LMFDB - Embedded newform 175.2.x.a.122.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [175,2,Mod(3,175)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			122.9
Character	$\chi$	$=$	175.122
Dual form			175.2.x.a.33.9

$q$-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} +(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} - 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}+ \cdots + 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

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{20}\right)$

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	0.549722	−	0.835348i	$-0.314734\pi$
$2$	0.0144040	+	0.00935405i	0.0101851	+	0.00661431i	−0.539536	+	0.841962i	$0.681400\pi$
$3$	1.05595	+	0.405343i	0.609656	+	0.234025i	0.643554	−	0.765400i	$-0.277459\pi$
$3$	1.05595	+	0.405343i	0.609656	+	0.234025i	−0.0338987	+	0.999425i	$0.510792\pi$
$4$	−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	0.990580	+	0.136938i	$0.0437262\pi$
$11$	3.39365	+	3.76903i	1.02322	+	1.13641i	0.0326443	+	0.999467i	$0.489607\pi$
$12$	−0.118375	−	2.25873i	−0.0341719	−	0.652039i
$13$	−0.145799	+	0.286147i	−0.0404375	+	0.0793630i	−0.910341	−	0.413859i	$-0.864181\pi$
$13$	−0.145799	+	0.286147i	−0.0404375	+	0.0793630i	0.869904	+	0.493222i	$0.164181\pi$
$14$	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	0.913177	−	0.407562i	$-0.133621\pi$
$17$	2.90424	+	2.35181i	0.704381	+	0.570397i	−0.208796	+	0.977959i	$0.566954\pi$
$18$	−0.00764859	−	0.0285449i	−0.00180279	−	0.00672810i
$19$	6.10342	+	2.71742i	1.40022	+	0.623419i	0.961400	−	0.275155i	$-0.0887293\pi$
$19$	6.10342	+	2.71742i	1.40022	+	0.623419i	0.438822	+	0.898574i	$0.355396\pi$
$20$	−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	−0.589511	−	0.807761i	$-0.700679\pi$
$23$	1.86170	−	2.86676i	0.388191	−	0.597762i	0.977702	+	0.209999i	$0.0673461\pi$
$24$	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	−0.582440	−	0.812874i	$-0.697902\pi$
$29$	1.99592	−	2.74715i	0.370633	−	0.510133i	0.953073	+	0.302741i	$0.0979018\pi$
$30$	0.0241916	−	0.0360780i	0.00441676	−	0.00658691i
$31$	0.746861	−	0.0784982i	0.134140	−	0.0140987i	−0.0372204	−	0.999307i	$-0.511850\pi$
$31$	0.746861	−	0.0784982i	0.134140	−	0.0140987i	0.171361	+	0.985208i	$0.445184\pi$
$32$	−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	−0.320928	−	0.947104i	$-0.603995\pi$
$37$	−3.29137	+	0.172493i	−0.541098	+	0.0283577i	−0.220170	+	0.975461i	$0.570661\pi$
$38$	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	0.380232	−	0.924891i	$-0.375844\pi$
$41$	7.88534	−	2.56210i	1.23148	−	0.400133i	0.851252	+	0.524758i	$0.175844\pi$
$42$	0.0301367	−	0.0416339i	0.00465019	−	0.00642425i
$43$	−3.99562	+	3.99562i	−0.609326	+	0.609326i	−0.942770	−	0.333444i	$-0.891789\pi$
$43$	−3.99562	+	3.99562i	−0.609326	+	0.609326i	0.333444	+	0.942770i	$0.391789\pi$
$44$	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	0.401480	−	0.915868i	$-0.368496\pi$
$47$	−3.96152	−	4.89207i	−0.577847	−	0.713581i	−0.979326	+	0.202287i	$0.935163\pi$
$48$	−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	0.311164	+	0.950356i	$0.399281\pi$
$53$	−4.04766	+	10.5445i	−0.555988	+	1.44840i	−0.867152	+	0.498043i	$0.834052\pi$
$54$	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	0.771595	−	0.636114i	$-0.219459\pi$
$59$	9.35373	+	1.98820i	1.21775	+	0.258841i	0.446157	+	0.894955i	$0.352792\pi$
$60$	−4.65012	+	1.98889i	−0.600328	+	0.256765i
$61$	0.570023	+	2.68175i	0.0729840	+	0.343363i	0.999455	−	0.0330028i	$-0.0105070\pi$
$61$	0.570023	+	2.68175i	0.0729840	+	0.343363i	−0.926471	+	0.376365i	$0.877174\pi$
$62$	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	−0.963653	−	0.267155i	$-0.913916\pi$
$67$	−4.10889	+	5.07406i	−0.501981	+	0.619895i	0.461672	+	0.887051i	$0.347250\pi$
$68$	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	0.348422	−	0.937338i	$-0.386718\pi$
$71$	−3.66851	−	2.66533i	−0.435372	−	0.316316i	−0.783793	+	0.621022i	$0.786718\pi$
$72$	−0.0918577	+	0.0743849i	−0.0108255	+	0.00876635i
$73$	0.528792	−	10.0900i	0.0618904	−	1.18094i	−0.774416	−	0.632677i	$-0.781956\pi$
$73$	0.528792	−	10.0900i	0.0618904	−	1.18094i	0.836306	−	0.548263i	$-0.184711\pi$
$74$	−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	−0.366321	−	0.930488i	$-0.619383\pi$
$79$	−8.16023	−	0.857674i	−0.918097	−	0.0964959i	−0.551776	+	0.833992i	$0.686050\pi$
$80$	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	0.0856324	−	0.996327i	$-0.472709\pi$
$83$	−1.28282	−	0.203179i	−0.140808	−	0.0223018i	−0.226441	+	0.974025i	$0.572709\pi$
$84$	−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	−0.259019	−	0.965872i	$-0.583399\pi$
$89$	−0.969707	+	0.206118i	−0.102789	+	0.0218484i	0.156230	+	0.987721i	$0.450066\pi$
$90$	−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	−0.744270	−	0.667879i	$-0.767202\pi$
$97$	−12.2690	+	1.94322i	−1.24573	+	0.197304i	−0.501457	+	0.865183i	$0.667202\pi$
$98$	−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	0.912472	−	0.409139i	$-0.134171\pi$
$101$	10.1944	+	5.88575i	1.01438	+	0.585654i	0.101911	+	0.994794i	$0.467504\pi$
$102$	−0.00379939	+	0.0724967i	−0.000376196	+	0.00717825i
$103$	11.4576	−	9.27815i	1.12895	−	0.914203i	0.131920	−	0.991260i	$-0.457886\pi$
$103$	11.4576	−	9.27815i	1.12895	−	0.914203i	0.997027	+	0.0770569i	$0.0245523\pi$
$104$	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	−0.705786	−	0.708425i	$-0.749406\pi$
$107$	2.68589	−	10.0239i	0.259655	−	0.969046i	0.965441	−	0.260621i	$-0.0839272\pi$
$108$	−6.71945	+	8.29783i	−0.646579	+	0.798459i
$109$	−1.89206	+	8.90145i	−0.181227	+	0.852604i	0.789750	+	0.613429i	$0.210210\pi$
$109$	−1.89206	+	8.90145i	−0.181227	+	0.852604i	−0.970976	+	0.239175i	$0.923123\pi$
$110$	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	0.773424	−	0.633889i	$-0.218542\pi$
$113$	7.60273	+	3.87378i	0.715204	+	0.364415i	−0.0582196	+	0.998304i	$0.518542\pi$
$114$	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	−0.954881	−	0.296989i	$-0.904017\pi$
$127$	−14.3784	+	7.32616i	−1.27588	+	0.650091i	−0.320996	+	0.947081i	$0.604017\pi$
$128$	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	−0.958722	−	0.284345i	$-0.908224\pi$
$131$	−1.21211	+	2.72244i	−0.105902	+	0.237860i	0.852820	+	0.522205i	$0.174891\pi$
$132$	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	0.989455	+	0.144839i	$0.0462664\pi$
$137$	8.41948	+	12.9649i	0.719324	+	1.10766i	−0.270131	+	0.962824i	$0.587067\pi$
$138$	0.0663116	−	0.00347524i	0.00564482	−	0.000295832i
$139$	−5.70394	+	17.5549i	−0.483801	+	1.48899i	0.349908	+	0.936784i	$0.386213\pi$
$139$	−5.70394	+	17.5549i	−0.483801	+	1.48899i	−0.833709	+	0.552204i	$0.813787\pi$
$140$	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	−0.921644	−	0.388036i	$-0.873154\pi$
$149$	−12.7732	+	7.37458i	−1.04642	+	0.604149i	−0.124773	+	0.992185i	$0.539820\pi$
$150$	−0.0943722	−	0.0229820i	−0.00770546	−	0.00187647i
$151$	−2.80622	+	4.86051i	−0.228367	+	0.395543i	−0.957324	−	0.289016i	$-0.906672\pi$
$151$	−2.80622	+	4.86051i	−0.228367	+	0.395543i	0.728957	+	0.684559i	$0.240005\pi$
$152$	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	0.998705	−	0.0508712i	$-0.0161998\pi$
$157$	1.35782	+	5.06744i	0.108366	+	0.404426i	−0.890340	+	0.455297i	$0.849533\pi$
$158$	−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	−0.753864	−	0.657031i	$-0.771812\pi$
$163$	−0.929553	−	17.7369i	−0.0728082	−	1.38926i	0.681055	−	0.732232i	$-0.261521\pi$
$164$	−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	0.928113	+	0.372297i	$0.121430\pi$
$167$	−0.899703	+	5.68050i	−0.0696211	+	0.439571i	−0.997735	+	0.0672731i	$0.978570\pi$
$168$	−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	0.614654	−	0.788797i	$-0.289295\pi$
$173$	1.89475	+	1.23047i	0.144055	+	0.0935507i	−0.470599	+	0.882347i	$0.655962\pi$
$174$	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	−0.807661	−	0.589648i	$-0.799267\pi$
$179$	−9.43793	−	21.1979i	−0.705424	−	1.58441i	0.102237	−	0.994760i	$-0.467400\pi$
$180$	7.68843	−	0.289545i	0.573061	−	0.0215814i
$181$	1.07470	+	1.47920i	0.0798820	+	0.109948i	0.847088	−	0.531453i	$-0.178354\pi$
$181$	1.07470	+	1.47920i	0.0798820	+	0.109948i	−0.767206	+	0.641401i	$0.778354\pi$
$182$	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	−0.760713	−	0.649089i	$-0.775150\pi$
$191$	−0.492886	+	0.547405i	−0.0356640	+	0.0396088i	0.725049	+	0.688697i	$0.241817\pi$
$192$	7.02590	+	5.68946i	0.507050	+	0.410601i
$193$	−3.73619	−	13.9437i	−0.268937	−	1.00369i	−0.959796	−	0.280697i	$-0.909434\pi$
$193$	−3.73619	−	13.9437i	−0.268937	−	1.00369i	0.690860	−	0.722989i	$-0.257232\pi$
$194$	−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	0.978195	+	0.207688i	$0.0665940\pi$
$197$	1.57277	+	9.93010i	0.112055	+	0.707490i	−0.866140	+	0.499802i	$0.833406\pi$
$198$	0.0816300	−	0.125699i	0.00580119	−	0.00893306i
$199$	3.19046	−	5.52604i	0.226166	−	0.391731i	−0.730503	−	0.682910i	$-0.760714\pi$
$199$	3.19046	−	5.52604i	0.226166	−	0.391731i	0.956669	+	0.291179i	$0.0940475\pi$
$200$	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	0.0815311	−	0.996671i	$-0.474019\pi$
$211$	8.73583	−	26.8861i	0.601399	−	1.85092i	0.519868	−	0.854246i	$-0.325981\pi$
$212$	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	−0.951816	−	0.306670i	$-0.900785\pi$
$223$	−18.8633	+	9.61132i	−1.26318	+	0.643622i	−0.311362	+	0.950291i	$0.600785\pi$
$224$	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	−0.621646	−	0.783299i	$-0.713536\pi$
$227$	−19.9144	−	1.04367i	−1.32176	−	0.0692707i	−0.700117	+	0.714028i	$0.746869\pi$
$228$	5.41542	−	14.1076i	0.358645	−	0.934302i
$229$	1.04973	−	9.98747i	0.0693678	−	0.659991i	−0.903493	−	0.428602i	$-0.859006\pi$
$229$	1.04973	−	9.98747i	0.0693678	−	0.659991i	0.972861	−	0.231389i	$-0.0743270\pi$
$230$	−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	−0.271510	−	0.962436i	$-0.587523\pi$
$233$	2.60583	−	1.00029i	0.170714	−	0.0655309i	0.442224	+	0.896905i	$0.354190\pi$
$234$	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	0.178075	−	0.984017i	$-0.443013\pi$
$239$	−3.96154	−	1.28718i	−0.256251	−	0.0832609i	−0.434325	+	0.900756i	$0.643013\pi$
$240$	7.41444	+	6.87626i	0.478600	+	0.443861i
$241$	−1.47575	+	6.94288i	−0.0950617	+	0.447230i	0.904713	+	0.426021i	$0.140085\pi$
$241$	−1.47575	+	6.94288i	−0.0950617	+	0.447230i	−0.999775	+	0.0212092i	$0.993248\pi$
$242$	−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	$-0.963041\pi$
$251$		−	3.67076i		−	0.231697i	0.993267	−	0.115848i	$-0.0369586\pi$
$252$	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	0.420698	−	0.907201i	$-0.361785\pi$
$257$	5.31329	+	1.42369i	0.331434	+	0.0888074i	−0.0892647	+	0.996008i	$0.528452\pi$
$258$	−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	0.119904	−	0.992786i	$-0.461741\pi$
$263$	17.4437	−	11.3281i	1.07563	−	0.698521i	0.955724	+	0.294265i	$0.0950748\pi$
$264$	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	0.995010	−	0.0997777i	$-0.0318132\pi$
$269$	0.0163748	+	0.155796i	0.000998391	+	0.00949906i	−0.994011	+	0.109277i	$0.965147\pi$
$270$	−0.198828	+	0.0501515i	−0.0121003	+	0.00305212i
$271$	1.38670	+	0.145748i	0.0842359	+	0.00885355i	0.146553	−	0.989203i	$-0.453182\pi$
$271$	1.38670	+	0.145748i	0.0842359	+	0.00885355i	−0.0623167	+	0.998056i	$0.519849\pi$
$272$	−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	−0.383367	−	0.923596i	$-0.625236\pi$
$277$	1.57183	−	29.9922i	0.0944419	−	1.80206i	0.477809	−	0.878464i	$-0.341431\pi$
$278$	−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	−0.381567	+	0.924341i	$0.624616\pi$
$281$	−23.1092	+	16.7898i	−1.37858	+	1.00160i	−0.997011	+	0.0772549i	$0.975384\pi$
$282$	0.0316498	−	0.118119i	0.00188472	−	0.00703385i
$283$	17.7097	−	21.8697i	1.05273	−	1.30002i	0.100404	−	0.994947i	$-0.467986\pi$
$283$	17.7097	−	21.8697i	1.05273	−	1.30002i	0.952329	−	0.305071i	$-0.0986803\pi$
$284$	−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	0.560986	−	0.827826i	$-0.310422\pi$
$293$	−4.56757	−	4.56757i	−0.266840	−	0.266840i	−0.827826	+	0.560986i	$0.810422\pi$
$294$	−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	−0.254080	−	0.967183i	$-0.581773\pi$
$307$	12.4946	−	12.4946i	0.713104	−	0.713104i	0.967183	+	0.254080i	$0.0817725\pi$
$308$	−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	−0.811470	−	0.584394i	$-0.801332\pi$
$311$	−5.55685	+	5.00341i	−0.315100	+	0.283717i	0.496371	+	0.868111i	$0.334666\pi$
$312$	0.0135903	+	0.0209273i	0.000769401	+	0.00118477i
$313$	−27.7944	+	1.45664i	−1.57103	+	0.0823343i	−0.817832	−	0.575458i	$-0.804824\pi$
$313$	−27.7944	+	1.45664i	−1.57103	+	0.0823343i	−0.753200	+	0.657792i	$0.771491\pi$
$314$	−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	0.844627	+	0.535356i	$0.179823\pi$
$317$	10.2406	+	26.6777i	0.575170	+	1.49837i	−0.269457	+	0.963012i	$0.586844\pi$
$318$	−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	0.780639	−	0.624983i	$-0.214894\pi$
$331$	15.2558	+	6.79232i	0.838535	+	0.373340i	0.0578965	+	0.998323i	$0.481561\pi$
$332$	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	0.380865	+	0.924631i	$0.375626\pi$
$337$	−10.8501	+	21.2946i	−0.591044	+	1.15999i	−0.971909	+	0.235358i	$0.924374\pi$
$338$	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	0.264596	−	0.964359i	$-0.414761\pi$
$347$	−3.42854	−	1.31609i	−0.184053	−	0.0706515i	−0.448649	+	0.893708i	$0.648095\pi$
$348$	−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	−0.366976	−	0.930230i	$-0.619607\pi$
$353$	−23.7134	−	9.10273i	−1.26214	−	0.484490i	−0.895162	+	0.445741i	$0.852940\pi$
$354$	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	0.418605	−	0.908168i	$-0.362519\pi$
$359$	−8.35258	−	7.52069i	−0.440832	−	0.396927i	−0.859437	+	0.511241i	$0.829186\pi$
$360$	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	0.471766	−	0.881724i	$-0.343617\pi$
$367$	−5.60548	−	4.53923i	−0.292604	−	0.236946i	−0.764370	+	0.644778i	$0.776950\pi$
$368$	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	−0.779404	−	0.626521i	$-0.784478\pi$
$373$	2.12375	−	3.27030i	0.109964	−	0.169329i	0.889368	+	0.457192i	$0.151145\pi$
$374$	−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	−0.872878	−	0.487939i	$-0.837749\pi$
$379$	−2.70772	+	3.72686i	−0.139086	+	0.191436i	0.733792	+	0.679375i	$0.237749\pi$
$380$	−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	0.901854	+	0.432042i	$0.142207\pi$
$383$	10.1910	+	26.5486i	0.520738	+	1.35657i	−0.381116	+	0.924527i	$0.624460\pi$
$384$	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	0.104205	−	0.994556i	$-0.466770\pi$
$389$	21.7783	−	19.6093i	1.10420	−	0.994230i	1.00000		0.000325536i	$0.000103621\pi$
$390$	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	0.759247	−	0.650803i	$-0.225568\pi$
$397$	−0.701171	−	0.865873i	−0.0351907	−	0.0434569i	−0.794438	+	0.607346i	$0.792234\pi$
$398$	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	0.738523	−	0.674229i	$-0.235524\pi$
$401$	−4.29812	−	7.44456i	−0.214638	−	0.371764i	−0.953160	+	0.302465i	$0.902190\pi$
$402$	−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	−0.183869	−	0.982951i	$-0.558862\pi$
$409$	−15.2011	−	3.23109i	−0.751645	−	0.159767i	−0.567775	+	0.823184i	$0.692196\pi$
$410$	−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	−0.705948	−	0.708264i	$-0.749479\pi$
$419$	−5.12758	+	3.72540i	−0.250499	+	0.181998i	0.455449	+	0.890262i	$0.349479\pi$
$420$	8.82419	+	10.0593i	0.430576	+	0.490842i
$421$	−17.9408	−	13.0347i	−0.874380	−	0.635274i	0.0573790	−	0.998352i	$-0.481726\pi$
$421$	−17.9408	−	13.0347i	−0.874380	−	0.635274i	−0.931759	+	0.363079i	$0.881726\pi$
$422$	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	0.991317	+	0.131491i	$0.0419764\pi$
$431$	1.01729	+	9.67888i	0.0490012	+	0.466215i	−0.942316	+	0.334724i	$0.891357\pi$
$432$	20.6209	+	5.52535i	0.992123	+	0.265839i
$433$	12.2911	+	1.94672i	0.590674	+	0.0935535i	0.444614	−	0.895722i	$-0.353341\pi$
$433$	12.2911	+	1.94672i	0.590674	+	0.0935535i	0.146060	+	0.989276i	$0.453341\pi$
$434$	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	0.404105	−	0.914713i	$-0.367583\pi$
$439$	23.9971	−	5.10075i	1.14532	−	0.243445i	0.741215	+	0.671267i	$0.234250\pi$
$440$	−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	0.0944121	−	0.995533i	$-0.469903\pi$
$443$	−6.76871	−	1.81367i	−0.321591	−	0.0861701i	−0.416003	+	0.909363i	$0.636570\pi$
$444$	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	$0.0865186\pi$
$449$			11.3776i			0.536943i	−0.963288	+	0.268472i	$0.913481\pi$
$450$	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	−0.994931	−	0.100558i	$-0.967937\pi$
$457$	−1.77469	+	6.62325i	−0.0830167	+	0.309822i	0.911915	+	0.410380i	$0.134604\pi$
$458$	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	0.161097	−	0.986939i	$-0.448497\pi$
$461$	−6.19822	−	2.01392i	−0.288680	−	0.0937978i	−0.449777	+	0.893141i	$0.648497\pi$
$462$	0.259193	−	0.0277049i	0.0120587	−	0.00128895i
$463$	3.99566	+	2.03589i	0.185694	+	0.0946158i	0.544366	−	0.838848i	$-0.316770\pi$
$463$	3.99566	+	2.03589i	0.185694	+	0.0946158i	−0.358672	+	0.933464i	$0.616770\pi$
$464$	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	0.735587	−	0.677430i	$-0.236906\pi$
$467$	37.5050	−	14.3968i	1.73552	−	0.666205i	0.999937	+	0.0112245i	$0.00357295\pi$
$468$	−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	0.0745845	−	0.997215i	$-0.476237\pi$
$479$	18.9438	−	8.43434i	0.865566	−	0.385375i	0.790982	+	0.611840i	$0.209570\pi$
$480$	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	0.918418	−	0.395611i	$-0.129467\pi$
$487$	4.04851	+	6.23415i	0.183455	+	0.282496i	−0.734963	+	0.678107i	$0.762800\pi$
$488$	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	−0.986949	−	0.161033i	$-0.948518\pi$
$491$	−6.27403	−	19.3095i	−0.283143	−	0.871425i	0.703806	−	0.710392i	$-0.251482\pi$
$492$	−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	−0.667709	−	0.744422i	$-0.732725\pi$
$499$	−7.97198	+	4.60262i	−0.356875	+	0.206042i	0.310834	+	0.950464i	$0.399392\pi$
$500$	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	0.946598	+	0.322415i	$0.104495\pi$
$503$	3.27358	+	20.6686i	0.145962	+	0.921565i	−0.800637	+	0.599150i	$0.795505\pi$
$504$	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	−0.628699	−	0.777648i	$-0.716412\pi$
$509$	4.74698	−	5.27205i	0.210406	−	0.233680i	0.839105	+	0.543969i	$0.183079\pi$
$510$	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	0.724706	−	0.689058i	$-0.241975\pi$
$521$	−6.21506	−	13.9592i	−0.272287	−	0.611566i	−0.996993	+	0.0774921i	$0.975309\pi$
$522$	−0.0936831	−	0.0359616i	−0.00410040	−	0.00157400i
$523$	−3.88934	−	2.52576i	−0.170069	−	0.110444i	0.456798	−	0.889571i	$-0.348996\pi$
$523$	−3.88934	−	2.52576i	−0.170069	−	0.110444i	−0.626867	+	0.779127i	$0.715663\pi$
$524$	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	−0.258074	−	0.966125i	$-0.583088\pi$
$541$	16.9732	−	18.8507i	0.729735	−	0.810453i	0.987809	+	0.155672i	$0.0497544\pi$
$542$	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	−0.999319	−	0.0368938i	$-0.988254\pi$
$547$	−1.41055	−	8.90589i	−0.0603110	−	0.380788i	0.939008	−	0.343895i	$-0.111746\pi$
$548$	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	−0.588306	−	0.808638i	$-0.700205\pi$
$557$	−16.3666	+	4.38542i	−0.693475	+	0.185816i	−0.105169	+	0.994454i	$0.533538\pi$
$558$	−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	0.838637	+	0.544691i	$0.183353\pi$
$563$	23.6121	+	36.3595i	0.995133	+	1.53237i	0.156496	+	0.987679i	$0.449980\pi$
$564$	−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	−0.809629	−	0.586942i	$-0.800332\pi$
$569$	4.01461	−	9.01696i	0.168301	−	0.378011i	0.977930	+	0.208931i	$0.0669984\pi$
$570$	0.245691	−	0.154461i	0.0102908	−	0.00646964i
$571$	−1.33258	+	0.593302i	−0.0557666	+	0.0248289i	−0.434430	−	0.900705i	$-0.643050\pi$
$571$	−1.33258	+	0.593302i	−0.0557666	+	0.0248289i	0.378664	+	0.925534i	$0.376384\pi$
$572$	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	−0.0650391	−	0.997883i	$-0.520717\pi$
$577$	−5.62157	−	0.294614i	−0.234029	−	0.0122649i	−0.168990	+	0.985618i	$0.554051\pi$
$578$	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	0.792007	−	0.610512i	$-0.209036\pi$
$587$	18.5011	+	9.42678i	0.763622	+	0.389085i	−0.0283850	+	0.999597i	$0.509036\pi$
$588$	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	−0.842862	−	0.538130i	$-0.819131\pi$
$593$	3.80233	−	14.1905i	0.156143	−	0.582733i	0.999005	−	0.0446033i	$-0.0142024\pi$
$594$	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	0.310479	−	0.950580i	$-0.399511\pi$
$599$	−8.74982	−	5.05171i	−0.357508	−	0.206407i	−0.667987	+	0.744173i	$0.732844\pi$
$600$	0.0695531	+	0.382215i	0.00283949	+	0.0156039i
$601$		−	22.6515i		−	0.923974i	−0.886887	−	0.461987i	$-0.847137\pi$
$601$		−	22.6515i		−	0.923974i	0.886887	−	0.461987i	$-0.152863\pi$
$602$	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	−0.154418	−	0.988006i	$-0.549350\pi$
$607$	−19.2701	−	5.16341i	−0.782150	−	0.209576i	−0.627732	+	0.778429i	$0.716017\pi$
$608$	−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	−0.994171	−	0.107815i	$-0.965614\pi$
$613$	−32.1875	+	20.9028i	−1.30004	+	0.844257i	−0.305871	+	0.952073i	$0.598948\pi$
$614$	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	0.144565	−	0.989495i	$-0.453822\pi$
$617$	−0.589114	−	0.0933065i	−0.0237168	−	0.00375638i	−0.168282	+	0.985739i	$0.553822\pi$
$618$	0.276642	+	0.0741259i	0.0111282	+	0.00298178i
$619$	0.290449	+	2.76344i	0.0116741	+	0.111072i	0.998807	−	0.0488294i	$-0.0155491\pi$
$619$	0.290449	+	2.76344i	0.0116741	+	0.111072i	−0.987133	+	0.159901i	$0.948882\pi$
$620$	−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	−0.0474420	−	0.998874i	$-0.515107\pi$
$631$	22.3034	−	16.2043i	0.887883	−	0.645085i	0.935325	+	0.353789i	$0.115107\pi$
$632$	−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	0.178511	−	0.983938i	$-0.442872\pi$
$641$	−1.48400	−	0.315435i	−0.0586146	−	0.0124589i	−0.237126	+	0.971479i	$0.576205\pi$
$642$	0.188204	−	0.0722447i	0.00742781	−	0.00285127i
$643$	−18.1864	−	18.1864i	−0.717201	−	0.717201i	0.250830	−	0.968031i	$-0.419297\pi$
$643$	−18.1864	−	18.1864i	−0.717201	−	0.717201i	−0.968031	+	0.250830i	$0.919297\pi$
$644$	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	−0.976420	−	0.215880i	$-0.930738\pi$
$647$	−2.70505	+	7.04689i	−0.106346	+	0.277042i	0.870073	+	0.492922i	$0.164071\pi$
$648$	−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	0.998188	+	0.0601643i	$0.0191625\pi$
$653$	21.7081	+	26.8073i	0.849503	+	1.04905i	−0.148686	+	0.988885i	$0.547504\pi$
$654$	−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	−0.619959	−	0.784634i	$-0.712851\pi$
$659$	−16.9511	+	5.50773i	−0.660319	+	0.214551i	−0.0403605	+	0.999185i	$0.512851\pi$
$660$	−23.2771	−	10.7769i	−0.906059	−	0.419489i
$661$	−29.1652	+	26.2604i	−1.13439	+	1.02141i	−0.134860	+	0.990865i	$0.543059\pi$
$661$	−29.1652	+	26.2604i	−1.13439	+	1.02141i	−0.999533	+	0.0305478i	$0.990275\pi$
$662$	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	0.991136	−	0.132850i	$-0.0424129\pi$
$673$	7.81076	+	15.3295i	0.301083	+	0.590908i	−0.690053	+	0.723759i	$0.742413\pi$
$674$	−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	−0.845274	−	0.534333i	$-0.820563\pi$
$677$	−0.346917	+	0.534205i	−0.0133331	+	0.0205312i	0.831941	+	0.554864i	$0.187230\pi$
$678$	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	0.860284	−	0.509816i	$-0.170286\pi$
$683$	14.1248	+	11.4381i	0.540471	+	0.437665i	−0.319812	+	0.947481i	$0.603620\pi$
$684$	−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	0.238740	−	0.971083i	$-0.423265\pi$
$691$	−18.4552	−	16.6171i	−0.702068	−	0.632145i	−0.940809	+	0.338938i	$0.889932\pi$
$692$	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	−0.984967	−	0.172743i	$-0.944737\pi$
$709$	−33.5426	−	30.2019i	−1.25972	−	1.13426i	−0.274754	−	0.961515i	$-0.588596\pi$
$710$	−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	−0.198558	−	0.980089i	$-0.563626\pi$
$719$	−28.4168	−	12.6520i	−1.05977	−	0.471839i	−0.861209	+	0.508250i	$0.830292\pi$
$720$	−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	0.998525	−	0.0542869i	$-0.0172886\pi$
$727$	9.91394	+	19.4572i	0.367688	+	0.721628i	−0.630838	+	0.775915i	$0.717289\pi$
$728$	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	0.932081	−	0.362250i	$-0.117991\pi$
$733$	−0.0807548	−	0.210373i	−0.00298275	−	0.00777032i	−0.935064	+	0.354480i	$0.884658\pi$
$734$	−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	−0.999999	−	0.00171350i	$-0.999455\pi$
$739$	−29.9797	+	26.9939i	−1.10282	+	0.992986i	−0.102824	+	0.994700i	$0.532788\pi$
$740$	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	−0.742477	−	0.669871i	$-0.766349\pi$
$743$	−1.97911	+	1.97911i	−0.0726064	+	0.0726064i	0.669871	+	0.742477i	$0.266349\pi$
$744$	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	0.998504	+	0.0546754i	$0.0174124\pi$
$751$	14.9793	+	25.9449i	0.546602	+	0.946743i	−0.451902	+	0.892068i	$0.649254\pi$
$752$	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	0.997884	+	0.0650131i	$0.0207089\pi$
$757$	29.2442	+	29.2442i	1.06290	+	1.06290i	0.0650131	+	0.997884i	$0.479291\pi$
$758$	−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	−0.674396	−	0.738370i	$-0.735596\pi$
$761$	−9.89316	−	46.5437i	−0.358627	−	1.68721i	0.315769	−	0.948836i	$-0.397738\pi$
$762$	−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	+	7.00513i	−0.453980	+	0.253271i
$766$	−0.101545	+	0.477733i	−0.00366898	+	0.0172612i
$767$	−1.93269	+	2.38667i	−0.0697852	+	0.0861776i
$768$	4.67702	−	17.4549i	0.168767	−	0.629848i
$769$	−30.0966	+	21.8665i	−1.08531	+	0.788525i	−0.978601	−	0.205765i	$-0.934032\pi$
$769$	−30.0966	+	21.8665i	−1.08531	+	0.788525i	−0.106710	+	0.994290i	$0.534032\pi$
$770$	−0.378463	−	0.349751i	−0.0136388	−	0.0126041i
$771$	5.03351	+	3.65706i	0.181277	+	0.131706i
$772$	−22.4337	+	18.1665i	−0.807407	+	0.653825i
$773$	−0.0181612	+	0.346537i	−0.000653213	+	0.0124641i	−0.998937	−	0.0461029i	$-0.985320\pi$
$773$	−0.0181612	+	0.346537i	−0.000653213	+	0.0124641i	0.998283	+	0.0585670i	$0.0186531\pi$
$774$	0.144615	+	0.0834938i	0.00519809	+	0.00300112i
$775$	−2.59354	+	2.71526i	−0.0931626	+	0.0975350i
$776$			0.853311i			0.0306321i
$777$	0.0174102	+	9.86311i	0.000624586	+	0.353837i
$778$	0.497121	−	0.0787362i	0.0178226	−	0.00282283i
$779$	55.0899	+	5.79018i	1.97380	+	0.207455i
$780$	0.108869	−	1.62060i	0.00389815	−	0.0580267i
$781$	−2.40393	−	22.8719i	−0.0860195	−	0.818421i
$782$	0.211917	+	0.0567829i	0.00757812	+	0.00203055i
$783$	−17.9077	−	2.83631i	−0.639970	−	0.101361i
$784$	2.82722	−	27.8444i	0.100972	−	0.994445i
$785$	9.59091	−	6.75480i	0.342314	−	0.241089i
$786$	−0.0566260	+	0.0120362i	−0.00201978	+	0.000429318i
$787$	−8.11239	+	5.26825i	−0.289175	+	0.187793i	−0.681072	−	0.732217i	$-0.738486\pi$
$787$	−8.11239	+	5.26825i	−0.289175	+	0.187793i	0.391896	+	0.920009i	$0.371819\pi$
$788$	16.8613	−	10.9499i	0.600659	−	0.390073i
$789$	23.0116	−	4.89126i	0.819234	−	0.174133i
$790$	−0.101775	+	0.298223i	−0.00362098	+	0.0106103i
$791$	3.49222	−	22.3038i	0.124169	−	0.793031i
$792$	−0.592092	−	0.0937781i	−0.0210391	−	0.00333226i
$793$	−0.850484	−	0.227886i	−0.0302016	−	0.00809249i
$794$	−0.00200022	−	0.0190308i	−7.09851e−5	−	0.000675378i
$795$	26.5153	+	10.6286i	0.940402	+	0.376958i
$796$	−12.6901	−	1.33378i	−0.449787	−	0.0472746i
$797$	47.4366	−	7.51322i	1.68029	−	0.266132i	0.757895	−	0.652377i	$-0.226228\pi$
$797$	47.4366	−	7.51322i	1.68029	−	0.266132i	0.922396	+	0.386245i	$0.126228\pi$
$798$	0.297073	−	0.172215i	0.0105163	−	0.00609636i
$799$		−	23.5245i		−	0.832235i
$800$	0.586320	−	0.847179i	0.0207296	−	0.0299523i
$801$	1.47727	+	0.852904i	0.0521969	+	0.0301359i
$802$	0.00772680	−	0.147436i	0.000272843	−	0.00520615i
$803$	39.8239	−	32.2487i	1.40535	−	1.13803i
$804$	11.9473	+	8.68023i	0.421349	+	0.306128i
$805$	1.85315	+	20.1374i	0.0653151	+	0.709750i
$806$	−0.00335106	+	0.00243469i	−0.000118036	+	8.57583e-5i
$807$	−0.0458598	+	0.171151i	−0.00161434	+	0.00602480i
$808$	0.508888	−	0.628425i	0.0179026	−	0.0221079i
$809$	6.71500	−	31.5916i	0.236087	−	1.11070i	−0.687163	−	0.726503i	$-0.741144\pi$
$809$	6.71500	−	31.5916i	0.236087	−	1.11070i	0.923250	−	0.384199i	$-0.125522\pi$
$810$	−0.0334544	−	0.00401483i	−0.00117547	−	0.000141067i
$811$	−25.8661	−	8.40440i	−0.908281	−	0.295118i	−0.182630	−	0.983182i	$-0.558461\pi$
$811$	−25.8661	−	8.40440i	−0.908281	−	0.295118i	−0.725651	+	0.688063i	$0.758461\pi$
$812$	1.90944	+	17.8638i	0.0670083	+	0.626895i
$813$	1.40521	+	0.715992i	0.0492830	+	0.0251109i
$814$	−0.0596895	−	0.280817i	−0.00209212	−	0.00984263i
$815$	−36.5156	+	15.6180i	−1.27909	+	0.547074i
$816$	−16.5309	−	3.51374i	−0.578696	−	0.123006i
$817$	−35.2447	+	13.5292i	−1.23306	+	0.473326i
$818$	−0.188732	−	0.188732i	−0.00659886	−	0.00659886i
$819$	−0.922080	−	1.13457i	−0.0322201	−	0.0396452i
$820$	−17.3154	+	32.7816i	−0.604680	+	1.14478i
$821$	−0.0494968	+	0.470930i	−0.00172745	+	0.0164356i	−0.995352	−	0.0963071i	$-0.969297\pi$
$821$	−0.0494968	+	0.470930i	−0.00172745	+	0.0164356i	0.993624	+	0.112743i	$0.0359636\pi$
$822$	−0.107619	+	0.280358i	−0.00375365	+	0.00977860i
$823$	−16.1570	−	0.846752i	−0.563197	−	0.0295159i	−0.231387	−	0.972862i	$-0.574326\pi$
$823$	−16.1570	−	0.846752i	−0.563197	−	0.0295159i	−0.331811	+	0.943346i	$0.607660\pi$
$824$	−0.506382	−	0.877080i	−0.0176407	−	0.0305545i
$825$	−25.1621	−	13.7682i	−0.876033	−	0.479347i
$826$	0.196589	−	0.387517i	0.00684021	−	0.0134835i
$827$	12.0127	−	6.12078i	0.417723	−	0.212841i	−0.232480	−	0.972601i	$-0.574684\pi$
$827$	12.0127	−	6.12078i	0.417723	−	0.212841i	0.650203	+	0.759761i	$0.274684\pi$
$828$	7.40172	+	9.14036i	0.257227	+	0.317649i
$829$	3.14458	−	1.40006i	0.109216	−	0.0486259i	−0.351402	−	0.936225i	$-0.614295\pi$
$829$	3.14458	−	1.40006i	0.109216	−	0.0486259i	0.460617	+	0.887599i	$0.347628\pi$
$830$	−0.0185587	+	0.0462985i	−0.000644180	+	0.00160705i
$831$	13.8169	−	31.0333i	0.479304	−	1.07653i
$832$	−1.81509	+	1.81509i	−0.0629271	+	0.0629271i
$833$	−26.1282	−	1.27684i	−0.905289	−	0.0442400i
$834$	−0.341022	+	0.110805i	−0.0118086	+	0.00383686i
$835$	12.6173	−	2.48839i	0.436639	−	0.0861142i
$836$	50.3546	−	45.3395i	1.74155	−	1.56810i
$837$	−2.18389	−	3.36289i	−0.0754861	−	0.116238i
$838$	−0.108705	+	0.00569699i	−0.00375516	+	0.000196799i
$839$	8.56984	−	26.3753i	0.295864	−	0.910575i	−0.687066	−	0.726595i	$-0.741102\pi$
$839$	8.56984	−	26.3753i	0.295864	−	0.910575i	0.982930	−	0.183980i	$-0.0588982\pi$
$840$	0.0660217	+	0.454904i	0.00227797	+	0.0156957i
$841$	5.39836	+	16.6145i	0.186150	+	0.572912i
$842$	−0.136491	−	0.355571i	−0.00470378	−	0.0122538i
$843$	−31.2079	+	8.36213i	−1.07486	+	0.288007i
$844$	−56.2215	+	5.90911i	−1.93522	+	0.203400i
$845$	16.0607	−	23.9520i	0.552505	−	0.823975i
$846$	−0.109344	+	0.150499i	−0.00375931	+	0.00517425i
$847$	38.0864	−	8.16580i	1.30866	−	0.280580i
$848$	−20.5017	−	40.2368i	−0.704030	−	1.38174i
$849$	27.5654	−	15.9149i	0.946042	−	0.546198i
$850$	−0.273078	−	0.168568i	−0.00936650	−	0.00578183i
$851$	−5.63304	+	9.75671i	−0.193098	+	0.334456i
$852$	−5.58599	+	8.60167i	−0.191373	+	0.294688i
$853$	−4.81360	−	30.3919i	−0.164815	−	1.04060i	−0.921941	−	0.387330i	$-0.873397\pi$
$853$	−4.81360	−	30.3919i	−0.164815	−	1.04060i	0.757126	−	0.653268i	$-0.226603\pi$
$854$	0.124422	+	0.00630047i	0.00425764	+	0.000215598i
$855$	−18.4419	+	17.9069i	−0.630701	+	0.612403i
$856$	−0.651240	−	0.289951i	−0.0222589	−	0.00991032i
$857$	−1.08695	−	4.05654i	−0.0371294	−	0.138569i	0.944873	−	0.327437i	$-0.106185\pi$
$857$	−1.08695	−	4.05654i	−0.0371294	−	0.138569i	−0.982002	+	0.188868i	$0.939518\pi$
$858$	−0.0245896	−	0.0199123i	−0.000839476	−	0.000679794i
$859$	−4.81200	+	5.34427i	−0.164183	+	0.182344i	−0.819623	−	0.572904i	$-0.805817\pi$
$859$	−4.81200	+	5.34427i	−0.164183	+	0.182344i	0.655439	+	0.755248i	$0.272484\pi$
$860$	0.371859	−	25.2640i	0.0126803	−	0.861497i
$861$	−6.46404	−	23.9549i	−0.220294	−	0.816381i
$862$	−0.0758837	+	0.148930i	−0.00258461	+	0.00507258i
$863$	−0.516497	−	9.85535i	−0.0175818	−	0.335480i	−0.993232	−	0.116148i	$-0.962945\pi$
$863$	−0.516497	−	9.85535i	−0.0175818	−	0.335480i	0.975650	−	0.219332i	$-0.0703879\pi$
$864$	0.736196	+	0.817629i	0.0250459	+	0.0278163i
$865$	1.12294	−	4.92542i	0.0381811	−	0.167469i
$866$	0.158831	+	0.143012i	0.00539730	+	0.00485975i
$867$	0.536908	−	3.38990i	0.0182343	−	0.115127i
$868$	−2.65337	+	2.95735i	−0.0900613	+	0.100379i
$869$	−24.4604	−	33.6668i	−0.829761	−	1.14207i
$870$	−0.0508272	−	0.138467i	−0.00172320	−	0.00469446i
$871$	−0.852855	−	1.91554i	−0.0288979	−	0.0649057i
$872$	0.583615	+	0.224029i	0.0197637	+	0.00758658i
$873$	17.9256	+	11.6410i	0.606690	+	0.393989i
$874$	0.392224			0.0132672
$875$	5.86130	−	28.9939i	0.198148	−	0.980172i
$876$	−22.8531			−0.772133
$877$	27.4507	+	17.8267i	0.926944	+	0.601965i	0.917390	−	0.397990i	$-0.130292\pi$
$877$	27.4507	+	17.8267i	0.926944	+	0.601965i	0.00955443	+	0.999954i	$0.496959\pi$
$878$	0.393367	+	0.150999i	0.0132755	+	0.00509598i
$879$	−2.97171	−	6.67457i	−0.100233	−	0.225128i
$880$	15.6247	+	42.5658i	0.526707	+	1.43489i
$881$	11.3837	+	15.6683i	0.383527	+	0.527880i	0.956515	−	0.291684i	$-0.0942157\pi$
$881$	11.3837	+	15.6683i	0.383527	+	0.527880i	−0.572988	+	0.819564i	$0.694216\pi$
$882$	0.161221	+	0.129615i	0.00542861	+	0.00436436i
$883$	5.72089	−	36.1203i	0.192523	−	1.21554i	−0.682289	−	0.731082i	$-0.739016\pi$
$883$	5.72089	−	36.1203i	0.192523	−	1.21554i	0.874813	−	0.484461i	$-0.160984\pi$
$884$	1.78352	+	1.60589i	0.0599863	+	0.0540119i
$885$	5.37612	−	23.5806i	0.180716	−	0.792655i
$886$	−0.0805312	−	0.0894389i	−0.00270550	−	0.00300476i
$887$	−0.598808	−	11.4259i	−0.0201060	−	0.383645i	−0.990086	−	0.140461i	$-0.955141\pi$
$887$	−0.598808	−	11.4259i	−0.0201060	−	0.383645i	0.969980	−	0.243184i	$-0.0781919\pi$
$888$	−0.116260	+	0.228174i	−0.00390144	+	0.00765701i
$889$	30.2433	+	30.1367i	1.01433	+	1.01075i
$890$	−0.000560326		0.0380684i	−1.87822e−5		0.00127606i
$891$	2.97749	−	3.30683i	0.0997496	−	0.110783i
$892$	32.9007	+	26.6424i	1.10160	+	0.892055i
$893$	−10.8850	−	40.6235i	−0.364253	−	1.35941i
$894$	−0.261747	−	0.116537i	−0.00875414	−	0.00389759i
$895$	−37.2248	+	36.1449i	−1.24429	+	1.20819i
$896$	0.789507	−	1.22044i	0.0263756	−	0.0407722i
$897$	0.194238	+	1.22637i	0.00648543	+	0.0409474i
$898$	−0.106427	+	0.163883i	−0.00355151	+	0.00546885i
$899$	1.27503	−	2.20841i	0.0425246	−	0.0736547i
$900$	−6.53191	−	15.9158i	−0.217730	−	0.530527i
$901$	−36.5540	+	21.1045i	−1.21779	+	0.703091i
$902$	0.327875	+	0.643490i	0.0109170	+	0.0214259i
$903$	11.3371	+	12.5465i	0.377275	+	0.417522i
$904$	0.344529	−	0.474204i	0.0114589	−	0.0157718i
$905$	2.27693	−	3.39569i	0.0756878	−	0.112877i
$906$	−0.108430	+	0.0113965i	−0.00360235	+	0.000378622i
$907$	−0.668595	+	0.179150i	−0.0222003	+	0.00594856i	−0.269902	−	0.962888i	$-0.586991\pi$
$907$	−0.668595	+	0.179150i	−0.0222003	+	0.00594856i	0.247702	+	0.968836i	$0.420325\pi$
$908$	14.2908	+	37.2289i	0.474258	+	1.23548i
$909$	−6.25905	−	19.2634i	−0.207600	−	0.638926i
$910$	0.0120876	−	0.0303099i	0.000400700	−	0.00100476i
$911$	7.30607	−	22.4858i	0.242061	−	0.744987i	−0.754045	−	0.656823i	$-0.771900\pi$
$911$	7.30607	−	22.4858i	0.242061	−	0.744987i	0.996106	−	0.0881643i	$-0.0281000\pi$
$912$	−30.1723	+	1.58127i	−0.999106	+	0.0523609i
$913$	−3.58767	−	5.52452i	−0.118734	−	0.182835i
$914$	−0.0875168	+	0.0788005i	−0.00289480	+	0.00260649i
$915$	6.80309	−	1.34171i	0.224903	−	0.0443555i
$916$	−19.0991	+	6.20568i	−0.631053	+	0.205042i
$917$	7.84279	+	0.810316i	0.258992	+	0.0267590i
$918$	0.242327	−	0.242327i	0.00799798	−	0.00799798i
$919$	−3.16025	+	7.09803i	−0.104247	+	0.234142i	−0.958137	−	0.286312i	$-0.907571\pi$
$919$	−3.16025	+	7.09803i	−0.104247	+	0.234142i	0.853890	+	0.520454i	$0.174237\pi$
$920$	−0.195356	+	0.487358i	−0.00644071	+	0.0160677i
$921$	18.2583	−	8.12912i	0.601632	−	0.267864i
$922$	−0.0704407	−	0.0869870i	−0.00231984	−	0.00286476i
$923$	1.29754	−	0.661131i	0.0427091	−	0.0217614i
$924$	−27.0667	−	13.7310i	−0.890429	−	0.451718i
$925$	11.9906	−	11.3047i	0.394249	−	0.371697i
$926$	0.0385095	+	0.0667005i	0.00126550	+	0.00219191i
$927$	−25.3331	−	1.32765i	−0.832048	−	0.0436058i
$928$	−0.250750	+	0.653225i	−0.00823126	+	0.0214432i
$929$	−5.76695	+	54.8689i	−0.189208	+	1.80019i	0.328365	+	0.944551i	$0.393502\pi$
$929$	−5.76695	+	54.8689i	−0.189208	+	1.80019i	−0.517573	+	0.855639i	$0.673164\pi$
$930$	0.0152357	−	0.0288442i	0.000499598	−	0.000945840i
$931$	−45.7106	+	9.88488i	−1.49810	+	0.323964i
$932$	−3.94681	−	3.94681i	−0.129282	−	0.129282i
$933$	−7.89587	+	3.03094i	−0.258499	+	0.0992286i
$934$	0.674889	+	0.143452i	0.0220831	+	0.00469390i
$935$	38.9664	−	16.6662i	1.27434	−	0.545043i
$936$	−0.00789225	−	0.0371301i	−0.000257966	−	0.00121364i
$937$	30.2515	+	15.4139i	0.988274	+	0.503551i	0.871915	−	0.489657i	$-0.162878\pi$
$937$	30.2515	+	15.4139i	0.988274	+	0.503551i	0.116358	+	0.993207i	$0.462878\pi$
$938$	0.174809	+	0.239714i	0.00570773	+	0.00782693i
$939$	−29.9400	−	9.72811i	−0.977057	−	0.317465i
$940$	27.9470	+	3.35389i	0.911532	+	0.109392i
$941$	4.83848	−	22.7633i	0.157730	−	0.742061i	−0.826181	−	0.563404i	$-0.809491\pi$
$941$	4.83848	−	22.7633i	0.157730	−	0.742061i	0.983911	−	0.178657i	$-0.0571753\pi$
$942$	−0.0641359	+	0.0792012i	−0.00208966	+	0.00258051i
$943$	7.33518	−	27.3753i	0.238866	−	0.891462i
$944$	−30.9319	+	22.4733i	−1.00675	+	0.731444i
$945$	28.6888	+	13.2209i	0.933245	+	0.430077i
$946$	−0.398202	−	0.289311i	−0.0129467	−	0.00940630i
$947$	25.0666	−	20.2986i	0.814556	−	0.659615i	−0.128699	−	0.991684i	$-0.541080\pi$
$947$	25.0666	−	20.2986i	0.814556	−	0.659615i	0.943255	+	0.332069i	$0.107747\pi$
$948$	−0.971287	+	18.5333i	−0.0315459	+	0.601932i
$949$	2.81012	+	1.62242i	0.0912202	+	0.0526660i
$950$	−0.549566	−	0.164737i	−0.0178303	−	0.00534477i
$951$			32.3214i			1.04809i
$952$	−0.588803	−	0.338561i	−0.0190832	−	0.0109728i
$953$	−28.1170	+	4.45329i	−0.910797	+	0.144256i	−0.594213	−	0.804308i	$-0.702536\pi$
$953$	−28.1170	+	4.45329i	−0.910797	+	0.144256i	−0.316585	+	0.948564i	$0.602536\pi$
$954$	0.331951	+	0.0348895i	0.0107473	+	0.00112959i
$955$	1.52885	+	0.612835i	0.0494724	+	0.0198309i
$956$	0.870679	+	8.28396i	0.0281598	+	0.267922i
$957$	18.8156	+	5.04162i	0.608222	+	0.162973i
$958$	0.351762	+	0.0557136i	0.0113649	+	0.00180002i
$959$	25.6832	−	31.8308i	0.829353	−	1.02787i
$960$	6.52921	−	19.1320i	0.210729	−	0.617484i
$961$	−29.7709	+	6.32801i	−0.960353	+	0.204129i
$962$	0.0152463	−	0.00990103i	0.000491559	−	0.000319222i
$963$	−14.9754	+	9.72513i	−0.482575	+	0.313388i
$964$	13.8837	−	2.95107i	0.447164	−	0.0950476i
$965$	−26.3905	+	18.5866i	−0.849541	+	0.598325i
$966$	−0.0632492	−	0.163904i	−0.00203501	−	0.00527354i
$967$	21.0805	+	3.33883i	0.677904	+	0.107369i	0.485886	−	0.874022i	$-0.338497\pi$
$967$	21.0805	+	3.33883i	0.677904	+	0.107369i	0.192018	+	0.981391i	$0.438497\pi$
$968$	0.976883	+	0.261755i	0.0313982	+	0.00841312i
$969$	2.95190	+	28.0854i	0.0948286	+	0.902234i
$970$	−0.0319755	+	0.475978i	−0.00102667	+	0.0152827i
$971$	52.9519	+	5.56547i	1.69931	+	0.178604i	0.903980	−	0.427575i	$-0.140632\pi$
$971$	52.9519	+	5.56547i	1.69931	+	0.178604i	0.795328	+	0.606179i	$0.207299\pi$
$972$	29.6775	−	4.70046i	0.951908	−	0.150767i
$973$	48.8361	−	0.0862044i	1.56561	−	0.00276359i
$974$			0.127666i			0.00409070i
$975$	0.242928	−	1.79992i	0.00777992	−	0.0576435i
$976$	−9.49319	−	5.48089i	−0.303870	−	0.175439i
$977$	−1.94719	+	37.1545i	−0.0622960	+	1.18868i	0.771362	+	0.636397i	$0.219576\pi$
$977$	−1.94719	+	37.1545i	−0.0622960	+	1.18868i	−0.833658	+	0.552282i	$0.813757\pi$
$978$	0.268139	−	0.217135i	0.00857416	−	0.00694321i
$979$	−4.06771	−	2.95536i	−0.130005	−	0.0944538i
$980$	5.24200	−	30.8583i	0.167450	−	0.985731i
$981$	12.6680	−	9.20384i	0.404458	−	0.293856i
$982$	0.0902509	−	0.336821i	0.00288002	−	0.0107484i
$983$	12.6142	−	15.5773i	0.402331	−	0.496838i	−0.535206	−	0.844721i	$-0.679766\pi$
$983$	12.6142	−	15.5773i	0.402331	−	0.496838i	0.937538	+	0.347883i	$0.113100\pi$
$984$	0.133939	−	0.630131i	0.00426980	−	0.0200879i
$985$	19.6326	−	10.9528i	0.625546	−	0.348986i
$986$	0.207277	+	0.0673484i	0.00660105	+	0.00214481i
$987$	−15.2206	+	11.0995i	−0.484477	+	0.353302i
$988$	3.82295	+	1.94789i	0.121624	+	0.0619707i
$989$	4.01586	+	18.8931i	0.127697	+	0.600766i
$990$	−0.326755	−	0.0744965i	−0.0103850	−	0.00236766i
$991$	38.8742	+	8.26297i	1.23488	+	0.262482i	0.778695	−	0.627403i	$-0.215882\pi$
$991$	38.8742	+	8.26297i	1.23488	+	0.262482i	0.456185	+	0.889885i	$0.349215\pi$
$992$	−0.144465	+	0.0554550i	−0.00458678	+	0.00176070i
$993$	13.3562	+	13.3562i	0.423847	+	0.423847i
$994$	−0.159901	+	0.129954i	−0.00507176	+	0.00412188i
$995$	−14.0581	−	2.43920i	−0.445673	−	0.0773278i
$996$	−0.307073	+	2.92160i	−0.00972997	+	0.0925745i
$997$	−4.08061	+	10.6304i	−0.129234	+	0.336667i	−0.982896	−	0.184161i	$-0.941043\pi$
$997$	−4.08061	+	10.6304i	−0.129234	+	0.336667i	0.853662	+	0.520828i	$0.174377\pi$
$998$	−0.157881	−	0.00827421i	−0.00499764	−	0.000261915i
$999$	8.79910	+	15.2405i	0.278391	+	0.482188i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.122.9	yes	288
5.2	odd	4		875.2.bb.a.493.10		288
5.3	odd	4		875.2.bb.b.493.9		288
5.4	even	2		875.2.bb.c.507.10		288
7.5	odd	6	inner	175.2.x.a.47.9	yes	288
25.6	even	5		875.2.bb.b.857.10		288
25.8	odd	20	inner	175.2.x.a.108.9	yes	288
25.17	odd	20		875.2.bb.c.143.10		288
25.19	even	10		875.2.bb.a.857.9		288
35.12	even	12		875.2.bb.a.243.9		288
35.19	odd	6		875.2.bb.c.257.10		288
35.33	even	12		875.2.bb.b.243.10		288
175.19	odd	30		875.2.bb.a.607.10		288
175.33	even	60	inner	175.2.x.a.33.9	✓	288
175.117	even	60		875.2.bb.c.768.10		288
175.131	odd	30		875.2.bb.b.607.9		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.9	✓	288	175.33	even	60	inner
175.2.x.a.47.9	yes	288	7.5	odd	6	inner
175.2.x.a.108.9	yes	288	25.8	odd	20	inner
175.2.x.a.122.9	yes	288	1.1	even	1	trivial
875.2.bb.a.243.9		288	35.12	even	12
875.2.bb.a.493.10		288	5.2	odd	4
875.2.bb.a.607.10		288	175.19	odd	30
875.2.bb.a.857.9		288	25.19	even	10
875.2.bb.b.243.10		288	35.33	even	12
875.2.bb.b.493.9		288	5.3	odd	4
875.2.bb.b.607.9		288	175.131	odd	30
875.2.bb.b.857.10		288	25.6	even	5
875.2.bb.c.143.10		288	25.17	odd	20
875.2.bb.c.257.10		288	35.19	odd	6
875.2.bb.c.507.10		288	5.4	even	2
875.2.bb.c.768.10		288	175.117	even	60

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 $\F_{q}$
Belyi maps

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} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) \) 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

Modular forms

Varieties

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