LMFDB - Embedded newform 225.2.q.a.106.25

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [225,2,Mod(16,225)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("225.16"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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

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

Self dual:	no
Analytic conductor:	$1.79663404548$
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			106.25
Character	$\chi$	$=$	225.106
Dual form			225.2.q.a.121.25

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.10306 + 0.447019i) q^{2} +(1.01562 + 1.40304i) q^{3} +(2.39595 + 1.06675i) q^{4} +(-1.89032 - 1.19444i) q^{5} +(1.50873 + 3.40468i) q^{6} +(-0.107339 + 0.185917i) q^{7} +(1.08313 + 0.786937i) q^{8} +(-0.937030 + 2.84991i) q^{9} +(-3.44153 - 3.35699i) q^{10} +(0.814318 + 0.173089i) q^{11} +(0.936691 + 4.44502i) q^{12} +(5.35109 - 1.13741i) q^{13} +(-0.308850 + 0.343013i) q^{14} +(-0.244010 - 3.86529i) q^{15} +(-1.58374 - 1.75893i) q^{16} +(-4.59284 - 3.33690i) q^{17} +(-3.24460 + 5.57466i) q^{18} +(-3.93045 - 2.85564i) q^{19} +(-3.25496 - 4.87830i) q^{20} +(-0.369865 + 0.0382202i) q^{21} +(1.63519 + 0.728032i) q^{22} +(-0.383475 + 0.425892i) q^{23} +(-0.00405749 + 2.31890i) q^{24} +(2.14664 + 4.51574i) q^{25} +11.7621 q^{26} +(-4.95020 + 1.57974i) q^{27} +(-0.455506 + 0.330945i) q^{28} +(0.0969420 + 0.922342i) q^{29} +(1.21469 - 8.23802i) q^{30} +(-0.107879 + 1.02640i) q^{31} +(-3.88325 - 6.72599i) q^{32} +(0.584188 + 1.31831i) q^{33} +(-8.16737 - 9.07079i) q^{34} +(0.424973 - 0.223234i) q^{35} +(-5.28520 + 5.82866i) q^{36} +(-2.04164 + 6.28353i) q^{37} +(-6.98945 - 7.76257i) q^{38} +(7.03050 + 6.35260i) q^{39} +(-1.10751 - 2.78129i) q^{40} +(9.61614 - 2.04397i) q^{41} +(-0.794935 - 0.0849575i) q^{42} +(2.16590 - 3.75145i) q^{43} +(1.76642 + 1.28338i) q^{44} +(5.17533 - 4.26802i) q^{45} +(-0.996854 + 0.724257i) q^{46} +(0.270140 + 2.57021i) q^{47} +(0.859356 - 4.00845i) q^{48} +(3.47696 + 6.02227i) q^{49} +(2.49589 + 10.4565i) q^{50} +(0.0172052 - 9.83295i) q^{51} +(14.0343 + 2.98307i) q^{52} +(-7.56450 + 5.49593i) q^{53} +(-11.1167 + 1.10945i) q^{54} +(-1.33258 - 1.29984i) q^{55} +(-0.262568 + 0.116903i) q^{56} +(0.0147238 - 8.41481i) q^{57} +(-0.208430 + 1.98308i) q^{58} +(-9.56875 + 2.03390i) q^{59} +(3.53864 - 9.52133i) q^{60} +(14.7519 + 3.13562i) q^{61} +(-0.685694 + 2.11035i) q^{62} +(-0.429267 - 0.480118i) q^{63} +(-3.69727 - 11.3790i) q^{64} +(-11.4738 - 4.24147i) q^{65} +(0.639273 + 3.03363i) q^{66} +(-1.12882 + 10.7400i) q^{67} +(-7.44460 - 12.8944i) q^{68} +(-0.987009 - 0.105485i) q^{69} +(0.993534 - 0.279503i) q^{70} +(-2.48919 + 1.80850i) q^{71} +(-3.25762 + 2.34943i) q^{72} +(1.33451 + 4.10721i) q^{73} +(-7.10256 + 12.3020i) q^{74} +(-4.15559 + 7.59810i) q^{75} +(-6.37091 - 11.0347i) q^{76} +(-0.119589 + 0.132817i) q^{77} +(11.9458 + 16.5027i) q^{78} +(-0.869419 - 8.27197i) q^{79} +(0.892860 + 5.21662i) q^{80} +(-7.24395 - 5.34090i) q^{81} +21.1370 q^{82} +(-3.17237 + 1.41243i) q^{83} +(-0.926950 - 0.302978i) q^{84} +(4.69624 + 11.7937i) q^{85} +(6.23199 - 6.92132i) q^{86} +(-1.19562 + 1.07276i) q^{87} +(0.745799 + 0.828294i) q^{88} +(-2.45204 - 7.54659i) q^{89} +(12.7919 - 6.66244i) q^{90} +(-0.362919 + 1.11695i) q^{91} +(-1.37311 + 0.611346i) q^{92} +(-1.54964 + 0.891071i) q^{93} +(-0.580813 + 5.52607i) q^{94} +(4.01893 + 10.0927i) q^{95} +(5.49291 - 12.2794i) q^{96} +(-1.06331 - 10.1167i) q^{97} +(4.62018 + 14.2195i) q^{98} +(-1.25633 + 2.15854i) 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} - 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}+ \cdots - 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

Character values

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

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

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 $

$2$	2.10306	+	0.447019i	1.48709	+	0.316090i	0.878633	−	0.477497i	$-0.158456\pi$
$2$	2.10306	+	0.447019i	1.48709	+	0.316090i	0.608456	+	0.793588i	$0.291789\pi$
$3$	1.01562	+	1.40304i	0.586369	+	0.810044i
$3$	1.01562	+	1.40304i	0.586369	+	0.810044i
$4$	2.39595	+	1.06675i	1.19797	+	0.533373i
$5$	−1.89032	−	1.19444i	−0.845378	−	0.534169i
$5$	−1.89032	−	1.19444i	−0.845378	−	0.534169i
$6$	1.50873	+	3.40468i	0.615935	+	1.38995i
$7$	−0.107339	+	0.185917i	−0.0405705	+	0.0702702i	−0.885598	−	0.464453i	$-0.846251\pi$
$7$	−0.107339	+	0.185917i	−0.0405705	+	0.0702702i	0.845027	+	0.534723i	$0.179584\pi$
$8$	1.08313	+	0.786937i	0.382943	+	0.278224i
$9$	−0.937030	+	2.84991i	−0.312343	+	0.949969i
$10$	−3.44153	−	3.35699i	−1.08831	−	1.06157i
$11$	0.814318	+	0.173089i	0.245526	+	0.0521882i	0.329031	−	0.944319i	$-0.393278\pi$
$11$	0.814318	+	0.173089i	0.245526	+	0.0521882i	−0.0835047	+	0.996507i	$0.526611\pi$
$12$	0.936691	+	4.44502i	0.270399	+	1.28317i
$13$	5.35109	−	1.13741i	1.48413	−	0.315461i	0.606606	−	0.795002i	$-0.292530\pi$
$13$	5.35109	−	1.13741i	1.48413	−	0.315461i	0.877519	+	0.479542i	$0.159197\pi$
$14$	−0.308850	+	0.343013i	−0.0825437	+	0.0916740i
$15$	−0.244010	−	3.86529i	−0.0630031	−	0.998013i
$16$	−1.58374	−	1.75893i	−0.395936	−	0.439731i
$17$	−4.59284	−	3.33690i	−1.11393	−	0.809316i	−0.130650	−	0.991429i	$-0.541706\pi$
$17$	−4.59284	−	3.33690i	−1.11393	−	0.809316i	−0.983278	+	0.182113i	$0.941706\pi$
$18$	−3.24460	+	5.57466i	−0.764759	+	1.31396i
$19$	−3.93045	−	2.85564i	−0.901706	−	0.655128i	0.0371973	−	0.999308i	$-0.488157\pi$
$19$	−3.93045	−	2.85564i	−0.901706	−	0.655128i	−0.938904	+	0.344180i	$0.888157\pi$
$20$	−3.25496	−	4.87830i	−0.727830	−	1.09082i
$21$	−0.369865	+	0.0382202i	−0.0807112	+	0.00834033i
$22$	1.63519	+	0.728032i	0.348623	+	0.155217i
$23$	−0.383475	+	0.425892i	−0.0799601	+	0.0888047i	−0.781797	−	0.623533i	$-0.785697\pi$
$23$	−0.383475	+	0.425892i	−0.0799601	+	0.0888047i	0.701837	+	0.712338i	$0.252363\pi$
$24$	−0.00405749	+	2.31890i	−0.000828233	+	0.473343i
$25$	2.14664	+	4.51574i	0.429328	+	0.903149i
$26$	11.7621			2.30674
$27$	−4.95020	+	1.57974i	−0.952666	+	0.304020i
$28$	−0.455506	+	0.330945i	−0.0860826	+	0.0625427i
$29$	0.0969420	+	0.922342i	0.0180017	+	0.171275i	0.999829	−	0.0185029i	$-0.00589000\pi$
$29$	0.0969420	+	0.922342i	0.0180017	+	0.171275i	−0.981827	+	0.189778i	$0.939223\pi$
$30$	1.21469	−	8.23802i	0.221771	−	1.50405i
$31$	−0.107879	+	1.02640i	−0.0193756	+	0.184346i	−0.999929	−	0.0119055i	$-0.996210\pi$
$31$	−0.107879	+	1.02640i	−0.0193756	+	0.184346i	0.980554	+	0.196252i	$0.0628769\pi$
$32$	−3.88325	−	6.72599i	−0.686469	−	1.18900i
$33$	0.584188	+	1.31831i	0.101694	+	0.229489i
$34$	−8.16737	−	9.07079i	−1.40069	−	1.55563i
$35$	0.424973	−	0.223234i	0.0718335	−	0.0377334i
$36$	−5.28520	+	5.82866i	−0.880867	+	0.971444i
$37$	−2.04164	+	6.28353i	−0.335644	+	1.03301i	0.630760	+	0.775978i	$0.282743\pi$
$37$	−2.04164	+	6.28353i	−0.335644	+	1.03301i	−0.966404	+	0.257028i	$0.917257\pi$
$38$	−6.98945	−	7.76257i	−1.13384	−	1.25925i
$39$	7.03050	+	6.35260i	1.12578	+	1.01723i
$40$	−1.10751	−	2.78129i	−0.175113	−	0.439761i
$41$	9.61614	−	2.04397i	1.50179	−	0.319215i	0.617655	−	0.786449i	$-0.288083\pi$
$41$	9.61614	−	2.04397i	1.50179	−	0.319215i	0.884134	+	0.467234i	$0.154749\pi$
$42$	−0.794935	−	0.0849575i	−0.122661	−	0.0131092i
$43$	2.16590	−	3.75145i	0.330296	−	0.572090i	−0.652273	−	0.757984i	$-0.726185\pi$
$43$	2.16590	−	3.75145i	0.330296	−	0.572090i	0.982570	+	0.185894i	$0.0595180\pi$
$44$	1.76642	+	1.28338i	0.266298	+	0.193477i
$45$	5.17533	−	4.26802i	0.771492	−	0.636239i
$46$	−0.996854	+	0.724257i	−0.146978	+	0.106786i
$47$	0.270140	+	2.57021i	0.0394040	+	0.374904i	0.996398	+	0.0847970i	$0.0270242\pi$
$47$	0.270140	+	2.57021i	0.0394040	+	0.374904i	−0.956994	+	0.290107i	$0.906309\pi$
$48$	0.859356	−	4.00845i	0.124037	−	0.578570i
$49$	3.47696	+	6.02227i	0.496708	+	0.860324i
$50$	2.49589	+	10.4565i	0.352972	+	1.47877i
$51$	0.0172052	−	9.83295i	0.00240921	−	1.37689i
$52$	14.0343	+	2.98307i	1.94620	+	0.413678i
$53$	−7.56450	+	5.49593i	−1.03906	+	0.754924i	−0.970103	−	0.242695i	$-0.921969\pi$
$53$	−7.56450	+	5.49593i	−1.03906	+	0.754924i	−0.0689615	+	0.997619i	$0.521969\pi$
$54$	−11.1167	+	1.10945i	−1.51280	+	0.150977i
$55$	−1.33258	−	1.29984i	−0.179685	−	0.175271i
$56$	−0.262568	+	0.116903i	−0.0350871	+	0.0156218i
$57$	0.0147238	−	8.41481i	0.00195022	−	1.11457i
$58$	−0.208430	+	1.98308i	−0.0273682	+	0.260391i
$59$	−9.56875	+	2.03390i	−1.24575	+	0.264791i	−0.783181	−	0.621794i	$-0.786404\pi$
$59$	−9.56875	+	2.03390i	−1.24575	+	0.264791i	−0.462565	+	0.886586i	$0.653071\pi$
$60$	3.53864	−	9.52133i	0.456837	−	1.22920i
$61$	14.7519	+	3.13562i	1.88879	+	0.401475i	0.998541	−	0.0539923i	$-0.0171946\pi$
$61$	14.7519	+	3.13562i	1.88879	+	0.401475i	0.890252	+	0.455468i	$0.150528\pi$
$62$	−0.685694	+	2.11035i	−0.0870832	+	0.268015i
$63$	−0.429267	−	0.480118i	−0.0540826	−	0.0604892i
$64$	−3.69727	−	11.3790i	−0.462158	−	1.42238i
$65$	−11.4738	−	4.24147i	−1.42316	−	0.526090i
$66$	0.639273	+	3.03363i	0.0786890	+	0.373414i
$67$	−1.12882	+	10.7400i	−0.137907	+	1.31210i	0.678489	+	0.734611i	$0.262635\pi$
$67$	−1.12882	+	10.7400i	−0.137907	+	1.31210i	−0.816397	+	0.577492i	$0.804032\pi$
$68$	−7.44460	−	12.8944i	−0.902790	−	1.56368i
$69$	−0.987009	−	0.105485i	−0.118822	−	0.0126989i
$70$	0.993534	−	0.279503i	0.118750	−	0.0334070i
$71$	−2.48919	+	1.80850i	−0.295413	+	0.214630i	−0.725612	−	0.688104i	$-0.758443\pi$
$71$	−2.48919	+	1.80850i	−0.295413	+	0.214630i	0.430199	+	0.902734i	$0.358443\pi$
$72$	−3.25762	+	2.34943i	−0.383914	+	0.276883i
$73$	1.33451	+	4.10721i	0.156193	+	0.480713i	0.998280	−	0.0586293i	$-0.0186730\pi$
$73$	1.33451	+	4.10721i	0.156193	+	0.480713i	−0.842087	+	0.539342i	$0.818673\pi$
$74$	−7.10256	+	12.3020i	−0.825656	+	1.43008i
$75$	−4.15559	+	7.59810i	−0.479846	+	0.877353i
$76$	−6.37091	−	11.0347i	−0.730794	−	1.26577i
$77$	−0.119589	+	0.132817i	−0.0136284	+	0.0151359i
$78$	11.9458	+	16.5027i	1.35260	+	1.86856i
$79$	−0.869419	−	8.27197i	−0.0978173	−	0.930669i	−0.927850	−	0.372954i	$-0.878345\pi$
$79$	−0.869419	−	8.27197i	−0.0978173	−	0.930669i	0.830033	−	0.557715i	$-0.188322\pi$
$80$	0.892860	+	5.21662i	0.0998248	+	0.583236i
$81$	−7.24395	−	5.34090i	−0.804883	−	0.593433i
$82$	21.1370			2.33419
$83$	−3.17237	+	1.41243i	−0.348213	+	0.155034i	−0.573388	−	0.819284i	$-0.694371\pi$
$83$	−3.17237	+	1.41243i	−0.348213	+	0.155034i	0.225175	+	0.974318i	$0.427705\pi$
$84$	−0.926950	−	0.302978i	−0.101139	−	0.0330577i
$85$	4.69624	+	11.7937i	0.509379	+	1.27920i
$86$	6.23199	−	6.92132i	0.672012	−	0.746345i
$87$	−1.19562	+	1.07276i	−0.128184	+	0.115012i
$88$	0.745799	+	0.828294i	0.0795025	+	0.0882964i
$89$	−2.45204	−	7.54659i	−0.259915	−	0.799937i	−0.992821	−	0.119607i	$-0.961837\pi$
$89$	−2.45204	−	7.54659i	−0.259915	−	0.799937i	0.732906	−	0.680330i	$-0.238163\pi$
$90$	12.7919	−	6.66244i	1.34839	−	0.702283i
$91$	−0.362919	+	1.11695i	−0.0380442	+	0.117088i
$92$	−1.37311	+	0.611346i	−0.143156	+	0.0637372i
$93$	−1.54964	+	0.891071i	−0.160690	+	0.0923998i
$94$	−0.580813	+	5.52607i	−0.0599063	+	0.569971i
$95$	4.01893	+	10.0927i	0.412334	+	1.03549i
$96$	5.49291	−	12.2794i	0.560618	−	1.25326i
$97$	−1.06331	−	10.1167i	−0.107962	−	1.02719i	−0.905622	−	0.424085i	$-0.860596\pi$
$97$	−1.06331	−	10.1167i	−0.107962	−	1.02719i	0.797660	−	0.603108i	$-0.206071\pi$
$98$	4.62018	+	14.2195i	0.466709	+	1.43638i
$99$	−1.25633	+	2.15854i	−0.126266	+	0.216942i
$100$	0.326091	+	13.1094i	0.0326091	+	1.31094i
$101$	2.82063	−	4.88547i	0.280663	−	0.486123i	−0.690885	−	0.722965i	$-0.742779\pi$
$101$	2.82063	−	4.88547i	0.280663	−	0.486123i	0.971548	+	0.236842i	$0.0761123\pi$
$102$	4.43170	−	20.6716i	0.438804	−	2.04679i
$103$	5.30676	+	2.36272i	0.522891	+	0.232806i	0.651170	−	0.758932i	$-0.274279\pi$
$103$	5.30676	+	2.36272i	0.522891	+	0.232806i	−0.128279	+	0.991738i	$0.540945\pi$
$104$	6.69098	+	2.97901i	0.656104	+	0.292116i
$105$	0.744816	+	0.369532i	0.0726866	+	0.0360627i
$106$	−18.3654	+	8.17680i	−1.78380	+	0.794201i
$107$	−5.55653			−0.537170			−0.268585	−	0.963256i	$-0.586556\pi$
$107$	−5.55653			−0.537170			−0.268585	+	0.963256i	$0.586556\pi$
$108$	−13.5456	−	1.49563i	−1.30343	−	0.143917i
$109$	2.89880	−	8.92159i	0.277655	−	0.854534i	−0.710850	−	0.703344i	$-0.751689\pi$
$109$	2.89880	−	8.92159i	0.277655	−	0.854534i	0.988505	−	0.151190i	$-0.0483105\pi$
$110$	−2.22144	−	3.32934i	−0.211806	−	0.317440i
$111$	−10.8896	+	3.51718i	−1.03359	+	0.333836i
$112$	0.497013	−	0.105643i	0.0469633	−	0.00998236i
$113$	7.04544	−	1.49755i	0.662779	−	0.140878i	0.135774	−	0.990740i	$-0.456648\pi$
$113$	7.04544	−	1.49755i	0.662779	−	0.140878i	0.527006	+	0.849862i	$0.323315\pi$
$114$	3.79255	−	17.6903i	0.355205	−	1.65685i
$115$	1.23359	−	0.347037i	0.115033	−	0.0323614i
$116$	−0.751636	+	2.31330i	−0.0697876	+	0.214784i
$117$	−1.77262	+	16.3159i	−0.163879	+	1.50841i
$118$	−21.0329			−1.93623
$119$	1.11338	−	0.495709i	0.102063	−	0.0454415i
$120$	2.77745	−	4.37862i	0.253545	−	0.399711i
$121$	−9.41585	−	4.19220i	−0.855986	−	0.381110i
$122$	29.6226	+	13.1888i	2.68190	+	1.19406i
$123$	12.6341	+	11.4159i	1.13918	+	1.02934i
$124$	−1.35337	+	2.34411i	−0.121537	+	0.210508i
$125$	1.33593	−	11.1002i	0.119489	−	0.992835i
$126$	−0.688153	−	1.20161i	−0.0613056	−	0.107048i
$127$	4.49371	+	13.8302i	0.398753	+	1.22723i	0.926000	+	0.377523i	$0.123224\pi$
$127$	4.49371	+	13.8302i	0.398753	+	1.22723i	−0.527248	+	0.849712i	$0.676776\pi$
$128$	−1.06529	−	10.1356i	−0.0941595	−	0.895868i
$129$	7.46315	−	0.771208i	0.657094	−	0.0679011i
$130$	−22.2342	−	14.0491i	−1.95007	−	1.23219i
$131$	1.85447	−	17.6441i	0.162026	−	1.54157i	−0.547447	−	0.836840i	$-0.684400\pi$
$131$	1.85447	−	17.6441i	0.162026	−	1.54157i	0.709473	−	0.704733i	$-0.248933\pi$
$132$	−0.00661719	+	3.78179i	−0.000575952	+	0.329162i
$133$	0.952805	−	0.424216i	0.0826186	−	0.0367842i
$134$	−7.17498	+	22.0823i	−0.619824	+	1.90762i
$135$	11.2444	+	2.92649i	0.967761	+	0.251872i
$136$	−2.34870	−	7.22856i	−0.201399	−	0.619844i
$137$	1.93506	+	2.14910i	0.165323	+	0.183610i	0.820114	−	0.572200i	$-0.193910\pi$
$137$	1.93506	+	2.14910i	0.165323	+	0.183610i	−0.654791	+	0.755810i	$0.727243\pi$
$138$	−2.02859	−	0.663054i	−0.172685	−	0.0564429i
$139$	14.3332	−	15.9187i	1.21573	−	1.35020i	0.297216	−	0.954810i	$-0.403942\pi$
$139$	14.3332	−	15.9187i	1.21573	−	1.35020i	0.918512	−	0.395393i	$-0.129392\pi$
$140$	1.25635	−	0.0815186i	0.106181	−	0.00688958i
$141$	−3.33174	+	2.98938i	−0.280583	+	0.251751i
$142$	−6.04336	+	2.69068i	−0.507148	+	0.225797i
$143$	4.55436			0.380855
$144$	6.49679	−	2.86536i	0.541399	−	0.238780i
$145$	0.918428	−	1.85931i	0.0762713	−	0.154408i
$146$	0.970561	+	9.23427i	0.0803242	+	0.764234i
$147$	−4.91820	+	10.9946i	−0.405646	+	0.906822i
$148$	−11.5946	+	12.8771i	−0.953071	+	1.05849i
$149$	2.89725	+	5.01818i	0.237352	+	0.411105i	0.959954	−	0.280159i	$-0.0903872\pi$
$149$	2.89725	+	5.01818i	0.237352	+	0.411105i	−0.722602	+	0.691265i	$0.757054\pi$
$150$	−12.1360	+	14.1216i	−0.990896	+	1.15303i
$151$	−11.7176	+	20.2954i	−0.953561	+	1.65162i	−0.215934	+	0.976408i	$0.569280\pi$
$151$	−11.7176	+	20.2954i	−0.953561	+	1.65162i	−0.737627	+	0.675209i	$0.764054\pi$
$152$	−2.00996	−	6.18603i	−0.163030	−	0.501753i
$153$	13.8135	−	9.96241i	1.11675	−	0.805413i
$154$	−0.310874	+	0.225863i	−0.0250509	+	0.0182006i
$155$	1.42989	−	1.81137i	0.114852	−	0.145492i
$156$	10.0681	+	22.7203i	0.806095	+	1.81908i
$157$	−6.02359	−	10.4332i	−0.480735	−	0.832657i	0.519021	−	0.854762i	$-0.326297\pi$
$157$	−6.02359	−	10.4332i	−0.480735	−	0.832657i	−0.999756	+	0.0221042i	$0.992963\pi$
$158$	1.86929	−	17.7851i	0.148713	−	1.41491i
$159$	−15.3937	−	5.03150i	−1.22080	−	0.399024i
$160$	−0.693174	+	17.3526i	−0.0548002	+	1.37184i
$161$	−0.0380188	−	0.117010i	−0.00299630	−	0.00922166i
$162$	−12.8470	−	14.4704i	−1.00935	−	1.13690i
$163$	−2.62184	+	8.06919i	−0.205358	+	0.632027i	0.794340	+	0.607473i	$0.207817\pi$
$163$	−2.62184	+	8.06919i	−0.205358	+	0.632027i	−0.999698	+	0.0245544i	$0.992183\pi$
$164$	25.2202	+	5.36072i	1.96937	+	0.418602i
$165$	0.470336	−	3.18981i	0.0366156	−	0.248326i
$166$	−7.30307	+	1.55231i	−0.566828	+	0.120483i
$167$	−1.30146	+	12.3826i	−0.100710	+	0.958193i	0.821161	+	0.570697i	$0.193327\pi$
$167$	−1.30146	+	12.3826i	−0.100710	+	0.958193i	−0.921871	+	0.387497i	$0.873340\pi$
$168$	−0.430688	−	0.249664i	−0.0332283	−	0.0192620i
$169$	15.4644	−	6.88518i	1.18957	−	0.529629i
$170$	4.60448	+	26.9021i	0.353148	+	2.06330i
$171$	11.8212	−	8.52559i	0.903993	−	0.651968i
$172$	9.19122	−	6.67781i	0.700824	−	0.509178i
$173$	0.438291	+	0.0931617i	0.0333227	+	0.00708295i	0.224543	−	0.974464i	$-0.427911\pi$
$173$	0.438291	+	0.0931617i	0.0333227	+	0.00708295i	−0.191220	+	0.981547i	$0.561244\pi$
$174$	−2.99402	+	1.72162i	−0.226976	+	0.130516i
$175$	−1.06997	−	0.0856199i	−0.0808825	−	0.00647225i
$176$	−0.985221	−	1.70645i	−0.0742638	−	0.128629i
$177$	−12.5719	−	11.3596i	−0.944959	−	0.853844i
$178$	−1.78331	−	16.9670i	−0.133665	−	1.27173i
$179$	16.8623	−	12.2512i	1.26035	−	0.915695i	0.261572	−	0.965184i	$-0.415759\pi$
$179$	16.8623	−	12.2512i	1.26035	−	0.915695i	0.998775	+	0.0494885i	$0.0157591\pi$
$180$	16.9527	−	4.70521i	1.26358	−	0.350706i
$181$	−11.8265	−	8.59247i	−0.879058	−	0.638673i	0.0539438	−	0.998544i	$-0.482821\pi$
$181$	−11.8265	−	8.59247i	−0.879058	−	0.638673i	−0.933002	+	0.359871i	$0.882821\pi$
$182$	−1.26254	+	2.18678i	−0.0935856	+	0.162095i
$183$	10.5830	+	23.8821i	0.782317	+	1.76542i
$184$	−0.750503	+	0.159524i	−0.0553278	+	0.0117603i
$185$	11.3647	−	9.43929i	0.835546	−	0.693990i
$186$	−3.65731	+	1.18126i	−0.268167	+	0.0866142i
$187$	−3.16246	−	3.51226i	−0.231262	−	0.256842i
$188$	−2.09452	+	6.44627i	−0.152759	+	0.470142i
$189$	0.237651	−	1.08990i	0.0172866	−	0.0792782i
$190$	3.94041	+	23.0222i	0.285867	+	1.67021i
$191$	15.7623	+	17.5058i	1.14052	+	1.26667i	0.959037	+	0.283279i	$0.0914223\pi$
$191$	15.7623	+	17.5058i	1.14052	+	1.26667i	0.181481	+	0.983395i	$0.441911\pi$
$192$	12.2102	−	16.7442i	0.881193	−	1.20841i
$193$	−0.567396	−	0.982758i	−0.0408420	−	0.0707405i	0.844882	−	0.534953i	$-0.179671\pi$
$193$	−0.567396	−	0.982758i	−0.0408420	−	0.0707405i	−0.885724	+	0.464213i	$0.846337\pi$
$194$	2.28615	−	21.7513i	0.164136	−	1.56165i
$195$	−5.70213	−	20.4060i	−0.408338	−	1.46130i
$196$	1.90639	+	18.1381i	0.136171	+	1.29558i
$197$	7.23157	−	5.25404i	0.515228	−	0.374335i	−0.299575	−	0.954073i	$-0.596845\pi$
$197$	7.23157	−	5.25404i	0.515228	−	0.374335i	0.814803	+	0.579738i	$0.196845\pi$
$198$	−3.60704	+	3.97794i	−0.256341	+	0.282700i
$199$	−11.5001			−0.815219			−0.407609	−	0.913156i	$-0.633637\pi$
$199$	−11.5001			−0.815219			−0.407609	+	0.913156i	$0.633637\pi$
$200$	−1.22853	+	6.58039i	−0.0868699	+	0.465304i
$201$	−16.2151	+	9.32400i	−1.14373	+	0.657665i
$202$	8.11586	−	9.01358i	0.571030	−	0.634193i
$203$	−0.181885	−	0.0809805i	−0.0127658	−	0.00568371i
$204$	10.5305	−	23.5409i	0.737281	−	1.64819i
$205$	−20.6190	−	7.62211i	−1.44009	−	0.532351i
$206$	10.1043	+	7.34117i	0.703997	+	0.511484i
$207$	−0.854426	−	1.49194i	−0.0593867	−	0.103697i
$208$	−10.4754	−	7.61080i	−0.726336	−	0.527714i
$209$	−2.70635	−	3.00571i	−0.187202	−	0.207909i
$210$	1.40121	+	1.11010i	0.0966924	+	0.0766039i
$211$	7.07729	−	7.86013i	0.487221	−	0.541114i	−0.448533	−	0.893766i	$-0.648053\pi$
$211$	7.07729	−	7.86013i	0.487221	−	0.541114i	0.935754	+	0.352652i	$0.114720\pi$
$212$	−23.9869	+	5.09858i	−1.64743	+	0.350172i
$213$	−5.06548	−	1.65568i	−0.347081	−	0.113445i
$214$	−11.6857	−	2.48388i	−0.798819	−	0.169794i
$215$	−8.57511	+	4.50441i	−0.584818	+	0.307198i
$216$	−6.60484	−	2.18444i	−0.449402	−	0.148632i
$217$	−0.179245	−	0.130229i	−0.0121680	−	0.00884054i
$218$	10.0845	−	17.4668i	0.683007	−	1.18300i
$219$	−4.40721	+	6.04374i	−0.297812	+	0.408398i
$220$	−1.80619	−	4.53589i	−0.121773	−	0.305809i
$221$	−28.3721	−	12.6321i	−1.90852	−	0.849726i
$222$	−24.4737	+	2.52900i	−1.64257	+	0.169735i
$223$	−6.61405	−	1.40586i	−0.442910	−	0.0941434i	−0.0189418	−	0.999821i	$-0.506030\pi$
$223$	−6.61405	−	1.40586i	−0.442910	−	0.0941434i	−0.423968	+	0.905677i	$0.639363\pi$
$224$	1.66731			0.111402
$225$	−14.8809	+	1.88634i	−0.992061	+	0.125756i
$226$	15.4864			1.03014
$227$	−2.89305	−	0.614937i	−0.192019	−	0.0408148i	0.110898	−	0.993832i	$-0.464627\pi$
$227$	−2.89305	−	0.614937i	−0.192019	−	0.0408148i	−0.302917	+	0.953017i	$0.597961\pi$
$228$	9.01174	−	20.1457i	0.596817	−	1.33418i
$229$	3.71690	+	1.65487i	0.245620	+	0.109357i	0.525854	−	0.850575i	$-0.323746\pi$
$229$	3.71690	+	1.65487i	0.245620	+	0.109357i	−0.280235	+	0.959931i	$0.590412\pi$
$230$	2.74946	−	0.178400i	0.181294	−	0.0117633i
$231$	−0.307803	−	0.0328961i	−0.0202520	−	0.00216440i
$232$	−0.620825	+	1.07530i	−0.0407591	+	0.0705969i
$233$	−17.2334	−	12.5208i	−1.12900	−	0.820263i	−0.143447	−	0.989658i	$-0.545819\pi$
$233$	−17.2334	−	12.5208i	−1.12900	−	0.820263i	−0.985548	+	0.169395i	$0.945819\pi$
$234$	−11.0215	+	33.5209i	−0.720495	+	2.19133i
$235$	2.55930	−	5.18119i	0.166951	−	0.337984i
$236$	−25.0959	−	5.33430i	−1.63360	−	0.347233i
$237$	10.7229	−	9.62101i	0.696526	−	0.624952i
$238$	2.56310	−	0.544803i	0.166141	−	0.0353144i
$239$	−11.7575	+	13.0580i	−0.760527	+	0.844651i	−0.991742	−	0.128252i	$-0.959063\pi$
$239$	−11.7575	+	13.0580i	−0.760527	+	0.844651i	0.231215	+	0.972903i	$0.425730\pi$
$240$	−6.41231	+	6.55082i	−0.413913	+	0.422854i
$241$	−12.0647	−	13.3992i	−0.777154	−	0.863117i	0.216420	−	0.976300i	$-0.430562\pi$
$241$	−12.0647	−	13.3992i	−0.777154	−	0.863117i	−0.993574	+	0.113183i	$0.963895\pi$
$242$	−17.9281	−	13.0255i	−1.15246	−	0.837313i
$243$	0.136378	−	15.5879i	0.00874864	−	0.999962i
$244$	32.0000	+	23.2494i	2.04859	+	1.48839i
$245$	0.620648	−	15.5370i	0.0396518	−	0.992624i
$246$	21.4672	+	29.6561i	1.36870	+	1.89080i
$247$	−24.2802	−	10.8102i	−1.54491	−	0.687839i
$248$	−0.924555	+	1.02682i	−0.0587093	+	0.0652033i
$249$	−5.20361	−	3.01646i	−0.329766	−	0.191160i
$250$	7.77157	−	22.7473i	0.491517	−	1.43867i
$251$	14.8913			0.939927			0.469964	−	0.882686i	$-0.344267\pi$
$251$	14.8913			0.939927			0.469964	+	0.882686i	$0.344267\pi$
$252$	−0.516339	−	1.60826i	−0.0325263	−	0.101311i
$253$	−0.385988	+	0.280437i	−0.0242669	+	0.0176309i
$254$	3.26817	+	31.0946i	0.205063	+	1.95105i
$255$	−11.7774	+	18.5669i	−0.737527	+	1.16270i
$256$	−0.210854	+	2.00615i	−0.0131784	+	0.125384i
$257$	−3.57122	−	6.18553i	−0.222766	−	0.385843i	0.732881	−	0.680357i	$-0.238175\pi$
$257$	−3.57122	−	6.18553i	−0.222766	−	0.385843i	−0.955647	+	0.294515i	$0.904842\pi$
$258$	16.0402	+	1.71428i	0.998620	+	0.106726i
$259$	−0.949069	−	1.05405i	−0.0589723	−	0.0654954i
$260$	−22.9662	−	22.4020i	−1.42430	−	1.38931i
$261$	−2.71943	−	0.587986i	−0.168328	−	0.0363954i
$262$	11.7873	−	36.2777i	0.728224	−	2.24124i
$263$	−15.9225	−	17.6837i	−0.981822	−	1.09042i	−0.995894	−	0.0905232i	$-0.971146\pi$
$263$	−15.9225	−	17.6837i	−0.981822	−	1.09042i	0.0140720	−	0.999901i	$-0.495521\pi$
$264$	−0.404679	+	1.88762i	−0.0249063	+	0.116175i
$265$	20.8639	−	1.35376i	1.28166	−	0.0831610i
$266$	2.19344	−	0.466230i	0.134488	−	0.0285864i
$267$	8.09781	−	11.1048i	0.495578	−	0.679601i
$268$	−14.1615	+	24.5284i	−0.865049	+	1.49831i
$269$	11.9262	+	8.66489i	0.727154	+	0.528308i	0.888662	−	0.458563i	$-0.151636\pi$
$269$	11.9262	+	8.66489i	0.727154	+	0.528308i	−0.161508	+	0.986871i	$0.551636\pi$
$270$	22.3394	+	11.1810i	1.35953	+	0.680456i
$271$	17.5938	−	12.7827i	1.06875	−	0.776492i	0.0930624	−	0.995660i	$-0.470334\pi$
$271$	17.5938	−	12.7827i	1.06875	−	0.776492i	0.975687	+	0.219168i	$0.0703344\pi$
$272$	1.40453	+	13.3633i	0.0851624	+	0.810266i
$273$	−1.93571	+	0.625208i	−0.117155	+	0.0378393i
$274$	3.10885	+	5.38469i	0.187813	+	0.325301i
$275$	0.966423	+	4.04881i	0.0582775	+	0.244152i
$276$	−2.25230	−	1.30562i	−0.135572	−	0.0785893i
$277$	20.4264	+	4.34177i	1.22730	+	0.260872i	0.775559	−	0.631275i	$-0.217468\pi$
$277$	20.4264	+	4.34177i	1.22730	+	0.260872i	0.451746	+	0.892147i	$0.350801\pi$
$278$	37.2596	−	27.0707i	2.23468	−	1.62359i
$279$	−2.82405	−	1.26921i	−0.169071	−	0.0759855i
$280$	0.635970	+	0.0926368i	0.0380065	+	0.00553611i
$281$	4.51247	−	2.00908i	0.269191	−	0.119852i	−0.267702	−	0.963502i	$-0.586264\pi$
$281$	4.51247	−	2.00908i	0.269191	−	0.119852i	0.536894	+	0.843650i	$0.319598\pi$
$282$	−8.34317	+	4.79749i	−0.496829	+	0.285686i
$283$	0.799696	−	7.60860i	0.0475370	−	0.452284i	−0.944701	−	0.327933i	$-0.893648\pi$
$283$	0.799696	−	7.60860i	0.0475370	−	0.452284i	0.992238	−	0.124352i	$-0.0396852\pi$
$284$	−7.89319	+	1.67775i	−0.468375	+	0.0995562i
$285$	−10.0788	+	15.8891i	−0.597016	+	0.941190i
$286$	9.57810	+	2.03589i	0.566365	+	0.120385i
$287$	−0.652181	+	2.00721i	−0.0384970	+	0.118482i
$288$	22.8072	−	4.76446i	1.34393	−	0.280748i
$289$	4.70604	+	14.4837i	0.276826	+	0.851983i
$290$	2.76266	−	3.49970i	0.162229	−	0.205509i
$291$	13.1142	−	11.7666i	0.768766	−	0.689768i
$292$	−1.18392	+	11.2643i	−0.0692837	+	0.659191i
$293$	7.63483	+	13.2239i	0.446032	+	0.772549i	0.998123	−	0.0612339i	$-0.0195036\pi$
$293$	7.63483	+	13.2239i	0.446032	+	0.772549i	−0.552092	+	0.833783i	$0.686170\pi$
$294$	−15.2581	+	20.9239i	−0.889870	+	1.22030i
$295$	20.5174	+	7.58454i	1.19457	+	0.441589i
$296$	−7.15611	+	5.19921i	−0.415940	+	0.302198i
$297$	−4.30447	+	0.429585i	−0.249770	+	0.0249271i
$298$	3.84987	+	11.8487i	0.223017	+	0.686375i
$299$	−1.56760	+	2.71516i	−0.0906564	+	0.157022i
$300$	−18.0618	+	13.7717i	−1.04280	+	0.795110i
$301$	0.464973	+	0.805356i	0.0268006	+	0.0464200i
$302$	−33.7152	+	37.4445i	−1.94009	+	2.15469i
$303$	9.71920	−	1.00434i	0.558353	−	0.0576977i
$304$	1.20197	+	11.4360i	0.0689376	+	0.655897i
$305$	−24.1406	−	23.5476i	−1.38229	−	1.34833i
$306$	33.5040	−	14.7767i	1.91529	−	0.844725i
$307$	−31.2444			−1.78321			−0.891606	−	0.452812i	$-0.850421\pi$
$307$	−31.2444			−1.78321			−0.891606	+	0.452812i	$0.850421\pi$
$308$	−0.428210	+	0.190651i	−0.0243995	+	0.0108634i
$309$	2.07467	+	9.84521i	0.118024	+	0.560075i
$310$	3.81686	−	3.17022i	0.216783	−	0.180057i
$311$	−15.8341	+	17.5855i	−0.897868	+	0.997183i	0.102129	+	0.994771i	$0.467435\pi$
$311$	−15.8341	+	17.5855i	−0.897868	+	0.997183i	−0.999997	+	0.00241224i	$0.999232\pi$
$312$	2.61582	+	12.4132i	0.148092	+	0.702761i
$313$	5.43570	+	6.03696i	0.307244	+	0.341229i	0.876916	−	0.480643i	$-0.159597\pi$
$313$	5.43570	+	6.03696i	0.307244	+	0.341229i	−0.569672	+	0.821872i	$0.692930\pi$
$314$	−8.00415	−	24.6343i	−0.451701	−	1.39019i
$315$	0.237983	+	1.42031i	0.0134088	+	0.0800254i
$316$	6.74100	−	20.7467i	0.379211	−	1.16709i
$317$	13.3172	−	5.92921i	0.747969	−	0.333017i	0.00289230	−	0.999996i	$-0.499079\pi$
$317$	13.3172	−	5.92921i	0.747969	−	0.333017i	0.745077	+	0.666978i	$0.232413\pi$
$318$	−30.1246	−	17.4628i	−1.68931	−	0.979266i
$319$	−0.0807052	+	0.767859i	−0.00451863	+	0.0429918i
$320$	−6.60249	+	25.9262i	−0.369091	+	1.44932i
$321$	−5.64332	−	7.79602i	−0.314980	−	0.435131i
$322$	−0.0276502	−	0.263074i	−0.00154088	−	0.0146605i
$323$	8.52296	+	26.2310i	0.474230	+	1.45953i
$324$	−11.6588	−	20.5240i	−0.647709	−	1.14022i
$325$	16.6231	+	21.7225i	0.922084	+	1.20495i
$326$	−9.12097	+	15.7980i	−0.505164	+	0.874969i
$327$	15.4614	−	4.99383i	0.855018	−	0.276159i
$328$	12.0240	+	5.35342i	0.663913	+	0.295593i
$329$	−0.506844	−	0.225661i	−0.0279432	−	0.0124411i
$330$	2.41505	−	6.49811i	0.132944	−	0.357709i
$331$	2.80280	−	1.24789i	0.154056	−	0.0685900i	−0.328260	−	0.944587i	$-0.606462\pi$
$331$	2.80280	−	1.24789i	0.154056	−	0.0685900i	0.482316	+	0.875997i	$0.339796\pi$
$332$	−9.10753			−0.499841
$333$	−15.9944	−	11.7064i	−0.876488	−	0.641504i
$334$	−8.27231	+	25.4596i	−0.452641	+	1.39308i
$335$	14.9621	−	18.9538i	0.817468	−	1.03556i
$336$	0.652998	+	0.590034i	0.0356240	+	0.0321890i
$337$	−13.1475	+	2.79458i	−0.716188	+	0.152230i	−0.551572	−	0.834127i	$-0.685972\pi$
$337$	−13.1475	+	2.79458i	−0.716188	+	0.152230i	−0.164616	+	0.986358i	$0.552638\pi$
$338$	35.6003	−	7.56708i	1.93640	−	0.411595i
$339$	9.25662	+	8.36407i	0.502750	+	0.454274i
$340$	−1.32889	+	33.2667i	−0.0720690	+	1.80414i
$341$	−0.265505	+	0.817140i	−0.0143779	+	0.0442506i
$342$	28.6719	−	12.6455i	1.55040	−	0.683791i
$343$	−2.99561			−0.161748
$344$	5.29809	−	2.35886i	0.285654	−	0.127181i
$345$	1.73977	+	1.37832i	0.0936660	+	0.0742063i
$346$	0.880108	+	0.391849i	0.0473149	+	0.0210660i
$347$	21.8117	+	9.71118i	1.17091	+	0.521323i	0.897690	−	0.440628i	$-0.145244\pi$
$347$	21.8117	+	9.71118i	1.17091	+	0.521323i	0.273222	+	0.961951i	$0.411911\pi$
$348$	−4.00902	+	1.29486i	−0.214906	+	0.0694117i
$349$	6.39557	−	11.0774i	0.342347	−	0.592962i	−0.642521	−	0.766268i	$-0.722112\pi$
$349$	6.39557	−	11.0774i	0.342347	−	0.592962i	0.984868	+	0.173306i	$0.0554449\pi$
$350$	−2.21195	−	0.658363i	−0.118234	−	0.0351910i
$351$	−24.6921	+	14.0837i	−1.31797	+	0.751733i
$352$	−1.99801	−	6.14924i	−0.106494	−	0.327756i
$353$	2.26851	+	21.5835i	0.120741	+	1.14877i	0.872254	+	0.489054i	$0.162658\pi$
$353$	2.26851	+	21.5835i	0.120741	+	1.14877i	−0.751513	+	0.659718i	$0.770676\pi$
$354$	−21.3614	−	29.5099i	−1.13535	−	1.56843i
$355$	6.86552	−	0.445472i	0.364384	−	0.0236432i
$356$	2.17534	−	20.6969i	0.115293	−	1.09694i
$357$	1.82627	+	1.05866i	0.0966565	+	0.0560304i
$358$	40.9389	−	18.2272i	2.16369	−	0.963337i
$359$	5.49096	−	16.8994i	0.289802	−	0.891919i	−0.695116	−	0.718897i	$-0.744647\pi$
$359$	5.49096	−	16.8994i	0.289802	−	0.891919i	0.984918	−	0.173021i	$-0.0553529\pi$
$360$	8.96420	−	0.550150i	0.472455	−	0.0289955i
$361$	1.42243	+	4.37778i	0.0748646	+	0.230410i
$362$	−21.0309	−	23.3572i	−1.10536	−	1.22763i
$363$	−3.68110	−	17.4685i	−0.193208	−	0.916857i
$364$	−2.06104	+	2.28901i	−0.108028	+	0.119977i
$365$	2.38314	−	9.35795i	0.124739	−	0.489817i
$366$	11.5809	+	54.9564i	0.605342	+	2.87262i
$367$	−25.3936	+	11.3060i	−1.32554	+	0.590167i	−0.942698	−	0.333648i	$-0.891720\pi$
$367$	−25.3936	+	11.3060i	−1.32554	+	0.590167i	−0.382839	+	0.923815i	$0.625054\pi$
$368$	1.35644			0.0707093
$369$	−3.18548	+	29.3204i	−0.165829	+	1.52636i
$370$	28.1201	−	14.7712i	1.46189	−	0.767917i
$371$	−0.209820	−	1.99630i	−0.0108933	−	0.103643i
$372$	−4.66339	+	0.481894i	−0.241786	+	0.0249850i
$373$	7.86934	−	8.73979i	0.407459	−	0.452529i	−0.504133	−	0.863626i	$-0.668188\pi$
$373$	7.86934	−	8.73979i	0.407459	−	0.452529i	0.911591	+	0.411097i	$0.134854\pi$
$374$	−5.08079	−	8.80018i	−0.262721	−	0.455047i
$375$	16.9309	−	9.39927i	0.874305	−	0.485376i
$376$	−1.73000	+	2.99645i	−0.0892179	+	0.154530i
$377$	1.56783	+	4.82527i	0.0807471	+	0.248514i
$378$	0.986999	−	2.18588i	0.0507657	−	0.112430i
$379$	−9.49787	+	6.90061i	−0.487873	+	0.354460i	−0.804366	−	0.594134i	$-0.797495\pi$
$379$	−9.49787	+	6.90061i	−0.487873	+	0.354460i	0.316493	+	0.948595i	$0.397495\pi$
$380$	−1.13723	+	28.4689i	−0.0583386	+	1.46042i
$381$	−14.8404	+	20.3511i	−0.760298	+	1.04262i
$382$	25.3236	+	43.8618i	1.29567	+	2.24416i
$383$	−3.80547	+	36.2067i	−0.194451	+	1.85007i	0.267988	+	0.963422i	$0.413641\pi$
$383$	−3.80547	+	36.2067i	−0.194451	+	1.85007i	−0.462439	+	0.886651i	$0.653025\pi$
$384$	13.1387	−	11.7886i	0.670481	−	0.601582i
$385$	0.384702	−	0.108225i	0.0196062	−	0.00551567i
$386$	−0.753956	−	2.32044i	−0.0383753	−	0.118107i
$387$	8.66176	+	9.68783i	0.440302	+	0.492460i
$388$	8.24429	−	25.3733i	0.418540	−	1.28814i
$389$	14.8350	+	3.15327i	0.752162	+	0.159877i	0.568011	−	0.823021i	$-0.307713\pi$
$389$	14.8350	+	3.15327i	0.752162	+	0.159877i	0.184151	+	0.982898i	$0.441046\pi$
$390$	−2.87007	−	45.4640i	−0.145332	−	2.30216i
$391$	3.18240	−	0.676440i	0.160941	−	0.0342090i
$392$	−0.973162	+	9.25902i	−0.0491521	+	0.467651i
$393$	26.6388	−	15.3178i	1.34375	−	0.772682i
$394$	17.5571	−	7.81692i	0.884513	−	0.393811i
$395$	−8.23686	+	16.6752i	−0.414442	+	0.839018i
$396$	−5.31271	+	3.83158i	−0.266974	+	0.192544i
$397$	5.32677	−	3.87012i	0.267343	−	0.194236i	−0.446035	−	0.895015i	$-0.647164\pi$
$397$	5.32677	−	3.87012i	0.267343	−	0.194236i	0.713378	+	0.700780i	$0.247164\pi$
$398$	−24.1854	−	5.14076i	−1.21230	−	0.257683i
$399$	1.56288	+	0.905978i	0.0782418	+	0.0453557i
$400$	4.54313	−	10.9276i	0.227156	−	0.546378i
$401$	12.0107	+	20.8032i	0.599786	+	1.03886i	0.992852	+	0.119350i	$0.0380810\pi$
$401$	12.0107	+	20.8032i	0.599786	+	1.03886i	−0.393066	+	0.919510i	$0.628586\pi$
$402$	−38.2694	+	12.3605i	−1.90870	+	0.616485i
$403$	0.590164	+	5.61504i	0.0293982	+	0.279705i
$404$	11.9696	−	8.69646i	0.595512	−	0.432665i
$405$	7.31403	+	18.7485i	0.363437	+	0.931619i
$406$	−0.346316	−	0.251613i	−0.0171874	−	0.0124873i
$407$	−2.75016	+	4.76341i	−0.136320	+	0.236113i
$408$	7.75655	−	10.6368i	0.384007	−	0.526600i
$409$	16.9095	−	3.59424i	0.836123	−	0.177724i	0.230097	−	0.973168i	$-0.426096\pi$
$409$	16.9095	−	3.59424i	0.836123	−	0.177724i	0.606027	+	0.795444i	$0.292762\pi$
$410$	−39.9558	−	25.2469i	−1.97328	−	1.24685i
$411$	−1.04998	+	4.89762i	−0.0517918	+	0.241582i
$412$	10.1943	+	11.3219i	0.502237	+	0.557791i
$413$	0.648967	−	1.99732i	0.0319336	−	0.0982815i
$414$	−1.12998	−	3.51959i	−0.0555357	−	0.172979i
$415$	7.68385	+	1.11925i	0.377186	+	0.0549417i
$416$	−28.4298	−	31.5745i	−1.39389	−	1.54807i
$417$	36.8916	+	3.94274i	1.80659	+	0.193077i
$418$	−4.34802	−	7.53099i	−0.212669	−	0.368353i
$419$	2.15825	−	20.5344i	0.105437	−	1.00317i	−0.806051	−	0.591845i	$-0.798400\pi$
$419$	2.15825	−	20.5344i	0.105437	−	1.00317i	0.911489	−	0.411325i	$-0.134934\pi$
$420$	1.39035	+	1.67991i	0.0678419	+	0.0819712i
$421$	−1.13080	−	10.7588i	−0.0551118	−	0.524354i	−0.986898	−	0.161346i	$-0.948416\pi$
$421$	−1.13080	−	10.7588i	−0.0551118	−	0.524354i	0.931786	−	0.363008i	$-0.118250\pi$
$422$	18.3976	−	13.3666i	0.895582	−	0.650678i
$423$	−7.57800	−	1.63849i	−0.368455	−	0.0796661i
$424$	−12.5183			−0.607941
$425$	5.20939	−	27.9032i	0.252692	−	1.35350i
$426$	−9.91289	−	5.74636i	−0.480281	−	0.278412i
$427$	−2.16643	+	2.40607i	−0.104841	+	0.116438i
$428$	−13.3132	−	5.92740i	−0.643516	−	0.286512i
$429$	4.62550	+	6.38994i	0.223321	+	0.308509i
$430$	−20.0475	+	5.63981i	−0.966779	+	0.271976i
$431$	−4.52152	−	3.28508i	−0.217794	−	0.158237i	0.473539	−	0.880773i	$-0.342976\pi$
$431$	−4.52152	−	3.28508i	−0.217794	−	0.158237i	−0.691333	+	0.722536i	$0.742976\pi$
$432$	10.6185	+	6.20513i	0.510882	+	0.298544i
$433$	−20.6700	−	15.0176i	−0.993337	−	0.721701i	−0.0326873	−	0.999466i	$-0.510407\pi$
$433$	−20.6700	−	15.0176i	−0.993337	−	0.721701i	−0.960649	+	0.277764i	$0.910407\pi$
$434$	−0.318749	−	0.354006i	−0.0153004	−	0.0169928i
$435$	3.54146	−	0.599769i	0.169800	−	0.0287567i
$436$	16.4625	−	18.2834i	0.788408	−	0.875616i
$437$	2.72342	−	0.578881i	0.130279	−	0.0276917i
$438$	−11.9703	+	10.7402i	−0.571964	+	0.513189i
$439$	−19.7486	−	4.19768i	−0.942547	−	0.200345i	−0.289085	−	0.957304i	$-0.593351\pi$
$439$	−19.7486	−	4.19768i	−0.942547	−	0.200345i	−0.653462	+	0.756959i	$0.726684\pi$
$440$	−0.420456	−	2.45655i	−0.0200445	−	0.117112i
$441$	−20.4209	+	4.26596i	−0.972424	+	0.203141i
$442$	−54.0215	−	39.2489i	−2.56954	−	1.86688i
$443$	−15.8802	+	27.5053i	−0.754490	+	1.30681i	0.191138	+	0.981563i	$0.438782\pi$
$443$	−15.8802	+	27.5053i	−0.754490	+	1.30681i	−0.945628	+	0.325252i	$0.894551\pi$
$444$	−29.8428	−	3.18941i	−1.41628	−	0.151363i
$445$	−4.37879	+	17.1943i	−0.207575	+	0.815088i
$446$	−13.2813	−	5.91322i	−0.628888	−	0.279999i
$447$	−4.09819	+	9.16152i	−0.193838	+	0.433325i
$448$	2.51242	+	0.534031i	0.118701	+	0.0252306i
$449$	−1.22065			−0.0576060			−0.0288030	−	0.999585i	$-0.509170\pi$
$449$	−1.22065			−0.0576060			−0.0288030	+	0.999585i	$0.509170\pi$
$450$	−32.1387	−	2.68498i	−1.51503	−	0.126571i
$451$	8.18439			0.385388
$452$	18.4780	+	3.92762i	0.869133	+	0.184740i
$453$	−40.3758	+	4.17225i	−1.89702	+	0.196030i
$454$	−5.80938	−	2.58650i	−0.272648	−	0.121391i
$455$	2.02016	−	1.67791i	0.0947066	−	0.0786617i
$456$	6.63788	−	9.10271i	0.310847	−	0.426274i
$457$	−2.87232	+	4.97500i	−0.134361	+	0.232721i	−0.925353	−	0.379106i	$-0.876232\pi$
$457$	−2.87232	+	4.97500i	−0.134361	+	0.232721i	0.790992	+	0.611827i	$0.209565\pi$
$458$	7.07711	+	5.14182i	0.330692	+	0.240262i
$459$	28.0069	+	9.26280i	1.30725	+	0.432351i
$460$	3.32583	+	0.484447i	0.155068	+	0.0225875i
$461$	29.7543	+	6.32448i	1.38580	+	0.294560i	0.839650	−	0.543128i	$-0.182760\pi$
$461$	29.7543	+	6.32448i	1.38580	+	0.294560i	0.546148	+	0.837689i	$0.316094\pi$
$462$	−0.632624	−	0.206777i	−0.0294323	−	0.00962012i
$463$	−25.3702	+	5.39259i	−1.17905	+	0.250615i	−0.755433	−	0.655226i	$-0.772573\pi$
$463$	−25.3702	+	5.39259i	−1.17905	+	0.250615i	−0.423618	+	0.905841i	$0.639240\pi$
$464$	1.46880	−	1.63127i	0.0681873	−	0.0757297i
$465$	3.99364	+	0.166531i	0.185201	+	0.00772269i
$466$	−30.6458	−	34.0356i	−1.41964	−	1.57667i
$467$	7.52196	+	5.46502i	0.348075	+	0.252891i	0.748061	−	0.663630i	$-0.230985\pi$
$467$	7.52196	+	5.46502i	0.348075	+	0.252891i	−0.399986	+	0.916521i	$0.630985\pi$
$468$	−21.6520	+	37.2011i	−1.00086	+	1.71962i
$469$	−1.87559	−	1.36270i	−0.0866067	−	0.0629234i
$470$	7.69847	−	9.75231i	0.355104	−	0.449841i
$471$	8.52045	−	19.0475i	0.392601	−	0.877661i
$472$	−11.9647	−	5.32704i	−0.550721	−	0.245197i
$473$	2.41306	−	2.67998i	0.110953	−	0.123225i
$474$	26.8517	−	15.4402i	1.23334	−	0.709193i
$475$	4.45807	−	23.8789i	0.204550	−	1.09564i
$476$	3.19640			0.146507
$477$	−8.57473	−	26.7080i	−0.392610	−	1.22287i
$478$	−30.5638	+	22.2059i	−1.39796	+	1.01568i
$479$	−0.329609	−	3.13602i	−0.0150602	−	0.143288i	0.984408	−	0.175901i	$-0.0562839\pi$
$479$	−0.329609	−	3.13602i	−0.0150602	−	0.143288i	−0.999468	+	0.0326127i	$0.989617\pi$
$480$	−25.0504	+	16.6511i	−1.14339	+	0.760016i
$481$	−3.77807	+	35.9459i	−0.172265	+	1.63899i
$482$	−19.3831	−	33.5724i	−0.882874	−	1.52918i
$483$	0.125556	−	0.172179i	0.00571302	−	0.00783443i
$484$	−18.0879	−	20.0886i	−0.822176	−	0.913119i
$485$	−10.0737	+	20.3938i	−0.457425	+	0.926036i
$486$	7.25489	−	32.7213i	0.329088	−	1.48427i
$487$	3.13902	−	9.66092i	0.142243	−	0.437778i	−0.854403	−	0.519610i	$-0.826077\pi$
$487$	3.13902	−	9.66092i	0.142243	−	0.437778i	0.996646	+	0.0818323i	$0.0260772\pi$
$488$	13.5107	+	15.0051i	0.611600	+	0.679251i
$489$	−13.9842	+	4.51669i	−0.632386	+	0.204252i
$490$	8.25062	−	32.3979i	0.372725	−	1.46359i
$491$	−12.7383	+	2.70762i	−0.574873	+	0.122193i	−0.486169	−	0.873865i	$-0.661606\pi$
$491$	−12.7383	+	2.70762i	−0.574873	+	0.122193i	−0.0887041	+	0.996058i	$0.528273\pi$
$492$	18.0929	+	40.8293i	0.815689	+	1.84073i
$493$	2.63252	−	4.55966i	0.118563	−	0.205357i
$494$	−46.2304	−	33.5883i	−2.08000	−	1.51121i
$495$	4.95311	−	2.57974i	0.222626	−	0.115951i
$496$	1.97621	−	1.43580i	0.0887343	−	0.0644692i
$497$	−0.0690438	−	0.656908i	−0.00309704	−	0.0294664i
$498$	−9.59510	−	8.66991i	−0.429967	−	0.388508i
$499$	−11.2205	−	19.4345i	−0.502298	−	0.870006i	−0.999996	−	0.00265559i	$-0.999155\pi$
$499$	−11.2205	−	19.4345i	−0.502298	−	0.870006i	0.497698	−	0.867350i	$-0.334179\pi$
$500$	15.0420	−	25.1705i	0.672696	−	1.12566i
$501$	−18.6950	+	10.7500i	−0.835232	+	0.480275i
$502$	31.3172	+	6.65668i	1.39776	+	0.297102i
$503$	−9.75752	+	7.08926i	−0.435066	+	0.316094i	−0.783672	−	0.621175i	$-0.786655\pi$
$503$	−9.75752	+	7.08926i	−0.435066	+	0.316094i	0.348605	+	0.937270i	$0.386655\pi$
$504$	−0.0871280	−	0.857835i	−0.00388099	−	0.0382110i
$505$	−11.1673	+	5.86606i	−0.496938	+	0.261036i
$506$	−0.937117	+	0.417231i	−0.0416599	+	0.0185482i
$507$	25.3661	+	14.7044i	1.12655	+	0.653044i
$508$	−3.98662	+	37.9302i	−0.176878	+	1.68288i
$509$	15.2446	−	3.24033i	0.675704	−	0.143625i	0.142736	−	0.989761i	$-0.454410\pi$
$509$	15.2446	−	3.24033i	0.675704	−	0.143625i	0.532968	+	0.846136i	$0.321077\pi$
$510$	−33.0683	+	33.7826i	−1.46429	+	1.49592i
$511$	−0.906848	−	0.192757i	−0.0401166	−	0.00852705i
$512$	−7.63887	+	23.5100i	−0.337594	+	1.03901i
$513$	23.9676	+	7.92689i	1.05820	+	0.349981i
$514$	−4.74544	−	14.6050i	−0.209312	−	0.644197i
$515$	−7.20937	−	10.8049i	−0.317683	−	0.476121i
$516$	18.7040	+	6.11351i	0.823398	+	0.269132i
$517$	−0.224894	+	2.13973i	−0.00989084	+	0.0941051i
$518$	−1.52477	−	2.64098i	−0.0669946	−	0.116038i
$519$	0.314428	+	0.709556i	0.0138019	+	0.0311461i
$520$	−9.08986	−	13.6232i	−0.398617	−	0.597419i
$521$	−2.61227	+	1.89793i	−0.114446	+	0.0831496i	−0.643536	−	0.765416i	$-0.722533\pi$
$521$	−2.61227	+	1.89793i	−0.114446	+	0.0831496i	0.529090	+	0.848566i	$0.322533\pi$
$522$	−5.45628	−	2.45221i	−0.238815	−	0.107330i
$523$	1.78463	+	5.49252i	0.0780363	+	0.240171i	0.982463	−	0.186458i	$-0.0597009\pi$
$523$	1.78463	+	5.49252i	0.0780363	+	0.240171i	−0.904427	+	0.426629i	$0.859701\pi$
$524$	23.2650	−	40.2962i	1.01634	−	1.76035i
$525$	−0.966560	−	1.58817i	−0.0421841	−	0.0693135i
$526$	−25.5810	−	44.3076i	−1.11538	−	1.93190i
$527$	3.92044	−	4.35410i	0.170777	−	0.189667i
$528$	1.39361	−	3.11541i	0.0606489	−	0.135581i
$529$	2.36982	+	22.5474i	0.103036	+	0.980320i
$530$	44.4832	+	6.47952i	1.93223	+	0.281452i
$531$	3.16978	−	29.1759i	0.137557	−	1.26613i
$532$	2.73540			0.118595
$533$	49.1320	−	21.8750i	2.12814	−	0.947510i
$534$	21.9942	−	19.7341i	0.951784	−	0.853979i
$535$	10.5036	+	6.63692i	0.454111	+	0.286939i
$536$	−9.67438	+	10.7445i	−0.417870	+	0.464091i
$537$	34.3145	+	11.2159i	1.48078	+	0.484001i
$538$	21.2082	+	23.5540i	0.914349	+	1.01549i
$539$	1.78896	+	5.50586i	0.0770561	+	0.237154i
$540$	23.8191	+	19.0066i	1.02501	+	0.817913i
$541$	−5.27423	+	16.2324i	−0.226757	+	0.697887i	0.771351	+	0.636409i	$0.219581\pi$
$541$	−5.27423	+	16.2324i	−0.226757	+	0.697887i	−0.998108	+	0.0614771i	$0.980419\pi$
$542$	42.7150	−	19.0180i	1.83477	−	0.816891i
$543$	0.0443033	−	25.3197i	0.00190124	−	1.08657i
$544$	−4.60876	+	43.8494i	−0.197599	+	1.88003i
$545$	−16.1360	+	13.4023i	−0.691188	+	0.574090i
$546$	−4.35040	+	0.449550i	−0.186180	+	0.0192390i
$547$	−2.66874	−	25.3914i	−0.114107	−	1.08566i	−0.890367	−	0.455243i	$-0.849552\pi$
$547$	−2.66874	−	25.3914i	−0.114107	−	1.08566i	0.776260	−	0.630413i	$-0.217114\pi$
$548$	2.34376	+	7.21334i	0.100120	+	0.308139i
$549$	−22.7593	+	39.1035i	−0.971341	+	1.66890i
$550$	0.222550	+	8.94690i	0.00948958	+	0.381497i
$551$	2.25285	−	3.90205i	0.0959745	−	0.166233i
$552$	−0.986045	−	0.890968i	−0.0419688	−	0.0379221i
$553$	1.63123	+	0.726268i	0.0693668	+	0.0308841i
$554$	41.0172	+	18.2620i	1.74265	+	0.775879i
$555$	24.7859	+	6.35830i	1.05210	+	0.269895i
$556$	51.3228	−	22.8504i	2.17657	−	0.969073i
$557$	−0.493147			−0.0208953			−0.0104477	−	0.999945i	$-0.503326\pi$
$557$	−0.493147			−0.0208953			−0.0104477	+	0.999945i	$0.503326\pi$
$558$	−5.37179	−	3.93163i	−0.227406	−	0.166439i
$559$	7.32299	−	22.5378i	0.309729	−	0.953249i
$560$	−1.06570	−	0.393951i	−0.0450340	−	0.0166475i
$561$	1.71598	−	8.00417i	0.0724488	−	0.337936i
$562$	10.3881	−	2.20806i	0.438196	−	0.0931414i
$563$	−23.1190	+	4.91409i	−0.974349	+	0.207104i	−0.667464	−	0.744642i	$-0.732620\pi$
$563$	−23.1190	+	4.91409i	−0.974349	+	0.207104i	−0.306885	+	0.951746i	$0.599287\pi$
$564$	−11.1716	+	3.60827i	−0.470409	+	0.151936i
$565$	−15.1069	−	5.58447i	−0.635552	−	0.234941i
$566$	5.08300	−	15.6439i	0.213655	−	0.657561i
$567$	1.77053	−	0.773487i	0.0743552	−	0.0324834i
$568$	−4.11929			−0.172842
$569$	−15.2203	+	6.77652i	−0.638069	+	0.284087i	−0.700162	−	0.713984i	$-0.746889\pi$
$569$	−15.2203	+	6.77652i	−0.638069	+	0.284087i	0.0620932	+	0.998070i	$0.480222\pi$
$570$	−28.2991	+	28.9104i	−1.18532	+	1.21092i
$571$	10.8886	+	4.84792i	0.455674	+	0.202879i	0.621721	−	0.783239i	$-0.286434\pi$
$571$	10.8886	+	4.84792i	0.455674	+	0.202879i	−0.166047	+	0.986118i	$0.553100\pi$
$572$	10.9120	+	4.85834i	0.456254	+	0.203138i
$573$	−8.55278	+	39.8943i	−0.357298	+	1.66661i
$574$	−2.26884	+	3.92974i	−0.0946995	+	0.164024i
$575$	−2.74640	−	0.817438i	−0.114533	−	0.0340895i
$576$	35.8936	+	0.125610i	1.49557	+	0.00523376i
$577$	−2.15829	−	6.64253i	−0.0898507	−	0.276532i	0.896027	−	0.444000i	$-0.146441\pi$
$577$	−2.15829	−	6.64253i	−0.0898507	−	0.276532i	−0.985878	+	0.167468i	$0.946441\pi$
$578$	3.42260	+	32.5638i	0.142361	+	1.35448i
$579$	0.802588	−	1.79419i	0.0333544	−	0.0745639i
$580$	4.18392	−	3.47510i	0.173728	−	0.144295i
$581$	0.0779251	−	0.741408i	0.00323288	−	0.0307588i
$582$	32.8398	−	18.8835i	1.36125	−	0.782747i
$583$	−7.11119	+	3.16611i	−0.294515	+	0.131127i
$584$	−1.78667	+	5.49881i	−0.0739330	+	0.227542i
$585$	22.8391	−	28.7250i	0.944282	−	1.18763i
$586$	10.1452	+	31.2236i	0.419093	+	1.28984i
$587$	16.4197	+	18.2360i	0.677715	+	0.752679i	0.979664	−	0.200645i	$-0.0643038\pi$
$587$	16.4197	+	18.2360i	0.677715	+	0.752679i	−0.301949	+	0.953324i	$0.597637\pi$
$588$	−23.5122	+	21.0961i	−0.969628	+	0.869990i
$589$	3.35502	−	3.72613i	0.138241	−	0.153533i
$590$	39.7589	+	25.1224i	1.63685	+	1.03427i
$591$	14.7161	+	4.81005i	0.605341	+	0.197859i
$592$	14.2857	−	6.36041i	0.587139	−	0.261411i
$593$	−46.1210			−1.89396			−0.946981	−	0.321290i	$-0.895884\pi$
$593$	−46.1210			−1.89396			−0.946981	+	0.321290i	$0.895884\pi$
$594$	−9.24459	−	1.02074i	−0.379310	−	0.0418813i
$595$	−2.69674	−	0.392813i	−0.110556	−	0.0161038i
$596$	1.58854	+	15.1139i	0.0650691	+	0.619091i
$597$	−11.6797	−	16.1350i	−0.478019	−	0.660363i
$598$	−4.51048	+	5.00939i	−0.184447	+	0.204849i
$599$	1.44188	+	2.49741i	0.0589136	+	0.102041i	0.893978	−	0.448111i	$-0.147903\pi$
$599$	1.44188	+	2.49741i	0.0589136	+	0.102041i	−0.835064	+	0.550152i	$0.814570\pi$
$600$	−10.4803	+	4.95951i	−0.427855	+	0.202471i
$601$	12.7488	−	22.0816i	0.520036	−	0.900728i	−0.479693	−	0.877436i	$-0.659252\pi$
$601$	12.7488	−	22.0816i	0.520036	−	0.900728i	0.999729	−	0.0232919i	$-0.00741470\pi$
$602$	0.617856	+	1.90157i	0.0251819	+	0.0775020i
$603$	−29.5503	−	13.2808i	−1.20338	−	0.540834i
$604$	−49.7247	+	36.1271i	−2.02327	+	1.46999i
$605$	12.7917	+	19.1713i	0.520055	+	0.779422i
$606$	20.8890	+	2.23249i	0.848558	+	0.0906885i
$607$	9.59799	+	16.6242i	0.389570	+	0.674756i	0.992392	−	0.123120i	$-0.0392901\pi$
$607$	9.59799	+	16.6242i	0.389570	+	0.674756i	−0.602821	+	0.797876i	$0.705957\pi$
$608$	−3.94407	+	37.5253i	−0.159953	+	1.52185i
$609$	−0.0711076	−	0.337437i	−0.00288142	−	0.0136736i
$610$	−40.2430	−	60.3134i	−1.62939	−	2.44202i
$611$	4.36893	+	13.4462i	0.176748	+	0.543974i
$612$	43.7237	−	9.13396i	1.76743	−	0.369218i
$613$	1.55330	−	4.78057i	0.0627372	−	0.193085i	−0.914775	−	0.403963i	$-0.867632\pi$
$613$	1.55330	−	4.78057i	0.0627372	−	0.193085i	0.977512	+	0.210878i	$0.0676323\pi$
$614$	−65.7089	−	13.9669i	−2.65179	−	0.563656i
$615$	−10.2470	−	36.6704i	−0.413198	−	1.47869i
$616$	−0.234048	+	0.0497484i	−0.00943006	+	0.00200442i
$617$	3.04669	−	28.9873i	0.122655	−	1.16698i	−0.744036	−	0.668139i	$-0.767091\pi$
$617$	3.04669	−	28.9873i	0.122655	−	1.16698i	0.866691	−	0.498845i	$-0.166242\pi$
$618$	−0.0378515	+	21.6325i	−0.00152261	+	0.870187i
$619$	−33.7213	+	15.0137i	−1.35537	+	0.603451i	−0.950444	−	0.310897i	$-0.899371\pi$
$619$	−33.7213	+	15.0137i	−1.35537	+	0.603451i	−0.404930	+	0.914348i	$0.632704\pi$
$620$	5.35821	−	2.81461i	0.215191	−	0.113037i
$621$	1.22548	−	2.71404i	0.0491768	−	0.108911i
$622$	−41.1611	+	29.9053i	−1.65041	+	1.19909i
$623$	1.66624	+	0.354171i	0.0667566	+	0.0141896i
$624$	0.0392417	−	22.4270i	0.00157093	−	0.897800i
$625$	−15.7839	+	19.3873i	−0.631355	+	0.775494i
$626$	8.73297	+	15.1260i	0.349040	+	0.604555i
$627$	1.46850	−	6.84978i	0.0586461	−	0.273554i
$628$	−3.30269	−	31.4230i	−0.131792	−	1.25391i
$629$	30.3444	−	22.0465i	1.20991	−	0.879053i
$630$	−0.134414	+	3.09338i	−0.00535517	+	0.123243i
$631$	−23.9259	−	17.3832i	−0.952474	−	0.692013i	−0.00108328	−	0.999999i	$-0.500345\pi$
$631$	−23.9259	−	17.3832i	−0.952474	−	0.692013i	−0.951391	+	0.307987i	$0.900345\pi$
$632$	5.56783	−	9.64376i	0.221476	−	0.383608i
$633$	18.2159	+	1.94680i	0.724017	+	0.0773784i
$634$	30.6574	−	6.51643i	1.21756	−	0.258800i
$635$	8.02477	−	31.5111i	0.318453	−	1.25048i
$636$	−31.5151	−	28.4763i	−1.24966	−	1.12916i
$637$	25.4553	+	28.2710i	1.00858	+	1.12014i
$638$	−0.512976	+	1.57878i	−0.0203089	+	0.0625044i
$639$	−2.82162	−	8.78859i	−0.111622	−	0.347671i
$640$	−10.0926	+	20.4320i	−0.398944	+	0.807644i
$641$	16.3402	+	18.1476i	0.645399	+	0.716788i	0.973712	−	0.227781i	$-0.0731470\pi$
$641$	16.3402	+	18.1476i	0.645399	+	0.716788i	−0.328314	+	0.944569i	$0.606480\pi$
$642$	−8.38328	−	18.9182i	−0.330862	−	0.746641i
$643$	1.87297	+	3.24409i	0.0738629	+	0.127934i	0.900591	−	0.434667i	$-0.143134\pi$
$643$	1.87297	+	3.24409i	0.0738629	+	0.127934i	−0.826728	+	0.562601i	$0.809801\pi$
$644$	0.0337286	−	0.320906i	0.00132909	−	0.0126455i
$645$	−15.0289	−	7.45643i	−0.591763	−	0.293597i
$646$	6.19855	+	58.9753i	0.243879	+	2.32035i
$647$	19.1798	−	13.9350i	0.754038	−	0.547840i	−0.143038	−	0.989717i	$-0.545687\pi$
$647$	19.1798	−	13.9350i	0.754038	−	0.547840i	0.897076	+	0.441877i	$0.145687\pi$
$648$	−3.64316	−	11.4854i	−0.143117	−	0.451189i
$649$	−8.14405			−0.319682
$650$	25.2490	+	53.1147i	0.990348	+	2.08333i
$651$	0.000671470	−	0.383751i	2.63170e−5	−	0.0150404i
$652$	−14.8896	+	16.5365i	−0.583120	+	0.647620i
$653$	15.7653	+	7.01917i	0.616944	+	0.274681i	0.691320	−	0.722549i	$-0.257030\pi$
$653$	15.7653	+	7.01917i	0.616944	+	0.274681i	−0.0743754	+	0.997230i	$0.523696\pi$
$654$	34.7486	−	3.59077i	1.35878	−	0.140410i
$655$	−24.5803	+	31.1380i	−0.960433	+	1.21666i
$656$	−18.8247	−	13.6769i	−0.734981	−	0.533995i
$657$	−12.9557	−	0.0453385i	−0.505448	−	0.00176882i
$658$	−0.965048	−	0.701149i	−0.0376215	−	0.0273336i
$659$	14.8203	+	16.4596i	0.577317	+	0.641175i	0.959097	−	0.283078i	$-0.0913555\pi$
$659$	14.8203	+	16.4596i	0.577317	+	0.641175i	−0.381780	+	0.924253i	$0.624689\pi$
$660$	4.52961	−	7.14089i	0.176315	−	0.277959i
$661$	−10.0159	+	11.1238i	−0.389575	+	0.432666i	−0.905747	−	0.423818i	$-0.860690\pi$
$661$	−10.0159	+	11.1238i	−0.389575	+	0.432666i	0.516173	+	0.856485i	$0.327356\pi$
$662$	6.45228	−	1.37147i	0.250775	−	0.0533039i
$663$	−11.0920	−	52.6366i	−0.430778	−	2.04423i
$664$	−4.54757	−	0.966615i	−0.176480	−	0.0375119i
$665$	−2.30781	−	0.336160i	−0.0894929	−	0.0130357i
$666$	−28.4043	−	31.7690i	−1.10064	−	1.23102i
$667$	−0.429993	−	0.312408i	−0.0166494	−	0.0120965i
$668$	−16.3273	+	28.2797i	−0.631722	+	1.09417i
$669$	−4.74489	−	10.7076i	−0.183448	−	0.413979i
$670$	39.9390	−	33.1726i	1.54298	−	1.28157i
$671$	11.4700	+	5.10679i	0.442796	+	0.197145i
$672$	1.69335	+	2.33929i	0.0653224	+	0.0902402i
$673$	−8.03882	−	1.70870i	−0.309874	−	0.0658657i	0.0503500	−	0.998732i	$-0.483966\pi$
$673$	−8.03882	−	1.70870i	−0.309874	−	0.0658657i	−0.360224	+	0.932866i	$0.617300\pi$
$674$	−28.8991			−1.11315
$675$	−17.7600	−	18.9627i	−0.683582	−	0.729874i
$676$	44.3966			1.70756
$677$	−3.98325	−	0.846666i	−0.153089	−	0.0325400i	0.130730	−	0.991418i	$-0.458268\pi$
$677$	−3.98325	−	0.846666i	−0.153089	−	0.0325400i	−0.283818	+	0.958878i	$0.591601\pi$
$678$	15.7283	+	21.7280i	0.604043	+	0.834460i
$679$	1.99500	+	0.888232i	0.0765611	+	0.0340872i
$680$	−4.19426	+	16.4697i	−0.160842	+	0.631584i
$681$	−2.07546	−	4.68360i	−0.0795319	−	0.179476i
$682$	−0.923650	+	1.59981i	−0.0353684	+	0.0612599i
$683$	−22.8029	−	16.5672i	−0.872527	−	0.633928i	0.0587367	−	0.998274i	$-0.481293\pi$
$683$	−22.8029	−	16.5672i	−0.872527	−	0.633928i	−0.931264	+	0.364345i	$0.881293\pi$
$684$	37.4177	−	7.81663i	1.43070	−	0.298876i
$685$	−1.09092	−	6.37379i	−0.0416818	−	0.243530i
$686$	−6.29995	−	1.33910i	−0.240533	−	0.0511269i
$687$	1.45311	+	6.89567i	0.0554398	+	0.263086i
$688$	−10.0287	+	2.13167i	−0.382342	+	0.0812693i
$689$	−34.2272	+	38.0132i	−1.30395	+	1.44819i
$690$	3.04270	+	3.67640i	0.115834	+	0.139958i
$691$	9.63302	+	10.6986i	0.366457	+	0.406992i	0.897969	−	0.440059i	$-0.145042\pi$
$691$	9.63302	+	10.6986i	0.366457	+	0.406992i	−0.531511	+	0.847051i	$0.678376\pi$
$692$	0.950744	+	0.690756i	0.0361419	+	0.0262586i
$693$	−0.266457	−	0.465270i	−0.0101219	−	0.0176741i
$694$	41.5302	+	30.1734i	1.57646	+	1.14537i
$695$	−46.1083	+	12.9713i	−1.74899	+	0.492028i
$696$	−2.13921	+	0.221056i	−0.0810865	+	0.00837911i
$697$	−50.9860	−	22.7004i	−1.93123	−	0.859839i
$698$	18.4021	−	20.4376i	0.696530	−	0.773575i
$699$	0.0645579	−	36.8954i	0.00244180	−	1.39551i
$700$	−2.47227	−	1.34653i	−0.0934430	−	0.0508941i
$701$	−29.8133			−1.12603			−0.563017	−	0.826446i	$-0.690359\pi$
$701$	−29.8133			−1.12603			−0.563017	+	0.826446i	$0.690359\pi$
$702$	−58.2248	+	18.5810i	−2.19755	+	0.701296i
$703$	25.9681	−	18.8669i	0.979404	−	0.711579i
$704$	−1.04117	−	9.90609i	−0.0392406	−	0.373350i
$705$	9.86869	−	1.67133i	0.371676	−	0.0629458i
$706$	−4.87741	+	46.4054i	−0.183564	+	1.74649i
$707$	0.605530	+	1.04881i	0.0227733	+	0.0394445i
$708$	−18.0037	−	40.6281i	−0.676620	−	1.52690i
$709$	8.07398	+	8.96707i	0.303225	+	0.336765i	0.875430	−	0.483345i	$-0.160578\pi$
$709$	8.07398	+	8.96707i	0.303225	+	0.336765i	−0.572205	+	0.820111i	$0.693912\pi$
$710$	14.6378	+	2.13217i	0.549345	+	0.0800188i
$711$	24.3890	+	5.27332i	0.914660	+	0.197765i
$712$	3.28283	−	10.1035i	0.123029	−	0.378645i
$713$	−0.395765	−	0.439542i	−0.0148215	−	0.0164610i
$714$	3.36751	+	3.04281i	0.126026	+	0.113874i
$715$	−8.60921	−	5.43990i	−0.321966	−	0.203441i
$716$	53.4701	−	11.3654i	1.99827	−	0.424745i
$717$	−30.2620	−	3.23421i	−1.13015	−	0.120784i
$718$	19.1022	−	33.0860i	0.712888	−	1.23476i
$719$	11.6486	+	8.46317i	0.434418	+	0.315623i	0.783413	−	0.621502i	$-0.213477\pi$
$719$	11.6486	+	8.46317i	0.434418	+	0.315623i	−0.348995	+	0.937125i	$0.613477\pi$
$720$	−15.7035	−	2.34356i	−0.585236	−	0.0873393i
$721$	−1.00890	+	0.733006i	−0.0375732	+	0.0272986i
$722$	1.03450	+	9.84260i	0.0385001	+	0.366304i
$723$	6.54642	−	30.5357i	0.243464	−	1.13563i
$724$	−19.1698	−	33.2030i	−0.712439	−	1.23398i
$725$	−3.95696	+	2.41770i	−0.146958	+	0.0897911i
$726$	0.0671604	−	38.3828i	0.00249256	−	1.42452i
$727$	11.8911	+	2.52754i	0.441018	+	0.0937412i	0.423068	−	0.906098i	$-0.360953\pi$
$727$	11.8911	+	2.52754i	0.441018	+	0.0937412i	0.0179491	+	0.999839i	$0.494286\pi$
$728$	−1.27206	+	0.924203i	−0.0471455	+	0.0342532i
$729$	22.0089	−	15.6400i	0.815143	−	0.579260i
$730$	9.19508	−	18.6150i	0.340325	−	0.688973i
$731$	−22.4658	+	10.0024i	−0.830928	+	0.369953i
$732$	−0.119875	+	68.5098i	−0.00443071	+	2.53219i
$733$	−4.40888	+	41.9477i	−0.162846	+	1.54937i	0.542224	+	0.840234i	$0.317582\pi$
$733$	−4.40888	+	41.9477i	−0.162846	+	1.54937i	−0.705069	+	0.709138i	$0.749084\pi$
$734$	−58.4584	+	12.4257i	−2.15774	+	0.458641i
$735$	22.4294	−	14.9089i	0.827320	−	0.549924i
$736$	4.35368	+	0.925403i	0.160479	+	0.0341108i
$737$	−2.77819	+	8.55040i	−0.102336	+	0.314958i
$738$	−19.8060	+	60.2386i	−0.729070	+	2.21741i
$739$	8.98032	+	27.6386i	0.330347	+	1.01670i	0.968969	+	0.247182i	$0.0795045\pi$
$739$	8.98032	+	27.6386i	0.330347	+	1.01670i	−0.638623	+	0.769520i	$0.720495\pi$
$740$	37.2984	−	10.4929i	1.37112	−	0.385726i
$741$	−9.49229	−	45.0451i	−0.348708	−	1.65477i
$742$	0.451122	−	4.29214i	0.0165612	−	0.157569i
$743$	−6.94670	−	12.0320i	−0.254850	−	0.441413i	0.710005	−	0.704197i	$-0.248693\pi$
$743$	−6.94670	−	12.0320i	−0.254850	−	0.441413i	−0.964855	+	0.262784i	$0.915359\pi$
$744$	−2.37967	−	0.254324i	−0.0872429	−	0.00932396i
$745$	0.517168	−	12.9466i	0.0189476	−	0.474325i
$746$	20.4566	−	14.8626i	0.748968	−	0.544157i
$747$	−1.05269	−	10.3644i	−0.0385159	−	0.379215i
$748$	−3.83039	−	11.7887i	−0.140053	−	0.431039i
$749$	0.596435	−	1.03305i	0.0217932	−	0.0377470i
$750$	39.8083	−	12.1988i	1.45359	−	0.445438i
$751$	3.34417	+	5.79228i	0.122031	+	0.211363i	0.920568	−	0.390582i	$-0.127726\pi$
$751$	3.34417	+	5.79228i	0.122031	+	0.211363i	−0.798538	+	0.601945i	$0.794393\pi$
$752$	4.09298	−	4.54571i	0.149256	−	0.165765i
$753$	15.1239	+	20.8930i	0.551144	+	0.761383i
$754$	1.14024	+	10.8487i	0.0415252	+	0.395086i
$755$	46.3915	−	24.3690i	1.68836	−	0.886878i
$756$	1.73204	−	2.35782i	0.0629937	−	0.0857531i
$757$	52.8193			1.91975			0.959875	−	0.280428i	$-0.0904765\pi$
$757$	52.8193			1.91975			0.959875	+	0.280428i	$0.0904765\pi$
$758$	−23.0593	+	10.2667i	−0.837552	+	0.372902i
$759$	−0.785480	−	0.256738i	−0.0285111	−	0.00931901i
$760$	−3.58935	+	14.0944i	−0.130199	+	0.511257i
$761$	−30.4351	+	33.8016i	−1.10327	+	1.22531i	−0.131017	+	0.991380i	$0.541824\pi$
$761$	−30.4351	+	33.8016i	−1.10327	+	1.22531i	−0.972254	+	0.233927i	$0.924842\pi$
$762$	−40.3077	+	36.1657i	−1.46019	+	1.31014i
$763$	1.34752	+	1.49658i	0.0487836	+	0.0541797i
$764$	19.0914	+	58.7573i	0.690703	+	2.12576i
$765$	−38.0114	+	2.33283i	−1.37430	+	0.0843438i
$766$	−24.1882	+	74.4437i	−0.873956	+	2.68976i
$767$	−48.8899	+	21.7672i	−1.76531	+	0.785967i
$768$	−3.02885	+	1.74165i	−0.109294	+	0.0628462i
$769$	3.85459	−	36.6740i	0.139000	−	1.32250i	−0.673349	−	0.739325i	$-0.735145\pi$
$769$	3.85459	−	36.6740i	0.139000	−	1.32250i	0.812349	−	0.583172i	$-0.198189\pi$
$770$	0.857431	−	0.0556348i	0.0308997	−	0.00200494i
$771$	5.05153	−	11.2927i	0.181926	−	0.406697i
$772$	−0.311099	−	2.95991i	−0.0111967	−	0.106529i
$773$	−11.0880	−	34.1253i	−0.398806	−	1.22740i	−0.925957	−	0.377628i	$-0.876740\pi$
$773$	−11.0880	−	34.1253i	−0.398806	−	1.22740i	0.527151	−	0.849772i	$-0.323260\pi$
$774$	13.8856	+	24.2461i	0.499107	+	0.871507i
$775$	−4.86652	+	1.71615i	−0.174810	+	0.0616459i
$776$	6.80950	−	11.7944i	0.244447	−	0.423394i
$777$	0.514975	−	2.40209i	0.0184746	−	0.0861746i
$778$	29.7893	+	13.2630i	1.06800	+	0.475503i
$779$	−43.6326	−	19.4265i	−1.56330	−	0.696026i
$780$	8.10595	−	54.9744i	0.290239	−	1.96840i
$781$	−2.34003	+	1.04185i	−0.0837327	+	0.0372802i
$782$	6.99516			0.250147
$783$	−1.93694	−	4.41263i	−0.0692206	−	0.157694i
$784$	5.08611	−	15.6534i	0.181647	−	0.559051i
$785$	−1.07523	+	26.9169i	−0.0383767	+	0.960704i
$786$	62.8704	−	20.3063i	2.24251	−	0.724301i
$787$	1.69173	−	0.359589i	0.0603037	−	0.0128179i	−0.177661	−	0.984092i	$-0.556853\pi$
$787$	1.69173	−	0.359589i	0.0603037	−	0.0128179i	0.237965	+	0.971274i	$0.423520\pi$
$788$	22.9312	−	4.87418i	0.816890	−	0.173635i
$789$	8.63971	−	40.2998i	0.307582	−	1.43471i
$790$	−24.7767	+	31.3868i	−0.881517	+	1.11669i
$791$	−0.477832	+	1.47062i	−0.0169898	+	0.0522891i
$792$	−3.05940	+	1.34932i	−0.108711	+	0.0479461i
$793$	82.5055			2.92986
$794$	12.9325	−	5.75794i	0.458958	−	0.204341i
$795$	23.0892	+	27.8979i	0.818889	+	0.989437i
$796$	−27.5536	−	12.2676i	−0.976611	−	0.434815i
$797$	−12.9904	−	5.78369i	−0.460143	−	0.204869i	0.163555	−	0.986534i	$-0.447704\pi$
$797$	−12.9904	−	5.78369i	−0.460143	−	0.204869i	−0.623698	+	0.781665i	$0.714370\pi$
$798$	2.88184	+	2.60397i	0.102016	+	0.0921794i
$799$	7.33582	−	12.7060i	0.259523	−	0.449506i
$800$	22.0369	−	31.9741i	0.779122	−	1.13045i
$801$	23.8047	+	0.0833050i	0.841098	+	0.00294344i
$802$	15.9598	+	49.1193i	0.563561	+	1.73446i
$803$	0.375807	+	3.57557i	0.0132619	+	0.126179i
$804$	−48.7969	+	5.04245i	−1.72093	+	0.177834i
$805$	−0.0678931	+	0.266597i	−0.00239292	+	0.00939632i
$806$	−1.26888	+	12.0726i	−0.0446944	+	0.425239i
$807$	−0.0446767	+	25.5332i	−0.00157269	+	0.898810i
$808$	6.89966	−	3.07193i	0.242729	−	0.108070i
$809$	−15.8154	+	48.6748i	−0.556040	+	1.71132i	0.137141	+	0.990552i	$0.456209\pi$
$809$	−15.8154	+	48.6748i	−0.556040	+	1.71132i	−0.693181	+	0.720764i	$0.743791\pi$
$810$	7.00093	+	42.6987i	0.245988	+	1.50028i
$811$	−4.48774	−	13.8118i	−0.157586	−	0.484999i	0.840828	−	0.541303i	$-0.182069\pi$
$811$	−4.48774	−	13.8118i	−0.157586	−	0.484999i	−0.998414	+	0.0563032i	$0.982069\pi$
$812$	−0.349402	−	0.388050i	−0.0122616	−	0.0136179i
$813$	35.8032	+	11.7025i	1.25567	+	0.410424i
$814$	−7.91308	+	8.78837i	−0.277353	+	0.308032i
$815$	14.5943	−	12.1217i	0.511214	−	0.424606i
$816$	−17.3227	+	15.5426i	−0.606415	+	0.544100i
$817$	−19.2257	+	8.55984i	−0.672623	+	0.299471i
$818$	37.1685			1.29957
$819$	−2.84314	−	2.08090i	−0.0993473	−	0.0727126i
$820$	−41.2713	−	40.2574i	−1.44125	−	1.40585i
$821$	−3.87368	−	36.8556i	−0.135192	−	1.28627i	−0.826182	−	0.563404i	$-0.809491\pi$
$821$	−3.87368	−	36.8556i	−0.135192	−	1.28627i	0.690989	−	0.722865i	$-0.257175\pi$
$822$	−4.39751	+	9.83064i	−0.153381	+	0.342883i
$823$	25.2628	−	28.0572i	0.880605	−	0.978011i	−0.119285	−	0.992860i	$-0.538060\pi$
$823$	25.2628	−	28.0572i	0.880605	−	0.978011i	0.999890	+	0.0148491i	$0.00472679\pi$
$824$	3.88858	+	6.73521i	0.135465	+	0.234632i
$825$	−4.69911	+	5.46798i	−0.163602	+	0.190371i
$826$	2.25766	−	3.91038i	0.0785539	−	0.136059i
$827$	−2.01840	−	6.21199i	−0.0701866	−	0.216012i	0.909811	−	0.415024i	$-0.136227\pi$
$827$	−2.01840	−	6.21199i	−0.0701866	−	0.216012i	−0.979997	+	0.199012i	$0.936227\pi$
$828$	−0.455639	−	4.48608i	−0.0158345	−	0.155902i
$829$	−15.0231	+	10.9149i	−0.521772	+	0.379090i	−0.817271	−	0.576253i	$-0.804514\pi$
$829$	−15.0231	+	10.9149i	−0.521772	+	0.379090i	0.295499	+	0.955343i	$0.404514\pi$
$830$	15.6593	+	5.78868i	0.543542	+	0.200928i
$831$	14.6538	+	33.0686i	0.508336	+	1.14714i
$832$	−32.7270	−	56.6848i	−1.13460	−	1.96519i
$833$	4.12656	−	39.2616i	0.142977	−	1.36033i
$834$	75.8228	+	24.7831i	2.62553	+	0.858168i
$835$	17.2504	−	21.8526i	0.596975	−	0.756239i
$836$	−3.27796	−	10.0885i	−0.113371	−	0.348919i
$837$	−1.08742	−	5.25128i	−0.0375866	−	0.181511i
$838$	13.7182	−	42.2203i	0.473887	−	1.45848i
$839$	−27.0809	−	5.75622i	−0.934936	−	0.198727i	−0.284837	−	0.958576i	$-0.591939\pi$
$839$	−27.0809	−	5.75622i	−0.934936	−	0.198727i	−0.650099	+	0.759849i	$0.725273\pi$
$840$	0.515931	+	0.986374i	0.0178013	+	0.0340331i
$841$	27.5250	−	5.85061i	0.949137	−	0.201745i
$842$	2.43127	−	23.1320i	0.0837871	−	0.797181i
$843$	7.40178	+	4.29070i	0.254931	+	0.147780i
$844$	25.3416	−	11.2828i	0.872294	−	0.388370i
$845$	−37.4566	−	5.45600i	−1.28854	−	0.187692i
$846$	−15.2046	−	6.83336i	−0.522743	−	0.234936i
$847$	1.79010	−	1.30058i	0.0615084	−	0.0446885i
$848$	21.6472	+	4.60125i	0.743367	+	0.158007i
$849$	11.4873	−	6.60545i	0.394245	−	0.226698i
$850$	23.4289	−	56.3535i	0.803606	−	1.93291i
$851$	−1.89319	−	3.27910i	−0.0648977	−	0.112406i
$852$	−10.3704	−	9.37049i	−0.355285	−	0.321028i
$853$	−2.16611	−	20.6091i	−0.0741660	−	0.705643i	−0.966917	−	0.255092i	$-0.917894\pi$
$853$	−2.16611	−	20.6091i	−0.0741660	−	0.705643i	0.892751	−	0.450551i	$-0.148772\pi$
$854$	−5.63170	+	4.09167i	−0.192713	+	0.140014i
$855$	−32.5293	+	1.99638i	−1.11248	+	0.0682749i
$856$	−6.01842	−	4.37264i	−0.205705	−	0.149454i
$857$	9.92764	−	17.1952i	0.339122	−	0.587376i	−0.645146	−	0.764059i	$-0.723203\pi$
$857$	9.92764	−	17.1952i	0.339122	−	0.587376i	0.984268	+	0.176683i	$0.0565368\pi$
$858$	6.87129	+	15.5061i	0.234582	+	0.529370i
$859$	−21.8604	+	4.64657i	−0.745867	+	0.158539i	−0.565141	−	0.824994i	$-0.691178\pi$
$859$	−21.8604	+	4.64657i	−0.745867	+	0.158539i	−0.180726	+	0.983533i	$0.557845\pi$
$860$	−25.3506	+	1.64488i	−0.864448	+	0.0560901i
$861$	−3.47856	+	1.12353i	−0.118549	+	0.0382897i
$862$	−8.04054	−	8.92992i	−0.273862	−	0.304154i
$863$	−8.57513	+	26.3915i	−0.291901	+	0.898378i	0.692344	+	0.721567i	$0.256578\pi$
$863$	−8.57513	+	26.3915i	−0.291901	+	0.898378i	−0.984245	+	0.176811i	$0.943422\pi$
$864$	29.8482	+	27.1605i	1.01545	+	0.924018i
$865$	−0.717236	−	0.699617i	−0.0243868	−	0.0237877i
$866$	−36.7571	−	40.8229i	−1.24906	−	1.38722i
$867$	−15.5416	+	21.3127i	−0.527822	+	0.723817i
$868$	−0.290541	−	0.503232i	−0.00986160	−	0.0170808i
$869$	0.723800	−	6.88650i	0.0245532	−	0.233608i
$870$	7.71602	+	0.321751i	0.261598	+	0.0109084i
$871$	6.17537	+	58.7547i	0.209244	+	1.99083i
$872$	10.1605	−	7.38204i	0.344078	−	0.249987i
$873$	29.8279	+	6.44931i	1.00952	+	0.218276i
$874$	5.98630			0.202490
$875$	1.92033	+	1.43987i	0.0649190	+	0.0486764i
$876$	−17.0066	+	9.77912i	−0.574600	+	0.330406i
$877$	−11.1114	+	12.3405i	−0.375205	+	0.416708i	−0.900942	−	0.433940i	$-0.857123\pi$
$877$	−11.1114	+	12.3405i	−0.375205	+	0.416708i	0.525736	+	0.850647i	$0.323790\pi$
$878$	−39.6560	−	17.6560i	−1.33832	−	0.595860i
$879$	−10.7996	+	24.1424i	−0.364260	+	0.814304i
$880$	−0.175865	+	4.40253i	−0.00592841	+	0.148409i
$881$	11.1788	+	8.12184i	0.376622	+	0.273632i	0.759951	−	0.649980i	$-0.225223\pi$
$881$	11.1788	+	8.12184i	0.376622	+	0.273632i	−0.383330	+	0.923612i	$0.625223\pi$
$882$	−44.8534	−	0.156965i	−1.51029	−	0.00528529i
$883$	−24.1939	−	17.5779i	−0.814188	−	0.591543i	0.100853	−	0.994901i	$-0.467843\pi$
$883$	−24.1939	−	17.5779i	−0.814188	−	0.591543i	−0.915042	+	0.403359i	$0.867843\pi$
$884$	−54.5030	−	60.5317i	−1.83313	−	2.03590i
$885$	10.1965	+	36.4897i	0.342751	+	1.22659i
$886$	−45.6924	+	50.7465i	−1.53507	+	1.70486i
$887$	32.1673	−	6.83737i	1.08007	−	0.229576i	0.366684	−	0.930346i	$-0.380493\pi$
$887$	32.1673	−	6.83737i	1.08007	−	0.229576i	0.713388	+	0.700769i	$0.247160\pi$
$888$	−14.5626	−	4.75986i	−0.488688	−	0.159730i
$889$	−3.05363	−	0.649070i	−0.102416	−	0.0217691i
$890$	−16.8950	+	34.2032i	−0.566323	+	1.14650i
$891$	−4.97443	−	5.60303i	−0.166650	−	0.187709i
$892$	−14.3472	−	10.4239i	−0.480381	−	0.349017i
$893$	6.27782	−	10.8735i	0.210079	−	0.363868i
$894$	−12.7141	+	17.4353i	−0.425224	+	0.583122i
$895$	−46.5084	+	3.01772i	−1.55461	+	0.100871i
$896$	1.99873	+	0.889892i	0.0667729	+	0.0297292i
$897$	−5.40155	+	0.558172i	−0.180353	+	0.0186368i
$898$	−2.56710	−	0.545654i	−0.0856652	−	0.0182087i
$899$	−0.957146			−0.0319226
$900$	−37.6662	−	11.3546i	−1.25554	−	0.378486i
$901$	53.0819			1.76841
$902$	17.2123	+	3.65858i	0.573106	+	0.121817i
$903$	−0.657710	+	1.47031i	−0.0218872	+	0.0489289i
$904$	8.80958	+	3.92228i	0.293002	+	0.130453i
$905$	12.0928	+	30.3686i	0.401977	+	1.00949i
$906$	−86.7779	−	9.27427i	−2.88300	−	0.308117i
$907$	1.05513	−	1.82754i	0.0350350	−	0.0606823i	−0.847976	−	0.530034i	$-0.822179\pi$
$907$	1.05513	−	1.82754i	0.0350350	−	0.0606823i	0.883011	+	0.469352i	$0.155512\pi$
$908$	−6.27562	−	4.55951i	−0.208264	−	0.151313i
$909$	11.2801	+	12.6164i	0.374139	+	0.418459i
$910$	4.99858	−	2.62570i	0.165701	−	0.0870411i
$911$	38.3653	+	8.15479i	1.27110	+	0.270180i	0.793593	−	0.608449i	$-0.208208\pi$
$911$	38.3653	+	8.15479i	1.27110	+	0.270180i	0.477505	+	0.878629i	$0.341541\pi$
$912$	−14.8243	+	13.3010i	−0.490883	+	0.440440i
$913$	−2.82779	+	0.601065i	−0.0935862	+	0.0198924i
$914$	−8.26458	+	9.17875i	−0.273368	+	0.303606i
$915$	8.52047	−	57.7857i	0.281678	−	1.91034i
$916$	7.14018	+	7.92997i	0.235918	+	0.262014i
$917$	3.08129	+	2.23869i	0.101753	+	0.0739280i
$918$	54.7595	+	31.9999i	1.80733	+	1.05615i
$919$	−9.51825	−	6.91541i	−0.313978	−	0.228118i	0.419624	−	0.907698i	$-0.362162\pi$
$919$	−9.51825	−	6.91541i	−0.313978	−	0.228118i	−0.733602	+	0.679580i	$0.762162\pi$
$920$	1.60923	+	0.594876i	0.0530549	+	0.0196125i
$921$	−31.7325	−	43.8371i	−1.04562	−	1.44448i
$922$	59.7480	+	26.6015i	1.96770	+	0.876075i
$923$	−11.2629	+	12.5087i	−0.370722	+	0.411729i
$924$	−0.702390	−	0.407165i	−0.0231069	−	0.0133948i
$925$	−32.7575	+	4.26894i	−1.07706	+	0.140362i
$926$	−55.7656			−1.83257
$927$	−11.7061	+	12.9098i	−0.384480	+	0.424015i
$928$	5.82721	−	4.23372i	0.191288	−	0.138979i
$929$	1.17760	+	11.2041i	0.0386359	+	0.367596i	0.996708	+	0.0810700i	$0.0258337\pi$
$929$	1.17760	+	11.2041i	0.0386359	+	0.367596i	−0.958073	+	0.286526i	$0.907500\pi$
$930$	8.32443	+	2.13546i	0.272969	+	0.0700245i
$931$	3.53141	−	33.5991i	0.115737	−	1.10117i
$932$	−27.9338	−	48.3828i	−0.915002	−	1.58483i
$933$	−40.7546	−	4.35559i	−1.33424	−	0.142596i
$934$	13.3762	+	14.8557i	0.437682	+	0.486095i
$935$	1.78288	+	10.4167i	0.0583065	+	0.340661i
$936$	−14.7596	+	16.2772i	−0.482431	+	0.532038i
$937$	−4.12125	+	12.6839i	−0.134635	+	0.414365i	−0.995533	−	0.0944128i	$-0.969903\pi$
$937$	−4.12125	+	12.6839i	−0.134635	+	0.414365i	0.860898	+	0.508778i	$0.169903\pi$
$938$	−3.33533	−	3.70426i	−0.108902	−	0.120948i
$939$	−2.94947	+	13.7578i	−0.0962523	+	0.448967i
$940$	11.6590	−	9.68375i	0.380274	−	0.315849i
$941$	23.6100	−	5.01846i	0.769664	−	0.163597i	0.193687	−	0.981063i	$-0.437955\pi$
$941$	23.6100	−	5.01846i	0.769664	−	0.163597i	0.575977	+	0.817466i	$0.304622\pi$
$942$	26.4336	−	36.2492i	0.861253	−	1.18106i
$943$	−2.81704	+	4.87926i	−0.0917354	+	0.158890i
$944$	18.7319	+	13.6095i	0.609672	+	0.442953i
$945$	−1.75105	+	1.77640i	−0.0569616	+	0.0577861i
$946$	6.27282	−	4.55747i	0.203947	−	0.148176i
$947$	−4.91815	−	46.7930i	−0.159818	−	1.52057i	−0.721034	−	0.692900i	$-0.756333\pi$
$947$	−4.91815	−	46.7930i	−0.159818	−	1.52057i	0.561216	−	0.827670i	$-0.310334\pi$
$948$	35.9546	−	11.6129i	1.16775	−	0.377168i
$949$	11.8127	+	20.4602i	0.383456	+	0.664165i
$950$	20.0499	−	48.2260i	0.650506	−	1.56466i
$951$	21.8441	+	12.6627i	0.708345	+	0.410617i
$952$	1.59602	+	0.339245i	0.0517274	+	0.0109950i
$953$	11.2586	−	8.17984i	0.364701	−	0.264971i	−0.390309	−	0.920684i	$-0.627632\pi$
$953$	11.2586	−	8.17984i	0.364701	−	0.264971i	0.755010	+	0.655713i	$0.227632\pi$
$954$	−6.09420	−	60.0016i	−0.197307	−	1.94262i
$955$	−8.88623	−	51.9186i	−0.287552	−	1.68005i
$956$	−42.0998	+	18.7440i	−1.36161	+	0.606226i
$957$	−1.15930	+	0.666621i	−0.0374749	+	0.0215488i
$958$	0.708674	−	6.74258i	0.0228962	−	0.217843i
$959$	−0.607263	+	0.129078i	−0.0196095	+	0.00416813i
$960$	−43.0810	+	17.0676i	−1.39043	+	0.550854i
$961$	29.2807	+	6.22381i	0.944540	+	0.200768i
$962$	−24.0140	+	73.9076i	−0.774244	+	2.38288i
$963$	5.20663	−	15.8356i	0.167781	−	0.510295i
$964$	−14.6128	−	44.9737i	−0.470648	−	1.44851i
$965$	−0.101282	+	2.53545i	−0.00326038	+	0.0816190i
$966$	0.341021	−	0.305977i	0.0109722	−	0.00984466i
$967$	0.527411	−	5.01798i	0.0169604	−	0.161367i	−0.982763	−	0.184868i	$-0.940814\pi$
$967$	0.527411	−	5.01798i	0.0169604	−	0.161367i	0.999724	+	0.0235002i	$0.00748103\pi$
$968$	−6.89955	−	11.9504i	−0.221760	−	0.384099i
$969$	−28.1470	+	38.5988i	−0.904211	+	1.23997i
$970$	−30.3021	+	38.3863i	−0.972943	+	1.23251i
$971$	28.3509	−	20.5981i	0.909824	−	0.661026i	−0.0311463	−	0.999515i	$-0.509916\pi$
$971$	28.3509	−	20.5981i	0.909824	−	0.661026i	0.940970	+	0.338489i	$0.109916\pi$
$972$	16.9550	−	37.2022i	0.543833	−	1.19326i
$973$	1.42104	+	4.37350i	0.0455563	+	0.140208i
$974$	10.9202	−	18.9143i	0.349905	−	0.606053i
$975$	−13.5948	+	45.3847i	−0.435381	+	1.45347i
$976$	−17.8480	−	30.9136i	−0.571300	−	0.989520i
$977$	14.9550	−	16.6092i	0.478452	−	0.531374i	−0.454802	−	0.890593i	$-0.650290\pi$
$977$	14.9550	−	16.6092i	0.478452	−	0.531374i	0.933254	+	0.359218i	$0.116957\pi$
$978$	−31.4286	+	3.24769i	−1.00498	+	0.103850i
$979$	−0.690508	−	6.56974i	−0.0220687	−	0.209970i
$980$	18.0611	−	36.5639i	0.576941	−	1.16799i
$981$	22.7095	+	16.6211i	0.725057	+	0.530671i
$982$	−27.9998			−0.893511
$983$	28.7204	−	12.7871i	0.916038	−	0.407847i	0.106096	−	0.994356i	$-0.466165\pi$
$983$	28.7204	−	12.7871i	0.916038	−	0.407847i	0.809942	+	0.586509i	$0.199498\pi$
$984$	4.70075	+	22.3071i	0.149854	+	0.711126i
$985$	−19.9456	+	1.29418i	−0.635520	+	0.0412360i
$986$	7.57460	−	8.41245i	0.241224	−	0.267907i
$987$	−0.198149	−	0.940307i	−0.00630717	−	0.0299303i
$988$	−46.6424	−	51.8016i	−1.48389	−	1.64803i
$989$	0.767144	+	2.36103i	0.0243938	+	0.0750763i
$990$	11.5699	−	3.21121i	0.367715	−	0.102059i
$991$	−1.67436	+	5.15314i	−0.0531877	+	0.163695i	−0.974122	−	0.226023i	$-0.927428\pi$
$991$	−1.67436	+	5.15314i	−0.0531877	+	0.163695i	0.920934	+	0.389718i	$0.127428\pi$
$992$	7.32245	−	3.26017i	0.232488	−	0.103510i
$993$	4.59741	+	2.66505i	0.145894	+	0.0845728i
$994$	0.148447	−	1.41238i	0.00470846	−	0.0447980i
$995$	21.7388	+	13.7361i	0.689168	+	0.435464i
$996$	−9.24980	−	12.7782i	−0.293091	−	0.404893i
$997$	4.70906	+	44.8037i	0.149137	+	1.41895i	0.771506	+	0.636223i	$0.219504\pi$
$997$	4.70906	+	44.8037i	0.149137	+	1.41895i	−0.622368	+	0.782725i	$0.713829\pi$
$998$	−14.9098	−	45.8876i	−0.471961	−	1.45255i
$999$	0.180208	−	34.3300i	0.00570154	−	1.08615i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.106.25	yes	224
3.2	odd	2		675.2.r.a.181.4		224
9.4	even	3	inner	225.2.q.a.31.4	✓	224
9.5	odd	6		675.2.r.a.631.25		224
25.21	even	5	inner	225.2.q.a.196.4	yes	224
75.71	odd	10		675.2.r.a.46.25		224
225.121	even	15	inner	225.2.q.a.121.25	yes	224
225.221	odd	30		675.2.r.a.496.4		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.4	✓	224	9.4	even	3	inner
225.2.q.a.106.25	yes	224	1.1	even	1	trivial
225.2.q.a.121.25	yes	224	225.121	even	15	inner
225.2.q.a.196.4	yes	224	25.21	even	5	inner
675.2.r.a.46.25		224	75.71	odd	10
675.2.r.a.181.4		224	3.2	odd	2
675.2.r.a.496.4		224	225.221	odd	30
675.2.r.a.631.25		224	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.10306 + 0.447019i) q^{2} +(1.01562 + 1.40304i) q^{3} +(2.39595 + 1.06675i) q^{4} +(-1.89032 - 1.19444i) q^{5} +(1.50873 + 3.40468i) q^{6} +(-0.107339 + 0.185917i) q^{7} +(1.08313 + 0.786937i) q^{8} +(-0.937030 + 2.84991i) q^{9} +(-3.44153 - 3.35699i) q^{10} +(0.814318 + 0.173089i) q^{11} +(0.936691 + 4.44502i) q^{12} +(5.35109 - 1.13741i) q^{13} +(-0.308850 + 0.343013i) q^{14} +(-0.244010 - 3.86529i) q^{15} +(-1.58374 - 1.75893i) q^{16} +(-4.59284 - 3.33690i) q^{17} +(-3.24460 + 5.57466i) q^{18} +(-3.93045 - 2.85564i) q^{19} +(-3.25496 - 4.87830i) q^{20} +(-0.369865 + 0.0382202i) q^{21} +(1.63519 + 0.728032i) q^{22} +(-0.383475 + 0.425892i) q^{23} +(-0.00405749 + 2.31890i) q^{24} +(2.14664 + 4.51574i) q^{25} +11.7621 q^{26} +(-4.95020 + 1.57974i) q^{27} +(-0.455506 + 0.330945i) q^{28} +(0.0969420 + 0.922342i) q^{29} +(1.21469 - 8.23802i) q^{30} +(-0.107879 + 1.02640i) q^{31} +(-3.88325 - 6.72599i) q^{32} +(0.584188 + 1.31831i) q^{33} +(-8.16737 - 9.07079i) q^{34} +(0.424973 - 0.223234i) q^{35} +(-5.28520 + 5.82866i) q^{36} +(-2.04164 + 6.28353i) q^{37} +(-6.98945 - 7.76257i) q^{38} +(7.03050 + 6.35260i) q^{39} +(-1.10751 - 2.78129i) q^{40} +(9.61614 - 2.04397i) q^{41} +(-0.794935 - 0.0849575i) q^{42} +(2.16590 - 3.75145i) q^{43} +(1.76642 + 1.28338i) q^{44} +(5.17533 - 4.26802i) q^{45} +(-0.996854 + 0.724257i) q^{46} +(0.270140 + 2.57021i) q^{47} +(0.859356 - 4.00845i) q^{48} +(3.47696 + 6.02227i) q^{49} +(2.49589 + 10.4565i) q^{50} +(0.0172052 - 9.83295i) q^{51} +(14.0343 + 2.98307i) q^{52} +(-7.56450 + 5.49593i) q^{53} +(-11.1167 + 1.10945i) q^{54} +(-1.33258 - 1.29984i) q^{55} +(-0.262568 + 0.116903i) q^{56} +(0.0147238 - 8.41481i) q^{57} +(-0.208430 + 1.98308i) q^{58} +(-9.56875 + 2.03390i) q^{59} +(3.53864 - 9.52133i) q^{60} +(14.7519 + 3.13562i) q^{61} +(-0.685694 + 2.11035i) q^{62} +(-0.429267 - 0.480118i) q^{63} +(-3.69727 - 11.3790i) q^{64} +(-11.4738 - 4.24147i) q^{65} +(0.639273 + 3.03363i) q^{66} +(-1.12882 + 10.7400i) q^{67} +(-7.44460 - 12.8944i) q^{68} +(-0.987009 - 0.105485i) q^{69} +(0.993534 - 0.279503i) q^{70} +(-2.48919 + 1.80850i) q^{71} +(-3.25762 + 2.34943i) q^{72} +(1.33451 + 4.10721i) q^{73} +(-7.10256 + 12.3020i) q^{74} +(-4.15559 + 7.59810i) q^{75} +(-6.37091 - 11.0347i) q^{76} +(-0.119589 + 0.132817i) q^{77} +(11.9458 + 16.5027i) q^{78} +(-0.869419 - 8.27197i) q^{79} +(0.892860 + 5.21662i) q^{80} +(-7.24395 - 5.34090i) q^{81} +21.1370 q^{82} +(-3.17237 + 1.41243i) q^{83} +(-0.926950 - 0.302978i) q^{84} +(4.69624 + 11.7937i) q^{85} +(6.23199 - 6.92132i) q^{86} +(-1.19562 + 1.07276i) q^{87} +(0.745799 + 0.828294i) q^{88} +(-2.45204 - 7.54659i) q^{89} +(12.7919 - 6.66244i) q^{90} +(-0.362919 + 1.11695i) q^{91} +(-1.37311 + 0.611346i) q^{92} +(-1.54964 + 0.891071i) q^{93} +(-0.580813 + 5.52607i) q^{94} +(4.01893 + 10.0927i) q^{95} +(5.49291 - 12.2794i) q^{96} +(-1.06331 - 10.1167i) q^{97} +(4.62018 + 14.2195i) q^{98} +(-1.25633 + 2.15854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20}+ \cdots - 20 q^{99}+O(q^{100}) \) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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