LMFDB - Embedded newform 225.2.q.a.16.14

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			16.14
Character	$\chi$	$=$	225.16
Dual form			225.2.q.a.211.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0861137 + 0.0383403i) q^{2} +(1.36636 - 1.06445i) q^{3} +(-1.33232 + 1.47969i) q^{4} +(-0.0996266 - 2.23385i) q^{5} +(-0.0768514 + 0.144050i) q^{6} +(0.322971 - 0.559402i) q^{7} +(0.116257 - 0.357802i) q^{8} +(0.733899 - 2.90885i) q^{9} +O(q^{10})$	\(q+(-0.0861137 + 0.0383403i) q^{2} +(1.36636 - 1.06445i) q^{3} +(-1.33232 + 1.47969i) q^{4} +(-0.0996266 - 2.23385i) q^{5} +(-0.0768514 + 0.144050i) q^{6} +(0.322971 - 0.559402i) q^{7} +(0.116257 - 0.357802i) q^{8} +(0.733899 - 2.90885i) q^{9} +(0.0942256 + 0.188545i) q^{10} +(5.40026 - 2.40435i) q^{11} +(-0.245378 + 3.43997i) q^{12} +(-0.255067 - 0.113563i) q^{13} +(-0.00636459 + 0.0605550i) q^{14} +(-2.51394 - 2.94620i) q^{15} +(-0.412549 - 3.92514i) q^{16} +(-0.735171 + 2.26262i) q^{17} +(0.0483273 + 0.278630i) q^{18} +(-0.791053 + 2.43461i) q^{19} +(3.43813 + 2.82877i) q^{20} +(-0.154159 - 1.10813i) q^{21} +(-0.372853 + 0.414095i) q^{22} +(-0.562173 + 5.34872i) q^{23} +(-0.222013 - 0.612637i) q^{24} +(-4.98015 + 0.445101i) q^{25} +0.0263188 q^{26} +(-2.09355 - 4.75574i) q^{27} +(0.397440 + 1.22320i) q^{28} +(-0.794901 - 0.168961i) q^{29} +(0.329443 + 0.157323i) q^{30} +(0.0411395 - 0.00874448i) q^{31} +(0.562233 + 0.973816i) q^{32} +(4.81941 - 9.03351i) q^{33} +(-0.0234414 - 0.223030i) q^{34} +(-1.28180 - 0.665736i) q^{35} +(3.32640 + 4.96144i) q^{36} +(-6.04934 + 4.39510i) q^{37} +(-0.0252232 - 0.239983i) q^{38} +(-0.469396 + 0.116337i) q^{39} +(-0.810857 - 0.224054i) q^{40} +(8.91562 + 3.96949i) q^{41} +(0.0557613 + 0.0895149i) q^{42} +(-0.429402 + 0.743746i) q^{43} +(-3.63716 + 11.1940i) q^{44} +(-6.57104 - 1.34962i) q^{45} +(-0.156661 - 0.482152i) q^{46} +(1.61125 + 0.342483i) q^{47} +(-4.74181 - 4.92404i) q^{48} +(3.29138 + 5.70084i) q^{49} +(0.411794 - 0.229270i) q^{50} +(1.40394 + 3.87412i) q^{51} +(0.507867 - 0.226117i) q^{52} +(-2.47058 - 7.60367i) q^{53} +(0.362620 + 0.329267i) q^{54} +(-5.90896 - 11.8238i) q^{55} +(-0.162608 - 0.180594i) q^{56} +(1.51065 + 4.16860i) q^{57} +(0.0749299 - 0.0159268i) q^{58} +(2.32377 + 1.03461i) q^{59} +(7.70882 + 0.205424i) q^{60} +(-10.8863 + 4.84692i) q^{61} +(-0.00320741 + 0.00233032i) q^{62} +(-1.39019 - 1.35002i) q^{63} +(6.30025 + 4.57740i) q^{64} +(-0.228271 + 0.581094i) q^{65} +(-0.0686697 + 0.962687i) q^{66} +(-10.8408 + 2.30428i) q^{67} +(-2.36849 - 4.10235i) q^{68} +(4.92530 + 7.90670i) q^{69} +(0.135905 + 0.00818463i) q^{70} +(1.96555 + 6.04933i) q^{71} +(-0.955471 - 0.600764i) q^{72} +(10.1015 + 7.33920i) q^{73} +(0.352422 - 0.610413i) q^{74} +(-6.33091 + 5.90928i) q^{75} +(-2.54853 - 4.41418i) q^{76} +(0.399128 - 3.79745i) q^{77} +(0.0359611 - 0.0280150i) q^{78} +(7.36881 + 1.56629i) q^{79} +(-8.72707 + 1.31262i) q^{80} +(-7.92278 - 4.26960i) q^{81} -0.919949 q^{82} +(-8.55130 - 9.49718i) q^{83} +(1.84508 + 1.24828i) q^{84} +(5.12760 + 1.41684i) q^{85} +(0.00846196 - 0.0805102i) q^{86} +(-1.26597 + 0.615268i) q^{87} +(-0.232464 - 2.21174i) q^{88} +(-7.14652 - 5.19225i) q^{89} +(0.617601 - 0.135715i) q^{90} +(-0.145907 + 0.106007i) q^{91} +(-7.16543 - 7.95802i) q^{92} +(0.0469035 - 0.0557390i) q^{93} +(-0.151882 + 0.0322835i) q^{94} +(5.51736 + 1.52454i) q^{95} +(1.80479 + 0.732118i) q^{96} +(12.9608 + 2.75489i) q^{97} +(-0.502005 - 0.364728i) q^{98} +(-3.03064 - 17.4731i) 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 $

$2$	−0.0861137	+	0.0383403i	−0.0608916	+	0.0271107i	−0.436957	−	0.899483i	$-0.643944\pi$
$2$	−0.0861137	+	0.0383403i	−0.0608916	+	0.0271107i	0.376065	+	0.926593i	$0.377277\pi$
$3$	1.36636	−	1.06445i	0.788870	−	0.614560i
$3$	1.36636	−	1.06445i	0.788870	−	0.614560i
$4$	−1.33232	+	1.47969i	−0.666158	+	0.739843i
$5$	−0.0996266	−	2.23385i	−0.0445544	−	0.999007i
$5$	−0.0996266	−	2.23385i	−0.0445544	−	0.999007i
$6$	−0.0768514	+	0.144050i	−0.0313745	+	0.0588083i
$7$	0.322971	−	0.559402i	0.122072	−	0.211434i	−0.798513	−	0.601978i	$-0.794380\pi$
$7$	0.322971	−	0.559402i	0.122072	−	0.211434i	0.920584	+	0.390544i	$0.127713\pi$
$8$	0.116257	−	0.357802i	0.0411030	−	0.126502i
$9$	0.733899	−	2.90885i	0.244633	−	0.969616i
$10$	0.0942256	+	0.188545i	0.0297968	+	0.0596232i
$11$	5.40026	−	2.40435i	1.62824	−	0.724938i	0.629591	−	0.776927i	$-0.283223\pi$
$11$	5.40026	−	2.40435i	1.62824	−	0.724938i	0.998648	+	0.0519884i	$0.0165559\pi$
$12$	−0.245378	+	3.43997i	−0.0708344	+	0.993034i
$13$	−0.255067	−	0.113563i	−0.0707428	−	0.0314967i	0.371060	−	0.928609i	$-0.378994\pi$
$13$	−0.255067	−	0.113563i	−0.0707428	−	0.0314967i	−0.441803	+	0.897112i	$0.645661\pi$
$14$	−0.00636459	+	0.0605550i	−0.00170101	+	0.0161840i
$15$	−2.51394	−	2.94620i	−0.649097	−	0.760706i
$16$	−0.412549	−	3.92514i	−0.103137	−	0.981286i
$17$	−0.735171	+	2.26262i	−0.178305	+	0.548767i	−0.999769	−	0.0214938i	$-0.993158\pi$
$17$	−0.735171	+	2.26262i	−0.178305	+	0.548767i	0.821464	+	0.570261i	$0.193158\pi$
$18$	0.0483273	+	0.278630i	0.0113909	+	0.0656736i
$19$	−0.791053	+	2.43461i	−0.181480	+	0.558538i	−0.999870	−	0.0161251i	$-0.994867\pi$
$19$	−0.791053	+	2.43461i	−0.181480	+	0.558538i	0.818390	+	0.574663i	$0.194867\pi$
$20$	3.43813	+	2.82877i	0.768789	+	0.632533i
$21$	−0.154159	−	1.10813i	−0.0336402	−	0.241814i
$22$	−0.372853	+	0.414095i	−0.0794925	+	0.0882853i
$23$	−0.562173	+	5.34872i	−0.117221	+	1.11528i	0.764863	+	0.644193i	$0.222807\pi$
$23$	−0.562173	+	5.34872i	−0.117221	+	1.11528i	−0.882084	+	0.471092i	$0.843860\pi$
$24$	−0.222013	−	0.612637i	−0.0453181	−	0.125054i
$25$	−4.98015	+	0.445101i	−0.996030	+	0.0890202i
$26$	0.0263188			0.00516154
$27$	−2.09355	−	4.75574i	−0.402903	−	0.915243i
$28$	0.397440	+	1.22320i	0.0751092	+	0.231162i
$29$	−0.794901	−	0.168961i	−0.147609	−	0.0313753i	0.133514	−	0.991047i	$-0.457374\pi$
$29$	−0.794901	−	0.168961i	−0.147609	−	0.0313753i	−0.281124	+	0.959672i	$0.590707\pi$
$30$	0.329443	+	0.157323i	0.0601478	+	0.0287231i
$31$	0.0411395	−	0.00874448i	0.00738888	−	0.00157055i	−0.204216	−	0.978926i	$-0.565464\pi$
$31$	0.0411395	−	0.00874448i	0.00738888	−	0.00157055i	0.211605	+	0.977355i	$0.432131\pi$
$32$	0.562233	+	0.973816i	0.0993896	+	0.172148i
$33$	4.81941	−	9.03351i	0.838951	−	1.57253i
$34$	−0.0234414	−	0.223030i	−0.00402016	−	0.0382493i
$35$	−1.28180	−	0.665736i	−0.216663	−	0.112530i
$36$	3.32640	+	4.96144i	0.554399	+	0.826907i
$37$	−6.04934	+	4.39510i	−0.994506	+	0.722551i	−0.960903	−	0.276885i	$-0.910698\pi$
$37$	−6.04934	+	4.39510i	−0.994506	+	0.722551i	−0.0336026	+	0.999435i	$0.510698\pi$
$38$	−0.0252232	−	0.239983i	−0.00409174	−	0.0389303i
$39$	−0.469396	+	0.116337i	−0.0751635	+	0.0186288i
$40$	−0.810857	−	0.224054i	−0.128208	−	0.0354260i
$41$	8.91562	+	3.96949i	1.39239	+	0.619930i	0.959549	−	0.281542i	$-0.0908457\pi$
$41$	8.91562	+	3.96949i	1.39239	+	0.619930i	0.432837	+	0.901472i	$0.357512\pi$
$42$	0.0557613	+	0.0895149i	0.00860416	+	0.0138125i
$43$	−0.429402	+	0.743746i	−0.0654832	+	0.113420i	−0.896908	−	0.442217i	$-0.854192\pi$
$43$	−0.429402	+	0.743746i	−0.0654832	+	0.113420i	0.831425	+	0.555637i	$0.187526\pi$
$44$	−3.63716	+	11.1940i	−0.548323	+	1.68756i
$45$	−6.57104	−	1.34962i	−0.979552	−	0.201189i
$46$	−0.156661	−	0.482152i	−0.0230984	−	0.0710894i
$47$	1.61125	+	0.342483i	0.235026	+	0.0499562i	0.323919	−	0.946085i	$-0.395000\pi$
$47$	1.61125	+	0.342483i	0.235026	+	0.0499562i	−0.0888930	+	0.996041i	$0.528333\pi$
$48$	−4.74181	−	4.92404i	−0.684421	−	0.710724i
$49$	3.29138	+	5.70084i	0.470197	+	0.814405i
$50$	0.411794	−	0.229270i	0.0582365	−	0.0324236i
$51$	1.40394	+	3.87412i	0.196590	+	0.542485i
$52$	0.507867	−	0.226117i	0.0704285	−	0.0313568i
$53$	−2.47058	−	7.60367i	−0.339361	−	1.04444i	−0.964534	−	0.263958i	$-0.914972\pi$
$53$	−2.47058	−	7.60367i	−0.339361	−	1.04444i	0.625174	−	0.780486i	$-0.285028\pi$
$54$	0.362620	+	0.329267i	0.0493463	+	0.0448076i
$55$	−5.90896	−	11.8238i	−0.796764	−	1.59432i
$56$	−0.162608	−	0.180594i	−0.0217293	−	0.0241329i
$57$	1.51065	+	4.16860i	0.200091	+	0.552145i
$58$	0.0749299	−	0.0159268i	0.00983878	−	0.00209130i
$59$	2.32377	+	1.03461i	0.302530	+	0.134695i	0.552387	−	0.833588i	$-0.313717\pi$
$59$	2.32377	+	1.03461i	0.302530	+	0.134695i	−0.249857	+	0.968283i	$0.580384\pi$
$60$	7.70882	+	0.205424i	0.995204	+	0.0265201i
$61$	−10.8863	+	4.84692i	−1.39385	+	0.620584i	−0.959898	−	0.280350i	$-0.909549\pi$
$61$	−10.8863	+	4.84692i	−1.39385	+	0.620584i	−0.433956	+	0.900934i	$0.642883\pi$
$62$	−0.00320741	+	0.00233032i	−0.000407342	+	0.000295951i
$63$	−1.39019	−	1.35002i	−0.175147	−	0.170086i
$64$	6.30025	+	4.57740i	0.787531	+	0.572175i
$65$	−0.228271	+	0.581094i	−0.0283136	+	0.0720759i
$66$	−0.0686697	+	0.962687i	−0.00845266	+	0.118499i
$67$	−10.8408	+	2.30428i	−1.32442	+	0.281513i	−0.815227	−	0.579142i	$-0.803388\pi$
$67$	−10.8408	+	2.30428i	−1.32442	+	0.281513i	−0.509189	+	0.860655i	$0.670054\pi$
$68$	−2.36849	−	4.10235i	−0.287222	−	0.497483i
$69$	4.92530	+	7.90670i	0.592937	+	0.951854i
$70$	0.135905	+	0.00818463i	0.0162437	+	0.000978250i
$71$	1.96555	+	6.04933i	0.233267	+	0.717923i	0.997347	+	0.0728005i	$0.0231937\pi$
$71$	1.96555	+	6.04933i	0.233267	+	0.717923i	−0.764079	+	0.645122i	$0.776806\pi$
$72$	−0.955471	−	0.600764i	−0.112603	−	0.0708007i
$73$	10.1015	+	7.33920i	1.18230	+	0.858989i	0.992429	−	0.122821i	$-0.0391941\pi$
$73$	10.1015	+	7.33920i	1.18230	+	0.858989i	0.189868	+	0.981810i	$0.439194\pi$
$74$	0.352422	−	0.610413i	0.0409682	−	0.0709590i
$75$	−6.33091	+	5.90928i	−0.731030	+	0.682345i
$76$	−2.54853	−	4.41418i	−0.292336	−	0.506341i
$77$	0.399128	−	3.79745i	0.0454848	−	0.432759i
$78$	0.0359611	−	0.0280150i	0.00407179	−	0.00317208i
$79$	7.36881	+	1.56629i	0.829056	+	0.176221i	0.602846	−	0.797857i	$-0.294033\pi$
$79$	7.36881	+	1.56629i	0.829056	+	0.176221i	0.226210	+	0.974079i	$0.427366\pi$
$80$	−8.72707	+	1.31262i	−0.975717	+	0.146755i
$81$	−7.92278	−	4.26960i	−0.880309	−	0.474400i
$82$	−0.919949			−0.101591
$83$	−8.55130	−	9.49718i	−0.938627	−	1.04245i	−0.999019	−	0.0442760i	$-0.985902\pi$
$83$	−8.55130	−	9.49718i	−0.938627	−	1.04245i	0.0603925	−	0.998175i	$-0.480765\pi$
$84$	1.84508	+	1.24828i	0.201314	+	0.136198i
$85$	5.12760	+	1.41684i	0.556166	+	0.153678i
$86$	0.00846196	−	0.0805102i	0.000912476	−	0.00868163i
$87$	−1.26597	+	0.615268i	−0.135727	+	0.0659637i
$88$	−0.232464	−	2.21174i	−0.0247807	−	0.235773i
$89$	−7.14652	−	5.19225i	−0.757529	−	0.550377i	0.140622	−	0.990063i	$-0.455090\pi$
$89$	−7.14652	−	5.19225i	−0.757529	−	0.550377i	−0.898151	+	0.439686i	$0.855090\pi$
$90$	0.617601	−	0.135715i	0.0651009	−	0.0143056i
$91$	−0.145907	+	0.106007i	−0.0152952	+	0.0111126i
$92$	−7.16543	−	7.95802i	−0.747048	−	0.829681i
$93$	0.0469035	−	0.0557390i	0.00486367	−	0.00577987i
$94$	−0.151882	+	0.0322835i	−0.0156654	+	0.00332979i
$95$	5.51736	+	1.52454i	0.566069	+	0.156415i
$96$	1.80479	+	0.732118i	0.184201	+	0.0747215i
$97$	12.9608	+	2.75489i	1.31597	+	0.279717i	0.811823	−	0.583904i	$-0.198475\pi$
$97$	12.9608	+	2.75489i	1.31597	+	0.279717i	0.504142	+	0.863621i	$0.331809\pi$
$98$	−0.502005	−	0.364728i	−0.0507101	−	0.0368431i
$99$	−3.03064	−	17.4731i	−0.304591	−	1.75611i
$100$	5.97652	−	7.96207i	0.597652	−	0.796207i
$101$	5.97629	−	10.3512i	0.594664	−	1.02999i	−0.398931	−	0.916981i	$-0.630619\pi$
$101$	5.97629	−	10.3512i	0.594664	−	1.02999i	0.993594	−	0.113006i	$-0.0360481\pi$
$102$	−0.269433	−	0.279787i	−0.0266778	−	0.0277031i
$103$	−3.15521	+	3.50421i	−0.310892	+	0.345280i	−0.878260	−	0.478184i	$-0.841295\pi$
$103$	−3.15521	+	3.50421i	−0.310892	+	0.345280i	0.567368	+	0.823465i	$0.307962\pi$
$104$	−0.0702864	+	0.0780609i	−0.00689215	+	0.00765450i
$105$	−2.46004	+	0.454767i	−0.240075	+	0.0443807i
$106$	0.504278	+	0.560058i	0.0489798	+	0.0543976i
$107$	4.90145			0.473841			0.236921	−	0.971529i	$-0.423862\pi$
$107$	4.90145			0.473841			0.236921	+	0.971529i	$0.423862\pi$
$108$	9.82627	+	3.23836i	0.945533	+	0.311611i
$109$	9.96264	−	7.23828i	0.954248	−	0.693302i	0.00244045	−	0.999997i	$-0.499223\pi$
$109$	9.96264	−	7.23828i	0.954248	−	0.693302i	0.951808	+	0.306695i	$0.0992232\pi$
$110$	0.962171	+	0.791641i	0.0917394	+	0.0754800i
$111$	−3.58724	+	12.4445i	−0.340486	+	1.18118i
$112$	−2.32897	−	1.03693i	−0.220067	−	0.0979803i
$113$	7.95515	+	3.54186i	0.748357	+	0.333190i	0.745232	−	0.666805i	$-0.232339\pi$
$113$	7.95515	+	3.54186i	0.748357	+	0.333190i	0.00312509	+	0.999995i	$0.499005\pi$
$114$	−0.289913	−	0.301055i	−0.0271529	−	0.0281964i
$115$	12.0042	+	0.722934i	1.11940	+	0.0674139i
$116$	1.30907	−	0.951094i	0.121544	−	0.0883069i
$117$	−0.517531	+	0.658607i	−0.0478457	+	0.0608882i
$118$	−0.239776			−0.0220732
$119$	1.02828	+	1.14202i	0.0942620	+	0.104689i
$120$	−1.34642	+	0.556977i	−0.122911	+	0.0508448i
$121$	16.0214	−	17.7936i	1.45649	−	1.61760i
$122$	0.751632	−	0.834772i	0.0680496	−	0.0755767i
$123$	16.4073	−	4.06645i	1.47940	−	0.366660i
$124$	−0.0418718	+	0.0725240i	−0.00376019	+	0.00651285i
$125$	1.49044	+	11.0805i	0.133309	+	0.991074i
$126$	0.171474	+	0.0629549i	0.0152761	+	0.00560846i
$127$	−16.5737	−	12.0415i	−1.47068	−	1.06851i	−0.980416	−	0.196940i	$-0.936900\pi$
$127$	−16.5737	−	12.0415i	−1.47068	−	1.06851i	−0.490266	−	0.871573i	$-0.663100\pi$
$128$	−2.91782	−	0.620202i	−0.257902	−	0.0548187i
$129$	0.204960	+	1.47330i	0.0180457	+	0.129717i
$130$	−0.00262205	−	0.0587922i	−0.000229969	−	0.00515642i
$131$	−4.83084	+	1.02683i	−0.422073	+	0.0897143i	−0.414051	−	0.910254i	$-0.635887\pi$
$131$	−4.83084	+	1.02683i	−0.422073	+	0.0897143i	−0.00802126	+	0.999968i	$0.502553\pi$
$132$	6.94579	+	19.1667i	0.604553	+	1.66825i
$133$	1.10644	+	1.22883i	0.0959405	+	0.106553i
$134$	0.845195	−	0.614070i	0.0730138	−	0.0530476i
$135$	−10.4150	+	5.15046i	−0.896383	+	0.443281i
$136$	0.724103	+	0.526091i	0.0620913	+	0.0451120i
$137$	−1.74119	−	16.5663i	−0.148760	−	1.41536i	−0.773139	−	0.634236i	$-0.781315\pi$
$137$	−1.74119	−	16.5663i	−0.148760	−	1.41536i	0.624379	−	0.781121i	$-0.285352\pi$
$138$	−0.727281	−	0.492038i	−0.0619103	−	0.0418850i
$139$	0.692041	−	6.58433i	0.0586981	−	0.558475i	−0.925167	−	0.379561i	$-0.876075\pi$
$139$	0.692041	−	6.58433i	0.0586981	−	0.558475i	0.983865	−	0.178914i	$-0.0572584\pi$
$140$	2.69284	−	1.00968i	0.227586	−	0.0853339i
$141$	2.56611	−	1.24714i	0.216106	−	0.105028i
$142$	−0.401194	−	0.445571i	−0.0336674	−	0.0373914i
$143$	−1.65047			−0.138019
$144$	−11.7204	−	1.68062i	−0.976701	−	0.140051i
$145$	−0.298241	+	1.79252i	−0.0247675	+	0.148861i
$146$	−1.15127	−	0.244710i	−0.0952797	−	0.0202523i
$147$	10.5655	+	4.28591i	0.871425	+	0.353496i
$148$	1.55626	−	14.8068i	0.127924	−	1.21711i
$149$	8.60564	+	14.9054i	0.705001	+	1.22110i	0.966691	+	0.255946i	$0.0823869\pi$
$149$	8.60564	+	14.9054i	0.705001	+	1.22110i	−0.261690	+	0.965152i	$0.584280\pi$
$150$	0.318614	−	0.751599i	0.0260148	−	0.0613678i
$151$	−0.171293	+	0.296689i	−0.0139397	+	0.0241442i	−0.872911	−	0.487879i	$-0.837771\pi$
$151$	−0.171293	+	0.296689i	−0.0139397	+	0.0241442i	0.858971	+	0.512024i	$0.171104\pi$
$152$	0.779144	+	0.566081i	0.0631969	+	0.0459152i
$153$	6.04209	+	3.79904i	0.488474	+	0.307134i
$154$	0.111225	+	0.342315i	0.00896276	+	0.0275845i
$155$	−0.0236324	−	0.0910283i	−0.00189820	−	0.00731157i
$156$	0.453241	−	0.849557i	0.0362884	−	0.0680190i
$157$	5.07964	+	8.79820i	0.405399	+	0.702173i	0.994368	−	0.105984i	$-0.0337991\pi$
$157$	5.07964	+	8.79820i	0.405399	+	0.702173i	−0.588968	+	0.808156i	$0.700466\pi$
$158$	−0.694608	+	0.147644i	−0.0552601	+	0.0117459i
$159$	−11.4694	−	7.75957i	−0.909585	−	0.615374i
$160$	2.11934	−	1.35296i	0.167549	−	0.106961i
$161$	2.81052	+	2.04196i	0.221500	+	0.160929i
$162$	0.845958	+	0.0639092i	0.0664648	+	0.00502118i
$163$	−13.1349	+	9.54309i	−1.02881	+	0.747473i	−0.968070	−	0.250681i	$-0.919345\pi$
$163$	−13.1349	+	9.54309i	−1.02881	+	0.747473i	−0.0607380	+	0.998154i	$0.519345\pi$
$164$	−17.7520	+	7.90371i	−1.38620	+	0.617176i
$165$	−20.6596	−	9.86584i	−1.60835	−	0.768055i
$166$	1.10051	+	0.489978i	0.0854161	+	0.0380297i
$167$	−17.2141	+	3.65896i	−1.33206	+	0.283139i	−0.818299	−	0.574792i	$-0.805083\pi$
$167$	−17.2141	+	3.65896i	−1.33206	+	0.283139i	−0.513764	+	0.857931i	$0.671749\pi$
$168$	−0.414414	−	0.0736697i	−0.0319727	−	0.00568374i
$169$	−8.64654	−	9.60295i	−0.665118	−	0.738688i
$170$	−0.495879	+	0.0745841i	−0.0380322	+	0.00572034i
$171$	6.50136	+	4.08781i	0.497172	+	0.312603i
$172$	−0.528412	−	1.62628i	−0.0402910	−	0.124003i
$173$	−13.0604	+	5.81488i	−0.992967	+	0.442097i	−0.837910	−	0.545808i	$-0.816223\pi$
$173$	−13.0604	+	5.81488i	−0.992967	+	0.442097i	−0.155057	+	0.987906i	$0.549556\pi$
$174$	0.0854282	−	0.101521i	0.00647630	−	0.00769628i
$175$	−1.35945	+	2.92966i	−0.102765	+	0.221461i
$176$	−11.6653	−	20.2049i	−0.879304	−	1.52300i
$177$	4.27641	−	1.05988i	0.321435	−	0.0796657i
$178$	0.814486	+	0.173124i	0.0610483	+	0.0129762i
$179$	−5.01429	−	15.4324i	−0.374786	−	1.15347i	−0.943623	−	0.331022i	$-0.892607\pi$
$179$	−5.01429	−	15.4324i	−0.374786	−	1.15347i	0.568837	−	0.822450i	$-0.307393\pi$
$180$	10.7517	−	7.92495i	0.801385	−	0.590691i
$181$	−4.83704	+	14.8869i	−0.359534	+	1.10653i	0.593799	+	0.804613i	$0.297627\pi$
$181$	−4.83704	+	14.8869i	−0.359534	+	1.10653i	−0.953333	+	0.301920i	$0.902373\pi$
$182$	0.00850021	−	0.0147228i	0.000630077	−	0.00109133i
$183$	−9.71542	+	18.2106i	−0.718185	+	1.34617i
$184$	1.84843	+	0.822972i	0.136268	+	0.0606703i
$185$	10.4207	+	13.0754i	0.766143	+	0.961325i
$186$	−0.00190198	+	0.00659819i	−0.000139460	+	0.000483803i
$187$	1.47003	+	13.9864i	0.107499	+	1.02278i
$188$	−2.65347	+	1.92786i	−0.193524	+	0.140603i
$189$	−3.33652	−	0.364832i	−0.242696	−	0.0265376i
$190$	−0.533572	+	0.0802535i	−0.0387094	+	0.00582220i
$191$	0.00915242	+	0.0870794i	0.000662246	+	0.00630085i	0.994848	−	0.101378i	$-0.0323250\pi$
$191$	0.00915242	+	0.0870794i	0.000662246	+	0.00630085i	−0.994186	+	0.107678i	$0.965658\pi$
$192$	13.4808	−	0.451899i	0.972895	−	0.0326130i
$193$	9.55089	+	16.5426i	0.687488	+	1.19076i	0.972648	+	0.232284i	$0.0746199\pi$
$193$	9.55089	+	16.5426i	0.687488	+	1.19076i	−0.285160	+	0.958480i	$0.592047\pi$
$194$	−1.22172	+	0.259685i	−0.0877146	+	0.0186443i
$195$	0.306644	+	1.03697i	0.0219592	+	0.0742589i
$196$	−12.8206	−	2.72510i	−0.915758	−	0.194650i
$197$	−6.93182	−	21.3339i	−0.493871	−	1.51998i	−0.818708	−	0.574210i	$-0.805309\pi$
$197$	−6.93182	−	21.3339i	−0.493871	−	1.51998i	0.324837	−	0.945770i	$-0.394691\pi$
$198$	0.930903	+	1.38848i	0.0661564	+	0.0986747i
$199$	3.83647			0.271960			0.135980	−	0.990712i	$-0.456582\pi$
$199$	3.83647			0.271960			0.135980	+	0.990712i	$0.456582\pi$
$200$	−0.419719	+	1.83365i	−0.0296786	+	0.129659i
$201$	−12.3597	+	14.6880i	−0.871785	+	1.03601i
$202$	−0.117771	+	1.12052i	−0.00828635	+	0.0788393i
$203$	−0.351247	+	0.390100i	−0.0246527	+	0.0273796i
$204$	−7.60296	−	3.08416i	−0.532314	−	0.215935i
$205$	7.97901	−	20.3116i	0.557278	−	1.41862i
$206$	0.137354	−	0.422733i	0.00956992	−	0.0294532i
$207$	15.1460	+	5.56069i	1.05272	+	0.386495i
$208$	−0.340524	+	1.04802i	−0.0236111	+	0.0726674i
$209$	1.58177	+	15.0495i	0.109413	+	1.04100i
$210$	0.194407	−	0.133480i	0.0134154	−	0.00921102i
$211$	2.00311	−	19.0583i	0.137900	−	1.31203i	−0.678524	−	0.734578i	$-0.737380\pi$
$211$	2.00311	−	19.0583i	0.137900	−	1.31203i	0.816424	−	0.577453i	$-0.195953\pi$
$212$	14.5426	+	6.47480i	0.998793	+	0.444691i
$213$	9.12485	+	6.17336i	0.625224	+	0.422992i
$214$	−0.422082	+	0.187923i	−0.0288530	+	0.0128462i
$215$	1.70420	+	0.885122i	0.116225	+	0.0603648i
$216$	−1.94500	+	0.196187i	−0.132341	+	0.0133488i
$217$	0.00839519	−	0.0258377i	0.000569903	−	0.00175398i
$218$	−0.580403	+	1.00529i	−0.0393098	+	0.0680866i
$219$	21.6146	−	0.724556i	1.46058	−	0.0489609i
$220$	25.3681	+	7.00964i	1.71032	+	0.472590i
$221$	0.444468	−	0.493632i	0.0298982	−	0.0332053i
$222$	−0.168216	−	1.20918i	−0.0112899	−	0.0811549i
$223$	−22.1731	+	9.87211i	−1.48482	+	0.661085i	−0.979426	−	0.201802i	$-0.935320\pi$
$223$	−22.1731	+	9.87211i	−1.48482	+	0.661085i	−0.505396	+	0.862888i	$0.668654\pi$
$224$	0.726339			0.0485306
$225$	−2.36019	+	14.8132i	−0.157346	+	0.987543i
$226$	−0.820844			−0.0546017
$227$	16.2273	−	7.22487i	1.07704	−	0.479531i	0.209969	−	0.977708i	$-0.432664\pi$
$227$	16.2273	−	7.22487i	1.07704	−	0.479531i	0.867076	+	0.498177i	$0.165997\pi$
$228$	−8.18089	−	3.31860i	−0.541793	−	0.219780i
$229$	−3.83232	+	4.25622i	−0.253247	+	0.281259i	−0.856341	−	0.516411i	$-0.827268\pi$
$229$	−3.83232	+	4.25622i	−0.253247	+	0.281259i	0.603094	+	0.797670i	$0.293934\pi$
$230$	−1.06145	+	0.397991i	−0.0699897	+	0.0262428i
$231$	−3.49683	−	5.61355i	−0.230075	−	0.369344i
$232$	−0.152867	+	0.264774i	−0.0100362	+	0.0173833i
$233$	−2.10216	+	6.46978i	−0.137717	+	0.423850i	−0.996003	−	0.0893227i	$-0.971530\pi$
$233$	−2.10216	+	6.46978i	−0.137717	+	0.423850i	0.858286	+	0.513172i	$0.171530\pi$
$234$	0.0193153	−	0.0765574i	0.00126268	−	0.00500471i
$235$	0.604530	−	3.63342i	0.0394352	−	0.237018i
$236$	−4.62690	+	2.06003i	−0.301186	+	0.134096i
$237$	11.7357	−	5.70360i	0.762316	−	0.370489i
$238$	−0.132334	−	0.0589189i	−0.00857795	−	0.00381915i
$239$	1.21016	−	11.5139i	0.0782787	−	0.744772i	−0.883033	−	0.469310i	$-0.844503\pi$
$239$	1.21016	−	11.5139i	0.0782787	−	0.744772i	0.961312	−	0.275462i	$-0.0888308\pi$
$240$	−10.5271	+	11.0830i	−0.679524	+	0.715407i
$241$	2.76063	+	26.2657i	0.177828	+	1.69192i	0.611815	+	0.791001i	$0.290440\pi$
$241$	2.76063	+	26.2657i	0.177828	+	1.69192i	−0.433987	+	0.900919i	$0.642894\pi$
$242$	−0.697453	+	2.14654i	−0.0448340	+	0.137985i
$243$	−15.3702	+	2.59957i	−0.985997	+	0.166763i
$244$	7.33214	−	22.5660i	0.469392	−	1.44464i
$245$	12.4069	−	7.92040i	0.792647	−	0.506015i
$246$	−1.25699	+	0.979239i	−0.0801424	+	0.0624340i
$247$	0.478253	−	0.531154i	0.0304305	−	0.0337965i
$248$	0.00165396	−	0.0157364i	0.000105027	−	0.000999263i
$249$	−21.7934	−	3.87418i	−1.38110	−	0.245516i
$250$	−0.553179	−	0.897044i	−0.0349861	−	0.0567340i
$251$	−1.93964			−0.122429			−0.0612144	−	0.998125i	$-0.519497\pi$
$251$	−1.93964			−0.122429			−0.0612144	+	0.998125i	$0.519497\pi$
$252$	3.84977	−	0.258391i	0.242513	−	0.0162771i
$253$	9.82431	+	30.2361i	0.617649	+	1.90093i
$254$	1.88890	+	0.401499i	0.118520	+	0.0251923i
$255$	8.51432	−	3.52214i	0.533187	−	0.220565i
$256$	−14.9597	+	3.17978i	−0.934980	+	0.198736i
$257$	−2.53536	−	4.39138i	−0.158152	−	0.273927i	0.776051	−	0.630671i	$-0.217220\pi$
$257$	−2.53536	−	4.39138i	−0.158152	−	0.273927i	−0.934202	+	0.356744i	$0.883887\pi$
$258$	−0.0741368	−	0.119013i	−0.00461556	−	0.00740945i
$259$	0.504869	+	4.80350i	0.0313710	+	0.298475i
$260$	−0.555708	−	1.11197i	−0.0344636	−	0.0689615i
$261$	−1.07486	+	2.18824i	−0.0665322	+	0.135449i
$262$	0.376633	−	0.273640i	0.0232685	−	0.0169055i
$263$	−0.626513	−	5.96087i	−0.0386324	−	0.367563i	−0.996710	−	0.0810533i	$-0.974172\pi$
$263$	−0.626513	−	5.96087i	−0.0386324	−	0.367563i	0.958077	−	0.286510i	$-0.0924951\pi$
$264$	−2.67192	−	2.77460i	−0.164445	−	0.170765i
$265$	−16.7393	+	6.27643i	−1.02829	+	0.385558i
$266$	−0.142393	−	0.0633975i	−0.00873069	−	0.00388715i
$267$	−15.2916	+	0.512600i	−0.935832	+	0.0313706i
$268$	11.0338	−	19.1110i	0.673994	−	1.16739i
$269$	1.33291	−	4.10227i	0.0812689	−	0.250120i	−0.902164	−	0.431394i	$-0.858022\pi$
$269$	1.33291	−	4.10227i	0.0812689	−	0.250120i	0.983433	+	0.181274i	$0.0580220\pi$
$270$	0.699407	−	0.842841i	0.0425645	−	0.0512936i
$271$	−8.40101	−	25.8556i	−0.510325	−	1.57062i	−0.791630	−	0.611000i	$-0.790767\pi$
$271$	−8.40101	−	25.8556i	−0.510325	−	1.57062i	0.281305	−	0.959618i	$-0.409233\pi$
$272$	9.18442	+	1.95221i	0.556887	+	0.118370i
$273$	−0.0865221	+	0.300155i	−0.00523655	+	0.0181662i
$274$	0.785099	+	1.35983i	0.0474296	+	0.0821504i
$275$	−25.8239	+	14.3777i	−1.55724	+	0.867007i
$276$	−18.2615	−	3.24631i	−1.09921	−	0.195405i
$277$	12.2157	−	5.43880i	0.733972	−	0.326786i	−0.00548865	−	0.999985i	$-0.501747\pi$
$277$	12.2157	−	5.43880i	0.733972	−	0.326786i	0.739461	+	0.673199i	$0.235080\pi$
$278$	0.192851	+	0.593534i	0.0115664	+	0.0355978i
$279$	0.00475591	−	0.126086i	0.000284729	−	0.00754858i
$280$	−0.387219	+	0.381232i	−0.0231408	+	0.0227830i
$281$	15.3773	+	17.0782i	0.917330	+	1.01880i	0.999754	+	0.0222013i	$0.00706746\pi$
$281$	15.3773	+	17.0782i	0.917330	+	1.01880i	−0.0824231	+	0.996597i	$0.526266\pi$
$282$	−0.173162	+	0.205782i	−0.0103116	+	0.0122541i
$283$	−11.6062	+	2.46697i	−0.689917	+	0.146646i	−0.539512	−	0.841978i	$-0.681391\pi$
$283$	−11.6062	+	2.46697i	−0.689917	+	0.146646i	−0.150405	+	0.988624i	$0.548058\pi$
$284$	−11.5698	−	5.15122i	−0.686543	−	0.305669i
$285$	9.16152	−	3.78987i	0.542681	−	0.224493i
$286$	0.142128	−	0.0632796i	0.00840422	−	0.00374180i
$287$	5.10003	−	3.70539i	0.301045	−	0.218722i
$288$	3.24530	−	0.920767i	0.191231	−	0.0542567i
$289$	9.17430	+	6.66552i	0.539665	+	0.392089i
$290$	−0.0430432	−	0.165795i	−0.00252758	−	0.00973583i
$291$	20.6415	−	10.0319i	1.21003	−	0.588079i
$292$	−24.3182	+	5.16899i	−1.42311	+	0.302492i
$293$	−7.39271	−	12.8045i	−0.431887	−	0.748050i	0.565149	−	0.824989i	$-0.308819\pi$
$293$	−7.39271	−	12.8045i	−0.431887	−	0.748050i	−0.997036	+	0.0769390i	$0.975485\pi$
$294$	−1.07416	+	0.0360074i	−0.0626460	+	0.00210000i
$295$	2.07965	−	5.29403i	0.121082	−	0.308230i
$296$	0.869299	+	2.67543i	0.0505270	+	0.155506i
$297$	−22.7401	−	20.6486i	−1.31952	−	1.19815i
$298$	−1.31254	−	0.953617i	−0.0760335	−	0.0552415i
$299$	0.750808	−	1.30044i	0.0434204	−	0.0752063i
$300$	−0.309118	−	17.2408i	−0.0178469	−	0.995397i
$301$	0.277369	+	0.480417i	0.0159873	+	0.0276908i
$302$	0.00337557	−	0.0321164i	0.000194242	−	0.00184809i
$303$	−2.85258	−	20.5050i	−0.163876	−	1.17798i
$304$	9.88255	+	2.10060i	0.566803	+	0.120478i
$305$	11.9118	+	23.8356i	0.682070	+	1.36482i
$306$	−0.665963	−	0.0954939i	−0.0380706	−	0.00545902i
$307$	6.64948			0.379506			0.189753	−	0.981832i	$-0.439231\pi$
$307$	6.64948			0.379506			0.189753	+	0.981832i	$0.439231\pi$
$308$	5.08727	+	5.64998i	0.289874	+	0.321938i
$309$	−0.581107	+	8.14659i	−0.0330580	+	0.463443i
$310$	0.00552513	+	0.00693271i	0.000313806	+	0.000393751i
$311$	−2.55826	+	24.3402i	−0.145066	+	1.38021i	0.643590	+	0.765371i	$0.277444\pi$
$311$	−2.55826	+	24.3402i	−0.145066	+	1.38021i	−0.788655	+	0.614836i	$0.789222\pi$
$312$	−0.0129449	+	0.181476i	−0.000732861	+	0.0102740i
$313$	−0.776631	−	7.38915i	−0.0438978	−	0.417660i	−0.994299	−	0.106632i	$-0.965993\pi$
$313$	−0.776631	−	7.38915i	−0.0438978	−	0.417660i	0.950401	−	0.311028i	$-0.100673\pi$
$314$	−0.774752	−	0.562891i	−0.0437218	−	0.0317658i
$315$	−2.87723	+	3.23996i	−0.162114	+	0.182551i
$316$	−12.1352	+	8.81674i	−0.682658	+	0.495980i
$317$	−1.47227	−	1.63512i	−0.0826910	−	0.0918377i	0.700379	−	0.713771i	$-0.253014\pi$
$317$	−1.47227	−	1.63512i	−0.0826910	−	0.0918377i	−0.783070	+	0.621933i	$0.786348\pi$
$318$	1.28518	+	0.228464i	0.0720693	+	0.0128116i
$319$	−4.69891	+	0.998784i	−0.263089	+	0.0559212i
$320$	9.59754	−	14.5298i	0.536519	−	0.812242i
$321$	6.69717	−	5.21734i	0.373799	−	0.291204i
$322$	−0.320314	−	0.0680847i	−0.0178504	−	0.00379421i
$323$	−4.92705	−	3.57971i	−0.274148	−	0.199181i
$324$	16.8733	−	6.03478i	0.937407	−	0.335266i
$325$	1.32082	+	0.452030i	0.0732658	+	0.0250741i
$326$	0.765214	−	1.32539i	0.0423813	−	0.0734065i
$327$	5.90781	−	20.4949i	0.326703	−	1.13337i
$328$	2.45680	−	2.72855i	0.135654	−	0.150659i
$329$	0.711974	−	0.790727i	0.0392524	−	0.0435942i
$330$	2.15734	+	0.0574884i	0.118757	+	0.00316463i
$331$	−12.0275	−	13.3579i	−0.661092	−	0.734217i	0.315593	−	0.948895i	$-0.397797\pi$
$331$	−12.0275	−	13.3579i	−0.661092	−	0.734217i	−0.976685	+	0.214678i	$0.931130\pi$
$332$	25.4459			1.39652
$333$	8.34508	+	20.8222i	0.457308	+	1.14105i
$334$	1.34208	−	0.975079i	0.0734354	−	0.0533539i
$335$	6.22745	+	23.9871i	0.340242	+	1.31056i
$336$	−4.28598	+	1.06226i	−0.233819	+	0.0579508i
$337$	−2.38823	−	1.06331i	−0.130095	−	0.0579221i	0.340657	−	0.940188i	$-0.389351\pi$
$337$	−2.38823	−	1.06331i	−0.130095	−	0.0579221i	−0.470752	+	0.882266i	$0.656017\pi$
$338$	1.11277	+	0.495435i	0.0605265	+	0.0269481i
$339$	14.6398	−	3.62838i	0.795122	−	0.197066i
$340$	−8.92806	+	5.69956i	−0.484192	+	0.309102i
$341$	0.201139	−	0.146136i	0.0108923	−	0.00791372i
$342$	−0.716585	−	0.102753i	−0.0387485	−	0.00555623i
$343$	8.77367			0.473734
$344$	0.216193	+	0.240107i	0.0116563	+	0.0129457i
$345$	17.1717	−	11.7901i	0.924491	−	0.634757i
$346$	0.901739	−	1.00148i	0.0484778	−	0.0538400i
$347$	0.794313	−	0.882174i	0.0426410	−	0.0473576i	−0.721447	−	0.692470i	$-0.756523\pi$
$347$	0.794313	−	0.882174i	0.0426410	−	0.0473576i	0.764088	+	0.645112i	$0.223189\pi$
$348$	0.776273	−	2.69298i	0.0416126	−	0.144359i
$349$	−9.82282	+	17.0136i	−0.525803	+	0.910718i	0.473745	+	0.880662i	$0.342902\pi$
$349$	−9.82282	+	17.0136i	−0.525803	+	0.910718i	−0.999548	+	0.0300560i	$0.990431\pi$
$350$	0.00474349	−	0.304406i	0.000253550	−	0.0162712i
$351$	−0.00608252	+	1.45078i	−0.000324661	+	0.0774370i
$352$	5.37759	+	3.90705i	0.286627	+	0.208246i
$353$	23.9164	+	5.08359i	1.27294	+	0.270572i	0.794347	−	0.607464i	$-0.207813\pi$
$353$	23.9164	+	5.08359i	1.27294	+	0.270572i	0.478594	+	0.878036i	$0.341147\pi$
$354$	−0.327621	+	0.255229i	−0.0174129	+	0.0135653i
$355$	13.3175	−	4.99340i	0.706817	−	0.265022i
$356$	17.2043	−	3.65689i	0.911827	−	0.193815i
$357$	2.62062	+	0.465863i	0.138698	+	0.0246561i
$358$	1.02348	+	1.13669i	0.0540927	+	0.0600760i
$359$	1.90435	−	1.38359i	0.100508	−	0.0730231i	−0.536396	−	0.843966i	$-0.680215\pi$
$359$	1.90435	−	1.38359i	0.100508	−	0.0730231i	0.636904	+	0.770943i	$0.280215\pi$
$360$	−1.24683	+	2.19423i	−0.0657135	+	0.115646i
$361$	10.0698	+	7.31610i	0.529987	+	0.385058i
$362$	−0.154232	−	1.46742i	−0.00810625	−	0.0771258i
$363$	2.95073	−	41.3665i	0.154873	−	2.17118i
$364$	0.0375360	−	0.357131i	0.00196742	−	0.0187188i
$365$	15.3883	−	23.2965i	0.805459	−	1.21939i
$366$	0.138431	−	1.94068i	0.00723590	−	0.101441i
$367$	−5.67343	−	6.30098i	−0.296151	−	0.328908i	0.576645	−	0.816995i	$-0.304362\pi$
$367$	−5.67343	−	6.30098i	−0.296151	−	0.328908i	−0.872795	+	0.488087i	$0.837695\pi$
$368$	21.2264			1.10650
$369$	18.0898	−	23.0210i	0.941718	−	1.19842i
$370$	−1.39868	−	0.726443i	−0.0727139	−	0.0377660i
$371$	−5.05143	−	1.07372i	−0.262257	−	0.0557445i
$372$	0.0199860	+	0.143664i	0.00103623	+	0.00744866i
$373$	0.718101	−	6.83227i	0.0371819	−	0.353762i	−0.960075	−	0.279743i	$-0.909751\pi$
$373$	0.718101	−	6.83227i	0.0371819	−	0.353762i	0.997257	−	0.0740189i	$-0.0235825\pi$
$374$	−0.662830	−	1.14806i	−0.0342741	−	0.0593646i
$375$	13.8312	+	13.5536i	0.714238	+	0.699903i
$376$	0.309860	−	0.536694i	0.0159798	−	0.0276779i
$377$	0.183565	+	0.133368i	0.00945408	+	0.00686879i
$378$	0.301308	−	0.0965063i	0.0154976	−	0.00496375i
$379$	−1.82815	−	5.62647i	−0.0939059	−	0.289013i	0.893061	−	0.449935i	$-0.148553\pi$
$379$	−1.82815	−	5.62647i	−0.0939059	−	0.289013i	−0.986967	+	0.160923i	$0.948553\pi$
$380$	−9.60671	+	6.13280i	−0.492814	+	0.314606i
$381$	−35.4633	+	1.18879i	−1.81684	+	0.0609035i
$382$	−0.00412680	−	0.00714783i	−0.000211146	−	0.000365715i
$383$	−17.8504	+	3.79423i	−0.912115	+	0.193876i	−0.639988	−	0.768385i	$-0.721061\pi$
$383$	−17.8504	+	3.79423i	−0.912115	+	0.193876i	−0.272128	+	0.962261i	$0.587727\pi$
$384$	−4.64698	+	2.25845i	−0.237140	+	0.115251i
$385$	−8.52268	−	0.513264i	−0.434356	−	0.0261584i
$386$	−1.45671	−	1.05836i	−0.0741447	−	0.0538693i
$387$	1.84831	+	1.79490i	0.0939547	+	0.0912399i
$388$	−21.3442	+	15.5075i	−1.08359	+	0.787272i
$389$	18.3000	−	8.14768i	0.927846	−	0.413104i	0.113536	−	0.993534i	$-0.463782\pi$
$389$	18.3000	−	8.14768i	0.927846	−	0.413104i	0.814310	+	0.580430i	$0.197116\pi$
$390$	−0.0661639	−	0.0775405i	−0.00335034	−	0.00392641i
$391$	−11.6888	−	5.20421i	−0.591130	−	0.263188i
$392$	2.42242	−	0.514901i	0.122351	−	0.0260064i
$393$	−5.50768	+	6.54520i	−0.277826	+	0.330162i
$394$	1.41487	+	1.57138i	0.0712803	+	0.0791648i
$395$	2.76472	−	16.6168i	0.139108	−	0.836084i
$396$	29.8924	+	18.7952i	1.50215	+	0.944497i
$397$	−5.88033	−	18.0978i	−0.295125	−	0.908302i	−0.983179	−	0.182643i	$-0.941535\pi$
$397$	−5.88033	−	18.0978i	−0.295125	−	0.908302i	0.688054	−	0.725659i	$-0.258465\pi$
$398$	−0.330372	+	0.147091i	−0.0165601	+	0.00737302i
$399$	2.81982	+	0.501275i	0.141168	+	0.0250951i
$400$	3.80164	+	19.3642i	0.190082	+	0.968209i
$401$	−14.9193	−	25.8410i	−0.745034	−	1.29044i	−0.950179	−	0.311705i	$-0.899100\pi$
$401$	−14.9193	−	25.8410i	−0.745034	−	1.29044i	0.205145	−	0.978732i	$-0.434233\pi$
$402$	0.501198	−	1.73871i	0.0249975	−	0.0867190i
$403$	−0.0114864	−	0.00244151i	−0.000572177	−	0.000121620i
$404$	7.35429	+	22.6342i	0.365889	+	1.12609i
$405$	−8.74831	+	18.1237i	−0.434707	+	0.900572i
$406$	0.0152907	−	0.0470599i	0.000758863	−	0.00233554i
$407$	−22.1006	+	38.2794i	−1.09549	+	1.89744i
$408$	1.54938	−	0.0519379i	0.0767060	−	0.00257131i
$409$	−29.9326	−	13.3269i	−1.48007	−	0.658971i	−0.501554	−	0.865126i	$-0.667238\pi$
$409$	−29.9326	−	13.3269i	−1.48007	−	0.658971i	−0.978519	+	0.206155i	$0.933905\pi$
$410$	0.0916514	+	2.05503i	0.00452634	+	0.101491i
$411$	−20.0131	−	20.7822i	−0.987174	−	1.02511i
$412$	−0.981404	−	9.33744i	−0.0483503	−	0.460023i
$413$	1.32927	−	0.965774i	0.0654093	−	0.0475227i
$414$	−1.51748	+	0.101851i	−0.0745800	+	0.00500571i
$415$	−20.3633	+	20.0485i	−0.999596	+	0.984140i
$416$	−0.0328174	−	0.312237i	−0.00160901	−	0.0153087i
$417$	−6.06310	−	9.73322i	−0.296911	−	0.476638i
$418$	−0.713214	−	1.23532i	−0.0348844	−	0.0604216i
$419$	5.17279	−	1.09951i	0.252707	−	0.0537146i	−0.0798161	−	0.996810i	$-0.525433\pi$
$419$	5.17279	−	1.09951i	0.252707	−	0.0537146i	0.332523	+	0.943095i	$0.392100\pi$
$420$	2.60464	−	4.24598i	0.127093	−	0.207183i
$421$	−10.9560	−	2.32876i	−0.533961	−	0.113497i	−0.0669632	−	0.997755i	$-0.521331\pi$
$421$	−10.9560	−	2.32876i	−0.533961	−	0.113497i	−0.466998	+	0.884259i	$0.654664\pi$
$422$	0.558207	+	1.71799i	0.0271731	+	0.0836302i
$423$	2.17873	−	4.43555i	0.105933	−	0.215664i
$424$	−3.00783			−0.146073
$425$	2.65416	−	11.5954i	0.128746	−	0.562461i
$426$	−1.02246	−	0.181762i	−0.0495385	−	0.00880637i
$427$	−0.804600	+	7.65526i	−0.0389373	+	0.370464i
$428$	−6.53028	+	7.25261i	−0.315653	+	0.350568i
$429$	−2.25514	+	1.75684i	−0.108879	+	0.0848211i
$430$	−0.180690	−	0.0108818i	−0.00871367	−	0.000524766i
$431$	2.72032	−	8.37228i	0.131033	−	0.403278i	−0.863919	−	0.503631i	$-0.831997\pi$
$431$	2.72032	−	8.37228i	0.131033	−	0.403278i	0.994952	+	0.100353i	$0.0319971\pi$
$432$	−17.8033	+	10.1794i	−0.856561	+	0.489759i
$433$	5.29618	−	16.3000i	0.254518	−	0.783327i	−0.739406	−	0.673260i	$-0.764894\pi$
$433$	5.29618	−	16.3000i	0.254518	−	0.783327i	0.993924	−	0.110067i	$-0.0351065\pi$
$434$	0.000267686		0.00254686i	1.28493e−5		0.000122253i
$435$	1.50054	+	2.76670i	0.0719454	+	0.132653i
$436$	−2.56300	+	24.3853i	−0.122745	+	1.16784i
$437$	−12.5773	−	5.59979i	−0.601656	−	0.267874i
$438$	−1.83353	+	0.891104i	−0.0876096	+	0.0425786i
$439$	−0.755550	+	0.336392i	−0.0360604	+	0.0160551i	−0.424688	−	0.905340i	$-0.639616\pi$
$439$	−0.755550	+	0.336392i	−0.0360604	+	0.0160551i	0.388627	+	0.921395i	$0.372949\pi$
$440$	−4.91754	+	0.739637i	−0.234435	+	0.0352608i
$441$	18.9984	−	5.39028i	0.904686	−	0.256680i
$442$	−0.0193488	+	0.0595495i	−0.000920329	+	0.00283248i
$443$	−7.57757	+	13.1247i	−0.360021	+	0.623575i	−0.987964	−	0.154685i	$-0.950564\pi$
$443$	−7.57757	+	13.1247i	−0.360021	+	0.623575i	0.627943	+	0.778259i	$0.283897\pi$
$444$	−13.6347	−	21.8880i	−0.647072	−	1.03876i
$445$	−10.8867	+	16.4815i	−0.516079	+	0.781299i
$446$	1.53091	−	1.70025i	0.0724907	−	0.0805091i
$447$	27.6245	+	11.2059i	1.30659	+	0.530023i
$448$	4.59540	−	2.04600i	0.217112	−	0.0966646i
$449$	−7.04917			−0.332671			−0.166335	−	0.986069i	$-0.553193\pi$
$449$	−7.04917			−0.332671			−0.166335	+	0.986069i	$0.553193\pi$
$450$	−0.364696	−	1.36611i	−0.0171919	−	0.0643989i
$451$	57.6907			2.71655
$452$	−15.8396	+	7.05225i	−0.745033	+	0.331710i
$453$	0.0817609	+	0.587718i	0.00384146	+	0.0276134i
$454$	−1.12039	+	1.24432i	−0.0525826	+	0.0583989i
$455$	0.251340	+	0.315372i	0.0117830	+	0.0147849i
$456$	1.66716	−	0.0558858i	0.0780718	−	0.00261709i
$457$	−3.18909	+	5.52366i	−0.149179	+	0.258386i	−0.930924	−	0.365212i	$-0.880996\pi$
$457$	−3.18909	+	5.52366i	−0.149179	+	0.258386i	0.781745	+	0.623598i	$0.214330\pi$
$458$	0.166830	−	0.513451i	0.00779548	−	0.0239920i
$459$	12.2996	−	1.24062i	0.574094	−	0.0579073i
$460$	−17.0631	+	16.7993i	−0.795573	+	0.783272i
$461$	2.88043	−	1.28245i	0.134155	−	0.0597297i	−0.338561	−	0.940944i	$-0.609940\pi$
$461$	2.88043	−	1.28245i	0.134155	−	0.0597297i	0.472716	+	0.881215i	$0.343274\pi$
$462$	0.516351	+	0.349334i	0.0240228	+	0.0162525i
$463$	22.9695	+	10.2267i	1.06748	+	0.475274i	0.863838	−	0.503770i	$-0.168054\pi$
$463$	22.9695	+	10.2267i	1.06748	+	0.475274i	0.203646	+	0.979045i	$0.434721\pi$
$464$	−0.335262	+	3.18981i	−0.0155642	+	0.148083i
$465$	−0.129185	−	0.0992222i	−0.00599083	−	0.00460132i
$466$	−0.0670286	−	0.637735i	−0.00310504	−	0.0295425i
$467$	−11.3694	+	34.9913i	−0.526111	+	1.61920i	0.235997	+	0.971754i	$0.424164\pi$
$467$	−11.3694	+	34.9913i	−0.526111	+	1.61920i	−0.762108	+	0.647449i	$0.775836\pi$
$468$	−0.285017	−	1.64326i	−0.0131749	−	0.0759595i
$469$	−2.21224	+	6.80858i	−0.102152	+	0.314391i
$470$	0.0872479	+	0.336065i	0.00402445	+	0.0155015i
$471$	16.3059	+	6.61452i	0.751335	+	0.304781i
$472$	0.640341	−	0.711170i	0.0294741	−	0.0327343i
$473$	−0.530656	+	5.04885i	−0.0243996	+	0.232146i
$474$	−0.791928	+	0.941109i	−0.0363745	+	0.0432266i
$475$	2.85592	−	12.4768i	0.131038	−	0.572476i
$476$	−3.05982			−0.140247
$477$	−23.9311	+	1.60622i	−1.09573	+	0.0735438i
$478$	0.337235	+	1.03790i	0.0154248	+	0.0474726i
$479$	−17.1732	−	3.65028i	−0.784665	−	0.166786i	−0.201878	−	0.979411i	$-0.564704\pi$
$479$	−17.1732	−	3.65028i	−0.784665	−	0.166786i	−0.582787	+	0.812625i	$0.698038\pi$
$480$	1.45564	−	4.10457i	0.0664404	−	0.187347i
$481$	2.04211	−	0.434064i	0.0931121	−	0.0197916i
$482$	−1.24476	−	2.15599i	−0.0566973	−	0.0982027i
$483$	6.01375	−	0.201591i	0.273635	−	0.00917269i
$484$	4.98335	+	47.4134i	0.226516	+	2.15515i
$485$	4.86278	−	29.2268i	0.220807	−	1.32712i
$486$	1.22391	−	0.813156i	0.0555179	−	0.0368855i
$487$	17.7188	−	12.8735i	0.802916	−	0.583352i	−0.108852	−	0.994058i	$-0.534718\pi$
$487$	17.7188	−	12.8735i	0.802916	−	0.583352i	0.911768	+	0.410706i	$0.134718\pi$
$488$	0.468623	+	4.45865i	0.0212135	+	0.201833i
$489$	−7.78897	+	27.0208i	−0.352229	+	1.22192i
$490$	−0.764733	+	1.15774i	−0.0345471	+	0.0523013i
$491$	23.6286	+	10.5201i	1.06634	+	0.474766i	0.863450	−	0.504435i	$-0.168299\pi$
$491$	23.6286	+	10.5201i	1.06634	+	0.474766i	0.202893	+	0.979201i	$0.434966\pi$
$492$	−15.8426	+	29.6955i	−0.714241	+	1.33877i
$493$	0.966684	−	1.67435i	0.0435373	−	0.0754088i
$494$	−0.0208196	+	0.0640761i	−0.000936717	+	0.00288292i
$495$	−38.7302	+	8.51077i	−1.74079	+	0.382531i
$496$	−0.0512954	−	0.157871i	−0.00230323	−	0.00708862i
$497$	4.01882	+	0.854226i	0.180269	+	0.0383173i
$498$	2.02525	−	0.501947i	0.0907537	−	0.0224928i
$499$	−11.6388	−	20.1590i	−0.521024	−	0.902440i	−0.999701	−	0.0244489i	$-0.992217\pi$
$499$	−11.6388	−	20.1590i	−0.521024	−	0.902440i	0.478677	−	0.877991i	$-0.341116\pi$
$500$	−18.3815	−	12.5574i	−0.822045	−	0.561584i
$501$	−19.6259	+	23.3229i	−0.876820	+	1.04199i
$502$	0.167029	−	0.0743663i	0.00745489	−	0.00331913i
$503$	−7.37389	−	22.6945i	−0.328786	−	1.01190i	−0.969703	−	0.244288i	$-0.921446\pi$
$503$	−7.37389	−	22.6945i	−0.328786	−	1.01190i	0.640917	−	0.767610i	$-0.278554\pi$
$504$	−0.644658	+	0.340463i	−0.0287153	+	0.0151654i
$505$	−23.7185	−	12.3189i	−1.05546	−	0.548183i
$506$	−2.00527	−	2.22708i	−0.0891451	−	0.0990056i
$507$	−22.0362	−	3.91733i	−0.978660	−	0.173975i
$508$	39.8991	−	8.48082i	1.77024	−	0.376276i
$509$	−6.28785	−	2.79953i	−0.278704	−	0.124087i	0.262625	−	0.964898i	$-0.415412\pi$
$509$	−6.28785	−	2.79953i	−0.278704	−	0.124087i	−0.541329	+	0.840811i	$0.682079\pi$
$510$	−0.598160	+	0.629747i	−0.0264870	+	0.0278856i
$511$	7.36807	−	3.28048i	0.325944	−	0.145120i
$512$	5.99293	−	4.35412i	0.264853	−	0.192427i
$513$	13.2345	−	1.33493i	0.584317	−	0.0589384i
$514$	0.386697	+	0.280951i	0.0170565	+	0.0123922i
$515$	8.14222	+	6.69914i	0.358789	+	0.295199i
$516$	−2.45310	−	1.65963i	−0.107992	−	0.0730611i
$517$	9.52463	−	2.02452i	0.418893	−	0.0890384i
$518$	−0.227644	−	0.394291i	−0.0100021	−	0.0173241i
$519$	−11.6557	+	21.8474i	−0.511627	+	0.958995i
$520$	0.181379	+	0.149232i	0.00795398	+	0.00654426i
$521$	1.59963	+	4.92314i	0.0700809	+	0.215687i	0.979963	−	0.199180i	$-0.0638280\pi$
$521$	1.59963	+	4.92314i	0.0700809	+	0.215687i	−0.909882	+	0.414867i	$0.863828\pi$
$522$	0.00866222	−	0.229648i	0.000379135	−	0.0100514i
$523$	−26.2991	−	19.1074i	−1.14998	−	0.835510i	−0.161503	−	0.986872i	$-0.551634\pi$
$523$	−26.2991	−	19.1074i	−1.14998	−	0.835510i	−0.988478	+	0.151362i	$0.951634\pi$
$524$	4.91682	−	8.51619i	0.214792	−	0.372031i
$525$	1.26097	+	5.45005i	0.0550330	+	0.237860i
$526$	0.282493	+	0.489292i	0.0123173	+	0.0213342i
$527$	−0.0104591	+	0.0995120i	−0.000455607	+	0.00433481i
$528$	−37.4461	−	15.1901i	−1.62963	−	0.661064i
$529$	−5.79534	−	1.23184i	−0.251971	−	0.0535582i
$530$	1.20084	−	1.18228i	0.0521613	−	0.0513548i
$531$	4.71494	−	6.00020i	0.204611	−	0.260387i
$532$	−3.29240			−0.142744
$533$	−1.82329	−	2.02497i	−0.0789756	−	0.0877112i
$534$	1.29717	−	0.630427i	0.0561338	−	0.0272813i
$535$	−0.488315	−	10.9491i	−0.0211117	−	0.473371i
$536$	−0.435841	+	4.14675i	−0.0188255	+	0.179112i
$537$	−23.2783	−	15.7488i	−1.00453	−	0.679612i
$538$	0.0425006	+	0.404366i	0.00183233	+	0.0174335i
$539$	31.4811	+	22.8724i	1.35599	+	0.985182i
$540$	6.25504	−	22.2730i	0.269174	−	0.958478i
$541$	9.31574	−	6.76828i	0.400515	−	0.290991i	−0.369236	−	0.929336i	$-0.620381\pi$
$541$	9.31574	−	6.76828i	0.400515	−	0.290991i	0.769751	+	0.638345i	$0.220381\pi$
$542$	1.71476	+	1.90443i	0.0736551	+	0.0818022i
$543$	9.23716	+	25.4897i	0.396404	+	1.09387i
$544$	−2.61672	+	0.556200i	−0.112191	+	0.0238469i
$545$	−17.1618	−	21.5339i	−0.735129	−	0.922411i
$546$	−0.00405728	−	0.0291647i	−0.000173635	−	0.00124813i
$547$	22.8102	+	4.84846i	0.975294	+	0.207305i	0.667879	−	0.744270i	$-0.267203\pi$
$547$	22.8102	+	4.84846i	0.975294	+	0.207305i	0.307415	+	0.951575i	$0.400536\pi$
$548$	26.8328	+	19.4952i	1.14624	+	0.832792i
$549$	6.10946	+	35.2239i	0.260745	+	1.50332i
$550$	1.67255	−	2.22821i	0.0713177	−	0.0950113i
$551$	1.04016	−	1.80162i	0.0443125	−	0.0767515i
$552$	3.40163	−	0.843075i	0.144783	−	0.0358836i
$553$	3.25610	−	3.61626i	0.138463	−	0.153779i
$554$	−0.843417	+	0.936710i	−0.0358334	+	0.0397970i
$555$	28.1566	+	6.77354i	1.19518	+	0.287521i
$556$	8.82072	+	9.79640i	0.374082	+	0.415460i
$557$	−13.9243			−0.589990			−0.294995	−	0.955499i	$-0.595318\pi$
$557$	−13.9243			−0.589990			−0.294995	+	0.955499i	$0.595318\pi$
$558$	0.00442463	+	0.0110401i	0.000187310	+	0.000467364i
$559$	0.193988	−	0.140941i	0.00820483	−	0.00596116i
$560$	−2.08431	+	5.30588i	−0.0880781	+	0.224214i
$561$	16.8963	+	17.5457i	0.713364	+	0.740779i
$562$	−1.97898	−	0.881097i	−0.0834781	−	0.0371668i
$563$	17.3991	+	7.74658i	0.733284	+	0.326479i	0.739184	−	0.673503i	$-0.235211\pi$
$563$	17.3991	+	7.74658i	0.733284	+	0.326479i	−0.00589976	+	0.999983i	$0.501878\pi$
$564$	−1.57350	+	5.45863i	−0.0662561	+	0.229850i
$565$	7.11943	−	18.1235i	0.299517	−	0.762459i
$566$	0.904869	−	0.657426i	0.0380345	−	0.0276337i
$567$	−4.94725	+	3.05306i	−0.207765	+	0.128217i
$568$	2.39297			0.100407
$569$	−11.8249	−	13.1329i	−0.495726	−	0.550559i	0.442416	−	0.896810i	$-0.354121\pi$
$569$	−11.8249	−	13.1329i	−0.495726	−	0.550559i	−0.938142	+	0.346251i	$0.887455\pi$
$570$	−0.643628	+	0.677615i	−0.0269586	+	0.0283822i
$571$	20.0655	−	22.2850i	0.839717	−	0.932600i	−0.158785	−	0.987313i	$-0.550758\pi$
$571$	20.0655	−	22.2850i	0.839717	−	0.932600i	0.998502	+	0.0547129i	$0.0174244\pi$
$572$	2.19895	−	2.44218i	0.0919427	−	0.102113i
$573$	0.105197	+	0.109240i	0.00439467	+	0.00456356i
$574$	−0.297117	+	0.514621i	−0.0124014	+	0.0214799i
$575$	0.418984	−	26.8876i	0.0174728	−	1.12129i
$576$	17.9387	−	14.9671i	0.747446	−	0.623630i
$577$	4.49517	+	3.26593i	0.187136	+	0.135962i	0.677409	−	0.735607i	$-0.263103\pi$
$577$	4.49517	+	3.26593i	0.187136	+	0.135962i	−0.490273	+	0.871569i	$0.663103\pi$
$578$	−1.04559	−	0.222247i	−0.0434909	−	0.00924427i
$579$	30.6588	+	12.4368i	1.27413	+	0.516856i
$580$	−2.25502	−	2.82951i	−0.0936345	−	0.117489i
$581$	−8.07456	+	1.71630i	−0.334989	+	0.0712041i
$582$	−1.39290	+	1.65528i	−0.0577374	+	0.0686138i
$583$	−31.6236	−	35.1216i	−1.30972	−	1.45459i
$584$	3.80036	−	2.76112i	0.157260	−	0.114256i
$585$	1.52279	+	1.09047i	0.0629595	+	0.0450854i
$586$	1.12754	+	0.819209i	0.0465784	+	0.0338412i
$587$	3.48300	+	33.1385i	0.143759	+	1.36777i	0.793941	+	0.607995i	$0.208026\pi$
$587$	3.48300	+	33.1385i	0.143759	+	1.36777i	−0.650182	+	0.759778i	$0.725307\pi$
$588$	−20.4183	+	9.92339i	−0.842038	+	0.409234i
$589$	−0.0112542	+	0.107076i	−0.000463719	+	0.00441200i
$590$	0.0238881	+	0.535623i	0.000983457	+	0.0220513i
$591$	−32.1803	−	21.7714i	−1.32372	−	0.895554i
$592$	19.7471	+	21.9313i	0.811600	+	0.901373i
$593$	−26.1795			−1.07506			−0.537532	−	0.843243i	$-0.680643\pi$
$593$	−26.1795			−1.07506			−0.537532	+	0.843243i	$0.680643\pi$
$594$	2.74991	+	0.906264i	0.112830	+	0.0371845i
$595$	2.44865	−	2.41079i	0.100385	−	0.0988327i
$596$	−33.5207	−	7.12505i	−1.37306	−	0.291854i
$597$	5.24201	−	4.08372i	0.214541	−	0.167136i
$598$	−0.0147957	+	0.140772i	−0.000605042	+	0.00575659i
$599$	−9.64381	−	16.7036i	−0.394036	−	0.682490i	0.598942	−	0.800792i	$-0.295588\pi$
$599$	−9.64381	−	16.7036i	−0.394036	−	0.682490i	−0.992978	+	0.118303i	$0.962255\pi$
$600$	1.37834	+	2.95221i	0.0562705	+	0.120523i
$601$	3.81131	−	6.60138i	0.155466	−	0.269276i	−0.777762	−	0.628559i	$-0.783645\pi$
$601$	3.81131	−	6.60138i	0.155466	−	0.269276i	0.933229	+	0.359283i	$0.116979\pi$
$602$	−0.0423046	−	0.0307361i	−0.00172421	−	0.00125271i
$603$	−1.25324	+	33.2254i	−0.0510360	+	1.35304i
$604$	−0.210790	−	0.648744i	−0.00857691	−	0.0263970i
$605$	−41.3444	−	34.0167i	−1.68089	−	1.38298i
$606$	1.03181	+	1.65640i	0.0419146	+	0.0672865i
$607$	3.78262	+	6.55168i	0.153532	+	0.265925i	0.932523	−	0.361110i	$-0.117602\pi$
$607$	3.78262	+	6.55168i	0.153532	+	0.265925i	−0.778992	+	0.627034i	$0.784269\pi$
$608$	−2.81562	+	0.598478i	−0.114188	+	0.0242715i
$609$	−0.0646905	+	0.906902i	−0.00262139	+	0.0367495i
$610$	−1.93964	−	1.59587i	−0.0785336	−	0.0646147i
$611$	−0.372084	−	0.270335i	−0.0150529	−	0.0109366i
$612$	−13.6713	+	3.87888i	−0.552631	+	0.156794i
$613$	−0.404949	+	0.294213i	−0.0163558	+	0.0118832i	−0.595933	−	0.803034i	$-0.703218\pi$
$613$	−0.404949	+	0.294213i	−0.0163558	+	0.0118832i	0.579577	+	0.814917i	$0.303218\pi$
$614$	−0.572611	+	0.254943i	−0.0231087	+	0.0102887i
$615$	−10.7184	−	36.2463i	−0.432209	−	1.46159i
$616$	−1.31233	−	0.584288i	−0.0528754	−	0.0235417i
$617$	21.6181	−	4.59508i	0.870313	−	0.184991i	0.248953	−	0.968516i	$-0.419914\pi$
$617$	21.6181	−	4.59508i	0.870313	−	0.184991i	0.621360	+	0.783525i	$0.286580\pi$
$618$	−0.262301	−	0.723813i	−0.0105513	−	0.0291160i
$619$	17.0008	+	18.8813i	0.683321	+	0.758905i	0.980629	−	0.195877i	$-0.0627552\pi$
$619$	17.0008	+	18.8813i	0.683321	+	0.758905i	−0.297307	+	0.954782i	$0.596089\pi$
$620$	0.166179	+	0.0863098i	0.00667391	+	0.00346628i
$621$	26.6140	−	8.52423i	1.06798	−	0.342066i
$622$	−0.712910	−	2.19411i	−0.0285851	−	0.0879758i
$623$	−5.21267	+	2.32083i	−0.208841	+	0.0929821i
$624$	0.650289	+	1.79445i	0.0260324	+	0.0718356i
$625$	24.6038	−	4.43334i	0.984151	−	0.177334i
$626$	0.350181	+	0.606531i	0.0139960	+	0.0242419i
$627$	18.1807	+	18.8794i	0.726066	+	0.753970i
$628$	−19.7863	−	4.20570i	−0.789558	−	0.167826i
$629$	−5.49717	−	16.9185i	−0.219186	−	0.674586i
$630$	0.123548	−	0.389319i	0.00492228	−	0.0155109i
$631$	−13.3579	+	41.1114i	−0.531770	+	1.63662i	0.218757	+	0.975779i	$0.429800\pi$
$631$	−13.3579	+	41.1114i	−0.531770	+	1.63662i	−0.750527	+	0.660840i	$0.770200\pi$
$632$	1.41710	−	2.45448i	0.0563691	−	0.0976341i
$633$	−17.5496	−	28.1728i	−0.697536	−	1.11977i
$634$	0.189474	+	0.0843593i	0.00752497	+	0.00335033i
$635$	−25.2477	+	38.2229i	−1.00193	+	1.51683i
$636$	26.7626	−	6.63296i	1.06121	−	0.263014i
$637$	−0.192117	−	1.82787i	−0.00761196	−	0.0724230i
$638$	0.366347	−	0.266167i	0.0145038	−	0.0105376i
$639$	19.0391	−	1.27788i	0.753174	−	0.0505520i
$640$	−1.09474	+	6.57976i	−0.0432736	+	0.260088i
$641$	2.74863	+	26.1515i	0.108564	+	1.03292i	0.904190	+	0.427131i	$0.140476\pi$
$641$	2.74863	+	26.1515i	0.108564	+	1.03292i	−0.795625	+	0.605789i	$0.792858\pi$
$642$	−0.376684	+	0.706056i	−0.0148665	+	0.0278658i
$643$	0.605320	+	1.04844i	0.0238715	+	0.0413466i	0.877714	−	0.479184i	$-0.159067\pi$
$643$	0.605320	+	1.04844i	0.0238715	+	0.0413466i	−0.853843	+	0.520531i	$0.825734\pi$
$644$	−6.76596	+	1.43815i	−0.266616	+	0.0566710i
$645$	3.27072	−	0.604630i	0.128784	−	0.0238073i
$646$	0.561534	+	0.119358i	0.0220933	+	0.00469607i
$647$	0.311454	+	0.958558i	0.0122445	+	0.0376848i	0.956992	−	0.290114i	$-0.0936932\pi$
$647$	0.311454	+	0.958558i	0.0122445	+	0.0376848i	−0.944748	+	0.327799i	$0.893693\pi$
$648$	−2.44875	+	2.33842i	−0.0961960	+	0.0918617i
$649$	15.0365			0.590236
$650$	−0.131072	+	0.0117145i	−0.00514105	+	0.000459482i
$651$	−0.0160321	−	0.0442400i	−0.000628346	−	0.00173390i
$652$	3.37910	−	32.1500i	0.132336	−	1.25909i
$653$	23.8737	−	26.5145i	0.934251	−	1.03759i	−0.0649606	−	0.997888i	$-0.520692\pi$
$653$	23.8737	−	26.5145i	0.934251	−	1.03759i	0.999212	−	0.0397029i	$-0.0126412\pi$
$654$	0.277035	+	1.99140i	0.0108329	+	0.0778697i
$655$	2.77506	+	10.6891i	0.108430	+	0.417656i
$656$	11.9027	−	36.6327i	0.464722	−	1.43027i
$657$	28.7621	−	23.9976i	1.12212	−	0.936236i
$658$	−0.0309940	+	0.0953897i	−0.00120827	+	0.00371868i
$659$	−1.59189	−	15.1459i	−0.0620114	−	0.589999i	−0.980768	−	0.195175i	$-0.937472\pi$
$659$	−1.59189	−	15.1459i	−0.0620114	−	0.589999i	0.918757	−	0.394823i	$-0.129194\pi$
$660$	42.1235	−	17.4253i	1.63965	−	0.678281i
$661$	−0.227402	+	2.16359i	−0.00884493	+	0.0841539i	−0.998054	−	0.0623579i	$-0.980138\pi$
$661$	−0.227402	+	2.16359i	−0.00884493	+	0.0841539i	0.989209	+	0.146512i	$0.0468046\pi$
$662$	1.54788	+	0.689161i	0.0601601	+	0.0267850i
$663$	0.0818594	−	1.14759i	0.00317916	−	0.0445689i
$664$	−4.39226	+	1.95556i	−0.170453	+	0.0758904i
$665$	2.63478	−	2.59404i	0.102172	−	0.100593i
$666$	−1.51695	−	1.47312i	−0.0587808	−	0.0570823i
$667$	1.35060	−	4.15671i	0.0522954	−	0.160949i
$668$	17.5204	−	30.3463i	0.677886	−	1.17413i
$669$	−19.7882	+	37.0910i	−0.765056	+	1.43402i
$670$	−1.45594	−	1.82686i	−0.0562480	−	0.0705778i
$671$	−47.1354	+	52.3492i	−1.81964	+	2.02092i
$672$	0.992443	−	0.773151i	0.0382843	−	0.0298249i
$673$	23.6039	−	10.5091i	0.909864	−	0.405098i	0.102216	−	0.994762i	$-0.467407\pi$
$673$	23.6039	−	10.5091i	0.909864	−	0.405098i	0.807648	+	0.589664i	$0.200740\pi$
$674$	0.246427			0.00949201
$675$	12.5430	+	22.7525i	0.482779	+	0.875742i
$676$	25.7293			0.989587
$677$	8.41574	−	3.74693i	0.323443	−	0.144006i	−0.238591	−	0.971120i	$-0.576686\pi$
$677$	8.41574	−	3.74693i	0.323443	−	0.144006i	0.562034	+	0.827114i	$0.310019\pi$
$678$	−1.12157	+	0.873746i	−0.0430737	+	0.0335560i
$679$	5.72704	−	6.36052i	0.219784	−	0.244094i
$680$	1.10307	−	1.66995i	0.0423007	−	0.0640396i
$681$	14.4819	−	27.1449i	0.554948	−	1.04020i
$682$	−0.0117179	+	0.0202961i	−0.000448703	+	0.000777177i
$683$	5.99517	−	18.4512i	0.229399	−	0.706016i	−0.768417	−	0.639950i	$-0.778955\pi$
$683$	5.99517	−	18.4512i	0.229399	−	0.706016i	0.997815	−	0.0660664i	$-0.0210449\pi$
$684$	−14.7105	+	4.17372i	−0.562472	+	0.159586i
$685$	−36.8332	+	5.54001i	−1.40732	+	0.211673i
$686$	−0.755534	+	0.336385i	−0.0288464	+	0.0128432i
$687$	−0.705813	+	9.89485i	−0.0269284	+	0.377512i
$688$	3.09646	+	1.37863i	0.118051	+	0.0525599i
$689$	−0.233333	+	2.22001i	−0.00888926	+	0.0845757i
$690$	−1.02668	+	1.67366i	−0.0390851	+	0.0637150i
$691$	−0.793047	−	7.54533i	−0.0301689	−	0.287038i	−0.999196	−	0.0400847i	$-0.987237\pi$
$691$	−0.793047	−	7.54533i	−0.0301689	−	0.287038i	0.969027	−	0.246953i	$-0.0794294\pi$
$692$	8.79642	−	27.0726i	0.334390	−	1.02915i
$693$	−10.7533	−	3.94795i	−0.408483	−	0.149970i
$694$	−0.0345784	+	0.106422i	−0.00131258	+	0.00403971i
$695$	−14.7773	−	0.889939i	−0.560536	−	0.0337573i
$696$	0.0729660	+	0.524497i	0.00276577	+	0.0198810i
$697$	−15.5360	+	17.2544i	−0.588467	+	0.653559i
$698$	0.193572	−	1.84172i	0.00732682	−	0.0697100i
$699$	4.01444	+	11.0777i	0.151840	+	0.418998i
$700$	−2.52376	−	5.91479i	−0.0953891	−	0.223558i
$701$	−9.96570			−0.376399			−0.188200	−	0.982131i	$-0.560265\pi$
$701$	−9.96570			−0.376399			−0.188200	+	0.982131i	$0.560265\pi$
$702$	−0.0550996	−	0.125165i	−0.00207960	−	0.00472406i
$703$	−5.91502	−	18.2046i	−0.223089	−	0.686598i
$704$	45.0286	+	9.57113i	1.69708	+	0.360725i
$705$	−3.04158	−	5.60806i	−0.114552	−	0.211212i
$706$	−2.25444	+	0.479195i	−0.0848468	+	0.0180348i
$707$	−3.86034	−	6.68630i	−0.145183	−	0.251464i
$708$	−4.12923	+	7.73984i	−0.155186	+	0.290881i
$709$	−2.60799	−	24.8133i	−0.0979450	−	0.931884i	−0.927592	−	0.373595i	$-0.878125\pi$
$709$	−2.60799	−	24.8133i	−0.0979450	−	0.931884i	0.829647	−	0.558289i	$-0.188542\pi$
$710$	−0.955367	+	0.940596i	−0.0358543	+	0.0352999i
$711$	9.96406	−	20.2853i	0.373681	−	0.760756i
$712$	−2.68863	+	1.95340i	−0.100761	+	0.0732069i
$713$	0.0236442	+	0.224960i	0.000885483	+	0.00842480i
$714$	−0.243533	+	0.0603581i	−0.00911398	+	0.00225885i
$715$	0.164431	+	3.68690i	0.00614936	+	0.137882i
$716$	29.5157	+	13.1412i	1.10305	+	0.491112i
$717$	−10.6024	−	17.0203i	−0.395955	−	0.635636i
$718$	−0.110943	+	0.192159i	−0.00414037	+	0.00717132i
$719$	−0.0734464	+	0.226045i	−0.00273909	+	0.00843004i	−0.952417	−	0.304799i	$-0.901411\pi$
$719$	−0.0734464	+	0.226045i	−0.00273909	+	0.00843004i	0.949678	+	0.313229i	$0.101411\pi$
$720$	−2.58658	+	26.3491i	−0.0963960	+	0.981971i
$721$	0.941224	+	2.89679i	0.0350530	+	0.107882i
$722$	−1.14765	−	0.243940i	−0.0427110	−	0.00907849i
$723$	31.7305	+	32.9499i	1.18007	+	1.22542i
$724$	−15.5834	−	26.9913i	−0.579154	−	1.00312i
$725$	4.03393	+	0.487642i	0.149816	+	0.0181106i
$726$	1.33191	+	3.67536i	0.0494317	+	0.136405i
$727$	−1.81932	+	0.810013i	−0.0674748	+	0.0300417i	−0.440197	−	0.897901i	$-0.645091\pi$
$727$	−1.81932	+	0.810013i	−0.0674748	+	0.0300417i	0.372722	+	0.927943i	$0.378425\pi$
$728$	0.0209670	+	0.0645297i	0.000777088	+	0.00239163i
$729$	−18.2341	+	19.9127i	−0.675338	+	0.737508i
$730$	−0.431947	+	2.59614i	−0.0159871	+	0.0960874i
$731$	−1.36713	−	1.51836i	−0.0505653	−	0.0561584i
$732$	−14.0020	−	38.6381i	−0.517528	−	1.42810i
$733$	46.8327	−	9.95460i	1.72981	−	0.367682i	0.767796	−	0.640695i	$-0.221354\pi$
$733$	46.8327	−	9.95460i	1.72981	−	0.367682i	0.962010	+	0.273013i	$0.0880203\pi$
$734$	0.730142	+	0.325080i	0.0269500	+	0.0119989i
$735$	8.52147	−	24.0286i	0.314319	−	0.886310i
$736$	−5.52474	+	2.45977i	−0.203644	+	0.0906684i
$737$	−53.0028	+	38.5088i	−1.95238	+	1.41849i
$738$	−0.675150	+	2.67599i	−0.0248526	+	0.0985046i
$739$	−18.8030	−	13.6612i	−0.691681	−	0.502536i	0.185531	−	0.982638i	$-0.440599\pi$
$739$	−18.8030	−	13.6612i	−0.691681	−	0.502536i	−0.877212	+	0.480103i	$0.840599\pi$
$740$	−33.2312	−	2.00129i	−1.22160	−	0.0735689i
$741$	0.0880818	−	1.23483i	0.00323576	−	0.0453625i
$742$	0.476164	−	0.101212i	0.0174805	−	0.00371560i
$743$	−19.5580	−	33.8755i	−0.717515	−	1.24277i	−0.961982	−	0.273114i	$-0.911946\pi$
$743$	−19.5580	−	33.8755i	−0.717515	−	1.24277i	0.244467	−	0.969658i	$-0.421387\pi$
$744$	−0.0144907	−	0.0232622i	−0.000531254	−	0.000852834i
$745$	32.4390	−	20.7087i	1.18847	−	0.758706i
$746$	0.200113	+	0.615885i	0.00732666	+	0.0225491i
$747$	−33.9016	+	17.9044i	−1.24040	+	0.655090i
$748$	−22.6540	−	16.4591i	−0.828311	−	0.601803i
$749$	1.58303	−	2.74188i	0.0578425	−	0.100186i
$750$	−1.71070	−	0.636857i	−0.0624660	−	0.0232547i
$751$	13.9704	+	24.1975i	0.509788	+	0.882979i	0.999936	+	0.0113398i	$0.00360966\pi$
$751$	13.9704	+	24.1975i	0.509788	+	0.882979i	−0.490147	+	0.871640i	$0.663057\pi$
$752$	0.679572	−	6.46570i	0.0247814	−	0.235780i
$753$	−2.65025	+	2.06464i	−0.0965805	+	0.0752398i
$754$	−0.0209208	−	0.00444686i	−0.000761892	−	0.000161945i
$755$	0.679823	+	0.353085i	0.0247413	+	0.0128501i
$756$	4.98514	−	4.45094i	0.181308	−	0.161879i
$757$	6.33909			0.230398			0.115199	−	0.993342i	$-0.463249\pi$
$757$	6.33909			0.230398			0.115199	+	0.993342i	$0.463249\pi$
$758$	0.373150	+	0.414425i	0.0135534	+	0.0150526i
$759$	45.6083	+	30.8560i	1.65548	+	1.12000i
$760$	1.18692	−	1.79688i	0.0430539	−	0.0651799i
$761$	2.49946	−	23.7808i	0.0906053	−	0.862052i	−0.850962	−	0.525227i	$-0.823980\pi$
$761$	2.49946	−	23.7808i	0.0906053	−	0.862052i	0.941567	−	0.336825i	$-0.109353\pi$
$762$	3.00830	−	1.46205i	0.108979	−	0.0529643i
$763$	−0.831467	−	7.91088i	−0.0301011	−	0.286393i
$764$	−0.141044	−	0.102475i	−0.00510280	−	0.00370740i
$765$	7.88452	−	13.8756i	0.285065	−	0.501673i
$766$	1.39170	−	1.01113i	0.0502841	−	0.0365335i
$767$	−0.475224	−	0.527790i	−0.0171593	−	0.0190574i
$768$	−17.0556	+	20.2685i	−0.615443	+	0.731378i
$769$	−24.8922	+	5.29100i	−0.897636	+	0.190798i	−0.633551	−	0.773701i	$-0.718403\pi$
$769$	−24.8922	+	5.29100i	−0.897636	+	0.190798i	−0.264085	+	0.964499i	$0.585070\pi$
$770$	0.753599	−	0.282563i	0.0271578	−	0.0101829i
$771$	−8.13863	−	3.30146i	−0.293105	−	0.118899i
$772$	−37.2027	−	7.90768i	−1.33895	−	0.284603i
$773$	31.6647	+	23.0058i	1.13890	+	0.827460i	0.986966	−	0.160931i	$-0.0514496\pi$
$773$	31.6647	+	23.0058i	1.13890	+	0.827460i	0.151935	+	0.988391i	$0.451450\pi$
$774$	−0.227982	−	0.0837009i	−0.00819463	−	0.00300857i
$775$	−0.200989	+	0.0618601i	−0.00721973	+	0.00222208i
$776$	2.49248	−	4.31711i	0.0894749	−	0.154975i
$777$	5.80292	+	6.02593i	0.208178	+	0.216179i
$778$	−1.26350	+	1.40325i	−0.0452985	+	0.0503091i
$779$	−16.7169	+	18.5660i	−0.598945	+	0.665196i
$780$	−1.94293	−	0.927834i	−0.0695682	−	0.0332218i
$781$	25.1591	+	27.9421i	0.900265	+	0.999845i
$782$	1.20610			0.0431301
$783$	0.860625	+	4.13407i	0.0307562	+	0.147740i
$784$	21.0188	−	15.2710i	0.750670	−	0.545394i
$785$	19.1478	−	12.2237i	0.683413	−	0.436282i
$786$	0.223342	−	0.774798i	0.00796635	−	0.0276361i
$787$	34.4527	+	15.3393i	1.22811	+	0.546789i	0.915202	−	0.402996i	$-0.132031\pi$
$787$	34.4527	+	15.3393i	1.22811	+	0.546789i	0.312905	+	0.949784i	$0.398698\pi$
$788$	40.8029	+	18.1666i	1.45354	+	0.647159i
$789$	−7.20108	−	7.47783i	−0.256365	−	0.266218i
$790$	0.399014	+	1.53694i	0.0141963	+	0.0546818i
$791$	4.55060	−	3.30621i	0.161801	−	0.117555i
$792$	−6.60423	−	0.946996i	−0.234671	−	0.0336500i
$793$	3.32718			0.118152
$794$	1.20025	+	1.33301i	0.0425953	+	0.0473069i
$795$	−16.1910	+	26.3940i	−0.574237	+	0.936099i
$796$	−5.11138	+	5.67677i	−0.181168	+	0.201208i
$797$	−32.4877	+	36.0812i	−1.15077	+	1.27806i	−0.196039	+	0.980596i	$0.562808\pi$
$797$	−32.4877	+	36.0812i	−1.15077	+	1.27806i	−0.954733	+	0.297465i	$0.903859\pi$
$798$	−0.262044	+	0.0649461i	−0.00927627	+	0.00229907i
$799$	−1.95946	+	3.39388i	−0.0693206	+	0.120067i
$800$	−3.23345	−	4.59950i	−0.114320	−	0.162617i
$801$	−20.3483	+	16.9775i	−0.718971	+	0.599872i
$802$	2.27551	+	1.65325i	0.0803509	+	0.0583784i
$803$	72.1969	+	15.3459i	2.54777	+	0.541546i
$804$	−5.26658	−	37.8575i	−0.185738	−	1.33513i
$805$	4.28143	−	6.48170i	0.150900	−	0.228450i
$806$	0.00108274		0.000230144i	3.81380e−5		8.10648e-6i
$807$	−2.54542	−	7.02401i	−0.0896030	−	0.247257i
$808$	−3.00891	−	3.34173i	−0.105853	−	0.117562i
$809$	28.4141	−	20.6440i	0.998986	−	0.725806i	0.0371156	−	0.999311i	$-0.488183\pi$
$809$	28.4141	−	20.6440i	0.998986	−	0.725806i	0.961871	+	0.273505i	$0.0881830\pi$
$810$	0.0584834	−	1.89611i	0.00205490	−	0.0666225i
$811$	13.0544	+	9.48461i	0.458404	+	0.333050i	0.792905	−	0.609346i	$-0.208568\pi$
$811$	13.0544	+	9.48461i	0.458404	+	0.333050i	−0.334501	+	0.942395i	$0.608568\pi$
$812$	−0.109253	−	1.03947i	−0.00383402	−	0.0364783i
$813$	−39.0008	−	26.3858i	−1.36782	−	0.925389i
$814$	0.435523	−	4.14373i	0.0152651	−	0.145238i
$815$	22.6264	+	28.3907i	0.792568	+	0.994483i
$816$	14.6273	−	7.10891i	0.512057	−	0.248862i
$817$	−1.47105	−	1.63377i	−0.0514656	−	0.0571584i
$818$	3.08857			0.107989
$819$	0.201278	+	0.502219i	0.00703324	+	0.0175489i
$820$	19.4243	+	38.8679i	0.678325	+	1.35733i
$821$	−48.6168	−	10.3338i	−1.69674	−	0.360653i	−0.744881	−	0.667197i	$-0.767494\pi$
$821$	−48.6168	−	10.3338i	−1.69674	−	0.360653i	−0.951856	+	0.306545i	$0.900827\pi$
$822$	2.52020	+	1.02233i	0.0879021	+	0.0356577i
$823$	−0.425552	+	4.04886i	−0.0148338	+	0.141134i	−0.999432	−	0.0336979i	$-0.989272\pi$
$823$	−0.425552	+	4.04886i	−0.0148338	+	0.141134i	0.984598	+	0.174832i	$0.0559383\pi$
$824$	0.887000	+	1.53633i	0.0309001	+	0.0535206i
$825$	−19.9805	+	47.1333i	−0.695633	+	1.64097i
$826$	−0.0774407	+	0.134131i	−0.00269451	+	0.00466702i
$827$	−28.2790	−	20.5459i	−0.983358	−	0.714451i	−0.0249015	−	0.999690i	$-0.507927\pi$
$827$	−28.2790	−	20.5459i	−0.983358	−	0.714451i	−0.958457	+	0.285238i	$0.907927\pi$
$828$	−28.4074	+	15.0028i	−0.987224	+	0.521382i
$829$	−3.28419	−	10.1077i	−0.114065	−	0.351055i	0.877686	−	0.479236i	$-0.159086\pi$
$829$	−3.28419	−	10.1077i	−0.114065	−	0.351055i	−0.991751	+	0.128181i	$0.959086\pi$
$830$	0.984896	−	2.50718i	0.0341863	−	0.0870256i
$831$	10.9018	−	20.4344i	0.378180	−	0.708861i
$832$	−1.08716	−	1.88302i	−0.0376905	−	0.0652819i
$833$	−15.3186	+	3.25606i	−0.530757	+	0.112816i
$834$	0.895291	+	0.605703i	0.0310014	+	0.0209738i
$835$	9.88854	+	38.0890i	0.342207	+	1.31813i
$836$	−24.3759	−	17.7102i	−0.843060	−	0.612519i
$837$	−0.127714	−	0.177342i	−0.00441444	−	0.00612984i
$838$	−0.403293	+	0.293009i	−0.0139315	+	0.0101218i
$839$	10.6973	−	4.76273i	0.369311	−	0.164428i	−0.213686	−	0.976902i	$-0.568547\pi$
$839$	10.6973	−	4.76273i	0.369311	−	0.164428i	0.582996	+	0.812475i	$0.301880\pi$
$840$	−0.123280	+	0.933077i	−0.00425357	+	0.0321942i
$841$	−25.8895	−	11.5267i	−0.892741	−	0.397474i
$842$	1.03274	−	0.219517i	0.0355907	−	0.00756504i
$843$	39.1898	+	6.96670i	1.34977	+	0.239946i
$844$	25.5316	+	28.3557i	0.878834	+	0.976044i
$845$	−20.5901	+	20.2718i	−0.708321	+	0.697369i
$846$	−0.0175582	+	0.465494i	−0.000603664	+	0.0160040i
$847$	−4.77932	−	14.7092i	−0.164219	−	0.505415i
$848$	−28.8263	+	12.8343i	−0.989898	+	0.440731i
$849$	−13.2323	+	15.7250i	−0.454132	+	0.539680i
$850$	0.216012	+	1.10029i	0.00740916	+	0.0377395i
$851$	−20.1074	−	34.8270i	−0.689273	−	1.19386i
$852$	−21.2918	+	5.27705i	−0.729445	+	0.180789i
$853$	−1.96066	−	0.416752i	−0.0671318	−	0.0142693i	0.174223	−	0.984706i	$-0.444259\pi$
$853$	−1.96066	−	0.416752i	−0.0671318	−	0.0142693i	−0.241355	+	0.970437i	$0.577592\pi$
$854$	−0.224218	−	0.690071i	−0.00767258	−	0.0236138i
$855$	8.48384	−	14.9303i	0.290141	−	0.510606i
$856$	0.569828	−	1.75375i	0.0194763	−	0.0599419i
$857$	9.33777	−	16.1735i	0.318972	−	0.552476i	−0.661302	−	0.750120i	$-0.729996\pi$
$857$	9.33777	−	16.1735i	0.318972	−	0.552476i	0.980274	+	0.197644i	$0.0633290\pi$
$858$	0.126841	−	0.237751i	0.00433028	−	0.00811669i
$859$	−20.7544	−	9.24045i	−0.708131	−	0.315280i	0.0208803	−	0.999782i	$-0.493353\pi$
$859$	−20.7544	−	9.24045i	−0.708131	−	0.315280i	−0.729011	+	0.684502i	$0.760020\pi$
$860$	−3.58023	+	1.34241i	−0.122085	+	0.0457759i
$861$	3.02430	−	10.4916i	0.103068	−	0.357554i
$862$	0.0867390	+	0.825266i	0.00295434	+	0.0281087i
$863$	−29.8923	+	21.7180i	−1.01754	+	0.739290i	−0.965778	−	0.259370i	$-0.916485\pi$
$863$	−29.8923	+	21.7180i	−1.01754	+	0.739290i	−0.0517667	+	0.998659i	$0.516485\pi$
$864$	3.45415	−	4.71256i	0.117513	−	0.160325i
$865$	14.2907	+	28.5957i	0.485899	+	0.972283i
$866$	0.168872	+	1.60671i	0.00573850	+	0.0545982i
$867$	19.6305	−	0.658047i	0.666688	−	0.0223485i
$868$	0.0270467	+	0.0468463i	0.000918025	+	0.00159007i
$869$	43.5594	−	9.25883i	1.47765	−	0.314084i
$870$	−0.235293	−	0.180719i	−0.00797718	−	0.00612696i
$871$	3.02681	+	0.643369i	0.102560	+	0.0217997i
$872$	−1.43165	−	4.40616i	−0.0484817	−	0.149211i
$873$	17.5254	−	35.6790i	0.593146	−	1.20755i
$874$	1.29778			0.0438981
$875$	6.67985	+	2.74494i	0.225820	+	0.0927958i
$876$	−27.7253	+	32.9481i	−0.936752	+	1.11321i
$877$	−5.82703	+	55.4405i	−0.196765	+	1.87209i	0.237612	+	0.971360i	$0.423635\pi$
$877$	−5.82703	+	55.4405i	−0.196765	+	1.87209i	−0.434376	+	0.900731i	$0.643031\pi$
$878$	0.0521658	−	0.0579360i	0.00176051	−	0.00195525i
$879$	−23.7309	−	9.62651i	−0.800424	−	0.324694i
$880$	−43.9724	+	28.0714i	−1.48231	+	0.946287i
$881$	−11.7219	+	36.0764i	−0.394922	+	1.21544i	0.534101	+	0.845421i	$0.320650\pi$
$881$	−11.7219	+	36.0764i	−0.394922	+	1.21544i	−0.929023	+	0.370023i	$0.879350\pi$
$882$	−1.42936	+	1.19258i	−0.0481290	+	0.0401563i
$883$	3.31780	−	10.2111i	0.111653	−	0.343632i	−0.879581	−	0.475748i	$-0.842177\pi$
$883$	3.31780	−	10.2111i	0.111653	−	0.343632i	0.991234	+	0.132116i	$0.0421773\pi$
$884$	0.138249	+	1.31535i	0.00464980	+	0.0442399i
$885$	−2.79366	−	9.44725i	−0.0939079	−	0.317566i
$886$	0.149326	−	1.42075i	0.00501672	−	0.0477309i
$887$	18.3849	+	8.18548i	0.617304	+	0.274841i	0.691471	−	0.722404i	$-0.256963\pi$
$887$	18.3849	+	8.18548i	0.617304	+	0.274841i	−0.0741668	+	0.997246i	$0.523630\pi$
$888$	4.03563	+	2.73028i	0.135427	+	0.0916223i
$889$	−12.0889	+	5.38232i	−0.405448	+	0.180517i
$890$	0.305589	−	1.83668i	0.0102434	−	0.0615658i
$891$	−53.0507	−	4.00779i	−1.77726	−	0.134266i
$892$	14.9340	−	45.9620i	0.500026	−	1.53892i
$893$	−2.10840	+	3.65186i	−0.0705549	+	0.122205i
$894$	−2.80848	+	0.0941449i	−0.0939298	+	0.00314868i
$895$	−33.9741	+	12.7386i	−1.13563	+	0.425806i
$896$	−1.28931	+	1.43193i	−0.0430730	+	0.0478374i
$897$	−0.358372	−	2.57607i	−0.0119657	−	0.0860124i
$898$	0.607030	−	0.270267i	0.0202569	−	0.00901893i
$899$	−0.0341793			−0.00113994
$900$	−18.7743	−	23.2281i	−0.625810	−	0.774271i
$901$	19.0205			0.633666
$902$	−4.96796	+	2.21188i	−0.165415	+	0.0736475i
$903$	0.890365	+	0.361179i	0.0296295	+	0.0120193i
$904$	2.19213	−	2.43460i	0.0729090	−	0.0809737i
$905$	33.7369	+	9.32208i	1.12145	+	0.309876i
$906$	−0.0295740	−	0.0474758i	−0.000982531	−	0.00157728i
$907$	4.60700	−	7.97957i	0.152973	−	0.264957i	−0.779346	−	0.626594i	$-0.784449\pi$
$907$	4.60700	−	7.97957i	0.152973	−	0.264957i	0.932319	+	0.361637i	$0.117782\pi$
$908$	−10.9294	+	33.6371i	−0.362704	+	1.11629i
$909$	−25.7242	−	24.9809i	−0.853218	−	0.828564i
$910$	−0.0337353	−	0.0175214i	−0.00111831	−	0.000580828i
$911$	−18.4111	+	8.19714i	−0.609986	+	0.271583i	−0.688393	−	0.725338i	$-0.741683\pi$
$911$	−18.4111	+	8.19714i	−0.609986	+	0.271583i	0.0784067	+	0.996921i	$0.475017\pi$
$912$	15.7391	−	7.64928i	0.521175	−	0.253293i
$913$	−69.0137	−	30.7269i	−2.28402	−	1.01691i
$914$	0.0628453	−	0.597933i	0.00207874	−	0.0197779i
$915$	41.6476	+	19.8885i	1.37683	+	0.657494i
$916$	−1.19201	−	11.3413i	−0.0393853	−	0.374726i
$917$	−0.985812	+	3.03402i	−0.0325544	+	0.100192i
$918$	−1.01160	+	0.578404i	−0.0333876	+	0.0190902i
$919$	−7.88600	+	24.2706i	−0.260135	+	0.800613i	0.732639	+	0.680617i	$0.238288\pi$
$919$	−7.88600	+	24.2706i	−0.260135	+	0.800613i	−0.992774	+	0.119996i	$0.961712\pi$
$920$	1.65424	−	4.21109i	0.0545387	−	0.138836i
$921$	9.08560	−	7.07802i	0.299381	−	0.233229i
$922$	−0.198875	+	0.220873i	−0.00654960	+	0.00727407i
$923$	0.185635	−	1.76620i	0.00611024	−	0.0581350i
$924$	12.9652	+	2.30480i	0.426523	+	0.0758223i
$925$	28.1704	−	24.5808i	0.926236	−	0.808213i
$926$	−2.37008			−0.0778858
$927$	7.87762	+	11.7498i	0.258735	+	0.385913i
$928$	−0.282382	−	0.869083i	−0.00926965	−	0.0285290i
$929$	3.87324	+	0.823283i	0.127077	+	0.0270110i	0.271011	−	0.962576i	$-0.412642\pi$
$929$	3.87324	+	0.823283i	0.127077	+	0.0270110i	−0.143934	+	0.989587i	$0.545975\pi$
$930$	0.0149288	+	0.00359139i	0.000489536	+	0.000117766i
$931$	−16.4830	+	3.50357i	−0.540208	+	0.114825i
$932$	−6.77251	−	11.7303i	−0.221841	−	0.384240i
$933$	22.4134	+	35.9807i	0.733781	+	1.17796i
$934$	−0.362519	−	3.44913i	−0.0118620	−	0.112859i
$935$	31.0969	−	4.67722i	1.01698	−	0.152962i
$936$	0.175484	+	0.261741i	0.00573588	+	0.00855528i
$937$	21.4103	−	15.5555i	0.699445	−	0.508176i	−0.180307	−	0.983610i	$-0.557709\pi$
$937$	21.4103	−	15.5555i	0.699445	−	0.508176i	0.879751	+	0.475434i	$0.157709\pi$
$938$	−0.0705387	−	0.671131i	−0.00230317	−	0.0219132i
$939$	−8.92653	−	9.26958i	−0.291306	−	0.302501i
$940$	4.57089	+	5.73537i	0.149086	+	0.187067i
$941$	−12.6770	−	5.64415i	−0.413257	−	0.183994i	0.189567	−	0.981868i	$-0.439291\pi$
$941$	−12.6770	−	5.64415i	−0.413257	−	0.183994i	−0.602825	+	0.797874i	$0.705958\pi$
$942$	−1.65776	+	0.0555708i	−0.0540128	+	0.00181060i
$943$	−26.2438	+	45.4556i	−0.854616	+	1.48024i
$944$	3.10233	−	9.54798i	0.100972	−	0.310760i
$945$	−0.482573	+	7.48963i	−0.0156981	+	0.243638i
$946$	−0.147878	−	0.455121i	−0.00480792	−	0.0147973i
$947$	39.1728	+	8.32644i	1.27295	+	0.270573i	0.794349	−	0.607462i	$-0.207812\pi$
$947$	39.1728	+	8.32644i	1.27295	+	0.270573i	0.478597	+	0.878035i	$0.341146\pi$
$948$	−7.19613	+	24.9642i	−0.233720	+	0.810799i
$949$	−1.74311	−	3.01915i	−0.0565836	−	0.0980057i
$950$	0.232432	+	1.18392i	0.00754109	+	0.0384115i
$951$	−3.75216	−	0.667016i	−0.121672	−	0.0216295i
$952$	0.528161	−	0.235152i	0.0171178	−	0.00762133i
$953$	−0.571072	−	1.75758i	−0.0184988	−	0.0569336i	0.941381	−	0.337345i	$-0.109529\pi$
$953$	−0.571072	−	1.75758i	−0.0184988	−	0.0569336i	−0.959880	+	0.280412i	$0.909529\pi$
$954$	1.99921	−	1.05584i	0.0647268	−	0.0341842i
$955$	0.193610	−	0.0291205i	0.00626508	−	0.000942318i
$956$	15.4246	+	17.1308i	0.498869	+	0.554050i
$957$	−5.35727	+	6.36645i	−0.173176	+	0.205798i
$958$	1.61880	−	0.344087i	0.0523012	−	0.0111170i
$959$	−9.82960	−	4.37642i	−0.317414	−	0.141322i
$960$	−2.35252	−	30.0691i	−0.0759274	−	0.970476i
$961$	−28.3183	+	12.6081i	−0.913493	+	0.406713i
$962$	−0.159211	+	0.115674i	−0.00513318	+	0.00372948i
$963$	3.59717	−	14.2576i	0.115917	−	0.459444i
$964$	−42.5430	−	30.9093i	−1.37022	−	0.995521i
$965$	36.0022	−	22.9833i	1.15895	−	0.739859i
$966$	−0.510137	+	0.247929i	−0.0164134	+	0.00797698i
$967$	51.0902	−	10.8596i	1.64295	−	0.349220i	0.708609	−	0.705601i	$-0.249323\pi$
$967$	51.0902	−	10.8596i	1.64295	−	0.349220i	0.934340	+	0.356382i	$0.115990\pi$
$968$	−4.50399	−	7.80113i	−0.144764	−	0.250738i
$969$	−10.5426	+	0.353404i	−0.338676	+	0.0113530i
$970$	0.701813	+	2.70327i	0.0225339	+	0.0867968i
$971$	10.3029	+	31.7090i	0.330635	+	1.01759i	0.968832	+	0.247718i	$0.0796806\pi$
$971$	10.3029	+	31.7090i	0.330635	+	1.01759i	−0.638197	+	0.769873i	$0.720319\pi$
$972$	16.6314	−	26.2065i	0.533452	−	0.840573i
$973$	−3.45978	−	2.51367i	−0.110915	−	0.0805847i
$974$	−1.03226	+	1.78793i	−0.0330757	+	0.0572889i
$975$	2.28588	−	0.788305i	0.0732068	−	0.0252460i
$976$	23.5160	+	40.7309i	0.752729	+	1.30376i
$977$	−2.77040	+	26.3586i	−0.0886329	+	0.843285i	0.856401	+	0.516312i	$0.172695\pi$
$977$	−2.77040	+	26.3586i	−0.0886329	+	0.843285i	−0.945033	+	0.326974i	$0.893971\pi$
$978$	−0.365248	−	2.62549i	−0.0116793	−	0.0839540i
$979$	−51.0770	−	10.8568i	−1.63243	−	0.346983i
$980$	−4.81019	+	28.9108i	−0.153656	+	0.923521i
$981$	−13.7435	−	34.2920i	−0.438796	−	1.09486i
$982$	−2.43809			−0.0778026
$983$	−4.21672	−	4.68314i	−0.134493	−	0.149369i	0.672136	−	0.740428i	$-0.265377\pi$
$983$	−4.21672	−	4.68314i	−0.134493	−	0.149369i	−0.806629	+	0.591058i	$0.798710\pi$
$984$	0.452477	−	6.34332i	0.0144244	−	0.202218i
$985$	−46.9662	+	17.6100i	−1.49647	+	0.561103i
$986$	−0.0190498	+	0.181247i	−0.000606671	+	0.00577209i
$987$	0.131127	−	1.83828i	0.00417381	−	0.0585131i
$988$	0.148757	+	1.41533i	0.00473260	+	0.0450277i
$989$	−3.73669	−	2.71486i	−0.118820	−	0.0863276i
$990$	3.00890	−	2.21782i	0.0956291	−	0.0704871i
$991$	−28.4252	+	20.6521i	−0.902956	+	0.656036i	−0.939224	−	0.343306i	$-0.888453\pi$
$991$	−28.4252	+	20.6521i	−0.902956	+	0.656036i	0.0362673	+	0.999342i	$0.488453\pi$
$992$	0.0316455	+	0.0351459i	0.00100475	+	0.00111588i
$993$	−30.6527	−	5.44909i	−0.972736	−	0.172922i
$994$	−0.378827	+	0.0805221i	−0.0120157	+	0.00255401i
$995$	−0.382214	−	8.57008i	−0.0121170	−	0.271690i
$996$	34.7683	−	27.0858i	1.10168	−	0.858247i
$997$	4.59624	+	0.976961i	0.145564	+	0.0309407i	0.280118	−	0.959966i	$-0.409627\pi$
$997$	4.59624	+	0.976961i	0.145564	+	0.0309407i	−0.134553	+	0.990906i	$0.542960\pi$
$998$	1.77516	+	1.28973i	0.0561918	+	0.0408257i
$999$	33.5666	+	19.5678i	1.06200	+	0.619096i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.16.14	✓	224
3.2	odd	2		675.2.r.a.316.15		224
9.4	even	3	inner	225.2.q.a.166.15	yes	224
9.5	odd	6		675.2.r.a.91.14		224
25.11	even	5	inner	225.2.q.a.61.15	yes	224
75.11	odd	10		675.2.r.a.586.14		224
225.86	odd	30		675.2.r.a.361.15		224
225.211	even	15	inner	225.2.q.a.211.14	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.16.14	✓	224	1.1	even	1	trivial
225.2.q.a.61.15	yes	224	25.11	even	5	inner
225.2.q.a.166.15	yes	224	9.4	even	3	inner
225.2.q.a.211.14	yes	224	225.211	even	15	inner
675.2.r.a.91.14		224	9.5	odd	6
675.2.r.a.316.15		224	3.2	odd	2
675.2.r.a.361.15		224	225.86	odd	30
675.2.r.a.586.14		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)

\(f(q)\)	\(=\)	\(q+(-0.0861137 + 0.0383403i) q^{2} +(1.36636 - 1.06445i) q^{3} +(-1.33232 + 1.47969i) q^{4} +(-0.0996266 - 2.23385i) q^{5} +(-0.0768514 + 0.144050i) q^{6} +(0.322971 - 0.559402i) q^{7} +(0.116257 - 0.357802i) q^{8} +(0.733899 - 2.90885i) q^{9} +O(q^{10})\)	\(q+(-0.0861137 + 0.0383403i) q^{2} +(1.36636 - 1.06445i) q^{3} +(-1.33232 + 1.47969i) q^{4} +(-0.0996266 - 2.23385i) q^{5} +(-0.0768514 + 0.144050i) q^{6} +(0.322971 - 0.559402i) q^{7} +(0.116257 - 0.357802i) q^{8} +(0.733899 - 2.90885i) q^{9} +(0.0942256 + 0.188545i) q^{10} +(5.40026 - 2.40435i) q^{11} +(-0.245378 + 3.43997i) q^{12} +(-0.255067 - 0.113563i) q^{13} +(-0.00636459 + 0.0605550i) q^{14} +(-2.51394 - 2.94620i) q^{15} +(-0.412549 - 3.92514i) q^{16} +(-0.735171 + 2.26262i) q^{17} +(0.0483273 + 0.278630i) q^{18} +(-0.791053 + 2.43461i) q^{19} +(3.43813 + 2.82877i) q^{20} +(-0.154159 - 1.10813i) q^{21} +(-0.372853 + 0.414095i) q^{22} +(-0.562173 + 5.34872i) q^{23} +(-0.222013 - 0.612637i) q^{24} +(-4.98015 + 0.445101i) q^{25} +0.0263188 q^{26} +(-2.09355 - 4.75574i) q^{27} +(0.397440 + 1.22320i) q^{28} +(-0.794901 - 0.168961i) q^{29} +(0.329443 + 0.157323i) q^{30} +(0.0411395 - 0.00874448i) q^{31} +(0.562233 + 0.973816i) q^{32} +(4.81941 - 9.03351i) q^{33} +(-0.0234414 - 0.223030i) q^{34} +(-1.28180 - 0.665736i) q^{35} +(3.32640 + 4.96144i) q^{36} +(-6.04934 + 4.39510i) q^{37} +(-0.0252232 - 0.239983i) q^{38} +(-0.469396 + 0.116337i) q^{39} +(-0.810857 - 0.224054i) q^{40} +(8.91562 + 3.96949i) q^{41} +(0.0557613 + 0.0895149i) q^{42} +(-0.429402 + 0.743746i) q^{43} +(-3.63716 + 11.1940i) q^{44} +(-6.57104 - 1.34962i) q^{45} +(-0.156661 - 0.482152i) q^{46} +(1.61125 + 0.342483i) q^{47} +(-4.74181 - 4.92404i) q^{48} +(3.29138 + 5.70084i) q^{49} +(0.411794 - 0.229270i) q^{50} +(1.40394 + 3.87412i) q^{51} +(0.507867 - 0.226117i) q^{52} +(-2.47058 - 7.60367i) q^{53} +(0.362620 + 0.329267i) q^{54} +(-5.90896 - 11.8238i) q^{55} +(-0.162608 - 0.180594i) q^{56} +(1.51065 + 4.16860i) q^{57} +(0.0749299 - 0.0159268i) q^{58} +(2.32377 + 1.03461i) q^{59} +(7.70882 + 0.205424i) q^{60} +(-10.8863 + 4.84692i) q^{61} +(-0.00320741 + 0.00233032i) q^{62} +(-1.39019 - 1.35002i) q^{63} +(6.30025 + 4.57740i) q^{64} +(-0.228271 + 0.581094i) q^{65} +(-0.0686697 + 0.962687i) q^{66} +(-10.8408 + 2.30428i) q^{67} +(-2.36849 - 4.10235i) q^{68} +(4.92530 + 7.90670i) q^{69} +(0.135905 + 0.00818463i) q^{70} +(1.96555 + 6.04933i) q^{71} +(-0.955471 - 0.600764i) q^{72} +(10.1015 + 7.33920i) q^{73} +(0.352422 - 0.610413i) q^{74} +(-6.33091 + 5.90928i) q^{75} +(-2.54853 - 4.41418i) q^{76} +(0.399128 - 3.79745i) q^{77} +(0.0359611 - 0.0280150i) q^{78} +(7.36881 + 1.56629i) q^{79} +(-8.72707 + 1.31262i) q^{80} +(-7.92278 - 4.26960i) q^{81} -0.919949 q^{82} +(-8.55130 - 9.49718i) q^{83} +(1.84508 + 1.24828i) q^{84} +(5.12760 + 1.41684i) q^{85} +(0.00846196 - 0.0805102i) q^{86} +(-1.26597 + 0.615268i) q^{87} +(-0.232464 - 2.21174i) q^{88} +(-7.14652 - 5.19225i) q^{89} +(0.617601 - 0.135715i) q^{90} +(-0.145907 + 0.106007i) q^{91} +(-7.16543 - 7.95802i) q^{92} +(0.0469035 - 0.0557390i) q^{93} +(-0.151882 + 0.0322835i) q^{94} +(5.51736 + 1.52454i) q^{95} +(1.80479 + 0.732118i) q^{96} +(12.9608 + 2.75489i) q^{97} +(-0.502005 - 0.364728i) q^{98} +(-3.03064 - 17.4731i) 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