LMFDB - Embedded newform 29.2.e.a.6.2

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			6.2
Root			$-1.41140 - 0.0891373i$ of defining polynomial
Character	$\chi$	$=$	29.6
Dual form			29.2.e.a.5.2

$q$-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 $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{14}\right)$

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	0.949887	−	0.312594i	$-0.101198\pi$
$2$	1.21127	+	0.965958i	0.856499	+	0.683035i	−0.0933873	+	0.995630i	$0.529769\pi$
$3$	−2.86109	−	0.653024i	−1.65185	−	0.377024i	−0.707692	−	0.706521i	$-0.750264\pi$
$3$	−2.86109	−	0.653024i	−1.65185	−	0.377024i	−0.944157	+	0.329497i	$0.893121\pi$
$4$	0.0890656	+	0.390222i	0.0445328	+	0.195111i
$5$	0.283269	−	0.355208i	0.126682	−	0.158854i	−0.714446	−	0.699691i	$-0.753321\pi$
$5$	0.283269	−	0.355208i	0.126682	−	0.158854i	0.841127	+	0.540837i	$0.181892\pi$
$6$	−2.83476	−	3.55468i	−1.15729	−	1.45119i
$7$	−0.759522	+	3.32768i	−0.287072	+	1.25775i	0.601449	+	0.798911i	$0.294590\pi$
$7$	−0.759522	+	3.32768i	−0.287072	+	1.25775i	−0.888522	+	0.458835i	$0.848267\pi$
$8$	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	0.782920	−	0.622122i	$-0.213729\pi$
$11$	−0.635522	−	1.31967i	−0.191617	−	0.397897i	−0.974537	+	0.224225i	$0.928015\pi$
$12$		−	1.17462i		−	0.339084i
$13$	−2.78085	+	1.33919i	−0.771270	+	0.371424i	−0.777765	−	0.628555i	$-0.783647\pi$
$13$	−2.78085	+	1.33919i	−0.771270	+	0.371424i	0.00649509	+	0.999979i	$0.497933\pi$
$14$	−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	$-0.888739\pi$
$17$		−	2.82403i		−	0.684927i	0.939531	−	0.342463i	$-0.111261\pi$
$18$	3.77259	+	7.83387i	0.889208	+	1.84646i
$19$	2.23472	−	0.510059i	0.512679	−	0.117016i	0.0416480	−	0.999132i	$-0.486739\pi$
$19$	2.23472	−	0.510059i	0.512679	−	0.117016i	0.471031	+	0.882117i	$0.343882\pi$
$20$	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	0.815336	−	0.578988i	$-0.196552\pi$
$23$	0.333001	+	0.417570i	0.0694356	+	0.0870695i	−0.745901	+	0.666057i	$0.767981\pi$
$24$	−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	0.338453	−	0.940983i	$-0.390096\pi$
$31$	−2.80406	−	2.23616i	−0.503624	−	0.401627i	−0.842078	+	0.539356i	$0.818668\pi$
$32$	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	0.476466	+	0.879193i	$0.341918\pi$
$37$	−3.08996	+	6.41637i	−0.507987	+	1.05484i	−0.984452	+	0.175652i	$0.943797\pi$
$38$	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	$0.112697\pi$
$41$			4.43991i			0.693398i	−0.937977	+	0.346699i	$0.887303\pi$
$42$	13.9819	−	6.73333i	2.15746	−	1.03898i
$43$	3.22518	−	2.57200i	0.491836	−	0.392226i	−0.345926	−	0.938262i	$-0.612435\pi$
$43$	3.22518	−	2.57200i	0.491836	−	0.392226i	0.837762	+	0.546036i	$0.183864\pi$
$44$	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	0.906570	−	0.422056i	$-0.138691\pi$
$47$	0.0778542	+	0.161666i	0.0113562	+	0.0235814i	−0.895214	+	0.445637i	$0.852977\pi$
$48$	−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	−0.631945	−	0.775013i	$-0.717743\pi$
$53$	1.92383	−	2.41240i	0.264258	−	0.331369i	0.896203	+	0.443644i	$0.146315\pi$
$54$	−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	0.338727	−	0.940885i	$-0.390004\pi$
$61$	1.84068	+	0.420124i	0.235675	+	0.0537913i	−0.103052	+	0.994676i	$0.532861\pi$
$62$	−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	−0.379676	−	0.925119i	$-0.623965\pi$
$67$	−10.9658	−	5.28086i	−1.33969	−	0.645160i	−0.960012	+	0.279960i	$0.909679\pi$
$68$	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	−0.176673	−	0.984270i	$-0.556534\pi$
$71$	4.06735	−	1.95873i	0.482706	−	0.232459i	0.659379	+	0.751811i	$0.270819\pi$
$72$	10.8750	−	8.67253i	1.28163	−	1.02207i
$73$	6.47043	−	5.16000i	0.757307	−	0.603932i	−0.166833	−	0.985985i	$-0.553354\pi$
$73$	6.47043	−	5.16000i	0.757307	−	0.603932i	0.924140	+	0.382053i	$0.124783\pi$
$74$	−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	0.227976	+	0.973667i	$0.426789\pi$
$79$	−6.00316	+	12.4657i	−0.675408	+	1.40250i	−0.903384	+	0.428832i	$0.858925\pi$
$80$	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	0.996011	−	0.0892328i	$-0.0284415\pi$
$83$	0.545892	+	2.39171i	0.0599194	+	0.262524i	−0.936091	+	0.351757i	$0.885584\pi$
$84$	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	−0.123204	−	0.992381i	$-0.539317\pi$
$89$	−10.5483	−	8.41200i	−1.11812	−	0.891671i	−0.994916	+	0.100711i	$0.967888\pi$
$90$	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	0.0169394	−	0.999857i	$-0.494608\pi$
$97$	4.58979	−	1.04759i	0.466023	−	0.106367i	0.449083	+	0.893490i	$0.351751\pi$
$98$	−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	−0.992141	−	0.125128i	$-0.960066\pi$
$101$	−10.9636	+	8.74320i	−1.09092	+	0.869981i	−0.0987809	+	0.995109i	$0.531494\pi$
$102$	−10.0385	+	8.00544i	−0.993961	+	0.792657i
$103$	7.75475	−	3.73449i	0.764099	−	0.367970i	−0.0108941	−	0.999941i	$-0.503468\pi$
$103$	7.75475	−	3.73449i	0.764099	−	0.367970i	0.774993	+	0.631970i	$0.217753\pi$
$104$			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	0.196613	−	0.980481i	$-0.437006\pi$
$107$	−4.62766	−	2.22856i	−0.447373	−	0.215443i	−0.643985	+	0.765038i	$0.722720\pi$
$108$	1.33133	−	2.76454i	0.128108	−	0.266018i
$109$	1.31423	−	5.75801i	0.125880	−	0.551518i	−0.872176	−	0.489193i	$-0.837291\pi$
$109$	1.31423	−	5.75801i	0.125880	−	0.551518i	0.998056	−	0.0623247i	$-0.0198514\pi$
$110$	−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	−0.345074	−	0.938576i	$-0.612146\pi$
$113$	−11.3020	−	2.57962i	−1.06321	−	0.242670i	−0.718133	+	0.695906i	$0.755003\pi$
$114$	−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	0.932203	+	0.361935i	$0.117884\pi$
$127$	7.14432	+	14.8353i	0.633956	+	1.31642i	−0.298247	+	0.954489i	$0.596402\pi$
$128$		−	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	−0.920525	−	0.390683i	$-0.872239\pi$
$131$	−8.52089	+	6.79518i	−0.744473	+	0.593698i	0.176052	+	0.984381i	$0.443667\pi$
$132$	−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	−0.573862	−	0.818952i	$-0.694556\pi$
$137$	4.96534	−	10.3106i	0.424217	−	0.880896i	0.998080	−	0.0619445i	$-0.0197302\pi$
$138$	0.540350	−	2.36743i	0.0459976	−	0.201529i
$139$	11.9086	+	14.9330i	1.01008	+	1.26660i	0.963507	+	0.267683i	$0.0862580\pi$
$139$	11.9086	+	14.9330i	1.01008	+	1.26660i	0.0465713	+	0.998915i	$0.485171\pi$
$140$	−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	0.403330	+	0.915054i	$0.367853\pi$
$149$	5.33389	+	23.3693i	0.436970	+	1.91449i	0.0336393	+	0.999434i	$0.489290\pi$
$150$	13.5887	−	17.0397i	1.10951	−	1.39128i
$151$	−5.05137	−	6.33421i	−0.411074	−	0.515471i	0.532591	−	0.846373i	$-0.321218\pi$
$151$	−5.05137	−	6.33421i	−0.411074	−	0.515471i	−0.943665	+	0.330902i	$0.892647\pi$
$152$	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	$0.0466811\pi$
$157$			3.66196i			0.292256i	−0.989266	+	0.146128i	$0.953319\pi$
$158$	−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	−0.948777	−	0.315948i	$-0.897678\pi$
$163$	−7.71445	−	16.0192i	−0.604242	−	1.25472i	0.344535	−	0.938774i	$-0.388037\pi$
$164$	−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	−0.793523	−	0.608540i	$-0.791756\pi$
$167$	2.39657	−	10.5000i	0.185452	−	0.812518i	0.978975	−	0.203978i	$-0.0653873\pi$
$168$	−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	−0.940608	−	0.339496i	$-0.889744\pi$
$179$	−5.35590	+	6.71609i	−0.400319	+	0.501984i	0.540289	+	0.841480i	$0.318315\pi$
$180$	0.636320	+	0.797920i	0.0474285	+	0.0594734i
$181$	−2.07216	+	9.07873i	−0.154022	+	0.674817i	0.837669	+	0.546178i	$0.183918\pi$
$181$	−2.07216	+	9.07873i	−0.154022	+	0.674817i	−0.991692	+	0.128638i	$0.958939\pi$
$182$	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	$0.148355\pi$
$191$			12.4211i			0.898759i	−0.893341	+	0.449379i	$0.851645\pi$
$192$	7.41352	+	15.3943i	0.535025	+	1.11099i
$193$	19.6240	−	4.47904i	1.41256	−	0.322408i	0.552891	−	0.833254i	$-0.313525\pi$
$193$	19.6240	−	4.47904i	1.41256	−	0.322408i	0.859673	+	0.510845i	$0.170667\pi$
$194$	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	0.548755	−	0.835983i	$-0.315102\pi$
$197$	−5.45115	−	6.83552i	−0.388378	−	0.487011i	−0.937133	+	0.348973i	$0.886531\pi$
$198$	7.94059	−	9.95718i	0.564313	−	0.707626i
$199$	−3.16689	−	13.8751i	−0.224495	−	0.983577i	−0.954048	−	0.299653i	$-0.903129\pi$
$199$	−3.16689	−	13.8751i	−0.224495	−	0.983577i	0.729553	−	0.683924i	$-0.239728\pi$
$200$	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	−0.912687	−	0.408659i	$-0.865997\pi$
$211$	−0.350565	+	0.727955i	−0.0241339	+	0.0501145i	0.888553	+	0.458773i	$0.151711\pi$
$212$	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	0.0570436	−	0.998372i	$-0.481833\pi$
$223$	−10.2733	−	4.94734i	−0.687949	−	0.331299i	−0.744992	+	0.667073i	$0.767547\pi$
$224$	−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	0.218010	+	0.975947i	$0.430044\pi$
$227$	−11.7817	+	14.7738i	−0.781980	+	0.980571i	−0.999989	+	0.00462481i	$0.998528\pi$
$228$	−0.599126	−	2.62494i	−0.0396781	−	0.173841i
$229$	23.8163	+	5.43593i	1.57383	+	0.359216i	0.918278	−	0.395935i	$-0.129580\pi$
$229$	23.8163	+	5.43593i	1.57383	+	0.359216i	0.655550	+	0.755152i	$0.272437\pi$
$230$	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	−0.904546	−	0.426377i	$-0.859790\pi$
$239$	1.47515	−	6.46307i	0.0954197	−	0.418061i	0.999965	+	0.00831561i	$0.00264697\pi$
$240$	−2.68441	+	5.57423i	−0.173278	+	0.359815i
$241$	−1.02548	−	0.493845i	−0.0660569	−	0.0318113i	0.400564	−	0.916269i	$-0.368814\pi$
$241$	−1.02548	−	0.493845i	−0.0660569	−	0.0318113i	−0.466621	+	0.884458i	$0.654529\pi$
$242$	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	−0.933854	−	0.357654i	$-0.883577\pi$
$251$	−25.6664	+	5.85818i	−1.62005	+	0.369765i	−0.686193	+	0.727420i	$0.740719\pi$
$252$	−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	−0.940430	−	0.339986i	$-0.889578\pi$
$257$	−3.85785	−	16.9024i	−0.240646	−	1.05434i	0.699784	−	0.714354i	$-0.253280\pi$
$258$	−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	0.737113	−	0.675770i	$-0.236189\pi$
$263$	3.92959	+	3.13374i	0.242309	+	0.193235i	−0.494804	+	0.869005i	$0.664760\pi$
$264$	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	−0.381772	−	0.924257i	$-0.624686\pi$
$269$	9.49420	−	19.7149i	0.578872	−	1.20204i	0.960644	−	0.277783i	$-0.0895997\pi$
$270$	−4.86164	−	2.34124i	−0.295870	−	0.142483i
$271$	7.60881	−	1.73666i	0.462202	−	0.105495i	0.0149223	−	0.999889i	$-0.495250\pi$
$271$	7.60881	−	1.73666i	0.462202	−	0.105495i	0.447280	+	0.894394i	$0.352393\pi$
$272$	−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	−0.482310	−	0.876000i	$-0.660202\pi$
$277$	−1.63340	+	0.786604i	−0.0981414	+	0.0472624i	0.384169	+	0.923263i	$0.374488\pi$
$278$			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	0.0570809	−	0.998370i	$-0.481821\pi$
$281$	−11.5311	−	5.55308i	−0.687887	−	0.331269i	−0.744967	+	0.667101i	$0.767535\pi$
$282$	0.353972	−	0.735031i	0.0210788	−	0.0437705i
$283$	4.54554	−	19.9153i	0.270204	−	1.18384i	−0.639568	−	0.768735i	$-0.720887\pi$
$283$	4.54554	−	19.9153i	0.270204	−	1.18384i	0.909772	−	0.415108i	$-0.136256\pi$
$284$	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	0.395092	−	0.918642i	$-0.370713\pi$
$293$	6.03337	+	1.37708i	0.352473	+	0.0804497i	−0.0426185	+	0.999091i	$0.513570\pi$
$294$	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	$-0.971440\pi$
$307$		−	3.13998i		−	0.179208i	0.995977	−	0.0896041i	$-0.0285602\pi$
$308$	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	−0.793583	−	0.608462i	$-0.791787\pi$
$311$	3.12006	−	6.47888i	0.176923	−	0.367384i	0.970506	+	0.241078i	$0.0775011\pi$
$312$	4.99548	−	21.8866i	0.282813	−	1.23909i
$313$	−1.29502	−	1.62390i	−0.0731988	−	0.0917884i	0.743884	−	0.668309i	$-0.232982\pi$
$313$	−1.29502	−	1.62390i	−0.0731988	−	0.0917884i	−0.817083	+	0.576520i	$0.804410\pi$
$314$	−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	0.478004	−	0.878358i	$-0.341360\pi$
$317$	−4.84220	−	3.86153i	−0.271965	−	0.216885i	−0.749969	+	0.661473i	$0.769932\pi$
$318$	−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	$-0.975462\pi$
$331$		−	2.80221i		−	0.154023i	0.997030	−	0.0770116i	$-0.0245378\pi$
$332$	−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	0.994557	+	0.104198i	$0.0332277\pi$
$337$	8.36969	+	17.3798i	0.455926	+	0.946740i	−0.538630	+	0.842542i	$0.681058\pi$
$338$	−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	0.129338	+	0.991601i	$0.458715\pi$
$353$	−16.2741	+	20.4071i	−0.866182	+	1.08616i	−0.995519	+	0.0945571i	$0.969857\pi$
$354$	−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	0.954964	−	0.296721i	$-0.0958931\pi$
$359$	2.41707	+	5.01910i	0.127568	+	0.264898i	−0.827396	+	0.561619i	$0.810179\pi$
$360$		−	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	−0.349444	−	0.936957i	$-0.613630\pi$
$367$	−4.93781	+	1.12702i	−0.257752	+	0.0588302i	0.0916923	+	0.995787i	$0.470772\pi$
$368$	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	0.977532	−	0.210789i	$-0.0676033\pi$
$373$	0.103290	+	0.452543i	0.00534815	+	0.0234318i	−0.972183	+	0.234221i	$0.924746\pi$
$374$	−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	0.574898	−	0.818225i	$-0.305042\pi$
$379$	−1.84723	−	1.47312i	−0.0948858	−	0.0756689i	−0.669784	+	0.742556i	$0.733613\pi$
$380$	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	−0.999862	−	0.0166410i	$-0.994703\pi$
$383$	−15.5310	−	19.4752i	−0.793595	−	0.995137i	0.206266	−	0.978496i	$-0.433869\pi$
$384$	−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	$-0.901268\pi$
$389$		−	12.0401i		−	0.610455i	0.952279	−	0.305227i	$-0.0987325\pi$
$390$	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	0.917331	−	0.398126i	$-0.130339\pi$
$397$	23.4717	+	11.3034i	1.17801	+	0.567300i	0.260679	+	0.965425i	$0.416053\pi$
$398$	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	−0.138961	−	0.990298i	$-0.544376\pi$
$401$	17.1700	−	21.5305i	0.857429	−	1.07518i	0.996391	−	0.0848846i	$-0.0270522\pi$
$402$	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	−0.231884	−	0.972743i	$-0.574489\pi$
$409$	−17.4503	−	3.98292i	−0.862862	−	0.196943i	−0.630978	+	0.775801i	$0.717346\pi$
$410$	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	−0.492536	−	0.870292i	$-0.663930\pi$
$419$	−2.44008	+	1.17508i	−0.119206	+	0.0574064i	0.373330	+	0.927698i	$0.378216\pi$
$420$	1.42413	−	1.13571i	0.0694904	−	0.0554168i
$421$	−10.8912	+	8.68543i	−0.530804	+	0.423302i	−0.851869	−	0.523755i	$-0.824531\pi$
$421$	−10.8912	+	8.68543i	−0.530804	+	0.423302i	0.321065	+	0.947057i	$0.395959\pi$
$422$	−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	−0.995266	−	0.0971837i	$-0.969017\pi$
$431$	−2.92161	−	12.8004i	−0.140729	−	0.616573i	0.854538	−	0.519389i	$-0.173841\pi$
$432$	−34.6812	−	7.91575i	−1.66860	−	0.380847i
$433$	4.40985	+	3.51674i	0.211924	+	0.169004i	0.723699	−	0.690116i	$-0.242440\pi$
$433$	4.40985	+	3.51674i	0.211924	+	0.169004i	−0.511775	+	0.859120i	$0.671012\pi$
$434$	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	0.923241	+	0.384220i	$0.125530\pi$
$439$	5.40856	+	23.6965i	0.258137	+	1.13097i	−0.665105	+	0.746750i	$0.731613\pi$
$440$	−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	−0.982779	−	0.184783i	$-0.940842\pi$
$443$	−4.74743	+	9.85815i	−0.225557	+	0.468375i	0.757222	+	0.653158i	$0.226556\pi$
$444$	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	−0.667632	−	0.744491i	$-0.732692\pi$
$449$	−1.91489	+	1.52708i	−0.0903693	+	0.0720671i	0.577263	+	0.816558i	$0.304121\pi$
$450$	−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	0.747653	+	0.664089i	$0.231181\pi$
$457$	−4.57686	+	20.0525i	−0.214097	+	0.938018i	−0.961750	+	0.273929i	$0.911677\pi$
$458$	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	−0.178311	−	0.983974i	$-0.557063\pi$
$461$	−16.4445	−	3.75334i	−0.765895	−	0.174811i	−0.587583	+	0.809164i	$0.699921\pi$
$462$	−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	0.752481	−	0.658614i	$-0.228857\pi$
$467$	24.7368	+	5.64601i	1.14468	+	0.261266i	0.392200	+	0.919880i	$0.371714\pi$
$468$	−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	−0.311997	−	0.950083i	$-0.600998\pi$
$479$	11.9244	−	9.50940i	0.544840	−	0.434495i	0.856837	+	0.515588i	$0.172426\pi$
$480$	−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	0.774300	−	0.632819i	$-0.218102\pi$
$487$	−0.329948	−	0.413741i	−0.0149514	−	0.0187484i	−0.789251	+	0.614071i	$0.789531\pi$
$488$	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	0.224455	−	0.974484i	$-0.427940\pi$
$491$	−14.9714	−	11.9393i	−0.675651	−	0.538813i	−0.900106	+	0.435671i	$0.856511\pi$
$492$	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	0.554123	−	0.832435i	$-0.313054\pi$
$499$	−8.50519	−	10.6652i	−0.380745	−	0.477439i	−0.934868	+	0.354996i	$0.884482\pi$
$500$	−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	−0.989990	−	0.141135i	$-0.954925\pi$
$503$	−40.8341	+	9.32013i	−1.82070	+	0.415564i	−0.830714	+	0.556699i	$0.812068\pi$
$504$	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	−0.380122	−	0.924936i	$-0.624118\pi$
$509$	2.39191	−	1.15189i	0.106020	−	0.0510564i	0.486142	+	0.873880i	$0.338404\pi$
$510$			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	−0.672136	−	0.740428i	$-0.734623\pi$
$541$	−22.2465	+	5.07761i	−0.956450	+	0.218304i	−0.284314	+	0.958731i	$0.591766\pi$
$542$	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	−0.990500	−	0.137510i	$-0.956090\pi$
$547$	−3.68955	−	16.1650i	−0.157754	−	0.691164i	0.832747	−	0.553654i	$-0.186767\pi$
$548$	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	0.920432	+	0.390903i	$0.127837\pi$
$557$	25.8835	+	32.4569i	1.09672	+	1.37524i	0.176287	+	0.984339i	$0.443591\pi$
$558$	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	$0.183591\pi$
$563$			25.8782i			1.09064i	−0.838229	+	0.545318i	$0.816409\pi$
$564$	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	0.829268	−	0.558852i	$-0.188758\pi$
$569$	−2.97456	−	6.17675i	−0.124700	−	0.258943i	−0.953968	+	0.299909i	$0.903044\pi$
$570$	−4.61614	+	1.05360i	−0.193349	+	0.0441306i
$571$	22.3415	+	10.7591i	0.934962	+	0.450254i	0.838389	−	0.545072i	$-0.183498\pi$
$571$	22.3415	+	10.7591i	0.934962	+	0.450254i	0.0965729	+	0.995326i	$0.469212\pi$
$572$	−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	−0.728916	−	0.684604i	$-0.759975\pi$
$577$	−40.4195	−	9.22548i	−1.68268	−	0.384062i	−0.953769	+	0.300542i	$0.902832\pi$
$578$	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	−0.999304	−	0.0373002i	$-0.988124\pi$
$587$	−2.00556	+	8.78692i	−0.0827782	+	0.362675i	0.916526	+	0.399975i	$0.130981\pi$
$588$	−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	−0.356333	−	0.934359i	$-0.615973\pi$
$593$	3.70166	−	1.78263i	0.152009	−	0.0732037i	0.508342	+	0.861155i	$0.330259\pi$
$594$	−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	0.800924	−	0.598766i	$-0.204342\pi$
$599$	43.6215	−	9.95632i	1.78233	−	0.406804i	0.981402	+	0.191962i	$0.0614850\pi$
$600$	−31.4129	−	15.1276i	−1.28243	−	0.617584i
$601$	1.92305	−	3.99326i	0.0784429	−	0.162888i	−0.858059	−	0.513552i	$-0.828330\pi$
$601$	1.92305	−	3.99326i	0.0784429	−	0.162888i	0.936502	+	0.350663i	$0.114044\pi$
$602$	−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	0.787520	−	0.616289i	$-0.211365\pi$
$607$	8.91682	+	7.11093i	0.361923	+	0.288624i	−0.425597	+	0.904913i	$0.639936\pi$
$608$	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	0.893484	+	0.449095i	$0.148253\pi$
$613$	7.01511	+	30.7352i	0.283338	+	1.24138i	−0.610146	+	0.792289i	$0.708889\pi$
$614$	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	−0.926861	−	0.375406i	$-0.877503\pi$
$617$	−1.37781	+	2.86105i	−0.0554685	+	0.115181i	0.871392	+	0.490587i	$0.163218\pi$
$618$	−35.2578	−	16.9793i	−1.41828	−	0.683006i
$619$	20.3526	−	4.64536i	0.818042	−	0.186713i	0.207030	−	0.978335i	$-0.433620\pi$
$619$	20.3526	−	4.64536i	0.818042	−	0.186713i	0.611011	+	0.791622i	$0.290763\pi$
$620$	−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	0.460314	+	0.887756i	$0.347737\pi$
$631$	−8.53059	+	37.3750i	−0.339597	+	1.48787i	−0.799912	+	0.600118i	$0.795120\pi$
$632$	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	0.0915256	−	0.995803i	$-0.470826\pi$
$641$	−6.53394	−	1.49133i	−0.258075	−	0.0589040i	−0.349601	+	0.936899i	$0.613683\pi$
$642$	5.19649	+	22.7673i	0.205089	+	0.898553i
$643$	8.38577	−	10.5154i	0.330702	−	0.414688i	−0.588485	−	0.808508i	$-0.700275\pi$
$643$	8.38577	−	10.5154i	0.330702	−	0.414688i	0.919187	+	0.393820i	$0.128847\pi$
$644$	−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	0.734099	−	0.679042i	$-0.237605\pi$
$647$	16.8109	+	8.09572i	0.660906	+	0.318276i	−0.0731932	+	0.997318i	$0.523319\pi$
$648$	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	−0.124148	−	0.992264i	$-0.539620\pi$
$653$	20.8420	−	16.6210i	0.815612	−	0.650429i	0.939760	+	0.341835i	$0.111048\pi$
$654$	−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	0.527243	+	0.849715i	$0.323226\pi$
$659$	−11.9581	+	24.8312i	−0.465821	+	0.967288i	−0.993064	+	0.117573i	$0.962489\pi$
$660$	−0.173938	+	0.762073i	−0.00677053	+	0.0296636i
$661$	−17.5288	−	21.9804i	−0.681792	−	0.854940i	0.313726	−	0.949514i	$-0.398423\pi$
$661$	−17.5288	−	21.9804i	−0.681792	−	0.854940i	−0.995518	+	0.0945737i	$0.969851\pi$
$662$	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	0.923495	−	0.383611i	$-0.125320\pi$
$673$	8.92427	+	11.1907i	0.344005	+	0.431369i	−0.579490	+	0.814980i	$0.696748\pi$
$674$	−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	−0.828611	−	0.559826i	$-0.810868\pi$
$677$	−34.6645	+	7.91194i	−1.33226	+	0.304080i	−0.503653	+	0.863906i	$0.668011\pi$
$678$	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	−0.502155	−	0.864778i	$-0.667459\pi$
$683$	−3.63615	+	1.75108i	−0.139133	+	0.0670031i	0.363022	+	0.931781i	$0.381745\pi$
$684$			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	−0.224300	−	0.974520i	$-0.572010\pi$
$691$	20.3907	−	25.5691i	0.775698	−	0.972695i	0.999998	+	0.00182516i	$0.000580967\pi$
$692$	−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	−0.532271	−	0.846574i	$-0.678661\pi$
$701$	10.8955	−	13.6626i	0.411519	−	0.516028i	0.943790	+	0.330546i	$0.107233\pi$
$702$	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	−0.344552	−	0.938767i	$-0.611969\pi$
$709$	4.64858	−	2.23864i	0.174581	−	0.0840739i	0.519133	+	0.854693i	$0.326255\pi$
$710$	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	0.469590	−	0.882885i	$-0.344402\pi$
$719$	−13.2905	−	16.6658i	−0.495653	−	0.621529i	−0.965243	+	0.261356i	$0.915830\pi$
$720$	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	0.410200	−	0.911996i	$-0.365459\pi$
$727$	−10.4522	−	8.33539i	−0.387652	−	0.309142i	−0.797852	+	0.602853i	$0.794030\pi$
$728$	−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	−0.972953	−	0.231003i	$-0.925799\pi$
$733$	−5.02821	+	10.4412i	−0.185721	+	0.385654i	0.787232	+	0.616657i	$0.211514\pi$
$734$	−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	−0.604798	−	0.796379i	$-0.706746\pi$
$739$	1.00676	−	0.802861i	0.0370341	−	0.0295337i	0.641832	+	0.766845i	$0.278175\pi$
$740$	−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	0.964668	−	0.263469i	$-0.0848667\pi$
$743$	4.28548	+	8.89888i	0.157219	+	0.326468i	−0.807449	+	0.589937i	$0.799152\pi$
$744$	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	0.590530	−	0.807015i	$-0.298919\pi$
$751$	21.1679	+	4.83144i	0.772429	+	0.176302i	0.181899	+	0.983317i	$0.441776\pi$
$752$	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	0.619888	−	0.784690i	$-0.287178\pi$
$757$	23.0543	+	5.26200i	0.837923	+	0.191251i	0.218035	+	0.975941i	$0.430035\pi$
$758$	−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	−0.178737	−	0.983897i	$-0.557201\pi$
$761$	11.2882	−	49.4568i	0.409196	−	1.79281i	0.587933	−	0.808910i	$-0.299942\pi$
$762$	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	−0.829527	−	0.558466i	$-0.811390\pi$
$769$	−13.0238	+	10.3861i	−0.469651	+	0.374534i	0.359877	+	0.933000i	$0.382819\pi$
$770$	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	−0.773121	−	0.634259i	$-0.781305\pi$
$773$	−33.2101	+	7.57999i	−1.19448	+	0.272633i	−0.421363	+	0.906892i	$0.638448\pi$
$774$	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	0.976471	−	0.215647i	$-0.0691860\pi$
$787$	0.0879573	+	0.385366i	0.00313534	+	0.0137368i	−0.973336	+	0.229384i	$0.926329\pi$
$788$	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	−0.940875	−	0.338755i	$-0.889994\pi$
$797$	−23.1489	+	18.4607i	−0.819978	+	0.653910i	0.120897	+	0.992665i	$0.461423\pi$
$798$	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	0.0664255	−	0.997791i	$-0.478841\pi$
$809$	−8.72210	−	1.99076i	−0.306653	−	0.0699915i	−0.373078	+	0.927800i	$0.621698\pi$
$810$	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	−0.599400	−	0.800450i	$-0.704594\pi$
$821$	−45.8145	−	22.0631i	−1.59894	−	0.770007i	−0.999537	+	0.0304427i	$0.990308\pi$
$822$	−50.7265	+	11.5780i	−1.76929	+	0.403829i
$823$	0.145552	+	0.302242i	0.00507362	+	0.0105355i	0.903490	−	0.428609i	$-0.140996\pi$
$823$	0.145552	+	0.302242i	0.00507362	+	0.0105355i	−0.898417	+	0.439144i	$0.855282\pi$
$824$		−	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	−0.214717	−	0.976676i	$-0.568883\pi$
$827$	19.8339	−	15.8170i	0.689693	−	0.550012i	0.904410	+	0.426664i	$0.140311\pi$
$828$	−1.08094	+	0.520555i	−0.0375654	+	0.0180905i
$829$		−	46.0845i		−	1.60058i	−0.599613	−	0.800290i	$-0.704679\pi$
$829$		−	46.0845i		−	1.60058i	0.599613	−	0.800290i	$-0.295321\pi$
$830$	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	0.167633	−	0.985850i	$-0.446388\pi$
$839$	−21.9036	−	17.4676i	−0.756198	−	0.603048i	−0.923830	+	0.382802i	$0.874959\pi$
$840$	−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	$-0.861390\pi$
$853$		−	24.6397i		−	0.843646i	0.906678	−	0.421823i	$-0.138610\pi$
$854$	−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	0.393409	−	0.919363i	$-0.371296\pi$
$857$	39.7397	−	19.1376i	1.35748	−	0.653729i	0.964074	+	0.265634i	$0.0855813\pi$
$858$		−	20.5548i		−	0.701729i
$859$	−3.63787	−	7.55411i	−0.124122	−	0.257743i	0.829643	−	0.558294i	$-0.188544\pi$
$859$	−3.63787	−	7.55411i	−0.124122	−	0.257743i	−0.953766	+	0.300551i	$0.902829\pi$
$860$	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	−0.597346	−	0.801984i	$-0.703778\pi$
$863$	8.48439	−	37.1725i	0.288812	−	1.26537i	0.886158	−	0.463384i	$-0.153365\pi$
$864$	−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	−0.795152	−	0.606410i	$-0.792609\pi$
$877$	5.45987	−	23.9212i	0.184367	−	0.807763i	0.979519	−	0.201353i	$-0.0645338\pi$
$878$	−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	0.797762	+	0.602973i	$0.206017\pi$
$881$	22.9079	+	47.5688i	0.771788	+	1.60264i	−0.0259735	+	0.999663i	$0.508269\pi$
$882$		−	40.4344i		−	1.36150i
$883$	−5.14964	+	2.47994i	−0.173299	+	0.0834565i	−0.518522	−	0.855064i	$-0.673518\pi$
$883$	−5.14964	+	2.47994i	−0.173299	+	0.0834565i	0.345223	+	0.938521i	$0.387803\pi$
$884$	−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	$0.194798\pi$
$887$			34.2192i			1.14897i	−0.818515	+	0.574485i	$0.805202\pi$
$888$	−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	−0.222711	−	0.974885i	$-0.571491\pi$
$907$	20.4293	−	42.4218i	0.678342	−	1.40859i	0.901053	−	0.433708i	$-0.142795\pi$
$908$	−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	$0.308154\pi$
$911$			49.7296i			1.64761i	−0.566870	+	0.823807i	$0.691846\pi$
$912$	−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	0.517136	−	0.855903i	$-0.326998\pi$
$919$	5.16544	+	2.48755i	0.170392	+	0.0820566i	−0.346743	+	0.937960i	$0.612713\pi$
$920$	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	0.657930	−	0.753079i	$-0.271432\pi$
$937$	14.6735	+	7.06636i	0.479361	+	0.230848i	−0.178569	+	0.983927i	$0.557147\pi$
$938$	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	0.179463	−	0.983765i	$-0.442564\pi$
$941$	32.5314	−	15.6663i	1.06049	−	0.510707i	0.881031	+	0.473058i	$0.156850\pi$
$942$	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	−0.0421251	−	0.999112i	$-0.513413\pi$
$947$	10.8759	−	2.48236i	0.353420	−	0.0806659i	0.395545	+	0.918446i	$0.370556\pi$
$948$	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	0.812766	+	0.582590i	$0.197961\pi$
$953$	10.2881	+	45.0753i	0.333266	+	1.46013i	−0.479500	+	0.877542i	$0.659182\pi$
$954$	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	0.428747	−	0.903425i	$-0.358955\pi$
$967$	37.5341	−	8.56691i	1.20702	−	0.275493i	0.778269	+	0.627931i	$0.216098\pi$
$968$	−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	0.178620	−	0.983918i	$-0.442837\pi$
$971$	36.6956	−	29.2637i	1.17762	−	0.939118i	0.998996	+	0.0448004i	$0.0142652\pi$
$972$	−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	−0.0258953	−	0.999665i	$-0.508244\pi$
$977$	−25.7436	−	12.3975i	−0.823610	−	0.396630i	−0.797715	+	0.603035i	$0.793958\pi$
$978$	−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	0.780107	−	0.625646i	$-0.215165\pi$
$983$	37.9840	+	8.66960i	1.21150	+	0.276517i	0.431395	+	0.902163i	$0.358022\pi$
$984$	−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	−0.778583	−	0.627541i	$-0.784061\pi$
$991$	0.203838	−	0.255604i	0.00647512	−	0.00811954i	0.785059	+	0.619422i	$0.212633\pi$
$992$	−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	0.679691	−	0.733499i	$-0.262114\pi$
$997$	−10.0271	−	20.8215i	−0.317562	−	0.659424i	−0.997253	+	0.0740747i	$0.976400\pi$
$998$		−	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.6.2	yes	12
3.2	odd	2		261.2.o.a.64.1		12
4.3	odd	2		464.2.y.d.209.2		12
5.2	odd	4		725.2.p.a.499.1		24
5.3	odd	4		725.2.p.a.499.4		24
5.4	even	2		725.2.q.a.151.1		12
29.2	odd	28		841.2.d.m.778.4		24
29.3	odd	28		841.2.d.l.605.1		24
29.4	even	14		841.2.e.e.270.2		12
29.5	even	14	inner	29.2.e.a.5.2	✓	12
29.6	even	14		841.2.e.f.651.1		12
29.7	even	7		841.2.e.a.236.1		12
29.8	odd	28		841.2.d.l.645.4		24
29.9	even	14		841.2.e.a.196.1		12
29.10	odd	28		841.2.d.k.571.4		24
29.11	odd	28		841.2.a.k.1.10		12
29.12	odd	4		841.2.d.m.574.1		24
29.13	even	14		841.2.b.e.840.3		12
29.14	odd	28		841.2.d.k.190.1		24
29.15	odd	28		841.2.d.k.190.4		24
29.16	even	7		841.2.b.e.840.10		12
29.17	odd	4		841.2.d.m.574.4		24
29.18	odd	28		841.2.a.k.1.3		12
29.19	odd	28		841.2.d.k.571.1		24
29.20	even	7		841.2.e.h.196.2		12
29.21	odd	28		841.2.d.l.645.1		24
29.22	even	14		841.2.e.h.236.2		12
29.23	even	7		841.2.e.e.651.2		12
29.24	even	7		841.2.e.i.63.1		12
29.25	even	7		841.2.e.f.270.1		12
29.26	odd	28		841.2.d.l.605.4		24
29.27	odd	28		841.2.d.m.778.1		24
29.28	even	2		841.2.e.i.267.1		12
87.5	odd	14		261.2.o.a.208.1		12
87.11	even	28		7569.2.a.bp.1.3		12
87.47	even	28		7569.2.a.bp.1.10		12
116.63	odd	14		464.2.y.d.353.2		12
145.34	even	14		725.2.q.a.701.1		12
145.63	odd	28		725.2.p.a.324.1		24
145.92	odd	28		725.2.p.a.324.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.e.a.5.2	✓	12	29.5	even	14	inner
29.2.e.a.6.2	yes	12	1.1	even	1	trivial
261.2.o.a.64.1		12	3.2	odd	2
261.2.o.a.208.1		12	87.5	odd	14
464.2.y.d.209.2		12	4.3	odd	2
464.2.y.d.353.2		12	116.63	odd	14
725.2.p.a.324.1		24	145.63	odd	28
725.2.p.a.324.4		24	145.92	odd	28
725.2.p.a.499.1		24	5.2	odd	4
725.2.p.a.499.4		24	5.3	odd	4
725.2.q.a.151.1		12	5.4	even	2
725.2.q.a.701.1		12	145.34	even	14
841.2.a.k.1.3		12	29.18	odd	28
841.2.a.k.1.10		12	29.11	odd	28
841.2.b.e.840.3		12	29.13	even	14
841.2.b.e.840.10		12	29.16	even	7
841.2.d.k.190.1		24	29.14	odd	28
841.2.d.k.190.4		24	29.15	odd	28
841.2.d.k.571.1		24	29.19	odd	28
841.2.d.k.571.4		24	29.10	odd	28
841.2.d.l.605.1		24	29.3	odd	28
841.2.d.l.605.4		24	29.26	odd	28
841.2.d.l.645.1		24	29.21	odd	28
841.2.d.l.645.4		24	29.8	odd	28
841.2.d.m.574.1		24	29.12	odd	4
841.2.d.m.574.4		24	29.17	odd	4
841.2.d.m.778.1		24	29.27	odd	28
841.2.d.m.778.4		24	29.2	odd	28
841.2.e.a.196.1		12	29.9	even	14
841.2.e.a.236.1		12	29.7	even	7
841.2.e.e.270.2		12	29.4	even	14
841.2.e.e.651.2		12	29.23	even	7
841.2.e.f.270.1		12	29.25	even	7
841.2.e.f.651.1		12	29.6	even	14
841.2.e.h.196.2		12	29.20	even	7
841.2.e.h.236.2		12	29.22	even	14
841.2.e.i.63.1		12	29.24	even	7
841.2.e.i.267.1		12	29.28	even	2
7569.2.a.bp.1.3		12	87.11	even	28
7569.2.a.bp.1.10		12	87.47	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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