LMFDB - Embedded newform 150.2.e.b.107.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,2,Mod(107,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("150.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	150.e (of order $4$, degree $2$, 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:	$1.19775603032$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.3
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	150.107
Dual form			150.2.e.b.143.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(0.448288 + 1.67303i) q^{3} -1.00000i q^{4} +(1.50000 + 0.866025i) q^{6} +(2.44949 + 2.44949i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.59808 + 1.50000i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(0.448288 + 1.67303i) q^{3} -1.00000i q^{4} +(1.50000 + 0.866025i) q^{6} +(2.44949 + 2.44949i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.59808 + 1.50000i) q^{9} -5.19615i q^{11} +(1.67303 - 0.448288i) q^{12} +3.46410 q^{14} -1.00000 q^{16} +(-2.12132 + 2.12132i) q^{17} +(-0.776457 + 2.89778i) q^{18} -1.00000i q^{19} +(-3.00000 + 5.19615i) q^{21} +(-3.67423 - 3.67423i) q^{22} +(-4.24264 - 4.24264i) q^{23} +(0.866025 - 1.50000i) q^{24} +(-3.67423 - 3.67423i) q^{27} +(2.44949 - 2.44949i) q^{28} -2.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(8.69333 - 2.32937i) q^{33} +3.00000i q^{34} +(1.50000 + 2.59808i) q^{36} +(-2.44949 - 2.44949i) q^{37} +(-0.707107 - 0.707107i) q^{38} +5.19615i q^{41} +(1.55291 + 5.79555i) q^{42} +(-2.44949 + 2.44949i) q^{43} -5.19615 q^{44} -6.00000 q^{46} +(-0.448288 - 1.67303i) q^{48} +5.00000i q^{49} +(-4.50000 - 2.59808i) q^{51} +(4.24264 + 4.24264i) q^{53} -5.19615 q^{54} -3.46410i q^{56} +(1.67303 - 0.448288i) q^{57} +10.3923 q^{59} +14.0000 q^{61} +(-1.41421 + 1.41421i) q^{62} +(-10.0382 - 2.68973i) q^{63} +1.00000i q^{64} +(4.50000 - 7.79423i) q^{66} +(3.67423 + 3.67423i) q^{67} +(2.12132 + 2.12132i) q^{68} +(5.19615 - 9.00000i) q^{69} +(2.89778 + 0.776457i) q^{72} +(-6.12372 + 6.12372i) q^{73} -3.46410 q^{74} -1.00000 q^{76} +(12.7279 - 12.7279i) q^{77} -14.0000i q^{79} +(4.50000 - 7.79423i) q^{81} +(3.67423 + 3.67423i) q^{82} +(2.12132 + 2.12132i) q^{83} +(5.19615 + 3.00000i) q^{84} +3.46410i q^{86} +(-3.67423 + 3.67423i) q^{88} -15.5885 q^{89} +(-4.24264 + 4.24264i) q^{92} +(-0.896575 - 3.34607i) q^{93} +(-1.50000 - 0.866025i) q^{96} +(4.89898 + 4.89898i) q^{97} +(3.53553 + 3.53553i) q^{98} +(7.79423 + 13.5000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{6}+O(q^{10}) $ 8 * q + 12 * q^6	$ 8 q + 12 q^{6} - 8 q^{16} - 24 q^{21} - 16 q^{31} + 12 q^{36} - 48 q^{46} - 36 q^{51} + 112 q^{61} + 36 q^{66} - 8 q^{76} + 36 q^{81} - 12 q^{96}+O(q^{100}) $ 8 * q + 12 * q^6 - 8 * q^16 - 24 * q^21 - 16 * q^31 + 12 * q^36 - 48 * q^46 - 36 * q^51 + 112 * q^61 + 36 * q^66 - 8 * q^76 + 36 * q^81 - 12 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	0.448288	+	1.67303i	0.258819	+	0.965926i
$3$	0.448288	+	1.67303i	0.258819	+	0.965926i
$4$		−	1.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$	1.50000	+	0.866025i	0.612372	+	0.353553i
$7$	2.44949	+	2.44949i	0.925820	+	0.925820i	0.997433	−	0.0716124i	$-0.0228145\pi$
$7$	2.44949	+	2.44949i	0.925820	+	0.925820i	−0.0716124	+	0.997433i	$0.522814\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.59808	+	1.50000i	−0.866025	+	0.500000i
$10$		0			0
$11$		−	5.19615i		−	1.56670i	−0.621582	−	0.783349i	$-0.713510\pi$
$11$		−	5.19615i		−	1.56670i	0.621582	−	0.783349i	$-0.286490\pi$
$12$	1.67303	−	0.448288i	0.482963	−	0.129410i
$13$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$13$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$14$	3.46410			0.925820
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−2.12132	+	2.12132i	−0.514496	+	0.514496i	−0.915901	−	0.401405i	$-0.868522\pi$
$17$	−2.12132	+	2.12132i	−0.514496	+	0.514496i	0.401405	+	0.915901i	$0.368522\pi$
$18$	−0.776457	+	2.89778i	−0.183013	+	0.683013i
$19$		−	1.00000i		−	0.229416i	−0.993399	−	0.114708i	$-0.963407\pi$
$19$		−	1.00000i		−	0.229416i	0.993399	−	0.114708i	$-0.0365932\pi$
$20$		0			0
$21$	−3.00000	+	5.19615i	−0.654654	+	1.13389i
$22$	−3.67423	−	3.67423i	−0.783349	−	0.783349i
$23$	−4.24264	−	4.24264i	−0.884652	−	0.884652i	0.109351	−	0.994003i	$-0.465123\pi$
$23$	−4.24264	−	4.24264i	−0.884652	−	0.884652i	−0.994003	+	0.109351i	$0.965123\pi$
$24$	0.866025	−	1.50000i	0.176777	−	0.306186i
$25$		0			0
$26$		0			0
$27$	−3.67423	−	3.67423i	−0.707107	−	0.707107i
$28$	2.44949	−	2.44949i	0.462910	−	0.462910i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$		0			0
$31$	−2.00000			−0.359211			−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000			−0.359211			−0.179605	+	0.983739i	$0.557482\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	8.69333	−	2.32937i	1.51331	−	0.405492i
$34$			3.00000i			0.514496i
$35$		0			0
$36$	1.50000	+	2.59808i	0.250000	+	0.433013i
$37$	−2.44949	−	2.44949i	−0.402694	−	0.402694i	0.476488	−	0.879181i	$-0.341910\pi$
$37$	−2.44949	−	2.44949i	−0.402694	−	0.402694i	−0.879181	+	0.476488i	$0.841910\pi$
$38$	−0.707107	−	0.707107i	−0.114708	−	0.114708i
$39$		0			0
$40$		0			0
$41$			5.19615i			0.811503i	0.913984	+	0.405751i	$0.132990\pi$
$41$			5.19615i			0.811503i	−0.913984	+	0.405751i	$0.867010\pi$
$42$	1.55291	+	5.79555i	0.239620	+	0.894274i
$43$	−2.44949	+	2.44949i	−0.373544	+	0.373544i	−0.868766	−	0.495222i	$-0.835087\pi$
$43$	−2.44949	+	2.44949i	−0.373544	+	0.373544i	0.495222	+	0.868766i	$0.335087\pi$
$44$	−5.19615			−0.783349
$45$		0			0
$46$	−6.00000			−0.884652
$47$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$47$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$48$	−0.448288	−	1.67303i	−0.0647048	−	0.241481i
$49$			5.00000i			0.714286i
$50$		0			0
$51$	−4.50000	−	2.59808i	−0.630126	−	0.363803i
$52$		0			0
$53$	4.24264	+	4.24264i	0.582772	+	0.582772i	0.935664	−	0.352892i	$-0.114802\pi$
$53$	4.24264	+	4.24264i	0.582772	+	0.582772i	−0.352892	+	0.935664i	$0.614802\pi$
$54$	−5.19615			−0.707107
$55$		0			0
$56$		−	3.46410i		−	0.462910i
$57$	1.67303	−	0.448288i	0.221599	−	0.0593772i
$58$		0			0
$59$	10.3923			1.35296			0.676481	−	0.736460i	$-0.263504\pi$
$59$	10.3923			1.35296			0.676481	+	0.736460i	$0.263504\pi$
$60$		0			0
$61$	14.0000			1.79252			0.896258	−	0.443533i	$-0.146275\pi$
$61$	14.0000			1.79252			0.896258	+	0.443533i	$0.146275\pi$
$62$	−1.41421	+	1.41421i	−0.179605	+	0.179605i
$63$	−10.0382	−	2.68973i	−1.26469	−	0.338874i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	4.50000	−	7.79423i	0.553912	−	0.959403i
$67$	3.67423	+	3.67423i	0.448879	+	0.448879i	0.894982	−	0.446103i	$-0.147188\pi$
$67$	3.67423	+	3.67423i	0.448879	+	0.448879i	−0.446103	+	0.894982i	$0.647188\pi$
$68$	2.12132	+	2.12132i	0.257248	+	0.257248i
$69$	5.19615	−	9.00000i	0.625543	−	1.08347i
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	2.89778	+	0.776457i	0.341506	+	0.0915064i
$73$	−6.12372	+	6.12372i	−0.716728	+	0.716728i	−0.967934	−	0.251206i	$-0.919173\pi$
$73$	−6.12372	+	6.12372i	−0.716728	+	0.716728i	0.251206	+	0.967934i	$0.419173\pi$
$74$	−3.46410			−0.402694
$75$		0			0
$76$	−1.00000			−0.114708
$77$	12.7279	−	12.7279i	1.45048	−	1.45048i
$78$		0			0
$79$		−	14.0000i		−	1.57512i	−0.616236	−	0.787562i	$-0.711343\pi$
$79$		−	14.0000i		−	1.57512i	0.616236	−	0.787562i	$-0.288657\pi$
$80$		0			0
$81$	4.50000	−	7.79423i	0.500000	−	0.866025i
$82$	3.67423	+	3.67423i	0.405751	+	0.405751i
$83$	2.12132	+	2.12132i	0.232845	+	0.232845i	0.813879	−	0.581034i	$-0.197352\pi$
$83$	2.12132	+	2.12132i	0.232845	+	0.232845i	−0.581034	+	0.813879i	$0.697352\pi$
$84$	5.19615	+	3.00000i	0.566947	+	0.327327i
$85$		0			0
$86$			3.46410i			0.373544i
$87$		0			0
$88$	−3.67423	+	3.67423i	−0.391675	+	0.391675i
$89$	−15.5885			−1.65237			−0.826187	−	0.563397i	$-0.809494\pi$
$89$	−15.5885			−1.65237			−0.826187	+	0.563397i	$0.809494\pi$
$90$		0			0
$91$		0			0
$92$	−4.24264	+	4.24264i	−0.442326	+	0.442326i
$93$	−0.896575	−	3.34607i	−0.0929705	−	0.346971i
$94$		0			0
$95$		0			0
$96$	−1.50000	−	0.866025i	−0.153093	−	0.0883883i
$97$	4.89898	+	4.89898i	0.497416	+	0.497416i	0.910633	−	0.413217i	$-0.135595\pi$
$97$	4.89898	+	4.89898i	0.497416	+	0.497416i	−0.413217	+	0.910633i	$0.635595\pi$
$98$	3.53553	+	3.53553i	0.357143	+	0.357143i
$99$	7.79423	+	13.5000i	0.783349	+	1.35680i
$100$		0			0
$101$			10.3923i			1.03407i	0.855963	+	0.517036i	$0.172965\pi$
$101$			10.3923i			1.03407i	−0.855963	+	0.517036i	$0.827035\pi$
$102$	−5.01910	+	1.34486i	−0.496965	+	0.133161i
$103$	9.79796	−	9.79796i	0.965422	−	0.965422i	−0.0340002	−	0.999422i	$-0.510825\pi$
$103$	9.79796	−	9.79796i	0.965422	−	0.965422i	0.999422	+	0.0340002i	$0.0108247\pi$
$104$		0			0
$105$		0			0
$106$	6.00000			0.582772
$107$	−6.36396	+	6.36396i	−0.615227	+	0.615227i	−0.944303	−	0.329076i	$-0.893263\pi$
$107$	−6.36396	+	6.36396i	−0.615227	+	0.615227i	0.329076	+	0.944303i	$0.393263\pi$
$108$	−3.67423	+	3.67423i	−0.353553	+	0.353553i
$109$			10.0000i			0.957826i	0.877862	+	0.478913i	$0.158969\pi$
$109$			10.0000i			0.957826i	−0.877862	+	0.478913i	$0.841031\pi$
$110$		0			0
$111$	3.00000	−	5.19615i	0.284747	−	0.493197i
$112$	−2.44949	−	2.44949i	−0.231455	−	0.231455i
$113$	6.36396	+	6.36396i	0.598671	+	0.598671i	0.939959	−	0.341288i	$-0.110863\pi$
$113$	6.36396	+	6.36396i	0.598671	+	0.598671i	−0.341288	+	0.939959i	$0.610863\pi$
$114$	0.866025	−	1.50000i	0.0811107	−	0.140488i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	7.34847	−	7.34847i	0.676481	−	0.676481i
$119$	−10.3923			−0.952661
$120$		0			0
$121$	−16.0000			−1.45455
$122$	9.89949	−	9.89949i	0.896258	−	0.896258i
$123$	−8.69333	+	2.32937i	−0.783851	+	0.210032i
$124$			2.00000i			0.179605i
$125$		0			0
$126$	−9.00000	+	5.19615i	−0.801784	+	0.462910i
$127$	−7.34847	−	7.34847i	−0.652071	−	0.652071i	0.301420	−	0.953491i	$-0.402539\pi$
$127$	−7.34847	−	7.34847i	−0.652071	−	0.652071i	−0.953491	+	0.301420i	$0.902539\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−5.19615	−	3.00000i	−0.457496	−	0.264135i
$130$		0			0
$131$			10.3923i			0.907980i	0.891007	+	0.453990i	$0.150000\pi$
$131$			10.3923i			0.907980i	−0.891007	+	0.453990i	$0.850000\pi$
$132$	−2.32937	−	8.69333i	−0.202746	−	0.756657i
$133$	2.44949	−	2.44949i	0.212398	−	0.212398i
$134$	5.19615			0.448879
$135$		0			0
$136$	3.00000			0.257248
$137$	−14.8492	+	14.8492i	−1.26866	+	1.26866i	−0.321874	+	0.946783i	$0.604313\pi$
$137$	−14.8492	+	14.8492i	−1.26866	+	1.26866i	−0.946783	+	0.321874i	$0.895687\pi$
$138$	−2.68973	−	10.0382i	−0.228965	−	0.854508i
$139$		−	7.00000i		−	0.593732i	−0.954919	−	0.296866i	$-0.904058\pi$
$139$		−	7.00000i		−	0.593732i	0.954919	−	0.296866i	$-0.0959415\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	2.59808	−	1.50000i	0.216506	−	0.125000i
$145$		0			0
$146$			8.66025i			0.716728i
$147$	−8.36516	+	2.24144i	−0.689947	+	0.184871i
$148$	−2.44949	+	2.44949i	−0.201347	+	0.201347i
$149$	20.7846			1.70274			0.851371	−	0.524564i	$-0.175772\pi$
$149$	20.7846			1.70274			0.851371	+	0.524564i	$0.175772\pi$
$150$		0			0
$151$	−14.0000			−1.13930			−0.569652	−	0.821886i	$-0.692922\pi$
$151$	−14.0000			−1.13930			−0.569652	+	0.821886i	$0.692922\pi$
$152$	−0.707107	+	0.707107i	−0.0573539	+	0.0573539i
$153$	2.32937	−	8.69333i	0.188319	−	0.702814i
$154$		−	18.0000i		−	1.45048i
$155$		0			0
$156$		0			0
$157$	−12.2474	−	12.2474i	−0.977453	−	0.977453i	0.0222985	−	0.999751i	$-0.492902\pi$
$157$	−12.2474	−	12.2474i	−0.977453	−	0.977453i	−0.999751	+	0.0222985i	$0.992902\pi$
$158$	−9.89949	−	9.89949i	−0.787562	−	0.787562i
$159$	−5.19615	+	9.00000i	−0.412082	+	0.713746i
$160$		0			0
$161$		−	20.7846i		−	1.63806i
$162$	−2.32937	−	8.69333i	−0.183013	−	0.683013i
$163$	3.67423	−	3.67423i	0.287788	−	0.287788i	−0.548417	−	0.836205i	$-0.684769\pi$
$163$	3.67423	−	3.67423i	0.287788	−	0.287788i	0.836205	+	0.548417i	$0.184769\pi$
$164$	5.19615			0.405751
$165$		0			0
$166$	3.00000			0.232845
$167$	8.48528	−	8.48528i	0.656611	−	0.656611i	−0.297966	−	0.954577i	$-0.596308\pi$
$167$	8.48528	−	8.48528i	0.656611	−	0.656611i	0.954577	+	0.297966i	$0.0963081\pi$
$168$	5.79555	−	1.55291i	0.447137	−	0.119810i
$169$			13.0000i			1.00000i
$170$		0			0
$171$	1.50000	+	2.59808i	0.114708	+	0.198680i
$172$	2.44949	+	2.44949i	0.186772	+	0.186772i
$173$	−8.48528	−	8.48528i	−0.645124	−	0.645124i	0.306687	−	0.951811i	$-0.400780\pi$
$173$	−8.48528	−	8.48528i	−0.645124	−	0.645124i	−0.951811	+	0.306687i	$0.900780\pi$
$174$		0			0
$175$		0			0
$176$			5.19615i			0.391675i
$177$	4.65874	+	17.3867i	0.350173	+	1.30686i
$178$	−11.0227	+	11.0227i	−0.826187	+	0.826187i
$179$	−15.5885			−1.16514			−0.582568	−	0.812782i	$-0.697952\pi$
$179$	−15.5885			−1.16514			−0.582568	+	0.812782i	$0.697952\pi$
$180$		0			0
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$	6.27603	+	23.4225i	0.463937	+	1.73144i
$184$			6.00000i			0.442326i
$185$		0			0
$186$	−3.00000	−	1.73205i	−0.219971	−	0.127000i
$187$	11.0227	+	11.0227i	0.806060	+	0.806060i
$188$		0			0
$189$		−	18.0000i		−	1.30931i
$190$		0			0
$191$		−	10.3923i		−	0.751961i	−0.926628	−	0.375980i	$-0.877306\pi$
$191$		−	10.3923i		−	0.751961i	0.926628	−	0.375980i	$-0.122694\pi$
$192$	−1.67303	+	0.448288i	−0.120741	+	0.0323524i
$193$	−6.12372	+	6.12372i	−0.440795	+	0.440795i	−0.892279	−	0.451484i	$-0.850895\pi$
$193$	−6.12372	+	6.12372i	−0.440795	+	0.440795i	0.451484	+	0.892279i	$0.350895\pi$
$194$	6.92820			0.497416
$195$		0			0
$196$	5.00000			0.357143
$197$	−4.24264	+	4.24264i	−0.302276	+	0.302276i	−0.841904	−	0.539628i	$-0.818565\pi$
$197$	−4.24264	+	4.24264i	−0.302276	+	0.302276i	0.539628	+	0.841904i	$0.318565\pi$
$198$	15.0573	+	4.03459i	1.07008	+	0.286726i
$199$			16.0000i			1.13421i	0.823646	+	0.567105i	$0.191937\pi$
$199$			16.0000i			1.13421i	−0.823646	+	0.567105i	$0.808063\pi$
$200$		0			0
$201$	−4.50000	+	7.79423i	−0.317406	+	0.549762i
$202$	7.34847	+	7.34847i	0.517036	+	0.517036i
$203$		0			0
$204$	−2.59808	+	4.50000i	−0.181902	+	0.315063i
$205$		0			0
$206$		−	13.8564i		−	0.965422i
$207$	17.3867	+	4.65874i	1.20846	+	0.323805i
$208$		0			0
$209$	−5.19615			−0.359425
$210$		0			0
$211$	23.0000			1.58339			0.791693	−	0.610920i	$-0.209200\pi$
$211$	23.0000			1.58339			0.791693	+	0.610920i	$0.209200\pi$
$212$	4.24264	−	4.24264i	0.291386	−	0.291386i
$213$		0			0
$214$			9.00000i			0.615227i
$215$		0			0
$216$			5.19615i			0.353553i
$217$	−4.89898	−	4.89898i	−0.332564	−	0.332564i
$218$	7.07107	+	7.07107i	0.478913	+	0.478913i
$219$	−12.9904	−	7.50000i	−0.877809	−	0.506803i
$220$		0			0
$221$		0			0
$222$	−1.55291	−	5.79555i	−0.104225	−	0.388972i
$223$	9.79796	−	9.79796i	0.656120	−	0.656120i	−0.298340	−	0.954460i	$-0.596433\pi$
$223$	9.79796	−	9.79796i	0.656120	−	0.656120i	0.954460	+	0.298340i	$0.0964329\pi$
$224$	−3.46410			−0.231455
$225$		0			0
$226$	9.00000			0.598671
$227$	8.48528	−	8.48528i	0.563188	−	0.563188i	−0.367024	−	0.930212i	$-0.619623\pi$
$227$	8.48528	−	8.48528i	0.563188	−	0.563188i	0.930212	+	0.367024i	$0.119623\pi$
$228$	−0.448288	−	1.67303i	−0.0296886	−	0.110799i
$229$		−	16.0000i		−	1.05731i	−0.848837	−	0.528655i	$-0.822697\pi$
$229$		−	16.0000i		−	1.05731i	0.848837	−	0.528655i	$-0.177303\pi$
$230$		0			0
$231$	27.0000	+	15.5885i	1.77647	+	1.02565i
$232$		0			0
$233$	−12.7279	−	12.7279i	−0.833834	−	0.833834i	0.154205	−	0.988039i	$-0.450718\pi$
$233$	−12.7279	−	12.7279i	−0.833834	−	0.833834i	−0.988039	+	0.154205i	$0.950718\pi$
$234$		0			0
$235$		0			0
$236$		−	10.3923i		−	0.676481i
$237$	23.4225	−	6.27603i	1.52145	−	0.407672i
$238$	−7.34847	+	7.34847i	−0.476331	+	0.476331i
$239$	20.7846			1.34444			0.672222	−	0.740349i	$-0.265340\pi$
$239$	20.7846			1.34444			0.672222	+	0.740349i	$0.265340\pi$
$240$		0			0
$241$	−1.00000			−0.0644157			−0.0322078	−	0.999481i	$-0.510254\pi$
$241$	−1.00000			−0.0644157			−0.0322078	+	0.999481i	$0.510254\pi$
$242$	−11.3137	+	11.3137i	−0.727273	+	0.727273i
$243$	15.0573	+	4.03459i	0.965926	+	0.258819i
$244$		−	14.0000i		−	0.896258i
$245$		0			0
$246$	−4.50000	+	7.79423i	−0.286910	+	0.496942i
$247$		0			0
$248$	1.41421	+	1.41421i	0.0898027	+	0.0898027i
$249$	−2.59808	+	4.50000i	−0.164646	+	0.285176i
$250$		0			0
$251$		−	5.19615i		−	0.327978i	−0.986462	−	0.163989i	$-0.947564\pi$
$251$		−	5.19615i		−	0.327978i	0.986462	−	0.163989i	$-0.0524362\pi$
$252$	−2.68973	+	10.0382i	−0.169437	+	0.632347i
$253$	−22.0454	+	22.0454i	−1.38598	+	1.38598i
$254$	−10.3923			−0.652071
$255$		0			0
$256$	1.00000			0.0625000
$257$	4.24264	−	4.24264i	0.264649	−	0.264649i	−0.562291	−	0.826940i	$-0.690080\pi$
$257$	4.24264	−	4.24264i	0.264649	−	0.264649i	0.826940	+	0.562291i	$0.190080\pi$
$258$	−5.79555	+	1.55291i	−0.360815	+	0.0966802i
$259$		−	12.0000i		−	0.745644i
$260$		0			0
$261$		0			0
$262$	7.34847	+	7.34847i	0.453990	+	0.453990i
$263$	12.7279	+	12.7279i	0.784837	+	0.784837i	0.980643	−	0.195805i	$-0.0627321\pi$
$263$	12.7279	+	12.7279i	0.784837	+	0.784837i	−0.195805	+	0.980643i	$0.562732\pi$
$264$	−7.79423	−	4.50000i	−0.479702	−	0.276956i
$265$		0			0
$266$		−	3.46410i		−	0.212398i
$267$	−6.98811	−	26.0800i	−0.427666	−	1.59607i
$268$	3.67423	−	3.67423i	0.224440	−	0.224440i
$269$	20.7846			1.26726			0.633630	−	0.773636i	$-0.281564\pi$
$269$	20.7846			1.26726			0.633630	+	0.773636i	$0.281564\pi$
$270$		0			0
$271$	−10.0000			−0.607457			−0.303728	−	0.952759i	$-0.598232\pi$
$271$	−10.0000			−0.607457			−0.303728	+	0.952759i	$0.598232\pi$
$272$	2.12132	−	2.12132i	0.128624	−	0.128624i
$273$		0			0
$274$			21.0000i			1.26866i
$275$		0			0
$276$	−9.00000	−	5.19615i	−0.541736	−	0.312772i
$277$	−9.79796	−	9.79796i	−0.588702	−	0.588702i	0.348578	−	0.937280i	$-0.386665\pi$
$277$	−9.79796	−	9.79796i	−0.588702	−	0.588702i	−0.937280	+	0.348578i	$0.886665\pi$
$278$	−4.94975	−	4.94975i	−0.296866	−	0.296866i
$279$	5.19615	−	3.00000i	0.311086	−	0.179605i
$280$		0			0
$281$		−	20.7846i		−	1.23991i	−0.784639	−	0.619953i	$-0.787152\pi$
$281$		−	20.7846i		−	1.23991i	0.784639	−	0.619953i	$-0.212848\pi$
$282$		0			0
$283$	6.12372	−	6.12372i	0.364018	−	0.364018i	−0.501272	−	0.865290i	$-0.667134\pi$
$283$	6.12372	−	6.12372i	0.364018	−	0.364018i	0.865290	+	0.501272i	$0.167134\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−12.7279	+	12.7279i	−0.751305	+	0.751305i
$288$	0.776457	−	2.89778i	0.0457532	−	0.170753i
$289$			8.00000i			0.470588i
$290$		0			0
$291$	−6.00000	+	10.3923i	−0.351726	+	0.609208i
$292$	6.12372	+	6.12372i	0.358364	+	0.358364i
$293$	−21.2132	−	21.2132i	−1.23929	−	1.23929i	−0.960292	−	0.278996i	$-0.909998\pi$
$293$	−21.2132	−	21.2132i	−1.23929	−	1.23929i	−0.278996	−	0.960292i	$-0.590002\pi$
$294$	−4.33013	+	7.50000i	−0.252538	+	0.437409i
$295$		0			0
$296$			3.46410i			0.201347i
$297$	−19.0919	+	19.0919i	−1.10782	+	1.10782i
$298$	14.6969	−	14.6969i	0.851371	−	0.851371i
$299$		0			0
$300$		0			0
$301$	−12.0000			−0.691669
$302$	−9.89949	+	9.89949i	−0.569652	+	0.569652i
$303$	−17.3867	+	4.65874i	−0.998838	+	0.267638i
$304$			1.00000i			0.0573539i
$305$		0			0
$306$	−4.50000	−	7.79423i	−0.257248	−	0.445566i
$307$	−1.22474	−	1.22474i	−0.0698999	−	0.0698999i	0.671293	−	0.741192i	$-0.265739\pi$
$307$	−1.22474	−	1.22474i	−0.0698999	−	0.0698999i	−0.741192	+	0.671293i	$0.765739\pi$
$308$	−12.7279	−	12.7279i	−0.725241	−	0.725241i
$309$	20.7846	+	12.0000i	1.18240	+	0.682656i
$310$		0			0
$311$			31.1769i			1.76788i	0.467600	+	0.883940i	$0.345119\pi$
$311$			31.1769i			1.76788i	−0.467600	+	0.883940i	$0.654881\pi$
$312$		0			0
$313$	14.6969	−	14.6969i	0.830720	−	0.830720i	−0.156895	−	0.987615i	$-0.550148\pi$
$313$	14.6969	−	14.6969i	0.830720	−	0.830720i	0.987615	+	0.156895i	$0.0501485\pi$
$314$	−17.3205			−0.977453
$315$		0			0
$316$	−14.0000			−0.787562
$317$	8.48528	−	8.48528i	0.476581	−	0.476581i	−0.427456	−	0.904036i	$-0.640590\pi$
$317$	8.48528	−	8.48528i	0.476581	−	0.476581i	0.904036	+	0.427456i	$0.140590\pi$
$318$	2.68973	+	10.0382i	0.150832	+	0.562914i
$319$		0			0
$320$		0			0
$321$	−13.5000	−	7.79423i	−0.753497	−	0.435031i
$322$	−14.6969	−	14.6969i	−0.819028	−	0.819028i
$323$	2.12132	+	2.12132i	0.118033	+	0.118033i
$324$	−7.79423	−	4.50000i	−0.433013	−	0.250000i
$325$		0			0
$326$		−	5.19615i		−	0.287788i
$327$	−16.7303	+	4.48288i	−0.925189	+	0.247904i
$328$	3.67423	−	3.67423i	0.202876	−	0.202876i
$329$		0			0
$330$		0			0
$331$	−13.0000			−0.714545			−0.357272	−	0.934000i	$-0.616293\pi$
$331$	−13.0000			−0.714545			−0.357272	+	0.934000i	$0.616293\pi$
$332$	2.12132	−	2.12132i	0.116423	−	0.116423i
$333$	10.0382	+	2.68973i	0.550090	+	0.147396i
$334$		−	12.0000i		−	0.656611i
$335$		0			0
$336$	3.00000	−	5.19615i	0.163663	−	0.283473i
$337$	3.67423	+	3.67423i	0.200148	+	0.200148i	0.800064	−	0.599915i	$-0.204799\pi$
$337$	3.67423	+	3.67423i	0.200148	+	0.200148i	−0.599915	+	0.800064i	$0.704799\pi$
$338$	9.19239	+	9.19239i	0.500000	+	0.500000i
$339$	−7.79423	+	13.5000i	−0.423324	+	0.733219i
$340$		0			0
$341$			10.3923i			0.562775i
$342$	2.89778	+	0.776457i	0.156694	+	0.0419860i
$343$	4.89898	−	4.89898i	0.264520	−	0.264520i
$344$	3.46410			0.186772
$345$		0			0
$346$	−12.0000			−0.645124
$347$	6.36396	−	6.36396i	0.341635	−	0.341635i	−0.515347	−	0.856982i	$-0.672337\pi$
$347$	6.36396	−	6.36396i	0.341635	−	0.341635i	0.856982	+	0.515347i	$0.172337\pi$
$348$		0			0
$349$		−	22.0000i		−	1.17763i	−0.808267	−	0.588817i	$-0.799594\pi$
$349$		−	22.0000i		−	1.17763i	0.808267	−	0.588817i	$-0.200406\pi$
$350$		0			0
$351$		0			0
$352$	3.67423	+	3.67423i	0.195837	+	0.195837i
$353$	12.7279	+	12.7279i	0.677439	+	0.677439i	0.959420	−	0.281981i	$-0.0909915\pi$
$353$	12.7279	+	12.7279i	0.677439	+	0.677439i	−0.281981	+	0.959420i	$0.590992\pi$
$354$	15.5885	+	9.00000i	0.828517	+	0.478345i
$355$		0			0
$356$			15.5885i			0.826187i
$357$	−4.65874	−	17.3867i	−0.246567	−	0.920200i
$358$	−11.0227	+	11.0227i	−0.582568	+	0.582568i
$359$	−10.3923			−0.548485			−0.274242	−	0.961661i	$-0.588427\pi$
$359$	−10.3923			−0.548485			−0.274242	+	0.961661i	$0.588427\pi$
$360$		0			0
$361$	18.0000			0.947368
$362$	−1.41421	+	1.41421i	−0.0743294	+	0.0743294i
$363$	−7.17260	−	26.7685i	−0.376464	−	1.40498i
$364$		0			0
$365$		0			0
$366$	21.0000	+	12.1244i	1.09769	+	0.633750i
$367$	−14.6969	−	14.6969i	−0.767174	−	0.767174i	0.210434	−	0.977608i	$-0.432512\pi$
$367$	−14.6969	−	14.6969i	−0.767174	−	0.767174i	−0.977608	+	0.210434i	$0.932512\pi$
$368$	4.24264	+	4.24264i	0.221163	+	0.221163i
$369$	−7.79423	−	13.5000i	−0.405751	−	0.702782i
$370$		0			0
$371$			20.7846i			1.07908i
$372$	−3.34607	+	0.896575i	−0.173485	+	0.0464853i
$373$	2.44949	−	2.44949i	0.126830	−	0.126830i	−0.640843	−	0.767672i	$-0.721415\pi$
$373$	2.44949	−	2.44949i	0.126830	−	0.126830i	0.767672	+	0.640843i	$0.221415\pi$
$374$	15.5885			0.806060
$375$		0			0
$376$		0			0
$377$		0			0
$378$	−12.7279	−	12.7279i	−0.654654	−	0.654654i
$379$			11.0000i			0.565032i	0.959263	+	0.282516i	$0.0911690\pi$
$379$			11.0000i			0.565032i	−0.959263	+	0.282516i	$0.908831\pi$
$380$		0			0
$381$	9.00000	−	15.5885i	0.461084	−	0.798621i
$382$	−7.34847	−	7.34847i	−0.375980	−	0.375980i
$383$	4.24264	+	4.24264i	0.216789	+	0.216789i	0.807144	−	0.590355i	$-0.201012\pi$
$383$	4.24264	+	4.24264i	0.216789	+	0.216789i	−0.590355	+	0.807144i	$0.701012\pi$
$384$	−0.866025	+	1.50000i	−0.0441942	+	0.0765466i
$385$		0			0
$386$			8.66025i			0.440795i
$387$	2.68973	−	10.0382i	0.136726	−	0.510270i
$388$	4.89898	−	4.89898i	0.248708	−	0.248708i
$389$	−10.3923			−0.526911			−0.263455	−	0.964672i	$-0.584862\pi$
$389$	−10.3923			−0.526911			−0.263455	+	0.964672i	$0.584862\pi$
$390$		0			0
$391$	18.0000			0.910299
$392$	3.53553	−	3.53553i	0.178571	−	0.178571i
$393$	−17.3867	+	4.65874i	−0.877041	+	0.235002i
$394$			6.00000i			0.302276i
$395$		0			0
$396$	13.5000	−	7.79423i	0.678401	−	0.391675i
$397$	19.5959	+	19.5959i	0.983491	+	0.983491i	0.999866	−	0.0163750i	$-0.00521255\pi$
$397$	19.5959	+	19.5959i	0.983491	+	0.983491i	−0.0163750	+	0.999866i	$0.505213\pi$
$398$	11.3137	+	11.3137i	0.567105	+	0.567105i
$399$	5.19615	+	3.00000i	0.260133	+	0.150188i
$400$		0			0
$401$		−	5.19615i		−	0.259483i	−0.991548	−	0.129742i	$-0.958585\pi$
$401$		−	5.19615i		−	0.259483i	0.991548	−	0.129742i	$-0.0414148\pi$
$402$	2.32937	+	8.69333i	0.116178	+	0.433584i
$403$		0			0
$404$	10.3923			0.517036
$405$		0			0
$406$		0			0
$407$	−12.7279	+	12.7279i	−0.630900	+	0.630900i
$408$	1.34486	+	5.01910i	0.0665807	+	0.248482i
$409$			5.00000i			0.247234i	0.992330	+	0.123617i	$0.0394494\pi$
$409$			5.00000i			0.247234i	−0.992330	+	0.123617i	$0.960551\pi$
$410$		0			0
$411$	−31.5000	−	18.1865i	−1.55378	−	0.897076i
$412$	−9.79796	−	9.79796i	−0.482711	−	0.482711i
$413$	25.4558	+	25.4558i	1.25260	+	1.25260i
$414$	15.5885	−	9.00000i	0.766131	−	0.442326i
$415$		0			0
$416$		0			0
$417$	11.7112	−	3.13801i	0.573501	−	0.153669i
$418$	−3.67423	+	3.67423i	−0.179713	+	0.179713i
$419$	−25.9808			−1.26924			−0.634622	−	0.772823i	$-0.718844\pi$
$419$	−25.9808			−1.26924			−0.634622	+	0.772823i	$0.718844\pi$
$420$		0			0
$421$	4.00000			0.194948			0.0974740	−	0.995238i	$-0.468924\pi$
$421$	4.00000			0.194948			0.0974740	+	0.995238i	$0.468924\pi$
$422$	16.2635	−	16.2635i	0.791693	−	0.791693i
$423$		0			0
$424$		−	6.00000i		−	0.291386i
$425$		0			0
$426$		0			0
$427$	34.2929	+	34.2929i	1.65955	+	1.65955i
$428$	6.36396	+	6.36396i	0.307614	+	0.307614i
$429$		0			0
$430$		0			0
$431$		−	10.3923i		−	0.500580i	−0.968171	−	0.250290i	$-0.919474\pi$
$431$		−	10.3923i		−	0.500580i	0.968171	−	0.250290i	$-0.0805259\pi$
$432$	3.67423	+	3.67423i	0.176777	+	0.176777i
$433$	−15.9217	+	15.9217i	−0.765147	+	0.765147i	−0.977248	−	0.212101i	$-0.931970\pi$
$433$	−15.9217	+	15.9217i	−0.765147	+	0.765147i	0.212101	+	0.977248i	$0.431970\pi$
$434$	−6.92820			−0.332564
$435$		0			0
$436$	10.0000			0.478913
$437$	−4.24264	+	4.24264i	−0.202953	+	0.202953i
$438$	−14.4889	+	3.88229i	−0.692306	+	0.185503i
$439$			4.00000i			0.190910i	0.995434	+	0.0954548i	$0.0304305\pi$
$439$			4.00000i			0.190910i	−0.995434	+	0.0954548i	$0.969569\pi$
$440$		0			0
$441$	−7.50000	−	12.9904i	−0.357143	−	0.618590i
$442$		0			0
$443$	−14.8492	−	14.8492i	−0.705509	−	0.705509i	0.260079	−	0.965587i	$-0.416252\pi$
$443$	−14.8492	−	14.8492i	−0.705509	−	0.705509i	−0.965587	+	0.260079i	$0.916252\pi$
$444$	−5.19615	−	3.00000i	−0.246598	−	0.142374i
$445$		0			0
$446$		−	13.8564i		−	0.656120i
$447$	9.31749	+	34.7733i	0.440702	+	1.64472i
$448$	−2.44949	+	2.44949i	−0.115728	+	0.115728i
$449$	−25.9808			−1.22611			−0.613054	−	0.790041i	$-0.710059\pi$
$449$	−25.9808			−1.22611			−0.613054	+	0.790041i	$0.710059\pi$
$450$		0			0
$451$	27.0000			1.27138
$452$	6.36396	−	6.36396i	0.299336	−	0.299336i
$453$	−6.27603	−	23.4225i	−0.294874	−	1.10048i
$454$		−	12.0000i		−	0.563188i
$455$		0			0
$456$	−1.50000	−	0.866025i	−0.0702439	−	0.0405554i
$457$	18.3712	+	18.3712i	0.859367	+	0.859367i	0.991264	−	0.131896i	$-0.0421066\pi$
$457$	18.3712	+	18.3712i	0.859367	+	0.859367i	−0.131896	+	0.991264i	$0.542107\pi$
$458$	−11.3137	−	11.3137i	−0.528655	−	0.528655i
$459$	15.5885			0.727607
$460$		0			0
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$	30.1146	−	8.06918i	1.40106	−	0.375412i
$463$	−24.4949	+	24.4949i	−1.13837	+	1.13837i	−0.149633	+	0.988742i	$0.547809\pi$
$463$	−24.4949	+	24.4949i	−1.13837	+	1.13837i	−0.988742	+	0.149633i	$0.952191\pi$
$464$		0			0
$465$		0			0
$466$	−18.0000			−0.833834
$467$	8.48528	−	8.48528i	0.392652	−	0.392652i	−0.482980	−	0.875632i	$-0.660445\pi$
$467$	8.48528	−	8.48528i	0.392652	−	0.392652i	0.875632	+	0.482980i	$0.160445\pi$
$468$		0			0
$469$			18.0000i			0.831163i
$470$		0			0
$471$	15.0000	−	25.9808i	0.691164	−	1.19713i
$472$	−7.34847	−	7.34847i	−0.338241	−	0.338241i
$473$	12.7279	+	12.7279i	0.585230	+	0.585230i
$474$	12.1244	−	21.0000i	0.556890	−	0.964562i
$475$		0			0
$476$			10.3923i			0.476331i
$477$	−17.3867	−	4.65874i	−0.796081	−	0.213309i
$478$	14.6969	−	14.6969i	0.672222	−	0.672222i
$479$	10.3923			0.474837			0.237418	−	0.971408i	$-0.423699\pi$
$479$	10.3923			0.474837			0.237418	+	0.971408i	$0.423699\pi$
$480$		0			0
$481$		0			0
$482$	−0.707107	+	0.707107i	−0.0322078	+	0.0322078i
$483$	34.7733	−	9.31749i	1.58224	−	0.423960i
$484$			16.0000i			0.727273i
$485$		0			0
$486$	13.5000	−	7.79423i	0.612372	−	0.353553i
$487$	−22.0454	−	22.0454i	−0.998973	−	0.998973i	0.00102669	−	0.999999i	$-0.499673\pi$
$487$	−22.0454	−	22.0454i	−0.998973	−	0.998973i	−0.999999	+	0.00102669i	$0.999673\pi$
$488$	−9.89949	−	9.89949i	−0.448129	−	0.448129i
$489$	7.79423	+	4.50000i	0.352467	+	0.203497i
$490$		0			0
$491$		−	31.1769i		−	1.40699i	−0.710698	−	0.703497i	$-0.751621\pi$
$491$		−	31.1769i		−	1.40699i	0.710698	−	0.703497i	$-0.248379\pi$
$492$	2.32937	+	8.69333i	0.105016	+	0.391926i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	2.00000			0.0898027
$497$		0			0
$498$	1.34486	+	5.01910i	0.0602648	+	0.224911i
$499$		−	20.0000i		−	0.895323i	−0.894203	−	0.447661i	$-0.852257\pi$
$499$		−	20.0000i		−	0.895323i	0.894203	−	0.447661i	$-0.147743\pi$
$500$		0			0
$501$	18.0000	+	10.3923i	0.804181	+	0.464294i
$502$	−3.67423	−	3.67423i	−0.163989	−	0.163989i
$503$	8.48528	+	8.48528i	0.378340	+	0.378340i	0.870503	−	0.492163i	$-0.163794\pi$
$503$	8.48528	+	8.48528i	0.378340	+	0.378340i	−0.492163	+	0.870503i	$0.663794\pi$
$504$	5.19615	+	9.00000i	0.231455	+	0.400892i
$505$		0			0
$506$			31.1769i			1.38598i
$507$	−21.7494	+	5.82774i	−0.965926	+	0.258819i
$508$	−7.34847	+	7.34847i	−0.326036	+	0.326036i
$509$	−10.3923			−0.460631			−0.230315	−	0.973116i	$-0.573976\pi$
$509$	−10.3923			−0.460631			−0.230315	+	0.973116i	$0.573976\pi$
$510$		0			0
$511$	−30.0000			−1.32712
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−3.67423	+	3.67423i	−0.162221	+	0.162221i
$514$		−	6.00000i		−	0.264649i
$515$		0			0
$516$	−3.00000	+	5.19615i	−0.132068	+	0.228748i
$517$		0			0
$518$	−8.48528	−	8.48528i	−0.372822	−	0.372822i
$519$	10.3923	−	18.0000i	0.456172	−	0.790112i
$520$		0			0
$521$			36.3731i			1.59353i	0.604287	+	0.796766i	$0.293458\pi$
$521$			36.3731i			1.59353i	−0.604287	+	0.796766i	$0.706542\pi$
$522$		0			0
$523$	−30.6186	+	30.6186i	−1.33886	+	1.33886i	−0.441692	+	0.897167i	$0.645622\pi$
$523$	−30.6186	+	30.6186i	−1.33886	+	1.33886i	−0.897167	+	0.441692i	$0.854378\pi$
$524$	10.3923			0.453990
$525$		0			0
$526$	18.0000			0.784837
$527$	4.24264	−	4.24264i	0.184812	−	0.184812i
$528$	−8.69333	+	2.32937i	−0.378329	+	0.101373i
$529$			13.0000i			0.565217i
$530$		0			0
$531$	−27.0000	+	15.5885i	−1.17170	+	0.676481i
$532$	−2.44949	−	2.44949i	−0.106199	−	0.106199i
$533$		0			0
$534$	−23.3827	−	13.5000i	−1.01187	−	0.584202i
$535$		0			0
$536$		−	5.19615i		−	0.224440i
$537$	−6.98811	−	26.0800i	−0.301559	−	1.12543i
$538$	14.6969	−	14.6969i	0.633630	−	0.633630i
$539$	25.9808			1.11907
$540$		0			0
$541$	8.00000			0.343947			0.171973	−	0.985102i	$-0.444986\pi$
$541$	8.00000			0.343947			0.171973	+	0.985102i	$0.444986\pi$
$542$	−7.07107	+	7.07107i	−0.303728	+	0.303728i
$543$	−0.896575	−	3.34607i	−0.0384757	−	0.143593i
$544$		−	3.00000i		−	0.128624i
$545$		0			0
$546$		0			0
$547$	−8.57321	−	8.57321i	−0.366564	−	0.366564i	0.499658	−	0.866223i	$-0.333459\pi$
$547$	−8.57321	−	8.57321i	−0.366564	−	0.366564i	−0.866223	+	0.499658i	$0.833459\pi$
$548$	14.8492	+	14.8492i	0.634328	+	0.634328i
$549$	−36.3731	+	21.0000i	−1.55236	+	0.896258i
$550$		0			0
$551$		0			0
$552$	−10.0382	+	2.68973i	−0.427254	+	0.114482i
$553$	34.2929	−	34.2929i	1.45828	−	1.45828i
$554$	−13.8564			−0.588702
$555$		0			0
$556$	−7.00000			−0.296866
$557$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$557$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$558$	1.55291	−	5.79555i	0.0657401	−	0.245345i
$559$		0			0
$560$		0			0
$561$	−13.5000	+	23.3827i	−0.569970	+	0.987218i
$562$	−14.6969	−	14.6969i	−0.619953	−	0.619953i
$563$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$563$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$564$		0			0
$565$		0			0
$566$		−	8.66025i		−	0.364018i
$567$	30.1146	−	8.06918i	1.26469	−	0.338874i
$568$		0			0
$569$	25.9808			1.08917			0.544585	−	0.838706i	$-0.316687\pi$
$569$	25.9808			1.08917			0.544585	+	0.838706i	$0.316687\pi$
$570$		0			0
$571$	20.0000			0.836974			0.418487	−	0.908223i	$-0.362561\pi$
$571$	20.0000			0.836974			0.418487	+	0.908223i	$0.362561\pi$
$572$		0			0
$573$	17.3867	−	4.65874i	0.726338	−	0.194622i
$574$			18.0000i			0.751305i
$575$		0			0
$576$	−1.50000	−	2.59808i	−0.0625000	−	0.108253i
$577$	−13.4722	−	13.4722i	−0.560855	−	0.560855i	0.368695	−	0.929550i	$-0.379805\pi$
$577$	−13.4722	−	13.4722i	−0.560855	−	0.560855i	−0.929550	+	0.368695i	$0.879805\pi$
$578$	5.65685	+	5.65685i	0.235294	+	0.235294i
$579$	−12.9904	−	7.50000i	−0.539862	−	0.311689i
$580$		0			0
$581$			10.3923i			0.431145i
$582$	3.10583	+	11.5911i	0.128741	+	0.480467i
$583$	22.0454	−	22.0454i	0.913027	−	0.913027i
$584$	8.66025			0.358364
$585$		0			0
$586$	−30.0000			−1.23929
$587$	−14.8492	+	14.8492i	−0.612894	+	0.612894i	−0.943699	−	0.330805i	$-0.892680\pi$
$587$	−14.8492	+	14.8492i	−0.612894	+	0.612894i	0.330805	+	0.943699i	$0.392680\pi$
$588$	2.24144	+	8.36516i	0.0924354	+	0.344974i
$589$			2.00000i			0.0824086i
$590$		0			0
$591$	−9.00000	−	5.19615i	−0.370211	−	0.213741i
$592$	2.44949	+	2.44949i	0.100673	+	0.100673i
$593$	−23.3345	−	23.3345i	−0.958234	−	0.958234i	0.0409281	−	0.999162i	$-0.486969\pi$
$593$	−23.3345	−	23.3345i	−0.958234	−	0.958234i	−0.999162	+	0.0409281i	$0.986969\pi$
$594$			27.0000i			1.10782i
$595$		0			0
$596$		−	20.7846i		−	0.851371i
$597$	−26.7685	+	7.17260i	−1.09556	+	0.293555i
$598$		0			0
$599$	−10.3923			−0.424618			−0.212309	−	0.977203i	$-0.568098\pi$
$599$	−10.3923			−0.424618			−0.212309	+	0.977203i	$0.568098\pi$
$600$		0			0
$601$	−5.00000			−0.203954			−0.101977	−	0.994787i	$-0.532517\pi$
$601$	−5.00000			−0.203954			−0.101977	+	0.994787i	$0.532517\pi$
$602$	−8.48528	+	8.48528i	−0.345834	+	0.345834i
$603$	−15.0573	−	4.03459i	−0.613180	−	0.164301i
$604$			14.0000i			0.569652i
$605$		0			0
$606$	−9.00000	+	15.5885i	−0.365600	+	0.633238i
$607$	4.89898	+	4.89898i	0.198843	+	0.198843i	0.799504	−	0.600661i	$-0.205096\pi$
$607$	4.89898	+	4.89898i	0.198843	+	0.198843i	−0.600661	+	0.799504i	$0.705096\pi$
$608$	0.707107	+	0.707107i	0.0286770	+	0.0286770i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−8.69333	−	2.32937i	−0.351407	−	0.0941593i
$613$	17.1464	−	17.1464i	0.692538	−	0.692538i	−0.270252	−	0.962790i	$-0.587107\pi$
$613$	17.1464	−	17.1464i	0.692538	−	0.692538i	0.962790	+	0.270252i	$0.0871070\pi$
$614$	−1.73205			−0.0698999
$615$		0			0
$616$	−18.0000			−0.725241
$617$	−21.2132	+	21.2132i	−0.854011	+	0.854011i	−0.990624	−	0.136613i	$-0.956378\pi$
$617$	−21.2132	+	21.2132i	−0.854011	+	0.854011i	0.136613	+	0.990624i	$0.456378\pi$
$618$	23.1822	−	6.21166i	0.932526	−	0.249869i
$619$			4.00000i			0.160774i	0.996764	+	0.0803868i	$0.0256155\pi$
$619$			4.00000i			0.160774i	−0.996764	+	0.0803868i	$0.974384\pi$
$620$		0			0
$621$			31.1769i			1.25109i
$622$	22.0454	+	22.0454i	0.883940	+	0.883940i
$623$	−38.1838	−	38.1838i	−1.52980	−	1.52980i
$624$		0			0
$625$		0			0
$626$		−	20.7846i		−	0.830720i
$627$	−2.32937	−	8.69333i	−0.0930261	−	0.347178i
$628$	−12.2474	+	12.2474i	−0.488726	+	0.488726i
$629$	10.3923			0.414368
$630$		0			0
$631$	−34.0000			−1.35352			−0.676759	−	0.736204i	$-0.736616\pi$
$631$	−34.0000			−1.35352			−0.676759	+	0.736204i	$0.736616\pi$
$632$	−9.89949	+	9.89949i	−0.393781	+	0.393781i
$633$	10.3106	+	38.4797i	0.409810	+	1.52943i
$634$		−	12.0000i		−	0.476581i
$635$		0			0
$636$	9.00000	+	5.19615i	0.356873	+	0.206041i
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$			20.7846i			0.820943i	0.911873	+	0.410471i	$0.134636\pi$
$641$			20.7846i			0.820943i	−0.911873	+	0.410471i	$0.865364\pi$
$642$	−15.0573	+	4.03459i	−0.594264	+	0.159233i
$643$	−22.0454	+	22.0454i	−0.869386	+	0.869386i	−0.992404	−	0.123018i	$-0.960743\pi$
$643$	−22.0454	+	22.0454i	−0.869386	+	0.869386i	0.123018	+	0.992404i	$0.460743\pi$
$644$	−20.7846			−0.819028
$645$		0			0
$646$	3.00000			0.118033
$647$	33.9411	−	33.9411i	1.33436	−	1.33436i	0.432941	−	0.901422i	$-0.357476\pi$
$647$	33.9411	−	33.9411i	1.33436	−	1.33436i	0.901422	−	0.432941i	$-0.142524\pi$
$648$	−8.69333	+	2.32937i	−0.341506	+	0.0915064i
$649$		−	54.0000i		−	2.11969i
$650$		0			0
$651$	6.00000	−	10.3923i	0.235159	−	0.407307i
$652$	−3.67423	−	3.67423i	−0.143894	−	0.143894i
$653$	4.24264	+	4.24264i	0.166027	+	0.166027i	0.785231	−	0.619203i	$-0.212544\pi$
$653$	4.24264	+	4.24264i	0.166027	+	0.166027i	−0.619203	+	0.785231i	$0.712544\pi$
$654$	−8.66025	+	15.0000i	−0.338643	+	0.586546i
$655$		0			0
$656$		−	5.19615i		−	0.202876i
$657$	6.72432	−	25.0955i	0.262341	−	0.979068i
$658$		0			0
$659$	25.9808			1.01207			0.506033	−	0.862514i	$-0.331111\pi$
$659$	25.9808			1.01207			0.506033	+	0.862514i	$0.331111\pi$
$660$		0			0
$661$	−20.0000			−0.777910			−0.388955	−	0.921257i	$-0.627164\pi$
$661$	−20.0000			−0.777910			−0.388955	+	0.921257i	$0.627164\pi$
$662$	−9.19239	+	9.19239i	−0.357272	+	0.357272i
$663$		0			0
$664$		−	3.00000i		−	0.116423i
$665$		0			0
$666$	9.00000	−	5.19615i	0.348743	−	0.201347i
$667$		0			0
$668$	−8.48528	−	8.48528i	−0.328305	−	0.328305i
$669$	20.7846	+	12.0000i	0.803579	+	0.463947i
$670$		0			0
$671$		−	72.7461i		−	2.80833i
$672$	−1.55291	−	5.79555i	−0.0599050	−	0.223568i
$673$	4.89898	−	4.89898i	0.188842	−	0.188842i	−0.606353	−	0.795195i	$-0.707368\pi$
$673$	4.89898	−	4.89898i	0.188842	−	0.188842i	0.795195	+	0.606353i	$0.207368\pi$
$674$	5.19615			0.200148
$675$		0			0
$676$	13.0000			0.500000
$677$	25.4558	−	25.4558i	0.978348	−	0.978348i	−0.0214229	−	0.999771i	$-0.506820\pi$
$677$	25.4558	−	25.4558i	0.978348	−	0.978348i	0.999771	+	0.0214229i	$0.00681965\pi$
$678$	4.03459	+	15.0573i	0.154947	+	0.578272i
$679$			24.0000i			0.921035i
$680$		0			0
$681$	18.0000	+	10.3923i	0.689761	+	0.398234i
$682$	7.34847	+	7.34847i	0.281387	+	0.281387i
$683$	−14.8492	−	14.8492i	−0.568190	−	0.568190i	0.363431	−	0.931621i	$-0.381605\pi$
$683$	−14.8492	−	14.8492i	−0.568190	−	0.568190i	−0.931621	+	0.363431i	$0.881605\pi$
$684$	2.59808	−	1.50000i	0.0993399	−	0.0573539i
$685$		0			0
$686$		−	6.92820i		−	0.264520i
$687$	26.7685	−	7.17260i	1.02128	−	0.273652i
$688$	2.44949	−	2.44949i	0.0933859	−	0.0933859i
$689$		0			0
$690$		0			0
$691$	37.0000			1.40755			0.703773	−	0.710425i	$-0.251497\pi$
$691$	37.0000			1.40755			0.703773	+	0.710425i	$0.251497\pi$
$692$	−8.48528	+	8.48528i	−0.322562	+	0.322562i
$693$	−13.9762	+	52.1600i	−0.530913	+	1.98139i
$694$		−	9.00000i		−	0.341635i
$695$		0			0
$696$		0			0
$697$	−11.0227	−	11.0227i	−0.417515	−	0.417515i
$698$	−15.5563	−	15.5563i	−0.588817	−	0.588817i
$699$	15.5885	−	27.0000i	0.589610	−	1.02123i
$700$		0			0
$701$		−	20.7846i		−	0.785024i	−0.919747	−	0.392512i	$-0.871606\pi$
$701$		−	20.7846i		−	0.785024i	0.919747	−	0.392512i	$-0.128394\pi$
$702$		0			0
$703$	−2.44949	+	2.44949i	−0.0923843	+	0.0923843i
$704$	5.19615			0.195837
$705$		0			0
$706$	18.0000			0.677439
$707$	−25.4558	+	25.4558i	−0.957366	+	0.957366i
$708$	17.3867	−	4.65874i	0.653431	−	0.175086i
$709$		−	40.0000i		−	1.50223i	−0.660171	−	0.751116i	$-0.729516\pi$
$709$		−	40.0000i		−	1.50223i	0.660171	−	0.751116i	$-0.270484\pi$
$710$		0			0
$711$	21.0000	+	36.3731i	0.787562	+	1.36410i
$712$	11.0227	+	11.0227i	0.413093	+	0.413093i
$713$	8.48528	+	8.48528i	0.317776	+	0.317776i
$714$	−15.5885	−	9.00000i	−0.583383	−	0.336817i
$715$		0			0
$716$			15.5885i			0.582568i
$717$	9.31749	+	34.7733i	0.347968	+	1.29863i
$718$	−7.34847	+	7.34847i	−0.274242	+	0.274242i
$719$	31.1769			1.16270			0.581351	−	0.813653i	$-0.302524\pi$
$719$	31.1769			1.16270			0.581351	+	0.813653i	$0.302524\pi$
$720$		0			0
$721$	48.0000			1.78761
$722$	12.7279	−	12.7279i	0.473684	−	0.473684i
$723$	−0.448288	−	1.67303i	−0.0166720	−	0.0622208i
$724$			2.00000i			0.0743294i
$725$		0			0
$726$	−24.0000	−	13.8564i	−0.890724	−	0.514259i
$727$	−4.89898	−	4.89898i	−0.181693	−	0.181693i	0.610400	−	0.792093i	$-0.291009\pi$
$727$	−4.89898	−	4.89898i	−0.181693	−	0.181693i	−0.792093	+	0.610400i	$0.791009\pi$
$728$		0			0
$729$			27.0000i			1.00000i
$730$		0			0
$731$		−	10.3923i		−	0.384373i
$732$	23.4225	−	6.27603i	0.865719	−	0.231969i
$733$	14.6969	−	14.6969i	0.542844	−	0.542844i	−0.381518	−	0.924362i	$-0.624598\pi$
$733$	14.6969	−	14.6969i	0.542844	−	0.542844i	0.924362	+	0.381518i	$0.124598\pi$
$734$	−20.7846			−0.767174
$735$		0			0
$736$	6.00000			0.221163
$737$	19.0919	−	19.0919i	0.703259	−	0.703259i
$738$	−15.0573	−	4.03459i	−0.554267	−	0.148515i
$739$			20.0000i			0.735712i	0.929883	+	0.367856i	$0.119908\pi$
$739$			20.0000i			0.735712i	−0.929883	+	0.367856i	$0.880092\pi$
$740$		0			0
$741$		0			0
$742$	14.6969	+	14.6969i	0.539542	+	0.539542i
$743$	12.7279	+	12.7279i	0.466942	+	0.466942i	0.900922	−	0.433980i	$-0.142891\pi$
$743$	12.7279	+	12.7279i	0.466942	+	0.466942i	−0.433980	+	0.900922i	$0.642891\pi$
$744$	−1.73205	+	3.00000i	−0.0635001	+	0.109985i
$745$		0			0
$746$		−	3.46410i		−	0.126830i
$747$	−8.69333	−	2.32937i	−0.318072	−	0.0852272i
$748$	11.0227	−	11.0227i	0.403030	−	0.403030i
$749$	−31.1769			−1.13918
$750$		0			0
$751$	−20.0000			−0.729810			−0.364905	−	0.931045i	$-0.618899\pi$
$751$	−20.0000			−0.729810			−0.364905	+	0.931045i	$0.618899\pi$
$752$		0			0
$753$	8.69333	−	2.32937i	0.316803	−	0.0848870i
$754$		0			0
$755$		0			0
$756$	−18.0000			−0.654654
$757$	24.4949	+	24.4949i	0.890282	+	0.890282i	0.994549	−	0.104267i	$-0.0332497\pi$
$757$	24.4949	+	24.4949i	0.890282	+	0.890282i	−0.104267	+	0.994549i	$0.533250\pi$
$758$	7.77817	+	7.77817i	0.282516	+	0.282516i
$759$	−46.7654	−	27.0000i	−1.69748	−	0.980038i
$760$		0			0
$761$			5.19615i			0.188360i	0.995555	+	0.0941802i	$0.0300230\pi$
$761$			5.19615i			0.188360i	−0.995555	+	0.0941802i	$0.969977\pi$
$762$	−4.65874	−	17.3867i	−0.168768	−	0.629852i
$763$	−24.4949	+	24.4949i	−0.886775	+	0.886775i
$764$	−10.3923			−0.375980
$765$		0			0
$766$	6.00000			0.216789
$767$		0			0
$768$	0.448288	+	1.67303i	0.0161762	+	0.0603704i
$769$			13.0000i			0.468792i	0.972141	+	0.234396i	$0.0753112\pi$
$769$			13.0000i			0.468792i	−0.972141	+	0.234396i	$0.924689\pi$
$770$		0			0
$771$	9.00000	+	5.19615i	0.324127	+	0.187135i
$772$	6.12372	+	6.12372i	0.220398	+	0.220398i
$773$	8.48528	+	8.48528i	0.305194	+	0.305194i	0.843042	−	0.537848i	$-0.180762\pi$
$773$	8.48528	+	8.48528i	0.305194	+	0.305194i	−0.537848	+	0.843042i	$0.680762\pi$
$774$	−5.19615	−	9.00000i	−0.186772	−	0.323498i
$775$		0			0
$776$		−	6.92820i		−	0.248708i
$777$	20.0764	−	5.37945i	0.720237	−	0.192987i
$778$	−7.34847	+	7.34847i	−0.263455	+	0.263455i
$779$	5.19615			0.186171
$780$		0			0
$781$		0			0
$782$	12.7279	−	12.7279i	0.455150	−	0.455150i
$783$		0			0
$784$		−	5.00000i		−	0.178571i
$785$		0			0
$786$	−9.00000	+	15.5885i	−0.321019	+	0.556022i
$787$	17.1464	+	17.1464i	0.611204	+	0.611204i	0.943260	−	0.332056i	$-0.107742\pi$
$787$	17.1464	+	17.1464i	0.611204	+	0.611204i	−0.332056	+	0.943260i	$0.607742\pi$
$788$	4.24264	+	4.24264i	0.151138	+	0.151138i
$789$	−15.5885	+	27.0000i	−0.554964	+	0.961225i
$790$		0			0
$791$			31.1769i			1.10852i
$792$	4.03459	−	15.0573i	0.143363	−	0.535038i
$793$		0			0
$794$	27.7128			0.983491
$795$		0			0
$796$	16.0000			0.567105
$797$	−29.6985	+	29.6985i	−1.05197	+	1.05197i	−0.0534012	+	0.998573i	$0.517006\pi$
$797$	−29.6985	+	29.6985i	−1.05197	+	1.05197i	−0.998573	+	0.0534012i	$0.982994\pi$
$798$	5.79555	−	1.55291i	0.205160	−	0.0549726i
$799$		0			0
$800$		0			0
$801$	40.5000	−	23.3827i	1.43100	−	0.826187i
$802$	−3.67423	−	3.67423i	−0.129742	−	0.129742i
$803$	31.8198	+	31.8198i	1.12290	+	1.12290i
$804$	7.79423	+	4.50000i	0.274881	+	0.158703i
$805$		0			0
$806$		0			0
$807$	9.31749	+	34.7733i	0.327991	+	1.22408i
$808$	7.34847	−	7.34847i	0.258518	−	0.258518i
$809$	20.7846			0.730748			0.365374	−	0.930861i	$-0.380941\pi$
$809$	20.7846			0.730748			0.365374	+	0.930861i	$0.380941\pi$
$810$		0			0
$811$	−44.0000			−1.54505			−0.772524	−	0.634985i	$-0.781006\pi$
$811$	−44.0000			−1.54505			−0.772524	+	0.634985i	$0.781006\pi$
$812$		0			0
$813$	−4.48288	−	16.7303i	−0.157221	−	0.586758i
$814$			18.0000i			0.630900i
$815$		0			0
$816$	4.50000	+	2.59808i	0.157532	+	0.0909509i
$817$	2.44949	+	2.44949i	0.0856968	+	0.0856968i
$818$	3.53553	+	3.53553i	0.123617	+	0.123617i
$819$		0			0
$820$		0			0
$821$		−	31.1769i		−	1.08808i	−0.839059	−	0.544041i	$-0.816894\pi$
$821$		−	31.1769i		−	1.08808i	0.839059	−	0.544041i	$-0.183106\pi$
$822$	−35.1337	+	9.41404i	−1.22543	+	0.328352i
$823$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$823$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$824$	−13.8564			−0.482711
$825$		0			0
$826$	36.0000			1.25260
$827$	−2.12132	+	2.12132i	−0.0737655	+	0.0737655i	−0.743027	−	0.669261i	$-0.766611\pi$
$827$	−2.12132	+	2.12132i	−0.0737655	+	0.0737655i	0.669261	+	0.743027i	$0.266611\pi$
$828$	4.65874	−	17.3867i	0.161903	−	0.604228i
$829$			44.0000i			1.52818i	0.645108	+	0.764092i	$0.276812\pi$
$829$			44.0000i			1.52818i	−0.645108	+	0.764092i	$0.723188\pi$
$830$		0			0
$831$	12.0000	−	20.7846i	0.416275	−	0.721010i
$832$		0			0
$833$	−10.6066	−	10.6066i	−0.367497	−	0.367497i
$834$	6.06218	−	10.5000i	0.209916	−	0.363585i
$835$		0			0
$836$			5.19615i			0.179713i
$837$	7.34847	+	7.34847i	0.254000	+	0.254000i
$838$	−18.3712	+	18.3712i	−0.634622	+	0.634622i
$839$	−20.7846			−0.717564			−0.358782	−	0.933421i	$-0.616808\pi$
$839$	−20.7846			−0.717564			−0.358782	+	0.933421i	$0.616808\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$	2.82843	−	2.82843i	0.0974740	−	0.0974740i
$843$	34.7733	−	9.31749i	1.19766	−	0.320911i
$844$		−	23.0000i		−	0.791693i
$845$		0			0
$846$		0			0
$847$	−39.1918	−	39.1918i	−1.34665	−	1.34665i
$848$	−4.24264	−	4.24264i	−0.145693	−	0.145693i
$849$	12.9904	+	7.50000i	0.445829	+	0.257399i
$850$		0			0
$851$			20.7846i			0.712487i
$852$		0			0
$853$	−7.34847	+	7.34847i	−0.251607	+	0.251607i	−0.821629	−	0.570022i	$-0.806935\pi$
$853$	−7.34847	+	7.34847i	−0.251607	+	0.251607i	0.570022	+	0.821629i	$0.306935\pi$
$854$	48.4974			1.65955
$855$		0			0
$856$	9.00000			0.307614
$857$	36.0624	−	36.0624i	1.23187	−	1.23187i	0.268625	−	0.963245i	$-0.413431\pi$
$857$	36.0624	−	36.0624i	1.23187	−	1.23187i	0.963245	−	0.268625i	$-0.0865692\pi$
$858$		0			0
$859$			7.00000i			0.238837i	0.992844	+	0.119418i	$0.0381030\pi$
$859$			7.00000i			0.238837i	−0.992844	+	0.119418i	$0.961897\pi$
$860$		0			0
$861$	−27.0000	−	15.5885i	−0.920158	−	0.531253i
$862$	−7.34847	−	7.34847i	−0.250290	−	0.250290i
$863$	−33.9411	−	33.9411i	−1.15537	−	1.15537i	−0.985460	−	0.169910i	$-0.945652\pi$
$863$	−33.9411	−	33.9411i	−1.15537	−	1.15537i	−0.169910	−	0.985460i	$-0.554348\pi$
$864$	5.19615			0.176777
$865$		0			0
$866$			22.5167i			0.765147i
$867$	−13.3843	+	3.58630i	−0.454553	+	0.121797i
$868$	−4.89898	+	4.89898i	−0.166282	+	0.166282i
$869$	−72.7461			−2.46774
$870$		0			0
$871$		0			0
$872$	7.07107	−	7.07107i	0.239457	−	0.239457i
$873$	−20.0764	−	5.37945i	−0.679483	−	0.182067i
$874$			6.00000i			0.202953i
$875$		0			0
$876$	−7.50000	+	12.9904i	−0.253402	+	0.438904i
$877$	−34.2929	−	34.2929i	−1.15799	−	1.15799i	−0.984908	−	0.173080i	$-0.944628\pi$
$877$	−34.2929	−	34.2929i	−1.15799	−	1.15799i	−0.173080	−	0.984908i	$-0.555372\pi$
$878$	2.82843	+	2.82843i	0.0954548	+	0.0954548i
$879$	25.9808	−	45.0000i	0.876309	−	1.51781i
$880$		0			0
$881$			20.7846i			0.700251i	0.936703	+	0.350126i	$0.113861\pi$
$881$			20.7846i			0.700251i	−0.936703	+	0.350126i	$0.886139\pi$
$882$	−14.4889	−	3.88229i	−0.487866	−	0.130723i
$883$	20.8207	−	20.8207i	0.700671	−	0.700671i	−0.263883	−	0.964555i	$-0.585003\pi$
$883$	20.8207	−	20.8207i	0.700671	−	0.700671i	0.964555	+	0.263883i	$0.0850034\pi$
$884$		0			0
$885$		0			0
$886$	−21.0000			−0.705509
$887$	−33.9411	+	33.9411i	−1.13963	+	1.13963i	−0.151115	+	0.988516i	$0.548286\pi$
$887$	−33.9411	+	33.9411i	−1.13963	+	1.13963i	−0.988516	+	0.151115i	$0.951714\pi$
$888$	−5.79555	+	1.55291i	−0.194486	+	0.0521124i
$889$		−	36.0000i		−	1.20740i
$890$		0			0
$891$	−40.5000	−	23.3827i	−1.35680	−	0.783349i
$892$	−9.79796	−	9.79796i	−0.328060	−	0.328060i
$893$		0			0
$894$	31.1769	+	18.0000i	1.04271	+	0.602010i
$895$		0			0
$896$			3.46410i			0.115728i
$897$		0			0
$898$	−18.3712	+	18.3712i	−0.613054	+	0.613054i
$899$		0			0
$900$		0			0
$901$	−18.0000			−0.599667
$902$	19.0919	−	19.0919i	0.635690	−	0.635690i
$903$	−5.37945	−	20.0764i	−0.179017	−	0.668100i
$904$		−	9.00000i		−	0.299336i
$905$		0			0
$906$	−21.0000	−	12.1244i	−0.697678	−	0.402805i
$907$	−17.1464	−	17.1464i	−0.569338	−	0.569338i	0.362605	−	0.931943i	$-0.381887\pi$
$907$	−17.1464	−	17.1464i	−0.569338	−	0.569338i	−0.931943	+	0.362605i	$0.881887\pi$
$908$	−8.48528	−	8.48528i	−0.281594	−	0.281594i
$909$	−15.5885	−	27.0000i	−0.517036	−	0.895533i
$910$		0			0
$911$			41.5692i			1.37725i	0.725118	+	0.688625i	$0.241785\pi$
$911$			41.5692i			1.37725i	−0.725118	+	0.688625i	$0.758215\pi$
$912$	−1.67303	+	0.448288i	−0.0553996	+	0.0148443i
$913$	11.0227	−	11.0227i	0.364798	−	0.364798i
$914$	25.9808			0.859367
$915$		0			0
$916$	−16.0000			−0.528655
$917$	−25.4558	+	25.4558i	−0.840626	+	0.840626i
$918$	11.0227	−	11.0227i	0.363803	−	0.363803i
$919$			26.0000i			0.857661i	0.903385	+	0.428830i	$0.141074\pi$
$919$			26.0000i			0.857661i	−0.903385	+	0.428830i	$0.858926\pi$
$920$		0			0
$921$	1.50000	−	2.59808i	0.0494267	−	0.0856095i
$922$		0			0
$923$		0			0
$924$	15.5885	−	27.0000i	0.512823	−	0.888235i
$925$		0			0
$926$			34.6410i			1.13837i
$927$	−10.7589	+	40.1528i	−0.353369	+	1.31879i
$928$		0			0
$929$	41.5692			1.36384			0.681921	−	0.731426i	$-0.261145\pi$
$929$	41.5692			1.36384			0.681921	+	0.731426i	$0.261145\pi$
$930$		0			0
$931$	5.00000			0.163868
$932$	−12.7279	+	12.7279i	−0.416917	+	0.416917i
$933$	−52.1600	+	13.9762i	−1.70764	+	0.457561i
$934$		−	12.0000i		−	0.392652i
$935$		0			0
$936$		0			0
$937$	6.12372	+	6.12372i	0.200053	+	0.200053i	0.800023	−	0.599970i	$-0.204821\pi$
$937$	6.12372	+	6.12372i	0.200053	+	0.200053i	−0.599970	+	0.800023i	$0.704821\pi$
$938$	12.7279	+	12.7279i	0.415581	+	0.415581i
$939$	31.1769	+	18.0000i	1.01742	+	0.587408i
$940$		0			0
$941$		−	20.7846i		−	0.677559i	−0.940866	−	0.338779i	$-0.889986\pi$
$941$		−	20.7846i		−	0.677559i	0.940866	−	0.338779i	$-0.110014\pi$
$942$	−7.76457	−	28.9778i	−0.252983	−	0.944147i
$943$	22.0454	−	22.0454i	0.717897	−	0.717897i
$944$	−10.3923			−0.338241
$945$		0			0
$946$	18.0000			0.585230
$947$	16.9706	−	16.9706i	0.551469	−	0.551469i	−0.375396	−	0.926865i	$-0.622493\pi$
$947$	16.9706	−	16.9706i	0.551469	−	0.551469i	0.926865	+	0.375396i	$0.122493\pi$
$948$	−6.27603	−	23.4225i	−0.203836	−	0.760726i
$949$		0			0
$950$		0			0
$951$	18.0000	+	10.3923i	0.583690	+	0.336994i
$952$	7.34847	+	7.34847i	0.238165	+	0.238165i
$953$	6.36396	+	6.36396i	0.206149	+	0.206149i	0.802628	−	0.596479i	$-0.203434\pi$
$953$	6.36396	+	6.36396i	0.206149	+	0.206149i	−0.596479	+	0.802628i	$0.703434\pi$
$954$	−15.5885	+	9.00000i	−0.504695	+	0.291386i
$955$		0			0
$956$		−	20.7846i		−	0.672222i
$957$		0			0
$958$	7.34847	−	7.34847i	0.237418	−	0.237418i
$959$	−72.7461			−2.34910
$960$		0			0
$961$	−27.0000			−0.870968
$962$		0			0
$963$	6.98811	−	26.0800i	0.225189	−	0.840416i
$964$			1.00000i			0.0322078i
$965$		0			0
$966$	18.0000	−	31.1769i	0.579141	−	1.00310i
$967$	−9.79796	−	9.79796i	−0.315081	−	0.315081i	0.531793	−	0.846874i	$-0.321518\pi$
$967$	−9.79796	−	9.79796i	−0.315081	−	0.315081i	−0.846874	+	0.531793i	$0.821518\pi$
$968$	11.3137	+	11.3137i	0.363636	+	0.363636i
$969$	−2.59808	+	4.50000i	−0.0834622	+	0.144561i
$970$		0			0
$971$			5.19615i			0.166752i	0.996518	+	0.0833762i	$0.0265703\pi$
$971$			5.19615i			0.166752i	−0.996518	+	0.0833762i	$0.973430\pi$
$972$	4.03459	−	15.0573i	0.129410	−	0.482963i
$973$	17.1464	−	17.1464i	0.549689	−	0.549689i
$974$	−31.1769			−0.998973
$975$		0			0
$976$	−14.0000			−0.448129
$977$	−6.36396	+	6.36396i	−0.203601	+	0.203601i	−0.801541	−	0.597940i	$-0.795986\pi$
$977$	−6.36396	+	6.36396i	−0.203601	+	0.203601i	0.597940	+	0.801541i	$0.295986\pi$
$978$	8.69333	−	2.32937i	0.277982	−	0.0744851i
$979$			81.0000i			2.58877i
$980$		0			0
$981$	−15.0000	−	25.9808i	−0.478913	−	0.829502i
$982$	−22.0454	−	22.0454i	−0.703497	−	0.703497i
$983$	21.2132	+	21.2132i	0.676596	+	0.676596i	0.959228	−	0.282632i	$-0.0912076\pi$
$983$	21.2132	+	21.2132i	0.676596	+	0.676596i	−0.282632	+	0.959228i	$0.591208\pi$
$984$	7.79423	+	4.50000i	0.248471	+	0.143455i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	20.7846			0.660912
$990$		0			0
$991$	−10.0000			−0.317660			−0.158830	−	0.987306i	$-0.550772\pi$
$991$	−10.0000			−0.317660			−0.158830	+	0.987306i	$0.550772\pi$
$992$	1.41421	−	1.41421i	0.0449013	−	0.0449013i
$993$	−5.82774	−	21.7494i	−0.184938	−	0.690197i
$994$		0			0
$995$		0			0
$996$	4.50000	+	2.59808i	0.142588	+	0.0823232i
$997$	44.0908	+	44.0908i	1.39637	+	1.39637i	0.810157	+	0.586214i	$0.199382\pi$
$997$	44.0908	+	44.0908i	1.39637	+	1.39637i	0.586214	+	0.810157i	$0.300618\pi$
$998$	−14.1421	−	14.1421i	−0.447661	−	0.447661i
$999$			18.0000i			0.569495i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.2.e.b.107.3	yes	8
3.2	odd	2	inner	150.2.e.b.107.1	✓	8
4.3	odd	2		1200.2.v.l.257.2		8
5.2	odd	4	inner	150.2.e.b.143.4	yes	8
5.3	odd	4	inner	150.2.e.b.143.1	yes	8
5.4	even	2	inner	150.2.e.b.107.2	yes	8
12.11	even	2		1200.2.v.l.257.4		8
15.2	even	4	inner	150.2.e.b.143.2	yes	8
15.8	even	4	inner	150.2.e.b.143.3	yes	8
15.14	odd	2	inner	150.2.e.b.107.4	yes	8
20.3	even	4		1200.2.v.l.593.4		8
20.7	even	4		1200.2.v.l.593.1		8
20.19	odd	2		1200.2.v.l.257.3		8
60.23	odd	4		1200.2.v.l.593.2		8
60.47	odd	4		1200.2.v.l.593.3		8
60.59	even	2		1200.2.v.l.257.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.e.b.107.1	✓	8	3.2	odd	2	inner
150.2.e.b.107.2	yes	8	5.4	even	2	inner
150.2.e.b.107.3	yes	8	1.1	even	1	trivial
150.2.e.b.107.4	yes	8	15.14	odd	2	inner
150.2.e.b.143.1	yes	8	5.3	odd	4	inner
150.2.e.b.143.2	yes	8	15.2	even	4	inner
150.2.e.b.143.3	yes	8	15.8	even	4	inner
150.2.e.b.143.4	yes	8	5.2	odd	4	inner
1200.2.v.l.257.1		8	60.59	even	2
1200.2.v.l.257.2		8	4.3	odd	2
1200.2.v.l.257.3		8	20.19	odd	2
1200.2.v.l.257.4		8	12.11	even	2
1200.2.v.l.593.1		8	20.7	even	4
1200.2.v.l.593.2		8	60.23	odd	4
1200.2.v.l.593.3		8	60.47	odd	4
1200.2.v.l.593.4		8	20.3	even	4

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.448288 + 1.67303i) q^{3} -1.00000i q^{4} +(1.50000 + 0.866025i) q^{6} +(2.44949 + 2.44949i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.59808 + 1.50000i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.448288 + 1.67303i) q^{3} -1.00000i q^{4} +(1.50000 + 0.866025i) q^{6} +(2.44949 + 2.44949i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.59808 + 1.50000i) q^{9} -5.19615i q^{11} +(1.67303 - 0.448288i) q^{12} +3.46410 q^{14} -1.00000 q^{16} +(-2.12132 + 2.12132i) q^{17} +(-0.776457 + 2.89778i) q^{18} -1.00000i q^{19} +(-3.00000 + 5.19615i) q^{21} +(-3.67423 - 3.67423i) q^{22} +(-4.24264 - 4.24264i) q^{23} +(0.866025 - 1.50000i) q^{24} +(-3.67423 - 3.67423i) q^{27} +(2.44949 - 2.44949i) q^{28} -2.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(8.69333 - 2.32937i) q^{33} +3.00000i q^{34} +(1.50000 + 2.59808i) q^{36} +(-2.44949 - 2.44949i) q^{37} +(-0.707107 - 0.707107i) q^{38} +5.19615i q^{41} +(1.55291 + 5.79555i) q^{42} +(-2.44949 + 2.44949i) q^{43} -5.19615 q^{44} -6.00000 q^{46} +(-0.448288 - 1.67303i) q^{48} +5.00000i q^{49} +(-4.50000 - 2.59808i) q^{51} +(4.24264 + 4.24264i) q^{53} -5.19615 q^{54} -3.46410i q^{56} +(1.67303 - 0.448288i) q^{57} +10.3923 q^{59} +14.0000 q^{61} +(-1.41421 + 1.41421i) q^{62} +(-10.0382 - 2.68973i) q^{63} +1.00000i q^{64} +(4.50000 - 7.79423i) q^{66} +(3.67423 + 3.67423i) q^{67} +(2.12132 + 2.12132i) q^{68} +(5.19615 - 9.00000i) q^{69} +(2.89778 + 0.776457i) q^{72} +(-6.12372 + 6.12372i) q^{73} -3.46410 q^{74} -1.00000 q^{76} +(12.7279 - 12.7279i) q^{77} -14.0000i q^{79} +(4.50000 - 7.79423i) q^{81} +(3.67423 + 3.67423i) q^{82} +(2.12132 + 2.12132i) q^{83} +(5.19615 + 3.00000i) q^{84} +3.46410i q^{86} +(-3.67423 + 3.67423i) q^{88} -15.5885 q^{89} +(-4.24264 + 4.24264i) q^{92} +(-0.896575 - 3.34607i) q^{93} +(-1.50000 - 0.866025i) q^{96} +(4.89898 + 4.89898i) q^{97} +(3.53553 + 3.53553i) q^{98} +(7.79423 + 13.5000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{6}+O(q^{10}) \) 8 * q + 12 * q^6	\( 8 q + 12 q^{6} - 8 q^{16} - 24 q^{21} - 16 q^{31} + 12 q^{36} - 48 q^{46} - 36 q^{51} + 112 q^{61} + 36 q^{66} - 8 q^{76} + 36 q^{81} - 12 q^{96}+O(q^{100}) \) 8 * q + 12 * q^6 - 8 * q^16 - 24 * q^21 - 16 * q^31 + 12 * q^36 - 48 * q^46 - 36 * q^51 + 112 * q^61 + 36 * q^66 - 8 * q^76 + 36 * q^81 - 12 * q^96

Introduction

L-functions

Modular forms

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