LMFDB - Embedded newform 1152.2.p.g.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.g.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	−0.972640	−	0.232319i	$-0.925369\pi$
$5$	−0.637560	+	1.10429i	−0.285126	+	0.493852i	0.687514	+	0.726171i	$0.258702\pi$
$6$		0			0
$7$	1.73560	−	1.00205i	0.655995	−	0.378739i	−0.134754	−	0.990879i	$-0.543024\pi$
$7$	1.73560	−	1.00205i	0.655995	−	0.378739i	0.790749	+	0.612140i	$0.209691\pi$
$8$		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	0.0754165	−	0.997152i	$-0.475971\pi$
$13$	−2.70573	−	1.56215i	−0.750434	−	0.433263i	−0.825851	+	0.563889i	$0.809305\pi$
$14$		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	$-0.516081\pi$
$23$	4.02692	−	6.97483i	0.839671	−	1.45435i	0.890170	−	0.455629i	$-0.150586\pi$
$24$		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	$-0.949813\pi$
$29$	−3.39145	−	5.87416i	−0.629776	−	1.09080i	0.357821	−	0.933790i	$-0.383520\pi$
$30$		0			0
$31$	−0.688426	−	0.397463i	−0.123645	−	0.0713865i	0.436902	−	0.899509i	$-0.356076\pi$
$31$	−0.688426	−	0.397463i	−0.123645	−	0.0713865i	−0.560547	+	0.828123i	$0.689409\pi$
$32$		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	$0.0207268\pi$
$37$			0.791602i			0.130138i	−0.997881	+	0.0650692i	$0.979273\pi$
$38$		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	0.923151	−	0.384437i	$-0.125605\pi$
$47$	0.881932	+	1.52755i	0.128643	+	0.222816i	−0.794508	+	0.607254i	$0.792271\pi$
$48$		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	$-0.685598\pi$
$53$	−8.01673			−1.10118			−0.550591	+	0.834775i	$0.685598\pi$
$54$		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	$-0.321822\pi$
$61$	11.9523	−	6.90065i	1.53033	−	0.883537i	0.999346	−	0.0361566i	$-0.0115115\pi$
$62$		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	$-0.483763\pi$
$71$	0.859283			0.101978			0.0509891	+	0.998699i	$0.483763\pi$
$72$		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	$-0.268771\pi$
$79$	14.6096	−	8.43483i	1.64370	−	0.948993i	0.979501	−	0.201441i	$-0.0645625\pi$
$80$		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	0.984795	−	0.173719i	$-0.0555783\pi$
$101$	3.43658	+	5.95234i	0.341953	+	0.592280i	−0.642842	+	0.765998i	$0.722245\pi$
$102$		0			0
$103$	−11.2396	−	6.48918i	−1.10747	−	0.639398i	−0.169297	−	0.985565i	$-0.554150\pi$
$103$	−11.2396	−	6.48918i	−1.10747	−	0.639398i	−0.938173	+	0.346167i	$0.887483\pi$
$104$		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	$-0.653541\pi$
$109$		−	18.4982i		−	1.77180i	0.463874	−	0.885901i	$-0.346459\pi$
$110$		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	$-0.966105\pi$
$127$		−	2.39548i		−	0.212564i	0.994336	−	0.106282i	$-0.0338947\pi$
$128$		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	$0.348296\pi$
$149$	−6.59328	+	11.4199i	−0.540143	+	0.935555i	−0.998895	+	0.0469907i	$0.985037\pi$
$150$		0			0
$151$	−15.3430	+	8.85829i	−1.24860	+	0.720877i	−0.970829	−	0.239771i	$-0.922927\pi$
$151$	−15.3430	+	8.85829i	−1.24860	+	0.720877i	−0.277767	+	0.960649i	$0.589594\pi$
$152$		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	0.501771	−	0.865001i	$-0.332682\pi$
$157$	0.0444019	+	0.0256355i	0.00354366	+	0.00204593i	−0.498227	+	0.867047i	$0.666015\pi$
$158$		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	−0.771684	−	0.636006i	$-0.780585\pi$
$167$	2.13169	−	3.69220i	0.164955	−	0.285711i	0.936639	+	0.350295i	$0.113919\pi$
$168$		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	$-0.886729\pi$
$173$	−10.1329	−	17.5507i	−0.770389	−	1.33435i	0.166961	−	0.985964i	$-0.446605\pi$
$174$		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	$-0.961954\pi$
$181$		−	3.20840i		−	0.238478i	0.992866	−	0.119239i	$-0.0380455\pi$
$182$		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	$0.229801\pi$
$191$	13.0957	+	22.6823i	0.947568	+	1.64124i	0.197043	+	0.980395i	$0.436866\pi$
$192$		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	$-0.780039\pi$
$197$	−21.6315			−1.54118			−0.770591	+	0.637330i	$0.780039\pi$
$198$		0			0
$199$			25.5228i			1.80926i	0.426193	+	0.904632i	$0.359855\pi$
$199$			25.5228i			1.80926i	−0.426193	+	0.904632i	$0.640145\pi$
$200$		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	0.0251097	−	0.999685i	$-0.492006\pi$
$223$	13.4909	−	7.78897i	0.903417	−	0.521588i	0.878307	+	0.478097i	$0.158673\pi$
$224$		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	0.431764	−	0.901987i	$-0.357891\pi$
$229$	−2.02018	−	1.16635i	−0.133497	−	0.0770748i	−0.565261	+	0.824912i	$0.691225\pi$
$230$		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	$0.386074\pi$
$239$	−9.83215	+	17.0298i	−0.635989	+	1.10156i	−0.986305	+	0.164933i	$0.947259\pi$
$240$		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	$-0.971690\pi$
$263$	−9.32405	−	16.1497i	−0.574946	−	0.995835i	0.421102	−	0.907013i	$-0.361643\pi$
$264$		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	$-0.390483\pi$
$269$	11.0645			0.674617			0.337308	+	0.941394i	$0.390483\pi$
$270$		0			0
$271$			13.9315i			0.846276i	0.906065	+	0.423138i	$0.139071\pi$
$271$			13.9315i			0.846276i	−0.906065	+	0.423138i	$0.860929\pi$
$272$		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	−0.246929	−	0.969034i	$-0.579421\pi$
$277$	7.80262	−	4.50485i	0.468814	−	0.270670i	0.715743	+	0.698364i	$0.246088\pi$
$278$		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	$-0.560732\pi$
$293$	12.9319	−	22.3987i	0.755490	−	1.30855i	0.945130	−	0.326694i	$-0.105935\pi$
$294$		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	−0.564554	−	0.825396i	$-0.690952\pi$
$311$	7.62787	−	13.2119i	0.432537	−	0.749176i	0.997091	+	0.0762203i	$0.0242852\pi$
$312$		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	0.859945	−	0.510386i	$-0.170498\pi$
$317$	−0.214277	−	0.371139i	−0.0120350	−	0.0208453i	−0.871980	+	0.489541i	$0.837164\pi$
$318$		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	−0.793382	−	0.608723i	$-0.791682\pi$
$349$	−12.3841	+	7.14994i	−0.662904	+	0.382728i	0.130479	+	0.991451i	$0.458349\pi$
$350$		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	$-0.306012\pi$
$359$	21.6909			1.14480			0.572401	+	0.819974i	$0.306012\pi$
$360$		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	0.162415	−	0.986723i	$-0.448072\pi$
$367$	21.0375	−	12.1460i	1.09815	−	0.634017i	0.935734	+	0.352706i	$0.114738\pi$
$368$		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	0.353612	−	0.935392i	$-0.384953\pi$
$373$	−5.40106	−	3.11830i	−0.279656	−	0.161460i	−0.633268	+	0.773933i	$0.718287\pi$
$374$		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	$0.385813\pi$
$383$	−12.4341	+	21.5366i	−0.635355	+	1.10047i	−0.986440	+	0.164124i	$0.947520\pi$
$384$		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	0.962729	−	0.270467i	$-0.0871779\pi$
$389$	4.87424	+	8.44243i	0.247134	+	0.428048i	−0.715596	+	0.698515i	$0.753845\pi$
$390$		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	$0.110349\pi$
$397$			13.5397i			0.679540i	−0.940509	+	0.339770i	$0.889651\pi$
$398$		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	−0.729170	−	0.684332i	$-0.760094\pi$
$421$	−10.2818	+	5.93622i	−0.501106	+	0.289314i	0.228064	+	0.973646i	$0.426760\pi$
$422$		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	$-0.553702\pi$
$431$	−6.97179			−0.335820			−0.167910	+	0.985802i	$0.553702\pi$
$432$		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	0.160861	−	0.986977i	$-0.448573\pi$
$439$	22.9646	−	13.2586i	1.09604	−	0.632798i	0.935178	+	0.354179i	$0.115240\pi$
$440$		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	0.940357	−	0.340188i	$-0.110491\pi$
$461$	3.76959	+	6.52912i	0.175567	+	0.304091i	−0.764790	+	0.644279i	$0.777157\pi$
$462$		0			0
$463$	−8.97193	−	5.17995i	−0.416961	−	0.240733i	0.276815	−	0.960923i	$-0.410721\pi$
$463$	−8.97193	−	5.17995i	−0.416961	−	0.240733i	−0.693776	+	0.720191i	$0.744054\pi$
$464$		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	0.910566	−	0.413364i	$-0.135646\pi$
$479$	2.12949	+	3.68839i	0.0972990	+	0.168527i	−0.813267	+	0.581891i	$0.802313\pi$
$480$		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	$-0.975832\pi$
$487$		−	3.34781i		−	0.151704i	0.997119	−	0.0758518i	$-0.0241676\pi$
$488$		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	$-0.507407\pi$
$503$	−1.04368			−0.0465355			−0.0232678	+	0.999729i	$0.507407\pi$
$504$		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	−0.988721	−	0.149771i	$-0.952146\pi$
$509$	−8.22698	+	14.2495i	−0.364654	+	0.631600i	0.624066	+	0.781371i	$0.285480\pi$
$510$		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	$0.261511\pi$
$541$			34.0615i			1.46442i	−0.681080	+	0.732209i	$0.738489\pi$
$542$		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	$-0.290395\pi$
$557$	28.8839			1.22385			0.611925	+	0.790916i	$0.290395\pi$
$558$		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	$-0.640070\pi$
$599$	13.9635	−	24.1855i	0.570534	−	0.988193i	0.996511	−	0.0834595i	$-0.0265969\pi$
$600$		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	0.365228	−	0.930918i	$-0.380991\pi$
$607$	−6.36525	−	3.67498i	−0.258358	−	0.149163i	−0.623585	+	0.781755i	$0.714325\pi$
$608$		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	$-0.901208\pi$
$613$		−	15.1229i		−	0.610810i	0.952223	−	0.305405i	$-0.0987918\pi$
$614$		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	$0.0648173\pi$
$631$			10.1597i			0.404451i	−0.979339	+	0.202225i	$0.935183\pi$
$632$		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	$-0.543238\pi$
$647$	−6.88907			−0.270837			−0.135419	+	0.990788i	$0.543238\pi$
$648$		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	$0.445872\pi$
$653$	−19.6489	+	34.0328i	−0.768919	+	1.33181i	−0.938149	+	0.346231i	$0.887462\pi$
$654$		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	0.323392	−	0.946265i	$-0.395177\pi$
$661$	−8.59746	−	4.96374i	−0.334402	−	0.193067i	−0.657794	+	0.753198i	$0.728510\pi$
$662$		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	0.990050	−	0.140713i	$-0.0449396\pi$
$677$	9.70944	+	16.8172i	0.373164	+	0.646339i	−0.616886	+	0.787052i	$0.711606\pi$
$678$		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	$-0.196569\pi$
$701$	43.1727			1.63061			0.815306	+	0.579030i	$0.196569\pi$
$702$		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	−0.909070	−	0.416643i	$-0.863207\pi$
$709$	−26.7011	+	15.4159i	−1.00278	+	0.578956i	−0.0937116	+	0.995599i	$0.529873\pi$
$710$		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	$-0.252507\pi$
$719$	37.6211			1.40303			0.701515	+	0.712654i	$0.252507\pi$
$720$		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	−0.384596	−	0.923085i	$-0.625659\pi$
$727$	5.99982	−	3.46400i	0.222521	−	0.128473i	0.607117	+	0.794612i	$0.292326\pi$
$728$		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	−0.0148649	−	0.999890i	$-0.504732\pi$
$733$	−24.0478	−	13.8840i	−0.888227	−	0.512818i	−0.873362	+	0.487071i	$0.838065\pi$
$734$		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	−0.935232	−	0.354035i	$-0.884809\pi$
$743$	−4.38888	+	7.60176i	−0.161012	+	0.278882i	0.774220	+	0.632917i	$0.218143\pi$
$744$		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	0.750553	−	0.660811i	$-0.229787\pi$
$751$	15.1697	+	8.75822i	0.553550	+	0.319592i	−0.197003	+	0.980403i	$0.563121\pi$
$752$		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	$0.241451\pi$
$757$			37.8512i			1.37573i	−0.725841	+	0.687863i	$0.758549\pi$
$758$		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	$-0.306569\pi$
$773$	31.7490			1.14193			0.570966	+	0.820974i	$0.306569\pi$
$774$		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	−0.715199	−	0.698921i	$-0.753664\pi$
$797$	6.99240	−	12.1112i	0.247684	−	0.429001i	0.962883	+	0.269920i	$0.0869973\pi$
$798$		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	$0.0188855\pi$
$821$	15.7727	+	27.3192i	0.550472	+	0.953445i	−0.447769	+	0.894149i	$0.647781\pi$
$822$		0			0
$823$	−30.3863	−	17.5435i	−1.05920	−	0.611528i	−0.133988	−	0.990983i	$-0.542778\pi$
$823$	−30.3863	−	17.5435i	−1.05920	−	0.611528i	−0.925210	+	0.379455i	$0.876112\pi$
$824$		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	$0.109486\pi$
$829$			19.4187i			0.674439i	−0.941426	+	0.337219i	$0.890514\pi$
$830$		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	0.995985	−	0.0895178i	$-0.0285326\pi$
$839$	12.1791	+	21.0948i	0.420468	+	0.728272i	−0.575517	+	0.817790i	$0.695199\pi$
$840$		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	−0.572451	−	0.819939i	$-0.694007\pi$
$853$	−4.33970	+	2.50553i	−0.148589	+	0.0857876i	0.423862	+	0.905727i	$0.360674\pi$
$854$		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	$-0.830827\pi$
$863$	−50.6493			−1.72412			−0.862061	+	0.506804i	$0.830827\pi$
$864$		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	0.753983	−	0.656893i	$-0.228130\pi$
$877$	16.6458	+	9.61046i	0.562089	+	0.324522i	−0.191895	+	0.981416i	$0.561463\pi$
$878$		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	$0.406623\pi$
$887$	−20.3846	+	35.3071i	−0.684447	+	1.18550i	−0.973610	+	0.228217i	$0.926710\pi$
$888$		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	0.977913	−	0.209012i	$-0.0670247\pi$
$911$	9.29470	+	16.0989i	0.307947	+	0.533380i	−0.669966	+	0.742392i	$0.733691\pi$
$912$		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	$0.0524546\pi$
$919$			9.94612i			0.328092i	−0.986453	+	0.164046i	$0.947545\pi$
$920$		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	−0.566181	−	0.824281i	$-0.691580\pi$
$941$	13.2138	−	22.8870i	0.430758	−	0.746094i	0.996939	+	0.0781866i	$0.0249130\pi$
$942$		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	0.869344	−	0.494207i	$-0.164541\pi$
$967$	27.2413	+	15.7278i	0.876021	+	0.505771i	0.00667646	+	0.999978i	$0.497875\pi$
$968$		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	0.978739	−	0.205110i	$-0.0657551\pi$
$983$	9.77391	+	16.9289i	0.311739	+	0.539948i	−0.667000	+	0.745058i	$0.732422\pi$
$984$		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	$0.110417\pi$
$991$			21.4045i			0.679938i	−0.940437	+	0.339969i	$0.889583\pi$
$992$		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	−0.291685	−	0.956514i	$-0.594216\pi$
$997$	12.3408	−	7.12499i	0.390838	−	0.225651i	0.682523	+	0.730864i	$0.260883\pi$
$998$		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.g.959.4	yes	24
3.2	odd	2		3456.2.p.g.2879.8		24
4.3	odd	2		1152.2.p.f.959.9	yes	24
8.3	odd	2		1152.2.p.f.959.4	yes	24
8.5	even	2	inner	1152.2.p.g.959.9	yes	24
9.2	odd	6		1152.2.p.f.191.4	✓	24
9.7	even	3		3456.2.p.f.575.5		24
12.11	even	2		3456.2.p.f.2879.8		24
24.5	odd	2		3456.2.p.g.2879.5		24
24.11	even	2		3456.2.p.f.2879.5		24
36.7	odd	6		3456.2.p.g.575.5		24
36.11	even	6	inner	1152.2.p.g.191.9	yes	24
72.11	even	6	inner	1152.2.p.g.191.4	yes	24
72.29	odd	6		1152.2.p.f.191.9	yes	24
72.43	odd	6		3456.2.p.g.575.8		24
72.61	even	6		3456.2.p.f.575.8		24

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