LMFDB - Embedded newform 175.2.x.a.108.9

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			108.9
Character	$\chi$	$=$	175.108
Dual form			175.2.x.a.47.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.000898858 + 0.0171512i) q^{2} +(0.879015 + 0.711812i) q^{3} +(1.98875 - 0.209026i) q^{4} +(1.43263 + 1.71685i) q^{5} +(-0.0114183 + 0.0157160i) q^{6} +(-2.51481 + 0.822022i) q^{7} +(0.0107461 + 0.0678483i) q^{8} +(-0.357745 - 1.68306i) q^{9} +O(q^{10})$	\(q+(0.000898858 + 0.0171512i) q^{2} +(0.879015 + 0.711812i) q^{3} +(1.98875 - 0.209026i) q^{4} +(1.43263 + 1.71685i) q^{5} +(-0.0114183 + 0.0157160i) q^{6} +(-2.51481 + 0.822022i) q^{7} +(0.0107461 + 0.0678483i) q^{8} +(-0.357745 - 1.68306i) q^{9} +(-0.0281584 + 0.0261145i) q^{10} +(-4.96090 - 1.05447i) q^{11} +(1.89693 + 1.23188i) q^{12} +(0.145799 + 0.286147i) q^{13} +(-0.0163592 - 0.0423932i) q^{14} +(0.0372227 + 2.52890i) q^{15} +(3.91086 - 0.831279i) q^{16} +(3.48884 + 1.33924i) q^{17} +(0.0285449 - 0.00764859i) q^{18} +(0.698358 - 6.64443i) q^{19} +(3.20800 + 3.11494i) q^{20} +(-2.79568 - 1.06750i) q^{21} +(0.0136263 - 0.0860334i) q^{22} +(-3.41354 + 0.178896i) q^{23} +(-0.0388492 + 0.0672888i) q^{24} +(-0.895167 + 4.91922i) q^{25} +(-0.00477673 + 0.00275784i) q^{26} +(2.42406 - 4.75748i) q^{27} +(-4.82951 + 2.16046i) q^{28} +(1.99592 + 2.74715i) q^{29} +(-0.0433403 + 0.00291154i) q^{30} +(0.305449 + 0.686049i) q^{31} +(0.0533314 + 0.199035i) q^{32} +(-3.61012 - 4.45813i) q^{33} +(-0.0198337 + 0.0610417i) q^{34} +(-5.01408 - 3.13991i) q^{35} +(-1.06327 - 3.27240i) q^{36} +(1.79507 - 2.76416i) q^{37} +(0.114588 + 0.00600530i) q^{38} +(-0.0755233 + 0.355309i) q^{39} +(-0.101090 + 0.115651i) q^{40} +(-7.88534 - 2.56210i) q^{41} +(0.0157961 - 0.0489089i) q^{42} +(-3.99562 - 3.99562i) q^{43} +(-10.0864 - 1.06012i) q^{44} +(2.37705 - 3.02538i) q^{45} +(-0.00613657 - 0.0583856i) q^{46} +(2.25590 + 5.87681i) 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} +(0.349771 + 0.538600i) q^{52} +(-7.10798 + 8.77763i) q^{53} +(0.0837755 + 0.0372993i) q^{54} +(-5.29674 - 10.0278i) q^{55} +(-0.0827972 - 0.161792i) q^{56} +(5.34345 - 5.34345i) q^{57} +(-0.0453229 + 0.0367018i) q^{58} +(6.39870 + 7.10647i) q^{59} +(0.602633 + 5.02157i) q^{60} +(-2.03745 - 1.83453i) q^{61} +(-0.0114920 + 0.00585548i) q^{62} +(2.28317 + 3.93850i) q^{63} +(7.60172 - 2.46995i) q^{64} +(-0.282397 + 0.660258i) q^{65} +(0.0732173 - 0.0659252i) q^{66} +(-2.33982 + 6.09544i) q^{67} +(7.21837 + 1.93416i) q^{68} +(-3.12789 - 2.27255i) q^{69} +(0.0493464 - 0.0888199i) q^{70} +(-3.66851 + 2.66533i) q^{71} +(0.110348 - 0.0423587i) q^{72} +(-8.47376 + 5.50292i) q^{73} +(0.0490223 + 0.0283030i) q^{74} +(-4.28842 + 3.68687i) q^{75} -13.3601i q^{76} +(13.3425 - 1.42617i) q^{77} +(-0.00616188 - 0.000975946i) q^{78} +(3.33735 - 7.49580i) q^{79} +(7.02998 + 5.52346i) q^{80} +(0.801517 - 0.356859i) q^{81} +(0.0368554 - 0.137546i) q^{82} +(1.28282 - 0.203179i) q^{83} +(-5.78305 - 1.53863i) q^{84} +(2.69893 + 7.90846i) q^{85} +(0.0649383 - 0.0721212i) q^{86} +(-0.201010 + 3.83550i) q^{87} +(0.0182337 - 0.347920i) q^{88} +(-0.663356 + 0.736732i) q^{89} +(0.0540257 + 0.0380499i) q^{90} +(-0.601877 - 0.599756i) q^{91} +(-6.75128 + 1.06930i) q^{92} +(-0.219844 + 0.820470i) q^{93} +(-0.0987668 + 0.0439738i) q^{94} +(12.4080 - 8.32000i) q^{95} +(-0.0947968 + 0.212917i) q^{96} +(12.2690 + 1.94322i) q^{97} +(0.0759884 + 0.0931634i) 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 $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{20}\right)$

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 $

$2$	0.000898858		0.0171512i	0.000635588		0.0121278i	0.998929	−	0.0462711i	$-0.0147338\pi$
$2$	0.000898858		0.0171512i	0.000635588		0.0121278i	−0.998293	+	0.0583989i	$0.981400\pi$
$3$	0.879015	+	0.711812i	0.507499	+	0.410965i	0.848578	−	0.529070i	$-0.177459\pi$
$3$	0.879015	+	0.711812i	0.507499	+	0.410965i	−0.341079	+	0.940035i	$0.610792\pi$
$4$	1.98875	−	0.209026i	0.994375	−	0.104513i
$5$	1.43263	+	1.71685i	0.640690	+	0.767800i
$5$	1.43263	+	1.71685i	0.640690	+	0.767800i
$6$	−0.0114183	+	0.0157160i	−0.00466152	+	0.00641603i
$7$	−2.51481	+	0.822022i	−0.950510	+	0.310695i
$7$	−2.51481	+	0.822022i	−0.950510	+	0.310695i
$8$	0.0107461	+	0.0678483i	0.00379932	+	0.0239880i
$9$	−0.357745	−	1.68306i	−0.119248	−	0.561019i
$10$	−0.0281584	+	0.0261145i	−0.00890447	+	0.00825813i
$11$	−4.96090	−	1.05447i	−1.49577	−	0.317935i	−0.613882	−	0.789398i	$-0.710393\pi$
$11$	−4.96090	−	1.05447i	−1.49577	−	0.317935i	−0.881886	+	0.471463i	$0.843726\pi$
$12$	1.89693	+	1.23188i	0.547596	+	0.355613i
$13$	0.145799	+	0.286147i	0.0404375	+	0.0793630i	0.910341	−	0.413859i	$-0.135819\pi$
$13$	0.145799	+	0.286147i	0.0404375	+	0.0793630i	−0.869904	+	0.493222i	$0.835819\pi$
$14$	−0.0163592	−	0.0423932i	−0.00437217	−	0.0113301i
$15$	0.0372227	+	2.52890i	0.00961085	+	0.652959i
$16$	3.91086	−	0.831279i	0.977715	−	0.207820i
$17$	3.48884	+	1.33924i	0.846169	+	0.324814i	0.742540	−	0.669802i	$-0.233621\pi$
$17$	3.48884	+	1.33924i	0.846169	+	0.324814i	0.103629	+	0.994616i	$0.466954\pi$
$18$	0.0285449	−	0.00764859i	0.00672810	−	0.00180279i
$19$	0.698358	−	6.64443i	0.160214	−	1.52434i	−0.558777	−	0.829318i	$-0.688729\pi$
$19$	0.698358	−	6.64443i	0.160214	−	1.52434i	0.718991	−	0.695019i	$-0.244604\pi$
$20$	3.20800	+	3.11494i	0.717331	+	0.696521i
$21$	−2.79568	−	1.06750i	−0.610068	−	0.232948i
$22$	0.0136263	−	0.0860334i	0.00290515	−	0.0183424i
$23$	−3.41354	+	0.178896i	−0.711772	+	0.0373024i	−0.404786	−	0.914412i	$-0.632654\pi$
$23$	−3.41354	+	0.178896i	−0.711772	+	0.0373024i	−0.306986	+	0.951714i	$0.599321\pi$
$24$	−0.0388492	+	0.0672888i	−0.00793006	+	0.0137353i
$25$	−0.895167	+	4.91922i	−0.179033	+	0.983843i
$26$	−0.00477673	+	0.00275784i	−0.000936793	+	0.000540858i
$27$	2.42406	−	4.75748i	0.466510	−	0.915577i
$28$	−4.82951	+	2.16046i	−0.912691	+	0.408288i
$29$	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	$0.697902\pi$
$30$	−0.0433403	+	0.00291154i	−0.00791281	+	0.000531571i
$31$	0.305449	+	0.686049i	0.0548602	+	0.123218i	0.938896	−	0.344202i	$-0.111850\pi$
$31$	0.305449	+	0.686049i	0.0548602	+	0.123218i	−0.884036	+	0.467420i	$0.845184\pi$
$32$	0.0533314	+	0.199035i	0.00942775	+	0.0351848i
$33$	−3.61012	−	4.45813i	−0.628441	−	0.776060i
$34$	−0.0198337	+	0.0610417i	−0.00340145	+	0.0104686i
$35$	−5.01408	−	3.13991i	−0.847534	−	0.530742i
$36$	−1.06327	−	3.27240i	−0.177211	−	0.545400i
$37$	1.79507	−	2.76416i	0.295107	−	0.454426i	−0.659752	−	0.751483i	$-0.729339\pi$
$37$	1.79507	−	2.76416i	0.295107	−	0.454426i	0.954860	+	0.297058i	$0.0960054\pi$
$38$	0.114588	+	0.00600530i	0.0185886	+	0.000974188i
$39$	−0.0755233	+	0.355309i	−0.0120934	+	0.0568950i
$40$	−0.101090	+	0.115651i	−0.0159838	+	0.0182860i
$41$	−7.88534	−	2.56210i	−1.23148	−	0.400133i	−0.380232	−	0.924891i	$-0.624156\pi$
$41$	−7.88534	−	2.56210i	−1.23148	−	0.400133i	−0.851252	+	0.524758i	$0.824156\pi$
$42$	0.0157961	−	0.0489089i	0.00243739	−	0.00754681i
$43$	−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	$0.891789\pi$
$44$	−10.0864	−	1.06012i	−1.52058	−	0.159820i
$45$	2.37705	−	3.02538i	0.354349	−	0.450998i
$46$	−0.00613657	−	0.0583856i	−0.000904788	−	0.00860849i
$47$	2.25590	+	5.87681i	0.329056	+	0.857221i	0.993905	+	0.110242i	$0.0351627\pi$
$47$	2.25590	+	5.87681i	0.329056	+	0.857221i	−0.664849	+	0.746978i	$0.731504\pi$
$48$	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
$52$	0.349771	+	0.538600i	0.0485045	+	0.0746903i
$53$	−7.10798	+	8.77763i	−0.976356	+	1.20570i	0.00225825	+	0.999997i	$0.499281\pi$
$53$	−7.10798	+	8.77763i	−0.976356	+	1.20570i	−0.978615	+	0.205702i	$0.934052\pi$
$54$	0.0837755	+	0.0372993i	0.0114004	+	0.00507579i
$55$	−5.29674	−	10.0278i	−0.714212	−	1.35215i
$56$	−0.0827972	−	0.161792i	−0.0110642	−	0.0216204i
$57$	5.34345	−	5.34345i	0.707757	−	0.707757i
$58$	−0.0453229	+	0.0367018i	−0.00595119	+	0.00481918i
$59$	6.39870	+	7.10647i	0.833039	+	0.925184i	0.998132	−	0.0610943i	$-0.0194590\pi$
$59$	6.39870	+	7.10647i	0.833039	+	0.925184i	−0.165093	+	0.986278i	$0.552792\pi$
$60$	0.602633	+	5.02157i	0.0777995	+	0.648282i
$61$	−2.03745	−	1.83453i	−0.260869	−	0.234887i	0.528309	−	0.849052i	$-0.322826\pi$
$61$	−2.03745	−	1.83453i	−0.260869	−	0.234887i	−0.789178	+	0.614165i	$0.789493\pi$
$62$	−0.0114920	+	0.00585548i	−0.00145949	+	0.000743647i
$63$	2.28317	+	3.93850i	0.287652	+	0.496204i
$64$	7.60172	−	2.46995i	0.950215	−	0.308744i
$65$	−0.282397	+	0.660258i	−0.0350270	+	0.0818949i
$66$	0.0732173	−	0.0659252i	0.00901243	−	0.00811483i
$67$	−2.33982	+	6.09544i	−0.285854	+	0.744676i	0.713190	+	0.700971i	$0.247250\pi$
$67$	−2.33982	+	6.09544i	−0.285854	+	0.744676i	−0.999044	+	0.0437055i	$0.986084\pi$
$68$	7.21837	+	1.93416i	0.875357	+	0.234551i
$69$	−3.12789	−	2.27255i	−0.376554	−	0.273582i
$70$	0.0493464	−	0.0888199i	0.00589802	−	0.0106160i
$71$	−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	$0.386718\pi$
$72$	0.110348	−	0.0423587i	0.0130046	−	0.00499202i
$73$	−8.47376	+	5.50292i	−0.991779	+	0.644069i	−0.935122	−	0.354325i	$-0.884711\pi$
$73$	−8.47376	+	5.50292i	−0.991779	+	0.644069i	−0.0566564	+	0.998394i	$0.518044\pi$
$74$	0.0490223	+	0.0283030i	0.00569873	+	0.00329016i
$75$	−4.28842	+	3.68687i	−0.495184	+	0.425723i
$76$		−	13.3601i		−	1.53251i
$77$	13.3425	−	1.42617i	1.52052	−	0.162528i
$78$	−0.00616188		0.000975946i	−0.000697695		0.000110504i
$79$	3.33735	−	7.49580i	0.375481	−	0.843344i	−0.622666	−	0.782488i	$-0.713950\pi$
$79$	3.33735	−	7.49580i	0.375481	−	0.843344i	0.998147	−	0.0608557i	$-0.0193829\pi$
$80$	7.02998	+	5.52346i	0.785976	+	0.617541i
$81$	0.801517	−	0.356859i	0.0890575	−	0.0396510i
$82$	0.0368554	−	0.137546i	0.00407000	−	0.0151894i
$83$	1.28282	−	0.203179i	0.140808	−	0.0223018i	−0.0856324	−	0.996327i	$-0.527291\pi$
$83$	1.28282	−	0.203179i	0.140808	−	0.0223018i	0.226441	+	0.974025i	$0.427291\pi$
$84$	−5.78305	−	1.53863i	−0.630983	−	0.167878i
$85$	2.69893	+	7.90846i	0.292740	+	0.857793i
$86$	0.0649383	−	0.0721212i	0.00700247	−	0.00777703i
$87$	−0.201010	+	3.83550i	−0.0215506	+	0.411209i
$88$	0.0182337	−	0.347920i	0.00194372	−	0.0370884i
$89$	−0.663356	+	0.736732i	−0.0703156	+	0.0780934i	−0.777276	−	0.629160i	$-0.783399\pi$
$89$	−0.663356	+	0.736732i	−0.0703156	+	0.0780934i	0.706960	+	0.707253i	$0.250066\pi$
$90$	0.0540257	+	0.0380499i	0.00569481	+	0.00401081i
$91$	−0.601877	−	0.599756i	−0.0630939	−	0.0628715i
$92$	−6.75128	+	1.06930i	−0.703870	+	0.111482i
$93$	−0.219844	+	0.820470i	−0.0227968	+	0.0850787i
$94$	−0.0987668	+	0.0439738i	−0.0101870	+	0.00453555i
$95$	12.4080	−	8.32000i	1.27303	−	0.853614i
$96$	−0.0947968	+	0.212917i	−0.00967515	+	0.0217308i
$97$	12.2690	+	1.94322i	1.24573	+	0.197304i	0.744270	−	0.667879i	$-0.232798\pi$
$97$	12.2690	+	1.94322i	1.24573	+	0.197304i	0.501457	+	0.865183i	$0.332798\pi$
$98$	0.0759884	+	0.0931634i	0.00767599	+	0.00941093i
$99$			8.72671i			0.877067i
$100$	−0.752018	+	9.97020i	−0.0752018	+	0.997020i
$101$	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	$0.467504\pi$
$102$	−0.0608843	+	0.0395387i	−0.00602845	+	0.00391492i
$103$	13.7639	−	5.28346i	1.35620	−	0.520595i	0.431780	−	0.901979i	$-0.357886\pi$
$103$	13.7639	−	5.28346i	1.35620	−	0.520595i	0.924417	+	0.381384i	$0.124552\pi$
$104$	−0.0178478	+	0.0129672i	−0.00175012	+	0.00127154i
$105$	−2.17242	−	6.32911i	−0.212006	−	0.617658i
$106$	−0.156936	−	0.114021i	−0.0152430	−	0.0110747i
$107$	−10.0239	−	2.68589i	−0.969046	−	0.259655i	−0.260621	−	0.965441i	$-0.583927\pi$
$107$	−10.0239	−	2.68589i	−0.969046	−	0.259655i	−0.708425	+	0.705786i	$0.750594\pi$
$108$	3.82641	−	9.96813i	0.368196	−	0.959184i
$109$	−6.76285	+	6.08930i	−0.647763	+	0.583249i	−0.926120	−	0.377229i	$-0.876877\pi$
$109$	−6.76285	+	6.08930i	−0.647763	+	0.583249i	0.278357	+	0.960478i	$0.410210\pi$
$110$	0.167228	−	0.0998592i	0.0159446	−	0.00952120i
$111$	3.54546	−	1.15199i	0.336520	−	0.109342i
$112$	−9.15175	+	5.30532i	−0.864759	+	0.501306i
$113$	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	$0.218542\pi$
$114$	0.0964498	+	0.0868438i	0.00903335	+	0.00813366i
$115$	−5.19746	−	5.60425i	−0.484666	−	0.522599i
$116$	4.54361	+	5.04619i	0.421864	+	0.468527i
$117$	0.429443	−	0.347756i	0.0397020	−	0.0321501i
$118$	−0.116133	+	0.116133i	−0.0106909	+	0.0106909i
$119$	−9.87467	−	0.500033i	−0.905210	−	0.0458379i
$120$	−0.171181	+	0.0297013i	−0.0156267	+	0.00271135i
$121$	13.4496	+	5.98816i	1.22269	+	0.544378i
$122$	0.0296330	−	0.0365938i	0.00268285	−	0.00331304i
$123$	−5.10760	−	7.86501i	−0.460536	−	0.709164i
$124$	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	$0.904017\pi$
$128$	0.196884	+	0.512900i	0.0174022	+	0.0453344i
$129$	−0.668078	−	6.35633i	−0.0588210	−	0.559644i
$130$	−0.0115781	−	0.00424998i	−0.00101546	−	0.000372748i
$131$	−2.96375	−	0.311503i	−0.258944	−	0.0272161i	−0.0258332	−	0.999666i	$-0.508224\pi$
$131$	−2.96375	−	0.311503i	−0.258944	−	0.0272161i	−0.233111	+	0.972450i	$0.574891\pi$
$132$	−8.11149	−	8.11149i	−0.706015	−	0.706015i
$133$	3.70563	+	17.2836i	0.321319	+	1.49867i
$134$	−0.106647	−	0.0346518i	−0.00921293	−	0.00299346i
$135$	11.6407	−	2.65394i	1.00187	−	0.228415i
$136$	−0.0533737	+	0.251104i	−0.00457676	+	0.0215320i
$137$	−15.4376	−	0.809052i	−1.31893	−	0.0691220i	−0.620162	−	0.784474i	$-0.712933\pi$
$137$	−15.4376	−	0.809052i	−1.31893	−	0.0691220i	−0.698764	+	0.715352i	$0.746266\pi$
$138$	0.0361654	−	0.0556899i	0.00307861	−	0.00474064i
$139$	5.70394	+	17.5549i	0.483801	+	1.48899i	0.833709	+	0.552204i	$0.186213\pi$
$139$	5.70394	+	17.5549i	0.483801	+	1.48899i	−0.349908	+	0.936784i	$0.613787\pi$
$140$	−10.6281	−	5.19643i	−0.898236	−	0.439178i
$141$	−2.20022	+	6.77157i	−0.185292	+	0.570269i
$142$	−0.0490111	−	0.0605237i	−0.00411292	−	0.00507903i
$143$	−0.421562	−	1.57329i	−0.0352528	−	0.131565i
$144$	−2.79818	−	6.28481i	−0.233182	−	0.523734i
$145$	−1.85704	+	7.36234i	−0.154219	+	0.611409i
$146$	−0.101999	−	0.140389i	−0.00844147	−	0.0116187i
$147$	7.90813	+	0.386457i	0.652251	+	0.0318745i
$148$	2.99216	−	5.87245i	0.245954	−	0.482712i
$149$	12.7732	−	7.37458i	1.04642	−	0.604149i	0.124773	−	0.992185i	$-0.460180\pi$
$149$	12.7732	−	7.37458i	1.04642	−	0.604149i	0.921644	+	0.388036i	$0.126846\pi$
$150$	−0.0670891	−	0.0702377i	−0.00547780	−	0.00573489i
$151$	−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	$0.240005\pi$
$152$	0.458318	−	0.0240194i	0.0371745	−	0.00194823i
$153$	1.00590	−	6.35103i	0.0813225	−	0.513450i
$154$	0.0364537	+	0.227559i	0.00293752	+	0.0183372i
$155$	−0.740252	+	1.50726i	−0.0594585	+	0.121066i
$156$	−0.0759281	+	0.722408i	−0.00607912	+	0.0578389i
$157$	5.06744	−	1.35782i	0.404426	−	0.108366i	−0.0508712	−	0.998705i	$-0.516200\pi$
$157$	5.06744	−	1.35782i	0.404426	−	0.108366i	0.455297	+	0.890340i	$0.349533\pi$
$158$	0.131562	+	0.0505019i	0.0104665	+	0.00401772i
$159$	−12.4960	+	2.65612i	−0.991000	+	0.210644i
$160$	−0.265311	+	0.376705i	−0.0209746	+	0.0297812i
$161$	8.43735	−	3.25590i	0.664957	−	0.256601i
$162$	0.00684101	+	0.0134262i	0.000537481	+	0.00105487i
$163$	−14.8958	−	9.67348i	−1.16673	−	0.757685i	−0.192074	−	0.981381i	$-0.561521\pi$
$163$	−14.8958	−	9.67348i	−1.16673	−	0.757685i	−0.974659	+	0.223695i	$0.928188\pi$
$164$	−16.2175	−	3.44714i	−1.26638	−	0.269177i
$165$	2.48200	−	12.5849i	0.193223	−	0.979731i
$166$	0.00463785	+	0.0218194i	0.000359967	+	0.00169351i
$167$	0.899703	+	5.68050i	0.0696211	+	0.439571i	0.997735	+	0.0672731i	$0.0214299\pi$
$167$	0.899703	+	5.68050i	0.0696211	+	0.439571i	−0.928113	+	0.372297i	$0.878570\pi$
$168$	0.0423856	−	0.201154i	0.00327012	−	0.0155193i
$169$	7.58059	−	10.4338i	0.583122	−	0.802599i
$170$	−0.133214	+	0.0533985i	−0.0102170	+	0.00409548i
$171$	−11.4328	+	1.20163i	−0.874287	+	0.0918912i
$172$	−8.78147	−	7.11110i	−0.669581	−	0.542216i
$173$	−0.118239	−	2.25614i	−0.00898956	−	0.171531i	−0.999435	−	0.0336229i	$-0.989295\pi$
$173$	−0.118239	−	2.25614i	−0.00898956	−	0.171531i	0.990445	−	0.137908i	$-0.0440379\pi$
$174$	−0.0659643			−0.00500074
$175$	−1.79253	−	13.1067i	−0.135503	−	0.990777i
$176$	−20.2779			−1.52851
$177$	0.566075	+	10.8014i	0.0425488	+	0.811880i
$178$	−0.0132321	−	0.0107152i	−0.000991789	−	0.000803135i
$179$	23.0769	−	2.42548i	1.72485	−	0.181289i	0.810369	−	0.585920i	$-0.199267\pi$
$179$	23.0769	−	2.42548i	1.72485	−	0.181289i	0.914480	+	0.404631i	$0.132600\pi$
$180$	4.09497	−	6.51360i	0.305221	−	0.485495i
$181$	−1.07470	+	1.47920i	−0.0798820	+	0.109948i	−0.847088	−	0.531453i	$-0.821646\pi$
$181$	−1.07470	+	1.47920i	−0.0798820	+	0.109948i	0.767206	+	0.641401i	$0.221646\pi$
$182$	0.00974556	−	0.0108620i	0.000722389	−	0.000805147i
$183$	−0.485109	−	3.06286i	−0.0358603	−	0.226413i
$184$	−0.0488201	−	0.229680i	−0.00359906	−	0.0169323i
$185$	7.31732	−	0.878143i	0.537980	−	0.0645624i
$186$	−0.0142697	−	0.00303311i	−0.00104630	−	0.000222399i
$187$	−15.8956	−	10.3227i	−1.16240	−	0.754873i
$188$	5.71482	+	11.2160i	0.416796	+	0.818008i
$189$	−2.18529	+	13.9568i	−0.158957	+	1.01521i
$190$	0.153851	+	0.205334i	0.0111615	+	0.0148965i
$191$	0.720510	−	0.153149i	0.0521342	−	0.0110815i	−0.181771	−	0.983341i	$-0.558183\pi$
$191$	0.720510	−	0.153149i	0.0521342	−	0.0110815i	0.233905	+	0.972259i	$0.424850\pi$
$192$	8.44016	+	3.23987i	0.609116	+	0.233818i
$193$	13.9437	−	3.73619i	1.00369	−	0.268937i	0.280697	−	0.959796i	$-0.409434\pi$
$193$	13.9437	−	3.73619i	1.00369	−	0.268937i	0.722989	+	0.690860i	$0.242768\pi$
$194$	−0.0223005	+	0.212175i	−0.00160108	+	0.0152333i
$195$	−0.718211	+	0.379363i	−0.0514321	+	0.0271667i
$196$	10.3694	−	9.40311i	0.740669	−	0.671651i
$197$	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	$-0.0665940\pi$
$198$	−0.149674	+	0.00784407i	−0.0106368	+	0.000557454i
$199$	−3.19046	+	5.52604i	−0.226166	+	0.391731i	−0.956669	−	0.291179i	$-0.905952\pi$
$199$	−3.19046	+	5.52604i	−0.226166	+	0.391731i	0.730503	+	0.682910i	$0.239286\pi$
$200$	−0.343380	−	0.00787307i	−0.0242806	−	0.000556710i
$201$	−6.39554	+	3.69247i	−0.451107	+	0.260447i
$202$	−0.0917845	+	0.180137i	−0.00645794	+	0.0126744i
$203$	−7.27758	−	5.26787i	−0.510786	−	0.369732i
$204$	4.96830	+	6.83828i	0.347851	+	0.478775i
$205$	−6.89799	−	17.2085i	−0.481777	−	1.20189i
$206$	0.102990	+	0.231319i	0.00717563	+	0.0161167i
$207$	1.52227	+	5.68118i	0.105805	+	0.394869i
$208$	0.808069	+	0.997882i	0.0560295	+	0.0691907i
$209$	−10.4708	+	32.2260i	−0.724284	+	2.22912i
$210$	0.106599	−	0.0429486i	0.00735605	−	0.00296374i
$211$	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	$0.474019\pi$
$212$	−12.3012	+	18.9423i	−0.844853	+	1.30096i
$213$	−5.12188	−	0.268427i	−0.350946	−	0.0183923i
$214$	0.0370563	−	0.174336i	0.00253312	−	0.0119174i
$215$	1.13566	−	12.5841i	0.0774515	−	0.858229i
$216$	0.348836	+	0.113344i	0.0237353	+	0.00771206i
$217$	−1.33209	−	1.47420i	−0.0904285	−	0.100075i
$218$	−0.110518	−	0.110518i	−0.00748521	−	0.00748521i
$219$	−11.3656	−	1.19457i	−0.768017	−	0.0807218i
$220$	−12.6300	−	18.8356i	−0.851512	−	1.26990i
$221$	0.125451	+	1.19358i	0.00843873	+	0.0802891i
$222$	0.0229449	+	0.0597735i	0.00153996	+	0.00401173i
$223$	18.8633	+	9.61132i	1.26318	+	0.643622i	0.951816	−	0.306670i	$-0.0992147\pi$
$223$	18.8633	+	9.61132i	1.26318	+	0.643622i	0.311362	+	0.950291i	$0.399215\pi$
$224$	−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
$227$	−10.8610	−	16.7245i	−0.720872	−	1.11004i	−0.989179	−	0.146712i	$-0.953131\pi$
$227$	−10.8610	−	16.7245i	−0.720872	−	1.11004i	0.268308	−	0.963333i	$-0.413536\pi$
$228$	9.50987	−	11.7437i	0.629807	−	0.777746i
$229$	9.17427	+	4.08465i	0.606253	+	0.269921i	0.686819	−	0.726828i	$-0.259006\pi$
$229$	9.17427	+	4.08465i	0.606253	+	0.269921i	−0.0805667	+	0.996749i	$0.525673\pi$
$230$	0.0914481	−	0.0941803i	0.00602991	−	0.00621007i
$231$	12.7434	+	8.24375i	0.838457	+	0.542399i
$232$	−0.164941	+	0.164941i	−0.0108289	+	0.0108289i
$233$	−2.16919	+	1.75658i	−0.142108	+	0.115077i	−0.697739	−	0.716352i	$-0.745810\pi$
$233$	−2.16919	+	1.75658i	−0.142108	+	0.115077i	0.555630	+	0.831429i	$0.312477\pi$
$234$	0.00635045	+	0.00705289i	0.000415142	+	0.000461062i
$235$	−6.85776	+	12.2923i	−0.447351	+	0.801862i
$236$	14.2108	+	12.7955i	0.925047	+	0.832916i
$237$	8.26918	−	4.21336i	0.537141	−	0.273687i
$238$	−0.000299749	−	0.169812i	−1.94298e−5	−	0.0110073i
$239$	−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	$0.443013\pi$
$240$	2.24779	+	9.85923i	0.145094	+	0.636410i
$241$	5.27483	−	4.74948i	0.339782	−	0.305941i	−0.481520	−	0.876435i	$-0.659915\pi$
$241$	5.27483	−	4.74948i	0.339782	−	0.305941i	0.821301	+	0.570494i	$0.193248\pi$
$242$	−0.0906150	+	0.236060i	−0.00582495	+	0.0151745i
$243$	−14.5140	−	3.88900i	−0.931071	−	0.249480i
$244$	−4.43544	−	3.22254i	−0.283950	−	0.206302i
$245$	15.1905	+	3.77460i	0.970488	+	0.241151i
$246$	0.130304	−	0.0946711i	0.00830785	−	0.00603601i
$247$	2.00311	−	0.768920i	0.127455	−	0.0489252i
$248$	−0.0432649	+	0.0280965i	−0.00274732	+	0.00178413i
$249$	1.27225	+	0.734532i	0.0806254	+	0.0465491i
$250$	−0.103256	−	0.161894i	−0.00653051	−	0.0102391i
$251$		−	3.67076i		−	0.231697i	−0.993267	−	0.115848i	$-0.963041\pi$
$251$		−	3.67076i		−	0.231697i	0.993267	−	0.115848i	$-0.0369586\pi$
$252$	5.36390	+	7.35544i	0.337894	+	0.463349i
$253$	17.1229	+	2.71200i	1.07651	+	0.170502i
$254$	0.112728	−	0.253192i	0.00707321	−	0.0158867i
$255$	−3.25694	+	8.87278i	−0.203958	+	0.555635i
$256$	14.5952	−	6.49819i	0.912198	−	0.406137i
$257$	1.42369	−	5.31329i	0.0888074	−	0.331434i	−0.907201	−	0.420698i	$-0.861785\pi$
$257$	1.42369	−	5.31329i	0.0888074	−	0.331434i	0.996008	+	0.0892647i	$0.0284517\pi$
$258$	0.108418	−	0.0171718i	0.00674984	−	0.00106907i
$259$	−2.24206	+	8.42694i	−0.139315	+	0.523624i
$260$	−0.423606	+	1.37212i	−0.0262709	+	0.0850951i
$261$	3.90958	−	4.34202i	0.241997	−	0.268765i
$262$	0.00267867	−	0.0511120i	0.000165489	−	0.00315771i
$263$	1.08855	−	20.7708i	0.0671229	−	1.28078i	−0.732703	−	0.680549i	$-0.761741\pi$
$263$	1.08855	−	20.7708i	0.0671229	−	1.28078i	0.799826	−	0.600232i	$-0.204925\pi$
$264$	0.263681	−	0.292848i	0.0162285	−	0.0180235i
$265$	−25.2530	+	0.371697i	−1.55128	+	0.0228331i
$266$	−0.293103	+	0.0790916i	−0.0179713	+	0.00484942i
$267$	−1.10751	+	0.175413i	−0.0677788	+	0.0107351i
$268$	−3.37921	+	12.6114i	−0.206418	+	0.770363i
$269$	0.143111	−	0.0637171i	0.00872562	−	0.00388490i	−0.402369	−	0.915477i	$-0.631813\pi$
$269$	0.143111	−	0.0637171i	0.00872562	−	0.00388490i	0.411095	+	0.911593i	$0.365147\pi$
$270$	0.0559816	+	0.197266i	0.00340693	+	0.0120052i
$271$	0.567128	−	1.27379i	0.0344506	−	0.0773772i	−0.895501	−	0.445060i	$-0.853182\pi$
$271$	0.567128	−	1.27379i	0.0344506	−	0.0773772i	0.929951	+	0.367683i	$0.119849\pi$
$272$	14.7577	+	2.33738i	0.894814	+	0.141725i
$273$	−0.102145	−	0.955618i	−0.00618212	−	0.0578366i
$274$		−	0.265502i		−	0.0160395i
$275$	9.62801	−	23.4598i	0.580591	−	1.41468i
$276$	−6.69562	−	3.86572i	−0.403029	−	0.232689i
$277$	25.1881	−	16.3574i	1.51341	−	0.982819i	0.521867	−	0.853027i	$-0.325236\pi$
$277$	25.1881	−	16.3574i	1.51341	−	0.982819i	0.991541	−	0.129792i	$-0.0414310\pi$
$278$	−0.295961	+	0.113609i	−0.0177506	+	0.00681381i
$279$	1.04539	−	0.759518i	0.0625857	−	0.0454712i
$280$	0.159156	−	0.373938i	0.00951137	−	0.0223471i
$281$	−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	$-0.624616\pi$
$282$	−0.118119	−	0.0316498i	−0.00703385	−	0.00188472i
$283$	−10.0848	+	26.2719i	−0.599482	+	1.56170i	0.211965	+	0.977277i	$0.432014\pi$
$283$	−10.0848	+	26.2719i	−0.599482	+	1.56170i	−0.811447	+	0.584426i	$0.801320\pi$
$284$	−6.73862	+	6.06748i	−0.399864	+	0.360039i
$285$	16.8291	+	1.51875i	0.996869	+	0.0899631i
$286$	0.0266049	−	0.00864446i	0.00157318	−	0.000511158i
$287$	21.9363	−	0.0387214i	1.29486	−	0.00228565i
$288$	0.315909	−	0.160964i	0.0186151	−	0.00948487i
$289$	−2.25500	−	2.03041i	−0.132647	−	0.119436i
$290$	−0.127942	−	0.0252329i	−0.00751304	−	0.00148173i
$291$	9.40141	+	10.4413i	0.551120	+	0.612081i
$292$	−15.7019	+	12.7152i	−0.918887	+	0.744100i
$293$	4.56757	−	4.56757i	0.266840	−	0.266840i	−0.560986	−	0.827826i	$-0.689578\pi$
$293$	4.56757	−	4.56757i	0.266840	−	0.266840i	0.827826	+	0.560986i	$0.189578\pi$
$294$	0.000480065		0.135981i	2.79979e−5		0.00793060i
$295$	−3.03383	+	21.1665i	−0.176636	+	1.23236i
$296$	0.206834	+	0.0920883i	0.0120220	+	0.00535252i
$297$	−17.0421	+	21.0453i	−0.988885	+	1.22117i
$298$	0.137964	+	0.212447i	0.00799207	+	0.0123067i
$299$	−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
$303$	4.77150	+	12.4302i	0.274115	+	0.714095i
$304$	−2.79219	−	26.5660i	−0.160143	−	1.52366i
$305$	0.230711	−	6.12620i	0.0132105	−	0.350785i
$306$	0.109832	+	0.0115438i	0.00627868	+	0.000659916i
$307$	−12.4946	−	12.4946i	−0.713104	−	0.713104i	0.254080	−	0.967183i	$-0.418227\pi$
$307$	−12.4946	−	12.4946i	−0.713104	−	0.713104i	−0.967183	+	0.254080i	$0.918227\pi$
$308$	26.2369	−	5.62524i	1.49498	−	0.320528i
$309$	15.8595	+	5.15306i	0.902215	+	0.293148i
$310$	−0.0265168	−	0.0113414i	−0.00150605	−	0.000644149i
$311$	1.55465	−	7.31407i	0.0881563	−	0.414743i	−0.911835	−	0.410557i	$-0.865334\pi$
$311$	1.55465	−	7.31407i	0.0881563	−	0.414743i	0.999991	−	0.00418591i	$-0.00133242\pi$
$312$	−0.0249187	−	0.00130593i	−0.00141074	−	7.39340e-5i
$313$	−15.1587	+	23.3423i	−0.856819	+	1.31939i	0.0894451	+	0.995992i	$0.471491\pi$
$313$	−15.1587	+	23.3423i	−0.856819	+	1.31939i	−0.946264	+	0.323394i	$0.895176\pi$
$314$	0.0278431	+	0.0856923i	0.00157128	+	0.00483590i
$315$	−3.49089	+	9.56226i	−0.196689	+	0.538772i
$316$	5.07033	−	15.6049i	0.285228	−	0.877843i
$317$	17.9833	+	22.2075i	1.01004	+	1.24730i	0.968722	+	0.248150i	$0.0798225\pi$
$317$	17.9833	+	22.2075i	1.01004	+	1.24730i	0.0413185	+	0.999146i	$0.486844\pi$
$318$	−0.0567878	−	0.211935i	−0.00318450	−	0.0118847i
$319$	−7.00477	−	15.7330i	−0.392192	−	0.880878i
$320$	15.1310	+	9.51252i	0.845846	+	0.531766i
$321$	−6.89929	−	9.49606i	−0.385081	−	0.530019i
$322$	0.0634266	+	0.141784i	0.00353463	+	0.00790134i
$323$	11.3350	−	22.2461i	0.630694	−	1.23781i
$324$	1.51943	−	0.877241i	0.0844125	−	0.0487356i
$325$	−1.53813	+	0.461069i	−0.0853204	+	0.0255755i
$326$	0.152523	−	0.264177i	0.00844745	−	0.0146314i
$327$	−10.2791	+	0.538704i	−0.568434	+	0.0297904i
$328$	0.0890975	−	0.562539i	0.00491959	−	0.0310610i
$329$	−10.5040	−	12.9247i	−0.579105	−	0.712560i
$330$	0.218077	+	0.0312573i	0.0120047	+	0.00172066i
$331$	−1.74558	+	16.6081i	−0.0959457	+	0.912863i	0.835624	+	0.549301i	$0.185106\pi$
$331$	−1.74558	+	16.6081i	−0.0959457	+	0.912863i	−0.931570	+	0.363561i	$0.881561\pi$
$332$	2.50875	−	0.672217i	0.137685	−	0.0368927i
$333$	−5.29442	−	2.03234i	−0.290132	−	0.111371i
$334$	−0.0966189	+	0.0205370i	−0.00528675	+	0.00112373i
$335$	−13.8171	+	4.71536i	−0.754906	+	0.257627i
$336$	−11.8209	−	1.85087i	−0.644884	−	0.100973i
$337$	−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	$-0.375626\pi$
$338$	0.185766	+	0.120638i	0.0101043	+	0.00656184i
$339$	9.44031	+	2.00660i	0.512728	+	0.108984i
$340$	7.02057	+	15.1638i	0.380744	+	0.822373i
$341$	−0.791882	−	3.72551i	−0.0428828	−	0.201748i
$342$	−0.0308859	−	0.195006i	−0.00167012	−	0.0105447i
$343$	−10.8064	+	15.0406i	−0.583493	+	0.812118i
$344$	0.228158	−	0.314033i	0.0123015	−	0.0169315i
$345$	−0.579471	−	8.62584i	−0.0311977	−	0.464399i
$346$	0.0385893	−	0.00405590i	0.00207457	−	0.000218046i
$347$	2.85404	+	2.31115i	0.153213	+	0.124069i	0.702862	−	0.711326i	$-0.251905\pi$
$347$	2.85404	+	2.31115i	0.153213	+	0.124069i	−0.549649	+	0.835396i	$0.685239\pi$
$348$	0.401961	+	7.66988i	0.0215474	+	0.411149i
$349$	−1.21897			−0.0652497			−0.0326249	−	0.999468i	$-0.510387\pi$
$349$	−1.21897			−0.0652497			−0.0326249	+	0.999468i	$0.510387\pi$
$350$	0.223186	−	0.0425252i	0.0119298	−	0.00227307i
$351$	1.71477			0.0915274
$352$	−0.0546944	−	1.04363i	−0.00291522	−	0.0556258i
$353$	−19.7399	−	15.9851i	−1.05065	−	0.850799i	−0.0615584	−	0.998103i	$-0.519607\pi$
$353$	−19.7399	−	15.9851i	−1.05065	−	0.850799i	−0.989091	+	0.147304i	$0.952940\pi$
$354$	−0.184748	+	0.0194178i	−0.00981924	+	0.00103204i
$355$	−9.83157	−	2.47987i	−0.521806	−	0.131618i
$356$	−1.16525	+	1.60383i	−0.0617583	+	0.0850031i
$357$	−8.32405	−	7.46845i	−0.440556	−	0.395272i
$358$	0.0623428	+	0.393617i	0.00329492	+	0.0208033i
$359$	−2.33682	−	10.9939i	−0.123333	−	0.580235i	−0.995799	−	0.0915616i	$-0.970814\pi$
$359$	−2.33682	−	10.9939i	−0.123333	−	0.580235i	0.872467	−	0.488674i	$-0.162519\pi$
$360$	0.230811	+	0.128767i	0.0121648	+	0.00678663i
$361$	−25.0759	−	5.33005i	−1.31979	−	0.280529i
$362$	−0.0263361	−	0.0171029i	−0.00138420	−	0.000898908i
$363$	7.55997	+	14.8373i	0.396796	+	0.778755i
$364$	−1.32235	−	1.06696i	−0.0693099	−	0.0559238i
$365$	−21.5874	−	6.66457i	−1.12994	−	0.348839i
$366$	0.0520958	−	0.0110733i	0.00272309	−	0.000578810i
$367$	−6.73383	−	2.58488i	−0.351503	−	0.134929i	0.176209	−	0.984353i	$-0.443617\pi$
$367$	−6.73383	−	2.58488i	−0.351503	−	0.134929i	−0.527712	+	0.849423i	$0.676950\pi$
$368$	−13.2012	+	3.53724i	−0.688158	+	0.184391i
$369$	−1.49122	+	14.1881i	−0.0776301	+	0.738601i
$370$	0.0216385	+	0.124712i	0.00112493	+	0.00648345i
$371$	10.6598	−	27.9170i	0.553431	−	1.44938i
$372$	−0.265716	+	1.67766i	−0.0137767	+	0.0869827i
$373$	−3.89404	+	0.204078i	−0.201626	+	0.0105667i	−0.152881	−	0.988245i	$-0.548855\pi$
$373$	−3.89404	+	0.204078i	−0.201626	+	0.0105667i	−0.0487442	+	0.998811i	$0.515522\pi$
$374$	0.162760	−	0.281908i	0.00841610	−	0.0145771i
$375$	−12.4735	−	2.08068i	−0.644130	−	0.107446i
$376$	−0.374489	+	0.216211i	−0.0193128	+	0.0111503i
$377$	−0.495085	+	0.971660i	−0.0254982	+	0.0500430i
$378$	−0.241340	−	0.0249353i	−0.0124132	−	0.00128253i
$379$	−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	$0.837749\pi$
$380$	22.9373	−	19.1400i	1.17666	−	0.981862i
$381$	−7.42397	−	16.6745i	−0.380342	−	0.854261i
$382$	0.00327433	+	0.0122200i	0.000167529	+	0.000625228i
$383$	−17.8962	−	22.1000i	−0.914454	−	1.12926i	−0.991222	−	0.132208i	$-0.957793\pi$
$383$	−17.8962	−	22.1000i	−0.914454	−	1.12926i	0.0767678	−	0.997049i	$-0.475540\pi$
$384$	−0.192024	+	0.590991i	−0.00979921	+	0.0301589i
$385$	21.5634	+	20.8640i	1.09897	+	1.06333i
$386$	0.0766136	+	0.235792i	0.00389953	+	0.0120015i
$387$	−5.29544	+	8.15426i	−0.269182	+	0.414504i
$388$	24.8061	+	1.30003i	1.25934	+	0.0659992i
$389$	6.09298	−	28.6652i	0.308926	−	1.45338i	−0.500282	−	0.865863i	$-0.666770\pi$
$389$	6.09298	−	28.6652i	0.308926	−	1.45338i	0.809208	−	0.587522i	$-0.199896\pi$
$390$	−0.00715211	−	0.0119772i	−0.000362161	−	0.000606489i
$391$	−12.1489	−	3.94741i	−0.614396	−	0.199629i
$392$	0.341216	+	0.338815i	0.0172340	+	0.0171128i
$393$	−2.38345	−	2.38345i	−0.120229	−	0.120229i
$394$	0.171727	+	0.0180493i	0.00865149	+	0.000909308i
$395$	17.6504	−	5.00895i	0.888086	−	0.252027i
$396$	1.82411	+	17.3552i	0.0916649	+	0.872134i
$397$	0.399283	+	1.04017i	0.0200394	+	0.0522045i	0.943235	−	0.332126i	$-0.107766\pi$
$397$	0.399283	+	1.04017i	0.0200394	+	0.0522045i	−0.923196	+	0.384330i	$0.874432\pi$
$398$	−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	$0.902190\pi$
$402$	−0.0690790	−	0.106372i	−0.00344535	−	0.00530537i
$403$	−0.151777	+	0.187429i	−0.00756055	+	0.00933650i
$404$	21.5044	+	9.57439i	1.06989	+	0.476344i
$405$	1.76095	+	0.864843i	0.0875022	+	0.0429744i
$406$	0.0838090	−	0.129555i	0.00415937	−	0.00642969i
$407$	−11.8199	+	11.8199i	−0.585890	+	0.585890i
$408$	−0.225655	+	0.182732i	−0.0111716	+	0.00904657i
$409$	−10.3987	−	11.5490i	−0.514185	−	0.571060i	0.429010	−	0.903300i	$-0.358862\pi$
$409$	−10.3987	−	11.5490i	−0.514185	−	0.571060i	−0.943195	+	0.332240i	$0.892196\pi$
$410$	0.288947	−	0.133777i	0.0142701	−	0.00660678i
$411$	−12.9940	−	11.6999i	−0.640947	−	0.577112i
$412$	26.2686	−	13.3845i	1.29416	−	0.659407i
$413$	−21.9332	−	12.6116i	−1.07926	−	0.620575i
$414$	−0.0960709	+	0.0312153i	−0.00472163	+	0.00153415i
$415$	2.18664	+	1.91134i	0.107338	+	0.0938240i
$416$	−0.0491778	+	0.0442799i	−0.00241114	+	0.00217100i
$417$	−7.48195	+	19.4912i	−0.366393	+	0.954486i
$418$	−0.562127	−	0.150621i	−0.0274945	−	0.00736713i
$419$	5.12758	+	3.72540i	0.250499	+	0.181998i	0.705948	−	0.708264i	$-0.250521\pi$
$419$	5.12758	+	3.72540i	0.250499	+	0.181998i	−0.455449	+	0.890262i	$0.650521\pi$
$420$	−5.64335	−	12.1329i	−0.275367	−	0.592026i
$421$	−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	$0.481726\pi$
$422$	−0.453278	+	0.173997i	−0.0220652	+	0.00847004i
$423$	9.08396	−	5.89920i	0.441677	−	0.286829i
$424$	−0.671930	−	0.387939i	−0.0326318	−	0.0188400i
$425$	−9.71111	+	15.9635i	−0.471058	+	0.774345i
$426$		−	0.0880879i		−	0.00426787i
$427$	6.63183	+	2.93866i	0.320937	+	0.142212i
$428$	−20.4964	−	3.24632i	−0.990732	−	0.156917i
$429$	0.749328	−	1.68302i	0.0361779	−	0.0812568i
$430$	0.216854	+	0.00816667i	0.0104576	+	0.000393832i
$431$	−8.89080	+	3.95844i	−0.428255	+	0.190671i	−0.609533	−	0.792761i	$-0.708643\pi$
$431$	−8.89080	+	3.95844i	−0.428255	+	0.190671i	0.181279	+	0.983432i	$0.441976\pi$
$432$	5.52535	−	20.6209i	0.265839	−	0.992123i
$433$	−12.2911	+	1.94672i	−0.590674	+	0.0935535i	−0.444614	−	0.895722i	$-0.646659\pi$
$433$	−12.2911	+	1.94672i	−0.590674	+	0.0935535i	−0.146060	+	0.989276i	$0.546659\pi$
$434$	0.0240870	−	0.0241722i	0.00115621	−	0.00116030i
$435$	−6.87297	+	5.14974i	−0.329534	+	0.246911i
$436$	−12.1768	+	13.5237i	−0.583163	+	0.647668i
$437$	−1.19521	+	22.8060i	−0.0571746	+	1.09096i
$438$	0.0102723	−	0.196008i	0.000490831	−	0.00936562i
$439$	16.4159	−	18.2318i	0.783490	−	0.870154i	−0.210727	−	0.977545i	$-0.567583\pi$
$439$	16.4159	−	18.2318i	0.783490	−	0.870154i	0.994217	+	0.107391i	$0.0342497\pi$
$440$	0.623449	−	0.467135i	0.0297218	−	0.0222698i
$441$	−8.97928	−	8.02776i	−0.427585	−	0.382274i
$442$	−0.0203587	+	0.00322450i	−0.000968363	+	0.000153374i
$443$	1.81367	−	6.76871i	0.0861701	−	0.321591i	−0.909363	−	0.416003i	$-0.863430\pi$
$443$	1.81367	−	6.76871i	0.0861701	−	0.321591i	0.995533	+	0.0944121i	$0.0300971\pi$
$444$	6.81023	−	3.03211i	0.323199	−	0.143898i
$445$	−2.21520	−	0.0834241i	−0.105011	−	0.00395468i
$446$	−0.147891	+	0.332168i	−0.00700282	+	0.0157286i
$447$	16.4771	+	2.60972i	0.779340	+	0.123435i
$448$	−17.0865	+	12.4602i	−0.807263	+	0.588691i
$449$		−	11.3776i		−	0.536943i	−0.963288	−	0.268472i	$-0.913481\pi$
$449$		−	11.3776i		−	0.536943i	0.963288	−	0.268472i	$-0.0865186\pi$
$450$	0.0120726	+	0.147265i	0.000569108	+	0.00694216i
$451$	36.4167	+	21.0252i	1.71480	+	0.990039i
$452$	14.3102	−	9.29316i	0.673095	−	0.437113i
$453$	−5.92648	+	2.27496i	−0.278450	+	0.106887i
$454$	0.277083	−	0.201313i	0.0130042	−	0.00944808i
$455$	0.167428	−	1.89256i	0.00784915	−	0.0887246i
$456$	0.419965	+	0.305123i	0.0196667	+	0.0142887i
$457$	6.62325	+	1.77469i	0.309822	+	0.0830167i	0.410380	−	0.911915i	$-0.365396\pi$
$457$	6.62325	+	1.77469i	0.309822	+	0.0830167i	−0.100558	+	0.994931i	$0.532063\pi$
$458$	−0.0618104	+	0.161021i	−0.00288821	+	0.00752404i
$459$	14.8286	−	13.3517i	0.692138	−	0.623204i
$460$	−11.5079	−	10.0591i	−0.536558	−	0.469006i
$461$	6.19822	−	2.01392i	0.288680	−	0.0937978i	−0.161097	−	0.986939i	$-0.551503\pi$
$461$	6.19822	−	2.01392i	0.288680	−	0.0937978i	0.449777	+	0.893141i	$0.351503\pi$
$462$	−0.129936	+	0.225976i	−0.00604516	+	0.0105133i
$463$	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	$0.316770\pi$
$464$	10.0894	+	9.08455i	0.468389	+	0.421740i
$465$	−1.72358	+	0.797986i	−0.0799291	+	0.0370057i
$466$	−0.0320772	−	0.0356254i	−0.00148595	−	0.00165031i
$467$	31.2205	−	25.2819i	1.44471	−	1.16991i	0.490248	−	0.871583i	$-0.336906\pi$
$467$	31.2205	−	25.2819i	1.44471	−	1.16991i	0.954465	−	0.298322i	$-0.0964271\pi$
$468$	0.781365	−	0.781365i	0.0361186	−	0.0361186i
$469$	0.873619	−	17.2523i	0.0403400	−	0.796636i
$470$	−0.216992	−	0.106570i	−0.0100091	−	0.00491571i
$471$	5.42086	+	2.41352i	0.249780	+	0.111209i
$472$	−0.413401	+	0.510507i	−0.0190283	+	0.0234980i
$473$	15.6086	+	24.0351i	0.717684	+	1.10514i
$474$	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
$478$	−0.0256376	−	0.0667882i	−0.00117264	−	0.00305482i
$479$	2.16757	+	20.6230i	0.0990386	+	0.942290i	0.925360	+	0.379090i	$0.123763\pi$
$479$	2.16757	+	20.6230i	0.0990386	+	0.942290i	−0.826321	+	0.563199i	$0.809570\pi$
$480$	−0.501355	+	0.142278i	−0.0228836	+	0.00649409i
$481$	1.05268	+	0.110641i	0.0479980	+	0.00504479i
$482$	0.0862007	+	0.0862007i	0.00392633	+	0.00392633i
$483$	9.73414	+	3.14383i	0.442919	+	0.143049i
$484$	27.9996	+	9.09763i	1.27271	+	0.413529i
$485$	14.2406	+	23.8479i	0.646634	+	1.08288i
$486$	0.0536552	−	0.252428i	0.00243385	−	0.0114504i
$487$	−7.42319	−	0.389033i	−0.336377	−	0.0176288i	−0.116600	−	0.993179i	$-0.537200\pi$
$487$	−7.42319	−	0.389033i	−0.336377	−	0.0176288i	−0.219777	+	0.975550i	$0.570533\pi$
$488$	0.102575	−	0.157952i	0.00464335	−	0.00715013i
$489$	−6.20797	−	19.1062i	−0.280734	−	0.864011i
$490$	−0.0510849	+	0.263929i	−0.00230778	+	0.0119231i
$491$	−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	$0.948518\pi$
$492$	−11.8017	−	14.5739i	−0.532063	−	0.657043i
$493$	3.28436	+	12.2574i	0.147920	+	0.552045i
$494$	0.0149884	+	0.0336646i	0.000674362	+	0.00151464i
$495$	−14.9825	+	12.5021i	−0.673412	+	0.561928i
$496$	1.76487	+	2.42913i	0.0792448	+	0.109071i
$497$	7.03465	−	9.71839i	0.315547	−	0.435929i
$498$	−0.0114546	+	0.0224808i	−0.000513291	+	0.00100739i
$499$	7.97198	−	4.60262i	0.356875	−	0.206042i	−0.310834	−	0.950464i	$-0.600608\pi$
$499$	7.97198	−	4.60262i	0.356875	−	0.206042i	0.667709	+	0.744422i	$0.267275\pi$
$500$	−18.1947	+	12.9925i	−0.813693	+	0.581041i
$501$	−3.25260	+	5.63367i	−0.145315	+	0.251694i
$502$	0.0629581	−	0.00329950i	0.00280996	−	0.000147264i
$503$	−3.27358	+	20.6686i	−0.145962	+	0.921565i	0.800637	+	0.599150i	$0.204495\pi$
$503$	−3.27358	+	20.6686i	−0.145962	+	0.921565i	−0.946598	+	0.322415i	$0.895505\pi$
$504$	−0.242685	+	0.197233i	−0.0108100	+	0.00878544i
$505$	4.49982	+	25.9344i	0.200239	+	1.15407i
$506$	−0.0311230	+	0.296116i	−0.00138359	+	0.0131640i
$507$	14.0903	−	3.77549i	0.625774	−	0.167676i
$508$	−30.1264	−	11.5644i	−1.33664	−	0.513089i
$509$	6.93922	−	1.47498i	0.307575	−	0.0653772i	−0.0515382	−	0.998671i	$-0.516412\pi$
$509$	6.93922	−	1.47498i	0.307575	−	0.0653772i	0.359114	+	0.933294i	$0.383079\pi$
$510$	−0.155107	−	0.0478852i	−0.00686824	−	0.00212039i
$511$	16.7864	−	20.8044i	0.742586	−	0.920334i
$512$	0.623407	+	1.22350i	0.0275509	+	0.0540718i
$513$	−29.9179	−	19.4289i	−1.32091	−	0.857807i
$514$	0.0924091	+	0.0196422i	0.00407599	+	0.000866379i
$515$	28.7894	+	16.0614i	1.26861	+	0.707748i
$516$	−2.65728	−	12.5015i	−0.116980	−	0.550349i
$517$	−4.99434	−	31.5330i	−0.219651	−	1.38682i
$518$	−0.146548	−	0.0308794i	−0.00643893	−	0.00135676i
$519$	1.50201	−	2.06734i	0.0659310	−	0.0907463i
$520$	−0.0478320	−	0.0120649i	−0.00209757	−	0.000529082i
$521$	−15.1966	+	1.59723i	−0.665775	+	0.0699757i	−0.431386	−	0.902167i	$-0.641975\pi$
$521$	−15.1966	+	1.59723i	−0.665775	+	0.0699757i	−0.234388	+	0.972143i	$0.575309\pi$
$522$	0.0779852	+	0.0631512i	0.00341332	+	0.00276405i
$523$	0.242708	+	4.63114i	0.0106129	+	0.202506i	0.998790	+	0.0491867i	$0.0156629\pi$
$523$	0.242708	+	4.63114i	0.0106129	+	0.202506i	−0.988177	+	0.153319i	$0.951004\pi$
$524$	−5.95927			−0.260332
$525$	7.75388	−	12.7970i	0.338407	−	0.558505i
$526$	0.357223			0.0155757
$527$	0.146877	+	2.80259i	0.00639808	+	0.122083i
$528$	−17.8246	−	14.4341i	−0.775717	−	0.628163i
$529$	−11.2538	+	1.18282i	−0.489294	+	0.0514268i
$530$	−0.0290739	−	0.432785i	−0.00126289	−	0.0187990i
$531$	9.67149	−	13.3117i	0.419707	−	0.577677i
$532$	10.9823	+	33.5981i	0.476143	+	1.45666i
$533$	−0.416539	−	2.62992i	−0.0180423	−	0.113915i
$534$	−0.00400405	−	0.0188376i	−0.000173272	−	0.000815181i
$535$	−9.74920	−	21.0574i	−0.421495	−	0.910391i
$536$	−0.438709	−	0.0932504i	−0.0189493	−	0.00402781i
$537$	22.0114	+	14.2944i	0.949863	+	0.616848i
$538$	0.00122146	+	0.00239725i	5.26610e−5	+	0.000103353i
$539$	−32.3816	+	14.5544i	−1.39477	+	0.626903i
$540$	22.5956	−	7.71122i	0.972361	−	0.331838i
$541$	−24.8117	+	5.27390i	−1.06674	+	0.226743i	−0.707652	−	0.706561i	$-0.750246\pi$
$541$	−24.8117	+	5.27390i	−1.06674	+	0.226743i	−0.359088	+	0.933304i	$0.616912\pi$
$542$	0.0223568	+	0.00858198i	0.000960308	+	0.000368628i
$543$	−1.99759	+	0.535254i	−0.0857249	+	0.0229699i
$544$	−0.0804917	+	0.765827i	−0.00345105	+	0.0328346i
$545$	−20.1431	−	2.88713i	−0.862834	−	0.123671i
$546$	0.0162982	−	0.00261088i	0.000697499	−	0.000111735i
$547$	−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	$0.988254\pi$
$548$	−30.8707	+	1.61787i	−1.31873	+	0.0691118i
$549$	−2.35873	+	4.08544i	−0.100668	+	0.174362i
$550$	0.411019	+	0.144045i	0.0175259	+	0.00614210i
$551$	19.6471	−	11.3433i	0.836995	−	0.483239i
$552$	0.120576	−	0.236643i	0.00513204	−	0.0100722i
$553$	−2.23108	+	21.5939i	−0.0948752	+	0.918266i
$554$	0.303190	+	0.417305i	0.0128813	+	0.0177296i
$555$	7.05711	+	4.43666i	0.299557	+	0.188326i
$556$	15.0131	+	33.7201i	0.636699	+	1.43005i
$557$	4.38542	+	16.3666i	0.185816	+	0.693475i	0.994454	+	0.105169i	$0.0335383\pi$
$557$	4.38542	+	16.3666i	0.185816	+	0.693475i	−0.808638	+	0.588306i	$0.799795\pi$
$558$	0.0139663	+	0.0172470i	0.000591242	+	0.000730123i
$559$	0.560777	−	1.72589i	0.0237183	−	0.0729975i
$560$	−22.2195	−	8.11166i	−0.938945	−	0.342780i
$561$	−6.62463	−	20.3885i	−0.279692	−	0.860804i
$562$	0.267194	−	0.411443i	0.0112709	−	0.0173557i
$563$	43.2943	+	2.26896i	1.82464	+	0.0956252i	0.933603	−	0.358310i	$-0.116647\pi$
$563$	43.2943	+	2.26896i	1.82464	+	0.0956252i	0.891035	+	0.453935i	$0.149980\pi$
$564$	−2.96025	+	13.9269i	−0.124649	+	0.586427i
$565$	17.5426	+	7.50308i	0.738022	+	0.315657i
$566$	−0.459661	−	0.149353i	−0.0193210	−	0.00627776i
$567$	−1.72232	+	1.55630i	−0.0723306	+	0.0653584i
$568$	−0.220260	−	0.220260i	−0.00924190	−	0.00924190i
$569$	−9.81623	−	1.03173i	−0.411518	−	0.0432522i	−0.103492	−	0.994630i	$-0.533002\pi$
$569$	−9.81623	−	1.03173i	−0.411518	−	0.0432522i	−0.308026	+	0.951378i	$0.599668\pi$
$570$	−0.0109215	+	0.290005i	−0.000457452	+	0.0121470i
$571$	0.152474	+	1.45070i	0.00638085	+	0.0607098i	0.997249	−	0.0741249i	$-0.0236163\pi$
$571$	0.152474	+	1.45070i	0.00638085	+	0.0607098i	−0.990868	+	0.134835i	$0.956950\pi$
$572$	−1.16724	−	3.04076i	−0.0488047	−	0.127141i
$573$	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
$577$	−3.06593	−	4.72112i	−0.127636	−	0.196543i	0.769075	−	0.639159i	$-0.220717\pi$
$577$	−3.06593	−	4.72112i	−0.127636	−	0.196543i	−0.896711	+	0.442616i	$0.854051\pi$
$578$	0.0327972	−	0.0405011i	0.00136418	−	0.00168462i
$579$	14.9161	+	6.64109i	0.619894	+	0.275994i
$580$	−2.15427	+	15.0300i	−0.0894514	+	0.624088i
$581$	−3.05904	+	1.56547i	−0.126911	+	0.0649466i
$582$	−0.170631	+	0.170631i	−0.00707288	+	0.00707288i
$583$	44.5177	−	36.0498i	1.84374	−	1.49303i
$584$	−0.464424	−	0.515795i	−0.0192180	−	0.0213437i
$585$	1.21228	+	0.239086i	0.0501215	+	0.00988499i
$586$	0.0824450	+	0.0742338i	0.00340577	+	0.00306657i
$587$	−18.5011	+	9.42678i	−0.763622	+	0.389085i	−0.792007	−	0.610512i	$-0.790964\pi$
$587$	−18.5011	+	9.42678i	−0.763622	+	0.389085i	0.0283850	+	0.999597i	$0.490964\pi$
$588$	15.8081	−	0.884438i	0.651914	−	0.0364736i
$589$	4.77172	−	1.55043i	0.196615	−	0.0638842i
$590$	−0.365759	−	0.0330082i	−0.0150581	−	0.00135893i
$591$	8.45086	−	7.60919i	0.347622	−	0.313000i
$592$	4.72247	−	12.3025i	0.194092	−	0.505628i
$593$	14.1905	+	3.80233i	0.582733	+	0.156143i	0.538130	−	0.842862i	$-0.319131\pi$
$593$	14.1905	+	3.80233i	0.582733	+	0.156143i	0.0446033	+	0.999005i	$0.485798\pi$
$594$	−0.376271	−	0.273377i	−0.0154386	−	0.0112168i
$595$	−13.2882	−	17.6697i	−0.544764	−	0.724388i
$596$	23.8611	−	17.3361i	0.977390	−	0.710116i
$597$	−6.73797	+	2.58646i	−0.275767	+	0.105857i
$598$	0.0158122	−	0.0102685i	0.000646608	−	0.000419912i
$599$	8.74982	+	5.05171i	0.357508	+	0.206407i	0.667987	−	0.744173i	$-0.267156\pi$
$599$	8.74982	+	5.05171i	0.357508	+	0.206407i	−0.310479	+	0.950580i	$0.600489\pi$
$600$	−0.296232	−	0.251342i	−0.0120936	−	0.0102610i
$601$		−	22.6515i		−	0.923974i	−0.886887	−	0.461987i	$-0.847137\pi$
$601$		−	22.6515i		−	0.923974i	0.886887	−	0.461987i	$-0.152863\pi$
$602$	−0.104022	+	0.234752i	−0.00423963	+	0.00956778i
$603$	11.0960	+	1.75744i	0.451865	+	0.0715684i
$604$	−4.56489	+	10.2529i	−0.185743	+	0.417185i
$605$	8.98749	+	31.6698i	0.365393	+	1.28756i
$606$	−0.208904	+	0.0930100i	−0.00848614	+	0.00377827i
$607$	−5.16341	+	19.2701i	−0.209576	+	0.782150i	0.778429	+	0.627732i	$0.216017\pi$
$607$	−5.16341	+	19.2701i	−0.209576	+	0.782150i	−0.988006	+	0.154418i	$0.950650\pi$
$608$	1.35972	−	0.215359i	0.0551440	−	0.00873395i
$609$	−2.64737	−	9.81081i	−0.107277	−	0.397554i
$610$	0.105279	−	0.00154960i	0.00426263	−	6.27413e-5i
$611$	−1.35272	+	1.50235i	−0.0547254	+	0.0607787i
$612$	0.672961	−	12.8409i	0.0272028	−	0.519061i
$613$	−2.00861	+	38.3266i	−0.0811272	+	1.54800i	0.590456	+	0.807070i	$0.298948\pi$
$613$	−2.00861	+	38.3266i	−0.0811272	+	1.54800i	−0.671584	+	0.740929i	$0.734386\pi$
$614$	0.203067	−	0.225528i	0.00819510	−	0.00910158i
$615$	6.18579	−	20.0366i	0.249435	−	0.807954i
$616$	0.240144	+	0.889942i	0.00967566	+	0.0358568i
$617$	−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	$0.453822\pi$
$618$	−0.0741259	+	0.276642i	−0.00298178	+	0.0111282i
$619$	2.53843	−	1.13018i	0.102028	−	0.0454258i	−0.355088	−	0.934833i	$-0.615549\pi$
$619$	2.53843	−	1.13018i	0.102028	−	0.0454258i	0.457116	+	0.889407i	$0.348882\pi$
$620$	−1.15712	+	3.15230i	−0.0464710	+	0.126599i
$621$	−7.42352	+	16.6735i	−0.297896	+	0.669084i
$622$	0.126843	+	0.0200899i	0.00508593	+	0.000805532i
$623$	1.06261	−	2.39804i	0.0425724	−	0.0960753i
$624$			1.45235i			0.0581404i
$625$	−23.3974	−	8.80703i	−0.935894	−	0.352281i
$626$	−0.413975	−	0.239009i	−0.0165458	−	0.00955270i
$627$	−32.1429	+	20.8738i	−1.28366	+	0.833620i
$628$	9.79405	−	3.75958i	0.390825	−	0.150024i
$629$	9.96459	−	7.23970i	0.397314	−	0.288666i
$630$	−0.167142	−	0.0512779i	−0.00665911	−	0.00204296i
$631$	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	$0.515107\pi$
$632$	0.544441	+	0.145882i	0.0216567	+	0.00580289i
$633$	−11.4589	+	29.8516i	−0.455452	+	1.18649i
$634$	−0.364721	+	0.328396i	−0.0144849	+	0.0130423i
$635$	−8.02093	−	35.1812i	−0.318301	−	1.39612i
$636$	−24.2963	+	7.89435i	−0.963411	+	0.313031i
$637$	2.00662	+	1.01352i	0.0795052	+	0.0401570i
$638$	0.263544	−	0.134282i	0.0104338	−	0.00531628i
$639$	5.79828	+	5.22080i	0.229377	+	0.206532i
$640$	−0.598512	+	1.07281i	−0.0236583	+	0.0424067i
$641$	1.01518	+	1.12747i	0.0400971	+	0.0445323i	0.762860	−	0.646564i	$-0.223795\pi$
$641$	1.01518	+	1.12747i	0.0400971	+	0.0445323i	−0.722763	+	0.691096i	$0.757128\pi$
$642$	0.156668	−	0.126867i	0.00618318	−	0.00500704i
$643$	18.1864	−	18.1864i	0.717201	−	0.717201i	−0.250830	−	0.968031i	$-0.580703\pi$
$643$	18.1864	−	18.1864i	0.717201	−	0.717201i	0.968031	+	0.250830i	$0.0807034\pi$
$644$	16.0992	−	8.23879i	0.634398	−	0.324654i
$645$	9.95579	−	10.2532i	0.392009	−	0.403721i
$646$	0.391737	+	0.174412i	0.0154127	+	0.00686216i
$647$	4.75026	−	5.86608i	0.186752	−	0.230620i	−0.675168	−	0.737664i	$-0.735929\pi$
$647$	4.75026	−	5.86608i	0.186752	−	0.230620i	0.861920	+	0.507045i	$0.169262\pi$
$648$	0.0328254	+	0.0505467i	0.00128950	+	0.00198566i
$649$	−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
$653$	12.3617	+	32.2034i	0.483751	+	1.26022i	0.930742	+	0.365677i	$0.119162\pi$
$653$	12.3617	+	32.2034i	0.483751	+	1.26022i	−0.446990	+	0.894539i	$0.647504\pi$
$654$	−0.0184789	−	0.175815i	−0.000722581	−	0.00687489i
$655$	−3.71114	−	5.53459i	−0.145006	−	0.216254i
$656$	−32.9683	−	3.46511i	−1.28720	−	0.135290i
$657$	12.2932	+	12.2932i	0.479602	+	0.479602i
$658$	0.212232	−	0.191774i	0.00827368	−	0.00747614i
$659$	−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	$0.712851\pi$
$660$	2.30550	−	25.5470i	0.0897416	−	0.994414i
$661$	8.15962	−	38.3880i	0.317372	−	1.49312i	−0.473311	−	0.880895i	$-0.656941\pi$
$661$	8.15962	−	38.3880i	0.317372	−	1.49312i	0.790684	−	0.612225i	$-0.209725\pi$
$662$	−0.286418	−	0.0150105i	−0.0111320	−	0.000583401i
$663$	−0.739334	+	1.13847i	−0.0287134	+	0.0442147i
$664$	0.0275707	+	0.0848540i	0.00106995	+	0.00329297i
$665$	−24.3645	+	31.1229i	−0.944816	+	1.20689i
$666$	0.0300981	−	0.0926326i	0.00116628	−	0.00358944i
$667$	−7.30461	−	9.02044i	−0.282836	−	0.349273i
$668$	2.97666	+	11.1090i	0.115170	+	0.429822i
$669$	9.73964	+	21.8756i	0.376556	+	0.845760i
$670$	−0.0932937	−	0.232741i	−0.00360425	−	0.00899157i
$671$	8.17313	+	11.2493i	0.315520	+	0.434276i
$672$	0.0633735	−	0.613371i	0.00244468	−	0.0236613i
$673$	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
$675$	21.2331	+	16.1832i	0.817263	+	0.622891i
$676$	12.8950	−	22.3347i	0.495960	−	0.859028i
$677$	−0.636093	+	0.0333362i	−0.0244470	+	0.00128122i	−0.0645556	−	0.997914i	$-0.520563\pi$
$677$	−0.636093	+	0.0333362i	−0.0244470	+	0.00128122i	0.0401085	+	0.999195i	$0.487230\pi$
$678$	−0.0259302	+	0.163717i	−0.000995842	+	0.00628750i
$679$	−32.4515	+	5.19856i	−1.24538	+	0.199502i
$680$	−0.507572	+	0.268103i	−0.0194645	+	0.0102813i
$681$	2.35771	−	22.4321i	0.0903476	−	0.859600i
$682$	0.0631853	−	0.0169304i	0.00241949	−	0.000648300i
$683$	−16.9681	−	6.51343i	−0.649265	−	0.249229i	0.0113716	−	0.999935i	$-0.496380\pi$
$683$	−16.9681	−	6.51343i	−0.649265	−	0.249229i	−0.660637	+	0.750706i	$0.729714\pi$
$684$	−22.4858	+	4.77950i	−0.859765	+	0.182749i
$685$	−20.7273	−	27.6632i	−0.791951	−	1.05696i
$686$	−0.267679	−	0.171824i	−0.0102200	−	0.00656028i
$687$	5.15681	+	10.1208i	0.196745	+	0.386133i
$688$	−18.9478	−	12.3048i	−0.722377	−	0.469117i
$689$	−3.54803	−	0.754158i	−0.135169	−	0.0287311i
$690$	0.147423	−	0.0176920i	0.00561229	−	0.000673525i
$691$	5.16326	+	24.2912i	0.196420	+	0.924081i	0.960353	+	0.278786i	$0.0899322\pi$
$691$	5.16326	+	24.2912i	0.196420	+	0.924081i	−0.763934	+	0.645295i	$0.776735\pi$
$692$	−0.706740	−	4.46218i	−0.0268662	−	0.169627i
$693$	−7.17355	−	21.9460i	−0.272501	−	0.833661i
$694$	−0.0370737	+	0.0510276i	−0.00140730	+	0.00193698i
$695$	−21.9676	+	34.9424i	−0.833278	+	1.32544i
$696$	−0.262392	+	0.0275786i	−0.00994596	+	0.00104536i
$697$	−24.0795	−	19.4992i	−0.912074	−	0.738583i
$698$	−0.00109568	−	0.0209068i	−4.14720e−5	−	0.000791333i
$699$	−3.15710			−0.119413
$700$	−6.30455	−	25.6914i	−0.238289	−	0.971042i
$701$	−7.79098			−0.294261			−0.147131	−	0.989117i	$-0.547004\pi$
$701$	−7.79098			−0.294261			−0.147131	+	0.989117i	$0.547004\pi$
$702$	0.00154133	+	0.0294103i	5.81738e−5	+	0.00111002i
$703$	−17.1127	−	13.8576i	−0.645417	−	0.522648i
$704$	−40.3159	+	4.23737i	−1.51946	+	0.159702i
$705$	−14.7779	+	5.92368i	−0.556567	+	0.223099i
$706$	0.256420	−	0.352932i	0.00965050	−	0.0132828i
$707$	−30.4753	−	6.42152i	−1.14614	−	0.241506i
$708$	3.38355	+	21.3629i	0.127162	+	0.802866i
$709$	−9.38432	−	44.1498i	−0.352436	−	1.65808i	−0.695319	−	0.718701i	$-0.744737\pi$
$709$	−9.38432	−	44.1498i	−0.352436	−	1.65808i	0.342884	−	0.939378i	$-0.388596\pi$
$710$	0.0336957	−	0.170853i	0.00126458	−	0.00641198i
$711$	−13.8098	−	2.93536i	−0.517907	−	0.110085i
$712$	−0.0571145	−	0.0370906i	−0.00214046	−	0.00139003i
$713$	−1.16539	−	2.28721i	−0.0436443	−	0.0856568i
$714$	0.120611	−	0.149481i	0.00451375	−	0.00559418i
$715$	2.09717	−	2.97769i	0.0784296	−	0.111359i
$716$	45.3872	−	9.64735i	1.69620	−	0.360539i
$717$	−4.39848	−	1.68842i	−0.164264	−	0.0630552i
$718$	0.186458	−	0.0499613i	0.00695856	−	0.00186454i
$719$	−3.25147	+	30.9356i	−0.121259	+	1.15370i	0.749503	+	0.662001i	$0.230292\pi$
$719$	−3.25147	+	30.9356i	−0.121259	+	1.15370i	−0.870762	+	0.491704i	$0.836374\pi$
$720$	6.78135	−	13.8078i	0.252726	−	0.514588i
$721$	−30.2705	+	24.6012i	−1.12733	+	0.916195i
$722$	0.0688773	−	0.434874i	0.00256335	−	0.0161843i
$723$	8.01739	−	0.420174i	0.298170	−	0.0156264i
$724$	−1.82812	+	3.16640i	−0.0679417	+	0.117678i
$725$	−15.3005	+	7.35921i	−0.568246	+	0.273314i
$726$	−0.247682	+	0.142999i	−0.00919235	+	0.00530721i
$727$	−9.91394	+	19.4572i	−0.367688	+	0.721628i	−0.998525	−	0.0542869i	$-0.982711\pi$
$727$	−9.91394	+	19.4572i	−0.367688	+	0.721628i	0.630838	+	0.775915i	$0.282711\pi$
$728$	0.0342246	−	0.0472814i	0.00126845	−	0.00175236i
$729$	−11.5369	−	15.8791i	−0.427291	−	0.588116i
$730$	0.0949015	−	0.376242i	0.00351246	−	0.0139253i
$731$	−8.58899	−	19.2912i	−0.317675	−	0.713510i
$732$	−1.60498	−	5.98986i	−0.0593217	−	0.221392i
$733$	0.141811	+	0.175122i	0.00523792	+	0.00646830i	0.779758	−	0.626081i	$-0.215342\pi$
$733$	0.141811	+	0.175122i	0.00523792	+	0.00646830i	−0.774520	+	0.632549i	$0.782009\pi$
$734$	0.0382810	−	0.117817i	0.00141298	−	0.00434870i
$735$	10.6659	+	14.1307i	0.393418	+	0.521220i
$736$	−0.217655	−	0.669875i	−0.00802289	−	0.0246919i
$737$	18.0351	−	27.7716i	0.664331	−	1.02298i
$738$	−0.244683	−	0.0128233i	−0.00900691	−	0.000472032i
$739$	−8.38752	+	39.4602i	−0.308540	+	1.45157i	0.501483	+	0.865167i	$0.332788\pi$
$739$	−8.38752	+	39.4602i	−0.308540	+	1.45157i	−0.810023	+	0.586398i	$0.800545\pi$
$740$	14.3688	−	3.27592i	0.528207	−	0.120425i
$741$	2.30809	+	0.749943i	0.0847897	+	0.0275498i
$742$	0.488393	+	0.157736i	0.0179295	+	0.00579066i
$743$	−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	$0.766349\pi$
$744$	−0.0580299	−	0.00609919i	−0.00212748	−	0.000223607i
$745$	30.9602	+	11.3646i	1.13429	+	0.416367i
$746$	−0.00700037	−	0.0666041i	−0.000256302	−	0.00243855i
$747$	−0.800886	−	2.08638i	−0.0293029	−	0.0763366i
$748$	−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	$0.649254\pi$
$752$	13.7078	+	21.1081i	0.499870	+	0.769733i
$753$	2.61289	−	3.22666i	0.0952192	−	0.117586i
$754$	−0.0171102	−	0.00761794i	−0.000623116	−	0.000277429i
$755$	−12.3650	+	2.14543i	−0.450010	+	0.0780803i
$756$	−1.42867	+	28.2134i	−0.0519601	+	1.02611i
$757$	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	$-0.0207089\pi$
$758$	0.0614863	−	0.0497906i	0.00223328	−	0.00180848i
$759$	13.1208	+	14.5721i	0.476256	+	0.528936i
$760$	0.697835	+	0.752453i	0.0253132	+	0.0272943i
$761$	35.3614	+	31.8396i	1.28185	+	1.15418i	0.979601	+	0.200954i	$0.0644043\pi$
$761$	35.3614	+	31.8396i	1.28185	+	1.15418i	0.302250	+	0.953229i	$0.402262\pi$
$762$	0.279315	−	0.142318i	0.0101185	−	0.00515565i
$763$	12.0018	−	20.8726i	0.434493	−	0.755641i
$764$	1.40090	−	0.455180i	0.0506828	−	0.0164679i

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)

\(f(q)\)	\(=\)	\(q+(0.000898858 + 0.0171512i) q^{2} +(0.879015 + 0.711812i) q^{3} +(1.98875 - 0.209026i) q^{4} +(1.43263 + 1.71685i) q^{5} +(-0.0114183 + 0.0157160i) q^{6} +(-2.51481 + 0.822022i) q^{7} +(0.0107461 + 0.0678483i) q^{8} +(-0.357745 - 1.68306i) q^{9} +O(q^{10})\)	\(q+(0.000898858 + 0.0171512i) q^{2} +(0.879015 + 0.711812i) q^{3} +(1.98875 - 0.209026i) q^{4} +(1.43263 + 1.71685i) q^{5} +(-0.0114183 + 0.0157160i) q^{6} +(-2.51481 + 0.822022i) q^{7} +(0.0107461 + 0.0678483i) q^{8} +(-0.357745 - 1.68306i) q^{9} +(-0.0281584 + 0.0261145i) q^{10} +(-4.96090 - 1.05447i) q^{11} +(1.89693 + 1.23188i) q^{12} +(0.145799 + 0.286147i) q^{13} +(-0.0163592 - 0.0423932i) q^{14} +(0.0372227 + 2.52890i) q^{15} +(3.91086 - 0.831279i) q^{16} +(3.48884 + 1.33924i) q^{17} +(0.0285449 - 0.00764859i) q^{18} +(0.698358 - 6.64443i) q^{19} +(3.20800 + 3.11494i) q^{20} +(-2.79568 - 1.06750i) q^{21} +(0.0136263 - 0.0860334i) q^{22} +(-3.41354 + 0.178896i) q^{23} +(-0.0388492 + 0.0672888i) q^{24} +(-0.895167 + 4.91922i) q^{25} +(-0.00477673 + 0.00275784i) q^{26} +(2.42406 - 4.75748i) q^{27} +(-4.82951 + 2.16046i) q^{28} +(1.99592 + 2.74715i) q^{29} +(-0.0433403 + 0.00291154i) q^{30} +(0.305449 + 0.686049i) q^{31} +(0.0533314 + 0.199035i) q^{32} +(-3.61012 - 4.45813i) q^{33} +(-0.0198337 + 0.0610417i) q^{34} +(-5.01408 - 3.13991i) q^{35} +(-1.06327 - 3.27240i) q^{36} +(1.79507 - 2.76416i) q^{37} +(0.114588 + 0.00600530i) q^{38} +(-0.0755233 + 0.355309i) q^{39} +(-0.101090 + 0.115651i) q^{40} +(-7.88534 - 2.56210i) q^{41} +(0.0157961 - 0.0489089i) q^{42} +(-3.99562 - 3.99562i) q^{43} +(-10.0864 - 1.06012i) q^{44} +(2.37705 - 3.02538i) q^{45} +(-0.00613657 - 0.0583856i) q^{46} +(2.25590 + 5.87681i) 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} +(0.349771 + 0.538600i) q^{52} +(-7.10798 + 8.77763i) q^{53} +(0.0837755 + 0.0372993i) q^{54} +(-5.29674 - 10.0278i) q^{55} +(-0.0827972 - 0.161792i) q^{56} +(5.34345 - 5.34345i) q^{57} +(-0.0453229 + 0.0367018i) q^{58} +(6.39870 + 7.10647i) q^{59} +(0.602633 + 5.02157i) q^{60} +(-2.03745 - 1.83453i) q^{61} +(-0.0114920 + 0.00585548i) q^{62} +(2.28317 + 3.93850i) q^{63} +(7.60172 - 2.46995i) q^{64} +(-0.282397 + 0.660258i) q^{65} +(0.0732173 - 0.0659252i) q^{66} +(-2.33982 + 6.09544i) q^{67} +(7.21837 + 1.93416i) q^{68} +(-3.12789 - 2.27255i) q^{69} +(0.0493464 - 0.0888199i) q^{70} +(-3.66851 + 2.66533i) q^{71} +(0.110348 - 0.0423587i) q^{72} +(-8.47376 + 5.50292i) q^{73} +(0.0490223 + 0.0283030i) q^{74} +(-4.28842 + 3.68687i) q^{75} -13.3601i q^{76} +(13.3425 - 1.42617i) q^{77} +(-0.00616188 - 0.000975946i) q^{78} +(3.33735 - 7.49580i) q^{79} +(7.02998 + 5.52346i) q^{80} +(0.801517 - 0.356859i) q^{81} +(0.0368554 - 0.137546i) q^{82} +(1.28282 - 0.203179i) q^{83} +(-5.78305 - 1.53863i) q^{84} +(2.69893 + 7.90846i) q^{85} +(0.0649383 - 0.0721212i) q^{86} +(-0.201010 + 3.83550i) q^{87} +(0.0182337 - 0.347920i) q^{88} +(-0.663356 + 0.736732i) q^{89} +(0.0540257 + 0.0380499i) q^{90} +(-0.601877 - 0.599756i) q^{91} +(-6.75128 + 1.06930i) q^{92} +(-0.219844 + 0.820470i) q^{93} +(-0.0987668 + 0.0439738i) q^{94} +(12.4080 - 8.32000i) q^{95} +(-0.0947968 + 0.212917i) q^{96} +(12.2690 + 1.94322i) q^{97} +(0.0759884 + 0.0931634i) 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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