LMFDB - Embedded newform 483.2.q.e.169.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(64,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("483.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (of order $11$, degree $10$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			169.1
Character	$\chi$	$=$	483.169
Dual form			483.2.q.e.463.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.322450 + 2.24269i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-3.00670 - 0.882847i) q^{4} +(-0.335539 - 0.387233i) q^{5} +(2.17397 - 0.638336i) q^{6} +(-0.841254 - 0.540641i) q^{7} +(1.06701 - 2.33642i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.322450 + 2.24269i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-3.00670 - 0.882847i) q^{4} +(-0.335539 - 0.387233i) q^{5} +(2.17397 - 0.638336i) q^{6} +(-0.841254 - 0.540641i) q^{7} +(1.06701 - 2.33642i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(0.976638 - 0.627647i) q^{10} +(-0.460099 - 3.20006i) q^{11} +(0.445963 + 3.10174i) q^{12} +(1.50615 - 0.967944i) q^{13} +(1.48375 - 1.71234i) q^{14} +(-0.212851 + 0.466079i) q^{15} +(-0.376549 - 0.241993i) q^{16} +(7.01395 - 2.05948i) q^{17} +(-1.48375 - 1.71234i) q^{18} +(-3.70816 - 1.08882i) q^{19} +(0.666998 + 1.46052i) q^{20} +(-0.142315 + 0.989821i) q^{21} +7.32511 q^{22} +(4.40226 - 1.90267i) q^{23} -2.56853 q^{24} +(0.674211 - 4.68924i) q^{25} +(1.68514 + 3.68994i) q^{26} +(0.959493 + 0.281733i) q^{27} +(2.05209 + 2.36824i) q^{28} +(5.42044 - 1.59158i) q^{29} +(-0.976638 - 0.627647i) q^{30} +(-1.42905 + 3.12918i) q^{31} +(4.02820 - 4.64879i) q^{32} +(-2.71975 + 1.74787i) q^{33} +(2.35713 + 16.3942i) q^{34} +(0.0729196 + 0.507167i) q^{35} +(2.63618 - 1.69417i) q^{36} +(-2.76396 + 3.18978i) q^{37} +(3.63757 - 7.96518i) q^{38} +(-1.50615 - 0.967944i) q^{39} +(-1.26276 + 0.370780i) q^{40} +(3.50052 + 4.03982i) q^{41} +(-2.17397 - 0.638336i) q^{42} +(-4.94848 - 10.8357i) q^{43} +(-1.44178 + 10.0278i) q^{44} +0.512382 q^{45} +(2.84759 + 10.4864i) q^{46} +3.86398 q^{47} +(-0.0637007 + 0.443048i) q^{48} +(0.415415 + 0.909632i) q^{49} +(10.2991 + 3.02410i) q^{50} +(-4.78707 - 5.52457i) q^{51} +(-5.38309 + 1.58062i) q^{52} +(-10.1092 - 6.49681i) q^{53} +(-0.941228 + 2.06100i) q^{54} +(-1.08479 + 1.25191i) q^{55} +(-2.16079 + 1.38865i) q^{56} +(0.550006 + 3.82538i) q^{57} +(1.82161 + 12.6696i) q^{58} +(-6.07498 + 3.90415i) q^{59} +(1.05146 - 1.21345i) q^{60} +(3.91429 - 8.57109i) q^{61} +(-6.55699 - 4.21392i) q^{62} +(0.959493 - 0.281733i) q^{63} +(8.54067 + 9.85645i) q^{64} +(-0.880191 - 0.258448i) q^{65} +(-3.04296 - 6.66315i) q^{66} +(-1.52451 + 10.6032i) q^{67} -22.9070 q^{68} +(-3.55949 - 3.21404i) q^{69} -1.16093 q^{70} +(1.30569 - 9.08129i) q^{71} +(1.06701 + 2.33642i) q^{72} +(-4.62665 - 1.35851i) q^{73} +(-6.26245 - 7.22726i) q^{74} +(-4.54556 + 1.33470i) q^{75} +(10.1881 + 6.54748i) q^{76} +(-1.34302 + 2.94081i) q^{77} +(2.65646 - 3.06571i) q^{78} +(-0.247281 + 0.158918i) q^{79} +(0.0326391 + 0.227010i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-10.1888 + 6.54795i) q^{82} +(-9.41662 + 10.8674i) q^{83} +(1.30176 - 2.85045i) q^{84} +(-3.15095 - 2.02499i) q^{85} +(25.8967 - 7.60395i) q^{86} +(-3.69949 - 4.26944i) q^{87} +(-7.96762 - 2.33951i) q^{88} +(-0.454172 - 0.994498i) q^{89} +(-0.165218 + 1.14911i) q^{90} -1.79036 q^{91} +(-14.9160 + 1.83423i) q^{92} +3.44005 q^{93} +(-1.24594 + 8.66571i) q^{94} +(0.822609 + 1.80126i) q^{95} +(-5.90206 - 1.73300i) q^{96} +(0.124757 + 0.143978i) q^{97} +(-2.17397 + 0.638336i) q^{98} +(2.71975 + 1.74787i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - q^{2} + 6 q^{3} - 3 q^{4} + 5 q^{5} + q^{6} + 6 q^{7} + 13 q^{8} - 6 q^{9}+O(q^{10}) $ 60 * q - q^2 + 6 * q^3 - 3 * q^4 + 5 * q^5 + q^6 + 6 * q^7 + 13 * q^8 - 6 * q^9	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} + 5 q^{5} + q^{6} + 6 q^{7} + 13 q^{8} - 6 q^{9} - 4 q^{10} - q^{11} + 3 q^{12} + 22 q^{13} + q^{14} + 6 q^{15} - 5 q^{16} + 9 q^{17} - q^{18} - 34 q^{19} + 67 q^{20} - 6 q^{21} - 28 q^{22} - 13 q^{23} + 42 q^{24} - 15 q^{25} - 4 q^{26} + 6 q^{27} + 14 q^{28} - 23 q^{29} + 4 q^{30} + 27 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 6 q^{35} - 3 q^{36} - 82 q^{37} + 2 q^{38} - 22 q^{39} + 57 q^{40} - 22 q^{41} - q^{42} + 25 q^{43} - 41 q^{44} + 16 q^{45} - 47 q^{46} - 90 q^{47} - 28 q^{48} - 6 q^{49} + 55 q^{50} - 9 q^{51} - 92 q^{52} - 17 q^{53} - 10 q^{54} + 21 q^{55} + 9 q^{56} - 32 q^{57} + 87 q^{58} + 38 q^{59} - 45 q^{60} + 23 q^{61} + q^{62} + 6 q^{63} - 75 q^{64} - 75 q^{65} + 61 q^{66} + 5 q^{67} + 88 q^{68} + 13 q^{69} - 18 q^{70} + 8 q^{71} + 13 q^{72} + 90 q^{73} + 79 q^{74} - 18 q^{75} - 85 q^{76} - 10 q^{77} - 18 q^{78} - 6 q^{79} - 147 q^{80} - 6 q^{81} + 112 q^{82} - 90 q^{83} - 3 q^{84} + 55 q^{85} - 8 q^{86} - 10 q^{87} - 210 q^{88} - 15 q^{89} - 4 q^{90} - 22 q^{91} + 39 q^{92} + 50 q^{93} + 144 q^{94} + 72 q^{95} + 7 q^{96} - 48 q^{97} - q^{98} - q^{99}+O(q^{100}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 + 5 * q^5 + q^6 + 6 * q^7 + 13 * q^8 - 6 * q^9 - 4 * q^10 - q^11 + 3 * q^12 + 22 * q^13 + q^14 + 6 * q^15 - 5 * q^16 + 9 * q^17 - q^18 - 34 * q^19 + 67 * q^20 - 6 * q^21 - 28 * q^22 - 13 * q^23 + 42 * q^24 - 15 * q^25 - 4 * q^26 + 6 * q^27 + 14 * q^28 - 23 * q^29 + 4 * q^30 + 27 * q^31 + 37 * q^32 + q^33 + 3 * q^34 + 6 * q^35 - 3 * q^36 - 82 * q^37 + 2 * q^38 - 22 * q^39 + 57 * q^40 - 22 * q^41 - q^42 + 25 * q^43 - 41 * q^44 + 16 * q^45 - 47 * q^46 - 90 * q^47 - 28 * q^48 - 6 * q^49 + 55 * q^50 - 9 * q^51 - 92 * q^52 - 17 * q^53 - 10 * q^54 + 21 * q^55 + 9 * q^56 - 32 * q^57 + 87 * q^58 + 38 * q^59 - 45 * q^60 + 23 * q^61 + q^62 + 6 * q^63 - 75 * q^64 - 75 * q^65 + 61 * q^66 + 5 * q^67 + 88 * q^68 + 13 * q^69 - 18 * q^70 + 8 * q^71 + 13 * q^72 + 90 * q^73 + 79 * q^74 - 18 * q^75 - 85 * q^76 - 10 * q^77 - 18 * q^78 - 6 * q^79 - 147 * q^80 - 6 * q^81 + 112 * q^82 - 90 * q^83 - 3 * q^84 + 55 * q^85 - 8 * q^86 - 10 * q^87 - 210 * q^88 - 15 * q^89 - 4 * q^90 - 22 * q^91 + 39 * q^92 + 50 * q^93 + 144 * q^94 + 72 * q^95 + 7 * q^96 - 48 * q^97 - q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{11}\right)$

Coefficient data

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

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

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

$2$	−0.322450	+	2.24269i	−0.228007	+	1.58582i	0.478482	+	0.878097i	$0.341187\pi$
$2$	−0.322450	+	2.24269i	−0.228007	+	1.58582i	−0.706489	+	0.707724i	$0.749722\pi$
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$4$	−3.00670	−	0.882847i	−1.50335	−	0.441423i
$5$	−0.335539	−	0.387233i	−0.150058	−	0.173176i	0.675744	−	0.737136i	$-0.263822\pi$
$5$	−0.335539	−	0.387233i	−0.150058	−	0.173176i	−0.825802	+	0.563961i	$0.809277\pi$
$6$	2.17397	−	0.638336i	0.887521	−	0.260600i
$7$	−0.841254	−	0.540641i	−0.317964	−	0.204343i
$7$	−0.841254	−	0.540641i	−0.317964	−	0.204343i
$8$	1.06701	−	2.33642i	0.377244	−	0.826050i
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$	0.976638	−	0.627647i	0.308840	−	0.198479i
$11$	−0.460099	−	3.20006i	−0.138725	−	0.964855i	−0.933660	−	0.358160i	$-0.883404\pi$
$11$	−0.460099	−	3.20006i	−0.138725	−	0.964855i	0.794935	−	0.606695i	$-0.207505\pi$
$12$	0.445963	+	3.10174i	0.128738	+	0.895395i
$13$	1.50615	−	0.967944i	0.417731	−	0.268459i	−0.314847	−	0.949142i	$-0.601953\pi$
$13$	1.50615	−	0.967944i	0.417731	−	0.268459i	0.732578	+	0.680683i	$0.238317\pi$
$14$	1.48375	−	1.71234i	0.396549	−	0.457643i
$15$	−0.212851	+	0.466079i	−0.0549580	+	0.120341i
$16$	−0.376549	−	0.241993i	−0.0941372	−	0.0604983i
$17$	7.01395	−	2.05948i	1.70113	−	0.499497i	0.720187	−	0.693780i	$-0.244056\pi$
$17$	7.01395	−	2.05948i	1.70113	−	0.499497i	0.980946	+	0.194283i	$0.0622380\pi$
$18$	−1.48375	−	1.71234i	−0.349724	−	0.403603i
$19$	−3.70816	−	1.08882i	−0.850711	−	0.249791i	−0.172820	−	0.984953i	$-0.555288\pi$
$19$	−3.70816	−	1.08882i	−0.850711	−	0.249791i	−0.677891	+	0.735162i	$0.737106\pi$
$20$	0.666998	+	1.46052i	0.149145	+	0.326583i
$21$	−0.142315	+	0.989821i	−0.0310556	+	0.215997i
$22$	7.32511			1.56172
$23$	4.40226	−	1.90267i	0.917934	−	0.396734i
$23$	4.40226	−	1.90267i	0.917934	−	0.396734i
$24$	−2.56853			−0.524300
$25$	0.674211	−	4.68924i	0.134842	−	0.937849i
$26$	1.68514	+	3.68994i	0.330483	+	0.723657i
$27$	0.959493	+	0.281733i	0.184655	+	0.0542195i
$28$	2.05209	+	2.36824i	0.387809	+	0.447556i
$29$	5.42044	−	1.59158i	1.00655	−	0.295550i	0.263409	−	0.964684i	$-0.415153\pi$
$29$	5.42044	−	1.59158i	1.00655	−	0.295550i	0.743141	+	0.669134i	$0.233335\pi$
$30$	−0.976638	−	0.627647i	−0.178309	−	0.114592i
$31$	−1.42905	+	3.12918i	−0.256665	+	0.562018i	−0.993471	−	0.114087i	$-0.963606\pi$
$31$	−1.42905	+	3.12918i	−0.256665	+	0.562018i	0.736806	+	0.676104i	$0.236333\pi$
$32$	4.02820	−	4.64879i	0.712092	−	0.821798i
$33$	−2.71975	+	1.74787i	−0.473447	+	0.304266i
$34$	2.35713	+	16.3942i	0.404244	+	2.81158i
$35$	0.0729196	+	0.507167i	0.0123257	+	0.0857269i
$36$	2.63618	−	1.69417i	0.439363	−	0.282362i
$37$	−2.76396	+	3.18978i	−0.454393	+	0.524397i	−0.936005	−	0.351987i	$-0.885506\pi$
$37$	−2.76396	+	3.18978i	−0.454393	+	0.524397i	0.481612	+	0.876384i	$0.340051\pi$
$38$	3.63757	−	7.96518i	0.590092	−	1.29212i
$39$	−1.50615	−	0.967944i	−0.241177	−	0.154995i
$40$	−1.26276	+	0.370780i	−0.199660	+	0.0586255i
$41$	3.50052	+	4.03982i	0.546690	+	0.630914i	0.960109	−	0.279627i	$-0.0902109\pi$
$41$	3.50052	+	4.03982i	0.546690	+	0.630914i	−0.413419	+	0.910541i	$0.635665\pi$
$42$	−2.17397	−	0.638336i	−0.335451	−	0.0984974i
$43$	−4.94848	−	10.8357i	−0.754636	−	1.65242i	−0.757851	−	0.652428i	$-0.773750\pi$
$43$	−4.94848	−	10.8357i	−0.754636	−	1.65242i	0.00321426	−	0.999995i	$-0.498977\pi$
$44$	−1.44178	+	10.0278i	−0.217357	+	1.51175i
$45$	0.512382			0.0763814
$46$	2.84759	+	10.4864i	0.419854	+	1.54614i
$47$	3.86398			0.563619			0.281810	−	0.959470i	$-0.409065\pi$
$47$	3.86398			0.563619			0.281810	+	0.959470i	$0.409065\pi$
$48$	−0.0637007	+	0.443048i	−0.00919441	+	0.0639485i
$49$	0.415415	+	0.909632i	0.0593450	+	0.129947i
$50$	10.2991	+	3.02410i	1.45652	+	0.427672i
$51$	−4.78707	−	5.52457i	−0.670324	−	0.773595i
$52$	−5.38309	+	1.58062i	−0.746500	+	0.219192i
$53$	−10.1092	−	6.49681i	−1.38861	−	0.892405i	−0.389025	−	0.921227i	$-0.627188\pi$
$53$	−10.1092	−	6.49681i	−1.38861	−	0.892405i	−0.999585	+	0.0288215i	$0.990825\pi$
$54$	−0.941228	+	2.06100i	−0.128085	+	0.280467i
$55$	−1.08479	+	1.25191i	−0.146273	+	0.168808i
$56$	−2.16079	+	1.38865i	−0.288748	+	0.185567i
$57$	0.550006	+	3.82538i	0.0728501	+	0.506683i
$58$	1.82161	+	12.6696i	0.239189	+	1.66360i
$59$	−6.07498	+	3.90415i	−0.790895	+	0.508277i	−0.872633	−	0.488377i	$-0.837589\pi$
$59$	−6.07498	+	3.90415i	−0.790895	+	0.508277i	0.0817381	+	0.996654i	$0.473953\pi$
$60$	1.05146	−	1.21345i	0.135742	−	0.156655i
$61$	3.91429	−	8.57109i	0.501173	−	1.09742i	−0.474913	−	0.880033i	$-0.657520\pi$
$61$	3.91429	−	8.57109i	0.501173	−	1.09742i	0.976086	−	0.217384i	$-0.0697522\pi$
$62$	−6.55699	−	4.21392i	−0.832738	−	0.535168i
$63$	0.959493	−	0.281733i	0.120885	−	0.0354950i
$64$	8.54067	+	9.85645i	1.06758	+	1.23206i
$65$	−0.880191	−	0.258448i	−0.109174	−	0.0320565i
$66$	−3.04296	−	6.66315i	−0.374562	−	0.820177i
$67$	−1.52451	+	10.6032i	−0.186248	+	1.29538i	0.655369	+	0.755309i	$0.272513\pi$
$67$	−1.52451	+	10.6032i	−0.186248	+	1.29538i	−0.841617	+	0.540075i	$0.818396\pi$
$68$	−22.9070			−2.77789
$69$	−3.55949	−	3.21404i	−0.428512	−	0.386924i
$70$	−1.16093			−0.138758
$71$	1.30569	−	9.08129i	0.154957	−	1.07775i	−0.752798	−	0.658251i	$-0.771297\pi$
$71$	1.30569	−	9.08129i	0.154957	−	1.07775i	0.907756	−	0.419499i	$-0.137794\pi$
$72$	1.06701	+	2.33642i	0.125748	+	0.275350i
$73$	−4.62665	−	1.35851i	−0.541508	−	0.159001i	−0.000471233	−	1.00000i	$-0.500150\pi$
$73$	−4.62665	−	1.35851i	−0.541508	−	0.159001i	−0.541037	+	0.840999i	$0.681968\pi$
$74$	−6.26245	−	7.22726i	−0.727996	−	0.840152i
$75$	−4.54556	+	1.33470i	−0.524876	+	0.154118i
$76$	10.1881	+	6.54748i	1.16865	+	0.751048i
$77$	−1.34302	+	2.94081i	−0.153052	+	0.335137i
$78$	2.65646	−	3.06571i	0.300784	−	0.347124i
$79$	−0.247281	+	0.158918i	−0.0278213	+	0.0178797i	−0.554478	−	0.832199i	$-0.687082\pi$
$79$	−0.247281	+	0.158918i	−0.0278213	+	0.0178797i	0.526656	+	0.850078i	$0.323446\pi$
$80$	0.0326391	+	0.227010i	0.00364917	+	0.0253805i
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	−10.1888	+	6.54795i	−1.12517	+	0.723100i
$83$	−9.41662	+	10.8674i	−1.03361	+	1.19285i	−0.0526533	+	0.998613i	$0.516768\pi$
$83$	−9.41662	+	10.8674i	−1.03361	+	1.19285i	−0.980955	+	0.194235i	$0.937778\pi$
$84$	1.30176	−	2.85045i	0.142034	−	0.311010i
$85$	−3.15095	−	2.02499i	−0.341769	−	0.219641i
$86$	25.8967	−	7.60395i	2.79251	−	0.819955i
$87$	−3.69949	−	4.26944i	−0.396627	−	0.457732i
$88$	−7.96762	−	2.33951i	−0.849351	−	0.249392i
$89$	−0.454172	−	0.994498i	−0.0481421	−	0.105417i	0.884033	−	0.467425i	$-0.154818\pi$
$89$	−0.454172	−	0.994498i	−0.0481421	−	0.105417i	−0.932175	+	0.362009i	$0.882091\pi$
$90$	−0.165218	+	1.14911i	−0.0174155	+	0.121127i
$91$	−1.79036			−0.187681
$92$	−14.9160	+	1.83423i	−1.55510	+	0.191232i
$93$	3.44005			0.356717
$94$	−1.24594	+	8.66571i	−0.128509	+	0.893799i
$95$	0.822609	+	1.80126i	0.0843979	+	0.184806i
$96$	−5.90206	−	1.73300i	−0.602377	−	0.176874i
$97$	0.124757	+	0.143978i	0.0126672	+	0.0146187i	0.762048	−	0.647521i	$-0.224194\pi$
$97$	0.124757	+	0.143978i	0.0126672	+	0.0146187i	−0.749381	+	0.662139i	$0.769649\pi$
$98$	−2.17397	+	0.638336i	−0.219604	+	0.0644817i
$99$	2.71975	+	1.74787i	0.273345	+	0.175668i
$100$	−6.16704	+	13.5039i	−0.616704	+	1.35039i
$101$	6.71547	−	7.75006i	0.668214	−	0.771160i	−0.315882	−	0.948799i	$-0.602300\pi$
$101$	6.71547	−	7.75006i	0.668214	−	0.771160i	0.984096	+	0.177639i	$0.0568458\pi$
$102$	13.9335	−	8.95451i	1.37962	−	0.886629i
$103$	0.0788827	+	0.548641i	0.00777254	+	0.0540592i	0.993339	−	0.115232i	$-0.0367612\pi$
$103$	0.0788827	+	0.548641i	0.00777254	+	0.0540592i	−0.985566	+	0.169291i	$0.945852\pi$
$104$	−0.654451	−	4.55180i	−0.0641742	−	0.446341i
$105$	0.431043	−	0.277015i	0.0420655	−	0.0270339i
$106$	17.8301	−	20.5770i	1.73181	−	1.99861i
$107$	3.59747	−	7.87736i	0.347780	−	0.761533i	−0.652213	−	0.758035i	$-0.726159\pi$
$107$	3.59747	−	7.87736i	0.347780	−	0.761533i	0.999994	−	0.00349758i	$-0.00111332\pi$
$108$	−2.63618	−	1.69417i	−0.253667	−	0.163022i
$109$	15.3396	−	4.50412i	1.46927	−	0.431417i	0.553408	−	0.832910i	$-0.313327\pi$
$109$	15.3396	−	4.50412i	1.46927	−	0.431417i	0.915862	+	0.401494i	$0.131509\pi$
$110$	−2.45786	−	2.83652i	−0.234348	−	0.270452i
$111$	4.04972	+	1.18910i	0.384382	+	0.112865i
$112$	0.185942	+	0.407155i	0.0175698	+	0.0384726i
$113$	0.663908	−	4.61758i	0.0624552	−	0.434386i	−0.934471	−	0.356039i	$-0.884127\pi$
$113$	0.663908	−	4.61758i	0.0624552	−	0.434386i	0.996926	−	0.0783464i	$-0.0249640\pi$
$114$	−8.75648			−0.820120
$115$	−2.21390	−	1.06628i	−0.206448	−	0.0994309i
$116$	−17.7028			−1.64366
$117$	−0.254795	+	1.77214i	−0.0235558	+	0.163834i
$118$	−6.79693	−	14.8832i	−0.625708	−	1.37011i
$119$	−7.01395	−	2.05948i	−0.642968	−	0.188792i
$120$	0.861844	+	0.994621i	0.0786752	+	0.0907960i
$121$	0.525720	−	0.154365i	0.0477927	−	0.0140332i
$122$	17.9601	+	11.5423i	1.62604	+	1.04499i
$123$	2.22058	−	4.86239i	0.200223	−	0.438427i
$124$	7.05931	−	8.14688i	0.633945	−	0.731611i
$125$	−4.19727	+	2.69742i	−0.375415	+	0.241265i
$126$	0.322450	+	2.24269i	0.0287261	+	0.199795i
$127$	−1.20095	−	8.35279i	−0.106567	−	0.741190i	−0.971110	−	0.238632i	$-0.923301\pi$
$127$	−1.20095	−	8.35279i	−0.106567	−	0.741190i	0.864543	−	0.502559i	$-0.167608\pi$
$128$	−14.5094	+	9.32464i	−1.28246	+	0.824190i
$129$	−7.80079	+	9.00259i	−0.686821	+	0.792634i
$130$	0.863436	−	1.89066i	0.0757283	−	0.165822i
$131$	10.8151	+	6.95047i	0.944923	+	0.607265i	0.919787	−	0.392419i	$-0.128362\pi$
$131$	10.8151	+	6.95047i	0.944923	+	0.607265i	0.0251365	+	0.999684i	$0.491998\pi$
$132$	9.72057	−	2.85422i	0.846067	−	0.248428i
$133$	2.53085	+	2.92076i	0.219452	+	0.253262i
$134$	−23.2881	−	6.83799i	−2.01178	−	0.590712i
$135$	−0.212851	−	0.466079i	−0.0183193	−	0.0401137i
$136$	2.67212	−	18.5850i	0.229133	−	1.59365i
$137$	3.89744			0.332981			0.166490	−	0.986043i	$-0.446757\pi$
$137$	3.89744			0.332981			0.166490	+	0.986043i	$0.446757\pi$
$138$	8.35585	−	6.94647i	0.711297	−	0.591323i
$139$	−10.7864			−0.914887			−0.457444	−	0.889239i	$-0.651235\pi$
$139$	−10.7864			−0.914887			−0.457444	+	0.889239i	$0.651235\pi$
$140$	0.228503	−	1.58928i	0.0193121	−	0.134318i
$141$	−1.60515	−	3.51480i	−0.135178	−	0.295999i
$142$	19.9455	+	5.85653i	1.67379	+	0.491469i
$143$	−3.79046	−	4.37442i	−0.316974	−	0.365807i
$144$	0.429473	−	0.126105i	0.0357894	−	0.0105087i
$145$	−2.43508	−	1.56493i	−0.202223	−	0.129961i
$146$	4.53857	−	9.93809i	0.375615	−	0.822482i
$147$	0.654861	−	0.755750i	0.0540120	−	0.0623332i
$148$	11.1265	−	7.15056i	0.914592	−	0.587773i
$149$	1.88534	+	13.1128i	0.154453	+	1.07425i	0.908638	+	0.417584i	$0.137123\pi$
$149$	1.88534	+	13.1128i	0.154453	+	1.07425i	−0.754185	+	0.656662i	$0.771968\pi$
$150$	−1.52760	−	10.6247i	−0.124728	−	0.867500i
$151$	2.73639	−	1.75857i	0.222684	−	0.143111i	−0.424542	−	0.905408i	$-0.639565\pi$
$151$	2.73639	−	1.75857i	0.222684	−	0.143111i	0.647227	+	0.762297i	$0.275929\pi$
$152$	−6.50057	+	7.50206i	−0.527266	+	0.608498i
$153$	−3.03671	+	6.64946i	−0.245503	+	0.537577i
$154$	−6.16227	−	3.96025i	−0.496570	−	0.319126i
$155$	1.69122	−	0.496588i	0.135842	−	0.0398869i
$156$	3.67399	+	4.24002i	0.294155	+	0.339473i
$157$	−21.4181	−	6.28891i	−1.70935	−	0.501910i	−0.726631	−	0.687027i	$-0.758915\pi$
$157$	−21.4181	−	6.28891i	−1.70935	−	0.501910i	−0.982716	+	0.185118i	$0.940733\pi$
$158$	−0.276668	−	0.605818i	−0.0220105	−	0.0481963i
$159$	−1.71018	+	11.8946i	−0.135626	+	0.943300i
$160$	−3.15178			−0.249170
$161$	−4.73207	−	0.779413i	−0.372940	−	0.0614264i
$162$	2.26575			0.178014
$163$	−0.893901	+	6.21722i	−0.0700157	+	0.486970i	0.924399	+	0.381427i	$0.124567\pi$
$163$	−0.893901	+	6.21722i	−0.0700157	+	0.486970i	−0.994415	+	0.105543i	$0.966342\pi$
$164$	−6.95848	−	15.2370i	−0.543366	−	1.18981i
$165$	1.58942	+	0.466694i	0.123736	+	0.0363321i
$166$	−21.3357	−	24.6227i	−1.65597	−	1.91110i
$167$	7.98124	−	2.34350i	0.617607	−	0.181346i	0.0420606	−	0.999115i	$-0.486608\pi$
$167$	7.98124	−	2.34350i	0.617607	−	0.181346i	0.575546	+	0.817769i	$0.304790\pi$
$168$	2.16079	+	1.38865i	0.166708	+	0.107137i
$169$	−4.06882	+	8.90948i	−0.312986	+	0.685345i
$170$	5.55746	−	6.41365i	0.426238	−	0.491904i
$171$	3.25120	−	2.08942i	0.248626	−	0.159782i
$172$	5.31237	+	36.9483i	0.405064	+	2.81728i
$173$	2.83040	+	19.6859i	0.215191	+	1.49669i	0.755460	+	0.655195i	$0.227414\pi$
$173$	2.83040	+	19.6859i	0.215191	+	1.49669i	−0.540268	+	0.841493i	$0.681677\pi$
$174$	10.7679	−	6.92013i	0.816314	−	0.524613i
$175$	−3.10238	+	3.58034i	−0.234518	+	0.270648i
$176$	−0.601143	+	1.31632i	−0.0453129	+	0.0992214i
$177$	6.07498	+	3.90415i	0.456623	+	0.293454i
$178$	2.37680	−	0.697891i	0.178149	−	0.0523091i
$179$	3.33296	+	3.84644i	0.249117	+	0.287496i	0.866511	−	0.499158i	$-0.166357\pi$
$179$	3.33296	+	3.84644i	0.249117	+	0.287496i	−0.617394	+	0.786654i	$0.711812\pi$
$180$	−1.54058	−	0.452355i	−0.114828	−	0.0337166i
$181$	4.89330	+	10.7148i	0.363716	+	0.796428i	0.999694	+	0.0247207i	$0.00786964\pi$
$181$	4.89330	+	10.7148i	0.363716	+	0.796428i	−0.635978	+	0.771707i	$0.719403\pi$
$182$	0.577303	−	4.01523i	0.0427925	−	0.297629i
$183$	−9.42260			−0.696538
$184$	0.251808	−	12.3157i	0.0185635	−	0.907924i
$185$	2.16261			0.158998
$186$	−1.10925	+	7.71497i	−0.0813338	+	0.565689i
$187$	−9.81758	−	21.4975i	−0.717932	−	1.57205i
$188$	−11.6178	−	3.41130i	−0.847317	−	0.248795i
$189$	−0.654861	−	0.755750i	−0.0476341	−	0.0549727i
$190$	−4.30493	+	1.26404i	−0.312312	+	0.0917031i
$191$	−12.8862	−	8.28143i	−0.932410	−	0.599224i	−0.0161769	−	0.999869i	$-0.505149\pi$
$191$	−12.8862	−	8.28143i	−0.932410	−	0.599224i	−0.916233	+	0.400646i	$0.868786\pi$
$192$	5.41782	−	11.8634i	0.390998	−	0.856166i
$193$	3.46861	−	4.00299i	0.249676	−	0.288141i	−0.617052	−	0.786922i	$-0.711673\pi$
$193$	3.46861	−	4.00299i	0.249676	−	0.288141i	0.866728	+	0.498781i	$0.166219\pi$
$194$	−0.363125	+	0.233366i	−0.0260709	+	0.0167547i
$195$	0.130553	+	0.908013i	0.00934907	+	0.0650242i
$196$	−0.445963	−	3.10174i	−0.0318545	−	0.221553i
$197$	−21.8497	+	14.0419i	−1.55672	+	1.00045i	−0.573253	+	0.819379i	$0.694319\pi$
$197$	−21.8497	+	14.0419i	−1.55672	+	1.00045i	−0.983471	+	0.181067i	$0.942045\pi$
$198$	−4.79692	+	5.53595i	−0.340903	+	0.393423i
$199$	−0.787671	+	1.72476i	−0.0558365	+	0.122265i	−0.935494	−	0.353343i	$-0.885045\pi$
$199$	−0.787671	+	1.72476i	−0.0558365	+	0.122265i	0.879657	+	0.475608i	$0.157772\pi$
$200$	−10.2367	−	6.57870i	−0.723841	−	0.465185i
$201$	10.2783	−	3.01798i	0.724975	−	0.212872i
$202$	15.2156	+	17.5597i	1.07056	+	1.23550i
$203$	−5.42044	−	1.59158i	−0.380440	−	0.111707i
$204$	9.51593	+	20.8370i	0.666248	+	1.45888i
$205$	0.389788	−	2.71103i	0.0272240	−	0.189347i
$206$	−1.25587			−0.0875005
$207$	−1.44492	+	4.57299i	−0.100429	+	0.317844i
$208$	−0.801375			−0.0555653
$209$	−1.77815	+	12.3673i	−0.122997	+	0.855465i
$210$	0.482268	+	1.05602i	0.0332797	+	0.0728723i
$211$	3.04858	+	0.895145i	0.209873	+	0.0616243i	0.384979	−	0.922925i	$-0.374209\pi$
$211$	3.04858	+	0.895145i	0.209873	+	0.0616243i	−0.175106	+	0.984550i	$0.556027\pi$
$212$	24.6597	+	28.4589i	1.69364	+	1.95456i
$213$	−8.80303	+	2.58480i	−0.603174	+	0.177108i
$214$	16.5065	+	10.6081i	1.12836	+	0.725152i
$215$	−2.53551	+	5.55200i	−0.172921	+	0.378643i
$216$	1.68203	−	1.94117i	0.114448	−	0.132080i
$217$	2.89396	−	1.85983i	0.196455	−	0.126254i
$218$	5.15508	+	35.8544i	0.349146	+	2.42837i
$219$	0.686238	+	4.77289i	0.0463717	+	0.322522i
$220$	4.36688	−	2.80642i	0.294415	−	0.189209i
$221$	8.57059	−	9.89099i	0.576521	−	0.665340i
$222$	−3.97263	+	8.69884i	−0.266625	+	0.583828i
$223$	−1.58259	−	1.01707i	−0.105978	−	0.0681080i	0.486578	−	0.873637i	$-0.338245\pi$
$223$	−1.58259	−	1.01707i	−0.105978	−	0.0681080i	−0.592556	+	0.805529i	$0.701881\pi$
$224$	−5.90206	+	1.73300i	−0.394348	+	0.115791i
$225$	3.10238	+	3.58034i	0.206825	+	0.238689i
$226$	10.1417	+	2.97788i	0.674618	+	0.198086i
$227$	−2.35273	−	5.15176i	−0.156156	−	0.341934i	0.815343	−	0.578979i	$-0.196549\pi$
$227$	−2.35273	−	5.15176i	−0.156156	−	0.341934i	−0.971499	+	0.237045i	$0.923821\pi$
$228$	1.72352	−	11.9873i	0.114143	−	0.793880i
$229$	21.4706			1.41882			0.709408	−	0.704798i	$-0.248962\pi$
$229$	21.4706			1.41882			0.709408	+	0.704798i	$0.248962\pi$
$230$	3.10521	−	4.62128i	0.204751	−	0.304718i
$231$	3.23297			0.212714
$232$	2.06504	−	14.3627i	0.135576	−	0.942955i
$233$	11.2623	+	24.6610i	0.737817	+	1.61559i	0.787112	+	0.616810i	$0.211575\pi$
$233$	11.2623	+	24.6610i	0.737817	+	1.61559i	−0.0492947	+	0.998784i	$0.515697\pi$
$234$	−3.89220	−	1.14285i	−0.254441	−	0.0747107i
$235$	−1.29652	−	1.49626i	−0.0845754	−	0.0976052i
$236$	21.7124	−	6.37534i	1.41336	−	0.414999i
$237$	0.247281	+	0.158918i	0.0160626	+	0.0103228i
$238$	6.88043	−	15.0660i	0.445992	−	0.976586i
$239$	2.69787	−	3.11351i	0.174511	−	0.201396i	−0.661755	−	0.749720i	$-0.730188\pi$
$239$	2.69787	−	3.11351i	0.174511	−	0.201396i	0.836266	+	0.548323i	$0.184734\pi$
$240$	0.192937	−	0.123993i	0.0124540	−	0.00800372i
$241$	−0.165600	−	1.15177i	−0.0106672	−	0.0741921i	0.983792	−	0.179311i	$-0.0573868\pi$
$241$	−0.165600	−	1.15177i	−0.0106672	−	0.0741921i	−0.994460	+	0.105119i	$0.966478\pi$
$242$	0.176675	+	1.22880i	0.0113571	+	0.0789904i
$243$	−0.841254	+	0.540641i	−0.0539664	+	0.0346821i
$244$	−19.3361	+	22.3150i	−1.23786	+	1.42857i
$245$	0.212851	−	0.466079i	0.0135986	−	0.0297767i
$246$	10.1888	+	6.54795i	0.649615	+	0.417482i
$247$	−6.63896	+	1.94938i	−0.422427	+	0.124036i
$248$	5.78628	+	6.67772i	0.367429	+	0.424036i
$249$	13.7971	+	4.05120i	0.874356	+	0.256734i
$250$	−4.69607	−	10.2830i	−0.297006	−	0.650352i
$251$	−1.10157	+	7.66157i	−0.0695303	+	0.483594i	0.925068	+	0.379800i	$0.124007\pi$
$251$	−1.10157	+	7.66157i	−0.0695303	+	0.483594i	−0.994599	+	0.103794i	$0.966902\pi$
$252$	−3.13363			−0.197400
$253$	−8.11413	−	13.2121i	−0.510131	−	0.830636i
$254$	19.1200			1.19969
$255$	−0.533046	+	3.70742i	−0.0333807	+	0.232168i
$256$	−5.39807	−	11.8201i	−0.337379	−	0.738757i
$257$	21.7505	+	6.38653i	1.35676	+	0.398381i	0.877619	−	0.479358i	$-0.159130\pi$
$257$	21.7505	+	6.38653i	1.35676	+	0.398381i	0.479140	+	0.877738i	$0.340949\pi$
$258$	−17.6747	−	20.3976i	−1.10038	−	1.26990i
$259$	4.04972	−	1.18910i	0.251637	−	0.0738874i
$260$	2.41830	+	1.55415i	0.149977	+	0.0963842i
$261$	−2.34679	+	5.13876i	−0.145263	+	0.318081i
$262$	−19.0751	+	22.0138i	−1.17846	+	1.36002i
$263$	7.08820	−	4.55531i	0.437077	−	0.280893i	−0.303541	−	0.952818i	$-0.598169\pi$
$263$	7.08820	−	4.55531i	0.437077	−	0.280893i	0.740618	+	0.671926i	$0.234533\pi$
$264$	1.18178	+	8.21947i	0.0727336	+	0.505873i
$265$	0.876265	+	6.09456i	0.0538286	+	0.374386i
$266$	−7.36642	+	4.73411i	−0.451664	+	0.290267i
$267$	−0.715957	+	0.826259i	−0.0438159	+	0.0505662i
$268$	13.9447	−	30.5347i	0.851809	−	1.86520i
$269$	19.8371	+	12.7485i	1.20949	+	0.777292i	0.980573	−	0.196153i	$-0.0628451\pi$
$269$	19.8371	+	12.7485i	1.20949	+	0.777292i	0.228917	+	0.973446i	$0.426481\pi$
$270$	1.11391	−	0.327072i	0.0677901	−	0.0199050i
$271$	7.36495	+	8.49961i	0.447389	+	0.516314i	0.933985	−	0.357313i	$-0.116307\pi$
$271$	7.36495	+	8.49961i	0.447389	+	0.516314i	−0.486596	+	0.873627i	$0.661762\pi$
$272$	−3.13947	−	0.921833i	−0.190359	−	0.0558943i
$273$	0.743744	+	1.62857i	0.0450134	+	0.0985657i
$274$	−1.25673	+	8.74075i	−0.0759218	+	0.528048i
$275$	−15.3161			−0.923594
$276$	7.86482	+	12.8061i	0.473407	+	0.770838i
$277$	−12.4835			−0.750061			−0.375031	−	0.927012i	$-0.622368\pi$
$277$	−12.4835			−0.750061			−0.375031	+	0.927012i	$0.622368\pi$
$278$	3.47806	−	24.1905i	0.208600	−	1.45085i
$279$	−1.42905	−	3.12918i	−0.0855549	−	0.187339i
$280$	1.26276	+	0.370780i	0.0754644	+	0.0221584i
$281$	3.01274	+	3.47689i	0.179725	+	0.207414i	0.838463	−	0.544959i	$-0.183455\pi$
$281$	3.01274	+	3.47689i	0.179725	+	0.207414i	−0.658738	+	0.752373i	$0.728909\pi$
$282$	8.40019	−	2.46652i	0.500224	−	0.146879i
$283$	1.60606	+	1.03215i	0.0954702	+	0.0613550i	0.587505	−	0.809221i	$-0.300110\pi$
$283$	1.60606	+	1.03215i	0.0954702	+	0.0613550i	−0.492035	+	0.870576i	$0.663747\pi$
$284$	−11.9432	+	26.1520i	−0.708699	+	1.55183i
$285$	1.29676	−	1.49654i	0.0768136	−	0.0886476i
$286$	11.0327	−	7.09029i	0.652378	−	0.419258i
$287$	−0.760736	−	5.29104i	−0.0449048	−	0.312320i
$288$	0.875411	+	6.08862i	0.0515841	+	0.358775i
$289$	30.6527	−	19.6993i	1.80310	−	1.15878i
$290$	4.29485	−	4.95652i	0.252202	−	0.291057i
$291$	0.0791405	−	0.173294i	0.00463930	−	0.0101586i
$292$	12.7116	+	8.16925i	0.743890	+	0.478069i
$293$	11.8648	−	3.48381i	0.693148	−	0.203526i	0.0838620	−	0.996477i	$-0.473275\pi$
$293$	11.8648	−	3.48381i	0.693148	−	0.203526i	0.609286	+	0.792951i	$0.291456\pi$
$294$	1.48375	+	1.71234i	0.0865342	+	0.0998658i
$295$	3.55021	+	1.04244i	0.206701	+	0.0606929i
$296$	4.50351	+	9.86130i	0.261761	+	0.573177i
$297$	0.460099	−	3.20006i	0.0266977	−	0.185686i
$298$	−30.0160			−1.73878
$299$	4.78878	−	7.12684i	0.276942	−	0.412156i
$300$	14.8455			0.857104
$301$	−1.69527	+	11.7909i	−0.0977140	+	0.679616i
$302$	3.06158	+	6.70393i	0.176174	+	0.385768i
$303$	−9.83941	−	2.88911i	−0.565259	−	0.165975i
$304$	1.13282	+	1.30734i	0.0649716	+	0.0749813i
$305$	−4.63240	+	1.36020i	−0.265251	+	0.0778846i
$306$	−13.9335	−	8.95451i	−0.796525	−	0.511896i
$307$	−9.67442	+	21.1840i	−0.552148	+	1.20904i	0.403623	+	0.914925i	$0.367751\pi$
$307$	−9.67442	+	21.1840i	−0.552148	+	1.20904i	−0.955771	+	0.294110i	$0.904977\pi$
$308$	6.63436	−	7.65645i	0.378027	−	0.436267i
$309$	0.466292	−	0.299668i	0.0265265	−	0.0170475i
$310$	0.568358	+	3.95302i	0.0322806	+	0.224516i
$311$	2.45752	+	17.0925i	0.139353	+	0.969224i	0.932751	+	0.360521i	$0.117401\pi$
$311$	2.45752	+	17.0925i	0.139353	+	0.969224i	−0.793398	+	0.608703i	$0.791690\pi$
$312$	−3.86860	+	2.48620i	−0.219016	+	0.140753i
$313$	21.0917	−	24.3412i	1.19218	−	1.37584i	0.283165	−	0.959071i	$-0.408616\pi$
$313$	21.0917	−	24.3412i	1.19218	−	1.37584i	0.909011	−	0.416773i	$-0.136839\pi$
$314$	21.0103	−	46.0062i	1.18568	−	2.59628i
$315$	−0.431043	−	0.277015i	−0.0242865	−	0.0156080i
$316$	0.883801	−	0.259507i	0.0497177	−	0.0145984i
$317$	−4.45074	−	5.13643i	−0.249978	−	0.288491i	0.616867	−	0.787067i	$-0.288402\pi$
$317$	−4.45074	−	5.13643i	−0.249978	−	0.288491i	−0.866846	+	0.498577i	$0.833856\pi$
$318$	−26.1244	−	7.67080i	−1.46498	−	0.430157i
$319$	−7.58711	−	16.6135i	−0.424797	−	0.930175i
$320$	0.951014	−	6.61445i	0.0531633	−	0.369759i
$321$	−8.65994			−0.483351
$322$	3.27384	−	10.3613i	0.182444	−	0.577410i
$323$	−28.2513			−1.57194
$324$	−0.445963	+	3.10174i	−0.0247757	+	0.172319i
$325$	−3.52346	−	7.71530i	−0.195446	−	0.427968i
$326$	−13.6551	−	4.00949i	−0.756284	−	0.222065i
$327$	−10.4694	−	12.0823i	−0.578959	−	0.668155i
$328$	13.1738	−	3.86818i	0.727402	−	0.213584i
$329$	−3.25059	−	2.08902i	−0.179211	−	0.115172i
$330$	−1.55916	+	3.41408i	−0.0858289	+	0.187939i
$331$	8.64200	−	9.97341i	0.475008	−	0.548188i	−0.466790	−	0.884368i	$-0.654590\pi$
$331$	8.64200	−	9.97341i	0.475008	−	0.548188i	0.941798	+	0.336180i	$0.109135\pi$
$332$	37.9072	−	24.3615i	2.08043	−	1.33701i
$333$	−0.600666	−	4.17773i	−0.0329163	−	0.228938i
$334$	2.68220	+	18.6551i	0.146763	+	1.02076i
$335$	4.61743	−	2.96744i	0.252277	−	0.162129i
$336$	0.293119	−	0.338277i	0.0159909	−	0.0184545i
$337$	−11.6186	+	25.4412i	−0.632906	+	1.38587i	0.272844	+	0.962058i	$0.412036\pi$
$337$	−11.6186	+	25.4412i	−0.632906	+	1.38587i	−0.905750	+	0.423813i	$0.860691\pi$
$338$	−18.6692	−	11.9980i	−1.01547	−	0.652604i
$339$	−4.47610	+	1.31430i	−0.243108	+	0.0713831i
$340$	7.68621	+	8.87036i	0.416843	+	0.481063i
$341$	10.6711	+	3.13331i	0.577871	+	0.169678i
$342$	3.63757	+	7.96518i	0.196697	+	0.430707i
$343$	0.142315	−	0.989821i	0.00768428	−	0.0534453i
$344$	−30.5967			−1.64967
$345$	−0.0502317	+	2.45679i	−0.00270438	+	0.132269i
$346$	−45.0619			−2.42255
$347$	4.25458	−	29.5913i	0.228398	−	1.58854i	−0.476462	−	0.879195i	$-0.658081\pi$
$347$	4.25458	−	29.5913i	0.228398	−	1.58854i	0.704860	−	0.709347i	$-0.251010\pi$
$348$	7.35399	+	16.1030i	0.394215	+	0.863211i
$349$	−32.1216	−	9.43174i	−1.71943	−	0.504870i	−0.734614	−	0.678485i	$-0.762637\pi$
$349$	−32.1216	−	9.43174i	−1.71943	−	0.504870i	−0.984814	+	0.173615i	$0.944455\pi$
$350$	−7.02922	−	8.11216i	−0.375728	−	0.433613i
$351$	1.71784	−	0.504404i	0.0916916	−	0.0269231i
$352$	−16.7298	−	10.7516i	−0.891701	−	0.573061i
$353$	−7.50779	+	16.4398i	−0.399599	+	0.875000i	0.597711	+	0.801711i	$0.296077\pi$
$353$	−7.50779	+	16.4398i	−0.399599	+	0.875000i	−0.997311	+	0.0732891i	$0.976650\pi$
$354$	−10.7147	+	12.3654i	−0.569479	+	0.657214i
$355$	−3.95468	+	2.54152i	−0.209893	+	0.134890i
$356$	0.487570	+	3.39112i	0.0258411	+	0.179729i
$357$	1.04033	+	7.23565i	0.0550601	+	0.382951i
$358$	−9.70108	+	6.23451i	−0.512718	+	0.329504i
$359$	7.77468	−	8.97245i	0.410332	−	0.473548i	−0.512536	−	0.858666i	$-0.671294\pi$
$359$	7.77468	−	8.97245i	0.410332	−	0.473548i	0.922867	+	0.385118i	$0.125839\pi$
$360$	0.546716	−	1.19714i	0.0288145	−	0.0630949i
$361$	−3.41885	−	2.19716i	−0.179939	−	0.115640i
$362$	−25.6079	+	7.51916i	−1.34592	+	0.395198i
$363$	−0.358808	−	0.414086i	−0.0188325	−	0.0217339i
$364$	5.38309	+	1.58062i	0.282150	+	0.0828468i
$365$	1.02636	+	2.24742i	0.0537223	+	0.117635i
$366$	3.03832	−	21.1320i	0.158815	−	1.10459i
$367$	−10.3542			−0.540484			−0.270242	−	0.962792i	$-0.587104\pi$
$367$	−10.3542			−0.540484			−0.270242	+	0.962792i	$0.587104\pi$
$368$	−2.11810	−	0.348869i	−0.110413	−	0.0181860i
$369$	−5.34545			−0.278273
$370$	−0.697333	+	4.85005i	−0.0362526	+	0.252142i
$371$	4.99199	+	10.9309i	0.259171	+	0.567506i
$372$	−10.3432	−	3.03704i	−0.536270	−	0.157463i
$373$	−6.29680	−	7.26690i	−0.326036	−	0.376266i	0.568941	−	0.822379i	$-0.307353\pi$
$373$	−6.29680	−	7.26690i	−0.326036	−	0.376266i	−0.894977	+	0.446113i	$0.852808\pi$
$374$	51.3779	−	15.0859i	2.65669	−	0.780074i
$375$	4.19727	+	2.69742i	0.216746	+	0.139294i
$376$	4.12290	−	9.02788i	0.212622	−	0.465577i
$377$	6.62343	−	7.64384i	0.341124	−	0.393678i
$378$	1.90607	−	1.22496i	0.0980378	−	0.0630051i
$379$	2.12620	+	14.7880i	0.109215	+	0.759609i	0.968662	+	0.248383i	$0.0798993\pi$
$379$	2.12620	+	14.7880i	0.109215	+	0.759609i	−0.859446	+	0.511226i	$0.829192\pi$
$380$	−0.883100	−	6.14210i	−0.0453021	−	0.315083i
$381$	−7.09907	+	4.56230i	−0.363696	+	0.233734i
$382$	22.7278	−	26.2293i	1.16286	−	1.34201i
$383$	13.4609	−	29.4753i	0.687821	−	1.50612i	−0.166317	−	0.986072i	$-0.553187\pi$
$383$	13.4609	−	29.4753i	0.687821	−	1.50612i	0.854138	−	0.520046i	$-0.174085\pi$
$384$	14.5094	+	9.32464i	0.740431	+	0.475846i
$385$	1.58942	−	0.466694i	0.0810041	−	0.0237850i
$386$	7.85901	+	9.06978i	0.400013	+	0.461639i
$387$	11.4296	+	3.35604i	0.581000	+	0.170597i
$388$	−0.247997	−	0.543039i	−0.0125902	−	0.0275686i
$389$	0.200766	−	1.39636i	0.0101792	−	0.0707982i	−0.984099	−	0.177623i	$-0.943159\pi$
$389$	0.200766	−	1.39636i	0.0101792	−	0.0707982i	0.994278	+	0.106825i	$0.0340684\pi$
$390$	−2.07849			−0.105248
$391$	26.9587	−	22.4116i	1.36336	−	1.13340i
$392$	2.56853			0.129731
$393$	1.82960	−	12.7251i	0.0922910	−	0.641898i
$394$	−24.4463	−	53.5298i	−1.23158	−	2.69679i
$395$	0.144511	+	0.0424322i	0.00727113	+	0.00213500i
$396$	−6.63436	−	7.65645i	−0.333389	−	0.384751i
$397$	−9.52031	+	2.79542i	−0.477811	+	0.140298i	−0.511765	−	0.859126i	$-0.671008\pi$
$397$	−9.52031	+	2.79542i	−0.477811	+	0.140298i	0.0339543	+	0.999423i	$0.489190\pi$
$398$	−3.61412	−	2.32265i	−0.181159	−	0.116424i
$399$	1.60546	−	3.51547i	0.0803735	−	0.175993i
$400$	−1.38864	+	1.60257i	−0.0694319	+	0.0801287i
$401$	16.7703	−	10.7776i	0.837469	−	0.538209i	−0.0501741	−	0.998740i	$-0.515978\pi$
$401$	16.7703	−	10.7776i	0.837469	−	0.538209i	0.887643	+	0.460532i	$0.152341\pi$
$402$	3.45415	+	24.0242i	0.172278	+	1.19822i
$403$	0.876509	+	6.09625i	0.0436620	+	0.303676i
$404$	−27.0335	+	17.3734i	−1.34497	+	0.864358i
$405$	−0.335539	+	0.387233i	−0.0166731	+	0.0192417i
$406$	5.31725	−	11.6432i	0.263891	−	0.577840i
$407$	11.4792	+	7.37723i	0.569003	+	0.365676i
$408$	−18.0156	+	5.28985i	−0.891904	+	0.261887i
$409$	17.4296	+	20.1149i	0.861841	+	0.994617i	0.999991	+	0.00420575i	$0.00133874\pi$
$409$	17.4296	+	20.1149i	0.861841	+	0.994617i	−0.138151	+	0.990411i	$0.544116\pi$
$410$	5.95432	+	1.74835i	0.294063	+	0.0863447i
$411$	−1.61905	−	3.54523i	−0.0798621	−	0.174874i
$412$	0.247189	−	1.71924i	0.0121782	−	0.0847009i
$413$	7.22134			0.355339
$414$	−9.78987	−	4.71508i	−0.481146	−	0.231733i
$415$	7.36784			0.361673
$416$	1.56730	−	10.9008i	0.0768434	−	0.534458i
$417$	4.48082	+	9.81162i	0.219427	+	0.480477i
$418$	−27.1627	−	7.97569i	−1.32857	−	0.390104i
$419$	−8.54588	−	9.86248i	−0.417494	−	0.481814i	0.507578	−	0.861606i	$-0.330541\pi$
$419$	−8.54588	−	9.86248i	−0.417494	−	0.481814i	−0.925072	+	0.379792i	$0.875995\pi$
$420$	−1.54058	+	0.452355i	−0.0751726	+	0.0220727i
$421$	26.9768	+	17.3370i	1.31477	+	0.844952i	0.994738	−	0.102454i	$-0.0326695\pi$
$421$	26.9768	+	17.3370i	1.31477	+	0.844952i	0.320033	+	0.947406i	$0.396306\pi$
$422$	−2.99055	+	6.54839i	−0.145578	+	0.318771i
$423$	−2.53037	+	2.92020i	−0.123031	+	0.141985i
$424$	−25.9659	+	16.6873i	−1.26102	+	0.810406i
$425$	−4.92852	−	34.2786i	−0.239069	−	1.66276i
$426$	−2.95838	−	20.5760i	−0.143334	−	0.996908i
$427$	−7.92679	+	5.09424i	−0.383604	+	0.246528i
$428$	−17.7710	+	20.5088i	−0.858994	+	0.991332i
$429$	−2.40450	+	5.26512i	−0.116090	+	0.254202i
$430$	−11.6338	−	7.47662i	−0.561034	−	0.360555i
$431$	6.72887	−	1.97578i	0.324118	−	0.0951698i	−0.115626	−	0.993293i	$-0.536887\pi$
$431$	6.72887	−	1.97578i	0.324118	−	0.0951698i	0.439744	+	0.898123i	$0.355069\pi$
$432$	−0.293119	−	0.338277i	−0.0141027	−	0.0162754i
$433$	20.7127	+	6.08181i	0.995391	+	0.292273i	0.738563	−	0.674184i	$-0.235505\pi$
$433$	20.7127	+	6.08181i	0.995391	+	0.292273i	0.256827	+	0.966457i	$0.417323\pi$
$434$	3.23787	+	7.08995i	0.155423	+	0.340329i
$435$	−0.411943	+	2.86513i	−0.0197512	+	0.137372i
$436$	−50.0981			−2.39926
$437$	−18.3959	+	2.26216i	−0.879997	+	0.108214i
$438$	−10.9254			−0.522036
$439$	−2.08716	+	14.5165i	−0.0996145	+	0.692834i	0.877415	+	0.479732i	$0.159266\pi$
$439$	−2.08716	+	14.5165i	−0.0996145	+	0.692834i	−0.977030	+	0.213103i	$0.931643\pi$
$440$	1.76752	+	3.87032i	0.0842630	+	0.184510i
$441$	−0.959493	−	0.281733i	−0.0456901	−	0.0134158i
$442$	19.4188	+	22.4105i	0.923660	+	1.06596i
$443$	−2.55551	+	0.750365i	−0.121416	+	0.0356509i	−0.341876	−	0.939745i	$-0.611062\pi$
$443$	−2.55551	+	0.750365i	−0.121416	+	0.0356509i	0.220460	+	0.975396i	$0.429244\pi$
$444$	−11.1265	−	7.15056i	−0.528040	−	0.339351i
$445$	−0.232710	+	0.509563i	−0.0110315	+	0.0241556i
$446$	2.79128	−	3.22131i	0.132171	−	0.152533i
$447$	11.1447	−	7.16224i	0.527124	−	0.338762i
$448$	−1.85606	−	12.9092i	−0.0876908	−	0.609903i
$449$	−3.85961	−	26.8442i	−0.182146	−	1.26686i	−0.851675	−	0.524070i	$-0.824413\pi$
$449$	−3.85961	−	26.8442i	−0.182146	−	1.26686i	0.669529	−	0.742786i	$-0.266496\pi$
$450$	−9.02995	+	5.80320i	−0.425676	+	0.273565i
$451$	11.3171	−	13.0606i	0.532901	−	0.615000i
$452$	−6.07279	+	13.2976i	−0.285640	+	0.625465i
$453$	−2.73639	−	1.75857i	−0.128567	−	0.0826249i
$454$	12.3124	−	3.61526i	0.577851	−	0.169672i
$455$	0.600737	+	0.693287i	0.0281630	+	0.0325018i
$456$	9.52455	+	2.79666i	0.446028	+	0.130966i
$457$	1.95857	+	4.28867i	0.0916181	+	0.200616i	0.949894	−	0.312574i	$-0.101191\pi$
$457$	1.95857	+	4.28867i	0.0916181	+	0.200616i	−0.858275	+	0.513189i	$0.828464\pi$
$458$	−6.92320	+	48.1519i	−0.323500	+	2.24999i
$459$	7.31006			0.341204
$460$	5.71519	+	5.16052i	0.266472	+	0.240610i
$461$	24.6815			1.14953			0.574767	−	0.818317i	$-0.305093\pi$
$461$	24.6815			1.14953			0.574767	+	0.818317i	$0.305093\pi$
$462$	−1.04247	+	7.25055i	−0.0485002	+	0.337326i
$463$	−12.6773	−	27.7593i	−0.589163	−	1.29009i	−0.935947	−	0.352141i	$-0.885454\pi$
$463$	−12.6773	−	27.7593i	−0.589163	−	1.29009i	0.346784	−	0.937945i	$-0.387274\pi$
$464$	−2.42621	−	0.712400i	−0.112634	−	0.0330724i
$465$	−1.15427	−	1.33210i	−0.0535281	−	0.0617747i
$466$	−58.9385	+	17.3059i	−2.73027	+	0.801680i
$467$	26.6002	+	17.0949i	1.23091	+	0.791058i	0.984033	−	0.177988i	$-0.0569589\pi$
$467$	26.6002	+	17.0949i	1.23091	+	0.791058i	0.246878	+	0.969047i	$0.420595\pi$
$468$	2.33062	−	5.10335i	0.107733	−	0.235902i
$469$	7.01500	−	8.09575i	0.323923	−	0.373827i
$470$	3.77371	−	2.42521i	0.174068	−	0.111867i
$471$	3.17679	+	22.0951i	0.146379	+	1.01809i
$472$	2.63969	+	18.3595i	0.121502	+	0.845063i
$473$	−32.3980	+	20.8209i	−1.48966	+	0.957347i
$474$	−0.436140	+	0.503332i	−0.0200326	+	0.0231188i
$475$	−7.60581	+	16.6544i	−0.348978	+	0.764156i
$476$	19.2706	+	12.3845i	0.883268	+	0.567642i
$477$	11.5301	−	3.38554i	0.527927	−	0.155013i
$478$	6.11271	+	7.05445i	0.279589	+	0.322663i
$479$	−23.9027	−	7.01848i	−1.09214	−	0.320683i	−0.314417	−	0.949285i	$-0.601809\pi$
$479$	−23.9027	−	7.01848i	−1.09214	−	0.320683i	−0.777727	+	0.628602i	$0.783627\pi$
$480$	1.30930	+	2.86696i	0.0597610	+	0.130858i
$481$	−1.07541	+	7.47965i	−0.0490345	+	0.341043i
$482$	2.63646			0.120088
$483$	1.25680	+	4.62822i	0.0571862	+	0.210592i
$484$	−1.71696			−0.0780438
$485$	0.0138919	−	0.0966202i	0.000630798	−	0.00438730i
$486$	−0.941228	−	2.06100i	−0.0426950	−	0.0934889i
$487$	9.29337	+	2.72878i	0.421123	+	0.123653i	0.485426	−	0.874278i	$-0.338664\pi$
$487$	9.29337	+	2.72878i	0.421123	+	0.123653i	−0.0643035	+	0.997930i	$0.520483\pi$
$488$	−15.8491	−	18.2909i	−0.717456	−	0.827988i
$489$	6.02672	−	1.76960i	0.272538	−	0.0800243i
$490$	0.976638	+	0.627647i	0.0441200	+	0.0283542i
$491$	−11.1317	+	24.3751i	−0.502369	+	1.10003i	0.473324	+	0.880889i	$0.343054\pi$
$491$	−11.1317	+	24.3751i	−0.502369	+	1.10003i	−0.975692	+	0.219145i	$0.929673\pi$
$492$	−10.9694	+	12.6593i	−0.494537	+	0.570726i
$493$	34.7408	−	22.3266i	1.56465	−	1.00554i
$494$	−2.23111	−	15.5177i	−0.100382	−	0.698175i
$495$	−0.235747	−	1.63965i	−0.0105960	−	0.0736970i
$496$	1.29535	−	0.832469i	0.0581628	−	0.0373790i
$497$	−6.00813	+	6.93375i	−0.269502	+	0.311021i
$498$	−13.5345	+	29.6363i	−0.606493	+	1.32804i
$499$	13.0360	+	8.37771i	0.583570	+	0.375038i	0.798864	−	0.601512i	$-0.205435\pi$
$499$	13.0360	+	8.37771i	0.583570	+	0.375038i	−0.215294	+	0.976549i	$0.569071\pi$
$500$	15.0013	−	4.40479i	0.670880	−	0.196988i
$501$	−5.44725	−	6.28646i	−0.243365	−	0.280858i
$502$	−16.8273	−	4.94095i	−0.751041	−	0.220525i
$503$	3.84243	+	8.41375i	0.171326	+	0.375151i	0.975745	−	0.218911i	$-0.0702506\pi$
$503$	3.84243	+	8.41375i	0.171326	+	0.375151i	−0.804419	+	0.594062i	$0.797523\pi$
$504$	0.365541	−	2.54239i	0.0162825	−	0.113247i
$505$	−5.25438			−0.233817
$506$	32.2470	−	13.9372i	1.43355	−	0.619586i
$507$	9.79460			0.434993
$508$	−3.76334	+	26.1746i	−0.166971	+	1.16131i
$509$	5.92874	+	12.9821i	0.262787	+	0.575423i	0.994326	−	0.106377i	$-0.0339249\pi$
$509$	5.92874	+	12.9821i	0.262787	+	0.575423i	−0.731539	+	0.681800i	$0.761198\pi$
$510$	−8.14271	−	2.39092i	−0.360565	−	0.105872i
$511$	3.15772	+	3.64420i	0.139689	+	0.161210i
$512$	−4.84802	+	1.42351i	−0.214254	+	0.0629108i
$513$	−3.25120	−	2.08942i	−0.143544	−	0.0922502i
$514$	−21.3365	+	46.7203i	−0.941111	+	2.06075i
$515$	0.185984	−	0.214636i	0.00819542	−	0.00945801i
$516$	31.4026	−	20.1812i	1.38242	−	0.888428i
$517$	−1.77781	−	12.3650i	−0.0781882	−	0.543811i
$518$	1.36096	+	9.46569i	0.0597972	+	0.415899i
$519$	16.7311	−	10.7524i	0.734414	−	0.471979i
$520$	−1.54301	+	1.78073i	−0.0676656	+	0.0780903i
$521$	−17.0047	+	37.2352i	−0.744991	+	1.63130i	0.0301744	+	0.999545i	$0.490394\pi$
$521$	−17.0047	+	37.2352i	−0.744991	+	1.63130i	−0.775165	+	0.631758i	$0.782334\pi$
$522$	−10.7679	−	6.92013i	−0.471299	−	0.302886i
$523$	−9.72011	+	2.85408i	−0.425031	+	0.124800i	−0.487251	−	0.873262i	$-0.662000\pi$
$523$	−9.72011	+	2.85408i	−0.425031	+	0.124800i	0.0622200	+	0.998062i	$0.480182\pi$
$524$	−26.3817	−	30.4461i	−1.15249	−	1.33004i
$525$	4.54556	+	1.33470i	0.198385	+	0.0582510i
$526$	7.93056	+	17.3655i	0.345789	+	0.757172i
$527$	−3.57879	+	24.8910i	−0.155894	+	1.08427i
$528$	1.44709			0.0629765
$529$	15.7597	−	16.7521i	0.685205	−	0.728350i
$530$	−13.9508			−0.605982
$531$	1.02770	−	7.14784i	0.0445986	−	0.310190i
$532$	−5.03092	−	11.0162i	−0.218118	−	0.477612i
$533$	9.18263	+	2.69626i	0.397744	+	0.116788i
$534$	−1.62218	−	1.87210i	−0.0701987	−	0.0810136i
$535$	−4.25746	+	1.25010i	−0.184066	+	0.0540467i
$536$	23.1468	+	14.8756i	0.999790	+	0.642526i
$537$	2.11428	−	4.62963i	0.0912380	−	0.199783i
$538$	−34.9875	+	40.3777i	−1.50842	+	1.74081i
$539$	2.71975	−	1.74787i	0.117148	−	0.0752863i
$540$	0.228503	+	1.58928i	0.00983322	+	0.0683915i
$541$	−5.60124	−	38.9575i	−0.240816	−	1.67491i	−0.648057	−	0.761591i	$-0.724418\pi$
$541$	−5.60124	−	38.9575i	−0.240816	−	1.67491i	0.407241	−	0.913321i	$-0.366491\pi$
$542$	−21.4368	+	13.7766i	−0.920790	+	0.591756i
$543$	7.71381	−	8.90221i	0.331031	−	0.382030i
$544$	18.6795	−	40.9024i	0.800876	−	1.75367i
$545$	−6.89119	−	4.42870i	−0.295186	−	0.189705i
$546$	−3.89220	+	1.14285i	−0.166571	+	0.0489096i
$547$	−28.4610	−	32.8458i	−1.21691	−	1.40438i	−0.887887	−	0.460061i	$-0.847827\pi$
$547$	−28.4610	−	32.8458i	−1.21691	−	1.40438i	−0.329019	−	0.944323i	$-0.606718\pi$
$548$	−11.7184	−	3.44084i	−0.500586	−	0.146985i
$549$	3.91429	+	8.57109i	0.167058	+	0.365805i
$550$	4.93867	−	34.3492i	0.210586	−	1.46466i
$551$	−21.8328			−0.930110
$552$	−11.3073	+	4.88707i	−0.481273	+	0.208007i
$553$	0.293944			0.0124998
$554$	4.02531	−	27.9966i	0.171019	−	1.18946i
$555$	−0.898379	−	1.96718i	−0.0381341	−	0.0835019i
$556$	32.4314	+	9.52270i	1.37540	+	0.403853i
$557$	−16.2584	−	18.7632i	−0.688891	−	0.795023i	0.298316	−	0.954467i	$-0.403575\pi$
$557$	−16.2584	−	18.7632i	−0.688891	−	0.795023i	−0.987207	+	0.159444i	$0.949030\pi$
$558$	7.47858	−	2.19591i	0.316594	−	0.0929603i
$559$	−17.9415	−	11.5303i	−0.758843	−	0.487679i
$560$	0.0952732	−	0.208619i	0.00402603	−	0.00881577i
$561$	−15.4764	+	17.8608i	−0.653416	+	0.754082i
$562$	−8.76905	+	5.63552i	−0.369900	+	0.237720i
$563$	−4.21848	−	29.3402i	−0.177788	−	1.23654i	−0.861867	−	0.507134i	$-0.830705\pi$
$563$	−4.21848	−	29.3402i	−0.177788	−	1.23654i	0.684079	−	0.729408i	$-0.260204\pi$
$564$	1.72319	+	11.9851i	0.0725594	+	0.504662i
$565$	−2.01085	+	1.29229i	−0.0845970	+	0.0543672i
$566$	−2.83267	+	3.26907i	−0.119066	+	0.137409i
$567$	−0.415415	+	0.909632i	−0.0174458	+	0.0382010i
$568$	−19.8245	−	12.7405i	−0.831819	−	0.534578i
$569$	−7.84234	+	2.30272i	−0.328768	+	0.0965349i	−0.441951	−	0.897039i	$-0.645713\pi$
$569$	−7.84234	+	2.30272i	−0.328768	+	0.0965349i	0.113183	+	0.993574i	$0.463895\pi$
$570$	2.93814	+	3.39080i	0.123065	+	0.142025i
$571$	18.7809	+	5.51457i	0.785956	+	0.230777i	0.649997	−	0.759937i	$-0.274770\pi$
$571$	18.7809	+	5.51457i	0.785956	+	0.230777i	0.135959	+	0.990714i	$0.456588\pi$
$572$	7.53483	+	16.4990i	0.315047	+	0.689856i
$573$	−2.17995	+	15.1619i	−0.0910688	+	0.633397i
$574$	12.1115			0.505523
$575$	−5.95402	−	21.9261i	−0.248300	−	0.914380i
$576$	−13.0420			−0.543415
$577$	3.95883	−	27.5342i	0.164808	−	1.14627i	−0.724606	−	0.689163i	$-0.757978\pi$
$577$	3.95883	−	27.5342i	0.164808	−	1.14627i	0.889414	−	0.457102i	$-0.151113\pi$
$578$	34.2954	+	75.0965i	1.42650	+	3.12360i
$579$	−5.08216	−	1.49226i	−0.211207	−	0.0620160i
$580$	5.93997	+	6.85509i	0.246644	+	0.284642i
$581$	13.7971	−	4.05120i	0.572400	−	0.168072i
$582$	0.363125	+	0.233366i	0.0150520	+	0.00967334i
$583$	−16.1389	+	35.3393i	−0.668407	+	1.46361i
$584$	−8.11072	+	9.36027i	−0.335624	+	0.387331i
$585$	0.771724	−	0.495957i	0.0319069	−	0.0205053i
$586$	3.98731	+	27.7324i	0.164714	+	1.14561i
$587$	−3.09805	−	21.5474i	−0.127870	−	0.889358i	−0.948247	−	0.317534i	$-0.897145\pi$
$587$	−3.09805	−	21.5474i	−0.127870	−	0.889358i	0.820376	−	0.571824i	$-0.193764\pi$
$588$	−2.63618	+	1.69417i	−0.108714	+	0.0698664i
$589$	8.70625	−	10.0475i	0.358735	−	0.414002i
$590$	−3.48262	+	7.62588i	−0.143377	+	0.313953i
$591$	21.8497	+	14.0419i	0.898775	+	0.577607i
$592$	1.81267	−	0.532249i	0.0745004	−	0.0218753i
$593$	28.7623	+	33.1935i	1.18113	+	1.36309i	0.917138	+	0.398569i	$0.130493\pi$
$593$	28.7623	+	33.1935i	1.18113	+	1.36309i	0.263990	+	0.964525i	$0.414961\pi$
$594$	7.02839	+	2.06372i	0.288378	+	0.0846755i
$595$	1.55596	+	3.40707i	0.0637879	+	0.139676i
$596$	5.90797	−	41.0908i	0.242000	−	1.68315i
$597$	1.89611			0.0776025
$598$	14.4391	+	13.0378i	0.590461	+	0.533155i
$599$	−6.60216			−0.269757			−0.134879	−	0.990862i	$-0.543064\pi$
$599$	−6.60216			−0.269757			−0.134879	+	0.990862i	$0.543064\pi$
$600$	−1.73174	+	12.0445i	−0.0706978	+	0.491714i
$601$	14.4205	+	31.5764i	0.588223	+	1.28803i	0.936510	+	0.350641i	$0.114036\pi$
$601$	14.4205	+	31.5764i	0.588223	+	1.28803i	−0.348287	+	0.937388i	$0.613236\pi$
$602$	−25.8967	−	7.60395i	−1.05547	−	0.309914i
$603$	−7.01500	−	8.09575i	−0.285673	−	0.329684i
$604$	−9.78006	+	2.87168i	−0.397945	+	0.116847i
$605$	−0.236175	−	0.151780i	−0.00960188	−	0.00617075i
$606$	9.65210	−	21.1352i	0.392090	−	0.858557i
$607$	−17.4032	+	20.0844i	−0.706376	+	0.815201i	−0.989599	−	0.143853i	$-0.954051\pi$
$607$	−17.4032	+	20.0844i	−0.706376	+	0.815201i	0.283223	+	0.959054i	$0.408596\pi$
$608$	−19.9989	+	12.8525i	−0.811063	+	0.521238i
$609$	0.803976	+	5.59177i	0.0325787	+	0.226590i
$610$	−1.55678	−	10.8276i	−0.0630322	−	0.438399i
$611$	5.81973	−	3.74011i	0.235441	−	0.151309i
$612$	15.0009	−	17.3120i	0.606376	−	0.699796i
$613$	9.74016	−	21.3280i	0.393401	−	0.861429i	−0.604495	−	0.796609i	$-0.706625\pi$
$613$	9.74016	−	21.3280i	0.393401	−	0.861429i	0.997897	−	0.0648205i	$-0.0206475\pi$
$614$	−44.3897	−	28.5275i	−1.79142	−	1.15128i
$615$	−2.62797	+	0.771641i	−0.105970	+	0.0311156i
$616$	5.43796	+	6.27574i	0.219102	+	0.252857i
$617$	10.7649	+	3.16087i	0.433380	+	0.127252i	0.491144	−	0.871078i	$-0.336579\pi$
$617$	10.7649	+	3.16087i	0.433380	+	0.127252i	−0.0577639	+	0.998330i	$0.518397\pi$
$618$	0.521706	+	1.14238i	0.0209861	+	0.0459532i
$619$	4.14237	−	28.8108i	0.166496	−	1.15801i	−0.719561	−	0.694429i	$-0.755657\pi$
$619$	4.14237	−	28.8108i	0.166496	−	1.15801i	0.886057	−	0.463576i	$-0.153434\pi$
$620$	−5.52341			−0.221826
$621$	4.75998	−	0.585338i	0.191011	−	0.0234888i
$622$	−39.1255			−1.56879
$623$	−0.155592	+	1.08217i	−0.00623368	+	0.0433562i
$624$	0.332903	+	0.728956i	0.0133268	+	0.0291816i
$625$	−20.2749	−	5.95326i	−0.810998	−	0.238130i
$626$	47.7887	+	55.1511i	1.91002	+	2.20428i
$627$	11.9884	−	3.52011i	0.478770	−	0.140579i
$628$	58.8456	+	37.8177i	2.34819	+	1.50909i
$629$	−12.8170	+	28.0653i	−0.511047	+	1.11904i
$630$	0.760248	−	0.877374i	0.0302890	−	0.0349554i
$631$	−19.5027	+	12.5337i	−0.776392	+	0.498957i	−0.867834	−	0.496854i	$-0.834489\pi$
$631$	−19.5027	+	12.5337i	−0.776392	+	0.498957i	0.0914424	+	0.995810i	$0.470852\pi$
$632$	0.107448	+	0.747320i	0.00427407	+	0.0297268i
$633$	−0.452175	−	3.14495i	−0.0179723	−	0.125000i
$634$	12.9546	−	8.32539i	0.514491	−	0.330644i
$635$	−2.83151	+	3.26773i	−0.112365	+	0.129676i
$636$	15.6431	−	34.2535i	0.620288	−	1.35824i
$637$	1.50615	+	0.967944i	0.0596758	+	0.0383513i
$638$	39.7053	−	11.6585i	1.57195	−	0.461566i
$639$	6.00813	+	6.93375i	0.237678	+	0.274295i
$640$	8.47928	+	2.48974i	0.335173	+	0.0984157i
$641$	−9.21854	−	20.1858i	−0.364110	−	0.797291i	−0.999681	−	0.0252481i	$-0.991962\pi$
$641$	−9.21854	−	20.1858i	−0.364110	−	0.797291i	0.635571	−	0.772043i	$-0.280765\pi$
$642$	2.79240	−	19.4216i	0.110207	−	0.766508i
$643$	37.2224			1.46791			0.733954	−	0.679199i	$-0.237673\pi$
$643$	37.2224			1.46791			0.733954	+	0.679199i	$0.237673\pi$
$644$	13.5398	+	6.52116i	0.533544	+	0.256970i
$645$	6.10357			0.240328
$646$	9.10963	−	63.3588i	0.358413	−	2.49282i
$647$	2.09404	+	4.58530i	0.0823250	+	0.180267i	0.946318	−	0.323237i	$-0.104771\pi$
$647$	2.09404	+	4.58530i	0.0823250	+	0.180267i	−0.863993	+	0.503504i	$0.832044\pi$
$648$	−2.46449	−	0.723640i	−0.0968144	−	0.0284273i
$649$	15.2886	+	17.6440i	0.600131	+	0.692588i
$650$	18.4392	−	5.41423i	0.723244	−	0.212364i
$651$	−2.89396	−	1.85983i	−0.113423	−	0.0728926i
$652$	8.17654	−	17.9041i	0.320218	−	0.701180i
$653$	−26.4718	+	30.5501i	−1.03592	+	1.19552i	−0.0555313	+	0.998457i	$0.517685\pi$
$653$	−26.4718	+	30.5501i	−1.03592	+	1.19552i	−0.980391	+	0.197061i	$0.936860\pi$
$654$	30.4728	−	19.5837i	1.19158	−	0.765783i
$655$	−0.937453	−	6.52013i	−0.0366293	−	0.254763i
$656$	−0.340509	−	2.36829i	−0.0132946	−	0.0924663i
$657$	4.05650	−	2.60696i	0.158259	−	0.101707i
$658$	5.73319	−	6.61645i	0.223503	−	0.257936i
$659$	−7.11584	+	15.5815i	−0.277194	+	0.606970i	−0.996109	−	0.0881277i	$-0.971912\pi$
$659$	−7.11584	+	15.5815i	−0.277194	+	0.606970i	0.718915	+	0.695098i	$0.244639\pi$
$660$	−4.36688	−	2.80642i	−0.169980	−	0.109240i
$661$	−36.2730	+	10.6507i	−1.41086	+	0.414265i	−0.896398	−	0.443250i	$-0.853825\pi$
$661$	−36.2730	+	10.6507i	−1.41086	+	0.414265i	−0.514459	+	0.857515i	$0.672007\pi$
$662$	19.5806	+	22.5973i	0.761023	+	0.878268i
$663$	−12.5575	−	3.68722i	−0.487694	−	0.143200i
$664$	15.3431	+	33.5968i	0.595429	+	1.30381i
$665$	0.281813	−	1.96005i	0.0109283	−	0.0760077i
$666$	9.56303			0.370560
$667$	20.8339	−	17.3199i	0.806692	−	0.670628i
$668$	−26.0661			−1.00853
$669$	−0.267727	+	1.86208i	−0.0103509	+	0.0719922i
$670$	5.16616	+	11.3123i	0.199586	+	0.437033i
$671$	−29.2290	−	8.58241i	−1.12837	−	0.331320i
$672$	4.02820	+	4.64879i	0.155391	+	0.179331i
$673$	−25.2256	+	7.40689i	−0.972374	+	0.285515i	−0.729073	−	0.684436i	$-0.760048\pi$
$673$	−25.2256	+	7.40689i	−0.972374	+	0.285515i	−0.243301	+	0.969951i	$0.578230\pi$
$674$	−53.3103	−	34.2605i	−2.05344	−	1.31966i
$675$	1.96801	−	4.30935i	0.0757489	−	0.165867i
$676$	20.0994	−	23.1960i	0.773055	−	0.892153i
$677$	−20.3903	+	13.1040i	−0.783662	+	0.503629i	−0.870247	−	0.492615i	$-0.836041\pi$
$677$	−20.3903	+	13.1040i	−0.783662	+	0.503629i	0.0865850	+	0.996244i	$0.472405\pi$
$678$	−1.50425	−	10.4623i	−0.0577705	−	0.401802i
$679$	−0.0271123	−	0.188570i	−0.00104048	−	0.00723667i
$680$	−8.09333	+	5.20127i	−0.310365	+	0.199459i
$681$	−3.70884	+	4.28023i	−0.142123	+	0.164019i
$682$	−10.4679	+	22.9216i	−0.400838	+	0.877713i
$683$	3.02413	+	1.94349i	0.115715	+	0.0743655i	0.597218	−	0.802079i	$-0.296273\pi$
$683$	3.02413	+	1.94349i	0.115715	+	0.0743655i	−0.481503	+	0.876444i	$0.659909\pi$
$684$	−11.6200	+	3.41195i	−0.444303	+	0.130459i
$685$	−1.30774	−	1.50922i	−0.0499663	−	0.0576642i
$686$	2.17397	+	0.638336i	0.0830027	+	0.0243718i
$687$	−8.91921	−	19.5303i	−0.340289	−	0.745129i
$688$	−0.758812	+	5.27765i	−0.0289294	+	0.201209i
$689$	−21.5146			−0.819640
$690$	−5.49361	−	0.904845i	−0.209138	−	0.0344469i
$691$	9.00117			0.342421			0.171210	−	0.985235i	$-0.445232\pi$
$691$	9.00117			0.342421			0.171210	+	0.985235i	$0.445232\pi$
$692$	8.86944	−	61.6883i	0.337165	−	2.34504i
$693$	−1.34302	−	2.94081i	−0.0510173	−	0.111712i
$694$	64.9921	+	19.0834i	2.46707	+	0.724397i
$695$	3.61925	+	4.17683i	0.137286	+	0.158436i
$696$	−13.9226	+	4.08804i	−0.527734	+	0.154957i
$697$	32.8724	+	21.1258i	1.24513	+	0.800197i
$698$	31.5101	−	68.9975i	1.19267	−	2.61159i
$699$	17.7539	−	20.4891i	0.671514	−	0.774968i
$700$	12.4888	−	8.02607i	0.472033	−	0.303357i
$701$	−0.434863	−	3.02454i	−0.0164246	−	0.114235i	0.979960	−	0.199195i	$-0.0638328\pi$
$701$	−0.434863	−	3.02454i	−0.0164246	−	0.114235i	−0.996384	+	0.0849600i	$0.972924\pi$
$702$	0.577303	+	4.01523i	0.0217889	+	0.151545i
$703$	13.7223	−	8.81879i	0.517547	−	0.332607i
$704$	27.6117	−	31.8656i	1.04066	−	1.20098i
$705$	−0.822453	+	1.80092i	−0.0309754	+	0.0678266i
$706$	−34.4484	−	22.1387i	−1.29648	−	0.833199i
$707$	−9.83941	+	2.88911i	−0.370049	+	0.108656i
$708$	−14.8189	−	17.1019i	−0.556927	−	0.642728i
$709$	42.8645	+	12.5862i	1.60981	+	0.472683i	0.958254	−	0.285917i	$-0.0922983\pi$
$709$	42.8645	+	12.5862i	1.60981	+	0.472683i	0.651556	+	0.758600i	$0.274116\pi$
$710$	−4.42465	−	9.68864i	−0.166054	−	0.363608i
$711$	0.0418326	−	0.290952i	0.00156884	−	0.0109115i
$712$	−2.80817			−0.105241
$713$	−0.337247	+	16.4945i	−0.0126300	+	0.617723i
$714$	−16.5628			−0.619846
$715$	−0.422072	+	2.93558i	−0.0157846	+	0.109784i
$716$	−6.62539	−	14.5076i	−0.247602	−	0.542174i
$717$	−3.95289	−	1.16067i	−0.147623	−	0.0433461i
$718$	17.6155	+	20.3294i	0.657404	+	0.758685i
$719$	39.1843	−	11.5055i	1.46133	−	0.429084i	0.548058	−	0.836440i	$-0.315367\pi$
$719$	39.1843	−	11.5055i	1.46133	−	0.429084i	0.913269	+	0.407356i	$0.133549\pi$
$720$	−0.192937	−	0.123993i	−0.00719034	−	0.00462095i
$721$	0.230257	−	0.504193i	0.00857524	−	0.0187771i
$722$	6.02996	−	6.95895i	0.224412	−	0.258985i
$723$	−0.978895	+	0.629098i	−0.0364055	+	0.0233964i
$724$	−5.25313	−	36.5364i	−0.195231	−	1.35786i
$725$	−3.80881	−	26.4908i	−0.141455	−	0.983845i
$726$	1.04436	−	0.671172i	0.0387600	−	0.0249095i
$727$	−1.95098	+	2.25156i	−0.0723580	+	0.0835056i	−0.790774	−	0.612108i	$-0.790322\pi$
$727$	−1.95098	+	2.25156i	−0.0723580	+	0.0835056i	0.718416	+	0.695613i	$0.244867\pi$
$728$	−1.91033	+	4.18304i	−0.0708016	+	0.155034i
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$	−5.37122	+	1.57713i	−0.198798	+	0.0583723i
$731$	−57.0242	−	65.8095i	−2.10912	−	2.43405i
$732$	28.3309	+	8.31871i	1.04714	+	0.307468i
$733$	−6.66846	−	14.6019i	−0.246305	−	0.539333i	0.745588	−	0.666407i	$-0.232169\pi$
$733$	−6.66846	−	14.6019i	−0.246305	−	0.539333i	−0.991893	+	0.127074i	$0.959441\pi$
$734$	3.33871	−	23.2212i	0.123234	−	0.857111i
$735$	−0.512382			−0.0188995
$736$	8.88806	−	28.1295i	0.327618	−	1.03687i
$737$	34.6322			1.27569
$738$	1.72364	−	11.9882i	0.0634481	−	0.441291i
$739$	19.1055	+	41.8352i	0.702807	+	1.53893i	0.836535	+	0.547914i	$0.184578\pi$
$739$	19.1055	+	41.8352i	0.702807	+	1.53893i	−0.133728	+	0.991018i	$0.542695\pi$
$740$	−6.50231	−	1.90925i	−0.239030	−	0.0701854i
$741$	4.53114	+	5.22921i	0.166456	+	0.192100i
$742$	−26.1244	+	7.67080i	−0.959055	+	0.281604i
$743$	−13.9181	−	8.94461i	−0.510605	−	0.328146i	0.259841	−	0.965651i	$-0.416330\pi$
$743$	−13.9181	−	8.94461i	−0.510605	−	0.328146i	−0.770446	+	0.637506i	$0.779966\pi$
$744$	3.67056	−	8.03741i	0.134569	−	0.294666i
$745$	4.44511	−	5.12993i	0.162856	−	0.187946i
$746$	18.3278	−	11.7786i	0.671029	−	0.431244i
$747$	−2.04643	−	14.2332i	−0.0748749	−	0.520766i
$748$	10.5395	+	73.3040i	0.385363	+	2.68026i
$749$	−7.28520	+	4.68192i	−0.266196	+	0.171074i
$750$	−7.40289	+	8.54339i	−0.270315	+	0.311961i
$751$	6.49614	−	14.2246i	0.237048	−	0.519062i	−0.753298	−	0.657679i	$-0.771538\pi$
$751$	6.49614	−	14.2246i	0.237048	−	0.519062i	0.990346	+	0.138617i	$0.0442657\pi$
$752$	−1.45498	−	0.935057i	−0.0530575	−	0.0340980i
$753$	7.42682	−	2.18071i	0.270648	−	0.0794695i
$754$	15.0070	+	17.3191i	0.546525	+	0.630723i
$755$	−1.59914	−	0.469551i	−0.0581988	−	0.0170887i
$756$	1.30176	+	2.85045i	0.0473445	+	0.103670i
$757$	5.81127	−	40.4183i	0.211214	−	1.46903i	−0.557896	−	0.829911i	$-0.688391\pi$
$757$	5.81127	−	40.4183i	0.211214	−	1.46903i	0.769110	−	0.639116i	$-0.220700\pi$
$758$	−33.8505			−1.22951
$759$	−8.64739	+	12.8694i	−0.313880	+	0.467128i
$760$	5.08624			0.184497
$761$	−4.90737	+	34.1315i	−0.177892	+	1.23727i	0.683738	+	0.729728i	$0.260353\pi$
$761$	−4.90737	+	34.1315i	−0.177892	+	1.23727i	−0.861630	+	0.507537i	$0.830556\pi$
$762$	−7.94272	−	17.3921i	−0.287734	−	0.630051i
$763$	−15.3396	−	4.50412i	−0.555332	−	0.163060i
$764$	31.4336	+	36.2763i	1.13723	+	1.31243i
$765$	3.59382	−	1.05524i	0.129935	−	0.0381523i
$766$	61.7635	+	39.6930i	2.23161	+	1.43417i
$767$	−5.37083	+	11.7605i	−0.193929	+	0.424646i
$768$	−8.50952	+	9.82051i	−0.307061	+	0.354367i
$769$	−44.6938	+	28.7229i	−1.61170	+	1.03578i	−0.650658	+	0.759371i	$0.725507\pi$
$769$	−44.6938	+	28.7229i	−1.61170	+	1.03578i	−0.961041	+	0.276405i	$0.910857\pi$
$770$	0.534144	+	3.71505i	0.0192492	+	0.133881i
$771$	−3.22610	−	22.4380i	−0.116185	−	0.808085i
$772$	−13.9631	+	8.97353i	−0.502542	+	0.322964i
$773$	22.0667	−	25.4664i	0.793685	−	0.915962i	−0.204332	−	0.978902i	$-0.565502\pi$
$773$	22.0667	−	25.4664i	0.793685	−	0.915962i	0.998017	+	0.0629399i	$0.0200476\pi$
$774$	−11.2120	+	24.5509i	−0.403008	+	0.882465i
$775$	13.7100	+	8.81089i	0.492478	+	0.316497i
$776$	0.469509	−	0.137860i	0.0168544	−	0.00494890i
$777$	−2.76396	−	3.18978i	−0.0991566	−	0.114433i
$778$	3.06686	+	0.900513i	0.109952	+	0.0322849i
$779$	−8.58190	−	18.7917i	−0.307478	−	0.673284i
$780$	0.409104	−	2.84538i	0.0146483	−	0.101881i
$781$	−29.6614			−1.06137
$782$	41.5694	+	67.6866i	1.48652	+	2.42047i
$783$	5.64927			0.201889
$784$	0.0637007	−	0.443048i	0.00227503	−	0.0158232i
$785$	4.75133	+	10.4040i	0.169582	+	0.371333i
$786$	27.9486	+	8.20644i	0.996892	+	0.292714i
$787$	0.0190701	+	0.0220081i	0.000679777	+	0.000784505i	0.756089	−	0.654468i	$-0.227108\pi$
$787$	0.0190701	+	0.0220081i	0.000679777	+	0.000784505i	−0.755410	+	0.655253i	$0.772562\pi$
$788$	78.0922	−	22.9299i	2.78192	−	0.816845i
$789$	−7.08820	−	4.55531i	−0.252347	−	0.162173i
$790$	−0.141760	+	0.310411i	−0.00504359	+	0.0110439i
$791$	−3.05497	+	3.52562i	−0.108622	+	0.125357i
$792$	6.98576	−	4.48948i	0.248228	−	0.159527i
$793$	−2.40083	−	16.6982i	−0.0852561	−	0.592969i
$794$	−3.19943	−	22.2525i	−0.113543	−	0.789711i
$795$	5.17979	−	3.32885i	0.183708	−	0.118062i
$796$	3.89099	−	4.49044i	0.137912	−	0.159159i
$797$	4.03161	−	8.82800i	0.142807	−	0.312704i	−0.824691	−	0.565584i	$-0.808651\pi$
$797$	4.03161	−	8.82800i	0.142807	−	0.312704i	0.967498	+	0.252881i	$0.0813780\pi$
$798$	7.36642	+	4.73411i	0.260769	+	0.167586i
$799$	27.1017	−	7.95779i	0.958791	−	0.281526i
$800$	−19.0835	−	22.0235i	−0.674702	−	0.778647i
$801$	1.04901	+	0.308017i	0.0370650	+	0.0108833i
$802$	18.7633	+	41.0858i	0.662554	+	1.45079i
$803$	−2.21859	+	15.4306i	−0.0782922	+	0.544535i
$804$	−33.5681			−1.18386
$805$	1.28598	+	2.09394i	0.0453249	+	0.0738016i
$806$	−13.9546			−0.491531
$807$	3.35585	−	23.3404i	0.118131	−	0.821622i
$808$	−10.9420	−	23.9595i	−0.384937	−	0.842894i
$809$	−6.23075	−	1.82951i	−0.219062	−	0.0643223i	0.170360	−	0.985382i	$-0.445507\pi$
$809$	−6.23075	−	1.82951i	−0.219062	−	0.0643223i	−0.389422	+	0.921060i	$0.627325\pi$
$810$	−0.760248	−	0.877374i	−0.0267124	−	0.0308278i
$811$	−0.0240761	+	0.00706937i	−0.000845425	+	0.000248239i	−0.282155	−	0.959369i	$-0.591049\pi$
$811$	−0.0240761	+	0.00706937i	−0.000845425	+	0.000248239i	0.281310	+	0.959617i	$0.409231\pi$
$812$	14.8925	+	9.57084i	0.522625	+	0.335870i
$813$	4.67200	−	10.2303i	0.163854	−	0.358791i
$814$	−20.2463	+	23.3655i	−0.709633	+	0.818960i
$815$	2.70745	−	1.73997i	0.0948378	−	0.0609485i
$816$	0.465656	+	3.23871i	0.0163012	+	0.113377i
$817$	6.55175	+	45.5684i	0.229217	+	1.59424i
$818$	−50.7316	+	32.6033i	−1.77379	+	1.13995i
$819$	1.17244	−	1.35307i	0.0409683	−	0.0472800i
$820$	−3.56540	+	7.80714i	−0.124509	+	0.272637i
$821$	−38.5765	−	24.7916i	−1.34633	−	0.865234i	−0.348919	−	0.937153i	$-0.613451\pi$
$821$	−38.5765	−	24.7916i	−1.34633	−	0.865234i	−0.997410	+	0.0719193i	$0.977088\pi$
$822$	8.47293	−	2.48788i	0.295527	−	0.0867746i
$823$	5.37168	+	6.19925i	0.187245	+	0.216092i	0.841609	−	0.540088i	$-0.181609\pi$
$823$	5.37168	+	6.19925i	0.187245	+	0.216092i	−0.654364	+	0.756180i	$0.727063\pi$
$824$	1.36603	+	0.401101i	0.0475877	+	0.0139730i
$825$	6.36253	+	13.9320i	0.221515	+	0.485050i
$826$	−2.32852	+	16.1952i	−0.0810197	+	0.563504i
$827$	47.9309			1.66672			0.833361	−	0.552729i	$-0.186414\pi$
$827$	47.9309			1.66672			0.833361	+	0.552729i	$0.186414\pi$
$828$	8.38170	−	12.4739i	0.291284	−	0.433500i
$829$	−10.8153			−0.375632			−0.187816	−	0.982204i	$-0.560141\pi$
$829$	−10.8153			−0.375632			−0.187816	+	0.982204i	$0.560141\pi$
$830$	−2.37576	+	16.5238i	−0.0824639	+	0.573549i
$831$	5.18583	+	11.3554i	0.179895	+	0.393914i
$832$	22.4040	+	6.57841i	0.776719	+	0.228065i
$833$	4.78707	+	5.52457i	0.165862	+	0.191415i
$834$	−23.4493	+	6.88532i	−0.811982	+	0.238419i
$835$	−3.58550	−	2.30426i	−0.124081	−	0.0797422i
$836$	16.2648	−	35.6150i	0.562530	−	1.23177i
$837$	−2.25276	+	2.59982i	−0.0778666	+	0.0898629i
$838$	24.8741	−	15.9856i	0.859262	−	0.552214i
$839$	0.145413	+	1.01137i	0.00502022	+	0.0349164i	0.992178	−	0.124834i	$-0.0398400\pi$
$839$	0.145413	+	1.01137i	0.00502022	+	0.0349164i	−0.987157	+	0.159751i	$0.948931\pi$
$840$	−0.187297	−	1.30268i	−0.00646235	−	0.0449466i
$841$	2.45167	−	1.57559i	0.0845403	−	0.0543308i
$842$	−47.5801	+	54.9104i	−1.63972	+	1.89234i
$843$	1.91115	−	4.18484i	0.0658236	−	0.144133i
$844$	−8.37590	−	5.38287i	−0.288310	−	0.185286i
$845$	4.81529	−	1.41390i	0.165651	−	0.0486395i
$846$	−5.73319	−	6.61645i	−0.197111	−	0.227478i
$847$	−0.525720	−	0.154365i	−0.0180640	−	0.00530406i
$848$	2.23444	+	4.89273i	0.0767308	+	0.168017i
$849$	0.271697	−	1.88969i	0.00932461	−	0.0648541i
$850$	78.4656			2.69135
$851$	−6.09857	+	19.3011i	−0.209056	+	0.661635i
$852$	28.7501			0.984961
$853$	−1.83351	+	12.7523i	−0.0627781	+	0.436631i	0.934056	+	0.357126i	$0.116243\pi$
$853$	−1.83351	+	12.7523i	−0.0627781	+	0.436631i	−0.996834	+	0.0795056i	$0.974666\pi$
$854$	−8.86881	−	19.4200i	−0.303484	−	0.664538i
$855$	−1.90000	−	0.557890i	−0.0649786	−	0.0190794i
$856$	−14.5663	−	16.8104i	−0.497866	−	0.574568i
$857$	−34.5996	+	10.1594i	−1.18190	+	0.347037i	−0.812906	−	0.582395i	$-0.802116\pi$
$857$	−34.5996	+	10.1594i	−1.18190	+	0.347037i	−0.368994	+	0.929432i	$0.620298\pi$
$858$	−11.0327	−	7.09029i	−0.376650	−	0.242059i
$859$	−16.9853	+	37.1927i	−0.579532	+	1.26900i	0.362033	+	0.932165i	$0.382083\pi$
$859$	−16.9853	+	37.1927i	−0.579532	+	1.26900i	−0.941565	+	0.336832i	$0.890644\pi$
$860$	12.5251	−	14.4547i	0.427102	−	0.492902i
$861$	−4.49688	+	2.88997i	−0.153253	+	0.0984898i
$862$	2.26133	+	15.7279i	0.0770211	+	0.535693i
$863$	4.92216	+	34.2344i	0.167552	+	1.16535i	0.883923	+	0.467632i	$0.154893\pi$
$863$	4.92216	+	34.2344i	0.167552	+	1.16535i	−0.716371	+	0.697719i	$0.754198\pi$
$864$	5.17474	−	3.32561i	0.176048	−	0.113139i
$865$	6.67330	−	7.70140i	0.226899	−	0.261855i
$866$	−20.3184	+	44.4912i	−0.690449	+	1.51187i
$867$	−30.6527	−	19.6993i	−1.04102	−	0.669023i
$868$	−10.3432	+	3.03704i	−0.351071	+	0.103084i
$869$	0.622321	+	0.718197i	0.0211108	+	0.0243632i
$870$	−6.29276	−	1.84772i	−0.213345	−	0.0626436i
$871$	7.96714	+	17.4456i	0.269956	+	0.591122i
$872$	5.84398	−	40.6458i	0.197902	−	1.37644i
$873$	−0.190510			−0.00644777
$874$	0.858447	−	41.9858i	0.0290374	−	1.42019i
$875$	4.98930			0.168669
$876$	2.15042	−	14.9565i	0.0726560	−	0.505333i
$877$	1.34211	+	2.93882i	0.0453200	+	0.0992368i	0.930938	−	0.365178i	$-0.118992\pi$
$877$	1.34211	+	2.93882i	0.0453200	+	0.0992368i	−0.885618	+	0.464415i	$0.846265\pi$
$878$	−31.8830	−	9.36169i	−1.07600	−	0.315942i
$879$	−8.09779	−	9.34535i	−0.273132	−	0.315211i
$880$	0.711429	−	0.208894i	0.0239823	−	0.00704183i
$881$	−6.34204	−	4.07578i	−0.213669	−	0.137317i	0.429429	−	0.903101i	$-0.358715\pi$
$881$	−6.34204	−	4.07578i	−0.213669	−	0.137317i	−0.643098	+	0.765784i	$0.722351\pi$
$882$	0.941228	−	2.06100i	0.0316928	−	0.0693975i
$883$	−17.5856	+	20.2948i	−0.591801	+	0.682975i	−0.970099	−	0.242709i	$-0.921964\pi$
$883$	−17.5856	+	20.2948i	−0.591801	+	0.682975i	0.378298	+	0.925684i	$0.376509\pi$
$884$	−34.5014	+	22.1727i	−1.16041	+	0.745749i
$885$	−0.526577	−	3.66243i	−0.0177007	−	0.123111i
$886$	−0.858812	−	5.97317i	−0.0288524	−	0.200673i
$887$	−15.5308	+	9.98107i	−0.521475	+	0.335132i	−0.774755	−	0.632261i	$-0.782127\pi$
$887$	−15.5308	+	9.98107i	−0.521475	+	0.335132i	0.253280	+	0.967393i	$0.418491\pi$
$888$	7.09933	−	8.19307i	0.238238	−	0.274941i
$889$	−3.50556	+	7.67610i	−0.117573	+	0.257448i
$890$	−1.06776	−	0.686205i	−0.0357912	−	0.0230016i
$891$	−3.10201	+	0.910832i	−0.103921	+	0.0305140i
$892$	3.86046	+	4.45521i	0.129258	+	0.149171i
$893$	−14.3283	−	4.20716i	−0.479477	−	0.140787i
$894$	12.4691	+	27.3035i	0.417028	+	0.913165i
$895$	0.371129	−	2.58126i	0.0124055	−	0.0862820i
$896$	17.2474			0.576195
$897$	−8.47213	−	1.39543i	−0.282876	−	0.0465921i
$898$	61.4478			2.05054
$899$	−2.76572	+	19.2360i	−0.0922419	+	0.641556i
$900$	−6.16704	−	13.5039i	−0.205568	−	0.450131i
$901$	−84.2857	−	24.7485i	−2.80796	−	0.824492i
$902$	25.6417	+	29.5921i	0.853775	+	0.985309i
$903$	11.4296	−	3.35604i	0.380354	−	0.111682i
$904$	−10.0802	−	6.47817i	−0.335263	−	0.215461i
$905$	2.50724	−	5.49010i	0.0833436	−	0.182497i
$906$	4.82628	−	5.56983i	0.160343	−	0.185045i
$907$	−39.9477	+	25.6728i	−1.32644	+	0.852452i	−0.995822	−	0.0913116i	$-0.970894\pi$
$907$	−39.9477	+	25.6728i	−1.32644	+	0.852452i	−0.330620	+	0.943764i	$0.607258\pi$
$908$	2.52574	+	17.5669i	0.0838195	+	0.582978i
$909$	1.45941	+	10.1504i	0.0484056	+	0.336668i
$910$	−1.74854	+	1.12372i	−0.0579634	+	0.0372508i
$911$	12.9235	−	14.9145i	0.428175	−	0.494140i	−0.500135	−	0.865947i	$-0.666716\pi$
$911$	12.9235	−	14.9145i	0.428175	−	0.494140i	0.928310	+	0.371807i	$0.121262\pi$
$912$	0.718611	−	1.57354i	0.0237956	−	0.0521051i
$913$	39.1088	+	25.1337i	1.29431	+	0.831804i
$914$	−10.2497	+	3.00959i	−0.339030	+	0.0995483i
$915$	3.16165	+	3.64874i	0.104521	+	0.120624i
$916$	−64.5556	−	18.9552i	−2.13298	−	0.626299i
$917$	−5.34057	−	11.6942i	−0.176361	−	0.386177i
$918$	−2.35713	+	16.3942i	−0.0777969	+	0.541089i
$919$	15.6557			0.516433			0.258217	−	0.966087i	$-0.416865\pi$
$919$	15.6557			0.516433			0.258217	+	0.966087i	$0.416865\pi$
$920$	−4.85353	+	4.03489i	−0.160016	+	0.133026i
$921$	23.2886			0.767384
$922$	−7.95857	+	55.3531i	−0.262102	+	1.82296i
$923$	−6.82361	−	14.9416i	−0.224602	−	0.491809i
$924$	−9.72057	−	2.85422i	−0.319783	−	0.0938968i
$925$	13.0942	+	15.1115i	0.430534	+	0.496862i
$926$	66.3434	−	19.4802i	2.18018	−	0.640158i
$927$	−0.466292	−	0.299668i	−0.0153151	−	0.00984239i
$928$	14.4357	−	31.6097i	0.473874	−	1.03764i
$929$	6.78107	−	7.82577i	0.222480	−	0.256755i	−0.633526	−	0.773721i	$-0.718393\pi$
$929$	6.78107	−	7.82577i	0.222480	−	0.256755i	0.856006	+	0.516966i	$0.172939\pi$
$930$	3.35968	−	2.15914i	0.110168	−	0.0708009i
$931$	−0.550006	−	3.82538i	−0.0180257	−	0.125372i
$932$	−12.0905	−	84.0910i	−0.396036	−	2.75449i
$933$	14.5270	−	9.33590i	0.475591	−	0.305644i
$934$	−46.9158	+	54.1438i	−1.53513	+	1.77164i
$935$	−5.03035	+	11.0149i	−0.164510	+	0.360227i
$936$	3.86860	+	2.48620i	0.126449	+	0.0812639i
$937$	−20.6580	+	6.06573i	−0.674867	+	0.198159i	−0.601169	−	0.799122i	$-0.705298\pi$
$937$	−20.6580	+	6.06573i	−0.674867	+	0.198159i	−0.0736978	+	0.997281i	$0.523480\pi$
$938$	15.8943	+	18.3430i	0.518966	+	0.598919i
$939$	−30.9033	−	9.07404i	−1.00849	−	0.296120i
$940$	2.57727	+	5.64343i	0.0840612	+	0.184068i
$941$	−3.56465	+	24.7927i	−0.116204	+	0.808217i	0.845470	+	0.534023i	$0.179320\pi$
$941$	−3.56465	+	24.7927i	−0.116204	+	0.808217i	−0.961674	+	0.274195i	$0.911589\pi$
$942$	−50.5768			−1.64788
$943$	23.0966	+	11.1240i	0.752130	+	0.362247i
$944$	3.23230			0.105203
$945$	−0.0729196	+	0.507167i	−0.00237208	+	0.0164981i
$946$	−36.2482	−	79.3724i	−1.17853	−	2.58062i
$947$	−36.6588	−	10.7640i	−1.19125	−	0.349783i	−0.374749	−	0.927126i	$-0.622271\pi$
$947$	−36.6588	−	10.7640i	−1.19125	−	0.349783i	−0.816501	+	0.577344i	$0.804089\pi$
$948$	−0.603200	−	0.696130i	−0.0195910	−	0.0226093i
$949$	−8.28339	+	2.43222i	−0.268890	+	0.0789532i
$950$	−34.8982	−	22.4277i	−1.13225	−	0.727650i
$951$	−2.82336	+	6.18229i	−0.0915536	+	0.200474i
$952$	−12.2958	+	14.1901i	−0.398508	+	0.459902i
$953$	21.0536	−	13.5303i	0.681992	−	0.438289i	−0.153239	−	0.988189i	$-0.548970\pi$
$953$	21.0536	−	13.5303i	0.681992	−	0.438289i	0.835231	+	0.549900i	$0.185334\pi$
$954$	3.87484	+	26.9501i	0.125453	+	0.872542i
$955$	1.11697	+	7.76869i	0.0361443	+	0.251389i
$956$	−10.8604	+	6.97959i	−0.351252	+	0.225736i
$957$	−11.9603	+	13.8030i	−0.386623	+	0.446186i
$958$	23.4477	−	51.3433i	0.757562	−	1.65883i
$959$	−3.27873	−	2.10711i	−0.105876	−	0.0680423i
$960$	−6.41178	+	1.88267i	−0.206939	+	0.0607629i
$961$	12.5511	+	14.4847i	0.404874	+	0.467249i
$962$	−16.4278	−	4.82363i	−0.529653	−	0.155520i
$963$	3.59747	+	7.87736i	0.115927	+	0.253844i
$964$	−0.518929	+	3.60923i	−0.0167136	+	0.116245i
$965$	−2.71394			−0.0873648
$966$	−10.7849	+	1.32623i	−0.346999	+	0.0426708i
$967$	−5.62563			−0.180908			−0.0904540	−	0.995901i	$-0.528832\pi$
$967$	−5.62563			−0.180908			−0.0904540	+	0.995901i	$0.528832\pi$
$968$	0.200285	−	1.39301i	0.00643740	−	0.0447731i
$969$	11.7360	+	25.6983i	0.377015	+	0.825547i
$970$	0.212210	+	0.0623104i	0.00681364	+	0.00200067i
$971$	−1.80855	−	2.08718i	−0.0580391	−	0.0669807i	0.725988	−	0.687708i	$-0.241383\pi$
$971$	−1.80855	−	2.08718i	−0.0580391	−	0.0669807i	−0.784027	+	0.620727i	$0.786837\pi$
$972$	3.00670	−	0.882847i	0.0964400	−	0.0283173i
$973$	9.07406	+	5.83155i	0.290901	+	0.186951i
$974$	−9.11646	+	19.9623i	−0.292110	+	0.639632i
$975$	−5.55439	+	6.41010i	−0.177883	+	0.205288i
$976$	−3.54807	+	2.28020i	−0.113571	+	0.0729876i
$977$	0.989416	+	6.88154i	0.0316542	+	0.220160i	0.999508	−	0.0313521i	$-0.00998132\pi$
$977$	0.989416	+	6.88154i	0.0316542	+	0.220160i	−0.967854	+	0.251512i	$0.919072\pi$
$978$	2.02536	+	14.0867i	0.0647638	+	0.450442i
$979$	−2.97349	+	1.91095i	−0.0950332	+	0.0610741i
$980$	−1.05146	+	1.21345i	−0.0335876	+	0.0387621i
$981$	−6.64133	+	14.5425i	−0.212041	+	0.464306i
$982$	−51.0764	−	32.8248i	−1.62991	−	1.04748i
$983$	26.9991	−	7.92764i	0.861136	−	0.252852i	0.178795	−	0.983886i	$-0.442780\pi$
$983$	26.9991	−	7.92764i	0.861136	−	0.252852i	0.682341	+	0.731034i	$0.260962\pi$
$984$	−8.99122	−	10.3764i	−0.286629	−	0.330788i
$985$	12.7689	+	3.74929i	0.406851	+	0.119462i
$986$	38.8694	+	85.1122i	1.23785	+	2.71052i
$987$	−0.549901	+	3.82465i	−0.0175036	+	0.121740i
$988$	21.6824			0.689808
$989$	−42.4011	−	38.2860i	−1.34828	−	1.21743i
$990$	3.75326			0.119286
$991$	1.35251	−	9.40691i	0.0429639	−	0.298820i	−0.956998	−	0.290094i	$-0.906313\pi$
$991$	1.35251	−	9.40691i	0.0429639	−	0.298820i	0.999962	−	0.00872600i	$-0.00277761\pi$
$992$	8.79041	+	19.2483i	0.279096	+	0.611135i
$993$	−12.6621	−	3.71794i	−0.401821	−	0.117985i
$994$	−13.6129	−	15.7102i	−0.431776	−	0.498296i
$995$	0.932178	−	0.273712i	0.0295520	−	0.00867726i
$996$	−37.9072	−	24.3615i	−1.20113	−	0.771922i
$997$	10.1677	−	22.2641i	0.322014	−	0.705112i	−0.677524	−	0.735500i	$-0.736947\pi$
$997$	10.1677	−	22.2641i	0.322014	−	0.705112i	0.999538	+	0.0303886i	$0.00967448\pi$
$998$	−22.9921	+	26.5342i	−0.727801	+	0.839927i
$999$	−3.55067	+	2.28188i	−0.112338	+	0.0721954i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.e.169.1	✓	60
23.3	even	11	inner	483.2.q.e.463.1	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.e.169.1	✓	60	1.1	even	1	trivial
483.2.q.e.463.1	yes	60	23.3	even	11	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.322450 + 2.24269i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-3.00670 - 0.882847i) q^{4} +(-0.335539 - 0.387233i) q^{5} +(2.17397 - 0.638336i) q^{6} +(-0.841254 - 0.540641i) q^{7} +(1.06701 - 2.33642i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.322450 + 2.24269i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-3.00670 - 0.882847i) q^{4} +(-0.335539 - 0.387233i) q^{5} +(2.17397 - 0.638336i) q^{6} +(-0.841254 - 0.540641i) q^{7} +(1.06701 - 2.33642i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(0.976638 - 0.627647i) q^{10} +(-0.460099 - 3.20006i) q^{11} +(0.445963 + 3.10174i) q^{12} +(1.50615 - 0.967944i) q^{13} +(1.48375 - 1.71234i) q^{14} +(-0.212851 + 0.466079i) q^{15} +(-0.376549 - 0.241993i) q^{16} +(7.01395 - 2.05948i) q^{17} +(-1.48375 - 1.71234i) q^{18} +(-3.70816 - 1.08882i) q^{19} +(0.666998 + 1.46052i) q^{20} +(-0.142315 + 0.989821i) q^{21} +7.32511 q^{22} +(4.40226 - 1.90267i) q^{23} -2.56853 q^{24} +(0.674211 - 4.68924i) q^{25} +(1.68514 + 3.68994i) q^{26} +(0.959493 + 0.281733i) q^{27} +(2.05209 + 2.36824i) q^{28} +(5.42044 - 1.59158i) q^{29} +(-0.976638 - 0.627647i) q^{30} +(-1.42905 + 3.12918i) q^{31} +(4.02820 - 4.64879i) q^{32} +(-2.71975 + 1.74787i) q^{33} +(2.35713 + 16.3942i) q^{34} +(0.0729196 + 0.507167i) q^{35} +(2.63618 - 1.69417i) q^{36} +(-2.76396 + 3.18978i) q^{37} +(3.63757 - 7.96518i) q^{38} +(-1.50615 - 0.967944i) q^{39} +(-1.26276 + 0.370780i) q^{40} +(3.50052 + 4.03982i) q^{41} +(-2.17397 - 0.638336i) q^{42} +(-4.94848 - 10.8357i) q^{43} +(-1.44178 + 10.0278i) q^{44} +0.512382 q^{45} +(2.84759 + 10.4864i) q^{46} +3.86398 q^{47} +(-0.0637007 + 0.443048i) q^{48} +(0.415415 + 0.909632i) q^{49} +(10.2991 + 3.02410i) q^{50} +(-4.78707 - 5.52457i) q^{51} +(-5.38309 + 1.58062i) q^{52} +(-10.1092 - 6.49681i) q^{53} +(-0.941228 + 2.06100i) q^{54} +(-1.08479 + 1.25191i) q^{55} +(-2.16079 + 1.38865i) q^{56} +(0.550006 + 3.82538i) q^{57} +(1.82161 + 12.6696i) q^{58} +(-6.07498 + 3.90415i) q^{59} +(1.05146 - 1.21345i) q^{60} +(3.91429 - 8.57109i) q^{61} +(-6.55699 - 4.21392i) q^{62} +(0.959493 - 0.281733i) q^{63} +(8.54067 + 9.85645i) q^{64} +(-0.880191 - 0.258448i) q^{65} +(-3.04296 - 6.66315i) q^{66} +(-1.52451 + 10.6032i) q^{67} -22.9070 q^{68} +(-3.55949 - 3.21404i) q^{69} -1.16093 q^{70} +(1.30569 - 9.08129i) q^{71} +(1.06701 + 2.33642i) q^{72} +(-4.62665 - 1.35851i) q^{73} +(-6.26245 - 7.22726i) q^{74} +(-4.54556 + 1.33470i) q^{75} +(10.1881 + 6.54748i) q^{76} +(-1.34302 + 2.94081i) q^{77} +(2.65646 - 3.06571i) q^{78} +(-0.247281 + 0.158918i) q^{79} +(0.0326391 + 0.227010i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-10.1888 + 6.54795i) q^{82} +(-9.41662 + 10.8674i) q^{83} +(1.30176 - 2.85045i) q^{84} +(-3.15095 - 2.02499i) q^{85} +(25.8967 - 7.60395i) q^{86} +(-3.69949 - 4.26944i) q^{87} +(-7.96762 - 2.33951i) q^{88} +(-0.454172 - 0.994498i) q^{89} +(-0.165218 + 1.14911i) q^{90} -1.79036 q^{91} +(-14.9160 + 1.83423i) q^{92} +3.44005 q^{93} +(-1.24594 + 8.66571i) q^{94} +(0.822609 + 1.80126i) q^{95} +(-5.90206 - 1.73300i) q^{96} +(0.124757 + 0.143978i) q^{97} +(-2.17397 + 0.638336i) q^{98} +(2.71975 + 1.74787i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} + 5 q^{5} + q^{6} + 6 q^{7} + 13 q^{8} - 6 q^{9}+O(q^{10}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 + 5 * q^5 + q^6 + 6 * q^7 + 13 * q^8 - 6 * q^9	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} + 5 q^{5} + q^{6} + 6 q^{7} + 13 q^{8} - 6 q^{9} - 4 q^{10} - q^{11} + 3 q^{12} + 22 q^{13} + q^{14} + 6 q^{15} - 5 q^{16} + 9 q^{17} - q^{18} - 34 q^{19} + 67 q^{20} - 6 q^{21} - 28 q^{22} - 13 q^{23} + 42 q^{24} - 15 q^{25} - 4 q^{26} + 6 q^{27} + 14 q^{28} - 23 q^{29} + 4 q^{30} + 27 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 6 q^{35} - 3 q^{36} - 82 q^{37} + 2 q^{38} - 22 q^{39} + 57 q^{40} - 22 q^{41} - q^{42} + 25 q^{43} - 41 q^{44} + 16 q^{45} - 47 q^{46} - 90 q^{47} - 28 q^{48} - 6 q^{49} + 55 q^{50} - 9 q^{51} - 92 q^{52} - 17 q^{53} - 10 q^{54} + 21 q^{55} + 9 q^{56} - 32 q^{57} + 87 q^{58} + 38 q^{59} - 45 q^{60} + 23 q^{61} + q^{62} + 6 q^{63} - 75 q^{64} - 75 q^{65} + 61 q^{66} + 5 q^{67} + 88 q^{68} + 13 q^{69} - 18 q^{70} + 8 q^{71} + 13 q^{72} + 90 q^{73} + 79 q^{74} - 18 q^{75} - 85 q^{76} - 10 q^{77} - 18 q^{78} - 6 q^{79} - 147 q^{80} - 6 q^{81} + 112 q^{82} - 90 q^{83} - 3 q^{84} + 55 q^{85} - 8 q^{86} - 10 q^{87} - 210 q^{88} - 15 q^{89} - 4 q^{90} - 22 q^{91} + 39 q^{92} + 50 q^{93} + 144 q^{94} + 72 q^{95} + 7 q^{96} - 48 q^{97} - q^{98} - q^{99}+O(q^{100}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 + 5 * q^5 + q^6 + 6 * q^7 + 13 * q^8 - 6 * q^9 - 4 * q^10 - q^11 + 3 * q^12 + 22 * q^13 + q^14 + 6 * q^15 - 5 * q^16 + 9 * q^17 - q^18 - 34 * q^19 + 67 * q^20 - 6 * q^21 - 28 * q^22 - 13 * q^23 + 42 * q^24 - 15 * q^25 - 4 * q^26 + 6 * q^27 + 14 * q^28 - 23 * q^29 + 4 * q^30 + 27 * q^31 + 37 * q^32 + q^33 + 3 * q^34 + 6 * q^35 - 3 * q^36 - 82 * q^37 + 2 * q^38 - 22 * q^39 + 57 * q^40 - 22 * q^41 - q^42 + 25 * q^43 - 41 * q^44 + 16 * q^45 - 47 * q^46 - 90 * q^47 - 28 * q^48 - 6 * q^49 + 55 * q^50 - 9 * q^51 - 92 * q^52 - 17 * q^53 - 10 * q^54 + 21 * q^55 + 9 * q^56 - 32 * q^57 + 87 * q^58 + 38 * q^59 - 45 * q^60 + 23 * q^61 + q^62 + 6 * q^63 - 75 * q^64 - 75 * q^65 + 61 * q^66 + 5 * q^67 + 88 * q^68 + 13 * q^69 - 18 * q^70 + 8 * q^71 + 13 * q^72 + 90 * q^73 + 79 * q^74 - 18 * q^75 - 85 * q^76 - 10 * q^77 - 18 * q^78 - 6 * q^79 - 147 * q^80 - 6 * q^81 + 112 * q^82 - 90 * q^83 - 3 * q^84 + 55 * q^85 - 8 * q^86 - 10 * q^87 - 210 * q^88 - 15 * q^89 - 4 * q^90 - 22 * q^91 + 39 * q^92 + 50 * q^93 + 144 * q^94 + 72 * q^95 + 7 * q^96 - 48 * q^97 - q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more