LMFDB - Embedded newform 525.2.n.c.211.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(106,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("525.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.n (of order $5$, degree $4$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			211.3
Character	$\chi$	$=$	525.211
Dual form			525.2.n.c.316.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0144696 + 0.0105128i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.617935 + 1.90181i) q^{4} +(-1.54334 - 1.61805i) q^{5} +(0.00552688 + 0.0170100i) q^{6} +1.00000 q^{7} +(-0.0221058 - 0.0680345i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.0144696 + 0.0105128i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.617935 + 1.90181i) q^{4} +(-1.54334 - 1.61805i) q^{5} +(0.00552688 + 0.0170100i) q^{6} +1.00000 q^{7} +(-0.0221058 - 0.0680345i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(0.0393417 + 0.00718776i) q^{10} +(3.99329 - 2.90130i) q^{11} +(1.61778 + 1.17538i) q^{12} +(-3.82422 - 2.77846i) q^{13} +(-0.0144696 + 0.0105128i) q^{14} +(-2.01578 + 0.967799i) q^{15} +(-3.23452 - 2.35001i) q^{16} +(0.930775 + 2.86463i) q^{17} +0.0178854 q^{18} +(-0.982720 - 3.02450i) q^{19} +(4.03091 - 1.93529i) q^{20} +(0.309017 - 0.951057i) q^{21} +(-0.0272806 + 0.0839610i) q^{22} +(5.67594 - 4.12381i) q^{23} -0.0715357 q^{24} +(-0.236196 + 4.99442i) q^{25} +0.0845440 q^{26} +(-0.809017 + 0.587785i) q^{27} +(-0.617935 + 1.90181i) q^{28} +(2.44073 - 7.51180i) q^{29} +(0.0189932 - 0.0351950i) q^{30} +(-2.99044 - 9.20362i) q^{31} +0.214579 q^{32} +(-1.52530 - 4.69440i) q^{33} +(-0.0435831 - 0.0316649i) q^{34} +(-1.54334 - 1.61805i) q^{35} +(1.61778 - 1.17538i) q^{36} +(0.116437 + 0.0845967i) q^{37} +(0.0460154 + 0.0334321i) q^{38} +(-3.82422 + 2.77846i) q^{39} +(-0.0759668 + 0.140769i) q^{40} +(-4.23948 - 3.08016i) q^{41} +(0.00552688 + 0.0170100i) q^{42} +7.50453 q^{43} +(3.05012 + 9.38729i) q^{44} +(0.297521 + 2.21619i) q^{45} +(-0.0387758 + 0.119340i) q^{46} +(-1.95797 + 6.02600i) q^{47} +(-3.23452 + 2.35001i) q^{48} +1.00000 q^{49} +(-0.0490874 - 0.0747501i) q^{50} +3.01205 q^{51} +(7.64722 - 5.55603i) q^{52} +(-3.42236 + 10.5329i) q^{53} +(0.00552688 - 0.0170100i) q^{54} +(-10.8575 - 1.98367i) q^{55} +(-0.0221058 - 0.0680345i) q^{56} -3.18015 q^{57} +(0.0436534 + 0.134351i) q^{58} +(3.03363 + 2.20406i) q^{59} +(-0.594947 - 4.43166i) q^{60} +(-8.93142 + 6.48905i) q^{61} +(0.140026 + 0.101735i) q^{62} +(-0.809017 - 0.587785i) q^{63} +(6.46593 - 4.69777i) q^{64} +(1.40638 + 10.4759i) q^{65} +(0.0714215 + 0.0518907i) q^{66} +(0.695086 + 2.13926i) q^{67} -6.02314 q^{68} +(-2.16802 - 6.67247i) q^{69} +(0.0393417 + 0.00718776i) q^{70} +(3.63058 - 11.1738i) q^{71} +(-0.0221058 + 0.0680345i) q^{72} +(3.10637 - 2.25691i) q^{73} -0.00257414 q^{74} +(4.67699 + 1.76800i) q^{75} +6.35928 q^{76} +(3.99329 - 2.90130i) q^{77} +(0.0261255 - 0.0804062i) q^{78} +(-3.10523 + 9.55693i) q^{79} +(1.18951 + 8.86049i) q^{80} +(0.309017 + 0.951057i) q^{81} +0.0937243 q^{82} +(-1.37795 - 4.24088i) q^{83} +(1.61778 + 1.17538i) q^{84} +(3.19862 - 5.92715i) q^{85} +(-0.108587 + 0.0788933i) q^{86} +(-6.38992 - 4.64255i) q^{87} +(-0.285663 - 0.207546i) q^{88} +(1.70738 - 1.24049i) q^{89} +(-0.0276032 - 0.0289395i) q^{90} +(-3.82422 - 2.77846i) q^{91} +(4.33534 + 13.3428i) q^{92} -9.67726 q^{93} +(-0.0350190 - 0.107777i) q^{94} +(-3.37713 + 6.25793i) q^{95} +(0.0663084 - 0.204076i) q^{96} +(-5.87431 + 18.0793i) q^{97} +(-0.0144696 + 0.0105128i) q^{98} -4.93598 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} - 6 q^{3} - 9 q^{4} - q^{5} + q^{6} + 24 q^{7} + 9 q^{8} - 6 q^{9}+O(q^{10}) $ 24 * q + q^2 - 6 * q^3 - 9 * q^4 - q^5 + q^6 + 24 * q^7 + 9 * q^8 - 6 * q^9	\( 24 q + q^{2} - 6 q^{3} - 9 q^{4} - q^{5} + q^{6} + 24 q^{7} + 9 q^{8} - 6 q^{9} - 16 q^{10} + 2 q^{11} + q^{12} + 8 q^{13} + q^{14} - 6 q^{15} + 13 q^{16} + 12 q^{17} - 4 q^{18} + 19 q^{19} + 11 q^{20} - 6 q^{21} - 19 q^{22} - 6 q^{24} + 9 q^{25} - 14 q^{26} - 6 q^{27} - 9 q^{28} + 5 q^{29} - 6 q^{30} + 17 q^{31} - 26 q^{32} + 7 q^{33} - 7 q^{34} - q^{35} + q^{36} + 22 q^{37} - 16 q^{38} + 8 q^{39} + 3 q^{40} + 37 q^{41} + q^{42} + 8 q^{43} + 13 q^{44} + 4 q^{45} + 24 q^{46} - 24 q^{47} + 13 q^{48} + 24 q^{49} - 21 q^{50} - 8 q^{51} + 23 q^{52} - 24 q^{53} + q^{54} - 55 q^{55} + 9 q^{56} - 26 q^{57} + 8 q^{58} - 39 q^{60} + 24 q^{62} - 6 q^{63} - q^{64} - 34 q^{65} + 16 q^{66} + 34 q^{67} + 22 q^{68} + 10 q^{69} - 16 q^{70} - 24 q^{71} + 9 q^{72} + 46 q^{73} + 10 q^{74} + 24 q^{75} - 20 q^{76} + 2 q^{77} - 14 q^{78} + 10 q^{79} + 6 q^{80} - 6 q^{81} - 78 q^{82} + 42 q^{83} + q^{84} - 22 q^{85} - 96 q^{86} - 10 q^{87} - 39 q^{88} + 29 q^{89} + 14 q^{90} + 8 q^{91} + 42 q^{92} - 58 q^{93} + 54 q^{94} - 42 q^{95} + 9 q^{96} - 32 q^{97} + q^{98} - 18 q^{99}+O(q^{100}) \) 24 * q + q^2 - 6 * q^3 - 9 * q^4 - q^5 + q^6 + 24 * q^7 + 9 * q^8 - 6 * q^9 - 16 * q^10 + 2 * q^11 + q^12 + 8 * q^13 + q^14 - 6 * q^15 + 13 * q^16 + 12 * q^17 - 4 * q^18 + 19 * q^19 + 11 * q^20 - 6 * q^21 - 19 * q^22 - 6 * q^24 + 9 * q^25 - 14 * q^26 - 6 * q^27 - 9 * q^28 + 5 * q^29 - 6 * q^30 + 17 * q^31 - 26 * q^32 + 7 * q^33 - 7 * q^34 - q^35 + q^36 + 22 * q^37 - 16 * q^38 + 8 * q^39 + 3 * q^40 + 37 * q^41 + q^42 + 8 * q^43 + 13 * q^44 + 4 * q^45 + 24 * q^46 - 24 * q^47 + 13 * q^48 + 24 * q^49 - 21 * q^50 - 8 * q^51 + 23 * q^52 - 24 * q^53 + q^54 - 55 * q^55 + 9 * q^56 - 26 * q^57 + 8 * q^58 - 39 * q^60 + 24 * q^62 - 6 * q^63 - q^64 - 34 * q^65 + 16 * q^66 + 34 * q^67 + 22 * q^68 + 10 * q^69 - 16 * q^70 - 24 * q^71 + 9 * q^72 + 46 * q^73 + 10 * q^74 + 24 * q^75 - 20 * q^76 + 2 * q^77 - 14 * q^78 + 10 * q^79 + 6 * q^80 - 6 * q^81 - 78 * q^82 + 42 * q^83 + q^84 - 22 * q^85 - 96 * q^86 - 10 * q^87 - 39 * q^88 + 29 * q^89 + 14 * q^90 + 8 * q^91 + 42 * q^92 - 58 * q^93 + 54 * q^94 - 42 * q^95 + 9 * q^96 - 32 * q^97 + q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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 $

$2$	−0.0144696	+	0.0105128i	−0.0102315	+	0.00743364i	−0.592889	−	0.805284i	$-0.702013\pi$
$2$	−0.0144696	+	0.0105128i	−0.0102315	+	0.00743364i	0.582658	+	0.812718i	$0.302013\pi$
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$	−0.617935	+	1.90181i	−0.308968	+	0.950904i
$5$	−1.54334	−	1.61805i	−0.690203	−	0.723616i
$5$	−1.54334	−	1.61805i	−0.690203	−	0.723616i
$6$	0.00552688	+	0.0170100i	0.00225634	+	0.00694430i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−0.0221058	−	0.0680345i	−0.00781556	−	0.0240538i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	0.0393417	+	0.00718776i	0.0124409	+	0.00227297i
$11$	3.99329	−	2.90130i	1.20402	−	0.874774i	0.209348	−	0.977841i	$-0.432866\pi$
$11$	3.99329	−	2.90130i	1.20402	−	0.874774i	0.994674	+	0.103067i	$0.0328658\pi$
$12$	1.61778	+	1.17538i	0.467011	+	0.339304i
$13$	−3.82422	−	2.77846i	−1.06065	−	0.770606i	−0.0864397	−	0.996257i	$-0.527549\pi$
$13$	−3.82422	−	2.77846i	−1.06065	−	0.770606i	−0.974208	+	0.225651i	$0.927549\pi$
$14$	−0.0144696	+	0.0105128i	−0.00386715	+	0.00280965i
$15$	−2.01578	+	0.967799i	−0.520472	+	0.249885i
$16$	−3.23452	−	2.35001i	−0.808629	−	0.587503i
$17$	0.930775	+	2.86463i	0.225746	+	0.694775i	0.998215	+	0.0597224i	$0.0190216\pi$
$17$	0.930775	+	2.86463i	0.225746	+	0.694775i	−0.772469	+	0.635053i	$0.780978\pi$
$18$	0.0178854			0.00421562
$19$	−0.982720	−	3.02450i	−0.225452	−	0.693868i	−0.998245	−	0.0592114i	$-0.981141\pi$
$19$	−0.982720	−	3.02450i	−0.225452	−	0.693868i	0.772794	−	0.634657i	$-0.218859\pi$
$20$	4.03091	−	1.93529i	0.901340	−	0.432743i
$21$	0.309017	−	0.951057i	0.0674330	−	0.207538i
$22$	−0.0272806	+	0.0839610i	−0.00581624	+	0.0179005i
$23$	5.67594	−	4.12381i	1.18352	−	0.859874i	0.190952	−	0.981599i	$-0.438843\pi$
$23$	5.67594	−	4.12381i	1.18352	−	0.859874i	0.992564	+	0.121725i	$0.0388426\pi$
$24$	−0.0715357			−0.0146022
$25$	−0.236196	+	4.99442i	−0.0472391	+	0.998884i
$26$	0.0845440			0.0165804
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	−0.617935	+	1.90181i	−0.116779	+	0.359408i
$29$	2.44073	−	7.51180i	0.453233	−	1.39491i	−0.419965	−	0.907540i	$-0.637958\pi$
$29$	2.44073	−	7.51180i	0.453233	−	1.39491i	0.873198	−	0.487366i	$-0.162042\pi$
$30$	0.0189932	−	0.0351950i	0.00346767	−	0.00642570i
$31$	−2.99044	−	9.20362i	−0.537099	−	1.65302i	−0.739070	−	0.673628i	$-0.764735\pi$
$31$	−2.99044	−	9.20362i	−0.537099	−	1.65302i	0.201971	−	0.979391i	$-0.435265\pi$
$32$	0.214579			0.0379325
$33$	−1.52530	−	4.69440i	−0.265521	−	0.817189i
$34$	−0.0435831	−	0.0316649i	−0.00747443	−	0.00543049i
$35$	−1.54334	−	1.61805i	−0.260872	−	0.273501i
$36$	1.61778	−	1.17538i	0.269629	−	0.195897i
$37$	0.116437	+	0.0845967i	0.0191422	+	0.0139076i	0.597315	−	0.802007i	$-0.296234\pi$
$37$	0.116437	+	0.0845967i	0.0191422	+	0.0139076i	−0.578173	+	0.815914i	$0.696234\pi$
$38$	0.0460154	+	0.0334321i	0.00746468	+	0.00542341i
$39$	−3.82422	+	2.77846i	−0.612365	+	0.444909i
$40$	−0.0759668	+	0.140769i	−0.0120114	+	0.0222575i
$41$	−4.23948	−	3.08016i	−0.662095	−	0.481040i	0.205275	−	0.978704i	$-0.434191\pi$
$41$	−4.23948	−	3.08016i	−0.662095	−	0.481040i	−0.867370	+	0.497664i	$0.834191\pi$
$42$	0.00552688	+	0.0170100i	0.000852816	+	0.00262470i
$43$	7.50453			1.14443			0.572215	−	0.820104i	$-0.306084\pi$
$43$	7.50453			1.14443			0.572215	+	0.820104i	$0.306084\pi$
$44$	3.05012	+	9.38729i	0.459822	+	1.41519i
$45$	0.297521	+	2.21619i	0.0443518	+	0.330370i
$46$	−0.0387758	+	0.119340i	−0.00571717	+	0.0175957i
$47$	−1.95797	+	6.02600i	−0.285599	+	0.878983i	0.700620	+	0.713535i	$0.252907\pi$
$47$	−1.95797	+	6.02600i	−0.285599	+	0.878983i	−0.986219	+	0.165448i	$0.947093\pi$
$48$	−3.23452	+	2.35001i	−0.466862	+	0.339195i
$49$	1.00000			0.142857
$50$	−0.0490874	−	0.0747501i	−0.00694201	−	0.0105713i
$51$	3.01205			0.421771
$52$	7.64722	−	5.55603i	1.06048	−	0.770483i
$53$	−3.42236	+	10.5329i	−0.470097	+	1.44681i	0.382361	+	0.924013i	$0.375111\pi$
$53$	−3.42236	+	10.5329i	−0.470097	+	1.44681i	−0.852458	+	0.522796i	$0.824889\pi$
$54$	0.00552688	−	0.0170100i	0.000752113	−	0.00231477i
$55$	−10.8575	−	1.98367i	−1.46402	−	0.267478i
$56$	−0.0221058	−	0.0680345i	−0.00295401	−	0.00909149i
$57$	−3.18015			−0.421221
$58$	0.0436534	+	0.134351i	0.00573197	+	0.0176412i
$59$	3.03363	+	2.20406i	0.394944	+	0.286944i	0.767479	−	0.641075i	$-0.221511\pi$
$59$	3.03363	+	2.20406i	0.394944	+	0.286944i	−0.372534	+	0.928018i	$0.621511\pi$
$60$	−0.594947	−	4.43166i	−0.0768073	−	0.572125i
$61$	−8.93142	+	6.48905i	−1.14355	+	0.830838i	−0.987610	−	0.156928i	$-0.949841\pi$
$61$	−8.93142	+	6.48905i	−1.14355	+	0.830838i	−0.155941	+	0.987766i	$0.549841\pi$
$62$	0.140026	+	0.101735i	0.0177833	+	0.0129203i
$63$	−0.809017	−	0.587785i	−0.101927	−	0.0740540i
$64$	6.46593	−	4.69777i	0.808241	−	0.587221i
$65$	1.40638	+	10.4759i	0.174440	+	1.29938i
$66$	0.0714215	+	0.0518907i	0.00879137	+	0.00638731i
$67$	0.695086	+	2.13926i	0.0849183	+	0.261352i	0.984495	−	0.175410i	$-0.0561252\pi$
$67$	0.695086	+	2.13926i	0.0849183	+	0.261352i	−0.899577	+	0.436762i	$0.856125\pi$
$68$	−6.02314			−0.730413
$69$	−2.16802	−	6.67247i	−0.260999	−	0.803271i
$70$	0.0393417	+	0.00718776i	0.00470223	+	0.000859102i
$71$	3.63058	−	11.1738i	0.430870	−	1.32608i	−0.466390	−	0.884579i	$-0.654446\pi$
$71$	3.63058	−	11.1738i	0.430870	−	1.32608i	0.897260	−	0.441503i	$-0.145554\pi$
$72$	−0.0221058	+	0.0680345i	−0.00260519	+	0.00801794i
$73$	3.10637	−	2.25691i	0.363573	−	0.264151i	−0.390968	−	0.920404i	$-0.627860\pi$
$73$	3.10637	−	2.25691i	0.363573	−	0.264151i	0.754541	+	0.656253i	$0.227860\pi$
$74$	−0.00257414			−0.000299238
$75$	4.67699	+	1.76800i	0.540052	+	0.204151i
$76$	6.35928			0.729460
$77$	3.99329	−	2.90130i	0.455078	−	0.330633i
$78$	0.0261255	−	0.0804062i	0.00295814	−	0.00910420i
$79$	−3.10523	+	9.55693i	−0.349366	+	1.07524i	0.609838	+	0.792526i	$0.291234\pi$
$79$	−3.10523	+	9.55693i	−0.349366	+	1.07524i	−0.959205	+	0.282713i	$0.908766\pi$
$80$	1.18951	+	8.86049i	0.132992	+	0.990633i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	0.0937243			0.0103501
$83$	−1.37795	−	4.24088i	−0.151249	−	0.465497i	0.846512	−	0.532369i	$-0.178698\pi$
$83$	−1.37795	−	4.24088i	−0.151249	−	0.465497i	−0.997762	+	0.0668719i	$0.978698\pi$
$84$	1.61778	+	1.17538i	0.176514	+	0.128245i
$85$	3.19862	−	5.92715i	0.346939	−	0.642889i
$86$	−0.108587	+	0.0788933i	−0.0117093	+	0.00850728i
$87$	−6.38992	−	4.64255i	−0.685071	−	0.497734i
$88$	−0.285663	−	0.207546i	−0.0304518	−	0.0221245i
$89$	1.70738	−	1.24049i	0.180982	−	0.131491i	−0.493606	−	0.869686i	$-0.664321\pi$
$89$	1.70738	−	1.24049i	0.180982	−	0.131491i	0.674588	+	0.738195i	$0.264321\pi$
$90$	−0.0276032	−	0.0289395i	−0.00290963	−	0.00305049i
$91$	−3.82422	−	2.77846i	−0.400887	−	0.291262i
$92$	4.33534	+	13.3428i	0.451990	+	1.39108i
$93$	−9.67726			−1.00349
$94$	−0.0350190	−	0.107777i	−0.00361193	−	0.0111164i
$95$	−3.37713	+	6.25793i	−0.346487	+	0.642050i
$96$	0.0663084	−	0.204076i	0.00676757	−	0.0208285i
$97$	−5.87431	+	18.0793i	−0.596446	+	1.83567i	−0.0490515	+	0.998796i	$0.515620\pi$
$97$	−5.87431	+	18.0793i	−0.596446	+	1.83567i	−0.547394	+	0.836875i	$0.684380\pi$
$98$	−0.0144696	+	0.0105128i	−0.00146165	+	0.00106195i
$99$	−4.93598			−0.496085
$100$	−9.35247	−	3.53543i	−0.935247	−	0.353543i
$101$	11.8789			1.18199			0.590995	−	0.806675i	$-0.298735\pi$
$101$	11.8789			1.18199			0.590995	+	0.806675i	$0.298735\pi$
$102$	−0.0435831	+	0.0316649i	−0.00431537	+	0.00313530i
$103$	−1.29250	+	3.97791i	−0.127354	+	0.391955i	−0.994323	−	0.106407i	$-0.966065\pi$
$103$	−1.29250	+	3.97791i	−0.127354	+	0.391955i	0.866969	+	0.498363i	$0.166065\pi$
$104$	−0.104494	+	0.321599i	−0.0102465	+	0.0315354i
$105$	−2.01578	+	0.967799i	−0.196720	+	0.0944475i
$106$	−0.0612101	−	0.188385i	−0.00594525	−	0.0182976i
$107$	9.80164			0.947560			0.473780	−	0.880643i	$-0.342889\pi$
$107$	9.80164			0.947560			0.473780	+	0.880643i	$0.342889\pi$
$108$	−0.617935	−	1.90181i	−0.0594608	−	0.183002i
$109$	9.26899	+	6.73432i	0.887808	+	0.645031i	0.935306	−	0.353841i	$-0.115125\pi$
$109$	9.26899	+	6.73432i	0.887808	+	0.645031i	−0.0474972	+	0.998871i	$0.515125\pi$
$110$	0.177957	−	0.0854390i	0.0169675	−	0.00814629i
$111$	0.116437	−	0.0845967i	0.0110517	−	0.00802956i
$112$	−3.23452	−	2.35001i	−0.305633	−	0.222055i
$113$	−8.15283	−	5.92338i	−0.766954	−	0.557225i	0.134081	−	0.990970i	$-0.457192\pi$
$113$	−8.15283	−	5.92338i	−0.766954	−	0.557225i	−0.901035	+	0.433746i	$0.857192\pi$
$114$	0.0460154	−	0.0334321i	0.00430973	−	0.00313121i
$115$	−15.4325	−	2.81953i	−1.43908	−	0.262922i
$116$	12.7778	+	9.28361i	1.18639	+	0.861962i
$117$	1.46072	+	4.49564i	0.135044	+	0.415622i
$118$	−0.0670659			−0.00617392
$119$	0.930775	+	2.86463i	0.0853240	+	0.262600i
$120$	0.110404	+	0.115749i	0.0100785	+	0.0105664i
$121$	4.12967	−	12.7098i	0.375425	−	1.15544i
$122$	0.0610159	−	0.187787i	0.00552412	−	0.0170015i
$123$	−4.23948	+	3.08016i	−0.382261	+	0.277729i
$124$	19.3514			1.73781
$125$	8.44577	−	7.32591i	0.755412	−	0.655250i
$126$	0.0178854			0.00159335
$127$	−5.22829	+	3.79857i	−0.463935	+	0.337069i	−0.795073	−	0.606514i	$-0.792568\pi$
$127$	−5.22829	+	3.79857i	−0.463935	+	0.337069i	0.331138	+	0.943582i	$0.392568\pi$
$128$	−0.176789	+	0.544102i	−0.0156261	+	0.0480923i
$129$	2.31903	−	7.13723i	0.204179	−	0.628398i
$130$	−0.130480	−	0.136797i	−0.0114439	−	0.0119979i
$131$	5.99952	+	18.4646i	0.524180	+	1.61326i	0.765931	+	0.642923i	$0.222278\pi$
$131$	5.99952	+	18.4646i	0.524180	+	1.61326i	−0.241751	+	0.970338i	$0.577722\pi$
$132$	9.87038			0.859106
$133$	−0.982720	−	3.02450i	−0.0852127	−	0.262258i
$134$	−0.0325470	−	0.0236468i	−0.00281164	−	0.00204277i
$135$	2.19966	+	0.401880i	0.189316	+	0.0345883i
$136$	0.174318	−	0.126650i	0.0149477	−	0.0108601i
$137$	0.839054	+	0.609609i	0.0716852	+	0.0520824i	0.623051	−	0.782181i	$-0.285893\pi$
$137$	0.839054	+	0.609609i	0.0716852	+	0.0520824i	−0.551365	+	0.834264i	$0.685893\pi$
$138$	0.101516	+	0.0737559i	0.00864164	+	0.00627852i
$139$	15.6491	−	11.3698i	1.32734	−	0.964371i	0.327533	−	0.944840i	$-0.393783\pi$
$139$	15.6491	−	11.3698i	1.32734	−	0.964371i	0.999809	−	0.0195310i	$-0.00621731\pi$
$140$	4.03091	−	1.93529i	0.340674	−	0.163562i
$141$	5.12603	+	3.72428i	0.431689	+	0.313641i
$142$	0.0649342	+	0.199847i	0.00544915	+	0.0167708i
$143$	−23.3324			−1.95115
$144$	1.23547	+	3.80240i	0.102956	+	0.316867i
$145$	−15.9214	+	7.64404i	−1.32220	+	0.634803i
$146$	−0.0212214	+	0.0653129i	−0.00175630	+	0.00540533i
$147$	0.309017	−	0.951057i	0.0254873	−	0.0784418i
$148$	−0.232837	+	0.169166i	−0.0191391	+	0.0139054i
$149$	−2.80943			−0.230158			−0.115079	−	0.993356i	$-0.536712\pi$
$149$	−2.80943			−0.230158			−0.115079	+	0.993356i	$0.536712\pi$
$150$	−0.0862604	+	0.0235859i	−0.00704313	+	0.00192578i
$151$	−20.0577			−1.63227			−0.816135	−	0.577862i	$-0.803887\pi$
$151$	−20.0577			−1.63227			−0.816135	+	0.577862i	$0.803887\pi$
$152$	−0.184047	+	0.133718i	−0.0149282	+	0.0108459i
$153$	0.930775	−	2.86463i	0.0752487	−	0.231592i
$154$	−0.0272806	+	0.0839610i	−0.00219833	+	0.00676577i
$155$	−10.2767	+	19.0430i	−0.825444	+	1.52957i
$156$	−2.92098	−	8.98984i	−0.233865	−	0.719763i
$157$	−4.01099			−0.320112			−0.160056	−	0.987108i	$-0.551167\pi$
$157$	−4.01099			−0.320112			−0.160056	+	0.987108i	$0.551167\pi$
$158$	−0.0555382	−	0.170929i	−0.00441838	−	0.0135984i
$159$	8.95985	+	6.50971i	0.710562	+	0.516253i
$160$	−0.331168	−	0.347200i	−0.0261811	−	0.0274485i
$161$	5.67594	−	4.12381i	0.447327	−	0.325002i
$162$	−0.0144696	−	0.0105128i	−0.00113684	−	0.000825960i
$163$	5.02098	+	3.64795i	0.393273	+	0.285730i	0.766796	−	0.641891i	$-0.221850\pi$
$163$	5.02098	+	3.64795i	0.393273	+	0.285730i	−0.373522	+	0.927621i	$0.621850\pi$
$164$	8.47760	−	6.15933i	0.661989	−	0.480963i
$165$	−5.24172	+	9.71307i	−0.408068	+	0.756162i
$166$	0.0645216	+	0.0468777i	0.00500785	+	0.00363841i
$167$	0.594794	+	1.83059i	0.0460266	+	0.141655i	0.971429	−	0.237331i	$-0.0762727\pi$
$167$	0.594794	+	1.83059i	0.0460266	+	0.141655i	−0.925402	+	0.378986i	$0.876273\pi$
$168$	−0.0715357			−0.00551910
$169$	2.88761	+	8.88714i	0.222124	+	0.683626i
$170$	0.0160279	+	0.119390i	0.00122929	+	0.00915676i
$171$	−0.982720	+	3.02450i	−0.0751505	+	0.231289i
$172$	−4.63731	+	14.2722i	−0.353592	+	1.08824i
$173$	14.7267	−	10.6995i	1.11965	−	0.813471i	0.135491	−	0.990779i	$-0.456739\pi$
$173$	14.7267	−	10.6995i	1.11965	−	0.813471i	0.984155	+	0.177308i	$0.0567387\pi$
$174$	0.141265			0.0107093
$175$	−0.236196	+	4.99442i	−0.0178547	+	0.377543i
$176$	−19.7344			−1.48754
$177$	3.03363	−	2.20406i	0.228021	−	0.165667i
$178$	−0.0116642	+	0.0358986i	−0.000874265	+	0.00269071i
$179$	−2.11171	+	6.49918i	−0.157837	+	0.485772i	−0.998437	−	0.0558840i	$-0.982202\pi$
$179$	−2.11171	+	6.49918i	−0.157837	+	0.485772i	0.840601	+	0.541656i	$0.182202\pi$
$180$	−4.39861	−	0.803631i	−0.327853	−	0.0598991i
$181$	−1.29379	−	3.98188i	−0.0961668	−	0.295971i	0.891389	−	0.453239i	$-0.149731\pi$
$181$	−1.29379	−	3.98188i	−0.0961668	−	0.295971i	−0.987556	+	0.157268i	$0.949731\pi$
$182$	0.0845440			0.00626682
$183$	3.41150	+	10.4995i	0.252185	+	0.776146i
$184$	−0.406033	−	0.295000i	−0.0299331	−	0.0217477i
$185$	−0.0428206	−	0.318963i	−0.00314823	−	0.0234507i
$186$	0.140026	−	0.101735i	0.0102672	−	0.00745955i
$187$	12.0280	+	8.73885i	0.879574	+	0.639048i
$188$	−10.2504	−	7.44736i	−0.747588	−	0.543154i
$189$	−0.809017	+	0.587785i	−0.0588473	+	0.0427551i
$190$	−0.0169224	−	0.126053i	−0.00122768	−	0.00914481i
$191$	−0.0323987	−	0.0235391i	−0.00234429	−	0.00170323i	0.586612	−	0.809868i	$-0.300461\pi$
$191$	−0.0323987	−	0.0235391i	−0.00234429	−	0.00170323i	−0.588957	+	0.808165i	$0.700461\pi$
$192$	−2.46976	−	7.60115i	−0.178240	−	0.548566i
$193$	−15.6002			−1.12292			−0.561462	−	0.827502i	$-0.689761\pi$
$193$	−15.6002			−1.12292			−0.561462	+	0.827502i	$0.689761\pi$
$194$	−0.105064	−	0.323354i	−0.00754317	−	0.0232155i
$195$	10.3978	+	1.89968i	0.744600	+	0.136039i
$196$	−0.617935	+	1.90181i	−0.0441382	+	0.135843i
$197$	7.87150	−	24.2260i	0.560821	−	1.72603i	−0.119231	−	0.992867i	$-0.538043\pi$
$197$	7.87150	−	24.2260i	0.560821	−	1.72603i	0.680052	−	0.733164i	$-0.261957\pi$
$198$	0.0714215	−	0.0518907i	0.00507570	−	0.00368771i
$199$	−1.12478			−0.0797335			−0.0398668	−	0.999205i	$-0.512693\pi$
$199$	−1.12478			−0.0797335			−0.0398668	+	0.999205i	$0.512693\pi$
$200$	0.345014	−	0.0943359i	0.0243962	−	0.00667056i
$201$	2.24935			0.158657
$202$	−0.171882	+	0.124879i	−0.0120936	+	0.00878649i
$203$	2.44073	−	7.51180i	0.171306	−	0.527225i
$204$	−1.86125	+	5.72834i	−0.130314	+	0.401064i
$205$	1.55909	+	11.6134i	0.108892	+	0.811118i
$206$	−0.0231169	−	0.0711464i	−0.00161063	−	0.00495700i
$207$	−7.01585			−0.487635
$208$	5.84009	+	17.9739i	0.404937	+	1.24627i
$209$	−12.6993	−	9.22656i	−0.878427	−	0.638214i
$210$	0.0189932	−	0.0351950i	0.00131066	−	0.00242869i
$211$	−16.3232	+	11.8595i	−1.12374	+	0.816443i	−0.984771	−	0.173855i	$-0.944378\pi$
$211$	−16.3232	+	11.8595i	−1.12374	+	0.816443i	−0.138965	+	0.990297i	$0.544378\pi$
$212$	−17.9168	−	13.0173i	−1.23053	−	0.894034i
$213$	−9.50497	−	6.90577i	−0.651270	−	0.473175i
$214$	−0.141825	+	0.103042i	−0.00969499	+	0.00704382i
$215$	−11.5821	−	12.1427i	−0.789889	−	0.828128i
$216$	0.0578736	+	0.0420476i	0.00393780	+	0.00286098i
$217$	−2.99044	−	9.20362i	−0.203004	−	0.624783i
$218$	−0.204914			−0.0138786
$219$	−1.18653	−	3.65175i	−0.0801780	−	0.246763i
$220$	10.4818	−	19.4230i	0.706681	−	1.30950i
$221$	4.39977	−	13.5411i	0.295961	−	0.910873i
$222$	−0.000795453		0.00244815i	−5.33873e−5		0.000164309i
$223$	9.62813	−	6.99525i	0.644747	−	0.468436i	−0.216730	−	0.976231i	$-0.569539\pi$
$223$	9.62813	−	6.99525i	0.644747	−	0.468436i	0.861478	+	0.507795i	$0.169539\pi$
$224$	0.214579			0.0143371
$225$	3.12673	−	3.90174i	0.208449	−	0.260116i
$226$	0.180239			0.0119893
$227$	2.92249	−	2.12332i	0.193973	−	0.140929i	−0.486560	−	0.873647i	$-0.661748\pi$
$227$	2.92249	−	2.12332i	0.193973	−	0.140929i	0.680533	+	0.732718i	$0.261748\pi$
$228$	1.96513	−	6.04804i	0.130144	−	0.400541i
$229$	6.06378	−	18.6624i	0.400706	−	1.23325i	−0.523722	−	0.851889i	$-0.675457\pi$
$229$	6.06378	−	18.6624i	0.400706	−	1.23325i	0.924428	−	0.381356i	$-0.124543\pi$
$230$	0.252942	−	0.121440i	0.0166785	−	0.00800754i
$231$	−1.52530	−	4.69440i	−0.100357	−	0.308869i
$232$	−0.565016			−0.0370951
$233$	0.701812	+	2.15996i	0.0459772	+	0.141503i	0.971410	−	0.237409i	$-0.0762982\pi$
$233$	0.701812	+	2.15996i	0.0459772	+	0.141503i	−0.925433	+	0.378912i	$0.876298\pi$
$234$	−0.0683976	−	0.0496937i	−0.00447129	−	0.00324858i
$235$	12.7722	−	6.13208i	0.833167	−	0.400013i
$236$	−6.06628	+	4.40741i	−0.394881	+	0.286898i
$237$	8.12961	+	5.90651i	0.528075	+	0.383669i
$238$	−0.0435831	−	0.0316649i	−0.00282507	−	0.00205253i
$239$	5.37575	−	3.90571i	0.347728	−	0.252639i	−0.400187	−	0.916433i	$-0.631055\pi$
$239$	5.37575	−	3.90571i	0.347728	−	0.252639i	0.747915	+	0.663794i	$0.231055\pi$
$240$	8.79441	+	1.60675i	0.567677	+	0.103715i
$241$	8.38371	+	6.09113i	0.540043	+	0.392364i	0.824101	−	0.566443i	$-0.191681\pi$
$241$	8.38371	+	6.09113i	0.540043	+	0.392364i	−0.284058	+	0.958807i	$0.591681\pi$
$242$	0.0738606	+	0.227320i	0.00474794	+	0.0146127i
$243$	1.00000			0.0641500
$244$	−6.82190	−	20.9957i	−0.436728	−	1.34411i
$245$	−1.54334	−	1.61805i	−0.0986005	−	0.103374i
$246$	0.0289624	−	0.0891371i	0.00184658	−	0.00568317i
$247$	−4.64532	+	14.2968i	−0.295574	+	0.909684i
$248$	−0.560058	+	0.406906i	−0.0355637	+	0.0258386i
$249$	−4.45913			−0.282586
$250$	−0.0451910	+	0.194791i	−0.00285813	+	0.0123197i
$251$	20.5340			1.29610			0.648048	−	0.761600i	$-0.275586\pi$
$251$	20.5340			1.29610			0.648048	+	0.761600i	$0.275586\pi$
$252$	1.61778	−	1.17538i	0.101910	−	0.0740421i
$253$	10.7013	−	32.9352i	0.672784	−	2.07062i
$254$	0.0357176	−	0.109927i	0.00224112	−	0.00689745i
$255$	−4.64862	−	4.87366i	−0.291108	−	0.305200i
$256$	4.93637	+	15.1926i	0.308523	+	0.949536i
$257$	−8.67344			−0.541035			−0.270517	−	0.962715i	$-0.587195\pi$
$257$	−8.67344			−0.541035			−0.270517	+	0.962715i	$0.587195\pi$
$258$	0.0414766	+	0.127652i	0.00258222	+	0.00794727i
$259$	0.116437	+	0.0845967i	0.00723507	+	0.00525658i
$260$	−20.7922	−	3.79876i	−1.28948	−	0.235589i
$261$	−6.38992	+	4.64255i	−0.395526	+	0.287367i
$262$	−0.280924	−	0.204103i	−0.0173556	−	0.0126096i
$263$	−5.22564	−	3.79665i	−0.322227	−	0.234111i	0.414898	−	0.909868i	$-0.363817\pi$
$263$	−5.22564	−	3.79665i	−0.322227	−	0.234111i	−0.737125	+	0.675756i	$0.763817\pi$
$264$	−0.285663	+	0.207546i	−0.0175813	+	0.0127736i
$265$	22.3247	−	10.7183i	1.37140	−	0.658423i
$266$	0.0460154	+	0.0334321i	0.00282138	+	0.00204985i
$267$	−0.652162	−	2.00715i	−0.0399117	−	0.122836i
$268$	−4.49797			−0.274757
$269$	−1.54147	−	4.74415i	−0.0939850	−	0.289256i	0.893003	−	0.450051i	$-0.148594\pi$
$269$	−1.54147	−	4.74415i	−0.0939850	−	0.289256i	−0.986988	+	0.160795i	$0.948594\pi$
$270$	−0.0360529	+	0.0173094i	−0.00219411	+	0.00105342i
$271$	4.21878	−	12.9841i	0.256273	−	0.788726i	−0.737304	−	0.675562i	$-0.763901\pi$
$271$	4.21878	−	12.9841i	0.256273	−	0.788726i	0.993576	−	0.113165i	$-0.0360988\pi$
$272$	3.72131	−	11.4530i	0.225638	−	0.694442i
$273$	−3.82422	+	2.77846i	−0.231452	+	0.168160i
$274$	−0.0185494			−0.00112061
$275$	13.5471	+	20.6294i	0.816920	+	1.24400i
$276$	14.0295			0.844474
$277$	3.81418	−	2.77116i	0.229172	−	0.166503i	−0.467274	−	0.884113i	$-0.654764\pi$
$277$	3.81418	−	2.77116i	0.229172	−	0.166503i	0.696446	+	0.717610i	$0.254764\pi$
$278$	−0.106909	+	0.329031i	−0.00641195	+	0.0197340i
$279$	−2.99044	+	9.20362i	−0.179033	+	0.551007i
$280$	−0.0759668	+	0.140769i	−0.00453988	+	0.00841254i
$281$	−6.34354	−	19.5234i	−0.378424	−	1.16467i	−0.941139	−	0.338019i	$-0.890243\pi$
$281$	−6.34354	−	19.5234i	−0.378424	−	1.16467i	0.562715	−	0.826651i	$-0.309757\pi$
$282$	−0.113324			−0.00674833
$283$	6.77462	+	20.8502i	0.402710	+	1.23941i	0.922793	+	0.385297i	$0.125901\pi$
$283$	6.77462	+	20.8502i	0.402710	+	1.23941i	−0.520083	+	0.854116i	$0.674099\pi$
$284$	19.0069	+	13.8093i	1.12785	+	0.819433i
$285$	4.90806	+	5.14565i	0.290728	+	0.304802i
$286$	0.337609	−	0.245287i	0.0199632	−	0.0145041i
$287$	−4.23948	−	3.08016i	−0.250248	−	0.181816i
$288$	−0.173598	−	0.126126i	−0.0102293	−	0.00743205i
$289$	6.41352	−	4.65970i	0.377266	−	0.274100i
$290$	0.150016	−	0.277983i	0.00880922	−	0.0163237i
$291$	15.3791	+	11.1736i	0.901541	+	0.655008i
$292$	2.37267	+	7.30234i	0.138850	+	0.427337i
$293$	−1.09631			−0.0640472			−0.0320236	−	0.999487i	$-0.510195\pi$
$293$	−1.09631			−0.0640472			−0.0320236	+	0.999487i	$0.510195\pi$
$294$	0.00552688	+	0.0170100i	0.000322334	+	0.000992043i
$295$	−1.11564	−	8.31018i	−0.0649548	−	0.483838i
$296$	0.00318156	−	0.00979183i	0.000184924	−	0.000569139i
$297$	−1.52530	+	4.69440i	−0.0885070	+	0.272396i
$298$	0.0406513	−	0.0295349i	0.00235486	−	0.00171091i
$299$	−33.1639			−1.91792
$300$	−6.25246	+	7.80223i	−0.360986	+	0.450462i
$301$	7.50453			0.432554
$302$	0.290226	−	0.210861i	0.0167006	−	0.0121337i
$303$	3.67077	−	11.2975i	0.210880	−	0.649022i
$304$	−3.92900	+	12.0922i	−0.225343	+	0.693535i
$305$	24.2839	+	4.43669i	1.39049	+	0.254044i
$306$	0.0166472	+	0.0512349i	0.000951660	+	0.00292891i
$307$	−14.6712			−0.837328			−0.418664	−	0.908141i	$-0.637501\pi$
$307$	−14.6712			−0.837328			−0.418664	+	0.908141i	$0.637501\pi$
$308$	3.05012	+	9.38729i	0.173796	+	0.534890i
$309$	3.38381	+	2.45849i	0.192498	+	0.139858i
$310$	−0.0514954	−	0.383580i	−0.00292474	−	0.0217859i
$311$	3.76312	−	2.73407i	0.213387	−	0.155035i	−0.475958	−	0.879468i	$-0.657898\pi$
$311$	3.76312	−	2.73407i	0.213387	−	0.155035i	0.689345	+	0.724433i	$0.257898\pi$
$312$	0.273568	+	0.198759i	0.0154878	+	0.0112525i
$313$	27.0340	+	19.6414i	1.52805	+	1.11020i	0.957309	+	0.289067i	$0.0933451\pi$
$313$	27.0340	+	19.6414i	1.52805	+	1.11020i	0.570744	+	0.821128i	$0.306655\pi$
$314$	0.0580373	−	0.0421666i	0.00327523	−	0.00237960i
$315$	0.297521	+	2.21619i	0.0167634	+	0.124868i
$316$	−16.2566	−	11.8111i	−0.914506	−	0.664428i
$317$	3.49020	+	10.7417i	0.196029	+	0.603316i	0.999963	+	0.00859736i	$0.00273666\pi$
$317$	3.49020	+	10.7417i	0.196029	+	0.603316i	−0.803934	+	0.594719i	$0.797263\pi$
$318$	−0.198080			−0.0111078
$319$	−12.0474	−	37.0781i	−0.674525	−	2.07598i
$320$	−17.5804	−	3.21195i	−0.982773	−	0.179554i
$321$	3.02887	−	9.32191i	0.169055	−	0.520298i
$322$	−0.0387758	+	0.119340i	−0.00216089	+	0.00665053i
$323$	7.74939	−	5.63026i	0.431188	−	0.313276i
$324$	−1.99968			−0.111093
$325$	14.7800	−	18.4435i	0.819850	−	1.02306i
$326$	−0.111001			−0.00614780
$327$	9.26899	−	6.73432i	0.512576	−	0.372409i
$328$	−0.115840	+	0.356520i	−0.00639621	+	0.0196855i
$329$	−1.95797	+	6.02600i	−0.107946	+	0.332224i
$330$	−0.0262657	−	0.195649i	−0.00144588	−	0.0107701i
$331$	−7.96609	−	24.5171i	−0.437856	−	1.34758i	−0.890132	−	0.455704i	$-0.849388\pi$
$331$	−7.96609	−	24.5171i	−0.437856	−	1.34758i	0.452276	−	0.891878i	$-0.350612\pi$
$332$	8.91682			0.489374
$333$	−0.0444751	−	0.136880i	−0.00243722	−	0.00750100i
$334$	−0.0278509	−	0.0202349i	−0.00152394	−	0.00110720i
$335$	2.38867	−	4.42629i	0.130507	−	0.241834i
$336$	−3.23452	+	2.35001i	−0.176457	+	0.128204i
$337$	15.3294	+	11.1375i	0.835048	+	0.606698i	0.920983	−	0.389603i	$-0.127388\pi$
$337$	15.3294	+	11.1375i	0.835048	+	0.606698i	−0.0859347	+	0.996301i	$0.527388\pi$
$338$	−0.135211	−	0.0982363i	−0.00735449	−	0.00534335i
$339$	−8.15283	+	5.92338i	−0.442801	+	0.321714i
$340$	9.29576	+	9.74576i	0.504133	+	0.528538i
$341$	−38.6441	−	28.0766i	−2.09270	−	1.52043i
$342$	−0.0175763	−	0.0540943i	−0.000950418	−	0.00292509i
$343$	1.00000			0.0539949
$344$	−0.165893	−	0.510567i	−0.00894437	−	0.0275279i
$345$	−7.45042	+	13.8059i	−0.401117	+	0.743283i
$346$	−0.100607	+	0.309635i	−0.00540864	+	0.0166461i
$347$	−6.20168	+	19.0868i	−0.332924	+	1.02463i	0.634812	+	0.772666i	$0.281077\pi$
$347$	−6.20168	+	19.0868i	−0.332924	+	1.02463i	−0.967736	+	0.251967i	$0.918923\pi$
$348$	12.7778	−	9.28361i	0.684962	−	0.497654i
$349$	−3.26562			−0.174805			−0.0874024	−	0.996173i	$-0.527857\pi$
$349$	−3.26562			−0.174805			−0.0874024	+	0.996173i	$0.527857\pi$
$350$	−0.0490874	−	0.0747501i	−0.00262383	−	0.00399556i
$351$	4.72700			0.252308
$352$	0.856875	−	0.622556i	0.0456716	−	0.0331823i
$353$	1.45254	−	4.47047i	0.0773110	−	0.237939i	−0.904931	−	0.425559i	$-0.860077\pi$
$353$	1.45254	−	4.47047i	0.0773110	−	0.237939i	0.982242	+	0.187620i	$0.0600774\pi$
$354$	−0.0207245	+	0.0637835i	−0.00110150	+	0.00339005i
$355$	−23.6830	+	11.3705i	−1.25696	+	0.603482i
$356$	1.30412	+	4.01366i	0.0691180	+	0.212723i
$357$	3.01205			0.159415
$358$	−0.0377687	−	0.116240i	−0.00199614	−	0.00614348i
$359$	3.35880	+	2.44031i	0.177271	+	0.128795i	0.672882	−	0.739749i	$-0.265056\pi$
$359$	3.35880	+	2.44031i	0.177271	+	0.128795i	−0.495611	+	0.868544i	$0.665056\pi$
$360$	0.144200	−	0.0692322i	0.00760002	−	0.00364886i
$361$	7.18945	−	5.22344i	0.378392	−	0.274918i
$362$	0.0605811	+	0.0440148i	0.00318407	+	0.00231336i
$363$	−10.8116	−	7.85510i	−0.567463	−	0.412286i
$364$	7.64722	−	5.55603i	0.400823	−	0.291215i
$365$	−8.44598	−	1.54309i	−0.442083	−	0.0807690i
$366$	−0.159742	−	0.116059i	−0.00834983	−	0.00606650i
$367$	5.93241	+	18.2581i	0.309669	+	0.953064i	0.977893	+	0.209104i	$0.0670547\pi$
$367$	5.93241	+	18.2581i	0.309669	+	0.953064i	−0.668224	+	0.743960i	$0.732945\pi$
$368$	−28.0499			−1.46220
$369$	1.61934	+	4.98380i	0.0842992	+	0.259446i
$370$	0.00397278	+	0.00416510i	0.000206535	+	0.000216533i
$371$	−3.42236	+	10.5329i	−0.177680	+	0.546842i
$372$	5.97992	−	18.4043i	0.310044	−	0.954219i
$373$	18.0704	−	13.1289i	0.935651	−	0.679790i	−0.0117192	−	0.999931i	$-0.503730\pi$
$373$	18.0704	−	13.1289i	0.935651	−	0.679790i	0.947370	+	0.320141i	$0.103730\pi$
$374$	−0.265909			−0.0137498
$375$	−4.35747	−	10.2962i	−0.225019	−	0.531695i
$376$	0.453259			0.0233750
$377$	−30.2051	+	21.9453i	−1.55564	+	1.13024i
$378$	0.00552688	−	0.0170100i	0.000284272	−	0.000874899i
$379$	−8.70554	+	26.7929i	−0.447174	+	1.37626i	0.432908	+	0.901438i	$0.357487\pi$
$379$	−8.70554	+	26.7929i	−0.447174	+	1.37626i	−0.880082	+	0.474821i	$0.842513\pi$
$380$	−9.81454	−	10.2897i	−0.503475	−	0.527848i
$381$	1.99703	+	6.14622i	0.102311	+	0.314880i
$382$	0.000716256	0		3.66468e−5	0
$383$	−1.91122	−	5.88213i	−0.0976588	−	0.300563i	0.890279	−	0.455416i	$-0.150510\pi$
$383$	−1.91122	−	5.88213i	−0.0976588	−	0.300563i	−0.987937	+	0.154853i	$0.950510\pi$
$384$	0.462841	+	0.336274i	0.0236192	+	0.0171604i
$385$	−10.8575	−	1.98367i	−0.553348	−	0.101097i
$386$	0.225728	−	0.164001i	0.0114892	−	0.00834742i
$387$	−6.07129	−	4.41105i	−0.308621	−	0.224226i
$388$	−30.7534	−	22.3436i	−1.56127	−	1.13433i
$389$	−2.76271	+	2.00722i	−0.140075	+	0.101770i	−0.655616	−	0.755095i	$-0.727591\pi$
$389$	−2.76271	+	2.00722i	−0.140075	+	0.101770i	0.515541	+	0.856865i	$0.327591\pi$
$390$	−0.170422	+	0.0818216i	−0.00862966	+	0.00414320i
$391$	17.0962	+	12.4211i	0.864593	+	0.628164i
$392$	−0.0221058	−	0.0680345i	−0.00111651	−	0.00343626i
$393$	19.4148			0.979349
$394$	0.140785	+	0.433291i	0.00709263	+	0.0218289i
$395$	20.2561	−	9.72517i	1.01919	−	0.489326i
$396$	3.05012	−	9.38729i	0.153274	−	0.471729i
$397$	4.44137	−	13.6691i	0.222906	−	0.686035i	−0.775591	−	0.631236i	$-0.782548\pi$
$397$	4.44137	−	13.6691i	0.222906	−	0.686035i	0.998497	−	0.0547992i	$-0.0174519\pi$
$398$	0.0162751	−	0.0118245i	0.000815795	−	0.000592710i
$399$	−3.18015			−0.159207
$400$	12.5009	−	15.5995i	0.625046	−	0.779973i
$401$	−5.45261			−0.272291			−0.136145	−	0.990689i	$-0.543471\pi$
$401$	−5.45261			−0.272291			−0.136145	+	0.990689i	$0.543471\pi$
$402$	−0.0325470	+	0.0236468i	−0.00162330	+	0.00117940i
$403$	−14.1358	+	43.5055i	−0.704154	+	2.16716i
$404$	−7.34036	+	22.5913i	−0.365197	+	1.12396i
$405$	1.06194	−	1.96781i	0.0527683	−	0.0977813i
$406$	0.0436534	+	0.134351i	0.00216648	+	0.00666774i
$407$	0.710408			0.0352136
$408$	−0.0665837	−	0.204923i	−0.00329638	−	0.0101452i
$409$	−6.15443	−	4.47146i	−0.304317	−	0.221099i	0.425137	−	0.905129i	$-0.360226\pi$
$409$	−6.15443	−	4.47146i	−0.304317	−	0.221099i	−0.729454	+	0.684030i	$0.760226\pi$
$410$	−0.144649	−	0.151651i	−0.00714368	−	0.00748951i
$411$	0.839054	−	0.609609i	0.0413875	−	0.0300698i
$412$	−6.76655	−	4.91618i	−0.333364	−	0.242203i
$413$	3.03363	+	2.20406i	0.149275	+	0.108455i
$414$	0.101516	−	0.0737559i	0.00498925	−	0.00362490i
$415$	−4.73533	+	8.77471i	−0.232448	+	0.430734i
$416$	−0.820596	−	0.596198i	−0.0402330	−	0.0292310i
$417$	−5.97744	−	18.3967i	−0.292716	−	0.900888i
$418$	0.280749			0.0137319
$419$	−4.96156	−	15.2701i	−0.242388	−	0.745994i	−0.996055	−	0.0887375i	$-0.971717\pi$
$419$	−4.96156	−	15.2701i	−0.242388	−	0.745994i	0.753667	−	0.657257i	$-0.228283\pi$
$420$	−0.594947	−	4.43166i	−0.0290304	−	0.216243i
$421$	−7.67402	+	23.6182i	−0.374009	+	1.15108i	0.570136	+	0.821550i	$0.306891\pi$
$421$	−7.67402	+	23.6182i	−0.374009	+	1.15108i	−0.944145	+	0.329531i	$0.893109\pi$
$422$	0.111514	−	0.343204i	0.00542840	−	0.0167069i
$423$	5.12603	−	3.72428i	0.249236	−	0.181080i
$424$	0.792257			0.0384754
$425$	−14.5270	+	3.97207i	−0.704663	+	0.192673i
$426$	0.210131			0.0101809
$427$	−8.93142	+	6.48905i	−0.432221	+	0.314027i
$428$	−6.05678	+	18.6408i	−0.292765	+	0.901039i
$429$	−7.21009	+	22.1904i	−0.348107	+	1.07136i
$430$	0.295241	+	0.0539408i	0.0142378	+	0.00260126i
$431$	9.40591	+	28.9484i	0.453067	+	1.39440i	0.873390	+	0.487022i	$0.161917\pi$
$431$	9.40591	+	28.9484i	0.453067	+	1.39440i	−0.420323	+	0.907375i	$0.638083\pi$
$432$	3.99808			0.192358
$433$	8.92590	+	27.4711i	0.428951	+	1.32018i	0.899160	+	0.437621i	$0.144179\pi$
$433$	8.92590	+	27.4711i	0.428951	+	1.32018i	−0.470208	+	0.882556i	$0.655821\pi$
$434$	0.140026	+	0.101735i	0.00672145	+	0.00488342i
$435$	2.34993	+	17.5043i	0.112671	+	0.839266i
$436$	−18.5350	+	13.4665i	−0.887666	+	0.644927i
$437$	−18.0503	−	13.1143i	−0.863465	−	0.627344i
$438$	0.0555585	+	0.0403656i	0.00265469	+	0.00192874i
$439$	3.24705	−	2.35912i	0.154973	−	0.112595i	−0.507596	−	0.861595i	$-0.669466\pi$
$439$	3.24705	−	2.35912i	0.154973	−	0.112595i	0.662570	+	0.749000i	$0.269466\pi$
$440$	0.105054	+	0.782533i	0.00500827	+	0.0373058i
$441$	−0.809017	−	0.587785i	−0.0385246	−	0.0279898i
$442$	0.0786915	+	0.242187i	0.00374297	+	0.0115197i
$443$	25.8920			1.23016			0.615082	−	0.788463i	$-0.289123\pi$
$443$	25.8920			1.23016			0.615082	+	0.788463i	$0.289123\pi$
$444$	0.0889360	+	0.273717i	0.00422072	+	0.0129900i
$445$	−4.64225	−	0.848144i	−0.220064	−	0.0402059i
$446$	−0.0657756	+	0.202436i	−0.00311456	+	0.00958564i
$447$	−0.868163	+	2.67193i	−0.0410627	+	0.126378i
$448$	6.46593	−	4.69777i	0.305486	−	0.221949i
$449$	−10.9541			−0.516954			−0.258477	−	0.966017i	$-0.583221\pi$
$449$	−10.9541			−0.516954			−0.258477	+	0.966017i	$0.583221\pi$
$450$	−0.00422445	+	0.0893270i	−0.000199142	+	0.00421091i
$451$	−25.8659			−1.21798
$452$	16.3031	−	11.8449i	0.766831	−	0.557135i
$453$	−6.19816	+	19.0760i	−0.291215	+	0.896267i
$454$	−0.0199653	+	0.0614469i	−0.000937018	+	0.00288384i
$455$	1.40638	+	10.4759i	0.0659322	+	0.491118i
$456$	0.0702996	+	0.216360i	0.00329208	+	0.0101320i
$457$	−8.51432			−0.398283			−0.199141	−	0.979971i	$-0.563815\pi$
$457$	−8.51432			−0.398283			−0.199141	+	0.979971i	$0.563815\pi$
$458$	0.108453	+	0.333784i	0.00506767	+	0.0155967i
$459$	−2.43680	−	1.77044i	−0.113740	−	0.0826370i
$460$	14.8985	−	27.6073i	0.694644	−	1.28720i
$461$	4.56788	−	3.31876i	0.212747	−	0.154570i	−0.476309	−	0.879278i	$-0.658025\pi$
$461$	4.56788	−	3.31876i	0.212747	−	0.154570i	0.689056	+	0.724708i	$0.258025\pi$
$462$	0.0714215	+	0.0518907i	0.00332283	+	0.00241417i
$463$	21.4246	+	15.5659i	0.995685	+	0.723407i	0.961159	−	0.275997i	$-0.0890079\pi$
$463$	21.4246	+	15.5659i	0.995685	+	0.723407i	0.0345259	+	0.999404i	$0.489008\pi$
$464$	−25.5474	+	18.5613i	−1.18601	+	0.861686i
$465$	14.9353	+	15.6583i	0.692609	+	0.726138i
$466$	−0.0328620	−	0.0238756i	−0.00152230	−	0.00110602i
$467$	−11.1283	−	34.2493i	−0.514955	−	1.58487i	−0.783365	−	0.621563i	$-0.786498\pi$
$467$	−11.1283	−	34.2493i	−0.514955	−	1.58487i	0.268410	−	0.963305i	$-0.413502\pi$
$468$	−9.45248			−0.436941
$469$	0.695086	+	2.13926i	0.0320961	+	0.0987816i
$470$	−0.120343	+	0.223000i	−0.00555102	+	0.0102862i
$471$	−1.23947	+	3.81468i	−0.0571115	+	0.175771i
$472$	0.0828914	−	0.255114i	0.00381539	−	0.0117426i
$473$	29.9678	−	21.7729i	1.37792	−	1.00112i
$474$	−0.179725			−0.00825507
$475$	15.3377	−	4.19374i	0.703744	−	0.192422i
$476$	−6.02314			−0.276070
$477$	8.95985	−	6.50971i	0.410243	−	0.298059i
$478$	−0.0367250	+	0.113028i	−0.00167976	+	0.00516977i
$479$	0.992042	−	3.05319i	0.0453276	−	0.139504i	−0.925831	−	0.377937i	$-0.876634\pi$
$479$	0.992042	−	3.05319i	0.0453276	−	0.139504i	0.971159	+	0.238433i	$0.0766337\pi$
$480$	−0.432543	+	0.207669i	−0.0197428	+	0.00947874i
$481$	−0.210234	−	0.647033i	−0.00958583	−	0.0295022i
$482$	−0.185343			−0.00844215
$483$	−2.16802	−	6.67247i	−0.0986482	−	0.303608i
$484$	21.6198	+	15.7077i	0.982717	+	0.713986i
$485$	38.3193	−	18.3975i	1.73999	−	0.835389i
$486$	−0.0144696	+	0.0105128i	−0.000656353	+	0.000476868i
$487$	6.59479	+	4.79139i	0.298838	+	0.217119i	0.727092	−	0.686540i	$-0.240871\pi$
$487$	6.59479	+	4.79139i	0.298838	+	0.217119i	−0.428254	+	0.903658i	$0.640871\pi$
$488$	0.638915	+	0.464199i	0.0289223	+	0.0210133i
$489$	5.02098	−	3.64795i	0.227056	−	0.164966i
$490$	0.0393417	+	0.00718776i	0.00177728	+	0.000324710i
$491$	14.9496	+	10.8615i	0.674667	+	0.490174i	0.871584	−	0.490246i	$-0.163093\pi$
$491$	14.9496	+	10.8615i	0.674667	+	0.490174i	−0.196917	+	0.980420i	$0.563093\pi$
$492$	−3.23815	−	9.96601i	−0.145987	−	0.449302i
$493$	23.7903			1.07146
$494$	−0.0830831	−	0.255704i	−0.00373809	−	0.0115046i
$495$	7.61790	+	7.98668i	0.342399	+	0.358975i
$496$	−11.9560	+	36.7968i	−0.536841	+	1.65223i
$497$	3.63058	−	11.1738i	0.162854	−	0.501212i
$498$	0.0645216	−	0.0468777i	0.00289128	−	0.00210064i
$499$	−11.6319			−0.520715			−0.260358	−	0.965512i	$-0.583840\pi$
$499$	−11.6319			−0.520715			−0.260358	+	0.965512i	$0.583840\pi$
$500$	8.71355	+	20.5892i	0.389682	+	0.920776i
$501$	1.92480			0.0859935
$502$	−0.297118	+	0.215869i	−0.0132610	+	0.00963470i
$503$	−9.61306	+	29.5860i	−0.428625	+	1.31917i	0.470855	+	0.882211i	$0.343946\pi$
$503$	−9.61306	+	29.5860i	−0.428625	+	1.31917i	−0.899480	+	0.436962i	$0.856054\pi$
$504$	−0.0221058	+	0.0680345i	−0.000984669	+	0.00303050i
$505$	−18.3331	−	19.2206i	−0.815813	−	0.855307i
$506$	0.191396	+	0.589057i	0.00850861	+	0.0261868i
$507$	9.34449			0.415004
$508$	−3.99342	−	12.2905i	−0.177179	−	0.545302i
$509$	17.3897	+	12.6344i	0.770786	+	0.560009i	0.902200	−	0.431319i	$-0.141952\pi$
$509$	17.3897	+	12.6344i	0.770786	+	0.560009i	−0.131414	+	0.991328i	$0.541952\pi$
$510$	0.118499	+	0.0216499i	0.00524723	+	0.000958674i
$511$	3.10637	−	2.25691i	0.137418	−	0.0998397i
$512$	−1.15682	−	0.840482i	−0.0511249	−	0.0371444i
$513$	2.57280	+	1.86925i	0.113592	+	0.0825292i
$514$	0.125501	−	0.0911818i	0.00553561	−	0.00402185i
$515$	8.43125	−	4.04794i	0.371525	−	0.178373i
$516$	12.1406	+	8.82070i	0.534462	+	0.388309i
$517$	9.66449	+	29.7442i	0.425044	+	1.30815i
$518$	−0.00257414			−0.000113101
$519$	−5.62508	−	17.3122i	−0.246914	−	0.759922i
$520$	0.681634	−	0.327260i	0.0298916	−	0.0143513i
$521$	−2.48790	+	7.65696i	−0.108997	+	0.335458i	−0.990648	−	0.136444i	$-0.956432\pi$
$521$	−2.48790	+	7.65696i	−0.108997	+	0.335458i	0.881651	+	0.471902i	$0.156432\pi$
$522$	0.0436534	−	0.134351i	0.00191066	−	0.00588040i
$523$	8.08621	−	5.87498i	0.353585	−	0.256895i	−0.396786	−	0.917911i	$-0.629875\pi$
$523$	8.08621	−	5.87498i	0.353585	−	0.256895i	0.750372	+	0.661016i	$0.229875\pi$
$524$	−38.8235			−1.69601
$525$	4.67699	+	1.76800i	0.204120	+	0.0771617i
$526$	0.115526			0.00503717
$527$	23.5816	−	17.1330i	1.02723	−	0.746325i
$528$	−6.09828	+	18.7686i	−0.265394	+	0.816797i
$529$	8.10308	−	24.9387i	0.352308	−	1.08429i
$530$	−0.210349	+	0.389784i	−0.00913699	+	0.0169311i
$531$	−1.15874	−	3.56624i	−0.0502851	−	0.154762i
$532$	6.35928			0.275710
$533$	7.65459	+	23.5584i	0.331557	+	1.02043i
$534$	0.0305372	+	0.0221865i	0.00132147	+	0.000960106i
$535$	−15.1273	−	15.8596i	−0.654009	−	0.685669i
$536$	0.130178	−	0.0945797i	0.00562282	−	0.00408522i
$537$	5.52853	+	4.01671i	0.238574	+	0.173334i
$538$	0.0721785	+	0.0524408i	0.00311184	+	0.00226088i
$539$	3.99329	−	2.90130i	0.172003	−	0.124968i
$540$	−2.12354	+	3.93499i	−0.0913828	+	0.169335i
$541$	7.73774	+	5.62180i	0.332671	+	0.241700i	0.741563	−	0.670883i	$-0.234085\pi$
$541$	7.73774	+	5.62180i	0.332671	+	0.241700i	−0.408892	+	0.912583i	$0.634085\pi$
$542$	0.0754544	+	0.232225i	0.00324104	+	0.00997491i
$543$	−4.18680			−0.179673
$544$	0.199724	+	0.614688i	0.00856311	+	0.0263545i
$545$	−3.40873	−	25.3911i	−0.146014	−	1.08763i
$546$	0.0261255	−	0.0804062i	0.00111807	−	0.00344107i
$547$	0.453003	−	1.39420i	0.0193690	−	0.0596117i	−0.940905	−	0.338671i	$-0.890023\pi$
$547$	0.453003	−	1.39420i	0.0193690	−	0.0596117i	0.960274	+	0.279059i	$0.0900226\pi$
$548$	−1.67784	+	1.21902i	−0.0716738	+	0.0520740i
$549$	11.0398			0.471169
$550$	−0.412893	−	0.156082i	−0.0176058	−	0.00665535i
$551$	−25.1180			−1.07006
$552$	−0.406033	+	0.295000i	−0.0172819	+	0.0125560i
$553$	−3.10523	+	9.55693i	−0.132048	+	0.406402i
$554$	−0.0260570	+	0.0801951i	−0.00110705	+	0.00340716i
$555$	−0.316585	−	0.0578403i	−0.0134383	−	0.00245519i
$556$	11.9530	+	36.7874i	0.506919	+	1.56014i
$557$	−2.82835			−0.119841			−0.0599204	−	0.998203i	$-0.519085\pi$
$557$	−2.82835			−0.119841			−0.0599204	+	0.998203i	$0.519085\pi$
$558$	−0.0534851	−	0.164610i	−0.00226420	−	0.00696850i
$559$	−28.6990	−	20.8510i	−1.21384	−	0.881905i
$560$	1.18951	+	8.86049i	0.0502661	+	0.374424i
$561$	12.0280	−	8.73885i	0.507822	−	0.368955i
$562$	0.297033	+	0.215807i	0.0125296	+	0.00910328i
$563$	28.8654	+	20.9720i	1.21653	+	0.883862i	0.995807	−	0.0914737i	$-0.0291577\pi$
$563$	28.8654	+	20.9720i	1.21653	+	0.883862i	0.220725	+	0.975336i	$0.429158\pi$
$564$	−10.2504	+	7.44736i	−0.431620	+	0.313590i
$565$	2.99826	+	22.3335i	0.126138	+	0.939578i
$566$	−0.317218	−	0.230473i	−0.0133337	−	0.00968749i
$567$	0.309017	+	0.951057i	0.0129775	+	0.0399406i
$568$	−0.840458			−0.0352648
$569$	6.00647	+	18.4860i	0.251804	+	0.774974i	0.994442	+	0.105281i	$0.0335743\pi$
$569$	6.00647	+	18.4860i	0.251804	+	0.774974i	−0.742638	+	0.669693i	$0.766426\pi$
$570$	−0.125112	−	0.0228582i	−0.00524038	−	0.000957423i
$571$	−3.11299	+	9.58079i	−0.130274	+	0.400943i	−0.994825	−	0.101602i	$-0.967603\pi$
$571$	−3.11299	+	9.58079i	−0.130274	+	0.400943i	0.864551	+	0.502546i	$0.167603\pi$
$572$	14.4179	−	44.3737i	0.602842	−	1.85536i
$573$	−0.0323987	+	0.0235391i	−0.00135348	+	0.000983358i
$574$	0.0937243			0.00391198
$575$	19.2554	+	29.3220i	0.803006	+	1.22281i
$576$	−7.99232			−0.333013
$577$	−29.5282	+	21.4535i	−1.22927	+	0.893120i	−0.996836	−	0.0794910i	$-0.974671\pi$
$577$	−29.5282	+	21.4535i	−1.22927	+	0.893120i	−0.232439	+	0.972611i	$0.574671\pi$
$578$	−0.0438146	+	0.134848i	−0.00182245	+	0.00560892i
$579$	−4.82072	+	14.8366i	−0.200342	+	0.616590i
$580$	−4.69912	−	35.0029i	−0.195120	−	1.45342i
$581$	−1.37795	−	4.24088i	−0.0571668	−	0.175941i
$582$	−0.339995			−0.0140932
$583$	16.8927	+	51.9903i	0.699623	+	2.15322i
$584$	−0.222216	−	0.161449i	−0.00919537	−	0.00668083i
$585$	5.01980	−	9.30183i	0.207543	−	0.384584i
$586$	0.0158631	−	0.0115252i	0.000655300	−	0.000476103i
$587$	20.9279	+	15.2050i	0.863786	+	0.627577i	0.928912	−	0.370300i	$-0.120745\pi$
$587$	20.9279	+	15.2050i	0.863786	+	0.627577i	−0.0651265	+	0.997877i	$0.520745\pi$
$588$	1.61778	+	1.17538i	0.0667159	+	0.0484720i
$589$	−24.8976	+	18.0892i	−1.02589	+	0.745352i
$590$	0.103506	+	0.108516i	0.00426126	+	0.00446755i
$591$	−20.6079	−	14.9725i	−0.847694	−	0.615886i
$592$	−0.177815	−	0.547259i	−0.00730816	−	0.0224922i
$593$	−19.4716			−0.799603			−0.399801	−	0.916602i	$-0.630921\pi$
$593$	−19.4716			−0.799603			−0.399801	+	0.916602i	$0.630921\pi$
$594$	−0.0272806	−	0.0839610i	−0.00111934	−	0.00344496i
$595$	3.19862	−	5.92715i	0.131131	−	0.242989i
$596$	1.73605	−	5.34301i	0.0711113	−	0.218858i
$597$	−0.347576	+	1.06973i	−0.0142253	+	0.0437811i
$598$	0.479867	−	0.348644i	0.0196232	−	0.0142571i
$599$	−37.9039			−1.54871			−0.774357	−	0.632749i	$-0.781926\pi$
$599$	−37.9039			−1.54871			−0.774357	+	0.632749i	$0.781926\pi$
$600$	0.0168964	−	0.357279i	0.000689794	−	0.0145859i
$601$	43.5352			1.77584			0.887920	−	0.459999i	$-0.152150\pi$
$601$	43.5352			1.77584			0.887920	+	0.459999i	$0.152150\pi$
$602$	−0.108587	+	0.0788933i	−0.00442569	+	0.00321545i
$603$	0.695086	−	2.13926i	0.0283061	−	0.0871172i
$604$	12.3943	−	38.1458i	0.504318	−	1.55213i
$605$	−26.9387	+	12.9336i	−1.09521	+	0.525824i
$606$	0.0656530	+	0.202059i	0.00266697	+	0.00820809i
$607$	−3.37472			−0.136976			−0.0684878	−	0.997652i	$-0.521817\pi$
$607$	−3.37472			−0.136976			−0.0684878	+	0.997652i	$0.521817\pi$
$608$	−0.210871	−	0.648993i	−0.00855194	−	0.0263202i
$609$	−6.38992	−	4.64255i	−0.258933	−	0.188126i
$610$	−0.398019	+	0.191093i	−0.0161153	+	0.00773714i
$611$	24.2307	−	17.6046i	0.980269	−	0.712207i
$612$	4.87282	+	3.54031i	0.196972	+	0.143109i
$613$	−25.5935	−	18.5948i	−1.03371	−	0.751037i	−0.0646651	−	0.997907i	$-0.520598\pi$
$613$	−25.5935	−	18.5948i	−1.03371	−	0.751037i	−0.969049	+	0.246870i	$0.920598\pi$
$614$	0.212285	−	0.154234i	0.00856714	−	0.00622439i
$615$	11.5268	+	2.10596i	0.464806	+	0.0849206i
$616$	−0.285663	−	0.207546i	−0.0115097	−	0.00836228i
$617$	−15.0761	−	46.3996i	−0.606943	−	1.86798i	−0.482839	−	0.875709i	$-0.660394\pi$
$617$	−15.0761	−	46.3996i	−0.606943	−	1.86798i	−0.124104	−	0.992269i	$-0.539606\pi$
$618$	−0.0748078			−0.00300921
$619$	0.296832	+	0.913555i	0.0119307	+	0.0367189i	0.956845	−	0.290600i	$-0.0938549\pi$
$619$	0.296832	+	0.913555i	0.0119307	+	0.0367189i	−0.944914	+	0.327319i	$0.893855\pi$
$620$	−29.8659	−	31.3117i	−1.19944	−	1.25751i
$621$	−2.16802	+	6.67247i	−0.0869995	+	0.267757i
$622$	−0.0257082	+	0.0791216i	−0.00103080	+	0.00317249i
$623$	1.70738	−	1.24049i	0.0684049	−	0.0496990i
$624$	18.8989			0.756562
$625$	−24.8884	−	2.35932i	−0.995537	−	0.0943728i
$626$	−0.597655			−0.0238871
$627$	−12.6993	+	9.22656i	−0.507160	+	0.368473i
$628$	2.47853	−	7.62814i	0.0989043	−	0.304396i
$629$	−0.133961	+	0.412290i	−0.00534139	+	0.0164391i
$630$	−0.0276032	−	0.0289395i	−0.00109974	−	0.00115298i
$631$	−6.16916	−	18.9867i	−0.245590	−	0.755850i	−0.995539	−	0.0943533i	$-0.969922\pi$
$631$	−6.16916	−	18.9867i	−0.245590	−	0.755850i	0.749948	−	0.661496i	$-0.230078\pi$
$632$	0.718844			0.0285941
$633$	6.23491	+	19.1891i	0.247816	+	0.762698i
$634$	−0.163427	−	0.118737i	−0.00649051	−	0.00471563i
$635$	14.2153	+	2.59715i	0.564118	+	0.103065i
$636$	−17.9168	+	13.0173i	−0.710448	+	0.516171i
$637$	−3.82422	−	2.77846i	−0.151521	−	0.110087i
$638$	0.564114	+	0.409852i	0.0223335	+	0.0162262i
$639$	−9.50497	+	6.90577i	−0.376011	+	0.273188i
$640$	1.15323	−	0.553680i	0.0455855	−	0.0218861i
$641$	24.5784	+	17.8572i	0.970788	+	0.705318i	0.955631	−	0.294567i	$-0.0951753\pi$
$641$	24.5784	+	17.8572i	0.970788	+	0.705318i	0.0151567	+	0.999885i	$0.495175\pi$
$642$	0.0541725	+	0.166726i	0.00213802	+	0.00658014i
$643$	−17.3209			−0.683069			−0.341535	−	0.939869i	$-0.610947\pi$
$643$	−17.3209			−0.683069			−0.341535	+	0.939869i	$0.610947\pi$
$644$	4.33534	+	13.3428i	0.170836	+	0.525780i
$645$	−15.1275	+	7.26288i	−0.595644	+	0.285975i
$646$	−0.0529407	+	0.162935i	−0.00208293	+	0.00641058i
$647$	1.55978	−	4.80050i	0.0613211	−	0.188727i	−0.915703	−	0.401856i	$-0.868365\pi$
$647$	1.55978	−	4.80050i	0.0613211	−	0.188727i	0.977024	+	0.213129i	$0.0683654\pi$
$648$	0.0578736	−	0.0420476i	0.00227349	−	0.00165179i
$649$	18.5088			0.726533
$650$	−0.0199689	+	0.422248i	−0.000783246	+	0.0165619i
$651$	−9.67726			−0.379282
$652$	−10.0403	+	7.29474i	−0.393210	+	0.285684i
$653$	10.0463	−	30.9193i	0.393142	−	1.20997i	−0.537257	−	0.843418i	$-0.680540\pi$
$653$	10.0463	−	30.9193i	0.393142	−	1.20997i	0.930399	−	0.366548i	$-0.119460\pi$
$654$	−0.0633220	+	0.194885i	−0.00247609	+	0.00762062i
$655$	20.6174	−	38.2047i	0.805590	−	1.49278i
$656$	6.47423	+	19.9256i	0.252776	+	0.777966i
$657$	−3.83968			−0.149800
$658$	−0.0350190	−	0.107777i	−0.00136518	−	0.00420159i
$659$	−11.4083	−	8.28858i	−0.444403	−	0.322877i	0.342979	−	0.939343i	$-0.388564\pi$
$659$	−11.4083	−	8.28858i	−0.444403	−	0.322877i	−0.787382	+	0.616466i	$0.788564\pi$
$660$	−15.2334	−	15.9708i	−0.592958	−	0.621663i
$661$	−10.9155	+	7.93054i	−0.424562	+	0.308462i	−0.779471	−	0.626439i	$-0.784512\pi$
$661$	−10.9155	+	7.93054i	−0.424562	+	0.308462i	0.354909	+	0.934901i	$0.384512\pi$
$662$	0.373008	+	0.271006i	0.0144974	+	0.0105330i
$663$	−11.5187	−	8.36886i	−0.447351	−	0.325020i
$664$	−0.258066	+	0.187496i	−0.0100149	+	0.00727624i
$665$	−3.37713	+	6.25793i	−0.130960	+	0.242672i
$666$	0.00208252	+	0.00151304i	8.06962e−5	+	5.86292e-5i
$667$	−17.1238	−	52.7017i	−0.663037	−	2.04062i
$668$	−3.84897			−0.148921
$669$	−3.67762	−	11.3185i	−0.142185	−	0.437600i
$670$	0.0119694	+	0.0891580i	0.000462418	+	0.00344447i
$671$	−16.8391	+	51.8254i	−0.650065	+	2.00070i
$672$	0.0663084	−	0.204076i	0.00255790	−	0.00787242i
$673$	13.9708	−	10.1503i	0.538533	−	0.391267i	−0.285007	−	0.958525i	$-0.591996\pi$
$673$	13.9708	−	10.1503i	0.538533	−	0.391267i	0.823540	+	0.567258i	$0.191996\pi$
$674$	−0.338896			−0.0130538
$675$	−2.74456	−	4.17940i	−0.105638	−	0.160865i
$676$	−18.6860			−0.718692
$677$	−18.0805	+	13.1362i	−0.694888	+	0.504866i	−0.878263	−	0.478177i	$-0.841298\pi$
$677$	−18.0805	+	13.1362i	−0.694888	+	0.504866i	0.183375	+	0.983043i	$0.441298\pi$
$678$	0.0556969	−	0.171417i	0.00213903	−	0.00658324i
$679$	−5.87431	+	18.0793i	−0.225435	+	0.693818i
$680$	−0.473958	−	0.0865927i	−0.0181755	−	0.00332068i
$681$	−1.11629	−	3.43560i	−0.0427764	−	0.131652i
$682$	0.854326			0.0327138
$683$	−0.380264	−	1.17033i	−0.0145504	−	0.0447815i	0.943518	−	0.331322i	$-0.107495\pi$
$683$	−0.380264	−	1.17033i	−0.0145504	−	0.0447815i	−0.958068	+	0.286541i	$0.907495\pi$
$684$	−5.14477	−	3.73789i	−0.196715	−	0.142922i
$685$	−0.308568	−	2.29847i	−0.0117898	−	0.0878200i
$686$	−0.0144696	+	0.0105128i	−0.000552450	+	0.000401379i
$687$	−15.8752	−	11.5340i	−0.605676	−	0.440049i
$688$	−24.2735	−	17.6357i	−0.925419	−	0.672357i
$689$	42.3532	−	30.7714i	1.61353	−	1.17230i
$690$	−0.0373332	−	0.278089i	−0.00142125	−	0.0105867i
$691$	11.3102	+	8.21731i	0.430258	+	0.312601i	0.781752	−	0.623589i	$-0.214326\pi$
$691$	11.3102	+	8.21731i	0.430258	+	0.312601i	−0.351494	+	0.936190i	$0.614326\pi$
$692$	11.2484	+	34.6189i	0.427599	+	1.31601i
$693$	−4.93598			−0.187502
$694$	−0.110919	−	0.341374i	−0.00421044	−	0.0129584i
$695$	−42.5488	−	7.77372i	−1.61397	−	0.294874i
$696$	−0.174600	+	0.537362i	−0.00661818	+	0.0203687i
$697$	4.87752	−	15.0115i	0.184749	−	0.568600i
$698$	0.0472521	−	0.0343307i	0.00178852	−	0.00129944i
$699$	2.27111			0.0859013
$700$	−9.35247	−	3.53543i	−0.353490	−	0.133627i
$701$	22.6795			0.856594			0.428297	−	0.903638i	$-0.359114\pi$
$701$	22.6795			0.856594			0.428297	+	0.903638i	$0.359114\pi$
$702$	−0.0683976	+	0.0496937i	−0.00258150	+	0.00187557i
$703$	0.141438	−	0.435300i	0.00533442	−	0.0164176i
$704$	12.1907	−	37.5191i	0.459454	−	1.41406i
$705$	−1.88513	−	14.0420i	−0.0709980	−	0.528853i
$706$	0.0259793	+	0.0799559i	0.000977742	+	0.00300918i
$707$	11.8789			0.446750
$708$	2.31711	+	7.13134i	0.0870824	+	0.268012i
$709$	42.4077	+	30.8110i	1.59266	+	1.15713i	0.900023	+	0.435843i	$0.143550\pi$
$709$	42.4077	+	30.8110i	1.59266	+	1.15713i	0.692634	+	0.721289i	$0.256450\pi$
$710$	0.223147	−	0.413499i	0.00837457	−	0.0155183i
$711$	8.12961	−	5.90651i	0.304884	−	0.221511i
$712$	−0.122139	−	0.0887391i	−0.00457735	−	0.00332564i
$713$	−54.9276	−	39.9072i	−2.05705	−	1.49454i
$714$	−0.0435831	+	0.0316649i	−0.00163105	+	0.00118503i
$715$	36.0098	+	37.7530i	1.34669	+	1.41188i
$716$	−11.0553	−	8.03214i	−0.413156	−	0.300175i
$717$	−2.05335	−	6.31957i	−0.0766839	−	0.236009i
$718$	−0.0742548			−0.00277117
$719$	−1.65985	−	5.10849i	−0.0619019	−	0.190514i	0.915323	−	0.402720i	$-0.131935\pi$
$719$	−1.65985	−	5.10849i	−0.0619019	−	0.190514i	−0.977225	+	0.212206i	$0.931935\pi$
$720$	4.24573	−	7.86747i	0.158229	−	0.293203i
$721$	−1.29250	+	3.97791i	−0.0481353	+	0.148145i
$722$	−0.0491154	+	0.151162i	−0.00182789	+	0.00562566i
$723$	8.38371	−	6.09113i	0.311794	−	0.226531i
$724$	8.37226			0.311152
$725$	36.9406	+	13.9643i	1.37194	+	0.518621i
$726$	0.239018			0.00887079
$727$	−16.1849	+	11.7590i	−0.600263	+	0.436117i	−0.845972	−	0.533227i	$-0.820979\pi$
$727$	−16.1849	+	11.7590i	−0.600263	+	0.436117i	0.245709	+	0.969344i	$0.420979\pi$
$728$	−0.104494	+	0.321599i	−0.00387280	+	0.0119192i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	0.138432	−	0.0664626i	0.00512359	−	0.00245989i
$731$	6.98503	+	21.4977i	0.258351	+	0.795122i
$732$	−22.0761			−0.815958
$733$	−0.481573	−	1.48213i	−0.0177873	−	0.0547437i	0.941769	−	0.336261i	$-0.109162\pi$
$733$	−0.481573	−	1.48213i	−0.0177873	−	0.0547437i	−0.959556	+	0.281517i	$0.909162\pi$
$734$	−0.277782	−	0.201820i	−0.0102531	−	0.00744933i
$735$	−2.01578	+	0.967799i	−0.0743531	+	0.0356978i
$736$	1.21794	−	0.884882i	0.0448937	−	0.0326172i
$737$	8.98229	+	6.52602i	0.330867	+	0.240389i
$738$	−0.0758246	−	0.0550898i	−0.00279114	−	0.00202788i
$739$	−0.316704	+	0.230099i	−0.0116501	+	0.00846433i	−0.593595	−	0.804764i	$-0.702292\pi$
$739$	−0.316704	+	0.230099i	−0.0116501	+	0.00846433i	0.581945	+	0.813228i	$0.302292\pi$
$740$	0.633068	+	0.115662i	0.0232720	+	0.00425183i
$741$	12.1616	+	8.83591i	0.446767	+	0.324595i
$742$	−0.0612101	−	0.188385i	−0.00224709	−	0.00691584i
$743$	−7.02511			−0.257726			−0.128863	−	0.991662i	$-0.541133\pi$
$743$	−7.02511			−0.257726			−0.128863	+	0.991662i	$0.541133\pi$
$744$	0.213923	+	0.658388i	0.00784281	+	0.0241377i
$745$	4.33591	+	4.54581i	0.158856	+	0.166546i
$746$	−0.123450	+	0.379940i	−0.00451982	+	0.0139106i
$747$	−1.37795	+	4.24088i	−0.0504164	+	0.155166i
$748$	−24.0521	+	17.4749i	−0.879434	+	0.638946i
$749$	9.80164			0.358144
$750$	0.171292	+	0.103173i	0.00625472	+	0.00376734i
$751$	−42.4390			−1.54862			−0.774311	−	0.632806i	$-0.781903\pi$
$751$	−42.4390			−1.54862			−0.774311	+	0.632806i	$0.781903\pi$
$752$	20.4943	−	14.8900i	0.747349	−	0.542981i
$753$	6.34536	−	19.5290i	0.231238	−	0.711676i
$754$	0.206349	−	0.635078i	0.00751480	−	0.0231282i
$755$	30.9558	+	32.4544i	1.12660	+	1.18114i
$756$	−0.617935	−	1.90181i	−0.0224741	−	0.0691681i
$757$	36.8287			1.33856			0.669281	−	0.743009i	$-0.266602\pi$
$757$	36.8287			1.33856			0.669281	+	0.743009i	$0.266602\pi$
$758$	−0.155702	−	0.479201i	−0.00565534	−	0.0174054i
$759$	−28.0163	−	20.3551i	−1.01693	−	0.738842i
$760$	0.500410	+	0.0914254i	0.0181518	+	0.00331635i
$761$	32.3903	−	23.5330i	1.17415	−	0.853069i	0.182649	−	0.983178i	$-0.441533\pi$
$761$	32.3903	−	23.5330i	1.17415	−	0.853069i	0.991500	+	0.130109i	$0.0415328\pi$
$762$	−0.0935098	−	0.0679388i	−0.00338750	−	0.00246116i
$763$	9.26899	+	6.73432i	0.335560	+	0.243799i
$764$	0.0647871	−	0.0470706i	0.00234391	−	0.00170295i
$765$	−6.07163	+	2.91506i	−0.219520	+	0.105394i
$766$	0.0894919	+	0.0650197i	0.00323347	+	0.00234926i
$767$	−5.47737	−	16.8576i	−0.197776	−	0.608693i
$768$	15.9744			0.576427
$769$	6.13185	+	18.8719i	0.221120	+	0.680538i	0.998662	+	0.0517070i	$0.0164662\pi$
$769$	6.13185	+	18.8719i	0.221120	+	0.680538i	−0.777542	+	0.628831i	$0.783534\pi$
$770$	0.177957	−	0.0854390i	0.00641311	−	0.00307901i
$771$	−2.68024	+	8.24894i	−0.0965265	+	0.297078i
$772$	9.63989	−	29.6685i	0.346947	−	1.06779i
$773$	−2.79069	+	2.02756i	−0.100374	+	0.0729261i	−0.636840	−	0.770996i	$-0.719759\pi$
$773$	−2.79069	+	2.02756i	−0.100374	+	0.0729261i	0.536466	+	0.843922i	$0.319759\pi$
$774$	0.134221			0.00482448
$775$	46.6731	−	12.7616i	1.67655	−	0.458412i
$776$	1.35987			0.0488165
$777$	0.116437	−	0.0845967i	0.00417717	−	0.00303489i
$778$	0.0188737	−	0.0580873i	0.000676655	−	0.00208253i
$779$	−5.14973	+	15.8492i	−0.184508	+	0.567858i
$780$	−10.0380	+	18.6007i	−0.359418	+	0.666012i
$781$	−17.9205	−	55.1535i	−0.641244	−	1.97355i
$782$	−0.377955			−0.0135156
$783$	2.44073	+	7.51180i	0.0872247	+	0.268450i
$784$	−3.23452	−	2.35001i	−0.115518	−	0.0839290i
$785$	6.19033	+	6.49000i	0.220942	+	0.231638i
$786$	−0.280924	+	0.204103i	−0.0100202	+	0.00728013i
$787$	−36.8748	−	26.7911i	−1.31444	−	0.954999i	−0.999984	−	0.00572884i	$-0.998176\pi$
$787$	−36.8748	−	26.7911i	−1.31444	−	0.954999i	−0.314460	−	0.949271i	$-0.601824\pi$
$788$	41.2091	+	29.9402i	1.46801	+	1.06657i
$789$	−5.22564	+	3.79665i	−0.186038	+	0.135164i
$790$	−0.190858	+	0.353666i	−0.00679042	+	0.0125829i
$791$	−8.15283	−	5.92338i	−0.289881	−	0.210611i
$792$	0.109114	+	0.335817i	0.00387718	+	0.0119327i
$793$	52.1853			1.85315
$794$	0.0794356	+	0.244478i	0.00281906	+	0.00867618i
$795$	−3.29504	−	24.5442i	−0.116863	−	0.870494i
$796$	0.695041	−	2.13912i	0.0246351	−	0.0758189i
$797$	−4.23389	+	13.0306i	−0.149972	+	0.461566i	−0.997617	−	0.0689977i	$-0.978020\pi$
$797$	−4.23389	+	13.0306i	−0.149972	+	0.461566i	0.847645	+	0.530564i	$0.178020\pi$
$798$	0.0460154	−	0.0334321i	0.00162893	−	0.00118348i
$799$	−19.0847			−0.675168
$800$	−0.0506825	+	1.07170i	−0.00179190	+	0.0378901i
$801$	−2.11044			−0.0745688
$802$	0.0788969	−	0.0573220i	0.00278595	−	0.00202411i
$803$	5.85667	−	18.0250i	0.206677	−	0.636087i
$804$	−1.38995	+	4.27783i	−0.0490198	+	0.150867i
$805$	−15.4325	−	2.81953i	−0.543923	−	0.0993753i
$806$	−0.252824	−	0.778112i	−0.00890534	−	0.0274078i
$807$	−4.98830			−0.175596
$808$	−0.262591	−	0.808172i	−0.00923792	−	0.0284314i
$809$	−6.53089	−	4.74497i	−0.229614	−	0.166824i	0.467030	−	0.884242i	$-0.345324\pi$
$809$	−6.53089	−	4.74497i	−0.229614	−	0.166824i	−0.696644	+	0.717417i	$0.745324\pi$
$810$	0.00532127	+	0.0396373i	0.000186970	+	0.00139271i
$811$	17.7751	−	12.9144i	0.624169	−	0.453485i	−0.230206	−	0.973142i	$-0.573940\pi$
$811$	17.7751	−	12.9144i	0.624169	−	0.453485i	0.854375	+	0.519657i	$0.173940\pi$
$812$	12.7778	+	9.28361i	0.448413	+	0.325791i
$813$	−11.0449	−	8.02460i	−0.387362	−	0.281435i
$814$	−0.0102793	+	0.00746835i	−0.000360289	+	0.000261765i
$815$	−1.84650	−	13.7542i	−0.0646800	−	0.481790i
$816$	−9.74252	−	7.07836i	−0.341057	−	0.247792i
$817$	−7.37486	−	22.6975i	−0.258014	−	0.794084i
$818$	0.136059			0.00475720
$819$	1.46072	+	4.49564i	0.0510418	+	0.157090i
$820$	−23.0500	−	4.21125i	−0.804939	−	0.147063i
$821$	−3.81358	+	11.7370i	−0.133095	+	0.409624i	−0.995289	−	0.0969542i	$-0.969090\pi$
$821$	−3.81358	+	11.7370i	−0.133095	+	0.409624i	0.862194	+	0.506579i	$0.169090\pi$
$822$	−0.00573208	+	0.0176415i	−0.000199929	+	0.000615319i
$823$	14.5477	−	10.5696i	0.507102	−	0.368432i	−0.304621	−	0.952474i	$-0.598530\pi$
$823$	14.5477	−	10.5696i	0.507102	−	0.368432i	0.811723	+	0.584042i	$0.198530\pi$
$824$	0.299207			0.0104234
$825$	23.8060	−	6.50920i	0.828820	−	0.226621i
$826$	−0.0670659			−0.00233352
$827$	−39.6010	+	28.7718i	−1.37706	+	1.00049i	−0.379914	+	0.925022i	$0.624046\pi$
$827$	−39.6010	+	28.7718i	−1.37706	+	1.00049i	−0.997148	+	0.0754721i	$0.975954\pi$
$828$	4.33534	−	13.3428i	0.150663	−	0.463694i
$829$	−9.83644	+	30.2735i	−0.341634	+	1.05144i	0.621728	+	0.783234i	$0.286431\pi$
$829$	−9.83644	+	30.2735i	−0.341634	+	1.05144i	−0.963361	+	0.268207i	$0.913569\pi$
$830$	−0.0237282	−	0.176748i	−0.000823619	−	0.00613500i
$831$	−1.45689	−	4.48384i	−0.0505389	−	0.155543i
$832$	−37.7797			−1.30977
$833$	0.930775	+	2.86463i	0.0322494	+	0.0992536i
$834$	0.279890	+	0.203352i	0.00969181	+	0.00704151i
$835$	2.04402	−	3.78763i	0.0707363	−	0.131076i
$836$	25.3945	−	18.4502i	0.878286	−	0.638112i
$837$	7.82907	+	5.68815i	0.270612	+	0.196611i
$838$	0.232323	+	0.168792i	0.00802545	+	0.00583083i
$839$	38.3307	−	27.8489i	1.32332	−	0.961451i	0.323439	−	0.946249i	$-0.395161\pi$
$839$	38.3307	−	27.8489i	1.32332	−	0.961451i	0.999884	−	0.0152015i	$-0.00483896\pi$
$840$	0.110404	+	0.115749i	0.00380930	+	0.00399371i
$841$	−27.0085	−	19.6228i	−0.931328	−	0.676649i
$842$	−0.137253	−	0.422420i	−0.00473004	−	0.0145576i
$843$	−20.5281			−0.707026
$844$	−12.4678	−	38.3721i	−0.429161	−	1.32082i
$845$	9.92331	−	18.3882i	0.341372	−	0.632573i
$846$	−0.0350190	+	0.107777i	−0.00120398	+	0.00370546i
$847$	4.12967	−	12.7098i	0.141897	−	0.436715i
$848$	35.8222	−	26.0263i	1.23014	−	0.893748i
$849$	21.9231			0.752400
$850$	0.168442	−	0.210193i	0.00577752	−	0.00720956i
$851$	1.00975			0.0346139
$852$	19.0069	−	13.8093i	0.651166	−	0.473100i
$853$	5.22996	−	16.0962i	0.179070	−	0.551122i	−0.820725	−	0.571323i	$-0.806430\pi$
$853$	5.22996	−	16.0962i	0.179070	−	0.551122i	0.999796	+	0.0202005i	$0.00643046\pi$
$854$	0.0610159	−	0.187787i	0.00208792	−	0.00642596i
$855$	6.41048	−	3.07774i	0.219234	−	0.105257i
$856$	−0.216673	−	0.666850i	−0.00740572	−	0.0227925i
$857$	9.61903			0.328580			0.164290	−	0.986412i	$-0.447467\pi$
$857$	9.61903			0.328580			0.164290	+	0.986412i	$0.447467\pi$
$858$	−0.128955	−	0.396883i	−0.00440246	−	0.0135494i
$859$	2.13064	+	1.54800i	0.0726967	+	0.0528172i	0.623540	−	0.781791i	$-0.285694\pi$
$859$	2.13064	+	1.54800i	0.0726967	+	0.0528172i	−0.550843	+	0.834609i	$0.685694\pi$
$860$	30.2501	−	14.5234i	1.03152	−	0.495245i
$861$	−4.23948	+	3.08016i	−0.144481	+	0.104972i
$862$	−0.440427	−	0.319989i	−0.0150010	−	0.0108989i
$863$	24.2235	+	17.5994i	0.824577	+	0.599090i	0.918020	−	0.396534i	$-0.129787\pi$
$863$	24.2235	+	17.5994i	0.824577	+	0.599090i	−0.0934427	+	0.995625i	$0.529787\pi$
$864$	−0.173598	+	0.126126i	−0.00590591	+	0.00429090i
$865$	−40.0407	−	7.31548i	−1.36142	−	0.248734i
$866$	−0.417951	−	0.303659i	−0.0142025	−	0.0103187i
$867$	−2.44975	−	7.53955i	−0.0831978	−	0.256056i
$868$	19.3514			0.656830
$869$	15.3274	+	47.1728i	0.519946	+	1.60023i
$870$	−0.218021	−	0.228575i	−0.00739159	−	0.00774941i
$871$	3.28567	−	10.1123i	0.111331	−	0.342641i
$872$	0.253268	−	0.779479i	0.00857673	−	0.0263965i
$873$	15.3791	−	11.1736i	0.520505	−	0.378169i
$874$	0.399048			0.0134980
$875$	8.44577	−	7.32591i	0.285519	−	0.247661i
$876$	7.67813			0.259420
$877$	24.7298	−	17.9673i	0.835067	−	0.606712i	−0.0859213	−	0.996302i	$-0.527383\pi$
$877$	24.7298	−	17.9673i	0.835067	−	0.606712i	0.920988	+	0.389590i	$0.127383\pi$
$878$	−0.0221825	+	0.0682709i	−0.000748625	+	0.00230403i
$879$	−0.338779	+	1.04265i	−0.0114267	+	0.0351678i
$880$	30.4570	+	31.9314i	1.02670	+	1.07641i
$881$	2.42324	+	7.45796i	0.0816410	+	0.251265i	0.983543	−	0.180676i	$-0.0578287\pi$
$881$	2.42324	+	7.45796i	0.0816410	+	0.251265i	−0.901902	+	0.431942i	$0.857829\pi$
$882$	0.0178854			0.000602231
$883$	3.06607	+	9.43638i	0.103181	+	0.317559i	0.989299	−	0.145900i	$-0.0466079\pi$
$883$	3.06607	+	9.43638i	0.103181	+	0.317559i	−0.886118	+	0.463460i	$0.846608\pi$
$884$	23.0338	+	16.7350i	0.774711	+	0.562860i
$885$	−8.24820	−	1.50696i	−0.277260	−	0.0506558i
$886$	−0.374646	+	0.272196i	−0.0125865	+	0.00914460i
$887$	−8.62265	−	6.26472i	−0.289520	−	0.210349i	0.433539	−	0.901135i	$-0.357265\pi$
$887$	−8.62265	−	6.26472i	−0.289520	−	0.210349i	−0.723059	+	0.690786i	$0.757265\pi$
$888$	−0.00832943	−	0.00605169i	−0.000279517	−	0.000203081i
$889$	−5.22829	+	3.79857i	−0.175351	+	0.127400i
$890$	0.0760876	−	0.0365305i	0.00255046	−	0.00122451i
$891$	3.99329	+	2.90130i	0.133780	+	0.0971971i
$892$	7.35406	+	22.6335i	0.246232	+	0.757825i
$893$	20.1498			0.674287
$894$	−0.0155274	−	0.0477884i	−0.000519314	−	0.00159828i
$895$	13.7751	−	6.61359i	0.460451	−	0.221068i
$896$	−0.176789	+	0.544102i	−0.00590612	+	0.0181772i
$897$	−10.2482	+	31.5407i	−0.342178	+	1.05311i
$898$	0.158500	−	0.115157i	0.00528923	−	0.00384285i
$899$	−76.4347			−2.54924
$900$	5.48824	+	8.35747i	0.182941	+	0.278582i
$901$	−33.3584			−1.11133
$902$	0.374268	−	0.271922i	0.0124618	−	0.00905401i
$903$	2.31903	−	7.13723i	0.0771724	−	0.237512i
$904$	−0.222770	+	0.685615i	−0.00740921	+	0.0228032i
$905$	−4.44614	+	8.23883i	−0.147795	+	0.273868i
$906$	−0.110856	−	0.341181i	−0.00368295	−	0.0113350i
$907$	9.78704			0.324973			0.162487	−	0.986711i	$-0.448049\pi$
$907$	9.78704			0.324973			0.162487	+	0.986711i	$0.448049\pi$
$908$	2.23223	+	6.87009i	0.0740791	+	0.227992i
$909$	−9.61020	−	6.98222i	−0.318750	−	0.231585i
$910$	−0.130480	−	0.136797i	−0.00432538	−	0.00453477i
$911$	−47.1466	+	34.2540i	−1.56204	+	1.13489i	−0.627720	+	0.778439i	$0.716012\pi$
$911$	−47.1466	+	34.2540i	−1.56204	+	1.13489i	−0.934316	+	0.356446i	$0.883988\pi$
$912$	10.2862	+	7.47339i	0.340612	+	0.247469i
$913$	−17.8066	−	12.9372i	−0.589312	−	0.428160i
$914$	0.123198	−	0.0895089i	0.00407504	−	0.00296069i
$915$	11.7237	−	21.7243i	0.387572	−	0.718184i
$916$	31.7453	+	23.0643i	1.04889	+	0.762066i
$917$	5.99952	+	18.4646i	0.198122	+	0.609755i
$918$	0.0538716			0.00177803
$919$	−17.0340	−	52.4251i	−0.561899	−	1.72935i	−0.676991	−	0.735991i	$-0.736717\pi$
$919$	−17.0340	−	52.4251i	−0.561899	−	1.72935i	0.115093	−	0.993355i	$-0.463283\pi$
$920$	0.149321	+	1.11227i	0.00492297	+	0.0366704i
$921$	−4.53364	+	13.9531i	−0.149389	+	0.459771i
$922$	−0.0312059	+	0.0960419i	−0.00102771	+	0.00316297i
$923$	−44.9300	+	32.6435i	−1.47889	+	1.07448i
$924$	9.87038			0.324712
$925$	−0.450013	+	0.561555i	−0.0147963	+	0.0184638i
$926$	−0.473644			−0.0155649
$927$	3.38381	−	2.45849i	0.111139	−	0.0807473i
$928$	0.523729	−	1.61187i	0.0171922	−	0.0529123i
$929$	2.96277	−	9.11847i	0.0972054	−	0.299167i	−0.890617	−	0.454755i	$-0.849727\pi$
$929$	2.96277	−	9.11847i	0.0972054	−	0.299167i	0.987822	+	0.155587i	$0.0497270\pi$
$930$	−0.380720	−	0.0695579i	−0.0124843	−	0.00228089i
$931$	−0.982720	−	3.02450i	−0.0322074	−	0.0991241i
$932$	−4.54150			−0.148762
$933$	−1.43739	−	4.42382i	−0.0470579	−	0.144829i
$934$	0.521075	+	0.378583i	0.0170501	+	0.0123876i
$935$	−4.42337	−	32.9490i	−0.144660	−	1.07755i
$936$	0.273568	−	0.198759i	0.00894186	−	0.00649664i
$937$	−3.78333	−	2.74875i	−0.123596	−	0.0897978i	0.524270	−	0.851552i	$-0.324338\pi$
$937$	−3.78333	−	2.74875i	−0.123596	−	0.0897978i	−0.647866	+	0.761754i	$0.724338\pi$
$938$	−0.0325470	−	0.0236468i	−0.00106270	−	0.000772096i
$939$	27.0340	−	19.6414i	0.882222	−	0.640972i
$940$	3.76965	+	28.0795i	0.122953	+	0.915853i
$941$	−6.22234	−	4.52079i	−0.202842	−	0.147374i	0.481727	−	0.876321i	$-0.340010\pi$
$941$	−6.22234	−	4.52079i	−0.202842	−	0.147374i	−0.684569	+	0.728948i	$0.740010\pi$
$942$	−0.0221683	−	0.0682269i	−0.000722282	−	0.00222295i
$943$	−36.7650			−1.19723
$944$	−4.63274	−	14.2581i	−0.150783	−	0.464062i
$945$	2.19966	+	0.401880i	0.0715549	+	0.0130731i
$946$	−0.204728	+	0.630088i	−0.00665628	+	0.0204859i
$947$	0.967549	−	2.97781i	0.0314411	−	0.0967658i	−0.934104	−	0.357000i	$-0.883800\pi$
$947$	0.967549	−	2.97781i	0.0314411	−	0.0967658i	0.965546	+	0.260234i	$0.0837997\pi$
$948$	−16.2566	+	11.8111i	−0.527990	+	0.383607i
$949$	−18.1501			−0.589179
$950$	−0.177843	+	0.221923i	−0.00576998	+	0.00720015i
$951$	11.2945			0.366250
$952$	0.174318	−	0.126650i	0.00564969	−	0.00410474i
$953$	−5.33167	+	16.4092i	−0.172710	+	0.531546i	−0.999521	−	0.0309329i	$-0.990152\pi$
$953$	−5.33167	+	16.4092i	−0.172710	+	0.531546i	0.826812	+	0.562479i	$0.190152\pi$
$954$	−0.0612101	+	0.188385i	−0.00198175	+	0.00609920i
$955$	0.0119148	+	0.0887517i	0.000385555	+	0.00287194i
$956$	4.10605	+	12.6371i	0.132799	+	0.408714i
$957$	−38.9862			−1.26025
$958$	0.0177430	+	0.0546075i	0.000573251	+	0.00176429i
$959$	0.839054	+	0.609609i	0.0270945	+	0.0196853i
$960$	−8.48738	+	15.7274i	−0.273929	+	0.507599i
$961$	−50.6845	+	36.8244i	−1.63498	+	1.18788i
$962$	0.00984408	+	0.00715215i	0.000317386	+	0.000230594i
$963$	−7.92969	−	5.76126i	−0.255531	−	0.185654i
$964$	−16.7647	+	12.1803i	−0.539956	+	0.392301i
$965$	24.0764	+	25.2419i	0.775046	+	0.812566i
$966$	0.101516	+	0.0737559i	0.00326623	+	0.00237306i
$967$	−7.02868	−	21.6321i	−0.226027	−	0.695640i	−0.998186	−	0.0602101i	$-0.980823\pi$
$967$	−7.02868	−	21.6321i	−0.226027	−	0.695640i	0.772159	−	0.635430i	$-0.219177\pi$
$968$	−0.955996			−0.0307269
$969$	−2.96000	−	9.10995i	−0.0950890	−	0.292654i
$970$	−0.361055	+	0.669045i	−0.0115928	+	0.0214817i
$971$	7.75427	−	23.8652i	0.248846	−	0.765870i	−0.746134	−	0.665796i	$-0.768092\pi$
$971$	7.75427	−	23.8652i	0.248846	−	0.765870i	0.994980	−	0.100074i	$-0.0319080\pi$
$972$	−0.617935	+	1.90181i	−0.0198203	+	0.0610005i
$973$	15.6491	−	11.3698i	0.501688	−	0.364498i
$974$	−0.145794			−0.00467156
$975$	−12.9735	−	19.7560i	−0.415485	−	0.632699i
$976$	44.1382			1.41283
$977$	−48.8346	+	35.4804i	−1.56236	+	1.13512i	−0.628315	+	0.777959i	$0.716255\pi$
$977$	−48.8346	+	35.4804i	−1.56236	+	1.13512i	−0.934043	+	0.357161i	$0.883745\pi$
$978$	−0.0343013	+	0.105569i	−0.00109683	+	0.00337571i
$979$	3.21906	−	9.90725i	0.102882	−	0.316637i
$980$	4.03091	−	1.93529i	0.128763	−	0.0618205i
$981$	−3.54044	−	10.8964i	−0.113038	−	0.347894i
$982$	−0.330499			−0.0105467
$983$	1.24657	+	3.83655i	0.0397594	+	0.122367i	0.968966	−	0.247193i	$-0.0795083\pi$
$983$	1.24657	+	3.83655i	0.0397594	+	0.122367i	−0.929207	+	0.369560i	$0.879508\pi$
$984$	0.303274	+	0.220341i	0.00966802	+	0.00702423i
$985$	−51.3474	+	24.6525i	−1.63606	+	0.785493i
$986$	−0.344235	+	0.250102i	−0.0109627	+	0.00796486i
$987$	5.12603	+	3.72428i	0.163163	+	0.118545i
$988$	−24.3193	−	17.6690i	−0.773700	−	0.562126i
$989$	42.5953	−	30.9473i	1.35445	−	0.984066i
$990$	−0.194190	−	0.0354787i	−0.00617175	−	0.00112759i
$991$	−38.0849	−	27.6703i	−1.20981	−	0.878975i	−0.214593	−	0.976704i	$-0.568842\pi$
$991$	−38.0849	−	27.6703i	−1.20981	−	0.878975i	−0.995213	+	0.0977282i	$0.968842\pi$
$992$	−0.641684	−	1.97490i	−0.0203735	−	0.0627032i
$993$	−25.7788			−0.818066
$994$	0.0649342	+	0.199847i	0.00205959	+	0.00633876i
$995$	1.73592	+	1.81995i	0.0550323	+	0.0576964i
$996$	2.75545	−	8.48040i	0.0873098	−	0.268712i
$997$	−16.5166	+	50.8330i	−0.523087	+	1.60990i	0.244979	+	0.969528i	$0.421219\pi$
$997$	−16.5166	+	50.8330i	−0.523087	+	1.60990i	−0.768067	+	0.640370i	$0.778781\pi$
$998$	0.168308	−	0.122283i	0.00532771	−	0.00387081i
$999$	−0.143924			−0.00455357

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.n.c.211.3	✓	24
25.16	even	5	inner	525.2.n.c.316.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.n.c.211.3	✓	24	1.1	even	1	trivial
525.2.n.c.316.3	yes	24	25.16	even	5	inner

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0144696 + 0.0105128i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.617935 + 1.90181i) q^{4} +(-1.54334 - 1.61805i) q^{5} +(0.00552688 + 0.0170100i) q^{6} +1.00000 q^{7} +(-0.0221058 - 0.0680345i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.0144696 + 0.0105128i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.617935 + 1.90181i) q^{4} +(-1.54334 - 1.61805i) q^{5} +(0.00552688 + 0.0170100i) q^{6} +1.00000 q^{7} +(-0.0221058 - 0.0680345i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(0.0393417 + 0.00718776i) q^{10} +(3.99329 - 2.90130i) q^{11} +(1.61778 + 1.17538i) q^{12} +(-3.82422 - 2.77846i) q^{13} +(-0.0144696 + 0.0105128i) q^{14} +(-2.01578 + 0.967799i) q^{15} +(-3.23452 - 2.35001i) q^{16} +(0.930775 + 2.86463i) q^{17} +0.0178854 q^{18} +(-0.982720 - 3.02450i) q^{19} +(4.03091 - 1.93529i) q^{20} +(0.309017 - 0.951057i) q^{21} +(-0.0272806 + 0.0839610i) q^{22} +(5.67594 - 4.12381i) q^{23} -0.0715357 q^{24} +(-0.236196 + 4.99442i) q^{25} +0.0845440 q^{26} +(-0.809017 + 0.587785i) q^{27} +(-0.617935 + 1.90181i) q^{28} +(2.44073 - 7.51180i) q^{29} +(0.0189932 - 0.0351950i) q^{30} +(-2.99044 - 9.20362i) q^{31} +0.214579 q^{32} +(-1.52530 - 4.69440i) q^{33} +(-0.0435831 - 0.0316649i) q^{34} +(-1.54334 - 1.61805i) q^{35} +(1.61778 - 1.17538i) q^{36} +(0.116437 + 0.0845967i) q^{37} +(0.0460154 + 0.0334321i) q^{38} +(-3.82422 + 2.77846i) q^{39} +(-0.0759668 + 0.140769i) q^{40} +(-4.23948 - 3.08016i) q^{41} +(0.00552688 + 0.0170100i) q^{42} +7.50453 q^{43} +(3.05012 + 9.38729i) q^{44} +(0.297521 + 2.21619i) q^{45} +(-0.0387758 + 0.119340i) q^{46} +(-1.95797 + 6.02600i) q^{47} +(-3.23452 + 2.35001i) q^{48} +1.00000 q^{49} +(-0.0490874 - 0.0747501i) q^{50} +3.01205 q^{51} +(7.64722 - 5.55603i) q^{52} +(-3.42236 + 10.5329i) q^{53} +(0.00552688 - 0.0170100i) q^{54} +(-10.8575 - 1.98367i) q^{55} +(-0.0221058 - 0.0680345i) q^{56} -3.18015 q^{57} +(0.0436534 + 0.134351i) q^{58} +(3.03363 + 2.20406i) q^{59} +(-0.594947 - 4.43166i) q^{60} +(-8.93142 + 6.48905i) q^{61} +(0.140026 + 0.101735i) q^{62} +(-0.809017 - 0.587785i) q^{63} +(6.46593 - 4.69777i) q^{64} +(1.40638 + 10.4759i) q^{65} +(0.0714215 + 0.0518907i) q^{66} +(0.695086 + 2.13926i) q^{67} -6.02314 q^{68} +(-2.16802 - 6.67247i) q^{69} +(0.0393417 + 0.00718776i) q^{70} +(3.63058 - 11.1738i) q^{71} +(-0.0221058 + 0.0680345i) q^{72} +(3.10637 - 2.25691i) q^{73} -0.00257414 q^{74} +(4.67699 + 1.76800i) q^{75} +6.35928 q^{76} +(3.99329 - 2.90130i) q^{77} +(0.0261255 - 0.0804062i) q^{78} +(-3.10523 + 9.55693i) q^{79} +(1.18951 + 8.86049i) q^{80} +(0.309017 + 0.951057i) q^{81} +0.0937243 q^{82} +(-1.37795 - 4.24088i) q^{83} +(1.61778 + 1.17538i) q^{84} +(3.19862 - 5.92715i) q^{85} +(-0.108587 + 0.0788933i) q^{86} +(-6.38992 - 4.64255i) q^{87} +(-0.285663 - 0.207546i) q^{88} +(1.70738 - 1.24049i) q^{89} +(-0.0276032 - 0.0289395i) q^{90} +(-3.82422 - 2.77846i) q^{91} +(4.33534 + 13.3428i) q^{92} -9.67726 q^{93} +(-0.0350190 - 0.107777i) q^{94} +(-3.37713 + 6.25793i) q^{95} +(0.0663084 - 0.204076i) q^{96} +(-5.87431 + 18.0793i) q^{97} +(-0.0144696 + 0.0105128i) q^{98} -4.93598 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} - 6 q^{3} - 9 q^{4} - q^{5} + q^{6} + 24 q^{7} + 9 q^{8} - 6 q^{9}+O(q^{10}) \) 24 * q + q^2 - 6 * q^3 - 9 * q^4 - q^5 + q^6 + 24 * q^7 + 9 * q^8 - 6 * q^9	\( 24 q + q^{2} - 6 q^{3} - 9 q^{4} - q^{5} + q^{6} + 24 q^{7} + 9 q^{8} - 6 q^{9} - 16 q^{10} + 2 q^{11} + q^{12} + 8 q^{13} + q^{14} - 6 q^{15} + 13 q^{16} + 12 q^{17} - 4 q^{18} + 19 q^{19} + 11 q^{20} - 6 q^{21} - 19 q^{22} - 6 q^{24} + 9 q^{25} - 14 q^{26} - 6 q^{27} - 9 q^{28} + 5 q^{29} - 6 q^{30} + 17 q^{31} - 26 q^{32} + 7 q^{33} - 7 q^{34} - q^{35} + q^{36} + 22 q^{37} - 16 q^{38} + 8 q^{39} + 3 q^{40} + 37 q^{41} + q^{42} + 8 q^{43} + 13 q^{44} + 4 q^{45} + 24 q^{46} - 24 q^{47} + 13 q^{48} + 24 q^{49} - 21 q^{50} - 8 q^{51} + 23 q^{52} - 24 q^{53} + q^{54} - 55 q^{55} + 9 q^{56} - 26 q^{57} + 8 q^{58} - 39 q^{60} + 24 q^{62} - 6 q^{63} - q^{64} - 34 q^{65} + 16 q^{66} + 34 q^{67} + 22 q^{68} + 10 q^{69} - 16 q^{70} - 24 q^{71} + 9 q^{72} + 46 q^{73} + 10 q^{74} + 24 q^{75} - 20 q^{76} + 2 q^{77} - 14 q^{78} + 10 q^{79} + 6 q^{80} - 6 q^{81} - 78 q^{82} + 42 q^{83} + q^{84} - 22 q^{85} - 96 q^{86} - 10 q^{87} - 39 q^{88} + 29 q^{89} + 14 q^{90} + 8 q^{91} + 42 q^{92} - 58 q^{93} + 54 q^{94} - 42 q^{95} + 9 q^{96} - 32 q^{97} + q^{98} - 18 q^{99}+O(q^{100}) \) 24 * q + q^2 - 6 * q^3 - 9 * q^4 - q^5 + q^6 + 24 * q^7 + 9 * q^8 - 6 * q^9 - 16 * q^10 + 2 * q^11 + q^12 + 8 * q^13 + q^14 - 6 * q^15 + 13 * q^16 + 12 * q^17 - 4 * q^18 + 19 * q^19 + 11 * q^20 - 6 * q^21 - 19 * q^22 - 6 * q^24 + 9 * q^25 - 14 * q^26 - 6 * q^27 - 9 * q^28 + 5 * q^29 - 6 * q^30 + 17 * q^31 - 26 * q^32 + 7 * q^33 - 7 * q^34 - q^35 + q^36 + 22 * q^37 - 16 * q^38 + 8 * q^39 + 3 * q^40 + 37 * q^41 + q^42 + 8 * q^43 + 13 * q^44 + 4 * q^45 + 24 * q^46 - 24 * q^47 + 13 * q^48 + 24 * q^49 - 21 * q^50 - 8 * q^51 + 23 * q^52 - 24 * q^53 + q^54 - 55 * q^55 + 9 * q^56 - 26 * q^57 + 8 * q^58 - 39 * q^60 + 24 * q^62 - 6 * q^63 - q^64 - 34 * q^65 + 16 * q^66 + 34 * q^67 + 22 * q^68 + 10 * q^69 - 16 * q^70 - 24 * q^71 + 9 * q^72 + 46 * q^73 + 10 * q^74 + 24 * q^75 - 20 * q^76 + 2 * q^77 - 14 * q^78 + 10 * q^79 + 6 * q^80 - 6 * q^81 - 78 * q^82 + 42 * q^83 + q^84 - 22 * q^85 - 96 * q^86 - 10 * q^87 - 39 * q^88 + 29 * q^89 + 14 * q^90 + 8 * q^91 + 42 * q^92 - 58 * q^93 + 54 * q^94 - 42 * q^95 + 9 * q^96 - 32 * q^97 + q^98 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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