LMFDB - Embedded newform 552.2.q.b.265.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(25,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("552.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.q (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			265.2
Character	$\chi$	$=$	552.265
Dual form			552.2.q.b.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 + 0.989821i) q^{3} +(-0.451280 + 0.132508i) q^{5} +(-0.325189 - 0.375288i) q^{7} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(-0.142315 + 0.989821i) q^{3} +(-0.451280 + 0.132508i) q^{5} +(-0.325189 - 0.375288i) q^{7} +(-0.959493 - 0.281733i) q^{9} +(3.66318 + 2.35418i) q^{11} +(1.44489 - 1.66749i) q^{13} +(-0.0669352 - 0.465545i) q^{15} +(2.21590 + 4.85214i) q^{17} +(-2.87917 + 6.30449i) q^{19} +(0.417748 - 0.268470i) q^{21} +(4.54766 + 1.52277i) q^{23} +(-4.02017 + 2.58361i) q^{25} +(0.415415 - 0.909632i) q^{27} +(-2.79905 - 6.12906i) q^{29} +(1.52056 + 10.5757i) q^{31} +(-2.85155 + 3.29086i) q^{33} +(0.196480 + 0.126270i) q^{35} +(-4.47341 - 1.31351i) q^{37} +(1.44489 + 1.66749i) q^{39} +(1.87203 - 0.549677i) q^{41} +(0.727796 - 5.06193i) q^{43} +0.470332 q^{45} +4.15181 q^{47} +(0.961111 - 6.68467i) q^{49} +(-5.11811 + 1.50281i) q^{51} +(4.82353 + 5.56665i) q^{53} +(-1.96507 - 0.576996i) q^{55} +(-5.83058 - 3.74708i) q^{57} +(-3.87925 + 4.47689i) q^{59} +(0.120262 + 0.836439i) q^{61} +(0.206286 + 0.451703i) q^{63} +(-0.431095 + 0.943966i) q^{65} +(-5.09955 + 3.27728i) q^{67} +(-2.15447 + 4.28466i) q^{69} +(11.4068 - 7.33068i) q^{71} +(-0.276252 + 0.604907i) q^{73} +(-1.98518 - 4.34694i) q^{75} +(-0.307729 - 2.14030i) q^{77} +(3.92181 - 4.52601i) q^{79} +(0.841254 + 0.540641i) q^{81} +(13.5725 + 3.98525i) q^{83} +(-1.64294 - 1.89605i) q^{85} +(6.46502 - 1.89830i) q^{87} +(2.08998 - 14.5361i) q^{89} -1.09565 q^{91} -10.6845 q^{93} +(0.463916 - 3.22661i) q^{95} +(9.30065 - 2.73092i) q^{97} +(-2.85155 - 3.29086i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} - 3 q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 - 3 * q^9	$ 30 q - 3 q^{3} - 3 q^{9} + 9 q^{11} + 13 q^{13} + 17 q^{17} - 9 q^{19} - 11 q^{21} - 12 q^{23} - 23 q^{25} - 3 q^{27} - q^{29} - 37 q^{31} + 9 q^{33} + 10 q^{35} + 7 q^{37} + 13 q^{39} + 16 q^{41} + 20 q^{43} - 22 q^{45} + 22 q^{47} + 19 q^{49} + 17 q^{51} + 25 q^{53} + 10 q^{55} + 24 q^{57} + 7 q^{59} + 8 q^{61} - 28 q^{65} - 23 q^{67} - q^{69} + 5 q^{71} + 34 q^{73} - 23 q^{75} + 62 q^{77} + 20 q^{79} - 3 q^{81} + 29 q^{83} - 46 q^{85} + 10 q^{87} - 67 q^{89} - 118 q^{91} - 26 q^{93} - 99 q^{95} - 41 q^{97} + 9 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 - 3 * q^9 + 9 * q^11 + 13 * q^13 + 17 * q^17 - 9 * q^19 - 11 * q^21 - 12 * q^23 - 23 * q^25 - 3 * q^27 - q^29 - 37 * q^31 + 9 * q^33 + 10 * q^35 + 7 * q^37 + 13 * q^39 + 16 * q^41 + 20 * q^43 - 22 * q^45 + 22 * q^47 + 19 * q^49 + 17 * q^51 + 25 * q^53 + 10 * q^55 + 24 * q^57 + 7 * q^59 + 8 * q^61 - 28 * q^65 - 23 * q^67 - q^69 + 5 * q^71 + 34 * q^73 - 23 * q^75 + 62 * q^77 + 20 * q^79 - 3 * q^81 + 29 * q^83 - 46 * q^85 + 10 * q^87 - 67 * q^89 - 118 * q^91 - 26 * q^93 - 99 * q^95 - 41 * q^97 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$1$	$1$	$1$

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
$3$	−0.142315	+	0.989821i	−0.0821655	+	0.571474i
$3$	−0.142315	+	0.989821i	−0.0821655	+	0.571474i
$4$		0			0
$5$	−0.451280	+	0.132508i	−0.201819	+	0.0592593i	−0.381080	−	0.924542i	$-0.624448\pi$
$5$	−0.451280	+	0.132508i	−0.201819	+	0.0592593i	0.179261	+	0.983802i	$0.442629\pi$
$6$		0			0
$7$	−0.325189	−	0.375288i	−0.122910	−	0.141846i	0.690959	−	0.722894i	$-0.257188\pi$
$7$	−0.325189	−	0.375288i	−0.122910	−	0.141846i	−0.813869	+	0.581048i	$0.802643\pi$
$8$		0			0
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$		0			0
$11$	3.66318	+	2.35418i	1.10449	+	0.709813i	0.960086	−	0.279706i	$-0.0902369\pi$
$11$	3.66318	+	2.35418i	1.10449	+	0.709813i	0.144405	+	0.989519i	$0.453873\pi$
$12$		0			0
$13$	1.44489	−	1.66749i	0.400741	−	0.462479i	−0.519133	−	0.854693i	$-0.673745\pi$
$13$	1.44489	−	1.66749i	0.400741	−	0.462479i	0.919874	+	0.392214i	$0.128291\pi$
$14$		0			0
$15$	−0.0669352	−	0.465545i	−0.0172826	−	0.120203i
$16$		0			0
$17$	2.21590	+	4.85214i	0.537434	+	1.17682i	0.962407	+	0.271611i	$0.0875565\pi$
$17$	2.21590	+	4.85214i	0.537434	+	1.17682i	−0.424973	+	0.905206i	$0.639716\pi$
$18$		0			0
$19$	−2.87917	+	6.30449i	−0.660526	+	1.44635i	0.221505	+	0.975159i	$0.428903\pi$
$19$	−2.87917	+	6.30449i	−0.660526	+	1.44635i	−0.882031	+	0.471191i	$0.843824\pi$
$20$		0			0
$21$	0.417748	−	0.268470i	0.0911600	−	0.0585850i
$22$		0			0
$23$	4.54766	+	1.52277i	0.948252	+	0.317519i
$23$	4.54766	+	1.52277i	0.948252	+	0.317519i
$24$		0			0
$25$	−4.02017	+	2.58361i	−0.804034	+	0.516722i
$26$		0			0
$27$	0.415415	−	0.909632i	0.0799467	−	0.175059i
$28$		0			0
$29$	−2.79905	−	6.12906i	−0.519770	−	1.13814i	−0.969527	−	0.244986i	$-0.921217\pi$
$29$	−2.79905	−	6.12906i	−0.519770	−	1.13814i	0.449757	−	0.893151i	$-0.351511\pi$
$30$		0			0
$31$	1.52056	+	10.5757i	0.273100	+	1.89945i	0.415418	+	0.909631i	$0.363635\pi$
$31$	1.52056	+	10.5757i	0.273100	+	1.89945i	−0.142318	+	0.989821i	$0.545456\pi$
$32$		0			0
$33$	−2.85155	+	3.29086i	−0.496390	+	0.572865i
$34$		0			0
$35$	0.196480	+	0.126270i	0.0332112	+	0.0213435i
$36$		0			0
$37$	−4.47341	−	1.31351i	−0.735424	−	0.215940i	−0.107489	−	0.994206i	$-0.534281\pi$
$37$	−4.47341	−	1.31351i	−0.735424	−	0.215940i	−0.627934	+	0.778266i	$0.716099\pi$
$38$		0			0
$39$	1.44489	+	1.66749i	0.231368	+	0.267013i
$40$		0			0
$41$	1.87203	−	0.549677i	0.292362	−	0.0858451i	−0.132263	−	0.991215i	$-0.542224\pi$
$41$	1.87203	−	0.549677i	0.292362	−	0.0858451i	0.424625	+	0.905370i	$0.360406\pi$
$42$		0			0
$43$	0.727796	−	5.06193i	0.110988	−	0.771937i	−0.855974	−	0.517018i	$-0.827042\pi$
$43$	0.727796	−	5.06193i	0.110988	−	0.771937i	0.966962	−	0.254919i	$-0.0820489\pi$
$44$		0			0
$45$	0.470332			0.0701130
$46$		0			0
$47$	4.15181			0.605604			0.302802	−	0.953053i	$-0.402078\pi$
$47$	4.15181			0.605604			0.302802	+	0.953053i	$0.402078\pi$
$48$		0			0
$49$	0.961111	−	6.68467i	0.137302	−	0.954953i
$50$		0			0
$51$	−5.11811	+	1.50281i	−0.716679	+	0.210436i
$52$		0			0
$53$	4.82353	+	5.56665i	0.662563	+	0.764639i	0.983194	−	0.182566i	$-0.0584402\pi$
$53$	4.82353	+	5.56665i	0.662563	+	0.764639i	−0.320630	+	0.947204i	$0.603895\pi$
$54$		0			0
$55$	−1.96507	−	0.576996i	−0.264970	−	0.0778022i
$56$		0			0
$57$	−5.83058	−	3.74708i	−0.772279	−	0.496313i
$58$		0			0
$59$	−3.87925	+	4.47689i	−0.505035	+	0.582842i	−0.949820	−	0.312796i	$-0.898734\pi$
$59$	−3.87925	+	4.47689i	−0.505035	+	0.582842i	0.444785	+	0.895637i	$0.353280\pi$
$60$		0			0
$61$	0.120262	+	0.836439i	0.0153979	+	0.107095i	0.996071	−	0.0885589i	$-0.0282262\pi$
$61$	0.120262	+	0.836439i	0.0153979	+	0.107095i	−0.980673	+	0.195654i	$0.937317\pi$
$62$		0			0
$63$	0.206286	+	0.451703i	0.0259896	+	0.0569092i
$64$		0			0
$65$	−0.431095	+	0.943966i	−0.0534708	+	0.117085i
$66$		0			0
$67$	−5.09955	+	3.27728i	−0.623009	+	0.400384i	−0.813715	−	0.581264i	$-0.802559\pi$
$67$	−5.09955	+	3.27728i	−0.623009	+	0.400384i	0.190706	+	0.981647i	$0.438922\pi$
$68$		0			0
$69$	−2.15447	+	4.28466i	−0.259367	+	0.515812i
$70$		0			0
$71$	11.4068	−	7.33068i	1.35373	−	0.869992i	0.355820	−	0.934555i	$-0.384202\pi$
$71$	11.4068	−	7.33068i	1.35373	−	0.869992i	0.997914	+	0.0645631i	$0.0205654\pi$
$72$		0			0
$73$	−0.276252	+	0.604907i	−0.0323328	+	0.0707990i	−0.925109	−	0.379701i	$-0.876027\pi$
$73$	−0.276252	+	0.604907i	−0.0323328	+	0.0707990i	0.892777	+	0.450500i	$0.148754\pi$
$74$		0			0
$75$	−1.98518	−	4.34694i	−0.229229	−	0.501941i
$76$		0			0
$77$	−0.307729	−	2.14030i	−0.0350690	−	0.243910i
$78$		0			0
$79$	3.92181	−	4.52601i	0.441238	−	0.509216i	−0.490951	−	0.871187i	$-0.663351\pi$
$79$	3.92181	−	4.52601i	0.441238	−	0.509216i	0.932189	+	0.361971i	$0.117896\pi$
$80$		0			0
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$		0			0
$83$	13.5725	+	3.98525i	1.48978	+	0.437438i	0.922470	−	0.386069i	$-0.126167\pi$
$83$	13.5725	+	3.98525i	1.48978	+	0.437438i	0.567307	+	0.823507i	$0.307985\pi$
$84$		0			0
$85$	−1.64294	−	1.89605i	−0.178202	−	0.205656i
$86$		0			0
$87$	6.46502	−	1.89830i	0.693123	−	0.203519i
$88$		0			0
$89$	2.08998	−	14.5361i	0.221537	−	1.54083i	−0.510689	−	0.859765i	$-0.670610\pi$
$89$	2.08998	−	14.5361i	0.221537	−	1.54083i	0.732227	−	0.681061i	$-0.238481\pi$
$90$		0			0
$91$	−1.09565			−0.114856
$92$		0			0
$93$	−10.6845			−1.10793
$94$		0			0
$95$	0.463916	−	3.22661i	0.0475968	−	0.331043i
$96$		0			0
$97$	9.30065	−	2.73092i	0.944338	−	0.277283i	0.226910	−	0.973916i	$-0.427138\pi$
$97$	9.30065	−	2.73092i	0.944338	−	0.277283i	0.717428	+	0.696633i	$0.245319\pi$
$98$		0			0
$99$	−2.85155	−	3.29086i	−0.286591	−	0.330744i
$100$		0			0
$101$	−6.60064	−	1.93812i	−0.656788	−	0.192850i	−0.0636765	−	0.997971i	$-0.520283\pi$
$101$	−6.60064	−	1.93812i	−0.656788	−	0.192850i	−0.593112	+	0.805120i	$0.702101\pi$
$102$		0			0
$103$	−4.05307	−	2.60475i	−0.399361	−	0.256654i	0.325510	−	0.945539i	$-0.394464\pi$
$103$	−4.05307	−	2.60475i	−0.399361	−	0.256654i	−0.724871	+	0.688885i	$0.758101\pi$
$104$		0			0
$105$	−0.152947	+	0.176510i	−0.0149261	+	0.0172256i
$106$		0			0
$107$	−0.0519187	−	0.361102i	−0.00501917	−	0.0349091i	0.987158	−	0.159747i	$-0.0510679\pi$
$107$	−0.0519187	−	0.361102i	−0.00501917	−	0.0349091i	−0.992177	+	0.124838i	$0.960159\pi$
$108$		0			0
$109$	−6.49439	−	14.2207i	−0.622049	−	1.36210i	−0.914019	−	0.405671i	$-0.867038\pi$
$109$	−6.49439	−	14.2207i	−0.622049	−	1.36210i	0.291970	−	0.956427i	$-0.405689\pi$
$110$		0			0
$111$	1.93677	−	4.24094i	0.183830	−	0.402533i
$112$		0			0
$113$	−7.62426	+	4.89982i	−0.717230	+	0.460936i	−0.847672	−	0.530520i	$-0.821997\pi$
$113$	−7.62426	+	4.89982i	−0.717230	+	0.460936i	0.130442	+	0.991456i	$0.458360\pi$
$114$		0			0
$115$	−2.25405	−	0.0845943i	−0.210191	−	0.00788846i
$116$		0			0
$117$	−1.85615	+	1.19288i	−0.171601	+	0.110281i
$118$		0			0
$119$	1.10037	−	2.40946i	0.100870	−	0.220875i
$120$		0			0
$121$	3.30715	+	7.24164i	0.300650	+	0.658331i
$122$		0			0
$123$	0.277665	+	1.93120i	0.0250362	+	0.174131i
$124$		0			0
$125$	3.01189	−	3.47590i	0.269391	−	0.310894i
$126$		0			0
$127$	−2.75122	−	1.76810i	−0.244131	−	0.156894i	0.412854	−	0.910797i	$-0.364532\pi$
$127$	−2.75122	−	1.76810i	−0.244131	−	0.156894i	−0.656985	+	0.753904i	$0.728168\pi$
$128$		0			0
$129$	4.90683	+	1.44078i	0.432023	+	0.126853i
$130$		0			0
$131$	−10.1086	−	11.6660i	−0.883194	−	1.01926i	−0.999660	−	0.0260652i	$-0.991702\pi$
$131$	−10.1086	−	11.6660i	−0.883194	−	1.01926i	0.116467	−	0.993195i	$-0.462843\pi$
$132$		0			0
$133$	3.30228	−	0.969636i	0.286344	−	0.0840781i
$134$		0			0
$135$	−0.0669352	+	0.465545i	−0.00576087	+	0.0400677i
$136$		0			0
$137$	6.46918			0.552700			0.276350	−	0.961057i	$-0.410875\pi$
$137$	6.46918			0.552700			0.276350	+	0.961057i	$0.410875\pi$
$138$		0			0
$139$	−20.3477			−1.72587			−0.862933	−	0.505318i	$-0.831375\pi$
$139$	−20.3477			−1.72587			−0.862933	+	0.505318i	$0.831375\pi$
$140$		0			0
$141$	−0.590865	+	4.10955i	−0.0497598	+	0.346087i
$142$		0			0
$143$	9.21848	−	2.70679i	0.770888	−	0.226353i
$144$		0			0
$145$	2.07530	+	2.39503i	0.172345	+	0.198896i
$146$		0			0
$147$	6.47985	+	1.90266i	0.534449	+	0.156928i
$148$		0			0
$149$	5.88773	+	3.78381i	0.482342	+	0.309982i	0.759119	−	0.650952i	$-0.225630\pi$
$149$	5.88773	+	3.78381i	0.482342	+	0.309982i	−0.276777	+	0.960934i	$0.589266\pi$
$150$		0			0
$151$	5.66905	−	6.54243i	0.461341	−	0.532415i	−0.476642	−	0.879097i	$-0.658146\pi$
$151$	5.66905	−	6.54243i	0.461341	−	0.532415i	0.937983	+	0.346682i	$0.112692\pi$
$152$		0			0
$153$	−0.759133	−	5.27989i	−0.0613723	−	0.426854i
$154$		0			0
$155$	−2.08756	−	4.57112i	−0.167677	−	0.367161i
$156$		0			0
$157$	6.50167	−	14.2367i	0.518889	−	1.13621i	−0.450969	−	0.892540i	$-0.648921\pi$
$157$	6.50167	−	14.2367i	0.518889	−	1.13621i	0.969858	−	0.243670i	$-0.0783513\pi$
$158$		0			0
$159$	−6.19645	+	3.98222i	−0.491411	+	0.315811i
$160$		0			0
$161$	−0.907372	−	2.20187i	−0.0715109	−	0.173532i
$162$		0			0
$163$	−18.5650	+	11.9310i	−1.45412	+	0.934508i	−0.455094	+	0.890443i	$0.650395\pi$
$163$	−18.5650	+	11.9310i	−1.45412	+	0.934508i	−0.999029	+	0.0440651i	$0.985969\pi$
$164$		0			0
$165$	0.850782	−	1.86295i	0.0662333	−	0.145031i
$166$		0			0
$167$	−2.21548	−	4.85122i	−0.171439	−	0.375398i	0.804337	−	0.594174i	$-0.202521\pi$
$167$	−2.21548	−	4.85122i	−0.171439	−	0.375398i	−0.975775	+	0.218776i	$0.929794\pi$
$168$		0			0
$169$	1.15727	+	8.04899i	0.0890207	+	0.619153i
$170$		0			0
$171$	4.53872	−	5.23796i	0.347085	−	0.400557i
$172$		0			0
$173$	14.3538	+	9.22461i	1.09130	+	0.701334i	0.957140	−	0.289626i	$-0.0935309\pi$
$173$	14.3538	+	9.22461i	1.09130	+	0.701334i	0.134157	+	0.990960i	$0.457167\pi$
$174$		0			0
$175$	2.27691	+	0.668562i	0.172118	+	0.0505385i
$176$		0			0
$177$	−3.87925	−	4.47689i	−0.291582	−	0.336504i
$178$		0			0
$179$	−6.38955	+	1.87614i	−0.477577	+	0.140229i	−0.511657	−	0.859190i	$-0.670968\pi$
$179$	−6.38955	+	1.87614i	−0.477577	+	0.140229i	0.0340799	+	0.999419i	$0.489150\pi$
$180$		0			0
$181$	1.44807	−	10.0715i	0.107634	−	0.748610i	−0.862503	−	0.506052i	$-0.831104\pi$
$181$	1.44807	−	10.0715i	0.107634	−	0.748610i	0.970137	−	0.242558i	$-0.0779865\pi$
$182$		0			0
$183$	−0.845040			−0.0624671
$184$		0			0
$185$	2.19281			0.161219
$186$		0			0
$187$	−3.30559	+	22.9909i	−0.241729	+	1.68126i
$188$		0			0
$189$	−0.476463	+	0.139902i	−0.0346576	+	0.0101764i
$190$		0			0
$191$	−7.34270	−	8.47392i	−0.531299	−	0.613152i	0.425125	−	0.905135i	$-0.360230\pi$
$191$	−7.34270	−	8.47392i	−0.531299	−	0.613152i	−0.956423	+	0.291983i	$0.905685\pi$
$192$		0			0
$193$	−9.55070	−	2.80434i	−0.687474	−	0.201861i	−0.0807043	−	0.996738i	$-0.525717\pi$
$193$	−9.55070	−	2.80434i	−0.687474	−	0.201861i	−0.606770	+	0.794877i	$0.707535\pi$
$194$		0			0
$195$	−0.873007	−	0.561048i	−0.0625173	−	0.0401775i
$196$		0			0
$197$	−11.9483	+	13.7891i	−0.851282	+	0.982431i	−0.999979	−	0.00645128i	$-0.997946\pi$
$197$	−11.9483	+	13.7891i	−0.851282	+	0.982431i	0.148697	+	0.988883i	$0.452492\pi$
$198$		0			0
$199$	−2.13987	−	14.8831i	−0.151691	−	1.05504i	−0.913385	−	0.407098i	$-0.866541\pi$
$199$	−2.13987	−	14.8831i	−0.151691	−	1.05504i	0.761693	−	0.647938i	$-0.224368\pi$
$200$		0			0
$201$	−2.51818	−	5.51405i	−0.177619	−	0.388931i
$202$		0			0
$203$	−1.38994	+	3.04355i	−0.0975549	+	0.213615i
$204$		0			0
$205$	−0.771973	+	0.496117i	−0.0539169	+	0.0346503i
$206$		0			0
$207$	−3.93443	−	2.74231i	−0.273462	−	0.190603i
$208$		0			0
$209$	−25.3888	+	16.3164i	−1.75618	+	1.12863i
$210$		0			0
$211$	7.81692	−	17.1167i	0.538139	−	1.17836i	−0.423965	−	0.905678i	$-0.639362\pi$
$211$	7.81692	−	17.1167i	0.538139	−	1.17836i	0.962104	−	0.272682i	$-0.0879106\pi$
$212$		0			0
$213$	5.63271	+	12.3339i	0.385947	+	0.845106i
$214$		0			0
$215$	0.342306	+	2.38079i	0.0233451	+	0.162368i
$216$		0			0
$217$	3.47447	−	4.00975i	0.235862	−	0.272199i
$218$		0			0
$219$	−0.559435	−	0.359527i	−0.0378031	−	0.0242946i
$220$		0			0
$221$	11.2926	+	3.31582i	0.759626	+	0.223046i
$222$		0			0
$223$	10.7627	+	12.4208i	0.720724	+	0.831760i	0.991394	−	0.130912i	$-0.0417907\pi$
$223$	10.7627	+	12.4208i	0.720724	+	0.831760i	−0.270670	+	0.962672i	$0.587245\pi$
$224$		0			0
$225$	4.58521	−	1.34634i	0.305681	−	0.0897560i
$226$		0			0
$227$	0.874734	−	6.08391i	0.0580581	−	0.403803i	−0.939982	−	0.341224i	$-0.889158\pi$
$227$	0.874734	−	6.08391i	0.0580581	−	0.403803i	0.998040	−	0.0625788i	$-0.0199325\pi$
$228$		0			0
$229$	14.0656			0.929479			0.464739	−	0.885448i	$-0.346148\pi$
$229$	14.0656			0.929479			0.464739	+	0.885448i	$0.346148\pi$
$230$		0			0
$231$	2.16231			0.142270
$232$		0			0
$233$	−0.203404	+	1.41471i	−0.0133254	+	0.0926804i	−0.995399	−	0.0958186i	$-0.969453\pi$
$233$	−0.203404	+	1.41471i	−0.0133254	+	0.0926804i	0.982073	+	0.188499i	$0.0603622\pi$
$234$		0			0
$235$	−1.87363	+	0.550148i	−0.122222	+	0.0358877i
$236$		0			0
$237$	3.92181	+	4.52601i	0.254749	+	0.293996i
$238$		0			0
$239$	12.8236	+	3.76535i	0.829489	+	0.243560i	0.668797	−	0.743445i	$-0.266809\pi$
$239$	12.8236	+	3.76535i	0.829489	+	0.243560i	0.160692	+	0.987005i	$0.448628\pi$
$240$		0			0
$241$	22.0438	+	14.1667i	1.41997	+	0.912556i	0.999987	+	0.00502171i	$0.00159847\pi$
$241$	22.0438	+	14.1667i	1.41997	+	0.912556i	0.419978	+	0.907534i	$0.362038\pi$
$242$		0			0
$243$	−0.654861	+	0.755750i	−0.0420093	+	0.0484814i
$244$		0			0
$245$	0.452041	+	3.14402i	0.0288799	+	0.200864i
$246$		0			0
$247$	6.35262	+	13.9103i	0.404208	+	0.885091i
$248$		0			0
$249$	−5.87626	+	12.8672i	−0.372393	+	0.815426i
$250$		0			0
$251$	−6.89256	+	4.42958i	−0.435055	+	0.279593i	−0.739782	−	0.672847i	$-0.765071\pi$
$251$	−6.89256	+	4.42958i	−0.435055	+	0.279593i	0.304727	+	0.952440i	$0.401435\pi$
$252$		0			0
$253$	13.0740	+	16.2842i	0.821956	+	1.02378i
$254$		0			0
$255$	2.11057	−	1.35638i	0.132169	−	0.0849398i
$256$		0			0
$257$	7.25177	−	15.8792i	0.452353	−	0.990515i	−0.536811	−	0.843702i	$-0.680371\pi$
$257$	7.25177	−	15.8792i	0.452353	−	0.990515i	0.989164	−	0.146812i	$-0.0469014\pi$
$258$		0			0
$259$	0.961758	+	2.10596i	0.0597608	+	0.130858i
$260$		0			0
$261$	0.958910	+	6.66937i	0.0593551	+	0.412824i
$262$		0			0
$263$	−16.6510	+	19.2162i	−1.02674	+	1.18492i	−0.0441731	+	0.999024i	$0.514065\pi$
$263$	−16.6510	+	19.2162i	−1.02674	+	1.18492i	−0.982569	+	0.185899i	$0.940480\pi$
$264$		0			0
$265$	−2.91439	−	1.87297i	−0.179030	−	0.115055i
$266$		0			0
$267$	14.0907	+	4.13741i	0.862339	+	0.253206i
$268$		0			0
$269$	−6.57502	−	7.58798i	−0.400886	−	0.462647i	0.519034	−	0.854754i	$-0.326292\pi$
$269$	−6.57502	−	7.58798i	−0.400886	−	0.462647i	−0.919920	+	0.392106i	$0.871746\pi$
$270$		0			0
$271$	−16.2603	+	4.77445i	−0.987742	+	0.290027i	−0.735417	−	0.677615i	$-0.763014\pi$
$271$	−16.2603	+	4.77445i	−0.987742	+	0.290027i	−0.252326	+	0.967642i	$0.581195\pi$
$272$		0			0
$273$	0.155928	−	1.08450i	0.00943718	−	0.0656370i
$274$		0			0
$275$	−20.8089			−1.25482
$276$		0			0
$277$	4.08137			0.245226			0.122613	−	0.992455i	$-0.460873\pi$
$277$	4.08137			0.245226			0.122613	+	0.992455i	$0.460873\pi$
$278$		0			0
$279$	1.52056	−	10.5757i	0.0910333	−	0.633150i
$280$		0			0
$281$	9.11129	−	2.67532i	0.543534	−	0.159596i	0.00157162	−	0.999999i	$-0.499500\pi$
$281$	9.11129	−	2.67532i	0.543534	−	0.159596i	0.541962	+	0.840403i	$0.317682\pi$
$282$		0			0
$283$	−3.83238	−	4.42281i	−0.227812	−	0.262909i	0.630323	−	0.776333i	$-0.282922\pi$
$283$	−3.83238	−	4.42281i	−0.227812	−	0.262909i	−0.858135	+	0.513424i	$0.828377\pi$
$284$		0			0
$285$	3.12774	+	0.918388i	0.185271	+	0.0544006i
$286$		0			0
$287$	−0.815050	−	0.523801i	−0.0481109	−	0.0309190i
$288$		0			0
$289$	−7.50044	+	8.65597i	−0.441203	+	0.509175i
$290$		0			0
$291$	1.37950	+	9.59463i	0.0808677	+	0.562447i
$292$		0			0
$293$	−0.966073	−	2.11541i	−0.0564386	−	0.123583i	0.879311	−	0.476247i	$-0.158003\pi$
$293$	−0.966073	−	2.11541i	−0.0564386	−	0.123583i	−0.935750	+	0.352664i	$0.885276\pi$
$294$		0			0
$295$	1.15741	−	2.53436i	0.0673867	−	0.147556i
$296$		0			0
$297$	3.66318	−	2.35418i	0.212559	−	0.136604i
$298$		0			0
$299$	9.11007	−	5.38296i	0.526849	−	0.311304i
$300$		0			0
$301$	−2.13635	+	1.37295i	−0.123137	+	0.0791356i
$302$		0			0
$303$	2.85776	−	6.25763i	0.164174	−	0.359491i
$304$		0			0
$305$	−0.165106	−	0.361533i	−0.00945397	−	0.0207013i
$306$		0			0
$307$	−1.41684	−	9.85433i	−0.0808632	−	0.562416i	−0.989467	−	0.144757i	$-0.953760\pi$
$307$	−1.41684	−	9.85433i	−0.0808632	−	0.562416i	0.908604	−	0.417659i	$-0.137149\pi$
$308$		0			0
$309$	3.15505	−	3.64112i	0.179485	−	0.207136i
$310$		0			0
$311$	24.7024	+	15.8753i	1.40075	+	0.900205i	0.999873	−	0.0159292i	$-0.00507065\pi$
$311$	24.7024	+	15.8753i	1.40075	+	0.900205i	0.400873	+	0.916134i	$0.368707\pi$
$312$		0			0
$313$	28.6965	+	8.42604i	1.62202	+	0.476268i	0.961560	−	0.274594i	$-0.0885435\pi$
$313$	28.6965	+	8.42604i	1.62202	+	0.476268i	0.660459	+	0.750862i	$0.270362\pi$
$314$		0			0
$315$	−0.152947	−	0.176510i	−0.00861758	−	0.00994522i
$316$		0			0
$317$	−18.6759	+	5.48375i	−1.04894	+	0.307998i	−0.760391	−	0.649466i	$-0.774993\pi$
$317$	−18.6759	+	5.48375i	−1.04894	+	0.307998i	−0.288554	+	0.957464i	$0.593174\pi$
$318$		0			0
$319$	4.17551	−	29.0413i	0.233784	−	1.62600i
$320$		0			0
$321$	0.364816			0.0203620
$322$		0			0
$323$	−36.9702			−2.05708
$324$		0			0
$325$	−1.50056	+	10.4366i	−0.0832362	+	0.578921i
$326$		0			0
$327$	15.0002	−	4.40446i	0.829514	−	0.243567i
$328$		0			0
$329$	−1.35012	−	1.55813i	−0.0744348	−	0.0859023i
$330$		0			0
$331$	13.2504	+	3.89067i	0.728308	+	0.213851i	0.624808	−	0.780779i	$-0.285177\pi$
$331$	13.2504	+	3.89067i	0.728308	+	0.213851i	0.103501	+	0.994629i	$0.466996\pi$
$332$		0			0
$333$	3.92215	+	2.52061i	0.214932	+	0.138129i
$334$		0			0
$335$	1.86706	−	2.15470i	0.102008	−	0.117724i
$336$		0			0
$337$	4.55418	+	31.6750i	0.248082	+	1.72545i	0.609275	+	0.792959i	$0.291460\pi$
$337$	4.55418	+	31.6750i	0.248082	+	1.72545i	−0.361193	+	0.932491i	$0.617630\pi$
$338$		0			0
$339$	−3.76490	−	8.24397i	−0.204481	−	0.447751i
$340$		0			0
$341$	−19.3271	+	42.3204i	−1.04662	+	2.29178i
$342$		0			0
$343$	−5.74545	+	3.69238i	−0.310225	+	0.199370i
$344$		0			0
$345$	0.404518	−	2.21906i	0.0217785	−	0.119470i
$346$		0			0
$347$	−3.16646	+	2.03496i	−0.169984	+	0.109242i	−0.622867	−	0.782328i	$-0.714032\pi$
$347$	−3.16646	+	2.03496i	−0.169984	+	0.109242i	0.452882	+	0.891570i	$0.350396\pi$
$348$		0			0
$349$	4.06432	−	8.89963i	0.217558	−	0.476386i	−0.769113	−	0.639113i	$-0.779302\pi$
$349$	4.06432	−	8.89963i	0.217558	−	0.476386i	0.986671	+	0.162727i	$0.0520289\pi$
$350$		0			0
$351$	−0.916576	−	2.00702i	−0.0489232	−	0.107127i
$352$		0			0
$353$	2.52765	+	17.5802i	0.134533	+	0.935698i	0.939542	+	0.342435i	$0.111252\pi$
$353$	2.52765	+	17.5802i	0.134533	+	0.935698i	−0.805008	+	0.593263i	$0.797839\pi$
$354$		0			0
$355$	−4.17627	+	4.81968i	−0.221654	+	0.255802i
$356$		0			0
$357$	2.22834	+	1.43207i	0.117936	+	0.0757931i
$358$		0			0
$359$	6.34158	+	1.86205i	0.334696	+	0.0982755i	0.444762	−	0.895649i	$-0.353288\pi$
$359$	6.34158	+	1.86205i	0.334696	+	0.0982755i	−0.110067	+	0.993924i	$0.535106\pi$
$360$		0			0
$361$	−19.0147	−	21.9441i	−1.00077	−	1.15495i
$362$		0			0
$363$	−7.63859	+	2.24289i	−0.400922	+	0.117721i
$364$		0			0
$365$	0.0445120	−	0.309588i	0.00232987	−	0.0162046i
$366$		0			0
$367$	4.63553			0.241973			0.120986	−	0.992654i	$-0.461394\pi$
$367$	4.63553			0.241973			0.120986	+	0.992654i	$0.461394\pi$
$368$		0			0
$369$	−1.95106			−0.101568
$370$		0			0
$371$	0.520539	−	3.62043i	0.0270251	−	0.187963i
$372$		0			0
$373$	−4.77131	+	1.40098i	−0.247049	+	0.0725402i	−0.402913	−	0.915238i	$-0.632002\pi$
$373$	−4.77131	+	1.40098i	−0.247049	+	0.0725402i	0.155864	+	0.987779i	$0.450184\pi$
$374$		0			0
$375$	3.01189	+	3.47590i	0.155533	+	0.179495i
$376$		0			0
$377$	−14.2645	−	4.18843i	−0.734658	−	0.215715i
$378$		0			0
$379$	9.56257	+	6.14549i	0.491196	+	0.315673i	0.762686	−	0.646769i	$-0.223880\pi$
$379$	9.56257	+	6.14549i	0.491196	+	0.315673i	−0.271490	+	0.962441i	$0.587516\pi$
$380$		0			0
$381$	2.14164	−	2.47159i	0.109720	−	0.126623i
$382$		0			0
$383$	−2.35936	−	16.4097i	−0.120558	−	0.838497i	−0.956927	−	0.290330i	$-0.906235\pi$
$383$	−2.35936	−	16.4097i	−0.120558	−	0.838497i	0.836369	−	0.548167i	$-0.184674\pi$
$384$		0			0
$385$	0.422479	+	0.925100i	0.0215315	+	0.0471475i
$386$		0			0
$387$	−2.12443	+	4.65184i	−0.107991	+	0.236467i
$388$		0			0
$389$	24.7577	−	15.9108i	1.25526	−	0.806709i	0.267635	−	0.963520i	$-0.413758\pi$
$389$	24.7577	−	15.9108i	1.25526	−	0.806709i	0.987629	+	0.156811i	$0.0501214\pi$
$390$		0			0
$391$	2.68847	+	25.4402i	0.135962	+	1.28656i
$392$		0			0
$393$	12.9858	−	8.34548i	0.655048	−	0.420974i
$394$		0			0
$395$	−1.17010	+	2.56217i	−0.0588743	+	0.128917i
$396$		0			0
$397$	−8.60230	−	18.8364i	−0.431737	−	0.945373i	−0.993042	−	0.117763i	$-0.962428\pi$
$397$	−8.60230	−	18.8364i	−0.431737	−	0.945373i	0.561304	−	0.827609i	$-0.310300\pi$
$398$		0			0
$399$	0.489803	+	3.40666i	0.0245208	+	0.170546i
$400$		0			0
$401$	5.25238	−	6.06157i	0.262291	−	0.302700i	−0.609294	−	0.792945i	$-0.708547\pi$
$401$	5.25238	−	6.06157i	0.262291	−	0.302700i	0.871585	+	0.490244i	$0.163092\pi$
$402$		0			0
$403$	19.8319	+	12.7452i	0.987899	+	0.634884i
$404$		0			0
$405$	−0.451280	−	0.132508i	−0.0224243	−	0.00658437i
$406$		0			0
$407$	−13.2947	−	15.3429i	−0.658992	−	0.760517i
$408$		0			0
$409$	−1.36834	+	0.401782i	−0.0676602	+	0.0198668i	−0.315388	−	0.948963i	$-0.602134\pi$
$409$	−1.36834	+	0.401782i	−0.0676602	+	0.0198668i	0.247727	+	0.968830i	$0.420316\pi$
$410$		0			0
$411$	−0.920661	+	6.40334i	−0.0454128	+	0.315853i
$412$		0			0
$413$	2.94161			0.144747
$414$		0			0
$415$	−6.65309			−0.326587
$416$		0			0
$417$	2.89577	−	20.1406i	0.141807	−	0.986287i
$418$		0			0
$419$	−19.9772	+	5.86582i	−0.975948	+	0.286564i	−0.730551	−	0.682858i	$-0.760737\pi$
$419$	−19.9772	+	5.86582i	−0.975948	+	0.286564i	−0.245397	+	0.969423i	$0.578918\pi$
$420$		0			0
$421$	−18.9194	−	21.8341i	−0.922073	−	1.06413i	−0.997753	−	0.0669965i	$-0.978658\pi$
$421$	−18.9194	−	21.8341i	−0.922073	−	1.06413i	0.0756805	−	0.997132i	$-0.475887\pi$
$422$		0			0
$423$	−3.98364	−	1.16970i	−0.193691	−	0.0568728i
$424$		0			0
$425$	−21.4443	−	13.7814i	−1.04020	−	0.668498i
$426$		0			0
$427$	0.274798	−	0.317133i	0.0132984	−	0.0153472i
$428$		0			0
$429$	1.36731	+	9.50987i	0.0660145	+	0.459141i
$430$		0			0
$431$	−3.54219	−	7.75632i	−0.170621	−	0.373609i	0.804933	−	0.593365i	$-0.202201\pi$
$431$	−3.54219	−	7.75632i	−0.170621	−	0.373609i	−0.975555	+	0.219756i	$0.929474\pi$
$432$		0			0
$433$	−8.16972	+	17.8892i	−0.392612	+	0.859700i	0.605354	+	0.795956i	$0.293031\pi$
$433$	−8.16972	+	17.8892i	−0.392612	+	0.859700i	−0.997966	+	0.0637440i	$0.979696\pi$
$434$		0			0
$435$	−2.66600	+	1.71333i	−0.127825	+	0.0821480i
$436$		0			0
$437$	−22.6937	+	24.2864i	−1.08559	+	1.16178i
$438$		0			0
$439$	19.9796	−	12.8401i	0.953573	−	0.612824i	0.0313607	−	0.999508i	$-0.490016\pi$
$439$	19.9796	−	12.8401i	0.953573	−	0.612824i	0.922212	+	0.386684i	$0.126380\pi$
$440$		0			0
$441$	−2.80547	+	6.14312i	−0.133594	+	0.292529i
$442$		0			0
$443$	−4.24525	−	9.29580i	−0.201698	−	0.441657i	0.781571	−	0.623816i	$-0.214419\pi$
$443$	−4.24525	−	9.29580i	−0.201698	−	0.441657i	−0.983269	+	0.182159i	$0.941691\pi$
$444$		0			0
$445$	0.982984	+	6.83681i	0.0465979	+	0.324096i
$446$		0			0
$447$	−4.58321	+	5.28931i	−0.216778	+	0.250176i
$448$		0			0
$449$	−23.0184	−	14.7930i	−1.08630	−	0.698125i	−0.130299	−	0.991475i	$-0.541594\pi$
$449$	−23.0184	−	14.7930i	−1.08630	−	0.698125i	−0.956005	+	0.293350i	$0.905230\pi$
$450$		0			0
$451$	8.15162	+	2.39353i	0.383845	+	0.112707i
$452$		0			0
$453$	5.66905	+	6.54243i	0.266355	+	0.307390i
$454$		0			0
$455$	0.494447	−	0.145183i	0.0231800	−	0.00680627i
$456$		0			0
$457$	4.61775	−	32.1172i	0.216009	−	1.50238i	−0.536559	−	0.843863i	$-0.680276\pi$
$457$	4.61775	−	32.1172i	0.216009	−	1.50238i	0.752568	−	0.658514i	$-0.228815\pi$
$458$		0			0
$459$	5.33418			0.248978
$460$		0			0
$461$	−14.0379			−0.653809			−0.326905	−	0.945057i	$-0.606006\pi$
$461$	−14.0379			−0.653809			−0.326905	+	0.945057i	$0.606006\pi$
$462$		0			0
$463$	−0.514703	+	3.57984i	−0.0239203	+	0.166369i	−0.998280	−	0.0586269i	$-0.981328\pi$
$463$	−0.514703	+	3.57984i	−0.0239203	+	0.166369i	0.974360	+	0.224996i	$0.0722369\pi$
$464$		0			0
$465$	4.82168	−	1.41577i	0.223600	−	0.0656549i
$466$		0			0
$467$	21.5409	+	24.8596i	0.996795	+	1.15036i	0.988626	+	0.150397i	$0.0480551\pi$
$467$	21.5409	+	24.8596i	0.996795	+	1.15036i	0.00816973	+	0.999967i	$0.497399\pi$
$468$		0			0
$469$	2.88824	+	0.848064i	0.133367	+	0.0391600i
$470$		0			0
$471$	13.1665	+	8.46158i	0.606679	+	0.389889i
$472$		0			0
$473$	14.5828	−	16.8294i	0.670516	−	0.773817i
$474$		0			0
$475$	−4.71360	−	32.7838i	−0.216275	−	1.50422i
$476$		0			0
$477$	−3.05984	−	6.70011i	−0.140100	−	0.306777i
$478$		0			0
$479$	−0.665726	+	1.45774i	−0.0304178	+	0.0666057i	−0.924231	−	0.381834i	$-0.875293\pi$
$479$	−0.665726	+	1.45774i	−0.0304178	+	0.0666057i	0.893813	+	0.448439i	$0.148020\pi$
$480$		0			0
$481$	−8.65386	+	5.56150i	−0.394582	+	0.253582i
$482$		0			0
$483$	2.30859	−	0.584778i	0.105044	−	0.0266083i
$484$		0			0
$485$	−3.83533	+	2.46482i	−0.174153	+	0.111922i
$486$		0			0
$487$	8.70010	−	19.0506i	0.394239	−	0.863263i	−0.603583	−	0.797300i	$-0.706261\pi$
$487$	8.70010	−	19.0506i	0.394239	−	0.863263i	0.997822	−	0.0659628i	$-0.0210119\pi$
$488$		0			0
$489$	−9.16749	−	20.0740i	−0.414568	−	0.907777i
$490$		0			0
$491$	1.78046	+	12.3834i	0.0803511	+	0.558854i	0.989737	+	0.142901i	$0.0456430\pi$
$491$	1.78046	+	12.3834i	0.0803511	+	0.558854i	−0.909386	+	0.415954i	$0.863448\pi$
$492$		0			0
$493$	23.5366	−	27.1627i	1.06004	−	1.22335i
$494$		0			0
$495$	1.72291	+	1.10725i	0.0774391	+	0.0497671i
$496$		0			0
$497$	−6.46047	−	1.89697i	−0.289792	−	0.0850905i
$498$		0			0
$499$	−22.1456	−	25.5573i	−0.991372	−	1.14410i	−0.989562	−	0.144106i	$-0.953969\pi$
$499$	−22.1456	−	25.5573i	−0.991372	−	1.14410i	−0.00180945	−	0.999998i	$-0.500576\pi$
$500$		0			0
$501$	5.11713	−	1.50253i	0.228617	−	0.0671279i
$502$		0			0
$503$	4.14500	−	28.8291i	0.184817	−	1.28543i	−0.660364	−	0.750946i	$-0.729598\pi$
$503$	4.14500	−	28.8291i	0.184817	−	1.28543i	0.845180	−	0.534481i	$-0.179493\pi$
$504$		0			0
$505$	3.23556			0.143980
$506$		0			0
$507$	−8.13176			−0.361144
$508$		0			0
$509$	4.20772	−	29.2653i	0.186504	−	1.29716i	−0.654471	−	0.756087i	$-0.727109\pi$
$509$	4.20772	−	29.2653i	0.186504	−	1.29716i	0.840975	−	0.541075i	$-0.181982\pi$
$510$		0			0
$511$	0.316848	−	0.0930350i	0.0140165	−	0.00411563i
$512$		0			0
$513$	4.53872	+	5.23796i	0.200389	+	0.231262i
$514$		0			0
$515$	2.17422	+	0.638409i	0.0958077	+	0.0281317i
$516$		0			0
$517$	15.2088	+	9.77413i	0.668884	+	0.429866i
$518$		0			0
$519$	−11.1735	+	12.8949i	−0.490461	+	0.566022i
$520$		0			0
$521$	−0.0106780	−	0.0742669i	−0.000467810	−	0.00325369i	0.989586	−	0.143941i	$-0.0459777\pi$
$521$	−0.0106780	−	0.0742669i	−0.000467810	−	0.00325369i	−0.990054	+	0.140688i	$0.955069\pi$
$522$		0			0
$523$	8.36486	+	18.3165i	0.365770	+	0.800924i	0.999623	+	0.0274702i	$0.00874513\pi$
$523$	8.36486	+	18.3165i	0.365770	+	0.800924i	−0.633853	+	0.773454i	$0.718528\pi$
$524$		0			0
$525$	−0.985796	+	2.15859i	−0.0430237	+	0.0942087i
$526$		0			0
$527$	−47.9454	+	30.8126i	−2.08853	+	1.34222i
$528$		0			0
$529$	18.3624	+	13.8500i	0.798364	+	0.602176i
$530$		0			0
$531$	4.98340	−	3.20263i	0.216261	−	0.138983i
$532$		0			0
$533$	1.78829	−	3.91582i	0.0774596	−	0.169613i
$534$		0			0
$535$	0.0712788	+	0.156079i	0.00308165	+	0.00674787i
$536$		0			0
$537$	−0.947716	−	6.59151i	−0.0408970	−	0.284445i
$538$		0			0
$539$	19.2577	−	22.2245i	0.829486	−	0.957278i
$540$		0			0
$541$	−26.1890	−	16.8306i	−1.12595	−	0.723605i	−0.161240	−	0.986915i	$-0.551549\pi$
$541$	−26.1890	−	16.8306i	−1.12595	−	0.723605i	−0.964711	+	0.263310i	$0.915186\pi$
$542$		0			0
$543$	9.76292	+	2.86665i	0.418967	+	0.123020i
$544$		0			0
$545$	4.81515	+	5.55698i	0.206258	+	0.238035i
$546$		0			0
$547$	13.6877	−	4.01907i	0.585244	−	0.171843i	0.0243110	−	0.999704i	$-0.492261\pi$
$547$	13.6877	−	4.01907i	0.585244	−	0.171843i	0.560933	+	0.827861i	$0.310443\pi$
$548$		0			0
$549$	0.120262	−	0.836439i	0.00513264	−	0.0356983i
$550$		0			0
$551$	46.6995			1.98947
$552$		0			0
$553$	−2.97389			−0.126463
$554$		0			0
$555$	−0.312070	+	2.17049i	−0.0132466	+	0.0921323i
$556$		0			0
$557$	35.5368	−	10.4345i	1.50574	−	0.442126i	0.578216	−	0.815884i	$-0.303749\pi$
$557$	35.5368	−	10.4345i	1.50574	−	0.442126i	0.927526	+	0.373758i	$0.121931\pi$
$558$		0			0
$559$	−7.38915	−	8.52754i	−0.312528	−	0.360676i
$560$		0			0
$561$	−22.2865	−	6.54389i	−0.940935	−	0.276283i
$562$		0			0
$563$	17.6996	+	11.3748i	0.745948	+	0.479392i	0.857575	−	0.514358i	$-0.171970\pi$
$563$	17.6996	+	11.3748i	0.745948	+	0.479392i	−0.111627	+	0.993750i	$0.535606\pi$
$564$		0			0
$565$	2.79142	−	3.22147i	0.117436	−	0.135528i
$566$		0			0
$567$	−0.0706703	−	0.491523i	−0.00296788	−	0.0206420i
$568$		0			0
$569$	−17.0234	−	37.2762i	−0.713660	−	1.56270i	−0.822582	−	0.568647i	$-0.807467\pi$
$569$	−17.0234	−	37.2762i	−0.713660	−	1.56270i	0.108921	−	0.994050i	$-0.465260\pi$
$570$		0			0
$571$	7.37115	−	16.1406i	0.308473	−	0.675461i	−0.690375	−	0.723452i	$-0.742554\pi$
$571$	7.37115	−	16.1406i	0.308473	−	0.675461i	0.998848	+	0.0479903i	$0.0152817\pi$
$572$		0			0
$573$	9.43265	−	6.06199i	0.394054	−	0.253243i
$574$		0			0
$575$	−22.2166	+	5.62758i	−0.926496	+	0.234686i
$576$		0			0
$577$	−35.2646	+	22.6632i	−1.46809	+	0.943481i	−0.469934	+	0.882701i	$0.655722\pi$
$577$	−35.2646	+	22.6632i	−1.46809	+	0.943481i	−0.998151	+	0.0607798i	$0.980641\pi$
$578$		0			0
$579$	4.13500	−	9.05439i	0.171845	−	0.376288i
$580$		0			0
$581$	−2.91802	−	6.38956i	−0.121060	−	0.265084i
$582$		0			0
$583$	4.56455	+	31.7471i	0.189044	+	1.31483i
$584$		0			0
$585$	0.679579	−	0.784276i	0.0280971	−	0.0324258i
$586$		0			0
$587$	14.4557	+	9.29011i	0.596650	+	0.383444i	0.803830	−	0.594859i	$-0.202792\pi$
$587$	14.4557	+	9.29011i	0.596650	+	0.383444i	−0.207180	+	0.978303i	$0.566429\pi$
$588$		0			0
$589$	−71.0524	−	20.8629i	−2.92766	−	0.859639i
$590$		0			0
$591$	−11.9483	−	13.7891i	−0.491488	−	0.567207i
$592$		0			0
$593$	36.6902	−	10.7732i	1.50669	−	0.442403i	0.578864	−	0.815424i	$-0.303496\pi$
$593$	36.6902	−	10.7732i	1.50669	−	0.442403i	0.927823	+	0.373020i	$0.121678\pi$
$594$		0			0
$595$	−0.177300	+	1.23315i	−0.00726861	+	0.0505543i
$596$		0			0
$597$	15.0362			0.615389
$598$		0			0
$599$	−39.5776			−1.61710			−0.808549	−	0.588429i	$-0.799747\pi$
$599$	−39.5776			−1.61710			−0.808549	+	0.588429i	$0.799747\pi$
$600$		0			0
$601$	−4.48789	+	31.2139i	−0.183065	+	1.27324i	0.666399	+	0.745596i	$0.267835\pi$
$601$	−4.48789	+	31.2139i	−0.183065	+	1.27324i	−0.849463	+	0.527647i	$0.823074\pi$
$602$		0			0
$603$	5.81630	−	1.70782i	0.236858	−	0.0695478i
$604$		0			0
$605$	−2.45202	−	2.82979i	−0.0996890	−	0.115047i
$606$		0			0
$607$	38.1414	+	11.1993i	1.54811	+	0.454567i	0.940536	−	0.339694i	$-0.110324\pi$
$607$	38.1414	+	11.1993i	1.54811	+	0.454567i	0.607577	+	0.794261i	$0.292142\pi$
$608$		0			0
$609$	−2.81476	−	1.80894i	−0.114060	−	0.0733019i
$610$		0			0
$611$	5.99892	−	6.92312i	0.242690	−	0.280080i
$612$		0			0
$613$	−2.07870	−	14.4577i	−0.0839581	−	0.583941i	−0.987759	−	0.155988i	$-0.950144\pi$
$613$	−2.07870	−	14.4577i	−0.0839581	−	0.583941i	0.903801	−	0.427953i	$-0.140765\pi$
$614$		0			0
$615$	−0.381204	−	0.834720i	−0.0153716	−	0.0336592i
$616$		0			0
$617$	8.87703	−	19.4380i	0.357376	−	0.782544i	−0.642492	−	0.766292i	$-0.722099\pi$
$617$	8.87703	−	19.4380i	0.357376	−	0.782544i	0.999868	−	0.0162516i	$-0.00517327\pi$
$618$		0			0
$619$	−34.0957	+	21.9120i	−1.37042	+	0.880718i	−0.998862	−	0.0476907i	$-0.984814\pi$
$619$	−34.0957	+	21.9120i	−1.37042	+	0.880718i	−0.371561	+	0.928408i	$0.621177\pi$
$620$		0			0
$621$	3.27432	−	3.50411i	0.131394	−	0.140615i
$622$		0			0
$623$	−6.13487	+	3.94264i	−0.245789	+	0.157959i
$624$		0			0
$625$	9.02728	−	19.7670i	0.361091	−	0.790679i
$626$		0			0
$627$	−12.5371	−	27.4525i	−0.500685	−	1.09635i
$628$		0			0
$629$	−3.53928	−	24.6162i	−0.141120	−	0.981513i
$630$		0			0
$631$	6.25220	−	7.21543i	0.248896	−	0.287242i	−0.617529	−	0.786548i	$-0.711866\pi$
$631$	6.25220	−	7.21543i	0.248896	−	0.287242i	0.866426	+	0.499306i	$0.166412\pi$
$632$		0			0
$633$	15.8300	+	10.1733i	0.629185	+	0.404353i
$634$		0			0
$635$	1.47586	+	0.433351i	0.0585677	+	0.0171970i
$636$		0			0
$637$	−9.75794	−	11.2613i	−0.386624	−	0.446188i
$638$		0			0
$639$	−13.0100	+	3.82008i	−0.514667	+	0.151120i
$640$		0			0
$641$	−0.911307	+	6.33828i	−0.0359945	+	0.250347i	−0.999872	−	0.0159988i	$-0.994907\pi$
$641$	−0.911307	+	6.33828i	−0.0359945	+	0.250347i	0.963878	+	0.266346i	$0.0858163\pi$
$642$		0			0
$643$	7.29558			0.287709			0.143855	−	0.989599i	$-0.454050\pi$
$643$	7.29558			0.287709			0.143855	+	0.989599i	$0.454050\pi$
$644$		0			0
$645$	−2.40527			−0.0947075
$646$		0			0
$647$	−4.02081	+	27.9653i	−0.158074	+	1.09943i	0.744103	+	0.668065i	$0.232877\pi$
$647$	−4.02081	+	27.9653i	−0.158074	+	1.09943i	−0.902177	+	0.431366i	$0.858032\pi$
$648$		0			0
$649$	−24.7498	+	7.26720i	−0.971515	+	0.285262i
$650$		0			0
$651$	3.47447	+	4.00975i	0.136175	+	0.157154i
$652$		0			0
$653$	10.0827	+	2.96056i	0.394568	+	0.115856i	0.472997	−	0.881064i	$-0.343172\pi$
$653$	10.0827	+	2.96056i	0.394568	+	0.115856i	−0.0784289	+	0.996920i	$0.524990\pi$
$654$		0			0
$655$	6.10765	+	3.92515i	0.238646	+	0.153368i
$656$		0			0
$657$	0.435483	−	0.502575i	0.0169898	−	0.0196073i
$658$		0			0
$659$	0.708207	+	4.92569i	0.0275878	+	0.191878i	0.998955	−	0.0457059i	$-0.0145537\pi$
$659$	0.708207	+	4.92569i	0.0275878	+	0.191878i	−0.971367	+	0.237584i	$0.923645\pi$
$660$		0			0
$661$	2.57867	+	5.64649i	0.100299	+	0.219623i	0.953129	−	0.302565i	$-0.0978430\pi$
$661$	2.57867	+	5.64649i	0.100299	+	0.219623i	−0.852830	+	0.522188i	$0.825116\pi$
$662$		0			0
$663$	−4.88918	+	10.7058i	−0.189880	+	0.415779i
$664$		0			0
$665$	−1.36177	+	0.875155i	−0.0528071	+	0.0339371i
$666$		0			0
$667$	−3.39598	−	32.1351i	−0.131493	−	1.24428i
$668$		0			0
$669$	−13.8261	+	8.88549i	−0.534547	+	0.343533i
$670$		0			0
$671$	−1.52859	+	3.34714i	−0.0590105	+	0.129215i
$672$		0			0
$673$	9.78087	+	21.4171i	0.377025	+	0.825569i	0.999092	+	0.0426054i	$0.0135658\pi$
$673$	9.78087	+	21.4171i	0.377025	+	0.825569i	−0.622067	+	0.782964i	$0.713707\pi$
$674$		0			0
$675$	0.680092	+	4.73015i	0.0261768	+	0.182063i
$676$		0			0
$677$	−9.09556	+	10.4968i	−0.349571	+	0.403426i	−0.903119	−	0.429391i	$-0.858728\pi$
$677$	−9.09556	+	10.4968i	−0.349571	+	0.403426i	0.553548	+	0.832817i	$0.313274\pi$
$678$		0			0
$679$	−4.04935	−	2.60236i	−0.155400	−	0.0998694i
$680$		0			0
$681$	5.89749	+	1.73166i	0.225992	+	0.0663574i
$682$		0			0
$683$	12.6910	+	14.6462i	0.485608	+	0.560421i	0.944687	−	0.327974i	$-0.106366\pi$
$683$	12.6910	+	14.6462i	0.485608	+	0.560421i	−0.459079	+	0.888395i	$0.651821\pi$
$684$		0			0
$685$	−2.91942	+	0.857218i	−0.111545	+	0.0327526i
$686$		0			0
$687$	−2.00174	+	13.9224i	−0.0763711	+	0.531173i
$688$		0			0
$689$	16.2518			0.619146
$690$		0			0
$691$	51.6354			1.96430			0.982152	−	0.188087i	$-0.0602288\pi$
$691$	51.6354			1.96430			0.982152	+	0.188087i	$0.0602288\pi$
$692$		0			0
$693$	−0.307729	+	2.14030i	−0.0116897	+	0.0813034i
$694$		0			0
$695$	9.18250	−	2.69623i	0.348312	−	0.102274i
$696$		0			0
$697$	6.81534	+	7.86532i	0.258149	+	0.297920i
$698$		0			0
$699$	−1.37136	−	0.402667i	−0.0518695	−	0.0152303i
$700$		0			0
$701$	−7.11103	−	4.56998i	−0.268580	−	0.172606i	0.399418	−	0.916769i	$-0.369212\pi$
$701$	−7.11103	−	4.56998i	−0.268580	−	0.172606i	−0.667998	+	0.744163i	$0.732849\pi$
$702$		0			0
$703$	21.1607	−	24.4208i	0.798091	−	0.921047i
$704$		0			0
$705$	−0.277903	−	1.93286i	−0.0104664	−	0.0727956i
$706$		0			0
$707$	1.41910	+	3.10740i	0.0533708	+	0.116866i
$708$		0			0
$709$	−18.0334	+	39.4876i	−0.677259	+	1.48299i	0.188264	+	0.982119i	$0.439714\pi$
$709$	−18.0334	+	39.4876i	−0.677259	+	1.48299i	−0.865522	+	0.500871i	$0.833013\pi$
$710$		0			0
$711$	−5.03807	+	3.23777i	−0.188942	+	0.121426i
$712$		0			0
$713$	−9.18935	+	50.4101i	−0.344144	+	1.88787i
$714$		0			0
$715$	−3.80145	+	2.44304i	−0.142166	+	0.0913646i
$716$		0			0
$717$	−5.55201	+	12.1572i	−0.207343	+	0.454019i
$718$		0			0
$719$	4.06050	+	8.89125i	0.151431	+	0.331588i	0.970111	−	0.242663i	$-0.0780208\pi$
$719$	4.06050	+	8.89125i	0.151431	+	0.331588i	−0.818680	+	0.574250i	$0.805294\pi$
$720$		0			0
$721$	0.340482	+	2.36811i	0.0126802	+	0.0881929i
$722$		0			0
$723$	−17.1596	+	19.8033i	−0.638174	+	0.736492i
$724$		0			0
$725$	27.0877	+	17.4082i	1.00601	+	0.646525i
$726$		0			0
$727$	−2.07797	−	0.610147i	−0.0770676	−	0.0226291i	0.242971	−	0.970033i	$-0.421878\pi$
$727$	−2.07797	−	0.610147i	−0.0770676	−	0.0226291i	−0.320039	+	0.947404i	$0.603696\pi$
$728$		0			0
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$		0			0
$731$	26.1739	−	7.68536i	0.968078	−	0.284253i
$732$		0			0
$733$	6.61154	−	45.9843i	0.244203	−	1.69847i	−0.386375	−	0.922342i	$-0.626273\pi$
$733$	6.61154	−	45.9843i	0.244203	−	1.69847i	0.630578	−	0.776126i	$-0.282818\pi$
$734$		0			0
$735$	−3.17635			−0.117161
$736$		0			0
$737$	−26.3959			−0.972305
$738$		0			0
$739$	−4.12325	+	28.6779i	−0.151676	+	1.05493i	0.761733	+	0.647891i	$0.224349\pi$
$739$	−4.12325	+	28.6779i	−0.151676	+	1.05493i	−0.913410	+	0.407042i	$0.866560\pi$
$740$		0			0
$741$	−14.6728	+	4.30832i	−0.539018	+	0.158270i
$742$		0			0
$743$	−24.5977	−	28.3872i	−0.902400	−	1.04143i	−0.998937	−	0.0460961i	$-0.985322\pi$
$743$	−24.5977	−	28.3872i	−0.902400	−	1.04143i	0.0965367	−	0.995329i	$-0.469223\pi$
$744$		0			0
$745$	−3.15840	−	0.927390i	−0.115715	−	0.0339770i
$746$		0			0
$747$	−11.9000	−	7.64764i	−0.435397	−	0.279812i
$748$		0			0
$749$	−0.118634	+	0.136911i	−0.00433479	+	0.00500262i
$750$		0			0
$751$	2.23070	+	15.5149i	0.0813995	+	0.566146i	0.989181	+	0.146702i	$0.0468658\pi$
$751$	2.23070	+	15.5149i	0.0813995	+	0.566146i	−0.907781	+	0.419444i	$0.862225\pi$
$752$		0			0
$753$	−3.40358	−	7.45280i	−0.124033	−	0.271595i
$754$		0			0
$755$	−1.69141	+	3.70366i	−0.0615566	+	0.134790i
$756$		0			0
$757$	−24.5992	+	15.8089i	−0.894073	+	0.574586i	−0.905027	−	0.425354i	$-0.860150\pi$
$757$	−24.5992	+	15.8089i	−0.894073	+	0.574586i	0.0109538	+	0.999940i	$0.496513\pi$
$758$		0			0
$759$	−17.9791	+	10.6235i	−0.652599	+	0.385607i
$760$		0			0
$761$	9.15427	−	5.88309i	0.331842	−	0.213262i	−0.364100	−	0.931360i	$-0.618623\pi$
$761$	9.15427	−	5.88309i	0.331842	−	0.213262i	0.695942	+	0.718098i	$0.254987\pi$
$762$		0			0
$763$	−3.22497	+	7.06169i	−0.116752	+	0.255650i
$764$		0			0
$765$	1.04221	+	2.28212i	0.0376811	+	0.0825102i
$766$		0			0
$767$	1.86009	+	12.9372i	0.0671641	+	0.467137i
$768$		0			0
$769$	−15.5966	+	17.9995i	−0.562429	+	0.649077i	−0.963733	−	0.266867i	$-0.914011\pi$
$769$	−15.5966	+	17.9995i	−0.562429	+	0.649077i	0.401305	+	0.915945i	$0.368557\pi$
$770$		0			0
$771$	14.6855	+	9.43780i	0.528885	+	0.339894i
$772$		0			0
$773$	33.2616	+	9.76650i	1.19634	+	0.351276i	0.818452	−	0.574576i	$-0.194833\pi$
$773$	33.2616	+	9.76650i	1.19634	+	0.351276i	0.377886	+	0.925852i	$0.376651\pi$
$774$		0			0
$775$	−33.4364	−	38.5876i	−1.20107	−	1.38611i
$776$		0			0
$777$	−2.22139	+	0.652260i	−0.0796921	+	0.0233997i
$778$		0			0
$779$	−1.92444	+	13.3848i	−0.0689504	+	0.479560i
$780$		0			0
$781$	59.0428			2.11272
$782$		0			0
$783$	−6.73795			−0.240795
$784$		0			0
$785$	−1.04760	+	7.28625i	−0.0373906	+	0.260057i
$786$		0			0
$787$	17.4671	−	5.12881i	0.622635	−	0.182822i	0.0448270	−	0.998995i	$-0.485726\pi$
$787$	17.4671	−	5.12881i	0.622635	−	0.182822i	0.577808	+	0.816173i	$0.303908\pi$
$788$		0			0
$789$	−16.6510	−	19.2162i	−0.592790	−	0.684116i
$790$		0			0
$791$	4.31817	+	1.26793i	0.153536	+	0.0450824i
$792$		0			0
$793$	1.56852	+	1.00803i	0.0556998	+	0.0357961i
$794$		0			0
$795$	2.26866	−	2.61818i	0.0804612	−	0.0928572i
$796$		0			0
$797$	6.29844	+	43.8066i	0.223102	+	1.55171i	0.726203	+	0.687481i	$0.241283\pi$
$797$	6.29844	+	43.8066i	0.223102	+	1.55171i	−0.503101	+	0.864228i	$0.667807\pi$
$798$		0			0
$799$	9.20000	+	20.1452i	0.325473	+	0.712686i
$800$		0			0
$801$	−6.10062	+	13.3585i	−0.215555	+	0.471999i
$802$		0			0
$803$	−2.43602	+	1.56554i	−0.0859653	+	0.0552465i
$804$		0			0
$805$	0.701244	+	0.873426i	0.0247156	+	0.0307842i
$806$		0			0
$807$	8.44647	−	5.42822i	0.297330	−	0.191082i
$808$		0			0
$809$	4.71211	−	10.3181i	0.165669	−	0.362765i	−0.808530	−	0.588455i	$-0.799736\pi$
$809$	4.71211	−	10.3181i	0.165669	−	0.362765i	0.974199	+	0.225690i	$0.0724637\pi$
$810$		0			0
$811$	−9.01183	−	19.7331i	−0.316448	−	0.692925i	0.682843	−	0.730565i	$-0.260743\pi$
$811$	−9.01183	−	19.7331i	−0.316448	−	0.692925i	−0.999291	+	0.0376403i	$0.988016\pi$
$812$		0			0
$813$	−2.41177	−	16.7743i	−0.0845846	−	0.588299i
$814$		0			0
$815$	6.79707	−	7.84424i	0.238091	−	0.274772i
$816$		0			0
$817$	29.8175	+	19.1625i	1.04318	+	0.670412i
$818$		0			0
$819$	1.05127	+	0.308681i	0.0367344	+	0.0107862i
$820$		0			0
$821$	−10.5114	−	12.1308i	−0.366852	−	0.423369i	0.542072	−	0.840332i	$-0.317640\pi$
$821$	−10.5114	−	12.1308i	−0.366852	−	0.423369i	−0.908924	+	0.416963i	$0.863095\pi$
$822$		0			0
$823$	−53.1273	+	15.5996i	−1.85190	+	0.543768i	−0.852110	+	0.523362i	$0.824678\pi$
$823$	−53.1273	+	15.5996i	−1.85190	+	0.543768i	−0.999792	+	0.0204056i	$0.993504\pi$
$824$		0			0
$825$	2.96142	−	20.5971i	0.103103	−	0.717099i
$826$		0			0
$827$	35.4095			1.23131			0.615655	−	0.788016i	$-0.288891\pi$
$827$	35.4095			1.23131			0.615655	+	0.788016i	$0.288891\pi$
$828$		0			0
$829$	−36.0703			−1.25277			−0.626386	−	0.779513i	$-0.715467\pi$
$829$	−36.0703			−1.25277			−0.626386	+	0.779513i	$0.715467\pi$
$830$		0			0
$831$	−0.580840	+	4.03983i	−0.0201491	+	0.140140i
$832$		0			0
$833$	34.5647	−	10.1491i	1.19760	−	0.351646i
$834$		0			0
$835$	1.64262	+	1.89569i	0.0568454	+	0.0656031i
$836$		0			0
$837$	10.2517	+	3.01016i	0.354349	+	0.104046i
$838$		0			0
$839$	2.17140	+	1.39548i	0.0749652	+	0.0481772i	0.577587	−	0.816329i	$-0.303995\pi$
$839$	2.17140	+	1.39548i	0.0749652	+	0.0481772i	−0.502621	+	0.864507i	$0.667631\pi$
$840$		0			0
$841$	−10.7397	+	12.3943i	−0.370335	+	0.427389i
$842$		0			0
$843$	1.35141	+	9.39929i	0.0465451	+	0.323729i
$844$		0			0
$845$	−1.58881	−	3.47900i	−0.0546566	−	0.119681i
$846$		0			0
$847$	1.64225	−	3.59604i	0.0564285	−	0.123561i
$848$		0			0
$849$	4.92319	−	3.16394i	0.168964	−	0.108586i
$850$		0			0
$851$	−18.3434	−	12.7854i	−0.628802	−	0.438276i
$852$		0			0
$853$	−30.7028	+	19.7315i	−1.05124	+	0.675593i	−0.947742	−	0.319037i	$-0.896641\pi$
$853$	−30.7028	+	19.7315i	−1.05124	+	0.675593i	−0.103500	+	0.994629i	$0.533004\pi$
$854$		0			0
$855$	−1.35416	+	2.96521i	−0.0463114	+	0.101408i
$856$		0			0
$857$	−8.13062	−	17.8036i	−0.277737	−	0.608158i	0.718433	−	0.695596i	$-0.244859\pi$
$857$	−8.13062	−	17.8036i	−0.277737	−	0.608158i	−0.996170	+	0.0874374i	$0.972132\pi$
$858$		0			0
$859$	1.15139	+	8.00812i	0.0392851	+	0.273234i	0.999991	−	0.00433594i	$-0.00138018\pi$
$859$	1.15139	+	8.00812i	0.0392851	+	0.273234i	−0.960706	+	0.277570i	$0.910471\pi$
$860$		0			0
$861$	0.634463	−	0.732210i	0.0216225	−	0.0249536i
$862$		0			0
$863$	20.5434	+	13.2025i	0.699307	+	0.449417i	0.841384	−	0.540438i	$-0.181742\pi$
$863$	20.5434	+	13.2025i	0.699307	+	0.449417i	−0.142077	+	0.989856i	$0.545378\pi$
$864$		0			0
$865$	−7.69991	−	2.26090i	−0.261805	−	0.0768728i
$866$		0			0
$867$	−7.50044	−	8.65597i	−0.254728	−	0.293972i
$868$		0			0
$869$	25.0213	−	7.34693i	0.848791	−	0.249227i
$870$		0			0
$871$	−1.90345	+	13.2388i	−0.0644959	+	0.448579i
$872$		0			0
$873$	−9.69330			−0.328068
$874$		0			0
$875$	−2.28390			−0.0772098
$876$		0			0
$877$	1.59751	−	11.1109i	0.0539441	−	0.375189i	−0.944910	−	0.327330i	$-0.893851\pi$
$877$	1.59751	−	11.1109i	0.0539441	−	0.375189i	0.998854	−	0.0478592i	$-0.0152399\pi$
$878$		0			0
$879$	2.23136	−	0.655187i	0.0752619	−	0.0220989i
$880$		0			0
$881$	24.2304	+	27.9633i	0.816341	+	0.942108i	0.999158	−	0.0410390i	$-0.0130668\pi$
$881$	24.2304	+	27.9633i	0.816341	+	0.942108i	−0.182816	+	0.983147i	$0.558521\pi$
$882$		0			0
$883$	14.4204	+	4.23421i	0.485285	+	0.142492i	0.515217	−	0.857059i	$-0.327711\pi$
$883$	14.4204	+	4.23421i	0.485285	+	0.142492i	−0.0299328	+	0.999552i	$0.509529\pi$
$884$		0			0
$885$	2.34385	+	1.50630i	0.0787877	+	0.0506338i
$886$		0			0
$887$	−18.9021	+	21.8142i	−0.634671	+	0.732450i	−0.978423	−	0.206611i	$-0.933757\pi$
$887$	−18.9021	+	21.8142i	−0.634671	+	0.732450i	0.343752	+	0.939061i	$0.388302\pi$
$888$		0			0
$889$	0.231119	+	1.60747i	0.00775148	+	0.0539127i
$890$		0			0
$891$	1.80890	+	3.96093i	0.0606003	+	0.132696i
$892$		0			0
$893$	−11.9538	+	26.1751i	−0.400017	+	0.875916i
$894$		0			0
$895$	2.63487	−	1.69333i	0.0880741	−	0.0566018i
$896$		0			0
$897$	4.03167	+	9.78342i	0.134613	+	0.326659i
$898$		0			0
$899$	60.5629	−	38.9214i	2.01989	−	1.29810i
$900$		0			0
$901$	−16.3217	+	35.7396i	−0.543756	+	1.19066i
$902$		0			0
$903$	−1.05494	−	2.31000i	−0.0351063	−	0.0768720i
$904$		0			0
$905$	0.681072	+	4.73696i	0.0226396	+	0.157462i
$906$		0			0
$907$	20.1456	−	23.2493i	0.668925	−	0.771981i	−0.315283	−	0.948998i	$-0.602099\pi$
$907$	20.1456	−	23.2493i	0.668925	−	0.771981i	0.984208	+	0.177017i	$0.0566448\pi$
$908$		0			0
$909$	5.78723	+	3.71923i	0.191950	+	0.123359i
$910$		0			0
$911$	48.4648	+	14.2306i	1.60571	+	0.471479i	0.957128	−	0.289665i	$-0.0935439\pi$
$911$	48.4648	+	14.2306i	1.60571	+	0.471479i	0.648583	+	0.761144i	$0.275362\pi$
$912$		0			0
$913$	40.3366	+	46.5509i	1.33495	+	1.54061i
$914$		0			0
$915$	0.381350	−	0.111974i	0.0126070	−	0.00370176i
$916$		0			0
$917$	−1.09089	+	7.58729i	−0.0360243	+	0.250554i
$918$		0			0
$919$	−50.4429			−1.66396			−0.831979	−	0.554807i	$-0.812792\pi$
$919$	−50.4429			−1.66396			−0.831979	+	0.554807i	$0.812792\pi$
$920$		0			0
$921$	9.95566			0.328050
$922$		0			0
$923$	4.25767	−	29.6127i	0.140143	−	0.974715i
$924$		0			0
$925$	21.3775	−	6.27699i	0.702887	−	0.206386i
$926$		0			0
$927$	3.15505	+	3.64112i	0.103625	+	0.119590i
$928$		0			0
$929$	2.50641	+	0.735948i	0.0822326	+	0.0241457i	0.322590	−	0.946539i	$-0.395446\pi$
$929$	2.50641	+	0.735948i	0.0822326	+	0.0241457i	−0.240357	+	0.970684i	$0.577265\pi$
$930$		0			0
$931$	39.3763	+	25.3056i	1.29051	+	0.829357i
$932$		0			0
$933$	−19.2292	+	22.1917i	−0.629536	+	0.726524i
$934$		0			0
$935$	−1.55473	−	10.8134i	−0.0508450	−	0.353635i
$936$		0			0
$937$	0.303704	+	0.665019i	0.00992157	+	0.0217252i	0.914528	−	0.404523i	$-0.132562\pi$
$937$	0.303704	+	0.665019i	0.00992157	+	0.0217252i	−0.904606	+	0.426248i	$0.859835\pi$
$938$		0			0
$939$	−12.4242	+	27.2052i	−0.405449	+	0.887809i
$940$		0			0
$941$	6.70316	−	4.30786i	0.218517	−	0.140432i	−0.426803	−	0.904344i	$-0.640360\pi$
$941$	6.70316	−	4.30786i	0.218517	−	0.140432i	0.645320	+	0.763912i	$0.276724\pi$
$942$		0			0
$943$	9.35037	+	0.350919i	0.304490	+	0.0114275i
$944$		0			0
$945$	0.196480	−	0.126270i	0.00639150	−	0.00410757i
$946$		0			0
$947$	1.41394	−	3.09610i	0.0459469	−	0.100610i	−0.885267	−	0.465084i	$-0.846024\pi$
$947$	1.41394	−	3.09610i	0.0459469	−	0.100610i	0.931213	+	0.364474i	$0.118751\pi$
$948$		0			0
$949$	0.609524	+	1.33467i	0.0197860	+	0.0433253i
$950$		0			0
$951$	−2.77007	−	19.2663i	−0.0898256	−	0.624751i
$952$		0			0
$953$	27.2329	−	31.4284i	0.882159	−	1.01807i	−0.117528	−	0.993070i	$-0.537497\pi$
$953$	27.2329	−	31.4284i	0.882159	−	1.01807i	0.999688	−	0.0249964i	$-0.00795743\pi$
$954$		0			0
$955$	4.43648	+	2.85115i	0.143561	+	0.0922611i
$956$		0			0
$957$	28.1515	+	8.26602i	0.910008	+	0.267202i
$958$		0			0
$959$	−2.10371	−	2.42781i	−0.0679323	−	0.0783980i
$960$		0			0
$961$	−79.7890	+	23.4282i	−2.57384	+	0.755747i
$962$		0			0
$963$	−0.0519187	+	0.361102i	−0.00167306	+	0.0116364i
$964$		0			0
$965$	4.68164			0.150707
$966$		0			0
$967$	−45.6025			−1.46648			−0.733238	−	0.679972i	$-0.761992\pi$
$967$	−45.6025			−1.46648			−0.733238	+	0.679972i	$0.761992\pi$
$968$		0			0
$969$	5.26141	−	36.5939i	0.169021	−	1.17557i
$970$		0			0
$971$	−47.9572	+	14.0815i	−1.53902	+	0.451897i	−0.937797	−	0.347185i	$-0.887138\pi$
$971$	−47.9572	+	14.0815i	−1.53902	+	0.451897i	−0.601222	+	0.799082i	$0.705319\pi$
$972$		0			0
$973$	6.61684	+	7.63624i	0.212126	+	0.244807i
$974$		0			0
$975$	−10.1169	−	2.97058i	−0.323999	−	0.0951346i
$976$		0			0
$977$	8.88843	+	5.71225i	0.284366	+	0.182751i	0.675046	−	0.737776i	$-0.264124\pi$
$977$	8.88843	+	5.71225i	0.284366	+	0.182751i	−0.390680	+	0.920527i	$0.627760\pi$
$978$		0			0
$979$	41.8767	−	48.3283i	1.33838	−	1.54458i
$980$		0			0
$981$	2.22488	+	15.4744i	0.0710349	+	0.494058i
$982$		0			0
$983$	0.285919	+	0.626075i	0.00911939	+	0.0199687i	0.914137	−	0.405406i	$-0.132870\pi$
$983$	0.285919	+	0.626075i	0.00911939	+	0.0199687i	−0.905018	+	0.425374i	$0.860142\pi$
$984$		0			0
$985$	3.56487	−	7.80599i	0.113586	−	0.248719i
$986$		0			0
$987$	1.73441	−	1.11464i	0.0552069	−	0.0354793i
$988$		0			0
$989$	11.0179	−	21.9117i	0.350349	−	0.696750i
$990$		0			0
$991$	−27.4572	+	17.6456i	−0.872205	+	0.560532i	−0.898427	−	0.439124i	$-0.855289\pi$
$991$	−27.4572	+	17.6456i	−0.872205	+	0.560532i	0.0262211	+	0.999656i	$0.491653\pi$
$992$		0			0
$993$	−5.73680	+	12.5618i	−0.182052	+	0.398638i
$994$		0			0
$995$	2.93781	+	6.43291i	0.0931348	+	0.203937i
$996$		0			0
$997$	−4.17859	−	29.0627i	−0.132337	−	0.920426i	−0.942497	−	0.334216i	$-0.891529\pi$
$997$	−4.17859	−	29.0627i	−0.132337	−	0.920426i	0.810159	−	0.586210i	$-0.199381\pi$
$998$		0			0
$999$	−3.05313	+	3.52350i	−0.0965969	+	0.111479i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.b.265.2	yes	30
23.2	even	11	inner	552.2.q.b.25.2	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.b.25.2	✓	30	23.2	even	11	inner
552.2.q.b.265.2	yes	30	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{3} +(-0.451280 + 0.132508i) q^{5} +(-0.325189 - 0.375288i) q^{7} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(-0.142315 + 0.989821i) q^{3} +(-0.451280 + 0.132508i) q^{5} +(-0.325189 - 0.375288i) q^{7} +(-0.959493 - 0.281733i) q^{9} +(3.66318 + 2.35418i) q^{11} +(1.44489 - 1.66749i) q^{13} +(-0.0669352 - 0.465545i) q^{15} +(2.21590 + 4.85214i) q^{17} +(-2.87917 + 6.30449i) q^{19} +(0.417748 - 0.268470i) q^{21} +(4.54766 + 1.52277i) q^{23} +(-4.02017 + 2.58361i) q^{25} +(0.415415 - 0.909632i) q^{27} +(-2.79905 - 6.12906i) q^{29} +(1.52056 + 10.5757i) q^{31} +(-2.85155 + 3.29086i) q^{33} +(0.196480 + 0.126270i) q^{35} +(-4.47341 - 1.31351i) q^{37} +(1.44489 + 1.66749i) q^{39} +(1.87203 - 0.549677i) q^{41} +(0.727796 - 5.06193i) q^{43} +0.470332 q^{45} +4.15181 q^{47} +(0.961111 - 6.68467i) q^{49} +(-5.11811 + 1.50281i) q^{51} +(4.82353 + 5.56665i) q^{53} +(-1.96507 - 0.576996i) q^{55} +(-5.83058 - 3.74708i) q^{57} +(-3.87925 + 4.47689i) q^{59} +(0.120262 + 0.836439i) q^{61} +(0.206286 + 0.451703i) q^{63} +(-0.431095 + 0.943966i) q^{65} +(-5.09955 + 3.27728i) q^{67} +(-2.15447 + 4.28466i) q^{69} +(11.4068 - 7.33068i) q^{71} +(-0.276252 + 0.604907i) q^{73} +(-1.98518 - 4.34694i) q^{75} +(-0.307729 - 2.14030i) q^{77} +(3.92181 - 4.52601i) q^{79} +(0.841254 + 0.540641i) q^{81} +(13.5725 + 3.98525i) q^{83} +(-1.64294 - 1.89605i) q^{85} +(6.46502 - 1.89830i) q^{87} +(2.08998 - 14.5361i) q^{89} -1.09565 q^{91} -10.6845 q^{93} +(0.463916 - 3.22661i) q^{95} +(9.30065 - 2.73092i) q^{97} +(-2.85155 - 3.29086i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} - 3 q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 - 3 * q^9	\( 30 q - 3 q^{3} - 3 q^{9} + 9 q^{11} + 13 q^{13} + 17 q^{17} - 9 q^{19} - 11 q^{21} - 12 q^{23} - 23 q^{25} - 3 q^{27} - q^{29} - 37 q^{31} + 9 q^{33} + 10 q^{35} + 7 q^{37} + 13 q^{39} + 16 q^{41} + 20 q^{43} - 22 q^{45} + 22 q^{47} + 19 q^{49} + 17 q^{51} + 25 q^{53} + 10 q^{55} + 24 q^{57} + 7 q^{59} + 8 q^{61} - 28 q^{65} - 23 q^{67} - q^{69} + 5 q^{71} + 34 q^{73} - 23 q^{75} + 62 q^{77} + 20 q^{79} - 3 q^{81} + 29 q^{83} - 46 q^{85} + 10 q^{87} - 67 q^{89} - 118 q^{91} - 26 q^{93} - 99 q^{95} - 41 q^{97} + 9 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 - 3 * q^9 + 9 * q^11 + 13 * q^13 + 17 * q^17 - 9 * q^19 - 11 * q^21 - 12 * q^23 - 23 * q^25 - 3 * q^27 - q^29 - 37 * q^31 + 9 * q^33 + 10 * q^35 + 7 * q^37 + 13 * q^39 + 16 * q^41 + 20 * q^43 - 22 * q^45 + 22 * q^47 + 19 * q^49 + 17 * q^51 + 25 * q^53 + 10 * q^55 + 24 * q^57 + 7 * q^59 + 8 * q^61 - 28 * q^65 - 23 * q^67 - q^69 + 5 * q^71 + 34 * q^73 - 23 * q^75 + 62 * q^77 + 20 * q^79 - 3 * q^81 + 29 * q^83 - 46 * q^85 + 10 * q^87 - 67 * q^89 - 118 * q^91 - 26 * q^93 - 99 * q^95 - 41 * q^97 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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