LMFDB - Embedded newform 54.2.e.a.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,2,Mod(7,54)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("54.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	54.e (of order $9$, degree $6$, 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:	$0.431192170915$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.1
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	54.25
Dual form			54.2.e.a.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 + 0.984808i) q^{2} +(-0.592396 + 1.62760i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.673648 + 0.565258i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(3.31908 - 1.20805i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.29813 - 1.92836i) q^{9} +O(q^{10})$	\(q+(-0.173648 + 0.984808i) q^{2} +(-0.592396 + 1.62760i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.673648 + 0.565258i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(3.31908 - 1.20805i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.29813 - 1.92836i) q^{9} +(-0.439693 - 0.761570i) q^{10} +(2.73783 + 2.29731i) q^{11} +(1.11334 - 1.32683i) q^{12} +(-0.641559 - 3.63846i) q^{13} +(0.613341 + 3.47843i) q^{14} +(-0.520945 - 1.43128i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-3.12449 - 5.41177i) q^{17} +(2.29813 - 1.92836i) q^{18} +(-2.08512 + 3.61154i) q^{19} +(0.826352 - 0.300767i) q^{20} +6.11776i q^{21} +(-2.73783 + 2.29731i) q^{22} +(-1.93969 - 0.705990i) q^{23} +(1.11334 + 1.32683i) q^{24} +(-0.733956 + 4.16247i) q^{25} +3.69459 q^{26} +(4.50000 - 2.59808i) q^{27} -3.53209 q^{28} +(0.0282185 - 0.160035i) q^{29} +(1.50000 - 0.264490i) q^{30} +(-1.53936 - 0.560282i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(-5.36097 + 3.09516i) q^{33} +(5.87211 - 2.13727i) q^{34} +(-1.55303 + 2.68993i) q^{35} +(1.50000 + 2.59808i) q^{36} +(3.85844 + 6.68302i) q^{37} +(-3.19459 - 2.68058i) q^{38} +(6.30200 + 1.11121i) q^{39} +(0.152704 + 0.866025i) q^{40} +(-1.33750 - 7.58532i) q^{41} +(-6.02481 - 1.06234i) q^{42} +(-8.29086 - 6.95686i) q^{43} +(-1.78699 - 3.09516i) q^{44} +2.63816 q^{45} +(1.03209 - 1.78763i) q^{46} +(6.02481 - 2.19285i) q^{47} +(-1.50000 + 0.866025i) q^{48} +(4.19459 - 3.51968i) q^{49} +(-3.97178 - 1.44561i) q^{50} +(10.6591 - 1.87949i) q^{51} +(-0.641559 + 3.63846i) q^{52} +0.716881 q^{53} +(1.77719 + 4.88279i) q^{54} -3.14290 q^{55} +(0.613341 - 3.47843i) q^{56} +(-4.64290 - 5.53320i) q^{57} +(0.152704 + 0.0555796i) q^{58} +(-5.35117 + 4.49016i) q^{59} +1.52314i q^{60} +(1.19207 - 0.433877i) q^{61} +(0.819078 - 1.41868i) q^{62} +(-9.95723 - 3.62414i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(2.48886 + 2.08840i) q^{65} +(-2.11721 - 5.81699i) q^{66} +(0.624485 + 3.54163i) q^{67} +(1.08512 + 6.15403i) q^{68} +(2.29813 - 2.73881i) q^{69} +(-2.37939 - 1.99654i) q^{70} +(6.76991 + 11.7258i) q^{71} +(-2.81908 + 1.02606i) q^{72} +(1.16385 - 2.01584i) q^{73} +(-7.25150 + 2.63933i) q^{74} +(-6.34002 - 3.66041i) q^{75} +(3.19459 - 2.68058i) q^{76} +(11.8623 + 4.31753i) q^{77} +(-2.18866 + 6.01330i) q^{78} +(-1.14930 + 6.51800i) q^{79} -0.879385 q^{80} +(1.56283 + 8.86327i) q^{81} +7.70233 q^{82} +(-0.773318 + 4.38571i) q^{83} +(2.09240 - 5.74881i) q^{84} +(5.16385 + 1.87949i) q^{85} +(8.29086 - 6.95686i) q^{86} +(0.243756 + 0.140732i) q^{87} +(3.35844 - 1.22237i) q^{88} +(-4.62449 + 8.00984i) q^{89} +(-0.458111 + 2.59808i) q^{90} +(-6.52481 - 11.3013i) q^{91} +(1.58125 + 1.32683i) q^{92} +(1.82383 - 2.17355i) q^{93} +(1.11334 + 6.31407i) q^{94} +(-0.636812 - 3.61154i) q^{95} +(-0.592396 - 1.62760i) q^{96} +(-8.64930 - 7.25762i) q^{97} +(2.73783 + 4.74205i) q^{98} +(-1.86184 - 10.5590i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{5} - 9 q^{6} + 3 q^{7} + 3 q^{8}+O(q^{10}) $ 6 * q - 3 * q^5 - 9 * q^6 + 3 * q^7 + 3 * q^8	$ 6 q - 3 q^{5} - 9 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{10} - 3 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{17} + 9 q^{19} + 6 q^{20} + 3 q^{22} - 6 q^{23} - 9 q^{25} + 18 q^{26} + 27 q^{27} - 12 q^{28} + 15 q^{29} + 9 q^{30} - 18 q^{31} - 9 q^{33} + 6 q^{34} + 3 q^{35} + 9 q^{36} + 15 q^{37} - 15 q^{38} + 3 q^{40} - 3 q^{41} - 9 q^{42} - 18 q^{43} - 3 q^{44} - 18 q^{45} - 3 q^{46} + 9 q^{47} - 9 q^{48} + 21 q^{49} - 9 q^{50} + 27 q^{51} - 12 q^{52} - 12 q^{53} - 18 q^{55} - 3 q^{56} - 27 q^{57} + 3 q^{58} - 6 q^{59} + 18 q^{61} - 12 q^{62} - 9 q^{63} - 3 q^{64} + 21 q^{65} + 18 q^{66} - 9 q^{67} - 15 q^{68} - 3 q^{70} + 12 q^{71} + 3 q^{73} - 3 q^{74} - 18 q^{75} + 15 q^{76} + 39 q^{77} + 18 q^{78} + 33 q^{79} + 6 q^{80} - 6 q^{82} - 18 q^{83} + 9 q^{84} + 27 q^{85} + 18 q^{86} + 9 q^{87} + 12 q^{88} - 15 q^{89} - 9 q^{90} - 12 q^{91} + 12 q^{92} + 27 q^{93} + 21 q^{95} - 12 q^{97} - 3 q^{98} - 45 q^{99}+O(q^{100}) $ 6 * q - 3 * q^5 - 9 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^10 - 3 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^17 + 9 * q^19 + 6 * q^20 + 3 * q^22 - 6 * q^23 - 9 * q^25 + 18 * q^26 + 27 * q^27 - 12 * q^28 + 15 * q^29 + 9 * q^30 - 18 * q^31 - 9 * q^33 + 6 * q^34 + 3 * q^35 + 9 * q^36 + 15 * q^37 - 15 * q^38 + 3 * q^40 - 3 * q^41 - 9 * q^42 - 18 * q^43 - 3 * q^44 - 18 * q^45 - 3 * q^46 + 9 * q^47 - 9 * q^48 + 21 * q^49 - 9 * q^50 + 27 * q^51 - 12 * q^52 - 12 * q^53 - 18 * q^55 - 3 * q^56 - 27 * q^57 + 3 * q^58 - 6 * q^59 + 18 * q^61 - 12 * q^62 - 9 * q^63 - 3 * q^64 + 21 * q^65 + 18 * q^66 - 9 * q^67 - 15 * q^68 - 3 * q^70 + 12 * q^71 + 3 * q^73 - 3 * q^74 - 18 * q^75 + 15 * q^76 + 39 * q^77 + 18 * q^78 + 33 * q^79 + 6 * q^80 - 6 * q^82 - 18 * q^83 + 9 * q^84 + 27 * q^85 + 18 * q^86 + 9 * q^87 + 12 * q^88 - 15 * q^89 - 9 * q^90 - 12 * q^91 + 12 * q^92 + 27 * q^93 + 21 * q^95 - 12 * q^97 - 3 * q^98 - 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$3$	−0.592396	+	1.62760i	−0.342020	+	0.939693i
$3$	−0.592396	+	1.62760i	−0.342020	+	0.939693i
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	−0.673648	+	0.565258i	−0.301265	+	0.252791i	−0.780870	−	0.624693i	$-0.785224\pi$
$5$	−0.673648	+	0.565258i	−0.301265	+	0.252791i	0.479606	+	0.877484i	$0.340780\pi$
$6$	−1.50000	−	0.866025i	−0.612372	−	0.353553i
$7$	3.31908	−	1.20805i	1.25449	−	0.456598i	0.372576	−	0.928002i	$-0.378475\pi$
$7$	3.31908	−	1.20805i	1.25449	−	0.456598i	0.881918	+	0.471403i	$0.156252\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−2.29813	−	1.92836i	−0.766044	−	0.642788i
$10$	−0.439693	−	0.761570i	−0.139043	−	0.240830i
$11$	2.73783	+	2.29731i	0.825486	+	0.692665i	0.954250	−	0.299011i	$-0.0966566\pi$
$11$	2.73783	+	2.29731i	0.825486	+	0.692665i	−0.128764	+	0.991675i	$0.541101\pi$
$12$	1.11334	−	1.32683i	0.321394	−	0.383022i
$13$	−0.641559	−	3.63846i	−0.177937	−	1.00913i	−0.934700	−	0.355439i	$-0.884331\pi$
$13$	−0.641559	−	3.63846i	−0.177937	−	1.00913i	0.756763	−	0.653689i	$-0.226780\pi$
$14$	0.613341	+	3.47843i	0.163922	+	0.929649i
$15$	−0.520945	−	1.43128i	−0.134507	−	0.369556i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−3.12449	−	5.41177i	−0.757799	−	1.31255i	−0.943971	−	0.330029i	$-0.892941\pi$
$17$	−3.12449	−	5.41177i	−0.757799	−	1.31255i	0.186172	−	0.982517i	$-0.440392\pi$
$18$	2.29813	−	1.92836i	0.541675	−	0.454519i
$19$	−2.08512	+	3.61154i	−0.478360	+	0.828544i	−0.999692	−	0.0248102i	$-0.992102\pi$
$19$	−2.08512	+	3.61154i	−0.478360	+	0.828544i	0.521332	+	0.853354i	$0.325435\pi$
$20$	0.826352	−	0.300767i	0.184778	−	0.0672537i
$21$			6.11776i			1.33500i
$22$	−2.73783	+	2.29731i	−0.583706	+	0.489788i
$23$	−1.93969	−	0.705990i	−0.404454	−	0.147209i	0.131779	−	0.991279i	$-0.457931\pi$
$23$	−1.93969	−	0.705990i	−0.404454	−	0.147209i	−0.536233	+	0.844070i	$0.680153\pi$
$24$	1.11334	+	1.32683i	0.227260	+	0.270838i
$25$	−0.733956	+	4.16247i	−0.146791	+	0.832494i
$26$	3.69459			0.724569
$27$	4.50000	−	2.59808i	0.866025	−	0.500000i
$28$	−3.53209			−0.667502
$29$	0.0282185	−	0.160035i	0.00524004	−	0.0297178i	−0.982076	−	0.188487i	$-0.939642\pi$
$29$	0.0282185	−	0.160035i	0.00524004	−	0.0297178i	0.987316	+	0.158770i	$0.0507527\pi$
$30$	1.50000	−	0.264490i	0.273861	−	0.0482891i
$31$	−1.53936	−	0.560282i	−0.276478	−	0.100630i	0.200060	−	0.979784i	$-0.435886\pi$
$31$	−1.53936	−	0.560282i	−0.276478	−	0.100630i	−0.476538	+	0.879154i	$0.658108\pi$
$32$	−0.766044	+	0.642788i	−0.135419	+	0.113630i
$33$	−5.36097	+	3.09516i	−0.933225	+	0.538797i
$34$	5.87211	−	2.13727i	1.00706	−	0.366539i
$35$	−1.55303	+	2.68993i	−0.262511	+	0.454682i
$36$	1.50000	+	2.59808i	0.250000	+	0.433013i
$37$	3.85844	+	6.68302i	0.634324	+	1.09868i	0.986658	+	0.162807i	$0.0520547\pi$
$37$	3.85844	+	6.68302i	0.634324	+	1.09868i	−0.352334	+	0.935874i	$0.614612\pi$
$38$	−3.19459	−	2.68058i	−0.518231	−	0.434848i
$39$	6.30200	+	1.11121i	1.00913	+	0.177937i
$40$	0.152704	+	0.866025i	0.0241446	+	0.136931i
$41$	−1.33750	−	7.58532i	−0.208882	−	1.18463i	−0.891213	−	0.453585i	$-0.850145\pi$
$41$	−1.33750	−	7.58532i	−0.208882	−	1.18463i	0.682331	−	0.731043i	$-0.260966\pi$
$42$	−6.02481	−	1.06234i	−0.929649	−	0.163922i
$43$	−8.29086	−	6.95686i	−1.26434	−	1.06091i	−0.995205	−	0.0978094i	$-0.968816\pi$
$43$	−8.29086	−	6.95686i	−1.26434	−	1.06091i	−0.269139	−	0.963101i	$-0.586739\pi$
$44$	−1.78699	−	3.09516i	−0.269399	−	0.466612i
$45$	2.63816			0.393273
$46$	1.03209	−	1.78763i	0.152173	−	0.263572i
$47$	6.02481	−	2.19285i	0.878810	−	0.319861i	0.137080	−	0.990560i	$-0.456228\pi$
$47$	6.02481	−	2.19285i	0.878810	−	0.319861i	0.741729	+	0.670699i	$0.234006\pi$
$48$	−1.50000	+	0.866025i	−0.216506	+	0.125000i
$49$	4.19459	−	3.51968i	0.599228	−	0.502812i
$50$	−3.97178	−	1.44561i	−0.561695	−	0.204440i
$51$	10.6591	−	1.87949i	1.49257	−	0.263181i
$52$	−0.641559	+	3.63846i	−0.0889683	+	0.504564i
$53$	0.716881			0.0984712			0.0492356	−	0.998787i	$-0.484321\pi$
$53$	0.716881			0.0984712			0.0492356	+	0.998787i	$0.484321\pi$
$54$	1.77719	+	4.88279i	0.241845	+	0.664463i
$55$	−3.14290			−0.423789
$56$	0.613341	−	3.47843i	0.0819611	−	0.464825i
$57$	−4.64290	−	5.53320i	−0.614968	−	0.732890i
$58$	0.152704	+	0.0555796i	0.0200510	+	0.00729796i
$59$	−5.35117	+	4.49016i	−0.696663	+	0.584569i	−0.920822	−	0.389983i	$-0.872481\pi$
$59$	−5.35117	+	4.49016i	−0.696663	+	0.584569i	0.224159	+	0.974552i	$0.428036\pi$
$60$			1.52314i			0.196637i
$61$	1.19207	−	0.433877i	0.152628	−	0.0555522i	−0.264576	−	0.964365i	$-0.585232\pi$
$61$	1.19207	−	0.433877i	0.152628	−	0.0555522i	0.417205	+	0.908813i	$0.363010\pi$
$62$	0.819078	−	1.41868i	0.104023	−	0.180173i
$63$	−9.95723	−	3.62414i	−1.25449	−	0.456598i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	2.48886	+	2.08840i	0.308705	+	0.259034i
$66$	−2.11721	−	5.81699i	−0.260611	−	0.716022i
$67$	0.624485	+	3.54163i	0.0762930	+	0.432679i	0.998898	+	0.0469331i	$0.0149448\pi$
$67$	0.624485	+	3.54163i	0.0762930	+	0.432679i	−0.922605	+	0.385746i	$0.873944\pi$
$68$	1.08512	+	6.15403i	0.131590	+	0.746286i
$69$	2.29813	−	2.73881i	0.276663	−	0.329714i
$70$	−2.37939	−	1.99654i	−0.284391	−	0.238632i
$71$	6.76991	+	11.7258i	0.803441	+	1.39160i	0.917338	+	0.398108i	$0.130333\pi$
$71$	6.76991	+	11.7258i	0.803441	+	1.39160i	−0.113897	+	0.993493i	$0.536334\pi$
$72$	−2.81908	+	1.02606i	−0.332232	+	0.120922i
$73$	1.16385	−	2.01584i	0.136218	−	0.235937i	−0.789844	−	0.613308i	$-0.789839\pi$
$73$	1.16385	−	2.01584i	0.136218	−	0.235937i	0.926062	+	0.377371i	$0.123172\pi$
$74$	−7.25150	+	2.63933i	−0.842969	+	0.306816i
$75$	−6.34002	−	3.66041i	−0.732083	−	0.422668i
$76$	3.19459	−	2.68058i	0.366445	−	0.307484i
$77$	11.8623	+	4.31753i	1.35184	+	0.492028i
$78$	−2.18866	+	6.01330i	−0.247817	+	0.680872i
$79$	−1.14930	+	6.51800i	−0.129306	+	0.733333i	0.849350	+	0.527830i	$0.176994\pi$
$79$	−1.14930	+	6.51800i	−0.129306	+	0.733333i	−0.978656	+	0.205503i	$0.934117\pi$
$80$	−0.879385			−0.0983183
$81$	1.56283	+	8.86327i	0.173648	+	0.984808i
$82$	7.70233			0.850580
$83$	−0.773318	+	4.38571i	−0.0848827	+	0.481394i	0.912499	+	0.409079i	$0.134150\pi$
$83$	−0.773318	+	4.38571i	−0.0848827	+	0.481394i	−0.997382	+	0.0723151i	$0.976961\pi$
$84$	2.09240	−	5.74881i	0.228299	−	0.627247i
$85$	5.16385	+	1.87949i	0.560098	+	0.203859i
$86$	8.29086	−	6.95686i	0.894026	−	0.750177i
$87$	0.243756	+	0.140732i	0.0261334	+	0.0150881i
$88$	3.35844	−	1.22237i	0.358011	−	0.130305i
$89$	−4.62449	+	8.00984i	−0.490194	+	0.849042i	−0.999936	−	0.0112857i	$-0.996408\pi$
$89$	−4.62449	+	8.00984i	−0.490194	+	0.849042i	0.509742	+	0.860327i	$0.329741\pi$
$90$	−0.458111	+	2.59808i	−0.0482891	+	0.273861i
$91$	−6.52481	−	11.3013i	−0.683986	−	1.18470i
$92$	1.58125	+	1.32683i	0.164857	+	0.138331i
$93$	1.82383	−	2.17355i	0.189122	−	0.225387i
$94$	1.11334	+	6.31407i	0.114832	+	0.651247i
$95$	−0.636812	−	3.61154i	−0.0653355	−	0.370536i
$96$	−0.592396	−	1.62760i	−0.0604612	−	0.166116i
$97$	−8.64930	−	7.25762i	−0.878203	−	0.736900i	0.0876055	−	0.996155i	$-0.472079\pi$
$97$	−8.64930	−	7.25762i	−0.878203	−	0.736900i	−0.965809	+	0.259255i	$0.916523\pi$
$98$	2.73783	+	4.74205i	0.276562	+	0.479020i
$99$	−1.86184	−	10.5590i	−0.187122	−	1.06122i
$100$	2.11334	−	3.66041i	0.211334	−	0.366041i
$101$	−8.80928	+	3.20631i	−0.876556	+	0.319040i	−0.740819	−	0.671705i	$-0.765562\pi$
$101$	−8.80928	+	3.20631i	−0.876556	+	0.319040i	−0.135737	+	0.990745i	$0.543340\pi$
$102$			10.8235i			1.07169i
$103$	−2.47178	+	2.07407i	−0.243552	+	0.204364i	−0.756390	−	0.654121i	$-0.773039\pi$
$103$	−2.47178	+	2.07407i	−0.243552	+	0.204364i	0.512838	+	0.858485i	$0.328594\pi$
$104$	−3.47178	−	1.26363i	−0.340436	−	0.123909i
$105$	−3.45811	−	4.12122i	−0.337477	−	0.402190i
$106$	−0.124485	+	0.705990i	−0.0120911	+	0.0685718i
$107$	−2.28312			−0.220717			−0.110359	−	0.993892i	$-0.535200\pi$
$107$	−2.28312			−0.220717			−0.110359	+	0.993892i	$0.535200\pi$
$108$	−5.11721	+	0.902302i	−0.492404	+	0.0868241i
$109$	10.4192			0.997980			0.498990	−	0.866608i	$-0.333704\pi$
$109$	10.4192			0.997980			0.498990	+	0.866608i	$0.333704\pi$
$110$	0.545759	−	3.09516i	0.0520361	−	0.295112i
$111$	−13.1630	+	2.32099i	−1.24937	+	0.220298i
$112$	3.31908	+	1.20805i	0.313623	+	0.114150i
$113$	8.52869	−	7.15642i	0.802311	−	0.673219i	−0.146448	−	0.989218i	$-0.546784\pi$
$113$	8.52869	−	7.15642i	0.802311	−	0.673219i	0.948759	+	0.315999i	$0.102340\pi$
$114$	6.25537	−	3.61154i	0.585869	−	0.338252i
$115$	1.70574	−	0.620838i	0.159061	−	0.0578934i
$116$	−0.0812519	+	0.140732i	−0.00754405	+	0.0130667i
$117$	−5.54189	+	9.59883i	−0.512348	+	0.887412i
$118$	−3.49273	−	6.04958i	−0.321531	−	0.556909i
$119$	−16.9081	−	14.1876i	−1.54996	−	1.30057i
$120$	−1.50000	−	0.264490i	−0.136931	−	0.0241446i
$121$	0.307934	+	1.74638i	0.0279940	+	0.158762i
$122$	0.220285	+	1.24930i	0.0199437	+	0.113106i
$123$	13.1382	+	2.31661i	1.18463	+	0.208882i
$124$	1.25490	+	1.05299i	0.112693	+	0.0945610i
$125$	−4.05690	−	7.02676i	−0.362861	−	0.628493i
$126$	5.29813	−	9.17664i	0.471995	−	0.817520i
$127$	4.95336	−	8.57948i	0.439540	−	0.761305i	−0.558114	−	0.829764i	$-0.688475\pi$
$127$	4.95336	−	8.57948i	0.439540	−	0.761305i	0.997654	+	0.0684588i	$0.0218082\pi$
$128$	0.939693	−	0.342020i	0.0830579	−	0.0302306i
$129$	16.2344	−	9.37295i	1.42936	−	0.825242i
$130$	−2.48886	+	2.08840i	−0.218287	+	0.183165i
$131$	8.48545	+	3.08845i	0.741377	+	0.269839i	0.684973	−	0.728569i	$-0.259814\pi$
$131$	8.48545	+	3.08845i	0.741377	+	0.269839i	0.0564046	+	0.998408i	$0.482036\pi$
$132$	6.09627	−	1.07494i	0.530612	−	0.0935612i
$133$	−2.55778	+	14.5059i	−0.221788	+	1.25782i
$134$	−3.59627			−0.310670
$135$	−1.56283	+	4.29385i	−0.134507	+	0.369556i
$136$	−6.24897			−0.535845
$137$	0.352044	−	1.99654i	0.0300772	−	0.170576i	−0.966069	−	0.258284i	$-0.916843\pi$
$137$	0.352044	−	1.99654i	0.0300772	−	0.170576i	0.996146	+	0.0877077i	$0.0279542\pi$
$138$	2.29813	+	2.73881i	0.195630	+	0.233143i
$139$	−0.155230	−	0.0564991i	−0.0131664	−	0.00479219i	0.335429	−	0.942066i	$-0.391119\pi$
$139$	−0.155230	−	0.0564991i	−0.0131664	−	0.00479219i	−0.348595	+	0.937273i	$0.613341\pi$
$140$	2.37939	−	1.99654i	0.201095	−	0.168739i
$141$			11.1050i			0.935210i
$142$	−12.7233	+	4.63089i	−1.06771	+	0.388616i
$143$	6.60220	−	11.4353i	0.552103	−	0.956271i
$144$	−0.520945	−	2.95442i	−0.0434120	−	0.246202i
$145$	0.0714517	+	0.123758i	0.00593374	+	0.0102775i
$146$	1.78312	+	1.49621i	0.147572	+	0.123828i
$147$	3.24376	+	8.91215i	0.267540	+	0.735061i
$148$	−1.34002	−	7.59964i	−0.110149	−	0.624687i
$149$	−1.00727	−	5.71253i	−0.0825191	−	0.467989i	−0.997864	−	0.0653193i	$-0.979193\pi$
$149$	−1.00727	−	5.71253i	−0.0825191	−	0.467989i	0.915345	−	0.402670i	$-0.131918\pi$
$150$	4.70574	−	5.60808i	0.384222	−	0.457898i
$151$	10.7626	+	9.03093i	0.875851	+	0.734926i	0.965322	−	0.261063i	$-0.0840730\pi$
$151$	10.7626	+	9.03093i	0.875851	+	0.734926i	−0.0894705	+	0.995989i	$0.528517\pi$
$152$	2.08512	+	3.61154i	0.169126	+	0.292934i
$153$	−3.25537	+	18.4621i	−0.263181	+	1.49257i
$154$	−6.31180	+	10.9324i	−0.508620	+	0.880955i
$155$	1.35369	−	0.492704i	0.108731	−	0.0395749i
$156$	−5.54189	−	3.19961i	−0.443706	−	0.256174i
$157$	−3.65657	+	3.06823i	−0.291826	+	0.244871i	−0.776933	−	0.629584i	$-0.783225\pi$
$157$	−3.65657	+	3.06823i	−0.291826	+	0.244871i	0.485106	+	0.874455i	$0.338781\pi$
$158$	−6.21941	−	2.26368i	−0.494790	−	0.180089i
$159$	−0.424678	+	1.16679i	−0.0336791	+	0.0925327i
$160$	0.152704	−	0.866025i	0.0120723	−	0.0684653i
$161$	−7.29086			−0.574600
$162$	−9.00000			−0.707107
$163$	−10.7169			−0.839411			−0.419705	−	0.907660i	$-0.637867\pi$
$163$	−10.7169			−0.839411			−0.419705	+	0.907660i	$0.637867\pi$
$164$	−1.33750	+	7.58532i	−0.104441	+	0.592314i
$165$	1.86184	−	5.11538i	0.144944	−	0.398231i
$166$	−4.18479	−	1.52314i	−0.324803	−	0.118219i
$167$	−9.88120	+	8.29131i	−0.764630	+	0.641601i	−0.939328	−	0.343021i	$-0.888550\pi$
$167$	−9.88120	+	8.29131i	−0.764630	+	0.641601i	0.174698	+	0.984622i	$0.444105\pi$
$168$	5.29813	+	3.05888i	0.408760	+	0.235998i
$169$	−0.610815	+	0.222318i	−0.0469857	+	0.0171014i
$170$	−2.74763	+	4.75903i	−0.210733	+	0.365001i
$171$	11.7562	−	4.27892i	0.899022	−	0.327217i
$172$	5.41147	+	9.37295i	0.412621	+	0.714681i
$173$	9.86097	+	8.27433i	0.749715	+	0.629086i	0.935428	−	0.353518i	$-0.115015\pi$
$173$	9.86097	+	8.27433i	0.749715	+	0.629086i	−0.185712	+	0.982604i	$0.559459\pi$
$174$	−0.180922	+	0.215615i	−0.0137157	+	0.0163457i
$175$	2.59240	+	14.7022i	0.195967	+	1.11138i
$176$	0.620615	+	3.51968i	0.0467806	+	0.265306i
$177$	−4.13816	−	11.3695i	−0.311043	−	0.854583i
$178$	−7.08512	−	5.94512i	−0.531052	−	0.445606i
$179$	4.48158	+	7.76233i	0.334969	+	0.580184i	0.983479	−	0.181023i	$-0.0579408\pi$
$179$	4.48158	+	7.76233i	0.334969	+	0.580184i	−0.648510	+	0.761206i	$0.724607\pi$
$180$	−2.47906	−	0.902302i	−0.184778	−	0.0672537i
$181$	0.992726	−	1.71945i	0.0737887	−	0.127806i	−0.826770	−	0.562540i	$-0.809824\pi$
$181$	0.992726	−	1.71945i	0.0737887	−	0.127806i	0.900559	+	0.434734i	$0.143158\pi$
$182$	12.2626	−	4.46324i	0.908967	−	0.330837i
$183$			2.19723i			0.162424i
$184$	−1.58125	+	1.32683i	−0.116571	+	0.0978151i
$185$	−6.37686	−	2.32099i	−0.468836	−	0.170642i
$186$	1.82383	+	2.17355i	0.133729	+	0.159372i
$187$	3.87820	−	21.9944i	0.283602	−	1.60839i
$188$	−6.41147			−0.467605
$189$	11.7973	−	14.0594i	0.858124	−	1.02267i
$190$	3.66725			0.266050
$191$	2.27853	−	12.9222i	0.164869	−	0.935018i	−0.784331	−	0.620343i	$-0.786993\pi$
$191$	2.27853	−	12.9222i	0.164869	−	0.935018i	0.949200	−	0.314675i	$-0.101895\pi$
$192$	1.70574	−	0.300767i	0.123101	−	0.0217060i
$193$	−5.40895	−	1.96870i	−0.389345	−	0.141710i	0.139928	−	0.990162i	$-0.455313\pi$
$193$	−5.40895	−	1.96870i	−0.389345	−	0.141710i	−0.529273	+	0.848452i	$0.677535\pi$
$194$	8.64930	−	7.25762i	0.620984	−	0.521067i
$195$	−4.87346	+	2.81369i	−0.348995	+	0.201493i
$196$	−5.14543	+	1.87278i	−0.367531	+	0.133770i
$197$	13.3405	−	23.1064i	0.950471	−	1.64626i	0.206062	−	0.978539i	$-0.433935\pi$
$197$	13.3405	−	23.1064i	0.950471	−	1.64626i	0.744409	−	0.667724i	$-0.232731\pi$
$198$	10.7219			0.761975
$199$	5.32160	+	9.21729i	0.377239	+	0.653396i	0.990659	−	0.136360i	$-0.0435404\pi$
$199$	5.32160	+	9.21729i	0.377239	+	0.653396i	−0.613421	+	0.789756i	$0.710207\pi$
$200$	3.23783	+	2.71686i	0.228949	+	0.192111i
$201$	−6.13429	−	1.08164i	−0.432679	−	0.0762930i
$202$	−1.62789	−	9.23222i	−0.114538	−	0.649576i
$203$	−0.0996702	−	0.565258i	−0.00699548	−	0.0396733i
$204$	−10.6591	−	1.87949i	−0.746286	−	0.131590i
$205$	5.18866	+	4.35381i	0.362392	+	0.304083i
$206$	−1.61334	−	2.79439i	−0.112407	−	0.194694i
$207$	3.09627	+	5.36289i	0.215205	+	0.372747i
$208$	1.84730	−	3.19961i	0.128087	−	0.221853i
$209$	−14.0055	+	5.09759i	−0.968782	+	0.352608i
$210$	4.65910	−	2.68993i	0.321508	−	0.185623i
$211$	−4.09105	+	3.43280i	−0.281640	+	0.236324i	−0.772653	−	0.634828i	$-0.781071\pi$
$211$	−4.09105	+	3.43280i	−0.281640	+	0.236324i	0.491014	+	0.871152i	$0.336626\pi$
$212$	−0.673648	−	0.245188i	−0.0462663	−	0.0168396i
$213$	−23.0954	+	4.07234i	−1.58247	+	0.279032i
$214$	0.396459	−	2.24843i	0.0271014	−	0.153700i
$215$	9.51754			0.649091
$216$		−	5.19615i		−	0.353553i
$217$	−5.78611			−0.392787
$218$	−1.80928	+	10.2609i	−0.122540	+	0.694957i
$219$	2.59152	+	3.08845i	0.175119	+	0.208698i
$220$	2.95336	+	1.07494i	0.199116	+	0.0724722i
$221$	−17.6860	+	14.8403i	−1.18969	+	0.998266i
$222$		−	13.3660i		−	0.897069i
$223$	17.9008	−	6.51536i	1.19873	−	0.436301i	0.335947	−	0.941881i	$-0.390944\pi$
$223$	17.9008	−	6.51536i	1.19873	−	0.436301i	0.862779	+	0.505580i	$0.168722\pi$
$224$	−1.76604	+	3.05888i	−0.117999	+	0.204380i
$225$	9.71348	−	8.15058i	0.647565	−	0.543372i
$226$	5.56670	+	9.64181i	0.370292	+	0.641364i
$227$	−2.65136	−	2.22475i	−0.175977	−	0.147662i	0.550545	−	0.834806i	$-0.314420\pi$
$227$	−2.65136	−	2.22475i	−0.175977	−	0.147662i	−0.726522	+	0.687143i	$0.758864\pi$
$228$	2.47044	+	6.78747i	0.163609	+	0.449511i
$229$	−5.02528	−	28.4998i	−0.332080	−	1.88332i	−0.454352	−	0.890822i	$-0.650129\pi$
$229$	−5.02528	−	28.4998i	−0.332080	−	1.88332i	0.122272	−	0.992497i	$-0.460982\pi$
$230$	0.315207	+	1.78763i	0.0207842	+	0.117873i
$231$	−14.0544	+	16.7494i	−0.924710	+	1.10203i
$232$	−0.124485	−	0.104455i	−0.00817285	−	0.00685784i
$233$	3.33022	+	5.76811i	0.218170	+	0.377882i	0.954249	−	0.299015i	$-0.0966579\pi$
$233$	3.33022	+	5.76811i	0.218170	+	0.377882i	−0.736078	+	0.676896i	$0.763325\pi$
$234$	−8.49067	−	7.12452i	−0.555052	−	0.465744i
$235$	−2.81908	+	4.88279i	−0.183896	+	0.318518i
$236$	6.56418	−	2.38917i	0.427292	−	0.155521i
$237$	−9.92783	−	5.73184i	−0.644882	−	0.372323i
$238$	16.9081	−	14.1876i	1.09599	−	0.919643i
$239$	−7.31908	−	2.66393i	−0.473432	−	0.172315i	0.0942745	−	0.995546i	$-0.469947\pi$
$239$	−7.31908	−	2.66393i	−0.473432	−	0.172315i	−0.567706	+	0.823231i	$0.692169\pi$
$240$	0.520945	−	1.43128i	0.0336268	−	0.0923889i
$241$	3.80200	−	21.5622i	0.244909	−	1.38895i	−0.575796	−	0.817593i	$-0.695308\pi$
$241$	3.80200	−	21.5622i	0.244909	−	1.38895i	0.820705	−	0.571352i	$-0.193581\pi$
$242$	−1.77332			−0.113993
$243$	−15.3516	−	2.70691i	−0.984808	−	0.173648i
$244$	−1.26857			−0.0812119
$245$	−0.836152	+	4.74205i	−0.0534198	+	0.302959i
$246$	−4.56283	+	12.5363i	−0.290916	+	0.799284i
$247$	14.4782	+	5.26963i	0.921224	+	0.335298i
$248$	−1.25490	+	1.05299i	−0.0796862	+	0.0668647i
$249$	−6.68004	−	3.85673i	−0.423331	−	0.244410i
$250$	7.62449	−	2.77509i	0.482215	−	0.175512i
$251$	−8.04236	+	13.9298i	−0.507629	+	0.879239i	0.492332	+	0.870407i	$0.336145\pi$
$251$	−8.04236	+	13.9298i	−0.507629	+	0.879239i	−0.999961	+	0.00883173i	$0.997189\pi$
$252$	8.11721	+	6.81115i	0.511336	+	0.429062i
$253$	−3.68866	−	6.38895i	−0.231904	−	0.401670i
$254$	7.58899	+	6.36792i	0.476176	+	0.399559i
$255$	−6.11809	+	7.29125i	−0.383130	+	0.456596i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	4.49138	+	25.4719i	0.280165	+	1.58889i	0.722063	+	0.691828i	$0.243194\pi$
$257$	4.49138	+	25.4719i	0.280165	+	1.58889i	−0.441898	+	0.897065i	$0.645695\pi$
$258$	6.41147	+	17.6154i	0.399161	+	1.09669i
$259$	20.8799	+	17.5203i	1.29741	+	1.08866i
$260$	−1.62449	−	2.81369i	−0.100746	−	0.174498i
$261$	−0.373455	+	0.313366i	−0.0231163	+	0.0193969i
$262$	−4.51501	+	7.82023i	−0.278939	+	0.483136i
$263$	29.5967	−	10.7723i	1.82501	−	0.664250i	0.830832	−	0.556523i	$-0.187865\pi$
$263$	29.5967	−	10.7723i	1.82501	−	0.664250i	0.994180	−	0.107727i	$-0.0343574\pi$
$264$			6.19031i			0.380987i
$265$	−0.482926	+	0.405223i	−0.0296659	+	0.0248926i
$266$	−13.8414	−	5.03785i	−0.848669	−	0.308890i
$267$	−10.2973	−	12.2718i	−0.630182	−	0.751021i
$268$	0.624485	−	3.54163i	0.0381465	−	0.216340i
$269$	−4.60906			−0.281019			−0.140510	−	0.990079i	$-0.544874\pi$
$269$	−4.60906			−0.281019			−0.140510	+	0.990079i	$0.544874\pi$
$270$	−3.95723	−	2.28471i	−0.240830	−	0.139043i
$271$	−1.31820			−0.0800750			−0.0400375	−	0.999198i	$-0.512748\pi$
$271$	−1.31820			−0.0800750			−0.0400375	+	0.999198i	$0.512748\pi$
$272$	1.08512	−	6.15403i	0.0657952	−	0.373143i
$273$	22.2592	−	3.92490i	1.34719	−	0.237546i
$274$	1.90508	+	0.693392i	0.115090	+	0.0418893i
$275$	−11.5719	+	9.70999i	−0.697813	+	0.585535i
$276$	−3.09627	+	1.78763i	−0.186373	+	0.107603i
$277$	−28.9624	+	10.5415i	−1.74018	+	0.633375i	−0.999269	−	0.0382227i	$-0.987830\pi$
$277$	−28.9624	+	10.5415i	−1.74018	+	0.633375i	−0.740916	+	0.671598i	$0.765608\pi$
$278$	0.0825961	−	0.143061i	0.00495378	−	0.00858021i
$279$	2.45723	+	4.25605i	0.147111	+	0.254803i
$280$	1.55303	+	2.68993i	0.0928115	+	0.160754i
$281$	16.4172	+	13.7756i	0.979365	+	0.821785i	0.983994	−	0.178204i	$-0.0570287\pi$
$281$	16.4172	+	13.7756i	0.979365	+	0.821785i	−0.00462815	+	0.999989i	$0.501473\pi$
$282$	−10.9363	−	1.92836i	−0.651247	−	0.114832i
$283$	−0.307934	−	1.74638i	−0.0183047	−	0.103811i	0.974287	−	0.225313i	$-0.0723403\pi$
$283$	−0.307934	−	1.74638i	−0.0183047	−	0.103811i	−0.992591	+	0.121501i	$0.961229\pi$
$284$	−2.35117	−	13.3341i	−0.139516	−	0.791235i
$285$	6.25537	+	1.10299i	0.370536	+	0.0653355i
$286$	10.1152	+	8.48762i	0.598121	+	0.501884i
$287$	−13.6027	−	23.5605i	−0.802940	−	1.39073i
$288$	3.00000			0.176777
$289$	−11.0248	+	19.0955i	−0.648519	+	1.12327i
$290$	−0.134285	+	0.0488759i	−0.00788551	+	0.00287009i
$291$	16.9363	−	9.77817i	0.992823	−	0.573207i
$292$	−1.78312	+	1.49621i	−0.104349	+	0.0875593i
$293$	29.0920	+	10.5886i	1.69957	+	0.618594i	0.995777	−	0.0918092i	$-0.0292650\pi$
$293$	29.0920	+	10.5886i	1.69957	+	0.618594i	0.703795	+	0.710403i	$0.251487\pi$
$294$	−9.34002	+	1.64690i	−0.544721	+	0.0960490i
$295$	1.06670	−	6.04958i	0.0621059	−	0.352220i
$296$	7.71688			0.448535
$297$	18.2888	+	3.22481i	1.06122	+	0.187122i
$298$	5.80066			0.336023
$299$	−1.32429	+	7.51044i	−0.0765858	+	0.434340i
$300$	4.70574	+	5.60808i	0.271686	+	0.323783i
$301$	−35.9222	−	13.0746i	−2.07052	−	0.753608i
$302$	−10.7626	+	9.03093i	−0.619320	+	0.519672i
$303$		−	16.2373i		−	0.932811i
$304$	−3.91875	+	1.42631i	−0.224756	+	0.0818044i
$305$	−0.557781	+	0.966105i	−0.0319385	+	0.0553190i
$306$	−17.6163	−	6.41182i	−1.00706	−	0.366539i
$307$	−4.26857	−	7.39338i	−0.243620	−	0.421963i	0.718123	−	0.695917i	$-0.245002\pi$
$307$	−4.26857	−	7.39338i	−0.243620	−	0.421963i	−0.961743	+	0.273954i	$0.911668\pi$
$308$	−9.67024	−	8.11430i	−0.551013	−	0.462355i
$309$	−1.91147	−	5.25173i	−0.108740	−	0.298761i
$310$	0.250152	+	1.41868i	0.0142077	+	0.0805759i
$311$	−3.12789	−	17.7391i	−0.177366	−	1.00589i	−0.935377	−	0.353652i	$-0.884940\pi$
$311$	−3.12789	−	17.7391i	−0.177366	−	1.00589i	0.758011	−	0.652242i	$-0.226171\pi$
$312$	4.11334	−	4.90209i	0.232872	−	0.277526i
$313$	13.1800	+	11.0594i	0.744980	+	0.625113i	0.934170	−	0.356828i	$-0.116142\pi$
$313$	13.1800	+	11.0594i	0.744980	+	0.625113i	−0.189190	+	0.981941i	$0.560586\pi$
$314$	−2.38666	−	4.13381i	−0.134687	−	0.233285i
$315$	8.75624	−	3.18701i	0.493358	−	0.179568i
$316$	3.30928	−	5.73184i	0.186161	−	0.322441i
$317$	−23.4094	+	8.52033i	−1.31480	+	0.478549i	−0.901790	−	0.432175i	$-0.857746\pi$
$317$	−23.4094	+	8.52033i	−1.31480	+	0.478549i	−0.413014	+	0.910725i	$0.635524\pi$
$318$	−1.07532	−	0.620838i	−0.0603011	−	0.0348148i
$319$	0.444907	−	0.373321i	0.0249100	−	0.0209020i
$320$	0.826352	+	0.300767i	0.0461945	+	0.0168134i
$321$	1.35251	−	3.71599i	0.0754898	−	0.207407i
$322$	1.26604	−	7.18009i	0.0705539	−	0.400131i
$323$	26.0597			1.45000
$324$	1.56283	−	8.86327i	0.0868241	−	0.492404i
$325$	15.6159			0.866212
$326$	1.86097	−	10.5541i	0.103069	−	0.584536i
$327$	−6.17230	+	16.9583i	−0.341329	+	0.937794i
$328$	−7.23783	−	2.63435i	−0.399642	−	0.145458i
$329$	17.3478	−	14.5565i	0.956413	−	0.802526i
$330$	4.71436	+	2.72183i	0.259517	+	0.149832i
$331$	−8.32547	+	3.03022i	−0.457609	+	0.166556i	−0.560531	−	0.828133i	$-0.689403\pi$
$331$	−8.32547	+	3.03022i	−0.457609	+	0.166556i	0.102922	+	0.994689i	$0.467181\pi$
$332$	2.22668	−	3.85673i	0.122205	−	0.211665i
$333$	4.02007	−	22.7989i	0.220298	−	1.24937i
$334$	−6.44949	−	11.1708i	−0.352901	−	0.611242i
$335$	−2.42262	−	2.03282i	−0.132362	−	0.111065i
$336$	−3.93242	+	4.68647i	−0.214531	+	0.255668i
$337$	3.65910	+	20.7518i	0.199324	+	1.13042i	0.906125	+	0.423010i	$0.139026\pi$
$337$	3.65910	+	20.7518i	0.199324	+	1.13042i	−0.706801	+	0.707412i	$0.749862\pi$
$338$	−0.112874	−	0.640140i	−0.00613953	−	0.0348190i
$339$	6.59539	+	18.1207i	0.358212	+	0.984180i
$340$	−4.20961	−	3.53228i	−0.228298	−	0.191565i
$341$	−2.92737	−	5.07035i	−0.158526	−	0.274575i
$342$	2.17247	+	12.3207i	0.117474	+	0.666225i
$343$	−2.69207	+	4.66280i	−0.145358	+	0.251767i
$344$	−10.1702	+	3.70167i	−0.548343	+	0.199580i
$345$			3.14403i			0.169269i
$346$	−9.86097	+	8.27433i	−0.530129	+	0.444831i
$347$	−20.7754	−	7.56164i	−1.11528	−	0.405930i	−0.282355	−	0.959310i	$-0.591116\pi$
$347$	−20.7754	−	7.56164i	−1.11528	−	0.405930i	−0.832929	+	0.553380i	$0.813338\pi$
$348$	−0.180922	−	0.215615i	−0.00969844	−	0.0115582i
$349$	0.381911	−	2.16593i	0.0204433	−	0.115939i	−0.972878	−	0.231317i	$-0.925697\pi$
$349$	0.381911	−	2.16593i	0.0204433	−	0.115939i	0.993322	+	0.115377i	$0.0368077\pi$
$350$	−14.9290			−0.797989
$351$	−12.3400	−	14.7063i	−0.658662	−	0.784962i
$352$	−3.57398			−0.190494
$353$	0.826352	−	4.68647i	0.0439823	−	0.249436i	−0.954887	−	0.296968i	$-0.904025\pi$
$353$	0.826352	−	4.68647i	0.0439823	−	0.249436i	0.998870	+	0.0475321i	$0.0151356\pi$
$354$	11.9153	−	2.10100i	0.633293	−	0.111667i
$355$	−11.1887	−	4.07234i	−0.593833	−	0.216137i
$356$	7.08512	−	5.94512i	0.375511	−	0.315091i
$357$	33.1079	−	19.1148i	1.75225	−	1.01166i
$358$	−8.42262	+	3.06558i	−0.445149	+	0.162021i
$359$	1.30288	−	2.25666i	0.0687634	−	0.119102i	−0.829594	−	0.558367i	$-0.811428\pi$
$359$	1.30288	−	2.25666i	0.0687634	−	0.119102i	0.898357	+	0.439266i	$0.144761\pi$
$360$	1.31908	−	2.28471i	0.0695215	−	0.120415i
$361$	0.804530	+	1.39349i	0.0423437	+	0.0733414i
$362$	1.52094	+	1.27622i	0.0799391	+	0.0670768i
$363$	−3.02481	−	0.533356i	−0.158762	−	0.0279940i
$364$	2.26604	+	12.8514i	0.118773	+	0.673595i
$365$	0.355448	+	2.01584i	0.0186050	+	0.105514i
$366$	−2.16385	−	0.381545i	−0.113106	−	0.0199437i
$367$	−10.9042	−	9.14971i	−0.569195	−	0.477611i	0.312184	−	0.950022i	$-0.398939\pi$
$367$	−10.9042	−	9.14971i	−0.569195	−	0.477611i	−0.881379	+	0.472411i	$0.843384\pi$
$368$	−1.03209	−	1.78763i	−0.0538014	−	0.0931867i
$369$	−11.5535	+	20.0112i	−0.601451	+	1.04174i
$370$	3.39306	−	5.87695i	0.176397	−	0.305528i
$371$	2.37939	−	0.866025i	0.123532	−	0.0449618i
$372$	−2.45723	+	1.41868i	−0.127402	+	0.0735554i
$373$	−1.76810	+	1.48362i	−0.0915489	+	0.0768187i	−0.687413	−	0.726266i	$-0.741254\pi$
$373$	−1.76810	+	1.48362i	−0.0915489	+	0.0768187i	0.595865	+	0.803085i	$0.296810\pi$
$374$	20.9868	+	7.63857i	1.08520	+	0.394981i
$375$	13.8400	−	2.44037i	0.714696	−	0.126020i
$376$	1.11334	−	6.31407i	0.0574162	−	0.325623i
$377$	−0.600385			−0.0309214
$378$	11.7973	+	14.0594i	0.606785	+	0.723139i
$379$	−6.02734			−0.309604			−0.154802	−	0.987946i	$-0.549474\pi$
$379$	−6.02734			−0.309604			−0.154802	+	0.987946i	$0.549474\pi$
$380$	−0.636812	+	3.61154i	−0.0326677	+	0.185268i
$381$	11.0296	+	13.1445i	0.565062	+	0.673414i
$382$	12.3302	+	4.48783i	0.630869	+	0.229618i
$383$	16.3007	−	13.6779i	0.832925	−	0.698907i	−0.123036	−	0.992402i	$-0.539263\pi$
$383$	16.3007	−	13.6779i	0.832925	−	0.698907i	0.955960	+	0.293495i	$0.0948185\pi$
$384$			1.73205i			0.0883883i
$385$	−10.4315	+	3.79677i	−0.531641	+	0.193501i
$386$	2.87804	−	4.98491i	0.146488	−	0.253725i
$387$	5.63816	+	31.9756i	0.286604	+	1.62541i
$388$	5.64543	+	9.77817i	0.286603	+	0.496411i
$389$	−15.8248	−	13.2785i	−0.802347	−	0.673249i	0.146421	−	0.989222i	$-0.453225\pi$
$389$	−15.8248	−	13.2785i	−0.802347	−	0.673249i	−0.948768	+	0.315973i	$0.897669\pi$
$390$	−1.92468	−	5.28801i	−0.0974599	−	0.267769i
$391$	2.23989	+	12.7030i	0.113276	+	0.642419i
$392$	−0.950837	−	5.39246i	−0.0480245	−	0.272361i
$393$	−10.0535	+	11.9813i	−0.507132	+	0.604376i
$394$	20.4388	+	17.1502i	1.02969	+	0.864015i
$395$	−2.91013	−	5.04049i	−0.146425	−	0.253615i
$396$	−1.86184	+	10.5590i	−0.0935612	+	0.530612i
$397$	12.2638	−	21.2416i	0.615504	−	1.06608i	−0.374792	−	0.927109i	$-0.622286\pi$
$397$	12.2638	−	21.2416i	0.615504	−	1.06608i	0.990296	−	0.138975i	$-0.0443807\pi$
$398$	−10.0013	+	3.64019i	−0.501322	+	0.182466i
$399$	−22.0945	−	12.7563i	−1.10611	−	0.638612i
$400$	−3.23783	+	2.71686i	−0.161891	+	0.135843i
$401$	−13.7433	−	5.00217i	−0.686310	−	0.249796i	−0.0247555	−	0.999694i	$-0.507881\pi$
$401$	−13.7433	−	5.00217i	−0.686310	−	0.249796i	−0.661554	+	0.749897i	$0.730103\pi$
$402$	2.13041	−	5.85327i	0.106255	−	0.291934i
$403$	−1.05097	+	5.96037i	−0.0523527	+	0.296907i
$404$	9.37464			0.466406
$405$	−6.06283	−	5.08732i	−0.301265	−	0.252791i
$406$	0.573978			0.0284860
$407$	−4.78921	+	27.1610i	−0.237392	+	1.34632i
$408$	3.70187	−	10.1708i	0.183270	−	0.503529i
$409$	33.9479	+	12.3560i	1.67862	+	0.610966i	0.993119	−	0.117110i	$-0.0373629\pi$
$409$	33.9479	+	12.3560i	1.67862	+	0.610966i	0.685497	+	0.728076i	$0.259585\pi$
$410$	−5.18866	+	4.35381i	−0.256250	+	0.215019i
$411$	3.04101	+	1.75573i	0.150002	+	0.0866037i
$412$	3.03209	−	1.10359i	0.149380	−	0.0543700i
$413$	−12.3366	+	21.3677i	−0.607045	+	1.05143i
$414$	−5.81908	+	2.11797i	−0.285992	+	0.104093i
$415$	−1.95811	−	3.39155i	−0.0961199	−	0.166485i
$416$	2.83022	+	2.37484i	0.138763	+	0.116436i
$417$	0.183915	−	0.219182i	0.00900637	−	0.0107334i
$418$	−2.58812	−	14.6779i	−0.126589	−	0.717921i
$419$	3.42309	+	19.4133i	0.167229	+	0.948401i	0.946737	+	0.322009i	$0.104358\pi$
$419$	3.42309	+	19.4133i	0.167229	+	0.948401i	−0.779508	+	0.626392i	$0.784531\pi$
$420$	1.84002	+	5.05542i	0.0897839	+	0.246679i
$421$	2.63041	+	2.20718i	0.128199	+	0.107571i	0.704633	−	0.709572i	$-0.251112\pi$
$421$	2.63041	+	2.20718i	0.128199	+	0.107571i	−0.576434	+	0.817144i	$0.695556\pi$
$422$	−2.67024	−	4.62500i	−0.129985	−	0.225141i
$423$	−18.0744	−	6.57856i	−0.878810	−	0.319861i
$424$	0.358441	−	0.620838i	0.0174074	−	0.0301505i
$425$	24.8195	−	9.03358i	1.20392	−	0.438193i
$426$		−	23.4517i		−	1.13624i
$427$	3.43242	−	2.88014i	0.166106	−	0.139380i
$428$	2.14543	+	0.780873i	0.103703	+	0.0377449i
$429$	14.7010	+	17.5200i	0.709770	+	0.845871i
$430$	−1.65270	+	9.37295i	−0.0797004	+	0.452004i
$431$	−28.7151			−1.38316			−0.691579	−	0.722300i	$-0.743085\pi$
$431$	−28.7151			−1.38316			−0.691579	+	0.722300i	$0.743085\pi$
$432$	5.11721	+	0.902302i	0.246202	+	0.0434120i
$433$	−14.1179			−0.678464			−0.339232	−	0.940703i	$-0.610167\pi$
$433$	−14.1179			−0.678464			−0.339232	+	0.940703i	$0.610167\pi$
$434$	1.00475	−	5.69821i	0.0482294	−	0.273523i
$435$	−0.243756	+	0.0429807i	−0.0116872	+	0.00206077i
$436$	−9.79086	−	3.56358i	−0.468897	−	0.170665i
$437$	6.59421	−	5.53320i	0.315444	−	0.264689i
$438$	−3.49154	+	2.01584i	−0.166832	+	0.0963207i
$439$	−14.5842	+	5.30823i	−0.696068	+	0.253348i	−0.665731	−	0.746192i	$-0.731880\pi$
$439$	−14.5842	+	5.30823i	−0.696068	+	0.253348i	−0.0303369	+	0.999540i	$0.509658\pi$
$440$	−1.57145	+	2.72183i	−0.0749160	+	0.129758i
$441$	−16.4270			−0.782236
$442$	−11.5437	−	19.9943i	−0.549078	−	0.951031i
$443$	−27.3897	−	22.9826i	−1.30132	−	1.09194i	−0.989915	−	0.141662i	$-0.954755\pi$
$443$	−27.3897	−	22.9826i	−1.30132	−	1.09194i	−0.311407	−	0.950277i	$-0.600800\pi$
$444$	13.1630	+	2.32099i	0.624687	+	0.110149i
$445$	−1.41235	−	8.00984i	−0.0669519	−	0.379703i
$446$	3.30793	+	18.7602i	0.156635	+	0.888322i
$447$	9.89440	+	1.74465i	0.467989	+	0.0825191i
$448$	−2.70574	−	2.27038i	−0.127834	−	0.107266i
$449$	12.8564	+	22.2679i	0.606730	+	1.05089i	0.991775	+	0.127990i	$0.0408525\pi$
$449$	12.8564	+	22.2679i	0.606730	+	1.05089i	−0.385045	+	0.922898i	$0.625814\pi$
$450$	6.34002	+	10.9812i	0.298872	+	0.517661i
$451$	13.7640	−	23.8399i	0.648121	−	1.12258i
$452$	−10.4620	+	3.80785i	−0.492090	+	0.179106i
$453$	−21.0744	+	12.1673i	−0.990164	+	0.571671i
$454$	2.65136	−	2.22475i	0.124434	−	0.104413i
$455$	10.7836	+	3.92490i	0.505542	+	0.184002i
$456$	−7.11334	+	1.25427i	−0.333113	+	0.0587368i
$457$	0.352921	−	2.00152i	0.0165090	−	0.0936270i	−0.975440	−	0.220265i	$-0.929308\pi$
$457$	0.352921	−	2.00152i	0.0165090	−	0.0936270i	0.991949	+	0.126638i	$0.0404188\pi$
$458$	28.9394			1.35225
$459$	−28.1204	−	16.2353i	−1.31255	−	0.757799i
$460$	−1.81521			−0.0846345
$461$	3.74628	−	21.2462i	0.174482	−	0.989535i	−0.764259	−	0.644910i	$-0.776895\pi$
$461$	3.74628	−	21.2462i	0.174482	−	0.989535i	0.938740	−	0.344625i	$-0.111994\pi$
$462$	−14.0544	−	16.7494i	−0.653869	−	0.779251i
$463$	20.2986	+	7.38809i	0.943356	+	0.343353i	0.767490	−	0.641061i	$-0.221505\pi$
$463$	20.2986	+	7.38809i	0.943356	+	0.343353i	0.175866	+	0.984414i	$0.443728\pi$
$464$	0.124485	−	0.104455i	0.00577908	−	0.00484922i
$465$			2.49514i			0.115709i
$466$	−6.25877	+	2.27801i	−0.289932	+	0.105527i
$467$	−12.2622	+	21.2387i	−0.567426	+	0.982810i	0.429394	+	0.903117i	$0.358727\pi$
$467$	−12.2622	+	21.2387i	−0.567426	+	0.982810i	−0.996819	+	0.0796928i	$0.974606\pi$
$468$	8.49067	−	7.12452i	0.392481	−	0.329331i
$469$	6.35117	+	11.0005i	0.293270	+	0.507958i
$470$	−4.31908	−	3.62414i	−0.199224	−	0.167169i
$471$	−2.82770	−	7.76903i	−0.130293	−	0.357978i
$472$	1.21301	+	6.87933i	0.0558334	+	0.316647i
$473$	−6.71688	−	38.0933i	−0.308843	−	1.75153i
$474$	7.36871	−	8.78168i	0.338456	−	0.403356i
$475$	−13.5025	−	11.3300i	−0.619538	−	0.519854i
$476$	11.0360	+	19.1148i	0.505832	+	0.876127i
$477$	−1.64749	−	1.38241i	−0.0754333	−	0.0632961i
$478$	3.89440	−	6.74530i	0.178126	−	0.308523i
$479$	−13.4620	+	4.89976i	−0.615094	+	0.223876i	−0.630730	−	0.776002i	$-0.717245\pi$
$479$	−13.4620	+	4.89976i	−0.615094	+	0.223876i	0.0156369	+	0.999878i	$0.495022\pi$
$480$	1.31908	+	0.761570i	0.0602074	+	0.0347608i
$481$	21.8405	−	18.3263i	0.995841	−	0.835609i
$482$	20.5744	+	7.48849i	0.937140	+	0.341091i
$483$	4.31908	−	11.8666i	0.196525	−	0.539948i
$484$	0.307934	−	1.74638i	0.0139970	−	0.0793808i
$485$	9.92902			0.450853
$486$	5.33157	−	14.6484i	0.241845	−	0.664463i
$487$	32.3114			1.46417			0.732084	−	0.681214i	$-0.238548\pi$
$487$	32.3114			1.46417			0.732084	+	0.681214i	$0.238548\pi$
$488$	0.220285	−	1.24930i	0.00997183	−	0.0565531i
$489$	6.34864	−	17.4427i	0.287095	−	0.788788i
$490$	−4.52481	−	1.64690i	−0.204410	−	0.0743993i
$491$	24.8576	−	20.8580i	1.12181	−	0.941307i	0.123112	−	0.992393i	$-0.460713\pi$
$491$	24.8576	−	20.8580i	1.12181	−	0.941307i	0.998694	+	0.0510857i	$0.0162682\pi$
$492$	−11.5535	−	6.67042i	−0.520872	−	0.300726i
$493$	−0.954241	+	0.347315i	−0.0429768	+	0.0156423i
$494$	−7.70368	+	13.3432i	−0.346605	+	0.600337i
$495$	7.22281	+	6.06066i	0.324641	+	0.272406i
$496$	−0.819078	−	1.41868i	−0.0367777	−	0.0637008i
$497$	36.6352	+	30.7406i	1.64331	+	1.37890i
$498$	4.95811	−	5.90885i	0.222178	−	0.264782i
$499$	−4.31180	−	24.4535i	−0.193023	−	1.09469i	−0.915206	−	0.402985i	$-0.867973\pi$
$499$	−4.31180	−	24.4535i	−0.193023	−	1.09469i	0.722184	−	0.691702i	$-0.243139\pi$
$500$	1.40895	+	7.99054i	0.0630101	+	0.357348i
$501$	−7.64131	−	20.9943i	−0.341389	−	0.937957i
$502$	−12.3216	−	10.3391i	−0.549940	−	0.461455i
$503$	7.46198	+	12.9245i	0.332713	+	0.576276i	0.983043	−	0.183376i	$-0.0587025\pi$
$503$	7.46198	+	12.9245i	0.332713	+	0.576276i	−0.650330	+	0.759652i	$0.725369\pi$
$504$	−8.11721	+	6.81115i	−0.361569	+	0.303393i
$505$	4.12196	−	7.13944i	0.183425	−	0.317701i
$506$	6.93242	−	2.52319i	0.308184	−	0.112170i
$507$		−	1.12586i		−	0.0500012i
$508$	−7.58899	+	6.36792i	−0.336707	+	0.282531i
$509$	−14.4595	−	5.26281i	−0.640904	−	0.233270i	0.00106632	−	0.999999i	$-0.499661\pi$
$509$	−14.4595	−	5.26281i	−0.640904	−	0.233270i	−0.641970	+	0.766729i	$0.721883\pi$
$510$	−6.11809	−	7.29125i	−0.270914	−	0.322862i
$511$	1.42767	−	8.09672i	0.0631564	−	0.358178i
$512$	−1.00000			−0.0441942
$513$			21.6692i			0.956720i
$514$	−25.8648			−1.14085
$515$	0.492726	−	2.79439i	0.0217121	−	0.123135i
$516$	−18.4611	+	3.25519i	−0.812705	+	0.143302i
$517$	21.5326	+	7.83721i	0.947001	+	0.344680i
$518$	−20.8799	+	17.5203i	−0.917408	+	0.769797i
$519$	−19.3089	+	11.1480i	−0.847565	+	0.489342i
$520$	3.05303	−	1.11121i	0.133884	−	0.0487299i
$521$	−6.69207	+	11.5910i	−0.293185	+	0.507811i	−0.974561	−	0.224122i	$-0.928048\pi$
$521$	−6.69207	+	11.5910i	−0.293185	+	0.507811i	0.681376	+	0.731933i	$0.261382\pi$
$522$	−0.243756	−	0.422197i	−0.0106689	−	0.0184791i
$523$	12.4402	+	21.5470i	0.543970	+	0.942184i	0.998671	+	0.0515397i	$0.0164129\pi$
$523$	12.4402	+	21.5470i	0.543970	+	0.942184i	−0.454701	+	0.890644i	$0.650254\pi$
$524$	−6.91740	−	5.80439i	−0.302188	−	0.253566i
$525$	−25.4650	−	4.49016i	−1.11138	−	0.195967i
$526$	5.46926	+	31.0177i	0.238471	+	1.35244i
$527$	1.77760	+	10.0813i	0.0774334	+	0.439147i
$528$	−6.09627	−	1.07494i	−0.265306	−	0.0467806i
$529$	−14.3550	−	12.0453i	−0.624132	−	0.523709i
$530$	−0.315207	−	0.545955i	−0.0136917	−	0.0237148i
$531$	20.9564			0.909428
$532$	7.36484	−	12.7563i	0.319306	−	0.553055i
$533$	−26.7408	+	9.73286i	−1.15827	+	0.421577i
$534$	13.8735	−	8.00984i	0.600363	−	0.346620i
$535$	1.53802	−	1.29055i	0.0664943	−	0.0557954i
$536$	3.37939	+	1.23000i	0.145967	+	0.0531277i
$537$	−15.2888	+	2.69583i	−0.659760	+	0.116334i
$538$	0.800355	−	4.53904i	0.0345057	−	0.195692i
$539$	19.5699			0.842934
$540$	2.93717	−	3.50038i	0.126396	−	0.150632i
$541$	−9.09421			−0.390991			−0.195495	−	0.980705i	$-0.562631\pi$
$541$	−9.09421			−0.390991			−0.195495	+	0.980705i	$0.562631\pi$
$542$	0.228903	−	1.29817i	0.00983223	−	0.0557614i
$543$	2.21048	+	2.63435i	0.0948610	+	0.113051i
$544$	5.87211	+	2.13727i	0.251765	+	0.0916349i
$545$	−7.01889	+	5.88954i	−0.300656	+	0.252280i
$546$			22.6026i			0.967303i
$547$	−20.8701	+	7.59608i	−0.892339	+	0.324785i	−0.747179	−	0.664623i	$-0.768592\pi$
$547$	−20.8701	+	7.59608i	−0.892339	+	0.324785i	−0.145160	+	0.989408i	$0.546370\pi$
$548$	−1.01367	+	1.75573i	−0.0433019	+	0.0750010i
$549$	−3.57620	−	1.30163i	−0.152628	−	0.0555522i
$550$	−7.55303	−	13.0822i	−0.322062	−	0.557828i
$551$	0.519134	+	0.435605i	0.0221158	+	0.0185574i
$552$	−1.22281	−	3.35965i	−0.0520463	−	0.142996i
$553$	4.05943	+	23.0222i	0.172625	+	0.979002i
$554$	−5.35204	−	30.3530i	−0.227387	−	1.28957i
$555$	7.55525	−	9.00400i	0.320703	−	0.382199i
$556$	0.126545	+	0.106183i	0.00536668	+	0.00450318i
$557$	1.35369	+	2.34466i	0.0573578	+	0.0993466i	0.893279	−	0.449504i	$-0.148399\pi$
$557$	1.35369	+	2.34466i	0.0573578	+	0.0993466i	−0.835921	+	0.548850i	$0.815066\pi$
$558$	−4.61809	+	1.68085i	−0.195499	+	0.0711559i
$559$	−19.9932	+	34.6292i	−0.845622	+	1.46466i
$560$	−2.91875	+	1.06234i	−0.123340	+	0.0448919i
$561$	33.5005	+	19.3415i	1.41439	+	0.816600i
$562$	−16.4172	+	13.7756i	−0.692516	+	0.581090i
$563$	−6.60859	−	2.40533i	−0.278519	−	0.101373i	0.198984	−	0.980003i	$-0.436236\pi$
$563$	−6.60859	−	2.40533i	−0.278519	−	0.101373i	−0.477503	+	0.878630i	$0.658458\pi$
$564$	3.79813	−	10.4353i	0.159930	−	0.439405i
$565$	−1.70011	+	9.64181i	−0.0715242	+	0.405634i
$566$	1.77332			0.0745381
$567$	15.8944	+	27.5299i	0.667502	+	1.15615i
$568$	13.5398			0.568119
$569$	4.34507	−	24.6421i	0.182155	−	1.03305i	−0.747401	−	0.664373i	$-0.768699\pi$
$569$	4.34507	−	24.6421i	0.182155	−	1.03305i	0.929556	−	0.368680i	$-0.120190\pi$
$570$	−2.17247	+	5.96880i	−0.0909946	+	0.250006i
$571$	−6.43242	−	2.34121i	−0.269188	−	0.0979765i	0.203899	−	0.978992i	$-0.434638\pi$
$571$	−6.43242	−	2.34121i	−0.269188	−	0.0979765i	−0.473088	+	0.881015i	$0.656861\pi$
$572$	−10.1152	+	8.48762i	−0.422936	+	0.354885i
$573$	19.6823	+	11.3636i	0.822241	+	0.474721i
$574$	25.5646	−	9.30477i	1.06705	−	0.388374i
$575$	4.36231	−	7.55574i	0.181921	−	0.315096i
$576$	−0.520945	+	2.95442i	−0.0217060	+	0.123101i
$577$	−2.10014	−	3.63754i	−0.0874298	−	0.151433i	0.818994	−	0.573802i	$-0.194532\pi$
$577$	−2.10014	−	3.63754i	−0.0874298	−	0.151433i	−0.906424	+	0.422369i	$0.861199\pi$
$578$	−16.8910	−	14.1732i	−0.702573	−	0.589529i
$579$	6.40848	−	7.63733i	0.266327	−	0.317397i
$580$	−0.0248149	−	0.140732i	−0.00103038	−	0.00584360i
$581$	2.73143	+	15.4907i	0.113319	+	0.642663i
$582$	6.68866	+	18.3770i	0.277254	+	0.761749i
$583$	1.96270	+	1.64690i	0.0812866	+	0.0682075i
$584$	−1.16385	−	2.01584i	−0.0481604	−	0.0834162i
$585$	−1.69253	−	9.59883i	−0.0699776	−	0.396863i
$586$	−15.4795	+	26.8113i	−0.639453	+	1.10757i
$587$	34.3491	−	12.5021i	1.41774	−	0.516015i	0.484348	−	0.874875i	$-0.339057\pi$
$587$	34.3491	−	12.5021i	1.41774	−	0.516015i	0.933391	+	0.358860i	$0.116835\pi$
$588$		−	9.48411i		−	0.391118i
$589$	5.23324	−	4.39121i	0.215632	−	0.180937i
$590$	5.77244	+	2.10100i	0.237648	+	0.0864967i
$591$	29.7050	+	35.4011i	1.22190	+	1.45621i
$592$	−1.34002	+	7.59964i	−0.0550746	+	0.312343i
$593$	−45.0660			−1.85064			−0.925320	−	0.379186i	$-0.876204\pi$
$593$	−45.0660			−1.85064			−0.925320	+	0.379186i	$0.876204\pi$
$594$	−6.35163	+	17.4510i	−0.260611	+	0.716022i
$595$	19.4097			0.795721
$596$	−1.00727	+	5.71253i	−0.0412595	+	0.233995i
$597$	−18.1545	+	3.20113i	−0.743015	+	0.131014i
$598$	−7.16637	−	2.60835i	−0.293055	−	0.106663i
$599$	12.4531	−	10.4494i	0.508820	−	0.426951i	−0.351893	−	0.936040i	$-0.614462\pi$
$599$	12.4531	−	10.4494i	0.508820	−	0.426951i	0.860714	+	0.509089i	$0.170018\pi$
$600$	−6.34002	+	3.66041i	−0.258830	+	0.149436i
$601$	39.0057	−	14.1969i	1.59107	−	0.579104i	0.613501	−	0.789694i	$-0.289761\pi$
$601$	39.0057	−	14.1969i	1.59107	−	0.579104i	0.977574	+	0.210590i	$0.0675386\pi$
$602$	19.1138	−	33.1061i	0.779021	−	1.34930i
$603$	5.39440	−	9.34337i	0.219677	−	0.380492i
$604$	−7.02481	−	12.1673i	−0.285836	−	0.495082i
$605$	−1.19459	−	1.00238i	−0.0485671	−	0.0407526i
$606$	15.9907	+	2.81959i	0.649576	+	0.114538i
$607$	−7.34565	−	41.6592i	−0.298151	−	1.69090i	−0.654114	−	0.756396i	$-0.726958\pi$
$607$	−7.34565	−	41.6592i	−0.298151	−	1.69090i	0.355963	−	0.934500i	$-0.384153\pi$
$608$	−0.724155	−	4.10689i	−0.0293684	−	0.166556i
$609$	0.979055	+	0.172634i	0.0396733	+	0.00699548i
$610$	−0.854570	−	0.717070i	−0.0346005	−	0.0290333i
$611$	−11.8439	−	20.5142i	−0.479153	−	0.829917i
$612$	9.37346	−	16.2353i	0.378899	−	0.656273i
$613$	−9.50686	+	16.4664i	−0.383979	+	0.665070i	−0.991627	−	0.129136i	$-0.958780\pi$
$613$	−9.50686	+	16.4664i	−0.383979	+	0.665070i	0.607648	+	0.794206i	$0.292113\pi$
$614$	8.02229	−	2.91987i	0.323753	−	0.117837i
$615$	−10.1600	+	5.86587i	−0.409690	+	0.236535i
$616$	9.67024	−	8.11430i	0.389625	−	0.326934i
$617$	−34.7550	−	12.6498i	−1.39918	−	0.509261i	−0.471246	−	0.882002i	$-0.656196\pi$
$617$	−34.7550	−	12.6498i	−1.39918	−	0.509261i	−0.927935	+	0.372741i	$0.878418\pi$
$618$	5.50387	−	0.970481i	0.221398	−	0.0390385i
$619$	−5.29648	+	30.0379i	−0.212884	+	1.20732i	0.671658	+	0.740862i	$0.265583\pi$
$619$	−5.29648	+	30.0379i	−0.212884	+	1.20732i	−0.884541	+	0.466462i	$0.845529\pi$
$620$	−1.44057			−0.0578547
$621$	−10.5628	+	1.86251i	−0.423872	+	0.0747401i
$622$	18.0128			0.722247
$623$	−5.67277	+	32.1719i	−0.227275	+	1.28894i
$624$	4.11334	+	4.90209i	0.164665	+	0.196241i
$625$	−13.1540	−	4.78768i	−0.526162	−	0.191507i
$626$	−13.1800	+	11.0594i	−0.526781	+	0.442021i
$627$		−	25.8151i		−	1.03096i
$628$	4.48545	−	1.63257i	0.178989	−	0.0651467i
$629$	24.1113	−	41.7620i	0.961380	−	1.66516i
$630$	1.61809	+	9.17664i	0.0644662	+	0.365606i
$631$	−6.86349	−	11.8879i	−0.273231	−	0.473251i	0.696456	−	0.717599i	$-0.254759\pi$
$631$	−6.86349	−	11.8879i	−0.273231	−	0.473251i	−0.969687	+	0.244349i	$0.921426\pi$
$632$	5.07011	+	4.25433i	0.201678	+	0.169228i
$633$	−3.16369	−	8.69216i	−0.125745	−	0.345482i
$634$	−4.32588	−	24.5333i	−0.171803	−	0.974342i
$635$	1.51279	+	8.57948i	0.0600334	+	0.340466i
$636$	0.798133	−	0.951178i	0.0316480	−	0.0377167i
$637$	−15.4973	−	13.0038i	−0.614026	−	0.515229i
$638$	0.290393	+	0.502975i	0.0114968	+	0.0199130i
$639$	7.05350	−	40.0024i	0.279032	−	1.58247i
$640$	−0.439693	+	0.761570i	−0.0173804	+	0.0301037i
$641$	−4.01367	+	1.46086i	−0.158530	+	0.0577004i	−0.420066	−	0.907493i	$-0.637993\pi$
$641$	−4.01367	+	1.46086i	−0.158530	+	0.0577004i	0.261536	+	0.965194i	$0.415771\pi$
$642$	3.42468	+	1.97724i	0.135161	+	0.0780354i
$643$	−16.1511	+	13.5524i	−0.636938	+	0.534454i	−0.903076	−	0.429481i	$-0.858697\pi$
$643$	−16.1511	+	13.5524i	−0.636938	+	0.534454i	0.266138	+	0.963935i	$0.414252\pi$
$644$	6.85117	+	2.49362i	0.269974	+	0.0982624i
$645$	−5.63816	+	15.4907i	−0.222002	+	0.609946i
$646$	−4.52523	+	25.6638i	−0.178043	+	1.00973i
$647$	−27.4023			−1.07730			−0.538648	−	0.842531i	$-0.681065\pi$
$647$	−27.4023			−1.07730			−0.538648	+	0.842531i	$0.681065\pi$
$648$	8.45723	+	3.07818i	0.332232	+	0.120922i
$649$	−24.9659			−0.979995
$650$	−2.71167	+	15.3786i	−0.106360	+	0.603199i
$651$	3.42767	−	9.41745i	0.134341	−	0.369099i
$652$	10.0706	+	3.66539i	0.394394	+	0.143548i
$653$	3.61540	−	3.03368i	0.141482	−	0.118717i	−0.569300	−	0.822130i	$-0.692786\pi$
$653$	3.61540	−	3.03368i	0.141482	−	0.118717i	0.710782	+	0.703413i	$0.248341\pi$
$654$	−15.6288	−	9.02330i	−0.611135	−	0.352839i
$655$	−7.46198	+	2.71594i	−0.291564	+	0.106121i
$656$	3.85117	−	6.67042i	0.150363	−	0.260436i
$657$	−6.56196	+	2.38836i	−0.256006	+	0.0931787i
$658$	11.3229	+	19.6119i	0.441414	+	0.764552i
$659$	16.1099	+	13.5178i	0.627554	+	0.526580i	0.900168	−	0.435543i	$-0.143444\pi$
$659$	16.1099	+	13.5178i	0.627554	+	0.526580i	−0.272614	+	0.962124i	$0.587888\pi$
$660$	−3.49912	+	4.17009i	−0.136203	+	0.162321i
$661$	4.40184	+	24.9641i	0.171212	+	0.970989i	0.942426	+	0.334414i	$0.108538\pi$
$661$	4.40184	+	24.9641i	0.171212	+	0.970989i	−0.771215	+	0.636575i	$0.780351\pi$
$662$	−1.53849	−	8.72518i	−0.0597949	−	0.339114i
$663$	−13.6769	−	37.5769i	−0.531166	−	1.45937i
$664$	3.41147	+	2.86257i	0.132391	+	0.111089i
$665$	−6.47653	−	11.2177i	−0.251149	−	0.435003i
$666$	21.7545	+	7.91799i	0.842969	+	0.306816i
$667$	−0.167718	+	0.290497i	−0.00649408	+	0.0112481i
$668$	12.1211	−	4.41171i	0.468979	−	0.170694i
$669$			32.9949i			1.27566i
$670$	2.42262	−	2.03282i	0.0935939	−	0.0785346i
$671$	4.26042	+	1.55067i	0.164472	+	0.0598628i
$672$	−3.93242	−	4.68647i	−0.151696	−	0.180785i
$673$	2.47090	−	14.0132i	0.0952464	−	0.540169i	−0.899425	−	0.437075i	$-0.856015\pi$
$673$	2.47090	−	14.0132i	0.0952464	−	0.540169i	0.994672	−	0.103094i	$-0.0328743\pi$
$674$	−21.0719			−0.811660
$675$	7.51161	+	20.6380i	0.289122	+	0.794356i
$676$	0.650015			0.0250006
$677$	8.07878	−	45.8170i	0.310493	−	1.76089i	−0.285958	−	0.958242i	$-0.592312\pi$
$677$	8.07878	−	45.8170i	0.310493	−	1.76089i	0.596450	−	0.802650i	$-0.296577\pi$
$678$	−18.9907	+	3.34857i	−0.729332	+	0.128601i
$679$	−37.4752	−	13.6399i	−1.43817	−	0.523450i
$680$	4.20961	−	3.53228i	0.161431	−	0.135457i
$681$	5.19166	−	2.99740i	0.198945	−	0.114861i
$682$	5.50165	−	2.00244i	0.210669	−	0.0766773i
$683$	5.10101	−	8.83522i	0.195185	−	0.338070i	−0.751776	−	0.659418i	$-0.770803\pi$
$683$	5.10101	−	8.83522i	0.195185	−	0.338070i	0.946961	+	0.321348i	$0.104136\pi$
$684$	−12.5107			−0.478360
$685$	0.891407	+	1.54396i	0.0340589	+	0.0589918i
$686$	−4.12449	−	3.46085i	−0.157474	−	0.132136i
$687$	49.3631	+	8.70404i	1.88332	+	0.332080i
$688$	−1.87939	−	10.6585i	−0.0716509	−	0.406352i
$689$	−0.459922	−	2.60835i	−0.0175216	−	0.0993701i
$690$	−3.09627	−	0.545955i	−0.117873	−	0.0207842i
$691$	−0.269915	−	0.226485i	−0.0102680	−	0.00861591i	0.637639	−	0.770335i	$-0.279911\pi$
$691$	−0.269915	−	0.226485i	−0.0102680	−	0.00861591i	−0.647907	+	0.761719i	$0.724356\pi$
$692$	−6.43629	−	11.1480i	−0.244671	−	0.423783i
$693$	−18.9354	−	32.7971i	−0.719297	−	1.24586i
$694$	11.0544	−	19.1467i	0.419618	−	0.726800i
$695$	0.136507	−	0.0496844i	0.00517800	−	0.00188464i
$696$	0.243756	−	0.140732i	0.00923954	−	0.00533445i
$697$	−36.8710	+	30.9384i	−1.39659	+	1.17188i
$698$	2.06670	+	0.752219i	0.0782259	+	0.0284719i
$699$	−11.3610	+	2.00324i	−0.429711	+	0.0757697i
$700$	2.59240	−	14.7022i	0.0979834	−	0.555691i
$701$	39.9358			1.50836			0.754178	−	0.656671i	$-0.228036\pi$
$701$	39.9358			1.50836			0.754178	+	0.656671i	$0.228036\pi$
$702$	16.6257	−	9.59883i	0.627495	−	0.362285i
$703$	−32.1813			−1.21374
$704$	0.620615	−	3.51968i	0.0233903	−	0.132653i
$705$	−6.27719	−	7.48086i	−0.236413	−	0.281746i
$706$	4.47178	+	1.62760i	0.168298	+	0.0612554i
$707$	−25.3653	+	21.2840i	−0.953960	+	0.800468i
$708$			12.0992i			0.454714i
$709$	46.2789	−	16.8441i	1.73804	−	0.632595i	0.738891	−	0.673825i	$-0.235350\pi$
$709$	46.2789	−	16.8441i	1.73804	−	0.632595i	0.999150	+	0.0412304i	$0.0131278\pi$
$710$	5.95336	−	10.3115i	0.223426	−	0.386985i
$711$	15.2103	−	12.7630i	0.570432	−	0.478649i
$712$	4.62449	+	8.00984i	0.173310	+	0.300182i
$713$	2.59034	+	2.17355i	0.0970089	+	0.0814001i
$714$	13.0753	+	35.9242i	0.489332	+	1.34443i
$715$	2.01636	+	11.4353i	0.0754075	+	0.427657i
$716$	−1.55644	−	8.82699i	−0.0581668	−	0.329880i
$717$	8.67159	−	10.3344i	0.323846	−	0.385945i
$718$	1.99613	+	1.67495i	0.0744949	+	0.0625086i
$719$	25.8050	+	44.6956i	0.962364	+	1.66686i	0.716536	+	0.697550i	$0.245726\pi$
$719$	25.8050	+	44.6956i	0.962364	+	1.66686i	0.245828	+	0.969314i	$0.420940\pi$
$720$	2.02094	+	1.69577i	0.0753162	+	0.0631978i
$721$	−5.69846	+	9.87003i	−0.212222	+	0.367579i
$722$	−1.51202	+	0.550331i	−0.0562716	+	0.0204812i
$723$	32.8423	+	18.9615i	1.22142	+	0.705186i
$724$	−1.52094	+	1.27622i	−0.0565255	+	0.0474305i
$725$	0.645430	+	0.234917i	0.0239707	+	0.00872461i
$726$	1.05051	−	2.88624i	0.0389880	−	0.107119i
$727$	−4.79932	+	27.2183i	−0.177997	+	1.00947i	0.756631	+	0.653842i	$0.226844\pi$
$727$	−4.79932	+	27.2183i	−0.177997	+	1.00947i	−0.934628	+	0.355628i	$0.884267\pi$
$728$	−13.0496			−0.483651
$729$	13.5000	−	23.3827i	0.500000	−	0.866025i
$730$	−2.04694			−0.0757607
$731$	−11.7442	+	66.6048i	−0.434376	+	2.46347i
$732$	0.751497	−	2.06472i	0.0277761	−	0.0763142i
$733$	−25.9072	−	9.42945i	−0.956904	−	0.348285i	−0.184084	−	0.982910i	$-0.558932\pi$
$733$	−25.9072	−	9.42945i	−0.956904	−	0.348285i	−0.772820	+	0.634626i	$0.781154\pi$
$734$	10.9042	−	9.14971i	0.402481	−	0.337722i
$735$	−7.22281	−	4.17009i	−0.266417	−	0.153816i
$736$	1.93969	−	0.705990i	0.0714980	−	0.0260232i
$737$	−6.42649	+	11.1310i	−0.236723	+	0.410016i
$738$	−17.7010	−	14.8529i	−0.651582	−	0.546743i
$739$	2.01320	+	3.48697i	0.0740569	+	0.128270i	0.900676	−	0.434492i	$-0.143072\pi$
$739$	2.01320	+	3.48697i	0.0740569	+	0.128270i	−0.826619	+	0.562762i	$0.809739\pi$
$740$	5.19846	+	4.36203i	0.191099	+	0.160351i
$741$	−17.1536	+	20.4429i	−0.630155	+	0.750989i
$742$	0.439693	+	2.49362i	0.0161416	+	0.0915437i
$743$	5.04979	+	28.6388i	0.185259	+	1.05066i	0.925622	+	0.378449i	$0.123542\pi$
$743$	5.04979	+	28.6388i	0.185259	+	1.05066i	−0.740363	+	0.672207i	$0.765347\pi$
$744$	−0.970437	−	2.66625i	−0.0355780	−	0.0977496i
$745$	3.90760	+	3.27887i	0.143164	+	0.120128i
$746$	−1.15405	−	1.99887i	−0.0422527	−	0.0731838i
$747$	10.2344	−	8.58770i	0.374458	−	0.314208i
$748$	−11.1668	+	19.3415i	−0.408300	+	0.707197i
$749$	−7.57785	+	2.75811i	−0.276889	+	0.100779i
$750$			14.0535i			0.513162i
$751$	31.1962	−	26.1768i	1.13837	−	0.955203i	0.138983	−	0.990295i	$-0.455617\pi$
$751$	31.1962	−	26.1768i	1.13837	−	0.955203i	0.999384	+	0.0350914i	$0.0111722\pi$
$752$	6.02481	+	2.19285i	0.219702	+	0.0799651i
$753$	−17.9078	−	21.3416i	−0.652595	−	0.777733i
$754$	0.104256	−	0.591264i	0.00379677	−	0.0215326i
$755$	−12.3550			−0.449646
$756$	−15.8944	+	9.17664i	−0.578074	+	0.333751i
$757$	32.9486			1.19754			0.598769	−	0.800922i	$-0.295657\pi$
$757$	32.9486			1.19754			0.598769	+	0.800922i	$0.295657\pi$
$758$	1.04664	−	5.93577i	0.0380156	−	0.215597i
$759$	12.5838	−	2.21886i	0.456762	−	0.0805395i
$760$	−3.44609	−	1.25427i	−0.125003	−	0.0454973i
$761$	−0.773318	+	0.648891i	−0.0280328	+	0.0235223i	−0.656696	−	0.754155i	$-0.728047\pi$
$761$	−0.773318	+	0.648891i	−0.0280328	+	0.0235223i	0.628664	+	0.777677i	$0.283602\pi$
$762$	−14.8601	+	8.57948i	−0.538324	+	0.310802i
$763$	34.5822	−	12.5869i	1.25196	−	0.455676i
$764$	−6.56077	+	11.3636i	−0.237360	+	0.411120i
$765$	−8.24288	−	14.2771i	−0.298022	−	0.516189i
$766$	10.6395	+	18.4282i	0.384421	+	0.665836i
$767$	19.7704	+	16.5893i	0.713867	+	0.599006i
$768$	−1.70574	−	0.300767i	−0.0615505	−	0.0108530i
$769$	−5.38831	−	30.5586i	−0.194307	−	1.10197i	−0.913402	−	0.407059i	$-0.866554\pi$
$769$	−5.38831	−	30.5586i	−0.194307	−	1.10197i	0.719094	−	0.694912i	$-0.244557\pi$
$770$	−1.92767	−	10.9324i	−0.0694684	−	0.393975i
$771$	−44.1186	−	7.77930i	−1.58889	−	0.280165i
$772$	4.40941	+	3.69994i	0.158698	+	0.133164i
$773$	−8.32295	−	14.4158i	−0.299356	−	0.518499i	0.676633	−	0.736320i	$-0.263438\pi$
$773$	−8.32295	−	14.4158i	−0.299356	−	0.518499i	−0.975989	+	0.217821i	$0.930105\pi$
$774$	−32.4688			−1.16707
$775$	3.46198	−	5.99633i	0.124358	−	0.215394i
$776$	−10.6099	+	3.86170i	−0.380875	+	0.138627i
$777$	−40.8851	+	23.6050i	−1.46674	+	0.846825i
$778$	15.8248	−	13.2785i	0.567345	−	0.476059i
$779$	30.1835	+	10.9859i	1.08144	+	0.393611i
$780$	5.54189	−	0.977185i	0.198431	−	0.0349888i
$781$	−8.40302	+	47.6559i	−0.300684	+	1.70526i
$782$	−12.8990			−0.461267
$783$	−0.288800	−	0.793471i	−0.0103209	−	0.0283564i
$784$	5.47565			0.195559
$785$	0.728903	−	4.13381i	0.0260157	−	0.147542i
$786$	−10.0535	−	11.9813i	−0.358596	−	0.427359i
$787$	1.93494	+	0.704262i	0.0689733	+	0.0251042i	0.376276	−	0.926507i	$-0.377204\pi$
$787$	1.93494	+	0.704262i	0.0689733	+	0.0251042i	−0.307303	+	0.951612i	$0.599427\pi$
$788$	−20.4388	+	17.1502i	−0.728103	+	0.610951i
$789$			54.5530i			1.94214i
$790$	5.46926	−	1.99065i	0.194587	−	0.0708240i
$791$	19.6621	−	34.0557i	0.699104	−	1.21088i
$792$	−10.0753	−	3.66712i	−0.358011	−	0.130305i
$793$	−2.34343	−	4.05893i	−0.0832175	−	0.144137i
$794$	18.7893	+	15.7661i	0.666806	+	0.559517i
$795$	−0.373455	−	1.02606i	−0.0132451	−	0.0363906i
$796$	−1.84817	−	10.4815i	−0.0655068	−	0.371507i
$797$	8.95336	+	50.7770i	0.317144	+	1.79862i	0.559935	+	0.828537i	$0.310826\pi$
$797$	8.95336	+	50.7770i	0.317144	+	1.79862i	−0.242791	+	0.970079i	$0.578063\pi$
$798$	16.3991	−	19.5437i	0.580524	−	0.691841i
$799$	−30.6917	−	25.7534i	−1.08579	−	0.911088i
$800$	−2.11334	−	3.66041i	−0.0747179	−	0.129415i
$801$	26.0736	−	9.49000i	0.921264	−	0.335313i
$802$	7.31268	−	12.6659i	0.258220	−	0.447250i
$803$	7.81743	−	2.84531i	0.275871	−	0.100409i
$804$	5.39440	+	3.11446i	0.190246	+	0.109838i
$805$	4.91147	−	4.12122i	0.173107	−	0.145254i
$806$	−5.68732	−	2.07001i	−0.200327	−	0.0729132i
$807$	2.73039	−	7.50168i	0.0961143	−	0.264072i
$808$	−1.62789	+	9.23222i	−0.0572689	+	0.324788i
$809$	25.9709			0.913088			0.456544	−	0.889701i	$-0.349087\pi$
$809$	25.9709			0.913088			0.456544	+	0.889701i	$0.349087\pi$
$810$	6.06283	−	5.08732i	0.213026	−	0.178750i
$811$	−14.4442			−0.507204			−0.253602	−	0.967309i	$-0.581615\pi$
$811$	−14.4442			−0.507204			−0.253602	+	0.967309i	$0.581615\pi$
$812$	−0.0996702	+	0.565258i	−0.00349774	+	0.0198367i
$813$	0.780897	−	2.14550i	0.0273873	−	0.0752459i
$814$	−25.9167	−	9.43290i	−0.908379	−	0.330623i
$815$	7.21941	−	6.05780i	0.252885	−	0.212196i
$816$	9.37346	+	5.41177i	0.328137	+	0.189450i
$817$	42.4124	−	15.4369i	1.48382	−	0.540067i
$818$	−18.0633	+	31.2866i	−0.631568	+	1.09391i
$819$	−6.79813	+	38.5541i	−0.237546	+	1.34719i
$820$	−3.38666	−	5.86587i	−0.118267	−	0.204845i
$821$	−5.12061	−	4.29671i	−0.178711	−	0.149956i	0.549044	−	0.835793i	$-0.314992\pi$
$821$	−5.12061	−	4.29671i	−0.178711	−	0.149956i	−0.727755	+	0.685837i	$0.759436\pi$
$822$	−2.25712	+	2.68993i	−0.0787262	+	0.0938222i
$823$	−1.34343	−	7.61895i	−0.0468289	−	0.265580i	0.952400	−	0.304852i	$-0.0986071\pi$
$823$	−1.34343	−	7.61895i	−0.0468289	−	0.265580i	−0.999229	+	0.0392725i	$0.987496\pi$
$824$	0.560307	+	3.17766i	0.0195192	+	0.110699i
$825$	−8.94878	−	24.5866i	−0.311556	−	0.855994i
$826$	−18.9008	−	15.8597i	−0.657643	−	0.551828i
$827$	−23.4038	−	40.5366i	−0.813830	−	1.40959i	−0.910165	−	0.414245i	$-0.864046\pi$
$827$	−23.4038	−	40.5366i	−0.813830	−	1.40959i	0.0963358	−	0.995349i	$-0.469288\pi$
$828$	−1.07532	−	6.09845i	−0.0373700	−	0.211936i
$829$	22.6648	−	39.2566i	0.787180	−	1.36344i	−0.140507	−	0.990080i	$-0.544873\pi$
$829$	22.6648	−	39.2566i	0.787180	−	1.36344i	0.927688	−	0.373357i	$-0.121793\pi$
$830$	3.68004	−	1.33943i	0.127736	−	0.0464922i
$831$		−	53.3839i		−	1.85187i
$832$	−2.83022	+	2.37484i	−0.0981203	+	0.0823327i
$833$	−32.1536	−	11.7030i	−1.11406	−	0.405484i
$834$	0.183915	+	0.219182i	0.00636846	+	0.00758964i
$835$	1.96972	−	11.1708i	0.0681650	−	0.386583i
$836$	14.9044			0.515478
$837$	−8.38279	+	1.47811i	−0.289752	+	0.0510910i
$838$	−19.7128			−0.680966
$839$	1.81924	−	10.3174i	0.0628071	−	0.356197i	−0.937166	−	0.348883i	$-0.886561\pi$
$839$	1.81924	−	10.3174i	0.0628071	−	0.356197i	0.999973	−	0.00731353i	$-0.00232799\pi$
$840$	−5.29813	+	0.934204i	−0.182803	+	0.0322331i
$841$	27.2263	+	9.90955i	0.938837	+	0.341709i
$842$	−2.63041	+	2.20718i	−0.0906501	+	0.0760645i
$843$	−32.1466	+	18.5599i	−1.10719	+	0.639235i
$844$	5.01842	−	1.82655i	0.172741	−	0.0628726i
$845$	0.285807	−	0.495032i	0.00983206	−	0.0170296i
$846$	9.61721	−	16.6575i	0.330647	−	0.572697i
$847$	3.13176	+	5.42437i	0.107609	+	0.186383i
$848$	0.549163	+	0.460802i	0.0188583	+	0.0158240i
$849$	3.02481	+	0.533356i	0.103811	+	0.0183047i
$850$	4.58647	+	26.0111i	0.157315	+	0.892175i
$851$	−2.76604	−	15.6870i	−0.0948188	−	0.537744i
$852$	23.0954	+	4.07234i	0.791235	+	0.139516i
$853$	27.4932	+	23.0695i	0.941349	+	0.789886i	0.977820	−	0.209449i	$-0.0671671\pi$
$853$	27.4932	+	23.0695i	0.941349	+	0.789886i	−0.0364705	+	0.999335i	$0.511612\pi$
$854$	2.24035	+	3.88040i	0.0766633	+	0.132785i
$855$	−5.50088	+	9.52780i	−0.188126	+	0.325844i
$856$	−1.14156	+	1.97724i	−0.0390177	+	0.0675806i
$857$	15.5488	−	5.65928i	0.531135	−	0.193317i	−0.0625099	−	0.998044i	$-0.519911\pi$
$857$	15.5488	−	5.65928i	0.531135	−	0.193317i	0.593645	+	0.804727i	$0.297688\pi$
$858$	−19.8066	+	11.4353i	−0.676186	+	0.390396i
$859$	10.8369	−	9.09321i	0.369749	−	0.310256i	−0.438913	−	0.898529i	$-0.644636\pi$
$859$	10.8369	−	9.09321i	0.369749	−	0.310256i	0.808662	+	0.588273i	$0.200192\pi$
$860$	−8.94356	−	3.25519i	−0.304973	−	0.111001i
$861$	46.4051	−	8.18248i	1.58148	−	0.278858i
$862$	4.98633	−	28.2789i	0.169835	−	0.963182i
$863$	−32.8939			−1.11972			−0.559861	−	0.828586i	$-0.689146\pi$
$863$	−32.8939			−1.11972			−0.559861	+	0.828586i	$0.689146\pi$
$864$	−1.77719	+	4.88279i	−0.0604612	+	0.166116i
$865$	−11.3200			−0.384890
$866$	2.45155	−	13.9034i	0.0833071	−	0.472458i
$867$	−24.5488	−	29.2561i	−0.833719	−	0.993588i
$868$	5.43717	+	1.97897i	0.184549	+	0.0671705i
$869$	−18.1205	+	15.2049i	−0.614694	+	0.515790i
$870$		−	0.247516i		−	0.00839158i
$871$	12.4855	−	4.54433i	0.423053	−	0.153979i
$872$	5.20961	−	9.02330i	0.176420	−	0.305568i
$873$	5.88191	+	33.3580i	0.199073	+	1.12900i
$874$	4.30406	+	7.45486i	0.145587	+	0.252164i
$875$	−21.9538	−	18.4215i	−0.742175	−	0.622759i
$876$	−1.37892	−	3.78855i	−0.0465893	−	0.128003i
$877$	4.15627	+	23.5714i	0.140347	+	0.795949i	0.970986	+	0.239137i	$0.0768645\pi$
$877$	4.15627	+	23.5714i	0.140347	+	0.795949i	−0.830639	+	0.556812i	$0.812024\pi$
$878$	−2.69506	−	15.2844i	−0.0909539	−	0.515825i
$879$	−34.4680	+	41.0773i	−1.16258	+	1.38550i
$880$	−2.40760	−	2.02022i	−0.0811603	−	0.0681016i
$881$	9.34183	+	16.1805i	0.314734	+	0.545136i	0.979381	−	0.202022i	$-0.0647512\pi$
$881$	9.34183	+	16.1805i	0.314734	+	0.545136i	−0.664647	+	0.747158i	$0.731418\pi$
$882$	2.85251	−	16.1774i	0.0960490	−	0.544721i
$883$	2.99407	−	5.18588i	0.100758	−	0.174519i	−0.811239	−	0.584715i	$-0.801206\pi$
$883$	2.99407	−	5.18588i	0.100758	−	0.174519i	0.911997	+	0.410196i	$0.134540\pi$
$884$	21.6951	−	7.89636i	0.729684	−	0.265583i
$885$	9.21436	+	5.31991i	0.309737	+	0.178827i
$886$	27.3897	−	22.9826i	0.920173	−	0.772117i
$887$	−7.36231	−	2.67966i	−0.247202	−	0.0899742i	0.215447	−	0.976515i	$-0.430879\pi$
$887$	−7.36231	−	2.67966i	−0.247202	−	0.0899742i	−0.462650	+	0.886541i	$0.653101\pi$
$888$	−4.57145	+	12.5600i	−0.153408	+	0.421485i
$889$	6.07620	−	34.4598i	0.203789	−	1.15575i
$890$	8.13341			0.272632
$891$	−16.0829	+	27.8564i	−0.538797	+	0.933225i
$892$	−19.0496			−0.637829
$893$	−4.64290	+	26.3312i	−0.155369	+	0.881140i
$894$	−3.43629	+	9.44113i	−0.114927	+	0.315759i
$895$	−7.40673	−	2.69583i	−0.247580	−	0.0901116i
$896$	2.70574	−	2.27038i	0.0903923	−	0.0758482i
$897$	−11.4394	−	6.60457i	−0.381952	−	0.220520i
$898$	−24.1621	+	8.79428i	−0.806299	+	0.293469i
$899$	−0.133103	+	0.230542i	−0.00443924	+	0.00768899i
$900$	−11.9153	+	4.33683i	−0.397178	+	0.144561i
$901$	−2.23989	−	3.87960i	−0.0746214	−	0.129248i
$902$	21.0876	+	17.6946i	0.702142	+	0.589167i
$903$	42.5604	−	50.7215i	1.41632	−	1.68790i
$904$	−1.93330	−	10.9643i	−0.0643005	−	0.364666i
$905$	0.303186	+	1.71945i	0.0100782	+	0.0571565i
$906$	−8.32295	−	22.8671i	−0.276511	−	0.759709i
$907$	−8.30928	−	6.97231i	−0.275905	−	0.231512i	0.494326	−	0.869276i	$-0.335415\pi$
$907$	−8.30928	−	6.97231i	−0.275905	−	0.231512i	−0.770231	+	0.637765i	$0.779859\pi$
$908$	1.73055	+	2.99740i	0.0574304	+	0.0994723i
$909$	26.4278	+	9.61894i	0.876556	+	0.319040i
$910$	−5.73783	+	9.93821i	−0.190207	+	0.329448i
$911$	−28.4402	+	10.3514i	−0.942265	+	0.342956i	−0.767060	−	0.641576i	$-0.778281\pi$
$911$	−28.4402	+	10.3514i	−0.942265	+	0.342956i	−0.175205	+	0.984532i	$0.556059\pi$
$912$		−	7.22308i		−	0.239180i
$913$	−12.1925	+	10.2308i	−0.403514	+	0.338588i
$914$	1.90983	+	0.695120i	0.0631714	+	0.0229925i
$915$	−1.24200	−	1.48016i	−0.0410593	−	0.0489326i
$916$	−5.02528	+	28.4998i	−0.166040	+	0.941660i
$917$	31.8949			1.05326
$918$	20.8717	−	24.8739i	0.688869	−	0.820962i
$919$	16.3492			0.539309			0.269655	−	0.962957i	$-0.413090\pi$
$919$	16.3492			0.539309			0.269655	+	0.962957i	$0.413090\pi$
$920$	0.315207	−	1.78763i	0.0103921	−	0.0589364i
$921$	14.5621	−	2.56769i	0.479838	−	0.0846084i
$922$	20.2729	+	7.37874i	0.667653	+	0.243006i
$923$	38.3207	−	32.1549i	1.26134	−	1.05839i
$924$	18.9354	−	10.9324i	0.622929	−	0.359648i
$925$	−30.6498	+	11.1556i	−1.00776	+	0.366794i
$926$	−10.8007	+	18.7073i	−0.354932	+	0.614760i
$927$	9.68004			0.317934
$928$	0.0812519	+	0.140732i	0.00266722	+	0.00461977i
$929$	−30.5107	−	25.6015i	−1.00102	−	0.839959i	−0.0138986	−	0.999903i	$-0.504424\pi$
$929$	−30.5107	−	25.6015i	−1.00102	−	0.839959i	−0.987126	+	0.159944i	$0.948869\pi$
$930$	−2.45723	−	0.433277i	−0.0805759	−	0.0142077i
$931$	3.96522	+	22.4879i	0.129955	+	0.737011i
$932$	−1.15657	−	6.55926i	−0.0378848	−	0.214856i
$933$	30.7251	+	5.41766i	1.00589	+	0.177366i
$934$	−18.7867	−	15.7639i	−0.614721	−	0.515812i
$935$	9.81996	+	17.0087i	0.321147	+	0.556243i
$936$	5.54189	+	9.59883i	0.181142	+	0.313748i
$937$	−24.4124	+	42.2835i	−0.797519	+	1.38134i	0.123709	+	0.992319i	$0.460521\pi$
$937$	−24.4124	+	42.2835i	−0.797519	+	1.38134i	−0.921228	+	0.389024i	$0.872812\pi$
$938$	−11.9363	+	4.34445i	−0.389734	+	0.141851i
$939$	−25.8080	+	14.9002i	−0.842212	+	0.486251i
$940$	4.31908	−	3.62414i	0.140873	−	0.118206i
$941$	−11.8751	−	4.32218i	−0.387117	−	0.140899i	0.141127	−	0.989991i	$-0.454927\pi$
$941$	−11.8751	−	4.32218i	−0.387117	−	0.140899i	−0.528245	+	0.849092i	$0.677150\pi$
$942$	8.14203	−	1.43566i	0.265282	−	0.0467763i
$943$	−2.76083	+	15.6574i	−0.0899050	+	0.509877i
$944$	−6.98545			−0.227357
$945$			16.1396i			0.525021i
$946$	38.6810			1.25763
$947$	6.60261	−	37.4452i	0.214556	−	1.21681i	−0.667120	−	0.744951i	$-0.732473\pi$
$947$	6.60261	−	37.4452i	0.214556	−	1.21681i	0.881675	−	0.471856i	$-0.156416\pi$
$948$	7.36871	+	8.78168i	0.239325	+	0.285216i
$949$	−8.08125	−	2.94134i	−0.262329	−	0.0954798i
$950$	13.5025	−	11.3300i	0.438080	−	0.367593i
$951$		−	43.1485i		−	1.39918i
$952$	−20.7408	+	7.54904i	−0.672214	+	0.244666i
$953$	−7.95353	+	13.7759i	−0.257640	+	0.446245i	−0.965609	−	0.259998i	$-0.916278\pi$
$953$	−7.95353	+	13.7759i	−0.257640	+	0.446245i	0.707969	+	0.706243i	$0.249612\pi$
$954$	1.64749	−	1.38241i	0.0533394	−	0.0447571i
$955$	5.76945	+	9.99298i	0.186695	+	0.323365i
$956$	5.96657	+	5.00654i	0.192973	+	0.161923i
$957$	0.344055	+	0.945283i	0.0111217	+	0.0305567i
$958$	−2.48767	−	14.1083i	−0.0803731	−	0.455818i
$959$	−1.24345	−	7.05196i	−0.0401531	−	0.227720i
$960$	−0.979055	+	1.16679i	−0.0315989	+	0.0376581i
$961$	−21.6917	−	18.2015i	−0.699731	−	0.587144i
$962$	14.2554	+	24.6910i	0.459611	+	0.796070i
$963$	5.24691	+	4.40268i	0.169079	+	0.141874i
$964$	−10.9474	+	18.9615i	−0.352593	+	0.610709i
$965$	4.75655	−	1.73124i	0.153119	−	0.0557307i
$966$	10.9363	+	6.31407i	0.351869	+	0.203152i
$967$	−45.3023	+	38.0132i	−1.45682	+	1.22242i	−0.529420	+	0.848360i	$0.677590\pi$
$967$	−45.3023	+	38.0132i	−1.45682	+	1.22242i	−0.927404	+	0.374060i	$0.877965\pi$
$968$	1.66637	+	0.606511i	0.0535593	+	0.0194940i
$969$	−15.4377	+	42.4147i	−0.495930	+	1.36256i
$970$	−1.72416	+	9.77817i	−0.0553593	+	0.313958i
$971$	−9.68004			−0.310647			−0.155324	−	0.987864i	$-0.549642\pi$
$971$	−9.68004			−0.310647			−0.155324	+	0.987864i	$0.549642\pi$
$972$	13.5000	+	7.79423i	0.433013	+	0.250000i
$973$	−0.583473			−0.0187053
$974$	−5.61081	+	31.8205i	−0.179782	+	1.01959i
$975$	−9.25078	+	25.4163i	−0.296262	+	0.813973i
$976$	1.19207	+	0.433877i	0.0381571	+	0.0138881i
$977$	2.64955	−	2.22324i	0.0847666	−	0.0711276i	−0.599420	−	0.800435i	$-0.704602\pi$
$977$	2.64955	−	2.22324i	0.0847666	−	0.0711276i	0.684186	+	0.729307i	$0.260158\pi$
$978$	16.0753	+	9.28109i	0.514032	+	0.296777i
$979$	−31.0621	+	11.3057i	−0.992750	+	0.361331i
$980$	2.40760	−	4.17009i	0.0769081	−	0.133209i
$981$	−23.9447	−	20.0920i	−0.764497	−	0.641489i
$982$	16.2246	+	28.1019i	0.517748	+	0.896767i
$983$	−32.2649	−	27.0735i	−1.02909	−	0.863510i	−0.0383486	−	0.999264i	$-0.512210\pi$
$983$	−32.2649	−	27.0735i	−1.02909	−	0.863510i	−0.990743	+	0.135754i	$0.956654\pi$
$984$	8.57532	−	10.2197i	0.273371	−	0.325791i
$985$	4.07428	+	23.1064i	0.129817	+	0.736231i
$986$	−0.176337	−	1.00005i	−0.00561570	−	0.0318482i
$987$	13.4153	+	36.8584i	0.427015	+	1.17321i
$988$	−11.8027	−	9.90366i	−0.375495	−	0.315077i
$989$	11.1702	+	19.3474i	0.355193	+	0.615213i
$990$	−7.22281	+	6.06066i	−0.229556	+	0.192620i
$991$	9.26786	−	16.0524i	0.294403	−	0.509921i	−0.680443	−	0.732801i	$-0.738213\pi$
$991$	9.26786	−	16.0524i	0.294403	−	0.509921i	0.974846	+	0.222880i	$0.0715458\pi$
$992$	1.53936	−	0.560282i	0.0488748	−	0.0177890i
$993$		−	15.3456i		−	0.486978i
$994$	−36.6352	+	30.7406i	−1.16200	+	0.975033i
$995$	−8.79503	−	3.20113i	−0.278821	−	0.101483i
$996$	4.95811	+	5.90885i	0.157104	+	0.187229i
$997$	−1.90879	+	10.8253i	−0.0604519	+	0.342839i	0.939548	+	0.342417i	$0.111246\pi$
$997$	−1.90879	+	10.8253i	−0.0604519	+	0.342839i	−1.00000		0.000422427i	$0.999866\pi$
$998$	24.8307			0.786002
$999$	34.7260	+	20.0490i	1.09868	+	0.634324i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.2.e.a.25.1	yes	6
3.2	odd	2		162.2.e.a.73.1		6
4.3	odd	2		432.2.u.a.241.1		6
9.2	odd	6		486.2.e.c.55.1		6
9.4	even	3		486.2.e.d.379.1		6
9.5	odd	6		486.2.e.a.379.1		6
9.7	even	3		486.2.e.b.55.1		6
27.2	odd	18		1458.2.c.a.487.1		6
27.4	even	9		486.2.e.d.109.1		6
27.5	odd	18		486.2.e.c.433.1		6
27.7	even	9		1458.2.c.d.973.3		6
27.11	odd	18		1458.2.a.d.1.3		3
27.13	even	9	inner	54.2.e.a.13.1	✓	6
27.14	odd	18		162.2.e.a.91.1		6
27.16	even	9		1458.2.a.a.1.1		3
27.20	odd	18		1458.2.c.a.973.1		6
27.22	even	9		486.2.e.b.433.1		6
27.23	odd	18		486.2.e.a.109.1		6
27.25	even	9		1458.2.c.d.487.3		6
108.67	odd	18		432.2.u.a.337.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.e.a.13.1	✓	6	27.13	even	9	inner
54.2.e.a.25.1	yes	6	1.1	even	1	trivial
162.2.e.a.73.1		6	3.2	odd	2
162.2.e.a.91.1		6	27.14	odd	18
432.2.u.a.241.1		6	4.3	odd	2
432.2.u.a.337.1		6	108.67	odd	18
486.2.e.a.109.1		6	27.23	odd	18
486.2.e.a.379.1		6	9.5	odd	6
486.2.e.b.55.1		6	9.7	even	3
486.2.e.b.433.1		6	27.22	even	9
486.2.e.c.55.1		6	9.2	odd	6
486.2.e.c.433.1		6	27.5	odd	18
486.2.e.d.109.1		6	27.4	even	9
486.2.e.d.379.1		6	9.4	even	3
1458.2.a.a.1.1		3	27.16	even	9
1458.2.a.d.1.3		3	27.11	odd	18
1458.2.c.a.487.1		6	27.2	odd	18
1458.2.c.a.973.1		6	27.20	odd	18
1458.2.c.d.487.3		6	27.25	even	9
1458.2.c.d.973.3		6	27.7	even	9

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:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	54.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(-0.592396 + 1.62760i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.673648 + 0.565258i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(3.31908 - 1.20805i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.29813 - 1.92836i) q^{9} +O(q^{10})\)	\(q+(-0.173648 + 0.984808i) q^{2} +(-0.592396 + 1.62760i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.673648 + 0.565258i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(3.31908 - 1.20805i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.29813 - 1.92836i) q^{9} +(-0.439693 - 0.761570i) q^{10} +(2.73783 + 2.29731i) q^{11} +(1.11334 - 1.32683i) q^{12} +(-0.641559 - 3.63846i) q^{13} +(0.613341 + 3.47843i) q^{14} +(-0.520945 - 1.43128i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-3.12449 - 5.41177i) q^{17} +(2.29813 - 1.92836i) q^{18} +(-2.08512 + 3.61154i) q^{19} +(0.826352 - 0.300767i) q^{20} +6.11776i q^{21} +(-2.73783 + 2.29731i) q^{22} +(-1.93969 - 0.705990i) q^{23} +(1.11334 + 1.32683i) q^{24} +(-0.733956 + 4.16247i) q^{25} +3.69459 q^{26} +(4.50000 - 2.59808i) q^{27} -3.53209 q^{28} +(0.0282185 - 0.160035i) q^{29} +(1.50000 - 0.264490i) q^{30} +(-1.53936 - 0.560282i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(-5.36097 + 3.09516i) q^{33} +(5.87211 - 2.13727i) q^{34} +(-1.55303 + 2.68993i) q^{35} +(1.50000 + 2.59808i) q^{36} +(3.85844 + 6.68302i) q^{37} +(-3.19459 - 2.68058i) q^{38} +(6.30200 + 1.11121i) q^{39} +(0.152704 + 0.866025i) q^{40} +(-1.33750 - 7.58532i) q^{41} +(-6.02481 - 1.06234i) q^{42} +(-8.29086 - 6.95686i) q^{43} +(-1.78699 - 3.09516i) q^{44} +2.63816 q^{45} +(1.03209 - 1.78763i) q^{46} +(6.02481 - 2.19285i) q^{47} +(-1.50000 + 0.866025i) q^{48} +(4.19459 - 3.51968i) q^{49} +(-3.97178 - 1.44561i) q^{50} +(10.6591 - 1.87949i) q^{51} +(-0.641559 + 3.63846i) q^{52} +0.716881 q^{53} +(1.77719 + 4.88279i) q^{54} -3.14290 q^{55} +(0.613341 - 3.47843i) q^{56} +(-4.64290 - 5.53320i) q^{57} +(0.152704 + 0.0555796i) q^{58} +(-5.35117 + 4.49016i) q^{59} +1.52314i q^{60} +(1.19207 - 0.433877i) q^{61} +(0.819078 - 1.41868i) q^{62} +(-9.95723 - 3.62414i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(2.48886 + 2.08840i) q^{65} +(-2.11721 - 5.81699i) q^{66} +(0.624485 + 3.54163i) q^{67} +(1.08512 + 6.15403i) q^{68} +(2.29813 - 2.73881i) q^{69} +(-2.37939 - 1.99654i) q^{70} +(6.76991 + 11.7258i) q^{71} +(-2.81908 + 1.02606i) q^{72} +(1.16385 - 2.01584i) q^{73} +(-7.25150 + 2.63933i) q^{74} +(-6.34002 - 3.66041i) q^{75} +(3.19459 - 2.68058i) q^{76} +(11.8623 + 4.31753i) q^{77} +(-2.18866 + 6.01330i) q^{78} +(-1.14930 + 6.51800i) q^{79} -0.879385 q^{80} +(1.56283 + 8.86327i) q^{81} +7.70233 q^{82} +(-0.773318 + 4.38571i) q^{83} +(2.09240 - 5.74881i) q^{84} +(5.16385 + 1.87949i) q^{85} +(8.29086 - 6.95686i) q^{86} +(0.243756 + 0.140732i) q^{87} +(3.35844 - 1.22237i) q^{88} +(-4.62449 + 8.00984i) q^{89} +(-0.458111 + 2.59808i) q^{90} +(-6.52481 - 11.3013i) q^{91} +(1.58125 + 1.32683i) q^{92} +(1.82383 - 2.17355i) q^{93} +(1.11334 + 6.31407i) q^{94} +(-0.636812 - 3.61154i) q^{95} +(-0.592396 - 1.62760i) q^{96} +(-8.64930 - 7.25762i) q^{97} +(2.73783 + 4.74205i) q^{98} +(-1.86184 - 10.5590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{5} - 9 q^{6} + 3 q^{7} + 3 q^{8}+O(q^{10}) \) 6 * q - 3 * q^5 - 9 * q^6 + 3 * q^7 + 3 * q^8	\( 6 q - 3 q^{5} - 9 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{10} - 3 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{17} + 9 q^{19} + 6 q^{20} + 3 q^{22} - 6 q^{23} - 9 q^{25} + 18 q^{26} + 27 q^{27} - 12 q^{28} + 15 q^{29} + 9 q^{30} - 18 q^{31} - 9 q^{33} + 6 q^{34} + 3 q^{35} + 9 q^{36} + 15 q^{37} - 15 q^{38} + 3 q^{40} - 3 q^{41} - 9 q^{42} - 18 q^{43} - 3 q^{44} - 18 q^{45} - 3 q^{46} + 9 q^{47} - 9 q^{48} + 21 q^{49} - 9 q^{50} + 27 q^{51} - 12 q^{52} - 12 q^{53} - 18 q^{55} - 3 q^{56} - 27 q^{57} + 3 q^{58} - 6 q^{59} + 18 q^{61} - 12 q^{62} - 9 q^{63} - 3 q^{64} + 21 q^{65} + 18 q^{66} - 9 q^{67} - 15 q^{68} - 3 q^{70} + 12 q^{71} + 3 q^{73} - 3 q^{74} - 18 q^{75} + 15 q^{76} + 39 q^{77} + 18 q^{78} + 33 q^{79} + 6 q^{80} - 6 q^{82} - 18 q^{83} + 9 q^{84} + 27 q^{85} + 18 q^{86} + 9 q^{87} + 12 q^{88} - 15 q^{89} - 9 q^{90} - 12 q^{91} + 12 q^{92} + 27 q^{93} + 21 q^{95} - 12 q^{97} - 3 q^{98} - 45 q^{99}+O(q^{100}) \) 6 * q - 3 * q^5 - 9 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^10 - 3 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^17 + 9 * q^19 + 6 * q^20 + 3 * q^22 - 6 * q^23 - 9 * q^25 + 18 * q^26 + 27 * q^27 - 12 * q^28 + 15 * q^29 + 9 * q^30 - 18 * q^31 - 9 * q^33 + 6 * q^34 + 3 * q^35 + 9 * q^36 + 15 * q^37 - 15 * q^38 + 3 * q^40 - 3 * q^41 - 9 * q^42 - 18 * q^43 - 3 * q^44 - 18 * q^45 - 3 * q^46 + 9 * q^47 - 9 * q^48 + 21 * q^49 - 9 * q^50 + 27 * q^51 - 12 * q^52 - 12 * q^53 - 18 * q^55 - 3 * q^56 - 27 * q^57 + 3 * q^58 - 6 * q^59 + 18 * q^61 - 12 * q^62 - 9 * q^63 - 3 * q^64 + 21 * q^65 + 18 * q^66 - 9 * q^67 - 15 * q^68 - 3 * q^70 + 12 * q^71 + 3 * q^73 - 3 * q^74 - 18 * q^75 + 15 * q^76 + 39 * q^77 + 18 * q^78 + 33 * q^79 + 6 * q^80 - 6 * q^82 - 18 * q^83 + 9 * q^84 + 27 * q^85 + 18 * q^86 + 9 * q^87 + 12 * q^88 - 15 * q^89 - 9 * q^90 - 12 * q^91 + 12 * q^92 + 27 * q^93 + 21 * q^95 - 12 * q^97 - 3 * q^98 - 45 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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