LMFDB - Embedded newform 750.2.m.c.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(31,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([0, 24]))

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

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

chi := DirichletCharacter("750.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.m (of order $25$, degree $20$, 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$6$ over $\Q(\zeta_{25})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			121.2
Character	$\chi$	$=$	750.121
Dual form			750.2.m.c.31.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0627905 + 0.998027i) q^{2} +(0.425779 - 0.904827i) q^{3} +(-0.992115 - 0.125333i) q^{4} +(-1.18727 + 1.89484i) q^{5} +(0.876307 + 0.481754i) q^{6} +(-0.762228 - 0.553791i) q^{7} +(0.187381 - 0.982287i) q^{8} +(-0.637424 - 0.770513i) q^{9} +O(q^{10})$	\(q+(-0.0627905 + 0.998027i) q^{2} +(0.425779 - 0.904827i) q^{3} +(-0.992115 - 0.125333i) q^{4} +(-1.18727 + 1.89484i) q^{5} +(0.876307 + 0.481754i) q^{6} +(-0.762228 - 0.553791i) q^{7} +(0.187381 - 0.982287i) q^{8} +(-0.637424 - 0.770513i) q^{9} +(-1.81655 - 1.30390i) q^{10} +(-0.00130650 + 0.0207663i) q^{11} +(-0.535827 + 0.844328i) q^{12} +(-2.18641 - 2.64292i) q^{13} +(0.600559 - 0.725951i) q^{14} +(1.20898 + 1.88105i) q^{15} +(0.968583 + 0.248690i) q^{16} +(-6.11991 + 0.773125i) q^{17} +(0.809017 - 0.587785i) q^{18} +(-1.13735 - 2.41699i) q^{19} +(1.41539 - 1.73109i) q^{20} +(-0.825626 + 0.453892i) q^{21} +(-0.0206432 - 0.00260785i) q^{22} +(0.729534 + 0.288843i) q^{23} +(-0.809017 - 0.587785i) q^{24} +(-2.18080 - 4.49935i) q^{25} +(2.77499 - 2.01615i) q^{26} +(-0.968583 + 0.248690i) q^{27} +(0.686810 + 0.644957i) q^{28} +(-0.623441 - 0.585450i) q^{29} +(-1.95325 + 1.08849i) q^{30} +(-2.36953 + 0.299341i) q^{31} +(-0.309017 + 0.951057i) q^{32} +(0.0182336 + 0.0100240i) q^{33} +(-0.387327 - 6.15638i) q^{34} +(1.95431 - 0.786800i) q^{35} +(0.535827 + 0.844328i) q^{36} +(-0.182989 - 0.0469836i) q^{37} +(2.48364 - 0.983341i) q^{38} +(-3.32231 + 0.853024i) q^{39} +(1.63880 + 1.52129i) q^{40} +(1.68407 - 0.666770i) q^{41} +(-0.401155 - 0.852497i) q^{42} +(-1.89189 - 5.82263i) q^{43} +(0.00389890 - 0.0204388i) q^{44} +(2.21679 - 0.293009i) q^{45} +(-0.334081 + 0.709958i) q^{46} +(-0.834789 - 4.37612i) q^{47} +(0.637424 - 0.770513i) q^{48} +(-1.88881 - 5.81316i) q^{49} +(4.62740 - 1.89398i) q^{50} +(-1.90619 + 5.86664i) q^{51} +(1.83792 + 2.89611i) q^{52} +(-2.11704 + 1.16385i) q^{53} +(-0.187381 - 0.982287i) q^{54} +(-0.0377975 - 0.0271307i) q^{55} +(-0.686810 + 0.644957i) q^{56} -2.67122 q^{57} +(0.623441 - 0.585450i) q^{58} +(0.418811 - 0.659941i) q^{59} +(-0.963693 - 2.01775i) q^{60} +(-7.22846 - 2.86195i) q^{61} +(-0.149967 - 2.38365i) q^{62} +(0.0591591 + 0.940307i) q^{63} +(-0.929776 - 0.368125i) q^{64} +(7.60374 - 1.00504i) q^{65} +(-0.0111491 + 0.0175682i) q^{66} +(-8.85687 + 8.31715i) q^{67} +6.16855 q^{68} +(0.571973 - 0.537119i) q^{69} +(0.662535 + 1.99986i) q^{70} +(2.08076 + 10.9077i) q^{71} +(-0.876307 + 0.481754i) q^{72} +(-3.62834 - 5.71735i) q^{73} +(0.0583809 - 0.179678i) q^{74} +(-4.99967 + 0.0575189i) q^{75} +(0.825452 + 2.54048i) q^{76} +(0.0124960 - 0.0151051i) q^{77} +(-0.642731 - 3.36932i) q^{78} +(-4.10237 + 8.71799i) q^{79} +(-1.62119 + 1.54004i) q^{80} +(-0.187381 + 0.982287i) q^{81} +(0.559710 + 1.72261i) q^{82} +(-1.36358 - 2.89775i) q^{83} +(0.876004 - 0.346834i) q^{84} +(5.80102 - 12.5141i) q^{85} +(5.92993 - 1.52255i) q^{86} +(-0.795179 + 0.314834i) q^{87} +(0.0201536 + 0.00517457i) q^{88} +(0.192938 + 0.304021i) q^{89} +(0.153238 + 2.23081i) q^{90} +(0.202920 + 3.22532i) q^{91} +(-0.687580 - 0.378000i) q^{92} +(-0.738045 + 2.27147i) q^{93} +(4.41990 - 0.558363i) q^{94} +(5.93014 + 0.714521i) q^{95} +(0.728969 + 0.684547i) q^{96} +(2.87727 + 2.70194i) q^{97} +(5.92029 - 1.52007i) q^{98} +(0.0168335 - 0.0122302i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 20 q^{5} - 5 q^{7}+O(q^{10}) $ 120 * q + 20 * q^5 - 5 * q^7	$ 120 q + 20 q^{5} - 5 q^{7} + 20 q^{10} + 10 q^{13} + 20 q^{14} + 15 q^{17} + 30 q^{18} - 5 q^{19} - 5 q^{21} + 10 q^{22} - 15 q^{23} - 30 q^{24} - 20 q^{25} - 10 q^{26} + 5 q^{28} - 5 q^{29} + 5 q^{30} + 55 q^{31} + 30 q^{32} + 10 q^{33} + 25 q^{34} - 10 q^{35} - 5 q^{37} - 35 q^{38} - 10 q^{39} - 5 q^{40} + 55 q^{41} + 5 q^{42} + 5 q^{43} + 15 q^{44} - 5 q^{45} - 10 q^{46} + 10 q^{47} - 25 q^{49} + 20 q^{50} + 15 q^{51} - 40 q^{52} + 30 q^{53} - 10 q^{55} - 5 q^{56} + 60 q^{57} + 5 q^{58} + 20 q^{59} - 20 q^{60} - 60 q^{61} + 25 q^{62} + 5 q^{63} + 15 q^{65} - 25 q^{66} + 95 q^{67} + 60 q^{68} - 10 q^{69} + 40 q^{70} - 90 q^{71} - 30 q^{74} - 55 q^{75} + 15 q^{76} + 95 q^{77} - 5 q^{78} - 90 q^{79} - 5 q^{80} - 45 q^{82} + 95 q^{83} - 5 q^{84} + 115 q^{85} - 15 q^{86} + 10 q^{87} + 65 q^{89} + 5 q^{90} - 85 q^{91} - 65 q^{92} - 30 q^{93} - 10 q^{94} - 55 q^{95} - 35 q^{98} + 10 q^{99}+O(q^{100}) $ 120 * q + 20 * q^5 - 5 * q^7 + 20 * q^10 + 10 * q^13 + 20 * q^14 + 15 * q^17 + 30 * q^18 - 5 * q^19 - 5 * q^21 + 10 * q^22 - 15 * q^23 - 30 * q^24 - 20 * q^25 - 10 * q^26 + 5 * q^28 - 5 * q^29 + 5 * q^30 + 55 * q^31 + 30 * q^32 + 10 * q^33 + 25 * q^34 - 10 * q^35 - 5 * q^37 - 35 * q^38 - 10 * q^39 - 5 * q^40 + 55 * q^41 + 5 * q^42 + 5 * q^43 + 15 * q^44 - 5 * q^45 - 10 * q^46 + 10 * q^47 - 25 * q^49 + 20 * q^50 + 15 * q^51 - 40 * q^52 + 30 * q^53 - 10 * q^55 - 5 * q^56 + 60 * q^57 + 5 * q^58 + 20 * q^59 - 20 * q^60 - 60 * q^61 + 25 * q^62 + 5 * q^63 + 15 * q^65 - 25 * q^66 + 95 * q^67 + 60 * q^68 - 10 * q^69 + 40 * q^70 - 90 * q^71 - 30 * q^74 - 55 * q^75 + 15 * q^76 + 95 * q^77 - 5 * q^78 - 90 * q^79 - 5 * q^80 - 45 * q^82 + 95 * q^83 - 5 * q^84 + 115 * q^85 - 15 * q^86 + 10 * q^87 + 65 * q^89 + 5 * q^90 - 85 * q^91 - 65 * q^92 - 30 * q^93 - 10 * q^94 - 55 * q^95 - 35 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{13}{25}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.0627905	+	0.998027i	−0.0443996	+	0.705711i
$2$	−0.0627905	+	0.998027i	−0.0443996	+	0.705711i
$3$	0.425779	−	0.904827i	0.245824	−	0.522402i
$3$	0.425779	−	0.904827i	0.245824	−	0.522402i
$4$	−0.992115	−	0.125333i	−0.496057	−	0.0626666i
$5$	−1.18727	+	1.89484i	−0.530961	+	0.847396i
$5$	−1.18727	+	1.89484i	−0.530961	+	0.847396i
$6$	0.876307	+	0.481754i	0.357751	+	0.196675i
$7$	−0.762228	−	0.553791i	−0.288095	−	0.209313i	0.434345	−	0.900746i	$-0.356980\pi$
$7$	−0.762228	−	0.553791i	−0.288095	−	0.209313i	−0.722441	+	0.691433i	$0.756980\pi$
$8$	0.187381	−	0.982287i	0.0662493	−	0.347291i
$9$	−0.637424	−	0.770513i	−0.212475	−	0.256838i
$10$	−1.81655	−	1.30390i	−0.574443	−	0.412330i
$11$	−0.00130650	+	0.0207663i	−0.000393925	+	0.00626126i	−0.998219	−	0.0596596i	$-0.980998\pi$
$11$	−0.00130650	+	0.0207663i	−0.000393925	+	0.00626126i	0.997825	+	0.0659208i	$0.0209985\pi$
$12$	−0.535827	+	0.844328i	−0.154680	+	0.243736i
$13$	−2.18641	−	2.64292i	−0.606401	−	0.733013i	0.374563	−	0.927201i	$-0.377793\pi$
$13$	−2.18641	−	2.64292i	−0.606401	−	0.733013i	−0.980964	+	0.194188i	$0.937793\pi$
$14$	0.600559	−	0.725951i	0.160506	−	0.194019i
$15$	1.20898	+	1.88105i	0.312159	+	0.485685i
$16$	0.968583	+	0.248690i	0.242146	+	0.0621725i
$17$	−6.11991	+	0.773125i	−1.48430	+	0.187510i	−0.825325	−	0.564657i	$-0.809008\pi$
$17$	−6.11991	+	0.773125i	−1.48430	+	0.187510i	−0.658972	+	0.752168i	$0.729008\pi$
$18$	0.809017	−	0.587785i	0.190687	−	0.138542i
$19$	−1.13735	−	2.41699i	−0.260926	−	0.554496i	0.730842	−	0.682547i	$-0.239128\pi$
$19$	−1.13735	−	2.41699i	−0.260926	−	0.554496i	−0.991768	+	0.128051i	$0.959128\pi$
$20$	1.41539	−	1.73109i	0.316491	−	0.387083i
$21$	−0.825626	+	0.453892i	−0.180166	+	0.0990474i
$22$	−0.0206432	−	0.00260785i	−0.00440116	−	0.000555995i
$23$	0.729534	+	0.288843i	0.152118	+	0.0602279i	0.442950	−	0.896546i	$-0.353932\pi$
$23$	0.729534	+	0.288843i	0.152118	+	0.0602279i	−0.290832	+	0.956774i	$0.593932\pi$
$24$	−0.809017	−	0.587785i	−0.165140	−	0.119981i
$25$	−2.18080	−	4.49935i	−0.436160	−	0.899869i
$26$	2.77499	−	2.01615i	0.544220	−	0.395399i
$27$	−0.968583	+	0.248690i	−0.186404	+	0.0478604i
$28$	0.686810	+	0.644957i	0.129795	+	0.121885i
$29$	−0.623441	−	0.585450i	−0.115770	−	0.108715i	0.624500	−	0.781024i	$-0.285303\pi$
$29$	−0.623441	−	0.585450i	−0.115770	−	0.108715i	−0.740271	+	0.672309i	$0.765303\pi$
$30$	−1.95325	+	1.08849i	−0.356614	+	0.198730i
$31$	−2.36953	+	0.299341i	−0.425580	+	0.0537633i	−0.335207	−	0.942145i	$-0.608806\pi$
$31$	−2.36953	+	0.299341i	−0.425580	+	0.0537633i	−0.0903736	+	0.995908i	$0.528806\pi$
$32$	−0.309017	+	0.951057i	−0.0546270	+	0.168125i
$33$	0.0182336	+	0.0100240i	0.00317406	+	0.00174495i
$34$	−0.387327	−	6.15638i	−0.0664260	−	1.05581i
$35$	1.95431	−	0.786800i	0.330339	−	0.132993i
$36$	0.535827	+	0.844328i	0.0893045	+	0.140721i
$37$	−0.182989	−	0.0469836i	−0.0300832	−	0.00772406i	0.233618	−	0.972328i	$-0.424943\pi$
$37$	−0.182989	−	0.0469836i	−0.0300832	−	0.00772406i	−0.263702	+	0.964604i	$0.584943\pi$
$38$	2.48364	−	0.983341i	0.402899	−	0.159519i
$39$	−3.32231	+	0.853024i	−0.531995	+	0.136593i
$40$	1.63880	+	1.52129i	0.259117	+	0.240537i
$41$	1.68407	−	0.666770i	0.263007	−	0.104132i	−0.232920	−	0.972496i	$-0.574828\pi$
$41$	1.68407	−	0.666770i	0.263007	−	0.104132i	0.495928	+	0.868364i	$0.334828\pi$
$42$	−0.401155	−	0.852497i	−0.0618995	−	0.131543i
$43$	−1.89189	−	5.82263i	−0.288510	−	0.887942i	−0.985325	−	0.170691i	$-0.945400\pi$
$43$	−1.89189	−	5.82263i	−0.288510	−	0.887942i	0.696815	−	0.717251i	$-0.254600\pi$
$44$	0.00389890	−	0.0204388i	0.000587782	−	0.00308126i
$45$	2.21679	−	0.293009i	0.330459	−	0.0436793i
$46$	−0.334081	+	0.709958i	−0.0492575	+	0.104678i
$47$	−0.834789	−	4.37612i	−0.121766	−	0.638322i	−0.989874	−	0.141947i	$-0.954664\pi$
$47$	−0.834789	−	4.37612i	−0.121766	−	0.638322i	0.868108	−	0.496376i	$-0.165336\pi$
$48$	0.637424	−	0.770513i	0.0920042	−	0.111214i
$49$	−1.88881	−	5.81316i	−0.269830	−	0.830452i
$50$	4.62740	−	1.89398i	0.654413	−	0.267849i
$51$	−1.90619	+	5.86664i	−0.266920	+	0.821494i
$52$	1.83792	+	2.89611i	0.254874	+	0.401618i
$53$	−2.11704	+	1.16385i	−0.290798	+	0.159867i	−0.620475	−	0.784226i	$-0.713060\pi$
$53$	−2.11704	+	1.16385i	−0.290798	+	0.159867i	0.329677	+	0.944094i	$0.393060\pi$
$54$	−0.187381	−	0.982287i	−0.0254994	−	0.133672i
$55$	−0.0377975	−	0.0271307i	−0.00509661	−	0.00365830i
$56$	−0.686810	+	0.644957i	−0.0917788	+	0.0861860i
$57$	−2.67122			−0.353812
$58$	0.623441	−	0.585450i	0.0818618	−	0.0768734i
$59$	0.418811	−	0.659941i	0.0545246	−	0.0859170i	−0.815972	−	0.578091i	$-0.803798\pi$
$59$	0.418811	−	0.659941i	0.0545246	−	0.0859170i	0.870497	+	0.492174i	$0.163798\pi$
$60$	−0.963693	−	2.01775i	−0.124412	−	0.260490i
$61$	−7.22846	−	2.86195i	−0.925509	−	0.366435i	−0.143463	−	0.989656i	$-0.545824\pi$
$61$	−7.22846	−	2.86195i	−0.925509	−	0.366435i	−0.782046	+	0.623221i	$0.785824\pi$
$62$	−0.149967	−	2.38365i	−0.0190458	−	0.302724i
$63$	0.0591591	+	0.940307i	0.00745335	+	0.118468i
$64$	−0.929776	−	0.368125i	−0.116222	−	0.0460156i
$65$	7.60374	−	1.00504i	0.943128	−	0.124660i
$66$	−0.0111491	+	0.0175682i	−0.00137236	+	0.00216250i
$67$	−8.85687	+	8.31715i	−1.08204	+	1.01610i	−0.0822286	+	0.996613i	$0.526204\pi$
$67$	−8.85687	+	8.31715i	−1.08204	+	1.01610i	−0.999810	+	0.0194884i	$0.993796\pi$
$68$	6.16855			0.748047
$69$	0.571973	−	0.537119i	0.0688575	−	0.0646615i
$70$	0.662535	+	1.99986i	0.0791881	+	0.239029i
$71$	2.08076	+	10.9077i	0.246940	+	1.29451i	0.862356	+	0.506303i	$0.168988\pi$
$71$	2.08076	+	10.9077i	0.246940	+	1.29451i	−0.615415	+	0.788203i	$0.711012\pi$
$72$	−0.876307	+	0.481754i	−0.103274	+	0.0567752i
$73$	−3.62834	−	5.71735i	−0.424665	−	0.669165i	0.562873	−	0.826543i	$-0.309696\pi$
$73$	−3.62834	−	5.71735i	−0.424665	−	0.669165i	−0.987538	+	0.157378i	$0.949696\pi$
$74$	0.0583809	−	0.179678i	0.00678664	−	0.0208871i
$75$	−4.99967	+	0.0575189i	−0.577312	+	0.00664171i
$76$	0.825452	+	2.54048i	0.0946859	+	0.291413i
$77$	0.0124960	−	0.0151051i	0.00142405	−	0.00172139i
$78$	−0.642731	−	3.36932i	−0.0727750	−	0.381500i
$79$	−4.10237	+	8.71799i	−0.461553	+	0.980850i	0.529615	+	0.848238i	$0.322336\pi$
$79$	−4.10237	+	8.71799i	−0.461553	+	0.980850i	−0.991168	+	0.132612i	$0.957664\pi$
$80$	−1.62119	+	1.54004i	−0.181255	+	0.172182i
$81$	−0.187381	+	0.982287i	−0.0208201	+	0.109143i
$82$	0.559710	+	1.72261i	0.0618097	+	0.190231i
$83$	−1.36358	−	2.89775i	−0.149672	−	0.318070i	0.815905	−	0.578186i	$-0.196239\pi$
$83$	−1.36358	−	2.89775i	−0.149672	−	0.318070i	−0.965577	+	0.260116i	$0.916239\pi$
$84$	0.876004	−	0.346834i	0.0955799	−	0.0378427i
$85$	5.80102	−	12.5141i	0.629209	−	1.35735i
$86$	5.92993	−	1.52255i	0.639441	−	0.164180i
$87$	−0.795179	+	0.314834i	−0.0852522	+	0.0337537i
$88$	0.0201536	+	0.00517457i	0.00214838	+	0.000551611i
$89$	0.192938	+	0.304021i	0.0204514	+	0.0322262i	0.854400	−	0.519616i	$-0.173925\pi$
$89$	0.192938	+	0.304021i	0.0204514	+	0.0322262i	−0.833948	+	0.551842i	$0.813925\pi$
$90$	0.153238	+	2.23081i	0.0161527	+	0.235148i
$91$	0.202920	+	3.22532i	0.0212718	+	0.338105i
$92$	−0.687580	−	0.378000i	−0.0716851	−	0.0394092i
$93$	−0.738045	+	2.27147i	−0.0765317	+	0.235540i
$94$	4.41990	−	0.558363i	0.455878	−	0.0575907i
$95$	5.93014	+	0.714521i	0.608419	+	0.0733083i
$96$	0.728969	+	0.684547i	0.0744000	+	0.0698663i
$97$	2.87727	+	2.70194i	0.292143	+	0.274340i	0.816735	−	0.577014i	$-0.195782\pi$
$97$	2.87727	+	2.70194i	0.292143	+	0.274340i	−0.524592	+	0.851354i	$0.675782\pi$
$98$	5.92029	−	1.52007i	0.598040	−	0.153551i
$99$	0.0168335	−	0.0122302i	0.00169183	−	0.00122918i
$100$	1.59969	+	4.73719i	0.159969	+	0.473719i
$101$	4.32917	+	3.14532i	0.430768	+	0.312971i	0.781956	−	0.623334i	$-0.214222\pi$
$101$	4.32917	+	3.14532i	0.430768	+	0.312971i	−0.351188	+	0.936305i	$0.614222\pi$
$102$	−5.73538	−	2.27080i	−0.567887	−	0.224842i
$103$	−1.71583	−	0.216760i	−0.169066	−	0.0213580i	0.0403446	−	0.999186i	$-0.487154\pi$
$103$	−1.71583	−	0.216760i	−0.169066	−	0.0213580i	−0.209410	+	0.977828i	$0.567154\pi$
$104$	−3.00580	+	1.65245i	−0.294742	+	0.162036i
$105$	0.120188	−	2.10332i	0.0117291	−	0.205263i
$106$	−1.02863	−	2.18594i	−0.0999089	−	0.212317i
$107$	−3.04739	+	2.21406i	−0.294603	+	0.214041i	−0.725262	−	0.688473i	$-0.758281\pi$
$107$	−3.04739	+	2.21406i	−0.294603	+	0.214041i	0.430659	+	0.902515i	$0.358281\pi$
$108$	0.992115	−	0.125333i	0.0954663	−	0.0120602i
$109$	12.4542	+	3.19769i	1.19289	+	0.306283i	0.792391	−	0.610013i	$-0.208836\pi$
$109$	12.4542	+	3.19769i	1.19289	+	0.306283i	0.400502	+	0.916296i	$0.368836\pi$
$110$	0.0294505	−	0.0360193i	0.00280799	−	0.00343431i
$111$	−0.120425	+	0.145569i	−0.0114302	+	0.0138168i
$112$	−0.600559	−	0.725951i	−0.0567475	−	0.0685960i
$113$	0.512743	−	0.807954i	0.0482348	−	0.0760059i	−0.819355	−	0.573287i	$-0.805668\pi$
$113$	0.512743	−	0.807954i	0.0482348	−	0.0760059i	0.867590	+	0.497281i	$0.165668\pi$
$114$	0.167727	−	2.66595i	0.0157091	−	0.249689i
$115$	−1.41346	+	1.03941i	−0.131806	+	0.0969258i
$116$	0.545149	+	0.658972i	0.0506158	+	0.0611840i
$117$	−0.642731	+	3.36932i	−0.0594205	+	0.311493i
$118$	0.632341	+	0.459423i	0.0582117	+	0.0422933i
$119$	5.09292	+	2.79986i	0.466867	+	0.256662i
$120$	2.07427	−	0.835097i	0.189354	−	0.0762335i
$121$	10.9128	+	1.37861i	0.992076	+	0.125328i
$122$	3.31018	−	7.03449i	0.299690	−	0.636873i
$123$	0.113730	−	1.80769i	0.0102547	−	0.162994i
$124$	2.38836			0.214481
$125$	11.1147	+	1.20966i	0.994130	+	0.108195i
$126$	−0.942166			−0.0839348
$127$	−0.336606	+	5.35020i	−0.0298689	+	0.474753i	0.954452	+	0.298365i	$0.0964414\pi$
$127$	−0.336606	+	5.35020i	−0.0298689	+	0.474753i	−0.984321	+	0.176388i	$0.943559\pi$
$128$	0.425779	−	0.904827i	0.0376339	−	0.0799762i
$129$	−6.07399	−	0.767324i	−0.534785	−	0.0675591i
$130$	0.525617	+	7.65184i	0.0460997	+	0.671111i
$131$	16.0331	+	8.81427i	1.40082	+	0.770107i	0.989927	−	0.141577i	$-0.0452174\pi$
$131$	16.0331	+	8.81427i	1.40082	+	0.770107i	0.410892	+	0.911684i	$0.365217\pi$
$132$	−0.0168335	−	0.0122302i	−0.00146517	−	0.00106451i
$133$	−0.471589	+	2.47215i	−0.0408919	+	0.214363i
$134$	−7.74461	−	9.36163i	−0.669033	−	0.808722i
$135$	0.678739	−	2.13057i	0.0584166	−	0.183370i
$136$	−0.387327	+	6.15638i	−0.0332130	+	0.527905i
$137$	−3.34246	+	5.26687i	−0.285565	+	0.449979i	−0.956582	−	0.291463i	$-0.905858\pi$
$137$	−3.34246	+	5.26687i	−0.285565	+	0.449979i	0.671017	+	0.741442i	$0.265858\pi$
$138$	0.500144	+	0.604571i	0.0425751	+	0.0514645i
$139$	8.42064	−	10.1788i	0.714229	−	0.863355i	−0.281122	−	0.959672i	$-0.590706\pi$
$139$	8.42064	−	10.1788i	0.714229	−	0.863355i	0.995351	+	0.0963175i	$0.0307064\pi$
$140$	−2.03751	+	0.535655i	−0.172201	+	0.0452711i
$141$	−4.31506	−	1.10792i	−0.363394	−	0.0933037i
$142$	−11.0168	+	1.39175i	−0.924512	+	0.116793i
$143$	0.0577400	−	0.0419506i	0.00482846	−	0.00350808i
$144$	−0.425779	−	0.904827i	−0.0354816	−	0.0754023i
$145$	1.84952	−	0.486233i	0.153594	−	0.0403795i
$146$	5.93389	−	3.26219i	0.491093	−	0.269980i
$147$	−6.06413	−	0.766077i	−0.500161	−	0.0631850i
$148$	0.175658	+	0.0695478i	0.0144390	+	0.00571679i
$149$	4.37396	+	3.17787i	0.358329	+	0.260341i	0.752355	−	0.658758i	$-0.228918\pi$
$149$	4.37396	+	3.17787i	0.358329	+	0.260341i	−0.394026	+	0.919099i	$0.628918\pi$
$150$	0.256526	−	4.99342i	0.0209453	−	0.407711i
$151$	−5.08628	+	3.69540i	−0.413916	+	0.300727i	−0.775185	−	0.631734i	$-0.782343\pi$
$151$	−5.08628	+	3.69540i	−0.413916	+	0.300727i	0.361269	+	0.932462i	$0.382343\pi$
$152$	−2.58730	+	0.664305i	−0.209858	+	0.0538823i
$153$	4.49668	+	4.22267i	0.363535	+	0.341382i
$154$	0.0142907	+	0.0134198i	0.00115157	+	0.00108140i
$155$	2.24606	−	4.84527i	0.180408	−	0.389181i
$156$	3.40303	−	0.429902i	0.272460	−	0.0344197i
$157$	0.963740	−	2.96609i	0.0769148	−	0.236720i	−0.905205	−	0.424974i	$-0.860283\pi$
$157$	0.963740	−	2.96609i	0.0769148	−	0.236720i	0.982120	+	0.188255i	$0.0602831\pi$
$158$	−8.44319	−	4.64169i	−0.671704	−	0.369273i
$159$	0.151693	+	2.41110i	0.0120301	+	0.191213i
$160$	−1.43521	−	1.71469i	−0.113463	−	0.135558i
$161$	−0.396113	−	0.624174i	−0.0312181	−	0.0491918i
$162$	−0.968583	−	0.248690i	−0.0760991	−	0.0195389i
$163$	0.330242	−	0.130752i	0.0258666	−	0.0102413i	−0.355156	−	0.934807i	$-0.615572\pi$
$163$	0.330242	−	0.130752i	0.0258666	−	0.0102413i	0.381022	+	0.924566i	$0.375572\pi$
$164$	−1.75436	+	0.450442i	−0.136992	+	0.0351736i
$165$	−0.0406420	+	0.0226485i	−0.00316397	+	0.00176318i
$166$	2.97765	−	1.17894i	0.231111	−	0.0915032i
$167$	−4.44432	−	9.44466i	−0.343912	−	0.730850i	0.655798	−	0.754936i	$-0.272332\pi$
$167$	−4.44432	−	9.44466i	−0.343912	−	0.730850i	−0.999710	+	0.0240865i	$0.992332\pi$
$168$	0.291145	+	0.896053i	0.0224624	+	0.0691320i
$169$	0.231342	−	1.21274i	0.0177955	−	0.0932874i
$170$	12.1252	+	6.57534i	0.929959	+	0.504306i
$171$	−1.13735	+	2.41699i	−0.0869753	+	0.184832i
$172$	1.14720	+	6.01383i	0.0874731	+	0.458550i
$173$	4.50826	−	5.44955i	0.342757	−	0.414322i	−0.570764	−	0.821114i	$-0.693353\pi$
$173$	4.50826	−	5.44955i	0.342757	−	0.414322i	0.913521	+	0.406792i	$0.133353\pi$
$174$	−0.264283	−	0.813379i	−0.0200352	−	0.0616621i
$175$	−0.829431	+	4.63724i	−0.0626991	+	0.350542i
$176$	−0.00642982	+	0.0197889i	−0.000484666	+	0.00149165i
$177$	−0.418811	−	0.659941i	−0.0314798	−	0.0496042i
$178$	−0.315536	+	0.173467i	−0.0236504	+	0.0130019i
$179$	3.42064	+	17.9316i	0.255671	+	1.34027i	0.846031	+	0.533134i	$0.178986\pi$
$179$	3.42064	+	17.9316i	0.255671	+	1.34027i	−0.590360	+	0.807140i	$0.701014\pi$
$180$	−2.23603	+	0.0128618i	−0.166664	+	0.000958664i
$181$	−7.45066	+	6.99663i	−0.553803	+	0.520056i	−0.910139	−	0.414302i	$-0.864026\pi$
$181$	−7.45066	+	6.99663i	−0.553803	+	0.520056i	0.356336	+	0.934358i	$0.384026\pi$
$182$	−3.23170			−0.239549
$183$	−5.66730	+	5.32195i	−0.418939	+	0.393410i
$184$	0.420428	−	0.662488i	0.0309943	−	0.0488393i
$185$	0.306283	−	0.290952i	0.0225184	−	0.0213912i
$186$	−2.22064	−	0.879215i	−0.162826	−	0.0644672i
$187$	−0.00805923	−	0.128098i	−0.000589349	−	0.00936744i
$188$	0.279733	+	4.44624i	0.0204017	+	0.324275i
$189$	0.876004	+	0.346834i	0.0637199	+	0.0252285i
$190$	−1.08547	+	5.87357i	−0.0787481	+	0.426114i
$191$	−1.38949	+	2.18949i	−0.100540	+	0.158426i	−0.890874	−	0.454251i	$-0.849907\pi$
$191$	−1.38949	+	2.18949i	−0.100540	+	0.158426i	0.790334	+	0.612676i	$0.209907\pi$
$192$	−0.728969	+	0.684547i	−0.0526088	+	0.0494029i
$193$	−25.1247			−1.80852			−0.904258	−	0.426987i	$-0.859575\pi$
$193$	−25.1247			−1.80852			−0.904258	+	0.426987i	$0.859575\pi$
$194$	−2.87727	+	2.70194i	−0.206576	+	0.193988i
$195$	2.32812	−	7.30800i	0.166720	−	0.523336i
$196$	1.14534	+	6.00406i	0.0818097	+	0.428861i
$197$	4.45161	−	2.44729i	0.317164	−	0.174363i	−0.315217	−	0.949019i	$-0.602077\pi$
$197$	4.45161	−	2.44729i	0.317164	−	0.174363i	0.632382	+	0.774657i	$0.282077\pi$
$198$	0.0111491	+	0.0175682i	0.000792333	+	0.00124852i
$199$	−2.10647	+	6.48304i	−0.149323	+	0.459570i	−0.997542	−	0.0700768i	$-0.977676\pi$
$199$	−2.10647	+	6.48304i	−0.149323	+	0.459570i	0.848218	+	0.529647i	$0.177676\pi$
$200$	−4.82829	+	1.29908i	−0.341412	+	0.0918588i
$201$	3.75451	+	11.5552i	0.264823	+	0.815041i
$202$	−3.41095	+	4.12313i	−0.239993	+	0.290102i
$203$	0.150987	+	0.791503i	0.0105972	+	0.0555526i
$204$	2.62644	−	5.58147i	0.183888	−	0.390781i
$205$	−0.736017	+	3.98266i	−0.0514057	+	0.278161i
$206$	0.324070	−	1.69883i	0.0225790	−	0.118363i
$207$	−0.242465	−	0.746231i	−0.0168525	−	0.0518666i
$208$	−1.46045	−	3.10362i	−0.101264	−	0.215197i
$209$	0.0516778	−	0.0204607i	0.00357463	−	0.00141530i
$210$	2.09162	+	0.252019i	0.144335	+	0.0173909i
$211$	−27.0653	+	6.94918i	−1.86325	+	0.478401i	−0.999667	−	0.0258057i	$-0.991785\pi$
$211$	−27.0653	+	6.94918i	−1.86325	+	0.478401i	−0.863583	+	0.504207i	$0.831785\pi$
$212$	2.24621	−	0.889339i	0.154271	−	0.0610801i
$213$	10.7555	+	2.76155i	0.736957	+	0.189218i
$214$	−2.01834	−	3.18040i	−0.137971	−	0.217408i
$215$	13.2791	+	3.32819i	0.905626	+	0.226981i
$216$	0.0627905	+	0.998027i	0.00427235	+	0.0679071i
$217$	1.97190	+	1.08406i	0.133861	+	0.0735907i
$218$	−3.97338	+	12.2288i	−0.269111	+	0.828240i
$219$	−6.71809	+	0.848692i	−0.453966	+	0.0573493i
$220$	0.0340991	+	0.0316540i	0.00229896	+	0.00213411i
$221$	15.4239	+	14.4840i	1.03753	+	0.974303i
$222$	−0.137720	−	0.129328i	−0.00924317	−	0.00867991i
$223$	−3.61150	+	0.927276i	−0.241844	+	0.0620950i	−0.367666	−	0.929958i	$-0.619843\pi$
$223$	−3.61150	+	0.927276i	−0.241844	+	0.0620950i	0.125822	+	0.992053i	$0.459843\pi$
$224$	0.762228	−	0.553791i	0.0509285	−	0.0370017i
$225$	−2.07671	+	4.54833i	−0.138447	+	0.303222i
$226$	0.774164	+	0.562463i	0.0514966	+	0.0374145i
$227$	−6.38155	−	2.52664i	−0.423558	−	0.167699i	0.146669	−	0.989186i	$-0.453145\pi$
$227$	−6.38155	−	2.52664i	−0.423558	−	0.167699i	−0.570227	+	0.821487i	$0.693145\pi$
$228$	2.65016	+	0.334793i	0.175511	+	0.0221722i
$229$	16.5451	−	9.09575i	1.09333	−	0.601064i	0.170146	−	0.985419i	$-0.445576\pi$
$229$	16.5451	−	9.09575i	1.09333	−	0.601064i	0.923186	+	0.384354i	$0.125576\pi$
$230$	−0.948610	−	1.47594i	−0.0625495	−	0.0973204i
$231$	−0.00834696	−	0.0177382i	−0.000549189	−	0.00116709i
$232$	−0.691901	+	0.502696i	−0.0454256	+	0.0330036i
$233$	−28.1536	+	3.55663i	−1.84440	+	0.233002i	−0.968418	−	0.249334i	$-0.919788\pi$
$233$	−28.1536	+	3.55663i	−1.84440	+	0.233002i	−0.875986	+	0.482336i	$0.839788\pi$
$234$	−3.32231	−	0.853024i	−0.217186	−	0.0557639i
$235$	9.28313	+	3.61383i	0.605565	+	0.235740i
$236$	−0.498221	+	0.602246i	−0.0324314	+	0.0392029i
$237$	6.14156	+	7.42388i	0.398938	+	0.482233i
$238$	−3.11412	+	4.90707i	−0.201858	+	0.318078i
$239$	1.14550	−	18.2072i	0.0740964	−	1.17773i	−0.768741	−	0.639560i	$-0.779117\pi$
$239$	1.14550	−	18.2072i	0.0740964	−	1.17773i	0.842837	−	0.538168i	$-0.180883\pi$
$240$	0.703204	+	2.12262i	0.0453916	+	0.137014i
$241$	−4.06987	−	4.91962i	−0.262163	−	0.316901i	0.622964	−	0.782251i	$-0.285928\pi$
$241$	−4.06987	−	4.91962i	−0.262163	−	0.316901i	−0.885127	+	0.465350i	$0.845928\pi$
$242$	−2.06111	+	10.8047i	−0.132493	+	0.694555i
$243$	0.809017	+	0.587785i	0.0518985	+	0.0377064i
$244$	6.81276	+	3.74535i	0.436142	+	0.239771i
$245$	13.2575	+	3.32278i	0.846991	+	0.212285i
$246$	1.79698	+	0.227011i	0.114571	+	0.0144737i
$247$	−3.90119	+	8.29045i	−0.248227	+	0.527509i
$248$	−0.149967	+	2.38365i	−0.00952289	+	0.151362i
$249$	−3.20255			−0.202953
$250$	−1.90517	+	11.0168i	−0.120494	+	0.696765i
$251$	−25.0906			−1.58370			−0.791852	−	0.610713i	$-0.790883\pi$
$251$	−25.0906			−1.58370			−0.791852	+	0.610713i	$0.790883\pi$
$252$	0.0591591	−	0.940307i	0.00372667	−	0.0592338i
$253$	−0.00695132	+	0.0147723i	−0.000437026	+	0.000928728i
$254$	−5.31850	−	0.671883i	−0.333713	−	0.0421577i
$255$	−8.85317	−	10.5772i	−0.554407	−	0.662369i
$256$	0.876307	+	0.481754i	0.0547692	+	0.0301096i
$257$	−0.624806	−	0.453948i	−0.0389743	−	0.0283165i	0.568128	−	0.822941i	$-0.307668\pi$
$257$	−0.624806	−	0.453948i	−0.0389743	−	0.0283165i	−0.607102	+	0.794624i	$0.707668\pi$
$258$	1.14720	−	6.01383i	0.0714215	−	0.374405i
$259$	0.113460	+	0.137150i	0.00705009	+	0.00852209i
$260$	−7.66975	+	0.0441170i	−0.475658	+	0.00273602i
$261$	−0.0537008	+	0.853550i	−0.00332400	+	0.0528334i
$262$	−9.80361	+	15.4480i	−0.605669	+	0.954382i
$263$	−7.82594	−	9.45994i	−0.482568	−	0.583325i	0.471895	−	0.881655i	$-0.343570\pi$
$263$	−7.82594	−	9.45994i	−0.482568	−	0.583325i	−0.954463	+	0.298330i	$0.903570\pi$
$264$	0.0132631	−	0.0160323i	0.000816286	−	0.000986721i
$265$	0.308180	−	5.39324i	0.0189314	−	0.331304i
$266$	−2.43766	−	0.625886i	−0.149463	−	0.0383755i
$267$	0.357236	−	0.0451293i	0.0218625	−	0.00276187i
$268$	9.82944	−	7.14151i	0.600429	−	0.436237i
$269$	9.11166	+	19.3633i	0.555547	+	1.18060i	0.963528	+	0.267608i	$0.0862331\pi$
$269$	9.11166	+	19.3633i	0.555547	+	1.18060i	−0.407980	+	0.912991i	$0.633767\pi$
$270$	2.08374	+	0.811179i	0.126813	+	0.0493668i
$271$	20.9282	−	11.5054i	1.27130	−	0.698903i	0.304032	−	0.952662i	$-0.401667\pi$
$271$	20.9282	−	11.5054i	1.27130	−	0.698903i	0.967267	+	0.253759i	$0.0816670\pi$
$272$	−6.11991	−	0.773125i	−0.371074	−	0.0468776i
$273$	3.00476	+	1.18967i	0.181856	+	0.0720019i
$274$	−5.04660	−	3.66657i	−0.304876	−	0.221506i
$275$	0.0962838	−	0.0394087i	0.00580613	−	0.00237643i
$276$	−0.634782	+	0.461196i	−0.0382094	+	0.0277607i
$277$	28.4340	−	7.30061i	1.70843	−	0.438651i	0.736986	−	0.675908i	$-0.236249\pi$
$277$	28.4340	−	7.30061i	1.70843	−	0.438651i	0.971447	+	0.237258i	$0.0762485\pi$
$278$	9.62998	+	9.04315i	0.577568	+	0.542372i
$279$	1.74104	+	1.63495i	0.104233	+	0.0978817i
$280$	−0.406662	−	2.06713i	−0.0243027	−	0.123534i
$281$	13.7063	−	1.73151i	0.817650	−	0.103293i	0.294627	−	0.955612i	$-0.404804\pi$
$281$	13.7063	−	1.73151i	0.817650	−	0.103293i	0.523022	+	0.852319i	$0.324804\pi$
$282$	1.37668	−	4.23698i	0.0819800	−	0.252309i
$283$	−27.6306	−	15.1901i	−1.64247	−	0.902956i	−0.989326	−	0.145722i	$-0.953449\pi$
$283$	−27.6306	−	15.1901i	−1.64247	−	0.902956i	−0.653144	−	0.757233i	$-0.726551\pi$
$284$	−0.697251	−	11.0825i	−0.0413742	−	0.657624i
$285$	3.17145	−	5.06152i	0.187860	−	0.299819i
$286$	0.0382423	+	0.0602602i	0.00226131	+	0.00356326i
$287$	−1.65290	−	0.424391i	−0.0975673	−	0.0250510i
$288$	0.929776	−	0.368125i	0.0547876	−	0.0216919i
$289$	20.3897	−	5.23519i	1.19939	−	0.307952i
$290$	0.369141	+	1.87640i	0.0216767	+	0.110186i
$291$	3.66987	−	1.45300i	0.215132	−	0.0851766i
$292$	2.88316	+	6.12702i	0.168724	+	0.358557i
$293$	−7.71102	−	23.7321i	−0.450483	−	1.38644i	−0.876357	−	0.481661i	$-0.840033\pi$
$293$	−7.71102	−	23.7321i	−0.450483	−	1.38644i	0.425875	−	0.904782i	$-0.359967\pi$
$294$	1.14534	−	6.00406i	0.0667973	−	0.350164i
$295$	0.753239	+	1.57710i	0.0438553	+	0.0918225i
$296$	−0.0804402	+	0.170944i	−0.00467549	+	0.00993592i
$297$	−0.00389890	−	0.0204388i	−0.000226237	−	0.00118598i
$298$	−3.44624	+	4.16579i	−0.199635	+	0.241318i
$299$	−0.831673	−	2.55963i	−0.0480969	−	0.148027i
$300$	4.96745	+	0.569559i	0.286796	+	0.0328835i
$301$	−1.78247	+	5.48588i	−0.102740	+	0.316201i
$302$	−3.36874	−	5.30828i	−0.193849	−	0.305457i
$303$	4.68924	−	2.57793i	0.269390	−	0.148098i
$304$	−0.500537	−	2.62390i	−0.0287077	−	0.150491i
$305$	14.0050	−	10.2988i	0.801925	−	0.589710i
$306$	−4.49668	+	4.22267i	−0.257058	+	0.241394i
$307$	25.2513			1.44117			0.720585	−	0.693367i	$-0.243873\pi$
$307$	25.2513			1.44117			0.720585	+	0.693367i	$0.243873\pi$
$308$	−0.0142907	+	0.0134198i	−0.000814286	+	0.000764666i
$309$	−0.926695	+	1.46024i	−0.0527178	+	0.0830700i
$310$	4.69467	+	2.54586i	0.266640	+	0.144595i
$311$	−14.2313	−	5.63458i	−0.806985	−	0.319508i	−0.0718384	−	0.997416i	$-0.522887\pi$
$311$	−14.2313	−	5.63458i	−0.806985	−	0.319508i	−0.735146	+	0.677908i	$0.762887\pi$
$312$	0.215376	+	3.42330i	0.0121933	+	0.193806i
$313$	−1.47651	−	23.4685i	−0.0834575	−	1.32652i	−0.787480	−	0.616341i	$-0.788614\pi$
$313$	−1.47651	−	23.4685i	−0.0834575	−	1.32652i	0.704022	−	0.710178i	$-0.251386\pi$
$314$	2.89972	+	1.14808i	0.163641	+	0.0647899i
$315$	−1.85196	−	1.00430i	−0.104346	−	0.0565858i
$316$	5.16268	−	8.13508i	0.290423	−	0.457634i
$317$	−10.6986	+	10.0466i	−0.600891	+	0.564274i	−0.924147	−	0.382037i	$-0.875223\pi$
$317$	−10.6986	+	10.0466i	−0.600891	+	0.564274i	0.323256	+	0.946312i	$0.395223\pi$
$318$	−2.41587			−0.135475
$319$	0.0129721	−	0.0121816i	0.000726300	−	0.000682041i
$320$	1.80143	−	1.32471i	0.100703	−	0.0740536i
$321$	0.705825	+	3.70006i	0.0393953	+	0.206517i
$322$	0.647814	−	0.356139i	0.0361013	−	0.0198468i
$323$	8.82912	+	13.9125i	0.491265	+	0.774110i
$324$	0.309017	−	0.951057i	0.0171676	−	0.0528365i
$325$	−7.12327	+	15.6011i	−0.395128	+	0.865393i
$326$	0.109758	+	0.337801i	0.00607894	+	0.0187090i
$327$	8.19608	−	9.90736i	0.453244	−	0.547878i
$328$	−0.339396	−	1.77918i	−0.0187400	−	0.0982387i
$329$	−1.78716	+	3.79790i	−0.0985291	+	0.209385i
$330$	−0.0200519	−	0.0419839i	−0.00110382	−	0.00231114i
$331$	3.27507	−	17.1685i	0.180014	−	0.943666i	−0.771539	−	0.636182i	$-0.780513\pi$
$331$	3.27507	−	17.1685i	0.180014	−	0.943666i	0.951553	−	0.307484i	$-0.0994871\pi$
$332$	0.989642	+	3.04580i	0.0543136	+	0.167160i
$333$	0.0804402	+	0.170944i	0.00440810	+	0.00936768i
$334$	9.70509	−	3.84252i	0.531039	−	0.210253i
$335$	−5.24418	−	26.6570i	−0.286520	−	1.45643i
$336$	−0.912566	+	0.234307i	−0.0497846	+	0.0127825i
$337$	10.8750	−	4.30571i	0.592398	−	0.234547i	−0.0527459	−	0.998608i	$-0.516797\pi$
$337$	10.8750	−	4.30571i	0.592398	−	0.234547i	0.645144	+	0.764061i	$0.276797\pi$
$338$	1.19582	+	0.307034i	0.0650439	+	0.0167004i
$339$	−0.512743	−	0.807954i	−0.0278484	−	0.0438820i
$340$	−7.32371	+	11.6884i	−0.397184	+	0.633892i
$341$	−0.00312040	−	0.0495974i	−0.000168979	−	0.00268585i
$342$	−2.34081	−	1.28687i	−0.126576	−	0.0695859i
$343$	−3.81759	+	11.7493i	−0.206131	+	0.634405i
$344$	−6.07399	+	0.767324i	−0.327488	+	0.0413713i
$345$	0.338667	+	1.72150i	0.0182332	+	0.0926823i
$346$	5.15572	+	4.84155i	0.277173	+	0.260283i
$347$	−16.7823	−	15.7597i	−0.900923	−	0.846023i	0.0877448	−	0.996143i	$-0.472034\pi$
$347$	−16.7823	−	15.7597i	−0.900923	−	0.846023i	−0.988668	+	0.150120i	$0.952034\pi$
$348$	0.828368	−	0.212689i	0.0444052	−	0.0114013i
$349$	18.0608	−	13.1219i	0.966772	−	0.702401i	0.0120584	−	0.999927i	$-0.496162\pi$
$349$	18.0608	−	13.1219i	0.966772	−	0.702401i	0.954714	+	0.297526i	$0.0961616\pi$
$350$	−4.57601	−	1.11897i	−0.244598	−	0.0598114i
$351$	2.77499	+	2.01615i	0.148118	+	0.107614i
$352$	−0.0193462	−	0.00765969i	−0.00103115	−	0.000408263i
$353$	−33.4570	−	4.22661i	−1.78074	−	0.224960i	−0.835082	−	0.550126i	$-0.814580\pi$
$353$	−33.4570	−	4.22661i	−1.78074	−	0.224960i	−0.945657	+	0.325166i	$0.894580\pi$
$354$	0.684936	−	0.376547i	0.0364039	−	0.0200132i
$355$	−23.1387	−	9.00765i	−1.22808	−	0.478077i
$356$	−0.153312	−	0.325805i	−0.00812554	−	0.0172677i
$357$	4.70185	−	3.41609i	0.248848	−	0.180799i
$358$	−18.1110	+	2.28796i	−0.957198	+	0.120922i
$359$	−1.83199	−	0.470374i	−0.0966885	−	0.0248254i	0.200036	−	0.979789i	$-0.435894\pi$
$359$	−1.83199	−	0.470374i	−0.0966885	−	0.0248254i	−0.296724	+	0.954963i	$0.595894\pi$
$360$	0.127565	−	2.23243i	0.00672327	−	0.117659i
$361$	7.56277	−	9.14182i	0.398041	−	0.481149i
$362$	−6.51500	−	7.87528i	−0.342421	−	0.413915i
$363$	5.89386	−	9.28724i	0.309348	−	0.487454i
$364$	0.202920	−	3.22532i	0.0106359	−	0.169053i
$365$	15.1412	−	0.0870936i	0.792529	−	0.00455869i
$366$	−4.95559	−	5.99028i	−0.259033	−	0.313117i
$367$	−0.781977	+	4.09927i	−0.0408189	+	0.213980i	−0.996853	−	0.0792765i	$-0.974739\pi$
$367$	−0.781977	+	4.09927i	−0.0408189	+	0.213980i	0.956034	+	0.293256i	$0.0947390\pi$
$368$	0.634782	+	0.461196i	0.0330903	+	0.0240415i
$369$	−1.58722	−	0.872582i	−0.0826274	−	0.0454248i
$370$	0.271146	+	0.323948i	0.0140962	+	0.0168412i
$371$	2.25820	+	0.285277i	0.117240	+	0.0148108i
$372$	1.01692	−	2.16106i	0.0527246	−	0.112046i
$373$	0.517501	−	8.22544i	0.0267952	−	0.425897i	−0.961646	−	0.274293i	$-0.911556\pi$
$373$	0.517501	−	8.22544i	0.0267952	−	0.425897i	0.988441	−	0.151604i	$-0.0484438\pi$
$374$	0.128351			0.00663688
$375$	5.82695	−	9.54184i	0.300902	−	0.492738i
$376$	−4.45503			−0.229750
$377$	−0.184198	+	2.92774i	−0.00948666	+	0.150786i
$378$	−0.401155	+	0.852497i	−0.0206332	+	0.0438477i
$379$	−29.8221	−	3.76741i	−1.53186	−	0.193519i	−0.686268	−	0.727349i	$-0.740752\pi$
$379$	−29.8221	−	3.76741i	−1.53186	−	0.193519i	−0.845592	+	0.533830i	$0.820752\pi$
$380$	−5.79382	−	1.45213i	−0.297217	−	0.0744927i
$381$	4.69768	+	2.58257i	0.240670	+	0.132309i
$382$	−2.09792	−	1.52423i	−0.107339	−	0.0779862i
$383$	0.978079	−	5.12727i	0.0499775	−	0.261991i	−0.948525	−	0.316703i	$-0.897424\pi$
$383$	0.978079	−	5.12727i	0.0499775	−	0.261991i	0.998502	+	0.0547120i	$0.0174241\pi$
$384$	−0.637424	−	0.770513i	−0.0325284	−	0.0393201i
$385$	0.0137856	+	0.0416117i	0.000702578	+	0.00212073i
$386$	1.57759	−	25.0751i	0.0802974	−	1.27629i
$387$	−3.28048	+	5.16920i	−0.166756	+	0.262765i
$388$	−2.51594	−	3.04125i	−0.127728	−	0.154396i
$389$	21.9808	−	26.5702i	1.11447	−	1.34716i	0.183097	−	0.983095i	$-0.441388\pi$
$389$	21.9808	−	26.5702i	1.11447	−	1.34716i	0.931373	−	0.364068i	$-0.118612\pi$
$390$	7.14739	+	2.78240i	0.361922	+	0.140892i
$391$	−4.68800	−	1.20367i	−0.237082	−	0.0608723i
$392$	−6.06413	+	0.766077i	−0.306285	+	0.0386927i
$393$	14.8020	−	10.7543i	0.746660	−	0.542480i
$394$	2.16295	+	4.59649i	0.108968	+	0.231568i
$395$	−11.6485	−	18.1239i	−0.586102	−	0.911912i
$396$	−0.0182336	+	0.0100240i	−0.000916273	+	0.000503725i
$397$	38.1880	+	4.82427i	1.91660	+	0.242123i	0.990743	−	0.135750i	$-0.0433444\pi$
$397$	38.1880	+	4.82427i	1.91660	+	0.242123i	0.925857	+	0.377873i	$0.123344\pi$
$398$	−6.33798	−	2.50938i	−0.317694	−	0.125784i
$399$	2.03608	+	1.47930i	0.101931	+	0.0740575i
$400$	−0.993345	−	4.90033i	−0.0496672	−	0.245017i
$401$	4.26746	−	3.10049i	0.213107	−	0.154831i	−0.476111	−	0.879385i	$-0.657954\pi$
$401$	4.26746	−	3.10049i	0.213107	−	0.154831i	0.689218	+	0.724554i	$0.257954\pi$
$402$	−11.7682	+	3.02155i	−0.586942	+	0.150701i
$403$	5.97190	+	5.60799i	0.297481	+	0.279354i
$404$	−3.90082	−	3.66311i	−0.194073	−	0.182247i
$405$	−1.63880	−	1.52129i	−0.0814327	−	0.0755936i
$406$	−0.799422	+	0.100990i	−0.0396746	+	0.00501207i
$407$	0.00121475	−	0.00373862i	6.02129e−5	−	0.000185316i
$408$	5.40555	+	2.97172i	0.267614	+	0.147122i
$409$	−2.17602	−	34.5868i	−0.107597	−	1.71021i	−0.568440	−	0.822724i	$-0.692453\pi$
$409$	−2.17602	−	34.5868i	−0.107597	−	1.71021i	0.460843	−	0.887481i	$-0.347547\pi$
$410$	−3.92859	−	0.984639i	−0.194019	−	0.0486278i
$411$	3.34246	+	5.26687i	0.164871	+	0.259796i
$412$	1.67513	+	0.430101i	0.0825279	+	0.0211896i
$413$	−0.684699	+	0.271092i	−0.0336918	+	0.0133395i
$414$	0.759983	−	0.195130i	0.0373511	−	0.00959014i
$415$	7.10969	+	0.856645i	0.349001	+	0.0420510i
$416$	3.18920	−	1.26269i	0.156363	−	0.0619087i
$417$	−5.62472	−	11.9531i	−0.275444	−	0.585348i
$418$	0.0171754	+	0.0528606i	0.000840079	+	0.00258550i
$419$	−1.42672	+	7.47912i	−0.0696998	+	0.365379i	−0.999999	−	0.00142246i	$-0.999547\pi$
$419$	−1.42672	+	7.47912i	−0.0696998	+	0.365379i	0.930299	+	0.366802i	$0.119547\pi$
$420$	−0.382855	+	2.07167i	−0.0186814	+	0.101087i
$421$	9.61103	−	20.4245i	0.468413	−	0.995428i	−0.521434	−	0.853292i	$-0.674603\pi$
$421$	9.61103	−	20.4245i	0.468413	−	0.995428i	0.989847	−	0.142137i	$-0.0453972\pi$
$422$	−5.23602	−	27.4482i	−0.254886	−	1.33616i
$423$	−2.83974	+	3.43266i	−0.138073	+	0.166901i
$424$	0.746543	+	2.29762i	0.0362554	+	0.111583i
$425$	16.8249	+	25.8496i	0.816126	+	1.25389i
$426$	−3.43145	+	10.5609i	−0.166254	+	0.511678i
$427$	3.92481	+	6.18452i	0.189935	+	0.299290i
$428$	3.30086	−	1.81466i	0.159553	−	0.0877150i
$429$	−0.0133735	−	0.0701064i	−0.000645680	−	0.00338477i
$430$	−4.15543	+	13.0439i	−0.200392	+	0.629033i
$431$	−23.6404	+	22.1998i	−1.13872	+	1.06933i	−0.141878	+	0.989884i	$0.545314\pi$
$431$	−23.6404	+	22.1998i	−1.13872	+	1.06933i	−0.996839	+	0.0794424i	$0.974686\pi$
$432$	−1.00000			−0.0481125
$433$	−25.9594	+	24.3775i	−1.24753	+	1.17151i	−0.269507	+	0.962998i	$0.586861\pi$
$433$	−25.9594	+	24.3775i	−1.24753	+	1.17151i	−0.978021	+	0.208508i	$0.933139\pi$
$434$	−1.20574	+	1.89994i	−0.0578772	+	0.0911998i
$435$	0.347531	−	1.88053i	0.0166628	−	0.0901643i
$436$	−11.9552	−	4.73339i	−0.572550	−	0.226688i
$437$	−0.131604	−	2.09179i	−0.00629549	−	0.100064i
$438$	−0.425185	−	6.75812i	−0.0203161	−	0.322915i
$439$	30.0502	+	11.8977i	1.43422	+	0.567846i	0.951423	−	0.307888i	$-0.0996221\pi$
$439$	30.0502	+	11.8977i	1.43422	+	0.567846i	0.482794	+	0.875734i	$0.339622\pi$
$440$	−0.0337327	+	0.0320442i	−0.00160814	+	0.00152765i
$441$	−3.27515	+	5.16081i	−0.155959	+	0.245753i
$442$	−15.4239	+	14.4840i	−0.733642	+	0.688936i
$443$	17.1440			0.814535			0.407267	−	0.913309i	$-0.366482\pi$
$443$	17.1440			0.814535			0.407267	+	0.913309i	$0.366482\pi$
$444$	0.137720	−	0.129328i	0.00653591	−	0.00613763i
$445$	−0.805138	+	0.00463122i	−0.0381672	+	0.000219541i
$446$	−0.698678	−	3.66260i	−0.0330834	−	0.173429i
$447$	4.73776	−	2.60461i	0.224089	−	0.123194i
$448$	0.504838	+	0.795497i	0.0238513	+	0.0375837i
$449$	0.913307	−	2.81087i	0.0431016	−	0.132653i	−0.927190	−	0.374591i	$-0.877783\pi$
$449$	0.913307	−	2.81087i	0.0431016	−	0.132653i	0.970292	+	0.241938i	$0.0777831\pi$
$450$	−4.40895	−	2.35820i	−0.207840	−	0.111167i
$451$	0.0116461	+	0.0358429i	0.000548392	+	0.00168778i
$452$	−0.609963	+	0.737319i	−0.0286903	+	0.0346806i
$453$	1.17806	+	6.17563i	0.0553503	+	0.290156i
$454$	2.92235	−	6.21031i	0.137153	−	0.291464i
$455$	−6.35237	−	3.44481i	−0.297804	−	0.161495i
$456$	−0.500537	+	2.62390i	−0.0234398	+	0.122876i
$457$	−0.341118	−	1.04985i	−0.0159568	−	0.0491100i	0.942761	−	0.333469i	$-0.108219\pi$
$457$	−0.341118	−	1.04985i	−0.0159568	−	0.0491100i	−0.958718	+	0.284359i	$0.908219\pi$
$458$	8.03893	+	17.0836i	0.375634	+	0.798264i
$459$	5.73538	−	2.27080i	0.267704	−	0.105992i
$460$	1.53259	−	0.854063i	0.0714573	−	0.0398209i
$461$	−38.3683	+	9.85131i	−1.78699	+	0.458821i	−0.989503	−	0.144513i	$-0.953839\pi$
$461$	−38.3683	+	9.85131i	−1.78699	+	0.458821i	−0.797488	+	0.603334i	$0.793839\pi$
$462$	0.0182273	−	0.00721670i	0.000848010	−	0.000335751i
$463$	3.15543	+	0.810177i	0.146645	+	0.0376521i	0.321299	−	0.946978i	$-0.395881\pi$
$463$	3.15543	+	0.810177i	0.146645	+	0.0376521i	−0.174654	+	0.984630i	$0.555881\pi$
$464$	−0.458259	−	0.722101i	−0.0212741	−	0.0335227i
$465$	−3.42780	−	4.09531i	−0.158961	−	0.189915i
$466$	−1.78183	−	28.3214i	−0.0825417	−	1.31196i
$467$	−14.6206	−	8.03775i	−0.676561	−	0.371943i	0.106130	−	0.994352i	$-0.466154\pi$
$467$	−14.6206	−	8.03775i	−0.676561	−	0.371943i	−0.782692	+	0.622409i	$0.786154\pi$
$468$	1.05995	−	3.26219i	0.0489962	−	0.150795i
$469$	11.3569	−	1.43471i	0.524414	−	0.0662489i
$470$	−4.18959	+	9.03790i	−0.193251	+	0.416887i
$471$	−2.27346	−	2.13492i	−0.104755	−	0.0983718i
$472$	−0.569774	−	0.535053i	−0.0262260	−	0.0246278i
$473$	0.123386	−	0.0316801i	0.00567329	−	0.00145665i
$474$	−7.79486	+	5.66330i	−0.358030	+	0.260124i
$475$	−8.39455	+	10.3883i	−0.385168	+	0.476648i
$476$	−4.70185	−	3.41609i	−0.215509	−	0.156576i
$477$	2.24621	+	0.889339i	0.102847	+	0.0407200i
$478$	18.0994	+	2.28648i	0.827847	+	0.104581i
$479$	−35.3070	+	19.4102i	−1.61322	+	0.886874i	−0.618327	+	0.785921i	$0.712189\pi$
$479$	−35.3070	+	19.4102i	−1.61322	+	0.886874i	−0.994891	+	0.100953i	$0.967811\pi$
$480$	−2.16258	+	0.568536i	−0.0987080	+	0.0259500i
$481$	0.275916	+	0.586351i	0.0125807	+	0.0267353i
$482$	5.16546	−	3.75293i	0.235280	−	0.170941i
$483$	−0.733426	+	0.0926532i	−0.0333720	+	0.00421587i
$484$	−10.6540	−	2.73548i	−0.484273	−	0.124340i
$485$	−8.53582	+	2.24404i	−0.387591	+	0.101897i
$486$	−0.637424	+	0.770513i	−0.0289141	+	0.0349512i
$487$	21.3775	+	25.8409i	0.968706	+	1.17096i	0.985253	+	0.171102i	$0.0547326\pi$
$487$	21.3775	+	25.8409i	0.968706	+	1.17096i	−0.0165472	+	0.999863i	$0.505267\pi$
$488$	−4.16573	+	6.56415i	−0.188574	+	0.297145i
$489$	0.0223022	−	0.354484i	0.00100854	−	0.0160303i
$490$	−4.14867	+	13.0227i	−0.187418	+	0.588306i
$491$	7.21900	+	8.72627i	0.325789	+	0.393811i	0.907823	−	0.419353i	$-0.137743\pi$
$491$	7.21900	+	8.72627i	0.325789	+	0.393811i	−0.582034	+	0.813164i	$0.697743\pi$
$492$	−0.339396	+	1.77918i	−0.0153012	+	0.0802116i
$493$	4.26803	+	3.10091i	0.192222	+	0.139658i
$494$	−8.02914	−	4.41406i	−0.361248	−	0.198598i
$495$	0.00318847	+	0.0464172i	0.000143311	+	0.00208630i
$496$	−2.36953	−	0.299341i	−0.106395	−	0.0134408i
$497$	4.45458	−	9.46647i	0.199815	−	0.424629i
$498$	0.201090	−	3.19623i	0.00901104	−	0.143226i
$499$	−4.44466			−0.198970			−0.0994851	−	0.995039i	$-0.531720\pi$
$499$	−4.44466			−0.198970			−0.0994851	+	0.995039i	$0.531720\pi$
$500$	−10.8755	−	2.59317i	−0.486365	−	0.115970i
$501$	−10.4381			−0.466339
$502$	1.57545	−	25.0411i	0.0703158	−	1.11764i
$503$	−6.81999	+	14.4932i	−0.304088	+	0.646220i	−0.997214	−	0.0745964i	$-0.976233\pi$
$503$	−6.81999	+	14.4932i	−0.304088	+	0.646220i	0.693126	+	0.720817i	$0.256233\pi$
$504$	0.934737	+	0.118085i	0.0416365	+	0.00525991i
$505$	−11.0997	+	4.46872i	−0.493932	+	0.198856i
$506$	−0.0143067	−	0.00786517i	−0.000636010	−	0.000349649i
$507$	−0.998816	−	0.725682i	−0.0443590	−	0.0322287i
$508$	1.00451	−	5.26582i	0.0445679	−	0.233633i
$509$	−3.19101	−	3.85727i	−0.141439	−	0.170971i	0.695037	−	0.718974i	$-0.255388\pi$
$509$	−3.19101	−	3.85727i	−0.141439	−	0.170971i	−0.836476	+	0.548004i	$0.815388\pi$
$510$	11.1122	−	8.17155i	0.492057	−	0.361843i
$511$	−0.400595	+	6.36727i	−0.0177213	+	0.281671i
$512$	−0.535827	+	0.844328i	−0.0236804	+	0.0373144i
$513$	1.70270	+	2.05821i	0.0751760	+	0.0908722i
$514$	0.492284	−	0.595069i	0.0217137	−	0.0262474i
$515$	2.44787	−	2.99386i	0.107866	−	0.131925i
$516$	5.92993	+	1.52255i	0.261051	+	0.0670264i
$517$	0.0919662	−	0.0116180i	0.00404467	−	0.000510961i
$518$	−0.144004	+	0.104625i	−0.00632716	+	0.00459695i
$519$	−3.01138	−	6.39951i	−0.132185	−	0.280907i
$520$	0.437558	−	7.65738i	0.0191882	−	0.335798i
$521$	−11.6236	+	6.39014i	−0.509240	+	0.279957i	−0.715589	−	0.698521i	$-0.753842\pi$
$521$	−11.6236	+	6.39014i	−0.509240	+	0.279957i	0.206349	+	0.978478i	$0.433842\pi$
$522$	−0.848493	−	0.107190i	−0.0371375	−	0.00469156i
$523$	22.8026	+	9.02819i	0.997088	+	0.394775i	0.809275	−	0.587430i	$-0.199860\pi$
$523$	22.8026	+	9.02819i	0.997088	+	0.394775i	0.187813	+	0.982205i	$0.439860\pi$
$524$	−14.8020	−	10.7543i	−0.646627	−	0.469802i
$525$	3.84274	+	2.72493i	0.167711	+	0.118926i
$526$	9.93266	−	7.21650i	0.433085	−	0.314654i
$527$	14.2699	−	3.66389i	0.621606	−	0.159601i
$528$	0.0151679	+	0.0142436i	0.000660097	+	0.000619873i
$529$	−16.3175	−	15.3231i	−0.709456	−	0.666224i
$530$	5.36325	+	0.646216i	0.232965	+	0.0280698i
$531$	−0.775453	+	0.0979625i	−0.0336518	+	0.00425121i
$532$	0.777713	−	2.39355i	0.0337181	−	0.103774i
$533$	−5.44428	−	2.99302i	−0.235818	−	0.129642i
$534$	0.0226093	+	0.359364i	0.000978399	+	0.0155512i
$535$	−0.577215	−	8.40299i	−0.0249552	−	0.363293i
$536$	6.51022	+	10.2585i	0.281199	+	0.443098i
$537$	17.6815	+	4.53983i	0.763012	+	0.195908i
$538$	−19.8972	+	7.87785i	−0.857828	+	0.339638i
$539$	0.123185	−	0.0316286i	0.00530597	−	0.00136234i
$540$	−0.940418	+	2.02870i	−0.0404691	+	0.0873012i
$541$	7.89167	−	3.12453i	0.339289	−	0.134334i	−0.192300	−	0.981336i	$-0.561595\pi$
$541$	7.89167	−	3.12453i	0.339289	−	0.134334i	0.531590	+	0.847002i	$0.321595\pi$
$542$	10.1686	+	21.6094i	0.436779	+	0.928202i
$543$	3.15841	+	9.72058i	0.135540	+	0.417150i
$544$	1.15587	−	6.05929i	0.0495576	−	0.259790i
$545$	−20.8455	+	19.8021i	−0.892923	+	0.848229i
$546$	−1.37599	+	2.92413i	−0.0588869	+	0.125141i
$547$	−1.79528	−	9.41121i	−0.0767608	−	0.402394i	−0.999842	−	0.0177885i	$-0.994337\pi$
$547$	−1.79528	−	9.41121i	−0.0767608	−	0.402394i	0.923081	−	0.384606i	$-0.125663\pi$
$548$	3.97622	−	4.80642i	0.169856	−	0.205320i
$549$	2.40242	+	7.39390i	0.102533	+	0.315564i
$550$	0.0332852	+	0.0985683i	0.00141929	+	0.00420297i
$551$	−0.705957	+	2.17271i	−0.0300748	+	0.0925607i
$552$	−0.420428	−	0.662488i	−0.0178946	−	0.0281974i
$553$	7.95489	−	4.37324i	0.338276	−	0.185969i
$554$	5.50081	+	28.8363i	0.233707	+	1.22514i
$555$	−0.132853	−	0.401015i	−0.00563928	−	0.0170221i
$556$	−9.62998	+	9.04315i	−0.408402	+	0.383515i
$557$	13.9718			0.592003			0.296002	−	0.955187i	$-0.404347\pi$
$557$	13.9718			0.592003			0.296002	+	0.955187i	$0.404347\pi$
$558$	−1.74104	+	1.63495i	−0.0737042	+	0.0692128i
$559$	−11.2523	+	17.7307i	−0.475920	+	0.749930i
$560$	2.08858	−	0.276064i	0.0882587	−	0.0116658i
$561$	−0.119338	−	0.0472492i	−0.00503845	−	0.00199486i
$562$	0.867466	+	13.7880i	0.0365919	+	0.581611i
$563$	0.00354396	+	0.0563296i	0.000149360	+	0.00237401i	0.998101	−	0.0616035i	$-0.0196214\pi$
$563$	0.00354396	+	0.0563296i	0.000149360	+	0.00237401i	−0.997951	+	0.0639775i	$0.979621\pi$
$564$	4.14218	+	1.64000i	0.174417	+	0.0690567i
$565$	0.922177	+	1.93082i	0.0387963	+	0.0812302i
$566$	16.8950	−	26.6223i	0.710151	−	1.11902i
$567$	0.686810	−	0.644957i	0.0288433	−	0.0270857i
$568$	11.1044			0.465930
$569$	−28.8174	+	27.0613i	−1.20809	+	1.13447i	−0.220834	+	0.975311i	$0.570878\pi$
$569$	−28.8174	+	27.0613i	−1.20809	+	1.13447i	−0.987253	+	0.159158i	$0.949122\pi$
$570$	4.85240	+	3.48300i	0.203244	+	0.145887i
$571$	−4.91434	−	25.7619i	−0.205659	−	1.07810i	−0.923995	−	0.382405i	$-0.875096\pi$
$571$	−4.91434	−	25.7619i	−0.205659	−	1.07810i	0.718336	−	0.695697i	$-0.244904\pi$
$572$	−0.0625425	+	0.0343831i	−0.00261504	+	0.00143763i
$573$	1.38949	+	2.18949i	0.0580468	+	0.0914671i
$574$	0.527340	−	1.62299i	0.0220108	−	0.0677421i
$575$	−0.291364	−	3.91233i	−0.0121507	−	0.163156i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	2.81855	−	3.40704i	0.117338	−	0.141837i	−0.708574	−	0.705637i	$-0.750661\pi$
$577$	2.81855	−	3.40704i	0.117338	−	0.141837i	0.825911	+	0.563800i	$0.190661\pi$
$578$	3.94458	+	20.6782i	0.164073	+	0.860099i
$579$	−10.6976	+	22.7335i	−0.444576	+	0.944772i
$580$	−1.89588	+	0.250593i	−0.0787221	+	0.0104053i
$581$	−0.565392	+	2.96389i	−0.0234564	+	0.122963i
$582$	1.21970	+	3.75386i	0.0505584	+	0.155603i
$583$	−0.0214029	−	0.0454836i	−0.000886419	−	0.00188374i
$584$	−6.29596	+	2.49275i	−0.260529	+	0.103151i
$585$	−5.62121	−	5.21814i	−0.232408	−	0.215744i
$586$	24.1694	−	6.20566i	0.998430	−	0.256353i
$587$	33.2869	−	13.1792i	1.37390	−	0.543965i	0.438874	−	0.898548i	$-0.355377\pi$
$587$	33.2869	−	13.1792i	1.37390	−	0.543965i	0.935024	+	0.354584i	$0.115377\pi$
$588$	5.92029	+	1.52007i	0.244149	+	0.0626868i
$589$	3.41849	+	5.38668i	0.140856	+	0.221954i
$590$	−1.62129	+	0.652725i	−0.0667473	+	0.0268723i
$591$	−0.318974	−	5.06995i	−0.0131208	−	0.208550i
$592$	−0.165556	−	0.0910151i	−0.00680431	−	0.00374070i
$593$	13.3792	−	41.1769i	0.549418	−	1.69093i	−0.160830	−	0.986982i	$-0.551417\pi$
$593$	13.3792	−	41.1769i	0.549418	−	1.69093i	0.710248	−	0.703952i	$-0.248583\pi$
$594$	0.0206432	−	0.00260785i	0.000847003	−	0.000107001i
$595$	−11.3519	+	6.32607i	−0.465383	+	0.259344i
$596$	−3.94118	−	3.70101i	−0.161437	−	0.151599i
$597$	4.96914	+	4.66633i	0.203373	+	0.190980i
$598$	2.60680	−	0.669311i	0.106600	−	0.0273702i
$599$	3.54160	−	2.57312i	0.144706	−	0.105135i	−0.513077	−	0.858343i	$-0.671494\pi$
$599$	3.54160	−	2.57312i	0.144706	−	0.105135i	0.657783	+	0.753208i	$0.271494\pi$
$600$	−0.880345	+	4.92189i	−0.0359399	+	0.200935i
$601$	−11.1993	−	8.13677i	−0.456829	−	0.331906i	0.335457	−	0.942056i	$-0.391109\pi$
$601$	−11.1993	−	8.13677i	−0.456829	−	0.331906i	−0.792286	+	0.610150i	$0.791109\pi$
$602$	−5.36313	−	2.12341i	−0.218585	−	0.0865439i
$603$	12.0541	+	1.52278i	0.490879	+	0.0620125i
$604$	5.50933	−	3.02878i	0.224172	−	0.123239i
$605$	−15.5687	+	19.0412i	−0.632957	+	0.774136i
$606$	2.27841	+	4.84186i	0.0925539	+	0.196687i
$607$	1.17463	−	0.853416i	0.0476766	−	0.0346391i	−0.563692	−	0.825985i	$-0.690619\pi$
$607$	1.17463	−	0.853416i	0.0476766	−	0.0346391i	0.611368	+	0.791346i	$0.290619\pi$
$608$	2.65016	−	0.334793i	0.107478	−	0.0135776i
$609$	0.780461	+	0.200388i	0.0316259	+	0.00812014i
$610$	9.39914	+	14.6241i	0.380560	+	0.592111i
$611$	−9.74052	+	11.7743i	−0.394059	+	0.476336i
$612$	−3.93198	−	4.75295i	−0.158941	−	0.192127i
$613$	6.96565	−	10.9761i	0.281340	−	0.443321i	−0.674042	−	0.738693i	$-0.735443\pi$
$613$	6.96565	−	10.9761i	0.281340	−	0.443321i	0.955382	+	0.295372i	$0.0954435\pi$
$614$	−1.58554	+	25.2015i	−0.0639874	+	1.01705i
$615$	3.29024	+	2.36170i	0.132675	+	0.0952331i
$616$	−0.0124960	−	0.0151051i	−0.000503479	−	0.000608602i
$617$	−4.17630	+	21.8929i	−0.168132	+	0.881377i	0.793819	+	0.608154i	$0.208090\pi$
$617$	−4.17630	+	21.8929i	−0.168132	+	0.881377i	−0.961951	+	0.273223i	$0.911910\pi$
$618$	−1.39917	−	1.01656i	−0.0562828	−	0.0408919i
$619$	24.0750	+	13.2354i	0.967657	+	0.531974i	0.885497	−	0.464645i	$-0.153818\pi$
$619$	24.0750	+	13.2354i	0.967657	+	0.531974i	0.0821599	+	0.996619i	$0.473818\pi$
$620$	−2.83562	+	4.52555i	−0.113881	+	0.181751i
$621$	−0.778446	−	0.0983407i	−0.0312380	−	0.00394627i
$622$	6.51706	−	13.8495i	0.261310	−	0.555312i
$623$	0.0213017	−	0.338581i	0.000853435	−	0.0135650i
$624$	−3.43007			−0.137313
$625$	−15.4882	+	19.6243i	−0.619529	+	0.784974i
$626$	23.5149			0.939845
$627$	0.00348995	−	0.0554712i	0.000139375	−	0.00221531i
$628$	−1.32789	+	2.82191i	−0.0529886	+	0.112606i
$629$	1.15620	+	0.146062i	0.0461008	+	0.00582389i
$630$	1.11860	−	1.78525i	0.0445662	−	0.0711260i
$631$	−11.8342	−	6.50591i	−0.471112	−	0.258996i	0.228466	−	0.973552i	$-0.426629\pi$
$631$	−11.8342	−	6.50591i	−0.471112	−	0.258996i	−0.699579	+	0.714556i	$0.746629\pi$
$632$	7.79486	+	5.66330i	0.310063	+	0.225274i
$633$	−5.23602	+	27.4482i	−0.208113	+	1.09097i
$634$	−9.35503	−	11.3083i	−0.371536	−	0.449109i
$635$	−9.73810	−	6.98992i	−0.386445	−	0.277386i
$636$	0.151693	−	2.41110i	0.00601504	−	0.0956063i
$637$	−11.2340	+	17.7019i	−0.445107	+	0.701376i
$638$	0.0113431	+	0.0137114i	0.000449077	+	0.000542841i
$639$	7.07821	−	8.55608i	0.280010	−	0.338473i
$640$	1.20898	+	1.88105i	0.0477893	+	0.0743551i
$641$	2.03253	+	0.521864i	0.0802799	+	0.0206124i	0.288616	−	0.957445i	$-0.406805\pi$
$641$	2.03253	+	0.521864i	0.0802799	+	0.0206124i	−0.208336	+	0.978057i	$0.566805\pi$
$642$	−3.73708	+	0.472103i	−0.147491	+	0.0186324i
$643$	1.72286	−	1.25173i	0.0679430	−	0.0493635i	−0.553295	−	0.832985i	$-0.686630\pi$
$643$	1.72286	−	1.25173i	0.0679430	−	0.0493635i	0.621238	+	0.783622i	$0.286630\pi$
$644$	0.314760	+	0.668898i	0.0124033	+	0.0263583i
$645$	8.66540	−	10.5982i	0.341200	−	0.417304i
$646$	−14.4394	+	7.93812i	−0.568110	+	0.312321i
$647$	−30.3324	−	3.83188i	−1.19249	−	0.150647i	−0.496071	−	0.868282i	$-0.665225\pi$
$647$	−30.3324	−	3.83188i	−1.19249	−	0.150647i	−0.696419	+	0.717635i	$0.745225\pi$
$648$	0.929776	+	0.368125i	0.0365251	+	0.0144613i
$649$	0.0131573	+	0.00955935i	0.000516470	+	0.000375237i
$650$	−15.1230	−	8.08881i	−0.593174	−	0.317269i
$651$	1.82048	−	1.32265i	0.0713502	−	0.0518389i
$652$	−0.344026	+	0.0883308i	−0.0134731	+	0.00345930i
$653$	13.9431	+	13.0935i	0.545637	+	0.512387i	0.907617	−	0.419799i	$-0.137899\pi$
$653$	13.9431	+	13.0935i	0.545637	+	0.512387i	−0.361980	+	0.932186i	$0.617899\pi$
$654$	9.37317	+	8.80200i	0.366520	+	0.344185i
$655$	−35.7372	+	19.9152i	−1.39637	+	0.778151i
$656$	1.79698	−	0.227011i	0.0701602	−	0.00886330i
$657$	−2.09250	+	6.44006i	−0.0816363	+	0.251251i
$658$	−3.67819	−	2.02210i	−0.143391	−	0.0788297i
$659$	−1.06400	−	16.9118i	−0.0414476	−	0.658791i	−0.962826	−	0.270124i	$-0.912935\pi$
$659$	−1.06400	−	16.9118i	−0.0414476	−	0.658791i	0.921378	−	0.388668i	$-0.127065\pi$
$660$	0.0431601	−	0.0173761i	0.00168000	−	0.000676365i
$661$	−26.3862	−	41.5780i	−1.02631	−	1.61720i	−0.756169	−	0.654376i	$-0.772931\pi$
$661$	−26.3862	−	41.5780i	−1.02631	−	1.61720i	−0.270136	−	0.962822i	$-0.587069\pi$
$662$	16.9290	+	4.34662i	0.657963	+	0.168936i
$663$	19.6728	−	7.78900i	0.764027	−	0.302500i
$664$	−3.10193	+	0.796441i	−0.120378	+	0.0309079i
$665$	−4.12442	−	3.82869i	−0.159938	−	0.148470i
$666$	−0.175658	+	0.0695478i	−0.00680660	+	0.00269492i
$667$	−0.285718	−	0.607182i	−0.0110631	−	0.0235102i
$668$	3.22555	+	9.92721i	0.124800	+	0.384095i
$669$	−0.698678	+	3.66260i	−0.0270124	+	0.141604i
$670$	26.9337	−	3.56002i	1.04054	−	0.137536i
$671$	0.0688760	−	0.146369i	0.00265893	−	0.00565051i
$672$	−0.176544	−	0.925478i	−0.00681035	−	0.0357011i
$673$	8.58836	−	10.3815i	0.331057	−	0.400179i	−0.578551	−	0.815646i	$-0.696382\pi$
$673$	8.58836	−	10.3815i	0.331057	−	0.400179i	0.909608	+	0.415467i	$0.136382\pi$
$674$	3.61437	+	11.1239i	0.139220	+	0.428476i
$675$	3.23123	+	3.81565i	0.124370	+	0.146864i
$676$	−0.381514	+	1.17418i	−0.0146736	+	0.0451607i
$677$	14.6596	+	23.0998i	0.563415	+	0.887799i	0.999929	−	0.0118978i	$-0.00378729\pi$
$677$	14.6596	+	23.0998i	0.563415	+	0.887799i	−0.436515	+	0.899697i	$0.643787\pi$
$678$	0.838555	−	0.460999i	0.0322045	−	0.0177046i
$679$	−0.696829	−	3.65290i	−0.0267418	−	0.140186i
$680$	−11.2055	−	8.04318i	−0.429710	−	0.308442i
$681$	−5.00330	+	4.69841i	−0.191727	+	0.180044i
$682$	0.0496954			0.00190294
$683$	10.3825	−	9.74985i	0.397277	−	0.373068i	−0.460004	−	0.887917i	$-0.652152\pi$
$683$	10.3825	−	9.74985i	0.397277	−	0.373068i	0.857281	+	0.514849i	$0.172152\pi$
$684$	1.43131	−	2.25538i	0.0547275	−	0.0862368i
$685$	−6.01147	−	12.5866i	−0.229686	−	0.480909i
$686$	−11.4864	−	4.54781i	−0.438555	−	0.173636i
$687$	−1.18552	−	18.8433i	−0.0452303	−	0.718915i
$688$	−0.384421	−	6.11019i	−0.0146559	−	0.232949i
$689$	7.70468	+	3.05050i	0.293525	+	0.116215i
$690$	−1.73937	+	0.229905i	−0.0662165	+	0.00875233i
$691$	4.80774	−	7.57579i	0.182895	−	0.288196i	−0.740493	−	0.672064i	$-0.765408\pi$
$691$	4.80774	−	7.57579i	0.182895	−	0.288196i	0.923388	+	0.383867i	$0.125408\pi$
$692$	−5.15572	+	4.84155i	−0.195991	+	0.184048i
$693$	−0.0196040			−0.000744693
$694$	16.7823	−	15.7597i	0.637049	−	0.598229i
$695$	9.28962	+	28.0407i	0.352375	+	1.06364i
$696$	0.160255	+	0.840089i	0.00607447	+	0.0318435i
$697$	−9.79085	+	5.38257i	−0.370855	+	0.203879i
$698$	11.9620	+	18.8491i	0.452768	+	0.713448i
$699$	−8.76909	+	26.9885i	−0.331677	+	1.02080i
$700$	1.40409	−	4.49672i	0.0530696	−	0.169960i
$701$	−0.0412127	−	0.126840i	−0.00155658	−	0.00479066i	0.950275	−	0.311411i	$-0.100802\pi$
$701$	−0.0412127	−	0.126840i	−0.00155658	−	0.00479066i	−0.951832	+	0.306621i	$0.900802\pi$
$702$	−2.18641	+	2.64292i	−0.0825207	+	0.0997504i
$703$	0.0945637	+	0.495720i	0.00356654	+	0.0186964i
$704$	0.00885933	−	0.0188270i	0.000333898	−	0.000709570i
$705$	7.22245	−	6.86094i	0.272013	−	0.258398i
$706$	6.31905	−	33.1256i	0.237821	−	1.24670i
$707$	−1.55796	−	4.79491i	−0.0585931	−	0.180331i
$708$	0.332796	+	0.707228i	0.0125072	+	0.0265792i
$709$	−12.7973	+	5.06681i	−0.480613	+	0.190288i	−0.595923	−	0.803041i	$-0.703214\pi$
$709$	−12.7973	+	5.06681i	−0.480613	+	0.190288i	0.115310	+	0.993329i	$0.463214\pi$
$710$	10.4428	−	22.5275i	0.391910	−	0.845440i
$711$	9.33228	−	2.39612i	0.349988	−	0.0898616i
$712$	0.334789	−	0.132552i	0.0125468	−	0.00496761i
$713$	−1.81511	−	0.466042i	−0.0679766	−	0.0174534i
$714$	3.11412	+	4.90707i	0.116543	+	0.183642i
$715$	0.0109367	+	0.159214i	0.000409009	+	0.00595428i
$716$	−1.14624	−	18.2190i	−0.0428370	−	0.680874i
$717$	−15.9867	−	8.78875i	−0.597033	−	0.328222i
$718$	0.584477	−	1.79884i	0.0218125	−	0.0671320i
$719$	−27.6893	+	3.49797i	−1.03264	+	0.130452i	−0.623342	−	0.781949i	$-0.714225\pi$
$719$	−27.6893	+	3.49797i	−1.03264	+	0.130452i	−0.409295	+	0.912402i	$0.634225\pi$
$720$	2.22001	+	0.267489i	0.0827349	+	0.00996871i
$721$	1.18781	+	1.11543i	0.0442365	+	0.0415409i
$722$	8.64891	+	8.12187i	0.321879	+	0.302265i
$723$	−6.18427	+	1.58785i	−0.229996	+	0.0590528i
$724$	8.26882	−	6.00765i	0.307308	−	0.223273i
$725$	−1.27454	+	4.08183i	−0.0473353	+	0.151595i
$726$	8.89884	+	6.46538i	0.330267	+	0.239953i
$727$	−21.6267	−	8.56263i	−0.802091	−	0.317570i	−0.0689265	−	0.997622i	$-0.521957\pi$
$727$	−21.6267	−	8.56263i	−0.802091	−	0.317570i	−0.733164	+	0.680052i	$0.761957\pi$
$728$	3.20621	+	0.405039i	0.118830	+	0.0150117i
$729$	0.876307	−	0.481754i	0.0324558	−	0.0178427i
$730$	−0.863805	+	15.1168i	−0.0319708	+	0.559499i
$731$	16.0798	+	34.1713i	0.594733	+	1.26387i
$732$	6.28963	−	4.56968i	0.232471	−	0.168900i
$733$	−12.4162	+	1.56854i	−0.458604	+	0.0579352i	−0.351242	−	0.936285i	$-0.614241\pi$
$733$	−12.4162	+	1.56854i	−0.458604	+	0.0579352i	−0.107363	+	0.994220i	$0.534241\pi$
$734$	−4.04208	−	1.03783i	−0.149196	−	0.0383070i
$735$	8.65132	−	10.5810i	0.319109	−	0.390285i
$736$	−0.500144	+	0.604571i	−0.0184356	+	0.0222848i
$737$	−0.161145	−	0.194790i	−0.00593584	−	0.00717520i
$738$	0.970522	−	1.52930i	0.0357254	−	0.0562942i
$739$	−1.35947	+	21.6082i	−0.0500089	+	0.794869i	0.890475	+	0.455032i	$0.150372\pi$
$739$	−1.35947	+	21.6082i	−0.0500089	+	0.794869i	−0.940484	+	0.339838i	$0.889628\pi$
$740$	−0.340334	+	0.250271i	−0.0125109	+	0.00920013i
$741$	5.84038	+	7.05981i	0.214552	+	0.259349i
$742$	−0.426507	+	2.23583i	−0.0156576	+	0.0820799i
$743$	12.4861	+	9.07172i	0.458072	+	0.332809i	0.792775	−	0.609515i	$-0.208636\pi$
$743$	12.4861	+	9.07172i	0.458072	+	0.332809i	−0.334702	+	0.942324i	$0.608636\pi$
$744$	2.09294	+	1.15060i	0.0767308	+	0.0421831i
$745$	−11.2146	+	4.51496i	−0.410871	+	0.165415i
$746$	8.17671	+	1.03296i	0.299371	+	0.0378193i
$747$	−1.36358	+	2.89775i	−0.0498907	+	0.106023i
$748$	−0.00805923	+	0.128098i	−0.000294675	+	0.00468372i
$749$	3.54894			0.129675
$750$	9.15713	+	6.41459i	0.334371	+	0.234228i
$751$	24.3636			0.889039			0.444520	−	0.895769i	$-0.353374\pi$
$751$	24.3636			0.889039			0.444520	+	0.895769i	$0.353374\pi$
$752$	0.279733	−	4.44624i	0.0102008	−	0.162138i
$753$	−10.6831	+	22.7026i	−0.389312	+	0.827330i
$754$	−2.91039	−	0.367668i	−0.105990	−	0.0133897i
$755$	−0.963406	−	14.0251i	−0.0350619	−	0.510425i
$756$	−0.825626	−	0.453892i	−0.0300277	−	0.0165079i
$757$	22.0039	+	15.9868i	0.799746	+	0.581049i	0.910840	−	0.412761i	$-0.135435\pi$
$757$	22.0039	+	15.9868i	0.799746	+	0.581049i	−0.111094	+	0.993810i	$0.535435\pi$
$758$	5.63253	−	29.5267i	0.204583	−	1.07246i
$759$	0.0104067	+	0.0125795i	0.000377738	+	0.000456607i
$760$	1.81306	−	5.69121i	0.0657666	−	0.206442i
$761$	0.855474	−	13.5974i	0.0310109	−	0.492904i	−0.951613	−	0.307298i	$-0.900575\pi$
$761$	0.855474	−	13.5974i	0.0310109	−	0.492904i	0.982624	−	0.185606i	$-0.0594249\pi$
$762$	−2.87245	+	4.52625i	−0.104058	+	0.163969i
$763$	−7.72207	−	9.33438i	−0.279558	−	0.337927i
$764$	1.65295	−	1.99807i	0.0598016	−	0.0722877i
$765$	−13.3400	+	3.50705i	−0.482309	+	0.126797i
$766$	5.05574	+	1.29809i	0.182671	+	0.0469020i
$767$	−2.65986	+	0.336019i	−0.0960420	+	0.0121329i
$768$	0.809017	−	0.587785i	0.0291929	−	0.0212099i
$769$	12.4679	+	26.4956i	0.449603	+	0.955455i	0.993234	+	0.116131i	$0.0370491\pi$
$769$	12.4679	+	26.4956i	0.449603	+	0.955455i	−0.543631	+	0.839324i	$0.682951\pi$
$770$	−0.0423952	+	0.0111456i	−0.00152782	+	0.000401658i
$771$	−0.676774	+	0.372060i	−0.0243734	+	0.0133994i
$772$	24.9266	+	3.14896i	0.897127	+	0.113334i
$773$	12.2919	+	4.86669i	0.442108	+	0.175043i	0.578623	−	0.815595i	$-0.303590\pi$
$773$	12.2919	+	4.86669i	0.442108	+	0.175043i	−0.136515	+	0.990638i	$0.543590\pi$
$774$	−4.95302	−	3.59858i	−0.178033	−	0.129348i
$775$	6.51431	+	10.0085i	0.234001	+	0.359517i
$776$	3.19323	−	2.32002i	0.114630	−	0.0832837i
$777$	0.172406	−	0.0442664i	0.00618504	−	0.00158805i
$778$	25.1376	+	23.6058i	0.901226	+	0.846308i
$779$	−3.52695	−	3.31203i	−0.126366	−	0.118666i
$780$	−3.22570	+	6.95858i	−0.115499	+	0.249157i
$781$	−0.229231	+	0.0289586i	−0.00820252	+	0.00103622i
$782$	1.49566	−	4.60317i	0.0534847	−	0.164609i
$783$	0.749450	+	0.412014i	0.0267832	+	0.0147242i
$784$	−0.383796	−	6.10026i	−0.0137070	−	0.217866i
$785$	4.47603	+	5.34766i	0.159756	+	0.190866i
$786$	9.80361	+	15.4480i	0.349683	+	0.551012i
$787$	8.12253	+	2.08551i	0.289537	+	0.0743405i	0.390665	−	0.920533i	$-0.372245\pi$
$787$	8.12253	+	2.08551i	0.289537	+	0.0743405i	−0.101128	+	0.994873i	$0.532245\pi$
$788$	−4.72324	+	1.87006i	−0.168258	+	0.0666182i
$789$	−11.8917	+	3.05328i	−0.423357	+	0.108700i
$790$	18.8195	−	10.4875i	0.669569	−	0.373130i
$791$	−0.838265	+	0.331893i	−0.0298053	+	0.0118007i
$792$	−0.00885933	−	0.0188270i	−0.000314802	−	0.000668989i
$793$	8.24048	+	25.3616i	0.292628	+	0.900617i
$794$	−7.21259	+	37.8097i	−0.255965	+	1.34182i
$795$	−4.74873	−	2.57518i	−0.168420	−	0.0913322i
$796$	2.90240	−	6.16790i	0.102873	−	0.218616i
$797$	−8.08596	−	42.3881i	−0.286419	−	1.50146i	−0.776684	−	0.629890i	$-0.783100\pi$
$797$	−8.08596	−	42.3881i	−0.286419	−	1.50146i	0.490265	−	0.871573i	$-0.336900\pi$
$798$	−1.60423	+	1.93918i	−0.0567890	+	0.0686461i
$799$	8.49212	+	26.1361i	0.300430	+	0.924627i
$800$	4.95304	−	0.683690i	0.175116	−	0.0241721i
$801$	0.111269	−	0.342451i	0.00393151	−	0.0120999i
$802$	2.82642	+	4.45372i	0.0998043	+	0.157266i
$803$	0.123468	−	0.0678773i	0.00435711	−	0.00239534i
$804$	−2.27666	−	11.9347i	−0.0802915	−	0.420903i
$805$	1.65300	−	0.00950817i	0.0582605	−	0.000335119i
$806$	−5.97190	+	5.60799i	−0.210351	+	0.197533i
$807$	21.4000			0.753314
$808$	3.90082	−	3.66311i	0.137230	−	0.128868i
$809$	2.81540	−	4.43636i	0.0989842	−	0.155974i	−0.791226	−	0.611523i	$-0.790557\pi$
$809$	2.81540	−	4.43636i	0.0989842	−	0.155974i	0.890211	+	0.455549i	$0.150557\pi$
$810$	1.62119	−	1.54004i	0.0569629	−	0.0541116i
$811$	5.81394	+	2.30190i	0.204155	+	0.0808307i	0.467977	−	0.883741i	$-0.344983\pi$
$811$	5.81394	+	2.30190i	0.204155	+	0.0808307i	−0.263822	+	0.964571i	$0.584983\pi$
$812$	−0.0505951	−	0.804186i	−0.00177554	−	0.0282214i
$813$	−1.49958	−	23.8352i	−0.0525927	−	0.835936i
$814$	0.00365497	+	0.00144710i	0.000128106	+	5.07209e-5i
$815$	−0.144332	+	0.780992i	−0.00505571	+	0.0273570i
$816$	−3.30528	+	5.20828i	−0.115708	+	0.182326i
$817$	−11.9215	+	11.1950i	−0.417080	+	0.391665i
$818$	34.6552			1.21169
$819$	2.35581	−	2.21225i	0.0823185	−	0.0773022i
$820$	1.22937	−	3.85901i	0.0429316	−	0.134763i
$821$	−1.83089	−	9.59784i	−0.0638984	−	0.334967i	0.935954	−	0.352121i	$-0.114539\pi$
$821$	−1.83089	−	9.59784i	−0.0638984	−	0.334967i	−0.999853	+	0.0171540i	$0.994539\pi$
$822$	−5.46635	+	3.00515i	−0.190661	+	0.104817i
$823$	25.0164	+	39.4195i	0.872015	+	1.37408i	0.926791	+	0.375577i	$0.122556\pi$
$823$	25.0164	+	39.4195i	0.872015	+	1.37408i	−0.0547757	+	0.998499i	$0.517444\pi$
$824$	−0.534435	+	1.64482i	−0.0186179	+	0.0573001i
$825$	0.00533763	−	0.103900i	0.000185832	−	0.00361732i
$826$	−0.227564	−	0.700370i	−0.00791796	−	0.0243690i
$827$	24.6631	−	29.8126i	0.857621	−	1.03669i	−0.141287	−	0.989969i	$-0.545124\pi$
$827$	24.6631	−	29.8126i	0.857621	−	1.03669i	0.998908	−	0.0467172i	$-0.0148760\pi$
$828$	0.147026	+	0.770736i	0.00510950	+	0.0267849i
$829$	6.97840	−	14.8299i	0.242370	−	0.515062i	−0.746219	−	0.665701i	$-0.768133\pi$
$829$	6.97840	−	14.8299i	0.242370	−	0.515062i	0.988589	+	0.150638i	$0.0481328\pi$
$830$	−1.30138	+	7.04187i	−0.0451714	+	0.244427i
$831$	5.50081	−	28.8363i	0.190821	−	1.00032i
$832$	1.05995	+	3.26219i	0.0367472	+	0.113096i
$833$	16.0537	+	34.1158i	0.556227	+	1.18204i
$834$	12.2827	−	4.86308i	0.425316	−	0.168395i
$835$	23.1727	+	2.79207i	0.801923	+	0.0966235i
$836$	−0.0538347	+	0.0138224i	−0.00186191	+	0.000478058i
$837$	2.22064	−	0.879215i	0.0767567	−	0.0303901i
$838$	−7.37478	−	1.89352i	−0.254758	−	0.0654106i
$839$	10.2956	+	16.2232i	0.355442	+	0.560087i	0.974254	−	0.225452i	$-0.0723859\pi$
$839$	10.2956	+	16.2232i	0.355442	+	0.560087i	−0.618812	+	0.785539i	$0.712386\pi$
$840$	−2.04354	−	0.512181i	−0.0705088	−	0.0176719i
$841$	−1.77500	−	28.2128i	−0.0612068	−	0.972855i
$842$	19.7807	+	10.8745i	0.681688	+	0.374761i
$843$	4.26915	−	13.1391i	0.147037	−	0.452534i
$844$	27.7228	−	3.50221i	0.954259	−	0.120551i
$845$	2.02327	+	1.87820i	0.0696027	+	0.0646119i
$846$	−3.24757	−	3.04968i	−0.111654	−	0.104850i
$847$	−7.55461	−	7.09425i	−0.259579	−	0.243761i
$848$	−2.33997	+	0.600801i	−0.0803548	+	0.0206316i
$849$	−25.5089	+	18.5333i	−0.875464	+	0.636062i
$850$	−26.8550	+	15.1686i	−0.921119	+	0.520277i
$851$	−0.119926	−	0.0871313i	−0.00411101	−	0.00298682i
$852$	−10.3246	−	4.08780i	−0.353715	−	0.140046i
$853$	−11.9336	−	1.50756i	−0.408598	−	0.0516179i	−0.0816519	−	0.996661i	$-0.526020\pi$
$853$	−11.9336	−	1.50756i	−0.408598	−	0.0516179i	−0.326946	+	0.945043i	$0.606020\pi$
$854$	−6.41875	+	3.52874i	−0.219645	+	0.120751i
$855$	−3.22946	−	5.02470i	−0.110445	−	0.171841i
$856$	1.60382	+	3.40829i	0.0548174	+	0.116493i
$857$	−13.5577	+	9.85021i	−0.463121	+	0.336477i	−0.794754	−	0.606931i	$-0.792400\pi$
$857$	−13.5577	+	9.85021i	−0.463121	+	0.336477i	0.331634	+	0.943408i	$0.392400\pi$
$858$	0.0708078	−	0.00894511i	0.00241734	−	0.000305381i
$859$	−14.8686	−	3.81760i	−0.507309	−	0.130255i	−0.0136441	−	0.999907i	$-0.504343\pi$
$859$	−14.8686	−	3.81760i	−0.507309	−	0.130255i	−0.493665	+	0.869652i	$0.664343\pi$
$860$	−12.7572	−	4.96626i	−0.435018	−	0.169348i
$861$	−1.08777	+	1.31489i	−0.0370711	+	0.0448112i
$862$	−20.6716	−	24.9877i	−0.704077	−	0.851083i
$863$	1.55178	−	2.44522i	0.0528233	−	0.0832363i	−0.816890	−	0.576794i	$-0.804304\pi$
$863$	1.55178	−	2.44522i	0.0528233	−	0.0832363i	0.869713	+	0.493557i	$0.164304\pi$
$864$	0.0627905	−	0.998027i	0.00213618	−	0.0339536i
$865$	4.97350	+	15.0125i	0.169104	+	0.510440i
$866$	−22.6994	−	27.4388i	−0.771356	−	0.932409i
$867$	3.94458	−	20.6782i	0.133965	−	0.702268i
$868$	−1.82048	−	1.32265i	−0.0617911	−	0.0448938i
$869$	−0.175680	−	0.0965810i	−0.00595954	−	0.00327629i
$870$	1.85499	+	0.464925i	0.0628902	+	0.0157624i
$871$	41.3463	+	5.22325i	1.40097	+	0.176983i
$872$	5.47473	−	11.6344i	0.185398	−	0.393990i
$873$	0.247837	−	3.93926i	0.00838801	−	0.133324i
$874$	2.09593			0.0708958
$875$	−7.80205	−	7.07727i	−0.263757	−	0.239255i
$876$	6.77148			0.228787
$877$	1.21066	−	19.2429i	0.0408810	−	0.649785i	−0.923224	−	0.384263i	$-0.874456\pi$
$877$	1.21066	−	19.2429i	0.0408810	−	0.649785i	0.964105	−	0.265522i	$-0.0855444\pi$
$878$	−13.7611	+	29.2438i	−0.464414	+	0.986931i
$879$	−24.7566	−	3.12749i	−0.835021	−	0.105488i
$880$	−0.0298629	−	0.0356782i	−0.00100668	−	0.00120271i
$881$	−15.3190	−	8.42171i	−0.516112	−	0.283735i	0.202336	−	0.979316i	$-0.435147\pi$
$881$	−15.3190	−	8.42171i	−0.516112	−	0.283735i	−0.718447	+	0.695581i	$0.755147\pi$
$882$	−4.94497	−	3.59273i	−0.166506	−	0.120974i
$883$	−4.57804	+	23.9989i	−0.154063	+	0.807628i	0.818414	+	0.574629i	$0.194854\pi$
$883$	−4.57804	+	23.9989i	−0.154063	+	0.807628i	−0.972477	+	0.232998i	$0.925146\pi$
$884$	−13.4870	−	16.3030i	−0.453617	−	0.548328i
$885$	1.74772	−	0.0100530i	0.0587489	−	0.000337928i
$886$	−1.07648	+	17.1101i	−0.0361650	+	0.574827i
$887$	−5.53415	+	8.72043i	−0.185819	+	0.292803i	−0.924448	−	0.381309i	$-0.875474\pi$
$887$	−5.53415	+	8.72043i	−0.185819	+	0.292803i	0.738629	+	0.674112i	$0.235474\pi$
$888$	0.120425	+	0.145569i	0.00404120	+	0.00488497i
$889$	3.21946	−	3.89166i	0.107977	−	0.130522i
$890$	0.0459330	−	0.803840i	0.00153968	−	0.0269448i
$891$	−0.0201536	−	0.00517457i	−0.000675172	−	0.000173355i
$892$	3.69924	−	0.467323i	0.123860	−	0.0156471i
$893$	−9.62759	+	6.99485i	−0.322175	+	0.234074i
$894$	2.30198	+	4.89196i	0.0769898	+	0.163612i
$895$	−38.0387	−	14.8081i	−1.27149	−	0.494979i
$896$	−0.825626	+	0.453892i	−0.0275822	+	0.0151635i
$897$	−2.67013	−	0.337316i	−0.0891530	−	0.0112626i
$898$	2.74798	+	1.08800i	0.0917011	+	0.0363070i
$899$	1.65251	+	1.20062i	0.0551144	+	0.0400429i
$900$	2.63039	−	4.25218i	0.0876797	−	0.141739i
$901$	12.0563	−	8.75941i	0.401653	−	0.291818i
$902$	−0.0365035	+	0.00937250i	−0.00121543	+	0.000312070i
$903$	4.20483	+	3.94860i	0.139928	+	0.131401i
$904$	−0.697564	−	0.655056i	−0.0232006	−	0.0217869i
$905$	−4.41156	−	22.4246i	−0.146645	−	0.745420i
$906$	−6.23742	+	0.787969i	−0.207224	+	0.0261785i
$907$	8.87696	−	27.3205i	0.294754	−	0.907161i	−0.688549	−	0.725190i	$-0.741752\pi$
$907$	8.87696	−	27.3205i	0.294754	−	0.907161i	0.983304	−	0.181972i	$-0.0582479\pi$
$908$	6.01456	+	3.30653i	0.199600	+	0.109731i
$909$	−0.336001	−	5.34058i	−0.0111445	−	0.177136i
$910$	3.83688	−	6.12353i	0.127191	−	0.202993i
$911$	−10.0484	−	15.8338i	−0.332919	−	0.524597i	0.636092	−	0.771613i	$-0.280550\pi$
$911$	−10.0484	−	15.8338i	−0.332919	−	0.524597i	−0.969011	+	0.247016i	$0.920550\pi$
$912$	−2.58730	−	0.664305i	−0.0856740	−	0.0219973i
$913$	0.0619570	−	0.0245305i	0.00205048	−	0.000811841i
$914$	1.06920	−	0.274524i	0.0353660	−	0.00908044i
$915$	−3.35562	−	17.0572i	−0.110933	−	0.563892i
$916$	−17.5547	+	6.95038i	−0.580022	+	0.229647i
$917$	−7.33962	−	15.5975i	−0.242376	−	0.515074i
$918$	1.90619	+	5.86664i	0.0629136	+	0.193628i
$919$	−9.46948	+	49.6408i	−0.312369	+	1.63750i	0.386529	+	0.922277i	$0.373674\pi$
$919$	−9.46948	+	49.6408i	−0.312369	+	1.63750i	−0.698899	+	0.715221i	$0.746326\pi$
$920$	0.756146	+	1.58319i	0.0249294	+	0.0521962i
$921$	10.7515	−	22.8481i	0.354274	−	0.752870i
$922$	−7.42271	−	38.9112i	−0.244454	−	1.28147i
$923$	24.2788	−	29.3480i	0.799145	−	0.966001i
$924$	0.00605795	+	0.0186445i	0.000199292	+	0.000613358i
$925$	0.187667	+	0.925794i	0.00617046	+	0.0304399i
$926$	−1.00671	+	3.09833i	−0.0330825	+	0.101818i
$927$	0.926695	+	1.46024i	0.0304367	+	0.0479605i
$928$	0.749450	−	0.412014i	0.0246019	−	0.0135250i
$929$	−0.236364	−	1.23907i	−0.00775487	−	0.0406524i	0.978199	−	0.207667i	$-0.0665872\pi$
$929$	−0.236364	−	1.23907i	−0.00775487	−	0.0406524i	−0.985954	+	0.167015i	$0.946587\pi$
$930$	4.30246	−	3.16389i	0.141083	−	0.103748i
$931$	−11.9021	+	11.1768i	−0.390077	+	0.366306i
$932$	28.3774			0.929532
$933$	−11.1577	+	10.4778i	−0.365288	+	0.343028i
$934$	8.93993	−	14.0871i	0.292523	−	0.460943i
$935$	0.252293	+	0.136815i	0.00825085	+	0.00447434i
$936$	3.18920	+	1.26269i	0.104242	+	0.0412724i
$937$	2.53919	+	40.3592i	0.0829517	+	1.31848i	0.790783	+	0.612097i	$0.209674\pi$
$937$	2.53919	+	40.3592i	0.0829517	+	1.31848i	−0.707831	+	0.706382i	$0.750326\pi$
$938$	0.718775	+	11.4246i	0.0234688	+	0.373026i
$939$	−21.8636	−	8.65642i	−0.713492	−	0.282492i
$940$	−8.75700	−	4.74881i	−0.285622	−	0.154889i
$941$	23.7968	−	37.4978i	0.775755	−	1.22239i	−0.194642	−	0.980874i	$-0.562354\pi$
$941$	23.7968	−	37.4978i	0.775755	−	1.22239i	0.970396	−	0.241519i	$-0.0776456\pi$
$942$	2.27346	−	2.13492i	0.0740732	−	0.0695594i
$943$	1.42118			0.0462799
$944$	0.569774	−	0.535053i	0.0185446	−	0.0174145i
$945$	−1.69724	+	1.24810i	−0.0552113	+	0.0406006i
$946$	0.0238701	+	0.125132i	0.000776085	+	0.00406838i
$947$	−46.6310	+	25.6356i	−1.51530	+	0.833046i	−0.999717	−	0.0237910i	$-0.992426\pi$
$947$	−46.6310	+	25.6356i	−1.51530	+	0.833046i	−0.515588	+	0.856837i	$0.672426\pi$
$948$	−5.16268	−	8.13508i	−0.167676	−	0.264215i
$949$	−7.17744	+	22.0899i	−0.232989	+	0.717068i
$950$	−9.84071	−	9.03027i	−0.319275	−	0.292981i
$951$	4.53523	+	13.9580i	0.147065	+	0.452619i
$952$	3.70458	−	4.47807i	0.120066	−	0.145135i
$953$	8.50076	+	44.5625i	0.275366	+	1.44352i	0.803979	+	0.594658i	$0.202713\pi$
$953$	8.50076	+	44.5625i	0.275366	+	1.44352i	−0.528612	+	0.848864i	$0.677287\pi$
$954$	−1.02863	+	2.18594i	−0.0333030	+	0.0707724i
$955$	−2.49902	−	5.23236i	−0.0808664	−	0.169315i
$956$	−3.41844	+	17.9201i	−0.110560	+	0.579577i
$957$	−0.00549902	−	0.0169242i	−0.000177758	−	0.000547083i
$958$	−17.1549	−	36.4561i	−0.554251	−	1.17784i
$959$	5.46446	−	2.16353i	0.176457	−	0.0698642i
$960$	−0.431624	−	2.19401i	−0.0139306	−	0.0708115i
$961$	−24.5010	+	6.29079i	−0.790355	+	0.202929i
$962$	−0.602518	+	0.238554i	−0.0194260	+	0.00769129i
$963$	3.64844	+	0.936761i	0.117569	+	0.0301867i
$964$	3.42118	+	5.39092i	0.110189	+	0.173630i
$965$	29.8297	−	47.6072i	0.960252	−	1.53253i
$966$	−0.0464182	−	0.737796i	−0.00149348	−	0.0237382i
$967$	1.37299	+	0.754806i	0.0441523	+	0.0242729i	0.503677	−	0.863892i	$-0.331980\pi$
$967$	1.37299	+	0.754806i	0.0441523	+	0.0242729i	−0.459525	+	0.888165i	$0.651980\pi$
$968$	3.39905	−	10.4612i	0.109250	−	0.336236i
$969$	16.3476	−	2.06519i	0.525162	−	0.0663433i
$970$	−1.70364	−	8.65988i	−0.0547006	−	0.278052i
$971$	43.4527	+	40.8048i	1.39446	+	1.30949i	0.897019	+	0.441993i	$0.145728\pi$
$971$	43.4527	+	40.8048i	1.39446	+	1.30949i	0.497445	+	0.867496i	$0.334272\pi$
$972$	−0.728969	−	0.684547i	−0.0233817	−	0.0219569i
$973$	−12.0554	+	3.09530i	−0.386478	+	0.0992306i
$974$	−27.1322	+	19.7127i	−0.869373	+	0.631637i
$975$	11.0833	+	13.0879i	0.354951	+	0.419150i
$976$	−6.28963	−	4.56968i	−0.201326	−	0.146272i
$977$	−31.3429	−	12.4095i	−1.00275	−	0.397017i	−0.191358	−	0.981520i	$-0.561289\pi$
$977$	−31.3429	−	12.4095i	−1.00275	−	0.397017i	−0.811391	+	0.584504i	$0.801289\pi$
$978$	0.352384	+	0.0445164i	0.0112680	+	0.00142348i
$979$	−0.00656546	+	0.00360939i	−0.000209833	+	0.000115357i
$980$	−12.7365	−	4.95819i	−0.406853	−	0.158384i
$981$	−5.47473	−	11.6344i	−0.174795	−	0.371457i
$982$	−9.16234	+	6.65683i	−0.292382	+	0.212428i
$983$	42.5481	−	5.37507i	1.35707	−	0.171438i	0.587100	−	0.809514i	$-0.300269\pi$
$983$	42.5481	−	5.37507i	1.35707	−	0.171438i	0.769973	+	0.638076i	$0.220269\pi$
$984$	−1.75436	−	0.450442i	−0.0559268	−	0.0143596i
$985$	−0.648027	+	11.3407i	−0.0206479	+	0.361343i
$986$	−3.36278	+	4.06490i	−0.107093	+	0.129453i
$987$	2.67551	+	3.23413i	0.0851623	+	0.102944i
$988$	4.90950	−	7.73613i	0.156192	−	0.246119i
$989$	0.301629	−	4.79426i	0.00959125	−	0.152449i
$990$	−0.0465258		0.000267620i	−0.00147869		8.50553e-6i
$991$	7.42377	+	8.97380i	0.235824	+	0.285062i	0.875128	−	0.483892i	$-0.160777\pi$
$991$	7.42377	+	8.97380i	0.235824	+	0.285062i	−0.639304	+	0.768954i	$0.720777\pi$
$992$	0.447535	−	2.34606i	0.0142092	−	0.0744874i
$993$	−14.1401	−	10.2734i	−0.448721	−	0.326015i
$994$	9.16808	+	5.04020i	0.290794	+	0.159865i
$995$	−9.78335	−	11.6885i	−0.310153	−	0.370550i
$996$	3.17729	+	0.401386i	0.100676	+	0.0127184i
$997$	−15.2411	+	32.3890i	−0.482691	+	1.02577i	0.504081	+	0.863656i	$0.331831\pi$
$997$	−15.2411	+	32.3890i	−0.482691	+	1.02577i	−0.986772	+	0.162114i	$0.948169\pi$
$998$	0.279082	−	4.43589i	0.00883420	−	0.140416i
$999$	0.188925			0.00597731

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.m.c.121.2	yes	120
125.31	even	25	inner	750.2.m.c.31.2	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.m.c.31.2	✓	120	125.31	even	25	inner
750.2.m.c.121.2	yes	120	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.m (of order \(25\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0627905 + 0.998027i) q^{2} +(0.425779 - 0.904827i) q^{3} +(-0.992115 - 0.125333i) q^{4} +(-1.18727 + 1.89484i) q^{5} +(0.876307 + 0.481754i) q^{6} +(-0.762228 - 0.553791i) q^{7} +(0.187381 - 0.982287i) q^{8} +(-0.637424 - 0.770513i) q^{9} +O(q^{10})\)	\(q+(-0.0627905 + 0.998027i) q^{2} +(0.425779 - 0.904827i) q^{3} +(-0.992115 - 0.125333i) q^{4} +(-1.18727 + 1.89484i) q^{5} +(0.876307 + 0.481754i) q^{6} +(-0.762228 - 0.553791i) q^{7} +(0.187381 - 0.982287i) q^{8} +(-0.637424 - 0.770513i) q^{9} +(-1.81655 - 1.30390i) q^{10} +(-0.00130650 + 0.0207663i) q^{11} +(-0.535827 + 0.844328i) q^{12} +(-2.18641 - 2.64292i) q^{13} +(0.600559 - 0.725951i) q^{14} +(1.20898 + 1.88105i) q^{15} +(0.968583 + 0.248690i) q^{16} +(-6.11991 + 0.773125i) q^{17} +(0.809017 - 0.587785i) q^{18} +(-1.13735 - 2.41699i) q^{19} +(1.41539 - 1.73109i) q^{20} +(-0.825626 + 0.453892i) q^{21} +(-0.0206432 - 0.00260785i) q^{22} +(0.729534 + 0.288843i) q^{23} +(-0.809017 - 0.587785i) q^{24} +(-2.18080 - 4.49935i) q^{25} +(2.77499 - 2.01615i) q^{26} +(-0.968583 + 0.248690i) q^{27} +(0.686810 + 0.644957i) q^{28} +(-0.623441 - 0.585450i) q^{29} +(-1.95325 + 1.08849i) q^{30} +(-2.36953 + 0.299341i) q^{31} +(-0.309017 + 0.951057i) q^{32} +(0.0182336 + 0.0100240i) q^{33} +(-0.387327 - 6.15638i) q^{34} +(1.95431 - 0.786800i) q^{35} +(0.535827 + 0.844328i) q^{36} +(-0.182989 - 0.0469836i) q^{37} +(2.48364 - 0.983341i) q^{38} +(-3.32231 + 0.853024i) q^{39} +(1.63880 + 1.52129i) q^{40} +(1.68407 - 0.666770i) q^{41} +(-0.401155 - 0.852497i) q^{42} +(-1.89189 - 5.82263i) q^{43} +(0.00389890 - 0.0204388i) q^{44} +(2.21679 - 0.293009i) q^{45} +(-0.334081 + 0.709958i) q^{46} +(-0.834789 - 4.37612i) q^{47} +(0.637424 - 0.770513i) q^{48} +(-1.88881 - 5.81316i) q^{49} +(4.62740 - 1.89398i) q^{50} +(-1.90619 + 5.86664i) q^{51} +(1.83792 + 2.89611i) q^{52} +(-2.11704 + 1.16385i) q^{53} +(-0.187381 - 0.982287i) q^{54} +(-0.0377975 - 0.0271307i) q^{55} +(-0.686810 + 0.644957i) q^{56} -2.67122 q^{57} +(0.623441 - 0.585450i) q^{58} +(0.418811 - 0.659941i) q^{59} +(-0.963693 - 2.01775i) q^{60} +(-7.22846 - 2.86195i) q^{61} +(-0.149967 - 2.38365i) q^{62} +(0.0591591 + 0.940307i) q^{63} +(-0.929776 - 0.368125i) q^{64} +(7.60374 - 1.00504i) q^{65} +(-0.0111491 + 0.0175682i) q^{66} +(-8.85687 + 8.31715i) q^{67} +6.16855 q^{68} +(0.571973 - 0.537119i) q^{69} +(0.662535 + 1.99986i) q^{70} +(2.08076 + 10.9077i) q^{71} +(-0.876307 + 0.481754i) q^{72} +(-3.62834 - 5.71735i) q^{73} +(0.0583809 - 0.179678i) q^{74} +(-4.99967 + 0.0575189i) q^{75} +(0.825452 + 2.54048i) q^{76} +(0.0124960 - 0.0151051i) q^{77} +(-0.642731 - 3.36932i) q^{78} +(-4.10237 + 8.71799i) q^{79} +(-1.62119 + 1.54004i) q^{80} +(-0.187381 + 0.982287i) q^{81} +(0.559710 + 1.72261i) q^{82} +(-1.36358 - 2.89775i) q^{83} +(0.876004 - 0.346834i) q^{84} +(5.80102 - 12.5141i) q^{85} +(5.92993 - 1.52255i) q^{86} +(-0.795179 + 0.314834i) q^{87} +(0.0201536 + 0.00517457i) q^{88} +(0.192938 + 0.304021i) q^{89} +(0.153238 + 2.23081i) q^{90} +(0.202920 + 3.22532i) q^{91} +(-0.687580 - 0.378000i) q^{92} +(-0.738045 + 2.27147i) q^{93} +(4.41990 - 0.558363i) q^{94} +(5.93014 + 0.714521i) q^{95} +(0.728969 + 0.684547i) q^{96} +(2.87727 + 2.70194i) q^{97} +(5.92029 - 1.52007i) q^{98} +(0.0168335 - 0.0122302i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 20 q^{5} - 5 q^{7}+O(q^{10}) \) 120 * q + 20 * q^5 - 5 * q^7	\( 120 q + 20 q^{5} - 5 q^{7} + 20 q^{10} + 10 q^{13} + 20 q^{14} + 15 q^{17} + 30 q^{18} - 5 q^{19} - 5 q^{21} + 10 q^{22} - 15 q^{23} - 30 q^{24} - 20 q^{25} - 10 q^{26} + 5 q^{28} - 5 q^{29} + 5 q^{30} + 55 q^{31} + 30 q^{32} + 10 q^{33} + 25 q^{34} - 10 q^{35} - 5 q^{37} - 35 q^{38} - 10 q^{39} - 5 q^{40} + 55 q^{41} + 5 q^{42} + 5 q^{43} + 15 q^{44} - 5 q^{45} - 10 q^{46} + 10 q^{47} - 25 q^{49} + 20 q^{50} + 15 q^{51} - 40 q^{52} + 30 q^{53} - 10 q^{55} - 5 q^{56} + 60 q^{57} + 5 q^{58} + 20 q^{59} - 20 q^{60} - 60 q^{61} + 25 q^{62} + 5 q^{63} + 15 q^{65} - 25 q^{66} + 95 q^{67} + 60 q^{68} - 10 q^{69} + 40 q^{70} - 90 q^{71} - 30 q^{74} - 55 q^{75} + 15 q^{76} + 95 q^{77} - 5 q^{78} - 90 q^{79} - 5 q^{80} - 45 q^{82} + 95 q^{83} - 5 q^{84} + 115 q^{85} - 15 q^{86} + 10 q^{87} + 65 q^{89} + 5 q^{90} - 85 q^{91} - 65 q^{92} - 30 q^{93} - 10 q^{94} - 55 q^{95} - 35 q^{98} + 10 q^{99}+O(q^{100}) \) 120 * q + 20 * q^5 - 5 * q^7 + 20 * q^10 + 10 * q^13 + 20 * q^14 + 15 * q^17 + 30 * q^18 - 5 * q^19 - 5 * q^21 + 10 * q^22 - 15 * q^23 - 30 * q^24 - 20 * q^25 - 10 * q^26 + 5 * q^28 - 5 * q^29 + 5 * q^30 + 55 * q^31 + 30 * q^32 + 10 * q^33 + 25 * q^34 - 10 * q^35 - 5 * q^37 - 35 * q^38 - 10 * q^39 - 5 * q^40 + 55 * q^41 + 5 * q^42 + 5 * q^43 + 15 * q^44 - 5 * q^45 - 10 * q^46 + 10 * q^47 - 25 * q^49 + 20 * q^50 + 15 * q^51 - 40 * q^52 + 30 * q^53 - 10 * q^55 - 5 * q^56 + 60 * q^57 + 5 * q^58 + 20 * q^59 - 20 * q^60 - 60 * q^61 + 25 * q^62 + 5 * q^63 + 15 * q^65 - 25 * q^66 + 95 * q^67 + 60 * q^68 - 10 * q^69 + 40 * q^70 - 90 * q^71 - 30 * q^74 - 55 * q^75 + 15 * q^76 + 95 * q^77 - 5 * q^78 - 90 * q^79 - 5 * q^80 - 45 * q^82 + 95 * q^83 - 5 * q^84 + 115 * q^85 - 15 * q^86 + 10 * q^87 + 65 * q^89 + 5 * q^90 - 85 * q^91 - 65 * q^92 - 30 * q^93 - 10 * q^94 - 55 * q^95 - 35 * q^98 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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