LMFDB - Embedded newform 1008.2.cz.g.607.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(367,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 4, 1]))

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

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

chi := DirichletCharacter("1008.367");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.cz (of order $6$, 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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			607.8
Character	$\chi$	$=$	1008.607
Dual form			1008.2.cz.g.367.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02195 - 1.39843i) q^{3} +(-3.67461 + 2.12154i) q^{5} +(2.04787 + 1.67518i) q^{7} +(-0.911216 - 2.85827i) q^{9} +O(q^{10})$	\(q+(1.02195 - 1.39843i) q^{3} +(-3.67461 + 2.12154i) q^{5} +(2.04787 + 1.67518i) q^{7} +(-0.911216 - 2.85827i) q^{9} +(-1.49616 - 0.863811i) q^{11} +(-2.74353 - 1.58398i) q^{13} +(-0.788464 + 7.30680i) q^{15} +(3.64191 - 2.10266i) q^{17} +(3.66963 - 6.35599i) q^{19} +(4.43545 - 1.15185i) q^{21} +(3.84515 - 2.22000i) q^{23} +(6.50184 - 11.2615i) q^{25} +(-4.92831 - 1.64675i) q^{27} +(-0.0835405 - 0.144696i) q^{29} +1.94485 q^{31} +(-2.73699 + 1.20951i) q^{33} +(-11.0791 - 1.81099i) q^{35} +(5.04487 - 8.73797i) q^{37} +(-5.01885 + 2.21788i) q^{39} +(5.21912 + 3.01326i) q^{41} +(3.51626 - 2.03012i) q^{43} +(9.41228 + 8.56983i) q^{45} -9.44670 q^{47} +(1.38756 + 6.86110i) q^{49} +(0.781447 - 7.24178i) q^{51} +(2.59479 + 4.49430i) q^{53} +7.33043 q^{55} +(-5.13821 - 11.6273i) q^{57} -6.67413 q^{59} -7.00089i q^{61} +(2.92205 - 7.37981i) q^{63} +13.4419 q^{65} +10.7195i q^{67} +(0.825057 - 7.64592i) q^{69} -2.30845i q^{71} +(2.81533 - 1.62543i) q^{73} +(-9.10386 - 20.6011i) q^{75} +(-1.61692 - 4.27532i) q^{77} +2.38834i q^{79} +(-7.33937 + 5.20900i) q^{81} +(0.341572 + 0.591621i) q^{83} +(-8.92174 + 15.4529i) q^{85} +(-0.287722 - 0.0310476i) q^{87} +(-8.57197 - 4.94903i) q^{89} +(-2.96496 - 7.83969i) q^{91} +(1.98755 - 2.71974i) q^{93} +31.1410i q^{95} +(-11.8382 + 6.83477i) q^{97} +(-1.10567 + 5.06355i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{3} - 3 q^{5} + 4 q^{7} + 17 q^{9}+O(q^{10}) $ 24 * q - 3 * q^3 - 3 * q^5 + 4 * q^7 + 17 * q^9	$ 24 q - 3 q^{3} - 3 q^{5} + 4 q^{7} + 17 q^{9} - 9 q^{11} - 3 q^{13} - 6 q^{15} - 3 q^{17} - 4 q^{19} + 13 q^{21} - 6 q^{23} + 15 q^{25} + 9 q^{27} + 18 q^{29} + 34 q^{31} - 21 q^{33} - 42 q^{35} - 3 q^{37} + 27 q^{39} + 36 q^{41} + 24 q^{43} + 21 q^{45} - 42 q^{47} + 30 q^{49} - 6 q^{51} - 12 q^{53} - 30 q^{55} - 13 q^{57} - 12 q^{59} - 3 q^{63} + 6 q^{69} + 48 q^{73} + 36 q^{75} - 48 q^{77} - 31 q^{81} - 48 q^{83} - 21 q^{85} + 15 q^{87} + 39 q^{89} + 9 q^{91} + 10 q^{93} + 3 q^{97} + 30 q^{99}+O(q^{100}) $ 24 * q - 3 * q^3 - 3 * q^5 + 4 * q^7 + 17 * q^9 - 9 * q^11 - 3 * q^13 - 6 * q^15 - 3 * q^17 - 4 * q^19 + 13 * q^21 - 6 * q^23 + 15 * q^25 + 9 * q^27 + 18 * q^29 + 34 * q^31 - 21 * q^33 - 42 * q^35 - 3 * q^37 + 27 * q^39 + 36 * q^41 + 24 * q^43 + 21 * q^45 - 42 * q^47 + 30 * q^49 - 6 * q^51 - 12 * q^53 - 30 * q^55 - 13 * q^57 - 12 * q^59 - 3 * q^63 + 6 * q^69 + 48 * q^73 + 36 * q^75 - 48 * q^77 - 31 * q^81 - 48 * q^83 - 21 * q^85 + 15 * q^87 + 39 * q^89 + 9 * q^91 + 10 * q^93 + 3 * q^97 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	1.02195	−	1.39843i	0.590026	−	0.807384i
$3$	1.02195	−	1.39843i	0.590026	−	0.807384i
$4$		0			0
$5$	−3.67461	+	2.12154i	−1.64334	+	0.948780i	−0.663699	+	0.748000i	$0.731014\pi$
$5$	−3.67461	+	2.12154i	−1.64334	+	0.948780i	−0.979636	+	0.200781i	$0.935652\pi$
$6$		0			0
$7$	2.04787	+	1.67518i	0.774023	+	0.633158i
$7$	2.04787	+	1.67518i	0.774023	+	0.633158i
$8$		0			0
$9$	−0.911216	−	2.85827i	−0.303739	−	0.952755i
$10$		0			0
$11$	−1.49616	−	0.863811i	−0.451111	−	0.260449i	0.257189	−	0.966361i	$-0.417204\pi$
$11$	−1.49616	−	0.863811i	−0.451111	−	0.260449i	−0.708299	+	0.705912i	$0.750537\pi$
$12$		0			0
$13$	−2.74353	−	1.58398i	−0.760919	−	0.439317i	0.0687067	−	0.997637i	$-0.478113\pi$
$13$	−2.74353	−	1.58398i	−0.760919	−	0.439317i	−0.829626	+	0.558320i	$0.811446\pi$
$14$		0			0
$15$	−0.788464	+	7.30680i	−0.203580	+	1.88661i
$16$		0			0
$17$	3.64191	−	2.10266i	0.883293	−	0.509970i	0.0115504	−	0.999933i	$-0.496323\pi$
$17$	3.64191	−	2.10266i	0.883293	−	0.509970i	0.871743	+	0.489964i	$0.162990\pi$
$18$		0			0
$19$	3.66963	−	6.35599i	0.841871	−	1.45816i	−0.0464402	−	0.998921i	$-0.514788\pi$
$19$	3.66963	−	6.35599i	0.841871	−	1.45816i	0.888311	−	0.459242i	$-0.151879\pi$
$20$		0			0
$21$	4.43545	−	1.15185i	0.967895	−	0.251354i
$22$		0			0
$23$	3.84515	−	2.22000i	0.801770	−	0.462902i	−0.0423200	−	0.999104i	$-0.513475\pi$
$23$	3.84515	−	2.22000i	0.801770	−	0.462902i	0.844090	+	0.536202i	$0.180142\pi$
$24$		0			0
$25$	6.50184	−	11.2615i	1.30037	−	2.25230i
$26$		0			0
$27$	−4.92831	−	1.64675i	−0.948453	−	0.316917i
$28$		0			0
$29$	−0.0835405	−	0.144696i	−0.0155131	−	0.0268694i	0.858165	−	0.513375i	$-0.171605\pi$
$29$	−0.0835405	−	0.144696i	−0.0155131	−	0.0268694i	−0.873678	+	0.486505i	$0.838271\pi$
$30$		0			0
$31$	1.94485			0.349306			0.174653	−	0.984630i	$-0.444120\pi$
$31$	1.94485			0.349306			0.174653	+	0.984630i	$0.444120\pi$
$32$		0			0
$33$	−2.73699	+	1.20951i	−0.476449	+	0.210548i
$34$		0			0
$35$	−11.0791	−	1.81099i	−1.87271	−	0.306113i
$36$		0			0
$37$	5.04487	−	8.73797i	0.829371	−	1.43651i	−0.0691613	−	0.997605i	$-0.522032\pi$
$37$	5.04487	−	8.73797i	0.829371	−	1.43651i	0.898532	−	0.438907i	$-0.144634\pi$
$38$		0			0
$39$	−5.01885	+	2.21788i	−0.803659	+	0.355146i
$40$		0			0
$41$	5.21912	+	3.01326i	0.815090	+	0.470593i	0.848720	−	0.528842i	$-0.177374\pi$
$41$	5.21912	+	3.01326i	0.815090	+	0.470593i	−0.0336303	+	0.999434i	$0.510707\pi$
$42$		0			0
$43$	3.51626	−	2.03012i	0.536225	−	0.309590i	−0.207323	−	0.978273i	$-0.566475\pi$
$43$	3.51626	−	2.03012i	0.536225	−	0.309590i	0.743548	+	0.668683i	$0.233142\pi$
$44$		0			0
$45$	9.41228	+	8.56983i	1.40310	+	1.27752i
$46$		0			0
$47$	−9.44670			−1.37794			−0.688971	−	0.724789i	$-0.741937\pi$
$47$	−9.44670			−1.37794			−0.688971	+	0.724789i	$0.741937\pi$
$48$		0			0
$49$	1.38756	+	6.86110i	0.198223	+	0.980157i
$50$		0			0
$51$	0.781447	−	7.24178i	0.109425	−	1.01405i
$52$		0			0
$53$	2.59479	+	4.49430i	0.356422	+	0.617340i	0.987360	−	0.158493i	$-0.0506634\pi$
$53$	2.59479	+	4.49430i	0.356422	+	0.617340i	−0.630939	+	0.775833i	$0.717330\pi$
$54$		0			0
$55$	7.33043			0.988435
$56$		0			0
$57$	−5.13821	−	11.6273i	−0.680572	−	1.54007i
$58$		0			0
$59$	−6.67413			−0.868898			−0.434449	−	0.900697i	$-0.643057\pi$
$59$	−6.67413			−0.868898			−0.434449	+	0.900697i	$0.643057\pi$
$60$		0			0
$61$		−	7.00089i		−	0.896372i	−0.893940	−	0.448186i	$-0.852070\pi$
$61$		−	7.00089i		−	0.896372i	0.893940	−	0.448186i	$-0.147930\pi$
$62$		0			0
$63$	2.92205	−	7.37981i	0.368144	−	0.929769i
$64$		0			0
$65$	13.4419			1.66726
$66$		0			0
$67$			10.7195i			1.30959i	0.755805	+	0.654797i	$0.227246\pi$
$67$			10.7195i			1.30959i	−0.755805	+	0.654797i	$0.772754\pi$
$68$		0			0
$69$	0.825057	−	7.64592i	0.0993252	−	0.920460i
$70$		0			0
$71$		−	2.30845i		−	0.273963i	−0.990574	−	0.136981i	$-0.956260\pi$
$71$		−	2.30845i		−	0.273963i	0.990574	−	0.136981i	$-0.0437401\pi$
$72$		0			0
$73$	2.81533	−	1.62543i	0.329509	−	0.190242i	−0.326114	−	0.945330i	$-0.605739\pi$
$73$	2.81533	−	1.62543i	0.329509	−	0.190242i	0.655623	+	0.755088i	$0.272406\pi$
$74$		0			0
$75$	−9.10386	−	20.6011i	−1.05122	−	2.37881i
$76$		0			0
$77$	−1.61692	−	4.27532i	−0.184265	−	0.487217i
$78$		0			0
$79$			2.38834i			0.268709i	0.990933	+	0.134355i	$0.0428961\pi$
$79$			2.38834i			0.268709i	−0.990933	+	0.134355i	$0.957104\pi$
$80$		0			0
$81$	−7.33937	+	5.20900i	−0.815486	+	0.578777i
$82$		0			0
$83$	0.341572	+	0.591621i	0.0374924	+	0.0649388i	0.884163	−	0.467179i	$-0.154730\pi$
$83$	0.341572	+	0.591621i	0.0374924	+	0.0649388i	−0.846670	+	0.532118i	$0.821396\pi$
$84$		0			0
$85$	−8.92174	+	15.4529i	−0.967698	+	1.67610i
$86$		0			0
$87$	−0.287722	−	0.0310476i	−0.0308471	−	0.00332865i
$88$		0			0
$89$	−8.57197	−	4.94903i	−0.908627	−	0.524596i	−0.0286381	−	0.999590i	$-0.509117\pi$
$89$	−8.57197	−	4.94903i	−0.908627	−	0.524596i	−0.879989	+	0.474994i	$0.842450\pi$
$90$		0			0
$91$	−2.96496	−	7.83969i	−0.310812	−	0.821823i
$92$		0			0
$93$	1.98755	−	2.71974i	0.206100	−	0.282024i
$94$		0			0
$95$			31.1410i			3.19500i
$96$		0			0
$97$	−11.8382	+	6.83477i	−1.20198	+	0.693966i	−0.960996	−	0.276562i	$-0.910805\pi$
$97$	−11.8382	+	6.83477i	−1.20198	+	0.693966i	−0.240988	+	0.970528i	$0.577471\pi$
$98$		0			0
$99$	−1.10567	+	5.06355i	−0.111124	+	0.508906i
$100$		0			0
$101$	−8.64741	−	4.99259i	−0.860450	−	0.496781i	0.00371322	−	0.999993i	$-0.498818\pi$
$101$	−8.64741	−	4.99259i	−0.860450	−	0.496781i	−0.864163	+	0.503212i	$0.832151\pi$
$102$		0			0
$103$	−2.39212	−	4.14327i	−0.235703	−	0.408249i	0.723774	−	0.690037i	$-0.242406\pi$
$103$	−2.39212	−	4.14327i	−0.235703	−	0.408249i	−0.959477	+	0.281788i	$0.909072\pi$
$104$		0			0
$105$	−13.8549	+	13.6426i	−1.35210	+	1.33138i
$106$		0			0
$107$	−7.92894	−	4.57778i	−0.766520	−	0.442550i	0.0651118	−	0.997878i	$-0.479260\pi$
$107$	−7.92894	−	4.57778i	−0.766520	−	0.442550i	−0.831632	+	0.555327i	$0.812593\pi$
$108$		0			0
$109$	1.40626	+	2.43572i	0.134695	+	0.233299i	0.925481	−	0.378794i	$-0.123661\pi$
$109$	1.40626	+	2.43572i	0.134695	+	0.233299i	−0.790786	+	0.612093i	$0.790328\pi$
$110$		0			0
$111$	−7.06381	−	15.9847i	−0.670467	−	1.51720i
$112$		0			0
$113$	8.95991	−	15.5190i	0.842877	−	1.45991i	−0.0445745	−	0.999006i	$-0.514193\pi$
$113$	8.95991	−	15.5190i	0.842877	−	1.45991i	0.887452	−	0.460900i	$-0.152473\pi$
$114$		0			0
$115$	−9.41962	+	16.3153i	−0.878384	+	1.52141i
$116$		0			0
$117$	−2.02748	+	9.28509i	−0.187441	+	0.858407i
$118$		0			0
$119$	10.9805	+	1.79487i	1.00658	+	0.164536i
$120$		0			0
$121$	−4.00766	−	6.94147i	−0.364333	−	0.631043i
$122$		0			0
$123$	9.54755	−	4.21916i	0.860873	−	0.380429i
$124$		0			0
$125$			33.9602i			3.03749i
$126$		0			0
$127$			8.93987i			0.793285i	0.917973	+	0.396642i	$0.129825\pi$
$127$			8.93987i			0.793285i	−0.917973	+	0.396642i	$0.870175\pi$
$128$		0			0
$129$	0.754487	−	6.99193i	0.0664289	−	0.615606i
$130$		0			0
$131$	9.77456	+	16.9300i	0.854007	+	1.47918i	0.877563	+	0.479461i	$0.159168\pi$
$131$	9.77456	+	16.9300i	0.854007	+	1.47918i	−0.0235563	+	0.999723i	$0.507499\pi$
$132$		0			0
$133$	18.1623	−	6.86896i	1.57487	−	0.595614i
$134$		0			0
$135$	21.6032	−	4.40444i	1.85931	−	0.379074i
$136$		0			0
$137$	6.42416	−	11.1270i	0.548853	−	0.950641i	−0.449501	−	0.893280i	$-0.648398\pi$
$137$	6.42416	−	11.1270i	0.548853	−	0.950641i	0.998354	−	0.0573608i	$-0.0182685\pi$
$138$		0			0
$139$	−2.22078	+	3.84650i	−0.188364	+	0.326256i	−0.944705	−	0.327922i	$-0.893652\pi$
$139$	−2.22078	+	3.84650i	−0.188364	+	0.326256i	0.756341	+	0.654178i	$0.226985\pi$
$140$		0			0
$141$	−9.65410	+	13.2106i	−0.813022	+	1.11253i
$142$		0			0
$143$	2.73652	+	4.73979i	0.228839	+	0.396361i
$144$		0			0
$145$	0.613957	+	0.354468i	0.0509864	+	0.0294370i
$146$		0			0
$147$	11.0128	+	5.07133i	0.908320	+	0.418276i
$148$		0			0
$149$	−2.69553	−	4.66879i	−0.220826	−	0.382483i	0.734233	−	0.678898i	$-0.237542\pi$
$149$	−2.69553	−	4.66879i	−0.220826	−	0.382483i	−0.955059	+	0.296415i	$0.904209\pi$
$150$		0			0
$151$	2.26042	+	1.30506i	0.183951	+	0.106204i	0.589148	−	0.808025i	$-0.299464\pi$
$151$	2.26042	+	1.30506i	0.183951	+	0.106204i	−0.405197	+	0.914229i	$0.632797\pi$
$152$		0			0
$153$	−9.32853	−	8.49358i	−0.754167	−	0.686665i
$154$		0			0
$155$	−7.14657	+	4.12608i	−0.574027	+	0.331414i
$156$		0			0
$157$		−	9.38214i		−	0.748777i	−0.927272	−	0.374388i	$-0.877853\pi$
$157$		−	9.38214i		−	0.748777i	0.927272	−	0.374388i	$-0.122147\pi$
$158$		0			0
$159$	8.93673	+	0.964346i	0.708729	+	0.0764776i
$160$		0			0
$161$	11.5933	+	1.89504i	0.913678	+	0.149350i
$162$		0			0
$163$	10.5275	+	6.07803i	0.824574	+	0.476068i	0.851991	−	0.523556i	$-0.175395\pi$
$163$	10.5275	+	6.07803i	0.824574	+	0.476068i	−0.0274172	+	0.999624i	$0.508728\pi$
$164$		0			0
$165$	7.49137	−	10.2511i	0.583202	−	0.798047i
$166$		0			0
$167$	1.63000	−	2.82325i	0.126133	−	0.218469i	−0.796042	−	0.605241i	$-0.793077\pi$
$167$	1.63000	−	2.82325i	0.126133	−	0.218469i	0.922175	+	0.386772i	$0.126410\pi$
$168$		0			0
$169$	−1.48202	−	2.56694i	−0.114002	−	0.197457i
$170$		0			0
$171$	−21.5109	−	4.69710i	−1.64498	−	0.359196i
$172$		0			0
$173$		−	9.52521i		−	0.724188i	−0.932142	−	0.362094i	$-0.882062\pi$
$173$		−	9.52521i		−	0.724188i	0.932142	−	0.362094i	$-0.117938\pi$
$174$		0			0
$175$	32.1800	−	12.1704i	2.43258	−	0.919996i
$176$		0			0
$177$	−6.82066	+	9.33331i	−0.512672	+	0.701534i
$178$		0			0
$179$	1.51383	−	0.874013i	0.113149	−	0.0653268i	−0.442357	−	0.896839i	$-0.645858\pi$
$179$	1.51383	−	0.874013i	0.113149	−	0.0653268i	0.555507	+	0.831512i	$0.312524\pi$
$180$		0			0
$181$			2.25839i			0.167865i	0.996471	+	0.0839324i	$0.0267480\pi$
$181$			2.25839i			0.167865i	−0.996471	+	0.0839324i	$0.973252\pi$
$182$		0			0
$183$	−9.79025	−	7.15459i	−0.723716	−	0.528882i
$184$		0			0
$185$			42.8115i			3.14756i
$186$		0			0
$187$	−7.26520			−0.531284
$188$		0			0
$189$	−7.33395	−	11.6281i	−0.533466	−	0.845821i
$190$		0			0
$191$		−	12.3640i		−	0.894626i	−0.894378	−	0.447313i	$-0.852381\pi$
$191$		−	12.3640i		−	0.894626i	0.894378	−	0.447313i	$-0.147619\pi$
$192$		0			0
$193$	22.7705			1.63906			0.819528	−	0.573040i	$-0.194236\pi$
$193$	22.7705			1.63906			0.819528	+	0.573040i	$0.194236\pi$
$194$		0			0
$195$	13.7370	−	18.7975i	0.983727	−	1.34612i
$196$		0			0
$197$	26.3375			1.87647			0.938234	−	0.346002i	$-0.112461\pi$
$197$	26.3375			1.87647			0.938234	+	0.346002i	$0.112461\pi$
$198$		0			0
$199$	−4.27112	−	7.39780i	−0.302772	−	0.524416i	0.673991	−	0.738740i	$-0.264579\pi$
$199$	−4.27112	−	7.39780i	−0.302772	−	0.524416i	−0.976763	+	0.214324i	$0.931245\pi$
$200$		0			0
$201$	14.9905	+	10.9548i	1.05735	+	0.772694i
$202$		0			0
$203$	0.0713119	−	0.436265i	0.00500512	−	0.0306198i
$204$		0			0
$205$	−25.5710			−1.78596
$206$		0			0
$207$	−9.84911	−	8.96757i	−0.684561	−	0.623289i
$208$		0			0
$209$	−10.9807	+	6.33973i	−0.759554	+	0.438529i
$210$		0			0
$211$	−4.17846	−	2.41243i	−0.287657	−	0.166079i	0.349228	−	0.937038i	$-0.386444\pi$
$211$	−4.17846	−	2.41243i	−0.287657	−	0.166079i	−0.636885	+	0.770959i	$0.719777\pi$
$212$		0			0
$213$	−3.22821	−	2.35913i	−0.221193	−	0.161645i
$214$		0			0
$215$	−8.61393	+	14.9198i	−0.587465	+	1.01752i
$216$		0			0
$217$	3.98281	+	3.25797i	0.270371	+	0.221166i
$218$		0			0
$219$	0.604087	−	5.59816i	0.0408204	−	0.378288i
$220$		0			0
$221$	−13.3223			−0.896153
$222$		0			0
$223$	13.2777	+	22.9976i	0.889139	+	1.54003i	0.840895	+	0.541198i	$0.182029\pi$
$223$	13.2777	+	22.9976i	0.889139	+	1.54003i	0.0482438	+	0.998836i	$0.484638\pi$
$224$		0			0
$225$	−38.1130	−	8.32231i	−2.54087	−	0.554821i
$226$		0			0
$227$	−2.08007	+	3.60278i	−0.138059	+	0.239125i	−0.926762	−	0.375649i	$-0.877420\pi$
$227$	−2.08007	+	3.60278i	−0.138059	+	0.239125i	0.788703	+	0.614775i	$0.210753\pi$
$228$		0			0
$229$	−2.90847	+	1.67921i	−0.192197	+	0.110965i	−0.593011	−	0.805195i	$-0.702061\pi$
$229$	−2.90847	+	1.67921i	−0.192197	+	0.110965i	0.400814	+	0.916160i	$0.368728\pi$
$230$		0			0
$231$	−7.63115	−	2.10804i	−0.502093	−	0.138699i
$232$		0			0
$233$	−4.91358	+	8.51057i	−0.321899	+	0.557546i	−0.980880	−	0.194614i	$-0.937655\pi$
$233$	−4.91358	+	8.51057i	−0.321899	+	0.557546i	0.658980	+	0.752160i	$0.270988\pi$
$234$		0			0
$235$	34.7129	−	20.0415i	2.26442	−	1.30736i
$236$		0			0
$237$	3.33993	+	2.44077i	0.216951	+	0.158545i
$238$		0			0
$239$	−5.74829	−	3.31878i	−0.371826	−	0.214674i	0.302430	−	0.953172i	$-0.402202\pi$
$239$	−5.74829	−	3.31878i	−0.371826	−	0.214674i	−0.674256	+	0.738498i	$0.735536\pi$
$240$		0			0
$241$	16.3656	+	9.44866i	1.05420	+	0.608642i	0.923822	−	0.382823i	$-0.125048\pi$
$241$	16.3656	+	9.44866i	1.05420	+	0.608642i	0.130377	+	0.991465i	$0.458381\pi$
$242$		0			0
$243$	−0.216086	+	15.5870i	−0.0138619	+	0.999904i
$244$		0			0
$245$	−19.6548	−	22.2681i	−1.25570	−	1.42266i
$246$		0			0
$247$	−20.1355	+	11.6252i	−1.28119	+	0.739696i
$248$		0			0
$249$	1.17641	+	0.126944i	0.0745521	+	0.00804478i
$250$		0			0
$251$	17.5972			1.11072			0.555362	−	0.831609i	$-0.312580\pi$
$251$	17.5972			1.11072			0.555362	+	0.831609i	$0.312580\pi$
$252$		0			0
$253$	−7.67064			−0.482249
$254$		0			0
$255$	12.4922	+	28.2686i	0.782292	+	1.77025i
$256$		0			0
$257$	−14.6238	+	8.44306i	−0.912208	+	0.526664i	−0.881141	−	0.472854i	$-0.843224\pi$
$257$	−14.6238	+	8.44306i	−0.912208	+	0.526664i	−0.0310671	+	0.999517i	$0.509891\pi$
$258$		0			0
$259$	24.9689	−	9.44318i	1.55149	−	0.586771i
$260$		0			0
$261$	−0.337457	+	0.370631i	−0.0208881	+	0.0229415i
$262$		0			0
$263$	11.7039	+	6.75726i	0.721694	+	0.416670i	0.815376	−	0.578932i	$-0.196530\pi$
$263$	11.7039	+	6.75726i	0.721694	+	0.416670i	−0.0936818	+	0.995602i	$0.529864\pi$
$264$		0			0
$265$	−19.0697	−	11.0099i	−1.17144	−	0.676331i
$266$		0			0
$267$	−15.6810	+	6.92962i	−0.959664	+	0.424086i
$268$		0			0
$269$	−0.860342	+	0.496719i	−0.0524560	+	0.0302855i	−0.525999	−	0.850485i	$-0.676308\pi$
$269$	−0.860342	+	0.496719i	−0.0524560	+	0.0302855i	0.473543	+	0.880771i	$0.342975\pi$
$270$		0			0
$271$	−2.60397	+	4.51021i	−0.158180	+	0.273976i	−0.934212	−	0.356717i	$-0.883896\pi$
$271$	−2.60397	+	4.51021i	−0.158180	+	0.273976i	0.776032	+	0.630693i	$0.217229\pi$
$272$		0			0
$273$	−13.9933	−	3.86553i	−0.846914	−	0.233952i
$274$		0			0
$275$	−19.4556	+	11.2327i	−1.17322	+	0.677358i
$276$		0			0
$277$	1.39265	−	2.41215i	0.0836765	−	0.144932i	−0.821150	−	0.570712i	$-0.806667\pi$
$277$	1.39265	−	2.41215i	0.0836765	−	0.144932i	0.904826	+	0.425781i	$0.140000\pi$
$278$		0			0
$279$	−1.77218	−	5.55891i	−0.106098	−	0.332803i
$280$		0			0
$281$	9.74790	+	16.8839i	0.581511	+	1.00721i	0.995301	+	0.0968339i	$0.0308716\pi$
$281$	9.74790	+	16.8839i	0.581511	+	1.00721i	−0.413790	+	0.910373i	$0.635795\pi$
$282$		0			0
$283$	−25.7862			−1.53283			−0.766417	−	0.642344i	$-0.777962\pi$
$283$	−25.7862			−1.53283			−0.766417	+	0.642344i	$0.777962\pi$
$284$		0			0
$285$	43.5486	+	31.8247i	2.57959	+	1.88513i
$286$		0			0
$287$	5.64035	+	14.9137i	0.332939	+	0.880330i
$288$		0			0
$289$	0.342346	−	0.592960i	0.0201380	−	0.0348800i
$290$		0			0
$291$	−2.54012	+	23.5397i	−0.148905	+	1.37992i
$292$		0			0
$293$	−6.06817	−	3.50346i	−0.354506	−	0.204674i	0.312162	−	0.950029i	$-0.398947\pi$
$293$	−6.06817	−	3.50346i	−0.354506	−	0.204674i	−0.666668	+	0.745355i	$0.732280\pi$
$294$		0			0
$295$	24.5248	−	14.1594i	1.42789	−	0.824393i
$296$		0			0
$297$	5.95108	+	6.72093i	0.345317	+	0.389988i
$298$		0			0
$299$	−14.0657			−0.813442
$300$		0			0
$301$	10.6017	+	1.73295i	0.611069	+	0.0998856i
$302$		0			0
$303$	−15.8190	+	6.99061i	−0.908781	+	0.401600i
$304$		0			0
$305$	14.8526	+	25.7255i	0.850460	+	1.47304i
$306$		0			0
$307$	−2.06699			−0.117970			−0.0589848	−	0.998259i	$-0.518786\pi$
$307$	−2.06699			−0.117970			−0.0589848	+	0.998259i	$0.518786\pi$
$308$		0			0
$309$	−8.23872	−	0.889025i	−0.468684	−	0.0505749i
$310$		0			0
$311$	−8.94436			−0.507188			−0.253594	−	0.967311i	$-0.581613\pi$
$311$	−8.94436			−0.507188			−0.253594	+	0.967311i	$0.581613\pi$
$312$		0			0
$313$			2.43193i			0.137461i	0.997635	+	0.0687303i	$0.0218948\pi$
$313$			2.43193i			0.137461i	−0.997635	+	0.0687303i	$0.978105\pi$
$314$		0			0
$315$	4.91915	+	33.3172i	0.277163	+	1.87721i
$316$		0			0
$317$	−8.99171			−0.505025			−0.252512	−	0.967594i	$-0.581257\pi$
$317$	−8.99171			−0.505025			−0.252512	+	0.967594i	$0.581257\pi$
$318$		0			0
$319$			0.288653i			0.0161614i
$320$		0			0
$321$	−14.5047	+	6.40979i	−0.809575	+	0.357760i
$322$		0			0
$323$		−	30.8639i		−	1.71731i
$324$		0			0
$325$	−35.6760	+	20.5975i	−1.97895	+	1.14255i
$326$		0			0
$327$	4.84332	+	0.522633i	0.267836	+	0.0289017i
$328$		0			0
$329$	−19.3456	−	15.8249i	−1.06656	−	0.872455i
$330$		0			0
$331$		−	4.44942i		−	0.244562i	−0.992496	−	0.122281i	$-0.960979\pi$
$331$		−	4.44942i		−	0.244562i	0.992496	−	0.122281i	$-0.0390209\pi$
$332$		0			0
$333$	−29.5724	−	6.45740i	−1.62056	−	0.353863i
$334$		0			0
$335$	−22.7418	−	39.3899i	−1.24252	−	2.15210i
$336$		0			0
$337$	3.15784	−	5.46953i	0.172018	−	0.297945i	−0.767107	−	0.641519i	$-0.778304\pi$
$337$	3.15784	−	5.46953i	0.172018	−	0.297945i	0.939125	+	0.343575i	$0.111638\pi$
$338$		0			0
$339$	−12.5456	−	28.3895i	−0.681386	−	1.54191i
$340$		0			0
$341$	−2.90982	−	1.67998i	−0.157576	−	0.0909763i
$342$		0			0
$343$	−8.65202	+	16.3751i	−0.467165	+	0.884170i
$344$		0			0
$345$	13.1893	+	29.8461i	0.710090	+	1.60686i
$346$		0			0
$347$		−	21.1224i		−	1.13391i	−0.823750	−	0.566954i	$-0.808122\pi$
$347$		−	21.1224i		−	1.13391i	0.823750	−	0.566954i	$-0.191878\pi$
$348$		0			0
$349$	3.42362	−	1.97663i	0.183262	−	0.105807i	−0.405562	−	0.914067i	$-0.632924\pi$
$349$	3.42362	−	1.97663i	0.183262	−	0.105807i	0.588825	+	0.808261i	$0.299591\pi$
$350$		0			0
$351$	10.9126	+	12.3242i	0.582469	+	0.657819i
$352$		0			0
$353$	16.0154	+	9.24652i	0.852416	+	0.492143i	0.861465	−	0.507816i	$-0.169547\pi$
$353$	16.0154	+	9.24652i	0.852416	+	0.492143i	−0.00904907	+	0.999959i	$0.502880\pi$
$354$		0			0
$355$	4.89747	+	8.48266i	0.259931	+	0.450213i
$356$		0			0
$357$	13.7316	−	13.5212i	0.726752	−	0.715617i
$358$		0			0
$359$	2.45699	+	1.41854i	0.129675	+	0.0748677i	0.563434	−	0.826161i	$-0.309480\pi$
$359$	2.45699	+	1.41854i	0.129675	+	0.0748677i	−0.433759	+	0.901029i	$0.642813\pi$
$360$		0			0
$361$	−17.4324	−	30.1938i	−0.917493	−	1.58914i
$362$		0			0
$363$	−13.8028	−	1.48944i	−0.724460	−	0.0781751i
$364$		0			0
$365$	−6.89682	+	11.9456i	−0.360996	+	0.625263i
$366$		0			0
$367$	−13.7720	+	23.8539i	−0.718895	+	1.24516i	0.242544	+	0.970141i	$0.422018\pi$
$367$	−13.7720	+	23.8539i	−0.718895	+	1.24516i	−0.961438	+	0.275021i	$0.911315\pi$
$368$		0			0
$369$	3.85696	−	17.6634i	0.200785	−	0.919519i
$370$		0			0
$371$	−2.21497	+	13.5505i	−0.114995	+	0.703506i
$372$		0			0
$373$	8.04596	+	13.9360i	0.416604	+	0.721580i	0.995595	−	0.0937541i	$-0.0298868\pi$
$373$	8.04596	+	13.9360i	0.416604	+	0.721580i	−0.578991	+	0.815334i	$0.696553\pi$
$374$		0			0
$375$	47.4910	+	34.7058i	2.45242	+	1.79220i
$376$		0			0
$377$			0.529305i			0.0272606i
$378$		0			0
$379$			9.15017i			0.470013i	0.971994	+	0.235006i	$0.0755111\pi$
$379$			9.15017i			0.470013i	−0.971994	+	0.235006i	$0.924489\pi$
$380$		0			0
$381$	12.5018	+	9.13614i	0.640486	+	0.468059i
$382$		0			0
$383$	−10.2333	−	17.7245i	−0.522895	−	0.905680i	−0.999645	−	0.0266416i	$-0.991519\pi$
$383$	−10.2333	−	17.7245i	−0.522895	−	0.905680i	0.476750	−	0.879039i	$-0.341815\pi$
$384$		0			0
$385$	15.0118	+	12.2798i	0.765071	+	0.625835i
$386$		0			0
$387$	−9.00668	−	8.20054i	−0.457835	−	0.416857i
$388$		0			0
$389$	2.57877	−	4.46656i	0.130749	−	0.226463i	−0.793217	−	0.608939i	$-0.791595\pi$
$389$	2.57877	−	4.46656i	0.130749	−	0.226463i	0.923965	+	0.382476i	$0.124929\pi$
$390$		0			0
$391$	9.33580	−	16.1701i	0.472132	−	0.817756i
$392$		0			0
$393$	33.6646	+	3.63269i	1.69816	+	0.183245i
$394$		0			0
$395$	−5.06695	−	8.77621i	−0.254946	−	0.441579i
$396$		0			0
$397$	−1.86688	−	1.07785i	−0.0936962	−	0.0540955i	0.452420	−	0.891805i	$-0.350561\pi$
$397$	−1.86688	−	1.07785i	−0.0936962	−	0.0540955i	−0.546116	+	0.837710i	$0.683894\pi$
$398$		0			0
$399$	8.95533	−	32.4185i	0.448327	−	1.62296i
$400$		0			0
$401$	11.3719	+	19.6967i	0.567884	+	0.983604i	0.996775	+	0.0802477i	$0.0255711\pi$
$401$	11.3719	+	19.6967i	0.567884	+	0.983604i	−0.428891	+	0.903356i	$0.641096\pi$
$402$		0			0
$403$	−5.33576	−	3.08061i	−0.265793	−	0.153456i
$404$		0			0
$405$	15.9182	−	34.7118i	0.790984	−	1.72484i
$406$		0			0
$407$	−15.0959	+	8.71562i	−0.748276	+	0.432017i
$408$		0			0
$409$		−	35.7603i		−	1.76823i	−0.467266	−	0.884117i	$-0.654761\pi$
$409$		−	35.7603i		−	1.76823i	0.467266	−	0.884117i	$-0.345239\pi$
$410$		0			0
$411$	−8.99509	−	20.3550i	−0.443695	−	1.00404i
$412$		0			0
$413$	−13.6678	−	11.1804i	−0.672547	−	0.550149i
$414$		0			0
$415$	−2.51029	−	1.44932i	−0.123225	−	0.0711442i
$416$		0			0
$417$	3.10953	+	7.03655i	0.152274	+	0.344581i
$418$		0			0
$419$	3.40403	−	5.89596i	0.166298	−	0.288036i	−0.770818	−	0.637056i	$-0.780152\pi$
$419$	3.40403	−	5.89596i	0.166298	−	0.288036i	0.937115	+	0.349020i	$0.113485\pi$
$420$		0			0
$421$	9.41938	+	16.3148i	0.459072	+	0.795137i	0.998912	−	0.0466311i	$-0.0148485\pi$
$421$	9.41938	+	16.3148i	0.459072	+	0.795137i	−0.539840	+	0.841768i	$0.681515\pi$
$422$		0			0
$423$	8.60798	+	27.0012i	0.418535	+	1.31284i
$424$		0			0
$425$		−	54.6846i		−	2.65259i
$426$		0			0
$427$	11.7277	−	14.3369i	0.567545	−	0.693812i
$428$		0			0
$429$	9.42486	+	1.01702i	0.455036	+	0.0491021i
$430$		0			0
$431$	25.6776	−	14.8249i	1.23684	−	0.714093i	0.268397	−	0.963308i	$-0.413506\pi$
$431$	25.6776	−	14.8249i	1.23684	−	0.714093i	0.968448	+	0.249216i	$0.0801729\pi$
$432$		0			0
$433$		−	31.0315i		−	1.49128i	−0.666351	−	0.745638i	$-0.732145\pi$
$433$		−	31.0315i		−	1.49128i	0.666351	−	0.745638i	$-0.267855\pi$
$434$		0			0
$435$	1.12314	−	0.496326i	0.0538503	−	0.0237970i
$436$		0			0
$437$		−	32.5863i		−	1.55881i
$438$		0			0
$439$	21.1077			1.00741			0.503707	−	0.863875i	$-0.331969\pi$
$439$	21.1077			1.00741			0.503707	+	0.863875i	$0.331969\pi$
$440$		0			0
$441$	18.3465	−	10.2180i	0.873642	−	0.486569i
$442$		0			0
$443$		−	29.9176i		−	1.42143i	−0.703481	−	0.710714i	$-0.748372\pi$
$443$		−	29.9176i		−	1.42143i	0.703481	−	0.710714i	$-0.251628\pi$
$444$		0			0
$445$	41.9982			1.99091
$446$		0			0
$447$	−9.28369	−	1.00179i	−0.439104	−	0.0473829i
$448$		0			0
$449$	−1.48470			−0.0700672			−0.0350336	−	0.999386i	$-0.511154\pi$
$449$	−1.48470			−0.0700672			−0.0350336	+	0.999386i	$0.511154\pi$
$450$		0			0
$451$	−5.20578	−	9.01667i	−0.245131	−	0.424578i
$452$		0			0
$453$	4.13508	−	1.82734i	0.194283	−	0.0858558i
$454$		0			0
$455$	27.5272	+	22.5175i	1.29050	+	1.05564i
$456$		0			0
$457$	−22.7741			−1.06533			−0.532663	−	0.846328i	$-0.678809\pi$
$457$	−22.7741			−1.06533			−0.532663	+	0.846328i	$0.678809\pi$
$458$		0			0
$459$	−21.4110	+	4.36524i	−0.999380	+	0.203752i
$460$		0			0
$461$	16.3426	−	9.43539i	0.761150	−	0.439450i	−0.0685586	−	0.997647i	$-0.521840\pi$
$461$	16.3426	−	9.43539i	0.761150	−	0.439450i	0.829708	+	0.558197i	$0.188507\pi$
$462$		0			0
$463$	−30.9200	−	17.8517i	−1.43697	−	0.829637i	−0.439335	−	0.898324i	$-0.644786\pi$
$463$	−30.9200	−	17.8517i	−1.43697	−	0.829637i	−0.997638	+	0.0686868i	$0.978119\pi$
$464$		0			0
$465$	−1.53345	+	14.2107i	−0.0711118	+	0.659003i
$466$		0			0
$467$	−7.24286	+	12.5450i	−0.335159	+	0.580513i	−0.983515	−	0.180824i	$-0.942124\pi$
$467$	−7.24286	+	12.5450i	−0.335159	+	0.580513i	0.648356	+	0.761337i	$0.275457\pi$
$468$		0			0
$469$	−17.9571	+	21.9521i	−0.829180	+	1.01366i
$470$		0			0
$471$	−13.1203	−	9.58813i	−0.604550	−	0.441798i
$472$		0			0
$473$	−7.01454			−0.322529
$474$		0			0
$475$	−47.7187	−	82.6512i	−2.18948	−	3.79230i
$476$		0			0
$477$	10.4815	−	11.5119i	0.479915	−	0.527093i
$478$		0			0
$479$	−16.2831	+	28.2032i	−0.743995	+	1.28864i	0.206668	+	0.978411i	$0.433738\pi$
$479$	−16.2831	+	28.2032i	−0.743995	+	1.28864i	−0.950663	+	0.310226i	$0.899595\pi$
$480$		0			0
$481$	−27.6815	+	15.9819i	−1.26217	+	0.728713i
$482$		0			0
$483$	14.4979	−	14.2757i	0.659676	−	0.649569i
$484$		0			0
$485$	29.0004	−	50.2302i	1.31684	−	2.28084i
$486$		0			0
$487$	−34.1298	+	19.7049i	−1.54657	+	0.892912i	−0.548169	+	0.836367i	$0.684675\pi$
$487$	−34.1298	+	19.7049i	−1.54657	+	0.892912i	−0.998400	+	0.0565448i	$0.981992\pi$
$488$		0			0
$489$	19.2583	−	8.51044i	0.870890	−	0.384856i
$490$		0			0
$491$	37.4605	+	21.6278i	1.69057	+	0.976049i	0.954058	+	0.299621i	$0.0968603\pi$
$491$	37.4605	+	21.6278i	1.69057	+	0.976049i	0.736509	+	0.676428i	$0.236473\pi$
$492$		0			0
$493$	−0.608494	−	0.351314i	−0.0274052	−	0.0158224i
$494$		0			0
$495$	−6.67960	−	20.9523i	−0.300226	−	0.941736i
$496$		0			0
$497$	3.86707	−	4.72741i	0.173462	−	0.212054i
$498$		0			0
$499$	−10.0407	+	5.79698i	−0.449482	+	0.259509i	−0.707611	−	0.706602i	$-0.750227\pi$
$499$	−10.0407	+	5.79698i	−0.449482	+	0.259509i	0.258129	+	0.966110i	$0.416894\pi$
$500$		0			0
$501$	−2.28233	−	5.16468i	−0.101967	−	0.230741i
$502$		0			0
$503$	19.5811			0.873077			0.436538	−	0.899686i	$-0.356204\pi$
$503$	19.5811			0.873077			0.436538	+	0.899686i	$0.356204\pi$
$504$		0			0
$505$	42.3678			1.88534
$506$		0			0
$507$	−5.10424	−	0.550790i	−0.226687	−	0.0244614i
$508$		0			0
$509$	−19.1690	+	11.0672i	−0.849652	+	0.490547i	−0.860533	−	0.509394i	$-0.829870\pi$
$509$	−19.1690	+	11.0672i	−0.849652	+	0.490547i	0.0108817	+	0.999941i	$0.496536\pi$
$510$		0			0
$511$	8.48831	+	1.38750i	0.375501	+	0.0613795i
$512$		0			0
$513$	−28.5518	+	25.2813i	−1.26059	+	1.11620i
$514$		0			0
$515$	17.5802	+	10.1499i	0.774677	+	0.447260i
$516$		0			0
$517$	14.1338	+	8.16016i	0.621604	+	0.358883i
$518$		0			0
$519$	−13.3203	−	9.73434i	−0.584698	−	0.427290i
$520$		0			0
$521$	18.8964	−	10.9099i	0.827868	−	0.477970i	−0.0252540	−	0.999681i	$-0.508039\pi$
$521$	18.8964	−	10.9099i	0.827868	−	0.477970i	0.853122	+	0.521711i	$0.174706\pi$
$522$		0			0
$523$	−20.8478	+	36.1095i	−0.911612	+	1.57896i	−0.0998248	+	0.995005i	$0.531828\pi$
$523$	−20.8478	+	36.1095i	−0.911612	+	1.57896i	−0.811787	+	0.583953i	$0.801505\pi$
$524$		0			0
$525$	15.8670	−	57.4391i	0.692493	−	2.50685i
$526$		0			0
$527$	7.08298	−	4.08936i	0.308539	−	0.178135i
$528$		0			0
$529$	−1.64321	+	2.84612i	−0.0714437	+	0.123744i
$530$		0			0
$531$	6.08157	+	19.0764i	0.263918	+	0.827847i
$532$		0			0
$533$	−9.54589	−	16.5340i	−0.413478	−	0.716165i
$534$		0			0
$535$	38.8477			1.67953
$536$		0			0
$537$	0.324824	−	3.01019i	0.0140172	−	0.129899i
$538$		0			0
$539$	3.85068	−	11.4639i	0.165860	−	0.493786i
$540$		0			0
$541$	−1.58040	+	2.73733i	−0.0679466	+	0.117687i	−0.897997	−	0.440001i	$-0.854978\pi$
$541$	−1.58040	+	2.73733i	−0.0679466	+	0.117687i	0.830051	+	0.557688i	$0.188311\pi$
$542$		0			0
$543$	3.15820	+	2.30797i	0.135531	+	0.0990446i
$544$		0			0
$545$	−10.3349	−	5.96687i	−0.442699	−	0.255593i
$546$		0			0
$547$	−8.24591	+	4.76078i	−0.352570	+	0.203556i	−0.665817	−	0.746116i	$-0.731917\pi$
$547$	−8.24591	+	4.76078i	−0.352570	+	0.203556i	0.313247	+	0.949672i	$0.398583\pi$
$548$		0			0
$549$	−20.0104	+	6.37932i	−0.854023	+	0.272263i
$550$		0			0
$551$	−1.22625			−0.0522400
$552$		0			0
$553$	−4.00089	+	4.89101i	−0.170135	+	0.207987i
$554$		0			0
$555$	59.8689	+	43.7514i	2.54129	+	1.85714i
$556$		0			0
$557$	12.5874	+	21.8021i	0.533347	+	0.923785i	0.999241	+	0.0389442i	$0.0123995\pi$
$557$	12.5874	+	21.8021i	0.533347	+	0.923785i	−0.465894	+	0.884841i	$0.654267\pi$
$558$		0			0
$559$	−12.8626			−0.544032
$560$		0			0
$561$	−7.42470	+	10.1599i	−0.313471	+	0.428950i
$562$		0			0
$563$	22.2170			0.936336			0.468168	−	0.883639i	$-0.344914\pi$
$563$	22.2170			0.936336			0.468168	+	0.883639i	$0.344914\pi$
$564$		0			0
$565$			76.0351i			3.19882i
$566$		0			0
$567$	−23.7561	−	1.62739i	−0.997662	−	0.0683441i
$568$		0			0
$569$	18.2175			0.763718			0.381859	−	0.924221i	$-0.375284\pi$
$569$	18.2175			0.763718			0.381859	+	0.924221i	$0.375284\pi$
$570$		0			0
$571$			22.9637i			0.960999i	0.876995	+	0.480500i	$0.159545\pi$
$571$			22.9637i			0.960999i	−0.876995	+	0.480500i	$0.840455\pi$
$572$		0			0
$573$	−17.2902	−	12.6354i	−0.722307	−	0.527852i
$574$		0			0
$575$		−	57.7363i		−	2.40777i
$576$		0			0
$577$	19.4632	−	11.2371i	0.810265	−	0.467806i	−0.0367832	−	0.999323i	$-0.511711\pi$
$577$	19.4632	−	11.2371i	0.810265	−	0.467806i	0.847048	+	0.531517i	$0.178378\pi$
$578$		0			0
$579$	23.2704	−	31.8429i	0.967085	−	1.32335i
$580$		0			0
$581$	−0.291573	+	1.78376i	−0.0120965	+	0.0740027i
$582$		0			0
$583$		−	8.96562i		−	0.371318i
$584$		0			0
$585$	−12.2485	−	38.4205i	−0.506411	−	1.58849i
$586$		0			0
$587$	19.4626	+	33.7103i	0.803309	+	1.39137i	0.917427	+	0.397905i	$0.130262\pi$
$587$	19.4626	+	33.7103i	0.803309	+	1.39137i	−0.114118	+	0.993467i	$0.536404\pi$
$588$		0			0
$589$	7.13689	−	12.3615i	0.294070	−	0.509345i
$590$		0			0
$591$	26.9157	−	36.8311i	1.10716	−	1.51503i
$592$		0			0
$593$	8.82756	+	5.09660i	0.362505	+	0.209292i	0.670179	−	0.742200i	$-0.266217\pi$
$593$	8.82756	+	5.09660i	0.362505	+	0.209292i	−0.307674	+	0.951492i	$0.599551\pi$
$594$		0			0
$595$	−44.1569	+	16.7001i	−1.81026	+	0.684636i
$596$		0			0
$597$	−14.7102	−	1.58735i	−0.602048	−	0.0649659i
$598$		0			0
$599$			27.1004i			1.10729i	0.832752	+	0.553647i	$0.186764\pi$
$599$			27.1004i			1.10729i	−0.832752	+	0.553647i	$0.813236\pi$
$600$		0			0
$601$	3.99531	−	2.30669i	0.162972	−	0.0940920i	−0.416296	−	0.909229i	$-0.636672\pi$
$601$	3.99531	−	2.30669i	0.162972	−	0.0940920i	0.579268	+	0.815137i	$0.303339\pi$
$602$		0			0
$603$	30.6392	−	9.76777i	1.24772	−	0.397774i
$604$		0			0
$605$	29.4532	+	17.0048i	1.19744	+	0.691344i
$606$		0			0
$607$	−5.88397	−	10.1913i	−0.238823	−	0.413654i	0.721554	−	0.692358i	$-0.243428\pi$
$607$	−5.88397	−	10.1913i	−0.238823	−	0.413654i	−0.960377	+	0.278705i	$0.910095\pi$
$608$		0			0
$609$	−0.537208	−	0.545568i	−0.0217688	−	0.0221075i
$610$		0			0
$611$	25.9173	+	14.9634i	1.04850	+	0.605353i
$612$		0			0
$613$	4.05852	+	7.02956i	0.163922	+	0.283921i	0.936272	−	0.351276i	$-0.114252\pi$
$613$	4.05852	+	7.02956i	0.163922	+	0.283921i	−0.772350	+	0.635197i	$0.780919\pi$
$614$		0			0
$615$	−26.1324	+	35.7593i	−1.05376	+	1.44195i
$616$		0			0
$617$	−12.5912	+	21.8085i	−0.506901	+	0.877979i	0.493067	+	0.869991i	$0.335876\pi$
$617$	−12.5912	+	21.8085i	−0.506901	+	0.877979i	−0.999968	+	0.00798740i	$0.997458\pi$
$618$		0			0
$619$	−15.6663	+	27.1347i	−0.629680	+	1.09064i	0.357936	+	0.933746i	$0.383481\pi$
$619$	−15.6663	+	27.1347i	−0.629680	+	1.09064i	−0.987616	+	0.156891i	$0.949853\pi$
$620$		0			0
$621$	−22.6059	+	4.60885i	−0.907142	+	0.184947i
$622$		0			0
$623$	−9.26379	−	24.4946i	−0.371146	−	0.981354i
$624$		0			0
$625$	−39.5386	−	68.4829i	−1.58154	−	2.73931i
$626$		0			0
$627$	−2.35614	+	21.8347i	−0.0940954	+	0.871995i
$628$		0			0
$629$		−	42.4305i		−	1.69182i
$630$		0			0
$631$			25.3631i			1.00969i	0.863210	+	0.504845i	$0.168450\pi$
$631$			25.3631i			1.00969i	−0.863210	+	0.504845i	$0.831550\pi$
$632$		0			0
$633$	−7.64382	+	3.37789i	−0.303815	+	0.134259i
$634$		0			0
$635$	−18.9663	−	32.8505i	−0.752653	−	1.30363i
$636$		0			0
$637$	7.06103	−	21.0215i	0.279768	−	0.832902i
$638$		0			0
$639$	−6.59817	+	2.10350i	−0.261020	+	0.0832131i
$640$		0			0
$641$	−7.87718	+	13.6437i	−0.311130	+	0.538893i	−0.978607	−	0.205737i	$-0.934041\pi$
$641$	−7.87718	+	13.6437i	−0.311130	+	0.538893i	0.667477	+	0.744630i	$0.267374\pi$
$642$		0			0
$643$	0.184285	−	0.319192i	0.00726751	−	0.0125877i	−0.862369	−	0.506281i	$-0.831020\pi$
$643$	0.184285	−	0.319192i	0.00726751	−	0.0125877i	0.869636	+	0.493693i	$0.164353\pi$
$644$		0			0
$645$	12.0612	+	27.2933i	0.474909	+	1.07467i
$646$		0			0
$647$	2.90611	+	5.03353i	0.114251	+	0.197889i	0.917480	−	0.397782i	$-0.130220\pi$
$647$	2.90611	+	5.03353i	0.114251	+	0.197889i	−0.803229	+	0.595670i	$0.796887\pi$
$648$		0			0
$649$	9.98559	+	5.76519i	0.391969	+	0.226303i
$650$		0			0
$651$	8.62630	−	2.24018i	0.338091	−	0.0877995i
$652$		0			0
$653$	−13.0326	−	22.5731i	−0.510006	−	0.883356i	−0.999933	−	0.0115922i	$-0.996310\pi$
$653$	−13.0326	−	22.5731i	−0.510006	−	0.883356i	0.489927	−	0.871763i	$-0.337023\pi$
$654$		0			0
$655$	−71.8354	−	41.4742i	−2.80684	−	1.62053i
$656$		0			0
$657$	−7.21128	−	6.56584i	−0.281339	−	0.256158i
$658$		0			0
$659$	15.4955	−	8.94635i	0.603620	−	0.348500i	−0.166844	−	0.985983i	$-0.553358\pi$
$659$	15.4955	−	8.94635i	0.603620	−	0.348500i	0.770464	+	0.637483i	$0.220024\pi$
$660$		0			0
$661$			45.2952i			1.76178i	0.473322	+	0.880890i	$0.343055\pi$
$661$			45.2952i			1.76178i	−0.473322	+	0.880890i	$0.656945\pi$
$662$		0			0
$663$	−13.6148	+	18.6303i	−0.528753	+	0.723540i
$664$		0			0
$665$	−52.1668	+	63.7728i	−2.02294	+	2.47300i
$666$		0			0
$667$	−0.642452	−	0.370920i	−0.0248758	−	0.0143621i
$668$		0			0
$669$	45.7297	+	4.93461i	1.76801	+	0.190783i
$670$		0			0
$671$	−6.04744	+	10.4745i	−0.233459	+	0.404363i
$672$		0			0
$673$	−14.6621	−	25.3955i	−0.565182	−	0.978925i	−0.997033	−	0.0769793i	$-0.975472\pi$
$673$	−14.6621	−	25.3955i	−0.565182	−	0.978925i	0.431850	−	0.901945i	$-0.357861\pi$
$674$		0			0
$675$	−50.5879	+	44.7933i	−1.94713	+	1.72410i
$676$		0			0
$677$		−	25.7271i		−	0.988772i	−0.869242	−	0.494386i	$-0.835393\pi$
$677$		−	25.7271i		−	0.988772i	0.869242	−	0.494386i	$-0.164607\pi$
$678$		0			0
$679$	−35.6925	−	5.83431i	−1.36975	−	0.223900i
$680$		0			0
$681$	2.91251	+	6.59072i	0.111608	+	0.252557i
$682$		0			0
$683$	−6.72920	+	3.88510i	−0.257486	+	0.148659i	−0.623187	−	0.782073i	$-0.714162\pi$
$683$	−6.72920	+	3.88510i	−0.257486	+	0.148659i	0.365701	+	0.930732i	$0.380829\pi$
$684$		0			0
$685$			54.5163i			2.08296i
$686$		0			0
$687$	−0.624073	+	5.78337i	−0.0238099	+	0.220649i
$688$		0			0
$689$		−	16.4404i		−	0.626328i
$690$		0			0
$691$	17.6126			0.670013			0.335007	−	0.942216i	$-0.391261\pi$
$691$	17.6126			0.670013			0.335007	+	0.942216i	$0.391261\pi$
$692$		0			0
$693$	−10.7466	+	8.51731i	−0.408231	+	0.323546i
$694$		0			0
$695$		−	18.8458i		−	0.714863i
$696$		0			0
$697$	25.3434			0.959952
$698$		0			0
$699$	6.87999	+	15.5687i	0.260225	+	0.588863i
$700$		0			0
$701$	6.19616			0.234026			0.117013	−	0.993130i	$-0.462668\pi$
$701$	6.19616			0.234026			0.117013	+	0.993130i	$0.462668\pi$
$702$		0			0
$703$	−37.0256	−	64.1302i	−1.39645	−	2.41872i
$704$		0			0
$705$	7.44838	−	69.0252i	0.280522	−	2.59964i
$706$		0			0
$707$	−9.34532	−	24.7101i	−0.351467	−	0.929320i
$708$		0			0
$709$	−21.6436			−0.812844			−0.406422	−	0.913686i	$-0.633224\pi$
$709$	−21.6436			−0.812844			−0.406422	+	0.913686i	$0.633224\pi$
$710$		0			0
$711$	6.82651	−	2.17629i	0.256014	−	0.0816173i
$712$		0			0
$713$	7.47825	−	4.31757i	0.280063	−	0.161694i
$714$		0			0
$715$	−20.1113	−	11.6112i	−0.752118	−	0.434236i
$716$		0			0
$717$	−10.5156	+	4.64695i	−0.392711	+	0.173543i
$718$		0			0
$719$	9.26360	−	16.0450i	0.345474	−	0.598379i	−0.639966	−	0.768403i	$-0.721051\pi$
$719$	9.26360	−	16.0450i	0.345474	−	0.598379i	0.985440	+	0.170025i	$0.0543848\pi$
$720$		0			0
$721$	2.04197	−	12.4921i	0.0760468	−	0.465231i
$722$		0			0
$723$	29.9382	−	13.2300i	1.11341	−	0.492029i
$724$		0			0
$725$	−2.17267			−0.0806908
$726$		0			0
$727$	0.667514	+	1.15617i	0.0247567	+	0.0428799i	0.878138	−	0.478407i	$-0.158786\pi$
$727$	0.667514	+	1.15617i	0.0247567	+	0.0428799i	−0.853382	+	0.521287i	$0.825452\pi$
$728$		0			0
$729$	21.5765	+	16.2314i	0.799128	+	0.601161i
$730$		0			0
$731$	8.53728	−	14.7870i	0.315763	−	0.546917i
$732$		0			0
$733$	−32.9319	+	19.0132i	−1.21637	+	0.702270i	−0.964139	−	0.265398i	$-0.914497\pi$
$733$	−32.9319	+	19.0132i	−1.21637	+	0.702270i	−0.252228	+	0.967668i	$0.581163\pi$
$734$		0			0
$735$	−51.2267	+	4.72888i	−1.88953	+	0.174428i
$736$		0			0
$737$	9.25961	−	16.0381i	0.341082	−	0.590772i
$738$		0			0
$739$	44.1512	−	25.4907i	1.62413	−	0.937691i	0.638328	−	0.769764i	$-0.279626\pi$
$739$	44.1512	−	25.4907i	1.62413	−	0.937691i	0.985800	−	0.167926i	$-0.0537071\pi$
$740$		0			0
$741$	−4.32049	+	40.0386i	−0.158717	+	1.47085i
$742$		0			0
$743$	5.62890	+	3.24985i	0.206504	+	0.119225i	0.599686	−	0.800236i	$-0.295292\pi$
$743$	5.62890	+	3.24985i	0.206504	+	0.119225i	−0.393181	+	0.919461i	$0.628626\pi$
$744$		0			0
$745$	19.8100	+	11.4373i	0.725784	+	0.419031i
$746$		0			0
$747$	1.37976	−	1.51540i	0.0504829	−	0.0554456i
$748$		0			0
$749$	−8.56887	−	22.6571i	−0.313100	−	0.827872i
$750$		0			0
$751$	20.9679	−	12.1058i	0.765130	−	0.441748i	−0.0660045	−	0.997819i	$-0.521025\pi$
$751$	20.9679	−	12.1058i	0.765130	−	0.441748i	0.831135	+	0.556071i	$0.187692\pi$
$752$		0			0
$753$	17.9835	−	24.6084i	0.655356	−	0.896781i
$754$		0			0
$755$	−11.0749			−0.403057
$756$		0			0
$757$	−0.855427			−0.0310910			−0.0155455	−	0.999879i	$-0.504948\pi$
$757$	−0.855427			−0.0310910			−0.0155455	+	0.999879i	$0.504948\pi$
$758$		0			0
$759$	−7.83905	+	10.7269i	−0.284539	+	0.389360i
$760$		0			0
$761$	−18.0333	+	10.4115i	−0.653708	+	0.377418i	−0.789875	−	0.613268i	$-0.789855\pi$
$761$	−18.0333	+	10.4115i	−0.653708	+	0.377418i	0.136168	+	0.990686i	$0.456521\pi$
$762$		0			0
$763$	−1.20041	+	7.34377i	−0.0434579	+	0.265862i
$764$		0			0
$765$	52.2981	+	11.4198i	1.89084	+	0.412882i
$766$		0			0
$767$	18.3107	+	10.5717i	0.661161	+	0.381721i
$768$		0			0
$769$	38.2601	+	22.0895i	1.37969	+	0.796567i	0.992122	−	0.125272i	$-0.0399804\pi$
$769$	38.2601	+	22.0895i	1.37969	+	0.796567i	0.387572	+	0.921839i	$0.373314\pi$
$770$		0			0
$771$	−3.13784	+	29.0788i	−0.113007	+	1.04725i
$772$		0			0
$773$	−39.8687	+	23.0182i	−1.43398	+	0.827906i	−0.997421	−	0.0717715i	$-0.977135\pi$
$773$	−39.8687	+	23.0182i	−1.43398	+	0.827906i	−0.436555	+	0.899678i	$0.643801\pi$
$774$		0			0
$775$	12.6451	−	21.9020i	0.454226	−	0.786742i
$776$		0			0
$777$	12.3114	−	44.5678i	0.441671	−	1.59886i
$778$		0			0
$779$	38.3045	−	22.1151i	1.37240	−	0.792356i
$780$		0			0
$781$	−1.99407	+	3.45382i	−0.0713533	+	0.123588i
$782$		0			0
$783$	0.173435	+	0.850678i	0.00619806	+	0.0304008i
$784$		0			0
$785$	19.9046	+	34.4757i	0.710424	+	1.23049i
$786$		0			0
$787$	46.6670			1.66350			0.831750	−	0.555151i	$-0.187339\pi$
$787$	46.6670			1.66350			0.831750	+	0.555151i	$0.187339\pi$
$788$		0			0
$789$	21.4104	−	9.46150i	0.762231	−	0.336838i
$790$		0			0
$791$	44.3459	−	16.7715i	1.57676	−	0.596327i
$792$		0			0
$793$	−11.0893	+	19.2072i	−0.393791	+	0.682066i
$794$		0			0
$795$	−34.8849	+	15.4160i	−1.23724	+	0.546749i
$796$		0			0
$797$	−41.3925	−	23.8980i	−1.46620	−	0.846509i	−0.466911	−	0.884304i	$-0.654633\pi$
$797$	−41.3925	−	23.8980i	−1.46620	−	0.846509i	−0.999285	+	0.0377956i	$0.987966\pi$
$798$		0			0
$799$	−34.4040	+	19.8632i	−1.21713	+	0.702709i
$800$		0			0
$801$	−6.33473	+	29.0106i	−0.223827	+	1.02504i
$802$		0			0
$803$	−5.61626			−0.198193
$804$		0			0
$805$	−46.6211	+	17.6320i	−1.64318	+	0.621447i
$806$		0			0
$807$	−0.184604	+	1.71075i	−0.00649837	+	0.0602213i
$808$		0			0
$809$	−6.40052	−	11.0860i	−0.225030	−	0.389764i	0.731298	−	0.682058i	$-0.238915\pi$
$809$	−6.40052	−	11.0860i	−0.225030	−	0.389764i	−0.956329	+	0.292294i	$0.905581\pi$
$810$		0			0
$811$	−6.23832			−0.219057			−0.109528	−	0.993984i	$-0.534934\pi$
$811$	−6.23832			−0.219057			−0.109528	+	0.993984i	$0.534934\pi$
$812$		0			0
$813$	3.64607	+	8.25070i	0.127873	+	0.289365i
$814$		0			0
$815$	−51.5791			−1.80674
$816$		0			0
$817$		−	29.7991i		−	1.04254i
$818$		0			0
$819$	−19.7062	+	15.6183i	−0.688590	+	0.545747i
$820$		0			0
$821$	48.9849			1.70959			0.854793	−	0.518970i	$-0.173684\pi$
$821$	48.9849			1.70959			0.854793	+	0.518970i	$0.173684\pi$
$822$		0			0
$823$			48.2516i			1.68195i	0.541078	+	0.840973i	$0.318017\pi$
$823$			48.2516i			1.68195i	−0.541078	+	0.840973i	$0.681983\pi$
$824$		0			0
$825$	−4.17461	+	38.6867i	−0.145341	+	1.34690i
$826$		0			0
$827$			54.8165i			1.90616i	0.302724	+	0.953078i	$0.402104\pi$
$827$			54.8165i			1.90616i	−0.302724	+	0.953078i	$0.597896\pi$
$828$		0			0
$829$	8.86621	−	5.11891i	0.307936	−	0.177787i	−0.338066	−	0.941122i	$-0.609773\pi$
$829$	8.86621	−	5.11891i	0.307936	−	0.177787i	0.646003	+	0.763335i	$0.276439\pi$
$830$		0			0
$831$	−1.94999	−	4.41264i	−0.0676444	−	0.153073i
$832$		0			0
$833$	19.4799	+	22.0700i	0.674939	+	0.764679i
$834$		0			0
$835$			13.8324i			0.478691i
$836$		0			0
$837$	−9.58483	−	3.20268i	−0.331300	−	0.110701i
$838$		0			0
$839$	−18.5397	−	32.1118i	−0.640063	−	1.10862i	−0.985418	−	0.170149i	$-0.945575\pi$
$839$	−18.5397	−	32.1118i	−0.640063	−	1.10862i	0.345356	−	0.938472i	$-0.387758\pi$
$840$		0			0
$841$	14.4860	−	25.0906i	0.499519	−	0.865192i
$842$		0			0
$843$	33.5728	+	3.62278i	1.15631	+	0.124775i
$844$		0			0
$845$	10.8917	+	6.28833i	0.374686	+	0.216325i
$846$		0			0
$847$	3.42103	−	20.9288i	0.117548	−	0.719122i
$848$		0			0
$849$	−26.3524	+	36.0603i	−0.904412	+	1.23759i
$850$		0			0
$851$		−	44.7984i		−	1.53567i
$852$		0			0
$853$	21.4862	−	12.4050i	0.735672	−	0.424741i	−0.0848215	−	0.996396i	$-0.527032\pi$
$853$	21.4862	−	12.4050i	0.735672	−	0.424741i	0.820494	+	0.571656i	$0.193699\pi$
$854$		0			0
$855$	89.0093	−	28.3762i	3.04405	−	0.970446i
$856$		0			0
$857$	−32.5657	−	18.8018i	−1.11242	−	0.642259i	−0.172968	−	0.984927i	$-0.555336\pi$
$857$	−32.5657	−	18.8018i	−1.11242	−	0.642259i	−0.939456	+	0.342669i	$0.888669\pi$
$858$		0			0
$859$	13.2177	+	22.8938i	0.450983	+	0.781125i	0.998447	−	0.0557036i	$-0.0177402\pi$
$859$	13.2177	+	22.8938i	0.450983	+	0.781125i	−0.547464	+	0.836829i	$0.684407\pi$
$860$		0			0
$861$	26.6200	+	7.35353i	0.907207	+	0.250608i
$862$		0			0
$863$	−3.84525	−	2.22006i	−0.130894	−	0.0755716i	0.433123	−	0.901335i	$-0.357411\pi$
$863$	−3.84525	−	2.22006i	−0.130894	−	0.0755716i	−0.564017	+	0.825763i	$0.690745\pi$
$864$		0			0
$865$	20.2081	+	35.0014i	0.687095	+	1.19008i
$866$		0			0
$867$	−0.479352	−	1.08473i	−0.0162796	−	0.0368392i
$868$		0			0
$869$	2.06307	−	3.57335i	0.0699849	−	0.121217i
$870$		0			0
$871$	16.9794	−	29.4093i	0.575326	−	0.996495i
$872$		0			0
$873$	30.3227	+	27.6087i	1.02627	+	0.934412i
$874$		0			0
$875$	−56.8893	+	69.5461i	−1.92321	+	2.35109i
$876$		0			0
$877$	2.34507	+	4.06179i	0.0791875	+	0.137157i	0.902900	−	0.429851i	$-0.141434\pi$
$877$	2.34507	+	4.06179i	0.0791875	+	0.137157i	−0.823712	+	0.567008i	$0.808101\pi$
$878$		0			0
$879$	−11.1007	+	4.90554i	−0.374419	+	0.165460i
$880$		0			0
$881$		−	30.4670i		−	1.02646i	−0.858251	−	0.513230i	$-0.828449\pi$
$881$		−	30.4670i		−	1.02646i	0.858251	−	0.513230i	$-0.171551\pi$
$882$		0			0
$883$			3.85163i			0.129618i	0.997898	+	0.0648089i	$0.0206438\pi$
$883$			3.85163i			0.129618i	−0.997898	+	0.0648089i	$0.979356\pi$
$884$		0			0
$885$	5.26231	−	48.7665i	0.176891	−	1.63927i
$886$		0			0
$887$	−24.6543	−	42.7024i	−0.827809	−	1.43381i	−0.899753	−	0.436399i	$-0.856254\pi$
$887$	−24.6543	−	42.7024i	−0.827809	−	1.43381i	0.0719438	−	0.997409i	$-0.477080\pi$
$888$		0			0
$889$	−14.9759	+	18.3077i	−0.502274	+	0.614020i
$890$		0			0
$891$	15.4805	−	1.45369i	0.518616	−	0.0487003i
$892$		0			0
$893$	−34.6659	+	60.0431i	−1.16005	+	2.00927i
$894$		0			0
$895$	−3.70850	+	6.42331i	−0.123961	+	0.214708i
$896$		0			0
$897$	−14.3745	+	19.6699i	−0.479952	+	0.656760i
$898$		0			0
$899$	−0.162474	−	0.281413i	−0.00541881	−	0.00938565i
$900$		0			0
$901$	18.9000	+	10.9119i	0.629649	+	0.363528i
$902$		0			0
$903$	13.2578	−	13.0547i	0.441193	−	0.434433i
$904$		0			0
$905$	−4.79126	−	8.29871i	−0.159267	−	0.275858i
$906$		0			0
$907$	10.2798	+	5.93502i	0.341334	+	0.197069i	0.660862	−	0.750508i	$-0.270191\pi$
$907$	10.2798	+	5.93502i	0.341334	+	0.197069i	−0.319528	+	0.947577i	$0.603524\pi$
$908$		0			0
$909$	−6.39048	+	29.2659i	−0.211959	+	0.970690i
$910$		0			0
$911$	−43.8316	+	25.3062i	−1.45221	+	0.838432i	−0.998606	−	0.0527737i	$-0.983194\pi$
$911$	−43.8316	+	25.3062i	−1.45221	+	0.838432i	−0.453600	+	0.891205i	$0.649860\pi$
$912$		0			0
$913$		−	1.18022i		−	0.0390594i
$914$		0			0
$915$	51.1541	+	5.51994i	1.69110	+	0.182484i
$916$		0			0
$917$	−8.34377	+	51.0446i	−0.275536	+	1.68564i
$918$		0			0
$919$	12.7763	+	7.37638i	0.421450	+	0.243324i	0.695698	−	0.718335i	$-0.255095\pi$
$919$	12.7763	+	7.37638i	0.421450	+	0.243324i	−0.274247	+	0.961659i	$0.588429\pi$
$920$		0			0
$921$	−2.11237	+	2.89055i	−0.0696051	+	0.0952468i
$922$		0			0
$923$	−3.65654	+	6.33331i	−0.120356	+	0.208464i
$924$		0			0
$925$	−65.6018	−	113.626i	−2.15697	−	3.73599i
$926$		0			0
$927$	−9.66284	+	10.6127i	−0.317369	+	0.348568i
$928$		0			0
$929$		−	32.2141i		−	1.05691i	−0.848961	−	0.528455i	$-0.822771\pi$
$929$		−	32.2141i		−	1.05691i	0.848961	−	0.528455i	$-0.177229\pi$
$930$		0			0
$931$	48.7009	+	16.3584i	1.59611	+	0.536125i
$932$		0			0
$933$	−9.14073	+	12.5081i	−0.299254	+	0.409496i
$934$		0			0
$935$	26.6968	−	15.4134i	0.873078	−	0.504072i
$936$		0			0
$937$		−	9.13415i		−	0.298400i	−0.988807	−	0.149200i	$-0.952330\pi$
$937$		−	9.13415i		−	0.298400i	0.988807	−	0.149200i	$-0.0476698\pi$
$938$		0			0
$939$	3.40088	+	2.48532i	0.110984	+	0.0811053i
$940$		0			0
$941$		−	2.03413i		−	0.0663106i	−0.999450	−	0.0331553i	$-0.989444\pi$
$941$		−	2.03413i		−	0.0663106i	0.999450	−	0.0331553i	$-0.0105556\pi$
$942$		0			0
$943$	26.7578			0.871353
$944$		0			0
$945$	51.6189	+	27.1696i	1.67916	+	0.883826i
$946$		0			0
$947$			22.5209i			0.731830i	0.930648	+	0.365915i	$0.119244\pi$
$947$			22.5209i			0.731830i	−0.930648	+	0.365915i	$0.880756\pi$
$948$		0			0
$949$	−10.2986			−0.334306
$950$		0			0
$951$	−9.18913	+	12.5743i	−0.297978	+	0.407749i
$952$		0			0
$953$	−7.47118			−0.242015			−0.121008	−	0.992652i	$-0.538613\pi$
$953$	−7.47118			−0.242015			−0.121008	+	0.992652i	$0.538613\pi$
$954$		0			0
$955$	26.2306	+	45.4328i	0.848803	+	1.47017i
$956$		0			0
$957$	0.403661	+	0.294990i	0.0130485	+	0.00953567i
$958$		0			0
$959$	31.7955	−	12.0250i	1.02673	−	0.388307i
$960$		0			0
$961$	−27.2175			−0.877985
$962$		0			0
$963$	−5.85953	+	26.8344i	−0.188821	+	0.864726i
$964$		0			0
$965$	−83.6726	+	48.3084i	−2.69352	+	1.55510i
$966$		0			0
$967$	−20.1482	−	11.6326i	−0.647922	−	0.374078i	0.139738	−	0.990189i	$-0.455374\pi$
$967$	−20.1482	−	11.6326i	−0.647922	−	0.374078i	−0.787659	+	0.616111i	$0.788707\pi$
$968$		0			0
$969$	−43.1610	−	31.5415i	−1.38653	−	1.01326i
$970$		0			0
$971$	−0.490476	+	0.849530i	−0.0157401	+	0.0272627i	−0.873788	−	0.486307i	$-0.838344\pi$
$971$	−0.490476	+	0.849530i	−0.0157401	+	0.0272627i	0.858048	+	0.513569i	$0.171677\pi$
$972$		0			0
$973$	−10.9914	+	4.15694i	−0.352369	+	0.133265i
$974$		0			0
$975$	−7.65502	+	70.9402i	−0.245157	+	2.27190i
$976$		0			0
$977$	−5.62908			−0.180090			−0.0900452	−	0.995938i	$-0.528701\pi$
$977$	−5.62908			−0.180090			−0.0900452	+	0.995938i	$0.528701\pi$
$978$		0			0
$979$	8.55005	+	14.8091i	0.273261	+	0.473302i
$980$		0			0
$981$	5.68052	−	6.23893i	0.181365	−	0.199194i
$982$		0			0
$983$	20.1171	−	34.8438i	0.641636	−	1.11135i	−0.343432	−	0.939178i	$-0.611589\pi$
$983$	20.1171	−	34.8438i	0.641636	−	1.11135i	0.985068	−	0.172168i	$-0.0550772\pi$
$984$		0			0
$985$	−96.7799	+	55.8759i	−3.08367	+	1.78036i
$986$		0			0
$987$	−41.9004	+	10.8812i	−1.33370	+	0.346352i
$988$		0			0
$989$	9.01371	−	15.6122i	0.286619	−	0.496439i
$990$		0			0
$991$	7.50739	−	4.33440i	0.238480	−	0.137687i	−0.375998	−	0.926621i	$-0.622700\pi$
$991$	7.50739	−	4.33440i	0.238480	−	0.137687i	0.614478	+	0.788934i	$0.289367\pi$
$992$		0			0
$993$	−6.22220	−	4.54710i	−0.197456	−	0.144298i
$994$		0			0
$995$	31.3894	+	18.1227i	0.995111	+	0.574528i
$996$		0			0
$997$	−22.1016	−	12.7604i	−0.699965	−	0.404125i	0.107369	−	0.994219i	$-0.465757\pi$
$997$	−22.1016	−	12.7604i	−0.699965	−	0.404125i	−0.807334	+	0.590094i	$0.799091\pi$
$998$		0			0
$999$	−39.2519	+	34.7558i	−1.24187	+	1.09962i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cz.g.607.8	yes	24
3.2	odd	2		3024.2.cz.h.1279.12		24
4.3	odd	2		1008.2.cz.h.607.5	yes	24
7.3	odd	6		1008.2.bf.g.31.12	✓	24
9.2	odd	6		3024.2.bf.g.2287.12		24
9.7	even	3		1008.2.bf.h.943.1	yes	24
12.11	even	2		3024.2.cz.g.1279.12		24
21.17	even	6		3024.2.bf.h.1711.1		24
28.3	even	6		1008.2.bf.h.31.1	yes	24
36.7	odd	6		1008.2.bf.g.943.12	yes	24
36.11	even	6		3024.2.bf.h.2287.12		24
63.38	even	6		3024.2.cz.g.2719.12		24
63.52	odd	6		1008.2.cz.h.367.5	yes	24
84.59	odd	6		3024.2.bf.g.1711.1		24
252.115	even	6	inner	1008.2.cz.g.367.8	yes	24
252.227	odd	6		3024.2.cz.h.2719.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.g.31.12	✓	24	7.3	odd	6
1008.2.bf.g.943.12	yes	24	36.7	odd	6
1008.2.bf.h.31.1	yes	24	28.3	even	6
1008.2.bf.h.943.1	yes	24	9.7	even	3
1008.2.cz.g.367.8	yes	24	252.115	even	6	inner
1008.2.cz.g.607.8	yes	24	1.1	even	1	trivial
1008.2.cz.h.367.5	yes	24	63.52	odd	6
1008.2.cz.h.607.5	yes	24	4.3	odd	2
3024.2.bf.g.1711.1		24	84.59	odd	6
3024.2.bf.g.2287.12		24	9.2	odd	6
3024.2.bf.h.1711.1		24	21.17	even	6
3024.2.bf.h.2287.12		24	36.11	even	6
3024.2.cz.g.1279.12		24	12.11	even	2
3024.2.cz.g.2719.12		24	63.38	even	6
3024.2.cz.h.1279.12		24	3.2	odd	2
3024.2.cz.h.2719.12		24	252.227	odd	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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.cz (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.02195 - 1.39843i) q^{3} +(-3.67461 + 2.12154i) q^{5} +(2.04787 + 1.67518i) q^{7} +(-0.911216 - 2.85827i) q^{9} +O(q^{10})\)	\(q+(1.02195 - 1.39843i) q^{3} +(-3.67461 + 2.12154i) q^{5} +(2.04787 + 1.67518i) q^{7} +(-0.911216 - 2.85827i) q^{9} +(-1.49616 - 0.863811i) q^{11} +(-2.74353 - 1.58398i) q^{13} +(-0.788464 + 7.30680i) q^{15} +(3.64191 - 2.10266i) q^{17} +(3.66963 - 6.35599i) q^{19} +(4.43545 - 1.15185i) q^{21} +(3.84515 - 2.22000i) q^{23} +(6.50184 - 11.2615i) q^{25} +(-4.92831 - 1.64675i) q^{27} +(-0.0835405 - 0.144696i) q^{29} +1.94485 q^{31} +(-2.73699 + 1.20951i) q^{33} +(-11.0791 - 1.81099i) q^{35} +(5.04487 - 8.73797i) q^{37} +(-5.01885 + 2.21788i) q^{39} +(5.21912 + 3.01326i) q^{41} +(3.51626 - 2.03012i) q^{43} +(9.41228 + 8.56983i) q^{45} -9.44670 q^{47} +(1.38756 + 6.86110i) q^{49} +(0.781447 - 7.24178i) q^{51} +(2.59479 + 4.49430i) q^{53} +7.33043 q^{55} +(-5.13821 - 11.6273i) q^{57} -6.67413 q^{59} -7.00089i q^{61} +(2.92205 - 7.37981i) q^{63} +13.4419 q^{65} +10.7195i q^{67} +(0.825057 - 7.64592i) q^{69} -2.30845i q^{71} +(2.81533 - 1.62543i) q^{73} +(-9.10386 - 20.6011i) q^{75} +(-1.61692 - 4.27532i) q^{77} +2.38834i q^{79} +(-7.33937 + 5.20900i) q^{81} +(0.341572 + 0.591621i) q^{83} +(-8.92174 + 15.4529i) q^{85} +(-0.287722 - 0.0310476i) q^{87} +(-8.57197 - 4.94903i) q^{89} +(-2.96496 - 7.83969i) q^{91} +(1.98755 - 2.71974i) q^{93} +31.1410i q^{95} +(-11.8382 + 6.83477i) q^{97} +(-1.10567 + 5.06355i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{3} - 3 q^{5} + 4 q^{7} + 17 q^{9}+O(q^{10}) \) 24 * q - 3 * q^3 - 3 * q^5 + 4 * q^7 + 17 * q^9	\( 24 q - 3 q^{3} - 3 q^{5} + 4 q^{7} + 17 q^{9} - 9 q^{11} - 3 q^{13} - 6 q^{15} - 3 q^{17} - 4 q^{19} + 13 q^{21} - 6 q^{23} + 15 q^{25} + 9 q^{27} + 18 q^{29} + 34 q^{31} - 21 q^{33} - 42 q^{35} - 3 q^{37} + 27 q^{39} + 36 q^{41} + 24 q^{43} + 21 q^{45} - 42 q^{47} + 30 q^{49} - 6 q^{51} - 12 q^{53} - 30 q^{55} - 13 q^{57} - 12 q^{59} - 3 q^{63} + 6 q^{69} + 48 q^{73} + 36 q^{75} - 48 q^{77} - 31 q^{81} - 48 q^{83} - 21 q^{85} + 15 q^{87} + 39 q^{89} + 9 q^{91} + 10 q^{93} + 3 q^{97} + 30 q^{99}+O(q^{100}) \) 24 * q - 3 * q^3 - 3 * q^5 + 4 * q^7 + 17 * q^9 - 9 * q^11 - 3 * q^13 - 6 * q^15 - 3 * q^17 - 4 * q^19 + 13 * q^21 - 6 * q^23 + 15 * q^25 + 9 * q^27 + 18 * q^29 + 34 * q^31 - 21 * q^33 - 42 * q^35 - 3 * q^37 + 27 * q^39 + 36 * q^41 + 24 * q^43 + 21 * q^45 - 42 * q^47 + 30 * q^49 - 6 * q^51 - 12 * q^53 - 30 * q^55 - 13 * q^57 - 12 * q^59 - 3 * q^63 + 6 * q^69 + 48 * q^73 + 36 * q^75 - 48 * q^77 - 31 * q^81 - 48 * q^83 - 21 * q^85 + 15 * q^87 + 39 * q^89 + 9 * q^91 + 10 * q^93 + 3 * q^97 + 30 * q^99

Introduction

L-functions

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