LMFDB - Embedded newform 207.2.o.a.11.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,2,Mod(5,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([55, 3]))

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

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

chi := DirichletCharacter("207.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.o (of order $66$, degree $20$, 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:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			11.9
Character	$\chi$	$=$	207.11
Dual form			207.2.o.a.113.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.796836 + 0.0379580i) q^{2} +(-1.59395 - 0.677724i) q^{3} +(-1.35744 + 0.129619i) q^{4} +(0.279785 + 0.266774i) q^{5} +(1.29585 + 0.479531i) q^{6} +(-0.0444620 - 0.230691i) q^{7} +(2.65597 - 0.381872i) q^{8} +(2.08138 + 2.16052i) q^{9} +O(q^{10})$	\(q+(-0.796836 + 0.0379580i) q^{2} +(-1.59395 - 0.677724i) q^{3} +(-1.35744 + 0.129619i) q^{4} +(0.279785 + 0.266774i) q^{5} +(1.29585 + 0.479531i) q^{6} +(-0.0444620 - 0.230691i) q^{7} +(2.65597 - 0.381872i) q^{8} +(2.08138 + 2.16052i) q^{9} +(-0.233069 - 0.201955i) q^{10} +(-3.40663 + 1.75624i) q^{11} +(2.25154 + 0.713359i) q^{12} +(6.25244 + 1.20506i) q^{13} +(0.0441855 + 0.182135i) q^{14} +(-0.265165 - 0.614843i) q^{15} +(0.576055 - 0.111026i) q^{16} +(1.94248 + 4.25343i) q^{17} +(-1.74053 - 1.64258i) q^{18} +(4.94633 + 2.25891i) q^{19} +(-0.414369 - 0.325864i) q^{20} +(-0.0854741 + 0.397843i) q^{21} +(2.64786 - 1.52874i) q^{22} +(-2.41253 + 4.14484i) q^{23} +(-4.49231 - 1.19133i) q^{24} +(-0.230799 - 4.84506i) q^{25} +(-5.02792 - 0.722905i) q^{26} +(-1.85339 - 4.85437i) q^{27} +(0.0902563 + 0.307385i) q^{28} +(0.111406 - 1.16670i) q^{29} +(0.234631 + 0.479864i) q^{30} +(0.690862 - 0.543300i) q^{31} +(-5.67011 + 1.37555i) q^{32} +(6.62026 - 0.490613i) q^{33} +(-1.70929 - 3.31556i) q^{34} +(0.0491026 - 0.0764051i) q^{35} +(-3.10539 - 2.66298i) q^{36} +(-1.01963 + 3.47253i) q^{37} +(-4.02716 - 1.61223i) q^{38} +(-9.14941 - 6.15824i) q^{39} +(0.844975 + 0.601704i) q^{40} +(-1.33060 + 1.39550i) q^{41} +(0.0530076 - 0.320261i) q^{42} +(-6.32434 + 8.04205i) q^{43} +(4.39664 - 2.82555i) q^{44} +(0.00596751 + 1.15974i) q^{45} +(1.76506 - 3.39434i) q^{46} +(5.95963 + 3.44080i) q^{47} +(-0.993450 - 0.213437i) q^{48} +(6.44733 - 2.58112i) q^{49} +(0.367817 + 3.85196i) q^{50} +(-0.213569 - 8.09624i) q^{51} +(-8.64350 - 0.825354i) q^{52} +(-0.729817 - 0.842253i) q^{53} +(1.66111 + 3.79779i) q^{54} +(-1.42164 - 0.417432i) q^{55} +(-0.206184 - 0.595730i) q^{56} +(-6.35331 - 6.95285i) q^{57} +(-0.0444869 + 0.933895i) q^{58} +(1.78919 - 9.28320i) q^{59} +(0.439640 + 0.800240i) q^{60} +(-2.28136 + 5.69856i) q^{61} +(-0.529881 + 0.459145i) q^{62} +(0.405870 - 0.576216i) q^{63} +(3.34015 - 0.980756i) q^{64} +(1.42786 + 2.00515i) q^{65} +(-5.25664 + 0.642230i) q^{66} +(2.98608 - 5.79219i) q^{67} +(-3.18812 - 5.52198i) q^{68} +(6.65451 - 4.97166i) q^{69} +(-0.0362265 + 0.0627462i) q^{70} +(6.03456 + 9.38995i) q^{71} +(6.35314 + 4.94347i) q^{72} +(-2.69531 + 5.90191i) q^{73} +(0.680665 - 2.80574i) q^{74} +(-2.91573 + 7.87922i) q^{75} +(-7.00713 - 2.42519i) q^{76} +(0.556614 + 0.707792i) q^{77} +(7.52434 + 4.55982i) q^{78} +(13.6469 - 4.72322i) q^{79} +(0.190790 + 0.122614i) q^{80} +(-0.335702 + 8.99374i) q^{81} +(1.00730 - 1.16249i) q^{82} +(-8.54740 + 8.14993i) q^{83} +(0.0644575 - 0.551126i) q^{84} +(-0.591231 + 1.70825i) q^{85} +(4.73420 - 6.64826i) q^{86} +(-0.968274 + 1.78416i) q^{87} +(-8.37727 + 5.96543i) q^{88} +(1.66158 - 11.5566i) q^{89} +(-0.0487766 - 0.923897i) q^{90} -1.49596i q^{91} +(2.73760 - 5.93907i) q^{92} +(-1.46941 + 0.397782i) q^{93} +(-4.87946 - 2.51554i) q^{94} +(0.781289 + 1.95157i) q^{95} +(9.97013 + 1.65020i) q^{96} +(-1.06773 - 0.259028i) q^{97} +(-5.03950 + 2.30146i) q^{98} +(-10.8849 - 3.70469i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9}+O(q^{10}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23} + 52 q^{24} + 11 q^{25} - 79 q^{27} - 44 q^{28} + 27 q^{29} - 66 q^{30} - 3 q^{31} - 33 q^{32} - 11 q^{34} + 23 q^{36} - 44 q^{37} - 33 q^{38} - 40 q^{39} - 77 q^{40} + 9 q^{41} - 22 q^{42} - 11 q^{43} - 36 q^{46} - 120 q^{47} - 56 q^{48} + 35 q^{49} - 3 q^{50} - 22 q^{51} - 38 q^{52} + 42 q^{54} - 44 q^{55} + 165 q^{56} + 11 q^{57} - 10 q^{58} - 9 q^{59} + 88 q^{60} - 11 q^{61} + 33 q^{63} - 22 q^{64} + 198 q^{65} + 33 q^{66} - 11 q^{67} + 3 q^{69} - 70 q^{70} + 14 q^{72} - 36 q^{73} + 231 q^{74} - 13 q^{75} - 11 q^{76} + 39 q^{77} + 3 q^{78} - 11 q^{79} + 172 q^{81} - 10 q^{82} + 66 q^{83} - 110 q^{84} + q^{85} - 33 q^{86} - 196 q^{87} - 99 q^{88} + 418 q^{90} + 63 q^{92} - 188 q^{93} - 42 q^{94} - 93 q^{95} - 82 q^{96} + 22 q^{97} + 242 q^{99}+O(q^{100}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.796836	+	0.0379580i	−0.563448	+	0.0268404i	−0.327374	−	0.944895i	$-0.606164\pi$
$2$	−0.796836	+	0.0379580i	−0.563448	+	0.0268404i	−0.236074	+	0.971735i	$0.575861\pi$
$3$	−1.59395	−	0.677724i	−0.920270	−	0.391284i
$3$	−1.59395	−	0.677724i	−0.920270	−	0.391284i
$4$	−1.35744	+	0.129619i	−0.678718	+	0.0648097i
$5$	0.279785	+	0.266774i	0.125124	+	0.119305i	0.750058	−	0.661372i	$-0.230026\pi$
$5$	0.279785	+	0.266774i	0.125124	+	0.119305i	−0.624934	+	0.780678i	$0.714874\pi$
$6$	1.29585	+	0.479531i	0.529027	+	0.195768i
$7$	−0.0444620	−	0.230691i	−0.0168051	−	0.0871929i	0.972558	−	0.232661i	$-0.0747433\pi$
$7$	−0.0444620	−	0.230691i	−0.0168051	−	0.0871929i	−0.989363	+	0.145468i	$0.953531\pi$
$8$	2.65597	−	0.381872i	0.939029	−	0.135012i
$9$	2.08138	+	2.16052i	0.693794	+	0.720174i
$10$	−0.233069	−	0.201955i	−0.0737029	−	0.0638639i
$11$	−3.40663	+	1.75624i	−1.02714	+	0.529526i	−0.887564	−	0.460685i	$-0.847604\pi$
$11$	−3.40663	+	1.75624i	−1.02714	+	0.529526i	−0.139574	+	0.990212i	$0.544573\pi$
$12$	2.25154	+	0.713359i	0.649963	+	0.205929i
$13$	6.25244	+	1.20506i	1.73412	+	0.334223i	0.955882	−	0.293751i	$-0.0949036\pi$
$13$	6.25244	+	1.20506i	1.73412	+	0.334223i	0.778234	+	0.627974i	$0.216116\pi$
$14$	0.0441855	+	0.182135i	0.0118091	+	0.0486776i
$15$	−0.265165	−	0.614843i	−0.0684654	−	0.158752i
$16$	0.576055	−	0.111026i	0.144014	−	0.0277564i
$17$	1.94248	+	4.25343i	0.471120	+	1.03161i	0.984810	+	0.173633i	$0.0555508\pi$
$17$	1.94248	+	4.25343i	0.471120	+	1.03161i	−0.513690	+	0.857976i	$0.671722\pi$
$18$	−1.74053	−	1.64258i	−0.410247	−	0.387159i
$19$	4.94633	+	2.25891i	1.13477	+	0.518231i	0.892081	−	0.451875i	$-0.149245\pi$
$19$	4.94633	+	2.25891i	1.13477	+	0.518231i	0.242685	+	0.970105i	$0.421972\pi$
$20$	−0.414369	−	0.325864i	−0.0926558	−	0.0728653i
$21$	−0.0854741	+	0.397843i	−0.0186520	+	0.0868165i
$22$	2.64786	−	1.52874i	0.564526	−	0.325930i
$23$	−2.41253	+	4.14484i	−0.503046	+	0.864259i
$23$	−2.41253	+	4.14484i	−0.503046	+	0.864259i
$24$	−4.49231	−	1.19133i	−0.916988	−	0.243179i
$25$	−0.230799	−	4.84506i	−0.0461597	−	0.969012i
$26$	−5.02792	−	0.722905i	−0.986056	−	0.141773i
$27$	−1.85339	−	4.85437i	−0.356685	−	0.934225i
$28$	0.0902563	+	0.307385i	0.0170568	+	0.0580903i
$29$	0.111406	−	1.16670i	0.0206876	−	0.216650i	−0.979217	−	0.202817i	$-0.934990\pi$
$29$	0.111406	−	1.16670i	0.0206876	−	0.216650i	0.999904	−	0.0138334i	$-0.00440346\pi$
$30$	0.234631	+	0.479864i	0.0428376	+	0.0876108i
$31$	0.690862	−	0.543300i	0.124082	−	0.0975796i	−0.554189	−	0.832391i	$-0.686972\pi$
$31$	0.690862	−	0.543300i	0.124082	−	0.0975796i	0.678272	+	0.734811i	$0.262729\pi$
$32$	−5.67011	+	1.37555i	−1.00234	+	0.243166i
$33$	6.62026	−	0.490613i	1.15244	−	0.0854047i
$34$	−1.70929	−	3.31556i	−0.293141	−	0.568614i
$35$	0.0491026	−	0.0764051i	0.00829985	−	0.0129148i
$36$	−3.10539	−	2.66298i	−0.517565	−	0.443830i
$37$	−1.01963	+	3.47253i	−0.167626	+	0.570880i	0.832239	+	0.554417i	$0.187059\pi$
$37$	−1.01963	+	3.47253i	−0.167626	+	0.570880i	−0.999864	+	0.0164632i	$0.994759\pi$
$38$	−4.02716	−	1.61223i	−0.653292	−	0.261539i
$39$	−9.14941	−	6.15824i	−1.46508	−	0.986108i
$40$	0.844975	+	0.601704i	0.133602	+	0.0951378i
$41$	−1.33060	+	1.39550i	−0.207805	+	0.217940i	−0.819386	−	0.573242i	$-0.805685\pi$
$41$	−1.33060	+	1.39550i	−0.207805	+	0.217940i	0.611581	+	0.791182i	$0.290534\pi$
$42$	0.0530076	−	0.320261i	0.00817924	−	0.0494173i
$43$	−6.32434	+	8.04205i	−0.964453	+	1.22640i	0.00957054	+	0.999954i	$0.496954\pi$
$43$	−6.32434	+	8.04205i	−0.964453	+	1.22640i	−0.974023	+	0.226447i	$0.927289\pi$
$44$	4.39664	−	2.82555i	0.662819	−	0.425968i
$45$	0.00596751	+	1.15974i	0.000889584	+	0.172884i
$46$	1.76506	−	3.39434i	0.260244	−	0.500468i
$47$	5.95963	+	3.44080i	0.869302	+	0.501892i	0.867116	−	0.498106i	$-0.165971\pi$
$47$	5.95963	+	3.44080i	0.869302	+	0.501892i	0.00218557	+	0.999998i	$0.499304\pi$
$48$	−0.993450	−	0.213437i	−0.143392	−	0.0308069i
$49$	6.44733	−	2.58112i	0.921048	−	0.368732i
$50$	0.367817	+	3.85196i	0.0520172	+	0.544749i
$51$	−0.213569	−	8.09624i	−0.0299057	−	1.13370i
$52$	−8.64350	−	0.825354i	−1.19864	−	0.114456i
$53$	−0.729817	−	0.842253i	−0.100248	−	0.115692i	0.703408	−	0.710786i	$-0.251660\pi$
$53$	−0.729817	−	0.842253i	−0.100248	−	0.115692i	−0.803657	+	0.595093i	$0.797115\pi$
$54$	1.66111	+	3.79779i	0.226049	+	0.516814i
$55$	−1.42164	−	0.417432i	−0.191694	−	0.0562866i
$56$	−0.206184	−	0.595730i	−0.0275525	−	0.0796078i
$57$	−6.35331	−	6.95285i	−0.841516	−	0.920928i
$58$	−0.0444869	+	0.933895i	−0.00584141	+	0.122626i
$59$	1.78919	−	9.28320i	0.232933	−	1.20857i	−0.657500	−	0.753455i	$-0.728386\pi$
$59$	1.78919	−	9.28320i	0.232933	−	1.20857i	0.890432	−	0.455115i	$-0.150402\pi$
$60$	0.439640	+	0.800240i	0.0567573	+	0.103311i
$61$	−2.28136	+	5.69856i	−0.292098	+	0.729625i	0.707636	+	0.706577i	$0.249761\pi$
$61$	−2.28136	+	5.69856i	−0.292098	+	0.729625i	−0.999734	+	0.0230485i	$0.992663\pi$
$62$	−0.529881	+	0.459145i	−0.0672950	+	0.0583115i
$63$	0.405870	−	0.576216i	0.0511348	−	0.0725964i
$64$	3.34015	−	0.980756i	0.417518	−	0.122594i
$65$	1.42786	+	2.00515i	0.177104	+	0.248708i
$66$	−5.25664	+	0.642230i	−0.647048	+	0.0790530i
$67$	2.98608	−	5.79219i	0.364808	−	0.707628i	−0.632976	−	0.774172i	$-0.718167\pi$
$67$	2.98608	−	5.79219i	0.364808	−	0.707628i	0.997784	+	0.0665434i	$0.0211971\pi$
$68$	−3.18812	−	5.52198i	−0.386616	−	0.669639i
$69$	6.65451	−	4.97166i	0.801109	−	0.598518i
$70$	−0.0362265	+	0.0627462i	−0.00432990	+	0.00749961i
$71$	6.03456	+	9.38995i	0.716170	+	1.11438i	0.988359	+	0.152138i	$0.0486160\pi$
$71$	6.03456	+	9.38995i	0.716170	+	1.11438i	−0.272189	+	0.962244i	$0.587748\pi$
$72$	6.35314	+	4.94347i	0.748725	+	0.582593i
$73$	−2.69531	+	5.90191i	−0.315462	+	0.690766i	−0.999242	−	0.0389224i	$-0.987607\pi$
$73$	−2.69531	+	5.90191i	−0.315462	+	0.690766i	0.683780	+	0.729688i	$0.260335\pi$
$74$	0.680665	−	2.80574i	0.0791257	−	0.326161i
$75$	−2.91573	+	7.87922i	−0.336679	+	0.909814i
$76$	−7.00713	−	2.42519i	−0.803773	−	0.278189i
$77$	0.556614	+	0.707792i	0.0634320	+	0.0806604i
$78$	7.52434	+	4.55982i	0.851964	+	0.516297i
$79$	13.6469	−	4.72322i	1.53539	−	0.531404i	0.576971	−	0.816765i	$-0.304235\pi$
$79$	13.6469	−	4.72322i	1.53539	−	0.531404i	0.958420	+	0.285361i	$0.0921134\pi$
$80$	0.190790	+	0.122614i	0.0213310	+	0.0137086i
$81$	−0.335702	+	8.99374i	−0.0373002	+	0.999304i
$82$	1.00730	−	1.16249i	0.111238	−	0.128375i
$83$	−8.54740	+	8.14993i	−0.938199	+	0.894571i	−0.994594	−	0.103838i	$-0.966888\pi$
$83$	−8.54740	+	8.14993i	−0.938199	+	0.894571i	0.0563953	+	0.998409i	$0.482039\pi$
$84$	0.0644575	−	0.551126i	0.00703289	−	0.0601328i
$85$	−0.591231	+	1.70825i	−0.0641280	+	0.185286i
$86$	4.73420	−	6.64826i	0.510502	−	0.716900i
$87$	−0.968274	+	1.78416i	−0.103810	+	0.191282i
$88$	−8.37727	+	5.96543i	−0.893020	+	0.635916i
$89$	1.66158	−	11.5566i	0.176127	−	1.22499i	−0.689493	−	0.724292i	$-0.742167\pi$
$89$	1.66158	−	11.5566i	0.176127	−	1.22499i	0.865620	−	0.500701i	$-0.166924\pi$
$90$	−0.0487766	−	0.923897i	−0.00514150	−	0.0973873i
$91$		−	1.49596i		−	0.156819i
$92$	2.73760	−	5.93907i	0.285414	−	0.619191i
$93$	−1.46941	+	0.397782i	−0.152371	+	0.0412481i
$94$	−4.87946	−	2.51554i	−0.503278	−	0.259458i
$95$	0.781289	+	1.95157i	0.0801586	+	0.200226i
$96$	9.97013	+	1.65020i	1.01757	+	0.168422i
$97$	−1.06773	−	0.259028i	−0.108411	−	0.0263003i	0.181186	−	0.983449i	$-0.442006\pi$
$97$	−1.06773	−	0.259028i	−0.108411	−	0.0263003i	−0.289598	+	0.957148i	$0.593521\pi$
$98$	−5.03950	+	2.30146i	−0.509066	+	0.232483i
$99$	−10.8849	−	3.70469i	−1.09397	−	0.372335i
$100$	0.941308	+	6.54694i	0.0941308	+	0.654694i
$101$	3.90074	+	4.09098i	0.388138	+	0.407067i	0.888594	−	0.458695i	$-0.151683\pi$
$101$	3.90074	+	4.09098i	0.388138	+	0.407067i	−0.500456	+	0.865762i	$0.666834\pi$
$102$	0.477497	+	6.44327i	0.0472792	+	0.637979i
$103$	−6.92999	−	0.330116i	−0.682832	−	0.0325273i	−0.296700	−	0.954971i	$-0.595886\pi$
$103$	−6.92999	−	0.330116i	−0.682832	−	0.0325273i	−0.386132	+	0.922443i	$0.626189\pi$
$104$	17.0665	+	0.812978i	1.67351	+	0.0797191i
$105$	−0.130049	+	0.0885083i	−0.0126915	+	0.00863752i
$106$	0.613515	+	0.643436i	0.0595898	+	0.0624960i
$107$	−0.843310	−	5.86535i	−0.0815259	−	0.567025i	−0.989113	−	0.147160i	$-0.952987\pi$
$107$	−0.843310	−	5.86535i	−0.0815259	−	0.567025i	0.907587	−	0.419865i	$-0.137922\pi$
$108$	3.14508	+	6.34927i	0.302636	+	0.610959i
$109$	−7.63347	+	3.48609i	−0.731154	+	0.333907i	−0.745966	−	0.665984i	$-0.768012\pi$
$109$	−7.63347	+	3.48609i	−0.731154	+	0.333907i	0.0148127	+	0.999890i	$0.495285\pi$
$110$	1.14866	+	0.278663i	0.109521	+	0.0265694i
$111$	3.97865	−	4.84403i	0.377637	−	0.459775i
$112$	−0.0512251	−	0.127954i	−0.00484032	−	0.0120905i
$113$	13.2759	+	6.84418i	1.24889	+	0.643846i	0.950537	−	0.310610i	$-0.100533\pi$
$113$	13.2759	+	6.84418i	1.24889	+	0.643846i	0.298350	+	0.954456i	$0.403564\pi$
$114$	5.32646	+	5.29913i	0.498869	+	0.496309i
$115$	−1.78073	+	0.516064i	−0.166054	+	0.0481233i
$116$			1.59816i			0.148385i
$117$	10.4102	+	16.0167i	0.962420	+	1.48075i
$118$	−1.07332	+	7.46511i	−0.0988072	+	0.687219i
$119$	0.894861	−	0.637228i	0.0820318	−	0.0584146i
$120$	−0.939063	−	1.53175i	−0.0857243	−	0.139829i
$121$	2.14013	−	3.00539i	0.194557	−	0.273217i
$122$	1.60156	−	4.62741i	0.144999	−	0.418946i
$123$	3.06668	−	1.32258i	0.276513	−	0.119253i
$124$	−0.867379	+	0.827044i	−0.0778929	+	0.0742708i
$125$	2.49376	−	2.87795i	0.223049	−	0.257412i
$126$	−0.301540	+	0.474556i	−0.0268633	+	0.0422768i
$127$	6.47355	+	4.16030i	0.574435	+	0.369167i	0.795372	−	0.606121i	$-0.207275\pi$
$127$	6.47355	+	4.16030i	0.574435	+	0.369167i	−0.220938	+	0.975288i	$0.570912\pi$
$128$	8.40303	−	2.90832i	0.742730	−	0.257061i
$129$	15.5310	−	8.53251i	1.36743	−	0.751246i
$130$	−1.21388	−	1.54358i	−0.106465	−	0.135381i
$131$	−15.1714	−	5.25089i	−1.32554	−	0.458772i	−0.429625	−	0.903007i	$-0.641354\pi$
$131$	−15.1714	−	5.25089i	−1.32554	−	0.458772i	−0.895910	+	0.444235i	$0.853476\pi$
$132$	−8.92299	+	1.52409i	−0.776646	+	0.132655i
$133$	0.301187	−	1.24151i	0.0261162	−	0.107652i
$134$	−2.15956	+	4.72877i	−0.186557	+	0.408504i
$135$	0.776472	−	1.85262i	0.0668280	−	0.159448i
$136$	6.78344	+	10.5552i	0.581675	+	0.905104i
$137$	−3.01824	+	5.22774i	−0.257866	+	0.446636i	−0.965670	−	0.259772i	$-0.916352\pi$
$137$	−3.01824	+	5.22774i	−0.257866	+	0.446636i	0.707804	+	0.706408i	$0.249686\pi$
$138$	−5.11384	+	4.21420i	−0.435319	+	0.358736i
$139$	−2.64473	−	4.58080i	−0.224323	−	0.388539i	0.731793	−	0.681527i	$-0.238684\pi$
$139$	−2.64473	−	4.58080i	−0.224323	−	0.388539i	−0.956116	+	0.292988i	$0.905350\pi$
$140$	−0.0567500	+	0.110080i	−0.00479625	+	0.00930343i
$141$	−7.16747	−	9.52345i	−0.603610	−	0.802019i
$142$	−5.16498	−	7.25320i	−0.433435	−	0.608675i
$143$	−23.4161	+	6.87560i	−1.95816	+	0.574967i
$144$	1.43886	+	1.01349i	0.119905	+	0.0844577i
$145$	0.342414	−	0.296704i	0.0284360	−	0.0246399i
$146$	1.92370	−	4.80516i	0.159206	−	0.397678i
$147$	−12.0260	−	0.255317i	−0.991891	−	0.0210582i
$148$	0.933971	−	4.84590i	0.0767720	−	0.398331i
$149$	0.541194	−	11.3611i	0.0443364	−	0.930735i	−0.861670	−	0.507470i	$-0.830581\pi$
$149$	0.541194	−	11.3611i	0.0443364	−	0.930735i	0.906006	−	0.423265i	$-0.139116\pi$
$150$	2.02428	−	6.38912i	0.165282	−	0.521670i
$151$	−6.50545	−	18.7963i	−0.529406	−	1.52962i	−0.819765	−	0.572700i	$-0.805896\pi$
$151$	−6.50545	−	18.7963i	−0.529406	−	1.52962i	0.290359	−	0.956918i	$-0.406225\pi$
$152$	14.0000	+	4.11076i	1.13555	+	0.333426i
$153$	−5.14659	+	13.0498i	−0.416078	+	1.05501i
$154$	−0.470397	−	0.542867i	−0.0379056	−	0.0437454i
$155$	0.338231	+	0.0322972i	0.0271674	+	0.00259417i
$156$	13.2180	+	7.17348i	1.05829	+	0.574338i
$157$	−0.810604	−	8.48903i	−0.0646932	−	0.677498i	−0.968409	−	0.249366i	$-0.919778\pi$
$157$	−0.810604	−	8.48903i	−0.0646932	−	0.677498i	0.903716	−	0.428132i	$-0.140828\pi$
$158$	−10.6950	+	4.28164i	−0.850851	+	0.340629i
$159$	0.592479	+	1.83713i	0.0469867	+	0.145694i
$160$	−1.95337	−	1.12778i	−0.154428	−	0.0891589i
$161$	1.06344	+	0.372259i	0.0838110	+	0.0293381i
$162$	−0.0738848	−	7.17928i	−0.00580493	−	0.564057i
$163$	−4.58506	+	2.94664i	−0.359129	+	0.230798i	−0.707746	−	0.706467i	$-0.750288\pi$
$163$	−4.58506	+	2.94664i	−0.359129	+	0.230798i	0.348617	+	0.937265i	$0.386652\pi$
$164$	1.62533	−	2.06677i	0.126917	−	0.161388i
$165$	1.98313	+	1.62885i	0.154387	+	0.126806i
$166$	6.50152	−	6.81860i	0.504616	−	0.529226i
$167$	−4.34608	−	3.09483i	−0.336310	−	0.239485i	0.399408	−	0.916773i	$-0.369216\pi$
$167$	−4.34608	−	3.09483i	−0.336310	−	0.239485i	−0.735718	+	0.677288i	$0.763155\pi$
$168$	−0.0750921	+	1.08930i	−0.00579348	+	0.0840415i
$169$	25.5721	+	10.2375i	1.96709	+	0.787502i
$170$	0.406273	−	1.38364i	0.0311597	−	0.106120i
$171$	5.41477	+	15.3883i	0.414078	+	1.17677i
$172$	7.54248	−	11.7363i	0.575109	−	0.894887i
$173$	−5.53556	−	10.7375i	−0.420861	−	0.816356i	−0.999999	−	0.00112702i	$-0.999641\pi$
$173$	−5.53556	−	10.7375i	−0.420861	−	0.816356i	0.579138	−	0.815229i	$-0.303389\pi$
$174$	0.703833	−	1.45844i	0.0533574	−	0.110564i
$175$	−1.10745	+	0.268664i	−0.0837152	+	0.0203091i
$176$	−1.76742	+	1.38991i	−0.133224	+	0.104769i
$177$	−9.14334	+	13.5844i	−0.687255	+	1.02107i
$178$	−0.885346	+	9.27176i	−0.0663595	+	0.694948i
$179$	−5.11481	−	17.4194i	−0.382298	−	1.30199i	−0.896013	−	0.444028i	$-0.853549\pi$
$179$	−5.11481	−	17.4194i	−0.382298	−	1.30199i	0.513715	−	0.857961i	$-0.328269\pi$
$180$	−0.158425	−	1.57350i	−0.0118083	−	0.117282i
$181$	−20.7095	−	2.97758i	−1.53933	−	0.221322i	−0.680178	−	0.733047i	$-0.738097\pi$
$181$	−20.7095	−	2.97758i	−1.53933	−	0.221322i	−0.859149	+	0.511725i	$0.829007\pi$
$182$	0.0567836	+	1.19204i	0.00420908	+	0.0883595i
$183$	7.49842	−	7.53711i	0.554300	−	0.557159i
$184$	−4.82481	+	11.9299i	−0.355690	+	0.879482i
$185$	−1.21166	+	0.699551i	−0.0890829	+	0.0514320i
$186$	1.15578	−	0.372743i	0.0847459	−	0.0273308i
$187$	−14.0874	−	11.0784i	−1.03017	−	0.810134i
$188$	−8.53582	−	3.89818i	−0.622538	−	0.284304i
$189$	−1.03745	+	0.643395i	−0.0754636	+	0.0468001i
$190$	−0.696637	−	1.52542i	−0.0505394	−	0.110666i
$191$	20.4310	−	3.93775i	1.47834	−	0.284926i	0.614587	−	0.788849i	$-0.289323\pi$
$191$	20.4310	−	3.93775i	1.47834	−	0.284926i	0.863749	+	0.503923i	$0.168110\pi$
$192$	−5.98872	−	0.700417i	−0.432199	−	0.0505482i
$193$	−0.0528748	−	0.217953i	−0.00380601	−	0.0156886i	0.969877	−	0.243596i	$-0.0783269\pi$
$193$	−0.0528748	−	0.217953i	−0.00380601	−	0.0156886i	−0.973683	+	0.227907i	$0.926812\pi$
$194$	0.860637	+	0.165874i	0.0617901	+	0.0119091i
$195$	−0.917008	−	4.16381i	−0.0656683	−	0.298177i
$196$	−8.41728	+	4.33941i	−0.601234	+	0.309958i
$197$	−6.05870	−	5.24989i	−0.431664	−	0.374039i	0.411755	−	0.911294i	$-0.364916\pi$
$197$	−6.05870	−	5.24989i	−0.431664	−	0.374039i	−0.843420	+	0.537255i	$0.819461\pi$
$198$	8.81410	+	2.53886i	0.626391	+	0.180429i
$199$	−5.31597	+	0.764321i	−0.376839	+	0.0541813i	−0.328132	−	0.944632i	$-0.606419\pi$
$199$	−5.31597	+	0.764321i	−0.376839	+	0.0541813i	−0.0487069	+	0.998813i	$0.515510\pi$
$200$	−2.46318	−	12.7802i	−0.174173	−	0.903698i
$201$	−8.68518	+	7.20874i	−0.612605	+	0.508466i
$202$	−3.26353	−	3.11177i	−0.229622	−	0.218944i
$203$	−0.274099	+	0.0261733i	−0.0192380	+	0.00183701i
$204$	1.33934	+	10.9625i	0.0937724	+	0.767525i
$205$	−0.744566	+	0.0354680i	−0.0520027	+	0.00247719i
$206$	5.53460			0.385614
$207$	−13.9764	+	3.41469i	−0.971427	+	0.237337i
$208$	3.73555			0.259013
$209$	−20.8175	+	0.991661i	−1.43998	+	0.0685946i
$210$	0.100268	−	0.0754630i	0.00691915	−	0.00520744i
$211$	−6.69948	+	0.639723i	−0.461211	+	0.0440403i	−0.323076	−	0.946373i	$-0.604717\pi$
$211$	−6.69948	+	0.639723i	−0.461211	+	0.0440403i	−0.138135	+	0.990413i	$0.544111\pi$
$212$	1.09985	+	1.04871i	0.0755381	+	0.0720255i
$213$	−3.25501	−	19.0569i	−0.223030	−	1.30576i
$214$	0.894618	+	4.64172i	0.0611548	+	0.317301i
$215$	−3.91487	+	0.562873i	−0.266992	+	0.0383876i
$216$	−6.77631	−	12.1853i	−0.461069	−	0.829107i
$217$	−0.156051	−	0.135219i	−0.0105935	−	0.00917928i
$218$	5.95030	−	3.06759i	0.403005	−	0.207764i
$219$	8.29606	−	7.58069i	0.560596	−	0.512256i
$220$	1.98390	+	0.382365i	0.133754	+	0.0257791i
$221$	7.01959	+	28.9352i	0.472189	+	1.94639i
$222$	−2.98647	+	4.01092i	−0.200439	+	0.269195i
$223$	13.6409	−	2.62907i	0.913462	−	0.176055i	0.289199	−	0.957269i	$-0.406611\pi$
$223$	13.6409	−	2.62907i	0.913462	−	0.176055i	0.624264	+	0.781214i	$0.285399\pi$
$224$	0.569431	+	1.24688i	0.0380467	+	0.0833107i
$225$	9.98747	−	10.5831i	0.665831	−	0.705537i
$226$	−10.8385	−	4.94977i	−0.720965	−	0.329254i
$227$	14.9986	+	11.7950i	0.995493	+	0.782864i	0.976183	−	0.216949i	$-0.0696106\pi$
$227$	14.9986	+	11.7950i	0.995493	+	0.782864i	0.0193100	+	0.999814i	$0.493853\pi$
$228$	9.52544	+	8.61454i	0.630838	+	0.570512i
$229$	−7.85163	+	4.53314i	−0.518851	+	0.299558i	−0.736464	−	0.676476i	$-0.763506\pi$
$229$	−7.85163	+	4.53314i	−0.518851	+	0.299558i	0.217614	+	0.976035i	$0.430173\pi$
$230$	1.39936	−	0.478812i	0.0922710	−	0.0315719i
$231$	−0.407530	−	1.50542i	−0.0268135	−	0.0990493i
$232$	−0.149637	−	3.14126i	−0.00982412	−	0.206234i
$233$	17.1275	+	2.46256i	1.12206	+	0.161328i	0.678277	−	0.734806i	$-0.262727\pi$
$233$	17.1275	+	2.46256i	1.12206	+	0.161328i	0.443783	+	0.896134i	$0.353636\pi$
$234$	−8.90316	−	12.3676i	−0.582018	−	0.808493i
$235$	0.749499	+	2.55256i	0.0488919	+	0.166511i
$236$	−1.22543	+	12.8333i	−0.0797686	+	0.835375i
$237$	−24.9535	−	1.72019i	−1.62090	−	0.111739i
$238$	−0.688870	+	0.541733i	−0.0446528	+	0.0351154i
$239$	−7.20807	+	1.74866i	−0.466251	+	0.113111i	−0.462000	−	0.886880i	$-0.652868\pi$
$239$	−7.20807	+	1.74866i	−0.466251	+	0.113111i	−0.00425060	+	0.999991i	$0.501353\pi$
$240$	−0.221013	−	0.324743i	−0.0142663	−	0.0209621i
$241$	0.554618	+	1.07581i	0.0357261	+	0.0692990i	0.906023	−	0.423229i	$-0.139103\pi$
$241$	0.554618	+	1.07581i	0.0357261	+	0.0692990i	−0.870297	+	0.492528i	$0.836073\pi$
$242$	−1.59125	+	2.47604i	−0.102290	+	0.159166i
$243$	6.63036	−	14.1081i	0.425338	−	0.905035i
$244$	2.35815	−	8.03113i	0.150965	−	0.514141i
$245$	2.49244	+	0.997824i	0.159236	+	0.0637487i
$246$	−2.39344	+	1.17028i	−0.152600	+	0.0746145i
$247$	28.2045	+	20.0844i	1.79461	+	1.27794i
$248$	1.62744	−	1.70681i	0.103343	−	0.108383i
$249$	19.1476	−	7.19784i	1.21343	−	0.456145i
$250$	−1.87788	+	2.38792i	−0.118767	+	0.151025i
$251$	−2.92061	+	1.87696i	−0.184348	+	0.118473i	−0.629560	−	0.776952i	$-0.716765\pi$
$251$	−2.92061	+	1.87696i	−0.184348	+	0.118473i	0.445212	+	0.895425i	$0.353128\pi$
$252$	−0.476253	+	0.834786i	−0.0300011	+	0.0525866i
$253$	0.939245	−	18.3569i	0.0590498	−	1.15409i
$254$	−5.31628	−	3.06935i	−0.333573	−	0.192588i
$255$	2.10012	−	2.32218i	0.131514	−	0.145421i
$256$	−13.0490	+	5.22405i	−0.815565	+	0.326503i
$257$	−0.366395	−	3.83706i	−0.0228551	−	0.239349i	−0.999680	−	0.0253079i	$-0.991943\pi$
$257$	−0.366395	−	3.83706i	−0.0228551	−	0.239349i	0.976825	−	0.214041i	$-0.0686627\pi$
$258$	−12.0518	+	7.38854i	−0.750312	+	0.459990i
$259$	0.846415	+	0.0808228i	0.0525937	+	0.00502209i
$260$	−2.19814	−	2.53679i	−0.136323	−	0.157325i
$261$	2.75255	−	2.18764i	0.170379	−	0.135412i
$262$	12.2885	+	3.60822i	0.759184	+	0.222917i
$263$	−5.06015	−	14.6203i	−0.312022	−	0.901529i	−0.986576	−	0.163303i	$-0.947785\pi$
$263$	−5.06015	−	14.6203i	−0.312022	−	0.901529i	0.674554	−	0.738226i	$-0.264336\pi$
$264$	17.3959	−	3.83114i	1.07064	−	0.235791i
$265$	0.0204999	−	0.430346i	0.00125930	−	0.0264360i
$266$	−0.192871	+	1.00071i	−0.0118257	+	0.0613576i
$267$	−10.4806	+	17.2945i	−0.641405	+	1.05841i
$268$	−3.30263	+	8.24958i	−0.201740	+	0.503923i
$269$	2.06562	−	1.78987i	0.125943	−	0.109131i	−0.589612	−	0.807687i	$-0.700719\pi$
$269$	2.06562	−	1.78987i	0.125943	−	0.109131i	0.715555	+	0.698556i	$0.246174\pi$
$270$	−0.548399	+	1.50571i	−0.0333745	+	0.0916344i
$271$	10.5127	−	3.08681i	0.638602	−	0.187511i	0.0536262	−	0.998561i	$-0.482922\pi$
$271$	10.5127	−	3.08681i	0.638602	−	0.187511i	0.584976	+	0.811051i	$0.301104\pi$
$272$	1.59121	+	2.23455i	0.0964815	+	0.135489i
$273$	−1.01385	+	2.38449i	−0.0613608	+	0.144316i
$274$	2.20661	−	4.28022i	0.133306	−	0.258578i
$275$	9.29533	+	16.1000i	0.560530	+	0.970866i
$276$	−8.38865	+	7.61127i	−0.504938	+	0.458145i
$277$	−8.96349	+	15.5252i	−0.538564	+	0.932821i	0.460417	+	0.887703i	$0.347700\pi$
$277$	−8.96349	+	15.5252i	−0.538564	+	0.932821i	−0.998982	+	0.0451180i	$0.985634\pi$
$278$	2.28129	+	3.54976i	0.136823	+	0.212901i
$279$	2.61176	+	0.361808i	0.156362	+	0.0216609i
$280$	0.101238	−	0.221681i	0.00605014	−	0.0132480i
$281$	1.03923	−	4.28376i	0.0619952	−	0.255548i	−0.932378	−	0.361486i	$-0.882270\pi$
$281$	1.03923	−	4.28376i	0.0619952	−	0.255548i	0.994373	+	0.105938i	$0.0337847\pi$
$282$	6.07280	+	7.31657i	0.361630	+	0.435695i
$283$	28.6357	+	9.91092i	1.70222	+	0.589143i	0.993239	−	0.116087i	$-0.0370350\pi$
$283$	28.6357	+	9.91092i	1.70222	+	0.589143i	0.708979	+	0.705230i	$0.249156\pi$
$284$	−9.40865	−	11.9641i	−0.558300	−	0.709937i
$285$	0.0772829	−	3.64020i	0.00457784	−	0.215627i
$286$	18.3979	−	6.36756i	1.08789	−	0.376522i
$287$	0.381089	+	0.244911i	0.0224950	+	0.0144567i
$288$	−14.7736	−	9.38733i	−0.870541	−	0.553154i
$289$	−3.18584	+	3.67666i	−0.187403	+	0.216274i
$290$	−0.261586	+	0.249422i	−0.0153609	+	0.0146465i
$291$	1.52636	+	1.13650i	0.0894769	+	0.0666230i
$292$	2.89371	−	8.36083i	0.169342	−	0.489280i
$293$	10.3436	−	14.5256i	0.604282	−	0.848595i	−0.393205	−	0.919451i	$-0.628634\pi$
$293$	10.3436	−	14.5256i	0.604282	−	0.848595i	0.997487	+	0.0708560i	$0.0225731\pi$
$294$	9.59248	−	0.253038i	0.559445	−	0.0147575i
$295$	2.97711	−	2.11999i	0.173334	−	0.123431i
$296$	−1.38204	+	9.61232i	−0.0803296	+	0.558705i
$297$	14.8393	+	13.2821i	0.861062	+	0.770703i
$298$			9.07345i			0.525611i
$299$	−20.0790	+	23.0082i	−1.16120	+	1.33060i
$300$	2.93661	−	11.0735i	0.169546	−	0.639327i
$301$	2.13642	+	1.10140i	0.123141	+	0.0634837i
$302$	5.89724	+	14.7306i	0.339348	+	0.847651i
$303$	−3.44505	−	9.16445i	−0.197913	−	0.526484i
$304$	3.10016	+	0.752090i	0.177806	+	0.0431353i
$305$	−2.15852	+	0.985762i	−0.123596	+	0.0564446i
$306$	3.60565	−	10.5939i	0.206121	−	0.605613i
$307$	3.03118	+	21.0823i	0.172999	+	1.20323i	0.872504	+	0.488606i	$0.162494\pi$
$307$	3.03118	+	21.0823i	0.172999	+	1.20323i	−0.699506	+	0.714627i	$0.746596\pi$
$308$	−0.847312	−	0.888635i	−0.0482801	−	0.0506347i
$309$	10.8224	+	5.22281i	0.615662	+	0.297115i
$310$	−0.270741	−	0.0128970i	−0.0153771	−	0.000732499i
$311$	−0.0135254		0.000644294i	−0.000766954		3.65345e-5i	0.0471984	−	0.998886i	$-0.484971\pi$
$311$	−0.0135254		0.000644294i	−0.000766954		3.65345e-5i	−0.0479654	+	0.998849i	$0.515274\pi$
$312$	−26.6523	−	12.8622i	−1.50889	−	0.728180i
$313$	−18.9946	−	19.9209i	−1.07364	−	1.12600i	−0.991597	−	0.129369i	$-0.958705\pi$
$313$	−18.9946	−	19.9209i	−1.07364	−	1.12600i	−0.0820402	−	0.996629i	$-0.526144\pi$
$314$	0.968145	+	6.73360i	0.0546356	+	0.379999i
$315$	0.267276	−	0.0529410i	0.0150593	−	0.00298289i
$316$	−17.9125	+	8.18037i	−1.00766	+	0.460182i
$317$	−1.09953	−	0.266744i	−0.0617559	−	0.0149818i	0.204762	−	0.978812i	$-0.434358\pi$
$317$	−1.09953	−	0.266744i	−0.0617559	−	0.0149818i	−0.266518	+	0.963830i	$0.585873\pi$
$318$	−0.541843	−	1.44140i	−0.0303850	−	0.0808297i
$319$	1.66948	+	4.17016i	0.0934729	+	0.233484i
$320$	1.19616	+	0.616665i	0.0668676	+	0.0344726i
$321$	−2.63089	+	9.92064i	−0.146842	+	0.553716i
$322$	−0.861520	−	0.256264i	−0.0480106	−	0.0142810i
$323$			25.4268i			1.41478i
$324$	−0.710069	−	12.2519i	−0.0394483	−	0.680663i
$325$	4.39553	−	30.5716i	0.243820	−	1.69581i
$326$	3.54169	−	2.52203i	0.196156	−	0.139682i
$327$	14.5300	−	0.383284i	0.803511	−	0.0211957i
$328$	−3.00115	+	4.21452i	−0.165711	+	0.232708i
$329$	0.528782	−	1.52782i	0.0291527	−	0.0842312i
$330$	−1.64206	−	1.22265i	−0.0903924	−	0.0673047i
$331$	21.7823	−	20.7694i	1.19726	−	1.14159i	0.210814	−	0.977526i	$-0.432388\pi$
$331$	21.7823	−	20.7694i	1.19726	−	1.14159i	0.986450	−	0.164063i	$-0.0524601\pi$
$332$	10.5462	−	12.1709i	0.578796	−	0.667966i
$333$	−9.62471	+	5.02473i	−0.527431	+	0.275354i
$334$	3.58059	+	2.30110i	0.195921	+	0.125911i
$335$	2.38067	−	0.823957i	0.130070	−	0.0450176i
$336$	−0.00506704	+	0.238670i	−0.000276430	+	0.0130205i
$337$	12.7077	+	16.1591i	0.692230	+	0.880243i	0.997401	−	0.0720552i	$-0.0229558\pi$
$337$	12.7077	+	16.1591i	0.692230	+	0.880243i	−0.305170	+	0.952298i	$0.598713\pi$
$338$	−20.7654	−	7.18697i	−1.12949	−	0.390920i
$339$	−16.5226	−	19.9067i	−0.897387	−	1.08118i
$340$	0.581136	−	2.39548i	0.0315165	−	0.129913i
$341$	−1.39935	+	3.06414i	−0.0757789	+	0.165933i
$342$	−4.89880	−	12.0564i	−0.264897	−	0.651938i
$343$	−1.77122	−	2.75607i	−0.0956366	−	0.148814i
$344$	−13.7263	+	23.7746i	−0.740070	+	1.28184i
$345$	3.18815	+	0.384257i	0.171644	+	0.0206877i
$346$	4.81851	+	8.34590i	0.259045	+	0.448679i
$347$	−6.65097	+	12.9011i	−0.357043	+	0.692566i	−0.997128	−	0.0757380i	$-0.975869\pi$
$347$	−6.65097	+	12.9011i	−0.357043	+	0.692566i	0.640085	+	0.768304i	$0.278899\pi$
$348$	1.08311	−	2.54739i	0.0580607	−	0.136554i
$349$	15.6359	+	21.9576i	0.836973	+	1.17536i	0.982547	+	0.186017i	$0.0595578\pi$
$349$	15.6359	+	21.9576i	0.836973	+	1.17536i	−0.145574	+	0.989347i	$0.546503\pi$
$350$	0.872257	−	0.256118i	0.0466241	−	0.0136901i
$351$	−5.73842	−	32.5851i	−0.306294	−	1.73927i
$352$	16.9002	−	14.6441i	0.900781	−	0.780531i
$353$	−5.10456	+	12.7506i	−0.271688	+	0.678645i	−0.999978	−	0.00662470i	$-0.997891\pi$
$353$	−5.10456	+	12.7506i	−0.271688	+	0.678645i	0.728290	+	0.685269i	$0.240316\pi$
$354$	6.77010	−	11.1716i	0.359827	−	0.593765i
$355$	−0.816621	+	4.23703i	−0.0433417	+	0.224878i
$356$	−0.757538	+	15.9027i	−0.0401494	+	0.842840i
$357$	−1.85823	+	0.409243i	−0.0983481	+	0.0216595i
$358$	4.73687	+	13.6863i	0.250351	+	0.723343i
$359$	−2.08983	−	0.613630i	−0.110297	−	0.0323861i	0.226118	−	0.974100i	$-0.427396\pi$
$359$	−2.08983	−	0.613630i	−0.110297	−	0.0323861i	−0.336415	+	0.941714i	$0.609215\pi$
$360$	0.458721	+	3.07796i	0.0241767	+	0.162223i
$361$	6.92116	+	7.98744i	0.364272	+	0.420392i
$362$	16.6151	+	1.58655i	0.873272	+	0.0833873i
$363$	−5.44809	+	3.34004i	−0.285950	+	0.175306i
$364$	0.193906	+	2.03067i	0.0101634	+	0.106436i
$365$	−2.32858	+	0.932225i	−0.121884	+	0.0487949i
$366$	−5.68892	+	6.29047i	−0.297365	+	0.328808i
$367$	−4.77141	−	2.75478i	−0.249066	−	0.143798i	0.370271	−	0.928924i	$-0.379265\pi$
$367$	−4.77141	−	2.75478i	−0.249066	−	0.143798i	−0.619336	+	0.785126i	$0.712598\pi$
$368$	−0.929565	+	2.65551i	−0.0484569	+	0.138428i
$369$	−5.78449	+	0.0297644i	−0.301129	+	0.00154948i
$370$	0.938940	−	0.603420i	0.0488132	−	0.0313703i
$371$	−0.161851	+	0.205810i	−0.00840288	+	0.0106851i
$372$	1.94307	−	0.730428i	0.100743	−	0.0378709i
$373$	−24.6581	+	25.8607i	−1.27675	+	1.33902i	−0.363513	+	0.931589i	$0.618423\pi$
$373$	−24.6581	+	25.8607i	−1.27675	+	1.33902i	−0.913237	+	0.407428i	$0.866426\pi$
$374$	11.6458	+	8.29296i	0.602192	+	0.428819i
$375$	−5.92540	+	2.89725i	−0.305986	+	0.149613i
$376$	17.1426	+	6.86285i	0.884061	+	0.353925i
$377$	2.10250	−	7.16045i	0.108284	−	0.368782i
$378$	0.802259	−	0.552060i	0.0412637	−	0.0283949i
$379$	14.7552	−	22.9595i	0.757923	−	1.17935i	−0.221031	−	0.975267i	$-0.570942\pi$
$379$	14.7552	−	22.9595i	0.757923	−	1.17935i	0.978953	−	0.204084i	$-0.0654215\pi$
$380$	−1.31351	−	2.54786i	−0.0673817	−	0.130702i
$381$	−7.49901	−	11.0186i	−0.384186	−	0.564500i
$382$	−16.1307	+	3.91327i	−0.825318	+	0.200220i
$383$	−1.34779	+	1.05992i	−0.0688691	+	0.0541593i	−0.652000	−	0.758219i	$-0.726070\pi$
$383$	−1.34779	+	1.05992i	−0.0688691	+	0.0541593i	0.583131	+	0.812378i	$0.301827\pi$
$384$	−15.3651	−	1.05921i	−0.784096	−	0.0540524i
$385$	−0.0330886	+	0.346520i	−0.00168635	+	0.0176603i
$386$	0.0504057	+	0.171666i	0.00256558	+	0.00873757i
$387$	−30.5384	+	3.07471i	−1.55235	+	0.156296i
$388$	1.48295	+	0.213216i	0.0752853	+	0.0108244i
$389$	−1.43853	−	30.1985i	−0.0729364	−	1.53112i	−0.678069	−	0.734998i	$-0.737183\pi$
$389$	−1.43853	−	30.1985i	−0.0729364	−	1.53112i	0.605133	−	0.796125i	$-0.293120\pi$
$390$	0.888755	+	3.28307i	0.0450039	+	0.166245i
$391$	−22.3161	−	2.21025i	−1.12857	−	0.111777i
$392$	16.1383	−	9.31745i	0.815107	−	0.470602i
$393$	20.6239	+	18.6517i	1.04034	+	0.940855i
$394$	5.02707	+	3.95333i	0.253260	+	0.199166i
$395$	5.07822	+	2.31915i	0.255513	+	0.116689i
$396$	15.2557	+	3.61799i	0.766630	+	0.181811i
$397$	−10.2978	−	22.5490i	−0.516830	−	1.13170i	−0.970626	−	0.240595i	$-0.922657\pi$
$397$	−10.2978	−	22.5490i	−0.516830	−	1.13170i	0.453795	−	0.891106i	$-0.350070\pi$
$398$	4.20695	−	0.810822i	0.210875	−	0.0406428i
$399$	−1.32148	+	1.77479i	−0.0661566	+	0.0888505i
$400$	−0.670878	−	2.76540i	−0.0335439	−	0.138270i
$401$	−1.79295	−	0.345564i	−0.0895358	−	0.0172566i	0.144287	−	0.989536i	$-0.453911\pi$
$401$	−1.79295	−	0.345564i	−0.0895358	−	0.0172566i	−0.233822	+	0.972279i	$0.575123\pi$
$402$	6.64703	−	6.07386i	0.331524	−	0.302937i
$403$	4.97429	−	2.56442i	0.247787	−	0.127743i
$404$	−5.82527	−	5.04763i	−0.289818	−	0.251129i
$405$	−2.49322	+	2.42676i	−0.123889	+	0.120586i
$406$	0.217419	−	0.0312601i	0.0107903	−	0.00155141i
$407$	−2.62510	−	13.6203i	−0.130122	−	0.675135i
$408$	−3.65896	−	21.4219i	−0.181145	−	1.06054i
$409$	−11.2837	−	10.7590i	−0.557942	−	0.531997i	0.357781	−	0.933805i	$-0.383533\pi$
$409$	−11.2837	−	10.7590i	−0.557942	−	0.531997i	−0.915724	+	0.401808i	$0.868382\pi$
$410$	0.591951	−	0.0565244i	0.0292344	−	0.00279154i
$411$	8.35390	−	6.28725i	0.412067	−	0.310127i
$412$	9.44981	−	0.450150i	0.465559	−	0.0221773i
$413$	−2.22110			−0.109293
$414$	11.0073	−	3.25146i	0.540979	−	0.159801i
$415$	−4.56563			−0.224118
$416$	−37.1096	+	1.76775i	−1.81945	+	0.0866711i
$417$	1.11106	+	9.09399i	0.0544087	+	0.445335i
$418$	16.5505	−	1.58038i	0.809512	−	0.0772991i
$419$	−8.23540	−	7.85244i	−0.402326	−	0.383617i	0.461724	−	0.887024i	$-0.347231\pi$
$419$	−8.23540	−	7.85244i	−0.402326	−	0.383617i	−0.864049	+	0.503407i	$0.832080\pi$
$420$	0.165061	−	0.137001i	0.00805413	−	0.00668498i
$421$	2.28323	+	11.8465i	0.111278	+	0.577365i	0.994173	+	0.107795i	$0.0343789\pi$
$421$	2.28323	+	11.8465i	0.111278	+	0.577365i	−0.882895	+	0.469570i	$0.844409\pi$
$422$	5.31411	−	0.764053i	0.258687	−	0.0371935i
$423$	4.97036	+	20.0375i	0.241667	+	0.974257i
$424$	−2.26001	−	1.95831i	−0.109756	−	0.0951038i
$425$	20.1598	−	10.3931i	0.977894	−	0.504140i
$426$	3.31708	+	15.0617i	0.160713	+	0.729741i
$427$	1.41604	+	0.272919i	0.0685268	+	0.0132075i
$428$	1.90500	+	7.85253i	0.0920819	+	0.379567i
$429$	41.9840	+	4.91028i	2.02701	+	0.237071i
$430$	3.09814	−	0.597118i	0.149406	−	0.0287956i
$431$	−0.377606	−	0.826843i	−0.0181887	−	0.0398276i	0.900320	−	0.435229i	$-0.143333\pi$
$431$	−0.377606	−	0.826843i	−0.0181887	−	0.0398276i	−0.918508	+	0.395402i	$0.870605\pi$
$432$	−1.60662	−	2.59061i	−0.0772983	−	0.124641i
$433$	−17.0457	−	7.78452i	−0.819165	−	0.374100i	−0.0386620	−	0.999252i	$-0.512310\pi$
$433$	−17.0457	−	7.78452i	−0.819165	−	0.374100i	−0.780503	+	0.625152i	$0.785037\pi$
$434$	0.129480	+	0.101824i	0.00621524	+	0.00488772i
$435$	−0.746876	+	0.240870i	−0.0358100	+	0.0115488i
$436$	9.91008	−	5.72159i	0.474607	−	0.274014i
$437$	−21.2960	+	15.0521i	−1.01873	+	0.720039i
$438$	−6.32286	+	6.35547i	−0.302118	+	0.303676i
$439$	0.329884	+	6.92511i	0.0157445	+	0.330518i	0.992974	+	0.118333i	$0.0377549\pi$
$439$	0.329884	+	6.92511i	0.0157445	+	0.330518i	−0.977230	+	0.212185i	$0.931942\pi$
$440$	−3.93526	−	0.565804i	−0.187606	−	0.0269737i
$441$	18.9959	+	8.55730i	0.904568	+	0.407490i
$442$	−6.69179	−	22.7901i	−0.318296	−	1.08402i
$443$	1.35217	−	14.1606i	0.0642435	−	0.672788i	−0.904790	−	0.425858i	$-0.859972\pi$
$443$	1.35217	−	14.1606i	0.0642435	−	0.672788i	0.969033	−	0.246930i	$-0.0794218\pi$
$444$	−4.77289	+	7.09117i	−0.226511	+	0.336532i
$445$	3.54788	−	2.79009i	0.168186	−	0.132263i
$446$	−10.7698	+	2.61272i	−0.509963	+	0.123716i
$447$	−8.56230	+	17.7422i	−0.404983	+	0.839179i
$448$	−0.374761	−	0.726934i	−0.0177058	−	0.0343444i
$449$	4.37526	−	6.80804i	0.206481	−	0.321291i	−0.722532	−	0.691338i	$-0.757022\pi$
$449$	4.37526	−	6.80804i	0.206481	−	0.321291i	0.929013	+	0.370046i	$0.120658\pi$
$450$	−7.55667	+	8.81207i	−0.356225	+	0.415405i
$451$	2.08205	−	7.09080i	0.0980398	−	0.333893i
$452$	−18.9083	−	7.56973i	−0.889370	−	0.356050i
$453$	−2.36928	+	34.3693i	−0.111318	+	1.61481i
$454$	−12.3992	−	8.82940i	−0.581921	−	0.414384i
$455$	0.399084	−	0.418547i	0.0187093	−	0.0196218i
$456$	−19.5293	−	16.0405i	−0.914545	−	0.751163i
$457$	−15.1667	+	19.2860i	−0.709468	+	0.902162i	−0.998477	−	0.0551641i	$-0.982432\pi$
$457$	−15.1667	+	19.2860i	−0.709468	+	0.902162i	0.289009	+	0.957326i	$0.406674\pi$
$458$	6.08440	−	3.91020i	0.284305	−	0.182712i
$459$	17.0476	−	17.3128i	0.795713	−	0.808092i
$460$	2.35033	−	0.931341i	0.109585	−	0.0434240i
$461$	−5.33985	−	3.08296i	−0.248702	−	0.143588i	0.370468	−	0.928845i	$-0.379197\pi$
$461$	−5.33985	−	3.08296i	−0.248702	−	0.143588i	−0.619170	+	0.785257i	$0.712531\pi$
$462$	0.381877	+	1.18410i	0.0177665	+	0.0550895i
$463$	−3.39283	+	1.35828i	−0.157678	+	0.0631248i	−0.449159	−	0.893452i	$-0.648276\pi$
$463$	−3.39283	+	1.35828i	−0.157678	+	0.0631248i	0.291481	+	0.956577i	$0.405852\pi$
$464$	−0.0653571	−	0.684450i	−0.00303413	−	0.0317748i
$465$	−0.517237	−	0.280708i	−0.0239863	−	0.0130175i
$466$	−13.7413	−	1.31213i	−0.636553	−	0.0607835i
$467$	26.8058	+	30.9355i	1.24042	+	1.43153i	0.862783	+	0.505574i	$0.168719\pi$
$467$	26.8058	+	30.9355i	1.24042	+	1.43153i	0.377641	+	0.925952i	$0.376735\pi$
$468$	−16.2072	−	20.3923i	−0.749179	−	0.942636i
$469$	−1.46897	−	0.431329i	−0.0678308	−	0.0199169i
$470$	−0.694118	−	2.00552i	−0.0320173	−	0.0925079i
$471$	−4.46115	+	14.0805i	−0.205559	+	0.648795i
$472$	1.20705	−	25.3392i	0.0555592	−	1.16633i
$473$	7.42092	−	38.5034i	0.341214	−	1.77039i
$474$	19.9492	+	0.423528i	0.916295	+	0.0194533i
$475$	9.80296	−	24.4866i	0.449791	−	1.12352i
$476$	−1.13212	+	0.980988i	−0.0518906	+	0.0449635i
$477$	0.300679	−	3.32983i	0.0137671	−	0.152463i
$478$	5.67727	−	1.66700i	0.259672	−	0.0762467i
$479$	20.3296	+	28.5490i	0.928885	+	1.30444i	0.952444	+	0.304714i	$0.0985607\pi$
$479$	20.3296	+	28.5490i	0.928885	+	1.30444i	−0.0235594	+	0.999722i	$0.507500\pi$
$480$	2.34926	+	3.12148i	0.107229	+	0.142475i
$481$	−10.5598	+	20.4831i	−0.481484	+	0.933949i
$482$	−0.482776	−	0.836192i	−0.0219898	−	0.0380875i
$483$	−1.44279	−	1.31408i	−0.0656492	−	0.0597929i
$484$	−2.51553	+	4.35703i	−0.114342	+	0.198047i
$485$	−0.229632	−	0.357315i	−0.0104271	−	0.0162248i
$486$	−4.74780	+	11.4935i	−0.215364	+	0.521357i
$487$	−3.02321	+	6.61991i	−0.136995	+	0.299977i	−0.965678	−	0.259740i	$-0.916363\pi$
$487$	−3.02321	+	6.61991i	−0.136995	+	0.299977i	0.828684	+	0.559717i	$0.189090\pi$
$488$	−3.88311	+	16.0064i	−0.175780	+	0.724576i
$489$	9.30538	−	1.58940i	0.420804	−	0.0718753i
$490$	−2.02395	−	0.700495i	−0.0914326	−	0.0316451i
$491$	−18.9054	−	24.0401i	−0.853188	−	1.08492i	−0.995469	−	0.0950903i	$-0.969686\pi$
$491$	−18.9054	−	24.0401i	−0.853188	−	1.08492i	0.142281	−	0.989826i	$-0.454556\pi$
$492$	−3.99139	+	2.19282i	−0.179946	+	0.0988598i
$493$	5.17887	−	1.79242i	0.233245	−	0.0807267i
$494$	−23.2368	−	14.9334i	−1.04547	−	0.671884i
$495$	−2.05711	−	3.94033i	−0.0924603	−	0.177105i
$496$	0.337655	−	0.389674i	0.0151611	−	0.0174969i
$497$	1.89787	−	1.80961i	0.0851309	−	0.0811722i
$498$	−14.9843	+	6.46230i	−0.671461	+	0.289583i
$499$	0.315628	−	0.911947i	0.0141295	−	0.0408244i	−0.937716	−	0.347404i	$-0.887063\pi$
$499$	0.315628	−	0.911947i	0.0141295	−	0.0408244i	0.951845	+	0.306579i	$0.0991845\pi$
$500$	−3.01208	+	4.22988i	−0.134704	+	0.189166i
$501$	4.83001	+	7.87846i	0.215789	+	0.351983i
$502$	2.25601	−	1.60649i	0.100690	−	0.0717014i
$503$	3.79981	−	26.4282i	0.169425	−	1.17838i	−0.710651	−	0.703544i	$-0.751600\pi$
$503$	3.79981	−	26.4282i	0.169425	−	1.17838i	0.880076	−	0.474832i	$-0.157491\pi$
$504$	0.857939	−	1.68541i	0.0382156	−	0.0750740i
$505$			2.18521i			0.0972406i
$506$	−0.0516326	+	14.6631i	−0.00229535	+	0.651855i
$507$	−33.8226	−	33.6490i	−1.50211	−	1.49440i
$508$	−9.32669	−	4.80824i	−0.413805	−	0.213331i
$509$	−10.7169	−	26.7695i	−0.475019	−	1.18654i	−0.951581	−	0.307398i	$-0.900542\pi$
$509$	−10.7169	−	26.7695i	−0.475019	−	1.18654i	0.476562	−	0.879141i	$-0.341883\pi$
$510$	−1.58530	+	1.93012i	−0.0701985	+	0.0854669i
$511$	1.48135	+	0.359372i	0.0655312	+	0.0158977i
$512$	−5.97740	+	2.72979i	−0.264166	+	0.120641i
$513$	1.79812	−	28.1980i	0.0793891	−	1.24497i
$514$	0.437603	+	3.04360i	0.0193019	+	0.134247i
$515$	−1.85084	−	1.94110i	−0.0815577	−	0.0855353i
$516$	−19.9764	+	13.5955i	−0.879410	+	0.598507i
$517$	−26.3451	−	1.25497i	−1.15866	−	0.0551937i
$518$	−0.677522	−	0.0322744i	−0.0297686	−	0.00141805i
$519$	1.54638	+	20.8666i	0.0678786	+	0.915944i
$520$	4.55807	+	4.78037i	0.199885	+	0.209633i
$521$	−3.47160	−	24.1455i	−0.152094	−	1.05783i	−0.912703	−	0.408624i	$-0.866009\pi$
$521$	−3.47160	−	24.1455i	−0.152094	−	1.05783i	0.760609	−	0.649210i	$-0.224900\pi$
$522$	−2.11029	+	1.84768i	−0.0923650	+	0.0808706i
$523$	−9.63233	+	4.39894i	−0.421192	+	0.192352i	−0.614725	−	0.788742i	$-0.710733\pi$
$523$	−9.63233	+	4.39894i	−0.421192	+	0.192352i	0.193532	+	0.981094i	$0.438006\pi$
$524$	21.2749	+	5.16123i	0.929398	+	0.225470i
$525$	1.94730	+	0.322305i	0.0849872	+	0.0140666i
$526$	4.58707	+	11.4579i	0.200006	+	0.499590i
$527$	3.65287	+	1.88319i	0.159122	+	0.0820329i
$528$	3.75916	−	1.01764i	0.163597	−	0.0442870i
$529$	−11.3594	−	19.9991i	−0.493889	−	0.869525i
$530$			0.343694i			0.0149291i
$531$	23.7805	−	15.4563i	1.03199	−	0.670747i
$532$	−0.247918	+	1.72431i	−0.0107486	+	0.0747583i
$533$	−10.0012	+	7.12181i	−0.433199	+	0.308480i
$534$	7.69489	−	14.1787i	0.332991	−	0.613574i
$535$	1.32878	−	1.86601i	0.0574482	−	0.0806747i
$536$	5.71908	−	16.5242i	0.247027	−	0.713737i
$537$	−3.65279	+	31.2322i	−0.157630	+	1.34777i
$538$	−1.57802	+	1.50464i	−0.0680335	+	0.0648698i
$539$	−17.4306	+	20.1160i	−0.750790	+	0.866458i
$540$	−0.813875	+	2.61546i	−0.0350236	+	0.112551i
$541$	−20.6175	−	13.2501i	−0.886416	−	0.569665i	0.0163169	−	0.999867i	$-0.494806\pi$
$541$	−20.6175	−	13.2501i	−0.886416	−	0.569665i	−0.902733	+	0.430202i	$0.858442\pi$
$542$	−8.25975	+	2.85873i	−0.354787	+	0.122793i
$543$	30.9921	+	18.7815i	1.33000	+	0.805990i
$544$	−16.8649	−	21.4454i	−0.723076	−	0.919466i
$545$	−3.06573	−	1.06106i	−0.131321	−	0.0454508i
$546$	0.717360	−	1.93853i	0.0307002	−	0.0829616i
$547$	8.06054	−	33.2260i	0.344644	−	1.42064i	−0.490899	−	0.871216i	$-0.663332\pi$
$547$	8.06054	−	33.2260i	0.344644	−	1.42064i	0.835543	−	0.549425i	$-0.185153\pi$
$548$	3.41945	−	7.48755i	0.146072	−	0.319852i
$549$	−17.0602	+	6.93195i	−0.728113	+	0.295848i
$550$	−8.01798	−	12.4762i	−0.341888	−	0.531988i
$551$	3.18652	−	5.51921i	0.135750	−	0.235126i
$552$	15.7757	−	15.7458i	0.671458	−	0.670185i
$553$	−1.69637	−	2.93820i	−0.0721370	−	0.124945i
$554$	6.55313	−	12.7113i	0.278416	−	0.540051i
$555$	2.40543	−	0.293883i	0.102105	−	0.0124747i
$556$	4.18381	+	5.87534i	0.177433	+	0.249170i
$557$	41.3548	−	12.1429i	1.75226	−	0.514510i	0.761268	−	0.648438i	$-0.224577\pi$
$557$	41.3548	−	12.1429i	1.75226	−	0.514510i	0.990991	+	0.133928i	$0.0427592\pi$
$558$	−2.09488	−	0.189164i	−0.0886832	−	0.00800796i
$559$	−49.2337	+	42.6613i	−2.08237	+	1.80438i
$560$	0.0198029	−	0.0494652i	0.000836824	−	0.00209029i
$561$	14.9465	+	27.2058i	0.631042	+	1.14863i
$562$	−0.665492	+	3.45290i	−0.0280721	+	0.145652i
$563$	−2.16638	+	45.4779i	−0.0913020	+	1.91667i	0.236013	+	0.971750i	$0.424159\pi$
$563$	−2.16638	+	45.4779i	−0.0913020	+	1.91667i	−0.327315	+	0.944915i	$0.606144\pi$
$564$	10.9638	+	11.9984i	0.461660	+	0.505225i
$565$	1.88853	+	5.45656i	0.0794512	+	0.229559i
$566$	−23.1942	−	6.81043i	−0.974925	−	0.286264i
$567$	2.08970	−	0.322436i	0.0877590	−	0.0135410i
$568$	19.6134	+	22.6350i	0.822959	+	0.949746i
$569$	20.6692	+	1.97367i	0.866499	+	0.0827406i	0.518831	−	0.854877i	$-0.326368\pi$
$569$	20.6692	+	1.97367i	0.866499	+	0.0827406i	0.347668	+	0.937618i	$0.386974\pi$
$570$	0.0765930	+	2.90358i	0.00320813	+	0.121618i
$571$	3.99356	+	41.8225i	0.167125	+	1.75022i	0.558063	+	0.829799i	$0.311545\pi$
$571$	3.99356	+	41.8225i	0.167125	+	1.75022i	−0.390938	+	0.920417i	$0.627849\pi$
$572$	30.8947	−	12.3684i	1.29177	−	0.517148i
$573$	−35.2348	−	7.56997i	−1.47195	−	0.316240i
$574$	−0.312962	−	0.180689i	−0.0130628	−	0.00754180i
$575$	20.6388	+	10.7322i	0.860698	+	0.447564i
$576$	9.07106	+	5.17513i	0.377961	+	0.215630i
$577$	29.7745	−	19.1349i	1.23953	−	0.796596i	0.254180	−	0.967157i	$-0.418194\pi$
$577$	29.7745	−	19.1349i	1.23953	−	0.796596i	0.985347	+	0.170561i	$0.0545581\pi$
$578$	2.39904	−	3.05063i	0.0997868	−	0.126889i
$579$	−0.0634318	+	0.383242i	−0.00263614	+	0.0159270i
$580$	−0.426347	+	0.447140i	−0.0177031	+	0.0185665i
$581$	2.26015	+	1.60944i	0.0937667	+	0.0667710i
$582$	−1.25940	−	0.847670i	−0.0522038	−	0.0351370i
$583$	3.96541	+	1.58751i	0.164231	+	0.0657480i
$584$	−4.90491	+	16.7046i	−0.202966	+	0.691240i
$585$	−1.36025	+	7.25841i	−0.0562392	+	0.300098i
$586$	−7.69082	+	11.9672i	−0.317705	+	0.494359i
$587$	−3.34422	−	6.48687i	−0.138031	−	0.267742i	0.809681	−	0.586870i	$-0.199640\pi$
$587$	−3.34422	−	6.48687i	−0.138031	−	0.267742i	−0.947711	+	0.319128i	$0.896610\pi$
$588$	16.3577	−	1.21223i	0.674580	−	0.0499916i
$589$	4.64450	−	1.12674i	0.191373	−	0.0464267i
$590$	−2.29180	+	1.80229i	−0.0943519	+	0.0741991i
$591$	6.09931	+	12.4742i	0.250892	+	0.513121i
$592$	−0.201822	+	2.11357i	−0.00829483	+	0.0868673i
$593$	−6.39725	−	21.7870i	−0.262703	−	0.894686i	−0.980181	−	0.198104i	$-0.936522\pi$
$593$	−6.39725	−	21.7870i	−0.262703	−	0.894686i	0.717478	−	0.696582i	$-0.245297\pi$
$594$	−12.3286	−	10.0204i	−0.505850	−	0.411140i
$595$	0.420365	+	0.0604393i	0.0172333	+	0.00247777i
$596$	0.737978	+	15.4921i	0.0302288	+	0.634580i
$597$	8.99141	+	2.38446i	0.367994	+	0.0975896i
$598$	15.1263	−	19.0959i	0.618561	−	0.780889i
$599$	30.1473	−	17.4056i	1.23179	−	0.711172i	0.264385	−	0.964417i	$-0.414831\pi$
$599$	30.1473	−	17.4056i	1.23179	−	0.711172i	0.967402	+	0.253245i	$0.0814978\pi$
$600$	−4.73525	+	22.0404i	−0.193316	+	0.899797i
$601$	5.97038	+	4.69516i	0.243537	+	0.191519i	0.732465	−	0.680804i	$-0.238370\pi$
$601$	5.97038	+	4.69516i	0.243537	+	0.191519i	−0.488928	+	0.872324i	$0.662612\pi$
$602$	−1.74418	−	0.796542i	−0.0710876	−	0.0324646i
$603$	18.7293	−	5.60426i	0.762717	−	0.228223i
$604$	11.2671	+	24.6715i	0.458451	+	1.00387i
$605$	1.40054	−	0.269931i	0.0569399	−	0.0109743i
$606$	3.09300	+	7.17180i	0.125645	+	0.291334i
$607$	2.07579	+	8.55652i	0.0842537	+	0.347299i	0.998298	−	0.0583154i	$-0.0185729\pi$
$607$	2.07579	+	8.55652i	0.0842537	+	0.347299i	−0.914044	+	0.405614i	$0.867058\pi$
$608$	−31.1535	−	6.00434i	−1.26344	−	0.243508i
$609$	0.454640	+	0.144044i	0.0184229	+	0.00583698i
$610$	1.68257	−	0.867424i	0.0681252	−	0.0351210i
$611$	33.1159	+	28.6951i	1.33973	+	1.16088i
$612$	5.29467	−	18.3813i	0.214024	−	0.743022i
$613$	−13.7387	+	1.97532i	−0.554900	+	0.0797826i	−0.414060	−	0.910250i	$-0.635890\pi$
$613$	−13.7387	+	1.97532i	−0.554900	+	0.0797826i	−0.140840	+	0.990032i	$0.544980\pi$
$614$	−3.21560	−	16.6841i	−0.129771	−	0.673316i
$615$	1.21084	+	0.448075i	0.0488258	+	0.0180681i
$616$	1.74864	+	1.66732i	0.0704546	+	0.0671784i
$617$	38.2619	−	3.65357i	1.54037	−	0.147087i	0.709959	−	0.704243i	$-0.248714\pi$
$617$	38.2619	−	3.65357i	1.54037	−	0.147087i	0.830408	+	0.557156i	$0.188107\pi$
$618$	−8.82190	−	3.75093i	−0.354869	−	0.150884i
$619$	0.891913	−	0.0424871i	0.0358490	−	0.00170770i	−0.0296497	−	0.999560i	$-0.509439\pi$
$619$	0.891913	−	0.0424871i	0.0358490	−	0.00170770i	0.0654988	+	0.997853i	$0.479136\pi$
$620$	−0.463314			−0.0186071
$621$	24.5920	+	4.02929i	0.986842	+	0.161690i
$622$	0.0108020			0.000433120
$623$	−2.73987	+	0.130516i	−0.109771	+	0.00522902i
$624$	−5.95429	−	2.53167i	−0.238362	−	0.101348i
$625$	−22.6775	+	2.16543i	−0.907098	+	0.0866174i
$626$	15.8917	+	15.1527i	0.635161	+	0.605625i
$627$	33.8543	+	12.5279i	1.35201	+	0.500315i
$628$	2.20069	+	11.4182i	0.0878169	+	0.455638i
$629$	−16.7508	+	2.40840i	−0.667897	+	0.0960291i
$630$	−0.210966	+	0.0523306i	−0.00840508	+	0.00208490i
$631$	10.3993	+	9.01107i	0.413991	+	0.358725i	0.836814	−	0.547487i	$-0.184416\pi$
$631$	10.3993	+	9.01107i	0.413991	+	0.358725i	−0.422823	+	0.906212i	$0.638961\pi$
$632$	34.4420	−	17.7561i	1.37003	−	0.706300i
$633$	11.1122	+	3.52071i	0.441671	+	0.139936i
$634$	0.886272	+	0.170815i	0.0351984	+	0.00678393i
$635$	0.701341	+	2.89097i	0.0278319	+	0.114725i
$636$	−1.04238	−	2.41699i	−0.0413331	−	0.0958397i
$637$	43.4220	−	8.36891i	1.72044	−	0.331588i
$638$	−1.48859	−	3.25956i	−0.0589340	−	0.129047i
$639$	−7.72697	+	32.5819i	−0.305674	+	1.28892i
$640$	3.12691	+	1.42801i	0.123602	+	0.0564471i
$641$	19.1788	+	15.0824i	0.757516	+	0.595717i	0.920423	−	0.390924i	$-0.127845\pi$
$641$	19.1788	+	15.0824i	0.757516	+	0.595717i	−0.162907	+	0.986641i	$0.552087\pi$
$642$	1.71982	−	8.00499i	0.0678759	−	0.315932i
$643$	9.96761	−	5.75480i	0.393084	−	0.226947i	−0.290411	−	0.956902i	$-0.593792\pi$
$643$	9.96761	−	5.75480i	0.393084	−	0.226947i	0.683496	+	0.729955i	$0.260459\pi$
$644$	−1.49181	−	0.367475i	−0.0587854	−	0.0144806i
$645$	6.62160	+	1.75600i	0.260725	+	0.0691426i
$646$	−0.965150	−	20.2610i	−0.0379733	−	0.797158i
$647$	−44.2974	−	6.36900i	−1.74151	−	0.250391i	−0.803082	−	0.595868i	$-0.796808\pi$
$647$	−44.2974	−	6.36900i	−1.74151	−	0.250391i	−0.938427	+	0.345477i	$0.887717\pi$
$648$	2.54284	+	24.0153i	0.0998920	+	0.943411i
$649$	10.2084	+	34.7667i	0.400716	+	1.36471i
$650$	−2.34208	+	24.5274i	−0.0918640	+	0.962044i
$651$	0.157097	+	0.321293i	0.00615713	+	0.0125925i
$652$	5.84198	−	4.59419i	0.228790	−	0.179922i
$653$	28.3243	−	6.87140i	1.10842	−	0.268899i	0.360544	−	0.932742i	$-0.382591\pi$
$653$	28.3243	−	6.87140i	1.10842	−	0.268899i	0.747871	+	0.663844i	$0.231076\pi$
$654$	−11.5635	+	0.856945i	−0.452168	+	0.0335092i
$655$	−2.84394	−	5.51647i	−0.111122	−	0.215546i
$656$	−0.611565	+	0.951614i	−0.0238776	+	0.0371543i
$657$	−18.3612	+	6.46084i	−0.716337	+	0.252062i
$658$	−0.363360	+	1.23749i	−0.0141653	+	0.0482424i
$659$	20.7797	+	8.31896i	0.809464	+	0.324061i	0.739215	−	0.673469i	$-0.235196\pi$
$659$	20.7797	+	8.31896i	0.809464	+	0.324061i	0.0702486	+	0.997530i	$0.477621\pi$
$660$	−2.90311	−	1.95401i	−0.113003	−	0.0760596i
$661$	−8.06507	−	5.74311i	−0.313695	−	0.223381i	0.412355	−	0.911023i	$-0.364706\pi$
$661$	−8.06507	−	5.74311i	−0.313695	−	0.223381i	−0.726050	+	0.687642i	$0.758646\pi$
$662$	−16.5686	+	17.3766i	−0.643956	+	0.675362i
$663$	8.42113	−	50.8787i	0.327049	−	1.97596i
$664$	−19.5895	+	24.9100i	−0.760218	+	0.966696i
$665$	0.415470	−	0.267007i	0.0161112	−	0.0103541i
$666$	7.47859	−	4.36923i	0.289789	−	0.169304i
$667$	4.56700	+	3.27644i	0.176835	+	0.126864i
$668$	6.30068	+	3.63770i	0.243780	+	0.140747i
$669$	−23.5248	−	5.05415i	−0.909520	−	0.195405i
$670$	−1.86573	+	0.746924i	−0.0720793	+	0.0288562i
$671$	−2.23629	−	23.4195i	−0.0863310	−	0.904099i
$672$	−0.0626072	−	2.37339i	−0.00241512	−	0.0915554i
$673$	−5.01345	−	0.478726i	−0.193254	−	0.0184535i	−0.00201998	−	0.999998i	$-0.500643\pi$
$673$	−5.01345	−	0.478726i	−0.193254	−	0.0184535i	−0.191234	+	0.981544i	$0.561249\pi$
$674$	−10.7393	−	12.3938i	−0.413662	−	0.477392i
$675$	−23.0920	+	10.1002i	−0.888810	+	0.388756i
$676$	−36.0395	−	10.5822i	−1.38613	−	0.407006i
$677$	−4.52122	−	13.0632i	−0.173765	−	0.502060i	0.824167	−	0.566347i	$-0.191644\pi$
$677$	−4.52122	−	13.0632i	−0.173765	−	0.502060i	−0.997931	+	0.0642871i	$0.979523\pi$
$678$	13.9215	+	15.2352i	0.534651	+	0.585104i
$679$	−0.0122820	+	0.257832i	−0.000471342	+	0.00989468i
$680$	−0.917963	+	4.76284i	−0.0352023	+	0.182647i
$681$	−15.9133	−	28.9657i	−0.609800	−	1.10997i
$682$	0.998742	−	2.49474i	0.0382438	−	0.0955284i
$683$	−12.9336	+	11.2070i	−0.494890	+	0.428825i	−0.866210	−	0.499680i	$-0.833451\pi$
$683$	−12.9336	+	11.2070i	−0.494890	+	0.428825i	0.371320	+	0.928505i	$0.378905\pi$
$684$	−9.34484	−	20.1868i	−0.357309	−	0.771862i
$685$	−2.23909	+	0.657455i	−0.0855511	+	0.0251201i
$686$	1.51598	+	2.12890i	0.0578805	+	0.0812818i
$687$	15.5874	−	1.90439i	0.594695	−	0.0726568i
$688$	−2.75030	+	5.33483i	−0.104854	+	0.203388i
$689$	−3.54817	−	6.14561i	−0.135175	−	0.234129i
$690$	−2.55502	−	0.185174i	−0.0972678	−	0.00704947i
$691$	−18.1907	+	31.5072i	−0.692008	+	1.19859i	0.279172	+	0.960241i	$0.409940\pi$
$691$	−18.1907	+	31.5072i	−0.692008	+	1.19859i	−0.971179	+	0.238351i	$0.923393\pi$
$692$	8.90596	+	13.8579i	0.338554	+	0.526800i
$693$	−0.370674	+	2.67576i	−0.0140807	+	0.101644i
$694$	4.81003	−	10.5325i	0.182586	−	0.399808i
$695$	0.482086	−	1.98719i	0.0182866	−	0.0753783i
$696$	−1.89039	+	5.10844i	−0.0716551	+	0.193635i
$697$	−8.52032	−	2.94891i	−0.322730	−	0.111698i
$698$	−13.2928	−	16.9031i	−0.503138	−	0.639792i
$699$	−25.6315	−	15.5329i	−0.969473	−	0.587509i
$700$	1.46847	−	0.508241i	0.0555028	−	0.0192097i
$701$	−7.34392	−	4.71965i	−0.277376	−	0.178259i	0.394555	−	0.918872i	$-0.370899\pi$
$701$	−7.34392	−	4.71965i	−0.277376	−	0.178259i	−0.671931	+	0.740613i	$0.734535\pi$
$702$	5.80945	+	25.7472i	0.219263	+	0.971766i
$703$	−12.8876	+	14.8730i	−0.486064	+	0.560947i
$704$	−9.65620	+	9.20717i	−0.363932	+	0.347008i
$705$	0.535262	−	4.57662i	0.0201592	−	0.172365i
$706$	3.58351	−	10.3539i	0.134867	−	0.389673i
$707$	0.770315	−	1.08176i	0.0289707	−	0.0406836i
$708$	10.6507	−	19.6252i	0.400277	−	0.737558i
$709$	−34.0133	+	24.2208i	−1.27740	+	0.909630i	−0.998711	−	0.0507520i	$-0.983838\pi$
$709$	−34.0133	+	24.2208i	−1.27740	+	0.909630i	−0.278686	+	0.960382i	$0.589899\pi$
$710$	0.489884	−	3.40722i	0.0183850	−	0.127871i
$711$	38.6089	+	19.6535i	1.44795	+	0.737063i
$712$		−	31.3285i		−	1.17408i
$713$	0.585170	+	4.17424i	0.0219148	+	0.156327i
$714$	1.46517	−	0.396635i	0.0548327	−	0.0148437i
$715$	−8.38572	−	4.32314i	−0.313608	−	0.161676i
$716$	9.20092	+	22.9828i	0.343855	+	0.858907i
$717$	12.6744	+	2.09780i	0.473335	+	0.0783436i
$718$	1.68854	+	0.409637i	0.0630159	+	0.0152875i
$719$	34.6424	−	15.8206i	1.29194	−	0.590010i	0.353496	−	0.935436i	$-0.384993\pi$
$719$	34.6424	−	15.8206i	1.29194	−	0.590010i	0.938446	+	0.345426i	$0.112266\pi$
$720$	0.132198	+	0.667412i	0.00492675	+	0.0248730i
$721$	0.231966	+	1.61336i	0.00863888	+	0.0600847i
$722$	−5.81822	−	6.10197i	−0.216532	−	0.227092i
$723$	−0.154935	−	2.09067i	−0.00576209	−	0.0777528i
$724$	28.4978	+	1.35752i	1.05911	+	0.0504518i
$725$	−5.67842	−	0.270497i	−0.210891	−	0.0100460i
$726$	4.21445	−	2.86826i	0.156413	−	0.106451i
$727$	−24.5288	−	25.7250i	−0.909721	−	0.954088i	0.0894002	−	0.995996i	$-0.471505\pi$
$727$	−24.5288	−	25.7250i	−0.909721	−	0.954088i	−0.999121	+	0.0419075i	$0.986657\pi$
$728$	−0.571265	−	3.97323i	−0.0211725	−	0.147258i
$729$	−20.1299	+	17.9941i	−0.745551	+	0.666448i
$730$	1.82012	−	0.831219i	0.0673655	−	0.0307648i
$731$	−46.4912	−	11.2787i	−1.71954	−	0.417156i
$732$	−9.20168	+	11.2031i	−0.340104	+	0.414078i
$733$	−6.24381	−	15.5963i	−0.230621	−	0.576062i	0.767246	−	0.641353i	$-0.221627\pi$
$733$	−6.24381	−	15.5963i	−0.230621	−	0.576062i	−0.997866	+	0.0652910i	$0.979202\pi$
$734$	3.90660	+	2.01399i	0.144195	+	0.0743378i
$735$	−3.29659	−	3.27968i	−0.121597	−	0.120973i
$736$	7.97783	−	26.8203i	0.294067	−	0.988608i
$737$			24.9761i			0.920007i
$738$	4.60816	−	0.243285i	0.169629	−	0.00895545i
$739$	1.77307	−	12.3320i	0.0652236	−	0.453640i	−0.930871	−	0.365348i	$-0.880950\pi$
$739$	1.77307	−	12.3320i	0.0652236	−	0.453640i	0.996095	−	0.0882921i	$-0.0281409\pi$
$740$	1.55407	−	1.10665i	0.0571289	−	0.0406813i
$741$	−31.3451	−	51.1284i	−1.15149	−	1.87825i
$742$	0.121157	−	0.170141i	0.00444780	−	0.00624606i
$743$	8.70997	−	25.1658i	0.319538	−	0.923244i	−0.664811	−	0.747012i	$-0.731488\pi$
$743$	8.70997	−	25.1658i	0.319538	−	0.923244i	0.984349	−	0.176232i	$-0.0563910\pi$
$744$	−3.75081	+	1.61762i	−0.137512	+	0.0593050i
$745$	3.18226	−	3.03428i	0.116589	−	0.111167i
$746$	18.6669	−	21.5427i	0.683443	−	0.788735i
$747$	−35.3985	−	1.50372i	−1.29516	−	0.0550184i
$748$	20.5587	+	13.2123i	0.751699	+	0.483088i
$749$	−1.31559	+	0.455329i	−0.0480705	+	0.0166374i
$750$	4.61160	−	2.53355i	0.168392	−	0.0925121i
$751$	−9.95533	−	12.6592i	−0.363275	−	0.461942i	0.569716	−	0.821842i	$-0.307053\pi$
$751$	−9.95533	−	12.6592i	−0.363275	−	0.461942i	−0.932991	+	0.359900i	$0.882811\pi$
$752$	3.81509	+	1.32042i	0.139122	+	0.0481506i
$753$	5.92739	−	1.01243i	0.216006	−	0.0368949i
$754$	−1.40355	+	5.78552i	−0.0511143	+	0.210696i
$755$	3.19423	−	6.99440i	0.116250	−	0.254552i
$756$	1.32488	−	1.00784i	0.0481854	−	0.0366549i
$757$	−19.0813	−	29.6912i	−0.693523	−	1.07914i	−0.992184	−	0.124784i	$-0.960176\pi$
$757$	−19.0813	−	29.6912i	−0.693523	−	1.07914i	0.298661	−	0.954359i	$-0.403460\pi$
$758$	−10.8860	+	18.8550i	−0.395396	+	0.684846i
$759$	−13.9380	+	28.6235i	−0.505919	+	1.03897i
$760$	2.82033	+	4.88496i	0.102304	+	0.177196i
$761$	5.30997	−	10.2999i	0.192486	−	0.373371i	−0.772766	−	0.634691i	$-0.781127\pi$
$761$	5.30997	−	10.2999i	0.192486	−	0.373371i	0.965252	+	0.261320i	$0.0841577\pi$
$762$	6.39373	+	8.49538i	0.231620	+	0.307755i
$763$	1.14361	+	1.60597i	0.0414014	+	0.0581401i
$764$	−27.2234	+	7.99351i	−0.984907	+	0.289195i
$765$	−4.92129	+	2.27815i	−0.177930	+	0.0823668i
$766$	1.03374	−	0.895741i	0.0373505	−	0.0323644i
$767$	22.3736	−	55.8866i	0.807865	−	2.01795i
$768$	24.3400	+	0.516748i	0.878295	+	0.0186465i
$769$	1.24548	−	6.46215i	0.0449130	−	0.233031i	−0.952535	−	0.304430i	$-0.901534\pi$
$769$	1.24548	−	6.46215i	0.0449130	−	0.233031i	0.997448	+	0.0713987i	$0.0227463\pi$
$770$	0.0132130	−	0.277376i	0.000476165	−	0.00999592i
$771$	−2.01645	+	6.36441i	−0.0726206	+	0.229209i
$772$	0.100025	+	0.289004i	0.00359999	+	0.0104015i
$773$	−48.8484	−	14.3432i	−1.75696	−	0.515889i	−0.765173	−	0.643824i	$-0.777347\pi$
$773$	−48.8484	−	14.3432i	−1.75696	−	0.515889i	−0.991783	+	0.127935i	$0.959165\pi$
$774$	24.2174	−	3.60922i	0.870476	−	0.129731i
$775$	−2.79177	−	3.22187i	−0.100283	−	0.115733i
$776$	−2.93477	−	0.280237i	−0.105352	−	0.0100599i
$777$	−1.29437	−	0.702463i	−0.0464353	−	0.0252007i
$778$	2.29255	+	24.0086i	0.0821918	+	0.860751i
$779$	−9.73391	+	3.89687i	−0.348754	+	0.139620i
$780$	1.78449	+	5.53325i	0.0638950	+	0.198122i
$781$	−37.0485	−	21.3900i	−1.32570	−	0.765393i
$782$	17.8662	+	0.914135i	0.638893	+	0.0326894i
$783$	−5.87006	+	1.62154i	−0.209779	+	0.0579491i
$784$	3.42745	−	2.20269i	0.122409	−	0.0786674i
$785$	2.03786	−	2.59135i	0.0727344	−	0.0924893i
$786$	−17.1419	−	14.0795i	−0.611431	−	0.502200i
$787$	28.2763	−	29.6553i	1.00794	−	1.05710i	0.00957529	−	0.999954i	$-0.496952\pi$
$787$	28.2763	−	29.6553i	1.00794	−	1.05710i	0.998366	−	0.0571442i	$-0.0181995\pi$
$788$	8.90479	+	6.34107i	0.317220	+	0.225891i
$789$	−1.84290	+	26.7335i	−0.0656091	+	0.951739i
$790$	−4.13454	−	1.65522i	−0.147100	−	0.0588901i
$791$	0.988618	−	3.36692i	0.0351512	−	0.119714i
$792$	−30.3247	−	5.68294i	−1.07754	−	0.201934i
$793$	−21.1312	+	32.8807i	−0.750390	+	1.16763i
$794$	9.06156	+	17.5770i	0.321583	+	0.623783i
$795$	−0.324332	+	0.672059i	−0.0115029	+	0.0238355i
$796$	7.11702	−	1.72657i	0.252256	−	0.0611967i
$797$	−39.2158	+	30.8396i	−1.38909	+	1.09240i	−0.405085	+	0.914279i	$0.632758\pi$
$797$	−39.2158	+	30.8396i	−1.38909	+	1.09240i	−0.984009	+	0.178117i	$0.942999\pi$
$798$	0.985634	−	1.46438i	0.0348911	−	0.0518383i
$799$	−3.05874	+	32.0326i	−0.108210	+	1.13323i
$800$	7.97328	+	27.1545i	0.281898	+	0.960057i
$801$	28.4266	−	20.4637i	1.00440	−	0.723051i
$802$	1.44181	+	0.207301i	0.0509120	+	0.00732004i
$803$	−1.18324	−	24.8392i	−0.0417556	−	0.876557i
$804$	10.8552	−	10.9112i	0.382833	−	0.384808i
$805$	0.198226	+	0.387852i	0.00698654	+	0.0136700i
$806$	−3.86635	+	2.23224i	−0.136186	+	0.0786273i
$807$	−4.50555	+	1.45305i	−0.158603	+	0.0511499i
$808$	11.9225	+	9.37595i	0.419432	+	0.329845i
$809$	−8.01382	−	3.65979i	−0.281751	−	0.128671i	0.269528	−	0.962993i	$-0.413132\pi$
$809$	−8.01382	−	3.65979i	−0.281751	−	0.128671i	−0.551278	+	0.834321i	$0.685860\pi$
$810$	1.89458	−	2.02836i	0.0665686	−	0.0712695i
$811$	−0.249122	−	0.545501i	−0.00874786	−	0.0191551i	0.905208	−	0.424970i	$-0.139715\pi$
$811$	−0.249122	−	0.545501i	−0.00874786	−	0.0191551i	−0.913956	+	0.405814i	$0.866988\pi$
$812$	0.368680	−	0.0710572i	0.0129381	−	0.00249362i
$813$	−18.8488	−	2.20448i	−0.661056	−	0.0773144i
$814$	2.60878	+	10.7535i	0.0914377	+	0.376911i
$815$	−2.06892	−	0.398751i	−0.0724710	−	0.0139676i
$816$	−1.02192	−	4.64017i	−0.0357743	−	0.162438i
$817$	−49.4486	+	25.4925i	−1.72999	+	0.891871i
$818$	9.39964	+	8.14483i	0.328651	+	0.284777i
$819$	3.23205	−	3.11366i	0.112937	−	0.108800i
$820$	1.00610	−	0.144656i	0.0351346	−	0.00505160i
$821$	−10.5645	−	54.8137i	−0.368703	−	1.91301i	−0.406342	−	0.913721i	$-0.633196\pi$
$821$	−10.5645	−	54.8137i	−0.368703	−	1.91301i	0.0376395	−	0.999291i	$-0.488016\pi$
$822$	−6.41804	+	5.32701i	−0.223855	+	0.185801i
$823$	6.66139	+	6.35162i	0.232201	+	0.221404i	0.797243	−	0.603659i	$-0.206291\pi$
$823$	6.66139	+	6.35162i	0.232201	+	0.221404i	−0.565041	+	0.825063i	$0.691140\pi$
$824$	−18.5319	+	1.76959i	−0.645591	+	0.0616464i
$825$	−3.90499	−	31.9623i	−0.135954	−	1.11278i
$826$	1.76985	−	0.0843085i	0.0615811	−	0.00293347i
$827$	41.6200			1.44727			0.723634	−	0.690184i	$-0.242470\pi$
$827$	41.6200			1.44727			0.723634	+	0.690184i	$0.242470\pi$
$828$	18.5295	−	6.44683i	0.643944	−	0.224043i
$829$	44.7610			1.55461			0.777306	−	0.629123i	$-0.216586\pi$
$829$	44.7610			1.55461			0.777306	+	0.629123i	$0.216586\pi$
$830$	3.63806	−	0.173302i	0.126279	−	0.00601540i
$831$	24.8092	−	18.6717i	0.860622	−	0.647715i
$832$	22.0660	−	2.10704i	0.764999	−	0.0730486i
$833$	23.5024	+	22.4095i	0.814311	+	0.776444i
$834$	−1.23052	−	7.20425i	−0.0426095	−	0.249463i
$835$	−0.390346	−	2.02531i	−0.0135085	−	0.0700887i
$836$	28.1299	−	4.04447i	0.972894	−	0.139881i
$837$	−3.91782	−	2.34676i	−0.135420	−	0.0811157i
$838$	6.86033	+	5.94451i	0.236986	+	0.205350i
$839$	−36.7734	+	18.9580i	−1.26956	+	0.654503i	−0.955526	−	0.294908i	$-0.904711\pi$
$839$	−36.7734	+	18.9580i	−1.26956	+	0.654503i	−0.314034	+	0.949412i	$0.601681\pi$
$840$	−0.311608	+	0.284738i	−0.0107515	+	0.00982438i
$841$	27.1272	+	5.22833i	0.935419	+	0.180287i
$842$	−2.26903	−	9.35308i	−0.0781961	−	0.322329i
$843$	−4.55969	+	6.12381i	−0.157044	+	0.210915i
$844$	9.01120	−	1.73677i	0.310178	−	0.0597819i
$845$	4.42358	+	9.68629i	0.152176	+	0.333219i
$846$	−4.72115	−	15.7780i	−0.162316	−	0.542457i
$847$	−0.788469	−	0.360082i	−0.0270921	−	0.0123726i
$848$	−0.513926	−	0.404156i	−0.0176483	−	0.0138788i
$849$	−38.9272	−	35.2047i	−1.33598	−	1.20822i
$850$	−15.6696	+	9.04683i	−0.537462	+	0.310304i
$851$	−11.9332	−	12.6038i	−0.409065	−	0.432051i
$852$	6.88862	+	25.4466i	0.236000	+	0.871787i
$853$	−1.82212	−	38.2510i	−0.0623882	−	1.30969i	−0.785458	−	0.618915i	$-0.787572\pi$
$853$	−1.82212	−	38.2510i	−0.0623882	−	1.30969i	0.723070	−	0.690775i	$-0.242731\pi$
$854$	−1.13871	−	0.163722i	−0.0389658	−	0.00560244i
$855$	−2.59024	+	5.74994i	−0.0885843	+	0.196644i
$856$	−4.47962	−	15.2562i	−0.153110	−	0.521446i
$857$	−4.47296	+	46.8430i	−0.152793	+	1.60013i	0.515941	+	0.856624i	$0.327442\pi$
$857$	−4.47296	+	46.8430i	−0.152793	+	1.60013i	−0.668735	+	0.743501i	$0.733164\pi$
$858$	−33.6408	−	2.31906i	−1.14848	−	0.0791714i
$859$	15.3297	−	12.0554i	0.523041	−	0.411324i	−0.321423	−	0.946936i	$-0.604161\pi$
$859$	15.3297	−	12.0554i	0.523041	−	0.411324i	0.844465	+	0.535611i	$0.179919\pi$
$860$	5.24123	−	1.27151i	0.178724	−	0.0433581i
$861$	−0.441457	−	0.648651i	−0.0150448	−	0.0221060i
$862$	0.332276	+	0.644525i	0.0113174	+	0.0219526i
$863$	−12.8951	+	20.0652i	−0.438956	+	0.683028i	−0.988292	−	0.152573i	$-0.951244\pi$
$863$	−12.8951	+	20.0652i	−0.438956	+	0.683028i	0.549337	+	0.835601i	$0.314880\pi$
$864$	17.1864	+	24.9754i	0.584692	+	0.849679i
$865$	1.31572	−	4.48093i	0.0447359	−	0.152356i
$866$	13.8781	+	5.55596i	0.471598	+	0.188799i
$867$	7.56985	−	3.70131i	0.257086	−	0.125703i
$868$	0.229357	+	0.163324i	0.00778488	+	0.00554359i
$869$	−38.1947	+	40.0574i	−1.29567	+	1.35886i
$870$	0.585995	−	0.220284i	0.0198671	−	0.00746832i
$871$	25.6502	−	32.6169i	0.869125	−	1.10518i
$872$	−18.9431	+	12.1740i	−0.641493	+	0.412263i
$873$	−1.66271	−	2.84599i	−0.0562744	−	0.0963220i
$874$	16.3981	−	12.8024i	0.554673	−	0.433048i
$875$	−0.774795	−	0.447328i	−0.0261928	−	0.0151224i
$876$	−10.2788	+	11.3656i	−0.347287	+	0.384009i
$877$	−5.32271	+	2.13089i	−0.179735	+	0.0719551i	−0.459785	−	0.888031i	$-0.652073\pi$
$877$	−5.32271	+	2.13089i	−0.179735	+	0.0719551i	0.280049	+	0.959986i	$0.409649\pi$
$878$	−0.525727	−	5.50566i	−0.0177424	−	0.185807i
$879$	−26.3316	+	16.1430i	−0.888144	+	0.544491i
$880$	−0.865291	−	0.0826253i	−0.0291690	−	0.00278530i
$881$	2.80418	+	3.23620i	0.0944753	+	0.109030i	0.801018	−	0.598640i	$-0.204292\pi$
$881$	2.80418	+	3.23620i	0.0944753	+	0.109030i	−0.706543	+	0.707670i	$0.749746\pi$
$882$	−15.4615	−	6.09772i	−0.520615	−	0.205321i
$883$	29.3754	+	8.62540i	0.988561	+	0.290268i	0.735754	−	0.677249i	$-0.236828\pi$
$883$	29.3754	+	8.62540i	0.988561	+	0.290268i	0.252807	+	0.967517i	$0.418646\pi$
$884$	−13.2792	−	38.3678i	−0.446628	−	1.29045i
$885$	−6.18215	+	1.36151i	−0.207811	+	0.0457667i
$886$	−0.539951	+	11.3350i	−0.0181400	+	0.380806i
$887$	−4.83235	+	25.0726i	−0.162254	+	0.841855i	0.806005	+	0.591908i	$0.201625\pi$
$887$	−4.83235	+	25.0726i	−0.162254	+	0.841855i	−0.968260	+	0.249947i	$0.919587\pi$
$888$	8.71741	−	14.3850i	0.292537	−	0.482727i
$889$	0.671915	−	1.67836i	0.0225353	−	0.0562905i
$890$	−2.72118	+	2.35791i	−0.0912140	+	0.0790374i
$891$	−14.6515	−	31.2279i	−0.490845	−	1.04617i
$892$	−18.1759	+	5.33692i	−0.608573	+	0.178693i
$893$	21.7059	+	30.4816i	0.726359	+	1.02003i
$894$	6.14929	−	14.4627i	0.205663	−	0.483704i
$895$	3.21601	−	6.23819i	0.107499	−	0.208520i
$896$	−1.04454	−	1.80919i	−0.0348955	−	0.0604408i
$897$	47.5981	−	23.0660i	1.58926	−	0.770150i
$898$	−3.22795	+	5.59097i	−0.107718	+	0.186573i
$899$	−0.556900	−	0.866553i	−0.0185736	−	0.0289012i
$900$	−12.1856	+	15.6604i	−0.406186	+	0.522013i
$901$	2.16482	−	4.74028i	0.0721205	−	0.157922i
$902$	−1.38990	+	5.72924i	−0.0462785	+	0.190763i
$903$	−2.65891	−	3.20348i	−0.0884830	−	0.106605i
$904$	37.8739	+	13.1083i	1.25967	+	0.435976i
$905$	−4.99987	−	6.35785i	−0.166201	−	0.211342i
$906$	0.583339	−	27.4766i	0.0193801	−	0.912849i
$907$	−3.36818	+	1.16574i	−0.111838	+	0.0387077i	−0.382414	−	0.923991i	$-0.624907\pi$
$907$	−3.36818	+	1.16574i	−0.111838	+	0.0387077i	0.270576	+	0.962699i	$0.412786\pi$
$908$	−21.8885	−	14.0669i	−0.726396	−	0.466827i
$909$	−0.719716	+	16.9425i	−0.0238715	+	0.561947i
$910$	−0.302117	+	0.348662i	−0.0100151	+	0.0115580i
$911$	−15.7107	+	14.9801i	−0.520519	+	0.496314i	−0.904175	−	0.427162i	$-0.859513\pi$
$911$	−15.7107	+	14.9801i	−0.520519	+	0.496314i	0.383656	+	0.923476i	$0.374665\pi$
$912$	−4.43180	−	3.29985i	−0.146752	−	0.109269i
$913$	14.8046	−	42.7751i	0.489961	−	1.41565i
$914$	11.3533	−	15.9435i	0.375534	−	0.527364i
$915$	4.10865	−	0.108381i	0.135828	−	0.00358298i
$916$	10.0705	−	7.17118i	0.332739	−	0.236942i
$917$	−0.536778	+	3.73338i	−0.0177260	+	0.123287i
$918$	−12.9270	+	14.4426i	−0.426654	+	0.476675i
$919$			48.6891i			1.60610i	0.595909	+	0.803052i	$0.296792\pi$
$919$			48.6891i			1.60610i	−0.595909	+	0.803052i	$0.703208\pi$
$920$	−4.53249	+	2.05066i	−0.149432	+	0.0676084i
$921$	9.45643	−	35.6586i	0.311600	−	1.17499i
$922$	4.37201	+	2.25393i	0.143984	+	0.0742292i
$923$	26.4153	+	65.9822i	0.869469	+	2.17183i
$924$	0.748327	+	1.99069i	0.0246182	+	0.0654888i
$925$	17.0599	+	4.13870i	0.560927	+	0.136079i
$926$	2.65197	−	1.21111i	0.0871492	−	0.0397997i
$927$	−13.7107	−	15.6595i	−0.450319	−	0.514325i
$928$	0.973168	+	6.76854i	0.0319458	+	0.222188i
$929$	−31.3269	−	32.8547i	−1.02780	−	1.07793i	−0.996922	−	0.0784037i	$-0.975018\pi$
$929$	−31.3269	−	32.8547i	−1.02780	−	1.07793i	−0.0308794	−	0.999523i	$-0.509831\pi$
$930$	0.422808	+	0.204045i	0.0138644	+	0.00669089i
$931$	37.7212	+	1.79688i	1.23626	+	0.0588904i
$932$	−23.5687	−	1.12272i	−0.772018	−	0.0367758i
$933$	0.0211222	+	0.0101934i	0.000691510	+	0.000333719i
$934$	−22.5341	−	23.6331i	−0.737338	−	0.773298i
$935$	−0.985991	−	6.85772i	−0.0322454	−	0.224271i
$936$	33.7655	+	38.5647i	1.10366	+	1.26053i
$937$	41.3027	−	18.8623i	1.34930	−	0.616204i	0.396005	−	0.918248i	$-0.370396\pi$
$937$	41.3027	−	18.8623i	1.34930	−	0.616204i	0.953294	+	0.302044i	$0.0976689\pi$
$938$	1.18690	+	0.287939i	0.0387537	+	0.00940155i
$939$	16.7756	+	44.6261i	0.547451	+	1.45632i
$940$	−1.34826	−	3.36779i	−0.0439754	−	0.109845i
$941$	−31.3775	−	16.1762i	−1.02288	−	0.527329i	−0.136668	−	0.990617i	$-0.543639\pi$
$941$	−31.3775	−	16.1762i	−1.02288	−	0.527329i	−0.886208	+	0.463287i	$0.846670\pi$
$942$	3.02034	−	11.3892i	0.0984079	−	0.371080i
$943$	−2.57400	−	8.88181i	−0.0838209	−	0.289232i
$944$		−	5.54628i		−	0.180516i
$945$	−0.461905	−	0.0967537i	−0.0150258	−	0.00314740i
$946$	−4.45174	+	30.9626i	−0.144739	+	1.00668i
$947$	7.20360	−	5.12966i	0.234085	−	0.166691i	−0.456995	−	0.889469i	$-0.651074\pi$
$947$	7.20360	−	5.12966i	0.234085	−	0.166691i	0.691081	+	0.722778i	$0.257135\pi$
$948$	34.0958	−	0.899406i	1.10738	−	0.0292113i
$949$	−23.9644	+	33.6533i	−0.777918	+	1.09243i
$950$	−6.88190	+	19.8839i	−0.223278	+	0.645120i
$951$	1.57183	+	1.17036i	0.0509699	+	0.0379514i
$952$	2.13339	−	2.03418i	0.0691436	−	0.0659282i
$953$	−10.7149	+	12.3657i	−0.347091	+	0.400564i	−0.902273	−	0.431164i	$-0.858103\pi$
$953$	−10.7149	+	12.3657i	−0.347091	+	0.400564i	0.555183	+	0.831728i	$0.312648\pi$
$954$	−0.113198	+	2.66475i	−0.00366493	+	0.0862743i
$955$	6.76678	+	4.34875i	0.218968	+	0.140722i
$956$	9.55783	−	3.30800i	0.309122	−	0.106988i
$957$	0.165140	−	7.77849i	0.00533823	−	0.251443i
$958$	−17.2831	−	21.9772i	−0.558390	−	0.710051i
$959$	1.34019	+	0.463844i	0.0432769	+	0.0149783i
$960$	−1.48870	−	1.79360i	−0.0480476	−	0.0578883i
$961$	−7.12641	+	29.3755i	−0.229884	+	0.947596i
$962$	7.63691	−	16.7225i	0.246224	−	0.539155i
$963$	10.9170	−	14.0300i	0.351794	−	0.452111i
$964$	−0.892305	−	1.38845i	−0.0287392	−	0.0447191i
$965$	0.0433507	−	0.0750857i	0.00139551	−	0.00241709i
$966$	1.19955	+	0.992345i	0.0385948	+	0.0319282i
$967$	−29.4043	−	50.9298i	−0.945579	−	1.63779i	−0.754588	−	0.656199i	$-0.772163\pi$
$967$	−29.4043	−	50.9298i	−0.945579	−	1.63779i	−0.190991	−	0.981592i	$-0.561170\pi$
$968$	4.53645	−	8.79949i	0.145807	−	0.282826i
$969$	17.2323	−	40.5291i	0.553582	−	1.30198i
$970$	0.196542	+	0.276005i	0.00631059	+	0.00886199i
$971$	−33.1227	+	9.72572i	−1.06296	+	0.312113i	−0.766042	−	0.642790i	$-0.777777\pi$
$971$	−33.1227	+	9.72572i	−1.06296	+	0.312113i	−0.296917	+	0.954903i	$0.595959\pi$
$972$	−7.17161	+	20.0103i	−0.230030	+	0.641830i
$973$	−0.939159	+	0.813786i	−0.0301081	+	0.0260888i
$974$	2.15773	−	5.38974i	0.0691380	−	0.172698i
$975$	−27.7254	+	45.7508i	−0.887922	+	1.46520i
$976$	−0.681503	+	3.53597i	−0.0218144	+	0.113184i
$977$	−2.89993	+	60.8771i	−0.0927771	+	1.94763i	0.175915	+	0.984405i	$0.443712\pi$
$977$	−2.89993	+	60.8771i	−0.0927771	+	1.94763i	−0.268692	+	0.963226i	$0.586591\pi$
$978$	−7.35453	+	1.61971i	−0.235172	+	0.0517926i
$979$	14.6357	+	42.2871i	0.467759	+	1.35150i
$980$	−3.51267	−	1.03141i	−0.112208	−	0.0329473i
$981$	−23.4199	−	9.23639i	−0.747741	−	0.294895i
$982$	15.9770	+	18.4385i	0.509847	+	0.588395i
$983$	24.7377	+	2.36216i	0.789009	+	0.0753412i	0.481777	−	0.876294i	$-0.339991\pi$
$983$	24.7377	+	2.36216i	0.789009	+	0.0753412i	0.307231	+	0.951635i	$0.400597\pi$
$984$	7.63998	−	4.68381i	0.243554	−	0.149314i
$985$	−0.294596	−	3.08515i	−0.00938660	−	0.0983009i
$986$	−4.05867	+	1.62485i	−0.129255	+	0.0517457i
$987$	−1.87829	+	2.07690i	−0.0597867	+	0.0661085i
$988$	−40.8892	−	23.6074i	−1.30086	−	0.751051i
$989$	−18.0754	−	45.6151i	−0.574765	−	1.45047i
$990$	1.78875	+	3.06171i	0.0568502	+	0.0973076i
$991$	23.1499	−	14.8775i	0.735380	−	0.472600i	−0.118576	−	0.992945i	$-0.537833\pi$
$991$	23.1499	−	14.8775i	0.735380	−	0.472600i	0.853956	+	0.520345i	$0.174197\pi$
$992$	−3.16992	+	4.03089i	−0.100645	+	0.127981i
$993$	−48.7959	+	18.3431i	−1.54849	+	0.582100i
$994$	−1.44360	+	1.51400i	−0.0457882	+	0.0480213i
$995$	−1.69123	−	1.20432i	−0.0536156	−	0.0381795i
$996$	−25.0586	+	12.2525i	−0.794013	+	0.388236i
$997$	−23.6765	−	9.47864i	−0.749842	−	0.300191i	−0.0349147	−	0.999390i	$-0.511116\pi$
$997$	−23.6765	−	9.47864i	−0.749842	−	0.300191i	−0.714927	+	0.699199i	$0.753540\pi$
$998$	−0.216888	+	0.738653i	−0.00686548	+	0.0233817i
$999$	18.7467	−	1.48631i	0.593120	−	0.0470247i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.o.a.11.9	✓	440
3.2	odd	2		621.2.s.a.494.14		440
9.4	even	3		621.2.s.a.287.14		440
9.5	odd	6	inner	207.2.o.a.149.9	yes	440
23.21	odd	22	inner	207.2.o.a.182.9	yes	440
69.44	even	22		621.2.s.a.251.14		440
207.67	odd	66		621.2.s.a.44.14		440
207.113	even	66	inner	207.2.o.a.113.9	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.9	✓	440	1.1	even	1	trivial
207.2.o.a.113.9	yes	440	207.113	even	66	inner
207.2.o.a.149.9	yes	440	9.5	odd	6	inner
207.2.o.a.182.9	yes	440	23.21	odd	22	inner
621.2.s.a.44.14		440	207.67	odd	66
621.2.s.a.251.14		440	69.44	even	22
621.2.s.a.287.14		440	9.4	even	3
621.2.s.a.494.14		440	3.2	odd	2

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.o (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.796836 + 0.0379580i) q^{2} +(-1.59395 - 0.677724i) q^{3} +(-1.35744 + 0.129619i) q^{4} +(0.279785 + 0.266774i) q^{5} +(1.29585 + 0.479531i) q^{6} +(-0.0444620 - 0.230691i) q^{7} +(2.65597 - 0.381872i) q^{8} +(2.08138 + 2.16052i) q^{9} +O(q^{10})\)	\(q+(-0.796836 + 0.0379580i) q^{2} +(-1.59395 - 0.677724i) q^{3} +(-1.35744 + 0.129619i) q^{4} +(0.279785 + 0.266774i) q^{5} +(1.29585 + 0.479531i) q^{6} +(-0.0444620 - 0.230691i) q^{7} +(2.65597 - 0.381872i) q^{8} +(2.08138 + 2.16052i) q^{9} +(-0.233069 - 0.201955i) q^{10} +(-3.40663 + 1.75624i) q^{11} +(2.25154 + 0.713359i) q^{12} +(6.25244 + 1.20506i) q^{13} +(0.0441855 + 0.182135i) q^{14} +(-0.265165 - 0.614843i) q^{15} +(0.576055 - 0.111026i) q^{16} +(1.94248 + 4.25343i) q^{17} +(-1.74053 - 1.64258i) q^{18} +(4.94633 + 2.25891i) q^{19} +(-0.414369 - 0.325864i) q^{20} +(-0.0854741 + 0.397843i) q^{21} +(2.64786 - 1.52874i) q^{22} +(-2.41253 + 4.14484i) q^{23} +(-4.49231 - 1.19133i) q^{24} +(-0.230799 - 4.84506i) q^{25} +(-5.02792 - 0.722905i) q^{26} +(-1.85339 - 4.85437i) q^{27} +(0.0902563 + 0.307385i) q^{28} +(0.111406 - 1.16670i) q^{29} +(0.234631 + 0.479864i) q^{30} +(0.690862 - 0.543300i) q^{31} +(-5.67011 + 1.37555i) q^{32} +(6.62026 - 0.490613i) q^{33} +(-1.70929 - 3.31556i) q^{34} +(0.0491026 - 0.0764051i) q^{35} +(-3.10539 - 2.66298i) q^{36} +(-1.01963 + 3.47253i) q^{37} +(-4.02716 - 1.61223i) q^{38} +(-9.14941 - 6.15824i) q^{39} +(0.844975 + 0.601704i) q^{40} +(-1.33060 + 1.39550i) q^{41} +(0.0530076 - 0.320261i) q^{42} +(-6.32434 + 8.04205i) q^{43} +(4.39664 - 2.82555i) q^{44} +(0.00596751 + 1.15974i) q^{45} +(1.76506 - 3.39434i) q^{46} +(5.95963 + 3.44080i) q^{47} +(-0.993450 - 0.213437i) q^{48} +(6.44733 - 2.58112i) q^{49} +(0.367817 + 3.85196i) q^{50} +(-0.213569 - 8.09624i) q^{51} +(-8.64350 - 0.825354i) q^{52} +(-0.729817 - 0.842253i) q^{53} +(1.66111 + 3.79779i) q^{54} +(-1.42164 - 0.417432i) q^{55} +(-0.206184 - 0.595730i) q^{56} +(-6.35331 - 6.95285i) q^{57} +(-0.0444869 + 0.933895i) q^{58} +(1.78919 - 9.28320i) q^{59} +(0.439640 + 0.800240i) q^{60} +(-2.28136 + 5.69856i) q^{61} +(-0.529881 + 0.459145i) q^{62} +(0.405870 - 0.576216i) q^{63} +(3.34015 - 0.980756i) q^{64} +(1.42786 + 2.00515i) q^{65} +(-5.25664 + 0.642230i) q^{66} +(2.98608 - 5.79219i) q^{67} +(-3.18812 - 5.52198i) q^{68} +(6.65451 - 4.97166i) q^{69} +(-0.0362265 + 0.0627462i) q^{70} +(6.03456 + 9.38995i) q^{71} +(6.35314 + 4.94347i) q^{72} +(-2.69531 + 5.90191i) q^{73} +(0.680665 - 2.80574i) q^{74} +(-2.91573 + 7.87922i) q^{75} +(-7.00713 - 2.42519i) q^{76} +(0.556614 + 0.707792i) q^{77} +(7.52434 + 4.55982i) q^{78} +(13.6469 - 4.72322i) q^{79} +(0.190790 + 0.122614i) q^{80} +(-0.335702 + 8.99374i) q^{81} +(1.00730 - 1.16249i) q^{82} +(-8.54740 + 8.14993i) q^{83} +(0.0644575 - 0.551126i) q^{84} +(-0.591231 + 1.70825i) q^{85} +(4.73420 - 6.64826i) q^{86} +(-0.968274 + 1.78416i) q^{87} +(-8.37727 + 5.96543i) q^{88} +(1.66158 - 11.5566i) q^{89} +(-0.0487766 - 0.923897i) q^{90} -1.49596i q^{91} +(2.73760 - 5.93907i) q^{92} +(-1.46941 + 0.397782i) q^{93} +(-4.87946 - 2.51554i) q^{94} +(0.781289 + 1.95157i) q^{95} +(9.97013 + 1.65020i) q^{96} +(-1.06773 - 0.259028i) q^{97} +(-5.03950 + 2.30146i) q^{98} +(-10.8849 - 3.70469i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9}+O(q^{10}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23} + 52 q^{24} + 11 q^{25} - 79 q^{27} - 44 q^{28} + 27 q^{29} - 66 q^{30} - 3 q^{31} - 33 q^{32} - 11 q^{34} + 23 q^{36} - 44 q^{37} - 33 q^{38} - 40 q^{39} - 77 q^{40} + 9 q^{41} - 22 q^{42} - 11 q^{43} - 36 q^{46} - 120 q^{47} - 56 q^{48} + 35 q^{49} - 3 q^{50} - 22 q^{51} - 38 q^{52} + 42 q^{54} - 44 q^{55} + 165 q^{56} + 11 q^{57} - 10 q^{58} - 9 q^{59} + 88 q^{60} - 11 q^{61} + 33 q^{63} - 22 q^{64} + 198 q^{65} + 33 q^{66} - 11 q^{67} + 3 q^{69} - 70 q^{70} + 14 q^{72} - 36 q^{73} + 231 q^{74} - 13 q^{75} - 11 q^{76} + 39 q^{77} + 3 q^{78} - 11 q^{79} + 172 q^{81} - 10 q^{82} + 66 q^{83} - 110 q^{84} + q^{85} - 33 q^{86} - 196 q^{87} - 99 q^{88} + 418 q^{90} + 63 q^{92} - 188 q^{93} - 42 q^{94} - 93 q^{95} - 82 q^{96} + 22 q^{97} + 242 q^{99}+O(q^{100}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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