LMFDB - Embedded newform 49.2.e.b.29.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,2,Mod(8,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([12]))

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

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

chi := DirichletCharacter("49.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	49.e (of order $7$, 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:	$0.391266969904$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{7})$
Coefficient field:	$\Q(\zeta_{21})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + x^{9} - x^{8} + x^{6} - x^{4} + x^{3} - x + 1 $ x^12 - x^11 + x^9 - x^8 + x^6 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			29.2
Root			$0.826239 - 0.563320i$ of defining polynomial
Character	$\chi$	$=$	49.29
Dual form			49.2.e.b.22.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.658322 + 0.317031i) q^{2} +(0.255779 + 1.12064i) q^{3} +(-0.914101 - 1.14625i) q^{4} +(-0.0575591 - 0.252183i) q^{5} +(-0.186893 + 0.818832i) q^{6} +(-2.16885 + 1.51528i) q^{7} +(-0.563561 - 2.46912i) q^{8} +(1.51249 - 0.728379i) q^{9} +O(q^{10})$	\(q+(0.658322 + 0.317031i) q^{2} +(0.255779 + 1.12064i) q^{3} +(-0.914101 - 1.14625i) q^{4} +(-0.0575591 - 0.252183i) q^{5} +(-0.186893 + 0.818832i) q^{6} +(-2.16885 + 1.51528i) q^{7} +(-0.563561 - 2.46912i) q^{8} +(1.51249 - 0.728379i) q^{9} +(0.0420574 - 0.184265i) q^{10} +(-3.38633 - 1.63077i) q^{11} +(1.05072 - 1.31756i) q^{12} +(2.38980 + 1.15087i) q^{13} +(-1.90819 + 0.309949i) q^{14} +(0.267884 - 0.129006i) q^{15} +(-0.240694 + 1.05455i) q^{16} +(-3.20407 + 4.01778i) q^{17} +1.22663 q^{18} +3.83757 q^{19} +(-0.236449 + 0.296497i) q^{20} +(-2.25283 - 2.04293i) q^{21} +(-1.71229 - 2.14714i) q^{22} +(0.752824 + 0.944011i) q^{23} +(2.62285 - 1.26310i) q^{24} +(4.44456 - 2.14039i) q^{25} +(1.20840 + 1.51528i) q^{26} +(3.35314 + 4.20471i) q^{27} +(3.71944 + 1.10092i) q^{28} +(0.581144 - 0.728732i) q^{29} +0.217253 q^{30} -4.29970 q^{31} +(-3.65090 + 4.57809i) q^{32} +(0.961355 - 4.21197i) q^{33} +(-3.38307 + 1.62920i) q^{34} +(0.506965 + 0.459729i) q^{35} +(-2.21747 - 1.06788i) q^{36} +(2.52543 - 3.16679i) q^{37} +(2.52636 + 1.21663i) q^{38} +(-0.678448 + 2.97247i) q^{39} +(-0.590232 + 0.284241i) q^{40} +(-1.90432 - 8.34336i) q^{41} +(-0.835418 - 2.05912i) q^{42} +(-1.08450 + 4.75152i) q^{43} +(1.22618 + 5.37225i) q^{44} +(-0.270742 - 0.339500i) q^{45} +(0.196319 + 0.860132i) q^{46} +(-10.7873 - 5.19488i) q^{47} -1.24333 q^{48} +(2.40784 - 6.57284i) q^{49} +3.60452 q^{50} +(-5.32202 - 2.56295i) q^{51} +(-0.865341 - 3.79131i) q^{52} +(-2.39053 - 2.99763i) q^{53} +(0.874424 + 3.83110i) q^{54} +(-0.216338 + 0.947838i) q^{55} +(4.96369 + 4.50121i) q^{56} +(0.981571 + 4.30054i) q^{57} +(0.613611 - 0.295499i) q^{58} +(1.19672 - 5.24319i) q^{59} +(-0.392746 - 0.189136i) q^{60} +(-8.51974 + 10.6834i) q^{61} +(-2.83058 - 1.36314i) q^{62} +(-2.17668 + 3.87160i) q^{63} +(-1.90577 + 0.917769i) q^{64} +(0.152674 - 0.668909i) q^{65} +(1.96821 - 2.46805i) q^{66} +14.3846 q^{67} +7.53421 q^{68} +(-0.865341 + 1.08510i) q^{69} +(0.187998 + 0.463373i) q^{70} +(4.94126 + 6.19615i) q^{71} +(-2.65084 - 3.32405i) q^{72} +(7.59732 - 3.65868i) q^{73} +(2.66651 - 1.28413i) q^{74} +(3.53543 + 4.43329i) q^{75} +(-3.50793 - 4.39881i) q^{76} +(9.81551 - 1.59434i) q^{77} +(-1.38900 + 1.74176i) q^{78} -8.64110 q^{79} +0.279793 q^{80} +(-0.714272 + 0.895669i) q^{81} +(1.39145 - 6.09634i) q^{82} +(10.3491 - 4.98384i) q^{83} +(-0.282382 + 4.44974i) q^{84} +(1.19764 + 0.576752i) q^{85} +(-2.22033 + 2.78421i) q^{86} +(0.965291 + 0.464860i) q^{87} +(-2.11816 + 9.28029i) q^{88} +(-6.56727 + 3.16263i) q^{89} +(-0.0706034 - 0.309334i) q^{90} +(-6.92701 + 1.12516i) q^{91} +(0.393912 - 1.72584i) q^{92} +(-1.09977 - 4.81842i) q^{93} +(-5.45456 - 6.83980i) q^{94} +(-0.220887 - 0.967770i) q^{95} +(-6.06422 - 2.92037i) q^{96} -8.15942 q^{97} +(3.66893 - 3.56369i) q^{98} -6.30961 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 2 q^{4} - 7 q^{5} - 7 q^{6} - 7 q^{7} + 6 q^{8} - 8 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 + 2 * q^4 - 7 * q^5 - 7 * q^6 - 7 * q^7 + 6 * q^8 - 8 * q^9	\( 12 q - 2 q^{2} + 2 q^{4} - 7 q^{5} - 7 q^{6} - 7 q^{7} + 6 q^{8} - 8 q^{9} + 14 q^{10} - 8 q^{11} - 14 q^{12} + 7 q^{13} - 28 q^{14} - 7 q^{15} + 16 q^{16} + 20 q^{18} - 14 q^{19} + 7 q^{20} + 21 q^{21} + 13 q^{22} - 2 q^{23} + 3 q^{25} - 7 q^{26} + 21 q^{27} + 14 q^{28} - 11 q^{29} + 42 q^{30} - 14 q^{31} - 24 q^{32} + 35 q^{33} - 42 q^{34} + 21 q^{35} - 13 q^{36} - 30 q^{37} + 21 q^{38} + 21 q^{41} - 35 q^{42} + 17 q^{43} - 6 q^{44} - 49 q^{45} - 16 q^{46} - 21 q^{47} + 7 q^{49} - 46 q^{50} + 7 q^{51} - 7 q^{52} + 6 q^{53} + 42 q^{54} - 28 q^{55} - 14 q^{56} + 7 q^{57} - 32 q^{58} + 14 q^{59} - 28 q^{60} - 7 q^{61} + 56 q^{62} + 14 q^{63} + 14 q^{64} + 14 q^{65} - 28 q^{66} + 48 q^{67} + 56 q^{68} - 7 q^{69} + 21 q^{70} - 39 q^{71} - 4 q^{72} + 42 q^{73} + 61 q^{74} + 7 q^{75} - 28 q^{76} + 21 q^{77} - 16 q^{79} + 42 q^{80} - 25 q^{81} + 28 q^{82} - 7 q^{83} + 42 q^{84} + 28 q^{85} + 17 q^{86} + 7 q^{87} - 11 q^{88} - 14 q^{89} - 14 q^{90} - 21 q^{91} + 16 q^{92} - 70 q^{93} - 49 q^{94} - 7 q^{95} - 70 q^{96} - 28 q^{97} - 28 q^{98} - 18 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 + 2 * q^4 - 7 * q^5 - 7 * q^6 - 7 * q^7 + 6 * q^8 - 8 * q^9 + 14 * q^10 - 8 * q^11 - 14 * q^12 + 7 * q^13 - 28 * q^14 - 7 * q^15 + 16 * q^16 + 20 * q^18 - 14 * q^19 + 7 * q^20 + 21 * q^21 + 13 * q^22 - 2 * q^23 + 3 * q^25 - 7 * q^26 + 21 * q^27 + 14 * q^28 - 11 * q^29 + 42 * q^30 - 14 * q^31 - 24 * q^32 + 35 * q^33 - 42 * q^34 + 21 * q^35 - 13 * q^36 - 30 * q^37 + 21 * q^38 + 21 * q^41 - 35 * q^42 + 17 * q^43 - 6 * q^44 - 49 * q^45 - 16 * q^46 - 21 * q^47 + 7 * q^49 - 46 * q^50 + 7 * q^51 - 7 * q^52 + 6 * q^53 + 42 * q^54 - 28 * q^55 - 14 * q^56 + 7 * q^57 - 32 * q^58 + 14 * q^59 - 28 * q^60 - 7 * q^61 + 56 * q^62 + 14 * q^63 + 14 * q^64 + 14 * q^65 - 28 * q^66 + 48 * q^67 + 56 * q^68 - 7 * q^69 + 21 * q^70 - 39 * q^71 - 4 * q^72 + 42 * q^73 + 61 * q^74 + 7 * q^75 - 28 * q^76 + 21 * q^77 - 16 * q^79 + 42 * q^80 - 25 * q^81 + 28 * q^82 - 7 * q^83 + 42 * q^84 + 28 * q^85 + 17 * q^86 + 7 * q^87 - 11 * q^88 - 14 * q^89 - 14 * q^90 - 21 * q^91 + 16 * q^92 - 70 * q^93 - 49 * q^94 - 7 * q^95 - 70 * q^96 - 28 * q^97 - 28 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{3}{7}\right)$

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 $

$2$	0.658322	+	0.317031i	0.465504	+	0.224175i	0.651908	−	0.758298i	$-0.273969\pi$
$2$	0.658322	+	0.317031i	0.465504	+	0.224175i	−0.186404	+	0.982473i	$0.559683\pi$
$3$	0.255779	+	1.12064i	0.147674	+	0.647002i	0.993528	+	0.113588i	$0.0362343\pi$
$3$	0.255779	+	1.12064i	0.147674	+	0.647002i	−0.845854	+	0.533415i	$0.820909\pi$
$4$	−0.914101	−	1.14625i	−0.457050	−	0.573123i
$5$	−0.0575591	−	0.252183i	−0.0257412	−	0.112780i	0.960425	−	0.278538i	$-0.0898499\pi$
$5$	−0.0575591	−	0.252183i	−0.0257412	−	0.112780i	−0.986166	+	0.165759i	$0.946993\pi$
$6$	−0.186893	+	0.818832i	−0.0762988	+	0.334287i
$7$	−2.16885	+	1.51528i	−0.819749	+	0.572723i
$7$	−2.16885	+	1.51528i	−0.819749	+	0.572723i
$8$	−0.563561	−	2.46912i	−0.199249	−	0.872966i
$9$	1.51249	−	0.728379i	0.504165	−	0.242793i
$10$	0.0420574	−	0.184265i	0.0132997	−	0.0582698i
$11$	−3.38633	−	1.63077i	−1.02102	−	0.491695i	−0.152997	−	0.988227i	$-0.548892\pi$
$11$	−3.38633	−	1.63077i	−1.02102	−	0.491695i	−0.868019	+	0.496532i	$0.834607\pi$
$12$	1.05072	−	1.31756i	0.303317	−	0.380348i
$13$	2.38980	+	1.15087i	0.662811	+	0.319193i	0.734871	−	0.678207i	$-0.237243\pi$
$13$	2.38980	+	1.15087i	0.662811	+	0.319193i	−0.0720595	+	0.997400i	$0.522957\pi$
$14$	−1.90819	+	0.309949i	−0.509986	+	0.0828374i
$15$	0.267884	−	0.129006i	0.0691673	−	0.0333092i
$16$	−0.240694	+	1.05455i	−0.0601734	+	0.263637i
$17$	−3.20407	+	4.01778i	−0.777102	+	0.974455i	−1.00000		0.000386753i	$-0.999877\pi$
$17$	−3.20407	+	4.01778i	−0.777102	+	0.974455i	0.222898	+	0.974842i	$0.428448\pi$
$18$	1.22663			0.289119
$19$	3.83757			0.880400			0.440200	−	0.897900i	$-0.354908\pi$
$19$	3.83757			0.880400			0.440200	+	0.897900i	$0.354908\pi$
$20$	−0.236449	+	0.296497i	−0.0528715	+	0.0662988i
$21$	−2.25283	−	2.04293i	−0.491608	−	0.445803i
$22$	−1.71229	−	2.14714i	−0.365061	−	0.457772i
$23$	0.752824	+	0.944011i	0.156975	+	0.196840i	0.854099	−	0.520110i	$-0.174109\pi$
$23$	0.752824	+	0.944011i	0.156975	+	0.196840i	−0.697125	+	0.716950i	$0.745538\pi$
$24$	2.62285	−	1.26310i	0.535387	−	0.257829i
$25$	4.44456	−	2.14039i	0.888912	−	0.428078i
$26$	1.20840	+	1.51528i	0.236986	+	0.297171i
$27$	3.35314	+	4.20471i	0.645313	+	0.809197i
$28$	3.71944	+	1.10092i	0.702907	+	0.208054i
$29$	0.581144	−	0.728732i	0.107916	−	0.135322i	−0.724940	−	0.688812i	$-0.758133\pi$
$29$	0.581144	−	0.728732i	0.107916	−	0.135322i	0.832856	+	0.553490i	$0.186704\pi$
$30$	0.217253			0.0396647
$31$	−4.29970			−0.772249			−0.386124	−	0.922447i	$-0.626186\pi$
$31$	−4.29970			−0.772249			−0.386124	+	0.922447i	$0.626186\pi$
$32$	−3.65090	+	4.57809i	−0.645395	+	0.809299i
$33$	0.961355	−	4.21197i	0.167350	−	0.733210i
$34$	−3.38307	+	1.62920i	−0.580192	+	0.279406i
$35$	0.506965	+	0.459729i	0.0856927	+	0.0777084i
$36$	−2.21747	−	1.06788i	−0.369579	−	0.177980i
$37$	2.52543	−	3.16679i	0.415178	−	0.520617i	−0.529636	−	0.848225i	$-0.677671\pi$
$37$	2.52543	−	3.16679i	0.415178	−	0.520617i	0.944814	+	0.327609i	$0.106243\pi$
$38$	2.52636	+	1.21663i	0.409830	+	0.197364i
$39$	−0.678448	+	2.97247i	−0.108639	+	0.475977i
$40$	−0.590232	+	0.284241i	−0.0933238	+	0.0449424i
$41$	−1.90432	−	8.34336i	−0.297404	−	1.30301i	−0.873977	−	0.485968i	$-0.838467\pi$
$41$	−1.90432	−	8.34336i	−0.297404	−	1.30301i	0.576573	−	0.817046i	$-0.304390\pi$
$42$	−0.835418	−	2.05912i	−0.128908	−	0.317729i
$43$	−1.08450	+	4.75152i	−0.165385	+	0.724600i	0.822417	+	0.568885i	$0.192625\pi$
$43$	−1.08450	+	4.75152i	−0.165385	+	0.724600i	−0.987802	+	0.155714i	$0.950232\pi$
$44$	1.22618	+	5.37225i	0.184854	+	0.809897i
$45$	−0.270742	−	0.339500i	−0.0403599	−	0.0506097i
$46$	0.196319	+	0.860132i	0.0289457	+	0.126819i
$47$	−10.7873	−	5.19488i	−1.57349	−	0.757751i	−0.575299	−	0.817943i	$-0.695114\pi$
$47$	−10.7873	−	5.19488i	−1.57349	−	0.757751i	−0.998187	+	0.0601929i	$0.980828\pi$
$48$	−1.24333			−0.179460
$49$	2.40784	−	6.57284i	0.343978	−	0.938978i
$50$	3.60452			0.509756
$51$	−5.32202	−	2.56295i	−0.745232	−	0.358885i
$52$	−0.865341	−	3.79131i	−0.120001	−	0.525760i
$53$	−2.39053	−	2.99763i	−0.328364	−	0.411756i	0.590056	−	0.807363i	$-0.299106\pi$
$53$	−2.39053	−	2.99763i	−0.328364	−	0.411756i	−0.918420	+	0.395607i	$0.870534\pi$
$54$	0.874424	+	3.83110i	0.118994	+	0.521347i
$55$	−0.216338	+	0.947838i	−0.0291710	+	0.127806i
$56$	4.96369	+	4.50121i	0.663302	+	0.601499i
$57$	0.981571	+	4.30054i	0.130012	+	0.569621i
$58$	0.613611	−	0.295499i	0.0805710	−	0.0388010i
$59$	1.19672	−	5.24319i	0.155800	−	0.682605i	−0.835334	−	0.549742i	$-0.814726\pi$
$59$	1.19672	−	5.24319i	0.155800	−	0.682605i	0.991134	−	0.132863i	$-0.0424169\pi$
$60$	−0.392746	−	0.189136i	−0.0507032	−	0.0244174i
$61$	−8.51974	+	10.6834i	−1.09084	+	1.36787i	−0.166617	+	0.986022i	$0.553284\pi$
$61$	−8.51974	+	10.6834i	−1.09084	+	1.36787i	−0.924224	+	0.381850i	$0.875287\pi$
$62$	−2.83058	−	1.36314i	−0.359485	−	0.173119i
$63$	−2.17668	+	3.87160i	−0.274236	+	0.487776i
$64$	−1.90577	+	0.917769i	−0.238221	+	0.114721i
$65$	0.152674	−	0.668909i	0.0189369	−	0.0829679i
$66$	1.96821	−	2.46805i	0.242269	−	0.303796i
$67$	14.3846			1.75736			0.878682	−	0.477408i	$-0.158424\pi$
$67$	14.3846			1.75736			0.878682	+	0.477408i	$0.158424\pi$
$68$	7.53421			0.913657
$69$	−0.865341	+	1.08510i	−0.104175	+	0.130631i
$70$	0.187998	+	0.463373i	0.0224700	+	0.0553837i
$71$	4.94126	+	6.19615i	0.586420	+	0.735347i	0.983193	−	0.182570i	$-0.0584415\pi$
$71$	4.94126	+	6.19615i	0.586420	+	0.735347i	−0.396773	+	0.917917i	$0.629870\pi$
$72$	−2.65084	−	3.32405i	−0.312404	−	0.391742i
$73$	7.59732	−	3.65868i	0.889199	−	0.428216i	0.0672234	−	0.997738i	$-0.478586\pi$
$73$	7.59732	−	3.65868i	0.889199	−	0.428216i	0.821976	+	0.569522i	$0.192872\pi$
$74$	2.66651	−	1.28413i	0.309976	−	0.149277i
$75$	3.53543	+	4.43329i	0.408236	+	0.511912i
$76$	−3.50793	−	4.39881i	−0.402387	−	0.504578i
$77$	9.81551	−	1.59434i	1.11858	−	0.181692i
$78$	−1.38900	+	1.74176i	−0.157274	+	0.197215i
$79$	−8.64110			−0.972200			−0.486100	−	0.873903i	$-0.661581\pi$
$79$	−8.64110			−0.972200			−0.486100	+	0.873903i	$0.661581\pi$
$80$	0.279793			0.0312818
$81$	−0.714272	+	0.895669i	−0.0793636	+	0.0995188i
$82$	1.39145	−	6.09634i	0.153660	−	0.673228i
$83$	10.3491	−	4.98384i	1.13596	−	0.547048i	0.231170	−	0.972913i	$-0.425745\pi$
$83$	10.3491	−	4.98384i	1.13596	−	0.547048i	0.904786	+	0.425866i	$0.140030\pi$
$84$	−0.282382	+	4.44974i	−0.0308103	+	0.485507i
$85$	1.19764	+	0.576752i	0.129902	+	0.0625576i
$86$	−2.22033	+	2.78421i	−0.239424	+	0.300229i
$87$	0.965291	+	0.464860i	0.103490	+	0.0498382i
$88$	−2.11816	+	9.28029i	−0.225797	+	0.989282i
$89$	−6.56727	+	3.16263i	−0.696129	+	0.335238i	−0.748263	−	0.663402i	$-0.769112\pi$
$89$	−6.56727	+	3.16263i	−0.696129	+	0.335238i	0.0521339	+	0.998640i	$0.483398\pi$
$90$	−0.0706034	−	0.309334i	−0.00744226	−	0.0326067i
$91$	−6.92701	+	1.12516i	−0.726148	+	0.117949i
$92$	0.393912	−	1.72584i	0.0410682	−	0.179932i
$93$	−1.09977	−	4.81842i	−0.114041	−	0.499647i
$94$	−5.45456	−	6.83980i	−0.562595	−	0.705472i
$95$	−0.220887	−	0.967770i	−0.0226625	−	0.0992911i
$96$	−6.06422	−	2.92037i	−0.618927	−	0.298059i
$97$	−8.15942			−0.828464			−0.414232	−	0.910171i	$-0.635950\pi$
$97$	−8.15942			−0.828464			−0.414232	+	0.910171i	$0.635950\pi$
$98$	3.66893	−	3.56369i	0.370618	−	0.359987i
$99$	−6.30961			−0.634140
$100$	−6.51619	−	3.13803i	−0.651619	−	0.313803i
$101$	4.11146	+	18.0135i	0.409105	+	1.79241i	0.588353	+	0.808604i	$0.299776\pi$
$101$	4.11146	+	18.0135i	0.409105	+	1.79241i	−0.179248	+	0.983804i	$0.557366\pi$
$102$	−2.69107	−	3.37449i	−0.266456	−	0.334125i
$103$	1.60149	+	7.01658i	0.157799	+	0.691364i	0.990485	+	0.137619i	$0.0439448\pi$
$103$	1.60149	+	7.01658i	0.157799	+	0.691364i	−0.832686	+	0.553746i	$0.813198\pi$
$104$	1.49483	−	6.54929i	0.146580	−	0.642211i
$105$	−0.385520	+	0.685715i	−0.0376229	+	0.0669189i
$106$	−0.623396	−	2.73128i	−0.0605496	−	0.265285i
$107$	−2.62819	+	1.26567i	−0.254077	+	0.122357i	−0.556587	−	0.830789i	$-0.687890\pi$
$107$	−2.62819	+	1.26567i	−0.254077	+	0.122357i	0.302510	+	0.953146i	$0.402175\pi$
$108$	1.75452	−	7.68706i	0.168829	−	0.739688i
$109$	−2.55309	−	1.22950i	−0.244542	−	0.117765i	0.307599	−	0.951516i	$-0.400475\pi$
$109$	−2.55309	−	1.22950i	−0.244542	−	0.117765i	−0.552141	+	0.833751i	$0.686189\pi$
$110$	−0.442914	+	0.555397i	−0.0422302	+	0.0529550i
$111$	4.19478	+	2.02010i	0.398151	+	0.191740i
$112$	−1.07591	−	2.65188i	−0.101664	−	0.250579i
$113$	0.00932794	−	0.00449210i	0.000877499	−	0.000422581i	−0.433445	−	0.901180i	$-0.642702\pi$
$113$	0.00932794	−	0.00449210i	0.000877499	−	0.000422581i	0.434322	+	0.900757i	$0.356988\pi$
$114$	−0.717216	+	3.14233i	−0.0671735	+	0.294306i
$115$	0.194731	−	0.244186i	0.0181588	−	0.0227704i
$116$	−1.36653			−0.126879
$117$	4.45282			0.411664
$118$	2.45008	−	3.07231i	0.225548	−	0.282829i
$119$	0.861094	−	13.5690i	0.0789364	−	1.24387i
$120$	−0.469501	−	0.588735i	−0.0428593	−	0.0537439i
$121$	1.94941	+	2.44448i	0.177219	+	0.222225i
$122$	−8.99571	+	4.33210i	−0.814433	+	0.392210i
$123$	8.86282	−	4.26811i	0.799134	−	0.384843i
$124$	3.93036	+	4.92851i	0.352956	+	0.442593i
$125$	−1.60198	−	2.00882i	−0.143285	−	0.179674i
$126$	−2.66037	+	1.85868i	−0.237005	+	0.165585i
$127$	0.142558	−	0.178761i	0.0126499	−	0.0158625i	−0.775466	−	0.631389i	$-0.782485\pi$
$127$	0.142558	−	0.178761i	0.0126499	−	0.0158625i	0.788116	+	0.615526i	$0.211057\pi$
$128$	10.1656			0.898522
$129$	−5.60214			−0.493241
$130$	0.312574	−	0.391955i	0.0274145	−	0.0343767i
$131$	2.39953	−	10.5130i	0.209648	−	0.918529i	−0.755153	−	0.655549i	$-0.772437\pi$
$131$	2.39953	−	10.5130i	0.209648	−	0.918529i	0.964801	−	0.262980i	$-0.0847055\pi$
$132$	−5.70673	+	2.74822i	−0.496707	+	0.239202i
$133$	−8.32313	+	5.81501i	−0.721707	+	0.504225i
$134$	9.46972	+	4.56038i	0.818059	+	0.393957i
$135$	0.867351	−	1.08762i	0.0746497	−	0.0936078i
$136$	11.7261	+	5.64698i	1.00550	+	0.484225i
$137$	−3.93312	+	17.2321i	−0.336029	+	1.47224i	0.471214	+	0.882019i	$0.343816\pi$
$137$	−3.93312	+	17.2321i	−0.336029	+	1.47224i	−0.807243	+	0.590219i	$0.799041\pi$
$138$	−0.913684	+	0.440007i	−0.0777780	+	0.0374559i
$139$	2.67608	+	11.7247i	0.226982	+	0.994475i	0.952085	+	0.305834i	$0.0989352\pi$
$139$	2.67608	+	11.7247i	0.226982	+	0.994475i	−0.725102	+	0.688641i	$0.758208\pi$
$140$	0.0635455	−	1.00135i	0.00537058	−	0.0846291i
$141$	3.06243	−	13.4174i	0.257903	−	1.12995i
$142$	1.28857	+	5.64559i	0.108134	+	0.473767i
$143$	−6.21584	−	7.79442i	−0.519795	−	0.651802i
$144$	0.404062	+	1.77031i	0.0336719	+	0.147526i
$145$	−0.217224	−	0.104609i	−0.0180394	−	0.00868734i
$146$	6.16140			0.509921
$147$	7.98167	+	1.01713i	0.658317	+	0.0838917i
$148$	−5.93841			−0.488135
$149$	18.2135	+	8.77114i	1.49211	+	0.718560i	0.989308	−	0.145844i	$-0.0465899\pi$
$149$	18.2135	+	8.77114i	1.49211	+	0.718560i	0.502798	+	0.864404i	$0.332304\pi$
$150$	0.921961	+	4.03937i	0.0752778	+	0.329813i
$151$	−12.8221	−	16.0784i	−1.04345	−	1.30844i	−0.949807	−	0.312837i	$-0.898720\pi$
$151$	−12.8221	−	16.0784i	−1.04345	−	1.30844i	−0.0936421	−	0.995606i	$-0.529851\pi$
$152$	−2.16271	−	9.47544i	−0.175419	−	0.768560i
$153$	−1.91968	+	8.41065i	−0.155197	+	0.679960i
$154$	6.96722	+	2.06223i	0.561435	+	0.166180i
$155$	0.247487	+	1.08431i	0.0198786	+	0.0870938i
$156$	4.02736	−	1.93947i	0.322447	−	0.155282i
$157$	−0.460717	+	2.01853i	−0.0367692	+	0.161096i	−0.989979	−	0.141212i	$-0.954900\pi$
$157$	−0.460717	+	2.01853i	−0.0367692	+	0.161096i	0.953210	+	0.302308i	$0.0977572\pi$
$158$	−5.68863	−	2.73950i	−0.452563	−	0.217943i
$159$	2.74782	−	3.44566i	0.217916	−	0.273258i
$160$	1.36466	+	0.657184i	0.107886	+	0.0519550i
$161$	−3.06321	−	0.906681i	−0.241415	−	0.0714565i
$162$	−0.754176	+	0.363192i	−0.0592537	+	0.0285351i
$163$	1.60556	−	7.03440i	0.125757	−	0.550977i	−0.872317	−	0.488941i	$-0.837383\pi$
$163$	1.60556	−	7.03440i	0.125757	−	0.550977i	0.998074	−	0.0620362i	$-0.0197594\pi$
$164$	−7.82280	+	9.80948i	−0.610858	+	0.765992i
$165$	−1.11752			−0.0869989
$166$	8.39304			0.651426
$167$	−5.99415	+	7.51642i	−0.463841	+	0.581638i	−0.957651	−	0.287932i	$-0.907032\pi$
$167$	−5.99415	+	7.51642i	−0.463841	+	0.581638i	0.493810	+	0.869570i	$0.335604\pi$
$168$	−3.77463	+	6.71383i	−0.291219	+	0.517983i
$169$	−3.71872	−	4.66313i	−0.286055	−	0.358702i
$170$	0.605583	+	0.759377i	0.0464461	+	0.0582416i
$171$	5.80431	−	2.79521i	0.443866	−	0.213755i
$172$	6.43775	−	3.10026i	0.490874	−	0.236392i
$173$	−8.41423	−	10.5511i	−0.639722	−	0.802186i	0.351246	−	0.936283i	$-0.385758\pi$
$173$	−8.41423	−	10.5511i	−0.639722	−	0.802186i	−0.990968	+	0.134097i	$0.957187\pi$
$174$	0.488097	+	0.612055i	0.0370026	+	0.0463997i
$175$	−6.39631	+	11.3769i	−0.483515	+	0.860016i
$176$	2.53479	−	3.17853i	0.191067	−	0.239590i
$177$	6.18183			0.464655
$178$	−5.32603			−0.399203
$179$	1.18524	−	1.48625i	0.0885891	−	0.111087i	−0.735561	−	0.677458i	$-0.763082\pi$
$179$	1.18524	−	1.48625i	0.0885891	−	0.111087i	0.824151	+	0.566371i	$0.191653\pi$
$180$	−0.141665	+	0.620674i	−0.0105591	+	0.0462623i
$181$	5.99532	−	2.88719i	0.445628	−	0.214603i	−0.197592	−	0.980284i	$-0.563312\pi$
$181$	5.99532	−	2.88719i	0.445628	−	0.214603i	0.643221	+	0.765681i	$0.277598\pi$
$182$	−4.91691	−	1.45536i	−0.364466	−	0.107879i
$183$	−14.1514	−	6.81498i	−1.04611	−	0.503778i
$184$	1.90662	−	2.39082i	0.140558	−	0.176254i
$185$	−0.943970	−	0.454592i	−0.0694021	−	0.0334223i
$186$	0.803584	−	3.52073i	0.0589216	−	0.258153i
$187$	17.4021	−	8.38041i	1.27257	−	0.612836i
$188$	3.90605	+	17.1135i	0.284878	+	1.24813i
$189$	−13.6438	−	4.03844i	−0.992440	−	0.293753i
$190$	0.161398	−	0.707132i	0.0117091	−	0.0513008i
$191$	−2.07383	−	9.08603i	−0.150057	−	0.657442i	−0.992867	−	0.119230i	$-0.961957\pi$
$191$	−2.07383	−	9.08603i	−0.150057	−	0.657442i	0.842810	−	0.538212i	$-0.180900\pi$
$192$	−1.51595	−	1.90094i	−0.109404	−	0.137188i
$193$	−0.366993	−	1.60790i	−0.0264167	−	0.115739i	0.960001	−	0.279998i	$-0.0903339\pi$
$193$	−0.366993	−	1.60790i	−0.0264167	−	0.115739i	−0.986417	+	0.164259i	$0.947477\pi$
$194$	−5.37152	−	2.58679i	−0.385653	−	0.185721i
$195$	0.788658			0.0564769
$196$	−9.73511	+	3.24826i	−0.695365	+	0.232019i
$197$	−1.05367			−0.0750711			−0.0375355	−	0.999295i	$-0.511951\pi$
$197$	−1.05367			−0.0750711			−0.0375355	+	0.999295i	$0.511951\pi$
$198$	−4.15376	−	2.00034i	−0.295195	−	0.142158i
$199$	−2.50088	−	10.9571i	−0.177283	−	0.776726i	−0.982878	−	0.184260i	$-0.941011\pi$
$199$	−2.50088	−	10.9571i	−0.177283	−	0.776726i	0.805595	−	0.592467i	$-0.201846\pi$
$200$	−7.78966	−	9.76792i	−0.550812	−	0.690697i
$201$	3.67929	+	16.1200i	0.259517	+	1.13702i
$202$	−3.00417	+	13.1621i	−0.211373	+	0.926084i
$203$	−0.156182	+	2.46111i	−0.0109619	+	0.172736i
$204$	1.92709	+	8.44314i	0.134923	+	0.591138i
$205$	−1.99444	+	0.960472i	−0.139298	+	0.0670822i
$206$	−1.17018	+	5.12689i	−0.0815302	+	0.357207i
$207$	1.82624	+	0.879470i	0.126932	+	0.0611274i
$208$	−1.78885	+	2.24315i	−0.124035	+	0.155535i
$209$	−12.9953	−	6.25820i	−0.898902	−	0.432888i
$210$	−0.471189	+	0.329199i	−0.0325151	+	0.0227169i
$211$	10.4730	−	5.04352i	0.720989	−	0.347210i	−0.0371439	−	0.999310i	$-0.511826\pi$
$211$	10.4730	−	5.04352i	0.720989	−	0.347210i	0.758133	+	0.652100i	$0.226112\pi$
$212$	−1.25084	+	5.48027i	−0.0859078	+	0.376387i
$213$	−5.67978	+	7.12222i	−0.389172	+	0.488007i
$214$	−2.13145			−0.145703
$215$	1.26067			0.0859772
$216$	8.49224	−	10.6489i	0.577824	−	0.724568i
$217$	9.32541	−	6.51525i	0.633050	−	0.442284i
$218$	−1.29097	−	1.61882i	−0.0874352	−	0.109640i
$219$	6.04330	+	7.57806i	0.408368	+	0.512078i
$220$	1.28421	−	0.618443i	0.0865814	−	0.0416954i
$221$	−12.2810	+	5.91423i	−0.826111	+	0.397834i
$222$	2.12108	+	2.65975i	0.142358	+	0.178511i
$223$	2.08508	+	2.61461i	0.139628	+	0.175087i	0.846729	−	0.532025i	$-0.178569\pi$
$223$	2.08508	+	2.61461i	0.139628	+	0.175087i	−0.707101	+	0.707113i	$0.749997\pi$
$224$	0.981180	−	15.4613i	0.0655578	−	1.03305i
$225$	5.16336	−	6.47465i	0.344224	−	0.431643i
$226$	0.00756492			0.000503211
$227$	0.859279			0.0570324			0.0285162	−	0.999593i	$-0.490922\pi$
$227$	0.859279			0.0570324			0.0285162	+	0.999593i	$0.490922\pi$
$228$	4.03223	−	5.05625i	0.267041	−	0.334858i
$229$	2.74806	−	12.0400i	0.181597	−	0.795627i	−0.799274	−	0.600967i	$-0.794782\pi$
$229$	2.74806	−	12.0400i	0.181597	−	0.795627i	0.980871	−	0.194660i	$-0.0623605\pi$
$230$	0.205610	−	0.0990167i	0.0135575	−	0.00652897i
$231$	4.29728	+	10.5919i	0.282741	+	0.696894i
$232$	−2.12684	−	1.02423i	−0.139634	−	0.0672441i
$233$	−7.85030	+	9.84396i	−0.514290	+	0.644900i	−0.969386	−	0.245543i	$-0.921034\pi$
$233$	−7.85030	+	9.84396i	−0.514290	+	0.644900i	0.455095	+	0.890443i	$0.349605\pi$
$234$	2.93139	+	1.41168i	0.191631	+	0.0922846i
$235$	−0.689153	+	3.01938i	−0.0449554	+	0.196962i
$236$	−7.10391	+	3.42106i	−0.462425	+	0.222692i
$237$	−2.21021	−	9.68357i	−0.143569	−	0.629016i
$238$	4.86869	−	8.65981i	0.315590	−	0.561332i
$239$	−1.13806	+	4.98615i	−0.0736148	+	0.322527i	−0.998305	−	0.0581919i	$-0.981466\pi$
$239$	−1.13806	+	4.98615i	−0.0736148	+	0.322527i	0.924691	+	0.380719i	$0.124324\pi$
$240$	0.0715651	+	0.313547i	0.00461951	+	0.0202394i
$241$	11.4094	+	14.3070i	0.734947	+	0.921594i	0.999080	−	0.0428923i	$-0.0136572\pi$
$241$	11.4094	+	14.3070i	0.734947	+	0.921594i	−0.264133	+	0.964486i	$0.585086\pi$
$242$	0.508361	+	2.22728i	0.0326787	+	0.143175i
$243$	13.3499	+	6.42897i	0.856396	+	0.412418i
$244$	20.0337			1.28253
$245$	−1.79615	−	0.228890i	−0.114752	−	0.0146232i
$246$	7.18771			0.458272
$247$	9.17104	+	4.41654i	0.583539	+	0.281018i
$248$	2.42314	+	10.6165i	0.153870	+	0.674147i
$249$	8.23217	+	10.3228i	0.521692	+	0.654181i
$250$	−0.417760	−	1.83032i	−0.0264214	−	0.115760i
$251$	4.38882	−	19.2287i	0.277020	−	1.21370i	−0.624521	−	0.781008i	$-0.714706\pi$
$251$	4.38882	−	19.2287i	0.277020	−	1.21370i	0.901541	−	0.432694i	$-0.142437\pi$
$252$	6.42751	−	1.04402i	0.404895	−	0.0657673i
$253$	−1.00984	−	4.42441i	−0.0634883	−	0.278160i
$254$	0.150522	−	0.0724874i	0.00944457	−	0.00454826i
$255$	−0.340001	+	1.48964i	−0.0212917	+	0.0932851i
$256$	10.5038	+	5.05836i	0.656487	+	0.316147i
$257$	−7.02113	+	8.80422i	−0.437966	+	0.549192i	−0.951006	−	0.309173i	$-0.899948\pi$
$257$	−7.02113	+	8.80422i	−0.437966	+	0.549192i	0.513040	+	0.858365i	$0.328519\pi$
$258$	−3.68801	−	1.77605i	−0.229605	−	0.110572i
$259$	−0.678709	+	10.6950i	−0.0421729	+	0.664557i
$260$	−0.906294	+	0.436448i	−0.0562060	+	0.0270674i
$261$	0.348184	−	1.52550i	0.0215521	−	0.0944258i
$262$	4.91263	−	6.16024i	0.303503	−	0.380581i
$263$	−2.68750			−0.165718			−0.0828590	−	0.996561i	$-0.526405\pi$
$263$	−2.68750			−0.165718			−0.0828590	+	0.996561i	$0.526405\pi$
$264$	−10.9416			−0.673412
$265$	−0.618354	+	0.775391i	−0.0379852	+	0.0476319i
$266$	−7.32284	+	1.18945i	−0.448992	+	0.0729300i
$267$	−5.22394	−	6.55062i	−0.319700	−	0.400891i
$268$	−13.1490	−	16.4883i	−0.803204	−	1.00719i
$269$	3.02202	−	1.45533i	0.184256	−	0.0887330i	−0.339481	−	0.940613i	$-0.610252\pi$
$269$	3.02202	−	1.45533i	0.184256	−	0.0887330i	0.523737	+	0.851880i	$0.324537\pi$
$270$	0.915807	−	0.441029i	0.0557342	−	0.0268402i
$271$	2.47743	+	3.10660i	0.150493	+	0.188712i	0.851363	−	0.524576i	$-0.175776\pi$
$271$	2.47743	+	3.10660i	0.150493	+	0.188712i	−0.700870	+	0.713289i	$0.747205\pi$
$272$	−3.46574	−	4.34590i	−0.210142	−	0.263509i
$273$	−3.03268	−	7.47490i	−0.183546	−	0.452401i
$274$	−8.05237	+	10.0973i	−0.486461	+	0.610003i
$275$	−18.5412			−1.11808
$276$	2.03480			0.122481
$277$	−7.23624	+	9.07396i	−0.434784	+	0.545202i	−0.950160	−	0.311762i	$-0.899081\pi$
$277$	−7.23624	+	9.07396i	−0.434784	+	0.545202i	0.515376	+	0.856964i	$0.327652\pi$
$278$	−1.95537	+	8.56702i	−0.117275	+	0.513816i
$279$	−6.50327	+	3.13181i	−0.389340	+	0.187496i
$280$	0.849421	−	1.51084i	0.0507626	−	0.0902902i
$281$	23.4050	+	11.2713i	1.39622	+	0.672386i	0.972392	−	0.233354i	$-0.0749700\pi$
$281$	23.4050	+	11.2713i	1.39622	+	0.672386i	0.423833	+	0.905740i	$0.360684\pi$
$282$	6.26980	−	7.86208i	0.373361	−	0.468180i
$283$	−11.5494	−	5.56191i	−0.686542	−	0.330621i	0.0578865	−	0.998323i	$-0.481564\pi$
$283$	−11.5494	−	5.56191i	−0.686542	−	0.330621i	−0.744429	+	0.667702i	$0.767278\pi$
$284$	2.58550	−	11.3278i	0.153421	−	0.672181i
$285$	1.02802	−	0.495070i	0.0608949	−	0.0293254i
$286$	−1.62095	−	7.10185i	−0.0958488	−	0.419941i
$287$	16.7727	+	15.2099i	0.990062	+	0.897814i
$288$	−2.18739	+	9.58357i	−0.128893	+	0.564717i
$289$	−2.09362	−	9.17276i	−0.123154	−	0.539574i
$290$	−0.109839	−	0.137733i	−0.00644995	−	0.00808798i
$291$	−2.08701	−	9.14378i	−0.122343	−	0.536018i
$292$	−11.1385	−	5.36400i	−0.651829	−	0.313904i
$293$	−11.1476			−0.651250			−0.325625	−	0.945499i	$-0.605575\pi$
$293$	−11.1476			−0.651250			−0.325625	+	0.945499i	$0.605575\pi$
$294$	4.93205	+	3.20004i	0.287643	+	0.186630i
$295$	−1.39112			−0.0809944
$296$	−9.24242	−	4.45091i	−0.537205	−	0.258704i
$297$	−4.49793	−	19.7067i	−0.260996	−	1.14350i
$298$	9.20960	+	11.5485i	0.533498	+	0.668985i
$299$	0.712667	+	3.12240i	0.0412146	+	0.180573i
$300$	1.84990	−	8.10495i	0.106804	−	0.467939i
$301$	−4.84776	−	11.9487i	−0.279420	−	0.688710i
$302$	−3.34372	−	14.6498i	−0.192409	−	0.843000i
$303$	−19.1350	+	9.21494i	−1.09928	+	0.529384i
$304$	−0.923680	+	4.04691i	−0.0529767	+	0.232106i
$305$	3.18456	+	1.53360i	0.182347	+	0.0878139i
$306$	−3.93020	+	4.92832i	−0.224675	+	0.281733i
$307$	−1.60980	−	0.775239i	−0.0918762	−	0.0442452i	0.387381	−	0.921920i	$-0.373380\pi$
$307$	−1.60980	−	0.775239i	−0.0918762	−	0.0442452i	−0.479257	+	0.877674i	$0.659094\pi$
$308$	−10.7999	−	9.79361i	−0.615380	−	0.558043i
$309$	−7.45344	+	3.58939i	−0.424011	+	0.204193i
$310$	−0.180834	+	0.792285i	−0.0102707	+	0.0449988i
$311$	12.7744	−	16.0186i	0.724372	−	0.908334i	−0.274204	−	0.961672i	$-0.588414\pi$
$311$	12.7744	−	16.0186i	0.724372	−	0.908334i	0.998577	+	0.0533372i	$0.0169858\pi$
$312$	7.72175			0.437158
$313$	−18.3887			−1.03939			−0.519696	−	0.854351i	$-0.673955\pi$
$313$	−18.3887			−1.03939			−0.519696	+	0.854351i	$0.673955\pi$
$314$	−0.943237	+	1.18278i	−0.0532299	+	0.0667482i
$315$	1.10164	+	0.326075i	0.0620703	+	0.0183722i
$316$	7.89884	+	9.90483i	0.444344	+	0.557190i
$317$	9.16368	+	11.4909i	0.514684	+	0.645393i	0.969471	−	0.245207i	$-0.0788560\pi$
$317$	9.16368	+	11.4909i	0.514684	+	0.645393i	−0.454787	+	0.890600i	$0.650285\pi$
$318$	2.90133	−	1.39721i	0.162698	−	0.0783514i
$319$	−3.15634	+	1.52001i	−0.176721	+	0.0851043i
$320$	0.341140	+	0.427776i	0.0190703	+	0.0239134i
$321$	−2.09060	−	2.62153i	−0.116686	−	0.146319i
$322$	−1.72913	−	1.56802i	−0.0963606	−	0.0873823i
$323$	−12.2959	+	15.4185i	−0.684161	+	0.857910i
$324$	1.67957			0.0933097
$325$	13.0849			0.725820
$326$	3.28710	−	4.12189i	0.182055	−	0.228290i
$327$	0.724806	−	3.17558i	0.0400818	−	0.175610i
$328$	−19.5276	+	9.40398i	−1.07823	+	0.519248i
$329$	31.2677	−	5.07883i	1.72384	−	0.280005i
$330$	−0.735688	−	0.354289i	−0.0404983	−	0.0195030i
$331$	−11.9872	+	15.0314i	−0.658874	+	0.826202i	−0.993220	−	0.116248i	$-0.962913\pi$
$331$	−11.9872	+	15.0314i	−0.658874	+	0.826202i	0.334346	+	0.942450i	$0.391485\pi$
$332$	−15.1728	−	7.30683i	−0.832715	−	0.401014i
$333$	1.51307	−	6.62921i	0.0829160	−	0.363279i
$334$	−6.32902	+	3.04789i	−0.346308	+	0.166773i
$335$	−0.827966	−	3.62756i	−0.0452366	−	0.198195i
$336$	2.69661	−	1.88400i	0.147112	−	0.102781i
$337$	−2.81943	+	12.3527i	−0.153584	+	0.672895i	0.838242	+	0.545298i	$0.183584\pi$
$337$	−2.81943	+	12.3527i	−0.153584	+	0.672895i	−0.991826	+	0.127597i	$0.959274\pi$
$338$	−0.969758	−	4.24879i	−0.0527479	−	0.231104i
$339$	0.00741992	+	0.00930428i	0.000402995	+	0.000505339i
$340$	−0.433662	−	1.90000i	−0.0235186	−	0.103042i
$341$	14.5602	+	7.01181i	0.788478	+	0.379711i
$342$	4.70727			0.254540
$343$	4.73745	+	17.9041i	0.255798	+	0.966730i
$344$	12.3433			0.665504
$345$	0.323453	+	0.155767i	0.0174141	+	0.00838619i
$346$	−2.19424	−	9.61360i	−0.117963	−	0.516830i
$347$	15.6915	+	19.6766i	0.842366	+	1.05629i	0.997656	+	0.0684242i	$0.0217971\pi$
$347$	15.6915	+	19.6766i	0.842366	+	1.05629i	−0.155291	+	0.987869i	$0.549631\pi$
$348$	−0.349530	−	1.53139i	−0.0187368	−	0.0820911i
$349$	0.212213	−	0.929768i	0.0113595	−	0.0497693i	−0.968931	−	0.247333i	$-0.920446\pi$
$349$	0.212213	−	0.929768i	0.0113595	−	0.0497693i	0.980290	+	0.197564i	$0.0633029\pi$
$350$	−7.81767	+	5.46186i	−0.417872	+	0.291949i
$351$	3.17428	+	13.9074i	0.169431	+	0.742324i
$352$	19.8289	−	9.54912i	1.05689	−	0.508970i
$353$	6.05456	−	26.5268i	0.322252	−	1.41188i	−0.511284	−	0.859412i	$-0.670830\pi$
$353$	6.05456	−	26.5268i	0.322252	−	1.41188i	0.833536	−	0.552466i	$-0.186313\pi$
$354$	4.06963	+	1.95983i	0.216298	+	0.104164i
$355$	1.27815	−	1.60274i	0.0678370	−	0.0850649i
$356$	9.62830	+	4.63675i	0.510299	+	0.245747i
$357$	15.4263	−	2.50570i	0.816445	−	0.132616i
$358$	1.25146	−	0.602670i	0.0661415	−	0.0318521i
$359$	4.75641	−	20.8392i	0.251034	−	1.09985i	−0.679509	−	0.733668i	$-0.737807\pi$
$359$	4.75641	−	20.8392i	0.251034	−	1.09985i	0.930542	−	0.366184i	$-0.119336\pi$
$360$	−0.685687	+	0.859824i	−0.0361389	+	0.0453167i
$361$	−4.27302			−0.224896
$362$	4.86218			0.255550
$363$	−2.24076	+	2.80983i	−0.117610	+	0.147478i
$364$	7.62169	+	6.91155i	0.399485	+	0.362264i
$365$	−1.35995	−	1.70532i	−0.0711830	−	0.0892607i
$366$	−7.15565	−	8.97290i	−0.374032	−	0.469021i
$367$	−1.77439	+	0.854500i	−0.0926223	+	0.0446045i	−0.479621	−	0.877476i	$-0.659226\pi$
$367$	−1.77439	+	0.854500i	−0.0926223	+	0.0446045i	0.386999	+	0.922080i	$0.373512\pi$
$368$	−1.17671	+	0.566671i	−0.0613400	+	0.0295398i
$369$	−8.95739	−	11.2322i	−0.466303	−	0.584726i
$370$	−0.477316	−	0.598536i	−0.0248145	−	0.0311164i
$371$	9.72696	+	2.87909i	0.504999	+	0.149475i
$372$	−4.51779	+	5.66513i	−0.234236	+	0.293723i
$373$	16.1255			0.834948			0.417474	−	0.908689i	$-0.362916\pi$
$373$	16.1255			0.834948			0.417474	+	0.908689i	$0.362916\pi$
$374$	14.1130			0.729768
$375$	1.84141	−	2.30906i	0.0950900	−	0.119239i
$376$	−6.74750	+	29.5627i	−0.347976	+	1.52458i
$377$	2.22749	−	1.07270i	0.114722	−	0.0552470i
$378$	−7.70170	−	6.98410i	−0.396133	−	0.359223i
$379$	−24.6941	−	11.8921i	−1.26845	−	0.610855i	−0.326056	−	0.945351i	$-0.605720\pi$
$379$	−24.6941	−	11.8921i	−1.26845	−	0.610855i	−0.942397	+	0.334496i	$0.891434\pi$
$380$	−0.907389	+	1.13783i	−0.0465481	+	0.0583695i
$381$	0.236791	+	0.114032i	0.0121312	+	0.00584205i
$382$	1.51531	−	6.63900i	0.0775299	−	0.339681i
$383$	5.46288	−	2.63078i	0.279140	−	0.134427i	−0.289076	−	0.957306i	$-0.593348\pi$
$383$	5.46288	−	2.63078i	0.279140	−	0.134427i	0.568216	+	0.822879i	$0.307634\pi$
$384$	2.60015	+	11.3920i	0.132688	+	0.581346i
$385$	−0.967037	−	2.38353i	−0.0492848	−	0.121476i
$386$	0.268155	−	1.17487i	0.0136487	−	0.0597991i
$387$	1.82060	+	7.97657i	0.0925463	+	0.405472i
$388$	7.45853	+	9.35270i	0.378650	+	0.474812i
$389$	4.72883	+	20.7184i	0.239761	+	1.05046i	0.941231	+	0.337763i	$0.109670\pi$
$389$	4.72883	+	20.7184i	0.239761	+	1.05046i	−0.701470	+	0.712699i	$0.747473\pi$
$390$	0.519190	+	0.250029i	0.0262902	+	0.0126607i
$391$	−6.20493			−0.313797
$392$	−17.5861	−	2.24106i	−0.888233	−	0.113191i
$393$	12.3951			0.625250
$394$	−0.693656	−	0.334047i	−0.0349459	−	0.0168290i
$395$	0.497374	+	2.17914i	0.0250256	+	0.109644i
$396$	5.76762	+	7.23237i	0.289834	+	0.363440i
$397$	−5.85024	−	25.6316i	−0.293615	−	1.28641i	−0.879454	−	0.475984i	$-0.842092\pi$
$397$	−5.85024	−	25.6316i	−0.293615	−	1.28641i	0.585839	−	0.810428i	$-0.300765\pi$
$398$	1.82735	−	8.00614i	0.0915967	−	0.401311i
$399$	−8.64542	−	7.83989i	−0.432812	−	0.392485i
$400$	1.18736	+	5.20218i	0.0593682	+	0.260109i
$401$	−24.2979	+	11.7012i	−1.21338	+	0.584332i	−0.927460	−	0.373922i	$-0.878013\pi$
$401$	−24.2979	+	11.7012i	−1.21338	+	0.584332i	−0.285918	+	0.958254i	$0.592298\pi$
$402$	−2.68839	+	11.7786i	−0.134085	+	0.587463i
$403$	−10.2754	−	4.94838i	−0.511855	−	0.246496i
$404$	16.8896	−	21.1789i	0.840288	−	1.05369i
$405$	0.266985	+	0.128573i	0.0132666	+	0.00638886i
$406$	−0.883066	+	1.57069i	−0.0438258	+	0.0779519i
$407$	−13.7162	+	6.60538i	−0.679888	+	0.327417i
$408$	−3.32895	+	14.5851i	−0.164808	+	0.722070i
$409$	−6.52047	+	8.17642i	−0.322417	+	0.404298i	−0.916454	−	0.400140i	$-0.868962\pi$
$409$	−6.52047	+	8.17642i	−0.322417	+	0.404298i	0.594038	+	0.804437i	$0.297533\pi$
$410$	−1.61748			−0.0798818
$411$	−20.3170			−1.00216
$412$	6.57880	−	8.24956i	0.324114	−	0.406427i
$413$	5.34939	+	13.1851i	0.263226	+	0.648795i
$414$	0.923433	+	1.15795i	0.0453843	+	0.0569101i
$415$	−1.85252	−	2.32299i	−0.0909366	−	0.114031i
$416$	−13.9937	+	6.73901i	−0.686098	+	0.330407i
$417$	−12.4547	+	5.99786i	−0.609908	+	0.293716i
$418$	−6.57103	−	8.23981i	−0.321400	−	0.403022i
$419$	1.57886	+	1.97983i	0.0771324	+	0.0967210i	0.818901	−	0.573935i	$-0.194584\pi$
$419$	1.57886	+	1.97983i	0.0771324	+	0.0967210i	−0.741768	+	0.670656i	$0.766013\pi$
$420$	1.13840	−	0.184911i	0.0555483	−	0.00902275i
$421$	23.8498	−	29.9067i	1.16237	−	1.45756i	0.298097	−	0.954536i	$-0.403648\pi$
$421$	23.8498	−	29.9067i	1.16237	−	1.45756i	0.864271	−	0.503027i	$-0.167780\pi$
$422$	8.49354			0.413459
$423$	−20.0995			−0.977272
$424$	−6.05430	+	7.59186i	−0.294023	+	0.368693i
$425$	−5.64109	+	24.7152i	−0.273633	+	1.19886i
$426$	−5.99709	+	2.88805i	−0.290560	+	0.139926i
$427$	2.28968	−	36.0806i	0.110805	−	1.74606i
$428$	3.85320	+	1.85561i	0.186252	+	0.0896941i
$429$	7.14486	−	8.95937i	0.344957	−	0.432563i
$430$	0.829929	+	0.399673i	0.0400227	+	0.0192739i
$431$	7.67071	−	33.6076i	0.369485	−	1.61882i	−0.358710	−	0.933449i	$-0.616783\pi$
$431$	7.67071	−	33.6076i	0.369485	−	1.61882i	0.728195	−	0.685370i	$-0.240360\pi$
$432$	−5.24115	+	2.52400i	−0.252165	+	0.121436i
$433$	−5.96946	−	26.1539i	−0.286874	−	1.25688i	−0.888789	−	0.458317i	$-0.848453\pi$
$433$	−5.96946	−	26.1539i	−0.286874	−	1.25688i	0.601915	−	0.798560i	$-0.294405\pi$
$434$	8.20466	−	1.33269i	0.393836	−	0.0639710i
$435$	0.0616683	−	0.270187i	0.00295677	−	0.0129545i
$436$	0.924469	+	4.05036i	0.0442740	+	0.193977i
$437$	2.88902	+	3.62271i	0.138200	+	0.173298i
$438$	1.57596	+	6.90471i	0.0753021	+	0.329920i
$439$	21.6152	+	10.4093i	1.03164	+	0.496810i	0.871557	−	0.490294i	$-0.163110\pi$
$439$	21.6152	+	10.4093i	1.03164	+	0.496810i	0.160080	+	0.987104i	$0.448825\pi$
$440$	2.46225			0.117383
$441$	−1.14567	−	11.6952i	−0.0545557	−	0.556915i
$442$	−9.95986			−0.473742
$443$	10.4083	+	5.01236i	0.494512	+	0.238144i	0.664481	−	0.747305i	$-0.268653\pi$
$443$	10.4083	+	5.01236i	0.494512	+	0.238144i	−0.169969	+	0.985449i	$0.554367\pi$
$444$	−1.51892	−	6.65483i	−0.0720848	−	0.315824i
$445$	1.17557	+	1.47411i	0.0557272	+	0.0698797i
$446$	0.543743	+	2.38229i	0.0257470	+	0.112805i
$447$	−5.17068	+	22.6542i	−0.244565	+	1.07151i
$448$	2.74265	−	4.87828i	0.129578	−	0.230477i
$449$	−6.63613	−	29.0748i	−0.313178	−	1.37212i	−0.849268	−	0.527963i	$-0.822956\pi$
$449$	−6.63613	−	29.0748i	−0.313178	−	1.37212i	0.536089	−	0.844161i	$-0.319901\pi$
$450$	5.45181	−	2.62546i	0.257001	−	0.123765i
$451$	−7.15745	+	31.3588i	−0.337031	+	1.47663i
$452$	−0.0136757	−	0.00658588i	−0.000643252	−	0.000309774i
$453$	14.7385	−	18.4815i	0.692476	−	0.868337i
$454$	0.565682	+	0.272418i	0.0265488	+	0.0127852i
$455$	0.682458	+	1.68211i	0.0319941	+	0.0788585i
$456$	10.0654	−	4.84724i	0.471355	−	0.226993i
$457$	−1.44215	+	6.31846i	−0.0674608	+	0.295565i	−0.997393	−	0.0721670i	$-0.977009\pi$
$457$	−1.44215	+	6.31846i	−0.0674608	+	0.295565i	0.929932	+	0.367732i	$0.119866\pi$
$458$	5.62617	−	7.05499i	0.262894	−	0.329658i
$459$	−27.6373			−1.29000
$460$	−0.457901			−0.0213497
$461$	−5.99718	+	7.52022i	−0.279316	+	0.350252i	−0.901624	−	0.432521i	$-0.857624\pi$
$461$	−5.99718	+	7.52022i	−0.279316	+	0.350252i	0.622307	+	0.782773i	$0.286195\pi$
$462$	−0.528955	+	8.33523i	−0.0246092	+	0.387790i
$463$	2.59801	+	3.25780i	0.120740	+	0.151403i	0.838528	−	0.544859i	$-0.183417\pi$
$463$	2.59801	+	3.25780i	0.120740	+	0.151403i	−0.717788	+	0.696262i	$0.754845\pi$
$464$	0.628605	+	0.788246i	0.0291823	+	0.0365934i
$465$	−1.15182	+	0.554687i	−0.0534144	+	0.0257230i
$466$	−8.28887	+	3.99171i	−0.383974	+	0.184912i
$467$	−0.583834	−	0.732105i	−0.0270166	−	0.0338778i	0.768140	−	0.640282i	$-0.221183\pi$
$467$	−0.583834	−	0.732105i	−0.0270166	−	0.0338778i	−0.795156	+	0.606405i	$0.792611\pi$
$468$	−4.07033	−	5.10403i	−0.188151	−	0.235934i
$469$	−31.1982	+	21.7968i	−1.44060	+	1.00648i
$470$	−1.41092	+	1.76924i	−0.0650809	+	0.0816089i
$471$	−2.37989			−0.109660
$472$	−13.6205			−0.626934
$473$	11.4211	−	14.3216i	0.525143	−	0.658508i
$474$	1.61496	−	7.07561i	0.0741777	−	0.324994i
$475$	17.0563	−	8.21390i	0.782598	−	0.376880i
$476$	−16.3406	+	11.4165i	−0.748970	+	0.523272i
$477$	−5.79907	−	2.79268i	−0.265521	−	0.127868i
$478$	−2.32997	+	2.92169i	−0.106570	+	0.133635i
$479$	5.99336	+	2.88625i	0.273843	+	0.131876i	0.565766	−	0.824566i	$-0.308581\pi$
$479$	5.99336	+	2.88625i	0.273843	+	0.131876i	−0.291922	+	0.956442i	$0.594295\pi$
$480$	−0.387417	+	1.69738i	−0.0176831	+	0.0774747i
$481$	9.67982	−	4.66156i	0.441362	−	0.212549i
$482$	2.97532	+	13.0357i	0.135522	+	0.593762i
$483$	0.232560	−	3.66466i	0.0105819	−	0.166748i
$484$	1.02002	−	4.46900i	0.0463645	−	0.203136i
$485$	0.469649	+	2.05766i	0.0213256	+	0.0934337i
$486$	6.75034	+	8.46466i	0.306202	+	0.383965i
$487$	−1.65154	−	7.23588i	−0.0748385	−	0.327889i	0.923625	−	0.383297i	$-0.125211\pi$
$487$	−1.65154	−	7.23588i	−0.0748385	−	0.327889i	−0.998464	+	0.0554076i	$0.982354\pi$
$488$	31.1801	+	15.0155i	1.41145	+	0.679721i
$489$	8.29371			0.375054
$490$	−1.10988	−	0.720119i	−0.0501393	−	0.0325317i
$491$	−8.22580			−0.371225			−0.185612	−	0.982623i	$-0.559427\pi$
$491$	−8.22580			−0.371225			−0.185612	+	0.982623i	$0.559427\pi$
$492$	−12.9938	−	6.25749i	−0.585807	−	0.282110i
$493$	1.06586	+	4.66982i	0.0480037	+	0.210318i
$494$	4.63731	+	5.81501i	0.208643	+	0.261629i
$495$	0.363175	+	1.59118i	0.0163235	+	0.0715180i
$496$	1.03491	−	4.53424i	0.0464688	−	0.203593i
$497$	−20.1058	−	5.95113i	−0.901867	−	0.266944i
$498$	2.14676	+	9.40558i	0.0961987	+	0.421474i
$499$	11.2435	−	5.41457i	0.503327	−	0.242389i	−0.164950	−	0.986302i	$-0.552746\pi$
$499$	11.2435	−	5.41457i	0.503327	−	0.242389i	0.668277	+	0.743913i	$0.267032\pi$
$500$	−0.838229	+	3.67252i	−0.0374868	+	0.164240i
$501$	−9.95639	−	4.79474i	−0.444819	−	0.214213i
$502$	8.98534	−	11.2673i	0.401035	−	0.502882i
$503$	28.4640	+	13.7075i	1.26915	+	0.611188i	0.942578	−	0.333986i	$-0.108394\pi$
$503$	28.4640	+	13.7075i	1.26915	+	0.611188i	0.326567	+	0.945174i	$0.394108\pi$
$504$	10.7861	+	3.19260i	0.480453	+	0.142210i
$505$	4.30604	−	2.07368i	0.191616	−	0.0922774i
$506$	0.737874	−	3.23284i	0.0328025	−	0.143717i
$507$	4.27452	−	5.36008i	0.189838	−	0.238049i
$508$	−0.335217			−0.0148728
$509$	−6.20074			−0.274843			−0.137421	−	0.990513i	$-0.543881\pi$
$509$	−6.20074			−0.274843			−0.137421	+	0.990513i	$0.543881\pi$
$510$	−0.696094	+	0.872874i	−0.0308235	+	0.0386515i
$511$	−10.9335	+	19.4472i	−0.483672	+	0.860294i
$512$	−7.36511	−	9.23555i	−0.325495	−	0.408158i
$513$	12.8679	+	16.1359i	0.568134	+	0.712417i
$514$	−7.41337	+	3.57009i	−0.326990	+	0.157470i
$515$	1.67728	−	0.807735i	0.0739098	−	0.0355931i
$516$	5.12092	+	6.42143i	0.225436	+	0.282688i
$517$	28.0576	+	35.1831i	1.23397	+	1.54735i
$518$	−3.83747	+	6.82560i	−0.168609	+	0.299900i
$519$	9.67182	−	12.1281i	0.424546	−	0.532364i
$520$	−1.73766			−0.0762014
$521$	37.6658			1.65017			0.825085	−	0.565008i	$-0.191127\pi$
$521$	37.6658			1.65017			0.825085	+	0.565008i	$0.191127\pi$
$522$	0.712847	−	0.893882i	0.0312005	−	0.0391241i
$523$	−2.56784	+	11.2504i	−0.112284	+	0.491947i	0.887247	+	0.461296i	$0.152615\pi$
$523$	−2.56784	+	11.2504i	−0.112284	+	0.491947i	−0.999530	+	0.0306511i	$0.990242\pi$
$524$	−14.2440	+	6.85953i	−0.622250	+	0.299660i
$525$	−14.3855	−	4.25798i	−0.627835	−	0.185834i
$526$	−1.76924	−	0.852020i	−0.0771424	−	0.0371498i
$527$	13.7765	−	17.2752i	0.600116	−	0.752521i
$528$	4.21033	+	2.02759i	0.183231	+	0.0882395i
$529$	4.79357	−	21.0020i	0.208416	−	0.913130i
$530$	−0.652899	+	0.314419i	−0.0283601	+	0.0136575i
$531$	−2.00899	−	8.80196i	−0.0871827	−	0.381972i
$532$	14.2736	+	4.22486i	0.618840	+	0.183171i
$533$	5.05116	−	22.1306i	0.218790	−	0.958581i
$534$	−1.36229	−	5.96857i	−0.0589519	−	0.258285i
$535$	0.470457	+	0.589934i	0.0203396	+	0.0255051i
$536$	−8.10662	−	35.5174i	−0.350153	−	1.53412i
$537$	1.96871	+	0.948080i	0.0849560	+	0.0409127i
$538$	2.45085			0.105664
$539$	−18.8725	+	18.3312i	−0.812897	+	0.789579i
$540$	−2.03953			−0.0877675
$541$	−2.01290	−	0.969363i	−0.0865414	−	0.0416762i	0.390112	−	0.920767i	$-0.372436\pi$
$541$	−2.01290	−	0.969363i	−0.0865414	−	0.0416762i	−0.476654	+	0.879091i	$0.658150\pi$
$542$	0.646057	+	2.83056i	0.0277505	+	0.121583i
$543$	4.76898	+	5.98012i	0.204657	+	0.256631i
$544$	−6.69599	−	29.3371i	−0.287088	−	1.25782i
$545$	−0.163106	+	0.714615i	−0.00698670	+	0.0306107i
$546$	0.373295	−	5.88234i	0.0159755	−	0.251741i
$547$	5.63344	+	24.6817i	0.240868	+	1.05531i	0.940229	+	0.340544i	$0.110611\pi$
$547$	5.63344	+	24.6817i	0.240868	+	1.05531i	−0.699360	+	0.714769i	$0.746532\pi$
$548$	23.3475	−	11.2436i	0.997356	−	0.480301i
$549$	−5.10448	+	22.3642i	−0.217854	+	0.954481i
$550$	−12.2061	−	5.87814i	−0.520469	−	0.250645i
$551$	2.23018	−	2.79656i	0.0950091	−	0.119138i
$552$	3.16692	+	1.52511i	0.134793	+	0.0649130i
$553$	18.7413	−	13.0937i	0.796960	−	0.556801i
$554$	−7.64050	+	3.67947i	−0.324614	+	0.156326i
$555$	0.267987	−	1.17413i	0.0113754	−	0.0498389i
$556$	10.9932	−	13.7850i	0.466214	−	0.584614i
$557$	−20.8421			−0.883108			−0.441554	−	0.897235i	$-0.645573\pi$
$557$	−20.8421			−0.883108			−0.441554	+	0.897235i	$0.645573\pi$
$558$	−5.27412			−0.223271
$559$	−8.06011	+	10.1071i	−0.340906	+	0.427483i
$560$	−0.606830	+	0.423965i	−0.0256432	+	0.0179158i
$561$	13.8425	+	17.3580i	0.584432	+	0.732854i
$562$	11.8347	+	14.8402i	0.499216	+	0.625997i
$563$	−28.8148	+	13.8765i	−1.21440	+	0.584823i	−0.927746	−	0.373211i	$-0.878257\pi$
$563$	−28.8148	+	13.8765i	−1.21440	+	0.584823i	−0.286652	+	0.958035i	$0.592542\pi$
$564$	−18.1790	+	8.75455i	−0.765474	+	0.368633i
$565$	−0.00166974	−	0.00209378i	−7.02464e−5	−	8.80862e-5i
$566$	−5.83994	−	7.32306i	−0.245471	−	0.307811i
$567$	0.191961	−	3.02490i	0.00806159	−	0.127034i
$568$	12.5143	−	15.6925i	0.525090	−	0.658442i
$569$	−19.1151			−0.801349			−0.400674	−	0.916221i	$-0.631224\pi$
$569$	−19.1151			−0.801349			−0.400674	+	0.916221i	$0.631224\pi$
$570$	0.833724			0.0349208
$571$	2.63603	−	3.30547i	0.110314	−	0.138330i	−0.723609	−	0.690210i	$-0.757518\pi$
$571$	2.63603	−	3.30547i	0.110314	−	0.138330i	0.833923	+	0.551880i	$0.186090\pi$
$572$	−3.25242	+	14.2498i	−0.135990	+	0.595813i
$573$	9.65173	−	4.64803i	0.403207	−	0.194174i
$574$	6.21982	+	15.3305i	0.259610	+	0.639883i
$575$	5.36652	+	2.58438i	0.223799	+	0.107776i
$576$	−2.21398	+	2.77624i	−0.0922491	+	0.115677i
$577$	−28.1347	−	13.5490i	−1.17126	−	0.564050i	−0.255909	−	0.966701i	$-0.582375\pi$
$577$	−28.1347	−	13.5490i	−1.17126	−	0.564050i	−0.915354	+	0.402650i	$0.868089\pi$
$578$	1.52977	−	6.70237i	0.0636301	−	0.278782i
$579$	1.70801	−	0.822535i	0.0709825	−	0.0341834i
$580$	0.0786562	+	0.344615i	0.00326602	+	0.0143094i
$581$	−14.8936	+	26.4909i	−0.617893	+	1.09903i
$582$	1.52494	−	6.68120i	0.0632108	−	0.276944i
$583$	3.20667	+	14.0493i	0.132807	+	0.581865i
$584$	−13.3153	−	16.6968i	−0.550990	−	0.690920i
$585$	−0.256300	−	1.12293i	−0.0105967	−	0.0464272i
$586$	−7.33871	−	3.53413i	−0.303159	−	0.145994i
$587$	−41.5631			−1.71549			−0.857747	−	0.514072i	$-0.828136\pi$
$587$	−41.5631			−1.71549			−0.857747	+	0.514072i	$0.828136\pi$
$588$	−6.13017	−	10.0787i	−0.252804	−	0.415640i
$589$	−16.5004			−0.679888
$590$	−0.915807	−	0.441029i	−0.0377032	−	0.0181569i
$591$	−0.269507	−	1.18079i	−0.0110861	−	0.0485712i
$592$	2.73167	+	3.42541i	0.112271	+	0.140784i
$593$	−1.41781	−	6.21181i	−0.0582223	−	0.255089i	0.937438	−	0.348153i	$-0.113191\pi$
$593$	−1.41781	−	6.21181i	−0.0582223	−	0.255089i	−0.995660	+	0.0930642i	$0.970334\pi$
$594$	3.28656	−	14.3993i	0.134849	−	0.590812i
$595$	−3.47144	+	0.563869i	−0.142315	+	0.0231164i
$596$	−6.59505	−	28.8948i	−0.270144	−	1.18358i
$597$	11.6393	−	5.60518i	0.476364	−	0.229405i
$598$	−0.520733	+	2.28148i	−0.0212944	+	0.0932967i
$599$	40.0702	+	19.2968i	1.63722	+	0.788445i	0.999840	+	0.0178981i	$0.00569744\pi$
$599$	40.0702	+	19.2968i	1.63722	+	0.788445i	0.637383	+	0.770547i	$0.280017\pi$
$600$	8.95390	−	11.2278i	0.365542	−	0.458375i
$601$	−17.4078	−	8.38317i	−0.710080	−	0.341956i	0.0437351	−	0.999043i	$-0.486074\pi$
$601$	−17.4078	−	8.38317i	−0.710080	−	0.341956i	−0.753815	+	0.657087i	$0.771789\pi$
$602$	0.596713	−	9.40296i	0.0243202	−	0.383236i
$603$	21.7567	−	10.4775i	0.886000	−	0.426675i
$604$	−6.70912	+	29.3946i	−0.272990	+	1.19605i
$605$	0.504249	−	0.632308i	0.0205006	−	0.0257070i
$606$	−15.5184			−0.630393
$607$	−11.4898			−0.466355			−0.233178	−	0.972434i	$-0.574912\pi$
$607$	−11.4898			−0.466355			−0.233178	+	0.972434i	$0.574912\pi$
$608$	−14.0106	+	17.5688i	−0.568206	+	0.712507i
$609$	−2.79797	+	0.454476i	−0.113379	+	0.0184163i
$610$	1.61027	+	2.01921i	0.0651978	+	0.0817554i
$611$	−19.8008	−	24.8294i	−0.801055	−	1.00449i
$612$	11.3954	−	5.48776i	0.460634	−	0.221829i
$613$	−7.56177	+	3.64156i	−0.305417	+	0.147081i	−0.580314	−	0.814392i	$-0.697070\pi$
$613$	−7.56177	+	3.64156i	−0.305417	+	0.147081i	0.274898	+	0.961474i	$0.411356\pi$
$614$	−0.813992	−	1.02071i	−0.0328501	−	0.0411927i
$615$	−1.58648	−	1.98938i	−0.0639730	−	0.0802196i
$616$	−9.46826	−	23.3372i	−0.381487	−	0.940282i
$617$	−29.3392	+	36.7902i	−1.18115	+	1.48112i	−0.339910	+	0.940458i	$0.610397\pi$
$617$	−29.3392	+	36.7902i	−1.18115	+	1.48112i	−0.841241	+	0.540660i	$0.818175\pi$
$618$	−6.04471			−0.243154
$619$	19.3218			0.776609			0.388305	−	0.921531i	$-0.373061\pi$
$619$	19.3218			0.776609			0.388305	+	0.921531i	$0.373061\pi$
$620$	1.01666	−	1.27485i	0.0408300	−	0.0511992i
$621$	−1.44497	+	6.33081i	−0.0579845	+	0.254047i
$622$	13.4881	−	6.49553i	0.540824	−	0.260447i
$623$	9.45117	−	16.8105i	0.378653	−	0.673500i
$624$	−2.97132	−	1.43091i	−0.118948	−	0.0572823i
$625$	14.9643	−	18.7646i	0.598571	−	0.750584i
$626$	−12.1057	−	5.82979i	−0.483841	−	0.233005i
$627$	3.68927	−	16.1638i	0.147335	−	0.645518i
$628$	2.73487	−	1.31705i	0.109133	−	0.0525559i
$629$	4.63180	+	20.2932i	0.184682	+	0.809144i
$630$	0.621856	+	0.563916i	0.0247754	+	0.0224669i
$631$	−0.00581131	+	0.0254610i	−0.000231345	+	0.00101359i	−0.975043	−	0.222014i	$-0.928737\pi$
$631$	−0.00581131	+	0.0254610i	−0.000231345	+	0.00101359i	0.974812	+	0.223028i	$0.0715940\pi$
$632$	4.86979	+	21.3359i	0.193710	+	0.848698i
$633$	8.33074	+	10.4464i	0.331117	+	0.415208i
$634$	2.38968	+	10.4699i	0.0949064	+	0.415812i
$635$	−0.0532860	−	0.0256612i	−0.00211459	−	0.00101833i
$636$	−6.46135			−0.256209
$637$	13.3187	−	12.9367i	0.527707	−	0.512570i
$638$	−2.55978			−0.101342
$639$	11.9868	+	5.77252i	0.474189	+	0.228357i
$640$	−0.585124	−	2.56359i	−0.0231290	−	0.101335i
$641$	16.3199	+	20.4645i	0.644598	+	0.808300i	0.991570	−	0.129575i	$-0.0413614\pi$
$641$	16.3199	+	20.4645i	0.644598	+	0.808300i	−0.346972	+	0.937876i	$0.612790\pi$
$642$	−0.545181	−	2.38859i	−0.0215166	−	0.0942703i
$643$	−1.66446	+	7.29249i	−0.0656400	+	0.287588i	−0.997085	−	0.0762934i	$-0.975691\pi$
$643$	−1.66446	+	7.29249i	−0.0656400	+	0.287588i	0.931445	+	0.363881i	$0.118549\pi$
$644$	1.76080	+	4.33999i	0.0693852	+	0.171019i
$645$	0.322454	+	1.41276i	0.0126966	+	0.0556275i
$646$	−12.9828	+	6.25218i	−0.510801	+	0.245989i
$647$	3.39776	−	14.8865i	0.133580	−	0.585250i	−0.863186	−	0.504886i	$-0.831535\pi$
$647$	3.39776	−	14.8865i	0.133580	−	0.585250i	0.996766	−	0.0803642i	$-0.0256083\pi$
$648$	2.61405	+	1.25886i	0.102690	+	0.0494527i
$649$	−12.6029	+	15.8036i	−0.494708	+	0.620344i
$650$	8.61408	+	4.14832i	0.337872	+	0.162711i
$651$	9.68650	+	8.78397i	0.379644	+	0.344271i
$652$	−9.53080	+	4.58979i	−0.373255	+	0.179750i
$653$	6.22154	−	27.2584i	0.243468	−	1.06670i	−0.694367	−	0.719621i	$-0.744316\pi$
$653$	6.22154	−	27.2584i	0.243468	−	1.06670i	0.937835	−	0.347081i	$-0.112827\pi$
$654$	1.48391	−	1.86077i	0.0580256	−	0.0727618i
$655$	−2.78932			−0.108988
$656$	9.25683			0.361418
$657$	8.82600	−	11.0675i	0.344335	−	0.431783i
$658$	22.1944	+	6.56933i	0.865226	+	0.256099i
$659$	−0.573070	−	0.718608i	−0.0223237	−	0.0279930i	0.770544	−	0.637386i	$-0.219984\pi$
$659$	−0.573070	−	0.718608i	−0.0223237	−	0.0279930i	−0.792868	+	0.609393i	$0.791413\pi$
$660$	1.02153	+	1.28095i	0.0397629	+	0.0498611i
$661$	−31.5584	+	15.1977i	−1.22748	+	0.591122i	−0.931384	−	0.364037i	$-0.881398\pi$
$661$	−31.5584	+	15.1977i	−1.22748	+	0.591122i	−0.296093	+	0.955159i	$0.595684\pi$
$662$	−12.6568	+	6.09521i	−0.491922	+	0.236897i
$663$	−9.76896	−	12.2499i	−0.379395	−	0.475746i
$664$	−18.1380	−	22.7444i	−0.703892	−	0.882653i
$665$	1.94552	+	1.76424i	0.0754439	+	0.0684145i
$666$	3.09776	−	3.88446i	0.120036	−	0.150520i
$667$	1.12543			0.0435768
$668$	14.0949			0.545349
$669$	−2.39672	+	3.00539i	−0.0926626	+	0.116195i
$670$	0.604980	−	2.65059i	0.0233724	−	0.102401i
$671$	46.2728	−	22.2838i	1.78634	−	0.860257i
$672$	17.5776	−	2.85514i	0.678070	−	0.110139i
$673$	28.4634	+	13.7072i	1.09718	+	0.528375i	0.892771	−	0.450510i	$-0.148758\pi$
$673$	28.4634	+	13.7072i	1.09718	+	0.528375i	0.204411	+	0.978885i	$0.434472\pi$
$674$	−5.77228	+	7.23821i	−0.222340	+	0.278806i
$675$	23.9030	+	11.5111i	0.920026	+	0.443061i
$676$	−1.94581	+	8.52513i	−0.0748387	+	0.327890i
$677$	−9.38776	+	4.52091i	−0.360801	+	0.173753i	−0.605498	−	0.795847i	$-0.707026\pi$
$677$	−9.38776	+	4.52091i	−0.360801	+	0.173753i	0.244697	+	0.969600i	$0.421312\pi$
$678$	0.00193495	+	0.00847756i	7.43112e−5	+	0.000325579i
$679$	17.6966	−	12.3638i	0.679132	−	0.474480i
$680$	0.749129	−	3.28215i	0.0287278	−	0.125865i
$681$	0.219786	+	0.962944i	0.00842220	+	0.0369001i
$682$	7.36232	+	9.23206i	0.281918	+	0.353514i
$683$	5.18944	+	22.7364i	0.198568	+	0.869985i	0.971790	+	0.235849i	$0.0757870\pi$
$683$	5.18944	+	22.7364i	0.198568	+	0.869985i	−0.773221	+	0.634136i	$0.781356\pi$
$684$	−8.50972	−	4.09806i	−0.325377	−	0.156693i
$685$	4.57203			0.174688
$686$	−2.55739	+	13.2886i	−0.0976415	+	0.507360i
$687$	14.1954			0.541590
$688$	−4.74967	−	2.28732i	−0.181079	−	0.0872033i
$689$	−2.26301	−	9.91491i	−0.0862140	−	0.377728i
$690$	0.163553	+	0.205089i	0.00622636	+	0.00780760i
$691$	1.99341	+	8.73369i	0.0758328	+	0.332245i	0.998587	−	0.0531441i	$-0.0169243\pi$
$691$	1.99341	+	8.73369i	0.0758328	+	0.332245i	−0.922754	+	0.385389i	$0.874067\pi$
$692$	−4.40272	+	19.2896i	−0.167366	+	0.733279i
$693$	13.6846	−	9.56084i	0.519836	−	0.363186i
$694$	4.09200	+	17.9282i	0.155330	+	0.680546i
$695$	2.80273	−	1.34972i	0.106314	−	0.0511979i
$696$	0.603795	−	2.64540i	0.0228868	−	0.100274i
$697$	39.6234	+	19.0816i	1.50084	+	0.722767i
$698$	0.434470	−	0.544808i	0.0164449	−	0.0206213i
$699$	−13.0395	−	6.27949i	−0.493199	−	0.237512i
$700$	18.8877	−	3.06793i	0.713886	−	0.115957i
$701$	−45.0009	+	21.6713i	−1.69966	+	0.818513i	−0.705731	+	0.708480i	$0.749381\pi$
$701$	−45.0009	+	21.6713i	−1.69966	+	0.818513i	−0.993928	+	0.110033i	$0.964904\pi$
$702$	−2.31939	+	10.1619i	−0.0875398	+	0.383537i
$703$	9.69152	−	12.1528i	0.365523	−	0.458351i
$704$	7.95022			0.299635
$705$	−3.55991			−0.134074
$706$	12.3957	−	15.5437i	0.466517	−	0.584994i
$707$	−36.2126	−	32.8386i	−1.36192	−	1.23502i
$708$	−5.65081	−	7.08590i	−0.212371	−	0.266304i
$709$	1.11191	+	1.39429i	0.0417586	+	0.0523636i	0.802272	−	0.596958i	$-0.203624\pi$
$709$	1.11191	+	1.39429i	0.0417586	+	0.0523636i	−0.760514	+	0.649322i	$0.775053\pi$
$710$	1.34955	−	0.649910i	0.0506478	−	0.0243907i
$711$	−13.0696	+	6.29399i	−0.490149	+	0.236043i
$712$	11.5100	+	14.4331i	0.431355	+	0.540902i
$713$	−3.23692	−	4.05896i	−0.121223	−	0.152009i
$714$	10.9498	+	3.24105i	0.409787	+	0.121293i
$715$	−1.60784	+	2.01617i	−0.0601298	+	0.0754004i
$716$	−2.78703			−0.104156
$717$	−5.87878			−0.219547
$718$	9.73793	−	12.2110i	0.363416	−	0.455710i
$719$	−2.70364	+	11.8454i	−0.100829	+	0.441759i	0.899163	+	0.437615i	$0.144177\pi$
$719$	−2.70364	+	11.8454i	−0.100829	+	0.441759i	−0.999991	+	0.00414497i	$0.998681\pi$
$720$	0.423185	−	0.203795i	0.0157712	−	0.00759500i
$721$	−14.1055	−	12.7912i	−0.525316	−	0.476370i
$722$	−2.81302	−	1.35468i	−0.104690	−	0.0504160i
$723$	−13.1147	+	16.4453i	−0.487741	+	0.611608i
$724$	−8.78976	−	4.23292i	−0.326669	−	0.157315i
$725$	1.02316	−	4.48277i	0.0379993	−	0.166486i
$726$	−2.36595	+	1.13938i	−0.0878085	+	0.0422864i
$727$	−8.06887	−	35.3520i	−0.299258	−	1.31113i	−0.871235	−	0.490866i	$-0.836681\pi$
$727$	−8.06887	−	35.3520i	−0.299258	−	1.31113i	0.571977	−	0.820269i	$-0.306177\pi$
$728$	6.68195	+	16.4695i	0.247649	+	0.610402i
$729$	−4.55470	+	19.9555i	−0.168693	+	0.739091i
$730$	−0.354644	−	1.55380i	−0.0131260	−	0.0575086i
$731$	−15.6157	−	19.5815i	−0.577569	−	0.724248i
$732$	5.12421	+	22.4506i	0.189396	+	0.829799i
$733$	4.20646	+	2.02572i	0.155369	+	0.0748218i	0.509952	−	0.860203i	$-0.329663\pi$
$733$	4.20646	+	2.02572i	0.155369	+	0.0748218i	−0.354583	+	0.935024i	$0.615377\pi$
$734$	−1.43902			−0.0531152
$735$	−0.202914	−	2.07139i	−0.00748460	−	0.0764042i
$736$	−7.07025			−0.260613
$737$	−48.7111	−	23.4580i	−1.79430	−	0.864087i
$738$	−2.33588	−	10.2342i	−0.0859851	−	0.376725i
$739$	−5.91557	−	7.41789i	−0.217608	−	0.272871i	0.661031	−	0.750359i	$-0.270119\pi$
$739$	−5.91557	−	7.41789i	−0.217608	−	0.272871i	−0.878639	+	0.477487i	$0.841548\pi$
$740$	0.341810	+	1.49757i	0.0125652	+	0.0550516i
$741$	−2.60359	+	11.4071i	−0.0956454	+	0.419050i
$742$	5.49071	+	4.97912i	0.201570	+	0.182789i
$743$	−0.942029	−	4.12730i	−0.0345597	−	0.151416i	0.954704	−	0.297557i	$-0.0961718\pi$
$743$	−0.942029	−	4.12730i	−0.0345597	−	0.151416i	−0.989264	+	0.146141i	$0.953315\pi$
$744$	−11.2775	+	5.43094i	−0.413452	+	0.199108i
$745$	1.16358	−	5.09798i	0.0426303	−	0.186776i
$746$	10.6158	+	5.11229i	0.388671	+	0.187174i
$747$	12.0228	−	15.0761i	0.439890	−	0.551604i
$748$	−25.5133	−	12.2866i	−0.932858	−	0.449241i
$749$	3.78232	−	6.72751i	0.138203	−	0.245818i
$750$	1.94428	−	0.936317i	0.0709952	−	0.0341895i
$751$	3.10685	−	13.6120i	0.113371	−	0.496709i	−0.886079	−	0.463534i	$-0.846581\pi$
$751$	3.10685	−	13.6120i	0.113371	−	0.496709i	0.999450	−	0.0331749i	$-0.0105618\pi$
$752$	8.07467	−	10.1253i	0.294453	−	0.369233i
$753$	22.6710			0.826177
$754$	1.80649			0.0657884
$755$	−3.31667	+	4.15897i	−0.120706	+	0.151361i
$756$	7.84276	+	19.3307i	0.285238	+	0.703050i
$757$	−1.94703	−	2.44150i	−0.0707659	−	0.0887377i	0.745189	−	0.666854i	$-0.232359\pi$
$757$	−1.94703	−	2.44150i	−0.0707659	−	0.0887377i	−0.815954	+	0.578116i	$0.803788\pi$
$758$	−12.4865	−	15.6576i	−0.453531	−	0.568710i
$759$	4.69988	−	2.26334i	0.170595	−	0.0821541i
$760$	−2.26506	+	1.09079i	−0.0821623	+	0.0395673i
$761$	7.73460	+	9.69888i	0.280379	+	0.351584i	0.902002	−	0.431733i	$-0.142098\pi$
$761$	7.73460	+	9.69888i	0.280379	+	0.351584i	−0.621623	+	0.783317i	$0.713526\pi$
$762$	0.119733	+	0.150140i	0.00433746	+	0.00543900i
$763$	7.40033	−	1.20204i	0.267910	−	0.0435167i
$764$	−8.51914	+	10.6827i	−0.308212	+	0.386485i
$765$	2.23151			0.0806806
$766$	4.43037			0.160076
$767$	8.89414	−	11.1529i	0.321149	−	0.402708i
$768$	−2.98195	+	13.0648i	−0.107602	+	0.471435i
$769$	−31.1973	+	15.0238i	−1.12500	+	0.541773i	−0.901435	−	0.432915i	$-0.857485\pi$
$769$	−31.1973	+	15.0238i	−1.12500	+	0.541773i	−0.223569	+	0.974688i	$0.571771\pi$
$770$	0.119033	−	1.87571i	0.00428966	−	0.0675960i
$771$	−11.6622	−	5.61623i	−0.420005	−	0.202264i
$772$	−1.50758	+	1.89045i	−0.0542591	+	0.0680387i
$773$	−3.93189	−	1.89350i	−0.141420	−	0.0681043i	0.361835	−	0.932242i	$-0.382150\pi$
$773$	−3.93189	−	1.89350i	−0.141420	−	0.0681043i	−0.503255	+	0.864138i	$0.667865\pi$
$774$	−1.33028	+	5.82833i	−0.0478159	+	0.209495i
$775$	−19.1103	+	9.20302i	−0.686461	+	0.330582i
$776$	4.59833	+	20.1466i	0.165070	+	0.723221i
$777$	−12.1589	+	1.97498i	−0.436198	+	0.0708518i
$778$	−3.45527	+	15.1385i	−0.123877	+	0.542743i
$779$	−7.30796	−	32.0183i	−0.261835	−	1.14717i
$780$	−0.720912	−	0.903996i	−0.0258128	−	0.0323682i
$781$	−6.62824	−	29.0402i	−0.237177	−	1.03914i
$782$	−4.08484	−	1.96716i	−0.146074	−	0.0703454i
$783$	5.01277			0.179142
$784$	6.35183	+	4.12123i	0.226851	+	0.147187i
$785$	0.535557			0.0191149
$786$	8.15996	+	3.92963i	0.291056	+	0.140165i
$787$	−6.98539	−	30.6050i	−0.249002	−	1.09095i	−0.932549	−	0.361043i	$-0.882421\pi$
$787$	−6.98539	−	30.6050i	−0.249002	−	1.09095i	0.683547	−	0.729907i	$-0.260437\pi$
$788$	0.963163	+	1.20777i	0.0343113	+	0.0430250i
$789$	−0.687405	−	3.01172i	−0.0244723	−	0.107220i
$790$	−0.363422	+	1.59226i	−0.0129300	+	0.0566499i
$791$	−0.0134241	+	0.0238772i	−0.000477307	+	0.000848974i
$792$	3.55585	+	15.5792i	0.126352	+	0.553583i
$793$	−32.6557	+	15.7261i	−1.15964	+	0.558452i
$794$	4.27467	−	18.7285i	0.151702	−	0.664651i
$795$	−1.02710	−	0.494624i	−0.0364274	−	0.0175425i
$796$	−10.2734	+	12.8825i	−0.364133	+	0.456608i
$797$	9.32295	+	4.48970i	0.330236	+	0.159033i	0.591653	−	0.806193i	$-0.298476\pi$
$797$	9.32295	+	4.48970i	0.330236	+	0.159033i	−0.261417	+	0.965226i	$0.584190\pi$
$798$	−3.20598	−	7.90203i	−0.113490	−	0.279729i
$799$	55.4351	−	26.6961i	1.96115	−	0.944441i
$800$	−6.42778	+	28.1619i	−0.227256	+	0.995675i
$801$	−7.62936	+	9.56692i	−0.269570	+	0.338030i
$802$	−19.7055			−0.695824
$803$	−31.6935			−1.11844
$804$	15.1143	−	18.9527i	0.533039	−	0.668410i
$805$	−0.0523341	+	0.824676i	−0.00184453	+	0.0290660i
$806$	−5.19574	−	6.51525i	−0.183012	−	0.229490i
$807$	2.40387	+	3.01436i	0.0846203	+	0.106111i
$808$	42.1604	−	20.3034i	1.48320	−	0.714270i
$809$	34.3743	−	16.5538i	1.20854	−	0.582001i	0.282439	−	0.959285i	$-0.408856\pi$
$809$	34.3743	−	16.5538i	1.20854	−	0.582001i	0.926097	+	0.377284i	$0.123142\pi$
$810$	0.135000	+	0.169285i	0.00474343	+	0.00594807i
$811$	−1.66424	−	2.08689i	−0.0584393	−	0.0732805i	0.751753	−	0.659445i	$-0.229209\pi$
$811$	−1.66424	−	2.08689i	−0.0584393	−	0.0732805i	−0.810192	+	0.586164i	$0.800637\pi$
$812$	2.96380	−	2.07068i	0.104009	−	0.0726666i
$813$	−2.84770	+	3.57091i	−0.0998733	+	0.125237i
$814$	−11.1238			−0.389889
$815$	−1.86637			−0.0653761
$816$	3.98373	−	4.99544i	0.139459	−	0.174875i
$817$	−4.16186	+	18.2343i	−0.145605	+	0.637937i
$818$	−6.88475	+	3.31552i	−0.240720	+	0.115924i
$819$	−9.65752	+	6.74728i	−0.337461	+	0.235769i
$820$	2.92406	+	1.40815i	0.102112	+	0.0491748i
$821$	8.37914	−	10.5071i	0.292434	−	0.366701i	−0.613811	−	0.789453i	$-0.710364\pi$
$821$	8.37914	−	10.5071i	0.292434	−	0.366701i	0.906245	+	0.422752i	$0.138936\pi$
$822$	−13.3751	−	6.44112i	−0.466511	−	0.224660i
$823$	−10.2282	+	44.8125i	−0.356531	+	1.56207i	0.405234	+	0.914213i	$0.367190\pi$
$823$	−10.2282	+	44.8125i	−0.356531	+	1.56207i	−0.761765	+	0.647853i	$0.775667\pi$
$824$	16.4223	−	7.90854i	0.572096	−	0.275507i
$825$	−4.74245	−	20.7780i	−0.165111	−	0.723398i
$826$	−0.658459	+	10.3759i	−0.0229107	+	0.361025i
$827$	−2.47685	+	10.8518i	−0.0861286	+	0.377354i	−0.999561	−	0.0296370i	$-0.990565\pi$
$827$	−2.47685	+	10.8518i	−0.0861286	+	0.377354i	0.913432	+	0.406991i	$0.133422\pi$
$828$	−0.661277	−	2.89724i	−0.0229810	−	0.100686i
$829$	18.1309	+	22.7354i	0.629712	+	0.789634i	0.989675	−	0.143333i	$-0.0457820\pi$
$829$	18.1309	+	22.7354i	0.629712	+	0.789634i	−0.359963	+	0.932967i	$0.617211\pi$
$830$	−0.483095	−	2.11658i	−0.0167685	−	0.0734675i
$831$	−12.0195	−	5.78830i	−0.416953	−	0.200794i
$832$	−5.61063			−0.194514
$833$	18.6933	+	30.7341i	0.647686	+	1.06487i
$834$	−10.1007			−0.349758
$835$	2.24053	+	1.07898i	0.0775367	+	0.0373397i
$836$	4.70556	+	20.6164i	0.162745	+	0.713033i
$837$	−14.4175	−	18.0790i	−0.498342	−	0.624901i
$838$	0.411731	+	1.80391i	0.0142230	+	0.0623151i
$839$	0.785984	−	3.44362i	0.0271352	−	0.118887i	−0.959546	−	0.281550i	$-0.909151\pi$
$839$	0.785984	−	3.44362i	0.0271352	−	0.118887i	0.986682	+	0.162663i	$0.0520085\pi$
$840$	1.91038	+	0.565454i	0.0659143	+	0.0195100i
$841$	6.25979	+	27.4259i	0.215855	+	0.945721i
$842$	25.1822	−	12.1271i	0.867835	−	0.417927i
$843$	−6.64452	+	29.1115i	−0.228849	+	1.00265i
$844$	−15.3545	−	7.39432i	−0.528523	−	0.254523i
$845$	−0.961914	+	1.20620i	−0.0330908	+	0.0414946i
$846$	−13.2319	−	6.37217i	−0.454924	−	0.219080i
$847$	−7.93205	−	2.34781i	−0.272548	−	0.0806718i
$848$	3.73653	−	1.79942i	0.128313	−	0.0617923i
$849$	3.27881	−	14.3654i	0.112528	−	0.493019i
$850$	−11.5491	+	14.4822i	−0.396133	+	0.496735i
$851$	4.89069			0.167651
$852$	13.3557			0.457559
$853$	22.6874	−	28.4491i	0.776802	−	0.974079i	−0.223197	−	0.974773i	$-0.571649\pi$
$853$	22.6874	−	28.4491i	0.776802	−	0.974079i	1.00000		0.000693882i	$0.000220870\pi$
$854$	12.9460	−	23.0267i	0.443003	−	0.787958i
$855$	−1.03899	−	1.30286i	−0.0355328	−	0.0445568i
$856$	4.60624	+	5.77605i	0.157438	+	0.197421i
$857$	23.3152	−	11.2280i	0.796432	−	0.383541i	0.00901278	−	0.999959i	$-0.497131\pi$
$857$	23.3152	−	11.2280i	0.796432	−	0.383541i	0.787419	+	0.616418i	$0.211417\pi$
$858$	7.54402	−	3.63301i	0.257549	−	0.124029i
$859$	−15.5741	−	19.5293i	−0.531381	−	0.666331i	0.441601	−	0.897212i	$-0.354411\pi$
$859$	−15.5741	−	19.5293i	−0.531381	−	0.666331i	−0.972982	+	0.230880i	$0.925839\pi$
$860$	−1.15238	−	1.44504i	−0.0392959	−	0.0492755i
$861$	−12.7548	+	22.6866i	−0.434681	+	0.773156i
$862$	15.7044	−	19.6927i	0.534895	−	0.670737i
$863$	27.8885			0.949334			0.474667	−	0.880165i	$-0.342568\pi$
$863$	27.8885			0.949334			0.474667	+	0.880165i	$0.342568\pi$
$864$	−31.4915			−1.07136
$865$	−2.17649	+	2.72924i	−0.0740030	+	0.0927968i
$866$	4.36178	−	19.1102i	0.148219	−	0.649391i
$867$	9.74386	−	4.69240i	0.330919	−	0.159362i
$868$	−15.9924	−	4.73362i	−0.542819	−	0.160669i
$869$	29.2616	+	14.0916i	0.992631	+	0.478026i
$870$	0.126255	−	0.158319i	0.00428045	−	0.00536752i
$871$	34.3764	+	16.5548i	1.16480	+	0.560938i
$872$	−1.59697	+	6.99680i	−0.0540803	+	0.236941i
$873$	−12.3411	+	5.94315i	−0.417682	+	0.201145i
$874$	0.753391	+	3.30082i	0.0254838	+	0.111652i
$875$	6.51838	+	1.92938i	0.220361	+	0.0652250i
$876$	3.16213	−	13.8542i	0.106839	−	0.468091i
$877$	4.10168	+	17.9706i	0.138504	+	0.606825i	0.995764	+	0.0919422i	$0.0293075\pi$
$877$	4.10168	+	17.9706i	0.138504	+	0.606825i	−0.857260	+	0.514883i	$0.827835\pi$
$878$	10.9297	+	13.7054i	0.368859	+	0.462534i
$879$	−2.85132	−	12.4925i	−0.0961727	−	0.421360i
$880$	−0.947470	−	0.456277i	−0.0319392	−	0.0153811i
$881$	15.8868			0.535239			0.267619	−	0.963525i	$-0.413763\pi$
$881$	15.8868			0.535239			0.267619	+	0.963525i	$0.413763\pi$
$882$	2.95352	−	8.06242i	0.0994503	−	0.271476i
$883$	14.2002			0.477874			0.238937	−	0.971035i	$-0.423201\pi$
$883$	14.2002			0.477874			0.238937	+	0.971035i	$0.423201\pi$
$884$	18.0053	+	8.67087i	0.605582	+	0.291633i
$885$	−0.355820	−	1.55895i	−0.0119608	−	0.0524035i
$886$	5.26292	+	6.59949i	0.176811	+	0.221714i
$887$	3.86344	+	16.9268i	0.129722	+	0.568347i	0.997454	+	0.0713153i	$0.0227197\pi$
$887$	3.86344	+	16.9268i	0.129722	+	0.568347i	−0.867732	+	0.497032i	$0.834423\pi$
$888$	2.62386	−	11.4959i	0.0880510	−	0.385776i
$889$	−0.0383123	+	0.603722i	−0.00128495	+	0.0202482i
$890$	0.306561	+	1.34313i	0.0102760	+	0.0450219i
$891$	3.87939	−	1.86821i	0.129964	−	0.0625875i
$892$	1.09101	−	4.78004i	0.0365298	−	0.160048i
$893$	−41.3970	−	19.9357i	−1.38530	−	0.667124i
$894$	−10.5861	+	13.2745i	−0.354051	+	0.443966i
$895$	−0.443027	−	0.213351i	−0.0148088	−	0.00713152i
$896$	−22.0477	+	15.4038i	−0.736563	+	0.514604i
$897$	−3.31680	+	1.59729i	−0.110745	+	0.0533319i
$898$	4.84890	−	21.2444i	0.161810	−	0.708936i
$899$	−2.49874	+	3.13333i	−0.0833378	+	0.104502i
$900$	−12.1414			−0.404712
$901$	19.7033			0.656410
$902$	−14.6536	+	18.3751i	−0.487912	+	0.611823i
$903$	12.1502	−	8.48881i	0.404334	−	0.282490i
$904$	−0.0163484	−	0.0205002i	−0.000543740	−	0.000681828i
$905$	−1.07319	−	1.34573i	−0.0356739	−	0.0447336i
$906$	15.5619	−	7.49421i	0.517009	−	0.248979i
$907$	−2.01064	+	0.968275i	−0.0667623	+	0.0321510i	−0.466967	−	0.884275i	$-0.654653\pi$
$907$	−2.01064	+	0.968275i	−0.0667623	+	0.0321510i	0.400205	+	0.916426i	$0.368939\pi$
$908$	−0.785468	−	0.984946i	−0.0260667	−	0.0326866i
$909$	19.3392	+	24.2506i	0.641440	+	0.804341i
$910$	−0.0840041	+	1.32373i	−0.00278471	+	0.0438812i
$911$	−11.5362	+	14.4660i	−0.382213	+	0.479279i	−0.935306	−	0.353840i	$-0.884876\pi$
$911$	−11.5362	+	14.4660i	−0.382213	+	0.479279i	0.553093	+	0.833119i	$0.313447\pi$
$912$	−4.77139			−0.157996
$913$	−43.1727			−1.42881
$914$	−2.95255	+	3.70238i	−0.0976615	+	0.122464i
$915$	−0.904076	+	3.96101i	−0.0298878	+	0.130947i
$916$	−16.3128	+	7.85585i	−0.538991	+	0.259564i
$917$	10.7260	+	26.4372i	0.354203	+	0.873034i
$918$	−18.1943	−	8.76189i	−0.600500	−	0.289186i
$919$	−15.2508	+	19.1239i	−0.503078	+	0.630840i	−0.966921	−	0.255078i	$-0.917899\pi$
$919$	−15.2508	+	19.1239i	−0.503078	+	0.630840i	0.463843	+	0.885918i	$0.346470\pi$
$920$	−0.712667	−	0.343202i	−0.0234959	−	0.0113150i
$921$	0.457012	−	2.00230i	0.0150590	−	0.0659780i
$922$	−6.33222	+	3.04944i	−0.208540	+	0.100428i
$923$	4.67769	+	20.4943i	0.153968	+	0.674577i
$924$	8.21274	−	14.6078i	0.270179	−	0.480561i
$925$	4.44627	−	19.4804i	0.146192	−	0.640511i
$926$	0.677501	+	2.96833i	0.0222641	+	0.0975453i
$927$	7.53297	+	9.44604i	0.247415	+	0.310249i
$928$	1.21450	+	5.32106i	0.0398678	+	0.174672i
$929$	16.9841	+	8.17913i	0.557232	+	0.268349i	0.691232	−	0.722633i	$-0.257068\pi$
$929$	16.9841	+	8.17913i	0.557232	+	0.268349i	−0.134001	+	0.990981i	$0.542782\pi$
$930$	−0.934121			−0.0306310
$931$	9.24028	−	25.2238i	0.302838	−	0.826676i
$932$	18.4596			0.604663
$933$	21.2186	+	10.2183i	0.694665	+	0.334533i
$934$	−0.152251	−	0.667054i	−0.00498180	−	0.0218267i
$935$	−3.11504	−	3.90614i	−0.101873	−	0.127744i
$936$	−2.50944	−	10.9946i	−0.0820235	−	0.359369i
$937$	−3.86556	+	16.9361i	−0.126282	+	0.553280i	0.871714	+	0.490014i	$0.163009\pi$
$937$	−3.86556	+	16.9361i	−0.126282	+	0.553280i	−0.997997	+	0.0632651i	$0.979849\pi$
$938$	−27.4487	+	4.45851i	−0.896231	+	0.145575i
$939$	−4.70345	−	20.6071i	−0.153491	−	0.672489i
$940$	4.09090	−	1.97007i	0.133431	−	0.0642568i
$941$	7.18111	−	31.4625i	0.234098	−	1.02565i	−0.712105	−	0.702073i	$-0.752258\pi$
$941$	7.18111	−	31.4625i	0.234098	−	1.02565i	0.946202	−	0.323575i	$-0.104885\pi$
$942$	−1.56673	−	0.754499i	−0.0510469	−	0.0245829i
$943$	6.44261	−	8.07877i	0.209800	−	0.263081i
$944$	5.24115	+	2.52400i	0.170585	+	0.0821494i
$945$	−0.233101	+	3.67318i	−0.00758276	+	0.119489i
$946$	12.0592	−	5.80738i	0.392077	−	0.188814i
$947$	−3.99576	+	17.5066i	−0.129845	+	0.568888i	0.867588	+	0.497283i	$0.165669\pi$
$947$	−3.99576	+	17.5066i	−0.129845	+	0.568888i	−0.997433	+	0.0716043i	$0.977188\pi$
$948$	−9.07940	+	11.3852i	−0.294885	+	0.369774i
$949$	22.3667			0.726055
$950$	13.8326			0.448789
$951$	−10.5333	+	13.2083i	−0.341565	+	0.428309i
$952$	−33.9889	+	5.52084i	−1.10159	+	0.178931i
$953$	−16.0421	−	20.1162i	−0.519655	−	0.651627i	0.450881	−	0.892584i	$-0.351110\pi$
$953$	−16.0421	−	20.1162i	−0.519655	−	0.651627i	−0.970536	+	0.240958i	$0.922539\pi$
$954$	−2.93229	−	3.67697i	−0.0949363	−	0.119046i
$955$	−2.17197	+	1.04597i	−0.0702834	+	0.0338467i
$956$	6.75566	−	3.25335i	0.218494	−	0.105221i
$957$	−2.51071	−	3.14833i	−0.0811598	−	0.101771i
$958$	3.03053	+	3.80016i	0.0979119	+	0.122778i
$959$	−17.5811	−	43.3337i	−0.567725	−	1.39932i
$960$	−0.392127	+	0.491711i	−0.0126558	+	0.0158699i
$961$	−12.5126			−0.403632
$962$	7.85029			0.253104
$963$	−3.05324	+	3.82864i	−0.0983892	+	0.123376i
$964$	5.96995	−	26.1561i	0.192279	−	0.842430i
$965$	−0.384361	+	0.185099i	−0.0123730	+	0.00595854i
$966$	1.31491	−	2.33880i	0.0423066	−	0.0752496i
$967$	−29.1779	−	14.0513i	−0.938297	−	0.451860i	−0.0987289	−	0.995114i	$-0.531478\pi$
$967$	−29.1779	−	14.0513i	−0.938297	−	0.451860i	−0.839568	+	0.543254i	$0.817192\pi$
$968$	4.93710	−	6.19093i	0.158685	−	0.198984i
$969$	−20.4237	−	9.83552i	−0.656103	−	0.315962i
$970$	−0.343164	+	1.50350i	−0.0110183	+	0.0482744i
$971$	18.4046	−	8.86317i	0.590630	−	0.284433i	−0.114599	−	0.993412i	$-0.536558\pi$
$971$	18.4046	−	8.86317i	0.590630	−	0.284433i	0.705229	+	0.708979i	$0.250844\pi$
$972$	−4.83396	−	21.1790i	−0.155049	−	0.679316i
$973$	−23.5702	−	21.3741i	−0.755627	−	0.685222i
$974$	1.20675	−	5.28713i	0.0386668	−	0.169411i
$975$	3.34685	+	14.6635i	0.107185	+	0.469607i
$976$	−9.21553	−	11.5559i	−0.294982	−	0.369896i
$977$	−0.550490	−	2.41186i	−0.0176118	−	0.0771621i	0.965358	−	0.260928i	$-0.0840284\pi$
$977$	−0.550490	−	2.41186i	−0.0176118	−	0.0771621i	−0.982970	+	0.183766i	$0.941171\pi$
$978$	5.45993	+	2.62936i	0.174589	+	0.0840777i
$979$	27.3964			0.875594
$980$	1.37950	+	2.26806i	0.0440665	+	0.0724505i
$981$	−4.75708			−0.151882
$982$	−5.41522	−	2.60783i	−0.172807	−	0.0832193i
$983$	13.4357	+	58.8656i	0.428532	+	1.87752i	0.477350	+	0.878714i	$0.341598\pi$
$983$	13.4357	+	58.8656i	0.428532	+	1.87752i	−0.0488176	+	0.998808i	$0.515545\pi$
$984$	−15.5332	−	19.4780i	−0.495181	−	0.620937i
$985$	0.0606484	+	0.265718i	0.00193242	+	0.00846648i
$986$	−0.778802	+	3.41215i	−0.0248021	+	0.108665i
$987$	13.6892	+	33.7408i	0.435731	+	1.07398i
$988$	−3.32081	−	14.5494i	−0.105649	−	0.462879i
$989$	−5.30192	+	2.55327i	−0.168591	+	0.0811893i
$990$	−0.265366	+	1.16264i	−0.00843388	+	0.0369512i
$991$	−16.6503	−	8.01838i	−0.528916	−	0.254712i	0.150314	−	0.988638i	$-0.451972\pi$
$991$	−16.6503	−	8.01838i	−0.528916	−	0.254712i	−0.679229	+	0.733926i	$0.737686\pi$
$992$	15.6978	−	19.6844i	0.498405	−	0.624980i
$993$	−19.9109	−	9.58858i	−0.631853	−	0.304284i
$994$	−11.3494	−	10.2919i	−0.359980	−	0.326440i
$995$	−2.61924	+	1.26136i	−0.0830354	+	0.0399877i
$996$	4.30745	−	18.8722i	0.136487	−	0.597988i
$997$	−19.8168	+	24.8494i	−0.627603	+	0.786989i	−0.989392	−	0.145271i	$-0.953595\pi$
$997$	−19.8168	+	24.8494i	−0.627603	+	0.786989i	0.361789	+	0.932260i	$0.382166\pi$
$998$	9.11840			0.288638
$999$	21.7836			0.689201

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.2.e.b.29.2	yes	12
3.2	odd	2		441.2.u.b.127.1		12
4.3	odd	2		784.2.u.b.225.2		12
7.2	even	3		343.2.g.b.116.1		12
7.3	odd	6		343.2.g.a.30.1		12
7.4	even	3		343.2.g.d.30.1		12
7.5	odd	6		343.2.g.c.116.1		12
7.6	odd	2		343.2.e.b.197.2		12
49.4	even	21		343.2.g.b.275.1		12
49.13	odd	14		2401.2.a.d.1.3		6
49.22	even	7	inner	49.2.e.b.22.2	✓	12
49.23	even	21		343.2.g.d.263.1		12
49.26	odd	42		343.2.g.a.263.1		12
49.27	odd	14		343.2.e.b.148.2		12
49.36	even	7		2401.2.a.c.1.3		6
49.45	odd	42		343.2.g.c.275.1		12
147.71	odd	14		441.2.u.b.316.1		12
196.71	odd	14		784.2.u.b.561.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.e.b.22.2	✓	12	49.22	even	7	inner
49.2.e.b.29.2	yes	12	1.1	even	1	trivial
343.2.e.b.148.2		12	49.27	odd	14
343.2.e.b.197.2		12	7.6	odd	2
343.2.g.a.30.1		12	7.3	odd	6
343.2.g.a.263.1		12	49.26	odd	42
343.2.g.b.116.1		12	7.2	even	3
343.2.g.b.275.1		12	49.4	even	21
343.2.g.c.116.1		12	7.5	odd	6
343.2.g.c.275.1		12	49.45	odd	42
343.2.g.d.30.1		12	7.4	even	3
343.2.g.d.263.1		12	49.23	even	21
441.2.u.b.127.1		12	3.2	odd	2
441.2.u.b.316.1		12	147.71	odd	14
784.2.u.b.225.2		12	4.3	odd	2
784.2.u.b.561.2		12	196.71	odd	14
2401.2.a.c.1.3		6	49.36	even	7
2401.2.a.d.1.3		6	49.13	odd	14

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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	49.e (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.658322 + 0.317031i) q^{2} +(0.255779 + 1.12064i) q^{3} +(-0.914101 - 1.14625i) q^{4} +(-0.0575591 - 0.252183i) q^{5} +(-0.186893 + 0.818832i) q^{6} +(-2.16885 + 1.51528i) q^{7} +(-0.563561 - 2.46912i) q^{8} +(1.51249 - 0.728379i) q^{9} +O(q^{10})\)	\(q+(0.658322 + 0.317031i) q^{2} +(0.255779 + 1.12064i) q^{3} +(-0.914101 - 1.14625i) q^{4} +(-0.0575591 - 0.252183i) q^{5} +(-0.186893 + 0.818832i) q^{6} +(-2.16885 + 1.51528i) q^{7} +(-0.563561 - 2.46912i) q^{8} +(1.51249 - 0.728379i) q^{9} +(0.0420574 - 0.184265i) q^{10} +(-3.38633 - 1.63077i) q^{11} +(1.05072 - 1.31756i) q^{12} +(2.38980 + 1.15087i) q^{13} +(-1.90819 + 0.309949i) q^{14} +(0.267884 - 0.129006i) q^{15} +(-0.240694 + 1.05455i) q^{16} +(-3.20407 + 4.01778i) q^{17} +1.22663 q^{18} +3.83757 q^{19} +(-0.236449 + 0.296497i) q^{20} +(-2.25283 - 2.04293i) q^{21} +(-1.71229 - 2.14714i) q^{22} +(0.752824 + 0.944011i) q^{23} +(2.62285 - 1.26310i) q^{24} +(4.44456 - 2.14039i) q^{25} +(1.20840 + 1.51528i) q^{26} +(3.35314 + 4.20471i) q^{27} +(3.71944 + 1.10092i) q^{28} +(0.581144 - 0.728732i) q^{29} +0.217253 q^{30} -4.29970 q^{31} +(-3.65090 + 4.57809i) q^{32} +(0.961355 - 4.21197i) q^{33} +(-3.38307 + 1.62920i) q^{34} +(0.506965 + 0.459729i) q^{35} +(-2.21747 - 1.06788i) q^{36} +(2.52543 - 3.16679i) q^{37} +(2.52636 + 1.21663i) q^{38} +(-0.678448 + 2.97247i) q^{39} +(-0.590232 + 0.284241i) q^{40} +(-1.90432 - 8.34336i) q^{41} +(-0.835418 - 2.05912i) q^{42} +(-1.08450 + 4.75152i) q^{43} +(1.22618 + 5.37225i) q^{44} +(-0.270742 - 0.339500i) q^{45} +(0.196319 + 0.860132i) q^{46} +(-10.7873 - 5.19488i) q^{47} -1.24333 q^{48} +(2.40784 - 6.57284i) q^{49} +3.60452 q^{50} +(-5.32202 - 2.56295i) q^{51} +(-0.865341 - 3.79131i) q^{52} +(-2.39053 - 2.99763i) q^{53} +(0.874424 + 3.83110i) q^{54} +(-0.216338 + 0.947838i) q^{55} +(4.96369 + 4.50121i) q^{56} +(0.981571 + 4.30054i) q^{57} +(0.613611 - 0.295499i) q^{58} +(1.19672 - 5.24319i) q^{59} +(-0.392746 - 0.189136i) q^{60} +(-8.51974 + 10.6834i) q^{61} +(-2.83058 - 1.36314i) q^{62} +(-2.17668 + 3.87160i) q^{63} +(-1.90577 + 0.917769i) q^{64} +(0.152674 - 0.668909i) q^{65} +(1.96821 - 2.46805i) q^{66} +14.3846 q^{67} +7.53421 q^{68} +(-0.865341 + 1.08510i) q^{69} +(0.187998 + 0.463373i) q^{70} +(4.94126 + 6.19615i) q^{71} +(-2.65084 - 3.32405i) q^{72} +(7.59732 - 3.65868i) q^{73} +(2.66651 - 1.28413i) q^{74} +(3.53543 + 4.43329i) q^{75} +(-3.50793 - 4.39881i) q^{76} +(9.81551 - 1.59434i) q^{77} +(-1.38900 + 1.74176i) q^{78} -8.64110 q^{79} +0.279793 q^{80} +(-0.714272 + 0.895669i) q^{81} +(1.39145 - 6.09634i) q^{82} +(10.3491 - 4.98384i) q^{83} +(-0.282382 + 4.44974i) q^{84} +(1.19764 + 0.576752i) q^{85} +(-2.22033 + 2.78421i) q^{86} +(0.965291 + 0.464860i) q^{87} +(-2.11816 + 9.28029i) q^{88} +(-6.56727 + 3.16263i) q^{89} +(-0.0706034 - 0.309334i) q^{90} +(-6.92701 + 1.12516i) q^{91} +(0.393912 - 1.72584i) q^{92} +(-1.09977 - 4.81842i) q^{93} +(-5.45456 - 6.83980i) q^{94} +(-0.220887 - 0.967770i) q^{95} +(-6.06422 - 2.92037i) q^{96} -8.15942 q^{97} +(3.66893 - 3.56369i) q^{98} -6.30961 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 2 q^{4} - 7 q^{5} - 7 q^{6} - 7 q^{7} + 6 q^{8} - 8 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 + 2 * q^4 - 7 * q^5 - 7 * q^6 - 7 * q^7 + 6 * q^8 - 8 * q^9	\( 12 q - 2 q^{2} + 2 q^{4} - 7 q^{5} - 7 q^{6} - 7 q^{7} + 6 q^{8} - 8 q^{9} + 14 q^{10} - 8 q^{11} - 14 q^{12} + 7 q^{13} - 28 q^{14} - 7 q^{15} + 16 q^{16} + 20 q^{18} - 14 q^{19} + 7 q^{20} + 21 q^{21} + 13 q^{22} - 2 q^{23} + 3 q^{25} - 7 q^{26} + 21 q^{27} + 14 q^{28} - 11 q^{29} + 42 q^{30} - 14 q^{31} - 24 q^{32} + 35 q^{33} - 42 q^{34} + 21 q^{35} - 13 q^{36} - 30 q^{37} + 21 q^{38} + 21 q^{41} - 35 q^{42} + 17 q^{43} - 6 q^{44} - 49 q^{45} - 16 q^{46} - 21 q^{47} + 7 q^{49} - 46 q^{50} + 7 q^{51} - 7 q^{52} + 6 q^{53} + 42 q^{54} - 28 q^{55} - 14 q^{56} + 7 q^{57} - 32 q^{58} + 14 q^{59} - 28 q^{60} - 7 q^{61} + 56 q^{62} + 14 q^{63} + 14 q^{64} + 14 q^{65} - 28 q^{66} + 48 q^{67} + 56 q^{68} - 7 q^{69} + 21 q^{70} - 39 q^{71} - 4 q^{72} + 42 q^{73} + 61 q^{74} + 7 q^{75} - 28 q^{76} + 21 q^{77} - 16 q^{79} + 42 q^{80} - 25 q^{81} + 28 q^{82} - 7 q^{83} + 42 q^{84} + 28 q^{85} + 17 q^{86} + 7 q^{87} - 11 q^{88} - 14 q^{89} - 14 q^{90} - 21 q^{91} + 16 q^{92} - 70 q^{93} - 49 q^{94} - 7 q^{95} - 70 q^{96} - 28 q^{97} - 28 q^{98} - 18 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 + 2 * q^4 - 7 * q^5 - 7 * q^6 - 7 * q^7 + 6 * q^8 - 8 * q^9 + 14 * q^10 - 8 * q^11 - 14 * q^12 + 7 * q^13 - 28 * q^14 - 7 * q^15 + 16 * q^16 + 20 * q^18 - 14 * q^19 + 7 * q^20 + 21 * q^21 + 13 * q^22 - 2 * q^23 + 3 * q^25 - 7 * q^26 + 21 * q^27 + 14 * q^28 - 11 * q^29 + 42 * q^30 - 14 * q^31 - 24 * q^32 + 35 * q^33 - 42 * q^34 + 21 * q^35 - 13 * q^36 - 30 * q^37 + 21 * q^38 + 21 * q^41 - 35 * q^42 + 17 * q^43 - 6 * q^44 - 49 * q^45 - 16 * q^46 - 21 * q^47 + 7 * q^49 - 46 * q^50 + 7 * q^51 - 7 * q^52 + 6 * q^53 + 42 * q^54 - 28 * q^55 - 14 * q^56 + 7 * q^57 - 32 * q^58 + 14 * q^59 - 28 * q^60 - 7 * q^61 + 56 * q^62 + 14 * q^63 + 14 * q^64 + 14 * q^65 - 28 * q^66 + 48 * q^67 + 56 * q^68 - 7 * q^69 + 21 * q^70 - 39 * q^71 - 4 * q^72 + 42 * q^73 + 61 * q^74 + 7 * q^75 - 28 * q^76 + 21 * q^77 - 16 * q^79 + 42 * q^80 - 25 * q^81 + 28 * q^82 - 7 * q^83 + 42 * q^84 + 28 * q^85 + 17 * q^86 + 7 * q^87 - 11 * q^88 - 14 * q^89 - 14 * q^90 - 21 * q^91 + 16 * q^92 - 70 * q^93 - 49 * q^94 - 7 * q^95 - 70 * q^96 - 28 * q^97 - 28 * q^98 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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