LMFDB - Embedded newform 287.2.bc.a.2.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(2,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([20, 39]))

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

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

chi := DirichletCharacter("287.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.bc (of order $60$, degree $16$, 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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$416$
Relative dimension:	$26$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			2.15
Character	$\chi$	$=$	287.2
Dual form			287.2.bc.a.144.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0396320 - 0.186454i) q^{2} +(2.77822 + 0.744421i) q^{3} +(1.79390 + 0.798694i) q^{4} +(-2.60706 + 0.274013i) q^{5} +(0.248906 - 0.488506i) q^{6} +(-1.73439 + 1.99797i) q^{7} +(0.444101 - 0.611253i) q^{8} +(4.56625 + 2.63632i) q^{9} +O(q^{10})$	\(q+(0.0396320 - 0.186454i) q^{2} +(2.77822 + 0.744421i) q^{3} +(1.79390 + 0.798694i) q^{4} +(-2.60706 + 0.274013i) q^{5} +(0.248906 - 0.488506i) q^{6} +(-1.73439 + 1.99797i) q^{7} +(0.444101 - 0.611253i) q^{8} +(4.56625 + 2.63632i) q^{9} +(-0.0522322 + 0.496956i) q^{10} +(-2.69871 - 3.33263i) q^{11} +(4.38927 + 3.55436i) q^{12} +(4.54204 + 2.31428i) q^{13} +(0.303791 + 0.402567i) q^{14} +(-7.44696 - 1.17948i) q^{15} +(2.53153 + 2.81154i) q^{16} +(1.74835 - 1.41579i) q^{17} +(0.672521 - 0.746911i) q^{18} +(0.391965 - 7.47914i) q^{19} +(-4.89565 - 1.59069i) q^{20} +(-6.30585 + 4.25967i) q^{21} +(-0.728337 + 0.371106i) q^{22} +(-6.87307 - 1.46092i) q^{23} +(1.68884 - 1.36759i) q^{24} +(1.83095 - 0.389181i) q^{25} +(0.611516 - 0.755160i) q^{26} +(4.62210 + 4.62210i) q^{27} +(-4.70709 + 2.19890i) q^{28} +(-0.331708 + 2.09432i) q^{29} +(-0.515057 + 1.34177i) q^{30} +(0.844092 - 8.03100i) q^{31} +(1.93320 - 1.11614i) q^{32} +(-5.01672 - 11.2677i) q^{33} +(-0.194688 - 0.382097i) q^{34} +(3.97420 - 5.68408i) q^{35} +(6.08576 + 8.37633i) q^{36} +(0.151717 + 1.44349i) q^{37} +(-1.37898 - 0.369496i) q^{38} +(10.8960 + 9.81076i) q^{39} +(-0.990308 + 1.71526i) q^{40} +(4.86499 + 4.16316i) q^{41} +(0.544319 + 1.34457i) q^{42} +(-6.84777 + 2.22498i) q^{43} +(-2.17946 - 8.13384i) q^{44} +(-12.6269 - 5.62185i) q^{45} +(-0.544786 + 1.22361i) q^{46} +(2.23309 + 3.43865i) q^{47} +(4.94015 + 9.69560i) q^{48} +(-0.983764 - 6.93053i) q^{49} -0.356812i q^{50} +(5.91124 - 2.63185i) q^{51} +(6.29954 + 7.77928i) q^{52} +(2.29824 - 0.882212i) q^{53} +(1.04499 - 0.678624i) q^{54} +(7.94889 + 7.94889i) q^{55} +(0.451019 + 1.94745i) q^{56} +(6.65659 - 20.4869i) q^{57} +(0.377348 + 0.144850i) q^{58} +(5.22067 - 5.79814i) q^{59} +(-12.4170 - 8.06372i) q^{60} +(-4.77620 + 4.30051i) q^{61} +(-1.46396 - 0.475668i) q^{62} +(-13.1870 + 4.55080i) q^{63} +(2.20672 + 6.79159i) q^{64} +(-12.4755 - 4.78890i) q^{65} +(-2.29974 + 0.488824i) q^{66} +(0.831479 + 2.16608i) q^{67} +(4.26714 - 1.14338i) q^{68} +(-18.0073 - 9.17519i) q^{69} +(-0.902312 - 0.966275i) q^{70} +(-8.07306 + 1.27865i) q^{71} +(3.63934 - 1.62034i) q^{72} +(-12.3177 + 7.11164i) q^{73} +(0.275157 + 0.0289202i) q^{74} +(5.37649 + 0.281770i) q^{75} +(6.67669 - 13.1037i) q^{76} +(11.3391 + 0.388148i) q^{77} +(2.26108 - 1.64277i) q^{78} +(1.78322 + 6.65508i) q^{79} +(-7.37025 - 6.63620i) q^{80} +(1.49143 + 2.58323i) q^{81} +(0.969045 - 0.742101i) q^{82} -1.77240 q^{83} +(-14.7142 + 2.60497i) q^{84} +(-4.17012 + 4.17012i) q^{85} +(0.143464 + 1.36497i) q^{86} +(-2.48061 + 5.57155i) q^{87} +(-3.23558 + 0.169570i) q^{88} +(-8.06042 - 0.422429i) q^{89} +(-1.54864 + 2.13152i) q^{90} +(-12.5015 + 5.06097i) q^{91} +(-11.1627 - 8.11021i) q^{92} +(8.32352 - 21.6835i) q^{93} +(0.729651 - 0.280087i) q^{94} +(1.02751 + 19.6060i) q^{95} +(6.20173 - 1.66175i) q^{96} +(4.87722 + 0.772476i) q^{97} +(-1.33121 - 0.0912438i) q^{98} +(-3.53709 - 22.3323i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 416 q - 10 q^{2} - 8 q^{3} - 54 q^{4} - 10 q^{5} - 16 q^{6} - 16 q^{7} - 40 q^{8}+O(q^{10}) $ 416 * q - 10 * q^2 - 8 * q^3 - 54 * q^4 - 10 * q^5 - 16 * q^6 - 16 * q^7 - 40 * q^8	\( 416 q - 10 q^{2} - 8 q^{3} - 54 q^{4} - 10 q^{5} - 16 q^{6} - 16 q^{7} - 40 q^{8} + 18 q^{10} - 12 q^{11} - 24 q^{12} - 32 q^{13} + 10 q^{14} - 32 q^{15} + 26 q^{16} - 2 q^{17} - 30 q^{18} - 4 q^{19} + 80 q^{20} - 20 q^{21} - 32 q^{22} - 6 q^{23} + 26 q^{24} - 42 q^{25} - 18 q^{26} - 92 q^{27} - 42 q^{28} - 128 q^{29} - 38 q^{30} - 38 q^{31} + 100 q^{33} - 56 q^{34} - 2 q^{35} - 120 q^{36} + 6 q^{38} - 10 q^{39} + 20 q^{40} - 44 q^{41} + 112 q^{42} - 76 q^{44} - 106 q^{45} + 90 q^{46} + 32 q^{47} - 20 q^{48} - 48 q^{51} - 20 q^{52} - 2 q^{53} + 72 q^{54} - 16 q^{55} - 166 q^{56} - 32 q^{57} - 14 q^{58} + 54 q^{59} + 62 q^{60} - 90 q^{61} - 40 q^{62} - 100 q^{63} - 8 q^{64} + 2 q^{65} + 22 q^{66} - 24 q^{67} - 42 q^{68} + 24 q^{69} + 222 q^{70} - 92 q^{71} - 30 q^{72} - 10 q^{74} - 32 q^{75} + 348 q^{76} + 80 q^{77} + 80 q^{78} + 10 q^{79} - 90 q^{80} + 120 q^{81} - 124 q^{82} + 432 q^{83} + 76 q^{85} - 54 q^{86} - 10 q^{87} - 130 q^{88} - 50 q^{89} + 80 q^{90} - 92 q^{92} - 16 q^{93} - 50 q^{94} - 52 q^{95} - 64 q^{96} - 4 q^{97} + 66 q^{98} - 124 q^{99}+O(q^{100}) \) 416 * q - 10 * q^2 - 8 * q^3 - 54 * q^4 - 10 * q^5 - 16 * q^6 - 16 * q^7 - 40 * q^8 + 18 * q^10 - 12 * q^11 - 24 * q^12 - 32 * q^13 + 10 * q^14 - 32 * q^15 + 26 * q^16 - 2 * q^17 - 30 * q^18 - 4 * q^19 + 80 * q^20 - 20 * q^21 - 32 * q^22 - 6 * q^23 + 26 * q^24 - 42 * q^25 - 18 * q^26 - 92 * q^27 - 42 * q^28 - 128 * q^29 - 38 * q^30 - 38 * q^31 + 100 * q^33 - 56 * q^34 - 2 * q^35 - 120 * q^36 + 6 * q^38 - 10 * q^39 + 20 * q^40 - 44 * q^41 + 112 * q^42 - 76 * q^44 - 106 * q^45 + 90 * q^46 + 32 * q^47 - 20 * q^48 - 48 * q^51 - 20 * q^52 - 2 * q^53 + 72 * q^54 - 16 * q^55 - 166 * q^56 - 32 * q^57 - 14 * q^58 + 54 * q^59 + 62 * q^60 - 90 * q^61 - 40 * q^62 - 100 * q^63 - 8 * q^64 + 2 * q^65 + 22 * q^66 - 24 * q^67 - 42 * q^68 + 24 * q^69 + 222 * q^70 - 92 * q^71 - 30 * q^72 - 10 * q^74 - 32 * q^75 + 348 * q^76 + 80 * q^77 + 80 * q^78 + 10 * q^79 - 90 * q^80 + 120 * q^81 - 124 * q^82 + 432 * q^83 + 76 * q^85 - 54 * q^86 - 10 * q^87 - 130 * q^88 - 50 * q^89 + 80 * q^90 - 92 * q^92 - 16 * q^93 - 50 * q^94 - 52 * q^95 - 64 * q^96 - 4 * q^97 + 66 * q^98 - 124 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{20}\right)$

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 $

$2$	0.0396320	−	0.186454i	0.0280240	−	0.131843i	−0.961912	−	0.273360i	$-0.911865\pi$
$2$	0.0396320	−	0.186454i	0.0280240	−	0.131843i	0.989936	+	0.141518i	$0.0451982\pi$
$3$	2.77822	+	0.744421i	1.60400	+	0.429792i	0.946249	−	0.323440i	$-0.104839\pi$
$3$	2.77822	+	0.744421i	1.60400	+	0.429792i	0.657755	+	0.753232i	$0.271506\pi$
$4$	1.79390	+	0.798694i	0.896948	+	0.399347i
$5$	−2.60706	+	0.274013i	−1.16591	+	0.122542i	−0.667645	−	0.744480i	$-0.732697\pi$
$5$	−2.60706	+	0.274013i	−1.16591	+	0.122542i	−0.498269	+	0.867023i	$0.666031\pi$
$6$	0.248906	−	0.488506i	0.101615	−	0.199432i
$7$	−1.73439	+	1.99797i	−0.655539	+	0.755161i
$7$	−1.73439	+	1.99797i	−0.655539	+	0.755161i
$8$	0.444101	−	0.611253i	0.157014	−	0.216111i
$9$	4.56625	+	2.63632i	1.52208	+	0.878774i
$10$	−0.0522322	+	0.496956i	−0.0165173	+	0.157151i
$11$	−2.69871	−	3.33263i	−0.813692	−	1.00483i	−0.999752	−	0.0222876i	$-0.992905\pi$
$11$	−2.69871	−	3.33263i	−0.813692	−	1.00483i	0.186059	−	0.982538i	$-0.440428\pi$
$12$	4.38927	+	3.55436i	1.26707	+	1.02606i
$13$	4.54204	+	2.31428i	1.25973	+	0.641867i	0.950973	−	0.309273i	$-0.100086\pi$
$13$	4.54204	+	2.31428i	1.25973	+	0.641867i	0.308761	+	0.951140i	$0.400086\pi$
$14$	0.303791	+	0.402567i	0.0811917	+	0.107591i
$15$	−7.44696	−	1.17948i	−1.92280	−	0.304541i
$16$	2.53153	+	2.81154i	0.632882	+	0.702886i
$17$	1.74835	−	1.41579i	0.424037	−	0.343379i	−0.393429	−	0.919355i	$-0.628711\pi$
$17$	1.74835	−	1.41579i	0.424037	−	0.343379i	0.817466	+	0.575976i	$0.195378\pi$
$18$	0.672521	−	0.746911i	0.158515	−	0.176049i
$19$	0.391965	−	7.47914i	0.0899230	−	1.71583i	−0.466155	−	0.884703i	$-0.654361\pi$
$19$	0.391965	−	7.47914i	0.0899230	−	1.71583i	0.556078	−	0.831130i	$-0.312305\pi$
$20$	−4.89565	−	1.59069i	−1.09470	−	0.355690i
$21$	−6.30585	+	4.25967i	−1.37605	+	0.929537i
$22$	−0.728337	+	0.371106i	−0.155282	+	0.0791201i
$23$	−6.87307	−	1.46092i	−1.43313	−	0.304622i	−0.575044	−	0.818122i	$-0.695015\pi$
$23$	−6.87307	−	1.46092i	−1.43313	−	0.304622i	−0.858089	+	0.513501i	$0.828348\pi$
$24$	1.68884	−	1.36759i	0.344733	−	0.279159i
$25$	1.83095	−	0.389181i	0.366190	−	0.0778361i
$26$	0.611516	−	0.755160i	0.119928	−	0.148099i
$27$	4.62210	+	4.62210i	0.889523	+	0.889523i
$28$	−4.70709	+	2.19890i	−0.889556	+	0.415553i
$29$	−0.331708	+	2.09432i	−0.0615966	+	0.388906i	0.937559	+	0.347826i	$0.113080\pi$
$29$	−0.331708	+	2.09432i	−0.0615966	+	0.388906i	−0.999156	+	0.0410801i	$0.986920\pi$
$30$	−0.515057	+	1.34177i	−0.0940360	+	0.244972i
$31$	0.844092	−	8.03100i	0.151603	−	1.44241i	−0.608988	−	0.793180i	$-0.708424\pi$
$31$	0.844092	−	8.03100i	0.151603	−	1.44241i	0.760591	−	0.649231i	$-0.224909\pi$
$32$	1.93320	−	1.11614i	0.341745	−	0.197307i
$33$	−5.01672	−	11.2677i	−0.873300	−	1.96146i
$34$	−0.194688	−	0.382097i	−0.0333887	−	0.0655291i
$35$	3.97420	−	5.68408i	0.671762	−	0.960784i
$36$	6.08576	+	8.37633i	1.01429	+	1.39605i
$37$	0.151717	+	1.44349i	0.0249422	+	0.237309i	0.999889	+	0.0148725i	$0.00473425\pi$
$37$	0.151717	+	1.44349i	0.0249422	+	0.237309i	−0.974947	+	0.222436i	$0.928599\pi$
$38$	−1.37898	−	0.369496i	−0.223700	−	0.0599402i
$39$	10.8960	+	9.81076i	1.74475	+	1.57098i
$40$	−0.990308	+	1.71526i	−0.156582	+	0.271207i
$41$	4.86499	+	4.16316i	0.759784	+	0.650176i
$41$	4.86499	+	4.16316i	0.759784	+	0.650176i
$42$	0.544319	+	1.34457i	0.0839902	+	0.207471i
$43$	−6.84777	+	2.22498i	−1.04428	+	0.339306i	−0.780420	−	0.625256i	$-0.784994\pi$
$43$	−6.84777	+	2.22498i	−1.04428	+	0.339306i	−0.263856	+	0.964562i	$0.584994\pi$
$44$	−2.17946	−	8.13384i	−0.328565	−	1.22622i
$45$	−12.6269	−	5.62185i	−1.88230	−	0.838055i
$46$	−0.544786	+	1.22361i	−0.0803243	+	0.180411i
$47$	2.23309	+	3.43865i	0.325729	+	0.501579i	0.963160	−	0.268928i	$-0.0866695\pi$
$47$	2.23309	+	3.43865i	0.325729	+	0.501579i	−0.637431	+	0.770508i	$0.720003\pi$
$48$	4.94015	+	9.69560i	0.713050	+	1.39944i
$49$	−0.983764	−	6.93053i	−0.140538	−	0.990075i
$50$		−	0.356812i		−	0.0504608i
$51$	5.91124	−	2.63185i	0.827739	−	0.368533i
$52$	6.29954	+	7.77928i	0.873589	+	1.07879i
$53$	2.29824	−	0.882212i	0.315688	−	0.121181i	−0.195365	−	0.980731i	$-0.562589\pi$
$53$	2.29824	−	0.882212i	0.315688	−	0.121181i	0.511053	+	0.859549i	$0.329256\pi$
$54$	1.04499	−	0.678624i	0.142205	−	0.0923491i
$55$	7.94889	+	7.94889i	1.07183	+	1.07183i
$56$	0.451019	+	1.94745i	0.0602699	+	0.260239i
$57$	6.65659	−	20.4869i	0.881687	−	2.71355i
$58$	0.377348	+	0.144850i	0.0495482	+	0.0190198i
$59$	5.22067	−	5.79814i	0.679673	−	0.754853i	−0.300330	−	0.953835i	$-0.597097\pi$
$59$	5.22067	−	5.79814i	0.679673	−	0.754853i	0.980003	+	0.198982i	$0.0637635\pi$
$60$	−12.4170	−	8.06372i	−1.60303	−	1.04102i
$61$	−4.77620	+	4.30051i	−0.611529	+	0.550624i	−0.915633	−	0.402015i	$-0.868310\pi$
$61$	−4.77620	+	4.30051i	−0.611529	+	0.550624i	0.304103	+	0.952639i	$0.401643\pi$
$62$	−1.46396	−	0.475668i	−0.185923	−	0.0604100i
$63$	−13.1870	+	4.55080i	−1.66140	+	0.573347i
$64$	2.20672	+	6.79159i	0.275840	+	0.848949i
$65$	−12.4755	−	4.78890i	−1.54740	−	0.593990i
$66$	−2.29974	+	0.488824i	−0.283078	+	0.0601701i
$67$	0.831479	+	2.16608i	0.101581	+	0.264628i	0.974947	−	0.222436i	$-0.0714009\pi$
$67$	0.831479	+	2.16608i	0.101581	+	0.264628i	−0.873366	+	0.487065i	$0.838068\pi$
$68$	4.26714	−	1.14338i	0.517467	−	0.138655i
$69$	−18.0073	−	9.17519i	−2.16783	−	1.10456i
$70$	−0.902312	−	0.966275i	−0.107847	−	0.115492i
$71$	−8.07306	+	1.27865i	−0.958096	+	0.151748i	−0.615851	−	0.787863i	$-0.711188\pi$
$71$	−8.07306	+	1.27865i	−0.958096	+	0.151748i	−0.342246	+	0.939611i	$0.611188\pi$
$72$	3.63934	−	1.62034i	0.428900	−	0.190959i
$73$	−12.3177	+	7.11164i	−1.44168	+	0.832354i	−0.997962	−	0.0638128i	$-0.979674\pi$
$73$	−12.3177	+	7.11164i	−1.44168	+	0.832354i	−0.443717	+	0.896167i	$0.646341\pi$
$74$	0.275157	+	0.0289202i	0.0319864	+	0.00336191i
$75$	5.37649	+	0.281770i	0.620824	+	0.0325360i
$76$	6.67669	−	13.1037i	0.765869	−	1.50310i
$77$	11.3391	+	0.388148i	1.29221	+	0.0442335i
$78$	2.26108	−	1.64277i	0.256017	−	0.186007i
$79$	1.78322	+	6.65508i	0.200628	+	0.748755i	0.990738	+	0.135789i	$0.0433569\pi$
$79$	1.78322	+	6.65508i	0.200628	+	0.748755i	−0.790110	+	0.612966i	$0.789976\pi$
$80$	−7.37025	−	6.63620i	−0.824019	−	0.741950i
$81$	1.49143	+	2.58323i	0.165715	+	0.287026i
$82$	0.969045	−	0.742101i	0.107013	−	0.0819513i
$83$	−1.77240			−0.194546			−0.0972728	−	0.995258i	$-0.531012\pi$
$83$	−1.77240			−0.194546			−0.0972728	+	0.995258i	$0.531012\pi$
$84$	−14.7142	+	2.60497i	−1.60545	+	0.284225i
$85$	−4.17012	+	4.17012i	−0.452313	+	0.452313i
$86$	0.143464	+	1.36497i	0.0154702	+	0.147189i
$87$	−2.48061	+	5.57155i	−0.265950	+	0.597332i
$88$	−3.23558	+	0.169570i	−0.344914	+	0.0180762i
$89$	−8.06042	−	0.422429i	−0.854403	−	0.0447774i	−0.379896	−	0.925029i	$-0.624040\pi$
$89$	−8.06042	−	0.422429i	−0.854403	−	0.0447774i	−0.474507	+	0.880252i	$0.657374\pi$
$90$	−1.54864	+	2.13152i	−0.163241	+	0.224682i
$91$	−12.5015	+	5.06097i	−1.31052	+	0.530534i
$92$	−11.1627	−	8.11021i	−1.16380	−	0.845548i
$93$	8.32352	−	21.6835i	0.863108	−	2.24847i
$94$	0.729651	−	0.280087i	0.0752578	−	0.0288888i
$95$	1.02751	+	19.6060i	0.105420	+	2.01153i
$96$	6.20173	−	1.66175i	0.632962	−	0.169602i
$97$	4.87722	+	0.772476i	0.495207	+	0.0784331i	0.399043	−	0.916932i	$-0.369343\pi$
$97$	4.87722	+	0.772476i	0.495207	+	0.0784331i	0.0961643	+	0.995365i	$0.469343\pi$
$98$	−1.33121	−	0.0912438i	−0.134473	−	0.00921702i
$99$	−3.53709	−	22.3323i	−0.355491	−	2.24448i
$100$	3.59537	+	0.764220i	0.359537	+	0.0764220i
$101$	3.97583	+	2.58193i	0.395610	+	0.256912i	0.727079	−	0.686554i	$-0.240878\pi$
$101$	3.97583	+	2.58193i	0.395610	+	0.256912i	−0.331469	+	0.943466i	$0.607544\pi$
$102$	−0.256445	−	1.20648i	−0.0253918	−	0.119459i
$103$	8.02156	−	7.22264i	0.790388	−	0.711668i	−0.171479	−	0.985188i	$-0.554855\pi$
$103$	8.02156	−	7.22264i	0.790388	−	0.711668i	0.961866	+	0.273520i	$0.0881879\pi$
$104$	3.43174	−	1.74856i	0.336510	−	0.171460i
$105$	15.2725	−	12.8331i	1.49045	−	1.25238i
$106$	−0.0734079	−	0.463479i	−0.00713001	−	0.0450171i
$107$	8.67498	+	9.63454i	0.838642	+	0.931406i	0.998445	−	0.0557426i	$-0.0177526\pi$
$107$	8.67498	+	9.63454i	0.838642	+	0.931406i	−0.159803	+	0.987149i	$0.551086\pi$
$108$	4.59992	+	11.9832i	0.442628	+	1.15308i
$109$	−1.31890	+	4.92220i	−0.126328	+	0.471461i	−0.999884	−	0.0152628i	$-0.995141\pi$
$109$	−1.31890	+	4.92220i	−0.126328	+	0.471461i	0.873556	+	0.486724i	$0.161808\pi$
$110$	1.79713	−	1.16707i	0.171350	−	0.111276i
$111$	−0.653063	+	4.12328i	−0.0619860	+	0.391364i
$112$	−10.0080	+	0.181590i	−0.945671	+	0.0171586i
$113$	−2.88514	−	2.09618i	−0.271412	−	0.197192i	0.443751	−	0.896150i	$-0.353647\pi$
$113$	−2.88514	−	2.09618i	−0.271412	−	0.197192i	−0.715163	+	0.698958i	$0.753647\pi$
$114$	−3.55604	−	2.05308i	−0.333054	−	0.192289i
$115$	18.3188	+	1.92539i	1.70824	+	0.179543i
$116$	−2.26777	+	3.49206i	−0.210557	+	0.324230i
$117$	14.6389	+	22.5419i	1.35336	+	2.08400i
$118$	−0.874179	−	1.20320i	−0.0804747	−	0.110764i
$119$	−0.203628	+	5.94868i	−0.0186666	+	0.545315i
$120$	−4.02817	+	4.02817i	−0.367720	+	0.367720i
$121$	−1.53636	+	7.22800i	−0.139669	+	0.657091i
$122$	0.612555	+	1.06098i	0.0554582	+	0.0960564i
$123$	10.4168	+	15.1878i	0.939256	+	1.36943i
$124$	7.92853	−	13.7326i	0.712003	−	1.23323i
$125$	7.79884	−	2.53400i	0.697550	−	0.226648i
$126$	0.325889	+	2.63911i	0.0290325	+	0.235111i
$127$	2.63137	−	1.91180i	0.233496	−	0.169645i	−0.464885	−	0.885371i	$-0.653904\pi$
$127$	2.63137	−	1.91180i	0.233496	−	0.169645i	0.698381	+	0.715726i	$0.253904\pi$
$128$	5.79386	−	0.608959i	0.512110	−	0.0538249i
$129$	−20.6809	+	1.08384i	−1.82085	+	0.0954269i
$130$	−1.38734	+	2.13631i	−0.121678	+	0.187367i
$131$	0.796293	+	1.78850i	0.0695725	+	0.156262i	0.944984	−	0.327115i	$-0.106077\pi$
$131$	0.796293	+	1.78850i	0.0695725	+	0.156262i	−0.875412	+	0.483378i	$0.839410\pi$
$132$		−	24.2200i		−	2.10808i
$133$	14.2633	+	13.7549i	1.23678	+	1.19270i
$134$	0.436826	−	0.0691865i	0.0377360	−	0.00597680i
$135$	−13.3166	−	10.7836i	−1.14611	−	0.928103i
$136$	−0.0889590	−	1.69744i	−0.00762817	−	0.145554i
$137$	−0.734110	+	2.73973i	−0.0627192	+	0.234071i	−0.990169	−	0.139877i	$-0.955329\pi$
$137$	−0.734110	+	2.73973i	−0.0627192	+	0.234071i	0.927450	+	0.373948i	$0.121996\pi$
$138$	−2.42441	+	2.99390i	−0.206380	+	0.254858i
$139$	0.992334	−	3.05409i	0.0841687	−	0.259045i	−0.900111	−	0.435660i	$-0.856515\pi$
$139$	0.992334	−	3.05409i	0.0841687	−	0.259045i	0.984280	+	0.176616i	$0.0565149\pi$
$140$	11.6691	−	7.02248i	0.986223	−	0.593508i
$141$	3.64420	+	11.2157i	0.306897	+	0.944531i
$142$	−0.0815427	+	1.55593i	−0.00684291	+	0.130571i
$143$	−4.54499	−	21.3825i	−0.380071	−	1.78810i
$144$	4.14743	+	19.5121i	0.345619	+	1.62601i
$145$	0.290911	−	5.55092i	0.0241589	−	0.460979i
$146$	0.837816	+	2.57853i	0.0693381	+	0.213401i
$147$	2.42612	−	19.9868i	0.200103	−	1.64849i
$148$	−0.880744	+	2.71065i	−0.0723967	+	0.222814i
$149$	−13.4491	+	16.6083i	−1.10180	+	1.36061i	−0.175207	+	0.984532i	$0.556059\pi$
$149$	−13.4491	+	16.6083i	−1.10180	+	1.36061i	−0.926590	+	0.376074i	$0.877274\pi$
$150$	0.265618	−	0.991300i	0.0216876	−	0.0809393i
$151$	−0.312283	−	5.95871i	−0.0254132	−	0.484913i	−0.981456	−	0.191686i	$-0.938604\pi$
$151$	−0.312283	−	5.95871i	−0.0254132	−	0.484913i	0.956043	−	0.293227i	$-0.0947290\pi$
$152$	−4.39758	−	3.56109i	−0.356691	−	0.288842i
$153$	11.7159	−	1.85561i	0.947172	−	0.150017i
$154$	0.521763	−	2.09884i	0.0420449	−	0.169129i
$155$			21.1686i			1.70030i
$156$	11.7104	+	26.3020i	0.937584	+	2.10585i
$157$	−1.70942	+	2.63228i	−0.136427	+	0.210079i	−0.900280	−	0.435311i	$-0.856638\pi$
$157$	−1.70942	+	2.63228i	−0.136427	+	0.210079i	0.763853	+	0.645390i	$0.223305\pi$
$158$	1.31154	−	0.0687347i	0.104340	−	0.00546824i
$159$	7.04175	−	0.740118i	0.558447	−	0.0586951i
$160$	−4.73415	+	3.43956i	−0.374267	+	0.271921i
$161$	14.8395	−	11.1984i	1.16951	−	0.882556i
$162$	0.540762	−	0.175704i	0.0424863	−	0.0138046i
$163$	−0.806957	+	1.39769i	−0.0632058	+	0.109476i	−0.895897	−	0.444262i	$-0.853466\pi$
$163$	−0.806957	+	1.39769i	−0.0632058	+	0.109476i	0.832691	+	0.553738i	$0.186799\pi$
$164$	5.40220	+	11.3539i	0.421841	+	0.886592i
$165$	16.1664	+	28.0011i	1.25855	+	2.17988i
$166$	−0.0702435	+	0.330470i	−0.00545195	+	0.0256494i
$167$	−7.29948	+	7.29948i	−0.564851	+	0.564851i	−0.930681	−	0.365831i	$-0.880785\pi$
$167$	−7.29948	+	7.29948i	−0.564851	+	0.564851i	0.365831	+	0.930681i	$0.380785\pi$
$168$	−0.196697	+	5.74620i	−0.0151755	+	0.443329i
$169$	7.63298	+	10.5059i	0.587152	+	0.808146i
$170$	0.612264	+	0.942803i	0.0469585	+	0.0723097i
$171$	21.5072	−	33.1182i	1.64470	−	2.53262i
$172$	−14.0613	−	1.47790i	−1.07216	−	0.112689i
$173$	0.494308	+	0.285389i	0.0375815	+	0.0216977i	0.518673	−	0.854973i	$-0.326426\pi$
$173$	0.494308	+	0.285389i	0.0375815	+	0.0216977i	−0.481092	+	0.876670i	$0.659760\pi$
$174$	0.940524	+	0.683331i	0.0713009	+	0.0518032i
$175$	−2.39802	+	4.33318i	−0.181273	+	0.327557i
$176$	2.53798	−	16.0242i	0.191308	−	1.20787i
$177$	18.8204	−	12.2221i	1.41463	−	0.918670i
$178$	−0.398214	+	1.48615i	−0.0298474	+	0.111392i
$179$	−4.60669	−	12.0008i	−0.344320	−	0.896986i	−0.990956	−	0.134186i	$-0.957158\pi$
$179$	−4.60669	−	12.0008i	−0.344320	−	0.896986i	0.646636	−	0.762799i	$-0.276175\pi$
$180$	−18.1612	−	20.1700i	−1.35365	−	1.50338i
$181$	−2.05975	−	13.0048i	−0.153100	−	0.966636i	−0.937905	−	0.346893i	$-0.887237\pi$
$181$	−2.05975	−	13.0048i	−0.153100	−	0.966636i	0.784805	−	0.619743i	$-0.212763\pi$
$182$	0.448177	+	2.53153i	0.0332211	+	0.187650i
$183$	−16.4707	+	8.39224i	−1.21755	+	0.620372i
$184$	−3.94533	+	3.55239i	−0.290853	+	0.261886i
$185$	−0.791072	−	3.72170i	−0.0581608	−	0.273625i
$186$	−3.71309	−	2.41131i	−0.272257	−	0.176806i
$187$	−9.43659	−	2.00581i	−0.690072	−	0.146679i
$188$	1.25950	+	7.95214i	0.0918582	+	0.579970i
$189$	−17.2513	+	1.21828i	−1.25485	+	0.0886167i
$190$	3.69633	+	0.585441i	0.268160	+	0.0424724i
$191$	4.58792	−	1.22933i	0.331970	−	0.0889511i	−0.0889840	−	0.996033i	$-0.528362\pi$
$191$	4.58792	−	1.22933i	0.331970	−	0.0889511i	0.420954	+	0.907082i	$0.361695\pi$
$192$	1.07495	+	20.5112i	0.0775777	+	1.48027i
$193$	−6.08294	+	2.33502i	−0.437860	+	0.168079i	−0.567305	−	0.823508i	$-0.692014\pi$
$193$	−6.08294	+	2.33502i	−0.437860	+	0.168079i	0.129445	+	0.991587i	$0.458680\pi$
$194$	0.337325	−	0.878761i	0.0242185	−	0.0630914i
$195$	−31.0947	−	22.5916i	−2.22674	−	1.61782i
$196$	3.77060	−	13.2184i	0.269329	−	0.944170i
$197$	−6.75526	+	9.29782i	−0.481292	+	0.662442i	−0.978753	−	0.205045i	$-0.934266\pi$
$197$	−6.75526	+	9.29782i	−0.481292	+	0.662442i	0.497460	+	0.867487i	$0.334266\pi$
$198$	−4.30412	−	0.225569i	−0.305880	−	0.0160305i
$199$	10.1709	−	0.533033i	0.720994	−	0.0377857i	0.311690	−	0.950184i	$-0.399105\pi$
$199$	10.1709	−	0.533033i	0.720994	−	0.0377857i	0.409304	+	0.912398i	$0.365772\pi$
$200$	0.575240	−	1.29201i	0.0406756	−	0.0913589i
$201$	0.697556	+	6.63680i	0.0492018	+	0.468124i
$202$	0.638981	−	0.638981i	0.0449585	−	0.0449585i
$203$	−3.60908	−	4.29512i	−0.253308	−	0.301458i
$204$	12.7062			0.889612
$205$	−13.8241	−	9.52054i	−0.965516	−	0.664943i
$206$	−1.02878	−	1.78190i	−0.0716784	−	0.124151i
$207$	−27.5327	−	24.7905i	−1.91365	−	1.72306i
$208$	4.99157	+	18.6288i	0.346103	+	1.29168i
$209$	−25.9830	+	18.8778i	−1.79728	+	1.30580i
$210$	−1.78750	−	3.35622i	−0.123349	−	0.231601i
$211$	2.96513	−	5.81939i	0.204128	−	0.400623i	−0.766134	−	0.642681i	$-0.777822\pi$
$211$	2.96513	−	5.81939i	0.204128	−	0.400623i	0.970262	+	0.242057i	$0.0778222\pi$
$212$	4.82743	+	0.252995i	0.331549	+	0.0173757i
$213$	−23.3806	−	2.45740i	−1.60201	−	0.168378i
$214$	2.14020	−	1.23565i	0.146301	−	0.0844670i
$215$	17.2429	−	7.67703i	1.17596	−	0.523569i
$216$	4.87795	−	0.772592i	0.331903	−	0.0525682i
$217$	14.5817	+	15.6154i	0.989871	+	1.06004i
$218$	0.865491	+	0.440990i	0.0586185	+	0.0298676i
$219$	−39.5153	+	10.5881i	−2.67020	+	0.715477i
$220$	7.91076	+	20.6082i	0.533343	+	1.38941i
$221$	11.2176	−	2.38438i	0.754578	−	0.160390i
$222$	0.742918	+	0.285179i	0.0498614	+	0.0191400i
$223$	−2.01967	−	6.21590i	−0.135247	−	0.416247i	0.860381	−	0.509651i	$-0.170225\pi$
$223$	−2.01967	−	6.21590i	−0.135247	−	0.416247i	−0.995628	+	0.0934033i	$0.970225\pi$
$224$	−1.12293	+	5.79830i	−0.0750289	+	0.387415i
$225$	9.38658	+	3.04988i	0.625772	+	0.203326i
$226$	−0.505184	+	0.454870i	−0.0336044	+	0.0302575i
$227$	12.0303	+	7.81259i	0.798481	+	0.518540i	0.878209	−	0.478277i	$-0.158738\pi$
$227$	12.0303	+	7.81259i	0.798481	+	0.518540i	−0.0797280	+	0.996817i	$0.525405\pi$
$228$	28.3040	−	31.4348i	1.87448	−	2.08182i
$229$	15.8836	+	6.09713i	1.04962	+	0.402910i	0.821192	−	0.570652i	$-0.193310\pi$
$229$	15.8836	+	6.09713i	1.04962	+	0.402910i	0.228424	+	0.973562i	$0.426643\pi$
$230$	1.08501	−	3.33930i	0.0715432	−	0.220187i
$231$	31.2136	+	9.51943i	2.05370	+	0.626333i
$232$	1.13285	+	1.13285i	0.0743751	+	0.0743751i
$233$	14.0521	−	9.12557i	0.920586	−	0.597836i	0.00501332	−	0.999987i	$-0.498404\pi$
$233$	14.0521	−	9.12557i	0.920586	−	0.597836i	0.915573	+	0.402152i	$0.131738\pi$
$234$	4.78318	−	1.83609i	0.312686	−	0.120029i
$235$	−6.76404	−	8.35289i	−0.441237	−	0.544882i
$236$	13.9963	−	6.23154i	0.911080	−	0.405639i
$237$			19.8167i			1.28723i
$238$	1.10108	+	0.273725i	0.0713726	+	0.0177430i
$239$	−4.20593	−	8.25461i	−0.272059	−	0.533946i	0.714040	−	0.700105i	$-0.246864\pi$
$239$	−4.20593	−	8.25461i	−0.272059	−	0.533946i	−0.986099	+	0.166159i	$0.946864\pi$
$240$	−15.5360	−	23.9234i	−1.00285	−	1.54425i
$241$	−6.39347	+	14.3600i	−0.411840	+	0.925007i	0.581897	+	0.813262i	$0.302311\pi$
$241$	−6.39347	+	14.3600i	−0.411840	+	0.925007i	−0.993737	+	0.111745i	$0.964356\pi$
$242$	1.28680	+	0.572919i	0.0827185	+	0.0368286i
$243$	−2.85491	−	10.6547i	−0.183143	−	0.683498i
$244$	−12.0028	+	3.89994i	−0.768400	+	0.249668i
$245$	4.46379	+	17.7988i	0.285181	+	1.13712i
$246$	3.24465	−	1.34034i	0.206871	−	0.0854569i
$247$	19.0892	−	33.0634i	1.21461	−	2.10377i
$248$	−4.53411	−	4.08253i	−0.287916	−	0.259241i
$249$	−4.92410	−	1.31941i	−0.312052	−	0.0836141i
$250$	−0.163390	−	1.55455i	−0.0103337	−	0.0983184i
$251$	15.8542	+	21.8215i	1.00071	+	1.37736i	0.924888	+	0.380239i	$0.124158\pi$
$251$	15.8542	+	21.8215i	1.00071	+	1.37736i	0.0758230	+	0.997121i	$0.475842\pi$
$252$	−27.2907	−	2.36868i	−1.71915	−	0.149213i
$253$	13.6797	+	26.8480i	0.860037	+	1.68792i
$254$	−0.252176	−	0.566397i	−0.0158229	−	0.0355389i
$255$	−14.6898	+	8.48116i	−0.919911	+	0.531111i
$256$	−1.37682	+	13.0995i	−0.0860511	+	0.818721i
$257$	4.08966	−	10.6539i	0.255106	−	0.664573i	−0.744891	−	0.667186i	$-0.767498\pi$
$257$	4.08966	−	10.6539i	0.255106	−	0.664573i	0.999997	+	0.00261308i	$0.000831769\pi$
$258$	−0.617539	+	3.89899i	−0.0384463	+	0.242740i
$259$	−3.14719	−	2.20046i	−0.195557	−	0.136730i
$260$	−18.5549	−	18.5549i	−1.15073	−	1.15073i
$261$	−7.03597	+	8.68870i	−0.435515	+	0.537817i
$262$	0.365032	−	0.0775899i	0.0225517	−	0.00479352i
$263$	−8.19311	+	6.63465i	−0.505209	+	0.409110i	−0.847753	−	0.530392i	$-0.822045\pi$
$263$	−8.19311	+	6.63465i	−0.505209	+	0.409110i	0.342544	+	0.939502i	$0.388712\pi$
$264$	−9.11538	−	1.93753i	−0.561013	−	0.119247i
$265$	−5.74992	+	2.92973i	−0.353215	+	0.179972i
$266$	3.12993	−	2.11431i	0.191909	−	0.129636i
$267$	−22.0791	−	7.17395i	−1.35122	−	0.439038i
$268$	−0.238446	+	4.54982i	−0.0145654	+	0.277924i
$269$	−0.0525515	+	0.0583643i	−0.00320412	+	0.00355854i	−0.744745	−	0.667349i	$-0.767429\pi$
$269$	−0.0525515	+	0.0583643i	−0.00320412	+	0.00355854i	0.741541	+	0.670908i	$0.234095\pi$
$270$	−2.53840	+	2.05556i	−0.154482	+	0.125097i
$271$	−6.86229	−	7.62135i	−0.416854	−	0.462964i	0.497746	−	0.867323i	$-0.334161\pi$
$271$	−6.86229	−	7.62135i	−0.416854	−	0.462964i	−0.914600	+	0.404359i	$0.867495\pi$
$272$	8.40654	+	1.33147i	0.509722	+	0.0807320i
$273$	−38.4995	+	4.75407i	−2.33009	+	0.287730i
$274$	0.481739	+	0.245458i	0.0291029	+	0.0148287i
$275$	−6.23821	−	5.05160i	−0.376178	−	0.304623i
$276$	−24.9751	−	30.8417i	−1.50332	−	1.85645i
$277$	0.872606	−	8.30229i	0.0524298	−	0.498836i	−0.936523	−	0.350606i	$-0.885976\pi$
$277$	0.872606	−	8.30229i	0.0524298	−	0.498836i	0.988953	−	0.148230i	$-0.0473577\pi$
$278$	−0.530118	−	0.306064i	−0.0317944	−	0.0183565i
$279$	25.0267	−	34.4462i	1.49831	−	2.06224i
$280$	−1.70946	−	4.95355i	−0.102160	−	0.296031i
$281$	4.25202	−	8.34507i	0.253654	−	0.497825i	−0.728705	−	0.684828i	$-0.759877\pi$
$281$	4.25202	−	8.34507i	0.253654	−	0.497825i	0.982359	+	0.187003i	$0.0598774\pi$
$282$	2.23563	−	0.234974i	0.133130	−	0.0139925i
$283$	9.28842	+	4.13547i	0.552139	+	0.245828i	0.663790	−	0.747919i	$-0.268947\pi$
$283$	9.28842	+	4.13547i	0.552139	+	0.245828i	−0.111650	+	0.993748i	$0.535614\pi$
$284$	−15.5035	−	4.15415i	−0.919963	−	0.246503i
$285$	−11.7405	+	55.2346i	−0.695445	+	3.27181i
$286$	−4.16698			−0.246398
$287$	−16.7557	+	2.49955i	−0.989056	+	0.147544i
$288$	11.7700			0.693553
$289$	−2.48222	+	11.6779i	−0.146013	+	0.686937i
$290$	−1.02346	−	0.274235i	−0.0600996	−	0.0161036i
$291$	12.9749	+	5.77681i	0.760604	+	0.338643i
$292$	−27.7767	+	2.91945i	−1.62551	+	0.170848i
$293$	7.21104	−	14.1525i	0.421274	−	0.826796i	−0.578663	−	0.815566i	$-0.696425\pi$
$293$	7.21104	−	14.1525i	0.421274	−	0.826796i	0.999937	−	0.0112294i	$-0.00357452\pi$
$294$	−3.63047	−	1.24448i	−0.211733	−	0.0725793i
$295$	−12.0218	+	16.5466i	−0.699938	+	0.963383i
$296$	0.949717	+	0.548320i	0.0552012	+	0.0318704i
$297$	2.93004	−	27.8775i	0.170018	−	1.61761i
$298$	2.56366	+	3.16586i	0.148509	+	0.183393i
$299$	−27.8367	−	22.5418i	−1.60984	−	1.30362i
$300$	9.41982	+	4.79964i	0.543854	+	0.277107i
$301$	7.43129	−	17.5406i	0.428333	−	1.01102i
$302$	−1.12340	−	0.177929i	−0.0646444	−	0.0102387i
$303$	9.12367	+	10.1329i	0.524141	+	0.582118i
$304$	22.0202	−	17.8316i	1.26295	−	1.02271i
$305$	11.2734	−	12.5204i	0.645516	−	0.716918i
$306$	0.118337	−	2.25801i	0.00676489	−	0.129082i
$307$	20.4721	+	6.65180i	1.16841	+	0.379638i	0.828048	−	0.560657i	$-0.189451\pi$
$307$	20.4721	+	6.65180i	1.16841	+	0.379638i	0.340359	+	0.940296i	$0.389451\pi$
$308$	20.0312	+	9.75279i	1.14138	+	0.555717i
$309$	27.6623	−	14.0946i	1.57365	−	0.801817i
$310$	3.94697	+	0.838954i	0.224173	+	0.0476494i
$311$	−17.8402	+	14.4467i	−1.01162	+	0.819196i	−0.983591	−	0.180411i	$-0.942257\pi$
$311$	−17.8402	+	14.4467i	−1.01162	+	0.819196i	−0.0280316	+	0.999607i	$0.508924\pi$
$312$	10.8358	−	2.30321i	0.613455	−	0.130394i
$313$	12.3554	−	15.2576i	0.698366	−	0.862410i	−0.297360	−	0.954765i	$-0.596106\pi$
$313$	12.3554	−	15.2576i	0.698366	−	0.862410i	0.995726	+	0.0923550i	$0.0294395\pi$
$314$	0.423050	+	0.423050i	0.0238741	+	0.0238741i
$315$	33.1322	−	15.4776i	1.86679	−	0.872065i
$316$	−2.11646	+	13.3628i	−0.119060	+	0.751715i
$317$	−0.924982	+	2.40966i	−0.0519522	+	0.135340i	−0.957101	−	0.289755i	$-0.906426\pi$
$317$	−0.924982	+	2.40966i	−0.0519522	+	0.135340i	0.905149	+	0.425095i	$0.139759\pi$
$318$	0.141081	−	1.34229i	0.00791141	−	0.0752720i
$319$	7.87478	−	4.54651i	0.440903	−	0.254556i
$320$	−7.61404	−	17.1014i	−0.425638	−	0.955999i
$321$	16.9288	+	33.2247i	0.944874	+	1.85442i
$322$	−1.49986	−	3.21069i	−0.0835840	−	0.178924i
$323$	−9.90358	−	13.6311i	−0.551050	−	0.758455i
$324$	0.612259	+	5.82525i	0.0340144	+	0.323625i
$325$	9.21692	+	2.46967i	0.511263	+	0.136992i
$326$	0.228623	+	0.205853i	0.0126623	+	0.0114012i
$327$	−7.32837	+	12.6931i	−0.405260	+	0.701931i
$328$	4.70529	−	1.12488i	0.259806	−	0.0621109i
$329$	−10.7434	−	1.50233i	−0.592301	−	0.0828264i
$330$	5.86161	−	1.90455i	0.322671	−	0.104842i
$331$	0.837868	+	3.12697i	0.0460534	+	0.171874i	0.985122	−	0.171856i	$-0.0549763\pi$
$331$	0.837868	+	3.12697i	0.0460534	+	0.171874i	−0.939069	+	0.343729i	$0.888310\pi$
$332$	−3.17949	−	1.41560i	−0.174497	−	0.0776913i
$333$	−3.11274	+	6.99132i	−0.170577	+	0.383122i
$334$	1.07172	+	1.65031i	0.0586420	+	0.0903008i
$335$	−2.76125	−	5.41926i	−0.150863	−	0.296086i
$336$	−27.9397	−	6.94570i	−1.52423	−	0.378919i
$337$			4.21756i			0.229745i	0.993380	+	0.114873i	$0.0366460\pi$
$337$			4.21756i			0.229745i	−0.993380	+	0.114873i	$0.963354\pi$
$338$	2.26137	−	1.00683i	0.123002	−	0.0547642i
$339$	−6.45511	−	7.97140i	−0.350594	−	0.432947i
$340$	−10.8114	+	4.15011i	−0.586331	+	0.225071i
$341$	−29.0423	+	18.8603i	−1.57273	+	1.02134i
$342$	−5.32265	−	5.32265i	−0.287816	−	0.287816i
$343$	15.5532	+	10.0547i	0.839795	+	0.542904i
$344$	−1.68108	+	5.17384i	−0.0906379	+	0.278955i
$345$	49.4603	+	18.9860i	2.66286	+	1.02217i
$346$	0.0728021	−	0.0808550i	0.00391387	−	0.00434679i
$347$	−15.2478	−	9.90203i	−0.818545	−	0.531569i	0.0661120	−	0.997812i	$-0.478941\pi$
$347$	−15.2478	−	9.90203i	−0.818545	−	0.531569i	−0.884657	+	0.466243i	$0.845607\pi$
$348$	−8.89992	+	8.01353i	−0.477086	+	0.429570i
$349$	−22.3657	−	7.26706i	−1.19721	−	0.388997i	−0.358476	−	0.933539i	$-0.616703\pi$
$349$	−22.3657	−	7.26706i	−1.19721	−	0.388997i	−0.838734	+	0.544542i	$0.816703\pi$
$350$	0.712899	+	0.618851i	0.0381060	+	0.0330790i
$351$	10.2969	+	31.6906i	0.549607	+	1.69152i
$352$	−8.93683	−	3.43053i	−0.476335	−	0.182848i
$353$	23.4060	−	4.97510i	1.24578	−	0.264798i	0.462583	−	0.886576i	$-0.346923\pi$
$353$	23.4060	−	4.97510i	1.24578	−	0.264798i	0.783194	+	0.621778i	$0.213589\pi$
$354$	−1.53297	−	3.99352i	−0.0814763	−	0.212253i
$355$	20.6966	−	5.54564i	1.09846	−	0.294332i
$356$	−14.1222	−	7.19561i	−0.748474	−	0.381366i
$357$	−4.99405	+	16.3751i	−0.264313	+	0.866664i
$358$	−2.42017	+	0.383318i	−0.127910	+	0.0202590i
$359$	25.6603	−	11.4247i	1.35430	−	0.602974i	0.404130	−	0.914702i	$-0.367574\pi$
$359$	25.6603	−	11.4247i	1.35430	−	0.602974i	0.950171	+	0.311728i	$0.100908\pi$
$360$	−9.04398	+	5.22155i	−0.476660	+	0.275200i
$361$	−36.8880	−	3.87709i	−1.94147	−	0.204057i
$362$	−2.50642	−	0.131356i	−0.131734	−	0.00690390i
$363$	−9.64901	+	18.9372i	−0.506441	+	0.993947i
$364$	−26.4686	−	0.906044i	−1.38733	−	0.0474896i
$365$	30.1644	−	21.9157i	1.57887	−	1.14712i
$366$	0.911998	+	3.40362i	0.0476709	+	0.177910i
$367$	22.1082	+	19.9063i	1.15404	+	1.03910i	0.998686	+	0.0512398i	$0.0163173\pi$
$367$	22.1082	+	19.9063i	1.15404	+	1.03910i	0.155350	+	0.987859i	$0.450349\pi$
$368$	−13.2919	−	23.0223i	−0.692889	−	1.20012i
$369$	11.2393	+	31.8357i	0.585095	+	1.65730i
$370$	−0.725277			−0.0377054
$371$	−2.22342	+	6.12192i	−0.115434	+	0.317834i
$372$	32.2500	−	32.2500i	1.67209	−	1.67209i
$373$	1.41985	+	13.5089i	0.0735169	+	0.699467i	0.967758	+	0.251881i	$0.0810493\pi$
$373$	1.41985	+	13.5089i	0.0735169	+	0.699467i	−0.894241	+	0.447585i	$0.852284\pi$
$374$	−0.747981	+	1.67999i	−0.0386772	+	0.0868704i
$375$	23.5532	−	1.23437i	1.21628	−	0.0637427i
$376$	3.09361	+	0.162129i	0.159540	+	0.00836116i
$377$	−6.35348	+	8.74482i	−0.327221	+	0.450381i
$378$	−0.456552	+	3.26486i	−0.0234825	+	0.167926i
$379$	−23.0412	−	16.7404i	−1.18354	−	0.859896i	−0.190978	−	0.981594i	$-0.561166\pi$
$379$	−23.0412	−	16.7404i	−1.18354	−	0.859896i	−0.992567	+	0.121699i	$0.961166\pi$
$380$	−13.8160	+	35.9918i	−0.708743	+	1.84634i
$381$	8.73370	−	3.35255i	0.447441	−	0.171756i
$382$	−0.0473848	−	0.904155i	−0.00242442	−	0.0462606i
$383$	−15.6717	+	4.19923i	−0.800788	+	0.214571i	−0.635930	−	0.771747i	$-0.719383\pi$
$383$	−15.6717	+	4.19923i	−0.800788	+	0.214571i	−0.164858	+	0.986317i	$0.552717\pi$
$384$	16.5499	+	2.62125i	0.844559	+	0.133765i
$385$	−29.6681	+	2.09514i	−1.51203	+	0.106778i
$386$	0.194295	+	1.22673i	0.00988934	+	0.0624388i
$387$	−37.1344	−	7.89316i	−1.88765	−	0.401232i
$388$	8.13226	+	5.28115i	0.412853	+	0.268110i
$389$	−4.52782	−	21.3017i	−0.229570	−	1.08004i	−0.930353	−	0.366666i	$-0.880499\pi$
$389$	−4.52782	−	21.3017i	−0.229570	−	1.08004i	0.700783	−	0.713374i	$-0.252834\pi$
$390$	−5.44464	+	4.90237i	−0.275700	+	0.248241i
$391$	−14.0849	+	7.17660i	−0.712303	+	0.362936i
$392$	−4.67320	−	2.47653i	−0.236032	−	0.125084i
$393$	0.880875	+	5.56163i	0.0444343	+	0.280547i
$394$	1.46589	+	1.62803i	0.0738504	+	0.0820192i
$395$	−6.47255	−	16.8616i	−0.325669	−	0.848398i
$396$	11.4915	−	42.8869i	0.577470	−	2.15515i
$397$	−20.4911	+	13.3070i	−1.02842	+	0.667862i	−0.944466	−	0.328608i	$-0.893420\pi$
$397$	−20.4911	+	13.3070i	−1.02842	+	0.667862i	−0.0839504	+	0.996470i	$0.526754\pi$
$398$	0.303706	−	1.91752i	0.0152234	−	0.0961167i
$399$	29.3870	+	48.8320i	1.47119	+	2.44466i
$400$	5.72930	+	4.16258i	0.286465	+	0.208129i
$401$	11.4128	+	6.58919i	0.569928	+	0.329048i	0.757121	−	0.653275i	$-0.226605\pi$
$401$	11.4128	+	6.58919i	0.569928	+	0.329048i	−0.187192	+	0.982323i	$0.559939\pi$
$402$	1.26510	+	0.132967i	0.0630975	+	0.00663182i
$403$	22.4199	−	34.5236i	1.11682	−	1.71974i
$404$	5.07005	+	7.80719i	0.252244	+	0.388422i
$405$	−4.59609	−	6.32598i	−0.228382	−	0.314340i
$406$	−0.943875	+	0.502702i	−0.0468437	+	0.0249487i
$407$	4.40119	−	4.40119i	0.218159	−	0.218159i
$408$	1.01646	−	4.78207i	0.0503223	−	0.236748i
$409$	−15.4966	−	26.8410i	−0.766259	−	1.32720i	−0.939578	−	0.342334i	$-0.888783\pi$
$409$	−15.4966	−	26.8410i	−0.766259	−	1.32720i	0.173319	−	0.984866i	$-0.444551\pi$
$410$	−2.32302	+	2.20023i	−0.114726	+	0.108662i
$411$	−4.07903	+	7.06509i	−0.201204	+	0.348495i
$412$	20.1585	−	6.54990i	0.993139	−	0.322691i
$413$	2.52982	+	20.4870i	0.124484	+	1.00810i
$414$	−5.71346	+	4.15107i	−0.280801	+	0.204014i
$415$	4.62074	−	0.485660i	0.226823	−	0.0238401i
$416$	11.3637	−	0.595548i	0.557153	−	0.0291992i
$417$	5.03045	−	7.74621i	0.246342	−	0.379334i
$418$	2.49007	+	5.59279i	0.121793	+	0.273552i
$419$		−	13.7341i		−	0.670955i	−0.942048	−	0.335478i	$-0.891102\pi$
$419$		−	13.7341i		−	0.670955i	0.942048	−	0.335478i	$-0.108898\pi$
$420$	37.6471	−	10.8232i	1.83699	−	0.528118i
$421$	−25.7021	+	4.07081i	−1.25264	+	0.198399i	−0.747280	−	0.664509i	$-0.768641\pi$
$421$	−25.7021	+	4.07081i	−1.25264	+	0.198399i	−0.505361	+	0.862908i	$0.668641\pi$
$422$	−0.967533	−	0.783493i	−0.0470988	−	0.0381398i
$423$	1.13143	+	21.5889i	0.0550118	+	1.04969i
$424$	0.481397	−	1.79660i	0.0233787	−	0.0872506i
$425$	2.65015	−	3.27266i	0.128551	−	0.158747i
$426$	−1.38481	+	4.26200i	−0.0670942	+	0.206495i
$427$	−0.308481	−	17.0015i	−0.0149285	−	0.822759i
$428$	7.86697	+	24.2120i	0.380264	+	1.17033i
$429$	3.29061	−	62.7886i	0.158872	−	3.03146i
$430$	−0.748041	−	3.51926i	−0.0360738	−	0.169714i
$431$	6.50150	+	30.5871i	0.313166	+	1.47333i	0.800087	+	0.599885i	$0.204787\pi$
$431$	6.50150	+	30.5871i	0.313166	+	1.47333i	−0.486920	+	0.873446i	$0.661880\pi$
$432$	−1.29427	+	24.6962i	−0.0622707	+	1.18820i
$433$	−0.761161	−	2.34261i	−0.0365791	−	0.112579i	0.931100	−	0.364765i	$-0.118851\pi$
$433$	−0.761161	−	2.34261i	−0.0365791	−	0.112579i	−0.967679	+	0.252186i	$0.918851\pi$
$434$	3.48945	−	2.09995i	0.167499	−	0.100801i
$435$	4.94043	−	15.2051i	0.236876	−	0.729028i
$436$	−6.29730	+	7.77651i	−0.301586	+	0.372428i
$437$	−13.6204	+	50.8320i	−0.651552	+	2.43162i
$438$	0.408121	+	7.78740i	0.0195008	+	0.372097i
$439$	−27.2840	−	22.0941i	−1.30219	−	1.05450i	−0.994687	−	0.102950i	$-0.967172\pi$
$439$	−27.2840	−	22.0941i	−1.30219	−	1.05450i	−0.307507	−	0.951546i	$-0.599495\pi$
$440$	8.38890	−	1.32867i	0.399925	−	0.0633419i
$441$	13.7790	−	34.2400i	0.656143	−	1.63048i
$442$		−	2.18606i		−	0.103980i
$443$	4.92510	+	11.0620i	0.233999	+	0.525570i	0.991933	−	0.126761i	$-0.0404581\pi$
$443$	4.92510	+	11.0620i	0.233999	+	0.525570i	−0.757935	+	0.652331i	$0.773791\pi$
$444$	−4.46476	+	6.87513i	−0.211888	+	0.326279i
$445$	21.1298	−	1.10736i	1.00165	−	0.0524941i
$446$	−1.23902	+	0.130226i	−0.0586693	+	0.00616640i
$447$	−49.7282	+	36.1296i	−2.35206	+	1.70887i
$448$	−17.3967	−	7.37032i	−0.821917	−	0.348215i
$449$	33.1262	−	10.7634i	1.56332	−	0.507954i	0.605629	−	0.795747i	$-0.292922\pi$
$449$	33.1262	−	10.7634i	1.56332	−	0.507954i	0.957693	+	0.287793i	$0.0929215\pi$
$450$	0.940671	−	1.62929i	0.0443436	−	0.0768054i
$451$	0.745068	−	27.4484i	0.0350839	−	1.29249i
$452$	−3.50144	−	6.06468i	−0.164694	−	0.285258i
$453$	3.56820	−	16.7871i	0.167649	−	0.788725i
$454$	1.93347	−	1.93347i	0.0907423	−	0.0907423i
$455$	31.2055	−	16.6199i	1.46294	−	0.779151i
$456$	−9.56647	−	13.1671i	−0.447991	−	0.616607i
$457$	−5.06487	−	7.79922i	−0.236925	−	0.364832i	0.700130	−	0.714016i	$-0.253126\pi$
$457$	−5.06487	−	7.79922i	−0.236925	−	0.364832i	−0.937054	+	0.349184i	$0.886459\pi$
$458$	1.76633	−	2.71991i	0.0825351	−	0.127093i
$459$	14.6250	+	1.53714i	0.682634	+	0.0717478i
$460$	31.3243	+	18.0851i	1.46050	+	0.843221i
$461$	−7.99229	−	5.80673i	−0.372238	−	0.270447i	0.385900	−	0.922540i	$-0.373891\pi$
$461$	−7.99229	−	5.80673i	−0.372238	−	0.270447i	−0.758138	+	0.652094i	$0.773891\pi$
$462$	3.01199	−	5.44261i	0.140130	−	0.253213i
$463$	2.49852	−	15.7750i	0.116116	−	0.733127i	−0.859090	−	0.511825i	$-0.828970\pi$
$463$	2.49852	−	15.7750i	0.116116	−	0.733127i	0.975205	−	0.221301i	$-0.0710305\pi$
$464$	−6.72800	+	4.36922i	−0.312340	+	0.202836i
$465$	−15.7584	+	58.8110i	−0.730776	+	2.72729i
$466$	−1.14458	−	2.98174i	−0.0530217	−	0.138126i
$467$	14.0267	+	15.5782i	0.649079	+	0.720875i	0.974423	−	0.224721i	$-0.0721469\pi$
$467$	14.0267	+	15.5782i	0.649079	+	0.720875i	−0.325344	+	0.945596i	$0.605480\pi$
$468$	8.25654	+	52.1297i	0.381659	+	2.40970i
$469$	−5.76987	−	2.09556i	−0.266428	−	0.0967639i
$470$	−1.82550	+	0.930138i	−0.0842040	+	0.0429041i
$471$	−6.70866	+	6.04051i	−0.309119	+	0.278332i
$472$	−1.22562	−	5.76611i	−0.0564139	−	0.265407i
$473$	25.8952	+	16.8165i	1.19066	+	0.773225i
$474$	3.69490	+	0.785375i	0.169712	+	0.0360735i
$475$	−2.19307	−	13.8465i	−0.100625	−	0.635320i
$476$	−5.11647	+	10.5087i	−0.234513	+	0.481665i
$477$	12.8201	+	2.03051i	0.586993	+	0.0929706i
$478$	−1.70579	+	0.457065i	−0.0780211	+	0.0209057i
$479$	1.71128	+	32.6532i	0.0781905	+	1.49196i	0.703002	+	0.711188i	$0.251842\pi$
$479$	1.71128	+	32.6532i	0.0781905	+	1.49196i	−0.624812	+	0.780775i	$0.714824\pi$
$480$	−15.7130	+	6.03164i	−0.717195	+	0.275305i
$481$	−2.65155	+	6.90751i	−0.120900	+	0.314955i
$482$	2.42408	+	1.76120i	0.110414	+	0.0802205i
$483$	49.5635	−	20.0647i	2.25522	−	0.912976i
$484$	−8.52903	+	11.7392i	−0.387683	+	0.533600i
$485$	−12.9269	−	0.677469i	−0.586980	−	0.0307623i
$486$	−2.09975	+	0.110043i	−0.0952466	+	0.00499166i
$487$	10.8169	−	24.2951i	0.490159	−	1.10092i	−0.484003	−	0.875066i	$-0.660818\pi$
$487$	10.8169	−	24.2951i	0.490159	−	1.10092i	0.974162	−	0.225850i	$-0.0725158\pi$
$488$	0.507583	+	4.82933i	0.0229772	+	0.218613i
$489$	−3.28237	+	3.28237i	−0.148434	+	0.148434i
$490$	3.49555	−	0.126891i	0.157913	−	0.00573235i
$491$	−3.78131			−0.170648			−0.0853241	−	0.996353i	$-0.527193\pi$
$491$	−3.78131			−0.170648			−0.0853241	+	0.996353i	$0.527193\pi$
$492$	6.55638	+	35.5651i	0.295585	+	1.60340i
$493$	2.38517	+	4.13124i	0.107423	+	0.186062i
$494$	−5.40825	−	4.86961i	−0.243329	−	0.219094i
$495$	15.3407	+	57.2525i	0.689515	+	2.57331i
$496$	24.7164	−	17.9575i	1.10980	−	0.806315i
$497$	11.4472	−	18.3474i	0.513475	−	0.822994i
$498$	−0.441160	+	0.865825i	−0.0197689	+	0.0387986i
$499$	−20.3134	−	1.06458i	−0.909353	−	0.0476572i	−0.408080	−	0.912946i	$-0.633802\pi$
$499$	−20.3134	−	1.06458i	−0.909353	−	0.0476572i	−0.501273	+	0.865289i	$0.667135\pi$
$500$	16.0142	+	1.68316i	0.716177	+	0.0752732i
$501$	−25.7134	+	14.8456i	−1.14879	+	0.663255i
$502$	4.69703	−	2.09125i	0.209639	−	0.0933372i
$503$	−3.48742	+	0.552353i	−0.155496	+	0.0246282i	−0.233697	−	0.972309i	$-0.575082\pi$
$503$	−3.48742	+	0.552353i	−0.155496	+	0.0246282i	0.0782009	+	0.996938i	$0.475082\pi$
$504$	−3.07465	+	10.0816i	−0.136956	+	0.449069i
$505$	−11.0727	−	5.64183i	−0.492730	−	0.251058i
$506$	5.54806	−	1.48660i	0.246641	−	0.0660873i
$507$	13.3853	+	34.8698i	0.594460	+	1.54862i
$508$	6.24735	−	1.32792i	0.277181	−	0.0589167i
$509$	−12.0672	−	4.63215i	−0.534867	−	0.205316i	0.0759160	−	0.997114i	$-0.475812\pi$
$509$	−12.0672	−	4.63215i	−0.534867	−	0.205316i	−0.610783	+	0.791798i	$0.709145\pi$
$510$	0.999158	+	3.07509i	0.0442435	+	0.136167i
$511$	7.15492	−	36.9448i	0.316515	−	1.63434i
$512$	13.4692	+	4.37640i	0.595259	+	0.193411i
$513$	36.3810	−	32.7576i	1.60626	−	1.44628i
$514$	−1.82438	−	1.18477i	−0.0804700	−	0.0522578i
$515$	−18.9336	+	21.0279i	−0.834314	+	0.926600i
$516$	−37.9651	−	14.5734i	−1.67132	−	0.641559i
$517$	5.43330	−	16.7220i	0.238956	−	0.735432i
$518$	−0.535013	+	0.499597i	−0.0235071	+	0.0219510i
$519$	1.16084	+	1.16084i	0.0509554	+	0.0509554i
$520$	−8.46762	+	5.49894i	−0.371330	+	0.241144i
$521$	−11.9517	+	4.58782i	−0.523612	+	0.200996i	−0.605794	−	0.795621i	$-0.707144\pi$
$521$	−11.9517	+	4.58782i	−0.523612	+	0.200996i	0.0821820	+	0.996617i	$0.473811\pi$
$522$	1.34119	+	1.65623i	0.0587023	+	0.0724913i
$523$	20.0567	−	8.92980i	0.877016	−	0.390473i	0.0816926	−	0.996658i	$-0.473967\pi$
$523$	20.0567	−	8.92980i	0.877016	−	0.390473i	0.795324	+	0.606185i	$0.207301\pi$
$524$			3.84439i			0.167943i
$525$	−9.88792	+	10.2534i	−0.431544	+	0.447494i
$526$	0.912346	+	1.79058i	0.0397802	+	0.0780730i
$527$	−9.89442	−	15.2361i	−0.431008	−	0.663694i
$528$	18.9798	−	42.6293i	0.825990	−	1.85520i
$529$	24.0932	+	10.7270i	1.04753	+	0.466391i
$530$	0.318378	+	1.18820i	0.0138295	+	0.0516123i
$531$	39.1246	−	12.7124i	1.69786	−	0.551669i
$532$	14.6009	+	36.0669i	0.633028	+	1.56370i
$533$	12.4622	+	30.1682i	0.539799	+	1.30673i
$534$	−2.21265	+	3.83242i	−0.0957506	+	0.165845i
$535$	−25.2562	−	22.7408i	−1.09192	−	0.983170i
$536$	1.69328	+	0.453714i	0.0731386	+	0.0195974i
$537$	−3.86471	−	36.7703i	−0.166775	−	1.58675i
$538$	0.00879953	+	0.0121115i	0.000379375	+	0.000522164i
$539$	−20.4420	+	21.9820i	−0.880499	+	0.946833i
$540$	−15.2758	−	29.9805i	−0.657368	−	1.29016i
$541$	−11.1506	−	25.0446i	−0.479401	−	1.07675i	−0.977749	−	0.209776i	$-0.932727\pi$
$541$	−11.1506	−	25.0446i	−0.479401	−	1.07675i	0.498348	−	0.866977i	$-0.333940\pi$
$542$	−1.69299	+	0.977450i	−0.0727203	+	0.0419851i
$543$	3.95858	−	37.6633i	0.169879	−	1.61629i
$544$	1.79971	−	4.68840i	0.0771619	−	0.201014i
$545$	2.08970	−	13.1939i	0.0895131	−	0.565163i
$546$	−0.639395	+	7.36678i	−0.0273636	+	0.315269i
$547$	22.7025	+	22.7025i	0.970688	+	0.970688i	0.999582	−	0.0288944i	$-0.00919865\pi$
$547$	22.7025	+	22.7025i	0.970688	+	0.970688i	−0.0288944	+	0.999582i	$0.509199\pi$
$548$	−3.50513	+	4.32847i	−0.149732	+	0.184903i
$549$	−33.1468	+	7.04557i	−1.41467	+	0.300698i
$550$	−1.18912	+	0.962932i	−0.0507043	+	0.0410595i
$551$	15.5337	+	3.30179i	0.661758	+	0.140661i
$552$	−13.6054	+	6.93232i	−0.579086	+	0.295059i
$553$	−16.3895	−	7.97969i	−0.696950	−	0.339331i
$554$	−1.51341	−	0.491737i	−0.0642986	−	0.0208919i
$555$	0.572743	−	10.9286i	0.0243116	−	0.463893i
$556$	4.21943	−	4.68615i	0.178944	−	0.198737i
$557$	−11.8451	+	9.59201i	−0.501895	+	0.406426i	−0.846555	−	0.532301i	$-0.821327\pi$
$557$	−11.8451	+	9.59201i	−0.501895	+	0.406426i	0.344660	+	0.938727i	$0.387994\pi$
$558$	−5.43077	−	6.03148i	−0.229903	−	0.255333i
$559$	−36.2521	−	5.74176i	−1.53330	−	0.242851i
$560$	26.0418	−	3.21575i	1.10047	−	0.135890i
$561$	−24.7237	−	12.5974i	−1.04384	−	0.531861i
$562$	−1.38745	−	1.12354i	−0.0585261	−	0.0473935i
$563$	−6.17915	−	7.63061i	−0.260420	−	0.321592i	0.630119	−	0.776498i	$-0.283006\pi$
$563$	−6.17915	−	7.63061i	−0.260420	−	0.321592i	−0.890539	+	0.454906i	$0.849673\pi$
$564$	−2.42059	+	23.0304i	−0.101925	+	0.969753i
$565$	8.09613	+	4.67430i	0.340607	+	0.196649i
$566$	1.13919	−	1.56796i	0.0478838	−	0.0659064i
$567$	−7.74795	−	1.50051i	−0.325383	−	0.0630154i
$568$	−2.80368	+	5.50253i	−0.117640	+	0.230881i
$569$	12.7203	−	1.33696i	0.533262	−	0.0560481i	0.165929	−	0.986138i	$-0.446938\pi$
$569$	12.7203	−	1.33696i	0.533262	−	0.0560481i	0.367333	+	0.930089i	$0.380271\pi$
$570$	9.83339	+	4.37811i	0.411875	+	0.183379i
$571$	−2.21741	−	0.594153i	−0.0927958	−	0.0248645i	0.212122	−	0.977243i	$-0.431962\pi$
$571$	−2.21741	−	0.594153i	−0.0927958	−	0.0248645i	−0.304918	+	0.952379i	$0.598629\pi$
$572$	8.92484	−	41.9881i	0.373166	−	1.75561i
$573$	13.6614			0.570712
$574$	−0.198010	+	3.22322i	−0.00826476	+	0.134534i
$575$	−13.1528			−0.548510
$576$	−7.82839	+	36.8297i	−0.326183	+	1.53457i
$577$	26.6567	+	7.14265i	1.10973	+	0.297352i	0.766723	−	0.641979i	$-0.221886\pi$
$577$	26.6567	+	7.14265i	1.10973	+	0.297352i	0.343012	+	0.939331i	$0.388553\pi$
$578$	2.07902	+	0.925638i	0.0864757	+	0.0385015i
$579$	−18.6380	+	1.95893i	−0.774567	+	0.0814103i
$580$	4.95535	−	9.72542i	0.205760	−	0.403826i
$581$	3.07403	−	3.54119i	0.127532	−	0.146913i
$582$	1.59133	−	2.19028i	0.0659627	−	0.0907899i
$583$	−9.14238	−	5.27835i	−0.378639	−	0.218607i
$584$	−1.12330	+	10.6875i	−0.0464827	+	0.442253i
$585$	−44.3412	−	54.7568i	−1.83328	−	2.26391i
$586$	−2.35299	−	1.90542i	−0.0972012	−	0.0787120i
$587$	−30.3359	−	15.4569i	−1.25210	−	0.637975i	−0.303009	−	0.952988i	$-0.597991\pi$
$587$	−30.3359	−	15.4569i	−1.25210	−	0.637975i	−0.949088	+	0.315012i	$0.897991\pi$
$588$	20.3156	−	33.9166i	0.837800	−	1.39870i
$589$	−59.7341	−	9.46096i	−2.46130	−	0.389832i
$590$	2.60873	+	2.89729i	0.107400	+	0.119280i
$591$	−25.6891	+	20.8026i	−1.05671	+	0.855704i
$592$	−3.67437	+	4.08080i	−0.151016	+	0.167720i
$593$	−0.791164	+	15.0963i	−0.0324892	+	0.619931i	0.933062	+	0.359717i	$0.117127\pi$
$593$	−0.791164	+	15.0963i	−0.0324892	+	0.619931i	−0.965551	+	0.260215i	$0.916207\pi$
$594$	−5.08173	−	1.65115i	−0.208506	−	0.0677477i
$595$	−1.09915	−	15.5644i	−0.0450606	−	0.638077i
$596$	−37.3913	+	19.0518i	−1.53161	+	0.780393i
$597$	28.6537	+	6.09053i	1.17272	+	0.249269i
$598$	−5.30622	+	4.29689i	−0.216987	+	0.175713i
$599$	−18.3582	+	3.90216i	−0.750097	+	0.159438i	−0.567070	−	0.823670i	$-0.691923\pi$
$599$	−18.3582	+	3.90216i	−0.750097	+	0.159438i	−0.183027	+	0.983108i	$0.558590\pi$
$600$	2.55994	−	3.16126i	0.104509	−	0.129058i
$601$	−9.94712	−	9.94712i	−0.405751	−	0.405751i	0.474503	−	0.880254i	$-0.342628\pi$
$601$	−9.94712	−	9.94712i	−0.405751	−	0.405751i	−0.880254	+	0.474503i	$0.842628\pi$
$602$	−2.97600	−	2.08076i	−0.121293	−	0.0848055i
$603$	−1.91374	+	12.0829i	−0.0779336	+	0.492053i
$604$	4.19898	−	10.9387i	0.170854	−	0.445091i
$605$	2.02481	−	19.2648i	0.0823204	−	0.783226i
$606$	2.25090	−	1.29956i	0.0914365	−	0.0527909i
$607$	−7.77279	−	17.4580i	−0.315488	−	0.708597i	0.684300	−	0.729201i	$-0.260108\pi$
$607$	−7.77279	−	17.4580i	−0.315488	−	0.708597i	−0.999788	+	0.0206034i	$0.993441\pi$
$608$	−7.58999	−	14.8962i	−0.307815	−	0.604120i
$609$	−6.82942	−	14.6194i	−0.276742	−	0.592409i
$610$	−1.88769	−	2.59819i	−0.0764304	−	0.105197i
$611$	2.18475	+	20.7865i	0.0883854	+	0.840931i
$612$	22.4991	+	6.02862i	0.909474	+	0.243693i
$613$	6.95597	+	6.26318i	0.280949	+	0.252968i	0.797542	−	0.603264i	$-0.206133\pi$
$613$	6.95597	+	6.26318i	0.280949	+	0.252968i	−0.516593	+	0.856231i	$0.672800\pi$
$614$	2.05160	−	3.55348i	0.0827960	−	0.143407i
$615$	−31.3190	−	36.7411i	−1.26290	−	1.48154i
$616$	5.27298	−	6.75870i	0.212454	−	0.272316i
$617$	44.8873	−	14.5848i	1.80709	−	0.587160i	0.807098	−	0.590417i	$-0.201037\pi$
$617$	44.8873	−	14.5848i	1.80709	−	0.587160i	0.999995	+	0.00325735i	$0.00103685\pi$
$618$	−1.53169	−	5.71634i	−0.0616135	−	0.229945i
$619$	−15.9405	−	7.09718i	−0.640704	−	0.285260i	0.0605569	−	0.998165i	$-0.480712\pi$
$619$	−15.9405	−	7.09718i	−0.640704	−	0.285260i	−0.701260	+	0.712905i	$0.747379\pi$
$620$	−16.9072	+	37.9743i	−0.679011	+	1.52508i
$621$	−25.0155	−	38.5205i	−1.00384	−	1.54577i
$622$	1.98660	+	3.89891i	0.0796552	+	0.156332i
$623$	14.8239	−	15.3718i	0.593909	−	0.615859i
$624$			55.4707i			2.22060i
$625$	−28.1878	+	12.5500i	−1.12751	+	0.502001i
$626$	−2.35517	−	2.90839i	−0.0941315	−	0.116243i
$627$	−86.2394	+	33.1042i	−3.44407	+	1.32206i
$628$	−5.16891	+	3.35673i	−0.206262	+	0.133948i
$629$	2.30893	+	2.30893i	0.0920632	+	0.0920632i
$630$	−1.57276	−	6.79104i	−0.0626604	−	0.270561i
$631$	4.41141	−	13.5769i	0.175616	−	0.540489i	−0.824045	−	0.566524i	$-0.808288\pi$
$631$	4.41141	−	13.5769i	0.175616	−	0.540489i	0.999661	+	0.0260346i	$0.00828799\pi$
$632$	4.85987	+	1.86553i	0.193315	+	0.0742068i
$633$	12.5698	−	13.9602i	0.499606	−	0.554869i
$634$	0.412631	+	0.267966i	0.0163877	+	0.0106423i
$635$	−6.33629	+	5.70522i	−0.251448	+	0.226405i
$636$	13.2233	+	4.29651i	0.524338	+	0.170368i
$637$	11.5709	−	33.7554i	0.458456	−	1.33744i
$638$	−0.535620	−	1.64847i	−0.0212054	−	0.0652635i
$639$	−40.2345	−	15.4446i	−1.59165	−	0.610978i
$640$	−14.9381	+	3.17519i	−0.590480	+	0.125510i
$641$	−12.1524	−	31.6580i	−0.479990	−	1.25042i	−0.933311	−	0.359069i	$-0.883094\pi$
$641$	−12.1524	−	31.6580i	−0.479990	−	1.25042i	0.453321	−	0.891347i	$-0.350239\pi$
$642$	6.86578	−	1.83968i	0.270971	−	0.0726064i
$643$	0.371517	+	0.189297i	0.0146512	+	0.00746515i	0.461301	−	0.887244i	$-0.347383\pi$
$643$	0.371517	+	0.189297i	0.0146512	+	0.00746515i	−0.446650	+	0.894709i	$0.647383\pi$
$644$	35.5645	−	8.23654i	1.40144	−	0.324565i
$645$	53.6194	−	8.49249i	2.11126	−	0.334391i
$646$	−2.93407	+	1.30633i	−0.115439	+	0.0513969i
$647$	18.6601	−	10.7734i	0.733604	−	0.423547i	−0.0861351	−	0.996283i	$-0.527452\pi$
$647$	18.6601	−	10.7734i	0.733604	−	0.423547i	0.819739	+	0.572737i	$0.194118\pi$
$648$	2.24136	+	0.235576i	0.0880488	+	0.00925430i
$649$	−33.4121	−	1.75106i	−1.31154	−	0.0687349i
$650$	0.825763	−	1.62065i	0.0323891	−	0.0635672i
$651$	28.8867	+	54.2378i	1.13216	+	2.12575i
$652$	−2.56393	+	1.86280i	−0.100411	+	0.0729529i
$653$	−4.45241	−	16.6166i	−0.174236	−	0.650258i	−0.996680	−	0.0814127i	$-0.974057\pi$
$653$	−4.45241	−	16.6166i	−0.174236	−	0.650258i	0.822444	−	0.568846i	$-0.192610\pi$
$654$	2.07624	+	1.86945i	0.0811874	+	0.0731014i
$655$	−2.56606	−	4.44455i	−0.100264	−	0.173663i
$656$	0.610943	+	24.2173i	0.0238533	+	0.945526i
$657$	−74.9943			−2.92581
$658$	−0.705897	+	1.94360i	−0.0275187	+	0.0757695i
$659$	−29.8420	+	29.8420i	−1.16248	+	1.16248i	−0.178547	+	0.983931i	$0.557140\pi$
$659$	−29.8420	+	29.8420i	−1.16248	+	1.16248i	−0.983931	+	0.178547i	$0.942860\pi$
$660$	6.63660	+	63.1430i	0.258329	+	2.45784i
$661$	8.65004	−	19.4283i	0.336447	−	0.755673i	−0.663524	−	0.748155i	$-0.730940\pi$
$661$	8.65004	−	19.4283i	0.336447	−	0.755673i	0.999972	−	0.00751856i	$-0.00239326\pi$
$662$	0.616241	−	0.0322958i	0.0239509	−	0.00125521i
$663$	32.9399	+	1.72631i	1.27928	+	0.0670442i
$664$	−0.787123	+	1.08338i	−0.0305463	+	0.0420434i
$665$	−40.9543	−	31.9516i	−1.58814	−	1.23903i
$666$	1.18019	+	0.857461i	0.0457316	+	0.0332259i
$667$	5.33948	−	13.9098i	0.206745	−	0.538590i
$668$	−18.9246	+	7.26446i	−0.732213	+	0.281070i
$669$	−0.983830	−	18.7726i	−0.0380371	−	0.725791i
$670$	−1.11987	+	0.300070i	−0.0432645	+	0.0115927i
$671$	27.2216	+	4.31148i	1.05088	+	0.166443i
$672$	−7.43611	+	15.2730i	−0.286854	+	0.589169i
$673$	3.24120	+	20.4641i	0.124939	+	0.788834i	0.967988	+	0.250997i	$0.0807584\pi$
$673$	3.24120	+	20.4641i	0.124939	+	0.788834i	−0.843049	+	0.537837i	$0.819242\pi$
$674$	0.786380	+	0.167150i	0.0302902	+	0.00643838i
$675$	10.2617	+	6.66400i	0.394972	+	0.256498i
$676$	5.30178	+	24.9429i	0.203915	+	0.959343i
$677$	−8.26982	+	7.44618i	−0.317835	+	0.286180i	−0.812570	−	0.582864i	$-0.801932\pi$
$677$	−8.26982	+	7.44618i	−0.317835	+	0.286180i	0.494734	+	0.869044i	$0.335265\pi$
$678$	−1.74213	+	0.887658i	−0.0669059	+	0.0340903i
$679$	−10.0024	+	8.40476i	−0.383857	+	0.322545i
$680$	0.697042	+	4.40095i	0.0267303	+	0.168769i
$681$	27.6070	+	30.6607i	1.05790	+	1.17492i
$682$	2.36557	+	6.16252i	0.0905824	+	0.235975i
$683$	−0.127906	+	0.477352i	−0.00489419	+	0.0182654i	−0.968330	−	0.249675i	$-0.919676\pi$
$683$	−0.127906	+	0.477352i	−0.00489419	+	0.0182654i	0.963436	+	0.267940i	$0.0863429\pi$
$684$	65.0331	−	42.2330i	2.48660	−	1.61482i
$685$	1.16315	−	7.34381i	0.0444415	−	0.280593i
$686$	2.49114	−	2.50147i	0.0951123	−	0.0955064i
$687$	39.5891	+	28.7632i	1.51042	+	1.09738i
$688$	−23.5909	−	13.6202i	−0.899396	−	0.519267i
$689$	12.4804	+	1.31174i	0.475465	+	0.0499734i
$690$	5.50023	−	8.46961i	0.209390	−	0.322432i
$691$	10.6526	+	16.4035i	0.405243	+	0.624020i	0.981093	−	0.193535i	$-0.0619954\pi$
$691$	10.6526	+	16.4035i	0.405243	+	0.624020i	−0.575850	+	0.817555i	$0.695329\pi$
$692$	0.658798	+	0.906758i	0.0250438	+	0.0344698i
$693$	50.7539	+	31.6660i	1.92798	+	1.20289i
$694$	−2.45057	+	2.45057i	−0.0930224	+	0.0930224i
$695$	−1.75022	+	8.23412i	−0.0663895	+	0.312338i
$696$	2.30398	+	3.99061i	0.0873322	+	0.151264i
$697$	14.3999	+	0.390874i	0.545433	+	0.0148054i
$698$	−2.24137	+	3.88216i	−0.0848370	+	0.146942i
$699$	45.8331	−	14.8921i	1.73357	−	0.563271i
$700$	−7.76268	+	5.85799i	−0.293402	+	0.221411i
$701$	34.8266	−	25.3030i	1.31538	−	0.955682i	0.315407	−	0.948957i	$-0.397859\pi$
$701$	34.8266	−	25.3030i	1.31538	−	0.955682i	0.999977	−	0.00672568i	$-0.00214087\pi$
$702$	6.31691	−	0.663934i	0.238416	−	0.0250586i
$703$	10.8556	−	0.568915i	0.409425	−	0.0214571i
$704$	16.6786	−	25.6827i	0.628597	−	0.967954i
$705$	−12.5739	−	28.2414i	−0.473560	−	1.06363i
$706$		−	4.56131i		−	0.171667i
$707$	−12.0543	+	3.46550i	−0.453348	+	0.130334i
$708$	43.5236	−	6.89346i	1.63572	−	0.259072i
$709$	5.76339	+	4.66710i	0.216449	+	0.175277i	0.731413	−	0.681935i	$-0.238861\pi$
$709$	5.76339	+	4.66710i	0.216449	+	0.175277i	−0.514964	+	0.857212i	$0.672195\pi$
$710$	−0.213758	−	4.07874i	−0.00802219	−	0.153073i
$711$	−9.40230	+	35.0899i	−0.352614	+	1.31597i
$712$	−3.83786	+	4.73936i	−0.143830	+	0.177615i
$713$	−17.5341	+	53.9645i	−0.656658	+	2.02098i
$714$	2.85528	+	1.58014i	0.106856	+	0.0591351i
$715$	17.7082	+	54.5002i	0.662248	+	2.03819i
$716$	1.32108	−	25.2076i	0.0493709	−	0.942053i
$717$	−5.54009	−	26.0641i	−0.206898	−	0.973380i
$718$	−1.11321	−	5.23725i	−0.0415447	−	0.195452i
$719$	0.982166	−	18.7408i	0.0366286	−	0.698916i	−0.917175	−	0.398485i	$-0.869536\pi$
$719$	0.982166	−	18.7408i	0.0366286	−	0.698916i	0.953804	−	0.300431i	$-0.0971305\pi$
$720$	−16.1592	−	49.7329i	−0.602217	−	1.85343i
$721$	0.518090	+	28.5537i	0.0192947	+	1.06340i
$722$	−2.18484	+	6.72425i	−0.0813113	+	0.250251i
$723$	−28.4523	+	35.1357i	−1.05815	+	1.30671i
$724$	6.69184	−	24.9743i	0.248700	−	0.928162i
$725$	0.207728	+	3.96369i	0.00771484	+	0.147208i
$726$	3.14851	+	2.54961i	0.116852	+	0.0946250i
$727$	−37.3011	+	5.90792i	−1.38342	+	0.219112i	−0.803376	−	0.595472i	$-0.796965\pi$
$727$	−37.3011	+	5.90792i	−1.38342	+	0.219112i	−0.580045	+	0.814584i	$0.696965\pi$
$728$	−2.45842	+	9.88919i	−0.0911149	+	0.366518i
$729$		−	40.6748i		−	1.50648i
$730$	−2.89079	−	6.49282i	−0.106993	−	0.240310i
$731$	−8.82222	+	13.5850i	−0.326302	+	0.502460i
$732$	−36.2496	+	1.89976i	−1.33982	+	0.0702171i
$733$	33.6887	−	3.54083i	1.24432	−	0.130783i	0.540613	−	0.841272i	$-0.318193\pi$
$733$	33.6887	−	3.54083i	1.24432	−	0.130783i	0.703709	+	0.710488i	$0.251526\pi$
$734$	4.58779	−	3.33322i	0.169338	−	0.123032i
$735$	−0.848383	+	52.7717i	−0.0312931	+	1.94651i
$736$	−14.9176	+	4.84703i	−0.549871	+	0.178664i
$737$	4.97481	−	8.61663i	0.183250	−	0.317398i
$738$	6.38132	−	0.833899i	0.234899	−	0.0306963i
$739$	−10.3727	−	17.9660i	−0.381565	−	0.660890i	0.609721	−	0.792616i	$-0.291281\pi$
$739$	−10.3727	−	17.9660i	−0.381565	−	0.660890i	−0.991286	+	0.131726i	$0.957948\pi$
$740$	1.55340	−	7.30817i	0.0571041	−	0.268654i
$741$	77.6469	−	77.6469i	2.85243	−	2.85243i
$742$	1.05334	+	0.657188i	0.0386692	+	0.0241261i
$743$	−22.7339	−	31.2905i	−0.834025	−	1.14794i	−0.987161	−	0.159731i	$-0.948937\pi$
$743$	−22.7339	−	31.2905i	−0.834025	−	1.14794i	0.153136	−	0.988205i	$-0.451063\pi$
$744$	−9.55762	−	14.7174i	−0.350399	−	0.539568i
$745$	30.5118	−	46.9841i	1.11787	−	1.72137i
$746$	2.57506	+	0.270650i	0.0942798	+	0.00990921i
$747$	−8.09319	−	4.67261i	−0.296114	−	0.170962i
$748$	−15.3262	−	11.1352i	−0.560383	−	0.407142i
$749$	−34.2953	+	0.622268i	−1.25312	+	0.0227372i
$750$	0.703307	−	4.44051i	0.0256811	−	0.162144i
$751$	24.9544	−	16.2056i	0.910599	−	0.591350i	−0.00209340	−	0.999998i	$-0.500666\pi$
$751$	24.9544	−	16.2056i	0.910599	−	0.591350i	0.912692	+	0.408648i	$0.134000\pi$
$752$	−4.01481	+	14.9835i	−0.146405	+	0.546391i
$753$	27.8021	+	72.4271i	1.01317	+	2.63939i
$754$	1.37870	+	1.53120i	0.0502094	+	0.0557632i
$755$	2.44691	+	15.4492i	0.0890520	+	0.562252i
$756$	−31.9202	−	11.5931i	−1.16092	−	0.421636i
$757$	−18.2725	+	9.31029i	−0.664124	+	0.338388i	−0.753347	−	0.657624i	$-0.771562\pi$
$757$	−18.2725	+	9.31029i	−0.664124	+	0.338388i	0.0892226	+	0.996012i	$0.471562\pi$
$758$	−4.03447	+	3.63265i	−0.146539	+	0.131944i
$759$	18.0191	+	84.7730i	0.654050	+	3.07706i
$760$	12.4405	+	8.07898i	0.451266	+	0.293055i
$761$	36.8878	+	7.84074i	1.33718	+	0.284227i	0.820350	−	0.571861i	$-0.193778\pi$
$761$	36.8878	+	7.84074i	1.33718	+	0.284227i	0.516830	+	0.856088i	$0.327112\pi$
$762$	−0.278962	−	1.76130i	−0.0101057	−	0.0638051i
$763$	−7.54691	−	11.1721i	−0.273216	−	0.404459i
$764$	9.21211	+	1.45905i	0.333282	+	0.0527868i
$765$	−30.0355	+	8.04800i	−1.08594	+	0.290976i
$766$	0.161860	+	3.08848i	0.00584825	+	0.111591i
$767$	37.1310	−	14.2533i	1.34072	−	0.514655i
$768$	−13.5767	+	35.3684i	−0.489906	+	1.27625i
$769$	27.7276	+	20.1453i	0.999882	+	0.726457i	0.962063	−	0.272828i	$-0.0879589\pi$
$769$	27.7276	+	20.1453i	0.999882	+	0.726457i	0.0378193	+	0.999285i	$0.487959\pi$
$770$	−0.785159	+	5.61477i	−0.0282952	+	0.202342i
$771$	19.2930	−	26.5545i	0.694819	−	0.956336i
$772$	−12.7771	−	0.669621i	−0.459859	−	0.0241002i
$773$	−28.7636	+	1.50744i	−1.03455	+	0.0542187i	−0.562045	−	0.827107i	$-0.689985\pi$
$773$	−28.7636	+	1.50744i	−1.03455	+	0.0542187i	−0.472510	+	0.881325i	$0.656652\pi$
$774$	−2.94342	+	6.61102i	−0.105799	+	0.237628i
$775$	−1.58002	−	15.0329i	−0.0567560	−	0.539997i
$776$	2.63816	−	2.63816i	0.0947044	−	0.0947044i
$777$	−7.10551	−	8.45618i	−0.254909	−	0.303364i
$778$	−4.15123			−0.148829
$779$	33.0438	−	34.7541i	1.18392	−	1.24520i
$780$	−37.7369	−	65.3622i	−1.35120	−	2.34034i
$781$	26.0481	+	23.4538i	0.932075	+	0.839244i
$782$	0.779893	+	2.91060i	0.0278889	+	0.104083i
$783$	−11.2133	+	8.14697i	−0.400732	+	0.291149i
$784$	16.9951	−	20.3107i	0.606966	−	0.725382i
$785$	3.73529	−	7.33091i	0.133318	−	0.261651i
$786$	1.07190	+	0.0561757i	0.0382333	+	0.00200372i
$787$	51.1069	+	5.37156i	1.82177	+	0.191475i	0.952841	−	0.303470i	$-0.0981451\pi$
$787$	51.1069	+	5.37156i	1.82177	+	0.191475i	0.868924	+	0.494945i	$0.164812\pi$
$788$	−19.5444	+	11.2839i	−0.696239	+	0.401974i
$789$	−27.7012	+	12.3334i	−0.986189	+	0.439080i
$790$	−3.40042	+	0.538574i	−0.120982	+	0.0191616i
$791$	9.19208	−	2.12883i	0.326833	−	0.0756925i
$792$	−15.2215	−	7.75574i	−0.540873	−	0.275588i
$793$	−31.6463	+	8.47959i	−1.12379	+	0.301119i
$794$	1.66905	+	4.34802i	0.0592323	+	0.154305i
$795$	−18.1555	+	3.85906i	−0.643908	+	0.136867i
$796$	18.6712	+	7.16722i	0.661784	+	0.254035i
$797$	7.25513	+	22.3290i	0.256990	+	0.790933i	0.993431	+	0.114432i	$0.0365048\pi$
$797$	7.25513	+	22.3290i	0.256990	+	0.790933i	−0.736441	+	0.676502i	$0.763495\pi$
$798$	10.2696	−	3.54401i	0.363539	−	0.125457i
$799$	8.77262	+	2.85040i	0.310353	+	0.100840i
$800$	3.10522	−	2.79596i	0.109786	−	0.0988520i
$801$	−35.6922	−	23.1788i	−1.26112	−	0.818983i
$802$	1.68089	−	1.86682i	0.0593543	−	0.0659196i
$803$	56.9424	+	21.8581i	2.00945	+	0.771357i
$804$	−4.04943	+	12.4629i	−0.142812	+	0.439531i
$805$	−35.6189	+	33.2611i	−1.25540	+	1.17230i
$806$	−5.54851	−	5.54851i	−0.195438	−	0.195438i
$807$	−0.189447	+	0.123028i	−0.00666885	+	0.00433080i
$808$	3.34389	−	1.28360i	0.117638	−	0.0451568i
$809$	26.5935	+	32.8402i	0.934977	+	1.15460i	0.987758	+	0.155995i	$0.0498583\pi$
$809$	26.5935	+	32.8402i	0.934977	+	1.15460i	−0.0527805	+	0.998606i	$0.516808\pi$
$810$	−1.36165	+	0.606247i	−0.0478436	+	0.0213014i
$811$			4.01660i			0.141042i	0.997510	+	0.0705209i	$0.0224662\pi$
$811$			4.01660i			0.141042i	−0.997510	+	0.0705209i	$0.977534\pi$
$812$	−3.04383	−	10.5875i	−0.106817	−	0.371550i
$813$	−13.3914	−	26.2822i	−0.469658	−	0.921756i
$814$	−0.646190	−	0.995045i	−0.0226489	−	0.0348763i
$815$	1.72080	−	3.86498i	0.0602771	−	0.135384i
$816$	22.3640	+	9.95711i	0.782897	+	0.348568i
$817$	13.9568	+	52.0876i	0.488288	+	1.82231i
$818$	−5.61876	+	1.82564i	−0.196455	+	0.0638322i
$819$	−70.4275	−	9.84845i	−2.46094	−	0.344133i
$820$	−17.1950	−	28.1201i	−0.600475	−	0.981996i
$821$	−27.9039	+	48.3310i	−0.973853	+	1.68676i	−0.290182	+	0.956972i	$0.593716\pi$
$821$	−27.9039	+	48.3310i	−0.973853	+	1.68676i	−0.683671	+	0.729790i	$0.739618\pi$
$822$	1.15565	+	1.04055i	0.0403080	+	0.0362935i
$823$	8.50361	+	2.27854i	0.296417	+	0.0794248i	0.403963	−	0.914775i	$-0.367632\pi$
$823$	8.50361	+	2.27854i	0.296417	+	0.0794248i	−0.107546	+	0.994200i	$0.534299\pi$
$824$	−0.852478	−	8.11079i	−0.0296975	−	0.282553i
$825$	−13.5706	−	18.6783i	−0.472466	−	0.650294i
$826$	3.92014	+	0.340245i	0.136399	+	0.0118387i
$827$	16.1600	+	31.7158i	0.561938	+	1.10287i	0.980837	+	0.194833i	$0.0624163\pi$
$827$	16.1600	+	31.7158i	0.561938	+	1.10287i	−0.418898	+	0.908033i	$0.637584\pi$
$828$	−29.5907	−	66.4618i	−1.02835	−	2.30971i
$829$	45.9516	−	26.5302i	1.59597	−	0.921432i	0.603713	−	0.797202i	$-0.293687\pi$
$829$	45.9516	−	26.5302i	1.59597	−	0.921432i	0.992253	−	0.124230i	$-0.0396462\pi$
$830$	0.0925761	−	0.880803i	0.00321336	−	0.0305731i
$831$	8.60469	−	22.4160i	0.298493	−	0.777601i
$832$	−5.69465	+	35.9546i	−0.197427	+	1.24650i
$833$	−11.5321	−	10.7242i	−0.399564	−	0.371571i
$834$	−1.24494	−	1.24494i	−0.0431088	−	0.0431088i
$835$	17.0300	−	21.0304i	0.589349	−	0.727785i
$836$	−61.6884	+	13.1123i	−2.13354	+	0.453498i
$837$	41.0216	−	33.2186i	1.41791	−	1.14820i
$838$	−2.56077	−	0.544310i	−0.0884605	−	0.0188029i
$839$	11.1433	−	5.67778i	0.384708	−	0.196019i	−0.250931	−	0.968005i	$-0.580737\pi$
$839$	11.1433	−	5.67778i	0.384708	−	0.196019i	0.635639	+	0.771986i	$0.280737\pi$
$840$	−1.06173	−	15.0346i	−0.0366332	−	0.518742i
$841$	23.3045	+	7.57209i	0.803603	+	0.261106i
$842$	−0.259606	+	4.95358i	−0.00894661	+	0.170712i
$843$	18.0253	−	20.0191i	0.620824	−	0.689494i
$844$	9.96705	−	8.07116i	0.343080	−	0.277821i
$845$	−22.7784	−	25.2980i	−0.783601	−	0.870277i
$846$	4.07017	+	0.644651i	0.139935	+	0.0221636i
$847$	−11.7767	−	15.6058i	−0.404651	−	0.536221i
$848$	8.29844	+	4.22826i	0.284969	+	0.145199i
$849$	22.7267	+	18.4037i	0.779979	+	0.631614i
$850$	−0.505169	−	0.623832i	−0.0173272	−	0.0213973i
$851$	1.06606	−	10.1429i	0.0365440	−	0.347693i
$852$	−39.9796	−	23.0822i	−1.36968	−	0.790784i
$853$	−25.2738	+	34.7864i	−0.865358	+	1.19106i	0.114907	+	0.993376i	$0.463343\pi$
$853$	−25.2738	+	34.7864i	−0.865358	+	1.19106i	−0.980265	+	0.197687i	$0.936657\pi$
$854$	−3.18221	−	0.616284i	−0.108893	−	0.0210888i
$855$	−46.9959	+	92.2346i	−1.60723	+	3.15436i
$856$	9.74171	−	1.02390i	0.332965	−	0.0349960i
$857$	−39.5182	−	17.5946i	−1.34991	−	0.601021i	−0.400862	−	0.916139i	$-0.631289\pi$
$857$	−39.5182	−	17.5946i	−1.34991	−	0.601021i	−0.949053	+	0.315118i	$0.897956\pi$
$858$	−11.5768	−	3.10198i	−0.395224	−	0.105900i
$859$	−9.50841	+	44.7335i	−0.324423	+	1.52629i	0.449658	+	0.893201i	$0.351546\pi$
$859$	−9.50841	+	44.7335i	−0.324423	+	1.52629i	−0.774080	+	0.633088i	$0.781787\pi$
$860$	37.0636			1.26386
$861$	−48.4116	−	5.52898i	−1.64986	−	0.188427i
$862$	5.96075			0.203024
$863$	9.67883	−	45.5353i	0.329471	−	1.55004i	−0.432020	−	0.901864i	$-0.642199\pi$
$863$	9.67883	−	45.5353i	0.329471	−	1.55004i	0.761491	−	0.648175i	$-0.224468\pi$
$864$	14.0943	+	3.77657i	0.479499	+	0.128481i
$865$	−1.36689	−	0.608579i	−0.0464757	−	0.0206923i
$866$	−0.466955	+	0.0490790i	−0.0158678	+	0.00166777i
$867$	−15.5894	+	30.5960i	−0.529445	+	1.03909i
$868$	13.6862	+	39.6587i	0.464539	+	1.34610i
$869$	17.3665	−	23.9030i	0.589119	−	0.810852i
$870$	−2.63925	−	1.52377i	−0.0894788	−	0.0516606i
$871$	−1.23631	+	11.7627i	−0.0418907	+	0.398563i
$872$	2.42298	+	2.99213i	0.0820526	+	0.101326i
$873$	20.2341	+	16.3852i	0.684820	+	0.554557i
$874$	8.93801	+	4.55414i	0.302333	+	0.154046i
$875$	−8.46340	+	19.9768i	−0.286115	+	0.675339i
$876$	−79.3430	−	12.5667i	−2.68075	−	0.424590i
$877$	14.3274	+	15.9122i	0.483802	+	0.537316i	0.934784	−	0.355217i	$-0.115593\pi$
$877$	14.3274	+	15.9122i	0.483802	+	0.537316i	−0.450982	+	0.892533i	$0.648926\pi$
$878$	−5.20085	+	4.21157i	−0.175520	+	0.142133i
$879$	30.5692	−	33.9506i	1.03107	−	1.14512i
$880$	−2.22584	+	42.4715i	−0.0750329	+	1.43171i
$881$	−12.2100	−	3.96728i	−0.411367	−	0.133661i	0.0960203	−	0.995379i	$-0.469389\pi$
$881$	−12.2100	−	3.96728i	−0.411367	−	0.133661i	−0.507387	+	0.861718i	$0.669389\pi$
$882$	−5.83809	−	3.92614i	−0.196579	−	0.132200i
$883$	−13.1322	+	6.69119i	−0.441934	+	0.225176i	−0.660775	−	0.750584i	$-0.729772\pi$
$883$	−13.1322	+	6.69119i	−0.441934	+	0.225176i	0.218841	+	0.975760i	$0.429772\pi$
$884$	22.0276	+	4.68211i	0.740869	+	0.157477i
$885$	−45.7169	+	37.0208i	−1.53676	+	1.24444i
$886$	2.25774	−	0.479896i	0.0758501	−	0.0161224i
$887$	21.6627	−	26.7513i	0.727363	−	0.898219i	−0.270555	−	0.962704i	$-0.587207\pi$
$887$	21.6627	−	26.7513i	0.727363	−	0.898219i	0.997919	+	0.0644854i	$0.0205406\pi$
$888$	2.23034	+	2.23034i	0.0748453	+	0.0748453i
$889$	−0.744106	+	8.57321i	−0.0249565	+	0.287536i
$890$	0.630942	−	3.98361i	0.0211492	−	0.133531i
$891$	4.58402	−	11.9418i	0.153571	−	0.400065i
$892$	1.34153	−	12.7638i	0.0449177	−	0.427363i
$893$	26.5935	−	15.3537i	0.889916	−	0.513794i
$894$	4.76568	+	10.7039i	0.159388	+	0.357992i
$895$	15.2983	+	30.0247i	0.511367	+	1.00361i
$896$	−8.83214	+	12.6321i	−0.295061	+	0.422010i
$897$	−60.5559	−	83.3481i	−2.02190	−	2.78291i
$898$	−0.694011	−	6.60307i	−0.0231594	−	0.220347i
$899$	16.5395	+	4.43175i	0.551623	+	0.147807i
$900$	14.4026	+	12.9682i	0.480088	+	0.432273i
$901$	2.76911	−	4.79624i	0.0922524	−	0.159786i
$902$	−5.08832	−	1.22675i	−0.169423	−	0.0408464i
$903$	33.7033	−	43.1996i	1.12158	−	1.43759i
$904$	−2.56259	+	0.832637i	−0.0852306	+	0.0276931i
$905$	8.93337	+	33.3398i	0.296955	+	1.10825i
$906$	−2.98859	−	1.33061i	−0.0992894	−	0.0442065i
$907$	13.5942	−	30.5330i	0.451387	−	1.01383i	−0.534308	−	0.845290i	$-0.679428\pi$
$907$	13.5942	−	30.5330i	0.451387	−	1.01383i	0.985695	−	0.168541i	$-0.0539056\pi$
$908$	15.3413	+	23.6235i	0.509119	+	0.783974i
$909$	11.3478	+	22.2713i	0.376383	+	0.738693i
$910$	−1.86210	−	6.47706i	−0.0617280	−	0.214713i
$911$		−	3.70784i		−	0.122846i	−0.998112	−	0.0614231i	$-0.980436\pi$
$911$		−	3.70784i		−	0.122846i	0.998112	−	0.0614231i	$-0.0195639\pi$
$912$	74.4511	−	33.1478i	2.46532	−	1.09763i
$913$	4.78318	+	5.90674i	0.158300	+	0.195485i
$914$	−1.65492	+	0.635266i	−0.0547400	+	0.0210127i
$915$	40.6405	−	26.3923i	1.34353	−	0.872502i
$916$	23.6237	+	23.6237i	0.780550	+	0.780550i
$917$	−4.95446	−	1.51100i	−0.163611	−	0.0498976i
$918$	0.866222	−	2.66596i	0.0285896	−	0.0879897i
$919$	7.90891	+	3.03595i	0.260891	+	0.100147i	0.485298	−	0.874349i	$-0.338711\pi$
$919$	7.90891	+	3.03595i	0.260891	+	0.100147i	−0.224407	+	0.974496i	$0.572044\pi$
$920$	9.31231	−	10.3424i	0.307018	−	0.340978i
$921$	51.9243	+	33.7200i	1.71096	+	1.11111i
$922$	−1.39944	+	1.26006i	−0.0460880	+	0.0414978i
$923$	−39.6273	−	12.8757i	−1.30435	−	0.423808i
$924$	48.3908	+	42.0070i	1.59194	+	1.38193i
$925$	0.839566	+	2.58392i	0.0276048	+	0.0849588i
$926$	−2.84229	−	1.09105i	−0.0934033	−	0.0358542i
$927$	55.6696	−	11.8329i	1.82843	−	0.388645i
$928$	1.69629	+	4.41898i	0.0556834	+	0.145060i
$929$	−26.0006	+	6.96685i	−0.853053	+	0.228575i	−0.658746	−	0.752366i	$-0.728913\pi$
$929$	−26.0006	+	6.96685i	−0.853053	+	0.228575i	−0.194308	+	0.980941i	$0.562246\pi$
$930$	10.3410	+	5.26900i	0.339094	+	0.172777i
$931$	−52.2200	+	4.64119i	−1.71144	+	0.152109i
$932$	32.4966	−	5.14696i	1.06446	−	0.168594i
$933$	−60.3182	+	26.8554i	−1.97473	+	0.879207i
$934$	3.46053	−	1.99794i	0.113232	−	0.0653745i
$935$	25.1514	+	2.64352i	0.822539	+	0.0864523i
$936$	20.2799	+	1.06283i	0.662870	+	0.0347395i
$937$	14.8776	−	29.1989i	0.486029	−	0.953886i	−0.509593	−	0.860416i	$-0.670204\pi$
$937$	14.8776	−	29.1989i	0.486029	−	0.953886i	0.995622	−	0.0934703i	$-0.0297960\pi$
$938$	−0.619396	+	0.992762i	−0.0202240	+	0.0324148i
$939$	45.6839	−	33.1913i	1.49084	−	1.08316i
$940$	−5.46258	−	20.3866i	−0.178170	−	0.664938i
$941$	−24.5636	−	22.1172i	−0.800751	−	0.720999i	0.163341	−	0.986570i	$-0.447773\pi$
$941$	−24.5636	−	22.1172i	−0.800751	−	0.720999i	−0.964091	+	0.265570i	$0.914440\pi$
$942$	0.860397	+	1.49025i	0.0280333	+	0.0485550i
$943$	−27.3554	−	35.7210i	−0.890813	−	1.16324i
$944$	29.5180			0.960728
$945$	44.6415	−	7.90322i	1.45219	−	0.257092i
$946$	4.16178	−	4.16178i	0.135311	−	0.135311i
$947$	4.98663	+	47.4446i	0.162044	+	1.54174i	0.709377	+	0.704829i	$0.248976\pi$
$947$	4.98663	+	47.4446i	0.162044	+	1.54174i	−0.547334	+	0.836914i	$0.684357\pi$
$948$	−15.8275	+	35.5491i	−0.514053	+	1.15458i
$949$	−72.4058	+	3.79463i	−2.35039	+	0.123179i
$950$	−2.66864	−	0.139858i	−0.0865823	−	0.00453758i
$951$	−4.36360	+	6.00598i	−0.141500	+	0.194757i
$952$	3.54572	+	2.76629i	0.114917	+	0.0896559i
$953$	−34.9916	−	25.4229i	−1.13349	−	0.823529i	−0.147291	−	0.989093i	$-0.547055\pi$
$953$	−34.9916	−	25.4229i	−1.13349	−	0.823529i	−0.986199	+	0.165564i	$0.947055\pi$
$954$	0.886683	−	2.30989i	0.0287074	−	0.0747854i
$955$	−11.6241	+	4.46209i	−0.376148	+	0.144390i
$956$	−0.952101	−	18.1672i	−0.0307931	−	0.587568i
$957$	25.2624	−	6.76903i	0.816616	−	0.218812i
$958$	6.15613	+	0.975035i	0.198896	+	0.0315020i
$959$	−4.20067	−	6.21850i	−0.135647	−	0.200806i
$960$	−8.42280	−	53.1795i	−0.271845	−	1.71636i
$961$	−33.4619	−	7.11255i	−1.07942	−	0.229437i
$962$	1.18285	+	0.768149i	0.0381365	+	0.0247661i
$963$	14.2123	+	66.8637i	0.457986	+	2.15465i
$964$	−22.9385	+	20.6539i	−0.738798	+	0.665217i
$965$	15.2188	−	7.75436i	0.489910	−	0.249622i
$966$	−1.77684	−	10.0365i	−0.0571689	−	0.322919i
$967$	7.41552	+	46.8197i	0.238467	+	1.50562i	0.758612	+	0.651543i	$0.225878\pi$
$967$	7.41552	+	46.8197i	0.238467	+	1.50562i	−0.520145	+	0.854078i	$0.674122\pi$
$968$	3.73584	+	4.14907i	0.120074	+	0.133356i
$969$	−17.3670	−	45.2426i	−0.557908	−	1.45340i
$970$	−0.638634	+	2.38342i	−0.0205053	+	0.0765269i
$971$	−26.3868	+	17.1358i	−0.846794	+	0.549915i	−0.893536	−	0.448992i	$-0.851783\pi$
$971$	−26.3868	+	17.1358i	−0.846794	+	0.549915i	0.0467414	+	0.998907i	$0.485116\pi$
$972$	3.38841	−	21.3936i	0.108683	−	0.686200i
$973$	4.38088	+	7.27965i	0.140445	+	0.233375i
$974$	−4.10122	−	2.97971i	−0.131411	−	0.0954760i
$975$	23.7681	+	13.7225i	0.761189	+	0.439473i
$976$	−24.1821	−	2.54165i	−0.774051	−	0.0813561i
$977$	−14.4807	+	22.2984i	−0.463280	+	0.713389i	−0.990677	−	0.136230i	$-0.956501\pi$
$977$	−14.4807	+	22.2984i	−0.463280	+	0.713389i	0.527397	+	0.849619i	$0.323168\pi$
$978$	0.481923	+	0.742097i	0.0154102	+	0.0237296i
$979$	20.3450	+	28.0024i	0.650228	+	0.894962i
$980$	−6.20818	+	35.4943i	−0.198313	+	1.13382i
$981$	−18.9989	+	18.9989i	−0.606589	+	0.606589i
$982$	−0.149861	+	0.705040i	−0.00478225	+	0.0224987i
$983$	−2.61643	−	4.53179i	−0.0834512	−	0.144542i	0.821279	−	0.570527i	$-0.193261\pi$
$983$	−2.61643	−	4.53179i	−0.0834512	−	0.144542i	−0.904730	+	0.425985i	$0.859928\pi$
$984$	13.9097	+	0.377569i	0.443425	+	0.0120365i
$985$	15.0637	−	26.0910i	0.479968	−	0.831329i
$986$	0.864813	−	0.280995i	0.0275413	−	0.00894870i
$987$	−28.7291	−	12.1714i	−0.914456	−	0.387420i
$988$	60.6516	−	44.0659i	1.92958	−	1.40192i
$989$	50.3157	−	5.28839i	1.59995	−	0.168161i
$990$	11.2829	−	0.591312i	0.358595	−	0.0187931i
$991$	20.5805	−	31.6912i	0.653762	−	1.00671i	−0.343943	−	0.938991i	$-0.611763\pi$
$991$	20.5805	−	31.6912i	0.653762	−	1.00671i	0.997705	−	0.0677146i	$-0.0215707\pi$
$992$	−7.33189	−	16.4677i	−0.232788	−	0.522850i
$993$			9.31111i			0.295479i
$994$	−2.96727	−	2.86151i	−0.0941160	−	0.0907616i
$995$	−26.3701	+	4.17661i	−0.835987	+	0.132407i
$996$	−7.77952	−	6.29973i	−0.246503	−	0.199615i
$997$	2.21434	+	42.2521i	0.0701289	+	1.33814i	0.776420	+	0.630216i	$0.217034\pi$
$997$	2.21434	+	42.2521i	0.0701289	+	1.33814i	−0.706291	+	0.707922i	$0.749633\pi$
$998$	−1.00356	+	3.74532i	−0.0317670	+	0.118556i
$999$	−5.97071	+	7.37322i	−0.188905	+	0.233278i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.bc.a.2.15	✓	416
7.4	even	3	inner	287.2.bc.a.207.15	yes	416
41.21	even	20	inner	287.2.bc.a.226.15	yes	416
287.144	even	60	inner	287.2.bc.a.144.15	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.bc.a.2.15	✓	416	1.1	even	1	trivial
287.2.bc.a.144.15	yes	416	287.144	even	60	inner
287.2.bc.a.207.15	yes	416	7.4	even	3	inner
287.2.bc.a.226.15	yes	416	41.21	even	20	inner

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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.bc (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0396320 - 0.186454i) q^{2} +(2.77822 + 0.744421i) q^{3} +(1.79390 + 0.798694i) q^{4} +(-2.60706 + 0.274013i) q^{5} +(0.248906 - 0.488506i) q^{6} +(-1.73439 + 1.99797i) q^{7} +(0.444101 - 0.611253i) q^{8} +(4.56625 + 2.63632i) q^{9} +O(q^{10})\)	\(q+(0.0396320 - 0.186454i) q^{2} +(2.77822 + 0.744421i) q^{3} +(1.79390 + 0.798694i) q^{4} +(-2.60706 + 0.274013i) q^{5} +(0.248906 - 0.488506i) q^{6} +(-1.73439 + 1.99797i) q^{7} +(0.444101 - 0.611253i) q^{8} +(4.56625 + 2.63632i) q^{9} +(-0.0522322 + 0.496956i) q^{10} +(-2.69871 - 3.33263i) q^{11} +(4.38927 + 3.55436i) q^{12} +(4.54204 + 2.31428i) q^{13} +(0.303791 + 0.402567i) q^{14} +(-7.44696 - 1.17948i) q^{15} +(2.53153 + 2.81154i) q^{16} +(1.74835 - 1.41579i) q^{17} +(0.672521 - 0.746911i) q^{18} +(0.391965 - 7.47914i) q^{19} +(-4.89565 - 1.59069i) q^{20} +(-6.30585 + 4.25967i) q^{21} +(-0.728337 + 0.371106i) q^{22} +(-6.87307 - 1.46092i) q^{23} +(1.68884 - 1.36759i) q^{24} +(1.83095 - 0.389181i) q^{25} +(0.611516 - 0.755160i) q^{26} +(4.62210 + 4.62210i) q^{27} +(-4.70709 + 2.19890i) q^{28} +(-0.331708 + 2.09432i) q^{29} +(-0.515057 + 1.34177i) q^{30} +(0.844092 - 8.03100i) q^{31} +(1.93320 - 1.11614i) q^{32} +(-5.01672 - 11.2677i) q^{33} +(-0.194688 - 0.382097i) q^{34} +(3.97420 - 5.68408i) q^{35} +(6.08576 + 8.37633i) q^{36} +(0.151717 + 1.44349i) q^{37} +(-1.37898 - 0.369496i) q^{38} +(10.8960 + 9.81076i) q^{39} +(-0.990308 + 1.71526i) q^{40} +(4.86499 + 4.16316i) q^{41} +(0.544319 + 1.34457i) q^{42} +(-6.84777 + 2.22498i) q^{43} +(-2.17946 - 8.13384i) q^{44} +(-12.6269 - 5.62185i) q^{45} +(-0.544786 + 1.22361i) q^{46} +(2.23309 + 3.43865i) q^{47} +(4.94015 + 9.69560i) q^{48} +(-0.983764 - 6.93053i) q^{49} -0.356812i q^{50} +(5.91124 - 2.63185i) q^{51} +(6.29954 + 7.77928i) q^{52} +(2.29824 - 0.882212i) q^{53} +(1.04499 - 0.678624i) q^{54} +(7.94889 + 7.94889i) q^{55} +(0.451019 + 1.94745i) q^{56} +(6.65659 - 20.4869i) q^{57} +(0.377348 + 0.144850i) q^{58} +(5.22067 - 5.79814i) q^{59} +(-12.4170 - 8.06372i) q^{60} +(-4.77620 + 4.30051i) q^{61} +(-1.46396 - 0.475668i) q^{62} +(-13.1870 + 4.55080i) q^{63} +(2.20672 + 6.79159i) q^{64} +(-12.4755 - 4.78890i) q^{65} +(-2.29974 + 0.488824i) q^{66} +(0.831479 + 2.16608i) q^{67} +(4.26714 - 1.14338i) q^{68} +(-18.0073 - 9.17519i) q^{69} +(-0.902312 - 0.966275i) q^{70} +(-8.07306 + 1.27865i) q^{71} +(3.63934 - 1.62034i) q^{72} +(-12.3177 + 7.11164i) q^{73} +(0.275157 + 0.0289202i) q^{74} +(5.37649 + 0.281770i) q^{75} +(6.67669 - 13.1037i) q^{76} +(11.3391 + 0.388148i) q^{77} +(2.26108 - 1.64277i) q^{78} +(1.78322 + 6.65508i) q^{79} +(-7.37025 - 6.63620i) q^{80} +(1.49143 + 2.58323i) q^{81} +(0.969045 - 0.742101i) q^{82} -1.77240 q^{83} +(-14.7142 + 2.60497i) q^{84} +(-4.17012 + 4.17012i) q^{85} +(0.143464 + 1.36497i) q^{86} +(-2.48061 + 5.57155i) q^{87} +(-3.23558 + 0.169570i) q^{88} +(-8.06042 - 0.422429i) q^{89} +(-1.54864 + 2.13152i) q^{90} +(-12.5015 + 5.06097i) q^{91} +(-11.1627 - 8.11021i) q^{92} +(8.32352 - 21.6835i) q^{93} +(0.729651 - 0.280087i) q^{94} +(1.02751 + 19.6060i) q^{95} +(6.20173 - 1.66175i) q^{96} +(4.87722 + 0.772476i) q^{97} +(-1.33121 - 0.0912438i) q^{98} +(-3.53709 - 22.3323i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 416 q - 10 q^{2} - 8 q^{3} - 54 q^{4} - 10 q^{5} - 16 q^{6} - 16 q^{7} - 40 q^{8}+O(q^{10}) \) 416 * q - 10 * q^2 - 8 * q^3 - 54 * q^4 - 10 * q^5 - 16 * q^6 - 16 * q^7 - 40 * q^8	\( 416 q - 10 q^{2} - 8 q^{3} - 54 q^{4} - 10 q^{5} - 16 q^{6} - 16 q^{7} - 40 q^{8} + 18 q^{10} - 12 q^{11} - 24 q^{12} - 32 q^{13} + 10 q^{14} - 32 q^{15} + 26 q^{16} - 2 q^{17} - 30 q^{18} - 4 q^{19} + 80 q^{20} - 20 q^{21} - 32 q^{22} - 6 q^{23} + 26 q^{24} - 42 q^{25} - 18 q^{26} - 92 q^{27} - 42 q^{28} - 128 q^{29} - 38 q^{30} - 38 q^{31} + 100 q^{33} - 56 q^{34} - 2 q^{35} - 120 q^{36} + 6 q^{38} - 10 q^{39} + 20 q^{40} - 44 q^{41} + 112 q^{42} - 76 q^{44} - 106 q^{45} + 90 q^{46} + 32 q^{47} - 20 q^{48} - 48 q^{51} - 20 q^{52} - 2 q^{53} + 72 q^{54} - 16 q^{55} - 166 q^{56} - 32 q^{57} - 14 q^{58} + 54 q^{59} + 62 q^{60} - 90 q^{61} - 40 q^{62} - 100 q^{63} - 8 q^{64} + 2 q^{65} + 22 q^{66} - 24 q^{67} - 42 q^{68} + 24 q^{69} + 222 q^{70} - 92 q^{71} - 30 q^{72} - 10 q^{74} - 32 q^{75} + 348 q^{76} + 80 q^{77} + 80 q^{78} + 10 q^{79} - 90 q^{80} + 120 q^{81} - 124 q^{82} + 432 q^{83} + 76 q^{85} - 54 q^{86} - 10 q^{87} - 130 q^{88} - 50 q^{89} + 80 q^{90} - 92 q^{92} - 16 q^{93} - 50 q^{94} - 52 q^{95} - 64 q^{96} - 4 q^{97} + 66 q^{98} - 124 q^{99}+O(q^{100}) \) 416 * q - 10 * q^2 - 8 * q^3 - 54 * q^4 - 10 * q^5 - 16 * q^6 - 16 * q^7 - 40 * q^8 + 18 * q^10 - 12 * q^11 - 24 * q^12 - 32 * q^13 + 10 * q^14 - 32 * q^15 + 26 * q^16 - 2 * q^17 - 30 * q^18 - 4 * q^19 + 80 * q^20 - 20 * q^21 - 32 * q^22 - 6 * q^23 + 26 * q^24 - 42 * q^25 - 18 * q^26 - 92 * q^27 - 42 * q^28 - 128 * q^29 - 38 * q^30 - 38 * q^31 + 100 * q^33 - 56 * q^34 - 2 * q^35 - 120 * q^36 + 6 * q^38 - 10 * q^39 + 20 * q^40 - 44 * q^41 + 112 * q^42 - 76 * q^44 - 106 * q^45 + 90 * q^46 + 32 * q^47 - 20 * q^48 - 48 * q^51 - 20 * q^52 - 2 * q^53 + 72 * q^54 - 16 * q^55 - 166 * q^56 - 32 * q^57 - 14 * q^58 + 54 * q^59 + 62 * q^60 - 90 * q^61 - 40 * q^62 - 100 * q^63 - 8 * q^64 + 2 * q^65 + 22 * q^66 - 24 * q^67 - 42 * q^68 + 24 * q^69 + 222 * q^70 - 92 * q^71 - 30 * q^72 - 10 * q^74 - 32 * q^75 + 348 * q^76 + 80 * q^77 + 80 * q^78 + 10 * q^79 - 90 * q^80 + 120 * q^81 - 124 * q^82 + 432 * q^83 + 76 * q^85 - 54 * q^86 - 10 * q^87 - 130 * q^88 - 50 * q^89 + 80 * q^90 - 92 * q^92 - 16 * q^93 - 50 * q^94 - 52 * q^95 - 64 * q^96 - 4 * q^97 + 66 * q^98 - 124 * q^99

Introduction

L-functions

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