LMFDB - Embedded newform 29.2.e.a.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,2,Mod(4,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(14))

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

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

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

chi := DirichletCharacter("29.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	29.e (of order $14$, degree $6$, 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:	$0.231566165862$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{14})$
Coefficient field:	12.0.7877952219361.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3x^{11} + 13x^{9} - 18x^{8} - 14x^{7} + 57x^{6} - 28x^{5} - 72x^{4} + 104x^{3} - 96x + 64 $ x^12 - 3x^11 + 13x^9 - 18x^8 - 14x^7 + 57x^6 - 28x^5 - 72x^4 + 104x^3 - 96*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			5.2
Root			$-1.41140 + 0.0891373i$ of defining polynomial
Character	$\chi$	$=$	29.5
Dual form			29.2.e.a.6.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.21127 - 0.965958i) q^{2} +(-2.86109 + 0.653024i) q^{3} +(0.0890656 - 0.390222i) q^{4} +(0.283269 + 0.355208i) q^{5} +(-2.83476 + 3.55468i) q^{6} +(-0.759522 - 3.32768i) q^{7} +(1.07536 + 2.23300i) q^{8} +(5.05647 - 2.43507i) q^{9} +O(q^{10})$	\(q+(1.21127 - 0.965958i) q^{2} +(-2.86109 + 0.653024i) q^{3} +(0.0890656 - 0.390222i) q^{4} +(0.283269 + 0.355208i) q^{5} +(-2.83476 + 3.55468i) q^{6} +(-0.759522 - 3.32768i) q^{7} +(1.07536 + 2.23300i) q^{8} +(5.05647 - 2.43507i) q^{9} +(0.686232 + 0.156628i) q^{10} +(-0.635522 + 1.31967i) q^{11} +1.17462i q^{12} +(-2.78085 - 1.33919i) q^{13} +(-4.13439 - 3.29707i) q^{14} +(-1.04242 - 0.831299i) q^{15} +(4.18077 + 2.01335i) q^{16} +2.82403i q^{17} +(3.77259 - 7.83387i) q^{18} +(2.23472 + 0.510059i) q^{19} +(0.163839 - 0.0789009i) q^{20} +(4.34612 + 9.02480i) q^{21} +(0.504960 + 2.21237i) q^{22} +(0.333001 - 0.417570i) q^{23} +(-4.53489 - 5.68657i) q^{24} +(1.06667 - 4.67340i) q^{25} +(-4.66197 + 1.06407i) q^{26} +(-5.99360 + 4.77973i) q^{27} -1.36618 q^{28} +(-3.83606 + 3.77951i) q^{29} -2.06565 q^{30} +(-2.80406 + 2.23616i) q^{31} +(2.17627 - 0.496719i) q^{32} +(0.956503 - 4.19071i) q^{33} +(2.72789 + 3.42067i) q^{34} +(0.966870 - 1.21242i) q^{35} +(-0.499859 - 2.19003i) q^{36} +(-3.08996 - 6.41637i) q^{37} +(3.19955 - 1.54082i) q^{38} +(8.83079 + 2.01557i) q^{39} +(-0.488564 + 1.01451i) q^{40} -4.43991i q^{41} +(13.9819 + 6.73333i) q^{42} +(3.22518 + 2.57200i) q^{43} +(0.458363 + 0.365532i) q^{44} +(2.29729 + 1.10632i) q^{45} -0.827457i q^{46} +(0.0778542 - 0.161666i) q^{47} +(-13.2763 - 3.03023i) q^{48} +(-4.18982 + 2.01771i) q^{49} +(-3.22228 - 6.69113i) q^{50} +(-1.84416 - 8.07978i) q^{51} +(-0.770259 + 0.965875i) q^{52} +(1.92383 + 2.41240i) q^{53} +(-2.64286 + 11.5791i) q^{54} +(-0.648782 + 0.148080i) q^{55} +(6.61396 - 5.27446i) q^{56} -6.72679 q^{57} +(-0.995668 + 8.28348i) q^{58} +13.2495 q^{59} +(-0.417234 + 0.332733i) q^{60} +(1.84068 - 0.420124i) q^{61} +(-1.23644 + 5.41721i) q^{62} +(-11.9436 - 14.9768i) q^{63} +(-3.63013 + 4.55204i) q^{64} +(-0.312039 - 1.36713i) q^{65} +(-2.88947 - 6.00004i) q^{66} +(-10.9658 + 5.28086i) q^{67} +(1.10200 + 0.251524i) q^{68} +(-0.680062 + 1.41216i) q^{69} -2.40252i q^{70} +(4.06735 + 1.95873i) q^{71} +(10.8750 + 8.67253i) q^{72} +(6.47043 + 5.16000i) q^{73} +(-9.94073 - 4.78720i) q^{74} +14.0676i q^{75} +(0.398073 - 0.826606i) q^{76} +(4.87415 + 1.11249i) q^{77} +(12.6435 - 6.08877i) q^{78} +(-6.00316 - 12.4657i) q^{79} +(0.469123 + 2.05536i) q^{80} +(3.52936 - 4.42568i) q^{81} +(-4.28877 - 5.37794i) q^{82} +(0.545892 - 2.39171i) q^{83} +(3.90876 - 0.892150i) q^{84} +(-1.00312 + 0.799958i) q^{85} +6.39102 q^{86} +(8.50718 - 13.3185i) q^{87} -3.63025 q^{88} +(-10.5483 + 8.41200i) q^{89} +(3.85131 - 0.879036i) q^{90} +(-2.34428 + 10.2709i) q^{91} +(-0.133286 - 0.167136i) q^{92} +(6.56239 - 8.22898i) q^{93} +(-0.0618598 - 0.271025i) q^{94} +(0.451848 + 0.938272i) q^{95} +(-5.90212 + 2.84231i) q^{96} +(4.58979 + 1.04759i) q^{97} +(-3.12599 + 6.49118i) q^{98} +8.22043i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 7 q^{2} - 7 q^{3} - q^{4} - q^{5} - 3 q^{6} - 11 q^{7} + 14 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q - 7 * q^2 - 7 * q^3 - q^4 - q^5 - 3 * q^6 - 11 * q^7 + 14 * q^8 - 3 * q^9	\( 12 q - 7 q^{2} - 7 q^{3} - q^{4} - q^{5} - 3 q^{6} - 11 q^{7} + 14 q^{8} - 3 q^{9} - 7 q^{10} + 7 q^{11} + 9 q^{13} - 7 q^{14} + 7 q^{15} + 9 q^{16} + 42 q^{18} - 7 q^{19} - 11 q^{20} - 7 q^{21} - 4 q^{22} - 5 q^{23} - 25 q^{24} + 13 q^{25} - 21 q^{26} - 7 q^{27} + 12 q^{28} - 15 q^{29} + 2 q^{30} - 21 q^{31} - 17 q^{33} - 13 q^{34} + 19 q^{35} - 40 q^{36} + 7 q^{37} + 28 q^{38} + 21 q^{39} + 35 q^{40} + 50 q^{42} + 7 q^{43} + 42 q^{44} + 16 q^{45} - 7 q^{47} - 14 q^{48} + 13 q^{49} - 28 q^{50} + 20 q^{51} - 6 q^{52} - 10 q^{53} - 38 q^{54} - 35 q^{55} - 21 q^{56} - 14 q^{57} - 57 q^{58} + 44 q^{59} - 28 q^{60} - 7 q^{61} + 37 q^{62} - 13 q^{63} - 26 q^{64} - 6 q^{65} + 21 q^{66} - 37 q^{67} + 14 q^{68} + 21 q^{69} - 21 q^{71} + 35 q^{72} + 14 q^{73} + 7 q^{76} - 7 q^{77} + 17 q^{78} + 49 q^{79} - 6 q^{80} + q^{81} + 22 q^{82} + 5 q^{83} + 21 q^{84} + 14 q^{85} - 44 q^{86} + 15 q^{87} - 66 q^{88} + 7 q^{89} + 28 q^{90} - 3 q^{91} - 6 q^{92} + 19 q^{93} + 66 q^{94} - 7 q^{95} + 30 q^{96} + 14 q^{97} - 42 q^{98}+O(q^{100}) \) 12 * q - 7 * q^2 - 7 * q^3 - q^4 - q^5 - 3 * q^6 - 11 * q^7 + 14 * q^8 - 3 * q^9 - 7 * q^10 + 7 * q^11 + 9 * q^13 - 7 * q^14 + 7 * q^15 + 9 * q^16 + 42 * q^18 - 7 * q^19 - 11 * q^20 - 7 * q^21 - 4 * q^22 - 5 * q^23 - 25 * q^24 + 13 * q^25 - 21 * q^26 - 7 * q^27 + 12 * q^28 - 15 * q^29 + 2 * q^30 - 21 * q^31 - 17 * q^33 - 13 * q^34 + 19 * q^35 - 40 * q^36 + 7 * q^37 + 28 * q^38 + 21 * q^39 + 35 * q^40 + 50 * q^42 + 7 * q^43 + 42 * q^44 + 16 * q^45 - 7 * q^47 - 14 * q^48 + 13 * q^49 - 28 * q^50 + 20 * q^51 - 6 * q^52 - 10 * q^53 - 38 * q^54 - 35 * q^55 - 21 * q^56 - 14 * q^57 - 57 * q^58 + 44 * q^59 - 28 * q^60 - 7 * q^61 + 37 * q^62 - 13 * q^63 - 26 * q^64 - 6 * q^65 + 21 * q^66 - 37 * q^67 + 14 * q^68 + 21 * q^69 - 21 * q^71 + 35 * q^72 + 14 * q^73 + 7 * q^76 - 7 * q^77 + 17 * q^78 + 49 * q^79 - 6 * q^80 + q^81 + 22 * q^82 + 5 * q^83 + 21 * q^84 + 14 * q^85 - 44 * q^86 + 15 * q^87 - 66 * q^88 + 7 * q^89 + 28 * q^90 - 3 * q^91 - 6 * q^92 + 19 * q^93 + 66 * q^94 - 7 * q^95 + 30 * q^96 + 14 * q^97 - 42 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{14}\right)$

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 $

$2$	1.21127	−	0.965958i	0.856499	−	0.683035i	−0.0933873	−	0.995630i	$-0.529769\pi$
$2$	1.21127	−	0.965958i	0.856499	−	0.683035i	0.949887	+	0.312594i	$0.101198\pi$
$3$	−2.86109	+	0.653024i	−1.65185	+	0.377024i	−0.944157	−	0.329497i	$-0.893121\pi$
$3$	−2.86109	+	0.653024i	−1.65185	+	0.377024i	−0.707692	+	0.706521i	$0.750264\pi$
$4$	0.0890656	−	0.390222i	0.0445328	−	0.195111i
$5$	0.283269	+	0.355208i	0.126682	+	0.158854i	0.841127	−	0.540837i	$-0.181892\pi$
$5$	0.283269	+	0.355208i	0.126682	+	0.158854i	−0.714446	+	0.699691i	$0.753321\pi$
$6$	−2.83476	+	3.55468i	−1.15729	+	1.45119i
$7$	−0.759522	−	3.32768i	−0.287072	−	1.25775i	−0.888522	−	0.458835i	$-0.848267\pi$
$7$	−0.759522	−	3.32768i	−0.287072	−	1.25775i	0.601449	−	0.798911i	$-0.294590\pi$
$8$	1.07536	+	2.23300i	0.380196	+	0.789485i
$9$	5.05647	−	2.43507i	1.68549	−	0.811689i
$10$	0.686232	+	0.156628i	0.217006	+	0.0495301i
$11$	−0.635522	+	1.31967i	−0.191617	+	0.397897i	−0.974537	−	0.224225i	$-0.928015\pi$
$11$	−0.635522	+	1.31967i	−0.191617	+	0.397897i	0.782920	+	0.622122i	$0.213729\pi$
$12$			1.17462i			0.339084i
$13$	−2.78085	−	1.33919i	−0.771270	−	0.371424i	0.00649509	−	0.999979i	$-0.497933\pi$
$13$	−2.78085	−	1.33919i	−0.771270	−	0.371424i	−0.777765	+	0.628555i	$0.783647\pi$
$14$	−4.13439	−	3.29707i	−1.10496	−	0.881178i
$15$	−1.04242	−	0.831299i	−0.269151	−	0.214640i
$16$	4.18077	+	2.01335i	1.04519	+	0.503339i
$17$			2.82403i			0.684927i	0.939531	+	0.342463i	$0.111261\pi$
$17$			2.82403i			0.684927i	−0.939531	+	0.342463i	$0.888739\pi$
$18$	3.77259	−	7.83387i	0.889208	−	1.84646i
$19$	2.23472	+	0.510059i	0.512679	+	0.117016i	0.471031	−	0.882117i	$-0.343882\pi$
$19$	2.23472	+	0.510059i	0.512679	+	0.117016i	0.0416480	+	0.999132i	$0.486739\pi$
$20$	0.163839	−	0.0789009i	0.0366356	−	0.0176428i
$21$	4.34612	+	9.02480i	0.948400	+	1.96937i
$22$	0.504960	+	2.21237i	0.107658	+	0.471680i
$23$	0.333001	−	0.417570i	0.0694356	−	0.0870695i	−0.745901	−	0.666057i	$-0.767981\pi$
$23$	0.333001	−	0.417570i	0.0694356	−	0.0870695i	0.815336	+	0.578988i	$0.196552\pi$
$24$	−4.53489	−	5.68657i	−0.925681	−	1.16077i
$25$	1.06667	−	4.67340i	0.213335	−	0.934680i
$26$	−4.66197	+	1.06407i	−0.914288	+	0.208680i
$27$	−5.99360	+	4.77973i	−1.15347	+	0.919860i
$28$	−1.36618			−0.258184
$29$	−3.83606	+	3.77951i	−0.712338	+	0.701837i
$29$	−3.83606	+	3.77951i	−0.712338	+	0.701837i
$30$	−2.06565			−0.377134
$31$	−2.80406	+	2.23616i	−0.503624	+	0.401627i	−0.842078	−	0.539356i	$-0.818668\pi$
$31$	−2.80406	+	2.23616i	−0.503624	+	0.401627i	0.338453	+	0.940983i	$0.390096\pi$
$32$	2.17627	−	0.496719i	0.384713	−	0.0878083i
$33$	0.956503	−	4.19071i	0.166506	−	0.729510i
$34$	2.72789	+	3.42067i	0.467829	+	0.586639i
$35$	0.966870	−	1.21242i	0.163431	−	0.204936i
$36$	−0.499859	−	2.19003i	−0.0833098	−	0.365004i
$37$	−3.08996	−	6.41637i	−0.507987	−	1.05484i	−0.984452	−	0.175652i	$-0.943797\pi$
$37$	−3.08996	−	6.41637i	−0.507987	−	1.05484i	0.476466	−	0.879193i	$-0.341918\pi$
$38$	3.19955	−	1.54082i	0.519035	−	0.249954i
$39$	8.83079	+	2.01557i	1.41406	+	0.322749i
$40$	−0.488564	+	1.01451i	−0.0772488	+	0.160409i
$41$		−	4.43991i		−	0.693398i	−0.937977	−	0.346699i	$-0.887303\pi$
$41$		−	4.43991i		−	0.693398i	0.937977	−	0.346699i	$-0.112697\pi$
$42$	13.9819	+	6.73333i	2.15746	+	1.03898i
$43$	3.22518	+	2.57200i	0.491836	+	0.392226i	0.837762	−	0.546036i	$-0.183864\pi$
$43$	3.22518	+	2.57200i	0.491836	+	0.392226i	−0.345926	+	0.938262i	$0.612435\pi$
$44$	0.458363	+	0.365532i	0.0691008	+	0.0551060i
$45$	2.29729	+	1.10632i	0.342460	+	0.164920i
$46$		−	0.827457i		−	0.122002i
$47$	0.0778542	−	0.161666i	0.0113562	−	0.0235814i	−0.895214	−	0.445637i	$-0.852977\pi$
$47$	0.0778542	−	0.161666i	0.0113562	−	0.0235814i	0.906570	+	0.422056i	$0.138691\pi$
$48$	−13.2763	−	3.03023i	−1.91627	−	0.437377i
$49$	−4.18982	+	2.01771i	−0.598545	+	0.288244i
$50$	−3.22228	−	6.69113i	−0.455699	−	0.946268i
$51$	−1.84416	−	8.07978i	−0.258234	−	1.13140i
$52$	−0.770259	+	0.965875i	−0.106816	+	0.133943i
$53$	1.92383	+	2.41240i	0.264258	+	0.331369i	0.896203	−	0.443644i	$-0.146315\pi$
$53$	1.92383	+	2.41240i	0.264258	+	0.331369i	−0.631945	+	0.775013i	$0.717743\pi$
$54$	−2.64286	+	11.5791i	−0.359648	+	1.57572i
$55$	−0.648782	+	0.148080i	−0.0874818	+	0.0199671i
$56$	6.61396	−	5.27446i	0.883828	−	0.704829i
$57$	−6.72679			−0.890986
$58$	−0.995668	+	8.28348i	−0.130738	+	1.08767i
$59$	13.2495			1.72494			0.862468	−	0.506112i	$-0.168918\pi$
$59$	13.2495			1.72494			0.862468	+	0.506112i	$0.168918\pi$
$60$	−0.417234	+	0.332733i	−0.0538647	+	0.0429557i
$61$	1.84068	−	0.420124i	0.235675	−	0.0537913i	−0.103052	−	0.994676i	$-0.532861\pi$
$61$	1.84068	−	0.420124i	0.235675	−	0.0537913i	0.338727	+	0.940885i	$0.390004\pi$
$62$	−1.23644	+	5.41721i	−0.157028	+	0.687987i
$63$	−11.9436	−	14.9768i	−1.50476	−	1.88690i
$64$	−3.63013	+	4.55204i	−0.453766	+	0.569004i
$65$	−0.312039	−	1.36713i	−0.0387037	−	0.169572i
$66$	−2.88947	−	6.00004i	−0.355669	−	0.738554i
$67$	−10.9658	+	5.28086i	−1.33969	+	0.645160i	−0.960012	−	0.279960i	$-0.909679\pi$
$67$	−10.9658	+	5.28086i	−1.33969	+	0.645160i	−0.379676	+	0.925119i	$0.623965\pi$
$68$	1.10200	+	0.251524i	0.133637	+	0.0305017i
$69$	−0.680062	+	1.41216i	−0.0818698	+	0.170004i
$70$		−	2.40252i		−	0.287156i
$71$	4.06735	+	1.95873i	0.482706	+	0.232459i	0.659379	−	0.751811i	$-0.270819\pi$
$71$	4.06735	+	1.95873i	0.482706	+	0.232459i	−0.176673	+	0.984270i	$0.556534\pi$
$72$	10.8750	+	8.67253i	1.28163	+	1.02207i
$73$	6.47043	+	5.16000i	0.757307	+	0.603932i	0.924140	−	0.382053i	$-0.124783\pi$
$73$	6.47043	+	5.16000i	0.757307	+	0.603932i	−0.166833	+	0.985985i	$0.553354\pi$
$74$	−9.94073	−	4.78720i	−1.15559	−	0.556501i
$75$			14.0676i			1.62438i
$76$	0.398073	−	0.826606i	0.0456621	−	0.0948182i
$77$	4.87415	+	1.11249i	0.555461	+	0.126780i
$78$	12.6435	−	6.08877i	1.43159	−	0.689417i
$79$	−6.00316	−	12.4657i	−0.675408	−	1.40250i	−0.903384	−	0.428832i	$-0.858925\pi$
$79$	−6.00316	−	12.4657i	−0.675408	−	1.40250i	0.227976	−	0.973667i	$-0.426789\pi$
$80$	0.469123	+	2.05536i	0.0524496	+	0.229797i
$81$	3.52936	−	4.42568i	0.392151	−	0.491742i
$82$	−4.28877	−	5.37794i	−0.473615	−	0.593895i
$83$	0.545892	−	2.39171i	0.0599194	−	0.262524i	−0.936091	−	0.351757i	$-0.885584\pi$
$83$	0.545892	−	2.39171i	0.0599194	−	0.262524i	0.996011	+	0.0892328i	$0.0284415\pi$
$84$	3.90876	−	0.892150i	0.426481	−	0.0973415i
$85$	−1.00312	+	0.799958i	−0.108803	+	0.0867677i
$86$	6.39102			0.689162
$87$	8.50718	−	13.3185i	0.912066	−	1.42790i
$88$	−3.63025			−0.386986
$89$	−10.5483	+	8.41200i	−1.11812	+	0.891671i	−0.994916	−	0.100711i	$-0.967888\pi$
$89$	−10.5483	+	8.41200i	−1.11812	+	0.891671i	−0.123204	+	0.992381i	$0.539317\pi$
$90$	3.85131	−	0.879036i	0.405964	−	0.0926585i
$91$	−2.34428	+	10.2709i	−0.245747	+	1.07669i
$92$	−0.133286	−	0.167136i	−0.0138960	−	0.0174251i
$93$	6.56239	−	8.22898i	0.680489	−	0.853306i
$94$	−0.0618598	−	0.271025i	−0.00638035	−	0.0279541i
$95$	0.451848	+	0.938272i	0.0463586	+	0.0962647i
$96$	−5.90212	+	2.84231i	−0.602382	+	0.290092i
$97$	4.58979	+	1.04759i	0.466023	+	0.106367i	0.449083	−	0.893490i	$-0.351751\pi$
$97$	4.58979	+	1.04759i	0.466023	+	0.106367i	0.0169394	+	0.999857i	$0.494608\pi$
$98$	−3.12599	+	6.49118i	−0.315772	+	0.655708i
$99$			8.22043i			0.826184i
$100$	−1.72866	−	0.832479i	−0.172866	−	0.0832479i
$101$	−10.9636	−	8.74320i	−1.09092	−	0.869981i	−0.0987809	−	0.995109i	$-0.531494\pi$
$101$	−10.9636	−	8.74320i	−1.09092	−	0.869981i	−0.992141	+	0.125128i	$0.960066\pi$
$102$	−10.0385	−	8.00544i	−0.993961	−	0.792657i
$103$	7.75475	+	3.73449i	0.764099	+	0.367970i	0.774993	−	0.631970i	$-0.217753\pi$
$103$	7.75475	+	3.73449i	0.764099	+	0.367970i	−0.0108941	+	0.999941i	$0.503468\pi$
$104$		−	7.64976i		−	0.750120i
$105$	−1.97456	+	4.10022i	−0.192697	+	0.400140i
$106$	4.66056	+	1.06374i	0.452674	+	0.103320i
$107$	−4.62766	+	2.22856i	−0.447373	+	0.215443i	−0.643985	−	0.765038i	$-0.722720\pi$
$107$	−4.62766	+	2.22856i	−0.447373	+	0.215443i	0.196613	+	0.980481i	$0.437006\pi$
$108$	1.33133	+	2.76454i	0.128108	+	0.266018i
$109$	1.31423	+	5.75801i	0.125880	+	0.551518i	0.998056	+	0.0623247i	$0.0198514\pi$
$109$	1.31423	+	5.75801i	0.125880	+	0.551518i	−0.872176	+	0.489193i	$0.837291\pi$
$110$	−0.642813	+	0.806062i	−0.0612898	+	0.0768550i
$111$	13.0307	+	16.3400i	1.23682	+	1.55092i
$112$	3.52442	−	15.4415i	0.333026	−	1.45908i
$113$	−11.3020	+	2.57962i	−1.06321	+	0.242670i	−0.718133	−	0.695906i	$-0.755003\pi$
$113$	−11.3020	+	2.57962i	−1.06321	+	0.242670i	−0.345074	+	0.938576i	$0.612146\pi$
$114$	−8.14798	+	6.49780i	−0.763129	+	0.608575i
$115$	0.242653			0.0226275
$116$	1.13319	+	1.83354i	0.105214	+	0.170240i
$117$	−17.3223			−1.60145
$118$	16.0487	−	12.7984i	1.47741	−	1.17819i
$119$	9.39746	−	2.14491i	0.861464	−	0.196624i
$120$	0.735322	−	3.22166i	0.0671254	−	0.294096i
$121$	5.52074	+	6.92278i	0.501885	+	0.629344i
$122$	1.82375	−	2.28691i	0.165114	−	0.207047i
$123$	2.89937	+	12.7030i	0.261427	+	1.14539i
$124$	0.622855	+	1.29337i	0.0559340	+	0.116148i
$125$	4.00886	−	1.93057i	0.358563	−	0.172675i
$126$	−28.9340	−	6.60399i	−2.57764	−	0.588331i
$127$	7.14432	−	14.8353i	0.633956	−	1.31642i	−0.298247	−	0.954489i	$-0.596402\pi$
$127$	7.14432	−	14.8353i	0.633956	−	1.31642i	0.932203	−	0.361935i	$-0.117884\pi$
$128$			13.4848i			1.19190i
$129$	−10.9071	−	5.25259i	−0.960318	−	0.462465i
$130$	−1.69856	−	1.35455i	−0.148973	−	0.118802i
$131$	−8.52089	−	6.79518i	−0.744473	−	0.593698i	0.176052	−	0.984381i	$-0.443667\pi$
$131$	−8.52089	−	6.79518i	−0.744473	−	0.593698i	−0.920525	+	0.390683i	$0.872239\pi$
$132$	−1.55012	−	0.746497i	−0.134920	−	0.0649742i
$133$		−	7.82382i		−	0.678412i
$134$	−8.18151	+	16.9891i	−0.706775	+	1.46763i
$135$	−3.39560	−	0.775023i	−0.292247	−	0.0667034i
$136$	−6.30605	+	3.03683i	−0.540739	+	0.260406i
$137$	4.96534	+	10.3106i	0.424217	+	0.880896i	0.998080	+	0.0619445i	$0.0197302\pi$
$137$	4.96534	+	10.3106i	0.424217	+	0.880896i	−0.573862	+	0.818952i	$0.694556\pi$
$138$	0.540350	+	2.36743i	0.0459976	+	0.201529i
$139$	11.9086	−	14.9330i	1.01008	−	1.26660i	0.0465713	−	0.998915i	$-0.485171\pi$
$139$	11.9086	−	14.9330i	1.01008	−	1.26660i	0.963507	−	0.267683i	$-0.0862580\pi$
$140$	−0.386997	−	0.485279i	−0.0327072	−	0.0410135i
$141$	−0.117176	+	0.513381i	−0.00986798	+	0.0432345i
$142$	6.81873	−	1.55633i	0.572215	−	0.130604i
$143$	3.53459	−	2.81874i	0.295577	−	0.235715i
$144$	26.0426			2.17022
$145$	−2.42915	−	0.291981i	−0.201730	−	0.0242477i
$146$	12.8218			1.06114
$147$	10.6698	−	8.50889i	0.880031	−	0.701801i
$148$	−2.77902	+	0.634293i	−0.228434	+	0.0521385i
$149$	5.33389	−	23.3693i	0.436970	−	1.91449i	0.0336393	−	0.999434i	$-0.489290\pi$
$149$	5.33389	−	23.3693i	0.436970	−	1.91449i	0.403330	−	0.915054i	$-0.367853\pi$
$150$	13.5887	+	17.0397i	1.10951	+	1.39128i
$151$	−5.05137	+	6.33421i	−0.411074	+	0.515471i	−0.943665	−	0.330902i	$-0.892647\pi$
$151$	−5.05137	+	6.33421i	−0.411074	+	0.515471i	0.532591	+	0.846373i	$0.321218\pi$
$152$	1.26415	+	5.53862i	0.102536	+	0.449241i
$153$	6.87669	+	14.2796i	0.555948	+	1.15444i
$154$	6.97855	−	3.36069i	0.562347	−	0.270812i
$155$	−1.58861	−	0.362589i	−0.127600	−	0.0291239i
$156$	1.57304	−	3.26645i	0.125944	−	0.261525i
$157$		−	3.66196i		−	0.292256i	−0.989266	−	0.146128i	$-0.953319\pi$
$157$		−	3.66196i		−	0.292256i	0.989266	−	0.146128i	$-0.0466811\pi$
$158$	−19.3128	−	9.30055i	−1.53644	−	0.739912i
$159$	−7.07960	−	5.64579i	−0.561449	−	0.447740i
$160$	0.792907	+	0.632322i	0.0626848	+	0.0499894i
$161$	−1.64246	−	0.790969i	−0.129444	−	0.0623371i
$162$		−	8.76992i		−	0.689030i
$163$	−7.71445	+	16.0192i	−0.604242	+	1.25472i	0.344535	+	0.938774i	$0.388037\pi$
$163$	−7.71445	+	16.0192i	−0.604242	+	1.25472i	−0.948777	+	0.315948i	$0.897678\pi$
$164$	−1.73255	−	0.395443i	−0.135289	−	0.0308789i
$165$	1.75952	−	0.847341i	0.136979	−	0.0659654i
$166$	−1.64907	−	3.42432i	−0.127992	−	0.265779i
$167$	2.39657	+	10.5000i	0.185452	+	0.812518i	0.978975	+	0.203978i	$0.0653873\pi$
$167$	2.39657	+	10.5000i	0.185452	+	0.812518i	−0.793523	+	0.608540i	$0.791756\pi$
$168$	−15.4788	+	19.4098i	−1.19421	+	1.49750i
$169$	−2.16564	−	2.71563i	−0.166588	−	0.208895i
$170$	−0.442321	+	1.93794i	−0.0339245	+	0.148633i
$171$	12.5418	−	2.86258i	0.959095	−	0.218907i
$172$	1.29090	−	1.02946i	0.0984305	−	0.0784957i
$173$	−5.10262			−0.387945			−0.193972	−	0.981007i	$-0.562137\pi$
$173$	−5.10262			−0.387945			−0.193972	+	0.981007i	$0.562137\pi$
$174$	−2.56062	−	24.3500i	−0.194120	−	1.84597i
$175$	−16.3618			−1.23683
$176$	−5.31394	+	4.23773i	−0.400554	+	0.319431i
$177$	−37.9079	+	8.65223i	−2.84933	+	0.650342i
$178$	−4.65125	+	20.3785i	−0.348626	+	1.52743i
$179$	−5.35590	−	6.71609i	−0.400319	−	0.501984i	0.540289	−	0.841480i	$-0.318315\pi$
$179$	−5.35590	−	6.71609i	−0.400319	−	0.501984i	−0.940608	+	0.339496i	$0.889744\pi$
$180$	0.636320	−	0.797920i	0.0474285	−	0.0594734i
$181$	−2.07216	−	9.07873i	−0.154022	−	0.674817i	−0.991692	−	0.128638i	$-0.958939\pi$
$181$	−2.07216	−	9.07873i	−0.154022	−	0.674817i	0.837669	−	0.546178i	$-0.183918\pi$
$182$	7.08174	+	14.7054i	0.524934	+	1.09004i
$183$	−4.99200	+	2.40402i	−0.369019	+	0.177710i
$184$	1.29053	+	0.294555i	0.0951391	+	0.0217149i
$185$	1.40386	−	2.91514i	0.103214	−	0.214325i
$186$		−	16.3065i		−	1.19565i
$187$	−3.72679	−	1.79473i	−0.272530	−	0.131244i
$188$	−0.0561515	−	0.0447793i	−0.00409527	−	0.00326587i
$189$	20.4577	+	16.3145i	1.48808	+	1.18670i
$190$	1.45364	+	0.700038i	0.105458	+	0.0507861i
$191$		−	12.4211i		−	0.898759i	−0.893341	−	0.449379i	$-0.851645\pi$
$191$		−	12.4211i		−	0.898759i	0.893341	−	0.449379i	$-0.148355\pi$
$192$	7.41352	−	15.3943i	0.535025	−	1.11099i
$193$	19.6240	+	4.47904i	1.41256	+	0.322408i	0.859673	−	0.510845i	$-0.170667\pi$
$193$	19.6240	+	4.47904i	1.41256	+	0.322408i	0.552891	+	0.833254i	$0.313525\pi$
$194$	6.57142	−	3.16463i	0.471800	−	0.227207i
$195$	1.78554	+	3.70771i	0.127865	+	0.265515i
$196$	0.414186	+	1.81467i	0.0295847	+	0.129619i
$197$	−5.45115	+	6.83552i	−0.388378	+	0.487011i	−0.937133	−	0.348973i	$-0.886531\pi$
$197$	−5.45115	+	6.83552i	−0.388378	+	0.487011i	0.548755	+	0.835983i	$0.315102\pi$
$198$	7.94059	+	9.95718i	0.564313	+	0.707626i
$199$	−3.16689	+	13.8751i	−0.224495	+	0.983577i	0.729553	+	0.683924i	$0.239728\pi$
$199$	−3.16689	+	13.8751i	−0.224495	+	0.983577i	−0.954048	+	0.299653i	$0.903129\pi$
$200$	11.5828	−	2.64369i	0.819025	−	0.186937i
$201$	27.9256	−	22.2699i	1.96972	−	1.57080i
$202$	−21.7255			−1.52860
$203$	15.4906	+	9.89456i	1.08722	+	0.694462i
$204$	−3.31716			−0.232248
$205$	1.57709	−	1.25769i	0.110149	−	0.0878408i
$206$	13.0005	−	2.96728i	0.905787	−	0.206740i
$207$	0.666999	−	2.92231i	0.0463596	−	0.203115i
$208$	−8.92986	−	11.1977i	−0.619174	−	0.776420i
$209$	−2.09332	+	2.62494i	−0.144798	+	0.181571i
$210$	1.56891	+	6.87383i	0.108265	+	0.474339i
$211$	−0.350565	−	0.727955i	−0.0241339	−	0.0501145i	0.888553	−	0.458773i	$-0.151711\pi$
$211$	−0.350565	−	0.727955i	−0.0241339	−	0.0501145i	−0.912687	+	0.408659i	$0.865997\pi$
$212$	1.11272	−	0.535858i	0.0764219	−	0.0368029i
$213$	−12.9162	−	2.94803i	−0.885000	−	0.201996i
$214$	−3.45266	+	7.16952i	−0.236019	+	0.490098i
$215$			1.87418i			0.127818i
$216$	−17.1184	−	8.24379i	−1.16476	−	0.560919i
$217$	9.57099	+	7.63261i	0.649721	+	0.518135i
$218$	7.15389	+	5.70504i	0.484522	+	0.386394i
$219$	−21.8821	−	10.5379i	−1.47865	−	0.712082i
$220$			0.266358i			0.0179578i
$221$	3.78190	−	7.85321i	0.254398	−	0.528264i
$222$	31.5675	+	7.20507i	2.11867	+	0.483572i
$223$	−10.2733	+	4.94734i	−0.687949	+	0.331299i	−0.744992	−	0.667073i	$-0.767547\pi$
$223$	−10.2733	+	4.94734i	−0.687949	+	0.331299i	0.0570436	+	0.998372i	$0.481833\pi$
$224$	−3.30584	−	6.86465i	−0.220881	−	0.458664i
$225$	−5.98644	−	26.2283i	−0.399096	−	1.74856i
$226$	−11.1981	+	14.0419i	−0.744884	+	0.934055i
$227$	−11.7817	−	14.7738i	−0.781980	−	0.980571i	−0.999989	−	0.00462481i	$-0.998528\pi$
$227$	−11.7817	−	14.7738i	−0.781980	−	0.980571i	0.218010	−	0.975947i	$-0.430044\pi$
$228$	−0.599126	+	2.62494i	−0.0396781	+	0.173841i
$229$	23.8163	−	5.43593i	1.57383	−	0.359216i	0.655550	−	0.755152i	$-0.272437\pi$
$229$	23.8163	−	5.43593i	1.57383	−	0.359216i	0.918278	+	0.395935i	$0.129580\pi$
$230$	0.293919	−	0.234393i	0.0193805	−	0.0154554i
$231$	−14.6718			−0.965337
$232$	−12.5648	−	4.50160i	−0.824917	−	0.295545i
$233$	20.2523			1.32677			0.663387	−	0.748276i	$-0.269118\pi$
$233$	20.2523			1.32677			0.663387	+	0.748276i	$0.269118\pi$
$234$	−20.9821	+	16.7326i	−1.37164	+	1.09385i
$235$	0.0794787	−	0.0181405i	0.00518462	−	0.00118335i
$236$	1.18007	−	5.17024i	0.0768162	−	0.336554i
$237$	25.3159	+	31.7452i	1.64445	+	2.06207i
$238$	9.31100	−	11.6756i	0.603542	−	0.756818i
$239$	1.47515	+	6.46307i	0.0954197	+	0.418061i	0.999965	−	0.00831561i	$-0.00264697\pi$
$239$	1.47515	+	6.46307i	0.0954197	+	0.418061i	−0.904546	+	0.426377i	$0.859790\pi$
$240$	−2.68441	−	5.57423i	−0.173278	−	0.359815i
$241$	−1.02548	+	0.493845i	−0.0660569	+	0.0318113i	−0.466621	−	0.884458i	$-0.654529\pi$
$241$	−1.02548	+	0.493845i	−0.0660569	+	0.0318113i	0.400564	+	0.916269i	$0.368814\pi$
$242$	13.3742	+	3.05258i	0.859728	+	0.196227i
$243$	2.77085	−	5.75374i	0.177750	−	0.369102i
$244$		−	0.755693i		−	0.0483783i
$245$	−1.90355	−	0.916701i	−0.121613	−	0.0585659i
$246$	15.7825	+	12.5861i	1.00625	+	0.802460i
$247$	−5.53135	−	4.41111i	−0.351952	−	0.280672i
$248$	−8.00872	−	3.85680i	−0.508554	−	0.244907i
$249$			7.19937i			0.456241i
$250$	2.99098	−	6.21083i	0.189166	−	0.392808i
$251$	−25.6664	−	5.85818i	−1.62005	−	0.369765i	−0.686193	−	0.727420i	$-0.740719\pi$
$251$	−25.6664	−	5.85818i	−1.62005	−	0.369765i	−0.933854	+	0.357654i	$0.883577\pi$
$252$	−6.90806	+	3.32674i	−0.435167	+	0.209565i
$253$	0.339427	+	0.704828i	0.0213396	+	0.0443122i
$254$	−5.67659	−	24.8708i	−0.356181	−	1.56053i
$255$	2.34761	−	2.94381i	0.147013	−	0.184349i
$256$	5.76547	+	7.22967i	0.360342	+	0.451854i
$257$	−3.85785	+	16.9024i	−0.240646	+	1.05434i	0.699784	+	0.714354i	$0.253280\pi$
$257$	−3.85785	+	16.9024i	−0.240646	+	1.05434i	−0.940430	+	0.339986i	$0.889578\pi$
$258$	−18.2853	+	4.17349i	−1.13839	+	0.259830i
$259$	−19.0048	+	15.1558i	−1.18090	+	0.941735i
$260$	−0.561277			−0.0348089
$261$	−10.1936	+	28.4520i	−0.630965	+	1.76114i
$262$	−16.8850			−1.04316
$263$	3.92959	−	3.13374i	0.242309	−	0.193235i	−0.494804	−	0.869005i	$-0.664760\pi$
$263$	3.92959	−	3.13374i	0.242309	−	0.193235i	0.737113	+	0.675770i	$0.236189\pi$
$264$	10.3864	−	2.37064i	0.639242	−	0.145903i
$265$	−0.311944	+	1.36672i	−0.0191626	+	0.0839568i
$266$	−7.55749	−	9.47679i	−0.463379	−	0.581059i
$267$	24.6864	−	30.9558i	1.51078	−	1.89446i
$268$	1.08403	+	4.74945i	0.0662177	+	0.290119i
$269$	9.49420	+	19.7149i	0.578872	+	1.20204i	0.960644	+	0.277783i	$0.0895997\pi$
$269$	9.49420	+	19.7149i	0.578872	+	1.20204i	−0.381772	+	0.924257i	$0.624686\pi$
$270$	−4.86164	+	2.34124i	−0.295870	+	0.142483i
$271$	7.60881	+	1.73666i	0.462202	+	0.105495i	0.447280	−	0.894394i	$-0.352393\pi$
$271$	7.60881	+	1.73666i	0.462202	+	0.105495i	0.0149223	+	0.999889i	$0.495250\pi$
$272$	−5.68577	+	11.8066i	−0.344750	+	0.715881i
$273$		−	30.9169i		−	1.87118i
$274$	15.9740	+	7.69268i	0.965025	+	0.464732i
$275$	5.48947	+	4.37771i	0.331028	+	0.263986i
$276$	0.490487	+	0.391150i	0.0295238	+	0.0235445i
$277$	−1.63340	−	0.786604i	−0.0981414	−	0.0472624i	0.384169	−	0.923263i	$-0.374488\pi$
$277$	−1.63340	−	0.786604i	−0.0981414	−	0.0472624i	−0.482310	+	0.876000i	$0.660202\pi$
$278$		−	29.5912i		−	1.77476i
$279$	−8.73344	+	18.1352i	−0.522857	+	1.08572i
$280$	3.74706	+	0.855241i	0.223930	+	0.0511104i
$281$	−11.5311	+	5.55308i	−0.687887	+	0.331269i	−0.744967	−	0.667101i	$-0.767535\pi$
$281$	−11.5311	+	5.55308i	−0.687887	+	0.331269i	0.0570809	+	0.998370i	$0.481821\pi$
$282$	0.353972	+	0.735031i	0.0210788	+	0.0437705i
$283$	4.54554	+	19.9153i	0.270204	+	1.18384i	0.909772	+	0.415108i	$0.136256\pi$
$283$	4.54554	+	19.9153i	0.270204	+	1.18384i	−0.639568	+	0.768735i	$0.720887\pi$
$284$	1.12660	−	1.41271i	0.0668516	−	0.0838292i
$285$	−1.90549	−	2.38941i	−0.112872	−	0.141536i
$286$	1.55857	−	6.82852i	0.0921599	−	0.403779i
$287$	−14.7746	+	3.37221i	−0.872118	+	0.199055i
$288$	9.79468	−	7.81100i	0.577157	−	0.460267i
$289$	9.02488			0.530875
$290$	−3.22440	+	1.99278i	−0.189343	+	0.117020i
$291$	−13.8159			−0.809902
$292$	2.58984	−	2.06533i	0.151559	−	0.120864i
$293$	6.03337	−	1.37708i	0.352473	−	0.0804497i	−0.0426185	−	0.999091i	$-0.513570\pi$
$293$	6.03337	−	1.37708i	0.352473	−	0.0804497i	0.395092	+	0.918642i	$0.370713\pi$
$294$	4.70482	−	20.6132i	0.274391	−	1.20218i
$295$	3.75316	+	4.70632i	0.218518	+	0.274013i
$296$	11.0049	−	13.7998i	0.639650	−	0.802095i
$297$	−2.49863	−	10.9472i	−0.144985	−	0.635222i
$298$	−16.1130	−	33.4589i	−0.933399	−	1.93822i
$299$	−1.48523	+	0.715251i	−0.0858933	+	0.0413640i
$300$	5.48947	+	1.25294i	0.316935	+	0.0723383i
$301$	6.10920	−	12.6859i	0.352128	−	0.731202i
$302$			12.5519i			0.722279i
$303$	37.0774	+	17.8555i	2.13004	+	1.02577i
$304$	8.31591	+	6.63172i	0.476950	+	0.380355i
$305$	0.670639	+	0.534817i	0.0384007	+	0.0306235i
$306$	22.1230	+	10.6539i	1.26469	+	0.609043i
$307$			3.13998i			0.179208i	0.995977	+	0.0896041i	$0.0285602\pi$
$307$			3.13998i			0.179208i	−0.995977	+	0.0896041i	$0.971440\pi$
$308$	0.868238	−	1.80292i	0.0494725	−	0.102731i
$309$	−24.6257	−	5.62066i	−1.40091	−	0.319748i
$310$	−2.27448	+	1.09533i	−0.129182	+	0.0622107i
$311$	3.12006	+	6.47888i	0.176923	+	0.367384i	0.970506	−	0.241078i	$-0.0775011\pi$
$311$	3.12006	+	6.47888i	0.176923	+	0.367384i	−0.793583	+	0.608462i	$0.791787\pi$
$312$	4.99548	+	21.8866i	0.282813	+	1.23909i
$313$	−1.29502	+	1.62390i	−0.0731988	+	0.0917884i	−0.817083	−	0.576520i	$-0.804410\pi$
$313$	−1.29502	+	1.62390i	−0.0731988	+	0.0917884i	0.743884	+	0.668309i	$0.232982\pi$
$314$	−3.53730	−	4.43563i	−0.199621	−	0.250317i
$315$	1.93663	−	8.48494i	0.109117	−	0.478072i
$316$	−5.39906	+	1.23230i	−0.303721	+	0.0693223i
$317$	−4.84220	+	3.86153i	−0.271965	+	0.216885i	−0.749969	−	0.661473i	$-0.769932\pi$
$317$	−4.84220	+	3.86153i	−0.271965	+	0.216885i	0.478004	+	0.878358i	$0.341360\pi$
$318$	−14.0289			−0.786703
$319$	−2.54982	−	7.46430i	−0.142762	−	0.417921i
$320$	−2.64522			−0.147872
$321$	11.7848	−	9.39809i	0.657765	−	0.524550i
$322$	−2.75351	+	0.628472i	−0.153447	+	0.0350234i
$323$	−1.44042	+	6.31089i	−0.0801471	+	0.351148i
$324$	−1.41265	−	1.77141i	−0.0784807	−	0.0984117i
$325$	−9.22483	+	11.5676i	−0.511702	+	0.641653i
$326$	6.12959	+	26.8555i	0.339486	+	1.48739i
$327$	−7.52025	−	15.6159i	−0.415871	−	0.863564i
$328$	9.91432	−	4.77449i	0.547427	−	0.263627i
$329$	−0.597105	−	0.136285i	−0.0329195	−	0.00751365i
$330$	1.31277	−	2.72599i	0.0722654	−	0.150061i
$331$			2.80221i			0.154023i	0.997030	+	0.0770116i	$0.0245378\pi$
$331$			2.80221i			0.154023i	−0.997030	+	0.0770116i	$0.975462\pi$
$332$	−0.884677	−	0.426038i	−0.0485530	−	0.0233819i
$333$	−31.2486	−	24.9199i	−1.71241	−	1.36560i
$334$	13.0455	+	10.4034i	0.713818	+	0.569251i
$335$	−4.98208	−	2.39924i	−0.272200	−	0.131085i
$336$			46.4809i			2.53574i
$337$	8.36969	−	17.3798i	0.455926	−	0.946740i	−0.538630	−	0.842542i	$-0.681058\pi$
$337$	8.36969	−	17.3798i	0.455926	−	0.946740i	0.994557	−	0.104198i	$-0.0332277\pi$
$338$	−5.24637	−	1.19745i	−0.285365	−	0.0651327i
$339$	30.6516	−	14.7610i	1.66477	−	0.801709i
$340$	0.222818	+	0.462687i	0.0120840	+	0.0250927i
$341$	−1.16897	−	5.12158i	−0.0633031	−	0.277349i
$342$	12.4264	−	15.5822i	0.671943	−	0.842590i
$343$	−5.00038	−	6.27028i	−0.269995	−	0.338563i
$344$	−2.27505	+	9.96766i	−0.122663	+	0.537420i
$345$	−0.694252	+	0.158458i	−0.0373773	+	0.00853111i
$346$	−6.18066	+	4.92891i	−0.332274	+	0.264980i
$347$	29.3654			1.57642			0.788209	−	0.615408i	$-0.211009\pi$
$347$	29.3654			1.57642			0.788209	+	0.615408i	$0.211009\pi$
$348$	−4.43949	−	4.50591i	−0.237981	−	0.241542i
$349$	8.51756			0.455935			0.227967	−	0.973669i	$-0.426792\pi$
$349$	8.51756			0.455935			0.227967	+	0.973669i	$0.426792\pi$
$350$	−19.8186	+	15.8048i	−1.05935	+	0.844800i
$351$	23.0683	−	5.26519i	1.23129	−	0.281035i
$352$	−0.727558	+	3.18764i	−0.0387789	+	0.169902i
$353$	−16.2741	−	20.4071i	−0.866182	−	1.08616i	−0.995519	−	0.0945571i	$-0.969857\pi$
$353$	−16.2741	−	20.4071i	−0.866182	−	1.08616i	0.129338	−	0.991601i	$-0.458715\pi$
$354$	−37.5591	+	47.0977i	−1.99625	+	2.50321i
$355$	0.456397	+	1.99960i	0.0242230	+	0.106128i
$356$	2.34306	+	4.86541i	0.124182	+	0.257866i
$357$	−25.4863	+	12.2735i	−1.34888	+	0.649585i
$358$	−12.9749	−	2.96144i	−0.685746	−	0.156517i
$359$	2.41707	−	5.01910i	0.127568	−	0.264898i	−0.827396	−	0.561619i	$-0.810179\pi$
$359$	2.41707	−	5.01910i	0.127568	−	0.264898i	0.954964	+	0.296721i	$0.0958931\pi$
$360$			6.31955i			0.333069i
$361$	−12.3846	−	5.96412i	−0.651822	−	0.313901i
$362$	−11.2796	−	8.99520i	−0.592844	−	0.472777i
$363$	−20.3160	−	16.2015i	−1.06632	−	0.850359i
$364$	3.79915	+	1.82958i	0.199130	+	0.0958958i
$365$			3.76002i			0.196808i
$366$	−3.72449	+	7.73399i	−0.194682	+	0.404262i
$367$	−4.93781	−	1.12702i	−0.257752	−	0.0588302i	0.0916923	−	0.995787i	$-0.470772\pi$
$367$	−4.93781	−	1.12702i	−0.257752	−	0.0588302i	−0.349444	+	0.936957i	$0.613630\pi$
$368$	2.23292	−	1.07532i	0.116399	−	0.0560548i
$369$	−10.8115	−	22.4503i	−0.562823	−	1.16871i
$370$	−1.11545	−	4.88709i	−0.0579893	−	0.254068i
$371$	6.56653	−	8.23416i	0.340917	−	0.427496i
$372$	−2.62665	−	3.29371i	−0.136185	−	0.170771i
$373$	0.103290	−	0.452543i	0.00534815	−	0.0234318i	−0.972183	−	0.234221i	$-0.924746\pi$
$373$	0.103290	−	0.452543i	0.00534815	−	0.0234318i	0.977532	+	0.210789i	$0.0676033\pi$
$374$	−6.24780	+	1.42602i	−0.323066	+	0.0737377i
$375$	−10.2090	+	8.14140i	−0.527190	+	0.420420i
$376$	0.444721			0.0229347
$377$	15.7290	−	5.37305i	0.810084	−	0.276726i
$378$	40.5390			2.08510
$379$	−1.84723	+	1.47312i	−0.0948858	+	0.0756689i	−0.669784	−	0.742556i	$-0.733613\pi$
$379$	−1.84723	+	1.47312i	−0.0948858	+	0.0756689i	0.574898	+	0.818225i	$0.305042\pi$
$380$	0.406379	−	0.0927532i	0.0208468	−	0.00475814i
$381$	−10.7527	+	47.1106i	−0.550877	+	2.41355i
$382$	−11.9983	−	15.0453i	−0.613884	−	0.769786i
$383$	−15.5310	+	19.4752i	−0.793595	+	0.995137i	0.206266	+	0.978496i	$0.433869\pi$
$383$	−15.5310	+	19.4752i	−0.793595	+	0.995137i	−0.999862	+	0.0166410i	$0.994703\pi$
$384$	−8.80588	−	38.5811i	−0.449373	−	1.96883i
$385$	0.985528	+	2.04647i	0.0502272	+	0.104298i
$386$	28.0965	−	13.5306i	1.43008	−	0.688688i
$387$	22.5710	+	5.15169i	1.14735	+	0.261875i
$388$	0.817585	−	1.69773i	0.0415066	−	0.0861893i
$389$			12.0401i			0.610455i	0.952279	+	0.305227i	$0.0987325\pi$
$389$			12.0401i			0.610455i	−0.952279	+	0.305227i	$0.901268\pi$
$390$	5.74427	+	2.76630i	0.290873	+	0.140077i
$391$	1.17923	+	0.940404i	0.0596362	+	0.0475583i
$392$	−9.01109	−	7.18610i	−0.455129	−	0.362953i
$393$	28.8164	+	13.8773i	1.45360	+	0.700015i
$394$			13.5453i			0.682400i
$395$	2.72740	−	5.66351i	0.137230	−	0.284962i
$396$	3.20779	+	0.732158i	0.161198	+	0.0367923i
$397$	23.4717	−	11.3034i	1.17801	−	0.567300i	0.260679	−	0.965425i	$-0.416053\pi$
$397$	23.4717	−	11.3034i	1.17801	−	0.567300i	0.917331	+	0.398126i	$0.130339\pi$
$398$	9.56676	+	19.8656i	0.479538	+	0.995771i
$399$	5.10915	+	22.3846i	0.255777	+	1.12063i
$400$	13.8687	−	17.3908i	0.693437	−	0.869542i
$401$	17.1700	+	21.5305i	0.857429	+	1.07518i	0.996391	+	0.0848846i	$0.0270522\pi$
$401$	17.1700	+	21.5305i	0.857429	+	1.07518i	−0.138961	+	0.990298i	$0.544376\pi$
$402$	12.3137	−	53.9500i	0.614153	−	2.69078i
$403$	10.7923	−	2.46328i	0.537605	−	0.122705i
$404$	−4.38827	+	3.49953i	−0.218325	+	0.174108i
$405$	2.57179			0.127793
$406$	28.3210	−	2.97822i	1.40555	−	0.147806i
$407$	10.4313			0.517058
$408$	16.0590	−	12.8067i	0.795041	−	0.634024i
$409$	−17.4503	+	3.98292i	−0.862862	+	0.196943i	−0.630978	−	0.775801i	$-0.717346\pi$
$409$	−17.4503	+	3.98292i	−0.862862	+	0.196943i	−0.231884	+	0.972743i	$0.574489\pi$
$410$	0.695414	−	3.04681i	0.0343440	−	0.150471i
$411$	−20.9393	−	26.2571i	−1.03286	−	1.29517i
$412$	2.14796	−	2.69346i	0.105823	−	0.132697i
$413$	−10.0633	−	44.0901i	−0.495181	−	2.16953i
$414$	−2.01491	−	4.18401i	−0.0990276	−	0.205633i
$415$	1.00419	−	0.483591i	0.0492936	−	0.0237386i
$416$	−6.71708	−	1.53313i	−0.329332	−	0.0751679i
$417$	−24.3201	+	50.5012i	−1.19096	+	2.47305i
$418$			5.20158i			0.254418i
$419$	−2.44008	−	1.17508i	−0.119206	−	0.0574064i	0.373330	−	0.927698i	$-0.378216\pi$
$419$	−2.44008	−	1.17508i	−0.119206	−	0.0574064i	−0.492536	+	0.870292i	$0.663930\pi$
$420$	1.42413	+	1.13571i	0.0694904	+	0.0554168i
$421$	−10.8912	−	8.68543i	−0.530804	−	0.423302i	0.321065	−	0.947057i	$-0.395959\pi$
$421$	−10.8912	−	8.68543i	−0.530804	−	0.423302i	−0.851869	+	0.523755i	$0.824531\pi$
$422$	−1.12780	−	0.543122i	−0.0549006	−	0.0264388i
$423$		−	1.00704i		−	0.0489639i
$424$	−3.31810	+	6.89010i	−0.161141	+	0.334613i
$425$	13.1978	+	3.01231i	0.640188	+	0.146119i
$426$	−18.4927	+	8.90559i	−0.895972	+	0.431477i
$427$	−2.79608	−	5.80611i	−0.135312	−	0.280978i
$428$	0.457469	+	2.00430i	0.0221126	+	0.0968816i
$429$	−8.27205	+	10.3728i	−0.399378	+	0.500805i
$430$	1.81038	+	2.27014i	0.0873041	+	0.109476i
$431$	−2.92161	+	12.8004i	−0.140729	+	0.616573i	0.854538	+	0.519389i	$0.173841\pi$
$431$	−2.92161	+	12.8004i	−0.140729	+	0.616573i	−0.995266	+	0.0971837i	$0.969017\pi$
$432$	−34.6812	+	7.91575i	−1.66860	+	0.380847i
$433$	4.40985	−	3.51674i	0.211924	−	0.169004i	−0.511775	−	0.859120i	$-0.671012\pi$
$433$	4.40985	−	3.51674i	0.211924	−	0.169004i	0.723699	+	0.690116i	$0.242440\pi$
$434$	18.9659			0.910391
$435$	7.14067	−	0.750907i	0.342369	−	0.0360032i
$436$	2.36396			0.113213
$437$	0.957149	−	0.763301i	0.0457866	−	0.0365136i
$438$	−36.6843	+	8.37295i	−1.75284	+	0.400075i
$439$	5.40856	−	23.6965i	0.258137	−	1.13097i	−0.665105	−	0.746750i	$-0.731613\pi$
$439$	5.40856	−	23.6965i	0.258137	−	1.13097i	0.923241	−	0.384220i	$-0.125530\pi$
$440$	−1.02834	−	1.28949i	−0.0490240	−	0.0614741i
$441$	−16.2724	+	20.4050i	−0.774877	+	0.971665i
$442$	−3.00495	−	13.1655i	−0.142931	−	0.626221i
$443$	−4.74743	−	9.85815i	−0.225557	−	0.468375i	0.757222	−	0.653158i	$-0.226556\pi$
$443$	−4.74743	−	9.85815i	−0.225557	−	0.468375i	−0.982779	+	0.184783i	$0.940842\pi$
$444$	7.53680	−	3.62953i	0.357681	−	0.172250i
$445$	−5.97602	−	1.36399i	−0.283290	−	0.0646592i
$446$	−7.66480	+	15.9161i	−0.362939	+	0.753650i
$447$			70.3448i			3.32719i
$448$	17.9049	+	8.62254i	0.845926	+	0.407377i
$449$	−1.91489	−	1.52708i	−0.0903693	−	0.0720671i	0.577263	−	0.816558i	$-0.304121\pi$
$449$	−1.91489	−	1.52708i	−0.0903693	−	0.0720671i	−0.667632	+	0.744491i	$0.732692\pi$
$450$	−32.5867	−	25.9870i	−1.53615	−	1.22504i
$451$	5.85924	+	2.82166i	0.275901	+	0.132867i
$452$			4.64006i			0.218250i
$453$	10.3160	−	21.4214i	0.484688	−	1.00647i
$454$	−28.5417	−	6.51447i	−1.33953	−	0.305739i
$455$	−4.31238	+	2.07673i	−0.202168	+	0.0973587i
$456$	−7.23370	−	15.0209i	−0.338749	−	0.703420i
$457$	−4.57686	−	20.0525i	−0.214097	−	0.938018i	−0.961750	−	0.273929i	$-0.911677\pi$
$457$	−4.57686	−	20.0525i	−0.214097	−	0.938018i	0.747653	−	0.664089i	$-0.231181\pi$
$458$	23.5972	−	29.5900i	1.10263	−	1.38265i
$459$	−13.4981	−	16.9261i	−0.630037	−	0.790041i
$460$	0.0216121	−	0.0946886i	0.00100767	−	0.00441488i
$461$	−16.4445	+	3.75334i	−0.765895	+	0.174811i	−0.587583	−	0.809164i	$-0.699921\pi$
$461$	−16.4445	+	3.75334i	−0.765895	+	0.174811i	−0.178311	+	0.983974i	$0.557063\pi$
$462$	−17.7716	+	14.1724i	−0.826810	+	0.659359i
$463$	−12.3851			−0.575585			−0.287793	−	0.957693i	$-0.592921\pi$
$463$	−12.3851			−0.575585			−0.287793	+	0.957693i	$0.592921\pi$
$464$	−23.6472	+	8.07792i	−1.09779	+	0.375008i
$465$	4.78192			0.221756
$466$	24.5311	−	19.5629i	1.13638	−	0.906234i
$467$	24.7368	−	5.64601i	1.14468	−	0.261266i	0.392200	−	0.919880i	$-0.371714\pi$
$467$	24.7368	−	5.64601i	1.14468	−	0.261266i	0.752481	+	0.658614i	$0.228857\pi$
$468$	−1.54282	+	6.75955i	−0.0713170	+	0.312460i
$469$	25.9018	+	32.4798i	1.19603	+	1.49978i
$470$	0.0787474	−	0.0987461i	0.00363235	−	0.00455482i
$471$	2.39135	+	10.4772i	0.110187	+	0.482763i
$472$	14.2479	+	29.5861i	0.655813	+	1.36181i
$473$	−5.44388	+	2.62163i	−0.250310	+	0.120543i
$474$	61.3290	+	13.9980i	2.81694	+	0.642947i
$475$	4.76742	−	9.89965i	0.218744	−	0.454227i
$476$		−	3.85813i		−	0.176837i
$477$	15.6021	+	7.51360i	0.714373	+	0.344024i
$478$	8.02986	+	6.40360i	0.367277	+	0.292894i
$479$	11.9244	+	9.50940i	0.544840	+	0.434495i	0.856837	−	0.515588i	$-0.172426\pi$
$479$	11.9244	+	9.50940i	0.544840	+	0.434495i	−0.311997	+	0.950083i	$0.600998\pi$
$480$	−2.68150	−	1.29134i	−0.122393	−	0.0589414i
$481$			21.9810i			1.00225i
$482$	−0.765102	+	1.58875i	−0.0348495	+	0.0723656i
$483$	5.21575	+	1.19046i	0.237325	+	0.0541679i
$484$	3.19313	−	1.53773i	0.145142	−	0.0698968i
$485$	0.928033	+	1.92708i	0.0421398	+	0.0875042i
$486$	−2.20161	−	9.64588i	−0.0998670	−	0.437546i
$487$	−0.329948	+	0.413741i	−0.0149514	+	0.0187484i	−0.789251	−	0.614071i	$-0.789531\pi$
$487$	−0.329948	+	0.413741i	−0.0149514	+	0.0187484i	0.774300	+	0.632819i	$0.218102\pi$
$488$	2.91753	+	3.65846i	0.132070	+	0.165611i
$489$	11.6108	−	50.8701i	0.525057	−	2.30042i
$490$	−3.19121	+	0.728374i	−0.144164	+	0.0329046i
$491$	−14.9714	+	11.9393i	−0.675651	+	0.538813i	−0.900106	−	0.435671i	$-0.856511\pi$
$491$	−14.9714	+	11.9393i	−0.675651	+	0.538813i	0.224455	+	0.974484i	$0.427940\pi$
$492$	5.21521			0.235120
$493$	−10.6734	−	10.8331i	−0.480707	−	0.487899i
$494$	−10.9609			−0.493155
$495$	−2.91996	+	2.32859i	−0.131242	+	0.104662i
$496$	−16.2253	+	3.70333i	−0.728539	+	0.166284i
$497$	3.42880	−	15.0226i	0.153803	−	0.673854i
$498$	6.95429	+	8.72040i	0.311629	+	0.390770i
$499$	−8.50519	+	10.6652i	−0.380745	+	0.477439i	−0.934868	−	0.354996i	$-0.884482\pi$
$499$	−8.50519	+	10.6652i	−0.380745	+	0.477439i	0.554123	+	0.832435i	$0.313054\pi$
$500$	−0.396297	−	1.73629i	−0.0177230	−	0.0776493i
$501$	−13.7136	−	28.4765i	−0.612677	−	1.27224i
$502$	−36.7477	+	17.6968i	−1.64013	+	0.789846i
$503$	−40.8341	−	9.32013i	−1.82070	−	0.415564i	−0.830714	−	0.556699i	$-0.812068\pi$
$503$	−40.8341	−	9.32013i	−1.82070	−	0.415564i	−0.989990	+	0.141135i	$0.954925\pi$
$504$	20.5996	−	42.7756i	0.917580	−	1.90538i
$505$		−	6.37104i		−	0.283508i
$506$	1.09197	+	0.525867i	0.0485442	+	0.0233776i
$507$	7.96946	+	6.35543i	0.353936	+	0.282255i
$508$	−5.15276	−	4.10919i	−0.228617	−	0.182316i
$509$	2.39191	+	1.15189i	0.106020	+	0.0510564i	0.486142	−	0.873880i	$-0.338404\pi$
$509$	2.39191	+	1.15189i	0.106020	+	0.0510564i	−0.380122	+	0.924936i	$0.624118\pi$
$510$		−	5.83345i		−	0.258309i
$511$	12.2564	−	25.4507i	0.542191	−	1.12587i
$512$	−12.3262	−	2.81338i	−0.544748	−	0.124335i
$513$	−15.8319	+	7.62425i	−0.698997	+	0.336619i
$514$	11.6541	+	24.1999i	0.514039	+	1.06741i
$515$	0.870159	+	3.81241i	0.0383438	+	0.167995i
$516$	−3.02112	+	3.78837i	−0.132998	+	0.166774i
$517$	0.163868	+	0.205484i	0.00720692	+	0.00903719i
$518$	−8.38009	+	36.7156i	−0.368200	+	1.61319i
$519$	14.5990	−	3.33213i	0.640826	−	0.146264i
$520$	2.71725	−	2.16694i	0.119159	−	0.0950265i
$521$	−6.45004			−0.282581			−0.141291	−	0.989968i	$-0.545125\pi$
$521$	−6.45004			−0.282581			−0.141291	+	0.989968i	$0.545125\pi$
$522$	15.1363	+	44.3097i	0.662497	+	1.93938i
$523$	−18.9831			−0.830074			−0.415037	−	0.909804i	$-0.636231\pi$
$523$	−18.9831			−0.830074			−0.415037	+	0.909804i	$0.636231\pi$
$524$	−3.41055	+	2.71982i	−0.148990	+	0.118816i
$525$	46.8124	−	10.6846i	2.04306	−	0.466315i
$526$	1.73274	−	7.59164i	0.0755511	−	0.331011i
$527$	−6.31499	−	7.91874i	−0.275085	−	0.344946i
$528$	12.4363	−	15.5946i	0.541221	−	0.678670i
$529$	5.05451	+	22.1452i	0.219761	+	0.962836i
$530$	0.942342	+	1.95679i	0.0409327	+	0.0849977i
$531$	66.9956	−	32.2634i	2.90736	−	1.40011i
$532$	−3.05303	−	0.696834i	−0.132366	−	0.0302116i
$533$	−5.94588	+	12.3467i	−0.257545	+	0.534797i
$534$		−	61.3419i		−	2.65453i
$535$	−2.10247	−	1.01250i	−0.0908979	−	0.0437741i
$536$	−23.5843	−	18.8079i	−1.01869	−	0.812376i
$537$	19.7095	+	15.7178i	0.850526	+	0.678272i
$538$	30.5439	+	14.7091i	1.31684	+	0.634156i
$539$		−	6.81149i		−	0.293392i
$540$	−0.604862	+	1.25601i	−0.0260291	+	0.0540500i
$541$	−22.2465	−	5.07761i	−0.956450	−	0.218304i	−0.284314	−	0.958731i	$-0.591766\pi$
$541$	−22.2465	−	5.07761i	−0.956450	−	0.218304i	−0.672136	+	0.740428i	$0.734623\pi$
$542$	10.8939	−	5.24622i	0.467932	−	0.225344i
$543$	11.8573	+	24.6219i	0.508844	+	1.05663i
$544$	1.40275	+	6.14583i	0.0601422	+	0.263500i
$545$	−1.67301	+	2.09789i	−0.0716639	+	0.0898637i
$546$	−29.8645	−	37.4488i	−1.27808	−	1.60266i
$547$	−3.68955	+	16.1650i	−0.157754	+	0.691164i	0.832747	+	0.553654i	$0.186767\pi$
$547$	−3.68955	+	16.1650i	−0.157754	+	0.691164i	−0.990500	+	0.137510i	$0.956090\pi$
$548$	4.46567	−	1.01926i	0.190764	−	0.0435407i
$549$	8.28433	−	6.60653i	0.353566	−	0.281960i
$550$	10.8779			0.463837
$551$	−10.5003	+	6.48950i	−0.447326	+	0.276462i
$552$	−3.88467			−0.165343
$553$	−36.9223	+	29.4446i	−1.57010	+	1.25211i
$554$	−2.73832	+	0.625003i	−0.116340	+	0.0265538i
$555$	−2.11290	+	9.25721i	−0.0896875	+	0.392947i
$556$	−4.76652	−	5.97703i	−0.202146	−	0.253483i
$557$	25.8835	−	32.4569i	1.09672	−	1.37524i	0.176287	−	0.984339i	$-0.443591\pi$
$557$	25.8835	−	32.4569i	1.09672	−	1.37524i	0.920432	−	0.390903i	$-0.127837\pi$
$558$	6.93924	+	30.4028i	0.293761	+	1.28705i
$559$	−5.52438	−	11.4715i	−0.233656	−	0.485192i
$560$	6.48329	−	3.12219i	0.273969	−	0.131937i
$561$	11.8347	+	2.70119i	0.499661	+	0.114044i
$562$	−8.60325	+	17.8648i	−0.362906	+	0.753582i
$563$		−	25.8782i		−	1.09064i	−0.838229	−	0.545318i	$-0.816409\pi$
$563$		−	25.8782i		−	1.09064i	0.838229	−	0.545318i	$-0.183591\pi$
$564$	0.189896	+	0.0914492i	0.00799607	+	0.00385070i
$565$	−4.11782	−	3.28385i	−0.173238	−	0.138153i
$566$	24.7432	+	19.7321i	1.04004	+	0.829401i
$567$	−17.4079	−	8.38319i	−0.731062	−	0.352061i
$568$			11.1887i			0.469469i
$569$	−2.97456	+	6.17675i	−0.124700	+	0.258943i	−0.953968	−	0.299909i	$-0.903044\pi$
$569$	−2.97456	+	6.17675i	−0.124700	+	0.258943i	0.829268	+	0.558852i	$0.188758\pi$
$570$	−4.61614	−	1.05360i	−0.193349	−	0.0441306i
$571$	22.3415	−	10.7591i	0.934962	−	0.450254i	0.0965729	−	0.995326i	$-0.469212\pi$
$571$	22.3415	−	10.7591i	0.934962	−	0.450254i	0.838389	+	0.545072i	$0.183498\pi$
$572$	−0.785124	−	1.63033i	−0.0328277	−	0.0681673i
$573$	8.11128	+	35.5378i	0.338853	+	1.48461i
$574$	−14.6387	+	18.3563i	−0.611007	+	0.766178i
$575$	−1.59627	−	2.00166i	−0.0665691	−	0.0834750i
$576$	−7.27111	+	31.8568i	−0.302963	+	1.32737i
$577$	−40.4195	+	9.22548i	−1.68268	+	0.384062i	−0.953769	−	0.300542i	$-0.902832\pi$
$577$	−40.4195	+	9.22548i	−1.68268	+	0.384062i	−0.728916	+	0.684604i	$0.759975\pi$
$578$	10.9316	−	8.71765i	0.454694	−	0.362607i
$579$	−59.0708			−2.45490
$580$	−0.330291	+	0.921900i	−0.0137146	+	0.0382798i
$581$	−8.37346			−0.347390
$582$	−16.7348	+	13.3456i	−0.693681	+	0.553192i
$583$	−4.40622	+	1.00569i	−0.182487	+	0.0416515i
$584$	−4.56426	+	19.9973i	−0.188870	+	0.827495i
$585$	−4.90687	−	6.15302i	−0.202874	−	0.254396i
$586$	5.97786	−	7.49600i	0.246943	−	0.309657i
$587$	−2.00556	−	8.78692i	−0.0827782	−	0.362675i	0.916526	−	0.399975i	$-0.130981\pi$
$587$	−2.00556	−	8.78692i	−0.0827782	−	0.362675i	−0.999304	+	0.0373002i	$0.988124\pi$
$588$	−2.37004	−	4.92144i	−0.0977389	−	0.202957i
$589$	−7.40686	+	3.56695i	−0.305194	+	0.146974i
$590$	9.09221	+	2.07524i	0.374321	+	0.0854362i
$591$	11.1324	−	23.1168i	0.457927	−	0.950896i
$592$		−	33.0466i		−	1.35821i
$593$	3.70166	+	1.78263i	0.152009	+	0.0732037i	0.508342	−	0.861155i	$-0.330259\pi$
$593$	3.70166	+	1.78263i	0.152009	+	0.0732037i	−0.356333	+	0.934359i	$0.615973\pi$
$594$	−13.6011	−	10.8465i	−0.558059	−	0.445037i
$595$	3.42390	+	2.73047i	0.140366	+	0.111938i
$596$	−8.64415	−	4.16280i	−0.354078	−	0.170515i
$597$		−	41.7658i		−	1.70936i
$598$	−1.10812	+	2.30104i	−0.0453145	+	0.0940964i
$599$	43.6215	+	9.95632i	1.78233	+	0.406804i	0.981402	−	0.191962i	$-0.0614850\pi$
$599$	43.6215	+	9.95632i	1.78233	+	0.406804i	0.800924	+	0.598766i	$0.204342\pi$
$600$	−31.4129	+	15.1276i	−1.28243	+	0.617584i
$601$	1.92305	+	3.99326i	0.0784429	+	0.162888i	0.936502	−	0.350663i	$-0.114044\pi$
$601$	1.92305	+	3.99326i	0.0784429	+	0.162888i	−0.858059	+	0.513552i	$0.828330\pi$
$602$	−4.85412	−	21.2673i	−0.197839	−	0.866790i
$603$	−42.5891	+	53.4050i	−1.73436	+	2.17482i
$604$	2.02185	+	2.53531i	0.0822677	+	0.103160i
$605$	−0.895175	+	3.92202i	−0.0363940	+	0.159453i
$606$	62.1586	−	14.1873i	2.52502	−	0.576319i
$607$	8.91682	−	7.11093i	0.361923	−	0.288624i	−0.425597	−	0.904913i	$-0.639936\pi$
$607$	8.91682	−	7.11093i	0.361923	−	0.288624i	0.787520	+	0.616289i	$0.211365\pi$
$608$	5.11669			0.207509
$609$	−50.7812	−	18.1935i	−2.05776	−	0.737237i
$610$	1.32894			0.0538071
$611$	−0.433002	+	0.345308i	−0.0175174	+	0.0139697i
$612$	6.18469	−	1.41161i	0.250001	−	0.0570612i
$613$	7.01511	−	30.7352i	0.283338	−	1.24138i	−0.610146	−	0.792289i	$-0.708889\pi$
$613$	7.01511	−	30.7352i	0.283338	−	1.24138i	0.893484	−	0.449095i	$-0.148253\pi$
$614$	3.03309	+	3.80338i	0.122406	+	0.153492i
$615$	−3.69089	+	4.62823i	−0.148831	+	0.186628i
$616$	2.75725	+	12.0803i	0.111093	+	0.486729i
$617$	−1.37781	−	2.86105i	−0.0554685	−	0.115181i	0.871392	−	0.490587i	$-0.163218\pi$
$617$	−1.37781	−	2.86105i	−0.0554685	−	0.115181i	−0.926861	+	0.375406i	$0.877503\pi$
$618$	−35.2578	+	16.9793i	−1.41828	+	0.683006i
$619$	20.3526	+	4.64536i	0.818042	+	0.186713i	0.611011	−	0.791622i	$-0.290763\pi$
$619$	20.3526	+	4.64536i	0.818042	+	0.186713i	0.207030	+	0.978335i	$0.433620\pi$
$620$	−0.282980	+	0.587615i	−0.0113648	+	0.0235992i
$621$			4.09441i			0.164303i
$622$	10.0376	+	4.83384i	0.402470	+	0.193819i
$623$	36.0042	+	28.7124i	1.44248	+	1.15034i
$624$	32.8615	+	26.2061i	1.31551	+	1.04909i
$625$	−19.7730	−	9.52219i	−0.790921	−	0.380887i
$626$			3.21792i			0.128614i
$627$	4.27502	−	8.87718i	0.170728	−	0.354520i
$628$	−1.42898	−	0.326154i	−0.0570223	−	0.0130150i
$629$	18.1200	−	8.72613i	0.722492	−	0.347934i
$630$	−5.85031	−	12.1483i	−0.233082	−	0.483999i
$631$	−8.53059	−	37.3750i	−0.339597	−	1.48787i	−0.799912	−	0.600118i	$-0.795120\pi$
$631$	−8.53059	−	37.3750i	−0.339597	−	1.48787i	0.460314	−	0.887756i	$-0.347737\pi$
$632$	21.3803	−	26.8101i	0.850464	−	1.06645i
$633$	1.47837	+	1.85382i	0.0587599	+	0.0736826i
$634$	−2.13515	+	9.35472i	−0.0847978	+	0.371524i
$635$	7.29339	−	1.66467i	0.289429	−	0.0660604i
$636$	−2.83366	+	2.25977i	−0.112362	+	0.0896057i
$637$	14.3534			0.568701
$638$	−10.2987	−	6.57829i	−0.407731	−	0.260437i
$639$	25.3361			1.00228
$640$	−4.78990	+	3.81982i	−0.189337	+	0.150991i
$641$	−6.53394	+	1.49133i	−0.258075	+	0.0589040i	−0.349601	−	0.936899i	$-0.613683\pi$
$641$	−6.53394	+	1.49133i	−0.258075	+	0.0589040i	0.0915256	+	0.995803i	$0.470826\pi$
$642$	5.19649	−	22.7673i	0.205089	−	0.898553i
$643$	8.38577	+	10.5154i	0.330702	+	0.414688i	0.919187	−	0.393820i	$-0.128847\pi$
$643$	8.38577	+	10.5154i	0.330702	+	0.414688i	−0.588485	+	0.808508i	$0.700275\pi$
$644$	−0.454940	+	0.570477i	−0.0179272	+	0.0224799i
$645$	−1.22388	−	5.36219i	−0.0481904	−	0.211136i
$646$	4.35132	+	9.03560i	0.171200	+	0.355501i
$647$	16.8109	−	8.09572i	0.660906	−	0.318276i	−0.0731932	−	0.997318i	$-0.523319\pi$
$647$	16.8109	−	8.09572i	0.660906	−	0.318276i	0.734099	+	0.679042i	$0.237605\pi$
$648$	13.6779	+	3.12188i	0.537317	+	0.122639i
$649$	−8.42033	+	17.4850i	−0.330527	+	0.686346i
$650$			22.9223i			0.899086i
$651$	−32.3677	−	15.5875i	−1.26859	−	0.610921i
$652$	5.56396	+	4.43711i	0.217901	+	0.173771i
$653$	20.8420	+	16.6210i	0.815612	+	0.650429i	0.939760	−	0.341835i	$-0.111048\pi$
$653$	20.8420	+	16.6210i	0.815612	+	0.650429i	−0.124148	+	0.992264i	$0.539620\pi$
$654$	−24.1934	−	11.6509i	−0.946038	−	0.455588i
$655$		−	4.95155i		−	0.193473i
$656$	8.93911	−	18.5623i	0.349014	−	0.724735i
$657$	45.2825	+	10.3354i	1.76664	+	0.403224i
$658$	−0.854903	+	0.411699i	−0.0333276	+	0.0160497i
$659$	−11.9581	−	24.8312i	−0.465821	−	0.967288i	−0.993064	−	0.117573i	$-0.962489\pi$
$659$	−11.9581	−	24.8312i	−0.465821	−	0.967288i	0.527243	−	0.849715i	$-0.323226\pi$
$660$	−0.173938	−	0.762073i	−0.00677053	−	0.0296636i
$661$	−17.5288	+	21.9804i	−0.681792	+	0.854940i	−0.995518	−	0.0945737i	$-0.969851\pi$
$661$	−17.5288	+	21.9804i	−0.681792	+	0.854940i	0.313726	+	0.949514i	$0.398423\pi$
$662$	2.70681	+	3.39424i	0.105203	+	0.131921i
$663$	−5.69202	+	24.9384i	−0.221060	+	0.968526i
$664$	5.92772	−	1.35296i	0.230040	−	0.0525051i
$665$	2.77908	−	2.21625i	0.107768	−	0.0859423i
$666$	−61.9222			−2.39943
$667$	0.300798	+	2.86040i	0.0116469	+	0.110755i
$668$	4.31080			0.166790
$669$	26.1620	−	20.8635i	1.01148	−	0.806628i
$670$	−8.35222	+	1.90634i	−0.322675	+	0.0736484i
$671$	−0.615367	+	2.69610i	−0.0237560	+	0.104082i
$672$	13.9411	+	17.4816i	0.537789	+	0.674366i
$673$	8.92427	−	11.1907i	0.344005	−	0.431369i	−0.579490	−	0.814980i	$-0.696748\pi$
$673$	8.92427	−	11.1907i	0.344005	−	0.431369i	0.923495	+	0.383611i	$0.125320\pi$
$674$	−6.65022	−	29.1365i	−0.256157	−	1.12230i
$675$	15.9444	+	33.1089i	0.613700	+	1.27436i
$676$	−1.25258	+	0.603212i	−0.0481763	+	0.0232005i
$677$	−34.6645	−	7.91194i	−1.33226	−	0.304080i	−0.503653	−	0.863906i	$-0.668011\pi$
$677$	−34.6645	−	7.91194i	−1.33226	−	0.304080i	−0.828611	+	0.559826i	$0.810868\pi$
$678$	22.8689	−	47.4878i	0.878275	−	1.82376i
$679$		−	16.0690i		−	0.616673i
$680$	−2.86502	−	1.37972i	−0.109868	−	0.0529098i
$681$	43.3561	+	34.5754i	1.66141	+	1.32493i
$682$	−6.36317	−	5.07446i	−0.243658	−	0.194311i
$683$	−3.63615	−	1.75108i	−0.139133	−	0.0670031i	0.363022	−	0.931781i	$-0.381745\pi$
$683$	−3.63615	−	1.75108i	−0.139133	−	0.0670031i	−0.502155	+	0.864778i	$0.667459\pi$
$684$		−	5.14904i		−	0.196879i
$685$	−2.25589	+	4.68441i	−0.0861932	+	0.178982i
$686$	−12.1137	−	2.76486i	−0.462501	−	0.105563i
$687$	−64.5908	+	31.1053i	−2.46429	+	1.18674i
$688$	8.30542	+	17.2464i	0.316641	+	0.657512i
$689$	−2.11922	−	9.28492i	−0.0807359	−	0.353727i
$690$	−0.687864	+	0.862554i	−0.0261865	+	0.0328369i
$691$	20.3907	+	25.5691i	0.775698	+	0.972695i	0.999998	−	0.00182516i	$-0.000580967\pi$
$691$	20.3907	+	25.5691i	0.775698	+	0.972695i	−0.224300	+	0.974520i	$0.572010\pi$
$692$	−0.454468	+	1.99115i	−0.0172763	+	0.0756923i
$693$	27.3550	−	6.24360i	1.03913	−	0.237175i
$694$	35.5695	−	28.3657i	1.35020	−	1.07675i
$695$	8.67766			0.329162
$696$	38.8885	+	4.67437i	1.47407	+	0.177182i
$697$	12.5384			0.474927
$698$	10.3171	−	8.22761i	0.390508	−	0.311420i
$699$	−57.9437	+	13.2253i	−2.19163	+	0.500226i
$700$	−1.45727	+	6.38472i	−0.0550796	+	0.241320i
$701$	10.8955	+	13.6626i	0.411519	+	0.516028i	0.943790	−	0.330546i	$-0.107233\pi$
$701$	10.8955	+	13.6626i	0.411519	+	0.516028i	−0.532271	+	0.846574i	$0.678661\pi$
$702$	22.8560	−	28.6606i	0.862646	−	1.08172i
$703$	−3.63245	−	15.9148i	−0.137001	−	0.600239i
$704$	−3.70018	−	7.68350i	−0.139456	−	0.289583i
$705$	−0.215549	+	0.103803i	−0.00811805	+	0.00390945i
$706$	−39.4247	−	8.99843i	−1.48377	−	0.338660i
$707$	−20.7675	+	43.1241i	−0.781041	+	1.62185i
$708$			15.5631i			0.584898i
$709$	4.64858	+	2.23864i	0.174581	+	0.0840739i	0.519133	−	0.854693i	$-0.326255\pi$
$709$	4.64858	+	2.23864i	0.174581	+	0.0840739i	−0.344552	+	0.938767i	$0.611969\pi$
$710$	2.48435	+	1.98121i	0.0932362	+	0.0743534i
$711$	−60.7095	−	48.4142i	−2.27679	−	1.81568i
$712$	−30.1272	−	14.5085i	−1.12906	−	0.543729i
$713$			1.91554i			0.0717375i
$714$	−19.0151	+	39.4853i	−0.711623	+	1.47770i
$715$	2.00248	+	0.457052i	0.0748884	+	0.0170928i
$716$	−3.09779	+	1.49182i	−0.115770	+	0.0557518i
$717$	−8.44108	−	17.5281i	−0.315238	−	0.654598i
$718$	−1.92051	−	8.41429i	−0.0716727	−	0.314019i
$719$	−13.2905	+	16.6658i	−0.495653	+	0.621529i	−0.965243	−	0.261356i	$-0.915830\pi$
$719$	−13.2905	+	16.6658i	−0.495653	+	0.621529i	0.469590	+	0.882885i	$0.344402\pi$
$720$	7.37706	+	9.25054i	0.274927	+	0.344747i
$721$	6.53730	−	28.6418i	0.243462	−	1.06668i
$722$	−20.7622	+	4.73885i	−0.772691	+	0.176362i
$723$	2.61149	−	2.08260i	0.0971225	−	0.0774526i
$724$	−3.72728			−0.138523
$725$	13.5713	+	21.9589i	0.504026	+	0.815534i
$726$	−40.2583			−1.49412
$727$	−10.4522	+	8.33539i	−0.387652	+	0.309142i	−0.797852	−	0.602853i	$-0.794030\pi$
$727$	−10.4522	+	8.33539i	−0.387652	+	0.309142i	0.410200	+	0.911996i	$0.365459\pi$
$728$	−25.4560	+	5.81016i	−0.943461	+	0.215339i
$729$	−7.94917	+	34.8276i	−0.294414	+	1.28991i
$730$	3.63202	+	4.55441i	0.134427	+	0.168566i
$731$	−7.26339	+	9.10801i	−0.268646	+	0.336872i
$732$	0.493486	+	2.16210i	0.0182398	+	0.0799137i
$733$	−5.02821	−	10.4412i	−0.185721	−	0.385654i	0.787232	−	0.616657i	$-0.211514\pi$
$733$	−5.02821	−	10.4412i	−0.185721	−	0.385654i	−0.972953	+	0.231003i	$0.925799\pi$
$734$	−7.06970	+	3.40459i	−0.260947	+	0.125666i
$735$	6.04485	+	1.37970i	0.222968	+	0.0508909i
$736$	0.517285	−	1.07415i	0.0190674	−	0.0395938i
$737$		−	17.8274i		−	0.656681i
$738$	−34.7817	−	16.7500i	−1.28033	−	0.616575i
$739$	1.00676	+	0.802861i	0.0370341	+	0.0295337i	0.641832	−	0.766845i	$-0.278175\pi$
$739$	1.00676	+	0.802861i	0.0370341	+	0.0295337i	−0.604798	+	0.796379i	$0.706746\pi$
$740$	−1.01251	−	0.807454i	−0.0372208	−	0.0296826i
$741$	18.7062	+	9.00845i	0.687191	+	0.330934i
$742$		−	16.3168i		−	0.599009i
$743$	4.28548	−	8.89888i	0.157219	−	0.326468i	−0.807449	−	0.589937i	$-0.799152\pi$
$743$	4.28548	−	8.89888i	0.157219	−	0.326468i	0.964668	+	0.263469i	$0.0848667\pi$
$744$	25.4322	+	5.80474i	0.932391	+	0.212812i
$745$	9.81189	−	4.72516i	0.359480	−	0.173116i
$746$	−0.312025	−	0.647926i	−0.0114240	−	0.0237223i
$747$	−3.06369	−	13.4229i	−0.112094	−	0.491118i
$748$	−1.03227	+	1.29443i	−0.0377436	+	0.0473290i
$749$	10.9308	+	13.7067i	0.399401	+	0.500833i
$750$	−4.50163	+	19.7229i	−0.164376	+	0.720179i
$751$	21.1679	−	4.83144i	0.772429	−	0.176302i	0.181899	−	0.983317i	$-0.441776\pi$
$751$	21.1679	−	4.83144i	0.772429	−	0.176302i	0.590530	+	0.807015i	$0.298919\pi$
$752$	0.650982	−	0.519140i	0.0237389	−	0.0189311i
$753$	77.2592			2.81548
$754$	13.8620	−	21.7018i	0.504823	−	0.790332i
$755$	−3.68086			−0.133960
$756$	8.18834	−	6.52999i	0.297807	−	0.237493i
$757$	23.0543	−	5.26200i	0.837923	−	0.191251i	0.218035	−	0.975941i	$-0.430035\pi$
$757$	23.0543	−	5.26200i	0.837923	−	0.191251i	0.619888	+	0.784690i	$0.287178\pi$
$758$	−0.814531	+	3.56869i	−0.0295851	+	0.129621i
$759$	−1.43140	−	1.79492i	−0.0519566	−	0.0651515i
$760$	−1.60926	+	2.01795i	−0.0583742	+	0.0731989i
$761$	11.2882	+	49.4568i	0.409196	+	1.79281i	0.587933	+	0.808910i	$0.299942\pi$
$761$	11.2882	+	49.4568i	0.409196	+	1.79281i	−0.178737	+	0.983897i	$0.557201\pi$
$762$	32.4824	+	67.4505i	1.17671	+	2.44347i
$763$	18.1627	−	8.74667i	0.657532	−	0.316651i
$764$	−4.84698	−	1.10629i	−0.175358	−	0.0400243i
$765$	−3.12427	+	6.48762i	−0.112958	+	0.234560i
$766$			38.5921i			1.39439i
$767$	−36.8449	−	17.7436i	−1.33039	−	0.640683i
$768$	−21.2167	−	16.9197i	−0.765590	−	0.610538i
$769$	−13.0238	−	10.3861i	−0.469651	−	0.374534i	0.359877	−	0.933000i	$-0.382819\pi$
$769$	−13.0238	−	10.3861i	−0.469651	−	0.374534i	−0.829527	+	0.558466i	$0.811390\pi$
$770$	3.17055	+	1.52686i	0.114259	+	0.0550241i
$771$		−	50.8784i		−	1.83234i
$772$	3.49564	−	7.25877i	0.125811	−	0.261249i
$773$	−33.2101	−	7.57999i	−1.19448	−	0.272633i	−0.421363	−	0.906892i	$-0.638448\pi$
$773$	−33.2101	−	7.57999i	−1.19448	−	0.272633i	−0.773121	+	0.634259i	$0.781305\pi$
$774$	32.3160	−	15.5626i	1.16157	−	0.559385i
$775$	7.45948	+	15.4898i	0.267952	+	0.556409i
$776$	2.59639	+	11.3755i	0.0932051	+	0.408358i
$777$	44.4771	−	55.7726i	1.59561	−	2.00083i
$778$	11.6302	+	14.5838i	0.416962	+	0.522854i
$779$	2.26462	−	9.92194i	0.0811383	−	0.355490i
$780$	1.60586	−	0.366527i	0.0574991	−	0.0131238i
$781$	−5.16978	+	4.12276i	−0.184989	+	0.147524i
$782$	2.33676			0.0835624
$783$	4.92675	−	40.9882i	0.176068	−	1.46480i
$784$	−21.5790			−0.770680
$785$	1.30076	−	1.03732i	0.0464259	−	0.0370235i
$786$	48.3094	−	11.0263i	1.72314	−	0.393295i
$787$	0.0879573	−	0.385366i	0.00313534	−	0.0137368i	−0.973336	−	0.229384i	$-0.926329\pi$
$787$	0.0879573	−	0.385366i	0.00313534	−	0.0137368i	0.976471	+	0.215647i	$0.0691860\pi$
$788$	2.18186	+	2.73597i	0.0777256	+	0.0974648i
$789$	−9.19648	+	11.5320i	−0.327403	+	0.410551i
$790$	−2.16708	−	9.49461i	−0.0771013	−	0.337803i
$791$	17.1683	+	35.6503i	0.610434	+	1.26758i
$792$	−18.3562	+	8.83989i	−0.652260	+	0.314112i
$793$	−5.68130	−	1.29672i	−0.201749	−	0.0460478i
$794$	17.5120	−	36.3641i	0.621479	−	1.29051i
$795$		−	4.11401i		−	0.145909i
$796$	5.13229	+	2.47158i	0.181909	+	0.0876029i
$797$	−23.1489	−	18.4607i	−0.819978	−	0.653910i	0.120897	−	0.992665i	$-0.461423\pi$
$797$	−23.1489	−	18.4607i	−0.819978	−	0.653910i	−0.940875	+	0.338755i	$0.889994\pi$
$798$	27.8112	+	22.1787i	0.984505	+	0.785117i
$799$	0.456549	+	0.219862i	0.0161515	+	0.00777817i
$800$		−	10.7004i		−	0.378316i
$801$	−32.8534	+	68.2209i	−1.16082	+	2.41047i
$802$	41.5951	+	9.49382i	1.46878	+	0.335238i
$803$	−10.9216	+	5.25958i	−0.385416	+	0.185606i
$804$	−6.20301	−	12.8807i	−0.218763	−	0.454266i
$805$	−0.184300	−	0.807473i	−0.00649573	−	0.0284597i
$806$	10.6930	−	13.4086i	0.376646	−	0.472299i
$807$	−40.0381	−	50.2061i	−1.40941	−	1.76734i
$808$	7.73376	−	33.8838i	0.272073	−	1.19203i
$809$	−8.72210	+	1.99076i	−0.306653	+	0.0699915i	−0.373078	−	0.927800i	$-0.621698\pi$
$809$	−8.72210	+	1.99076i	−0.306653	+	0.0699915i	0.0664255	+	0.997791i	$0.478841\pi$
$810$	3.11514	−	2.48424i	0.109455	−	0.0872875i
$811$	18.3209			0.643333			0.321667	−	0.946853i	$-0.395757\pi$
$811$	18.3209			0.643333			0.321667	+	0.946853i	$0.395757\pi$
$812$	5.24075	−	5.16349i	0.183914	−	0.181203i
$813$	−22.9035			−0.803262
$814$	12.6351	−	10.0762i	0.442860	−	0.353169i
$815$	−7.87541	+	1.79751i	−0.275864	+	0.0629641i
$816$	8.55746	−	37.4927i	0.299571	−	1.31251i
$817$	5.89550	+	7.39272i	0.206257	+	0.258639i
$818$	−17.2898	+	21.6807i	−0.604522	+	0.758047i
$819$	13.1567	+	57.6432i	0.459732	+	2.01422i
$820$	−0.350313	−	0.727432i	−0.0122335	−	0.0254030i
$821$	−45.8145	+	22.0631i	−1.59894	+	0.770007i	−0.999537	−	0.0304427i	$-0.990308\pi$
$821$	−45.8145	+	22.0631i	−1.59894	+	0.770007i	−0.599400	+	0.800450i	$0.704594\pi$
$822$	−50.7265	−	11.5780i	−1.76929	−	0.403829i
$823$	0.145552	−	0.302242i	0.00507362	−	0.0105355i	−0.898417	−	0.439144i	$-0.855282\pi$
$823$	0.145552	−	0.302242i	0.00507362	−	0.0105355i	0.903490	+	0.428609i	$0.140996\pi$
$824$			21.3323i			0.743145i
$825$	−18.5646	−	8.94024i	−0.646337	−	0.311259i
$826$	−54.7785	−	43.6844i	−1.90599	−	1.51998i
$827$	19.8339	+	15.8170i	0.689693	+	0.550012i	0.904410	−	0.426664i	$-0.140311\pi$
$827$	19.8339	+	15.8170i	0.689693	+	0.550012i	−0.214717	+	0.976676i	$0.568883\pi$
$828$	−1.08094	−	0.520555i	−0.0375654	−	0.0180905i
$829$			46.0845i			1.60058i	0.599613	+	0.800290i	$0.295321\pi$
$829$			46.0845i			1.60058i	−0.599613	+	0.800290i	$0.704679\pi$
$830$	0.749217	−	1.55576i	0.0260057	−	0.0540014i
$831$	5.18697	+	1.18389i	0.179934	+	0.0410687i
$832$	16.1909	−	7.79712i	0.561318	−	0.270317i
$833$	−5.69806	−	11.8321i	−0.197426	−	0.409960i
$834$	19.3237	+	84.6629i	0.669127	+	2.93164i
$835$	−3.05083	+	3.82562i	−0.105578	+	0.132391i
$836$	0.837867	+	1.05065i	0.0289782	+	0.0363376i
$837$	6.11814	−	26.8053i	0.211474	−	0.926528i
$838$	−4.09068	+	0.933670i	−0.141310	+	0.0322531i
$839$	−21.9036	+	17.4676i	−0.756198	+	0.603048i	−0.923830	−	0.382802i	$-0.874959\pi$
$839$	−21.9036	+	17.4676i	−0.756198	+	0.603048i	0.167633	+	0.985850i	$0.446388\pi$
$840$	−11.2791			−0.389168
$841$	0.430668	−	28.9968i	0.0148506	−	0.999890i
$842$	−21.5820			−0.743764
$843$	29.3651	−	23.4179i	1.01139	−	0.806555i
$844$	−0.315287	+	0.0719623i	−0.0108526	+	0.00247704i
$845$	0.351154	−	1.53851i	0.0120801	−	0.0529262i
$846$	−0.972757	−	1.21980i	−0.0334441	−	0.0419376i
$847$	18.8437	−	23.6293i	0.647477	−	0.811911i
$848$	3.18607	+	13.9591i	0.109410	+	0.479356i
$849$	−26.0104	−	54.0111i	−0.892674	−	1.85366i
$850$	18.8959	−	9.09979i	0.648124	−	0.312120i
$851$	−3.70825	−	0.846383i	−0.127117	−	0.0290136i
$852$	−2.30077	+	4.77760i	−0.0788231	+	0.163678i
$853$			24.6397i			0.843646i	0.906678	+	0.421823i	$0.138610\pi$
$853$			24.6397i			0.843646i	−0.906678	+	0.421823i	$0.861390\pi$
$854$	−8.99528	−	4.33190i	−0.307812	−	0.148234i
$855$	4.56951	+	3.64406i	0.156274	+	0.124624i
$856$	−9.95277	−	7.93707i	−0.340179	−	0.271283i
$857$	39.7397	+	19.1376i	1.35748	+	0.653729i	0.964074	−	0.265634i	$-0.0855813\pi$
$857$	39.7397	+	19.1376i	1.35748	+	0.653729i	0.393409	+	0.919363i	$0.371296\pi$
$858$			20.5548i			0.701729i
$859$	−3.63787	+	7.55411i	−0.124122	+	0.257743i	−0.953766	−	0.300551i	$-0.902829\pi$
$859$	−3.63787	+	7.55411i	−0.124122	+	0.257743i	0.829643	+	0.558294i	$0.188544\pi$
$860$	0.731345	+	0.166925i	0.0249387	+	0.00569209i
$861$	40.0693	−	19.2964i	1.36556	−	0.657618i
$862$	8.82578	+	18.3269i	0.300607	+	0.624217i
$863$	8.48439	+	37.1725i	0.288812	+	1.26537i	0.886158	+	0.463384i	$0.153365\pi$
$863$	8.48439	+	37.1725i	0.288812	+	1.26537i	−0.597346	+	0.801984i	$0.703778\pi$
$864$	−10.6695	+	13.3791i	−0.362983	+	0.455166i
$865$	−1.44541	−	1.81249i	−0.0491455	−	0.0616265i
$866$	1.94451	−	8.51947i	0.0660772	−	0.289503i
$867$	−25.8210	+	5.89346i	−0.876926	+	0.200153i
$868$	3.83086	−	3.05501i	0.130028	−	0.103694i
$869$	20.2658			0.687469
$870$	7.92395	−	7.80714i	0.268647	−	0.264687i
$871$	37.5664			1.27289
$872$	−11.4444	+	9.12659i	−0.387556	+	0.309065i
$873$	25.7591	−	5.87934i	0.871813	−	0.198986i
$874$	0.422052	−	1.84913i	0.0142761	−	0.0625478i
$875$	−9.46913	−	11.8739i	−0.320115	−	0.401411i
$876$	−6.06104	+	7.60031i	−0.204784	+	0.256791i
$877$	5.45987	+	23.9212i	0.184367	+	0.807763i	0.979519	+	0.201353i	$0.0645338\pi$
$877$	5.45987	+	23.9212i	0.184367	+	0.807763i	−0.795152	+	0.606410i	$0.792609\pi$
$878$	−16.3385	−	33.9273i	−0.551399	−	1.14499i
$879$	−16.3627	+	7.87987i	−0.551901	+	0.265781i
$880$	−3.01055	−	0.687138i	−0.101486	−	0.0231634i
$881$	22.9079	−	47.5688i	0.771788	−	1.60264i	−0.0259735	−	0.999663i	$-0.508269\pi$
$881$	22.9079	−	47.5688i	0.771788	−	1.60264i	0.797762	−	0.602973i	$-0.206017\pi$
$882$			40.4344i			1.36150i
$883$	−5.14964	−	2.47994i	−0.173299	−	0.0834565i	0.345223	−	0.938521i	$-0.387803\pi$
$883$	−5.14964	−	2.47994i	−0.173299	−	0.0834565i	−0.518522	+	0.855064i	$0.673518\pi$
$884$	−2.72766	−	2.17523i	−0.0917410	−	0.0731610i
$885$	−13.8115	−	11.0143i	−0.464268	−	0.370241i
$886$	−15.2730	−	7.35509i	−0.513106	−	0.247099i
$887$		−	34.2192i		−	1.14897i	−0.818515	−	0.574485i	$-0.805202\pi$
$887$		−	34.2192i		−	1.14897i	0.818515	−	0.574485i	$-0.194798\pi$
$888$	−22.4745	+	46.6688i	−0.754196	+	1.56610i
$889$	−54.7936	−	12.5063i	−1.83772	−	0.419447i
$890$	−8.55615	+	4.12042i	−0.286803	+	0.138117i
$891$	3.59747	+	7.47022i	0.120520	+	0.250262i
$892$	1.01557	+	4.44949i	0.0340037	+	0.148980i
$893$	0.256441	−	0.321567i	0.00858148	−	0.0107608i
$894$	67.9501	+	85.2067i	2.27259	+	2.84974i
$895$	0.868447	−	3.80492i	0.0290290	−	0.127184i
$896$	44.8730	−	10.2420i	1.49910	−	0.342161i
$897$	3.78231	−	3.01629i	0.126288	−	0.100711i
$898$	−3.79455			−0.126626
$899$	2.30494	−	19.1760i	0.0768742	−	0.639556i
$900$	−10.7681			−0.358935
$901$	−6.81269	+	5.43294i	−0.226964	+	0.180998i
$902$	9.82274	−	2.24198i	0.327061	−	0.0746496i
$903$	−9.19476	+	40.2849i	−0.305982	+	1.34060i
$904$	−17.9140	−	22.4635i	−0.595811	−	0.747124i
$905$	2.63786	−	3.30777i	0.0876853	−	0.109954i
$906$	−8.19668	−	35.9120i	−0.272316	−	1.19310i
$907$	20.4293	+	42.4218i	0.678342	+	1.40859i	0.901053	+	0.433708i	$0.142795\pi$
$907$	20.4293	+	42.4218i	0.678342	+	1.40859i	−0.222711	+	0.974885i	$0.571491\pi$
$908$	−6.81440	+	3.28164i	−0.226144	+	0.108905i
$909$	−76.7275	−	17.5126i	−2.54489	−	0.580855i
$910$	−3.21743	+	6.68107i	−0.106657	+	0.221475i
$911$		−	49.7296i		−	1.64761i	−0.566870	−	0.823807i	$-0.691846\pi$
$911$		−	49.7296i		−	1.64761i	0.566870	−	0.823807i	$-0.308154\pi$
$912$	−28.1232	−	13.5434i	−0.931252	−	0.448468i
$913$	2.80935	+	2.24038i	0.0929759	+	0.0741458i
$914$	−24.9137	−	19.8680i	−0.824073	−	0.657177i
$915$	−2.26801	−	1.09221i	−0.0749780	−	0.0361075i
$916$		−	9.77782i		−	0.323068i
$917$	−16.1404	+	33.5159i	−0.533003	+	1.10679i
$918$	−32.6997	−	7.46350i	−1.07925	−	0.246332i
$919$	5.16544	−	2.48755i	0.170392	−	0.0820566i	−0.346743	−	0.937960i	$-0.612713\pi$
$919$	5.16544	−	2.48755i	0.170392	−	0.0820566i	0.517136	+	0.855903i	$0.326998\pi$
$920$	0.260939	+	0.541845i	0.00860289	+	0.0178641i
$921$	−2.05049	−	8.98376i	−0.0675658	−	0.296025i
$922$	−16.2932	+	20.4310i	−0.536587	+	0.672859i
$923$	−8.68760	−	10.8939i	−0.285956	−	0.358577i
$924$	−1.30676	+	5.72528i	−0.0429892	+	0.188348i
$925$	−33.2823	+	7.59646i	−1.09431	+	0.249770i
$926$	−15.0018	+	11.9635i	−0.492988	+	0.393145i
$927$	48.3054			1.58656
$928$	−6.47093	+	10.1307i	−0.212419	+	0.332555i
$929$	−7.62389			−0.250132			−0.125066	−	0.992148i	$-0.539914\pi$
$929$	−7.62389			−0.250132			−0.125066	+	0.992148i	$0.539914\pi$
$930$	5.79221	−	4.61913i	0.189934	−	0.151467i
$931$	−10.3922	+	2.37195i	−0.340590	+	0.0777375i
$932$	1.80379	−	7.90290i	0.0590850	−	0.258868i
$933$	−13.1576	−	16.4992i	−0.430762	−	0.540158i
$934$	24.5092	−	30.7335i	0.801965	−	1.00563i
$935$	−0.418183	−	1.83218i	−0.0136760	−	0.0599186i
$936$	−18.6277	−	38.6807i	−0.608864	−	1.26432i
$937$	14.6735	−	7.06636i	0.479361	−	0.230848i	−0.178569	−	0.983927i	$-0.557147\pi$
$937$	14.6735	−	7.06636i	0.479361	−	0.230848i	0.657930	+	0.753079i	$0.271432\pi$
$938$	62.7483	+	14.3219i	2.04881	+	0.467626i
$939$	2.64471	−	5.49180i	0.0863070	−	0.179218i
$940$		−	0.0326300i		−	0.00106427i
$941$	32.5314	+	15.6663i	1.06049	+	0.510707i	0.881031	−	0.473058i	$-0.156850\pi$
$941$	32.5314	+	15.6663i	1.06049	+	0.510707i	0.179463	+	0.983765i	$0.442564\pi$
$942$	13.0171	+	10.3808i	0.424119	+	0.338224i
$943$	−1.85398	−	1.47850i	−0.0603737	−	0.0481465i
$944$	55.3931	+	26.6759i	1.80289	+	0.868227i
$945$			11.8881i			0.386721i
$946$	−4.06163	+	8.43407i	−0.132055	+	0.274215i
$947$	10.8759	+	2.48236i	0.353420	+	0.0806659i	0.395545	−	0.918446i	$-0.370556\pi$
$947$	10.8759	+	2.48236i	0.353420	+	0.0806659i	−0.0421251	+	0.999112i	$0.513413\pi$
$948$	14.6424	−	7.05143i	0.475565	−	0.229020i
$949$	−11.0831	−	23.0143i	−0.359773	−	0.747077i
$950$	−3.78800	−	16.5963i	−0.122899	−	0.538455i
$951$	11.3323	−	14.2102i	0.367475	−	0.460798i
$952$	14.8952	+	18.6780i	0.482756	+	0.605357i
$953$	10.2881	−	45.0753i	0.333266	−	1.46013i	−0.479500	−	0.877542i	$-0.659182\pi$
$953$	10.2881	−	45.0753i	0.333266	−	1.46013i	0.812766	−	0.582590i	$-0.197961\pi$
$954$	26.1563	−	5.97000i	0.846841	−	0.193286i
$955$	4.41207	−	3.51851i	0.142771	−	0.113856i
$956$	2.65342			0.0858176
$957$	12.1696	+	19.6909i	0.393388	+	0.636517i
$958$	23.6294			0.763431
$959$	30.5392	−	24.3542i	0.986163	−	0.786438i
$960$	7.56820	−	1.72739i	0.244263	−	0.0557514i
$961$	−4.03582	+	17.6821i	−0.130188	+	0.570390i
$962$	21.2328	+	26.6250i	0.684572	+	0.858426i
$963$	−17.9729	+	22.5373i	−0.579169	+	0.726255i
$964$	0.101374	+	0.444149i	0.00326504	+	0.0143051i
$965$	3.96787	+	8.23936i	0.127730	+	0.265234i
$966$	7.46764	−	3.59622i	0.240267	−	0.115707i
$967$	37.5341	+	8.56691i	1.20702	+	0.275493i	0.778269	−	0.627931i	$-0.216098\pi$
$967$	37.5341	+	8.56691i	1.20702	+	0.275493i	0.428747	+	0.903425i	$0.358955\pi$
$968$	−9.52182	+	19.7723i	−0.306043	+	0.635505i
$969$		−	18.9966i		−	0.610260i
$970$	2.98558	+	1.43778i	0.0958612	+	0.0461643i
$971$	36.6956	+	29.2637i	1.17762	+	0.939118i	0.998996	−	0.0448004i	$-0.0142652\pi$
$971$	36.6956	+	29.2637i	1.17762	+	0.939118i	0.178620	+	0.983918i	$0.442837\pi$
$972$	−1.99845	−	1.59371i	−0.0641002	−	0.0511182i
$973$	−58.7371	−	28.2863i	−1.88302	−	0.906817i
$974$			0.819869i			0.0262703i
$975$	18.8391	−	39.1199i	0.603335	−	1.25284i
$976$	8.54134	+	1.94950i	0.273402	+	0.0624021i
$977$	−25.7436	+	12.3975i	−0.823610	+	0.396630i	−0.797715	−	0.603035i	$-0.793958\pi$
$977$	−25.7436	+	12.3975i	−0.823610	+	0.396630i	−0.0258953	+	0.999665i	$0.508244\pi$
$978$	−35.0746	−	72.8331i	−1.12156	−	2.32894i
$979$	−4.39742	−	19.2664i	−0.140542	−	0.615755i
$980$	−0.527258	+	0.661160i	−0.0168426	+	0.0211200i
$981$	20.6665	+	25.9150i	0.659831	+	0.827402i
$982$	−6.60161	+	28.9235i	−0.210666	+	0.922987i
$983$	37.9840	−	8.66960i	1.21150	−	0.276517i	0.431395	−	0.902163i	$-0.358022\pi$
$983$	37.9840	−	8.66960i	1.21150	−	0.276517i	0.780107	+	0.625646i	$0.215165\pi$
$984$	−25.2479	+	20.1345i	−0.804873	+	0.641865i
$985$	−3.97217			−0.126564
$986$	−23.3928	−	2.81179i	−0.744978	−	0.0895457i
$987$	1.79737			0.0572108
$988$	−2.21396	+	1.76558i	−0.0704356	+	0.0561705i
$989$	2.14798	−	0.490263i	0.0683018	−	0.0155894i
$990$	−1.28755	+	5.64112i	−0.0409210	+	0.179287i
$991$	0.203838	+	0.255604i	0.00647512	+	0.00811954i	0.785059	−	0.619422i	$-0.212633\pi$
$991$	0.203838	+	0.255604i	0.00647512	+	0.00811954i	−0.778583	+	0.627541i	$0.784061\pi$
$992$	−4.99164	+	6.25932i	−0.158485	+	0.198734i
$993$	−1.82991	−	8.01735i	−0.0580704	−	0.254423i
$994$	−10.3579	−	21.5085i	−0.328534	−	0.682208i
$995$	−5.82561	+	2.80547i	−0.184684	+	0.0889393i
$996$	2.80935	+	0.641216i	0.0890177	+	0.0203177i
$997$	−10.0271	+	20.8215i	−0.317562	+	0.659424i	−0.997253	−	0.0740747i	$-0.976400\pi$
$997$	−10.0271	+	20.8215i	−0.317562	+	0.659424i	0.679691	+	0.733499i	$0.262114\pi$
$998$			21.1341i			0.668988i
$999$	49.1885	+	23.6879i	1.55626	+	0.749453i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.2.e.a.5.2	✓	12
3.2	odd	2		261.2.o.a.208.1		12
4.3	odd	2		464.2.y.d.353.2		12
5.2	odd	4		725.2.p.a.324.4		24
5.3	odd	4		725.2.p.a.324.1		24
5.4	even	2		725.2.q.a.701.1		12
29.2	odd	28		841.2.d.k.571.4		24
29.3	odd	28		841.2.d.k.190.4		24
29.4	even	14		841.2.e.h.196.2		12
29.5	even	14		841.2.e.f.270.1		12
29.6	even	14	inner	29.2.e.a.6.2	yes	12
29.7	even	7		841.2.e.f.651.1		12
29.8	odd	28		841.2.a.k.1.10		12
29.9	even	14		841.2.b.e.840.10		12
29.10	odd	28		841.2.d.l.645.1		24
29.11	odd	28		841.2.d.l.605.4		24
29.12	odd	4		841.2.d.m.778.4		24
29.13	even	14		841.2.e.a.236.1		12
29.14	odd	28		841.2.d.m.574.1		24
29.15	odd	28		841.2.d.m.574.4		24
29.16	even	7		841.2.e.h.236.2		12
29.17	odd	4		841.2.d.m.778.1		24
29.18	odd	28		841.2.d.l.605.1		24
29.19	odd	28		841.2.d.l.645.4		24
29.20	even	7		841.2.b.e.840.3		12
29.21	odd	28		841.2.a.k.1.3		12
29.22	even	14		841.2.e.e.651.2		12
29.23	even	7		841.2.e.i.267.1		12
29.24	even	7		841.2.e.e.270.2		12
29.25	even	7		841.2.e.a.196.1		12
29.26	odd	28		841.2.d.k.190.1		24
29.27	odd	28		841.2.d.k.571.1		24
29.28	even	2		841.2.e.i.63.1		12
87.8	even	28		7569.2.a.bp.1.3		12
87.35	odd	14		261.2.o.a.64.1		12
87.50	even	28		7569.2.a.bp.1.10		12
116.35	odd	14		464.2.y.d.209.2		12
145.64	even	14		725.2.q.a.151.1		12
145.93	odd	28		725.2.p.a.499.4		24
145.122	odd	28		725.2.p.a.499.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.e.a.5.2	✓	12	1.1	even	1	trivial
29.2.e.a.6.2	yes	12	29.6	even	14	inner
261.2.o.a.64.1		12	87.35	odd	14
261.2.o.a.208.1		12	3.2	odd	2
464.2.y.d.209.2		12	116.35	odd	14
464.2.y.d.353.2		12	4.3	odd	2
725.2.p.a.324.1		24	5.3	odd	4
725.2.p.a.324.4		24	5.2	odd	4
725.2.p.a.499.1		24	145.122	odd	28
725.2.p.a.499.4		24	145.93	odd	28
725.2.q.a.151.1		12	145.64	even	14
725.2.q.a.701.1		12	5.4	even	2
841.2.a.k.1.3		12	29.21	odd	28
841.2.a.k.1.10		12	29.8	odd	28
841.2.b.e.840.3		12	29.20	even	7
841.2.b.e.840.10		12	29.9	even	14
841.2.d.k.190.1		24	29.26	odd	28
841.2.d.k.190.4		24	29.3	odd	28
841.2.d.k.571.1		24	29.27	odd	28
841.2.d.k.571.4		24	29.2	odd	28
841.2.d.l.605.1		24	29.18	odd	28
841.2.d.l.605.4		24	29.11	odd	28
841.2.d.l.645.1		24	29.10	odd	28
841.2.d.l.645.4		24	29.19	odd	28
841.2.d.m.574.1		24	29.14	odd	28
841.2.d.m.574.4		24	29.15	odd	28
841.2.d.m.778.1		24	29.17	odd	4
841.2.d.m.778.4		24	29.12	odd	4
841.2.e.a.196.1		12	29.25	even	7
841.2.e.a.236.1		12	29.13	even	14
841.2.e.e.270.2		12	29.24	even	7
841.2.e.e.651.2		12	29.22	even	14
841.2.e.f.270.1		12	29.5	even	14
841.2.e.f.651.1		12	29.7	even	7
841.2.e.h.196.2		12	29.4	even	14
841.2.e.h.236.2		12	29.16	even	7
841.2.e.i.63.1		12	29.28	even	2
841.2.e.i.267.1		12	29.23	even	7
7569.2.a.bp.1.3		12	87.8	even	28
7569.2.a.bp.1.10		12	87.50	even	28

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	29.e (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.21127 - 0.965958i) q^{2} +(-2.86109 + 0.653024i) q^{3} +(0.0890656 - 0.390222i) q^{4} +(0.283269 + 0.355208i) q^{5} +(-2.83476 + 3.55468i) q^{6} +(-0.759522 - 3.32768i) q^{7} +(1.07536 + 2.23300i) q^{8} +(5.05647 - 2.43507i) q^{9} +O(q^{10})\)	\(q+(1.21127 - 0.965958i) q^{2} +(-2.86109 + 0.653024i) q^{3} +(0.0890656 - 0.390222i) q^{4} +(0.283269 + 0.355208i) q^{5} +(-2.83476 + 3.55468i) q^{6} +(-0.759522 - 3.32768i) q^{7} +(1.07536 + 2.23300i) q^{8} +(5.05647 - 2.43507i) q^{9} +(0.686232 + 0.156628i) q^{10} +(-0.635522 + 1.31967i) q^{11} +1.17462i q^{12} +(-2.78085 - 1.33919i) q^{13} +(-4.13439 - 3.29707i) q^{14} +(-1.04242 - 0.831299i) q^{15} +(4.18077 + 2.01335i) q^{16} +2.82403i q^{17} +(3.77259 - 7.83387i) q^{18} +(2.23472 + 0.510059i) q^{19} +(0.163839 - 0.0789009i) q^{20} +(4.34612 + 9.02480i) q^{21} +(0.504960 + 2.21237i) q^{22} +(0.333001 - 0.417570i) q^{23} +(-4.53489 - 5.68657i) q^{24} +(1.06667 - 4.67340i) q^{25} +(-4.66197 + 1.06407i) q^{26} +(-5.99360 + 4.77973i) q^{27} -1.36618 q^{28} +(-3.83606 + 3.77951i) q^{29} -2.06565 q^{30} +(-2.80406 + 2.23616i) q^{31} +(2.17627 - 0.496719i) q^{32} +(0.956503 - 4.19071i) q^{33} +(2.72789 + 3.42067i) q^{34} +(0.966870 - 1.21242i) q^{35} +(-0.499859 - 2.19003i) q^{36} +(-3.08996 - 6.41637i) q^{37} +(3.19955 - 1.54082i) q^{38} +(8.83079 + 2.01557i) q^{39} +(-0.488564 + 1.01451i) q^{40} -4.43991i q^{41} +(13.9819 + 6.73333i) q^{42} +(3.22518 + 2.57200i) q^{43} +(0.458363 + 0.365532i) q^{44} +(2.29729 + 1.10632i) q^{45} -0.827457i q^{46} +(0.0778542 - 0.161666i) q^{47} +(-13.2763 - 3.03023i) q^{48} +(-4.18982 + 2.01771i) q^{49} +(-3.22228 - 6.69113i) q^{50} +(-1.84416 - 8.07978i) q^{51} +(-0.770259 + 0.965875i) q^{52} +(1.92383 + 2.41240i) q^{53} +(-2.64286 + 11.5791i) q^{54} +(-0.648782 + 0.148080i) q^{55} +(6.61396 - 5.27446i) q^{56} -6.72679 q^{57} +(-0.995668 + 8.28348i) q^{58} +13.2495 q^{59} +(-0.417234 + 0.332733i) q^{60} +(1.84068 - 0.420124i) q^{61} +(-1.23644 + 5.41721i) q^{62} +(-11.9436 - 14.9768i) q^{63} +(-3.63013 + 4.55204i) q^{64} +(-0.312039 - 1.36713i) q^{65} +(-2.88947 - 6.00004i) q^{66} +(-10.9658 + 5.28086i) q^{67} +(1.10200 + 0.251524i) q^{68} +(-0.680062 + 1.41216i) q^{69} -2.40252i q^{70} +(4.06735 + 1.95873i) q^{71} +(10.8750 + 8.67253i) q^{72} +(6.47043 + 5.16000i) q^{73} +(-9.94073 - 4.78720i) q^{74} +14.0676i q^{75} +(0.398073 - 0.826606i) q^{76} +(4.87415 + 1.11249i) q^{77} +(12.6435 - 6.08877i) q^{78} +(-6.00316 - 12.4657i) q^{79} +(0.469123 + 2.05536i) q^{80} +(3.52936 - 4.42568i) q^{81} +(-4.28877 - 5.37794i) q^{82} +(0.545892 - 2.39171i) q^{83} +(3.90876 - 0.892150i) q^{84} +(-1.00312 + 0.799958i) q^{85} +6.39102 q^{86} +(8.50718 - 13.3185i) q^{87} -3.63025 q^{88} +(-10.5483 + 8.41200i) q^{89} +(3.85131 - 0.879036i) q^{90} +(-2.34428 + 10.2709i) q^{91} +(-0.133286 - 0.167136i) q^{92} +(6.56239 - 8.22898i) q^{93} +(-0.0618598 - 0.271025i) q^{94} +(0.451848 + 0.938272i) q^{95} +(-5.90212 + 2.84231i) q^{96} +(4.58979 + 1.04759i) q^{97} +(-3.12599 + 6.49118i) q^{98} +8.22043i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 7 q^{2} - 7 q^{3} - q^{4} - q^{5} - 3 q^{6} - 11 q^{7} + 14 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q - 7 * q^2 - 7 * q^3 - q^4 - q^5 - 3 * q^6 - 11 * q^7 + 14 * q^8 - 3 * q^9	\( 12 q - 7 q^{2} - 7 q^{3} - q^{4} - q^{5} - 3 q^{6} - 11 q^{7} + 14 q^{8} - 3 q^{9} - 7 q^{10} + 7 q^{11} + 9 q^{13} - 7 q^{14} + 7 q^{15} + 9 q^{16} + 42 q^{18} - 7 q^{19} - 11 q^{20} - 7 q^{21} - 4 q^{22} - 5 q^{23} - 25 q^{24} + 13 q^{25} - 21 q^{26} - 7 q^{27} + 12 q^{28} - 15 q^{29} + 2 q^{30} - 21 q^{31} - 17 q^{33} - 13 q^{34} + 19 q^{35} - 40 q^{36} + 7 q^{37} + 28 q^{38} + 21 q^{39} + 35 q^{40} + 50 q^{42} + 7 q^{43} + 42 q^{44} + 16 q^{45} - 7 q^{47} - 14 q^{48} + 13 q^{49} - 28 q^{50} + 20 q^{51} - 6 q^{52} - 10 q^{53} - 38 q^{54} - 35 q^{55} - 21 q^{56} - 14 q^{57} - 57 q^{58} + 44 q^{59} - 28 q^{60} - 7 q^{61} + 37 q^{62} - 13 q^{63} - 26 q^{64} - 6 q^{65} + 21 q^{66} - 37 q^{67} + 14 q^{68} + 21 q^{69} - 21 q^{71} + 35 q^{72} + 14 q^{73} + 7 q^{76} - 7 q^{77} + 17 q^{78} + 49 q^{79} - 6 q^{80} + q^{81} + 22 q^{82} + 5 q^{83} + 21 q^{84} + 14 q^{85} - 44 q^{86} + 15 q^{87} - 66 q^{88} + 7 q^{89} + 28 q^{90} - 3 q^{91} - 6 q^{92} + 19 q^{93} + 66 q^{94} - 7 q^{95} + 30 q^{96} + 14 q^{97} - 42 q^{98}+O(q^{100}) \) 12 * q - 7 * q^2 - 7 * q^3 - q^4 - q^5 - 3 * q^6 - 11 * q^7 + 14 * q^8 - 3 * q^9 - 7 * q^10 + 7 * q^11 + 9 * q^13 - 7 * q^14 + 7 * q^15 + 9 * q^16 + 42 * q^18 - 7 * q^19 - 11 * q^20 - 7 * q^21 - 4 * q^22 - 5 * q^23 - 25 * q^24 + 13 * q^25 - 21 * q^26 - 7 * q^27 + 12 * q^28 - 15 * q^29 + 2 * q^30 - 21 * q^31 - 17 * q^33 - 13 * q^34 + 19 * q^35 - 40 * q^36 + 7 * q^37 + 28 * q^38 + 21 * q^39 + 35 * q^40 + 50 * q^42 + 7 * q^43 + 42 * q^44 + 16 * q^45 - 7 * q^47 - 14 * q^48 + 13 * q^49 - 28 * q^50 + 20 * q^51 - 6 * q^52 - 10 * q^53 - 38 * q^54 - 35 * q^55 - 21 * q^56 - 14 * q^57 - 57 * q^58 + 44 * q^59 - 28 * q^60 - 7 * q^61 + 37 * q^62 - 13 * q^63 - 26 * q^64 - 6 * q^65 + 21 * q^66 - 37 * q^67 + 14 * q^68 + 21 * q^69 - 21 * q^71 + 35 * q^72 + 14 * q^73 + 7 * q^76 - 7 * q^77 + 17 * q^78 + 49 * q^79 - 6 * q^80 + q^81 + 22 * q^82 + 5 * q^83 + 21 * q^84 + 14 * q^85 - 44 * q^86 + 15 * q^87 - 66 * q^88 + 7 * q^89 + 28 * q^90 - 3 * q^91 - 6 * q^92 + 19 * q^93 + 66 * q^94 - 7 * q^95 + 30 * q^96 + 14 * q^97 - 42 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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