LMFDB - Embedded newform 950.2.bb.d.193.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(143,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([27, 34]))

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

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

chi := DirichletCharacter("950.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.bb (of order $36$, degree $12$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			193.7
Character	$\chi$	$=$	950.193
Dual form			950.2.bb.d.507.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0871557 + 0.996195i) q^{2} +(0.0142429 - 0.0305440i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(0.0316692 + 0.0115266i) q^{6} +(2.42021 + 0.648494i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(1.92763 + 2.29726i) q^{9} +O(q^{10})$	\(q+(0.0871557 + 0.996195i) q^{2} +(0.0142429 - 0.0305440i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(0.0316692 + 0.0115266i) q^{6} +(2.42021 + 0.648494i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(1.92763 + 2.29726i) q^{9} +(1.13265 - 1.96182i) q^{11} +(-0.00872262 + 0.0325533i) q^{12} +(-1.32944 + 0.619927i) q^{13} +(-0.435091 + 2.46752i) q^{14} +(0.939693 - 0.342020i) q^{16} +(1.99433 - 0.174481i) q^{17} +(-2.12052 + 2.12052i) q^{18} +(1.72838 - 4.00159i) q^{19} +(0.0542785 - 0.0646866i) q^{21} +(2.05307 + 0.957361i) q^{22} +(-2.55260 + 3.64549i) q^{23} +(-0.0331896 - 0.00585222i) q^{24} +(-0.733436 - 1.27035i) q^{26} +(0.195283 - 0.0523258i) q^{27} +(-2.49605 - 0.218376i) q^{28} +(2.41338 - 2.02507i) q^{29} +(3.21213 - 1.85453i) q^{31} +(0.422618 + 0.906308i) q^{32} +(-0.0437894 - 0.0625378i) q^{33} +(0.347635 + 1.97154i) q^{34} +(-2.29726 - 1.92763i) q^{36} +(8.01239 + 8.01239i) q^{37} +(4.13700 + 1.37304i) q^{38} +0.0494359i q^{39} +(1.23073 + 3.38141i) q^{41} +(0.0691711 + 0.0484341i) q^{42} +(-3.13537 + 2.19541i) q^{43} +(-0.774781 + 2.12869i) q^{44} +(-3.85409 - 2.22516i) q^{46} +(-0.895748 + 10.2384i) q^{47} +(0.00293729 - 0.0335734i) q^{48} +(-0.625296 - 0.361015i) q^{49} +(0.0230757 - 0.0634001i) q^{51} +(1.20159 - 0.841363i) q^{52} +(0.451332 + 0.316026i) q^{53} +(0.0691467 + 0.189979i) q^{54} -2.50559i q^{56} +(-0.0976074 - 0.109786i) q^{57} +(2.22770 + 2.22770i) q^{58} +(-3.05382 - 2.56246i) q^{59} +(0.911575 + 5.16980i) q^{61} +(2.12743 + 3.03828i) q^{62} +(3.17552 + 6.80992i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(0.0584833 - 0.0490733i) q^{66} +(-1.37428 - 0.120234i) q^{67} +(-1.93374 + 0.518143i) q^{68} +(0.0749915 + 0.129889i) q^{69} +(7.95714 + 1.40306i) q^{71} +(1.72008 - 2.45653i) q^{72} +(-3.37102 - 1.57193i) q^{73} +(-7.28358 + 8.68023i) q^{74} +(-1.00726 + 4.24092i) q^{76} +(4.01349 - 4.01349i) q^{77} +(-0.0492478 + 0.00430862i) q^{78} +(11.5411 - 4.20061i) q^{79} +(-1.56106 + 8.85320i) q^{81} +(-3.26128 + 1.52076i) q^{82} +(-1.54270 + 5.75745i) q^{83} +(-0.0422212 + 0.0731292i) q^{84} +(-2.46032 - 2.93210i) q^{86} +(-0.0274802 - 0.102557i) q^{87} +(-2.18812 - 0.586305i) q^{88} +(-8.99243 - 3.27298i) q^{89} +(-3.61954 + 0.638222i) q^{91} +(1.88079 - 4.03336i) q^{92} +(-0.0108946 - 0.124525i) q^{93} -10.2776 q^{94} +0.0337016 q^{96} +(0.712763 + 8.14692i) q^{97} +(0.305143 - 0.654382i) q^{98} +(6.69015 - 1.17965i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{6}+O(q^{10}) $ 96 * q - 12 * q^6	$ 96 q - 12 q^{6} + 12 q^{26} - 72 q^{31} + 12 q^{36} - 24 q^{41} + 12 q^{51} - 72 q^{61} - 36 q^{66} + 168 q^{71} - 12 q^{76} + 12 q^{81} - 48 q^{86} - 72 q^{91}+O(q^{100}) $ 96 * q - 12 * q^6 + 12 * q^26 - 72 * q^31 + 12 * q^36 - 24 * q^41 + 12 * q^51 - 72 * q^61 - 36 * q^66 + 168 * q^71 - 12 * q^76 + 12 * q^81 - 48 * q^86 - 72 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	0.0871557	+	0.996195i	0.0616284	+	0.704416i
$2$	0.0871557	+	0.996195i	0.0616284	+	0.704416i
$3$	0.0142429	−	0.0305440i	0.00822315	−	0.0176346i	−0.902153	−	0.431416i	$-0.858014\pi$
$3$	0.0142429	−	0.0305440i	0.00822315	−	0.0176346i	0.910376	+	0.413781i	$0.135792\pi$
$4$	−0.984808	+	0.173648i	−0.492404	+	0.0868241i
$5$		0			0
$5$		0			0
$6$	0.0316692	+	0.0115266i	0.0129289	+	0.00470573i
$7$	2.42021	+	0.648494i	0.914754	+	0.245108i	0.685342	−	0.728222i	$-0.259653\pi$
$7$	2.42021	+	0.648494i	0.914754	+	0.245108i	0.229412	+	0.973329i	$0.426320\pi$
$8$	−0.258819	−	0.965926i	−0.0915064	−	0.341506i
$9$	1.92763	+	2.29726i	0.642544	+	0.765754i
$10$		0			0
$11$	1.13265	−	1.96182i	0.341508	−	0.591510i	−0.643205	−	0.765694i	$-0.722396\pi$
$11$	1.13265	−	1.96182i	0.341508	−	0.591510i	0.984713	+	0.174185i	$0.0557289\pi$
$12$	−0.00872262	+	0.0325533i	−0.00251800	+	0.00939732i
$13$	−1.32944	+	0.619927i	−0.368719	+	0.171937i	−0.598142	−	0.801390i	$-0.704094\pi$
$13$	−1.32944	+	0.619927i	−0.368719	+	0.171937i	0.229422	+	0.973327i	$0.426316\pi$
$14$	−0.435091	+	2.46752i	−0.116283	+	0.659473i
$15$		0			0
$16$	0.939693	−	0.342020i	0.234923	−	0.0855050i
$17$	1.99433	−	0.174481i	0.483697	−	0.0423180i	0.157300	−	0.987551i	$-0.449721\pi$
$17$	1.99433	−	0.174481i	0.483697	−	0.0423180i	0.326397	+	0.945233i	$0.394165\pi$
$18$	−2.12052	+	2.12052i	−0.499811	+	0.499811i
$19$	1.72838	−	4.00159i	0.396518	−	0.918027i
$19$	1.72838	−	4.00159i	0.396518	−	0.918027i
$20$		0			0
$21$	0.0542785	−	0.0646866i	0.0118445	−	0.0141158i
$22$	2.05307	+	0.957361i	0.437715	+	0.204110i
$23$	−2.55260	+	3.64549i	−0.532254	+	0.760137i	−0.991770	−	0.128032i	$-0.959134\pi$
$23$	−2.55260	+	3.64549i	−0.532254	+	0.760137i	0.459516	+	0.888169i	$0.348023\pi$
$24$	−0.0331896	−	0.00585222i	−0.00677480	−	0.00119458i
$25$		0			0
$26$	−0.733436	−	1.27035i	−0.143839	−	0.249136i
$27$	0.195283	−	0.0523258i	0.0375821	−	0.0100701i
$28$	−2.49605	−	0.218376i	−0.471710	−	0.0412693i
$29$	2.41338	−	2.02507i	0.448154	−	0.376046i	−0.390596	−	0.920562i	$-0.627731\pi$
$29$	2.41338	−	2.02507i	0.448154	−	0.376046i	0.838750	+	0.544516i	$0.183287\pi$
$30$		0			0
$31$	3.21213	−	1.85453i	0.576916	−	0.333083i	−0.182991	−	0.983115i	$-0.558578\pi$
$31$	3.21213	−	1.85453i	0.576916	−	0.333083i	0.759907	+	0.650032i	$0.225244\pi$
$32$	0.422618	+	0.906308i	0.0747091	+	0.160214i
$33$	−0.0437894	−	0.0625378i	−0.00762276	−	0.0108864i
$34$	0.347635	+	1.97154i	0.0596189	+	0.338116i
$35$		0			0
$36$	−2.29726	−	1.92763i	−0.382877	−	0.321272i
$37$	8.01239	+	8.01239i	1.31723	+	1.31723i	0.915960	+	0.401269i	$0.131431\pi$
$37$	8.01239	+	8.01239i	1.31723	+	1.31723i	0.401269	+	0.915960i	$0.368569\pi$
$38$	4.13700	+	1.37304i	0.671110	+	0.222737i
$39$			0.0494359i			0.00791608i
$40$		0			0
$41$	1.23073	+	3.38141i	0.192208	+	0.528087i	0.997937	−	0.0641969i	$-0.0204486\pi$
$41$	1.23073	+	3.38141i	0.192208	+	0.528087i	−0.805729	+	0.592284i	$0.798226\pi$
$42$	0.0691711	+	0.0484341i	0.0106733	+	0.00747355i
$43$	−3.13537	+	2.19541i	−0.478139	+	0.334797i	−0.787675	−	0.616091i	$-0.788715\pi$
$43$	−3.13537	+	2.19541i	−0.478139	+	0.334797i	0.309536	+	0.950888i	$0.399826\pi$
$44$	−0.774781	+	2.12869i	−0.116803	+	0.320913i
$45$		0			0
$46$	−3.85409	−	2.22516i	−0.568255	−	0.328082i
$47$	−0.895748	+	10.2384i	−0.130658	+	1.49343i	0.594080	+	0.804406i	$0.297516\pi$
$47$	−0.895748	+	10.2384i	−0.130658	+	1.49343i	−0.724738	+	0.689024i	$0.758039\pi$
$48$	0.00293729	−	0.0335734i	0.000423961	−	0.00484590i
$49$	−0.625296	−	0.361015i	−0.0893281	−	0.0515736i
$50$		0			0
$51$	0.0230757	−	0.0634001i	0.00323125	−	0.00887779i
$52$	1.20159	−	0.841363i	0.166631	−	0.116676i
$53$	0.451332	+	0.316026i	0.0619953	+	0.0434095i	0.604163	−	0.796861i	$-0.293507\pi$
$53$	0.451332	+	0.316026i	0.0619953	+	0.0434095i	−0.542168	+	0.840270i	$0.682396\pi$
$54$	0.0691467	+	0.189979i	0.00940967	+	0.0258529i
$55$		0			0
$56$		−	2.50559i		−	0.334823i
$57$	−0.0976074	−	0.109786i	−0.0129284	−	0.0145415i
$58$	2.22770	+	2.22770i	0.292512	+	0.292512i
$59$	−3.05382	−	2.56246i	−0.397573	−	0.333604i	0.421981	−	0.906604i	$-0.361335\pi$
$59$	−3.05382	−	2.56246i	−0.397573	−	0.333604i	−0.819555	+	0.573001i	$0.805779\pi$
$60$		0			0
$61$	0.911575	+	5.16980i	0.116715	+	0.661925i	0.985887	+	0.167414i	$0.0535417\pi$
$61$	0.911575	+	5.16980i	0.116715	+	0.661925i	−0.869171	+	0.494511i	$0.835347\pi$
$62$	2.12743	+	3.03828i	0.270183	+	0.385862i
$63$	3.17552	+	6.80992i	0.400078	+	0.857969i
$64$	−0.866025	+	0.500000i	−0.108253	+	0.0625000i
$65$		0			0
$66$	0.0584833	−	0.0490733i	0.00719880	−	0.00604051i
$67$	−1.37428	−	0.120234i	−0.167895	−	0.0146889i	0.00289801	−	0.999996i	$-0.499078\pi$
$67$	−1.37428	−	0.120234i	−0.167895	−	0.0146889i	−0.170793	+	0.985307i	$0.554633\pi$
$68$	−1.93374	+	0.518143i	−0.234500	+	0.0628341i
$69$	0.0749915	+	0.129889i	0.00902791	+	0.0156368i
$70$		0			0
$71$	7.95714	+	1.40306i	0.944339	+	0.166513i	0.624558	−	0.780979i	$-0.285279\pi$
$71$	7.95714	+	1.40306i	0.944339	+	0.166513i	0.319782	+	0.947491i	$0.396390\pi$
$72$	1.72008	−	2.45653i	0.202713	−	0.289504i
$73$	−3.37102	−	1.57193i	−0.394548	−	0.183981i	0.215211	−	0.976568i	$-0.430956\pi$
$73$	−3.37102	−	1.57193i	−0.394548	−	0.183981i	−0.609759	+	0.792587i	$0.708734\pi$
$74$	−7.28358	+	8.68023i	−0.846699	+	1.00906i
$75$		0			0
$76$	−1.00726	+	4.24092i	−0.115540	+	0.486467i
$77$	4.01349	−	4.01349i	0.457380	−	0.457380i
$78$	−0.0492478	+	0.00430862i	−0.00557622	+	0.000487856i
$79$	11.5411	−	4.20061i	1.29847	−	0.472605i	0.401973	−	0.915651i	$-0.368325\pi$
$79$	11.5411	−	4.20061i	1.29847	−	0.472605i	0.896499	+	0.443046i	$0.146102\pi$
$80$		0			0
$81$	−1.56106	+	8.85320i	−0.173451	+	0.983689i
$82$	−3.26128	+	1.52076i	−0.360148	+	0.167940i
$83$	−1.54270	+	5.75745i	−0.169334	+	0.631962i	0.828114	+	0.560560i	$0.189414\pi$
$83$	−1.54270	+	5.75745i	−0.169334	+	0.631962i	−0.997448	+	0.0714024i	$0.977253\pi$
$84$	−0.0422212	+	0.0731292i	−0.00460671	+	0.00797905i
$85$		0			0
$86$	−2.46032	−	2.93210i	−0.265303	−	0.316176i
$87$	−0.0274802	−	0.102557i	−0.00294618	−	0.0109953i
$88$	−2.18812	−	0.586305i	−0.233254	−	0.0625003i
$89$	−8.99243	−	3.27298i	−0.953196	−	0.346935i	−0.181832	−	0.983330i	$-0.558203\pi$
$89$	−8.99243	−	3.27298i	−0.953196	−	0.346935i	−0.771364	+	0.636394i	$0.780425\pi$
$90$		0			0
$91$	−3.61954	+	0.638222i	−0.379431	+	0.0669038i
$92$	1.88079	−	4.03336i	0.196086	−	0.420507i
$93$	−0.0108946	−	0.124525i	−0.00112971	−	0.0129127i
$94$	−10.2776			−1.06005
$95$		0			0
$96$	0.0337016			0.00343966
$97$	0.712763	+	8.14692i	0.0723701	+	0.827194i	0.942464	+	0.334308i	$0.108503\pi$
$97$	0.712763	+	8.14692i	0.0723701	+	0.827194i	−0.870094	+	0.492886i	$0.835942\pi$
$98$	0.305143	−	0.654382i	0.0308241	−	0.0661025i
$99$	6.69015	−	1.17965i	0.672385	−	0.118560i
$100$		0			0
$101$	−10.3584	−	3.77015i	−1.03070	−	0.375144i	−0.229352	−	0.973344i	$-0.573661\pi$
$101$	−10.3584	−	3.77015i	−1.03070	−	0.375144i	−0.801347	+	0.598200i	$0.795883\pi$
$102$	0.0651700	+	0.0174623i	0.00645279	+	0.00172902i
$103$	−4.51187	−	16.8385i	−0.444567	−	1.65915i	−0.717076	−	0.696995i	$-0.754520\pi$
$103$	−4.51187	−	16.8385i	−0.444567	−	1.65915i	0.272509	−	0.962153i	$-0.412147\pi$
$104$	0.942887	+	1.12369i	0.0924576	+	0.110187i
$105$		0			0
$106$	−0.275487	+	0.477158i	−0.0267577	+	0.0463457i
$107$	3.23442	−	12.0710i	0.312683	−	1.16695i	−0.613444	−	0.789738i	$-0.710216\pi$
$107$	3.23442	−	12.0710i	0.312683	−	1.16695i	0.926127	−	0.377211i	$-0.123117\pi$
$108$	−0.183229	+	0.0854413i	−0.0176313	+	0.00822159i
$109$	3.02363	−	17.1478i	0.289611	−	1.64246i	−0.398723	−	0.917071i	$-0.630547\pi$
$109$	3.02363	−	17.1478i	0.289611	−	1.64246i	0.688334	−	0.725394i	$-0.258342\pi$
$110$		0			0
$111$	0.358851	−	0.130611i	0.0340606	−	0.0123970i
$112$	2.49605	−	0.218376i	0.235855	−	0.0206346i
$113$	−2.86466	+	2.86466i	−0.269485	+	0.269485i	−0.828893	−	0.559408i	$-0.811029\pi$
$113$	−2.86466	+	2.86466i	−0.269485	+	0.269485i	0.559408	+	0.828893i	$0.311029\pi$
$114$	0.100861	−	0.106804i	0.00944652	−	0.0100032i
$115$		0			0
$116$	−2.02507	+	2.41338i	−0.188023	+	0.224077i
$117$	−3.98680	−	1.85908i	−0.368580	−	0.171872i
$118$	2.28655	−	3.26553i	0.210494	−	0.300617i
$119$	4.93986	+	0.871030i	0.452836	+	0.0798472i
$120$		0			0
$121$	2.93419	+	5.08216i	0.266744	+	0.462015i
$122$	−5.07068	+	1.35868i	−0.459078	+	0.123009i
$123$	0.120811	+	0.0105696i	0.0108932	+	0.000953028i
$124$	−2.84130	+	2.38413i	−0.255156	+	0.214102i
$125$		0			0
$126$	−6.50724	+	3.75696i	−0.579711	+	0.334696i
$127$	−1.18157	−	2.53389i	−0.104847	−	0.224846i	0.846884	−	0.531777i	$-0.178476\pi$
$127$	−1.18157	−	2.53389i	−0.104847	−	0.224846i	−0.951732	+	0.306931i	$0.900698\pi$
$128$	−0.573576	−	0.819152i	−0.0506975	−	0.0724035i
$129$	0.0223998	+	0.127036i	0.00197220	+	0.0111849i
$130$		0			0
$131$	−3.50214	−	2.93865i	−0.305984	−	0.256751i	0.476846	−	0.878987i	$-0.341780\pi$
$131$	−3.50214	−	2.93865i	−0.305984	−	0.256751i	−0.782830	+	0.622236i	$0.786224\pi$
$132$	0.0539838	+	0.0539838i	0.00469868	+	0.00469868i
$133$	6.77805	−	8.56384i	0.587732	−	0.742579i
$134$		−	1.37953i		−	0.119174i
$135$		0			0
$136$	−0.684707	−	1.88122i	−0.0587132	−	0.161313i
$137$	−7.07218	−	4.95199i	−0.604217	−	0.423077i	0.231034	−	0.972946i	$-0.425789\pi$
$137$	−7.07218	−	4.95199i	−0.604217	−	0.423077i	−0.835251	+	0.549868i	$0.814678\pi$
$138$	−0.122859	+	0.0860267i	−0.0104584	+	0.00732308i
$139$	−1.37577	+	3.77990i	−0.116691	+	0.320607i	−0.984264	−	0.176703i	$-0.943457\pi$
$139$	−1.37577	+	3.77990i	−0.116691	+	0.320607i	0.867573	+	0.497310i	$0.165679\pi$
$140$		0			0
$141$	0.299965	+	0.173185i	0.0252616	+	0.0145848i
$142$	−0.704209	+	8.04915i	−0.0590959	+	0.675470i
$143$	−0.289611	+	3.31027i	−0.0242185	+	0.276819i
$144$	2.59709	+	1.49943i	0.216424	+	0.124953i
$145$		0			0
$146$	1.27215	−	3.49519i	0.105284	−	0.289264i
$147$	−0.0199329	+	0.0139572i	−0.00164404	+	0.00115117i
$148$	−9.28200	−	6.49933i	−0.762976	−	0.534242i
$149$	−3.99086	−	10.9648i	−0.326944	−	0.898270i	−0.988881	−	0.148711i	$-0.952488\pi$
$149$	−3.99086	−	10.9648i	−0.326944	−	0.898270i	0.661937	−	0.749559i	$-0.269735\pi$
$150$		0			0
$151$		−	5.28871i		−	0.430389i	−0.976571	−	0.215195i	$-0.930961\pi$
$151$		−	5.28871i		−	0.430389i	0.976571	−	0.215195i	$-0.0690386\pi$
$152$	−4.31257	−	0.633802i	−0.349796	−	0.0514081i
$153$	4.24517	+	4.24517i	0.343202	+	0.343202i
$154$	4.34802	+	3.64842i	0.350373	+	0.293998i
$155$		0			0
$156$	−0.00858446	−	0.0486849i	−0.000687307	−	0.00389791i
$157$	−8.22978	−	11.7533i	−0.656808	−	0.938019i	0.343191	−	0.939266i	$-0.388492\pi$
$157$	−8.22978	−	11.7533i	−0.656808	−	0.938019i	−0.999999	+	0.00124661i	$0.999603\pi$
$158$	5.19049	+	11.1310i	0.412933	+	0.885538i
$159$	0.0160810	−	0.00928437i	0.00127531	−	0.000736299i
$160$		0			0
$161$	−8.54191	+	7.16751i	−0.673197	+	0.564879i
$162$	−8.95557	−	0.783511i	−0.703616	−	0.0615584i
$163$	17.0295	−	4.56304i	1.33385	−	0.357405i	0.479703	−	0.877431i	$-0.340745\pi$
$163$	17.0295	−	4.56304i	1.33385	−	0.357405i	0.854150	+	0.520026i	$0.174078\pi$
$164$	−1.79921	−	3.11632i	−0.140495	−	0.243344i
$165$		0			0
$166$	−5.87000	−	1.03504i	−0.455600	−	0.0803346i
$167$	1.37363	−	1.96174i	0.106294	−	0.151804i	−0.762481	−	0.647011i	$-0.776019\pi$
$167$	1.37363	−	1.96174i	0.106294	−	0.151804i	0.868775	+	0.495207i	$0.164908\pi$
$168$	−0.0765308	−	0.0356869i	−0.00590448	−	0.00275330i
$169$	−6.97315	+	8.31027i	−0.536396	+	0.639252i
$170$		0			0
$171$	12.5244	−	3.74304i	0.957764	−	0.286238i
$172$	2.70651	−	2.70651i	0.206369	−	0.206369i
$173$	4.27900	−	0.374364i	0.325326	−	0.0284623i	0.0766770	−	0.997056i	$-0.475569\pi$
$173$	4.27900	−	0.374364i	0.325326	−	0.0284623i	0.248649	+	0.968594i	$0.420013\pi$
$174$	0.0997720	−	0.0363141i	0.00756370	−	0.00275296i
$175$		0			0
$176$	0.393367	−	2.23089i	0.0296511	−	0.168160i
$177$	−0.121763	+	0.0567791i	−0.00915228	+	0.00426778i
$178$	2.47678	−	9.24347i	0.185643	−	0.692828i
$179$	−3.95757	+	6.85471i	−0.295802	+	0.512345i	−0.975171	−	0.221452i	$-0.928920\pi$
$179$	−3.95757	+	6.85471i	−0.295802	+	0.512345i	0.679369	+	0.733797i	$0.262254\pi$
$180$		0			0
$181$	7.27360	+	8.66834i	0.540643	+	0.644313i	0.965332	−	0.261026i	$-0.0840610\pi$
$181$	7.27360	+	8.66834i	0.540643	+	0.644313i	−0.424689	+	0.905339i	$0.639617\pi$
$182$	−0.951257	−	3.55014i	−0.0705118	−	0.263154i
$183$	0.170890	+	0.0457898i	0.0126326	+	0.00338488i
$184$	4.18193	+	1.52210i	0.308296	+	0.112211i
$185$		0			0
$186$	0.123102	−	0.0217062i	0.00902628	−	0.00159158i
$187$	1.91659	−	4.11014i	0.140155	−	0.300563i
$188$	−0.895748	−	10.2384i	−0.0653291	−	0.746715i
$189$	0.506558			0.0368467
$190$		0			0
$191$	6.14107			0.444352			0.222176	−	0.975007i	$-0.428684\pi$
$191$	6.14107			0.444352			0.222176	+	0.975007i	$0.428684\pi$
$192$	0.00293729	+	0.0335734i	0.000211981	+	0.00242295i
$193$	6.16774	−	13.2268i	0.443964	−	0.952084i	−0.549237	−	0.835667i	$-0.685081\pi$
$193$	6.16774	−	13.2268i	0.443964	−	0.952084i	0.993200	−	0.116417i	$-0.0371408\pi$
$194$	−8.05379	+	1.42010i	−0.578229	+	0.101957i
$195$		0			0
$196$	0.678486	+	0.246949i	0.0484633	+	0.0176392i
$197$	−17.6627	−	4.73270i	−1.25841	−	0.337191i	−0.432832	−	0.901475i	$-0.642486\pi$
$197$	−17.6627	−	4.73270i	−1.25841	−	0.337191i	−0.825581	+	0.564284i	$0.809152\pi$
$198$	1.75825	+	6.56188i	0.124953	+	0.466332i
$199$	13.7474	+	16.3835i	0.974527	+	1.16140i	0.986877	+	0.161473i	$0.0516244\pi$
$199$	13.7474	+	16.3835i	0.974527	+	1.16140i	−0.0123499	+	0.999924i	$0.503931\pi$
$200$		0			0
$201$	−0.0232462	+	0.0402637i	−0.00163966	+	0.00283998i
$202$	2.85301	−	10.6476i	0.200737	−	0.749160i
$203$	7.15414	−	3.33603i	0.502123	−	0.234144i
$204$	−0.0117159	+	0.0664440i	−0.000820274	+	0.00465201i
$205$		0			0
$206$	16.3812	−	5.96227i	1.14133	−	0.415411i
$207$	−13.2951	+	1.16317i	−0.924075	+	0.0808461i
$208$	−1.03723	+	1.03723i	−0.0719193	+	0.0719193i
$209$	−5.89271	−	7.92318i	−0.407608	−	0.548058i
$210$		0			0
$211$	10.4174	−	12.4150i	0.717165	−	0.854684i	−0.277187	−	0.960816i	$-0.589402\pi$
$211$	10.4174	−	12.4150i	0.717165	−	0.854684i	0.994352	+	0.106132i	$0.0338466\pi$
$212$	−0.499353	−	0.232852i	−0.0342957	−	0.0159923i
$213$	0.156188	−	0.223060i	0.0107018	−	0.0152838i
$214$	12.3070	+	2.17005i	0.841288	+	0.148342i
$215$		0			0
$216$	−0.101086	−	0.175086i	−0.00687801	−	0.0119131i
$217$	8.97670	−	2.40530i	0.609378	−	0.163282i
$218$	17.3461	+	1.51759i	1.17483	+	0.102784i
$219$	−0.0960263	+	0.0805756i	−0.00648885	+	0.00544479i
$220$		0			0
$221$	−2.54317	+	1.46830i	−0.171072	+	0.0987687i
$222$	0.161390	+	0.346102i	0.0108318	+	0.0232288i
$223$	−8.11099	−	11.5837i	−0.543152	−	0.775701i	0.449938	−	0.893060i	$-0.351446\pi$
$223$	−8.11099	−	11.5837i	−0.543152	−	0.775701i	−0.993090	+	0.117359i	$0.962557\pi$
$224$	0.435091	+	2.46752i	0.0290707	+	0.164868i
$225$		0			0
$226$	−3.10343	−	2.60409i	−0.206437	−	0.173221i
$227$	−11.9434	−	11.9434i	−0.792709	−	0.792709i	0.189225	−	0.981934i	$-0.439402\pi$
$227$	−11.9434	−	11.9434i	−0.792709	−	0.792709i	−0.981934	+	0.189225i	$0.939402\pi$
$228$	0.115189	+	0.0911688i	0.00762856	+	0.00603780i
$229$			0.954813i			0.0630958i	0.999502	+	0.0315479i	$0.0100437\pi$
$229$			0.954813i			0.0630958i	−0.999502	+	0.0315479i	$0.989956\pi$
$230$		0			0
$231$	−0.0654244	−	0.179752i	−0.00430461	−	0.0118268i
$232$	−2.58070	−	1.80702i	−0.169431	−	0.118637i
$233$	−23.6607	+	16.5674i	−1.55006	+	1.08537i	−0.589332	+	0.807891i	$0.700609\pi$
$233$	−23.6607	+	16.5674i	−1.55006	+	1.08537i	−0.960733	+	0.277476i	$0.910502\pi$
$234$	1.50453	−	4.13366i	0.0983541	−	0.270226i
$235$		0			0
$236$	3.45239	+	1.99324i	0.224732	+	0.129749i
$237$	0.0360750	−	0.412340i	0.00234333	−	0.0267843i
$238$	−0.437179	+	4.99698i	−0.0283381	+	0.323906i
$239$	−11.2999	−	6.52400i	−0.730929	−	0.422002i	0.0878328	−	0.996135i	$-0.472006\pi$
$239$	−11.2999	−	6.52400i	−0.730929	−	0.422002i	−0.818762	+	0.574133i	$0.805339\pi$
$240$		0			0
$241$	−4.49546	+	12.3512i	−0.289578	+	0.795609i	0.706547	+	0.707666i	$0.250252\pi$
$241$	−4.49546	+	12.3512i	−0.289578	+	0.795609i	−0.996125	+	0.0879435i	$0.971971\pi$
$242$	−4.80709	+	3.36596i	−0.309011	+	0.216372i
$243$	0.745006	+	0.521659i	0.0477921	+	0.0334644i
$244$	−1.79545	−	4.93296i	−0.114942	−	0.315801i
$245$		0			0
$246$			0.121273i			0.00773205i
$247$	0.182915	+	6.39133i	0.0116386	+	0.406670i
$248$	−2.62270	−	2.62270i	−0.166541	−	0.166541i
$249$	0.153883	+	0.129123i	0.00975195	+	0.00818286i
$250$		0			0
$251$	−4.25357	−	24.1232i	−0.268483	−	1.52264i	−0.758930	−	0.651172i	$-0.774278\pi$
$251$	−4.25357	−	24.1232i	−0.268483	−	1.52264i	0.490447	−	0.871471i	$-0.336833\pi$
$252$	−4.30981	−	6.15504i	−0.271492	−	0.387731i
$253$	4.26056	+	9.13681i	0.267859	+	0.574426i
$254$	2.42126	−	1.39792i	0.151924	−	0.0877131i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−26.5727	−	2.32481i	−1.65756	−	0.145018i	−0.780421	−	0.625254i	$-0.784995\pi$
$257$	−26.5727	−	2.32481i	−1.65756	−	0.145018i	−0.877139	+	0.480237i	$0.840551\pi$
$258$	−0.124600	+	0.0333865i	−0.00775727	+	0.00207855i
$259$	14.1957	+	24.5877i	0.882078	+	1.52780i
$260$		0			0
$261$	9.30423	+	1.64059i	0.575918	+	0.101550i
$262$	2.62223	−	3.74493i	0.162002	−	0.231363i
$263$	12.0893	+	5.63732i	0.745457	+	0.347612i	0.757952	−	0.652310i	$-0.226200\pi$
$263$	12.0893	+	5.63732i	0.745457	+	0.347612i	−0.0124959	+	0.999922i	$0.503978\pi$
$264$	−0.0490733	+	0.0584833i	−0.00302026	+	0.00359940i
$265$		0			0
$266$	9.12200	+	6.00587i	0.559306	+	0.368244i
$267$	−0.228048	+	0.228048i	−0.0139563	+	0.0139563i
$268$	1.37428	−	0.120234i	0.0839477	−	0.00734447i
$269$	11.9636	−	4.35441i	0.729436	−	0.265493i	0.0495100	−	0.998774i	$-0.484234\pi$
$269$	11.9636	−	4.35441i	0.729436	−	0.265493i	0.679926	+	0.733281i	$0.262012\pi$
$270$		0			0
$271$	1.02817	−	5.83105i	0.0624570	−	0.354211i	−0.937523	−	0.347923i	$-0.886887\pi$
$271$	1.02817	−	5.83105i	0.0624570	−	0.354211i	0.999980	−	0.00628846i	$-0.00200169\pi$
$272$	1.81438	−	0.846061i	0.110013	−	0.0513000i
$273$	−0.0320589	+	0.119645i	−0.00194029	+	0.00724127i
$274$	4.31677	−	7.47686i	0.260786	−	0.451694i
$275$		0			0
$276$	−0.0964072	−	0.114894i	−0.00580303	−	0.00691578i
$277$	−1.48760	−	5.55179i	−0.0893811	−	0.333575i	0.906727	−	0.421719i	$-0.138573\pi$
$277$	−1.48760	−	5.55179i	−0.0893811	−	0.333575i	−0.996108	+	0.0881440i	$0.971906\pi$
$278$	−3.88543	−	1.04110i	−0.233032	−	0.0624408i
$279$	10.4522	+	3.80427i	0.625754	+	0.227756i
$280$		0			0
$281$	−3.50468	+	0.617970i	−0.209072	+	0.0368650i	−0.277203	−	0.960811i	$-0.589407\pi$
$281$	−3.50468	+	0.617970i	−0.209072	+	0.0368650i	0.0681312	+	0.997676i	$0.478296\pi$
$282$	−0.146382	+	0.313918i	−0.00871694	+	0.0186935i
$283$	−2.10050	−	24.0089i	−0.124862	−	1.42718i	−0.757553	−	0.652774i	$-0.773605\pi$
$283$	−2.10050	−	24.0089i	−0.124862	−	1.42718i	0.632691	−	0.774404i	$-0.281950\pi$
$284$	−8.07990			−0.479454
$285$		0			0
$286$	−3.32292			−0.196488
$287$	0.785810	+	8.98185i	0.0463849	+	0.530182i
$288$	−1.26737	+	2.71789i	−0.0746808	+	0.160153i
$289$	−12.7948	+	2.25607i	−0.752636	+	0.132710i
$290$		0			0
$291$	0.258992	+	0.0942652i	0.0151824	+	0.00552592i
$292$	3.59277	+	0.962679i	0.210251	+	0.0563365i
$293$	−4.23639	−	15.8104i	−0.247493	−	0.923655i	−0.972114	−	0.234508i	$-0.924652\pi$
$293$	−4.23639	−	15.8104i	−0.247493	−	0.923655i	0.724621	−	0.689147i	$-0.242015\pi$
$294$	−0.0156413	−	0.0186406i	−0.000912221	−	0.00108714i
$295$		0			0
$296$	5.66562	−	9.81314i	0.329307	−	0.570377i
$297$	0.118534	−	0.442375i	0.00687805	−	0.0256692i
$298$	10.5752	−	4.93131i	0.612607	−	0.285663i
$299$	1.13358	−	6.42887i	0.0655568	−	0.371791i
$300$		0			0
$301$	−9.01197	+	3.28009i	−0.519441	+	0.189061i
$302$	5.26859	−	0.460941i	0.303173	−	0.0265242i
$303$	−0.262689	+	0.262689i	−0.0150911	+	0.0150911i
$304$	0.255525	−	4.35140i	0.0146553	−	0.249570i
$305$		0			0
$306$	−3.85903	+	4.59901i	−0.220606	+	0.262908i
$307$	17.0189	+	7.93605i	0.971321	+	0.452934i	0.842478	−	0.538731i	$-0.181096\pi$
$307$	17.0189	+	7.93605i	0.971321	+	0.452934i	0.128843	+	0.991665i	$0.458874\pi$
$308$	−3.25558	+	4.64945i	−0.185504	+	0.264927i
$309$	−0.578578	−	0.102019i	−0.0329142	−	0.00580366i
$310$		0			0
$311$	−13.3331	−	23.0937i	−0.756052	−	1.30952i	−0.944849	−	0.327505i	$-0.893792\pi$
$311$	−13.3331	−	23.0937i	−0.756052	−	1.30952i	0.188797	−	0.982016i	$-0.439541\pi$
$312$	0.0477514	−	0.0127950i	0.00270339	−	0.000724372i
$313$	26.9533	+	2.35811i	1.52349	+	0.133288i	0.817912	−	0.575343i	$-0.195131\pi$
$313$	26.9533	+	2.35811i	1.52349	+	0.133288i	0.705579	+	0.708631i	$0.250687\pi$
$314$	10.9913	−	9.22283i	0.620278	−	0.520475i
$315$		0			0
$316$	−10.6363	+	6.14087i	−0.598339	+	0.345451i
$317$	9.24944	+	19.8355i	0.519500	+	1.11407i	0.974666	+	0.223665i	$0.0718022\pi$
$317$	9.24944	+	19.8355i	0.519500	+	1.11407i	−0.455166	+	0.890407i	$0.650420\pi$
$318$	0.0106506	+	0.0152106i	0.000597256	+	0.000852969i
$319$	−1.23928	−	7.02832i	−0.0693865	−	0.393510i
$320$		0			0
$321$	−0.322630	−	0.270719i	−0.0180074	−	0.0151100i
$322$	−7.88471	−	7.88471i	−0.439398	−	0.439398i
$323$	2.74877	−	8.28207i	0.152945	−	0.460826i
$324$		−	8.98978i		−	0.499432i
$325$		0			0
$326$	6.02989	+	16.5670i	0.333965	+	0.917561i
$327$	−0.480699	−	0.336589i	−0.0265827	−	0.0186134i
$328$	2.94765	−	2.06397i	0.162757	−	0.113964i
$329$	−8.80747	+	24.1983i	−0.485571	+	1.33410i
$330$		0			0
$331$	5.54135	+	3.19930i	0.304580	+	0.175850i	0.644499	−	0.764605i	$-0.277066\pi$
$331$	5.54135	+	3.19930i	0.304580	+	0.175850i	−0.339918	+	0.940455i	$0.610399\pi$
$332$	0.519496	−	5.93787i	0.0285111	−	0.325883i
$333$	−2.96162	+	33.8515i	−0.162296	+	1.85505i
$334$	2.07400	+	1.19742i	0.113484	+	0.0655200i
$335$		0			0
$336$	0.0288810	−	0.0793498i	0.00157559	−	0.00432889i
$337$	22.2434	−	15.5750i	1.21168	−	0.848425i	0.219789	−	0.975547i	$-0.429463\pi$
$337$	22.2434	−	15.5750i	1.21168	−	0.848425i	0.991887	+	0.127122i	$0.0405741\pi$
$338$	−8.88640	−	6.22232i	−0.483356	−	0.338450i
$339$	0.0466972	+	0.128299i	0.00253624	+	0.00696827i
$340$		0			0
$341$		−	8.40215i		−	0.455002i
$342$	4.82037	+	12.1505i	0.260656	+	0.657024i
$343$	−13.6813	−	13.6813i	−0.738719	−	0.738719i
$344$	2.93210	+	2.46032i	0.158088	+	0.132652i
$345$		0			0
$346$	0.745878	+	4.23009i	0.0400987	+	0.227411i
$347$	−8.77253	−	12.5285i	−0.470934	−	0.672564i	0.511476	−	0.859297i	$-0.329099\pi$
$347$	−8.77253	−	12.5285i	−0.470934	−	0.672564i	−0.982411	+	0.186734i	$0.940210\pi$
$348$	0.0448716	+	0.0962274i	0.00240537	+	0.00515833i
$349$	−12.9778	+	7.49275i	−0.694687	+	0.401078i	−0.805366	−	0.592778i	$-0.798031\pi$
$349$	−12.9778	+	7.49275i	−0.694687	+	0.401078i	0.110678	+	0.993856i	$0.464698\pi$
$350$		0			0
$351$	−0.227178	+	0.190625i	−0.0121258	+	0.0101748i
$352$	2.25669	+	0.197435i	0.120282	+	0.0105233i
$353$	17.7025	−	4.74337i	0.942209	−	0.252464i	0.245156	−	0.969484i	$-0.421161\pi$
$353$	17.7025	−	4.74337i	0.942209	−	0.252464i	0.697053	+	0.717020i	$0.254494\pi$
$354$	−0.0671754	−	0.116351i	−0.00357033	−	0.00618399i
$355$		0			0
$356$	9.42417	+	1.66173i	0.499480	+	0.0880718i
$357$	0.0969627	−	0.138477i	0.00513181	−	0.00732899i
$358$	−7.17355	−	3.34508i	−0.379134	−	0.176793i
$359$	0.238793	−	0.284583i	0.0126030	−	0.0150197i	−0.759706	−	0.650267i	$-0.774657\pi$
$359$	0.238793	−	0.284583i	0.0126030	−	0.0150197i	0.772309	+	0.635247i	$0.219102\pi$
$360$		0			0
$361$	−13.0254	−	13.8325i	−0.685547	−	0.728028i
$362$	−8.00142	+	8.00142i	−0.420545	+	0.420545i
$363$	0.197021	−	0.0172371i	0.0103409	−	0.000904714i
$364$	3.45372	−	1.25705i	0.181024	−	0.0658874i
$365$		0			0
$366$	−0.0307215	+	0.174231i	−0.00160584	+	0.00910718i
$367$	3.35924	−	1.56644i	0.175351	−	0.0817674i	−0.332961	−	0.942941i	$-0.608048\pi$
$367$	3.35924	−	1.56644i	0.175351	−	0.0817674i	0.508312	+	0.861173i	$0.330270\pi$
$368$	−1.15183	+	4.29868i	−0.0600432	+	0.224084i
$369$	−5.39559	+	9.34543i	−0.280883	+	0.486504i
$370$		0			0
$371$	0.887379	+	1.05754i	0.0460704	+	0.0549046i
$372$	0.0323527	+	0.120742i	0.00167741	+	0.00626017i
$373$	−18.0426	−	4.83451i	−0.934212	−	0.250321i	−0.240562	−	0.970634i	$-0.577332\pi$
$373$	−18.0426	−	4.83451i	−0.934212	−	0.250321i	−0.693650	+	0.720312i	$0.743998\pi$
$374$	4.26154	+	1.55107i	0.220359	+	0.0802041i
$375$		0			0
$376$	10.1214	−	1.78468i	0.521972	−	0.0920378i
$377$	−1.95305	+	4.18832i	−0.100587	+	0.215710i
$378$	0.0441495	+	0.504631i	0.00227080	+	0.0259554i
$379$	−6.07584			−0.312095			−0.156047	−	0.987750i	$-0.549875\pi$
$379$	−6.07584			−0.312095			−0.156047	+	0.987750i	$0.549875\pi$
$380$		0			0
$381$	−0.0942241			−0.00482725
$382$	0.535229	+	6.11770i	0.0273847	+	0.313009i
$383$	−10.4541	+	22.4188i	−0.534177	+	1.14555i	0.435282	+	0.900294i	$0.356649\pi$
$383$	−10.4541	+	22.4188i	−0.534177	+	1.14555i	−0.969459	+	0.245253i	$0.921129\pi$
$384$	−0.0331896	+	0.00585222i	−0.00169370	+	0.000298645i
$385$		0			0
$386$	13.7140	+	4.99149i	0.698024	+	0.254060i
$387$	−11.0873	−	2.97083i	−0.563598	−	0.151016i
$388$	−2.11663	−	7.89938i	−0.107456	−	0.401030i
$389$	−19.6393	−	23.4052i	−0.995751	−	1.18669i	−0.982402	−	0.186779i	$-0.940195\pi$
$389$	−19.6393	−	23.4052i	−0.995751	−	1.18669i	−0.0133492	−	0.999911i	$-0.504249\pi$
$390$		0			0
$391$	−4.45466	+	7.71570i	−0.225282	+	0.390200i
$392$	−0.186875	+	0.697428i	−0.00943862	+	0.0352254i
$393$	−0.139639	+	0.0651146i	−0.00704385	+	0.00328460i
$394$	3.17528	−	18.0079i	0.159968	−	0.907226i
$395$		0			0
$396$	−6.38367	+	2.32346i	−0.320791	+	0.116758i
$397$	15.6888	−	1.37259i	0.787397	−	0.0688883i	0.313638	−	0.949543i	$-0.398452\pi$
$397$	15.6888	−	1.37259i	0.787397	−	0.0688883i	0.473759	+	0.880654i	$0.342897\pi$
$398$	−15.1230	+	15.1230i	−0.758048	+	0.758048i
$399$	−0.165035	−	0.329003i	−0.00826208	−	0.0164708i
$400$		0			0
$401$	−22.9103	+	27.3034i	−1.14408	+	1.36347i	−0.222666	+	0.974895i	$0.571476\pi$
$401$	−22.9103	+	27.3034i	−1.14408	+	1.36347i	−0.921418	+	0.388572i	$0.872968\pi$
$402$	−0.0421365	−	0.0196486i	−0.00210158	−	0.000979982i
$403$	−3.12066	+	4.45676i	−0.155451	+	0.222007i
$404$	10.8557	+	1.91415i	0.540092	+	0.0952327i
$405$		0			0
$406$	3.94686	+	6.83617i	0.195880	+	0.339273i
$407$	24.7941	−	6.64356i	1.22900	−	0.329309i
$408$	−0.0672122	−	0.00588031i	−0.00332750	−	0.000291119i
$409$	−20.5222	+	17.2202i	−1.01476	+	0.851482i	−0.988960	−	0.148186i	$-0.952657\pi$
$409$	−20.5222	+	17.2202i	−1.01476	+	0.851482i	−0.0257968	+	0.999667i	$0.508212\pi$
$410$		0			0
$411$	−0.251982	+	0.145482i	−0.0124294	+	0.00717610i
$412$	7.36730	+	15.7992i	0.362961	+	0.778372i
$413$	−5.72915	−	8.18208i	−0.281913	−	0.402614i
$414$	−2.31749	−	13.1432i	−0.113899	−	0.645951i
$415$		0			0
$416$	−1.12369	−	0.942887i	−0.0550934	−	0.0462288i
$417$	0.0958585	+	0.0958585i	0.00469421	+	0.00469421i
$418$	7.37945	−	6.56084i	0.360941	−	0.320901i
$419$		−	0.718949i		−	0.0351229i	−0.999846	−	0.0175615i	$-0.994410\pi$
$419$		−	0.718949i		−	0.0351229i	0.999846	−	0.0175615i	$-0.00559028\pi$
$420$		0			0
$421$	6.15540	+	16.9118i	0.299996	+	0.824231i	0.994499	+	0.104742i	$0.0334017\pi$
$421$	6.15540	+	16.9118i	0.299996	+	0.824231i	−0.694504	+	0.719489i	$0.744376\pi$
$422$	13.2757	+	9.29575i	0.646251	+	0.452510i
$423$	−25.2471	+	17.6782i	−1.22755	+	0.859543i
$424$	0.188445	−	0.517747i	0.00915167	−	0.0251440i
$425$		0			0
$426$	0.235823	+	0.136153i	0.0114257	+	0.00659662i
$427$	−1.14638	+	13.1032i	−0.0554771	+	0.634106i
$428$	−1.08917	+	12.4493i	−0.0526471	+	0.601759i
$429$	0.0969841	+	0.0559938i	0.00468244	+	0.00270341i
$430$		0			0
$431$	6.61722	−	18.1807i	0.318740	−	0.875731i	−0.672072	−	0.740486i	$-0.734595\pi$
$431$	6.61722	−	18.1807i	0.318740	−	0.875731i	0.990812	−	0.135246i	$-0.0431823\pi$
$432$	0.165609	−	0.115961i	0.00796787	−	0.00557916i
$433$	−29.9536	−	20.9737i	−1.43948	−	1.00793i	−0.993614	−	0.112832i	$-0.964008\pi$
$433$	−29.9536	−	20.9737i	−1.43948	−	1.00793i	−0.445864	−	0.895101i	$-0.647103\pi$
$434$	3.17852	+	8.73290i	0.152574	+	0.419193i
$435$		0			0
$436$			17.4124i			0.833901i
$437$	10.1759	+	16.5152i	0.486778	+	0.790031i
$438$	−0.0886382	−	0.0886382i	−0.00423530	−	0.00423530i
$439$	3.19469	+	2.68066i	0.152474	+	0.127941i	0.715834	−	0.698271i	$-0.246047\pi$
$439$	3.19469	+	2.68066i	0.152474	+	0.127941i	−0.563359	+	0.826212i	$0.690491\pi$
$440$		0			0
$441$	−0.375995	−	2.13238i	−0.0179045	−	0.101542i
$442$	−1.68437	−	2.40552i	−0.0801171	−	0.114419i
$443$	16.1962	+	34.7328i	0.769504	+	1.65021i	0.759716	+	0.650255i	$0.225338\pi$
$443$	16.1962	+	34.7328i	0.769504	+	1.65021i	0.00978754	+	0.999952i	$0.496884\pi$
$444$	−0.330719	+	0.190940i	−0.0156952	+	0.00906163i
$445$		0			0
$446$	10.8327	−	9.08971i	0.512943	−	0.430410i
$447$	−0.391750	−	0.0342737i	−0.0185292	−	0.00162109i
$448$	−2.42021	+	0.648494i	−0.114344	+	0.0306385i
$449$	12.0948	+	20.9488i	0.570788	+	0.988633i	0.996485	+	0.0837679i	$0.0266954\pi$
$449$	12.0948	+	20.9488i	0.570788	+	0.988633i	−0.425698	+	0.904866i	$0.639971\pi$
$450$		0			0
$451$	8.02769	+	1.41550i	0.378009	+	0.0666532i
$452$	2.32370	−	3.31858i	0.109298	−	0.156093i
$453$	−0.161539	−	0.0753267i	−0.00758974	−	0.00353915i
$454$	10.8570	−	12.9388i	0.509543	−	0.607250i
$455$		0			0
$456$	−0.0807825	+	0.122696i	−0.00378299	+	0.00574578i
$457$	−1.31749	+	1.31749i	−0.0616295	+	0.0616295i	−0.737250	−	0.675620i	$-0.763876\pi$
$457$	−1.31749	+	1.31749i	−0.0616295	+	0.0616295i	0.675620	+	0.737250i	$0.263876\pi$
$458$	−0.951180	+	0.0832175i	−0.0444457	+	0.00388850i
$459$	0.380328	−	0.138428i	0.0177522	−	0.00646128i
$460$		0			0
$461$	−6.34841	+	36.0036i	−0.295675	+	1.67686i	0.368772	+	0.929520i	$0.379778\pi$
$461$	−6.34841	+	36.0036i	−0.295675	+	1.67686i	−0.664447	+	0.747335i	$0.731333\pi$
$462$	0.173366	−	0.0808418i	0.00806571	−	0.00376110i
$463$	−0.119756	+	0.446936i	−0.00556554	+	0.0207709i	−0.968653	−	0.248419i	$-0.920089\pi$
$463$	−0.119756	+	0.446936i	−0.00556554	+	0.0207709i	0.963087	+	0.269190i	$0.0867558\pi$
$464$	1.57522	−	2.72837i	0.0731280	−	0.126661i
$465$		0			0
$466$	−18.5665	−	22.1267i	−0.860078	−	1.02500i
$467$	9.09391	+	33.9389i	0.420816	+	1.57051i	0.772893	+	0.634536i	$0.218809\pi$
$467$	9.09391	+	33.9389i	0.420816	+	1.57051i	−0.352077	+	0.935971i	$0.614525\pi$
$468$	4.24906	+	1.13853i	0.196413	+	0.0526286i
$469$	−3.24809	−	1.18221i	−0.149983	−	0.0545892i
$470$		0			0
$471$	−0.476211	+	0.0839688i	−0.0219426	+	0.00386908i
$472$	−1.68476	+	3.61298i	−0.0775473	+	0.166301i
$473$	0.755697	+	8.63765i	0.0347470	+	0.397160i
$474$	0.413915			0.0190117
$475$		0			0
$476$	−5.01606			−0.229911
$477$	0.144007	+	1.64601i	0.00659364	+	0.0753657i
$478$	5.51432	−	11.8255i	0.252219	−	0.540886i
$479$	−32.9500	+	5.80997i	−1.50552	+	0.265464i	−0.864725	−	0.502245i	$-0.832508\pi$
$479$	−32.9500	+	5.80997i	−1.50552	+	0.265464i	−0.640798	+	0.767709i	$0.721397\pi$
$480$		0			0
$481$	−15.6191	−	5.68487i	−0.712168	−	0.259208i
$482$	−12.6960	−	3.40188i	−0.578286	−	0.154951i
$483$	0.0972630	+	0.362991i	0.00442562	+	0.0165166i
$484$	−3.77212	−	4.49544i	−0.171460	−	0.204338i
$485$		0			0
$486$	−0.454742	+	0.787636i	−0.0206275	+	0.0357279i
$487$	−0.995535	+	3.71539i	−0.0451120	+	0.168360i	−0.984807	−	0.173654i	$-0.944443\pi$
$487$	−0.995535	+	3.71539i	−0.0451120	+	0.168360i	0.939695	+	0.342014i	$0.111109\pi$
$488$	4.75771	−	2.21856i	0.215371	−	0.100429i
$489$	0.103176	−	0.585140i	0.00466578	−	0.0264610i
$490$		0			0
$491$	−16.2992	+	5.93241i	−0.735571	+	0.267726i	−0.682521	−	0.730866i	$-0.739116\pi$
$491$	−16.2992	+	5.93241i	−0.735571	+	0.267726i	−0.0530499	+	0.998592i	$0.516894\pi$
$492$	−0.120811	+	0.0105696i	−0.00544658	+	0.000476514i
$493$	4.45975	−	4.45975i	0.200857	−	0.200857i
$494$	−6.35106	+	0.739260i	−0.285748	+	0.0332609i
$495$		0			0
$496$	2.38413	−	2.84130i	0.107051	−	0.127578i
$497$	18.3481	+	8.55586i	0.823025	+	0.383783i
$498$	−0.115220	+	0.164551i	−0.00516314	+	0.00737373i
$499$	23.6560	+	4.17119i	1.05899	+	0.186728i	0.675907	−	0.736987i	$-0.263752\pi$
$499$	23.6560	+	4.17119i	1.05899	+	0.186728i	0.383081	+	0.923715i	$0.374863\pi$
$500$		0			0
$501$	−0.0403551	−	0.0698970i	−0.00180293	−	0.00312277i
$502$	23.6607	−	6.33986i	1.05603	−	0.282962i
$503$	37.0567	+	3.24204i	1.65228	+	0.144556i	0.874843	−	0.484407i	$-0.160965\pi$
$503$	37.0567	+	3.24204i	1.65228	+	0.144556i	0.777436	+	0.628963i	$0.216520\pi$
$504$	5.75599	−	4.82985i	0.256392	−	0.215139i
$505$		0			0
$506$	−8.73071	+	5.04068i	−0.388127	+	0.224085i
$507$	0.154511	+	0.331350i	0.00686209	+	0.0147158i
$508$	1.60362	+	2.29021i	0.0711493	+	0.101612i
$509$	−5.03122	−	28.5334i	−0.223005	−	1.26472i	−0.866463	−	0.499241i	$-0.833612\pi$
$509$	−5.03122	−	28.5334i	−0.223005	−	1.26472i	0.643458	−	0.765481i	$-0.277499\pi$
$510$		0			0
$511$	−7.13919	−	5.99049i	−0.315819	−	0.265004i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	0.128137	−	0.871879i	0.00565737	−	0.0384944i
$514$		−	26.6742i		−	1.17655i
$515$		0			0
$516$	−0.0441191	−	0.121216i	−0.00194223	−	0.00533624i
$517$	19.0714	+	13.3539i	0.838758	+	0.587304i
$518$	−23.2569	+	16.2846i	−1.02185	+	0.715506i
$519$	0.0495108	−	0.136030i	0.00217328	−	0.00597105i
$520$		0			0
$521$	−19.2902	−	11.1372i	−0.845119	−	0.487930i	0.0138821	−	0.999904i	$-0.495581\pi$
$521$	−19.2902	−	11.1372i	−0.845119	−	0.487930i	−0.859001	+	0.511974i	$0.828914\pi$
$522$	−0.823427	+	9.41182i	−0.0360404	+	0.411944i
$523$	−2.87934	+	32.9110i	−0.125905	+	1.43910i	0.626000	+	0.779823i	$0.284691\pi$
$523$	−2.87934	+	32.9110i	−0.125905	+	1.43910i	−0.751904	+	0.659272i	$0.770864\pi$
$524$	3.95923	+	2.28586i	0.172960	+	0.0998583i
$525$		0			0
$526$	−4.56222	+	12.5346i	−0.198922	+	0.546534i
$527$	6.08248	−	4.25900i	0.264957	−	0.185525i
$528$	−0.0625378	−	0.0437894i	−0.00272161	−	0.00190569i
$529$	1.09263	+	3.00198i	0.0475058	+	0.130521i
$530$		0			0
$531$		−	11.9549i		−	0.518799i
$532$	−5.18799	+	9.61074i	−0.224928	+	0.416678i
$533$	−3.73240	−	3.73240i	−0.161668	−	0.161668i
$534$	−0.247056	−	0.207305i	−0.0106912	−	0.00897096i
$535$		0			0
$536$	0.239553	+	1.35857i	0.0103471	+	0.0586815i
$537$	0.153003	+	0.218511i	0.00660257	+	0.00942945i
$538$	5.38054	+	11.5386i	0.231972	+	0.497465i
$539$	−1.41649	+	0.817811i	−0.0610125	+	0.0352256i
$540$		0			0
$541$	−2.75479	+	2.31154i	−0.118438	+	0.0993809i	−0.700083	−	0.714062i	$-0.746854\pi$
$541$	−2.75479	+	2.31154i	−0.118438	+	0.0993809i	0.581645	+	0.813443i	$0.302409\pi$
$542$	5.89847	+	0.516049i	0.253361	+	0.0221662i
$543$	0.368363	−	0.0987027i	0.0158080	−	0.00423574i
$544$	1.00098	+	1.73374i	0.0429165	+	0.0743335i
$545$		0			0
$546$	−0.121984	−	0.0215091i	−0.00522044	−	0.000920505i
$547$	10.4196	−	14.8808i	0.445511	−	0.636255i	−0.532099	−	0.846682i	$-0.678597\pi$
$547$	10.4196	−	14.8808i	0.445511	−	0.636255i	0.977610	+	0.210427i	$0.0674855\pi$
$548$	7.82464	+	3.64869i	0.334252	+	0.155864i
$549$	−10.1192	+	12.0596i	−0.431877	+	0.514691i
$550$		0			0
$551$	−3.93224	−	13.1575i	−0.167519	−	0.560527i
$552$	0.106054	−	0.106054i	0.00451396	−	0.00451396i
$553$	30.6559	−	2.68204i	1.30362	−	0.114052i
$554$	5.40101	−	1.96581i	0.229467	−	0.0835192i
$555$		0			0
$556$	0.698498	−	3.96138i	0.0296229	−	0.168000i
$557$	−36.9623	+	17.2358i	−1.56614	+	0.730304i	−0.995839	−	0.0911299i	$-0.970952\pi$
$557$	−36.9623	+	17.2358i	−1.56614	+	0.730304i	−0.570303	+	0.821434i	$0.693174\pi$
$558$	−2.87883	+	10.7439i	−0.121871	+	0.454827i
$559$	2.80728	−	4.86236i	0.118735	−	0.205656i
$560$		0			0
$561$	−0.0982424	−	0.117081i	−0.00414780	−	0.00494315i
$562$	−0.921072	−	3.43749i	−0.0388531	−	0.145002i
$563$	−31.4324	−	8.42229i	−1.32472	−	0.354957i	−0.473975	−	0.880539i	$-0.657181\pi$
$563$	−31.4324	−	8.42229i	−1.32472	−	0.354957i	−0.850743	+	0.525581i	$0.823848\pi$
$564$	−0.325481	−	0.118466i	−0.0137052	−	0.00498830i
$565$		0			0
$566$	23.7344	−	4.18502i	0.997632	−	0.175909i
$567$	−9.51934	+	20.4143i	−0.399775	+	0.857320i
$568$	−0.704209	−	8.04915i	−0.0295480	−	0.337735i
$569$	18.2602			0.765506			0.382753	−	0.923851i	$-0.374976\pi$
$569$	18.2602			0.765506			0.382753	+	0.923851i	$0.374976\pi$
$570$		0			0
$571$	43.3406			1.81375			0.906873	−	0.421404i	$-0.138463\pi$
$571$	43.3406			1.81375			0.906873	+	0.421404i	$0.138463\pi$
$572$	−0.289611	−	3.31027i	−0.0121093	−	0.138409i
$573$	0.0874667	−	0.187573i	0.00365397	−	0.00783597i
$574$	−8.87918	+	1.56564i	−0.370610	+	0.0653485i
$575$		0			0
$576$	−2.81801	−	1.02567i	−0.117417	−	0.0427363i
$577$	9.25703	+	2.48041i	0.385375	+	0.103261i	0.446305	−	0.894881i	$-0.352740\pi$
$577$	9.25703	+	2.48041i	0.385375	+	0.103261i	−0.0609294	+	0.998142i	$0.519406\pi$
$578$	−3.36263	−	12.5495i	−0.139867	−	0.521990i
$579$	−0.316152	−	0.376776i	−0.0131388	−	0.0156583i
$580$		0			0
$581$	−7.46734	+	12.9338i	−0.309798	+	0.536585i
$582$	−0.0713339	+	0.266222i	−0.00295689	+	0.0110352i
$583$	1.13119	−	0.527482i	0.0468490	−	0.0218461i
$584$	−0.645886	+	3.66300i	−0.0267269	+	0.151576i
$585$		0			0
$586$	15.3810	−	5.59824i	0.635385	−	0.231261i
$587$	29.7356	−	2.60153i	1.22732	−	0.107376i	0.545003	−	0.838434i	$-0.316529\pi$
$587$	29.7356	−	2.60153i	1.22732	−	0.107376i	0.682316	+	0.731058i	$0.260973\pi$
$588$	0.0172064	−	0.0172064i	0.000709582	−	0.000709582i
$589$	−1.86925	−	16.0590i	−0.0770213	−	0.661698i
$590$		0			0
$591$	−0.396123	+	0.472081i	−0.0162943	+	0.0194188i
$592$	10.2696	+	4.78879i	0.422077	+	0.196818i
$593$	−12.9858	+	18.5456i	−0.533261	+	0.761575i	−0.991896	−	0.127049i	$-0.959449\pi$
$593$	−12.9858	+	18.5456i	−0.533261	+	0.761575i	0.458636	+	0.888624i	$0.348338\pi$
$594$	0.451023	+	0.0795275i	0.0185057	+	0.00326305i
$595$		0			0
$596$	5.83424	+	10.1052i	0.238980	+	0.413925i
$597$	0.696222	−	0.186552i	0.0284945	−	0.00763507i
$598$	6.50321	+	0.568957i	0.265936	+	0.0232664i
$599$	−11.9367	+	10.0161i	−0.487719	+	0.409245i	−0.853208	−	0.521571i	$-0.825346\pi$
$599$	−11.9367	+	10.0161i	−0.487719	+	0.409245i	0.365489	+	0.930816i	$0.380902\pi$
$600$		0			0
$601$	−6.37915	+	3.68300i	−0.260211	+	0.150233i	−0.624431	−	0.781080i	$-0.714669\pi$
$601$	−6.37915	+	3.68300i	−0.260211	+	0.150233i	0.364220	+	0.931313i	$0.381336\pi$
$602$	−4.05305	−	8.69179i	−0.165190	−	0.354251i
$603$	−2.37290	−	3.38886i	−0.0966321	−	0.138005i
$604$	0.918375	+	5.20836i	0.0373681	+	0.211925i
$605$		0			0
$606$	−0.284584	−	0.238795i	−0.0115605	−	0.00970037i
$607$	−4.74573	−	4.74573i	−0.192623	−	0.192623i	0.604205	−	0.796829i	$-0.293491\pi$
$607$	−4.74573	−	4.74573i	−0.192623	−	0.192623i	−0.796829	+	0.604205i	$0.793491\pi$
$608$	4.35711	−	0.124698i	0.176704	−	0.00505715i
$609$		−	0.266031i		−	0.0107801i
$610$		0			0
$611$	−5.15624	−	14.1667i	−0.208599	−	0.573122i
$612$	−4.91784	−	3.44351i	−0.198792	−	0.139196i
$613$	−20.8858	+	14.6244i	−0.843571	+	0.590675i	−0.913482	−	0.406879i	$-0.866617\pi$
$613$	−20.8858	+	14.6244i	−0.843571	+	0.590675i	0.0699114	+	0.997553i	$0.477728\pi$
$614$	−6.42256	+	17.6458i	−0.259193	+	0.712128i
$615$		0			0
$616$	−4.91550	−	2.83797i	−0.198051	−	0.114345i
$617$	−1.71835	+	19.6408i	−0.0691782	+	0.790710i	0.879795	+	0.475353i	$0.157680\pi$
$617$	−1.71835	+	19.6408i	−0.0691782	+	0.790710i	−0.948973	+	0.315357i	$0.897876\pi$
$618$	0.0512043	−	0.585268i	0.00205974	−	0.0235429i
$619$	−21.3938	−	12.3517i	−0.859889	−	0.496457i	0.00408588	−	0.999992i	$-0.498699\pi$
$619$	−21.3938	−	12.3517i	−0.859889	−	0.496457i	−0.863975	+	0.503534i	$0.832033\pi$
$620$		0			0
$621$	−0.307725	+	0.845467i	−0.0123486	+	0.0339274i
$622$	21.8437	−	15.2951i	0.875853	−	0.613279i
$623$	−19.6411	−	13.7528i	−0.786904	−	0.550996i
$624$	0.0169081	+	0.0464546i	0.000676865	+	0.00185967i
$625$		0			0
$626$			27.0563i			1.08139i
$627$	−0.325935	+	0.0671380i	−0.0130166	+	0.00268124i
$628$	10.1457	+	10.1457i	0.404857	+	0.404857i
$629$	17.3774	+	14.5814i	0.692882	+	0.581397i
$630$		0			0
$631$	−6.57225	−	37.2731i	−0.261637	−	1.48382i	−0.778443	−	0.627715i	$-0.783990\pi$
$631$	−6.57225	−	37.2731i	−0.261637	−	1.48382i	0.516806	−	0.856102i	$-0.327121\pi$
$632$	−7.04452	−	10.0606i	−0.280216	−	0.400190i
$633$	−0.230830	−	0.495016i	−0.00917466	−	0.0196751i
$634$	−18.9539	+	10.9430i	−0.752754	+	0.434603i
$635$		0			0
$636$	−0.0142245	+	0.0119358i	−0.000564037	+	0.000473284i
$637$	1.05509	+	0.0923088i	0.0418044	+	0.00365741i
$638$	6.89356	−	1.84712i	0.272919	−	0.0731284i
$639$	12.1153	+	20.9842i	0.479272	+	0.830124i
$640$		0			0
$641$	−11.9059	−	2.09933i	−0.470255	−	0.0829187i	−0.0665013	−	0.997786i	$-0.521184\pi$
$641$	−11.9059	−	2.09933i	−0.470255	−	0.0829187i	−0.403754	+	0.914868i	$0.632295\pi$
$642$	0.241569	−	0.344997i	0.00953399	−	0.0136159i
$643$	−25.6938	−	11.9812i	−1.01326	−	0.472493i	−0.156213	−	0.987723i	$-0.549929\pi$
$643$	−25.6938	−	11.9812i	−1.01326	−	0.472493i	−0.857052	+	0.515230i	$0.827706\pi$
$644$	7.16751	−	8.54191i	0.282440	−	0.336598i
$645$		0			0
$646$	8.49012	+	2.01648i	0.334039	+	0.0793372i
$647$	−5.49556	+	5.49556i	−0.216053	+	0.216053i	−0.806833	−	0.590780i	$-0.798820\pi$
$647$	−5.49556	+	5.49556i	−0.216053	+	0.216053i	0.590780	+	0.806833i	$0.298820\pi$
$648$	8.95557	−	0.783511i	0.351808	−	0.0307792i
$649$	−8.48599	+	3.08865i	−0.333104	+	0.121240i
$650$		0			0
$651$	0.0543868	−	0.308443i	0.00213159	−	0.0120888i
$652$	−15.9784	+	7.45086i	−0.625763	+	0.291798i
$653$	−0.0479315	+	0.178883i	−0.00187571	+	0.00700023i	−0.966857	−	0.255317i	$-0.917820\pi$
$653$	−0.0479315	+	0.178883i	−0.00187571	+	0.00700023i	0.964982	+	0.262317i	$0.0844868\pi$
$654$	0.293412	−	0.508205i	0.0114733	−	0.0198724i
$655$		0			0
$656$	2.31302	+	2.75655i	0.0903082	+	0.107625i
$657$	−2.88694	−	10.7742i	−0.112630	−	0.420342i
$658$	−24.8739	−	6.66493i	−0.969684	−	0.259826i
$659$	39.2370	+	14.2811i	1.52846	+	0.556313i	0.963243	−	0.268632i	$-0.0865716\pi$
$659$	39.2370	+	14.2811i	1.52846	+	0.556313i	0.565213	+	0.824945i	$0.308794\pi$
$660$		0			0
$661$	41.9180	−	7.39128i	1.63042	−	0.287487i	0.717787	−	0.696263i	$-0.245155\pi$
$661$	41.9180	−	7.39128i	1.63042	−	0.287487i	0.912635	+	0.408776i	$0.134044\pi$
$662$	−2.70417	+	5.79910i	−0.105100	+	0.225389i
$663$	0.00862565	+	0.0985917i	0.000334993	+	0.00382898i
$664$	5.96055			0.231314
$665$		0			0
$666$	−33.9808			−1.31673
$667$	1.22197	+	13.9672i	0.0473148	+	0.540810i
$668$	−1.01211	+	2.17047i	−0.0391595	+	0.0839779i
$669$	−0.469337	+	0.0827567i	−0.0181456	+	0.00319956i
$670$		0			0
$671$	11.1747	+	4.06725i	0.431394	+	0.157015i
$672$	0.0815650	+	0.0218553i	0.00314644	+	0.000843086i
$673$	−10.1698	−	37.9542i	−0.392017	−	1.46303i	−0.826803	−	0.562492i	$-0.809843\pi$
$673$	−10.1698	−	37.9542i	−0.392017	−	1.46303i	0.434786	−	0.900534i	$-0.356824\pi$
$674$	17.4544	+	20.8013i	0.672318	+	0.801237i
$675$		0			0
$676$	5.42414	−	9.39489i	0.208621	−	0.361342i
$677$	8.30083	−	30.9791i	0.319027	−	1.19062i	−0.601155	−	0.799133i	$-0.705293\pi$
$677$	8.30083	−	30.9791i	0.319027	−	1.19062i	0.920182	−	0.391492i	$-0.128041\pi$
$678$	−0.123741	+	0.0577015i	−0.00475226	+	0.00221601i
$679$	−3.55819	+	20.1795i	−0.136551	+	0.774418i
$680$		0			0
$681$	−0.534907	+	0.194690i	−0.0204977	+	0.00746054i
$682$	8.37018	−	0.732296i	0.320511	−	0.0280411i
$683$	−20.5729	+	20.5729i	−0.787201	+	0.787201i	−0.981035	−	0.193833i	$-0.937908\pi$
$683$	−20.5729	+	20.5729i	−0.787201	+	0.787201i	0.193833	+	0.981035i	$0.437908\pi$
$684$	−11.6841	+	5.86101i	−0.446754	+	0.224101i
$685$		0			0
$686$	12.4368	−	14.8216i	0.474839	−	0.565891i
$687$	0.0291639	+	0.0135993i	0.00111267	+	0.000518847i
$688$	−2.19541	+	3.13537i	−0.0836992	+	0.119535i
$689$	−0.795931	−	0.140344i	−0.0303225	−	0.00534668i
$690$		0			0
$691$	−3.53645	−	6.12530i	−0.134533	−	0.233018i	0.790886	−	0.611963i	$-0.209620\pi$
$691$	−3.53645	−	6.12530i	−0.134533	−	0.233018i	−0.925419	+	0.378946i	$0.876287\pi$
$692$	−4.14898	+	1.11172i	−0.157721	+	0.0422611i
$693$	16.9566	+	1.48351i	0.644127	+	0.0563538i
$694$	11.7162	−	9.83108i	0.444742	−	0.373183i
$695$		0			0
$696$	−0.0919504	+	0.0530876i	−0.00348537	+	0.00201228i
$697$	3.04448	+	6.52891i	0.115318	+	0.247300i
$698$	−8.59534	−	12.2754i	−0.325338	−	0.464631i
$699$	0.169038	+	0.958662i	0.00639360	+	0.0362599i
$700$		0			0
$701$	27.4876	+	23.0648i	1.03819	+	0.871145i	0.991803	−	0.127778i	$-0.0407846\pi$
$701$	27.4876	+	23.0648i	1.03819	+	0.871145i	0.0463877	+	0.998924i	$0.485229\pi$
$702$	−0.209699	−	0.209699i	−0.00791458	−	0.00791458i
$703$	45.9108	−	18.2138i	1.73156	−	0.686947i
$704$			2.26531i			0.0853771i
$705$		0			0
$706$	6.26819	+	17.2217i	0.235907	+	0.648148i
$707$	−22.6246	−	15.8419i	−0.850885	−	0.595796i
$708$	0.110054	−	0.0770604i	0.00413607	−	0.00289611i
$709$	10.6544	−	29.2727i	0.400134	−	1.09936i	−0.562084	−	0.827080i	$-0.690000\pi$
$709$	10.6544	−	29.2727i	0.400134	−	1.09936i	0.962218	−	0.272279i	$-0.0877774\pi$
$710$		0			0
$711$	31.8968	+	18.4156i	1.19622	+	0.690641i
$712$	−0.834041	+	9.53313i	−0.0312570	+	0.357269i
$713$	−1.43863	+	16.4437i	−0.0538773	+	0.615820i
$714$	0.146401	+	0.0845247i	0.00547892	+	0.00316326i
$715$		0			0
$716$	2.70714	−	7.43779i	0.101170	−	0.277963i
$717$	−0.360213	+	0.252224i	−0.0134524	+	0.00941946i
$718$	0.304312	+	0.213082i	0.0113568	+	0.00795213i
$719$	−4.66030	−	12.8041i	−0.173800	−	0.477512i	0.821955	−	0.569552i	$-0.192883\pi$
$719$	−4.66030	−	12.8041i	−0.173800	−	0.477512i	−0.995755	+	0.0920405i	$0.970661\pi$
$720$		0			0
$721$		−	43.6787i		−	1.62668i
$722$	12.6447	−	14.1814i	0.470586	−	0.527777i
$723$	0.313226	+	0.313226i	0.0116490	+	0.0116490i
$724$	−8.66834	−	7.27360i	−0.322156	−	0.270321i
$725$		0			0
$726$	0.0343430	+	0.194769i	0.00127459	+	0.00722856i
$727$	−26.4965	−	37.8409i	−0.982701	−	1.40344i	−0.913958	−	0.405808i	$-0.866990\pi$
$727$	−26.4965	−	37.8409i	−0.982701	−	1.40344i	−0.0687426	−	0.997634i	$-0.521899\pi$
$728$	1.55328	+	3.33102i	0.0575684	+	0.123456i
$729$	−23.3296	+	13.4693i	−0.864059	+	0.498865i
$730$		0			0
$731$	−5.86991	+	4.92544i	−0.217106	+	0.182174i
$732$	−0.176245	−	0.0154194i	−0.00651421	−	0.000569919i
$733$	3.07234	−	0.823232i	0.113480	−	0.0304068i	−0.201632	−	0.979461i	$-0.564625\pi$
$733$	3.07234	−	0.823232i	0.113480	−	0.0304068i	0.315112	+	0.949055i	$0.397958\pi$
$734$	1.85326	+	3.20993i	0.0684049	+	0.118481i
$735$		0			0
$736$	−4.38271	−	0.772790i	−0.161549	−	0.0284854i
$737$	−1.79247	+	2.55991i	−0.0660263	+	0.0942954i
$738$	−9.78012	−	4.56055i	−0.360011	−	0.167876i
$739$	8.50050	−	10.1305i	0.312696	−	0.372657i	−0.586690	−	0.809811i	$-0.699569\pi$
$739$	8.50050	−	10.1305i	0.312696	−	0.372657i	0.899386	+	0.437155i	$0.144014\pi$
$740$		0			0
$741$	0.197822	+	0.0854441i	0.00726718	+	0.00313887i
$742$	−0.976172	+	0.976172i	−0.0358364	+	0.0358364i
$743$	28.0679	−	2.45562i	1.02971	−	0.0900879i	0.440241	−	0.897879i	$-0.354893\pi$
$743$	28.0679	−	2.45562i	1.02971	−	0.0900879i	0.589468	+	0.807792i	$0.299337\pi$
$744$	−0.117463	+	0.0427529i	−0.00430639	+	0.00156740i
$745$		0			0
$746$	3.24359	−	18.3953i	0.118756	−	0.673501i
$747$	−16.2001	+	7.55425i	−0.592732	+	0.276396i
$748$	−1.17375	+	4.38051i	−0.0429167	+	0.160167i
$749$	15.6560	−	27.1169i	0.572056	−	0.990831i
$750$		0			0
$751$	21.1956	+	25.2599i	0.773439	+	0.921748i	0.998617	−	0.0525691i	$-0.0167410\pi$
$751$	21.1956	+	25.2599i	0.773439	+	0.921748i	−0.225179	+	0.974318i	$0.572297\pi$
$752$	2.66003	+	9.92735i	0.0970012	+	0.362013i
$753$	−0.797403	−	0.213664i	−0.0290590	−	0.00778633i
$754$	−4.34260	−	1.58058i	−0.158148	−	0.0575613i
$755$		0			0
$756$	−0.498862	+	0.0879629i	−0.0181434	+	0.00319918i
$757$	17.6731	−	37.9001i	0.642341	−	1.37750i	−0.267909	−	0.963444i	$-0.586333\pi$
$757$	17.6731	−	37.9001i	0.642341	−	1.37750i	0.910250	−	0.414060i	$-0.135890\pi$
$758$	−0.529544	−	6.05272i	−0.0192339	−	0.219845i
$759$	0.339758			0.0123324
$760$		0			0
$761$	8.04964			0.291799			0.145900	−	0.989299i	$-0.453392\pi$
$761$	8.04964			0.291799			0.145900	+	0.989299i	$0.453392\pi$
$762$	−0.00821217	−	0.0938656i	−0.000297496	−	0.00340039i
$763$	18.4381	−	39.5406i	0.667503	−	1.43147i
$764$	−6.04777	+	1.06638i	−0.218801	+	0.0385805i
$765$		0			0
$766$	−23.2446	−	8.46035i	−0.839862	−	0.305685i
$767$	5.64840	+	1.51348i	0.203952	+	0.0546487i
$768$	−0.00872262	−	0.0325533i	−0.000314750	−	0.00117466i
$769$	−6.10714	−	7.27821i	−0.220229	−	0.262459i	0.644606	−	0.764515i	$-0.277022\pi$
$769$	−6.10714	−	7.27821i	−0.220229	−	0.262459i	−0.864835	+	0.502056i	$0.832577\pi$
$770$		0			0
$771$	−0.449482	+	0.778526i	−0.0161877	+	0.0280379i
$772$	−3.77724	+	14.0968i	−0.135946	+	0.507356i
$773$	23.3042	−	10.8669i	0.838195	−	0.390857i	0.0443788	−	0.999015i	$-0.485869\pi$
$773$	23.3042	−	10.8669i	0.838195	−	0.390857i	0.793816	+	0.608158i	$0.208091\pi$
$774$	1.99320	−	11.3040i	0.0716441	−	0.406314i
$775$		0			0
$776$	7.68484	−	2.79705i	0.275870	−	0.100408i
$777$	0.953195	−	0.0833937i	0.0341957	−	0.00299173i
$778$	21.6044	−	21.6044i	0.774557	−	0.774557i
$779$	15.6582	+	0.919484i	0.561012	+	0.0329439i
$780$		0			0
$781$	11.7652	−	14.0213i	0.420993	−	0.501720i
$782$	−8.07459	−	3.76524i	−0.288747	−	0.134645i
$783$	0.365328	−	0.521743i	0.0130558	−	0.0186456i
$784$	−0.711061	−	0.125379i	−0.0253950	−	0.00447783i
$785$		0			0
$786$	−0.0770372	−	0.133432i	−0.00274783	−	0.00475937i
$787$	22.1285	−	5.92931i	0.788795	−	0.211357i	0.158136	−	0.987417i	$-0.449451\pi$
$787$	22.1285	−	5.92931i	0.788795	−	0.211357i	0.630659	+	0.776060i	$0.282785\pi$
$788$	18.2161	+	1.59371i	0.648923	+	0.0567734i
$789$	0.344373	−	0.288963i	0.0122600	−	0.0102874i
$790$		0			0
$791$	−8.79080	+	5.07537i	−0.312565	+	0.180459i
$792$	−2.87100	−	6.15687i	−0.102016	−	0.218775i
$793$	−4.41678	−	6.30781i	−0.156844	−	0.223997i
$794$	2.73473	+	15.5094i	0.0970521	+	0.550410i
$795$		0			0
$796$	−16.3835	−	13.7474i	−0.580698	−	0.487264i
$797$	−10.5852	−	10.5852i	−0.374947	−	0.374947i	0.494328	−	0.869275i	$-0.335414\pi$
$797$	−10.5852	−	10.5852i	−0.374947	−	0.374947i	−0.869275	+	0.494328i	$0.835414\pi$
$798$	0.313368	−	0.193082i	0.0110931	−	0.00683501i
$799$			20.5752i			0.727897i
$800$		0			0
$801$	−9.81522	−	26.9671i	−0.346804	−	0.952835i
$802$	−29.1963	−	20.4434i	−1.03096	−	0.721883i
$803$	−6.90204	+	4.83286i	−0.243568	+	0.170548i
$804$	0.0159014	−	0.0436886i	0.000560798	−	0.00154078i
$805$		0			0
$806$	−4.71179	−	2.72035i	−0.165966	−	0.0958203i
$807$	0.0373959	−	0.427437i	0.00131640	−	0.0150465i
$808$	−0.960733	+	10.9812i	−0.0337985	+	0.386318i
$809$	12.2226	+	7.05673i	0.429724	+	0.248101i	0.699229	−	0.714898i	$-0.253527\pi$
$809$	12.2226	+	7.05673i	0.429724	+	0.248101i	−0.269505	+	0.962999i	$0.586860\pi$
$810$		0			0
$811$	−7.02538	+	19.3021i	−0.246695	+	0.677788i	0.753108	+	0.657897i	$0.228554\pi$
$811$	−7.02538	+	19.3021i	−0.246695	+	0.677788i	−0.999802	+	0.0198904i	$0.993668\pi$
$812$	−6.46616	+	4.52765i	−0.226918	+	0.158890i
$813$	−0.163460	−	0.114456i	−0.00573278	−	0.00401414i
$814$	8.77923	+	24.1207i	0.307712	+	0.845431i
$815$		0			0
$816$		−	0.0674690i		−	0.00236189i
$817$	3.36600	+	16.3410i	0.117762	+	0.571698i
$818$	−18.9432	−	18.9432i	−0.662335	−	0.662335i
$819$	−8.44330	−	7.08477i	−0.295033	−	0.247562i
$820$		0			0
$821$	3.47874	+	19.7289i	0.121409	+	0.688544i	0.983376	+	0.181580i	$0.0581212\pi$
$821$	3.47874	+	19.7289i	0.121409	+	0.688544i	−0.861967	+	0.506964i	$0.830768\pi$
$822$	−0.166890	−	0.238344i	−0.00582096	−	0.00831320i
$823$	21.3543	+	45.7944i	0.744364	+	1.59629i	0.801548	+	0.597930i	$0.204010\pi$
$823$	21.3543	+	45.7944i	0.744364	+	1.59629i	−0.0571842	+	0.998364i	$0.518212\pi$
$824$	−15.0970	+	8.71626i	−0.525929	+	0.303645i
$825$		0			0
$826$	7.65161	−	6.42047i	0.266234	−	0.223397i
$827$	−44.4196	−	3.88621i	−1.54462	−	0.135137i	−0.717260	−	0.696806i	$-0.754604\pi$
$827$	−44.4196	−	3.88621i	−1.54462	−	0.135137i	−0.827362	+	0.561669i	$0.810159\pi$
$828$	12.8912	−	3.45418i	0.447999	−	0.120041i
$829$	0.701985	+	1.21587i	0.0243809	+	0.0422290i	0.877958	−	0.478737i	$-0.158905\pi$
$829$	0.701985	+	1.21587i	0.0243809	+	0.0422290i	−0.853578	+	0.520966i	$0.825572\pi$
$830$		0			0
$831$	−0.190762	−	0.0336365i	−0.00661746	−	0.00116684i
$832$	0.841363	−	1.20159i	0.0291690	−	0.0416577i
$833$	−1.31004	−	0.610882i	−0.0453902	−	0.0211658i
$834$	−0.0871391	+	0.103848i	−0.00301738	+	0.00359597i
$835$		0			0
$836$	7.17904	+	6.77955i	0.248292	+	0.234476i
$837$	0.530234	−	0.530234i	0.0183276	−	0.0183276i
$838$	0.716213	−	0.0626605i	0.0247412	−	0.00216457i
$839$	35.0809	−	12.7684i	1.21113	−	0.440815i	0.344033	−	0.938957i	$-0.388207\pi$
$839$	35.0809	−	12.7684i	1.21113	−	0.440815i	0.867095	+	0.498143i	$0.165984\pi$
$840$		0			0
$841$	−3.31228	+	18.7849i	−0.114217	+	0.647755i
$842$	−16.3110	+	7.60593i	−0.562113	+	0.262118i
$843$	−0.0310416	+	0.115849i	−0.00106913	+	0.00399005i
$844$	−8.10332	+	14.0354i	−0.278928	+	0.483117i
$845$		0			0
$846$	−19.8113	−	23.6102i	−0.681128	−	0.811737i
$847$	3.80560	+	14.2027i	0.130762	+	0.488011i
$848$	0.532201	+	0.142603i	0.0182759	+	0.00489700i
$849$	−0.763244	−	0.277798i	−0.0261945	−	0.00953401i
$850$		0			0
$851$	−49.6615	+	8.75667i	−1.70238	+	0.300175i
$852$	−0.115081	+	0.246793i	−0.00394262	+	0.00845498i
$853$	−3.49410	−	39.9377i	−0.119636	−	1.36744i	−0.784338	−	0.620334i	$-0.786997\pi$
$853$	−3.49410	−	39.9377i	−0.119636	−	1.36744i	0.664702	−	0.747108i	$-0.268558\pi$
$854$	−13.1532			−0.450094
$855$		0			0
$856$	−12.4968			−0.427133
$857$	−3.36514	−	38.4638i	−0.114951	−	1.31390i	−0.806356	−	0.591430i	$-0.798564\pi$
$857$	−3.36514	−	38.4638i	−0.114951	−	1.31390i	0.691405	−	0.722467i	$-0.256992\pi$
$858$	−0.0473280	+	0.101495i	−0.00161575	+	0.00346499i
$859$	−8.45858	+	1.49148i	−0.288603	+	0.0508885i	−0.316075	−	0.948734i	$-0.602365\pi$
$859$	−8.45858	+	1.49148i	−0.288603	+	0.0508885i	0.0274724	+	0.999623i	$0.491254\pi$
$860$		0			0
$861$	0.285534	+	0.103926i	0.00973097	+	0.00354178i
$862$	18.6882	+	5.00749i	0.636523	+	0.170556i
$863$	−8.12122	−	30.3088i	−0.276450	−	1.03172i	−0.954864	−	0.297044i	$-0.903999\pi$
$863$	−8.12122	−	30.3088i	−0.276450	−	1.03172i	0.678414	−	0.734680i	$-0.262668\pi$
$864$	0.129953	+	0.154872i	0.00442110	+	0.00526886i
$865$		0			0
$866$	18.2833	−	31.6676i	0.621291	−	1.07611i
$867$	−0.113326	+	0.422938i	−0.00384875	+	0.0143637i
$868$	−8.42264	+	3.92754i	−0.285883	+	0.133310i
$869$	4.83123	−	27.3993i	0.163888	−	0.929457i
$870$		0			0
$871$	1.90156	−	0.692111i	0.0644319	−	0.0234513i
$872$	−17.3461	+	1.51759i	−0.587413	+	0.0513920i
$873$	−17.3417	+	17.3417i	−0.586927	+	0.586927i
$874$	−15.5655	+	11.5766i	−0.526511	+	0.391583i
$875$		0			0
$876$	0.0805756	−	0.0960263i	0.00272240	−	0.00324443i
$877$	−49.8867	−	23.2626i	−1.68455	−	0.785521i	−0.998308	−	0.0581520i	$-0.981479\pi$
$877$	−49.8867	−	23.2626i	−1.68455	−	0.785521i	−0.686247	−	0.727369i	$-0.740743\pi$
$878$	−2.39203	+	3.41617i	−0.0807270	+	0.115290i
$879$	−0.543253	−	0.0957902i	−0.0183235	−	0.00323092i
$880$		0			0
$881$	−8.19028	−	14.1860i	−0.275938	−	0.477938i	0.694434	−	0.719557i	$-0.255655\pi$
$881$	−8.19028	−	14.1860i	−0.275938	−	0.477938i	−0.970371	+	0.241619i	$0.922322\pi$
$882$	2.09149	−	0.560413i	0.0704242	−	0.0188701i
$883$	14.3824	+	1.25830i	0.484006	+	0.0423450i	0.326548	−	0.945181i	$-0.394115\pi$
$883$	14.3824	+	1.25830i	0.484006	+	0.0423450i	0.157458	+	0.987526i	$0.449670\pi$
$884$	2.24957	−	1.88761i	0.0756612	−	0.0634873i
$885$		0			0
$886$	−33.1891	+	19.1617i	−1.11501	+	0.643751i
$887$	−10.6137	−	22.7613i	−0.356375	−	0.764248i	0.643625	−	0.765341i	$-0.277430\pi$
$887$	−10.6137	−	22.7613i	−0.356375	−	0.764248i	−0.999999	+	0.00109317i	$0.999652\pi$
$888$	−0.219038	−	0.312818i	−0.00735043	−	0.0104975i
$889$	−1.21644	−	6.89878i	−0.0407981	−	0.231378i
$890$		0			0
$891$	15.6002	+	13.0901i	0.522627	+	0.438536i
$892$	9.99925	+	9.99925i	0.334800	+	0.334800i
$893$	39.4218	+	21.2804i	1.31920	+	0.712120i
$894$		−	0.393247i		−	0.0131521i
$895$		0			0
$896$	−0.856961	−	2.35448i	−0.0286291	−	0.0786577i
$897$	−0.180218	−	0.126190i	−0.00601731	−	0.00421336i
$898$	−19.8149	+	13.8746i	−0.661232	+	0.463000i
$899$	3.99657	−	10.9805i	0.133293	−	0.366220i
$900$		0			0
$901$	0.955247	+	0.551512i	0.0318239	+	0.0183735i
$902$	−0.710453	+	8.12051i	−0.0236555	+	0.270384i
$903$	−0.0281696	+	0.321980i	−0.000937425	+	0.0107148i
$904$	3.50848	+	2.02562i	0.116690	+	0.0673712i
$905$		0			0
$906$	0.0609610	−	0.167489i	0.00202529	−	0.00556445i
$907$	−21.5559	+	15.0936i	−0.715751	+	0.501174i	−0.873817	−	0.486254i	$-0.838363\pi$
$907$	−21.5559	+	15.0936i	−0.715751	+	0.501174i	0.158066	+	0.987429i	$0.449474\pi$
$908$	13.8359	+	9.68797i	0.459159	+	0.321507i
$909$	−11.3062	−	31.0634i	−0.375002	−	1.03031i
$910$		0			0
$911$		−	18.8117i		−	0.623259i	−0.950204	−	0.311630i	$-0.899125\pi$
$911$		−	18.8117i		−	0.623259i	0.950204	−	0.311630i	$-0.100875\pi$
$912$	−0.129270	−	0.0697814i	−0.00428056	−	0.00231069i
$913$	9.54771	+	9.54771i	0.315983	+	0.315983i
$914$	−1.42730	−	1.19765i	−0.0472109	−	0.0396147i
$915$		0			0
$916$	−0.165802	−	0.940308i	−0.00547824	−	0.0310686i
$917$	−6.57023	−	9.38326i	−0.216968	−	0.309863i
$918$	0.171049	+	0.366816i	0.00564547	+	0.0121067i
$919$	44.5039	−	25.6944i	1.46805	−	0.847579i	0.468690	−	0.883363i	$-0.344726\pi$
$919$	44.5039	−	25.6944i	1.46805	−	0.847579i	0.999360	+	0.0357836i	$0.0113927\pi$
$920$		0			0
$921$	0.484798	−	0.406794i	0.0159746	−	0.0134043i
$922$	−36.4199	−	3.18633i	−1.19943	−	0.104936i
$923$	−11.4483	+	3.06757i	−0.376826	+	0.100970i
$924$	0.0956440	+	0.165660i	0.00314646	+	0.00544982i
$925$		0			0
$926$	−0.455673	−	0.0803474i	−0.0149743	−	0.00264038i
$927$	29.9853	−	42.8234i	0.984846	−	1.40651i
$928$	2.85528	+	1.33144i	0.0937290	+	0.0437066i
$929$	−25.5464	+	30.4450i	−0.838150	+	0.998869i	0.161777	+	0.986827i	$0.448277\pi$
$929$	−25.5464	+	30.4450i	−0.838150	+	0.998869i	−0.999928	+	0.0120414i	$0.996167\pi$
$930$		0			0
$931$	−2.52538	+	1.87821i	−0.0827661	+	0.0615557i
$932$	20.4243	−	20.4243i	0.669022	−	0.669022i
$933$	−0.895276	+	0.0783265i	−0.0293100	+	0.00256429i
$934$	−33.0172	+	12.0173i	−1.08036	+	0.393217i
$935$		0			0
$936$	−0.763869	+	4.33212i	−0.0249678	+	0.141600i
$937$	−48.2472	+	22.4980i	−1.57617	+	0.734978i	−0.996788	−	0.0800807i	$-0.974482\pi$
$937$	−48.2472	+	22.4980i	−1.57617	+	0.734978i	−0.579378	+	0.815059i	$0.696704\pi$
$938$	0.894619	−	3.33876i	0.0292103	−	0.109014i
$939$	0.455920	−	0.789677i	0.0148784	−	0.0257701i
$940$		0			0
$941$	26.6612	+	31.7736i	0.869131	+	1.03579i	0.999020	+	0.0442612i	$0.0140934\pi$
$941$	26.6612	+	31.7736i	0.869131	+	1.03579i	−0.129889	+	0.991529i	$0.541462\pi$
$942$	−0.125154	−	0.467080i	−0.00407773	−	0.0152183i
$943$	−15.4685	−	4.14476i	−0.503722	−	0.134972i
$944$	−3.74606	−	1.36346i	−0.121924	−	0.0443767i
$945$		0			0
$946$	−8.53892	+	1.50564i	−0.277624	+	0.0489527i
$947$	−0.0304341	+	0.0652661i	−0.000988975	+	0.00212086i	−0.906802	−	0.421558i	$-0.861484\pi$
$947$	−0.0304341	+	0.0652661i	−0.000988975	+	0.00212086i	0.905813	+	0.423678i	$0.139261\pi$
$948$	0.0360750	+	0.412340i	0.00117166	+	0.0133922i
$949$	5.45604			0.177110
$950$		0			0
$951$	0.737595			0.0239181
$952$	−0.437179	−	4.99698i	−0.0141690	−	0.161953i
$953$	17.1783	−	36.8390i	0.556460	−	1.19333i	−0.403960	−	0.914777i	$-0.632367\pi$
$953$	17.1783	−	36.8390i	0.556460	−	1.19333i	0.960420	−	0.278556i	$-0.0898557\pi$
$954$	−1.62720	+	0.286919i	−0.0526824	+	0.00928934i
$955$		0			0
$956$	12.2611	+	4.46268i	0.396552	+	0.144333i
$957$	−0.232324	−	0.0622511i	−0.00750997	−	0.00201229i
$958$	−8.65965	−	32.3182i	−0.279780	−	1.04415i
$959$	−13.9048	−	16.5711i	−0.449011	−	0.535110i
$960$		0			0
$961$	−8.62146	+	14.9328i	−0.278112	+	0.481703i
$962$	4.30195	−	16.0551i	0.138700	−	0.517637i
$963$	33.9651	−	15.8382i	1.09451	−	0.510378i
$964$	2.28241	−	12.9442i	0.0735113	−	0.416903i
$965$		0			0
$966$	−0.353132	+	0.128530i	−0.0113618	+	0.00413537i
$967$	14.9591	−	1.30875i	0.481053	−	0.0420867i	0.155950	−	0.987765i	$-0.450156\pi$
$967$	14.9591	−	1.30875i	0.481053	−	0.0420867i	0.325104	+	0.945678i	$0.394601\pi$
$968$	4.14957	−	4.14957i	0.133372	−	0.133372i
$969$	−0.213817	−	0.201919i	−0.00686880	−	0.00648658i
$970$		0			0
$971$	−20.9172	+	24.9281i	−0.671265	+	0.799982i	−0.988956	−	0.148212i	$-0.952648\pi$
$971$	−20.9172	+	24.9281i	−0.671265	+	0.799982i	0.317691	+	0.948194i	$0.397093\pi$
$972$	−0.824273	−	0.384365i	−0.0264386	−	0.0123285i
$973$	−5.78090	+	8.25599i	−0.185327	+	0.264675i
$974$	−3.78801	−	0.667929i	−0.121376	−	0.0214018i
$975$		0			0
$976$	2.62478	+	4.54625i	0.0840170	+	0.145522i
$977$	−6.14893	+	1.64760i	−0.196722	+	0.0527114i	−0.355834	−	0.934549i	$-0.615803\pi$
$977$	−6.14893	+	1.64760i	−0.196722	+	0.0527114i	0.159113	+	0.987260i	$0.449137\pi$
$978$	0.591906	+	0.0517851i	0.0189271	+	0.00165590i
$979$	−16.6063	+	13.9343i	−0.530740	+	0.445344i
$980$		0			0
$981$	45.2215	−	26.1087i	1.44381	−	0.833586i
$982$	−7.33040	−	15.7201i	−0.233923	−	0.501648i
$983$	−23.1147	−	33.0111i	−0.737243	−	1.05289i	−0.996208	−	0.0870053i	$-0.972270\pi$
$983$	−23.1147	−	33.0111i	−0.737243	−	1.05289i	0.258965	−	0.965887i	$-0.416619\pi$
$984$	−0.0210588	−	0.119430i	−0.000671328	−	0.00380729i
$985$		0			0
$986$	4.83147	+	4.05409i	0.153866	+	0.129108i
$987$	0.613670	+	0.613670i	0.0195333	+	0.0195333i
$988$	−1.28998	−	6.26246i	−0.0410397	−	0.199236i
$989$		−	17.0340i		−	0.541648i
$990$		0			0
$991$	7.99654	+	21.9703i	0.254019	+	0.697910i	0.999507	+	0.0313919i	$0.00999400\pi$
$991$	7.99654	+	21.9703i	0.254019	+	0.697910i	−0.745489	+	0.666518i	$0.767784\pi$
$992$	3.03828	+	2.12743i	0.0964655	+	0.0675458i
$993$	0.176645	−	0.123688i	0.00560565	−	0.00392512i
$994$	−6.92416	+	19.0240i	−0.219621	+	0.603404i
$995$		0			0
$996$	−0.173967	−	0.100440i	−0.00551237	−	0.00318257i
$997$	−1.72131	+	19.6747i	−0.0545146	+	0.623105i	0.918966	+	0.394336i	$0.129025\pi$
$997$	−1.72131	+	19.6747i	−0.0545146	+	0.623105i	−0.973481	+	0.228768i	$0.926530\pi$
$998$	−2.09356	+	23.9295i	−0.0662705	+	0.757476i
$999$	1.98394	+	1.14543i	0.0627689	+	0.0362397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.d.193.7	yes	96
5.2	odd	4	inner	950.2.bb.d.307.2	yes	96
5.3	odd	4	inner	950.2.bb.d.307.7	yes	96
5.4	even	2	inner	950.2.bb.d.193.2	✓	96
19.13	odd	18	inner	950.2.bb.d.393.2	yes	96
95.13	even	36	inner	950.2.bb.d.507.2	yes	96
95.32	even	36	inner	950.2.bb.d.507.7	yes	96
95.89	odd	18	inner	950.2.bb.d.393.7	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.bb.d.193.2	✓	96	5.4	even	2	inner
950.2.bb.d.193.7	yes	96	1.1	even	1	trivial
950.2.bb.d.307.2	yes	96	5.2	odd	4	inner
950.2.bb.d.307.7	yes	96	5.3	odd	4	inner
950.2.bb.d.393.2	yes	96	19.13	odd	18	inner
950.2.bb.d.393.7	yes	96	95.89	odd	18	inner
950.2.bb.d.507.2	yes	96	95.13	even	36	inner
950.2.bb.d.507.7	yes	96	95.32	even	36	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0871557 + 0.996195i) q^{2} +(0.0142429 - 0.0305440i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(0.0316692 + 0.0115266i) q^{6} +(2.42021 + 0.648494i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(1.92763 + 2.29726i) q^{9} +O(q^{10})\)	\(q+(0.0871557 + 0.996195i) q^{2} +(0.0142429 - 0.0305440i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(0.0316692 + 0.0115266i) q^{6} +(2.42021 + 0.648494i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(1.92763 + 2.29726i) q^{9} +(1.13265 - 1.96182i) q^{11} +(-0.00872262 + 0.0325533i) q^{12} +(-1.32944 + 0.619927i) q^{13} +(-0.435091 + 2.46752i) q^{14} +(0.939693 - 0.342020i) q^{16} +(1.99433 - 0.174481i) q^{17} +(-2.12052 + 2.12052i) q^{18} +(1.72838 - 4.00159i) q^{19} +(0.0542785 - 0.0646866i) q^{21} +(2.05307 + 0.957361i) q^{22} +(-2.55260 + 3.64549i) q^{23} +(-0.0331896 - 0.00585222i) q^{24} +(-0.733436 - 1.27035i) q^{26} +(0.195283 - 0.0523258i) q^{27} +(-2.49605 - 0.218376i) q^{28} +(2.41338 - 2.02507i) q^{29} +(3.21213 - 1.85453i) q^{31} +(0.422618 + 0.906308i) q^{32} +(-0.0437894 - 0.0625378i) q^{33} +(0.347635 + 1.97154i) q^{34} +(-2.29726 - 1.92763i) q^{36} +(8.01239 + 8.01239i) q^{37} +(4.13700 + 1.37304i) q^{38} +0.0494359i q^{39} +(1.23073 + 3.38141i) q^{41} +(0.0691711 + 0.0484341i) q^{42} +(-3.13537 + 2.19541i) q^{43} +(-0.774781 + 2.12869i) q^{44} +(-3.85409 - 2.22516i) q^{46} +(-0.895748 + 10.2384i) q^{47} +(0.00293729 - 0.0335734i) q^{48} +(-0.625296 - 0.361015i) q^{49} +(0.0230757 - 0.0634001i) q^{51} +(1.20159 - 0.841363i) q^{52} +(0.451332 + 0.316026i) q^{53} +(0.0691467 + 0.189979i) q^{54} -2.50559i q^{56} +(-0.0976074 - 0.109786i) q^{57} +(2.22770 + 2.22770i) q^{58} +(-3.05382 - 2.56246i) q^{59} +(0.911575 + 5.16980i) q^{61} +(2.12743 + 3.03828i) q^{62} +(3.17552 + 6.80992i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(0.0584833 - 0.0490733i) q^{66} +(-1.37428 - 0.120234i) q^{67} +(-1.93374 + 0.518143i) q^{68} +(0.0749915 + 0.129889i) q^{69} +(7.95714 + 1.40306i) q^{71} +(1.72008 - 2.45653i) q^{72} +(-3.37102 - 1.57193i) q^{73} +(-7.28358 + 8.68023i) q^{74} +(-1.00726 + 4.24092i) q^{76} +(4.01349 - 4.01349i) q^{77} +(-0.0492478 + 0.00430862i) q^{78} +(11.5411 - 4.20061i) q^{79} +(-1.56106 + 8.85320i) q^{81} +(-3.26128 + 1.52076i) q^{82} +(-1.54270 + 5.75745i) q^{83} +(-0.0422212 + 0.0731292i) q^{84} +(-2.46032 - 2.93210i) q^{86} +(-0.0274802 - 0.102557i) q^{87} +(-2.18812 - 0.586305i) q^{88} +(-8.99243 - 3.27298i) q^{89} +(-3.61954 + 0.638222i) q^{91} +(1.88079 - 4.03336i) q^{92} +(-0.0108946 - 0.124525i) q^{93} -10.2776 q^{94} +0.0337016 q^{96} +(0.712763 + 8.14692i) q^{97} +(0.305143 - 0.654382i) q^{98} +(6.69015 - 1.17965i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{6}+O(q^{10}) \) 96 * q - 12 * q^6	\( 96 q - 12 q^{6} + 12 q^{26} - 72 q^{31} + 12 q^{36} - 24 q^{41} + 12 q^{51} - 72 q^{61} - 36 q^{66} + 168 q^{71} - 12 q^{76} + 12 q^{81} - 48 q^{86} - 72 q^{91}+O(q^{100}) \) 96 * q - 12 * q^6 + 12 * q^26 - 72 * q^31 + 12 * q^36 - 24 * q^41 + 12 * q^51 - 72 * q^61 - 36 * q^66 + 168 * q^71 - 12 * q^76 + 12 * q^81 - 48 * q^86 - 72 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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