LMFDB - Embedded newform 175.2.x.a.33.9

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			33.9
Character	$\chi$	$=$	175.33
Dual form			175.2.x.a.122.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0144040 - 0.00935405i) q^{2} +(1.05595 - 0.405343i) q^{3} +(-0.813353 + 1.82682i) q^{4} +(-0.770525 + 2.09912i) q^{5} +(0.0114183 - 0.0157160i) q^{6} +(-0.822022 + 2.51481i) q^{7} +(0.0107461 + 0.0678483i) q^{8} +(-1.27870 + 1.15134i) q^{9} +O(q^{10})$	\(q+(0.0144040 - 0.00935405i) q^{2} +(1.05595 - 0.405343i) q^{3} +(-0.813353 + 1.82682i) q^{4} +(-0.770525 + 2.09912i) q^{5} +(0.0114183 - 0.0157160i) q^{6} +(-0.822022 + 2.51481i) q^{7} +(0.0107461 + 0.0678483i) q^{8} +(-1.27870 + 1.15134i) q^{9} +(0.00853662 + 0.0374431i) q^{10} +(3.39365 - 3.76903i) q^{11} +(-0.118375 + 2.25873i) q^{12} +(-0.145799 - 0.286147i) q^{13} +(0.0116833 + 0.0439125i) q^{14} +(0.0372227 + 2.52890i) q^{15} +(-2.67534 - 2.97126i) q^{16} +(2.90424 - 2.35181i) q^{17} +(-0.00764859 + 0.0285449i) q^{18} +(6.10342 - 2.71742i) q^{19} +(-3.20800 - 3.11494i) q^{20} +(0.151343 + 2.98873i) q^{21} +(0.0136263 - 0.0860334i) q^{22} +(1.86170 + 2.86676i) q^{23} +(0.0388492 + 0.0672888i) q^{24} +(-3.81258 - 3.23484i) q^{25} +(-0.00477673 - 0.00275784i) q^{26} +(-2.42406 + 4.75748i) q^{27} +(-3.92552 - 3.54712i) q^{28} +(1.99592 + 2.74715i) q^{29} +(0.0241916 + 0.0360780i) q^{30} +(0.746861 + 0.0784982i) q^{31} +(-0.199035 - 0.0533314i) q^{32} +(2.05579 - 5.35552i) q^{33} +(0.0198337 - 0.0610417i) q^{34} +(-4.64549 - 3.66325i) q^{35} +(-1.06327 - 3.27240i) q^{36} +(-3.29137 - 0.172493i) q^{37} +(0.0624947 - 0.0962334i) q^{38} +(-0.269945 - 0.243060i) q^{39} +(-0.150702 - 0.0297215i) q^{40} +(7.88534 + 2.56210i) q^{41} +(0.0301367 + 0.0416339i) q^{42} +(-3.99562 - 3.99562i) q^{43} +(4.12511 + 9.26514i) q^{44} +(-1.43154 - 3.57127i) q^{45} +(0.0536317 + 0.0238784i) q^{46} +(-3.96152 + 4.89207i) q^{47} +(-4.02942 - 2.05309i) q^{48} +(-5.64856 - 4.13446i) q^{49} +(-0.0851752 - 0.0109315i) q^{50} +(2.11346 - 3.66061i) q^{51} +(0.641326 - 0.0336105i) q^{52} +(-4.04766 - 10.5445i) q^{53} +(0.00958565 + 0.0912013i) q^{54} +(5.29674 + 10.0278i) q^{55} +(-0.179459 - 0.0287484i) q^{56} +(5.34345 - 5.34345i) q^{57} +(0.0544462 + 0.0208999i) q^{58} +(9.35373 - 1.98820i) q^{59} +(-4.65012 - 1.98889i) q^{60} +(0.570023 - 2.68175i) q^{61} +(0.0114920 - 0.00585548i) q^{62} +(-1.84430 - 4.16211i) q^{63} +(7.60172 - 2.46995i) q^{64} +(0.712999 - 0.0855661i) q^{65} +(-0.0204842 - 0.0963707i) q^{66} +(-4.10889 - 5.07406i) q^{67} +(1.93416 + 7.21837i) q^{68} +(3.12789 + 2.27255i) q^{69} +(-0.101180 - 0.00931112i) q^{70} +(-3.66851 + 2.66533i) q^{71} +(-0.0918577 - 0.0743849i) q^{72} +(0.528792 + 10.0900i) q^{73} +(-0.0490223 + 0.0283030i) q^{74} +(-5.33714 - 1.87045i) q^{75} +13.3601i q^{76} +(6.68874 + 11.6326i) q^{77} +(-0.00616188 - 0.000975946i) q^{78} +(-8.16023 + 0.857674i) q^{79} +(8.29845 - 3.32641i) q^{80} +(-0.0917101 + 0.872564i) q^{81} +(0.137546 - 0.0368554i) q^{82} +(-1.28282 + 0.203179i) q^{83} +(-5.58297 - 2.15442i) q^{84} +(2.69893 + 7.90846i) q^{85} +(-0.0949280 - 0.0201776i) q^{86} +(3.22114 + 2.09183i) q^{87} +(0.292191 + 0.189751i) q^{88} +(-0.969707 - 0.206118i) q^{89} +(-0.0540257 - 0.0380499i) q^{90} +(0.839457 - 0.131438i) q^{91} +(-6.75128 + 1.06930i) q^{92} +(0.820470 - 0.219844i) q^{93} +(-0.0113010 + 0.107521i) q^{94} +(1.00134 + 14.9056i) q^{95} +(-0.231790 + 0.0243621i) q^{96} +(-12.2690 - 1.94322i) q^{97} +(-0.120036 - 0.00671581i) q^{98} +8.72671i 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 $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{20}\right)$

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 $

$2$	0.0144040	−	0.00935405i	0.0101851	−	0.00661431i	−0.539536	−	0.841962i	$-0.681400\pi$
$2$	0.0144040	−	0.00935405i	0.0101851	−	0.00661431i	0.549722	+	0.835348i	$0.314734\pi$
$3$	1.05595	−	0.405343i	0.609656	−	0.234025i	−0.0338987	−	0.999425i	$-0.510792\pi$
$3$	1.05595	−	0.405343i	0.609656	−	0.234025i	0.643554	+	0.765400i	$0.277459\pi$
$4$	−0.813353	+	1.82682i	−0.406677	+	0.913411i
$5$	−0.770525	+	2.09912i	−0.344589	+	0.938754i
$5$	−0.770525	+	2.09912i	−0.344589	+	0.938754i
$6$	0.0114183	−	0.0157160i	0.00466152	−	0.00641603i
$7$	−0.822022	+	2.51481i	−0.310695	+	0.950510i
$7$	−0.822022	+	2.51481i	−0.310695	+	0.950510i
$8$	0.0107461	+	0.0678483i	0.00379932	+	0.0239880i
$9$	−1.27870	+	1.15134i	−0.426232	+	0.383781i
$10$	0.00853662	+	0.0374431i	0.00269952	+	0.0118406i
$11$	3.39365	−	3.76903i	1.02322	−	1.13641i	0.0326443	−	0.999467i	$-0.489607\pi$
$11$	3.39365	−	3.76903i	1.02322	−	1.13641i	0.990580	−	0.136938i	$-0.0437262\pi$
$12$	−0.118375	+	2.25873i	−0.0341719	+	0.652039i
$13$	−0.145799	−	0.286147i	−0.0404375	−	0.0793630i	0.869904	−	0.493222i	$-0.164181\pi$
$13$	−0.145799	−	0.286147i	−0.0404375	−	0.0793630i	−0.910341	+	0.413859i	$0.864181\pi$
$14$	0.0116833	+	0.0439125i	0.00312249	+	0.0117361i
$15$	0.0372227	+	2.52890i	0.00961085	+	0.652959i
$16$	−2.67534	−	2.97126i	−0.668835	−	0.742816i
$17$	2.90424	−	2.35181i	0.704381	−	0.570397i	−0.208796	−	0.977959i	$-0.566954\pi$
$17$	2.90424	−	2.35181i	0.704381	−	0.570397i	0.913177	+	0.407562i	$0.133621\pi$
$18$	−0.00764859	+	0.0285449i	−0.00180279	+	0.00672810i
$19$	6.10342	−	2.71742i	1.40022	−	0.623419i	0.438822	−	0.898574i	$-0.355396\pi$
$19$	6.10342	−	2.71742i	1.40022	−	0.623419i	0.961400	+	0.275155i	$0.0887293\pi$
$20$	−3.20800	−	3.11494i	−0.717331	−	0.696521i
$21$	0.151343	+	2.98873i	0.0330257	+	0.652194i
$22$	0.0136263	−	0.0860334i	0.00290515	−	0.0183424i
$23$	1.86170	+	2.86676i	0.388191	+	0.597762i	0.977702	−	0.209999i	$-0.0673461\pi$
$23$	1.86170	+	2.86676i	0.388191	+	0.597762i	−0.589511	+	0.807761i	$0.700679\pi$
$24$	0.0388492	+	0.0672888i	0.00793006	+	0.0137353i
$25$	−3.81258	−	3.23484i	−0.762516	−	0.646969i
$26$	−0.00477673	−	0.00275784i	−0.000936793	−	0.000540858i
$27$	−2.42406	+	4.75748i	−0.466510	+	0.915577i
$28$	−3.92552	−	3.54712i	−0.741853	−	0.670342i
$29$	1.99592	+	2.74715i	0.370633	+	0.510133i	0.953073	−	0.302741i	$-0.0979018\pi$
$29$	1.99592	+	2.74715i	0.370633	+	0.510133i	−0.582440	+	0.812874i	$0.697902\pi$
$30$	0.0241916	+	0.0360780i	0.00441676	+	0.00658691i
$31$	0.746861	+	0.0784982i	0.134140	+	0.0140987i	0.171361	−	0.985208i	$-0.445184\pi$
$31$	0.746861	+	0.0784982i	0.134140	+	0.0140987i	−0.0372204	+	0.999307i	$0.511850\pi$
$32$	−0.199035	−	0.0533314i	−0.0351848	−	0.00942775i
$33$	2.05579	−	5.35552i	0.357867	−	0.932276i
$34$	0.0198337	−	0.0610417i	0.00340145	−	0.0104686i
$35$	−4.64549	−	3.66325i	−0.785232	−	0.619202i
$36$	−1.06327	−	3.27240i	−0.177211	−	0.545400i
$37$	−3.29137	−	0.172493i	−0.541098	−	0.0283577i	−0.220170	−	0.975461i	$-0.570661\pi$
$37$	−3.29137	−	0.172493i	−0.541098	−	0.0283577i	−0.320928	+	0.947104i	$0.603995\pi$
$38$	0.0624947	−	0.0962334i	0.0101380	−	0.0156111i
$39$	−0.269945	−	0.243060i	−0.0432258	−	0.0389207i
$40$	−0.150702	−	0.0297215i	−0.0238280	−	0.00469937i
$41$	7.88534	+	2.56210i	1.23148	+	0.400133i	0.851252	−	0.524758i	$-0.175844\pi$
$41$	7.88534	+	2.56210i	1.23148	+	0.400133i	0.380232	+	0.924891i	$0.375844\pi$
$42$	0.0301367	+	0.0416339i	0.00465019	+	0.00642425i
$43$	−3.99562	−	3.99562i	−0.609326	−	0.609326i	0.333444	−	0.942770i	$-0.391789\pi$
$43$	−3.99562	−	3.99562i	−0.609326	−	0.609326i	−0.942770	+	0.333444i	$0.891789\pi$
$44$	4.12511	+	9.26514i	0.621883	+	1.39677i
$45$	−1.43154	−	3.57127i	−0.213401	−	0.532374i
$46$	0.0536317	+	0.0238784i	0.00790756	+	0.00352067i
$47$	−3.96152	+	4.89207i	−0.577847	+	0.713581i	−0.979326	−	0.202287i	$-0.935163\pi$
$47$	−3.96152	+	4.89207i	−0.577847	+	0.713581i	0.401480	+	0.915868i	$0.368496\pi$
$48$	−4.02942	−	2.05309i	−0.581596	−	0.296338i
$49$	−5.64856	−	4.13446i	−0.806937	−	0.590638i
$50$	−0.0851752	−	0.0109315i	−0.0120456	−	0.00154595i
$51$	2.11346	−	3.66061i	0.295943	−	0.512588i
$52$	0.641326	−	0.0336105i	0.0889360	−	0.00466094i
$53$	−4.04766	−	10.5445i	−0.555988	−	1.44840i	−0.867152	−	0.498043i	$-0.834052\pi$
$53$	−4.04766	−	10.5445i	−0.555988	−	1.44840i	0.311164	−	0.950356i	$-0.399281\pi$
$54$	0.00958565	+	0.0912013i	0.00130444	+	0.0124109i
$55$	5.29674	+	10.0278i	0.714212	+	1.35215i
$56$	−0.179459	−	0.0287484i	−0.0239812	−	0.00384166i
$57$	5.34345	−	5.34345i	0.707757	−	0.707757i
$58$	0.0544462	+	0.0208999i	0.00714913	+	0.00274429i
$59$	9.35373	−	1.98820i	1.21775	−	0.258841i	0.446157	−	0.894955i	$-0.352792\pi$
$59$	9.35373	−	1.98820i	1.21775	−	0.258841i	0.771595	+	0.636114i	$0.219459\pi$
$60$	−4.65012	−	1.98889i	−0.600328	−	0.256765i
$61$	0.570023	−	2.68175i	0.0729840	−	0.343363i	−0.926471	−	0.376365i	$-0.877174\pi$
$61$	0.570023	−	2.68175i	0.0729840	−	0.343363i	0.999455	+	0.0330028i	$0.0105070\pi$
$62$	0.0114920	−	0.00585548i	0.00145949	−	0.000743647i
$63$	−1.84430	−	4.16211i	−0.232359	−	0.524377i
$64$	7.60172	−	2.46995i	0.950215	−	0.308744i
$65$	0.712999	−	0.0855661i	0.0884366	−	0.0106132i
$66$	−0.0204842	−	0.0963707i	−0.00252143	−	0.0118624i
$67$	−4.10889	−	5.07406i	−0.501981	−	0.619895i	0.461672	−	0.887051i	$-0.347250\pi$
$67$	−4.10889	−	5.07406i	−0.501981	−	0.619895i	−0.963653	+	0.267155i	$0.913916\pi$
$68$	1.93416	+	7.21837i	0.234551	+	0.875357i
$69$	3.12789	+	2.27255i	0.376554	+	0.273582i
$70$	−0.101180	−	0.00931112i	−0.0120933	−	0.00111289i
$71$	−3.66851	+	2.66533i	−0.435372	+	0.316316i	−0.783793	−	0.621022i	$-0.786718\pi$
$71$	−3.66851	+	2.66533i	−0.435372	+	0.316316i	0.348422	+	0.937338i	$0.386718\pi$
$72$	−0.0918577	−	0.0743849i	−0.0108255	−	0.00876635i
$73$	0.528792	+	10.0900i	0.0618904	+	1.18094i	0.836306	+	0.548263i	$0.184711\pi$
$73$	0.528792	+	10.0900i	0.0618904	+	1.18094i	−0.774416	+	0.632677i	$0.781956\pi$
$74$	−0.0490223	+	0.0283030i	−0.00569873	+	0.00329016i
$75$	−5.33714	−	1.87045i	−0.616279	−	0.215980i
$76$			13.3601i			1.53251i
$77$	6.68874	+	11.6326i	0.762253	+	1.32566i
$78$	−0.00616188		0.000975946i	−0.000697695		0.000110504i
$79$	−8.16023	+	0.857674i	−0.918097	+	0.0964959i	−0.551776	−	0.833992i	$-0.686050\pi$
$79$	−8.16023	+	0.857674i	−0.918097	+	0.0964959i	−0.366321	+	0.930488i	$0.619383\pi$
$80$	8.29845	−	3.32641i	0.927794	−	0.371904i
$81$	−0.0917101	+	0.872564i	−0.0101900	+	0.0969515i
$82$	0.137546	−	0.0368554i	0.0151894	−	0.00407000i
$83$	−1.28282	+	0.203179i	−0.140808	+	0.0223018i	−0.226441	−	0.974025i	$-0.572709\pi$
$83$	−1.28282	+	0.203179i	−0.140808	+	0.0223018i	0.0856324	+	0.996327i	$0.472709\pi$
$84$	−5.58297	−	2.15442i	−0.609152	−	0.235066i
$85$	2.69893	+	7.90846i	0.292740	+	0.857793i
$86$	−0.0949280	−	0.0201776i	−0.0102363	−	0.00217580i
$87$	3.22114	+	2.09183i	0.345342	+	0.224268i
$88$	0.292191	+	0.189751i	0.0311476	+	0.0202275i
$89$	−0.969707	−	0.206118i	−0.102789	−	0.0218484i	0.156230	−	0.987721i	$-0.450066\pi$
$89$	−0.969707	−	0.206118i	−0.102789	−	0.0218484i	−0.259019	+	0.965872i	$0.583399\pi$
$90$	−0.0540257	−	0.0380499i	−0.00569481	−	0.00401081i
$91$	0.839457	−	0.131438i	0.0879990	−	0.0137785i
$92$	−6.75128	+	1.06930i	−0.703870	+	0.111482i
$93$	0.820470	−	0.219844i	0.0850787	−	0.0227968i
$94$	−0.0113010	+	0.107521i	−0.00116560	+	0.0110900i
$95$	1.00134	+	14.9056i	0.102735	+	1.52929i
$96$	−0.231790	+	0.0243621i	−0.0236570	+	0.00248645i
$97$	−12.2690	−	1.94322i	−1.24573	−	0.197304i	−0.501457	−	0.865183i	$-0.667202\pi$
$97$	−12.2690	−	1.94322i	−1.24573	−	0.197304i	−0.744270	+	0.667879i	$0.767202\pi$
$98$	−0.120036	−	0.00671581i	−0.0121254	−	0.000678400i
$99$			8.72671i			0.877067i
$100$	9.01046	−	4.33384i	0.901046	−	0.433384i
$101$	10.1944	−	5.88575i	1.01438	−	0.585654i	0.101911	−	0.994794i	$-0.467504\pi$
$101$	10.1944	−	5.88575i	1.01438	−	0.585654i	0.912472	+	0.409139i	$0.134171\pi$
$102$	−0.00379939	−	0.0724967i	−0.000376196	−	0.00717825i
$103$	11.4576	+	9.27815i	1.12895	+	0.914203i	0.997027	−	0.0770569i	$-0.0245523\pi$
$103$	11.4576	+	9.27815i	1.12895	+	0.914203i	0.131920	+	0.991260i	$0.457886\pi$
$104$	0.0178478	−	0.0129672i	0.00175012	−	0.00127154i
$105$	−6.39030	−	1.98520i	−0.623630	−	0.193736i
$106$	−0.156936	−	0.114021i	−0.0152430	−	0.0110747i
$107$	2.68589	+	10.0239i	0.259655	+	0.969046i	0.965441	+	0.260621i	$0.0839272\pi$
$107$	2.68589	+	10.0239i	0.259655	+	0.969046i	−0.705786	+	0.708425i	$0.749406\pi$
$108$	−6.71945	−	8.29783i	−0.646579	−	0.798459i
$109$	−1.89206	−	8.90145i	−0.181227	−	0.852604i	−0.970976	−	0.239175i	$-0.923123\pi$
$109$	−1.89206	−	8.90145i	−0.181227	−	0.852604i	0.789750	−	0.613429i	$-0.210210\pi$
$110$	0.170095	+	0.0948942i	0.0162179	+	0.00904780i
$111$	−3.54546	+	1.15199i	−0.336520	+	0.109342i
$112$	9.67136	−	4.28553i	0.913857	−	0.404944i
$113$	7.60273	−	3.87378i	0.715204	−	0.364415i	−0.0582196	−	0.998304i	$-0.518542\pi$
$113$	7.60273	−	3.87378i	0.715204	−	0.364415i	0.773424	+	0.633889i	$0.218542\pi$
$114$	0.0269840	−	0.126950i	0.00252729	−	0.0118899i
$115$	−7.45216	+	1.69901i	−0.694917	+	0.158433i
$116$	−6.64194	+	1.41179i	−0.616689	+	0.131081i
$117$	0.515887	+	0.198031i	0.0476938	+	0.0183079i
$118$	0.116133	−	0.116133i	0.0106909	−	0.0106909i
$119$	3.52700	+	9.23685i	0.323320	+	0.846741i
$120$	−0.171181	+	0.0297013i	−0.0156267	+	0.00271135i
$121$	−1.53891	−	14.6418i	−0.139901	−	1.33107i
$122$	−0.0168746	−	0.0439598i	−0.00152775	−	0.00397994i
$123$	9.36510	−	0.490804i	0.844422	−	0.0442543i
$124$	−0.750864	+	1.30053i	−0.0674296	+	0.116791i
$125$	9.72801	−	5.51053i	0.870099	−	0.492876i
$126$	−0.0654978	−	0.0426993i	−0.00583501	−	0.00380396i
$127$	−14.3784	−	7.32616i	−1.27588	−	0.650091i	−0.320996	−	0.947081i	$-0.604017\pi$
$127$	−14.3784	−	7.32616i	−1.27588	−	0.650091i	−0.954881	+	0.296989i	$0.904017\pi$
$128$	0.345742	−	0.426956i	0.0305596	−	0.0377379i
$129$	−5.83879	−	2.59960i	−0.514076	−	0.228882i
$130$	0.00946962	−	0.00790192i	0.000830541	−	0.000693044i
$131$	−1.21211	−	2.72244i	−0.105902	−	0.237860i	0.852820	−	0.522205i	$-0.174891\pi$
$131$	−1.21211	−	2.72244i	−0.105902	−	0.237860i	−0.958722	+	0.284345i	$0.908224\pi$
$132$	8.11149	+	8.11149i	0.706015	+	0.706015i
$133$	1.81665	+	17.5827i	0.157523	+	1.52462i
$134$	−0.106647	−	0.0346518i	−0.00921293	−	0.00299346i
$135$	−8.11871	−	8.75413i	−0.698747	−	0.753436i
$136$	0.190775	+	0.171775i	0.0163588	+	0.0147296i
$137$	8.41948	−	12.9649i	0.719324	−	1.10766i	−0.270131	−	0.962824i	$-0.587067\pi$
$137$	8.41948	−	12.9649i	0.719324	−	1.10766i	0.989455	−	0.144839i	$-0.0462664\pi$
$138$	0.0663116	+	0.00347524i	0.00564482	+	0.000295832i
$139$	−5.70394	−	17.5549i	−0.483801	−	1.48899i	−0.833709	−	0.552204i	$-0.813787\pi$
$139$	−5.70394	−	17.5549i	−0.483801	−	1.48899i	0.349908	−	0.936784i	$-0.386213\pi$
$140$	10.4705	−	5.50698i	0.884921	−	0.465424i
$141$	−2.20022	+	6.77157i	−0.185292	+	0.570269i
$142$	−0.0279095	+	0.0727067i	−0.00234211	+	0.00610141i
$143$	−1.57329	−	0.421562i	−0.131565	−	0.0352528i
$144$	6.84189	+	0.719112i	0.570158	+	0.0599260i
$145$	−7.30449	+	2.07292i	−0.606605	+	0.172147i
$146$	0.101999	+	0.140389i	0.00844147	+	0.0116187i
$147$	−7.64050	−	2.07620i	−0.630178	−	0.171242i
$148$	2.99216	−	5.87245i	0.245954	−	0.482712i
$149$	−12.7732	−	7.37458i	−1.04642	−	0.604149i	−0.124773	−	0.992185i	$-0.539820\pi$
$149$	−12.7732	−	7.37458i	−1.04642	−	0.604149i	−0.921644	+	0.388036i	$0.873154\pi$
$150$	−0.0943722	+	0.0229820i	−0.00770546	+	0.00187647i
$151$	−2.80622	−	4.86051i	−0.228367	−	0.395543i	0.728957	−	0.684559i	$-0.240005\pi$
$151$	−2.80622	−	4.86051i	−0.228367	−	0.395543i	−0.957324	+	0.289016i	$0.906672\pi$
$152$	0.249960	+	0.384905i	0.0202745	+	0.0312199i
$153$	−1.00590	+	6.35103i	−0.0813225	+	0.513450i
$154$	0.205157	+	0.104989i	0.0165320	+	0.00846026i
$155$	−0.740252	+	1.50726i	−0.0594585	+	0.121066i
$156$	0.663588	−	0.295448i	0.0531295	−	0.0236548i
$157$	1.35782	−	5.06744i	0.108366	−	0.404426i	−0.890340	−	0.455297i	$-0.849533\pi$
$157$	1.35782	−	5.06744i	0.108366	−	0.404426i	0.998705	+	0.0508712i	$0.0161998\pi$
$158$	−0.109517	+	0.0886851i	−0.00871270	+	0.00705541i
$159$	−8.54828	−	9.49383i	−0.677923	−	0.752910i
$160$	0.265311	−	0.376705i	0.0209746	−	0.0297812i
$161$	−8.73973	+	2.32528i	−0.688787	+	0.183257i
$162$	0.00684101	+	0.0134262i	0.000537481	+	0.00105487i
$163$	−0.929553	+	17.7369i	−0.0728082	+	1.38926i	0.681055	+	0.732232i	$0.261521\pi$
$163$	−0.929553	+	17.7369i	−0.0728082	+	1.38926i	−0.753864	+	0.657031i	$0.771812\pi$
$164$	−11.0941	+	12.3212i	−0.866302	+	0.962126i
$165$	9.65782	+	8.44190i	0.751860	+	0.657201i
$166$	−0.0165772	+	0.0149262i	−0.00128664	+	0.00115850i
$167$	−0.899703	−	5.68050i	−0.0696211	−	0.439571i	−0.997735	−	0.0672731i	$-0.978570\pi$
$167$	−0.899703	−	5.68050i	−0.0696211	−	0.439571i	0.928113	−	0.372297i	$-0.121430\pi$
$168$	−0.201154	+	0.0423856i	−0.0155193	+	0.00327012i
$169$	7.58059	−	10.4338i	0.583122	−	0.802599i
$170$	0.112851	+	0.0886674i	0.00865531	+	0.00680048i
$171$	−4.67575	+	10.5019i	−0.357563	+	0.803100i
$172$	10.5491	−	4.04943i	0.804363	−	0.308766i
$173$	1.89475	−	1.23047i	0.144055	−	0.0935507i	−0.470599	−	0.882347i	$-0.655962\pi$
$173$	1.89475	−	1.23047i	0.144055	−	0.0935507i	0.614654	+	0.788797i	$0.289295\pi$
$174$	0.0659643			0.00500074
$175$	11.2691	−	6.92881i	0.851860	−	0.523769i
$176$	−20.2779			−1.52851
$177$	9.07122	−	5.89092i	0.681834	−	0.442788i
$178$	−0.0158957	+	0.00610177i	−0.00119143	+	0.000457347i
$179$	−9.43793	+	21.1979i	−0.705424	+	1.58441i	0.102237	+	0.994760i	$0.467400\pi$
$179$	−9.43793	+	21.1979i	−0.705424	+	1.58441i	−0.807661	+	0.589648i	$0.799267\pi$
$180$	7.68843	+	0.289545i	0.573061	+	0.0215814i
$181$	1.07470	−	1.47920i	0.0798820	−	0.109948i	−0.767206	−	0.641401i	$-0.778354\pi$
$181$	1.07470	−	1.47920i	0.0798820	−	0.109948i	0.847088	+	0.531453i	$0.178354\pi$
$182$	0.0108620	−	0.00974556i	0.000805147	−	0.000722389i
$183$	−0.485109	−	3.06286i	−0.0358603	−	0.226413i
$184$	−0.174499	+	0.157120i	−0.0128642	+	0.0115830i
$185$	2.89817	−	6.77606i	0.213077	−	0.498186i
$186$	0.00976159	−	0.0108413i	0.000715754	−	0.000794926i
$187$	0.991941	−	18.9274i	0.0725379	−	1.38411i
$188$	−5.71482	−	11.2160i	−0.416796	−	0.818008i
$189$	−9.97154	−	10.0068i	−0.725322	−	0.727888i
$190$	0.153851	+	0.205334i	0.0111615	+	0.0148965i
$191$	−0.492886	−	0.547405i	−0.0356640	−	0.0396088i	0.725049	−	0.688697i	$-0.241817\pi$
$191$	−0.492886	−	0.547405i	−0.0356640	−	0.0396088i	−0.760713	+	0.649089i	$0.775150\pi$
$192$	7.02590	−	5.68946i	0.507050	−	0.410601i
$193$	−3.73619	+	13.9437i	−0.268937	+	1.00369i	0.690860	+	0.722989i	$0.257232\pi$
$193$	−3.73619	+	13.9437i	−0.268937	+	1.00369i	−0.959796	+	0.280697i	$0.909434\pi$
$194$	−0.194899	+	0.0867746i	−0.0139929	+	0.00623006i
$195$	0.718211	−	0.379363i	0.0514321	−	0.0271667i
$196$	12.1472	−	6.95613i	0.867657	−	0.496866i
$197$	1.57277	−	9.93010i	0.112055	−	0.707490i	−0.866140	−	0.499802i	$-0.833406\pi$
$197$	1.57277	−	9.93010i	0.112055	−	0.707490i	0.978195	−	0.207688i	$-0.0665940\pi$
$198$	0.0816300	+	0.125699i	0.00580119	+	0.00893306i
$199$	3.19046	+	5.52604i	0.226166	+	0.391731i	0.956669	−	0.291179i	$-0.0940475\pi$
$199$	3.19046	+	5.52604i	0.226166	+	0.391731i	−0.730503	+	0.682910i	$0.760714\pi$
$200$	0.178508	−	0.293439i	0.0126224	−	0.0207493i
$201$	−6.39554	−	3.69247i	−0.451107	−	0.260447i
$202$	0.0917845	−	0.180137i	0.00645794	−	0.0126744i
$203$	−8.54926	+	2.76115i	−0.600040	+	0.193795i
$204$	4.96830	+	6.83828i	0.347851	+	0.478775i
$205$	−11.4540	+	14.5781i	−0.799983	+	1.01818i
$206$	0.251823	+	0.0264676i	0.0175453	+	0.00184409i
$207$	−5.68118	−	1.52227i	−0.394869	−	0.105805i
$208$	−0.460157	+	1.19875i	−0.0319061	+	0.0831183i
$209$	10.4708	−	32.2260i	0.724284	−	2.22912i
$210$	−0.110615	+	0.0311804i	−0.00763319	+	0.00215165i
$211$	8.73583	+	26.8861i	0.601399	+	1.85092i	0.519868	+	0.854246i	$0.325981\pi$
$211$	8.73583	+	26.8861i	0.601399	+	1.85092i	0.0815311	+	0.996671i	$0.474019\pi$
$212$	22.5551	+	1.18206i	1.54909	+	0.0811844i
$213$	−2.79341	+	4.30147i	−0.191401	+	0.294732i
$214$	0.132451	+	0.119260i	0.00905419	+	0.00815243i
$215$	11.4660	−	5.30854i	0.781974	−	0.362040i
$216$	−0.348836	−	0.113344i	−0.0237353	−	0.00771206i
$217$	−0.811344	+	1.81369i	−0.0550776	+	0.123121i
$218$	−0.110518	−	0.110518i	−0.00748521	−	0.00748521i
$219$	4.64827	+	10.4402i	0.314101	+	0.705483i
$220$	−22.6271	+	1.52006i	−1.52552	+	0.102482i
$221$	−1.09640	−	0.488148i	−0.0737518	−	0.0328364i
$222$	−0.0402929	+	0.0497576i	−0.00270428	+	0.00333951i
$223$	−18.8633	−	9.61132i	−1.26318	−	0.643622i	−0.311362	−	0.950291i	$-0.600785\pi$
$223$	−18.8633	−	9.61132i	−1.26318	−	0.643622i	−0.951816	+	0.306670i	$0.900785\pi$
$224$	0.297730	−	0.456697i	0.0198929	−	0.0305144i
$225$	8.59956	−	0.253207i	0.573304	−	0.0168805i
$226$	0.0732739	−	0.126914i	0.00487411	−	0.00844220i
$227$	−19.9144	+	1.04367i	−1.32176	+	0.0692707i	−0.700117	−	0.714028i	$-0.746869\pi$
$227$	−19.9144	+	1.04367i	−1.32176	+	0.0692707i	−0.621646	+	0.783299i	$0.713536\pi$
$228$	5.41542	+	14.1076i	0.358645	+	0.934302i
$229$	1.04973	+	9.98747i	0.0693678	+	0.659991i	0.972861	+	0.231389i	$0.0743270\pi$
$229$	1.04973	+	9.98747i	0.0693678	+	0.659991i	−0.903493	+	0.428602i	$0.859006\pi$
$230$	−0.0914481	+	0.0941803i	−0.00602991	+	0.00621007i
$231$	11.7782	+	9.57228i	0.774949	+	0.629810i
$232$	−0.164941	+	0.164941i	−0.0108289	+	0.0108289i
$233$	2.60583	+	1.00029i	0.170714	+	0.0655309i	0.442224	−	0.896905i	$-0.354190\pi$
$233$	2.60583	+	1.00029i	0.170714	+	0.0655309i	−0.271510	+	0.962436i	$0.587523\pi$
$234$	0.00928321	−	0.00197321i	0.000606863	−	0.000128993i
$235$	−7.21657	−	12.0851i	−0.470757	−	0.788348i
$236$	−3.97581	+	18.7047i	−0.258803	+	1.21757i
$237$	−8.26918	+	4.21336i	−0.537141	+	0.273687i
$238$	0.137205	+	0.100056i	0.00889366	+	0.00648564i
$239$	−3.96154	+	1.28718i	−0.256251	+	0.0832609i	−0.434325	−	0.900756i	$-0.643013\pi$
$239$	−3.96154	+	1.28718i	−0.256251	+	0.0832609i	0.178075	+	0.984017i	$0.443013\pi$
$240$	7.41444	−	6.87626i	0.478600	−	0.443861i
$241$	−1.47575	−	6.94288i	−0.0950617	−	0.447230i	−0.999775	−	0.0212092i	$-0.993248\pi$
$241$	−1.47575	−	6.94288i	−0.0950617	−	0.447230i	0.904713	−	0.426021i	$-0.140085\pi$
$242$	−0.159127	−	0.196505i	−0.0102290	−	0.0126318i
$243$	−3.88900	−	14.5140i	−0.249480	−	0.931071i
$244$	4.43544	+	3.22254i	0.283950	+	0.206302i
$245$	13.0311	−	8.67127i	0.832525	−	0.553987i
$246$	0.130304	−	0.0946711i	0.00830785	−	0.00603601i
$247$	−1.66746	−	1.35028i	−0.106098	−	0.0859163i
$248$	0.00269988	+	0.0515167i	0.000171442	+	0.00327132i
$249$	−1.27225	+	0.734532i	−0.0806254	+	0.0465491i
$250$	0.0885762	−	0.170370i	0.00560205	−	0.0107751i
$251$			3.67076i			0.231697i	0.993267	+	0.115848i	$0.0369586\pi$
$251$			3.67076i			0.231697i	−0.993267	+	0.115848i	$0.963041\pi$
$252$	9.10350	+	0.0160693i	0.573467	+	0.00101227i
$253$	17.1229	+	2.71200i	1.07651	+	0.170502i
$254$	−0.275635	+	0.0289704i	−0.0172949	+	0.00181777i
$255$	6.05558	+	7.25699i	0.379215	+	0.454450i
$256$	−1.66999	+	15.8889i	−0.104374	+	0.993055i
$257$	5.31329	−	1.42369i	0.331434	−	0.0888074i	−0.0892647	−	0.996008i	$-0.528452\pi$
$257$	5.31329	−	1.42369i	0.331434	−	0.0888074i	0.420698	+	0.907201i	$0.361785\pi$
$258$	−0.108418	+	0.0171718i	−0.00674984	+	0.00106907i
$259$	3.13937	−	8.13538i	0.195071	−	0.505508i
$260$	−0.423606	+	1.37212i	−0.0262709	+	0.0850951i
$261$	−5.71509	−	1.21478i	−0.353755	−	0.0751930i
$262$	−0.0429249	−	0.0278758i	−0.00265191	−	0.00172217i
$263$	17.4437	+	11.3281i	1.07563	+	0.698521i	0.955724	−	0.294265i	$-0.0950748\pi$
$263$	17.4437	+	11.3281i	1.07563	+	0.698521i	0.119904	+	0.992786i	$0.461741\pi$
$264$	0.385454	+	0.0819308i	0.0237231	+	0.00504249i
$265$	25.2530	−	0.371697i	1.55128	−	0.0228331i
$266$	0.190637	+	0.236268i	0.0116887	+	0.0144865i
$267$	−1.10751	+	0.175413i	−0.0677788	+	0.0107351i
$268$	12.6114	−	3.37921i	0.770363	−	0.206418i
$269$	0.0163748	−	0.155796i	0.000998391	−	0.00949906i	−0.994011	−	0.109277i	$-0.965147\pi$
$269$	0.0163748	−	0.155796i	0.000998391	−	0.00949906i	0.995010	+	0.0997777i	$0.0318132\pi$
$270$	−0.198828	−	0.0501515i	−0.0121003	−	0.00305212i
$271$	1.38670	−	0.145748i	0.0842359	−	0.00885355i	−0.0623167	−	0.998056i	$-0.519849\pi$
$271$	1.38670	−	0.145748i	0.0842359	−	0.00885355i	0.146553	+	0.989203i	$0.453182\pi$
$272$	−14.7577	−	2.33738i	−0.894814	−	0.141725i
$273$	0.833151	−	0.479061i	0.0504246	−	0.0289941i
$274$		−	0.265502i		−	0.0160395i
$275$	−25.1308	+	3.39181i	−1.51544	+	0.204534i
$276$	−6.69562	+	3.86572i	−0.403029	+	0.232689i
$277$	1.57183	+	29.9922i	0.0944419	+	1.80206i	0.477809	+	0.878464i	$0.341431\pi$
$277$	1.57183	+	29.9922i	0.0944419	+	1.80206i	−0.383367	+	0.923596i	$0.625236\pi$
$278$	−0.246369	−	0.199506i	−0.0147762	−	0.0119655i
$279$	−1.04539	+	0.759518i	−0.0625857	+	0.0454712i
$280$	0.198624	−	0.354554i	0.0118701	−	0.0211887i
$281$	−23.1092	−	16.7898i	−1.37858	−	1.00160i	−0.997011	−	0.0772549i	$-0.975384\pi$
$281$	−23.1092	−	16.7898i	−1.37858	−	1.00160i	−0.381567	−	0.924341i	$-0.624616\pi$
$282$	0.0316498	+	0.118119i	0.00188472	+	0.00703385i
$283$	17.7097	+	21.8697i	1.05273	+	1.30002i	0.952329	+	0.305071i	$0.0986803\pi$
$283$	17.7097	+	21.8697i	1.05273	+	1.30002i	0.100404	+	0.994947i	$0.467986\pi$
$284$	−1.88528	−	8.86956i	−0.111871	−	0.526312i
$285$	7.09926	+	15.3338i	0.420524	+	0.908295i
$286$	−0.0266049	+	0.00864446i	−0.00157318	+	0.000511158i
$287$	−12.9251	+	17.7240i	−0.762947	+	1.04622i
$288$	0.315909	−	0.160964i	0.0186151	−	0.00948487i
$289$	−0.630888	+	2.96810i	−0.0371111	+	0.174594i
$290$	−0.0858235	+	0.0981849i	−0.00503973	+	0.00576562i
$291$	−13.7432	+	2.92120i	−0.805638	+	0.171244i
$292$	−18.8626	−	7.24069i	−1.10385	−	0.423729i
$293$	−4.56757	+	4.56757i	−0.266840	+	0.266840i	−0.827826	−	0.560986i	$-0.810422\pi$
$293$	−4.56757	+	4.56757i	−0.266840	+	0.266840i	0.560986	+	0.827826i	$0.310422\pi$
$294$	−0.129474	+	0.0415640i	−0.00755110	+	0.00242406i
$295$	−3.03383	+	21.1665i	−0.176636	+	1.23236i
$296$	−0.0236660	−	0.225167i	−0.00137556	−	0.0130876i
$297$	9.70468	+	25.2816i	0.563123	+	1.46698i
$298$	−0.252966	+	0.0132574i	−0.0146539	+	0.000767981i
$299$	0.548882	−	0.950692i	0.0317427	−	0.0549799i
$300$	7.75795	−	8.22866i	0.447905	−	0.475082i
$301$	13.3327	−	6.76374i	0.768485	−	0.389855i
$302$	−0.0858861	−	0.0437612i	−0.00494219	−	0.00251817i
$303$	8.37910	−	10.3473i	0.481367	−	0.594438i
$304$	−24.4029	−	10.8649i	−1.39960	−	0.623143i
$305$	5.19009	+	3.26290i	0.297183	+	0.186833i
$306$	0.0449188	+	0.100889i	0.00256784	+	0.00576746i
$307$	12.4946	+	12.4946i	0.713104	+	0.713104i	0.967183	−	0.254080i	$-0.0817725\pi$
$307$	12.4946	+	12.4946i	0.713104	+	0.713104i	−0.254080	+	0.967183i	$0.581773\pi$
$308$	−26.6910	+	2.75771i	−1.52086	+	0.157135i
$309$	15.8595	+	5.15306i	0.902215	+	0.293148i
$310$	0.00343644	+	0.0286349i	0.000195177	+	0.00162635i
$311$	−5.55685	−	5.00341i	−0.315100	−	0.283717i	0.496371	−	0.868111i	$-0.334666\pi$
$311$	−5.55685	−	5.00341i	−0.315100	−	0.283717i	−0.811470	+	0.584394i	$0.801332\pi$
$312$	0.0135903	−	0.0209273i	0.000769401	−	0.00118477i
$313$	−27.7944	−	1.45664i	−1.57103	−	0.0823343i	−0.753200	−	0.657792i	$-0.771491\pi$
$313$	−27.7944	−	1.45664i	−1.57103	−	0.0823343i	−0.817832	+	0.575458i	$0.804824\pi$
$314$	−0.0278431	−	0.0856923i	−0.00157128	−	0.00483590i
$315$	10.1578	−	0.664379i	0.572329	−	0.0374335i
$316$	5.07033	−	15.6049i	0.285228	−	0.877843i
$317$	10.2406	−	26.6777i	0.575170	−	1.49837i	−0.269457	−	0.963012i	$-0.586844\pi$
$317$	10.2406	−	26.6777i	0.575170	−	1.49837i	0.844627	−	0.535356i	$-0.179823\pi$
$318$	−0.211935	−	0.0567878i	−0.0118847	−	0.00318450i
$319$	17.1275	+	1.80018i	0.958958	+	0.100791i
$320$	−0.672606	+	17.8601i	−0.0375998	+	0.998407i
$321$	6.89929	+	9.49606i	0.385081	+	0.530019i
$322$	−0.104136	+	0.115245i	−0.00580328	+	0.00642236i
$323$	11.3350	−	22.2461i	0.630694	−	1.23781i
$324$	−1.51943	−	0.877241i	−0.0844125	−	0.0487356i
$325$	−0.369770	+	1.56260i	−0.0205112	+	0.0866773i
$326$	0.152523	+	0.264177i	0.00844745	+	0.0146314i
$327$	−5.60607	−	8.63259i	−0.310016	−	0.477383i
$328$	−0.0890975	+	0.562539i	−0.00491959	+	0.0310610i
$329$	−9.04617	−	13.9839i	−0.498732	−	0.770955i
$330$	0.218077	+	0.0312573i	0.0120047	+	0.00172066i
$331$	15.2558	−	6.79232i	0.838535	−	0.373340i	0.0578965	−	0.998323i	$-0.481561\pi$
$331$	15.2558	−	6.79232i	0.838535	−	0.373340i	0.780639	+	0.624983i	$0.214894\pi$
$332$	0.672217	−	2.50875i	0.0368927	−	0.137685i
$333$	4.40726	−	3.56893i	0.241517	−	0.195576i
$334$	−0.0660950	−	0.0734059i	−0.00361656	−	0.00401659i
$335$	13.8171	−	4.71536i	0.754906	−	0.257627i
$336$	8.47541	−	8.44554i	0.462371	−	0.460742i
$337$	−10.8501	−	21.2946i	−0.591044	−	1.15999i	−0.971909	−	0.235358i	$-0.924374\pi$
$337$	−10.8501	−	21.2946i	−0.591044	−	1.15999i	0.380865	−	0.924631i	$-0.375626\pi$
$338$	0.0115924	−	0.221197i	0.000630546	−	0.0120315i
$339$	6.45792	−	7.17225i	0.350746	−	0.389543i
$340$	−16.6425	−	1.50192i	−0.902568	−	0.0814529i
$341$	2.83045	−	2.54854i	0.153277	−	0.138011i
$342$	0.0308859	+	0.195006i	0.00167012	+	0.0105447i
$343$	15.0406	−	10.8064i	0.812118	−	0.583493i
$344$	0.228158	−	0.314033i	0.0123015	−	0.0169315i
$345$	−7.18046	+	4.81476i	−0.386583	+	0.259218i
$346$	0.0157821	−	0.0354472i	0.000848452	−	0.00190566i
$347$	−3.42854	+	1.31609i	−0.184053	+	0.0706515i	−0.448649	−	0.893708i	$-0.648095\pi$
$347$	−3.42854	+	1.31609i	−0.184053	+	0.0706515i	0.264596	+	0.964359i	$0.414761\pi$
$348$	−6.44133	+	4.18305i	−0.345291	+	0.224235i
$349$	1.21897			0.0652497			0.0326249	−	0.999468i	$-0.489613\pi$
$349$	1.21897			0.0652497			0.0326249	+	0.999468i	$0.489613\pi$
$350$	0.0975067	−	0.205214i	0.00521195	−	0.0109691i
$351$	1.71477			0.0915274
$352$	−0.876464	+	0.569183i	−0.0467157	+	0.0303375i
$353$	−23.7134	+	9.10273i	−1.26214	+	0.484490i	−0.895162	−	0.445741i	$-0.852940\pi$
$353$	−23.7134	+	9.10273i	−1.26214	+	0.484490i	−0.366976	+	0.930230i	$0.619607\pi$
$354$	0.0755576	−	0.169705i	0.00401584	−	0.00901973i
$355$	−2.76815	−	9.75433i	−0.146918	−	0.517706i
$356$	1.16525	−	1.60383i	0.0617583	−	0.0850031i
$357$	7.46845	+	8.32405i	0.395272	+	0.440556i
$358$	0.0623428	+	0.393617i	0.00329492	+	0.0208033i
$359$	−8.35258	+	7.52069i	−0.440832	+	0.396927i	−0.859437	−	0.511241i	$-0.829186\pi$
$359$	−8.35258	+	7.52069i	−0.440832	+	0.396927i	0.418605	+	0.908168i	$0.362519\pi$
$360$	0.226921	−	0.135505i	0.0119598	−	0.00714172i
$361$	17.1539	−	19.0514i	0.902838	−	1.00270i
$362$	0.00164347	−	0.0313592i	8.63787e−5	−	0.00164820i
$363$	−7.55997	−	14.8373i	−0.396796	−	0.778755i
$364$	−0.442661	+	1.64044i	−0.0232017	+	0.0859826i
$365$	−21.5874	−	6.66457i	−1.12994	−	0.348839i
$366$	−0.0356376	−	0.0395796i	−0.00186281	−	0.00206886i
$367$	−5.60548	+	4.53923i	−0.292604	+	0.236946i	−0.764370	−	0.644778i	$-0.776950\pi$
$367$	−5.60548	+	4.53923i	−0.292604	+	0.236946i	0.471766	+	0.881724i	$0.343617\pi$
$368$	3.53724	−	13.2012i	0.184391	−	0.688158i
$369$	−13.0328	+	5.80259i	−0.678462	+	0.302071i
$370$	−0.0216385	−	0.124712i	−0.00112493	−	0.00648345i
$371$	29.8447	−	1.51127i	1.54946	−	0.0784614i
$372$	−0.265716	+	1.67766i	−0.0137767	+	0.0869827i
$373$	2.12375	+	3.27030i	0.109964	+	0.169329i	0.889368	−	0.457192i	$-0.151145\pi$
$373$	2.12375	+	3.27030i	0.109964	+	0.169329i	−0.779404	+	0.626521i	$0.784478\pi$
$374$	−0.162760	−	0.281908i	−0.00841610	−	0.0145771i
$375$	8.03868	−	9.76204i	0.415116	−	0.504110i
$376$	−0.374489	−	0.216211i	−0.0193128	−	0.0111503i
$377$	0.495085	−	0.971660i	0.0254982	−	0.0500430i
$378$	−0.237234	−	0.0508634i	−0.0122020	−	0.00261613i
$379$	−2.70772	−	3.72686i	−0.139086	−	0.191436i	0.733792	−	0.679375i	$-0.237749\pi$
$379$	−2.70772	−	3.72686i	−0.139086	−	0.191436i	−0.872878	+	0.487939i	$0.837749\pi$
$380$	−28.0444	−	10.2943i	−1.43865	−	0.528086i
$381$	−18.1525	−	1.90791i	−0.929983	−	0.0977451i
$382$	−0.0122200	−	0.00327433i	−0.000625228	−	0.000167529i
$383$	10.1910	−	26.5486i	0.520738	−	1.35657i	−0.381116	−	0.924527i	$-0.624460\pi$
$383$	10.1910	−	26.5486i	0.520738	−	1.35657i	0.901854	−	0.432042i	$-0.142207\pi$
$384$	0.192024	−	0.590991i	0.00979921	−	0.0301589i
$385$	−29.5721	+	5.07723i	−1.50713	+	0.258760i
$386$	0.0766136	+	0.235792i	0.00389953	+	0.0120015i
$387$	9.70951	+	0.508854i	0.493562	+	0.0258665i
$388$	13.5289	−	20.8327i	0.686827	−	1.05762i
$389$	21.7783	+	19.6093i	1.10420	+	0.994230i	1.00000		0.000325536i	$-0.000103621\pi$
$389$	21.7783	+	19.6093i	1.10420	+	0.994230i	0.104205	+	0.994556i	$0.466770\pi$
$390$	0.00679651	−	0.0121825i	0.000344154	−	0.000616885i
$391$	12.1489	+	3.94741i	0.614396	+	0.199629i
$392$	0.219816	−	0.427674i	0.0111024	−	0.0216008i
$393$	−2.38345	−	2.38345i	−0.120229	−	0.120229i
$394$	−0.0702325	−	0.157745i	−0.00353826	−	0.00794706i
$395$	4.48730	−	17.7901i	0.225781	−	0.895119i
$396$	−15.9421	−	7.09790i	−0.801122	−	0.356683i
$397$	−0.701171	+	0.865873i	−0.0351907	+	0.0434569i	−0.794438	−	0.607346i	$-0.792234\pi$
$397$	−0.701171	+	0.865873i	−0.0351907	+	0.0434569i	0.759247	+	0.650803i	$0.225568\pi$
$398$	0.0976462	+	0.0497532i	0.00489456	+	0.00249390i
$399$	9.04534	+	17.8302i	0.452833	+	0.892627i
$400$	0.588369	+	19.9825i	0.0294184	+	0.999125i
$401$	−4.29812	+	7.44456i	−0.214638	+	0.371764i	−0.953160	−	0.302465i	$-0.902190\pi$
$401$	−4.29812	+	7.44456i	−0.214638	+	0.371764i	0.738523	+	0.674229i	$0.235524\pi$
$402$	−0.126661	+	0.00663801i	−0.00631726	+	0.000331074i
$403$	−0.0864297	−	0.225157i	−0.00430537	−	0.0112159i
$404$	2.46055	+	23.4106i	0.122417	+	1.16472i
$405$	−1.76095	−	0.864843i	−0.0875022	−	0.0429744i
$406$	−0.0973153	+	0.119742i	−0.00482968	+	0.00594268i
$407$	−11.8199	+	11.8199i	−0.585890	+	0.585890i
$408$	0.271078	+	0.104057i	0.0134203	+	0.00515159i
$409$	−15.2011	+	3.23109i	−0.751645	+	0.159767i	−0.567775	−	0.823184i	$-0.692196\pi$
$409$	−15.2011	+	3.23109i	−0.751645	+	0.159767i	−0.183869	+	0.982951i	$0.558862\pi$
$410$	−0.0286191	+	0.317124i	−0.00141339	+	0.0156616i
$411$	3.63537	−	17.1031i	0.179320	−	0.843633i
$412$	−26.2686	+	13.3845i	−1.29416	+	0.659407i
$413$	−2.68904	+	25.1572i	−0.132319	+	1.23791i
$414$	−0.0960709	+	0.0312153i	−0.00472163	+	0.00153415i
$415$	0.561951	−	2.84935i	0.0275851	−	0.139869i
$416$	0.0137586	+	0.0647291i	0.000674571	+	0.00317361i
$417$	−13.1389	−	16.2251i	−0.643413	−	0.794548i
$418$	−0.150621	−	0.562127i	−0.00736713	−	0.0274945i
$419$	−5.12758	−	3.72540i	−0.250499	−	0.181998i	0.455449	−	0.890262i	$-0.349479\pi$
$419$	−5.12758	−	3.72540i	−0.250499	−	0.181998i	−0.705948	+	0.708264i	$0.749479\pi$
$420$	8.82419	−	10.0593i	0.430576	−	0.490842i
$421$	−17.9408	+	13.0347i	−0.874380	+	0.635274i	−0.931759	−	0.363079i	$-0.881726\pi$
$421$	−17.9408	+	13.0347i	−0.874380	+	0.635274i	0.0573790	+	0.998352i	$0.481726\pi$
$422$	0.377325	+	0.305552i	0.0183679	+	0.0148740i
$423$	−0.566871	−	10.8165i	−0.0275622	−	0.525918i
$424$	0.671930	−	0.387939i	0.0326318	−	0.0188400i
$425$	−18.6804	−	0.428307i	−0.906131	−	0.0207759i
$426$			0.0880879i			0.00426787i
$427$	6.27552	+	3.63796i	0.303694	+	0.176053i
$428$	−20.4964	−	3.24632i	−0.990732	−	0.156917i
$429$	−1.83220	+	0.192572i	−0.0884594	+	0.00929746i
$430$	0.115499	−	0.183718i	0.00556988	−	0.00885965i
$431$	1.01729	−	9.67888i	0.0490012	−	0.466215i	−0.942316	−	0.334724i	$-0.891357\pi$
$431$	1.01729	−	9.67888i	0.0490012	−	0.466215i	0.991317	−	0.131491i	$-0.0419764\pi$
$432$	20.6209	−	5.52535i	0.992123	−	0.265839i
$433$	12.2911	−	1.94672i	0.590674	−	0.0935535i	0.146060	−	0.989276i	$-0.453341\pi$
$433$	12.2911	−	1.94672i	0.590674	−	0.0935535i	0.444614	+	0.895722i	$0.353341\pi$
$434$	0.00527873	+	0.0337136i	0.000253387	+	0.00161831i
$435$	−6.87297	+	5.14974i	−0.329534	+	0.246911i
$436$	17.8003	+	3.78356i	0.852478	+	0.181200i
$437$	19.1529	+	12.4381i	0.916209	+	0.594993i
$438$	0.164612	+	0.106900i	0.00786545	+	0.00510788i
$439$	23.9971	+	5.10075i	1.14532	+	0.243445i	0.741215	−	0.671267i	$-0.234250\pi$
$439$	23.9971	+	5.10075i	1.14532	+	0.243445i	0.404105	+	0.914713i	$0.367583\pi$
$440$	−0.623449	+	0.467135i	−0.0297218	+	0.0222698i
$441$	11.9830	−	1.21671i	0.570618	−	0.0579384i
$442$	−0.0203587	+	0.00322450i	−0.000968363	+	0.000153374i
$443$	−6.76871	+	1.81367i	−0.321591	+	0.0861701i	−0.416003	−	0.909363i	$-0.636570\pi$
$443$	−6.76871	+	1.81367i	−0.321591	+	0.0861701i	0.0944121	+	0.995533i	$0.469903\pi$
$444$	0.779231	−	7.41389i	0.0369807	−	0.351848i
$445$	1.17985	−	1.87671i	0.0559302	−	0.0889645i
$446$	−0.361611	+	0.0380068i	−0.0171228	+	0.00179968i
$447$	−16.4771	−	2.60972i	−0.779340	−	0.123435i
$448$	−0.0373287	+	21.1472i	−0.00176361	+	0.999114i
$449$		−	11.3776i		−	0.536943i	−0.963288	−	0.268472i	$-0.913481\pi$
$449$		−	11.3776i		−	0.536943i	0.963288	−	0.268472i	$-0.0865186\pi$
$450$	0.121499	−	0.0840879i	0.00572753	−	0.00396394i
$451$	36.4167	−	21.0252i	1.71480	−	0.990039i
$452$	0.893007	+	17.0396i	0.0420035	+	0.801474i
$453$	−4.93341	−	3.99500i	−0.231792	−	0.187701i
$454$	−0.277083	+	0.201313i	−0.0130042	+	0.00944808i
$455$	−0.370918	+	1.86339i	−0.0173889	+	0.0873573i
$456$	0.419965	+	0.305123i	0.0196667	+	0.0142887i
$457$	−1.77469	−	6.62325i	−0.0830167	−	0.309822i	0.911915	−	0.410380i	$-0.134604\pi$
$457$	−1.77469	−	6.62325i	−0.0830167	−	0.309822i	−0.994931	+	0.100558i	$0.967937\pi$
$458$	0.108544	+	0.134040i	0.00507191	+	0.00626328i
$459$	4.14863	+	19.5178i	0.193641	+	0.911011i
$460$	2.95745	−	14.9957i	0.137892	−	0.699176i
$461$	−6.19822	+	2.01392i	−0.288680	+	0.0937978i	−0.449777	−	0.893141i	$-0.648497\pi$
$461$	−6.19822	+	2.01392i	−0.288680	+	0.0937978i	0.161097	+	0.986939i	$0.448497\pi$
$462$	0.259193	+	0.0277049i	0.0120587	+	0.00128895i
$463$	3.99566	−	2.03589i	0.185694	−	0.0946158i	−0.358672	−	0.933464i	$-0.616770\pi$
$463$	3.99566	−	2.03589i	0.185694	−	0.0946158i	0.544366	+	0.838848i	$0.316770\pi$
$464$	2.82274	−	13.2800i	0.131043	−	0.616507i
$465$	−0.170714	+	1.89166i	−0.00791667	+	0.0877235i
$466$	0.0468911	−	0.00996701i	0.00217219	−	0.000461713i
$467$	37.5050	+	14.3968i	1.73552	+	0.666205i	0.999937	−	0.0112245i	$-0.00357295\pi$
$467$	37.5050	+	14.3968i	1.73552	+	0.666205i	0.735587	+	0.677430i	$0.236906\pi$
$468$	−0.781365	+	0.781365i	−0.0361186	+	0.0361186i
$469$	16.1379	−	6.16210i	0.745180	−	0.284539i
$470$	−0.216992	−	0.106570i	−0.0100091	−	0.00491571i
$471$	−0.620259	−	5.90137i	−0.0285800	−	0.271921i
$472$	0.235412	+	0.613269i	0.0108357	+	0.0282280i
$473$	−28.6193	+	1.49988i	−1.31592	+	0.0689643i
$474$	−0.0796971	+	0.138039i	−0.00366061	+	0.00634036i
$475$	−32.0602	−	9.38324i	−1.47102	−	0.430533i
$476$	−19.7428	−	1.06962i	−0.904909	−	0.0490261i
$477$	17.3161	+	8.82298i	0.792849	+	0.403977i
$478$	−0.0450215	+	0.0555969i	−0.00205924	+	0.00254294i
$479$	18.9438	+	8.43434i	0.865566	+	0.385375i	0.790982	−	0.611840i	$-0.209570\pi$
$479$	18.9438	+	8.43434i	0.865566	+	0.385375i	0.0745845	+	0.997215i	$0.476237\pi$
$480$	0.127461	−	0.505326i	0.00581778	−	0.0230649i
$481$	0.430521	+	0.966966i	0.0196301	+	0.0440898i
$482$	−0.0862007	−	0.0862007i	−0.00392633	−	0.00392633i
$483$	−8.28622	+	5.99797i	−0.377036	+	0.272917i
$484$	27.9996	+	9.09763i	1.27271	+	0.413529i
$485$	13.5326	−	24.2567i	0.614484	−	1.10144i
$486$	−0.191781	−	0.172681i	−0.00869938	−	0.00783296i
$487$	4.04851	−	6.23415i	0.183455	−	0.282496i	−0.734963	−	0.678107i	$-0.762800\pi$
$487$	4.04851	−	6.23415i	0.183455	−	0.282496i	0.918418	+	0.395611i	$0.129467\pi$
$488$	0.188077	+	0.00985672i	0.00851387	+	0.000446193i
$489$	6.20797	+	19.1062i	0.280734	+	0.864011i
$490$	0.106588	−	0.246794i	0.00481514	−	0.0111490i
$491$	−6.27403	+	19.3095i	−0.283143	+	0.871425i	0.703806	+	0.710392i	$0.251482\pi$
$491$	−6.27403	+	19.3095i	−0.283143	+	0.871425i	−0.986949	+	0.161033i	$0.948518\pi$
$492$	−6.72052	+	17.5076i	−0.302984	+	0.789302i
$493$	12.2574	+	3.28436i	0.552045	+	0.147920i
$494$	−0.0366486	−	0.00385192i	−0.00164890	−	0.000173306i
$495$	−18.3184	−	6.72415i	−0.823350	−	0.302228i
$496$	−1.76487	−	2.42913i	−0.0792448	−	0.109071i
$497$	−3.68720	−	11.4166i	−0.165393	−	0.512103i
$498$	−0.0114546	+	0.0224808i	−0.000513291	+	0.00100739i
$499$	−7.97198	−	4.60262i	−0.356875	−	0.206042i	0.310834	−	0.950464i	$-0.399392\pi$
$499$	−7.97198	−	4.60262i	−0.356875	−	0.206042i	−0.667709	+	0.744422i	$0.732725\pi$
$500$	2.15444	+	22.2533i	0.0963495	+	0.995199i
$501$	−3.25260	−	5.63367i	−0.145315	−	0.251694i
$502$	0.0343365	+	0.0528736i	0.00153251	+	0.00235986i
$503$	3.27358	−	20.6686i	0.145962	−	0.921565i	−0.800637	−	0.599150i	$-0.795505\pi$
$503$	3.27358	−	20.6686i	0.145962	−	0.921565i	0.946598	−	0.322415i	$-0.104495\pi$
$504$	0.262573	−	0.169859i	0.0116959	−	0.00756611i
$505$	4.49982	+	25.9344i	0.200239	+	1.15407i
$506$	0.272005	−	0.121105i	0.0120921	−	0.00538376i
$507$	3.77549	−	14.0903i	0.167676	−	0.625774i
$508$	25.0783	−	20.3080i	1.11267	−	0.901022i
$509$	4.74698	+	5.27205i	0.210406	+	0.233680i	0.839105	−	0.543969i	$-0.183079\pi$
$509$	4.74698	+	5.27205i	0.210406	+	0.233680i	−0.628699	+	0.777648i	$0.716412\pi$
$510$	0.155107	+	0.0478852i	0.00686824	+	0.00212039i
$511$	−25.8090	−	6.96436i	−1.14172	−	0.308085i
$512$	0.623407	+	1.22350i	0.0275509	+	0.0540718i
$513$	−1.86698	+	35.6241i	−0.0824291	+	1.57284i
$514$	0.0632152	−	0.0702076i	0.00278830	−	0.00309672i
$515$	−28.3043	+	16.9017i	−1.24723	+	0.744778i
$516$	9.49799	−	8.55203i	0.418126	−	0.376482i
$517$	4.99434	+	31.5330i	0.219651	+	1.38682i
$518$	−0.0308794	−	0.146548i	−0.00135676	−	0.00643893i
$519$	1.50201	−	2.06734i	0.0659310	−	0.0907463i
$520$	0.0134675	+	0.0474562i	0.000590588	+	0.00208109i
$521$	−6.21506	+	13.9592i	−0.272287	+	0.611566i	−0.996993	−	0.0774921i	$-0.975309\pi$
$521$	−6.21506	+	13.9592i	−0.272287	+	0.611566i	0.724706	+	0.689058i	$0.241975\pi$
$522$	−0.0936831	+	0.0359616i	−0.00410040	+	0.00157400i
$523$	−3.88934	+	2.52576i	−0.170069	+	0.110444i	−0.626867	−	0.779127i	$-0.715663\pi$
$523$	−3.88934	+	2.52576i	−0.170069	+	0.110444i	0.456798	+	0.889571i	$0.348996\pi$
$524$	5.95927			0.260332
$525$	9.09106	−	11.8843i	0.396767	−	0.518675i
$526$	0.357223			0.0155757
$527$	2.35367	−	1.52849i	0.102528	−	0.0665822i
$528$	−21.4126	+	8.21952i	−0.931863	+	0.357709i
$529$	4.60253	−	10.3374i	0.200110	−	0.449454i
$530$	0.360266	−	0.241571i	0.0156490	−	0.0104932i
$531$	−9.67149	+	13.3117i	−0.419707	+	0.577677i
$532$	−33.5981	−	10.9823i	−1.45666	−	0.476143i
$533$	−0.416539	−	2.62992i	−0.0180423	−	0.113915i
$534$	−0.0143118	+	0.0128864i	−0.000619332	+	0.000557649i
$535$	−23.1109	−	2.08566i	−0.999169	−	0.0901707i
$536$	0.300112	−	0.333308i	0.0129628	−	0.0143967i
$537$	−1.37359	+	26.2097i	−0.0592748	+	1.13103i
$538$	−0.00122146	−	0.00239725i	−5.26610e−5	−	0.000103353i
$539$	−34.7521	+	7.25866i	−1.49688	+	0.312653i
$540$	22.5956	−	7.71122i	0.972361	−	0.331838i
$541$	16.9732	+	18.8507i	0.729735	+	0.810453i	0.987809	−	0.155672i	$-0.0497544\pi$
$541$	16.9732	+	18.8507i	0.729735	+	0.810453i	−0.258074	+	0.966125i	$0.583088\pi$
$542$	0.0186106	−	0.0150706i	0.000799395	−	0.000647337i
$543$	0.535254	−	1.99759i	0.0229699	−	0.0857249i
$544$	−0.703472	+	0.313206i	−0.0301611	+	0.0134286i
$545$	20.1431	+	2.88713i	0.862834	+	0.123671i
$546$	0.00751952	−	0.0146937i	0.000321806	−	0.000628833i
$547$	−1.41055	+	8.90589i	−0.0603110	+	0.380788i	0.939008	+	0.343895i	$0.111746\pi$
$547$	−1.41055	+	8.90589i	−0.0603110	+	0.380788i	−0.999319	+	0.0368938i	$0.988254\pi$
$548$	16.8365	+	25.9259i	0.719218	+	1.10750i
$549$	2.35873	+	4.08544i	0.100668	+	0.174362i
$550$	−0.330256	+	0.283930i	−0.0140822	+	0.0121068i
$551$	19.6471	+	11.3433i	0.836995	+	0.483239i
$552$	−0.120576	+	0.236643i	−0.00513204	+	0.0100722i
$553$	4.55100	−	21.2265i	0.193528	−	0.902641i
$554$	0.303190	+	0.417305i	0.0128813	+	0.0177296i
$555$	0.313705	−	8.32996i	0.0133160	−	0.353587i
$556$	36.7090	+	3.85827i	1.55681	+	0.163627i
$557$	−16.3666	−	4.38542i	−0.693475	−	0.185816i	−0.105169	−	0.994454i	$-0.533538\pi$
$557$	−16.3666	−	4.38542i	−0.693475	−	0.185816i	−0.588306	+	0.808638i	$0.700205\pi$
$558$	−0.00795316	+	0.0207187i	−0.000336684	+	0.000877092i
$559$	−0.560777	+	1.72589i	−0.0237183	+	0.0729975i
$560$	1.54380	+	23.6034i	0.0652373	+	0.997426i
$561$	−6.62463	−	20.3885i	−0.279692	−	0.860804i
$562$	−0.489917	−	0.0256755i	−0.0206659	−	0.00108305i
$563$	23.6121	−	36.3595i	0.995133	−	1.53237i	0.156496	−	0.987679i	$-0.449980\pi$
$563$	23.6121	−	36.3595i	0.995133	−	1.53237i	0.838637	−	0.544691i	$-0.183353\pi$
$564$	−10.5809	−	9.52709i	−0.445536	−	0.401163i
$565$	2.27343	+	18.9439i	0.0956439	+	0.796974i
$566$	0.459661	+	0.149353i	0.0193210	+	0.00627776i
$567$	−2.11895	−	0.947901i	−0.0889874	−	0.0398081i
$568$	−0.220260	−	0.220260i	−0.00924190	−	0.00924190i
$569$	4.01461	+	9.01696i	0.168301	+	0.378011i	0.977930	−	0.208931i	$-0.0669984\pi$
$569$	4.01461	+	9.01696i	0.168301	+	0.378011i	−0.809629	+	0.586942i	$0.800332\pi$
$570$	0.245691	+	0.154461i	0.0102908	+	0.00646964i
$571$	−1.33258	−	0.593302i	−0.0557666	−	0.0248289i	0.378664	−	0.925534i	$-0.376384\pi$
$571$	−1.33258	−	0.593302i	−0.0557666	−	0.0248289i	−0.434430	+	0.900705i	$0.643050\pi$
$572$	2.04976	−	2.53124i	0.0857047	−	0.105836i
$573$	−0.742352	−	0.378247i	−0.0310122	−	0.0158015i
$574$	−0.0203817	+	0.376199i	−0.000850716	+	0.0157022i
$575$	2.17566	−	16.9521i	0.0907312	−	0.706950i
$576$	−6.87654	+	11.9105i	−0.286522	+	0.496271i
$577$	−5.62157	+	0.294614i	−0.234029	+	0.0122649i	−0.168990	−	0.985618i	$-0.554051\pi$
$577$	−5.62157	+	0.294614i	−0.234029	+	0.0122649i	−0.0650391	+	0.997883i	$0.520717\pi$
$578$	0.0186764	+	0.0486537i	0.000776837	+	0.00202373i
$579$	1.70671	+	16.2383i	0.0709286	+	0.674841i
$580$	2.15427	−	15.0300i	0.0894514	−	0.624088i
$581$	0.543552	−	3.39308i	0.0225504	−	0.140769i
$582$	−0.170631	+	0.170631i	−0.00707288	+	0.00707288i
$583$	−53.4789	−	20.5286i	−2.21487	−	0.850209i
$584$	−0.678903	+	0.144305i	−0.0280932	+	0.00597140i
$585$	−0.813193	+	0.930320i	−0.0336214	+	0.0384640i
$586$	−0.0230659	+	0.108516i	−0.000952842	+	0.00448277i
$587$	18.5011	−	9.42678i	0.763622	−	0.389085i	−0.0283850	−	0.999597i	$-0.509036\pi$
$587$	18.5011	−	9.42678i	0.763622	−	0.389085i	0.792007	+	0.610512i	$0.209036\pi$
$588$	10.0073	−	12.2691i	0.412693	−	0.505971i
$589$	4.77172	−	1.55043i	0.196615	−	0.0638842i
$590$	0.154294	+	0.333261i	0.00635217	+	0.0137201i
$591$	−2.36432	−	11.1232i	−0.0972551	−	0.457549i
$592$	8.29300	+	10.2410i	0.340840	+	0.420903i
$593$	3.80233	+	14.1905i	0.156143	+	0.582733i	0.999005	+	0.0446033i	$0.0142024\pi$
$593$	3.80233	+	14.1905i	0.156143	+	0.582733i	−0.842862	+	0.538130i	$0.819131\pi$
$594$	0.376271	+	0.273377i	0.0154386	+	0.0112168i
$595$	−22.1069	+	0.286359i	−0.906293	+	0.0117396i
$596$	23.8611	−	17.3361i	0.977390	−	0.710116i
$597$	5.60893	+	4.54202i	0.229558	+	0.185892i
$598$	−0.000986734	−	0.0188280i	−4.03506e−5	−	0.000769935i
$599$	−8.74982	+	5.05171i	−0.357508	+	0.206407i	−0.667987	−	0.744173i	$-0.732844\pi$
$599$	−8.74982	+	5.05171i	−0.357508	+	0.206407i	0.310479	+	0.950580i	$0.399511\pi$
$600$	0.0695531	−	0.382215i	0.00283949	−	0.0156039i
$601$			22.6515i			0.923974i	0.886887	+	0.461987i	$0.152863\pi$
$601$			22.6515i			0.923974i	−0.886887	+	0.461987i	$0.847137\pi$
$602$	0.128776	−	0.222140i	0.00524850	−	0.00905373i
$603$	11.0960	+	1.75744i	0.451865	+	0.0715684i
$604$	11.1617	−	1.17315i	0.454165	−	0.0477346i
$605$	31.9206	+	8.05151i	1.29776	+	0.327340i
$606$	0.0239029	−	0.227421i	0.000970990	−	0.00923835i
$607$	−19.2701	+	5.16341i	−0.782150	+	0.209576i	−0.627732	−	0.778429i	$-0.716017\pi$
$607$	−19.2701	+	5.16341i	−0.782150	+	0.209576i	−0.154418	+	0.988006i	$0.549350\pi$
$608$	−1.35972	+	0.215359i	−0.0551440	+	0.00873395i
$609$	−7.90841	+	6.38103i	−0.320465	+	0.258572i
$610$	0.105279	−	0.00154960i	0.00426263	−	6.27413e-5i
$611$	1.97744	+	0.420317i	0.0799986	+	0.0170042i
$612$	−10.7840	−	7.00323i	−0.435919	−	0.283089i
$613$	−32.1875	−	20.9028i	−1.30004	−	0.844257i	−0.305871	−	0.952073i	$-0.598948\pi$
$613$	−32.1875	−	20.9028i	−1.30004	−	0.844257i	−0.994171	+	0.107815i	$0.965614\pi$
$614$	0.296847	+	0.0630967i	0.0119798	+	0.00254638i
$615$	−6.18579	+	20.0366i	−0.249435	+	0.807954i
$616$	−0.717375	+	0.578825i	−0.0289039	+	0.0233215i
$617$	−0.589114	+	0.0933065i	−0.0237168	+	0.00375638i	−0.168282	−	0.985739i	$-0.553822\pi$
$617$	−0.589114	+	0.0933065i	−0.0237168	+	0.00375638i	0.144565	+	0.989495i	$0.453822\pi$
$618$	0.276642	−	0.0741259i	0.0111282	−	0.00298178i
$619$	0.290449	−	2.76344i	0.0116741	−	0.111072i	−0.987133	−	0.159901i	$-0.948882\pi$
$619$	0.290449	−	2.76344i	0.0116741	−	0.111072i	0.998807	+	0.0488294i	$0.0155491\pi$
$620$	−2.15141	−	2.57824i	−0.0864028	−	0.103545i
$621$	−18.1514	+	1.90779i	−0.728392	+	0.0765571i
$622$	−0.126843	−	0.0200899i	−0.00508593	−	0.000805532i
$623$	1.31547	−	2.26920i	0.0527031	−	0.0909134i
$624$			1.45235i			0.0581404i
$625$	4.07156	+	24.6662i	0.162862	+	0.986649i
$626$	−0.413975	+	0.239009i	−0.0165458	+	0.00955270i
$627$	−2.00583	−	38.2734i	−0.0801050	−	1.52849i
$628$	8.15292	+	6.60211i	0.325337	+	0.263453i
$629$	−9.96459	+	7.23970i	−0.397314	+	0.288666i
$630$	0.140099	−	0.104587i	0.00558166	−	0.00416683i
$631$	22.3034	+	16.2043i	0.887883	+	0.645085i	0.935325	−	0.353789i	$-0.115107\pi$
$631$	22.3034	+	16.2043i	0.887883	+	0.645085i	−0.0474420	+	0.998874i	$0.515107\pi$
$632$	−0.145882	−	0.544441i	−0.00580289	−	0.0216567i
$633$	20.1227	+	24.8495i	0.799807	+	0.987680i
$634$	−0.102039	−	0.480056i	−0.00405249	−	0.0190655i
$635$	26.4574	−	24.5369i	1.04993	−	0.973719i
$636$	24.2963	−	7.89435i	0.963411	−	0.313031i
$637$	−0.359510	+	2.21912i	−0.0142443	+	0.0879248i
$638$	0.263544	−	0.134282i	0.0104338	−	0.00531628i
$639$	1.62220	−	7.63186i	0.0641733	−	0.301912i
$640$	0.629828	+	1.05473i	0.0248961	+	0.0416920i
$641$	−1.48400	+	0.315435i	−0.0586146	+	0.0124589i	−0.237126	−	0.971479i	$-0.576205\pi$
$641$	−1.48400	+	0.315435i	−0.0586146	+	0.0124589i	0.178511	+	0.983938i	$0.442872\pi$
$642$	0.188204	+	0.0722447i	0.00742781	+	0.00285127i
$643$	−18.1864	+	18.1864i	−0.717201	+	0.717201i	−0.968031	−	0.250830i	$-0.919297\pi$
$643$	−18.1864	+	18.1864i	−0.717201	+	0.717201i	0.250830	+	0.968031i	$0.419297\pi$
$644$	2.86062	−	17.8572i	0.112724	−	0.703672i
$645$	9.95579	−	10.2532i	0.392009	−	0.403721i
$646$	−0.0448227	−	0.426460i	−0.00176353	−	0.0167788i
$647$	−2.70505	−	7.04689i	−0.106346	−	0.277042i	0.870073	−	0.492922i	$-0.164071\pi$
$647$	−2.70505	−	7.04689i	−0.106346	−	0.277042i	−0.976420	+	0.215880i	$0.930738\pi$
$648$	−0.0601875	+	0.00315429i	−0.00236439	+	0.000123912i
$649$	24.2497	−	42.0017i	0.951885	−	1.64871i
$650$	0.00929046	+	0.0259665i	0.000364402	+	0.00101849i
$651$	−0.121578	+	2.24404i	−0.00476501	+	0.0879510i
$652$	−31.6461	−	16.1245i	−1.23936	−	0.631484i
$653$	21.7081	−	26.8073i	0.849503	−	1.04905i	−0.148686	−	0.988885i	$-0.547504\pi$
$653$	21.7081	−	26.8073i	0.849503	−	1.04905i	0.998188	−	0.0601643i	$-0.0191625\pi$
$654$	−0.161499	−	0.0719041i	−0.00631512	−	0.00281167i
$655$	6.64867	−	0.446648i	0.259785	−	0.0174520i
$656$	−13.4833	−	30.2839i	−0.526433	−	1.18239i
$657$	−12.2932	−	12.2932i	−0.479602	−	0.479602i
$658$	−0.261107	−	0.116805i	−0.0101790	−	0.00455353i
$659$	−16.9511	−	5.50773i	−0.660319	−	0.214551i	−0.0403605	−	0.999185i	$-0.512851\pi$
$659$	−16.9511	−	5.50773i	−0.660319	−	0.214551i	−0.619959	+	0.784634i	$0.712851\pi$
$660$	−23.2771	+	10.7769i	−0.906059	+	0.419489i
$661$	−29.1652	−	26.2604i	−1.13439	−	1.02141i	−0.999533	−	0.0305478i	$-0.990275\pi$
$661$	−29.1652	−	26.2604i	−1.13439	−	1.02141i	−0.134860	−	0.990865i	$-0.543059\pi$
$662$	0.156209	−	0.240540i	0.00607122	−	0.00934885i
$663$	−1.35562	−	0.0710448i	−0.0526477	−	0.00275915i
$664$	−0.0275707	−	0.0848540i	−0.00106995	−	0.00329297i
$665$	−38.3080	−	9.73459i	−1.48552	−	0.377491i
$666$	0.0300981	−	0.0926326i	0.00116628	−	0.00358944i
$667$	−4.15963	+	10.8362i	−0.161061	+	0.419579i
$668$	11.1090	+	2.97666i	0.429822	+	0.115170i
$669$	−23.8146	−	2.50302i	−0.920727	−	0.0967724i
$670$	0.154913	−	0.197165i	0.00598480	−	0.00761716i
$671$	−8.17313	−	11.2493i	−0.315520	−	0.434276i
$672$	0.129270	−	0.602934i	0.00498672	−	0.0232587i
$673$	7.81076	−	15.3295i	0.301083	−	0.590908i	−0.690053	−	0.723759i	$-0.742413\pi$
$673$	7.81076	−	15.3295i	0.301083	−	0.590908i	0.991136	+	0.132850i	$0.0424129\pi$
$674$	−0.355475	−	0.205234i	−0.0136924	−	0.00790531i
$675$	24.6316	−	10.2968i	0.948071	−	0.396325i
$676$	12.8950	+	22.3347i	0.495960	+	0.859028i
$677$	−0.346917	−	0.534205i	−0.0133331	−	0.0205312i	0.831941	−	0.554864i	$-0.187230\pi$
$677$	−0.346917	−	0.534205i	−0.0133331	−	0.0205312i	−0.845274	+	0.534333i	$0.820563\pi$
$678$	0.0259302	−	0.163717i	0.000995842	−	0.00628750i
$679$	14.9722	−	29.2568i	0.574580	−	1.12277i
$680$	−0.507572	+	0.268103i	−0.0194645	+	0.0102813i
$681$	−20.6056	+	9.17421i	−0.789609	+	0.351557i
$682$	0.0169304	−	0.0631853i	0.000648300	−	0.00241949i
$683$	14.1248	−	11.4381i	0.540471	−	0.437665i	−0.319812	−	0.947481i	$-0.603620\pi$
$683$	14.1248	−	11.4381i	0.540471	−	0.437665i	0.860284	+	0.509816i	$0.170286\pi$
$684$	−15.3821	−	17.0835i	−0.588148	−	0.653204i
$685$	20.7273	+	27.6632i	0.791951	+	1.05696i
$686$	0.115561	−	0.296347i	0.00441214	−	0.0113146i
$687$	5.15681	+	10.1208i	0.196745	+	0.386133i
$688$	−1.18241	+	22.5617i	−0.0450788	+	0.860155i
$689$	−2.42714	+	2.69561i	−0.0924665	+	0.102694i
$690$	−0.0583897	+	0.136518i	−0.00222286	+	0.00519715i
$691$	−18.4552	+	16.6171i	−0.702068	+	0.632145i	−0.940809	−	0.338938i	$-0.889932\pi$
$691$	−18.4552	+	16.6171i	−0.702068	+	0.632145i	0.238740	+	0.971083i	$0.423265\pi$
$692$	0.706740	+	4.46218i	0.0268662	+	0.169627i
$693$	−21.9460	−	7.17355i	−0.833661	−	0.272501i
$694$	−0.0370737	+	0.0510276i	−0.00140730	+	0.00193698i
$695$	41.2448	+	1.55327i	1.56451	+	0.0589190i
$696$	−0.107312	+	0.241028i	−0.00406767	+	0.00913613i
$697$	28.9265	−	11.1038i	1.09567	−	0.420588i
$698$	0.0175580	−	0.0114023i	0.000664578	−	0.000431582i
$699$	3.15710			0.119413
$700$	3.49198	+	26.2221i	0.131984	+	0.991103i
$701$	−7.79098			−0.294261			−0.147131	−	0.989117i	$-0.547004\pi$
$701$	−7.79098			−0.294261			−0.147131	+	0.989117i	$0.547004\pi$
$702$	0.0246994	−	0.0160400i	0.000932220	−	0.000605391i
$703$	−20.5574	+	7.89123i	−0.775335	+	0.297623i
$704$	16.4883	−	37.0332i	0.621425	−	1.39574i
$705$	−12.5190	−	9.83618i	−0.471493	−	0.370452i
$706$	−0.256420	+	0.352932i	−0.00965050	+	0.0132828i
$707$	6.42152	+	30.4753i	0.241506	+	1.14614i
$708$	3.38355	+	21.3629i	0.127162	+	0.802866i
$709$	−33.5426	+	30.2019i	−1.25972	+	1.13426i	−0.274754	+	0.961515i	$0.588596\pi$
$709$	−33.5426	+	30.2019i	−1.25972	+	1.13426i	−0.984967	+	0.172743i	$0.944737\pi$
$710$	−0.131115	−	0.114608i	−0.00492065	−	0.00430115i
$711$	9.44698	−	10.4919i	0.354289	−	0.393478i
$712$	0.00356414	−	0.0680079i	0.000133572	−	0.00254870i
$713$	1.16539	+	2.28721i	0.0436443	+	0.0856568i
$714$	0.185439	+	0.0500392i	0.00693988	+	0.00187267i
$715$	2.09717	−	2.97769i	0.0784296	−	0.111359i
$716$	−31.0485	−	34.4828i	−1.16034	−	1.28868i
$717$	−3.66145	+	2.96499i	−0.136740	+	0.110729i
$718$	−0.0499613	+	0.186458i	−0.00186454	+	0.00695856i
$719$	−28.4168	+	12.6520i	−1.05977	+	0.471839i	−0.861209	−	0.508250i	$-0.830292\pi$
$719$	−28.4168	+	12.6520i	−1.05977	+	0.471839i	−0.198558	+	0.980089i	$0.563626\pi$
$720$	−6.78135	+	13.8078i	−0.252726	+	0.514588i
$721$	−32.7512	+	21.1868i	−1.21972	+	0.789036i
$722$	0.0688773	−	0.434874i	0.00256335	−	0.0161843i
$723$	−4.37258	−	6.73318i	−0.162618	−	0.250409i
$724$	1.82812	+	3.16640i	0.0679417	+	0.117678i
$725$	1.27699	−	16.9302i	0.0474262	−	0.628773i
$726$	−0.247682	−	0.142999i	−0.00919235	−	0.00530721i
$727$	9.91394	−	19.4572i	0.367688	−	0.721628i	−0.630838	−	0.775915i	$-0.717289\pi$
$727$	9.91394	−	19.4572i	0.367688	−	0.721628i	0.998525	+	0.0542869i	$0.0172886\pi$
$728$	0.0179388	+	0.0555432i	0.000664855	+	0.00205857i
$729$	−11.5369	−	15.8791i	−0.427291	−	0.588116i
$730$	−0.373286	+	0.105934i	−0.0138159	+	0.00392078i
$731$	−21.0011	−	2.20731i	−0.776755	−	0.0816403i
$732$	5.98986	+	1.60498i	0.221392	+	0.0593217i
$733$	−0.0807548	+	0.210373i	−0.00298275	+	0.00777032i	−0.935064	−	0.354480i	$-0.884658\pi$
$733$	−0.0807548	+	0.210373i	−0.00298275	+	0.00777032i	0.932081	+	0.362250i	$0.117991\pi$
$734$	−0.0382810	+	0.117817i	−0.00141298	+	0.00434870i
$735$	10.2454	−	14.4385i	0.377907	−	0.532573i
$736$	−0.217655	−	0.669875i	−0.00802289	−	0.0246919i
$737$	−33.0684	−	1.73304i	−1.21809	−	0.0638375i
$738$	−0.133447	+	0.205490i	−0.00491224	+	0.00756419i
$739$	−29.9797	−	26.9939i	−1.10282	−	0.992986i	−0.102824	−	0.994700i	$-0.532788\pi$
$739$	−29.9797	−	26.9939i	−1.10282	−	0.992986i	−0.999999	+	0.00171350i	$0.999455\pi$
$740$	10.0214	+	10.8058i	0.368395	+	0.397228i
$741$	−2.30809	−	0.749943i	−0.0847897	−	0.0275498i
$742$	0.415746	−	0.300937i	0.0152625	−	0.0110478i
$743$	−1.97911	−	1.97911i	−0.0726064	−	0.0726064i	0.669871	−	0.742477i	$-0.266349\pi$
$743$	−1.97911	−	1.97911i	−0.0726064	−	0.0726064i	−0.742477	+	0.669871i	$0.766349\pi$
$744$	0.0237329	+	0.0533050i	0.000870090	+	0.00195426i
$745$	25.3221	−	21.1300i	0.927732	−	0.774145i
$746$	0.0611810	+	0.0272395i	0.00224000	+	0.000997310i
$747$	1.40641	−	1.73678i	0.0514580	−	0.0635454i
$748$	33.7701	+	17.2067i	1.23476	+	0.629141i
$749$	−27.4161	−	1.48535i	−1.00176	−	0.0542734i
$750$	0.0244743	−	0.215806i	0.000893675	−	0.00788014i
$751$	14.9793	−	25.9449i	0.546602	−	0.946743i	−0.451902	−	0.892068i	$-0.649254\pi$
$751$	14.9793	−	25.9449i	0.546602	−	0.946743i	0.998504	−	0.0546754i	$-0.0174124\pi$
$752$	25.1340	−	1.31722i	0.916543	−	0.0480340i
$753$	1.48792	+	3.87616i	0.0542228	+	0.141255i
$754$	−0.00195776	−	0.0186268i	−7.12973e−5	−	0.000678349i
$755$	12.3650	−	2.14543i	0.450010	−	0.0780803i
$756$	26.3910	−	10.0771i	0.959832	−	0.366502i
$757$	29.2442	−	29.2442i	1.06290	−	1.06290i	0.0650131	−	0.997884i	$-0.479291\pi$
$757$	29.2442	−	29.2442i	1.06290	−	1.06290i	0.997884	−	0.0650131i	$-0.0207089\pi$
$758$	−0.0738631	−	0.0283534i	−0.00268283	−	0.00102984i
$759$	19.1803	−	4.07689i	0.696199	−	0.147982i
$760$	−1.00056	+	0.228117i	−0.0362942	+	0.00827466i
$761$	−9.89316	+	46.5437i	−0.358627	+	1.68721i	0.315769	+	0.948836i	$0.397738\pi$
$761$	−9.89316	+	46.5437i	−0.358627	+	1.68721i	−0.674396	+	0.738370i	$0.735596\pi$
$762$	−0.279315	+	0.142318i	−0.0101185	+	0.00515565i
$763$	23.9408	+	2.55901i	0.866714	+	0.0926424i
$764$	1.40090	−	0.455180i	0.0506828	−	0.0164679i
$765$	−12.5565

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)

\(f(q)\)	\(=\)	\(q+(0.0144040 - 0.00935405i) q^{2} +(1.05595 - 0.405343i) q^{3} +(-0.813353 + 1.82682i) q^{4} +(-0.770525 + 2.09912i) q^{5} +(0.0114183 - 0.0157160i) q^{6} +(-0.822022 + 2.51481i) q^{7} +(0.0107461 + 0.0678483i) q^{8} +(-1.27870 + 1.15134i) q^{9} +O(q^{10})\)	\(q+(0.0144040 - 0.00935405i) q^{2} +(1.05595 - 0.405343i) q^{3} +(-0.813353 + 1.82682i) q^{4} +(-0.770525 + 2.09912i) q^{5} +(0.0114183 - 0.0157160i) q^{6} +(-0.822022 + 2.51481i) q^{7} +(0.0107461 + 0.0678483i) q^{8} +(-1.27870 + 1.15134i) q^{9} +(0.00853662 + 0.0374431i) q^{10} +(3.39365 - 3.76903i) q^{11} +(-0.118375 + 2.25873i) q^{12} +(-0.145799 - 0.286147i) q^{13} +(0.0116833 + 0.0439125i) q^{14} +(0.0372227 + 2.52890i) q^{15} +(-2.67534 - 2.97126i) q^{16} +(2.90424 - 2.35181i) q^{17} +(-0.00764859 + 0.0285449i) q^{18} +(6.10342 - 2.71742i) q^{19} +(-3.20800 - 3.11494i) q^{20} +(0.151343 + 2.98873i) q^{21} +(0.0136263 - 0.0860334i) q^{22} +(1.86170 + 2.86676i) q^{23} +(0.0388492 + 0.0672888i) q^{24} +(-3.81258 - 3.23484i) q^{25} +(-0.00477673 - 0.00275784i) q^{26} +(-2.42406 + 4.75748i) q^{27} +(-3.92552 - 3.54712i) q^{28} +(1.99592 + 2.74715i) q^{29} +(0.0241916 + 0.0360780i) q^{30} +(0.746861 + 0.0784982i) q^{31} +(-0.199035 - 0.0533314i) q^{32} +(2.05579 - 5.35552i) q^{33} +(0.0198337 - 0.0610417i) q^{34} +(-4.64549 - 3.66325i) q^{35} +(-1.06327 - 3.27240i) q^{36} +(-3.29137 - 0.172493i) q^{37} +(0.0624947 - 0.0962334i) q^{38} +(-0.269945 - 0.243060i) q^{39} +(-0.150702 - 0.0297215i) q^{40} +(7.88534 + 2.56210i) q^{41} +(0.0301367 + 0.0416339i) q^{42} +(-3.99562 - 3.99562i) q^{43} +(4.12511 + 9.26514i) q^{44} +(-1.43154 - 3.57127i) q^{45} +(0.0536317 + 0.0238784i) q^{46} +(-3.96152 + 4.89207i) q^{47} +(-4.02942 - 2.05309i) q^{48} +(-5.64856 - 4.13446i) q^{49} +(-0.0851752 - 0.0109315i) q^{50} +(2.11346 - 3.66061i) q^{51} +(0.641326 - 0.0336105i) q^{52} +(-4.04766 - 10.5445i) q^{53} +(0.00958565 + 0.0912013i) q^{54} +(5.29674 + 10.0278i) q^{55} +(-0.179459 - 0.0287484i) q^{56} +(5.34345 - 5.34345i) q^{57} +(0.0544462 + 0.0208999i) q^{58} +(9.35373 - 1.98820i) q^{59} +(-4.65012 - 1.98889i) q^{60} +(0.570023 - 2.68175i) q^{61} +(0.0114920 - 0.00585548i) q^{62} +(-1.84430 - 4.16211i) q^{63} +(7.60172 - 2.46995i) q^{64} +(0.712999 - 0.0855661i) q^{65} +(-0.0204842 - 0.0963707i) q^{66} +(-4.10889 - 5.07406i) q^{67} +(1.93416 + 7.21837i) q^{68} +(3.12789 + 2.27255i) q^{69} +(-0.101180 - 0.00931112i) q^{70} +(-3.66851 + 2.66533i) q^{71} +(-0.0918577 - 0.0743849i) q^{72} +(0.528792 + 10.0900i) q^{73} +(-0.0490223 + 0.0283030i) q^{74} +(-5.33714 - 1.87045i) q^{75} +13.3601i q^{76} +(6.68874 + 11.6326i) q^{77} +(-0.00616188 - 0.000975946i) q^{78} +(-8.16023 + 0.857674i) q^{79} +(8.29845 - 3.32641i) q^{80} +(-0.0917101 + 0.872564i) q^{81} +(0.137546 - 0.0368554i) q^{82} +(-1.28282 + 0.203179i) q^{83} +(-5.58297 - 2.15442i) q^{84} +(2.69893 + 7.90846i) q^{85} +(-0.0949280 - 0.0201776i) q^{86} +(3.22114 + 2.09183i) q^{87} +(0.292191 + 0.189751i) q^{88} +(-0.969707 - 0.206118i) q^{89} +(-0.0540257 - 0.0380499i) q^{90} +(0.839457 - 0.131438i) q^{91} +(-6.75128 + 1.06930i) q^{92} +(0.820470 - 0.219844i) q^{93} +(-0.0113010 + 0.107521i) q^{94} +(1.00134 + 14.9056i) q^{95} +(-0.231790 + 0.0243621i) q^{96} +(-12.2690 - 1.94322i) q^{97} +(-0.120036 - 0.00671581i) q^{98} +8.72671i 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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