LMFDB - Embedded newform 722.2.i.b.501.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(7,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(114))

chi = DirichletCharacter(H, H._module([50]))

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

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

chi := DirichletCharacter("722.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.i (of order $57$, degree $36$, 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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$612$
Relative dimension:	$17$ over $\Q(\zeta_{57})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{57}]$

Embedding invariants

Embedding label			501.12
Character	$\chi$	$=$	722.501
Dual form			722.2.i.b.49.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.926494 - 0.376309i) q^{2} +(0.477385 + 0.106984i) q^{3} +(0.716783 + 0.697297i) q^{4} +(-0.0291194 - 1.05640i) q^{5} +(-0.402035 - 0.278765i) q^{6} +(-0.154422 - 0.609798i) q^{7} +(-0.401695 - 0.915773i) q^{8} +(-2.49662 - 1.17818i) q^{9} +O(q^{10})$	\(q+(-0.926494 - 0.376309i) q^{2} +(0.477385 + 0.106984i) q^{3} +(0.716783 + 0.697297i) q^{4} +(-0.0291194 - 1.05640i) q^{5} +(-0.402035 - 0.278765i) q^{6} +(-0.154422 - 0.609798i) q^{7} +(-0.401695 - 0.915773i) q^{8} +(-2.49662 - 1.17818i) q^{9} +(-0.370554 + 0.989705i) q^{10} +(-0.471774 + 5.69347i) q^{11} +(0.267581 + 0.409563i) q^{12} +(1.53303 + 4.90138i) q^{13} +(-0.0864018 + 0.623085i) q^{14} +(0.0991171 - 0.507424i) q^{15} +(0.0275543 + 0.999620i) q^{16} +(-2.59615 + 2.52558i) q^{17} +(1.86974 + 2.03108i) q^{18} +(-4.11767 + 1.42997i) q^{19} +(0.715751 - 0.777513i) q^{20} +(-0.00847974 - 0.307629i) q^{21} +(2.57960 - 5.09743i) q^{22} +(6.86081 - 1.53754i) q^{23} +(-0.0937898 - 0.480151i) q^{24} +(3.87728 - 0.213915i) q^{25} +(0.424089 - 5.11799i) q^{26} +(-2.22401 - 1.73101i) q^{27} +(0.314523 - 0.544771i) q^{28} +(7.70302 + 2.17821i) q^{29} +(-0.282780 + 0.432827i) q^{30} +(-0.196656 - 0.153064i) q^{31} +(0.350638 - 0.936511i) q^{32} +(-0.834330 + 2.66750i) q^{33} +(3.35572 - 1.36297i) q^{34} +(-0.639694 + 0.180888i) q^{35} +(-0.967990 - 2.58539i) q^{36} +(-0.800262 + 9.65772i) q^{37} +(4.35311 + 0.224658i) q^{38} +(0.207475 + 2.50385i) q^{39} +(-0.955725 + 0.451017i) q^{40} +(-6.06987 - 5.28625i) q^{41} +(-0.107907 + 0.288208i) q^{42} +(3.07472 + 8.21222i) q^{43} +(-4.30820 + 3.75201i) q^{44} +(-1.17193 + 2.67174i) q^{45} +(-6.93509 - 1.15726i) q^{46} +(-10.0475 - 6.96678i) q^{47} +(-0.0937898 + 0.480151i) q^{48} +(5.80831 - 3.14330i) q^{49} +(-3.67277 - 1.26086i) q^{50} +(-1.50956 + 0.927924i) q^{51} +(-2.31886 + 4.58220i) q^{52} +(2.62124 + 1.81753i) q^{53} +(1.40913 + 2.44069i) q^{54} +(6.02831 + 0.332591i) q^{55} +(-0.496406 + 0.386369i) q^{56} +(-2.11870 + 0.242120i) q^{57} +(-6.31712 - 4.91681i) q^{58} +(0.524415 + 0.456713i) q^{59} +(0.424871 - 0.294599i) q^{60} +(4.04667 + 5.50569i) q^{61} +(0.124601 + 0.215816i) q^{62} +(-0.332922 + 1.70437i) q^{63} +(-0.677282 + 0.735724i) q^{64} +(5.13317 - 1.76222i) q^{65} +(1.77681 - 2.15746i) q^{66} +(1.47504 + 0.163257i) q^{67} -3.62195 q^{68} +3.43974 q^{69} +(0.660742 + 0.0731309i) q^{70} +(-0.485397 + 0.660406i) q^{71} +(-0.0760681 + 2.75961i) q^{72} +(-3.90023 + 3.79421i) q^{73} +(4.37573 - 8.64668i) q^{74} +(1.87384 + 0.312688i) q^{75} +(-3.94859 - 1.84626i) q^{76} +(3.54472 - 0.591509i) q^{77} +(0.749999 - 2.39788i) q^{78} +(3.14883 + 8.41016i) q^{79} +(1.05520 - 0.0582168i) q^{80} +(4.38853 + 5.32870i) q^{81} +(3.63443 + 7.18183i) q^{82} +(-8.48221 + 4.59034i) q^{83} +(0.208431 - 0.226416i) q^{84} +(2.74361 + 2.66903i) q^{85} +(0.241623 - 8.76562i) q^{86} +(3.44427 + 1.86395i) q^{87} +(5.40344 - 1.85500i) q^{88} +(-4.09558 - 3.98424i) q^{89} +(2.09119 - 2.03434i) q^{90} +(2.75212 - 1.69172i) q^{91} +(5.98983 + 3.68194i) q^{92} +(-0.0775052 - 0.0941093i) q^{93} +(6.68728 + 10.2356i) q^{94} +(1.63052 + 4.30826i) q^{95} +(0.267581 - 0.409563i) q^{96} +(4.53528 - 0.501965i) q^{97} +(-6.56422 + 0.726527i) q^{98} +(7.88580 - 13.6586i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 612 q + 17 q^{2} - 19 q^{3} + 17 q^{4} + q^{5} - 2 q^{7} - 34 q^{8} + 4 q^{9}+O(q^{10}) $ 612 * q + 17 * q^2 - 19 * q^3 + 17 * q^4 + q^5 - 2 * q^7 - 34 * q^8 + 4 * q^9	\( 612 q + 17 q^{2} - 19 q^{3} + 17 q^{4} + q^{5} - 2 q^{7} - 34 q^{8} + 4 q^{9} + q^{10} - 28 q^{11} + 4 q^{13} - 18 q^{14} - 52 q^{15} + 17 q^{16} + 18 q^{17} - 46 q^{18} - 12 q^{19} - 2 q^{20} - 65 q^{21} + 33 q^{22} + 39 q^{23} + 20 q^{25} - 8 q^{26} + 158 q^{27} - 37 q^{28} - 42 q^{29} - 29 q^{30} + 12 q^{31} + 17 q^{32} + 60 q^{33} - q^{34} - 14 q^{35} + 23 q^{36} - 6 q^{37} + 76 q^{38} - 108 q^{39} + q^{40} + 8 q^{41} + 11 q^{42} + 7 q^{43} - 5 q^{44} - 101 q^{45} - 21 q^{46} + 105 q^{47} - 62 q^{49} - 78 q^{50} - 3 q^{51} + 4 q^{52} + 146 q^{53} - 79 q^{54} + 4 q^{55} - 21 q^{56} - 28 q^{57} + 8 q^{58} - 4 q^{59} - 14 q^{60} - 93 q^{61} - 6 q^{62} - 95 q^{63} - 34 q^{64} - 76 q^{65} - 16 q^{66} - 6 q^{67} + 78 q^{68} + 38 q^{69} + 81 q^{70} - 151 q^{71} + 23 q^{72} + 7 q^{73} - 35 q^{74} - 12 q^{75} - 7 q^{76} + 78 q^{77} - 3 q^{78} - 10 q^{79} + q^{80} + 58 q^{81} - 30 q^{82} + 67 q^{83} - 22 q^{84} - 6 q^{85} - 12 q^{86} - 109 q^{87} + 10 q^{88} - 25 q^{89} - 73 q^{90} + 37 q^{91} + q^{92} + 56 q^{93} - 39 q^{94} - 29 q^{95} - 153 q^{97} + 164 q^{98} - 116 q^{99}+O(q^{100}) \) 612 * q + 17 * q^2 - 19 * q^3 + 17 * q^4 + q^5 - 2 * q^7 - 34 * q^8 + 4 * q^9 + q^10 - 28 * q^11 + 4 * q^13 - 18 * q^14 - 52 * q^15 + 17 * q^16 + 18 * q^17 - 46 * q^18 - 12 * q^19 - 2 * q^20 - 65 * q^21 + 33 * q^22 + 39 * q^23 + 20 * q^25 - 8 * q^26 + 158 * q^27 - 37 * q^28 - 42 * q^29 - 29 * q^30 + 12 * q^31 + 17 * q^32 + 60 * q^33 - q^34 - 14 * q^35 + 23 * q^36 - 6 * q^37 + 76 * q^38 - 108 * q^39 + q^40 + 8 * q^41 + 11 * q^42 + 7 * q^43 - 5 * q^44 - 101 * q^45 - 21 * q^46 + 105 * q^47 - 62 * q^49 - 78 * q^50 - 3 * q^51 + 4 * q^52 + 146 * q^53 - 79 * q^54 + 4 * q^55 - 21 * q^56 - 28 * q^57 + 8 * q^58 - 4 * q^59 - 14 * q^60 - 93 * q^61 - 6 * q^62 - 95 * q^63 - 34 * q^64 - 76 * q^65 - 16 * q^66 - 6 * q^67 + 78 * q^68 + 38 * q^69 + 81 * q^70 - 151 * q^71 + 23 * q^72 + 7 * q^73 - 35 * q^74 - 12 * q^75 - 7 * q^76 + 78 * q^77 - 3 * q^78 - 10 * q^79 + q^80 + 58 * q^81 - 30 * q^82 + 67 * q^83 - 22 * q^84 - 6 * q^85 - 12 * q^86 - 109 * q^87 + 10 * q^88 - 25 * q^89 - 73 * q^90 + 37 * q^91 + q^92 + 56 * q^93 - 39 * q^94 - 29 * q^95 - 153 * q^97 + 164 * q^98 - 116 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{7}{57}\right)$

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 $

$2$	−0.926494	−	0.376309i	−0.655130	−	0.266091i
$2$	−0.926494	−	0.376309i	−0.655130	−	0.266091i
$3$	0.477385	+	0.106984i	0.275618	+	0.0617675i	0.354298	−	0.935132i	$-0.384720\pi$
$3$	0.477385	+	0.106984i	0.275618	+	0.0617675i	−0.0786802	+	0.996900i	$0.525071\pi$
$4$	0.716783	+	0.697297i	0.358391	+	0.348648i
$5$	−0.0291194	−	1.05640i	−0.0130226	−	0.472436i	−0.977821	−	0.209444i	$-0.932835\pi$
$5$	−0.0291194	−	1.05640i	−0.0130226	−	0.472436i	0.964798	−	0.262992i	$-0.0847093\pi$
$6$	−0.402035	−	0.278765i	−0.164130	−	0.113805i
$7$	−0.154422	−	0.609798i	−0.0583660	−	0.230482i	0.933343	−	0.358986i	$-0.116877\pi$
$7$	−0.154422	−	0.609798i	−0.0583660	−	0.230482i	−0.991709	+	0.128504i	$0.958983\pi$
$8$	−0.401695	−	0.915773i	−0.142021	−	0.323775i
$9$	−2.49662	−	1.17818i	−0.832207	−	0.392728i
$10$	−0.370554	+	0.989705i	−0.117179	+	0.312972i
$11$	−0.471774	+	5.69347i	−0.142245	+	1.71665i	0.435299	+	0.900286i	$0.356643\pi$
$11$	−0.471774	+	5.69347i	−0.142245	+	1.71665i	−0.577544	+	0.816360i	$0.695989\pi$
$12$	0.267581	+	0.409563i	0.0772440	+	0.118231i
$13$	1.53303	+	4.90138i	0.425187	+	1.35940i	0.882592	+	0.470139i	$0.155796\pi$
$13$	1.53303	+	4.90138i	0.425187	+	1.35940i	−0.457406	+	0.889258i	$0.651221\pi$
$14$	−0.0864018	+	0.623085i	−0.0230919	+	0.166526i
$15$	0.0991171	−	0.507424i	0.0255919	−	0.131016i
$16$	0.0275543	+	0.999620i	0.00688859	+	0.249905i
$17$	−2.59615	+	2.52558i	−0.629659	+	0.612542i	−0.941265	−	0.337669i	$-0.890361\pi$
$17$	−2.59615	+	2.52558i	−0.629659	+	0.612542i	0.311605	+	0.950212i	$0.399133\pi$
$18$	1.86974	+	2.03108i	0.440703	+	0.478731i
$19$	−4.11767	+	1.42997i	−0.944658	+	0.328058i
$19$	−4.11767	+	1.42997i	−0.944658	+	0.328058i
$20$	0.715751	−	0.777513i	0.160047	−	0.173857i
$21$	−0.00847974	−	0.307629i	−0.00185043	−	0.0671302i
$22$	2.57960	−	5.09743i	0.549973	−	1.08678i
$23$	6.86081	−	1.53754i	1.43058	−	0.320600i	0.566543	−	0.824032i	$-0.308281\pi$
$23$	6.86081	−	1.53754i	1.43058	−	0.320600i	0.864035	+	0.503432i	$0.167930\pi$
$24$	−0.0937898	−	0.480151i	−0.0191448	−	0.0980105i
$25$	3.87728	−	0.213915i	0.775455	−	0.0427831i
$26$	0.424089	−	5.11799i	0.0831707	−	1.00372i
$27$	−2.22401	−	1.73101i	−0.428010	−	0.333134i
$28$	0.314523	−	0.544771i	0.0594394	−	0.102952i
$29$	7.70302	+	2.17821i	1.43041	+	0.404483i	0.897248	−	0.441527i	$-0.145563\pi$
$29$	7.70302	+	2.17821i	1.43041	+	0.404483i	0.533167	+	0.846010i	$0.321002\pi$
$30$	−0.282780	+	0.432827i	−0.0516283	+	0.0790230i
$31$	−0.196656	−	0.153064i	−0.0353205	−	0.0274910i	0.596399	−	0.802688i	$-0.296598\pi$
$31$	−0.196656	−	0.153064i	−0.0353205	−	0.0274910i	−0.631719	+	0.775197i	$0.717650\pi$
$32$	0.350638	−	0.936511i	0.0619845	−	0.165553i
$33$	−0.834330	+	2.66750i	−0.145238	+	0.464353i
$34$	3.35572	−	1.36297i	0.575501	−	0.233748i
$35$	−0.639694	+	0.180888i	−0.108128	+	0.0305757i
$36$	−0.967990	−	2.58539i	−0.161332	−	0.430898i
$37$	−0.800262	+	9.65772i	−0.131562	+	1.58772i	0.536686	+	0.843782i	$0.319676\pi$
$37$	−0.800262	+	9.65772i	−0.131562	+	1.58772i	−0.668249	+	0.743938i	$0.732956\pi$
$38$	4.35311	+	0.224658i	0.706167	+	0.0364443i
$39$	0.207475	+	2.50385i	0.0332226	+	0.400937i
$40$	−0.955725	+	0.451017i	−0.151113	+	0.0713121i
$41$	−6.06987	−	5.28625i	−0.947954	−	0.825574i	0.0368365	−	0.999321i	$-0.488272\pi$
$41$	−6.06987	−	5.28625i	−0.947954	−	0.825574i	−0.984790	+	0.173748i	$0.944412\pi$
$42$	−0.107907	+	0.288208i	−0.0166505	+	0.0444714i
$43$	3.07472	+	8.21222i	0.468891	+	1.25235i	0.930834	+	0.365443i	$0.119082\pi$
$43$	3.07472	+	8.21222i	0.468891	+	1.25235i	−0.461943	+	0.886910i	$0.652847\pi$
$44$	−4.30820	+	3.75201i	−0.649485	+	0.565637i
$45$	−1.17193	+	2.67174i	−0.174701	+	0.398279i
$46$	−6.93509	−	1.15726i	−1.02252	−	0.170629i
$47$	−10.0475	−	6.96678i	−1.46558	−	1.01621i	−0.990686	−	0.136165i	$-0.956522\pi$
$47$	−10.0475	−	6.96678i	−1.46558	−	1.01621i	−0.474891	−	0.880044i	$-0.657513\pi$
$48$	−0.0937898	+	0.480151i	−0.0135374	+	0.0693039i
$49$	5.80831	−	3.14330i	0.829758	−	0.449043i
$50$	−3.67277	−	1.26086i	−0.519408	−	0.178313i
$51$	−1.50956	+	0.927924i	−0.211381	+	0.129935i
$52$	−2.31886	+	4.58220i	−0.321569	+	0.635437i
$53$	2.62124	+	1.81753i	0.360055	+	0.249657i	0.735994	−	0.676988i	$-0.236715\pi$
$53$	2.62124	+	1.81753i	0.360055	+	0.249657i	−0.375939	+	0.926644i	$0.622680\pi$
$54$	1.40913	+	2.44069i	0.191758	+	0.332135i
$55$	6.02831	+	0.332591i	0.812858	+	0.0448466i
$56$	−0.496406	+	0.386369i	−0.0663351	+	0.0516307i
$57$	−2.11870	+	0.242120i	−0.280628	+	0.0320695i
$58$	−6.31712	−	4.91681i	−0.829479	−	0.645609i
$59$	0.524415	+	0.456713i	0.0682730	+	0.0594590i	0.690215	−	0.723604i	$-0.257516\pi$
$59$	0.524415	+	0.456713i	0.0682730	+	0.0594590i	−0.621942	+	0.783063i	$0.713656\pi$
$60$	0.424871	−	0.294599i	0.0548506	−	0.0380325i
$61$	4.04667	+	5.50569i	0.518123	+	0.704931i	0.983648	−	0.180104i	$-0.0576433\pi$
$61$	4.04667	+	5.50569i	0.518123	+	0.704931i	−0.465525	+	0.885035i	$0.654135\pi$
$62$	0.124601	+	0.215816i	0.0158244	+	0.0274087i
$63$	−0.332922	+	1.70437i	−0.0419442	+	0.214731i
$64$	−0.677282	+	0.735724i	−0.0846602	+	0.0919655i
$65$	5.13317	−	1.76222i	0.636691	−	0.218576i
$66$	1.77681	−	2.15746i	0.218710	−	0.265565i
$67$	1.47504	+	0.163257i	0.180204	+	0.0199450i	0.199657	−	0.979866i	$-0.436017\pi$
$67$	1.47504	+	0.163257i	0.180204	+	0.0199450i	−0.0194531	+	0.999811i	$0.506192\pi$
$68$	−3.62195			−0.439226
$69$	3.43974			0.414096
$70$	0.660742	+	0.0731309i	0.0789738	+	0.00874082i
$71$	−0.485397	+	0.660406i	−0.0576060	+	0.0783758i	−0.833615	−	0.552347i	$-0.813733\pi$
$71$	−0.485397	+	0.660406i	−0.0576060	+	0.0783758i	0.776009	+	0.630722i	$0.217241\pi$
$72$	−0.0760681	+	2.75961i	−0.00896471	+	0.325223i
$73$	−3.90023	+	3.79421i	−0.456488	+	0.444078i	−0.889244	−	0.457433i	$-0.848769\pi$
$73$	−3.90023	+	3.79421i	−0.456488	+	0.444078i	0.432756	+	0.901511i	$0.357541\pi$
$74$	4.37573	−	8.64668i	0.508668	−	1.00516i
$75$	1.87384	+	0.312688i	0.216372	+	0.0361061i
$76$	−3.94859	−	1.84626i	−0.452934	−	0.211780i
$77$	3.54472	−	0.591509i	0.403958	−	0.0674087i
$78$	0.749999	−	2.39788i	0.0849207	−	0.271506i
$79$	3.14883	+	8.41016i	0.354271	+	0.946217i	0.985357	+	0.170504i	$0.0545395\pi$
$79$	3.14883	+	8.41016i	0.354271	+	0.946217i	−0.631086	+	0.775713i	$0.717390\pi$
$80$	1.05520	−	0.0582168i	0.117974	−	0.00650883i
$81$	4.38853	+	5.32870i	0.487615	+	0.592078i
$82$	3.63443	+	7.18183i	0.401356	+	0.793100i
$83$	−8.48221	+	4.59034i	−0.931043	+	0.503855i	−0.869326	−	0.494238i	$-0.835447\pi$
$83$	−8.48221	+	4.59034i	−0.931043	+	0.503855i	−0.0617168	+	0.998094i	$0.519658\pi$
$84$	0.208431	−	0.226416i	0.0227417	−	0.0247040i
$85$	2.74361	+	2.66903i	0.297587	+	0.289497i
$86$	0.241623	−	8.76562i	0.0260549	−	0.945222i
$87$	3.44427	+	1.86395i	0.369264	+	0.199836i
$88$	5.40344	−	1.85500i	0.576008	−	0.197744i
$89$	−4.09558	−	3.98424i	−0.434130	−	0.422328i	0.447489	−	0.894289i	$-0.352318\pi$
$89$	−4.09558	−	3.98424i	−0.434130	−	0.422328i	−0.881619	+	0.471961i	$0.843546\pi$
$90$	2.09119	−	2.03434i	0.220431	−	0.214438i
$91$	2.75212	−	1.69172i	0.288500	−	0.177341i
$92$	5.98983	+	3.68194i	0.624483	+	0.383868i
$93$	−0.0775052	−	0.0941093i	−0.00803691	−	0.00975868i
$94$	6.68728	+	10.2356i	0.689740	+	1.05573i
$95$	1.63052	+	4.30826i	0.167288	+	0.442018i
$96$	0.267581	−	0.409563i	0.0273099	−	0.0418009i
$97$	4.53528	−	0.501965i	0.460488	−	0.0509668i	0.123228	−	0.992378i	$-0.460675\pi$
$97$	4.53528	−	0.501965i	0.460488	−	0.0509668i	0.337260	+	0.941412i	$0.390500\pi$
$98$	−6.56422	+	0.726527i	−0.663086	+	0.0733903i
$99$	7.88580	−	13.6586i	0.792552	−	1.37274i
$100$	2.92833	+	2.55028i	0.292833	+	0.255028i
$101$	−5.40020	−	2.54842i	−0.537340	−	0.253577i	0.138838	−	0.990315i	$-0.455663\pi$
$101$	−5.40020	−	2.54842i	−0.537340	−	0.253577i	−0.676178	+	0.736738i	$0.736365\pi$
$102$	1.74779	−	0.291654i	0.173057	−	0.0288780i
$103$	−0.397103	+	1.56812i	−0.0391277	+	0.154512i	−0.985881	−	0.167449i	$-0.946447\pi$
$103$	−0.397103	+	1.56812i	−0.0391277	+	0.154512i	0.946753	+	0.321961i	$0.104342\pi$
$104$	3.87274	−	3.37277i	0.379753	−	0.330727i
$105$	−0.324732	+	0.0179160i	−0.0316906	+	0.00174842i
$106$	−1.74461	−	2.67033i	−0.169452	−	0.259365i
$107$	−13.3550	+	10.3946i	−1.29107	+	1.00488i	−0.292253	+	0.956341i	$0.594405\pi$
$107$	−13.3550	+	10.3946i	−1.29107	+	1.00488i	−0.998821	+	0.0485422i	$0.984542\pi$
$108$	−0.387098	−	2.79155i	−0.0372486	−	0.268617i
$109$	1.15140	−	0.798365i	0.110284	−	0.0764695i	−0.513382	−	0.858160i	$-0.671607\pi$
$109$	1.15140	−	0.798365i	0.110284	−	0.0764695i	0.623666	+	0.781691i	$0.285643\pi$
$110$	−5.46004	−	2.57665i	−0.520594	−	0.245674i
$111$	−1.41526	+	4.52483i	−0.134330	+	0.429478i
$112$	0.605312	−	0.171166i	0.0571966	−	0.0161737i
$113$	4.83271	−	19.0839i	0.454623	−	1.79527i	−0.138738	−	0.990329i	$-0.544304\pi$
$113$	4.83271	−	19.0839i	0.454623	−	1.79527i	0.593361	−	0.804937i	$-0.297801\pi$
$114$	2.05407	+	0.572963i	0.192381	+	0.0536629i
$115$	−1.82404	−	7.20298i	−0.170093	−	0.671681i
$116$	4.00253	+	6.93259i	0.371626	+	0.643675i
$117$	1.94732	−	14.0431i	0.180030	−	1.29828i
$118$	−0.314002	−	0.620485i	−0.0289062	−	0.0571202i
$119$	1.94099	+	1.19313i	0.177931	+	0.109374i
$120$	−0.504500	+	0.113061i	−0.0460544	+	0.0103210i
$121$	−21.3430	−	3.56152i	−1.94028	−	0.323775i
$122$	−1.67737	−	6.62379i	−0.151862	−	0.599689i
$123$	−2.33211	−	3.17296i	−0.210280	−	0.286096i
$124$	−0.0342289	−	0.246841i	−0.00307385	−	0.0221670i
$125$	−0.775233	−	9.35568i	−0.0693390	−	0.836797i
$126$	0.949821	−	1.45381i	0.0846168	−	0.129516i
$127$	4.69753	−	8.13635i	0.416838	−	0.721985i	−0.578781	−	0.815483i	$-0.696472\pi$
$127$	4.69753	−	8.13635i	0.416838	−	0.721985i	0.995619	+	0.0934981i	$0.0298049\pi$
$128$	0.904357	−	0.426776i	0.0799346	−	0.0377221i
$129$	0.589247	+	4.24934i	0.0518803	+	0.374133i
$130$	−5.41899	−	0.298974i	−0.475277	−	0.0262218i
$131$	−1.08895	+	7.85292i	−0.0951417	+	0.686113i	0.881647	+	0.471909i	$0.156435\pi$
$131$	−1.08895	+	7.85292i	−0.0951417	+	0.686113i	−0.976789	+	0.214204i	$0.931284\pi$
$132$	−2.45807	+	1.33024i	−0.213948	+	0.115783i
$133$	1.50785	+	2.29013i	0.130747	+	0.198579i
$134$	−1.30518	−	0.706327i	−0.112750	−	0.0610173i
$135$	−1.76388	+	2.39984i	−0.151810	+	0.206546i
$136$	3.35572	+	1.36297i	0.287750	+	0.116874i
$137$	0.940588	+	0.104104i	0.0803599	+	0.00889423i	0.150098	−	0.988671i	$-0.452041\pi$
$137$	0.940588	+	0.104104i	0.0803599	+	0.00889423i	−0.0697384	+	0.997565i	$0.522216\pi$
$138$	−3.18690	−	1.29441i	−0.271287	−	0.110187i
$139$	−1.29889	+	1.57715i	−0.110170	+	0.133772i	−0.824098	−	0.566447i	$-0.808318\pi$
$139$	−1.29889	+	1.57715i	−0.110170	+	0.133772i	0.713928	+	0.700219i	$0.246914\pi$
$140$	−0.584654	−	0.316399i	−0.0494123	−	0.0267406i
$141$	−4.05118	−	4.40076i	−0.341171	−	0.370611i
$142$	0.698234	−	0.429203i	0.0585945	−	0.0360179i
$143$	−28.6291	+	6.41593i	−2.39408	+	0.536527i
$144$	1.10894	−	2.52814i	0.0924120	−	0.210678i
$145$	2.07675	−	8.20089i	0.172465	−	0.681047i
$146$	5.04134	−	2.04761i	0.417224	−	0.169462i
$147$	3.10908	−	0.879165i	0.256433	−	0.0725123i
$148$	−7.30791	+	6.36447i	−0.600707	+	0.523156i
$149$	4.05318	+	20.7500i	0.332050	+	1.69991i	0.656763	+	0.754097i	$0.271925\pi$
$149$	4.05318	+	20.7500i	0.332050	+	1.69991i	−0.324713	+	0.945812i	$0.605268\pi$
$150$	−1.61843	−	0.994847i	−0.132144	−	0.0812289i
$151$	−2.73785	−	0.939904i	−0.222803	−	0.0764883i	0.211038	−	0.977478i	$-0.432316\pi$
$151$	−2.73785	−	0.939904i	−0.222803	−	0.0764883i	−0.433841	+	0.900990i	$0.642842\pi$
$152$	2.96358	+	3.19644i	0.240378	+	0.259265i
$153$	9.45720	−	3.24666i	0.764569	−	0.262477i
$154$	−3.50675	−	0.785882i	−0.282582	−	0.0633281i
$155$	−0.155970	+	0.212204i	−0.0125278	+	0.0170447i
$156$	−1.59721	+	1.93939i	−0.127879	+	0.155275i
$157$	−16.0385	−	3.59430i	−1.28001	−	0.286857i	−0.474929	−	0.880024i	$-0.657526\pi$
$157$	−16.0385	−	3.59430i	−1.28001	−	0.286857i	−0.805079	+	0.593167i	$0.797877\pi$
$158$	0.247447	−	8.97690i	0.0196858	−	0.714164i
$159$	1.05689	+	1.14809i	0.0838171	+	0.0910497i
$160$	−0.999540	−	0.343143i	−0.0790206	−	0.0271278i
$161$	−1.99705	−	3.94628i	−0.157390	−	0.311010i
$162$	−2.06071	−	6.58846i	−0.161905	−	0.517638i
$163$	−7.67829	+	5.97626i	−0.601410	+	0.468096i	−0.868577	−	0.495554i	$-0.834965\pi$
$163$	−7.67829	+	5.97626i	−0.601410	+	0.468096i	0.267167	+	0.963650i	$0.413913\pi$
$164$	−0.664688	−	8.02159i	−0.0519034	−	0.626381i
$165$	2.84224	+	0.803710i	0.221268	+	0.0625687i
$166$	9.58610	−	1.06099i	0.744026	−	0.0823488i
$167$	0.954629	+	0.269943i	0.0738714	+	0.0208888i	0.308839	−	0.951114i	$-0.400060\pi$
$167$	0.954629	+	0.269943i	0.0738714	+	0.0208888i	−0.234967	+	0.972003i	$0.575498\pi$
$168$	−0.278312	+	0.131339i	−0.0214723	+	0.0101330i
$169$	−10.9902	+	7.62044i	−0.845400	+	0.586187i
$170$	−1.53756	−	3.50529i	−0.117926	−	0.268843i
$171$	11.9650	+	1.28128i	0.914988	+	0.0979816i
$172$	−3.52245	+	8.03037i	−0.268584	+	0.612310i
$173$	−4.54971	−	23.2920i	−0.345908	−	1.77086i	−0.596350	−	0.802724i	$-0.703383\pi$
$173$	−4.54971	−	23.2920i	−0.345908	−	1.77086i	0.250442	−	0.968131i	$-0.419424\pi$
$174$	−2.48968	−	3.02305i	−0.188742	−	0.229176i
$175$	−0.729182	−	2.33132i	−0.0551209	−	0.176231i
$176$	−5.70431	−	0.314715i	−0.429978	−	0.0237226i
$177$	0.201486	+	0.274132i	0.0151447	+	0.0206050i
$178$	2.29522	+	5.23258i	0.172034	+	0.392198i
$179$	19.6700	−	3.28234i	1.47020	−	0.245333i	0.625355	−	0.780340i	$-0.284954\pi$
$179$	19.6700	−	3.28234i	1.47020	−	0.245333i	0.844848	+	0.535007i	$0.179691\pi$
$180$	−2.70301	+	1.09787i	−0.201471	+	0.0818303i
$181$	7.09034	−	2.87985i	0.527021	−	0.214057i	−0.0972576	−	0.995259i	$-0.531007\pi$
$181$	7.09034	−	2.87985i	0.527021	−	0.214057i	0.624279	+	0.781202i	$0.285393\pi$
$182$	−3.18643	+	0.531721i	−0.236194	+	0.0394138i
$183$	1.34279	+	3.06126i	0.0992622	+	0.226295i
$184$	−4.16400	−	5.66532i	−0.306974	−	0.417653i
$185$	10.2257	+	0.564168i	0.751809	+	0.0414785i
$186$	0.0363939	+	0.116358i	0.00266853	+	0.00853176i
$187$	−13.1545	−	15.9726i	−0.961952	−	1.16803i
$188$	−2.34396	−	11.9998i	−0.170951	−	0.875172i
$189$	−0.712133	+	1.62350i	−0.0518001	+	0.118092i
$190$	0.110568	−	4.60516i	0.00802148	−	0.334093i
$191$	−3.47911	−	7.93158i	−0.251740	−	0.573909i	0.743784	−	0.668420i	$-0.233029\pi$
$191$	−3.47911	−	7.93158i	−0.251740	−	0.573909i	−0.995524	+	0.0945112i	$0.969871\pi$
$192$	−0.402035	+	0.278765i	−0.0290144	+	0.0201181i
$193$	20.4724	−	9.66118i	1.47364	−	0.695427i	0.489366	−	0.872079i	$-0.337228\pi$
$193$	20.4724	−	9.66118i	1.47364	−	0.695427i	0.984273	+	0.176652i	$0.0565266\pi$
$194$	−4.39081	−	1.24160i	−0.315242	−	0.0891418i
$195$	2.63903	−	0.292087i	0.188985	−	0.0209168i
$196$	6.35511	+	1.79705i	0.453936	+	0.128361i
$197$	−0.859703	−	10.3751i	−0.0612513	−	0.739193i	−0.956141	−	0.292906i	$-0.905378\pi$
$197$	−0.859703	−	10.3751i	−0.0612513	−	0.739193i	0.894890	−	0.446287i	$-0.147254\pi$
$198$	−12.4460	+	9.68711i	−0.884499	+	0.688433i
$199$	3.74772	+	11.9821i	0.265669	+	0.849391i	0.987541	+	0.157364i	$0.0502996\pi$
$199$	3.74772	+	11.9821i	0.265669	+	0.849391i	−0.721872	+	0.692027i	$0.756718\pi$
$200$	−1.75338	−	3.46478i	−0.123983	−	0.244997i
$201$	0.686694	+	0.235742i	0.0484357	+	0.0166280i
$202$	4.04426	+	4.39324i	0.284553	+	0.309107i
$203$	0.138752	−	5.03365i	0.00973846	−	0.353293i
$204$	−1.72907	−	0.387493i	−0.121059	−	0.0271299i
$205$	−5.40764	+	6.56613i	−0.377686	+	0.458599i
$206$	0.958014	−	1.30342i	0.0667480	−	0.0908139i
$207$	−18.9403	−	4.24463i	−1.31645	−	0.295022i
$208$	−4.85727	+	1.66750i	−0.336791	+	0.115621i
$209$	−6.19888	−	24.1184i	−0.428786	−	1.66831i
$210$	0.307604	+	0.105601i	0.0212267	+	0.00728714i
$211$	−4.29919	−	2.64271i	−0.295969	−	0.181931i	0.367727	−	0.929934i	$-0.380136\pi$
$211$	−4.29919	−	2.64271i	−0.295969	−	0.181931i	−0.663696	+	0.748002i	$0.731013\pi$
$212$	0.611504	+	3.13056i	0.0419982	+	0.215008i
$213$	−0.302374	+	0.263338i	−0.0207183	+	0.0180436i
$214$	16.2849	−	4.60493i	1.11321	−	0.314786i
$215$	8.58585	−	3.48727i	0.585550	−	0.237830i
$216$	−0.691843	+	2.73202i	−0.0470739	+	0.185891i
$217$	−0.0629699	+	0.143557i	−0.00427467	+	0.00974528i
$218$	−1.36720	+	0.306397i	−0.0925985	+	0.0207518i
$219$	−2.26783	+	1.39403i	−0.153246	+	0.0941999i
$220$	4.08907	+	4.44192i	0.275685	+	0.299474i
$221$	−16.3588	−	8.85293i	−1.10041	−	0.595513i
$222$	3.01397	−	3.65966i	0.202284	−	0.245620i
$223$	9.46299	+	3.84353i	0.633688	+	0.257382i	0.670465	−	0.741942i	$-0.266095\pi$
$223$	9.46299	+	3.84353i	0.633688	+	0.257382i	−0.0367762	+	0.999324i	$0.511709\pi$
$224$	−0.625229	−	0.0692003i	−0.0417749	−	0.00462364i
$225$	−9.93212	−	4.03408i	−0.662141	−	0.268939i
$226$	−11.6589	+	15.8626i	−0.775541	+	1.05516i
$227$	−26.2783	−	14.2211i	−1.74415	−	0.943889i	−0.933676	−	0.358118i	$-0.883419\pi$
$227$	−26.2783	−	14.2211i	−1.74415	−	0.943889i	−0.810477	−	0.585771i	$-0.800792\pi$
$228$	−1.68747	−	1.30381i	−0.111756	−	0.0863471i
$229$	−17.7250	+	9.59228i	−1.17130	+	0.633876i	−0.940722	−	0.339178i	$-0.889851\pi$
$229$	−17.7250	+	9.59228i	−1.17130	+	0.633876i	−0.230578	+	0.973054i	$0.574062\pi$
$230$	−1.02058	+	7.35992i	−0.0672954	+	0.485299i
$231$	1.75548	+	0.0968524i	0.115502	+	0.00637242i
$232$	−1.09952	−	7.92920i	−0.0721873	−	0.520577i
$233$	18.4923	−	8.72674i	1.21147	−	0.571708i	0.288836	−	0.957379i	$-0.406732\pi$
$233$	18.4923	−	8.72674i	1.21147	−	0.571708i	0.922636	+	0.385671i	$0.126030\pi$
$234$	−7.08872	+	12.2780i	−0.463404	+	0.802640i
$235$	−7.06712	+	10.8170i	−0.461008	+	0.705625i
$236$	0.0574267	+	0.693037i	0.00373816	+	0.0451129i
$237$	0.603449	+	4.35176i	0.0391982	+	0.282677i
$238$	−1.34934	−	1.83584i	−0.0874645	−	0.119000i
$239$	−1.82900	−	7.22254i	−0.118308	−	0.467187i	0.881681	−	0.471846i	$-0.156412\pi$
$239$	−1.82900	−	7.22254i	−0.118308	−	0.467187i	−0.999989	+	0.00465815i	$0.998517\pi$
$240$	0.509963	+	0.0850977i	0.0329179	+	0.00549303i
$241$	24.7584	−	5.54849i	1.59483	−	0.357410i	0.671376	−	0.741117i	$-0.265704\pi$
$241$	24.7584	−	5.54849i	1.59483	−	0.357410i	0.923455	+	0.383707i	$0.125353\pi$
$242$	18.4340	+	11.3313i	1.18498	+	0.728405i
$243$	5.34255	+	10.5572i	0.342725	+	0.677242i
$244$	−0.938519	+	6.76811i	−0.0600825	+	0.433284i
$245$	−3.48971	−	6.04436i	−0.222950	−	0.386160i
$246$	0.966677	+	3.81732i	0.0616331	+	0.243384i
$247$	−13.3213	−	17.9901i	−0.847617	−	1.14468i
$248$	−0.0611757	+	0.241577i	−0.00388466	+	0.0153402i
$249$	−4.54037	+	1.28389i	−0.287734	+	0.0813635i
$250$	−2.80238	+	8.95971i	−0.177238	+	0.566662i
$251$	25.7753	+	12.1637i	1.62692	+	0.767764i	0.999937	−	0.0112662i	$-0.00358623\pi$
$251$	25.7753	+	12.1637i	1.62692	+	0.767764i	0.626987	+	0.779030i	$0.284288\pi$
$252$	−1.42709	+	0.989519i	−0.0898980	+	0.0623339i
$253$	5.51720	+	39.7872i	0.346864	+	2.50140i
$254$	−7.41402	+	5.77056i	−0.465197	+	0.362077i
$255$	1.02422	+	1.56768i	0.0641388	+	0.0981718i
$256$	−0.998482	+	0.0550878i	−0.0624051	+	0.00344299i
$257$	2.63333	−	2.29337i	0.164263	−	0.143056i	−0.570714	−	0.821149i	$-0.693333\pi$
$257$	2.63333	−	2.29337i	0.164263	−	0.143056i	0.734977	+	0.678092i	$0.237193\pi$
$258$	1.05313	−	4.15873i	0.0655652	−	0.258911i
$259$	6.01284	−	1.00337i	0.373620	−	0.0623461i
$260$	4.90816	+	2.31621i	0.304391	+	0.143646i
$261$	−16.6652	−	14.5137i	−1.03155	−	0.898377i
$262$	3.96403	−	6.86590i	0.244899	−	0.424177i
$263$	−27.7441	+	3.07072i	−1.71078	+	0.189349i	−0.911412	−	0.411496i	$-0.865006\pi$
$263$	−27.7441	+	3.07072i	−1.71078	+	0.189349i	−0.799366	+	0.600845i	$0.794831\pi$
$264$	2.77797	−	0.307466i	0.170973	−	0.0189232i
$265$	1.84371	−	2.82200i	0.113258	−	0.173354i
$266$	−0.535219	−	2.68921i	−0.0328164	−	0.164886i
$267$	−1.52891	−	2.34018i	−0.0935680	−	0.143217i
$268$	0.943442	+	1.14556i	0.0576299	+	0.0699761i
$269$	−16.5222	−	10.1561i	−1.00737	−	0.619230i	−0.0813462	−	0.996686i	$-0.525922\pi$
$269$	−16.5222	−	10.1561i	−1.00737	−	0.619230i	−0.926028	+	0.377455i	$0.876799\pi$
$270$	2.53731	−	1.55968i	0.154416	−	0.0949189i
$271$	−3.00811	+	2.92633i	−0.182730	+	0.177762i	−0.782974	−	0.622055i	$-0.786298\pi$
$271$	−3.00811	+	2.92633i	−0.182730	+	0.177762i	0.600244	+	0.799817i	$0.295070\pi$
$272$	−2.59615	−	2.52558i	−0.157415	−	0.153136i
$273$	1.49481	−	0.513168i	0.0904698	−	0.0310583i
$274$	−0.832274	−	0.450404i	−0.0502795	−	0.0272099i
$275$	−0.611279	+	22.1761i	−0.0368615	+	1.33727i
$276$	2.46554	+	2.39852i	0.148408	+	0.144374i
$277$	8.59798	−	9.33989i	0.516602	−	0.561180i	−0.421816	−	0.906682i	$-0.638607\pi$
$277$	8.59798	−	9.33989i	0.516602	−	0.561180i	0.938418	+	0.345502i	$0.112291\pi$
$278$	1.79691	−	0.972438i	0.107771	−	0.0583230i
$279$	0.310639	+	0.613839i	0.0185974	+	0.0367496i
$280$	0.422615	+	0.513152i	0.0252561	+	0.0306667i
$281$	11.4907	−	0.633958i	0.685476	−	0.0378188i	0.290997	−	0.956724i	$-0.406013\pi$
$281$	11.4907	−	0.633958i	0.685476	−	0.0378188i	0.394479	+	0.918905i	$0.370925\pi$
$282$	2.09735	+	5.60178i	0.124895	+	0.333581i
$283$	5.24744	−	16.7770i	0.311928	−	0.997290i	−0.657818	−	0.753177i	$-0.728521\pi$
$283$	5.24744	−	16.7770i	0.311928	−	0.997290i	0.969747	−	0.244114i	$-0.0784970\pi$
$284$	−0.808423	+	0.134902i	−0.0479711	+	0.00800496i
$285$	0.317470	+	2.23114i	0.0188053	+	0.132161i
$286$	28.9391	+	4.82907i	1.71120	+	0.285549i
$287$	−2.28623	+	4.51771i	−0.134952	+	0.266672i
$288$	−1.97879	+	1.92500i	−0.116601	+	0.113432i
$289$	−0.106951	+	3.87998i	−0.00629124	+	0.228234i
$290$	−5.01017	+	6.81658i	−0.294207	+	0.400283i
$291$	2.21878	+	0.245574i	0.130067	+	0.0143958i
$292$	−5.44131			−0.318428
$293$	24.3765			1.42409			0.712046	−	0.702133i	$-0.247769\pi$
$293$	24.3765			1.42409			0.712046	+	0.702133i	$0.247769\pi$
$294$	−3.21138	−	0.355436i	−0.187292	−	0.0207294i
$295$	0.467201	−	0.567291i	0.0272015	−	0.0330289i
$296$	9.16575	−	3.14660i	0.532748	−	0.182893i
$297$	10.9047	−	11.8457i	0.632755	−	0.687355i
$298$	4.05318	−	20.7500i	0.234795	−	1.20202i
$299$	18.0539	+	31.2703i	1.04409	+	1.80841i
$300$	1.12510	+	1.53075i	0.0649576	+	0.0883779i
$301$	4.53300	−	3.14311i	0.261278	−	0.181166i
$302$	2.18291	+	1.90109i	0.125612	+	0.109396i
$303$	−2.30533	−	1.79431i	−0.132438	−	0.103081i
$304$	−1.54289	−	4.07670i	−0.0884906	−	0.233815i
$305$	5.69837	−	4.43522i	0.326288	−	0.253960i
$306$	−9.98379	−	0.550821i	−0.570735	−	0.0314883i
$307$	0.524971	+	0.909277i	0.0299617	+	0.0518952i	0.880617	−	0.473828i	$-0.157128\pi$
$307$	0.524971	+	0.909277i	0.0299617	+	0.0518952i	−0.850656	+	0.525723i	$0.823795\pi$
$308$	2.95325	+	2.04774i	0.168277	+	0.116681i
$309$	−0.357336	+	0.706115i	−0.0203281	+	0.0401695i
$310$	0.224359	−	0.137913i	0.0127428	−	0.00783295i
$311$	19.2148	+	6.59646i	1.08957	+	0.374051i	0.810213	−	0.586135i	$-0.199351\pi$
$311$	19.2148	+	6.59646i	1.08957	+	0.374051i	0.279360	+	0.960186i	$0.409878\pi$
$312$	2.20962	−	1.19579i	0.125095	−	0.0676981i
$313$	−2.53056	+	12.9550i	−0.143035	+	0.732262i	0.839084	+	0.544002i	$0.183092\pi$
$313$	−2.53056	+	12.9550i	−0.143035	+	0.732262i	−0.982119	+	0.188260i	$0.939715\pi$
$314$	13.5070	+	9.36552i	0.762242	+	0.528527i
$315$	1.81019	+	0.302068i	0.101993	+	0.0170196i
$316$	−3.60735	+	8.22393i	−0.202929	+	0.462632i
$317$	15.7206	−	13.6911i	0.882956	−	0.768967i	−0.0909648	−	0.995854i	$-0.528995\pi$
$317$	15.7206	−	13.6911i	0.882956	−	0.768967i	0.973921	+	0.226887i	$0.0728547\pi$
$318$	−0.547168	−	1.46142i	−0.0306837	−	0.0819524i
$319$	−16.0356	+	42.8293i	−0.897823	+	2.39798i
$320$	0.796940	+	0.694056i	0.0445503	+	0.0387989i
$321$	−7.48752	+	3.53345i	−0.417913	+	0.197218i
$322$	0.365234	+	4.40771i	0.0203537	+	0.245632i
$323$	7.07859	−	14.1119i	0.393863	−	0.785207i
$324$	−0.570062	+	6.87963i	−0.0316701	+	0.382202i
$325$	6.99247	+	18.6761i	0.387872	+	1.03596i
$326$	9.36281	−	2.64755i	0.518558	−	0.146634i
$327$	0.635075	−	0.257945i	0.0351197	−	0.0142644i
$328$	−2.40277	+	7.68208i	−0.132671	+	0.424172i
$329$	−2.69678	+	7.20277i	−0.148678	+	0.397101i
$330$	−2.33088	−	1.81419i	−0.128311	−	0.0998681i
$331$	1.01423	−	1.55239i	0.0557469	−	0.0853269i	−0.808205	−	0.588901i	$-0.799561\pi$
$331$	1.01423	−	1.55239i	0.0557469	−	0.0853269i	0.863952	+	0.503574i	$0.167982\pi$
$332$	−9.28073	−	2.62434i	−0.509346	−	0.144029i
$333$	13.3765	−	23.1688i	0.733029	−	1.26964i
$334$	−0.782876	−	0.609337i	−0.0428371	−	0.0333414i
$335$	0.129512	−	1.56298i	0.00707602	−	0.0853948i
$336$	0.307279	−	0.0169530i	0.0167634	−	0.000924864i
$337$	4.84658	+	24.8118i	0.264010	+	1.35158i	0.843730	+	0.536769i	$0.180355\pi$
$337$	4.84658	+	24.8118i	0.264010	+	1.35158i	−0.579719	+	0.814816i	$0.696838\pi$
$338$	13.0500	−	2.92457i	0.709826	−	0.159076i
$339$	4.34875	−	8.59336i	0.236191	−	0.466727i
$340$	0.105469	+	3.82623i	0.00571987	+	0.207506i
$341$	0.964240	−	1.04744i	0.0522165	−	0.0567223i
$342$	−10.6034	−	5.68964i	−0.573364	−	0.307661i
$343$	−5.79600	−	6.29614i	−0.312955	−	0.339959i
$344$	6.28543	−	6.11456i	0.338888	−	0.329675i
$345$	−0.100163	−	3.63374i	−0.00539261	−	0.195634i
$346$	−4.54971	+	23.2920i	−0.244594	+	1.25218i
$347$	−3.14448	+	22.6763i	−0.168804	+	1.21733i	0.697046	+	0.717026i	$0.254497\pi$
$347$	−3.14448	+	22.6763i	−0.168804	+	1.21733i	−0.865851	+	0.500303i	$0.833222\pi$
$348$	1.16907	+	3.73772i	0.0626687	+	0.200363i
$349$	8.54124	+	13.0733i	0.457202	+	0.699800i	0.989139	−	0.146984i	$-0.0469566\pi$
$349$	8.54124	+	13.0733i	0.457202	+	0.699800i	−0.531937	+	0.846784i	$0.678536\pi$
$350$	−0.201716	+	2.43436i	−0.0107822	+	0.130122i
$351$	5.07487	−	13.5544i	0.270877	−	0.723480i
$352$	5.16658	+	2.43817i	0.275379	+	0.129955i
$353$	1.55422	+	3.54327i	0.0827230	+	0.188589i	0.952267	−	0.305266i	$-0.0987453\pi$
$353$	1.55422	+	3.54327i	0.0827230	+	0.188589i	−0.869544	+	0.493855i	$0.835587\pi$
$354$	−0.0835175	−	0.329803i	−0.00443891	−	0.0175288i
$355$	0.711787	+	0.493542i	0.0377777	+	0.0261945i
$356$	−0.157441	−	5.71166i	−0.00834435	−	0.302718i
$357$	0.798956	+	0.777236i	0.0422852	+	0.0411357i
$358$	−19.4593	−	4.36093i	−1.02846	−	0.230482i
$359$	−4.92498	−	2.00036i	−0.259931	−	0.105575i	0.242623	−	0.970121i	$-0.421992\pi$
$359$	−4.92498	−	2.00036i	−0.259931	−	0.105575i	−0.502554	+	0.864546i	$0.667606\pi$
$360$	2.91746			0.153764
$361$	14.9104	−	11.7763i	0.784756	−	0.619804i
$362$	−7.65287			−0.402226
$363$	−9.80782	−	3.98359i	−0.514777	−	0.209084i
$364$	3.15230	+	0.706447i	0.165225	+	0.0370279i
$365$	4.12177	+	4.00972i	0.215743	+	0.209878i
$366$	−0.0921091	−	3.34155i	−0.00481462	−	0.174665i
$367$	12.8147	+	8.88551i	0.668921	+	0.463820i	0.854940	−	0.518727i	$-0.173594\pi$
$367$	12.8147	+	8.88551i	0.668921	+	0.463820i	−0.186019	+	0.982546i	$0.559559\pi$
$368$	1.72600	+	6.81584i	0.0899742	+	0.355300i
$369$	8.92598	+	20.3492i	0.464668	+	1.05934i
$370$	−9.26176	−	4.37073i	−0.481496	−	0.227223i
$371$	0.703549	−	1.87910i	0.0365264	−	0.0975578i
$372$	0.0100678	−	0.121500i	0.000521990	−	0.00629948i
$373$	−14.4272	−	22.0824i	−0.747010	−	1.14338i	−0.985074	−	0.172134i	$-0.944934\pi$
$373$	−14.4272	−	22.0824i	−0.747010	−	1.14338i	0.238064	−	0.971250i	$-0.423487\pi$
$374$	6.17691	+	19.7487i	0.319401	+	1.02118i
$375$	0.630827	−	4.54920i	0.0325758	−	0.234919i
$376$	−2.34396	+	11.9998i	−0.120880	+	0.618840i
$377$	1.13277	+	41.0947i	0.0583404	+	2.11648i
$378$	1.27073	−	1.23618i	0.0653591	−	0.0635823i
$379$	−19.1387	−	20.7902i	−0.983090	−	1.06792i	−0.997684	−	0.0680265i	$-0.978330\pi$
$379$	−19.1387	−	20.7902i	−0.983090	−	1.06792i	0.0145939	−	0.999894i	$-0.495354\pi$
$380$	−1.83541	+	4.22504i	−0.0941543	+	0.216740i
$381$	3.11299	−	3.38161i	0.159483	−	0.173245i
$382$	0.238650	+	8.65778i	0.0122104	+	0.442971i
$383$	0.316326	−	0.625077i	0.0161635	−	0.0319399i	−0.884030	−	0.467431i	$-0.845180\pi$
$383$	0.316326	−	0.625077i	0.0161635	−	0.0319399i	0.900193	+	0.435491i	$0.143425\pi$
$384$	0.477385	−	0.106984i	0.0243614	−	0.00545953i
$385$	−0.728090	−	3.72741i	−0.0371069	−	0.189967i
$386$	−22.6032	+	1.24705i	−1.15047	+	0.0634733i
$387$	1.99909	−	24.1254i	0.101619	−	1.22636i
$388$	3.60083	+	2.80264i	0.182804	+	0.142282i
$389$	0.633204	−	1.09674i	0.0321047	−	0.0556070i	−0.849527	−	0.527546i	$-0.823112\pi$
$389$	0.633204	−	1.09674i	0.0321047	−	0.0556070i	0.881631	+	0.471939i	$0.156446\pi$
$390$	−2.55496	−	0.722473i	−0.129375	−	0.0365839i
$391$	−13.9285	+	21.3192i	−0.704396	+	1.07816i
$392$	−5.21172	−	4.05644i	−0.263232	−	0.204881i
$393$	−1.35999	+	3.63236i	−0.0686022	+	0.183228i
$394$	−3.10773	+	9.93595i	−0.156565	+	0.500566i
$395$	8.79279	−	3.57132i	0.442414	−	0.179693i
$396$	15.1765	−	4.29150i	0.762648	−	0.215656i
$397$	−7.57172	−	20.2232i	−0.380014	−	1.01497i	−0.977097	−	0.212792i	$-0.931744\pi$
$397$	−7.57172	−	20.2232i	−0.380014	−	1.01497i	0.597084	−	0.802179i	$-0.296326\pi$
$398$	1.03675	−	12.5117i	0.0519675	−	0.627154i
$399$	0.474817	+	1.25459i	0.0237706	+	0.0628080i
$400$	0.320670	+	3.86991i	0.0160335	+	0.193495i
$401$	14.3216	−	6.75852i	0.715186	−	0.337504i	−0.0344031	−	0.999408i	$-0.510953\pi$
$401$	14.3216	−	6.75852i	0.715186	−	0.337504i	0.749589	+	0.661904i	$0.230251\pi$
$402$	−0.547506	−	0.476823i	−0.0273071	−	0.0237818i
$403$	0.448742	−	1.19854i	0.0223534	−	0.0597034i
$404$	−2.09377	−	5.59220i	−0.104169	−	0.278222i
$405$	5.50144	−	4.79121i	0.273369	−	0.238077i
$406$	−2.02276	+	4.61143i	−0.100388	+	0.228862i
$407$	−54.6084	−	9.11253i	−2.70684	−	0.451691i
$408$	1.45615	+	1.00967i	0.0720902	+	0.0499863i
$409$	−0.501369	+	2.56673i	−0.0247911	+	0.126917i	−0.991793	−	0.127851i	$-0.959192\pi$
$409$	−0.501369	+	2.56673i	−0.0247911	+	0.126917i	0.967002	+	0.254768i	$0.0819990\pi$
$410$	7.48104	−	4.04854i	0.369462	−	0.199943i
$411$	0.437885	+	0.150326i	0.0215993	+	0.00741504i
$412$	−1.37809	+	0.847106i	−0.0678934	+	0.0417339i
$413$	0.197522	−	0.390314i	0.00971942	−	0.0192061i
$414$	15.9508	+	11.0601i	0.783940	+	0.543572i
$415$	5.09623	+	8.82693i	0.250164	+	0.433297i
$416$	5.12773	+	0.282905i	0.251408	+	0.0138706i
$417$	−0.788800	+	0.613947i	−0.0386277	+	0.0300651i
$418$	−3.33277	+	24.6783i	−0.163011	+	1.20705i
$419$	25.4833	+	19.8344i	1.24494	+	0.968976i	1.00000		0.000562042i	$-0.000178904\pi$
$419$	25.4833	+	19.8344i	1.24494	+	0.968976i	0.244941	+	0.969538i	$0.421232\pi$
$420$	−0.245255	−	0.213593i	−0.0119672	−	0.0104223i
$421$	14.4340	−	10.0083i	0.703468	−	0.487774i	−0.163242	−	0.986586i	$-0.552195\pi$
$421$	14.4340	−	10.0083i	0.703468	−	0.487774i	0.866710	+	0.498812i	$0.166230\pi$
$422$	2.98870	+	4.06628i	0.145488	+	0.197943i
$423$	16.8766	+	29.2312i	0.820570	+	1.42127i
$424$	0.611504	−	3.13056i	0.0296972	−	0.152033i
$425$	−9.52574	+	10.3477i	−0.462066	+	0.501938i
$426$	0.379244	−	0.130195i	0.0183744	−	0.00630796i
$427$	2.73247	−	3.31785i	0.132233	−	0.160562i
$428$	−16.8207	−	1.86172i	−0.813061	−	0.0899895i
$429$	−14.3535			−0.692993
$430$	−9.26703			−0.446896
$431$	−8.35185	−	0.924382i	−0.402294	−	0.0445259i	−0.0934153	−	0.995627i	$-0.529778\pi$
$431$	−8.35185	−	0.924382i	−0.402294	−	0.0445259i	−0.308879	+	0.951101i	$0.599954\pi$
$432$	1.66907	−	2.27086i	0.0803034	−	0.109257i
$433$	0.102776	−	3.72851i	0.00493908	−	0.179181i	−0.993128	−	0.117034i	$-0.962661\pi$
$433$	0.102776	−	3.72851i	0.00493908	−	0.179181i	0.998067	−	0.0621469i	$-0.0197947\pi$
$434$	0.112363	−	0.109308i	0.00539360	−	0.00524697i
$435$	1.86878	−	3.69280i	0.0896009	−	0.177056i
$436$	1.38200	+	0.230616i	0.0661859	+	0.0110445i
$437$	−26.0519	+	16.1418i	−1.24623	+	0.772169i
$438$	2.62572	−	0.438155i	0.125462	−	0.0209359i
$439$	6.45698	−	20.6441i	0.308175	−	0.985290i	−0.663341	−	0.748317i	$-0.730862\pi$
$439$	6.45698	−	20.6441i	0.308175	−	0.985290i	0.971516	−	0.236973i	$-0.0761553\pi$
$440$	−2.11697	−	5.65417i	−0.100922	−	0.269552i
$441$	−18.2045	+	1.00437i	−0.866882	+	0.0478272i
$442$	11.8249	+	14.3582i	0.562452	+	0.682948i
$443$	4.14806	+	8.19680i	0.197080	+	0.389442i	0.969288	−	0.245929i	$-0.0790930\pi$
$443$	4.14806	+	8.19680i	0.197080	+	0.389442i	−0.772207	+	0.635371i	$0.780847\pi$
$444$	−4.16958	+	2.25647i	−0.197880	+	0.107087i
$445$	−4.08969	+	4.44258i	−0.193870	+	0.210599i
$446$	−7.32104	−	7.12202i	−0.346661	−	0.337237i
$447$	−0.285003	+	10.3394i	−0.0134802	+	0.489036i
$448$	0.553230	+	0.299393i	0.0261377	+	0.0141450i
$449$	33.2965	−	11.4307i	1.57136	−	0.539448i	0.604907	−	0.796296i	$-0.293210\pi$
$449$	33.2965	−	11.4307i	1.57136	−	0.539448i	0.966452	+	0.256848i	$0.0826838\pi$
$450$	7.68399	+	7.47510i	0.362227	+	0.352380i
$451$	32.9607	−	32.0647i	1.55206	−	1.50987i
$452$	16.7712	−	10.3092i	0.788849	−	0.484904i
$453$	−1.20645	−	0.741603i	−0.0566840	−	0.0348436i
$454$	18.9952	+	23.0646i	0.891487	+	1.08247i
$455$	−1.86727	−	2.85807i	−0.0875391	−	0.133989i
$456$	1.07280	+	1.84299i	0.0502383	+	0.0863058i
$457$	4.21809	−	6.45627i	0.197314	−	0.302011i	−0.724778	−	0.688983i	$-0.758058\pi$
$457$	4.21809	−	6.45627i	0.197314	−	0.302011i	0.922092	+	0.386971i	$0.126479\pi$
$458$	20.0318	−	2.21711i	0.936023	−	0.103599i
$459$	10.1457	−	1.12292i	0.473559	−	0.0524135i
$460$	3.71517	−	6.43487i	0.173221	−	0.300027i
$461$	22.0107	+	19.1691i	1.02514	+	0.892795i	0.994288	−	0.106729i	$-0.0340379\pi$
$461$	22.0107	+	19.1691i	1.02514	+	0.892795i	0.0308511	+	0.999524i	$0.490178\pi$
$462$	−1.58999	−	0.750336i	−0.0739732	−	0.0349088i
$463$	−6.72035	+	1.12143i	−0.312321	+	0.0521172i	−0.318679	−	0.947863i	$-0.603239\pi$
$463$	−6.72035	+	1.12143i	−0.312321	+	0.0521172i	0.00635815	+	0.999980i	$0.497976\pi$
$464$	−1.96513	+	7.76011i	−0.0912288	+	0.360254i
$465$	−0.0971601	+	0.0846168i	−0.00450569	+	0.00392401i
$466$	−20.4170	+	1.12644i	−0.945799	+	0.0521812i
$467$	−14.4618	−	22.1354i	−0.669211	−	1.02430i	−0.996835	−	0.0794952i	$-0.974669\pi$
$467$	−14.4618	−	22.1354i	−0.669211	−	1.02430i	0.327625	−	0.944808i	$-0.393752\pi$
$468$	11.1880	−	8.70797i	0.517165	−	0.402526i
$469$	−0.128224	−	0.924685i	−0.00592084	−	0.0426980i
$470$	10.6182	−	7.36249i	0.489781	−	0.339606i
$471$	−7.27198	−	3.43173i	−0.335075	−	0.158126i
$472$	0.207591	−	0.663705i	0.00955514	−	0.0305495i
$473$	−48.2066	+	13.6315i	−2.21654	+	0.626779i
$474$	1.07852	−	4.25896i	0.0495379	−	0.195621i
$475$	−15.6594	+	6.42522i	−0.718504	+	0.294809i
$476$	0.559309	+	2.20866i	0.0256359	+	0.101234i
$477$	−4.40287	−	7.62599i	−0.201593	−	0.349170i
$478$	−1.02336	+	7.37991i	−0.0468072	+	0.337549i
$479$	12.5477	+	24.7950i	0.573321	+	1.13291i	0.976040	+	0.217589i	$0.0698193\pi$
$479$	12.5477	+	24.7950i	0.573321	+	1.13291i	−0.402720	+	0.915323i	$0.631935\pi$
$480$	−0.440454	−	0.270746i	−0.0201039	−	0.0123578i
$481$	−48.5630	+	10.8832i	−2.21428	+	0.496232i
$482$	−25.0265	−	4.17618i	−1.13993	−	0.190220i
$483$	−0.531171	−	2.09755i	−0.0241691	−	0.0954417i
$484$	−12.8149	−	17.4353i	−0.582495	−	0.792513i
$485$	−0.662340	−	4.77645i	−0.0300753	−	0.216888i
$486$	−0.977080	−	11.7916i	−0.0443212	−	0.534878i
$487$	−11.6883	+	17.8903i	−0.529649	+	0.810688i	−0.997316	−	0.0732169i	$-0.976673\pi$
$487$	−11.6883	+	17.8903i	−0.529649	+	0.810688i	0.467667	+	0.883905i	$0.345095\pi$
$488$	3.41643	−	5.91744i	0.154655	−	0.267870i
$489$	−4.30487	+	2.03152i	−0.194673	+	0.0918683i
$490$	0.958649	+	6.91328i	0.0433074	+	0.312310i
$491$	−0.910152	−	0.0502145i	−0.0410746	−	0.00226615i	0.0345388	−	0.999403i	$-0.489004\pi$
$491$	−0.910152	−	0.0502145i	−0.0410746	−	0.00226615i	−0.0756134	+	0.997137i	$0.524091\pi$
$492$	0.540873	−	3.90050i	0.0243845	−	0.175848i
$493$	−25.4994	+	13.7996i	−1.14844	+	0.621503i
$494$	5.57232	+	21.6806i	0.250710	+	0.975457i
$495$	−14.6586	−	7.93282i	−0.658853	−	0.356554i
$496$	0.147587	−	0.200799i	0.00662684	−	0.00901614i
$497$	0.477670	+	0.194013i	0.0214264	+	0.00870267i
$498$	4.68977	+	0.519064i	0.210154	+	0.0232598i
$499$	15.0553	+	6.11495i	0.673970	+	0.273743i	0.687520	−	0.726165i	$-0.258699\pi$
$499$	15.0553	+	6.11495i	0.673970	+	0.273743i	−0.0135504	+	0.999908i	$0.504313\pi$
$500$	5.96801	−	7.24655i	0.266898	−	0.324076i
$501$	0.426846	+	0.230997i	0.0190701	+	0.0103202i
$502$	−19.3034	−	20.9691i	−0.861552	−	0.935895i
$503$	10.2302	−	6.28847i	0.456141	−	0.280389i	−0.276488	−	0.961017i	$-0.589170\pi$
$503$	10.2302	−	6.28847i	0.456141	−	0.280389i	0.732629	+	0.680629i	$0.238293\pi$
$504$	1.69455	−	0.379758i	0.0754813	−	0.0169158i
$505$	−2.53489	+	5.77897i	−0.112801	+	0.257161i
$506$	9.86063	−	38.9388i	0.438359	−	1.73104i
$507$	−6.06182	+	2.46210i	−0.269215	+	0.109346i
$508$	9.04056	−	2.55643i	0.401110	−	0.113423i
$509$	−2.42849	+	2.11498i	−0.107641	+	0.0937447i	−0.708898	−	0.705311i	$-0.750807\pi$
$509$	−2.42849	+	2.11498i	−0.107641	+	0.0937447i	0.601257	+	0.799056i	$0.294667\pi$
$510$	−0.358997	−	1.83787i	−0.0158967	−	0.0813821i
$511$	2.91598	+	1.79245i	0.128995	+	0.0792932i
$512$	0.945817	+	0.324699i	0.0417996	+	0.0143498i
$513$	11.6330	+	3.94747i	0.513610	+	0.174285i
$514$	−3.30278	+	1.13385i	−0.145679	+	0.0500118i
$515$	1.66813	+	0.373836i	0.0735066	+	0.0164732i
$516$	−2.54069	+	3.45673i	−0.111848	+	0.152174i
$517$	44.4053	−	53.9184i	1.95294	−	2.37133i
$518$	−5.94844	−	1.33308i	−0.261359	−	0.0585720i
$519$	0.319917	−	11.6060i	0.0140428	−	0.509446i
$520$	−3.67576	−	3.99294i	−0.161193	−	0.175102i
$521$	−30.8804	−	10.6013i	−1.35289	−	0.464449i	−0.449508	−	0.893276i	$-0.648401\pi$
$521$	−30.8804	−	10.6013i	−1.35289	−	0.464449i	−0.903387	+	0.428827i	$0.858927\pi$
$522$	9.97855	+	19.7182i	0.436749	+	0.863040i
$523$	−6.93924	−	22.1860i	−0.303432	−	0.970125i	−0.973667	−	0.227976i	$-0.926789\pi$
$523$	−6.93924	−	22.1860i	−0.303432	−	0.970125i	0.670235	−	0.742149i	$-0.266193\pi$
$524$	−6.25635	+	4.86951i	−0.273310	+	0.212726i
$525$	−0.0986849	−	1.19095i	−0.00430696	−	0.0519773i
$526$	26.8603	+	7.59538i	1.17117	+	0.331174i
$527$	0.897123	−	0.0992935i	0.0390793	−	0.00432529i
$528$	−2.68948	−	0.760512i	−0.117045	−	0.0330971i
$529$	23.9065	−	11.2817i	1.03941	−	0.490510i
$530$	−2.77013	+	1.92077i	−0.120327	+	0.0834327i
$531$	−0.771173	−	1.75810i	−0.0334661	−	0.0762949i
$532$	−0.516097	+	2.69294i	−0.0223757	+	0.116754i
$533$	16.6046	−	37.8547i	0.719225	−	1.63967i
$534$	0.535899	+	2.74351i	0.0231906	+	0.118723i
$535$	11.3697	+	13.8055i	0.491556	+	0.596864i
$536$	−0.443009	−	1.41638i	−0.0191351	−	0.0611783i
$537$	9.74130	+	0.537443i	0.420368	+	0.0231924i
$538$	11.4858	+	15.6270i	0.495190	+	0.673730i
$539$	15.1561	+	34.5524i	0.652818	+	1.48828i
$540$	−2.93772	+	0.490219i	−0.126419	+	0.0210957i
$541$	34.4364	−	13.9869i	1.48054	−	0.601342i	0.513981	−	0.857801i	$-0.328170\pi$
$541$	34.4364	−	13.9869i	1.48054	−	0.601342i	0.966555	+	0.256460i	$0.0825561\pi$
$542$	3.88820	−	1.57925i	0.167013	−	0.0678347i
$543$	3.69292	−	0.616239i	0.158478	−	0.0264454i
$544$	1.45492	+	3.31689i	0.0623793	+	0.142210i
$545$	−0.876920	−	1.19309i	−0.0375631	−	0.0511065i
$546$	−1.57804	−	0.0870629i	−0.0675339	−	0.00372595i
$547$	3.73648	+	11.9462i	0.159760	+	0.510783i	0.999480	−	0.0322373i	$-0.0102632\pi$
$547$	3.73648	+	11.9462i	0.159760	+	0.510783i	−0.839720	+	0.543020i	$0.817281\pi$
$548$	0.601605	+	0.730489i	0.0256993	+	0.0312049i
$549$	−3.61628	−	18.5133i	−0.154339	−	0.790130i
$550$	8.91141	−	20.3160i	0.379984	−	0.866276i
$551$	−34.8332	+	2.04596i	−1.48395	+	0.0871608i
$552$	−1.38173	−	3.15002i	−0.0588102	−	0.134074i
$553$	4.64225	−	3.21887i	0.197409	−	0.136880i
$554$	−11.4807	+	5.41785i	−0.487767	+	0.230183i
$555$	4.82124	+	1.36332i	0.204650	+	0.0578696i
$556$	−2.03076	+	0.224765i	−0.0861235	+	0.00953215i
$557$	−1.01169	−	0.286078i	−0.0428666	−	0.0121215i	0.250603	−	0.968090i	$-0.419371\pi$
$557$	−1.01169	−	0.286078i	−0.0428666	−	0.0121215i	−0.293469	+	0.955969i	$0.594810\pi$
$558$	−0.0568116	−	0.685614i	−0.00240503	−	0.0290244i
$559$	−35.5376	+	27.6600i	−1.50308	+	1.16989i
$560$	−0.198446	−	0.634467i	−0.00838587	−	0.0268111i
$561$	−4.57093	−	9.03241i	−0.192985	−	0.381349i
$562$	−10.8846	−	3.73669i	−0.459139	−	0.157623i
$563$	22.4398	+	24.3761i	0.945724	+	1.02733i	0.999586	+	0.0287819i	$0.00916284\pi$
$563$	22.4398	+	24.3761i	0.945724	+	1.02733i	−0.0538615	+	0.998548i	$0.517153\pi$
$564$	0.164817	−	5.97926i	0.00694006	−	0.251772i
$565$	−20.3010	−	4.54956i	−0.854069	−	0.191401i
$566$	−11.1751	+	13.5691i	−0.469723	+	0.570354i
$567$	2.57175	−	3.49899i	0.108003	−	0.146944i
$568$	0.799764	+	0.179231i	0.0335573	+	0.00752038i
$569$	−3.44978	+	1.18431i	−0.144622	+	0.0496488i	−0.396060	−	0.918225i	$-0.629623\pi$
$569$	−3.44978	+	1.18431i	−0.144622	+	0.0496488i	0.251438	+	0.967873i	$0.419097\pi$
$570$	0.545464	−	2.18660i	0.0228470	−	0.0915867i
$571$	−41.8200	−	14.3568i	−1.75011	−	0.600815i	−0.751828	−	0.659359i	$-0.770828\pi$
$571$	−41.8200	−	14.3568i	−1.75011	−	0.600815i	−0.998285	+	0.0585446i	$0.981354\pi$
$572$	−24.9946	−	15.3641i	−1.04508	−	0.642407i
$573$	−0.812320	−	4.15863i	−0.0339352	−	0.173729i
$574$	3.81823	−	3.32530i	0.159370	−	0.138795i
$575$	26.2724	−	7.42911i	1.09563	−	0.309815i
$576$	2.55773	−	1.03886i	0.106572	−	0.0432859i
$577$	4.94179	−	19.5147i	0.205730	−	0.812408i	−0.777326	−	0.629098i	$-0.783424\pi$
$577$	4.94179	−	19.5147i	0.205730	−	0.812408i	0.983055	−	0.183309i	$-0.0586810\pi$
$578$	1.55916	−	3.55454i	0.0648527	−	0.147849i
$579$	10.8068	−	2.42187i	0.449117	−	0.100649i
$580$	7.20703	−	4.43015i	0.299256	−	0.183952i
$581$	4.10902	+	4.46359i	0.170471	+	0.185181i
$582$	−1.96327	−	1.06247i	−0.0813803	−	0.0440408i
$583$	−11.5847	+	14.0665i	−0.479789	+	0.582575i
$584$	5.04134	+	2.04761i	0.208612	+	0.0847309i
$585$	−14.8918	−	1.64822i	−0.615700	−	0.0681457i
$586$	−22.5847	−	9.17311i	−0.932965	−	0.378938i
$587$	−5.64544	+	7.68090i	−0.233012	+	0.317025i	−0.906526	−	0.422150i	$-0.861275\pi$
$587$	−5.64544	+	7.68090i	−0.233012	+	0.317025i	0.673514	+	0.739175i	$0.264784\pi$
$588$	2.84157	+	1.53778i	0.117185	+	0.0634171i
$589$	1.02864	+	0.349052i	0.0423844	+	0.0143825i
$590$	−0.646336	+	0.349779i	−0.0266092	+	0.0144002i
$591$	0.699562	−	5.04487i	0.0287761	−	0.207518i
$592$	−9.67611	−	0.533846i	−0.397686	−	0.0219409i
$593$	−1.55918	−	11.2440i	−0.0640279	−	0.461735i	−0.995255	−	0.0972971i	$-0.968980\pi$
$593$	−1.55918	−	11.2440i	−0.0640279	−	0.461735i	0.931228	−	0.364438i	$-0.118739\pi$
$594$	−14.5608	+	6.87139i	−0.597436	+	0.281937i
$595$	1.20390	−	2.08521i	0.0493549	−	0.0854852i
$596$	−11.5637	+	17.6995i	−0.473667	+	0.725001i
$597$	0.507204	+	6.12104i	0.0207585	+	0.250517i
$598$	−4.95954	−	35.7656i	−0.202811	−	1.46256i
$599$	11.5023	+	15.6494i	0.469971	+	0.639419i	0.974609	−	0.223912i	$-0.0718829\pi$
$599$	11.5023	+	15.6494i	0.469971	+	0.639419i	−0.504638	+	0.863331i	$0.668374\pi$
$600$	−0.466361	−	1.84162i	−0.0190391	−	0.0751837i
$601$	5.27919	+	0.880942i	0.215343	+	0.0359344i	0.271282	−	0.962500i	$-0.412552\pi$
$601$	5.27919	+	0.880942i	0.215343	+	0.0359344i	−0.0559396	+	0.998434i	$0.517815\pi$
$602$	−5.38257	+	1.20626i	−0.219377	+	0.0491636i
$603$	−3.49026	−	2.14546i	−0.142134	−	0.0873697i
$604$	−1.30705	−	2.58280i	−0.0531831	−	0.105093i
$605$	−3.14089	+	22.6505i	−0.127695	+	0.920873i
$606$	1.46066	+	2.52994i	0.0593352	+	0.102772i
$607$	5.52777	+	21.8287i	0.224365	+	0.885999i	0.974440	+	0.224646i	$0.0721227\pi$
$607$	5.52777	+	21.8287i	0.224365	+	0.885999i	−0.750075	+	0.661353i	$0.769983\pi$
$608$	−0.104626	+	4.35764i	−0.00424313	+	0.176726i
$609$	0.604760	−	2.38814i	0.0245061	−	0.0967725i
$610$	−6.94852	+	1.96485i	−0.281337	+	0.0795546i
$611$	18.7437	−	59.9269i	0.758288	−	2.42438i
$612$	9.04264	+	4.26733i	0.365527	+	0.172496i
$613$	4.38150	−	3.03806i	0.176967	−	0.122706i	−0.478012	−	0.878353i	$-0.658642\pi$
$613$	4.38150	−	3.03806i	0.176967	−	0.122706i	0.654979	+	0.755647i	$0.272678\pi$
$614$	−0.144213	−	1.03999i	−0.00581998	−	0.0419706i
$615$	−3.28400	+	2.55604i	−0.132424	+	0.103069i
$616$	−1.96559	−	3.00855i	−0.0791957	−	0.121218i
$617$	−28.7585	+	1.58665i	−1.15777	+	0.0638760i	−0.623770	−	0.781608i	$-0.714400\pi$
$617$	−28.7585	+	1.58665i	−1.15777	+	0.0638760i	−0.534001	+	0.845484i	$0.679312\pi$
$618$	0.596787	−	0.519743i	0.0240063	−	0.0209071i
$619$	6.32509	−	24.9772i	0.254227	−	1.00392i	−0.702208	−	0.711972i	$-0.747802\pi$
$619$	6.32509	−	24.9772i	0.254227	−	1.00392i	0.956435	−	0.291947i	$-0.0943031\pi$
$620$	−0.259766	+	0.0433472i	−0.0104324	+	0.00174087i
$621$	−17.9200	−	8.45664i	−0.719104	−	0.339353i
$622$	−15.3201	−	13.3423i	−0.614281	−	0.534978i
$623$	−1.79714	+	3.11273i	−0.0720007	+	0.124709i
$624$	−2.49719	+	0.276388i	−0.0999674	+	0.0110644i
$625$	9.43727	−	1.04452i	0.377491	−	0.0417807i
$626$	7.21965	−	11.0505i	0.288555	−	0.441666i
$627$	−0.378955	−	12.1770i	−0.0151340	−	0.486301i
$628$	−8.98979	−	13.7599i	−0.358732	−	0.549080i
$629$	−22.3137	−	27.0940i	−0.889706	−	1.08031i
$630$	−1.56346	−	0.961056i	−0.0622898	−	0.0382894i
$631$	−5.27995	+	3.24557i	−0.210191	+	0.129204i	−0.624769	−	0.780810i	$-0.714807\pi$
$631$	−5.27995	+	3.24557i	−0.210191	+	0.129204i	0.414577	+	0.910014i	$0.363929\pi$
$632$	6.43693	−	6.26194i	0.256047	−	0.249087i
$633$	−1.76964	−	1.72153i	−0.0703369	−	0.0684248i
$634$	−19.7171	+	6.76889i	−0.783067	+	0.268827i
$635$	−8.73203	−	4.72554i	−0.346520	−	0.187527i
$636$	−0.0429984	+	1.55990i	−0.00170500	+	0.0618541i
$637$	24.3108	+	23.6499i	0.963230	+	0.937044i
$638$	30.9740	−	33.6467i	1.22627	−	1.33209i
$639$	1.98993	−	1.07690i	0.0787205	−	0.0426014i
$640$	−0.477181	−	0.942935i	−0.0188622	−	0.0372728i
$641$	13.1562	+	15.9746i	0.519637	+	0.630960i	0.964324	−	0.264726i	$-0.0852815\pi$
$641$	13.1562	+	15.9746i	0.519637	+	0.630960i	−0.444687	+	0.895686i	$0.646685\pi$
$642$	8.26681	−	0.456093i	0.326265	−	0.0180005i
$643$	9.02100	+	24.0940i	0.355754	+	0.950176i	0.984936	+	0.172918i	$0.0553196\pi$
$643$	9.02100	+	24.0940i	0.355754	+	0.950176i	−0.629183	+	0.777258i	$0.716610\pi$
$644$	1.32028	−	4.22116i	0.0520262	−	0.166337i
$645$	4.47184	−	0.746218i	0.176078	−	0.0293823i
$646$	−11.8687	+	10.4109i	−0.466968	+	0.409610i
$647$	−42.3960	−	7.07464i	−1.66676	−	0.278133i	−0.745334	−	0.666692i	$-0.767710\pi$
$647$	−42.3960	−	7.07464i	−1.66676	−	0.278133i	−0.921424	+	0.388559i	$0.872973\pi$
$648$	3.11703	−	6.15942i	0.122448	−	0.241965i
$649$	−2.84769	+	2.77027i	−0.111782	+	0.108743i
$650$	0.549493	−	19.9346i	0.0215529	−	0.781899i
$651$	−0.0454192	+	0.0617951i	−0.00178012	+	0.00242194i
$652$	−9.67089	−	1.07037i	−0.378741	−	0.0419191i
$653$	3.06971			0.120127			0.0600636	−	0.998195i	$-0.480870\pi$
$653$	3.06971			0.120127			0.0600636	+	0.998195i	$0.480870\pi$
$654$	−0.685460			−0.0268036
$655$	8.32752	+	0.921690i	0.325383	+	0.0360134i
$656$	5.11699	−	6.21322i	0.199785	−	0.242585i
$657$	14.2077	−	4.87750i	0.554294	−	0.190289i
$658$	5.20902	−	5.65850i	0.203069	−	0.220591i
$659$	−7.11882	+	36.4444i	−0.277310	+	1.41967i	0.539121	+	0.842228i	$0.318757\pi$
$659$	−7.11882	+	36.4444i	−0.277310	+	1.41967i	−0.816431	+	0.577443i	$0.804050\pi$
$660$	1.47685	+	2.55797i	0.0574861	+	0.0995689i
$661$	−6.25851	−	8.51502i	−0.243428	−	0.331196i	0.666851	−	0.745191i	$-0.267642\pi$
$661$	−6.25851	−	8.51502i	−0.243428	−	0.331196i	−0.910279	+	0.413995i	$0.864133\pi$
$662$	−1.52385	+	1.05662i	−0.0592262	+	0.0410665i
$663$	−6.86231	−	5.97639i	−0.266510	−	0.232104i
$664$	7.61098	+	5.92386i	0.295363	+	0.229890i
$665$	2.37538	−	1.65958i	0.0921133	−	0.0643558i
$666$	−21.1119	+	16.4321i	−0.818070	+	0.636729i
$667$	56.1980	+	3.10053i	2.17600	+	0.120053i
$668$	0.496031	+	0.859151i	0.0191920	+	0.0332415i
$669$	4.10629	+	2.84724i	0.158758	+	0.110081i
$670$	−0.708157	+	1.39936i	−0.0273585	+	0.0540619i
$671$	−33.2556	+	20.4421i	−1.28382	+	0.789160i
$672$	−0.291071	−	0.0999250i	−0.0112283	−	0.00385469i
$673$	−12.1827	+	6.59294i	−0.469608	+	0.254139i	−0.693475	−	0.720481i	$-0.743921\pi$
$673$	−12.1827	+	6.59294i	−0.469608	+	0.254139i	0.223867	+	0.974620i	$0.428132\pi$
$674$	4.84658	−	24.8118i	0.186683	−	0.955715i
$675$	−8.99337	−	6.23587i	−0.346155	−	0.240019i
$676$	−13.1913	−	2.20124i	−0.507357	−	0.0846630i
$677$	0.226631	−	0.516667i	0.00871014	−	0.0198571i	−0.911364	−	0.411600i	$-0.864970\pi$
$677$	0.226631	−	0.516667i	0.00871014	−	0.0198571i	0.920075	+	0.391743i	$0.128128\pi$
$678$	−7.26285	+	6.32522i	−0.278928	+	0.242919i
$679$	−1.00644	−	2.68809i	−0.0386238	−	0.103160i
$680$	1.34213	−	3.58467i	0.0514683	−	0.137466i
$681$	−11.0234	−	9.60031i	−0.422419	−	0.367885i
$682$	−1.28753	+	0.607598i	−0.0493019	+	0.0232661i
$683$	−0.679375	−	8.19884i	−0.0259956	−	0.313720i	−0.997160	−	0.0753099i	$-0.976005\pi$
$683$	−0.679375	−	8.19884i	−0.0259956	−	0.313720i	0.971165	−	0.238410i	$-0.0766262\pi$
$684$	7.68289	+	9.26157i	0.293763	+	0.354125i
$685$	0.0825862	−	0.996668i	0.00315546	−	0.0380807i
$686$	3.00067	+	8.01442i	0.114566	+	0.305992i
$687$	−9.48786	+	2.68291i	−0.361985	+	0.102359i
$688$	−8.12438	+	3.29984i	−0.309739	+	0.125805i
$689$	−4.88995	+	15.6340i	−0.186292	+	0.595609i
$690$	−1.27461	+	3.40433i	−0.0485235	+	0.129601i
$691$	5.10303	+	3.97184i	0.194128	+	0.151096i	0.706613	−	0.707600i	$-0.250222\pi$
$691$	5.10303	+	3.97184i	0.194128	+	0.151096i	−0.512485	+	0.858696i	$0.671275\pi$
$692$	12.9803	−	19.8678i	0.493436	−	0.755259i
$693$	−9.54673	−	2.69956i	−0.362650	−	0.102548i
$694$	11.4467	−	19.8262i	0.434509	−	0.752591i
$695$	1.70392	+	1.32622i	0.0646335	+	0.0503063i
$696$	0.323404	−	3.90291i	0.0122586	−	0.147939i
$697$	29.1091	−	1.60600i	1.10259	−	0.0608314i
$698$	−2.99379	−	15.3265i	−0.113317	−	0.580118i
$699$	9.76158	−	2.18762i	0.369217	−	0.0827434i
$700$	1.10296	−	2.17951i	0.0416880	−	0.0823777i
$701$	1.27027	+	46.0831i	0.0479775	+	1.74053i	0.515798	+	0.856710i	$0.327495\pi$
$701$	1.27027	+	46.0831i	0.0479775	+	1.74053i	−0.467821	+	0.883823i	$0.654961\pi$
$702$	−9.80248	+	10.6483i	−0.369971	+	0.401896i
$703$	−10.5150	−	40.9116i	−0.396582	−	1.54301i
$704$	−3.86930	−	4.20318i	−0.145830	−	0.158413i
$705$	−4.53099	+	4.40781i	−0.170647	+	0.166008i
$706$	−0.106612	−	3.86769i	−0.00401240	−	0.145562i
$707$	−0.720110	+	3.68656i	−0.0270825	+	0.138647i
$708$	−0.0467296	+	0.336989i	−0.00175620	+	0.0126648i
$709$	7.54835	+	24.1334i	0.283484	+	0.906350i	0.981695	+	0.190458i	$0.0609972\pi$
$709$	7.54835	+	24.1334i	0.283484	+	0.906350i	−0.698211	+	0.715892i	$0.746020\pi$
$710$	−0.473742	−	0.725116i	−0.0177792	−	0.0272131i
$711$	2.04727	−	24.7069i	0.0767787	−	0.926581i
$712$	−2.00348	+	5.35107i	−0.0750838	+	0.200540i
$713$	−1.58456	−	0.747773i	−0.0593423	−	0.0280043i
$714$	−0.447746	−	1.02076i	−0.0167565	−	0.0382009i
$715$	7.61144	+	30.0569i	0.284652	+	1.12406i
$716$	16.3879	+	11.3631i	0.612443	+	0.424658i
$717$	−0.100435	−	3.64361i	−0.00375082	−	0.136073i
$718$	3.81022	+	3.70664i	0.142196	+	0.138330i
$719$	−7.23515	−	1.62143i	−0.269826	−	0.0604693i	0.0816681	−	0.996660i	$-0.473975\pi$
$719$	−7.23515	−	1.62143i	−0.269826	−	0.0604693i	−0.351494	+	0.936190i	$0.614326\pi$
$720$	−2.70301	−	1.09787i	−0.100735	−	0.0409152i
$721$	1.01756			0.0378960
$722$	−18.2459	+	5.29974i	−0.679042	+	0.197236i
$723$	12.4129			0.461641
$724$	7.09034	+	2.87985i	0.263510	+	0.107029i
$725$	30.3327	+	6.79771i	1.12653	+	0.252461i
$726$	7.58782	+	7.38155i	0.281610	+	0.273955i
$727$	−0.784487	−	28.4597i	−0.0290950	−	1.05551i	−0.863496	−	0.504355i	$-0.831730\pi$
$727$	−0.784487	−	28.4597i	−0.0290950	−	1.05551i	0.834401	−	0.551157i	$-0.185814\pi$
$728$	−2.65475	−	1.84076i	−0.0983914	−	0.0682231i
$729$	−3.66291	−	14.4645i	−0.135663	−	0.535723i
$730$	−2.30990	−	5.26604i	−0.0854932	−	0.194905i
$731$	−28.7231	−	13.5547i	−1.06236	−	0.501340i
$732$	−1.17212	+	3.13058i	−0.0433227	+	0.115710i
$733$	−4.25054	+	51.2964i	−0.156997	+	1.89468i	0.230907	+	0.972976i	$0.425831\pi$
$733$	−4.25054	+	51.2964i	−0.156997	+	1.89468i	−0.387904	+	0.921700i	$0.626801\pi$
$734$	−8.52903	−	13.0547i	−0.314812	−	0.481856i
$735$	−1.01928	−	3.25883i	−0.0375968	−	0.120204i
$736$	0.965731	−	6.96435i	0.0355973	−	0.256709i
$737$	−1.62538	+	8.32106i	−0.0598718	+	0.306510i
$738$	−0.612278	−	22.2123i	−0.0225383	−	0.817647i
$739$	−3.12349	+	3.03858i	−0.114900	+	0.111776i	−0.752503	−	0.658589i	$-0.771154\pi$
$739$	−3.12349	+	3.03858i	−0.114900	+	0.111776i	0.637604	+	0.770365i	$0.279926\pi$
$740$	6.93622	+	7.53474i	0.254980	+	0.276983i
$741$	−4.43475	−	10.0134i	−0.162915	−	0.367850i
$742$	−1.35896	+	1.47622i	−0.0498888	+	0.0541937i
$743$	−0.770766	−	27.9620i	−0.0282767	−	1.02583i	−0.872137	−	0.489262i	$-0.837266\pi$
$743$	−0.770766	−	27.9620i	−0.0282767	−	1.02583i	0.843860	−	0.536563i	$-0.180278\pi$
$744$	−0.0550493	+	0.108780i	−0.00201821	+	0.00398809i
$745$	21.8023	−	4.88601i	0.798774	−	0.179010i
$746$	5.05686	+	25.8883i	0.185145	+	0.947838i
$747$	26.5851	−	1.46674i	0.972699	−	0.0536653i
$748$	1.70874	−	20.6215i	0.0624779	−	0.753996i
$749$	8.40091	+	6.53869i	0.306962	+	0.238918i
$750$	−2.29636	+	3.97742i	−0.0838513	+	0.145235i
$751$	−20.7996	−	5.88156i	−0.758988	−	0.214621i	−0.129444	−	0.991587i	$-0.541319\pi$
$751$	−20.7996	−	5.88156i	−0.758988	−	0.214621i	−0.629543	+	0.776965i	$0.716758\pi$
$752$	6.68728	−	10.2356i	0.243860	−	0.373256i
$753$	11.0034	+	8.56430i	0.400987	+	0.312101i
$754$	14.4148	−	38.5002i	0.524956	−	1.40210i
$755$	−0.913190	+	2.91963i	−0.0332344	+	0.106256i
$756$	−1.64251	+	0.667129i	−0.0597374	+	0.0242632i
$757$	−30.4931	+	8.62263i	−1.10829	+	0.313395i	−0.776601	−	0.629993i	$-0.783058\pi$
$757$	−30.4931	+	8.62263i	−1.10829	+	0.313395i	−0.331691	+	0.943388i	$0.607619\pi$
$758$	9.90836	+	26.4641i	0.359888	+	0.961218i
$759$	−1.62278	+	19.5840i	−0.0589032	+	0.710856i
$760$	3.29042	−	3.22380i	0.119356	−	0.116939i
$761$	−1.94671	−	23.4933i	−0.0705683	−	0.851633i	−0.936318	−	0.351155i	$-0.885789\pi$
$761$	−1.94671	−	23.4933i	−0.0705683	−	0.851633i	0.865749	−	0.500478i	$-0.166842\pi$
$762$	−4.15670	+	1.96159i	−0.150581	+	0.0710610i
$763$	−0.664644	−	0.578839i	−0.0240617	−	0.0209554i
$764$	3.03690	−	8.11119i	0.109871	−	0.293453i
$765$	−3.70516	−	9.89604i	−0.133960	−	0.357792i
$766$	−0.528296	+	0.460094i	−0.0190881	+	0.0166239i
$767$	−1.43458	+	3.27051i	−0.0517997	+	0.118091i
$768$	−0.482553	−	0.0805239i	−0.0174126	−	0.00290566i
$769$	2.60251	+	1.80454i	0.0938489	+	0.0650734i	0.615803	−	0.787900i	$-0.288832\pi$
$769$	2.60251	+	1.80454i	0.0938489	+	0.0650734i	−0.521954	+	0.852974i	$0.674797\pi$
$770$	−0.728090	+	3.72741i	−0.0262385	+	0.134327i
$771$	1.50247	−	0.813094i	0.0541100	−	0.0292829i
$772$	21.4110	+	7.35041i	0.770599	+	0.264547i
$773$	−33.2662	+	20.4487i	−1.19650	+	0.735488i	−0.971076	−	0.238772i	$-0.923255\pi$
$773$	−33.2662	+	20.4487i	−1.19650	+	0.735488i	−0.225428	+	0.974260i	$0.572378\pi$
$774$	−10.9308	+	21.5998i	−0.392898	+	0.776388i
$775$	−0.795232	−	0.551402i	−0.0285656	−	0.0198069i
$776$	−2.28149	−	3.95165i	−0.0819007	−	0.141856i
$777$	2.97778	+	0.164289i	0.106827	+	0.00589383i
$778$	−0.999373	+	0.777844i	−0.0358293	+	0.0278870i
$779$	32.5529	+	13.0873i	1.16633	+	0.468901i
$780$	2.09528	+	1.63082i	0.0750231	+	0.0583928i
$781$	−3.53100	−	3.07515i	−0.126349	−	0.110038i
$782$	20.9273	−	14.5107i	0.748359	−	0.518901i
$783$	−13.3611	−	18.1784i	−0.477485	−	0.649642i
$784$	3.30215	+	5.71949i	0.117934	+	0.204268i
$785$	−3.32999	+	17.0477i	−0.118852	+	0.608458i
$786$	2.62691	−	2.85359i	0.0936988	−	0.101784i
$787$	19.8736	−	6.82263i	0.708419	−	0.243200i	0.0531394	−	0.998587i	$-0.483077\pi$
$787$	19.8736	−	6.82263i	0.708419	−	0.243200i	0.655279	+	0.755387i	$0.272551\pi$
$788$	6.61828	−	8.03614i	0.235767	−	0.286275i
$789$	−13.5732	−	1.50228i	−0.483217	−	0.0534824i
$790$	−9.49040			−0.337653
$791$	−12.3836			−0.440311
$792$	−15.6759	−	1.73500i	−0.557018	−	0.0616507i
$793$	−20.7818	+	28.2746i	−0.737983	+	1.00406i
$794$	−0.595012	+	21.5859i	−0.0211162	+	0.766056i
$795$	1.18207	−	1.14993i	0.0419236	−	0.0407839i
$796$	−5.66880	+	11.2019i	−0.200925	+	0.397039i
$797$	6.19641	+	1.03400i	0.219488	+	0.0366261i	0.273317	−	0.961924i	$-0.411879\pi$
$797$	6.19641	+	1.03400i	0.219488	+	0.0366261i	−0.0538285	+	0.998550i	$0.517142\pi$
$798$	0.0321981	−	1.34105i	0.00113980	−	0.0474726i
$799$	43.6800	−	7.28890i	1.54529	−	0.257863i
$800$	1.15918	−	3.70612i	0.0409834	−	0.131031i
$801$	5.53094	+	14.7725i	0.195426	+	0.521960i
$802$	−15.8122	+	0.872381i	−0.558347	+	0.0308048i
$803$	−19.7622	−	23.9959i	−0.697392	−	0.846796i
$804$	0.327828	+	0.647806i	0.0115616	+	0.0228463i
$805$	−4.11069	+	2.22460i	−0.144883	+	0.0784067i
$806$	−0.866777	+	0.941571i	−0.0305309	+	0.0331654i
$807$	−6.80088	−	6.61600i	−0.239402	−	0.232894i
$808$	−0.164536	+	5.96904i	−0.00578834	+	0.209990i
$809$	−0.436986	−	0.236485i	−0.0153636	−	0.00831438i	0.468247	−	0.883597i	$-0.344886\pi$
$809$	−0.436986	−	0.236485i	−0.0153636	−	0.00831438i	−0.483611	+	0.875283i	$0.660675\pi$
$810$	−6.90003	+	2.36878i	−0.242442	+	0.0832306i
$811$	−13.3663	−	13.0030i	−0.469355	−	0.456596i	0.424187	−	0.905575i	$-0.360560\pi$
$811$	−13.3663	−	13.0030i	−0.469355	−	0.456596i	−0.893543	+	0.448979i	$0.851788\pi$
$812$	3.60940	−	3.51128i	0.126665	−	0.123222i
$813$	−1.74910	+	1.07517i	−0.0613435	+	0.0377077i
$814$	47.1652	+	28.9924i	1.65314	+	1.01618i
$815$	6.53690	+	7.93732i	0.228978	+	0.278032i
$816$	−0.969166	−	1.48342i	−0.0339276	−	0.0519301i
$817$	−24.4039	−	29.4184i	−0.853785	−	1.02922i
$818$	1.43040	−	2.18939i	0.0500128	−	0.0765503i
$819$	−8.86415	+	0.981084i	−0.309739	+	0.0342819i
$820$	−8.45464	+	0.935760i	−0.295249	+	0.0326782i
$821$	0.791964	−	1.37172i	0.0276397	−	0.0478734i	−0.851875	−	0.523746i	$-0.824534\pi$
$821$	0.791964	−	1.37172i	0.0276397	−	0.0478734i	0.879514	+	0.475872i	$0.157868\pi$
$822$	−0.349129	−	0.304056i	−0.0121773	−	0.0106052i
$823$	−9.56680	−	4.51468i	−0.333478	−	0.157372i	0.252721	−	0.967539i	$-0.418675\pi$
$823$	−9.56680	−	4.51468i	−0.333478	−	0.157372i	−0.586199	+	0.810167i	$0.699376\pi$
$824$	1.59556	−	0.266252i	0.0555840	−	0.00927533i
$825$	−2.66431	+	10.5211i	−0.0927594	+	0.366298i
$826$	−0.329882	+	0.287294i	−0.0114781	+	0.00999624i
$827$	8.70862	−	0.480468i	0.302828	−	0.0167075i	0.0969635	−	0.995288i	$-0.469087\pi$
$827$	8.70862	−	0.480468i	0.302828	−	0.0167075i	0.205865	+	0.978580i	$0.433999\pi$
$828$	−10.6163	−	16.2495i	−0.368943	−	0.564710i
$829$	8.13426	−	6.33115i	0.282515	−	0.219890i	−0.463035	−	0.886340i	$-0.653240\pi$
$829$	8.13426	−	6.33115i	0.282515	−	0.219890i	0.745550	+	0.666450i	$0.232187\pi$
$830$	−1.39997	−	10.0959i	−0.0485937	−	0.350432i
$831$	5.10377	−	3.53887i	0.177048	−	0.122762i
$832$	−4.64436	−	2.19172i	−0.161014	−	0.0759844i
$833$	−7.14061	+	22.8298i	−0.247408	+	0.791006i
$834$	0.961852	−	0.271986i	0.0333062	−	0.00941810i
$835$	0.257370	−	1.01633i	0.00890665	−	0.0351716i
$836$	12.3745	−	21.6101i	0.427980	−	0.747402i
$837$	0.172409	+	0.680828i	0.00595933	+	0.0235329i
$838$	−16.1462	−	27.9661i	−0.557762	−	0.966073i
$839$	2.13635	−	15.4062i	0.0737549	−	0.531882i	−0.917276	−	0.398251i	$-0.869617\pi$
$839$	2.13635	−	15.4062i	0.0737549	−	0.531882i	0.991031	−	0.133631i	$-0.0426635\pi$
$840$	0.146850	+	0.290184i	0.00506682	+	0.0100123i
$841$	29.8863	+	18.3710i	1.03056	+	0.633483i
$842$	−17.1392	+	3.84098i	−0.590655	+	0.132369i
$843$	5.55330	+	0.926681i	0.191266	+	0.0319166i
$844$	−1.23884	−	4.89206i	−0.0426426	−	0.168392i
$845$	8.37025	+	11.3881i	0.287945	+	0.391764i
$846$	−4.63613	−	33.4334i	−0.159394	−	1.14946i
$847$	1.12402	+	13.5649i	0.0386219	+	0.466097i
$848$	−1.74461	+	2.67033i	−0.0599102	+	0.0916994i
$849$	4.29993	−	7.44770i	0.147573	−	0.255604i
$850$	12.7195	−	6.00247i	0.436275	−	0.205883i
$851$	9.35872	+	67.4902i	0.320813	+	2.31354i
$852$	−0.400361	−	0.0220885i	−0.0137161	−	0.000756741i
$853$	−5.48541	+	39.5579i	−0.187817	+	1.35444i	0.628940	+	0.777454i	$0.283489\pi$
$853$	−5.48541	+	39.5579i	−0.187817	+	1.35444i	−0.816757	+	0.576982i	$0.804230\pi$
$854$	−3.78015	+	2.04572i	−0.129354	+	0.0700029i
$855$	1.00512	−	12.6771i	0.0343745	−	0.433549i
$856$	14.8837	+	8.05467i	0.508715	+	0.275303i
$857$	22.1102	−	30.0820i	0.755270	−	1.02758i	−0.243071	−	0.970009i	$-0.578155\pi$
$857$	22.1102	−	30.0820i	0.755270	−	1.02758i	0.998341	−	0.0575739i	$-0.0183365\pi$
$858$	13.2984	+	5.40135i	0.454001	+	0.184399i
$859$	30.6793	+	3.39559i	1.04677	+	0.115856i	0.616904	−	0.787039i	$-0.288387\pi$
$859$	30.6793	+	3.39559i	1.04677	+	0.115856i	0.429862	+	0.902895i	$0.358562\pi$
$860$	8.58585	+	3.48727i	0.292775	+	0.118915i
$861$	−1.57473	+	1.91209i	−0.0536668	+	0.0651640i
$862$	7.39008	+	3.99931i	0.251707	+	0.136217i
$863$	−20.2348	−	21.9809i	−0.688802	−	0.748238i	0.289101	−	0.957299i	$-0.406644\pi$
$863$	−20.2348	−	21.9809i	−0.688802	−	0.748238i	−0.977903	+	0.209060i	$0.932959\pi$
$864$	−2.40093	+	1.47585i	−0.0816814	+	0.0502094i
$865$	−24.4731	+	5.48456i	−0.832111	+	0.186481i
$866$	−1.49829	+	3.41577i	−0.0509141	+	0.116072i
$867$	−0.466155	+	1.84080i	−0.0158314	+	0.0625169i
$868$	−0.145237	+	0.0589904i	−0.00492968	+	0.00200226i
$869$	−49.3685	+	13.9601i	−1.67471	+	0.473564i
$870$	−3.12104	+	2.71812i	−0.105813	+	0.0921529i
$871$	1.46109	+	7.47999i	0.0495073	+	0.253450i
$872$	−1.19363	−	0.733725i	−0.0404216	−	0.0248471i
$873$	−11.9143	−	4.09018i	−0.403238	−	0.138432i
$874$	30.2112	−	5.15175i	1.02191	−	0.174261i
$875$	−5.58536	+	1.91746i	−0.188820	+	0.0648219i
$876$	−2.59760	−	0.582135i	−0.0877647	−	0.0196685i
$877$	19.7599	−	26.8843i	0.667244	−	0.907818i	−0.332129	−	0.943234i	$-0.607767\pi$
$877$	19.7599	−	26.8843i	0.667244	−	0.907818i	0.999373	+	0.0354158i	$0.0112756\pi$
$878$	−13.7509	+	16.6968i	−0.464071	+	0.563491i
$879$	11.6370	+	2.60791i	0.392506	+	0.0879626i
$880$	−0.166359	+	6.03519i	−0.00560796	+	0.203446i
$881$	34.8018	+	37.8049i	1.17250	+	1.27368i	0.954661	+	0.297694i	$0.0962175\pi$
$881$	34.8018	+	37.8049i	1.17250	+	1.27368i	0.217842	+	0.975984i	$0.430098\pi$
$882$	17.2443	+	5.91999i	0.580647	+	0.199336i
$883$	−19.6495	−	38.8286i	−0.661260	−	1.30668i	−0.938299	−	0.345826i	$-0.887599\pi$
$883$	−19.6495	−	38.8286i	−0.661260	−	1.30668i	0.277039	−	0.960859i	$-0.410647\pi$
$884$	−5.55257	−	17.7526i	−0.186753	−	0.597083i
$885$	0.283726	−	0.220833i	0.00953734	−	0.00742321i
$886$	−0.758625	−	9.15524i	−0.0254865	−	0.307576i
$887$	41.4476	+	11.7203i	1.39167	+	0.393528i	0.883784	−	0.467895i	$-0.154987\pi$
$887$	41.4476	+	11.7203i	1.39167	+	0.393528i	0.507889	+	0.861422i	$0.330426\pi$
$888$	4.71222	−	0.521549i	0.158132	−	0.0175020i
$889$	−5.68694	−	1.60811i	−0.190734	−	0.0539343i
$890$	5.46085	−	2.57704i	0.183048	−	0.0863826i
$891$	−32.4092	+	22.4720i	−1.08575	+	0.752841i
$892$	4.10282	+	9.35349i	0.137373	+	0.313178i
$893$	51.3345	+	14.3193i	1.71784	+	0.479176i
$894$	4.15486	−	9.47212i	0.138959	−	0.316795i
$895$	−4.04024	−	20.6838i	−0.135050	−	0.691382i
$896$	−0.399900	−	0.485572i	−0.0133597	−	0.0162218i
$897$	5.27323	+	16.8595i	0.176068	+	0.562921i
$898$	−35.1505	−	1.93931i	−1.17299	−	0.0647155i
$899$	−1.18144	−	1.60741i	−0.0394033	−	0.0536101i
$900$	−4.30622	−	9.81719i	−0.143541	−	0.327240i
$901$	−11.3955	+	1.90156i	−0.379638	+	0.0633503i
$902$	−42.6041	+	17.3043i	−1.41856	+	0.576170i
$903$	2.50025	−	1.01551i	0.0832030	−	0.0337941i
$904$	−19.4178	+	3.24026i	−0.645828	+	0.107770i
$905$	−3.24874	−	7.40637i	−0.107992	−	0.246196i
$906$	0.838698	+	1.14109i	0.0278639	+	0.0379102i
$907$	44.0555	+	2.43061i	1.46284	+	0.0807071i	0.768920	−	0.639346i	$-0.220795\pi$
$907$	44.0555	+	2.43061i	1.46284	+	0.0807071i	0.693919	+	0.720053i	$0.255882\pi$
$908$	−8.91950	−	28.5172i	−0.296004	−	0.946378i
$909$	10.4797	+	12.7249i	0.347591	+	0.422057i
$910$	0.654497	+	3.35066i	0.0216964	+	0.111073i
$911$	0.526295	−	1.19983i	0.0174369	−	0.0397522i	−0.906839	−	0.421477i	$-0.861512\pi$
$911$	0.526295	−	1.19983i	0.0174369	−	0.0397522i	0.924276	+	0.381725i	$0.124670\pi$
$912$	−0.300407	−	2.11122i	−0.00994747	−	0.0699095i
$913$	−22.1333	−	50.4588i	−0.732505	−	1.66994i
$914$	−6.33759	+	4.39439i	−0.209629	+	0.145353i
$915$	3.19481	−	1.50767i	0.105617	−	0.0498420i
$916$	−19.3936	−	5.48400i	−0.640784	−	0.181196i
$917$	4.95685	−	0.548624i	0.163690	−	0.0181172i
$918$	−9.82246	−	2.77753i	−0.324189	−	0.0916721i
$919$	0.826369	+	9.97279i	0.0272594	+	0.328972i	0.996546	+	0.0830393i	$0.0264627\pi$
$919$	0.826369	+	9.97279i	0.0272594	+	0.328972i	−0.969287	+	0.245933i	$0.920906\pi$
$920$	−5.86359	+	4.56381i	−0.193317	+	0.150464i
$921$	0.153335	+	0.490239i	0.00505255	+	0.0161539i
$922$	−13.1792	−	26.0429i	−0.434035	−	0.857677i
$923$	−3.98103	−	1.36669i	−0.131037	−	0.0449851i
$924$	1.19076	+	1.29351i	0.0391732	+	0.0425534i
$925$	−1.03690	+	37.6168i	−0.0340931	+	1.23683i
$926$	6.64837	+	1.48993i	0.218479	+	0.0489623i
$927$	2.83896	−	3.44715i	0.0932435	−	0.113219i
$928$	4.74088	−	6.45020i	0.155627	−	0.211738i
$929$	51.9428	+	11.6407i	1.70419	+	0.381917i	0.958659	−	0.284556i	$-0.0918463\pi$
$929$	51.9428	+	11.6407i	1.70419	+	0.381917i	0.745528	+	0.666474i	$0.232197\pi$
$930$	0.121860	−	0.0418347i	0.00399596	−	0.00137181i
$931$	−19.4219	+	21.2488i	−0.636526	+	0.696400i
$932$	19.3401	+	6.63947i	0.633506	+	0.217483i
$933$	8.46715	+	5.20474i	0.277202	+	0.170395i
$934$	5.06899	+	25.9504i	0.165862	+	0.849123i
$935$	−16.4904	+	14.3615i	−0.539294	+	0.469672i
$936$	−13.6425	+	3.85773i	−0.445919	+	0.126094i
$937$	43.7300	−	17.7616i	1.42860	−	0.580246i	0.474638	−	0.880181i	$-0.342579\pi$
$937$	43.7300	−	17.7616i	1.42860	−	0.580246i	0.953960	+	0.299935i	$0.0969649\pi$
$938$	−0.229169	+	0.904968i	−0.00748263	+	0.0295482i
$939$	−2.59404	+	5.91381i	−0.0846531	+	0.192990i
$940$	−12.6083	+	2.82558i	−0.411236	+	0.0921602i
$941$	6.64404	−	4.08407i	0.216589	−	0.133137i	−0.411130	−	0.911577i	$-0.634866\pi$
$941$	6.64404	−	4.08407i	0.216589	−	0.133137i	0.627719	+	0.778440i	$0.283989\pi$
$942$	5.44606	+	5.91599i	0.177442	+	0.192753i
$943$	−49.7720	−	26.9353i	−1.62080	−	0.877133i
$944$	−0.442090	+	0.536800i	−0.0143888	+	0.0174714i
$945$	1.73580	+	0.705022i	0.0564656	+	0.0229344i
$946$	49.7928	+	5.51107i	1.61890	+	0.179180i
$947$	−52.0550	−	21.1429i	−1.69156	−	0.687052i	−0.692161	−	0.721743i	$-0.743341\pi$
$947$	−52.0550	−	21.1429i	−1.69156	−	0.687052i	−0.999398	+	0.0346907i	$0.988955\pi$
$948$	−2.60193	+	3.54005i	−0.0845066	+	0.114975i
$949$	−24.5760	−	13.2999i	−0.797771	−	0.431732i
$950$	16.9263	−	0.0601350i	0.549160	−	0.00195104i
$951$	8.96950	−	4.85405i	0.290856	−	0.157403i
$952$	0.312943	−	2.25678i	0.0101426	−	0.0731428i
$953$	31.7372	+	1.75099i	1.02807	+	0.0567202i	0.561261	−	0.827639i	$-0.310316\pi$
$953$	31.7372	+	1.75099i	1.02807	+	0.0567202i	0.466808	+	0.884359i	$0.345404\pi$
$954$	1.20950	+	8.72227i	0.0391590	+	0.282394i
$955$	−8.27760	+	3.90629i	−0.267857	+	0.126405i
$956$	3.72526	−	6.45234i	0.120484	−	0.208684i
$957$	−12.2372	+	18.7305i	−0.395574	+	0.605471i
$958$	−2.29481	−	27.6943i	−0.0741420	−	0.894761i
$959$	−0.0817648	−	0.589645i	−0.00264032	−	0.0190406i
$960$	0.306194	+	0.416592i	0.00988237	+	0.0134454i
$961$	−7.59480	−	29.9912i	−0.244994	−	0.967458i
$962$	49.0888	+	8.19146i	1.58269	+	0.264103i
$963$	45.5891	−	10.2167i	1.46909	−	0.329230i
$964$	21.6154	+	13.2869i	0.696184	+	0.427943i
$965$	−10.8022	−	21.3457i	−0.347735	−	0.687144i
$966$	−0.297200	+	2.14325i	−0.00956225	+	0.0689579i
$967$	−6.10022	−	10.5659i	−0.196170	−	0.339776i	0.751114	−	0.660173i	$-0.229517\pi$
$967$	−6.10022	−	10.5659i	−0.196170	−	0.339776i	−0.947283	+	0.320397i	$0.896184\pi$
$968$	5.31185	+	20.9760i	0.170729	+	0.674195i
$969$	4.88897	−	5.97951i	0.157056	−	0.192089i
$970$	−1.18377	+	4.67460i	−0.0380086	+	0.150092i
$971$	−27.8465	+	7.87423i	−0.893635	+	0.252696i	−0.687808	−	0.725892i	$-0.741427\pi$
$971$	−27.8465	+	7.87423i	−0.893635	+	0.252696i	−0.205827	+	0.978588i	$0.565988\pi$
$972$	−3.53203	+	11.2925i	−0.113290	+	0.362208i
$973$	1.16232	+	0.548513i	0.0372623	+	0.0175845i
$974$	17.5615	−	12.1768i	0.562705	−	0.390171i
$975$	1.34005	+	9.66375i	0.0429160	+	0.309488i
$976$	−5.39209	+	4.19684i	−0.172597	+	0.134337i
$977$	9.21545	+	14.1053i	0.294828	+	0.451269i	0.953601	−	0.301074i	$-0.0973450\pi$
$977$	9.21545	+	14.1053i	0.294828	+	0.451269i	−0.658772	+	0.752342i	$0.728924\pi$
$978$	4.75291	−	0.262225i	0.151981	−	0.00838505i
$979$	24.6163	−	21.4384i	0.786741	−	0.685174i
$980$	1.71335	−	6.76586i	0.0547309	−	0.216127i
$981$	−3.81524	+	0.636651i	−0.121811	+	0.0203267i
$982$	0.824354	+	0.389022i	0.0263062	+	0.0124142i
$983$	30.4997	+	26.5622i	0.972790	+	0.847203i	0.988276	−	0.152677i	$-0.0487894\pi$
$983$	30.4997	+	26.5622i	0.972790	+	0.847203i	−0.0154865	+	0.999880i	$0.504930\pi$
$984$	−1.96891	+	3.41025i	−0.0627665	+	0.108715i
$985$	−10.9352	+	1.21031i	−0.348424	+	0.0385635i
$986$	28.8180	−	3.18958i	0.917752	−	0.101577i
$987$	−2.05798	+	3.14998i	−0.0655063	+	0.100265i
$988$	2.99590	−	22.1839i	0.0953123	−	0.705763i
$989$	33.7217	+	51.6150i	1.07229	+	1.64126i
$990$	10.5959	+	12.8659i	0.336759	+	0.408904i
$991$	37.8522	+	23.2676i	1.20241	+	0.739121i	0.972230	−	0.234026i	$-0.0751901\pi$
$991$	37.8522	+	23.2676i	1.20241	+	0.739121i	0.230184	+	0.973147i	$0.426067\pi$
$992$	−0.212301	+	0.130501i	−0.00674055	+	0.00414340i
$993$	0.650257	−	0.632580i	0.0206353	−	0.0200743i
$994$	−0.369550	−	0.359504i	−0.0117214	−	0.0114028i
$995$	12.5488	−	4.30800i	0.397823	−	0.136573i
$996$	−4.14971	−	2.24571i	−0.131489	−	0.0711582i
$997$	0.00691910	−	0.251012i	0.000219130	−	0.00794963i	−0.999503	−	0.0315289i	$-0.989962\pi$
$997$	0.00691910	−	0.251012i	0.000219130	−	0.00794963i	0.999722	+	0.0235793i	$0.00750622\pi$
$998$	−11.6476	−	11.3309i	−0.368697	−	0.358674i
$999$	18.4974	−	20.0936i	0.585233	−	0.635732i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.i.b.501.12	yes	612
361.49	even	57	inner	722.2.i.b.49.12	✓	612

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.i.b.49.12	✓	612	361.49	even	57	inner
722.2.i.b.501.12	yes	612	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.i (of order \(57\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.926494 - 0.376309i) q^{2} +(0.477385 + 0.106984i) q^{3} +(0.716783 + 0.697297i) q^{4} +(-0.0291194 - 1.05640i) q^{5} +(-0.402035 - 0.278765i) q^{6} +(-0.154422 - 0.609798i) q^{7} +(-0.401695 - 0.915773i) q^{8} +(-2.49662 - 1.17818i) q^{9} +O(q^{10})\)	\(q+(-0.926494 - 0.376309i) q^{2} +(0.477385 + 0.106984i) q^{3} +(0.716783 + 0.697297i) q^{4} +(-0.0291194 - 1.05640i) q^{5} +(-0.402035 - 0.278765i) q^{6} +(-0.154422 - 0.609798i) q^{7} +(-0.401695 - 0.915773i) q^{8} +(-2.49662 - 1.17818i) q^{9} +(-0.370554 + 0.989705i) q^{10} +(-0.471774 + 5.69347i) q^{11} +(0.267581 + 0.409563i) q^{12} +(1.53303 + 4.90138i) q^{13} +(-0.0864018 + 0.623085i) q^{14} +(0.0991171 - 0.507424i) q^{15} +(0.0275543 + 0.999620i) q^{16} +(-2.59615 + 2.52558i) q^{17} +(1.86974 + 2.03108i) q^{18} +(-4.11767 + 1.42997i) q^{19} +(0.715751 - 0.777513i) q^{20} +(-0.00847974 - 0.307629i) q^{21} +(2.57960 - 5.09743i) q^{22} +(6.86081 - 1.53754i) q^{23} +(-0.0937898 - 0.480151i) q^{24} +(3.87728 - 0.213915i) q^{25} +(0.424089 - 5.11799i) q^{26} +(-2.22401 - 1.73101i) q^{27} +(0.314523 - 0.544771i) q^{28} +(7.70302 + 2.17821i) q^{29} +(-0.282780 + 0.432827i) q^{30} +(-0.196656 - 0.153064i) q^{31} +(0.350638 - 0.936511i) q^{32} +(-0.834330 + 2.66750i) q^{33} +(3.35572 - 1.36297i) q^{34} +(-0.639694 + 0.180888i) q^{35} +(-0.967990 - 2.58539i) q^{36} +(-0.800262 + 9.65772i) q^{37} +(4.35311 + 0.224658i) q^{38} +(0.207475 + 2.50385i) q^{39} +(-0.955725 + 0.451017i) q^{40} +(-6.06987 - 5.28625i) q^{41} +(-0.107907 + 0.288208i) q^{42} +(3.07472 + 8.21222i) q^{43} +(-4.30820 + 3.75201i) q^{44} +(-1.17193 + 2.67174i) q^{45} +(-6.93509 - 1.15726i) q^{46} +(-10.0475 - 6.96678i) q^{47} +(-0.0937898 + 0.480151i) q^{48} +(5.80831 - 3.14330i) q^{49} +(-3.67277 - 1.26086i) q^{50} +(-1.50956 + 0.927924i) q^{51} +(-2.31886 + 4.58220i) q^{52} +(2.62124 + 1.81753i) q^{53} +(1.40913 + 2.44069i) q^{54} +(6.02831 + 0.332591i) q^{55} +(-0.496406 + 0.386369i) q^{56} +(-2.11870 + 0.242120i) q^{57} +(-6.31712 - 4.91681i) q^{58} +(0.524415 + 0.456713i) q^{59} +(0.424871 - 0.294599i) q^{60} +(4.04667 + 5.50569i) q^{61} +(0.124601 + 0.215816i) q^{62} +(-0.332922 + 1.70437i) q^{63} +(-0.677282 + 0.735724i) q^{64} +(5.13317 - 1.76222i) q^{65} +(1.77681 - 2.15746i) q^{66} +(1.47504 + 0.163257i) q^{67} -3.62195 q^{68} +3.43974 q^{69} +(0.660742 + 0.0731309i) q^{70} +(-0.485397 + 0.660406i) q^{71} +(-0.0760681 + 2.75961i) q^{72} +(-3.90023 + 3.79421i) q^{73} +(4.37573 - 8.64668i) q^{74} +(1.87384 + 0.312688i) q^{75} +(-3.94859 - 1.84626i) q^{76} +(3.54472 - 0.591509i) q^{77} +(0.749999 - 2.39788i) q^{78} +(3.14883 + 8.41016i) q^{79} +(1.05520 - 0.0582168i) q^{80} +(4.38853 + 5.32870i) q^{81} +(3.63443 + 7.18183i) q^{82} +(-8.48221 + 4.59034i) q^{83} +(0.208431 - 0.226416i) q^{84} +(2.74361 + 2.66903i) q^{85} +(0.241623 - 8.76562i) q^{86} +(3.44427 + 1.86395i) q^{87} +(5.40344 - 1.85500i) q^{88} +(-4.09558 - 3.98424i) q^{89} +(2.09119 - 2.03434i) q^{90} +(2.75212 - 1.69172i) q^{91} +(5.98983 + 3.68194i) q^{92} +(-0.0775052 - 0.0941093i) q^{93} +(6.68728 + 10.2356i) q^{94} +(1.63052 + 4.30826i) q^{95} +(0.267581 - 0.409563i) q^{96} +(4.53528 - 0.501965i) q^{97} +(-6.56422 + 0.726527i) q^{98} +(7.88580 - 13.6586i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 612 q + 17 q^{2} - 19 q^{3} + 17 q^{4} + q^{5} - 2 q^{7} - 34 q^{8} + 4 q^{9}+O(q^{10}) \) 612 * q + 17 * q^2 - 19 * q^3 + 17 * q^4 + q^5 - 2 * q^7 - 34 * q^8 + 4 * q^9	\( 612 q + 17 q^{2} - 19 q^{3} + 17 q^{4} + q^{5} - 2 q^{7} - 34 q^{8} + 4 q^{9} + q^{10} - 28 q^{11} + 4 q^{13} - 18 q^{14} - 52 q^{15} + 17 q^{16} + 18 q^{17} - 46 q^{18} - 12 q^{19} - 2 q^{20} - 65 q^{21} + 33 q^{22} + 39 q^{23} + 20 q^{25} - 8 q^{26} + 158 q^{27} - 37 q^{28} - 42 q^{29} - 29 q^{30} + 12 q^{31} + 17 q^{32} + 60 q^{33} - q^{34} - 14 q^{35} + 23 q^{36} - 6 q^{37} + 76 q^{38} - 108 q^{39} + q^{40} + 8 q^{41} + 11 q^{42} + 7 q^{43} - 5 q^{44} - 101 q^{45} - 21 q^{46} + 105 q^{47} - 62 q^{49} - 78 q^{50} - 3 q^{51} + 4 q^{52} + 146 q^{53} - 79 q^{54} + 4 q^{55} - 21 q^{56} - 28 q^{57} + 8 q^{58} - 4 q^{59} - 14 q^{60} - 93 q^{61} - 6 q^{62} - 95 q^{63} - 34 q^{64} - 76 q^{65} - 16 q^{66} - 6 q^{67} + 78 q^{68} + 38 q^{69} + 81 q^{70} - 151 q^{71} + 23 q^{72} + 7 q^{73} - 35 q^{74} - 12 q^{75} - 7 q^{76} + 78 q^{77} - 3 q^{78} - 10 q^{79} + q^{80} + 58 q^{81} - 30 q^{82} + 67 q^{83} - 22 q^{84} - 6 q^{85} - 12 q^{86} - 109 q^{87} + 10 q^{88} - 25 q^{89} - 73 q^{90} + 37 q^{91} + q^{92} + 56 q^{93} - 39 q^{94} - 29 q^{95} - 153 q^{97} + 164 q^{98} - 116 q^{99}+O(q^{100}) \) 612 * q + 17 * q^2 - 19 * q^3 + 17 * q^4 + q^5 - 2 * q^7 - 34 * q^8 + 4 * q^9 + q^10 - 28 * q^11 + 4 * q^13 - 18 * q^14 - 52 * q^15 + 17 * q^16 + 18 * q^17 - 46 * q^18 - 12 * q^19 - 2 * q^20 - 65 * q^21 + 33 * q^22 + 39 * q^23 + 20 * q^25 - 8 * q^26 + 158 * q^27 - 37 * q^28 - 42 * q^29 - 29 * q^30 + 12 * q^31 + 17 * q^32 + 60 * q^33 - q^34 - 14 * q^35 + 23 * q^36 - 6 * q^37 + 76 * q^38 - 108 * q^39 + q^40 + 8 * q^41 + 11 * q^42 + 7 * q^43 - 5 * q^44 - 101 * q^45 - 21 * q^46 + 105 * q^47 - 62 * q^49 - 78 * q^50 - 3 * q^51 + 4 * q^52 + 146 * q^53 - 79 * q^54 + 4 * q^55 - 21 * q^56 - 28 * q^57 + 8 * q^58 - 4 * q^59 - 14 * q^60 - 93 * q^61 - 6 * q^62 - 95 * q^63 - 34 * q^64 - 76 * q^65 - 16 * q^66 - 6 * q^67 + 78 * q^68 + 38 * q^69 + 81 * q^70 - 151 * q^71 + 23 * q^72 + 7 * q^73 - 35 * q^74 - 12 * q^75 - 7 * q^76 + 78 * q^77 - 3 * q^78 - 10 * q^79 + q^80 + 58 * q^81 - 30 * q^82 + 67 * q^83 - 22 * q^84 - 6 * q^85 - 12 * q^86 - 109 * q^87 + 10 * q^88 - 25 * q^89 - 73 * q^90 + 37 * q^91 + q^92 + 56 * q^93 - 39 * q^94 - 29 * q^95 - 153 * q^97 + 164 * q^98 - 116 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more