LMFDB - Embedded newform 950.2.bb.d.193.1

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			193.1
Character	$\chi$	$=$	950.193
Dual form			950.2.bb.d.507.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0871557 - 0.996195i) q^{2} +(-1.07287 + 2.30077i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(2.38552 + 0.868257i) q^{6} +(3.67829 + 0.985594i) q^{7} +(0.258819 + 0.965926i) q^{8} +(-2.21412 - 2.63869i) q^{9} +O(q^{10})$	\(q+(-0.0871557 - 0.996195i) q^{2} +(-1.07287 + 2.30077i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(2.38552 + 0.868257i) q^{6} +(3.67829 + 0.985594i) q^{7} +(0.258819 + 0.965926i) q^{8} +(-2.21412 - 2.63869i) q^{9} +(1.53833 - 2.66446i) q^{11} +(0.657042 - 2.45211i) q^{12} +(1.02095 - 0.476076i) q^{13} +(0.661259 - 3.75019i) q^{14} +(0.939693 - 0.342020i) q^{16} +(4.95805 - 0.433773i) q^{17} +(-2.43568 + 2.43568i) q^{18} +(-4.19007 + 1.20139i) q^{19} +(-6.21392 + 7.40547i) q^{21} +(-2.78840 - 1.30025i) q^{22} +(4.72305 - 6.74521i) q^{23} +(-2.50005 - 0.440826i) q^{24} +(-0.563246 - 0.975571i) q^{26} +(1.09013 - 0.292098i) q^{27} +(-3.79355 - 0.331893i) q^{28} +(0.0437215 - 0.0366867i) q^{29} +(2.29763 - 1.32654i) q^{31} +(-0.422618 - 0.906308i) q^{32} +(4.47989 + 6.39794i) q^{33} +(-0.864245 - 4.90137i) q^{34} +(2.63869 + 2.21412i) q^{36} +(5.15977 + 5.15977i) q^{37} +(1.56201 + 4.06941i) q^{38} +2.85973i q^{39} +(1.26518 + 3.47605i) q^{41} +(7.91887 + 5.54485i) q^{42} +(-6.82487 + 4.77882i) q^{43} +(-1.05228 + 2.89111i) q^{44} +(-7.13119 - 4.11719i) q^{46} +(-0.349595 + 3.99588i) q^{47} +(-0.221255 + 2.52895i) q^{48} +(6.49621 + 3.75059i) q^{49} +(-4.32130 + 11.8727i) q^{51} +(-0.922769 + 0.646130i) q^{52} +(8.73114 + 6.11361i) q^{53} +(-0.385997 - 1.06052i) q^{54} +3.80804i q^{56} +(1.73125 - 10.9293i) q^{57} +(-0.0403577 - 0.0403577i) q^{58} +(6.83880 + 5.73843i) q^{59} +(-2.32335 - 13.1763i) q^{61} +(-1.52174 - 2.17327i) q^{62} +(-5.54350 - 11.8881i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(5.98315 - 5.02046i) q^{66} +(2.31577 + 0.202604i) q^{67} +(-4.80740 + 1.28814i) q^{68} +(10.4520 + 18.1033i) q^{69} +(-2.94420 - 0.519143i) q^{71} +(1.97572 - 2.82162i) q^{72} +(9.70143 + 4.52385i) q^{73} +(4.69043 - 5.58984i) q^{74} +(3.91779 - 1.91074i) q^{76} +(8.28449 - 8.28449i) q^{77} +(2.84885 - 0.249242i) q^{78} +(-9.59702 + 3.49303i) q^{79} +(1.29692 - 7.35520i) q^{81} +(3.35256 - 1.56332i) q^{82} +(-1.63918 + 6.11750i) q^{83} +(4.83357 - 8.37200i) q^{84} +(5.35547 + 6.38240i) q^{86} +(0.0375003 + 0.139953i) q^{87} +(2.97182 + 0.796297i) q^{88} +(9.61510 + 3.49961i) q^{89} +(4.22456 - 0.744904i) q^{91} +(-3.48000 + 7.46289i) q^{92} +(0.587006 + 6.70951i) q^{93} +4.01115 q^{94} +2.53861 q^{96} +(-0.299410 - 3.42227i) q^{97} +(3.17013 - 6.79837i) q^{98} +(-10.4367 + 1.84028i) 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
$3$	−1.07287	+	2.30077i	−0.619419	+	1.32835i	0.306948	+	0.951726i	$0.400692\pi$
$3$	−1.07287	+	2.30077i	−0.619419	+	1.32835i	−0.926367	+	0.376622i	$0.877086\pi$
$4$	−0.984808	+	0.173648i	−0.492404	+	0.0868241i
$5$		0			0
$5$		0			0
$6$	2.38552	+	0.868257i	0.973884	+	0.354465i
$7$	3.67829	+	0.985594i	1.39026	+	0.372519i	0.874838	−	0.484416i	$-0.160968\pi$
$7$	3.67829	+	0.985594i	1.39026	+	0.372519i	0.515423	+	0.856936i	$0.327635\pi$
$8$	0.258819	+	0.965926i	0.0915064	+	0.341506i
$9$	−2.21412	−	2.63869i	−0.738041	−	0.879563i
$10$		0			0
$11$	1.53833	−	2.66446i	0.463823	−	0.803366i	−0.535324	−	0.844647i	$-0.679811\pi$
$11$	1.53833	−	2.66446i	0.463823	−	0.803366i	0.999148	+	0.0412811i	$0.0131439\pi$
$12$	0.657042	−	2.45211i	0.189672	−	0.707864i
$13$	1.02095	−	0.476076i	0.283160	−	0.132040i	−0.275850	−	0.961201i	$-0.588959\pi$
$13$	1.02095	−	0.476076i	0.283160	−	0.132040i	0.559010	+	0.829161i	$0.311181\pi$
$14$	0.661259	−	3.75019i	0.176729	−	1.00228i
$15$		0			0
$16$	0.939693	−	0.342020i	0.234923	−	0.0855050i
$17$	4.95805	−	0.433773i	1.20250	−	0.105205i	0.531760	−	0.846895i	$-0.321531\pi$
$17$	4.95805	−	0.433773i	1.20250	−	0.105205i	0.670743	+	0.741690i	$0.265975\pi$
$18$	−2.43568	+	2.43568i	−0.574094	+	0.574094i
$19$	−4.19007	+	1.20139i	−0.961267	+	0.275618i
$19$	−4.19007	+	1.20139i	−0.961267	+	0.275618i
$20$		0			0
$21$	−6.21392	+	7.40547i	−1.35599	+	1.61601i
$22$	−2.78840	−	1.30025i	−0.594488	−	0.277214i
$23$	4.72305	−	6.74521i	0.984824	−	1.40647i	0.0723312	−	0.997381i	$-0.476956\pi$
$23$	4.72305	−	6.74521i	0.984824	−	1.40647i	0.912493	−	0.409093i	$-0.134155\pi$
$24$	−2.50005	−	0.440826i	−0.510320	−	0.0899832i
$25$		0			0
$26$	−0.563246	−	0.975571i	−0.110462	−	0.191325i
$27$	1.09013	−	0.292098i	0.209795	−	0.0562143i
$28$	−3.79355	−	0.331893i	−0.716914	−	0.0627218i
$29$	0.0437215	−	0.0366867i	0.00811888	−	0.00681255i	−0.638719	−	0.769440i	$-0.720535\pi$
$29$	0.0437215	−	0.0366867i	0.00811888	−	0.00681255i	0.646838	+	0.762627i	$0.276091\pi$
$30$		0			0
$31$	2.29763	−	1.32654i	0.412667	−	0.238253i	−0.279268	−	0.960213i	$-0.590092\pi$
$31$	2.29763	−	1.32654i	0.412667	−	0.238253i	0.691935	+	0.721960i	$0.256759\pi$
$32$	−0.422618	−	0.906308i	−0.0747091	−	0.160214i
$33$	4.47989	+	6.39794i	0.779848	+	1.11374i
$34$	−0.864245	−	4.90137i	−0.148217	−	0.840579i
$35$		0			0
$36$	2.63869	+	2.21412i	0.439782	+	0.369021i
$37$	5.15977	+	5.15977i	0.848261	+	0.848261i	0.989916	−	0.141655i	$-0.0452423\pi$
$37$	5.15977	+	5.15977i	0.848261	+	0.848261i	−0.141655	+	0.989916i	$0.545242\pi$
$38$	1.56201	+	4.06941i	0.253391	+	0.660146i
$39$			2.85973i			0.457924i
$40$		0			0
$41$	1.26518	+	3.47605i	0.197588	+	0.542868i	0.998430	−	0.0560070i	$-0.0178369\pi$
$41$	1.26518	+	3.47605i	0.197588	+	0.542868i	−0.800843	+	0.598875i	$0.795615\pi$
$42$	7.91887	+	5.54485i	1.22191	+	0.855589i
$43$	−6.82487	+	4.77882i	−1.04078	+	0.728764i	−0.963354	−	0.268234i	$-0.913560\pi$
$43$	−6.82487	+	4.77882i	−1.04078	+	0.728764i	−0.0774289	+	0.996998i	$0.524671\pi$
$44$	−1.05228	+	2.89111i	−0.158637	+	0.435851i
$45$		0			0
$46$	−7.13119	−	4.11719i	−1.05144	−	0.607047i
$47$	−0.349595	+	3.99588i	−0.0509936	+	0.582860i	0.927117	+	0.374773i	$0.122279\pi$
$47$	−0.349595	+	3.99588i	−0.0509936	+	0.582860i	−0.978110	+	0.208087i	$0.933276\pi$
$48$	−0.221255	+	2.52895i	−0.0319354	+	0.365023i
$49$	6.49621	+	3.75059i	0.928030	+	0.535798i
$50$		0			0
$51$	−4.32130	+	11.8727i	−0.605104	+	1.66251i
$52$	−0.922769	+	0.646130i	−0.127965	+	0.0896021i
$53$	8.73114	+	6.11361i	1.19931	+	0.839769i	0.990409	−	0.138167i	$-0.0441211\pi$
$53$	8.73114	+	6.11361i	1.19931	+	0.839769i	0.208905	+	0.977936i	$0.433010\pi$
$54$	−0.385997	−	1.06052i	−0.0525276	−	0.144318i
$55$		0			0
$56$			3.80804i			0.508871i
$57$	1.73125	−	10.9293i	0.229310	−	1.44762i
$58$	−0.0403577	−	0.0403577i	−0.00529923	−	0.00529923i
$59$	6.83880	+	5.73843i	0.890336	+	0.747080i	0.968277	−	0.249878i	$-0.0803904\pi$
$59$	6.83880	+	5.73843i	0.890336	+	0.747080i	−0.0779418	+	0.996958i	$0.524835\pi$
$60$		0			0
$61$	−2.32335	−	13.1763i	−0.297474	−	1.68706i	−0.656974	−	0.753913i	$-0.728164\pi$
$61$	−2.32335	−	13.1763i	−0.297474	−	1.68706i	0.359500	−	0.933145i	$-0.382947\pi$
$62$	−1.52174	−	2.17327i	−0.193261	−	0.276006i
$63$	−5.54350	−	11.8881i	−0.698416	−	1.49776i
$64$	−0.866025	+	0.500000i	−0.108253	+	0.0625000i
$65$		0			0
$66$	5.98315	−	5.02046i	0.736475	−	0.617976i
$67$	2.31577	+	0.202604i	0.282917	+	0.0247520i	0.227731	−	0.973724i	$-0.426869\pi$
$67$	2.31577	+	0.202604i	0.282917	+	0.0247520i	0.0551857	+	0.998476i	$0.482425\pi$
$68$	−4.80740	+	1.28814i	−0.582983	+	0.156210i
$69$	10.4520	+	18.1033i	1.25827	+	2.17939i
$70$		0			0
$71$	−2.94420	−	0.519143i	−0.349413	−	0.0616109i	−0.00381249	−	0.999993i	$-0.501214\pi$
$71$	−2.94420	−	0.519143i	−0.349413	−	0.0616109i	−0.345600	+	0.938382i	$0.612325\pi$
$72$	1.97572	−	2.82162i	0.232841	−	0.332531i
$73$	9.70143	+	4.52385i	1.13547	+	0.529477i	0.897157	−	0.441713i	$-0.145629\pi$
$73$	9.70143	+	4.52385i	1.13547	+	0.529477i	0.238310	+	0.971189i	$0.423407\pi$
$74$	4.69043	−	5.58984i	0.545252	−	0.649806i
$75$		0			0
$76$	3.91779	−	1.91074i	0.449401	−	0.219177i
$77$	8.28449	−	8.28449i	0.944105	−	0.944105i
$78$	2.84885	−	0.249242i	0.322569	−	0.0282211i
$79$	−9.59702	+	3.49303i	−1.07975	+	0.392997i	−0.819814	−	0.572629i	$-0.805923\pi$
$79$	−9.59702	+	3.49303i	−1.07975	+	0.392997i	−0.259935	+	0.965626i	$0.583701\pi$
$80$		0			0
$81$	1.29692	−	7.35520i	0.144102	−	0.817244i
$82$	3.35256	−	1.56332i	0.370228	−	0.172640i
$83$	−1.63918	+	6.11750i	−0.179923	+	0.671483i	0.815737	+	0.578423i	$0.196332\pi$
$83$	−1.63918	+	6.11750i	−0.179923	+	0.671483i	−0.995660	+	0.0930601i	$0.970335\pi$
$84$	4.83357	−	8.37200i	0.527386	−	0.913460i
$85$		0			0
$86$	5.35547	+	6.38240i	0.577495	+	0.688231i
$87$	0.0375003	+	0.139953i	0.00402045	+	0.0150045i
$88$	2.97182	+	0.796297i	0.316797	+	0.0848856i
$89$	9.61510	+	3.49961i	1.01920	+	0.370958i	0.796959	−	0.604034i	$-0.206441\pi$
$89$	9.61510	+	3.49961i	1.01920	+	0.370958i	0.222240	+	0.974992i	$0.428663\pi$
$90$		0			0
$91$	4.22456	−	0.744904i	0.442854	−	0.0780872i
$92$	−3.48000	+	7.46289i	−0.362815	+	0.778060i
$93$	0.587006	+	6.70951i	0.0608697	+	0.695744i
$94$	4.01115			0.413718
$95$		0			0
$96$	2.53861			0.259096
$97$	−0.299410	−	3.42227i	−0.0304005	−	0.347479i	−0.996128	−	0.0879195i	$-0.971978\pi$
$97$	−0.299410	−	3.42227i	−0.0304005	−	0.347479i	0.965727	−	0.259560i	$-0.0835774\pi$
$98$	3.17013	−	6.79837i	0.320232	−	0.686739i
$99$	−10.4367	+	1.84028i	−1.04893	+	0.184955i
$100$		0			0
$101$	−17.1040	−	6.22535i	−1.70191	−	0.619445i	−0.705871	−	0.708341i	$-0.749444\pi$
$101$	−17.1040	−	6.22535i	−1.70191	−	0.619445i	−0.996041	+	0.0888957i	$0.971666\pi$
$102$	12.2041	+	3.27009i	1.20839	+	0.323787i
$103$	−2.02796	−	7.56846i	−0.199821	−	0.745743i	−0.990966	−	0.134114i	$-0.957181\pi$
$103$	−2.02796	−	7.56846i	−0.199821	−	0.745743i	0.791145	−	0.611629i	$-0.209485\pi$
$104$	0.724096	+	0.862944i	0.0710034	+	0.0846186i
$105$		0			0
$106$	5.32938	−	9.23075i	0.517635	−	0.896570i
$107$	−3.85139	+	14.3736i	−0.372328	+	1.38955i	0.484882	+	0.874580i	$0.338863\pi$
$107$	−3.85139	+	14.3736i	−0.372328	+	1.38955i	−0.857210	+	0.514967i	$0.827804\pi$
$108$	−1.02284	+	0.476959i	−0.0984230	+	0.0458954i
$109$	−0.567012	+	3.21569i	−0.0543099	+	0.308007i	−0.999847	−	0.0175083i	$-0.994427\pi$
$109$	−0.567012	+	3.21569i	−0.0543099	+	0.308007i	0.945537	+	0.325515i	$0.105538\pi$
$110$		0			0
$111$	−17.4072	+	6.33569i	−1.65222	+	0.601357i
$112$	3.79355	−	0.331893i	0.358457	−	0.0313609i
$113$	−5.75233	+	5.75233i	−0.541134	+	0.541134i	−0.923861	−	0.382727i	$-0.874985\pi$
$113$	−5.75233	+	5.75233i	−0.541134	+	0.541134i	0.382727	+	0.923861i	$0.374985\pi$
$114$	−11.0386	−	0.772115i	−1.03386	−	0.0723152i
$115$		0			0
$116$	−0.0366867	+	0.0437215i	−0.00340628	+	0.00405944i
$117$	−3.51673	−	1.63988i	−0.325121	−	0.151607i
$118$	5.12056	−	7.31291i	0.471385	−	0.673208i
$119$	18.6646	+	3.29108i	1.71098	+	0.301693i
$120$		0			0
$121$	0.767094	+	1.32865i	0.0697358	+	0.120786i
$122$	−12.9237	+	3.46290i	−1.17006	+	0.313516i
$123$	−9.35495	−	0.818452i	−0.843507	−	0.0737973i
$124$	−2.03237	+	1.70536i	−0.182513	+	0.153146i
$125$		0			0
$126$	−11.3597	+	6.55852i	−1.01200	+	0.584280i
$127$	−6.58054	−	14.1120i	−0.583929	−	1.25224i	−0.947226	−	0.320566i	$-0.896127\pi$
$127$	−6.58054	−	14.1120i	−0.583929	−	1.25224i	0.363297	−	0.931673i	$-0.381651\pi$
$128$	0.573576	+	0.819152i	0.0506975	+	0.0724035i
$129$	−3.67280	−	20.8295i	−0.323372	−	1.83393i
$130$		0			0
$131$	11.1836	+	9.38417i	0.977118	+	0.819899i	0.983652	−	0.180080i	$-0.0576355\pi$
$131$	11.1836	+	9.38417i	0.977118	+	0.819899i	−0.00653440	+	0.999979i	$0.502080\pi$
$132$	−5.52282	−	5.52282i	−0.480700	−	0.480700i
$133$	−16.5963	+	0.289358i	−1.43909	+	0.0250906i
$134$		−	2.32462i		−	0.200816i
$135$		0			0
$136$	1.70223	+	4.67684i	0.145965	+	0.401035i
$137$	−6.93202	−	4.85385i	−0.592242	−	0.414692i	0.238666	−	0.971102i	$-0.423290\pi$
$137$	−6.93202	−	4.85385i	−0.592242	−	0.414692i	−0.830908	+	0.556409i	$0.812179\pi$
$138$	17.1235	−	11.9900i	1.45765	−	1.02066i
$139$	4.81008	−	13.2156i	0.407986	−	1.12093i	−0.550262	−	0.834992i	$-0.685472\pi$
$139$	4.81008	−	13.2156i	0.407986	−	1.12093i	0.958248	−	0.285940i	$-0.0923057\pi$
$140$		0			0
$141$	−8.81853	−	5.09138i	−0.742654	−	0.428772i
$142$	−0.260563	+	2.97825i	−0.0218659	+	0.249929i
$143$	0.302067	−	3.45264i	0.0252601	−	0.288724i
$144$	−2.98308	−	1.72228i	−0.248590	−	0.143524i
$145$		0			0
$146$	3.66110	−	10.0588i	0.302995	−	0.832471i
$147$	−15.5988	+	10.9224i	−1.28657	+	0.900863i
$148$	−5.97737	−	4.18540i	−0.491337	−	0.344038i
$149$	−6.02283	−	16.5476i	−0.493410	−	1.35563i	−0.897541	−	0.440931i	$-0.854648\pi$
$149$	−6.02283	−	16.5476i	−0.493410	−	1.35563i	0.404131	−	0.914701i	$-0.367574\pi$
$150$		0			0
$151$		−	10.6852i		−	0.869547i	−0.900540	−	0.434773i	$-0.856828\pi$
$151$		−	10.6852i		−	0.869547i	0.900540	−	0.434773i	$-0.143172\pi$
$152$	−2.24492	−	3.73635i	−0.182087	−	0.303058i
$153$	−12.1223	−	12.1223i	−0.980032	−	0.980032i
$154$	−8.97500	−	7.53092i	−0.723226	−	0.606859i
$155$		0			0
$156$	−0.496587	−	2.81629i	−0.0397588	−	0.225483i
$157$	5.22015	+	7.45514i	0.416613	+	0.594985i	0.971529	−	0.236921i	$-0.0761384\pi$
$157$	5.22015	+	7.45514i	0.416613	+	0.594985i	−0.554916	+	0.831907i	$0.687250\pi$
$158$	4.31617	+	9.25607i	0.343376	+	0.736373i
$159$	−23.4333	+	13.5292i	−1.85838	+	1.07294i
$160$		0			0
$161$	24.0208	−	20.1558i	1.89310	−	1.58850i
$162$	−7.44024	−	0.650937i	−0.584561	−	0.0511424i
$163$	−21.5602	+	5.77704i	−1.68872	+	0.452492i	−0.970060	−	0.242865i	$-0.921913\pi$
$163$	−21.5602	+	5.77704i	−1.68872	+	0.452492i	−0.718664	+	0.695357i	$0.755246\pi$
$164$	−1.84957	−	3.20355i	−0.144427	−	0.250155i
$165$		0			0
$166$	6.23708	+	1.09977i	0.484092	+	0.0853584i
$167$	−7.23681	+	10.3352i	−0.560001	+	0.799765i	−0.994916	−	0.100707i	$-0.967890\pi$
$167$	−7.23681	+	10.3352i	−0.560001	+	0.799765i	0.434915	+	0.900472i	$0.356779\pi$
$168$	−8.76141	−	4.08551i	−0.675958	−	0.315204i
$169$	−7.54055	+	8.98648i	−0.580042	+	0.691268i
$170$		0			0
$171$	12.4474	+	8.39626i	0.951879	+	0.642078i
$172$	5.89135	−	5.89135i	0.449211	−	0.449211i
$173$	2.37258	−	0.207574i	0.180384	−	0.0157815i	0.00339410	−	0.999994i	$-0.498920\pi$
$173$	2.37258	−	0.207574i	0.180384	−	0.0157815i	0.176990	+	0.984213i	$0.443364\pi$
$174$	0.136152	−	0.0495553i	0.0103217	−	0.00375678i
$175$		0			0
$176$	0.534256	−	3.02991i	0.0402710	−	0.228388i
$177$	−20.5399	+	9.57791i	−1.54387	+	0.719920i
$178$	2.64828	−	9.88353i	0.198497	−	0.740802i
$179$	10.5874	−	18.3378i	0.791336	−	1.37063i	−0.133804	−	0.991008i	$-0.542719\pi$
$179$	10.5874	−	18.3378i	0.791336	−	1.37063i	0.925140	−	0.379627i	$-0.123948\pi$
$180$		0			0
$181$	0.144240	+	0.171898i	0.0107213	+	0.0127771i	0.771378	−	0.636377i	$-0.219568\pi$
$181$	0.144240	+	0.171898i	0.0107213	+	0.0127771i	−0.760657	+	0.649154i	$0.775123\pi$
$182$	−1.11026	−	4.14356i	−0.0822982	−	0.307141i
$183$	32.8083	+	8.79096i	2.42526	+	0.649847i
$184$	7.73779	+	2.81633i	0.570437	+	0.207622i
$185$		0			0
$186$	6.63282	−	1.16954i	0.486342	−	0.0857552i
$187$	6.47133	−	13.8778i	0.473231	−	1.01485i
$188$	−0.349595	−	3.99588i	−0.0254968	−	0.291430i
$189$	4.29768			0.312610
$190$		0			0
$191$	15.1253			1.09443			0.547213	−	0.836994i	$-0.315689\pi$
$191$	15.1253			1.09443			0.547213	+	0.836994i	$0.315689\pi$
$192$	−0.221255	−	2.52895i	−0.0159677	−	0.182512i
$193$	4.85228	−	10.4057i	0.349274	−	0.749022i	−0.650672	−	0.759359i	$-0.725513\pi$
$193$	4.85228	−	10.4057i	0.349274	−	0.749022i	0.999947	+	0.0103373i	$0.00329052\pi$
$194$	−3.38315	+	0.596541i	−0.242896	+	0.0428292i
$195$		0			0
$196$	−7.04880	−	2.56555i	−0.503486	−	0.183254i
$197$	−3.10467	−	0.831893i	−0.221198	−	0.0592699i	0.146518	−	0.989208i	$-0.453193\pi$
$197$	−3.10467	−	0.831893i	−0.221198	−	0.0592699i	−0.367716	+	0.929938i	$0.619860\pi$
$198$	2.74290	+	10.2366i	0.194929	+	0.727486i
$199$	7.99574	+	9.52895i	0.566803	+	0.675490i	0.970972	−	0.239195i	$-0.0768835\pi$
$199$	7.99574	+	9.52895i	0.566803	+	0.675490i	−0.404168	+	0.914685i	$0.632439\pi$
$200$		0			0
$201$	−2.95065	+	5.11068i	−0.208123	+	0.360480i
$202$	−4.71095	+	17.5815i	−0.331461	+	1.23703i
$203$	0.196978	−	0.0918526i	0.0138252	−	0.00644679i
$204$	2.19398	−	12.4427i	0.153610	−	0.871163i
$205$		0			0
$206$	−7.36291	+	2.67988i	−0.512998	+	0.186716i
$207$	−28.2559	+	2.47207i	−1.96392	+	0.171821i
$208$	0.796551	−	0.796551i	0.0552309	−	0.0552309i
$209$	−3.24463	+	13.0124i	−0.224436	+	0.900087i
$210$		0			0
$211$	−17.5168	+	20.8757i	−1.20590	+	1.43714i	−0.337468	+	0.941337i	$0.609571\pi$
$211$	−17.5168	+	20.8757i	−1.20590	+	1.43714i	−0.868435	+	0.495803i	$0.834874\pi$
$212$	−9.66011	−	4.50458i	−0.663459	−	0.309376i
$213$	4.35316	−	6.21696i	0.298274	−	0.425979i
$214$	14.6546	+	2.58399i	1.00177	+	0.176638i
$215$		0			0
$216$	0.564290	+	0.977380i	0.0383951	+	0.0665023i
$217$	9.75877	−	2.61485i	0.662468	−	0.177508i
$218$	3.25287	+	0.284589i	0.220312	+	0.0192748i
$219$	−20.8166	+	17.4672i	−1.40666	+	1.18033i
$220$		0			0
$221$	4.85541	−	2.80327i	0.326610	−	0.188568i
$222$	7.82872	+	16.7887i	0.525429	+	1.12679i
$223$	−11.5059	−	16.4321i	−0.770490	−	1.10037i	−0.992126	−	0.125244i	$-0.960029\pi$
$223$	−11.5059	−	16.4321i	−0.770490	−	1.10037i	0.221636	−	0.975129i	$-0.428860\pi$
$224$	−0.661259	−	3.75019i	−0.0441822	−	0.250570i
$225$		0			0
$226$	6.23179	+	5.22910i	0.414533	+	0.347834i
$227$	−1.75515	−	1.75515i	−0.116493	−	0.116493i	0.646457	−	0.762950i	$-0.276250\pi$
$227$	−1.75515	−	1.75515i	−0.116493	−	0.116493i	−0.762950	+	0.646457i	$0.776250\pi$
$228$	0.192900	+	11.0639i	0.0127751	+	0.732724i
$229$		−	16.1219i		−	1.06537i	−0.846315	−	0.532683i	$-0.821184\pi$
$229$		−	16.1219i		−	1.06537i	0.846315	−	0.532683i	$-0.178816\pi$
$230$		0			0
$231$	10.1725	+	27.9488i	0.669303	+	1.83890i
$232$	0.0467526	+	0.0327365i	0.00306946	+	0.00214926i
$233$	16.5224	−	11.5691i	1.08242	−	0.757917i	0.110651	−	0.993859i	$-0.464706\pi$
$233$	16.5224	−	11.5691i	1.08242	−	0.757917i	0.971767	+	0.235942i	$0.0758175\pi$
$234$	−1.32713	+	3.64627i	−0.0867574	+	0.238364i
$235$		0			0
$236$	−7.73137	−	4.46371i	−0.503269	−	0.290563i
$237$	2.25966	−	25.8281i	0.146781	−	1.67771i
$238$	1.65182	−	18.8804i	0.107072	−	1.22384i
$239$	−9.01693	−	5.20593i	−0.583257	−	0.336743i	0.179170	−	0.983818i	$-0.442659\pi$
$239$	−9.01693	−	5.20593i	−0.583257	−	0.336743i	−0.762427	+	0.647075i	$0.775992\pi$
$240$		0			0
$241$	2.08529	−	5.72929i	0.134325	−	0.369056i	−0.854234	−	0.519889i	$-0.825973\pi$
$241$	2.08529	−	5.72929i	0.134325	−	0.369056i	0.988559	+	0.150833i	$0.0481956\pi$
$242$	1.25673	−	0.879974i	0.0807859	−	0.0565669i
$243$	18.3046	+	12.8170i	1.17424	+	0.822213i
$244$	4.57610	+	12.5727i	0.292955	+	0.804886i
$245$		0			0
$246$			9.39068i			0.598728i
$247$	−3.70589	+	3.22135i	−0.235800	+	0.204970i
$248$	1.87601	+	1.87601i	0.119127	+	0.119127i
$249$	−12.3163	−	10.3346i	−0.780515	−	0.654930i
$250$		0			0
$251$	−4.63523	−	26.2877i	−0.292573	−	1.65926i	−0.676907	−	0.736069i	$-0.736680\pi$
$251$	−4.63523	−	26.2877i	−0.292573	−	1.65926i	0.384334	−	0.923194i	$-0.374431\pi$
$252$	7.52363	+	10.7449i	0.473944	+	0.676862i
$253$	−10.7068	−	22.9607i	−0.673129	−	1.44353i
$254$	−13.4848	+	7.78545i	−0.846111	+	0.488502i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	23.0946	+	2.02051i	1.44060	+	0.126036i	0.780506	−	0.625148i	$-0.214961\pi$
$257$	23.0946	+	2.02051i	1.44060	+	0.126036i	0.660093	+	0.751184i	$0.270517\pi$
$258$	−20.4301	+	5.47423i	−1.27192	+	0.340810i
$259$	13.8937	+	24.0645i	0.863311	+	1.49530i
$260$		0			0
$261$	−0.193610	−	0.0341386i	−0.0119841	−	0.00211313i
$262$	8.37375	−	11.9590i	0.517332	−	0.738826i
$263$	0.0373827	+	0.0174318i	0.00230512	+	0.00107489i	0.423770	−	0.905770i	$-0.360706\pi$
$263$	0.0373827	+	0.0174318i	0.00230512	+	0.00107489i	−0.421465	+	0.906845i	$0.638484\pi$
$264$	−5.02046	+	5.98315i	−0.308988	+	0.368237i
$265$		0			0
$266$	1.73472	+	16.5080i	0.106363	+	1.01217i
$267$	−18.3675	+	18.3675i	−1.12407	+	1.12407i
$268$	−2.31577	+	0.202604i	−0.141458	+	0.0123760i
$269$	12.8238	−	4.66749i	0.781883	−	0.284582i	0.0799253	−	0.996801i	$-0.474532\pi$
$269$	12.8238	−	4.66749i	0.781883	−	0.284582i	0.701958	+	0.712219i	$0.252310\pi$
$270$		0			0
$271$	−4.60153	+	26.0966i	−0.279523	+	1.58525i	0.444694	+	0.895683i	$0.353313\pi$
$271$	−4.60153	+	26.0966i	−0.279523	+	1.58525i	−0.724217	+	0.689572i	$0.757799\pi$
$272$	4.51068	−	2.10337i	0.273500	−	0.127535i
$273$	−2.81853	+	10.5189i	−0.170585	+	0.636633i
$274$	−4.23121	+	7.32868i	−0.255617	+	0.442742i
$275$		0			0
$276$	−13.4368	−	16.0133i	−0.808800	−	0.963890i
$277$	0.539718	+	2.01426i	0.0324285	+	0.121025i	0.980243	−	0.197798i	$-0.0633791\pi$
$277$	0.539718	+	2.01426i	0.0324285	+	0.121025i	−0.947814	+	0.318823i	$0.896712\pi$
$278$	−13.5845	−	3.63996i	−0.814746	−	0.218310i
$279$	−8.58756	−	3.12562i	−0.514124	−	0.187126i
$280$		0			0
$281$	−9.77971	+	1.72443i	−0.583409	+	0.102871i	−0.457560	−	0.889179i	$-0.651277\pi$
$281$	−9.77971	+	1.72443i	−0.583409	+	0.102871i	−0.125849	+	0.992049i	$0.540165\pi$
$282$	−4.30342	+	9.22871i	−0.256265	+	0.549562i
$283$	1.33303	+	15.2366i	0.0792404	+	0.905722i	0.926931	+	0.375231i	$0.122437\pi$
$283$	1.33303	+	15.2366i	0.0792404	+	0.905722i	−0.847691	+	0.530491i	$0.822008\pi$
$284$	2.98962			0.177401
$285$		0			0
$286$	−3.46583			−0.204939
$287$	1.22772	+	14.0329i	0.0724698	+	0.828333i
$288$	−1.45574	+	3.12184i	−0.0857801	+	0.183956i
$289$	7.65234	−	1.34931i	0.450137	−	0.0793714i
$290$		0			0
$291$	8.19508	+	2.98276i	0.480404	+	0.174853i
$292$	−10.3396	−	2.77049i	−0.605079	−	0.162130i
$293$	1.96177	+	7.32144i	0.114608	+	0.427723i	0.999257	−	0.0385341i	$-0.0122688\pi$
$293$	1.96177	+	7.32144i	0.114608	+	0.427723i	−0.884649	+	0.466257i	$0.845602\pi$
$294$	12.2403	+	14.5875i	0.713871	+	0.850759i
$295$		0			0
$296$	−3.64851	+	6.31940i	−0.212065	+	0.367308i
$297$	0.898686	−	3.35394i	0.0521470	−	0.194615i
$298$	−15.9597	+	7.44213i	−0.924521	+	0.431111i
$299$	1.61076	−	9.13505i	0.0931524	−	0.528294i
$300$		0			0
$301$	−29.8138	+	10.8513i	−1.71844	+	0.625460i
$302$	−10.6445	+	0.931274i	−0.612523	+	0.0535888i
$303$	32.6734	−	32.6734i	1.87703	−	1.87703i
$304$	−3.52647	+	2.56203i	−0.202257	+	0.146942i
$305$		0			0
$306$	−11.0197	+	13.1327i	−0.629952	+	0.750748i
$307$	7.46761	+	3.48221i	0.426199	+	0.198740i	0.623869	−	0.781529i	$-0.285560\pi$
$307$	7.46761	+	3.48221i	0.426199	+	0.198740i	−0.197670	+	0.980269i	$0.563337\pi$
$308$	−6.72004	+	9.59721i	−0.382910	+	0.546852i
$309$	19.5890	+	3.45407i	1.11438	+	0.196495i
$310$		0			0
$311$	10.7053	+	18.5421i	0.607040	+	1.05142i	0.991725	+	0.128377i	$0.0409767\pi$
$311$	10.7053	+	18.5421i	0.607040	+	1.05142i	−0.384685	+	0.923048i	$0.625690\pi$
$312$	−2.76229	+	0.740153i	−0.156384	+	0.0419029i
$313$	−12.5945	−	1.10187i	−0.711881	−	0.0622815i	−0.274538	−	0.961576i	$-0.588525\pi$
$313$	−12.5945	−	1.10187i	−0.711881	−	0.0622815i	−0.437343	+	0.899295i	$0.644080\pi$
$314$	6.97181	−	5.85004i	0.393442	−	0.330137i
$315$		0			0
$316$	8.84467	−	5.10647i	0.497551	−	0.287261i
$317$	−10.8923	−	23.3586i	−0.611773	−	1.31195i	−0.931258	−	0.364360i	$-0.881288\pi$
$317$	−10.8923	−	23.3586i	−0.611773	−	1.31195i	0.319486	−	0.947591i	$-0.396490\pi$
$318$	15.5201	+	22.1650i	0.870324	+	1.24295i
$319$	−0.0304923	−	0.172931i	−0.00170724	−	0.00968225i
$320$		0			0
$321$	−28.9382	−	24.2821i	−1.61518	−	1.35529i
$322$	−22.1727	−	22.1727i	−1.23563	−	1.23563i
$323$	−20.2534	+	7.77409i	−1.12693	+	0.432562i
$324$			7.46866i			0.414926i
$325$		0			0
$326$	7.63415	+	20.9746i	0.422816	+	1.16168i
$327$	−6.79022	−	4.75456i	−0.375500	−	0.262928i
$328$	−3.03015	+	2.12174i	−0.167312	+	0.117153i
$329$	−5.22423	+	14.3534i	−0.288021	+	0.791331i
$330$		0			0
$331$	−22.7112	−	13.1123i	−1.24832	−	0.720717i	−0.277545	−	0.960713i	$-0.589521\pi$
$331$	−22.7112	−	13.1123i	−1.24832	−	0.720717i	−0.970774	+	0.239996i	$0.922854\pi$
$332$	0.551984	−	6.30920i	0.0302940	−	0.346262i
$333$	2.19066	−	25.0394i	0.120048	−	1.37215i
$334$	10.9266	+	6.30850i	0.597879	+	0.345186i
$335$		0			0
$336$	−3.30636	+	9.08415i	−0.180377	+	0.495581i
$337$	−10.3006	+	7.21257i	−0.561110	+	0.392894i	−0.819442	−	0.573163i	$-0.805716\pi$
$337$	−10.3006	+	7.21257i	−0.561110	+	0.392894i	0.258331	+	0.966056i	$0.416827\pi$
$338$	9.60948	+	6.72863i	0.522687	+	0.365989i
$339$	−7.06330	−	19.4063i	−0.383626	−	1.05400i
$340$		0			0
$341$		−	8.16260i		−	0.442030i
$342$	7.27944	−	13.1318i	0.393627	−	0.710089i
$343$	1.34951	+	1.34951i	0.0728668	+	0.0728668i
$344$	−6.38240	−	5.35547i	−0.344116	−	0.288747i
$345$		0			0
$346$	−0.413568	−	2.34546i	−0.0222335	−	0.126093i
$347$	3.06520	+	4.37756i	0.164548	+	0.235000i	0.892955	−	0.450145i	$-0.148628\pi$
$347$	3.06520	+	4.37756i	0.164548	+	0.235000i	−0.728407	+	0.685145i	$0.759739\pi$
$348$	−0.0612331	−	0.131315i	−0.00328244	−	0.00703922i
$349$	15.6767	−	9.05092i	0.839152	−	0.484485i	−0.0178239	−	0.999841i	$-0.505674\pi$
$349$	15.6767	−	9.05092i	0.839152	−	0.484485i	0.856976	+	0.515357i	$0.172340\pi$
$350$		0			0
$351$	0.973901	−	0.817200i	0.0519830	−	0.0436189i
$352$	−3.06495	−	0.268148i	−0.163362	−	0.0142923i
$353$	25.1387	−	6.73589i	1.33800	−	0.358515i	0.482306	−	0.876003i	$-0.339799\pi$
$353$	25.1387	−	6.73589i	1.33800	−	0.358515i	0.855691	+	0.517488i	$0.173133\pi$
$354$	11.3316	+	19.6270i	0.602270	+	1.04316i
$355$		0			0
$356$	−10.0767	−	1.77680i	−0.534066	−	0.0941702i
$357$	−27.5966	+	39.4121i	−1.46057	+	2.08591i
$358$	−19.1908	−	8.94882i	−1.01427	−	0.472960i
$359$	−4.51445	+	5.38011i	−0.238264	+	0.283951i	−0.871905	−	0.489676i	$-0.837115\pi$
$359$	−4.51445	+	5.38011i	−0.238264	+	0.283951i	0.633641	+	0.773627i	$0.281560\pi$
$360$		0			0
$361$	16.1133	−	10.0678i	0.848069	−	0.529885i
$362$	0.158673	−	0.158673i	0.00833966	−	0.00833966i
$363$	−3.87989	+	0.339447i	−0.203642	+	0.0178163i
$364$	−4.03103	+	1.46717i	−0.211283	+	0.0769008i
$365$		0			0
$366$	5.89808	−	33.4497i	0.308297	−	1.74844i
$367$	31.1863	−	14.5424i	1.62791	−	0.759107i	0.628092	−	0.778139i	$-0.283836\pi$
$367$	31.1863	−	14.5424i	1.62791	−	0.759107i	0.999819	+	0.0190316i	$0.00605831\pi$
$368$	2.13122	−	7.95380i	0.111097	−	0.414621i
$369$	6.37096	−	11.0348i	0.331659	−	0.574450i
$370$		0			0
$371$	26.0901	+	31.0930i	1.35453	+	1.61427i
$372$	−1.74318	−	6.50564i	−0.0903798	−	0.337302i
$373$	−13.0250	−	3.49005i	−0.674411	−	0.180708i	−0.0946700	−	0.995509i	$-0.530180\pi$
$373$	−13.0250	−	3.49005i	−0.674411	−	0.180708i	−0.579741	+	0.814801i	$0.696846\pi$
$374$	−14.3890	−	5.23717i	−0.744038	−	0.270808i
$375$		0			0
$376$	−3.95021	+	0.696528i	−0.203716	+	0.0359207i
$377$	0.0271718	−	0.0582701i	0.00139942	−	0.00300106i
$378$	−0.374568	−	4.28133i	−0.0192657	−	0.220208i
$379$	−32.5876			−1.67391			−0.836955	−	0.547271i	$-0.815667\pi$
$379$	−32.5876			−1.67391			−0.836955	+	0.547271i	$0.815667\pi$
$380$		0			0
$381$	39.5285			2.02511
$382$	−1.31825	−	15.0677i	−0.0674477	−	0.770931i
$383$	−11.0305	+	23.6550i	−0.563634	+	1.20872i	0.393568	+	0.919295i	$0.371240\pi$
$383$	−11.0305	+	23.6550i	−0.563634	+	1.20872i	−0.957202	+	0.289421i	$0.906537\pi$
$384$	−2.50005	+	0.440826i	−0.127580	+	0.0224958i
$385$		0			0
$386$	−10.7890	−	3.92689i	−0.549148	−	0.199874i
$387$	27.7209	+	7.42780i	1.40913	+	0.377576i
$388$	0.889133	+	3.31829i	0.0451389	+	0.168461i
$389$	7.04248	+	8.39290i	0.357068	+	0.425537i	0.914437	−	0.404728i	$-0.132634\pi$
$389$	7.04248	+	8.39290i	0.357068	+	0.425537i	−0.557369	+	0.830265i	$0.688189\pi$
$390$		0			0
$391$	20.4912	−	35.4918i	1.03628	−	1.79490i
$392$	−1.94145	+	7.24558i	−0.0980579	+	0.365957i
$393$	−33.5893	+	15.6630i	−1.69436	+	0.790091i
$394$	−0.558138	+	3.16536i	−0.0281186	+	0.159468i
$395$		0			0
$396$	9.95862	−	3.62464i	0.500440	−	0.182145i
$397$	26.0360	−	2.27785i	1.30671	−	0.114322i	0.587562	−	0.809179i	$-0.300088\pi$
$397$	26.0360	−	2.27785i	1.30671	−	0.114322i	0.719148	+	0.694857i	$0.244532\pi$
$398$	8.79582	−	8.79582i	0.440895	−	0.440895i
$399$	17.1399	−	38.4948i	0.858068	−	1.92715i
$400$		0			0
$401$	−1.74028	+	2.07399i	−0.0869056	+	0.103570i	−0.807745	−	0.589532i	$-0.799312\pi$
$401$	−1.74028	+	2.07399i	−0.0869056	+	0.103570i	0.720839	+	0.693102i	$0.243757\pi$
$402$	5.34840	+	2.49400i	0.266754	+	0.124389i
$403$	1.71423	−	2.44818i	0.0853919	−	0.121952i
$404$	17.9252	+	3.16069i	0.891811	+	0.157250i
$405$		0			0
$406$	−0.108671	−	0.188223i	−0.00539324	−	0.00934137i
$407$	21.6854	−	5.81060i	1.07491	−	0.288021i
$408$	−12.5866	−	1.10118i	−0.623128	−	0.0545166i
$409$	2.26586	−	1.90128i	0.112039	−	0.0940122i	−0.585047	−	0.810999i	$-0.698924\pi$
$409$	2.26586	−	1.90128i	0.112039	−	0.0940122i	0.697086	+	0.716987i	$0.254479\pi$
$410$		0			0
$411$	18.6047	−	10.7414i	0.917702	−	0.529835i
$412$	3.31140	+	7.10133i	0.163141	+	0.349857i
$413$	19.4993	+	27.8479i	0.959497	+	1.37030i
$414$	4.92534	+	27.9330i	0.242067	+	1.37283i
$415$		0			0
$416$	−0.862944	−	0.724096i	−0.0423093	−	0.0355017i
$417$	25.2454	+	25.2454i	1.23627	+	1.23627i
$418$	13.2457	+	2.09818i	0.647867	+	0.102625i
$419$			15.6042i			0.762314i	0.924510	+	0.381157i	$0.124474\pi$
$419$			15.6042i			0.762314i	−0.924510	+	0.381157i	$0.875526\pi$
$420$		0			0
$421$	8.08571	+	22.2153i	0.394073	+	1.08271i	0.965124	+	0.261793i	$0.0843138\pi$
$421$	8.08571	+	22.2153i	0.394073	+	1.08271i	−0.571051	+	0.820915i	$0.693464\pi$
$422$	22.3229	+	15.6307i	1.08666	+	0.760889i
$423$	11.3179	−	7.92491i	0.550297	−	0.385322i
$424$	−3.64551	+	10.0160i	−0.177042	+	0.486418i
$425$		0			0
$426$	−6.57270	−	3.79475i	−0.318448	−	0.183856i
$427$	4.44059	−	50.7562i	0.214895	−	2.45627i
$428$	1.29693	−	14.8240i	0.0626896	−	0.716545i
$429$	7.61965	+	4.39921i	0.367880	+	0.212396i
$430$		0			0
$431$	4.31659	−	11.8597i	0.207923	−	0.571263i	−0.791269	−	0.611469i	$-0.790579\pi$
$431$	4.31659	−	11.8597i	0.207923	−	0.571263i	0.999191	+	0.0402056i	$0.0128013\pi$
$432$	0.924479	−	0.647327i	0.0444790	−	0.0311445i
$433$	−1.52894	−	1.07057i	−0.0734760	−	0.0514485i	0.536261	−	0.844052i	$-0.319836\pi$
$433$	−1.52894	−	1.07057i	−0.0734760	−	0.0514485i	−0.609737	+	0.792604i	$0.708725\pi$
$434$	−3.45544	−	9.49374i	−0.165866	−	0.455714i
$435$		0			0
$436$		−	3.26529i		−	0.156379i
$437$	−11.6862	+	33.9371i	−0.559029	+	1.62343i
$438$	19.2151	+	19.2151i	0.918131	+	0.918131i
$439$	−24.8804	−	20.8771i	−1.18748	−	0.996411i	−0.999900	−	0.0141610i	$-0.995492\pi$
$439$	−24.8804	−	20.8771i	−1.18748	−	0.996411i	−0.187577	−	0.982250i	$-0.560063\pi$
$440$		0			0
$441$	−4.48677	−	25.4457i	−0.213656	−	1.21170i
$442$	−3.21578	−	4.59261i	−0.152959	−	0.218448i
$443$	−5.63973	−	12.0945i	−0.267952	−	0.574625i	0.725585	−	0.688132i	$-0.241569\pi$
$443$	−5.63973	−	12.0945i	−0.267952	−	0.574625i	−0.993537	+	0.113508i	$0.963791\pi$
$444$	16.0425	−	9.26216i	0.761345	−	0.439563i
$445$		0			0
$446$	−15.3667	+	12.8942i	−0.727636	+	0.610559i
$447$	44.5338	+	3.89621i	2.10638	+	0.184284i
$448$	−3.67829	+	0.985594i	−0.173783	+	0.0465649i
$449$	−7.83146	−	13.5645i	−0.369590	−	0.640148i	0.619912	−	0.784671i	$-0.287168\pi$
$449$	−7.83146	−	13.5645i	−0.369590	−	0.640148i	−0.989501	+	0.144524i	$0.953835\pi$
$450$		0			0
$451$	11.2081	+	1.97628i	0.527767	+	0.0930596i
$452$	4.66606	−	6.66383i	0.219473	−	0.313440i
$453$	24.5841	+	11.4637i	1.15506	+	0.538614i
$454$	−1.59550	+	1.90144i	−0.0748805	+	0.0892391i
$455$		0			0
$456$	11.0050	−	1.15645i	0.515355	−	0.0541556i
$457$	−7.42897	+	7.42897i	−0.347513	+	0.347513i	−0.859182	−	0.511670i	$-0.829027\pi$
$457$	−7.42897	+	7.42897i	−0.347513	+	0.347513i	0.511670	+	0.859182i	$0.329027\pi$
$458$	−16.0606	+	1.40512i	−0.750461	+	0.0656568i
$459$	5.27819	−	1.92110i	0.246365	−	0.0896694i
$460$		0			0
$461$	5.49699	−	31.1750i	0.256020	−	1.45196i	−0.537419	−	0.843315i	$-0.680601\pi$
$461$	5.49699	−	31.1750i	0.256020	−	1.45196i	0.793440	−	0.608649i	$-0.208288\pi$
$462$	26.9559	−	12.5697i	1.25410	−	0.584796i
$463$	9.65175	−	36.0208i	0.448555	−	1.67403i	−0.257821	−	0.966193i	$-0.583004\pi$
$463$	9.65175	−	36.0208i	0.448555	−	1.67403i	0.706376	−	0.707837i	$-0.250329\pi$
$464$	0.0285372	−	0.0494279i	0.00132481	−	0.00229463i
$465$		0			0
$466$	−12.9651	−	15.4512i	−0.600597	−	0.715763i
$467$	1.03224	+	3.85238i	0.0477664	+	0.178267i	0.985688	−	0.168581i	$-0.0539186\pi$
$467$	1.03224	+	3.85238i	0.0477664	+	0.178267i	−0.937921	+	0.346848i	$0.887252\pi$
$468$	3.74806	+	1.00429i	0.173254	+	0.0464233i
$469$	8.31838	+	3.02764i	0.384107	+	0.139804i
$470$		0			0
$471$	−22.7531	+	4.01198i	−1.04841	+	0.184862i
$472$	−3.77289	+	8.09099i	−0.173661	+	0.372418i
$473$	2.23411	+	25.5360i	0.102725	+	1.17415i
$474$	−25.9267			−1.19085
$475$		0			0
$476$	−18.9526			−0.868689
$477$	−3.19990	−	36.5751i	−0.146514	−	1.67466i
$478$	−4.40024	+	9.43634i	−0.201262	+	0.431608i
$479$	−11.6376	+	2.05202i	−0.531735	+	0.0937593i	−0.433068	−	0.901361i	$-0.642569\pi$
$479$	−11.6376	+	2.05202i	−0.531735	+	0.0937593i	−0.0986673	+	0.995120i	$0.531458\pi$
$480$		0			0
$481$	7.72431	+	2.81142i	0.352198	+	0.128190i
$482$	−5.88923	−	1.57801i	−0.268247	−	0.0718766i
$483$	20.6028	+	76.8906i	0.937459	+	3.49864i
$484$	−0.986157	−	1.17526i	−0.0448253	−	0.0534207i
$485$		0			0
$486$	11.1729	−	19.3520i	0.506813	−	0.877826i
$487$	2.93019	−	10.9356i	0.132780	−	0.495541i	−0.867217	−	0.497930i	$-0.834094\pi$
$487$	2.93019	−	10.9356i	0.132780	−	0.495541i	0.999997	+	0.00238899i	$0.000760439\pi$
$488$	12.1260	−	5.65447i	0.548920	−	0.255966i
$489$	9.83957	−	55.8029i	0.444961	−	2.52350i
$490$		0			0
$491$	11.6627	−	4.24486i	0.526328	−	0.191568i	−0.0651699	−	0.997874i	$-0.520759\pi$
$491$	11.6627	−	4.24486i	0.526328	−	0.191568i	0.591498	+	0.806306i	$0.298537\pi$
$492$	9.35495	−	0.818452i	0.421754	−	0.0368987i
$493$	0.200860	−	0.200860i	0.00904626	−	0.00904626i
$494$	3.53208	+	3.41103i	0.158916	+	0.153469i
$495$		0			0
$496$	1.70536	−	2.03237i	0.0765731	−	0.0912563i
$497$	−10.3180	−	4.81134i	−0.462824	−	0.215818i
$498$	−9.22186	+	13.1702i	−0.413241	+	0.590170i
$499$	−18.4265	−	3.24910i	−0.824885	−	0.145450i	−0.254757	−	0.967005i	$-0.581995\pi$
$499$	−18.4265	−	3.24910i	−0.824885	−	0.145450i	−0.570128	+	0.821556i	$0.693107\pi$
$500$		0			0
$501$	−16.0149	−	27.7385i	−0.715491	−	1.23927i
$502$	−25.7837	+	6.90871i	−1.15078	+	0.308351i
$503$	−23.9313	−	2.09372i	−1.06704	−	0.0933543i	−0.459919	−	0.887961i	$-0.652122\pi$
$503$	−23.9313	−	2.09372i	−1.06704	−	0.0933543i	−0.607125	+	0.794606i	$0.707677\pi$
$504$	10.0482	−	8.43147i	0.447584	−	0.375568i
$505$		0			0
$506$	−21.9402	+	12.6672i	−0.975361	+	0.563125i
$507$	−12.5858	−	26.9903i	−0.558955	−	1.19868i
$508$	8.93110	+	12.7549i	0.396253	+	0.565908i
$509$	−0.782200	−	4.43607i	−0.0346704	−	0.196626i	0.962553	−	0.271094i	$-0.0873853\pi$
$509$	−0.782200	−	4.43607i	−0.0346704	−	0.196626i	−0.997223	+	0.0744679i	$0.976274\pi$
$510$		0			0
$511$	31.2259	+	26.2017i	1.38135	+	1.15909i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−4.21677	+	2.53358i	−0.186175	+	0.111860i
$514$		−	23.1828i		−	1.02255i
$515$		0			0
$516$	7.23400	+	19.8752i	0.318459	+	0.874959i
$517$	10.1091	+	7.07846i	0.444597	+	0.311310i
$518$	22.7621	−	15.9382i	1.00011	−	0.700283i
$519$	−2.06788	+	5.68145i	−0.0907698	+	0.249388i
$520$		0			0
$521$	−23.7841	−	13.7318i	−1.04200	−	0.601600i	−0.121602	−	0.992579i	$-0.538803\pi$
$521$	−23.7841	−	13.7318i	−1.04200	−	0.601600i	−0.920400	+	0.390979i	$0.872137\pi$
$522$	−0.0171345	+	0.195848i	−0.000749957	+	0.00857205i
$523$	−1.06026	+	12.1189i	−0.0463621	+	0.529921i	0.937131	+	0.348977i	$0.113471\pi$
$523$	−1.06026	+	12.1189i	−0.0463621	+	0.529921i	−0.983493	+	0.180944i	$0.942085\pi$
$524$	−12.6433	−	7.29959i	−0.552324	−	0.318884i
$525$		0			0
$526$	0.0141074	−	0.0387597i	0.000615112	−	0.00169001i
$527$	10.8163	−	7.57369i	0.471167	−	0.329915i
$528$	6.39794	+	4.47989i	0.278435	+	0.194962i
$529$	−15.3242	−	42.1030i	−0.666271	−	1.83057i
$530$		0			0
$531$		−	30.7511i		−	1.33448i
$532$	16.2940	−	3.16689i	0.706433	−	0.137302i
$533$	2.94655	+	2.94655i	0.127629	+	0.127629i
$534$	19.8984	+	16.6968i	0.861089	+	0.722540i
$535$		0			0
$536$	0.403666	+	2.28930i	0.0174357	+	0.0988828i
$537$	30.8323	+	44.0331i	1.33051	+	1.90017i
$538$	−5.76740	−	12.3682i	−0.248650	−	0.533233i
$539$	19.9866	−	11.5393i	0.860884	−	0.497031i
$540$		0			0
$541$	−21.4279	+	17.9802i	−0.921259	+	0.773028i	−0.974227	−	0.225568i	$-0.927576\pi$
$541$	−21.4279	+	17.9802i	−0.921259	+	0.773028i	0.0529684	+	0.998596i	$0.483132\pi$
$542$	26.3983	+	2.30955i	1.13391	+	0.0992039i
$543$	−0.550248	+	0.147438i	−0.0236134	+	0.00632719i
$544$	−2.48849	−	4.31020i	−0.106693	−	0.184798i
$545$		0			0
$546$	10.7245	+	1.89102i	0.458968	+	0.0809284i
$547$	13.2417	−	18.9111i	0.566173	−	0.808579i	−0.429346	−	0.903140i	$-0.641256\pi$
$547$	13.2417	−	18.9111i	0.566173	−	0.808579i	0.995519	+	0.0945609i	$0.0301447\pi$
$548$	7.66956	+	3.57638i	0.327628	+	0.152775i
$549$	−29.6241	+	35.3046i	−1.26433	+	1.50677i
$550$		0			0
$551$	−0.139121	+	0.206246i	−0.00592675	+	0.00878639i
$552$	−14.7813	+	14.7813i	−0.629134	+	0.629134i
$553$	−38.7433	+	3.38960i	−1.64753	+	0.144140i
$554$	1.95955	−	0.713219i	0.0832534	−	0.0303018i
$555$		0			0
$556$	−2.44214	+	13.8501i	−0.103570	+	0.587374i
$557$	−14.9149	+	6.95491i	−0.631963	+	0.294689i	−0.712082	−	0.702096i	$-0.752248\pi$
$557$	−14.9149	+	6.95491i	−0.631963	+	0.294689i	0.0801192	+	0.996785i	$0.474470\pi$
$558$	−2.36527	+	8.82730i	−0.100130	+	0.373689i
$559$	−4.69276	+	8.12810i	−0.198483	+	0.343782i
$560$		0			0
$561$	24.9867	+	29.7780i	1.05494	+	1.25723i
$562$	2.57022	+	9.59221i	0.108418	+	0.404623i
$563$	−11.5200	−	3.08679i	−0.485512	−	0.130093i	0.00775608	−	0.999970i	$-0.497531\pi$
$563$	−11.5200	−	3.08679i	−0.485512	−	0.130093i	−0.493268	+	0.869877i	$0.664198\pi$
$564$	9.56866	+	3.48271i	0.402913	+	0.146648i
$565$		0			0
$566$	15.0624	−	2.65591i	0.633122	−	0.111636i
$567$	12.0197	−	25.7763i	0.504779	−	1.08250i
$568$	−0.260563	−	2.97825i	−0.0109330	−	0.124964i
$569$	−3.24545			−0.136056			−0.0680282	−	0.997683i	$-0.521671\pi$
$569$	−3.24545			−0.136056			−0.0680282	+	0.997683i	$0.521671\pi$
$570$		0			0
$571$	−36.4316			−1.52461			−0.762307	−	0.647215i	$-0.775934\pi$
$571$	−36.4316			−1.52461			−0.762307	+	0.647215i	$0.775934\pi$
$572$	0.302067	+	3.45264i	0.0126301	+	0.144362i
$573$	−16.2274	+	34.7997i	−0.677908	+	1.45378i
$574$	13.8725	−	2.44609i	0.579025	−	0.102098i
$575$		0			0
$576$	3.23683	+	1.17811i	0.134868	+	0.0490880i
$577$	−40.5711	−	10.8710i	−1.68900	−	0.452565i	−0.718866	−	0.695149i	$-0.755339\pi$
$577$	−40.5711	−	10.8710i	−1.68900	−	0.452565i	−0.970131	+	0.242583i	$0.922005\pi$
$578$	−2.01112	−	7.50562i	−0.0836517	−	0.312193i
$579$	18.7353	+	22.3279i	0.778614	+	0.927916i
$580$		0			0
$581$	−12.0587	+	20.8863i	−0.500281	+	0.866512i
$582$	2.25717	−	8.42386i	0.0935625	−	0.349180i
$583$	29.7208	−	13.8591i	1.23091	−	0.573983i
$584$	−1.85879	+	10.5417i	−0.0769172	+	0.436219i
$585$		0			0
$586$	7.12260	−	2.59241i	0.294232	−	0.107092i
$587$	5.40236	−	0.472645i	0.222979	−	0.0195082i	0.0248814	−	0.999690i	$-0.492079\pi$
$587$	5.40236	−	0.472645i	0.222979	−	0.0195082i	0.198098	+	0.980182i	$0.436524\pi$
$588$	13.4651	−	13.4651i	0.555293	−	0.555293i
$589$	−8.03354	+	8.31864i	−0.331016	+	0.342763i
$590$		0			0
$591$	5.24488	−	6.25061i	0.215746	−	0.257116i
$592$	6.61335	+	3.08385i	0.271807	+	0.126746i
$593$	−0.0817611	+	0.116767i	−0.00335753	+	0.00479504i	−0.820827	−	0.571176i	$-0.806487\pi$
$593$	−0.0817611	+	0.116767i	−0.00335753	+	0.00479504i	0.817470	+	0.575972i	$0.195376\pi$
$594$	−3.41950	−	0.602951i	−0.140304	−	0.0247394i
$595$		0			0
$596$	8.80479	+	15.2503i	0.360658	+	0.624679i
$597$	−30.5022	+	8.17305i	−1.24837	+	0.334501i
$598$	−9.24068	−	0.808454i	−0.377879	−	0.0330602i
$599$	−4.28307	+	3.59392i	−0.175001	+	0.146844i	−0.726081	−	0.687609i	$-0.758660\pi$
$599$	−4.28307	+	3.59392i	−0.175001	+	0.146844i	0.551080	+	0.834453i	$0.314216\pi$
$600$		0			0
$601$	9.62613	−	5.55765i	0.392658	−	0.226701i	−0.290653	−	0.956829i	$-0.593873\pi$
$601$	9.62613	−	5.55765i	0.392658	−	0.226701i	0.683311	+	0.730127i	$0.260539\pi$
$602$	13.4085	+	28.7546i	0.546489	+	1.17195i
$603$	−4.59280	−	6.55919i	−0.187033	−	0.267111i
$604$	1.85546	+	10.5228i	0.0754976	+	0.428168i
$605$		0			0
$606$	−35.3967	−	29.7013i	−1.43789	−	1.20653i
$607$	19.7401	+	19.7401i	0.801225	+	0.801225i	0.983287	−	0.182062i	$-0.0582771\pi$
$607$	19.7401	+	19.7401i	0.801225	+	0.801225i	−0.182062	+	0.983287i	$0.558277\pi$
$608$	2.85963	+	3.28976i	0.115973	+	0.133417i
$609$			0.551747i			0.0223579i
$610$		0			0
$611$	1.54543	+	4.24603i	0.0625213	+	0.171776i
$612$	14.0432	+	9.83314i	0.567662	+	0.397481i
$613$	35.3822	−	24.7749i	1.42907	−	1.00065i	0.434063	−	0.900883i	$-0.357080\pi$
$613$	35.3822	−	24.7749i	1.42907	−	1.00065i	0.995011	−	0.0997658i	$-0.0318094\pi$
$614$	2.81811	−	7.74269i	0.113730	−	0.312470i
$615$		0			0
$616$	10.1464	+	5.85802i	0.408809	+	0.236026i
$617$	0.979167	−	11.1919i	0.0394198	−	0.450570i	−0.950677	−	0.310183i	$-0.899610\pi$
$617$	0.979167	−	11.1919i	0.0394198	−	0.450570i	0.990097	−	0.140387i	$-0.0448347\pi$
$618$	1.73363	−	19.8155i	0.0697369	−	0.797096i
$619$	−20.7309	−	11.9690i	−0.833245	−	0.481074i	0.0217175	−	0.999764i	$-0.493087\pi$
$619$	−20.7309	−	11.9690i	−0.833245	−	0.481074i	−0.854962	+	0.518690i	$0.826420\pi$
$620$		0			0
$621$	3.17845	−	8.73272i	0.127547	−	0.350432i
$622$	17.5385	−	12.2806i	0.703230	−	0.492407i
$623$	31.9179	+	22.3492i	1.27876	+	0.895400i
$624$	0.978086	+	2.68727i	0.0391548	+	0.107577i
$625$		0			0
$626$			12.6426i			0.505298i
$627$	−26.4575	−	21.4257i	−1.05661	−	0.855660i
$628$	−6.43541	−	6.43541i	−0.256801	−	0.256801i
$629$	27.8206	+	23.3442i	1.10928	+	0.930795i
$630$		0			0
$631$	5.76360	+	32.6870i	0.229445	+	1.30125i	0.854002	+	0.520270i	$0.174169\pi$
$631$	5.76360	+	32.6870i	0.229445	+	1.30125i	−0.624557	+	0.780979i	$0.714720\pi$
$632$	−5.85790	−	8.36595i	−0.233015	−	0.332780i
$633$	−29.2369	−	62.6987i	−1.16206	−	2.49205i
$634$	−22.3204	+	12.8867i	−0.886457	+	0.511796i
$635$		0			0
$636$	20.7280	−	17.3928i	0.821918	−	0.689671i
$637$	8.41787	+	0.736468i	0.333528	+	0.0291799i
$638$	−0.169615	+	0.0454482i	−0.00671512	+	0.00179931i
$639$	5.14898	+	8.91829i	0.203690	+	0.352802i
$640$		0			0
$641$	21.5474	+	3.79939i	0.851071	+	0.150067i	0.582136	−	0.813091i	$-0.302217\pi$
$641$	21.5474	+	3.79939i	0.851071	+	0.150067i	0.268935	+	0.963158i	$0.413328\pi$
$642$	−21.6675	+	30.9444i	−0.855149	+	1.22128i
$643$	−24.2804	−	11.3221i	−0.957524	−	0.446501i	−0.119923	−	0.992783i	$-0.538265\pi$
$643$	−24.2804	−	11.3221i	−0.957524	−	0.446501i	−0.837601	+	0.546282i	$0.816043\pi$
$644$	−20.1558	+	24.0208i	−0.794250	+	0.946550i
$645$		0			0
$646$	9.50971	+	19.4988i	0.374155	+	0.767170i
$647$	−11.3164	+	11.3164i	−0.444894	+	0.444894i	−0.893653	−	0.448759i	$-0.851866\pi$
$647$	−11.3164	+	11.3164i	−0.444894	+	0.444894i	0.448759	+	0.893653i	$0.351866\pi$
$648$	7.44024	−	0.650937i	0.292280	−	0.0255712i
$649$	25.8101	−	9.39413i	1.01314	−	0.368752i
$650$		0			0
$651$	−4.45367	+	25.2580i	−0.174553	+	0.989940i
$652$	20.2295	−	9.43316i	0.792247	−	0.369431i
$653$	−3.76530	+	14.0523i	−0.147347	+	0.549908i	0.852292	+	0.523066i	$0.175212\pi$
$653$	−3.76530	+	14.0523i	−0.147347	+	0.549908i	−0.999640	+	0.0268423i	$0.991455\pi$
$654$	−4.14466	+	7.17877i	−0.162069	+	0.280712i
$655$		0			0
$656$	2.37776	+	2.83370i	0.0928359	+	0.110637i
$657$	−9.54312	−	35.6154i	−0.372313	−	1.38949i
$658$	14.7541	+	3.95336i	0.575176	+	0.154118i
$659$	−6.78690	−	2.47023i	−0.264380	−	0.0962264i	0.206429	−	0.978462i	$-0.433816\pi$
$659$	−6.78690	−	2.47023i	−0.264380	−	0.0962264i	−0.470809	+	0.882235i	$0.656038\pi$
$660$		0			0
$661$	−17.5261	+	3.09032i	−0.681686	+	0.120200i	−0.503759	−	0.863844i	$-0.668050\pi$
$661$	−17.5261	+	3.09032i	−0.681686	+	0.120200i	−0.177927	+	0.984044i	$0.556939\pi$
$662$	−11.0830	+	23.7676i	−0.430753	+	0.923752i
$663$	1.24047	+	14.1787i	0.0481760	+	0.550654i
$664$	−6.33330			−0.245780
$665$		0			0
$666$	−25.1351			−0.973964
$667$	−0.0409608	−	0.468184i	−0.00158601	−	0.0181282i
$668$	5.33217	−	11.4349i	0.206308	−	0.442429i
$669$	50.1506	−	8.84290i	1.93893	−	0.341886i
$670$		0			0
$671$	−38.6819	−	14.0791i	−1.49330	−	0.543517i
$672$	9.33775	+	2.50204i	0.360211	+	0.0965184i
$673$	6.39572	+	23.8692i	0.246537	+	0.920089i	0.972605	+	0.232465i	$0.0746792\pi$
$673$	6.39572	+	23.8692i	0.246537	+	0.920089i	−0.726068	+	0.687623i	$0.758654\pi$
$674$	8.08288	+	9.63281i	0.311341	+	0.371042i
$675$		0			0
$676$	5.86551	−	10.1594i	0.225596	−	0.390744i
$677$	−5.31278	+	19.8276i	−0.204187	+	0.762035i	0.785509	+	0.618850i	$0.212401\pi$
$677$	−5.31278	+	19.8276i	−0.204187	+	0.762035i	−0.989696	+	0.143185i	$0.954266\pi$
$678$	−18.7168	+	8.72779i	−0.718814	+	0.335189i
$679$	2.27165	−	12.8832i	0.0871781	−	0.494411i
$680$		0			0
$681$	5.92123	−	2.15515i	0.226902	−	0.0825856i
$682$	−8.13154	+	0.711418i	−0.311373	+	0.0272416i
$683$	−25.6579	+	25.6579i	−0.981772	+	0.981772i	−0.999837	−	0.0180646i	$-0.994250\pi$
$683$	−25.6579	+	25.6579i	−0.981772	+	0.981772i	0.0180646	+	0.999837i	$0.494250\pi$
$684$	−13.7163	−	6.10723i	−0.524457	−	0.233516i
$685$		0			0
$686$	1.22676	−	1.46199i	0.0468379	−	0.0558192i
$687$	37.0928	+	17.2966i	1.41518	+	0.659908i
$688$	−4.77882	+	6.82487i	−0.182191	+	0.260196i
$689$	11.8246	+	2.08500i	0.450481	+	0.0794320i
$690$		0			0
$691$	9.39675	+	16.2756i	0.357469	+	0.619155i	0.987537	−	0.157385i	$-0.0503064\pi$
$691$	9.39675	+	16.2756i	0.357469	+	0.619155i	−0.630068	+	0.776540i	$0.716973\pi$
$692$	−2.30049	+	0.616414i	−0.0874515	+	0.0234326i
$693$	−40.2031	−	3.51731i	−1.52719	−	0.133612i
$694$	4.09375	−	3.43506i	0.155397	−	0.130393i
$695$		0			0
$696$	−0.125478	+	0.0724450i	−0.00475624	+	0.00274602i
$697$	7.78063	+	16.6856i	0.294712	+	0.632013i
$698$	−10.3828	−	14.8282i	−0.392994	−	0.561254i
$699$	8.89151	+	50.4263i	0.336308	+	1.90730i
$700$		0			0
$701$	−2.65628	−	2.22888i	−0.100326	−	0.0841837i	0.591245	−	0.806492i	$-0.298637\pi$
$701$	−2.65628	−	2.22888i	−0.100326	−	0.0841837i	−0.691571	+	0.722308i	$0.743081\pi$
$702$	−0.898972	−	0.898972i	−0.0339295	−	0.0339295i
$703$	−27.8187	−	15.4209i	−1.04920	−	0.581610i
$704$			3.07666i			0.115956i
$705$		0			0
$706$	−8.90124	−	24.4559i	−0.335002	−	0.920412i
$707$	−56.7777	−	39.7562i	−2.13535	−	1.49519i
$708$	18.5647	−	12.9991i	0.697703	−	0.488537i
$709$	−8.54815	+	23.4859i	−0.321033	+	0.882030i	0.669260	+	0.743029i	$0.266611\pi$
$709$	−8.54815	+	23.4859i	−0.321033	+	0.882030i	−0.990292	+	0.139001i	$0.955611\pi$
$710$		0			0
$711$	30.4660	+	17.5896i	1.14257	+	0.659660i
$712$	−0.891793	+	10.1932i	−0.0334214	+	0.382008i
$713$	1.90404	−	21.7633i	0.0713070	−	0.815043i
$714$	41.6673	+	24.0566i	1.55936	+	0.900297i
$715$		0			0
$716$	−7.24218	+	19.8977i	−0.270653	+	0.743613i
$717$	21.6516	−	15.1606i	0.808593	−	0.566183i
$718$	5.75310	+	4.02836i	0.214704	+	0.150337i
$719$	−0.0911921	−	0.250548i	−0.00340089	−	0.00934388i	0.937981	−	0.346688i	$-0.112694\pi$
$719$	−0.0911921	−	0.250548i	−0.00340089	−	0.00934388i	−0.941381	+	0.337344i	$0.890471\pi$
$720$		0			0
$721$		−	29.8377i		−	1.11121i
$722$	−11.4339	−	15.1745i	−0.425525	−	0.564738i
$723$	10.9445	+	10.9445i	0.407031	+	0.407031i
$724$	−0.171898	−	0.144240i	−0.00638855	−	0.00536063i
$725$		0			0
$726$	0.676310	+	3.83554i	0.0251002	+	0.142350i
$727$	6.73291	+	9.61560i	0.249710	+	0.356623i	0.924364	−	0.381511i	$-0.124596\pi$
$727$	6.73291	+	9.61560i	0.249710	+	0.356623i	−0.674654	+	0.738134i	$0.735707\pi$
$728$	1.81292	+	3.88782i	0.0671912	+	0.144092i
$729$	−29.7232	+	17.1607i	−1.10086	+	0.635581i
$730$		0			0
$731$	−31.7651	+	26.6541i	−1.17487	+	0.985837i
$732$	−33.8364	−	2.96030i	−1.25063	−	0.109416i
$733$	8.44220	−	2.26208i	0.311820	−	0.0835519i	−0.0995153	−	0.995036i	$-0.531729\pi$
$733$	8.44220	−	2.26208i	0.311820	−	0.0835519i	0.411335	+	0.911484i	$0.365063\pi$
$734$	−17.2051	−	29.8002i	−0.635053	−	1.09994i
$735$		0			0
$736$	−8.10929	−	1.42989i	−0.298912	−	0.0527063i
$737$	4.10225	−	5.85861i	0.151108	−	0.215805i
$738$	−11.5481	−	5.38497i	−0.425091	−	0.198223i
$739$	−12.7373	+	15.1798i	−0.468551	+	0.558397i	−0.947628	−	0.319376i	$-0.896527\pi$
$739$	−12.7373	+	15.1798i	−0.468551	+	0.558397i	0.479078	+	0.877773i	$0.340971\pi$
$740$		0			0
$741$	−3.43566	−	11.9825i	−0.126212	−	0.440187i
$742$	28.7007	−	28.7007i	1.05364	−	1.05364i
$743$	−4.81540	+	0.421293i	−0.176660	+	0.0154557i	−0.175142	−	0.984543i	$-0.556039\pi$
$743$	−4.81540	+	0.421293i	−0.176660	+	0.0154557i	−0.00151753	+	0.999999i	$0.500483\pi$
$744$	−6.32896	+	2.30355i	−0.232031	+	0.0844523i
$745$		0			0
$746$	−2.34156	+	13.2797i	−0.0857306	+	0.486203i
$747$	19.7715	−	9.21962i	0.723403	−	0.337328i
$748$	−3.96316	+	14.7907i	−0.144907	+	0.540802i
$749$	−28.3330	+	49.0742i	−1.03527	+	1.79313i
$750$		0			0
$751$	−7.54694	−	8.99409i	−0.275392	−	0.328199i	0.610566	−	0.791966i	$-0.290942\pi$
$751$	−7.54694	−	8.99409i	−0.275392	−	0.328199i	−0.885957	+	0.463766i	$0.846498\pi$
$752$	1.03816	+	3.87447i	0.0378579	+	0.141287i
$753$	65.4548	+	17.5386i	2.38530	+	0.639140i
$754$	−0.0604165	−	0.0219898i	−0.00220024	−	0.000800822i
$755$		0			0
$756$	−4.23239	+	0.746285i	−0.153931	+	0.0271421i
$757$	−6.43621	+	13.8025i	−0.233928	+	0.501660i	−0.987870	−	0.155280i	$-0.950372\pi$
$757$	−6.43621	+	13.8025i	−0.233928	+	0.501660i	0.753943	+	0.656940i	$0.228150\pi$
$758$	2.84019	+	32.4636i	0.103160	+	1.17913i
$759$	64.3142			2.33446
$760$		0			0
$761$	29.4990			1.06934			0.534669	−	0.845062i	$-0.320436\pi$
$761$	29.4990			1.06934			0.534669	+	0.845062i	$0.320436\pi$
$762$	−3.44514	−	39.3781i	−0.124804	−	1.42652i
$763$	−5.25499	+	11.2694i	−0.190244	+	0.407979i
$764$	−14.8955	+	2.62647i	−0.538899	+	0.0950225i
$765$		0			0
$766$	24.5264	+	8.92688i	0.886175	+	0.322541i
$767$	9.71400	+	2.60286i	0.350752	+	0.0939837i
$768$	0.657042	+	2.45211i	0.0237090	+	0.0884830i
$769$	−4.03390	−	4.80742i	−0.145466	−	0.173360i	0.688391	−	0.725339i	$-0.258317\pi$
$769$	−4.03390	−	4.80742i	−0.145466	−	0.173360i	−0.833858	+	0.551979i	$0.813873\pi$
$770$		0			0
$771$	−29.4261	+	50.9674i	−1.05975	+	1.83555i
$772$	−2.97162	+	11.0902i	−0.106951	+	0.399147i
$773$	−2.47233	+	1.15287i	−0.0889235	+	0.0414657i	−0.466571	−	0.884484i	$-0.654511\pi$
$773$	−2.47233	+	1.15287i	−0.0889235	+	0.0414657i	0.377648	+	0.925949i	$0.376733\pi$
$774$	4.98350	−	28.2628i	0.179128	−	1.01589i
$775$		0			0
$776$	3.22817	−	1.17496i	0.115884	−	0.0421785i
$777$	−70.2729	+	6.14809i	−2.52103	+	0.220561i
$778$	7.74717	−	7.74717i	0.277750	−	0.277750i
$779$	−9.47728	−	13.0449i	−0.339559	−	0.467382i
$780$		0			0
$781$	−5.91239	+	7.04611i	−0.211562	+	0.252130i
$782$	−37.1427	−	17.3199i	−1.32822	−	0.619359i
$783$	0.0369458	−	0.0527641i	0.00132034	−	0.00188563i
$784$	7.38722	+	1.30257i	0.263829	+	0.0465202i
$785$		0			0
$786$	18.5309	+	32.0964i	0.660974	+	1.14484i
$787$	−47.6256	+	12.7612i	−1.69767	+	0.454889i	−0.972351	−	0.233524i	$-0.924974\pi$
$787$	−47.6256	+	12.7612i	−1.69767	+	0.454889i	−0.725319	+	0.688413i	$0.758308\pi$
$788$	3.20196	+	0.280135i	0.114065	+	0.00997940i
$789$	−0.0802132	+	0.0673069i	−0.00285567	+	0.00239619i
$790$		0			0
$791$	−26.8282	+	15.4893i	−0.953901	+	0.550735i
$792$	−4.47880	−	9.60482i	−0.159147	−	0.341292i
$793$	−8.64496	−	12.3463i	−0.306992	−	0.438430i
$794$	−4.53837	−	25.7384i	−0.161061	−	0.913422i
$795$		0			0
$796$	−9.52895	−	7.99574i	−0.337745	−	0.283402i
$797$	10.0334	+	10.0334i	0.355400	+	0.355400i	0.862114	−	0.506714i	$-0.169140\pi$
$797$	10.0334	+	10.0334i	0.355400	+	0.355400i	−0.506714	+	0.862114i	$0.669140\pi$
$798$	−39.8421	−	13.7196i	−1.41040	−	0.485670i
$799$			19.9634i			0.706255i
$800$		0			0
$801$	−12.0546	−	33.1199i	−0.425930	−	1.17023i
$802$	2.21777	+	1.55290i	0.0783123	+	0.0548348i
$803$	26.9776	−	18.8899i	0.952019	−	0.666611i
$804$	2.01837	−	5.54542i	0.0711823	−	0.195572i
$805$		0			0
$806$	−2.58827	−	1.49434i	−0.0911678	−	0.0526357i
$807$	−3.01943	+	34.5122i	−0.106289	+	1.21489i
$808$	1.58638	−	18.1324i	0.0558087	−	0.637897i
$809$	−31.2174	−	18.0234i	−1.09755	−	0.633669i	−0.161971	−	0.986796i	$-0.551785\pi$
$809$	−31.2174	−	18.0234i	−1.09755	−	0.633669i	−0.935575	+	0.353127i	$0.885118\pi$
$810$		0			0
$811$	−0.626949	+	1.72253i	−0.0220152	+	0.0604862i	−0.950213	−	0.311600i	$-0.899135\pi$
$811$	−0.626949	+	1.72253i	−0.0220152	+	0.0604862i	0.928198	+	0.372086i	$0.121357\pi$
$812$	−0.178036	+	0.124662i	−0.00624783	+	0.00437478i
$813$	−55.1053	−	38.5852i	−1.93263	−	1.35324i
$814$	−7.67849	−	21.0965i	−0.269131	−	0.739432i
$815$		0			0
$816$			12.6347i			0.442301i
$817$	22.8554	−	28.2229i	0.799610	−	0.987395i
$818$	−2.09153	−	2.09153i	−0.0731285	−	0.0731285i
$819$	−11.3193	−	9.49800i	−0.395527	−	0.331887i
$820$		0			0
$821$	5.26544	+	29.8618i	0.183765	+	1.04218i	0.927532	+	0.373745i	$0.121926\pi$
$821$	5.26544	+	29.8618i	0.183765	+	1.04218i	−0.743767	+	0.668440i	$0.766963\pi$
$822$	−12.3221	−	17.5977i	−0.429781	−	0.613791i
$823$	−15.2503	−	32.7044i	−0.531592	−	1.14000i	−0.970418	−	0.241431i	$-0.922383\pi$
$823$	−15.2503	−	32.7044i	−0.531592	−	1.14000i	0.438826	−	0.898572i	$-0.355395\pi$
$824$	6.78570	−	3.91772i	0.236391	−	0.136480i
$825$		0			0
$826$	26.0424	−	21.8522i	0.906132	−	0.760335i
$827$	9.80334	+	0.857681i	0.340896	+	0.0298245i	0.256318	−	0.966592i	$-0.417490\pi$
$827$	9.80334	+	0.857681i	0.340896	+	0.0298245i	0.0845773	+	0.996417i	$0.473046\pi$
$828$	27.3974	−	7.34111i	0.952125	−	0.255121i
$829$	2.91653	+	5.05158i	0.101295	+	0.175449i	0.912219	−	0.409704i	$-0.134368\pi$
$829$	2.91653	+	5.05158i	0.101295	+	0.175449i	−0.810923	+	0.585153i	$0.801035\pi$
$830$		0			0
$831$	−5.21338	−	0.919259i	−0.180850	−	0.0318888i
$832$	−0.646130	+	0.922769i	−0.0224005	+	0.0319913i
$833$	33.8354	+	15.7777i	1.17233	+	0.546665i
$834$	22.9491	−	27.3496i	0.794661	−	0.947040i
$835$		0			0
$836$	0.935760	−	13.3781i	0.0323639	−	0.462693i
$837$	2.11723	−	2.11723i	0.0731821	−	0.0731821i
$838$	15.5448	−	1.35999i	0.536986	−	0.0469802i
$839$	10.6088	−	3.86129i	0.366257	−	0.133307i	−0.152334	−	0.988329i	$-0.548679\pi$
$839$	10.6088	−	3.86129i	0.366257	−	0.133307i	0.518591	+	0.855022i	$0.326457\pi$
$840$		0			0
$841$	−5.03523	+	28.5562i	−0.173629	+	0.984697i
$842$	21.4261	−	9.99113i	0.738391	−	0.344317i
$843$	6.52481	−	24.3509i	0.224726	−	0.838690i
$844$	13.6256	−	23.6003i	0.469013	−	0.812355i
$845$		0			0
$846$	−8.88118	−	10.5842i	−0.305341	−	0.363891i
$847$	1.51209	+	5.64318i	0.0519559	+	0.193902i
$848$	10.2956	+	2.75869i	0.353551	+	0.0947337i
$849$	−36.4860	−	13.2798i	−1.25220	−	0.455762i
$850$		0			0
$851$	59.1736	−	10.4339i	2.02845	−	0.357670i
$852$	−3.20746	+	6.87842i	−0.109886	+	0.235651i
$853$	1.48267	+	16.9470i	0.0507656	+	0.580253i	0.978394	+	0.206749i	$0.0662883\pi$
$853$	1.48267	+	16.9470i	0.0507656	+	0.580253i	−0.927628	+	0.373504i	$0.878156\pi$
$854$	−50.9501			−1.74348
$855$		0			0
$856$	−14.8806			−0.508610
$857$	0.683107	+	7.80795i	0.0233345	+	0.266715i	0.998896	+	0.0469860i	$0.0149616\pi$
$857$	0.683107	+	7.80795i	0.0233345	+	0.266715i	−0.975561	+	0.219729i	$0.929483\pi$
$858$	3.71837	−	7.97407i	0.126943	−	0.272230i
$859$	−15.2179	+	2.68333i	−0.519228	+	0.0915540i	−0.427120	−	0.904195i	$-0.640472\pi$
$859$	−15.2179	+	2.68333i	−0.519228	+	0.0915540i	−0.0921086	+	0.995749i	$0.529361\pi$
$860$		0			0
$861$	−33.6035	−	12.2307i	−1.14520	−	0.416820i
$862$	−12.1908	−	3.26652i	−0.415221	−	0.111258i
$863$	10.4844	+	39.1283i	0.356893	+	1.33194i	0.878085	+	0.478504i	$0.158821\pi$
$863$	10.4844	+	39.1283i	0.356893	+	1.33194i	−0.521192	+	0.853439i	$0.674513\pi$
$864$	−0.725438	−	0.864543i	−0.0246799	−	0.0294123i
$865$		0			0
$866$	−0.933244	+	1.61643i	−0.0317129	+	0.0549284i
$867$	−5.10547	+	19.0539i	−0.173391	+	0.647103i
$868$	−9.15645	+	4.26972i	−0.310790	+	0.144924i
$869$	−5.45632	+	30.9443i	−0.185093	+	1.04971i
$870$		0			0
$871$	2.46074	−	0.895636i	0.0833790	−	0.0303475i
$872$	−3.25287	+	0.284589i	−0.110156	+	0.00963741i
$873$	−8.36739	+	8.36739i	−0.283193	+	0.283193i
$874$	34.8265	+	8.68396i	1.17802	+	0.293739i
$875$		0			0
$876$	17.4672	−	20.8166i	0.590163	−	0.703329i
$877$	−19.6708	−	9.17267i	−0.664237	−	0.309739i	0.0611009	−	0.998132i	$-0.480539\pi$
$877$	−19.6708	−	9.17267i	−0.664237	−	0.309739i	−0.725338	+	0.688393i	$0.758317\pi$
$878$	−18.6292	+	26.6053i	−0.628706	+	0.897885i
$879$	−18.9496	−	3.34133i	−0.639155	−	0.112700i
$880$		0			0
$881$	−20.7295	−	35.9046i	−0.698395	−	1.20966i	−0.969023	−	0.246972i	$-0.920564\pi$
$881$	−20.7295	−	35.9046i	−0.698395	−	1.20966i	0.270627	−	0.962684i	$-0.412769\pi$
$882$	−24.9579	+	6.68744i	−0.840375	+	0.225178i
$883$	−19.0353	−	1.66537i	−0.640589	−	0.0560443i	−0.237766	−	0.971322i	$-0.576415\pi$
$883$	−19.0353	−	1.66537i	−0.640589	−	0.0560443i	−0.402823	+	0.915278i	$0.631971\pi$
$884$	−4.29486	+	3.60381i	−0.144452	+	0.121209i
$885$		0			0
$886$	−11.5569	+	6.67237i	−0.388261	+	0.224163i
$887$	1.24830	+	2.67699i	0.0419138	+	0.0898845i	0.926150	−	0.377156i	$-0.123098\pi$
$887$	1.24830	+	2.67699i	0.0419138	+	0.0898845i	−0.884236	+	0.467041i	$0.845320\pi$
$888$	−10.6251	−	15.1742i	−0.356555	−	0.509214i
$889$	−10.2964	−	58.3938i	−0.345330	−	1.95846i
$890$		0			0
$891$	−17.6026	−	14.7703i	−0.589708	−	0.494824i
$892$	14.1845	+	14.1845i	0.474931	+	0.474931i
$893$	−3.33580	−	17.1630i	−0.111628	−	0.574339i
$894$		−	44.7039i		−	1.49512i
$895$		0			0
$896$	1.30243	+	3.57839i	0.0435110	+	0.119546i
$897$	19.2895	+	13.5067i	0.644058	+	0.450974i
$898$	−12.8303	+	8.98388i	−0.428153	+	0.299796i
$899$	0.0517896	−	0.142291i	0.00172728	−	0.00474566i
$900$		0			0
$901$	45.9413	+	26.5242i	1.53053	+	0.883650i
$902$	0.991917	−	11.3377i	0.0330272	−	0.377503i
$903$	7.01979	−	80.2366i	0.233604	−	2.67011i
$904$	−7.04514	−	4.06751i	−0.234318	−	0.135284i
$905$		0			0
$906$	9.27748	−	25.4897i	0.308224	−	0.846837i
$907$	−34.8176	+	24.3795i	−1.15610	+	0.809509i	−0.984453	−	0.175650i	$-0.943797\pi$
$907$	−34.8176	+	24.3795i	−1.15610	+	0.809509i	−0.171646	+	0.985159i	$0.554908\pi$
$908$	2.03326	+	1.42371i	0.0674762	+	0.0472474i
$909$	21.4436	+	58.9158i	0.711240	+	1.95412i
$910$		0			0
$911$		−	29.5661i		−	0.979568i	−0.871844	−	0.489784i	$-0.837076\pi$
$911$		−	29.5661i		−	0.979568i	0.871844	−	0.489784i	$-0.162924\pi$
$912$	−2.11119	−	10.8623i	−0.0699086	−	0.359687i
$913$	13.7783	+	13.7783i	0.455994	+	0.455994i
$914$	8.04818	+	6.75322i	0.266210	+	0.223377i
$915$		0			0
$916$	2.79954	+	15.8770i	0.0924994	+	0.524590i
$917$	31.8876	+	45.5402i	1.05302	+	1.50387i
$918$	−2.37382	−	5.09067i	−0.0783476	−	0.168017i
$919$	3.33276	−	1.92417i	0.109938	−	0.0634726i	−0.444023	−	0.896015i	$-0.646449\pi$
$919$	3.33276	−	1.92417i	0.109938	−	0.0634726i	0.553961	+	0.832543i	$0.313116\pi$
$920$		0			0
$921$	−16.0235	+	13.4453i	−0.527992	+	0.443038i
$922$	−31.5355	−	2.75899i	−1.03856	−	0.0908627i
$923$	−3.25303	+	0.871648i	−0.107075	+	0.0286906i
$924$	−14.8712	−	25.7578i	−0.489228	−	0.847368i
$925$		0			0
$926$	−36.7250	−	6.47560i	−1.20686	−	0.212801i
$927$	−15.4807	+	22.1087i	−0.508452	+	0.726144i
$928$	−0.0517270	−	0.0241207i	−0.00169802	−	0.000791800i
$929$	19.0818	−	22.7409i	0.626055	−	0.746103i	−0.356044	−	0.934469i	$-0.615875\pi$
$929$	19.0818	−	22.7409i	0.626055	−	0.746103i	0.982099	+	0.188366i	$0.0603191\pi$
$930$		0			0
$931$	−31.7255	−	7.91072i	−1.03976	−	0.259263i
$932$	−14.2624	+	14.2624i	−0.467181	+	0.467181i
$933$	−54.1463	+	4.73719i	−1.77267	+	0.155089i
$934$	3.74775	−	1.36407i	0.122630	−	0.0446337i
$935$		0			0
$936$	0.673803	−	3.82133i	0.0220239	−	0.124904i
$937$	−32.3022	+	15.0628i	−1.05527	+	0.492079i	−0.871248	−	0.490843i	$-0.836689\pi$
$937$	−32.3022	+	15.0628i	−1.05527	+	0.492079i	−0.184020	+	0.982923i	$0.558911\pi$
$938$	2.29113	−	8.55061i	0.0748080	−	0.279187i
$939$	16.0473	−	27.7947i	0.523684	−	0.907047i
$940$		0			0
$941$	−10.7222	−	12.7783i	−0.349535	−	0.416559i	0.562419	−	0.826852i	$-0.309871\pi$
$941$	−10.7222	−	12.7783i	−0.349535	−	0.416559i	−0.911954	+	0.410293i	$0.865426\pi$
$942$	5.97977	+	22.3168i	0.194831	+	0.727121i
$943$	29.4222	+	7.88366i	0.958119	+	0.256727i
$944$	8.38903	+	3.05336i	0.273040	+	0.0993783i
$945$		0			0
$946$	25.2441	−	4.45122i	0.820757	−	0.144722i
$947$	3.03806	−	6.51514i	0.0987237	−	0.211714i	−0.850743	−	0.525582i	$-0.823847\pi$
$947$	3.03806	−	6.51514i	0.0987237	−	0.211714i	0.949466	+	0.313869i	$0.101625\pi$
$948$	2.25966	+	25.8281i	0.0733904	+	0.838856i
$949$	12.0584			0.391431
$950$		0			0
$951$	65.4287			2.12167
$952$	1.65182	+	18.8804i	0.0535360	+	0.611919i
$953$	23.4072	−	50.1970i	0.758235	−	1.62604i	−0.0213720	−	0.999772i	$-0.506803\pi$
$953$	23.4072	−	50.1970i	0.758235	−	1.62604i	0.779607	−	0.626269i	$-0.215419\pi$
$954$	−36.1570	+	6.37545i	−1.17063	+	0.206413i
$955$		0			0
$956$	9.78394	+	3.56106i	0.316435	+	0.115173i
$957$	0.430587	+	0.115375i	0.0139189	+	0.00372956i
$958$	3.05850	+	11.4145i	0.0988156	+	0.368785i
$959$	−20.7140	−	24.6860i	−0.668890	−	0.797152i
$960$		0			0
$961$	−11.9806	+	20.7510i	−0.386471	+	0.669387i
$962$	2.12750	−	7.93995i	0.0685934	−	0.255994i
$963$	46.4549	−	21.6623i	1.49699	−	0.698057i
$964$	−1.05873	+	6.00435i	−0.0340994	+	0.193387i
$965$		0			0
$966$	74.8024	−	27.2258i	2.40673	−	0.875977i
$967$	−6.17912	+	0.540603i	−0.198707	+	0.0173846i	−0.186075	−	0.982536i	$-0.559577\pi$
$967$	−6.17912	+	0.540603i	−0.198707	+	0.0173846i	−0.0126324	+	0.999920i	$0.504021\pi$
$968$	−1.08483	+	1.08483i	−0.0348679	+	0.0348679i
$969$	3.84281	−	54.9389i	0.123449	−	1.76489i
$970$		0			0
$971$	37.4392	−	44.6183i	1.20148	−	1.43187i	0.328233	−	0.944597i	$-0.393547\pi$
$971$	37.4392	−	44.6183i	1.20148	−	1.43187i	0.873249	−	0.487274i	$-0.162009\pi$
$972$	−20.2522	−	9.44375i	−0.649589	−	0.302908i
$973$	30.7181	−	43.8699i	0.984776	−	1.40641i
$974$	−11.1494	−	1.96594i	−0.357250	−	0.0629928i
$975$		0			0
$976$	−6.68981	−	11.5871i	−0.214135	−	0.370893i
$977$	−37.6124	+	10.0782i	−1.20333	+	0.322430i	−0.804140	−	0.594440i	$-0.797374\pi$
$977$	−37.6124	+	10.0782i	−1.20333	+	0.322430i	−0.399186	+	0.916870i	$0.630707\pi$
$978$	−56.4482	−	4.93858i	−1.80501	−	0.157918i
$979$	24.1158	−	20.2355i	0.770743	−	0.646730i
$980$		0			0
$981$	9.74064	−	5.62376i	0.310995	−	0.179553i
$982$	−5.24517	−	11.2483i	−0.167380	−	0.358948i
$983$	−6.22159	−	8.88535i	−0.198438	−	0.283399i	0.707584	−	0.706629i	$-0.249785\pi$
$983$	−6.22159	−	8.88535i	−0.198438	−	0.283399i	−0.906022	+	0.423230i	$0.860896\pi$
$984$	−1.63067	−	9.24802i	−0.0519840	−	0.294816i
$985$		0			0
$986$	−0.217601	−	0.182589i	−0.00692984	−	0.00581483i
$987$	−27.4190	−	27.4190i	−0.872757	−	0.872757i
$988$	3.09021	−	3.81593i	0.0983126	−	0.121401i
$989$			68.6058i			2.18154i
$990$		0			0
$991$	−20.2642	−	55.6755i	−0.643715	−	1.76859i	−0.639731	−	0.768599i	$-0.720954\pi$
$991$	−20.2642	−	55.6755i	−0.643715	−	1.76859i	−0.00398388	−	0.999992i	$-0.501268\pi$
$992$	−2.17327	−	1.52174i	−0.0690015	−	0.0483154i
$993$	54.5343	−	38.1854i	1.73060	−	1.21178i
$994$	−3.89376	+	10.6980i	−0.123503	+	0.339321i
$995$		0			0
$996$	13.9238	+	8.03891i	0.441192	+	0.254723i
$997$	0.482526	−	5.51530i	0.0152818	−	0.174671i	−0.984718	−	0.174156i	$-0.944280\pi$
$997$	0.482526	−	5.51530i	0.0152818	−	0.174671i	1.00000		0.000515454i	$-0.000164074\pi$
$998$	−1.63075	+	18.6396i	−0.0516206	+	0.590026i
$999$	7.13196	+	4.11764i	0.225645	+	0.130276i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.d.193.1	✓	96
5.2	odd	4	inner	950.2.bb.d.307.8	yes	96
5.3	odd	4	inner	950.2.bb.d.307.1	yes	96
5.4	even	2	inner	950.2.bb.d.193.8	yes	96
19.13	odd	18	inner	950.2.bb.d.393.8	yes	96
95.13	even	36	inner	950.2.bb.d.507.8	yes	96
95.32	even	36	inner	950.2.bb.d.507.1	yes	96
95.89	odd	18	inner	950.2.bb.d.393.1	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.bb.d.193.1	✓	96	1.1	even	1	trivial
950.2.bb.d.193.8	yes	96	5.4	even	2	inner
950.2.bb.d.307.1	yes	96	5.3	odd	4	inner
950.2.bb.d.307.8	yes	96	5.2	odd	4	inner
950.2.bb.d.393.1	yes	96	95.89	odd	18	inner
950.2.bb.d.393.8	yes	96	19.13	odd	18	inner
950.2.bb.d.507.1	yes	96	95.32	even	36	inner
950.2.bb.d.507.8	yes	96	95.13	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)

\(f(q)\)	\(=\)	\(q+(-0.0871557 - 0.996195i) q^{2} +(-1.07287 + 2.30077i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(2.38552 + 0.868257i) q^{6} +(3.67829 + 0.985594i) q^{7} +(0.258819 + 0.965926i) q^{8} +(-2.21412 - 2.63869i) q^{9} +O(q^{10})\)	\(q+(-0.0871557 - 0.996195i) q^{2} +(-1.07287 + 2.30077i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(2.38552 + 0.868257i) q^{6} +(3.67829 + 0.985594i) q^{7} +(0.258819 + 0.965926i) q^{8} +(-2.21412 - 2.63869i) q^{9} +(1.53833 - 2.66446i) q^{11} +(0.657042 - 2.45211i) q^{12} +(1.02095 - 0.476076i) q^{13} +(0.661259 - 3.75019i) q^{14} +(0.939693 - 0.342020i) q^{16} +(4.95805 - 0.433773i) q^{17} +(-2.43568 + 2.43568i) q^{18} +(-4.19007 + 1.20139i) q^{19} +(-6.21392 + 7.40547i) q^{21} +(-2.78840 - 1.30025i) q^{22} +(4.72305 - 6.74521i) q^{23} +(-2.50005 - 0.440826i) q^{24} +(-0.563246 - 0.975571i) q^{26} +(1.09013 - 0.292098i) q^{27} +(-3.79355 - 0.331893i) q^{28} +(0.0437215 - 0.0366867i) q^{29} +(2.29763 - 1.32654i) q^{31} +(-0.422618 - 0.906308i) q^{32} +(4.47989 + 6.39794i) q^{33} +(-0.864245 - 4.90137i) q^{34} +(2.63869 + 2.21412i) q^{36} +(5.15977 + 5.15977i) q^{37} +(1.56201 + 4.06941i) q^{38} +2.85973i q^{39} +(1.26518 + 3.47605i) q^{41} +(7.91887 + 5.54485i) q^{42} +(-6.82487 + 4.77882i) q^{43} +(-1.05228 + 2.89111i) q^{44} +(-7.13119 - 4.11719i) q^{46} +(-0.349595 + 3.99588i) q^{47} +(-0.221255 + 2.52895i) q^{48} +(6.49621 + 3.75059i) q^{49} +(-4.32130 + 11.8727i) q^{51} +(-0.922769 + 0.646130i) q^{52} +(8.73114 + 6.11361i) q^{53} +(-0.385997 - 1.06052i) q^{54} +3.80804i q^{56} +(1.73125 - 10.9293i) q^{57} +(-0.0403577 - 0.0403577i) q^{58} +(6.83880 + 5.73843i) q^{59} +(-2.32335 - 13.1763i) q^{61} +(-1.52174 - 2.17327i) q^{62} +(-5.54350 - 11.8881i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(5.98315 - 5.02046i) q^{66} +(2.31577 + 0.202604i) q^{67} +(-4.80740 + 1.28814i) q^{68} +(10.4520 + 18.1033i) q^{69} +(-2.94420 - 0.519143i) q^{71} +(1.97572 - 2.82162i) q^{72} +(9.70143 + 4.52385i) q^{73} +(4.69043 - 5.58984i) q^{74} +(3.91779 - 1.91074i) q^{76} +(8.28449 - 8.28449i) q^{77} +(2.84885 - 0.249242i) q^{78} +(-9.59702 + 3.49303i) q^{79} +(1.29692 - 7.35520i) q^{81} +(3.35256 - 1.56332i) q^{82} +(-1.63918 + 6.11750i) q^{83} +(4.83357 - 8.37200i) q^{84} +(5.35547 + 6.38240i) q^{86} +(0.0375003 + 0.139953i) q^{87} +(2.97182 + 0.796297i) q^{88} +(9.61510 + 3.49961i) q^{89} +(4.22456 - 0.744904i) q^{91} +(-3.48000 + 7.46289i) q^{92} +(0.587006 + 6.70951i) q^{93} +4.01115 q^{94} +2.53861 q^{96} +(-0.299410 - 3.42227i) q^{97} +(3.17013 - 6.79837i) q^{98} +(-10.4367 + 1.84028i) 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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