LMFDB - Embedded newform 225.2.q.a.16.18

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			16.18
Character	$\chi$	$=$	225.16
Dual form			225.2.q.a.211.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.520318 - 0.231661i) q^{2} +(-1.62589 - 0.597061i) q^{3} +(-1.12120 + 1.24522i) q^{4} +(2.21056 + 0.336764i) q^{5} +(-0.984295 + 0.0659928i) q^{6} +(1.58872 - 2.75174i) q^{7} +(-0.646919 + 1.99101i) q^{8} +(2.28704 + 1.94151i) q^{9} +O(q^{10})$	\(q+(0.520318 - 0.231661i) q^{2} +(-1.62589 - 0.597061i) q^{3} +(-1.12120 + 1.24522i) q^{4} +(2.21056 + 0.336764i) q^{5} +(-0.984295 + 0.0659928i) q^{6} +(1.58872 - 2.75174i) q^{7} +(-0.646919 + 1.99101i) q^{8} +(2.28704 + 1.94151i) q^{9} +(1.22821 - 0.336876i) q^{10} +(1.73440 - 0.772206i) q^{11} +(2.56641 - 1.35516i) q^{12} +(5.02577 + 2.23762i) q^{13} +(0.189169 - 1.79982i) q^{14} +(-3.39306 - 1.86738i) q^{15} +(-0.225661 - 2.14702i) q^{16} +(0.888735 - 2.73524i) q^{17} +(1.63976 + 0.480388i) q^{18} +(-1.39039 + 4.27917i) q^{19} +(-2.89782 + 2.37505i) q^{20} +(-4.22603 + 3.52546i) q^{21} +(0.723552 - 0.803585i) q^{22} +(0.335381 - 3.19093i) q^{23} +(2.24057 - 2.85091i) q^{24} +(4.77318 + 1.48888i) q^{25} +3.13337 q^{26} +(-2.55927 - 4.52218i) q^{27} +(1.64524 + 5.06353i) q^{28} +(-1.75597 - 0.373243i) q^{29} +(-2.19807 - 0.185594i) q^{30} +(-7.35558 + 1.56348i) q^{31} +(-2.70827 - 4.69086i) q^{32} +(-3.28100 + 0.219977i) q^{33} +(-0.171223 - 1.62908i) q^{34} +(4.43864 - 5.54787i) q^{35} +(-4.98182 + 0.671035i) q^{36} +(-4.57619 + 3.32479i) q^{37} +(0.267871 + 2.54863i) q^{38} +(-6.83536 - 6.63882i) q^{39} +(-2.10055 + 4.18340i) q^{40} +(-0.974346 - 0.433807i) q^{41} +(-1.38217 + 2.81337i) q^{42} +(-3.64392 + 6.31145i) q^{43} +(-0.983045 + 3.02550i) q^{44} +(4.40181 + 5.06203i) q^{45} +(-0.564709 - 1.73800i) q^{46} +(7.34730 + 1.56172i) q^{47} +(-0.915004 + 3.62556i) q^{48} +(-1.54804 - 2.68128i) q^{49} +(2.82849 - 0.331069i) q^{50} +(-3.07809 + 3.91658i) q^{51} +(-8.42120 + 3.74936i) q^{52} +(-0.982710 - 3.02447i) q^{53} +(-2.37924 - 1.76009i) q^{54} +(4.09406 - 1.12293i) q^{55} +(4.45097 + 4.94330i) q^{56} +(4.81554 - 6.12731i) q^{57} +(-1.00013 + 0.212584i) q^{58} +(-12.0714 - 5.37452i) q^{59} +(6.12959 - 2.13139i) q^{60} +(0.958206 - 0.426621i) q^{61} +(-3.46504 + 2.51750i) q^{62} +(8.97598 - 3.20881i) q^{63} +(0.997243 + 0.724540i) q^{64} +(10.3562 + 6.63890i) q^{65} +(-1.65620 + 0.874537i) q^{66} +(12.7060 - 2.70075i) q^{67} +(2.40952 + 4.17341i) q^{68} +(-2.45048 + 4.98787i) q^{69} +(1.02428 - 3.91491i) q^{70} +(-2.10454 - 6.47710i) q^{71} +(-5.34510 + 3.29751i) q^{72} +(-0.173732 - 0.126223i) q^{73} +(-1.61085 + 2.79007i) q^{74} +(-6.87172 - 5.27063i) q^{75} +(-3.76959 - 6.52912i) q^{76} +(0.630566 - 5.99944i) q^{77} +(-5.09451 - 1.87081i) q^{78} +(4.79399 + 1.01899i) q^{79} +(0.224201 - 4.82212i) q^{80} +(1.46107 + 8.88061i) q^{81} -0.607465 q^{82} +(-10.0251 - 11.1340i) q^{83} +(0.348258 - 9.21506i) q^{84} +(2.88574 - 5.74714i) q^{85} +(-0.433882 + 4.12812i) q^{86} +(2.63217 + 1.65527i) q^{87} +(0.415453 + 3.95277i) q^{88} +(-2.15019 - 1.56220i) q^{89} +(3.46301 + 1.61414i) q^{90} +(14.1419 - 10.2747i) q^{91} +(3.59737 + 3.99529i) q^{92} +(12.8929 + 1.84969i) q^{93} +(4.18472 - 0.889490i) q^{94} +(-4.51461 + 8.99114i) q^{95} +(1.60262 + 9.24382i) q^{96} +(-13.1990 - 2.80553i) q^{97} +(-1.42662 - 1.03650i) q^{98} +(5.46589 + 1.60130i) 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 $

$2$	0.520318	−	0.231661i	0.367920	−	0.163809i	−0.214445	−	0.976736i	$-0.568794\pi$
$2$	0.520318	−	0.231661i	0.367920	−	0.163809i	0.582365	+	0.812927i	$0.302127\pi$
$3$	−1.62589	−	0.597061i	−0.938708	−	0.344713i
$3$	−1.62589	−	0.597061i	−0.938708	−	0.344713i
$4$	−1.12120	+	1.24522i	−0.560598	+	0.622608i
$5$	2.21056	+	0.336764i	0.988594	+	0.150605i
$5$	2.21056	+	0.336764i	0.988594	+	0.150605i
$6$	−0.984295	+	0.0659928i	−0.401837	+	0.0269414i
$7$	1.58872	−	2.75174i	0.600478	−	1.04006i	−0.392270	−	0.919850i	$-0.628310\pi$
$7$	1.58872	−	2.75174i	0.600478	−	1.04006i	0.992749	−	0.120209i	$-0.0383565\pi$
$8$	−0.646919	+	1.99101i	−0.228720	+	0.703929i
$9$	2.28704	+	1.94151i	0.762345	+	0.647171i
$10$	1.22821	−	0.336876i	0.388394	−	0.106530i
$11$	1.73440	−	0.772206i	0.522942	−	0.232829i	−0.128250	−	0.991742i	$-0.540936\pi$
$11$	1.73440	−	0.772206i	0.522942	−	0.232829i	0.651192	+	0.758913i	$0.274269\pi$
$12$	2.56641	−	1.35516i	0.740859	−	0.391201i
$13$	5.02577	+	2.23762i	1.39390	+	0.620604i	0.959908	−	0.280314i	$-0.0904385\pi$
$13$	5.02577	+	2.23762i	1.39390	+	0.620604i	0.433990	+	0.900917i	$0.357105\pi$
$14$	0.189169	−	1.79982i	0.0505575	−	0.481023i
$15$	−3.39306	−	1.86738i	−0.876085	−	0.482156i
$16$	−0.225661	−	2.14702i	−0.0564153	−	0.536756i
$17$	0.888735	−	2.73524i	0.215550	−	0.663394i	−0.783564	−	0.621311i	$-0.786600\pi$
$17$	0.888735	−	2.73524i	0.215550	−	0.663394i	0.999114	−	0.0420835i	$-0.0133995\pi$
$18$	1.63976	+	0.480388i	0.386495	+	0.113228i
$19$	−1.39039	+	4.27917i	−0.318976	+	0.981708i	0.655110	+	0.755533i	$0.272622\pi$
$19$	−1.39039	+	4.27917i	−0.318976	+	0.981708i	−0.974087	+	0.226175i	$0.927378\pi$
$20$	−2.89782	+	2.37505i	−0.647972	+	0.531077i
$21$	−4.22603	+	3.52546i	−0.922196	+	0.769319i
$22$	0.723552	−	0.803585i	0.154262	−	0.171325i
$23$	0.335381	−	3.19093i	0.0699317	−	0.665356i	−0.902264	−	0.431185i	$-0.858096\pi$
$23$	0.335381	−	3.19093i	0.0699317	−	0.665356i	0.972195	−	0.234171i	$-0.0752376\pi$
$24$	2.24057	−	2.85091i	0.457355	−	0.581940i
$25$	4.77318	+	1.48888i	0.954636	+	0.297775i
$26$	3.13337			0.614504
$27$	−2.55927	−	4.52218i	−0.492531	−	0.870295i
$28$	1.64524	+	5.06353i	0.310921	+	0.956918i
$29$	−1.75597	−	0.373243i	−0.326076	−	0.0693095i	0.0419654	−	0.999119i	$-0.486638\pi$
$29$	−1.75597	−	0.373243i	−0.326076	−	0.0693095i	−0.368041	+	0.929810i	$0.619971\pi$
$30$	−2.19807	−	0.185594i	−0.401311	−	0.0338846i
$31$	−7.35558	+	1.56348i	−1.32110	+	0.280809i	−0.813893	−	0.581015i	$-0.802656\pi$
$31$	−7.35558	+	1.56348i	−1.32110	+	0.280809i	−0.507208	+	0.861824i	$0.669322\pi$
$32$	−2.70827	−	4.69086i	−0.478759	−	0.829234i
$33$	−3.28100	+	0.219977i	−0.571149	+	0.0382931i
$34$	−0.171223	−	1.62908i	−0.0293646	−	0.279385i
$35$	4.43864	−	5.54787i	0.750268	−	0.937761i
$36$	−4.98182	+	0.671035i	−0.830303	+	0.111839i
$37$	−4.57619	+	3.32479i	−0.752320	+	0.546593i	−0.896545	−	0.442952i	$-0.853931\pi$
$37$	−4.57619	+	3.32479i	−0.752320	+	0.546593i	0.144225	+	0.989545i	$0.453931\pi$
$38$	0.267871	+	2.54863i	0.0434545	+	0.413442i
$39$	−6.83536	−	6.63882i	−1.09453	−	1.06306i
$40$	−2.10055	+	4.18340i	−0.332127	+	0.661453i
$41$	−0.974346	−	0.433807i	−0.152167	−	0.0677492i	0.329240	−	0.944246i	$-0.393207\pi$
$41$	−0.974346	−	0.433807i	−0.152167	−	0.0677492i	−0.481407	+	0.876497i	$0.659874\pi$
$42$	−1.38217	+	2.81337i	−0.213274	+	0.434112i
$43$	−3.64392	+	6.31145i	−0.555692	+	0.962488i	0.442157	+	0.896938i	$0.354213\pi$
$43$	−3.64392	+	6.31145i	−0.555692	+	0.962488i	−0.997849	+	0.0655498i	$0.979120\pi$
$44$	−0.983045	+	3.02550i	−0.148200	+	0.456111i
$45$	4.40181	+	5.06203i	0.656183	+	0.754602i
$46$	−0.564709	−	1.73800i	−0.0832618	−	0.256253i
$47$	7.34730	+	1.56172i	1.07171	+	0.227800i	0.709794	−	0.704409i	$-0.248788\pi$
$47$	7.34730	+	1.56172i	1.07171	+	0.227800i	0.361920	+	0.932209i	$0.382121\pi$
$48$	−0.915004	+	3.62556i	−0.132069	+	0.523304i
$49$	−1.54804	−	2.68128i	−0.221149	−	0.383040i
$50$	2.82849	−	0.331069i	0.400008	−	0.0468202i
$51$	−3.07809	+	3.91658i	−0.431019	+	0.548431i
$52$	−8.42120	+	3.74936i	−1.16781	+	0.519943i
$53$	−0.982710	−	3.02447i	−0.134986	−	0.415443i	0.860602	−	0.509278i	$-0.170087\pi$
$53$	−0.982710	−	3.02447i	−0.134986	−	0.415443i	−0.995588	+	0.0938349i	$0.970087\pi$
$54$	−2.37924	−	1.76009i	−0.323774	−	0.239518i
$55$	4.09406	−	1.12293i	0.552043	−	0.151415i
$56$	4.45097	+	4.94330i	0.594786	+	0.660576i
$57$	4.81554	−	6.12731i	0.637834	−	0.811582i
$58$	−1.00013	+	0.212584i	−0.131323	+	0.0279136i
$59$	−12.0714	−	5.37452i	−1.57156	−	0.699703i	−0.578321	−	0.815809i	$-0.696292\pi$
$59$	−12.0714	−	5.37452i	−1.57156	−	0.699703i	−0.993237	+	0.116106i	$0.962959\pi$
$60$	6.12959	−	2.13139i	0.791326	−	0.275161i
$61$	0.958206	−	0.426621i	0.122686	−	0.0546232i	−0.344476	−	0.938795i	$-0.611943\pi$
$61$	0.958206	−	0.426621i	0.122686	−	0.0546232i	0.467162	+	0.884172i	$0.345277\pi$
$62$	−3.46504	+	2.51750i	−0.440061	+	0.319723i
$63$	8.97598	−	3.20881i	1.13087	−	0.404272i
$64$	0.997243	+	0.724540i	0.124655	+	0.0905675i
$65$	10.3562	+	6.63890i	1.28453	+	0.823454i
$66$	−1.65620	+	0.874537i	−0.203865	+	0.107648i
$67$	12.7060	−	2.70075i	1.55229	−	0.329949i	0.649610	−	0.760268i	$-0.274932\pi$
$67$	12.7060	−	2.70075i	1.55229	−	0.329949i	0.902677	+	0.430319i	$0.141599\pi$
$68$	2.40952	+	4.17341i	0.292197	+	0.506101i
$69$	−2.45048	+	4.98787i	−0.295003	+	0.600468i
$70$	1.02428	−	3.91491i	0.122425	−	0.467922i
$71$	−2.10454	−	6.47710i	−0.249763	−	0.768690i	−0.994817	−	0.101686i	$-0.967576\pi$
$71$	−2.10454	−	6.47710i	−0.249763	−	0.768690i	0.745054	−	0.667004i	$-0.232424\pi$
$72$	−5.34510	+	3.29751i	−0.629926	+	0.388616i
$73$	−0.173732	−	0.126223i	−0.0203337	−	0.0147733i	0.577572	−	0.816340i	$-0.304000\pi$
$73$	−0.173732	−	0.126223i	−0.0203337	−	0.0147733i	−0.597906	+	0.801566i	$0.704000\pi$
$74$	−1.61085	+	2.79007i	−0.187257	+	0.324339i
$75$	−6.87172	−	5.27063i	−0.793477	−	0.608600i
$76$	−3.76959	−	6.52912i	−0.432402	−	0.748941i
$77$	0.630566	−	5.99944i	0.0718597	−	0.683699i
$78$	−5.09451	−	1.87081i	−0.576840	−	0.211828i
$79$	4.79399	+	1.01899i	0.539366	+	0.114646i	0.469537	−	0.882913i	$-0.344421\pi$
$79$	4.79399	+	1.01899i	0.539366	+	0.114646i	0.0698299	+	0.997559i	$0.477754\pi$
$80$	0.224201	−	4.82212i	0.0250665	−	0.539130i
$81$	1.46107	+	8.88061i	0.162341	+	0.986735i
$82$	−0.607465			−0.0670833
$83$	−10.0251	−	11.1340i	−1.10039	−	1.22211i	−0.973133	−	0.230243i	$-0.926048\pi$
$83$	−10.0251	−	11.1340i	−1.10039	−	1.22211i	−0.127261	−	0.991869i	$-0.540619\pi$
$84$	0.348258	−	9.21506i	0.0379980	−	1.00545i
$85$	2.88574	−	5.74714i	0.313002	−	0.623365i
$86$	−0.433882	+	4.12812i	−0.0467867	+	0.445146i
$87$	2.63217	+	1.65527i	0.282198	+	0.177464i
$88$	0.415453	+	3.95277i	0.0442874	+	0.421367i
$89$	−2.15019	−	1.56220i	−0.227920	−	0.165593i	0.467965	−	0.883747i	$-0.344987\pi$
$89$	−2.15019	−	1.56220i	−0.227920	−	0.165593i	−0.695884	+	0.718154i	$0.744987\pi$
$90$	3.46301	+	1.61414i	0.365033	+	0.170145i
$91$	14.1419	−	10.2747i	1.48247	−	1.07708i
$92$	3.59737	+	3.99529i	0.375052	+	0.416537i
$93$	12.8929	+	1.84969i	1.33693	+	0.191804i
$94$	4.18472	−	0.889490i	0.431621	−	0.0917439i
$95$	−4.51461	+	8.99114i	−0.463189	+	0.922472i
$96$	1.60262	+	9.24382i	0.163566	+	0.943444i
$97$	−13.1990	−	2.80553i	−1.34015	−	0.284858i	−0.518612	−	0.855010i	$-0.673551\pi$
$97$	−13.1990	−	2.80553i	−1.34015	−	0.284858i	−0.821539	+	0.570152i	$0.806884\pi$
$98$	−1.42662	−	1.03650i	−0.144110	−	0.104702i
$99$	5.46589	+	1.60130i	0.549342	+	0.160937i
$100$	−7.20565	+	4.27431i	−0.720565	+	0.427431i
$101$	−6.60846	+	11.4462i	−0.657566	+	1.13894i	0.323678	+	0.946167i	$0.395081\pi$
$101$	−6.60846	+	11.4462i	−0.657566	+	1.13894i	−0.981244	+	0.192771i	$0.938253\pi$
$102$	−0.694271	+	2.75094i	−0.0687431	+	0.272384i
$103$	−3.65814	+	4.06278i	−0.360447	+	0.400317i	−0.895906	−	0.444244i	$-0.853472\pi$
$103$	−3.65814	+	4.06278i	−0.360447	+	0.400317i	0.535458	+	0.844562i	$0.320139\pi$
$104$	−7.70639	+	8.55881i	−0.755674	+	0.839261i
$105$	−10.5292	+	6.37008i	−1.02754	+	0.621656i
$106$	−1.21197	−	1.34603i	−0.117717	−	0.130738i
$107$	11.8545			1.14602			0.573009	−	0.819549i	$-0.305776\pi$
$107$	11.8545			1.14602			0.573009	+	0.819549i	$0.305776\pi$
$108$	8.50054	+	1.88342i	0.817964	+	0.181232i
$109$	3.14760	−	2.28686i	0.301485	−	0.219042i	−0.426749	−	0.904370i	$-0.640341\pi$
$109$	3.14760	−	2.28686i	0.301485	−	0.219042i	0.728234	+	0.685328i	$0.240341\pi$
$110$	1.87008	−	1.53271i	0.178305	−	0.146138i
$111$	9.42548	−	2.67349i	0.894627	−	0.253756i
$112$	−6.26655	−	2.79005i	−0.592134	−	0.263635i
$113$	−19.0568	−	8.48462i	−1.79271	−	0.798166i	−0.974888	−	0.222695i	$-0.928515\pi$
$113$	−19.0568	−	8.48462i	−1.79271	−	0.798166i	−0.817822	−	0.575471i	$-0.804819\pi$
$114$	1.08616	−	4.30372i	0.101728	−	0.403080i
$115$	1.81597	−	6.94082i	0.169340	−	0.647235i
$116$	2.43356	−	1.76808i	0.225950	−	0.164162i
$117$	7.14976	+	14.8751i	0.660996	+	1.37520i
$118$	−7.52601			−0.692826
$119$	−6.11473	−	6.79109i	−0.560536	−	0.622539i
$120$	5.91301	−	5.54758i	0.539782	−	0.506423i
$121$	−4.94858	+	5.49596i	−0.449871	+	0.499633i
$122$	0.399741	−	0.443957i	0.0361908	−	0.0401940i
$123$	1.32517	+	1.28707i	0.119487	+	0.116051i
$124$	6.30019	−	10.9122i	0.565774	−	0.979949i
$125$	10.0500	+	4.89869i	0.898901	+	0.438152i
$126$	3.92701	−	3.74898i	0.349846	−	0.333986i
$127$	−8.35355	−	6.06921i	−0.741258	−	0.538555i	0.151847	−	0.988404i	$-0.451478\pi$
$127$	−8.35355	−	6.06921i	−0.741258	−	0.538555i	−0.893105	+	0.449849i	$0.851478\pi$
$128$	11.2831	+	2.39829i	0.997292	+	0.211981i
$129$	9.69293	−	8.08608i	0.853415	−	0.711940i
$130$	6.92651	+	1.05521i	0.607495	+	0.0925476i
$131$	3.39927	−	0.722537i	0.296996	−	0.0631284i	−0.0570039	−	0.998374i	$-0.518155\pi$
$131$	3.39927	−	0.722537i	0.296996	−	0.0631284i	0.354000	+	0.935246i	$0.384821\pi$
$132$	3.40473	−	4.33219i	0.296344	−	0.377069i
$133$	9.56622	+	10.6244i	0.829496	+	0.921249i
$134$	5.98551	−	4.34873i	0.517069	−	0.375673i
$135$	−4.13451	−	10.8584i	−0.355842	−	0.934546i
$136$	4.87096	+	3.53896i	0.417682	+	0.303463i
$137$	−0.305626	−	2.90784i	−0.0261114	−	0.248433i	−0.999790	−	0.0205067i	$-0.993472\pi$
$137$	−0.305626	−	2.90784i	−0.0261114	−	0.248433i	0.973678	−	0.227927i	$-0.0731946\pi$
$138$	−0.119535	+	3.16295i	−0.0101755	+	0.269249i
$139$	−0.474674	+	4.51623i	−0.0402614	+	0.383061i	0.955774	+	0.294102i	$0.0950206\pi$
$139$	−0.474674	+	4.51623i	−0.0402614	+	0.383061i	−0.996035	+	0.0889589i	$0.971646\pi$
$140$	1.93170	+	11.7473i	0.163258	+	0.992830i
$141$	−11.0135	−	6.92597i	−0.927501	−	0.583272i
$142$	−2.59552	−	2.88261i	−0.217811	−	0.241904i
$143$	10.4446			0.873423
$144$	3.65237	−	5.34844i	0.304364	−	0.445703i
$145$	−3.75599	−	1.41643i	−0.311918	−	0.117628i
$146$	−0.119637	−	0.0254296i	−0.00990120	−	0.00210457i
$147$	0.916052	+	5.28375i	0.0755547	+	0.435796i
$148$	0.990722	−	9.42609i	0.0814368	−	0.774820i
$149$	10.6857	+	18.5083i	0.875411	+	1.51626i	0.856325	+	0.516438i	$0.172742\pi$
$149$	10.6857	+	18.5083i	0.875411	+	1.51626i	0.0190860	+	0.999818i	$0.493924\pi$
$150$	−4.79647	−	1.15050i	−0.391630	−	0.0939377i
$151$	−10.4131	+	18.0359i	−0.847402	+	1.46774i	0.0361159	+	0.999348i	$0.488501\pi$
$151$	−10.4131	+	18.0359i	−0.847402	+	1.46774i	−0.883518	+	0.468397i	$0.844832\pi$
$152$	−7.62040	−	5.53655i	−0.618096	−	0.449073i
$153$	7.34308	−	4.53011i	0.593653	−	0.366238i
$154$	−1.06174	−	3.26769i	−0.0855573	−	0.263318i
$155$	−16.7865	+	0.979071i	−1.34832	+	0.0786409i
$156$	15.9305	−	1.06807i	1.27546	−	0.0855144i
$157$	6.10055	+	10.5665i	0.486877	+	0.843296i	0.999886	−	0.0150873i	$-0.00480263\pi$
$157$	6.10055	+	10.5665i	0.486877	+	0.843296i	−0.513009	+	0.858383i	$0.671469\pi$
$158$	2.73046	−	0.580378i	0.217224	−	0.0461724i
$159$	−0.208016	+	5.50419i	−0.0164967	+	0.436511i
$160$	−4.40709	−	11.2815i	−0.348411	−	0.891880i
$161$	−8.24779	−	5.99237i	−0.650017	−	0.472265i
$162$	2.81751	+	4.28227i	0.221364	+	0.336447i
$163$	−1.97156	+	1.43242i	−0.154424	+	0.112196i	−0.662314	−	0.749226i	$-0.730426\pi$
$163$	−1.97156	+	1.43242i	−0.154424	+	0.112196i	0.507890	+	0.861422i	$0.330426\pi$
$164$	1.63262	−	0.726887i	0.127486	−	0.0567604i
$165$	−7.32694	−	0.618650i	−0.570402	−	0.0481618i
$166$	−7.79553	−	3.47079i	−0.605050	−	0.269386i
$167$	4.18740	−	0.890059i	0.324031	−	0.0688748i	−0.0430245	−	0.999074i	$-0.513699\pi$
$167$	4.18740	−	0.890059i	0.324031	−	0.0688748i	0.367055	+	0.930199i	$0.380366\pi$
$168$	−4.28533	−	10.6948i	−0.330620	−	0.825119i
$169$	11.5528	+	12.8306i	0.888674	+	0.986973i
$170$	0.170116	−	3.65885i	0.0130473	−	0.280621i
$171$	−11.4879	+	7.08716i	−0.878503	+	0.541969i
$172$	−3.77357	−	11.6138i	−0.287732	−	0.885547i
$173$	−3.56921	+	1.58911i	−0.271362	+	0.120818i	−0.537907	−	0.843004i	$-0.680785\pi$
$173$	−3.56921	+	1.58911i	−0.271362	+	0.120818i	0.266545	+	0.963823i	$0.414118\pi$
$174$	1.75303	+	0.251500i	0.132897	+	0.0190662i
$175$	11.6802	−	10.7691i	0.882942	−	0.814070i
$176$	−2.04933	−	3.54955i	−0.154474	−	0.267557i
$177$	16.4178	+	15.9457i	1.23404	+	1.19855i
$178$	−1.48068	−	0.314729i	−0.110982	−	0.0235899i
$179$	6.86538	+	21.1295i	0.513142	+	1.57929i	0.786637	+	0.617416i	$0.211820\pi$
$179$	6.86538	+	21.1295i	0.513142	+	1.57929i	−0.273495	+	0.961874i	$0.588180\pi$
$180$	−11.2386	−	0.194330i	−0.837676	−	0.0144845i
$181$	7.16149	−	22.0408i	0.532309	−	1.63828i	−0.217083	−	0.976153i	$-0.569654\pi$
$181$	7.16149	−	22.0408i	0.532309	−	1.63828i	0.749393	−	0.662126i	$-0.230346\pi$
$182$	4.97803	−	8.62221i	0.368996	−	0.639121i
$183$	−1.81266	+	0.121531i	−0.133995	+	0.00898382i
$184$	6.13622	+	2.73202i	0.452368	+	0.201407i
$185$	−11.2356	+	5.80857i	−0.826059	+	0.427055i
$186$	7.13688	−	2.02434i	0.523302	−	0.148432i
$187$	−0.570748	−	5.43030i	−0.0417372	−	0.397103i
$188$	−10.1824	+	7.39798i	−0.742631	+	0.539553i
$189$	−16.5098	−	0.142037i	−1.20091	−	0.0103317i
$190$	−0.266138	+	5.72411i	−0.0193077	+	0.415270i
$191$	0.791639	+	7.53194i	0.0572810	+	0.544992i	0.985103	+	0.171968i	$0.0550125\pi$
$191$	0.791639	+	7.53194i	0.0572810	+	0.544992i	−0.927822	+	0.373024i	$0.878321\pi$
$192$	−1.18881	−	1.77344i	−0.0857952	−	0.127987i
$193$	−5.75178	−	9.96237i	−0.414022	−	0.717107i	0.581303	−	0.813687i	$-0.302543\pi$
$193$	−5.75178	−	9.96237i	−0.414022	−	0.717107i	−0.995325	+	0.0965798i	$0.969210\pi$
$194$	−7.51759	+	1.59791i	−0.539731	+	0.114723i
$195$	−12.8743	−	16.9774i	−0.921946	−	1.21578i
$196$	5.07443	+	1.07860i	0.362459	+	0.0770431i
$197$	−1.04613	−	3.21965i	−0.0745335	−	0.229390i	0.906848	−	0.421457i	$-0.138481\pi$
$197$	−1.04613	−	3.21965i	−0.0745335	−	0.229390i	−0.981382	+	0.192066i	$0.938481\pi$
$198$	3.21496	−	0.433045i	0.228477	−	0.0307752i
$199$	−16.4429			−1.16560			−0.582802	−	0.812614i	$-0.698044\pi$
$199$	−16.4429			−1.16560			−0.582802	+	0.812614i	$0.698044\pi$
$200$	−6.05223	+	8.54027i	−0.427957	+	0.603888i
$201$	−22.2711	−	3.19515i	−1.57088	−	0.225369i
$202$	−0.786871	+	7.48658i	−0.0553640	+	0.526754i
$203$	−3.81681	+	4.23899i	−0.267887	+	0.297519i
$204$	−1.42583	−	8.22414i	−0.0998283	−	0.575805i
$205$	−2.00776	−	1.28708i	−0.140228	−	0.0898936i
$206$	−0.962211	+	2.96138i	−0.0670404	+	0.206329i
$207$	6.96226	−	6.64664i	0.483911	−	0.461973i
$208$	3.67010	−	11.2954i	0.254475	−	0.783195i
$209$	0.892910	+	8.49547i	0.0617638	+	0.587644i
$210$	−4.00282	+	5.75366i	−0.276221	+	0.397040i
$211$	0.988953	−	9.40926i	0.0680823	−	0.647760i	−0.906265	−	0.422710i	$-0.861079\pi$
$211$	0.988953	−	9.40926i	0.0680823	−	0.647760i	0.974347	−	0.225050i	$-0.0722545\pi$
$212$	4.86793	+	2.16734i	0.334331	+	0.148854i
$213$	−0.445479	+	11.7876i	−0.0305237	+	0.807672i
$214$	6.16811	−	2.74622i	0.421644	−	0.187728i
$215$	−10.1806	+	12.7247i	−0.694310	+	0.867819i
$216$	10.6594	−	2.17004i	0.725277	−	0.147653i
$217$	−7.38365	+	22.7245i	−0.501235	+	1.54264i
$218$	1.10797	−	1.91907i	0.0750415	−	0.129976i
$219$	0.207105	+	0.308954i	0.0139949	+	0.0208772i
$220$	−3.19196	+	6.35701i	−0.215202	+	0.428589i
$221$	10.5870	−	11.7581i	0.712160	−	0.790933i
$222$	4.28491	−	3.57457i	0.287584	−	0.239910i
$223$	1.13308	−	0.504480i	0.0758767	−	0.0337825i	−0.368447	−	0.929649i	$-0.620111\pi$
$223$	1.13308	−	0.504480i	0.0758767	−	0.0337825i	0.444324	+	0.895866i	$0.353444\pi$
$224$	−17.2107			−1.14994
$225$	8.02577	+	12.6723i	0.535051	+	0.844820i
$226$	−11.8811			−0.790321
$227$	−22.1073	+	9.84279i	−1.46731	+	0.653289i	−0.976015	−	0.217704i	$-0.930143\pi$
$227$	−22.1073	+	9.84279i	−1.46731	+	0.653289i	−0.491296	+	0.870993i	$0.663477\pi$
$228$	2.23065	+	12.8663i	0.147729	+	0.852092i
$229$	2.50498	−	2.78206i	0.165534	−	0.183844i	−0.654671	−	0.755914i	$-0.727193\pi$
$229$	2.50498	−	2.78206i	0.165534	−	0.183844i	0.820205	+	0.572070i	$0.193860\pi$
$230$	−0.663031	−	4.03212i	−0.0437190	−	0.265870i
$231$	−4.60726	+	9.37794i	−0.303136	+	0.617023i
$232$	1.87910	−	3.25470i	0.123369	−	0.213681i
$233$	2.75742	−	8.48645i	0.180644	−	0.555966i	−0.819202	−	0.573505i	$-0.805583\pi$
$233$	2.75742	−	8.48645i	0.180644	−	0.555966i	0.999846	+	0.0175392i	$0.00558319\pi$
$234$	7.16613	+	6.08347i	0.468464	+	0.397689i
$235$	15.7157	+	5.92658i	1.02518	+	0.386608i
$236$	20.2268	−	9.00556i	1.31665	−	0.586212i
$237$	−7.18610	−	4.51908i	−0.466788	−	0.293546i
$238$	−4.75483	−	2.11699i	−0.308210	−	0.137224i
$239$	−0.680615	+	6.47562i	−0.0440253	+	0.418873i	0.950207	+	0.311621i	$0.100872\pi$
$239$	−0.680615	+	6.47562i	−0.0440253	+	0.418873i	−0.994232	+	0.107252i	$0.965795\pi$
$240$	−3.24363	+	7.70638i	−0.209375	+	0.497445i
$241$	−2.63541	−	25.0743i	−0.169762	−	1.61518i	−0.665290	−	0.746585i	$-0.731692\pi$
$241$	−2.63541	−	25.0743i	−0.169762	−	1.61518i	0.495528	−	0.868592i	$-0.334975\pi$
$242$	−1.30164	+	4.00604i	−0.0836726	+	0.257518i
$243$	2.92674	−	15.3112i	0.187750	−	0.982217i
$244$	−0.543103	+	1.67150i	−0.0347686	+	0.107007i
$245$	−2.51908	−	6.44847i	−0.160938	−	0.411978i
$246$	0.987672	+	0.362694i	0.0629717	+	0.0231245i
$247$	−16.5629	+	18.3950i	−1.05387	+	1.17044i
$248$	1.64556	−	15.6565i	0.104493	−	0.994187i
$249$	9.65200	+	24.0882i	0.611671	+	1.52653i
$250$	6.36404	+	0.220683i	0.402497	+	0.0139572i
$251$	28.2055			1.78032			0.890159	−	0.455650i	$-0.150593\pi$
$251$	28.2055			1.78032			0.890159	+	0.455650i	$0.150593\pi$
$252$	−6.06818	+	14.7747i	−0.382260	+	0.930721i
$253$	−1.88237	−	5.79335i	−0.118344	−	0.364225i
$254$	−5.75250	−	1.22273i	−0.360944	−	0.0767210i
$255$	−8.12328	+	7.62125i	−0.508700	+	0.477261i
$256$	4.01493	−	0.853400i	0.250933	−	0.0533375i
$257$	−13.6020	−	23.5593i	−0.848468	−	1.46959i	−0.882575	−	0.470172i	$-0.844192\pi$
$257$	−13.6020	−	23.5593i	−0.848468	−	1.46959i	0.0341065	−	0.999418i	$-0.489141\pi$
$258$	3.17018	−	6.45281i	0.197367	−	0.401734i
$259$	1.87870	+	17.8746i	0.116737	+	1.11067i
$260$	−19.8782	+	5.45224i	−1.23280	+	0.338134i
$261$	−3.29131	−	4.26286i	−0.203727	−	0.263864i
$262$	1.60132	−	1.16343i	0.0989298	−	0.0718767i
$263$	−1.60354	−	15.2566i	−0.0988784	−	0.940765i	−0.925689	−	0.378285i	$-0.876514\pi$
$263$	−1.60354	−	15.2566i	−0.0988784	−	0.940765i	0.826811	−	0.562480i	$-0.190153\pi$
$264$	1.68456	−	6.67482i	0.103678	−	0.410807i
$265$	−1.15381	−	7.01672i	−0.0708780	−	0.431034i
$266$	7.43872	+	3.31193i	0.456097	+	0.203068i
$267$	2.56324	+	3.82377i	0.156868	+	0.234011i
$268$	−10.8829	+	18.8498i	−0.664781	+	1.15143i
$269$	5.41294	−	16.6593i	0.330033	−	1.01574i	−0.639084	−	0.769137i	$-0.720687\pi$
$269$	5.41294	−	16.6593i	0.330033	−	1.01574i	0.969117	−	0.246600i	$-0.0793134\pi$
$270$	−4.66673	−	4.69204i	−0.284008	−	0.285548i
$271$	−2.30906	−	7.10654i	−0.140265	−	0.431692i	0.856107	−	0.516799i	$-0.172877\pi$
$271$	−2.30906	−	7.10654i	−0.140265	−	0.431692i	−0.996372	+	0.0851075i	$0.972877\pi$
$272$	−6.07319	−	1.29090i	−0.368241	−	0.0782720i
$273$	−29.1277	+	8.26192i	−1.76289	+	0.500034i
$274$	−0.832653	−	1.44220i	−0.0503024	−	0.0871264i
$275$	9.42834	−	1.10357i	0.568550	−	0.0665477i
$276$	−3.46350	−	8.64375i	−0.208478	−	0.520293i
$277$	5.12669	−	2.28255i	0.308033	−	0.137145i	−0.246898	−	0.969041i	$-0.579411\pi$
$277$	5.12669	−	2.28255i	0.308033	−	0.137145i	0.554931	+	0.831896i	$0.312745\pi$
$278$	0.799249	+	2.45984i	0.0479358	+	0.147531i
$279$	−19.8580	−	10.7052i	−1.18887	−	0.640904i
$280$	8.17442	+	12.4264i	0.488515	+	0.742620i
$281$	6.80056	+	7.55279i	0.405688	+	0.450562i	0.911019	−	0.412363i	$-0.135297\pi$
$281$	6.80056	+	7.55279i	0.405688	+	0.450562i	−0.505332	+	0.862925i	$0.668630\pi$
$282$	−7.33498	−	1.05232i	−0.436792	−	0.0626649i
$283$	−11.5913	+	2.46381i	−0.689033	+	0.146459i	−0.539105	−	0.842238i	$-0.681237\pi$
$283$	−11.5913	+	2.46381i	−0.689033	+	0.146459i	−0.149928	+	0.988697i	$0.547904\pi$
$284$	10.4250	+	4.64150i	0.618609	+	0.275422i
$285$	12.7085	−	11.9231i	0.752787	−	0.706264i
$286$	5.43452	−	2.41961i	0.321350	−	0.143074i
$287$	−2.74168	+	1.99195i	−0.161836	+	0.117581i
$288$	2.91345	−	15.9863i	0.171677	−	0.942002i
$289$	7.06157	+	5.13053i	0.415387	+	0.301796i
$290$	−2.28244	+	0.133123i	−0.134029	+	0.00781726i
$291$	19.7850	+	12.4421i	1.15982	+	0.729367i
$292$	0.351963	−	0.0748120i	0.0205971	−	0.00437804i
$293$	−8.45858	−	14.6507i	−0.494156	−	0.855903i	0.505822	−	0.862638i	$-0.331189\pi$
$293$	−8.45858	−	14.6507i	−0.494156	−	0.855903i	−0.999977	+	0.00673521i	$0.997856\pi$
$294$	1.70067	+	2.53702i	0.0991853	+	0.147962i
$295$	−24.8746	−	15.9459i	−1.44825	−	0.928407i
$296$	−3.65928	−	11.2621i	−0.212691	−	0.654597i
$297$	−7.93086	−	5.86701i	−0.460195	−	0.340438i
$298$	9.84762	+	7.15472i	0.570457	+	0.414462i
$299$	8.82564	−	15.2865i	0.510400	−	0.884039i
$300$	14.2676	−	2.64735i	0.823741	−	0.152845i
$301$	11.5783	+	20.0542i	0.667363	+	1.15591i
$302$	−1.23989	+	11.7967i	−0.0713474	+	0.678825i
$303$	17.5787	−	14.6646i	1.00987	−	0.842458i
$304$	9.50123	+	2.01955i	0.544933	+	0.115829i
$305$	2.26185	−	0.620383i	0.129513	−	0.0355231i
$306$	2.77129	−	4.05820i	0.158424	−	0.231992i
$307$	−1.52786			−0.0871995			−0.0435997	−	0.999049i	$-0.513883\pi$
$307$	−1.52786			−0.0871995			−0.0435997	+	0.999049i	$0.513883\pi$
$308$	6.76360	+	7.51174i	0.385392	+	0.428021i
$309$	8.37346	−	4.42149i	0.476349	−	0.251530i
$310$	−8.50750	+	4.39820i	−0.483194	+	0.249801i
$311$	0.956654	−	9.10196i	0.0542469	−	0.516125i	−0.933334	−	0.359010i	$-0.883114\pi$
$311$	0.956654	−	9.10196i	0.0542469	−	0.516125i	0.987580	−	0.157114i	$-0.0502191\pi$
$312$	17.6399	−	9.31450i	0.998661	−	0.527330i
$313$	0.0373152	+	0.355030i	0.00210918	+	0.0200675i	0.995526	−	0.0944894i	$-0.0301218\pi$
$313$	0.0373152	+	0.355030i	0.00210918	+	0.0200675i	−0.993417	+	0.114557i	$0.963455\pi$
$314$	5.62206	+	4.08467i	0.317271	+	0.230511i
$315$	20.9226	−	4.07049i	1.17885	−	0.229346i
$316$	−6.64388	+	4.82706i	−0.373747	+	0.271543i
$317$	12.0031	+	13.3308i	0.674164	+	0.748735i	0.979042	−	0.203657i	$-0.0652826\pi$
$317$	12.0031	+	13.3308i	0.674164	+	0.748735i	−0.304879	+	0.952391i	$0.598616\pi$
$318$	1.16687	+	2.91212i	0.0654348	+	0.163304i
$319$	−3.33378	+	0.708617i	−0.186656	+	0.0396749i
$320$	1.96047	+	1.93748i	0.109594	+	0.108308i
$321$	−19.2741	−	7.07787i	−1.07578	−	0.395048i
$322$	−5.67967	−	1.20725i	−0.316516	−	0.0672775i
$323$	10.4689	+	7.60609i	0.582504	+	0.423214i
$324$	−12.6964	−	8.13757i	−0.705357	−	0.452087i
$325$	20.6574	+	18.1633i	1.14587	+	1.00752i
$326$	−0.694002	+	1.20205i	−0.0384372	+	0.0665752i
$327$	−6.48304	+	1.83888i	−0.358513	+	0.101690i
$328$	1.49404	−	1.65929i	0.0824943	−	0.0916192i
$329$	15.9702	−	17.7367i	0.880467	−	0.977857i
$330$	−3.95566	+	1.37547i	−0.217752	+	0.0757171i
$331$	8.74392	+	9.71111i	0.480609	+	0.533771i	0.933873	−	0.357606i	$-0.116407\pi$
$331$	8.74392	+	9.71111i	0.480609	+	0.533771i	−0.453263	+	0.891377i	$0.649740\pi$
$332$	25.1043			1.37778
$333$	−16.9210	−	1.28080i	−0.927267	−	0.0701872i
$334$	1.97259	−	1.43317i	0.107935	−	0.0784195i
$335$	28.9970	−	1.69125i	1.58427	−	0.0924026i
$336$	8.52290	+	8.27783i	0.464962	+	0.451593i
$337$	21.3210	+	9.49273i	1.16143	+	0.517102i	0.894699	−	0.446669i	$-0.147390\pi$
$337$	21.3210	+	9.49273i	1.16143	+	0.517102i	0.266731	+	0.963771i	$0.414057\pi$
$338$	8.98347	+	3.99970i	0.488636	+	0.217555i
$339$	25.9184	+	25.1731i	1.40769	+	1.36722i
$340$	3.92095	+	10.0370i	0.212643	+	0.544335i
$341$	−11.5502	+	8.39172i	−0.625479	+	0.454437i
$342$	−4.33556	+	6.34887i	−0.234440	+	0.343308i
$343$	12.4044			0.669777
$344$	−10.2089	−	11.3381i	−0.550424	−	0.611308i
$345$	−7.09666	+	10.2008i	−0.382071	+	0.549190i
$346$	−1.48899	+	1.65369i	−0.0800485	+	0.0889029i
$347$	5.32071	−	5.90924i	0.285630	−	0.317225i	−0.583206	−	0.812325i	$-0.698202\pi$
$347$	5.32071	−	5.90924i	0.285630	−	0.317225i	0.868836	+	0.495100i	$0.164869\pi$
$348$	−5.01235	+	1.42173i	−0.268690	+	0.0762125i
$349$	3.94486	−	6.83270i	0.211163	−	0.365746i	−0.740915	−	0.671598i	$-0.765608\pi$
$349$	3.94486	−	6.83270i	0.211163	−	0.365746i	0.952079	+	0.305852i	$0.0989414\pi$
$350$	3.58265	−	8.30922i	0.191501	−	0.444147i
$351$	−2.74337	−	28.4541i	−0.146430	−	1.51877i
$352$	−8.31954	−	6.04450i	−0.443433	−	0.322173i
$353$	−3.90052	−	0.829082i	−0.207604	−	0.0441276i	0.102936	−	0.994688i	$-0.467176\pi$
$353$	−3.90052	−	0.829082i	−0.207604	−	0.0441276i	−0.310540	+	0.950560i	$0.600510\pi$
$354$	12.2365	+	4.49349i	0.650361	+	0.238826i
$355$	−2.47096	−	15.0268i	−0.131145	−	0.797538i
$356$	4.35607	−	0.925911i	0.230871	−	0.0490732i
$357$	5.88718	+	14.6924i	0.311582	+	0.777606i
$358$	8.46704	+	9.40360i	0.447497	+	0.496996i
$359$	−4.35344	+	3.16296i	−0.229766	+	0.166935i	−0.696712	−	0.717351i	$-0.745354\pi$
$359$	−4.35344	+	3.16296i	−0.229766	+	0.166935i	0.466946	+	0.884286i	$0.345354\pi$
$360$	−12.9262	+	5.48933i	−0.681268	+	0.289313i
$361$	−1.00678	−	0.731470i	−0.0529885	−	0.0384984i
$362$	−1.37973	−	13.1273i	−0.0725170	−	0.689953i
$363$	11.3273	−	5.98122i	0.594528	−	0.313933i
$364$	−3.06164	+	29.1296i	−0.160474	+	1.52681i
$365$	−0.341537	−	0.337531i	−0.0178769	−	0.0176672i
$366$	−0.915004	+	0.483156i	−0.0478280	+	0.0252550i
$367$	7.71153	+	8.56452i	0.402539	+	0.447064i	0.909999	−	0.414611i	$-0.136082\pi$
$367$	7.71153	+	8.56452i	0.402539	+	0.447064i	−0.507460	+	0.861675i	$0.669416\pi$
$368$	−6.92669			−0.361079
$369$	−1.38612	−	2.88383i	−0.0721587	−	0.150126i
$370$	−4.50048	+	5.62516i	−0.233969	+	0.292438i
$371$	−9.88380	−	2.10087i	−0.513141	−	0.109072i
$372$	−16.7587	+	13.9805i	−0.868898	+	0.724856i
$373$	1.50209	−	14.2914i	0.0777751	−	0.739981i	−0.884249	−	0.467016i	$-0.845329\pi$
$373$	1.50209	−	14.2914i	0.0777751	−	0.739981i	0.962024	−	0.272965i	$-0.0880043\pi$
$374$	−1.55496	−	2.69327i	−0.0804049	−	0.139265i
$375$	−13.4154	−	13.9652i	−0.692769	−	0.721160i
$376$	−7.86250	+	13.6183i	−0.405478	+	0.702308i
$377$	−7.98994	−	5.80503i	−0.411503	−	0.298974i
$378$	−8.62326	+	3.75077i	−0.443533	+	0.192919i
$379$	2.36999	+	7.29407i	0.121738	+	0.374671i	0.993293	−	0.115627i	$-0.0368878\pi$
$379$	2.36999	+	7.29407i	0.121738	+	0.374671i	−0.871555	+	0.490298i	$0.836888\pi$
$380$	−6.13414	−	15.7025i	−0.314675	−	0.805521i
$381$	9.95827	+	14.8555i	0.510177	+	0.761068i
$382$	2.15676	+	3.73561i	0.110349	+	0.191131i
$383$	15.0744	−	3.20417i	0.770268	−	0.163726i	0.194017	−	0.980998i	$-0.437848\pi$
$383$	15.0744	−	3.20417i	0.770268	−	0.163726i	0.576251	+	0.817273i	$0.304515\pi$
$384$	−16.9131	−	10.6360i	−0.863094	−	0.542768i
$385$	3.41430	−	13.0498i	0.174009	−	0.665079i
$386$	−5.30064	−	3.85114i	−0.269796	−	0.196018i
$387$	−20.5875	+	7.35981i	−1.04652	+	0.374120i
$388$	18.2921	−	13.2900i	0.928642	−	0.674698i
$389$	6.57053	−	2.92539i	0.333139	−	0.148323i	−0.233349	−	0.972393i	$-0.574968\pi$
$389$	6.57053	−	2.92539i	0.333139	−	0.148323i	0.566488	+	0.824070i	$0.308302\pi$
$390$	−10.6317	−	5.85120i	−0.538358	−	0.296287i
$391$	−8.42992	−	3.75324i	−0.426319	−	0.189810i
$392$	6.33992	−	1.34759i	0.320214	−	0.0680636i
$393$	−5.95824	−	0.854807i	−0.300553	−	0.0431193i
$394$	−1.29018	−	1.43289i	−0.0649985	−	0.0721882i
$395$	10.2543	+	3.86700i	0.515948	+	0.194570i
$396$	−8.12230	+	5.01084i	−0.408161	+	0.251804i
$397$	3.92783	+	12.0886i	0.197132	+	0.606710i	0.999945	+	0.0104793i	$0.00333573\pi$
$397$	3.92783	+	12.0886i	0.197132	+	0.606710i	−0.802813	+	0.596231i	$0.796664\pi$
$398$	−8.55552	+	3.80916i	−0.428850	+	0.190936i
$399$	−9.21022	−	22.9857i	−0.461088	−	1.15072i
$400$	2.11953	−	10.5841i	0.105976	−	0.529205i
$401$	13.8845	+	24.0487i	0.693361	+	1.20094i	0.970730	+	0.240173i	$0.0772040\pi$
$401$	13.8845	+	24.0487i	0.693361	+	1.20094i	−0.277370	+	0.960763i	$0.589463\pi$
$402$	−12.3282	+	3.49684i	−0.614877	+	0.174406i
$403$	−40.4659	−	8.60130i	−2.01575	−	0.428461i
$404$	−6.84358	−	21.0624i	−0.340481	−	1.04789i
$405$	0.239109	+	20.1232i	0.0118814	+	0.999929i
$406$	−1.00395	+	3.08983i	−0.0498250	+	0.153346i
$407$	−5.36953	+	9.30029i	−0.266158	+	0.460998i
$408$	−5.80667	−	8.66222i	−0.287473	−	0.428844i
$409$	−5.32589	−	2.37124i	−0.263348	−	0.117250i	0.270815	−	0.962631i	$-0.412707\pi$
$409$	−5.32589	−	2.37124i	−0.263348	−	0.117250i	−0.534164	+	0.845381i	$0.679373\pi$
$410$	−1.34284	−	0.204572i	−0.0663182	−	0.0101031i
$411$	−1.23924	+	4.91030i	−0.0611273	+	0.242207i
$412$	−0.957536	−	9.11034i	−0.0471744	−	0.448834i
$413$	−33.9672	+	24.6786i	−1.67142	+	1.21436i
$414$	2.08283	−	5.07125i	0.102365	−	0.249238i
$415$	−18.4115	−	27.9884i	−0.903787	−	1.37390i
$416$	−3.11479	−	29.6353i	−0.152715	−	1.45299i
$417$	3.46823	−	7.05948i	0.169840	−	0.345704i
$418$	2.43266	+	4.21349i	0.118985	+	0.206089i
$419$	18.2995	−	3.88968i	0.893988	−	0.190023i	0.262062	−	0.965051i	$-0.415598\pi$
$419$	18.2995	−	3.88968i	0.893988	−	0.190023i	0.631927	+	0.775028i	$0.282264\pi$
$420$	3.87314	−	20.2532i	0.188990	−	0.988254i
$421$	36.0784	+	7.66869i	1.75835	+	0.373749i	0.970308	−	0.241871i	$-0.0777612\pi$
$421$	36.0784	+	7.66869i	1.75835	+	0.373749i	0.788043	+	0.615620i	$0.211095\pi$
$422$	−1.66518	−	5.12491i	−0.0810598	−	0.249477i
$423$	13.7715	+	17.8366i	0.669591	+	0.867244i
$424$	6.65749			0.323316
$425$	8.31453	−	11.7326i	0.403314	−	0.569115i
$426$	2.49893	+	6.23649i	0.121073	+	0.302159i
$427$	0.348369	−	3.31451i	0.0168588	−	0.160400i
$428$	−13.2912	+	14.7614i	−0.642456	+	0.713520i
$429$	−16.9818	−	6.23608i	−0.819889	−	0.301081i
$430$	−2.34932	+	8.97934i	−0.113294	+	0.433022i
$431$	−11.1912	+	34.4429i	−0.539060	+	1.65906i	0.195648	+	0.980674i	$0.437319\pi$
$431$	−11.1912	+	34.4429i	−0.539060	+	1.65906i	−0.734709	+	0.678383i	$0.762681\pi$
$432$	−9.13170	+	6.51529i	−0.439349	+	0.313467i
$433$	−11.0444	+	33.9911i	−0.530758	+	1.63351i	0.221881	+	0.975074i	$0.428780\pi$
$433$	−11.0444	+	33.9911i	−0.530758	+	1.63351i	−0.752640	+	0.658433i	$0.771220\pi$
$434$	1.42253	+	13.5345i	0.0682837	+	0.649676i
$435$	5.26113	+	4.54551i	0.252252	+	0.217940i
$436$	−0.681439	+	6.48346i	−0.0326350	+	0.310501i
$437$	13.1882	+	5.87178i	0.630879	+	0.280885i
$438$	0.179333	+	0.112776i	0.00856887	+	0.00538865i
$439$	−13.7122	+	6.10506i	−0.654447	+	0.291379i	−0.706973	−	0.707241i	$-0.749940\pi$
$439$	−13.7122	+	6.10506i	−0.654447	+	0.291379i	0.0525255	+	0.998620i	$0.483273\pi$
$440$	−0.412765	+	8.87776i	−0.0196778	+	0.423230i
$441$	1.66532	−	9.13773i	0.0793010	−	0.435130i
$442$	2.78473	−	8.57053i	0.132456	−	0.407659i
$443$	2.61065	−	4.52178i	0.124036	−	0.214836i	−0.797320	−	0.603557i	$-0.793750\pi$
$443$	2.61065	−	4.52178i	0.124036	−	0.214836i	0.921356	+	0.388721i	$0.127083\pi$
$444$	−7.23875	+	14.7343i	−0.343536	+	0.699257i
$445$	−4.22704	−	4.17746i	−0.200381	−	0.198031i
$446$	0.472694	−	0.524980i	0.0223827	−	0.0248585i
$447$	−6.32329	−	36.4724i	−0.299081	−	1.72509i
$448$	3.57808	−	1.59306i	0.169048	−	0.0752652i
$449$	−7.57157			−0.357324			−0.178662	−	0.983910i	$-0.557177\pi$
$449$	−7.57157			−0.357324			−0.178662	+	0.983910i	$0.557177\pi$
$450$	7.11162	+	4.73437i	0.335245	+	0.223180i
$451$	−2.02490			−0.0953486
$452$	31.9316	−	14.2169i	1.50193	−	0.668704i
$453$	27.6990	−	23.1072i	1.30141	−	1.08567i
$454$	−9.22262	+	10.2428i	−0.432839	+	0.480717i
$455$	34.7216	−	17.9503i	1.62778	−	0.841525i
$456$	9.08428	+	13.5517i	0.425410	+	0.634615i
$457$	17.7105	−	30.6754i	0.828461	−	1.43494i	−0.0707840	−	0.997492i	$-0.522550\pi$
$457$	17.7105	−	30.6754i	0.828461	−	1.43494i	0.899245	−	0.437445i	$-0.144117\pi$
$458$	0.658892	−	2.02786i	0.0307880	−	0.0947557i
$459$	−14.6438	+	2.98120i	−0.683514	+	0.139150i
$460$	6.60675	+	10.0433i	0.308041	+	0.468271i
$461$	−13.0894	+	5.82776i	−0.609633	+	0.271426i	−0.688244	−	0.725479i	$-0.741618\pi$
$461$	−13.0894	+	5.82776i	−0.609633	+	0.271426i	0.0786113	+	0.996905i	$0.474951\pi$
$462$	−0.224744	+	5.94683i	−0.0104560	+	0.276672i
$463$	−11.2969	−	5.02972i	−0.525013	−	0.233751i	0.127076	−	0.991893i	$-0.459441\pi$
$463$	−11.2969	−	5.02972i	−0.525013	−	0.233751i	−0.652089	+	0.758142i	$0.726107\pi$
$464$	−0.405107	+	3.85434i	−0.0188066	+	0.178933i
$465$	27.8776	+	8.43070i	1.29279	+	0.390965i
$466$	−0.531243	−	5.05444i	−0.0246094	−	0.234142i
$467$	−6.79392	+	20.9095i	−0.314385	+	0.967578i	0.661622	+	0.749838i	$0.269869\pi$
$467$	−6.79392	+	20.9095i	−0.314385	+	0.967578i	−0.976007	+	0.217740i	$0.930131\pi$
$468$	−26.5390	−	7.77494i	−1.22677	−	0.359397i
$469$	12.7545	−	39.2543i	0.588948	−	1.81260i
$470$	9.55014	−	0.557011i	0.440515	−	0.0256930i
$471$	−3.61000	−	20.8223i	−0.166340	−	0.959442i
$472$	18.5099	−	20.5573i	0.851988	−	0.946228i
$473$	−1.44628	+	13.7605i	−0.0665001	+	0.632707i
$474$	−4.78595	−	0.686623i	−0.219826	−	0.0315376i
$475$	−13.0077	+	18.3551i	−0.596835	+	0.842191i
$476$	15.3122			0.701833
$477$	3.62455	−	8.82501i	0.165957	−	0.404070i
$478$	1.14601	+	3.52705i	0.0524172	+	0.161324i
$479$	5.00389	+	1.06361i	0.228633	+	0.0485975i	0.320804	−	0.947146i	$-0.396047\pi$
$479$	5.00389	+	1.06361i	0.228633	+	0.0485975i	−0.0921702	+	0.995743i	$0.529380\pi$
$480$	0.429701	+	20.9738i	0.0196131	+	0.957317i
$481$	−30.4385	+	6.46990i	−1.38788	+	0.295002i
$482$	−7.17998	−	12.4361i	−0.327039	−	0.566448i
$483$	9.83219	+	14.6674i	0.447380	+	0.667388i
$484$	−1.29532	−	12.3241i	−0.0588780	−	0.560187i
$485$	−28.2323	−	10.6467i	−1.28196	−	0.483443i
$486$	−2.02418	−	8.64473i	−0.0918185	−	0.392133i
$487$	−5.27361	+	3.83150i	−0.238970	+	0.173622i	−0.700824	−	0.713334i	$-0.747184\pi$
$487$	−5.27361	+	3.83150i	−0.238970	+	0.173622i	0.461854	+	0.886956i	$0.347184\pi$
$488$	0.229525	+	2.18379i	0.0103901	+	0.0988554i
$489$	4.06078	−	1.15182i	0.183635	−	0.0520870i
$490$	−2.80458	−	2.77168i	−0.126698	−	0.125212i
$491$	−14.1331	−	6.29244i	−0.637816	−	0.283974i	0.0622407	−	0.998061i	$-0.480175\pi$
$491$	−14.1331	−	6.29244i	−0.637816	−	0.283974i	−0.700057	+	0.714087i	$0.746842\pi$
$492$	−3.08845	+	0.207067i	−0.139238	+	0.00933531i
$493$	−2.58150	+	4.47130i	−0.116265	+	0.201377i
$494$	−4.35659	+	13.4082i	−0.196012	+	0.603264i
$495$	11.5434	+	5.38049i	0.518839	+	0.241835i
$496$	5.01669	+	15.4398i	0.225256	+	0.693267i
$497$	−21.1668	−	4.49914i	−0.949460	−	0.201814i
$498$	10.6024	+	10.2975i	0.475105	+	0.461443i
$499$	4.06654	+	7.04346i	0.182044	+	0.315309i	0.942576	−	0.333991i	$-0.108395\pi$
$499$	4.06654	+	7.04346i	0.182044	+	0.315309i	−0.760533	+	0.649300i	$0.775062\pi$
$500$	−17.3680	+	7.02204i	−0.776719	+	0.314035i
$501$	−7.33967	−	1.05300i	−0.327912	−	0.0470444i
$502$	14.6759	−	6.53411i	0.655015	−	0.291632i
$503$	−2.99913	−	9.23038i	−0.133725	−	0.411562i	0.861665	−	0.507478i	$-0.169422\pi$
$503$	−2.99913	−	9.23038i	−0.133725	−	0.411562i	−0.995389	+	0.0959155i	$0.969422\pi$
$504$	0.582048	+	19.9471i	0.0259265	+	0.888515i
$505$	−18.4631	+	23.0770i	−0.821596	+	1.02691i
$506$	−2.32152	−	2.57831i	−0.103204	−	0.114620i
$507$	−11.1228	−	27.7589i	−0.493983	−	1.23282i
$508$	16.9235	−	3.59719i	0.750857	−	0.159600i
$509$	−24.7092	−	11.0012i	−1.09522	−	0.487622i	−0.222045	−	0.975036i	$-0.571273\pi$
$509$	−24.7092	−	11.0012i	−1.09522	−	0.487622i	−0.873171	+	0.487415i	$0.837940\pi$
$510$	−2.46115	+	5.84732i	−0.108981	+	0.258924i
$511$	−0.623344	+	0.277531i	−0.0275751	+	0.0122772i
$512$	−16.7729	+	12.1862i	−0.741265	+	0.538561i
$513$	22.9096	−	4.66395i	1.01148	−	0.205919i
$514$	−12.5351	−	9.10730i	−0.552901	−	0.401706i
$515$	−9.45475	+	7.74909i	−0.416626	+	0.341466i
$516$	−0.798772	+	21.1359i	−0.0351640	+	0.930455i
$517$	13.9492	−	2.96498i	0.613483	−	0.130400i
$518$	5.11836	+	8.86527i	0.224888	+	0.389517i
$519$	6.75194	−	0.452688i	0.296377	−	0.0198708i
$520$	−19.9178	+	16.3246i	−0.873452	+	0.715879i
$521$	−9.60176	−	29.5512i	−0.420661	−	1.29466i	−0.907088	−	0.420940i	$-0.861700\pi$
$521$	−9.60176	−	29.5512i	−0.420661	−	1.29466i	0.486428	−	0.873721i	$-0.338300\pi$
$522$	−2.70007	−	1.45557i	−0.118179	−	0.0637088i
$523$	14.8951	+	10.8219i	0.651315	+	0.473208i	0.863719	−	0.503974i	$-0.168129\pi$
$523$	14.8951	+	10.8219i	0.651315	+	0.473208i	−0.212404	+	0.977182i	$0.568129\pi$
$524$	−2.91154	+	5.04293i	−0.127191	+	0.220301i
$525$	−25.4206	+	10.5356i	−1.10945	+	0.459812i
$526$	−4.36871	−	7.56683i	−0.190485	−	0.329929i
$527$	−2.26067	+	21.5088i	−0.0984763	+	0.936939i
$528$	1.21269	+	6.99475i	0.0527756	+	0.304407i
$529$	12.4278	+	2.64161i	0.540340	+	0.114853i
$530$	−2.22585	−	3.38364i	−0.0966846	−	0.146976i
$531$	−17.1730	−	35.7284i	−0.745243	−	1.55048i
$532$	−23.9552			−1.03859
$533$	−3.92615	−	4.36043i	−0.170060	−	0.188871i
$534$	2.21952	+	1.39577i	0.0960479	+	0.0604010i
$535$	26.2051	+	3.99217i	1.13295	+	0.172596i
$536$	−2.84254	+	27.0450i	−0.122779	+	1.16816i
$537$	1.45323	−	38.4532i	0.0627116	−	1.65938i
$538$	−1.04286	−	9.92211i	−0.0449607	−	0.427772i
$539$	−4.75543	−	3.45502i	−0.204831	−	0.148818i
$540$	18.1567	+	7.02609i	0.781340	+	0.302355i
$541$	2.72761	−	1.98173i	0.117269	−	0.0852011i	−0.527605	−	0.849490i	$-0.676910\pi$
$541$	2.72761	−	1.98173i	0.117269	−	0.0852011i	0.644874	+	0.764289i	$0.276910\pi$
$542$	−2.84775	−	3.16275i	−0.122321	−	0.135852i
$543$	−24.8035	+	31.5601i	−1.06442	+	1.35437i
$544$	−15.2376	+	3.23885i	−0.653306	+	0.138864i
$545$	7.72809	−	3.99526i	0.331035	−	0.171138i
$546$	−13.2417	+	11.0466i	−0.566693	+	0.472750i
$547$	24.5702	+	5.22256i	1.05055	+	0.223301i	0.700663	−	0.713493i	$-0.252888\pi$
$547$	24.5702	+	5.22256i	1.05055	+	0.223301i	0.349884	+	0.936793i	$0.386221\pi$
$548$	3.96355	+	2.87969i	0.169314	+	0.123014i
$549$	3.01974	+	0.884671i	0.128879	+	0.0377569i
$550$	4.65008	−	2.75838i	0.198280	−	0.117618i
$551$	4.03865	−	6.99514i	0.172052	−	0.298003i
$552$	−8.34563	−	8.10567i	−0.355214	−	0.345000i
$553$	10.4203	−	11.5729i	0.443116	−	0.492131i
$554$	2.13873	−	2.37530i	0.0908661	−	0.100917i
$555$	21.7360	−	2.73575i	0.922640	−	0.116126i
$556$	−5.09147	−	5.65465i	−0.215926	−	0.239811i
$557$	−11.3371			−0.480368			−0.240184	−	0.970727i	$-0.577208\pi$
$557$	−11.3371			−0.480368			−0.240184	+	0.970727i	$0.577208\pi$
$558$	−12.8124	−	0.969806i	−0.542394	−	0.0410552i
$559$	−32.4361	+	23.5662i	−1.37190	+	0.996745i
$560$	−12.9130	−	8.27793i	−0.545675	−	0.349806i
$561$	−2.31425	+	9.16985i	−0.0977077	+	0.387151i
$562$	5.28814	+	2.35443i	0.223067	+	0.0993157i
$563$	36.9447	+	16.4488i	1.55703	+	0.693236i	0.991333	−	0.131375i	$-0.0419392\pi$
$563$	36.9447	+	16.4488i	1.55703	+	0.693236i	0.565700	+	0.824611i	$0.308606\pi$
$564$	20.9726	−	5.94876i	0.883105	−	0.250488i
$565$	−39.2689	−	25.1734i	−1.65205	−	1.05905i
$566$	−5.46041	+	3.96722i	−0.229518	+	0.166755i
$567$	26.7583	+	10.0883i	1.12374	+	0.423669i
$568$	14.2574			0.598229
$569$	0.647023	+	0.718591i	0.0271246	+	0.0301249i	0.756554	−	0.653931i	$-0.226881\pi$
$569$	0.647023	+	0.718591i	0.0271246	+	0.0301249i	−0.729430	+	0.684056i	$0.760215\pi$
$570$	3.85035	−	9.14787i	0.161274	−	0.383162i
$571$	−1.81559	+	2.01642i	−0.0759801	+	0.0843844i	−0.779936	−	0.625859i	$-0.784749\pi$
$571$	−1.81559	+	2.01642i	−0.0759801	+	0.0843844i	0.703956	+	0.710243i	$0.251415\pi$
$572$	−11.7105	+	13.0058i	−0.489640	+	0.543800i
$573$	3.20991	−	12.7188i	0.134096	−	0.531334i
$574$	−0.965090	+	1.67159i	−0.0402821	+	0.0697706i
$575$	6.35174	−	14.7316i	0.264886	−	0.614349i
$576$	0.874029	+	3.59321i	0.0364179	+	0.149717i
$577$	13.0220	+	9.46105i	0.542114	+	0.393869i	0.824870	−	0.565323i	$-0.191249\pi$
$577$	13.0220	+	9.46105i	0.542114	+	0.393869i	−0.282756	+	0.959192i	$0.591249\pi$
$578$	4.86281	+	1.03362i	0.202266	+	0.0429930i
$579$	3.40361	+	19.6319i	0.141449	+	0.815873i
$580$	5.97496	−	3.08893i	0.248097	−	0.128261i
$581$	−46.5648	+	9.89764i	−1.93183	+	0.410623i
$582$	13.1768	+	1.89043i	0.546197	+	0.0783608i
$583$	−4.03993	−	4.48680i	−0.167317	−	0.185824i
$584$	0.363702	−	0.264245i	0.0150501	−	0.0109345i
$585$	10.7956	+	35.2902i	0.446343	+	1.45907i
$586$	−7.79514	−	5.66350i	−0.322014	−	0.233957i
$587$	1.32848	+	12.6397i	0.0548323	+	0.521695i	0.987121	+	0.159978i	$0.0511424\pi$
$587$	1.32848	+	12.6397i	0.0548323	+	0.521695i	−0.932288	+	0.361716i	$0.882191\pi$
$588$	−7.60648	−	4.78344i	−0.313686	−	0.197266i
$589$	3.53672	−	33.6496i	0.145728	−	1.38651i
$590$	−16.6367	−	2.53449i	−0.684923	−	0.104343i
$591$	−0.221440	+	5.85939i	−0.00910880	+	0.241023i
$592$	8.17108	+	9.07490i	0.335829	+	0.372976i
$593$	43.6874			1.79403			0.897014	−	0.442003i	$-0.145732\pi$
$593$	43.6874			1.79403			0.897014	+	0.442003i	$0.145732\pi$
$594$	−5.48572	−	1.21544i	−0.225082	−	0.0498703i
$595$	−11.2300	−	17.0714i	−0.460385	−	0.699858i
$596$	−35.0276	−	7.44535i	−1.43479	−	0.304973i
$597$	26.7343	+	9.81740i	1.09416	+	0.401799i
$598$	1.05087	−	9.99837i	0.0429733	−	0.408864i
$599$	−1.44797	−	2.50795i	−0.0591624	−	0.102472i	0.834927	−	0.550360i	$-0.185510\pi$
$599$	−1.44797	−	2.50795i	−0.0591624	−	0.102472i	−0.894090	+	0.447888i	$0.852176\pi$
$600$	14.9393	−	10.2720i	0.609895	−	0.419352i
$601$	−11.7991	+	20.4366i	−0.481295	+	0.833627i	−0.999770	−	0.0214662i	$-0.993167\pi$
$601$	−11.7991	+	20.4366i	−0.481295	+	0.833627i	0.518475	+	0.855093i	$0.326500\pi$
$602$	10.6702	+	7.75233i	0.434884	+	0.315962i
$603$	34.3026	+	18.4922i	1.39691	+	0.753059i
$604$	−10.7835	−	33.1883i	−0.438776	−	1.35041i
$605$	−12.7900	+	10.4827i	−0.519987	+	0.426181i
$606$	5.74931	−	11.7025i	0.233550	−	0.475383i
$607$	−13.9749	−	24.2052i	−0.567224	−	0.982461i	−0.996839	−	0.0794485i	$-0.974684\pi$
$607$	−13.9749	−	24.2052i	−0.567224	−	0.982461i	0.429615	−	0.903012i	$-0.358649\pi$
$608$	23.8385	−	5.06703i	0.966779	−	0.205495i
$609$	8.73665	−	4.61327i	0.354027	−	0.186939i
$610$	1.03316	−	0.846777i	0.0418315	−	0.0342850i
$611$	33.4314	+	24.2893i	1.35249	+	0.982640i
$612$	−2.59207	+	14.2229i	−0.104778	+	0.574925i
$613$	13.2567	−	9.63154i	0.535432	−	0.389014i	−0.286954	−	0.957944i	$-0.592643\pi$
$613$	13.2567	−	9.63154i	0.535432	−	0.389014i	0.822386	+	0.568930i	$0.192643\pi$
$614$	−0.794972	+	0.353944i	−0.0320825	+	0.0142840i
$615$	2.49593	+	3.29141i	0.100646	+	0.132722i
$616$	11.5370	+	5.13661i	0.464840	+	0.206960i
$617$	−5.88161	+	1.25017i	−0.236785	+	0.0503301i	−0.324775	−	0.945791i	$-0.605289\pi$
$617$	−5.88161	+	1.25017i	−0.236785	+	0.0503301i	0.0879908	+	0.996121i	$0.471955\pi$
$618$	3.33258	−	4.24038i	0.134056	−	0.170573i
$619$	−16.3337	−	18.1404i	−0.656508	−	0.729126i	0.319325	−	0.947645i	$-0.396544\pi$
$619$	−16.3337	−	18.1404i	−0.656508	−	0.729126i	−0.975833	+	0.218519i	$0.929877\pi$
$620$	17.6018	−	22.0005i	0.706906	−	0.883563i
$621$	−15.2883	+	6.64980i	−0.613499	+	0.266847i
$622$	−1.61080	−	4.95753i	−0.0645872	−	0.198779i
$623$	−7.71482	+	3.43486i	−0.309088	+	0.137615i
$624$	−12.7112	+	16.1738i	−0.508856	+	0.647470i
$625$	20.5665	+	14.2133i	0.822660	+	0.568534i
$626$	0.101662	+	0.176084i	0.00406324	+	0.00703773i
$627$	3.62054	−	14.3458i	0.144590	−	0.572917i
$628$	−19.9974	−	4.25059i	−0.797985	−	0.169617i
$629$	5.02711	+	15.4719i	0.200444	+	0.616903i
$630$	9.94343	−	6.96489i	0.396156	−	0.277488i
$631$	9.64049	−	29.6704i	0.383782	−	1.18116i	−0.553578	−	0.832797i	$-0.686738\pi$
$631$	9.64049	−	29.6704i	0.383782	−	1.18116i	0.937360	−	0.348362i	$-0.113262\pi$
$632$	−5.13015	+	8.88569i	−0.204067	+	0.353454i
$633$	−7.22583	+	14.7079i	−0.287201	+	0.584588i
$634$	9.33368	+	4.15562i	0.370688	+	0.165041i
$635$	−16.4222	−	16.2295i	−0.651694	−	0.644050i
$636$	−6.62068	−	6.43031i	−0.262527	−	0.254978i
$637$	−1.78041	−	16.9394i	−0.0705423	−	0.671165i
$638$	−1.57047	+	1.14101i	−0.0621754	+	0.0451731i
$639$	7.76221	−	18.8993i	0.307068	−	0.747646i
$640$	24.1343	+	9.10131i	0.953992	+	0.359761i
$641$	0.262265	+	2.49529i	0.0103589	+	0.0985579i	0.998480	−	0.0551211i	$-0.0175545\pi$
$641$	0.262265	+	2.49529i	0.0103589	+	0.0985579i	−0.988121	+	0.153679i	$0.950888\pi$
$642$	−11.6683	+	0.782312i	−0.460512	+	0.0308754i
$643$	7.75566	+	13.4332i	0.305854	+	0.529754i	0.977451	−	0.211162i	$-0.0677249\pi$
$643$	7.75566	+	13.4332i	0.305854	+	0.529754i	−0.671597	+	0.740916i	$0.734392\pi$
$644$	16.7092	−	3.55165i	0.658434	−	0.139955i
$645$	24.1499	−	14.6106i	0.950903	−	0.575291i
$646$	7.20918	+	1.53236i	0.283641	+	0.0602899i
$647$	−3.80099	−	11.6982i	−0.149432	−	0.459905i	0.848122	−	0.529801i	$-0.177733\pi$
$647$	−3.80099	−	11.6982i	−0.149432	−	0.459905i	−0.997554	+	0.0698957i	$0.977733\pi$
$648$	−18.6266	−	2.83604i	−0.731721	−	0.111410i
$649$	−25.0869			−0.984745
$650$	14.9561	+	4.66520i	0.586628	+	0.182984i
$651$	25.5730	−	32.5391i	1.00228	−	1.27531i
$652$	0.426833	−	4.06104i	0.0167161	−	0.159043i
$653$	−11.6984	+	12.9924i	−0.457792	+	0.508430i	−0.927208	−	0.374548i	$-0.877798\pi$
$653$	−11.6984	+	12.9924i	−0.457792	+	0.508430i	0.469415	+	0.882978i	$0.344465\pi$
$654$	−2.94725	+	2.45867i	−0.115246	+	0.0961414i
$655$	7.75763	−	0.452463i	0.303116	−	0.0176792i
$656$	−0.711521	+	2.18984i	−0.0277802	+	0.0854987i
$657$	−0.152266	−	0.625979i	−0.00594047	−	0.0244218i
$658$	4.20069	−	12.9284i	0.163760	−	0.504002i
$659$	−0.260923	−	2.48251i	−0.0101641	−	0.0967050i	0.988264	−	0.152757i	$-0.0488153\pi$
$659$	−0.260923	−	2.48251i	−0.0101641	−	0.0967050i	−0.998428	+	0.0560523i	$0.982149\pi$
$660$	8.98530	−	8.43000i	0.349752	−	0.328137i
$661$	0.585257	−	5.56835i	0.0227639	−	0.216584i	−0.977227	−	0.212199i	$-0.931938\pi$
$661$	0.585257	−	5.56835i	0.0227639	−	0.216584i	0.999990	−	0.00438491i	$-0.00139577\pi$
$662$	6.79930	+	3.02724i	0.264262	+	0.117657i
$663$	−24.2336	+	12.7962i	−0.941155	+	0.496965i
$664$	28.6533	−	12.7573i	1.11196	−	0.495077i
$665$	17.5688	+	26.7074i	0.681290	+	1.03567i
$666$	−9.10103	+	3.25351i	−0.352658	+	0.126071i
$667$	−1.77991	+	5.47801i	−0.0689185	+	0.212109i
$668$	−3.58658	+	6.21214i	−0.138769	+	0.240355i
$669$	−2.14347	+	0.143711i	−0.0828714	+	0.00555617i
$670$	14.6958	−	7.59744i	0.567750	−	0.293515i
$671$	1.33248	−	1.47987i	0.0514397	−	0.0571296i
$672$	27.9827	+	10.2758i	1.07946	+	0.396399i
$673$	19.8035	−	8.81709i	0.763369	−	0.339874i	0.0121495	−	0.999926i	$-0.496133\pi$
$673$	19.8035	−	8.81709i	0.763369	−	0.339874i	0.751220	+	0.660052i	$0.229466\pi$
$674$	13.2928			0.512020
$675$	−5.48287	−	25.3956i	−0.211036	−	0.977478i
$676$	−28.9298			−1.11269
$677$	4.07701	−	1.81520i	0.156692	−	0.0697638i	−0.326892	−	0.945062i	$-0.606001\pi$
$677$	4.07701	−	1.81520i	0.156692	−	0.0697638i	0.483584	+	0.875298i	$0.339335\pi$
$678$	19.3174	+	7.09376i	0.741881	+	0.272434i
$679$	−28.6895	+	31.8629i	−1.10100	+	1.22279i
$680$	9.57578	+	9.46346i	0.367214	+	0.362907i
$681$	41.8207	−	2.80390i	1.60257	−	0.107446i
$682$	−4.06575	+	7.04209i	−0.155686	+	0.269656i
$683$	8.58695	−	26.4279i	0.328570	−	1.01124i	−0.641233	−	0.767346i	$-0.721577\pi$
$683$	8.58695	−	26.4279i	0.328570	−	1.01124i	0.969803	−	0.243889i	$-0.0784233\pi$
$684$	4.05518	−	22.2510i	0.155054	−	0.850789i
$685$	0.303648	−	6.53088i	0.0116018	−	0.249532i
$686$	6.45426	−	2.87362i	0.246425	−	0.109715i
$687$	−5.73388	+	3.02770i	−0.218761	+	0.115514i
$688$	14.3731	+	6.39933i	0.547970	+	0.243972i
$689$	1.82873	−	17.3992i	0.0696692	−	0.662858i
$690$	−1.32941	+	6.95166i	−0.0506097	+	0.264645i
$691$	3.51242	+	33.4184i	0.133619	+	1.27130i	0.831679	+	0.555257i	$0.187380\pi$
$691$	3.51242	+	33.4184i	0.133619	+	1.27130i	−0.698060	+	0.716039i	$0.745953\pi$
$692$	2.02300	−	6.22614i	0.0769028	−	0.236682i
$693$	13.0901	−	12.4967i	0.497252	−	0.474710i
$694$	1.39952	−	4.30728i	0.0531251	−	0.163502i
$695$	−2.57020	+	9.82355i	−0.0974932	+	0.372628i
$696$	−4.99847	+	4.16984i	−0.189466	+	0.158058i
$697$	−2.05250	+	2.27953i	−0.0777441	+	0.0863435i
$698$	0.469715	−	4.46904i	0.0177790	−	0.169156i
$699$	−9.55019	+	12.1517i	−0.361221	+	0.459619i
$700$	0.314065	+	26.6187i	0.0118705	+	1.00609i
$701$	2.58517			0.0976406			0.0488203	−	0.998808i	$-0.484454\pi$
$701$	2.58517			0.0976406			0.0488203	+	0.998808i	$0.484454\pi$
$702$	−8.01913	−	14.1697i	−0.302662	−	0.534800i
$703$	−7.86469	−	24.2050i	−0.296622	−	0.912910i
$704$	2.28912	+	0.486567i	0.0862743	+	0.0183382i
$705$	−22.0135	−	19.0192i	−0.829078	−	0.716306i
$706$	−2.22158	+	0.472211i	−0.0836102	+	0.0177719i
$707$	20.9979	+	36.3695i	0.789709	+	1.36782i
$708$	−38.2634	+	2.56540i	−1.43803	+	0.0964136i
$709$	−4.81920	−	45.8516i	−0.180989	−	1.72199i	−0.588248	−	0.808680i	$-0.700182\pi$
$709$	−4.81920	−	45.8516i	−0.180989	−	1.72199i	0.407259	−	0.913313i	$-0.366484\pi$
$710$	−4.76679	−	7.24628i	−0.178895	−	0.271948i
$711$	8.98564	+	11.6381i	0.336988	+	0.436462i
$712$	4.50136	−	3.27043i	0.168696	−	0.122565i
$713$	2.52203	+	23.9955i	0.0944508	+	0.898640i
$714$	6.46686	+	6.28091i	0.242016	+	0.235057i
$715$	23.0885	+	3.51737i	0.863461	+	0.131542i
$716$	−34.0082	−	15.1414i	−1.27094	−	0.565861i
$717$	4.97294	−	10.1223i	0.185718	−	0.378023i
$718$	−1.53244	+	2.65426i	−0.0571901	+	0.0990562i
$719$	−3.94501	+	12.1415i	−0.147124	+	0.452801i	−0.997278	−	0.0737330i	$-0.976509\pi$
$719$	−3.94501	+	12.1415i	−0.147124	+	0.452801i	0.850154	+	0.526534i	$0.176509\pi$
$720$	9.87497	−	10.5931i	0.368018	−	0.394781i
$721$	5.36795	+	16.5208i	0.199913	+	0.615268i
$722$	−0.693300	−	0.147365i	−0.0258019	−	0.00548437i
$723$	−10.6860	+	42.3415i	−0.397416	+	1.57470i
$724$	19.4161	+	33.6297i	0.721593	+	1.24984i
$725$	−7.82585	−	4.39598i	−0.290645	−	0.163263i
$726$	4.50818	−	5.73622i	0.167314	−	0.212891i
$727$	−25.9153	+	11.5382i	−0.961144	+	0.427929i	−0.826482	−	0.562963i	$-0.809661\pi$
$727$	−25.9153	+	11.5382i	−0.961144	+	0.427929i	−0.134661	+	0.990892i	$0.542995\pi$
$728$	11.3083	+	34.8035i	0.419115	+	1.28990i
$729$	−13.9003	+	23.1470i	−0.514826	+	0.857295i
$730$	−0.255901	−	0.0965030i	−0.00947131	−	0.00357173i
$731$	14.0249	+	15.5762i	0.518729	+	0.576107i
$732$	1.88101	−	2.39341i	0.0695243	−	0.0884629i
$733$	−24.6701	+	5.24380i	−0.911212	+	0.193684i	−0.639587	−	0.768719i	$-0.720895\pi$
$733$	−24.6701	+	5.24380i	−0.911212	+	0.193684i	−0.271626	+	0.962403i	$0.587561\pi$
$734$	5.99651	+	2.66982i	0.221335	+	0.0985448i
$735$	0.245616	+	11.9885i	0.00905968	+	0.442204i
$736$	−15.8765	+	7.06868i	−0.585216	+	0.260555i
$737$	19.9518	−	14.4958i	0.734934	−	0.533961i
$738$	−1.38930	−	1.17940i	−0.0511407	−	0.0434144i
$739$	−35.4878	−	25.7834i	−1.30544	−	0.948457i	−0.305445	−	0.952210i	$-0.598805\pi$
$739$	−35.4878	−	25.7834i	−1.30544	−	0.948457i	−0.999993	+	0.00375305i	$0.998805\pi$
$740$	5.36442	−	20.5033i	0.197200	−	0.753717i
$741$	37.9124	−	20.0191i	1.39275	−	0.735421i
$742$	−5.62940	+	1.19657i	−0.206662	+	0.0439274i
$743$	13.2513	+	22.9519i	0.486143	+	0.842024i	0.999873	−	0.0159278i	$-0.00507018\pi$
$743$	13.2513	+	22.9519i	0.486143	+	0.842024i	−0.513730	+	0.857952i	$0.671737\pi$
$744$	−12.0234	+	24.4732i	−0.440798	+	0.897231i
$745$	17.3886	+	44.5123i	0.637069	+	1.63080i
$746$	−2.52919	−	7.78405i	−0.0926003	−	0.284994i
$747$	−1.31097	−	44.9276i	−0.0479658	−	1.64381i
$748$	7.40182	+	5.37774i	0.270637	+	0.196629i
$749$	18.8334	−	32.6205i	0.688159	−	1.19193i
$750$	−10.2155	−	4.15853i	−0.373016	−	0.151848i
$751$	7.23895	+	12.5382i	0.264153	+	0.457527i	0.967341	−	0.253477i	$-0.0815742\pi$
$751$	7.23895	+	12.5382i	0.264153	+	0.457527i	−0.703188	+	0.711004i	$0.748241\pi$
$752$	1.69504	−	16.1272i	0.0618118	−	0.588100i
$753$	−45.8591	−	16.8404i	−1.67120	−	0.613699i
$754$	−5.50210	−	1.16951i	−0.200375	−	0.0425910i
$755$	−29.0926	+	36.3629i	−1.05879	+	1.32338i
$756$	18.6876	−	20.3990i	0.679662	−	0.741905i
$757$	21.1038			0.767029			0.383515	−	0.923535i	$-0.374714\pi$
$757$	21.1038			0.767029			0.383515	+	0.923535i	$0.374714\pi$
$758$	2.92289	+	3.24620i	0.106164	+	0.117907i
$759$	−0.398452	+	10.5432i	−0.0144629	+	0.382695i
$760$	−14.9809	−	14.8052i	−0.543413	−	0.537040i
$761$	3.15080	−	29.9779i	0.114216	−	1.08670i	−0.775866	−	0.630898i	$-0.782687\pi$
$761$	3.15080	−	29.9779i	0.114216	−	1.08670i	0.890083	−	0.455799i	$-0.150647\pi$
$762$	8.62289	+	5.42262i	0.312374	+	0.196441i
$763$	−1.29221	−	12.2945i	−0.0467810	−	0.445092i
$764$	−10.2665	−	7.45903i	−0.371428	−	0.269858i
$765$	17.7579	−	7.54122i	0.642039	−	0.272653i
$766$	7.10122	−	5.15934i	0.256578	−	0.186415i
$767$	−48.6418	−	54.0222i	−1.75635	−	1.95063i
$768$	−7.03737	−	1.00962i

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)

\(f(q)\)	\(=\)	\(q+(0.520318 - 0.231661i) q^{2} +(-1.62589 - 0.597061i) q^{3} +(-1.12120 + 1.24522i) q^{4} +(2.21056 + 0.336764i) q^{5} +(-0.984295 + 0.0659928i) q^{6} +(1.58872 - 2.75174i) q^{7} +(-0.646919 + 1.99101i) q^{8} +(2.28704 + 1.94151i) q^{9} +O(q^{10})\)	\(q+(0.520318 - 0.231661i) q^{2} +(-1.62589 - 0.597061i) q^{3} +(-1.12120 + 1.24522i) q^{4} +(2.21056 + 0.336764i) q^{5} +(-0.984295 + 0.0659928i) q^{6} +(1.58872 - 2.75174i) q^{7} +(-0.646919 + 1.99101i) q^{8} +(2.28704 + 1.94151i) q^{9} +(1.22821 - 0.336876i) q^{10} +(1.73440 - 0.772206i) q^{11} +(2.56641 - 1.35516i) q^{12} +(5.02577 + 2.23762i) q^{13} +(0.189169 - 1.79982i) q^{14} +(-3.39306 - 1.86738i) q^{15} +(-0.225661 - 2.14702i) q^{16} +(0.888735 - 2.73524i) q^{17} +(1.63976 + 0.480388i) q^{18} +(-1.39039 + 4.27917i) q^{19} +(-2.89782 + 2.37505i) q^{20} +(-4.22603 + 3.52546i) q^{21} +(0.723552 - 0.803585i) q^{22} +(0.335381 - 3.19093i) q^{23} +(2.24057 - 2.85091i) q^{24} +(4.77318 + 1.48888i) q^{25} +3.13337 q^{26} +(-2.55927 - 4.52218i) q^{27} +(1.64524 + 5.06353i) q^{28} +(-1.75597 - 0.373243i) q^{29} +(-2.19807 - 0.185594i) q^{30} +(-7.35558 + 1.56348i) q^{31} +(-2.70827 - 4.69086i) q^{32} +(-3.28100 + 0.219977i) q^{33} +(-0.171223 - 1.62908i) q^{34} +(4.43864 - 5.54787i) q^{35} +(-4.98182 + 0.671035i) q^{36} +(-4.57619 + 3.32479i) q^{37} +(0.267871 + 2.54863i) q^{38} +(-6.83536 - 6.63882i) q^{39} +(-2.10055 + 4.18340i) q^{40} +(-0.974346 - 0.433807i) q^{41} +(-1.38217 + 2.81337i) q^{42} +(-3.64392 + 6.31145i) q^{43} +(-0.983045 + 3.02550i) q^{44} +(4.40181 + 5.06203i) q^{45} +(-0.564709 - 1.73800i) q^{46} +(7.34730 + 1.56172i) q^{47} +(-0.915004 + 3.62556i) q^{48} +(-1.54804 - 2.68128i) q^{49} +(2.82849 - 0.331069i) q^{50} +(-3.07809 + 3.91658i) q^{51} +(-8.42120 + 3.74936i) q^{52} +(-0.982710 - 3.02447i) q^{53} +(-2.37924 - 1.76009i) q^{54} +(4.09406 - 1.12293i) q^{55} +(4.45097 + 4.94330i) q^{56} +(4.81554 - 6.12731i) q^{57} +(-1.00013 + 0.212584i) q^{58} +(-12.0714 - 5.37452i) q^{59} +(6.12959 - 2.13139i) q^{60} +(0.958206 - 0.426621i) q^{61} +(-3.46504 + 2.51750i) q^{62} +(8.97598 - 3.20881i) q^{63} +(0.997243 + 0.724540i) q^{64} +(10.3562 + 6.63890i) q^{65} +(-1.65620 + 0.874537i) q^{66} +(12.7060 - 2.70075i) q^{67} +(2.40952 + 4.17341i) q^{68} +(-2.45048 + 4.98787i) q^{69} +(1.02428 - 3.91491i) q^{70} +(-2.10454 - 6.47710i) q^{71} +(-5.34510 + 3.29751i) q^{72} +(-0.173732 - 0.126223i) q^{73} +(-1.61085 + 2.79007i) q^{74} +(-6.87172 - 5.27063i) q^{75} +(-3.76959 - 6.52912i) q^{76} +(0.630566 - 5.99944i) q^{77} +(-5.09451 - 1.87081i) q^{78} +(4.79399 + 1.01899i) q^{79} +(0.224201 - 4.82212i) q^{80} +(1.46107 + 8.88061i) q^{81} -0.607465 q^{82} +(-10.0251 - 11.1340i) q^{83} +(0.348258 - 9.21506i) q^{84} +(2.88574 - 5.74714i) q^{85} +(-0.433882 + 4.12812i) q^{86} +(2.63217 + 1.65527i) q^{87} +(0.415453 + 3.95277i) q^{88} +(-2.15019 - 1.56220i) q^{89} +(3.46301 + 1.61414i) q^{90} +(14.1419 - 10.2747i) q^{91} +(3.59737 + 3.99529i) q^{92} +(12.8929 + 1.84969i) q^{93} +(4.18472 - 0.889490i) q^{94} +(-4.51461 + 8.99114i) q^{95} +(1.60262 + 9.24382i) q^{96} +(-13.1990 - 2.80553i) q^{97} +(-1.42662 - 1.03650i) q^{98} +(5.46589 + 1.60130i) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more