LMFDB - Embedded newform 850.2.g.i.599.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [850,2,Mod(149,850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(850, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("850.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 850 = 2 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	850.g (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.78728417181$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.23045668864.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 26x^{6} + 237x^{4} + 892x^{2} + 1156 $ x^8 + 26x^6 + 237x^4 + 892*x^2 + 1156
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 170)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			599.3
Root			$3.26843i$ of defining polynomial
Character	$\chi$	$=$	850.599
Dual form			850.2.g.i.149.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(1.60402 + 1.60402i) q^{3} +1.00000 q^{4} +(-1.60402 - 1.60402i) q^{6} +(2.26843 - 2.26843i) q^{7} -1.00000 q^{8} +2.14578i q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(1.60402 + 1.60402i) q^{3} +1.00000 q^{4} +(-1.60402 - 1.60402i) q^{6} +(2.26843 - 2.26843i) q^{7} -1.00000 q^{8} +2.14578i q^{9} +(-1.82843 - 1.82843i) q^{11} +(1.60402 + 1.60402i) q^{12} -5.68265i q^{13} +(-2.26843 + 2.26843i) q^{14} +1.00000 q^{16} +(4.07862 - 0.604023i) q^{17} -2.14578i q^{18} -4.35383i q^{19} +7.27723 q^{21} +(1.82843 + 1.82843i) q^{22} +(3.41421 - 3.41421i) q^{23} +(-1.60402 - 1.60402i) q^{24} +5.68265i q^{26} +(1.37019 - 1.37019i) q^{27} +(2.26843 - 2.26843i) q^{28} +(-6.01824 + 6.01824i) q^{29} +(-1.16402 + 1.16402i) q^{31} -1.00000 q^{32} -5.86568i q^{33} +(-4.07862 + 0.604023i) q^{34} +2.14578i q^{36} +(-3.09686 - 3.09686i) q^{37} +4.35383i q^{38} +(9.11510 - 9.11510i) q^{39} +(5.53686 + 5.53686i) q^{41} -7.27723 q^{42} -7.20805 q^{43} +(-1.82843 - 1.82843i) q^{44} +(-3.41421 + 3.41421i) q^{46} +4.89069i q^{47} +(1.60402 + 1.60402i) q^{48} -3.29156i q^{49} +(7.51107 + 5.57334i) q^{51} -5.68265i q^{52} +1.14578 q^{53} +(-1.37019 + 1.37019i) q^{54} +(-2.26843 + 2.26843i) q^{56} +(6.98364 - 6.98364i) q^{57} +(6.01824 - 6.01824i) q^{58} +8.01068i q^{59} +(-4.51863 - 4.51863i) q^{61} +(1.16402 - 1.16402i) q^{62} +(4.86756 + 4.86756i) q^{63} +1.00000 q^{64} +5.86568i q^{66} +14.0729i q^{67} +(4.07862 - 0.604023i) q^{68} +10.9530 q^{69} +(-4.37207 + 4.37207i) q^{71} -2.14578i q^{72} +(3.62981 + 3.62981i) q^{73} +(3.09686 + 3.09686i) q^{74} -4.35383i q^{76} -8.29532 q^{77} +(-9.11510 + 9.11510i) q^{78} +(1.29344 + 1.29344i) q^{79} +10.8330 q^{81} +(-5.53686 - 5.53686i) q^{82} +12.1572 q^{83} +7.27723 q^{84} +7.20805 q^{86} -19.3068 q^{87} +(1.82843 + 1.82843i) q^{88} -16.2925 q^{89} +(-12.8907 - 12.8907i) q^{91} +(3.41421 - 3.41421i) q^{92} -3.73423 q^{93} -4.89069i q^{94} +(-1.60402 - 1.60402i) q^{96} +(12.5312 + 12.5312i) q^{97} +3.29156i q^{98} +(3.92341 - 3.92341i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} - 4 q^{7} - 8 q^{8}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^4 - 4 * q^7 - 8 * q^8	$ 8 q - 8 q^{2} + 8 q^{4} - 4 q^{7} - 8 q^{8} + 8 q^{11} + 4 q^{14} + 8 q^{16} + 12 q^{17} + 16 q^{21} - 8 q^{22} + 16 q^{23} + 12 q^{27} - 4 q^{28} - 24 q^{29} + 4 q^{31} - 8 q^{32} - 12 q^{34} + 20 q^{37} + 4 q^{39} - 16 q^{42} - 32 q^{43} + 8 q^{44} - 16 q^{46} + 4 q^{51} + 20 q^{53} - 12 q^{54} + 4 q^{56} + 40 q^{57} + 24 q^{58} - 16 q^{61} - 4 q^{62} - 64 q^{63} + 8 q^{64} + 12 q^{68} - 8 q^{69} + 4 q^{71} + 28 q^{73} - 20 q^{74} - 8 q^{77} - 4 q^{78} - 8 q^{79} - 8 q^{81} + 56 q^{83} + 16 q^{84} + 32 q^{86} - 44 q^{87} - 8 q^{88} + 44 q^{89} - 44 q^{91} + 16 q^{92} - 20 q^{93} - 20 q^{97} + 4 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 - 4 * q^7 - 8 * q^8 + 8 * q^11 + 4 * q^14 + 8 * q^16 + 12 * q^17 + 16 * q^21 - 8 * q^22 + 16 * q^23 + 12 * q^27 - 4 * q^28 - 24 * q^29 + 4 * q^31 - 8 * q^32 - 12 * q^34 + 20 * q^37 + 4 * q^39 - 16 * q^42 - 32 * q^43 + 8 * q^44 - 16 * q^46 + 4 * q^51 + 20 * q^53 - 12 * q^54 + 4 * q^56 + 40 * q^57 + 24 * q^58 - 16 * q^61 - 4 * q^62 - 64 * q^63 + 8 * q^64 + 12 * q^68 - 8 * q^69 + 4 * q^71 + 28 * q^73 - 20 * q^74 - 8 * q^77 - 4 * q^78 - 8 * q^79 - 8 * q^81 + 56 * q^83 + 16 * q^84 + 32 * q^86 - 44 * q^87 - 8 * q^88 + 44 * q^89 - 44 * q^91 + 16 * q^92 - 20 * q^93 - 20 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/850\mathbb{Z}\right)^\times$.

$n$	$477$	$751$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	1.60402	+	1.60402i	0.926083	+	0.926083i	0.997450	−	0.0713668i	$-0.0227361\pi$
$3$	1.60402	+	1.60402i	0.926083	+	0.926083i	−0.0713668	+	0.997450i	$0.522736\pi$
$4$	1.00000			0.500000
$5$		0			0
$5$		0			0
$6$	−1.60402	−	1.60402i	−0.654840	−	0.654840i
$7$	2.26843	−	2.26843i	0.857387	−	0.857387i	−0.133643	−	0.991030i	$-0.542668\pi$
$7$	2.26843	−	2.26843i	0.857387	−	0.857387i	0.991030	+	0.133643i	$0.0426675\pi$
$8$	−1.00000			−0.353553
$9$			2.14578i			0.715261i
$10$		0			0
$11$	−1.82843	−	1.82843i	−0.551292	−	0.551292i	0.375522	−	0.926813i	$-0.377463\pi$
$11$	−1.82843	−	1.82843i	−0.551292	−	0.551292i	−0.926813	+	0.375522i	$0.877463\pi$
$12$	1.60402	+	1.60402i	0.463042	+	0.463042i
$13$		−	5.68265i		−	1.57608i	−0.615623	−	0.788041i	$-0.711095\pi$
$13$		−	5.68265i		−	1.57608i	0.615623	−	0.788041i	$-0.288905\pi$
$14$	−2.26843	+	2.26843i	−0.606264	+	0.606264i
$15$		0			0
$16$	1.00000			0.250000
$17$	4.07862	−	0.604023i	0.989211	−	0.146497i
$17$	4.07862	−	0.604023i	0.989211	−	0.146497i
$18$		−	2.14578i		−	0.505766i
$19$		−	4.35383i		−	0.998837i	−0.866361	−	0.499418i	$-0.833547\pi$
$19$		−	4.35383i		−	0.998837i	0.866361	−	0.499418i	$-0.166453\pi$
$20$		0			0
$21$	7.27723			1.58802
$22$	1.82843	+	1.82843i	0.389822	+	0.389822i
$23$	3.41421	−	3.41421i	0.711913	−	0.711913i	−0.255022	−	0.966935i	$-0.582083\pi$
$23$	3.41421	−	3.41421i	0.711913	−	0.711913i	0.966935	+	0.255022i	$0.0820828\pi$
$24$	−1.60402	−	1.60402i	−0.327420	−	0.327420i
$25$		0			0
$26$			5.68265i			1.11446i
$27$	1.37019	−	1.37019i	0.263692	−	0.263692i
$28$	2.26843	−	2.26843i	0.428693	−	0.428693i
$29$	−6.01824	+	6.01824i	−1.11756	+	1.11756i	−0.125460	+	0.992099i	$0.540041\pi$
$29$	−6.01824	+	6.01824i	−1.11756	+	1.11756i	−0.992099	+	0.125460i	$0.959959\pi$
$30$		0			0
$31$	−1.16402	+	1.16402i	−0.209064	+	0.209064i	−0.803870	−	0.594806i	$-0.797229\pi$
$31$	−1.16402	+	1.16402i	−0.209064	+	0.209064i	0.594806	+	0.803870i	$0.297229\pi$
$32$	−1.00000			−0.176777
$33$		−	5.86568i		−	1.02108i
$34$	−4.07862	+	0.604023i	−0.699478	+	0.103589i
$35$		0			0
$36$			2.14578i			0.357630i
$37$	−3.09686	−	3.09686i	−0.509120	−	0.509120i	0.405136	−	0.914256i	$-0.367224\pi$
$37$	−3.09686	−	3.09686i	−0.509120	−	0.509120i	−0.914256	+	0.405136i	$0.867224\pi$
$38$			4.35383i			0.706284i
$39$	9.11510	−	9.11510i	1.45958	−	1.45958i
$40$		0			0
$41$	5.53686	+	5.53686i	0.864713	+	0.864713i	0.991881	−	0.127168i	$-0.0405889\pi$
$41$	5.53686	+	5.53686i	0.864713	+	0.864713i	−0.127168	+	0.991881i	$0.540589\pi$
$42$	−7.27723			−1.12290
$43$	−7.20805			−1.09922			−0.549608	−	0.835422i	$-0.685223\pi$
$43$	−7.20805			−1.09922			−0.549608	+	0.835422i	$0.685223\pi$
$44$	−1.82843	−	1.82843i	−0.275646	−	0.275646i
$45$		0			0
$46$	−3.41421	+	3.41421i	−0.503398	+	0.503398i
$47$			4.89069i			0.713381i	0.934223	+	0.356690i	$0.116095\pi$
$47$			4.89069i			0.713381i	−0.934223	+	0.356690i	$0.883905\pi$
$48$	1.60402	+	1.60402i	0.231521	+	0.231521i
$49$		−	3.29156i		−	0.470223i
$50$		0			0
$51$	7.51107	+	5.57334i	1.05176	+	0.780423i
$52$		−	5.68265i		−	0.788041i
$53$	1.14578			0.157385			0.0786926	−	0.996899i	$-0.474925\pi$
$53$	1.14578			0.157385			0.0786926	+	0.996899i	$0.474925\pi$
$54$	−1.37019	+	1.37019i	−0.186459	+	0.186459i
$55$		0			0
$56$	−2.26843	+	2.26843i	−0.303132	+	0.303132i
$57$	6.98364	−	6.98364i	0.925006	−	0.925006i
$58$	6.01824	−	6.01824i	0.790233	−	0.790233i
$59$			8.01068i			1.04290i	0.853281	+	0.521451i	$0.174609\pi$
$59$			8.01068i			1.04290i	−0.853281	+	0.521451i	$0.825391\pi$
$60$		0			0
$61$	−4.51863	−	4.51863i	−0.578551	−	0.578551i	0.355953	−	0.934504i	$-0.384156\pi$
$61$	−4.51863	−	4.51863i	−0.578551	−	0.578551i	−0.934504	+	0.355953i	$0.884156\pi$
$62$	1.16402	−	1.16402i	0.147831	−	0.147831i
$63$	4.86756	+	4.86756i	0.613255	+	0.613255i
$64$	1.00000			0.125000
$65$		0			0
$66$			5.86568i			0.722015i
$67$			14.0729i			1.71928i	0.510897	+	0.859642i	$0.329313\pi$
$67$			14.0729i			1.71928i	−0.510897	+	0.859642i	$0.670687\pi$
$68$	4.07862	−	0.604023i	0.494606	−	0.0732486i
$69$	10.9530			1.31858
$70$		0			0
$71$	−4.37207	+	4.37207i	−0.518869	+	0.518869i	−0.917229	−	0.398360i	$-0.869579\pi$
$71$	−4.37207	+	4.37207i	−0.518869	+	0.518869i	0.398360	+	0.917229i	$0.369579\pi$
$72$		−	2.14578i		−	0.252883i
$73$	3.62981	+	3.62981i	0.424838	+	0.424838i	0.886865	−	0.462028i	$-0.152878\pi$
$73$	3.62981	+	3.62981i	0.424838	+	0.424838i	−0.462028	+	0.886865i	$0.652878\pi$
$74$	3.09686	+	3.09686i	0.360003	+	0.360003i
$75$		0			0
$76$		−	4.35383i		−	0.499418i
$77$	−8.29532			−0.945340
$78$	−9.11510	+	9.11510i	−1.03208	+	1.03208i
$79$	1.29344	+	1.29344i	0.145524	+	0.145524i	0.776115	−	0.630591i	$-0.217188\pi$
$79$	1.29344	+	1.29344i	0.145524	+	0.145524i	−0.630591	+	0.776115i	$0.717188\pi$
$80$		0			0
$81$	10.8330			1.20366
$82$	−5.53686	−	5.53686i	−0.611444	−	0.611444i
$83$	12.1572			1.33443			0.667215	−	0.744865i	$-0.267486\pi$
$83$	12.1572			1.33443			0.667215	+	0.744865i	$0.267486\pi$
$84$	7.27723			0.794011
$85$		0			0
$86$	7.20805			0.777264
$87$	−19.3068			−2.06990
$88$	1.82843	+	1.82843i	0.194911	+	0.194911i
$89$	−16.2925			−1.72700			−0.863498	−	0.504351i	$-0.831732\pi$
$89$	−16.2925			−1.72700			−0.863498	+	0.504351i	$0.831732\pi$
$90$		0			0
$91$	−12.8907	−	12.8907i	−1.35131	−	1.35131i
$92$	3.41421	−	3.41421i	0.355956	−	0.355956i
$93$	−3.73423			−0.387221
$94$		−	4.89069i		−	0.504436i
$95$		0			0
$96$	−1.60402	−	1.60402i	−0.163710	−	0.163710i
$97$	12.5312	+	12.5312i	1.27235	+	1.27235i	0.944852	+	0.327497i	$0.106205\pi$
$97$	12.5312	+	12.5312i	1.27235	+	1.27235i	0.327497	+	0.944852i	$0.393795\pi$
$98$			3.29156i			0.332498i
$99$	3.92341	−	3.92341i	0.394317	−	0.394317i
$100$		0			0
$101$	7.65685			0.761885			0.380943	−	0.924599i	$-0.375599\pi$
$101$	7.65685			0.761885			0.380943	+	0.924599i	$0.375599\pi$
$102$	−7.51107	−	5.57334i	−0.743707	−	0.551843i
$103$		−	7.58767i		−	0.747635i	−0.927502	−	0.373817i	$-0.878049\pi$
$103$		−	7.58767i		−	0.747635i	0.927502	−	0.373817i	$-0.121951\pi$
$104$			5.68265i			0.557229i
$105$		0			0
$106$	−1.14578			−0.111288
$107$	3.85422	+	3.85422i	0.372601	+	0.372601i	0.868424	−	0.495823i	$-0.165133\pi$
$107$	3.85422	+	3.85422i	0.372601	+	0.372601i	−0.495823	+	0.868424i	$0.665133\pi$
$108$	1.37019	−	1.37019i	0.131846	−	0.131846i
$109$	6.01824	+	6.01824i	0.576443	+	0.576443i	0.933921	−	0.357479i	$-0.116364\pi$
$109$	6.01824	+	6.01824i	0.576443	+	0.576443i	−0.357479	+	0.933921i	$0.616364\pi$
$110$		0			0
$111$		−	9.93487i		−	0.942976i
$112$	2.26843	−	2.26843i	0.214347	−	0.214347i
$113$	5.57823	−	5.57823i	0.524756	−	0.524756i	−0.394248	−	0.919004i	$-0.628995\pi$
$113$	5.57823	−	5.57823i	0.524756	−	0.524756i	0.919004	+	0.394248i	$0.128995\pi$
$114$	−6.98364	+	6.98364i	−0.654078	+	0.654078i
$115$		0			0
$116$	−6.01824	+	6.01824i	−0.558779	+	0.558779i
$117$	12.1937			1.12731
$118$		−	8.01068i		−	0.737443i
$119$	7.88189	−	10.6223i	0.722532	−	0.973741i
$120$		0			0
$121$		−	4.31371i		−	0.392155i
$122$	4.51863	+	4.51863i	0.409097	+	0.409097i
$123$			17.7625i			1.60159i
$124$	−1.16402	+	1.16402i	−0.104532	+	0.104532i
$125$		0			0
$126$	−4.86756	−	4.86756i	−0.433637	−	0.433637i
$127$	6.76992			0.600733			0.300367	−	0.953824i	$-0.402891\pi$
$127$	6.76992			0.600733			0.300367	+	0.953824i	$0.402891\pi$
$128$	−1.00000			−0.0883883
$129$	−11.5619	−	11.5619i	−1.01797	−	1.01797i
$130$		0			0
$131$	7.32804	−	7.32804i	0.640254	−	0.640254i	−0.310364	−	0.950618i	$-0.600451\pi$
$131$	7.32804	−	7.32804i	0.640254	−	0.640254i	0.950618	+	0.310364i	$0.100451\pi$
$132$		−	5.86568i		−	0.510542i
$133$	−9.87636	−	9.87636i	−0.856389	−	0.856389i
$134$		−	14.0729i		−	1.21572i
$135$		0			0
$136$	−4.07862	+	0.604023i	−0.349739	+	0.0517946i
$137$			1.74115i			0.148756i	0.997230	+	0.0743782i	$0.0236972\pi$
$137$			1.74115i			0.148756i	−0.997230	+	0.0743782i	$0.976303\pi$
$138$	−10.9530			−0.932378
$139$	−0.587666	+	0.587666i	−0.0498452	+	0.0498452i	−0.731590	−	0.681745i	$-0.761221\pi$
$139$	−0.587666	+	0.587666i	−0.0498452	+	0.0498452i	0.681745	+	0.731590i	$0.261221\pi$
$140$		0			0
$141$	−7.84478	+	7.84478i	−0.660650	+	0.660650i
$142$	4.37207	−	4.37207i	0.366896	−	0.366896i
$143$	−10.3903	+	10.3903i	−0.868881	+	0.868881i
$144$			2.14578i			0.178815i
$145$		0			0
$146$	−3.62981	−	3.62981i	−0.300406	−	0.300406i
$147$	5.27975	−	5.27975i	0.435466	−	0.435466i
$148$	−3.09686	−	3.09686i	−0.254560	−	0.254560i
$149$	2.44881			0.200614			0.100307	−	0.994957i	$-0.468017\pi$
$149$	2.44881			0.200614			0.100307	+	0.994957i	$0.468017\pi$
$150$		0			0
$151$		−	4.53686i		−	0.369205i	−0.982813	−	0.184602i	$-0.940900\pi$
$151$		−	4.53686i		−	0.369205i	0.982813	−	0.184602i	$-0.0590997\pi$
$152$			4.35383i			0.353142i
$153$	1.29610	+	8.75183i	0.104784	+	0.707544i
$154$	8.29532			0.668456
$155$		0			0
$156$	9.11510	−	9.11510i	0.729792	−	0.729792i
$157$		−	23.5074i		−	1.87610i	−0.346504	−	0.938048i	$-0.612631\pi$
$157$		−	23.5074i		−	1.87610i	0.346504	−	0.938048i	$-0.387369\pi$
$158$	−1.29344	−	1.29344i	−0.102901	−	0.102901i
$159$	1.83786	+	1.83786i	0.145752	+	0.145752i
$160$		0			0
$161$		−	15.4898i		−	1.22077i
$162$	−10.8330			−0.851118
$163$	−16.0479	+	16.0479i	−1.25697	+	1.25697i	−0.304440	+	0.952532i	$0.598469\pi$
$163$	−16.0479	+	16.0479i	−1.25697	+	1.25697i	−0.952532	+	0.304440i	$0.901531\pi$
$164$	5.53686	+	5.53686i	0.432356	+	0.432356i
$165$		0			0
$166$	−12.1572			−0.943585
$167$	14.4364	+	14.4364i	1.11712	+	1.11712i	0.992162	+	0.124957i	$0.0398792\pi$
$167$	14.4364	+	14.4364i	1.11712	+	1.11712i	0.124957	+	0.992162i	$0.460121\pi$
$168$	−7.27723			−0.561451
$169$	−19.2925			−1.48404
$170$		0			0
$171$	9.34237			0.714429
$172$	−7.20805			−0.549608
$173$	−6.65873	−	6.65873i	−0.506254	−	0.506254i	0.407120	−	0.913375i	$-0.366533\pi$
$173$	−6.65873	−	6.65873i	−0.506254	−	0.506254i	−0.913375	+	0.407120i	$0.866533\pi$
$174$	19.3068			1.46364
$175$		0			0
$176$	−1.82843	−	1.82843i	−0.137823	−	0.137823i
$177$	−12.8493	+	12.8493i	−0.965814	+	0.965814i
$178$	16.2925			1.22117
$179$			6.65763i			0.497615i	0.968553	+	0.248807i	$0.0800386\pi$
$179$			6.65763i			0.497615i	−0.968553	+	0.248807i	$0.919961\pi$
$180$		0			0
$181$	0.0853971	+	0.0853971i	0.00634752	+	0.00634752i	0.710273	−	0.703926i	$-0.248571\pi$
$181$	0.0853971	+	0.0853971i	0.00634752	+	0.00634752i	−0.703926	+	0.710273i	$0.748571\pi$
$182$	12.8907	+	12.8907i	0.955522	+	0.955522i
$183$		−	14.4960i		−	1.07157i
$184$	−3.41421	+	3.41421i	−0.251699	+	0.251699i
$185$		0			0
$186$	3.73423			0.273807
$187$	−8.56188	−	6.35305i	−0.626106	−	0.464581i
$188$			4.89069i			0.356690i
$189$		−	6.21635i		−	0.452173i
$190$		0			0
$191$	−9.52253			−0.689026			−0.344513	−	0.938781i	$-0.611956\pi$
$191$	−9.52253			−0.689026			−0.344513	+	0.938781i	$0.611956\pi$
$192$	1.60402	+	1.60402i	0.115760	+	0.115760i
$193$	−11.6318	+	11.6318i	−0.837278	+	0.837278i	−0.988500	−	0.151222i	$-0.951679\pi$
$193$	−11.6318	+	11.6318i	−0.837278	+	0.837278i	0.151222	+	0.988500i	$0.451679\pi$
$194$	−12.5312	−	12.5312i	−0.899687	−	0.899687i
$195$		0			0
$196$		−	3.29156i		−	0.235112i
$197$	−16.3414	+	16.3414i	−1.16428	+	1.16428i	−0.180745	+	0.983530i	$0.557851\pi$
$197$	−16.3414	+	16.3414i	−1.16428	+	1.16428i	−0.983530	+	0.180745i	$0.942149\pi$
$198$	−3.92341	+	3.92341i	−0.278824	+	0.278824i
$199$	6.99322	−	6.99322i	0.495737	−	0.495737i	−0.414371	−	0.910108i	$-0.635999\pi$
$199$	6.99322	−	6.99322i	0.495737	−	0.495737i	0.910108	+	0.414371i	$0.135999\pi$
$200$		0			0
$201$	−22.5733	+	22.5733i	−1.59220	+	1.59220i
$202$	−7.65685			−0.538734
$203$			27.3039i			1.91636i
$204$	7.51107	+	5.57334i	0.525880	+	0.390212i
$205$		0			0
$206$			7.58767i			0.528658i
$207$	7.32616	+	7.32616i	0.509203	+	0.509203i
$208$		−	5.68265i		−	0.394021i
$209$	−7.96066	+	7.96066i	−0.550650	+	0.550650i
$210$		0			0
$211$	11.8907	+	11.8907i	0.818589	+	0.818589i	0.985904	−	0.167315i	$-0.0535096\pi$
$211$	11.8907	+	11.8907i	0.818589	+	0.818589i	−0.167315	+	0.985904i	$0.553510\pi$
$212$	1.14578			0.0786926
$213$	−14.0258			−0.961031
$214$	−3.85422	−	3.85422i	−0.263469	−	0.263469i
$215$		0			0
$216$	−1.37019	+	1.37019i	−0.0932293	+	0.0932293i
$217$			5.28099i			0.358497i
$218$	−6.01824	−	6.01824i	−0.407606	−	0.407606i
$219$			11.6446i			0.786870i
$220$		0			0
$221$	−3.43245	−	23.1774i	−0.230892	−	1.55908i
$222$			9.93487i			0.666785i
$223$	9.25144			0.619522			0.309761	−	0.950814i	$-0.399751\pi$
$223$	9.25144			0.619522			0.309761	+	0.950814i	$0.399751\pi$
$224$	−2.26843	+	2.26843i	−0.151566	+	0.151566i
$225$		0			0
$226$	−5.57823	+	5.57823i	−0.371059	+	0.371059i
$227$	14.5205	−	14.5205i	0.963760	−	0.963760i	−0.0356061	−	0.999366i	$-0.511336\pi$
$227$	14.5205	−	14.5205i	0.963760	−	0.963760i	0.999366	+	0.0356061i	$0.0113362\pi$
$228$	6.98364	−	6.98364i	0.462503	−	0.462503i
$229$			15.1618i			1.00192i	0.865471	+	0.500959i	$0.167019\pi$
$229$			15.1618i			1.00192i	−0.865471	+	0.500959i	$0.832981\pi$
$230$		0			0
$231$	−13.3059	−	13.3059i	−0.875463	−	0.875463i
$232$	6.01824	−	6.01824i	0.395117	−	0.395117i
$233$	−6.28745	−	6.28745i	−0.411904	−	0.411904i	0.470497	−	0.882402i	$-0.344075\pi$
$233$	−6.28745	−	6.28745i	−0.411904	−	0.411904i	−0.882402	+	0.470497i	$0.844075\pi$
$234$	−12.1937			−0.797128
$235$		0			0
$236$			8.01068i			0.521451i
$237$			4.14943i			0.269534i
$238$	−7.88189	+	10.6223i	−0.510907	+	0.688539i
$239$	0.0827385			0.00535191			0.00267595	−	0.999996i	$-0.499148\pi$
$239$	0.0827385			0.00535191			0.00267595	+	0.999996i	$0.499148\pi$
$240$		0			0
$241$	−0.829206	+	0.829206i	−0.0534138	+	0.0534138i	−0.733309	−	0.679895i	$-0.762025\pi$
$241$	−0.829206	+	0.829206i	−0.0534138	+	0.0534138i	0.679895	+	0.733309i	$0.262025\pi$
$242$			4.31371i			0.277296i
$243$	13.2658	+	13.2658i	0.851000	+	0.851000i
$244$	−4.51863	−	4.51863i	−0.289275	−	0.289275i
$245$		0			0
$246$		−	17.7625i		−	1.13250i
$247$	−24.7413			−1.57425
$248$	1.16402	−	1.16402i	0.0739153	−	0.0739153i
$249$	19.5005	+	19.5005i	1.23579	+	1.23579i
$250$		0			0
$251$	−18.1245			−1.14401			−0.572005	−	0.820250i	$-0.693834\pi$
$251$	−18.1245			−1.14401			−0.572005	+	0.820250i	$0.693834\pi$
$252$	4.86756	+	4.86756i	0.306627	+	0.306627i
$253$	−12.4853			−0.784943
$254$	−6.76992			−0.424783
$255$		0			0
$256$	1.00000			0.0625000
$257$	−25.3539			−1.58154			−0.790768	−	0.612116i	$-0.790318\pi$
$257$	−25.3539			−1.58154			−0.790768	+	0.612116i	$0.790318\pi$
$258$	11.5619	+	11.5619i	0.719811	+	0.719811i
$259$	−14.0500			−0.873026
$260$		0			0
$261$	−12.9138	−	12.9138i	−0.799346	−	0.799346i
$262$	−7.32804	+	7.32804i	−0.452728	+	0.452728i
$263$	2.11385			0.130345			0.0651727	−	0.997874i	$-0.479240\pi$
$263$	2.11385			0.130345			0.0651727	+	0.997874i	$0.479240\pi$
$264$			5.86568i			0.361008i
$265$		0			0
$266$	9.87636	+	9.87636i	0.605559	+	0.605559i
$267$	−26.1335	−	26.1335i	−1.59934	−	1.59934i
$268$			14.0729i			0.859642i
$269$	−15.1898	+	15.1898i	−0.926139	+	0.926139i	−0.997454	−	0.0713148i	$-0.977281\pi$
$269$	−15.1898	+	15.1898i	−0.926139	+	0.926139i	0.0713148	+	0.997454i	$0.477281\pi$
$270$		0			0
$271$	22.5922			1.37238			0.686189	−	0.727423i	$-0.259282\pi$
$271$	22.5922			1.37238			0.686189	+	0.727423i	$0.259282\pi$
$272$	4.07862	−	0.604023i	0.247303	−	0.0366243i
$273$		−	41.3539i		−	2.50285i
$274$		−	1.74115i		−	0.105187i
$275$		0			0
$276$	10.9530			0.659291
$277$	−18.0756	−	18.0756i	−1.08606	−	1.08606i	−0.995930	−	0.0901277i	$-0.971272\pi$
$277$	−18.0756	−	18.0756i	−1.08606	−	1.08606i	−0.0901277	−	0.995930i	$-0.528728\pi$
$278$	0.587666	−	0.587666i	0.0352459	−	0.0352459i
$279$	−2.49773	−	2.49773i	−0.149535	−	0.149535i
$280$		0			0
$281$			15.8248i			0.944027i	0.881591	+	0.472014i	$0.156473\pi$
$281$			15.8248i			0.944027i	−0.881591	+	0.472014i	$0.843527\pi$
$282$	7.84478	−	7.84478i	0.467150	−	0.467150i
$283$	12.4325	−	12.4325i	0.739032	−	0.739032i	−0.233358	−	0.972391i	$-0.574972\pi$
$283$	12.4325	−	12.4325i	0.739032	−	0.739032i	0.972391	+	0.233358i	$0.0749715\pi$
$284$	−4.37207	+	4.37207i	−0.259434	+	0.259434i
$285$		0			0
$286$	10.3903	−	10.3903i	0.614391	−	0.614391i
$287$	25.1200			1.48279
$288$		−	2.14578i		−	0.126441i
$289$	16.2703	−	4.92717i	0.957077	−	0.289833i
$290$		0			0
$291$			40.2006i			2.35660i
$292$	3.62981	+	3.62981i	0.212419	+	0.212419i
$293$		−	29.6524i		−	1.73231i	−0.499773	−	0.866157i	$-0.666583\pi$
$293$		−	29.6524i		−	1.73231i	0.499773	−	0.866157i	$-0.333417\pi$
$294$	−5.27975	+	5.27975i	−0.307921	+	0.307921i
$295$		0			0
$296$	3.09686	+	3.09686i	0.180001	+	0.180001i
$297$	−5.01057			−0.290743
$298$	−2.44881			−0.141856
$299$	−19.4018	−	19.4018i	−1.12203	−	1.12203i
$300$		0			0
$301$	−16.3510	+	16.3510i	−0.942454	+	0.942454i
$302$			4.53686i			0.261067i
$303$	12.2818	+	12.2818i	0.705569	+	0.705569i
$304$		−	4.35383i		−	0.249709i
$305$		0			0
$306$	−1.29610	−	8.75183i	−0.0740932	−	0.500309i
$307$		−	32.0116i		−	1.82700i	−0.406842	−	0.913499i	$-0.633370\pi$
$307$		−	32.0116i		−	1.82700i	0.406842	−	0.913499i	$-0.366630\pi$
$308$	−8.29532			−0.472670
$309$	12.1708	−	12.1708i	0.692372	−	0.692372i
$310$		0			0
$311$	8.72792	−	8.72792i	0.494915	−	0.494915i	−0.414936	−	0.909851i	$-0.636196\pi$
$311$	8.72792	−	8.72792i	0.494915	−	0.494915i	0.909851	+	0.414936i	$0.136196\pi$
$312$	−9.11510	+	9.11510i	−0.516041	+	0.516041i
$313$	−1.39030	+	1.39030i	−0.0785845	+	0.0785845i	−0.745307	−	0.666722i	$-0.767697\pi$
$313$	−1.39030	+	1.39030i	−0.0785845	+	0.0785845i	0.666722	+	0.745307i	$0.267697\pi$
$314$			23.5074i			1.32660i
$315$		0			0
$316$	1.29344	+	1.29344i	0.0727619	+	0.0727619i
$317$	8.08540	−	8.08540i	0.454121	−	0.454121i	−0.442599	−	0.896720i	$-0.645943\pi$
$317$	8.08540	−	8.08540i	0.454121	−	0.454121i	0.896720	+	0.442599i	$0.145943\pi$
$318$	−1.83786	−	1.83786i	−0.103062	−	0.103062i
$319$	22.0078			1.23220
$320$		0			0
$321$			12.3645i			0.690120i
$322$			15.4898i			0.863214i
$323$	−2.62981	−	17.7576i	−0.146327	−	0.988060i
$324$	10.8330			0.601831
$325$		0			0
$326$	16.0479	−	16.0479i	0.888813	−	0.888813i
$327$			19.3068i			1.06767i
$328$	−5.53686	−	5.53686i	−0.305722	−	0.305722i
$329$	11.0942	+	11.0942i	0.611643	+	0.611643i
$330$		0			0
$331$			18.4784i			1.01566i	0.861457	+	0.507831i	$0.169553\pi$
$331$			18.4784i			1.01566i	−0.861457	+	0.507831i	$0.830447\pi$
$332$	12.1572			0.667215
$333$	6.64518	−	6.64518i	0.364154	−	0.364154i
$334$	−14.4364	−	14.4364i	−0.789922	−	0.789922i
$335$		0			0
$336$	7.27723			0.397006
$337$	1.83708	+	1.83708i	0.100072	+	0.100072i	0.755370	−	0.655298i	$-0.227457\pi$
$337$	1.83708	+	1.83708i	0.100072	+	0.100072i	−0.655298	+	0.755370i	$0.727457\pi$
$338$	19.2925			1.04937
$339$	17.8952			0.971936
$340$		0			0
$341$	4.25665			0.230510
$342$	−9.34237			−0.505177
$343$	8.41233	+	8.41233i	0.454223	+	0.454223i
$344$	7.20805			0.388632
$345$		0			0
$346$	6.65873	+	6.65873i	0.357976	+	0.357976i
$347$	−9.15522	+	9.15522i	−0.491478	+	0.491478i	−0.908772	−	0.417294i	$-0.862979\pi$
$347$	−9.15522	+	9.15522i	−0.491478	+	0.491478i	0.417294	+	0.908772i	$0.362979\pi$
$348$	−19.3068			−1.03495
$349$		−	20.3698i		−	1.09037i	−0.838315	−	0.545186i	$-0.816459\pi$
$349$		−	20.3698i		−	1.09037i	0.838315	−	0.545186i	$-0.183541\pi$
$350$		0			0
$351$	−7.78628	−	7.78628i	−0.415601	−	0.415601i
$352$	1.82843	+	1.82843i	0.0974555	+	0.0974555i
$353$			33.1680i			1.76536i	0.469978	+	0.882678i	$0.344262\pi$
$353$			33.1680i			1.76536i	−0.469978	+	0.882678i	$0.655738\pi$
$354$	12.8493	−	12.8493i	0.682934	−	0.682934i
$355$		0			0
$356$	−16.2925			−0.863498
$357$	29.6811	−	4.39562i	1.57089	−	0.232641i
$358$		−	6.65763i		−	0.351867i
$359$			17.2272i			0.909217i	0.890691	+	0.454609i	$0.150221\pi$
$359$			17.2272i			0.909217i	−0.890691	+	0.454609i	$0.849779\pi$
$360$		0			0
$361$	0.0441757			0.00232503
$362$	−0.0853971	−	0.0853971i	−0.00448837	−	0.00448837i
$363$	6.91929	−	6.91929i	0.363169	−	0.363169i
$364$	−12.8907	−	12.8907i	−0.675656	−	0.675656i
$365$		0			0
$366$			14.4960i			0.757716i
$367$	16.4879	−	16.4879i	0.860663	−	0.860663i	−0.130752	−	0.991415i	$-0.541739\pi$
$367$	16.4879	−	16.4879i	0.860663	−	0.860663i	0.991415	+	0.130752i	$0.0417391\pi$
$368$	3.41421	−	3.41421i	0.177978	−	0.177978i
$369$	−11.8809	+	11.8809i	−0.618495	+	0.618495i
$370$		0			0
$371$	2.59913	−	2.59913i	0.134940	−	0.134940i
$372$	−3.73423			−0.193611
$373$			10.6098i			0.549355i	0.961536	+	0.274678i	$0.0885711\pi$
$373$			10.6098i			0.549355i	−0.961536	+	0.274678i	$0.911429\pi$
$374$	8.56188	+	6.35305i	0.442724	+	0.328508i
$375$		0			0
$376$		−	4.89069i		−	0.252218i
$377$	34.1995	+	34.1995i	1.76136	+	1.76136i
$378$			6.21635i			0.319734i
$379$	19.6872	−	19.6872i	1.01126	−	1.01126i	0.0113269	−	0.999936i	$-0.496394\pi$
$379$	19.6872	−	19.6872i	1.01126	−	1.01126i	0.999936	−	0.0113269i	$-0.00360553\pi$
$380$		0			0
$381$	10.8591	+	10.8591i	0.556329	+	0.556329i
$382$	9.52253			0.487215
$383$	−0.426776			−0.0218073			−0.0109036	−	0.999941i	$-0.503471\pi$
$383$	−0.426776			−0.0218073			−0.0109036	+	0.999941i	$0.503471\pi$
$384$	−1.60402	−	1.60402i	−0.0818550	−	0.0818550i
$385$		0			0
$386$	11.6318	−	11.6318i	0.592045	−	0.592045i
$387$		−	15.4669i		−	0.786227i
$388$	12.5312	+	12.5312i	0.636175	+	0.636175i
$389$			0.807061i			0.0409196i	0.999791	+	0.0204598i	$0.00651302\pi$
$389$			0.807061i			0.0409196i	−0.999791	+	0.0204598i	$0.993487\pi$
$390$		0			0
$391$	11.8630	−	15.9876i	0.599939	−	0.808525i
$392$			3.29156i			0.166249i
$393$	23.5087			1.18586
$394$	16.3414	−	16.3414i	0.823267	−	0.823267i
$395$		0			0
$396$	3.92341	−	3.92341i	0.197159	−	0.197159i
$397$	18.9138	−	18.9138i	0.949258	−	0.949258i	−0.0495157	−	0.998773i	$-0.515768\pi$
$397$	18.9138	−	18.9138i	0.949258	−	0.949258i	0.998773	+	0.0495157i	$0.0157678\pi$
$398$	−6.99322	+	6.99322i	−0.350539	+	0.350539i
$399$		−	31.6838i		−	1.58618i
$400$		0			0
$401$	−10.9226	−	10.9226i	−0.545450	−	0.545450i	0.379671	−	0.925121i	$-0.376037\pi$
$401$	−10.9226	−	10.9226i	−0.545450	−	0.545450i	−0.925121	+	0.379671i	$0.876037\pi$
$402$	22.5733	−	22.5733i	1.12586	−	1.12586i
$403$	6.61471	+	6.61471i	0.329502	+	0.329502i
$404$	7.65685			0.380943
$405$		0			0
$406$		−	27.3039i		−	1.35507i
$407$			11.3248i			0.561348i
$408$	−7.51107	−	5.57334i	−0.371853	−	0.275921i
$409$	−9.19581			−0.454703			−0.227352	−	0.973813i	$-0.573007\pi$
$409$	−9.19581			−0.454703			−0.227352	+	0.973813i	$0.573007\pi$
$410$		0			0
$411$	−2.79285	+	2.79285i	−0.137761	+	0.137761i
$412$		−	7.58767i		−	0.373817i
$413$	18.1717	+	18.1717i	0.894170	+	0.894170i
$414$	−7.32616	−	7.32616i	−0.360061	−	0.360061i
$415$		0			0
$416$			5.68265i			0.278615i
$417$	−1.88526			−0.0923216
$418$	7.96066	−	7.96066i	0.389369	−	0.389369i
$419$	−6.93774	−	6.93774i	−0.338931	−	0.338931i	0.517034	−	0.855965i	$-0.327036\pi$
$419$	−6.93774	−	6.93774i	−0.338931	−	0.338931i	−0.855965	+	0.517034i	$0.827036\pi$
$420$		0			0
$421$	−17.0410			−0.830528			−0.415264	−	0.909701i	$-0.636311\pi$
$421$	−17.0410			−0.830528			−0.415264	+	0.909701i	$0.636311\pi$
$422$	−11.8907	−	11.8907i	−0.578830	−	0.578830i
$423$	−10.4944			−0.510253
$424$	−1.14578			−0.0556441
$425$		0			0
$426$	14.0258			0.679552
$427$	−20.5004			−0.992083
$428$	3.85422	+	3.85422i	0.186301	+	0.186301i
$429$	−33.3326			−1.60931
$430$		0			0
$431$	13.8152	+	13.8152i	0.665455	+	0.665455i	0.956660	−	0.291206i	$-0.0940564\pi$
$431$	13.8152	+	13.8152i	0.665455	+	0.665455i	−0.291206	+	0.956660i	$0.594056\pi$
$432$	1.37019	−	1.37019i	0.0659231	−	0.0659231i
$433$	−16.7404			−0.804491			−0.402245	−	0.915532i	$-0.631770\pi$
$433$	−16.7404			−0.804491			−0.402245	+	0.915532i	$0.631770\pi$
$434$		−	5.28099i		−	0.253496i
$435$		0			0
$436$	6.01824	+	6.01824i	0.288221	+	0.288221i
$437$	−14.8649	−	14.8649i	−0.711085	−	0.711085i
$438$		−	11.6446i		−	0.556401i
$439$	−7.98755	+	7.98755i	−0.381225	+	0.381225i	−0.871543	−	0.490318i	$-0.836880\pi$
$439$	−7.98755	+	7.98755i	−0.381225	+	0.381225i	0.490318	+	0.871543i	$0.336880\pi$
$440$		0			0
$441$	7.06298			0.336332
$442$	3.43245	+	23.1774i	0.163265	+	1.10243i
$443$		−	19.7084i		−	0.936376i	−0.883629	−	0.468188i	$-0.844907\pi$
$443$		−	19.7084i		−	0.936376i	0.883629	−	0.468188i	$-0.155093\pi$
$444$		−	9.93487i		−	0.471488i
$445$		0			0
$446$	−9.25144			−0.438069
$447$	3.92794	+	3.92794i	0.185785	+	0.185785i
$448$	2.26843	−	2.26843i	0.107173	−	0.107173i
$449$	6.43042	+	6.43042i	0.303470	+	0.303470i	0.842370	−	0.538900i	$-0.181160\pi$
$449$	6.43042	+	6.43042i	0.303470	+	0.303470i	−0.538900	+	0.842370i	$0.681160\pi$
$450$		0			0
$451$		−	20.2475i		−	0.953418i
$452$	5.57823	−	5.57823i	0.262378	−	0.262378i
$453$	7.27723	−	7.27723i	0.341914	−	0.341914i
$454$	−14.5205	+	14.5205i	−0.681481	+	0.681481i
$455$		0			0
$456$	−6.98364	+	6.98364i	−0.327039	+	0.327039i
$457$	−7.73959			−0.362043			−0.181021	−	0.983479i	$-0.557940\pi$
$457$	−7.73959			−0.362043			−0.181021	+	0.983479i	$0.557940\pi$
$458$		−	15.1618i		−	0.708464i
$459$	4.76085	−	6.41609i	0.222217	−	0.299478i
$460$		0			0
$461$			25.0045i			1.16458i	0.812982	+	0.582289i	$0.197843\pi$
$461$			25.0045i			1.16458i	−0.812982	+	0.582289i	$0.802157\pi$
$462$	13.3059	+	13.3059i	0.619046	+	0.619046i
$463$		−	29.7745i		−	1.38374i	−0.722024	−	0.691868i	$-0.756788\pi$
$463$		−	29.7745i		−	1.38374i	0.722024	−	0.691868i	$-0.243212\pi$
$464$	−6.01824	+	6.01824i	−0.279390	+	0.279390i
$465$		0			0
$466$	6.28745	+	6.28745i	0.291260	+	0.291260i
$467$	−12.3104			−0.569659			−0.284829	−	0.958578i	$-0.591937\pi$
$467$	−12.3104			−0.569659			−0.284829	+	0.958578i	$0.591937\pi$
$468$	12.1937			0.563655
$469$	31.9235	+	31.9235i	1.47409	+	1.47409i
$470$		0			0
$471$	37.7065	−	37.7065i	1.73742	−	1.73742i
$472$		−	8.01068i		−	0.368722i
$473$	13.1794	+	13.1794i	0.605989	+	0.605989i
$474$		−	4.14943i		−	0.190590i
$475$		0			0
$476$	7.88189	−	10.6223i	0.361266	−	0.486871i
$477$			2.45860i			0.112571i
$478$	−0.0827385			−0.00378437
$479$	4.61361	−	4.61361i	0.210801	−	0.210801i	−0.593807	−	0.804608i	$-0.702376\pi$
$479$	4.61361	−	4.61361i	0.210801	−	0.210801i	0.804608	+	0.593807i	$0.202376\pi$
$480$		0			0
$481$	−17.5983	+	17.5983i	−0.802416	+	0.802416i
$482$	0.829206	−	0.829206i	0.0377693	−	0.0377693i
$483$	24.8460	−	24.8460i	1.13053	−	1.13053i
$484$		−	4.31371i		−	0.196078i
$485$		0			0
$486$	−13.2658	−	13.2658i	−0.601748	−	0.601748i
$487$	−9.85234	+	9.85234i	−0.446452	+	0.446452i	−0.894173	−	0.447721i	$-0.852236\pi$
$487$	−9.85234	+	9.85234i	−0.446452	+	0.446452i	0.447721	+	0.894173i	$0.352236\pi$
$488$	4.51863	+	4.51863i	0.204549	+	0.204549i
$489$	−51.4825			−2.32812
$490$		0			0
$491$		−	0.302247i		−	0.0136402i	−0.999977	−	0.00682010i	$-0.997829\pi$
$491$		−	0.302247i		−	0.0136402i	0.999977	−	0.00682010i	$-0.00217092\pi$
$492$			17.7625i			0.800796i
$493$	−20.9110	+	28.1813i	−0.941782	+	1.26922i
$494$	24.7413			1.11316
$495$		0			0
$496$	−1.16402	+	1.16402i	−0.0522660	+	0.0522660i
$497$			19.8355i			0.889742i
$498$	−19.5005	−	19.5005i	−0.873838	−	0.873838i
$499$	−11.6941	−	11.6941i	−0.523500	−	0.523500i	0.395127	−	0.918627i	$-0.370701\pi$
$499$	−11.6941	−	11.6941i	−0.523500	−	0.523500i	−0.918627	+	0.395127i	$0.870701\pi$
$500$		0			0
$501$			46.3125i			2.06909i
$502$	18.1245			0.808937
$503$	0.399884	−	0.399884i	0.0178300	−	0.0178300i	−0.698136	−	0.715966i	$-0.745987\pi$
$503$	0.399884	−	0.399884i	0.0178300	−	0.0178300i	0.715966	+	0.698136i	$0.245987\pi$
$504$	−4.86756	−	4.86756i	−0.216818	−	0.216818i
$505$		0			0
$506$	12.4853			0.555038
$507$	−30.9456	−	30.9456i	−1.37434	−	1.37434i
$508$	6.76992			0.300367
$509$	−9.94842			−0.440956			−0.220478	−	0.975392i	$-0.570762\pi$
$509$	−9.94842			−0.440956			−0.220478	+	0.975392i	$0.570762\pi$
$510$		0			0
$511$	16.4680			0.728500
$512$	−1.00000			−0.0441942
$513$	−5.96555	−	5.96555i	−0.263386	−	0.263386i
$514$	25.3539			1.11831
$515$		0			0
$516$	−11.5619	−	11.5619i	−0.508983	−	0.508983i
$517$	8.94227	−	8.94227i	0.393281	−	0.393281i
$518$	14.0500			0.617323
$519$		−	21.3615i		−	0.937667i
$520$		0			0
$521$	−8.68265	−	8.68265i	−0.380394	−	0.380394i	0.490850	−	0.871244i	$-0.336686\pi$
$521$	−8.68265	−	8.68265i	−0.380394	−	0.380394i	−0.871244	+	0.490850i	$0.836686\pi$
$522$	12.9138	+	12.9138i	0.565223	+	0.565223i
$523$			13.1024i			0.572927i	0.958091	+	0.286464i	$0.0924798\pi$
$523$			13.1024i			0.572927i	−0.958091	+	0.286464i	$0.907520\pi$
$524$	7.32804	−	7.32804i	0.320127	−	0.320127i
$525$		0			0
$526$	−2.11385			−0.0921681
$527$	−4.04450	+	5.45069i	−0.176181	+	0.237436i
$528$		−	5.86568i		−	0.255271i
$529$		−	0.313708i		−	0.0136395i
$530$		0			0
$531$	−17.1892			−0.745947
$532$	−9.87636	−	9.87636i	−0.428195	−	0.428195i
$533$	31.4640	−	31.4640i	1.36286	−	1.36286i
$534$	26.1335	+	26.1335i	1.13091	+	1.13091i
$535$		0			0
$536$		−	14.0729i		−	0.607859i
$537$	−10.6790	+	10.6790i	−0.460833	+	0.460833i
$538$	15.1898	−	15.1898i	0.654879	−	0.654879i
$539$	−6.01838	+	6.01838i	−0.259230	+	0.259230i
$540$		0			0
$541$	7.74601	−	7.74601i	0.333027	−	0.333027i	−0.520708	−	0.853735i	$-0.674332\pi$
$541$	7.74601	−	7.74601i	0.333027	−	0.333027i	0.853735	+	0.520708i	$0.174332\pi$
$542$	−22.5922			−0.970418
$543$			0.273958i			0.0117567i
$544$	−4.07862	+	0.604023i	−0.174869	+	0.0258973i
$545$		0			0
$546$			41.3539i			1.76979i
$547$	−10.2981	−	10.2981i	−0.440316	−	0.440316i	0.451802	−	0.892118i	$-0.350781\pi$
$547$	−10.2981	−	10.2981i	−0.440316	−	0.440316i	−0.892118	+	0.451802i	$0.850781\pi$
$548$			1.74115i			0.0743782i
$549$	9.69599	−	9.69599i	0.413815	−	0.413815i
$550$		0			0
$551$	26.2024	+	26.2024i	1.11626	+	1.11626i
$552$	−10.9530			−0.466189
$553$	5.86818			0.249540
$554$	18.0756	+	18.0756i	0.767959	+	0.767959i
$555$		0			0
$556$	−0.587666	+	0.587666i	−0.0249226	+	0.0249226i
$557$			5.85876i			0.248243i	0.992267	+	0.124122i	$0.0396113\pi$
$557$			5.85876i			0.248243i	−0.992267	+	0.124122i	$0.960389\pi$
$558$	2.49773	+	2.49773i	0.105737	+	0.105737i
$559$			40.9608i			1.73246i
$560$		0			0
$561$	−3.54301	−	23.9239i	−0.149586	−	1.01007i
$562$		−	15.8248i		−	0.667528i
$563$	15.8330			0.667280			0.333640	−	0.942701i	$-0.391723\pi$
$563$	15.8330			0.667280			0.333640	+	0.942701i	$0.391723\pi$
$564$	−7.84478	+	7.84478i	−0.330325	+	0.330325i
$565$		0			0
$566$	−12.4325	+	12.4325i	−0.522575	+	0.522575i
$567$	24.5738	−	24.5738i	1.03200	−	1.03200i
$568$	4.37207	−	4.37207i	0.183448	−	0.183448i
$569$		−	15.0288i		−	0.630039i	−0.949085	−	0.315019i	$-0.897989\pi$
$569$		−	15.0288i		−	0.630039i	0.949085	−	0.315019i	$-0.102011\pi$
$570$		0			0
$571$	4.81410	+	4.81410i	0.201464	+	0.201464i	0.800627	−	0.599163i	$-0.204500\pi$
$571$	4.81410	+	4.81410i	0.201464	+	0.201464i	−0.599163	+	0.800627i	$0.704500\pi$
$572$	−10.3903	+	10.3903i	−0.434440	+	0.434440i
$573$	−15.2744	−	15.2744i	−0.638096	−	0.638096i
$574$	−25.1200			−1.04849
$575$		0			0
$576$			2.14578i			0.0894076i
$577$			22.6806i			0.944204i	0.881544	+	0.472102i	$0.156505\pi$
$577$			22.6806i			0.944204i	−0.881544	+	0.472102i	$0.843495\pi$
$578$	−16.2703	+	4.92717i	−0.676756	+	0.204943i
$579$	−37.3155			−1.55078
$580$		0			0
$581$	27.5779	−	27.5779i	1.14412	−	1.14412i
$582$		−	40.2006i		−	1.66637i
$583$	−2.09498	−	2.09498i	−0.0867652	−	0.0867652i
$584$	−3.62981	−	3.62981i	−0.150203	−	0.150203i
$585$		0			0
$586$			29.6524i			1.22493i
$587$	40.9919			1.69192			0.845959	−	0.533248i	$-0.179029\pi$
$587$	40.9919			1.69192			0.845959	+	0.533248i	$0.179029\pi$
$588$	5.27975	−	5.27975i	0.217733	−	0.217733i
$589$	5.06794	+	5.06794i	0.208821	+	0.208821i
$590$		0			0
$591$	−52.4239			−2.15643
$592$	−3.09686	−	3.09686i	−0.127280	−	0.127280i
$593$	−12.4390			−0.510809			−0.255405	−	0.966834i	$-0.582209\pi$
$593$	−12.4390			−0.510809			−0.255405	+	0.966834i	$0.582209\pi$
$594$	5.01057			0.205586
$595$		0			0
$596$	2.44881			0.100307
$597$	22.4346			0.918187
$598$	19.4018	+	19.4018i	0.793397	+	0.793397i
$599$	15.4382			0.630789			0.315395	−	0.948961i	$-0.397863\pi$
$599$	15.4382			0.630789			0.315395	+	0.948961i	$0.397863\pi$
$600$		0			0
$601$	1.63560	+	1.63560i	0.0667176	+	0.0667176i	0.739678	−	0.672961i	$-0.234978\pi$
$601$	1.63560	+	1.63560i	0.0667176	+	0.0667176i	−0.672961	+	0.739678i	$0.734978\pi$
$602$	16.3510	−	16.3510i	0.666415	−	0.666415i
$603$	−30.1975			−1.22974
$604$		−	4.53686i		−	0.184602i
$605$		0			0
$606$	−12.2818	−	12.2818i	−0.498913	−	0.498913i
$607$	18.4798	+	18.4798i	0.750070	+	0.750070i	0.974492	−	0.224422i	$-0.0720494\pi$
$607$	18.4798	+	18.4798i	0.750070	+	0.750070i	−0.224422	+	0.974492i	$0.572049\pi$
$608$			4.35383i			0.176571i
$609$	−43.7961	+	43.7961i	−1.77471	+	1.77471i
$610$		0			0
$611$	27.7921			1.12435
$612$	1.29610	+	8.75183i	0.0523918	+	0.353772i
$613$			41.1938i			1.66380i	0.554923	+	0.831902i	$0.312748\pi$
$613$			41.1938i			1.66380i	−0.554923	+	0.831902i	$0.687252\pi$
$614$			32.0116i			1.29188i
$615$		0			0
$616$	8.29532			0.334228
$617$	−26.9435	−	26.9435i	−1.08471	−	1.08471i	−0.996064	−	0.0886418i	$-0.971747\pi$
$617$	−26.9435	−	26.9435i	−1.08471	−	1.08471i	−0.0886418	−	0.996064i	$-0.528253\pi$
$618$	−12.1708	+	12.1708i	−0.489581	+	0.489581i
$619$	24.1574	+	24.1574i	0.970966	+	0.970966i	0.999590	−	0.0286241i	$-0.00911257\pi$
$619$	24.1574	+	24.1574i	0.970966	+	0.970966i	−0.0286241	+	0.999590i	$0.509113\pi$
$620$		0			0
$621$		−	9.35621i		−	0.375452i
$622$	−8.72792	+	8.72792i	−0.349958	+	0.349958i
$623$	−36.9583	+	36.9583i	−1.48070	+	1.48070i
$624$	9.11510	−	9.11510i	0.364896	−	0.364896i
$625$		0			0
$626$	1.39030	−	1.39030i	0.0555677	−	0.0555677i
$627$	−25.5382			−1.01990
$628$		−	23.5074i		−	0.938048i
$629$	−14.5015	−	10.7603i	−0.578212	−	0.429043i
$630$		0			0
$631$			31.9751i			1.27291i	0.771314	+	0.636454i	$0.219600\pi$
$631$			31.9751i			1.27291i	−0.771314	+	0.636454i	$0.780400\pi$
$632$	−1.29344	−	1.29344i	−0.0514504	−	0.0514504i
$633$			38.1459i			1.51616i
$634$	−8.08540	+	8.08540i	−0.321112	+	0.321112i
$635$		0			0
$636$	1.83786	+	1.83786i	0.0728759	+	0.0728759i
$637$	−18.7048			−0.741111
$638$	−22.0078			−0.871298
$639$	−9.38150	−	9.38150i	−0.371126	−	0.371126i
$640$		0			0
$641$	−32.0152	+	32.0152i	−1.26453	+	1.26453i	−0.315649	+	0.948876i	$0.602222\pi$
$641$	−32.0152	+	32.0152i	−1.26453	+	1.26453i	−0.948876	+	0.315649i	$0.897778\pi$
$642$		−	12.3645i		−	0.487988i
$643$	−24.9629	−	24.9629i	−0.984439	−	0.984439i	0.0154416	−	0.999881i	$-0.495085\pi$
$643$	−24.9629	−	24.9629i	−0.984439	−	0.984439i	−0.999881	+	0.0154416i	$0.995085\pi$
$644$		−	15.4898i		−	0.610384i
$645$		0			0
$646$	2.62981	+	17.7576i	0.103469	+	0.698664i
$647$			24.6950i			0.970861i	0.874275	+	0.485430i	$0.161337\pi$
$647$			24.6950i			0.970861i	−0.874275	+	0.485430i	$0.838663\pi$
$648$	−10.8330			−0.425559
$649$	14.6469	−	14.6469i	0.574943	−	0.574943i
$650$		0			0
$651$	−8.47084	+	8.47084i	−0.331998	+	0.331998i
$652$	−16.0479	+	16.0479i	−0.628486	+	0.628486i
$653$	−11.2541	+	11.2541i	−0.440407	+	0.440407i	−0.892149	−	0.451742i	$-0.850803\pi$
$653$	−11.2541	+	11.2541i	−0.440407	+	0.440407i	0.451742	+	0.892149i	$0.350803\pi$
$654$		−	19.3068i		−	0.754955i
$655$		0			0
$656$	5.53686	+	5.53686i	0.216178	+	0.216178i
$657$	−7.78879	+	7.78879i	−0.303870	+	0.303870i
$658$	−11.0942	−	11.0942i	−0.432497	−	0.432497i
$659$	−2.52086			−0.0981989			−0.0490994	−	0.998794i	$-0.515635\pi$
$659$	−2.52086			−0.0981989			−0.0490994	+	0.998794i	$0.515635\pi$
$660$		0			0
$661$		−	12.1208i		−	0.471443i	−0.971821	−	0.235722i	$-0.924255\pi$
$661$		−	12.1208i		−	0.471443i	0.971821	−	0.235722i	$-0.0757454\pi$
$662$		−	18.4784i		−	0.718182i
$663$	31.6713	−	42.6828i	1.23001	−	1.65766i
$664$	−12.1572			−0.471793
$665$		0			0
$666$	−6.64518	+	6.64518i	−0.257496	+	0.257496i
$667$			41.0951i			1.59121i
$668$	14.4364	+	14.4364i	0.558559	+	0.558559i
$669$	14.8395	+	14.8395i	0.573729	+	0.573729i
$670$		0			0
$671$			16.5240i			0.637900i
$672$	−7.27723			−0.280725
$673$	16.4469	−	16.4469i	0.633981	−	0.633981i	−0.315083	−	0.949064i	$-0.602032\pi$
$673$	16.4469	−	16.4469i	0.633981	−	0.633981i	0.949064	+	0.315083i	$0.102032\pi$
$674$	−1.83708	−	1.83708i	−0.0707618	−	0.0707618i
$675$		0			0
$676$	−19.2925			−0.742018
$677$	1.45511	+	1.45511i	0.0559245	+	0.0559245i	0.734516	−	0.678591i	$-0.237409\pi$
$677$	1.45511	+	1.45511i	0.0559245	+	0.0559245i	−0.678591	+	0.734516i	$0.737409\pi$
$678$	−17.8952			−0.687262
$679$	56.8523			2.18179
$680$		0			0
$681$	46.5825			1.78504
$682$	−4.25665			−0.162995
$683$	−9.73834	−	9.73834i	−0.372627	−	0.372627i	0.495806	−	0.868433i	$-0.334873\pi$
$683$	−9.73834	−	9.73834i	−0.372627	−	0.372627i	−0.868433	+	0.495806i	$0.834873\pi$
$684$	9.34237			0.357214
$685$		0			0
$686$	−8.41233	−	8.41233i	−0.321184	−	0.321184i
$687$	−24.3199	+	24.3199i	−0.927860	+	0.927860i
$688$	−7.20805			−0.274804
$689$		−	6.51107i		−	0.248052i
$690$		0			0
$691$	14.3615	+	14.3615i	0.546338	+	0.546338i	0.925380	−	0.379041i	$-0.123746\pi$
$691$	14.3615	+	14.3615i	0.546338	+	0.546338i	−0.379041	+	0.925380i	$0.623746\pi$
$692$	−6.65873	−	6.65873i	−0.253127	−	0.253127i
$693$		−	17.8000i		−	0.676164i
$694$	9.15522	−	9.15522i	0.347527	−	0.347527i
$695$		0			0
$696$	19.3068			0.731822
$697$	25.9272	+	19.2384i	0.982061	+	0.728705i
$698$			20.3698i			0.771009i
$699$		−	20.1704i		−	0.762916i
$700$		0			0
$701$	−41.7527			−1.57698			−0.788489	−	0.615048i	$-0.789136\pi$
$701$	−41.7527			−1.57698			−0.788489	+	0.615048i	$0.789136\pi$
$702$	7.78628	+	7.78628i	0.293874	+	0.293874i
$703$	−13.4832	+	13.4832i	−0.508528	+	0.508528i
$704$	−1.82843	−	1.82843i	−0.0689114	−	0.0689114i
$705$		0			0
$706$		−	33.1680i		−	1.24830i
$707$	17.3691	−	17.3691i	0.653230	−	0.653230i
$708$	−12.8493	+	12.8493i	−0.482907	+	0.482907i
$709$	36.3578	−	36.3578i	1.36545	−	1.36545i	0.498637	−	0.866811i	$-0.333834\pi$
$709$	36.3578	−	36.3578i	1.36545	−	1.36545i	0.866811	−	0.498637i	$-0.166166\pi$
$710$		0			0
$711$	−2.77545	+	2.77545i	−0.104087	+	0.104087i
$712$	16.2925			0.610586
$713$			7.94842i			0.297671i
$714$	−29.6811	+	4.39562i	−1.11079	+	0.164502i
$715$		0			0
$716$			6.65763i			0.248807i
$717$	0.132714	+	0.132714i	0.00495631	+	0.00495631i
$718$		−	17.2272i		−	0.642914i
$719$	−31.1026	+	31.1026i	−1.15993	+	1.15993i	−0.175443	+	0.984490i	$0.556136\pi$
$719$	−31.1026	+	31.1026i	−1.15993	+	1.15993i	−0.984490	+	0.175443i	$0.943864\pi$
$720$		0			0
$721$	−17.2121	−	17.2121i	−0.641012	−	0.641012i
$722$	−0.0441757			−0.00164405
$723$	−2.66013			−0.0989313
$724$	0.0853971	+	0.0853971i	0.00317376	+	0.00317376i
$725$		0			0
$726$	−6.91929	+	6.91929i	−0.256799	+	0.256799i
$727$		−	34.1619i		−	1.26699i	−0.773745	−	0.633497i	$-0.781619\pi$
$727$		−	34.1619i		−	1.26699i	0.773745	−	0.633497i	$-0.218381\pi$
$728$	12.8907	+	12.8907i	0.477761	+	0.477761i
$729$			10.0583i			0.372530i
$730$		0			0
$731$	−29.3989	+	4.35383i	−1.08736	+	0.161032i
$732$		−	14.4960i		−	0.535786i
$733$	9.63393			0.355837			0.177919	−	0.984045i	$-0.443064\pi$
$733$	9.63393			0.355837			0.177919	+	0.984045i	$0.443064\pi$
$734$	−16.4879	+	16.4879i	−0.608581	+	0.608581i
$735$		0			0
$736$	−3.41421	+	3.41421i	−0.125850	+	0.125850i
$737$	25.7314	−	25.7314i	0.947827	−	0.947827i
$738$	11.8809	−	11.8809i	0.437342	−	0.437342i
$739$			34.3768i			1.26457i	0.774736	+	0.632285i	$0.217883\pi$
$739$			34.3768i			1.26457i	−0.774736	+	0.632285i	$0.782117\pi$
$740$		0			0
$741$	−39.6856	−	39.6856i	−1.45789	−	1.45789i
$742$	−2.59913	+	2.59913i	−0.0954170	+	0.0954170i
$743$	10.4068	+	10.4068i	0.381789	+	0.381789i	0.871746	−	0.489958i	$-0.162988\pi$
$743$	10.4068	+	10.4068i	0.381789	+	0.381789i	−0.489958	+	0.871746i	$0.662988\pi$
$744$	3.73423			0.136903
$745$		0			0
$746$		−	10.6098i		−	0.388453i
$747$			26.0868i			0.954466i
$748$	−8.56188	−	6.35305i	−0.313053	−	0.232291i
$749$	17.4861			0.638927
$750$		0			0
$751$	−2.95895	+	2.95895i	−0.107974	+	0.107974i	−0.759030	−	0.651056i	$-0.774326\pi$
$751$	−2.95895	+	2.95895i	−0.107974	+	0.107974i	0.651056	+	0.759030i	$0.274326\pi$
$752$			4.89069i			0.178345i
$753$	−29.0722	−	29.0722i	−1.05945	−	1.05945i
$754$	−34.1995	−	34.1995i	−1.24547	−	1.24547i
$755$		0			0
$756$		−	6.21635i		−	0.226086i
$757$	−23.3964			−0.850357			−0.425178	−	0.905110i	$-0.639789\pi$
$757$	−23.3964			−0.850357			−0.425178	+	0.905110i	$0.639789\pi$
$758$	−19.6872	+	19.6872i	−0.715071	+	0.715071i
$759$	−20.0267	−	20.0267i	−0.726923	−	0.726923i
$760$		0			0
$761$	26.2704			0.952302			0.476151	−	0.879363i	$-0.342032\pi$
$761$	26.2704			0.952302			0.476151	+	0.879363i	$0.342032\pi$
$762$	−10.8591	−	10.8591i	−0.393384	−	0.393384i
$763$	27.3039			0.988468
$764$	−9.52253			−0.344513
$765$		0			0
$766$	0.426776			0.0154201
$767$	45.5219			1.64370
$768$	1.60402	+	1.60402i	0.0578802	+	0.0578802i
$769$	−27.1033			−0.977369			−0.488685	−	0.872461i	$-0.662523\pi$
$769$	−27.1033			−0.977369			−0.488685	+	0.872461i	$0.662523\pi$
$770$		0			0
$771$	−40.6683	−	40.6683i	−1.46463	−	1.46463i
$772$	−11.6318	+	11.6318i	−0.418639	+	0.418639i
$773$	−31.6782			−1.13939			−0.569693	−	0.821857i	$-0.692938\pi$
$773$	−31.6782			−1.13939			−0.569693	+	0.821857i	$0.692938\pi$
$774$			15.4669i			0.555946i
$775$		0			0
$776$	−12.5312	−	12.5312i	−0.449843	−	0.449843i
$777$	−22.5366	−	22.5366i	−0.808495	−	0.808495i
$778$		−	0.807061i		−	0.0289345i
$779$	24.1066	−	24.1066i	0.863707	−	0.863707i
$780$		0			0
$781$	15.9880			0.572096
$782$	−11.8630	+	15.9876i	−0.424221	+	0.571714i
$783$			16.4922i			0.589383i
$784$		−	3.29156i		−	0.117556i
$785$		0			0
$786$	−23.5087			−0.838527
$787$	12.3579	+	12.3579i	0.440513	+	0.440513i	0.892184	−	0.451671i	$-0.149172\pi$
$787$	12.3579	+	12.3579i	0.440513	+	0.440513i	−0.451671	+	0.892184i	$0.649172\pi$
$788$	−16.3414	+	16.3414i	−0.582138	+	0.582138i
$789$	3.39066	+	3.39066i	0.120711	+	0.120711i
$790$		0			0
$791$		−	25.3077i		−	0.899837i
$792$	−3.92341	+	3.92341i	−0.139412	+	0.139412i
$793$	−25.6777	+	25.6777i	−0.911844	+	0.911844i
$794$	−18.9138	+	18.9138i	−0.671227	+	0.671227i
$795$		0			0
$796$	6.99322	−	6.99322i	0.247868	−	0.247868i
$797$	14.1900			0.502634			0.251317	−	0.967905i	$-0.419136\pi$
$797$	14.1900			0.502634			0.251317	+	0.967905i	$0.419136\pi$
$798$			31.6838i			1.12160i
$799$	2.95409	+	19.9473i	0.104508	+	0.705684i
$800$		0			0
$801$		−	34.9601i		−	1.23525i
$802$	10.9226	+	10.9226i	0.385691	+	0.385691i
$803$		−	13.2737i		−	0.468419i
$804$	−22.5733	+	22.5733i	−0.796100	+	0.796100i
$805$		0			0
$806$	−6.61471	−	6.61471i	−0.232993	−	0.232993i
$807$	−48.7296			−1.71536
$808$	−7.65685			−0.269367
$809$	−17.2453	−	17.2453i	−0.606312	−	0.606312i	0.335668	−	0.941980i	$-0.391038\pi$
$809$	−17.2453	−	17.2453i	−0.606312	−	0.606312i	−0.941980	+	0.335668i	$0.891038\pi$
$810$		0			0
$811$	−9.10566	+	9.10566i	−0.319743	+	0.319743i	−0.848668	−	0.528925i	$-0.822595\pi$
$811$	−9.10566	+	9.10566i	−0.319743	+	0.319743i	0.528925	+	0.848668i	$0.322595\pi$
$812$			27.3039i			0.958180i
$813$	36.2384	+	36.2384i	1.27094	+	1.27094i
$814$		−	11.3248i		−	0.396933i
$815$		0			0
$816$	7.51107	+	5.57334i	0.262940	+	0.195106i
$817$			31.3826i			1.09794i
$818$	9.19581			0.321524
$819$	27.6606	−	27.6606i	0.966540	−	0.966540i
$820$		0			0
$821$	13.4527	−	13.4527i	0.469503	−	0.469503i	−0.432251	−	0.901754i	$-0.642280\pi$
$821$	13.4527	−	13.4527i	0.469503	−	0.469503i	0.901754	+	0.432251i	$0.142280\pi$
$822$	2.79285	−	2.79285i	0.0974117	−	0.0974117i
$823$	11.4872	−	11.4872i	0.400417	−	0.400417i	−0.477963	−	0.878380i	$-0.658625\pi$
$823$	11.4872	−	11.4872i	0.400417	−	0.400417i	0.878380	+	0.477963i	$0.158625\pi$
$824$			7.58767i			0.264329i
$825$		0			0
$826$	−18.1717	−	18.1717i	−0.632274	−	0.632274i
$827$	−12.4889	+	12.4889i	−0.434283	+	0.434283i	−0.890082	−	0.455800i	$-0.849353\pi$
$827$	−12.4889	+	12.4889i	−0.434283	+	0.434283i	0.455800	+	0.890082i	$0.349353\pi$
$828$	7.32616	+	7.32616i	0.254602	+	0.254602i
$829$	1.81004			0.0628654			0.0314327	−	0.999506i	$-0.489993\pi$
$829$	1.81004			0.0628654			0.0314327	+	0.999506i	$0.489993\pi$
$830$		0			0
$831$		−	57.9874i		−	2.01156i
$832$		−	5.68265i		−	0.197010i
$833$	−1.98818	−	13.4250i	−0.0688864	−	0.465150i
$834$	1.88526			0.0652813
$835$		0			0
$836$	−7.96066	+	7.96066i	−0.275325	+	0.275325i
$837$			3.18984i			0.110257i
$838$	6.93774	+	6.93774i	0.239660	+	0.239660i
$839$	−19.0797	−	19.0797i	−0.658705	−	0.658705i	0.296368	−	0.955074i	$-0.404224\pi$
$839$	−19.0797	−	19.0797i	−0.658705	−	0.658705i	−0.955074	+	0.296368i	$0.904224\pi$
$840$		0			0
$841$		−	43.4384i		−	1.49787i
$842$	17.0410			0.587272
$843$	−25.3833	+	25.3833i	−0.874248	+	0.874248i
$844$	11.8907	+	11.8907i	0.409294	+	0.409294i
$845$		0			0
$846$	10.4944			0.360803
$847$	−9.78535	−	9.78535i	−0.336229	−	0.336229i
$848$	1.14578			0.0393463
$849$	39.8839			1.36881
$850$		0			0
$851$	−21.1467			−0.724899
$852$	−14.0258			−0.480516
$853$	−12.8918	−	12.8918i	−0.441407	−	0.441407i	0.451078	−	0.892485i	$-0.351040\pi$
$853$	−12.8918	−	12.8918i	−0.441407	−	0.441407i	−0.892485	+	0.451078i	$0.851040\pi$
$854$	20.5004			0.701509
$855$		0			0
$856$	−3.85422	−	3.85422i	−0.131734	−	0.131734i
$857$	−7.32470	+	7.32470i	−0.250207	+	0.250207i	−0.821055	−	0.570848i	$-0.806614\pi$
$857$	−7.32470	+	7.32470i	−0.250207	+	0.250207i	0.570848	+	0.821055i	$0.306614\pi$
$858$	33.3326			1.13796
$859$			54.5456i			1.86107i	0.366202	+	0.930535i	$0.380658\pi$
$859$			54.5456i			1.86107i	−0.366202	+	0.930535i	$0.619342\pi$
$860$		0			0
$861$	40.2931	+	40.2931i	1.37318	+	1.37318i
$862$	−13.8152	−	13.8152i	−0.470548	−	0.470548i
$863$			1.42063i			0.0483589i	0.999708	+	0.0241794i	$0.00769730\pi$
$863$			1.42063i			0.0483589i	−0.999708	+	0.0241794i	$0.992303\pi$
$864$	−1.37019	+	1.37019i	−0.0466147	+	0.0466147i
$865$		0			0
$866$	16.7404			0.568861
$867$	34.0012	+	18.1947i	1.15474	+	0.617923i
$868$			5.28099i			0.179249i
$869$		−	4.72994i		−	0.160452i
$870$		0			0
$871$	79.9716			2.70973
$872$	−6.01824	−	6.01824i	−0.203803	−	0.203803i
$873$	−26.8892	+	26.8892i	−0.910062	+	0.910062i
$874$	14.8649	+	14.8649i	0.502813	+	0.502813i
$875$		0			0
$876$			11.6446i			0.393435i
$877$	20.4621	−	20.4621i	0.690958	−	0.690958i	−0.271485	−	0.962443i	$-0.587515\pi$
$877$	20.4621	−	20.4621i	0.690958	−	0.690958i	0.962443	+	0.271485i	$0.0875147\pi$
$878$	7.98755	−	7.98755i	0.269567	−	0.269567i
$879$	47.5632	−	47.5632i	1.60427	−	1.60427i
$880$		0			0
$881$	13.0607	−	13.0607i	0.440026	−	0.440026i	−0.451994	−	0.892021i	$-0.649287\pi$
$881$	13.0607	−	13.0607i	0.440026	−	0.440026i	0.892021	+	0.451994i	$0.149287\pi$
$882$	−7.06298			−0.237823
$883$			13.7927i			0.464162i	0.972696	+	0.232081i	$0.0745535\pi$
$883$			13.7927i			0.464162i	−0.972696	+	0.232081i	$0.925446\pi$
$884$	−3.43245	−	23.1774i	−0.115446	−	0.779539i
$885$		0			0
$886$			19.7084i			0.662118i
$887$	14.8015	+	14.8015i	0.496987	+	0.496987i	0.910499	−	0.413512i	$-0.135698\pi$
$887$	14.8015	+	14.8015i	0.496987	+	0.496987i	−0.413512	+	0.910499i	$0.635698\pi$
$888$			9.93487i			0.333392i
$889$	15.3571	−	15.3571i	0.515061	−	0.515061i
$890$		0			0
$891$	−19.8073	−	19.8073i	−0.663569	−	0.663569i
$892$	9.25144			0.309761
$893$	21.2932			0.712551
$894$	−3.92794	−	3.92794i	−0.131370	−	0.131370i
$895$		0			0
$896$	−2.26843	+	2.26843i	−0.0757830	+	0.0757830i
$897$		−	62.2418i		−	2.07819i
$898$	−6.43042	−	6.43042i	−0.214586	−	0.214586i
$899$		−	14.0107i		−	0.467282i
$900$		0			0
$901$	4.67321	−	0.692079i	0.155687	−	0.0230565i
$902$			20.2475i			0.674168i
$903$	−52.4546			−1.74558
$904$	−5.57823	+	5.57823i	−0.185529	+	0.185529i
$905$		0			0
$906$	−7.27723	+	7.27723i	−0.241770	+	0.241770i
$907$	−20.0606	+	20.0606i	−0.666103	+	0.666103i	−0.956812	−	0.290709i	$-0.906109\pi$
$907$	−20.0606	+	20.0606i	−0.666103	+	0.666103i	0.290709	+	0.956812i	$0.406109\pi$
$908$	14.5205	−	14.5205i	0.481880	−	0.481880i
$909$			16.4299i			0.544947i
$910$		0			0
$911$	−19.9375	−	19.9375i	−0.660560	−	0.660560i	0.294952	−	0.955512i	$-0.404696\pi$
$911$	−19.9375	−	19.9375i	−0.660560	−	0.660560i	−0.955512	+	0.294952i	$0.904696\pi$
$912$	6.98364	−	6.98364i	0.231252	−	0.231252i
$913$	−22.2286	−	22.2286i	−0.735660	−	0.735660i
$914$	7.73959			0.256003
$915$		0			0
$916$			15.1618i			0.500959i
$917$		−	33.2463i		−	1.09789i
$918$	−4.76085	+	6.41609i	−0.157131	+	0.211763i
$919$	−5.49805			−0.181364			−0.0906820	−	0.995880i	$-0.528905\pi$
$919$	−5.49805			−0.181364			−0.0906820	+	0.995880i	$0.528905\pi$
$920$		0			0
$921$	51.3473	−	51.3473i	1.69195	−	1.69195i
$922$		−	25.0045i		−	0.823481i
$923$	24.8449	+	24.8449i	0.817780	+	0.817780i
$924$	−13.3059	−	13.3059i	−0.437732	−	0.437732i
$925$		0			0
$926$			29.7745i			0.978449i
$927$	16.2815			0.534754
$928$	6.01824	−	6.01824i	0.197558	−	0.197558i
$929$	−7.24530	−	7.24530i	−0.237711	−	0.237711i	0.578191	−	0.815901i	$-0.303759\pi$
$929$	−7.24530	−	7.24530i	−0.237711	−	0.237711i	−0.815901	+	0.578191i	$0.803759\pi$
$930$		0			0
$931$	−14.3309			−0.469676
$932$	−6.28745	−	6.28745i	−0.205952	−	0.205952i
$933$	27.9996			0.916665
$934$	12.3104			0.402810
$935$		0			0
$936$	−12.1937			−0.398564
$937$	−18.3456			−0.599326			−0.299663	−	0.954045i	$-0.596874\pi$
$937$	−18.3456			−0.599326			−0.299663	+	0.954045i	$0.596874\pi$
$938$	−31.9235	−	31.9235i	−1.04234	−	1.04234i
$939$	−4.46016			−0.145552
$940$		0			0
$941$	−0.741002	−	0.741002i	−0.0241560	−	0.0241560i	0.694926	−	0.719082i	$-0.255437\pi$
$941$	−0.741002	−	0.741002i	−0.0241560	−	0.0241560i	−0.719082	+	0.694926i	$0.755437\pi$
$942$	−37.7065	+	37.7065i	−1.22854	+	1.22854i
$943$	37.8081			1.23120
$944$			8.01068i			0.260726i
$945$		0			0
$946$	−13.1794	−	13.1794i	−0.428499	−	0.428499i
$947$	−25.4030	−	25.4030i	−0.825487	−	0.825487i	0.161402	−	0.986889i	$-0.448399\pi$
$947$	−25.4030	−	25.4030i	−0.825487	−	0.825487i	−0.986889	+	0.161402i	$0.948399\pi$
$948$			4.14943i			0.134767i
$949$	20.6269	−	20.6269i	0.669579	−	0.669579i
$950$		0			0
$951$	25.9383			0.841108
$952$	−7.88189	+	10.6223i	−0.255453	+	0.344269i
$953$			0.289066i			0.00936376i	0.999989	+	0.00468188i	$0.00149029\pi$
$953$			0.289066i			0.00936376i	−0.999989	+	0.00468188i	$0.998510\pi$
$954$		−	2.45860i		−	0.0796001i
$955$		0			0
$956$	0.0827385			0.00267595
$957$	35.3011	+	35.3011i	1.14112	+	1.14112i
$958$	−4.61361	+	4.61361i	−0.149059	+	0.149059i
$959$	3.94968	+	3.94968i	0.127542	+	0.127542i
$960$		0			0
$961$			28.2901i			0.912585i
$962$	17.5983	−	17.5983i	0.567394	−	0.567394i
$963$	−8.27031	+	8.27031i	−0.266507	+	0.266507i
$964$	−0.829206	+	0.829206i	−0.0267069	+	0.0267069i
$965$		0			0
$966$	−24.8460	+	24.8460i	−0.799408	+	0.799408i
$967$	31.1696			1.00235			0.501173	−	0.865347i	$-0.332902\pi$
$967$	31.1696			1.00235			0.501173	+	0.865347i	$0.332902\pi$
$968$			4.31371i			0.138648i
$969$	24.2654	−	32.7019i	0.779516	−	1.05054i
$970$		0			0
$971$		−	19.6962i		−	0.632081i	−0.948746	−	0.316041i	$-0.897646\pi$
$971$		−	19.6962i		−	0.632081i	0.948746	−	0.316041i	$-0.102354\pi$
$972$	13.2658	+	13.2658i	0.425500	+	0.425500i
$973$			2.66616i			0.0854732i
$974$	9.85234	−	9.85234i	0.315689	−	0.315689i
$975$		0			0
$976$	−4.51863	−	4.51863i	−0.144638	−	0.144638i
$977$	20.4047			0.652806			0.326403	−	0.945231i	$-0.394163\pi$
$977$	20.4047			0.652806			0.326403	+	0.945231i	$0.394163\pi$
$978$	51.4825			1.64623
$979$	29.7896	+	29.7896i	0.952079	+	0.952079i
$980$		0			0
$981$	−12.9138	+	12.9138i	−0.412307	+	0.412307i
$982$			0.302247i			0.00964508i
$983$	−16.9814	−	16.9814i	−0.541623	−	0.541623i	0.382382	−	0.924004i	$-0.375104\pi$
$983$	−16.9814	−	16.9814i	−0.541623	−	0.541623i	−0.924004	+	0.382382i	$0.875104\pi$
$984$		−	17.7625i		−	0.566248i
$985$		0			0
$986$	20.9110	−	28.1813i	0.665941	−	0.897474i
$987$			35.5907i			1.13286i
$988$	−24.7413			−0.787124
$989$	−24.6098	+	24.6098i	−0.782546	+	0.782546i
$990$		0			0
$991$	18.5907	−	18.5907i	0.590552	−	0.590552i	−0.347228	−	0.937781i	$-0.612877\pi$
$991$	18.5907	−	18.5907i	0.590552	−	0.590552i	0.937781	+	0.347228i	$0.112877\pi$
$992$	1.16402	−	1.16402i	0.0369576	−	0.0369576i
$993$	−29.6397	+	29.6397i	−0.940588	+	0.940588i
$994$		−	19.8355i		−	0.629143i
$995$		0			0
$996$	19.5005	+	19.5005i	0.617897	+	0.617897i
$997$	−23.5532	+	23.5532i	−0.745937	+	0.745937i	−0.973713	−	0.227777i	$-0.926854\pi$
$997$	−23.5532	+	23.5532i	−0.745937	+	0.745937i	0.227777	+	0.973713i	$0.426854\pi$
$998$	11.6941	+	11.6941i	0.370170	+	0.370170i
$999$	−8.48654			−0.268502

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.g.i.599.3		8
5.2	odd	4		170.2.h.b.21.3	✓	8
5.3	odd	4		850.2.h.n.701.2		8
5.4	even	2		850.2.g.l.599.2		8
15.2	even	4		1530.2.q.g.361.2		8
17.13	even	4		850.2.g.l.149.2		8
20.7	even	4		1360.2.bt.b.1041.2		8
85.2	odd	8		2890.2.b.o.2311.3		8
85.13	odd	4		850.2.h.n.251.2		8
85.32	odd	8		2890.2.b.o.2311.6		8
85.42	odd	8		2890.2.a.be.1.1		4
85.47	odd	4		170.2.h.b.81.3	yes	8
85.64	even	4	inner	850.2.g.i.149.3		8
85.77	odd	8		2890.2.a.bd.1.4		4
255.47	even	4		1530.2.q.g.1441.2		8
340.47	even	4		1360.2.bt.b.81.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.h.b.21.3	✓	8	5.2	odd	4
170.2.h.b.81.3	yes	8	85.47	odd	4
850.2.g.i.149.3		8	85.64	even	4	inner
850.2.g.i.599.3		8	1.1	even	1	trivial
850.2.g.l.149.2		8	17.13	even	4
850.2.g.l.599.2		8	5.4	even	2
850.2.h.n.251.2		8	85.13	odd	4
850.2.h.n.701.2		8	5.3	odd	4
1360.2.bt.b.81.2		8	340.47	even	4
1360.2.bt.b.1041.2		8	20.7	even	4
1530.2.q.g.361.2		8	15.2	even	4
1530.2.q.g.1441.2		8	255.47	even	4
2890.2.a.bd.1.4		4	85.77	odd	8
2890.2.a.be.1.1		4	85.42	odd	8
2890.2.b.o.2311.3		8	85.2	odd	8
2890.2.b.o.2311.6		8	85.32	odd	8

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:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	850.g (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(1.60402 + 1.60402i) q^{3} +1.00000 q^{4} +(-1.60402 - 1.60402i) q^{6} +(2.26843 - 2.26843i) q^{7} -1.00000 q^{8} +2.14578i q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(1.60402 + 1.60402i) q^{3} +1.00000 q^{4} +(-1.60402 - 1.60402i) q^{6} +(2.26843 - 2.26843i) q^{7} -1.00000 q^{8} +2.14578i q^{9} +(-1.82843 - 1.82843i) q^{11} +(1.60402 + 1.60402i) q^{12} -5.68265i q^{13} +(-2.26843 + 2.26843i) q^{14} +1.00000 q^{16} +(4.07862 - 0.604023i) q^{17} -2.14578i q^{18} -4.35383i q^{19} +7.27723 q^{21} +(1.82843 + 1.82843i) q^{22} +(3.41421 - 3.41421i) q^{23} +(-1.60402 - 1.60402i) q^{24} +5.68265i q^{26} +(1.37019 - 1.37019i) q^{27} +(2.26843 - 2.26843i) q^{28} +(-6.01824 + 6.01824i) q^{29} +(-1.16402 + 1.16402i) q^{31} -1.00000 q^{32} -5.86568i q^{33} +(-4.07862 + 0.604023i) q^{34} +2.14578i q^{36} +(-3.09686 - 3.09686i) q^{37} +4.35383i q^{38} +(9.11510 - 9.11510i) q^{39} +(5.53686 + 5.53686i) q^{41} -7.27723 q^{42} -7.20805 q^{43} +(-1.82843 - 1.82843i) q^{44} +(-3.41421 + 3.41421i) q^{46} +4.89069i q^{47} +(1.60402 + 1.60402i) q^{48} -3.29156i q^{49} +(7.51107 + 5.57334i) q^{51} -5.68265i q^{52} +1.14578 q^{53} +(-1.37019 + 1.37019i) q^{54} +(-2.26843 + 2.26843i) q^{56} +(6.98364 - 6.98364i) q^{57} +(6.01824 - 6.01824i) q^{58} +8.01068i q^{59} +(-4.51863 - 4.51863i) q^{61} +(1.16402 - 1.16402i) q^{62} +(4.86756 + 4.86756i) q^{63} +1.00000 q^{64} +5.86568i q^{66} +14.0729i q^{67} +(4.07862 - 0.604023i) q^{68} +10.9530 q^{69} +(-4.37207 + 4.37207i) q^{71} -2.14578i q^{72} +(3.62981 + 3.62981i) q^{73} +(3.09686 + 3.09686i) q^{74} -4.35383i q^{76} -8.29532 q^{77} +(-9.11510 + 9.11510i) q^{78} +(1.29344 + 1.29344i) q^{79} +10.8330 q^{81} +(-5.53686 - 5.53686i) q^{82} +12.1572 q^{83} +7.27723 q^{84} +7.20805 q^{86} -19.3068 q^{87} +(1.82843 + 1.82843i) q^{88} -16.2925 q^{89} +(-12.8907 - 12.8907i) q^{91} +(3.41421 - 3.41421i) q^{92} -3.73423 q^{93} -4.89069i q^{94} +(-1.60402 - 1.60402i) q^{96} +(12.5312 + 12.5312i) q^{97} +3.29156i q^{98} +(3.92341 - 3.92341i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} - 4 q^{7} - 8 q^{8}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^4 - 4 * q^7 - 8 * q^8	\( 8 q - 8 q^{2} + 8 q^{4} - 4 q^{7} - 8 q^{8} + 8 q^{11} + 4 q^{14} + 8 q^{16} + 12 q^{17} + 16 q^{21} - 8 q^{22} + 16 q^{23} + 12 q^{27} - 4 q^{28} - 24 q^{29} + 4 q^{31} - 8 q^{32} - 12 q^{34} + 20 q^{37} + 4 q^{39} - 16 q^{42} - 32 q^{43} + 8 q^{44} - 16 q^{46} + 4 q^{51} + 20 q^{53} - 12 q^{54} + 4 q^{56} + 40 q^{57} + 24 q^{58} - 16 q^{61} - 4 q^{62} - 64 q^{63} + 8 q^{64} + 12 q^{68} - 8 q^{69} + 4 q^{71} + 28 q^{73} - 20 q^{74} - 8 q^{77} - 4 q^{78} - 8 q^{79} - 8 q^{81} + 56 q^{83} + 16 q^{84} + 32 q^{86} - 44 q^{87} - 8 q^{88} + 44 q^{89} - 44 q^{91} + 16 q^{92} - 20 q^{93} - 20 q^{97} + 4 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 - 4 * q^7 - 8 * q^8 + 8 * q^11 + 4 * q^14 + 8 * q^16 + 12 * q^17 + 16 * q^21 - 8 * q^22 + 16 * q^23 + 12 * q^27 - 4 * q^28 - 24 * q^29 + 4 * q^31 - 8 * q^32 - 12 * q^34 + 20 * q^37 + 4 * q^39 - 16 * q^42 - 32 * q^43 + 8 * q^44 - 16 * q^46 + 4 * q^51 + 20 * q^53 - 12 * q^54 + 4 * q^56 + 40 * q^57 + 24 * q^58 - 16 * q^61 - 4 * q^62 - 64 * q^63 + 8 * q^64 + 12 * q^68 - 8 * q^69 + 4 * q^71 + 28 * q^73 - 20 * q^74 - 8 * q^77 - 4 * q^78 - 8 * q^79 - 8 * q^81 + 56 * q^83 + 16 * q^84 + 32 * q^86 - 44 * q^87 - 8 * q^88 + 44 * q^89 - 44 * q^91 + 16 * q^92 - 20 * q^93 - 20 * q^97 + 4 * q^99

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