LMFDB - Embedded newform 240.2.bb.a.173.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(173,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2, 3]))

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

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

chi := DirichletCharacter("240.173");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bb (of order $4$, degree $2$, 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:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			173.13
Character	$\chi$	$=$	240.173
Dual form			240.2.bb.a.197.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.898057 - 1.09247i) q^{2} +(-1.70651 - 0.296326i) q^{3} +(-0.386989 + 1.96220i) q^{4} +(-2.17873 - 0.503115i) q^{5} +(1.20882 + 2.13044i) q^{6} +(-2.12944 - 2.12944i) q^{7} +(2.49119 - 1.33939i) q^{8} +(2.82438 + 1.01137i) q^{9} +O(q^{10})$	\(q+(-0.898057 - 1.09247i) q^{2} +(-1.70651 - 0.296326i) q^{3} +(-0.386989 + 1.96220i) q^{4} +(-2.17873 - 0.503115i) q^{5} +(1.20882 + 2.13044i) q^{6} +(-2.12944 - 2.12944i) q^{7} +(2.49119 - 1.33939i) q^{8} +(2.82438 + 1.01137i) q^{9} +(1.40699 + 2.83203i) q^{10} +(2.92724 + 2.92724i) q^{11} +(1.24185 - 3.23385i) q^{12} +3.82476i q^{13} +(-0.413995 + 4.23870i) q^{14} +(3.56895 + 1.50419i) q^{15} +(-3.70048 - 1.51870i) q^{16} +(4.54825 + 4.54825i) q^{17} +(-1.43156 - 3.99382i) q^{18} +(-2.02084 + 2.02084i) q^{19} +(1.83036 - 4.08042i) q^{20} +(3.00290 + 4.26492i) q^{21} +(0.569101 - 5.82676i) q^{22} +(-2.64430 - 2.64430i) q^{23} +(-4.64815 + 1.54749i) q^{24} +(4.49375 + 2.19231i) q^{25} +(4.17844 - 3.43485i) q^{26} +(-4.52015 - 2.56285i) q^{27} +(5.00245 - 3.35432i) q^{28} +(-0.843557 - 0.843557i) q^{29} +(-1.56184 - 5.24982i) q^{30} +1.38749 q^{31} +(1.66410 + 5.40655i) q^{32} +(-4.12797 - 5.86280i) q^{33} +(0.884248 - 9.05341i) q^{34} +(3.56812 + 5.71082i) q^{35} +(-3.07752 + 5.15062i) q^{36} +6.69746i q^{37} +(4.02254 + 0.392882i) q^{38} +(1.13338 - 6.52701i) q^{39} +(-6.10150 + 1.66483i) q^{40} -2.65508 q^{41} +(1.96253 - 7.11073i) q^{42} -6.23355 q^{43} +(-6.87666 + 4.61104i) q^{44} +(-5.64474 - 3.62449i) q^{45} +(-0.514093 + 5.26356i) q^{46} +(3.32248 + 3.32248i) q^{47} +(5.86489 + 3.68823i) q^{48} +2.06899i q^{49} +(-1.64061 - 6.87811i) q^{50} +(-6.41388 - 9.10941i) q^{51} +(-7.50495 - 1.48014i) q^{52} +3.88396i q^{53} +(1.25951 + 7.23973i) q^{54} +(-4.90494 - 7.85042i) q^{55} +(-8.15698 - 2.45267i) q^{56} +(4.04742 - 2.84976i) q^{57} +(-0.164000 + 1.67912i) q^{58} +(-10.3658 + 10.3658i) q^{59} +(-4.33267 + 6.42090i) q^{60} +(3.84345 + 3.84345i) q^{61} +(-1.24604 - 1.51579i) q^{62} +(-3.86069 - 8.16798i) q^{63} +(4.41204 - 6.67337i) q^{64} +(1.92429 - 8.33313i) q^{65} +(-2.69780 + 9.77481i) q^{66} +10.0836 q^{67} +(-10.6847 + 7.16446i) q^{68} +(3.72897 + 5.29612i) q^{69} +(3.03454 - 9.02671i) q^{70} +5.37152 q^{71} +(8.39069 - 1.26345i) q^{72} +(-2.68667 + 2.68667i) q^{73} +(7.31679 - 6.01470i) q^{74} +(-7.01901 - 5.07282i) q^{75} +(-3.18325 - 4.74734i) q^{76} -12.4668i q^{77} +(-8.14841 + 4.62344i) q^{78} +5.55500i q^{79} +(7.29827 + 5.17061i) q^{80} +(6.95426 + 5.71299i) q^{81} +(2.38441 + 2.90060i) q^{82} -1.35478 q^{83} +(-9.53073 + 4.24183i) q^{84} +(-7.62112 - 12.1977i) q^{85} +(5.59808 + 6.80998i) q^{86} +(1.18957 + 1.68951i) q^{87} +(11.2131 + 3.37158i) q^{88} +5.23963i q^{89} +(1.10964 + 9.42171i) q^{90} +(8.14458 - 8.14458i) q^{91} +(6.21198 - 4.16534i) q^{92} +(-2.36777 - 0.411150i) q^{93} +(0.645941 - 6.61349i) q^{94} +(5.41958 - 3.38615i) q^{95} +(-1.23771 - 9.71947i) q^{96} +(-6.28272 + 6.28272i) q^{97} +(2.26031 - 1.85807i) q^{98} +(5.30713 + 11.2282i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 4 q^{4} - 4 q^{6}+O(q^{10}) $ 88 * q - 4 * q^4 - 4 * q^6	$ 88 q - 4 q^{4} - 4 q^{6} - 12 q^{10} + 4 q^{12} - 4 q^{15} - 12 q^{16} + 16 q^{18} - 8 q^{19} - 4 q^{21} - 20 q^{22} - 12 q^{24} - 36 q^{28} - 16 q^{30} - 16 q^{31} - 4 q^{33} + 28 q^{34} - 20 q^{36} + 24 q^{39} - 4 q^{40} - 20 q^{42} - 40 q^{43} + 8 q^{45} - 36 q^{46} + 16 q^{48} - 4 q^{51} + 24 q^{52} - 24 q^{54} + 12 q^{57} + 44 q^{58} - 56 q^{60} - 24 q^{61} - 32 q^{63} - 28 q^{64} + 12 q^{66} - 8 q^{67} - 12 q^{69} - 28 q^{70} + 64 q^{72} - 24 q^{75} - 36 q^{76} + 20 q^{78} - 8 q^{81} - 48 q^{82} + 48 q^{84} - 24 q^{85} - 12 q^{87} + 60 q^{88} + 76 q^{90} - 8 q^{91} - 20 q^{94} + 48 q^{96} - 8 q^{97} - 32 q^{99}+O(q^{100}) $ 88 * q - 4 * q^4 - 4 * q^6 - 12 * q^10 + 4 * q^12 - 4 * q^15 - 12 * q^16 + 16 * q^18 - 8 * q^19 - 4 * q^21 - 20 * q^22 - 12 * q^24 - 36 * q^28 - 16 * q^30 - 16 * q^31 - 4 * q^33 + 28 * q^34 - 20 * q^36 + 24 * q^39 - 4 * q^40 - 20 * q^42 - 40 * q^43 + 8 * q^45 - 36 * q^46 + 16 * q^48 - 4 * q^51 + 24 * q^52 - 24 * q^54 + 12 * q^57 + 44 * q^58 - 56 * q^60 - 24 * q^61 - 32 * q^63 - 28 * q^64 + 12 * q^66 - 8 * q^67 - 12 * q^69 - 28 * q^70 + 64 * q^72 - 24 * q^75 - 36 * q^76 + 20 * q^78 - 8 * q^81 - 48 * q^82 + 48 * q^84 - 24 * q^85 - 12 * q^87 + 60 * q^88 + 76 * q^90 - 8 * q^91 - 20 * q^94 + 48 * q^96 - 8 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.898057	−	1.09247i	−0.635022	−	0.772494i
$2$	−0.898057	−	1.09247i	−0.635022	−	0.772494i
$3$	−1.70651	−	0.296326i	−0.985256	−	0.171084i
$3$	−1.70651	−	0.296326i	−0.985256	−	0.171084i
$4$	−0.386989	+	1.96220i	−0.193494	+	0.981101i
$5$	−2.17873	−	0.503115i	−0.974359	−	0.225000i
$5$	−2.17873	−	0.503115i	−0.974359	−	0.225000i
$6$	1.20882	+	2.13044i	0.493498	+	0.869747i
$7$	−2.12944	−	2.12944i	−0.804851	−	0.804851i	0.178999	−	0.983849i	$-0.442714\pi$
$7$	−2.12944	−	2.12944i	−0.804851	−	0.804851i	−0.983849	+	0.178999i	$0.942714\pi$
$8$	2.49119	−	1.33939i	0.880768	−	0.473547i
$9$	2.82438	+	1.01137i	0.941461	+	0.337123i
$10$	1.40699	+	2.83203i	0.444928	+	0.895566i
$11$	2.92724	+	2.92724i	0.882597	+	0.882597i	0.993798	−	0.111201i	$-0.0354696\pi$
$11$	2.92724	+	2.92724i	0.882597	+	0.882597i	−0.111201	+	0.993798i	$0.535470\pi$
$12$	1.24185	−	3.23385i	0.358492	−	0.933533i
$13$			3.82476i			1.06080i	0.847748	+	0.530399i	$0.177958\pi$
$13$			3.82476i			1.06080i	−0.847748	+	0.530399i	$0.822042\pi$
$14$	−0.413995	+	4.23870i	−0.110645	+	1.13284i
$15$	3.56895	+	1.50419i	0.921499	+	0.388380i
$16$	−3.70048	−	1.51870i	−0.925120	−	0.379675i
$17$	4.54825	+	4.54825i	1.10311	+	1.10311i	0.994033	+	0.109079i	$0.0347901\pi$
$17$	4.54825	+	4.54825i	1.10311	+	1.10311i	0.109079	+	0.994033i	$0.465210\pi$
$18$	−1.43156	−	3.99382i	−0.337422	−	0.941353i
$19$	−2.02084	+	2.02084i	−0.463612	+	0.463612i	−0.899837	−	0.436225i	$-0.856315\pi$
$19$	−2.02084	+	2.02084i	−0.463612	+	0.463612i	0.436225	+	0.899837i	$0.356315\pi$
$20$	1.83036	−	4.08042i	0.409281	−	0.912409i
$21$	3.00290	+	4.26492i	0.655287	+	0.930682i
$22$	0.569101	−	5.82676i	0.121333	−	1.24227i
$23$	−2.64430	−	2.64430i	−0.551376	−	0.551376i	0.375462	−	0.926838i	$-0.377484\pi$
$23$	−2.64430	−	2.64430i	−0.551376	−	0.551376i	−0.926838	+	0.375462i	$0.877484\pi$
$24$	−4.64815	+	1.54749i	−0.948799	+	0.315880i
$25$	4.49375	+	2.19231i	0.898750	+	0.438461i
$26$	4.17844	−	3.43485i	0.819460	−	0.673630i
$27$	−4.52015	−	2.56285i	−0.869904	−	0.493222i
$28$	5.00245	−	3.35432i	0.945374	−	0.633906i
$29$	−0.843557	−	0.843557i	−0.156645	−	0.156645i	0.624433	−	0.781078i	$-0.285330\pi$
$29$	−0.843557	−	0.843557i	−0.156645	−	0.156645i	−0.781078	+	0.624433i	$0.785330\pi$
$30$	−1.56184	−	5.24982i	−0.285151	−	0.958483i
$31$	1.38749			0.249201			0.124600	−	0.992207i	$-0.460235\pi$
$31$	1.38749			0.249201			0.124600	+	0.992207i	$0.460235\pi$
$32$	1.66410	+	5.40655i	0.294174	+	0.955752i
$33$	−4.12797	−	5.86280i	−0.718587	−	1.02058i
$34$	0.884248	−	9.05341i	0.151647	−	1.55265i
$35$	3.56812	+	5.71082i	0.603122	+	0.965305i
$36$	−3.07752	+	5.15062i	−0.512919	+	0.858437i
$37$			6.69746i			1.10106i	0.834817	+	0.550528i	$0.185574\pi$
$37$			6.69746i			1.10106i	−0.834817	+	0.550528i	$0.814426\pi$
$38$	4.02254	+	0.392882i	0.652542	+	0.0637338i
$39$	1.13338	−	6.52701i	0.181485	−	1.04516i
$40$	−6.10150	+	1.66483i	−0.964732	+	0.263232i
$41$	−2.65508			−0.414654			−0.207327	−	0.978272i	$-0.566476\pi$
$41$	−2.65508			−0.414654			−0.207327	+	0.978272i	$0.566476\pi$
$42$	1.96253	−	7.11073i	0.302824	−	1.09721i
$43$	−6.23355			−0.950607			−0.475304	−	0.879822i	$-0.657662\pi$
$43$	−6.23355			−0.950607			−0.475304	+	0.879822i	$0.657662\pi$
$44$	−6.87666	+	4.61104i	−1.03670	+	0.695140i
$45$	−5.64474	−	3.62449i	−0.841468	−	0.540307i
$46$	−0.514093	+	5.26356i	−0.0757989	+	0.776070i
$47$	3.32248	+	3.32248i	0.484634	+	0.484634i	0.906608	−	0.421974i	$-0.138663\pi$
$47$	3.32248	+	3.32248i	0.484634	+	0.484634i	−0.421974	+	0.906608i	$0.638663\pi$
$48$	5.86489	+	3.68823i	0.846524	+	0.532351i
$49$			2.06899i			0.295570i
$50$	−1.64061	−	6.87811i	−0.232017	−	0.972712i
$51$	−6.41388	−	9.10941i	−0.898123	−	1.27557i
$52$	−7.50495	−	1.48014i	−1.04075	−	0.205258i
$53$			3.88396i			0.533503i	0.963765	+	0.266751i	$0.0859503\pi$
$53$			3.88396i			0.533503i	−0.963765	+	0.266751i	$0.914050\pi$
$54$	1.25951	+	7.23973i	0.171397	+	0.985202i
$55$	−4.90494	−	7.85042i	−0.661382	−	1.05855i
$56$	−8.15698	−	2.45267i	−1.09002	−	0.327752i
$57$	4.04742	−	2.84976i	0.536094	−	0.377460i
$58$	−0.164000	+	1.67912i	−0.0215343	+	0.220480i
$59$	−10.3658	+	10.3658i	−1.34951	+	1.34951i	−0.463316	+	0.886193i	$0.653340\pi$
$59$	−10.3658	+	10.3658i	−1.34951	+	1.34951i	−0.886193	+	0.463316i	$0.846660\pi$
$60$	−4.33267	+	6.42090i	−0.559345	+	0.828935i
$61$	3.84345	+	3.84345i	0.492104	+	0.492104i	0.908968	−	0.416865i	$-0.136871\pi$
$61$	3.84345	+	3.84345i	0.492104	+	0.492104i	−0.416865	+	0.908968i	$0.636871\pi$
$62$	−1.24604	−	1.51579i	−0.158248	−	0.192506i
$63$	−3.86069	−	8.16798i	−0.486401	−	1.02907i
$64$	4.41204	−	6.67337i	0.551506	−	0.834171i
$65$	1.92429	−	8.33313i	0.238679	−	1.03360i
$66$	−2.69780	+	9.77481i	−0.332076	+	1.20320i
$67$	10.0836			1.23191			0.615955	−	0.787781i	$-0.288770\pi$
$67$	10.0836			1.23191			0.615955	+	0.787781i	$0.288770\pi$
$68$	−10.6847	+	7.16446i	−1.29571	+	0.868819i
$69$	3.72897	+	5.29612i	0.448915	+	0.637578i
$70$	3.03454	−	9.02671i	0.362696	−	1.07890i
$71$	5.37152			0.637482			0.318741	−	0.947842i	$-0.396740\pi$
$71$	5.37152			0.637482			0.318741	+	0.947842i	$0.396740\pi$
$72$	8.39069	−	1.26345i	0.988852	−	0.148899i
$73$	−2.68667	+	2.68667i	−0.314451	+	0.314451i	−0.846631	−	0.532180i	$-0.821373\pi$
$73$	−2.68667	+	2.68667i	−0.314451	+	0.314451i	0.532180	+	0.846631i	$0.321373\pi$
$74$	7.31679	−	6.01470i	0.850560	−	0.699195i
$75$	−7.01901	−	5.07282i	−0.810486	−	0.585758i
$76$	−3.18325	−	4.74734i	−0.365144	−	0.544557i
$77$		−	12.4668i		−	1.42072i
$78$	−8.14841	+	4.62344i	−0.922625	+	0.523501i
$79$			5.55500i			0.624986i	0.949920	+	0.312493i	$0.101164\pi$
$79$			5.55500i			0.624986i	−0.949920	+	0.312493i	$0.898836\pi$
$80$	7.29827	+	5.17061i	0.815972	+	0.578092i
$81$	6.95426	+	5.71299i	0.772696	+	0.634776i
$82$	2.38441	+	2.90060i	0.263314	+	0.320318i
$83$	−1.35478			−0.148706			−0.0743530	−	0.997232i	$-0.523689\pi$
$83$	−1.35478			−0.148706			−0.0743530	+	0.997232i	$0.523689\pi$
$84$	−9.53073	+	4.24183i	−1.03989	+	0.462822i
$85$	−7.62112	−	12.1977i	−0.826627	−	1.32303i
$86$	5.59808	+	6.80998i	0.603657	+	0.734339i
$87$	1.18957	+	1.68951i	0.127536	+	0.181135i
$88$	11.2131	+	3.37158i	1.19532	+	0.359412i
$89$			5.23963i			0.555400i	0.960668	+	0.277700i	$0.0895721\pi$
$89$			5.23963i			0.555400i	−0.960668	+	0.277700i	$0.910428\pi$
$90$	1.10964	+	9.42171i	0.116966	+	0.993136i
$91$	8.14458	−	8.14458i	0.853784	−	0.853784i
$92$	6.21198	−	4.16534i	0.647643	−	0.434267i
$93$	−2.36777	−	0.411150i	−0.245527	−	0.0426342i
$94$	0.645941	−	6.61349i	0.0666237	−	0.682130i
$95$	5.41958	−	3.38615i	0.556037	−	0.347412i
$96$	−1.23771	−	9.71947i	−0.126323	−	0.991989i
$97$	−6.28272	+	6.28272i	−0.637913	+	0.637913i	−0.950040	−	0.312127i	$-0.898959\pi$
$97$	−6.28272	+	6.28272i	−0.637913	+	0.637913i	0.312127	+	0.950040i	$0.398959\pi$
$98$	2.26031	−	1.85807i	0.228326	−	0.187693i
$99$	5.30713	+	11.2282i	0.533387	+	1.12847i
$100$	−6.04078	+	7.96925i	−0.604078	+	0.796925i
$101$	−11.7523	−	11.7523i	−1.16939	−	1.16939i	−0.982352	−	0.187040i	$-0.940110\pi$
$101$	−11.7523	−	11.7523i	−1.16939	−	1.16939i	−0.187040	−	0.982352i	$-0.559890\pi$
$102$	−4.19174	+	15.1878i	−0.415045	+	1.50381i
$103$	−7.99433	+	7.99433i	−0.787705	+	0.787705i	−0.981117	−	0.193413i	$-0.938044\pi$
$103$	−7.99433	+	7.99433i	−0.787705	+	0.787705i	0.193413	+	0.981117i	$0.438044\pi$
$104$	5.12286	+	9.52820i	0.502338	+	0.934317i
$105$	−4.39678	−	10.8029i	−0.429082	−	1.05426i
$106$	4.24312	−	3.48802i	0.412128	−	0.338786i
$107$	9.47431			0.915916			0.457958	−	0.888974i	$-0.348581\pi$
$107$	9.47431			0.915916			0.457958	+	0.888974i	$0.348581\pi$
$108$	6.77809	−	7.87766i	0.652222	−	0.758028i
$109$	7.26909	−	7.26909i	0.696253	−	0.696253i	−0.267347	−	0.963600i	$-0.586147\pi$
$109$	7.26909	−	7.26909i	0.696253	−	0.696253i	0.963600	+	0.267347i	$0.0861471\pi$
$110$	−4.17145	+	12.4086i	−0.397732	+	1.18312i
$111$	1.98463	−	11.4293i	0.188373	−	1.08482i
$112$	4.64595	+	11.1139i	0.439001	+	1.05017i
$113$	12.9233	−	12.9233i	1.21572	−	1.21572i	0.246601	−	0.969117i	$-0.420686\pi$
$113$	12.9233	−	12.9233i	1.21572	−	1.21572i	0.969117	−	0.246601i	$-0.0793138\pi$
$114$	−6.74809	−	1.86244i	−0.632017	−	0.174434i
$115$	4.43084	+	7.09162i	0.413178	+	0.661297i
$116$	1.98168	−	1.32878i	0.183994	−	0.123374i
$117$	−3.86824	+	10.8026i	−0.357619	+	0.998699i
$118$	20.6334	+	2.01526i	1.89946	+	0.185520i
$119$		−	19.3704i		−	1.77568i
$120$	10.9056	−	1.03302i	0.995544	−	0.0943013i
$121$			6.13752i			0.557956i
$122$	0.747225	−	7.65050i	0.0676506	−	0.692644i
$123$	4.53093	+	0.786770i	0.408541	+	0.0709406i
$124$	−0.536943	+	2.72254i	−0.0482189	+	0.244491i
$125$	−8.68770	−	7.03732i	−0.777052	−	0.629437i
$126$	−5.45617	+	11.5530i	−0.486074	+	1.02922i
$127$	−5.95234	+	5.95234i	−0.528185	+	0.528185i	−0.920031	−	0.391846i	$-0.871837\pi$
$127$	−5.95234	+	5.95234i	−0.528185	+	0.528185i	0.391846	+	0.920031i	$0.371837\pi$
$128$	−11.2527	+	1.17303i	−0.994610	+	0.103682i
$129$	10.6376	+	1.84716i	0.936592	+	0.162634i
$130$	−10.8318	+	5.38138i	−0.950014	+	0.471979i
$131$	6.51499	−	6.51499i	0.569217	−	0.569217i	−0.362692	−	0.931909i	$-0.618142\pi$
$131$	6.51499	−	6.51499i	0.569217	−	0.569217i	0.931909	+	0.362692i	$0.118142\pi$
$132$	13.1015	−	5.83106i	1.14034	−	0.507529i
$133$	8.60649			0.746277
$134$	−9.05566	−	11.0161i	−0.782290	−	0.951644i
$135$	8.55879	+	7.85793i	0.736624	+	0.676303i
$136$	17.4224	+	5.23865i	1.49396	+	0.449210i
$137$	−7.87520	+	7.87520i	−0.672824	+	0.672824i	−0.958366	−	0.285542i	$-0.907826\pi$
$137$	−7.87520	+	7.87520i	−0.672824	+	0.672824i	0.285542	+	0.958366i	$0.407826\pi$
$138$	2.43704	−	8.83000i	0.207454	−	0.751660i
$139$	9.10718	+	9.10718i	0.772461	+	0.772461i	0.978536	−	0.206075i	$-0.0660691\pi$
$139$	9.10718	+	9.10718i	0.772461	+	0.772461i	−0.206075	+	0.978536i	$0.566069\pi$
$140$	−12.5866	+	4.79135i	−1.06376	+	0.404943i
$141$	−4.68533	−	6.65440i	−0.394576	−	0.560402i
$142$	−4.82392	−	5.86823i	−0.404815	−	0.492451i
$143$	−11.1960	+	11.1960i	−0.936257	+	0.936257i
$144$	−8.91560	−	8.03194i	−0.742966	−	0.669329i
$145$	1.41348	+	2.26229i	0.117383	+	0.187873i
$146$	5.34790	+	0.522330i	0.442595	+	0.0432283i
$147$	0.613095	−	3.53076i	0.0505672	−	0.291212i
$148$	−13.1418	−	2.59184i	−1.08025	−	0.213048i
$149$	−4.17118	+	4.17118i	−0.341717	+	0.341717i	−0.857012	−	0.515296i	$-0.827682\pi$
$149$	−4.17118	+	4.17118i	−0.341717	+	0.341717i	0.515296	+	0.857012i	$0.327682\pi$
$150$	0.761563	+	12.2237i	0.0621814	+	0.998065i
$151$			4.13255i			0.336302i	0.985761	+	0.168151i	$0.0537796\pi$
$151$			4.13255i			0.336302i	−0.985761	+	0.168151i	$0.946220\pi$
$152$	−2.32759	+	7.74099i	−0.188793	+	0.627877i
$153$	8.24603	+	17.4459i	0.666652	+	1.41042i
$154$	−13.6196	+	11.1958i	−1.09750	+	0.902187i
$155$	−3.02297	−	0.698067i	−0.242811	−	0.0560701i
$156$	12.3687	+	4.74979i	0.990289	+	0.380288i
$157$	−20.1683			−1.60961			−0.804803	−	0.593542i	$-0.797729\pi$
$157$	−20.1683			−1.60961			−0.804803	+	0.593542i	$0.797729\pi$
$158$	6.06868	−	4.98870i	0.482798	−	0.396880i
$159$	1.15092	−	6.62803i	0.0912738	−	0.525637i
$160$	−0.905517	−	12.6167i	−0.0715874	−	0.997434i
$161$			11.2617i			0.887550i
$162$	−0.00404632	−	12.7279i	−0.000317909	−	1.00000i
$163$		−	5.54371i		−	0.434217i	−0.976147	−	0.217108i	$-0.930337\pi$
$163$		−	5.54371i		−	0.434217i	0.976147	−	0.217108i	$-0.0696625\pi$
$164$	1.02749	−	5.20981i	0.0802333	−	0.406818i
$165$	6.04407	+	14.8503i	0.470530	+	1.15610i
$166$	1.21667	+	1.48005i	0.0944316	+	0.114875i
$167$	−3.75517	+	3.75517i	−0.290584	+	0.290584i	−0.837311	−	0.546727i	$-0.815873\pi$
$167$	−3.75517	+	3.75517i	−0.290584	+	0.290584i	0.546727	+	0.837311i	$0.315873\pi$
$168$	13.1932	+	6.60264i	1.01788	+	0.509405i
$169$	−1.62879			−0.125291
$170$	−6.48145	+	19.2801i	−0.497104	+	1.47872i
$171$	−7.75143	+	3.66381i	−0.592767	+	0.280178i
$172$	2.41231	−	12.2315i	0.183937	−	0.932642i
$173$	4.82930			0.367165			0.183582	−	0.983004i	$-0.441231\pi$
$173$	4.82930			0.367165			0.183582	+	0.983004i	$0.441231\pi$
$174$	0.777437	−	2.81685i	0.0589374	−	0.213545i
$175$	−4.90078	−	14.2375i	−0.370464	−	1.07626i
$176$	−6.38660	−	15.2778i	−0.481408	−	1.15161i
$177$	20.7610	−	14.6177i	1.56049	−	1.09873i
$178$	5.72415	−	4.70548i	0.429043	−	0.352691i
$179$	−11.2085	−	11.2085i	−0.837761	−	0.837761i	0.150803	−	0.988564i	$-0.451814\pi$
$179$	−11.2085	−	11.2085i	−0.837761	−	0.837761i	−0.988564	+	0.150803i	$0.951814\pi$
$180$	9.29644	−	9.67348i	0.692916	−	0.721019i
$181$	17.3401	−	17.3401i	1.28888	−	1.28888i	0.353411	−	0.935468i	$-0.385022\pi$
$181$	17.3401	−	17.3401i	1.28888	−	1.28888i	0.935468	−	0.353411i	$-0.114978\pi$
$182$	−16.2120	−	1.58343i	−1.20171	−	0.117372i
$183$	−5.41999	−	7.69782i	−0.400657	−	0.569039i
$184$	−10.1292	−	3.04569i	−0.746737	−	0.224532i
$185$	3.36959	−	14.5920i	0.247737	−	1.07282i
$186$	1.67722	+	2.95596i	0.122980	+	0.216742i
$187$			26.6277i			1.94721i
$188$	−7.80515	+	5.23362i	−0.569249	+	0.381701i
$189$	4.16794	+	15.0828i	0.303173	+	1.09711i
$190$	−8.56637	−	2.87978i	−0.621470	−	0.208921i
$191$			5.45453i			0.394676i	0.980336	+	0.197338i	$0.0632296\pi$
$191$			5.45453i			0.394676i	−0.980336	+	0.197338i	$0.936770\pi$
$192$	−9.50671	+	10.0808i	−0.686088	+	0.727519i
$193$	−6.53795	−	6.53795i	−0.470612	−	0.470612i	0.431501	−	0.902113i	$-0.357984\pi$
$193$	−6.53795	−	6.53795i	−0.470612	−	0.470612i	−0.902113	+	0.431501i	$0.857984\pi$
$194$	12.5059	+	1.22146i	0.897873	+	0.0876954i
$195$	−5.75316	+	13.6504i	−0.411992	+	0.977524i
$196$	−4.05977	−	0.800675i	−0.289984	−	0.0571911i
$197$	6.76577			0.482041			0.241021	−	0.970520i	$-0.422518\pi$
$197$	6.76577			0.482041			0.241021	+	0.970520i	$0.422518\pi$
$198$	7.50037	−	15.8814i	0.533028	−	1.12864i
$199$	2.72711			0.193319			0.0966597	−	0.995317i	$-0.469184\pi$
$199$	2.72711			0.193319			0.0966597	+	0.995317i	$0.469184\pi$
$200$	14.1311	−	0.557459i	0.999223	−	0.0394183i
$201$	−17.2078	−	2.98804i	−1.21375	−	0.210760i
$202$	−2.28482	+	23.3932i	−0.160759	+	1.64594i
$203$			3.59260i			0.252151i
$204$	20.3566	−	9.06010i	1.42525	−	0.634334i
$205$	5.78471	+	1.33581i	0.404022	+	0.0932971i
$206$	15.9129	+	1.55422i	1.10871	+	0.108288i
$207$	−4.79416	−	10.1429i	−0.333217	−	0.704980i
$208$	5.80867	−	14.1534i	0.402759	−	0.981365i
$209$	−11.8310			−0.818366
$210$	−7.85333	+	14.5050i	−0.541931	+	1.00094i
$211$	−1.60522	−	1.60522i	−0.110508	−	0.110508i	0.649691	−	0.760198i	$-0.274898\pi$
$211$	−1.60522	−	1.60522i	−0.110508	−	0.110508i	−0.760198	+	0.649691i	$0.774898\pi$
$212$	−7.62112	−	1.50305i	−0.523420	−	0.103230i
$213$	−9.16657	−	1.59172i	−0.628083	−	0.109063i
$214$	−8.50847	−	10.3504i	−0.581627	−	0.707540i
$215$	13.5812	+	3.13619i	0.926233	+	0.213886i
$216$	−14.6932	−	0.330286i	−0.999747	−	0.0224731i
$217$	−2.95457	−	2.95457i	−0.200569	−	0.200569i
$218$	−14.4693	−	1.41322i	−0.979987	−	0.0957155i
$219$	5.38098	−	3.78871i	0.363613	−	0.256018i
$220$	17.3023	−	6.58647i	1.16652	−	0.444059i
$221$	−17.3960	+	17.3960i	−1.17018	+	1.17018i
$222$	−14.2685	+	8.09602i	−0.957640	+	0.543369i
$223$	6.16926	+	6.16926i	0.413124	+	0.413124i	0.882825	−	0.469701i	$-0.155638\pi$
$223$	6.16926	+	6.16926i	0.413124	+	0.413124i	−0.469701	+	0.882825i	$0.655638\pi$
$224$	7.96930	−	15.0565i	0.532471	−	1.00600i
$225$	10.4748	+	10.7367i	0.698323	+	0.715783i
$226$	−25.7241	−	2.51248i	−1.71114	−	0.167128i
$227$			15.9373i			1.05779i	0.848686	+	0.528897i	$0.177394\pi$
$227$			15.9373i			1.05779i	−0.848686	+	0.528897i	$0.822606\pi$
$228$	4.02551	+	9.04468i	0.266596	+	0.598999i
$229$	−18.0573	−	18.0573i	−1.19326	−	1.19326i	−0.976146	−	0.217115i	$-0.930335\pi$
$229$	−18.0573	−	18.0573i	−1.19326	−	1.19326i	−0.217115	−	0.976146i	$-0.569665\pi$
$230$	3.76825	−	11.2092i	0.248471	−	0.739116i
$231$	−3.69422	+	21.2747i	−0.243062	+	1.39977i
$232$	−3.23132	−	0.971604i	−0.212146	−	0.0637890i
$233$	2.38354	+	2.38354i	0.156151	+	0.156151i	0.780859	−	0.624708i	$-0.214782\pi$
$233$	2.38354	+	2.38354i	0.156151	+	0.156151i	−0.624708	+	0.780859i	$0.714782\pi$
$234$	15.2754	−	5.47538i	0.998585	−	0.357937i
$235$	−5.56721	−	8.91039i	−0.363165	−	0.581250i
$236$	−16.3283	−	24.3512i	−1.06288	−	1.58513i
$237$	1.64609	−	9.47968i	0.106925	−	0.615771i
$238$	−21.1616	+	17.3957i	−1.37170	+	1.12760i
$239$	4.65924			0.301381			0.150691	−	0.988581i	$-0.451850\pi$
$239$	4.65924			0.301381			0.150691	+	0.988581i	$0.451850\pi$
$240$	−10.9224	−	10.9864i	−0.705039	−	0.709168i
$241$	−21.7499			−1.40104			−0.700518	−	0.713635i	$-0.747048\pi$
$241$	−21.7499			−1.40104			−0.700518	+	0.713635i	$0.747048\pi$
$242$	6.70506	−	5.51184i	0.431018	−	0.354314i
$243$	−10.1746	−	11.8100i	−0.652704	−	0.757613i
$244$	−9.02900	+	6.05426i	−0.578023	+	0.387584i
$245$	1.04094	−	4.50777i	0.0665031	−	0.287991i
$246$	−3.20951	−	5.65648i	−0.204631	−	0.360644i
$247$	−7.72922	−	7.72922i	−0.491799	−	0.491799i
$248$	3.45650	−	1.85840i	0.219488	−	0.118008i
$249$	2.31194	+	0.401456i	0.146514	+	0.0254412i
$250$	0.113974	+	15.8110i	0.00720837	+	0.999974i
$251$	3.41489	+	3.41489i	0.215546	+	0.215546i	0.806618	−	0.591073i	$-0.201295\pi$
$251$	3.41489	+	3.41489i	0.215546	+	0.215546i	−0.591073	+	0.806618i	$0.701295\pi$
$252$	17.5213	−	4.41454i	1.10374	−	0.278090i
$253$		−	15.4810i		−	0.973285i
$254$	11.8483	+	1.15723i	0.743428	+	0.0726108i
$255$	9.39106	+	23.0739i	0.588091	+	1.44494i
$256$	11.3871	+	11.2398i	0.711693	+	0.702490i
$257$	−10.2183	−	10.2183i	−0.637399	−	0.637399i	0.312514	−	0.949913i	$-0.398829\pi$
$257$	−10.2183	−	10.2183i	−0.637399	−	0.637399i	−0.949913	+	0.312514i	$0.898829\pi$
$258$	−7.53523	−	13.2802i	−0.469123	−	0.826788i
$259$	14.2618	−	14.2618i	0.886186	−	0.886186i
$260$	15.6066	+	7.00068i	0.967881	+	0.434164i
$261$	−1.52938	−	3.23568i	−0.0946662	−	0.200283i
$262$	−12.9683	−	1.26661i	−0.801182	−	0.0782516i
$263$	10.1554	+	10.1554i	0.626208	+	0.626208i	0.947112	−	0.320904i	$-0.103987\pi$
$263$	10.1554	+	10.1554i	0.626208	+	0.626208i	−0.320904	+	0.947112i	$0.603987\pi$
$264$	−18.1361	−	9.07638i	−1.11620	−	0.558612i
$265$	1.95408	−	8.46211i	0.120038	−	0.519823i
$266$	−7.72911	−	9.40235i	−0.473902	−	0.576495i
$267$	1.55264	−	8.94150i	0.0950200	−	0.547211i
$268$	−3.90225	+	19.7861i	−0.238368	+	1.20863i
$269$	13.4591	+	13.4591i	0.820618	+	0.820618i	0.986197	−	0.165579i	$-0.0529492\pi$
$269$	13.4591	+	13.4591i	0.820618	+	0.820618i	−0.165579	+	0.986197i	$0.552949\pi$
$270$	0.898285	−	16.4071i	0.0546679	−	0.998505i
$271$	−2.61645			−0.158938			−0.0794689	−	0.996837i	$-0.525322\pi$
$271$	−2.61645			−0.158938			−0.0794689	+	0.996837i	$0.525322\pi$
$272$	−9.92326	−	23.7381i	−0.601686	−	1.43934i
$273$	−16.3123	+	11.4854i	−0.987265	+	0.695127i
$274$	15.6758	+	1.53106i	0.947011	+	0.0924947i
$275$	6.73689	+	19.5717i	0.406250	+	1.18022i
$276$	−11.8351	+	5.26745i	−0.712391	+	0.317063i
$277$		−	12.0608i		−	0.724664i	−0.932049	−	0.362332i	$-0.881981\pi$
$277$		−	12.0608i		−	0.724664i	0.932049	−	0.362332i	$-0.118019\pi$
$278$	1.77057	−	18.1281i	0.106192	−	1.08725i
$279$	3.91880	+	1.40327i	0.234613	+	0.0840113i
$280$	16.5379	+	9.44761i	0.988329	+	0.564603i
$281$	−2.60207			−0.155227			−0.0776134	−	0.996984i	$-0.524730\pi$
$281$	−2.60207			−0.155227			−0.0776134	+	0.996984i	$0.524730\pi$
$282$	−3.06206	+	11.0946i	−0.182343	+	0.660675i
$283$	−7.11274			−0.422809			−0.211404	−	0.977399i	$-0.567804\pi$
$283$	−7.11274			−0.422809			−0.211404	+	0.977399i	$0.567804\pi$
$284$	−2.07872	+	10.5400i	−0.123349	+	0.625434i
$285$	−10.2520	+	4.17256i	−0.607276	+	0.247161i
$286$	22.2860	+	2.17667i	1.31780	+	0.128709i
$287$	5.65382	+	5.65382i	0.333735	+	0.333735i
$288$	−0.767961	+	16.9532i	−0.0452525	+	0.998976i
$289$			24.3731i			1.43371i
$290$	1.20211	−	3.57585i	0.0705900	−	0.209981i
$291$	12.5833	−	8.85982i	0.737645	−	0.519372i
$292$	−4.23208	−	6.31151i	−0.247664	−	0.369353i
$293$			4.42114i			0.258286i	0.991626	+	0.129143i	$0.0412226\pi$
$293$			4.42114i			0.258286i	−0.991626	+	0.129143i	$0.958777\pi$
$294$	−4.40785	+	2.50103i	−0.257071	+	0.145863i
$295$	27.7994	−	17.3691i	1.61855	−	1.01127i
$296$	8.97055	+	16.6846i	0.521402	+	0.969776i
$297$	−5.72949	−	20.7337i	−0.332459	−	1.20309i
$298$	8.30286	+	0.810941i	0.480972	+	0.0469766i
$299$	10.1138	−	10.1138i	0.584898	−	0.584898i
$300$	12.6702	−	11.8096i	0.731513	−	0.681828i
$301$	13.2739	+	13.2739i	0.765097	+	0.765097i
$302$	4.51469	−	3.71126i	0.259791	−	0.213559i
$303$	16.5729	+	23.5379i	0.952087	+	1.35222i
$304$	10.5471	−	4.40902i	0.604919	−	0.252875i
$305$	−6.44016	−	10.3076i	−0.368762	−	0.590209i
$306$	11.6538	−	24.6760i	0.666203	−	1.41063i
$307$	29.9499			1.70933			0.854665	−	0.519179i	$-0.173762\pi$
$307$	29.9499			1.70933			0.854665	+	0.519179i	$0.173762\pi$
$308$	24.4623	+	4.82450i	1.39387	+	0.274901i
$309$	16.0114	−	11.2735i	0.910855	−	0.641327i
$310$	1.95218	+	3.92941i	0.110876	+	0.223176i
$311$	4.45934			0.252866			0.126433	−	0.991975i	$-0.459647\pi$
$311$	4.45934			0.252866			0.126433	+	0.991975i	$0.459647\pi$
$312$	−5.91878	−	17.7780i	−0.335085	−	1.00648i
$313$	10.2148	−	10.2148i	0.577374	−	0.577374i	−0.356805	−	0.934179i	$-0.616134\pi$
$313$	10.2148	−	10.2148i	0.577374	−	0.577374i	0.934179	+	0.356805i	$0.116134\pi$
$314$	18.1123	+	22.0333i	1.02214	+	1.24341i
$315$	4.30198	+	19.7382i	0.242389	+	1.11212i
$316$	−10.9000	−	2.14972i	−0.613175	−	0.120931i
$317$			12.3959i			0.696222i	0.937453	+	0.348111i	$0.113177\pi$
$317$			12.3959i			0.696222i	−0.937453	+	0.348111i	$0.886823\pi$
$318$	−8.27453	+	4.69500i	−0.464013	+	0.263283i
$319$		−	4.93860i		−	0.276508i
$320$	−12.9701	+	12.3197i	−0.725053	+	0.688693i
$321$	−16.1680	−	2.80749i	−0.902412	−	0.156699i
$322$	12.3031	−	10.1137i	0.685627	−	0.563614i
$323$	−18.3825			−1.02283
$324$	−13.9013	+	11.4348i	−0.772292	+	0.635267i
$325$	−8.38504	+	17.1875i	−0.465118	+	0.953392i
$326$	−6.05635	+	4.97856i	−0.335430	+	0.275737i
$327$	−14.5588	+	10.2508i	−0.805105	+	0.566870i
$328$	−6.61431	+	3.55620i	−0.365214	+	0.196358i
$329$		−	14.1500i		−	0.780116i
$330$	10.7956	−	19.9394i	0.594280	−	1.09763i
$331$	−3.32345	+	3.32345i	−0.182673	+	0.182673i	−0.792520	−	0.609846i	$-0.791231\pi$
$331$	−3.32345	+	3.32345i	−0.182673	+	0.182673i	0.609846	+	0.792520i	$0.291231\pi$
$332$	0.524283	−	2.65835i	0.0287738	−	0.145896i
$333$	−6.77361	+	18.9162i	−0.371192	+	1.03660i
$334$	7.47477	+	0.730061i	0.409001	+	0.0399472i
$335$	−21.9695	−	5.07322i	−1.20032	−	0.277180i
$336$	−4.63505	−	20.3428i	−0.252863	−	1.10979i
$337$	23.8025	−	23.8025i	1.29660	−	1.29660i	0.365980	−	0.930623i	$-0.380734\pi$
$337$	23.8025	−	23.8025i	1.29660	−	1.29660i	0.930623	−	0.365980i	$-0.119266\pi$
$338$	1.46274	+	1.77940i	0.0795627	+	0.0967868i
$339$	−25.8832	+	18.2242i	−1.40578	+	0.989804i
$340$	26.8837	−	10.2338i	1.45797	−	0.555006i
$341$	4.06152	+	4.06152i	0.219944	+	0.219944i
$342$	10.9638	+	5.17792i	0.592856	+	0.279990i
$343$	−10.5003	+	10.5003i	−0.566961	+	0.566961i
$344$	−15.5290	+	8.34918i	−0.837265	+	0.450158i
$345$	−5.45986	−	13.4149i	−0.293949	−	0.722235i
$346$	−4.33698	−	5.27587i	−0.233158	−	0.283633i
$347$	−0.669706			−0.0359517			−0.0179758	−	0.999838i	$-0.505722\pi$
$347$	−0.669706			−0.0359517			−0.0179758	+	0.999838i	$0.505722\pi$
$348$	−3.77551	+	1.68036i	−0.202389	+	0.0900770i
$349$	−7.86448	+	7.86448i	−0.420976	+	0.420976i	−0.885540	−	0.464564i	$-0.846211\pi$
$349$	−7.86448	+	7.86448i	−0.420976	+	0.420976i	0.464564	+	0.885540i	$0.346211\pi$
$350$	−11.1529	+	18.1401i	−0.596148	+	0.969627i
$351$	9.80230	−	17.2885i	0.523208	−	0.922792i
$352$	−10.9551	+	20.6975i	−0.583907	+	1.10318i
$353$	−6.77427	+	6.77427i	−0.360558	+	0.360558i	−0.864018	−	0.503460i	$-0.832060\pi$
$353$	−6.77427	+	6.77427i	−0.360558	+	0.360558i	0.503460	+	0.864018i	$0.332060\pi$
$354$	−34.6140	−	9.55328i	−1.83971	−	0.507751i
$355$	−11.7031	−	2.70249i	−0.621136	−	0.143433i
$356$	−10.2812	−	2.02768i	−0.544903	−	0.107467i
$357$	−5.73995	+	33.0559i	−0.303791	+	1.74950i
$358$	−2.17910	+	22.3108i	−0.115169	+	1.17916i
$359$			13.6099i			0.718301i	0.933280	+	0.359151i	$0.116934\pi$
$359$			13.6099i			0.718301i	−0.933280	+	0.359151i	$0.883066\pi$
$360$	−18.9167	−	1.46876i	−0.996999	−	0.0774106i
$361$			10.8324i			0.570127i
$362$	−34.5159	−	3.37118i	−1.81412	−	0.177185i
$363$	1.81871	−	10.4738i	0.0954573	−	0.549730i
$364$	12.8295	+	19.1332i	0.672446	+	1.00285i
$365$	7.20524	−	4.50184i	0.377140	−	0.235637i
$366$	−3.54219	+	12.8343i	−0.185153	+	0.670858i
$367$	−25.1103	+	25.1103i	−1.31075	+	1.31075i	−0.389886	+	0.920863i	$0.627486\pi$
$367$	−25.1103	+	25.1103i	−1.31075	+	1.31075i	−0.920863	+	0.389886i	$0.872514\pi$
$368$	5.76928	+	13.8011i	0.300745	+	0.719432i
$369$	−7.49896	−	2.68527i	−0.390380	−	0.139789i
$370$	−18.9674	+	9.42324i	−0.986069	+	0.489891i
$371$	8.27064	−	8.27064i	0.429390	−	0.429390i
$372$	1.72306	−	4.48694i	0.0893365	−	0.232637i
$373$	24.1055			1.24814			0.624068	−	0.781370i	$-0.285479\pi$
$373$	24.1055			1.24814			0.624068	+	0.781370i	$0.285479\pi$
$374$	29.0900	−	23.9131i	1.50421	−	1.23652i
$375$	12.7403	+	14.5837i	0.657909	+	0.753098i
$376$	12.7270	+	3.82682i	0.656347	+	0.197353i
$377$	3.22640	−	3.22640i	0.166168	−	0.166168i
$378$	12.7345	−	18.0986i	0.654992	−	0.930890i
$379$	−13.7770	−	13.7770i	−0.707677	−	0.707677i	0.258369	−	0.966046i	$-0.416815\pi$
$379$	−13.7770	−	13.7770i	−0.707677	−	0.707677i	−0.966046	+	0.258369i	$0.916815\pi$
$380$	4.54700	+	11.9447i	0.233256	+	0.612751i
$381$	11.9216	−	8.39392i	0.610761	−	0.430033i
$382$	5.95892	−	4.89847i	0.304885	−	0.250628i
$383$	24.2856	−	24.2856i	1.24093	−	1.24093i	0.281319	−	0.959614i	$-0.409228\pi$
$383$	24.2856	−	24.2856i	1.24093	−	1.24093i	0.959614	−	0.281319i	$-0.0907721\pi$
$384$	19.5505	+	1.33269i	0.997685	+	0.0680084i
$385$	−6.27221	+	27.1617i	−0.319661	+	1.38429i
$386$	−1.27108	+	13.0140i	−0.0646961	+	0.662394i
$387$	−17.6059	−	6.30442i	−0.894959	−	0.320472i
$388$	−9.89663	−	14.7593i	−0.502425	−	0.749290i
$389$	4.67054	−	4.67054i	0.236806	−	0.236806i	−0.578720	−	0.815526i	$-0.696448\pi$
$389$	4.67054	−	4.67054i	0.236806	−	0.236806i	0.815526	+	0.578720i	$0.196448\pi$
$390$	20.0793	−	5.97366i	1.01676	−	0.302488i
$391$		−	24.0539i		−	1.21646i
$392$	2.77119	+	5.15424i	0.139966	+	0.260328i
$393$	−13.0485	+	9.18736i	−0.658209	+	0.463441i
$394$	−6.07605	−	7.39142i	−0.306107	−	0.372374i
$395$	2.79480	−	12.1029i	0.140622	−	0.608961i
$396$	−24.0858	+	6.06848i	−1.21036	+	0.304953i
$397$	26.1442			1.31214			0.656071	−	0.754699i	$-0.272217\pi$
$397$	26.1442			1.31214			0.656071	+	0.754699i	$0.272217\pi$
$398$	−2.44910	−	2.97929i	−0.122762	−	0.149338i
$399$	−14.6871	−	2.55033i	−0.735275	−	0.127676i
$400$	−13.2996	−	14.9372i	−0.664979	−	0.746862i
$401$			18.1955i			0.908642i	0.890838	+	0.454321i	$0.150118\pi$
$401$			18.1955i			0.908642i	−0.890838	+	0.454321i	$0.849882\pi$
$402$	12.1893	+	21.4825i	0.607945	+	1.07145i
$403$			5.30682i			0.264351i
$404$	27.6083	−	18.5123i	1.37356	−	0.921022i
$405$	−12.2772	−	15.9459i	−0.610059	−	0.792356i
$406$	3.92481	−	3.22636i	0.194785	−	0.160121i
$407$	−19.6051	+	19.6051i	−0.971789	+	0.971789i
$408$	−28.1793	−	14.1025i	−1.39508	−	0.698180i
$409$	24.5643			1.21463			0.607314	−	0.794462i	$-0.292247\pi$
$409$	24.5643			1.21463			0.607314	+	0.794462i	$0.292247\pi$
$410$	−3.73566	−	7.51927i	−0.184491	−	0.371350i
$411$	15.7728	−	11.1055i	0.778014	−	0.547795i
$412$	−12.5928	−	18.7802i	−0.620402	−	0.925235i
$413$	44.1465			2.17231
$414$	−6.77540	+	14.3464i	−0.332993	+	0.705086i
$415$	2.95169	+	0.681608i	0.144893	+	0.0334588i
$416$	−20.6787	+	6.36479i	−1.01386	+	0.312059i
$417$	−12.8428	−	18.2402i	−0.628917	−	0.893228i
$418$	10.6249	+	12.9250i	0.519680	+	0.632183i
$419$	−10.9549	−	10.9549i	−0.535182	−	0.535182i	0.386928	−	0.922110i	$-0.373536\pi$
$419$	−10.9549	−	10.9549i	−0.535182	−	0.535182i	−0.922110	+	0.386928i	$0.873536\pi$
$420$	22.8990	−	4.44677i	1.11736	−	0.216980i
$421$	−8.82488	+	8.82488i	−0.430098	+	0.430098i	−0.888662	−	0.458564i	$-0.848364\pi$
$421$	−8.82488	+	8.82488i	−0.430098	+	0.430098i	0.458564	+	0.888662i	$0.348364\pi$
$422$	−0.312078	+	3.19523i	−0.0151917	+	0.155541i
$423$	6.02370	+	12.7442i	0.292882	+	0.619645i
$424$	5.20216	+	9.67568i	0.252639	+	0.469892i
$425$	10.4675	+	30.4098i	0.507750	+	1.47509i
$426$	6.49319	+	11.4437i	0.314596	+	0.554448i
$427$		−	16.3688i		−	0.792140i
$428$	−3.66645	+	18.5905i	−0.177225	+	0.898607i
$429$	22.4238	−	15.7885i	1.08263	−	0.762275i
$430$	−8.77052	−	17.6536i	−0.422952	−	0.851332i
$431$			0.399838i			0.0192595i	0.999954	+	0.00962976i	$0.00306530\pi$
$431$			0.399838i			0.0192595i	−0.999954	+	0.00962976i	$0.996935\pi$
$432$	12.8345	+	16.3486i	0.617501	+	0.786570i
$433$	−2.81479	−	2.81479i	−0.135270	−	0.135270i	0.636230	−	0.771500i	$-0.280493\pi$
$433$	−2.81479	−	2.81479i	−0.135270	−	0.135270i	−0.771500	+	0.636230i	$0.780493\pi$
$434$	−0.574414	+	5.88116i	−0.0275727	+	0.282305i
$435$	−1.74175	−	4.27948i	−0.0835104	−	0.205186i
$436$	11.4504	+	17.0765i	0.548374	+	0.817816i
$437$	10.6874			0.511249
$438$	−8.97148	−	2.47608i	−0.428674	−	0.118312i
$439$	4.64758			0.221817			0.110909	−	0.993831i	$-0.464624\pi$
$439$	4.64758			0.221817			0.110909	+	0.993831i	$0.464624\pi$
$440$	−22.7340	−	12.9872i	−1.08380	−	0.619142i
$441$	−2.09251	+	5.84361i	−0.0996434	+	0.278267i
$442$	34.6271	+	3.38204i	1.64704	+	0.160867i
$443$		−	33.7852i		−	1.60518i	−0.596529	−	0.802591i	$-0.703454\pi$
$443$		−	33.7852i		−	1.60518i	0.596529	−	0.802591i	$-0.296546\pi$
$444$	21.6586	+	8.31727i	1.02787	+	0.394720i
$445$	2.63614	−	11.4158i	0.124965	−	0.541159i
$446$	1.19940	−	12.2801i	0.0567931	−	0.581479i
$447$	8.35421	−	5.88215i	0.395141	−	0.278216i
$448$	−23.6057	+	4.81535i	−1.11526	+	0.227504i
$449$	9.64441			0.455148			0.227574	−	0.973761i	$-0.426921\pi$
$449$	9.64441			0.455148			0.227574	+	0.973761i	$0.426921\pi$
$450$	2.32260	−	21.0857i	0.109488	−	0.993988i
$451$	−7.77207	−	7.77207i	−0.365973	−	0.365973i
$452$	20.3569	+	30.3592i	0.957508	+	1.42798i
$453$	1.22458	−	7.05225i	0.0575358	−	0.331344i
$454$	17.4110	−	14.3126i	0.817139	−	0.671722i
$455$	−21.8425	+	13.6472i	−1.02399	+	0.639791i
$456$	6.26592	−	12.5204i	0.293429	−	0.586321i
$457$	−12.1950	−	12.1950i	−0.570460	−	0.570460i	0.361797	−	0.932257i	$-0.382163\pi$
$457$	−12.1950	−	12.1950i	−0.570460	−	0.570460i	−0.932257	+	0.361797i	$0.882163\pi$
$458$	−3.51062	+	35.9436i	−0.164040	+	1.67953i
$459$	−8.90228	−	32.2153i	−0.415523	−	1.50368i
$460$	−15.6299	+	5.94983i	−0.728747	+	0.277412i
$461$	3.33005	−	3.33005i	0.155096	−	0.155096i	−0.625294	−	0.780390i	$-0.715021\pi$
$461$	3.33005	−	3.33005i	0.155096	−	0.155096i	0.780390	+	0.625294i	$0.215021\pi$
$462$	26.5596	−	15.0700i	1.23567	−	0.701122i
$463$	3.26673	+	3.26673i	0.151818	+	0.151818i	0.778929	−	0.627112i	$-0.215763\pi$
$463$	3.26673	+	3.26673i	0.151818	+	0.151818i	−0.627112	+	0.778929i	$0.715763\pi$
$464$	1.84045	+	4.40268i	0.0854409	+	0.204389i
$465$	4.95189	+	2.08705i	0.229638	+	0.0967845i
$466$	0.463396	−	4.74450i	0.0214664	−	0.219785i
$467$		−	33.0741i		−	1.53048i	−0.643742	−	0.765242i	$-0.722619\pi$
$467$		−	33.0741i		−	1.53048i	0.643742	−	0.765242i	$-0.277381\pi$
$468$	−19.6999	−	11.7708i	−0.910628	−	0.544104i
$469$	−21.4724	−	21.4724i	−0.991504	−	0.991504i
$470$	−4.73468	+	14.0841i	−0.218394	+	0.649649i
$471$	34.4175	+	5.97640i	1.58587	+	0.275378i
$472$	−11.9392	+	39.7070i	−0.549548	+	1.82766i
$473$	−18.2471	−	18.2471i	−0.839004	−	0.839004i
$474$	−11.8346	+	6.71498i	−0.543580	+	0.308429i
$475$	−13.5114	+	4.65085i	−0.619947	+	0.213396i
$476$	38.0086	+	7.49613i	1.74212	+	0.343584i
$477$	−3.92812	+	10.9698i	−0.179856	+	0.502272i
$478$	−4.18426	−	5.09009i	−0.191384	−	0.232815i
$479$	−27.6867			−1.26504			−0.632518	−	0.774546i	$-0.717979\pi$
$479$	−27.6867			−1.26504			−0.632518	+	0.774546i	$0.717979\pi$
$480$	−2.19337	+	21.7988i	−0.100113	+	0.994976i
$481$	−25.6162			−1.16800
$482$	19.5327	+	23.7612i	0.889688	+	1.08229i
$483$	3.33715	−	19.2183i	0.151846	−	0.874464i
$484$	−12.0431	−	2.37515i	−0.547412	−	0.107961i
$485$	16.8493	−	10.5274i	0.765087	−	0.478026i
$486$	−3.76471	+	21.7216i	−0.170771	+	0.985311i
$487$	−28.8225	−	28.8225i	−1.30607	−	1.30607i	−0.924227	−	0.381843i	$-0.875289\pi$
$487$	−28.8225	−	28.8225i	−1.30607	−	1.30607i	−0.381843	−	0.924227i	$-0.624711\pi$
$488$	14.7227	+	4.42687i	0.666464	+	0.200395i
$489$	−1.64275	+	9.46042i	−0.0742875	+	0.427815i
$490$	−5.85943	+	2.91104i	−0.264702	+	0.131507i
$491$	−2.93822	−	2.93822i	−0.132600	−	0.132600i	0.637692	−	0.770292i	$-0.279889\pi$
$491$	−2.93822	−	2.93822i	−0.132600	−	0.132600i	−0.770292	+	0.637692i	$0.779889\pi$
$492$	−3.29722	+	8.58614i	−0.148650	+	0.387093i
$493$		−	7.67341i		−	0.345593i
$494$	−1.50268	+	15.3852i	−0.0676087	+	0.692214i
$495$	−5.91375	−	27.1333i	−0.265803	−	1.21955i
$496$	−5.13438	−	2.10718i	−0.230540	−	0.0946154i
$497$	−11.4383	−	11.4383i	−0.513078	−	0.513078i
$498$	−1.63768	−	2.88626i	−0.0733861	−	0.129337i
$499$	−4.06607	+	4.06607i	−0.182022	+	0.182022i	−0.792237	−	0.610214i	$-0.791083\pi$
$499$	−4.06607	+	4.06607i	−0.182022	+	0.182022i	0.610214	+	0.792237i	$0.291083\pi$
$500$	17.1707	−	14.3237i	0.767897	−	0.640574i
$501$	7.52100	−	5.29549i	0.336013	−	0.236585i
$502$	0.663906	−	6.79743i	0.0296316	−	0.303384i
$503$	−15.4387	−	15.4387i	−0.688376	−	0.688376i	0.273497	−	0.961873i	$-0.411820\pi$
$503$	−15.4387	−	15.4387i	−0.688376	−	0.688376i	−0.961873	+	0.273497i	$0.911820\pi$
$504$	−20.5579	−	15.1770i	−0.915720	−	0.676037i
$505$	19.6923	+	31.5177i	0.876295	+	1.40252i
$506$	−16.9126	+	13.9029i	−0.751857	+	0.618057i
$507$	2.77955	+	0.482652i	0.123444	+	0.0214353i
$508$	−9.37621	−	13.9832i	−0.416002	−	0.620403i
$509$	−11.3533	−	11.3533i	−0.503227	−	0.503227i	0.409212	−	0.912439i	$-0.365804\pi$
$509$	−11.3533	−	11.3533i	−0.503227	−	0.503227i	−0.912439	+	0.409212i	$0.865804\pi$
$510$	16.7739	−	30.9811i	0.742760	−	1.37187i
$511$	11.4422			0.506173
$512$	2.05296	−	22.5341i	0.0907290	−	0.995876i
$513$	14.3136	−	3.95538i	0.631961	−	0.174634i
$514$	−1.98659	+	20.3398i	−0.0876246	+	0.897149i
$515$	21.4396	−	13.3954i	0.944740	−	0.590274i
$516$	−7.74116	+	20.1584i	−0.340786	+	0.887423i
$517$			19.4514i			0.855473i
$518$	−28.3885	−	2.77271i	−1.24732	−	0.121826i
$519$	−8.24126	−	1.43105i	−0.361751	−	0.0628160i
$520$	−6.36757	−	23.3368i	−0.279236	−	1.02339i
$521$	20.3718			0.892506			0.446253	−	0.894907i	$-0.352758\pi$
$521$	20.3718			0.892506			0.446253	+	0.894907i	$0.352758\pi$
$522$	−2.16141	+	4.57662i	−0.0946025	+	0.200313i
$523$	41.7664			1.82632			0.913159	−	0.407604i	$-0.133636\pi$
$523$	41.7664			1.82632			0.913159	+	0.407604i	$0.133636\pi$
$524$	10.2625	+	15.3050i	0.448319	+	0.668600i
$525$	4.14430	+	25.7488i	0.180872	+	1.12377i
$526$	1.97436	−	20.2146i	0.0860863	−	0.881398i
$527$	6.31065	+	6.31065i	0.274896	+	0.274896i
$528$	6.37160	+	27.9643i	0.277288	+	1.21699i
$529$		−	9.01531i		−	0.391970i
$530$	−10.9995	+	5.46468i	−0.477787	+	0.237370i
$531$	−39.7605	+	18.7933i	−1.72546	+	0.815559i
$532$	−3.33062	+	16.8877i	−0.144401	+	0.732174i
$533$		−	10.1550i		−	0.439864i
$534$	−11.1627	+	6.33376i	−0.483057	+	0.274089i
$535$	−20.6420	−	4.76667i	−0.892431	−	0.206081i
$536$	25.1202	−	13.5059i	1.08503	−	0.583368i
$537$	15.8061	+	22.4488i	0.682082	+	0.968737i
$538$	2.61666	−	26.7908i	0.112812	−	1.15503i
$539$	−6.05643	+	6.05643i	−0.260869	+	0.260869i
$540$	−18.7310	+	13.7532i	−0.806054	+	0.591842i
$541$	−20.4942	−	20.4942i	−0.881113	−	0.881113i	0.112535	−	0.993648i	$-0.464103\pi$
$541$	−20.4942	−	20.4942i	−0.881113	−	0.881113i	−0.993648	+	0.112535i	$0.964103\pi$
$542$	2.34972	+	2.85839i	0.100929	+	0.122778i
$543$	−34.7294	+	24.4528i	−1.49038	+	1.04937i
$544$	−17.0216	+	32.1591i	−0.729794	+	1.37881i
$545$	−19.4946	+	12.1802i	−0.835057	+	0.521743i
$546$	27.1968	+	7.50619i	1.16392	+	0.321235i
$547$	10.5384			0.450588			0.225294	−	0.974291i	$-0.427666\pi$
$547$	10.5384			0.450588			0.225294	+	0.974291i	$0.427666\pi$
$548$	−12.4051	−	18.5004i	−0.529921	−	0.790296i
$549$	6.96823	+	14.7425i	0.297397	+	0.629196i
$550$	15.3314	−	24.9364i	0.653735	−	1.06329i
$551$	3.40939			0.145245
$552$	16.3832	+	8.19908i	0.697313	+	0.348976i
$553$	11.8290	−	11.8290i	0.503020	−	0.503020i
$554$	−13.1761	+	10.8313i	−0.559798	+	0.460177i
$555$	−10.0742	+	23.9029i	−0.427628	+	1.01462i
$556$	−21.3945	+	14.3458i	−0.907330	+	0.608396i
$557$			23.7749i			1.00737i	0.863886	+	0.503687i	$0.168024\pi$
$557$			23.7749i			1.00737i	−0.863886	+	0.503687i	$0.831976\pi$
$558$	−1.98628	−	5.54139i	−0.0840859	−	0.234586i
$559$		−	23.8418i		−	1.00840i
$560$	−4.53072	−	26.5517i	−0.191458	−	1.12201i
$561$	7.89047	−	45.4405i	0.333136	−	1.91850i
$562$	2.33681	+	2.84269i	0.0985724	+	0.119912i
$563$	5.63612			0.237534			0.118767	−	0.992922i	$-0.462106\pi$
$563$	5.63612			0.237534			0.118767	+	0.992922i	$0.462106\pi$
$564$	14.8705	−	6.61838i	0.626159	−	0.278684i
$565$	−34.6582	+	21.6544i	−1.45808	+	0.911009i
$566$	6.38765	+	7.77047i	0.268493	+	0.326617i
$567$	−2.64322	−	26.9741i	−0.111005	−	1.13281i
$568$	13.3815	−	7.19458i	0.561474	−	0.301878i
$569$			8.82620i			0.370014i	0.982737	+	0.185007i	$0.0592307\pi$
$569$			8.82620i			0.370014i	−0.982737	+	0.185007i	$0.940769\pi$
$570$	13.7653	+	7.45283i	0.576564	+	0.312165i
$571$	−1.54350	+	1.54350i	−0.0645936	+	0.0645936i	−0.738666	−	0.674072i	$-0.764544\pi$
$571$	−1.54350	+	1.54350i	−0.0645936	+	0.0645936i	0.674072	+	0.738666i	$0.264544\pi$
$572$	−17.6361	−	26.3016i	−0.737403	−	1.09972i
$573$	1.61632	−	9.30823i	0.0675227	−	0.388857i
$574$	1.09919	−	11.2541i	0.0458793	−	0.469737i
$575$	−6.08572	−	17.6800i	−0.253792	−	0.737306i
$576$	19.2105	−	14.3859i	0.800439	−	0.599414i
$577$	−0.768842	+	0.768842i	−0.0320073	+	0.0320073i	−0.722929	−	0.690922i	$-0.757205\pi$
$577$	−0.768842	+	0.768842i	−0.0320073	+	0.0320073i	0.690922	+	0.722929i	$0.257205\pi$
$578$	26.6269	−	21.8884i	1.10753	−	0.910438i
$579$	9.21974	+	13.0945i	0.383159	+	0.544188i
$580$	−4.98608	+	1.89805i	−0.207035	+	0.0788123i
$581$	2.88491	+	2.88491i	0.119686	+	0.119686i
$582$	−20.9796	−	5.79027i	−0.869632	−	0.240014i
$583$	−11.3693	+	11.3693i	−0.470868	+	0.470868i
$584$	−3.09449	+	10.2915i	−0.128051	+	0.425866i
$585$	13.8628	−	21.5898i	0.573157	−	0.892627i
$586$	4.82997	−	3.97043i	0.199524	−	0.164017i
$587$	−0.262771			−0.0108457			−0.00542286	−	0.999985i	$-0.501726\pi$
$587$	−0.262771			−0.0108457			−0.00542286	+	0.999985i	$0.501726\pi$
$588$	6.69080	+	2.56938i	0.275924	+	0.105959i
$589$	−2.80389	+	2.80389i	−0.115532	+	0.115532i
$590$	−43.9407	−	14.7717i	−1.80901	−	0.608140i
$591$	−11.5459	−	2.00488i	−0.474934	−	0.0824696i
$592$	10.1714	−	24.7838i	0.418044	−	1.01861i
$593$	−10.9183	+	10.9183i	−0.448362	+	0.448362i	−0.894810	−	0.446448i	$-0.852689\pi$
$593$	−10.9183	+	10.9183i	−0.448362	+	0.448362i	0.446448	+	0.894810i	$0.352689\pi$
$594$	−17.5056	+	24.8793i	−0.718262	+	1.02081i
$595$	−9.74553	+	42.2029i	−0.399528	+	1.73015i
$596$	−6.57050	−	9.79891i	−0.269138	−	0.401379i
$597$	−4.65385	−	0.808113i	−0.190469	−	0.0330739i
$598$	−20.1319	−	1.96628i	−0.823253	−	0.0804072i
$599$			48.0234i			1.96218i	0.193545	+	0.981091i	$0.438001\pi$
$599$			48.0234i			1.96218i	−0.193545	+	0.981091i	$0.561999\pi$
$600$	−24.2802	−	3.23611i	−0.991235	−	0.132114i
$601$			42.1359i			1.71876i	0.511337	+	0.859380i	$0.329150\pi$
$601$			42.1359i			1.71876i	−0.511337	+	0.859380i	$0.670850\pi$
$602$	2.58066	−	26.4222i	0.105180	−	1.07689i
$603$	28.4800	+	10.1983i	1.15979	+	0.415305i
$604$	−8.10889	−	1.59925i	−0.329946	−	0.0650725i
$605$	3.08788	−	13.3720i	0.125540	−	0.543650i
$606$	10.8311	−	39.2438i	0.439983	−	1.59417i
$607$	14.3583	−	14.3583i	0.582787	−	0.582787i	−0.352881	−	0.935668i	$-0.614798\pi$
$607$	14.3583	−	14.3583i	0.582787	−	0.582787i	0.935668	+	0.352881i	$0.114798\pi$
$608$	−14.2886	−	7.56288i	−0.579481	−	0.306715i
$609$	1.06458	−	6.13082i	0.0431390	−	0.248434i
$610$	−5.47708	+	16.2925i	−0.221761	+	0.659662i
$611$	−12.7077	+	12.7077i	−0.514098	+	0.514098i
$612$	−37.4236	+	9.42899i	−1.51276	+	0.381144i
$613$	35.1551			1.41990			0.709951	−	0.704251i	$-0.248717\pi$
$613$	35.1551			1.41990			0.709951	+	0.704251i	$0.248717\pi$
$614$	−26.8967	−	32.7194i	−1.08546	−	1.32045i
$615$	−9.47586	−	3.99374i	−0.382103	−	0.161043i
$616$	−16.6979	−	31.0570i	−0.672778	−	1.25132i
$617$	14.6639	−	14.6639i	0.590344	−	0.590344i	−0.347380	−	0.937724i	$-0.612929\pi$
$617$	14.6639	−	14.6639i	0.590344	−	0.590344i	0.937724	+	0.347380i	$0.112929\pi$
$618$	−26.6951	−	7.36772i	−1.07383	−	0.296373i
$619$	3.72169	+	3.72169i	0.149587	+	0.149587i	0.777934	−	0.628346i	$-0.216268\pi$
$619$	3.72169	+	3.72169i	0.149587	+	0.149587i	−0.628346	+	0.777934i	$0.716268\pi$
$620$	2.53961	−	5.66154i	0.101993	−	0.227373i
$621$	5.17569	+	18.7296i	0.207693	+	0.751594i
$622$	−4.00474	−	4.87171i	−0.160576	−	0.195338i
$623$	11.1575	−	11.1575i	0.447014	−	0.447014i
$624$	−14.1066	+	22.4318i	−0.564716	+	0.897990i
$625$	15.3876	+	19.7033i	0.615504	+	0.788134i
$626$	−20.3328	−	1.98591i	−0.812663	−	0.0793729i
$627$	20.1897	+	3.50583i	0.806300	+	0.140009i
$628$	7.80491	−	39.5743i	0.311450	−	1.57919i
$629$	−30.4617	+	30.4617i	−1.21459	+	1.21459i
$630$	17.7000	−	22.4258i	0.705186	−	0.893467i
$631$			31.9724i			1.27280i	0.771359	+	0.636400i	$0.219577\pi$
$631$			31.9724i			1.27280i	−0.771359	+	0.636400i	$0.780423\pi$
$632$	7.44033	+	13.8385i	0.295961	+	0.550468i
$633$	2.26366	+	3.21499i	0.0899723	+	0.127784i
$634$	13.5422	−	11.1322i	0.537828	−	0.442116i
$635$	15.9633	−	9.97384i	0.633483	−	0.395800i
$636$	12.5602	+	4.82331i	0.498042	+	0.191257i
$637$	−7.91338			−0.313540
$638$	−5.39528	+	4.43514i	−0.213601	+	0.175589i
$639$	15.1712	+	5.43259i	0.600164	+	0.214910i
$640$	25.1069	+	3.10570i	0.992436	+	0.122764i
$641$			22.6325i			0.893930i	0.894551	+	0.446965i	$0.147495\pi$
$641$			22.6325i			0.893930i	−0.894551	+	0.446965i	$0.852505\pi$
$642$	11.4527	+	20.1844i	0.452003	+	0.796615i
$643$			13.0421i			0.514329i	0.966368	+	0.257165i	$0.0827883\pi$
$643$			13.0421i			0.514329i	−0.966368	+	0.257165i	$0.917212\pi$
$644$	−22.0978	−	4.35817i	−0.870777	−	0.171736i
$645$	−22.2472	−	9.37643i	−0.875984	−	0.369197i
$646$	16.5086	+	20.0824i	0.649521	+	0.790132i
$647$	29.6121	−	29.6121i	1.16417	−	1.16417i	0.180621	−	0.983553i	$-0.442189\pi$
$647$	29.6121	−	29.6121i	1.16417	−	1.16417i	0.983553	−	0.180621i	$-0.0578107\pi$
$648$	24.9763	+	4.91762i	0.981163	+	0.193183i
$649$	−60.6863			−2.38215
$650$	26.3071	−	6.27494i	1.03185	−	0.246124i
$651$	4.16650	+	5.91753i	0.163298	+	0.231926i
$652$	10.8779	+	2.14535i	0.426011	+	0.0840186i
$653$	−28.5044			−1.11546			−0.557732	−	0.830021i	$-0.688328\pi$
$653$	−28.5044			−1.11546			−0.557732	+	0.830021i	$0.688328\pi$
$654$	24.2734	+	6.69933i	0.949163	+	0.261964i
$655$	−17.4722	+	10.9166i	−0.682695	+	0.426548i
$656$	9.82507	+	4.03228i	0.383605	+	0.157434i
$657$	−10.3054	+	4.87097i	−0.402052	+	0.190035i
$658$	−15.4585	+	12.7075i	−0.602635	+	0.495391i
$659$	−1.45554	−	1.45554i	−0.0566997	−	0.0566997i	0.678188	−	0.734888i	$-0.262765\pi$
$659$	−1.45554	−	1.45554i	−0.0566997	−	0.0566997i	−0.734888	+	0.678188i	$0.762765\pi$
$660$	−31.4783	+	6.11278i	−1.22529	+	0.237940i
$661$	15.7799	−	15.7799i	0.613765	−	0.613765i	−0.330160	−	0.943925i	$-0.607103\pi$
$661$	15.7799	−	15.7799i	0.613765	−	0.613765i	0.943925	+	0.330160i	$0.107103\pi$
$662$	6.61541	+	0.646128i	0.257115	+	0.0251125i
$663$	34.8413	−	24.5316i	1.35312	−	0.952727i
$664$	−3.37500	+	1.81458i	−0.130976	+	0.0704194i
$665$	−18.7512	−	4.33005i	−0.727142	−	0.167912i
$666$	26.7485	−	9.58784i	1.03648	−	0.371521i
$667$			4.46124i			0.172740i
$668$	−5.91519	−	8.82161i	−0.228866	−	0.341318i
$669$	−8.69982	−	12.3560i	−0.336354	−	0.477712i
$670$	14.1875	+	28.5571i	0.548112	+	1.10326i
$671$			22.5014i			0.868659i
$672$	−18.0614	+	23.3326i	−0.696732	+	0.900075i
$673$	−0.659734	−	0.659734i	−0.0254309	−	0.0254309i	0.694277	−	0.719708i	$-0.255724\pi$
$673$	−0.659734	−	0.659734i	−0.0254309	−	0.0254309i	−0.719708	+	0.694277i	$0.755724\pi$
$674$	−47.3795	−	4.62756i	−1.82499	−	0.178247i
$675$	−14.6939	−	21.4264i	−0.565568	−	0.824702i
$676$	0.630323	−	3.19601i	0.0242432	−	0.122923i
$677$	41.0728			1.57856			0.789278	−	0.614036i	$-0.210455\pi$
$677$	41.0728			1.57856			0.789278	+	0.614036i	$0.210455\pi$
$678$	43.1541	+	11.9103i	1.65732	+	0.457413i
$679$	26.7573			1.02685
$680$	−35.3232	−	20.1791i	−1.35458	−	0.773833i
$681$	4.72263	−	27.1972i	0.180971	−	1.04220i
$682$	0.789622	−	8.08458i	0.0302362	−	0.309574i
$683$			37.5396i			1.43641i	0.695830	+	0.718207i	$0.255037\pi$
$683$			37.5396i			1.43641i	−0.695830	+	0.718207i	$0.744963\pi$
$684$	−4.18941	−	16.6277i	−0.160186	−	0.635777i
$685$	21.1201	−	13.1958i	0.806957	−	0.504187i
$686$	20.9011	+	2.04141i	0.798007	+	0.0779415i
$687$	25.4642	+	36.1659i	0.971520	+	1.37982i
$688$	23.0671	+	9.46690i	0.879426	+	0.360922i
$689$	−14.8552			−0.565939
$690$	−9.75216	+	18.0121i	−0.371258	+	0.685709i
$691$	−29.6548	−	29.6548i	−1.12812	−	1.12812i	−0.990483	−	0.137638i	$-0.956049\pi$
$691$	−29.6548	−	29.6548i	−1.12812	−	1.12812i	−0.137638	−	0.990483i	$-0.543951\pi$
$692$	−1.86888	+	9.47606i	−0.0710443	+	0.360226i
$693$	12.6085	−	35.2109i	0.478957	−	1.33755i
$694$	0.601433	+	0.731634i	0.0228301	+	0.0277725i
$695$	−15.2602	−	24.4241i	−0.578851	−	0.926458i
$696$	5.22637	+	2.61558i	0.198105	+	0.0991433i
$697$	−12.0760	−	12.0760i	−0.457410	−	0.457410i
$698$	15.6545	+	1.52897i	0.592530	+	0.0578725i
$699$	−3.36124	−	4.77385i	−0.127134	−	0.180564i
$700$	29.8335	−	4.10656i	1.12760	−	0.155213i
$701$	−16.0824	+	16.0824i	−0.607422	+	0.607422i	−0.942272	−	0.334849i	$-0.891315\pi$
$701$	−16.0824	+	16.0824i	−0.607422	+	0.607422i	0.334849	+	0.942272i	$0.391315\pi$
$702$	−27.6902	+	4.81731i	−1.04510	+	0.181818i
$703$	−13.5345	−	13.5345i	−0.510463	−	0.510463i
$704$	32.4497	−	6.61945i	1.22299	−	0.249480i
$705$	6.86014	+	16.8554i	0.258368	+	0.634812i
$706$	13.4844	+	1.31702i	0.507492	+	0.0495668i
$707$			50.0513i			1.88237i
$708$	20.6486	+	46.3942i	0.776022	+	1.74360i
$709$	24.7407	+	24.7407i	0.929157	+	0.929157i	0.997651	−	0.0684944i	$-0.0218195\pi$
$709$	24.7407	+	24.7407i	0.929157	+	0.929157i	−0.0684944	+	0.997651i	$0.521820\pi$
$710$	7.55765	+	15.2123i	0.283634	+	0.570907i
$711$	−5.61815	+	15.6894i	−0.210697	+	0.588400i
$712$	7.01793	+	13.0529i	0.263008	+	0.489179i
$713$	−3.66895	−	3.66895i	−0.137403	−	0.137403i
$714$	41.2674	−	23.4153i	1.54439	−	0.876295i
$715$	30.0260	−	18.7602i	1.12291	−	0.701593i
$716$	26.3309	−	17.6558i	0.984031	−	0.659826i
$717$	−7.95107	−	1.38066i	−0.296938	−	0.0515615i
$718$	14.8684	−	12.2224i	0.554884	−	0.456137i
$719$	13.4644			0.502137			0.251068	−	0.967969i	$-0.419218\pi$
$719$	13.4644			0.502137			0.251068	+	0.967969i	$0.419218\pi$
$720$	15.3837	+	21.9850i	0.573317	+	0.819334i
$721$	34.0468			1.26797
$722$	11.8341	−	9.72813i	0.440420	−	0.362043i
$723$	37.1165	+	6.44507i	1.38038	+	0.239695i
$724$	27.3144	+	40.7352i	1.01513	+	1.51391i
$725$	−1.94140	−	5.64007i	−0.0721018	−	0.209467i
$726$	−13.0756	+	7.41914i	−0.485281	+	0.275350i
$727$	16.7234	+	16.7234i	0.620235	+	0.620235i	0.945592	−	0.325356i	$-0.105484\pi$
$727$	16.7234	+	16.7234i	0.620235	+	0.620235i	−0.325356	+	0.945592i	$0.605484\pi$
$728$	9.38088	−	31.1985i	0.347679	−	1.15629i
$729$	13.8636	+	23.1690i	0.513465	+	0.858110i
$730$	−11.3888	−	3.82862i	−0.421520	−	0.141704i
$731$	−28.3517	−	28.3517i	−1.04863	−	1.04863i
$732$	17.2022	−	7.65615i	0.635810	−	0.282979i
$733$			48.3320i			1.78518i	0.450867	+	0.892591i	$0.351115\pi$
$733$			48.3320i			1.78518i	−0.450867	+	0.892591i	$0.648885\pi$
$734$	49.9828	+	4.88183i	1.84490	+	0.180192i
$735$	−3.11215	+	7.38412i	−0.114793	+	0.272367i
$736$	9.89617	−	18.6969i	0.364778	−	0.689179i
$737$	29.5172	+	29.5172i	1.08728	+	1.08728i
$738$	3.80091	+	10.6039i	0.139914	+	0.390336i
$739$	−21.0974	+	21.0974i	−0.776080	+	0.776080i	−0.979162	−	0.203081i	$-0.934904\pi$
$739$	−21.0974	+	21.0974i	−0.776080	+	0.776080i	0.203081	+	0.979162i	$0.434904\pi$
$740$	27.3284	+	12.2588i	1.00461	+	0.450641i
$741$	10.8997	+	15.4804i	0.400409	+	0.568687i
$742$	−16.4629	−	1.60794i	−0.604374	−	0.0590293i
$743$	12.2403	+	12.2403i	0.449053	+	0.449053i	0.895040	−	0.445986i	$-0.147147\pi$
$743$	12.2403	+	12.2403i	0.449053	+	0.449053i	−0.445986	+	0.895040i	$0.647147\pi$
$744$	−6.44926	+	2.14713i	−0.236441	+	0.0787176i
$745$	11.1865	−	6.98931i	0.409841	−	0.256068i
$746$	−21.6481	−	26.3346i	−0.792594	−	0.964178i
$747$	−3.82641	−	1.37018i	−0.140001	−	0.0501322i
$748$	−52.2489	−	10.3046i	−1.91041	−	0.376774i
$749$	−20.1749	−	20.1749i	−0.737176	−	0.737176i
$750$	4.49071	−	27.0154i	0.163977	−	0.986464i
$751$	29.0583			1.06035			0.530177	−	0.847887i	$-0.322126\pi$
$751$	29.0583			1.06035			0.530177	+	0.847887i	$0.322126\pi$
$752$	−7.24892	−	17.3406i	−0.264341	−	0.632348i
$753$	−4.81563	−	6.83948i	−0.175491	−	0.249244i
$754$	−6.42225	−	0.627262i	−0.233884	−	0.0228435i
$755$	2.07914	−	9.00371i	0.0756678	−	0.327679i
$756$	−31.2085	+	2.34146i	−1.13504	+	0.0851583i
$757$		−	25.6342i		−	0.931691i	−0.884866	−	0.465846i	$-0.845750\pi$
$757$		−	25.6342i		−	0.931691i	0.884866	−	0.465846i	$-0.154250\pi$
$758$	−2.67846	+	27.4235i	−0.0972860	+	0.996067i
$759$	−4.58744	+	26.4186i	−0.166513	+	0.958935i
$760$	8.96580	−	15.6945i	0.325224	−	0.569300i
$761$	34.7046			1.25804			0.629020	−	0.777389i	$-0.283456\pi$
$761$	34.7046			1.25804			0.629020	+	0.777389i	$0.283456\pi$
$762$	−19.8764	−	5.48578i	−0.720045	−	0.198729i
$763$	−30.9581			−1.12076
$764$	−10.7029	−	2.11084i	−0.387217	−	0.0763676i
$765$	−9.18858	−	42.1587i	−0.332214	−	1.52425i
$766$	−48.3411	−	4.72148i	−1.74663	−	0.170594i
$767$	−39.6466	−	39.6466i	−1.43156	−	1.43156i
$768$	−16.1016	−	22.5552i	−0.581016	−	0.813892i
$769$		−	5.49454i		−	0.198138i	−0.995081	−	0.0990691i	$-0.968414\pi$
$769$		−	5.49454i		−	0.198138i	0.995081	−	0.0990691i	$-0.0315865\pi$
$770$	35.3062	−	17.5406i	1.27235	−	0.632118i
$771$	14.4097	+	20.4656i	0.518952	+	0.737050i
$772$	15.3589	−	10.2987i	0.552779	−	0.370657i
$773$			27.3609i			0.984103i	0.870566	+	0.492051i	$0.163753\pi$
$773$			27.3609i			0.984103i	−0.870566	+	0.492051i	$0.836247\pi$
$774$	8.92371	+	24.8957i	0.320756	+	0.894858i
$775$	6.23504	+	3.04180i	0.223969	+	0.109265i
$776$	−7.23640	+	24.0665i	−0.259772	+	0.863936i
$777$	−28.5641	+	20.1118i	−1.02473	+	0.721508i
$778$	−9.29684	−	0.908024i	−0.333308	−	0.0325542i
$779$	5.36549	−	5.36549i	0.192239	−	0.192239i
$780$	−24.5584	−	16.5714i	−0.879332	−	0.593352i
$781$	15.7237	+	15.7237i	0.562640	+	0.562640i
$782$	−26.2782	+	21.6018i	−0.939707	+	0.772477i
$783$	1.65109	+	5.97492i	0.0590052	+	0.213526i
$784$	3.14218	−	7.65625i	0.112221	−	0.273437i
$785$	43.9413	+	10.1470i	1.56833	+	0.362161i
$786$	21.7552	+	6.00433i	0.775982	+	0.214167i
$787$	38.9292			1.38768			0.693838	−	0.720131i	$-0.255918\pi$
$787$	38.9292			1.38768			0.693838	+	0.720131i	$0.255918\pi$
$788$	−2.61828	+	13.2758i	−0.0932724	+	0.472932i
$789$	−14.3210	−	20.3396i	−0.509841	−	0.724110i
$790$	−15.7319	+	7.81580i	−0.559716	+	0.278074i
$791$	−55.0385			−1.95694
$792$	28.2600	+	20.8632i	1.00418	+	0.741341i
$793$	−14.7003	+	14.7003i	−0.522022	+	0.522022i
$794$	−23.4790	−	28.5618i	−0.833238	−	1.01362i
$795$	−5.84221	+	13.8617i	−0.207202	+	0.491623i
$796$	−1.05536	+	5.35114i	−0.0374062	+	0.189666i
$797$		−	23.1152i		−	0.818784i	−0.912359	−	0.409392i	$-0.865741\pi$
$797$		−	23.1152i		−	0.818784i	0.912359	−	0.409392i	$-0.134259\pi$
$798$	10.4037	+	18.3356i	0.368286	+	0.649072i
$799$			30.2229i			1.06921i
$800$	−4.37475	+	27.9439i	−0.154671	+	0.987966i
$801$	−5.29920	+	14.7987i	−0.187238	+	0.522887i
$802$	19.8781	−	16.3406i	0.701921	−	0.577007i
$803$	−15.7291			−0.555068
$804$	12.5224	−	32.6089i	0.441630	−	1.15003i
$805$	5.66595	−	24.5363i	0.199699	−	0.864792i
$806$	5.79755	−	4.76582i	0.204210	−	0.167869i
$807$	−18.9799	−	26.9565i	−0.668124	−	0.948913i
$808$	−45.0180	−	13.5362i	−1.58373	−	0.476201i
$809$		−	22.0206i		−	0.774203i	−0.922037	−	0.387102i	$-0.873476\pi$
$809$		−	22.0206i		−	0.774203i	0.922037	−	0.387102i	$-0.126524\pi$
$810$	−6.39479	+	27.7328i	−0.224690	+	0.974430i
$811$	−13.5094	+	13.5094i	−0.474381	+	0.474381i	−0.903329	−	0.428948i	$-0.858884\pi$
$811$	−13.5094	+	13.5094i	−0.474381	+	0.474381i	0.428948	+	0.903329i	$0.358884\pi$
$812$	−7.04941	−	1.39030i	−0.247386	−	0.0487898i
$813$	4.46500	+	0.775321i	0.156594	+	0.0271917i
$814$	39.0245	+	3.81153i	1.36781	+	0.133594i
$815$	−2.78912	+	12.0783i	−0.0976987	+	0.423083i
$816$	9.89997	+	43.4500i	0.346568	+	1.52105i
$817$	12.5970	−	12.5970i	0.440713	−	0.440713i
$818$	−22.0602	−	26.8358i	−0.771316	−	0.938293i
$819$	31.2406	−	14.7662i	1.09163	−	0.515973i
$820$	−4.85975	+	10.8338i	−0.169710	+	0.378334i
$821$	−1.40441	−	1.40441i	−0.0490142	−	0.0490142i	0.682175	−	0.731189i	$-0.261034\pi$
$821$	−1.40441	−	1.40441i	−0.0490142	−	0.0490142i	−0.731189	+	0.682175i	$0.761034\pi$
$822$	−26.2973	−	7.25793i	−0.917224	−	0.253149i
$823$	−13.2359	+	13.2359i	−0.461373	+	0.461373i	−0.899105	−	0.437732i	$-0.855782\pi$
$823$	−13.2359	+	13.2359i	−0.461373	+	0.461373i	0.437732	+	0.899105i	$0.355782\pi$
$824$	−9.20782	+	30.6229i	−0.320770	+	1.06680i
$825$	−5.69700	−	35.3957i	−0.198344	−	1.23232i
$826$	−39.6460	−	48.2288i	−1.37946	−	1.67809i
$827$	−8.66513			−0.301316			−0.150658	−	0.988586i	$-0.548139\pi$
$827$	−8.66513			−0.301316			−0.150658	+	0.988586i	$0.548139\pi$
$828$	21.7577	−	5.48192i	0.756132	−	0.190510i
$829$	−13.0794	+	13.0794i	−0.454266	+	0.454266i	−0.896768	−	0.442501i	$-0.854091\pi$
$829$	−13.0794	+	13.0794i	−0.454266	+	0.454266i	0.442501	+	0.896768i	$0.354091\pi$
$830$	−1.90615	−	3.83677i	−0.0661635	−	0.133176i
$831$	−3.57393	+	20.5819i	−0.123978	+	0.713980i
$832$	25.5240	+	16.8750i	0.884887	+	0.585036i
$833$	−9.41027	+	9.41027i	−0.326046	+	0.326046i
$834$	−8.39334	+	30.4112i	−0.290638	+	1.05305i
$835$	10.0708	−	6.29222i	0.348514	−	0.217751i
$836$	4.57846	−	23.2148i	0.158349	−	0.802900i
$837$	−6.27167	−	3.55594i	−0.216781	−	0.122911i
$838$	−2.12980	+	21.8060i	−0.0735726	+	0.753277i
$839$		−	32.7312i		−	1.13001i	−0.825088	−	0.565004i	$-0.808875\pi$
$839$		−	32.7312i		−	1.13001i	0.825088	−	0.565004i	$-0.191125\pi$
$840$	−25.4226	−	21.0231i	−0.877163	−	0.725366i
$841$		−	27.5768i		−	0.950925i
$842$	17.5662	+	1.71569i	0.605370	+	0.0591266i
$843$	4.44048	+	0.771063i	0.152938	+	0.0265568i
$844$	3.77096	−	2.52856i	0.129802	−	0.0870366i
$845$	3.54869	+	0.819467i	0.122079	+	0.0281905i
$846$	8.51307	−	18.0257i	0.292685	−	0.619738i
$847$	13.0694	−	13.0694i	0.449071	−	0.449071i
$848$	5.89858	−	14.3725i	0.202558	−	0.493554i
$849$	12.1380	+	2.10769i	0.416575	+	0.0723358i
$850$	23.8214	−	38.7452i	0.817069	−	1.32895i
$851$	17.7101	−	17.7101i	0.607096	−	0.607096i
$852$	6.67064	−	17.3707i	0.228532	−	0.595110i
$853$	−14.6057			−0.500089			−0.250045	−	0.968234i	$-0.580445\pi$
$853$	−14.6057			−0.500089			−0.250045	+	0.968234i	$0.580445\pi$
$854$	−17.8824	+	14.7001i	−0.611923	+	0.503026i
$855$	18.7316	−	4.08259i	0.640608	−	0.139622i
$856$	23.6023	−	12.6898i	0.806710	−	0.433730i
$857$	−15.0381	+	15.0381i	−0.513692	+	0.513692i	−0.915656	−	0.401964i	$-0.868328\pi$
$857$	−15.0381	+	15.0381i	−0.513692	+	0.513692i	0.401964	+	0.915656i	$0.368328\pi$
$858$	−37.3863	−	10.3184i	−1.27635	−	0.352266i
$859$	10.2451	+	10.2451i	0.349557	+	0.349557i	0.859945	−	0.510387i	$-0.170498\pi$
$859$	10.2451	+	10.2451i	0.349557	+	0.349557i	−0.510387	+	0.859945i	$0.670498\pi$
$860$	−11.4096	+	25.4355i	−0.389065	+	0.867342i
$861$	−7.97295	−	11.3237i	−0.271718	−	0.385911i
$862$	0.436812	−	0.359077i	0.0148779	−	0.0122302i
$863$	20.5930	−	20.5930i	0.700995	−	0.700995i	−0.263629	−	0.964624i	$-0.584920\pi$
$863$	20.5930	−	20.5930i	0.700995	−	0.700995i	0.964624	+	0.263629i	$0.0849196\pi$
$864$	6.33421	−	28.7033i	0.215494	−	0.976505i
$865$	−10.5217	−	2.42969i	−0.357750	−	0.0826119i
$866$	−0.547237	+	5.60291i	−0.0185959	+	0.190395i
$867$	7.22238	−	41.5930i	0.245285	−	1.41257i
$868$	6.94085	−	4.65408i	0.235588	−	0.157970i
$869$	−16.2608	+	16.2608i	−0.551611	+	0.551611i
$870$	−3.11103	+	5.74603i	−0.105474	+	0.194809i
$871$			38.5674i			1.30681i
$872$	8.37250	−	27.8449i	0.283529	−	0.942946i
$873$	−24.0989	+	11.3906i	−0.815626	+	0.385515i
$874$	−9.59791	−	11.6757i	−0.324654	−	0.394937i
$875$	3.51438	+	33.4854i	0.118808	+	1.13201i
$876$	5.35185	+	12.0248i	0.180822	+	0.406279i
$877$	−12.6122			−0.425883			−0.212941	−	0.977065i	$-0.568304\pi$
$877$	−12.6122			−0.425883			−0.212941	+	0.977065i	$0.568304\pi$
$878$	−4.17379	−	5.07735i	−0.140859	−	0.171352i
$879$	1.31010	−	7.54474i	0.0441885	−	0.254478i
$880$	6.22819	+	36.4995i	0.209952	+	1.23040i
$881$		−	54.9606i		−	1.85167i	−0.377929	−	0.925835i	$-0.623364\pi$
$881$		−	54.9606i		−	1.85167i	0.377929	−	0.925835i	$-0.376636\pi$
$882$	8.26317	−	2.96188i	0.278236	−	0.0997318i
$883$		−	53.0273i		−	1.78451i	−0.451532	−	0.892255i	$-0.649122\pi$
$883$		−	53.0273i		−	1.78451i	0.451532	−	0.892255i	$-0.350878\pi$
$884$	−27.4023	−	40.8664i	−0.921641	−	1.37449i
$885$	−52.5870	+	21.4029i	−1.76769	+	0.719450i
$886$	−36.9094	+	30.3410i	−1.23999	+	1.01933i
$887$	12.4037	−	12.4037i	0.416476	−	0.416476i	−0.467511	−	0.883987i	$-0.654849\pi$
$887$	12.4037	−	12.4037i	0.416476	−	0.416476i	0.883987	+	0.467511i	$0.154849\pi$
$888$	−10.3643	−	31.1308i	−0.347802	−	1.04468i
$889$	25.3502			0.850220
$890$	−14.8388	+	7.37209i	−0.497397	+	0.247113i
$891$	3.63352	+	37.0801i	0.121728	+	1.24223i
$892$	−14.4928	+	9.71791i	−0.485254	+	0.325380i
$893$	−13.4284			−0.449364
$894$	−13.9286	−	3.84424i	−0.465843	−	0.128570i
$895$	18.7811	+	30.0594i	0.627784	+	1.00478i
$896$	26.4599	+	21.4641i	0.883962	+	0.717064i
$897$	−20.2564	+	14.2624i	−0.676341	+	0.476208i
$898$	−8.66122	−	10.5362i	−0.289029	−	0.351599i
$899$	−1.17043	−	1.17043i	−0.0390359	−	0.0390359i
$900$	−25.1213	+	16.3988i	−0.837377	+	0.546625i
$901$	−17.6652	+	17.6652i	−0.588513	+	0.588513i
$902$	−1.51101	+	15.4705i	−0.0503111	+	0.515112i
$903$	−18.7188	−	26.5856i	−0.622921	−	0.884713i
$904$	14.8849	−	49.5036i	0.495066	−	1.64647i
$905$	−46.5035	+	29.0554i	−1.54583	+	0.965833i
$906$	−8.80412	+	4.99550i	−0.292497	+	0.165964i
$907$			13.2167i			0.438853i	0.975629	+	0.219426i	$0.0704186\pi$
$907$			13.2167i			0.438853i	−0.975629	+	0.219426i	$0.929581\pi$
$908$	−31.2721	−	6.16754i	−1.03780	−	0.204677i
$909$	−21.3070	−	45.0787i	−0.706708	−	1.49517i
$910$	34.5250	+	11.6064i	1.14449	+	0.384748i
$911$			38.6519i			1.28059i	0.768127	+	0.640297i	$0.221189\pi$
$911$			38.6519i			1.28059i	−0.768127	+	0.640297i	$0.778811\pi$
$912$	−19.3053	+	4.39867i	−0.639263	+	0.145654i
$913$	−3.96576	−	3.96576i	−0.131248	−	0.131248i
$914$	−2.37090	+	24.2746i	−0.0784224	+	0.802932i
$915$	7.93582	+	19.4984i	0.262350	+	0.644596i
$916$	42.4201	−	28.4441i	1.40160	−	0.939820i
$917$	−27.7465			−0.916270
$918$	−27.1995	+	38.6566i	−0.897718	+	1.27586i
$919$	28.3921			0.936568			0.468284	−	0.883578i	$-0.344872\pi$
$919$	28.3921			0.936568			0.468284	+	0.883578i	$0.344872\pi$
$920$	20.5365	+	11.7319i	0.677070	+	0.386790i
$921$	−51.1099	−	8.87493i	−1.68413	−	0.292439i
$922$	−6.62856	−	0.647413i	−0.218300	−	0.0213214i
$923$			20.5448i			0.676239i
$924$	−40.3156	−	15.4819i	−1.32629	−	0.509317i
$925$	−14.6829	+	30.0967i	−0.482770	+	0.989575i
$926$	0.635103	−	6.50253i	0.0208708	−	0.213686i
$927$	−30.6643	+	14.4938i	−1.00715	+	0.476039i
$928$	3.15697	−	5.96450i	0.103633	−	0.195794i
$929$	54.4255			1.78564			0.892822	−	0.450410i	$-0.148722\pi$
$929$	54.4255			1.78564			0.892822	+	0.450410i	$0.148722\pi$
$930$	−2.16704	−	7.28408i	−0.0710599	−	0.238854i
$931$	−4.18109	−	4.18109i	−0.137030	−	0.137030i
$932$	−5.59939	+	3.75458i	−0.183414	+	0.122985i
$933$	−7.60993	−	1.32142i	−0.249138	−	0.0432613i
$934$	−36.1325	+	29.7024i	−1.18229	+	0.971891i
$935$	13.3968	−	58.0145i	0.438121	−	1.89728i
$936$	4.83239	+	32.0924i	0.157952	+	1.04897i
$937$	−30.3898	−	30.3898i	−0.992791	−	0.992791i	0.00718307	−	0.999974i	$-0.497714\pi$
$937$	−30.3898	−	30.3898i	−0.992791	−	0.992791i	−0.999974	+	0.00718307i	$0.997714\pi$
$938$	−4.17456	+	42.7414i	−0.136304	+	1.39556i
$939$	−20.4586	+	14.4048i	−0.667641	+	0.470082i
$940$	19.6384	−	7.47577i	0.640535	−	0.243833i
$941$	33.7798	−	33.7798i	1.10119	−	1.10119i	0.106922	−	0.994267i	$-0.465900\pi$
$941$	33.7798	−	33.7798i	1.10119	−	1.10119i	0.994267	−	0.106922i	$-0.0340995\pi$
$942$	−24.3798	−	42.9673i	−0.794337	−	1.39995i
$943$	7.02084	+	7.02084i	0.228630	+	0.228630i
$944$	54.1009	−	22.6158i	1.76083	−	0.736082i
$945$	−1.49244	−	34.9583i	−0.0485492	−	1.13720i
$946$	−3.54752	+	36.3214i	−0.115340	+	1.18091i
$947$			0.231368i			0.00751845i	0.999993	+	0.00375923i	$0.00119660\pi$
$947$			0.231368i			0.00751845i	−0.999993	+	0.00375923i	$0.998803\pi$
$948$	17.9640	+	6.89849i	0.583445	+	0.224053i
$949$	−10.2759	−	10.2759i	−0.333569	−	0.333569i
$950$	17.2150	+	10.5841i	0.558527	+	0.343395i
$951$	3.67322	−	21.1538i	0.119112	−	0.685958i
$952$	−25.9446	−	48.2553i	−0.840869	−	1.56396i
$953$	28.2451	+	28.2451i	0.914950	+	0.914950i	0.996656	−	0.0817066i	$-0.0260370\pi$
$953$	28.2451	+	28.2451i	0.914950	+	0.914950i	−0.0817066	+	0.996656i	$0.526037\pi$
$954$	15.5119	−	5.56013i	0.502215	−	0.180016i
$955$	2.74425	−	11.8840i	0.0888020	−	0.384556i
$956$	−1.80308	+	9.14238i	−0.0583156	+	0.295686i
$957$	−1.46343	+	8.42778i	−0.0473061	+	0.272432i
$958$	24.8642	+	30.2469i	0.803326	+	0.977233i
$959$	33.5395			1.08305
$960$	25.7844	−	17.1804i	0.832187	−	0.554495i
$961$	−29.0749			−0.937899
$962$	23.0048	+	27.9850i	0.741704	+	0.902272i
$963$	26.7591	+	9.58203i	0.862299	+	0.308777i
$964$	8.41698	−	42.6777i	0.271093	−	1.37456i
$965$	10.9551	+	17.5338i	0.352657	+	0.564433i
$966$	−23.9924	+	13.6134i	−0.771944	+	0.438004i
$967$	24.2968	+	24.2968i	0.781332	+	0.781332i	0.980056	−	0.198723i	$-0.0636795\pi$
$967$	24.2968	+	24.2968i	0.781332	+	0.781332i	−0.198723	+	0.980056i	$0.563680\pi$
$968$	8.22056	+	15.2897i	0.264219	+	0.491430i
$969$	31.3701	+	5.44723i	1.00775	+	0.174990i
$970$	−26.6325	−	8.95314i	−0.855119	−	0.287468i
$971$	−19.7408	−	19.7408i	−0.633512	−	0.633512i	0.315435	−	0.948947i	$-0.397850\pi$
$971$	−19.7408	−	19.7408i	−0.633512	−	0.633512i	−0.948947	+	0.315435i	$0.897850\pi$
$972$	27.1111	−	15.3944i	0.869590	−	0.493775i
$973$		−	38.7863i		−	1.24343i
$974$	−5.60352	+	57.3719i	−0.179548	+	1.83831i
$975$	19.4023	−	26.8460i	0.621371	−	0.859761i
$976$	−8.38556	−	20.0597i	−0.268415	−	0.642094i
$977$	−0.855791	−	0.855791i	−0.0273792	−	0.0273792i	0.693285	−	0.720664i	$-0.256163\pi$
$977$	−0.855791	−	0.855791i	−0.0273792	−	0.0273792i	−0.720664	+	0.693285i	$0.756163\pi$
$978$	11.8105	−	6.70134i	0.377659	−	0.214285i
$979$	−15.3377	+	15.3377i	−0.490194	+	0.490194i
$980$	8.44233	+	3.78699i	0.269680	+	0.120971i
$981$	27.8824	−	13.1790i	0.890218	−	0.420772i
$982$	−0.571234	+	5.84860i	−0.0182288	+	0.186636i
$983$	2.64752	+	2.64752i	0.0844427	+	0.0844427i	0.748066	−	0.663624i	$-0.230982\pi$
$983$	2.64752	+	2.64752i	0.0844427	+	0.0844427i	−0.663624	+	0.748066i	$0.730982\pi$
$984$	12.3412	−	4.10872i	0.393423	−	0.130981i
$985$	−14.7408	−	3.40396i	−0.469681	−	0.108459i
$986$	−8.38299	+	6.89116i	−0.266969	+	0.219459i
$987$	−4.19302	+	24.1472i	−0.133465	+	0.768614i
$988$	18.1574	−	12.1752i	0.577665	−	0.387344i
$989$	16.4834	+	16.4834i	0.524142	+	0.524142i
$990$	−24.3315	+	30.8278i	−0.773305	+	0.979773i
$991$	−56.4625			−1.79359			−0.896794	−	0.442447i	$-0.854110\pi$
$991$	−56.4625			−1.79359			−0.896794	+	0.442447i	$0.854110\pi$
$992$	2.30892	+	7.50154i	0.0733084	+	0.238174i
$993$	6.65633	−	4.68668i	0.211232	−	0.148727i
$994$	−2.22378	+	22.7682i	−0.0705340	+	0.722165i
$995$	−5.94163	−	1.37205i	−0.188362	−	0.0434968i
$996$	−1.68243	+	4.38115i	−0.0533100	+	0.138822i
$997$			30.4515i			0.964408i	0.876059	+	0.482204i	$0.160164\pi$
$997$			30.4515i			0.964408i	−0.876059	+	0.482204i	$0.839836\pi$
$998$	8.09364	+	0.790507i	0.256200	+	0.0250231i
$999$	17.1646	−	30.2736i	0.543065	−	0.957813i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bb.a.173.13	✓	88
3.2	odd	2	inner	240.2.bb.a.173.32	yes	88
4.3	odd	2		960.2.bb.a.593.43		88
5.2	odd	4		240.2.bf.a.77.35	yes	88
12.11	even	2		960.2.bb.a.593.2		88
15.2	even	4		240.2.bf.a.77.10	yes	88
16.5	even	4		240.2.bf.a.53.10	yes	88
16.11	odd	4		960.2.bf.a.113.23		88
20.7	even	4		960.2.bf.a.17.23		88
48.5	odd	4		240.2.bf.a.53.35	yes	88
48.11	even	4		960.2.bf.a.113.24		88
60.47	odd	4		960.2.bf.a.17.24		88
80.27	even	4		960.2.bb.a.497.2		88
80.37	odd	4	inner	240.2.bb.a.197.32	yes	88
240.107	odd	4		960.2.bb.a.497.43		88
240.197	even	4	inner	240.2.bb.a.197.13	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bb.a.173.13	✓	88	1.1	even	1	trivial
240.2.bb.a.173.32	yes	88	3.2	odd	2	inner
240.2.bb.a.197.13	yes	88	240.197	even	4	inner
240.2.bb.a.197.32	yes	88	80.37	odd	4	inner
240.2.bf.a.53.10	yes	88	16.5	even	4
240.2.bf.a.53.35	yes	88	48.5	odd	4
240.2.bf.a.77.10	yes	88	15.2	even	4
240.2.bf.a.77.35	yes	88	5.2	odd	4
960.2.bb.a.497.2		88	80.27	even	4
960.2.bb.a.497.43		88	240.107	odd	4
960.2.bb.a.593.2		88	12.11	even	2
960.2.bb.a.593.43		88	4.3	odd	2
960.2.bf.a.17.23		88	20.7	even	4
960.2.bf.a.17.24		88	60.47	odd	4
960.2.bf.a.113.23		88	16.11	odd	4
960.2.bf.a.113.24		88	48.11	even	4

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bb (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.898057 - 1.09247i) q^{2} +(-1.70651 - 0.296326i) q^{3} +(-0.386989 + 1.96220i) q^{4} +(-2.17873 - 0.503115i) q^{5} +(1.20882 + 2.13044i) q^{6} +(-2.12944 - 2.12944i) q^{7} +(2.49119 - 1.33939i) q^{8} +(2.82438 + 1.01137i) q^{9} +O(q^{10})\)	\(q+(-0.898057 - 1.09247i) q^{2} +(-1.70651 - 0.296326i) q^{3} +(-0.386989 + 1.96220i) q^{4} +(-2.17873 - 0.503115i) q^{5} +(1.20882 + 2.13044i) q^{6} +(-2.12944 - 2.12944i) q^{7} +(2.49119 - 1.33939i) q^{8} +(2.82438 + 1.01137i) q^{9} +(1.40699 + 2.83203i) q^{10} +(2.92724 + 2.92724i) q^{11} +(1.24185 - 3.23385i) q^{12} +3.82476i q^{13} +(-0.413995 + 4.23870i) q^{14} +(3.56895 + 1.50419i) q^{15} +(-3.70048 - 1.51870i) q^{16} +(4.54825 + 4.54825i) q^{17} +(-1.43156 - 3.99382i) q^{18} +(-2.02084 + 2.02084i) q^{19} +(1.83036 - 4.08042i) q^{20} +(3.00290 + 4.26492i) q^{21} +(0.569101 - 5.82676i) q^{22} +(-2.64430 - 2.64430i) q^{23} +(-4.64815 + 1.54749i) q^{24} +(4.49375 + 2.19231i) q^{25} +(4.17844 - 3.43485i) q^{26} +(-4.52015 - 2.56285i) q^{27} +(5.00245 - 3.35432i) q^{28} +(-0.843557 - 0.843557i) q^{29} +(-1.56184 - 5.24982i) q^{30} +1.38749 q^{31} +(1.66410 + 5.40655i) q^{32} +(-4.12797 - 5.86280i) q^{33} +(0.884248 - 9.05341i) q^{34} +(3.56812 + 5.71082i) q^{35} +(-3.07752 + 5.15062i) q^{36} +6.69746i q^{37} +(4.02254 + 0.392882i) q^{38} +(1.13338 - 6.52701i) q^{39} +(-6.10150 + 1.66483i) q^{40} -2.65508 q^{41} +(1.96253 - 7.11073i) q^{42} -6.23355 q^{43} +(-6.87666 + 4.61104i) q^{44} +(-5.64474 - 3.62449i) q^{45} +(-0.514093 + 5.26356i) q^{46} +(3.32248 + 3.32248i) q^{47} +(5.86489 + 3.68823i) q^{48} +2.06899i q^{49} +(-1.64061 - 6.87811i) q^{50} +(-6.41388 - 9.10941i) q^{51} +(-7.50495 - 1.48014i) q^{52} +3.88396i q^{53} +(1.25951 + 7.23973i) q^{54} +(-4.90494 - 7.85042i) q^{55} +(-8.15698 - 2.45267i) q^{56} +(4.04742 - 2.84976i) q^{57} +(-0.164000 + 1.67912i) q^{58} +(-10.3658 + 10.3658i) q^{59} +(-4.33267 + 6.42090i) q^{60} +(3.84345 + 3.84345i) q^{61} +(-1.24604 - 1.51579i) q^{62} +(-3.86069 - 8.16798i) q^{63} +(4.41204 - 6.67337i) q^{64} +(1.92429 - 8.33313i) q^{65} +(-2.69780 + 9.77481i) q^{66} +10.0836 q^{67} +(-10.6847 + 7.16446i) q^{68} +(3.72897 + 5.29612i) q^{69} +(3.03454 - 9.02671i) q^{70} +5.37152 q^{71} +(8.39069 - 1.26345i) q^{72} +(-2.68667 + 2.68667i) q^{73} +(7.31679 - 6.01470i) q^{74} +(-7.01901 - 5.07282i) q^{75} +(-3.18325 - 4.74734i) q^{76} -12.4668i q^{77} +(-8.14841 + 4.62344i) q^{78} +5.55500i q^{79} +(7.29827 + 5.17061i) q^{80} +(6.95426 + 5.71299i) q^{81} +(2.38441 + 2.90060i) q^{82} -1.35478 q^{83} +(-9.53073 + 4.24183i) q^{84} +(-7.62112 - 12.1977i) q^{85} +(5.59808 + 6.80998i) q^{86} +(1.18957 + 1.68951i) q^{87} +(11.2131 + 3.37158i) q^{88} +5.23963i q^{89} +(1.10964 + 9.42171i) q^{90} +(8.14458 - 8.14458i) q^{91} +(6.21198 - 4.16534i) q^{92} +(-2.36777 - 0.411150i) q^{93} +(0.645941 - 6.61349i) q^{94} +(5.41958 - 3.38615i) q^{95} +(-1.23771 - 9.71947i) q^{96} +(-6.28272 + 6.28272i) q^{97} +(2.26031 - 1.85807i) q^{98} +(5.30713 + 11.2282i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 4 q^{4} - 4 q^{6}+O(q^{10}) \) 88 * q - 4 * q^4 - 4 * q^6	\( 88 q - 4 q^{4} - 4 q^{6} - 12 q^{10} + 4 q^{12} - 4 q^{15} - 12 q^{16} + 16 q^{18} - 8 q^{19} - 4 q^{21} - 20 q^{22} - 12 q^{24} - 36 q^{28} - 16 q^{30} - 16 q^{31} - 4 q^{33} + 28 q^{34} - 20 q^{36} + 24 q^{39} - 4 q^{40} - 20 q^{42} - 40 q^{43} + 8 q^{45} - 36 q^{46} + 16 q^{48} - 4 q^{51} + 24 q^{52} - 24 q^{54} + 12 q^{57} + 44 q^{58} - 56 q^{60} - 24 q^{61} - 32 q^{63} - 28 q^{64} + 12 q^{66} - 8 q^{67} - 12 q^{69} - 28 q^{70} + 64 q^{72} - 24 q^{75} - 36 q^{76} + 20 q^{78} - 8 q^{81} - 48 q^{82} + 48 q^{84} - 24 q^{85} - 12 q^{87} + 60 q^{88} + 76 q^{90} - 8 q^{91} - 20 q^{94} + 48 q^{96} - 8 q^{97} - 32 q^{99}+O(q^{100}) \) 88 * q - 4 * q^4 - 4 * q^6 - 12 * q^10 + 4 * q^12 - 4 * q^15 - 12 * q^16 + 16 * q^18 - 8 * q^19 - 4 * q^21 - 20 * q^22 - 12 * q^24 - 36 * q^28 - 16 * q^30 - 16 * q^31 - 4 * q^33 + 28 * q^34 - 20 * q^36 + 24 * q^39 - 4 * q^40 - 20 * q^42 - 40 * q^43 + 8 * q^45 - 36 * q^46 + 16 * q^48 - 4 * q^51 + 24 * q^52 - 24 * q^54 + 12 * q^57 + 44 * q^58 - 56 * q^60 - 24 * q^61 - 32 * q^63 - 28 * q^64 + 12 * q^66 - 8 * q^67 - 12 * q^69 - 28 * q^70 + 64 * q^72 - 24 * q^75 - 36 * q^76 + 20 * q^78 - 8 * q^81 - 48 * q^82 + 48 * q^84 - 24 * q^85 - 12 * q^87 + 60 * q^88 + 76 * q^90 - 8 * q^91 - 20 * q^94 + 48 * q^96 - 8 * q^97 - 32 * q^99

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