LMFDB - Embedded newform 1152.2.p.f.959.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(191,1152)]

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([3, 3, 1]))

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

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

chi := DirichletCharacter("1152.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1152 = 2^{7} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1152.p (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:	$9.19876631285$
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			959.4
Character	$\chi$	$=$	1152.959
Dual form			1152.2.p.f.191.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.944152 + 1.45209i) q^{3} +(0.637560 - 1.10429i) q^{5} +(-1.73560 + 1.00205i) q^{7} +(-1.21715 - 2.74200i) q^{9} +O(q^{10})$	\(q+(-0.944152 + 1.45209i) q^{3} +(0.637560 - 1.10429i) q^{5} +(-1.73560 + 1.00205i) q^{7} +(-1.21715 - 2.74200i) q^{9} +(0.511856 - 0.295520i) q^{11} +(2.70573 + 1.56215i) q^{13} +(1.00157 + 1.96841i) q^{15} -4.34448i q^{17} +4.36512 q^{19} +(0.183601 - 3.46634i) q^{21} +(-4.02692 + 6.97483i) q^{23} +(1.68703 + 2.92203i) q^{25} +(5.13081 + 0.821440i) q^{27} +(3.39145 + 5.87416i) q^{29} +(0.688426 + 0.397463i) q^{31} +(-0.0541469 + 1.02228i) q^{33} +2.55547i q^{35} -0.791602i q^{37} +(-4.82301 + 2.45406i) q^{39} +(-3.81955 - 2.20522i) q^{41} +(2.84849 + 4.93373i) q^{43} +(-3.80396 - 0.404101i) q^{45} +(-0.881932 - 1.52755i) q^{47} +(-1.49179 + 2.58386i) q^{49} +(6.30860 + 4.10185i) q^{51} +8.01673 q^{53} -0.753647i q^{55} +(-4.12134 + 6.33857i) q^{57} +(6.66747 + 3.84947i) q^{59} +(-11.9523 + 6.90065i) q^{61} +(4.86011 + 3.53936i) q^{63} +(3.45013 - 1.99193i) q^{65} +(0.968787 - 1.67799i) q^{67} +(-6.32608 - 12.4328i) q^{69} -0.859283 q^{71} +13.9420 q^{73} +(-5.83588 - 0.309108i) q^{75} +(-0.592252 + 1.02581i) q^{77} +(-14.6096 + 8.43483i) q^{79} +(-6.03708 + 6.67486i) q^{81} +(5.89251 - 3.40204i) q^{83} +(-4.79755 - 2.76987i) q^{85} +(-11.7319 - 0.621400i) q^{87} -4.00854i q^{89} -6.26142 q^{91} +(-1.22713 + 0.624394i) q^{93} +(2.78303 - 4.82035i) q^{95} +(5.03373 + 8.71868i) q^{97} +(-1.43332 - 1.04381i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{7} - 4 q^{9}+O(q^{10}) $ 24 * q - 12 * q^7 - 4 * q^9	$ 24 q - 12 q^{7} - 4 q^{9} - 20 q^{15} + 12 q^{23} - 12 q^{25} + 36 q^{31} + 4 q^{33} - 20 q^{39} - 12 q^{41} - 12 q^{47} + 12 q^{49} + 4 q^{57} + 92 q^{63} - 48 q^{65} + 24 q^{73} - 84 q^{79} - 20 q^{81} - 68 q^{87} - 24 q^{95} - 12 q^{97}+O(q^{100}) $ 24 * q - 12 * q^7 - 4 * q^9 - 20 * q^15 + 12 * q^23 - 12 * q^25 + 36 * q^31 + 4 * q^33 - 20 * q^39 - 12 * q^41 - 12 * q^47 + 12 * q^49 + 4 * q^57 + 92 * q^63 - 48 * q^65 + 24 * q^73 - 84 * q^79 - 20 * q^81 - 68 * q^87 - 24 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$641$	$901$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

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
$3$	−0.944152	+	1.45209i	−0.545107	+	0.838367i
$3$	−0.944152	+	1.45209i	−0.545107	+	0.838367i
$4$		0			0
$5$	0.637560	−	1.10429i	0.285126	−	0.493852i	−0.687514	−	0.726171i	$-0.741298\pi$
$5$	0.637560	−	1.10429i	0.285126	−	0.493852i	0.972640	+	0.232319i	$0.0746314\pi$
$6$		0			0
$7$	−1.73560	+	1.00205i	−0.655995	+	0.378739i	−0.790749	−	0.612140i	$-0.790309\pi$
$7$	−1.73560	+	1.00205i	−0.655995	+	0.378739i	0.134754	+	0.990879i	$0.456976\pi$
$8$		0			0
$9$	−1.21715	−	2.74200i	−0.405718	−	0.913998i
$10$		0			0
$11$	0.511856	−	0.295520i	0.154330	−	0.0891027i	−0.420846	−	0.907132i	$-0.638267\pi$
$11$	0.511856	−	0.295520i	0.154330	−	0.0891027i	0.575176	+	0.818029i	$0.304933\pi$
$12$		0			0
$13$	2.70573	+	1.56215i	0.750434	+	0.433263i	0.825851	−	0.563889i	$-0.190695\pi$
$13$	2.70573	+	1.56215i	0.750434	+	0.433263i	−0.0754165	+	0.997152i	$0.524029\pi$
$14$		0			0
$15$	1.00157	+	1.96841i	0.258605	+	0.508242i
$16$		0			0
$17$		−	4.34448i		−	1.05369i	−0.849961	−	0.526846i	$-0.823374\pi$
$17$		−	4.34448i		−	1.05369i	0.849961	−	0.526846i	$-0.176626\pi$
$18$		0			0
$19$	4.36512			1.00143			0.500714	−	0.865613i	$-0.333071\pi$
$19$	4.36512			1.00143			0.500714	+	0.865613i	$0.333071\pi$
$20$		0			0
$21$	0.183601	−	3.46634i	0.0400650	−	0.756418i
$22$		0			0
$23$	−4.02692	+	6.97483i	−0.839671	+	1.45435i	0.0504988	+	0.998724i	$0.483919\pi$
$23$	−4.02692	+	6.97483i	−0.839671	+	1.45435i	−0.890170	+	0.455629i	$0.849414\pi$
$24$		0			0
$25$	1.68703	+	2.92203i	0.337407	+	0.584406i
$26$		0			0
$27$	5.13081	+	0.821440i	0.987425	+	0.158086i
$28$		0			0
$29$	3.39145	+	5.87416i	0.629776	+	1.09080i	0.987597	+	0.157013i	$0.0501865\pi$
$29$	3.39145	+	5.87416i	0.629776	+	1.09080i	−0.357821	+	0.933790i	$0.616480\pi$
$30$		0			0
$31$	0.688426	+	0.397463i	0.123645	+	0.0713865i	0.560547	−	0.828123i	$-0.310591\pi$
$31$	0.688426	+	0.397463i	0.123645	+	0.0713865i	−0.436902	+	0.899509i	$0.643924\pi$
$32$		0			0
$33$	−0.0541469	+	1.02228i	−0.00942576	+	0.177956i
$34$		0			0
$35$			2.55547i			0.431953i
$36$		0			0
$37$		−	0.791602i		−	0.130138i	−0.997881	−	0.0650692i	$-0.979273\pi$
$37$		−	0.791602i		−	0.130138i	0.997881	−	0.0650692i	$-0.0207268\pi$
$38$		0			0
$39$	−4.82301	+	2.45406i	−0.772300	+	0.392964i
$40$		0			0
$41$	−3.81955	−	2.20522i	−0.596513	−	0.344397i	0.171156	−	0.985244i	$-0.445250\pi$
$41$	−3.81955	−	2.20522i	−0.596513	−	0.344397i	−0.767669	+	0.640847i	$0.778583\pi$
$42$		0			0
$43$	2.84849	+	4.93373i	0.434391	+	0.752387i	0.997246	−	0.0741685i	$-0.0236303\pi$
$43$	2.84849	+	4.93373i	0.434391	+	0.752387i	−0.562855	+	0.826556i	$0.690297\pi$
$44$		0			0
$45$	−3.80396	−	0.404101i	−0.567060	−	0.0602398i
$46$		0			0
$47$	−0.881932	−	1.52755i	−0.128643	−	0.222816i	0.794508	−	0.607254i	$-0.207729\pi$
$47$	−0.881932	−	1.52755i	−0.128643	−	0.222816i	−0.923151	+	0.384437i	$0.874395\pi$
$48$		0			0
$49$	−1.49179	+	2.58386i	−0.213114	+	0.369123i
$50$		0			0
$51$	6.30860	+	4.10185i	0.883381	+	0.574375i
$52$		0			0
$53$	8.01673			1.10118			0.550591	−	0.834775i	$-0.314402\pi$
$53$	8.01673			1.10118			0.550591	+	0.834775i	$0.314402\pi$
$54$		0			0
$55$		−	0.753647i		−	0.101622i
$56$		0			0
$57$	−4.12134	+	6.33857i	−0.545885	+	0.839564i
$58$		0			0
$59$	6.66747	+	3.84947i	0.868031	+	0.501158i	0.866694	−	0.498841i	$-0.166241\pi$
$59$	6.66747	+	3.84947i	0.868031	+	0.501158i	0.00133778	+	0.999999i	$0.499574\pi$
$60$		0			0
$61$	−11.9523	+	6.90065i	−1.53033	+	0.883537i	−0.530986	+	0.847381i	$0.678178\pi$
$61$	−11.9523	+	6.90065i	−1.53033	+	0.883537i	−0.999346	+	0.0361566i	$0.988488\pi$
$62$		0			0
$63$	4.86011	+	3.53936i	0.612316	+	0.445917i
$64$		0			0
$65$	3.45013	−	1.99193i	0.427936	−	0.247069i
$66$		0			0
$67$	0.968787	−	1.67799i	0.118356	−	0.204999i	−0.800760	−	0.598985i	$-0.795571\pi$
$67$	0.968787	−	1.67799i	0.118356	−	0.204999i	0.919116	+	0.393986i	$0.128904\pi$
$68$		0			0
$69$	−6.32608	−	12.4328i	−0.761571	−	1.49673i
$70$		0			0
$71$	−0.859283			−0.101978			−0.0509891	−	0.998699i	$-0.516237\pi$
$71$	−0.859283			−0.101978			−0.0509891	+	0.998699i	$0.516237\pi$
$72$		0			0
$73$	13.9420			1.63179			0.815895	−	0.578201i	$-0.196245\pi$
$73$	13.9420			1.63179			0.815895	+	0.578201i	$0.196245\pi$
$74$		0			0
$75$	−5.83588	−	0.309108i	−0.673869	−	0.0356927i
$76$		0			0
$77$	−0.592252	+	1.02581i	−0.0674933	+	0.116902i
$78$		0			0
$79$	−14.6096	+	8.43483i	−1.64370	+	0.948993i	−0.664204	+	0.747552i	$0.731229\pi$
$79$	−14.6096	+	8.43483i	−1.64370	+	0.948993i	−0.979501	+	0.201441i	$0.935437\pi$
$80$		0			0
$81$	−6.03708	+	6.67486i	−0.670786	+	0.741651i
$82$		0			0
$83$	5.89251	−	3.40204i	0.646787	−	0.373422i	−0.140437	−	0.990090i	$-0.544851\pi$
$83$	5.89251	−	3.40204i	0.646787	−	0.373422i	0.787224	+	0.616667i	$0.211518\pi$
$84$		0			0
$85$	−4.79755	−	2.76987i	−0.520368	−	0.300435i
$86$		0			0
$87$	−11.7319	−	0.621400i	−1.25779	−	0.0666210i
$88$		0			0
$89$		−	4.00854i		−	0.424904i	−0.977172	−	0.212452i	$-0.931855\pi$
$89$		−	4.00854i		−	0.424904i	0.977172	−	0.212452i	$-0.0681449\pi$
$90$		0			0
$91$	−6.26142			−0.656375
$92$		0			0
$93$	−1.22713	+	0.624394i	−0.127248	+	0.0647466i
$94$		0			0
$95$	2.78303	−	4.82035i	0.285533	−	0.494557i
$96$		0			0
$97$	5.03373	+	8.71868i	0.511098	+	0.885248i	0.999917	+	0.0128629i	$0.00409451\pi$
$97$	5.03373	+	8.71868i	0.511098	+	0.885248i	−0.488819	+	0.872385i	$0.662572\pi$
$98$		0			0
$99$	−1.43332	−	1.04381i	−0.144054	−	0.104907i
$100$		0			0
$101$	−3.43658	−	5.95234i	−0.341953	−	0.592280i	0.642842	−	0.765998i	$-0.277755\pi$
$101$	−3.43658	−	5.95234i	−0.341953	−	0.592280i	−0.984795	+	0.173719i	$0.944422\pi$
$102$		0			0
$103$	11.2396	+	6.48918i	1.10747	+	0.639398i	0.938173	−	0.346167i	$-0.112517\pi$
$103$	11.2396	+	6.48918i	1.10747	+	0.639398i	0.169297	+	0.985565i	$0.445850\pi$
$104$		0			0
$105$	−3.71078	−	2.41275i	−0.362135	−	0.235460i
$106$		0			0
$107$			5.85328i			0.565858i	0.959141	+	0.282929i	$0.0913061\pi$
$107$			5.85328i			0.565858i	−0.959141	+	0.282929i	$0.908694\pi$
$108$		0			0
$109$			18.4982i			1.77180i	0.463874	+	0.885901i	$0.346459\pi$
$109$			18.4982i			1.77180i	−0.463874	+	0.885901i	$0.653541\pi$
$110$		0			0
$111$	1.14948	+	0.747392i	0.109104	+	0.0709393i
$112$		0			0
$113$	−2.22994	−	1.28745i	−0.209775	−	0.121114i	0.391432	−	0.920207i	$-0.371980\pi$
$113$	−2.22994	−	1.28745i	−0.209775	−	0.121114i	−0.601207	+	0.799094i	$0.705313\pi$
$114$		0			0
$115$	5.13481	+	8.89375i	0.478823	+	0.829346i
$116$		0			0
$117$	0.990130	−	9.32048i	0.0915375	−	0.861678i
$118$		0			0
$119$	4.35339	+	7.54029i	0.399074	+	0.691217i
$120$		0			0
$121$	−5.32534	+	9.22375i	−0.484121	+	0.838523i
$122$		0			0
$123$	6.80841	−	3.46428i	0.613894	−	0.312364i
$124$		0			0
$125$	10.6779			0.955064
$126$		0			0
$127$			2.39548i			0.212564i	0.994336	+	0.106282i	$0.0338947\pi$
$127$			2.39548i			0.212564i	−0.994336	+	0.106282i	$0.966105\pi$
$128$		0			0
$129$	−9.85366	−	0.521917i	−0.867566	−	0.0459522i
$130$		0			0
$131$	−9.35661	−	5.40204i	−0.817491	−	0.471978i	0.0320597	−	0.999486i	$-0.489793\pi$
$131$	−9.35661	−	5.40204i	−0.817491	−	0.471978i	−0.849550	+	0.527508i	$0.823127\pi$
$132$		0			0
$133$	−7.57611	+	4.37407i	−0.656932	+	0.379280i
$134$		0			0
$135$	4.17831	−	5.14217i	0.359611	−	0.442567i
$136$		0			0
$137$	15.4536	−	8.92216i	1.32029	−	0.762272i	0.336518	−	0.941677i	$-0.390751\pi$
$137$	15.4536	−	8.92216i	1.32029	−	0.762272i	0.983775	+	0.179406i	$0.0574174\pi$
$138$		0			0
$139$	3.62278	−	6.27484i	0.307280	−	0.532225i	−0.670486	−	0.741922i	$-0.733914\pi$
$139$	3.62278	−	6.27484i	0.307280	−	0.532225i	0.977766	+	0.209697i	$0.0672478\pi$
$140$		0			0
$141$	3.05083	+	0.161593i	0.256926	+	0.0136086i
$142$		0			0
$143$	1.84659			0.154420
$144$		0			0
$145$	8.64900			0.718260
$146$		0			0
$147$	−2.34353	−	4.60579i	−0.193291	−	0.379879i
$148$		0			0
$149$	6.59328	−	11.4199i	0.540143	−	0.935555i	−0.458753	−	0.888564i	$-0.651704\pi$
$149$	6.59328	−	11.4199i	0.540143	−	0.935555i	0.998895	−	0.0469907i	$-0.0149631\pi$
$150$		0			0
$151$	15.3430	−	8.85829i	1.24860	−	0.720877i	0.277767	−	0.960649i	$-0.410406\pi$
$151$	15.3430	−	8.85829i	1.24860	−	0.720877i	0.970829	+	0.239771i	$0.0770725\pi$
$152$		0			0
$153$	−11.9126	+	5.28790i	−0.963073	+	0.427502i
$154$		0			0
$155$	0.877826	−	0.506813i	0.0705087	−	0.0407082i
$156$		0			0
$157$	−0.0444019	−	0.0256355i	−0.00354366	−	0.00204593i	0.498227	−	0.867047i	$-0.333985\pi$
$157$	−0.0444019	−	0.0256355i	−0.00354366	−	0.00204593i	−0.501771	+	0.865001i	$0.667318\pi$
$158$		0			0
$159$	−7.56902	+	11.6410i	−0.600262	+	0.923195i
$160$		0			0
$161$		−	16.1407i		−	1.27206i
$162$		0			0
$163$	−21.6728			−1.69754			−0.848772	−	0.528759i	$-0.822658\pi$
$163$	−21.6728			−1.69754			−0.848772	+	0.528759i	$0.822658\pi$
$164$		0			0
$165$	1.09437	+	0.711558i	0.0851963	+	0.0553947i
$166$		0			0
$167$	−2.13169	+	3.69220i	−0.164955	+	0.285711i	−0.936639	−	0.350295i	$-0.886081\pi$
$167$	−2.13169	+	3.69220i	−0.164955	+	0.285711i	0.771684	+	0.636006i	$0.219415\pi$
$168$		0			0
$169$	−1.61935	−	2.80480i	−0.124566	−	0.215754i
$170$		0			0
$171$	−5.31303	−	11.9691i	−0.406297	−	0.915304i
$172$		0			0
$173$	10.1329	+	17.5507i	0.770389	+	1.33435i	0.937350	+	0.348390i	$0.113271\pi$
$173$	10.1329	+	17.5507i	0.770389	+	1.33435i	−0.166961	+	0.985964i	$0.553395\pi$
$174$		0			0
$175$	−5.85603	−	3.38098i	−0.442675	−	0.255578i
$176$		0			0
$177$	−11.8849	+	6.04732i	−0.893324	+	0.454544i
$178$		0			0
$179$			8.24861i			0.616530i	0.951300	+	0.308265i	$0.0997484\pi$
$179$			8.24861i			0.616530i	−0.951300	+	0.308265i	$0.900252\pi$
$180$		0			0
$181$			3.20840i			0.238478i	0.992866	+	0.119239i	$0.0380455\pi$
$181$			3.20840i			0.238478i	−0.992866	+	0.119239i	$0.961954\pi$
$182$		0			0
$183$	1.26438	−	23.8711i	0.0934653	−	1.76460i
$184$		0			0
$185$	−0.874155	−	0.504693i	−0.0642691	−	0.0371058i
$186$		0			0
$187$	−1.28388	−	2.22375i	−0.0938868	−	0.162617i
$188$		0			0
$189$	−9.72816	+	3.71564i	−0.707620	+	0.270273i
$190$		0			0
$191$	−13.0957	−	22.6823i	−0.947568	−	1.64124i	−0.750525	−	0.660842i	$-0.770199\pi$
$191$	−13.0957	−	22.6823i	−0.947568	−	1.64124i	−0.197043	−	0.980395i	$-0.563134\pi$
$192$		0			0
$193$	7.90828	−	13.6975i	0.569250	−	0.985971i	−0.427390	−	0.904067i	$-0.640567\pi$
$193$	7.90828	−	13.6975i	0.569250	−	0.985971i	0.996640	−	0.0819032i	$-0.0260998\pi$
$194$		0			0
$195$	−0.364973	+	6.89060i	−0.0261363	+	0.493446i
$196$		0			0
$197$	21.6315			1.54118			0.770591	−	0.637330i	$-0.219961\pi$
$197$	21.6315			1.54118			0.770591	+	0.637330i	$0.219961\pi$
$198$		0			0
$199$		−	25.5228i		−	1.80926i	−0.426193	−	0.904632i	$-0.640145\pi$
$199$		−	25.5228i		−	1.80926i	0.426193	−	0.904632i	$-0.359855\pi$
$200$		0			0
$201$	1.52191	+	2.99105i	0.107348	+	0.210972i
$202$		0			0
$203$	−11.7724	−	6.79679i	−0.826260	−	0.477041i
$204$		0			0
$205$	−4.87038	+	2.81192i	−0.340162	+	0.196393i
$206$		0			0
$207$	24.0263	+	2.55236i	1.66995	+	0.177401i
$208$		0			0
$209$	2.23431	−	1.28998i	0.154551	−	0.0892299i
$210$		0			0
$211$	9.66851	−	16.7463i	0.665607	−	1.15287i	−0.313513	−	0.949584i	$-0.601506\pi$
$211$	9.66851	−	16.7463i	0.665607	−	1.15287i	0.979120	−	0.203282i	$-0.0651608\pi$
$212$		0			0
$213$	0.811294	−	1.24776i	0.0555889	−	0.0854951i
$214$		0			0
$215$	7.26434			0.495424
$216$		0			0
$217$	−1.59311			−0.108147
$218$		0			0
$219$	−13.1634	+	20.2451i	−0.889499	+	1.36804i
$220$		0			0
$221$	6.78675	−	11.7550i	0.456526	−	0.790727i
$222$		0			0
$223$	−13.4909	+	7.78897i	−0.903417	+	0.521588i	−0.878307	−	0.478097i	$-0.841327\pi$
$223$	−13.4909	+	7.78897i	−0.903417	+	0.521588i	−0.0251097	+	0.999685i	$0.507994\pi$
$224$		0			0
$225$	5.95881	−	8.18240i	0.397254	−	0.545493i
$226$		0			0
$227$	−0.727162	+	0.419827i	−0.0482634	+	0.0278649i	−0.523938	−	0.851757i	$-0.675537\pi$
$227$	−0.727162	+	0.419827i	−0.0482634	+	0.0278649i	0.475674	+	0.879622i	$0.342204\pi$
$228$		0			0
$229$	2.02018	+	1.16635i	0.133497	+	0.0770748i	0.565261	−	0.824912i	$-0.308775\pi$
$229$	2.02018	+	1.16635i	0.133497	+	0.0770748i	−0.431764	+	0.901987i	$0.642109\pi$
$230$		0			0
$231$	−0.930396	−	1.82853i	−0.0612156	−	0.120308i
$232$		0			0
$233$		−	27.6912i		−	1.81411i	−0.421013	−	0.907055i	$-0.638325\pi$
$233$		−	27.6912i		−	1.81411i	0.421013	−	0.907055i	$-0.361675\pi$
$234$		0			0
$235$	−2.24914			−0.146718
$236$		0			0
$237$	1.54548	−	29.1782i	0.100390	−	1.89533i
$238$		0			0
$239$	9.83215	−	17.0298i	0.635989	−	1.10156i	−0.350316	−	0.936632i	$-0.613926\pi$
$239$	9.83215	−	17.0298i	0.635989	−	1.10156i	0.986305	−	0.164933i	$-0.0527409\pi$
$240$		0			0
$241$	9.14488	+	15.8394i	0.589074	+	1.02031i	0.994354	+	0.106113i	$0.0338405\pi$
$241$	9.14488	+	15.8394i	0.589074	+	1.02031i	−0.405280	+	0.914192i	$0.632826\pi$
$242$		0			0
$243$	−3.99260	−	15.0685i	−0.256126	−	0.966644i
$244$		0			0
$245$	1.90222	+	3.29474i	0.121528	+	0.210493i
$246$		0			0
$247$	11.8108	+	6.81899i	0.751506	+	0.433882i
$248$		0			0
$249$	−0.623341	+	11.7685i	−0.0395026	+	0.745799i
$250$		0			0
$251$		−	29.0275i		−	1.83220i	−0.400951	−	0.916100i	$-0.631320\pi$
$251$		−	29.0275i		−	1.83220i	0.400951	−	0.916100i	$-0.368680\pi$
$252$		0			0
$253$			4.76015i			0.299268i
$254$		0			0
$255$	8.55173	−	4.35132i	0.535530	−	0.272490i
$256$		0			0
$257$	−0.930520	−	0.537236i	−0.0580443	−	0.0335119i	0.470697	−	0.882295i	$-0.344002\pi$
$257$	−0.930520	−	0.537236i	−0.0580443	−	0.0335119i	−0.528741	+	0.848783i	$0.677336\pi$
$258$		0			0
$259$	0.793224	+	1.37390i	0.0492885	+	0.0853702i
$260$		0			0
$261$	11.9790	−	16.4491i	0.741481	−	1.01817i
$262$		0			0
$263$	9.32405	+	16.1497i	0.574946	+	0.995835i	0.996048	+	0.0888218i	$0.0283102\pi$
$263$	9.32405	+	16.1497i	0.574946	+	0.995835i	−0.421102	+	0.907013i	$0.638357\pi$
$264$		0			0
$265$	5.11115	−	8.85277i	0.313975	−	0.543821i
$266$		0			0
$267$	5.82077	+	3.78467i	0.356225	+	0.231618i
$268$		0			0
$269$	−11.0645			−0.674617			−0.337308	−	0.941394i	$-0.609517\pi$
$269$	−11.0645			−0.674617			−0.337308	+	0.941394i	$0.609517\pi$
$270$		0			0
$271$		−	13.9315i		−	0.846276i	−0.906065	−	0.423138i	$-0.860929\pi$
$271$		−	13.9315i		−	0.846276i	0.906065	−	0.423138i	$-0.139071\pi$
$272$		0			0
$273$	5.91173	−	9.09217i	0.357794	−	0.550283i
$274$		0			0
$275$	1.72704	+	0.997105i	0.104144	+	0.0601277i
$276$		0			0
$277$	−7.80262	+	4.50485i	−0.468814	+	0.270670i	−0.715743	−	0.698364i	$-0.753912\pi$
$277$	−7.80262	+	4.50485i	−0.468814	+	0.270670i	0.246929	+	0.969034i	$0.420579\pi$
$278$		0			0
$279$	0.251922	−	2.37144i	0.0150821	−	0.141974i
$280$		0			0
$281$	−17.4492	+	10.0743i	−1.04093	+	0.600981i	−0.920096	−	0.391692i	$-0.871890\pi$
$281$	−17.4492	+	10.0743i	−1.04093	+	0.600981i	−0.120833	+	0.992673i	$0.538557\pi$
$282$		0			0
$283$	3.26653	−	5.65780i	0.194175	−	0.336322i	−0.752455	−	0.658644i	$-0.771130\pi$
$283$	3.26653	−	5.65780i	0.194175	−	0.336322i	0.946630	+	0.322323i	$0.104464\pi$
$284$		0			0
$285$	4.37199	+	8.59236i	0.258975	+	0.508967i
$286$		0			0
$287$	8.83894			0.521746
$288$		0			0
$289$	−1.87454			−0.110267
$290$		0			0
$291$	−17.4130	−	0.922309i	−1.02077	−	0.0540667i
$292$		0			0
$293$	−12.9319	+	22.3987i	−0.755490	+	1.30855i	0.189640	+	0.981854i	$0.439268\pi$
$293$	−12.9319	+	22.3987i	−0.755490	+	1.30855i	−0.945130	+	0.326694i	$0.894065\pi$
$294$		0			0
$295$	8.50183	−	4.90853i	0.494996	−	0.285786i
$296$		0			0
$297$	2.86899	−	1.09580i	0.166476	−	0.0635848i
$298$		0			0
$299$	−21.7915	+	12.5813i	−1.26024	+	0.727597i
$300$		0			0
$301$	−9.88769	−	5.70866i	−0.569917	−	0.329042i
$302$		0			0
$303$	11.8880	+	0.629670i	0.682949	+	0.0361736i
$304$		0			0
$305$			17.5983i			1.00768i
$306$		0			0
$307$	−11.1149			−0.634361			−0.317181	−	0.948365i	$-0.602736\pi$
$307$	−11.1149			−0.634361			−0.317181	+	0.948365i	$0.602736\pi$
$308$		0			0
$309$	−20.0348	+	10.1942i	−1.13974	+	0.579926i
$310$		0			0
$311$	−7.62787	+	13.2119i	−0.432537	+	0.749176i	−0.997091	−	0.0762203i	$-0.975715\pi$
$311$	−7.62787	+	13.2119i	−0.432537	+	0.749176i	0.564554	+	0.825396i	$0.309048\pi$
$312$		0			0
$313$	10.9143	+	18.9041i	0.616912	+	1.06852i	0.990046	+	0.140745i	$0.0449498\pi$
$313$	10.9143	+	18.9041i	0.616912	+	1.06852i	−0.373134	+	0.927777i	$0.621717\pi$
$314$		0			0
$315$	7.00708	−	3.11039i	0.394804	−	0.175251i
$316$		0			0
$317$	0.214277	+	0.371139i	0.0120350	+	0.0208453i	0.871980	−	0.489541i	$-0.162836\pi$
$317$	0.214277	+	0.371139i	0.0120350	+	0.0208453i	−0.859945	+	0.510386i	$0.829502\pi$
$318$		0			0
$319$	3.47186	+	2.00448i	0.194387	+	0.112229i
$320$		0			0
$321$	−8.49951	−	5.52639i	−0.474397	−	0.308453i
$322$		0			0
$323$		−	18.9642i		−	1.05520i
$324$		0			0
$325$			10.5416i			0.584744i
$326$		0			0
$327$	−26.8611	−	17.4651i	−1.48542	−	0.965821i
$328$		0			0
$329$	3.06136	+	1.76748i	0.168778	+	0.0974443i
$330$		0			0
$331$	6.61374	+	11.4553i	0.363524	+	0.629642i	0.988538	−	0.150971i	$-0.0482401\pi$
$331$	6.61374	+	11.4553i	0.363524	+	0.629642i	−0.625014	+	0.780614i	$0.714907\pi$
$332$		0			0
$333$	−2.17057	+	0.963500i	−0.118946	+	0.0527995i
$334$		0			0
$335$	−1.23532	−	2.13964i	−0.0674927	−	0.116901i
$336$		0			0
$337$	−5.99838	+	10.3895i	−0.326752	+	0.565952i	−0.981865	−	0.189579i	$-0.939288\pi$
$337$	−5.99838	+	10.3895i	−0.326752	+	0.565952i	0.655113	+	0.755531i	$0.272621\pi$
$338$		0			0
$339$	3.97490	−	2.02252i	0.215887	−	0.109848i
$340$		0			0
$341$	0.469834			0.0254429
$342$		0			0
$343$		−	20.0081i		−	1.08034i
$344$		0			0
$345$	−17.7626	−	0.940828i	−0.956306	−	0.0506525i
$346$		0			0
$347$	−4.31331	−	2.49029i	−0.231551	−	0.133686i	0.379737	−	0.925095i	$-0.376015\pi$
$347$	−4.31331	−	2.49029i	−0.231551	−	0.133686i	−0.611287	+	0.791409i	$0.709348\pi$
$348$		0			0
$349$	12.3841	−	7.14994i	0.662904	−	0.382728i	−0.130479	−	0.991451i	$-0.541651\pi$
$349$	12.3841	−	7.14994i	0.662904	−	0.382728i	0.793382	+	0.608723i	$0.208318\pi$
$350$		0			0
$351$	12.5994	+	10.2377i	0.672505	+	0.546449i
$352$		0			0
$353$	3.97052	−	2.29238i	0.211329	−	0.122011i	−0.390600	−	0.920561i	$-0.627732\pi$
$353$	3.97052	−	2.29238i	0.211329	−	0.122011i	0.601929	+	0.798550i	$0.294399\pi$
$354$		0			0
$355$	−0.547844	+	0.948894i	−0.0290766	+	0.0503621i
$356$		0			0
$357$	−15.0595	−	0.797652i	−0.797031	−	0.0422162i
$358$		0			0
$359$	−21.6909			−1.14480			−0.572401	−	0.819974i	$-0.693988\pi$
$359$	−21.6909			−1.14480			−0.572401	+	0.819974i	$0.693988\pi$
$360$		0			0
$361$	0.0543064			0.00285823
$362$		0			0
$363$	−8.36583	−	16.4415i	−0.439092	−	0.862956i
$364$		0			0
$365$	8.88887	−	15.3960i	0.465265	−	0.805862i
$366$		0			0
$367$	−21.0375	+	12.1460i	−1.09815	+	0.634017i	−0.935734	−	0.352706i	$-0.885262\pi$
$367$	−21.0375	+	12.1460i	−1.09815	+	0.634017i	−0.162415	+	0.986723i	$0.551928\pi$
$368$		0			0
$369$	−1.39772	+	13.1573i	−0.0727623	+	0.684940i
$370$		0			0
$371$	−13.9138	+	8.03316i	−0.722371	+	0.417061i
$372$		0			0
$373$	5.40106	+	3.11830i	0.279656	+	0.161460i	0.633268	−	0.773933i	$-0.281713\pi$
$373$	5.40106	+	3.11830i	0.279656	+	0.161460i	−0.353612	+	0.935392i	$0.615047\pi$
$374$		0			0
$375$	−10.0816	+	15.5054i	−0.520612	+	0.800694i
$376$		0			0
$377$			21.1918i			1.09143i
$378$		0			0
$379$	−29.0842			−1.49395			−0.746976	−	0.664851i	$-0.768495\pi$
$379$	−29.0842			−1.49395			−0.746976	+	0.664851i	$0.768495\pi$
$380$		0			0
$381$	−3.47846	−	2.26170i	−0.178207	−	0.115870i
$382$		0			0
$383$	12.4341	−	21.5366i	0.635355	−	1.10047i	−0.351084	−	0.936344i	$-0.614187\pi$
$383$	12.4341	−	21.5366i	0.635355	−	1.10047i	0.986440	−	0.164124i	$-0.0524797\pi$
$384$		0			0
$385$	0.755192	+	1.30803i	0.0384881	+	0.0666634i
$386$		0			0
$387$	10.0612	−	13.8157i	0.511441	−	0.702290i
$388$		0			0
$389$	−4.87424	−	8.44243i	−0.247134	−	0.428048i	0.715596	−	0.698515i	$-0.246155\pi$
$389$	−4.87424	−	8.44243i	−0.247134	−	0.428048i	−0.962729	+	0.270467i	$0.912822\pi$
$390$		0			0
$391$	30.3020	+	17.4949i	1.53244	+	0.884755i
$392$		0			0
$393$	16.6783	−	8.48633i	0.841310	−	0.428078i
$394$		0			0
$395$			21.5109i			1.08233i
$396$		0			0
$397$		−	13.5397i		−	0.679540i	−0.940509	−	0.339770i	$-0.889651\pi$
$397$		−	13.5397i		−	0.679540i	0.940509	−	0.339770i	$-0.110349\pi$
$398$		0			0
$399$	0.801442	−	15.1310i	0.0401223	−	0.757498i
$400$		0			0
$401$	−17.4749	−	10.0891i	−0.872655	−	0.503827i	−0.00442521	−	0.999990i	$-0.501409\pi$
$401$	−17.4749	−	10.0891i	−0.872655	−	0.503827i	−0.868230	+	0.496163i	$0.834742\pi$
$402$		0			0
$403$	1.24180	+	2.15086i	0.0618583	+	0.107142i
$404$		0			0
$405$	3.52196	+	10.9223i	0.175007	+	0.542733i
$406$		0			0
$407$	−0.233934	−	0.405186i	−0.0115957	−	0.0200843i
$408$		0			0
$409$	−6.93069	+	12.0043i	−0.342701	+	0.593575i	−0.984933	−	0.172935i	$-0.944675\pi$
$409$	−6.93069	+	12.0043i	−0.342701	+	0.593575i	0.642233	+	0.766510i	$0.278008\pi$
$410$		0			0
$411$	−1.63477	+	30.8640i	−0.0806372	+	1.52241i
$412$		0			0
$413$	−15.4294			−0.759232
$414$		0			0
$415$		−	8.67602i		−	0.425889i
$416$		0			0
$417$	5.69120	+	11.1850i	0.278699	+	0.547733i
$418$		0			0
$419$	23.3421	+	13.4766i	1.14034	+	0.658373i	0.946514	−	0.322663i	$-0.104578\pi$
$419$	23.3421	+	13.4766i	1.14034	+	0.658373i	0.193822	+	0.981037i	$0.437912\pi$
$420$		0			0
$421$	10.2818	−	5.93622i	0.501106	−	0.289314i	−0.228064	−	0.973646i	$-0.573240\pi$
$421$	10.2818	−	5.93622i	0.501106	−	0.289314i	0.729170	+	0.684332i	$0.239906\pi$
$422$		0			0
$423$	−3.11509	+	4.27752i	−0.151461	+	0.207980i
$424$		0			0
$425$	12.6947	−	7.32929i	0.615784	−	0.355523i
$426$		0			0
$427$	13.8296	−	23.9535i	0.669260	−	1.15919i
$428$		0			0
$429$	−1.74346	+	2.68142i	−0.0841752	+	0.129460i
$430$		0			0
$431$	6.97179			0.335820			0.167910	−	0.985802i	$-0.446298\pi$
$431$	6.97179			0.335820			0.167910	+	0.985802i	$0.446298\pi$
$432$		0			0
$433$	−11.5779			−0.556396			−0.278198	−	0.960524i	$-0.589737\pi$
$433$	−11.5779			−0.556396			−0.278198	+	0.960524i	$0.589737\pi$
$434$		0			0
$435$	−8.16597	+	12.5592i	−0.391528	+	0.602166i
$436$		0			0
$437$	−17.5780	+	30.4460i	−0.840870	+	1.45643i
$438$		0			0
$439$	−22.9646	+	13.2586i	−1.09604	+	0.632798i	−0.935178	−	0.354179i	$-0.884760\pi$
$439$	−22.9646	+	13.2586i	−1.09604	+	0.632798i	−0.160861	+	0.986977i	$0.551427\pi$
$440$		0			0
$441$	8.90069	+	0.945535i	0.423842	+	0.0450255i
$442$		0			0
$443$	27.6626	−	15.9710i	1.31429	−	0.758805i	0.331485	−	0.943460i	$-0.392450\pi$
$443$	27.6626	−	15.9710i	1.31429	−	0.758805i	0.982803	+	0.184656i	$0.0591170\pi$
$444$		0			0
$445$	−4.42657	−	2.55568i	−0.209840	−	0.121151i
$446$		0			0
$447$	10.3577	+	20.3562i	0.489903	+	0.962815i
$448$		0			0
$449$		−	4.03758i		−	0.190545i	−0.995451	−	0.0952726i	$-0.969628\pi$
$449$		−	4.03758i		−	0.190545i	0.995451	−	0.0952726i	$-0.0303723\pi$
$450$		0			0
$451$	−2.60674			−0.122747
$452$		0			0
$453$	−1.62307	+	30.6431i	−0.0762583	+	1.43974i
$454$		0			0
$455$	−3.99203	+	6.91440i	−0.187149	+	0.324152i
$456$		0			0
$457$	−5.80314	−	10.0513i	−0.271459	−	0.470181i	0.697776	−	0.716316i	$-0.254173\pi$
$457$	−5.80314	−	10.0513i	−0.271459	−	0.470181i	−0.969236	+	0.246134i	$0.920840\pi$
$458$		0			0
$459$	3.56873	−	22.2907i	0.166574	−	1.04044i
$460$		0			0
$461$	−3.76959	−	6.52912i	−0.175567	−	0.304091i	0.764790	−	0.644279i	$-0.222843\pi$
$461$	−3.76959	−	6.52912i	−0.175567	−	0.304091i	−0.940357	+	0.340188i	$0.889509\pi$
$462$		0			0
$463$	8.97193	+	5.17995i	0.416961	+	0.240733i	0.693776	−	0.720191i	$-0.255946\pi$
$463$	8.97193	+	5.17995i	0.416961	+	0.240733i	−0.276815	+	0.960923i	$0.589279\pi$
$464$		0			0
$465$	−0.0928612	+	1.75319i	−0.00430633	+	0.0813025i
$466$		0			0
$467$			11.1707i			0.516919i	0.966022	+	0.258460i	$0.0832149\pi$
$467$			11.1707i			0.516919i	−0.966022	+	0.258460i	$0.916785\pi$
$468$		0			0
$469$			3.88309i			0.179304i
$470$		0			0
$471$	0.0791472	−	0.0402720i	0.00364691	−	0.00185563i
$472$		0			0
$473$	2.91604	+	1.68357i	0.134079	+	0.0774108i
$474$		0			0
$475$	7.36411	+	12.7550i	0.337889	+	0.585240i
$476$		0			0
$477$	−9.75759	−	21.9818i	−0.446769	−	1.00648i
$478$		0			0
$479$	−2.12949	−	3.68839i	−0.0972990	−	0.168527i	0.813267	−	0.581891i	$-0.197687\pi$
$479$	−2.12949	−	3.68839i	−0.0972990	−	0.168527i	−0.910566	+	0.413364i	$0.864354\pi$
$480$		0			0
$481$	1.23660	−	2.14186i	0.0563842	−	0.0976604i
$482$		0			0
$483$	23.4378	+	15.2393i	1.06646	+	0.693411i
$484$		0			0
$485$	12.8372			0.582909
$486$		0			0
$487$			3.34781i			0.151704i	0.997119	+	0.0758518i	$0.0241676\pi$
$487$			3.34781i			0.151704i	−0.997119	+	0.0758518i	$0.975832\pi$
$488$		0			0
$489$	20.4624	−	31.4709i	0.925342	−	1.42316i
$490$		0			0
$491$	19.8656	+	11.4694i	0.896521	+	0.517607i	0.876070	−	0.482184i	$-0.160156\pi$
$491$	19.8656	+	11.4694i	0.896521	+	0.517607i	0.0204512	+	0.999791i	$0.493490\pi$
$492$		0			0
$493$	25.5202	−	14.7341i	1.14937	−	0.663590i
$494$		0			0
$495$	−2.06650	+	0.917304i	−0.0928822	+	0.0412298i
$496$		0			0
$497$	1.49137	−	0.861044i	0.0668971	−	0.0386231i
$498$		0			0
$499$	−9.05609	+	15.6856i	−0.405406	+	0.702185i	−0.994369	−	0.105976i	$-0.966203\pi$
$499$	−9.05609	+	15.6856i	−0.405406	+	0.702185i	0.588962	+	0.808161i	$0.299537\pi$
$500$		0			0
$501$	−3.34878	−	6.58142i	−0.149613	−	0.294036i
$502$		0			0
$503$	1.04368			0.0465355			0.0232678	−	0.999729i	$-0.492593\pi$
$503$	1.04368			0.0465355			0.0232678	+	0.999729i	$0.492593\pi$
$504$		0			0
$505$	−8.76412			−0.389998
$506$		0			0
$507$	5.60175	+	0.296707i	0.248783	+	0.0131772i
$508$		0			0
$509$	8.22698	−	14.2495i	0.364654	−	0.631600i	−0.624066	−	0.781371i	$-0.714520\pi$
$509$	8.22698	−	14.2495i	0.364654	−	0.631600i	0.988721	+	0.149771i	$0.0478538\pi$
$510$		0			0
$511$	−24.1978	+	13.9706i	−1.07045	+	0.618022i
$512$		0			0
$513$	22.3966	+	3.58569i	0.988835	+	0.158312i
$514$		0			0
$515$	14.3318	−	8.27448i	0.631536	−	0.364617i
$516$		0			0
$517$	−0.902845	−	0.521258i	−0.0397071	−	0.0229249i
$518$		0			0
$519$	−35.0522	−	1.85660i	−1.53862	−	0.0814959i
$520$		0			0
$521$			16.3281i			0.715349i	0.933846	+	0.357674i	$0.116430\pi$
$521$			16.3281i			0.715349i	−0.933846	+	0.357674i	$0.883570\pi$
$522$		0			0
$523$	27.3714			1.19687			0.598434	−	0.801172i	$-0.295790\pi$
$523$	27.3714			1.19687			0.598434	+	0.801172i	$0.295790\pi$
$524$		0			0
$525$	10.4385	−	5.31135i	0.455573	−	0.231806i
$526$		0			0
$527$	1.72677	−	2.99086i	0.0752194	−	0.130284i
$528$		0			0
$529$	−20.9322	−	36.2556i	−0.910095	−	1.57633i
$530$		0			0
$531$	2.43988	−	22.9676i	0.105882	−	0.996708i
$532$		0			0
$533$	−6.88977	−	11.9334i	−0.298429	−	0.516894i
$534$		0			0
$535$	6.46370	+	3.73182i	0.279450	+	0.161341i
$536$		0			0
$537$	−11.9778	−	7.78795i	−0.516879	−	0.336075i
$538$		0			0
$539$			1.76342i			0.0759560i
$540$		0			0
$541$		−	34.0615i		−	1.46442i	−0.681080	−	0.732209i	$-0.738489\pi$
$541$		−	34.0615i		−	1.46442i	0.681080	−	0.732209i	$-0.261511\pi$
$542$		0			0
$543$	−4.65890	−	3.02922i	−0.199932	−	0.129996i
$544$		0			0
$545$	20.4273	+	11.7937i	0.875008	+	0.505186i
$546$		0			0
$547$	9.75947	+	16.9039i	0.417285	+	0.722758i	0.995665	−	0.0930088i	$-0.0296485\pi$
$547$	9.75947	+	16.9039i	0.417285	+	0.722758i	−0.578381	+	0.815767i	$0.696315\pi$
$548$		0			0
$549$	33.4693	+	24.3739i	1.42843	+	1.04025i
$550$		0			0
$551$	14.8041	+	25.6414i	0.630675	+	1.09236i
$552$		0			0
$553$	16.9042	−	29.2790i	0.718841	−	1.24507i
$554$		0			0
$555$	1.55820	−	0.792847i	0.0661418	−	0.0336545i
$556$		0			0
$557$	−28.8839			−1.22385			−0.611925	−	0.790916i	$-0.709605\pi$
$557$	−28.8839			−1.22385			−0.611925	+	0.790916i	$0.709605\pi$
$558$		0			0
$559$			17.7991i			0.752823i
$560$		0			0
$561$	4.44127	+	0.235240i	0.187511	+	0.00993185i
$562$		0			0
$563$	−11.2983	−	6.52308i	−0.476167	−	0.274915i	0.242651	−	0.970114i	$-0.421983\pi$
$563$	−11.2983	−	6.52308i	−0.476167	−	0.274915i	−0.718818	+	0.695199i	$0.755316\pi$
$564$		0			0
$565$	−2.84344	+	1.64166i	−0.119624	+	0.0690651i
$566$		0			0
$567$	3.78941	−	17.6343i	0.159140	−	0.740572i
$568$		0			0
$569$	−27.6452	+	15.9610i	−1.15895	+	0.669118i	−0.951051	−	0.309033i	$-0.899995\pi$
$569$	−27.6452	+	15.9610i	−1.15895	+	0.669118i	−0.207895	+	0.978151i	$0.566661\pi$
$570$		0			0
$571$	−0.687930	+	1.19153i	−0.0287890	+	0.0498639i	−0.880061	−	0.474861i	$-0.842498\pi$
$571$	−0.687930	+	1.19153i	−0.0287890	+	0.0498639i	0.851272	+	0.524725i	$0.175832\pi$
$572$		0			0
$573$	45.3012	+	2.39946i	1.89248	+	0.100239i
$574$		0			0
$575$	−27.1742			−1.13324
$576$		0			0
$577$	−6.26407			−0.260777			−0.130388	−	0.991463i	$-0.541622\pi$
$577$	−6.26407			−0.260777			−0.130388	+	0.991463i	$0.541622\pi$
$578$		0			0
$579$	12.4235	+	24.4161i	0.516303	+	1.01470i
$580$		0			0
$581$	−6.81802	+	11.8092i	−0.282859	+	0.489927i
$582$		0			0
$583$	4.10341	−	2.36911i	0.169946	−	0.0981184i
$584$		0			0
$585$	−9.66121	−	7.03575i	−0.399442	−	0.290892i
$586$		0			0
$587$	−7.05203	+	4.07149i	−0.291069	+	0.168049i	−0.638424	−	0.769685i	$-0.720413\pi$
$587$	−7.05203	+	4.07149i	−0.291069	+	0.168049i	0.347355	+	0.937734i	$0.387080\pi$
$588$		0			0
$589$	3.00507	+	1.73498i	0.123822	+	0.0714884i
$590$		0			0
$591$	−20.4234	+	31.4110i	−0.840108	+	1.29208i
$592$		0			0
$593$			15.5710i			0.639424i	0.947515	+	0.319712i	$0.103586\pi$
$593$			15.5710i			0.639424i	−0.947515	+	0.319712i	$0.896414\pi$
$594$		0			0
$595$	11.1022			0.455145
$596$		0			0
$597$	37.0615	+	24.0974i	1.51683	+	0.986242i
$598$		0			0
$599$	−13.9635	+	24.1855i	−0.570534	+	0.988193i	0.425978	+	0.904734i	$0.359930\pi$
$599$	−13.9635	+	24.1855i	−0.570534	+	0.988193i	−0.996511	+	0.0834595i	$0.973403\pi$
$600$		0			0
$601$	−14.1416	−	24.4940i	−0.576849	−	0.999132i	−0.995838	−	0.0911407i	$-0.970949\pi$
$601$	−14.1416	−	24.4940i	−0.576849	−	0.999132i	0.418989	−	0.907991i	$-0.362385\pi$
$602$		0			0
$603$	−5.78020	−	0.614040i	−0.235388	−	0.0250056i
$604$		0			0
$605$	6.79044	+	11.7614i	0.276071	+	0.478169i
$606$		0			0
$607$	6.36525	+	3.67498i	0.258358	+	0.149163i	0.623585	−	0.781755i	$-0.285675\pi$
$607$	6.36525	+	3.67498i	0.258358	+	0.149163i	−0.365228	+	0.930918i	$0.619009\pi$
$608$		0			0
$609$	20.9845	−	10.6774i	0.850335	−	0.432670i
$610$		0			0
$611$		−	5.51085i		−	0.222945i
$612$		0			0
$613$			15.1229i			0.610810i	0.952223	+	0.305405i	$0.0987918\pi$
$613$			15.1229i			0.610810i	−0.952223	+	0.305405i	$0.901208\pi$
$614$		0			0
$615$	0.515215	−	9.72713i	0.0207755	−	0.392236i
$616$		0			0
$617$	−2.69036	−	1.55328i	−0.108310	−	0.0625327i	0.444867	−	0.895597i	$-0.353251\pi$
$617$	−2.69036	−	1.55328i	−0.108310	−	0.0625327i	−0.553176	+	0.833064i	$0.686584\pi$
$618$		0			0
$619$	18.8905	+	32.7193i	0.759273	+	1.31510i	0.943222	+	0.332163i	$0.107778\pi$
$619$	18.8905	+	32.7193i	0.759273	+	1.31510i	−0.183949	+	0.982936i	$0.558888\pi$
$620$		0			0
$621$	−26.3908	+	32.4787i	−1.05903	+	1.30332i
$622$		0			0
$623$	4.01675	+	6.95721i	0.160928	+	0.278735i
$624$		0			0
$625$	−1.62734	+	2.81864i	−0.0650937	+	0.112746i
$626$		0			0
$627$	−0.236358	+	4.46237i	−0.00943922	+	0.178210i
$628$		0			0
$629$	−3.43910			−0.137126
$630$		0			0
$631$		−	10.1597i		−	0.404451i	−0.979339	−	0.202225i	$-0.935183\pi$
$631$		−	10.1597i		−	0.404451i	0.979339	−	0.202225i	$-0.0648173\pi$
$632$		0			0
$633$	15.1887	+	29.8507i	0.603698	+	1.18646i
$634$		0			0
$635$	2.64529	+	1.52726i	0.104975	+	0.0606075i
$636$		0			0
$637$	−8.07279	+	4.66082i	−0.319855	+	0.184669i
$638$		0			0
$639$	1.04588	+	2.35615i	0.0413743	+	0.0932078i
$640$		0			0
$641$	−15.8959	+	9.17749i	−0.627850	+	0.362489i	−0.779919	−	0.625881i	$-0.784740\pi$
$641$	−15.8959	+	9.17749i	−0.627850	+	0.362489i	0.152069	+	0.988370i	$0.451406\pi$
$642$		0			0
$643$	19.6141	−	33.9726i	0.773503	−	1.33975i	−0.162128	−	0.986770i	$-0.551836\pi$
$643$	19.6141	−	33.9726i	0.773503	−	1.33975i	0.935632	−	0.352978i	$-0.114831\pi$
$644$		0			0
$645$	−6.85864	+	10.5485i	−0.270059	+	0.415347i
$646$		0			0
$647$	6.88907			0.270837			0.135419	−	0.990788i	$-0.456762\pi$
$647$	6.88907			0.270837			0.135419	+	0.990788i	$0.456762\pi$
$648$		0			0
$649$	4.55038			0.178618
$650$		0			0
$651$	1.50414	−	2.31335i	0.0589518	−	0.0906672i
$652$		0			0
$653$	19.6489	−	34.0328i	0.768919	−	1.33181i	−0.169230	−	0.985577i	$-0.554128\pi$
$653$	19.6489	−	34.0328i	0.768919	−	1.33181i	0.938149	−	0.346231i	$-0.112538\pi$
$654$		0			0
$655$	−11.9308	+	6.88825i	−0.466175	+	0.269146i
$656$		0			0
$657$	−16.9696	−	38.2289i	−0.662046	−	1.49145i
$658$		0			0
$659$	−17.4932	+	10.0997i	−0.681439	+	0.393429i	−0.800397	−	0.599470i	$-0.795378\pi$
$659$	−17.4932	+	10.0997i	−0.681439	+	0.393429i	0.118958	+	0.992899i	$0.462045\pi$
$660$		0			0
$661$	8.59746	+	4.96374i	0.334402	+	0.193067i	0.657794	−	0.753198i	$-0.271490\pi$
$661$	8.59746	+	4.96374i	0.334402	+	0.193067i	−0.323392	+	0.946265i	$0.604823\pi$
$662$		0			0
$663$	10.6616	+	20.9535i	0.414064	+	0.813767i
$664$		0			0
$665$			11.1549i			0.432569i
$666$		0			0
$667$	−54.6283			−2.11522
$668$		0			0
$669$	1.42714	−	26.9440i	0.0551764	−	1.04172i
$670$		0			0
$671$	−4.07856	+	7.06428i	−0.157451	+	0.272713i
$672$		0			0
$673$	−15.1836	−	26.2987i	−0.585284	−	1.01374i	−0.994840	−	0.101456i	$-0.967650\pi$
$673$	−15.1836	−	26.2987i	−0.585284	−	1.01374i	0.409556	−	0.912285i	$-0.365683\pi$
$674$		0			0
$675$	6.25559	+	16.3782i	0.240778	+	0.630397i
$676$		0			0
$677$	−9.70944	−	16.8172i	−0.373164	−	0.646339i	0.616886	−	0.787052i	$-0.288394\pi$
$677$	−9.70944	−	16.8172i	−0.373164	−	0.646339i	−0.990050	+	0.140713i	$0.955060\pi$
$678$		0			0
$679$	−17.4731	−	10.0881i	−0.670556	−	0.387146i
$680$		0			0
$681$	0.0769231	−	1.45229i	0.00294770	−	0.0556518i
$682$		0			0
$683$			32.8315i			1.25626i	0.778107	+	0.628132i	$0.216180\pi$
$683$			32.8315i			1.25626i	−0.778107	+	0.628132i	$0.783820\pi$
$684$		0			0
$685$		−	22.7536i		−	0.869372i
$686$		0			0
$687$	−3.60101	+	1.83228i	−0.137387	+	0.0699058i
$688$		0			0
$689$	21.6911	+	12.5234i	0.826365	+	0.477102i
$690$		0			0
$691$	12.8082	+	22.1845i	0.487247	+	0.843937i	0.999892	−	0.0146636i	$-0.00466773\pi$
$691$	12.8082	+	22.1845i	0.487247	+	0.843937i	−0.512645	+	0.858601i	$0.671334\pi$
$692$		0			0
$693$	3.53363	+	0.375383i	0.134231	+	0.0142596i
$694$		0			0
$695$	−4.61948	−	8.00117i	−0.175227	−	0.303502i
$696$		0			0
$697$	−9.58053	+	16.5940i	−0.362888	+	0.628541i
$698$		0			0
$699$	40.2102	+	26.1447i	1.52089	+	0.988883i
$700$		0			0
$701$	−43.1727			−1.63061			−0.815306	−	0.579030i	$-0.803431\pi$
$701$	−43.1727			−1.63061			−0.815306	+	0.579030i	$0.803431\pi$
$702$		0			0
$703$		−	3.45544i		−	0.130324i
$704$		0			0
$705$	2.12353	−	3.26596i	0.0799767	−	0.123003i
$706$		0			0
$707$	11.9291	+	6.88725i	0.448639	+	0.259022i
$708$		0			0
$709$	26.7011	−	15.4159i	1.00278	−	0.578956i	0.0937116	−	0.995599i	$-0.470127\pi$
$709$	26.7011	−	15.4159i	1.00278	−	0.578956i	0.909070	+	0.416643i	$0.136793\pi$
$710$		0			0
$711$	40.9104	+	29.7929i	1.53426	+	1.11732i
$712$		0			0
$713$	−5.54448	+	3.20111i	−0.207642	+	0.119882i
$714$		0			0
$715$	1.17731	−	2.03917i	0.0440290	−	0.0762605i
$716$		0			0
$717$	15.4458	+	30.3559i	0.576834	+	1.13366i
$718$		0			0
$719$	−37.6211			−1.40303			−0.701515	−	0.712654i	$-0.747493\pi$
$719$	−37.6211			−1.40303			−0.701515	+	0.712654i	$0.747493\pi$
$720$		0			0
$721$	−26.0099			−0.968660
$722$		0			0
$723$	−31.6345	−	1.67558i	−1.17650	−	0.0623154i
$724$		0			0
$725$	−11.4430	+	19.8198i	−0.424981	+	0.736089i
$726$		0			0
$727$	−5.99982	+	3.46400i	−0.222521	+	0.128473i	−0.607117	−	0.794612i	$-0.707674\pi$
$727$	−5.99982	+	3.46400i	−0.222521	+	0.128473i	0.384596	+	0.923085i	$0.374341\pi$
$728$		0			0
$729$	25.6505	+	8.42931i	0.950018	+	0.312197i
$730$		0			0
$731$	21.4345	−	12.3752i	0.792785	−	0.457715i
$732$		0			0
$733$	24.0478	+	13.8840i	0.888227	+	0.512818i	0.873362	−	0.487071i	$-0.161935\pi$
$733$	24.0478	+	13.8840i	0.888227	+	0.512818i	0.0148649	+	0.999890i	$0.495268\pi$
$734$		0			0
$735$	−6.58025	−	0.348535i	−0.242716	−	0.0128559i
$736$		0			0
$737$		−	1.14518i		−	0.0421834i
$738$		0			0
$739$	−2.09459			−0.0770509			−0.0385254	−	0.999258i	$-0.512266\pi$
$739$	−2.09459			−0.0770509			−0.0385254	+	0.999258i	$0.512266\pi$
$740$		0			0
$741$	−21.0531	+	10.7123i	−0.773403	+	0.393526i
$742$		0			0
$743$	4.38888	−	7.60176i	0.161012	−	0.278882i	−0.774220	−	0.632917i	$-0.781857\pi$
$743$	4.38888	−	7.60176i	0.161012	−	0.278882i	0.935232	+	0.354035i	$0.115191\pi$
$744$		0			0
$745$	−8.40723	−	14.5617i	−0.308017	−	0.533501i
$746$		0			0
$747$	−16.5005	−	12.0164i	−0.603720	−	0.439658i
$748$		0			0
$749$	−5.86528	−	10.1590i	−0.214312	−	0.371200i
$750$		0			0
$751$	−15.1697	−	8.75822i	−0.553550	−	0.319592i	0.197003	−	0.980403i	$-0.436879\pi$
$751$	−15.1697	−	8.75822i	−0.553550	−	0.319592i	−0.750553	+	0.660811i	$0.770213\pi$
$752$		0			0
$753$	42.1507	+	27.4064i	1.53606	+	0.998744i
$754$		0			0
$755$		−	22.5908i		−	0.822162i
$756$		0			0
$757$		−	37.8512i		−	1.37573i	−0.725841	−	0.687863i	$-0.758549\pi$
$757$		−	37.8512i		−	1.37573i	0.725841	−	0.687863i	$-0.241451\pi$
$758$		0			0
$759$	−6.91218	−	4.49430i	−0.250896	−	0.163133i
$760$		0			0
$761$	19.4553	+	11.2325i	0.705253	+	0.407178i	0.809301	−	0.587394i	$-0.199846\pi$
$761$	19.4553	+	11.2325i	0.705253	+	0.407178i	−0.104048	+	0.994572i	$0.533180\pi$
$762$		0			0
$763$	−18.5361	−	32.1054i	−0.671051	−	1.16229i
$764$		0			0
$765$	−1.75561	+	16.5262i	−0.0634742	+	0.597507i
$766$		0			0
$767$	12.0269	+	20.8312i	0.434267	+	0.752172i
$768$		0			0
$769$	0.296079	−	0.512824i	0.0106769	−	0.0184929i	−0.860638	−	0.509218i	$-0.829935\pi$
$769$	0.296079	−	0.512824i	0.0106769	−	0.0184929i	0.871314	+	0.490725i	$0.163268\pi$
$770$		0			0
$771$	1.65867	−	0.843970i	0.0597355	−	0.0303948i
$772$		0			0
$773$	−31.7490			−1.14193			−0.570966	−	0.820974i	$-0.693431\pi$
$773$	−31.7490			−1.14193			−0.570966	+	0.820974i	$0.693431\pi$
$774$		0			0
$775$			2.68214i			0.0963452i
$776$		0			0
$777$	−2.74396	−	0.145339i	−0.0984391	−	0.00521400i
$778$		0			0
$779$	−16.6728	−	9.62604i	−0.597365	−	0.344889i
$780$		0			0
$781$	−0.439829	+	0.253935i	−0.0157383	+	0.00908652i
$782$		0			0
$783$	12.5756	+	32.9251i	0.449415	+	1.17665i
$784$		0			0
$785$	−0.0566178	+	0.0326883i	−0.00202077	+	0.00116669i
$786$		0			0
$787$	21.3225	−	36.9317i	0.760065	−	1.31647i	−0.182751	−	0.983159i	$-0.558500\pi$
$787$	21.3225	−	36.9317i	0.760065	−	1.31647i	0.942816	−	0.333313i	$-0.108166\pi$
$788$		0			0
$789$	−32.2543	−	1.70841i	−1.14828	−	0.0608208i
$790$		0			0
$791$	5.16037			0.183482
$792$		0			0
$793$	−43.1195			−1.53122
$794$		0			0
$795$	8.02935	+	15.7802i	0.284772	+	0.559667i
$796$		0			0
$797$	−6.99240	+	12.1112i	−0.247684	+	0.429001i	−0.962883	−	0.269920i	$-0.913003\pi$
$797$	−6.99240	+	12.1112i	−0.247684	+	0.429001i	0.715199	+	0.698921i	$0.246336\pi$
$798$		0			0
$799$	−6.63642	+	3.83154i	−0.234780	+	0.135550i
$800$		0			0
$801$	−10.9914	+	4.87900i	−0.388361	+	0.172391i
$802$		0			0
$803$	7.13630	−	4.12015i	0.251835	−	0.145397i
$804$		0			0
$805$	−17.8239	−	10.2907i	−0.628212	−	0.362698i
$806$		0			0
$807$	10.4466	−	16.0668i	0.367738	−	0.565576i
$808$		0			0
$809$			20.1516i			0.708491i	0.935152	+	0.354245i	$0.115262\pi$
$809$			20.1516i			0.708491i	−0.935152	+	0.354245i	$0.884738\pi$
$810$		0			0
$811$	42.4802			1.49168			0.745840	−	0.666125i	$-0.232048\pi$
$811$	42.4802			1.49168			0.745840	+	0.666125i	$0.232048\pi$
$812$		0			0
$813$	20.2298	+	13.1534i	0.709489	+	0.461310i
$814$		0			0
$815$	−13.8177	+	23.9330i	−0.484013	+	0.838335i
$816$		0			0
$817$	12.4340	+	21.5364i	0.435011	+	0.753462i
$818$		0			0
$819$	7.62111	+	17.1688i	0.266303	+	0.599926i
$820$		0			0
$821$	−15.7727	−	27.3192i	−0.550472	−	0.953445i	−0.998240	−	0.0592958i	$-0.981114\pi$
$821$	−15.7727	−	27.3192i	−0.550472	−	0.953445i	0.447769	−	0.894149i	$-0.352219\pi$
$822$		0			0
$823$	30.3863	+	17.5435i	1.05920	+	0.611528i	0.925210	−	0.379455i	$-0.123888\pi$
$823$	30.3863	+	17.5435i	1.05920	+	0.611528i	0.133988	+	0.990983i	$0.457222\pi$
$824$		0			0
$825$	−3.07848	+	1.56640i	−0.107179	+	0.0545351i
$826$		0			0
$827$		−	20.8003i		−	0.723299i	−0.932314	−	0.361649i	$-0.882214\pi$
$827$		−	20.8003i		−	0.723299i	0.932314	−	0.361649i	$-0.117786\pi$
$828$		0			0
$829$		−	19.4187i		−	0.674439i	−0.941426	−	0.337219i	$-0.890514\pi$
$829$		−	19.4187i		−	0.674439i	0.941426	−	0.337219i	$-0.109486\pi$
$830$		0			0
$831$	0.825403	−	15.5834i	0.0286329	−	0.540582i
$832$		0			0
$833$	11.2256	+	6.48108i	0.388943	+	0.224556i
$834$		0			0
$835$	2.71817	+	4.70800i	0.0940660	+	0.162927i
$836$		0			0
$837$	3.20569	+	2.60481i	0.110805	+	0.0900354i
$838$		0			0
$839$	−12.1791	−	21.0948i	−0.420468	−	0.728272i	0.575517	−	0.817790i	$-0.304801\pi$
$839$	−12.1791	−	21.0948i	−0.420468	−	0.728272i	−0.995985	+	0.0895178i	$0.971467\pi$
$840$		0			0
$841$	−8.50381	+	14.7290i	−0.293235	+	0.507897i
$842$		0			0
$843$	1.84587	−	34.8495i	0.0635750	−	1.20028i
$844$		0			0
$845$	−4.12974			−0.142067
$846$		0			0
$847$		−	21.3450i		−	0.733423i
$848$		0			0
$849$	5.13156	+	10.0851i	0.176115	+	0.346121i
$850$		0			0
$851$	5.52129	+	3.18772i	0.189267	+	0.109274i
$852$		0			0
$853$	4.33970	−	2.50553i	0.148589	−	0.0857876i	−0.423862	−	0.905727i	$-0.639326\pi$
$853$	4.33970	−	2.50553i	0.148589	−	0.0857876i	0.572451	+	0.819939i	$0.305993\pi$
$854$		0			0
$855$	−16.6047	−	1.76395i	−0.567870	−	0.0603258i
$856$		0			0
$857$	21.1673	−	12.2210i	0.723062	−	0.417460i	−0.0928163	−	0.995683i	$-0.529587\pi$
$857$	21.1673	−	12.2210i	0.723062	−	0.417460i	0.815879	+	0.578223i	$0.196254\pi$
$858$		0			0
$859$	−15.3223	+	26.5391i	−0.522791	+	0.905501i	0.476857	+	0.878981i	$0.341776\pi$
$859$	−15.3223	+	26.5391i	−0.522791	+	0.905501i	−0.999648	+	0.0265200i	$0.991557\pi$
$860$		0			0
$861$	−8.34530	+	12.8350i	−0.284407	+	0.437415i
$862$		0			0
$863$	50.6493			1.72412			0.862061	−	0.506804i	$-0.169173\pi$
$863$	50.6493			1.72412			0.862061	+	0.506804i	$0.169173\pi$
$864$		0			0
$865$	25.8413			0.878631
$866$		0			0
$867$	1.76986	−	2.72202i	0.0601075	−	0.0924445i
$868$		0			0
$869$	−4.98533	+	8.63484i	−0.169116	+	0.292917i
$870$		0			0
$871$	5.24255	−	3.02679i	0.177637	−	0.102559i
$872$		0			0
$873$	17.7798	−	24.4144i	0.601754	−	0.826304i
$874$		0			0
$875$	−18.5326	+	10.6998i	−0.626518	+	0.361720i
$876$		0			0
$877$	−16.6458	−	9.61046i	−0.562089	−	0.324522i	0.191895	−	0.981416i	$-0.438537\pi$
$877$	−16.6458	−	9.61046i	−0.562089	−	0.324522i	−0.753983	+	0.656893i	$0.771870\pi$
$878$		0			0
$879$	−20.3154	−	39.9262i	−0.685220	−	1.34668i
$880$		0			0
$881$			49.2749i			1.66011i	0.557679	+	0.830057i	$0.311692\pi$
$881$			49.2749i			1.66011i	−0.557679	+	0.830057i	$0.688308\pi$
$882$		0			0
$883$	−12.5060			−0.420861			−0.210431	−	0.977609i	$-0.567487\pi$
$883$	−12.5060			−0.420861			−0.210431	+	0.977609i	$0.567487\pi$
$884$		0			0
$885$	−0.899369	+	16.9799i	−0.0302320	+	0.570772i
$886$		0			0
$887$	20.3846	−	35.3071i	0.684447	−	1.18550i	−0.289163	−	0.957280i	$-0.593377\pi$
$887$	20.3846	−	35.3071i	0.684447	−	1.18550i	0.973610	−	0.228217i	$-0.0732897\pi$
$888$		0			0
$889$	−2.40039	−	4.15759i	−0.0805064	−	0.139441i
$890$		0			0
$891$	−1.11756	+	5.20064i	−0.0374396	+	0.174228i
$892$		0			0
$893$	−3.84974	−	6.66795i	−0.128827	−	0.223134i
$894$		0			0
$895$	9.10883	+	5.25899i	0.304475	+	0.175789i
$896$		0			0
$897$	2.30522	−	43.5220i	0.0769692	−	1.45316i
$898$		0			0
$899$			5.39190i			0.179830i
$900$		0			0
$901$		−	34.8286i		−	1.16031i
$902$		0			0
$903$	17.6250	−	8.96801i	0.586523	−	0.298437i
$904$		0			0
$905$	3.54299	+	2.04555i	0.117773	+	0.0679963i
$906$		0			0
$907$	19.2179	+	33.2864i	0.638120	+	1.10526i	0.985845	+	0.167660i	$0.0536210\pi$
$907$	19.2179	+	33.2864i	0.638120	+	1.10526i	−0.347725	+	0.937597i	$0.613046\pi$
$908$		0			0
$909$	−12.1384	+	16.6680i	−0.402606	+	0.552843i
$910$		0			0
$911$	−9.29470	−	16.0989i	−0.307947	−	0.533380i	0.669966	−	0.742392i	$-0.266309\pi$
$911$	−9.29470	−	16.0989i	−0.307947	−	0.533380i	−0.977913	+	0.209012i	$0.932975\pi$
$912$		0			0
$913$	2.01074	−	3.48271i	0.0665459	−	0.115261i
$914$		0			0
$915$	−25.5544	−	16.6155i	−0.844802	−	0.549291i
$916$		0			0
$917$	21.6524			0.715027
$918$		0			0
$919$		−	9.94612i		−	0.328092i	−0.986453	−	0.164046i	$-0.947545\pi$
$919$		−	9.94612i		−	0.328092i	0.986453	−	0.164046i	$-0.0524546\pi$
$920$		0			0
$921$	10.4942	−	16.1399i	0.345794	−	0.531827i
$922$		0			0
$923$	−2.32499	−	1.34233i	−0.0765279	−	0.0441834i
$924$		0			0
$925$	2.31308	−	1.33546i	0.0760537	−	0.0439096i
$926$		0			0
$927$	4.11300	−	38.7172i	0.135089	−	1.27164i
$928$		0			0
$929$	−50.8877	+	29.3800i	−1.66957	+	0.963927i	−0.701701	+	0.712472i	$0.747576\pi$
$929$	−50.8877	+	29.3800i	−1.66957	+	0.963927i	−0.967869	+	0.251455i	$0.919091\pi$
$930$		0			0
$931$	−6.51187	+	11.2789i	−0.213418	+	0.369651i
$932$		0			0
$933$	−11.9830	−	23.5504i	−0.392305	−	0.771005i
$934$		0			0
$935$	−3.27421			−0.107078
$936$		0			0
$937$	−24.7412			−0.808260			−0.404130	−	0.914702i	$-0.632426\pi$
$937$	−24.7412			−0.808260			−0.404130	+	0.914702i	$0.632426\pi$
$938$		0			0
$939$	−37.7553	−	1.99978i	−1.23210	−	0.0652602i
$940$		0			0
$941$	−13.2138	+	22.8870i	−0.430758	+	0.746094i	−0.996939	−	0.0781866i	$-0.975087\pi$
$941$	−13.2138	+	22.8870i	−0.430758	+	0.746094i	0.566181	+	0.824281i	$0.308420\pi$
$942$		0			0
$943$	30.7620	−	17.7605i	1.00175	−	0.578360i
$944$		0			0
$945$	−2.09916	+	13.1116i	−0.0682857	+	0.426521i
$946$		0			0
$947$	−38.1787	+	22.0425i	−1.24064	+	0.716285i	−0.969225	−	0.246176i	$-0.920826\pi$
$947$	−38.1787	+	22.0425i	−1.24064	+	0.716285i	−0.271418	+	0.962462i	$0.587492\pi$
$948$		0			0
$949$	37.7233	+	21.7796i	1.22455	+	0.706995i
$950$		0			0
$951$	−0.741239	−	0.0392611i	−0.0240363	−	0.00127313i
$952$		0			0
$953$			22.2969i			0.722267i	0.932514	+	0.361134i	$0.117610\pi$
$953$			22.2969i			0.722267i	−0.932514	+	0.361134i	$0.882390\pi$
$954$		0			0
$955$	−33.3971			−1.08070
$956$		0			0
$957$	−6.18866	+	3.14894i	−0.200051	+	0.101791i
$958$		0			0
$959$	−17.8809	+	30.9706i	−0.577404	+	1.00009i
$960$		0			0
$961$	−15.1840	−	26.2995i	−0.489808	−	0.848372i
$962$		0			0
$963$	16.0497	−	7.12434i	0.517193	−	0.229579i
$964$		0			0
$965$	−10.0840	−	17.4660i	−0.324616	−	0.562251i
$966$		0			0
$967$	−27.2413	−	15.7278i	−0.876021	−	0.505771i	−0.00667646	−	0.999978i	$-0.502125\pi$
$967$	−27.2413	−	15.7278i	−0.876021	−	0.505771i	−0.869344	+	0.494207i	$0.835459\pi$
$968$		0			0
$969$	27.5378	+	17.9051i	0.884642	+	0.575195i
$970$		0			0
$971$		−	21.2276i		−	0.681226i	−0.940204	−	0.340613i	$-0.889365\pi$
$971$		−	21.2276i		−	0.681226i	0.940204	−	0.340613i	$-0.110635\pi$
$972$		0			0
$973$			14.5208i			0.465516i
$974$		0			0
$975$	−15.3074	−	9.95290i	−0.490230	−	0.318748i
$976$		0			0
$977$	−41.7574	−	24.1087i	−1.33594	−	0.771305i	−0.349736	−	0.936848i	$-0.613729\pi$
$977$	−41.7574	−	24.1087i	−1.33594	−	0.771305i	−0.986203	+	0.165543i	$0.947062\pi$
$978$		0			0
$979$	−1.18460	−	2.05179i	−0.0378601	−	0.0655756i
$980$		0			0
$981$	50.7219	−	22.5151i	1.61942	−	0.718852i
$982$		0			0
$983$	−9.77391	−	16.9289i	−0.311739	−	0.539948i	0.667000	−	0.745058i	$-0.267578\pi$
$983$	−9.77391	−	16.9289i	−0.311739	−	0.539948i	−0.978739	+	0.205110i	$0.934245\pi$
$984$		0			0
$985$	13.7914	−	23.8874i	0.439430	−	0.761115i
$986$		0			0
$987$	−5.45694	+	2.77662i	−0.173696	+	0.0883807i
$988$		0			0
$989$	−45.8826			−1.45898
$990$		0			0
$991$		−	21.4045i		−	0.679938i	−0.940437	−	0.339969i	$-0.889583\pi$
$991$		−	21.4045i		−	0.679938i	0.940437	−	0.339969i	$-0.110417\pi$
$992$		0			0
$993$	−22.8786	−	1.21181i	−0.726031	−	0.0384555i
$994$		0			0
$995$	−28.1845	−	16.2723i	−0.893509	−	0.515868i
$996$		0			0
$997$	−12.3408	+	7.12499i	−0.390838	+	0.225651i	−0.682523	−	0.730864i	$-0.739117\pi$
$997$	−12.3408	+	7.12499i	−0.390838	+	0.225651i	0.291685	+	0.956514i	$0.405784\pi$
$998$		0			0
$999$	0.650253	−	4.06156i	0.0205731	−	0.128502i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.p.f.959.4	yes	24
3.2	odd	2		3456.2.p.f.2879.5		24
4.3	odd	2		1152.2.p.g.959.9	yes	24
8.3	odd	2		1152.2.p.g.959.4	yes	24
8.5	even	2	inner	1152.2.p.f.959.9	yes	24
9.2	odd	6		1152.2.p.g.191.4	yes	24
9.7	even	3		3456.2.p.g.575.8		24
12.11	even	2		3456.2.p.g.2879.5		24
24.5	odd	2		3456.2.p.f.2879.8		24
24.11	even	2		3456.2.p.g.2879.8		24
36.7	odd	6		3456.2.p.f.575.8		24
36.11	even	6	inner	1152.2.p.f.191.9	yes	24
72.11	even	6	inner	1152.2.p.f.191.4	✓	24
72.29	odd	6		1152.2.p.g.191.9	yes	24
72.43	odd	6		3456.2.p.f.575.5		24
72.61	even	6		3456.2.p.g.575.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.p.f.191.4	✓	24	72.11	even	6	inner
1152.2.p.f.191.9	yes	24	36.11	even	6	inner
1152.2.p.f.959.4	yes	24	1.1	even	1	trivial
1152.2.p.f.959.9	yes	24	8.5	even	2	inner
1152.2.p.g.191.4	yes	24	9.2	odd	6
1152.2.p.g.191.9	yes	24	72.29	odd	6
1152.2.p.g.959.4	yes	24	8.3	odd	2
1152.2.p.g.959.9	yes	24	4.3	odd	2
3456.2.p.f.575.5		24	72.43	odd	6
3456.2.p.f.575.8		24	36.7	odd	6
3456.2.p.f.2879.5		24	3.2	odd	2
3456.2.p.f.2879.8		24	24.5	odd	2
3456.2.p.g.575.5		24	72.61	even	6
3456.2.p.g.575.8		24	9.7	even	3
3456.2.p.g.2879.5		24	12.11	even	2
3456.2.p.g.2879.8		24	24.11	even	2

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.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.944152 + 1.45209i) q^{3} +(0.637560 - 1.10429i) q^{5} +(-1.73560 + 1.00205i) q^{7} +(-1.21715 - 2.74200i) q^{9} +O(q^{10})\)	\(q+(-0.944152 + 1.45209i) q^{3} +(0.637560 - 1.10429i) q^{5} +(-1.73560 + 1.00205i) q^{7} +(-1.21715 - 2.74200i) q^{9} +(0.511856 - 0.295520i) q^{11} +(2.70573 + 1.56215i) q^{13} +(1.00157 + 1.96841i) q^{15} -4.34448i q^{17} +4.36512 q^{19} +(0.183601 - 3.46634i) q^{21} +(-4.02692 + 6.97483i) q^{23} +(1.68703 + 2.92203i) q^{25} +(5.13081 + 0.821440i) q^{27} +(3.39145 + 5.87416i) q^{29} +(0.688426 + 0.397463i) q^{31} +(-0.0541469 + 1.02228i) q^{33} +2.55547i q^{35} -0.791602i q^{37} +(-4.82301 + 2.45406i) q^{39} +(-3.81955 - 2.20522i) q^{41} +(2.84849 + 4.93373i) q^{43} +(-3.80396 - 0.404101i) q^{45} +(-0.881932 - 1.52755i) q^{47} +(-1.49179 + 2.58386i) q^{49} +(6.30860 + 4.10185i) q^{51} +8.01673 q^{53} -0.753647i q^{55} +(-4.12134 + 6.33857i) q^{57} +(6.66747 + 3.84947i) q^{59} +(-11.9523 + 6.90065i) q^{61} +(4.86011 + 3.53936i) q^{63} +(3.45013 - 1.99193i) q^{65} +(0.968787 - 1.67799i) q^{67} +(-6.32608 - 12.4328i) q^{69} -0.859283 q^{71} +13.9420 q^{73} +(-5.83588 - 0.309108i) q^{75} +(-0.592252 + 1.02581i) q^{77} +(-14.6096 + 8.43483i) q^{79} +(-6.03708 + 6.67486i) q^{81} +(5.89251 - 3.40204i) q^{83} +(-4.79755 - 2.76987i) q^{85} +(-11.7319 - 0.621400i) q^{87} -4.00854i q^{89} -6.26142 q^{91} +(-1.22713 + 0.624394i) q^{93} +(2.78303 - 4.82035i) q^{95} +(5.03373 + 8.71868i) q^{97} +(-1.43332 - 1.04381i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{7} - 4 q^{9}+O(q^{10}) \) 24 * q - 12 * q^7 - 4 * q^9	\( 24 q - 12 q^{7} - 4 q^{9} - 20 q^{15} + 12 q^{23} - 12 q^{25} + 36 q^{31} + 4 q^{33} - 20 q^{39} - 12 q^{41} - 12 q^{47} + 12 q^{49} + 4 q^{57} + 92 q^{63} - 48 q^{65} + 24 q^{73} - 84 q^{79} - 20 q^{81} - 68 q^{87} - 24 q^{95} - 12 q^{97}+O(q^{100}) \) 24 * q - 12 * q^7 - 4 * q^9 - 20 * q^15 + 12 * q^23 - 12 * q^25 + 36 * q^31 + 4 * q^33 - 20 * q^39 - 12 * q^41 - 12 * q^47 + 12 * q^49 + 4 * q^57 + 92 * q^63 - 48 * q^65 + 24 * q^73 - 84 * q^79 - 20 * q^81 - 68 * q^87 - 24 * q^95 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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