LMFDB - Embedded newform 175.2.x.a.3.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(3,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

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

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

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, 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:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			3.7
Character	$\chi$	$=$	175.3
Dual form			175.2.x.a.117.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.423319 + 0.651855i) q^{2} +(0.402507 - 1.04857i) q^{3} +(0.567758 + 1.27521i) q^{4} +(0.567586 - 2.16283i) q^{5} +(0.513123 + 0.706254i) q^{6} +(1.24404 - 2.33503i) q^{7} +(-2.60695 - 0.412900i) q^{8} +(1.29196 + 1.16328i) q^{9} +O(q^{10})$	\(q+(-0.423319 + 0.651855i) q^{2} +(0.402507 - 1.04857i) q^{3} +(0.567758 + 1.27521i) q^{4} +(0.567586 - 2.16283i) q^{5} +(0.513123 + 0.706254i) q^{6} +(1.24404 - 2.33503i) q^{7} +(-2.60695 - 0.412900i) q^{8} +(1.29196 + 1.16328i) q^{9} +(1.16958 + 1.28555i) q^{10} +(-0.888306 - 0.986564i) q^{11} +(1.56566 - 0.0820529i) q^{12} +(1.79077 + 0.912442i) q^{13} +(0.995478 + 1.79939i) q^{14} +(-2.03941 - 1.46571i) q^{15} +(-0.495338 + 0.550128i) q^{16} +(-0.585165 + 0.722619i) q^{17} +(-1.30520 + 0.349728i) q^{18} +(4.81455 + 2.14358i) q^{19} +(3.08031 - 0.504177i) q^{20} +(-1.94770 - 2.24432i) q^{21} +(1.01913 - 0.161415i) q^{22} +(-0.960654 - 0.623856i) q^{23} +(-1.48227 + 2.56736i) q^{24} +(-4.35569 - 2.45519i) q^{25} +(-1.35285 + 0.781066i) q^{26} +(4.74204 - 2.41619i) q^{27} +(3.68396 + 0.260667i) q^{28} +(-4.04060 + 5.56140i) q^{29} +(1.81875 - 0.708941i) q^{30} +(-9.74492 + 1.02423i) q^{31} +(-1.51519 - 5.65478i) q^{32} +(-1.39203 + 0.534349i) q^{33} +(-0.223331 - 0.687341i) q^{34} +(-4.34419 - 4.01597i) q^{35} +(-0.749906 + 2.30797i) q^{36} +(0.401079 + 7.65304i) q^{37} +(-3.43539 + 2.23097i) q^{38} +(1.67755 - 1.51047i) q^{39} +(-2.37270 + 5.40404i) q^{40} +(0.0622653 - 0.0202312i) q^{41} +(2.28747 - 0.319555i) q^{42} +(-3.34331 - 3.34331i) q^{43} +(0.753729 - 1.69290i) q^{44} +(3.24928 - 2.13402i) q^{45} +(0.813327 - 0.362116i) q^{46} +(-0.145063 + 0.117470i) q^{47} +(0.377469 + 0.740824i) q^{48} +(-3.90475 - 5.80972i) q^{49} +(3.44427 - 1.79995i) q^{50} +(0.522180 + 0.904443i) q^{51} +(-0.146828 + 2.80164i) q^{52} +(-10.4278 - 4.00284i) q^{53} +(-0.432393 + 4.11394i) q^{54} +(-2.63796 + 1.36130i) q^{55} +(-4.20727 + 5.57365i) q^{56} +(4.18557 - 4.18557i) q^{57} +(-1.91476 - 4.98813i) q^{58} +(-4.71962 - 1.00319i) q^{59} +(0.711181 - 3.43284i) q^{60} +(0.951026 + 4.47423i) q^{61} +(3.45756 - 6.78585i) q^{62} +(4.32354 - 1.56960i) q^{63} +(2.91943 + 0.948580i) q^{64} +(2.98987 - 3.35524i) q^{65} +(0.240954 - 1.13360i) q^{66} +(6.60139 + 5.34570i) q^{67} +(-1.25372 - 0.335933i) q^{68} +(-1.04082 + 0.756203i) q^{69} +(4.45681 - 1.13174i) q^{70} +(8.72491 + 6.33902i) q^{71} +(-2.88774 - 3.56607i) q^{72} +(1.64457 + 0.0861882i) q^{73} +(-5.15845 - 2.97823i) q^{74} +(-4.32762 + 3.57900i) q^{75} +7.35658i q^{76} +(-3.40874 + 0.846904i) q^{77} +(0.274469 + 1.73293i) q^{78} +(10.3787 + 1.09084i) q^{79} +(0.908689 + 1.38358i) q^{80} +(-0.0796638 - 0.757950i) q^{81} +(-0.0131703 + 0.0491522i) q^{82} +(0.978599 - 6.17863i) q^{83} +(1.75614 - 3.75795i) q^{84} +(1.23077 + 1.67576i) q^{85} +(3.59464 - 0.764065i) q^{86} +(4.20513 + 6.47533i) q^{87} +(1.90842 + 2.93870i) q^{88} +(15.3519 - 3.26314i) q^{89} +(0.0155886 + 3.02143i) q^{90} +(4.35836 - 3.04639i) q^{91} +(0.250126 - 1.57923i) q^{92} +(-2.84842 + 10.6304i) q^{93} +(-0.0151652 - 0.144287i) q^{94} +(7.36887 - 9.19641i) q^{95} +(-6.53929 - 0.687307i) q^{96} +(2.72136 + 17.1820i) q^{97} +(5.44005 - 0.0859631i) q^{98} -2.30795i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{20}\right)$

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 $

$2$	−0.423319	+	0.651855i	−0.299332	+	0.460931i	−0.956049	−	0.293206i	$-0.905278\pi$
$2$	−0.423319	+	0.651855i	−0.299332	+	0.460931i	0.656717	+	0.754137i	$0.271944\pi$
$3$	0.402507	−	1.04857i	0.232387	−	0.605390i	−0.766953	−	0.641703i	$-0.778228\pi$
$3$	0.402507	−	1.04857i	0.232387	−	0.605390i	0.999340	+	0.0363135i	$0.0115615\pi$
$4$	0.567758	+	1.27521i	0.283879	+	0.637603i
$5$	0.567586	−	2.16283i	0.253832	−	0.967248i
$5$	0.567586	−	2.16283i	0.253832	−	0.967248i
$6$	0.513123	+	0.706254i	0.209482	+	0.288327i
$7$	1.24404	−	2.33503i	0.470201	−	0.882559i
$7$	1.24404	−	2.33503i	0.470201	−	0.882559i
$8$	−2.60695	−	0.412900i	−0.921695	−	0.145982i
$9$	1.29196	+	1.16328i	0.430652	+	0.387761i
$10$	1.16958	+	1.28555i	0.369855	+	0.406527i
$11$	−0.888306	−	0.986564i	−0.267834	−	0.297460i	0.594192	−	0.804323i	$-0.297472\pi$
$11$	−0.888306	−	0.986564i	−0.267834	−	0.297460i	−0.862027	+	0.506863i	$0.830805\pi$
$12$	1.56566	−	0.0820529i	0.451968	−	0.0236866i
$13$	1.79077	+	0.912442i	0.496670	+	0.253066i	0.684336	−	0.729167i	$-0.260092\pi$
$13$	1.79077	+	0.912442i	0.496670	+	0.253066i	−0.187666	+	0.982233i	$0.560092\pi$
$14$	0.995478	+	1.79939i	0.266053	+	0.480908i
$15$	−2.03941	−	1.46571i	−0.526575	−	0.378444i
$16$	−0.495338	+	0.550128i	−0.123834	+	0.137532i
$17$	−0.585165	+	0.722619i	−0.141923	+	0.175261i	−0.843151	−	0.537676i	$-0.819302\pi$
$17$	−0.585165	+	0.722619i	−0.141923	+	0.175261i	0.701228	+	0.712937i	$0.252636\pi$
$18$	−1.30520	+	0.349728i	−0.307639	+	0.0824316i
$19$	4.81455	+	2.14358i	1.10453	+	0.491770i	0.876266	−	0.481828i	$-0.160027\pi$
$19$	4.81455	+	2.14358i	1.10453	+	0.491770i	0.228268	+	0.973598i	$0.426694\pi$
$20$	3.08031	−	0.504177i	0.688778	−	0.112737i
$21$	−1.94770	−	2.24432i	−0.425023	−	0.489750i
$22$	1.01913	−	0.161415i	0.217280	−	0.0344138i
$23$	−0.960654	−	0.623856i	−0.200310	−	0.130083i	0.440586	−	0.897710i	$-0.354771\pi$
$23$	−0.960654	−	0.623856i	−0.200310	−	0.130083i	−0.640897	+	0.767627i	$0.721437\pi$
$24$	−1.48227	+	2.56736i	−0.302566	+	0.524060i
$25$	−4.35569	−	2.45519i	−0.871139	−	0.491037i
$26$	−1.35285	+	0.781066i	−0.265315	+	0.153180i
$27$	4.74204	−	2.41619i	0.912607	−	0.464996i
$28$	3.68396	+	0.260667i	0.696202	+	0.0492614i
$29$	−4.04060	+	5.56140i	−0.750320	+	1.03273i	0.247638	+	0.968853i	$0.420346\pi$
$29$	−4.04060	+	5.56140i	−0.750320	+	1.03273i	−0.997958	+	0.0638742i	$0.979654\pi$
$30$	1.81875	−	0.708941i	0.332057	−	0.129434i
$31$	−9.74492	+	1.02423i	−1.75024	+	0.183958i	−0.924780	−	0.380503i	$-0.875751\pi$
$31$	−9.74492	+	1.02423i	−1.75024	+	0.183958i	−0.825460	+	0.564461i	$0.809084\pi$
$32$	−1.51519	−	5.65478i	−0.267851	−	0.999634i
$33$	−1.39203	+	0.534349i	−0.242321	+	0.0930182i
$34$	−0.223331	−	0.687341i	−0.0383009	−	0.117878i
$35$	−4.34419	−	4.01597i	−0.734302	−	0.678823i
$36$	−0.749906	+	2.30797i	−0.124984	+	0.384662i
$37$	0.401079	+	7.65304i	0.0659369	+	1.25815i	0.808549	+	0.588430i	$0.200254\pi$
$37$	0.401079	+	7.65304i	0.0659369	+	1.25815i	−0.742612	+	0.669722i	$0.766413\pi$
$38$	−3.43539	+	2.23097i	−0.557295	+	0.361911i
$39$	1.67755	−	1.51047i	0.268623	−	0.241869i
$40$	−2.37270	+	5.40404i	−0.375157	+	0.854453i
$41$	0.0622653	−	0.0202312i	0.00972421	−	0.00315959i	−0.304151	−	0.952624i	$-0.598373\pi$
$41$	0.0622653	−	0.0202312i	0.00972421	−	0.00315959i	0.313875	+	0.949464i	$0.398373\pi$
$42$	2.28747	−	0.319555i	0.352964	−	0.0493085i
$43$	−3.34331	−	3.34331i	−0.509850	−	0.509850i	0.404630	−	0.914480i	$-0.367400\pi$
$43$	−3.34331	−	3.34331i	−0.509850	−	0.509850i	−0.914480	+	0.404630i	$0.867400\pi$
$44$	0.753729	−	1.69290i	0.113629	−	0.255215i
$45$	3.24928	−	2.13402i	0.484374	−	0.318121i
$46$	0.813327	−	0.362116i	0.119919	−	0.0533912i
$47$	−0.145063	+	0.117470i	−0.0211596	+	0.0171347i	−0.639842	−	0.768507i	$-0.721000\pi$
$47$	−0.145063	+	0.117470i	−0.0211596	+	0.0171347i	0.618682	+	0.785641i	$0.287667\pi$
$48$	0.377469	+	0.740824i	0.0544829	+	0.106929i
$49$	−3.90475	−	5.80972i	−0.557822	−	0.829961i
$50$	3.44427	−	1.79995i	0.487094	−	0.254551i
$51$	0.522180	+	0.904443i	0.0731199	+	0.126647i
$52$	−0.146828	+	2.80164i	−0.0203614	+	0.388518i
$53$	−10.4278	−	4.00284i	−1.43236	−	0.549832i	−0.486292	−	0.873796i	$-0.661651\pi$
$53$	−10.4278	−	4.00284i	−1.43236	−	0.549832i	−0.946069	+	0.323964i	$0.894984\pi$
$54$	−0.432393	+	4.11394i	−0.0588412	+	0.559837i
$55$	−2.63796	+	1.36130i	−0.355703	+	0.183557i
$56$	−4.20727	+	5.57365i	−0.562220	+	0.744810i
$57$	4.18557	−	4.18557i	0.554392	−	0.554392i
$58$	−1.91476	−	4.98813i	−0.251421	−	0.654974i
$59$	−4.71962	−	1.00319i	−0.614442	−	0.130604i	−0.109831	−	0.993950i	$-0.535031\pi$
$59$	−4.71962	−	1.00319i	−0.614442	−	0.130604i	−0.504612	+	0.863347i	$0.668364\pi$
$60$	0.711181	−	3.43284i	0.0918131	−	0.443178i
$61$	0.951026	+	4.47423i	0.121766	+	0.572866i	0.996153	+	0.0876354i	$0.0279310\pi$
$61$	0.951026	+	4.47423i	0.121766	+	0.572866i	−0.874386	+	0.485231i	$0.838736\pi$
$62$	3.45756	−	6.78585i	0.439111	−	0.861804i
$63$	4.32354	−	1.56960i	0.544715	−	0.197750i
$64$	2.91943	+	0.948580i	0.364929	+	0.118573i
$65$	2.98987	−	3.35524i	0.370848	−	0.416167i
$66$	0.240954	−	1.13360i	0.0296594	−	0.139536i
$67$	6.60139	+	5.34570i	0.806488	+	0.653081i	0.941217	−	0.337801i	$-0.109683\pi$
$67$	6.60139	+	5.34570i	0.806488	+	0.653081i	−0.134730	+	0.990882i	$0.543017\pi$
$68$	−1.25372	−	0.335933i	−0.152036	−	0.0407379i
$69$	−1.04082	+	0.756203i	−0.125300	+	0.0910361i
$70$	4.45681	−	1.13174i	0.532691	−	0.135269i
$71$	8.72491	+	6.33902i	1.03546	+	0.752303i	0.969393	−	0.245513i	$-0.0789563\pi$
$71$	8.72491	+	6.33902i	1.03546	+	0.752303i	0.0660625	+	0.997815i	$0.478956\pi$
$72$	−2.88774	−	3.56607i	−0.340324	−	0.420265i
$73$	1.64457	+	0.0861882i	0.192482	+	0.0100876i	0.148333	−	0.988937i	$-0.452609\pi$
$73$	1.64457	+	0.0861882i	0.192482	+	0.0100876i	0.0441488	+	0.999025i	$0.485942\pi$
$74$	−5.15845	−	2.97823i	−0.599658	−	0.346213i
$75$	−4.32762	+	3.57900i	−0.499710	+	0.413267i
$76$			7.35658i			0.843857i
$77$	−3.40874	+	0.846904i	−0.388462	+	0.0965136i
$78$	0.274469	+	1.73293i	0.0310775	+	0.196216i
$79$	10.3787	+	1.09084i	1.16769	+	0.122729i	0.668465	−	0.743744i	$-0.266952\pi$
$79$	10.3787	+	1.09084i	1.16769	+	0.122729i	0.499224	+	0.866473i	$0.333618\pi$
$80$	0.908689	+	1.38358i	0.101595	+	0.154689i
$81$	−0.0796638	−	0.757950i	−0.00885153	−	0.0842167i
$82$	−0.0131703	+	0.0491522i	−0.00145442	+	0.00542796i
$83$	0.978599	−	6.17863i	0.107415	−	0.678193i	−0.873946	−	0.486022i	$-0.838447\pi$
$83$	0.978599	−	6.17863i	0.107415	−	0.678193i	0.981362	−	0.192170i	$-0.0615526\pi$
$84$	1.75614	−	3.75795i	0.191611	−	0.410026i
$85$	1.23077	+	1.67576i	0.133496	+	0.181762i
$86$	3.59464	−	0.764065i	0.387620	−	0.0823912i
$87$	4.20513	+	6.47533i	0.450837	+	0.694228i
$88$	1.90842	+	2.93870i	0.203438	+	0.313267i
$89$	15.3519	−	3.26314i	1.62729	−	0.345892i	0.698248	−	0.715856i	$-0.253963\pi$
$89$	15.3519	−	3.26314i	1.62729	−	0.345892i	0.929046	+	0.369964i	$0.120630\pi$
$90$	0.0155886	+	3.02143i	0.00164319	+	0.318487i
$91$	4.35836	−	3.04639i	0.456880	−	0.319349i
$92$	0.250126	−	1.57923i	0.0260774	−	0.164646i
$93$	−2.84842	+	10.6304i	−0.295367	+	1.10233i
$94$	−0.0151652	−	0.144287i	−0.00156417	−	0.0148821i
$95$	7.36887	−	9.19641i	0.756030	−	0.943532i
$96$	−6.53929	−	0.687307i	−0.667413	−	0.0701479i
$97$	2.72136	+	17.1820i	0.276312	+	1.74457i	0.601461	+	0.798902i	$0.294586\pi$
$97$	2.72136	+	17.1820i	0.276312	+	1.74457i	−0.325149	+	0.945663i	$0.605414\pi$
$98$	5.44005	−	0.0859631i	0.549528	−	0.00868358i
$99$		−	2.30795i		−	0.231958i
$100$	0.657888	−	6.94836i	0.0657888	−	0.694836i
$101$	−3.07011	−	1.77253i	−0.305487	−	0.176373i	0.339418	−	0.940636i	$-0.389770\pi$
$101$	−3.07011	−	1.77253i	−0.305487	−	0.176373i	−0.644905	+	0.764262i	$0.723103\pi$
$102$	−0.810614	−	0.0424825i	−0.0802628	−	0.00420639i
$103$	−4.00546	−	4.94633i	−0.394669	−	0.487376i	0.540617	−	0.841269i	$-0.318191\pi$
$103$	−4.00546	−	4.94633i	−0.394669	−	0.487376i	−0.935286	+	0.353893i	$0.884858\pi$
$104$	−4.29169	−	3.11810i	−0.420835	−	0.305755i
$105$	−5.95957	+	2.93871i	−0.581595	+	0.286789i
$106$	7.02354	−	5.10290i	0.682186	−	0.495637i
$107$	−9.52075	−	2.55108i	−0.920406	−	0.246622i	−0.232647	−	0.972561i	$-0.574739\pi$
$107$	−9.52075	−	2.55108i	−0.920406	−	0.246622i	−0.687759	+	0.725939i	$0.741405\pi$
$108$	5.77347	+	4.67527i	0.555553	+	0.449878i
$109$	−2.25184	+	10.5941i	−0.215687	+	1.01473i	0.728430	+	0.685120i	$0.240250\pi$
$109$	−2.25184	+	10.5941i	−0.215687	+	1.01473i	−0.944118	+	0.329609i	$0.893083\pi$
$110$	0.229332	−	2.29583i	0.0218660	−	0.218899i
$111$	8.18615	+	2.65984i	0.776995	+	0.252461i
$112$	0.668350	+	1.84101i	0.0631531	+	0.173959i
$113$	−3.00115	+	5.89008i	−0.282324	+	0.554092i	−0.988002	−	0.154440i	$-0.950643\pi$
$113$	−3.00115	+	5.89008i	−0.282324	+	0.554092i	0.705678	+	0.708533i	$0.250643\pi$
$114$	0.956551	+	4.50022i	0.0895892	+	0.421484i
$115$	−1.89455	+	1.72364i	−0.176668	+	0.160730i
$116$	−9.38601	−	1.99506i	−0.871470	−	0.185237i
$117$	1.25217	+	3.26200i	0.115763	+	0.301572i
$118$	2.65184	−	2.65184i	0.244122	−	0.244122i
$119$	0.959372	+	2.26534i	0.0879455	+	0.207664i
$120$	4.71146	+	4.66309i	0.430095	+	0.425680i
$121$	0.965593	−	9.18700i	0.0877811	−	0.835182i
$122$	−3.31913	−	1.27410i	−0.300500	−	0.115351i
$123$	0.00384843	−	0.0734325i	0.000347002	−	0.00662118i
$124$	−6.83886	−	11.8453i	−0.614148	−	1.06374i
$125$	−7.78239	+	8.02711i	−0.696078	+	0.717966i
$126$	−0.807091	+	3.48276i	−0.0719014	+	0.310269i
$127$	−8.39463	−	16.4754i	−0.744903	−	1.46195i	−0.881927	−	0.471387i	$-0.843754\pi$
$127$	−8.39463	−	16.4754i	−0.744903	−	1.46195i	0.137023	−	0.990568i	$-0.456246\pi$
$128$	7.24505	−	5.86692i	0.640378	−	0.518568i
$129$	−4.85139	+	2.15998i	−0.427141	+	0.190175i
$130$	0.921459	+	3.36930i	0.0808173	+	0.295507i
$131$	6.81590	−	15.3088i	0.595508	−	1.33753i	−0.324594	−	0.945853i	$-0.605228\pi$
$131$	6.81590	−	15.3088i	0.595508	−	1.33753i	0.920102	−	0.391679i	$-0.128106\pi$
$132$	−1.47174	−	1.47174i	−0.128098	−	0.128098i
$133$	10.9948	−	8.57545i	0.953370	−	0.743586i
$134$	−6.27911	+	2.04021i	−0.542433	+	0.176247i
$135$	−2.53430	−	11.6276i	−0.218118	−	1.00075i
$136$	1.82386	−	1.64221i	0.156395	−	0.140819i
$137$	−2.76974	+	1.79869i	−0.236635	+	0.153673i	−0.657509	−	0.753446i	$-0.728390\pi$
$137$	−2.76974	+	1.79869i	−0.236635	+	0.153673i	0.420874	+	0.907119i	$0.361723\pi$
$138$	−0.0523334	−	0.998581i	−0.00445492	−	0.0850048i
$139$	2.66592	−	8.20486i	0.226120	−	0.695927i	−0.772055	−	0.635555i	$-0.780771\pi$
$139$	2.66592	−	8.20486i	0.226120	−	0.695927i	0.998176	−	0.0603721i	$-0.0192287\pi$
$140$	2.65474	−	7.81983i	0.224367	−	0.660897i
$141$	0.0647859	+	0.199391i	0.00545596	+	0.0167917i
$142$	−7.82554	+	3.00394i	−0.656705	+	0.252085i
$143$	−0.690568	−	2.57723i	−0.0577482	−	0.215519i
$144$	−1.27991	+	0.134524i	−0.106659	+	0.0112103i
$145$	9.73500	+	11.8957i	0.808448	+	0.987885i
$146$	−0.752360	+	1.03553i	−0.0622658	+	0.0857015i
$147$	−7.66357	+	1.75594i	−0.632080	+	0.144827i
$148$	−9.53148	+	4.85653i	−0.783483	+	0.399205i
$149$	0.0342344	−	0.0197652i	0.00280459	−	0.00161923i	−0.498597	−	0.866834i	$-0.666151\pi$
$149$	0.0342344	−	0.0197652i	0.00280459	−	0.00161923i	0.501402	+	0.865215i	$0.332818\pi$
$150$	−0.501023	−	4.33604i	−0.0409083	−	0.354036i
$151$	4.89690	−	8.48169i	0.398504	−	0.690230i	−0.595037	−	0.803698i	$-0.702863\pi$
$151$	4.89690	−	8.48169i	0.398504	−	0.690230i	0.993542	+	0.113468i	$0.0361960\pi$
$152$	−11.6662	−	7.57612i	−0.946254	−	0.614505i
$153$	−1.59662	+	0.252879i	−0.129079	+	0.0204441i
$154$	0.890929	−	2.58052i	0.0717931	−	0.207944i
$155$	−3.31584	+	21.6580i	−0.266334	+	1.73961i
$156$	2.87861	+	1.28164i	0.230473	+	0.102613i
$157$	−12.7152	+	3.40702i	−1.01478	+	0.271910i	−0.727626	−	0.685974i	$-0.759376\pi$
$157$	−12.7152	+	3.40702i	−1.01478	+	0.271910i	−0.287156	+	0.957884i	$0.592710\pi$
$158$	−5.10455	+	6.30360i	−0.406096	+	0.501487i
$159$	−8.39448	+	9.32301i	−0.665725	+	0.739363i
$160$	−13.0904	+	0.0675377i	−1.03488	+	0.00533933i
$161$	−2.65181	+	1.46706i	−0.208992	+	0.115621i
$162$	0.527797	+	0.268926i	0.0414676	+	0.0211288i
$163$	−3.48720	+	0.182756i	−0.273138	+	0.0143146i	−0.188413	−	0.982090i	$-0.560334\pi$
$163$	−3.48720	+	0.182756i	−0.273138	+	0.0143146i	−0.0847249	+	0.996404i	$0.527001\pi$
$164$	0.0611506	+	0.0679147i	0.00477506	+	0.00530324i
$165$	0.365613	+	3.31401i	0.0284629	+	0.257995i
$166$	3.61331	+	3.25344i	0.280447	+	0.252516i
$167$	18.9176	+	2.99626i	1.46389	+	0.231857i	0.836979	−	0.547235i	$-0.184319\pi$
$167$	18.9176	+	2.99626i	1.46389	+	0.231857i	0.626910	+	0.779092i	$0.284319\pi$
$168$	4.15088	+	6.65503i	0.320247	+	0.513447i
$169$	−5.26691	−	7.24928i	−0.405147	−	0.557637i
$170$	−1.61336	+	0.0929018i	−0.123739	+	0.00712524i
$171$	3.72661	+	8.37009i	0.284981	+	0.640077i
$172$	2.36522	−	6.16160i	0.180346	−	0.469818i
$173$	−2.70053	+	4.15845i	−0.205317	+	0.316161i	−0.926296	−	0.376796i	$-0.877026\pi$
$173$	−2.70053	+	4.15845i	−0.205317	+	0.316161i	0.720979	+	0.692957i	$0.243692\pi$
$174$	−6.00109			−0.454941
$175$	−11.1516	+	7.11635i	−0.842980	+	0.537945i
$176$	0.982748			0.0740774
$177$	−2.95159	+	4.54504i	−0.221855	+	0.341626i
$178$	−4.37165	+	11.3885i	−0.327669	+	0.853607i
$179$	8.23757	+	18.5019i	0.615705	+	1.38290i	0.904899	+	0.425626i	$0.139946\pi$
$179$	8.23757	+	18.5019i	0.615705	+	1.38290i	−0.289194	+	0.957270i	$0.593387\pi$
$180$	4.56612	+	2.93189i	0.340339	+	0.218530i
$181$	−2.67679	−	3.68429i	−0.198965	−	0.273851i	0.697863	−	0.716231i	$-0.254134\pi$
$181$	−2.67679	−	3.68429i	−0.198965	−	0.273851i	−0.896828	+	0.442380i	$0.854134\pi$
$182$	0.140827	+	4.13061i	0.0104388	+	0.306181i
$183$	5.07431	+	0.803693i	0.375104	+	0.0594107i
$184$	2.24679	+	2.02301i	0.165635	+	0.149139i
$185$	16.7799	+	3.47629i	1.23368	+	0.255582i
$186$	−5.72372	−	6.35683i	−0.419683	−	0.466105i
$187$	1.23272	−	0.0646039i	0.0901451	−	0.00472430i
$188$	−0.232159	−	0.118291i	−0.0169319	−	0.00862725i
$189$	0.257382	−	14.0787i	0.0187218	−	1.02407i
$190$	2.87534	+	8.69645i	0.208599	+	0.630907i
$191$	−10.3573	+	11.5029i	−0.749427	+	0.832323i	−0.990403	−	0.138208i	$-0.955866\pi$
$191$	−10.3573	+	11.5029i	−0.749427	+	0.832323i	0.240976	+	0.970531i	$0.422532\pi$
$192$	2.16974	−	2.67940i	0.156587	−	0.193369i
$193$	7.57383	−	2.02940i	0.545176	−	0.146080i	0.0242890	−	0.999705i	$-0.492268\pi$
$193$	7.57383	−	2.02940i	0.545176	−	0.146080i	0.520887	+	0.853625i	$0.325601\pi$
$194$	−12.3522	−	5.49953i	−0.886833	−	0.394843i
$195$	−2.31475	−	4.48558i	−0.165763	−	0.321219i
$196$	5.19164	−	8.27788i	0.370831	−	0.591277i
$197$	−16.1577	+	2.55912i	−1.15119	+	0.182330i	−0.702718	−	0.711469i	$-0.748030\pi$
$197$	−16.1577	+	2.55912i	−1.15119	+	0.182330i	−0.448469	+	0.893799i	$0.648030\pi$
$198$	1.50445	+	0.976999i	0.106916	+	0.0694323i
$199$	13.6561	−	23.6530i	0.968053	−	1.67672i	0.266874	−	0.963731i	$-0.414009\pi$
$199$	13.6561	−	23.6530i	0.968053	−	1.67672i	0.701179	−	0.712985i	$-0.252657\pi$
$200$	10.3413	+	8.19901i	0.731242	+	0.579758i
$201$	8.26242	−	4.77031i	0.582786	−	0.336472i
$202$	2.45507	−	1.25092i	0.172738	−	0.0880144i
$203$	7.95942	+	16.3535i	0.558641	+	1.14779i
$204$	−0.856878	+	1.17939i	−0.0599935	+	0.0825739i
$205$	−0.00841585	−	0.146152i	−0.000587789	−	0.0102077i
$206$	4.91987	−	0.517100i	0.342784	−	0.0360280i
$207$	−0.515402	−	1.92351i	−0.0358229	−	0.133693i
$208$	−1.38899	+	0.533185i	−0.0963095	+	0.0369697i
$209$	−2.16202	−	6.65402i	−0.149550	−	0.460268i
$210$	0.607190	−	5.12879i	0.0419001	−	0.353920i
$211$	4.53761	−	13.9653i	0.312382	−	0.961413i	−0.664437	−	0.747345i	$-0.731328\pi$
$211$	4.53761	−	13.9653i	0.312382	−	0.961413i	0.976819	−	0.214068i	$-0.0686715\pi$
$212$	−0.815998	−	15.5702i	−0.0560430	−	1.06936i
$213$	10.1587	−	6.59714i	0.696063	−	0.452029i
$214$	5.69325	−	5.12622i	0.389182	−	0.350421i
$215$	−9.12864	+	5.33341i	−0.622568	+	0.363736i
$216$	−13.3599	+	4.34090i	−0.909027	+	0.295361i
$217$	−9.73141	+	24.0289i	−0.660611	+	1.63119i
$218$	−5.95255	−	5.95255i	−0.403158	−	0.403158i
$219$	0.752324	−	1.68975i	0.0508373	−	0.114183i
$220$	−3.23366	−	2.59106i	−0.218013	−	0.174689i
$221$	−1.70724	+	0.760113i	−0.114842	+	0.0511307i
$222$	−5.19919	+	4.21022i	−0.348947	+	0.282571i
$223$	−9.81559	−	19.2642i	−0.657301	−	1.29003i	−0.943346	−	0.331809i	$-0.892341\pi$
$223$	−9.81559	−	19.2642i	−0.657301	−	1.29003i	0.286046	−	0.958216i	$-0.407659\pi$
$224$	−15.0891	−	3.49672i	−1.00818	−	0.233634i
$225$	−2.77129	−	8.23890i	−0.184753	−	0.549260i
$226$	−2.56903	−	4.44970i	−0.170890	−	0.295989i
$227$	0.492014	−	9.38818i	0.0326561	−	0.623116i	−0.932457	−	0.361281i	$-0.882339\pi$
$227$	0.492014	−	9.38818i	0.0326561	−	0.623116i	0.965113	−	0.261834i	$-0.0843273\pi$
$228$	7.71385	+	2.96107i	0.510862	+	0.196102i
$229$	−0.325389	+	3.09587i	−0.0215023	+	0.204581i	−0.999999	−	0.00168368i	$-0.999464\pi$
$229$	−0.325389	+	3.09587i	−0.0215023	+	0.204581i	0.978496	+	0.206265i	$0.0661307\pi$
$230$	−0.321565	−	1.96462i	−0.0212033	−	0.129543i
$231$	−0.484007	+	3.91517i	−0.0318454	+	0.257600i
$232$	12.8299	−	12.8299i	0.842326	−	0.842326i
$233$	10.4487	+	27.2198i	0.684516	+	1.78323i	0.619024	+	0.785372i	$0.287528\pi$
$233$	10.4487	+	27.2198i	0.684516	+	1.78323i	0.0654920	+	0.997853i	$0.479138\pi$
$234$	−2.65642	−	0.564639i	−0.173656	−	0.0369116i
$235$	0.171732	+	0.380422i	0.0112025	+	0.0248160i
$236$	−1.40033	−	6.58805i	−0.0911540	−	0.428846i
$237$	5.32129	−	10.4436i	0.345655	−	0.678386i
$238$	−1.88279	−	0.333592i	−0.122043	−	0.0216236i
$239$	3.05660	+	0.993150i	0.197715	+	0.0642416i	0.406201	−	0.913784i	$-0.366853\pi$
$239$	3.05660	+	0.993150i	0.197715	+	0.0642416i	−0.208485	+	0.978025i	$0.566853\pi$
$240$	1.81653	−	0.395921i	0.117256	−	0.0255566i
$241$	5.57588	−	26.2325i	0.359174	−	1.68978i	−0.313295	−	0.949656i	$-0.601433\pi$
$241$	5.57588	−	26.2325i	0.359174	−	1.68978i	0.672469	−	0.740125i	$-0.265234\pi$
$242$	5.57983	+	4.51846i	0.358685	+	0.290458i
$243$	14.5955	+	3.91085i	0.936301	+	0.250881i
$244$	−5.16561	+	3.75303i	−0.330694	+	0.240263i
$245$	−14.7817	+	5.14781i	−0.944371	+	0.328882i
$246$	0.0462382	+	0.0335940i	0.00294804	+	0.00214188i
$247$	6.66586	+	8.23165i	0.424138	+	0.523767i
$248$	25.8274	+	1.35356i	1.64004	+	0.0859510i
$249$	−6.08480	−	3.51306i	−0.385609	−	0.222631i
$250$	−1.93807	−	8.47102i	−0.122574	−	0.535754i
$251$			13.7541i			0.868150i	0.900877	+	0.434075i	$0.142925\pi$
$251$			13.7541i			0.868150i	−0.900877	+	0.434075i	$0.857075\pi$
$252$	4.45628	+	4.62225i	0.280719	+	0.291175i
$253$	0.237881	+	1.50192i	0.0149555	+	0.0944250i
$254$	14.2932	+	1.50227i	0.896833	+	0.0942610i
$255$	2.25254	−	0.616040i	0.141060	−	0.0385779i
$256$	1.39915	+	13.3120i	0.0874468	+	0.832000i
$257$	2.39177	−	8.92621i	0.149195	−	0.556802i	−0.850338	−	0.526237i	$-0.823603\pi$
$257$	2.39177	−	8.92621i	0.149195	−	0.556802i	0.999533	−	0.0305651i	$-0.00973070\pi$
$258$	0.645695	−	4.07676i	0.0401992	−	0.253808i
$259$	18.3691	+	8.58412i	1.14140	+	0.533391i
$260$	5.97615	+	1.90774i	0.370625	+	0.118313i
$261$	−11.6898	+	2.48474i	−0.723578	+	0.153801i
$262$	7.09379	+	10.9235i	0.438256	+	0.674854i
$263$	−4.57051	−	7.03797i	−0.281830	−	0.433980i	0.669198	−	0.743084i	$-0.266638\pi$
$263$	−4.57051	−	7.03797i	−0.281830	−	0.433980i	−0.951028	+	0.309104i	$0.899971\pi$
$264$	3.84957	−	0.818252i	0.236925	−	0.0503599i
$265$	−14.5761	+	20.2815i	−0.895404	+	1.24588i
$266$	0.935639	+	10.7972i	0.0573677	+	0.662017i
$267$	2.75761	−	17.4109i	0.168763	−	1.06553i
$268$	−3.06887	+	11.4532i	−0.187461	+	0.699615i
$269$	0.460334	+	4.37978i	0.0280670	+	0.267040i	0.999552	+	0.0299378i	$0.00953093\pi$
$269$	0.460334	+	4.37978i	0.0280670	+	0.267040i	−0.971485	+	0.237102i	$0.923802\pi$
$270$	8.65235	+	3.27021i	0.526565	+	0.199019i
$271$	−3.41350	−	0.358773i	−0.207355	−	0.0217939i	0.000281350	−	1.00000i	$-0.499910\pi$
$271$	−3.41350	−	0.358773i	−0.207355	−	0.0217939i	−0.207636	+	0.978206i	$0.566577\pi$
$272$	−0.107679	−	0.679856i	−0.00652898	−	0.0412223i
$273$	−1.44007	−	5.79622i	−0.0871572	−	0.350803i
$274$		−	2.56689i		−	0.155072i
$275$	1.44699	+	6.47813i	0.0872568	+	0.390646i
$276$	−1.55525	−	0.897924i	−0.0936150	−	0.0540487i
$277$	−7.68850	−	0.402937i	−0.461957	−	0.0242102i	−0.180062	−	0.983655i	$-0.557630\pi$
$277$	−7.68850	−	0.402937i	−0.461957	−	0.0242102i	−0.281895	+	0.959445i	$0.590963\pi$
$278$	4.21984	+	5.21107i	0.253089	+	0.312539i
$279$	−13.7815	−	10.0128i	−0.825076	−	0.599453i
$280$	9.66688	+	12.2631i	0.577707	+	0.732863i
$281$	19.6291	−	14.2614i	1.17097	−	0.850761i	0.179847	−	0.983695i	$-0.442440\pi$
$281$	19.6291	−	14.2614i	1.17097	−	0.850761i	0.991125	+	0.132934i	$0.0424398\pi$
$282$	−0.157399	−	0.0421749i	−0.00937296	−	0.00251148i
$283$	−5.63377	−	4.56213i	−0.334893	−	0.271191i	0.447093	−	0.894488i	$-0.352459\pi$
$283$	−5.63377	−	4.56213i	−0.334893	−	0.271191i	−0.781985	+	0.623297i	$0.785793\pi$
$284$	−3.12991	+	14.7251i	−0.185726	+	0.873772i
$285$	−6.67702	−	11.4284i	−0.395512	−	0.676958i
$286$	1.97231	+	0.640843i	0.116625	+	0.0378939i
$287$	0.0302197	−	0.170560i	0.00178381	−	0.0100678i
$288$	4.62055	−	9.06833i	0.272268	−	0.534357i
$289$	3.35474	+	15.7828i	0.197338	+	0.928400i
$290$	−11.8753	+	1.31012i	−0.697341	+	0.0769330i
$291$	19.1118	+	4.06234i	1.12035	+	0.238138i
$292$	0.823809	+	2.14610i	0.0482098	+	0.125591i
$293$	22.0206	−	22.0206i	1.28645	−	1.28645i	0.349529	−	0.936925i	$-0.386342\pi$
$293$	22.0206	−	22.0206i	1.28645	−	1.28645i	0.936925	−	0.349529i	$-0.113658\pi$
$294$	2.09952	−	5.73885i	0.122446	−	0.334697i
$295$	−4.84852	+	9.63836i	−0.282291	+	0.561167i
$296$	2.11435	−	20.1167i	0.122894	−	1.16926i
$297$	−6.59611	−	2.53201i	−0.382745	−	0.146922i
$298$	−0.00160802	+	0.0306828i	−9.31501e−5	+	0.00177741i
$299$	−1.15108	−	1.99372i	−0.0665684	−	0.115300i
$300$	−7.02100	−	3.48660i	−0.405358	−	0.201299i
$301$	−11.9659	+	3.64755i	−0.689705	+	0.210241i
$302$	3.45587	+	6.78253i	0.198863	+	0.390291i
$303$	−3.09435	+	2.50576i	−0.177766	+	0.143952i
$304$	−3.56407	+	1.58683i	−0.204414	+	0.0910108i
$305$	10.2168	+	0.482597i	0.585012	+	0.0276334i
$306$	0.511039	−	1.14781i	0.0292141	−	0.0656160i
$307$	2.33566	+	2.33566i	0.133303	+	0.133303i	0.770610	−	0.637307i	$-0.219952\pi$
$307$	2.33566	+	2.33566i	0.133303	+	0.133303i	−0.637307	+	0.770610i	$0.719952\pi$
$308$	−3.01532	−	3.86601i	−0.171814	−	0.220286i
$309$	−6.79877	+	2.20905i	−0.386768	+	0.125669i
$310$	−12.7142	−	11.3297i	−0.722118	−	0.643483i
$311$	−4.59090	+	4.13366i	−0.260326	+	0.234399i	−0.788950	−	0.614458i	$-0.789375\pi$
$311$	−4.59090	+	4.13366i	−0.260326	+	0.234399i	0.528624	+	0.848856i	$0.322708\pi$
$312$	−4.99696	+	3.24507i	−0.282897	+	0.183716i
$313$	−0.586184	−	11.1851i	−0.0331331	−	0.632216i	−0.963845	−	0.266463i	$-0.914145\pi$
$313$	−0.586184	−	11.1851i	−0.0331331	−	0.632216i	0.930712	−	0.365753i	$-0.119189\pi$
$314$	3.16170	−	9.73071i	0.178425	−	0.549136i
$315$	−0.940792	−	10.2420i	−0.0530076	−	0.577070i
$316$	4.50152	+	13.8542i	0.253230	+	0.779362i
$317$	−8.39567	+	3.22280i	−0.471548	+	0.181010i	−0.582525	−	0.812813i	$-0.697935\pi$
$317$	−8.39567	+	3.22280i	−0.471548	+	0.181010i	0.110977	+	0.993823i	$0.464602\pi$
$318$	−2.52370	−	9.41859i	−0.141522	−	0.528168i
$319$	9.07597	−	0.953923i	0.508157	−	0.0534094i
$320$	3.70865	−	5.77584i	0.207320	−	0.322879i
$321$	−6.50714	+	8.95630i	−0.363193	+	0.499892i
$322$	0.166253	−	2.34963i	0.00926494	−	0.130940i
$323$	−4.36630	+	2.22474i	−0.242947	+	0.123788i
$324$	0.921313	−	0.531920i	0.0511840	−	0.0295511i
$325$	−5.55982	−	8.37098i	−0.308403	−	0.464339i
$326$	1.35707	−	2.35051i	0.0751610	−	0.130183i
$327$	10.2022	+	6.62539i	0.564183	+	0.366385i
$328$	−0.170676	+	0.0270324i	−0.00942401	+	0.00149262i
$329$	0.0938322	+	0.484864i	0.00517314	+	0.0267314i
$330$	−2.31502	−	1.16456i	−0.127438	−	0.0641068i
$331$	−6.60155	−	2.93920i	−0.362854	−	0.161553i	0.217208	−	0.976125i	$-0.430305\pi$
$331$	−6.60155	−	2.93920i	−0.362854	−	0.161553i	−0.580062	+	0.814572i	$0.696972\pi$
$332$	8.43463	−	2.26005i	0.462910	−	0.124036i
$333$	−8.38447	+	10.3540i	−0.459466	+	0.567394i
$334$	−9.96132	+	11.0632i	−0.545059	+	0.605349i
$335$	15.3087	−	11.2436i	0.836404	−	0.614301i
$336$	2.19943	+	0.0402094i	0.119989	+	0.00219360i
$337$	9.03950	+	4.60585i	0.492413	+	0.250897i	0.682521	−	0.730866i	$-0.260884\pi$
$337$	9.03950	+	4.60585i	0.492413	+	0.250897i	−0.190108	+	0.981763i	$0.560884\pi$
$338$	6.95506	−	0.364499i	0.378305	−	0.0198261i
$339$	4.96815	+	5.51769i	0.269833	+	0.299680i
$340$	−1.43816	+	2.52091i	−0.0779952	+	0.136716i
$341$	9.66695	+	8.70416i	0.523494	+	0.471356i
$342$	−7.03363	−	1.11402i	−0.380335	−	0.0602392i
$343$	−18.4235	+	1.89023i	−0.994778	+	0.102063i
$344$	7.33539	+	10.0963i	0.395498	+	0.544356i
$345$	1.04478	+	2.68034i	0.0562492	+	0.144305i
$346$	−1.56752	−	3.52070i	−0.0842703	−	0.189274i
$347$	−2.87267	+	7.48356i	−0.154213	+	0.401738i	−0.988821	−	0.149105i	$-0.952361\pi$
$347$	−2.87267	+	7.48356i	−0.154213	+	0.401738i	0.834608	+	0.550844i	$0.185694\pi$
$348$	−5.86988	+	9.03883i	−0.314659	+	0.484532i
$349$	−8.82065			−0.472158			−0.236079	−	0.971734i	$-0.575862\pi$
$349$	−8.82065			−0.472158			−0.236079	+	0.971734i	$0.575862\pi$
$350$	0.0818548	−	10.2817i	0.00437532	−	0.549580i
$351$	10.6965			0.570939
$352$	−4.23285	+	6.51801i	−0.225612	+	0.347411i
$353$	6.03343	−	15.7176i	0.321127	−	0.836565i	−0.674070	−	0.738668i	$-0.735455\pi$
$353$	6.03343	−	15.7176i	0.321127	−	0.836565i	0.995197	−	0.0978967i	$-0.0312115\pi$
$354$	−1.71324	−	3.84801i	−0.0910579	−	0.204519i
$355$	18.6624	−	15.2726i	0.990495	−	0.810584i
$356$	12.8773	+	17.7241i	0.682497	+	0.939376i
$357$	2.76151	−	0.0941494i	0.146155	−	0.00498292i
$358$	−15.5477	−	2.46251i	−0.821720	−	0.130148i
$359$	−10.2724	−	9.24932i	−0.542157	−	0.488161i	0.351947	−	0.936020i	$-0.385520\pi$
$359$	−10.2724	−	9.24932i	−0.542157	−	0.488161i	−0.894104	+	0.447859i	$0.852187\pi$
$360$	−9.35185	+	4.22166i	−0.492886	+	0.222501i
$361$	5.87151	+	6.52098i	0.309027	+	0.343209i
$362$	3.53476	−	0.185249i	0.185783	−	0.00973647i
$363$	−9.24451	−	4.71031i	−0.485211	−	0.247227i
$364$	6.35927	+	3.82819i	0.333316	+	0.200652i
$365$	1.11984	−	3.50801i	0.0586153	−	0.183618i
$366$	−2.67195	+	2.96750i	−0.139665	+	0.155114i
$367$	0.653967	−	0.807582i	0.0341368	−	0.0421554i	−0.759792	−	0.650167i	$-0.774699\pi$
$367$	0.653967	−	0.807582i	0.0341368	−	0.0421554i	0.793928	+	0.608011i	$0.208032\pi$
$368$	0.819049	−	0.219464i	0.0426959	−	0.0114403i
$369$	0.103979	+	0.0462943i	0.00541292	+	0.00240999i
$370$	−9.36929	+	9.46647i	−0.487086	+	0.492138i
$371$	−22.3192	+	19.3695i	−1.15876	+	1.00561i
$372$	−15.1732	+	2.40320i	−0.786695	+	0.124600i
$373$	−18.4553	−	11.9850i	−0.955577	−	0.620559i	−0.0301748	−	0.999545i	$-0.509606\pi$
$373$	−18.4553	−	11.9850i	−0.955577	−	0.620559i	−0.925403	+	0.378985i	$0.876273\pi$
$374$	−0.479720	+	0.830899i	−0.0248057	+	0.0429648i
$375$	5.28448	+	11.3913i	0.272890	+	0.588245i
$376$	0.426675	−	0.246341i	0.0220041	−	0.0127041i
$377$	−12.3102	+	6.27237i	−0.634009	+	0.323044i
$378$	9.06828	+	6.12754i	0.466422	+	0.315167i
$379$	−17.8299	+	24.5408i	−0.915862	+	1.26058i	0.0492625	+	0.998786i	$0.484313\pi$
$379$	−17.8299	+	24.5408i	−0.915862	+	1.26058i	−0.965125	+	0.261790i	$0.915687\pi$
$380$	15.9110	+	4.17549i	0.816220	+	0.214198i
$381$	−20.6544	+	2.17087i	−1.05816	+	0.111217i
$382$	−3.11380	−	11.6209i	−0.159316	−	0.594575i
$383$	−19.9640	+	7.66347i	−1.02011	+	0.391585i	−0.810212	−	0.586137i	$-0.800648\pi$
$383$	−19.9640	+	7.66347i	−1.02011	+	0.391585i	−0.209902	+	0.977722i	$0.567315\pi$
$384$	−3.23567	−	9.95838i	−0.165120	−	0.508186i
$385$	−0.103043	+	7.85323i	−0.00525156	+	0.400238i
$386$	−1.88327	+	5.79612i	−0.0958562	+	0.295015i
$387$	−0.430196	−	8.20863i	−0.0218681	−	0.417268i
$388$	−20.3655	+	13.2255i	−1.03390	+	0.671423i
$389$	15.6392	−	14.0816i	0.792938	−	0.713964i	−0.169481	−	0.985533i	$-0.554209\pi$
$389$	15.6392	−	14.0816i	0.792938	−	0.713964i	0.962419	+	0.271569i	$0.0875426\pi$
$390$	3.90383	+	0.389956i	0.197678	+	0.0197462i
$391$	1.01295	−	0.329128i	0.0512271	−	0.0166447i
$392$	7.78066	+	16.7579i	0.392982	+	0.846403i
$393$	−13.3088	−	13.3088i	−0.671340	−	0.671340i
$394$	5.17168	−	11.6158i	0.260545	−	0.585195i
$395$	8.25008	−	21.8281i	0.415107	−	1.09829i
$396$	2.94311	−	1.31036i	0.147897	−	0.0658479i
$397$	3.98282	−	3.22523i	0.199892	−	0.161869i	−0.524148	−	0.851627i	$-0.675616\pi$
$397$	3.98282	−	3.22523i	0.199892	−	0.161869i	0.724040	+	0.689758i	$0.242283\pi$
$398$	9.63744	+	18.9145i	0.483081	+	0.948100i
$399$	−4.56645	−	14.9804i	−0.228608	−	0.749960i
$400$	3.50821	−	1.18004i	0.175410	−	0.0590022i
$401$	−17.1661	−	29.7326i	−0.857235	−	1.48477i	−0.874556	−	0.484924i	$-0.838847\pi$
$401$	−17.1661	−	29.7326i	−0.857235	−	1.48477i	0.0173216	−	0.999850i	$-0.494486\pi$
$402$	−0.388093	+	7.40526i	−0.0193563	+	0.369341i
$403$	−18.3854	−	7.05751i	−0.915844	−	0.351560i
$404$	0.517259	−	4.92139i	0.0257346	−	0.244848i
$405$	−1.68454	−	0.257902i	−0.0837053	−	0.0128153i
$406$	−14.0295	−	1.73437i	−0.696272	−	0.0860755i
$407$	7.19393	−	7.19393i	0.356590	−	0.356590i
$408$	−0.987852	−	2.57344i	−0.0489060	−	0.127404i
$409$	25.6660	+	5.45549i	1.26910	+	0.269756i	0.792777	−	0.609512i	$-0.208634\pi$
$409$	25.6660	+	5.45549i	1.26910	+	0.269756i	0.476327	+	0.879268i	$0.341968\pi$
$410$	0.0988328	+	0.0563833i	0.00488100	+	0.00278457i
$411$	0.771207	+	3.62824i	0.0380408	+	0.178968i
$412$	4.03345	−	7.91610i	0.198714	−	0.389998i
$413$	−8.21385	+	9.77247i	−0.404177	+	0.480872i
$414$	1.47203	+	0.478291i	0.0723462	+	0.0235067i
$415$	−12.8079	−	5.62345i	−0.628715	−	0.276044i
$416$	2.44630	−	11.5089i	0.119940	−	0.564272i
$417$	−7.53028	−	6.09790i	−0.368760	−	0.298616i
$418$	5.25268	+	1.40745i	0.256917	+	0.0688407i
$419$	−20.8379	+	15.1396i	−1.01800	+	0.739617i	−0.965871	−	0.259023i	$-0.916599\pi$
$419$	−20.8379	+	15.1396i	−1.01800	+	0.739617i	−0.0521248	+	0.998641i	$0.516599\pi$
$420$	−7.13106	−	5.93120i	−0.347960	−	0.289413i
$421$	−9.53283	−	6.92601i	−0.464602	−	0.337553i	0.330732	−	0.943725i	$-0.392704\pi$
$421$	−9.53283	−	6.92601i	−0.464602	−	0.337553i	−0.795334	+	0.606172i	$0.792704\pi$
$422$	7.18251	+	8.86966i	0.349639	+	0.431768i
$423$	−0.324066	−	0.0169836i	−0.0157566	−	0.000825770i
$424$	25.5318	+	14.7408i	1.23994	+	0.715877i
$425$	4.32296	−	1.71082i	0.209695	−	0.0829867i
$426$			9.41470i			0.456144i
$427$	11.6306	+	3.34542i	0.562843	+	0.161896i
$428$	−2.15233	−	13.5893i	−0.104037	−	0.656864i
$429$	−2.98036	−	0.313248i	−0.143893	−	0.0151238i
$430$	0.387724	−	8.20828i	0.0186977	−	0.395839i
$431$	1.62917	+	15.5005i	0.0784745	+	0.746635i	0.961033	+	0.276433i	$0.0891523\pi$
$431$	1.62917	+	15.5005i	0.0784745	+	0.746635i	−0.882559	+	0.470202i	$0.844181\pi$
$432$	−1.01970	+	3.80556i	−0.0490602	+	0.183095i
$433$	−0.121416	+	0.766591i	−0.00583489	+	0.0368400i	−0.990434	−	0.137987i	$-0.955937\pi$
$433$	−0.121416	+	0.766591i	−0.00583489	+	0.0368400i	0.984599	+	0.174827i	$0.0559367\pi$
$434$	−11.5439	−	16.5154i	−0.554123	−	0.792763i
$435$	16.3918	−	5.41969i	0.785928	−	0.259854i
$436$	−14.7881	+	3.14331i	−0.708223	+	0.150537i
$437$	−3.28784	−	5.06282i	−0.157279	−	0.242188i
$438$	0.782996	+	1.20571i	0.0374130	+	0.0576110i
$439$	10.3322	−	2.19617i	0.493128	−	0.104818i	0.0453661	−	0.998970i	$-0.485555\pi$
$439$	10.3322	−	2.19617i	0.493128	−	0.104818i	0.447762	+	0.894153i	$0.352221\pi$
$440$	7.43911	−	2.45962i	0.354646	−	0.117258i
$441$	1.71358	−	12.0482i	0.0815991	−	0.573726i
$442$	0.227225	−	1.43464i	0.0108080	−	0.0682391i
$443$	−7.03490	+	26.2546i	−0.334238	+	1.24739i	0.570455	+	0.821329i	$0.306767\pi$
$443$	−7.03490	+	26.2546i	−0.334238	+	1.24739i	−0.904693	+	0.426064i	$0.859900\pi$
$444$	1.25591	+	11.9492i	0.0596028	+	0.567083i
$445$	1.65588	−	35.0556i	0.0784960	−	1.66180i
$446$	16.7126	+	1.75656i	0.791364	+	0.0831757i
$447$	−0.00694557	−	0.0438526i	−0.000328514	−	0.00207416i
$448$	5.84684	−	5.63690i	0.276237	−	0.266318i
$449$			39.0168i			1.84131i	0.390372	+	0.920657i	$0.372346\pi$
$449$			39.0168i			1.84131i	−0.390372	+	0.920657i	$0.627654\pi$
$450$	6.54370	+	1.68121i	0.308473	+	0.0792529i
$451$	−0.0752701	−	0.0434572i	−0.00354433	−	0.00204632i
$452$	−9.21499	−	0.482937i	−0.433437	−	0.0227154i
$453$	−6.92257	−	8.54866i	−0.325251	−	0.401651i
$454$	5.91145	+	4.29492i	0.277438	+	0.201571i
$455$	−4.11509	−	11.1555i	−0.192919	−	0.522977i
$456$	−12.6398	+	9.18334i	−0.591912	+	0.430049i
$457$	22.2310	+	5.95677i	1.03992	+	0.278646i	0.738080	−	0.674713i	$-0.235732\pi$
$457$	22.2310	+	5.95677i	1.03992	+	0.278646i	0.301840	+	0.953359i	$0.402399\pi$
$458$	−1.88031	−	1.52265i	−0.0878613	−	0.0711487i
$459$	−1.02889	+	4.84056i	−0.0480246	+	0.225938i
$460$	−3.27364	−	1.43733i	−0.152634	−	0.0670158i
$461$	23.0880	+	7.50175i	1.07532	+	0.349391i	0.792556	−	0.609799i	$-0.208750\pi$
$461$	23.0880	+	7.50175i	1.07532	+	0.349391i	0.282760	+	0.959191i	$0.408750\pi$
$462$	−2.34724	−	1.97287i	−0.109203	−	0.0917863i
$463$	2.79874	−	5.49284i	0.130069	−	0.255274i	−0.816783	−	0.576945i	$-0.804245\pi$
$463$	2.79874	−	5.49284i	0.130069	−	0.255274i	0.946851	+	0.321671i	$0.104245\pi$
$464$	−1.05803	−	4.97762i	−0.0491176	−	0.231080i
$465$	21.3752	+	12.1944i	0.991249	+	0.565499i
$466$	−22.1665	−	4.71162i	−1.02684	−	0.218262i
$467$	−10.5121	−	27.3851i	−0.486444	−	1.26723i	−0.928864	−	0.370422i	$-0.879213\pi$
$467$	−10.5121	−	27.3851i	−0.486444	−	1.26723i	0.442420	−	0.896808i	$-0.354120\pi$
$468$	−3.44880	+	3.44880i	−0.159421	+	0.159421i
$469$	20.6947	−	8.76422i	0.955594	−	0.404694i
$470$	−0.320677	−	0.0490956i	−0.0147917	−	0.00226461i
$471$	−1.54546	+	14.7041i	−0.0712109	+	0.677527i
$472$	11.8896	+	4.56399i	0.547263	+	0.210075i
$473$	−0.328506	+	6.26828i	−0.0151047	+	0.288216i
$474$	4.55512	+	7.88970i	0.209224	+	0.362386i
$475$	−15.7078	−	21.1574i	−0.720725	−	0.970768i
$476$	−2.34409	+	2.50956i	−0.107441	+	0.115026i
$477$	−8.81577	−	17.3019i	−0.403646	−	0.792200i
$478$	−1.94131	+	1.57204i	−0.0887934	+	0.0719035i
$479$	8.30871	−	3.69927i	0.379635	−	0.169024i	−0.208043	−	0.978120i	$-0.566709\pi$
$479$	8.30871	−	3.69927i	0.379635	−	0.169024i	0.587677	+	0.809096i	$0.300043\pi$
$480$	−5.19814	+	13.7533i	−0.237261	+	0.627748i
$481$	−6.26471	+	14.0708i	−0.285646	+	0.641572i
$482$	14.7394	+	14.7394i	0.671360	+	0.671360i
$483$	0.470937	+	3.37110i	0.0214284	+	0.153390i
$484$	12.2635	−	3.98466i	0.557433	−	0.181121i
$485$	38.7063	+	3.86640i	1.75756	+	0.175564i
$486$	−8.72786	+	7.85860i	−0.395904	+	0.356473i
$487$	−0.445473	+	0.289294i	−0.0201863	+	0.0131091i	−0.554693	−	0.832055i	$-0.687164\pi$
$487$	−0.445473	+	0.289294i	−0.0201863	+	0.0131091i	0.534506	+	0.845164i	$0.320498\pi$
$488$	−0.631868	−	12.0568i	−0.0286033	−	0.545784i
$489$	−1.21199	+	3.73011i	−0.0548080	+	0.168682i
$490$	2.90177	−	11.8147i	0.131089	−	0.533735i
$491$	1.98288	+	6.10267i	0.0894861	+	0.275410i	0.985777	−	0.168056i	$-0.0537489\pi$
$491$	1.98288	+	6.10267i	0.0894861	+	0.275410i	−0.896291	+	0.443466i	$0.853749\pi$
$492$	0.0958265	−	0.0367843i	0.00432019	−	0.00165837i
$493$	−1.65436	−	6.17415i	−0.0745086	−	0.278070i
$494$	−8.18762	+	0.860554i	−0.368379	+	0.0387181i
$495$	−4.99171	−	1.30996i	−0.224361	−	0.0588783i
$496$	4.26357	−	5.86830i	0.191440	−	0.263494i
$497$	25.6559	−	12.4870i	1.15082	−	0.560118i
$498$	4.86582	−	2.47926i	0.218043	−	0.111098i
$499$	−5.43364	+	3.13711i	−0.243243	+	0.140437i	−0.616666	−	0.787225i	$-0.711517\pi$
$499$	−5.43364	+	3.13711i	−0.243243	+	0.140437i	0.373423	+	0.927661i	$0.378184\pi$
$500$	−14.6547	−	5.36669i	−0.655379	−	0.240006i
$501$	10.7562	−	18.6303i	0.480553	−	0.832343i
$502$	−8.96567	−	5.82237i	−0.400157	−	0.259865i
$503$	4.92568	−	0.780151i	0.219625	−	0.0347852i	−0.0456521	−	0.998957i	$-0.514537\pi$
$503$	4.92568	−	0.780151i	0.219625	−	0.0347852i	0.265277	+	0.964172i	$0.414537\pi$
$504$	−11.9193	+	2.30666i	−0.530929	+	0.102747i
$505$	−5.57623	+	5.63407i	−0.248139	+	0.250713i
$506$	−1.07973	−	0.480729i	−0.0480001	−	0.0213710i
$507$	−9.72131	+	2.60482i	−0.431739	+	0.115684i
$508$	16.2434	−	20.0589i	0.720684	−	0.889971i
$509$	−15.1400	+	16.8147i	−0.671070	+	0.745298i	−0.978494	−	0.206274i	$-0.933866\pi$
$509$	−15.1400	+	16.8147i	−0.671070	+	0.745298i	0.307425	+	0.951572i	$0.400533\pi$
$510$	−0.551976	+	1.72911i	−0.0244419	+	0.0765663i
$511$	2.24715	−	3.73290i	0.0994082	−	0.165134i
$512$	7.34327	+	3.74158i	0.324530	+	0.165356i
$513$	28.0101	−	1.46795i	1.23668	−	0.0648115i
$514$	4.80611	+	5.33772i	0.211988	+	0.235437i
$515$	−12.9715	+	5.85567i	−0.571593	+	0.258032i
$516$	−5.50883	−	4.96017i	−0.242513	−	0.218359i
$517$	0.244752	+	0.0387649i	0.0107642	+	0.00170488i
$518$	−13.3716	+	8.34013i	−0.587513	+	0.366444i
$519$	3.27343	+	4.50548i	0.143687	+	0.197769i
$520$	−9.17982	+	7.51242i	−0.402562	+	0.329442i
$521$	12.5522	+	28.1927i	0.549921	+	1.23514i	0.948140	+	0.317853i	$0.102962\pi$
$521$	12.5522	+	28.1927i	0.549921	+	1.23514i	−0.398219	+	0.917290i	$0.630372\pi$
$522$	3.32882	−	8.67186i	0.145698	−	0.379557i
$523$	−16.6846	+	25.6920i	−0.729567	+	1.12343i	0.257987	+	0.966149i	$0.416941\pi$
$523$	−16.6846	+	25.6920i	−0.729567	+	1.12343i	−0.987553	+	0.157286i	$0.949726\pi$
$524$	23.3916			1.02187
$525$	2.97337	+	14.5575i	0.129769	+	0.635343i
$526$	6.52252			0.284395
$527$	4.96226	−	7.64121i	0.216159	−	0.332856i
$528$	0.395563	−	1.03048i	0.0172147	−	0.0448457i
$529$	−8.82128	−	19.8129i	−0.383534	−	0.861432i
$530$	−7.05026	−	18.0871i	−0.306244	−	0.785652i
$531$	−4.93056	−	6.78633i	−0.213968	−	0.294502i
$532$	17.1778	+	9.15184i	0.744754	+	0.396783i
$533$	0.129963	+	0.0205840i	0.00562930	+	0.000891594i
$534$	10.1820	+	9.16792i	0.440619	+	0.396735i
$535$	−10.9214	+	19.1438i	−0.472173	+	0.827660i
$536$	−15.0022	−	16.6617i	−0.647998	−	0.719675i
$537$	22.7161	−	1.19050i	0.980273	−	0.0513739i
$538$	−3.04985	−	1.55398i	−0.131488	−	0.0669966i
$539$	−2.26305	+	9.01310i	−0.0974764	+	0.388222i
$540$	13.3888	−	9.83344i	0.576161	−	0.423164i
$541$	26.4951	−	29.4258i	1.13911	−	1.26511i	0.179509	−	0.983756i	$-0.442549\pi$
$541$	26.4951	−	29.4258i	1.13911	−	1.26511i	0.959603	−	0.281356i	$-0.0907841\pi$
$542$	1.67887	−	2.07323i	0.0721135	−	0.0890528i
$543$	−4.94065	+	1.32384i	−0.212023	+	0.0568115i
$544$	4.97289	+	2.21407i	0.213211	+	0.0949276i
$545$	21.6351	+	10.8834i	0.926747	+	0.466194i
$546$	4.38790	+	1.51493i	0.187785	+	0.0648331i
$547$	37.0235	−	5.86395i	1.58301	−	0.250724i	0.697932	−	0.716164i	$-0.254104\pi$
$547$	37.0235	−	5.86395i	1.58301	−	0.250724i	0.885079	+	0.465440i	$0.154104\pi$
$548$	−3.86625	−	2.51077i	−0.165158	−	0.107255i
$549$	−3.97611	+	6.88682i	−0.169696	+	0.293922i
$550$	−4.83534	−	1.79909i	−0.206179	−	0.0767134i
$551$	−31.3750	+	18.1143i	−1.33662	+	0.771697i
$552$	3.02561	−	1.54162i	0.128778	−	0.0656159i
$553$	15.4586	−	22.8774i	0.657365	−	0.972848i
$554$	3.51735	−	4.84122i	0.149438	−	0.205684i
$555$	10.3991	−	16.1956i	0.441419	−	0.687464i
$556$	11.9765	−	1.25878i	0.507916	−	0.0533841i
$557$	−1.55832	−	5.81572i	−0.0660280	−	0.246420i	0.925021	−	0.379915i	$-0.124047\pi$
$557$	−1.55832	−	5.81572i	−0.0660280	−	0.246420i	−0.991050	+	0.133495i	$0.957380\pi$
$558$	12.3609	−	4.74490i	0.523278	−	0.200868i
$559$	−2.93652	−	9.03767i	−0.124201	−	0.382253i
$560$	4.36114	−	0.400599i	0.184292	−	0.0169284i
$561$	0.428435	−	1.31859i	0.0180885	−	0.0556708i
$562$	0.986964	+	18.8324i	0.0416326	+	0.794397i
$563$	−25.3462	+	16.4600i	−1.06822	+	0.693708i	−0.954018	−	0.299750i	$-0.903097\pi$
$563$	−25.3462	+	16.4600i	−1.06822	+	0.693708i	−0.114199	+	0.993458i	$0.536430\pi$
$564$	−0.217481	+	0.195821i	−0.00915761	+	0.00824555i
$565$	11.0359	+	9.83410i	0.464282	+	0.413724i
$566$	5.35873	−	1.74116i	0.225244	−	0.0731863i
$567$	−1.86894	−	0.756899i	−0.0784882	−	0.0317868i
$568$	−20.1280	−	20.1280i	−0.844552	−	0.844552i
$569$	2.02703	−	4.55278i	0.0849775	−	0.190863i	−0.866059	−	0.499943i	$-0.833354\pi$
$569$	2.02703	−	4.55278i	0.0849775	−	0.190863i	0.951036	+	0.309080i	$0.100021\pi$
$570$	10.2761	+	0.485400i	0.430420	+	0.0203312i
$571$	−2.23119	+	0.993391i	−0.0933725	+	0.0415721i	−0.452891	−	0.891566i	$-0.649607\pi$
$571$	−2.23119	+	0.993391i	−0.0933725	+	0.0415721i	0.359519	+	0.933138i	$0.382941\pi$
$572$	2.89443	−	2.34386i	0.121022	−	0.0980018i
$573$	7.89270	+	15.4903i	0.329722	+	0.647117i
$574$	0.0983877	+	0.0919002i	0.00410662	+	0.00383584i
$575$	2.65263	+	5.07591i	0.110622	+	0.211680i
$576$	2.66831	+	4.62165i	0.111180	+	0.192569i
$577$	−1.27197	+	24.2706i	−0.0529527	+	1.01040i	0.834938	+	0.550343i	$0.185503\pi$
$577$	−1.27197	+	24.2706i	−0.0529527	+	1.01040i	−0.887891	+	0.460054i	$0.847830\pi$
$578$	−11.7082	−	4.49437i	−0.486998	−	0.186941i
$579$	0.920556	−	8.75851i	0.0382570	−	0.363991i
$580$	−9.64235	+	19.1680i	−0.400377	+	0.795908i
$581$	−13.2099	−	9.97149i	−0.548038	−	0.413687i
$582$	−10.7384	+	10.7384i	−0.445123	+	0.445123i
$583$	5.31398	+	13.8434i	0.220083	+	0.573335i
$584$	−4.25172	−	0.903731i	−0.175937	−	0.0373966i
$585$	7.76588	−	0.856758i	0.321080	−	0.0354226i
$586$	5.03247	+	23.6759i	0.207890	+	0.978044i
$587$	4.09368	−	8.03430i	0.168964	−	0.331611i	−0.790961	−	0.611866i	$-0.790419\pi$
$587$	4.09368	−	8.03430i	0.168964	−	0.331611i	0.959926	+	0.280255i	$0.0904191\pi$
$588$	−6.59023	−	8.77567i	−0.271777	−	0.361903i
$589$	−49.1130	−	15.9578i	−2.02366	−	0.657528i
$590$	−4.23034	−	7.24063i	−0.174160	−	0.298092i
$591$	−3.82016	+	17.9724i	−0.157140	+	0.739287i
$592$	−4.40882	−	3.57019i	−0.181202	−	0.146734i
$593$	24.7752	+	6.63849i	1.01740	+	0.272610i	0.728716	−	0.684816i	$-0.240117\pi$
$593$	24.7752	+	6.63849i	1.01740	+	0.272610i	0.288679	+	0.957426i	$0.406784\pi$
$594$	4.44277	−	3.22786i	0.182289	−	0.132441i
$595$	5.44408	−	0.789186i	0.223186	−	0.0323535i
$596$	0.0446416	+	0.0324340i	0.00182859	+	0.00132855i
$597$	−19.3051	−	23.8398i	−0.790104	−	0.975697i
$598$	1.78689	+	0.0936469i	0.0730714	+	0.00382951i
$599$	−23.1803	−	13.3832i	−0.947123	−	0.546822i	−0.0549370	−	0.998490i	$-0.517496\pi$
$599$	−23.1803	−	13.3832i	−0.947123	−	0.546822i	−0.892186	+	0.451668i	$0.850829\pi$
$600$	12.7596	−	7.54339i	0.520910	−	0.307958i
$601$		−	3.83116i		−	0.156276i	−0.996943	−	0.0781382i	$-0.975102\pi$
$601$		−	3.83116i		−	0.156276i	0.996943	−	0.0781382i	$-0.0248975\pi$
$602$	2.68775	−	9.34413i	0.109544	−	0.380838i
$603$	2.31015	+	14.5857i	0.0940764	+	0.593975i
$604$	13.5961	+	1.42901i	0.553219	+	0.0581457i
$605$	−19.3219	−	7.30283i	−0.785546	−	0.296902i
$606$	−0.323490	−	3.07780i	−0.0131409	−	0.125027i
$607$	−8.71399	+	32.5210i	−0.353690	+	1.31999i	0.528435	+	0.848974i	$0.322779\pi$
$607$	−8.71399	+	32.5210i	−0.353690	+	1.31999i	−0.882125	+	0.471015i	$0.843888\pi$
$608$	4.82648	−	30.4732i	0.195740	−	1.23585i
$609$	20.3514	−	1.76358i	0.824682	−	0.0714637i
$610$	−4.63955	+	6.45557i	−0.187850	+	0.261379i
$611$	−0.366959	+	0.0779995i	−0.0148456	+	0.00315552i
$612$	−1.22897	−	1.89244i	−0.0496780	−	0.0764974i
$613$	24.1890	+	37.2478i	0.976985	+	1.50442i	0.859363	+	0.511366i	$0.170860\pi$
$613$	24.1890	+	37.2478i	0.976985	+	1.50442i	0.117622	+	0.993058i	$0.462473\pi$
$614$	−2.51124	+	0.533781i	−0.101346	+	0.0215417i
$615$	−0.156638	−	0.0500028i	−0.00631625	−	0.00201631i
$616$	9.23610	−	0.800364i	0.372133	−	0.0322476i
$617$	−5.46815	+	34.5246i	−0.220140	+	1.38991i	0.591762	+	0.806112i	$0.298432\pi$
$617$	−5.46815	+	34.5246i	−0.220140	+	1.38991i	−0.811902	+	0.583794i	$0.801568\pi$
$618$	1.43807	−	5.36695i	0.0578476	−	0.215890i
$619$	1.39751	+	13.2964i	0.0561706	+	0.534427i	0.986037	+	0.166529i	$0.0532559\pi$
$619$	1.39751	+	13.2964i	0.0561706	+	0.534427i	−0.929866	+	0.367898i	$0.880077\pi$
$620$	−29.5010	+	8.06812i	−1.18479	+	0.324023i
$621$	−6.06282	−	0.637228i	−0.243293	−	0.0255711i
$622$	−0.751132	−	4.74246i	−0.0301176	−	0.190155i
$623$	11.4787	−	39.9066i	0.459885	−	1.59882i
$624$			1.67106i			0.0668960i
$625$	12.9441	+	21.3881i	0.517765	+	0.855523i
$626$	7.53917	+	4.35274i	0.301326	+	0.173971i
$627$	−7.84740	−	0.411265i	−0.313395	−	0.0164243i
$628$	−11.5638	−	14.2801i	−0.461446	−	0.569838i
$629$	−5.76493	−	4.18846i	−0.229863	−	0.167005i
$630$	7.07454	+	3.72237i	0.281856	+	0.148303i
$631$	11.1996	−	8.13699i	0.445849	−	0.323928i	−0.342106	−	0.939662i	$-0.611140\pi$
$631$	11.1996	−	8.13699i	0.445849	−	0.323928i	0.787955	+	0.615733i	$0.211140\pi$
$632$	−26.6062	−	7.12911i	−1.05834	−	0.283581i
$633$	−12.8171	−	10.3791i	−0.509436	−	0.412533i
$634$	1.45326	−	6.83703i	0.0577162	−	0.271533i
$635$	−40.3982	+	8.80499i	−1.60315	+	0.349415i
$636$	−16.6548	−	5.41147i	−0.660405	−	0.214579i
$637$	−1.69147	−	13.9667i	−0.0670186	−	0.553382i
$638$	−3.22021	+	6.32003i	−0.127489	+	0.250212i
$639$	3.89813	+	18.3393i	0.154208	+	0.725490i
$640$	−8.57699	−	18.9998i	−0.339035	−	0.751033i
$641$	2.29399	+	0.487602i	0.0906070	+	0.0192591i	0.252992	−	0.967468i	$-0.418585\pi$
$641$	2.29399	+	0.487602i	0.0906070	+	0.0192591i	−0.162385	+	0.986727i	$0.551919\pi$
$642$	−3.08361	−	8.03308i	−0.121700	−	0.317041i
$643$	16.5284	−	16.5284i	0.651816	−	0.651816i	−0.301614	−	0.953430i	$-0.597525\pi$
$643$	16.5284	−	16.5284i	0.651816	−	0.651816i	0.953430	+	0.301614i	$0.0975254\pi$
$644$	−3.37639	−	2.54867i	−0.133048	−	0.100432i
$645$	1.91809	+	11.7187i	0.0755247	+	0.461424i
$646$	0.398131	−	3.78797i	0.0156643	−	0.149036i
$647$	−10.9473	−	4.20226i	−0.430381	−	0.165208i	0.133527	−	0.991045i	$-0.457370\pi$
$647$	−10.9473	−	4.20226i	−0.430381	−	0.165208i	−0.563909	+	0.825837i	$0.690703\pi$
$648$	−0.105278	+	2.00883i	−0.00413572	+	0.0789143i
$649$	3.20276	+	5.54735i	0.125719	+	0.217752i
$650$	7.81024	−	0.0805937i	0.306343	−	0.00316115i
$651$	21.2789	+	19.8758i	0.833986	+	0.778994i
$652$	−2.21293	−	4.34313i	−0.0866652	−	0.170090i
$653$	16.1758	−	13.0989i	0.633008	−	0.512600i	−0.258261	−	0.966075i	$-0.583149\pi$
$653$	16.1758	−	13.0989i	0.633008	−	0.512600i	0.891269	+	0.453475i	$0.149816\pi$
$654$	−8.63758	+	3.84570i	−0.337756	+	0.150379i
$655$	−29.2417	−	23.4307i	−1.14257	−	0.915513i
$656$	−0.0197126	+	0.0442752i	−0.000769648	+	0.00172866i
$657$	2.02445	+	2.02445i	0.0789813	+	0.0789813i
$658$	−0.355782	−	0.144087i	−0.0138698	−	0.00561711i
$659$	30.5370	−	9.92209i	1.18955	−	0.386510i	0.353646	−	0.935379i	$-0.384942\pi$
$659$	30.5370	−	9.92209i	1.18955	−	0.386510i	0.835908	+	0.548870i	$0.184942\pi$
$660$	−4.01846	+	2.34779i	−0.156418	+	0.0913875i
$661$	−7.51696	+	6.76830i	−0.292376	+	0.263256i	−0.802244	−	0.596996i	$-0.796361\pi$
$661$	−7.51696	+	6.76830i	−0.292376	+	0.263256i	0.509868	+	0.860252i	$0.329694\pi$
$662$	4.71049	−	3.05903i	0.183079	−	0.118893i
$663$	0.109852	+	2.09611i	0.00426631	+	0.0814060i
$664$	−5.10231	+	15.7033i	−0.198008	+	0.609406i
$665$	−12.3068	−	28.6472i	−0.477236	−	1.11089i
$666$	−3.19997	−	9.84849i	−0.123996	−	0.381621i
$667$	7.35113	−	2.82183i	0.284637	−	0.109262i
$668$	6.91979	+	25.8250i	0.267735	+	0.999199i
$669$	−24.1506	+	2.53833i	−0.933716	+	0.0981375i
$670$	0.848692	+	14.7387i	0.0327878	+	0.569404i
$671$	3.56931	−	4.91273i	0.137792	−	0.189654i
$672$	−9.73998	+	14.4144i	−0.375728	+	0.556048i
$673$	10.0639	−	5.12781i	0.387935	−	0.197663i	−0.249135	−	0.968469i	$-0.580146\pi$
$673$	10.0639	−	5.12781i	0.387935	−	0.197663i	0.637070	+	0.770806i	$0.280146\pi$
$674$	−6.82894	+	3.94269i	−0.263041	+	0.151867i
$675$	−26.5871	−	1.11841i	−1.02334	−	0.0430478i
$676$	6.25399	−	10.8322i	0.240538	−	0.416624i
$677$	20.5086	+	13.3184i	0.788208	+	0.511868i	0.874863	−	0.484370i	$-0.160951\pi$
$677$	20.5086	+	13.3184i	0.788208	+	0.511868i	−0.0866551	+	0.996238i	$0.527618\pi$
$678$	−5.69985	+	0.902768i	−0.218901	+	0.0346706i
$679$	43.5059	+	15.0205i	1.66960	+	0.576435i
$680$	−2.51664	−	4.87681i	−0.0965086	−	0.187017i
$681$	−9.64609	−	4.29471i	−0.369639	−	0.164574i
$682$	−9.76605	+	2.61681i	−0.373961	+	0.100203i
$683$	−10.3756	+	12.8128i	−0.397012	+	0.490269i	−0.935978	−	0.352058i	$-0.885482\pi$
$683$	−10.3756	+	12.8128i	−0.397012	+	0.490269i	0.538966	+	0.842328i	$0.318815\pi$
$684$	−8.55778	+	9.50438i	−0.327215	+	0.363409i
$685$	2.31820	+	7.01141i	0.0885740	+	0.267892i
$686$	6.56689	−	12.8096i	0.250725	−	0.489074i
$687$	3.11525	+	1.58730i	0.118854	+	0.0605593i
$688$	3.49532	−	0.183182i	0.133258	−	0.00698375i
$689$	−15.0213	−	16.6829i	−0.572267	−	0.635567i
$690$	−2.18947	−	0.453592i	−0.0833516	−	0.0172680i
$691$	−20.8963	−	18.8151i	−0.794932	−	0.715760i	0.167917	−	0.985801i	$-0.446296\pi$
$691$	−20.8963	−	18.8151i	−0.794932	−	0.715760i	−0.962849	+	0.270041i	$0.912963\pi$
$692$	−6.83613	−	1.08274i	−0.259870	−	0.0411594i
$693$	−5.38914	−	2.87117i	−0.204716	−	0.109067i
$694$	−3.66214	−	5.04050i	−0.139013	−	0.191335i
$695$	−16.2326	−	10.4229i	−0.615738	−	0.395363i
$696$	−8.28889	−	18.6172i	−0.314190	−	0.705681i
$697$	−0.0218160	+	0.0568327i	−0.000826341	+	0.00215269i
$698$	3.73395	−	5.74978i	0.141332	−	0.217632i
$699$	32.7474			1.23862
$700$	−15.4062	−	10.1802i	−0.582300	−	0.384775i
$701$	−35.1051			−1.32590			−0.662951	−	0.748663i	$-0.730696\pi$
$701$	−35.1051			−1.32590			−0.662951	+	0.748663i	$0.730696\pi$
$702$	−4.52805	+	6.97258i	−0.170900	+	0.263163i
$703$	−14.4739	+	37.7057i	−0.545892	+	1.42210i
$704$	−1.65751	−	3.72283i	−0.0624698	−	0.140310i
$705$	0.468020	−	0.0269499i	0.0176267	−	0.00101499i
$706$	7.69154	+	10.5865i	0.289475	+	0.398428i
$707$	−7.95823	+	4.96372i	−0.299300	+	0.186680i
$708$	−7.47165	−	1.18339i	−0.280802	−	0.0444746i
$709$	−39.0403	−	35.1521i	−1.46619	−	1.32016i	−0.842767	−	0.538278i	$-0.819075\pi$
$709$	−39.0403	−	35.1521i	−1.46619	−	1.32016i	−0.623423	−	0.781885i	$-0.714258\pi$
$710$	2.05536	+	18.6303i	0.0771363	+	0.699184i
$711$	12.1398	+	13.4826i	0.455278	+	0.505638i
$712$	−41.3689	+	2.16805i	−1.55036	+	0.0812511i
$713$	10.0005	+	5.09550i	0.374521	+	0.190828i
$714$	−1.10763	+	1.83996i	−0.0414520	+	0.0688588i
$715$	−5.96608	+	0.0307811i	−0.223119	+	0.00115115i
$716$	−18.9168	+	21.0092i	−0.706953	+	0.785151i
$717$	2.27169	−	2.80530i	0.0848377	−	0.104766i
$718$	10.3777	−	2.78070i	0.387293	−	0.103775i
$719$	−2.53041	−	1.12661i	−0.0943685	−	0.0420156i	0.359009	−	0.933334i	$-0.383115\pi$
$719$	−2.53041	−	1.12661i	−0.0943685	−	0.0420156i	−0.453378	+	0.891318i	$0.649781\pi$
$720$	−0.435506	+	2.84458i	−0.0162303	+	0.106011i
$721$	−16.5328	+	3.19947i	−0.615712	+	0.119154i
$722$	−6.73625	+	1.06692i	−0.250697	+	0.0397066i
$723$	−25.2621	−	16.4054i	−0.939508	−	0.610124i
$724$	3.17846	−	5.50525i	0.118126	−	0.204601i
$725$	31.2539	−	14.3033i	1.16074	−	0.531213i
$726$	6.98382	−	4.03211i	0.259194	−	0.149646i
$727$	−5.31536	+	2.70831i	−0.197136	+	0.100446i	−0.549772	−	0.835315i	$-0.685285\pi$
$727$	−5.31536	+	2.70831i	−0.197136	+	0.100446i	0.352636	+	0.935761i	$0.385285\pi$
$728$	−12.6199	+	6.14222i	−0.467724	+	0.227646i
$729$	11.3195	−	15.5799i	0.419239	−	0.577033i
$730$	1.81266	+	2.21498i	0.0670895	+	0.0819802i
$731$	4.37233	−	0.459550i	0.161716	−	0.0169971i
$732$	1.85611	+	6.92710i	0.0686038	+	0.256033i
$733$	28.1255	−	10.7964i	1.03884	−	0.398773i	0.221641	−	0.975128i	$-0.428859\pi$
$733$	28.1255	−	10.7964i	1.03884	−	0.398773i	0.817199	+	0.576355i	$0.195525\pi$
$734$	0.249589	+	0.768156i	0.00921250	+	0.0283532i
$735$	−0.551932	+	17.5717i	−0.0203583	+	0.648140i
$736$	−2.07219	+	6.37755i	−0.0763820	+	0.235080i
$737$	−0.590180	−	11.2613i	−0.0217396	−	0.414816i
$738$	−0.0741934	+	0.0481817i	−0.00273110	+	0.00177359i
$739$	−33.5727	+	30.2290i	−1.23499	+	1.11199i	−0.245198	+	0.969473i	$0.578853\pi$
$739$	−33.5727	+	30.2290i	−1.23499	+	1.11199i	−0.989792	+	0.142517i	$0.954480\pi$
$740$	5.09393	+	23.3715i	0.187257	+	0.859154i
$741$	11.3145	−	3.67629i	0.415648	−	0.135052i
$742$	−3.17791	−	22.7484i	−0.116665	−	0.835119i
$743$	23.4363	+	23.4363i	0.859793	+	0.859793i	0.991313	−	0.131520i	$-0.0419858\pi$
$743$	23.4363	+	23.4363i	0.859793	+	0.859793i	−0.131520	+	0.991313i	$0.541986\pi$
$744$	11.8150	−	26.5369i	0.433159	−	0.972891i
$745$	−0.0233179	−	0.0852617i	−0.000854303	−	0.00312375i
$746$	15.6249	−	6.95667i	0.572070	−	0.254702i
$747$	8.45180	−	6.84413i	0.309235	−	0.250414i
$748$	0.782267	+	1.53529i	0.0286025	+	0.0561356i
$749$	−17.8010	+	19.0576i	−0.650434	+	0.696351i
$750$	−9.66250	−	1.37745i	−0.352825	−	0.0502972i
$751$	19.3994	+	33.6008i	0.707894	+	1.22611i	0.965637	+	0.259895i	$0.0836881\pi$
$751$	19.3994	+	33.6008i	0.707894	+	1.22611i	−0.257742	+	0.966214i	$0.582979\pi$
$752$	0.00723178	−	0.137991i	0.000263716	−	0.00503200i
$753$	14.4221	+	5.53611i	0.525569	+	0.201747i
$754$	1.12248	−	10.6797i	0.0408784	−	0.388932i
$755$	−15.5651	−	15.4053i	−0.566470	−	0.560655i
$756$	18.0993	−	7.66505i	0.658265	−	0.278775i
$757$	2.63808	−	2.63808i	0.0958825	−	0.0958825i	−0.657538	−	0.753421i	$-0.728402\pi$
$757$	2.63808	−	2.63808i	0.0958825	−	0.0958825i	0.753421	+	0.657538i	$0.228402\pi$
$758$	−8.44928	−	22.0111i	−0.306892	−	0.799480i
$759$	1.67061	+	0.355100i	0.0606394	+	0.0128893i
$760$	−23.0075	+	20.9320i	−0.834568	+	0.759282i
$761$	−8.25480	−	38.8358i	−0.299236	−	1.40780i	−0.828809	−	0.559532i	$-0.810981\pi$
$761$	−8.25480	−	38.8358i	−0.299236	−	1.40780i	0.529573	−	0.848265i	$-0.322352\pi$
$762$	7.32833	−	14.3827i	0.265477	−	0.521029i
$763$	21.9362	+	18.4375i	0.794142	+	0.667483i
$764$	−20.5490	−	6.67679i	−0.743438	−	0.241558i
$765$	−0.359282	+	3.59675i	−0.0129899	+	0.130041i
$766$	3.45569	−	16.2577i	0.124859	−

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.423319 + 0.651855i) q^{2} +(0.402507 - 1.04857i) q^{3} +(0.567758 + 1.27521i) q^{4} +(0.567586 - 2.16283i) q^{5} +(0.513123 + 0.706254i) q^{6} +(1.24404 - 2.33503i) q^{7} +(-2.60695 - 0.412900i) q^{8} +(1.29196 + 1.16328i) q^{9} +O(q^{10})\)	\(q+(-0.423319 + 0.651855i) q^{2} +(0.402507 - 1.04857i) q^{3} +(0.567758 + 1.27521i) q^{4} +(0.567586 - 2.16283i) q^{5} +(0.513123 + 0.706254i) q^{6} +(1.24404 - 2.33503i) q^{7} +(-2.60695 - 0.412900i) q^{8} +(1.29196 + 1.16328i) q^{9} +(1.16958 + 1.28555i) q^{10} +(-0.888306 - 0.986564i) q^{11} +(1.56566 - 0.0820529i) q^{12} +(1.79077 + 0.912442i) q^{13} +(0.995478 + 1.79939i) q^{14} +(-2.03941 - 1.46571i) q^{15} +(-0.495338 + 0.550128i) q^{16} +(-0.585165 + 0.722619i) q^{17} +(-1.30520 + 0.349728i) q^{18} +(4.81455 + 2.14358i) q^{19} +(3.08031 - 0.504177i) q^{20} +(-1.94770 - 2.24432i) q^{21} +(1.01913 - 0.161415i) q^{22} +(-0.960654 - 0.623856i) q^{23} +(-1.48227 + 2.56736i) q^{24} +(-4.35569 - 2.45519i) q^{25} +(-1.35285 + 0.781066i) q^{26} +(4.74204 - 2.41619i) q^{27} +(3.68396 + 0.260667i) q^{28} +(-4.04060 + 5.56140i) q^{29} +(1.81875 - 0.708941i) q^{30} +(-9.74492 + 1.02423i) q^{31} +(-1.51519 - 5.65478i) q^{32} +(-1.39203 + 0.534349i) q^{33} +(-0.223331 - 0.687341i) q^{34} +(-4.34419 - 4.01597i) q^{35} +(-0.749906 + 2.30797i) q^{36} +(0.401079 + 7.65304i) q^{37} +(-3.43539 + 2.23097i) q^{38} +(1.67755 - 1.51047i) q^{39} +(-2.37270 + 5.40404i) q^{40} +(0.0622653 - 0.0202312i) q^{41} +(2.28747 - 0.319555i) q^{42} +(-3.34331 - 3.34331i) q^{43} +(0.753729 - 1.69290i) q^{44} +(3.24928 - 2.13402i) q^{45} +(0.813327 - 0.362116i) q^{46} +(-0.145063 + 0.117470i) q^{47} +(0.377469 + 0.740824i) q^{48} +(-3.90475 - 5.80972i) q^{49} +(3.44427 - 1.79995i) q^{50} +(0.522180 + 0.904443i) q^{51} +(-0.146828 + 2.80164i) q^{52} +(-10.4278 - 4.00284i) q^{53} +(-0.432393 + 4.11394i) q^{54} +(-2.63796 + 1.36130i) q^{55} +(-4.20727 + 5.57365i) q^{56} +(4.18557 - 4.18557i) q^{57} +(-1.91476 - 4.98813i) q^{58} +(-4.71962 - 1.00319i) q^{59} +(0.711181 - 3.43284i) q^{60} +(0.951026 + 4.47423i) q^{61} +(3.45756 - 6.78585i) q^{62} +(4.32354 - 1.56960i) q^{63} +(2.91943 + 0.948580i) q^{64} +(2.98987 - 3.35524i) q^{65} +(0.240954 - 1.13360i) q^{66} +(6.60139 + 5.34570i) q^{67} +(-1.25372 - 0.335933i) q^{68} +(-1.04082 + 0.756203i) q^{69} +(4.45681 - 1.13174i) q^{70} +(8.72491 + 6.33902i) q^{71} +(-2.88774 - 3.56607i) q^{72} +(1.64457 + 0.0861882i) q^{73} +(-5.15845 - 2.97823i) q^{74} +(-4.32762 + 3.57900i) q^{75} +7.35658i q^{76} +(-3.40874 + 0.846904i) q^{77} +(0.274469 + 1.73293i) q^{78} +(10.3787 + 1.09084i) q^{79} +(0.908689 + 1.38358i) q^{80} +(-0.0796638 - 0.757950i) q^{81} +(-0.0131703 + 0.0491522i) q^{82} +(0.978599 - 6.17863i) q^{83} +(1.75614 - 3.75795i) q^{84} +(1.23077 + 1.67576i) q^{85} +(3.59464 - 0.764065i) q^{86} +(4.20513 + 6.47533i) q^{87} +(1.90842 + 2.93870i) q^{88} +(15.3519 - 3.26314i) q^{89} +(0.0155886 + 3.02143i) q^{90} +(4.35836 - 3.04639i) q^{91} +(0.250126 - 1.57923i) q^{92} +(-2.84842 + 10.6304i) q^{93} +(-0.0151652 - 0.144287i) q^{94} +(7.36887 - 9.19641i) q^{95} +(-6.53929 - 0.687307i) q^{96} +(2.72136 + 17.1820i) q^{97} +(5.44005 - 0.0859631i) q^{98} -2.30795i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

L-functions

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