LMFDB - Embedded newform 225.2.q.a.16.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, degree $8$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			16.2
Character	$\chi$	$=$	225.16
Dual form			225.2.q.a.211.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.43895 + 1.08589i) q^{2} +(-1.70795 - 0.287957i) q^{3} +(3.43105 - 3.81057i) q^{4} +(0.156246 - 2.23060i) q^{5} +(4.47828 - 1.15233i) q^{6} +(0.0677783 - 0.117395i) q^{7} +(-2.58030 + 7.94134i) q^{8} +(2.83416 + 0.983632i) q^{9} +O(q^{10})$	\(q+(-2.43895 + 1.08589i) q^{2} +(-1.70795 - 0.287957i) q^{3} +(3.43105 - 3.81057i) q^{4} +(0.156246 - 2.23060i) q^{5} +(4.47828 - 1.15233i) q^{6} +(0.0677783 - 0.117395i) q^{7} +(-2.58030 + 7.94134i) q^{8} +(2.83416 + 0.983632i) q^{9} +(2.04111 + 5.60999i) q^{10} +(-3.84795 + 1.71322i) q^{11} +(-6.95733 + 5.52025i) q^{12} +(-1.38801 - 0.617982i) q^{13} +(-0.0378292 + 0.359921i) q^{14} +(-0.909179 + 3.76476i) q^{15} +(-1.25824 - 11.9714i) q^{16} +(1.49050 - 4.58730i) q^{17} +(-7.98049 + 0.678560i) q^{18} +(-0.0886646 + 0.272882i) q^{19} +(-7.96377 - 8.24870i) q^{20} +(-0.149567 + 0.180988i) q^{21} +(7.52458 - 8.35690i) q^{22} +(-0.581968 + 5.53705i) q^{23} +(6.69377 - 12.8204i) q^{24} +(-4.95117 - 0.697047i) q^{25} +4.05635 q^{26} +(-4.55735 - 2.49611i) q^{27} +(-0.214793 - 0.661064i) q^{28} +(-4.07656 - 0.866500i) q^{29} +(-1.87067 - 10.1693i) q^{30} +(-9.47469 + 2.01391i) q^{31} +(7.71834 + 13.3686i) q^{32} +(7.06542 - 1.81804i) q^{33} +(1.34604 + 12.8067i) q^{34} +(-0.251272 - 0.169529i) q^{35} +(13.4723 - 7.42487i) q^{36} +(-8.14328 + 5.91644i) q^{37} +(-0.0800710 - 0.761824i) q^{38} +(2.19270 + 1.45517i) q^{39} +(17.3108 + 6.99642i) q^{40} +(-6.23965 - 2.77807i) q^{41} +(0.168252 - 0.603833i) q^{42} +(2.22316 - 3.85063i) q^{43} +(-6.67418 + 20.5410i) q^{44} +(2.63692 - 6.16820i) q^{45} +(-4.59324 - 14.1365i) q^{46} +(6.81762 + 1.44913i) q^{47} +(-1.29823 + 20.8087i) q^{48} +(3.49081 + 6.04626i) q^{49} +(12.8326 - 3.67637i) q^{50} +(-3.86665 + 7.40566i) q^{51} +(-7.11720 + 3.16878i) q^{52} +(-1.22682 - 3.77578i) q^{53} +(13.8256 + 1.13910i) q^{54} +(3.22028 + 8.85093i) q^{55} +(0.757388 + 0.841165i) q^{56} +(0.230013 - 0.440536i) q^{57} +(10.8834 - 2.31335i) q^{58} +(2.28974 + 1.01946i) q^{59} +(11.2264 + 16.3816i) q^{60} +(-0.993544 + 0.442354i) q^{61} +(20.9214 - 15.2003i) q^{62} +(0.307568 - 0.266049i) q^{63} +(-13.8646 - 10.0733i) q^{64} +(-1.59535 + 2.99954i) q^{65} +(-15.2580 + 12.1064i) q^{66} +(-8.73827 + 1.85738i) q^{67} +(-12.3662 - 21.4189i) q^{68} +(2.58841 - 9.28941i) q^{69} +(0.796930 + 0.140618i) q^{70} +(-0.994371 - 3.06036i) q^{71} +(-15.1243 + 19.9690i) q^{72} +(-2.15376 - 1.56480i) q^{73} +(13.4364 - 23.2726i) q^{74} +(8.25562 + 2.61625i) q^{75} +(0.735621 + 1.27413i) q^{76} +(-0.0596835 + 0.567851i) q^{77} +(-6.92803 - 1.16806i) q^{78} +(-3.63910 - 0.773514i) q^{79} +(-26.8999 + 0.936151i) q^{80} +(7.06494 + 5.57554i) q^{81} +18.2349 q^{82} +(-0.682979 - 0.758525i) q^{83} +(0.176496 + 1.19091i) q^{84} +(-9.99956 - 4.04147i) q^{85} +(-1.24082 + 11.8056i) q^{86} +(6.71303 + 2.65381i) q^{87} +(-3.67638 - 34.9785i) q^{88} +(5.75217 + 4.17920i) q^{89} +(0.266675 + 17.9073i) q^{90} +(-0.166625 + 0.121060i) q^{91} +(19.1026 + 21.2155i) q^{92} +(16.7622 - 0.711339i) q^{93} +(-18.2014 + 3.86883i) q^{94} +(0.594837 + 0.240412i) q^{95} +(-9.33293 - 25.0553i) q^{96} +(-2.06543 - 0.439021i) q^{97} +(-15.0795 - 10.9559i) q^{98} +(-12.5909 + 1.07057i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−2.43895	+	1.08589i	−1.72460	+	0.767840i	−0.727985	+	0.685593i	$0.759543\pi$
$2$	−2.43895	+	1.08589i	−1.72460	+	0.767840i	−0.996612	+	0.0822469i	$0.973790\pi$
$3$	−1.70795	−	0.287957i	−0.986083	−	0.166252i
$3$	−1.70795	−	0.287957i	−0.986083	−	0.166252i
$4$	3.43105	−	3.81057i	1.71553	−	1.90528i
$5$	0.156246	−	2.23060i	0.0698755	−	0.997556i
$5$	0.156246	−	2.23060i	0.0698755	−	0.997556i
$6$	4.47828	−	1.15233i	1.82825	−	0.470436i
$7$	0.0677783	−	0.117395i	0.0256178	−	0.0443713i	−0.852932	−	0.522022i	$-0.825178\pi$
$7$	0.0677783	−	0.117395i	0.0256178	−	0.0443713i	0.878550	+	0.477650i	$0.158511\pi$
$8$	−2.58030	+	7.94134i	−0.912272	+	2.80769i
$9$	2.83416	+	0.983632i	0.944720	+	0.327877i
$10$	2.04111	+	5.60999i	0.645456	+	1.77403i
$11$	−3.84795	+	1.71322i	−1.16020	+	0.516554i	−0.894310	−	0.447449i	$-0.852333\pi$
$11$	−3.84795	+	1.71322i	−1.16020	+	0.516554i	−0.265891	+	0.964003i	$0.585666\pi$
$12$	−6.95733	+	5.52025i	−2.00841	+	1.59356i
$13$	−1.38801	−	0.617982i	−0.384965	−	0.171398i	0.205123	−	0.978736i	$-0.434240\pi$
$13$	−1.38801	−	0.617982i	−0.384965	−	0.171398i	−0.590088	+	0.807339i	$0.700907\pi$
$14$	−0.0378292	+	0.359921i	−0.0101103	+	0.0961930i
$15$	−0.909179	+	3.76476i	−0.234749	+	0.972056i
$16$	−1.25824	−	11.9714i	−0.314560	−	2.99284i
$17$	1.49050	−	4.58730i	0.361500	−	1.11258i	−0.590643	−	0.806933i	$-0.701126\pi$
$17$	1.49050	−	4.58730i	0.361500	−	1.11258i	0.952144	−	0.305651i	$-0.0988741\pi$
$18$	−7.98049	+	0.678560i	−1.88102	+	0.159938i
$19$	−0.0886646	+	0.272882i	−0.0203411	+	0.0626033i	−0.960712	−	0.277548i	$-0.910478\pi$
$19$	−0.0886646	+	0.272882i	−0.0203411	+	0.0626033i	0.940371	+	0.340151i	$0.110478\pi$
$20$	−7.96377	−	8.24870i	−1.78075	−	1.84447i
$21$	−0.149567	+	0.180988i	−0.0326381	+	0.0394948i
$22$	7.52458	−	8.35690i	1.60425	−	1.78170i
$23$	−0.581968	+	5.53705i	−0.121349	+	1.15456i	0.749155	+	0.662394i	$0.230460\pi$
$23$	−0.581968	+	5.53705i	−0.121349	+	1.15456i	−0.870504	+	0.492161i	$0.836207\pi$
$24$	6.69377	−	12.8204i	1.36636	−	2.61694i
$25$	−4.95117	−	0.697047i	−0.990235	−	0.139409i
$26$	4.05635			0.795515
$27$	−4.55735	−	2.49611i	−0.877063	−	0.480376i
$28$	−0.214793	−	0.661064i	−0.0405920	−	0.124929i
$29$	−4.07656	−	0.866500i	−0.756998	−	0.160905i	−0.186784	−	0.982401i	$-0.559806\pi$
$29$	−4.07656	−	0.866500i	−0.756998	−	0.160905i	−0.570214	+	0.821496i	$0.693140\pi$
$30$	−1.87067	−	10.1693i	−0.341536	−	1.85665i
$31$	−9.47469	+	2.01391i	−1.70170	+	0.361708i	−0.953414	−	0.301663i	$-0.902458\pi$
$31$	−9.47469	+	2.01391i	−1.70170	+	0.361708i	−0.748290	+	0.663372i	$0.769125\pi$
$32$	7.71834	+	13.3686i	1.36442	+	2.36325i
$33$	7.06542	−	1.81804i	1.22993	−	0.316480i
$34$	1.34604	+	12.8067i	0.230844	+	2.19633i
$35$	−0.251272	−	0.169529i	−0.0424728	−	0.0286556i
$36$	13.4723	−	7.42487i	2.24539	−	1.23748i
$37$	−8.14328	+	5.91644i	−1.33875	+	0.972657i	−0.339258	+	0.940693i	$0.610176\pi$
$37$	−8.14328	+	5.91644i	−1.33875	+	0.972657i	−0.999489	+	0.0319638i	$0.989824\pi$
$38$	−0.0800710	−	0.761824i	−0.0129892	−	0.123584i
$39$	2.19270	+	1.45517i	0.351112	+	0.233014i
$40$	17.3108	+	6.99642i	2.73708	+	1.10623i
$41$	−6.23965	−	2.77807i	−0.974470	−	0.433862i	−0.143177	−	0.989697i	$-0.545732\pi$
$41$	−6.23965	−	2.77807i	−0.974470	−	0.433862i	−0.831293	+	0.555835i	$0.812399\pi$
$42$	0.168252	−	0.603833i	0.0259619	−	0.0931734i
$43$	2.22316	−	3.85063i	0.339029	−	0.587216i	−0.645221	−	0.763996i	$-0.723235\pi$
$43$	2.22316	−	3.85063i	0.339029	−	0.587216i	0.984250	+	0.176780i	$0.0565682\pi$
$44$	−6.67418	+	20.5410i	−1.00617	+	3.09667i
$45$	2.63692	−	6.16820i	0.393089	−	0.919501i
$46$	−4.59324	−	14.1365i	−0.677237	−	2.08432i
$47$	6.81762	+	1.44913i	0.994453	+	0.211377i	0.676272	−	0.736652i	$-0.263595\pi$
$47$	6.81762	+	1.44913i	0.994453	+	0.211377i	0.318181	+	0.948030i	$0.396928\pi$
$48$	−1.29823	+	20.8087i	−0.187384	+	3.00348i
$49$	3.49081	+	6.04626i	0.498687	+	0.863752i
$50$	12.8326	−	3.67637i	1.81480	−	0.519917i
$51$	−3.86665	+	7.40566i	−0.541439	+	1.03700i
$52$	−7.11720	+	3.16878i	−0.986978	+	0.439431i
$53$	−1.22682	−	3.77578i	−0.168517	−	0.518643i	0.830761	−	0.556629i	$-0.187906\pi$
$53$	−1.22682	−	3.77578i	−0.168517	−	0.518643i	−0.999278	+	0.0379864i	$0.987906\pi$
$54$	13.8256	+	1.13910i	1.88143	+	0.155011i
$55$	3.22028	+	8.85093i	0.434222	+	1.19346i
$56$	0.757388	+	0.841165i	0.101210	+	0.112405i
$57$	0.230013	−	0.440536i	0.0304659	−	0.0583504i
$58$	10.8834	−	2.31335i	1.42907	−	0.303757i
$59$	2.28974	+	1.01946i	0.298098	+	0.132722i	0.550336	−	0.834943i	$-0.314500\pi$
$59$	2.28974	+	1.01946i	0.298098	+	0.132722i	−0.252237	+	0.967665i	$0.581166\pi$
$60$	11.2264	+	16.3816i	1.44933	+	2.11485i
$61$	−0.993544	+	0.442354i	−0.127210	+	0.0566377i	−0.469355	−	0.883010i	$-0.655513\pi$
$61$	−0.993544	+	0.442354i	−0.127210	+	0.0566377i	0.342144	+	0.939647i	$0.388847\pi$
$62$	20.9214	−	15.2003i	2.65702	−	1.93044i
$63$	0.307568	−	0.266049i	0.0387500	−	0.0335190i
$64$	−13.8646	−	10.0733i	−1.73308	−	1.25916i
$65$	−1.59535	+	2.99954i	−0.197878	+	0.372048i
$66$	−15.2580	+	12.1064i	−1.87813	+	1.49019i
$67$	−8.73827	+	1.85738i	−1.06755	+	0.226915i	−0.708001	−	0.706212i	$-0.750403\pi$
$67$	−8.73827	+	1.85738i	−1.06755	+	0.226915i	−0.359548	+	0.933126i	$0.617069\pi$
$68$	−12.3662	−	21.4189i	−1.49963	−	2.59743i
$69$	2.58841	−	9.28941i	0.311607	−	1.11831i
$70$	0.796930	+	0.140618i	0.0952514	+	0.0168071i
$71$	−0.994371	−	3.06036i	−0.118010	−	0.363198i	0.874553	−	0.484930i	$-0.161155\pi$
$71$	−0.994371	−	3.06036i	−0.118010	−	0.363198i	−0.992563	+	0.121732i	$0.961155\pi$
$72$	−15.1243	+	19.9690i	−1.78242	+	2.35336i
$73$	−2.15376	−	1.56480i	−0.252079	−	0.183146i	0.454569	−	0.890712i	$-0.349793\pi$
$73$	−2.15376	−	1.56480i	−0.252079	−	0.183146i	−0.706647	+	0.707566i	$0.749793\pi$
$74$	13.4364	−	23.2726i	1.56195	−	2.70539i
$75$	8.25562	+	2.61625i	0.953277	+	0.302098i
$76$	0.735621	+	1.27413i	0.0843816	+	0.146153i
$77$	−0.0596835	+	0.567851i	−0.00680157	+	0.0647126i
$78$	−6.92803	−	1.16806i	−0.784445	−	0.132256i
$79$	−3.63910	−	0.773514i	−0.409431	−	0.0870272i	−0.00140804	−	0.999999i	$-0.500448\pi$
$79$	−3.63910	−	0.773514i	−0.409431	−	0.0870272i	−0.408023	+	0.912972i	$0.633782\pi$
$80$	−26.8999	+	0.936151i	−3.00750	+	0.104665i
$81$	7.06494	+	5.57554i	0.784993	+	0.619504i
$82$	18.2349			2.01370
$83$	−0.682979	−	0.758525i	−0.0749667	−	0.0832589i	0.704495	−	0.709709i	$-0.251174\pi$
$83$	−0.682979	−	0.758525i	−0.0749667	−	0.0832589i	−0.779461	+	0.626450i	$0.784507\pi$
$84$	0.176496	+	1.19091i	0.0192573	+	0.129939i
$85$	−9.99956	−	4.04147i	−1.08460	−	0.438359i
$86$	−1.24082	+	11.8056i	−0.133801	+	1.27303i
$87$	6.71303	+	2.65381i	0.719712	+	0.284518i
$88$	−3.67638	−	34.9785i	−0.391904	−	3.72872i
$89$	5.75217	+	4.17920i	0.609729	+	0.442994i	0.849319	−	0.527880i	$-0.177013\pi$
$89$	5.75217	+	4.17920i	0.609729	+	0.442994i	−0.239590	+	0.970874i	$0.577013\pi$
$90$	0.266675	+	17.9073i	0.0281100	+	1.88760i
$91$	−0.166625	+	0.121060i	−0.0174671	+	0.0126906i
$92$	19.1026	+	21.2155i	1.99158	+	2.21187i
$93$	16.7622	−	0.711339i	1.73816	−	0.0737624i
$94$	−18.2014	+	3.86883i	−1.87733	+	0.399040i
$95$	0.594837	+	0.240412i	0.0610290	+	0.0246658i
$96$	−9.33293	−	25.0553i	−0.952538	−	2.55720i
$97$	−2.06543	−	0.439021i	−0.209713	−	0.0445758i	0.101857	−	0.994799i	$-0.467522\pi$
$97$	−2.06543	−	0.439021i	−0.209713	−	0.0445758i	−0.311570	+	0.950223i	$0.600855\pi$
$98$	−15.0795	−	10.9559i	−1.52326	−	1.10671i
$99$	−12.5909	+	1.07057i	−1.26543	+	0.107596i
$100$	−19.6439	+	16.4752i	−1.96439	+	1.64752i
$101$	5.35748	−	9.27942i	0.533089	−	0.923337i	−0.466164	−	0.884698i	$-0.654364\pi$
$101$	5.35748	−	9.27942i	0.533089	−	0.923337i	0.999253	−	0.0386390i	$-0.0123022\pi$
$102$	1.38882	−	22.2608i	0.137514	−	2.20415i
$103$	7.81798	−	8.68274i	0.770328	−	0.855536i	−0.222519	−	0.974928i	$-0.571428\pi$
$103$	7.81798	−	8.68274i	0.770328	−	0.855536i	0.992847	+	0.119392i	$0.0380946\pi$
$104$	8.48909	−	9.42809i	0.832423	−	0.924500i
$105$	0.380343	+	0.361902i	0.0371176	+	0.0353180i
$106$	7.09224	+	7.87673i	0.688859	+	0.765056i
$107$	−16.9444			−1.63808			−0.819040	−	0.573736i	$-0.805494\pi$
$107$	−16.9444			−1.63808			−0.819040	+	0.573736i	$0.805494\pi$
$108$	−25.1481	+	8.80183i	−2.41988	+	0.846956i
$109$	12.8760	−	9.35498i	1.23330	−	0.896045i	0.236167	−	0.971713i	$-0.424109\pi$
$109$	12.8760	−	9.35498i	1.23330	−	0.896045i	0.997133	+	0.0756679i	$0.0241089\pi$
$110$	−17.4652	−	18.0901i	−1.66524	−	1.72482i
$111$	15.6120	−	7.76005i	1.48182	−	0.736551i
$112$	−1.49066	−	0.663686i	−0.140854	−	0.0627124i
$113$	5.23305	+	2.32990i	0.492284	+	0.219179i	0.637837	−	0.770172i	$-0.279829\pi$
$113$	5.23305	+	2.32990i	0.492284	+	0.219179i	−0.145553	+	0.989350i	$0.546496\pi$
$114$	−0.0826160	+	1.32421i	−0.00773770	+	0.124024i
$115$	12.2600	+	2.16328i	1.14325	+	0.201727i
$116$	−17.2887	+	12.5610i	−1.60522	+	1.16626i
$117$	−3.32598	−	3.11675i	−0.307487	−	0.288144i
$118$	−6.69157			−0.616009
$119$	−0.437504	−	0.485898i	−0.0401060	−	0.0445422i
$120$	−27.5512	−	16.9343i	−2.51507	−	1.54588i
$121$	4.51116	−	5.01015i	0.410106	−	0.455468i
$122$	1.94285	−	2.15776i	0.175898	−	0.195354i
$123$	9.85702	+	6.54155i	0.888778	+	0.589832i
$124$	−24.8340	+	43.0138i	−2.23016	+	3.86275i
$125$	−2.32844	+	10.9352i	−0.208262	+	0.978073i
$126$	−0.461244	+	0.982865i	−0.0410909	+	0.0875605i
$127$	8.56598	+	6.22355i	0.760108	+	0.552251i	0.898944	−	0.438065i	$-0.144336\pi$
$127$	8.56598	+	6.22355i	0.760108	+	0.552251i	−0.138835	+	0.990315i	$0.544336\pi$
$128$	14.5549	+	3.09374i	1.28648	+	0.273451i
$129$	−4.90586	+	5.93649i	−0.431937	+	0.522679i
$130$	0.633790	−	9.04810i	0.0555871	−	0.793571i
$131$	−14.0896	+	2.99484i	−1.23102	+	0.261661i	−0.777096	−	0.629382i	$-0.783308\pi$
$131$	−14.0896	+	2.99484i	−1.23102	+	0.261661i	−0.453920	+	0.891042i	$0.649975\pi$
$132$	17.3141	−	33.1611i	1.50700	−	2.88630i
$133$	0.0260255	+	0.0289043i	0.00225670	+	0.00250632i
$134$	19.2953	−	14.0188i	1.66686	−	1.21104i
$135$	−6.27989	+	9.77563i	−0.540487	+	0.841352i
$136$	32.5833	+	23.6732i	2.79400	+	2.02996i
$137$	−0.657469	−	6.25540i	−0.0561714	−	0.534435i	−0.986036	−	0.166533i	$-0.946743\pi$
$137$	−0.657469	−	6.25540i	−0.0561714	−	0.534435i	0.929865	−	0.367902i	$-0.119924\pi$
$138$	3.77429	+	25.4671i	0.321289	+	2.16790i
$139$	1.27730	−	12.1527i	0.108339	−	1.03078i	−0.796387	−	0.604787i	$-0.793258\pi$
$139$	1.27730	−	12.1527i	0.108339	−	1.03078i	0.904726	−	0.425993i	$-0.140075\pi$
$140$	−1.50813	+	0.375828i	−0.127460	+	0.0317633i
$141$	−11.2268	−	4.43822i	−0.945471	−	0.373766i
$142$	5.74843	+	6.38428i	0.482398	+	0.535757i
$143$	6.39974			0.535173
$144$	8.20934	−	35.1664i	0.684112	−	2.93053i
$145$	−2.56976	+	8.95780i	−0.213407	+	0.743905i
$146$	6.95211	+	1.47772i	0.575360	+	0.122297i
$147$	−4.22105	−	11.3319i	−0.348147	−	0.934639i
$148$	−5.39502	+	51.3302i	−0.443468	+	4.21931i
$149$	1.29104	+	2.23615i	0.105766	+	0.183193i	0.914051	−	0.405599i	$-0.132937\pi$
$149$	1.29104	+	2.23615i	0.105766	+	0.183193i	−0.808285	+	0.588792i	$0.799604\pi$
$150$	−22.9760	+	2.58380i	−1.87598	+	0.210967i
$151$	−0.949443	+	1.64448i	−0.0772646	+	0.133826i	−0.902069	−	0.431592i	$-0.857952\pi$
$151$	−0.949443	+	1.64448i	−0.0772646	+	0.133826i	0.824804	+	0.565418i	$0.191285\pi$
$152$	−1.93826	−	1.40823i	−0.157214	−	0.114223i
$153$	8.73654	−	11.5350i	0.706308	−	0.932553i
$154$	−0.471058	−	1.44977i	−0.0379590	−	0.116826i
$155$	3.01184	+	21.4489i	0.241917	+	1.72282i
$156$	13.0683	−	3.36266i	1.04630	−	0.269228i
$157$	−4.79460	−	8.30449i	−0.382651	−	0.662771i	0.608789	−	0.793332i	$-0.291655\pi$
$157$	−4.79460	−	8.30449i	−0.382651	−	0.662771i	−0.991440	+	0.130561i	$0.958322\pi$
$158$	9.71552	−	2.06510i	0.772926	−	0.164290i
$159$	1.00809	+	6.80210i	0.0799465	+	0.539442i
$160$	31.0259	−	15.1278i	2.45281	−	1.19595i
$161$	0.610580	+	0.443612i	0.0481205	+	0.0349616i
$162$	−23.2854	−	5.92671i	−1.82948	−	0.465646i
$163$	−2.81593	+	2.04590i	−0.220561	+	0.160247i	−0.692579	−	0.721342i	$-0.743526\pi$
$163$	−2.81593	+	2.04590i	−0.220561	+	0.160247i	0.472018	+	0.881589i	$0.343526\pi$
$164$	−31.9946	+	14.2449i	−2.49836	+	1.11234i
$165$	−2.95137	−	16.0442i	−0.229764	−	1.24904i
$166$	2.48943	+	1.10836i	0.193217	+	0.0860257i
$167$	3.16977	−	0.673754i	0.245284	−	0.0521367i	−0.0836291	−	0.996497i	$-0.526651\pi$
$167$	3.16977	−	0.673754i	0.245284	−	0.0521367i	0.328913	+	0.944360i	$0.393318\pi$
$168$	−1.05136	−	1.65476i	−0.0811141	−	0.127668i
$169$	−7.15402	−	7.94535i	−0.550310	−	0.611181i
$170$	28.7770	−	1.00148i	2.20709	−	0.0768097i
$171$	−0.519705	+	0.686177i	−0.0397428	+	0.0524733i
$172$	−7.04530	−	21.6832i	−0.537199	−	1.65333i
$173$	8.06575	−	3.59110i	0.613228	−	0.273026i	−0.0765296	−	0.997067i	$-0.524384\pi$
$173$	8.06575	−	3.59110i	0.613228	−	0.273026i	0.689757	+	0.724041i	$0.257717\pi$
$174$	−19.2545	+	0.817105i	−1.45968	+	0.0619446i
$175$	−0.417412	+	0.534001i	−0.0315534	+	0.0403666i
$176$	25.3512	+	43.9095i	1.91092	+	3.30980i
$177$	−3.61719	−	2.40052i	−0.271885	−	0.180434i
$178$	−18.5674	−	3.94662i	−1.39169	−	0.295812i
$179$	−2.38835	−	7.35058i	−0.178513	−	0.549408i	0.821263	−	0.570550i	$-0.193270\pi$
$179$	−2.38835	−	7.35058i	−0.178513	−	0.549408i	−0.999776	+	0.0211418i	$0.993270\pi$
$180$	−14.4569	−	31.2116i	−1.07756	−	2.32637i
$181$	5.40260	−	16.6275i	0.401572	−	1.23591i	−0.522152	−	0.852852i	$-0.674871\pi$
$181$	5.40260	−	16.6275i	0.401572	−	1.23591i	0.923724	−	0.383059i	$-0.125129\pi$
$182$	0.274932	−	0.476197i	0.0203793	−	0.0352981i
$183$	1.82430	−	0.469419i	0.134856	−	0.0347005i
$184$	−42.4700	−	18.9088i	−3.13093	−	1.39398i
$185$	11.9249	+	19.0888i	0.876734	+	1.40344i
$186$	−40.1097	+	19.9368i	−2.94098	+	1.46184i
$187$	2.12366	+	20.2053i	0.155297	+	1.47755i
$188$	28.9136	−	21.0070i	2.10874	−	1.53209i
$189$	−0.601921	+	0.365830i	−0.0437833	+	0.0266102i
$190$	−1.71184	+	0.0595741i	−0.124190	+	0.00432196i
$191$	1.35520	+	12.8939i	0.0980588	+	0.932967i	0.927361	+	0.374167i	$0.122071\pi$
$191$	1.35520	+	12.8939i	0.0980588	+	0.932967i	−0.829302	+	0.558800i	$0.811262\pi$
$192$	20.7794	+	21.1970i	1.49962	+	1.52976i
$193$	−5.50484	−	9.53467i	−0.396247	−	0.686321i	0.597012	−	0.802232i	$-0.296354\pi$
$193$	−5.50484	−	9.53467i	−0.396247	−	0.686321i	−0.993260	+	0.115912i	$0.963021\pi$
$194$	5.51421	−	1.17208i	0.395897	−	0.0841505i
$195$	3.58850	−	4.66367i	0.256978	−	0.333972i
$196$	35.0169	+	7.44306i	2.50120	+	0.531647i
$197$	−2.44849	−	7.53567i	−0.174447	−	0.536894i	0.825160	−	0.564899i	$-0.191085\pi$
$197$	−2.44849	−	7.53567i	−0.174447	−	0.536894i	−0.999608	+	0.0280045i	$0.991085\pi$
$198$	29.5460	−	16.2834i	2.09974	−	1.15721i
$199$	16.8130			1.19184			0.595919	−	0.803044i	$-0.296788\pi$
$199$	16.8130			1.19184			0.595919	+	0.803044i	$0.296788\pi$
$200$	18.3110	−	37.5203i	1.29478	−	2.65309i
$201$	15.4593	−	0.656050i	1.09042	−	0.0462742i
$202$	−2.99018	+	28.4497i	−0.210388	+	2.00171i
$203$	−0.378025	+	0.419840i	−0.0265322	+	0.0294670i
$204$	14.9531	+	40.1433i	1.04693	+	2.81060i
$205$	−7.17170	+	13.4841i	−0.500893	+	0.941772i
$206$	−9.63914	+	29.6662i	−0.671591	+	2.06694i
$207$	−7.09581	+	15.1205i	−0.493193	+	1.05094i
$208$	−5.65163	+	17.3939i	−0.391870	+	1.20605i
$209$	−0.126329	−	1.20194i	−0.00873833	−	0.0831397i
$210$	−1.32062	−	0.469651i	−0.0911316	−	0.0324090i
$211$	0.579817	−	5.51659i	0.0399163	−	0.379778i	−0.956267	−	0.292494i	$-0.905515\pi$
$211$	0.579817	−	5.51659i	0.0399163	−	0.379778i	0.996184	−	0.0872836i	$-0.0278186\pi$
$212$	−18.5972	−	8.27999i	−1.27726	−	0.568672i
$213$	0.817079	+	5.51327i	0.0559853	+	0.377763i
$214$	41.3266	−	18.3998i	2.82503	−	1.25778i
$215$	−8.24186	−	5.56064i	−0.562090	−	0.379232i
$216$	31.5817	−	29.7508i	2.14887	−	2.02428i
$217$	−0.405755	+	1.24878i	−0.0275444	+	0.0847730i
$218$	−21.2455	+	36.7983i	−1.43893	+	2.49229i
$219$	3.22791	+	3.29278i	0.218122	+	0.222506i
$220$	44.7760	+	18.0969i	3.01880	+	1.22009i
$221$	−4.90371	+	5.44612i	−0.329859	+	0.366346i
$222$	−29.6502	+	35.8792i	−1.98999	+	2.40806i
$223$	−0.394418	+	0.175606i	−0.0264122	+	0.0117595i	−0.419900	−	0.907570i	$-0.637935\pi$
$223$	−0.394418	+	0.175606i	−0.0264122	+	0.0117595i	0.393488	+	0.919330i	$0.371268\pi$
$224$	2.09254			0.139814
$225$	−13.3468	−	6.84568i	−0.889786	−	0.456378i
$226$	−15.2932			−1.01729
$227$	3.42683	−	1.52572i	0.227447	−	0.101266i	−0.289849	−	0.957072i	$-0.593605\pi$
$227$	3.42683	−	1.52572i	0.227447	−	0.101266i	0.517296	+	0.855806i	$0.326939\pi$
$228$	−0.889506	−	2.38798i	−0.0589089	−	0.158148i
$229$	−8.37065	+	9.29655i	−0.553148	+	0.614333i	−0.953267	−	0.302130i	$-0.902302\pi$
$229$	−8.37065	+	9.29655i	−0.553148	+	0.614333i	0.400119	+	0.916463i	$0.368969\pi$
$230$	−32.2507	+	8.03691i	−2.12655	+	0.529938i
$231$	0.265453	−	0.952672i	0.0174655	−	0.0626812i
$232$	17.3999	−	30.1375i	1.14236	−	1.97862i
$233$	−3.16431	+	9.73874i	−0.207301	+	0.638006i	0.792310	+	0.610118i	$0.208878\pi$
$233$	−3.16431	+	9.73874i	−0.207301	+	0.638006i	−0.999611	+	0.0278877i	$0.991122\pi$
$234$	11.4963	+	3.98995i	0.751540	+	0.260831i
$235$	4.29766	−	14.9810i	0.280349	−	0.977252i
$236$	11.7409	−	5.22739i	0.764269	−	0.340274i
$237$	5.99265	+	2.36903i	0.389264	+	0.153885i
$238$	1.59468	+	0.709998i	0.103368	+	0.0460223i
$239$	3.03062	−	28.8345i	0.196035	−	1.86515i	−0.247499	−	0.968888i	$-0.579609\pi$
$239$	3.03062	−	28.8345i	0.196035	−	1.86515i	0.443534	−	0.896258i	$-0.353725\pi$
$240$	46.2132	+	6.14714i	2.98305	+	0.396796i
$241$	−1.07447	−	10.2229i	−0.0692130	−	0.658517i	−0.973043	−	0.230625i	$-0.925923\pi$
$241$	−1.07447	−	10.2229i	−0.0692130	−	0.658517i	0.903830	−	0.427892i	$-0.140744\pi$
$242$	−5.56202	+	17.1181i	−0.357540	+	1.10040i
$243$	−10.4610	−	11.5571i	−0.671075	−	0.741390i
$244$	−1.72328	+	5.30371i	−0.110322	+	0.339535i
$245$	14.0322	−	6.84191i	0.896487	−	0.437113i
$246$	−31.1442	−	5.25087i	−1.98568	−	0.334783i
$247$	0.291704	−	0.323970i	0.0185607	−	0.0206137i
$248$	8.45439	−	80.4382i	0.536854	−	5.10783i
$249$	0.948069	+	1.49219i	0.0600814	+	0.0945636i
$250$	−6.19547	−	29.1988i	−0.391836	−	1.84669i
$251$	−21.4617			−1.35465			−0.677325	−	0.735684i	$-0.736861\pi$
$251$	−21.4617			−1.35465			−0.677325	+	0.735684i	$0.736861\pi$
$252$	0.0414862	−	2.08484i	0.00261339	−	0.131332i
$253$	−7.24680	−	22.3033i	−0.455602	−	1.40220i
$254$	−27.6501	−	5.87721i	−1.73492	−	0.368769i
$255$	15.9149	+	9.78206i	0.996632	+	0.612577i
$256$	−5.33185	+	1.13332i	−0.333240	+	0.0708325i
$257$	−2.60345	−	4.50931i	−0.162399	−	0.281283i	0.773330	−	0.634004i	$-0.218590\pi$
$257$	−2.60345	−	4.50931i	−0.162399	−	0.281283i	−0.935729	+	0.352721i	$0.885256\pi$
$258$	5.51876	−	19.8060i	0.343583	−	1.23307i
$259$	0.142625	+	1.35699i	0.00886231	+	0.0843193i
$260$	5.95626	+	16.3708i	0.369391	+	1.01527i
$261$	−10.7013	−	6.46563i	−0.662395	−	0.400213i
$262$	31.1118	−	22.6040i	1.92209	−	1.39648i
$263$	1.03927	+	9.88798i	0.0640841	+	0.609719i	0.978686	+	0.205363i	$0.0658376\pi$
$263$	1.03927	+	9.88798i	0.0640841	+	0.609719i	−0.914602	+	0.404356i	$0.867496\pi$
$264$	−3.79324	+	60.8000i	−0.233458	+	3.74198i
$265$	−8.61395	+	2.14661i	−0.529150	+	0.131865i
$266$	−0.0948618	−	0.0422352i	−0.00581635	−	0.00258960i
$267$	−8.62097	−	8.79423i	−0.527595	−	0.538198i
$268$	−22.9038	+	39.6705i	−1.39907	+	2.42326i
$269$	−9.33714	+	28.7368i	−0.569295	+	1.75211i	0.0855346	+	0.996335i	$0.472740\pi$
$269$	−9.33714	+	28.7368i	−0.569295	+	1.75211i	−0.654830	+	0.755776i	$0.727260\pi$
$270$	4.70108	−	30.6615i	0.286099	−	1.86600i
$271$	−2.74971	−	8.46274i	−0.167033	−	0.514075i	0.832147	−	0.554555i	$-0.187111\pi$
$271$	−2.74971	−	8.46274i	−0.167033	−	0.514075i	−0.999180	+	0.0404798i	$0.987111\pi$
$272$	−56.7916	−	12.0714i	−3.44350	−	0.731938i
$273$	0.319447	−	0.158784i	0.0193338	−	0.00961003i
$274$	8.39621	+	14.5427i	0.507233	+	0.878554i
$275$	20.2461	−	5.80023i	1.22088	−	0.349767i
$276$	−26.5170	−	41.7357i	−1.59613	−	2.51220i
$277$	−7.47005	+	3.32588i	−0.448832	+	0.199833i	−0.618689	−	0.785636i	$-0.712336\pi$
$277$	−7.47005	+	3.32588i	−0.448832	+	0.199833i	0.169858	+	0.985469i	$0.445669\pi$
$278$	10.0812	+	31.0269i	0.604633	+	1.86087i
$279$	−28.8337	−	3.61186i	−1.72623	−	0.216237i
$280$	1.99464	−	1.55800i	0.119203	−	0.0931085i
$281$	−17.0445	−	18.9299i	−1.01679	−	1.12926i	−0.991569	−	0.129581i	$-0.958637\pi$
$281$	−17.0445	−	18.9299i	−1.01679	−	1.12926i	−0.0252237	−	0.999682i	$-0.508030\pi$
$282$	32.2011	−	1.36652i	1.91755	−	0.0813753i
$283$	−10.4407	+	2.21925i	−0.620637	+	0.131920i	−0.507490	−	0.861658i	$-0.669426\pi$
$283$	−10.4407	+	2.21925i	−0.620637	+	0.131920i	−0.113147	+	0.993578i	$0.536093\pi$
$284$	−15.0734	−	6.71113i	−0.894445	−	0.398232i
$285$	−0.946721	−	0.581899i	−0.0560789	−	0.0344687i
$286$	−15.6086	+	6.94941i	−0.922957	+	0.410927i
$287$	−0.749046	+	0.544214i	−0.0442148	+	0.0321239i
$288$	8.72528	+	45.4806i	0.514142	+	2.67997i
$289$	−5.06843	−	3.68243i	−0.298143	−	0.216614i
$290$	−3.45966	−	24.6381i	−0.203158	−	1.44680i
$291$	3.40123	+	1.34458i	0.199383	+	0.0788207i
$292$	−13.3524	+	2.83815i	−0.781392	+	0.166090i
$293$	9.74076	+	16.8715i	0.569061	+	0.985643i	0.996659	+	0.0816741i	$0.0260267\pi$
$293$	9.74076	+	16.8715i	0.569061	+	0.985643i	−0.427598	+	0.903969i	$0.640640\pi$
$294$	22.6001	+	23.0543i	1.31807	+	1.34456i
$295$	2.63177	−	4.94821i	0.153227	−	0.288096i
$296$	−25.9724	−	79.9347i	−1.50961	−	4.64611i
$297$	21.8128	+	1.79716i	1.26571	+	0.104282i
$298$	−5.57701	−	4.05193i	−0.323067	−	0.234722i
$299$	4.22958	−	7.32585i	0.244603	−	0.423665i
$300$	38.2948	−	22.4821i	2.21095	−	1.29801i
$301$	−0.301364	−	0.521978i	−0.0173703	−	0.0300863i
$302$	0.529915	−	5.04180i	0.0304932	−	0.290123i
$303$	−11.8224	+	14.3060i	−0.679177	+	0.821860i
$304$	3.37832	+	0.718085i	0.193760	+	0.0411850i
$305$	0.831479	+	2.28532i	0.0476103	+	0.130857i
$306$	−8.78219	+	37.6203i	−0.502045	+	2.15061i
$307$	−4.81680			−0.274909			−0.137455	−	0.990508i	$-0.543892\pi$
$307$	−4.81680			−0.274909			−0.137455	+	0.990508i	$0.543892\pi$
$308$	1.95906	+	2.17575i	0.111628	+	0.123975i
$309$	−15.8529	+	12.5784i	−0.901842	+	0.715561i
$310$	−30.6369	−	49.0423i	−1.74006	−	2.78542i
$311$	−0.259321	+	2.46728i	−0.0147048	+	0.139907i	−0.999411	−	0.0343163i	$-0.989075\pi$
$311$	−0.259321	+	2.46728i	−0.0147048	+	0.139907i	0.984706	+	0.174223i	$0.0557413\pi$
$312$	−17.2138	+	13.6582i	−0.974539	+	0.773242i
$313$	1.23582	+	11.7580i	0.0698524	+	0.664601i	0.972290	+	0.233780i	$0.0751095\pi$
$313$	1.23582	+	11.7580i	0.0698524	+	0.664601i	−0.902437	+	0.430822i	$0.858224\pi$
$314$	20.7115	+	15.0478i	1.16882	+	0.849198i
$315$	−0.545392	−	0.727632i	−0.0307294	−	0.0409974i
$316$	−15.4335	+	11.2131i	−0.868200	+	0.630784i
$317$	19.4738	+	21.6279i	1.09376	+	1.21474i	0.975090	+	0.221809i	$0.0711963\pi$
$317$	19.4738	+	21.6279i	1.09376	+	1.21474i	0.118670	+	0.992934i	$0.462137\pi$
$318$	−9.84500	−	15.4953i	−0.552080	−	0.868933i
$319$	17.1709	−	3.64979i	0.961386	−	0.204349i
$320$	−24.6357	+	29.3526i	−1.37718	+	1.64086i
$321$	28.9402	+	4.87928i	1.61528	+	0.272335i
$322$	−1.97089	−	0.418925i	−0.109833	−	0.0233458i
$323$	1.11964	+	0.813463i	0.0622982	+	0.0452623i
$324$	45.4861	−	7.79147i	2.52701	−	0.432859i
$325$	6.44152	+	4.02725i	0.357311	+	0.223392i
$326$	4.64630	−	8.04763i	0.257335	−	0.445717i
$327$	−24.6854	+	12.2701i	−1.36511	+	0.678536i
$328$	38.1618	−	42.3829i	2.10713	−	2.34021i
$329$	0.632208	−	0.702138i	0.0348548	−	0.0387101i
$330$	24.6205	+	35.9261i	1.35531	+	1.97767i
$331$	6.75763	+	7.50511i	0.371433	+	0.412518i	0.899664	−	0.436583i	$-0.143811\pi$
$331$	6.75763	+	7.50511i	0.371433	+	0.412518i	−0.528231	+	0.849100i	$0.677145\pi$
$332$	−5.23375			−0.287239
$333$	−28.8990	+	8.75816i	−1.58365	+	0.479944i
$334$	−6.99927	+	5.08527i	−0.382983	+	0.278254i
$335$	2.77774	+	19.7818i	0.151764	+	1.08080i
$336$	2.35486	+	1.56279i	0.128468	+	0.0852571i
$337$	11.0106	+	4.90222i	0.599784	+	0.267041i	0.684088	−	0.729399i	$-0.260200\pi$
$337$	11.0106	+	4.90222i	0.599784	+	0.267041i	−0.0843046	+	0.996440i	$0.526867\pi$
$338$	26.0761	+	11.6098i	1.41835	+	0.631491i
$339$	−8.26685	−	5.48624i	−0.448994	−	0.297972i
$340$	−49.7093	+	24.2375i	−2.69587	+	1.31446i
$341$	33.0079	−	23.9816i	1.78748	−	1.29868i
$342$	0.522420	−	2.23789i	0.0282493	−	0.121011i
$343$	1.89530			0.102337
$344$	24.8427	+	27.5906i	1.33943	+	1.48759i
$345$	−20.3166	−	7.22514i	−1.09381	−	0.388989i
$346$	−15.7724	+	17.5170i	−0.847930	+	0.941721i
$347$	7.31074	−	8.11940i	0.392461	−	0.435872i	−0.514240	−	0.857646i	$-0.671926\pi$
$347$	7.31074	−	8.11940i	0.392461	−	0.435872i	0.906701	+	0.421774i	$0.138593\pi$
$348$	33.1453	−	16.4751i	1.77677	−	0.883158i
$349$	−6.04219	+	10.4654i	−0.323431	+	0.560199i	−0.981194	−	0.193026i	$-0.938170\pi$
$349$	−6.04219	+	10.4654i	−0.323431	+	0.560199i	0.657763	+	0.753225i	$0.271503\pi$
$350$	0.438181	−	1.75566i	0.0234218	−	0.0938442i
$351$	4.78310	+	6.28099i	0.255303	+	0.335254i
$352$	−52.6030	−	38.2183i	−2.80375	−	2.03704i
$353$	−5.22268	−	1.11012i	−0.277975	−	0.0590855i	0.0668144	−	0.997765i	$-0.478716\pi$
$353$	−5.22268	−	1.11012i	−0.277975	−	0.0590855i	−0.344790	+	0.938680i	$0.612050\pi$
$354$	11.4288	+	1.92689i	0.607436	+	0.102413i
$355$	−6.98181	+	1.73988i	−0.370556	+	0.0923430i
$356$	35.6611	−	7.58001i	1.89004	−	0.401740i
$357$	0.607316	+	0.955870i	0.0321426	+	0.0505900i
$358$	13.8070	+	15.3342i	0.729721	+	0.810437i
$359$	−10.7786	+	7.83115i	−0.568875	+	0.413312i	−0.834697	−	0.550710i	$-0.814357\pi$
$359$	−10.7786	+	7.83115i	−0.568875	+	0.413312i	0.265821	+	0.964022i	$0.414357\pi$
$360$	42.1797	+	36.8564i	2.22307	+	1.94250i
$361$	15.3047	+	11.1195i	0.805512	+	0.585238i
$362$	4.87896	+	46.4202i	0.256432	+	2.43979i
$363$	−9.14753	+	7.25805i	−0.480121	+	0.380949i
$364$	−0.110391	+	1.05030i	−0.00578607	+	0.0550508i
$365$	−3.82696	+	4.55969i	−0.200312	+	0.238665i
$366$	−3.93963	+	3.12588i	−0.205928	+	0.163392i
$367$	−20.1860	−	22.4188i	−1.05370	−	1.17025i	−0.984989	−	0.172617i	$-0.944778\pi$
$367$	−20.1860	−	22.4188i	−1.05370	−	1.17025i	−0.0687125	−	0.997637i	$-0.521889\pi$
$368$	67.0183			3.49357
$369$	−14.9516	−	14.0110i	−0.778348	−	0.729385i
$370$	−49.8125	−	33.6076i	−2.58963	−	1.74718i
$371$	−0.526411	−	0.111892i	−0.0273299	−	0.00580915i
$372$	54.8013	−	66.3141i	2.84131	−	3.43822i
$373$	2.31816	−	22.0558i	0.120030	−	1.14201i	−0.754250	−	0.656587i	$-0.771999\pi$
$373$	2.31816	−	22.0558i	0.120030	−	1.14201i	0.874280	−	0.485422i	$-0.161334\pi$
$374$	−27.1202	−	46.9735i	−1.40235	−	2.42894i
$375$	7.12572	−	18.0062i	0.367970	−	0.929837i
$376$	−29.0995	+	50.4019i	−1.50069	+	2.59928i
$377$	5.12283	+	3.72195i	0.263839	+	0.191690i
$378$	1.07080	−	1.54586i	0.0550762	−	0.0795105i
$379$	0.203894	+	0.627522i	0.0104734	+	0.0322337i	0.956157	−	0.292856i	$-0.0946056\pi$
$379$	0.203894	+	0.627522i	0.0104734	+	0.0322337i	−0.945683	+	0.325089i	$0.894606\pi$
$380$	2.95702	−	1.44180i	0.151692	−	0.0739628i
$381$	−12.8381	−	13.0961i	−0.657717	−	0.670935i
$382$	−17.3066	−	29.9759i	−0.885482	−	1.53370i
$383$	−34.2266	+	7.27509i	−1.74890	+	0.371740i	−0.967614	−	0.252435i	$-0.918769\pi$
$383$	−34.2266	+	7.27509i	−1.74890	+	0.371740i	−0.781285	+	0.624175i	$0.785435\pi$
$384$	−23.9681	−	9.47514i	−1.22312	−	0.483526i
$385$	1.25732	+	0.221855i	0.0640791	+	0.0113068i
$386$	23.7796	+	17.2769i	1.21035	+	0.879372i
$387$	10.0884	−	8.72653i	0.512822	−	0.443595i
$388$	−8.75952	+	6.36416i	−0.444697	+	0.323091i
$389$	14.9067	−	6.63687i	0.755797	−	0.336503i	0.00759323	−	0.999971i	$-0.497583\pi$
$389$	14.9067	−	6.63687i	0.755797	−	0.336503i	0.748204	+	0.663468i	$0.230916\pi$
$390$	−3.68795	+	15.2712i	−0.186746	+	0.773286i
$391$	24.5327	+	10.9227i	1.24067	+	0.552383i
$392$	−57.0227	+	12.1206i	−2.88008	+	0.612181i
$393$	24.9267	−	1.05782i	1.25739	−	0.0533599i
$394$	14.1546	+	15.7203i	0.713100	+	0.791978i
$395$	−2.29400	+	7.99652i	−0.115424	+	0.402349i
$396$	−39.1205	+	51.6516i	−1.96588	+	2.59559i
$397$	9.36909	+	28.8351i	0.470221	+	1.44719i	0.852295	+	0.523061i	$0.175210\pi$
$397$	9.36909	+	28.8351i	0.470221	+	1.44719i	−0.382074	+	0.924132i	$0.624790\pi$
$398$	−41.0059	+	18.2570i	−2.05544	+	0.915142i
$399$	−0.0361270	−	0.0568612i	−0.00180861	−	0.00284662i
$400$	−2.11484	+	60.1493i	−0.105742	+	3.00747i
$401$	10.2811	+	17.8074i	0.513413	+	0.889258i	0.999879	+	0.0155583i	$0.00495256\pi$
$401$	10.2811	+	17.8074i	0.513413	+	0.889258i	−0.486466	+	0.873700i	$0.661714\pi$
$402$	−36.9921	+	18.3872i	−1.84500	+	0.917070i
$403$	14.3955	+	3.05987i	0.717093	+	0.152423i
$404$	−16.9781	−	52.2532i	−0.844692	−	2.59969i
$405$	13.5407	−	14.8879i	0.672842	−	0.739786i
$406$	0.466085	−	1.43446i	0.0231314	−	0.0711911i
$407$	21.1988	−	36.7174i	1.05078	−	1.82001i
$408$	−48.8337	−	49.8152i	−2.41763	−	2.46622i
$409$	33.2039	+	14.7833i	1.64183	+	0.730989i	0.999375	−	0.0353363i	$-0.0112502\pi$
$409$	33.2039	+	14.7833i	1.64183	+	0.730989i	0.642453	+	0.766325i	$0.277917\pi$
$410$	2.84913	−	40.6747i	0.140709	−	2.00878i
$411$	−0.678367	+	10.8732i	−0.0334614	+	0.536336i
$412$	−6.26231	−	59.5819i	−0.308522	−	2.93539i
$413$	0.274874	−	0.199708i	0.0135257	−	0.00982697i
$414$	0.887164	−	44.5833i	0.0436017	−	2.19115i
$415$	−1.79868	+	1.40494i	−0.0882938	+	0.0689657i
$416$	−2.45161	−	23.3255i	−0.120200	−	1.14363i
$417$	−5.68103	+	20.3884i	−0.278201	+	0.998424i
$418$	1.61328	+	2.79428i	0.0789081	+	0.136673i
$419$	−8.65750	+	1.84021i	−0.422947	+	0.0899001i	−0.414468	−	0.910064i	$-0.636032\pi$
$419$	−8.65750	+	1.84021i	−0.422947	+	0.0899001i	−0.00847886	+	0.999964i	$0.502699\pi$
$420$	2.68403	−	0.207617i	0.130967	−	0.0101307i
$421$	−17.0085	−	3.61527i	−0.828944	−	0.176197i	−0.226148	−	0.974093i	$-0.572613\pi$
$421$	−17.0085	−	3.61527i	−0.828944	−	0.176197i	−0.602796	+	0.797896i	$0.705947\pi$
$422$	4.57627	+	14.0843i	0.222769	+	0.685613i
$423$	17.8968	+	10.8131i	0.870174	+	0.525751i
$424$	33.1503			1.60992
$425$	−10.5773	+	21.6736i	−0.513075	+	1.05132i
$426$	−7.97961	−	12.5593i	−0.386614	−	0.608501i
$427$	−0.0154103	+	0.146620i	−0.000745759	+	0.00709542i
$428$	−58.1372	+	64.5680i	−2.81017	+	3.12101i
$429$	−10.9304	−	1.84285i	−0.527725	−	0.0889737i
$430$	26.1397	+	4.61235i	1.26057	+	0.222427i
$431$	7.00874	−	21.5707i	0.337599	−	1.03902i	−0.627829	−	0.778352i	$-0.716056\pi$
$431$	7.00874	−	21.5707i	0.337599	−	1.03902i	0.965428	−	0.260671i	$-0.0839439\pi$
$432$	−24.1475	+	57.6984i	−1.16180	+	2.77601i
$433$	3.84650	−	11.8383i	0.184851	−	0.568912i	−0.815095	−	0.579327i	$-0.803315\pi$
$433$	3.84650	−	11.8383i	0.184851	−	0.568912i	0.999946	+	0.0104152i	$0.00331531\pi$
$434$	−0.366428	−	3.48633i	−0.0175891	−	0.167349i
$435$	6.96848	−	14.5595i	0.334113	−	0.698072i
$436$	8.53051	−	81.1624i	0.408537	−	3.88697i
$437$	−1.45936	−	0.649749i	−0.0698107	−	0.0310817i
$438$	−11.4483	−	4.52577i	−0.547021	−	0.216250i
$439$	19.6180	−	8.73448i	0.936314	−	0.416874i	0.118888	−	0.992908i	$-0.462067\pi$
$439$	19.6180	−	8.73448i	0.936314	−	0.416874i	0.817426	+	0.576034i	$0.195400\pi$
$440$	−78.5975	+	2.73529i	−3.74699	+	0.130400i
$441$	3.94623	+	20.5698i	0.187916	+	0.979512i
$442$	6.04601	−	18.6077i	0.287579	−	0.885078i
$443$	17.1128	−	29.6402i	0.813053	−	1.40825i	−0.0976653	−	0.995219i	$-0.531137\pi$
$443$	17.1128	−	29.6402i	0.813053	−	1.40825i	0.910718	−	0.413029i	$-0.135529\pi$
$444$	23.9953	−	86.1156i	1.13877	−	4.08687i
$445$	10.2209	−	12.1778i	0.484517	−	0.577284i
$446$	0.771277	−	0.856590i	0.0365210	−	0.0405607i
$447$	−1.56112	−	4.19100i	−0.0738383	−	0.198227i
$448$	−2.12228	+	0.944898i	−0.100268	+	0.0446422i
$449$	−14.0727			−0.664132			−0.332066	−	0.943256i	$-0.607746\pi$
$449$	−14.0727			−0.664132			−0.332066	+	0.943256i	$0.607746\pi$
$450$	39.9858	+	2.20311i	1.88495	+	0.103856i
$451$	28.7693			1.35469
$452$	26.8331	−	11.9469i	1.26212	−	0.561933i
$453$	2.09514	−	2.53529i	0.0984382	−	0.119118i
$454$	−6.70110	+	7.44233i	−0.314498	+	0.349286i
$455$	0.244003	+	0.390590i	0.0114390	+	0.0183112i
$456$	2.90494	+	2.96332i	0.136036	+	0.138770i
$457$	3.44104	−	5.96005i	0.160965	−	0.278799i	−0.774250	−	0.632880i	$-0.781873\pi$
$457$	3.44104	−	5.96005i	0.160965	−	0.278799i	0.935215	+	0.354080i	$0.115206\pi$
$458$	10.3206	−	31.7634i	0.482248	−	1.48421i
$459$	−18.2431	+	17.1855i	−0.851517	+	0.802149i
$460$	50.3082	−	39.2954i	2.34563	−	1.83216i
$461$	−11.1884	+	4.98140i	−0.521096	+	0.232007i	−0.650392	−	0.759599i	$-0.725395\pi$
$461$	−11.1884	+	4.98140i	−0.521096	+	0.232007i	0.129295	+	0.991606i	$0.458728\pi$
$462$	0.387071	+	2.61177i	0.0180082	+	0.121511i
$463$	−27.3439	−	12.1743i	−1.27078	−	0.565788i	−0.343148	−	0.939281i	$-0.611493\pi$
$463$	−27.3439	−	12.1743i	−1.27078	−	0.565788i	−0.927633	+	0.373493i	$0.878160\pi$
$464$	−5.24388	+	49.8922i	−0.243441	+	2.31619i
$465$	1.03232	−	37.5009i	0.0478726	−	1.73906i
$466$	−2.85761	−	27.1884i	−0.132376	−	1.25948i
$467$	10.7168	−	32.9830i	0.495915	−	1.52627i	−0.319611	−	0.947549i	$-0.603552\pi$
$467$	10.7168	−	32.9830i	0.495915	−	1.52627i	0.815526	−	0.578720i	$-0.196448\pi$
$468$	−23.2882	+	1.98014i	−1.07650	+	0.0915318i
$469$	−0.374217	+	1.15172i	−0.0172797	+	0.0531816i
$470$	5.78592	+	41.2046i	0.266885	+	1.90063i
$471$	5.79758	+	15.5643i	0.267138	+	0.717164i
$472$	−14.0040	+	15.5531i	−0.644589	+	0.715888i
$473$	−1.95765	+	18.6258i	−0.0900128	+	0.856415i
$474$	−17.1883	+	0.729420i	−0.789483	+	0.0335034i
$475$	0.629205	−	1.28928i	0.0288699	−	0.0591563i
$476$	−3.35265			−0.153668
$477$	0.236956	−	11.9079i	0.0108494	−	0.545226i
$478$	23.9195	+	73.6167i	1.09405	+	3.36715i
$479$	5.22924	+	1.11151i	0.238930	+	0.0507862i	0.325820	−	0.945432i	$-0.394360\pi$
$479$	5.22924	+	1.11151i	0.238930	+	0.0507862i	−0.0868901	+	0.996218i	$0.527693\pi$
$480$	−57.3467	+	16.9033i	−2.61751	+	0.771524i
$481$	14.9592	−	3.17968i	0.682082	−	0.144981i
$482$	13.7216	+	23.7665i	0.625000	+	1.08253i
$483$	−0.915097	−	0.933487i	−0.0416383	−	0.0424751i
$484$	−3.61350	−	34.3802i	−0.164250	−	1.56274i
$485$	−1.30200	+	4.53856i	−0.0591207	+	0.206085i
$486$	38.0636	+	16.8277i	1.72660	+	0.763321i
$487$	−14.9722	+	10.8779i	−0.678455	+	0.492926i	−0.872845	−	0.487998i	$-0.837727\pi$
$487$	−14.9722	+	10.8779i	−0.678455	+	0.492926i	0.194390	+	0.980924i	$0.437727\pi$
$488$	−0.949246	−	9.03147i	−0.0429703	−	0.408836i
$489$	5.39860	−	2.68341i	0.244133	−	0.121348i
$490$	−26.7943	+	31.9245i	−1.21045	+	1.44220i
$491$	−30.9697	−	13.7886i	−1.39764	−	0.622270i	−0.436849	−	0.899535i	$-0.643906\pi$
$491$	−30.9697	−	13.7886i	−1.39764	−	0.622270i	−0.960794	+	0.277264i	$0.910572\pi$
$492$	58.7470	−	15.1165i	2.64852	−	0.681503i
$493$	−10.0510	+	17.4089i	−0.452675	+	0.784057i
$494$	−0.359655	+	1.10690i	−0.0161816	+	0.0498019i
$495$	0.420735	+	28.2525i	0.0189106	+	1.26986i
$496$	36.0306	+	110.891i	1.61782	+	4.97915i
$497$	−0.426669	−	0.0906913i	−0.0191387	−	0.00406806i
$498$	−3.93264	−	2.60987i	−0.176226	−	0.116951i
$499$	−1.25899	−	2.18064i	−0.0563603	−	0.0976189i	0.836469	−	0.548015i	$-0.184616\pi$
$499$	−1.25899	−	2.18064i	−0.0563603	−	0.0976189i	−0.892829	+	0.450396i	$0.851283\pi$
$500$	33.6803	+	46.3919i	1.50623	+	2.07471i
$501$	−5.60780	+	0.237979i	−0.250538	+	0.0106321i
$502$	52.3439	−	23.3050i	2.33622	−	1.04015i
$503$	7.30399	+	22.4794i	0.325669	+	1.00231i	0.971138	+	0.238519i	$0.0766620\pi$
$503$	7.30399	+	22.4794i	0.325669	+	1.00231i	−0.645469	+	0.763787i	$0.723338\pi$
$504$	1.31916	+	3.12899i	0.0587603	+	0.139376i
$505$	−19.8616	−	13.4003i	−0.883830	−	0.596305i
$506$	41.8935	+	46.5275i	1.86239	+	2.06840i
$507$	9.93077	+	15.6303i	0.441041	+	0.694165i
$508$	53.1056	−	11.2879i	2.35618	−	0.500822i
$509$	17.2765	+	7.69197i	0.765766	+	0.340941i	0.752172	−	0.658967i	$-0.229006\pi$
$509$	17.2765	+	7.69197i	0.765766	+	0.340941i	0.0135935	+	0.999908i	$0.495673\pi$
$510$	−49.4379	−	6.57608i	−2.18915	−	0.291194i
$511$	−0.329678	+	0.146782i	−0.0145841	+	0.00649326i
$512$	−12.3030	+	8.93867i	−0.543722	+	0.395037i
$513$	1.08522	−	1.02230i	0.0479135	−	0.0451357i
$514$	11.2463	+	8.17091i	0.496053	+	0.360404i
$515$	−18.1462	−	18.7954i	−0.799618	−	0.828226i
$516$	5.78916	+	39.0625i	0.254854	+	1.71963i
$517$	−28.7165	+	6.10389i	−1.26295	+	0.268449i
$518$	−1.82140	−	3.15475i	−0.0800276	−	0.138612i
$519$	−14.8100	+	3.81082i	−0.650085	+	0.167276i
$520$	−19.7039	−	20.4089i	−0.864074	−	0.894989i
$521$	−0.835113	−	2.57021i	−0.0365870	−	0.112603i	0.931095	−	0.364777i	$-0.118855\pi$
$521$	−0.835113	−	2.57021i	−0.0365870	−	0.112603i	−0.967682	+	0.252174i	$0.918855\pi$
$522$	33.1209	+	4.14890i	1.44966	+	0.181592i
$523$	−10.4857	−	7.61829i	−0.458507	−	0.333125i	0.334438	−	0.942418i	$-0.391453\pi$
$523$	−10.4857	−	7.61829i	−0.458507	−	0.333125i	−0.792945	+	0.609293i	$0.791453\pi$
$524$	−36.9302	+	63.9649i	−1.61330	+	2.79432i
$525$	0.866687	−	0.791847i	0.0378253	−	0.0345591i
$526$	−13.2720	−	22.9877i	−0.578686	−	1.00231i
$527$	−4.88367	+	46.4650i	−0.212736	+	2.02405i
$528$	−30.6544	−	82.2952i	−1.33406	−	3.58144i
$529$	−7.82290	−	1.66281i	−0.340126	−	0.0722960i
$530$	18.6780	−	14.5893i	0.811320	−	0.633717i
$531$	5.48672	+	5.14156i	0.238103	+	0.223125i
$532$	0.199437			0.00864667
$533$	6.94391	+	7.71199i	0.300774	+	0.334043i
$534$	30.5757	+	12.0872i	1.32314	+	0.523066i
$535$	−2.64751	+	37.7963i	−0.114462	+	1.63408i
$536$	7.79727	−	74.1861i	0.336791	−	3.20435i
$537$	1.96252	+	13.2421i	0.0846888	+	0.571440i
$538$	−8.43215	−	80.2266i	−0.363536	−	3.45881i
$539$	−23.7910	−	17.2852i	−1.02475	−	0.744526i
$540$	15.7041	+	57.4707i	0.675796	+	2.47314i
$541$	0.557272	−	0.404882i	0.0239590	−	0.0174072i	−0.575741	−	0.817632i	$-0.695286\pi$
$541$	0.557272	−	0.404882i	0.0239590	−	0.0174072i	0.599700	+	0.800225i	$0.295286\pi$
$542$	15.8960	+	17.6543i	0.682792	+	0.758317i
$543$	−14.0153	+	26.8431i	−0.601456	+	1.15195i
$544$	72.8298	−	15.4804i	3.12255	−	0.663719i
$545$	−18.8554	−	30.1830i	−0.807677	−	1.29290i
$546$	−0.606694	+	0.734150i	−0.0259641	+	0.0314187i
$547$	38.4262	+	8.16774i	1.64299	+	0.349227i	0.934353	−	0.356350i	$-0.115979\pi$
$547$	38.4262	+	8.16774i	1.64299	+	0.349227i	0.708633	+	0.705577i	$0.249312\pi$
$548$	−26.0924	−	18.9573i	−1.11461	−	0.809814i
$549$	−3.25098	+	0.276422i	−0.138748	+	0.0117974i
$550$	−43.0807	+	36.1315i	−1.83697	+	1.54065i
$551$	0.597899	−	1.03559i	0.0254713	−	0.0441176i
$552$	67.0915	+	44.5248i	2.85560	+	1.89510i
$553$	−0.337459	+	0.374786i	−0.0143502	+	0.0159375i
$554$	14.6075	−	16.2233i	0.620614	−	0.689262i
$555$	−14.8703	−	36.0366i	−0.631207	−	1.52967i
$556$	−41.9263	−	46.5639i	−1.77807	−	1.97475i
$557$	17.5295			0.742748			0.371374	−	0.928483i	$-0.378887\pi$
$557$	17.5295			0.742748			0.371374	+	0.928483i	$0.378887\pi$
$558$	74.2461	−	22.5011i	3.14309	−	0.952548i
$559$	−5.46540	+	3.97084i	−0.231162	+	0.167949i
$560$	−1.71333	+	3.22138i	−0.0724014	+	0.136128i
$561$	2.19116	−	35.1210i	0.0925108	−	1.48281i
$562$	62.1265	+	27.6605i	2.62065	+	1.16679i
$563$	14.4900	+	6.45136i	0.610681	+	0.271893i	0.688685	−	0.725060i	$-0.258188\pi$
$563$	14.4900	+	6.45136i	0.610681	+	0.271893i	−0.0780046	+	0.996953i	$0.524855\pi$
$564$	−55.4320	+	27.5529i	−2.33411	+	1.16019i
$565$	6.01473	−	11.3088i	0.253042	−	0.475765i
$566$	23.0545	−	16.7501i	0.969055	−	0.704059i
$567$	1.13339	−	0.451491i	0.0475980	−	0.0189608i
$568$	26.8691			1.12740
$569$	−28.3146	−	31.4465i	−1.18701	−	1.31831i	−0.936697	−	0.350141i	$-0.886134\pi$
$569$	−28.3146	−	31.4465i	−1.18701	−	1.31831i	−0.250311	−	0.968165i	$-0.580533\pi$
$570$	2.94088	+	0.391187i	0.123180	+	0.0163850i
$571$	−9.09406	+	10.1000i	−0.380574	+	0.422671i	−0.902749	−	0.430168i	$-0.858454\pi$
$571$	−9.09406	+	10.1000i	−0.380574	+	0.422671i	0.522174	+	0.852839i	$0.325121\pi$
$572$	21.9578	−	24.3866i	0.918103	−	1.01966i
$573$	1.39828	−	22.4123i	0.0584138	−	0.936286i
$574$	1.23593	−	2.14069i	0.0515867	−	0.0893507i
$575$	6.74101	−	27.0093i	0.281120	−	1.12636i
$576$	−29.3863	−	42.1869i	−1.22443	−	1.75779i
$577$	8.62008	+	6.26285i	0.358858	+	0.260726i	0.752576	−	0.658506i	$-0.228811\pi$
$577$	8.62008	+	6.26285i	0.358858	+	0.260726i	−0.393717	+	0.919232i	$0.628811\pi$
$578$	16.3604	+	3.47750i	0.680501	+	0.144645i
$579$	6.65640	+	17.8699i	0.276631	+	0.742646i
$580$	25.3173	+	40.5269i	1.05124	+	1.68279i
$581$	−0.135339	+	0.0287671i	−0.00561479	+	0.00119346i
$582$	−9.75548	+	0.413995i	−0.404378	+	0.0171606i
$583$	11.1895	+	12.4272i	0.463421	+	0.514681i
$584$	17.9839	−	13.0661i	0.744180	−	0.540678i
$585$	−7.47191	+	6.93196i	−0.308925	+	0.286601i
$586$	−42.0778	−	30.5713i	−1.73822	−	1.26289i
$587$	0.698379	+	6.64463i	0.0288252	+	0.274253i	0.999435	+	0.0335965i	$0.0106961\pi$
$587$	0.698379	+	6.64463i	0.0288252	+	0.274253i	−0.970610	+	0.240657i	$0.922637\pi$
$588$	−57.6636	−	22.7957i	−2.37801	−	0.940079i
$589$	0.290511	−	2.76403i	0.0119703	−	0.113890i
$590$	−1.04553	+	14.9262i	−0.0430440	+	0.614503i
$591$	2.01193	+	13.5756i	0.0827599	+	0.558425i
$592$	81.0740	+	90.0418i	3.33212	+	3.70070i
$593$	−13.1850			−0.541442			−0.270721	−	0.962658i	$-0.587262\pi$
$593$	−13.1850			−0.541442			−0.270721	+	0.962658i	$0.587262\pi$
$594$	−55.1519	+	19.3031i	−2.26291	+	0.792018i
$595$	−1.15220	+	0.899978i	−0.0472357	+	0.0368955i
$596$	12.9507	+	2.75275i	0.530480	+	0.112757i
$597$	−28.7156	−	4.84141i	−1.17525	−	0.198146i
$598$	−2.36066	+	22.4602i	−0.0965348	+	0.918467i
$599$	−4.22052	−	7.31016i	−0.172446	−	0.298685i	0.766829	−	0.641852i	$-0.221834\pi$
$599$	−4.22052	−	7.31016i	−0.172446	−	0.298685i	−0.939274	+	0.343167i	$0.888500\pi$
$600$	−42.0784	+	58.8100i	−1.71784	+	2.40091i
$601$	−13.2046	+	22.8711i	−0.538628	+	0.932931i	0.460351	+	0.887737i	$0.347724\pi$
$601$	−13.2046	+	22.8711i	−0.538628	+	0.932931i	−0.998978	+	0.0451933i	$0.985610\pi$
$602$	1.30182	+	0.945829i	0.0530583	+	0.0385491i
$603$	−26.5926	−	3.33113i	−1.08294	−	0.135654i
$604$	3.00883	+	9.26023i	0.122428	+	0.376793i
$605$	−10.4708	−	10.8454i	−0.425699	−	0.440929i
$606$	13.2994	−	47.7295i	0.540250	−	1.93888i
$607$	15.9189	+	27.5724i	0.646129	+	1.11913i	0.984040	+	0.177950i	$0.0569466\pi$
$607$	15.9189	+	27.5724i	0.646129	+	1.11913i	−0.337910	+	0.941178i	$0.609720\pi$
$608$	−4.33238	+	0.920875i	−0.175701	+	0.0373464i
$609$	0.766543	−	0.608208i	0.0310619	−	0.0246459i
$610$	−4.50954	−	4.67088i	−0.182586	−	0.189118i
$611$	−8.56740	−	6.22458i	−0.346600	−	0.251820i
$612$	−13.9795	−	72.8685i	−0.565089	−	2.94554i
$613$	−16.4747	+	11.9696i	−0.665407	+	0.483446i	−0.868485	−	0.495716i	$-0.834906\pi$
$613$	−16.4747	+	11.9696i	−0.665407	+	0.483446i	0.203078	+	0.979163i	$0.434906\pi$
$614$	11.7479	−	5.23051i	0.474107	−	0.211086i
$615$	16.1317	−	20.9650i	0.650494	−	0.845391i
$616$	−4.35549	−	1.93919i	−0.175488	−	0.0781322i
$617$	−26.7830	+	5.69291i	−1.07824	+	0.229188i	−0.712603	−	0.701568i	$-0.752484\pi$
$617$	−26.7830	+	5.69291i	−1.07824	+	0.229188i	−0.365642	+	0.930756i	$0.619151\pi$
$618$	25.0057	−	47.8927i	1.00588	−	1.92652i
$619$	−20.1573	−	22.3869i	−0.810190	−	0.899807i	0.186387	−	0.982476i	$-0.440322\pi$
$619$	−20.1573	−	22.3869i	−0.810190	−	0.899807i	−0.996577	+	0.0826697i	$0.973655\pi$
$620$	92.0664	+	62.1156i	3.69748	+	2.49462i
$621$	16.4733	−	23.7816i	0.661051	−	0.954325i
$622$	−2.04672	−	6.29916i	−0.0820661	−	0.252573i
$623$	0.880491	−	0.392020i	0.0352761	−	0.0157060i
$624$	14.6614	−	28.0805i	0.586926	−	1.12412i
$625$	24.0282	+	6.90241i	0.961130	+	0.276096i
$626$	−15.7820	−	27.3352i	−0.630775	−	1.09253i
$627$	−0.130344	+	2.08922i	−0.00520544	+	0.0834354i
$628$	−48.0954	−	10.2230i	−1.91921	−	0.407941i
$629$	15.0029	+	46.1742i	0.598205	+	1.84108i
$630$	2.12031	+	1.18242i	0.0844753	+	0.0471088i
$631$	−14.5309	+	44.7216i	−0.578466	+	1.78034i	0.0455932	+	0.998960i	$0.485482\pi$
$631$	−14.5309	+	44.7216i	−0.578466	+	1.78034i	−0.624060	+	0.781377i	$0.714518\pi$
$632$	15.5327	−	26.9034i	0.617857	−	1.07016i
$633$	−2.57884	+	9.25508i	−0.102500	+	0.367857i
$634$	−70.9812	−	31.6029i	−2.81902	−	1.25511i
$635$	15.2207	−	18.1349i	0.604014	−	0.719661i
$636$	29.3787	+	19.4970i	1.16494	+	0.773105i
$637$	−1.10880	−	10.5495i	−0.0439323	−	0.417988i
$638$	−37.9157	+	27.5473i	−1.50110	+	1.09061i
$639$	0.192058	−	9.65165i	0.00759771	−	0.381813i
$640$	9.17506	−	31.9828i	0.362676	−	1.26423i
$641$	2.31632	+	22.0383i	0.0914891	+	0.870460i	0.939975	+	0.341243i	$0.110848\pi$
$641$	2.31632	+	22.0383i	0.0914891	+	0.870460i	−0.848486	+	0.529218i	$0.822486\pi$
$642$	−75.8820	+	19.5256i	−2.99482	+	0.770612i
$643$	−2.55849	−	4.43143i	−0.100897	−	0.174759i	0.811157	−	0.584828i	$-0.198838\pi$
$643$	−2.55849	−	4.43143i	−0.100897	−	0.174759i	−0.912054	+	0.410069i	$0.865505\pi$
$644$	3.78535	−	0.804600i	0.149164	−	0.0317057i
$645$	12.4754	+	11.8706i	0.491220	+	0.467403i
$646$	−3.61406	−	0.768193i	−0.142193	−	0.0302241i
$647$	−2.24133	−	6.89811i	−0.0881158	−	0.271193i	0.897283	−	0.441456i	$-0.145538\pi$
$647$	−2.24133	−	6.89811i	−0.0881158	−	0.271193i	−0.985399	+	0.170264i	$0.945538\pi$
$648$	−62.5069	+	41.7185i	−2.45550	+	1.63886i
$649$	−10.5573			−0.414412
$650$	−20.0837	−	2.82747i	−0.787747	−	0.110902i
$651$	1.05260	−	2.01602i	0.0412548	−	0.0790139i
$652$	−1.86559	+	17.7499i	−0.0730621	+	0.695139i
$653$	15.2667	−	16.9554i	0.597434	−	0.663517i	−0.366265	−	0.930511i	$-0.619364\pi$
$653$	15.2667	−	16.9554i	0.597434	−	0.663517i	0.963698	+	0.266993i	$0.0860302\pi$
$654$	46.8825	−	56.7317i	1.83325	−	2.21838i
$655$	4.47885	+	31.8963i	0.175003	+	1.24629i
$656$	−25.4063	+	78.1926i	−0.991949	+	3.05291i
$657$	−4.56492	−	6.55340i	−0.178094	−	0.255672i
$658$	−0.779478	+	2.39899i	−0.0303872	+	0.0935223i
$659$	−0.318857	−	3.03372i	−0.0124209	−	0.118177i	0.986555	−	0.163432i	$-0.0522565\pi$
$659$	−0.318857	−	3.03372i	−0.0124209	−	0.118177i	−0.998975	+	0.0452553i	$0.985590\pi$
$660$	−71.2639	−	43.8021i	−2.77394	−	1.70500i
$661$	0.769037	−	7.31690i	0.0299121	−	0.284594i	−0.969333	−	0.245750i	$-0.920966\pi$
$661$	0.769037	−	7.31690i	0.0299121	−	0.284594i	0.999245	−	0.0388442i	$-0.0123676\pi$
$662$	−24.6312	−	10.9665i	−0.957320	−	0.426226i
$663$	9.94352	−	7.88962i	0.386174	−	0.306407i
$664$	7.78599	−	3.46655i	0.302155	−	0.134528i
$665$	0.0685403	−	0.0535364i	0.00265788	−	0.00207605i
$666$	60.9727	−	52.7418i	2.36264	−	2.04370i
$667$	7.17028	−	22.0679i	0.277634	−	0.854471i
$668$	8.30824	−	14.3903i	0.321455	−	0.556777i
$669$	0.724213	−	0.186351i	0.0279997	−	0.00720473i
$670$	−28.2556	−	45.2305i	−1.09161	−	1.74741i
$671$	3.06526	−	3.40431i	0.118333	−	0.131422i
$672$	−3.57395	−	0.602563i	−0.137868	−	0.0232444i
$673$	−44.7482	+	19.9232i	−1.72492	+	0.767983i	−0.728349	+	0.685206i	$0.759712\pi$
$673$	−44.7482	+	19.9232i	−1.72492	+	0.767983i	−0.996568	+	0.0827765i	$0.973621\pi$
$674$	−32.1775			−1.23943
$675$	20.8243	+	15.5354i	0.801529	+	0.597956i
$676$	−54.8221			−2.10854
$677$	−12.9325	+	5.75790i	−0.497035	+	0.221294i	−0.639915	−	0.768446i	$-0.721030\pi$
$677$	−12.9325	+	5.75790i	−0.497035	+	0.221294i	0.142880	+	0.989740i	$0.454364\pi$
$678$	26.1199	+	4.40378i	1.00313	+	0.169126i
$679$	−0.191530	+	0.212716i	−0.00735026	+	0.00816329i
$680$	57.8965	−	68.9816i	2.22023	−	2.64533i
$681$	−6.29219	+	1.61907i	−0.241117	+	0.0620430i
$682$	−54.4631	+	94.3328i	−2.08550	+	3.61219i
$683$	2.59574	−	7.98887i	0.0993233	−	0.305686i	−0.889033	−	0.457843i	$-0.848622\pi$
$683$	2.59574	−	7.98887i	0.0993233	−	0.305686i	0.988356	+	0.152158i	$0.0486221\pi$
$684$	0.831591	+	4.33468i	0.0317967	+	0.165741i
$685$	−14.0560	+	0.489168i	−0.537053	+	0.0186901i
$686$	−4.62254	+	2.05809i	−0.176489	+	0.0785782i
$687$	16.9736	−	13.4676i	0.647584	−	0.513822i
$688$	−48.8945	−	21.7692i	−1.86409	−	0.829944i
$689$	−0.630518	+	5.99898i	−0.0240208	+	0.228543i
$690$	57.3967	−	4.43979i	2.18506	−	0.169020i
$691$	−2.66759	−	25.3804i	−0.101480	−	0.965517i	−0.920233	−	0.391371i	$-0.872001\pi$
$691$	−2.66759	−	25.3804i	−0.101480	−	0.965517i	0.818753	−	0.574146i	$-0.194666\pi$
$692$	13.9899	−	43.0563i	0.531814	−	1.63676i
$693$	−0.727708	+	1.55067i	−0.0276434	+	0.0589052i
$694$	−9.01374	+	27.7415i	−0.342157	+	1.05305i
$695$	−26.9083	−	4.74798i	−1.02069	−	0.180101i
$696$	−38.3964	+	46.4628i	−1.45541	+	1.76117i
$697$	−22.0441	+	24.4824i	−0.834979	+	0.927338i
$698$	3.37234	−	32.0857i	0.127645	−	1.21446i
$699$	8.20881	−	15.7221i	0.310486	−	0.594663i
$700$	0.602683	+	3.42276i	0.0227793	+	0.129368i
$701$	11.4130			0.431063			0.215532	−	0.976497i	$-0.430852\pi$
$701$	11.4130			0.431063			0.215532	+	0.976497i	$0.430852\pi$
$702$	−18.4862	−	10.1251i	−0.697717	−	0.382147i
$703$	−0.892467	−	2.74673i	−0.0336600	−	0.103595i
$704$	70.6081	+	15.0082i	2.66114	+	0.565644i
$705$	−11.6541	+	24.3492i	−0.438918	+	0.917043i
$706$	13.9433	−	2.96374i	0.524764	−	0.111542i
$707$	−0.726241	−	1.25789i	−0.0273131	−	0.0473077i
$708$	−21.5581	+	5.54722i	−0.810204	+	0.208477i
$709$	0.940531	+	8.94855i	0.0353224	+	0.336070i	0.997885	+	0.0650093i	$0.0207077\pi$
$709$	0.940531	+	8.94855i	0.0353224	+	0.336070i	−0.962562	+	0.271061i	$0.912626\pi$
$710$	15.1390	−	11.8249i	0.568155	−	0.443782i
$711$	−9.55294	−	5.77180i	−0.358263	−	0.216459i
$712$	−48.0307	+	34.8964i	−1.80003	+	1.30780i
$713$	−5.63715	−	53.6339i	−0.211113	−	2.00861i
$714$	−2.51918	−	1.67184i	−0.0942780	−	0.0625670i
$715$	0.999936	−	14.2753i	0.0373955	−	0.533865i
$716$	−36.2044	−	16.1192i	−1.35302	−	0.602404i
$717$	−13.4792	+	48.3750i	−0.503391	+	1.80660i
$718$	17.7848	−	30.8042i	0.663723	−	1.14960i
$719$	9.37500	−	28.8533i	0.349629	−	1.07605i	−0.609430	−	0.792840i	$-0.708602\pi$
$719$	9.37500	−	28.8533i	0.349629	−	1.07605i	0.959059	−	0.283207i	$-0.0913982\pi$
$720$	−77.1595	−	23.8064i	−2.87557	−	0.887212i
$721$	−0.489425	−	1.50630i	−0.0182272	−	0.0560974i
$722$	−49.4020	−	10.5007i	−1.83855	−	0.390796i
$723$	−1.10863	+	17.7696i	−0.0412303	+	0.660860i
$724$	−44.8236	−	77.6367i	−1.66585	−	2.88534i
$725$	19.5798	+	7.13175i	0.727174	+	0.264866i
$726$	14.4289	−	27.6352i	0.535507	−	1.02564i
$727$	25.1041	−	11.1771i	0.931061	−	0.414535i	0.115566	−	0.993300i	$-0.463132\pi$
$727$	25.1041	−	11.1771i	0.931061	−	0.414535i	0.815495	+	0.578765i	$0.196465\pi$
$728$	−0.531439	−	1.63560i	−0.0196964	−	0.0606194i
$729$	14.5389	+	22.7513i	0.538478	+	0.842640i
$730$	4.38244	−	15.2765i	0.162201	−	0.565409i
$731$	−14.3504	−	15.9377i	−0.530767	−	0.589477i
$732$	4.47051	−	8.56222i	0.165235	−	0.316469i
$733$	6.48313	−	1.37803i	0.239460	−	0.0508988i	−0.0866183	−	0.996242i	$-0.527606\pi$
$733$	6.48313	−	1.37803i	0.239460	−	0.0508988i	0.326078	+	0.945343i	$0.394273\pi$
$734$	73.5770	+	32.7586i	2.71578	+	1.20914i
$735$	−25.9365	+	7.64492i	−0.956682	+	0.281987i
$736$	−78.5142	+	34.9568i	−2.89407	+	1.28852i
$737$	30.4423	−	22.1176i	1.12136	−	0.814714i
$738$	51.6806	+	17.9364i	1.90239	+	0.660248i
$739$	−38.6512	−	28.0817i	−1.42181	−	1.03300i	−0.991470	−	0.130335i	$-0.958395\pi$
$739$	−38.6512	−	28.0817i	−1.42181	−	1.03300i	−0.430337	−	0.902668i	$-0.641605\pi$
$740$	113.654	+	20.0543i	4.17801	+	0.737210i
$741$	−0.591504	+	0.469325i	−0.0217294	+	0.0172411i
$742$	1.40539	−	0.298725i	0.0515936	−	0.0109666i
$743$	17.2283	+	29.8402i	0.632044	+	1.09473i	0.987133	+	0.159900i	$0.0511170\pi$
$743$	17.2283	+	29.8402i	0.632044	+	1.09473i	−0.355090	+	0.934832i	$0.615550\pi$
$744$	−37.6024	+	134.950i	−1.37857	+	4.94749i
$745$	5.18969	−	2.53041i	0.190136	−	0.0927072i
$746$	18.2963	+	56.3103i	0.669877	+	2.06167i
$747$	−1.18956	−	2.82158i	−0.0435239	−	0.103236i
$748$	84.2799	+	61.2329i	3.08158	+	2.23890i
$749$	−1.14847	+	1.98920i	−0.0419640	+	0.0726838i
$750$	2.17352	+	51.6540i	0.0793657	+	1.88614i
$751$	0.682040	+	1.18133i	0.0248880	+	0.0431072i	0.878201	−	0.478292i	$-0.158744\pi$
$751$	0.682040	+	1.18133i	0.0248880	+	0.0431072i	−0.853313	+	0.521399i	$0.825410\pi$
$752$	8.76985	−	83.4395i	0.319803	−	3.04273i
$753$	36.6554	+	6.18005i	1.33580	+	0.225214i
$754$	−16.5360	−	3.51482i	−0.602204	−	0.128002i
$755$	3.51984	+	2.37478i	0.128100	+	0.0864269i
$756$	−0.671201	+	3.54884i	−0.0244113	+	0.129070i
$757$	−46.5288			−1.69112			−0.845559	−	0.533882i	$-0.820733\pi$
$757$	−46.5288			−1.69112			−0.845559	+	0.533882i	$0.820733\pi$
$758$	−1.17871	−	1.30909i	−0.0428126	−	0.0475482i
$759$	5.95473	+	40.1797i	0.216143	+	1.45843i
$760$	−3.44405	+	4.10346i	−0.124929	+	0.148848i
$761$	−2.05258	+	19.5290i	−0.0744058	+	0.707924i	0.892197	+	0.451646i	$0.149163\pi$
$761$	−2.05258	+	19.5290i	−0.0744058	+	0.707924i	−0.966603	+	0.256278i	$0.917504\pi$
$762$	45.5325	+	18.0000i	1.64947	+	0.652071i
$763$	−0.225517	−	2.14565i	−0.00816427	−	0.0776778i
$764$	53.7827	+	39.0754i	1.94579	+	1.41370i
$765$	−24.3650	−	21.2901i	−0.880920	−	0.769744i
$766$	75.5770	−	54.9099i	2.73071	−	1.98398i
$767$	−2.54818	−	2.83004i	−0.0920093	−	0.102187i
$768$	9.43286	−	0.400303i	0.340379	−	0.0144447i
$769$	31.3047	−	6.65402i	1.12888	−	0.239950i	0.394635	−	0.918838i	$-0.370871\pi$
$769$	31.3047	−	6.65402i	1.12888	−	0.239950i	0.734242	+	0.678888i	$0.237538\pi$
$770$	−3.30746	+	0.824222i	−0.119192	+	0.0297029i
$771$	3.14807	+	8.45134i	0.113375	+	0.304368i
$772$	−55.2199	−	11.7374i	−1.98741	−	0.422437i
$773$	−28.9715	−	21.0490i	−1.04203	−	0.757080i	−0.0713505	−	0.997451i	$-0.522731\pi$
$773$	−28.9715	−	21.0490i	−1.04203	−	0.757080i	−0.970681	+	0.240371i	$0.922731\pi$
$774$	−15.1290	+	32.2385i	−0.543802	+	1.15879i
$775$	48.3146	−	3.36690i	1.73551	−	0.120943i
$776$	8.81584	−	15.2695i	0.316470	−	0.548142i
$777$	0.147159	−	2.35874i	0.00527929	−	0.0846192i
$778$	−29.1497	+	32.3740i	−1.04507	+	1.16066i
$779$	1.31132	−	1.45637i	0.0469830	−	0.0521799i
$780$	−5.45889	−	29.6755i	−0.195459	−	1.06255i
$781$	9.06935	+	10.0725i	0.324527	+	0.360424i
$782$	−71.6948			−2.56380
$783$	16.4154	+	14.1245i	0.586640	+	0.504768i
$784$	67.9897	−	49.3974i	2.42820	−	1.76419i
$785$	−19.2732	+	9.39730i	−0.687889	+	0.335404i
$786$	−59.6463	+	29.6476i	−2.12751	+	1.05750i
$787$	−5.63966	−	2.51094i	−0.201032	−	0.0895052i	0.303751	−	0.952751i	$-0.401761\pi$
$787$	−5.63966	−	2.51094i	−0.201032	−	0.0895052i	−0.504783	+	0.863246i	$0.668428\pi$
$788$	−37.1161	−	16.5251i	−1.32220	−	0.588684i
$789$	1.07230	−	17.1874i	0.0381750	−	0.611888i
$790$	−3.08840	−	21.9941i	−0.109880	−	0.782516i
$791$	0.628207	−	0.456419i	0.0223365	−	0.0162284i
$792$	23.9865	−	102.751i	0.852321	−	3.65109i
$793$	1.65242			0.0586791
$794$	−54.1625	−	60.1535i	−1.92215	−	2.13477i
$795$	15.3303	−	1.18584i	0.543709	−	0.0420573i
$796$	57.6861	−	64.0669i	2.04463	−	2.27079i
$797$	22.5944	−	25.0936i	0.800334	−	0.888861i	−0.195438	−	0.980716i	$-0.562613\pi$
$797$	22.5944	−	25.0936i	0.800334	−	0.888861i	0.995772	+	0.0918548i	$0.0292796\pi$
$798$	0.149857	+	0.0994516i	0.00530488	+	0.00352055i
$799$	16.8093	−	29.1146i	0.594670	−	1.03000i
$800$	−28.8963	−	71.5701i	−1.02164	−	2.53038i
$801$	12.1918	+	17.5025i	0.430776	+	0.618422i
$802$	−44.4119	−	32.2671i	−1.56824	−	1.13939i
$803$	10.9684	+	2.33140i	0.387066	+	0.0822735i
$804$	50.5418	−	61.1598i	1.78247	−	2.15694i
$805$	1.08492	−	1.29265i	0.0382385	−	0.0455599i
$806$	−38.4326	+	8.16911i	−1.35373	+	0.287745i
$807$	24.2223	−	46.3921i	0.852665	−	1.63308i
$808$	59.8671	+	66.4892i	2.10612	+	2.33908i
$809$	−20.7943	+	15.1079i	−0.731089	+	0.531167i	−0.889908	−	0.456141i	$-0.849231\pi$
$809$	−20.7943	+	15.1079i	−0.731089	+	0.531167i	0.158819	+	0.987308i	$0.449231\pi$
$810$	−16.8584	+	51.0145i	−0.592344	+	1.79247i
$811$	5.81417	+	4.22424i	0.204163	+	0.148333i	0.685169	−	0.728384i	$-0.259728\pi$
$811$	5.81417	+	4.22424i	0.204163	+	0.148333i	−0.481006	+	0.876717i	$0.659728\pi$
$812$	0.302804	+	2.88098i	0.0106263	+	0.101103i
$813$	2.25945	+	15.2457i	0.0792424	+	0.534690i
$814$	−11.8317	+	112.571i	−0.414702	+	3.94562i
$815$	4.12360	+	6.60089i	0.144443	+	0.231219i
$816$	93.5209	+	36.9709i	3.27389	+	1.29424i
$817$	0.853650	+	0.948075i	0.0298654	+	0.0331689i
$818$	−97.0357			−3.39277
$819$	−0.591322	+	0.179207i	−0.0206625	+	0.00626199i
$820$	26.7757	+	73.5930i	0.935048	+	2.56998i
$821$	0.496319	+	0.105496i	0.0173217	+	0.00368183i	0.216564	−	0.976268i	$-0.430515\pi$
$821$	0.496319	+	0.105496i	0.0173217	+	0.00368183i	−0.199243	+	0.979950i	$0.563848\pi$
$822$	−10.1526	−	27.2558i	−0.354113	−	0.950656i
$823$	−1.61052	+	15.3230i	−0.0561391	+	0.534128i	0.929923	+	0.367753i	$0.119873\pi$
$823$	−1.61052	+	15.3230i	−0.0561391	+	0.534128i	−0.986063	+	0.166375i	$0.946794\pi$
$824$	48.7799	+	84.4892i	1.69933	+	2.94332i
$825$	−36.2494	+	4.07649i	−1.26204	+	0.141925i
$826$	−0.453543	+	0.785560i	−0.0157808	+	0.0273331i
$827$	−35.2637	−	25.6206i	−1.22624	−	0.890915i	−0.229637	−	0.973276i	$-0.573754\pi$
$827$	−35.2637	−	25.6206i	−1.22624	−	0.890915i	−0.996603	+	0.0823613i	$0.973754\pi$
$828$	33.2715	+	78.9182i	1.15626	+	2.74260i
$829$	11.6434	+	35.8348i	0.404394	+	1.24460i	0.921401	+	0.388614i	$0.127046\pi$
$829$	11.6434	+	35.8348i	0.404394	+	1.24460i	−0.517007	+	0.855981i	$0.672954\pi$
$830$	2.86128	−	5.37974i	0.0993166	−	0.186734i
$831$	13.7161	−	3.52937i	0.475808	−	0.122432i
$832$	13.0192	+	22.5499i	0.451359	+	0.781777i
$833$	32.9391	−	7.00142i	1.14127	−	0.242585i
$834$	−8.28380	−	55.8952i	−0.286845	−	1.93549i
$835$	−1.00761	−	7.17576i	−0.0348699	−	0.248327i
$836$	−5.01350	−	3.64252i	−0.173396	−	0.125979i
$837$	48.2064	+	14.4718i	1.66626	+	0.500217i
$838$	19.1169	−	13.8893i	0.660384	−	0.479797i
$839$	25.5368	−	11.3697i	0.881630	−	0.392527i	0.0845629	−	0.996418i	$-0.473051\pi$
$839$	25.5368	−	11.3697i	0.881630	−	0.392527i	0.797067	+	0.603891i	$0.206384\pi$
$840$	−3.85538	+	2.08661i	−0.133023	+	0.0719950i
$841$	−10.6253	−	4.73069i	−0.366390	−	0.163127i
$842$	45.4086	−	9.65190i	1.56489	−	0.332627i
$843$	23.6602	+	37.2393i	0.814900	+	1.28259i
$844$	−19.0320	−	21.1371i	−0.655108	−	0.727571i
$845$	−18.8407	+	14.7164i	−0.648140	+	0.506258i
$846$	−55.3913	−	6.93860i	−1.90439	−	0.238554i
$847$	−0.282410	−	0.869169i	−0.00970373	−	0.0298650i
$848$	−43.6575	+	19.4376i	−1.49921	+	0.667489i
$849$	18.4712	−	0.783867i	0.633932	−	0.0269022i
$850$	2.26241	−	64.3465i	0.0776000	−	2.20707i
$851$	−28.0205	−	48.5330i	−0.960531	−	1.66369i
$852$	23.8121	+	15.8028i	0.815790	+	0.541394i
$853$	23.1484	+	4.92035i	0.792587	+	0.168470i	0.586377	−	0.810038i	$-0.300554\pi$
$853$	23.1484	+	4.92035i	0.792587	+	0.168470i	0.206210	+	0.978508i	$0.433887\pi$
$854$	−0.121628	−	0.374332i	−0.00416201	−	0.0128094i
$855$	1.44939	+	1.26647i	0.0495680	+	0.0433123i
$856$	43.7217	−	134.561i	1.49438	−	4.59922i
$857$	24.1294	−	41.7934i	0.824245	−	1.42763i	−0.0782494	−	0.996934i	$-0.524933\pi$
$857$	24.1294	−	41.7934i	0.824245	−	1.42763i	0.902495	−	0.430701i	$-0.141734\pi$
$858$	28.6598	−	7.37460i	0.978430	−	0.251765i
$859$	8.83897	+	3.93536i	0.301582	+	0.134273i	0.551948	−	0.833878i	$-0.313884\pi$
$859$	8.83897	+	3.93536i	0.301582	+	0.134273i	−0.250367	+	0.968151i	$0.580551\pi$
$860$	−49.4674	+	12.3273i	−1.68683	+	0.420359i
$861$	1.43604	−	0.713795i	0.0489401	−	0.0243261i
$862$	6.32943	+	60.2205i	0.215581	+	2.05112i
$863$	−7.67590	+	5.57686i	−0.261291	+	0.189839i	−0.710716	−	0.703479i	$-0.751629\pi$
$863$	−7.67590	+	5.57686i	−0.261291	+	0.189839i	0.449425	+	0.893318i	$0.351629\pi$
$864$	−1.80583	−	80.1910i	−0.0614356	−	2.72815i
$865$	−6.75008	−	18.5526i	−0.229510	−	0.630807i
$866$	3.47368	+	33.0499i	0.118040	+	1.12308i
$867$	7.59623	+	7.74889i	0.257981	+	0.263166i
$868$	3.36641	+	5.83080i	0.114264	+	0.197910i
$869$	15.3283	−	3.25812i	0.519976	−	0.110524i
$870$	−1.18581	+	43.0768i	−0.0402027	+	1.46044i
$871$	13.2766	+	2.82204i	0.449862	+	0.0956211i
$872$	41.0671	+	126.391i	1.39071	+	4.28016i
$873$	−5.42193	−	3.27588i	−0.183505	−	0.110872i
$874$	4.26486			0.144261
$875$	1.12592	+	1.01452i	0.0380632	+	0.0342969i
$876$	23.6225	−	1.00247i	0.798130	−	0.0338704i
$877$	−2.11673	+	20.1393i	−0.0714769	+	0.680057i	0.898849	+	0.438258i	$0.144404\pi$
$877$	−2.11673	+	20.1393i	−0.0714769	+	0.680057i	−0.970326	+	0.241800i	$0.922262\pi$
$878$	−38.3625	+	42.6059i	−1.29467	+	1.43788i
$879$	−11.7784	−	31.6205i	−0.397276	−	1.06653i
$880$	101.906	−	49.6877i	3.43524	−	1.67497i
$881$	−5.94159	+	18.2863i	−0.200177	+	0.616083i	0.799700	+	0.600400i	$0.204992\pi$
$881$	−5.94159	+	18.2863i	−0.200177	+	0.616083i	−0.999877	+	0.0156823i	$0.995008\pi$
$882$	−31.9611	−	45.8834i	−1.07619	−	1.54497i
$883$	−1.91625	+	5.89762i	−0.0644870	+	0.198471i	−0.978109	−	0.208095i	$-0.933274\pi$
$883$	−1.91625	+	5.89762i	−0.0644870	+	0.198471i	0.913622	+	0.406566i	$0.133274\pi$
$884$	3.92794	+	37.3718i	0.132111	+	1.25695i
$885$	−5.91979	+	7.69344i	−0.198992	+	0.258612i
$886$	−9.55119	+	90.8735i	−0.320879	+	3.05296i
$887$	−32.9404	−	14.6660i	−1.10603	−	0.492437i	−0.229270	−	0.973363i	$-0.573634\pi$
$887$	−32.9404	−	14.6660i	−1.10603	−	0.492437i	−0.876761	+	0.480926i	$0.840301\pi$
$888$	21.3416	+	144.003i	0.716178	+	4.83243i
$889$	1.31120	−	0.583786i	0.0439764	−	0.0195795i
$890$	−11.7044	+	40.7999i	−0.392334	+	1.36761i
$891$	−36.7376	−	9.35062i	−1.23076	−	0.313258i
$892$	−0.684110	+	2.10547i	−0.0229057	+	0.0704964i
$893$	−0.999923	+	1.73192i	−0.0334612	+	0.0579564i
$894$	8.35844	+	8.52642i	0.279548	+	0.285166i
$895$	−16.7694	+	4.17895i	−0.560539	+	0.139687i
$896$	1.34970	−	1.49899i	0.0450903	−	0.0500778i
$897$	−9.33343	+	11.2942i	−0.311634	+	0.377103i
$898$	34.3226	−	15.2814i	1.14536	−	0.509947i
$899$	40.3692			1.34639
$900$	−71.8794	+	27.3710i	−2.39598	+	0.912366i
$901$	−19.1492			−0.637953
$902$	−70.1669	+	31.2403i	−2.33630	+	1.04019i
$903$	0.364406	+	0.978291i	0.0121267	+	0.0325555i
$904$	−32.0054	+	35.5455i	−1.06448	+	1.18223i
$905$	−36.2452	−	14.6490i	−1.20483	−	0.486950i
$906$	−2.35689	+	8.45854i	−0.0783024	+	0.281016i
$907$	4.37588	−	7.57925i	0.145299	−	0.251665i	−0.784186	−	0.620526i	$-0.786919\pi$
$907$	4.37588	−	7.57925i	0.145299	−	0.251665i	0.929484	+	0.368862i	$0.120252\pi$
$908$	5.94376	−	18.2930i	0.197251	−	0.607075i
$909$	24.3115	−	21.0296i	0.806361	−	0.697508i
$910$	−1.01925	−	0.687669i	−0.0337878	−	0.0227960i
$911$	−17.5961	+	7.83427i	−0.582984	+	0.259561i	−0.676968	−	0.736013i	$-0.736706\pi$
$911$	−17.5961	+	7.83427i	−0.582984	+	0.259561i	0.0939841	+	0.995574i	$0.470040\pi$
$912$	−5.56322	−	2.19926i	−0.184217	−	0.0728249i
$913$	3.92759	+	1.74867i	0.129984	+	0.0578727i
$914$	−1.92055	+	18.2728i	−0.0635263	+	0.604412i
$915$	−0.762047	−	4.14263i	−0.0251925	−	0.136951i
$916$	6.70501	+	63.7939i	0.221540	+	2.10781i
$917$	−0.603390	+	1.85704i	−0.0199257	+	0.0613250i
$918$	25.8326	−	61.7245i	0.852601	−	2.03721i
$919$	−5.09770	+	15.6891i	−0.168158	+	0.517536i	−0.999255	−	0.0385906i	$-0.987713\pi$
$919$	−5.09770	+	15.6891i	−0.168158	+	0.517536i	0.831097	+	0.556127i	$0.187713\pi$
$920$	−48.8139	+	91.7792i	−1.60935	+	3.02587i
$921$	8.22683	+	1.38703i	0.271083	+	0.0457043i
$922$	21.8787	−	24.2988i	0.720537	−	0.800237i
$923$	−0.511050	+	4.86232i	−0.0168214	+	0.160045i
$924$	−2.71944	−	4.28019i	−0.0894630	−	0.140808i
$925$	44.4429	−	23.6171i	1.46127	−	0.776525i
$926$	79.9104			2.62602
$927$	30.6980	−	16.9183i	1.00826	−	0.555669i
$928$	−19.8804	−	61.1856i	−0.652607	−	2.00852i
$929$	22.1301	+	4.70389i	0.726064	+	0.154330i	0.556094	−	0.831120i	$-0.312300\pi$
$929$	22.1301	+	4.70389i	0.726064	+	0.154330i	0.169970	+	0.985449i	$0.445633\pi$
$930$	38.2041	+	92.5837i	1.25276	+	3.03594i
$931$	−1.95943	+	0.416489i	−0.0642176	+	0.0136499i
$932$	26.2532	+	45.4719i	0.859953	+	1.48948i
$933$	1.15338	−	4.13931i	0.0377599	−	0.135515i
$934$	9.67810	+	92.0810i	0.316677	+	3.01298i
$935$	45.4017	−	1.58004i	1.48479	−	0.0516727i
$936$	33.3332	−	18.3706i	1.08953	−	0.600461i
$937$	−43.9818	+	31.9547i	−1.43682	+	1.04391i	−0.448129	+	0.893969i	$0.647909\pi$
$937$	−43.9818	+	31.9547i	−1.43682	+	1.04391i	−0.988694	+	0.149944i	$0.952091\pi$
$938$	−0.337947	−	3.21535i	−0.0110344	−	0.104985i
$939$	1.27510	−	20.4379i	0.0416112	−	0.666966i
$940$	−42.3406	−	67.7771i	−1.38100	−	2.21064i
$941$	45.7840	+	20.3843i	1.49252	+	0.664511i	0.980866	−	0.194684i	$-0.0623682\pi$
$941$	45.7840	+	20.3843i	1.49252	+	0.664511i	0.511649	+	0.859195i	$0.329035\pi$
$942$	−31.0411	−	31.6649i	−1.01137	−	1.03170i
$943$	19.0136	−	32.9325i	0.619169	−	1.07243i
$944$	9.32324	−	28.6940i	0.303446	−	0.933909i
$945$	0.721974	+	1.39981i	0.0234858	+	0.0455357i
$946$	−15.4509	−	47.5531i	−0.502354	−	1.54609i
$947$	33.7933	+	7.18299i	1.09813	+	0.233416i	0.721133	−	0.692797i	$-0.243622\pi$
$947$	33.7933	+	7.18299i	1.09813	+	0.233416i	0.377002	+	0.926213i	$0.376955\pi$
$948$	29.5884	−	14.7071i	0.960987	−	0.477666i
$949$	2.02243	+	3.50294i	0.0656507	+	0.113710i
$950$	−0.134582	+	3.82774i	−0.00436643	+	0.124188i
$951$	−27.0324	−	42.5469i	−0.876584	−	1.37968i
$952$	4.98757	−	2.22061i	0.161648	−	0.0719703i
$953$	−9.45452	−	29.0980i	−0.306262	−	0.942577i	−0.979203	−	0.202881i	$-0.934969\pi$
$953$	−9.45452	−	29.0980i	−0.306262	−	0.942577i	0.672941	−	0.739696i	$-0.265031\pi$
$954$	12.3528	+	29.3001i	0.399935	+	0.948625i
$955$	28.9728	−	1.00829i	0.937539	−	0.0326275i
$956$	−99.4774	−	110.481i	−3.21733	−	3.57321i
$957$	−30.3780	+	1.28915i	−0.981980	+	0.0416724i
$958$	−13.9608	+	2.96747i	−0.451054	+	0.0958745i
$959$	−0.778917	−	0.346796i	−0.0251526	−	0.0111986i
$960$	50.5288	−	43.0386i	1.63081	−	1.38907i
$961$	57.3940	−	25.5535i	1.85142	−	0.824305i
$962$	−33.0320	+	23.9992i	−1.06499	+	0.773764i
$963$	−48.0233	−	16.6671i	−1.54753	−	0.537089i
$964$	−42.6418	−	30.9811i	−1.37340	−	0.997833i
$965$	−22.1282	+	10.7894i	−0.712331	+	0.347322i
$966$	3.24554	+	1.28303i	0.104423	+	0.0412809i
$967$	37.9711	−	8.07100i	1.22107	−	0.259546i	0.448095	−	0.893986i	$-0.352103\pi$
$967$	37.9711	−	8.07100i	1.22107	−	0.259546i	0.772972	+	0.634440i	$0.218769\pi$
$968$	28.1472	+	48.7523i	0.904684	+	1.56696i
$969$	−1.67803	−	1.71176i	−0.0539062	−	0.0549896i
$970$	−1.75287	−	12.4831i	−0.0562813	−	0.400809i
$971$	−2.15683	−	6.63803i	−0.0692158	−	0.213024i	0.910465	−	0.413585i	$-0.135724\pi$
$971$	−2.15683	−	6.63803i	−0.0692158	−	0.213024i	−0.979681	+	0.200561i	$0.935724\pi$
$972$	−79.9315	+	0.209334i	−2.56380	+	0.00671440i
$973$	−1.34010	−	0.973640i	−0.0429617	−	0.0312135i
$974$	24.7042	−	42.7889i	0.791573	−	1.37104i
$975$	−9.84210	−	8.73321i	−0.315199	−	0.279687i
$976$	6.54570	+	11.3375i	0.209523	+	0.362904i
$977$	−4.88978	+	46.5231i	−0.156438	+	1.48841i	0.581504	+	0.813543i	$0.302464\pi$
$977$	−4.88978	+	46.5231i	−0.156438	+	1.48841i	−0.737942	+	0.674864i	$0.764202\pi$
$978$	−10.2530	+	12.4070i	−0.327855	+	0.396732i
$979$	−29.2940	−	6.22662i	−0.936239	−	0.199004i
$980$	22.0738	−	76.9457i	0.705121	−	2.45794i
$981$	45.6946	−	13.8483i	1.45892	−	0.442141i
$982$	90.5064			2.88817
$983$	2.06002	+	2.28788i	0.0657044	+	0.0729721i	0.775101	−	0.631838i	$-0.217699\pi$
$983$	2.06002	+	2.28788i	0.0657044	+	0.0729721i	−0.709396	+	0.704810i	$0.751032\pi$
$984$	−77.3827	+	61.3988i	−2.46687	+	1.95732i
$985$	−17.1916	+	4.28418i	−0.547771	+	0.136505i
$986$	5.60980	−	53.3737i	0.178652	−	1.69976i
$987$	−1.28196	+	1.01717i	−0.0408054	+	0.0323767i
$988$	−0.233659	−	2.22311i	−0.00743367	−	0.0707266i
$989$	20.0273	+	14.5507i	0.636832	+	0.462686i
$990$	−31.7053	−	68.4496i	−1.00766	−	2.17547i
$991$	−17.0227	+	12.3677i	−0.540744	+	0.392874i	−0.824361	−	0.566064i	$-0.808466\pi$
$991$	−17.0227	+	12.3677i	−0.540744	+	0.392874i	0.283617	+	0.958938i	$0.408466\pi$
$992$	−100.052	−	111.119i	−3.17665	−	3.52803i
$993$	−9.38051	−	14.7642i	−0.297682	−	0.468529i
$994$	1.13910	−	0.242124i	0.0361302	−	0.00767971i
$995$	2.62696	−	37.5030i	0.0832804	−	1.18893i
$996$	8.93896	+	1.50710i	0.283242	+	0.0477542i
$997$	−54.1067	−	11.5007i	−1.71358	−	0.364232i	−0.756483	−	0.654013i	$-0.773084\pi$
$997$	−54.1067	−	11.5007i	−1.71358	−	0.364232i	−0.957093	+	0.289781i	$0.906418\pi$
$998$	5.43856	+	3.95134i	0.172155	+	0.125078i
$999$	51.8799	−	6.63679i	1.64141	−	0.209979i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.16.2	✓	224
3.2	odd	2		675.2.r.a.316.27		224
9.4	even	3	inner	225.2.q.a.166.27	yes	224
9.5	odd	6		675.2.r.a.91.2		224
25.11	even	5	inner	225.2.q.a.61.27	yes	224
75.11	odd	10		675.2.r.a.586.2		224
225.86	odd	30		675.2.r.a.361.27		224
225.211	even	15	inner	225.2.q.a.211.2	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.16.2	✓	224	1.1	even	1	trivial
225.2.q.a.61.27	yes	224	25.11	even	5	inner
225.2.q.a.166.27	yes	224	9.4	even	3	inner
225.2.q.a.211.2	yes	224	225.211	even	15	inner
675.2.r.a.91.2		224	9.5	odd	6
675.2.r.a.316.27		224	3.2	odd	2
675.2.r.a.361.27		224	225.86	odd	30
675.2.r.a.586.2		224	75.11	odd	10

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.43895 + 1.08589i) q^{2} +(-1.70795 - 0.287957i) q^{3} +(3.43105 - 3.81057i) q^{4} +(0.156246 - 2.23060i) q^{5} +(4.47828 - 1.15233i) q^{6} +(0.0677783 - 0.117395i) q^{7} +(-2.58030 + 7.94134i) q^{8} +(2.83416 + 0.983632i) q^{9} +O(q^{10})\)	\(q+(-2.43895 + 1.08589i) q^{2} +(-1.70795 - 0.287957i) q^{3} +(3.43105 - 3.81057i) q^{4} +(0.156246 - 2.23060i) q^{5} +(4.47828 - 1.15233i) q^{6} +(0.0677783 - 0.117395i) q^{7} +(-2.58030 + 7.94134i) q^{8} +(2.83416 + 0.983632i) q^{9} +(2.04111 + 5.60999i) q^{10} +(-3.84795 + 1.71322i) q^{11} +(-6.95733 + 5.52025i) q^{12} +(-1.38801 - 0.617982i) q^{13} +(-0.0378292 + 0.359921i) q^{14} +(-0.909179 + 3.76476i) q^{15} +(-1.25824 - 11.9714i) q^{16} +(1.49050 - 4.58730i) q^{17} +(-7.98049 + 0.678560i) q^{18} +(-0.0886646 + 0.272882i) q^{19} +(-7.96377 - 8.24870i) q^{20} +(-0.149567 + 0.180988i) q^{21} +(7.52458 - 8.35690i) q^{22} +(-0.581968 + 5.53705i) q^{23} +(6.69377 - 12.8204i) q^{24} +(-4.95117 - 0.697047i) q^{25} +4.05635 q^{26} +(-4.55735 - 2.49611i) q^{27} +(-0.214793 - 0.661064i) q^{28} +(-4.07656 - 0.866500i) q^{29} +(-1.87067 - 10.1693i) q^{30} +(-9.47469 + 2.01391i) q^{31} +(7.71834 + 13.3686i) q^{32} +(7.06542 - 1.81804i) q^{33} +(1.34604 + 12.8067i) q^{34} +(-0.251272 - 0.169529i) q^{35} +(13.4723 - 7.42487i) q^{36} +(-8.14328 + 5.91644i) q^{37} +(-0.0800710 - 0.761824i) q^{38} +(2.19270 + 1.45517i) q^{39} +(17.3108 + 6.99642i) q^{40} +(-6.23965 - 2.77807i) q^{41} +(0.168252 - 0.603833i) q^{42} +(2.22316 - 3.85063i) q^{43} +(-6.67418 + 20.5410i) q^{44} +(2.63692 - 6.16820i) q^{45} +(-4.59324 - 14.1365i) q^{46} +(6.81762 + 1.44913i) q^{47} +(-1.29823 + 20.8087i) q^{48} +(3.49081 + 6.04626i) q^{49} +(12.8326 - 3.67637i) q^{50} +(-3.86665 + 7.40566i) q^{51} +(-7.11720 + 3.16878i) q^{52} +(-1.22682 - 3.77578i) q^{53} +(13.8256 + 1.13910i) q^{54} +(3.22028 + 8.85093i) q^{55} +(0.757388 + 0.841165i) q^{56} +(0.230013 - 0.440536i) q^{57} +(10.8834 - 2.31335i) q^{58} +(2.28974 + 1.01946i) q^{59} +(11.2264 + 16.3816i) q^{60} +(-0.993544 + 0.442354i) q^{61} +(20.9214 - 15.2003i) q^{62} +(0.307568 - 0.266049i) q^{63} +(-13.8646 - 10.0733i) q^{64} +(-1.59535 + 2.99954i) q^{65} +(-15.2580 + 12.1064i) q^{66} +(-8.73827 + 1.85738i) q^{67} +(-12.3662 - 21.4189i) q^{68} +(2.58841 - 9.28941i) q^{69} +(0.796930 + 0.140618i) q^{70} +(-0.994371 - 3.06036i) q^{71} +(-15.1243 + 19.9690i) q^{72} +(-2.15376 - 1.56480i) q^{73} +(13.4364 - 23.2726i) q^{74} +(8.25562 + 2.61625i) q^{75} +(0.735621 + 1.27413i) q^{76} +(-0.0596835 + 0.567851i) q^{77} +(-6.92803 - 1.16806i) q^{78} +(-3.63910 - 0.773514i) q^{79} +(-26.8999 + 0.936151i) q^{80} +(7.06494 + 5.57554i) q^{81} +18.2349 q^{82} +(-0.682979 - 0.758525i) q^{83} +(0.176496 + 1.19091i) q^{84} +(-9.99956 - 4.04147i) q^{85} +(-1.24082 + 11.8056i) q^{86} +(6.71303 + 2.65381i) q^{87} +(-3.67638 - 34.9785i) q^{88} +(5.75217 + 4.17920i) q^{89} +(0.266675 + 17.9073i) q^{90} +(-0.166625 + 0.121060i) q^{91} +(19.1026 + 21.2155i) q^{92} +(16.7622 - 0.711339i) q^{93} +(-18.2014 + 3.86883i) q^{94} +(0.594837 + 0.240412i) q^{95} +(-9.33293 - 25.0553i) q^{96} +(-2.06543 - 0.439021i) q^{97} +(-15.0795 - 10.9559i) q^{98} +(-12.5909 + 1.07057i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

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