LMFDB - Embedded newform 225.2.q.a.196.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			196.27
Character	$\chi$	$=$	225.196
Dual form			225.2.q.a.31.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.69452 + 1.88195i) q^{2} +(-1.49464 - 0.875245i) q^{3} +(-0.461298 + 4.38896i) q^{4} +(-2.12223 + 0.704374i) q^{5} +(-0.885523 - 4.29596i) q^{6} +(-1.03406 + 1.79105i) q^{7} +(-4.94396 + 3.59200i) q^{8} +(1.46789 + 2.61635i) q^{9} +O(q^{10})$	\(q+(1.69452 + 1.88195i) q^{2} +(-1.49464 - 0.875245i) q^{3} +(-0.461298 + 4.38896i) q^{4} +(-2.12223 + 0.704374i) q^{5} +(-0.885523 - 4.29596i) q^{6} +(-1.03406 + 1.79105i) q^{7} +(-4.94396 + 3.59200i) q^{8} +(1.46789 + 2.61635i) q^{9} +(-4.92175 - 2.80036i) q^{10} +(1.63896 + 1.82025i) q^{11} +(4.53089 - 6.15617i) q^{12} +(-1.19441 + 1.32652i) q^{13} +(-5.12291 + 1.08891i) q^{14} +(3.78847 + 0.804686i) q^{15} +(-6.50420 - 1.38251i) q^{16} +(3.67466 - 2.66979i) q^{17} +(-2.43648 + 7.19596i) q^{18} +(5.85004 - 4.25031i) q^{19} +(-2.11249 - 9.63931i) q^{20} +(3.11316 - 1.77192i) q^{21} +(-0.648378 + 6.16890i) q^{22} +(-2.31553 + 0.492181i) q^{23} +(10.5333 - 1.04156i) q^{24} +(4.00772 - 2.98968i) q^{25} -4.52040 q^{26} +(0.0959772 - 5.19527i) q^{27} +(-7.38384 - 5.36467i) q^{28} +(-7.47301 + 3.32720i) q^{29} +(4.90524 + 8.49327i) q^{30} +(6.20029 + 2.76055i) q^{31} +(-2.30859 - 3.99860i) q^{32} +(-0.856491 - 4.15511i) q^{33} +(11.2512 + 2.39152i) q^{34} +(0.932951 - 4.52939i) q^{35} +(-12.1602 + 5.23561i) q^{36} +(1.53985 + 4.73917i) q^{37} +(17.9119 + 3.80729i) q^{38} +(2.94624 - 0.937275i) q^{39} +(7.96211 - 11.1054i) q^{40} +(-3.20347 + 3.55781i) q^{41} +(8.60997 + 2.85628i) q^{42} +(4.14034 - 7.17127i) q^{43} +(-8.74507 + 6.35367i) q^{44} +(-4.95809 - 4.51855i) q^{45} +(-4.84997 - 3.52371i) q^{46} +(-9.25434 + 4.12030i) q^{47} +(8.51140 + 7.75912i) q^{48} +(1.36143 + 2.35806i) q^{49} +(12.4176 + 2.47626i) q^{50} +(-7.82901 + 0.774155i) q^{51} +(-5.27108 - 5.85413i) q^{52} +(-2.52356 - 1.83348i) q^{53} +(9.93988 - 8.62285i) q^{54} +(-4.76039 - 2.70855i) q^{55} +(-1.32108 - 12.5692i) q^{56} +(-12.4638 + 1.23245i) q^{57} +(-18.9248 - 8.42585i) q^{58} +(6.99016 - 7.76336i) q^{59} +(-5.27935 + 16.2562i) q^{60} +(-1.76446 - 1.95963i) q^{61} +(5.31128 + 16.3465i) q^{62} +(-6.20391 - 0.0764024i) q^{63} +(-0.496397 + 1.52775i) q^{64} +(1.60044 - 3.65649i) q^{65} +(6.36839 - 8.65279i) q^{66} +(-1.48939 - 0.663118i) q^{67} +(10.0225 + 17.3595i) q^{68} +(3.89166 + 1.29102i) q^{69} +(10.1050 - 5.91936i) q^{70} +(8.24169 + 5.98794i) q^{71} +(-16.6551 - 7.66247i) q^{72} +(-0.608028 + 1.87132i) q^{73} +(-6.30959 + 10.9285i) q^{74} +(-8.60680 + 0.960767i) q^{75} +(15.9558 + 27.6363i) q^{76} +(-4.95496 + 1.05321i) q^{77} +(6.75636 + 3.95645i) q^{78} +(13.6290 - 6.06801i) q^{79} +(14.7772 - 1.64738i) q^{80} +(-4.69058 + 7.68104i) q^{81} -12.1240 q^{82} +(-0.424422 - 4.03811i) q^{83} +(6.34077 + 14.4809i) q^{84} +(-5.91793 + 8.25424i) q^{85} +(20.5119 - 4.35993i) q^{86} +(14.0816 + 1.56775i) q^{87} +(-14.6413 - 3.11211i) q^{88} +(0.105993 - 0.326212i) q^{89} +(0.102122 - 16.9877i) q^{90} +(-1.14078 - 3.51095i) q^{91} +(-1.09201 - 10.3898i) q^{92} +(-6.85104 - 9.55279i) q^{93} +(-23.4358 - 10.4343i) q^{94} +(-9.42133 + 13.1407i) q^{95} +(-0.0492408 + 7.99705i) q^{96} +(-10.0640 + 4.48076i) q^{97} +(-2.13079 + 6.55791i) q^{98} +(-2.35660 + 6.96004i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.69452	+	1.88195i	1.19821	+	1.33074i	0.930080	+	0.367358i	$0.119737\pi$
$2$	1.69452	+	1.88195i	1.19821	+	1.33074i	0.268125	+	0.963384i	$0.413596\pi$
$3$	−1.49464	−	0.875245i	−0.862930	−	0.505323i
$3$	−1.49464	−	0.875245i	−0.862930	−	0.505323i
$4$	−0.461298	+	4.38896i	−0.230649	+	2.19448i
$5$	−2.12223	+	0.704374i	−0.949090	+	0.315005i
$5$	−2.12223	+	0.704374i	−0.949090	+	0.315005i
$6$	−0.885523	−	4.29596i	−0.361513	−	1.75382i
$7$	−1.03406	+	1.79105i	−0.390839	+	0.676953i	−0.992560	−	0.121753i	$-0.961148\pi$
$7$	−1.03406	+	1.79105i	−0.390839	+	0.676953i	0.601721	+	0.798706i	$0.294482\pi$
$8$	−4.94396	+	3.59200i	−1.74795	+	1.26996i
$9$	1.46789	+	2.61635i	0.489298	+	0.872117i
$10$	−4.92175	−	2.80036i	−1.55640	−	0.885552i
$11$	1.63896	+	1.82025i	0.494166	+	0.548827i	0.937707	−	0.347427i	$-0.112945\pi$
$11$	1.63896	+	1.82025i	0.494166	+	0.548827i	−0.443541	+	0.896254i	$0.646278\pi$
$12$	4.53089	−	6.15617i	1.30796	−	1.77713i
$13$	−1.19441	+	1.32652i	−0.331269	+	0.367911i	−0.885651	−	0.464351i	$-0.846288\pi$
$13$	−1.19441	+	1.32652i	−0.331269	+	0.367911i	0.554383	+	0.832262i	$0.312954\pi$
$14$	−5.12291	+	1.08891i	−1.36916	+	0.291023i
$15$	3.78847	+	0.804686i	0.978178	+	0.207769i
$16$	−6.50420	−	1.38251i	−1.62605	−	0.345628i
$17$	3.67466	−	2.66979i	0.891235	−	0.647520i	−0.0449649	−	0.998989i	$-0.514318\pi$
$17$	3.67466	−	2.66979i	0.891235	−	0.647520i	0.936200	+	0.351469i	$0.114318\pi$
$18$	−2.43648	+	7.19596i	−0.574283	+	1.69610i
$19$	5.85004	−	4.25031i	1.34209	−	0.975087i	0.342728	−	0.939435i	$-0.388649\pi$
$19$	5.85004	−	4.25031i	1.34209	−	0.975087i	0.999364	−	0.0356524i	$-0.0113509\pi$
$20$	−2.11249	−	9.63931i	−0.472367	−	2.15542i
$21$	3.11316	−	1.77192i	0.679347	−	0.386664i
$22$	−0.648378	+	6.16890i	−0.138235	+	1.31521i
$23$	−2.31553	+	0.492181i	−0.482821	+	0.102627i	−0.442891	−	0.896576i	$-0.646047\pi$
$23$	−2.31553	+	0.492181i	−0.482821	+	0.102627i	−0.0399305	+	0.999202i	$0.512714\pi$
$24$	10.5333	−	1.04156i	2.15010	−	0.212608i
$25$	4.00772	−	2.98968i	0.801543	−	0.597937i
$26$	−4.52040			−0.886523
$27$	0.0959772	−	5.19527i	0.0184708	−	0.999829i
$28$	−7.38384	−	5.36467i	−1.39541	−	1.01383i
$29$	−7.47301	+	3.32720i	−1.38770	+	0.617845i	−0.958429	−	0.285330i	$-0.907897\pi$
$29$	−7.47301	+	3.32720i	−1.38770	+	0.617845i	−0.429273	+	0.903175i	$0.641230\pi$
$30$	4.90524	+	8.49327i	0.895571	+	1.55065i
$31$	6.20029	+	2.76055i	1.11361	+	0.495809i	0.879259	−	0.476344i	$-0.158038\pi$
$31$	6.20029	+	2.76055i	1.11361	+	0.495809i	0.234346	+	0.972153i	$0.424705\pi$
$32$	−2.30859	−	3.99860i	−0.408105	−	0.706859i
$33$	−0.856491	−	4.15511i	−0.149096	−	0.723313i
$34$	11.2512	+	2.39152i	1.92956	+	0.410141i
$35$	0.932951	−	4.52939i	0.157698	−	0.765606i
$36$	−12.1602	+	5.23561i	−2.02670	+	0.872601i
$37$	1.53985	+	4.73917i	0.253150	+	0.779115i	0.994189	+	0.107653i	$0.0343334\pi$
$37$	1.53985	+	4.73917i	0.253150	+	0.779115i	−0.741039	+	0.671462i	$0.765667\pi$
$38$	17.9119	+	3.80729i	2.90569	+	0.617624i
$39$	2.94624	−	0.937275i	0.471776	−	0.150084i
$40$	7.96211	−	11.1054i	1.25892	−	1.75592i
$41$	−3.20347	+	3.55781i	−0.500297	+	0.555636i	−0.939410	−	0.342796i	$-0.888626\pi$
$41$	−3.20347	+	3.55781i	−0.500297	+	0.555636i	0.439113	+	0.898432i	$0.355293\pi$
$42$	8.60997	+	2.85628i	1.32855	+	0.440733i
$43$	4.14034	−	7.17127i	0.631395	−	1.09361i	−0.355871	−	0.934535i	$-0.615816\pi$
$43$	4.14034	−	7.17127i	0.631395	−	1.09361i	0.987267	−	0.159074i	$-0.0508508\pi$
$44$	−8.74507	+	6.35367i	−1.31837	+	0.957851i
$45$	−4.95809	−	4.51855i	−0.739109	−	0.673586i
$46$	−4.84997	−	3.52371i	−0.715088	−	0.519542i
$47$	−9.25434	+	4.12030i	−1.34988	+	0.601007i	−0.949045	−	0.315141i	$-0.897948\pi$
$47$	−9.25434	+	4.12030i	−1.34988	+	0.601007i	−0.400839	+	0.916148i	$0.631281\pi$
$48$	8.51140	+	7.75912i	1.22851	+	1.11993i
$49$	1.36143	+	2.35806i	0.194489	+	0.336866i
$50$	12.4176	+	2.47626i	1.75611	+	0.350196i
$51$	−7.82901	+	0.774155i	−1.09628	+	0.108403i
$52$	−5.27108	−	5.85413i	−0.730967	−	0.811821i
$53$	−2.52356	−	1.83348i	−0.346638	−	0.251847i	0.400819	−	0.916157i	$-0.368726\pi$
$53$	−2.52356	−	1.83348i	−0.346638	−	0.251847i	−0.747457	+	0.664310i	$0.768726\pi$
$54$	9.93988	−	8.62285i	1.35265	−	1.17342i
$55$	−4.76039	−	2.70855i	−0.641891	−	0.365221i
$56$	−1.32108	−	12.5692i	−0.176537	−	1.67963i
$57$	−12.4638	+	1.23245i	−1.65087	+	0.163242i
$58$	−18.9248	−	8.42585i	−2.48494	−	1.10637i
$59$	6.99016	−	7.76336i	0.910041	−	1.01070i	−0.0898499	−	0.995955i	$-0.528639\pi$
$59$	6.99016	−	7.76336i	0.910041	−	1.01070i	0.999891	−	0.0147480i	$-0.00469459\pi$
$60$	−5.27935	+	16.2562i	−0.681561	+	2.09867i
$61$	−1.76446	−	1.95963i	−0.225916	−	0.250905i	0.619521	−	0.784980i	$-0.287327\pi$
$61$	−1.76446	−	1.95963i	−0.225916	−	0.250905i	−0.845437	+	0.534075i	$0.820660\pi$
$62$	5.31128	+	16.3465i	0.674534	+	2.07600i
$63$	−6.20391	−	0.0764024i	−0.781619	−	0.00962580i
$64$	−0.496397	+	1.52775i	−0.0620496	+	0.190969i
$65$	1.60044	−	3.65649i	0.198510	−	0.453532i
$66$	6.36839	−	8.65279i	0.783895	−	1.06509i
$67$	−1.48939	−	0.663118i	−0.181958	−	0.0810127i	0.313736	−	0.949510i	$-0.398419\pi$
$67$	−1.48939	−	0.663118i	−0.181958	−	0.0810127i	−0.495693	+	0.868498i	$0.665086\pi$
$68$	10.0225	+	17.3595i	1.21541	+	2.10515i
$69$	3.89166	+	1.29102i	0.468501	+	0.155421i
$70$	10.1050	−	5.91936i	1.20778	−	0.707498i
$71$	8.24169	+	5.98794i	0.978109	+	0.710638i	0.957285	−	0.289145i	$-0.0933711\pi$
$71$	8.24169	+	5.98794i	0.978109	+	0.710638i	0.0208238	+	0.999783i	$0.493371\pi$
$72$	−16.6551	−	7.66247i	−1.96283	−	0.903030i
$73$	−0.608028	+	1.87132i	−0.0711643	+	0.219021i	−0.980313	−	0.197451i	$-0.936734\pi$
$73$	−0.608028	+	1.87132i	−0.0711643	+	0.219021i	0.909148	+	0.416472i	$0.136734\pi$
$74$	−6.30959	+	10.9285i	−0.733475	+	1.27042i
$75$	−8.60680	+	0.960767i	−0.993827	+	0.110940i
$76$	15.9558	+	27.6363i	1.83026	+	3.17010i
$77$	−4.95496	+	1.05321i	−0.564670	+	0.120024i
$78$	6.75636	+	3.95645i	0.765007	+	0.447980i
$79$	13.6290	−	6.06801i	1.53338	−	0.682704i	0.545525	−	0.838094i	$-0.316330\pi$
$79$	13.6290	−	6.06801i	1.53338	−	0.682704i	0.987853	+	0.155390i	$0.0496635\pi$
$80$	14.7772	−	1.64738i	1.65214	−	0.184183i
$81$	−4.69058	+	7.68104i	−0.521176	+	0.853449i
$82$	−12.1240			−1.33887
$83$	−0.424422	−	4.03811i	−0.0465864	−	0.443240i	−0.992808	−	0.119720i	$-0.961800\pi$
$83$	−0.424422	−	4.03811i	−0.0465864	−	0.443240i	0.946221	−	0.323520i	$-0.104866\pi$
$84$	6.34077	+	14.4809i	0.691835	+	1.58000i
$85$	−5.91793	+	8.25424i	−0.641890	+	0.895298i
$86$	20.5119	−	4.35993i	2.21185	−	0.470144i
$87$	14.0816	+	1.56775i	1.50970	+	0.168081i
$88$	−14.6413	−	3.11211i	−1.56077	−	0.331752i
$89$	0.105993	−	0.326212i	0.0112352	−	0.0345784i	−0.945282	−	0.326255i	$-0.894213\pi$
$89$	0.105993	−	0.326212i	0.0112352	−	0.0345784i	0.956517	+	0.291677i	$0.0942131\pi$
$90$	0.102122	−	16.9877i	0.0107646	−	1.79066i
$91$	−1.14078	−	3.51095i	−0.119586	−	0.368048i
$92$	−1.09201	−	10.3898i	−0.113850	−	1.08321i
$93$	−6.85104	−	9.55279i	−0.710420	−	0.990579i
$94$	−23.4358	−	10.4343i	−2.41722	−	1.07622i
$95$	−9.42133	+	13.1407i	−0.966608	+	1.34821i
$96$	−0.0492408	+	7.99705i	−0.00502561	+	0.816195i
$97$	−10.0640	+	4.48076i	−1.02184	+	0.454953i	−0.848098	−	0.529839i	$-0.822252\pi$
$97$	−10.0640	+	4.48076i	−1.02184	+	0.454953i	−0.173742	+	0.984791i	$0.555586\pi$
$98$	−2.13079	+	6.55791i	−0.215243	+	0.662449i
$99$	−2.35660	+	6.96004i	−0.236847	+	0.699510i
$100$	11.2729	+	18.9688i	1.12729	+	1.89688i
$101$	6.38861	−	11.0654i	0.635691	−	1.10105i	−0.350677	−	0.936496i	$-0.614049\pi$
$101$	6.38861	−	11.0654i	0.635691	−	1.10105i	0.986368	−	0.164553i	$-0.0526180\pi$
$102$	−14.7233	−	13.4220i	−1.45783	−	1.32898i
$103$	0.959675	−	9.13070i	0.0945596	−	0.899674i	−0.839693	−	0.543062i	$-0.817265\pi$
$103$	0.959675	−	9.13070i	0.0945596	−	0.899674i	0.934252	−	0.356613i	$-0.116068\pi$
$104$	1.14023	−	10.8486i	0.111809	−	1.06379i
$105$	−5.35875	+	5.95324i	−0.522960	+	0.580977i
$106$	−0.825708	−	7.85609i	−0.0801999	−	0.763051i
$107$	0.980681			0.0948061			0.0474030	−	0.998876i	$-0.484905\pi$
$107$	0.980681			0.0948061			0.0474030	+	0.998876i	$0.484905\pi$
$108$	22.7575	+	2.81781i	2.18985	+	0.271144i
$109$	−2.74384	−	8.44467i	−0.262812	−	0.808853i	−0.992189	−	0.124741i	$-0.960190\pi$
$109$	−2.74384	−	8.44467i	−0.262812	−	0.808853i	0.729377	−	0.684112i	$-0.239810\pi$
$110$	−2.96920	−	13.5485i	−0.283103	−	1.29180i
$111$	1.84641	−	8.43110i	0.175254	−	0.800244i
$112$	9.20190	−	10.2197i	0.869498	−	0.965675i
$113$	4.53863	−	5.04065i	0.426958	−	0.474185i	−0.490830	−	0.871255i	$-0.663306\pi$
$113$	4.53863	−	5.04065i	0.426958	−	0.474185i	0.917788	+	0.397070i	$0.129973\pi$
$114$	−23.4395	−	21.3678i	−2.19531	−	2.00128i
$115$	4.56740	−	2.67552i	0.425913	−	0.249493i
$116$	−11.1557	−	34.3336i	−1.03578	−	3.18779i
$117$	−5.22391	−	1.17779i	−0.482951	−	0.108887i
$118$	26.4552			2.43540
$119$	0.981908	+	9.34223i	0.0900113	+	0.856401i
$120$	−21.6205	+	9.62983i	−1.97367	+	0.879079i
$121$	0.522693	−	4.97309i	0.0475175	−	0.452099i
$122$	0.698024	−	6.64126i	0.0631962	−	0.601271i
$123$	7.90198	−	2.51382i	0.712497	−	0.226664i
$124$	−14.9761	+	25.9394i	−1.34490	+	2.32943i
$125$	−6.39944	+	9.16773i	−0.572383	+	0.819986i
$126$	−10.3689	−	11.8049i	−0.923731	−	1.05167i
$127$	3.08193	−	9.48521i	0.273477	−	0.841676i	−0.716141	−	0.697955i	$-0.754093\pi$
$127$	3.08193	−	9.48521i	0.273477	−	0.841676i	0.989618	−	0.143721i	$-0.0459067\pi$
$128$	−12.1523	+	5.41057i	−1.07412	+	0.478231i
$129$	−12.4649	+	7.09466i	−1.09748	+	0.624650i
$130$	9.59332	−	3.18405i	0.841390	−	0.279259i
$131$	−12.5686	−	5.59591i	−1.09813	−	0.488917i	−0.223986	−	0.974592i	$-0.571907\pi$
$131$	−12.5686	−	5.59591i	−1.09813	−	0.488917i	−0.874139	+	0.485675i	$0.838574\pi$
$132$	18.6317	−	1.84236i	1.62168	−	0.160357i
$133$	1.56320	+	14.8728i	0.135546	+	1.28964i
$134$	−1.27584	−	3.92662i	−0.110215	−	0.339208i
$135$	3.45572	+	11.0932i	0.297421	+	0.954746i
$136$	−8.57746	+	26.3987i	−0.735511	+	2.26367i
$137$	8.34276	+	1.77331i	0.712770	+	0.151504i	0.550005	−	0.835161i	$-0.314626\pi$
$137$	8.34276	+	1.77331i	0.712770	+	0.151504i	0.162764	+	0.986665i	$0.447959\pi$
$138$	4.16484	+	9.51158i	0.354535	+	0.809679i
$139$	9.12603	−	1.93980i	0.774060	−	0.164532i	0.196086	−	0.980587i	$-0.437177\pi$
$139$	9.12603	−	1.93980i	0.774060	−	0.164532i	0.577974	+	0.816055i	$0.303843\pi$
$140$	19.4489	+	6.18409i	1.64374	+	0.522651i
$141$	17.4382	+	1.94145i	1.46856	+	0.163500i
$142$	2.69667	+	25.6571i	0.226300	+	2.15310i
$143$	−4.37219			−0.365621
$144$	−5.93034	−	19.0466i	−0.494195	−	1.58722i
$145$	13.5158	−	12.3249i	1.12243	−	1.02352i
$146$	−4.55205	+	2.02670i	−0.376730	+	0.167731i
$147$	0.0290383	−	4.71603i	0.00239504	−	0.388971i
$148$	−21.5104	+	4.57217i	−1.76814	+	0.375830i
$149$	−3.47298	−	6.01538i	−0.284518	−	0.492799i	0.687974	−	0.725735i	$-0.258500\pi$
$149$	−3.47298	−	6.01538i	−0.284518	−	0.492799i	−0.972492	+	0.232936i	$0.925167\pi$
$150$	−16.3925	−	14.5695i	−1.33844	−	1.18960i
$151$	0.394205	−	0.682783i	0.0320800	−	0.0555641i	−0.849540	−	0.527525i	$-0.823120\pi$
$151$	0.394205	−	0.682783i	0.0320800	−	0.0555641i	0.881620	+	0.471961i	$0.156454\pi$
$152$	−13.6553	+	42.0267i	−1.10759	+	3.40881i
$153$	12.3791	+	5.69522i	1.00079	+	0.460431i
$154$	−10.3783	−	7.54031i	−0.836311	−	0.607616i
$155$	−15.1029	−	1.49119i	−1.21309	−	0.119776i
$156$	2.75457	+	13.3633i	0.220542	+	1.06992i
$157$	−1.94393	−	3.36698i	−0.155142	−	0.268714i	0.777969	−	0.628303i	$-0.216250\pi$
$157$	−1.94393	−	3.36698i	−0.155142	−	0.268714i	−0.933111	+	0.359589i	$0.882917\pi$
$158$	34.5142	+	15.3667i	2.74580	+	1.22251i
$159$	2.16708	+	4.94912i	0.171860	+	0.392491i
$160$	7.71587	+	6.85983i	0.609993	+	0.542318i
$161$	1.51288	−	4.65617i	0.119232	−	0.366958i
$162$	−22.4036	+	4.18822i	−1.76020	+	0.329057i
$163$	2.59370	+	7.98258i	0.203154	+	0.625244i	0.999784	+	0.0207767i	$0.00661392\pi$
$163$	2.59370	+	7.98258i	0.203154	+	0.625244i	−0.796630	+	0.604467i	$0.793386\pi$
$164$	−14.1373	−	15.7011i	−1.10394	−	1.22605i
$165$	4.74442	+	8.21482i	0.369353	+	0.639523i
$166$	6.88033	−	7.64139i	0.534018	−	0.593087i
$167$	9.87343	+	4.39594i	0.764029	+	0.340168i	0.751482	−	0.659754i	$-0.229339\pi$
$167$	9.87343	+	4.39594i	0.764029	+	0.340168i	0.0125472	+	0.999921i	$0.496006\pi$
$168$	−9.02662	+	19.9427i	−0.696419	+	1.53862i
$169$	1.02581	+	9.75997i	0.0789088	+	0.750767i
$170$	−25.5621	+	2.84970i	−1.96053	+	0.218562i
$171$	19.7075	+	9.06677i	1.50707	+	0.693353i
$172$	29.5645	+	21.4799i	2.25427	+	1.63783i
$173$	−11.0146	−	12.2329i	−0.837422	−	0.930051i	0.160957	−	0.986961i	$-0.448542\pi$
$173$	−11.0146	−	12.2329i	−0.837422	−	0.930051i	−0.998379	+	0.0569100i	$0.981875\pi$
$174$	20.9110	+	29.1574i	1.58526	+	2.21042i
$175$	1.21044	+	10.2695i	0.0915009	+	0.776305i
$176$	−8.14362	−	14.1052i	−0.613849	−	1.06322i
$177$	−17.2426	+	5.48532i	−1.29603	+	0.412302i
$178$	0.793522	−	0.353299i	0.0594770	−	0.0264809i
$179$	−0.422707	−	0.307115i	−0.0315946	−	0.0229548i	0.571876	−	0.820340i	$-0.306216\pi$
$179$	−0.422707	−	0.307115i	−0.0315946	−	0.0229548i	−0.603471	+	0.797385i	$0.706216\pi$
$180$	22.1189	−	19.6765i	1.64865	−	1.46660i
$181$	−18.6716	+	13.5657i	−1.38785	+	1.00833i	−0.391756	+	0.920069i	$0.628132\pi$
$181$	−18.6716	+	13.5657i	−1.38785	+	1.00833i	−0.996097	+	0.0882646i	$0.971868\pi$
$182$	4.67438	−	8.09626i	0.346488	−	0.600134i
$183$	0.922074	+	4.47328i	0.0681616	+	0.330674i
$184$	9.67997	−	10.7507i	0.713617	−	0.792552i
$185$	−6.60606	−	8.97298i	−0.485687	−	0.659706i
$186$	6.36869	−	29.0807i	0.466975	−	2.13230i
$187$	10.8823	+	2.31311i	0.795794	+	0.169151i
$188$	−13.8148	−	42.5176i	−1.00755	−	3.10092i
$189$	9.20574	+	5.54413i	0.669619	+	0.403276i
$190$	−40.6949	+	4.53672i	−2.95232	+	0.329128i
$191$	0.982006	+	0.208732i	0.0710555	+	0.0151033i	0.243302	−	0.969951i	$-0.421769\pi$
$191$	0.982006	+	0.208732i	0.0710555	+	0.0151033i	−0.172247	+	0.985054i	$0.555103\pi$
$192$	2.07909	−	1.84897i	0.150046	−	0.133438i
$193$	6.92614	+	11.9964i	0.498554	+	0.863521i	0.999999	−	0.00166856i	$-0.000531120\pi$
$193$	6.92614	+	11.9964i	0.498554	+	0.863521i	−0.501444	+	0.865190i	$0.667198\pi$
$194$	−25.4861	−	11.3472i	−1.82980	−	0.814679i
$195$	−5.59240	+	4.06436i	−0.400480	+	0.291055i
$196$	−10.9775	+	4.88748i	−0.784104	+	0.349105i
$197$	6.40803	+	4.65571i	0.456553	+	0.331705i	0.792178	−	0.610291i	$-0.208947\pi$
$197$	6.40803	+	4.65571i	0.456553	+	0.331705i	−0.335624	+	0.941996i	$0.608947\pi$
$198$	−17.0918	+	7.35890i	−1.21466	+	0.522974i
$199$	14.6161			1.03611			0.518053	−	0.855348i	$-0.326657\pi$
$199$	14.6161			1.03611			0.518053	+	0.855348i	$0.326657\pi$
$200$	−9.07505	+	29.1766i	−0.641703	+	2.06310i
$201$	1.64571	+	2.29470i	0.116079	+	0.161856i
$202$	31.6502	−	6.72746i	2.22690	−	0.473342i
$203$	1.76839	−	16.8251i	0.124116	−	1.18089i
$204$	0.213773	−	34.7183i	0.0149671	−	2.43077i
$205$	4.29246	−	9.80692i	0.299799	−	0.684945i
$206$	18.8097	−	13.6661i	1.31054	−	0.952160i
$207$	−4.68667	−	5.33577i	−0.325746	−	0.370861i
$208$	9.60259	−	6.97669i	0.665820	−	0.483746i
$209$	17.3246	+	3.68246i	1.19837	+	0.254721i
$210$	−20.2842	+	0.00295802i	−1.39974	+	0.000204123i
$211$	−13.0287	+	2.76934i	−0.896933	+	0.190649i	−0.633238	−	0.773957i	$-0.718275\pi$
$211$	−13.0287	+	2.76934i	−0.896933	+	0.190649i	−0.263695	+	0.964606i	$0.584941\pi$
$212$	9.21118	−	10.2300i	0.632626	−	0.702603i
$213$	−7.07744	−	16.1633i	−0.484938	−	1.10749i
$214$	1.66178	+	1.84560i	0.113597	+	0.126162i
$215$	−3.73549	+	18.1354i	−0.254758	+	1.23683i
$216$	18.1869	+	26.0299i	1.23746	+	1.77111i
$217$	−11.3558	+	8.25045i	−0.770880	+	0.560077i
$218$	11.2430	−	19.4734i	0.761471	−	1.31891i
$219$	2.54664	−	2.26477i	0.172086	−	0.153039i
$220$	14.0837	−	19.6437i	0.949522	−	1.32438i
$221$	−0.847490	+	8.06333i	−0.0570084	+	0.542398i
$222$	18.9957	−	10.8118i	1.27491	−	0.725639i
$223$	2.44141	+	2.71146i	0.163489	+	0.181573i	0.819323	−	0.573332i	$-0.194350\pi$
$223$	2.44141	+	2.71146i	0.163489	+	0.181573i	−0.655834	+	0.754905i	$0.727683\pi$
$224$	9.54893			0.638014
$225$	13.7050	+	6.09705i	0.913664	+	0.406470i
$226$	17.1771			1.14260
$227$	10.5152	+	11.6783i	0.697915	+	0.775114i	0.983043	−	0.183376i	$-0.0587026\pi$
$227$	10.5152	+	11.6783i	0.697915	+	0.775114i	−0.285127	+	0.958490i	$0.592036\pi$
$228$	0.340327	−	55.2715i	0.0225387	−	3.66045i
$229$	−0.627978	+	5.97482i	−0.0414980	+	0.394827i	0.953983	+	0.299862i	$0.0969406\pi$
$229$	−0.627978	+	5.97482i	−0.0414980	+	0.394827i	−0.995481	+	0.0949650i	$0.969726\pi$
$230$	12.7747	+	4.06193i	0.842342	+	0.267835i
$231$	8.32769	+	2.76263i	0.547921	+	0.181768i
$232$	24.9950	−	43.2926i	1.64100	−	2.84230i
$233$	−0.484321	+	0.351880i	−0.0317289	+	0.0230524i	−0.603537	−	0.797335i	$-0.706242\pi$
$233$	−0.484321	+	0.351880i	−0.0317289	+	0.0230524i	0.571808	+	0.820388i	$0.306242\pi$
$234$	−6.63546	−	11.8269i	−0.433773	−	0.773151i
$235$	16.7376	−	15.2627i	1.09184	−	0.995630i
$236$	30.8485	+	34.2608i	2.00807	+	2.23019i
$237$	−25.6814	−	2.85920i	−1.66818	−	0.185725i
$238$	−15.9178	+	17.6785i	−1.03180	+	1.14593i
$239$	−1.14937	+	0.244307i	−0.0743469	+	0.0158029i	−0.244935	−	0.969540i	$-0.578767\pi$
$239$	−1.14937	+	0.244307i	−0.0743469	+	0.0158029i	0.170588	+	0.985342i	$0.445433\pi$
$240$	−23.5285	−	10.4714i	−1.51876	−	0.675928i
$241$	−17.5785	−	3.73642i	−1.13233	−	0.240684i	−0.396621	−	0.917982i	$-0.629817\pi$
$241$	−17.5785	−	3.73642i	−1.13233	−	0.240684i	−0.735709	+	0.677298i	$0.763151\pi$
$242$	10.2448	−	7.44331i	0.658563	−	0.478474i
$243$	13.7335	−	7.37498i	0.881006	−	0.473105i
$244$	9.41469	−	6.84017i	0.602714	−	0.437897i
$245$	−4.55021	−	4.04539i	−0.290702	−	0.258450i
$246$	18.1209	+	10.6114i	1.15535	+	0.676560i
$247$	−1.34920	+	12.8368i	−0.0858477	+	0.816787i
$248$	−40.5699	+	8.62339i	−2.57619	+	0.547586i
$249$	−2.89997	+	6.40699i	−0.183778	+	0.406026i
$250$	−28.0972	+	3.49144i	−1.77702	+	0.220818i
$251$	0.313172			0.0197673			0.00988364	−	0.999951i	$-0.496854\pi$
$251$	0.313172			0.0197673			0.00988364	+	0.999951i	$0.496854\pi$
$252$	3.19718	−	27.1935i	0.201403	−	1.71303i
$253$	−4.69096	−	3.40818i	−0.294918	−	0.214270i
$254$	23.0731	−	10.2728i	1.44773	−	0.644573i
$255$	16.0697	−	7.15748i	1.00632	−	0.448219i
$256$	−27.8398	−	12.3951i	−1.73999	−	0.774692i
$257$	1.48530	+	2.57262i	0.0926507	+	0.160476i	0.908626	−	0.417611i	$-0.137133\pi$
$257$	1.48530	+	2.57262i	0.0926507	+	0.160476i	−0.815975	+	0.578087i	$0.803799\pi$
$258$	−34.4739	−	11.4364i	−2.14625	−	0.711998i
$259$	−10.0804	−	2.14265i	−0.626365	−	0.133138i
$260$	15.3099	+	8.71099i	0.949482	+	0.540233i
$261$	−19.6747	−	14.6680i	−1.21783	−	0.907929i
$262$	−10.7665	−	33.1359i	−0.665158	−	2.04714i
$263$	7.94955	+	1.68973i	0.490190	+	0.104193i	0.446374	−	0.894847i	$-0.352715\pi$
$263$	7.94955	+	1.68973i	0.490190	+	0.104193i	0.0438160	+	0.999040i	$0.486048\pi$
$264$	19.1596	+	17.4662i	1.17919	+	1.07497i
$265$	6.64704	+	2.11353i	0.408324	+	0.129833i
$266$	−25.3411	+	28.1441i	−1.55376	+	1.72563i
$267$	−0.443936	+	0.394800i	−0.0271685	+	0.0241614i
$268$	3.59745	−	6.23097i	0.219749	−	0.380617i
$269$	18.6230	−	13.5304i	1.13547	−	0.824965i	0.148986	−	0.988839i	$-0.452399\pi$
$269$	18.6230	−	13.5304i	1.13547	−	0.824965i	0.986481	+	0.163874i	$0.0523992\pi$
$270$	−15.0210	+	25.3010i	−0.914149	+	1.53977i
$271$	−18.3049	−	13.2993i	−1.11194	−	0.807874i	−0.128974	−	0.991648i	$-0.541169\pi$
$271$	−18.3049	−	13.2993i	−1.11194	−	0.807874i	−0.982969	+	0.183774i	$0.941169\pi$
$272$	−27.5917	+	12.2846i	−1.67299	+	0.744865i
$273$	−1.36789	+	6.24606i	−0.0827885	+	0.378029i
$274$	10.7997	+	18.7056i	0.652432	+	1.13005i
$275$	12.0105	+	2.39507i	0.724259	+	0.144428i
$276$	−7.46146	+	16.4848i	−0.449127	+	0.992268i
$277$	−6.92921	−	7.69566i	−0.416336	−	0.462388i	0.498100	−	0.867120i	$-0.334031\pi$
$277$	−6.92921	−	7.69566i	−0.416336	−	0.462388i	−0.914435	+	0.404732i	$0.867365\pi$
$278$	19.1148	+	13.8877i	1.14643	+	0.832931i
$279$	1.87880	+	20.2743i	0.112481	+	1.21379i
$280$	11.6571	+	25.7443i	0.696643	+	1.53851i
$281$	2.65920	+	25.3006i	0.158635	+	1.50931i	0.727060	+	0.686574i	$0.240886\pi$
$281$	2.65920	+	25.3006i	0.158635	+	1.50931i	−0.568425	+	0.822735i	$0.692447\pi$
$282$	25.8956	+	36.1076i	1.54206	+	2.15018i
$283$	−15.1378	−	6.73980i	−0.899851	−	0.400639i	−0.0959386	−	0.995387i	$-0.530585\pi$
$283$	−15.1378	−	6.73980i	−0.899851	−	0.400639i	−0.803912	+	0.594748i	$0.797252\pi$
$284$	−30.0827	+	33.4102i	−1.78508	+	1.98253i
$285$	25.5829	−	11.3947i	1.51540	−	0.674963i
$286$	−7.40876	−	8.22826i	−0.438089	−	0.486547i
$287$	−3.05963	−	9.41657i	−0.180604	−	0.555842i
$288$	7.07297	−	11.9096i	0.416779	−	0.701780i
$289$	1.12201	−	3.45318i	0.0660004	−	0.203128i
$290$	46.0977	+	4.55148i	2.70695	+	0.267272i
$291$	18.9637	+	2.11130i	1.11167	+	0.123767i
$292$	−7.93266	−	3.53185i	−0.464224	−	0.206686i
$293$	−6.06420	−	10.5035i	−0.354274	−	0.613621i	0.632719	−	0.774381i	$-0.281939\pi$
$293$	−6.06420	−	10.5035i	−0.354274	−	0.613621i	−0.986993	+	0.160760i	$0.948605\pi$
$294$	8.92455	−	7.93675i	0.520490	−	0.462880i
$295$	−9.36642	+	21.3993i	−0.545334	+	1.24592i
$296$	−24.6360	−	17.8991i	−1.43194	−	1.04037i
$297$	9.61400	−	8.34014i	0.557861	−	0.483944i
$298$	5.43564	−	16.7292i	0.314878	−	0.969095i
$299$	2.11279	−	3.65946i	0.122186	−	0.211632i
$300$	−0.246470	−	38.2181i	−0.0142299	−	2.20652i
$301$	8.56274	+	14.8311i	0.493548	+	0.854851i
$302$	1.95295	−	0.415113i	0.112380	−	0.0238871i
$303$	−19.2336	+	10.9472i	−1.10494	+	0.628899i
$304$	−43.9259	+	19.5571i	−2.51933	+	1.12168i
$305$	5.12490	+	2.91595i	0.293451	+	0.166967i
$306$	10.2585	+	32.9476i	0.586440	+	1.88349i
$307$	−11.7705			−0.671776			−0.335888	−	0.941902i	$-0.609036\pi$
$307$	−11.7705			−0.671776			−0.335888	+	0.941902i	$0.609036\pi$
$308$	−2.33678	−	22.2330i	−0.133150	−	1.26684i
$309$	−9.42596	+	12.8071i	−0.536224	+	0.728573i
$310$	−22.7858	−	30.9498i	−1.29414	−	1.75783i
$311$	−9.67624	+	2.05675i	−0.548689	+	0.116628i	−0.473911	−	0.880573i	$-0.657158\pi$
$311$	−9.67624	+	2.05675i	−0.548689	+	0.116628i	−0.0747782	+	0.997200i	$0.523825\pi$
$312$	−11.1994	+	15.2167i	−0.634041	+	0.861478i
$313$	33.6648	+	7.15567i	1.90285	+	0.404462i	0.999691	−	0.0248538i	$-0.00791202\pi$
$313$	33.6648	+	7.15567i	1.90285	+	0.404462i	0.903154	+	0.429316i	$0.141245\pi$
$314$	3.04248	−	9.36378i	0.171697	−	0.528429i
$315$	13.2199	−	4.20773i	0.744859	−	0.237079i
$316$	20.3452	+	62.6162i	1.14451	+	3.52243i
$317$	−2.32443	−	22.1155i	−0.130553	−	1.24213i	−0.842034	−	0.539425i	$-0.818642\pi$
$317$	−2.32443	−	22.1155i	−0.130553	−	1.24213i	0.711481	−	0.702706i	$-0.248025\pi$
$318$	−5.64187	+	12.4647i	−0.316380	+	0.698987i
$319$	−18.3043	−	8.14961i	−1.02485	−	0.456290i
$320$	−0.0226404	−	3.59189i	−0.00126564	−	0.200793i
$321$	−1.46576	−	0.858336i	−0.0818110	−	0.0479077i
$322$	11.3263	−	5.04280i	0.631190	−	0.281024i
$323$	10.1495	−	31.2368i	0.564731	−	1.73806i
$324$	−31.5481	−	24.1300i	−1.75267	−	1.34056i
$325$	−0.820957	+	8.88722i	−0.0455385	+	0.492974i
$326$	−10.6278	+	18.4078i	−0.588618	+	1.01952i
$327$	−3.29010	+	15.0233i	−0.181943	+	0.830789i
$328$	3.05817	−	29.0965i	0.168859	−	1.60659i
$329$	2.18991	−	20.8356i	0.120734	−	1.14871i
$330$	−7.42039	+	22.8489i	−0.408479	+	1.25779i
$331$	1.36800	+	13.0156i	0.0751920	+	0.715404i	0.965563	+	0.260169i	$0.0837781\pi$
$331$	1.36800	+	13.0156i	0.0751920	+	0.715404i	−0.890371	+	0.455235i	$0.849555\pi$
$332$	17.9189			0.983426
$333$	−10.1390	+	10.9854i	−0.555614	+	0.601995i
$334$	8.45777	+	26.0303i	0.462788	+	1.42432i
$335$	3.62790	+	0.358203i	0.198214	+	0.0195707i
$336$	−22.6983	+	7.22092i	−1.23829	+	0.393933i
$337$	9.72209	−	10.7975i	0.529596	−	0.588176i	−0.417680	−	0.908594i	$-0.637157\pi$
$337$	9.72209	−	10.7975i	0.529596	−	0.588176i	0.947276	+	0.320418i	$0.103823\pi$
$338$	−16.6295	+	18.4690i	−0.904528	+	1.00458i
$339$	−11.1954	+	3.56155i	−0.608051	+	0.193437i
$340$	−33.4976	−	29.7812i	−1.81666	−	1.61511i
$341$	5.13715	+	15.8105i	0.278192	+	0.856188i
$342$	16.3315	+	52.4525i	0.883108	+	2.83630i
$343$	−20.1081			−1.08573
$344$	5.28954	+	50.3266i	0.285193	+	2.71343i
$345$	−9.16835	+	0.00133701i	−0.493608	+	7.19822e-5i
$346$	4.35739	−	41.4578i	0.234255	−	2.22878i
$347$	−1.16703	+	11.1035i	−0.0626493	+	0.596068i	0.917490	+	0.397759i	$0.130212\pi$
$347$	−1.16703	+	11.1035i	−0.0626493	+	0.596068i	−0.980139	+	0.198310i	$0.936455\pi$
$348$	−13.3766	+	61.0802i	−0.717061	+	3.27424i
$349$	4.08628	−	7.07765i	0.218734	−	0.378858i	−0.735687	−	0.677321i	$-0.763141\pi$
$349$	4.08628	−	7.07765i	0.218734	−	0.378858i	0.954421	+	0.298463i	$0.0964740\pi$
$350$	−17.2757	+	19.6799i	−0.923424	+	1.05194i
$351$	6.77700	+	6.33257i	0.361730	+	0.338008i
$352$	3.49476	−	10.7558i	0.186272	−	0.573285i
$353$	−20.5995	+	9.17150i	−1.09640	+	0.488150i	−0.873566	−	0.486706i	$-0.838198\pi$
$353$	−20.5995	+	9.17150i	−1.09640	+	0.488150i	−0.222836	+	0.974856i	$0.571532\pi$
$354$	−39.5410	−	23.1548i	−2.10158	−	1.23066i
$355$	−21.7085	−	6.90255i	−1.15217	−	0.366349i
$356$	1.38284	+	0.615679i	0.0732903	+	0.0326309i
$357$	6.70914	−	14.8227i	0.355085	−	0.784499i
$358$	−0.138310	−	1.31593i	−0.00730989	−	0.0695489i
$359$	−7.75846	−	23.8781i	−0.409476	−	1.26024i	−0.917100	−	0.398658i	$-0.869476\pi$
$359$	−7.75846	−	23.8781i	−0.409476	−	1.26024i	0.507624	−	0.861579i	$-0.330524\pi$
$360$	40.7432	+	4.53008i	2.14736	+	0.238756i
$361$	10.2866	−	31.6589i	0.541400	−	1.66626i
$362$	−57.1695	−	12.1518i	−3.00476	−	0.638682i
$363$	−5.13391	+	6.97549i	−0.269460	+	0.366118i
$364$	15.9357	−	3.38723i	0.835256	−	0.177539i
$365$	−0.0277319	−	4.39965i	−0.00145155	−	0.230288i
$366$	−6.85602	+	9.31534i	−0.358370	+	0.486921i
$367$	0.674667	+	6.41903i	0.0352173	+	0.335071i	0.997918	+	0.0645007i	$0.0205455\pi$
$367$	0.674667	+	6.41903i	0.0352173	+	0.335071i	−0.962700	+	0.270570i	$0.912788\pi$
$368$	15.7411			0.820562
$369$	−14.0108	−	3.15891i	−0.729374	−	0.164446i
$370$	5.69263	−	27.6372i	0.295946	−	1.43679i
$371$	5.89338	−	2.62390i	0.305969	−	0.136226i
$372$	45.0872	−	25.6623i	2.33766	−	1.33053i
$373$	23.5755	−	5.01112i	1.22069	−	0.259466i	0.447875	−	0.894096i	$-0.352181\pi$
$373$	23.5755	−	5.01112i	1.22069	−	0.259466i	0.772816	+	0.634630i	$0.218848\pi$
$374$	14.0871	+	24.3996i	0.728428	+	1.26167i
$375$	17.5889	−	8.10137i	0.908285	−	0.418353i
$376$	30.9530	−	53.6121i	1.59628	−	2.76484i
$377$	4.51220	−	13.8871i	0.232390	−	0.715224i
$378$	5.16549	+	26.7194i	0.265684	+	1.37430i
$379$	−0.345496	−	0.251018i	−0.0177469	−	0.0128939i	0.578876	−	0.815415i	$-0.303491\pi$
$379$	−0.345496	−	0.251018i	−0.0177469	−	0.0128939i	−0.596623	+	0.802521i	$0.703491\pi$
$380$	−53.3282	−	47.4117i	−2.73568	−	2.43217i
$381$	−12.9083	+	11.4795i	−0.661310	+	0.588114i
$382$	1.27120	+	2.20179i	0.0650404	+	0.112653i
$383$	20.8402	+	9.27864i	1.06488	+	0.474117i	0.862953	−	0.505283i	$-0.168612\pi$
$383$	20.8402	+	9.27864i	1.06488	+	0.474117i	0.201930	+	0.979400i	$0.435279\pi$
$384$	22.8989	+	2.54942i	1.16856	+	0.130100i
$385$	9.77370	−	5.72529i	0.498114	−	0.291788i
$386$	−10.8402	+	33.3628i	−0.551753	+	1.69812i
$387$	24.8401	+	0.305911i	1.26270	+	0.0155503i
$388$	−15.0234	−	46.2373i	−0.762698	−	2.34734i
$389$	8.29913	+	9.21712i	0.420783	+	0.467327i	0.915846	−	0.401531i	$-0.131522\pi$
$389$	8.29913	+	9.21712i	0.420783	+	0.467327i	−0.495063	+	0.868857i	$0.664855\pi$
$390$	−17.1254	−	3.63750i	−0.867177	−	0.184192i
$391$	−7.19475	+	7.99058i	−0.363854	+	0.404101i
$392$	−15.2010	−	6.76791i	−0.767765	−	0.341831i
$393$	13.8878	+	19.3645i	0.700545	+	0.976809i
$394$	2.09670	+	19.9488i	0.105630	+	1.00501i
$395$	−24.6496	+	22.4776i	−1.24026	+	1.13097i
$396$	−29.4602	−	13.5537i	−1.48043	−	0.681098i
$397$	−2.26012	−	1.64207i	−0.113432	−	0.0824133i	0.529623	−	0.848233i	$-0.322333\pi$
$397$	−2.26012	−	1.64207i	−0.113432	−	0.0824133i	−0.643055	+	0.765820i	$0.722333\pi$
$398$	24.7672	+	27.5068i	1.24147	+	1.37879i
$399$	10.6809	−	23.5977i	0.534716	−	1.18136i
$400$	−30.2003	+	13.9048i	−1.51001	+	0.695240i
$401$	−18.1027	−	31.3549i	−0.904008	−	1.56579i	−0.822244	−	0.569136i	$-0.807278\pi$
$401$	−18.1027	−	31.3549i	−0.904008	−	1.56579i	−0.0817642	−	0.996652i	$-0.526055\pi$
$402$	−1.52984	+	6.98555i	−0.0763014	+	0.348408i
$403$	−11.0676	+	4.92761i	−0.551316	+	0.245462i
$404$	45.6186	+	33.1438i	2.26961	+	1.64897i
$405$	4.54416	−	19.6049i	0.225801	−	0.974173i
$406$	34.6605	−	25.1824i	1.72017	−	1.24978i
$407$	−6.10273	+	10.5702i	−0.302501	+	0.523947i
$408$	35.9255	−	31.9492i	1.77858	−	1.58172i
$409$	−14.8526	+	16.4955i	−0.734414	+	0.815649i	−0.988450	−	0.151546i	$-0.951575\pi$
$409$	−14.8526	+	16.4955i	−0.734414	+	0.815649i	0.254037	+	0.967195i	$0.418242\pi$
$410$	25.7298	−	8.53979i	1.27071	−	0.421750i
$411$	−10.9173	−	9.95241i	−0.538512	−	0.490916i
$412$	39.6316	+	8.42395i	1.95251	+	0.415018i
$413$	6.67630	+	20.5475i	0.328519	+	1.01108i
$414$	2.10002	−	17.8616i	0.103210	−	0.877851i
$415$	3.74506	+	8.27084i	0.183838	+	0.405999i
$416$	8.06163	+	1.71355i	0.395254	+	0.0840138i
$417$	−15.3379	−	5.08821i	−0.751101	−	0.249171i
$418$	22.4267	+	38.8441i	1.09692	+	1.89993i
$419$	−29.2051	−	13.0030i	−1.42676	−	0.635236i	−0.459308	−	0.888277i	$-0.651903\pi$
$419$	−29.2051	−	13.0030i	−1.42676	−	0.635236i	−0.967456	+	0.253041i	$0.918569\pi$
$420$	−23.6566	−	26.2656i	−1.15432	−	1.28163i
$421$	−1.27594	+	0.568087i	−0.0621857	+	0.0276869i	−0.437594	−	0.899173i	$-0.644169\pi$
$421$	−1.27594	+	0.568087i	−0.0621857	+	0.0276869i	0.375408	+	0.926860i	$0.377503\pi$
$422$	−27.2891	−	19.8267i	−1.32841	−	0.965150i
$423$	−24.3645	−	18.1644i	−1.18464	−	0.883185i
$424$	19.0622			0.925745
$425$	6.74513	−	21.6858i	0.327187	−	1.05192i
$426$	18.4257	−	40.7084i	0.892730	−	1.97233i
$427$	5.33436	−	1.13385i	0.258148	−	0.0548710i
$428$	−0.452387	+	4.30417i	−0.0218669	+	0.208050i
$429$	6.53485	+	3.82674i	0.315506	+	0.184757i
$430$	−40.4599	+	23.7008i	−1.95115	+	1.14295i
$431$	−0.506575	+	0.368048i	−0.0244009	+	0.0177283i	−0.599919	−	0.800061i	$-0.704800\pi$
$431$	−0.506575	+	0.368048i	−0.0244009	+	0.0177283i	0.575518	+	0.817789i	$0.304800\pi$
$432$	−7.80676	+	33.6584i	−0.375603	+	1.61939i
$433$	−4.64257	+	3.37302i	−0.223108	+	0.162097i	−0.693724	−	0.720241i	$-0.744031\pi$
$433$	−4.64257	+	3.37302i	−0.223108	+	0.162097i	0.470617	+	0.882338i	$0.344031\pi$
$434$	−34.7695	−	7.39049i	−1.66899	−	0.354755i
$435$	−30.9886	+	6.59155i	−1.48579	+	0.316041i
$436$	38.3291	−	8.14710i	1.83563	−	0.390175i
$437$	−11.4540	+	12.7210i	−0.547920	+	0.608527i
$438$	8.57753	+	0.954968i	0.409850	+	0.0456301i
$439$	−15.5049	−	17.2199i	−0.740007	−	0.821861i	0.249190	−	0.968455i	$-0.419836\pi$
$439$	−15.5049	−	17.2199i	−0.740007	−	0.821861i	−0.989197	+	0.146594i	$0.953169\pi$
$440$	33.2643	−	3.70835i	1.58581	−	0.176789i
$441$	−4.17108	+	7.02334i	−0.198623	+	0.334445i
$442$	−16.6109	+	12.0685i	−0.790100	+	0.574041i
$443$	10.9667	−	18.9950i	0.521046	−	0.902477i	−0.478655	−	0.878003i	$-0.658875\pi$
$443$	10.9667	−	18.9950i	0.521046	−	0.902477i	0.999700	−	0.0244742i	$-0.00779117\pi$
$444$	36.1520	+	11.9931i	1.71570	+	0.569167i
$445$	0.00483427	+	0.766955i	0.000229167	+	0.0363572i
$446$	−0.965829	+	9.18925i	−0.0457333	+	0.435124i
$447$	−0.0740764	+	12.0305i	−0.00350369	+	0.569025i
$448$	−2.22298	−	2.46887i	−0.105026	−	0.116643i
$449$	−12.6712			−0.597990			−0.298995	−	0.954255i	$-0.596651\pi$
$449$	−12.6712			−0.597990			−0.298995	+	0.954255i	$0.596651\pi$
$450$	11.7489	+	36.1237i	0.553850	+	1.70289i
$451$	−11.7265			−0.552178
$452$	20.0296	+	22.2451i	0.942112	+	1.04632i
$453$	−1.18680	+	0.675489i	−0.0557606	+	0.0317372i
$454$	−4.15982	+	39.5781i	−0.195230	+	1.85749i
$455$	4.89401	+	6.64751i	0.229435	+	0.311640i
$456$	57.1934	−	50.8630i	2.67833	−	2.38188i
$457$	0.0638731	−	0.110631i	0.00298786	−	0.00517512i	−0.864528	−	0.502585i	$-0.832382\pi$
$457$	0.0638731	−	0.110631i	0.00298786	−	0.00517512i	0.867515	+	0.497410i	$0.165716\pi$
$458$	−12.3084	+	8.94261i	−0.575136	+	0.417861i
$459$	−13.5176	−	19.3471i	−0.630948	−	0.903043i
$460$	9.63581	+	21.2804i	0.449272	+	0.992203i
$461$	−4.84829	−	5.38457i	−0.225807	−	0.250785i	0.619586	−	0.784929i	$-0.287301\pi$
$461$	−4.84829	−	5.38457i	−0.225807	−	0.250785i	−0.845393	+	0.534144i	$0.820634\pi$
$462$	8.91227	+	20.3536i	0.414636	+	0.946937i
$463$	15.2392	−	16.9248i	0.708225	−	0.786564i	−0.276438	−	0.961032i	$-0.589154\pi$
$463$	15.2392	−	16.9248i	0.708225	−	0.786564i	0.984663	+	0.174468i	$0.0558206\pi$
$464$	53.2058	−	11.3092i	2.47002	−	0.525018i
$465$	21.2682	+	15.4475i	0.986290	+	0.716362i
$466$	−1.48291	−	0.315203i	−0.0686945	−	0.0146015i
$467$	−7.87672	+	5.72277i	−0.364491	+	0.264818i	−0.754923	−	0.655814i	$-0.772326\pi$
$467$	−7.87672	+	5.72277i	−0.364491	+	0.264818i	0.390432	+	0.920632i	$0.372326\pi$
$468$	7.57907	−	22.3842i	0.350343	−	1.03471i
$469$	2.72780	−	1.98186i	0.125958	−	0.0915138i
$470$	57.0859	+	5.63641i	2.63318	+	0.259988i
$471$	−0.0414626	+	6.73383i	−0.00191050	+	0.310278i
$472$	−6.67311	+	63.4904i	−0.307155	+	2.92238i
$473$	19.8394	−	4.21699i	0.912216	−	0.193897i
$474$	−38.1367	−	53.1761i	−1.75168	−	2.44246i
$475$	10.7382	−	34.5238i	0.492704	−	1.58406i
$476$	−41.4556			−1.90012
$477$	1.09270	−	9.29388i	0.0500311	−	0.425537i
$478$	−2.40741	−	1.74909i	−0.110112	−	0.0800013i
$479$	−10.2812	+	4.57749i	−0.469761	+	0.209151i	−0.627944	−	0.778259i	$-0.716103\pi$
$479$	−10.2812	+	4.57749i	−0.469761	+	0.209151i	0.158183	+	0.987410i	$0.449436\pi$
$480$	−5.52841	−	17.0063i	−0.252336	−	0.776226i
$481$	−8.12582	−	3.61785i	−0.370506	−	0.164960i
$482$	−22.7553	−	39.4133i	−1.03648	−	1.79523i
$483$	−6.33651	+	5.63516i	−0.288321	+	0.256409i
$484$	21.5856	+	4.58816i	0.981163	+	0.208553i
$485$	18.2019	−	16.5980i	0.826506	−	0.753676i
$486$	37.1511	+	13.3488i	1.68521	+	0.605514i
$487$	−2.45081	−	7.54283i	−0.111057	−	0.341798i	0.880047	−	0.474886i	$-0.157511\pi$
$487$	−2.45081	−	7.54283i	−0.111057	−	0.341798i	−0.991104	+	0.133088i	$0.957511\pi$
$488$	15.7624	+	3.35040i	0.713531	+	0.151666i
$489$	3.11007	−	14.2012i	0.140642	−	0.642200i
$490$	−0.0971844	−	15.4183i	−0.00439035	−	0.696526i
$491$	9.84430	−	10.9332i	0.444267	−	0.493409i	−0.478867	−	0.877888i	$-0.658952\pi$
$491$	9.84430	−	10.9332i	0.444267	−	0.493409i	0.923134	+	0.384479i	$0.125619\pi$
$492$	7.38791	+	35.8411i	0.333073	+	1.61584i
$493$	−18.5778	+	32.1777i	−0.836702	+	1.44921i
$494$	−26.4445	+	19.2131i	−1.18980	+	0.864437i
$495$	0.0987738	−	16.4307i	0.00443955	−	0.738506i
$496$	−36.5114	−	26.5271i	−1.63941	−	1.19110i
$497$	−19.2471	+	8.56938i	−0.863352	+	0.384389i
$498$	−16.9717	+	5.39914i	−0.760520	+	0.241941i
$499$	−11.7212	−	20.3017i	−0.524714	−	0.908831i	−0.999586	−	0.0287762i	$-0.990839\pi$
$499$	−11.7212	−	20.3017i	−0.524714	−	0.908831i	0.474872	−	0.880055i	$-0.342494\pi$
$500$	−37.2847	−	32.3159i	−1.66742	−	1.44521i
$501$	−10.9097	−	15.2120i	−0.487410	−	0.679623i
$502$	0.530676	+	0.589376i	0.0236852	+	0.0263051i
$503$	−11.6643	−	8.47463i	−0.520087	−	0.377865i	0.296550	−	0.955017i	$-0.404164\pi$
$503$	−11.6643	−	8.47463i	−0.520087	−	0.377865i	−0.816637	+	0.577152i	$0.804164\pi$
$504$	30.9463	−	21.9067i	1.37846	−	0.975802i
$505$	−5.76393	+	27.9833i	−0.256491	+	1.24524i
$506$	−1.53488	−	14.6034i	−0.0682336	−	0.649200i
$507$	7.00914	−	15.4855i	0.311287	−	0.687734i
$508$	40.2085	+	17.9020i	1.78396	+	0.794272i
$509$	0.258484	−	0.287075i	0.0114571	−	0.0127244i	−0.737389	−	0.675468i	$-0.763942\pi$
$509$	0.258484	−	0.287075i	0.0114571	−	0.0127244i	0.748846	+	0.662744i	$0.230608\pi$
$510$	40.7004	+	18.1139i	1.80224	+	0.802095i
$511$	−2.72289	−	3.02407i	−0.120453	−	0.133777i
$512$	−15.6267	−	48.0942i	−0.690611	−	2.12548i
$513$	−21.5200	−	30.8005i	−0.950131	−	1.35987i
$514$	−2.32468	+	7.15462i	−0.102537	+	0.315577i
$515$	4.39477	+	20.0534i	0.193657	+	0.883659i
$516$	−25.3881	−	57.9809i	−1.11765	−	2.55246i
$517$	−22.6675	−	10.0922i	−0.996915	−	0.443855i
$518$	−13.0490	−	22.6016i	−0.573342	−	0.993057i
$519$	5.75601	+	27.9242i	0.252661	+	1.22574i
$520$	5.22162	+	23.8263i	0.228983	+	1.04485i
$521$	35.3256	+	25.6656i	1.54764	+	1.12443i	0.945304	+	0.326190i	$0.105765\pi$
$521$	35.3256	+	25.6656i	1.54764	+	1.12443i	0.602340	+	0.798240i	$0.294235\pi$
$522$	−5.73456	−	61.8821i	−0.250995	−	2.70851i
$523$	−6.03504	+	18.5739i	−0.263894	+	0.812182i	0.728052	+	0.685522i	$0.240426\pi$
$523$	−6.03504	+	18.5739i	−0.263894	+	0.812182i	−0.991946	+	0.126660i	$0.959574\pi$
$524$	30.3581	−	52.5818i	1.32620	−	2.29705i
$525$	7.17919	−	16.4087i	0.313326	−	0.716134i
$526$	10.2907	+	17.8239i	0.448694	+	0.777161i
$527$	30.1540	−	6.40943i	1.31353	−	0.279199i
$528$	−0.173698	+	28.2098i	−0.00755924	+	1.22767i
$529$	−15.8921	+	7.07563i	−0.690962	+	0.307636i
$530$	7.28596	+	16.0908i	0.316482	+	0.698940i
$531$	30.5725	+	6.89293i	1.32673	+	0.299128i
$532$	−65.9973			−2.86135
$533$	−0.893274	−	8.49894i	−0.0386920	−	0.368130i
$534$	−1.49525	−	0.166472i	−0.0647059	−	0.00720395i
$535$	−2.08123	+	0.690766i	−0.0899795	+	0.0298644i
$536$	9.74539	−	2.07145i	0.420937	−	0.0894728i
$537$	0.362994	+	0.828999i	0.0156644	+	0.0357739i
$538$	57.0207	+	12.1201i	2.45834	+	0.522536i
$539$	−2.06094	+	6.34291i	−0.0887708	+	0.273208i
$540$	−50.2815	+	10.0498i	−2.16377	+	0.432474i
$541$	−5.67479	−	17.4652i	−0.243978	−	0.750888i	−0.995803	−	0.0915249i	$-0.970826\pi$
$541$	−5.67479	−	17.4652i	−0.243978	−	0.750888i	0.751824	−	0.659363i	$-0.229174\pi$
$542$	−5.98935	−	56.9848i	−0.257264	−	2.44771i
$543$	39.7807	−	3.93363i	1.70715	−	0.168808i
$544$	−19.1587	−	8.53001i	−0.821423	−	0.365721i
$545$	11.7713	+	15.9888i	0.504225	+	0.684887i
$546$	−14.0727	+	8.00976i	−0.602257	+	0.342786i
$547$	35.1535	−	15.6513i	1.50306	−	0.669203i	0.520278	−	0.853997i	$-0.325828\pi$
$547$	35.1535	−	15.6513i	1.50306	−	0.669203i	0.982777	+	0.184794i	$0.0591616\pi$
$548$	−11.6315	+	35.7980i	−0.496872	+	1.52922i
$549$	2.53704	−	7.49297i	0.108278	−	0.319792i
$550$	15.8446	+	26.6616i	0.675614	+	1.13686i
$551$	−29.5758	+	51.2268i	−1.25997	+	2.18234i
$552$	−23.8776	+	7.59607i	−1.01630	+	0.323310i
$553$	−3.22511	+	30.6849i	−0.137146	+	1.30485i
$554$	2.74121	−	26.0809i	0.116463	−	1.10807i
$555$	2.02013	+	19.1933i	0.0857495	+	0.814710i
$556$	4.30388	+	40.9486i	0.182525	+	1.73661i
$557$	34.0992			1.44483			0.722414	−	0.691461i	$-0.243032\pi$
$557$	34.0992			1.44483			0.722414	+	0.691461i	$0.243032\pi$
$558$	−34.9717	+	37.8910i	−1.48047	+	1.60405i
$559$	4.56761	+	14.0577i	0.193189	+	0.594576i
$560$	−12.3300	+	28.1702i	−0.521039	+	1.19041i
$561$	−14.2406	−	12.9820i	−0.601239	−	0.548099i
$562$	−43.1085	+	47.8769i	−1.81842	+	2.01956i
$563$	−16.6117	+	18.4492i	−0.700100	+	0.777540i	−0.983392	−	0.181494i	$-0.941907\pi$
$563$	−16.6117	+	18.4492i	−0.700100	+	0.777540i	0.283292	+	0.959034i	$0.408573\pi$
$564$	−16.5652	+	75.6399i	−0.697519	+	3.18501i
$565$	−6.08150	+	13.8943i	−0.255851	+	0.584538i
$566$	−12.9674	−	39.9094i	−0.545058	−	1.67752i
$567$	−8.90678	−	16.3438i	−0.374050	−	0.686373i
$568$	−62.2553			−2.61217
$569$	2.96097	+	28.1717i	0.124130	+	1.18102i	0.862297	+	0.506403i	$0.169025\pi$
$569$	2.96097	+	28.1717i	0.124130	+	1.18102i	−0.738167	+	0.674618i	$0.764308\pi$
$570$	64.7949	+	28.8372i	2.71396	+	1.20786i
$571$	−3.33890	+	31.7675i	−0.139729	+	1.32943i	0.669884	+	0.742465i	$0.266344\pi$
$571$	−3.33890	+	31.7675i	−0.139729	+	1.32943i	−0.809613	+	0.586964i	$0.800323\pi$
$572$	2.01689	−	19.1894i	0.0843303	−	0.802349i
$573$	−1.28505	−	1.17147i	−0.0536839	−	0.0489391i
$574$	12.5369	−	21.7146i	0.523282	−	0.906351i
$575$	−7.80852	+	8.89522i	−0.325638	+	0.370956i
$576$	−4.72579	+	0.943829i	−0.196908	+	0.0393262i
$577$	−4.21265	+	12.9652i	−0.175375	+	0.539748i	−0.999650	−	0.0264408i	$-0.991583\pi$
$577$	−4.21265	+	12.9652i	−0.175375	+	0.539748i	0.824276	+	0.566189i	$0.191583\pi$
$578$	8.39998	−	3.73991i	0.349393	−	0.155560i
$579$	0.147730	−	23.9924i	0.00613945	−	0.997090i
$580$	47.8585	+	65.0060i	1.98722	+	2.69923i
$581$	7.67133	+	3.41550i	0.318260	+	0.141699i
$582$	28.1610	+	39.2665i	1.16731	+	1.62765i
$583$	−0.798637	−	7.59853i	−0.0330762	−	0.314699i
$584$	−3.71570	−	11.4358i	−0.153757	−	0.473215i
$585$	11.9159	−	1.18004i	0.492663	−	0.0487885i
$586$	9.49120	−	29.2109i	0.392078	−	1.20669i
$587$	38.8559	+	8.25908i	1.60376	+	0.340889i	0.920941	−	0.389703i	$-0.127422\pi$
$587$	38.8559	+	8.25908i	1.60376	+	0.340889i	0.682815	+	0.730592i	$0.260756\pi$
$588$	20.6851	+	2.30294i	0.853038	+	0.0949718i
$589$	48.0051	−	10.2038i	1.97802	−	0.420441i
$590$	−56.1441	+	18.6344i	−2.31141	+	0.767165i
$591$	−5.50281	−	12.5672i	−0.226355	−	0.516945i
$592$	−3.46354	−	32.9534i	−0.142351	−	1.35438i
$593$	16.9892			0.697663			0.348832	−	0.937185i	$-0.386579\pi$
$593$	16.9892			0.697663			0.348832	+	0.937185i	$0.386579\pi$
$594$	31.9869	+	3.96057i	1.31244	+	0.162504i
$595$	−8.66425	−	19.1347i	−0.355200	−	0.784447i
$596$	28.0034	−	12.4679i	1.14706	−	0.510705i
$597$	−21.8458	−	12.7927i	−0.894088	−	0.523568i
$598$	10.4671	−	2.22485i	0.428032	−	0.0909810i
$599$	−7.81800	−	13.5412i	−0.319435	−	0.553277i	0.660935	−	0.750443i	$-0.270160\pi$
$599$	−7.81800	−	13.5412i	−0.319435	−	0.553277i	−0.980370	+	0.197166i	$0.936826\pi$
$600$	39.1006	−	35.6656i	1.59627	−	1.45604i
$601$	−0.702116	+	1.21610i	−0.0286399	+	0.0496058i	−0.879990	−	0.474992i	$-0.842451\pi$
$601$	−0.702116	+	1.21610i	−0.0286399	+	0.0496058i	0.851350	+	0.524598i	$0.175784\pi$
$602$	−13.4017	+	41.2462i	−0.546213	+	1.68107i
$603$	−0.451312	−	4.87014i	−0.0183788	−	0.198328i
$604$	2.81486	+	2.04512i	0.114535	+	0.0832147i
$605$	2.39364	+	10.9222i	0.0973152	+	0.444051i
$606$	−53.1938	−	17.6465i	−2.16085	−	0.716842i
$607$	−3.79337	−	6.57031i	−0.153968	−	0.266681i	0.778715	−	0.627378i	$-0.215872\pi$
$607$	−3.79337	−	6.57031i	−0.153968	−	0.266681i	−0.932683	+	0.360698i	$0.882539\pi$
$608$	−30.5006	−	13.5798i	−1.23696	−	0.550732i
$609$	−17.3691	+	23.5996i	−0.703833	+	0.956305i
$610$	3.19656	+	14.5859i	0.129425	+	0.590568i
$611$	5.58777	−	17.1974i	0.226057	−	0.695732i
$612$	−30.7066	+	51.7043i	−1.24124	+	2.09002i
$613$	9.44377	+	29.0649i	0.381430	+	1.17392i	0.939037	+	0.343816i	$0.111720\pi$
$613$	9.44377	+	29.0649i	0.381430	+	1.17392i	−0.557607	+	0.830105i	$0.688280\pi$
$614$	−19.9453	−	22.1515i	−0.804925	−	0.893960i
$615$	−14.9991	+	10.9009i	−0.604824	+	0.439565i
$616$	20.7140	−	23.0052i	0.834590	−	0.926906i
$617$	0.925938	+	0.412254i	0.0372768	+	0.0165967i	0.425290	−	0.905057i	$-0.360172\pi$
$617$	0.925938	+	0.412254i	0.0372768	+	0.0165967i	−0.388014	+	0.921654i	$0.626839\pi$
$618$	−40.0749	+	3.96272i	−1.61205	+	0.159404i
$619$	−4.81309	−	45.7935i	−0.193454	−	1.84059i	−0.473724	−	0.880673i	$-0.657091\pi$
$619$	−4.81309	−	45.7935i	−0.193454	−	1.84059i	0.280270	−	0.959921i	$-0.409576\pi$
$620$	13.5117	−	65.5981i	0.542644	−	2.63448i
$621$	2.33477	+	12.0770i	0.0936912	+	0.484634i
$622$	−20.2673	−	14.7250i	−0.812644	−	0.590420i
$623$	0.474659	+	0.527162i	0.0190168	+	0.0211203i
$624$	−20.4587	+	2.02302i	−0.819004	+	0.0809855i
$625$	7.12357	−	23.9636i	0.284943	−	0.958545i
$626$	43.5789	+	75.4809i	1.74176	+	3.01682i
$627$	−22.6710	−	20.6673i	−0.905393	−	0.825371i
$628$	15.6743	−	6.97863i	0.625471	−	0.278478i
$629$	18.3110	+	13.3037i	0.730108	+	0.530455i
$630$	30.3202	+	17.7492i	1.20798	+	0.707146i
$631$	−6.24556	+	4.53767i	−0.248632	+	0.180642i	−0.705120	−	0.709088i	$-0.749107\pi$
$631$	−6.24556	+	4.53767i	−0.248632	+	0.180642i	0.456488	+	0.889729i	$0.349107\pi$
$632$	−45.5848	+	78.9552i	−1.81327	+	3.14067i
$633$	21.8971	+	7.26415i	0.870330	+	0.288724i
$634$	37.6815	−	41.8496i	1.49653	−	1.66206i
$635$	0.140565	+	22.3006i	0.00557816	+	0.884973i
$636$	−22.7212	+	7.22820i	−0.900954	+	0.286617i
$637$	−4.75411	−	1.01052i	−0.188365	−	0.0400382i
$638$	−15.6798	−	48.2575i	−0.620770	−	1.91053i
$639$	−3.56863	+	30.3528i	−0.141173	+	1.20074i
$640$	21.9790	−	20.0422i	0.868795	−	0.792239i
$641$	−27.3002	−	5.80283i	−1.07829	−	0.229198i	−0.365669	−	0.930745i	$-0.619160\pi$
$641$	−27.3002	−	5.80283i	−1.07829	−	0.229198i	−0.712623	+	0.701547i	$0.752493\pi$
$642$	−0.868416	−	4.21297i	−0.0342737	−	0.166273i
$643$	−3.87285	−	6.70797i	−0.152730	−	0.264537i	0.779500	−	0.626402i	$-0.215473\pi$
$643$	−3.87285	−	6.70797i	−0.152730	−	0.264537i	−0.932230	+	0.361866i	$0.882140\pi$
$644$	19.7379	+	8.78787i	0.777782	+	0.346291i
$645$	21.4562	−	23.8365i	0.844835	−	0.938560i
$646$	75.9847	−	33.8305i	2.98958	−	1.33105i
$647$	−27.8778	−	20.2544i	−1.09599	−	0.796283i	−0.115588	−	0.993297i	$-0.536875\pi$
$647$	−27.8778	−	20.2544i	−1.09599	−	0.796283i	−0.980401	+	0.197015i	$0.936875\pi$
$648$	−4.40025	−	54.8233i	−0.172858	−	2.15366i
$649$	25.5879			1.00441
$650$	−18.1165	+	13.5146i	−0.710586	+	0.530085i
$651$	24.1939	−	2.39237i	0.948236	−	0.0937643i
$652$	−36.2317	+	7.70129i	−1.41894	+	0.301606i
$653$	1.25103	−	11.9028i	0.0489567	−	0.465792i	−0.942389	−	0.334518i	$-0.891427\pi$
$653$	1.25103	−	11.9028i	0.0489567	−	0.465792i	0.991346	−	0.131274i	$-0.0419067\pi$
$654$	−33.8482	+	19.2654i	−1.32357	+	0.753336i
$655$	30.6151	+	3.02280i	1.19623	+	0.118111i
$656$	25.7547	−	18.7119i	1.00555	−	0.730576i
$657$	−5.78855	+	1.15608i	−0.225833	+	0.0451030i
$658$	42.9225	−	31.1850i	1.67329	−	1.21572i
$659$	−9.12961	−	1.94056i	−0.355639	−	0.0755934i	0.0266278	−	0.999645i	$-0.491523\pi$
$659$	−9.12961	−	1.94056i	−0.355639	−	0.0755934i	−0.382267	+	0.924052i	$0.624856\pi$
$660$	−38.2431	+	17.0336i	−1.48861	+	0.663033i
$661$	−4.71132	+	1.00142i	−0.183249	+	0.0389508i	−0.298622	−	0.954371i	$-0.596527\pi$
$661$	−4.71132	+	1.00142i	−0.183249	+	0.0389508i	0.115373	+	0.993322i	$0.463194\pi$
$662$	−22.1767	+	24.6297i	−0.861922	+	0.957261i
$663$	8.32408	−	11.3100i	0.323281	−	0.439244i
$664$	16.6032	+	18.4397i	0.644329	+	0.715600i
$665$	−13.7935	−	30.4624i	−0.534888	−	1.18128i
$666$	−37.8547	−	0.466188i	−1.46684	−	0.0180644i
$667$	15.6664	−	11.3823i	0.606605	−	0.440724i
$668$	−23.8482	+	41.3063i	−0.922714	+	1.59819i
$669$	−1.27584	−	6.18950i	−0.0493267	−	0.239300i
$670$	5.47342	+	7.43452i	0.211457	+	0.287221i
$671$	0.675140	−	6.42352i	0.0260635	−	0.247977i
$672$	−14.2722	−	8.35765i	−0.550562	−	0.322403i
$673$	−11.9310	−	13.2507i	−0.459907	−	0.510779i	0.467929	−	0.883766i	$-0.345000\pi$
$673$	−11.9310	−	13.2507i	−0.459907	−	0.510779i	−0.927837	+	0.372987i	$0.878334\pi$
$674$	36.7946			1.41728
$675$	−15.1476	−	21.1081i	−0.583030	−	0.812451i
$676$	−43.3093			−1.66574
$677$	10.2517	+	11.3857i	0.394005	+	0.437586i	0.907209	−	0.420680i	$-0.138208\pi$
$677$	10.2517	+	11.3857i	0.394005	+	0.437586i	−0.513205	+	0.858266i	$0.671542\pi$
$678$	−25.6735	−	15.0341i	−0.985985	−	0.577382i
$679$	2.38150	−	22.6584i	0.0913935	−	0.869551i
$680$	−0.391213	−	62.0658i	−0.0150024	−	2.38012i
$681$	−5.49502	−	26.6581i	−0.210570	−	1.02154i
$682$	−21.0497	+	36.4591i	−0.806034	+	1.39609i
$683$	−22.9889	+	16.7024i	−0.879645	+	0.639100i	−0.933158	−	0.359468i	$-0.882958\pi$
$683$	−22.9889	+	16.7024i	−0.879645	+	0.639100i	0.0535124	+	0.998567i	$0.482958\pi$
$684$	−48.8848	+	82.3131i	−1.86916	+	3.14732i
$685$	−18.9543	+	2.11305i	−0.724207	+	0.0807355i
$686$	−34.0735	−	37.8425i	−1.30093	−	1.44483i
$687$	6.16803	−	8.38056i	0.235325	−	0.319738i
$688$	−36.8439	+	40.9193i	−1.40466	+	1.56004i
$689$	5.44631	−	1.15765i	0.207488	−	0.0441029i
$690$	−15.5385	−	17.2521i	−0.591539	−	0.656778i
$691$	−21.4992	−	4.56981i	−0.817870	−	0.173844i	−0.220065	−	0.975485i	$-0.570627\pi$
$691$	−21.4992	−	4.56981i	−0.817870	−	0.173844i	−0.597805	+	0.801642i	$0.703960\pi$
$692$	58.7708	−	42.6995i	2.23413	−	1.62319i
$693$	−10.0289	−	11.4179i	−0.380967	−	0.433730i
$694$	−22.8739	+	16.6188i	−0.868280	+	0.630842i
$695$	−18.0012	+	10.5448i	−0.682824	+	0.399988i
$696$	−75.2500	+	42.8300i	−2.85235	+	1.62347i
$697$	−2.27302	+	21.6263i	−0.0860966	+	0.819155i
$698$	20.2441	−	4.30301i	0.766250	−	0.162871i
$699$	1.03187	−	0.102034i	0.0390287	−	0.00385928i
$700$	−45.6310	+	0.575266i	−1.72469	+	0.0217430i
$701$	6.44692			0.243497			0.121748	−	0.992561i	$-0.461150\pi$
$701$	6.44692			0.243497			0.121748	+	0.992561i	$0.461150\pi$
$702$	−0.433855	+	23.4847i	−0.0163748	+	0.886371i
$703$	29.1511	+	21.1795i	1.09946	+	0.798801i
$704$	−3.59447	+	1.60036i	−0.135472	+	0.0603159i
$705$	−38.3753	+	8.16277i	−1.44530	+	0.307428i
$706$	−52.1666	−	23.2261i	−1.96332	−	0.874124i
$707$	13.2125	+	22.8847i	0.496906	+	0.860666i
$708$	−16.1209	−	78.2075i	−0.605859	−	2.93922i
$709$	4.80312	+	1.02094i	0.180385	+	0.0383420i	0.297218	−	0.954809i	$-0.403941\pi$
$709$	4.80312	+	1.02094i	0.180385	+	0.0383420i	−0.116833	+	0.993152i	$0.537274\pi$
$710$	−23.7952	−	52.5509i	−0.893017	−	1.97220i
$711$	35.8819	+	26.7510i	1.34568	+	1.00324i
$712$	0.647729	+	1.99351i	0.0242747	+	0.0747098i
$713$	−15.7156	−	3.34046i	−0.588555	−	0.125101i
$714$	39.2643	−	12.4910i	1.46943	−	0.467464i
$715$	9.27880	−	3.07966i	0.347007	−	0.115173i
$716$	1.54291	−	1.71358i	0.0576613	−	0.0640393i
$717$	1.93173	+	0.640833i	0.0721417	+	0.0239324i
$718$	31.7906	−	55.0629i	1.18641	−	2.05493i
$719$	38.7957	−	28.1867i	1.44683	−	1.05119i	0.460277	−	0.887775i	$-0.347750\pi$
$719$	38.7957	−	28.1867i	1.44683	−	1.05119i	0.986558	−	0.163412i	$-0.0522498\pi$
$720$	26.0015	+	36.2442i	0.969018	+	1.35074i
$721$	15.3612	+	11.1605i	0.572080	+	0.415640i
$722$	77.0113	−	34.2877i	2.86607	−	1.27605i
$723$	23.0032	+	20.9701i	0.855499	+	0.779886i
$724$	−50.9263	−	88.2070i	−1.89266	−	3.27819i
$725$	−20.0024	+	35.6764i	−0.742871	+	1.32499i
$726$	−21.8270	+	2.15832i	−0.810077	+	0.0801028i
$727$	6.94241	+	7.71033i	0.257480	+	0.285960i	0.858000	−	0.513649i	$-0.171707\pi$
$727$	6.94241	+	7.71033i	0.257480	+	0.285960i	−0.600521	+	0.799609i	$0.705040\pi$
$728$	18.2513	+	13.2603i	0.676437	+	0.491461i
$729$	−26.9816	−	0.997254i	−0.999318	−	0.0369353i
$730$	8.23293	−	7.50747i	0.304715	−	0.277864i
$731$	−3.93151	−	37.4058i	−0.145412	−	1.38350i
$732$	−20.0584	+	1.98343i	−0.741379	+	0.0733097i
$733$	−8.79421	−	3.91543i	−0.324822	−	0.144620i	0.237847	−	0.971303i	$-0.423558\pi$
$733$	−8.79421	−	3.91543i	−0.324822	−	0.144620i	−0.562668	+	0.826683i	$0.690225\pi$
$734$	−10.9371	+	12.1469i	−0.403695	+	0.448349i
$735$	3.26022	+	10.0289i	0.120255	+	0.369923i
$736$	7.31365	+	8.12263i	0.269585	+	0.299404i
$737$	−1.23401	−	3.79789i	−0.0454553	−	0.139897i
$738$	−17.7967	−	31.7205i	−0.655104	−	1.16765i
$739$	−10.9628	+	33.7400i	−0.403273	+	1.24115i	0.519056	+	0.854740i	$0.326284\pi$
$739$	−10.9628	+	33.7400i	−0.403273	+	1.24115i	−0.922329	+	0.386406i	$0.873716\pi$
$740$	42.4294	−	24.8545i	1.55974	−	0.913671i
$741$	13.2519	−	18.0055i	0.486822	−	0.661449i
$742$	14.9245	+	6.64481i	0.547895	+	0.243939i
$743$	1.41943	+	2.45852i	0.0520738	+	0.0901944i	0.890887	−	0.454224i	$-0.150084\pi$
$743$	1.41943	+	2.45852i	0.0520738	+	0.0901944i	−0.838814	+	0.544419i	$0.816750\pi$
$744$	68.1849	+	22.6197i	2.49978	+	0.829279i
$745$	11.6075	+	10.3197i	0.425268	+	0.378086i
$746$	49.3797	+	35.8765i	1.80792	+	1.31353i
$747$	9.94210	−	7.03794i	0.363762	−	0.257505i
$748$	−15.1721	+	46.6951i	−0.554749	+	1.70734i
$749$	−1.01409	+	1.75645i	−0.0370539	+	0.0641793i
$750$	45.0510	+	19.3735i	1.64503	+	0.707420i
$751$	−19.4018	−	33.6049i	−0.707983	−	1.22626i	−0.965604	−	0.260016i	$-0.916272\pi$
$751$	−19.4018	−	33.6049i	−0.707983	−	1.22626i	0.257622	−	0.966246i	$-0.417061\pi$
$752$	65.8884	−	14.0050i	2.40270	−	0.510710i
$753$	−0.468080	−	0.274103i	−0.0170578	−	0.00998885i
$754$	33.7809	−	15.0402i	1.23023	−	0.547734i
$755$	−0.355659	+	1.72669i	−0.0129438	+	0.0628407i
$756$	−28.5796	+	37.8461i	−1.03943	+	1.37645i
$757$	32.7437			1.19009			0.595046	−	0.803692i	$-0.297134\pi$
$757$	32.7437			1.19009			0.595046	+	0.803692i	$0.297134\pi$
$758$	−0.113046	−	1.07556i	−0.00410602	−	0.0390662i
$759$	4.02830	+	9.19974i	0.146218	+	0.333929i
$760$	−0.622811	−	98.8087i	−0.0225917	−	3.58417i
$761$	0.437407	−	0.0929737i	0.0158560	−	0.00337029i	−0.199977	−	0.979801i	$-0.564087\pi$
$761$	0.437407	−	0.0929737i	0.0158560	−	0.00337029i	0.215833	+	0.976430i	$0.430753\pi$
$762$	−43.4772	−	4.84047i	−1.57501	−	0.175352i
$763$	17.9621	+	3.81797i	0.650273	+	0.138220i
$764$	−1.36911	+	4.21370i	−0.0495328	+	0.152446i
$765$	−30.2829	−	3.36703i	−1.09488	−	0.121735i
$766$	17.8521	+	54.9431i	0.645022	+	1.98517i
$767$	1.94918	+	18.5452i	0.0703808	+	0.669629i
$768$	30.7617	+	42.8928i	1.11002	+	1.54776i
$769$	−6.84396	−	3.04713i	−0.246800	−	0.109882i	0.279609	−	0.960114i	$-0.409795\pi$
$769$	−6.84396	−	3.04713i	−0.246800	−	0.109882i	−0.526409	+	0.850232i	$0.676462\pi$
$770$	27.3364	+	8.69204i	0.985137	+	0.313239i
$771$	0.0316805	−	5.14514i	0.00114095	−	0.185298i
$772$	−55.8469	+	24.8646i	−2.00997	+	0.894897i
$773$	−5.48853	+	16.8920i	−0.197409	+	0.607562i	0.802531	+	0.596610i	$0.203486\pi$
$773$	−5.48853	+	16.8920i	−0.197409	+	0.607562i	−0.999940	+	0.0109516i	$0.996514\pi$
$774$	41.5163	+	47.2663i	1.49227	+	1.69895i
$775$	33.1022	−	7.47343i	1.18906	−	0.268453i
$776$	33.6609	−	58.3024i	1.20836	−	2.09293i
$777$	13.1912	+	12.0253i	0.473232	+	0.431406i
$778$	−3.28316	+	31.2372i	−0.117707	+	1.11991i
$779$	−3.61864	+	34.4290i	−0.129651	+	1.23355i
$780$	−15.2586	−	26.4197i	−0.546345	−	0.945978i
$781$	2.60826	+	24.8160i	0.0933310	+	0.887985i
$782$	−27.2295			−0.973726
$783$	16.5684	+	39.1436i	0.592108	+	1.39888i
$784$	−5.59494	−	17.2195i	−0.199819	−	0.614981i
$785$	6.49706	+	5.77625i	0.231890	+	0.206163i
$786$	−12.9100	+	58.9496i	−0.460484	+	2.10266i
$787$	9.21203	−	10.2310i	0.328373	−	0.364695i	−0.556239	−	0.831022i	$-0.687756\pi$
$787$	9.21203	−	10.2310i	0.328373	−	0.364695i	0.884613	+	0.466327i	$0.154423\pi$
$788$	−23.3897	+	25.9769i	−0.833225	+	0.925390i
$789$	−10.4028	−	9.48333i	−0.370349	−	0.337616i
$790$	−84.0710	−	8.30081i	−2.99111	−	0.295329i
$791$	4.33484	+	13.3413i	0.154129	+	0.474361i
$792$	−13.3495	−	42.8750i	−0.474354	−	1.52350i
$793$	4.70698			0.167150
$794$	−0.739510	−	7.03597i	−0.0262442	−	0.249697i
$795$	−8.08507	−	8.97674i	−0.286748	−	0.318372i
$796$	−6.74238	+	64.1494i	−0.238977	+	2.27372i
$797$	−2.44389	+	23.2520i	−0.0865669	+	0.823629i	0.861969	+	0.506961i	$0.169231\pi$
$797$	−2.44389	+	23.2520i	−0.0865669	+	0.823629i	−0.948536	+	0.316669i	$0.897436\pi$
$798$	62.5087	−	19.8856i	2.21279	−	0.703944i
$799$	−23.0062	+	39.8478i	−0.813899	+	1.40972i
$800$	−21.2067	−	9.12329i	−0.749771	−	0.322557i
$801$	1.00907	−	0.201530i	0.0356538	−	0.00712072i
$802$	28.3330	−	87.1999i	1.00047	−	3.07914i
$803$	−4.40281	+	1.96026i	−0.155372	+	0.0691759i
$804$	−10.8305	+	6.16440i	−0.381963	+	0.217402i
$805$	0.0690018	+	10.9471i	0.00243199	+	0.385835i
$806$	−28.0278	−	12.4788i	−0.987236	−	0.439546i
$807$	−39.6772	+	3.92339i	−1.39670	+	0.138110i
$808$	8.16185	+	77.6548i	0.287133	+	2.73189i
$809$	−3.98567	−	12.2666i	−0.140129	−	0.431272i	0.856224	−	0.516605i	$-0.172805\pi$
$809$	−3.98567	−	12.2666i	−0.140129	−	0.431272i	−0.996352	+	0.0853332i	$0.972805\pi$
$810$	44.5956	−	24.6689i	1.56693	−	0.866776i
$811$	−5.74344	+	17.6765i	−0.201679	+	0.620705i	0.798154	+	0.602454i	$0.205810\pi$
$811$	−5.74344	+	17.6765i	−0.201679	+	0.620705i	−0.999833	+	0.0182520i	$0.994190\pi$
$812$	73.0288	+	15.5228i	2.56281	+	0.544742i
$813$	15.7191	+	35.8989i	0.551292	+	1.25903i
$814$	−30.2339	+	6.42641i	−1.05970	+	0.225246i
$815$	−11.1271	−	15.1139i	−0.389767	−	0.529418i
$816$	51.9917	+	5.78843i	1.82007	+	0.202635i
$817$	−6.25895	−	59.5500i	−0.218973	−	2.08339i
$818$	−56.2117			−1.96540
$819$	7.51134	−	8.13837i	0.262467	−	0.284378i
$820$	41.0621	+	23.3634i	1.43395	+	0.815884i
$821$	31.8397	−	14.1760i	1.11121	−	0.494744i	0.232742	−	0.972538i	$-0.425230\pi$
$821$	31.8397	−	14.1760i	1.11121	−	0.494744i	0.878472	+	0.477794i	$0.158563\pi$
$822$	0.230350	−	37.4104i	0.00803437	−	1.30484i
$823$	−25.4303	+	5.40537i	−0.886444	+	0.188419i	−0.628564	−	0.777758i	$-0.716357\pi$
$823$	−25.4303	+	5.40537i	−0.886444	+	0.188419i	−0.257879	+	0.966177i	$0.583024\pi$
$824$	28.0528	+	48.5890i	0.977267	+	1.69268i
$825$	−15.8551	−	14.0919i	−0.552002	−	0.490616i
$826$	−27.3564	+	47.3826i	−0.951850	+	1.64865i
$827$	−10.5951	+	32.6084i	−0.368428	+	1.13390i	0.579379	+	0.815058i	$0.303295\pi$
$827$	−10.5951	+	32.6084i	−0.368428	+	1.13390i	−0.947807	+	0.318846i	$0.896705\pi$
$828$	25.5804	−	18.1082i	0.888981	−	0.629304i
$829$	−11.1943	−	8.13310i	−0.388792	−	0.282474i	0.376168	−	0.926551i	$-0.377242\pi$
$829$	−11.1943	−	8.13310i	−0.388792	−	0.282474i	−0.764960	+	0.644077i	$0.777242\pi$
$830$	−9.21926	+	21.0631i	−0.320005	+	0.731111i
$831$	3.62107	+	17.5670i	0.125614	+	0.609392i
$832$	−1.43370	−	2.48324i	−0.0497046	−	0.0860908i
$833$	11.2983	+	5.03033i	0.391463	+	0.174291i
$834$	−16.4146	−	37.4873i	−0.568391	−	1.29808i
$835$	−24.0501	−	2.37460i	−0.832287	−	0.0821764i
$836$	−24.1540	+	74.3384i	−0.835384	+	2.57105i
$837$	14.9369	−	31.9472i	0.516294	−	1.10426i
$838$	−25.0176	−	76.9964i	−0.864220	−	2.65980i
$839$	24.2283	+	26.9083i	0.836455	+	0.928977i	0.998326	−	0.0578349i	$-0.0184197\pi$
$839$	24.2283	+	26.9083i	0.836455	+	0.928977i	−0.161872	+	0.986812i	$0.551753\pi$
$840$	5.10942	−	48.6812i	0.176292	−	1.67966i
$841$	25.3708	−	28.1771i	0.874855	−	0.971625i
$842$	−3.23122	−	1.43863i	−0.111355	−	0.0495786i
$843$	18.1697	−	40.1428i	0.625798	−	1.38259i
$844$	−6.14439	−	58.4600i	−0.211499	−	2.01228i
$845$	−9.05168	−	19.9903i	−0.311387	−	0.687689i
$846$	−7.10150	−	76.6328i	−0.244154	−	2.63469i
$847$	8.36655	+	6.07866i	0.287478	+	0.208865i
$848$	13.8790	+	15.4142i	0.476606	+	0.529324i
$849$	16.7266	+	23.3229i	0.574056	+	0.800439i
$850$	52.2415	−	24.0530i	1.79187	−	0.825011i
$851$	−5.89809	−	10.2158i	−0.202184	−	0.350193i
$852$	74.2050	−	23.6065i	2.54222	−	0.808746i
$853$	−28.5948	+	12.7312i	−0.979066	+	0.435908i	−0.832943	−	0.553358i	$-0.813346\pi$
$853$	−28.5948	+	12.7312i	−0.979066	+	0.435908i	−0.146123	+	0.989266i	$0.546679\pi$
$854$	11.1730	+	8.11768i	0.382333	+	0.277781i
$855$	−48.2103	−	5.36031i	−1.64876	−	0.183319i
$856$	−4.84845	+	3.52261i	−0.165717	+	0.120400i
$857$	6.62700	−	11.4783i	0.226374	−	0.392091i	−0.730357	−	0.683066i	$-0.760646\pi$
$857$	6.62700	−	11.4783i	0.226374	−	0.392091i	0.956731	+	0.290975i	$0.0939795\pi$
$858$	3.87168	+	18.7828i	0.132177	+	0.641233i
$859$	−18.1786	+	20.1893i	−0.620244	+	0.688851i	−0.968632	−	0.248499i	$-0.920063\pi$
$859$	−18.1786	+	20.1893i	−0.620244	+	0.688851i	0.348388	+	0.937351i	$0.386729\pi$
$860$	−77.8725	−	24.7608i	−2.65543	−	0.844335i
$861$	−3.66876	+	16.7523i	−0.125031	+	0.570917i
$862$	−1.55105	−	0.329686i	−0.0528290	−	0.0112291i
$863$	17.1394	+	52.7496i	0.583431	+	1.79562i	0.605481	+	0.795859i	$0.292981\pi$
$863$	17.1394	+	52.7496i	0.583431	+	1.79562i	−0.0220503	+	0.999757i	$0.507019\pi$
$864$	−20.9954	+	11.6100i	−0.714277	+	0.394980i
$865$	31.9920	+	18.2027i	1.08776	+	0.618910i
$866$	−14.2148	−	3.02145i	−0.483038	−	0.102673i
$867$	−4.69937	+	4.17923i	−0.159599	+	0.141934i
$868$	−30.9725	−	53.6460i	−1.05128	−	1.82086i
$869$	33.3827	+	14.8629i	1.13243	+	0.504190i
$870$	−64.9157	−	47.1496i	−2.20085	−	1.59852i
$871$	2.65857	−	1.18367i	0.0900823	−	0.0401072i
$872$	43.8987	+	31.8943i	1.48660	+	1.08008i
$873$	−26.4961	−	19.7536i	−0.896756	−	0.668557i
$874$	−43.3493			−1.46631
$875$	−9.80243	−	20.9417i	−0.331383	−	0.707960i
$876$	8.76524	+	12.2219i	0.296150	+	0.412938i
$877$	44.2699	−	9.40986i	1.49489	−	0.317748i	0.613331	−	0.789826i	$-0.289829\pi$
$877$	44.2699	−	9.40986i	1.49489	−	0.317748i	0.881557	+	0.472077i	$0.156496\pi$
$878$	6.13376	−	58.3588i	0.207004	−	1.96952i
$879$	−0.129345	+	21.0066i	−0.00436271	+	0.708535i
$880$	27.2179	+	24.1983i	0.917517	+	0.815723i
$881$	3.25840	−	2.36737i	0.109778	−	0.0797587i	−0.531542	−	0.847032i	$-0.678387\pi$
$881$	3.25840	−	2.36737i	0.109778	−	0.0797587i	0.641320	+	0.767273i	$0.278387\pi$
$882$	−20.2856	+	4.05141i	−0.683051	+	0.136418i
$883$	−23.5316	+	17.0967i	−0.791900	+	0.575349i	−0.908527	−	0.417827i	$-0.862792\pi$
$883$	−23.5316	+	17.0967i	−0.791900	+	0.575349i	0.116626	+	0.993176i	$0.462792\pi$
$884$	−34.9987	−	7.43920i	−1.17713	−	0.250208i
$885$	32.7291	−	23.7863i	1.10018	−	0.799569i
$886$	54.3309	−	11.5484i	1.82528	−	0.387976i
$887$	8.44114	−	9.37484i	0.283426	−	0.314776i	−0.584574	−	0.811340i	$-0.698738\pi$
$887$	8.44114	−	9.37484i	0.283426	−	0.314776i	0.868000	+	0.496564i	$0.165405\pi$
$888$	21.1559	+	48.3153i	0.709945	+	1.62136i
$889$	13.8016	+	15.3282i	0.462890	+	0.514091i
$890$	−1.43518	+	1.30872i	−0.0481074	+	0.0438683i
$891$	−21.6691	+	4.05090i	−0.725943	+	0.135710i
$892$	−13.0267	+	9.46448i	−0.436167	+	0.316894i
$893$	−36.6258	+	63.4377i	−1.22563	+	2.12286i
$894$	−22.7664	+	20.2466i	−0.761423	+	0.677146i
$895$	1.11341	+	0.354024i	0.0372171	+	0.0118337i
$896$	2.87568	−	27.3603i	0.0960698	−	0.914044i
$897$	−6.36079	+	3.62037i	−0.212381	+	0.120881i
$898$	−21.4715	−	23.8466i	−0.716515	−	0.795770i
$899$	−55.5197			−1.85169
$900$	−33.0818	+	57.3380i	−1.10273	+	1.91127i
$901$	−14.1682			−0.472012
$902$	−19.8707	−	22.0687i	−0.661622	−	0.734806i
$903$	0.182638	−	29.6616i	0.00607780	−	0.987078i
$904$	−4.33277	+	41.2235i	−0.144106	+	1.37107i
$905$	30.0702	−	41.9414i	0.999566	−	1.39418i
$906$	−3.28229	−	1.08887i	−0.109047	−	0.0361752i
$907$	3.40353	−	5.89509i	0.113012	−	0.195743i	−0.803971	−	0.594668i	$-0.797283\pi$
$907$	3.40353	−	5.89509i	0.113012	−	0.195743i	0.916983	+	0.398925i	$0.130617\pi$
$908$	−56.1061	+	40.7634i	−1.86195	+	1.35278i
$909$	38.3288	+	0.472027i	1.27129	+	0.0156561i
$910$	−4.21731	+	20.4746i	−0.139802	+	0.678727i
$911$	−17.3545	−	19.2742i	−0.574981	−	0.638581i	0.383567	−	0.923513i	$-0.374696\pi$
$911$	−17.3545	−	19.2742i	−0.574981	−	0.638581i	−0.958548	+	0.284932i	$0.908029\pi$
$912$	82.7707	+	9.21516i	2.74081	+	0.305145i
$913$	6.65476	−	7.39086i	0.220240	−	0.244602i
$914$	0.316437	−	0.0672608i	0.0104668	−	0.00222479i
$915$	−5.10771	−	8.84383i	−0.168856	−	0.292368i
$916$	−25.9336	−	5.51235i	−0.856869	−	0.182133i
$917$	23.0193	−	16.7245i	0.760165	−	0.552292i
$918$	13.5044	−	58.2234i	0.445712	−	1.92166i
$919$	1.07405	−	0.780342i	0.0354296	−	0.0257411i	−0.569930	−	0.821694i	$-0.693030\pi$
$919$	1.07405	−	0.780342i	0.0354296	−	0.0257411i	0.605359	+	0.795952i	$0.293030\pi$
$920$	−12.9706	+	29.6338i	−0.427628	+	0.976996i
$921$	17.5926	+	10.3020i	0.579696	+	0.339464i
$922$	1.91800	−	18.2485i	0.0631658	−	0.600983i
$923$	−17.7871	+	3.78076i	−0.585468	+	0.124445i
$924$	−15.9666	+	35.2755i	−0.525264	+	1.16048i
$925$	20.3399	+	14.3896i	0.668772	+	0.473127i
$926$	57.6748			1.89531
$927$	25.2978	−	10.8920i	0.830889	−	0.357742i
$928$	30.5563	+	22.2004i	1.00306	+	0.728765i
$929$	30.7141	−	13.6748i	1.00770	−	0.448655i	0.164566	−	0.986366i	$-0.447377\pi$
$929$	30.7141	−	13.6748i	1.00770	−	0.448655i	0.843129	+	0.537711i	$0.180711\pi$
$930$	6.96786	+	66.2019i	0.228485	+	2.17085i
$931$	17.9869	+	8.00827i	0.589496	+	0.262460i
$932$	−1.32097	−	2.28799i	−0.0432698	−	0.0749455i
$933$	16.2627	+	5.39498i	0.532415	+	0.176624i
$934$	−24.1172	−	5.12627i	−0.789140	−	0.167737i
$935$	−24.7241	+	2.75627i	−0.808564	+	0.0901397i
$936$	30.0574	−	12.9413i	0.982458	−	0.423000i
$937$	5.34347	+	16.4455i	0.174563	+	0.537251i	0.999613	−	0.0278089i	$-0.00885300\pi$
$937$	5.34347	+	16.4455i	0.174563	+	0.537251i	−0.825050	+	0.565060i	$0.808853\pi$
$938$	8.35207	+	1.77529i	0.272705	+	0.0579652i
$939$	−44.0537	−	40.1601i	−1.43764	−	1.31057i
$940$	59.2665	+	80.5014i	1.93306	+	2.62566i
$941$	24.2742	−	26.9592i	0.791316	−	0.878845i	−0.203652	−	0.979043i	$-0.565281\pi$
$941$	24.2742	−	26.9592i	0.791316	−	0.878845i	0.994967	+	0.100198i	$0.0319478\pi$
$942$	−12.7430	+	11.3326i	−0.415189	+	0.369235i
$943$	5.66663	−	9.81489i	0.184531	−	0.319617i
$944$	−56.1983	+	40.8305i	−1.82910	+	1.32892i
$945$	−23.4418	−	5.28165i	−0.762563	−	0.171812i
$946$	41.5544	+	30.1910i	1.35105	+	0.981595i
$947$	10.7100	−	4.76839i	0.348028	−	0.154952i	−0.225276	−	0.974295i	$-0.572328\pi$
$947$	10.7100	−	4.76839i	0.348028	−	0.154952i	0.573303	+	0.819343i	$0.305662\pi$
$948$	24.3957	−	111.396i	0.792336	−	3.61796i
$949$	−1.75611	−	3.04168i	−0.0570059	−	0.0987370i
$950$	83.1683	−	38.2923i	2.69834	−	1.24237i
$951$	−15.8823	+	35.0891i	−0.515019	+	1.13784i
$952$	−38.4118	−	42.6606i	−1.24493	−	1.38264i
$953$	0.574496	+	0.417395i	0.0186097	+	0.0135208i	0.597051	−	0.802203i	$-0.296339\pi$
$953$	0.574496	+	0.417395i	0.0186097	+	0.0135208i	−0.578442	+	0.815724i	$0.696339\pi$
$954$	19.3422	−	13.6922i	0.626228	−	0.443303i
$955$	−2.23107	+	0.248722i	−0.0721957	+	0.00804847i
$956$	−0.542050	−	5.15726i	−0.0175311	−	0.166798i
$957$	20.2254	+	28.2015i	0.653796	+	0.911624i
$958$	−26.0363	−	11.5921i	−0.841196	−	0.374524i
$959$	−11.8030	+	13.1086i	−0.381139	+	0.423298i
$960$	−3.10994	+	5.38840i	−0.100373	+	0.173910i
$961$	10.0799	+	11.1949i	0.325159	+	0.361126i
$962$	−6.96073	−	21.4229i	−0.224423	−	0.690703i
$963$	1.43954	+	2.56581i	0.0463884	+	0.0826820i
$964$	24.5079	−	75.4277i	0.789348	−	2.42936i
$965$	−23.1488	−	20.5806i	−0.745187	−	0.662512i
$966$	−21.3424	−	2.37613i	−0.686681	−	0.0764507i
$967$	25.5114	+	11.3584i	0.820392	+	0.365262i	0.773625	−	0.633644i	$-0.218441\pi$
$967$	25.5114	+	11.3584i	0.820392	+	0.365262i	0.0467673	+	0.998906i	$0.485108\pi$
$968$	15.2792	+	26.4643i	0.491090	+	0.850594i
$969$	−42.5096	+	37.8045i	−1.36561	+	1.21446i
$970$	62.0801	+	6.12952i	1.99327	+	0.196807i
$971$	−24.9120	−	18.0996i	−0.799465	−	0.580845i	0.111292	−	0.993788i	$-0.464501\pi$
$971$	−24.9120	−	18.0996i	−0.799465	−	0.580845i	−0.910757	+	0.412942i	$0.864501\pi$
$972$	26.0333	+	63.6780i	0.835018	+	2.04247i
$973$	−5.96262	+	18.3511i	−0.191153	+	0.588308i
$974$	10.0423	−	17.3938i	0.321776	−	0.557333i
$975$	9.00553	−	12.5647i	0.288408	−	0.402391i
$976$	8.76719	+	15.1852i	0.280631	+	0.486067i
$977$	−24.5833	+	5.22535i	−0.786491	+	0.167174i	−0.583615	−	0.812031i	$-0.698362\pi$
$977$	−24.5833	+	5.22535i	−0.786491	+	0.167174i	−0.202876	+	0.979204i	$0.565029\pi$
$978$	31.9960	−	18.2112i	1.02312	−	0.582329i
$979$	0.767507	−	0.341716i	0.0245296	−	0.0109213i
$980$	19.8541	−	18.1046i	0.634215	−	0.578329i
$981$	18.0666	−	19.5747i	0.576821	−	0.624973i
$982$	37.2571			1.18892
$983$	−4.95289	−	47.1236i	−0.157973	−	1.50301i	−0.730381	−	0.683040i	$-0.760658\pi$
$983$	−4.95289	−	47.1236i	−0.157973	−	1.50301i	0.572409	−	0.819968i	$-0.306009\pi$
$984$	−30.0374	+	40.8121i	−0.957558	+	1.30104i
$985$	−16.8787	−	5.36683i	−0.537799	−	0.171001i
$986$	−92.0373	+	19.5631i	−2.93106	+	0.623017i
$987$	−21.5094	+	29.2250i	−0.684652	+	0.930243i
$988$	−55.7179	−	11.8432i	−1.77262	−	0.376782i
$989$	−6.05751	+	18.6431i	−0.192617	+	0.592816i
$990$	31.0892	−	27.6563i	0.988080	−	0.878974i
$991$	14.2923	+	43.9872i	0.454010	+	1.39730i	0.872294	+	0.488982i	$0.162632\pi$
$991$	14.2923	+	43.9872i	0.454010	+	1.39730i	−0.418284	+	0.908316i	$0.637368\pi$
$992$	−3.27562	−	31.1655i	−0.104001	−	0.989504i
$993$	9.34720	−	20.6510i	0.296624	−	0.655340i
$994$	−48.7418	−	21.7012i	−1.54600	−	0.688321i
$995$	−31.0187	+	10.2952i	−0.983359	+	0.326379i
$996$	−26.7823	−	15.6834i	−0.848628	−	0.496948i
$997$	−47.2632	+	21.0429i	−1.49684	+	0.666436i	−0.981659	−	0.190645i	$-0.938942\pi$
$997$	−47.2632	+	21.0429i	−1.49684	+	0.666436i	−0.515182	+	0.857081i	$0.672275\pi$
$998$	18.3451	−	56.4605i	0.580705	−	1.78722i
$999$	24.7690	−	7.54508i	0.783658	−	0.238716i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.196.27	yes	224
3.2	odd	2		675.2.r.a.46.2		224
9.4	even	3	inner	225.2.q.a.121.2	yes	224
9.5	odd	6		675.2.r.a.496.27		224
25.6	even	5	inner	225.2.q.a.106.2	yes	224
75.56	odd	10		675.2.r.a.181.27		224
225.31	even	15	inner	225.2.q.a.31.27	✓	224
225.131	odd	30		675.2.r.a.631.2		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.27	✓	224	225.31	even	15	inner
225.2.q.a.106.2	yes	224	25.6	even	5	inner
225.2.q.a.121.2	yes	224	9.4	even	3	inner
225.2.q.a.196.27	yes	224	1.1	even	1	trivial
675.2.r.a.46.2		224	3.2	odd	2
675.2.r.a.181.27		224	75.56	odd	10
675.2.r.a.496.27		224	9.5	odd	6
675.2.r.a.631.2		224	225.131	odd	30

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.69452 + 1.88195i) q^{2} +(-1.49464 - 0.875245i) q^{3} +(-0.461298 + 4.38896i) q^{4} +(-2.12223 + 0.704374i) q^{5} +(-0.885523 - 4.29596i) q^{6} +(-1.03406 + 1.79105i) q^{7} +(-4.94396 + 3.59200i) q^{8} +(1.46789 + 2.61635i) q^{9} +O(q^{10})\)	\(q+(1.69452 + 1.88195i) q^{2} +(-1.49464 - 0.875245i) q^{3} +(-0.461298 + 4.38896i) q^{4} +(-2.12223 + 0.704374i) q^{5} +(-0.885523 - 4.29596i) q^{6} +(-1.03406 + 1.79105i) q^{7} +(-4.94396 + 3.59200i) q^{8} +(1.46789 + 2.61635i) q^{9} +(-4.92175 - 2.80036i) q^{10} +(1.63896 + 1.82025i) q^{11} +(4.53089 - 6.15617i) q^{12} +(-1.19441 + 1.32652i) q^{13} +(-5.12291 + 1.08891i) q^{14} +(3.78847 + 0.804686i) q^{15} +(-6.50420 - 1.38251i) q^{16} +(3.67466 - 2.66979i) q^{17} +(-2.43648 + 7.19596i) q^{18} +(5.85004 - 4.25031i) q^{19} +(-2.11249 - 9.63931i) q^{20} +(3.11316 - 1.77192i) q^{21} +(-0.648378 + 6.16890i) q^{22} +(-2.31553 + 0.492181i) q^{23} +(10.5333 - 1.04156i) q^{24} +(4.00772 - 2.98968i) q^{25} -4.52040 q^{26} +(0.0959772 - 5.19527i) q^{27} +(-7.38384 - 5.36467i) q^{28} +(-7.47301 + 3.32720i) q^{29} +(4.90524 + 8.49327i) q^{30} +(6.20029 + 2.76055i) q^{31} +(-2.30859 - 3.99860i) q^{32} +(-0.856491 - 4.15511i) q^{33} +(11.2512 + 2.39152i) q^{34} +(0.932951 - 4.52939i) q^{35} +(-12.1602 + 5.23561i) q^{36} +(1.53985 + 4.73917i) q^{37} +(17.9119 + 3.80729i) q^{38} +(2.94624 - 0.937275i) q^{39} +(7.96211 - 11.1054i) q^{40} +(-3.20347 + 3.55781i) q^{41} +(8.60997 + 2.85628i) q^{42} +(4.14034 - 7.17127i) q^{43} +(-8.74507 + 6.35367i) q^{44} +(-4.95809 - 4.51855i) q^{45} +(-4.84997 - 3.52371i) q^{46} +(-9.25434 + 4.12030i) q^{47} +(8.51140 + 7.75912i) q^{48} +(1.36143 + 2.35806i) q^{49} +(12.4176 + 2.47626i) q^{50} +(-7.82901 + 0.774155i) q^{51} +(-5.27108 - 5.85413i) q^{52} +(-2.52356 - 1.83348i) q^{53} +(9.93988 - 8.62285i) q^{54} +(-4.76039 - 2.70855i) q^{55} +(-1.32108 - 12.5692i) q^{56} +(-12.4638 + 1.23245i) q^{57} +(-18.9248 - 8.42585i) q^{58} +(6.99016 - 7.76336i) q^{59} +(-5.27935 + 16.2562i) q^{60} +(-1.76446 - 1.95963i) q^{61} +(5.31128 + 16.3465i) q^{62} +(-6.20391 - 0.0764024i) q^{63} +(-0.496397 + 1.52775i) q^{64} +(1.60044 - 3.65649i) q^{65} +(6.36839 - 8.65279i) q^{66} +(-1.48939 - 0.663118i) q^{67} +(10.0225 + 17.3595i) q^{68} +(3.89166 + 1.29102i) q^{69} +(10.1050 - 5.91936i) q^{70} +(8.24169 + 5.98794i) q^{71} +(-16.6551 - 7.66247i) q^{72} +(-0.608028 + 1.87132i) q^{73} +(-6.30959 + 10.9285i) q^{74} +(-8.60680 + 0.960767i) q^{75} +(15.9558 + 27.6363i) q^{76} +(-4.95496 + 1.05321i) q^{77} +(6.75636 + 3.95645i) q^{78} +(13.6290 - 6.06801i) q^{79} +(14.7772 - 1.64738i) q^{80} +(-4.69058 + 7.68104i) q^{81} -12.1240 q^{82} +(-0.424422 - 4.03811i) q^{83} +(6.34077 + 14.4809i) q^{84} +(-5.91793 + 8.25424i) q^{85} +(20.5119 - 4.35993i) q^{86} +(14.0816 + 1.56775i) q^{87} +(-14.6413 - 3.11211i) q^{88} +(0.105993 - 0.326212i) q^{89} +(0.102122 - 16.9877i) q^{90} +(-1.14078 - 3.51095i) q^{91} +(-1.09201 - 10.3898i) q^{92} +(-6.85104 - 9.55279i) q^{93} +(-23.4358 - 10.4343i) q^{94} +(-9.42133 + 13.1407i) q^{95} +(-0.0492408 + 7.99705i) q^{96} +(-10.0640 + 4.48076i) q^{97} +(-2.13079 + 6.55791i) q^{98} +(-2.35660 + 6.96004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

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