LMFDB - Embedded newform 840.2.cp.b.521.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(521,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.521"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.cp (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.12
Character	$\chi$	$=$	840.521
Dual form			840.2.cp.b.761.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.46285 - 0.927396i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.49899 - 2.18014i) q^{7} +(1.27987 - 2.71329i) q^{9} +(-5.52920 - 3.19228i) q^{11} +0.186273i q^{13} +(1.53457 + 0.803169i) q^{15} +(3.85223 - 6.67225i) q^{17} +(-5.08695 + 2.93695i) q^{19} +(-4.21466 - 1.79907i) q^{21} +(0.256657 - 0.148181i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-0.644024 - 5.15609i) q^{27} -8.18311i q^{29} +(5.76880 + 3.33062i) q^{31} +(-11.0489 + 0.457915i) q^{33} +(1.13856 - 2.38824i) q^{35} +(1.69885 + 2.94249i) q^{37} +(0.172749 + 0.272490i) q^{39} +9.67409 q^{41} -0.268806 q^{43} +(2.98971 - 0.248240i) q^{45} +(2.93140 + 5.07734i) q^{47} +(-2.50604 + 6.53604i) q^{49} +(-0.552580 - 13.3331i) q^{51} +(2.72386 + 1.57262i) q^{53} -6.38457i q^{55} +(-4.71774 + 9.01394i) q^{57} +(-3.55719 + 6.16123i) q^{59} +(5.46516 - 3.15531i) q^{61} +(-7.83387 + 1.27689i) q^{63} +(-0.161317 + 0.0931364i) q^{65} +(0.460841 - 0.798199i) q^{67} +(0.238028 - 0.454789i) q^{69} -7.44163i q^{71} +(-5.90097 - 3.40693i) q^{73} +(0.0717222 + 1.73057i) q^{75} +(1.32860 + 16.8396i) q^{77} +(0.455092 + 0.788242i) q^{79} +(-5.72385 - 6.94533i) q^{81} -1.79069 q^{83} +7.70445 q^{85} +(-7.58898 - 11.9707i) q^{87} +(-3.80761 - 6.59498i) q^{89} +(0.406101 - 0.279222i) q^{91} +(11.5277 - 0.477758i) q^{93} +(-5.08695 - 2.93695i) q^{95} +10.2378i q^{97} +(-15.7383 + 10.9166i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{5} - 2 q^{7} + 8 q^{9} + 6 q^{19} - 14 q^{21} + 24 q^{23} - 16 q^{25} + 24 q^{27} + 42 q^{31} + 18 q^{33} + 2 q^{35} + 6 q^{37} + 12 q^{39} + 44 q^{41} - 20 q^{43} + 10 q^{45} + 4 q^{47} + 16 q^{49}+ \cdots - 8 q^{99}+O(q^{100}) $ 32 * q + 16 * q^5 - 2 * q^7 + 8 * q^9 + 6 * q^19 - 14 * q^21 + 24 * q^23 - 16 * q^25 + 24 * q^27 + 42 * q^31 + 18 * q^33 + 2 * q^35 + 6 * q^37 + 12 * q^39 + 44 * q^41 - 20 * q^43 + 10 * q^45 + 4 * q^47 + 16 * q^49 - 36 * q^51 + 12 * q^59 - 18 * q^61 + 34 * q^63 - 6 * q^65 - 6 * q^67 - 34 * q^69 - 6 * q^73 + 40 * q^77 - 2 * q^79 - 12 * q^81 - 88 * q^83 - 72 * q^87 - 6 * q^89 - 26 * q^91 + 50 * q^93 + 6 * q^95 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	1.46285	−	0.927396i	0.844578	−	0.535432i
$3$	1.46285	−	0.927396i	0.844578	−	0.535432i
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−1.49899	−	2.18014i	−0.566566	−	0.824016i
$7$	−1.49899	−	2.18014i	−0.566566	−	0.824016i
$8$		0			0
$9$	1.27987	−	2.71329i	0.426625	−	0.904429i
$10$		0			0
$11$	−5.52920	−	3.19228i	−1.66712	−	0.962510i	−0.969182	−	0.246347i	$-0.920770\pi$
$11$	−5.52920	−	3.19228i	−1.66712	−	0.962510i	−0.697934	−	0.716162i	$-0.745897\pi$
$12$		0			0
$13$			0.186273i			0.0516628i	0.999666	+	0.0258314i	$0.00822330\pi$
$13$			0.186273i			0.0516628i	−0.999666	+	0.0258314i	$0.991777\pi$
$14$		0			0
$15$	1.53457	+	0.803169i	0.396225	+	0.207377i
$16$		0			0
$17$	3.85223	−	6.67225i	0.934302	−	1.61826i	0.158429	−	0.987370i	$-0.449357\pi$
$17$	3.85223	−	6.67225i	0.934302	−	1.61826i	0.775874	−	0.630888i	$-0.217309\pi$
$18$		0			0
$19$	−5.08695	+	2.93695i	−1.16703	+	0.673783i	−0.952978	−	0.303040i	$-0.901998\pi$
$19$	−5.08695	+	2.93695i	−1.16703	+	0.673783i	−0.214048	+	0.976823i	$0.568665\pi$
$20$		0			0
$21$	−4.21466	−	1.79907i	−0.919714	−	0.392588i
$22$		0			0
$23$	0.256657	−	0.148181i	0.0535166	−	0.0308978i	−0.473003	−	0.881061i	$-0.656830\pi$
$23$	0.256657	−	0.148181i	0.0535166	−	0.0308978i	0.526520	+	0.850163i	$0.323497\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−0.644024	−	5.15609i	−0.123942	−	0.992289i
$28$		0			0
$29$		−	8.18311i		−	1.51957i	−0.650177	−	0.759783i	$-0.725305\pi$
$29$		−	8.18311i		−	1.51957i	0.650177	−	0.759783i	$-0.274695\pi$
$30$		0			0
$31$	5.76880	+	3.33062i	1.03611	+	0.598197i	0.918728	−	0.394891i	$-0.129217\pi$
$31$	5.76880	+	3.33062i	1.03611	+	0.598197i	0.117379	+	0.993087i	$0.462551\pi$
$32$		0			0
$33$	−11.0489	+	0.457915i	−1.92337	+	0.0797127i
$34$		0			0
$35$	1.13856	−	2.38824i	0.192452	−	0.403686i
$36$		0			0
$37$	1.69885	+	2.94249i	0.279289	+	0.483742i	0.971208	−	0.238233i	$-0.0765681\pi$
$37$	1.69885	+	2.94249i	0.279289	+	0.483742i	−0.691920	+	0.721975i	$0.743235\pi$
$38$		0			0
$39$	0.172749	+	0.272490i	0.0276619	+	0.0436333i
$40$		0			0
$41$	9.67409			1.51084			0.755419	−	0.655242i	$-0.227433\pi$
$41$	9.67409			1.51084			0.755419	+	0.655242i	$0.227433\pi$
$42$		0			0
$43$	−0.268806			−0.0409926			−0.0204963	−	0.999790i	$-0.506525\pi$
$43$	−0.268806			−0.0409926			−0.0204963	+	0.999790i	$0.506525\pi$
$44$		0			0
$45$	2.98971	−	0.248240i	0.445680	−	0.0370054i
$46$		0			0
$47$	2.93140	+	5.07734i	0.427589	+	0.740606i	0.996658	−	0.0816835i	$-0.0260297\pi$
$47$	2.93140	+	5.07734i	0.427589	+	0.740606i	−0.569069	+	0.822290i	$0.692696\pi$
$48$		0			0
$49$	−2.50604	+	6.53604i	−0.358005	+	0.933720i
$50$		0			0
$51$	−0.552580	−	13.3331i	−0.0773767	−	1.86700i
$52$		0			0
$53$	2.72386	+	1.57262i	0.374151	+	0.216016i	0.675270	−	0.737570i	$-0.264027\pi$
$53$	2.72386	+	1.57262i	0.374151	+	0.216016i	−0.301120	+	0.953586i	$0.597360\pi$
$54$		0			0
$55$		−	6.38457i		−	0.860895i
$56$		0			0
$57$	−4.71774	+	9.01394i	−0.624880	+	1.19393i
$58$		0			0
$59$	−3.55719	+	6.16123i	−0.463107	+	0.802124i	−0.999114	−	0.0420891i	$-0.986599\pi$
$59$	−3.55719	+	6.16123i	−0.463107	+	0.802124i	0.536007	+	0.844213i	$0.319932\pi$
$60$		0			0
$61$	5.46516	−	3.15531i	0.699742	−	0.403996i	−0.107510	−	0.994204i	$-0.534288\pi$
$61$	5.46516	−	3.15531i	0.699742	−	0.403996i	0.807251	+	0.590208i	$0.200954\pi$
$62$		0			0
$63$	−7.83387	+	1.27689i	−0.986975	+	0.160873i
$64$		0			0
$65$	−0.161317	+	0.0931364i	−0.0200089	+	0.0115521i
$66$		0			0
$67$	0.460841	−	0.798199i	0.0563006	−	0.0975156i	−0.836501	−	0.547965i	$-0.815403\pi$
$67$	0.460841	−	0.798199i	0.0563006	−	0.0975156i	0.892802	+	0.450449i	$0.148736\pi$
$68$		0			0
$69$	0.238028	−	0.454789i	0.0286553	−	0.0547501i
$70$		0			0
$71$		−	7.44163i		−	0.883159i	−0.897222	−	0.441579i	$-0.854418\pi$
$71$		−	7.44163i		−	0.883159i	0.897222	−	0.441579i	$-0.145582\pi$
$72$		0			0
$73$	−5.90097	−	3.40693i	−0.690656	−	0.398751i	0.113202	−	0.993572i	$-0.463889\pi$
$73$	−5.90097	−	3.40693i	−0.690656	−	0.398751i	−0.803858	+	0.594821i	$0.797223\pi$
$74$		0			0
$75$	0.0717222	+	1.73057i	0.00828176	+	0.199828i
$76$		0			0
$77$	1.32860	+	16.8396i	0.151408	+	1.91906i
$78$		0			0
$79$	0.455092	+	0.788242i	0.0512018	+	0.0886842i	0.890490	−	0.455002i	$-0.150361\pi$
$79$	0.455092	+	0.788242i	0.0512018	+	0.0886842i	−0.839289	+	0.543686i	$0.817028\pi$
$80$		0			0
$81$	−5.72385	−	6.94533i	−0.635983	−	0.771703i
$82$		0			0
$83$	−1.79069			−0.196554			−0.0982770	−	0.995159i	$-0.531333\pi$
$83$	−1.79069			−0.196554			−0.0982770	+	0.995159i	$0.531333\pi$
$84$		0			0
$85$	7.70445			0.835665
$86$		0			0
$87$	−7.58898	−	11.9707i	−0.813624	−	1.28339i
$88$		0			0
$89$	−3.80761	−	6.59498i	−0.403606	−	0.699067i	0.590552	−	0.807000i	$-0.298910\pi$
$89$	−3.80761	−	6.59498i	−0.403606	−	0.699067i	−0.994158	+	0.107933i	$0.965577\pi$
$90$		0			0
$91$	0.406101	−	0.279222i	0.0425710	−	0.0292704i
$92$		0			0
$93$	11.5277	−	0.477758i	1.19537	−	0.0495412i
$94$		0			0
$95$	−5.08695	−	2.93695i	−0.521910	−	0.301325i
$96$		0			0
$97$			10.2378i			1.03949i	0.854320	+	0.519747i	$0.173974\pi$
$97$			10.2378i			1.03949i	−0.854320	+	0.519747i	$0.826026\pi$
$98$		0			0
$99$	−15.7383	+	10.9166i	−1.58175	+	1.09716i
$100$		0			0
$101$	2.89920	−	5.02156i	0.288481	−	0.499664i	−0.684966	−	0.728575i	$-0.740183\pi$
$101$	2.89920	−	5.02156i	0.288481	−	0.499664i	0.973447	+	0.228911i	$0.0735164\pi$
$102$		0			0
$103$	1.75128	−	1.01110i	0.172559	−	0.0996267i	−0.411233	−	0.911530i	$-0.634902\pi$
$103$	1.75128	−	1.01110i	0.172559	−	0.0996267i	0.583792	+	0.811903i	$0.301568\pi$
$104$		0			0
$105$	−0.549294	−	4.54954i	−0.0536056	−	0.443989i
$106$		0			0
$107$	0.633070	−	0.365503i	0.0612012	−	0.0353345i	−0.469087	−	0.883152i	$-0.655417\pi$
$107$	0.633070	−	0.365503i	0.0612012	−	0.0353345i	0.530288	+	0.847817i	$0.322084\pi$
$108$		0			0
$109$	−4.20454	+	7.28248i	−0.402722	+	0.697535i	−0.994053	−	0.108894i	$-0.965269\pi$
$109$	−4.20454	+	7.28248i	−0.402722	+	0.697535i	0.591332	+	0.806429i	$0.298602\pi$
$110$		0			0
$111$	5.21401	+	2.72892i	0.494892	+	0.259018i
$112$		0			0
$113$			13.7653i			1.29493i	0.762094	+	0.647467i	$0.224172\pi$
$113$			13.7653i			1.29493i	−0.762094	+	0.647467i	$0.775828\pi$
$114$		0			0
$115$	0.256657	+	0.148181i	0.0239334	+	0.0138179i
$116$		0			0
$117$	0.505411	+	0.238406i	0.0467253	+	0.0220406i
$118$		0			0
$119$	−20.3209	+	1.60326i	−1.86282	+	0.146971i
$120$		0			0
$121$	14.8813	+	25.7752i	1.35285	+	2.34320i
$122$		0			0
$123$	14.1518	−	8.97171i	1.27602	−	0.808952i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	15.6325			1.38716			0.693581	−	0.720378i	$-0.256032\pi$
$127$	15.6325			1.38716			0.693581	+	0.720378i	$0.256032\pi$
$128$		0			0
$129$	−0.393224	+	0.249290i	−0.0346214	+	0.0219488i
$130$		0			0
$131$	−6.01615	−	10.4203i	−0.525633	−	0.910423i	−0.999554	−	0.0298561i	$-0.990495\pi$
$131$	−6.01615	−	10.4203i	−0.525633	−	0.910423i	0.473921	−	0.880567i	$-0.342838\pi$
$132$		0			0
$133$	14.0283	+	6.68780i	1.21641	+	0.579906i
$134$		0			0
$135$	4.14329	−	3.13578i	0.356598	−	0.269885i
$136$		0			0
$137$	−13.9423	−	8.04958i	−1.19117	−	0.687722i	−0.232597	−	0.972573i	$-0.574722\pi$
$137$	−13.9423	−	8.04958i	−1.19117	−	0.687722i	−0.958572	+	0.284851i	$0.908056\pi$
$138$		0			0
$139$		−	5.98676i		−	0.507790i	−0.967232	−	0.253895i	$-0.918288\pi$
$139$		−	5.98676i		−	0.507790i	0.967232	−	0.253895i	$-0.0817118\pi$
$140$		0			0
$141$	8.99691	+	4.70883i	0.757677	+	0.396555i
$142$		0			0
$143$	0.594636	−	1.02994i	0.0497259	−	0.0861278i
$144$		0			0
$145$	7.08678	−	4.09155i	0.588525	−	0.339785i
$146$		0			0
$147$	2.39553	+	11.8853i	0.197580	+	0.980287i
$148$		0			0
$149$	7.96751	−	4.60004i	0.652724	−	0.376850i	−0.136775	−	0.990602i	$-0.543674\pi$
$149$	7.96751	−	4.60004i	0.652724	−	0.376850i	0.789499	+	0.613752i	$0.210341\pi$
$150$		0			0
$151$	8.48055	−	14.6887i	0.690138	−	1.19535i	−0.281655	−	0.959516i	$-0.590883\pi$
$151$	8.48055	−	14.6887i	0.690138	−	1.19535i	0.971792	−	0.235838i	$-0.0757834\pi$
$152$		0			0
$153$	−13.1734	−	18.9918i	−1.06500	−	1.53540i
$154$		0			0
$155$			6.66124i			0.535043i
$156$		0			0
$157$	−9.96405	−	5.75274i	−0.795217	−	0.459119i	0.0465787	−	0.998915i	$-0.485168\pi$
$157$	−9.96405	−	5.75274i	−0.795217	−	0.459119i	−0.841796	+	0.539796i	$0.818502\pi$
$158$		0			0
$159$	5.44304	−	0.225583i	0.431662	−	0.0178899i
$160$		0			0
$161$	−0.707782	−	0.337426i	−0.0557810	−	0.0265929i
$162$		0			0
$163$	−3.55503	−	6.15749i	−0.278451	−	0.482292i	0.692549	−	0.721371i	$-0.256488\pi$
$163$	−3.55503	−	6.15749i	−0.278451	−	0.482292i	−0.971000	+	0.239079i	$0.923154\pi$
$164$		0			0
$165$	−5.92102	−	9.33968i	−0.460951	−	0.727093i
$166$		0			0
$167$	13.7041			1.06045			0.530227	−	0.847856i	$-0.322107\pi$
$167$	13.7041			1.06045			0.530227	+	0.847856i	$0.322107\pi$
$168$		0			0
$169$	12.9653			0.997331
$170$		0			0
$171$	1.45814	+	17.5613i	0.111506	+	1.34294i
$172$		0			0
$173$	6.51565	+	11.2854i	0.495375	+	0.858015i	0.999986	−	0.00533192i	$-0.00169721\pi$
$173$	6.51565	+	11.2854i	0.495375	+	0.858015i	−0.504610	+	0.863347i	$0.668364\pi$
$174$		0			0
$175$	2.63755	−	0.208095i	0.199380	−	0.0157305i
$176$		0			0
$177$	0.510259	+	12.3119i	0.0383534	+	0.925419i
$178$		0			0
$179$	7.68352	+	4.43608i	0.574293	+	0.331568i	0.758862	−	0.651251i	$-0.225756\pi$
$179$	7.68352	+	4.43608i	0.574293	+	0.331568i	−0.184569	+	0.982820i	$0.559089\pi$
$180$		0			0
$181$		−	16.2986i		−	1.21147i	−0.795668	−	0.605733i	$-0.792880\pi$
$181$		−	16.2986i		−	1.21147i	0.795668	−	0.605733i	$-0.207120\pi$
$182$		0			0
$183$	5.06850	−	9.68412i	0.374674	−	0.715870i
$184$		0			0
$185$	−1.69885	+	2.94249i	−0.124902	+	0.216336i
$186$		0			0
$187$	−42.5994	+	24.5948i	−3.11518	+	1.79855i
$188$		0			0
$189$	−10.2756	+	9.13300i	−0.747441	+	0.664328i
$190$		0			0
$191$	−8.26384	+	4.77113i	−0.597950	+	0.345227i	−0.768235	−	0.640168i	$-0.778865\pi$
$191$	−8.26384	+	4.77113i	−0.597950	+	0.345227i	0.170285	+	0.985395i	$0.445531\pi$
$192$		0			0
$193$	−6.93115	+	12.0051i	−0.498915	+	0.864147i	−0.999999	−	0.00125197i	$-0.999601\pi$
$193$	−6.93115	+	12.0051i	−0.498915	+	0.864147i	0.501084	+	0.865399i	$0.332935\pi$
$194$		0			0
$195$	−0.149609	+	0.285850i	−0.0107137	+	0.0204701i
$196$		0			0
$197$			26.2096i			1.86736i	0.358110	+	0.933679i	$0.383421\pi$
$197$			26.2096i			1.86736i	−0.358110	+	0.933679i	$0.616579\pi$
$198$		0			0
$199$	14.2763	+	8.24244i	1.01202	+	0.584291i	0.911783	−	0.410673i	$-0.134706\pi$
$199$	14.2763	+	8.24244i	1.01202	+	0.584291i	0.100238	+	0.994963i	$0.468039\pi$
$200$		0			0
$201$	−0.0661050	−	1.59503i	−0.00466268	−	0.112505i
$202$		0			0
$203$	−17.8403	+	12.2664i	−1.25215	+	0.860934i
$204$		0			0
$205$	4.83704	+	8.37801i	0.337834	+	0.585145i
$206$		0			0
$207$	−0.0735687	−	0.886035i	−0.00511338	−	0.0615837i
$208$		0			0
$209$	37.5023			2.59409
$210$		0			0
$211$	25.5398			1.75823			0.879116	−	0.476607i	$-0.158134\pi$
$211$	25.5398			1.75823			0.879116	+	0.476607i	$0.158134\pi$
$212$		0			0
$213$	−6.90134	−	10.8860i	−0.472872	−	0.745897i
$214$		0			0
$215$	−0.134403	−	0.232793i	−0.00916622	−	0.0158764i
$216$		0			0
$217$	−1.38617	−	17.5694i	−0.0940995	−	1.19269i
$218$		0			0
$219$	−11.7918	+	0.488704i	−0.796817	+	0.0330236i
$220$		0			0
$221$	1.24286	+	0.717565i	0.0836038	+	0.0482687i
$222$		0			0
$223$			25.7724i			1.72585i	0.505332	+	0.862925i	$0.331370\pi$
$223$			25.7724i			1.72585i	−0.505332	+	0.862925i	$0.668630\pi$
$224$		0			0
$225$	1.70984	+	2.46505i	0.113989	+	0.164336i
$226$		0			0
$227$	6.73748	−	11.6697i	0.447182	−	0.774542i	−0.551019	−	0.834493i	$-0.685761\pi$
$227$	6.73748	−	11.6697i	0.447182	−	0.774542i	0.998201	+	0.0599504i	$0.0190942\pi$
$228$		0			0
$229$	4.38539	−	2.53190i	0.289794	−	0.167313i	−0.348055	−	0.937474i	$-0.613158\pi$
$229$	4.38539	−	2.53190i	0.289794	−	0.167313i	0.637849	+	0.770161i	$0.279824\pi$
$230$		0			0
$231$	17.5606	+	23.4018i	1.15540	+	1.53972i
$232$		0			0
$233$	−2.66056	+	1.53607i	−0.174299	+	0.100632i	−0.584611	−	0.811313i	$-0.698753\pi$
$233$	−2.66056	+	1.53607i	−0.174299	+	0.100632i	0.410312	+	0.911945i	$0.365420\pi$
$234$		0			0
$235$	−2.93140	+	5.07734i	−0.191224	+	0.331209i
$236$		0			0
$237$	1.39674	+	0.731032i	0.0907283	+	0.0474856i
$238$		0			0
$239$			22.8326i			1.47692i	0.674299	+	0.738459i	$0.264446\pi$
$239$			22.8326i			1.47692i	−0.674299	+	0.738459i	$0.735554\pi$
$240$		0			0
$241$	−16.3478	−	9.43842i	−1.05306	−	0.607982i	−0.129552	−	0.991573i	$-0.541354\pi$
$241$	−16.3478	−	9.43842i	−1.05306	−	0.607982i	−0.923503	+	0.383591i	$0.874687\pi$
$242$		0			0
$243$	−14.8142	−	4.85172i	−0.950332	−	0.311238i
$244$		0			0
$245$	−6.91339	+	1.09773i	−0.441680	+	0.0701311i
$246$		0			0
$247$	−0.547074	−	0.947560i	−0.0348095	−	0.0602918i
$248$		0			0
$249$	−2.61952	+	1.66068i	−0.166005	+	0.105241i
$250$		0			0
$251$	−3.16383			−0.199699			−0.0998495	−	0.995003i	$-0.531836\pi$
$251$	−3.16383			−0.199699			−0.0998495	+	0.995003i	$0.531836\pi$
$252$		0			0
$253$	−1.89214			−0.118958
$254$		0			0
$255$	11.2705	−	7.14508i	0.705785	−	0.447442i
$256$		0			0
$257$	−1.44622	−	2.50492i	−0.0902125	−	0.156253i	0.817388	−	0.576088i	$-0.195421\pi$
$257$	−1.44622	−	2.50492i	−0.0902125	−	0.156253i	−0.907600	+	0.419835i	$0.862088\pi$
$258$		0			0
$259$	3.86848	−	8.11449i	0.240376	−	0.504210i
$260$		0			0
$261$	−22.2031	−	10.4733i	−1.37434	−	0.648284i
$262$		0			0
$263$	6.36015	+	3.67203i	0.392184	+	0.226427i	0.683106	−	0.730319i	$-0.260629\pi$
$263$	6.36015	+	3.67203i	0.392184	+	0.226427i	−0.290922	+	0.956747i	$0.593962\pi$
$264$		0			0
$265$			3.14524i			0.193211i
$266$		0			0
$267$	−11.6861	−	6.11632i	−0.715180	−	0.374313i
$268$		0			0
$269$	−9.55236	+	16.5452i	−0.582418	+	1.00878i	0.412774	+	0.910833i	$0.364560\pi$
$269$	−9.55236	+	16.5452i	−0.582418	+	1.00878i	−0.995192	+	0.0979438i	$0.968773\pi$
$270$		0			0
$271$	15.3258	−	8.84835i	0.930976	−	0.537499i	0.0438557	−	0.999038i	$-0.486036\pi$
$271$	15.3258	−	8.84835i	0.930976	−	0.537499i	0.887120	+	0.461539i	$0.152702\pi$
$272$		0			0
$273$	0.335117	−	0.785077i	0.0202822	−	0.0475150i
$274$		0			0
$275$	5.52920	−	3.19228i	0.333423	−	0.192502i
$276$		0			0
$277$	−9.88120	+	17.1147i	−0.593704	+	1.02832i	0.400025	+	0.916504i	$0.369001\pi$
$277$	−9.88120	+	17.1147i	−0.593704	+	1.02832i	−0.993728	+	0.111820i	$0.964332\pi$
$278$		0			0
$279$	16.4203	−	11.3896i	0.983055	−	0.681880i
$280$		0			0
$281$		−	4.51698i		−	0.269460i	−0.990882	−	0.134730i	$-0.956983\pi$
$281$		−	4.51698i		−	0.269460i	0.990882	−	0.134730i	$-0.0430168\pi$
$282$		0			0
$283$	0.652832	+	0.376913i	0.0388068	+	0.0224051i	0.519278	−	0.854605i	$-0.326201\pi$
$283$	0.652832	+	0.376913i	0.0388068	+	0.0224051i	−0.480471	+	0.877011i	$0.659534\pi$
$284$		0			0
$285$	−10.1652	+	0.421289i	−0.602133	+	0.0249550i
$286$		0			0
$287$	−14.5014	−	21.0909i	−0.855990	−	1.24496i
$288$		0			0
$289$	−21.1793	−	36.6836i	−1.24584	−	2.15786i
$290$		0			0
$291$	9.49453	+	14.9764i	0.556579	+	0.877935i
$292$		0			0
$293$	−3.44976			−0.201537			−0.100769	−	0.994910i	$-0.532130\pi$
$293$	−3.44976			−0.201537			−0.100769	+	0.994910i	$0.532130\pi$
$294$		0			0
$295$	−7.11438			−0.414215
$296$		0			0
$297$	−12.8988	+	30.5649i	−0.748462	+	1.77356i
$298$		0			0
$299$	0.0276020	+	0.0478081i	0.00159627	+	0.00276482i
$300$		0			0
$301$	0.402939	+	0.586036i	0.0232250	+	0.0337786i
$302$		0			0
$303$	−0.415874	−	10.0345i	−0.0238913	−	0.576468i
$304$		0			0
$305$	5.46516	+	3.15531i	0.312934	+	0.180673i
$306$		0			0
$307$		−	7.65577i		−	0.436938i	−0.975844	−	0.218469i	$-0.929894\pi$
$307$		−	7.65577i		−	0.436938i	0.975844	−	0.218469i	$-0.0701062\pi$
$308$		0			0
$309$	1.62417	−	3.10322i	0.0923959	−	0.176536i
$310$		0			0
$311$	16.5003	−	28.5794i	0.935649	−	1.62059i	0.162176	−	0.986762i	$-0.448149\pi$
$311$	16.5003	−	28.5794i	0.935649	−	1.62059i	0.773473	−	0.633830i	$-0.218518\pi$
$312$		0			0
$313$	15.8777	−	9.16700i	0.897461	−	0.518149i	0.0210856	−	0.999778i	$-0.493288\pi$
$313$	15.8777	−	9.16700i	0.897461	−	0.518149i	0.876376	+	0.481628i	$0.159954\pi$
$314$		0			0
$315$	−5.02276	−	6.14589i	−0.283000	−	0.346281i
$316$		0			0
$317$	2.30074	−	1.32833i	0.129222	−	0.0746066i	−0.433995	−	0.900915i	$-0.642897\pi$
$317$	2.30074	−	1.32833i	0.129222	−	0.0746066i	0.563218	+	0.826309i	$0.309563\pi$
$318$		0			0
$319$	−26.1228	+	45.2460i	−1.46260	+	2.53329i
$320$		0			0
$321$	0.587122	−	1.12178i	0.0327699	−	0.0626118i
$322$		0			0
$323$			45.2552i			2.51807i
$324$		0			0
$325$	−0.161317	−	0.0931364i	−0.00894826	−	0.00516628i
$326$		0			0
$327$	0.603117	+	14.5525i	0.0333525	+	0.804753i
$328$		0			0
$329$	6.67517	−	14.0018i	0.368014	−	0.771943i
$330$		0			0
$331$	−1.81649	−	3.14626i	−0.0998435	−	0.172934i	0.811776	−	0.583969i	$-0.198501\pi$
$331$	−1.81649	−	3.14626i	−0.0998435	−	0.172934i	−0.911620	+	0.411035i	$0.865168\pi$
$332$		0			0
$333$	10.1581	−	0.843442i	0.556661	−	0.0462203i
$334$		0			0
$335$	0.921681			0.0503568
$336$		0			0
$337$	−0.531227			−0.0289378			−0.0144689	−	0.999895i	$-0.504606\pi$
$337$	−0.531227			−0.0289378			−0.0144689	+	0.999895i	$0.504606\pi$
$338$		0			0
$339$	12.7659	+	20.1366i	0.693349	+	1.09367i
$340$		0			0
$341$	−21.2646	−	36.8313i	−1.15154	−	1.99453i
$342$		0			0
$343$	18.0060	−	4.33396i	0.972234	−	0.234012i
$344$		0			0
$345$	0.512873	−	0.0212557i	0.0276121	−	0.00114437i
$346$		0			0
$347$	−3.54279	−	2.04543i	−0.190187	−	0.109804i	0.401883	−	0.915691i	$-0.368356\pi$
$347$	−3.54279	−	2.04543i	−0.190187	−	0.109804i	−0.592070	+	0.805886i	$0.701689\pi$
$348$		0			0
$349$		−	16.0422i		−	0.858719i	−0.903134	−	0.429359i	$-0.858739\pi$
$349$		−	16.0422i		−	0.858719i	0.903134	−	0.429359i	$-0.141261\pi$
$350$		0			0
$351$	0.960439	−	0.119964i	0.0512644	−	0.00640321i
$352$		0			0
$353$	8.44835	−	14.6330i	0.449660	−	0.778835i	−0.548703	−	0.836017i	$-0.684878\pi$
$353$	8.44835	−	14.6330i	0.449660	−	0.778835i	0.998364	+	0.0571826i	$0.0182117\pi$
$354$		0			0
$355$	6.44464	−	3.72081i	0.342046	−	0.197480i
$356$		0			0
$357$	−28.2396	+	21.1909i	−1.49460	+	1.12154i
$358$		0			0
$359$	−7.48646	+	4.32231i	−0.395120	+	0.228123i	−0.684376	−	0.729129i	$-0.739925\pi$
$359$	−7.48646	+	4.32231i	−0.395120	+	0.228123i	0.289256	+	0.957252i	$0.406592\pi$
$360$		0			0
$361$	7.75136	−	13.4257i	0.407966	−	0.706618i
$362$		0			0
$363$	45.6731	+	23.9045i	2.39721	+	1.25466i
$364$		0			0
$365$		−	6.81385i		−	0.356653i
$366$		0			0
$367$	8.61874	+	4.97603i	0.449895	+	0.259747i	0.707786	−	0.706427i	$-0.249694\pi$
$367$	8.61874	+	4.97603i	0.449895	+	0.259747i	−0.257891	+	0.966174i	$0.583028\pi$
$368$		0			0
$369$	12.3816	−	26.2486i	0.644561	−	1.36645i
$370$		0			0
$371$	−0.654510	−	8.29575i	−0.0339805	−	0.430694i
$372$		0			0
$373$	−3.22411	−	5.58432i	−0.166938	−	0.289145i	0.770404	−	0.637556i	$-0.220055\pi$
$373$	−3.22411	−	5.58432i	−0.166938	−	0.289145i	−0.937342	+	0.348411i	$0.886721\pi$
$374$		0			0
$375$	−1.46285	+	0.927396i	−0.0755414	+	0.0478905i
$376$		0			0
$377$	1.52429			0.0785050
$378$		0			0
$379$	8.30224			0.426458			0.213229	−	0.977002i	$-0.431602\pi$
$379$	8.30224			0.426458			0.213229	+	0.977002i	$0.431602\pi$
$380$		0			0
$381$	22.8681	−	14.4975i	1.17157	−	0.742731i
$382$		0			0
$383$	−15.3085	−	26.5152i	−0.782230	−	1.35486i	−0.930640	−	0.365936i	$-0.880749\pi$
$383$	−15.3085	−	26.5152i	−0.782230	−	1.35486i	0.148410	−	0.988926i	$-0.452584\pi$
$384$		0			0
$385$	−13.9193	+	9.57042i	−0.709391	+	0.487754i
$386$		0			0
$387$	−0.344038	+	0.729349i	−0.0174884	+	0.0370749i
$388$		0			0
$389$	−5.50194	−	3.17655i	−0.278959	−	0.161057i	0.353993	−	0.935248i	$-0.384824\pi$
$389$	−5.50194	−	3.17655i	−0.278959	−	0.161057i	−0.632952	+	0.774191i	$0.718157\pi$
$390$		0			0
$391$		−	2.28330i		−	0.115472i
$392$		0			0
$393$	−18.4645	−	9.66397i	−0.931408	−	0.487483i
$394$		0			0
$395$	−0.455092	+	0.788242i	−0.0228982	+	0.0396608i
$396$		0			0
$397$	−10.3123	+	5.95380i	−0.517559	+	0.298813i	−0.735935	−	0.677052i	$-0.763257\pi$
$397$	−10.3123	+	5.95380i	−0.517559	+	0.298813i	0.218376	+	0.975865i	$0.429924\pi$
$398$		0			0
$399$	26.7235	−	3.22650i	1.33785	−	0.161527i
$400$		0			0
$401$	22.0659	−	12.7397i	1.10192	−	0.636192i	0.165193	−	0.986261i	$-0.447175\pi$
$401$	22.0659	−	12.7397i	1.10192	−	0.636192i	0.936724	+	0.350069i	$0.113842\pi$
$402$		0			0
$403$	−0.620404	+	1.07457i	−0.0309045	+	0.0535282i
$404$		0			0
$405$	3.15291	−	8.42966i	0.156669	−	0.418873i
$406$		0			0
$407$		−	21.6928i		−	1.07527i
$408$		0			0
$409$	−20.9193	−	12.0778i	−1.03439	−	0.597208i	−0.116154	−	0.993231i	$-0.537057\pi$
$409$	−20.9193	−	12.0778i	−1.03439	−	0.597208i	−0.918240	+	0.396023i	$0.870390\pi$
$410$		0			0
$411$	−27.8606	+	1.15467i	−1.37426	+	0.0569555i
$412$		0			0
$413$	18.7646	−	1.48047i	0.923344	−	0.0728491i
$414$		0			0
$415$	−0.895346	−	1.55078i	−0.0439508	−	0.0761250i
$416$		0			0
$417$	−5.55209	−	8.75774i	−0.271887	−	0.428869i
$418$		0			0
$419$	−9.60952			−0.469456			−0.234728	−	0.972061i	$-0.575420\pi$
$419$	−9.60952			−0.469456			−0.234728	+	0.972061i	$0.575420\pi$
$420$		0			0
$421$	7.26725			0.354184			0.177092	−	0.984194i	$-0.443331\pi$
$421$	7.26725			0.354184			0.177092	+	0.984194i	$0.443331\pi$
$422$		0			0
$423$	17.5281	−	1.45538i	0.852246	−	0.0707631i
$424$		0			0
$425$	3.85223	+	6.67225i	0.186860	+	0.323652i
$426$		0			0
$427$	−15.0713	−	7.18503i	−0.729349	−	0.347708i
$428$		0			0
$429$	−0.0852971	−	2.05811i	−0.00411818	−	0.0993665i
$430$		0			0
$431$	10.1889	+	5.88259i	0.490784	+	0.283354i	0.724900	−	0.688854i	$-0.241886\pi$
$431$	10.1889	+	5.88259i	0.490784	+	0.283354i	−0.234115	+	0.972209i	$0.575219\pi$
$432$		0			0
$433$		−	5.08112i		−	0.244183i	−0.992519	−	0.122092i	$-0.961040\pi$
$433$		−	5.08112i		−	0.244183i	0.992519	−	0.122092i	$-0.0389602\pi$
$434$		0			0
$435$	6.57242	−	12.5576i	0.315124	−	0.602090i
$436$		0			0
$437$	−0.870399	+	1.50758i	−0.0416368	+	0.0721171i
$438$		0			0
$439$	15.2664	−	8.81403i	0.728623	−	0.420671i	−0.0892949	−	0.996005i	$-0.528461\pi$
$439$	15.2664	−	8.81403i	0.728623	−	0.420671i	0.817918	+	0.575334i	$0.195128\pi$
$440$		0			0
$441$	14.5267	+	15.1649i	0.691749	+	0.722138i
$442$		0			0
$443$	−21.5228	+	12.4262i	−1.02258	+	0.590387i	−0.914851	−	0.403793i	$-0.867692\pi$
$443$	−21.5228	+	12.4262i	−1.02258	+	0.590387i	−0.107731	+	0.994180i	$0.534358\pi$
$444$		0			0
$445$	3.80761	−	6.59498i	0.180498	−	0.312632i
$446$		0			0
$447$	7.38923	−	14.1182i	0.349498	−	0.667769i
$448$		0			0
$449$			18.0711i			0.852830i	0.904528	+	0.426415i	$0.140224\pi$
$449$			18.0711i			0.852830i	−0.904528	+	0.426415i	$0.859776\pi$
$450$		0			0
$451$	−53.4899	−	30.8824i	−2.51874	−	1.45420i
$452$		0			0
$453$	−1.21649	−	29.3523i	−0.0571556	−	1.37909i
$454$		0			0
$455$	0.444864	+	0.212083i	0.0208555	+	0.00994261i
$456$		0			0
$457$	9.46311	+	16.3906i	0.442665	+	0.766719i	0.997886	−	0.0649839i	$-0.0206996\pi$
$457$	9.46311	+	16.3906i	0.442665	+	0.766719i	−0.555221	+	0.831703i	$0.687366\pi$
$458$		0			0
$459$	−36.8836	−	15.5653i	−1.72158	−	0.726527i
$460$		0			0
$461$	−15.4024			−0.717363			−0.358681	−	0.933460i	$-0.616774\pi$
$461$	−15.4024			−0.717363			−0.358681	+	0.933460i	$0.616774\pi$
$462$		0			0
$463$	−13.3839			−0.622004			−0.311002	−	0.950409i	$-0.600665\pi$
$463$	−13.3839			−0.622004			−0.311002	+	0.950409i	$0.600665\pi$
$464$		0			0
$465$	6.17760	+	9.74441i	0.286479	+	0.451886i
$466$		0			0
$467$	−10.7413	−	18.6044i	−0.497046	−	0.860909i	0.502948	−	0.864317i	$-0.332249\pi$
$467$	−10.7413	−	18.6044i	−0.497046	−	0.860909i	−0.999994	+	0.00340761i	$0.998915\pi$
$468$		0			0
$469$	−2.43098	+	0.191798i	−0.112252	+	0.00885639i
$470$		0			0
$471$	−19.9110	+	0.825199i	−0.917450	+	0.0380231i
$472$		0			0
$473$	1.48628	+	0.858106i	0.0683394	+	0.0394558i
$474$		0			0
$475$		−	5.87390i		−	0.269513i
$476$		0			0
$477$	7.75317	−	5.37785i	0.354993	−	0.246235i
$478$		0			0
$479$	7.81022	−	13.5277i	0.356858	−	0.618096i	−0.630576	−	0.776127i	$-0.717181\pi$
$479$	7.81022	−	13.5277i	0.356858	−	0.618096i	0.987434	+	0.158031i	$0.0505147\pi$
$480$		0			0
$481$	−0.548105	+	0.316449i	−0.0249915	+	0.0144288i
$482$		0			0
$483$	−1.34831	+	0.162790i	−0.0613501	+	0.00740718i
$484$		0			0
$485$	−8.86623	+	5.11892i	−0.402595	+	0.232438i
$486$		0			0
$487$	1.75816	−	3.04523i	0.0796700	−	0.137993i	−0.823438	−	0.567407i	$-0.807947\pi$
$487$	1.75816	−	3.04523i	0.0796700	−	0.137993i	0.903108	+	0.429414i	$0.141280\pi$
$488$		0			0
$489$	−10.9109	−	5.71058i	−0.493408	−	0.258241i
$490$		0			0
$491$		−	20.2108i		−	0.912099i	−0.889955	−	0.456049i	$-0.849264\pi$
$491$		−	20.2108i		−	0.912099i	0.889955	−	0.456049i	$-0.150736\pi$
$492$		0			0
$493$	−54.5998	−	31.5232i	−2.45905	−	1.41973i
$494$		0			0
$495$	−17.3232	−	8.17144i	−0.778618	−	0.367279i
$496$		0			0
$497$	−16.2238	+	11.1550i	−0.727737	+	0.500368i
$498$		0			0
$499$	−0.763061	−	1.32166i	−0.0341593	−	0.0591656i	0.848440	−	0.529291i	$-0.177542\pi$
$499$	−0.763061	−	1.32166i	−0.0341593	−	0.0591656i	−0.882600	+	0.470125i	$0.844209\pi$
$500$		0			0
$501$	20.0471	−	12.7091i	0.895636	−	0.567801i
$502$		0			0
$503$	4.12243			0.183810			0.0919050	−	0.995768i	$-0.470704\pi$
$503$	4.12243			0.183810			0.0919050	+	0.995768i	$0.470704\pi$
$504$		0			0
$505$	5.79840			0.258025
$506$		0			0
$507$	18.9663	−	12.0240i	0.842324	−	0.534003i
$508$		0			0
$509$	−5.26336	−	9.11640i	−0.233294	−	0.404077i	0.725481	−	0.688242i	$-0.241617\pi$
$509$	−5.26336	−	9.11640i	−0.233294	−	0.404077i	−0.958776	+	0.284164i	$0.908284\pi$
$510$		0			0
$511$	1.41793	+	17.9719i	0.0627256	+	0.795031i
$512$		0			0
$513$	18.4193	+	24.3373i	0.813231	+	1.07452i
$514$		0			0
$515$	1.75128	+	1.01110i	0.0771705	+	0.0445544i
$516$		0			0
$517$		−	37.4315i		−	1.64623i
$518$		0			0
$519$	19.9975	+	10.4663i	0.877792	+	0.459421i
$520$		0			0
$521$	3.90299	−	6.76018i	0.170993	−	0.296169i	−0.767774	−	0.640720i	$-0.778636\pi$
$521$	3.90299	−	6.76018i	0.170993	−	0.296169i	0.938767	+	0.344552i	$0.111969\pi$
$522$		0			0
$523$	0.611446	−	0.353019i	0.0267367	−	0.0154364i	−0.486572	−	0.873640i	$-0.661753\pi$
$523$	0.611446	−	0.353019i	0.0267367	−	0.0154364i	0.513309	+	0.858204i	$0.328420\pi$
$524$		0			0
$525$	3.66537	−	2.75047i	0.159970	−	0.120040i
$526$		0			0
$527$	44.4455	−	25.6606i	1.93607	−	1.11779i
$528$		0			0
$529$	−11.4561	+	19.8425i	−0.498091	+	0.862718i
$530$		0			0
$531$	12.1644	+	17.5373i	0.527892	+	0.761053i
$532$		0			0
$533$			1.80202i			0.0780541i
$534$		0			0
$535$	0.633070	+	0.365503i	0.0273700	+	0.0158021i
$536$		0			0
$537$	15.3539	−	0.636330i	0.662568	−	0.0274597i
$538$		0			0
$539$	34.7213	−	28.1390i	1.49555	−	1.21203i
$540$		0			0
$541$	15.5718	+	26.9711i	0.669484	+	1.15958i	0.978049	+	0.208376i	$0.0668179\pi$
$541$	15.5718	+	26.9711i	0.669484	+	1.15958i	−0.308565	+	0.951203i	$0.599849\pi$
$542$		0			0
$543$	−15.1153	−	23.8424i	−0.648658	−	1.02318i
$544$		0			0
$545$	−8.40908			−0.360205
$546$		0			0
$547$	3.60254			0.154033			0.0770167	−	0.997030i	$-0.475461\pi$
$547$	3.60254			0.154033			0.0770167	+	0.997030i	$0.475461\pi$
$548$		0			0
$549$	−1.56655	−	18.8669i	−0.0668586	−	0.805221i
$550$		0			0
$551$	24.0334	+	41.6270i	1.02386	+	1.77337i
$552$		0			0
$553$	1.03630	−	2.17373i	0.0440680	−	0.0924366i
$554$		0			0
$555$	0.243690	+	5.87993i	0.0103441	+	0.249589i
$556$		0			0
$557$	13.5235	+	7.80780i	0.573009	+	0.330827i	0.758350	−	0.651847i	$-0.226006\pi$
$557$	13.5235	+	7.80780i	0.573009	+	0.330827i	−0.185341	+	0.982674i	$0.559339\pi$
$558$		0			0
$559$		−	0.0500713i		−	0.00211779i
$560$		0			0
$561$	−39.5076	+	75.4851i	−1.66801	+	3.18698i
$562$		0			0
$563$	−9.23761	+	16.0000i	−0.389319	+	0.674320i	−0.992358	−	0.123392i	$-0.960623\pi$
$563$	−9.23761	+	16.0000i	−0.389319	+	0.674320i	0.603039	+	0.797711i	$0.293956\pi$
$564$		0			0
$565$	−11.9211	+	6.88267i	−0.501526	+	0.289556i
$566$		0			0
$567$	−6.56180	+	22.8898i	−0.275570	+	0.961281i
$568$		0			0
$569$	3.92281	−	2.26483i	0.164453	−	0.0949468i	−0.415515	−	0.909586i	$-0.636399\pi$
$569$	3.92281	−	2.26483i	0.164453	−	0.0949468i	0.579967	+	0.814640i	$0.303065\pi$
$570$		0			0
$571$	−19.4533	+	33.6941i	−0.814094	+	1.41005i	0.0958818	+	0.995393i	$0.469433\pi$
$571$	−19.4533	+	33.6941i	−0.814094	+	1.41005i	−0.909976	+	0.414660i	$0.863900\pi$
$572$		0			0
$573$	−7.66405	+	14.6433i	−0.320170	+	0.611733i
$574$		0			0
$575$			0.296362i			0.0123591i
$576$		0			0
$577$	−2.37456	−	1.37095i	−0.0988540	−	0.0570734i	0.449758	−	0.893150i	$-0.351510\pi$
$577$	−2.37456	−	1.37095i	−0.0988540	−	0.0570734i	−0.548612	+	0.836077i	$0.684844\pi$
$578$		0			0
$579$	0.994235	+	23.9896i	0.0413190	+	0.996975i
$580$		0			0
$581$	2.68424	+	3.90396i	0.111361	+	0.161964i
$582$		0			0
$583$	−10.0405	−	17.3907i	−0.415835	−	0.720247i
$584$		0			0
$585$	0.0462403	+	0.556902i	0.00191180	+	0.0230251i
$586$		0			0
$587$	16.5793			0.684302			0.342151	−	0.939645i	$-0.388845\pi$
$587$	16.5793			0.684302			0.342151	+	0.939645i	$0.388845\pi$
$588$		0			0
$589$	−39.1274			−1.61222
$590$		0			0
$591$	24.3067	+	38.3408i	0.999844	+	1.57713i
$592$		0			0
$593$	−7.24841	−	12.5546i	−0.297657	−	0.515556i	0.677943	−	0.735115i	$-0.262872\pi$
$593$	−7.24841	−	12.5546i	−0.297657	−	0.515556i	−0.975599	+	0.219558i	$0.929538\pi$
$594$		0			0
$595$	−11.5489	−	16.7968i	−0.473460	−	0.688602i
$596$		0			0
$597$	28.5281	−	1.18233i	1.16758	−	0.0483896i
$598$		0			0
$599$	−22.6646	−	13.0854i	−0.926051	−	0.534656i	−0.0404906	−	0.999180i	$-0.512892\pi$
$599$	−22.6646	−	13.0854i	−0.926051	−	0.534656i	−0.885560	+	0.464524i	$0.846225\pi$
$600$		0			0
$601$			39.8722i			1.62642i	0.581970	+	0.813211i	$0.302282\pi$
$601$			39.8722i			1.62642i	−0.581970	+	0.813211i	$0.697718\pi$
$602$		0			0
$603$	−1.57593	−	2.27199i	−0.0641766	−	0.0925224i
$604$		0			0
$605$	−14.8813	+	25.7752i	−0.605013	+	1.04791i
$606$		0			0
$607$	−9.68625	+	5.59236i	−0.393153	+	0.226987i	−0.683525	−	0.729927i	$-0.739554\pi$
$607$	−9.68625	+	5.59236i	−0.393153	+	0.226987i	0.290373	+	0.956914i	$0.406221\pi$
$608$		0			0
$609$	−14.7219	+	34.4890i	−0.596563	+	1.39757i
$610$		0			0
$611$	−0.945770	+	0.546041i	−0.0382618	+	0.0220904i
$612$		0			0
$613$	8.86155	−	15.3487i	0.357915	−	0.619926i	−0.629698	−	0.776840i	$-0.716821\pi$
$613$	8.86155	−	15.3487i	0.357915	−	0.619926i	0.987612	+	0.156914i	$0.0501546\pi$
$614$		0			0
$615$	14.8456	+	7.76993i	0.598633	+	0.313314i
$616$		0			0
$617$		−	13.5065i		−	0.543752i	−0.962332	−	0.271876i	$-0.912356\pi$
$617$		−	13.5065i		−	0.543752i	0.962332	−	0.271876i	$-0.0876441\pi$
$618$		0			0
$619$	−4.61699	−	2.66562i	−0.185573	−	0.107140i	0.404336	−	0.914611i	$-0.367503\pi$
$619$	−4.61699	−	2.66562i	−0.185573	−	0.107140i	−0.589908	+	0.807470i	$0.700836\pi$
$620$		0			0
$621$	−0.929326	−	1.22791i	−0.0372926	−	0.0492744i
$622$		0			0
$623$	−8.67041	+	18.1870i	−0.347373	+	0.728646i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	54.8603	−	34.7795i	2.19091	−	1.38896i
$628$		0			0
$629$	26.1774			1.04376
$630$		0			0
$631$	−18.6464			−0.742300			−0.371150	−	0.928573i	$-0.621036\pi$
$631$	−18.6464			−0.742300			−0.371150	+	0.928573i	$0.621036\pi$
$632$		0			0
$633$	37.3610	−	23.6855i	1.48497	−	0.941415i
$634$		0			0
$635$	7.81626	+	13.5382i	0.310179	+	0.537246i
$636$		0			0
$637$	−1.21749	−	0.466807i	−0.0482385	−	0.0184956i
$638$		0			0
$639$	−20.1913	−	9.52435i	−0.798754	−	0.376777i
$640$		0			0
$641$	−6.24029	−	3.60283i	−0.246477	−	0.142303i	0.371673	−	0.928364i	$-0.378784\pi$
$641$	−6.24029	−	3.60283i	−0.246477	−	0.142303i	−0.618150	+	0.786060i	$0.712118\pi$
$642$		0			0
$643$		−	17.2991i		−	0.682211i	−0.940025	−	0.341106i	$-0.889199\pi$
$643$		−	17.2991i		−	0.682211i	0.940025	−	0.341106i	$-0.110801\pi$
$644$		0			0
$645$	−0.412503	−	0.215897i	−0.0162423	−	0.00850094i
$646$		0			0
$647$	−21.1985	+	36.7169i	−0.833399	+	1.44349i	0.0619275	+	0.998081i	$0.480275\pi$
$647$	−21.1985	+	36.7169i	−0.833399	+	1.44349i	−0.895327	+	0.445410i	$0.853058\pi$
$648$		0			0
$649$	39.3368	−	22.7111i	1.54410	−	0.891489i
$650$		0			0
$651$	−18.3215	−	24.4159i	−0.718077	−	0.956934i
$652$		0			0
$653$	−40.6027	+	23.4420i	−1.58891	+	0.917355i	−0.595418	+	0.803416i	$0.703013\pi$
$653$	−40.6027	+	23.4420i	−1.58891	+	0.917355i	−0.993488	+	0.113939i	$0.963653\pi$
$654$		0			0
$655$	6.01615	−	10.4203i	0.235070	−	0.407154i
$656$		0			0
$657$	−16.7965	+	11.6506i	−0.655293	+	0.454533i
$658$		0			0
$659$			13.9569i			0.543682i	0.962342	+	0.271841i	$0.0876324\pi$
$659$			13.9569i			0.543682i	−0.962342	+	0.271841i	$0.912368\pi$
$660$		0			0
$661$	0.214647	+	0.123927i	0.00834881	+	0.00482019i	0.504169	−	0.863605i	$-0.331799\pi$
$661$	0.214647	+	0.123927i	0.00834881	+	0.00482019i	−0.495820	+	0.868425i	$0.665132\pi$
$662$		0			0
$663$	2.48359	−	0.102931i	0.0964545	−	0.00399749i
$664$		0			0
$665$	1.22233	+	15.4927i	0.0474000	+	0.600783i
$666$		0			0
$667$	−1.21258	−	2.10025i	−0.0469513	−	0.0813220i
$668$		0			0
$669$	23.9012	+	37.7013i	0.924075	+	1.45761i
$670$		0			0
$671$	−40.2906			−1.55540
$672$		0			0
$673$	32.7763			1.26343			0.631716	−	0.775200i	$-0.282351\pi$
$673$	32.7763			1.26343			0.631716	+	0.775200i	$0.282351\pi$
$674$		0			0
$675$	4.78731	+	2.02030i	0.184264	+	0.0777615i
$676$		0			0
$677$	−5.77061	−	9.99498i	−0.221782	−	0.384138i	0.733567	−	0.679617i	$-0.237854\pi$
$677$	−5.77061	−	9.99498i	−0.221782	−	0.384138i	−0.955349	+	0.295479i	$0.904521\pi$
$678$		0			0
$679$	22.3199	−	15.3465i	0.856561	−	0.588943i
$680$		0			0
$681$	−0.966453	−	23.3193i	−0.0370346	−	0.893597i
$682$		0			0
$683$	30.5108	+	17.6154i	1.16746	+	0.674034i	0.953081	−	0.302716i	$-0.0978933\pi$
$683$	30.5108	+	17.6154i	1.16746	+	0.674034i	0.214381	+	0.976750i	$0.431227\pi$
$684$		0			0
$685$		−	16.0992i		−	0.615117i
$686$		0			0
$687$	4.06710	−	7.77079i	0.155169	−	0.296474i
$688$		0			0
$689$	−0.292936	+	0.507381i	−0.0111600	+	0.0193297i
$690$		0			0
$691$	−12.5509	+	7.24625i	−0.477458	+	0.275660i	−0.719356	−	0.694641i	$-0.755563\pi$
$691$	−12.5509	+	7.24625i	−0.477458	+	0.275660i	0.241899	+	0.970301i	$0.422230\pi$
$692$		0			0
$693$	47.3912	+	17.9478i	1.80024	+	0.681779i
$694$		0			0
$695$	5.18468	−	2.99338i	0.196666	−	0.113545i
$696$		0			0
$697$	37.2668	−	64.5480i	1.41158	−	2.44493i
$698$		0			0
$699$	−2.46745	+	4.71444i	−0.0933277	+	0.178316i
$700$		0			0
$701$		−	15.1922i		−	0.573801i	−0.957960	−	0.286901i	$-0.907375\pi$
$701$		−	15.1922i		−	0.573801i	0.957960	−	0.286901i	$-0.0926250\pi$
$702$		0			0
$703$	−17.2839	−	9.97885i	−0.651874	−	0.376360i
$704$		0			0
$705$	0.420493	+	10.1460i	0.0158367	+	0.382119i
$706$		0			0
$707$	−15.2936	+	1.20662i	−0.575175	+	0.0453796i
$708$		0			0
$709$	3.59857	+	6.23291i	0.135147	+	0.234082i	0.925654	−	0.378372i	$-0.123516\pi$
$709$	3.59857	+	6.23291i	0.135147	+	0.234082i	−0.790506	+	0.612454i	$0.790183\pi$
$710$		0			0
$711$	2.72119	−	0.225944i	0.102052	−	0.00847355i
$712$		0			0
$713$	1.97413			0.0739319
$714$		0			0
$715$	1.18927			0.0444762
$716$		0			0
$717$	21.1749	+	33.4007i	0.790789	+	1.24737i
$718$		0			0
$719$	−7.67282	−	13.2897i	−0.286148	−	0.495622i	0.686739	−	0.726904i	$-0.259041\pi$
$719$	−7.67282	−	13.2897i	−0.286148	−	0.495622i	−0.972887	+	0.231282i	$0.925708\pi$
$720$		0			0
$721$	−4.82950	−	2.30240i	−0.179860	−	0.0857459i
$722$		0			0
$723$	−32.6676	+	1.35389i	−1.21492	+	0.0503516i
$724$		0			0
$725$	7.08678	+	4.09155i	0.263196	+	0.151957i
$726$		0			0
$727$			35.1502i			1.30365i	0.758370	+	0.651824i	$0.225996\pi$
$727$			35.1502i			1.30365i	−0.758370	+	0.651824i	$0.774004\pi$
$728$		0			0
$729$	−26.1705	+	6.64128i	−0.969277	+	0.245973i
$730$		0			0
$731$	−1.03550	+	1.79354i	−0.0382995	+	0.0663366i
$732$		0			0
$733$	−27.4367	+	15.8406i	−1.01340	+	0.585086i	−0.912185	−	0.409779i	$-0.865606\pi$
$733$	−27.4367	+	15.8406i	−1.01340	+	0.585086i	−0.101214	+	0.994865i	$0.532273\pi$
$734$		0			0
$735$	−9.09525	+	8.01726i	−0.335483	+	0.295721i
$736$		0			0
$737$	−5.09616	+	2.94227i	−0.187719	+	0.108380i
$738$		0			0
$739$	−11.7713	+	20.3886i	−0.433016	+	0.750006i	−0.997131	−	0.0756904i	$-0.975884\pi$
$739$	−11.7713	+	20.3886i	−0.433016	+	0.750006i	0.564115	+	0.825696i	$0.309217\pi$
$740$		0			0
$741$	−1.67905	−	0.878786i	−0.0616815	−	0.0322830i
$742$		0			0
$743$		−	28.3130i		−	1.03870i	−0.854560	−	0.519352i	$-0.826173\pi$
$743$		−	28.3130i		−	1.03870i	0.854560	−	0.519352i	$-0.173827\pi$
$744$		0			0
$745$	7.96751	+	4.60004i	0.291907	+	0.168532i
$746$		0			0
$747$	−2.29186	+	4.85866i	−0.0838548	+	0.177769i
$748$		0			0
$749$	−1.74582	−	0.832295i	−0.0637907	−	0.0304114i
$750$		0			0
$751$	−26.4096	−	45.7427i	−0.963699	−	1.66917i	−0.713072	−	0.701091i	$-0.752697\pi$
$751$	−26.4096	−	45.7427i	−0.963699	−	1.66917i	−0.250627	−	0.968084i	$-0.580637\pi$
$752$		0			0
$753$	−4.62821	+	2.93412i	−0.168661	+	0.106925i
$754$		0			0
$755$	16.9611			0.617278
$756$		0			0
$757$	39.3857			1.43150			0.715750	−	0.698357i	$-0.246085\pi$
$757$	39.3857			1.43150			0.715750	+	0.698357i	$0.246085\pi$
$758$		0			0
$759$	−2.76792	+	1.75476i	−0.100469	+	0.0636938i
$760$		0			0
$761$	6.19194	+	10.7248i	0.224458	+	0.388772i	0.956157	−	0.292856i	$-0.0946056\pi$
$761$	6.19194	+	10.7248i	0.224458	+	0.388772i	−0.731699	+	0.681628i	$0.761272\pi$
$762$		0			0
$763$	22.1794	−	1.74989i	0.802949	−	0.0633503i
$764$		0			0
$765$	9.86073	−	20.9044i	0.356515	−	0.755800i
$766$		0			0
$767$	−1.14767	−	0.662608i	−0.0414400	−	0.0239254i
$768$		0			0
$769$			38.5632i			1.39062i	0.718708	+	0.695312i	$0.244734\pi$
$769$			38.5632i			1.39062i	−0.718708	+	0.695312i	$0.755266\pi$
$770$		0			0
$771$	−4.43865	−	2.32311i	−0.159854	−	0.0836649i
$772$		0			0
$773$	−16.1494	+	27.9717i	−0.580855	+	1.00607i	0.414523	+	0.910039i	$0.363948\pi$
$773$	−16.1494	+	27.9717i	−0.580855	+	1.00607i	−0.995378	+	0.0960319i	$0.969385\pi$
$774$		0			0
$775$	−5.76880	+	3.33062i	−0.207221	+	0.119639i
$776$		0			0
$777$	−1.86633	−	15.4579i	−0.0669542	−	0.554550i
$778$		0			0
$779$	−49.2116	+	28.4123i	−1.76319	+	1.01798i
$780$		0			0
$781$	−23.7558	+	41.1462i	−0.850049	+	1.47233i
$782$		0			0
$783$	−42.1928	+	5.27012i	−1.50785	+	0.188339i
$784$		0			0
$785$		−	11.5055i		−	0.410649i
$786$		0			0
$787$	34.2715	+	19.7866i	1.22165	+	0.705318i	0.965269	−	0.261259i	$-0.0841377\pi$
$787$	34.2715	+	19.7866i	1.22165	+	0.705318i	0.256377	+	0.966577i	$0.417471\pi$
$788$		0			0
$789$	12.7094	−	0.526732i	0.452466	−	0.0187522i
$790$		0			0
$791$	30.0104	−	20.6341i	1.06705	−	0.733666i
$792$		0			0
$793$	0.587748	+	1.01801i	0.0208716	+	0.0361506i
$794$		0			0
$795$	2.91688	+	4.60102i	0.103451	+	0.163181i
$796$		0			0
$797$	−12.9298			−0.457998			−0.228999	−	0.973427i	$-0.573545\pi$
$797$	−12.9298			−0.457998			−0.228999	+	0.973427i	$0.573545\pi$
$798$		0			0
$799$	45.1697			1.59799
$800$		0			0
$801$	−22.7673	+	1.89040i	−0.804444	+	0.0667941i
$802$		0			0
$803$	21.7518	+	37.6751i	0.767603	+	1.32953i
$804$		0			0
$805$	−0.0616715	−	0.781670i	−0.00217363	−	0.0275502i
$806$		0			0
$807$	1.37023	+	33.0620i	0.0482345	+	1.16384i
$808$		0			0
$809$	−21.2251	−	12.2543i	−0.746234	−	0.430838i	0.0780978	−	0.996946i	$-0.475115\pi$
$809$	−21.2251	−	12.2543i	−0.746234	−	0.430838i	−0.824331	+	0.566108i	$0.808449\pi$
$810$		0			0
$811$		−	28.4376i		−	0.998579i	−0.866435	−	0.499289i	$-0.833594\pi$
$811$		−	28.4376i		−	0.998579i	0.866435	−	0.499289i	$-0.166406\pi$
$812$		0			0
$813$	14.2135	−	27.1569i	0.498487	−	0.952434i
$814$		0			0
$815$	3.55503	−	6.15749i	0.124527	−	0.215687i
$816$		0			0
$817$	1.36740	−	0.789471i	0.0478394	−	0.0276201i
$818$		0			0
$819$	−0.237850	−	1.45924i	−0.00831116	−	0.0509899i
$820$		0			0
$821$	8.66190	−	5.00095i	0.302302	−	0.174534i	−0.341174	−	0.940000i	$-0.610825\pi$
$821$	8.66190	−	5.00095i	0.302302	−	0.174534i	0.643477	+	0.765466i	$0.277491\pi$
$822$		0			0
$823$	−23.4186	+	40.5621i	−0.816320	+	1.41391i	0.0920564	+	0.995754i	$0.470656\pi$
$823$	−23.4186	+	40.5621i	−0.816320	+	1.41391i	−0.908376	+	0.418154i	$0.862677\pi$
$824$		0			0
$825$	5.12789	−	9.79759i	0.178530	−	0.341108i
$826$		0			0
$827$			8.37360i			0.291179i	0.989345	+	0.145589i	$0.0465078\pi$
$827$			8.37360i			0.291179i	−0.989345	+	0.145589i	$0.953492\pi$
$828$		0			0
$829$	40.9987	+	23.6706i	1.42394	+	0.822114i	0.996633	−	0.0819904i	$-0.0261277\pi$
$829$	40.9987	+	23.6706i	1.42394	+	0.822114i	0.427311	+	0.904105i	$0.359461\pi$
$830$		0			0
$831$	1.41740	+	34.2001i	0.0491691	+	1.18639i
$832$		0			0
$833$	33.9563	+	41.8992i	1.17651	+	1.45172i
$834$		0			0
$835$	6.85204	+	11.8681i	0.237125	+	0.410712i
$836$		0			0
$837$	13.4577	−	31.8894i	0.465167	−	1.10226i
$838$		0			0
$839$	−14.0087			−0.483634			−0.241817	−	0.970322i	$-0.577743\pi$
$839$	−14.0087			−0.483634			−0.241817	+	0.970322i	$0.577743\pi$
$840$		0			0
$841$	−37.9633			−1.30908
$842$		0			0
$843$	−4.18903	−	6.60768i	−0.144278	−	0.227580i
$844$		0			0
$845$	6.48265	+	11.2283i	0.223010	+	0.386265i
$846$		0			0
$847$	33.8867	−	71.0804i	1.16436	−	2.44235i
$848$		0			0
$849$	1.30454	−	0.0540660i	0.0447718	−	0.00185554i
$850$		0			0
$851$	0.872040	+	0.503472i	0.0298931	+	0.0172588i
$852$		0			0
$853$			18.1485i			0.621392i	0.950509	+	0.310696i	$0.100562\pi$
$853$			18.1485i			0.621392i	−0.950509	+	0.310696i	$0.899438\pi$
$854$		0			0
$855$	−14.4794	+	10.0434i	−0.495186	+	0.343478i
$856$		0			0
$857$	21.2325	−	36.7758i	0.725290	−	1.25624i	−0.233565	−	0.972341i	$-0.575039\pi$
$857$	21.2325	−	36.7758i	0.725290	−	1.25624i	0.958855	−	0.283897i	$-0.0916275\pi$
$858$		0			0
$859$	30.9486	−	17.8682i	1.05595	−	0.609655i	0.131644	−	0.991297i	$-0.457975\pi$
$859$	30.9486	−	17.8682i	1.05595	−	0.609655i	0.924310	+	0.381642i	$0.124641\pi$
$860$		0			0
$861$	−40.7730	−	17.4043i	−1.38954	−	0.593138i
$862$		0			0
$863$	−5.53956	+	3.19826i	−0.188569	+	0.108870i	−0.591312	−	0.806443i	$-0.701390\pi$
$863$	−5.53956	+	3.19826i	−0.188569	+	0.108870i	0.402744	+	0.915313i	$0.368057\pi$
$864$		0			0
$865$	−6.51565	+	11.2854i	−0.221539	+	0.383716i
$866$		0			0
$867$	−65.0024	−	34.0211i	−2.20760	−	1.15542i
$868$		0			0
$869$		−	5.81113i		−	0.197129i
$870$		0			0
$871$	0.148683	+	0.0858421i	0.00503792	+	0.00290865i
$872$		0			0
$873$	27.7782	+	13.1031i	0.940149	+	0.443474i
$874$		0			0
$875$	1.49899	+	2.18014i	0.0506752	+	0.0737022i
$876$		0			0
$877$	21.6364	+	37.4753i	0.730608	+	1.26545i	0.956624	+	0.291327i	$0.0940966\pi$
$877$	21.6364	+	37.4753i	0.730608	+	1.26545i	−0.226016	+	0.974124i	$0.572570\pi$
$878$		0			0
$879$	−5.04649	+	3.19929i	−0.170214	+	0.107909i
$880$		0			0
$881$	51.4321			1.73279			0.866396	−	0.499357i	$-0.166430\pi$
$881$	51.4321			1.73279			0.866396	+	0.499357i	$0.166430\pi$
$882$		0			0
$883$	13.8503			0.466101			0.233051	−	0.972465i	$-0.425129\pi$
$883$	13.8503			0.466101			0.233051	+	0.972465i	$0.425129\pi$
$884$		0			0
$885$	−10.4073	+	6.59785i	−0.349837	+	0.221784i
$886$		0			0
$887$	17.7602	+	30.7615i	0.596328	+	1.03287i	0.993358	+	0.115065i	$0.0367077\pi$
$887$	17.7602	+	30.7615i	0.596328	+	1.03287i	−0.397030	+	0.917806i	$0.629959\pi$
$888$		0			0
$889$	−23.4331	−	34.0811i	−0.785919	−	1.14304i
$890$		0			0
$891$	9.47681	+	56.6742i	0.317485	+	1.89866i
$892$		0			0
$893$	−29.8238	−	17.2188i	−0.998015	−	0.576204i
$894$		0			0
$895$			8.87216i			0.296564i
$896$		0			0
$897$	0.0847148	+	0.0443382i	0.00282854	+	0.00148041i
$898$		0			0
$899$	27.2548	−	47.2067i	0.908999	−	1.57443i
$900$		0			0
$901$	20.9858	−	12.1162i	0.699140	−	0.403649i
$902$		0			0
$903$	1.13293	+	0.483600i	0.0377015	+	0.0160932i
$904$		0			0
$905$	14.1150	−	8.14930i	0.469199	−	0.270892i
$906$		0			0
$907$	10.1629	−	17.6026i	0.337453	−	0.584486i	−0.646500	−	0.762914i	$-0.723768\pi$
$907$	10.1629	−	17.6026i	0.337453	−	0.584486i	0.983953	+	0.178428i	$0.0571012\pi$
$908$		0			0
$909$	−9.91432	−	14.2933i	−0.328837	−	0.474080i
$910$		0			0
$911$			36.1989i			1.19932i	0.800254	+	0.599661i	$0.204698\pi$
$911$			36.1989i			1.19932i	−0.800254	+	0.599661i	$0.795302\pi$
$912$		0			0
$913$	9.90109	+	5.71640i	0.327678	+	0.189185i
$914$		0			0
$915$	10.9209	−	0.452611i	0.361035	−	0.0149629i
$916$		0			0
$917$	−13.6995	+	28.7360i	−0.452398	+	0.948946i
$918$		0			0
$919$	−22.6036	−	39.1506i	−0.745624	−	1.29146i	−0.949903	−	0.312546i	$-0.898818\pi$
$919$	−22.6036	−	39.1506i	−0.745624	−	1.29146i	0.204279	−	0.978913i	$-0.434515\pi$
$920$		0			0
$921$	−7.09993	−	11.1993i	−0.233951	−	0.369028i
$922$		0			0
$923$	1.38617			0.0456264
$924$		0			0
$925$	−3.39769			−0.111715
$926$		0			0
$927$	−0.501991	−	6.04580i	−0.0164875	−	0.198570i
$928$		0			0
$929$	−18.8963	−	32.7294i	−0.619969	−	1.07382i	−0.989491	−	0.144596i	$-0.953812\pi$
$929$	−18.8963	−	32.7294i	−0.619969	−	1.07382i	0.369522	−	0.929222i	$-0.379521\pi$
$930$		0			0
$931$	−6.44793	−	40.6086i	−0.211322	−	1.33089i
$932$		0			0
$933$	−2.36688	−	57.1099i	−0.0774882	−	1.86969i
$934$		0			0
$935$	−42.5994	−	24.5948i	−1.39315	−	0.804336i
$936$		0			0
$937$		−	22.9137i		−	0.748557i	−0.927316	−	0.374278i	$-0.877890\pi$
$937$		−	22.9137i		−	0.748557i	0.927316	−	0.374278i	$-0.122110\pi$
$938$		0			0
$939$	14.7253	−	28.1349i	0.480542	−	0.918147i
$940$		0			0
$941$	−24.0405	+	41.6393i	−0.783697	+	1.35740i	0.146077	+	0.989273i	$0.453335\pi$
$941$	−24.0405	+	41.6393i	−0.783697	+	1.35740i	−0.929774	+	0.368130i	$0.879998\pi$
$942$		0			0
$943$	2.48292	−	1.43351i	0.0808550	−	0.0466816i
$944$		0			0
$945$	−13.0472	−	4.33244i	−0.424426	−	0.140934i
$946$		0			0
$947$	21.6521	−	12.5008i	0.703597	−	0.406222i	−0.105088	−	0.994463i	$-0.533513\pi$
$947$	21.6521	−	12.5008i	0.703597	−	0.406222i	0.808686	+	0.588241i	$0.200179\pi$
$948$		0			0
$949$	0.634618	−	1.09919i	0.0206006	−	0.0356812i
$950$		0			0
$951$	2.13375	−	4.07685i	0.0691916	−	0.132201i
$952$		0			0
$953$		−	41.8152i		−	1.35453i	−0.735741	−	0.677263i	$-0.763166\pi$
$953$		−	41.8152i		−	1.35453i	0.735741	−	0.677263i	$-0.236834\pi$
$954$		0			0
$955$	−8.26384	−	4.77113i	−0.267411	−	0.154390i
$956$		0			0
$957$	3.74717	+	90.4144i	0.121129	+	2.92268i
$958$		0			0
$959$	3.35016	+	42.4624i	0.108182	+	1.37118i
$960$		0			0
$961$	6.68604	+	11.5806i	0.215679	+	0.373566i
$962$		0			0
$963$	−0.181465	−	2.18550i	−0.00584762	−	0.0704267i
$964$		0			0
$965$	−13.8623			−0.446243
$966$		0			0
$967$	43.9591			1.41363			0.706814	−	0.707399i	$-0.250132\pi$
$967$	43.9591			1.41363			0.706814	+	0.707399i	$0.250132\pi$
$968$		0			0
$969$	41.9695	+	66.2017i	1.34825	+	2.12670i
$970$		0			0
$971$	6.34320	+	10.9867i	0.203563	+	0.352582i	0.949674	−	0.313240i	$-0.101414\pi$
$971$	6.34320	+	10.9867i	0.203563	+	0.352582i	−0.746111	+	0.665822i	$0.768081\pi$
$972$		0			0
$973$	−13.0520	+	8.97411i	−0.418427	+	0.287697i
$974$		0			0
$975$	−0.322357	+	0.0133599i	−0.0103237	+	0.000427859i
$976$		0			0
$977$	5.52395	+	3.18925i	0.176727	+	0.102033i	0.585754	−	0.810489i	$-0.300799\pi$
$977$	5.52395	+	3.18925i	0.176727	+	0.102033i	−0.409027	+	0.912522i	$0.634132\pi$
$978$		0			0
$979$			48.6199i			1.55390i
$980$		0			0
$981$	14.3782	+	20.7288i	0.459059	+	0.661819i
$982$		0			0
$983$	−2.32496	+	4.02694i	−0.0741546	+	0.128440i	−0.900718	−	0.434404i	$-0.856959\pi$
$983$	−2.32496	+	4.02694i	−0.0741546	+	0.128440i	0.826564	+	0.562843i	$0.190293\pi$
$984$		0			0
$985$	−22.6982	+	13.1048i	−0.723225	+	0.417554i
$986$		0			0
$987$	−3.22040	−	26.6731i	−0.102507	−	0.849013i
$988$		0			0
$989$	−0.0689909	+	0.0398319i	−0.00219378	+	0.00126658i
$990$		0			0
$991$	8.85455	−	15.3365i	0.281274	−	0.487181i	−0.690425	−	0.723404i	$-0.742576\pi$
$991$	8.85455	−	15.3365i	0.281274	−	0.487181i	0.971699	+	0.236223i	$0.0759097\pi$
$992$		0			0
$993$	−5.57509	−	2.91790i	−0.176920	−	0.0925969i
$994$		0			0
$995$			16.4849i			0.522606i
$996$		0			0
$997$	−11.6266	−	6.71259i	−0.368217	−	0.212590i	0.304462	−	0.952524i	$-0.401523\pi$
$997$	−11.6266	−	6.71259i	−0.368217	−	0.212590i	−0.672679	+	0.739934i	$0.734857\pi$
$998$		0			0
$999$	14.0776	−	10.6544i	0.445396	−	0.337091i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.cp.b.521.12	yes	32
3.2	odd	2		840.2.cp.a.521.8	✓	32
7.5	odd	6		840.2.cp.a.761.8	yes	32
21.5	even	6	inner	840.2.cp.b.761.12	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.cp.a.521.8	✓	32	3.2	odd	2
840.2.cp.a.761.8	yes	32	7.5	odd	6
840.2.cp.b.521.12	yes	32	1.1	even	1	trivial
840.2.cp.b.761.12	yes	32	21.5	even	6	inner

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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.cp (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.46285 - 0.927396i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.49899 - 2.18014i) q^{7} +(1.27987 - 2.71329i) q^{9} +(-5.52920 - 3.19228i) q^{11} +0.186273i q^{13} +(1.53457 + 0.803169i) q^{15} +(3.85223 - 6.67225i) q^{17} +(-5.08695 + 2.93695i) q^{19} +(-4.21466 - 1.79907i) q^{21} +(0.256657 - 0.148181i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-0.644024 - 5.15609i) q^{27} -8.18311i q^{29} +(5.76880 + 3.33062i) q^{31} +(-11.0489 + 0.457915i) q^{33} +(1.13856 - 2.38824i) q^{35} +(1.69885 + 2.94249i) q^{37} +(0.172749 + 0.272490i) q^{39} +9.67409 q^{41} -0.268806 q^{43} +(2.98971 - 0.248240i) q^{45} +(2.93140 + 5.07734i) q^{47} +(-2.50604 + 6.53604i) q^{49} +(-0.552580 - 13.3331i) q^{51} +(2.72386 + 1.57262i) q^{53} -6.38457i q^{55} +(-4.71774 + 9.01394i) q^{57} +(-3.55719 + 6.16123i) q^{59} +(5.46516 - 3.15531i) q^{61} +(-7.83387 + 1.27689i) q^{63} +(-0.161317 + 0.0931364i) q^{65} +(0.460841 - 0.798199i) q^{67} +(0.238028 - 0.454789i) q^{69} -7.44163i q^{71} +(-5.90097 - 3.40693i) q^{73} +(0.0717222 + 1.73057i) q^{75} +(1.32860 + 16.8396i) q^{77} +(0.455092 + 0.788242i) q^{79} +(-5.72385 - 6.94533i) q^{81} -1.79069 q^{83} +7.70445 q^{85} +(-7.58898 - 11.9707i) q^{87} +(-3.80761 - 6.59498i) q^{89} +(0.406101 - 0.279222i) q^{91} +(11.5277 - 0.477758i) q^{93} +(-5.08695 - 2.93695i) q^{95} +10.2378i q^{97} +(-15.7383 + 10.9166i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{5} - 2 q^{7} + 8 q^{9} + 6 q^{19} - 14 q^{21} + 24 q^{23} - 16 q^{25} + 24 q^{27} + 42 q^{31} + 18 q^{33} + 2 q^{35} + 6 q^{37} + 12 q^{39} + 44 q^{41} - 20 q^{43} + 10 q^{45} + 4 q^{47} + 16 q^{49}+ \cdots - 8 q^{99}+O(q^{100}) \) 32 * q + 16 * q^5 - 2 * q^7 + 8 * q^9 + 6 * q^19 - 14 * q^21 + 24 * q^23 - 16 * q^25 + 24 * q^27 + 42 * q^31 + 18 * q^33 + 2 * q^35 + 6 * q^37 + 12 * q^39 + 44 * q^41 - 20 * q^43 + 10 * q^45 + 4 * q^47 + 16 * q^49 - 36 * q^51 + 12 * q^59 - 18 * q^61 + 34 * q^63 - 6 * q^65 - 6 * q^67 - 34 * q^69 - 6 * q^73 + 40 * q^77 - 2 * q^79 - 12 * q^81 - 88 * q^83 - 72 * q^87 - 6 * q^89 - 26 * q^91 + 50 * q^93 + 6 * q^95 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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