LMFDB - Embedded newform 85.2.l.a.26.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [85,2,Mod(26,85)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(85, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("85.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 85 = 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	85.l (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.678728417181$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			26.2
Character	$\chi$	$=$	85.26
Dual form			85.2.l.a.36.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27691 + 1.27691i) q^{2} +(0.635552 + 0.263254i) q^{3} -1.26102i q^{4} +(-0.382683 + 0.923880i) q^{5} +(-1.14770 + 0.475393i) q^{6} +(1.66158 + 4.01142i) q^{7} +(-0.943613 - 0.943613i) q^{8} +(-1.78670 - 1.78670i) q^{9} +O(q^{10})$	\(q+(-1.27691 + 1.27691i) q^{2} +(0.635552 + 0.263254i) q^{3} -1.26102i q^{4} +(-0.382683 + 0.923880i) q^{5} +(-1.14770 + 0.475393i) q^{6} +(1.66158 + 4.01142i) q^{7} +(-0.943613 - 0.943613i) q^{8} +(-1.78670 - 1.78670i) q^{9} +(-0.691061 - 1.66837i) q^{10} +(0.0485041 - 0.0200910i) q^{11} +(0.331970 - 0.801445i) q^{12} +3.02508i q^{13} +(-7.24394 - 3.00054i) q^{14} +(-0.486431 + 0.486431i) q^{15} +4.93187 q^{16} +(3.12202 - 2.69314i) q^{17} +4.56292 q^{18} +(5.52988 - 5.52988i) q^{19} +(1.16503 + 0.482572i) q^{20} +2.98689i q^{21} +(-0.0362810 + 0.0875901i) q^{22} +(0.962654 - 0.398744i) q^{23} +(-0.351305 - 0.848125i) q^{24} +(-0.707107 - 0.707107i) q^{25} +(-3.86277 - 3.86277i) q^{26} +(-1.45495 - 3.51255i) q^{27} +(5.05848 - 2.09529i) q^{28} +(-0.161016 + 0.388726i) q^{29} -1.24226i q^{30} +(-1.27892 - 0.529745i) q^{31} +(-4.41035 + 4.41035i) q^{32} +0.0361159 q^{33} +(-0.547638 + 7.42546i) q^{34} -4.34193 q^{35} +(-2.25306 + 2.25306i) q^{36} +(0.311301 + 0.128945i) q^{37} +14.1224i q^{38} +(-0.796365 + 1.92260i) q^{39} +(1.23289 - 0.510679i) q^{40} +(2.52291 + 6.09084i) q^{41} +(-3.81400 - 3.81400i) q^{42} +(-7.06729 - 7.06729i) q^{43} +(-0.0253352 - 0.0611647i) q^{44} +(2.33443 - 0.966953i) q^{45} +(-0.720064 + 1.73839i) q^{46} -6.13168i q^{47} +(3.13446 + 1.29834i) q^{48} +(-8.38087 + 8.38087i) q^{49} +1.80583 q^{50} +(2.69319 - 0.889748i) q^{51} +3.81469 q^{52} +(-8.52974 + 8.52974i) q^{53} +(6.34307 + 2.62739i) q^{54} +0.0525004i q^{55} +(2.21733 - 5.35312i) q^{56} +(4.97030 - 2.05876i) q^{57} +(-0.290767 - 0.701974i) q^{58} +(3.60468 + 3.60468i) q^{59} +(0.613400 + 0.613400i) q^{60} +(-2.28486 - 5.51614i) q^{61} +(2.30951 - 0.956630i) q^{62} +(4.19844 - 10.1359i) q^{63} -1.39954i q^{64} +(-2.79481 - 1.15765i) q^{65} +(-0.0461170 + 0.0461170i) q^{66} +0.916040 q^{67} +(-3.39611 - 3.93693i) q^{68} +0.716788 q^{69} +(5.54427 - 5.54427i) q^{70} +(3.86169 + 1.59956i) q^{71} +3.37190i q^{72} +(2.06289 - 4.98025i) q^{73} +(-0.562156 + 0.232853i) q^{74} +(-0.263254 - 0.635552i) q^{75} +(-6.97330 - 6.97330i) q^{76} +(0.161187 + 0.161187i) q^{77} +(-1.43810 - 3.47188i) q^{78} +(9.22305 - 3.82031i) q^{79} +(-1.88734 + 4.55645i) q^{80} +4.96488i q^{81} +(-10.9990 - 4.55595i) q^{82} +(-4.61746 + 4.61746i) q^{83} +3.76653 q^{84} +(1.29339 + 3.91499i) q^{85} +18.0487 q^{86} +(-0.204668 + 0.204668i) q^{87} +(-0.0647272 - 0.0268109i) q^{88} -10.2159i q^{89} +(-1.74615 + 4.21559i) q^{90} +(-12.1349 + 5.02642i) q^{91} +(-0.502825 - 1.21393i) q^{92} +(-0.673362 - 0.673362i) q^{93} +(7.82963 + 7.82963i) q^{94} +(2.99275 + 7.22514i) q^{95} +(-3.96405 + 1.64196i) q^{96} +(-7.35663 + 17.7605i) q^{97} -21.4033i q^{98} +(-0.122559 - 0.0507655i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{6} - 24 q^{9}+O(q^{10}) $ 24 * q - 8 * q^6 - 24 * q^9	$ 24 q - 8 q^{6} - 24 q^{9} - 8 q^{11} + 24 q^{12} - 8 q^{15} - 24 q^{16} - 8 q^{17} + 8 q^{18} - 8 q^{19} - 32 q^{22} - 16 q^{23} - 8 q^{24} + 16 q^{26} + 24 q^{27} + 48 q^{28} - 8 q^{29} + 16 q^{34} - 32 q^{35} - 24 q^{36} + 24 q^{37} + 8 q^{39} + 16 q^{40} + 16 q^{41} - 24 q^{42} + 8 q^{43} + 16 q^{44} + 16 q^{45} + 8 q^{46} + 80 q^{48} + 8 q^{50} - 56 q^{51} - 48 q^{52} + 24 q^{53} - 32 q^{54} + 64 q^{56} + 32 q^{57} - 64 q^{58} + 32 q^{59} + 24 q^{60} + 32 q^{61} - 32 q^{62} - 56 q^{63} + 8 q^{65} + 96 q^{66} + 16 q^{67} - 40 q^{68} + 96 q^{69} - 24 q^{71} - 64 q^{74} - 8 q^{75} - 8 q^{76} + 24 q^{77} - 112 q^{78} - 32 q^{80} - 80 q^{82} - 96 q^{83} - 64 q^{84} - 16 q^{86} - 48 q^{87} - 8 q^{88} - 24 q^{91} + 80 q^{92} + 64 q^{93} + 56 q^{94} - 16 q^{95} - 168 q^{96} - 40 q^{97} - 8 q^{99}+O(q^{100}) $ 24 * q - 8 * q^6 - 24 * q^9 - 8 * q^11 + 24 * q^12 - 8 * q^15 - 24 * q^16 - 8 * q^17 + 8 * q^18 - 8 * q^19 - 32 * q^22 - 16 * q^23 - 8 * q^24 + 16 * q^26 + 24 * q^27 + 48 * q^28 - 8 * q^29 + 16 * q^34 - 32 * q^35 - 24 * q^36 + 24 * q^37 + 8 * q^39 + 16 * q^40 + 16 * q^41 - 24 * q^42 + 8 * q^43 + 16 * q^44 + 16 * q^45 + 8 * q^46 + 80 * q^48 + 8 * q^50 - 56 * q^51 - 48 * q^52 + 24 * q^53 - 32 * q^54 + 64 * q^56 + 32 * q^57 - 64 * q^58 + 32 * q^59 + 24 * q^60 + 32 * q^61 - 32 * q^62 - 56 * q^63 + 8 * q^65 + 96 * q^66 + 16 * q^67 - 40 * q^68 + 96 * q^69 - 24 * q^71 - 64 * q^74 - 8 * q^75 - 8 * q^76 + 24 * q^77 - 112 * q^78 - 32 * q^80 - 80 * q^82 - 96 * q^83 - 64 * q^84 - 16 * q^86 - 48 * q^87 - 8 * q^88 - 24 * q^91 + 80 * q^92 + 64 * q^93 + 56 * q^94 - 16 * q^95 - 168 * q^96 - 40 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/85\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$1$	$e\left(\frac{1}{8}\right)$

Coefficient data

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

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

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

$2$	−1.27691	+	1.27691i	−0.902915	+	0.902915i	−0.995687	−	0.0927724i	$-0.970427\pi$
$2$	−1.27691	+	1.27691i	−0.902915	+	0.902915i	0.0927724	+	0.995687i	$0.470427\pi$
$3$	0.635552	+	0.263254i	0.366936	+	0.151990i	0.558530	−	0.829484i	$-0.311366\pi$
$3$	0.635552	+	0.263254i	0.366936	+	0.151990i	−0.191594	+	0.981474i	$0.561366\pi$
$4$		−	1.26102i		−	0.630511i
$5$	−0.382683	+	0.923880i	−0.171141	+	0.413171i
$5$	−0.382683	+	0.923880i	−0.171141	+	0.413171i
$6$	−1.14770	+	0.475393i	−0.468546	+	0.194078i
$7$	1.66158	+	4.01142i	0.628020	+	1.51617i	0.842080	+	0.539353i	$0.181331\pi$
$7$	1.66158	+	4.01142i	0.628020	+	1.51617i	−0.214060	+	0.976821i	$0.568669\pi$
$8$	−0.943613	−	0.943613i	−0.333617	−	0.333617i
$9$	−1.78670	−	1.78670i	−0.595565	−	0.595565i
$10$	−0.691061	−	1.66837i	−0.218533	−	0.527585i
$11$	0.0485041	−	0.0200910i	0.0146245	−	0.00605768i	−0.375359	−	0.926879i	$-0.622481\pi$
$11$	0.0485041	−	0.0200910i	0.0146245	−	0.00605768i	0.389984	+	0.920822i	$0.372481\pi$
$12$	0.331970	−	0.801445i	0.0958313	−	0.231357i
$13$			3.02508i			0.839006i	0.907754	+	0.419503i	$0.137796\pi$
$13$			3.02508i			0.839006i	−0.907754	+	0.419503i	$0.862204\pi$
$14$	−7.24394	−	3.00054i	−1.93602	−	0.801928i
$15$	−0.486431	+	0.486431i	−0.125596	+	0.125596i
$16$	4.93187			1.23297
$17$	3.12202	−	2.69314i	0.757200	−	0.653183i
$17$	3.12202	−	2.69314i	0.757200	−	0.653183i
$18$	4.56292			1.07549
$19$	5.52988	−	5.52988i	1.26864	−	1.26864i	0.321851	−	0.946790i	$-0.395695\pi$
$19$	5.52988	−	5.52988i	1.26864	−	1.26864i	0.946790	−	0.321851i	$-0.104305\pi$
$20$	1.16503	+	0.482572i	0.260509	+	0.107906i
$21$			2.98689i			0.651792i
$22$	−0.0362810	+	0.0875901i	−0.00773514	+	0.0186743i
$23$	0.962654	−	0.398744i	0.200727	−	0.0831439i	−0.280055	−	0.959984i	$-0.590353\pi$
$23$	0.962654	−	0.398744i	0.200727	−	0.0831439i	0.480782	+	0.876840i	$0.340353\pi$
$24$	−0.351305	−	0.848125i	−0.0717098	−	0.173123i
$25$	−0.707107	−	0.707107i	−0.141421	−	0.141421i
$26$	−3.86277	−	3.86277i	−0.757551	−	0.757551i
$27$	−1.45495	−	3.51255i	−0.280005	−	0.675991i
$28$	5.05848	−	2.09529i	0.955964	−	0.395973i
$29$	−0.161016	+	0.388726i	−0.0298999	+	0.0721847i	−0.938124	−	0.346299i	$-0.887438\pi$
$29$	−0.161016	+	0.388726i	−0.0298999	+	0.0721847i	0.908224	+	0.418484i	$0.137438\pi$
$30$		−	1.24226i		−	0.226805i
$31$	−1.27892	−	0.529745i	−0.229701	−	0.0951451i	0.264865	−	0.964286i	$-0.414673\pi$
$31$	−1.27892	−	0.529745i	−0.229701	−	0.0951451i	−0.494565	+	0.869141i	$0.664673\pi$
$32$	−4.41035	+	4.41035i	−0.779647	+	0.779647i
$33$	0.0361159			0.00628698
$34$	−0.547638	+	7.42546i	−0.0939192	+	1.27346i
$35$	−4.34193			−0.733920
$36$	−2.25306	+	2.25306i	−0.375510	+	0.375510i
$37$	0.311301	+	0.128945i	0.0511775	+	0.0211984i	0.408125	−	0.912926i	$-0.366183\pi$
$37$	0.311301	+	0.128945i	0.0511775	+	0.0211984i	−0.356948	+	0.934124i	$0.616183\pi$
$38$			14.1224i			2.29095i
$39$	−0.796365	+	1.92260i	−0.127520	+	0.307862i
$40$	1.23289	−	0.510679i	0.194937	−	0.0807455i
$41$	2.52291	+	6.09084i	0.394012	+	0.951230i	0.989057	+	0.147537i	$0.0471345\pi$
$41$	2.52291	+	6.09084i	0.394012	+	0.951230i	−0.595044	+	0.803693i	$0.702865\pi$
$42$	−3.81400	−	3.81400i	−0.588513	−	0.588513i
$43$	−7.06729	−	7.06729i	−1.07775	−	1.07775i	−0.996711	−	0.0810414i	$-0.974175\pi$
$43$	−7.06729	−	7.06729i	−1.07775	−	1.07775i	−0.0810414	−	0.996711i	$-0.525825\pi$
$44$	−0.0253352	−	0.0611647i	−0.00381943	−	0.00922092i
$45$	2.33443	−	0.966953i	0.347996	−	0.144145i
$46$	−0.720064	+	1.73839i	−0.106168	+	0.256311i
$47$		−	6.13168i		−	0.894398i	−0.894435	−	0.447199i	$-0.852422\pi$
$47$		−	6.13168i		−	0.894398i	0.894435	−	0.447199i	$-0.147578\pi$
$48$	3.13446	+	1.29834i	0.452420	+	0.187399i
$49$	−8.38087	+	8.38087i	−1.19727	+	1.19727i
$50$	1.80583			0.255383
$51$	2.69319	−	0.889748i	0.377122	−	0.124590i
$52$	3.81469			0.529002
$53$	−8.52974	+	8.52974i	−1.17165	+	1.17165i	−0.189834	+	0.981816i	$0.560795\pi$
$53$	−8.52974	+	8.52974i	−1.17165	+	1.17165i	−0.981816	+	0.189834i	$0.939205\pi$
$54$	6.34307	+	2.62739i	0.863183	+	0.357542i
$55$			0.0525004i			0.00707916i
$56$	2.21733	−	5.35312i	0.296304	−	0.715340i
$57$	4.97030	−	2.05876i	0.658332	−	0.272690i
$58$	−0.290767	−	0.701974i	−0.0381796	−	0.0921737i
$59$	3.60468	+	3.60468i	0.469290	+	0.469290i	0.901684	−	0.432395i	$-0.142331\pi$
$59$	3.60468	+	3.60468i	0.469290	+	0.469290i	−0.432395	+	0.901684i	$0.642331\pi$
$60$	0.613400	+	0.613400i	0.0791896	+	0.0791896i
$61$	−2.28486	−	5.51614i	−0.292547	−	0.706270i	0.707453	−	0.706760i	$-0.249844\pi$
$61$	−2.28486	−	5.51614i	−0.292547	−	0.706270i	−1.00000		0.000490243i	$0.999844\pi$
$62$	2.30951	−	0.956630i	0.293308	−	0.121492i
$63$	4.19844	−	10.1359i	0.528954	−	1.27701i
$64$		−	1.39954i		−	0.174943i
$65$	−2.79481	−	1.15765i	−0.346653	−	0.143588i
$66$	−0.0461170	+	0.0461170i	−0.00567661	+	0.00567661i
$67$	0.916040			0.111912			0.0559561	−	0.998433i	$-0.482179\pi$
$67$	0.916040			0.111912			0.0559561	+	0.998433i	$0.482179\pi$
$68$	−3.39611	−	3.93693i	−0.411839	−	0.477423i
$69$	0.716788			0.0862912
$70$	5.54427	−	5.54427i	0.662667	−	0.662667i
$71$	3.86169	+	1.59956i	0.458298	+	0.189833i	0.599875	−	0.800094i	$-0.295217\pi$
$71$	3.86169	+	1.59956i	0.458298	+	0.189833i	−0.141577	+	0.989927i	$0.545217\pi$
$72$			3.37190i			0.397382i
$73$	2.06289	−	4.98025i	0.241443	−	0.582895i	−0.755984	−	0.654590i	$-0.772841\pi$
$73$	2.06289	−	4.98025i	0.241443	−	0.582895i	0.997427	+	0.0716959i	$0.0228411\pi$
$74$	−0.562156	+	0.232853i	−0.0653493	+	0.0270686i
$75$	−0.263254	−	0.635552i	−0.0303980	−	0.0733873i
$76$	−6.97330	−	6.97330i	−0.799892	−	0.799892i
$77$	0.161187	+	0.161187i	0.0183690	+	0.0183690i
$78$	−1.43810	−	3.47188i	−0.162833	−	0.393113i
$79$	9.22305	−	3.82031i	1.03767	−	0.429819i	0.202198	−	0.979345i	$-0.435192\pi$
$79$	9.22305	−	3.82031i	1.03767	−	0.429819i	0.835477	+	0.549526i	$0.185192\pi$
$80$	−1.88734	+	4.55645i	−0.211011	+	0.509427i
$81$			4.96488i			0.551653i
$82$	−10.9990	−	4.55595i	−1.21464	−	0.503120i
$83$	−4.61746	+	4.61746i	−0.506833	+	0.506833i	−0.913553	−	0.406720i	$-0.866672\pi$
$83$	−4.61746	+	4.61746i	−0.506833	+	0.506833i	0.406720	+	0.913553i	$0.366672\pi$
$84$	3.76653			0.410962
$85$	1.29339	+	3.91499i	0.140288	+	0.424640i
$86$	18.0487			1.94624
$87$	−0.204668	+	0.204668i	−0.0219427	+	0.0219427i
$88$	−0.0647272	−	0.0268109i	−0.00689994	−	0.00285805i
$89$		−	10.2159i		−	1.08289i	−0.840738	−	0.541443i	$-0.817878\pi$
$89$		−	10.2159i		−	1.08289i	0.840738	−	0.541443i	$-0.182122\pi$
$90$	−1.74615	+	4.21559i	−0.184061	+	0.444362i
$91$	−12.1349	+	5.02642i	−1.27208	+	0.526912i
$92$	−0.502825	−	1.21393i	−0.0524231	−	0.126561i
$93$	−0.673362	−	0.673362i	−0.0698244	−	0.0698244i
$94$	7.82963	+	7.82963i	0.807565	+	0.807565i
$95$	2.99275	+	7.22514i	0.307050	+	0.741283i
$96$	−3.96405	+	1.64196i	−0.404579	+	0.167582i
$97$	−7.35663	+	17.7605i	−0.746952	+	1.80330i	−0.172036	+	0.985091i	$0.555035\pi$
$97$	−7.35663	+	17.7605i	−0.746952	+	1.80330i	−0.574916	+	0.818212i	$0.694965\pi$
$98$		−	21.4033i		−	2.16206i
$99$	−0.122559	−	0.0507655i	−0.0123176	−	0.00510212i
$100$	−0.891677	+	0.891677i	−0.0891677	+	0.0891677i
$101$	−13.2926			−1.32266			−0.661331	−	0.750094i	$-0.730008\pi$
$101$	−13.2926			−1.32266			−0.661331	+	0.750094i	$0.730008\pi$
$102$	−2.30284	+	4.57510i	−0.228015	+	0.453003i
$103$	−6.91299			−0.681157			−0.340579	−	0.940216i	$-0.610623\pi$
$103$	−6.91299			−0.681157			−0.340579	+	0.940216i	$0.610623\pi$
$104$	2.85450	−	2.85450i	0.279907	−	0.279907i
$105$	−2.75952	−	1.14303i	−0.269302	−	0.111549i
$106$		−	21.7835i		−	2.11580i
$107$	5.64104	−	13.6187i	0.545339	−	1.31657i	−0.375572	−	0.926793i	$-0.622554\pi$
$107$	5.64104	−	13.6187i	0.545339	−	1.31657i	0.920911	−	0.389773i	$-0.127446\pi$
$108$	−4.42940	+	1.83472i	−0.426220	+	0.176546i
$109$	−1.81709	−	4.38684i	−0.174046	−	0.420183i	0.812652	−	0.582749i	$-0.198023\pi$
$109$	−1.81709	−	4.38684i	−0.174046	−	0.420183i	−0.986698	+	0.162566i	$0.948023\pi$
$110$	−0.0670386	−	0.0670386i	−0.00639188	−	0.00639188i
$111$	0.163903	+	0.163903i	0.0155569	+	0.0155569i
$112$	8.19471	+	19.7838i	0.774328	+	1.86939i
$113$	2.78393	−	1.15314i	0.261890	−	0.108478i	−0.247875	−	0.968792i	$-0.579732\pi$
$113$	2.78393	−	1.15314i	0.261890	−	0.108478i	0.509765	+	0.860314i	$0.329732\pi$
$114$	−3.71778	+	8.97551i	−0.348202	+	0.840633i
$115$			1.04197i			0.0971641i
$116$	0.490192	+	0.203044i	0.0455132	+	0.0188522i
$117$	5.40490	−	5.40490i	0.499683	−	0.499683i
$118$	−9.20574			−0.847457
$119$	15.9908	+	8.04884i	1.46588	+	0.737836i
$120$	0.918004			0.0838020
$121$	−7.77623	+	7.77623i	−0.706930	+	0.706930i
$122$	9.96122	+	4.12607i	0.901846	+	0.373557i
$123$			4.53522i			0.408927i
$124$	−0.668020	+	1.61274i	−0.0599900	+	0.144829i
$125$	0.923880	−	0.382683i	0.0826343	−	0.0342282i
$126$	7.58167	+	18.3038i	0.675429	+	1.63063i
$127$	0.00585984	+	0.00585984i	0.000519977	+	0.000519977i	0.707367	−	0.706847i	$-0.249883\pi$
$127$	0.00585984	+	0.00585984i	0.000519977	+	0.000519977i	−0.706847	+	0.707367i	$0.749883\pi$
$128$	−7.03360	−	7.03360i	−0.621689	−	0.621689i
$129$	−2.63114	−	6.35213i	−0.231659	−	0.559274i
$130$	5.04695	−	2.09051i	0.442647	−	0.183350i
$131$	3.13210	−	7.56157i	0.273653	−	0.660657i	−0.725981	−	0.687715i	$-0.758614\pi$
$131$	3.13210	−	7.56157i	0.273653	−	0.660657i	0.999634	+	0.0270577i	$0.00861380\pi$
$132$		−	0.0455430i		−	0.00396401i
$133$	31.3710	+	12.9943i	2.72021	+	1.12675i
$134$	−1.16971	+	1.16971i	−0.101047	+	0.101047i
$135$	3.80196			0.327221
$136$	−5.48726	−	0.404693i	−0.470528	−	0.0347021i
$137$	−2.23387			−0.190852			−0.0954260	−	0.995437i	$-0.530421\pi$
$137$	−2.23387			−0.190852			−0.0954260	+	0.995437i	$0.530421\pi$
$138$	−0.915277	+	0.915277i	−0.0779136	+	0.0779136i
$139$	−18.2335	−	7.55257i	−1.54655	−	0.640601i	−0.563859	−	0.825871i	$-0.690684\pi$
$139$	−18.2335	−	7.55257i	−1.54655	−	0.640601i	−0.982688	+	0.185270i	$0.940684\pi$
$140$			5.47526i			0.462744i
$141$	1.61419	−	3.89701i	0.135940	−	0.328187i
$142$	−6.97355	+	2.88854i	−0.585207	+	0.242401i
$143$	0.0607770	+	0.146729i	0.00508243	+	0.0122701i
$144$	−8.81175	−	8.81175i	−0.734313	−	0.734313i
$145$	−0.297518	−	0.297518i	−0.0247076	−	0.0247076i
$146$	3.72523	+	8.99349i	0.308302	+	0.744306i
$147$	−7.53279	+	3.12018i	−0.621294	+	0.257348i
$148$	0.162602	−	0.392557i	0.0133658	−	0.0322680i
$149$			10.1835i			0.834263i	0.908846	+	0.417132i	$0.136965\pi$
$149$			10.1835i			0.834263i	−0.908846	+	0.417132i	$0.863035\pi$
$150$	1.14770	+	0.475393i	0.0937093	+	0.0388157i
$151$	10.8529	−	10.8529i	0.883200	−	0.883200i	−0.110659	−	0.993858i	$-0.535296\pi$
$151$	10.8529	−	10.8529i	0.883200	−	0.883200i	0.993858	+	0.110659i	$0.0352961\pi$
$152$	−10.4361			−0.846482
$153$	−10.3899	−	0.766271i	−0.839975	−	0.0619494i
$154$	−0.411645			−0.0331713
$155$	0.978842	−	0.978842i	0.0786225	−	0.0786225i
$156$	2.42443	+	1.00423i	0.194110	+	0.0804030i
$157$		−	9.41222i		−	0.751177i	−0.926787	−	0.375588i	$-0.877441\pi$
$157$		−	9.41222i		−	0.751177i	0.926787	−	0.375588i	$-0.122559\pi$
$158$	−6.89884	+	16.6553i	−0.548842	+	1.32502i
$159$	−7.66659	+	3.17561i	−0.608000	+	0.251842i
$160$	−2.38686	−	5.76240i	−0.188698	−	0.455558i
$161$	3.19906	+	3.19906i	0.252121	+	0.252121i
$162$	−6.33972	−	6.33972i	−0.498096	−	0.498096i
$163$	−4.76262	−	11.4980i	−0.373037	−	0.900592i	−0.993232	−	0.116144i	$-0.962947\pi$
$163$	−4.76262	−	11.4980i	−0.373037	−	0.900592i	0.620195	−	0.784448i	$-0.287053\pi$
$164$	7.68068	−	3.18144i	0.599761	−	0.248429i
$165$	−0.0138210	+	0.0333668i	−0.00107596	+	0.00259760i
$166$		−	11.7922i		−	0.915253i
$167$	11.6432	+	4.82277i	0.900977	+	0.373197i	0.784596	−	0.620008i	$-0.212870\pi$
$167$	11.6432	+	4.82277i	0.900977	+	0.373197i	0.116382	+	0.993205i	$0.462870\pi$
$168$	2.81846	−	2.81846i	0.217449	−	0.217449i
$169$	3.84890			0.296069
$170$	−6.65066	−	3.34755i	−0.510082	−	0.256746i
$171$	−19.7604			−1.51112
$172$	−8.91201	+	8.91201i	−0.679534	+	0.679534i
$173$	11.2681	+	4.66741i	0.856699	+	0.354856i	0.767416	−	0.641150i	$-0.221542\pi$
$173$	11.2681	+	4.66741i	0.856699	+	0.354856i	0.0892832	+	0.996006i	$0.471542\pi$
$174$		−	0.522687i		−	0.0396248i
$175$	1.66158	−	4.01142i	0.125604	−	0.303235i
$176$	0.239216	−	0.0990864i	0.0180316	−	0.00746892i
$177$	1.34202	+	3.23991i	0.100872	+	0.243527i
$178$	13.0449	+	13.0449i	0.977754	+	0.977754i
$179$	9.80106	+	9.80106i	0.732566	+	0.732566i	0.971127	−	0.238562i	$-0.0766759\pi$
$179$	9.80106	+	9.80106i	0.732566	+	0.732566i	−0.238562	+	0.971127i	$0.576676\pi$
$180$	−1.21935	−	2.94377i	−0.0908849	−	0.219415i
$181$	1.88863	−	0.782297i	0.140381	−	0.0581476i	−0.311387	−	0.950283i	$-0.600794\pi$
$181$	1.88863	−	0.782297i	0.140381	−	0.0581476i	0.451768	+	0.892136i	$0.350794\pi$
$182$	9.07686	−	21.9135i	0.672822	−	1.62434i
$183$		−	4.10730i		−	0.303620i
$184$	−1.28463	−	0.532112i	−0.0947043	−	0.0392278i
$185$	−0.238259	+	0.238259i	−0.0175172	+	0.0175172i
$186$	1.71965			0.126091
$187$	0.0973225	−	0.193353i	0.00711693	−	0.0141394i
$188$	−7.73218			−0.563927
$189$	11.6728	−	11.6728i	0.849071	−	0.849071i
$190$	−13.0474	−	5.40440i	−0.946556	−	0.392076i
$191$			3.08056i			0.222902i	0.993770	+	0.111451i	$0.0355498\pi$
$191$			3.08056i			0.222902i	−0.993770	+	0.111451i	$0.964450\pi$
$192$	0.368435	−	0.889482i	0.0265895	−	0.0641928i
$193$	19.0706	−	7.89931i	1.37273	−	0.568605i	0.430205	−	0.902731i	$-0.358441\pi$
$193$	19.0706	−	7.89931i	1.37273	−	0.568605i	0.942528	+	0.334126i	$0.108441\pi$
$194$	−13.2848	−	32.0724i	−0.953794	−	2.30266i
$195$	−1.47149	−	1.47149i	−0.105376	−	0.105376i
$196$	10.5685	+	10.5685i	0.754890	+	0.754890i
$197$	−6.97881	−	16.8483i	−0.497219	−	1.20039i	−0.950975	−	0.309268i	$-0.899916\pi$
$197$	−6.97881	−	16.8483i	−0.497219	−	1.20039i	0.453756	−	0.891126i	$-0.350084\pi$
$198$	0.221320	−	0.0916738i	0.0157285	−	0.00651497i
$199$	−10.2053	+	24.6377i	−0.723432	+	1.74652i	−0.0601040	+	0.998192i	$0.519143\pi$
$199$	−10.2053	+	24.6377i	−0.723432	+	1.74652i	−0.663328	+	0.748328i	$0.730857\pi$
$200$			1.33447i			0.0943613i
$201$	0.582192	+	0.241152i	0.0410646	+	0.0170095i
$202$	16.9735	−	16.9735i	1.19425	−	1.19425i
$203$	−1.82689			−0.128222
$204$	−1.12199	−	3.39617i	−0.0785551	−	0.237779i
$205$	−6.59268			−0.460453
$206$	8.82730	−	8.82730i	0.615027	−	0.615027i
$207$	−2.43240	−	1.00754i	−0.169064	−	0.0700285i
$208$			14.9193i			1.03447i
$209$	0.157121	−	0.379323i	0.0108683	−	0.0262383i
$210$	4.98323	−	2.06412i	0.343876	−	0.142438i
$211$	2.98710	+	7.21149i	0.205640	+	0.496460i	0.992728	−	0.120382i	$-0.0384119\pi$
$211$	2.98710	+	7.21149i	0.205640	+	0.496460i	−0.787087	+	0.616842i	$0.788412\pi$
$212$	10.7562	+	10.7562i	0.738738	+	0.738738i
$213$	2.03321	+	2.03321i	0.139313	+	0.139313i
$214$	10.1868	+	24.5930i	0.696352	+	1.68114i
$215$	9.23386	−	3.82479i	0.629744	−	0.260849i
$216$	−1.94158	+	4.68739i	−0.132108	+	0.318937i
$217$		−	6.01049i		−	0.408019i
$218$	7.92189	+	3.28135i	0.536538	+	0.222241i
$219$	2.62215	−	2.62215i	0.177188	−	0.177188i
$220$	0.0662042			0.00446348
$221$	8.14696	+	9.44435i	0.548024	+	0.635295i
$222$	−0.418579			−0.0280932
$223$	3.37213	−	3.37213i	0.225815	−	0.225815i	−0.585127	−	0.810942i	$-0.698955\pi$
$223$	3.37213	−	3.37213i	0.225815	−	0.225815i	0.810942	+	0.585127i	$0.198955\pi$
$224$	−25.0199	−	10.3636i	−1.67171	−	0.692447i
$225$			2.52677i			0.168451i
$226$	−2.08238	+	5.02731i	−0.138518	+	0.334411i
$227$	−10.3577	+	4.29029i	−0.687464	+	0.284757i	−0.698943	−	0.715177i	$-0.746346\pi$
$227$	−10.3577	+	4.29029i	−0.687464	+	0.284757i	0.0114793	+	0.999934i	$0.496346\pi$
$228$	−2.59614	−	6.26765i	−0.171934	−	0.415085i
$229$	−14.6007	−	14.6007i	−0.964838	−	0.964838i	0.0345640	−	0.999402i	$-0.488996\pi$
$229$	−14.6007	−	14.6007i	−0.964838	−	0.964838i	−0.999402	+	0.0345640i	$0.988996\pi$
$230$	−1.33051	−	1.33051i	−0.0877309	−	0.0877309i
$231$	0.0600097	+	0.144876i	0.00394835	+	0.00953215i
$232$	0.518744	−	0.214871i	0.0340572	−	0.0141069i
$233$	−1.17044	+	2.82569i	−0.0766781	+	0.185117i	−0.957570	−	0.288199i	$-0.906943\pi$
$233$	−1.17044	+	2.82569i	−0.0766781	+	0.185117i	0.880892	+	0.473317i	$0.156943\pi$
$234$			13.8032i			0.902342i
$235$	5.66494	+	2.34649i	0.369540	+	0.153068i
$236$	4.54558	−	4.54558i	0.295892	−	0.295892i
$237$	6.86745			0.446089
$238$	−30.6966	+	10.1412i	−1.98976	+	0.657358i
$239$	4.94072			0.319588			0.159794	−	0.987150i	$-0.448917\pi$
$239$	4.94072			0.319588			0.159794	+	0.987150i	$0.448917\pi$
$240$	−2.39901	+	2.39901i	−0.154856	+	0.154856i
$241$	1.53527	+	0.635928i	0.0988952	+	0.0409637i	0.431583	−	0.902073i	$-0.357955\pi$
$241$	1.53527	+	0.635928i	0.0988952	+	0.0409637i	−0.332687	+	0.943037i	$0.607955\pi$
$242$		−	19.8592i		−	1.27659i
$243$	−5.67187	+	13.6931i	−0.363850	+	0.878413i
$244$	−6.95597	+	2.88126i	−0.445311	+	0.184454i
$245$	−4.53570	−	10.9501i	−0.289775	−	0.699579i
$246$	−5.79109	−	5.79109i	−0.369226	−	0.369226i
$247$	16.7283	+	16.7283i	1.06440	+	1.06440i
$248$	0.706929	+	1.70668i	0.0448900	+	0.108374i
$249$	−4.15021	+	1.71907i	−0.263009	+	0.108942i
$250$	−0.691061	+	1.66837i	−0.0437065	+	0.105517i
$251$			9.14240i			0.577063i	0.957470	+	0.288531i	$0.0931670\pi$
$251$			9.14240i			0.577063i	−0.957470	+	0.288531i	$0.906833\pi$
$252$	−12.7816	−	5.29432i	−0.805167	−	0.333511i
$253$	0.0386814	−	0.0386814i	0.00243188	−	0.00243188i
$254$	−0.0149650			−0.000938989
$255$	−0.208619	+	2.82867i	−0.0130642	+	0.177138i
$256$	20.7617			1.29761
$257$	−11.7749	+	11.7749i	−0.734498	+	0.734498i	−0.971507	−	0.237009i	$-0.923833\pi$
$257$	−11.7749	+	11.7749i	−0.734498	+	0.734498i	0.237009	+	0.971507i	$0.423833\pi$
$258$	11.4709	+	4.75139i	0.714145	+	0.295809i
$259$			1.46301i			0.0909070i
$260$	−1.45982	+	3.52431i	−0.0905341	+	0.218569i
$261$	0.982222	−	0.406850i	0.0607980	−	0.0251834i
$262$	5.65605	+	13.6549i	0.349432	+	0.843603i
$263$	15.3640	+	15.3640i	0.947387	+	0.947387i	0.998683	−	0.0512969i	$-0.0163355\pi$
$263$	15.3640	+	15.3640i	0.947387	+	0.947387i	−0.0512969	+	0.998683i	$0.516335\pi$
$264$	−0.0340795	−	0.0340795i	−0.00209745	−	0.00209745i
$265$	−4.61626	−	11.1446i	−0.283575	−	0.684610i
$266$	−56.6507	+	23.4655i	−3.47348	+	1.43876i
$267$	2.68939	−	6.49276i	0.164588	−	0.397350i
$268$		−	1.15515i		−	0.0705618i
$269$	−21.4082	−	8.86758i	−1.30528	−	0.540666i	−0.381779	−	0.924254i	$-0.624688\pi$
$269$	−21.4082	−	8.86758i	−1.30528	−	0.540666i	−0.923504	+	0.383588i	$0.874688\pi$
$270$	−4.85478	+	4.85478i	−0.295452	+	0.295452i
$271$	−3.95595			−0.240307			−0.120153	−	0.992755i	$-0.538339\pi$
$271$	−3.95595			−0.240307			−0.120153	+	0.992755i	$0.538339\pi$
$272$	15.3974	−	13.2822i	0.933603	−	0.805353i
$273$	−9.03556			−0.546857
$274$	2.85246	−	2.85246i	0.172323	−	0.172323i
$275$	−0.0485041	−	0.0200910i	−0.00292491	−	0.00121154i
$276$		−	0.903885i		−	0.0544075i
$277$	−6.47115	+	15.6227i	−0.388814	+	0.938679i	0.601378	+	0.798964i	$0.294618\pi$
$277$	−6.47115	+	15.6227i	−0.388814	+	0.938679i	−0.990192	+	0.139714i	$0.955382\pi$
$278$	32.9266	−	13.6387i	1.97481	−	0.817992i
$279$	1.33854	+	3.23153i	0.0801366	+	0.193467i
$280$	4.09710	+	4.09710i	0.244848	+	0.244848i
$281$	3.30210	+	3.30210i	0.196987	+	0.196987i	0.798707	−	0.601720i	$-0.205518\pi$
$281$	3.30210	+	3.30210i	0.196987	+	0.196987i	−0.601720	+	0.798707i	$0.705518\pi$
$282$	2.91496	+	7.03733i	0.173583	+	0.419067i
$283$	−8.03809	+	3.32949i	−0.477815	+	0.197917i	−0.608575	−	0.793497i	$-0.708258\pi$
$283$	−8.03809	+	3.32949i	−0.477815	+	0.197917i	0.130760	+	0.991414i	$0.458258\pi$
$284$	2.01708	−	4.86967i	0.119692	−	0.288962i
$285$			5.37981i			0.318672i
$286$	−0.264967	−	0.109753i	−0.0156678	−	0.00648982i
$287$	−20.2409	+	20.2409i	−1.19478	+	1.19478i
$288$	15.7599			0.928661
$289$	2.49398	−	16.8161i	0.146705	−	0.989180i
$290$	0.759811			0.0446176
$291$	−9.35105	+	9.35105i	−0.548168	+	0.548168i
$292$	−6.28021	−	2.60135i	−0.367521	−	0.152232i
$293$		−	0.739100i		−	0.0431787i	−0.999767	−	0.0215893i	$-0.993127\pi$
$293$		−	0.739100i		−	0.0431787i	0.999767	−	0.0215893i	$-0.00687263\pi$
$294$	5.63452	−	13.6029i	0.328612	−	0.793339i
$295$	−4.70974	+	1.95084i	−0.274212	+	0.113582i
$296$	−0.172073	−	0.415421i	−0.0100015	−	0.0241459i
$297$	−0.141142	−	0.141142i	−0.00818987	−	0.00818987i
$298$	−13.0034	−	13.0034i	−0.753269	−	0.753269i
$299$	1.20623	+	2.91210i	0.0697582	+	0.168411i
$300$	−0.801445	+	0.331970i	−0.0462715	+	0.0191663i
$301$	16.6070	−	40.0928i	0.957210	−	2.31091i
$302$			27.7165i			1.59491i
$303$	−8.44813	−	3.49933i	−0.485333	−	0.201031i
$304$	27.2726	−	27.2726i	1.56419	−	1.56419i
$305$	5.97063			0.341877
$306$	14.2455	−	12.2886i	0.814361	−	0.702491i
$307$	−2.86108			−0.163290			−0.0816451	−	0.996661i	$-0.526017\pi$
$307$	−2.86108			−0.163290			−0.0816451	+	0.996661i	$0.526017\pi$
$308$	0.203261	−	0.203261i	0.0115818	−	0.0115818i
$309$	−4.39357	−	1.81988i	−0.249941	−	0.103529i
$310$			2.49979i			0.141979i
$311$	7.84424	−	18.9377i	0.444806	−	1.07386i	−0.529435	−	0.848350i	$-0.677596\pi$
$311$	7.84424	−	18.9377i	0.444806	−	1.07386i	0.974242	−	0.225507i	$-0.0724038\pi$
$312$	2.56565	−	1.06273i	0.145251	−	0.0601650i
$313$	3.23958	+	7.82103i	0.183112	+	0.442071i	0.988605	−	0.150534i	$-0.0480994\pi$
$313$	3.23958	+	7.82103i	0.183112	+	0.442071i	−0.805493	+	0.592605i	$0.798099\pi$
$314$	12.0186	+	12.0186i	0.678249	+	0.678249i
$315$	7.75771	+	7.75771i	0.437097	+	0.437097i
$316$	−4.81750	−	11.6305i	−0.271005	−	0.654265i
$317$	−19.4863	+	8.07149i	−1.09446	+	0.453340i	−0.855560	−	0.517704i	$-0.826787\pi$
$317$	−19.4863	+	8.07149i	−1.09446	+	0.453340i	−0.238900	+	0.971044i	$0.576787\pi$
$318$	5.73460	−	13.8446i	0.321581	−	0.776364i
$319$			0.0220898i			0.00123679i
$320$	1.29301	+	0.535581i	0.0722813	+	0.0299399i
$321$	7.17035	−	7.17035i	0.400210	−	0.400210i
$322$	−8.16985			−0.455288
$323$	2.37163	−	32.1571i	0.131961	−	1.78927i
$324$	6.26082			0.347823
$325$	2.13905	−	2.13905i	0.118653	−	0.118653i
$326$	20.7634	+	8.60048i	1.14998	+	0.476337i
$327$		−	3.26643i		−	0.180634i
$328$	3.36675	−	8.12805i	0.185897	−	0.448796i
$329$	24.5967	−	10.1883i	1.35606	−	0.561699i
$330$	−0.0249583	−	0.0602547i	−0.00137391	−	0.00331691i
$331$	10.7665	+	10.7665i	0.591780	+	0.591780i	0.938112	−	0.346332i	$-0.112573\pi$
$331$	10.7665	+	10.7665i	0.591780	+	0.591780i	−0.346332	+	0.938112i	$0.612573\pi$
$332$	5.82272	+	5.82272i	0.319563	+	0.319563i
$333$	−0.325814	−	0.786585i	−0.0178545	−	0.0431046i
$334$	−21.0256	+	8.70910i	−1.15047	+	0.476541i
$335$	−0.350554	+	0.846311i	−0.0191528	+	0.0462389i
$336$			14.7309i			0.803638i
$337$	10.6003	+	4.39079i	0.577435	+	0.239182i	0.652235	−	0.758017i	$-0.273832\pi$
$337$	10.6003	+	4.39079i	0.577435	+	0.239182i	−0.0747994	+	0.997199i	$0.523832\pi$
$338$	−4.91472	+	4.91472i	−0.267326	+	0.267326i
$339$	2.07290			0.112585
$340$	4.93688	−	1.63100i	0.267740	−	0.0884532i
$341$	−0.0726759			−0.00393562
$342$	25.2324	−	25.2324i	1.36441	−	1.36441i
$343$	−19.4648	−	8.06258i	−1.05100	−	0.435338i
$344$			13.3376i			0.719114i
$345$	−0.274303	+	0.662226i	−0.0147680	+	0.0356530i
$346$	−20.3483	+	8.42854i	−1.09393	+	0.453121i
$347$	−5.73424	−	13.8437i	−0.307830	−	0.743168i	−0.999775	−	0.0212172i	$-0.993246\pi$
$347$	−5.73424	−	13.8437i	−0.307830	−	0.743168i	0.691945	−	0.721950i	$-0.256754\pi$
$348$	0.258091	+	0.258091i	0.0138351	+	0.0138351i
$349$	−3.20791	−	3.20791i	−0.171715	−	0.171715i	0.616017	−	0.787733i	$-0.288745\pi$
$349$	−3.20791	−	3.20791i	−0.171715	−	0.171715i	−0.787733	+	0.616017i	$0.788745\pi$
$350$	3.00054	+	7.24394i	0.160386	+	0.387205i
$351$	10.6257	−	4.40133i	0.567160	−	0.234925i
$352$	−0.125311	+	0.302528i	−0.00667912	+	0.0161248i
$353$		−	7.71469i		−	0.410612i	−0.978698	−	0.205306i	$-0.934181\pi$
$353$		−	7.71469i		−	0.410612i	0.978698	−	0.205306i	$-0.0658189\pi$
$354$	−5.85073	−	2.42345i	−0.310963	−	0.128805i
$355$	−2.95561	+	2.95561i	−0.156867	+	0.156867i
$356$	−12.8825			−0.682771
$357$	8.04411	+	9.32511i	0.425739	+	0.493537i
$358$	−25.0302			−1.32289
$359$	−7.79826	+	7.79826i	−0.411577	+	0.411577i	−0.882287	−	0.470711i	$-0.843997\pi$
$359$	−7.79826	+	7.79826i	−0.411577	+	0.411577i	0.470711	+	0.882287i	$0.343997\pi$
$360$	−3.11523	−	1.29037i	−0.164187	−	0.0680084i
$361$		−	42.1592i		−	2.21890i
$362$	−1.41269	+	3.41055i	−0.0742496	+	0.179254i
$363$	−6.98933	+	2.89507i	−0.366844	+	0.151952i
$364$	6.33843	+	15.3023i	0.332224	+	0.802059i
$365$	3.81172	+	3.81172i	0.199515	+	0.199515i
$366$	5.24467	+	5.24467i	0.274143	+	0.274143i
$367$	−6.13386	−	14.8084i	−0.320185	−	0.772995i	−0.999243	−	0.0389098i	$-0.987611\pi$
$367$	−6.13386	−	14.8084i	−0.320185	−	0.772995i	0.679058	−	0.734085i	$-0.262389\pi$
$368$	4.74768	−	1.96655i	0.247490	−	0.102514i
$369$	6.37481	−	15.3902i	0.331860	−	0.801180i
$370$		−	0.608473i		−	0.0316330i
$371$	−48.3892	−	20.0435i	−2.51224	−	1.04061i
$372$	−0.849124	+	0.849124i	−0.0440250	+	0.0440250i
$373$	−10.2501			−0.530732			−0.265366	−	0.964148i	$-0.585493\pi$
$373$	−10.2501			−0.530732			−0.265366	+	0.964148i	$0.585493\pi$
$374$	0.122623	+	0.371168i	0.00634066	+	0.0191926i
$375$	0.687917			0.0355239
$376$	−5.78593	+	5.78593i	−0.298387	+	0.298387i
$377$	−1.17593	−	0.487085i	−0.0605634	−	0.0250862i
$378$			29.8103i			1.53328i
$379$	−5.33919	+	12.8899i	−0.274256	+	0.662112i	−0.999656	−	0.0262152i	$-0.991654\pi$
$379$	−5.33919	+	12.8899i	−0.274256	+	0.662112i	0.725401	+	0.688327i	$0.241654\pi$
$380$	9.11105	−	3.77392i	0.467387	−	0.193598i
$381$	0.00218161	+	0.00526686i	0.000111767	+	0.000269830i
$382$	−3.93362	−	3.93362i	−0.201261	−	0.201261i
$383$	−3.97525	−	3.97525i	−0.203126	−	0.203126i	0.598212	−	0.801338i	$-0.295878\pi$
$383$	−3.97525	−	3.97525i	−0.203126	−	0.203126i	−0.801338	+	0.598212i	$0.795878\pi$
$384$	−2.61860	−	6.32185i	−0.133630	−	0.322611i
$385$	−0.210601	+	0.0872339i	−0.0107332	+	0.00444585i
$386$	−14.2648	+	34.4383i	−0.726060	+	1.75286i
$387$			25.2542i			1.28374i
$388$	22.3963	+	9.27687i	1.13700	+	0.470962i
$389$	−25.3255	+	25.3255i	−1.28406	+	1.28406i	−0.345717	+	0.938339i	$0.612364\pi$
$389$	−25.3255	+	25.3255i	−1.28406	+	1.28406i	−0.938339	+	0.345717i	$0.887636\pi$
$390$	3.75794			0.190291
$391$	1.93155	−	3.83745i	0.0976825	−	0.194068i
$392$	15.8166			0.798858
$393$	3.98123	−	3.98123i	0.200827	−	0.200827i
$394$	30.4252	+	12.6025i	1.53280	+	0.634907i
$395$			9.98296i			0.502297i
$396$	−0.0640163	+	0.154549i	−0.00321694	+	0.00776638i
$397$	3.59405	−	1.48870i	0.180380	−	0.0747159i	−0.290665	−	0.956825i	$-0.593877\pi$
$397$	3.59405	−	1.48870i	0.180380	−	0.0747159i	0.471046	+	0.882109i	$0.343877\pi$
$398$	−18.4290	−	44.4915i	−0.923761	−	2.23016i
$399$	16.5171	+	16.5171i	0.826891	+	0.826891i
$400$	−3.48736	−	3.48736i	−0.174368	−	0.174368i
$401$	14.0592	+	33.9420i	0.702085	+	1.69498i	0.718890	+	0.695124i	$0.244650\pi$
$401$	14.0592	+	33.9420i	0.702085	+	1.69498i	−0.0168056	+	0.999859i	$0.505350\pi$
$402$	−1.05134	+	0.435479i	−0.0524360	+	0.0217197i
$403$	1.60252	−	3.86883i	0.0798273	−	0.192720i
$404$			16.7622i			0.833952i
$405$	−4.58695	−	1.89998i	−0.227927	−	0.0944106i
$406$	2.33278	−	2.33278i	0.115774	−	0.115774i
$407$	0.0176900			0.000876860
$408$	−3.38090	−	1.70175i	−0.167380	−	0.0842491i
$409$	−22.3529			−1.10528			−0.552641	−	0.833419i	$-0.686380\pi$
$409$	−22.3529			−1.10528			−0.552641	+	0.833419i	$0.686380\pi$
$410$	8.41829	−	8.41829i	0.415750	−	0.415750i
$411$	−1.41974	−	0.588075i	−0.0700306	−	0.0290076i
$412$			8.71743i			0.429477i
$413$	−8.47041	+	20.4494i	−0.416802	+	1.00625i
$414$	4.39251	−	1.81944i	0.215880	−	0.0894204i
$415$	−2.49895	−	6.03301i	−0.122669	−	0.296149i
$416$	−13.3416	−	13.3416i	−0.654128	−	0.654128i
$417$	−9.60011	−	9.60011i	−0.470119	−	0.470119i
$418$	0.283733	+	0.684993i	0.0138778	+	0.0335041i
$419$	20.2014	−	8.36768i	0.986901	−	0.408788i	0.169924	−	0.985457i	$-0.445648\pi$
$419$	20.2014	−	8.36768i	0.986901	−	0.408788i	0.816978	+	0.576669i	$0.195648\pi$
$420$	−1.44139	+	3.47982i	−0.0703325	+	0.169798i
$421$			20.6111i			1.00453i	0.864715	+	0.502263i	$0.167499\pi$
$421$			20.6111i			1.00453i	−0.864715	+	0.502263i	$0.832501\pi$
$422$	−13.0227	−	5.39419i	−0.633937	−	0.262585i
$423$	−10.9555	+	10.9555i	−0.532672	+	0.532672i
$424$	16.0975			0.781766
$425$	−4.11194	−	0.303261i	−0.199458	−	0.0147103i
$426$	−5.19248			−0.251576
$427$	18.3311	−	18.3311i	0.887103	−	0.887103i
$428$	−17.1734	−	7.11347i	−0.830109	−	0.343842i
$429$			0.109254i			0.00527481i
$430$	−6.90692	+	16.6748i	−0.333081	+	0.804130i
$431$	20.6074	−	8.53585i	0.992621	−	0.411157i	0.173535	−	0.984828i	$-0.444481\pi$
$431$	20.6074	−	8.53585i	0.992621	−	0.411157i	0.819086	+	0.573670i	$0.194481\pi$
$432$	−7.17561	−	17.3234i	−0.345236	−	0.833475i
$433$	−6.31536	−	6.31536i	−0.303497	−	0.303497i	0.538883	−	0.842380i	$-0.318846\pi$
$433$	−6.31536	−	6.31536i	−0.303497	−	0.303497i	−0.842380	+	0.538883i	$0.818846\pi$
$434$	7.67489	+	7.67489i	0.368406	+	0.368406i
$435$	−0.110765	−	0.267412i	−0.00531080	−	0.0128214i
$436$	−5.53190	+	2.29139i	−0.264930	+	0.109738i
$437$	3.11835	−	7.52837i	0.149171	−	0.360131i
$438$			6.69652i			0.319972i
$439$	20.5695	+	8.52016i	0.981728	+	0.406645i	0.815066	−	0.579369i	$-0.196701\pi$
$439$	20.5695	+	8.52016i	0.981728	+	0.406645i	0.166663	+	0.986014i	$0.446701\pi$
$440$	0.0495401	−	0.0495401i	0.00236173	−	0.00236173i
$441$	29.9481			1.42610
$442$	−22.4626	−	1.65665i	−1.06844	−	0.0787987i
$443$	−6.17421			−0.293346			−0.146673	−	0.989185i	$-0.546856\pi$
$443$	−6.17421			−0.293346			−0.146673	+	0.989185i	$0.546856\pi$
$444$	0.206685	−	0.206685i	0.00980882	−	0.00980882i
$445$	9.43828	+	3.90946i	0.447418	+	0.185326i
$446$			8.61184i			0.407783i
$447$	−2.68085	+	6.47214i	−0.126800	+	0.306122i
$448$	5.61414	−	2.32545i	0.265243	−	0.109867i
$449$	11.5947	+	27.9922i	0.547189	+	1.32103i	0.919561	+	0.392948i	$0.128545\pi$
$449$	11.5947	+	27.9922i	0.547189	+	1.32103i	−0.372371	+	0.928084i	$0.621455\pi$
$450$	−3.22647	−	3.22647i	−0.152097	−	0.152097i
$451$	0.244743	+	0.244743i	0.0115245	+	0.0115245i
$452$	−1.45414	−	3.51060i	−0.0683968	−	0.165125i
$453$	9.75470	−	4.04053i	0.458316	−	0.189841i
$454$	7.74754	−	18.7042i	0.363610	−	0.877833i
$455$		−	13.1347i		−	0.615763i
$456$	−6.63271	−	2.74736i	−0.310605	−	0.128657i
$457$	18.0847	−	18.0847i	0.845965	−	0.845965i	−0.143662	−	0.989627i	$-0.545888\pi$
$457$	18.0847	−	18.0847i	0.845965	−	0.845965i	0.989627	+	0.143662i	$0.0458877\pi$
$458$	37.2876			1.74233
$459$	−14.0022	−	7.04787i	−0.653565	−	0.328966i
$460$	1.31395			0.0612630
$461$	−9.93945	+	9.93945i	−0.462926	+	0.462926i	−0.899613	−	0.436687i	$-0.856152\pi$
$461$	−9.93945	+	9.93945i	−0.462926	+	0.462926i	0.436687	+	0.899613i	$0.356152\pi$
$462$	−0.261622	−	0.108367i	−0.0121717	−	0.00504170i
$463$			25.1233i			1.16758i	0.811905	+	0.583789i	$0.198431\pi$
$463$			25.1233i			1.16758i	−0.811905	+	0.583789i	$0.801569\pi$
$464$	−0.794108	+	1.91715i	−0.0368656	+	0.0890013i
$465$	0.879790	−	0.364421i	0.0407993	−	0.0168996i
$466$	−2.11362	−	5.10272i	−0.0979114	−	0.236379i
$467$	−15.7614	−	15.7614i	−0.729352	−	0.729352i	0.241139	−	0.970491i	$-0.422479\pi$
$467$	−15.7614	−	15.7614i	−0.729352	−	0.729352i	−0.970491	+	0.241139i	$0.922479\pi$
$468$	−6.81569	−	6.81569i	−0.315055	−	0.315055i
$469$	1.52208	+	3.67462i	0.0702830	+	0.169678i
$470$	−10.2299	+	4.23737i	−0.471871	+	0.195455i
$471$	2.47781	−	5.98196i	0.114171	−	0.275634i
$472$		−	6.80285i		−	0.313126i
$473$	−0.484782	−	0.200803i	−0.0222903	−	0.00923294i
$474$	−8.76915	+	8.76915i	−0.402780	+	0.402780i
$475$	−7.82043			−0.358826
$476$	10.1498	−	20.1648i	0.465213	−	0.924250i
$477$	30.4801			1.39559
$478$	−6.30887	+	6.30887i	−0.288561	+	0.288561i
$479$	24.7134	+	10.2366i	1.12919	+	0.467724i	0.867504	−	0.497430i	$-0.165723\pi$
$479$	24.7134	+	10.2366i	1.12919	+	0.467724i	0.261681	+	0.965154i	$0.415723\pi$
$480$		−	4.29066i		−	0.195841i
$481$	−0.390068	+	0.941709i	−0.0177856	+	0.0429382i
$482$	−2.77243	+	1.14838i	−0.126281	+	0.0523072i
$483$	1.19100	+	2.87534i	0.0541926	+	0.130832i
$484$	9.80599	+	9.80599i	0.445727	+	0.445727i
$485$	−13.5933	−	13.5933i	−0.617239	−	0.617239i
$486$	−10.2424	−	24.7274i	−0.464606	−	1.12166i
$487$	−21.3841	+	8.85760i	−0.969008	+	0.401376i	−0.810343	−	0.585956i	$-0.800719\pi$
$487$	−21.3841	+	8.85760i	−0.969008	+	0.401376i	−0.158665	+	0.987332i	$0.550719\pi$
$488$	−3.04908	+	7.36113i	−0.138025	+	0.333223i
$489$		−	8.56135i		−	0.387158i
$490$	19.7741	+	8.19069i	0.893302	+	0.370018i
$491$	−5.50823	+	5.50823i	−0.248583	+	0.248583i	−0.820389	−	0.571806i	$-0.806243\pi$
$491$	−5.50823	+	5.50823i	−0.248583	+	0.248583i	0.571806	+	0.820389i	$0.306243\pi$
$492$	5.71901			0.257833
$493$	0.544201	+	1.64725i	0.0245096	+	0.0741883i
$494$	−42.7213			−1.92212
$495$	0.0938023	−	0.0938023i	0.00421610	−	0.00421610i
$496$	−6.30746	−	2.61263i	−0.283213	−	0.117311i
$497$			18.1487i			0.814079i
$498$	3.10435	−	7.49457i	0.139109	−	0.335840i
$499$	−8.12796	+	3.36671i	−0.363858	+	0.150715i	−0.557119	−	0.830432i	$-0.688093\pi$
$499$	−8.12796	+	3.36671i	−0.363858	+	0.150715i	0.193262	+	0.981147i	$0.438093\pi$
$500$	−0.482572	−	1.16503i	−0.0215813	−	0.0521018i
$501$	6.13025	+	6.13025i	0.273879	+	0.273879i
$502$	−11.6741	−	11.6741i	−0.521039	−	0.521039i
$503$	−3.00003	−	7.24271i	−0.133765	−	0.322937i	0.842778	−	0.538262i	$-0.180919\pi$
$503$	−3.00003	−	7.24271i	−0.133765	−	0.322937i	−0.976542	+	0.215325i	$0.930919\pi$
$504$	−13.5261	+	5.60269i	−0.602500	+	0.249564i
$505$	5.08685	−	12.2807i	0.226362	−	0.546486i
$506$			0.0987858i			0.00439156i
$507$	2.44618	+	1.01324i	0.108639	+	0.0449996i
$508$	0.00738938	−	0.00738938i	0.000327851	−	0.000327851i
$509$	2.52868			0.112082			0.0560409	−	0.998428i	$-0.482152\pi$
$509$	2.52868			0.112082			0.0560409	+	0.998428i	$0.482152\pi$
$510$	−3.34558	−	3.87836i	−0.148145	−	0.171737i
$511$	23.4055			1.03540
$512$	−12.4437	+	12.4437i	−0.549940	+	0.549940i
$513$	−27.4697	−	11.3783i	−1.21282	−	0.502365i
$514$		−	30.0711i		−	1.32638i
$515$	2.64549	−	6.38677i	0.116574	−	0.281435i
$516$	−8.01017	+	3.31792i	−0.352628	+	0.146063i
$517$	−0.123192	−	0.297412i	−0.00541797	−	0.0130801i
$518$	−1.86814	−	1.86814i	−0.0820813	−	0.0820813i
$519$	5.93276	+	5.93276i	0.260419	+	0.260419i
$520$	1.54485	+	3.72959i	0.0677459	+	0.163553i
$521$	9.33885	−	3.86828i	0.409142	−	0.169472i	−0.168613	−	0.985682i	$-0.553929\pi$
$521$	9.33885	−	3.86828i	0.409142	−	0.169472i	0.577755	+	0.816210i	$0.303929\pi$
$522$	−0.734701	+	1.77373i	−0.0321570	+	0.0776339i
$523$		−	5.80494i		−	0.253833i	−0.991913	−	0.126916i	$-0.959492\pi$
$523$		−	5.80494i		−	0.253833i	0.991913	−	0.126916i	$-0.0405079\pi$
$524$	−9.53530	−	3.94965i	−0.416552	−	0.172541i
$525$	2.11205	−	2.11205i	0.0921773	−	0.0921773i
$526$	−39.2371			−1.71082
$527$	−5.41948	+	1.79043i	−0.236076	+	0.0779925i
$528$	0.178119			0.00775164
$529$	−15.4958	+	15.4958i	−0.673728	+	0.673728i
$530$	20.1253	+	8.33618i	0.874188	+	0.362101i
$531$		−	12.8809i		−	0.558985i
$532$	16.3861	−	39.5595i	0.710427	−	1.71512i
$533$	−18.4253	+	7.63200i	−0.798087	+	0.330579i
$534$	4.85658	+	11.7248i	0.210165	+	0.507382i
$535$	10.4233	+	10.4233i	0.450637	+	0.450637i
$536$	−0.864387	−	0.864387i	−0.0373358	−	0.0373358i
$537$	3.64892	+	8.80926i	0.157462	+	0.380148i
$538$	38.6596	−	16.0133i	1.66674	−	0.690384i
$539$	−0.238126	+	0.574887i	−0.0102568	+	0.0247621i
$540$		−	4.79435i		−	0.206316i
$541$	39.1174	+	16.2030i	1.68179	+	0.696620i	0.999409	−	0.0343783i	$-0.0109451\pi$
$541$	39.1174	+	16.2030i	1.68179	+	0.696620i	0.682380	+	0.730998i	$0.260945\pi$
$542$	5.05141	−	5.05141i	0.216976	−	0.216976i
$543$	1.40627			0.0603487
$544$	−1.89149	+	25.6469i	−0.0810971	+	1.09960i
$545$	4.74828			0.203394
$546$	11.5376	−	11.5376i	0.493766	−	0.493766i
$547$	18.4832	+	7.65599i	0.790285	+	0.327347i	0.741058	−	0.671441i	$-0.234324\pi$
$547$	18.4832	+	7.65599i	0.790285	+	0.327347i	0.0492266	+	0.998788i	$0.484324\pi$
$548$			2.81695i			0.120334i
$549$	−5.77332	+	13.9380i	−0.246399	+	0.594860i
$550$	0.0875901	−	0.0362810i	0.00373485	−	0.00154703i
$551$	1.25921	+	3.04001i	0.0536443	+	0.129509i
$552$	−0.676370	−	0.676370i	−0.0287882	−	0.0287882i
$553$	30.6498	+	30.6498i	1.30336	+	1.30336i
$554$	−11.6858	−	28.2120i	−0.496482	−	1.19861i
$555$	−0.214149	+	0.0887034i	−0.00909012	+	0.00376525i
$556$	−9.52395	+	22.9929i	−0.403906	+	0.975114i
$557$		−	25.8965i		−	1.09727i	−0.836062	−	0.548636i	$-0.815147\pi$
$557$		−	25.8965i		−	1.09727i	0.836062	−	0.548636i	$-0.184853\pi$
$558$	−5.83560	−	2.41718i	−0.247041	−	0.102328i
$559$	21.3791	−	21.3791i	0.904240	−	0.904240i
$560$	−21.4138			−0.904899
$561$	0.112755	−	0.0972653i	0.00476050	−	0.00410655i
$562$	−8.43299			−0.355724
$563$	19.8208	−	19.8208i	0.835349	−	0.835349i	−0.152894	−	0.988243i	$-0.548859\pi$
$563$	19.8208	−	19.8208i	0.835349	−	0.835349i	0.988243	+	0.152894i	$0.0488593\pi$
$564$	−4.91421	−	2.03553i	−0.206925	−	0.0857113i
$565$			3.01331i			0.126771i
$566$	6.01248	−	14.5154i	0.252724	−	0.610129i
$567$	−19.9162	+	8.24956i	−0.836402	+	0.346449i
$568$	−2.13457	−	5.15331i	−0.0895645	−	0.216228i
$569$	−27.7130	−	27.7130i	−1.16179	−	1.16179i	−0.984084	−	0.177706i	$-0.943132\pi$
$569$	−27.7130	−	27.7130i	−1.16179	−	1.16179i	−0.177706	−	0.984084i	$-0.556868\pi$
$570$	−6.86956	−	6.86956i	−0.287734	−	0.287734i
$571$	1.48008	+	3.57322i	0.0619392	+	0.149535i	0.951819	−	0.306661i	$-0.0992118\pi$
$571$	1.48008	+	3.57322i	0.0619392	+	0.149535i	−0.889880	+	0.456196i	$0.849212\pi$
$572$	0.185028	−	0.0766411i	0.00773641	−	0.00320452i
$573$	−0.810972	+	1.95786i	−0.0338788	+	0.0817908i
$574$		−	51.6918i		−	2.15757i
$575$	−0.962654	−	0.398744i	−0.0401454	−	0.0166288i
$576$	−2.50055	+	2.50055i	−0.104190	+	0.104190i
$577$	14.4808			0.602845			0.301423	−	0.953491i	$-0.402539\pi$
$577$	14.4808			0.602845			0.301423	+	0.953491i	$0.402539\pi$
$578$	18.2881	+	24.6573i	0.760684	+	1.02561i
$579$	14.1999			0.590128
$580$	−0.375177	+	0.375177i	−0.0155784	+	0.0155784i
$581$	−26.1949	−	10.8503i	−1.08675	−	0.450145i
$582$		−	23.8810i		−	0.989898i
$583$	−0.242356	+	0.585099i	−0.0100374	+	0.0242323i
$584$	−6.64600	+	2.75286i	−0.275013	+	0.113914i
$585$	2.92511	+	7.06184i	0.120938	+	0.291971i
$586$	0.943767	+	0.943767i	0.0389867	+	0.0389867i
$587$	22.0937	+	22.0937i	0.911905	+	0.911905i	0.996422	−	0.0845171i	$-0.0269347\pi$
$587$	22.0937	+	22.0937i	0.911905	+	0.911905i	−0.0845171	+	0.996422i	$0.526935\pi$
$588$	3.93462	+	9.49900i	0.162261	+	0.391732i
$589$	−10.0017	+	4.14284i	−0.412113	+	0.170703i
$590$	3.52289	−	8.50500i	0.145035	−	0.350145i
$591$		−	12.5452i		−	0.516041i
$592$	1.53529	+	0.635939i	0.0631002	+	0.0261369i
$593$	1.41805	−	1.41805i	0.0582323	−	0.0582323i	−0.677391	−	0.735623i	$-0.736889\pi$
$593$	1.41805	−	1.41805i	0.0582323	−	0.0582323i	0.735623	+	0.677391i	$0.236889\pi$
$594$	0.360452			0.0147895
$595$	−13.5556	+	11.6934i	−0.555724	+	0.479384i
$596$	12.8416			0.526012
$597$	−12.9720	+	12.9720i	−0.530907	+	0.530907i
$598$	−5.25876	−	2.17825i	−0.215047	−	0.0890753i
$599$		−	36.0451i		−	1.47276i	−0.676567	−	0.736381i	$-0.736533\pi$
$599$		−	36.0451i		−	1.47276i	0.676567	−	0.736381i	$-0.263467\pi$
$600$	−0.351305	+	0.848125i	−0.0143420	+	0.0346246i
$601$	−35.8417	+	14.8461i	−1.46201	+	0.605586i	−0.965022	−	0.262168i	$-0.915562\pi$
$601$	−35.8417	+	14.8461i	−1.46201	+	0.605586i	−0.496993	+	0.867755i	$0.665562\pi$
$602$	29.9894	+	72.4007i	1.22228	+	2.95083i
$603$	−1.63669	−	1.63669i	−0.0666510	−	0.0666510i
$604$	−13.6858	−	13.6858i	−0.556867	−	0.556867i
$605$	−4.20846	−	10.1601i	−0.171098	−	0.413068i
$606$	15.2559	−	6.31920i	0.619728	−	0.256700i
$607$	−11.0800	+	26.7496i	−0.449725	+	1.08573i	0.522701	+	0.852516i	$0.324925\pi$
$607$	−11.0800	+	26.7496i	−0.449725	+	1.08573i	−0.972425	+	0.233215i	$0.925075\pi$
$608$			48.7774i			1.97818i
$609$	−1.16108	−	0.480936i	−0.0470494	−	0.0194885i
$610$	−7.62399	+	7.62399i	−0.308686	+	0.308686i
$611$	18.5488			0.750405
$612$	−0.966284	+	13.1019i	−0.0390597	+	0.529613i
$613$	9.10707			0.367831			0.183915	−	0.982942i	$-0.441123\pi$
$613$	9.10707			0.367831			0.183915	+	0.982942i	$0.441123\pi$
$614$	3.65335	−	3.65335i	0.147437	−	0.147437i
$615$	−4.19000	−	1.73555i	−0.168957	−	0.0699842i
$616$		−	0.304197i		−	0.0122564i
$617$	−1.93466	+	4.67068i	−0.0778864	+	0.188035i	−0.958027	−	0.286680i	$-0.907449\pi$
$617$	−1.93466	+	4.67068i	−0.0778864	+	0.188035i	0.880140	+	0.474714i	$0.157449\pi$
$618$	7.93404	−	3.28639i	0.319154	−	0.132198i
$619$	6.45177	+	15.5760i	0.259319	+	0.626051i	0.998894	−	0.0470233i	$-0.0149735\pi$
$619$	6.45177	+	15.5760i	0.259319	+	0.626051i	−0.739575	+	0.673074i	$0.764974\pi$
$620$	−1.23434	−	1.23434i	−0.0495723	−	0.0495723i
$621$	−2.80122	−	2.80122i	−0.112409	−	0.112409i
$622$	14.1654	+	34.1982i	0.567979	+	1.37122i
$623$	40.9803	−	16.9746i	1.64184	−	0.680074i
$624$	−3.92757	+	9.48199i	−0.157229	+	0.379583i
$625$			1.00000i			0.0400000i
$626$	−14.1235	−	5.85013i	−0.564487	−	0.233818i
$627$	0.199717	−	0.199717i	0.00797592	−	0.00797592i
$628$	−11.8690			−0.473625
$629$	1.31915	−	0.435808i	0.0525981	−	0.0173768i
$630$	−19.8119			−0.789323
$631$	1.91845	−	1.91845i	0.0763722	−	0.0763722i	−0.667889	−	0.744261i	$-0.732802\pi$
$631$	1.91845	−	1.91845i	0.0763722	−	0.0763722i	0.744261	+	0.667889i	$0.232802\pi$
$632$	−12.3079	−	5.09809i	−0.489581	−	0.202791i
$633$			5.36965i			0.213424i
$634$	14.5757	−	35.1889i	0.578876	−	1.39753i
$635$	−0.00765625	+	0.00317132i	−0.000303829	+	0.000125850i
$636$	4.00451	+	9.66773i	0.158789	+	0.383351i
$637$	−25.3528	−	25.3528i	−1.00451	−	1.00451i
$638$	−0.0282068	−	0.0282068i	−0.00111672	−	0.00111672i
$639$	−4.04173	−	9.75760i	−0.159888	−	0.386005i
$640$	9.18985	−	3.80656i	0.363261	−	0.150467i
$641$	−8.72988	+	21.0758i	−0.344809	+	0.832443i	0.652406	+	0.757870i	$0.273760\pi$
$641$	−8.72988	+	21.0758i	−0.344809	+	0.832443i	−0.997215	+	0.0745739i	$0.976240\pi$
$642$			18.3118i			0.722711i
$643$	−17.8097	−	7.37702i	−0.702346	−	0.290921i	0.00278691	−	0.999996i	$-0.499113\pi$
$643$	−17.8097	−	7.37702i	−0.702346	−	0.290921i	−0.705133	+	0.709075i	$0.749113\pi$
$644$	4.03408	−	4.03408i	0.158965	−	0.158965i
$645$	6.87550			0.270722
$646$	38.0335	+	44.0903i	1.49641	+	1.73471i
$647$	12.8098			0.503606			0.251803	−	0.967778i	$-0.418976\pi$
$647$	12.8098			0.503606			0.251803	+	0.967778i	$0.418976\pi$
$648$	4.68492	−	4.68492i	0.184041	−	0.184041i
$649$	0.247264	+	0.102420i	0.00970595	+	0.00402033i
$650$			5.46278i			0.214268i
$651$	1.58229	−	3.81998i	0.0620148	−	0.149717i
$652$	−14.4992	+	6.00577i	−0.567833	+	0.235204i
$653$	−15.9656	−	38.5442i	−0.624780	−	1.50835i	−0.846030	−	0.533136i	$-0.821013\pi$
$653$	−15.9656	−	38.5442i	−0.624780	−	1.50835i	0.221249	−	0.975217i	$-0.428987\pi$
$654$	4.17095	+	4.17095i	0.163097	+	0.163097i
$655$	5.78738	+	5.78738i	0.226131	+	0.226131i
$656$	12.4427	+	30.0392i	0.485804	+	1.17284i
$657$	−12.5840	+	5.21244i	−0.490947	+	0.203357i
$658$	−18.3983	+	44.4175i	−0.717242	+	1.73158i
$659$		−	34.3290i		−	1.33727i	−0.743592	−	0.668633i	$-0.766880\pi$
$659$		−	34.3290i		−	1.33727i	0.743592	−	0.668633i	$-0.233120\pi$
$660$	0.0420762	+	0.0174285i	0.00163781	+	0.000678405i
$661$	−19.5875	+	19.5875i	−0.761865	+	0.761865i	−0.976659	−	0.214794i	$-0.931092\pi$
$661$	−19.5875	+	19.5875i	−0.761865	+	0.761865i	0.214794	+	0.976659i	$0.431092\pi$
$662$	−27.4958			−1.06865
$663$	2.69156	+	8.14710i	0.104531	+	0.316407i
$664$	8.71419			0.338176
$665$	−24.0103	+	24.0103i	−0.931081	+	0.931081i
$666$	1.42044	+	0.588365i	0.0550409	+	0.0227987i
$667$			0.438413i			0.0169754i
$668$	6.08161	−	14.6823i	0.235305	−	0.568076i
$669$	3.03089	−	1.25544i	0.117181	−	0.0485380i
$670$	−0.633040	−	1.52829i	−0.0244565	−	0.0590431i
$671$	−0.221650	−	0.221650i	−0.00855671	−	0.00855671i
$672$	−13.1732	−	13.1732i	−0.508168	−	0.508168i
$673$	13.8561	+	33.4517i	0.534115	+	1.28947i	0.928777	+	0.370640i	$0.120862\pi$
$673$	13.8561	+	33.4517i	0.534115	+	1.28947i	−0.394662	+	0.918826i	$0.629138\pi$
$674$	−19.1423	+	7.92902i	−0.737336	+	0.305414i
$675$	−1.45495	+	3.51255i	−0.0560009	+	0.135198i
$676$		−	4.85355i		−	0.186675i
$677$	15.8129	+	6.54992i	0.607739	+	0.251734i	0.665262	−	0.746610i	$-0.268320\pi$
$677$	15.8129	+	6.54992i	0.607739	+	0.251734i	−0.0575224	+	0.998344i	$0.518320\pi$
$678$	−2.64692	+	2.64692i	−0.101654	+	0.101654i
$679$	−83.4684			−3.20322
$680$	2.47377	−	4.91469i	0.0948647	−	0.188470i
$681$	−7.71229			−0.295536
$682$	0.0928009	−	0.0928009i	0.00355353	−	0.00355353i
$683$	8.17654	+	3.38683i	0.312866	+	0.129594i	0.533591	−	0.845743i	$-0.320842\pi$
$683$	8.17654	+	3.38683i	0.312866	+	0.129594i	−0.220725	+	0.975336i	$0.570842\pi$
$684$			24.9183i			0.952776i
$685$	0.854864	−	2.06382i	0.0326627	−	0.0788546i
$686$	35.1501	−	14.5596i	1.34204	−	0.555890i
$687$	−5.43580	−	13.1232i	−0.207389	−	0.500680i
$688$	−34.8550	−	34.8550i	−1.32883	−	1.32883i
$689$	−25.8031	−	25.8031i	−0.983021	−	0.983021i
$690$	−0.495344	−	1.19587i	−0.0188574	−	0.0455259i
$691$	1.29190	−	0.535121i	0.0491461	−	0.0203570i	−0.357975	−	0.933731i	$-0.616533\pi$
$691$	1.29190	−	0.535121i	0.0491461	−	0.0203570i	0.407121	+	0.913374i	$0.366533\pi$
$692$	5.88570	−	14.2093i	0.223741	−	0.540158i
$693$		−	0.575985i		−	0.0218799i
$694$	24.9993	+	10.3551i	0.948962	+	0.393073i
$695$	13.9553	−	13.9553i	0.529356	−	0.529356i
$696$	0.386254			0.0146409
$697$	24.2801	+	12.2212i	0.919673	+	0.462910i
$698$	8.19245			0.310089
$699$	−1.48775	+	1.48775i	−0.0562720	+	0.0562720i
$700$	−5.05848	−	2.09529i	−0.191193	−	0.0791946i
$701$		−	2.36331i		−	0.0892608i	−0.999004	−	0.0446304i	$-0.985789\pi$
$701$		−	2.36331i		−	0.0892608i	0.999004	−	0.0446304i	$-0.0142110\pi$
$702$	−7.94805	+	19.1883i	−0.299980	+	0.724215i
$703$	2.43451	−	1.00841i	0.0918191	−	0.0380327i
$704$	−0.0281182	−	0.0678834i	−0.00105975	−	0.00255845i
$705$	2.98264	+	2.98264i	0.112333	+	0.112333i
$706$	9.85100	+	9.85100i	0.370747	+	0.370747i
$707$	−22.0867	−	53.3221i	−0.830657	−	2.00538i
$708$	4.08560	−	1.69231i	0.153546	−	0.0636009i
$709$	12.4474	−	30.0507i	0.467472	−	1.12858i	−0.497791	−	0.867297i	$-0.665855\pi$
$709$	12.4474	−	30.0507i	0.467472	−	1.12858i	0.965263	−	0.261280i	$-0.0841447\pi$
$710$		−	7.54812i		−	0.283276i
$711$	−23.3045	−	9.65306i	−0.873988	−	0.362018i
$712$	−9.63987	+	9.63987i	−0.361270	+	0.361270i
$713$	−1.44239			−0.0540179
$714$	−22.1790	−	1.63573i	−0.830028	−	0.0612158i
$715$	−0.158818			−0.00593945
$716$	12.3594	−	12.3594i	0.461891	−	0.461891i
$717$	3.14009	+	1.30067i	0.117269	+	0.0485743i
$718$		−	19.9154i		−	0.743237i
$719$	−6.28758	+	15.1796i	−0.234487	+	0.566102i	−0.996695	−	0.0812299i	$-0.974115\pi$
$719$	−6.28758	+	15.1796i	−0.234487	+	0.566102i	0.762208	+	0.647332i	$0.224115\pi$
$720$	11.5131	−	4.76888i	0.429068	−	0.177726i
$721$	−11.4865	−	27.7309i	−0.427780	−	1.03275i
$722$	53.8336	+	53.8336i	2.00348	+	2.00348i
$723$	0.808332	+	0.808332i	0.0300622	+	0.0300622i
$724$	−0.986493	−	2.38160i	−0.0366627	−	0.0885116i
$725$	0.388726	−	0.161016i	0.0144369	−	0.00597997i
$726$	5.22801	−	12.6215i	0.194030	−	0.468429i
$727$		−	32.4709i		−	1.20428i	−0.798391	−	0.602139i	$-0.794315\pi$
$727$		−	32.4709i		−	1.20428i	0.798391	−	0.602139i	$-0.205685\pi$
$728$	16.1936	+	6.70761i	0.600175	+	0.248600i
$729$	3.32256	−	3.32256i	0.123058	−	0.123058i
$730$	−9.73448			−0.360289
$731$	−41.0974	−	3.03099i	−1.52004	−	0.112105i
$732$	−5.17939			−0.191436
$733$	−6.10533	+	6.10533i	−0.225506	+	0.225506i	−0.810812	−	0.585307i	$-0.800974\pi$
$733$	−6.10533	+	6.10533i	−0.225506	+	0.225506i	0.585307	+	0.810812i	$0.300974\pi$
$734$	26.7415	+	11.0767i	0.987048	+	0.408849i
$735$		−	8.15343i		−	0.300744i
$736$	−2.48704	+	6.00424i	−0.0916734	+	0.221319i
$737$	0.0444317	−	0.0184042i	0.00163666	−	0.000677928i
$738$	11.5118	+	27.7920i	0.423756	+	1.02304i
$739$	−7.49715	−	7.49715i	−0.275787	−	0.275787i	0.555637	−	0.831425i	$-0.312474\pi$
$739$	−7.49715	−	7.49715i	−0.275787	−	0.275787i	−0.831425	+	0.555637i	$0.812474\pi$
$740$	0.300450	+	0.300450i	0.0110448	+	0.0110448i
$741$	6.22792	+	15.0355i	0.228788	+	0.552344i
$742$	87.3827	−	36.1951i	3.20792	−	1.32876i
$743$	−8.55008	+	20.6417i	−0.313672	+	0.757272i	0.685891	+	0.727705i	$0.259413\pi$
$743$	−8.55008	+	20.6417i	−0.313672	+	0.757272i	−0.999563	+	0.0295670i	$0.990587\pi$
$744$			1.27079i			0.0465893i
$745$	−9.40831	−	3.89705i	−0.344694	−	0.142777i
$746$	13.0886	−	13.0886i	0.479206	−	0.479206i
$747$	16.5000			0.603704
$748$	−0.243822	−	0.122726i	−0.00891502	−	0.00448730i
$749$	64.0032			2.33863
$750$	−0.878411	+	0.878411i	−0.0320750	+	0.0320750i
$751$	6.59640	+	2.73232i	0.240706	+	0.0997037i	0.499775	−	0.866155i	$-0.333416\pi$
$751$	6.59640	+	2.73232i	0.240706	+	0.0997037i	−0.259069	+	0.965859i	$0.583416\pi$
$752$		−	30.2406i		−	1.10276i
$753$	−2.40678	+	5.81047i	−0.0877078	+	0.211745i
$754$	2.12353	−	0.879593i	0.0773342	−	0.0320329i
$755$	5.87357	+	14.1800i	0.213761	+	0.516065i
$756$	−14.7197	−	14.7197i	−0.535349	−	0.535349i
$757$	12.7467	+	12.7467i	0.463287	+	0.463287i	0.899731	−	0.436444i	$-0.143762\pi$
$757$	12.7467	+	12.7467i	0.463287	+	0.463287i	−0.436444	+	0.899731i	$0.643762\pi$
$758$	−9.64166	−	23.2770i	−0.350201	−	0.845460i
$759$	0.0347671	−	0.0144010i	0.00126197	−	0.000522724i
$760$	3.99373	−	9.64173i	0.144868	−	0.349742i
$761$		−	49.9437i		−	1.81046i	−0.424923	−	0.905230i	$-0.639699\pi$
$761$		−	49.9437i		−	1.81046i	0.424923	−	0.905230i	$-0.360301\pi$
$762$	−0.00951106	−	0.00393961i	−0.000344549	−	0.000142717i
$763$	14.5782	−	14.5782i	0.527767	−	0.527767i
$764$	3.88466			0.140542
$765$	4.68399	−	9.30580i	0.169350	−	0.336452i
$766$	10.1521			0.366811
$767$	−10.9044	+	10.9044i	−0.393737	+	0.393737i
$768$	13.1952	+	5.46561i	0.476139	+	0.197223i
$769$			43.9115i			1.58349i	0.610852	+	0.791745i	$0.290827\pi$
$769$			43.9115i			1.58349i	−0.610852	+	0.791745i	$0.709173\pi$
$770$	0.157530	−	0.380310i	0.00567697	−	0.0137054i
$771$	−10.5834	+	4.38377i	−0.381151	+	0.157878i
$772$	−9.96120	−	24.0485i	−0.358511	−	0.865523i
$773$	6.84309	+	6.84309i	0.246129	+	0.246129i	0.819380	−	0.573251i	$-0.194318\pi$
$773$	6.84309	+	6.84309i	0.246129	+	0.246129i	−0.573251	+	0.819380i	$0.694318\pi$
$774$	−32.2475	−	32.2475i	−1.15911	−	1.15911i
$775$	0.529745	+	1.27892i	0.0190290	+	0.0459401i
$776$	23.7008	−	9.81720i	0.850810	−	0.352417i
$777$	−0.385144	+	0.929820i	−0.0138170	+	0.0333571i
$778$		−	64.6771i		−	2.31879i
$779$	47.6330	+	19.7302i	1.70663	+	0.706909i
$780$	−1.85558	+	1.85558i	−0.0664405	+	0.0664405i
$781$	0.219445			0.00785234
$782$	2.43367	+	7.36651i	0.0870280	+	0.263426i
$783$	1.59969			0.0571683
$784$	−41.3334	+	41.3334i	−1.47619	+	1.47619i
$785$	8.69576	+	3.60190i	0.310365	+	0.128557i
$786$			10.1674i			0.362659i
$787$	7.59181	−	18.3283i	0.270619	−	0.653332i	−0.728891	−	0.684630i	$-0.759964\pi$
$787$	7.59181	−	18.3283i	0.270619	−	0.653332i	0.999510	+	0.0312976i	$0.00996398\pi$
$788$	−21.2461	+	8.80043i	−0.756861	+	0.313502i
$789$	5.72000	+	13.8093i	0.203637	+	0.491624i
$790$	−12.7474	−	12.7474i	−0.453532	−	0.453532i
$791$	9.25147	+	9.25147i	0.328944	+	0.328944i
$792$	0.0677450	+	0.163551i	0.00240721	+	0.00581152i
$793$	16.6868	−	6.91188i	0.592564	−	0.245448i
$794$	−2.68835	+	6.49024i	−0.0954059	+	0.230330i
$795$		−	8.29826i		−	0.294309i
$796$	31.0687	+	12.8691i	1.10120	+	0.456132i
$797$	−3.93230	+	3.93230i	−0.139289	+	0.139289i	−0.773313	−	0.634024i	$-0.781402\pi$
$797$	−3.93230	+	3.93230i	−0.139289	+	0.139289i	0.634024	+	0.773313i	$0.281402\pi$
$798$	−42.1819			−1.49322
$799$	−16.5135	−	19.1432i	−0.584205	−	0.677238i
$800$	6.23717			0.220517
$801$	−18.2528	+	18.2528i	−0.644929	+	0.644929i
$802$	−61.2935	−	25.3886i	−2.16435	−	0.896502i
$803$		−	0.283008i		−	0.00998714i
$804$	0.304097	−	0.734156i	0.0107247	−	0.0258917i
$805$	−4.17977	+	1.73132i	−0.147318	+	0.0610210i
$806$	2.89388	+	6.98644i	0.101933	+	0.246087i
$807$	−11.2716	−	11.2716i	−0.396780	−	0.396780i
$808$	12.5430	+	12.5430i	0.441263	+	0.441263i
$809$	11.8801	+	28.6811i	0.417683	+	1.00838i	0.983017	+	0.183513i	$0.0587471\pi$
$809$	11.8801	+	28.6811i	0.417683	+	1.00838i	−0.565335	+	0.824862i	$0.691253\pi$
$810$	8.28325	−	3.43103i	0.291044	−	0.120554i
$811$	−17.9749	+	43.3953i	−0.631185	+	1.52382i	0.206949	+	0.978352i	$0.433647\pi$
$811$	−17.9749	+	43.3953i	−0.631185	+	1.52382i	−0.838134	+	0.545464i	$0.816353\pi$
$812$			2.30374i			0.0808455i
$813$	−2.51421	−	1.04142i	−0.0881773	−	0.0365242i
$814$	−0.0225886	+	0.0225886i	−0.000791730	+	0.000791730i
$815$	12.4453			0.435941
$816$	13.2824	−	4.38812i	0.464979	−	0.153615i
$817$	−78.1626			−2.73456
$818$	28.5428	−	28.5428i	0.997976	−	0.997976i
$819$	30.6620	+	12.7006i	1.07142	+	0.443795i
$820$			8.31351i			0.290320i
$821$	6.40739	−	15.4688i	0.223619	−	0.539865i	−0.771757	−	0.635918i	$-0.780622\pi$
$821$	6.40739	−	15.4688i	0.223619	−	0.539865i	0.995376	+	0.0960527i	$0.0306217\pi$
$822$	2.56381	−	1.06196i	0.0894231	−	0.0370402i
$823$	−10.1792	−	24.5749i	−0.354826	−	0.856626i	−0.996010	−	0.0892387i	$-0.971557\pi$
$823$	−10.1792	−	24.5749i	−0.354826	−	0.856626i	0.641184	−	0.767387i	$-0.278443\pi$
$824$	6.52318	+	6.52318i	0.227246	+	0.227246i
$825$	−0.0255378	−	0.0255378i	−0.000889113	−	0.000889113i
$826$	−15.2961	−	36.9281i	−0.532220	−	1.28489i
$827$	31.8605	−	13.1970i	1.10790	−	0.458906i	0.247684	−	0.968841i	$-0.420330\pi$
$827$	31.8605	−	13.1970i	1.10790	−	0.458906i	0.860213	+	0.509934i	$0.170330\pi$
$828$	−1.27052	+	3.06731i	−0.0441537	+	0.106597i
$829$		−	7.29346i		−	0.253312i	−0.991947	−	0.126656i	$-0.959576\pi$
$829$		−	7.29346i		−	0.253312i	0.991947	−	0.126656i	$-0.0404245\pi$
$830$	10.8946	+	4.51269i	0.378157	+	0.156638i
$831$	−8.22551	+	8.22551i	−0.285340	+	0.285340i
$832$	4.23372			0.146778
$833$	−3.59436	+	48.7361i	−0.124537	+	1.68861i
$834$	24.5170			0.848956
$835$	−8.91131	+	8.91131i	−0.308389	+	0.308389i
$836$	−0.478334	−	0.198133i	−0.0165435	−	0.00685256i
$837$			5.26302i			0.181917i
$838$	−15.1106	+	36.4802i	−0.521987	+	1.26019i
$839$	−32.8053	+	13.5884i	−1.13257	+	0.469124i	−0.868652	−	0.495422i	$-0.835013\pi$
$839$	−32.8053	+	13.5884i	−1.13257	+	0.469124i	−0.263913	+	0.964546i	$0.585013\pi$
$840$	1.52534	+	3.68250i	0.0526293	+	0.127058i
$841$	20.3809	+	20.3809i	0.702790	+	0.702790i
$842$	−26.3187	−	26.3187i	−0.907001	−	0.907001i
$843$	1.22936	+	2.96795i	0.0423415	+	0.102222i
$844$	9.09385	−	3.76680i	0.313023	−	0.129658i
$845$	−1.47291	+	3.55592i	−0.0506697	+	0.122327i
$846$		−	27.9784i		−	0.961916i
$847$	−44.1146	−	18.2728i	−1.51579	−	0.627862i
$848$	−42.0676	+	42.0676i	−1.44461	+	1.44461i
$849$	−5.98513			−0.205409
$850$	5.63783	−	4.86335i	0.193376	−	0.166812i
$851$	0.351091			0.0120352
$852$	2.56393	−	2.56393i	0.0878386	−	0.0878386i
$853$	0.220643	+	0.0913933i	0.00755467	+	0.00312925i	0.386458	−	0.922307i	$-0.373699\pi$
$853$	0.220643	+	0.0913933i	0.00755467	+	0.00312925i	−0.378903	+	0.925436i	$0.623699\pi$
$854$			46.8144i			1.60196i
$855$	7.56199	−	18.2563i	0.258615	−	0.624351i
$856$	−18.1737	+	7.52779i	−0.621164	+	0.257295i
$857$	−6.96291	−	16.8099i	−0.237848	−	0.574217i	0.759211	−	0.650844i	$-0.225585\pi$
$857$	−6.96291	−	16.8099i	−0.237848	−	0.574217i	−0.997060	+	0.0766273i	$0.975585\pi$
$858$	−0.139507	−	0.139507i	−0.00476271	−	0.00476271i
$859$	−14.2525	−	14.2525i	−0.486288	−	0.486288i	0.420845	−	0.907133i	$-0.361734\pi$
$859$	−14.2525	−	14.2525i	−0.486288	−	0.486288i	−0.907133	+	0.420845i	$0.861734\pi$
$860$	−4.82314	−	11.6441i	−0.164468	−	0.397061i
$861$	−18.1927	+	7.53565i	−0.620004	+	0.256814i
$862$	−15.4143	+	37.2134i	−0.525013	+	1.26749i
$863$			14.7597i			0.502424i	0.967932	+	0.251212i	$0.0808292\pi$
$863$			14.7597i			0.502424i	−0.967932	+	0.251212i	$0.919171\pi$
$864$	21.9084	+	9.07476i	0.745339	+	0.308730i
$865$	−8.62424	+	8.62424i	−0.293233	+	0.293233i
$866$	16.1284			0.548064
$867$	6.01196	−	10.0309i	0.204177	−	0.340669i
$868$	−7.57936			−0.257260
$869$	0.370602	−	0.370602i	0.0125718	−	0.0125718i
$870$	0.482900	+	0.200024i	0.0163718	+	0.00678144i
$871$			2.77109i			0.0938949i
$872$	−2.42485	+	5.85411i	−0.0821158	+	0.198245i
$873$	44.8766	−	18.5885i	1.51884	−	0.629126i
$874$	5.63121	+	13.5950i	0.190479	+	0.459856i
$875$	3.07021	+	3.07021i	0.103792	+	0.103792i
$876$	−3.30658	−	3.30658i	−0.111719	−	0.111719i
$877$	16.3627	+	39.5030i	0.552528	+	1.33392i	0.915574	+	0.402149i	$0.131737\pi$
$877$	16.3627	+	39.5030i	0.552528	+	1.33392i	−0.363046	+	0.931771i	$0.618263\pi$
$878$	−37.1450	+	15.3860i	−1.25358	+	0.519251i
$879$	0.194571	−	0.469737i	0.00656273	−	0.0158438i
$880$			0.258925i			0.00872837i
$881$	−40.3580	−	16.7168i	−1.35970	−	0.563205i	−0.420721	−	0.907190i	$-0.638223\pi$
$881$	−40.3580	−	16.7168i	−1.35970	−	0.563205i	−0.938975	+	0.343985i	$0.888223\pi$
$882$	−38.2412	+	38.2412i	−1.28765	+	1.28765i
$883$	41.4824			1.39599			0.697997	−	0.716101i	$-0.254075\pi$
$883$	41.4824			1.39599			0.697997	+	0.716101i	$0.254075\pi$
$884$	11.9095	−	10.2735i	0.400561	−	0.345535i
$885$	−3.50686			−0.117882
$886$	7.88394	−	7.88394i	0.264866	−	0.264866i
$887$	30.3770	+	12.5826i	1.01996	+	0.422481i	0.829078	−	0.559132i	$-0.188866\pi$
$887$	30.3770	+	12.5826i	1.01996	+	0.422481i	0.190881	+	0.981613i	$0.438866\pi$
$888$		−	0.309321i		−	0.0103801i
$889$	−0.0137697	+	0.0332429i	−0.000461819	+	0.00111493i
$890$	−17.0439	+	7.05983i	−0.571314	+	0.236646i
$891$	0.0997496	+	0.240817i	0.00334174	+	0.00806767i
$892$	−4.25233	−	4.25233i	−0.142378	−	0.142378i
$893$	−33.9075	−	33.9075i	−1.13467	−	1.13467i
$894$	−4.84115	−	11.6876i	−0.161912	−	0.390891i
$895$	−12.8057	+	5.30430i	−0.428048	+	0.177303i
$896$	16.5278	−	39.9017i	0.552155	−	1.33302i
$897$			2.16834i			0.0723988i
$898$	−50.5491	−	20.9381i	−1.68685	−	0.698714i
$899$	0.411852	−	0.411852i	0.0137360	−	0.0137360i
$900$	3.18631			0.106210
$901$	−3.65820	+	49.6018i	−0.121872	+	1.65248i
$902$	−0.625031			−0.0208113
$903$	21.1092	−	21.1092i	0.702470	−	0.702470i
$904$	−3.71507	−	1.53883i	−0.123561	−	0.0511808i
$905$			2.04424i			0.0679528i
$906$	−7.29650	+	17.6153i	−0.242410	+	0.585230i
$907$	33.6731	−	13.9479i	1.11810	−	0.463131i	0.254379	−	0.967105i	$-0.418129\pi$
$907$	33.6731	−	13.9479i	1.11810	−	0.463131i	0.863719	+	0.503973i	$0.168129\pi$
$908$	5.41015	+	13.0613i	0.179542	+	0.433453i
$909$	23.7498	+	23.7498i	0.787731	+	0.787731i
$910$	16.7719	+	16.7719i	0.555982	+	0.555982i
$911$	−11.4322	−	27.5999i	−0.378767	−	0.914425i	−0.992197	−	0.124676i	$-0.960211\pi$
$911$	−11.4322	−	27.5999i	−0.378767	−	0.914425i	0.613430	−	0.789749i	$-0.289789\pi$
$912$	24.5128	−	10.1535i	0.811701	−	0.336218i
$913$	−0.131196	+	0.316736i	−0.00434196	+	0.0104824i
$914$			46.1852i			1.52767i
$915$	3.79465	+	1.57180i	0.125447	+	0.0519619i
$916$	−18.4117	+	18.4117i	−0.608341	+	0.608341i
$917$	35.5369			1.17353
$918$	26.8791	−	8.88004i	0.887143	−	0.293085i
$919$	11.6218			0.383368			0.191684	−	0.981457i	$-0.438605\pi$
$919$	11.6218			0.383368			0.191684	+	0.981457i	$0.438605\pi$
$920$	0.983215	−	0.983215i	0.0324156	−	0.0324156i
$921$	−1.81836	−	0.753191i	−0.0599171	−	0.0248185i
$922$		−	25.3837i		−	0.835966i
$923$	−4.83880	+	11.6819i	−0.159271	+	0.384515i
$924$	0.182692	−	0.0756735i	0.00601012	−	0.00248947i
$925$	−0.128945	−	0.311301i	−0.00423968	−	0.0102355i
$926$	−32.0803	−	32.0803i	−1.05422	−	1.05422i
$927$	12.3514	+	12.3514i	0.405674	+	0.405674i
$928$	−1.00428	−	2.42455i	−0.0329672	−	0.0795899i
$929$	−4.65849	+	1.92961i	−0.152840	+	0.0633085i	−0.457792	−	0.889059i	$-0.651360\pi$
$929$	−4.65849	+	1.92961i	−0.152840	+	0.0633085i	0.304952	+	0.952368i	$0.401360\pi$
$930$	−0.658082	+	1.58875i	−0.0215794	+	0.0520972i
$931$			92.6904i			3.03781i
$932$	3.56326	+	1.47595i	0.116718	+	0.0483464i
$933$	9.97085	−	9.97085i	0.326431	−	0.326431i
$934$	40.2520			1.31709
$935$	0.141391	+	0.163907i	0.00462398	+	0.00536034i
$936$	−10.2003			−0.333406
$937$	24.6863	−	24.6863i	0.806465	−	0.806465i	−0.177632	−	0.984097i	$-0.556844\pi$
$937$	24.6863	−	24.6863i	0.806465	−	0.806465i	0.984097	+	0.177632i	$0.0568437\pi$
$938$	−6.63574	−	2.74861i	−0.216665	−	0.0897454i
$939$			5.82351i			0.190043i
$940$	2.95898	−	7.14360i	0.0965112	−	0.232999i
$941$	10.2169	−	4.23196i	0.333060	−	0.137958i	−0.209885	−	0.977726i	$-0.567309\pi$
$941$	10.2169	−	4.23196i	0.333060	−	0.137958i	0.542945	+	0.839768i	$0.317309\pi$
$942$	4.47450	+	10.8024i	0.145787	+	0.351961i
$943$	4.85738	+	4.85738i	0.158178	+	0.158178i
$944$	17.7778	+	17.7778i	0.578619	+	0.578619i
$945$	6.31728	+	15.2513i	0.205501	+	0.496123i
$946$	0.875434	−	0.362616i	0.0284628	−	0.0117897i
$947$	4.39774	−	10.6171i	0.142907	−	0.345008i	−0.836178	−	0.548458i	$-0.815215\pi$
$947$	4.39774	−	10.6171i	0.142907	−	0.345008i	0.979086	+	0.203449i	$0.0652152\pi$
$948$		−	8.66000i		−	0.281264i
$949$	15.0657	+	6.24040i	0.489052	+	0.202572i
$950$	9.98602	−	9.98602i	0.323989	−	0.323989i
$951$	−14.5094			−0.470500
$952$	−7.49414	−	22.6841i	−0.242887	−	0.735196i
$953$	−0.704896			−0.0228338			−0.0114169	−	0.999935i	$-0.503634\pi$
$953$	−0.704896			−0.0228338			−0.0114169	+	0.999935i	$0.503634\pi$
$954$	−38.9205	+	38.9205i	−1.26010	+	1.26010i
$955$	−2.84607	−	1.17888i	−0.0920966	−	0.0381477i
$956$		−	6.23035i		−	0.201504i
$957$	−0.00581524	+	0.0140392i	−0.000187980	+	0.000453824i
$958$	−44.6282	+	18.4856i	−1.44187	+	0.597243i
$959$	−3.71176	−	8.96097i	−0.119859	−	0.289365i
$960$	0.680780	+	0.680780i	0.0219721	+	0.0219721i
$961$	−20.5653	−	20.5653i	−0.663397	−	0.663397i
$962$	−0.704397	−	1.70057i	−0.0227107	−	0.0548284i
$963$	−34.4112	+	14.2536i	−1.10889	+	0.459316i
$964$	0.801919	−	1.93600i	0.0258281	−	0.0623545i
$965$			20.6419i			0.664486i
$966$	−5.19237	−	2.15075i	−0.167062	−	0.0691993i
$967$	28.2521	−	28.2521i	0.908527	−	0.908527i	−0.0876267	−	0.996153i	$-0.527928\pi$
$967$	28.2521	−	28.2521i	0.908527	−	0.908527i	0.996153	+	0.0876267i	$0.0279283\pi$
$968$	14.6755			0.471688
$969$	9.97281	−	19.8132i	0.320373	−	0.636492i
$970$	34.7149			1.11463
$971$	30.5851	−	30.5851i	0.981521	−	0.981521i	−0.0183111	−	0.999832i	$-0.505829\pi$
$971$	30.5851	−	30.5851i	0.981521	−	0.981521i	0.999832	+	0.0183111i	$0.00582892\pi$
$972$	17.2673	+	7.15235i	0.553849	+	0.229412i
$973$		−	85.6915i		−	2.74714i
$974$	15.9953	−	38.6161i	0.512523	−	1.23734i
$975$	1.92260	−	0.796365i	0.0615723	−	0.0255041i
$976$	−11.2686	−	27.2049i	−0.360700	−	0.870807i
$977$	−34.5543	−	34.5543i	−1.10549	−	1.10549i	−0.993736	−	0.111753i	$-0.964353\pi$
$977$	−34.5543	−	34.5543i	−1.10549	−	1.10549i	−0.111753	−	0.993736i	$-0.535647\pi$
$978$	10.9321	+	10.9321i	0.349571	+	0.349571i
$979$	−0.205249	−	0.495514i	−0.00655977	−	0.0158367i
$980$	−13.8084	+	5.71961i	−0.441092	+	0.182706i
$981$	−4.59137	+	11.0845i	−0.146591	+	0.353902i
$982$		−	14.0671i		−	0.448898i
$983$	−45.1621	−	18.7068i	−1.44045	−	0.596653i	−0.480542	−	0.876972i	$-0.659560\pi$
$983$	−45.1621	−	18.7068i	−1.44045	−	0.596653i	−0.959907	+	0.280318i	$0.909560\pi$
$984$	4.27949	−	4.27949i	0.136425	−	0.136425i
$985$	18.2365			0.581063
$986$	−2.79829	−	1.40850i	−0.0891158	−	0.0448557i
$987$	18.3146			0.582961
$988$	21.0948	−	21.0948i	0.671114	−	0.671114i
$989$	−9.62140	−	3.98531i	−0.305943	−	0.126726i
$990$			0.239555i			0.00761356i
$991$	5.56191	−	13.4276i	0.176680	−	0.426543i	−0.810586	−	0.585619i	$-0.800851\pi$
$991$	5.56191	−	13.4276i	0.176680	−	0.426543i	0.987266	+	0.159076i	$0.0508515\pi$
$992$	7.97684	−	3.30411i	0.253265	−	0.104906i
$993$	4.00834	+	9.67699i	0.127201	+	0.307090i
$994$	−23.1743	−	23.1743i	−0.735044	−	0.735044i
$995$	−18.8569	−	18.8569i	−0.597803	−	0.597803i
$996$	2.16779	+	5.23350i	0.0686890	+	0.165830i
$997$	−40.8392	+	16.9161i	−1.29339	+	0.535740i	−0.919994	−	0.391933i	$-0.871807\pi$
$997$	−40.8392	+	16.9161i	−1.29339	+	0.535740i	−0.373396	+	0.927672i	$0.621807\pi$
$998$	6.07971	−	14.6777i	0.192450	−	0.464615i
$999$		−	1.28107i		−	0.0405312i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	85.2.l.a.26.2	✓	24
3.2	odd	2		765.2.be.b.451.5		24
5.2	odd	4		425.2.n.f.349.2		24
5.3	odd	4		425.2.n.c.349.5		24
5.4	even	2		425.2.m.b.26.5		24
17.2	even	8	inner	85.2.l.a.36.2	yes	24
17.6	odd	16		1445.2.a.p.1.3		12
17.7	odd	16		1445.2.d.j.866.20		24
17.10	odd	16		1445.2.d.j.866.19		24
17.11	odd	16		1445.2.a.q.1.3		12
51.2	odd	8		765.2.be.b.631.5		24
85.2	odd	8		425.2.n.c.274.5		24
85.19	even	8		425.2.m.b.376.5		24
85.53	odd	8		425.2.n.f.274.2		24
85.74	odd	16		7225.2.a.bs.1.10		12
85.79	odd	16		7225.2.a.bq.1.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.26.2	✓	24	1.1	even	1	trivial
85.2.l.a.36.2	yes	24	17.2	even	8	inner
425.2.m.b.26.5		24	5.4	even	2
425.2.m.b.376.5		24	85.19	even	8
425.2.n.c.274.5		24	85.2	odd	8
425.2.n.c.349.5		24	5.3	odd	4
425.2.n.f.274.2		24	85.53	odd	8
425.2.n.f.349.2		24	5.2	odd	4
765.2.be.b.451.5		24	3.2	odd	2
765.2.be.b.631.5		24	51.2	odd	8
1445.2.a.p.1.3		12	17.6	odd	16
1445.2.a.q.1.3		12	17.11	odd	16
1445.2.d.j.866.19		24	17.10	odd	16
1445.2.d.j.866.20		24	17.7	odd	16
7225.2.a.bq.1.10		12	85.79	odd	16
7225.2.a.bs.1.10		12	85.74	odd	16

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:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	85.l (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27691 + 1.27691i) q^{2} +(0.635552 + 0.263254i) q^{3} -1.26102i q^{4} +(-0.382683 + 0.923880i) q^{5} +(-1.14770 + 0.475393i) q^{6} +(1.66158 + 4.01142i) q^{7} +(-0.943613 - 0.943613i) q^{8} +(-1.78670 - 1.78670i) q^{9} +O(q^{10})\)	\(q+(-1.27691 + 1.27691i) q^{2} +(0.635552 + 0.263254i) q^{3} -1.26102i q^{4} +(-0.382683 + 0.923880i) q^{5} +(-1.14770 + 0.475393i) q^{6} +(1.66158 + 4.01142i) q^{7} +(-0.943613 - 0.943613i) q^{8} +(-1.78670 - 1.78670i) q^{9} +(-0.691061 - 1.66837i) q^{10} +(0.0485041 - 0.0200910i) q^{11} +(0.331970 - 0.801445i) q^{12} +3.02508i q^{13} +(-7.24394 - 3.00054i) q^{14} +(-0.486431 + 0.486431i) q^{15} +4.93187 q^{16} +(3.12202 - 2.69314i) q^{17} +4.56292 q^{18} +(5.52988 - 5.52988i) q^{19} +(1.16503 + 0.482572i) q^{20} +2.98689i q^{21} +(-0.0362810 + 0.0875901i) q^{22} +(0.962654 - 0.398744i) q^{23} +(-0.351305 - 0.848125i) q^{24} +(-0.707107 - 0.707107i) q^{25} +(-3.86277 - 3.86277i) q^{26} +(-1.45495 - 3.51255i) q^{27} +(5.05848 - 2.09529i) q^{28} +(-0.161016 + 0.388726i) q^{29} -1.24226i q^{30} +(-1.27892 - 0.529745i) q^{31} +(-4.41035 + 4.41035i) q^{32} +0.0361159 q^{33} +(-0.547638 + 7.42546i) q^{34} -4.34193 q^{35} +(-2.25306 + 2.25306i) q^{36} +(0.311301 + 0.128945i) q^{37} +14.1224i q^{38} +(-0.796365 + 1.92260i) q^{39} +(1.23289 - 0.510679i) q^{40} +(2.52291 + 6.09084i) q^{41} +(-3.81400 - 3.81400i) q^{42} +(-7.06729 - 7.06729i) q^{43} +(-0.0253352 - 0.0611647i) q^{44} +(2.33443 - 0.966953i) q^{45} +(-0.720064 + 1.73839i) q^{46} -6.13168i q^{47} +(3.13446 + 1.29834i) q^{48} +(-8.38087 + 8.38087i) q^{49} +1.80583 q^{50} +(2.69319 - 0.889748i) q^{51} +3.81469 q^{52} +(-8.52974 + 8.52974i) q^{53} +(6.34307 + 2.62739i) q^{54} +0.0525004i q^{55} +(2.21733 - 5.35312i) q^{56} +(4.97030 - 2.05876i) q^{57} +(-0.290767 - 0.701974i) q^{58} +(3.60468 + 3.60468i) q^{59} +(0.613400 + 0.613400i) q^{60} +(-2.28486 - 5.51614i) q^{61} +(2.30951 - 0.956630i) q^{62} +(4.19844 - 10.1359i) q^{63} -1.39954i q^{64} +(-2.79481 - 1.15765i) q^{65} +(-0.0461170 + 0.0461170i) q^{66} +0.916040 q^{67} +(-3.39611 - 3.93693i) q^{68} +0.716788 q^{69} +(5.54427 - 5.54427i) q^{70} +(3.86169 + 1.59956i) q^{71} +3.37190i q^{72} +(2.06289 - 4.98025i) q^{73} +(-0.562156 + 0.232853i) q^{74} +(-0.263254 - 0.635552i) q^{75} +(-6.97330 - 6.97330i) q^{76} +(0.161187 + 0.161187i) q^{77} +(-1.43810 - 3.47188i) q^{78} +(9.22305 - 3.82031i) q^{79} +(-1.88734 + 4.55645i) q^{80} +4.96488i q^{81} +(-10.9990 - 4.55595i) q^{82} +(-4.61746 + 4.61746i) q^{83} +3.76653 q^{84} +(1.29339 + 3.91499i) q^{85} +18.0487 q^{86} +(-0.204668 + 0.204668i) q^{87} +(-0.0647272 - 0.0268109i) q^{88} -10.2159i q^{89} +(-1.74615 + 4.21559i) q^{90} +(-12.1349 + 5.02642i) q^{91} +(-0.502825 - 1.21393i) q^{92} +(-0.673362 - 0.673362i) q^{93} +(7.82963 + 7.82963i) q^{94} +(2.99275 + 7.22514i) q^{95} +(-3.96405 + 1.64196i) q^{96} +(-7.35663 + 17.7605i) q^{97} -21.4033i q^{98} +(-0.122559 - 0.0507655i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{6} - 24 q^{9}+O(q^{10}) \) 24 * q - 8 * q^6 - 24 * q^9	\( 24 q - 8 q^{6} - 24 q^{9} - 8 q^{11} + 24 q^{12} - 8 q^{15} - 24 q^{16} - 8 q^{17} + 8 q^{18} - 8 q^{19} - 32 q^{22} - 16 q^{23} - 8 q^{24} + 16 q^{26} + 24 q^{27} + 48 q^{28} - 8 q^{29} + 16 q^{34} - 32 q^{35} - 24 q^{36} + 24 q^{37} + 8 q^{39} + 16 q^{40} + 16 q^{41} - 24 q^{42} + 8 q^{43} + 16 q^{44} + 16 q^{45} + 8 q^{46} + 80 q^{48} + 8 q^{50} - 56 q^{51} - 48 q^{52} + 24 q^{53} - 32 q^{54} + 64 q^{56} + 32 q^{57} - 64 q^{58} + 32 q^{59} + 24 q^{60} + 32 q^{61} - 32 q^{62} - 56 q^{63} + 8 q^{65} + 96 q^{66} + 16 q^{67} - 40 q^{68} + 96 q^{69} - 24 q^{71} - 64 q^{74} - 8 q^{75} - 8 q^{76} + 24 q^{77} - 112 q^{78} - 32 q^{80} - 80 q^{82} - 96 q^{83} - 64 q^{84} - 16 q^{86} - 48 q^{87} - 8 q^{88} - 24 q^{91} + 80 q^{92} + 64 q^{93} + 56 q^{94} - 16 q^{95} - 168 q^{96} - 40 q^{97} - 8 q^{99}+O(q^{100}) \) 24 * q - 8 * q^6 - 24 * q^9 - 8 * q^11 + 24 * q^12 - 8 * q^15 - 24 * q^16 - 8 * q^17 + 8 * q^18 - 8 * q^19 - 32 * q^22 - 16 * q^23 - 8 * q^24 + 16 * q^26 + 24 * q^27 + 48 * q^28 - 8 * q^29 + 16 * q^34 - 32 * q^35 - 24 * q^36 + 24 * q^37 + 8 * q^39 + 16 * q^40 + 16 * q^41 - 24 * q^42 + 8 * q^43 + 16 * q^44 + 16 * q^45 + 8 * q^46 + 80 * q^48 + 8 * q^50 - 56 * q^51 - 48 * q^52 + 24 * q^53 - 32 * q^54 + 64 * q^56 + 32 * q^57 - 64 * q^58 + 32 * q^59 + 24 * q^60 + 32 * q^61 - 32 * q^62 - 56 * q^63 + 8 * q^65 + 96 * q^66 + 16 * q^67 - 40 * q^68 + 96 * q^69 - 24 * q^71 - 64 * q^74 - 8 * q^75 - 8 * q^76 + 24 * q^77 - 112 * q^78 - 32 * q^80 - 80 * q^82 - 96 * q^83 - 64 * q^84 - 16 * q^86 - 48 * q^87 - 8 * q^88 - 24 * q^91 + 80 * q^92 + 64 * q^93 + 56 * q^94 - 16 * q^95 - 168 * q^96 - 40 * q^97 - 8 * q^99

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