LMFDB - Embedded newform 936.2.g.f.469.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(469,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.469"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			469.19
Character	$\chi$	$=$	936.469
Dual form			936.2.g.f.469.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.21070 - 0.730889i) q^{2} +(0.931601 - 1.76978i) q^{4} -2.32782i q^{5} -4.85152 q^{7} +(-0.165621 - 2.82357i) q^{8} +(-1.70138 - 2.81830i) q^{10} +3.45836i q^{11} -1.00000i q^{13} +(-5.87375 + 3.54592i) q^{14} +(-2.26424 - 3.29746i) q^{16} +0.641186 q^{17} -5.60660i q^{19} +(-4.11973 - 2.16860i) q^{20} +(2.52768 + 4.18704i) q^{22} -9.37422 q^{23} -0.418756 q^{25} +(-0.730889 - 1.21070i) q^{26} +(-4.51968 + 8.58612i) q^{28} -5.01794i q^{29} +2.89128 q^{31} +(-5.15140 - 2.33733i) q^{32} +(0.776285 - 0.468636i) q^{34} +11.2935i q^{35} +5.74279i q^{37} +(-4.09780 - 6.78792i) q^{38} +(-6.57278 + 0.385537i) q^{40} +2.69012 q^{41} -0.307649i q^{43} +(6.12053 + 3.22181i) q^{44} +(-11.3494 + 6.85152i) q^{46} -8.30199 q^{47} +16.5372 q^{49} +(-0.506988 + 0.306064i) q^{50} +(-1.76978 - 0.931601i) q^{52} +1.60785i q^{53} +8.05044 q^{55} +(0.803515 + 13.6986i) q^{56} +(-3.66756 - 6.07523i) q^{58} -0.256735i q^{59} -11.1218i q^{61} +(3.50047 - 2.11320i) q^{62} +(-7.94514 + 0.935288i) q^{64} -2.32782 q^{65} -9.58901i q^{67} +(0.597329 - 1.13476i) q^{68} +(8.25428 + 13.6730i) q^{70} +11.6411 q^{71} +5.74279 q^{73} +(4.19735 + 6.95282i) q^{74} +(-9.92244 - 5.22311i) q^{76} -16.7783i q^{77} +8.80552 q^{79} +(-7.67589 + 5.27074i) q^{80} +(3.25693 - 1.96618i) q^{82} -13.4617i q^{83} -1.49257i q^{85} +(-0.224858 - 0.372472i) q^{86} +(9.76493 - 0.572778i) q^{88} -3.75972 q^{89} +4.85152i q^{91} +(-8.73303 + 16.5903i) q^{92} +(-10.0512 + 6.06784i) q^{94} -13.0512 q^{95} -1.98241 q^{97} +(20.0217 - 12.0869i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{4} - 8 q^{7} + 12 q^{10} - 4 q^{16} + 4 q^{22} - 24 q^{25} + 8 q^{28} + 40 q^{31} - 16 q^{34} - 36 q^{40} - 24 q^{46} + 24 q^{49} - 4 q^{52} - 16 q^{55} - 24 q^{58} + 8 q^{64} - 16 q^{70} - 16 q^{76}+ \cdots - 16 q^{97}+O(q^{100}) $ 24 * q + 8 * q^4 - 8 * q^7 + 12 * q^10 - 4 * q^16 + 4 * q^22 - 24 * q^25 + 8 * q^28 + 40 * q^31 - 16 * q^34 - 36 * q^40 - 24 * q^46 + 24 * q^49 - 4 * q^52 - 16 * q^55 - 24 * q^58 + 8 * q^64 - 16 * q^70 - 16 * q^76 + 68 * q^82 + 28 * q^88 + 12 * q^94 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$1$	$1$	$-1$	$1$

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 $

$2$	1.21070	−	0.730889i	0.856096	−	0.516817i
$2$	1.21070	−	0.730889i	0.856096	−	0.516817i
$3$		0			0
$3$		0			0
$4$	0.931601	−	1.76978i	0.465801	−	0.884890i
$5$		−	2.32782i		−	1.04103i	−0.853851	−	0.520517i	$-0.825739\pi$
$5$		−	2.32782i		−	1.04103i	0.853851	−	0.520517i	$-0.174261\pi$
$6$		0			0
$7$	−4.85152			−1.83370			−0.916851	−	0.399230i	$-0.869278\pi$
$7$	−4.85152			−1.83370			−0.916851	+	0.399230i	$0.869278\pi$
$8$	−0.165621	−	2.82357i	−0.0585560	−	0.998284i
$9$		0			0
$10$	−1.70138	−	2.81830i	−0.538024	−	0.891225i
$11$			3.45836i			1.04273i	0.853332	+	0.521367i	$0.174578\pi$
$11$			3.45836i			1.04273i	−0.853332	+	0.521367i	$0.825422\pi$
$12$		0			0
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	−5.87375	+	3.54592i	−1.56982	+	0.947688i
$15$		0			0
$16$	−2.26424	−	3.29746i	−0.566060	−	0.824364i
$17$	0.641186			0.155510			0.0777552	−	0.996972i	$-0.475225\pi$
$17$	0.641186			0.155510			0.0777552	+	0.996972i	$0.475225\pi$
$18$		0			0
$19$		−	5.60660i		−	1.28624i	−0.765765	−	0.643121i	$-0.777639\pi$
$19$		−	5.60660i		−	1.28624i	0.765765	−	0.643121i	$-0.222361\pi$
$20$	−4.11973	−	2.16860i	−0.921200	−	0.484914i
$21$		0			0
$22$	2.52768	+	4.18704i	0.538903	+	0.892681i
$23$	−9.37422			−1.95466			−0.977330	−	0.211722i	$-0.932093\pi$
$23$	−9.37422			−1.95466			−0.977330	+	0.211722i	$0.932093\pi$
$24$		0			0
$25$	−0.418756			−0.0837511
$26$	−0.730889	−	1.21070i	−0.143339	−	0.237438i
$27$		0			0
$28$	−4.51968	+	8.58612i	−0.854139	+	1.62262i
$29$		−	5.01794i		−	0.931808i	−0.884835	−	0.465904i	$-0.845729\pi$
$29$		−	5.01794i		−	0.931808i	0.884835	−	0.465904i	$-0.154271\pi$
$30$		0			0
$31$	2.89128			0.519288			0.259644	−	0.965704i	$-0.416395\pi$
$31$	2.89128			0.519288			0.259644	+	0.965704i	$0.416395\pi$
$32$	−5.15140	−	2.33733i	−0.910647	−	0.413186i
$33$		0			0
$34$	0.776285	−	0.468636i	0.133132	−	0.0803704i
$35$			11.2935i			1.90895i
$36$		0			0
$37$			5.74279i			0.944110i	0.881569	+	0.472055i	$0.156488\pi$
$37$			5.74279i			0.944110i	−0.881569	+	0.472055i	$0.843512\pi$
$38$	−4.09780	−	6.78792i	−0.664751	−	1.10115i
$39$		0			0
$40$	−6.57278	+	0.385537i	−1.03925	+	0.0609587i
$41$	2.69012			0.420126			0.210063	−	0.977688i	$-0.432633\pi$
$41$	2.69012			0.420126			0.210063	+	0.977688i	$0.432633\pi$
$42$		0			0
$43$		−	0.307649i		−	0.0469161i	−0.999725	−	0.0234580i	$-0.992532\pi$
$43$		−	0.307649i		−	0.0469161i	0.999725	−	0.0234580i	$-0.00746761\pi$
$44$	6.12053	+	3.22181i	0.922705	+	0.485706i
$45$		0			0
$46$	−11.3494	+	6.85152i	−1.67338	+	1.01020i
$47$	−8.30199			−1.21097			−0.605485	−	0.795857i	$-0.707021\pi$
$47$	−8.30199			−1.21097			−0.605485	+	0.795857i	$0.707021\pi$
$48$		0			0
$49$	16.5372			2.36246
$50$	−0.506988	+	0.306064i	−0.0716990	+	0.0432840i
$51$		0			0
$52$	−1.76978	−	0.931601i	−0.245424	−	0.129190i
$53$			1.60785i			0.220855i	0.993884	+	0.110428i	$0.0352221\pi$
$53$			1.60785i			0.220855i	−0.993884	+	0.110428i	$0.964778\pi$
$54$		0			0
$55$	8.05044			1.08552
$56$	0.803515	+	13.6986i	0.107374	+	1.83056i
$57$		0			0
$58$	−3.66756	−	6.07523i	−0.481574	−	0.797717i
$59$		−	0.256735i		−	0.0334241i	−0.999860	−	0.0167120i	$-0.994680\pi$
$59$		−	0.256735i		−	0.0334241i	0.999860	−	0.0167120i	$-0.00531985\pi$
$60$		0			0
$61$		−	11.1218i		−	1.42400i	−0.702180	−	0.712000i	$-0.747790\pi$
$61$		−	11.1218i		−	1.42400i	0.702180	−	0.712000i	$-0.252210\pi$
$62$	3.50047	−	2.11320i	0.444561	−	0.268377i
$63$		0			0
$64$	−7.94514	+	0.935288i	−0.993142	+	0.116911i
$65$	−2.32782			−0.288731
$66$		0			0
$67$		−	9.58901i		−	1.17148i	−0.810498	−	0.585742i	$-0.800803\pi$
$67$		−	9.58901i		−	1.17148i	0.810498	−	0.585742i	$-0.199197\pi$
$68$	0.597329	−	1.13476i	0.0724368	−	0.137610i
$69$		0			0
$70$	8.25428	+	13.6730i	0.986575	+	1.63424i
$71$	11.6411			1.38155			0.690773	−	0.723072i	$-0.257271\pi$
$71$	11.6411			1.38155			0.690773	+	0.723072i	$0.257271\pi$
$72$		0			0
$73$	5.74279			0.672143			0.336072	−	0.941836i	$-0.390902\pi$
$73$	5.74279			0.672143			0.336072	+	0.941836i	$0.390902\pi$
$74$	4.19735	+	6.95282i	0.487932	+	0.808248i
$75$		0			0
$76$	−9.92244	−	5.22311i	−1.13818	−	0.599132i
$77$		−	16.7783i		−	1.91206i
$78$		0			0
$79$	8.80552			0.990699			0.495349	−	0.868694i	$-0.335040\pi$
$79$	8.80552			0.990699			0.495349	+	0.868694i	$0.335040\pi$
$80$	−7.67589	+	5.27074i	−0.858191	+	0.589287i
$81$		0			0
$82$	3.25693	−	1.96618i	0.359668	−	0.217128i
$83$		−	13.4617i		−	1.47762i	−0.673916	−	0.738808i	$-0.735389\pi$
$83$		−	13.4617i		−	1.47762i	0.673916	−	0.738808i	$-0.264611\pi$
$84$		0			0
$85$		−	1.49257i		−	0.161892i
$86$	−0.224858	−	0.372472i	−0.0242470	−	0.0401647i
$87$		0			0
$88$	9.76493	−	0.572778i	1.04095	−	0.0610583i
$89$	−3.75972			−0.398530			−0.199265	−	0.979946i	$-0.563855\pi$
$89$	−3.75972			−0.398530			−0.199265	+	0.979946i	$0.563855\pi$
$90$		0			0
$91$			4.85152i			0.508577i
$92$	−8.73303	+	16.5903i	−0.910482	+	1.72966i
$93$		0			0
$94$	−10.0512	+	6.06784i	−1.03671	+	0.625850i
$95$	−13.0512			−1.33902
$96$		0			0
$97$	−1.98241			−0.201283			−0.100641	−	0.994923i	$-0.532090\pi$
$97$	−1.98241			−0.201283			−0.100641	+	0.994923i	$0.532090\pi$
$98$	20.0217	−	12.0869i	2.02249	−	1.22096i
$99$		0			0
$100$	−0.390113	+	0.741105i	−0.0390113	+	0.0741105i
$101$			7.54587i			0.750842i	0.926854	+	0.375421i	$0.122502\pi$
$101$			7.54587i			0.750842i	−0.926854	+	0.375421i	$0.877498\pi$
$102$		0			0
$103$	14.2185			1.40099			0.700495	−	0.713657i	$-0.252962\pi$
$103$	14.2185			1.40099			0.700495	+	0.713657i	$0.252962\pi$
$104$	−2.82357	+	0.165621i	−0.276874	+	0.0162405i
$105$		0			0
$106$	1.17516	+	1.94663i	0.114142	+	0.189073i
$107$			9.87361i			0.954518i	0.878763	+	0.477259i	$0.158370\pi$
$107$			9.87361i			0.954518i	−0.878763	+	0.477259i	$0.841630\pi$
$108$		0			0
$109$		−	20.0611i		−	1.92151i	−0.277402	−	0.960754i	$-0.589473\pi$
$109$		−	20.0611i		−	1.92151i	0.277402	−	0.960754i	$-0.410527\pi$
$110$	9.74669	−	5.88398i	0.929311	−	0.561016i
$111$		0			0
$112$	10.9850	+	15.9977i	1.03798	+	1.51164i
$113$	0.200024			0.0188167			0.00940835	−	0.999956i	$-0.497005\pi$
$113$	0.200024			0.0188167			0.00940835	+	0.999956i	$0.497005\pi$
$114$		0			0
$115$			21.8215i			2.03487i
$116$	−8.88065	−	4.67472i	−0.824548	−	0.434037i
$117$		0			0
$118$	−0.187645	−	0.310830i	−0.0172741	−	0.0286142i
$119$	−3.11072			−0.285160
$120$		0			0
$121$	−0.960244			−0.0872949
$122$	−8.12880	−	13.4652i	−0.735947	−	1.21908i
$123$		0			0
$124$	2.69352	−	5.11692i	0.241885	−	0.459513i
$125$		−	10.6643i		−	0.953846i
$126$		0			0
$127$	3.57016			0.316801			0.158400	−	0.987375i	$-0.449366\pi$
$127$	3.57016			0.316801			0.158400	+	0.987375i	$0.449366\pi$
$128$	−8.93561	+	6.93937i	−0.789804	+	0.613360i
$129$		0			0
$130$	−2.81830	+	1.70138i	−0.247181	+	0.149221i
$131$			4.37676i			0.382399i	0.981551	+	0.191199i	$0.0612377\pi$
$131$			4.37676i			0.382399i	−0.981551	+	0.191199i	$0.938762\pi$
$132$		0			0
$133$			27.2005i			2.35858i
$134$	−7.00850	−	11.6094i	−0.605442	−	1.00290i
$135$		0			0
$136$	−0.106194	−	1.81043i	−0.00910606	−	0.155244i
$137$	−17.1279			−1.46334			−0.731669	−	0.681661i	$-0.761258\pi$
$137$	−17.1279			−1.46334			−0.731669	+	0.681661i	$0.761258\pi$
$138$		0			0
$139$		−	8.84820i		−	0.750494i	−0.926925	−	0.375247i	$-0.877558\pi$
$139$		−	8.84820i		−	0.750494i	0.926925	−	0.375247i	$-0.122442\pi$
$140$	19.9870	+	10.5210i	1.68921	+	0.889188i
$141$		0			0
$142$	14.0939	−	8.50836i	1.18274	−	0.714006i
$143$	3.45836			0.289202
$144$		0			0
$145$	−11.6809			−0.970044
$146$	6.95282	−	4.19735i	0.575419	−	0.347375i
$147$		0			0
$148$	10.1635	+	5.34999i	0.835433	+	0.439767i
$149$		−	10.0600i		−	0.824150i	−0.911150	−	0.412075i	$-0.864804\pi$
$149$		−	10.0600i		−	0.824150i	0.911150	−	0.412075i	$-0.135196\pi$
$150$		0			0
$151$	−16.0647			−1.30733			−0.653664	−	0.756785i	$-0.726769\pi$
$151$	−16.0647			−1.30733			−0.653664	+	0.756785i	$0.726769\pi$
$152$	−15.8306	+	0.928572i	−1.28403	+	0.0753171i
$153$		0			0
$154$	−12.2631	−	20.3135i	−0.988187	−	1.63691i
$155$		−	6.73037i		−	0.540597i
$156$		0			0
$157$			4.34163i			0.346500i	0.984878	+	0.173250i	$0.0554268\pi$
$157$			4.34163i			0.346500i	−0.984878	+	0.173250i	$0.944573\pi$
$158$	10.6609	−	6.43586i	0.848133	−	0.512010i
$159$		0			0
$160$	−5.44089	+	11.9915i	−0.430140	+	0.948014i
$161$	45.4792			3.58426
$162$		0			0
$163$		−	17.8171i		−	1.39554i	−0.716322	−	0.697770i	$-0.754176\pi$
$163$		−	17.8171i		−	1.39554i	0.716322	−	0.697770i	$-0.245824\pi$
$164$	2.50612	−	4.76092i	0.195695	−	0.371765i
$165$		0			0
$166$	−9.83904	−	16.2981i	−0.763657	−	1.26498i
$167$	17.1464			1.32683			0.663414	−	0.748252i	$-0.269107\pi$
$167$	17.1464			1.32683			0.663414	+	0.748252i	$0.269107\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	−1.09090	−	1.80705i	−0.0836683	−	0.138595i
$171$		0			0
$172$	−0.544471	−	0.286606i	−0.0415155	−	0.0218535i
$173$			25.0119i			1.90162i	0.309771	+	0.950811i	$0.399748\pi$
$173$			25.0119i			1.90162i	−0.309771	+	0.950811i	$0.600252\pi$
$174$		0			0
$175$	2.03160			0.153575
$176$	11.4038	−	7.83055i	0.859593	−	0.590250i
$177$		0			0
$178$	−4.55190	+	2.74794i	−0.341180	+	0.205967i
$179$			13.5506i			1.01282i	0.862294	+	0.506408i	$0.169027\pi$
$179$			13.5506i			1.01282i	−0.862294	+	0.506408i	$0.830973\pi$
$180$		0			0
$181$		−	1.85179i		−	0.137642i	−0.997629	−	0.0688212i	$-0.978076\pi$
$181$		−	1.85179i		−	0.137642i	0.997629	−	0.0688212i	$-0.0219238\pi$
$182$	3.54592	+	5.87375i	0.262841	+	0.435391i
$183$		0			0
$184$	1.55257	+	26.4688i	0.114457	+	1.95131i
$185$	13.3682			0.982850
$186$		0			0
$187$			2.21745i			0.162156i
$188$	−7.73415	+	14.6927i	−0.564071	+	1.07157i
$189$		0			0
$190$	−15.8011	+	9.53896i	−1.14633	+	0.692029i
$191$	2.04057			0.147651			0.0738253	−	0.997271i	$-0.476479\pi$
$191$	2.04057			0.147651			0.0738253	+	0.997271i	$0.476479\pi$
$192$		0			0
$193$	13.8109			0.994130			0.497065	−	0.867713i	$-0.334411\pi$
$193$	13.8109			0.994130			0.497065	+	0.867713i	$0.334411\pi$
$194$	−2.40011	+	1.44892i	−0.172318	+	0.104026i
$195$		0			0
$196$	15.4061	−	29.2673i	1.10044	−	2.09052i
$197$		−	1.51068i		−	0.107632i	−0.998551	−	0.0538158i	$-0.982862\pi$
$197$		−	1.51068i		−	0.107632i	0.998551	−	0.0538158i	$-0.0171384\pi$
$198$		0			0
$199$	18.5086			1.31204			0.656019	−	0.754745i	$-0.272239\pi$
$199$	18.5086			1.31204			0.656019	+	0.754745i	$0.272239\pi$
$200$	0.0693548	+	1.18239i	0.00490413	+	0.0836074i
$201$		0			0
$202$	5.51520	+	9.13580i	0.388048	+	0.642793i
$203$			24.3446i			1.70866i
$204$		0			0
$205$		−	6.26212i		−	0.437365i
$206$	17.2144	−	10.3922i	1.19938	−	0.724056i
$207$		0			0
$208$	−3.29746	+	2.26424i	−0.228638	+	0.156997i
$209$	19.3896			1.34121
$210$		0			0
$211$			6.32310i			0.435300i	0.976027	+	0.217650i	$0.0698391\pi$
$211$			6.32310i			0.435300i	−0.976027	+	0.217650i	$0.930161\pi$
$212$	2.84554	+	1.49788i	0.195433	+	0.102875i
$213$		0			0
$214$	7.21652	+	11.9540i	0.493311	+	0.817159i
$215$	−0.716153			−0.0488412
$216$		0			0
$217$	−14.0271			−0.952220
$218$	−14.6625	−	24.2881i	−0.993068	−	1.64500i
$219$		0			0
$220$	7.49980	−	14.2475i	0.505637	−	0.960567i
$221$		−	0.641186i		−	0.0431308i
$222$		0			0
$223$	−19.6426			−1.31537			−0.657684	−	0.753294i	$-0.728464\pi$
$223$	−19.6426			−1.31537			−0.657684	+	0.753294i	$0.728464\pi$
$224$	24.9921	+	11.3396i	1.66985	+	0.757659i
$225$		0			0
$226$	0.242170	−	0.146196i	0.0161089	−	0.00972479i
$227$			24.5929i			1.63229i	0.577847	+	0.816145i	$0.303893\pi$
$227$			24.5929i			1.63229i	−0.577847	+	0.816145i	$0.696107\pi$
$228$		0			0
$229$		−	12.3978i		−	0.819273i	−0.912249	−	0.409636i	$-0.865656\pi$
$229$		−	12.3978i		−	0.819273i	0.912249	−	0.409636i	$-0.134344\pi$
$230$	15.9491	+	26.4194i	1.05165	+	1.74204i
$231$		0			0
$232$	−14.1685	+	0.831078i	−0.930209	+	0.0545629i
$233$	11.2290			0.735636			0.367818	−	0.929898i	$-0.380105\pi$
$233$	11.2290			0.735636			0.367818	+	0.929898i	$0.380105\pi$
$234$		0			0
$235$			19.3256i			1.26066i
$236$	−0.454365	−	0.239175i	−0.0295766	−	0.0155690i
$237$		0			0
$238$	−3.76616	+	2.27360i	−0.244124	+	0.147375i
$239$	−26.1610			−1.69221			−0.846107	−	0.533014i	$-0.821059\pi$
$239$	−26.1610			−1.69221			−0.846107	+	0.533014i	$0.821059\pi$
$240$		0			0
$241$	−5.90801			−0.380568			−0.190284	−	0.981729i	$-0.560941\pi$
$241$	−5.90801			−0.380568			−0.190284	+	0.981729i	$0.560941\pi$
$242$	−1.16257	+	0.701832i	−0.0747328	+	0.0451155i
$243$		0			0
$244$	−19.6831	−	10.3611i	−1.26008	−	0.663300i
$245$		−	38.4957i		−	2.45940i
$246$		0			0
$247$	−5.60660			−0.356739
$248$	−0.478857	−	8.16373i	−0.0304074	−	0.518397i
$249$		0			0
$250$	−7.79444	−	12.9113i	−0.492964	−	0.816584i
$251$			6.60905i			0.417160i	0.978005	+	0.208580i	$0.0668841\pi$
$251$			6.60905i			0.417160i	−0.978005	+	0.208580i	$0.933116\pi$
$252$		0			0
$253$		−	32.4194i		−	2.03819i
$254$	4.32240	−	2.60939i	0.271212	−	0.163728i
$255$		0			0
$256$	−5.74645	+	14.9325i	−0.359153	+	0.933279i
$257$	0.441161			0.0275189			0.0137594	−	0.999905i	$-0.495620\pi$
$257$	0.441161			0.0275189			0.0137594	+	0.999905i	$0.495620\pi$
$258$		0			0
$259$		−	27.8613i		−	1.73122i
$260$	−2.16860	+	4.11973i	−0.134491	+	0.255495i
$261$		0			0
$262$	3.19892	+	5.29895i	0.197630	+	0.327370i
$263$	10.7552			0.663195			0.331598	−	0.943421i	$-0.392412\pi$
$263$	10.7552			0.663195			0.331598	+	0.943421i	$0.392412\pi$
$264$		0			0
$265$	3.74279			0.229918
$266$	19.8806	+	32.9317i	1.21896	+	2.01917i
$267$		0			0
$268$	−16.9704	−	8.93313i	−1.03663	−	0.545678i
$269$		−	18.4754i		−	1.12646i	−0.826299	−	0.563232i	$-0.809558\pi$
$269$		−	18.4754i		−	1.12646i	0.826299	−	0.563232i	$-0.190442\pi$
$270$		0			0
$271$	0.185849			0.0112895			0.00564477	−	0.999984i	$-0.498203\pi$
$271$	0.185849			0.0112895			0.00564477	+	0.999984i	$0.498203\pi$
$272$	−1.45180	−	2.11428i	−0.0880281	−	0.128197i
$273$		0			0
$274$	−20.7368	+	12.5186i	−1.25276	+	0.756277i
$275$		−	1.44821i		−	0.0873302i
$276$		0			0
$277$			25.5315i			1.53404i	0.641623	+	0.767021i	$0.278262\pi$
$277$			25.5315i			1.53404i	−0.641623	+	0.767021i	$0.721738\pi$
$278$	−6.46705	−	10.7125i	−0.387868	−	0.642495i
$279$		0			0
$280$	31.8880	−	1.87044i	1.90567	−	0.111780i
$281$	−16.0583			−0.957959			−0.478980	−	0.877826i	$-0.658993\pi$
$281$	−16.0583			−0.957959			−0.478980	+	0.877826i	$0.658993\pi$
$282$		0			0
$283$			18.8655i			1.12144i	0.828006	+	0.560720i	$0.189475\pi$
$283$			18.8655i			1.12144i	−0.828006	+	0.560720i	$0.810525\pi$
$284$	10.8449	−	20.6022i	0.643525	−	1.22252i
$285$		0			0
$286$	4.18704	−	2.52768i	0.247585	−	0.149465i
$287$	−13.0512			−0.770386
$288$		0			0
$289$	−16.5889			−0.975817
$290$	−14.1421	+	8.53743i	−0.830451	+	0.501335i
$291$		0			0
$292$	5.34999	−	10.1635i	0.313085	−	0.594773i
$293$		−	32.3450i		−	1.88961i	−0.327630	−	0.944806i	$-0.606250\pi$
$293$		−	32.3450i		−	1.88961i	0.327630	−	0.944806i	$-0.393750\pi$
$294$		0			0
$295$	−0.597634			−0.0347956
$296$	16.2152	−	0.951129i	0.942490	−	0.0552832i
$297$		0			0
$298$	−7.35277	−	12.1797i	−0.425935	−	0.705551i
$299$			9.37422i			0.542125i
$300$		0			0
$301$			1.49257i			0.0860301i
$302$	−19.4496	+	11.7415i	−1.11920	+	0.675649i
$303$		0			0
$304$	−18.4875	+	12.6947i	−1.06033	+	0.728090i
$305$	−25.8896			−1.48243
$306$		0			0
$307$		−	0.888356i		−	0.0507012i	−0.999679	−	0.0253506i	$-0.991930\pi$
$307$		−	0.888356i		−	0.0507012i	0.999679	−	0.0253506i	$-0.00807021\pi$
$308$	−29.6939	−	15.6307i	−1.69197	−	0.890640i
$309$		0			0
$310$	−4.91916	−	8.14848i	−0.279389	−	0.462803i
$311$	20.3848			1.15592			0.577958	−	0.816066i	$-0.303850\pi$
$311$	20.3848			1.15592			0.577958	+	0.816066i	$0.303850\pi$
$312$		0			0
$313$	12.7182			0.718878			0.359439	−	0.933169i	$-0.382968\pi$
$313$	12.7182			0.718878			0.359439	+	0.933169i	$0.382968\pi$
$314$	3.17325	+	5.25642i	0.179077	+	0.296637i
$315$		0			0
$316$	8.20324	−	15.5838i	0.461468	−	0.876659i
$317$			14.1169i			0.792887i	0.918059	+	0.396443i	$0.129756\pi$
$317$			14.1169i			0.792887i	−0.918059	+	0.396443i	$0.870244\pi$
$318$		0			0
$319$	17.3538			0.971628
$320$	2.17718	+	18.4949i	0.121708	+	1.03389i
$321$		0			0
$322$	55.0618	−	33.2403i	3.06847	−	1.85241i
$323$		−	3.59487i		−	0.200024i
$324$		0			0
$325$			0.418756i			0.0232284i
$326$	−13.0223	−	21.5712i	−0.721239	−	1.19472i
$327$		0			0
$328$	−0.445541	−	7.59575i	−0.0246009	−	0.419405i
$329$	40.2773			2.22056
$330$		0			0
$331$		−	10.0151i		−	0.550478i	−0.961376	−	0.275239i	$-0.911243\pi$
$331$		−	10.0151i		−	0.550478i	0.961376	−	0.275239i	$-0.0887569\pi$
$332$	−23.8243	−	12.5410i	−1.30753	−	0.688275i
$333$		0			0
$334$	20.7592	−	12.5321i	1.13589	−	0.685727i
$335$	−22.3215			−1.21955
$336$		0			0
$337$	−7.43522			−0.405022			−0.202511	−	0.979280i	$-0.564910\pi$
$337$	−7.43522			−0.405022			−0.202511	+	0.979280i	$0.564910\pi$
$338$	−1.21070	+	0.730889i	−0.0658535	+	0.0397551i
$339$		0			0
$340$	−2.64151	−	1.39048i	−0.143256	−	0.0754092i
$341$			9.99907i			0.541480i
$342$		0			0
$343$	−46.2701			−2.49835
$344$	−0.868670	+	0.0509532i	−0.0468356	+	0.00274721i
$345$		0			0
$346$	18.2810	+	30.2820i	0.982791	+	1.62797i
$347$		−	2.98167i		−	0.160065i	−0.996792	−	0.0800323i	$-0.974498\pi$
$347$		−	2.98167i		−	0.160065i	0.996792	−	0.0800323i	$-0.0255023\pi$
$348$		0			0
$349$			18.9038i			1.01189i	0.862564	+	0.505947i	$0.168857\pi$
$349$			18.9038i			1.01189i	−0.862564	+	0.505947i	$0.831143\pi$
$350$	2.45966	−	1.48488i	0.131475	−	0.0793699i
$351$		0			0
$352$	8.08333	−	17.8154i	0.430843	−	0.949563i
$353$	−8.51716			−0.453323			−0.226661	−	0.973974i	$-0.572781\pi$
$353$	−8.51716			−0.453323			−0.226661	+	0.973974i	$0.572781\pi$
$354$		0			0
$355$		−	27.0984i		−	1.43824i
$356$	−3.50256	+	6.65388i	−0.185635	+	0.352655i
$357$		0			0
$358$	9.90396	+	16.4057i	0.523440	+	0.867068i
$359$	−13.5572			−0.715520			−0.357760	−	0.933814i	$-0.616459\pi$
$359$	−13.5572			−0.715520			−0.357760	+	0.933814i	$0.616459\pi$
$360$		0			0
$361$	−12.4339			−0.654418
$362$	−1.35345	−	2.24197i	−0.0711359	−	0.117835i
$363$		0			0
$364$	8.58612	+	4.51968i	0.450035	+	0.236896i
$365$		−	13.3682i		−	0.699724i
$366$		0			0
$367$	−12.1678			−0.635154			−0.317577	−	0.948233i	$-0.602869\pi$
$367$	−12.1678			−0.635154			−0.317577	+	0.948233i	$0.602869\pi$
$368$	21.2255	+	30.9111i	1.10645	+	1.61135i
$369$		0			0
$370$	16.1849	−	9.77068i	0.841414	−	0.507953i
$371$		−	7.80053i		−	0.404983i
$372$		0			0
$373$			22.9957i			1.19067i	0.803476	+	0.595337i	$0.202982\pi$
$373$			22.9957i			1.19067i	−0.803476	+	0.595337i	$0.797018\pi$
$374$	1.62071	+	2.68467i	0.0838049	+	0.138821i
$375$		0			0
$376$	1.37499	+	23.4413i	0.0709095	+	1.20889i
$377$	−5.01794			−0.258437
$378$		0			0
$379$			29.0303i			1.49118i	0.666402	+	0.745592i	$0.267833\pi$
$379$			29.0303i			1.49118i	−0.666402	+	0.745592i	$0.732167\pi$
$380$	−12.1585	+	23.0977i	−0.623717	+	1.18489i
$381$		0			0
$382$	2.47053	−	1.49143i	0.126403	−	0.0763083i
$383$	11.8113			0.603528			0.301764	−	0.953383i	$-0.402425\pi$
$383$	11.8113			0.603528			0.301764	+	0.953383i	$0.402425\pi$
$384$		0			0
$385$	−39.0569			−1.99052
$386$	16.7209	−	10.0942i	0.851071	−	0.513783i
$387$		0			0
$388$	−1.84681	+	3.50842i	−0.0937577	+	0.178113i
$389$		−	15.5223i		−	0.787014i	−0.919322	−	0.393507i	$-0.871262\pi$
$389$		−	15.5223i		−	0.787014i	0.919322	−	0.393507i	$-0.128738\pi$
$390$		0			0
$391$	−6.01061			−0.303970
$392$	−2.73892	−	46.6941i	−0.138336	−	2.35841i
$393$		0			0
$394$	−1.10414	−	1.82899i	−0.0556259	−	0.0921430i
$395$		−	20.4977i		−	1.03135i
$396$		0			0
$397$			29.5094i			1.48103i	0.672038	+	0.740516i	$0.265419\pi$
$397$			29.5094i			1.48103i	−0.672038	+	0.740516i	$0.734581\pi$
$398$	22.4084	−	13.5277i	1.12323	−	0.678083i
$399$		0			0
$400$	0.948162	+	1.38083i	0.0474081	+	0.0690414i
$401$	−31.3317			−1.56463			−0.782315	−	0.622883i	$-0.785961\pi$
$401$	−31.3317			−1.56463			−0.782315	+	0.622883i	$0.785961\pi$
$402$		0			0
$403$		−	2.89128i		−	0.144025i
$404$	13.3545	+	7.02974i	0.664412	+	0.349743i
$405$		0			0
$406$	17.7932	+	29.4741i	0.883064	+	1.46278i
$407$	−19.8606			−0.984455
$408$		0			0
$409$	30.0717			1.48695			0.743476	−	0.668763i	$-0.233176\pi$
$409$	30.0717			1.48695			0.743476	+	0.668763i	$0.233176\pi$
$410$	−4.57692	−	7.58156i	−0.226038	−	0.374427i
$411$		0			0
$412$	13.2460	−	25.1636i	0.652582	−	1.23972i
$413$			1.24556i			0.0612898i
$414$		0			0
$415$	−31.3365			−1.53825
$416$	−2.33733	+	5.15140i	−0.114597	+	0.252568i
$417$		0			0
$418$	23.4751	−	14.1717i	1.14820	−	0.693159i
$419$			18.5621i			0.906818i	0.891303	+	0.453409i	$0.149792\pi$
$419$			18.5621i			0.906818i	−0.891303	+	0.453409i	$0.850208\pi$
$420$		0			0
$421$		−	17.5208i		−	0.853910i	−0.904273	−	0.426955i	$-0.859586\pi$
$421$		−	17.5208i		−	0.853910i	0.904273	−	0.426955i	$-0.140414\pi$
$422$	4.62149	+	7.65539i	0.224970	+	0.372659i
$423$		0			0
$424$	4.53989	−	0.266294i	0.220477	−	0.0129324i
$425$	−0.268500			−0.0130242
$426$		0			0
$427$			53.9576i			2.61119i
$428$	17.4741	+	9.19827i	0.844643	+	0.444615i
$429$		0			0
$430$	−0.867048	+	0.523428i	−0.0418128	+	0.0252420i
$431$	−24.5625			−1.18313			−0.591567	−	0.806256i	$-0.701491\pi$
$431$	−24.5625			−1.18313			−0.591567	+	0.806256i	$0.701491\pi$
$432$		0			0
$433$	−9.65650			−0.464062			−0.232031	−	0.972708i	$-0.574537\pi$
$433$	−9.65650			−0.464062			−0.232031	+	0.972708i	$0.574537\pi$
$434$	−16.9826	+	10.2522i	−0.815192	+	0.492123i
$435$		0			0
$436$	−35.5038	−	18.6890i	−1.70032	−	0.895039i
$437$			52.5575i			2.51417i
$438$		0			0
$439$	2.89778			0.138303			0.0691517	−	0.997606i	$-0.477971\pi$
$439$	2.89778			0.138303			0.0691517	+	0.997606i	$0.477971\pi$
$440$	−1.33332	−	22.7310i	−0.0635637	−	1.08366i
$441$		0			0
$442$	−0.468636	−	0.776285i	−0.0222907	−	0.0369241i
$443$		−	28.2220i		−	1.34087i	−0.741969	−	0.670434i	$-0.766108\pi$
$443$		−	28.2220i		−	1.34087i	0.741969	−	0.670434i	$-0.233892\pi$
$444$		0			0
$445$			8.75196i			0.414883i
$446$	−23.7814	+	14.3566i	−1.12608	+	0.679805i
$447$		0			0
$448$	38.5460	−	4.53757i	1.82113	−	0.214380i
$449$	25.7865			1.21694			0.608471	−	0.793576i	$-0.291783\pi$
$449$	25.7865			1.21694			0.608471	+	0.793576i	$0.291783\pi$
$450$		0			0
$451$			9.30340i			0.438080i
$452$	0.186343	−	0.353999i	0.00876483	−	0.0166507i
$453$		0			0
$454$	17.9747	+	29.7747i	0.843595	+	1.39740i
$455$	11.2935			0.529446
$456$		0			0
$457$	1.90289			0.0890137			0.0445068	−	0.999009i	$-0.485828\pi$
$457$	1.90289			0.0890137			0.0445068	+	0.999009i	$0.485828\pi$
$458$	−9.06146	−	15.0101i	−0.423414	−	0.701376i
$459$		0			0
$460$	38.6193	+	20.3290i	1.80063	+	0.947842i
$461$			36.9540i			1.72112i	0.509349	+	0.860560i	$0.329886\pi$
$461$			36.9540i			1.72112i	−0.509349	+	0.860560i	$0.670114\pi$
$462$		0			0
$463$	2.01877			0.0938202			0.0469101	−	0.998899i	$-0.485063\pi$
$463$	2.01877			0.0938202			0.0469101	+	0.998899i	$0.485063\pi$
$464$	−16.5464	+	11.3618i	−0.768149	+	0.527459i
$465$		0			0
$466$	13.5950	−	8.20716i	0.629775	−	0.380189i
$467$		−	19.8606i		−	0.919041i	−0.888167	−	0.459520i	$-0.848021\pi$
$467$		−	19.8606i		−	0.919041i	0.888167	−	0.459520i	$-0.151979\pi$
$468$		0			0
$469$			46.5212i			2.14815i
$470$	14.1248	+	23.3975i	0.651531	+	1.07925i
$471$		0			0
$472$	−0.724911	+	0.0425208i	−0.0333667	+	0.00195718i
$473$	1.06396			0.0489210
$474$		0			0
$475$			2.34779i			0.107724i
$476$	−2.89795	+	5.50530i	−0.132828	+	0.252335i
$477$		0			0
$478$	−31.6732	+	19.1208i	−1.44870	+	0.874564i
$479$	28.3272			1.29430			0.647151	−	0.762362i	$-0.275961\pi$
$479$	28.3272			1.29430			0.647151	+	0.762362i	$0.275961\pi$
$480$		0			0
$481$	5.74279			0.261849
$482$	−7.15284	+	4.31810i	−0.325803	+	0.196684i
$483$		0			0
$484$	−0.894564	+	1.69942i	−0.0406620	+	0.0772463i
$485$			4.61469i			0.209542i
$486$		0			0
$487$	−0.908676			−0.0411760			−0.0205880	−	0.999788i	$-0.506554\pi$
$487$	−0.908676			−0.0411760			−0.0205880	+	0.999788i	$0.506554\pi$
$488$	−31.4032	+	1.84201i	−1.42156	+	0.0833837i
$489$		0			0
$490$	−28.1361	−	46.6069i	−1.27106	−	2.10548i
$491$		−	30.1024i		−	1.35850i	−0.733906	−	0.679251i	$-0.762305\pi$
$491$		−	30.1024i		−	1.35850i	0.733906	−	0.679251i	$-0.237695\pi$
$492$		0			0
$493$		−	3.21743i		−	0.144906i
$494$	−6.78792	+	4.09780i	−0.305403	+	0.184369i
$495$		0			0
$496$	−6.54654	−	9.53386i	−0.293948	−	0.428083i
$497$	−56.4770			−2.53334
$498$		0			0
$499$			7.50251i			0.335859i	0.985799	+	0.167929i	$0.0537080\pi$
$499$			7.50251i			0.335859i	−0.985799	+	0.167929i	$0.946292\pi$
$500$	−18.8735	−	9.93489i	−0.844048	−	0.444302i
$501$		0			0
$502$	4.83049	+	8.00160i	0.215595	+	0.357129i
$503$	21.3770			0.953155			0.476578	−	0.879132i	$-0.341877\pi$
$503$	21.3770			0.953155			0.476578	+	0.879132i	$0.341877\pi$
$504$		0			0
$505$	17.5654			0.781652
$506$	−23.6950	−	39.2503i	−1.05337	−	1.74489i
$507$		0			0
$508$	3.32597	−	6.31840i	0.147566	−	0.280334i
$509$			17.2562i			0.764867i	0.923983	+	0.382434i	$0.124914\pi$
$509$			17.2562i			0.764867i	−0.923983	+	0.382434i	$0.875086\pi$
$510$		0			0
$511$	−27.8613			−1.23251
$512$	3.95674	+	22.2788i	0.174865	+	0.984592i
$513$		0			0
$514$	0.534115	−	0.322440i	0.0235588	−	0.0142222i
$515$		−	33.0981i		−	1.45848i
$516$		0			0
$517$		−	28.7113i		−	1.26272i
$518$	−20.3635	−	33.7317i	−0.894721	−	1.48209i
$519$		0			0
$520$	0.385537	+	6.57278i	0.0169069	+	0.288235i
$521$	−23.4875			−1.02901			−0.514503	−	0.857489i	$-0.672024\pi$
$521$	−23.4875			−1.02901			−0.514503	+	0.857489i	$0.672024\pi$
$522$		0			0
$523$		−	29.4495i		−	1.28774i	−0.765136	−	0.643869i	$-0.777328\pi$
$523$		−	29.4495i		−	1.28774i	0.765136	−	0.643869i	$-0.222672\pi$
$524$	7.74589	+	4.07739i	0.338381	+	0.178122i
$525$		0			0
$526$	13.0214	−	7.86088i	0.567759	−	0.342751i
$527$	1.85384			0.0807547
$528$		0			0
$529$	64.8760			2.82070
$530$	4.53141	−	2.73557i	0.196832	−	0.118826i
$531$		0			0
$532$	48.1389	+	25.3400i	2.08709	+	1.09863i
$533$		−	2.69012i		−	0.116522i
$534$		0			0
$535$	22.9840			0.993685
$536$	−27.0753	+	1.58814i	−1.16947	+	0.0685973i
$537$		0			0
$538$	−13.5035	−	22.3682i	−0.582176	−	0.964362i
$539$			57.1917i			2.46342i
$540$		0			0
$541$		−	21.0811i		−	0.906348i	−0.891422	−	0.453174i	$-0.850292\pi$
$541$		−	21.0811i		−	0.906348i	0.891422	−	0.453174i	$-0.149708\pi$
$542$	0.225008	−	0.135835i	0.00966493	−	0.00583462i
$543$		0			0
$544$	−3.30300	−	1.49866i	−0.141615	−	0.0642547i
$545$	−46.6987			−2.00035
$546$		0			0
$547$		−	26.6432i		−	1.13918i	−0.821928	−	0.569591i	$-0.807102\pi$
$547$		−	26.6432i		−	1.13918i	0.821928	−	0.569591i	$-0.192898\pi$
$548$	−15.9564	+	30.3126i	−0.681623	+	1.29489i
$549$		0			0
$550$	−1.05848	−	1.75335i	−0.0451337	−	0.0747630i
$551$	−28.1336			−1.19853
$552$		0			0
$553$	−42.7202			−1.81665
$554$	18.6607	+	30.9111i	0.792818	+	1.31329i
$555$		0			0
$556$	−15.6594	−	8.24299i	−0.664105	−	0.349581i
$557$		−	25.0383i		−	1.06091i	−0.847714	−	0.530453i	$-0.822022\pi$
$557$		−	25.0383i		−	1.06091i	0.847714	−	0.530453i	$-0.177978\pi$
$558$		0			0
$559$	−0.307649			−0.0130122
$560$	37.2397	−	25.5711i	1.57367	−	1.08058i
$561$		0			0
$562$	−19.4419	+	11.7369i	−0.820105	+	0.495089i
$563$		−	4.04508i		−	0.170480i	−0.996360	−	0.0852400i	$-0.972834\pi$
$563$		−	4.04508i		−	0.170480i	0.996360	−	0.0852400i	$-0.0271657\pi$
$564$		0			0
$565$		−	0.465621i		−	0.0195888i
$566$	13.7886	+	22.8405i	0.579579	+	0.960060i
$567$		0			0
$568$	−1.92801	−	32.8695i	−0.0808977	−	1.37917i
$569$	8.42913			0.353367			0.176684	−	0.984268i	$-0.443463\pi$
$569$	8.42913			0.353367			0.176684	+	0.984268i	$0.443463\pi$
$570$		0			0
$571$		−	27.4502i		−	1.14875i	−0.818591	−	0.574377i	$-0.805245\pi$
$571$		−	27.4502i		−	1.14875i	0.818591	−	0.574377i	$-0.194755\pi$
$572$	3.22181	−	6.12053i	0.134711	−	0.255912i
$573$		0			0
$574$	−15.8011	+	9.53896i	−0.659524	+	0.398148i
$575$	3.92551			0.163705
$576$		0			0
$577$	−2.23961			−0.0932363			−0.0466182	−	0.998913i	$-0.514844\pi$
$577$	−2.23961			−0.0932363			−0.0466182	+	0.998913i	$0.514844\pi$
$578$	−20.0842	+	12.1246i	−0.835393	+	0.504318i
$579$		0			0
$580$	−10.8819	+	20.6726i	−0.451847	+	0.858382i
$581$			65.3098i			2.70951i
$582$		0			0
$583$	−5.56053			−0.230294
$584$	−0.951129	−	16.2152i	−0.0393580	−	0.670990i
$585$		0			0
$586$	−23.6406	−	39.1601i	−0.976584	−	1.61769i
$587$		−	9.30148i		−	0.383913i	−0.981403	−	0.191957i	$-0.938517\pi$
$587$		−	9.30148i		−	0.383913i	0.981403	−	0.191957i	$-0.0614833\pi$
$588$		0			0
$589$		−	16.2102i		−	0.667930i
$590$	−0.723557	+	0.436804i	−0.0297884	+	0.0179829i
$591$		0			0
$592$	18.9366	−	13.0031i	0.778290	−	0.534422i
$593$	21.4386			0.880376			0.440188	−	0.897906i	$-0.354912\pi$
$593$	21.4386			0.880376			0.440188	+	0.897906i	$0.354912\pi$
$594$		0			0
$595$			7.24121i			0.296861i
$596$	−17.8040	−	9.37194i	−0.729282	−	0.383890i
$597$		0			0
$598$	6.85152	+	11.3494i	0.280179	+	0.464111i
$599$	9.89839			0.404437			0.202219	−	0.979340i	$-0.435185\pi$
$599$	9.89839			0.404437			0.202219	+	0.979340i	$0.435185\pi$
$600$		0			0
$601$	−29.1142			−1.18759			−0.593797	−	0.804615i	$-0.702372\pi$
$601$	−29.1142			−1.18759			−0.593797	+	0.804615i	$0.702372\pi$
$602$	1.09090	+	1.80705i	0.0444618	+	0.0736500i
$603$		0			0
$604$	−14.9659	+	28.4310i	−0.608954	+	1.15684i
$605$			2.23528i			0.0908769i
$606$		0			0
$607$	19.0734			0.774166			0.387083	−	0.922045i	$-0.373483\pi$
$607$	19.0734			0.774166			0.387083	+	0.922045i	$0.373483\pi$
$608$	−13.1045	+	28.8818i	−0.531457	+	1.17131i
$609$		0			0
$610$	−31.3445	+	18.9224i	−1.26910	+	0.766146i
$611$			8.30199i			0.335863i
$612$		0			0
$613$			0.580305i			0.0234383i	0.999931	+	0.0117192i	$0.00373041\pi$
$613$			0.580305i			0.0234383i	−0.999931	+	0.0117192i	$0.996270\pi$
$614$	−0.649290	−	1.07554i	−0.0262032	−	0.0434051i
$615$		0			0
$616$	−47.3747	+	2.77884i	−1.90878	+	0.111963i
$617$	−26.4405			−1.06445			−0.532227	−	0.846602i	$-0.678645\pi$
$617$	−26.4405			−1.06445			−0.532227	+	0.846602i	$0.678645\pi$
$618$		0			0
$619$		−	0.0220395i		−	0.000885841i	−1.00000		0.000442921i	$-0.999859\pi$
$619$		−	0.0220395i		−	0.000885841i	1.00000		0.000442921i	$-0.000140986\pi$
$620$	−11.9113	−	6.27002i	−0.478368	−	0.251810i
$621$		0			0
$622$	24.6799	−	14.8990i	0.989575	−	0.597397i
$623$	18.2404			0.730784
$624$		0			0
$625$	−26.9184			−1.07674
$626$	15.3980	−	9.29563i	0.615428	−	0.371528i
$627$		0			0
$628$	7.68373	+	4.04467i	0.306614	+	0.161400i
$629$			3.68220i			0.146819i
$630$		0			0
$631$	21.2096			0.844341			0.422171	−	0.906516i	$-0.361268\pi$
$631$	21.2096			0.844341			0.422171	+	0.906516i	$0.361268\pi$
$632$	−1.45838	−	24.8630i	−0.0580113	−	0.988999i
$633$		0			0
$634$	10.3179	+	17.0914i	0.409777	+	0.678787i
$635$		−	8.31070i		−	0.329800i
$636$		0			0
$637$		−	16.5372i		−	0.655229i
$638$	21.0103	−	12.6837i	0.831807	−	0.502154i
$639$		0			0
$640$	16.1536	+	20.8005i	0.638528	+	0.822212i
$641$	−17.2504			−0.681351			−0.340675	−	0.940181i	$-0.610656\pi$
$641$	−17.2504			−0.681351			−0.340675	+	0.940181i	$0.610656\pi$
$642$		0			0
$643$		−	30.5119i		−	1.20327i	−0.798771	−	0.601636i	$-0.794516\pi$
$643$		−	30.5119i		−	1.20327i	0.798771	−	0.601636i	$-0.205484\pi$
$644$	42.3685	−	80.4882i	1.66955	−	3.17168i
$645$		0			0
$646$	−2.62745	−	4.35232i	−0.103376	−	0.171240i
$647$	29.9239			1.17643			0.588216	−	0.808704i	$-0.299831\pi$
$647$	29.9239			1.17643			0.588216	+	0.808704i	$0.299831\pi$
$648$		0			0
$649$	0.887882			0.0348524
$650$	0.306064	+	0.506988i	0.0120048	+	0.0198857i
$651$		0			0
$652$	−31.5323	−	16.5984i	−1.23490	−	0.650044i
$653$			25.1810i			0.985408i	0.870197	+	0.492704i	$0.163992\pi$
$653$			25.1810i			0.985408i	−0.870197	+	0.492704i	$0.836008\pi$
$654$		0			0
$655$	10.1883			0.398090
$656$	−6.09107	−	8.87055i	−0.237816	−	0.346337i
$657$		0			0
$658$	48.7638	−	29.4382i	1.90101	−	1.14762i
$659$		−	11.7183i		−	0.456480i	−0.973605	−	0.228240i	$-0.926703\pi$
$659$		−	11.7183i		−	0.456480i	0.973605	−	0.228240i	$-0.0732971\pi$
$660$		0			0
$661$		−	20.3418i		−	0.791203i	−0.918422	−	0.395602i	$-0.870536\pi$
$661$		−	20.3418i		−	0.791203i	0.918422	−	0.395602i	$-0.129464\pi$
$662$	−7.31990	−	12.1253i	−0.284496	−	0.471262i
$663$		0			0
$664$	−38.0102	+	2.22955i	−1.47508	+	0.0865233i
$665$	63.3180			2.45537
$666$		0			0
$667$			47.0393i			1.82137i
$668$	15.9736	−	30.3453i	0.618037	−	1.17410i
$669$		0			0
$670$	−27.0247	+	16.3145i	−1.04406	+	0.630286i
$671$	38.4631			1.48485
$672$		0			0
$673$	21.5020			0.828843			0.414422	−	0.910085i	$-0.363984\pi$
$673$	21.5020			0.828843			0.414422	+	0.910085i	$0.363984\pi$
$674$	−9.00184	+	5.43432i	−0.346738	+	0.209322i
$675$		0			0
$676$	−0.931601	+	1.76978i	−0.0358308	+	0.0680684i
$677$			30.2735i			1.16351i	0.813366	+	0.581753i	$0.197633\pi$
$677$			30.2735i			1.16351i	−0.813366	+	0.581753i	$0.802367\pi$
$678$		0			0
$679$	9.61769			0.369093
$680$	−4.21437	+	0.247201i	−0.161614	+	0.00947971i
$681$		0			0
$682$	7.30821	+	12.1059i	0.279846	+	0.463559i
$683$		−	30.0657i		−	1.15043i	−0.818001	−	0.575216i	$-0.804918\pi$
$683$		−	30.0657i		−	1.15043i	0.818001	−	0.575216i	$-0.195082\pi$
$684$		0			0
$685$			39.8708i			1.52338i
$686$	−56.0193	+	33.8183i	−2.13883	+	1.29119i
$687$		0			0
$688$	−1.01446	+	0.696591i	−0.0386759	+	0.0265573i
$689$	1.60785			0.0612543
$690$		0			0
$691$			23.3134i			0.886884i	0.896303	+	0.443442i	$0.146243\pi$
$691$			23.3134i			0.886884i	−0.896303	+	0.443442i	$0.853757\pi$
$692$	44.2656	+	23.3011i	1.68273	+	0.885777i
$693$		0			0
$694$	−2.17927	−	3.60992i	−0.0827241	−	0.137031i
$695$	−20.5970			−0.781290
$696$		0			0
$697$	1.72487			0.0653339
$698$	13.8166	+	22.8868i	0.522964	+	0.866279i
$699$		0			0
$700$	1.89264	−	3.59548i	0.0715351	−	0.135897i
$701$		−	45.8471i		−	1.73162i	−0.500371	−	0.865811i	$-0.666803\pi$
$701$		−	45.8471i		−	1.73162i	0.500371	−	0.865811i	$-0.333197\pi$
$702$		0			0
$703$	32.1975			1.21435
$704$	−3.23456	−	27.4771i	−0.121907	−	1.03558i
$705$		0			0
$706$	−10.3117	+	6.22510i	−0.388088	+	0.234285i
$707$		−	36.6089i		−	1.37682i
$708$		0			0
$709$		−	20.5059i		−	0.770115i	−0.922892	−	0.385058i	$-0.874182\pi$
$709$		−	20.5059i		−	0.770115i	0.922892	−	0.385058i	$-0.125818\pi$
$710$	−19.8060	−	32.8081i	−0.743304	−	1.23127i
$711$		0			0
$712$	0.622690	+	10.6158i	0.0233363	+	0.397846i
$713$	−27.1035			−1.01503
$714$		0			0
$715$		−	8.05044i		−	0.301070i
$716$	23.9815	+	12.6237i	0.896230	+	0.471770i
$717$		0			0
$718$	−16.4137	+	9.90879i	−0.612554	+	0.369793i
$719$	6.80948			0.253951			0.126975	−	0.991906i	$-0.459473\pi$
$719$	6.80948			0.253951			0.126975	+	0.991906i	$0.459473\pi$
$720$		0			0
$721$	−68.9813			−2.56900
$722$	−15.0538	+	9.08784i	−0.560245	+	0.338214i
$723$		0			0
$724$	−3.27726	−	1.72513i	−0.121798	−	0.0641139i
$725$			2.10129i			0.0780400i
$726$		0			0
$727$	−9.00081			−0.333821			−0.166911	−	0.985972i	$-0.553379\pi$
$727$	−9.00081			−0.333821			−0.166911	+	0.985972i	$0.553379\pi$
$728$	13.6986	−	0.803515i	0.507705	−	0.0297802i
$729$		0			0
$730$	−9.77068	−	16.1849i	−0.361629	−	0.599031i
$731$		−	0.197260i		−	0.00729593i
$732$		0			0
$733$			37.1422i			1.37188i	0.727658	+	0.685940i	$0.240609\pi$
$733$			37.1422i			1.37188i	−0.727658	+	0.685940i	$0.759391\pi$
$734$	−14.7316	+	8.89331i	−0.543753	+	0.328258i
$735$		0			0
$736$	48.2903	+	21.9107i	1.78000	+	0.807638i
$737$	33.1622			1.22155
$738$		0			0
$739$		−	20.5071i		−	0.754366i	−0.926139	−	0.377183i	$-0.876893\pi$
$739$		−	20.5071i		−	0.754366i	0.926139	−	0.377183i	$-0.123107\pi$
$740$	12.4538	−	23.6588i	0.457812	−	0.869714i
$741$		0			0
$742$	−5.70132	−	9.44412i	−0.209302	−	0.346704i
$743$	−18.7137			−0.686541			−0.343270	−	0.939237i	$-0.611535\pi$
$743$	−18.7137			−0.686541			−0.343270	+	0.939237i	$0.611535\pi$
$744$		0			0
$745$	−23.4180			−0.857968
$746$	16.8073	+	27.8410i	0.615361	+	1.01933i
$747$		0			0
$748$	3.92440	+	2.06578i	0.143490	+	0.0755323i
$749$		−	47.9020i		−	1.75030i
$750$		0			0
$751$	−5.05601			−0.184497			−0.0922483	−	0.995736i	$-0.529405\pi$
$751$	−5.05601			−0.184497			−0.0922483	+	0.995736i	$0.529405\pi$
$752$	18.7977	+	27.3755i	0.685481	+	0.998280i
$753$		0			0
$754$	−6.07523	+	3.66756i	−0.221247	+	0.133565i
$755$			37.3958i			1.36097i
$756$		0			0
$757$		−	32.6509i		−	1.18672i	−0.804938	−	0.593359i	$-0.797801\pi$
$757$		−	32.6509i		−	1.18672i	0.804938	−	0.593359i	$-0.202199\pi$
$758$	21.2179	+	35.1470i	0.770669	+	1.27660i
$759$		0			0
$760$	2.16155	+	36.8509i	0.0784076	+	1.33672i
$761$	−9.57114			−0.346953			−0.173477	−	0.984838i	$-0.555500\pi$
$761$	−9.57114			−0.346953			−0.173477	+	0.984838i	$0.555500\pi$
$762$		0			0
$763$			97.3269i			3.52347i
$764$	1.90100	−	3.61136i	0.0687758	−	0.130655i
$765$		0			0
$766$	14.2999	−	8.63274i	0.516678	−	0.311914i
$767$	−0.256735			−0.00927017
$768$		0			0
$769$	21.4464			0.773376			0.386688	−	0.922211i	$-0.373619\pi$
$769$	21.4464			0.773376			0.386688	+	0.922211i	$0.373619\pi$
$770$	−47.2863	+	28.5463i	−1.70408	+	1.02874i
$771$		0			0
$772$	12.8663	−	24.4423i	0.463067	−	0.879696i
$773$		−	13.4164i		−	0.482555i	−0.970456	−	0.241278i	$-0.922434\pi$
$773$		−	13.4164i		−	0.482555i	0.970456	−	0.241278i	$-0.0775664\pi$
$774$		0			0
$775$	−1.21074			−0.0434910
$776$	0.328329	+	5.59747i	0.0117863	+	0.200938i
$777$		0			0
$778$	−11.3451	−	18.7929i	−0.406742	−	0.673760i
$779$		−	15.0824i		−	0.540384i
$780$		0			0
$781$			40.2591i			1.44058i
$782$	−7.27707	+	4.39309i	−0.260227	+	0.157097i
$783$		0			0
$784$	−37.4442	−	54.5308i	−1.33729	−	1.94753i
$785$	10.1065			0.360718
$786$		0			0
$787$		−	21.1342i		−	0.753351i	−0.926345	−	0.376676i	$-0.877067\pi$
$787$		−	21.1342i		−	0.753351i	0.926345	−	0.376676i	$-0.122933\pi$
$788$	−2.67357	−	1.40735i	−0.0952422	−	0.0501349i
$789$		0			0
$790$	−14.9815	−	24.8166i	−0.533019	−	0.882935i
$791$	−0.970421			−0.0345042
$792$		0			0
$793$	−11.1218			−0.394946
$794$	21.5681	+	35.7271i	0.765423	+	1.26791i
$795$		0			0
$796$	17.2426	−	32.7561i	0.611148	−	1.16101i
$797$			8.10762i			0.287187i	0.989637	+	0.143593i	$0.0458657\pi$
$797$			8.10762i			0.287187i	−0.989637	+	0.143593i	$0.954134\pi$
$798$		0			0
$799$	−5.32312			−0.188318
$800$	2.15718	+	0.978771i	0.0762677	+	0.0346048i
$801$		0			0
$802$	−37.9334	+	22.9000i	−1.33947	+	0.808627i
$803$			19.8606i			0.700867i
$804$		0			0
$805$		−	105.867i		−	3.73134i
$806$	−2.11320	−	3.50047i	−0.0744344	−	0.123299i
$807$		0			0
$808$	21.3063	−	1.24976i	0.749554	−	0.0439663i
$809$	−24.3604			−0.856466			−0.428233	−	0.903668i	$-0.640864\pi$
$809$	−24.3604			−0.856466			−0.428233	+	0.903668i	$0.640864\pi$
$810$		0			0
$811$		−	13.0002i		−	0.456499i	−0.973603	−	0.228249i	$-0.926700\pi$
$811$		−	13.0002i		−	0.456499i	0.973603	−	0.228249i	$-0.0733001\pi$
$812$	43.0846	+	22.6795i	1.51197	+	0.795894i
$813$		0			0
$814$	−24.0453	+	14.5159i	−0.842788	+	0.508783i
$815$	−41.4750			−1.45280
$816$		0			0
$817$	−1.72487			−0.0603454
$818$	36.4079	−	21.9791i	1.27297	−	0.768482i
$819$		0			0
$820$	−11.0826	−	5.83380i	−0.387020	−	0.203725i
$821$		−	5.77192i		−	0.201441i	−0.994915	−	0.100721i	$-0.967885\pi$
$821$		−	5.77192i		−	0.201441i	0.994915	−	0.100721i	$-0.0321148\pi$
$822$		0			0
$823$	−16.5936			−0.578418			−0.289209	−	0.957266i	$-0.593392\pi$
$823$	−16.5936			−0.578418			−0.289209	+	0.957266i	$0.593392\pi$
$824$	−2.35489	−	40.1470i	−0.0820363	−	1.39859i
$825$		0			0
$826$	0.910363	+	1.50800i	0.0316756	+	0.0524699i
$827$		−	28.4866i		−	0.990577i	−0.868728	−	0.495289i	$-0.835062\pi$
$827$		−	28.4866i		−	0.990577i	0.868728	−	0.495289i	$-0.164938\pi$
$828$		0			0
$829$		−	5.11118i		−	0.177519i	−0.996053	−	0.0887593i	$-0.971710\pi$
$829$		−	5.11118i		−	0.177519i	0.996053	−	0.0887593i	$-0.0282902\pi$
$830$	−37.9392	+	22.9035i	−1.31689	+	0.794993i
$831$		0			0
$832$	0.935288	+	7.94514i	0.0324253	+	0.275448i
$833$	10.6034			0.367387
$834$		0			0
$835$		−	39.9138i		−	1.38127i
$836$	18.0634	−	34.3154i	0.624736	−	1.18682i
$837$		0			0
$838$	13.5668	+	22.4732i	0.468659	+	0.776323i
$839$	7.99678			0.276080			0.138040	−	0.990427i	$-0.455920\pi$
$839$	7.99678			0.276080			0.138040	+	0.990427i	$0.455920\pi$
$840$		0			0
$841$	3.82027			0.131733
$842$	−12.8057	−	21.2124i	−0.441315	−	0.731029i
$843$		0			0
$844$	11.1905	+	5.89061i	0.385193	+	0.202763i
$845$			2.32782i			0.0800795i
$846$		0			0
$847$	4.65864			0.160073
$848$	5.30182	−	3.64056i	0.182065	−	0.125017i
$849$		0			0
$850$	−0.325074	+	0.196244i	−0.0111499	+	0.00673111i
$851$		−	53.8342i		−	1.84541i
$852$		0			0
$853$		−	9.26357i		−	0.317178i	−0.987345	−	0.158589i	$-0.949305\pi$
$853$		−	9.26357i		−	0.317178i	0.987345	−	0.158589i	$-0.0506946\pi$
$854$	39.4370	+	65.3266i	1.34951	+	2.23543i
$855$		0			0
$856$	27.8789	−	1.63528i	0.952880	−	0.0558927i
$857$	30.4342			1.03961			0.519807	−	0.854284i	$-0.326004\pi$
$857$	30.4342			1.03961			0.519807	+	0.854284i	$0.326004\pi$
$858$		0			0
$859$			26.7734i			0.913496i	0.889596	+	0.456748i	$0.150986\pi$
$859$			26.7734i			0.913496i	−0.889596	+	0.456748i	$0.849014\pi$
$860$	−0.667169	+	1.26743i	−0.0227503	+	0.0432191i
$861$		0			0
$862$	−29.7379	+	17.9525i	−1.01288	+	0.611464i
$863$	−24.5043			−0.834136			−0.417068	−	0.908875i	$-0.636942\pi$
$863$	−24.5043			−0.834136			−0.417068	+	0.908875i	$0.636942\pi$
$864$		0			0
$865$	58.2233			1.97965
$866$	−11.6912	+	7.05784i	−0.397282	+	0.239835i
$867$		0			0
$868$	−13.0676	+	24.8248i	−0.443545	+	0.842610i
$869$			30.4527i			1.03304i
$870$		0			0
$871$	−9.58901			−0.324911
$872$	−56.6441	+	3.32255i	−1.91821	+	0.112516i
$873$		0			0
$874$	38.4137	+	63.6315i	1.29936	+	2.15237i
$875$			51.7382i			1.74907i
$876$		0			0
$877$			11.7307i			0.396118i	0.980190	+	0.198059i	$0.0634637\pi$
$877$			11.7307i			0.396118i	−0.980190	+	0.198059i	$0.936536\pi$
$878$	3.50835	−	2.11796i	0.118401	−	0.0714776i
$879$		0			0
$880$	−18.2281	−	26.5460i	−0.614470	−	0.894865i
$881$	−27.1663			−0.915255			−0.457628	−	0.889144i	$-0.651301\pi$
$881$	−27.1663			−0.915255			−0.457628	+	0.889144i	$0.651301\pi$
$882$		0			0
$883$		−	12.5347i		−	0.421827i	−0.977505	−	0.210913i	$-0.932356\pi$
$883$		−	12.5347i		−	0.421827i	0.977505	−	0.210913i	$-0.0676438\pi$
$884$	−1.13476	−	0.597329i	−0.0381660	−	0.0200904i
$885$		0			0
$886$	−20.6272	−	34.1684i	−0.692983	−	1.14791i
$887$	25.4941			0.856007			0.428003	−	0.903777i	$-0.359217\pi$
$887$	25.4941			0.856007			0.428003	+	0.903777i	$0.359217\pi$
$888$		0			0
$889$	−17.3207			−0.580918
$890$	6.39672	+	10.5960i	0.214418	+	0.355179i
$891$		0			0
$892$	−18.2991	+	34.7631i	−0.612700	+	1.16396i
$893$			46.5459i			1.55760i
$894$		0			0
$895$	31.5433			1.05438
$896$	43.3513	−	33.6665i	1.44826	−	1.12472i
$897$		0			0
$898$	31.2198	−	18.8471i	1.04182	−	0.628936i
$899$		−	14.5082i		−	0.483877i
$900$		0			0
$901$			1.03093i			0.0343453i
$902$	6.79975	+	11.2636i	0.226407	+	0.375038i
$903$		0			0
$904$	−0.0331283	−	0.564783i	−0.00110183	−	0.0187844i
$905$	−4.31064			−0.143290
$906$		0			0
$907$			15.3279i			0.508954i	0.967079	+	0.254477i	$0.0819034\pi$
$907$			15.3279i			0.508954i	−0.967079	+	0.254477i	$0.918097\pi$
$908$	43.5241	+	22.9108i	1.44440	+	0.760322i
$909$		0			0
$910$	13.6730	−	8.25428i	0.453257	−	0.273627i
$911$	30.7673			1.01937			0.509684	−	0.860362i	$-0.329762\pi$
$911$	30.7673			1.01937			0.509684	+	0.860362i	$0.329762\pi$
$912$		0			0
$913$	46.5555			1.54076
$914$	2.30384	−	1.39081i	0.0762042	−	0.0460038i
$915$		0			0
$916$	−21.9415	−	11.5499i	−0.724966	−	0.381618i
$917$		−	21.2339i		−	0.701206i
$918$		0			0
$919$	44.6602			1.47320			0.736601	−	0.676327i	$-0.236429\pi$
$919$	44.6602			1.47320			0.736601	+	0.676327i	$0.236429\pi$
$920$	61.6147	−	3.61411i	2.03138	−	0.119154i
$921$		0			0
$922$	27.0093	+	44.7403i	0.889504	+	1.47344i
$923$		−	11.6411i		−	0.383172i
$924$		0			0
$925$		−	2.40483i		−	0.0790702i
$926$	2.44413	−	1.47550i	0.0803191	−	0.0484879i
$927$		0			0
$928$	−11.7286	+	25.8494i	−0.385010	+	0.848548i
$929$	44.5282			1.46092			0.730462	−	0.682953i	$-0.239305\pi$
$929$	44.5282			1.46092			0.730462	+	0.682953i	$0.239305\pi$
$930$		0			0
$931$		−	92.7176i		−	3.03870i
$932$	10.4609	−	19.8729i	0.342660	−	0.650957i
$933$		0			0
$934$	−14.5159	−	24.0453i	−0.474976	−	0.786787i
$935$	5.16183			0.168810
$936$		0			0
$937$	53.9513			1.76251			0.881257	−	0.472638i	$-0.156698\pi$
$937$	53.9513			1.76251			0.881257	+	0.472638i	$0.156698\pi$
$938$	34.0019	+	56.3234i	1.11020	+	1.83902i
$939$		0			0
$940$	34.2020	+	18.0037i	1.11555	+	0.587216i
$941$			55.4218i			1.80670i	0.428904	+	0.903350i	$0.358900\pi$
$941$			55.4218i			1.80670i	−0.428904	+	0.903350i	$0.641100\pi$
$942$		0			0
$943$	−25.2178			−0.821203
$944$	−0.846573	+	0.581310i	−0.0275536	+	0.0189200i
$945$		0			0
$946$	1.28814	−	0.777638i	0.0418811	−	0.0252832i
$947$			16.6074i			0.539669i	0.962907	+	0.269834i	$0.0869689\pi$
$947$			16.6074i			0.539669i	−0.962907	+	0.269834i	$0.913031\pi$
$948$		0			0
$949$		−	5.74279i		−	0.186419i
$950$	1.71598	+	2.84248i	0.0556737	+	0.0922222i
$951$		0			0
$952$	0.515202	+	8.78336i	0.0166978	+	0.284670i
$953$	−7.51944			−0.243579			−0.121789	−	0.992556i	$-0.538863\pi$
$953$	−7.51944			−0.243579			−0.121789	+	0.992556i	$0.538863\pi$
$954$		0			0
$955$		−	4.75009i		−	0.153709i
$956$	−24.3716	+	46.2992i	−0.788234	+	1.49742i
$957$		0			0
$958$	34.2958	−	20.7040i	1.10805	−	0.668917i
$959$	83.0964			2.68332
$960$		0			0
$961$	−22.6405			−0.730340
$962$	6.95282	−	4.19735i	0.224168	−	0.135328i
$963$		0			0
$964$	−5.50391	+	10.4559i	−0.177269	+	0.336761i
$965$		−	32.1493i		−	1.03492i
$966$		0			0
$967$	52.0597			1.67413			0.837063	−	0.547107i	$-0.184271\pi$
$967$	52.0597			1.67413			0.837063	+	0.547107i	$0.184271\pi$
$968$	0.159037	+	2.71132i	0.00511163	+	0.0871451i
$969$		0			0
$970$	3.37283	+	5.58702i	0.108295	+	0.179388i
$971$		−	22.4547i		−	0.720606i	−0.932835	−	0.360303i	$-0.882673\pi$
$971$		−	22.4547i		−	0.720606i	0.932835	−	0.360303i	$-0.117327\pi$
$972$		0			0
$973$			42.9272i			1.37618i
$974$	−1.10014	+	0.664142i	−0.0352506	+	0.0212805i
$975$		0			0
$976$	−36.6736	+	25.1824i	−1.17389	+	0.806069i
$977$	−10.2681			−0.328504			−0.164252	−	0.986418i	$-0.552521\pi$
$977$	−10.2681			−0.328504			−0.164252	+	0.986418i	$0.552521\pi$
$978$		0			0
$979$		−	13.0025i		−	0.415560i
$980$	−68.1290	−	35.8627i	−2.17630	−	1.14559i
$981$		0			0
$982$	−22.0015	−	36.4450i	−0.702097	−	1.16301i
$983$	42.4380			1.35356			0.676782	−	0.736184i	$-0.263374\pi$
$983$	42.4380			1.35356			0.676782	+	0.736184i	$0.263374\pi$
$984$		0			0
$985$	−3.51660			−0.112048
$986$	−2.35159	−	3.89535i	−0.0748898	−	0.124053i
$987$		0			0
$988$	−5.22311	+	9.92244i	−0.166169	+	0.315675i
$989$			2.88397i			0.0917050i
$990$		0			0
$991$	5.40792			0.171788			0.0858941	−	0.996304i	$-0.472625\pi$
$991$	5.40792			0.171788			0.0858941	+	0.996304i	$0.472625\pi$
$992$	−14.8941	−	6.75787i	−0.472888	−	0.214563i
$993$		0			0
$994$	−68.3769	+	41.2785i	−2.16878	+	1.30927i
$995$		−	43.0846i		−	1.36587i
$996$		0			0
$997$			27.2901i			0.864285i	0.901805	+	0.432142i	$0.142242\pi$
$997$			27.2901i			0.864285i	−0.901805	+	0.432142i	$0.857758\pi$
$998$	5.48351	+	9.08331i	0.173577	+	0.287527i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.g.f.469.19	yes	24
3.2	odd	2	inner	936.2.g.f.469.6	yes	24
4.3	odd	2		3744.2.g.f.1873.7		24
8.3	odd	2		3744.2.g.f.1873.8		24
8.5	even	2	inner	936.2.g.f.469.20	yes	24
12.11	even	2		3744.2.g.f.1873.4		24
24.5	odd	2	inner	936.2.g.f.469.5	✓	24
24.11	even	2		3744.2.g.f.1873.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.g.f.469.5	✓	24	24.5	odd	2	inner
936.2.g.f.469.6	yes	24	3.2	odd	2	inner
936.2.g.f.469.19	yes	24	1.1	even	1	trivial
936.2.g.f.469.20	yes	24	8.5	even	2	inner
3744.2.g.f.1873.3		24	24.11	even	2
3744.2.g.f.1873.4		24	12.11	even	2
3744.2.g.f.1873.7		24	4.3	odd	2
3744.2.g.f.1873.8		24	8.3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.21070 - 0.730889i) q^{2} +(0.931601 - 1.76978i) q^{4} -2.32782i q^{5} -4.85152 q^{7} +(-0.165621 - 2.82357i) q^{8} +(-1.70138 - 2.81830i) q^{10} +3.45836i q^{11} -1.00000i q^{13} +(-5.87375 + 3.54592i) q^{14} +(-2.26424 - 3.29746i) q^{16} +0.641186 q^{17} -5.60660i q^{19} +(-4.11973 - 2.16860i) q^{20} +(2.52768 + 4.18704i) q^{22} -9.37422 q^{23} -0.418756 q^{25} +(-0.730889 - 1.21070i) q^{26} +(-4.51968 + 8.58612i) q^{28} -5.01794i q^{29} +2.89128 q^{31} +(-5.15140 - 2.33733i) q^{32} +(0.776285 - 0.468636i) q^{34} +11.2935i q^{35} +5.74279i q^{37} +(-4.09780 - 6.78792i) q^{38} +(-6.57278 + 0.385537i) q^{40} +2.69012 q^{41} -0.307649i q^{43} +(6.12053 + 3.22181i) q^{44} +(-11.3494 + 6.85152i) q^{46} -8.30199 q^{47} +16.5372 q^{49} +(-0.506988 + 0.306064i) q^{50} +(-1.76978 - 0.931601i) q^{52} +1.60785i q^{53} +8.05044 q^{55} +(0.803515 + 13.6986i) q^{56} +(-3.66756 - 6.07523i) q^{58} -0.256735i q^{59} -11.1218i q^{61} +(3.50047 - 2.11320i) q^{62} +(-7.94514 + 0.935288i) q^{64} -2.32782 q^{65} -9.58901i q^{67} +(0.597329 - 1.13476i) q^{68} +(8.25428 + 13.6730i) q^{70} +11.6411 q^{71} +5.74279 q^{73} +(4.19735 + 6.95282i) q^{74} +(-9.92244 - 5.22311i) q^{76} -16.7783i q^{77} +8.80552 q^{79} +(-7.67589 + 5.27074i) q^{80} +(3.25693 - 1.96618i) q^{82} -13.4617i q^{83} -1.49257i q^{85} +(-0.224858 - 0.372472i) q^{86} +(9.76493 - 0.572778i) q^{88} -3.75972 q^{89} +4.85152i q^{91} +(-8.73303 + 16.5903i) q^{92} +(-10.0512 + 6.06784i) q^{94} -13.0512 q^{95} -1.98241 q^{97} +(20.0217 - 12.0869i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{4} - 8 q^{7} + 12 q^{10} - 4 q^{16} + 4 q^{22} - 24 q^{25} + 8 q^{28} + 40 q^{31} - 16 q^{34} - 36 q^{40} - 24 q^{46} + 24 q^{49} - 4 q^{52} - 16 q^{55} - 24 q^{58} + 8 q^{64} - 16 q^{70} - 16 q^{76}+ \cdots - 16 q^{97}+O(q^{100}) \) 24 * q + 8 * q^4 - 8 * q^7 + 12 * q^10 - 4 * q^16 + 4 * q^22 - 24 * q^25 + 8 * q^28 + 40 * q^31 - 16 * q^34 - 36 * q^40 - 24 * q^46 + 24 * q^49 - 4 * q^52 - 16 * q^55 - 24 * q^58 + 8 * q^64 - 16 * q^70 - 16 * q^76 + 68 * q^82 + 28 * q^88 + 12 * q^94 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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