LMFDB - Embedded newform 405.2.e.i.136.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(136,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("405.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.e (of order $3$, degree $2$, not 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:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			136.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	405.136
Dual form			405.2.e.i.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 + 2.36603i) q^{2} +(-2.73205 - 4.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.633975 - 1.09808i) q^{7} +9.46410 q^{8} +O(q^{10})$	\(q+(-1.36603 + 2.36603i) q^{2} +(-2.73205 - 4.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.633975 - 1.09808i) q^{7} +9.46410 q^{8} -2.73205 q^{10} +(-1.13397 + 1.96410i) q^{11} +(2.73205 + 4.73205i) q^{13} +(1.73205 + 3.00000i) q^{14} +(-7.46410 + 12.9282i) q^{16} -0.732051 q^{17} -2.46410 q^{19} +(2.73205 - 4.73205i) q^{20} +(-3.09808 - 5.36603i) q^{22} +(1.73205 + 3.00000i) q^{23} +(-0.500000 + 0.866025i) q^{25} -14.9282 q^{26} -6.92820 q^{28} +(-3.59808 + 6.23205i) q^{29} +(1.50000 + 2.59808i) q^{31} +(-10.9282 - 18.9282i) q^{32} +(1.00000 - 1.73205i) q^{34} +1.26795 q^{35} +0.732051 q^{37} +(3.36603 - 5.83013i) q^{38} +(4.73205 + 8.19615i) q^{40} +(1.59808 + 2.76795i) q^{41} +(5.09808 - 8.83013i) q^{43} +12.3923 q^{44} -9.46410 q^{46} +(-2.63397 + 4.56218i) q^{47} +(2.69615 + 4.66987i) q^{49} +(-1.36603 - 2.36603i) q^{50} +(14.9282 - 25.8564i) q^{52} -3.26795 q^{53} -2.26795 q^{55} +(6.00000 - 10.3923i) q^{56} +(-9.83013 - 17.0263i) q^{58} +(-5.86603 - 10.1603i) q^{59} +(-2.00000 + 3.46410i) q^{61} -8.19615 q^{62} +29.8564 q^{64} +(-2.73205 + 4.73205i) q^{65} +(1.73205 + 3.00000i) q^{67} +(2.00000 + 3.46410i) q^{68} +(-1.73205 + 3.00000i) q^{70} +0.267949 q^{71} +9.66025 q^{73} +(-1.00000 + 1.73205i) q^{74} +(6.73205 + 11.6603i) q^{76} +(1.43782 + 2.49038i) q^{77} +(-4.26795 + 7.39230i) q^{79} -14.9282 q^{80} -8.73205 q^{82} +(-4.09808 + 7.09808i) q^{83} +(-0.366025 - 0.633975i) q^{85} +(13.9282 + 24.1244i) q^{86} +(-10.7321 + 18.5885i) q^{88} +5.19615 q^{89} +6.92820 q^{91} +(9.46410 - 16.3923i) q^{92} +(-7.19615 - 12.4641i) q^{94} +(-1.23205 - 2.13397i) q^{95} +(-3.83013 + 6.63397i) q^{97} -14.7321 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 4 q^{4} + 2 q^{5} + 6 q^{7} + 24 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 4 * q^4 + 2 * q^5 + 6 * q^7 + 24 * q^8	$ 4 q - 2 q^{2} - 4 q^{4} + 2 q^{5} + 6 q^{7} + 24 q^{8} - 4 q^{10} - 8 q^{11} + 4 q^{13} - 16 q^{16} + 4 q^{17} + 4 q^{19} + 4 q^{20} - 2 q^{22} - 2 q^{25} - 32 q^{26} - 4 q^{29} + 6 q^{31} - 16 q^{32} + 4 q^{34} + 12 q^{35} - 4 q^{37} + 10 q^{38} + 12 q^{40} - 4 q^{41} + 10 q^{43} + 8 q^{44} - 24 q^{46} - 14 q^{47} - 10 q^{49} - 2 q^{50} + 32 q^{52} - 20 q^{53} - 16 q^{55} + 24 q^{56} - 22 q^{58} - 20 q^{59} - 8 q^{61} - 12 q^{62} + 64 q^{64} - 4 q^{65} + 8 q^{68} + 8 q^{71} + 4 q^{73} - 4 q^{74} + 20 q^{76} + 30 q^{77} - 24 q^{79} - 32 q^{80} - 28 q^{82} - 6 q^{83} + 2 q^{85} + 28 q^{86} - 36 q^{88} + 24 q^{92} - 8 q^{94} + 2 q^{95} + 2 q^{97} - 52 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 4 * q^4 + 2 * q^5 + 6 * q^7 + 24 * q^8 - 4 * q^10 - 8 * q^11 + 4 * q^13 - 16 * q^16 + 4 * q^17 + 4 * q^19 + 4 * q^20 - 2 * q^22 - 2 * q^25 - 32 * q^26 - 4 * q^29 + 6 * q^31 - 16 * q^32 + 4 * q^34 + 12 * q^35 - 4 * q^37 + 10 * q^38 + 12 * q^40 - 4 * q^41 + 10 * q^43 + 8 * q^44 - 24 * q^46 - 14 * q^47 - 10 * q^49 - 2 * q^50 + 32 * q^52 - 20 * q^53 - 16 * q^55 + 24 * q^56 - 22 * q^58 - 20 * q^59 - 8 * q^61 - 12 * q^62 + 64 * q^64 - 4 * q^65 + 8 * q^68 + 8 * q^71 + 4 * q^73 - 4 * q^74 + 20 * q^76 + 30 * q^77 - 24 * q^79 - 32 * q^80 - 28 * q^82 - 6 * q^83 + 2 * q^85 + 28 * q^86 - 36 * q^88 + 24 * q^92 - 8 * q^94 + 2 * q^95 + 2 * q^97 - 52 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.36603	+	2.36603i	−0.965926	+	1.67303i	−0.258819	+	0.965926i	$0.583333\pi$
$2$	−1.36603	+	2.36603i	−0.965926	+	1.67303i	−0.707107	+	0.707107i	$0.750000\pi$
$3$		0			0
$3$		0			0
$4$	−2.73205	−	4.73205i	−1.36603	−	2.36603i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	0.633975	−	1.09808i	0.239620	−	0.415034i	−0.720985	−	0.692950i	$-0.756311\pi$
$7$	0.633975	−	1.09808i	0.239620	−	0.415034i	0.960605	+	0.277916i	$0.0896439\pi$
$8$	9.46410			3.34607
$9$		0			0
$10$	−2.73205			−0.863950
$11$	−1.13397	+	1.96410i	−0.341906	+	0.592199i	−0.984787	−	0.173768i	$-0.944406\pi$
$11$	−1.13397	+	1.96410i	−0.341906	+	0.592199i	0.642880	+	0.765967i	$0.277739\pi$
$12$		0			0
$13$	2.73205	+	4.73205i	0.757735	+	1.31243i	0.944003	+	0.329936i	$0.107027\pi$
$13$	2.73205	+	4.73205i	0.757735	+	1.31243i	−0.186269	+	0.982499i	$0.559640\pi$
$14$	1.73205	+	3.00000i	0.462910	+	0.801784i
$15$		0			0
$16$	−7.46410	+	12.9282i	−1.86603	+	3.23205i
$17$	−0.732051			−0.177548			−0.0887742	−	0.996052i	$-0.528295\pi$
$17$	−0.732051			−0.177548			−0.0887742	+	0.996052i	$0.528295\pi$
$18$		0			0
$19$	−2.46410			−0.565304			−0.282652	−	0.959223i	$-0.591214\pi$
$19$	−2.46410			−0.565304			−0.282652	+	0.959223i	$0.591214\pi$
$20$	2.73205	−	4.73205i	0.610905	−	1.05812i
$21$		0			0
$22$	−3.09808	−	5.36603i	−0.660512	−	1.14404i
$23$	1.73205	+	3.00000i	0.361158	+	0.625543i	0.988152	−	0.153481i	$-0.0490483\pi$
$23$	1.73205	+	3.00000i	0.361158	+	0.625543i	−0.626994	+	0.779024i	$0.715715\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−14.9282			−2.92766
$27$		0			0
$28$	−6.92820			−1.30931
$29$	−3.59808	+	6.23205i	−0.668146	+	1.15726i	0.310276	+	0.950646i	$0.399579\pi$
$29$	−3.59808	+	6.23205i	−0.668146	+	1.15726i	−0.978422	+	0.206616i	$0.933755\pi$
$30$		0			0
$31$	1.50000	+	2.59808i	0.269408	+	0.466628i	0.968709	−	0.248199i	$-0.0798387\pi$
$31$	1.50000	+	2.59808i	0.269408	+	0.466628i	−0.699301	+	0.714827i	$0.746505\pi$
$32$	−10.9282	−	18.9282i	−1.93185	−	3.34607i
$33$		0			0
$34$	1.00000	−	1.73205i	0.171499	−	0.297044i
$35$	1.26795			0.214323
$36$		0			0
$37$	0.732051			0.120348			0.0601742	−	0.998188i	$-0.480834\pi$
$37$	0.732051			0.120348			0.0601742	+	0.998188i	$0.480834\pi$
$38$	3.36603	−	5.83013i	0.546041	−	0.945771i
$39$		0			0
$40$	4.73205	+	8.19615i	0.748203	+	1.29593i
$41$	1.59808	+	2.76795i	0.249578	+	0.432281i	0.963409	−	0.268037i	$-0.0863749\pi$
$41$	1.59808	+	2.76795i	0.249578	+	0.432281i	−0.713831	+	0.700318i	$0.753042\pi$
$42$		0			0
$43$	5.09808	−	8.83013i	0.777449	−	1.34658i	−0.155958	−	0.987764i	$-0.549847\pi$
$43$	5.09808	−	8.83013i	0.777449	−	1.34658i	0.933408	−	0.358818i	$-0.116820\pi$
$44$	12.3923			1.86821
$45$		0			0
$46$	−9.46410			−1.39541
$47$	−2.63397	+	4.56218i	−0.384205	+	0.665462i	−0.991659	−	0.128893i	$-0.958858\pi$
$47$	−2.63397	+	4.56218i	−0.384205	+	0.665462i	0.607454	+	0.794355i	$0.292191\pi$
$48$		0			0
$49$	2.69615	+	4.66987i	0.385165	+	0.667125i
$50$	−1.36603	−	2.36603i	−0.193185	−	0.334607i
$51$		0			0
$52$	14.9282	−	25.8564i	2.07017	−	3.58564i
$53$	−3.26795			−0.448887			−0.224444	−	0.974487i	$-0.572056\pi$
$53$	−3.26795			−0.448887			−0.224444	+	0.974487i	$0.572056\pi$
$54$		0			0
$55$	−2.26795			−0.305810
$56$	6.00000	−	10.3923i	0.801784	−	1.38873i
$57$		0			0
$58$	−9.83013	−	17.0263i	−1.29076	−	2.23566i
$59$	−5.86603	−	10.1603i	−0.763691	−	1.32275i	−0.940936	−	0.338585i	$-0.890052\pi$
$59$	−5.86603	−	10.1603i	−0.763691	−	1.32275i	0.177244	−	0.984167i	$-0.443282\pi$
$60$		0			0
$61$	−2.00000	+	3.46410i	−0.256074	+	0.443533i	−0.965187	−	0.261562i	$-0.915762\pi$
$61$	−2.00000	+	3.46410i	−0.256074	+	0.443533i	0.709113	+	0.705095i	$0.249096\pi$
$62$	−8.19615			−1.04091
$63$		0			0
$64$	29.8564			3.73205
$65$	−2.73205	+	4.73205i	−0.338869	+	0.586939i
$66$		0			0
$67$	1.73205	+	3.00000i	0.211604	+	0.366508i	0.952217	−	0.305424i	$-0.0987981\pi$
$67$	1.73205	+	3.00000i	0.211604	+	0.366508i	−0.740613	+	0.671932i	$0.765465\pi$
$68$	2.00000	+	3.46410i	0.242536	+	0.420084i
$69$		0			0
$70$	−1.73205	+	3.00000i	−0.207020	+	0.358569i
$71$	0.267949			0.0317997			0.0158999	−	0.999874i	$-0.494939\pi$
$71$	0.267949			0.0317997			0.0158999	+	0.999874i	$0.494939\pi$
$72$		0			0
$73$	9.66025			1.13065			0.565324	−	0.824869i	$-0.308751\pi$
$73$	9.66025			1.13065			0.565324	+	0.824869i	$0.308751\pi$
$74$	−1.00000	+	1.73205i	−0.116248	+	0.201347i
$75$		0			0
$76$	6.73205	+	11.6603i	0.772219	+	1.33752i
$77$	1.43782	+	2.49038i	0.163855	+	0.283805i
$78$		0			0
$79$	−4.26795	+	7.39230i	−0.480182	+	0.831699i	−0.999742	−	0.0227349i	$-0.992763\pi$
$79$	−4.26795	+	7.39230i	−0.480182	+	0.831699i	0.519560	+	0.854434i	$0.326096\pi$
$80$	−14.9282			−1.66902
$81$		0			0
$82$	−8.73205			−0.964294
$83$	−4.09808	+	7.09808i	−0.449822	+	0.779115i	−0.998374	−	0.0570015i	$-0.981846\pi$
$83$	−4.09808	+	7.09808i	−0.449822	+	0.779115i	0.548552	+	0.836117i	$0.315179\pi$
$84$		0			0
$85$	−0.366025	−	0.633975i	−0.0397010	−	0.0687642i
$86$	13.9282	+	24.1244i	1.50192	+	2.60140i
$87$		0			0
$88$	−10.7321	+	18.5885i	−1.14404	+	1.98154i
$89$	5.19615			0.550791			0.275396	−	0.961331i	$-0.411191\pi$
$89$	5.19615			0.550791			0.275396	+	0.961331i	$0.411191\pi$
$90$		0			0
$91$	6.92820			0.726273
$92$	9.46410	−	16.3923i	0.986701	−	1.70902i
$93$		0			0
$94$	−7.19615	−	12.4641i	−0.742226	−	1.28557i
$95$	−1.23205	−	2.13397i	−0.126406	−	0.218941i
$96$		0			0
$97$	−3.83013	+	6.63397i	−0.388890	+	0.673578i	−0.992301	−	0.123853i	$-0.960475\pi$
$97$	−3.83013	+	6.63397i	−0.388890	+	0.673578i	0.603410	+	0.797431i	$0.293808\pi$
$98$	−14.7321			−1.48816
$99$		0			0
$100$	5.46410			0.546410
$101$	7.33013	−	12.6962i	0.729375	−	1.26331i	−0.227773	−	0.973714i	$-0.573144\pi$
$101$	7.33013	−	12.6962i	0.729375	−	1.26331i	0.957148	−	0.289600i	$-0.0935223\pi$
$102$		0			0
$103$	3.73205	+	6.46410i	0.367730	+	0.636927i	0.989210	−	0.146503i	$-0.0468018\pi$
$103$	3.73205	+	6.46410i	0.367730	+	0.636927i	−0.621480	+	0.783430i	$0.713468\pi$
$104$	25.8564	+	44.7846i	2.53543	+	4.39149i
$105$		0			0
$106$	4.46410	−	7.73205i	0.433592	−	0.751003i
$107$	15.4641			1.49497			0.747486	−	0.664278i	$-0.231261\pi$
$107$	15.4641			1.49497			0.747486	+	0.664278i	$0.231261\pi$
$108$		0			0
$109$	−19.9282			−1.90878			−0.954388	−	0.298570i	$-0.903490\pi$
$109$	−19.9282			−1.90878			−0.954388	+	0.298570i	$0.903490\pi$
$110$	3.09808	−	5.36603i	0.295390	−	0.511630i
$111$		0			0
$112$	9.46410	+	16.3923i	0.894274	+	1.54893i
$113$	2.56218	+	4.43782i	0.241029	+	0.417475i	0.961008	−	0.276521i	$-0.0891816\pi$
$113$	2.56218	+	4.43782i	0.241029	+	0.417475i	−0.719978	+	0.693997i	$0.755848\pi$
$114$		0			0
$115$	−1.73205	+	3.00000i	−0.161515	+	0.279751i
$116$	39.3205			3.65082
$117$		0			0
$118$	32.0526			2.95068
$119$	−0.464102	+	0.803848i	−0.0425441	+	0.0736886i
$120$		0			0
$121$	2.92820	+	5.07180i	0.266200	+	0.461072i
$122$	−5.46410	−	9.46410i	−0.494697	−	0.856840i
$123$		0			0
$124$	8.19615	−	14.1962i	0.736036	−	1.27485i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	16.5885			1.47199			0.735994	−	0.676988i	$-0.236715\pi$
$127$	16.5885			1.47199			0.735994	+	0.676988i	$0.236715\pi$
$128$	−18.9282	+	32.7846i	−1.67303	+	2.89778i
$129$		0			0
$130$	−7.46410	−	12.9282i	−0.654645	−	1.13388i
$131$	−7.79423	−	13.5000i	−0.680985	−	1.17950i	−0.974681	−	0.223602i	$-0.928219\pi$
$131$	−7.79423	−	13.5000i	−0.680985	−	1.17950i	0.293696	−	0.955899i	$-0.405115\pi$
$132$		0			0
$133$	−1.56218	+	2.70577i	−0.135458	+	0.234620i
$134$	−9.46410			−0.817574
$135$		0			0
$136$	−6.92820			−0.594089
$137$	4.73205	−	8.19615i	0.404286	−	0.700245i	−0.589952	−	0.807439i	$-0.700853\pi$
$137$	4.73205	−	8.19615i	0.404286	−	0.700245i	0.994238	+	0.107194i	$0.0341866\pi$
$138$		0			0
$139$	−10.6962	−	18.5263i	−0.907236	−	1.57138i	−0.817888	−	0.575378i	$-0.804855\pi$
$139$	−10.6962	−	18.5263i	−0.907236	−	1.57138i	−0.0893482	−	0.996000i	$-0.528478\pi$
$140$	−3.46410	−	6.00000i	−0.292770	−	0.507093i
$141$		0			0
$142$	−0.366025	+	0.633975i	−0.0307162	+	0.0532020i
$143$	−12.3923			−1.03630
$144$		0			0
$145$	−7.19615			−0.597608
$146$	−13.1962	+	22.8564i	−1.09212	+	1.89161i
$147$		0			0
$148$	−2.00000	−	3.46410i	−0.164399	−	0.284747i
$149$	−4.00000	−	6.92820i	−0.327693	−	0.567581i	0.654361	−	0.756182i	$-0.272938\pi$
$149$	−4.00000	−	6.92820i	−0.327693	−	0.567581i	−0.982054	+	0.188602i	$0.939604\pi$
$150$		0			0
$151$	7.69615	−	13.3301i	0.626304	−	1.08479i	−0.361983	−	0.932185i	$-0.617900\pi$
$151$	7.69615	−	13.3301i	0.626304	−	1.08479i	0.988287	−	0.152606i	$-0.0487665\pi$
$152$	−23.3205			−1.89154
$153$		0			0
$154$	−7.85641			−0.633087
$155$	−1.50000	+	2.59808i	−0.120483	+	0.208683i
$156$		0			0
$157$	−2.56218	−	4.43782i	−0.204484	−	0.354177i	0.745484	−	0.666523i	$-0.232218\pi$
$157$	−2.56218	−	4.43782i	−0.204484	−	0.354177i	−0.949968	+	0.312347i	$0.898885\pi$
$158$	−11.6603	−	20.1962i	−0.927640	−	1.60672i
$159$		0			0
$160$	10.9282	−	18.9282i	0.863950	−	1.49641i
$161$	4.39230			0.346162
$162$		0			0
$163$	9.26795			0.725922			0.362961	−	0.931804i	$-0.381766\pi$
$163$	9.26795			0.725922			0.362961	+	0.931804i	$0.381766\pi$
$164$	8.73205	−	15.1244i	0.681859	−	1.18101i
$165$		0			0
$166$	−11.1962	−	19.3923i	−0.868990	−	1.50513i
$167$	−0.169873	−	0.294229i	−0.0131452	−	0.0227681i	0.859378	−	0.511341i	$-0.170851\pi$
$167$	−0.169873	−	0.294229i	−0.0131452	−	0.0227681i	−0.872523	+	0.488573i	$0.837518\pi$
$168$		0			0
$169$	−8.42820	+	14.5981i	−0.648323	+	1.12293i
$170$	2.00000			0.153393
$171$		0			0
$172$	−55.7128			−4.24806
$173$	7.73205	−	13.3923i	0.587857	−	1.01820i	−0.406656	−	0.913581i	$-0.633305\pi$
$173$	7.73205	−	13.3923i	0.587857	−	1.01820i	0.994513	−	0.104617i	$-0.0333615\pi$
$174$		0			0
$175$	0.633975	+	1.09808i	0.0479240	+	0.0830068i
$176$	−16.9282	−	29.3205i	−1.27601	−	2.21012i
$177$		0			0
$178$	−7.09808	+	12.2942i	−0.532023	+	0.921491i
$179$	16.1244			1.20519			0.602595	−	0.798047i	$-0.294133\pi$
$179$	16.1244			1.20519			0.602595	+	0.798047i	$0.294133\pi$
$180$		0			0
$181$	19.5359			1.45209			0.726046	−	0.687646i	$-0.241356\pi$
$181$	19.5359			1.45209			0.726046	+	0.687646i	$0.241356\pi$
$182$	−9.46410	+	16.3923i	−0.701526	+	1.21508i
$183$		0			0
$184$	16.3923	+	28.3923i	1.20846	+	2.09311i
$185$	0.366025	+	0.633975i	0.0269107	+	0.0466107i
$186$		0			0
$187$	0.830127	−	1.43782i	0.0607049	−	0.105144i
$188$	28.7846			2.09933
$189$		0			0
$190$	6.73205			0.488394
$191$	8.06218	−	13.9641i	0.583359	−	1.01041i	−0.411719	−	0.911311i	$-0.635072\pi$
$191$	8.06218	−	13.9641i	0.583359	−	1.01041i	0.995078	−	0.0990961i	$-0.0315951\pi$
$192$		0			0
$193$	4.36603	+	7.56218i	0.314273	+	0.544337i	0.979283	−	0.202498i	$-0.0649058\pi$
$193$	4.36603	+	7.56218i	0.314273	+	0.544337i	−0.665009	+	0.746835i	$0.731572\pi$
$194$	−10.4641	−	18.1244i	−0.751279	−	1.30125i
$195$		0			0
$196$	14.7321	−	25.5167i	1.05229	−	1.82262i
$197$	−13.8564			−0.987228			−0.493614	−	0.869681i	$-0.664324\pi$
$197$	−13.8564			−0.987228			−0.493614	+	0.869681i	$0.664324\pi$
$198$		0			0
$199$	−2.00000			−0.141776			−0.0708881	−	0.997484i	$-0.522583\pi$
$199$	−2.00000			−0.141776			−0.0708881	+	0.997484i	$0.522583\pi$
$200$	−4.73205	+	8.19615i	−0.334607	+	0.579555i
$201$		0			0
$202$	20.0263	+	34.6865i	1.40904	+	2.44054i
$203$	4.56218	+	7.90192i	0.320202	+	0.554606i
$204$		0			0
$205$	−1.59808	+	2.76795i	−0.111614	+	0.193322i
$206$	−20.3923			−1.42080
$207$		0			0
$208$	−81.5692			−5.65581
$209$	2.79423	−	4.83975i	0.193281	−	0.334772i
$210$		0			0
$211$	−9.42820	−	16.3301i	−0.649064	−	1.12421i	−0.983347	−	0.181739i	$-0.941827\pi$
$211$	−9.42820	−	16.3301i	−0.649064	−	1.12421i	0.334282	−	0.942473i	$-0.391506\pi$
$212$	8.92820	+	15.4641i	0.613192	+	1.06208i
$213$		0			0
$214$	−21.1244	+	36.5885i	−1.44403	+	2.50114i
$215$	10.1962			0.695372
$216$		0			0
$217$	3.80385			0.258222
$218$	27.2224	−	47.1506i	1.84374	−	3.19344i
$219$		0			0
$220$	6.19615	+	10.7321i	0.417745	+	0.723555i
$221$	−2.00000	−	3.46410i	−0.134535	−	0.233021i
$222$		0			0
$223$	12.3923	−	21.4641i	0.829850	−	1.43734i	−0.0683053	−	0.997664i	$-0.521759\pi$
$223$	12.3923	−	21.4641i	0.829850	−	1.43734i	0.898155	−	0.439678i	$-0.144907\pi$
$224$	−27.7128			−1.85164
$225$		0			0
$226$	−14.0000			−0.931266
$227$	10.0263	−	17.3660i	0.665468	−	1.15262i	−0.313691	−	0.949525i	$-0.601566\pi$
$227$	10.0263	−	17.3660i	0.665468	−	1.15262i	0.979158	−	0.203098i	$-0.0651011\pi$
$228$		0			0
$229$	6.00000	+	10.3923i	0.396491	+	0.686743i	0.993290	−	0.115648i	$-0.0368944\pi$
$229$	6.00000	+	10.3923i	0.396491	+	0.686743i	−0.596799	+	0.802391i	$0.703561\pi$
$230$	−4.73205	−	8.19615i	−0.312022	−	0.540438i
$231$		0			0
$232$	−34.0526	+	58.9808i	−2.23566	+	3.87228i
$233$	−10.0526			−0.658565			−0.329283	−	0.944231i	$-0.606807\pi$
$233$	−10.0526			−0.658565			−0.329283	+	0.944231i	$0.606807\pi$
$234$		0			0
$235$	−5.26795			−0.343643
$236$	−32.0526	+	55.5167i	−2.08644	+	3.61383i
$237$		0			0
$238$	−1.26795	−	2.19615i	−0.0821889	−	0.142355i
$239$	−3.73205	−	6.46410i	−0.241406	−	0.418128i	0.719709	−	0.694276i	$-0.244275\pi$
$239$	−3.73205	−	6.46410i	−0.241406	−	0.418128i	−0.961115	+	0.276148i	$0.910942\pi$
$240$		0			0
$241$	−9.16025	+	15.8660i	−0.590064	+	1.02202i	0.404159	+	0.914689i	$0.367564\pi$
$241$	−9.16025	+	15.8660i	−0.590064	+	1.02202i	−0.994223	+	0.107332i	$0.965769\pi$
$242$	−16.0000			−1.02852
$243$		0			0
$244$	21.8564			1.39921
$245$	−2.69615	+	4.66987i	−0.172251	+	0.298347i
$246$		0			0
$247$	−6.73205	−	11.6603i	−0.428350	−	0.741924i
$248$	14.1962	+	24.5885i	0.901457	+	1.56137i
$249$		0			0
$250$	1.36603	−	2.36603i	0.0863950	−	0.149641i
$251$	−10.3923			−0.655956			−0.327978	−	0.944685i	$-0.606367\pi$
$251$	−10.3923			−0.655956			−0.327978	+	0.944685i	$0.606367\pi$
$252$		0			0
$253$	−7.85641			−0.493928
$254$	−22.6603	+	39.2487i	−1.42183	+	2.46268i
$255$		0			0
$256$	−21.8564	−	37.8564i	−1.36603	−	2.36603i
$257$	−5.19615	−	9.00000i	−0.324127	−	0.561405i	0.657208	−	0.753709i	$-0.271737\pi$
$257$	−5.19615	−	9.00000i	−0.324127	−	0.561405i	−0.981335	+	0.192304i	$0.938404\pi$
$258$		0			0
$259$	0.464102	−	0.803848i	0.0288379	−	0.0499487i
$260$	29.8564			1.85162
$261$		0			0
$262$	42.5885			2.63112
$263$	−6.66025	+	11.5359i	−0.410689	+	0.711334i	−0.994965	−	0.100221i	$-0.968045\pi$
$263$	−6.66025	+	11.5359i	−0.410689	+	0.711334i	0.584276	+	0.811555i	$0.301378\pi$
$264$		0			0
$265$	−1.63397	−	2.83013i	−0.100374	−	0.173853i
$266$	−4.26795	−	7.39230i	−0.261685	−	0.453251i
$267$		0			0
$268$	9.46410	−	16.3923i	0.578112	−	1.00132i
$269$	6.66025			0.406083			0.203041	−	0.979170i	$-0.434917\pi$
$269$	6.66025			0.406083			0.203041	+	0.979170i	$0.434917\pi$
$270$		0			0
$271$	10.9282			0.663841			0.331921	−	0.943307i	$-0.392303\pi$
$271$	10.9282			0.663841			0.331921	+	0.943307i	$0.392303\pi$
$272$	5.46410	−	9.46410i	0.331310	−	0.573845i
$273$		0			0
$274$	12.9282	+	22.3923i	0.781021	+	1.35277i
$275$	−1.13397	−	1.96410i	−0.0683812	−	0.118440i
$276$		0			0
$277$	−7.09808	+	12.2942i	−0.426482	+	0.738689i	−0.996558	−	0.0829037i	$-0.973581\pi$
$277$	−7.09808	+	12.2942i	−0.426482	+	0.738689i	0.570075	+	0.821592i	$0.306914\pi$
$278$	58.4449			3.50529
$279$		0			0
$280$	12.0000			0.717137
$281$	4.26795	−	7.39230i	0.254605	−	0.440988i	−0.710184	−	0.704017i	$-0.751388\pi$
$281$	4.26795	−	7.39230i	0.254605	−	0.440988i	0.964788	+	0.263029i	$0.0847214\pi$
$282$		0			0
$283$	−2.66025	−	4.60770i	−0.158136	−	0.273899i	0.776061	−	0.630658i	$-0.217215\pi$
$283$	−2.66025	−	4.60770i	−0.158136	−	0.273899i	−0.934196	+	0.356759i	$0.883882\pi$
$284$	−0.732051	−	1.26795i	−0.0434392	−	0.0752389i
$285$		0			0
$286$	16.9282	−	29.3205i	1.00099	−	1.73376i
$287$	4.05256			0.239215
$288$		0			0
$289$	−16.4641			−0.968477
$290$	9.83013	−	17.0263i	0.577245	−	0.999818i
$291$		0			0
$292$	−26.3923	−	45.7128i	−1.54449	−	2.67514i
$293$	12.6340	+	21.8827i	0.738085	+	1.27840i	0.953357	+	0.301846i	$0.0976029\pi$
$293$	12.6340	+	21.8827i	0.738085	+	1.27840i	−0.215272	+	0.976554i	$0.569064\pi$
$294$		0			0
$295$	5.86603	−	10.1603i	0.341533	−	0.591553i
$296$	6.92820			0.402694
$297$		0			0
$298$	21.8564			1.26611
$299$	−9.46410	+	16.3923i	−0.547323	+	0.947991i
$300$		0			0
$301$	−6.46410	−	11.1962i	−0.372585	−	0.645335i
$302$	21.0263	+	36.4186i	1.20993	+	2.09565i
$303$		0			0
$304$	18.3923	−	31.8564i	1.05487	−	1.82709i
$305$	−4.00000			−0.229039
$306$		0			0
$307$	−24.0526			−1.37275			−0.686376	−	0.727247i	$-0.740800\pi$
$307$	−24.0526			−1.37275			−0.686376	+	0.727247i	$0.740800\pi$
$308$	7.85641	−	13.6077i	0.447660	−	0.775370i
$309$		0			0
$310$	−4.09808	−	7.09808i	−0.232755	−	0.403144i
$311$	8.13397	+	14.0885i	0.461235	+	0.798883i	0.999023	−	0.0441973i	$-0.0140730\pi$
$311$	8.13397	+	14.0885i	0.461235	+	0.798883i	−0.537787	+	0.843080i	$0.680740\pi$
$312$		0			0
$313$	11.4641	−	19.8564i	0.647989	−	1.12235i	−0.335613	−	0.942000i	$-0.608943\pi$
$313$	11.4641	−	19.8564i	0.647989	−	1.12235i	0.983602	−	0.180351i	$-0.0577232\pi$
$314$	14.0000			0.790066
$315$		0			0
$316$	46.6410			2.62376
$317$	−2.09808	+	3.63397i	−0.117840	+	0.204104i	−0.918911	−	0.394464i	$-0.870930\pi$
$317$	−2.09808	+	3.63397i	−0.117840	+	0.204104i	0.801072	+	0.598568i	$0.204264\pi$
$318$		0			0
$319$	−8.16025	−	14.1340i	−0.456887	−	0.791351i
$320$	14.9282	+	25.8564i	0.834512	+	1.44542i
$321$		0			0
$322$	−6.00000	+	10.3923i	−0.334367	+	0.579141i
$323$	1.80385			0.100369
$324$		0			0
$325$	−5.46410			−0.303094
$326$	−12.6603	+	21.9282i	−0.701187	+	1.21449i
$327$		0			0
$328$	15.1244	+	26.1962i	0.835103	+	1.44644i
$329$	3.33975	+	5.78461i	0.184126	+	0.318916i
$330$		0			0
$331$	−3.23205	+	5.59808i	−0.177650	+	0.307698i	−0.941075	−	0.338198i	$-0.890183\pi$
$331$	−3.23205	+	5.59808i	−0.177650	+	0.307698i	0.763425	+	0.645896i	$0.223516\pi$
$332$	44.7846			2.45787
$333$		0			0
$334$	0.928203			0.0507890
$335$	−1.73205	+	3.00000i	−0.0946320	+	0.163908i
$336$		0			0
$337$	3.66025	+	6.33975i	0.199387	+	0.345348i	0.948330	−	0.317286i	$-0.102772\pi$
$337$	3.66025	+	6.33975i	0.199387	+	0.345348i	−0.748943	+	0.662634i	$0.769438\pi$
$338$	−23.0263	−	39.8827i	−1.25246	−	2.16933i
$339$		0			0
$340$	−2.00000	+	3.46410i	−0.108465	+	0.187867i
$341$	−6.80385			−0.368449
$342$		0			0
$343$	15.7128			0.848412
$344$	48.2487	−	83.5692i	2.60140	−	4.50575i
$345$		0			0
$346$	21.1244	+	36.5885i	1.13565	+	1.96701i
$347$	1.29423	+	2.24167i	0.0694778	+	0.120339i	0.898672	−	0.438622i	$-0.144533\pi$
$347$	1.29423	+	2.24167i	0.0694778	+	0.120339i	−0.829194	+	0.558961i	$0.811200\pi$
$348$		0			0
$349$	−4.42820	+	7.66987i	−0.237036	+	0.410559i	−0.959863	−	0.280471i	$-0.909509\pi$
$349$	−4.42820	+	7.66987i	−0.237036	+	0.410559i	0.722826	+	0.691030i	$0.242843\pi$
$350$	−3.46410			−0.185164
$351$		0			0
$352$	49.5692			2.64205
$353$	−9.75833	+	16.9019i	−0.519384	+	0.899599i	0.480363	+	0.877070i	$0.340505\pi$
$353$	−9.75833	+	16.9019i	−0.519384	+	0.899599i	−0.999746	+	0.0225287i	$0.992828\pi$
$354$		0			0
$355$	0.133975	+	0.232051i	0.00711063	+	0.0123160i
$356$	−14.1962	−	24.5885i	−0.752395	−	1.30319i
$357$		0			0
$358$	−22.0263	+	38.1506i	−1.16413	+	2.01632i
$359$	−18.1244			−0.956567			−0.478283	−	0.878206i	$-0.658741\pi$
$359$	−18.1244			−0.956567			−0.478283	+	0.878206i	$0.658741\pi$
$360$		0			0
$361$	−12.9282			−0.680432
$362$	−26.6865	+	46.2224i	−1.40261	+	2.42940i
$363$		0			0
$364$	−18.9282	−	32.7846i	−0.992107	−	1.71838i
$365$	4.83013	+	8.36603i	0.252820	+	0.437898i
$366$		0			0
$367$	15.5885	−	27.0000i	0.813711	−	1.40939i	−0.0965390	−	0.995329i	$-0.530777\pi$
$367$	15.5885	−	27.0000i	0.813711	−	1.40939i	0.910250	−	0.414059i	$-0.135889\pi$
$368$	−51.7128			−2.69572
$369$		0			0
$370$	−2.00000			−0.103975
$371$	−2.07180	+	3.58846i	−0.107562	+	0.186303i
$372$		0			0
$373$	9.02628	+	15.6340i	0.467363	+	0.809497i	0.999305	−	0.0372845i	$-0.0118708\pi$
$373$	9.02628	+	15.6340i	0.467363	+	0.809497i	−0.531942	+	0.846781i	$0.678537\pi$
$374$	2.26795	+	3.92820i	0.117273	+	0.203123i
$375$		0			0
$376$	−24.9282	+	43.1769i	−1.28557	+	2.22668i
$377$	−39.3205			−2.02511
$378$		0			0
$379$	−18.3923			−0.944749			−0.472375	−	0.881398i	$-0.656603\pi$
$379$	−18.3923			−0.944749			−0.472375	+	0.881398i	$0.656603\pi$
$380$	−6.73205	+	11.6603i	−0.345347	+	0.598158i
$381$		0			0
$382$	22.0263	+	38.1506i	1.12696	+	1.95196i
$383$	4.73205	+	8.19615i	0.241797	+	0.418804i	0.961226	−	0.275762i	$-0.0889300\pi$
$383$	4.73205	+	8.19615i	0.241797	+	0.418804i	−0.719430	+	0.694565i	$0.755597\pi$
$384$		0			0
$385$	−1.43782	+	2.49038i	−0.0732782	+	0.126922i
$386$	−23.8564			−1.21426
$387$		0			0
$388$	41.8564			2.12494
$389$	10.2679	−	17.7846i	0.520606	−	0.901716i	−0.479107	−	0.877756i	$-0.659040\pi$
$389$	10.2679	−	17.7846i	0.520606	−	0.901716i	0.999713	−	0.0239591i	$-0.00762716\pi$
$390$		0			0
$391$	−1.26795	−	2.19615i	−0.0641229	−	0.111064i
$392$	25.5167	+	44.1962i	1.28879	+	2.23224i
$393$		0			0
$394$	18.9282	−	32.7846i	0.953589	−	1.65166i
$395$	−8.53590			−0.429488
$396$		0			0
$397$	−6.39230			−0.320821			−0.160410	−	0.987050i	$-0.551282\pi$
$397$	−6.39230			−0.320821			−0.160410	+	0.987050i	$0.551282\pi$
$398$	2.73205	−	4.73205i	0.136945	−	0.237196i
$399$		0			0
$400$	−7.46410	−	12.9282i	−0.373205	−	0.646410i
$401$	5.53590	+	9.58846i	0.276450	+	0.478825i	0.970500	−	0.241102i	$-0.0775088\pi$
$401$	5.53590	+	9.58846i	0.276450	+	0.478825i	−0.694050	+	0.719927i	$0.744175\pi$
$402$		0			0
$403$	−8.19615	+	14.1962i	−0.408279	+	0.707161i
$404$	−80.1051			−3.98538
$405$		0			0
$406$	−24.9282			−1.23717
$407$	−0.830127	+	1.43782i	−0.0411479	+	0.0712702i
$408$		0			0
$409$	−4.92820	−	8.53590i	−0.243684	−	0.422073i	0.718077	−	0.695964i	$-0.245023\pi$
$409$	−4.92820	−	8.53590i	−0.243684	−	0.422073i	−0.961761	+	0.273891i	$0.911689\pi$
$410$	−4.36603	−	7.56218i	−0.215623	−	0.373469i
$411$		0			0
$412$	20.3923	−	35.3205i	1.00466	−	1.74012i
$413$	−14.8756			−0.731983
$414$		0			0
$415$	−8.19615			−0.402333
$416$	59.7128	−	103.426i	2.92766	−	5.07086i
$417$		0			0
$418$	7.63397	+	13.2224i	0.373390	+	0.646730i
$419$	−0.196152	−	0.339746i	−0.00958267	−	0.0165977i	0.861194	−	0.508276i	$-0.169717\pi$
$419$	−0.196152	−	0.339746i	−0.00958267	−	0.0165977i	−0.870777	+	0.491678i	$0.836384\pi$
$420$		0			0
$421$	3.89230	−	6.74167i	0.189699	−	0.328569i	−0.755451	−	0.655206i	$-0.772582\pi$
$421$	3.89230	−	6.74167i	0.189699	−	0.328569i	0.945150	+	0.326637i	$0.105915\pi$
$422$	51.5167			2.50779
$423$		0			0
$424$	−30.9282			−1.50201
$425$	0.366025	−	0.633975i	0.0177548	−	0.0307523i
$426$		0			0
$427$	2.53590	+	4.39230i	0.122721	+	0.212559i
$428$	−42.2487	−	73.1769i	−2.04217	−	3.53714i
$429$		0			0
$430$	−13.9282	+	24.1244i	−0.671678	+	1.16338i
$431$	38.6603			1.86220			0.931099	−	0.364765i	$-0.118851\pi$
$431$	38.6603			1.86220			0.931099	+	0.364765i	$0.118851\pi$
$432$		0			0
$433$	−28.5359			−1.37135			−0.685674	−	0.727909i	$-0.740492\pi$
$433$	−28.5359			−1.37135			−0.685674	+	0.727909i	$0.740492\pi$
$434$	−5.19615	+	9.00000i	−0.249423	+	0.432014i
$435$		0			0
$436$	54.4449	+	94.3013i	2.60744	+	4.51621i
$437$	−4.26795	−	7.39230i	−0.204164	−	0.353622i
$438$		0			0
$439$	7.69615	−	13.3301i	0.367317	−	0.636212i	−0.621828	−	0.783154i	$-0.713610\pi$
$439$	7.69615	−	13.3301i	0.367317	−	0.636212i	0.989145	+	0.146942i	$0.0469430\pi$
$440$	−21.4641			−1.02326
$441$		0			0
$442$	10.9282			0.519802
$443$	−8.83013	+	15.2942i	−0.419532	+	0.726651i	−0.995892	−	0.0905449i	$-0.971139\pi$
$443$	−8.83013	+	15.2942i	−0.419532	+	0.726651i	0.576360	+	0.817196i	$0.304472\pi$
$444$		0			0
$445$	2.59808	+	4.50000i	0.123161	+	0.213320i
$446$	33.8564	+	58.6410i	1.60315	+	2.77673i
$447$		0			0
$448$	18.9282	−	32.7846i	0.894274	−	1.54893i
$449$	16.1244			0.760955			0.380478	−	0.924790i	$-0.375760\pi$
$449$	16.1244			0.760955			0.380478	+	0.924790i	$0.375760\pi$
$450$		0			0
$451$	−7.24871			−0.341328
$452$	14.0000	−	24.2487i	0.658505	−	1.14056i
$453$		0			0
$454$	27.3923	+	47.4449i	1.28558	+	2.22670i
$455$	3.46410	+	6.00000i	0.162400	+	0.281284i
$456$		0			0
$457$	0.366025	−	0.633975i	0.0171219	−	0.0296561i	−0.857337	−	0.514755i	$-0.827883\pi$
$457$	0.366025	−	0.633975i	0.0171219	−	0.0296561i	0.874459	+	0.485099i	$0.161216\pi$
$458$	−32.7846			−1.53192
$459$		0			0
$460$	18.9282			0.882532
$461$	0.526279	−	0.911543i	0.0245113	−	0.0424548i	−0.853510	−	0.521077i	$-0.825530\pi$
$461$	0.526279	−	0.911543i	0.0245113	−	0.0424548i	0.878021	+	0.478622i	$0.158864\pi$
$462$		0			0
$463$	−5.19615	−	9.00000i	−0.241486	−	0.418265i	0.719652	−	0.694335i	$-0.244301\pi$
$463$	−5.19615	−	9.00000i	−0.241486	−	0.418265i	−0.961138	+	0.276069i	$0.910968\pi$
$464$	−53.7128	−	93.0333i	−2.49355	−	4.31896i
$465$		0			0
$466$	13.7321	−	23.7846i	0.636125	−	1.10180i
$467$	35.3731			1.63687			0.818435	−	0.574599i	$-0.194842\pi$
$467$	35.3731			1.63687			0.818435	+	0.574599i	$0.194842\pi$
$468$		0			0
$469$	4.39230			0.202818
$470$	7.19615	−	12.4641i	0.331934	−	0.574926i
$471$		0			0
$472$	−55.5167	−	96.1577i	−2.55536	−	4.42602i
$473$	11.5622	+	20.0263i	0.531630	+	0.920809i
$474$		0			0
$475$	1.23205	−	2.13397i	0.0565304	−	0.0979135i
$476$	5.07180			0.232465
$477$		0			0
$478$	20.3923			0.932722
$479$	−18.0622	+	31.2846i	−0.825282	+	1.42943i	0.0764216	+	0.997076i	$0.475650\pi$
$479$	−18.0622	+	31.2846i	−0.825282	+	1.42943i	−0.901704	+	0.432355i	$0.857683\pi$
$480$		0			0
$481$	2.00000	+	3.46410i	0.0911922	+	0.157949i
$482$	−25.0263	−	43.3468i	−1.13992	−	1.97439i
$483$		0			0
$484$	16.0000	−	27.7128i	0.727273	−	1.25967i
$485$	−7.66025			−0.347834
$486$		0			0
$487$	3.60770			0.163480			0.0817401	−	0.996654i	$-0.473952\pi$
$487$	3.60770			0.163480			0.0817401	+	0.996654i	$0.473952\pi$
$488$	−18.9282	+	32.7846i	−0.856840	+	1.48409i
$489$		0			0
$490$	−7.36603	−	12.7583i	−0.332763	−	0.576363i
$491$	−19.0622	−	33.0167i	−0.860264	−	1.49002i	−0.871674	−	0.490086i	$-0.836965\pi$
$491$	−19.0622	−	33.0167i	−0.860264	−	1.49002i	0.0114100	−	0.999935i	$-0.496368\pi$
$492$		0			0
$493$	2.63397	−	4.56218i	0.118628	−	0.205470i
$494$	36.7846			1.65502
$495$		0			0
$496$	−44.7846			−2.01089
$497$	0.169873	−	0.294229i	0.00761984	−	0.0131980i
$498$		0			0
$499$	5.16025	+	8.93782i	0.231005	+	0.400112i	0.958104	−	0.286420i	$-0.0924654\pi$
$499$	5.16025	+	8.93782i	0.231005	+	0.400112i	−0.727099	+	0.686532i	$0.759132\pi$
$500$	2.73205	+	4.73205i	0.122181	+	0.211624i
$501$		0			0
$502$	14.1962	−	24.5885i	0.633605	−	1.09744i
$503$	−27.3205			−1.21816			−0.609081	−	0.793108i	$-0.708461\pi$
$503$	−27.3205			−1.21816			−0.609081	+	0.793108i	$0.708461\pi$
$504$		0			0
$505$	14.6603			0.652373
$506$	10.7321	−	18.5885i	0.477098	−	0.826358i
$507$		0			0
$508$	−45.3205	−	78.4974i	−2.01077	−	3.48276i
$509$	17.3923	+	30.1244i	0.770900	+	1.33524i	0.937070	+	0.349141i	$0.113527\pi$
$509$	17.3923	+	30.1244i	0.770900	+	1.33524i	−0.166170	+	0.986097i	$0.553140\pi$
$510$		0			0
$511$	6.12436	−	10.6077i	0.270926	−	0.469257i
$512$	43.7128			1.93185
$513$		0			0
$514$	28.3923			1.25233
$515$	−3.73205	+	6.46410i	−0.164454	+	0.284842i
$516$		0			0
$517$	−5.97372	−	10.3468i	−0.262724	−	0.455051i
$518$	1.26795	+	2.19615i	0.0557105	+	0.0964934i
$519$		0			0
$520$	−25.8564	+	44.7846i	−1.13388	+	1.96394i
$521$	−12.5359			−0.549208			−0.274604	−	0.961557i	$-0.588547\pi$
$521$	−12.5359			−0.549208			−0.274604	+	0.961557i	$0.588547\pi$
$522$		0			0
$523$	−26.2487			−1.14778			−0.573888	−	0.818934i	$-0.694566\pi$
$523$	−26.2487			−1.14778			−0.573888	+	0.818934i	$0.694566\pi$
$524$	−42.5885	+	73.7654i	−1.86049	+	3.22246i
$525$		0			0
$526$	−18.1962	−	31.5167i	−0.793390	−	1.37419i
$527$	−1.09808	−	1.90192i	−0.0478330	−	0.0828491i
$528$		0			0
$529$	5.50000	−	9.52628i	0.239130	−	0.414186i
$530$	8.92820			0.387816
$531$		0			0
$532$	17.0718			0.740156
$533$	−8.73205	+	15.1244i	−0.378227	+	0.655109i
$534$		0			0
$535$	7.73205	+	13.3923i	0.334286	+	0.579000i
$536$	16.3923	+	28.3923i	0.708040	+	1.22636i
$537$		0			0
$538$	−9.09808	+	15.7583i	−0.392246	+	0.679390i
$539$	−12.2295			−0.526761
$540$		0			0
$541$	−17.5359			−0.753927			−0.376964	−	0.926228i	$-0.623032\pi$
$541$	−17.5359			−0.753927			−0.376964	+	0.926228i	$0.623032\pi$
$542$	−14.9282	+	25.8564i	−0.641221	+	1.11063i
$543$		0			0
$544$	8.00000	+	13.8564i	0.342997	+	0.594089i
$545$	−9.96410	−	17.2583i	−0.426815	−	0.739266i
$546$		0			0
$547$	3.07180	−	5.32051i	0.131341	−	0.227488i	−0.792853	−	0.609413i	$-0.791405\pi$
$547$	3.07180	−	5.32051i	0.131341	−	0.227488i	0.924194	+	0.381924i	$0.124739\pi$
$548$	−51.7128			−2.20906
$549$		0			0
$550$	6.19615			0.264205
$551$	8.86603	−	15.3564i	0.377705	−	0.654205i
$552$		0			0
$553$	5.41154	+	9.37307i	0.230122	+	0.398583i
$554$	−19.3923	−	33.5885i	−0.823900	−	1.42704i
$555$		0			0
$556$	−58.4449	+	101.229i	−2.47861	+	4.29309i
$557$	9.46410			0.401007			0.200503	−	0.979693i	$-0.435742\pi$
$557$	9.46410			0.401007			0.200503	+	0.979693i	$0.435742\pi$
$558$		0			0
$559$	55.7128			2.35640
$560$	−9.46410	+	16.3923i	−0.399931	+	0.692701i
$561$		0			0
$562$	11.6603	+	20.1962i	0.491858	+	0.851923i
$563$	−6.63397	−	11.4904i	−0.279589	−	0.484262i	0.691694	−	0.722191i	$-0.256865\pi$
$563$	−6.63397	−	11.4904i	−0.279589	−	0.484262i	−0.971283	+	0.237929i	$0.923531\pi$
$564$		0			0
$565$	−2.56218	+	4.43782i	−0.107792	+	0.186701i
$566$	14.5359			0.610989
$567$		0			0
$568$	2.53590			0.106404
$569$	16.4545	−	28.5000i	0.689808	−	1.19478i	−0.282092	−	0.959387i	$-0.591028\pi$
$569$	16.4545	−	28.5000i	0.689808	−	1.19478i	0.971900	−	0.235395i	$-0.0756383\pi$
$570$		0			0
$571$	−0.892305	−	1.54552i	−0.0373418	−	0.0646779i	0.846750	−	0.531990i	$-0.178556\pi$
$571$	−0.892305	−	1.54552i	−0.0373418	−	0.0646779i	−0.884092	+	0.467312i	$0.845222\pi$
$572$	33.8564	+	58.6410i	1.41561	+	2.45190i
$573$		0			0
$574$	−5.53590	+	9.58846i	−0.231064	+	0.400214i
$575$	−3.46410			−0.144463
$576$		0			0
$577$	18.7321			0.779825			0.389913	−	0.920852i	$-0.372505\pi$
$577$	18.7321			0.779825			0.389913	+	0.920852i	$0.372505\pi$
$578$	22.4904	−	38.9545i	0.935477	−	1.62029i
$579$		0			0
$580$	19.6603	+	34.0526i	0.816348	+	1.41396i
$581$	5.19615	+	9.00000i	0.215573	+	0.373383i
$582$		0			0
$583$	3.70577	−	6.41858i	0.153477	−	0.265831i
$584$	91.4256			3.78322
$585$		0			0
$586$	−69.0333			−2.85174
$587$	2.83013	−	4.90192i	0.116812	−	0.202324i	−0.801691	−	0.597739i	$-0.796066\pi$
$587$	2.83013	−	4.90192i	0.116812	−	0.202324i	0.918503	+	0.395415i	$0.129399\pi$
$588$		0			0
$589$	−3.69615	−	6.40192i	−0.152297	−	0.263787i
$590$	16.0263	+	27.7583i	0.659791	+	1.14279i
$591$		0			0
$592$	−5.46410	+	9.46410i	−0.224573	+	0.388972i
$593$	27.8564			1.14393			0.571963	−	0.820280i	$-0.306182\pi$
$593$	27.8564			1.14393			0.571963	+	0.820280i	$0.306182\pi$
$594$		0			0
$595$	−0.928203			−0.0380526
$596$	−21.8564	+	37.8564i	−0.895273	+	1.55066i
$597$		0			0
$598$	−25.8564	−	44.7846i	−1.05735	−	1.83138i
$599$	8.40192	+	14.5526i	0.343293	+	0.594601i	0.985042	−	0.172313i	$-0.0551242\pi$
$599$	8.40192	+	14.5526i	0.343293	+	0.594601i	−0.641749	+	0.766915i	$0.721791\pi$
$600$		0			0
$601$	−8.62436	+	14.9378i	−0.351795	+	0.609326i	−0.986564	−	0.163375i	$-0.947762\pi$
$601$	−8.62436	+	14.9378i	−0.351795	+	0.609326i	0.634769	+	0.772702i	$0.281095\pi$
$602$	35.3205			1.43956
$603$		0			0
$604$	−84.1051			−3.42219
$605$	−2.92820	+	5.07180i	−0.119048	+	0.206198i
$606$		0			0
$607$	2.90192	+	5.02628i	0.117785	+	0.204010i	0.918890	−	0.394514i	$-0.129087\pi$
$607$	2.90192	+	5.02628i	0.117785	+	0.204010i	−0.801104	+	0.598525i	$0.795754\pi$
$608$	26.9282	+	46.6410i	1.09208	+	1.89154i
$609$		0			0
$610$	5.46410	−	9.46410i	0.221235	−	0.383190i
$611$	−28.7846			−1.16450
$612$		0			0
$613$	−5.46410			−0.220693			−0.110346	−	0.993893i	$-0.535196\pi$
$613$	−5.46410			−0.220693			−0.110346	+	0.993893i	$0.535196\pi$
$614$	32.8564	−	56.9090i	1.32598	−	2.29666i
$615$		0			0
$616$	13.6077	+	23.5692i	0.548270	+	0.949631i
$617$	3.46410	+	6.00000i	0.139459	+	0.241551i	0.927292	−	0.374338i	$-0.122130\pi$
$617$	3.46410	+	6.00000i	0.139459	+	0.241551i	−0.787833	+	0.615889i	$0.788797\pi$
$618$		0			0
$619$	−7.92820	+	13.7321i	−0.318661	+	0.551938i	−0.980209	−	0.197965i	$-0.936567\pi$
$619$	−7.92820	+	13.7321i	−0.318661	+	0.551938i	0.661548	+	0.749903i	$0.269900\pi$
$620$	16.3923			0.658331
$621$		0			0
$622$	−44.4449			−1.78208
$623$	3.29423	−	5.70577i	0.131980	−	0.228597i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	31.3205	+	54.2487i	1.25182	+	2.16821i
$627$		0			0
$628$	−14.0000	+	24.2487i	−0.558661	+	0.967629i
$629$	−0.535898			−0.0213677
$630$		0			0
$631$	22.7128			0.904183			0.452091	−	0.891972i	$-0.350678\pi$
$631$	22.7128			0.904183			0.452091	+	0.891972i	$0.350678\pi$
$632$	−40.3923	+	69.9615i	−1.60672	+	2.78292i
$633$		0			0
$634$	−5.73205	−	9.92820i	−0.227649	−	0.394299i
$635$	8.29423	+	14.3660i	0.329146	+	0.570098i
$636$		0			0
$637$	−14.7321	+	25.5167i	−0.583705	+	1.01101i
$638$	44.5885			1.76527
$639$		0			0
$640$	−37.8564			−1.49641
$641$	13.3301	−	23.0885i	0.526508	−	0.911939i	−0.473015	−	0.881055i	$-0.656834\pi$
$641$	13.3301	−	23.0885i	0.526508	−	0.911939i	0.999523	−	0.0308846i	$-0.00983245\pi$
$642$		0			0
$643$	−12.1699	−	21.0788i	−0.479933	−	0.831268i	0.519802	−	0.854287i	$-0.326006\pi$
$643$	−12.1699	−	21.0788i	−0.479933	−	0.831268i	−0.999735	+	0.0230185i	$0.992672\pi$
$644$	−12.0000	−	20.7846i	−0.472866	−	0.819028i
$645$		0			0
$646$	−2.46410	+	4.26795i	−0.0969488	+	0.167920i
$647$	−4.53590			−0.178325			−0.0891623	−	0.996017i	$-0.528419\pi$
$647$	−4.53590			−0.178325			−0.0891623	+	0.996017i	$0.528419\pi$
$648$		0			0
$649$	26.6077			1.04444
$650$	7.46410	−	12.9282i	0.292766	−	0.507086i
$651$		0			0
$652$	−25.3205	−	43.8564i	−0.991628	−	1.71755i
$653$	−5.26795	−	9.12436i	−0.206151	−	0.357064i	0.744348	−	0.667792i	$-0.232760\pi$
$653$	−5.26795	−	9.12436i	−0.206151	−	0.357064i	−0.950499	+	0.310728i	$0.899427\pi$
$654$		0			0
$655$	7.79423	−	13.5000i	0.304546	−	0.527489i
$656$	−47.7128			−1.86287
$657$		0			0
$658$	−18.2487			−0.711409
$659$	2.73205	−	4.73205i	0.106426	−	0.184335i	−0.807894	−	0.589328i	$-0.799393\pi$
$659$	2.73205	−	4.73205i	0.106426	−	0.184335i	0.914320	+	0.404993i	$0.132726\pi$
$660$		0			0
$661$	8.16025	+	14.1340i	0.317397	+	0.549748i	0.979944	−	0.199272i	$-0.0638579\pi$
$661$	8.16025	+	14.1340i	0.317397	+	0.549748i	−0.662547	+	0.749020i	$0.730525\pi$
$662$	−8.83013	−	15.2942i	−0.343193	−	0.594427i
$663$		0			0
$664$	−38.7846	+	67.1769i	−1.50513	+	2.60697i
$665$	−3.12436			−0.121157
$666$		0			0
$667$	−24.9282			−0.965224
$668$	−0.928203	+	1.60770i	−0.0359133	+	0.0622036i
$669$		0			0
$670$	−4.73205	−	8.19615i	−0.182815	−	0.316645i
$671$	−4.53590	−	7.85641i	−0.175106	−	0.303293i
$672$		0			0
$673$	−5.19615	+	9.00000i	−0.200297	+	0.346925i	−0.948624	−	0.316405i	$-0.897524\pi$
$673$	−5.19615	+	9.00000i	−0.200297	+	0.346925i	0.748327	+	0.663330i	$0.230857\pi$
$674$	−20.0000			−0.770371
$675$		0			0
$676$	92.1051			3.54250
$677$	−9.00000	+	15.5885i	−0.345898	+	0.599113i	−0.985517	−	0.169580i	$-0.945759\pi$
$677$	−9.00000	+	15.5885i	−0.345898	+	0.599113i	0.639618	+	0.768693i	$0.279092\pi$
$678$		0			0
$679$	4.85641	+	8.41154i	0.186372	+	0.322805i
$680$	−3.46410	−	6.00000i	−0.132842	−	0.230089i
$681$		0			0
$682$	9.29423	−	16.0981i	0.355894	−	0.616427i
$683$	40.3923			1.54557			0.772784	−	0.634669i	$-0.218863\pi$
$683$	40.3923			1.54557			0.772784	+	0.634669i	$0.218863\pi$
$684$		0			0
$685$	9.46410			0.361605
$686$	−21.4641	+	37.1769i	−0.819503	+	1.41942i
$687$		0			0
$688$	76.1051	+	131.818i	2.90148	+	5.02551i
$689$	−8.92820	−	15.4641i	−0.340137	−	0.589135i
$690$		0			0
$691$	−18.8564	+	32.6603i	−0.717332	+	1.24245i	0.244722	+	0.969593i	$0.421303\pi$
$691$	−18.8564	+	32.6603i	−0.717332	+	1.24245i	−0.962053	+	0.272861i	$0.912030\pi$
$692$	−84.4974			−3.21211
$693$		0			0
$694$	−7.07180			−0.268442
$695$	10.6962	−	18.5263i	0.405728	−	0.702742i
$696$		0			0
$697$	−1.16987	−	2.02628i	−0.0443121	−	0.0767508i
$698$	−12.0981	−	20.9545i	−0.457919	−	0.793139i
$699$		0			0
$700$	3.46410	−	6.00000i	0.130931	−	0.226779i
$701$	31.1962			1.17826			0.589131	−	0.808037i	$-0.299470\pi$
$701$	31.1962			1.17826			0.589131	+	0.808037i	$0.299470\pi$
$702$		0			0
$703$	−1.80385			−0.0680334
$704$	−33.8564	+	58.6410i	−1.27601	+	2.21012i
$705$		0			0
$706$	−26.6603	−	46.1769i	−1.00337	−	1.73789i
$707$	−9.29423	−	16.0981i	−0.349545	−	0.605430i
$708$		0			0
$709$	14.7321	−	25.5167i	0.553274	−	0.958298i	−0.444762	−	0.895649i	$-0.646712\pi$
$709$	14.7321	−	25.5167i	0.553274	−	0.958298i	0.998036	−	0.0626494i	$-0.0199550\pi$
$710$	−0.732051			−0.0274734
$711$		0			0
$712$	49.1769			1.84298
$713$	−5.19615	+	9.00000i	−0.194597	+	0.337053i
$714$		0			0
$715$	−6.19615	−	10.7321i	−0.231723	−	0.401356i
$716$	−44.0526	−	76.3013i	−1.64632	−	2.85151i
$717$		0			0
$718$	24.7583	−	42.8827i	0.923973	−	1.60037i
$719$	−39.5885			−1.47640			−0.738200	−	0.674582i	$-0.764324\pi$
$719$	−39.5885			−1.47640			−0.738200	+	0.674582i	$0.764324\pi$
$720$		0			0
$721$	9.46410			0.352462
$722$	17.6603	−	30.5885i	0.657247	−	1.13838i
$723$		0			0
$724$	−53.3731	−	92.4449i	−1.98359	−	3.43569i
$725$	−3.59808	−	6.23205i	−0.133629	−	0.231453i
$726$		0			0
$727$	−6.19615	+	10.7321i	−0.229803	+	0.398030i	−0.957749	−	0.287604i	$-0.907141\pi$
$727$	−6.19615	+	10.7321i	−0.229803	+	0.398030i	0.727947	+	0.685633i	$0.240475\pi$
$728$	65.5692			2.43016
$729$		0			0
$730$	−26.3923			−0.976823
$731$	−3.73205	+	6.46410i	−0.138035	+	0.239083i
$732$		0			0
$733$	3.39230	+	5.87564i	0.125298	+	0.217022i	0.921849	−	0.387549i	$-0.126678\pi$
$733$	3.39230	+	5.87564i	0.125298	+	0.217022i	−0.796552	+	0.604571i	$0.793345\pi$
$734$	42.5885	+	73.7654i	1.57197	+	2.72273i
$735$		0			0
$736$	37.8564	−	65.5692i	1.39541	−	2.41691i
$737$	−7.85641			−0.289394
$738$		0			0
$739$	15.5359			0.571497			0.285749	−	0.958305i	$-0.407758\pi$
$739$	15.5359			0.571497			0.285749	+	0.958305i	$0.407758\pi$
$740$	2.00000	−	3.46410i	0.0735215	−	0.127343i
$741$		0			0
$742$	−5.66025	−	9.80385i	−0.207794	−	0.359911i
$743$	−22.9545	−	39.7583i	−0.842118	−	1.45859i	−0.888100	−	0.459649i	$-0.847975\pi$
$743$	−22.9545	−	39.7583i	−0.842118	−	1.45859i	0.0459822	−	0.998942i	$-0.485358\pi$
$744$		0			0
$745$	4.00000	−	6.92820i	0.146549	−	0.253830i
$746$	−49.3205			−1.80575
$747$		0			0
$748$	−9.07180			−0.331698
$749$	9.80385	−	16.9808i	0.358225	−	0.620464i
$750$		0			0
$751$	−3.60770	−	6.24871i	−0.131647	−	0.228019i	0.792665	−	0.609658i	$-0.208693\pi$
$751$	−3.60770	−	6.24871i	−0.131647	−	0.228019i	−0.924311	+	0.381639i	$0.875360\pi$
$752$	−39.3205	−	68.1051i	−1.43387	−	2.48354i
$753$		0			0
$754$	53.7128	−	93.0333i	1.95611	−	3.38807i
$755$	15.3923			0.560183
$756$		0			0
$757$	53.1769			1.93275			0.966374	−	0.257141i	$-0.0827805\pi$
$757$	53.1769			1.93275			0.966374	+	0.257141i	$0.0827805\pi$
$758$	25.1244	−	43.5167i	0.912558	−	1.58060i
$759$		0			0
$760$	−11.6603	−	20.1962i	−0.422962	−	0.732591i
$761$	−17.7224	−	30.6962i	−0.642438	−	1.11273i	−0.984887	−	0.173198i	$-0.944590\pi$
$761$	−17.7224	−	30.6962i	−0.642438	−	1.11273i	0.342449	−	0.939536i	$-0.388744\pi$
$762$		0			0
$763$	−12.6340	+	21.8827i	−0.457381	+	0.792206i
$764$	−88.1051			−3.18753
$765$		0			0
$766$	−25.8564			−0.934230
$767$	32.0526	−	55.5167i	1.15735	−	2.00459i
$768$		0			0
$769$	8.23205	+	14.2583i	0.296855	+	0.514169i	0.975415	−	0.220377i	$-0.0707287\pi$
$769$	8.23205	+	14.2583i	0.296855	+	0.514169i	−0.678559	+	0.734545i	$0.737395\pi$
$770$	−3.92820	−	6.80385i	−0.141563	−	0.245194i
$771$		0			0
$772$	23.8564	−	41.3205i	0.858611	−	1.48716i
$773$	43.5167			1.56519			0.782593	−	0.622534i	$-0.213897\pi$
$773$	43.5167			1.56519			0.782593	+	0.622534i	$0.213897\pi$
$774$		0			0
$775$	−3.00000			−0.107763
$776$	−36.2487	+	62.7846i	−1.30125	+	2.25384i
$777$		0			0
$778$	28.0526	+	48.5885i	1.00573	+	1.74198i
$779$	−3.93782	−	6.82051i	−0.141087	−	0.244370i
$780$		0			0
$781$	−0.303848	+	0.526279i	−0.0108725	+	0.0188318i
$782$	6.92820			0.247752
$783$		0			0
$784$	−80.4974			−2.87491
$785$	2.56218	−	4.43782i	0.0914480	−	0.158393i
$786$		0			0
$787$	4.97372	+	8.61474i	0.177294	+	0.307082i	0.940953	−	0.338538i	$-0.109932\pi$
$787$	4.97372	+	8.61474i	0.177294	+	0.307082i	−0.763659	+	0.645620i	$0.776599\pi$
$788$	37.8564	+	65.5692i	1.34858	+	2.33581i
$789$		0			0
$790$	11.6603	−	20.1962i	0.414853	−	0.718547i
$791$	6.49742			0.231022
$792$		0			0
$793$	−21.8564			−0.776144
$794$	8.73205	−	15.1244i	0.309889	−	0.536743i
$795$		0			0
$796$	5.46410	+	9.46410i	0.193670	+	0.335446i
$797$	−18.1962	−	31.5167i	−0.644541	−	1.11638i	−0.984407	−	0.175904i	$-0.943715\pi$
$797$	−18.1962	−	31.5167i	−0.644541	−	1.11638i	0.339867	−	0.940474i	$-0.389618\pi$
$798$		0			0
$799$	1.92820	−	3.33975i	0.0682149	−	0.118152i
$800$	21.8564			0.772741
$801$		0			0
$802$	−30.2487			−1.06812
$803$	−10.9545	+	18.9737i	−0.386575	+	0.669568i
$804$		0			0
$805$	2.19615	+	3.80385i	0.0774042	+	0.134068i
$806$	−22.3923	−	38.7846i	−0.788735	−	1.36613i
$807$		0			0
$808$	69.3731	−	120.158i	2.44054	−	4.22713i
$809$	13.4449			0.472696			0.236348	−	0.971668i	$-0.424049\pi$
$809$	13.4449			0.472696			0.236348	+	0.971668i	$0.424049\pi$
$810$		0			0
$811$	−11.5359			−0.405080			−0.202540	−	0.979274i	$-0.564920\pi$
$811$	−11.5359			−0.405080			−0.202540	+	0.979274i	$0.564920\pi$
$812$	24.9282	−	43.1769i	0.874808	−	1.51521i
$813$		0			0
$814$	−2.26795	−	3.92820i	−0.0794916	−	0.137683i
$815$	4.63397	+	8.02628i	0.162321	+	0.281148i
$816$		0			0
$817$	−12.5622	+	21.7583i	−0.439495	+	0.761228i
$818$	26.9282			0.941523
$819$		0			0
$820$	17.4641			0.609873
$821$	−17.1340	+	29.6769i	−0.597980	+	1.03573i	0.395139	+	0.918621i	$0.370696\pi$
$821$	−17.1340	+	29.6769i	−0.597980	+	1.03573i	−0.993119	+	0.117110i	$0.962637\pi$
$822$		0			0
$823$	11.9282	+	20.6603i	0.415791	+	0.720171i	0.995511	−	0.0946445i	$-0.0301714\pi$
$823$	11.9282	+	20.6603i	0.415791	+	0.720171i	−0.579720	+	0.814816i	$0.696838\pi$
$824$	35.3205	+	61.1769i	1.23045	+	2.13120i
$825$		0			0
$826$	20.3205	−	35.1962i	0.707041	−	1.22463i
$827$	32.3923			1.12639			0.563195	−	0.826324i	$-0.309572\pi$
$827$	32.3923			1.12639			0.563195	+	0.826324i	$0.309572\pi$
$828$		0			0
$829$	17.7846			0.617685			0.308843	−	0.951113i	$-0.400058\pi$
$829$	17.7846			0.617685			0.308843	+	0.951113i	$0.400058\pi$
$830$	11.1962	−	19.3923i	0.388624	−	0.673117i
$831$		0			0
$832$	81.5692	+	141.282i	2.82790	+	4.89807i
$833$	−1.97372	−	3.41858i	−0.0683854	−	0.118447i
$834$		0			0
$835$	0.169873	−	0.294229i	0.00587870	−	0.0101822i
$836$	−30.5359			−1.05611
$837$		0			0
$838$	1.07180			0.0370246
$839$	11.4019	−	19.7487i	0.393638	−	0.681801i	−0.599288	−	0.800533i	$-0.704550\pi$
$839$	11.4019	−	19.7487i	0.393638	−	0.681801i	0.992926	+	0.118732i	$0.0378830\pi$
$840$		0			0
$841$	−11.3923	−	19.7321i	−0.392838	−	0.680416i
$842$	10.6340	+	18.4186i	0.366471	+	0.634746i
$843$		0			0
$844$	−51.5167	+	89.2295i	−1.77328	+	3.07141i
$845$	−16.8564			−0.579878
$846$		0			0
$847$	7.42563			0.255148
$848$	24.3923	−	42.2487i	0.837635	−	1.45083i
$849$		0			0
$850$	1.00000	+	1.73205i	0.0342997	+	0.0594089i
$851$	1.26795	+	2.19615i	0.0434647	+	0.0752831i
$852$		0			0
$853$	−27.7583	+	48.0788i	−0.950427	+	1.64619i	−0.205925	+	0.978568i	$0.566020\pi$
$853$	−27.7583	+	48.0788i	−0.950427	+	1.64619i	−0.744502	+	0.667620i	$0.767313\pi$
$854$	−13.8564			−0.474156
$855$		0			0
$856$	146.354			5.00227
$857$	−26.2487	+	45.4641i	−0.896639	+	1.55302i	−0.0648758	+	0.997893i	$0.520665\pi$
$857$	−26.2487	+	45.4641i	−0.896639	+	1.55302i	−0.831763	+	0.555131i	$0.812668\pi$
$858$		0			0
$859$	5.50000	+	9.52628i	0.187658	+	0.325032i	0.944469	−	0.328601i	$-0.106577\pi$
$859$	5.50000	+	9.52628i	0.187658	+	0.325032i	−0.756811	+	0.653633i	$0.773244\pi$
$860$	−27.8564	−	48.2487i	−0.949896	−	1.64527i
$861$		0			0
$862$	−52.8109	+	91.4711i	−1.79875	+	3.11552i
$863$	−1.12436			−0.0382735			−0.0191368	−	0.999817i	$-0.506092\pi$
$863$	−1.12436			−0.0382735			−0.0191368	+	0.999817i	$0.506092\pi$
$864$		0			0
$865$	15.4641			0.525795
$866$	38.9808	−	67.5167i	1.32462	−	2.29431i
$867$		0			0
$868$	−10.3923	−	18.0000i	−0.352738	−	0.610960i
$869$	−9.67949	−	16.7654i	−0.328354	−	0.568726i
$870$		0			0
$871$	−9.46410	+	16.3923i	−0.320679	+	0.555432i
$872$	−188.603			−6.38689
$873$		0			0
$874$	23.3205			0.788828
$875$	−0.633975	+	1.09808i	−0.0214323	+	0.0371218i
$876$		0			0
$877$	−13.2679	−	22.9808i	−0.448027	−	0.776005i	0.550231	−	0.835013i	$-0.314540\pi$
$877$	−13.2679	−	22.9808i	−0.448027	−	0.776005i	−0.998258	+	0.0590075i	$0.981206\pi$
$878$	21.0263	+	36.4186i	0.709603	+	1.22907i
$879$		0			0
$880$	16.9282	−	29.3205i	0.570650	−	0.988394i
$881$	8.94744			0.301447			0.150723	−	0.988576i	$-0.451840\pi$
$881$	8.94744			0.301447			0.150723	+	0.988576i	$0.451840\pi$
$882$		0			0
$883$	−19.8038			−0.666453			−0.333226	−	0.942847i	$-0.608137\pi$
$883$	−19.8038			−0.666453			−0.333226	+	0.942847i	$0.608137\pi$
$884$	−10.9282	+	18.9282i	−0.367555	+	0.636624i
$885$		0			0
$886$	−24.1244	−	41.7846i	−0.810474	−	1.40378i
$887$	22.0981	+	38.2750i	0.741981	+	1.28515i	0.951592	+	0.307364i	$0.0994468\pi$
$887$	22.0981	+	38.2750i	0.741981	+	1.28515i	−0.209611	+	0.977785i	$0.567220\pi$
$888$		0			0
$889$	10.5167	−	18.2154i	0.352717	−	0.610925i
$890$	−14.1962			−0.475856
$891$		0			0
$892$	−135.426			−4.53439
$893$	6.49038	−	11.2417i	0.217192	−	0.376188i
$894$		0			0
$895$	8.06218	+	13.9641i	0.269489	+	0.466768i
$896$	24.0000	+	41.5692i	0.801784	+	1.38873i
$897$		0			0
$898$	−22.0263	+	38.1506i	−0.735026	+	1.27310i
$899$	−21.5885			−0.720015
$900$		0			0
$901$	2.39230			0.0796992
$902$	9.90192	−	17.1506i	0.329698	−	0.571054i
$903$		0			0
$904$	24.2487	+	42.0000i	0.806500	+	1.39690i
$905$	9.76795	+	16.9186i	0.324698	+	0.562393i
$906$		0			0
$907$	15.0000	−	25.9808i	0.498067	−	0.862677i	−0.501931	−	0.864908i	$-0.667377\pi$
$907$	15.0000	−	25.9808i	0.498067	−	0.862677i	0.999998	+	0.00223080i	$0.000710087\pi$
$908$	−109.569			−3.63618
$909$		0			0
$910$	−18.9282			−0.627464
$911$	−3.79423	+	6.57180i	−0.125708	+	0.217733i	−0.922010	−	0.387167i	$-0.873454\pi$
$911$	−3.79423	+	6.57180i	−0.125708	+	0.217733i	0.796301	+	0.604900i	$0.206787\pi$
$912$		0			0
$913$	−9.29423	−	16.0981i	−0.307594	−	0.532769i
$914$	1.00000	+	1.73205i	0.0330771	+	0.0572911i
$915$		0			0
$916$	32.7846	−	56.7846i	1.08323	−	1.87622i
$917$	−19.7654			−0.652710
$918$		0			0
$919$	46.9615			1.54912			0.774559	−	0.632502i	$-0.217972\pi$
$919$	46.9615			1.54912			0.774559	+	0.632502i	$0.217972\pi$
$920$	−16.3923	+	28.3923i	−0.540438	+	0.936067i
$921$		0			0
$922$	1.43782	+	2.49038i	0.0473522	+	0.0820163i
$923$	0.732051	+	1.26795i	0.0240957	+	0.0417351i
$924$		0			0
$925$	−0.366025	+	0.633975i	−0.0120348	+	0.0208450i
$926$	28.3923			0.933029
$927$		0			0
$928$	157.282			5.16304
$929$	14.1865	−	24.5718i	0.465445	−	0.806175i	−0.533776	−	0.845626i	$-0.679228\pi$
$929$	14.1865	−	24.5718i	0.465445	−	0.806175i	0.999222	+	0.0394511i	$0.0125609\pi$
$930$		0			0
$931$	−6.64359	−	11.5070i	−0.217735	−	0.377128i
$932$	27.4641	+	47.5692i	0.899617	+	1.55818i
$933$		0			0
$934$	−48.3205	+	83.6936i	−1.58110	+	2.73854i
$935$	1.66025			0.0542961
$936$		0			0
$937$	−31.8564			−1.04070			−0.520352	−	0.853952i	$-0.674199\pi$
$937$	−31.8564			−1.04070			−0.520352	+	0.853952i	$0.674199\pi$
$938$	−6.00000	+	10.3923i	−0.195907	+	0.339321i
$939$		0			0
$940$	14.3923	+	24.9282i	0.469425	+	0.813068i
$941$	−13.5885	−	23.5359i	−0.442971	−	0.767248i	0.554937	−	0.831892i	$-0.312742\pi$
$941$	−13.5885	−	23.5359i	−0.442971	−	0.767248i	−0.997908	+	0.0646438i	$0.979409\pi$
$942$		0			0
$943$	−5.53590	+	9.58846i	−0.180274	+	0.312243i
$944$	175.138			5.70027
$945$		0			0
$946$	−63.1769			−2.05406
$947$	−1.14359	+	1.98076i	−0.0371618	+	0.0643661i	−0.884008	−	0.467472i	$-0.845165\pi$
$947$	−1.14359	+	1.98076i	−0.0371618	+	0.0643661i	0.846846	+	0.531838i	$0.178498\pi$
$948$		0			0
$949$	26.3923	+	45.7128i	0.856730	+	1.48390i
$950$	3.36603	+	5.83013i	0.109208	+	0.189154i
$951$		0			0
$952$	−4.39230	+	7.60770i	−0.142355	+	0.246567i
$953$	−15.6077			−0.505583			−0.252791	−	0.967521i	$-0.581349\pi$
$953$	−15.6077			−0.505583			−0.252791	+	0.967521i	$0.581349\pi$
$954$		0			0
$955$	16.1244			0.521772
$956$	−20.3923	+	35.3205i	−0.659534	+	1.14235i
$957$		0			0
$958$	−49.3468	−	85.4711i	−1.59432	−	2.76145i
$959$	−6.00000	−	10.3923i	−0.193750	−	0.335585i
$960$		0			0
$961$	11.0000	−	19.0526i	0.354839	−	0.614599i
$962$	−10.9282			−0.352339
$963$		0			0
$964$	100.105			3.22417
$965$	−4.36603	+	7.56218i	−0.140547	+	0.243435i
$966$		0			0
$967$	18.0981	+	31.3468i	0.581995	+	1.00804i	0.995243	+	0.0974261i	$0.0310610\pi$
$967$	18.0981	+	31.3468i	0.581995	+	1.00804i	−0.413248	+	0.910619i	$0.635606\pi$
$968$	27.7128	+	48.0000i	0.890724	+	1.54278i
$969$		0			0
$970$	10.4641	−	18.1244i	0.335982	−	0.581938i
$971$	41.4449			1.33003			0.665014	−	0.746830i	$-0.268425\pi$
$971$	41.4449			1.33003			0.665014	+	0.746830i	$0.268425\pi$
$972$		0			0
$973$	−27.1244			−0.869567
$974$	−4.92820	+	8.53590i	−0.157910	+	0.273508i
$975$		0			0
$976$	−29.8564	−	51.7128i	−0.955680	−	1.65529i
$977$	−0.732051	−	1.26795i	−0.0234204	−	0.0405653i	0.854078	−	0.520145i	$-0.174122\pi$
$977$	−0.732051	−	1.26795i	−0.0234204	−	0.0405653i	−0.877498	+	0.479580i	$0.840789\pi$
$978$		0			0
$979$	−5.89230	+	10.2058i	−0.188319	+	0.326178i
$980$	29.4641			0.941196
$981$		0			0
$982$	104.158			3.32381
$983$	8.70577	−	15.0788i	0.277671	−	0.480940i	−0.693135	−	0.720808i	$-0.743771\pi$
$983$	8.70577	−	15.0788i	0.277671	−	0.480940i	0.970806	+	0.239868i	$0.0771042\pi$
$984$		0			0
$985$	−6.92820	−	12.0000i	−0.220751	−	0.382352i
$986$	7.19615	+	12.4641i	0.229172	+	0.396938i
$987$		0			0
$988$	−36.7846	+	63.7128i	−1.17027	+	2.02697i
$989$	35.3205			1.12313
$990$		0			0
$991$	3.14359			0.0998595			0.0499298	−	0.998753i	$-0.484100\pi$
$991$	3.14359			0.0998595			0.0499298	+	0.998753i	$0.484100\pi$
$992$	32.7846	−	56.7846i	1.04091	−	1.80291i
$993$		0			0
$994$	0.464102	+	0.803848i	0.0147204	+	0.0254965i
$995$	−1.00000	−	1.73205i	−0.0317021	−	0.0549097i
$996$		0			0
$997$	9.75833	−	16.9019i	0.309049	−	0.535289i	−0.669105	−	0.743168i	$-0.733322\pi$
$997$	9.75833	−	16.9019i	0.309049	−	0.535289i	0.978155	+	0.207878i	$0.0666558\pi$
$998$	−28.1962			−0.892534
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.e.i.136.1		4
3.2	odd	2		405.2.e.l.136.2		4
9.2	odd	6		405.2.a.g.1.1	✓	2
9.4	even	3	inner	405.2.e.i.271.1		4
9.5	odd	6		405.2.e.l.271.2		4
9.7	even	3		405.2.a.h.1.2	yes	2
36.7	odd	6		6480.2.a.bi.1.1		2
36.11	even	6		6480.2.a.br.1.1		2
45.2	even	12		2025.2.b.g.649.1		4
45.7	odd	12		2025.2.b.h.649.4		4
45.29	odd	6		2025.2.a.m.1.2		2
45.34	even	6		2025.2.a.g.1.1		2
45.38	even	12		2025.2.b.g.649.4		4
45.43	odd	12		2025.2.b.h.649.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.2.a.g.1.1	✓	2	9.2	odd	6
405.2.a.h.1.2	yes	2	9.7	even	3
405.2.e.i.136.1		4	1.1	even	1	trivial
405.2.e.i.271.1		4	9.4	even	3	inner
405.2.e.l.136.2		4	3.2	odd	2
405.2.e.l.271.2		4	9.5	odd	6
2025.2.a.g.1.1		2	45.34	even	6
2025.2.a.m.1.2		2	45.29	odd	6
2025.2.b.g.649.1		4	45.2	even	12
2025.2.b.g.649.4		4	45.38	even	12
2025.2.b.h.649.1		4	45.43	odd	12
2025.2.b.h.649.4		4	45.7	odd	12
6480.2.a.bi.1.1		2	36.7	odd	6
6480.2.a.br.1.1		2	36.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 + 2.36603i) q^{2} +(-2.73205 - 4.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.633975 - 1.09808i) q^{7} +9.46410 q^{8} +O(q^{10})\)	\(q+(-1.36603 + 2.36603i) q^{2} +(-2.73205 - 4.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.633975 - 1.09808i) q^{7} +9.46410 q^{8} -2.73205 q^{10} +(-1.13397 + 1.96410i) q^{11} +(2.73205 + 4.73205i) q^{13} +(1.73205 + 3.00000i) q^{14} +(-7.46410 + 12.9282i) q^{16} -0.732051 q^{17} -2.46410 q^{19} +(2.73205 - 4.73205i) q^{20} +(-3.09808 - 5.36603i) q^{22} +(1.73205 + 3.00000i) q^{23} +(-0.500000 + 0.866025i) q^{25} -14.9282 q^{26} -6.92820 q^{28} +(-3.59808 + 6.23205i) q^{29} +(1.50000 + 2.59808i) q^{31} +(-10.9282 - 18.9282i) q^{32} +(1.00000 - 1.73205i) q^{34} +1.26795 q^{35} +0.732051 q^{37} +(3.36603 - 5.83013i) q^{38} +(4.73205 + 8.19615i) q^{40} +(1.59808 + 2.76795i) q^{41} +(5.09808 - 8.83013i) q^{43} +12.3923 q^{44} -9.46410 q^{46} +(-2.63397 + 4.56218i) q^{47} +(2.69615 + 4.66987i) q^{49} +(-1.36603 - 2.36603i) q^{50} +(14.9282 - 25.8564i) q^{52} -3.26795 q^{53} -2.26795 q^{55} +(6.00000 - 10.3923i) q^{56} +(-9.83013 - 17.0263i) q^{58} +(-5.86603 - 10.1603i) q^{59} +(-2.00000 + 3.46410i) q^{61} -8.19615 q^{62} +29.8564 q^{64} +(-2.73205 + 4.73205i) q^{65} +(1.73205 + 3.00000i) q^{67} +(2.00000 + 3.46410i) q^{68} +(-1.73205 + 3.00000i) q^{70} +0.267949 q^{71} +9.66025 q^{73} +(-1.00000 + 1.73205i) q^{74} +(6.73205 + 11.6603i) q^{76} +(1.43782 + 2.49038i) q^{77} +(-4.26795 + 7.39230i) q^{79} -14.9282 q^{80} -8.73205 q^{82} +(-4.09808 + 7.09808i) q^{83} +(-0.366025 - 0.633975i) q^{85} +(13.9282 + 24.1244i) q^{86} +(-10.7321 + 18.5885i) q^{88} +5.19615 q^{89} +6.92820 q^{91} +(9.46410 - 16.3923i) q^{92} +(-7.19615 - 12.4641i) q^{94} +(-1.23205 - 2.13397i) q^{95} +(-3.83013 + 6.63397i) q^{97} -14.7321 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 4 q^{4} + 2 q^{5} + 6 q^{7} + 24 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 4 * q^4 + 2 * q^5 + 6 * q^7 + 24 * q^8	\( 4 q - 2 q^{2} - 4 q^{4} + 2 q^{5} + 6 q^{7} + 24 q^{8} - 4 q^{10} - 8 q^{11} + 4 q^{13} - 16 q^{16} + 4 q^{17} + 4 q^{19} + 4 q^{20} - 2 q^{22} - 2 q^{25} - 32 q^{26} - 4 q^{29} + 6 q^{31} - 16 q^{32} + 4 q^{34} + 12 q^{35} - 4 q^{37} + 10 q^{38} + 12 q^{40} - 4 q^{41} + 10 q^{43} + 8 q^{44} - 24 q^{46} - 14 q^{47} - 10 q^{49} - 2 q^{50} + 32 q^{52} - 20 q^{53} - 16 q^{55} + 24 q^{56} - 22 q^{58} - 20 q^{59} - 8 q^{61} - 12 q^{62} + 64 q^{64} - 4 q^{65} + 8 q^{68} + 8 q^{71} + 4 q^{73} - 4 q^{74} + 20 q^{76} + 30 q^{77} - 24 q^{79} - 32 q^{80} - 28 q^{82} - 6 q^{83} + 2 q^{85} + 28 q^{86} - 36 q^{88} + 24 q^{92} - 8 q^{94} + 2 q^{95} + 2 q^{97} - 52 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 4 * q^4 + 2 * q^5 + 6 * q^7 + 24 * q^8 - 4 * q^10 - 8 * q^11 + 4 * q^13 - 16 * q^16 + 4 * q^17 + 4 * q^19 + 4 * q^20 - 2 * q^22 - 2 * q^25 - 32 * q^26 - 4 * q^29 + 6 * q^31 - 16 * q^32 + 4 * q^34 + 12 * q^35 - 4 * q^37 + 10 * q^38 + 12 * q^40 - 4 * q^41 + 10 * q^43 + 8 * q^44 - 24 * q^46 - 14 * q^47 - 10 * q^49 - 2 * q^50 + 32 * q^52 - 20 * q^53 - 16 * q^55 + 24 * q^56 - 22 * q^58 - 20 * q^59 - 8 * q^61 - 12 * q^62 + 64 * q^64 - 4 * q^65 + 8 * q^68 + 8 * q^71 + 4 * q^73 - 4 * q^74 + 20 * q^76 + 30 * q^77 - 24 * q^79 - 32 * q^80 - 28 * q^82 - 6 * q^83 + 2 * q^85 + 28 * q^86 - 36 * q^88 + 24 * q^92 - 8 * q^94 + 2 * q^95 + 2 * q^97 - 52 * q^98

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