LMFDB - Embedded newform 1152.2.i.k.385.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(385,1152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1152.385");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1152 = 2^{7} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1152.i (of order $3$, 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:	$9.19876631285$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 3 x^{10} - 8 x^{9} + 22 x^{8} - 42 x^{7} + 51 x^{6} - 126 x^{5} + 198 x^{4} + \cdots + 729 $ x^12 - 2x^11 + 3x^10 - 8x^9 + 22x^8 - 42x^7 + 51x^6 - 126x^5 + 198x^4 - 216x^3 + 243x^2 - 486*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			385.1
Root			$-1.15879 - 1.28733i$ of defining polynomial
Character	$\chi$	$=$	1152.385
Dual form			1152.2.i.k.769.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.69425 - 0.359877i) q^{3} +(-1.74260 - 3.01828i) q^{5} +(1.34988 - 2.33807i) q^{7} +(2.74098 + 1.21944i) q^{9} +O(q^{10})$	\(q+(-1.69425 - 0.359877i) q^{3} +(-1.74260 - 3.01828i) q^{5} +(1.34988 - 2.33807i) q^{7} +(2.74098 + 1.21944i) q^{9} +(2.84274 - 4.92377i) q^{11} +(1.76055 + 3.04937i) q^{13} +(1.86620 + 5.74085i) q^{15} +7.65970 q^{17} +2.02060 q^{19} +(-3.12846 + 3.47548i) q^{21} +(0.0370909 + 0.0642434i) q^{23} +(-3.57334 + 6.18921i) q^{25} +(-4.20506 - 3.05246i) q^{27} +(2.46032 - 4.26140i) q^{29} +(-3.72257 - 6.44769i) q^{31} +(-6.58827 + 7.31907i) q^{33} -9.40925 q^{35} -5.00631 q^{37} +(-1.88542 - 5.79997i) q^{39} +(0.482053 + 0.834941i) q^{41} +(0.255495 - 0.442530i) q^{43} +(-1.09582 - 10.3980i) q^{45} +(2.83509 - 4.91053i) q^{47} +(-0.144369 - 0.250055i) q^{49} +(-12.9775 - 2.75655i) q^{51} +10.4058 q^{53} -19.8151 q^{55} +(-3.42340 - 0.727166i) q^{57} +(4.47636 + 7.75329i) q^{59} +(-1.46032 + 2.52935i) q^{61} +(6.55114 - 4.76248i) q^{63} +(6.13589 - 10.6277i) q^{65} +(-1.56829 - 2.71635i) q^{67} +(-0.0397217 - 0.122193i) q^{69} -8.19647 q^{71} +5.21796 q^{73} +(8.28150 - 9.20012i) q^{75} +(-7.67474 - 13.2930i) q^{77} +(0.716260 - 1.24060i) q^{79} +(6.02592 + 6.68493i) q^{81} +(-1.74052 + 3.01467i) q^{83} +(-13.3478 - 23.1191i) q^{85} +(-5.70198 + 6.33447i) q^{87} -12.4058 q^{89} +9.50616 q^{91} +(3.98660 + 12.2637i) q^{93} +(-3.52110 - 6.09873i) q^{95} +(-3.50265 + 6.06677i) q^{97} +(13.7962 - 10.0294i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} - 2 q^{5} + 6 q^{7} - 2 q^{9}+O(q^{10}) $ 12 * q + 4 * q^3 - 2 * q^5 + 6 * q^7 - 2 * q^9	$ 12 q + 4 q^{3} - 2 q^{5} + 6 q^{7} - 2 q^{9} + 4 q^{11} + 10 q^{13} + 4 q^{15} + 4 q^{17} + 4 q^{19} + 2 q^{21} + 8 q^{23} - 14 q^{25} - 14 q^{27} - 2 q^{29} + 8 q^{31} - 10 q^{33} + 8 q^{35} + 22 q^{39} - 2 q^{41} - 2 q^{43} + 10 q^{45} - 14 q^{47} - 18 q^{49} - 38 q^{51} + 24 q^{53} - 16 q^{55} - 38 q^{57} + 6 q^{59} + 14 q^{61} - 16 q^{63} - 8 q^{65} + 4 q^{67} - 50 q^{69} - 28 q^{71} + 60 q^{73} + 50 q^{75} + 2 q^{77} + 16 q^{79} + 22 q^{81} + 24 q^{83} + 16 q^{85} - 36 q^{87} - 48 q^{89} - 52 q^{91} + 42 q^{93} - 20 q^{95} - 14 q^{97} + 68 q^{99}+O(q^{100}) $ 12 * q + 4 * q^3 - 2 * q^5 + 6 * q^7 - 2 * q^9 + 4 * q^11 + 10 * q^13 + 4 * q^15 + 4 * q^17 + 4 * q^19 + 2 * q^21 + 8 * q^23 - 14 * q^25 - 14 * q^27 - 2 * q^29 + 8 * q^31 - 10 * q^33 + 8 * q^35 + 22 * q^39 - 2 * q^41 - 2 * q^43 + 10 * q^45 - 14 * q^47 - 18 * q^49 - 38 * q^51 + 24 * q^53 - 16 * q^55 - 38 * q^57 + 6 * q^59 + 14 * q^61 - 16 * q^63 - 8 * q^65 + 4 * q^67 - 50 * q^69 - 28 * q^71 + 60 * q^73 + 50 * q^75 + 2 * q^77 + 16 * q^79 + 22 * q^81 + 24 * q^83 + 16 * q^85 - 36 * q^87 - 48 * q^89 - 52 * q^91 + 42 * q^93 - 20 * q^95 - 14 * q^97 + 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−1.69425	−	0.359877i	−0.978177	−	0.207775i
$3$	−1.69425	−	0.359877i	−0.978177	−	0.207775i
$4$		0			0
$5$	−1.74260	−	3.01828i	−0.779317	−	1.34982i	−0.932336	−	0.361593i	$-0.882233\pi$
$5$	−1.74260	−	3.01828i	−0.779317	−	1.34982i	0.153019	−	0.988223i	$-0.451100\pi$
$6$		0			0
$7$	1.34988	−	2.33807i	0.510208	−	0.883706i	−0.489722	−	0.871879i	$-0.662902\pi$
$7$	1.34988	−	2.33807i	0.510208	−	0.883706i	0.999930	−	0.0118274i	$-0.00376488\pi$
$8$		0			0
$9$	2.74098	+	1.21944i	0.913659	+	0.406481i
$10$		0			0
$11$	2.84274	−	4.92377i	0.857119	−	1.48457i	−0.0175468	−	0.999846i	$-0.505586\pi$
$11$	2.84274	−	4.92377i	0.857119	−	1.48457i	0.874665	−	0.484727i	$-0.161081\pi$
$12$		0			0
$13$	1.76055	+	3.04937i	0.488289	+	0.845742i	0.999909	−	0.0134701i	$-0.00428779\pi$
$13$	1.76055	+	3.04937i	0.488289	+	0.845742i	−0.511620	+	0.859212i	$0.670954\pi$
$14$		0			0
$15$	1.86620	+	5.74085i	0.481851	+	1.48228i
$16$		0			0
$17$	7.65970			1.85775			0.928875	−	0.370392i	$-0.120777\pi$
$17$	7.65970			1.85775			0.928875	+	0.370392i	$0.120777\pi$
$18$		0			0
$19$	2.02060			0.463557			0.231778	−	0.972769i	$-0.425546\pi$
$19$	2.02060			0.463557			0.231778	+	0.972769i	$0.425546\pi$
$20$		0			0
$21$	−3.12846	+	3.47548i	−0.682685	+	0.758412i
$22$		0			0
$23$	0.0370909	+	0.0642434i	0.00773399	+	0.0133957i	0.869866	−	0.493287i	$-0.164205\pi$
$23$	0.0370909	+	0.0642434i	0.00773399	+	0.0133957i	−0.862133	+	0.506683i	$0.830872\pi$
$24$		0			0
$25$	−3.57334	+	6.18921i	−0.714669	+	1.23784i
$26$		0			0
$27$	−4.20506	−	3.05246i	−0.809263	−	0.587446i
$28$		0			0
$29$	2.46032	−	4.26140i	0.456870	−	0.791321i	−0.541924	−	0.840428i	$-0.682304\pi$
$29$	2.46032	−	4.26140i	0.456870	−	0.791321i	0.998794	+	0.0491062i	$0.0156373\pi$
$30$		0			0
$31$	−3.72257	−	6.44769i	−0.668594	−	1.15804i	−0.978297	−	0.207205i	$-0.933563\pi$
$31$	−3.72257	−	6.44769i	−0.668594	−	1.15804i	0.309704	−	0.950833i	$-0.399770\pi$
$32$		0			0
$33$	−6.58827	+	7.31907i	−1.14687	+	1.27409i
$34$		0			0
$35$	−9.40925			−1.59045
$36$		0			0
$37$	−5.00631			−0.823033			−0.411516	−	0.911402i	$-0.635001\pi$
$37$	−5.00631			−0.823033			−0.411516	+	0.911402i	$0.635001\pi$
$38$		0			0
$39$	−1.88542	−	5.79997i	−0.301909	−	0.928739i
$40$		0			0
$41$	0.482053	+	0.834941i	0.0752841	+	0.130396i	0.901210	−	0.433383i	$-0.142680\pi$
$41$	0.482053	+	0.834941i	0.0752841	+	0.130396i	−0.825926	+	0.563779i	$0.809347\pi$
$42$		0			0
$43$	0.255495	−	0.442530i	0.0389626	−	0.0674852i	−0.845887	−	0.533363i	$-0.820928\pi$
$43$	0.255495	−	0.442530i	0.0389626	−	0.0674852i	0.884849	+	0.465878i	$0.154261\pi$
$44$		0			0
$45$	−1.09582	−	10.3980i	−0.163355	−	1.55005i
$46$		0			0
$47$	2.83509	−	4.91053i	0.413541	−	0.716274i	−0.581733	−	0.813380i	$-0.697625\pi$
$47$	2.83509	−	4.91053i	0.413541	−	0.716274i	0.995274	+	0.0971059i	$0.0309586\pi$
$48$		0			0
$49$	−0.144369	−	0.250055i	−0.0206242	−	0.0357221i
$50$		0			0
$51$	−12.9775	−	2.75655i	−1.81721	−	0.385994i
$52$		0			0
$53$	10.4058			1.42935			0.714676	−	0.699455i	$-0.246574\pi$
$53$	10.4058			1.42935			0.714676	+	0.699455i	$0.246574\pi$
$54$		0			0
$55$	−19.8151			−2.67187
$56$		0			0
$57$	−3.42340	−	0.727166i	−0.453441	−	0.0963155i
$58$		0			0
$59$	4.47636	+	7.75329i	0.582773	+	1.00939i	0.995149	+	0.0983788i	$0.0313657\pi$
$59$	4.47636	+	7.75329i	0.582773	+	1.00939i	−0.412376	+	0.911014i	$0.635301\pi$
$60$		0			0
$61$	−1.46032	+	2.52935i	−0.186975	+	0.323849i	−0.944240	−	0.329258i	$-0.893202\pi$
$61$	−1.46032	+	2.52935i	−0.186975	+	0.323849i	0.757266	+	0.653107i	$0.226535\pi$
$62$		0			0
$63$	6.55114	−	4.76248i	0.825366	−	0.600016i
$64$		0			0
$65$	6.13589	−	10.6277i	0.761064	−	1.31820i
$66$		0			0
$67$	−1.56829	−	2.71635i	−0.191597	−	0.331855i	0.754183	−	0.656665i	$-0.228033\pi$
$67$	−1.56829	−	2.71635i	−0.191597	−	0.331855i	−0.945780	+	0.324809i	$0.894700\pi$
$68$		0			0
$69$	−0.0397217	−	0.122193i	−0.00478193	−	0.0147103i
$70$		0			0
$71$	−8.19647			−0.972742			−0.486371	−	0.873752i	$-0.661680\pi$
$71$	−8.19647			−0.972742			−0.486371	+	0.873752i	$0.661680\pi$
$72$		0			0
$73$	5.21796			0.610716			0.305358	−	0.952238i	$-0.401224\pi$
$73$	5.21796			0.610716			0.305358	+	0.952238i	$0.401224\pi$
$74$		0			0
$75$	8.28150	−	9.20012i	0.956265	−	1.06234i
$76$		0			0
$77$	−7.67474	−	13.2930i	−0.874617	−	1.51488i
$78$		0			0
$79$	0.716260	−	1.24060i	0.0805855	−	0.139578i	−0.822916	−	0.568163i	$-0.807654\pi$
$79$	0.716260	−	1.24060i	0.0805855	−	0.139578i	0.903502	+	0.428585i	$0.140988\pi$
$80$		0			0
$81$	6.02592	+	6.68493i	0.669546	+	0.742770i
$82$		0			0
$83$	−1.74052	+	3.01467i	−0.191047	+	0.330903i	−0.945597	−	0.325339i	$-0.894522\pi$
$83$	−1.74052	+	3.01467i	−0.191047	+	0.330903i	0.754551	+	0.656242i	$0.227855\pi$
$84$		0			0
$85$	−13.3478	−	23.1191i	−1.44778	−	2.50762i
$86$		0			0
$87$	−5.70198	+	6.33447i	−0.611316	+	0.679126i
$88$		0			0
$89$	−12.4058			−1.31502			−0.657509	−	0.753447i	$-0.728390\pi$
$89$	−12.4058			−1.31502			−0.657509	+	0.753447i	$0.728390\pi$
$90$		0			0
$91$	9.50616			0.996516
$92$		0			0
$93$	3.98660	+	12.2637i	0.413392	+	1.27168i
$94$		0			0
$95$	−3.52110	−	6.09873i	−0.361258	−	0.625717i
$96$		0			0
$97$	−3.50265	+	6.06677i	−0.355640	+	0.615987i	−0.987227	−	0.159318i	$-0.949071\pi$
$97$	−3.50265	+	6.06677i	−0.355640	+	0.615987i	0.631587	+	0.775305i	$0.282404\pi$
$98$		0			0
$99$	13.7962	−	10.0294i	1.38657	−	1.00799i
$100$		0			0
$101$	−4.44237	+	7.69441i	−0.442032	+	0.765623i	−0.997840	−	0.0656882i	$-0.979076\pi$
$101$	−4.44237	+	7.69441i	−0.442032	+	0.765623i	0.555808	+	0.831311i	$0.312409\pi$
$102$		0			0
$103$	2.65012	+	4.59014i	0.261124	+	0.452280i	0.966541	−	0.256513i	$-0.0825736\pi$
$103$	2.65012	+	4.59014i	0.261124	+	0.452280i	−0.705417	+	0.708792i	$0.749240\pi$
$104$		0			0
$105$	15.9416	+	3.38617i	1.55574	+	0.330456i
$106$		0			0
$107$	−7.53993			−0.728912			−0.364456	−	0.931221i	$-0.618745\pi$
$107$	−7.53993			−0.728912			−0.364456	+	0.931221i	$0.618745\pi$
$108$		0			0
$109$	−13.8840			−1.32984			−0.664922	−	0.746913i	$-0.731535\pi$
$109$	−13.8840			−1.32984			−0.664922	+	0.746913i	$0.731535\pi$
$110$		0			0
$111$	8.48195	+	1.80166i	0.805072	+	0.171006i
$112$		0			0
$113$	1.36549	+	2.36510i	0.128454	+	0.222489i	0.923078	−	0.384613i	$-0.125665\pi$
$113$	1.36549	+	2.36510i	0.128454	+	0.222489i	−0.794624	+	0.607102i	$0.792332\pi$
$114$		0			0
$115$	0.129270	−	0.223902i	0.0120545	−	0.0208789i
$116$		0			0
$117$	1.10710	+	10.5051i	0.102352	+	0.971200i
$118$		0			0
$119$	10.3397	−	17.9089i	0.947839	−	1.64171i
$120$		0			0
$121$	−10.6624	−	18.4677i	−0.969305	−	1.67889i
$122$		0			0
$123$	−0.516244	−	1.58808i	−0.0465481	−	0.143192i
$124$		0			0
$125$	7.48166			0.669180
$126$		0			0
$127$	5.89964			0.523509			0.261754	−	0.965135i	$-0.415699\pi$
$127$	5.89964			0.523509			0.261754	+	0.965135i	$0.415699\pi$
$128$		0			0
$129$	−0.592129	+	0.657810i	−0.0521340	+	0.0579170i
$130$		0			0
$131$	0.566027	+	0.980388i	0.0494540	+	0.0856569i	0.889693	−	0.456560i	$-0.150919\pi$
$131$	0.566027	+	0.980388i	0.0494540	+	0.0856569i	−0.840239	+	0.542217i	$0.817585\pi$
$132$		0			0
$133$	2.72757	−	4.72429i	0.236510	−	0.409648i
$134$		0			0
$135$	−1.88542	+	18.0113i	−0.162271	+	1.55016i
$136$		0			0
$137$	3.18182	−	5.51107i	0.271841	−	0.470843i	−0.697492	−	0.716592i	$-0.745701\pi$
$137$	3.18182	−	5.51107i	0.271841	−	0.470843i	0.969333	+	0.245750i	$0.0790341\pi$
$138$		0			0
$139$	11.2001	+	19.3992i	0.949983	+	1.64542i	0.745453	+	0.666559i	$0.232233\pi$
$139$	11.2001	+	19.3992i	0.949983	+	1.64542i	0.204531	+	0.978860i	$0.434433\pi$
$140$		0			0
$141$	−6.57054	+	7.29938i	−0.553340	+	0.614719i
$142$		0			0
$143$	20.0192			1.67409
$144$		0			0
$145$	−17.1495			−1.42418
$146$		0			0
$147$	0.154609	+	0.475611i	0.0127519	+	0.0392277i
$148$		0			0
$149$	−0.939215	−	1.62677i	−0.0769435	−	0.133270i	0.824986	−	0.565153i	$-0.191183\pi$
$149$	−0.939215	−	1.62677i	−0.0769435	−	0.133270i	−0.901930	+	0.431883i	$0.857849\pi$
$150$		0			0
$151$	−0.183779	+	0.318315i	−0.0149557	+	0.0259041i	−0.873406	−	0.486992i	$-0.838094\pi$
$151$	−0.183779	+	0.318315i	−0.0149557	+	0.0259041i	0.858451	+	0.512896i	$0.171427\pi$
$152$		0			0
$153$	20.9951	+	9.34057i	1.69735	+	0.755141i
$154$		0			0
$155$	−12.9739	+	22.4715i	−1.04209	+	1.80496i
$156$		0			0
$157$	7.15363	+	12.3905i	0.570922	+	0.988866i	0.996472	+	0.0839309i	$0.0267475\pi$
$157$	7.15363	+	12.3905i	0.570922	+	0.988866i	−0.425550	+	0.904935i	$0.639919\pi$
$158$		0			0
$159$	−17.6301	−	3.74482i	−1.39816	−	0.296984i
$160$		0			0
$161$	0.200274			0.0157838
$162$		0			0
$163$	−3.02958			−0.237295			−0.118648	−	0.992936i	$-0.537856\pi$
$163$	−3.02958			−0.237295			−0.118648	+	0.992936i	$0.537856\pi$
$164$		0			0
$165$	33.5718	+	7.13099i	2.61356	+	0.555147i
$166$		0			0
$167$	0.629519	+	1.09036i	0.0487137	+	0.0843745i	0.889354	−	0.457219i	$-0.151154\pi$
$167$	0.629519	+	1.09036i	0.0487137	+	0.0843745i	−0.840640	+	0.541594i	$0.817821\pi$
$168$		0			0
$169$	0.300915	−	0.521200i	0.0231473	−	0.0400923i
$170$		0			0
$171$	5.53841	+	2.46400i	0.423533	+	0.188427i
$172$		0			0
$173$	7.14845	−	12.3815i	0.543487	−	0.941347i	−0.455214	−	0.890382i	$-0.650437\pi$
$173$	7.14845	−	12.3815i	0.543487	−	0.941347i	0.998700	−	0.0509644i	$-0.0162295\pi$
$174$		0			0
$175$	9.64719	+	16.7094i	0.729259	+	1.26311i
$176$		0			0
$177$	−4.79386	−	14.7470i	−0.360329	−	1.10845i
$178$		0			0
$179$	−12.7991			−0.956647			−0.478324	−	0.878184i	$-0.658755\pi$
$179$	−12.7991			−0.956647			−0.478324	+	0.878184i	$0.658755\pi$
$180$		0			0
$181$	−10.4986			−0.780355			−0.390177	−	0.920740i	$-0.627586\pi$
$181$	−10.4986			−0.780355			−0.390177	+	0.920740i	$0.627586\pi$
$182$		0			0
$183$	3.38440	−	3.75981i	0.250182	−	0.277933i
$184$		0			0
$185$	8.72403	+	15.1105i	0.641403	+	1.11094i
$186$		0			0
$187$	21.7746	−	37.7146i	1.59231	−	2.75797i
$188$		0			0
$189$	−12.8132	+	5.71124i	−0.932022	+	0.415431i
$190$		0			0
$191$	4.09526	−	7.09320i	0.296323	−	0.513246i	−0.678969	−	0.734167i	$-0.737573\pi$
$191$	4.09526	−	7.09320i	0.296323	−	0.513246i	0.975292	+	0.220921i	$0.0709062\pi$
$192$		0			0
$193$	−1.46146	−	2.53132i	−0.105198	−	0.182208i	0.808621	−	0.588330i	$-0.200214\pi$
$193$	−1.46146	−	2.53132i	−0.105198	−	0.182208i	−0.913819	+	0.406122i	$0.866881\pi$
$194$		0			0
$195$	−14.2204	+	15.7978i	−1.01834	+	1.13130i
$196$		0			0
$197$	−4.44174			−0.316461			−0.158230	−	0.987402i	$-0.550579\pi$
$197$	−4.44174			−0.316461			−0.158230	+	0.987402i	$0.550579\pi$
$198$		0			0
$199$	−14.6898			−1.04133			−0.520665	−	0.853761i	$-0.674316\pi$
$199$	−14.6898			−1.04133			−0.520665	+	0.853761i	$0.674316\pi$
$200$		0			0
$201$	1.67952	+	5.16658i	0.118464	+	0.364422i
$202$		0			0
$203$	−6.64228	−	11.5048i	−0.466197	−	0.807477i
$204$		0			0
$205$	1.68006	−	2.90994i	0.117340	−	0.203239i
$206$		0			0
$207$	0.0233242	+	0.221320i	0.00162115	+	0.0153828i
$208$		0			0
$209$	5.74404	−	9.94896i	0.397323	−	0.688184i
$210$		0			0
$211$	2.04700	+	3.54551i	0.140921	+	0.244083i	0.927844	−	0.372969i	$-0.121660\pi$
$211$	2.04700	+	3.54551i	0.140921	+	0.244083i	−0.786923	+	0.617052i	$0.788327\pi$
$212$		0			0
$213$	13.8869	+	2.94972i	0.951514	+	0.202111i
$214$		0			0
$215$	−1.78091			−0.121457
$216$		0			0
$217$	−20.1002			−1.36449
$218$		0			0
$219$	−8.84054	−	1.87782i	−0.597388	−	0.126892i
$220$		0			0
$221$	13.4853	+	23.3572i	0.907120	+	1.57118i
$222$		0			0
$223$	−6.24612	+	10.8186i	−0.418271	+	0.724467i	−0.995766	−	0.0919276i	$-0.970697\pi$
$223$	−6.24612	+	10.8186i	−0.418271	+	0.724467i	0.577494	+	0.816395i	$0.304030\pi$
$224$		0			0
$225$	−17.3419	+	12.6070i	−1.15612	+	0.840467i
$226$		0			0
$227$	−4.52721	+	7.84136i	−0.300482	+	0.520449i	−0.976245	−	0.216669i	$-0.930481\pi$
$227$	−4.52721	+	7.84136i	−0.300482	+	0.520449i	0.675764	+	0.737118i	$0.263814\pi$
$228$		0			0
$229$	13.1073	+	22.7024i	0.866152	+	1.50022i	0.865899	+	0.500219i	$0.166747\pi$
$229$	13.1073	+	22.7024i	0.866152	+	1.50022i	0.000252919		1.00000i	$0.499919\pi$
$230$		0			0
$231$	8.21908	+	25.2837i	0.540776	+	1.66355i
$232$		0			0
$233$	1.41840			0.0929224			0.0464612	−	0.998920i	$-0.485206\pi$
$233$	1.41840			0.0929224			0.0464612	+	0.998920i	$0.485206\pi$
$234$		0			0
$235$	−19.7618			−1.28912
$236$		0			0
$237$	−1.65999	+	1.84412i	−0.107828	+	0.119788i
$238$		0			0
$239$	8.18200	+	14.1716i	0.529250	+	0.916688i	0.999418	+	0.0341107i	$0.0108599\pi$
$239$	8.18200	+	14.1716i	0.529250	+	0.916688i	−0.470168	+	0.882577i	$0.655807\pi$
$240$		0			0
$241$	−5.17500	+	8.96336i	−0.333351	+	0.577381i	−0.983167	−	0.182711i	$-0.941513\pi$
$241$	−5.17500	+	8.96336i	−0.333351	+	0.577381i	0.649816	+	0.760092i	$0.274846\pi$
$242$		0			0
$243$	−7.80366	−	13.4945i	−0.500605	−	0.865676i
$244$		0			0
$245$	−0.503157	+	0.871493i	−0.0321455	+	0.0556776i
$246$		0			0
$247$	3.55737	+	6.16154i	0.226350	+	0.392049i
$248$		0			0
$249$	4.03379	−	4.48124i	0.255631	−	0.283987i
$250$		0			0
$251$	26.9624			1.70185			0.850927	−	0.525283i	$-0.176041\pi$
$251$	26.9624			1.70185			0.850927	+	0.525283i	$0.176041\pi$
$252$		0			0
$253$	0.421759			0.0265158
$254$		0			0
$255$	14.2946	+	43.9732i	0.895160	+	2.75371i
$256$		0			0
$257$	−14.8380	−	25.7001i	−0.925568	−	1.60313i	−0.790646	−	0.612274i	$-0.790255\pi$
$257$	−14.8380	−	25.7001i	−0.925568	−	1.60313i	−0.134922	−	0.990856i	$-0.543078\pi$
$258$		0			0
$259$	−6.75794	+	11.7051i	−0.419918	+	0.727319i
$260$		0			0
$261$	11.9402	−	8.68017i	0.739080	−	0.537289i
$262$		0			0
$263$	1.46961	−	2.54544i	0.0906200	−	0.156959i	−0.817152	−	0.576422i	$-0.804448\pi$
$263$	1.46961	−	2.54544i	0.0906200	−	0.156959i	0.907772	+	0.419464i	$0.137782\pi$
$264$		0			0
$265$	−18.1333	−	31.4078i	−1.11392	−	1.92936i
$266$		0			0
$267$	21.0186	+	4.46458i	1.28632	+	0.273228i
$268$		0			0
$269$	13.4251			0.818541			0.409270	−	0.912413i	$-0.365783\pi$
$269$	13.4251			0.818541			0.409270	+	0.912413i	$0.365783\pi$
$270$		0			0
$271$	−31.3320			−1.90329			−0.951643	−	0.307207i	$-0.900606\pi$
$271$	−31.3320			−1.90329			−0.951643	+	0.307207i	$0.900606\pi$
$272$		0			0
$273$	−16.1058	−	3.42104i	−0.974769	−	0.207051i
$274$		0			0
$275$	20.3162	+	35.1887i	1.22511	+	2.12196i
$276$		0			0
$277$	4.78089	−	8.28075i	0.287256	−	0.497542i	−0.685898	−	0.727698i	$-0.740590\pi$
$277$	4.78089	−	8.28075i	0.287256	−	0.497542i	0.973154	+	0.230156i	$0.0739236\pi$
$278$		0			0
$279$	−2.34090	−	22.2124i	−0.140146	−	1.32982i
$280$		0			0
$281$	3.39152	−	5.87429i	0.202321	−	0.350431i	−0.746955	−	0.664875i	$-0.768485\pi$
$281$	3.39152	−	5.87429i	0.202321	−	0.350431i	0.949276	+	0.314444i	$0.101818\pi$
$282$		0			0
$283$	9.61895	+	16.6605i	0.571787	+	0.990364i	0.996383	+	0.0849812i	$0.0270830\pi$
$283$	9.61895	+	16.6605i	0.571787	+	0.990364i	−0.424595	+	0.905383i	$0.639584\pi$
$284$		0			0
$285$	3.77084	+	11.5999i	0.223366	+	0.687122i
$286$		0			0
$287$	2.60286			0.153642
$288$		0			0
$289$	41.6710			2.45124
$290$		0			0
$291$	8.11766	−	9.01811i	0.475866	−	0.528651i
$292$		0			0
$293$	5.63884	+	9.76676i	0.329425	+	0.570580i	0.982398	−	0.186801i	$-0.0598119\pi$
$293$	5.63884	+	9.76676i	0.329425	+	0.570580i	−0.652973	+	0.757381i	$0.726479\pi$
$294$		0			0
$295$	15.6011	−	27.0218i	0.908329	−	1.57327i
$296$		0			0
$297$	−26.9835	+	12.0274i	−1.56574	+	0.697900i
$298$		0			0
$299$	−0.130601	+	0.226207i	−0.00755285	+	0.0130819i
$300$		0			0
$301$	−0.689776	−	1.19473i	−0.0397580	−	0.0688629i
$302$		0			0
$303$	10.2955	−	11.4376i	0.591463	−	0.657071i
$304$		0			0
$305$	10.1790			0.582850
$306$		0			0
$307$	22.2819			1.27169			0.635846	−	0.771816i	$-0.280651\pi$
$307$	22.2819			1.27169			0.635846	+	0.771816i	$0.280651\pi$
$308$		0			0
$309$	−2.83808	−	8.73056i	−0.161453	−	0.496664i
$310$		0			0
$311$	12.0604	+	20.8893i	0.683884	+	1.18452i	0.973786	+	0.227466i	$0.0730441\pi$
$311$	12.0604	+	20.8893i	0.683884	+	1.18452i	−0.289902	+	0.957056i	$0.593623\pi$
$312$		0			0
$313$	14.5297	−	25.1661i	0.821265	−	1.42247i	−0.0834762	−	0.996510i	$-0.526602\pi$
$313$	14.5297	−	25.1661i	0.821265	−	1.42247i	0.904741	−	0.425962i	$-0.140064\pi$
$314$		0			0
$315$	−25.7905	−	11.4741i	−1.45313	−	0.646490i
$316$		0			0
$317$	16.2862	−	28.2085i	0.914724	−	1.58435i	0.107418	−	0.994214i	$-0.465742\pi$
$317$	16.2862	−	28.2085i	0.914724	−	1.58435i	0.807305	−	0.590134i	$-0.200925\pi$
$318$		0			0
$319$	−13.9881	−	24.2281i	−0.783183	−	1.35651i
$320$		0			0
$321$	12.7745	+	2.71344i	0.713005	+	0.151450i
$322$		0			0
$323$	15.4772			0.861173
$324$		0			0
$325$	−25.1642			−1.39586
$326$		0			0
$327$	23.5230	+	4.99652i	1.30082	+	0.276308i
$328$		0			0
$329$	−7.65409	−	13.2573i	−0.421984	−	0.730897i
$330$		0			0
$331$	−8.05963	+	13.9597i	−0.442997	+	0.767293i	−0.997910	−	0.0646148i	$-0.979418\pi$
$331$	−8.05963	+	13.9597i	−0.442997	+	0.767293i	0.554913	+	0.831908i	$0.312751\pi$
$332$		0			0
$333$	−13.7222	−	6.10492i	−0.751972	−	0.334547i
$334$		0			0
$335$	−5.46581	+	9.46706i	−0.298629	+	0.517241i
$336$		0			0
$337$	12.6119	+	21.8445i	0.687015	+	1.18995i	0.972799	+	0.231651i	$0.0744128\pi$
$337$	12.6119	+	21.8445i	0.687015	+	1.18995i	−0.285783	+	0.958294i	$0.592254\pi$
$338$		0			0
$339$	−1.46234	−	4.49847i	−0.0794233	−	0.244324i
$340$		0			0
$341$	−42.3292			−2.29226
$342$		0			0
$343$	18.1188			0.978325
$344$		0			0
$345$	−0.299592	+	0.332824i	−0.0161295	+	0.0179187i
$346$		0			0
$347$	−2.16774	−	3.75464i	−0.116371	−	0.201560i	0.801956	−	0.597383i	$-0.203793\pi$
$347$	−2.16774	−	3.75464i	−0.116371	−	0.201560i	−0.918327	+	0.395823i	$0.870459\pi$
$348$		0			0
$349$	−9.77744	+	16.9350i	−0.523374	+	0.906511i	0.476255	+	0.879307i	$0.341994\pi$
$349$	−9.77744	+	16.9350i	−0.523374	+	0.906511i	−0.999630	+	0.0272042i	$0.991340\pi$
$350$		0			0
$351$	1.90484	−	18.1968i	0.101673	−	0.971271i
$352$		0			0
$353$	9.13835	−	15.8281i	0.486385	−	0.842444i	−0.513492	−	0.858094i	$-0.671648\pi$
$353$	9.13835	−	15.8281i	0.486385	−	0.842444i	0.999878	+	0.0156502i	$0.00498183\pi$
$354$		0			0
$355$	14.2832	+	24.7392i	0.758074	+	1.31302i
$356$		0			0
$357$	−23.9631	+	26.6212i	−1.26826	+	1.40894i
$358$		0			0
$359$	−3.41976			−0.180488			−0.0902440	−	0.995920i	$-0.528765\pi$
$359$	−3.41976			−0.180488			−0.0902440	+	0.995920i	$0.528765\pi$
$360$		0			0
$361$	−14.9172			−0.785115
$362$		0			0
$363$	11.4186	+	35.1261i	0.599321	+	1.84364i
$364$		0			0
$365$	−9.09285	−	15.7493i	−0.475941	−	0.824355i
$366$		0			0
$367$	5.46341	−	9.46291i	0.285188	−	0.493960i	−0.687467	−	0.726216i	$-0.741277\pi$
$367$	5.46341	−	9.46291i	0.285188	−	0.493960i	0.972655	+	0.232256i	$0.0746107\pi$
$368$		0			0
$369$	0.303134	+	2.87639i	0.0157805	+	0.149739i
$370$		0			0
$371$	14.0467	−	24.3296i	0.729267	−	1.26313i
$372$		0			0
$373$	10.4603	+	18.1178i	0.541615	+	0.938104i	0.998812	+	0.0487387i	$0.0155202\pi$
$373$	10.4603	+	18.1178i	0.541615	+	0.938104i	−0.457197	+	0.889366i	$0.651147\pi$
$374$		0			0
$375$	−12.6758	−	2.69247i	−0.654576	−	0.139039i
$376$		0			0
$377$	17.3261			0.892338
$378$		0			0
$379$	−18.0219			−0.925725			−0.462862	−	0.886430i	$-0.653178\pi$
$379$	−18.0219			−0.925725			−0.462862	+	0.886430i	$0.653178\pi$
$380$		0			0
$381$	−9.99548	−	2.12314i	−0.512084	−	0.108772i
$382$		0			0
$383$	−12.4732	−	21.6042i	−0.637350	−	1.10392i	−0.986012	−	0.166674i	$-0.946697\pi$
$383$	−12.4732	−	21.6042i	−0.637350	−	1.10392i	0.348662	−	0.937249i	$-0.386636\pi$
$384$		0			0
$385$	−26.7481	+	46.3290i	−1.36321	+	2.36115i
$386$		0			0
$387$	1.23995	−	0.901403i	0.0630300	−	0.0458209i
$388$		0			0
$389$	−6.96347	+	12.0611i	−0.353062	+	0.611522i	−0.986784	−	0.162039i	$-0.948193\pi$
$389$	−6.96347	+	12.0611i	−0.353062	+	0.611522i	0.633722	+	0.773561i	$0.281526\pi$
$390$		0			0
$391$	0.284105	+	0.492085i	0.0143678	+	0.0248858i
$392$		0			0
$393$	−0.606174	−	1.86472i	−0.0305774	−	0.0940629i
$394$		0			0
$395$	−4.99263			−0.251206
$396$		0			0
$397$	−6.54840			−0.328655			−0.164327	−	0.986406i	$-0.552545\pi$
$397$	−6.54840			−0.328655			−0.164327	+	0.986406i	$0.552545\pi$
$398$		0			0
$399$	−6.32135	+	7.02255i	−0.316464	+	0.351567i
$400$		0			0
$401$	−12.1738	−	21.0857i	−0.607933	−	1.05297i	−0.991581	−	0.129491i	$-0.958666\pi$
$401$	−12.1738	−	21.0857i	−0.607933	−	1.05297i	0.383648	−	0.923480i	$-0.374668\pi$
$402$		0			0
$403$	13.1076	−	22.7030i	0.652934	−	1.13092i
$404$		0			0
$405$	9.67622	−	29.8371i	0.480815	−	1.48262i
$406$		0			0
$407$	−14.2317	+	24.6499i	−0.705437	+	1.22185i
$408$		0			0
$409$	8.08792	+	14.0087i	0.399922	+	0.692685i	0.993716	−	0.111932i	$-0.0357040\pi$
$409$	8.08792	+	14.0087i	0.399922	+	0.692685i	−0.593794	+	0.804617i	$0.702371\pi$
$410$		0			0
$411$	−7.37411	+	8.19208i	−0.363738	+	0.404086i
$412$		0			0
$413$	24.1703			1.18934
$414$		0			0
$415$	12.1322			0.595544
$416$		0			0
$417$	−11.9945	−	36.8978i	−0.587374	−	1.80689i
$418$		0			0
$419$	−17.2436	−	29.8668i	−0.842405	−	1.45909i	−0.887856	−	0.460121i	$-0.847806\pi$
$419$	−17.2436	−	29.8668i	−0.842405	−	1.45909i	0.0454518	−	0.998967i	$-0.485527\pi$
$420$		0			0
$421$	15.6909	−	27.1774i	0.764728	−	1.32455i	−0.175662	−	0.984451i	$-0.556207\pi$
$421$	15.6909	−	27.1774i	0.764728	−	1.32455i	0.940390	−	0.340097i	$-0.110460\pi$
$422$		0			0
$423$	13.7590	−	10.0024i	0.668987	−	0.486333i
$424$		0			0
$425$	−27.3708	+	47.4075i	−1.32768	+	2.29960i
$426$		0			0
$427$	3.94252	+	6.82864i	0.190792	+	0.330461i
$428$		0			0
$429$	−33.9175	−	7.20443i	−1.63755	−	0.347833i
$430$		0			0
$431$	−12.1491			−0.585200			−0.292600	−	0.956235i	$-0.594520\pi$
$431$	−12.1491			−0.585200			−0.292600	+	0.956235i	$0.594520\pi$
$432$		0			0
$433$	2.40374			0.115517			0.0577583	−	0.998331i	$-0.481605\pi$
$433$	2.40374			0.115517			0.0577583	+	0.998331i	$0.481605\pi$
$434$		0			0
$435$	29.0555	+	6.17169i	1.39310	+	0.295910i
$436$		0			0
$437$	0.0749458	+	0.129810i	0.00358514	+	0.00620965i
$438$		0			0
$439$	−18.6941	+	32.3792i	−0.892222	+	1.54537i	−0.0550162	+	0.998485i	$0.517521\pi$
$439$	−18.6941	+	32.3792i	−0.892222	+	1.54537i	−0.837206	+	0.546888i	$0.815812\pi$
$440$		0			0
$441$	−0.0907850	−	0.861444i	−0.00432310	−	0.0410212i
$442$		0			0
$443$	−4.22340	+	7.31515i	−0.200660	+	0.347553i	−0.948741	−	0.316054i	$-0.897642\pi$
$443$	−4.22340	+	7.31515i	−0.200660	+	0.347553i	0.748081	+	0.663607i	$0.230975\pi$
$444$		0			0
$445$	21.6185	+	37.4443i	1.02481	+	1.77503i
$446$		0			0
$447$	1.00583	+	3.09415i	0.0475741	+	0.146348i
$448$		0			0
$449$	18.6531			0.880295			0.440147	−	0.897926i	$-0.354926\pi$
$449$	18.6531			0.880295			0.440147	+	0.897926i	$0.354926\pi$
$450$		0			0
$451$	5.48141			0.258109
$452$		0			0
$453$	0.425922	−	0.473167i	0.0200116	−	0.0222313i
$454$		0			0
$455$	−16.5655	−	28.6922i	−0.776601	−	1.34511i
$456$		0			0
$457$	−8.91748	+	15.4455i	−0.417142	+	0.722511i	−0.995651	−	0.0931650i	$-0.970302\pi$
$457$	−8.91748	+	15.4455i	−0.417142	+	0.722511i	0.578509	+	0.815676i	$0.303635\pi$
$458$		0			0
$459$	−32.2095	−	23.3809i	−1.50341	−	1.09133i
$460$		0			0
$461$	10.0563	−	17.4181i	0.468370	−	0.811240i	−0.530977	−	0.847386i	$-0.678175\pi$
$461$	10.0563	−	17.4181i	0.468370	−	0.811240i	0.999347	+	0.0361463i	$0.0115082\pi$
$462$		0			0
$463$	4.10747	+	7.11435i	0.190890	+	0.330632i	0.945546	−	0.325490i	$-0.105529\pi$
$463$	4.10747	+	7.11435i	0.190890	+	0.330632i	−0.754655	+	0.656122i	$0.772196\pi$
$464$		0			0
$465$	30.0681	−	33.4034i	1.39438	−	1.54905i
$466$		0			0
$467$	−19.3274			−0.894364			−0.447182	−	0.894443i	$-0.647572\pi$
$467$	−19.3274			−0.894364			−0.447182	+	0.894443i	$0.647572\pi$
$468$		0			0
$469$	−8.46802			−0.391017
$470$		0			0
$471$	−7.66102	−	23.5670i	−0.353001	−	1.08591i
$472$		0			0
$473$	−1.45261	−	2.51600i	−0.0667911	−	0.115686i
$474$		0			0
$475$	−7.22029	+	12.5059i	−0.331290	+	0.573811i
$476$		0			0
$477$	28.5222	+	12.6893i	1.30594	+	0.581005i
$478$		0			0
$479$	−21.1597	+	36.6498i	−0.966814	+	1.67457i	−0.262152	+	0.965027i	$0.584432\pi$
$479$	−21.1597	+	36.6498i	−0.966814	+	1.67457i	−0.704661	+	0.709544i	$0.748901\pi$
$480$		0			0
$481$	−8.81387	−	15.2661i	−0.401878	−	0.696073i
$482$		0			0
$483$	−0.339314	−	0.0720738i	−0.0154393	−	0.00327947i
$484$		0			0
$485$	24.4149			1.10863
$486$		0			0
$487$	1.36060			0.0616547			0.0308273	−	0.999525i	$-0.490186\pi$
$487$	1.36060			0.0616547			0.0308273	+	0.999525i	$0.490186\pi$
$488$		0			0
$489$	5.13287	+	1.09028i	0.232116	+	0.0493040i
$490$		0			0
$491$	−15.6328	−	27.0768i	−0.705497	−	1.22196i	−0.966512	−	0.256622i	$-0.917390\pi$
$491$	−15.6328	−	27.0768i	−0.705497	−	1.22196i	0.261015	−	0.965335i	$-0.415943\pi$
$492$		0			0
$493$	18.8453	−	32.6410i	0.848750	−	1.47008i
$494$		0			0
$495$	−54.3127	−	24.1634i	−2.44118	−	1.08606i
$496$		0			0
$497$	−11.0643	+	19.1639i	−0.496301	+	0.859618i
$498$		0			0
$499$	−7.37981	−	12.7822i	−0.330366	−	0.572210i	0.652218	−	0.758032i	$-0.273839\pi$
$499$	−7.37981	−	12.7822i	−0.330366	−	0.572210i	−0.982584	+	0.185821i	$0.940505\pi$
$500$		0			0
$501$	−0.674169	−	2.07389i	−0.0301196	−	0.0926547i
$502$		0			0
$503$	44.6336			1.99011			0.995056	−	0.0993124i	$-0.0316643\pi$
$503$	44.6336			1.99011			0.995056	+	0.0993124i	$0.0316643\pi$
$504$		0			0
$505$	30.9652			1.37793
$506$		0			0
$507$	−0.697393	+	0.774751i	−0.0309723	+	0.0344079i
$508$		0			0
$509$	−0.854549	−	1.48012i	−0.0378772	−	0.0656053i	0.846465	−	0.532444i	$-0.178726\pi$
$509$	−0.854549	−	1.48012i	−0.0378772	−	0.0656053i	−0.884343	+	0.466839i	$0.845393\pi$
$510$		0			0
$511$	7.04364	−	12.1999i	0.311592	−	0.539694i
$512$		0			0
$513$	−8.49673	−	6.16779i	−0.375140	−	0.272315i
$514$		0			0
$515$	9.23621	−	15.9976i	0.406996	−	0.704938i
$516$		0			0
$517$	−16.1189	−	27.9187i	−0.708907	−	1.22786i
$518$		0			0
$519$	−16.5671	+	18.4048i	−0.727214	+	0.807880i
$520$		0			0
$521$	−10.6018			−0.464475			−0.232237	−	0.972659i	$-0.574605\pi$
$521$	−10.6018			−0.464475			−0.232237	+	0.972659i	$0.574605\pi$
$522$		0			0
$523$	−27.1565			−1.18747			−0.593736	−	0.804660i	$-0.702348\pi$
$523$	−27.1565			−1.18747			−0.593736	+	0.804660i	$0.702348\pi$
$524$		0			0
$525$	−10.3314	−	31.7818i	−0.450901	−	1.38707i
$526$		0			0
$527$	−28.5138	−	49.3874i	−1.24208	−	2.15135i
$528$		0			0
$529$	11.4972	−	19.9138i	0.499880	−	0.865818i
$530$		0			0
$531$	2.81491	+	26.7103i	0.122157	+	1.15913i
$532$		0			0
$533$	−1.69736	+	2.93991i	−0.0735208	+	0.127342i
$534$		0			0
$535$	13.1391	+	22.7576i	0.568053	+	0.983897i
$536$		0			0
$537$	21.6848	+	4.60609i	0.935770	+	0.198767i
$538$		0			0
$539$	−1.64162			−0.0707094
$540$		0			0
$541$	35.1225			1.51003			0.755017	−	0.655705i	$-0.227629\pi$
$541$	35.1225			1.51003			0.755017	+	0.655705i	$0.227629\pi$
$542$		0			0
$543$	17.7873	+	3.77820i	0.763325	+	0.162138i
$544$		0			0
$545$	24.1943	+	41.9057i	1.03637	+	1.79504i
$546$		0			0
$547$	13.0029	−	22.5218i	0.555966	−	0.962961i	−0.441862	−	0.897083i	$-0.645682\pi$
$547$	13.0029	−	22.5218i	0.555966	−	0.962961i	0.997828	−	0.0658781i	$-0.0209849\pi$
$548$		0			0
$549$	−7.08709	+	5.15210i	−0.302470	+	0.219886i
$550$		0			0
$551$	4.97131	−	8.61057i	0.211785	−	0.366822i
$552$		0			0
$553$	−1.93373	−	3.34932i	−0.0822307	−	0.142428i
$554$		0			0
$555$	−9.34279	−	28.7405i	−0.396580	−	1.21997i
$556$		0			0
$557$	−28.8670			−1.22314			−0.611568	−	0.791192i	$-0.709461\pi$
$557$	−28.8670			−1.22314			−0.611568	+	0.791192i	$0.709461\pi$
$558$		0			0
$559$	1.79925			0.0761000
$560$		0			0
$561$	−50.4642	+	56.0619i	−2.13060	+	2.36694i
$562$		0			0
$563$	0.876491	+	1.51813i	0.0369397	+	0.0639815i	0.883904	−	0.467668i	$-0.154906\pi$
$563$	0.876491	+	1.51813i	0.0369397	+	0.0639815i	−0.846964	+	0.531649i	$0.821572\pi$
$564$		0			0
$565$	4.75901	−	8.24285i	0.200213	−	0.346779i
$566$		0			0
$567$	23.7641	−	5.06511i	0.997998	−	0.212715i
$568$		0			0
$569$	−13.3974	+	23.2049i	−0.561647	+	0.972801i	0.435706	+	0.900089i	$0.356499\pi$
$569$	−13.3974	+	23.2049i	−0.561647	+	0.972801i	−0.997353	+	0.0727120i	$0.976835\pi$
$570$		0			0
$571$	−12.6759	−	21.9553i	−0.530471	−	0.918803i	−0.999368	−	0.0355497i	$-0.988682\pi$
$571$	−12.6759	−	21.9553i	−0.530471	−	0.918803i	0.468897	−	0.883253i	$-0.344652\pi$
$572$		0			0
$573$	−9.49108	+	10.5439i	−0.396496	+	0.440477i
$574$		0			0
$575$	−0.530154			−0.0221090
$576$		0			0
$577$	33.8507			1.40922			0.704612	−	0.709593i	$-0.251121\pi$
$577$	33.8507			1.40922			0.704612	+	0.709593i	$0.251121\pi$
$578$		0			0
$579$	1.56511	+	4.81463i	0.0650438	+	0.200089i
$580$		0			0
$581$	4.69900	+	8.13890i	0.194947	+	0.337659i
$582$		0			0
$583$	29.5811	−	51.2360i	1.22513	−	2.12198i
$584$		0			0
$585$	29.7782	−	21.6479i	1.23118	−	0.895028i
$586$		0			0
$587$	−11.2279	+	19.4474i	−0.463427	+	0.802679i	−0.999129	−	0.0417284i	$-0.986714\pi$
$587$	−11.2279	+	19.4474i	−0.463427	+	0.802679i	0.535702	+	0.844407i	$0.320047\pi$
$588$		0			0
$589$	−7.52182	−	13.0282i	−0.309931	−	0.536817i
$590$		0			0
$591$	7.52543	+	1.59848i	0.309555	+	0.0657526i
$592$		0			0
$593$	−9.35530			−0.384176			−0.192088	−	0.981378i	$-0.561526\pi$
$593$	−9.35530			−0.384176			−0.192088	+	0.981378i	$0.561526\pi$
$594$		0			0
$595$	−72.0721			−2.95467
$596$		0			0
$597$	24.8882	+	5.28651i	1.01860	+	0.216362i
$598$		0			0
$599$	12.2259	+	21.1759i	0.499538	+	0.865226i	1.00000		0.000533153i	$-0.000169708\pi$
$599$	12.2259	+	21.1759i	0.499538	+	0.865226i	−0.500462	+	0.865759i	$0.666836\pi$
$600$		0			0
$601$	−6.64643	+	11.5120i	−0.271114	+	0.469583i	−0.969147	−	0.246482i	$-0.920725\pi$
$601$	−6.64643	+	11.5120i	−0.271114	+	0.469583i	0.698034	+	0.716065i	$0.254059\pi$
$602$		0			0
$603$	−0.986201	−	9.35790i	−0.0401612	−	0.381083i
$604$		0			0
$605$	−37.1605	+	64.3639i	−1.51079	+	2.61677i
$606$		0			0
$607$	18.1403	+	31.4198i	0.736290	+	1.27529i	0.954155	+	0.299313i	$0.0967576\pi$
$607$	18.1403	+	31.4198i	0.736290	+	1.27529i	−0.217864	+	0.975979i	$0.569909\pi$
$608$		0			0
$609$	7.11340	+	21.8824i	0.288250	+	0.886719i
$610$		0			0
$611$	19.9653			0.807710
$612$		0			0
$613$	−6.73390			−0.271980			−0.135990	−	0.990710i	$-0.543421\pi$
$613$	−6.73390			−0.271980			−0.135990	+	0.990710i	$0.543421\pi$
$614$		0			0
$615$	−3.89366	+	4.32556i	−0.157007	+	0.174424i
$616$		0			0
$617$	0.553446	+	0.958597i	0.0222809	+	0.0385917i	0.876951	−	0.480580i	$-0.159574\pi$
$617$	0.553446	+	0.958597i	0.0222809	+	0.0385917i	−0.854670	+	0.519172i	$0.826241\pi$
$618$		0			0
$619$	7.60418	−	13.1708i	0.305638	−	0.529380i	−0.671765	−	0.740764i	$-0.734464\pi$
$619$	7.60418	−	13.1708i	0.305638	−	0.529380i	0.977403	+	0.211384i	$0.0677970\pi$
$620$		0			0
$621$	0.0401307	−	0.383365i	0.00161039	−	0.0153839i
$622$		0			0
$623$	−16.7464	+	29.0057i	−0.670932	+	1.16209i
$624$		0			0
$625$	4.82915	+	8.36432i	0.193166	+	0.334573i
$626$		0			0
$627$	−13.3122	+	14.7889i	−0.531640	+	0.590612i
$628$		0			0
$629$	−38.3469			−1.52899
$630$		0			0
$631$	−29.2163			−1.16308			−0.581541	−	0.813517i	$-0.697550\pi$
$631$	−29.2163			−1.16308			−0.581541	+	0.813517i	$0.697550\pi$
$632$		0			0
$633$	−2.19219	−	6.74365i	−0.0871316	−	0.268036i
$634$		0			0
$635$	−10.2807	−	17.8068i	−0.407979	−	0.706641i
$636$		0			0
$637$	0.508339	−	0.880468i	0.0201411	−	0.0348854i
$638$		0			0
$639$	−22.4663	−	9.99513i	−0.888755	−	0.395401i
$640$		0			0
$641$	−13.4412	+	23.2809i	−0.530897	+	0.919540i	0.468453	+	0.883488i	$0.344811\pi$
$641$	−13.4412	+	23.2809i	−0.530897	+	0.919540i	−0.999350	+	0.0360519i	$0.988522\pi$
$642$		0			0
$643$	−6.36207	−	11.0194i	−0.250896	−	0.434564i	0.712877	−	0.701289i	$-0.247392\pi$
$643$	−6.36207	−	11.0194i	−0.250896	−	0.434564i	−0.963773	+	0.266725i	$0.914058\pi$
$644$		0			0
$645$	3.01730	+	0.640907i	0.118806	+	0.0252357i
$646$		0			0
$647$	−47.3838			−1.86285			−0.931425	−	0.363933i	$-0.881434\pi$
$647$	−47.3838			−1.86285			−0.931425	+	0.363933i	$0.881434\pi$
$648$		0			0
$649$	50.9006			1.99802
$650$		0			0
$651$	34.0547	+	7.23358i	1.33471	+	0.283506i
$652$		0			0
$653$	−4.13506	−	7.16213i	−0.161817	−	0.280276i	0.773703	−	0.633548i	$-0.218402\pi$
$653$	−4.13506	−	7.16213i	−0.161817	−	0.280276i	−0.935521	+	0.353272i	$0.885069\pi$
$654$		0			0
$655$	1.97272	−	3.41686i	0.0770807	−	0.133508i
$656$		0			0
$657$	14.3023	+	6.36301i	0.557987	+	0.248245i
$658$		0			0
$659$	1.00770	−	1.74539i	0.0392544	−	0.0679906i	−0.845731	−	0.533610i	$-0.820835\pi$
$659$	1.00770	−	1.74539i	0.0392544	−	0.0679906i	0.884985	+	0.465619i	$0.154168\pi$
$660$		0			0
$661$	−1.70432	−	2.95196i	−0.0662902	−	0.114818i	0.830975	−	0.556309i	$-0.187783\pi$
$661$	−1.70432	−	2.95196i	−0.0662902	−	0.114818i	−0.897266	+	0.441491i	$0.854450\pi$
$662$		0			0
$663$	−14.4418	−	44.4261i	−0.560872	−	1.72537i
$664$		0			0
$665$	−19.0123			−0.737266
$666$		0			0
$667$	0.365022			0.0141337
$668$		0			0
$669$	14.4759	−	16.0816i	0.559669	−	0.621750i
$670$		0			0
$671$	8.30261	+	14.3805i	0.320519	+	0.555155i
$672$		0			0
$673$	7.56791	−	13.1080i	0.291722	−	0.505277i	−0.682495	−	0.730890i	$-0.739105\pi$
$673$	7.56791	−	13.1080i	0.291722	−	0.505277i	0.974217	+	0.225613i	$0.0724386\pi$
$674$		0			0
$675$	33.9184	−	15.1185i	1.30552	−	0.581912i
$676$		0			0
$677$	−9.31110	+	16.1273i	−0.357855	+	0.619822i	−0.987602	−	0.156978i	$-0.949825\pi$
$677$	−9.31110	+	16.1273i	−0.357855	+	0.619822i	0.629748	+	0.776800i	$0.283158\pi$
$678$		0			0
$679$	9.45634	+	16.3789i	0.362901	+	0.628563i
$680$		0			0
$681$	10.4922	−	11.6560i	0.402060	−	0.446659i
$682$		0			0
$683$	38.4656			1.47185			0.735923	−	0.677066i	$-0.236749\pi$
$683$	38.4656			1.47185			0.735923	+	0.677066i	$0.236749\pi$
$684$		0			0
$685$	−22.1786			−0.847401
$686$		0			0
$687$	−14.0369	−	43.1806i	−0.535542	−	1.64744i
$688$		0			0
$689$	18.3200	+	31.7312i	0.697938	+	1.20886i
$690$		0			0
$691$	11.2999	−	19.5720i	0.429869	−	0.744555i	−0.566992	−	0.823723i	$-0.691893\pi$
$691$	11.2999	−	19.5720i	0.429869	−	0.744555i	0.996861	+	0.0791683i	$0.0252264\pi$
$692$		0			0
$693$	−4.82618	−	45.7948i	−0.183331	−	1.73960i
$694$		0			0
$695$	39.0348	−	67.6103i	1.48068	−	2.56460i
$696$		0			0
$697$	3.69238	+	6.39540i	0.139859	+	0.242243i
$698$		0			0
$699$	−2.40312	−	0.510449i	−0.0908945	−	0.0193069i
$700$		0			0
$701$	−37.8883			−1.43102			−0.715510	−	0.698602i	$-0.753806\pi$
$701$	−37.8883			−1.43102			−0.715510	+	0.698602i	$0.753806\pi$
$702$		0			0
$703$	−10.1157			−0.381523
$704$		0			0
$705$	33.4814	+	7.11181i	1.26098	+	0.267846i
$706$		0			0
$707$	11.9934	+	20.7731i	0.451057	+	0.781253i
$708$		0			0
$709$	7.75701	−	13.4355i	0.291321	−	0.504582i	−0.682802	−	0.730604i	$-0.739239\pi$
$709$	7.75701	−	13.4355i	0.291321	−	0.504582i	0.974122	+	0.226022i	$0.0725720\pi$
$710$		0			0
$711$	3.47609	−	2.52701i	0.130364	−	0.0947704i
$712$		0			0
$713$	0.276147	−	0.478301i	0.0103418	−	0.0179125i
$714$		0			0
$715$	−34.8855	−	60.4235i	−1.30464	−	2.25971i
$716$		0			0
$717$	−8.76233	−	26.9548i	−0.327235	−	1.00665i
$718$		0			0
$719$	29.8701			1.11397			0.556983	−	0.830524i	$-0.311959\pi$
$719$	29.8701			1.11397			0.556983	+	0.830524i	$0.311959\pi$
$720$		0			0
$721$	14.3094			0.532910
$722$		0			0
$723$	11.9935	−	13.3238i	0.446041	−	0.495518i
$724$		0			0
$725$	17.5831	+	30.4549i	0.653021	+	1.13107i
$726$		0			0
$727$	−2.80759	+	4.86288i	−0.104128	+	0.180354i	−0.913381	−	0.407105i	$-0.866538\pi$
$727$	−2.80759	+	4.86288i	−0.104128	+	0.180354i	0.809254	+	0.587459i	$0.199872\pi$
$728$		0			0
$729$	8.36500	+	25.6715i	0.309815	+	0.950797i
$730$		0			0
$731$	1.95701	−	3.38965i	0.0723828	−	0.125371i
$732$		0			0
$733$	6.02803	+	10.4409i	0.222650	+	0.385642i	0.955612	−	0.294628i	$-0.0951958\pi$
$733$	6.02803	+	10.4409i	0.222650	+	0.385642i	−0.732962	+	0.680270i	$0.761863\pi$
$734$		0			0
$735$	1.16610	−	1.29545i	0.0430124	−	0.0477835i
$736$		0			0
$737$	−17.8329			−0.656885
$738$		0			0
$739$	−43.8187			−1.61190			−0.805948	−	0.591986i	$-0.798344\pi$
$739$	−43.8187			−1.61190			−0.805948	+	0.591986i	$0.798344\pi$
$740$		0			0
$741$	−3.80968	−	11.7194i	−0.139952	−	0.430523i
$742$		0			0
$743$	15.0004	+	25.9814i	0.550310	+	0.953164i	0.998252	+	0.0591018i	$0.0188236\pi$
$743$	15.0004	+	25.9814i	0.550310	+	0.953164i	−0.447942	+	0.894062i	$0.647843\pi$
$744$		0			0
$745$	−3.27336	+	5.66963i	−0.119927	+	0.207719i
$746$		0			0
$747$	−8.44694	+	6.14067i	−0.309058	+	0.224676i
$748$		0			0
$749$	−10.1780	+	17.6288i	−0.371897	+	0.644144i
$750$		0			0
$751$	4.69583	+	8.13342i	0.171353	+	0.296793i	0.938893	−	0.344208i	$-0.111853\pi$
$751$	4.69583	+	8.13342i	0.171353	+	0.296793i	−0.767540	+	0.641001i	$0.778519\pi$
$752$		0			0
$753$	−45.6812	−	9.70316i	−1.66471	−	0.353603i
$754$		0			0
$755$	1.28102			0.0466210
$756$		0			0
$757$	21.7285			0.789737			0.394868	−	0.918738i	$-0.370790\pi$
$757$	21.7285			0.789737			0.394868	+	0.918738i	$0.370790\pi$
$758$		0			0
$759$	−0.714567	−	0.151781i	−0.0259371	−	0.00550932i
$760$		0			0
$761$	−6.78398	−	11.7502i	−0.245919	−	0.425944i	0.716471	−	0.697617i	$-0.245756\pi$
$761$	−6.78398	−	11.7502i	−0.245919	−	0.425944i	−0.962390	+	0.271673i	$0.912423\pi$
$762$		0			0
$763$	−18.7417	+	32.4617i	−0.678497	+	1.17519i
$764$		0			0
$765$	−8.39365	−	79.6459i	−0.303473	−	2.87961i
$766$		0			0
$767$	−15.7617	+	27.3001i	−0.569124	+	0.985751i
$768$		0			0
$769$	−21.3949	−	37.0571i	−0.771520	−	1.33631i	−0.936730	−	0.350054i	$-0.886163\pi$
$769$	−21.3949	−	37.0571i	−0.771520	−	1.33631i	0.165209	−	0.986259i	$-0.447170\pi$
$770$		0			0
$771$	15.8904	+	48.8823i	0.572278	+	1.76045i
$772$		0			0
$773$	12.4288			0.447034			0.223517	−	0.974700i	$-0.428246\pi$
$773$	12.4288			0.447034			0.223517	+	0.974700i	$0.428246\pi$
$774$		0			0
$775$	53.2081			1.91129
$776$		0			0
$777$	15.6620	−	17.3993i	0.561873	−	0.624198i
$778$		0			0
$779$	0.974036	+	1.68708i	0.0348984	+	0.0604459i
$780$		0			0
$781$	−23.3004	+	40.3576i	−0.833756	+	1.44411i
$782$		0			0
$783$	−23.3535	+	10.4094i	−0.834586	+	0.372001i
$784$		0			0
$785$	24.9319	−	43.1833i	0.889858	−	1.54128i
$786$		0			0
$787$	21.5079	+	37.2527i	0.766673	+	1.32792i	0.939357	+	0.342940i	$0.111423\pi$
$787$	21.5079	+	37.2527i	0.766673	+	1.32792i	−0.172684	+	0.984977i	$0.555244\pi$
$788$		0			0
$789$	−3.40593	+	3.78374i	−0.121254	+	0.134705i
$790$		0			0
$791$	7.37300			0.262154
$792$		0			0
$793$	−10.2839			−0.365191
$794$		0			0
$795$	19.4194	+	59.7384i	0.688736	+	2.11870i
$796$		0			0
$797$	−13.6697	−	23.6766i	−0.484205	−	0.838668i	0.515630	−	0.856811i	$-0.327558\pi$
$797$	−13.6697	−	23.6766i	−0.484205	−	0.838668i	−0.999835	+	0.0181431i	$0.994225\pi$
$798$		0			0
$799$	21.7160	−	37.6132i	0.768256	−	1.33066i
$800$		0			0
$801$	−34.0041	−	15.1282i	−1.20148	−	0.534530i
$802$		0			0
$803$	14.8333	−	25.6921i	0.523456	−	0.906653i
$804$		0			0
$805$	−0.348998	−	0.604482i	−0.0123006	−	0.0213052i
$806$		0			0
$807$	−22.7454	−	4.83137i	−0.800677	−	0.170072i
$808$		0			0
$809$	18.2692			0.642311			0.321156	−	0.947026i	$-0.395929\pi$
$809$	18.2692			0.642311			0.321156	+	0.947026i	$0.395929\pi$
$810$		0			0
$811$	33.6619			1.18203			0.591015	−	0.806660i	$-0.298727\pi$
$811$	33.6619			1.18203			0.591015	+	0.806660i	$0.298727\pi$
$812$		0			0
$813$	53.0843	+	11.2757i	1.86175	+	0.395455i
$814$		0			0
$815$	5.27936	+	9.14412i	0.184928	+	0.320305i
$816$		0			0
$817$	0.516252	−	0.894175i	0.0180614	−	0.0312832i
$818$		0			0
$819$	26.0562	+	11.5922i	0.910476	+	0.405065i
$820$		0			0
$821$	21.5703	−	37.3609i	0.752810	−	1.30391i	−0.193645	−	0.981072i	$-0.562031\pi$
$821$	21.5703	−	37.3609i	0.752810	−	1.30391i	0.946456	−	0.322834i	$-0.104636\pi$
$822$		0			0
$823$	−8.45533	−	14.6451i	−0.294734	−	0.510494i	0.680189	−	0.733037i	$-0.261898\pi$
$823$	−8.45533	−	14.6451i	−0.294734	−	0.510494i	−0.974923	+	0.222542i	$0.928564\pi$
$824$		0			0
$825$	−21.7571	−	66.9298i	−0.757487	−	2.33020i
$826$		0			0
$827$	−12.2376			−0.425542			−0.212771	−	0.977102i	$-0.568249\pi$
$827$	−12.2376			−0.425542			−0.212771	+	0.977102i	$0.568249\pi$
$828$		0			0
$829$	−11.4794			−0.398696			−0.199348	−	0.979929i	$-0.563882\pi$
$829$	−11.4794			−0.398696			−0.199348	+	0.979929i	$0.563882\pi$
$830$		0			0
$831$	−11.0801	+	12.3091i	−0.384364	+	0.426999i
$832$		0			0
$833$	−1.10582	−	1.91534i	−0.0383146	−	0.0663627i
$834$		0			0
$835$	2.19401	−	3.80013i	0.0759267	−	0.131509i
$836$		0			0
$837$	−4.02766	+	38.4759i	−0.139216	+	1.32992i
$838$		0			0
$839$	−22.5224	+	39.0100i	−0.777560	+	1.34677i	0.155784	+	0.987791i	$0.450210\pi$
$839$	−22.5224	+	39.0100i	−0.777560	+	1.34677i	−0.933344	+	0.358983i	$0.883124\pi$
$840$		0			0
$841$	2.39367	+	4.14596i	0.0825403	+	0.142964i
$842$		0			0
$843$	−7.86012	+	8.73200i	−0.270717	+	0.300746i
$844$		0			0
$845$	−2.09750			−0.0721563
$846$		0			0
$847$	−57.5717			−1.97819
$848$		0			0
$849$	−10.3012	−	31.6887i	−0.353536	−	1.08755i
$850$		0			0
$851$	−0.185689	−	0.321622i	−0.00636533	−	0.0110251i
$852$		0			0
$853$	6.84105	−	11.8490i	0.234233	−	0.405703i	−0.724817	−	0.688942i	$-0.758075\pi$
$853$	6.84105	−	11.8490i	0.234233	−	0.405703i	0.959049	+	0.283239i	$0.0914088\pi$
$854$		0			0
$855$	−2.21421	−	21.0103i	−0.0757243	−	0.718536i
$856$		0			0
$857$	−14.9348	+	25.8679i	−0.510164	+	0.883631i	0.489766	+	0.871854i	$0.337082\pi$
$857$	−14.9348	+	25.8679i	−0.510164	+	0.883631i	−0.999931	+	0.0117768i	$0.996251\pi$
$858$		0			0
$859$	−3.77095	−	6.53148i	−0.128663	−	0.222851i	0.794496	−	0.607270i	$-0.207735\pi$
$859$	−3.77095	−	6.53148i	−0.128663	−	0.222851i	−0.923159	+	0.384418i	$0.874402\pi$
$860$		0			0
$861$	−4.40990	−	0.936709i	−0.150289	−	0.0319230i
$862$		0			0
$863$	−17.0591			−0.580698			−0.290349	−	0.956921i	$-0.593771\pi$
$863$	−17.0591			−0.580698			−0.290349	+	0.956921i	$0.593771\pi$
$864$		0			0
$865$	−49.8277			−1.69419
$866$		0			0
$867$	−70.6012	−	14.9964i	−2.39774	−	0.509306i
$868$		0			0
$869$	−4.07228	−	7.05340i	−0.138143	−	0.239270i
$870$		0			0
$871$	5.52210	−	9.56456i	0.187109	−	0.324083i
$872$		0			0
$873$	−16.9988	+	12.3576i	−0.575321	+	0.418241i
$874$		0			0
$875$	10.0994	−	17.4926i	0.341421	−	0.591358i
$876$		0			0
$877$	7.74247	+	13.4103i	0.261445	+	0.452835i	0.966626	−	0.256192i	$-0.0824678\pi$
$877$	7.74247	+	13.4103i	0.261445	+	0.452835i	−0.705181	+	0.709027i	$0.749134\pi$
$878$		0			0
$879$	−6.03879	−	18.5766i	−0.203683	−	0.626575i
$880$		0			0
$881$	−26.5541			−0.894631			−0.447316	−	0.894376i	$-0.647620\pi$
$881$	−26.5541			−0.894631			−0.447316	+	0.894376i	$0.647620\pi$
$882$		0			0
$883$	32.2262			1.08450			0.542250	−	0.840217i	$-0.317573\pi$
$883$	32.2262			1.08450			0.542250	+	0.840217i	$0.317573\pi$
$884$		0			0
$885$	−36.1567	+	40.1673i	−1.21539	+	1.35021i
$886$		0			0
$887$	18.4763	+	32.0018i	0.620373	+	1.07452i	0.989416	+	0.145105i	$0.0463519\pi$
$887$	18.4763	+	32.0018i	0.620373	+	1.07452i	−0.369044	+	0.929412i	$0.620315\pi$
$888$		0			0
$889$	7.96383	−	13.7938i	0.267098	−	0.462628i
$890$		0			0
$891$	50.0452	−	10.6667i	1.67658	−	0.357348i
$892$		0			0
$893$	5.72858	−	9.92220i	0.191700	−	0.332034i
$894$		0			0
$895$	22.3037	+	38.6312i	0.745531	+	1.29130i
$896$		0			0
$897$	0.302678	−	0.336252i	0.0101061	−	0.0112271i
$898$		0			0
$899$	−36.6349			−1.22184
$900$		0			0
$901$	79.7057			2.65538
$902$		0			0
$903$	0.738700	+	2.27240i	0.0245824	+	0.0756208i
$904$		0			0
$905$	18.2949	+	31.6877i	0.608144	+	1.05334i
$906$		0			0
$907$	0.591871	−	1.02515i	0.0196528	−	0.0340396i	−0.856032	−	0.516923i	$-0.827077\pi$
$907$	0.591871	−	1.02515i	0.0196528	−	0.0340396i	0.875685	+	0.482884i	$0.160411\pi$
$908$		0			0
$909$	−21.5593	+	15.6730i	−0.715078	+	0.519840i
$910$		0			0
$911$	26.7752	−	46.3760i	0.887103	−	1.53651i	0.0438179	−	0.999040i	$-0.486048\pi$
$911$	26.7752	−	46.3760i	0.887103	−	1.53651i	0.843285	−	0.537467i	$-0.180619\pi$
$912$		0			0
$913$	9.89569	+	17.1398i	0.327500	+	0.567246i
$914$		0			0
$915$	−17.2458	−	3.66320i	−0.570130	−	0.121102i
$916$		0			0
$917$	3.05628			0.100927
$918$		0			0
$919$	1.67908			0.0553878			0.0276939	−	0.999616i	$-0.491184\pi$
$919$	1.67908			0.0553878			0.0276939	+	0.999616i	$0.491184\pi$
$920$		0			0
$921$	−37.7511	−	8.01872i	−1.24394	−	0.264226i
$922$		0			0
$923$	−14.4303	−	24.9940i	−0.474980	−	0.822689i
$924$		0			0
$925$	17.8893	−	30.9851i	0.588196	−	1.01879i
$926$		0			0
$927$	1.66650	+	15.8131i	0.0547350	+	0.519371i
$928$		0			0
$929$	−14.2756	+	24.7261i	−0.468368	+	0.811237i	−0.999346	−	0.0361482i	$-0.988491\pi$
$929$	−14.2756	+	24.7261i	−0.468368	+	0.811237i	0.530978	+	0.847385i	$0.321825\pi$
$930$		0			0
$931$	−0.291712	−	0.505260i	−0.00956047	−	0.0165592i
$932$		0			0
$933$	−12.9158	−	39.7320i	−0.422846	−	1.30077i
$934$		0			0
$935$	−151.778			−4.96366
$936$		0			0
$937$	33.8620			1.10622			0.553111	−	0.833108i	$-0.313441\pi$
$937$	33.8620			1.10622			0.553111	+	0.833108i	$0.313441\pi$
$938$		0			0
$939$	−33.6736	+	37.4088i	−1.09890	+	1.22079i
$940$		0			0
$941$	8.28984	+	14.3584i	0.270241	+	0.468071i	0.968923	−	0.247361i	$-0.0795633\pi$
$941$	8.28984	+	14.3584i	0.270241	+	0.468071i	−0.698682	+	0.715432i	$0.746230\pi$
$942$		0			0
$943$	−0.0357596	+	0.0619374i	−0.00116449	+	0.00201696i
$944$		0			0
$945$	39.5664	+	28.7213i	1.28710	+	0.934306i
$946$		0			0
$947$	27.8930	−	48.3121i	0.906401	−	1.56993i	0.0873743	−	0.996176i	$-0.472152\pi$
$947$	27.8930	−	48.3121i	0.906401	−	1.56993i	0.819026	−	0.573756i	$-0.194514\pi$
$948$		0			0
$949$	9.18649	+	15.9115i	0.298206	+	0.516508i
$950$		0			0
$951$	−37.7445	+	41.9313i	−1.22395	+	1.35972i
$952$		0			0
$953$	−44.5366			−1.44268			−0.721341	−	0.692580i	$-0.756474\pi$
$953$	−44.5366			−1.44268			−0.721341	+	0.692580i	$0.756474\pi$
$954$		0			0
$955$	−28.5457			−0.923717
$956$		0			0
$957$	14.9802	+	46.0825i	0.484242	+	1.48963i
$958$		0			0
$959$	−8.59017	−	14.8786i	−0.277391	−	0.480455i
$960$		0			0
$961$	−12.2151	+	21.1572i	−0.394035	+	0.682489i
$962$		0			0
$963$	−20.6668	−	9.19451i	−0.665977	−	0.296289i
$964$		0			0
$965$	−5.09348	+	8.82216i	−0.163965	+	0.283996i
$966$		0			0
$967$	−14.0863	−	24.3982i	−0.452986	−	0.784595i	0.545584	−	0.838056i	$-0.316308\pi$
$967$	−14.0863	−	24.3982i	−0.452986	−	0.784595i	−0.998570	+	0.0534616i	$0.982975\pi$
$968$		0			0
$969$	−26.2222	−	5.56988i	−0.842380	−	0.178930i
$970$		0			0
$971$	30.8598			0.990338			0.495169	−	0.868797i	$-0.335106\pi$
$971$	30.8598			0.990338			0.495169	+	0.868797i	$0.335106\pi$
$972$		0			0
$973$	60.4755			1.93876
$974$		0			0
$975$	42.6345	+	9.05602i	1.36540	+	0.290025i
$976$		0			0
$977$	−14.6967	−	25.4555i	−0.470190	−	0.814393i	0.529229	−	0.848479i	$-0.322481\pi$
$977$	−14.6967	−	25.4555i	−0.470190	−	0.814393i	−0.999419	+	0.0340864i	$0.989148\pi$
$978$		0			0
$979$	−35.2666	+	61.0836i	−1.12713	+	1.95224i
$980$		0			0
$981$	−38.0557	−	16.9307i	−1.21502	−	0.540557i
$982$		0			0
$983$	−7.08964	+	12.2796i	−0.226124	+	0.391659i	−0.956656	−	0.291220i	$-0.905939\pi$
$983$	−7.08964	+	12.2796i	−0.226124	+	0.391659i	0.730532	+	0.682879i	$0.239272\pi$
$984$		0			0
$985$	7.74020	+	13.4064i	0.246623	+	0.427164i
$986$		0			0
$987$	8.19697	+	25.2157i	0.260912	+	0.802624i
$988$		0			0
$989$	0.0379061			0.00120535
$990$		0			0
$991$	46.0022			1.46131			0.730654	−	0.682748i	$-0.239215\pi$
$991$	46.0022			1.46131			0.730654	+	0.682748i	$0.239215\pi$
$992$		0			0
$993$	18.6788	−	20.7507i	0.592754	−	0.658505i
$994$		0			0
$995$	25.5985	+	44.3378i	0.811526	+	1.40560i
$996$		0			0
$997$	−30.1749	+	52.2645i	−0.955650	+	1.65523i	−0.222777	+	0.974869i	$0.571512\pi$
$997$	−30.1749	+	52.2645i	−0.955650	+	1.65523i	−0.732873	+	0.680365i	$0.761821\pi$
$998$		0			0
$999$	21.0518	+	15.2816i	0.666050	+	0.483487i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.i.k.385.1	yes	12
3.2	odd	2		3456.2.i.l.1153.6		12
4.3	odd	2		1152.2.i.i.385.6	✓	12
8.3	odd	2		1152.2.i.l.385.1	yes	12
8.5	even	2		1152.2.i.j.385.6	yes	12
9.4	even	3	inner	1152.2.i.k.769.1	yes	12
9.5	odd	6		3456.2.i.l.2305.6		12
12.11	even	2		3456.2.i.k.1153.6		12
24.5	odd	2		3456.2.i.j.1153.1		12
24.11	even	2		3456.2.i.i.1153.1		12
36.23	even	6		3456.2.i.k.2305.6		12
36.31	odd	6		1152.2.i.i.769.6	yes	12
72.5	odd	6		3456.2.i.j.2305.1		12
72.13	even	6		1152.2.i.j.769.6	yes	12
72.59	even	6		3456.2.i.i.2305.1		12
72.67	odd	6		1152.2.i.l.769.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.i.i.385.6	✓	12	4.3	odd	2
1152.2.i.i.769.6	yes	12	36.31	odd	6
1152.2.i.j.385.6	yes	12	8.5	even	2
1152.2.i.j.769.6	yes	12	72.13	even	6
1152.2.i.k.385.1	yes	12	1.1	even	1	trivial
1152.2.i.k.769.1	yes	12	9.4	even	3	inner
1152.2.i.l.385.1	yes	12	8.3	odd	2
1152.2.i.l.769.1	yes	12	72.67	odd	6
3456.2.i.i.1153.1		12	24.11	even	2
3456.2.i.i.2305.1		12	72.59	even	6
3456.2.i.j.1153.1		12	24.5	odd	2
3456.2.i.j.2305.1		12	72.5	odd	6
3456.2.i.k.1153.6		12	12.11	even	2
3456.2.i.k.2305.6		12	36.23	even	6
3456.2.i.l.1153.6		12	3.2	odd	2
3456.2.i.l.2305.6		12	9.5	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:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.69425 - 0.359877i) q^{3} +(-1.74260 - 3.01828i) q^{5} +(1.34988 - 2.33807i) q^{7} +(2.74098 + 1.21944i) q^{9} +O(q^{10})\)	\(q+(-1.69425 - 0.359877i) q^{3} +(-1.74260 - 3.01828i) q^{5} +(1.34988 - 2.33807i) q^{7} +(2.74098 + 1.21944i) q^{9} +(2.84274 - 4.92377i) q^{11} +(1.76055 + 3.04937i) q^{13} +(1.86620 + 5.74085i) q^{15} +7.65970 q^{17} +2.02060 q^{19} +(-3.12846 + 3.47548i) q^{21} +(0.0370909 + 0.0642434i) q^{23} +(-3.57334 + 6.18921i) q^{25} +(-4.20506 - 3.05246i) q^{27} +(2.46032 - 4.26140i) q^{29} +(-3.72257 - 6.44769i) q^{31} +(-6.58827 + 7.31907i) q^{33} -9.40925 q^{35} -5.00631 q^{37} +(-1.88542 - 5.79997i) q^{39} +(0.482053 + 0.834941i) q^{41} +(0.255495 - 0.442530i) q^{43} +(-1.09582 - 10.3980i) q^{45} +(2.83509 - 4.91053i) q^{47} +(-0.144369 - 0.250055i) q^{49} +(-12.9775 - 2.75655i) q^{51} +10.4058 q^{53} -19.8151 q^{55} +(-3.42340 - 0.727166i) q^{57} +(4.47636 + 7.75329i) q^{59} +(-1.46032 + 2.52935i) q^{61} +(6.55114 - 4.76248i) q^{63} +(6.13589 - 10.6277i) q^{65} +(-1.56829 - 2.71635i) q^{67} +(-0.0397217 - 0.122193i) q^{69} -8.19647 q^{71} +5.21796 q^{73} +(8.28150 - 9.20012i) q^{75} +(-7.67474 - 13.2930i) q^{77} +(0.716260 - 1.24060i) q^{79} +(6.02592 + 6.68493i) q^{81} +(-1.74052 + 3.01467i) q^{83} +(-13.3478 - 23.1191i) q^{85} +(-5.70198 + 6.33447i) q^{87} -12.4058 q^{89} +9.50616 q^{91} +(3.98660 + 12.2637i) q^{93} +(-3.52110 - 6.09873i) q^{95} +(-3.50265 + 6.06677i) q^{97} +(13.7962 - 10.0294i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} - 2 q^{5} + 6 q^{7} - 2 q^{9}+O(q^{10}) \) 12 * q + 4 * q^3 - 2 * q^5 + 6 * q^7 - 2 * q^9	\( 12 q + 4 q^{3} - 2 q^{5} + 6 q^{7} - 2 q^{9} + 4 q^{11} + 10 q^{13} + 4 q^{15} + 4 q^{17} + 4 q^{19} + 2 q^{21} + 8 q^{23} - 14 q^{25} - 14 q^{27} - 2 q^{29} + 8 q^{31} - 10 q^{33} + 8 q^{35} + 22 q^{39} - 2 q^{41} - 2 q^{43} + 10 q^{45} - 14 q^{47} - 18 q^{49} - 38 q^{51} + 24 q^{53} - 16 q^{55} - 38 q^{57} + 6 q^{59} + 14 q^{61} - 16 q^{63} - 8 q^{65} + 4 q^{67} - 50 q^{69} - 28 q^{71} + 60 q^{73} + 50 q^{75} + 2 q^{77} + 16 q^{79} + 22 q^{81} + 24 q^{83} + 16 q^{85} - 36 q^{87} - 48 q^{89} - 52 q^{91} + 42 q^{93} - 20 q^{95} - 14 q^{97} + 68 q^{99}+O(q^{100}) \) 12 * q + 4 * q^3 - 2 * q^5 + 6 * q^7 - 2 * q^9 + 4 * q^11 + 10 * q^13 + 4 * q^15 + 4 * q^17 + 4 * q^19 + 2 * q^21 + 8 * q^23 - 14 * q^25 - 14 * q^27 - 2 * q^29 + 8 * q^31 - 10 * q^33 + 8 * q^35 + 22 * q^39 - 2 * q^41 - 2 * q^43 + 10 * q^45 - 14 * q^47 - 18 * q^49 - 38 * q^51 + 24 * q^53 - 16 * q^55 - 38 * q^57 + 6 * q^59 + 14 * q^61 - 16 * q^63 - 8 * q^65 + 4 * q^67 - 50 * q^69 - 28 * q^71 + 60 * q^73 + 50 * q^75 + 2 * q^77 + 16 * q^79 + 22 * q^81 + 24 * q^83 + 16 * q^85 - 36 * q^87 - 48 * q^89 - 52 * q^91 + 42 * q^93 - 20 * q^95 - 14 * q^97 + 68 * q^99

Introduction

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