LMFDB - Embedded newform 950.2.bb.d.193.4

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			193.4
Character	$\chi$	$=$	950.193
Dual form			950.2.bb.d.507.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0871557 - 0.996195i) q^{2} +(1.36591 - 2.92920i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-3.03710 - 1.10542i) q^{6} +(2.44739 + 0.655775i) q^{7} +(0.258819 + 0.965926i) q^{8} +(-4.78616 - 5.70392i) q^{9} +O(q^{10})$	\(q+(-0.0871557 - 0.996195i) q^{2} +(1.36591 - 2.92920i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-3.03710 - 1.10542i) q^{6} +(2.44739 + 0.655775i) q^{7} +(0.258819 + 0.965926i) q^{8} +(-4.78616 - 5.70392i) q^{9} +(1.97115 - 3.41412i) q^{11} +(-0.836508 + 3.12189i) q^{12} +(3.34937 - 1.56183i) q^{13} +(0.439976 - 2.49523i) q^{14} +(0.939693 - 0.342020i) q^{16} +(-3.64591 + 0.318976i) q^{17} +(-5.26508 + 5.26508i) q^{18} +(4.35498 - 0.184704i) q^{19} +(5.26381 - 6.27316i) q^{21} +(-3.57293 - 1.66608i) q^{22} +(-0.904036 + 1.29110i) q^{23} +(3.18292 + 0.561234i) q^{24} +(-1.84781 - 3.20050i) q^{26} +(-13.8797 + 3.71907i) q^{27} +(-2.52408 - 0.220828i) q^{28} +(-4.66306 + 3.91277i) q^{29} +(-3.71476 + 2.14472i) q^{31} +(-0.422618 - 0.906308i) q^{32} +(-7.30826 - 10.4373i) q^{33} +(0.635524 + 3.60423i) q^{34} +(5.70392 + 4.78616i) q^{36} +(4.92208 + 4.92208i) q^{37} +(-0.563563 - 4.32231i) q^{38} -11.9443i q^{39} +(-2.93537 - 8.06485i) q^{41} +(-6.70806 - 4.69704i) q^{42} +(5.02897 - 3.52132i) q^{43} +(-1.34834 + 3.70454i) q^{44} +(1.36498 + 0.788070i) q^{46} +(-1.11739 + 12.7719i) q^{47} +(0.281689 - 3.21972i) q^{48} +(-0.502521 - 0.290131i) q^{49} +(-4.04564 + 11.1153i) q^{51} +(-3.02727 + 2.11972i) q^{52} +(0.774207 + 0.542106i) q^{53} +(4.91461 + 13.5028i) q^{54} +2.53372i q^{56} +(5.40748 - 13.0089i) q^{57} +(4.30429 + 4.30429i) q^{58} +(7.62033 + 6.39421i) q^{59} +(-0.438632 - 2.48761i) q^{61} +(2.46032 + 3.51370i) q^{62} +(-7.97309 - 17.0983i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(-9.76060 + 8.19011i) q^{66} +(-11.4932 - 1.00553i) q^{67} +(3.53513 - 0.947235i) q^{68} +(2.54706 + 4.41163i) q^{69} +(-5.43677 - 0.958650i) q^{71} +(4.27082 - 6.09936i) q^{72} +(5.28326 + 2.46362i) q^{73} +(4.47437 - 5.33234i) q^{74} +(-4.25675 + 0.938133i) q^{76} +(7.06305 - 7.06305i) q^{77} +(-11.8988 + 1.04101i) q^{78} +(14.1589 - 5.15341i) q^{79} +(-4.18566 + 23.7380i) q^{81} +(-7.77833 + 3.62709i) q^{82} +(-4.68290 + 17.4768i) q^{83} +(-4.09452 + 7.09191i) q^{84} +(-3.94623 - 4.70293i) q^{86} +(5.09198 + 19.0035i) q^{87} +(3.80796 + 1.02034i) q^{88} +(-2.15275 - 0.783537i) q^{89} +(9.22140 - 1.62598i) q^{91} +(0.666105 - 1.42847i) q^{92} +(1.20829 + 13.8108i) q^{93} +12.8207 q^{94} -3.23202 q^{96} +(-0.681237 - 7.78657i) q^{97} +(-0.245229 + 0.525895i) q^{98} +(-28.9081 + 5.09728i) 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
$3$	1.36591	−	2.92920i	0.788609	−	1.69118i	0.0681534	−	0.997675i	$-0.478289\pi$
$3$	1.36591	−	2.92920i	0.788609	−	1.69118i	0.720455	−	0.693502i	$-0.243933\pi$
$4$	−0.984808	+	0.173648i	−0.492404	+	0.0868241i
$5$		0			0
$5$		0			0
$6$	−3.03710	−	1.10542i	−1.23989	−	0.451284i
$7$	2.44739	+	0.655775i	0.925025	+	0.247860i	0.689732	−	0.724065i	$-0.257728\pi$
$7$	2.44739	+	0.655775i	0.925025	+	0.247860i	0.235293	+	0.971924i	$0.424395\pi$
$8$	0.258819	+	0.965926i	0.0915064	+	0.341506i
$9$	−4.78616	−	5.70392i	−1.59539	−	1.90131i
$10$		0			0
$11$	1.97115	−	3.41412i	0.594323	−	1.02940i	−0.399319	−	0.916812i	$-0.630754\pi$
$11$	1.97115	−	3.41412i	0.594323	−	1.02940i	0.993642	−	0.112585i	$-0.0359131\pi$
$12$	−0.836508	+	3.12189i	−0.241479	+	0.901212i
$13$	3.34937	−	1.56183i	0.928947	−	0.433175i	0.101574	−	0.994828i	$-0.467612\pi$
$13$	3.34937	−	1.56183i	0.928947	−	0.433175i	0.827373	+	0.561653i	$0.189834\pi$
$14$	0.439976	−	2.49523i	0.117589	−	0.666878i
$15$		0			0
$16$	0.939693	−	0.342020i	0.234923	−	0.0855050i
$17$	−3.64591	+	0.318976i	−0.884263	+	0.0773630i	−0.520233	−	0.854024i	$-0.674155\pi$
$17$	−3.64591	+	0.318976i	−0.884263	+	0.0773630i	−0.364030	+	0.931387i	$0.618599\pi$
$18$	−5.26508	+	5.26508i	−1.24099	+	1.24099i
$19$	4.35498	−	0.184704i	0.999102	−	0.0423740i
$19$	4.35498	−	0.184704i	0.999102	−	0.0423740i
$20$		0			0
$21$	5.26381	−	6.27316i	1.14866	−	1.36892i
$22$	−3.57293	−	1.66608i	−0.761751	−	0.355210i
$23$	−0.904036	+	1.29110i	−0.188505	+	0.269212i	−0.902269	−	0.431173i	$-0.858100\pi$
$23$	−0.904036	+	1.29110i	−0.188505	+	0.269212i	0.713765	+	0.700386i	$0.246989\pi$
$24$	3.18292	+	0.561234i	0.649710	+	0.114561i
$25$		0			0
$26$	−1.84781	−	3.20050i	−0.362385	−	0.627669i
$27$	−13.8797	+	3.71907i	−2.67116	+	0.715735i
$28$	−2.52408	−	0.220828i	−0.477006	−	0.0417326i
$29$	−4.66306	+	3.91277i	−0.865908	+	0.726583i	−0.963232	−	0.268670i	$-0.913416\pi$
$29$	−4.66306	+	3.91277i	−0.865908	+	0.726583i	0.0973245	+	0.995253i	$0.468972\pi$
$30$		0			0
$31$	−3.71476	+	2.14472i	−0.667190	+	0.385202i	−0.795011	−	0.606595i	$-0.792535\pi$
$31$	−3.71476	+	2.14472i	−0.667190	+	0.385202i	0.127821	+	0.991797i	$0.459202\pi$
$32$	−0.422618	−	0.906308i	−0.0747091	−	0.160214i
$33$	−7.30826	−	10.4373i	−1.27220	−	1.81690i
$34$	0.635524	+	3.60423i	0.108991	+	0.618121i
$35$		0			0
$36$	5.70392	+	4.78616i	0.950654	+	0.797693i
$37$	4.92208	+	4.92208i	0.809186	+	0.809186i	0.984511	−	0.175325i	$-0.0560976\pi$
$37$	4.92208	+	4.92208i	0.809186	+	0.809186i	−0.175325	+	0.984511i	$0.556098\pi$
$38$	−0.563563	−	4.32231i	−0.0914220	−	0.701172i
$39$		−	11.9443i		−	1.91262i
$40$		0			0
$41$	−2.93537	−	8.06485i	−0.458427	−	1.25952i	−0.926656	−	0.375911i	$-0.877330\pi$
$41$	−2.93537	−	8.06485i	−0.458427	−	1.25952i	0.468229	−	0.883607i	$-0.344892\pi$
$42$	−6.70806	−	4.69704i	−1.03508	−	0.724768i
$43$	5.02897	−	3.52132i	0.766911	−	0.536997i	−0.123396	−	0.992357i	$-0.539379\pi$
$43$	5.02897	−	3.52132i	0.766911	−	0.536997i	0.890307	+	0.455361i	$0.150490\pi$
$44$	−1.34834	+	3.70454i	−0.203270	+	0.558481i
$45$		0			0
$46$	1.36498	+	0.788070i	0.201255	+	0.116195i
$47$	−1.11739	+	12.7719i	−0.162989	+	1.86297i	0.271692	+	0.962384i	$0.412417\pi$
$47$	−1.11739	+	12.7719i	−0.162989	+	1.86297i	−0.434681	+	0.900584i	$0.643139\pi$
$48$	0.281689	−	3.21972i	0.0406583	−	0.464727i
$49$	−0.502521	−	0.290131i	−0.0717887	−	0.0414472i
$50$		0			0
$51$	−4.04564	+	11.1153i	−0.566503	+	1.55645i
$52$	−3.02727	+	2.11972i	−0.419807	+	0.293952i
$53$	0.774207	+	0.542106i	0.106346	+	0.0744639i	0.625540	−	0.780192i	$-0.284879\pi$
$53$	0.774207	+	0.542106i	0.106346	+	0.0744639i	−0.519194	+	0.854656i	$0.673768\pi$
$54$	4.91461	+	13.5028i	0.668794	+	1.83750i
$55$		0			0
$56$			2.53372i			0.338583i
$57$	5.40748	−	13.0089i	0.716238	−	1.72307i
$58$	4.30429	+	4.30429i	0.565181	+	0.565181i
$59$	7.62033	+	6.39421i	0.992082	+	0.832456i	0.985868	−	0.167525i	$-0.0535774\pi$
$59$	7.62033	+	6.39421i	0.992082	+	0.832456i	0.00621438	+	0.999981i	$0.498022\pi$
$60$		0			0
$61$	−0.438632	−	2.48761i	−0.0561611	−	0.318506i	0.943766	−	0.330615i	$-0.107256\pi$
$61$	−0.438632	−	2.48761i	−0.0561611	−	0.318506i	−0.999927	+	0.0121099i	$0.996145\pi$
$62$	2.46032	+	3.51370i	0.312461	+	0.446240i
$63$	−7.97309	−	17.0983i	−1.00451	−	2.15419i
$64$	−0.866025	+	0.500000i	−0.108253	+	0.0625000i
$65$		0			0
$66$	−9.76060	+	8.19011i	−1.20145	+	1.00813i
$67$	−11.4932	−	1.00553i	−1.40412	−	0.122845i	−0.640228	−	0.768185i	$-0.721160\pi$
$67$	−11.4932	−	1.00553i	−1.40412	−	0.122845i	−0.763896	+	0.645340i	$0.776716\pi$
$68$	3.53513	−	0.947235i	0.428697	−	0.114869i
$69$	2.54706	+	4.41163i	0.306629	+	0.531098i
$70$		0			0
$71$	−5.43677	−	0.958650i	−0.645226	−	0.113771i	−0.158547	−	0.987351i	$-0.550681\pi$
$71$	−5.43677	−	0.958650i	−0.645226	−	0.113771i	−0.486679	+	0.873581i	$0.661792\pi$
$72$	4.27082	−	6.09936i	0.503321	−	0.718816i
$73$	5.28326	+	2.46362i	0.618359	+	0.288345i	0.706446	−	0.707767i	$-0.250298\pi$
$73$	5.28326	+	2.46362i	0.618359	+	0.288345i	−0.0880868	+	0.996113i	$0.528075\pi$
$74$	4.47437	−	5.33234i	0.520135	−	0.619872i
$75$		0			0
$76$	−4.25675	+	0.938133i	−0.488283	+	0.107611i
$77$	7.06305	−	7.06305i	0.804909	−	0.804909i
$78$	−11.8988	+	1.04101i	−1.34728	+	0.117872i
$79$	14.1589	−	5.15341i	1.59300	−	0.579804i	0.615020	−	0.788512i	$-0.289148\pi$
$79$	14.1589	−	5.15341i	1.59300	−	0.579804i	0.977978	+	0.208708i	$0.0669258\pi$
$80$		0			0
$81$	−4.18566	+	23.7380i	−0.465073	+	2.63756i
$82$	−7.77833	+	3.62709i	−0.858973	+	0.400545i
$83$	−4.68290	+	17.4768i	−0.514015	+	1.91833i	−0.142925	+	0.989734i	$0.545651\pi$
$83$	−4.68290	+	17.4768i	−0.514015	+	1.91833i	−0.371090	+	0.928597i	$0.621016\pi$
$84$	−4.09452	+	7.09191i	−0.446748	+	0.773791i
$85$		0			0
$86$	−3.94623	−	4.70293i	−0.425533	−	0.507130i
$87$	5.09198	+	19.0035i	0.545918	+	2.03739i
$88$	3.80796	+	1.02034i	0.405930	+	0.108769i
$89$	−2.15275	−	0.783537i	−0.228191	−	0.0830548i	0.225394	−	0.974268i	$-0.427633\pi$
$89$	−2.15275	−	0.783537i	−0.228191	−	0.0830548i	−0.453585	+	0.891213i	$0.649855\pi$
$90$		0			0
$91$	9.22140	−	1.62598i	0.966666	−	0.170449i
$92$	0.666105	−	1.42847i	0.0694463	−	0.148928i
$93$	1.20829	+	13.8108i	0.125293	+	1.43211i
$94$	12.8207			1.32235
$95$		0			0
$96$	−3.23202			−0.329867
$97$	−0.681237	−	7.78657i	−0.0691691	−	0.790606i	−0.948991	−	0.315303i	$-0.897894\pi$
$97$	−0.681237	−	7.78657i	−0.0691691	−	0.790606i	0.879822	−	0.475303i	$-0.157662\pi$
$98$	−0.245229	+	0.525895i	−0.0247719	+	0.0531234i
$99$	−28.9081	+	5.09728i	−2.90538	+	0.512296i
$100$		0			0
$101$	14.4675	+	5.26572i	1.43957	+	0.523959i	0.939657	−	0.342119i	$-0.111145\pi$
$101$	14.4675	+	5.26572i	1.43957	+	0.523959i	0.499909	+	0.866078i	$0.333367\pi$
$102$	11.4256	+	3.06148i	1.13130	+	0.303132i
$103$	2.69162	+	10.0453i	0.265213	+	0.989790i	0.962120	+	0.272627i	$0.0878926\pi$
$103$	2.69162	+	10.0453i	0.265213	+	0.989790i	−0.696906	+	0.717162i	$0.745441\pi$
$104$	2.37550	+	2.83101i	0.232937	+	0.277603i
$105$		0			0
$106$	0.472566	−	0.818509i	0.0458997	−	0.0795006i
$107$	2.20164	−	8.21663i	0.212841	−	0.794332i	−0.774075	−	0.633094i	$-0.781785\pi$
$107$	2.20164	−	8.21663i	0.212841	−	0.794332i	0.986916	−	0.161238i	$-0.0515486\pi$
$108$	13.0231	−	6.07276i	1.25315	−	0.584351i
$109$	−1.23485	+	7.00316i	−0.118277	+	0.670781i	0.866799	+	0.498658i	$0.166174\pi$
$109$	−1.23485	+	7.00316i	−0.118277	+	0.670781i	−0.985075	+	0.172123i	$0.944937\pi$
$110$		0			0
$111$	21.1409	−	7.69466i	2.00661	−	0.730345i
$112$	2.52408	−	0.220828i	0.238503	−	0.0208663i
$113$	4.04575	−	4.04575i	0.380592	−	0.380592i	−0.490723	−	0.871315i	$-0.663267\pi$
$113$	4.04575	−	4.04575i	0.380592	−	0.380592i	0.871315	+	0.490723i	$0.163267\pi$
$114$	−13.4307	−	4.25310i	−1.25790	−	0.398339i
$115$		0			0
$116$	3.91277	−	4.66306i	0.363291	−	0.432954i
$117$	−24.9392	−	11.6293i	−2.30563	−	1.07513i
$118$	5.70573	−	8.14862i	0.525255	−	0.750142i
$119$	−9.13212	−	1.61024i	−0.837140	−	0.147610i
$120$		0			0
$121$	−2.27083	−	3.93319i	−0.206439	−	0.357563i
$122$	−2.43991	+	0.653772i	−0.220899	+	0.0591898i
$123$	−27.6330	−	2.41758i	−2.49159	−	0.217986i
$124$	3.28590	−	2.75719i	0.295082	−	0.247603i
$125$		0			0
$126$	−16.3384	+	9.43297i	−1.45554	+	0.840356i
$127$	1.27125	+	2.72621i	0.112805	+	0.241912i	0.954603	−	0.297882i	$-0.0962801\pi$
$127$	1.27125	+	2.72621i	0.112805	+	0.241912i	−0.841798	+	0.539793i	$0.818502\pi$
$128$	0.573576	+	0.819152i	0.0506975	+	0.0724035i
$129$	−3.44555	−	19.5407i	−0.303364	−	1.72046i
$130$		0			0
$131$	−13.8905	−	11.6555i	−1.21362	−	1.01835i	−0.999134	−	0.0416173i	$-0.986749\pi$
$131$	−13.8905	−	11.6555i	−1.21362	−	1.01835i	−0.214483	−	0.976728i	$-0.568807\pi$
$132$	9.00964	+	9.00964i	0.784189	+	0.784189i
$133$	10.7795	+	2.40385i	0.934697	+	0.208440i
$134$			11.5372i			0.996658i
$135$		0			0
$136$	−1.25174	−	3.43912i	−0.107336	−	0.294902i
$137$	−2.54287	−	1.78054i	−0.217252	−	0.152121i	0.459885	−	0.887979i	$-0.347891\pi$
$137$	−2.54287	−	1.78054i	−0.217252	−	0.152121i	−0.677137	+	0.735857i	$0.736780\pi$
$138$	4.17285	−	2.92186i	0.355217	−	0.248725i
$139$	5.24754	−	14.4175i	0.445091	−	1.22288i	−0.491013	−	0.871152i	$-0.663373\pi$
$139$	5.24754	−	14.4175i	0.445091	−	1.22288i	0.936104	−	0.351725i	$-0.114405\pi$
$140$		0			0
$141$	35.8851	+	20.7183i	3.02207	+	1.74480i
$142$	−0.481156	+	5.49964i	−0.0403777	+	0.461519i
$143$	1.26979	−	14.5138i	0.106185	−	1.21370i
$144$	−6.44838	−	3.72297i	−0.537365	−	0.310248i
$145$		0			0
$146$	1.99378	−	5.47787i	0.165007	−	0.453352i
$147$	−1.53625	+	1.07569i	−0.126708	+	0.0887217i
$148$	−5.70202	−	3.99260i	−0.468703	−	0.328189i
$149$	1.25031	+	3.43520i	0.102429	+	0.281422i	0.980312	−	0.197453i	$-0.0632669\pi$
$149$	1.25031	+	3.43520i	0.102429	+	0.281422i	−0.877883	+	0.478875i	$0.841045\pi$
$150$		0			0
$151$		−	16.9102i		−	1.37613i	−0.725649	−	0.688065i	$-0.758460\pi$
$151$		−	16.9102i		−	1.37613i	0.725649	−	0.688065i	$-0.241540\pi$
$152$	1.30556	+	4.15879i	0.105895	+	0.337322i
$153$	19.2693	+	19.2693i	1.55783	+	1.55783i
$154$	−7.65176	−	6.42059i	−0.616596	−	0.517386i
$155$		0			0
$156$	2.07411	+	11.7628i	0.166061	+	0.941781i
$157$	5.15180	+	7.35754i	0.411159	+	0.587195i	0.970308	−	0.241871i	$-0.0777612\pi$
$157$	5.15180	+	7.35754i	0.411159	+	0.587195i	−0.559150	+	0.829067i	$0.688872\pi$
$158$	−6.36783	−	13.6558i	−0.506597	−	1.08640i
$159$	2.64543	−	1.52734i	0.209797	−	0.121126i
$160$		0			0
$161$	−3.05920	+	2.56697i	−0.241098	+	0.202306i
$162$	24.0125	+	2.10082i	1.88660	+	0.165056i
$163$	6.29963	−	1.68798i	0.493425	−	0.132213i	−0.00352169	−	0.999994i	$-0.501121\pi$
$163$	6.29963	−	1.68798i	0.493425	−	0.132213i	0.496947	+	0.867781i	$0.334454\pi$
$164$	4.29122	+	7.43261i	0.335088	+	0.580389i
$165$		0			0
$166$	17.8185	+	3.14188i	1.38298	+	0.243857i
$167$	6.38626	−	9.12052i	0.494184	−	0.705767i	−0.492153	−	0.870509i	$-0.663790\pi$
$167$	6.38626	−	9.12052i	0.494184	−	0.705767i	0.986337	+	0.164741i	$0.0526789\pi$
$168$	7.42178	+	3.46083i	0.572603	+	0.267009i
$169$	0.422682	−	0.503732i	0.0325140	−	0.0387487i
$170$		0			0
$171$	−21.8972	−	23.9565i	−1.67452	−	1.83200i
$172$	−4.34110	+	4.34110i	−0.331006	+	0.331006i
$173$	−7.99455	+	0.699433i	−0.607815	+	0.0531769i	−0.386908	−	0.922118i	$-0.626457\pi$
$173$	−7.99455	+	0.699433i	−0.607815	+	0.0531769i	−0.220906	+	0.975295i	$0.570901\pi$
$174$	18.4874	−	6.72887i	1.40153	−	0.510114i
$175$		0			0
$176$	0.684572	−	3.88240i	0.0516015	−	0.292647i
$177$	29.1386	−	13.5876i	2.19019	−	1.02130i
$178$	−0.592931	+	2.21285i	−0.0444421	+	0.165860i
$179$	−2.05678	+	3.56245i	−0.153731	+	0.266270i	−0.932596	−	0.360921i	$-0.882462\pi$
$179$	−2.05678	+	3.56245i	−0.153731	+	0.266270i	0.778865	+	0.627191i	$0.215796\pi$
$180$		0			0
$181$	−13.3606	−	15.9226i	−0.993087	−	1.18352i	−0.983007	−	0.183566i	$-0.941236\pi$
$181$	−13.3606	−	15.9226i	−0.993087	−	1.18352i	−0.0100800	−	0.999949i	$-0.503209\pi$
$182$	−2.42349	−	9.04460i	−0.179641	−	0.670430i
$183$	−7.88584	−	2.11300i	−0.582938	−	0.156198i
$184$	−1.48109	−	0.539071i	−0.109187	−	0.0397409i
$185$		0			0
$186$	13.6529	−	2.40738i	1.00108	−	0.176517i
$187$	−6.09759	+	13.0763i	−0.445900	+	0.956236i
$188$	−1.11739	−	12.7719i	−0.0814943	−	0.931484i
$189$	−36.4080			−2.64829
$190$		0			0
$191$	2.70813			0.195953			0.0979766	−	0.995189i	$-0.468763\pi$
$191$	2.70813			0.195953			0.0979766	+	0.995189i	$0.468763\pi$
$192$	0.281689	+	3.21972i	0.0203292	+	0.232363i
$193$	−5.11958	+	10.9790i	−0.368516	+	0.790284i	0.631375	+	0.775478i	$0.282491\pi$
$193$	−5.11958	+	10.9790i	−0.368516	+	0.790284i	−0.999890	+	0.0148063i	$0.995287\pi$
$194$	−7.69757	+	1.35729i	−0.552653	+	0.0974476i
$195$		0			0
$196$	0.545267	+	0.198461i	0.0389477	+	0.0141758i
$197$	20.2186	+	5.41756i	1.44052	+	0.385985i	0.892715	−	0.450622i	$-0.148798\pi$
$197$	20.2186	+	5.41756i	1.44052	+	0.385985i	0.547803	+	0.836608i	$0.315464\pi$
$198$	7.59739	+	28.3539i	0.539923	+	2.01502i
$199$	−10.6962	−	12.7472i	−0.758231	−	0.903625i	0.239504	−	0.970895i	$-0.423015\pi$
$199$	−10.6962	−	12.7472i	−0.758231	−	0.903625i	−0.997735	+	0.0672708i	$0.978571\pi$
$200$		0			0
$201$	−18.6441	+	32.2926i	−1.31506	+	2.27774i
$202$	3.98476	−	14.8713i	0.280367	−	1.04634i
$203$	−13.9782	+	6.51814i	−0.981077	+	0.457484i
$204$	2.05402	−	11.6490i	0.143811	−	0.815590i
$205$		0			0
$206$	9.77245	−	3.55688i	0.680879	−	0.247820i
$207$	11.6912	−	1.02285i	0.812594	−	0.0710927i
$208$	2.61319	−	2.61319i	0.181192	−	0.181192i
$209$	7.95370	−	15.2325i	0.550169	−	1.05366i
$210$		0			0
$211$	8.58756	−	10.2343i	0.591192	−	0.704555i	−0.384643	−	0.923066i	$-0.625675\pi$
$211$	8.58756	−	10.2343i	0.591192	−	0.704555i	0.975835	+	0.218510i	$0.0701197\pi$
$212$	−0.856581	−	0.399430i	−0.0588302	−	0.0274330i
$213$	−10.2342	+	14.6160i	−0.701237	+	1.00147i
$214$	−8.37725	−	1.47713i	−0.572657	−	0.100975i
$215$		0			0
$216$	−7.18469	−	12.4442i	−0.488856	−	0.846723i
$217$	−10.4979	+	2.81290i	−0.712644	+	0.190952i
$218$	7.08414	+	0.619782i	0.479798	+	0.0419769i
$219$	14.4329	−	12.1107i	0.975286	−	0.818362i
$220$		0			0
$221$	−11.7133	+	6.76267i	−0.787921	+	0.454907i
$222$	−9.50793	−	20.3898i	−0.638131	−	1.36848i
$223$	6.72312	+	9.60162i	0.450214	+	0.642972i	0.978537	−	0.206071i	$-0.0660679\pi$
$223$	6.72312	+	9.60162i	0.450214	+	0.642972i	−0.528323	+	0.849043i	$0.677179\pi$
$224$	−0.439976	−	2.49523i	−0.0293971	−	0.166719i
$225$		0			0
$226$	−4.38296	−	3.67774i	−0.291550	−	0.244640i
$227$	−7.27903	−	7.27903i	−0.483126	−	0.483126i	0.423002	−	0.906129i	$-0.360976\pi$
$227$	−7.27903	−	7.27903i	−0.483126	−	0.483126i	−0.906129	+	0.423002i	$0.860976\pi$
$228$	−3.06635	+	13.7503i	−0.203074	+	0.910635i
$229$		−	1.66662i		−	0.110134i	−0.998483	−	0.0550668i	$-0.982463\pi$
$229$		−	1.66662i		−	0.110134i	0.998483	−	0.0550668i	$-0.0175372\pi$
$230$		0			0
$231$	−11.0416	−	30.3366i	−0.726485	−	1.99600i
$232$	−4.98633	−	3.49147i	−0.327369	−	0.229226i
$233$	2.19866	−	1.53952i	0.144039	−	0.100857i	−0.499336	−	0.866409i	$-0.666423\pi$
$233$	2.19866	−	1.53952i	0.144039	−	0.100857i	0.643375	+	0.765551i	$0.277534\pi$
$234$	−9.41149	+	25.8578i	−0.615248	+	1.69038i
$235$		0			0
$236$	−8.61490	−	4.97382i	−0.560782	−	0.323768i
$237$	4.24437	−	48.5133i	0.275701	−	3.15128i
$238$	−0.808195	+	9.23771i	−0.0523875	+	0.598792i
$239$	−2.95516	−	1.70617i	−0.191154	−	0.110363i	0.401369	−	0.915917i	$-0.368535\pi$
$239$	−2.95516	−	1.70617i	−0.191154	−	0.110363i	−0.592523	+	0.805554i	$0.701868\pi$
$240$		0			0
$241$	1.67023	−	4.58892i	0.107589	−	0.295599i	−0.874202	−	0.485562i	$-0.838615\pi$
$241$	1.67023	−	4.58892i	0.107589	−	0.295599i	0.981791	+	0.189964i	$0.0608371\pi$
$242$	−3.72031	+	2.60499i	−0.239150	+	0.167455i
$243$	28.5042	+	19.9589i	1.82855	+	1.28036i
$244$	0.863937	+	2.37365i	0.0553079	+	0.151957i
$245$		0			0
$246$			27.7386i			1.76855i
$247$	14.2980	−	7.42041i	0.909757	−	0.472149i
$248$	−3.03309	−	3.03309i	−0.192601	−	0.192601i
$249$	44.7967	+	37.5889i	2.83888	+	2.38210i
$250$		0			0
$251$	2.11295	+	11.9832i	0.133368	+	0.756370i	0.975982	+	0.217851i	$0.0699047\pi$
$251$	2.11295	+	11.9832i	0.133368	+	0.756370i	−0.842614	+	0.538519i	$0.818984\pi$
$252$	10.8211	+	15.4541i	0.681663	+	0.973515i
$253$	2.62598	+	5.63143i	0.165094	+	0.354045i
$254$	2.60504	−	1.50402i	0.163454	−	0.0943705i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	22.5912	+	1.97647i	1.40920	+	0.123289i	0.766211	−	0.642588i	$-0.222139\pi$
$257$	22.5912	+	1.97647i	1.40920	+	0.123289i	0.642987	+	0.765877i	$0.277695\pi$
$258$	−19.1660	+	5.13552i	−1.19323	+	0.319724i
$259$	8.81846	+	15.2740i	0.547952	+	0.949081i
$260$		0			0
$261$	44.6363	+	7.87058i	2.76292	+	0.487177i
$262$	−10.4005	+	14.8535i	−0.642545	+	0.917650i
$263$	−9.76593	−	4.55393i	−0.602193	−	0.280807i	0.0975174	−	0.995234i	$-0.468910\pi$
$263$	−9.76593	−	4.55393i	−0.602193	−	0.280807i	−0.699710	+	0.714427i	$0.746688\pi$
$264$	8.19011	−	9.76060i	0.504067	−	0.600723i
$265$		0			0
$266$	1.45521	−	10.9479i	0.0892246	−	0.671261i
$267$	−5.23560	+	5.23560i	−0.320414	+	0.320414i
$268$	11.4932	−	1.00553i	0.702062	−	0.0614225i
$269$	5.02541	−	1.82910i	0.306405	−	0.111522i	−0.184242	−	0.982881i	$-0.558983\pi$
$269$	5.02541	−	1.82910i	0.306405	−	0.111522i	0.490646	+	0.871359i	$0.336761\pi$
$270$		0			0
$271$	−5.36280	+	30.4140i	−0.325767	+	1.84752i	0.178463	+	0.983947i	$0.442888\pi$
$271$	−5.36280	+	30.4140i	−0.325767	+	1.84752i	−0.504230	+	0.863570i	$0.668224\pi$
$272$	−3.31694	+	1.54671i	−0.201119	+	0.0937833i
$273$	7.83277	−	29.2323i	0.474061	−	1.76922i
$274$	−1.55214	+	2.68838i	−0.0937679	+	0.162411i
$275$		0			0
$276$	−3.27443	−	3.90232i	−0.197098	−	0.234892i
$277$	2.79061	+	10.4147i	0.167671	+	0.625758i	0.997684	+	0.0680138i	$0.0216662\pi$
$277$	2.79061	+	10.4147i	0.167671	+	0.625758i	−0.830013	+	0.557744i	$0.811667\pi$
$278$	−14.8200	−	3.97101i	−0.888844	−	0.238165i
$279$	30.0127	+	10.9237i	1.79682	+	0.653987i
$280$		0			0
$281$	−11.8294	+	2.08583i	−0.705680	+	0.124430i	−0.514960	−	0.857214i	$-0.672193\pi$
$281$	−11.8294	+	2.08583i	−0.705680	+	0.124430i	−0.190720	+	0.981645i	$0.561082\pi$
$282$	17.5119	−	37.5543i	1.04282	−	2.23633i
$283$	1.33827	+	15.2965i	0.0795521	+	0.909285i	0.926176	+	0.377092i	$0.123076\pi$
$283$	1.33827	+	15.2965i	0.0795521	+	0.909285i	−0.846624	+	0.532192i	$0.821368\pi$
$284$	5.52064			0.327590
$285$		0			0
$286$	−14.5692			−0.861494
$287$	−1.89524	−	21.6627i	−0.111873	−	1.27871i
$288$	−3.14679	+	6.74832i	−0.185426	+	0.397648i
$289$	−3.55082	+	0.626106i	−0.208872	+	0.0368298i
$290$		0			0
$291$	−23.7390	−	8.64027i	−1.39160	−	0.506502i
$292$	−5.63080	−	1.50877i	−0.329518	−	0.0882940i
$293$	−0.751065	−	2.80301i	−0.0438777	−	0.163754i	0.940511	−	0.339764i	$-0.110347\pi$
$293$	−0.751065	−	2.80301i	−0.0438777	−	0.163754i	−0.984388	+	0.176011i	$0.943681\pi$
$294$	1.20549	+	1.43665i	0.0703058	+	0.0837872i
$295$		0			0
$296$	−3.48044	+	6.02830i	−0.202296	+	0.350388i
$297$	−14.6616	+	54.7180i	−0.850755	+	3.17506i
$298$	3.31315	−	1.54495i	0.191926	−	0.0894965i
$299$	−1.01147	+	5.73631i	−0.0584946	+	0.331740i
$300$		0			0
$301$	14.6170	−	5.32016i	0.842512	−	0.306649i
$302$	−16.8458	+	1.47382i	−0.969368	+	0.0848087i
$303$	35.1856	−	35.1856i	2.02136	−	2.02136i
$304$	4.02917	−	1.66306i	0.231089	−	0.0953829i
$305$		0			0
$306$	17.5166	−	20.8754i	1.00136	−	1.19337i
$307$	21.4864	+	10.0192i	1.22629	+	0.571829i	0.924367	−	0.381503i	$-0.124594\pi$
$307$	21.4864	+	10.0192i	1.22629	+	0.571829i	0.301923	+	0.953332i	$0.402371\pi$
$308$	−5.72926	+	8.18223i	−0.326455	+	0.466226i
$309$	33.1011	+	5.83662i	1.88306	+	0.332034i
$310$		0			0
$311$	−11.1882	−	19.3786i	−0.634427	−	1.09886i	−0.986636	−	0.162939i	$-0.947903\pi$
$311$	−11.1882	−	19.3786i	−0.634427	−	1.09886i	0.352209	−	0.935921i	$-0.385431\pi$
$312$	11.5373	−	3.09141i	0.653171	−	0.175017i
$313$	8.58311	+	0.750925i	0.485146	+	0.0424448i	0.327105	−	0.944988i	$-0.393927\pi$
$313$	8.58311	+	0.750925i	0.485146	+	0.0424448i	0.158040	+	0.987433i	$0.449482\pi$
$314$	6.88053	−	5.77345i	0.388291	−	0.325815i
$315$		0			0
$316$	−13.0489	+	7.53378i	−0.734057	+	0.423808i
$317$	7.38229	+	15.8314i	0.414631	+	0.889178i	0.997084	+	0.0763141i	$0.0243152\pi$
$317$	7.38229	+	15.8314i	0.414631	+	0.889178i	−0.582453	+	0.812864i	$0.697907\pi$
$318$	−1.75210	−	2.50225i	−0.0982526	−	0.140319i
$319$	4.16712	+	23.6329i	0.233314	+	1.32319i
$320$		0			0
$321$	−21.0609	−	17.6722i	−1.17551	−	0.986367i
$322$	2.82383	+	2.82383i	0.157366	+	0.157366i
$323$	−15.8190	+	2.06255i	−0.880190	+	0.114763i
$324$		−	24.1042i		−	1.33912i
$325$		0			0
$326$	−2.23061	−	6.12854i	−0.123542	−	0.339429i
$327$	18.8270	+	13.1828i	1.04114	+	0.729011i
$328$	7.03032	−	4.92268i	0.388184	−	0.271810i
$329$	−11.1102	+	30.5249i	−0.612523	+	1.68289i
$330$		0			0
$331$	26.5373	+	15.3213i	1.45862	+	0.842137i	0.998944	−	0.0459480i	$-0.0146308\pi$
$331$	26.5373	+	15.3213i	1.45862	+	0.842137i	0.459680	+	0.888085i	$0.347964\pi$
$332$	1.57694	−	18.0245i	0.0865457	−	0.989222i
$333$	4.51731	−	51.6331i	0.247547	−	2.82948i
$334$	−9.64242	−	5.56705i	−0.527609	−	0.304615i
$335$		0			0
$336$	2.80081	−	7.69517i	0.152797	−	0.419806i
$337$	7.96380	−	5.57631i	0.433816	−	0.303761i	−0.336194	−	0.941793i	$-0.609140\pi$
$337$	7.96380	−	5.57631i	0.433816	−	0.303761i	0.770010	+	0.638032i	$0.220251\pi$
$338$	−0.538655	−	0.377170i	−0.0292990	−	0.0205153i
$339$	−6.32469	−	17.3770i	−0.343510	−	0.943786i
$340$		0			0
$341$			16.9102i			0.915738i
$342$	−21.9568	+	23.9018i	−1.18729	+	1.29246i
$343$	−13.5809	−	13.5809i	−0.733298	−	0.733298i
$344$	4.70293	+	3.94623i	0.253565	+	0.212766i
$345$		0			0
$346$	1.39354	+	7.90317i	0.0749173	+	0.424877i
$347$	−8.11237	−	11.5857i	−0.435495	−	0.621951i	0.540081	−	0.841613i	$-0.318394\pi$
$347$	−8.11237	−	11.5857i	−0.435495	−	0.621951i	−0.975576	+	0.219662i	$0.929505\pi$
$348$	−8.31455	−	17.8306i	−0.445707	−	0.955821i
$349$	2.06292	−	1.19103i	0.110426	−	0.0637542i	−0.443770	−	0.896141i	$-0.646359\pi$
$349$	2.06292	−	1.19103i	0.110426	−	0.0637542i	0.554196	+	0.832386i	$0.313026\pi$
$350$		0			0
$351$	−40.6798	+	34.1344i	−2.17133	+	1.82196i
$352$	−3.92729	−	0.343593i	−0.209325	−	0.0183136i
$353$	−2.40113	+	0.643381i	−0.127799	+	0.0342437i	−0.322152	−	0.946688i	$-0.604406\pi$
$353$	−2.40113	+	0.643381i	−0.127799	+	0.0342437i	0.194352	+	0.980932i	$0.437739\pi$
$354$	−16.0755	−	27.8435i	−0.854401	−	1.47987i
$355$		0			0
$356$	2.25611	+	0.397812i	0.119573	+	0.0210840i
$357$	−17.1904	+	24.5504i	−0.909811	+	1.29935i
$358$	3.72816	+	1.73847i	0.197039	+	0.0918809i
$359$	−17.3352	+	20.6593i	−0.914916	+	1.09035i	0.0806929	+	0.996739i	$0.474287\pi$
$359$	−17.3352	+	20.6593i	−0.914916	+	1.09035i	−0.995608	+	0.0936149i	$0.970158\pi$
$360$		0			0
$361$	18.9318	−	1.60876i	0.996409	−	0.0846718i
$362$	−14.6975	+	14.6975i	−0.772485	+	0.772485i
$363$	−14.6229	+	1.27933i	−0.767501	+	0.0671476i
$364$	−8.79896	+	3.20256i	−0.461191	+	0.167860i
$365$		0			0
$366$	−1.41767	+	8.03999i	−0.0741027	+	0.420257i
$367$	3.32673	−	1.55128i	0.173654	−	0.0809761i	−0.333847	−	0.942627i	$-0.608347\pi$
$367$	3.32673	−	1.55128i	0.173654	−	0.0809761i	0.507501	+	0.861651i	$0.330569\pi$
$368$	−0.407935	+	1.52243i	−0.0212651	+	0.0793623i
$369$	−31.9522	+	55.3428i	−1.66336	+	2.88103i
$370$		0			0
$371$	1.53928	+	1.83445i	0.0799156	+	0.0952398i
$372$	−3.58815	−	13.3911i	−0.186037	−	0.694298i
$373$	30.3773	+	8.13958i	1.57288	+	0.421452i	0.936712	−	0.350100i	$-0.113852\pi$
$373$	30.3773	+	8.13958i	1.57288	+	0.421452i	0.636167	+	0.771552i	$0.280519\pi$
$374$	13.5580	+	4.93471i	0.701068	+	0.255168i
$375$		0			0
$376$	−12.6259	+	2.22628i	−0.651130	+	0.114812i
$377$	−9.50718	+	20.3882i	−0.489645	+	1.05005i
$378$	3.17316	+	36.2694i	0.163210	+	1.86550i
$379$	23.5065			1.20745			0.603723	−	0.797194i	$-0.293683\pi$
$379$	23.5065			1.20745			0.603723	+	0.797194i	$0.293683\pi$
$380$		0			0
$381$	9.72203			0.498075
$382$	−0.236029	−	2.69782i	−0.0120763	−	0.138033i
$383$	2.24823	−	4.82135i	0.114879	−	0.246359i	−0.840458	−	0.541876i	$-0.817714\pi$
$383$	2.24823	−	4.82135i	0.114879	−	0.246359i	0.955337	+	0.295517i	$0.0954919\pi$
$384$	3.18292	−	0.561234i	0.162428	−	0.0286404i
$385$		0			0
$386$	11.3834	+	4.14322i	0.579400	+	0.210884i
$387$	−44.1548	−	11.8312i	−2.24452	−	0.601416i
$388$	2.02301	+	7.54998i	0.102703	+	0.383292i
$389$	−15.7557	−	18.7770i	−0.798848	−	0.952030i	0.200771	−	0.979638i	$-0.435655\pi$
$389$	−15.7557	−	18.7770i	−0.798848	−	0.952030i	−0.999619	+	0.0276084i	$0.991211\pi$
$390$		0			0
$391$	2.88421	−	4.99559i	0.145861	−	0.252638i
$392$	0.150183	−	0.560489i	0.00758537	−	0.0283090i
$393$	−53.1144	+	24.7677i	−2.67927	+	1.24936i
$394$	3.63478	−	20.6139i	0.183118	−	1.03851i
$395$		0			0
$396$	27.5838	−	10.0397i	1.38614	−	0.504513i
$397$	−32.4668	+	2.84048i	−1.62946	+	0.142560i	−0.864884	−	0.501971i	$-0.832608\pi$
$397$	−32.4668	+	2.84048i	−1.62946	+	0.142560i	−0.764578	+	0.644531i	$0.777053\pi$
$398$	−11.7665	+	11.7665i	−0.589799	+	0.589799i
$399$	21.7651	−	28.2918i	1.08962	−	1.41636i
$400$		0			0
$401$	−11.1685	+	13.3101i	−0.557730	+	0.664676i	−0.969064	−	0.246808i	$-0.920618\pi$
$401$	−11.1685	+	13.3101i	−0.557730	+	0.664676i	0.411335	+	0.911484i	$0.365063\pi$
$402$	33.7947	+	15.7587i	1.68552	+	0.785973i
$403$	−9.09239	+	12.9853i	−0.452924	+	0.646843i
$404$	−15.1620	−	2.67348i	−0.754340	−	0.133010i
$405$		0			0
$406$	7.71162	+	13.3569i	0.382721	+	0.662892i
$407$	26.5068	−	7.10246i	1.31389	−	0.352056i
$408$	−11.7836	−	1.03094i	−0.583377	−	0.0510389i
$409$	−10.1412	+	8.50946i	−0.501449	+	0.420766i	−0.858108	−	0.513469i	$-0.828360\pi$
$409$	−10.1412	+	8.50946i	−0.501449	+	0.420766i	0.356659	+	0.934235i	$0.383916\pi$
$410$		0			0
$411$	−8.68888	+	5.01653i	−0.428591	+	0.247447i
$412$	−4.39507	−	9.42526i	−0.216530	−	0.464349i
$413$	14.4567	+	20.6463i	0.711369	+	1.01594i
$414$	−2.03791	−	11.5576i	−0.100158	−	0.568023i
$415$		0			0
$416$	−2.83101	−	2.37550i	−0.138801	−	0.116468i
$417$	−35.0641	−	35.0641i	−1.71710	−	1.71710i
$418$	−15.8678	−	6.59584i	−0.776118	−	0.322613i
$419$		−	5.51559i		−	0.269454i	−0.990883	−	0.134727i	$-0.956984\pi$
$419$		−	5.51559i		−	0.269454i	0.990883	−	0.134727i	$-0.0430157\pi$
$420$		0			0
$421$	−4.35404	−	11.9626i	−0.212203	−	0.583023i	0.787231	−	0.616658i	$-0.211514\pi$
$421$	−4.35404	−	11.9626i	−0.212203	−	0.583023i	−0.999434	+	0.0336350i	$0.989292\pi$
$422$	−10.9438	−	7.66291i	−0.532734	−	0.373025i
$423$	78.1978	−	54.7547i	3.80211	−	2.66226i
$424$	−0.323254	+	0.888134i	−0.0156986	+	0.0431316i
$425$		0			0
$426$	15.4523	+	8.92141i	0.748668	+	0.432244i
$427$	0.557808	−	6.37578i	0.0269942	−	0.308546i
$428$	−0.741389	+	8.47411i	−0.0358364	+	0.409612i
$429$	−40.7793	−	23.5439i	−1.96884	−	1.13671i
$430$		0			0
$431$	−8.13482	+	22.3502i	−0.391840	+	1.07657i	0.574320	+	0.818631i	$0.305266\pi$
$431$	−8.13482	+	22.3502i	−0.391840	+	1.07657i	−0.966160	+	0.257942i	$0.916956\pi$
$432$	−11.7707	+	8.24193i	−0.566318	+	0.396540i
$433$	11.4226	+	7.99820i	0.548936	+	0.384369i	0.814889	−	0.579617i	$-0.196798\pi$
$433$	11.4226	+	7.99820i	0.548936	+	0.384369i	−0.265953	+	0.963986i	$0.585687\pi$
$434$	3.71715	+	10.2128i	0.178429	+	0.490230i
$435$		0			0
$436$		−	7.11120i		−	0.340565i
$437$	−3.69859	+	5.78969i	−0.176928	+	0.276958i
$438$	−13.3225	−	13.3225i	−0.636573	−	0.636573i
$439$	−11.1903	−	9.38976i	−0.534083	−	0.448149i	0.335426	−	0.942067i	$-0.391120\pi$
$439$	−11.1903	−	9.38976i	−0.534083	−	0.448149i	−0.869508	+	0.493918i	$0.835564\pi$
$440$		0			0
$441$	0.750263	+	4.25495i	0.0357268	+	0.202617i
$442$	7.75782	+	11.0793i	0.369002	+	0.526989i
$443$	4.32586	+	9.27683i	0.205528	+	0.440755i	0.981870	−	0.189556i	$-0.0607049\pi$
$443$	4.32586	+	9.27683i	0.205528	+	0.440755i	−0.776342	+	0.630312i	$0.782927\pi$
$444$	−19.4836	+	11.2488i	−0.924649	+	0.533847i
$445$		0			0
$446$	8.97912	−	7.53438i	0.425174	−	0.356763i
$447$	11.7702	+	1.02976i	0.556712	+	0.0487060i
$448$	−2.44739	+	0.655775i	−0.115628	+	0.0309825i
$449$	−6.29574	−	10.9045i	−0.297114	−	0.514617i	0.678360	−	0.734730i	$-0.262691\pi$
$449$	−6.29574	−	10.9045i	−0.297114	−	0.514617i	−0.975475	+	0.220112i	$0.929358\pi$
$450$		0			0
$451$	−33.3204	−	5.87529i	−1.56900	−	0.276657i
$452$	−3.28175	+	4.68682i	−0.154360	+	0.220450i
$453$	−49.5333	−	23.0978i	−2.32728	−	1.08523i
$454$	−6.61692	+	7.88574i	−0.310548	+	0.370096i
$455$		0			0
$456$	13.9652	+	1.85627i	0.653981	+	0.0869277i
$457$	−17.8182	+	17.8182i	−0.833499	+	0.833499i	−0.987994	−	0.154494i	$-0.950625\pi$
$457$	−17.8182	+	17.8182i	−0.833499	+	0.833499i	0.154494	+	0.987994i	$0.450625\pi$
$458$	−1.66028	+	0.145256i	−0.0775799	+	0.00678736i
$459$	49.4180	−	17.9867i	2.30663	−	0.839546i
$460$		0			0
$461$	2.41039	−	13.6700i	0.112263	−	0.636676i	−0.875806	−	0.482664i	$-0.839669\pi$
$461$	2.41039	−	13.6700i	0.112263	−	0.636676i	0.988069	−	0.154012i	$-0.0492195\pi$
$462$	−29.2588	+	13.6436i	−1.36124	+	0.634758i
$463$	−0.652191	+	2.43401i	−0.0303099	+	0.113118i	−0.979423	−	0.201816i	$-0.935316\pi$
$463$	−0.652191	+	2.43401i	−0.0303099	+	0.113118i	0.949114	+	0.314934i	$0.101982\pi$
$464$	−3.04359	+	5.27166i	−0.141295	+	0.244731i
$465$		0			0
$466$	−1.72528	−	2.05611i	−0.0799223	−	0.0952476i
$467$	−10.3044	−	38.4564i	−0.476829	−	1.77955i	−0.614330	−	0.789049i	$-0.710573\pi$
$467$	−10.3044	−	38.4564i	−0.476829	−	1.77955i	0.137500	−	0.990502i	$-0.456093\pi$
$468$	26.5797	+	7.12201i	1.22865	+	0.329215i
$469$	−27.4690	−	9.99790i	−1.26840	−	0.461660i
$470$		0			0
$471$	28.5886	−	5.04095i	1.31729	−	0.232275i
$472$	−4.20405	+	9.01562i	−0.193507	+	0.414977i
$473$	−2.10940	−	24.1106i	−0.0969904	−	1.10861i
$474$	−48.6986			−2.23680
$475$		0			0
$476$	9.27300			0.425027
$477$	−0.613350	−	7.01062i	−0.0280834	−	0.320994i
$478$	−1.44211	+	3.09262i	−0.0659607	+	0.141453i
$479$	3.02245	−	0.532939i	0.138099	−	0.0243506i	−0.104171	−	0.994559i	$-0.533219\pi$
$479$	3.02245	−	0.532939i	0.138099	−	0.0243506i	0.242270	+	0.970209i	$0.422108\pi$
$480$		0			0
$481$	24.1733	+	8.79838i	1.10221	+	0.401171i
$482$	−4.71703	−	1.26392i	−0.214855	−	0.0575702i
$483$	3.34059	+	12.4673i	0.152002	+	0.567280i
$484$	2.91932	+	3.47911i	0.132696	+	0.158141i
$485$		0			0
$486$	17.3986	−	30.1353i	0.789218	−	1.36696i
$487$	−3.75668	+	14.0201i	−0.170231	+	0.635312i	0.827084	+	0.562079i	$0.189998\pi$
$487$	−3.75668	+	14.0201i	−0.170231	+	0.635312i	−0.997315	+	0.0732327i	$0.976668\pi$
$488$	2.28932	−	1.06753i	0.103633	−	0.0483247i
$489$	3.66029	−	20.7585i	0.165524	−	0.938734i
$490$		0			0
$491$	11.6629	−	4.24495i	0.526340	−	0.191572i	−0.0651635	−	0.997875i	$-0.520757\pi$
$491$	11.6629	−	4.24495i	0.526340	−	0.191572i	0.591503	+	0.806303i	$0.298535\pi$
$492$	27.6330	−	2.41758i	1.24579	−	0.108993i
$493$	15.7530	−	15.7530i	0.709480	−	0.709480i
$494$	−8.63832	−	13.5968i	−0.388656	−	0.611750i
$495$		0			0
$496$	−2.75719	+	3.28590i	−0.123802	+	0.147541i
$497$	−12.6772	−	5.91149i	−0.568651	−	0.265166i
$498$	33.5416	−	47.9024i	1.50304	−	2.14656i
$499$	−24.0876	−	4.24730i	−1.07831	−	0.190135i	−0.393842	−	0.919178i	$-0.628854\pi$
$499$	−24.0876	−	4.24730i	−1.07831	−	0.190135i	−0.684468	+	0.729043i	$0.739965\pi$
$500$		0			0
$501$	−17.9928	−	31.1645i	−0.803860	−	1.39233i
$502$	11.7534	−	3.14931i	0.524580	−	0.140561i
$503$	−10.0264	−	0.877199i	−0.447056	−	0.0391124i	−0.138595	−	0.990349i	$-0.544259\pi$
$503$	−10.0264	−	0.877199i	−0.447056	−	0.0391124i	−0.308462	+	0.951237i	$0.599814\pi$
$504$	14.4521	−	12.1268i	0.643750	−	0.540170i
$505$		0			0
$506$	5.38113	−	3.10680i	0.239221	−	0.138114i
$507$	−0.898190	−	1.92617i	−0.0398900	−	0.0855444i
$508$	−1.72534	−	2.46404i	−0.0765495	−	0.109324i
$509$	−1.85157	−	10.5008i	−0.0820694	−	0.465439i	−0.997951	−	0.0639893i	$-0.979618\pi$
$509$	−1.85157	−	10.5008i	−0.0820694	−	0.465439i	0.915881	−	0.401449i	$-0.131493\pi$
$510$		0			0
$511$	11.3146	+	9.49407i	0.500528	+	0.419993i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−59.7591	+	18.7601i	−2.63843	+	0.828279i
$514$		−	22.6775i		−	1.00026i
$515$		0			0
$516$	6.78641	+	18.6455i	0.298755	+	0.820823i
$517$	41.4022	+	28.9901i	1.82087	+	1.27498i
$518$	14.4473	−	10.1161i	0.634779	−	0.444477i
$519$	−8.87106	+	24.3730i	−0.389396	+	1.06986i
$520$		0			0
$521$	19.5360	+	11.2791i	0.855886	+	0.494146i	0.862632	−	0.505831i	$-0.168814\pi$
$521$	19.5360	+	11.2791i	0.855886	+	0.494146i	−0.00674670	+	0.999977i	$0.502148\pi$
$522$	3.95032	−	45.1524i	0.172901	−	1.97627i
$523$	−0.525149	+	6.00248i	−0.0229632	+	0.262470i	0.976031	+	0.217631i	$0.0698330\pi$
$523$	−0.525149	+	6.00248i	−0.0229632	+	0.262470i	−0.998994	+	0.0448390i	$0.985723\pi$
$524$	15.7034	+	9.06636i	0.686006	+	0.396066i
$525$		0			0
$526$	−3.68544	+	10.1257i	−0.160693	+	0.441500i
$527$	12.8596	−	9.00436i	0.560171	−	0.392236i
$528$	−10.4373	−	7.30826i	−0.454224	−	0.318051i
$529$	7.01681	+	19.2785i	0.305079	+	0.838197i
$530$		0			0
$531$		−	74.0695i		−	3.21434i
$532$	−11.0331	−	0.495496i	−0.478346	−	0.0214825i
$533$	−22.4276	−	22.4276i	−0.971446	−	0.971446i
$534$	5.67199	+	4.75937i	0.245451	+	0.205958i
$535$		0			0
$536$	−2.00341	−	11.3619i	−0.0865339	−	0.490758i
$537$	7.62577	+	10.8907i	0.329076	+	0.469969i
$538$	−2.26013	−	4.84687i	−0.0974413	−	0.208963i
$539$	−1.98108	+	1.14378i	−0.0853313	+	0.0492661i
$540$		0			0
$541$	−25.3958	+	21.3096i	−1.09185	+	0.916173i	−0.996851	−	0.0793037i	$-0.974730\pi$
$541$	−25.3958	+	21.3096i	−1.09185	+	0.916173i	−0.0950024	+	0.995477i	$0.530286\pi$
$542$	30.7656	+	2.69164i	1.32150	+	0.115616i
$543$	−64.8899	+	17.3872i	−2.78469	+	0.746156i
$544$	1.82992	+	3.16951i	0.0784571	+	0.135892i
$545$		0			0
$546$	−29.8037	−	5.25520i	−1.27548	−	0.224902i
$547$	−2.03107	+	2.90067i	−0.0868423	+	0.124024i	−0.860223	−	0.509919i	$-0.829675\pi$
$547$	−2.03107	+	2.90067i	−0.0868423	+	0.124024i	0.773380	+	0.633942i	$0.218564\pi$
$548$	2.81342	+	1.31192i	0.120184	+	0.0560425i
$549$	−12.0898	+	14.4080i	−0.515978	+	0.614919i
$550$		0			0
$551$	−19.5848	+	17.9013i	−0.834342	+	0.762622i
$552$	−3.60208	+	3.60208i	−0.153315	+	0.153315i
$553$	38.0317	−	3.32734i	1.61727	−	0.141493i
$554$	10.1318	−	3.68769i	0.430460	−	0.156675i
$555$		0			0
$556$	−2.66425	+	15.1097i	−0.112989	+	0.640794i
$557$	3.50860	−	1.63609i	0.148664	−	0.0693232i	−0.346862	−	0.937916i	$-0.612753\pi$
$557$	3.50860	−	1.63609i	0.148664	−	0.0693232i	0.495526	+	0.868593i	$0.334975\pi$
$558$	8.26639	−	30.8506i	0.349944	−	1.30601i
$559$	11.3441	−	19.6486i	0.479806	−	0.831048i
$560$		0			0
$561$	29.9745	+	35.7222i	1.26552	+	1.50819i
$562$	3.10889	+	11.6025i	0.131141	+	0.489424i
$563$	−4.19083	−	1.12293i	−0.176622	−	0.0473258i	0.169424	−	0.985543i	$-0.445809\pi$
$563$	−4.19083	−	1.12293i	−0.176622	−	0.0473258i	−0.346046	+	0.938217i	$0.612476\pi$
$564$	−38.9377	−	14.1722i	−1.63957	−	0.596755i
$565$		0			0
$566$	15.1217	−	2.66636i	0.635612	−	0.112076i
$567$	−25.8107	+	55.3513i	−1.08395	+	2.32454i
$568$	−0.481156	−	5.49964i	−0.0201888	−	0.230760i
$569$	10.7883			0.452270			0.226135	−	0.974096i	$-0.427391\pi$
$569$	10.7883			0.452270			0.226135	+	0.974096i	$0.427391\pi$
$570$		0			0
$571$	−20.2403			−0.847029			−0.423514	−	0.905889i	$-0.639204\pi$
$571$	−20.2403			−0.847029			−0.423514	+	0.905889i	$0.639204\pi$
$572$	1.26979	+	14.5138i	0.0530925	+	0.606850i
$573$	3.69906	−	7.93265i	0.154530	−	0.331391i
$574$	−21.4151	+	3.77606i	−0.893850	+	0.157610i
$575$		0			0
$576$	6.99690	+	2.54666i	0.291537	+	0.106111i
$577$	−15.6233	−	4.18625i	−0.650406	−	0.174276i	−0.0814936	−	0.996674i	$-0.525969\pi$
$577$	−15.6233	−	4.18625i	−0.650406	−	0.174276i	−0.568912	+	0.822398i	$0.692636\pi$
$578$	0.933198	+	3.48274i	0.0388159	+	0.144863i
$579$	25.1668	+	29.9926i	1.04590	+	1.24645i
$580$		0			0
$581$	−22.9217	+	39.7016i	−0.950954	+	1.64710i
$582$	−6.53841	+	24.4017i	−0.271026	+	1.01148i
$583$	3.37689	−	1.57467i	0.139857	−	0.0652162i
$584$	−1.01227	+	5.74087i	−0.0418880	+	0.237559i
$585$		0			0
$586$	−2.72689	+	0.992506i	−0.112647	+	0.0410000i
$587$	−39.8641	+	3.48766i	−1.64537	+	0.143951i	−0.871833	−	0.489804i	$-0.837068\pi$
$587$	−39.8641	+	3.48766i	−1.64537	+	0.143951i	−0.773534	+	0.633755i	$0.781513\pi$
$588$	1.32612	−	1.32612i	0.0546882	−	0.0546882i
$589$	−15.7816	+	10.0263i	−0.650268	+	0.413128i
$590$		0			0
$591$	43.4860	−	51.8246i	1.78877	−	2.13178i
$592$	6.30870	+	2.94179i	0.259286	+	0.120907i
$593$	−4.60785	+	6.58069i	−0.189222	+	0.270237i	−0.902542	−	0.430601i	$-0.858302\pi$
$593$	−4.60785	+	6.58069i	−0.189222	+	0.270237i	0.713320	+	0.700838i	$0.247190\pi$
$594$	55.7876	+	9.83686i	2.28899	+	0.403611i
$595$		0			0
$596$	−1.82783	−	3.16590i	−0.0748709	−	0.129680i
$597$	−51.9491	+	13.9197i	−2.12614	+	0.569696i
$598$	5.80264	+	0.507665i	0.237288	+	0.0207600i
$599$	−5.00661	+	4.20105i	−0.204565	+	0.171650i	−0.739314	−	0.673360i	$-0.764850\pi$
$599$	−5.00661	+	4.20105i	−0.204565	+	0.171650i	0.534750	+	0.845010i	$0.320406\pi$
$600$		0			0
$601$	6.10772	−	3.52629i	0.249139	−	0.143841i	−0.370231	−	0.928940i	$-0.620721\pi$
$601$	6.10772	−	3.52629i	0.249139	−	0.143841i	0.619370	+	0.785099i	$0.287388\pi$
$602$	−6.57388	−	14.0977i	−0.267931	−	0.574580i
$603$	49.2731	+	70.3692i	2.00655	+	2.86566i
$604$	2.93642	+	16.6533i	0.119481	+	0.677612i
$605$		0			0
$606$	−38.1183	−	31.9851i	−1.54845	−	1.29931i
$607$	−8.39622	−	8.39622i	−0.340792	−	0.340792i	0.515873	−	0.856665i	$-0.327468\pi$
$607$	−8.39622	−	8.39622i	−0.340792	−	0.340792i	−0.856665	+	0.515873i	$0.827468\pi$
$608$	−2.00789	−	3.86890i	−0.0814309	−	0.156904i
$609$			49.8482i			2.01995i
$610$		0			0
$611$	16.2050	+	44.5228i	0.655584	+	1.80120i
$612$	−22.3227	−	15.6305i	−0.902340	−	0.631825i
$613$	−35.3794	+	24.7729i	−1.42896	+	1.00057i	−0.433936	+	0.900944i	$0.642875\pi$
$613$	−35.3794	+	24.7729i	−1.42896	+	1.00057i	−0.995025	+	0.0996252i	$0.968236\pi$
$614$	8.10846	−	22.2778i	0.327231	−	0.899060i
$615$		0			0
$616$	8.65044	+	4.99433i	0.348536	+	0.201227i
$617$	−0.949913	+	10.8576i	−0.0382421	+	0.437109i	0.952804	+	0.303587i	$0.0981843\pi$
$617$	−0.949913	+	10.8576i	−0.0382421	+	0.437109i	−0.991046	+	0.133522i	$0.957371\pi$
$618$	2.92946	−	33.4839i	0.117840	−	1.34692i
$619$	31.1894	+	18.0072i	1.25361	+	0.723770i	0.971824	−	0.235708i	$-0.0757409\pi$
$619$	31.1894	+	18.0072i	1.25361	+	0.723770i	0.281783	+	0.959478i	$0.409074\pi$
$620$		0			0
$621$	7.74612	−	21.2823i	0.310841	−	0.854029i
$622$	−18.3297	+	12.8346i	−0.734956	+	0.514622i
$623$	−4.75479	−	3.32934i	−0.190497	−	0.133387i
$624$	−4.08519	−	11.2240i	−0.163539	−	0.449318i
$625$		0			0
$626$		−	8.61589i		−	0.344360i
$627$	−33.7551	−	44.1043i	−1.34805	−	1.76136i
$628$	−6.35116	−	6.35116i	−0.253439	−	0.253439i
$629$	−19.5155	−	16.3754i	−0.778134	−	0.652932i
$630$		0			0
$631$	−4.49012	−	25.4647i	−0.178749	−	1.01374i	−0.933727	−	0.357986i	$-0.883464\pi$
$631$	−4.49012	−	25.4647i	−0.178749	−	1.01374i	0.754978	−	0.655750i	$-0.227647\pi$
$632$	8.64240	+	12.3426i	0.343776	+	0.490963i
$633$	−18.2484	−	39.1338i	−0.725308	−	1.55543i
$634$	15.1277	−	8.73399i	0.600798	−	0.346871i
$635$		0			0
$636$	−2.34002	+	1.96351i	−0.0927880	+	0.0778584i
$637$	−2.13626	−	0.186899i	−0.0846418	−	0.00740520i
$638$	23.1798	−	6.21100i	0.917696	−	0.245896i
$639$	20.5532	+	35.5992i	0.813072	+	1.40828i
$640$		0			0
$641$	20.2511	+	3.57082i	0.799872	+	0.141039i	0.558620	−	0.829424i	$-0.311331\pi$
$641$	20.2511	+	3.57082i	0.799872	+	0.141039i	0.241252	+	0.970463i	$0.422442\pi$
$642$	−15.7694	+	22.5210i	−0.622368	+	0.888834i
$643$	14.6946	+	6.85219i	0.579497	+	0.270224i	0.690187	−	0.723631i	$-0.257528\pi$
$643$	14.6946	+	6.85219i	0.579497	+	0.270224i	−0.110690	+	0.993855i	$0.535306\pi$
$644$	2.56697	−	3.05920i	0.101153	−	0.120549i
$645$		0			0
$646$	3.43341	+	15.5790i	0.135086	+	0.612948i
$647$	15.8182	−	15.8182i	0.621877	−	0.621877i	−0.324134	−	0.946011i	$-0.605073\pi$
$647$	15.8182	−	15.8182i	0.621877	−	0.621877i	0.946011	+	0.324134i	$0.105073\pi$
$648$	−24.0125	+	2.10082i	−0.943301	+	0.0825281i
$649$	36.8514	−	13.4128i	1.44654	−	0.526499i
$650$		0			0
$651$	−6.09962	+	34.5927i	−0.239063	+	1.35579i
$652$	−5.91081	+	2.75626i	−0.231485	+	0.107943i
$653$	7.36581	−	27.4896i	0.288246	−	1.07575i	−0.658188	−	0.752854i	$-0.728677\pi$
$653$	7.36581	−	27.4896i	0.288246	−	1.07575i	0.946434	−	0.322896i	$-0.104657\pi$
$654$	11.4918	−	19.9043i	0.449363	−	0.778320i
$655$		0			0
$656$	−5.51668	−	6.57453i	−0.215390	−	0.256692i
$657$	−11.2342	−	41.9266i	−0.438288	−	1.63571i
$658$	31.3771	+	8.40747i	1.22321	+	0.327757i
$659$	−37.6974	−	13.7207i	−1.46848	−	0.534484i	−0.520794	−	0.853682i	$-0.674364\pi$
$659$	−37.6974	−	13.7207i	−1.46848	−	0.534484i	−0.947688	+	0.319199i	$0.896586\pi$
$660$		0			0
$661$	−29.2704	+	5.16115i	−1.13848	+	0.200746i	−0.710943	−	0.703250i	$-0.751731\pi$
$661$	−29.2704	+	5.16115i	−1.13848	+	0.200746i	−0.427542	+	0.903995i	$0.640620\pi$
$662$	12.9502	−	27.7717i	0.503322	−	1.07938i
$663$	3.80994	+	43.5478i	0.147966	+	1.69126i
$664$	−18.0933			−0.702158
$665$		0			0
$666$	−51.8303			−2.00838
$667$	−0.836195	−	9.55775i	−0.0323776	−	0.370077i
$668$	−4.70547	+	10.0909i	−0.182060	+	0.390430i
$669$	37.3083	−	6.57846i	1.44242	−	0.254338i
$670$		0			0
$671$	−9.35761	−	3.40589i	−0.361246	−	0.131483i
$672$	−7.91000	−	2.11948i	−0.305135	−	0.0817606i
$673$	3.54088	+	13.2147i	0.136491	+	0.509391i	0.999987	+	0.00503589i	$0.00160298\pi$
$673$	3.54088	+	13.2147i	0.136491	+	0.509391i	−0.863496	+	0.504355i	$0.831730\pi$
$674$	−6.24918	−	7.44749i	−0.240710	−	0.286866i
$675$		0			0
$676$	−0.328788	+	0.569478i	−0.0126457	+	0.0219030i
$677$	0.691310	−	2.58000i	0.0265692	−	0.0991575i	−0.951368	−	0.308057i	$-0.900321\pi$
$677$	0.691310	−	2.58000i	0.0265692	−	0.0991575i	0.977937	+	0.208899i	$0.0669880\pi$
$678$	−16.7596	+	7.81513i	−0.643648	+	0.300138i
$679$	3.43899	−	19.5035i	0.131976	−	0.748475i
$680$		0			0
$681$	−31.2643	+	11.3793i	−1.19805	+	0.436054i
$682$	16.8458	−	1.47382i	0.645061	−	0.0564355i
$683$	2.33396	−	2.33396i	0.0893066	−	0.0893066i	−0.661042	−	0.750349i	$-0.729886\pi$
$683$	2.33396	−	2.33396i	0.0893066	−	0.0893066i	0.750349	+	0.661042i	$0.229886\pi$
$684$	25.7245	+	19.7901i	0.983602	+	0.756694i
$685$		0			0
$686$	−12.3455	+	14.7129i	−0.471355	+	0.561739i
$687$	−4.88188	−	2.27646i	−0.186255	−	0.0868523i
$688$	3.52132	−	5.02897i	0.134249	−	0.191728i
$689$	3.43978	+	0.606526i	0.131045	+	0.0231068i
$690$		0			0
$691$	15.0419	+	26.0534i	0.572222	+	0.991118i	0.996337	+	0.0855098i	$0.0272519\pi$
$691$	15.0419	+	26.0534i	0.572222	+	0.991118i	−0.424115	+	0.905608i	$0.639415\pi$
$692$	7.75164	−	2.07705i	0.294673	−	0.0789574i
$693$	−74.0920	−	6.48221i	−2.81452	−	0.246239i
$694$	−10.8345	+	9.09126i	−0.411274	+	0.345100i
$695$		0			0
$696$	−17.0381	+	9.83695i	−0.645828	+	0.372869i
$697$	13.2746	+	28.4674i	0.502810	+	1.07828i
$698$	−1.36629	−	1.95126i	−0.0517148	−	0.0738565i
$699$	−1.50639	−	8.54316i	−0.0569769	−	0.323132i
$700$		0			0
$701$	1.51859	+	1.27425i	0.0573562	+	0.0481276i	0.671015	−	0.741444i	$-0.265859\pi$
$701$	1.51859	+	1.27425i	0.0573562	+	0.0481276i	−0.613659	+	0.789571i	$0.710303\pi$
$702$	37.5500	+	37.5500i	1.41723	+	1.41723i
$703$	22.3447	+	20.5265i	0.842747	+	0.774171i
$704$			3.94229i			0.148581i
$705$		0			0
$706$	0.850205	+	2.33592i	0.0319979	+	0.0879134i
$707$	31.9543	+	22.3747i	1.20177	+	0.841485i
$708$	−26.3365	+	18.4410i	−0.989786	+	0.693056i
$709$	−0.457833	+	1.25789i	−0.0171943	+	0.0472409i	−0.947993	−	0.318292i	$-0.896891\pi$
$709$	−0.457833	+	1.25789i	−0.0171943	+	0.0472409i	0.930799	+	0.365533i	$0.119113\pi$
$710$		0			0
$711$	−97.1613	−	56.0961i	−3.64383	−	2.10377i
$712$	0.199666	−	2.28219i	0.00748280	−	0.0855287i
$713$	0.589238	−	6.73502i	0.0220671	−	0.252228i
$714$	25.9552	+	14.9853i	0.971350	+	0.560809i
$715$		0			0
$716$	1.40692	−	3.86549i	0.0525792	−	0.144460i
$717$	−9.03419	+	6.32581i	−0.337388	+	0.236242i
$718$	22.0915	+	15.4686i	0.824448	+	0.577284i
$719$	12.0709	+	33.1646i	0.450170	+	1.23683i	0.932605	+	0.360900i	$0.117530\pi$
$719$	12.0709	+	33.1646i	0.450170	+	1.23683i	−0.482435	+	0.875932i	$0.660247\pi$
$720$		0			0
$721$			26.3497i			0.981316i
$722$	−3.25266	−	18.7195i	−0.121051	−	0.696668i
$723$	−11.1605	−	11.1605i	−0.415064	−	0.415064i
$724$	15.9226	+	13.3606i	0.591758	+	0.496544i
$725$		0			0
$726$	2.54893	+	14.4557i	0.0945998	+	0.536502i
$727$	5.97690	+	8.53589i	0.221671	+	0.316579i	0.914548	−	0.404477i	$-0.132546\pi$
$727$	5.97690	+	8.53589i	0.221671	+	0.316579i	−0.692878	+	0.721055i	$0.743657\pi$
$728$	3.95725	+	8.48636i	0.146666	+	0.314525i
$729$	34.7732	−	20.0763i	1.28790	−	0.743567i
$730$		0			0
$731$	−17.2120	+	14.4425i	−0.636607	+	0.534177i
$732$	8.13296	+	0.711542i	0.300603	+	0.0262993i
$733$	1.49475	−	0.400516i	0.0552097	−	0.0147934i	−0.231108	−	0.972928i	$-0.574235\pi$
$733$	1.49475	−	0.400516i	0.0552097	−	0.0147934i	0.286318	+	0.958135i	$0.407569\pi$
$734$	−1.83532	−	3.17887i	−0.0677429	−	0.117334i
$735$		0			0
$736$	1.55219	+	0.273694i	0.0572146	+	0.0100885i
$737$	−26.0879	+	37.2573i	−0.960959	+	1.37239i
$738$	57.9170	+	27.0071i	2.13195	+	0.994146i
$739$	−11.1902	+	13.3359i	−0.411638	+	0.490571i	−0.931532	−	0.363660i	$-0.881527\pi$
$739$	−11.1902	+	13.3359i	−0.411638	+	0.490571i	0.519894	+	0.854231i	$0.325971\pi$
$740$		0			0
$741$	−2.20616	−	52.0172i	−0.0810452	−	1.91090i
$742$	1.69331	−	1.69331i	0.0621633	−	0.0621633i
$743$	8.20317	−	0.717685i	0.300945	−	0.0263293i	0.0643168	−	0.997930i	$-0.479513\pi$
$743$	8.20317	−	0.717685i	0.300945	−	0.0263293i	0.236628	+	0.971600i	$0.423958\pi$
$744$	−13.0275	+	4.74161i	−0.477610	+	0.173836i
$745$		0			0
$746$	5.46105	−	30.9712i	0.199943	−	1.13393i
$747$	122.100	−	56.9360i	4.46739	−	2.08318i
$748$	3.73428	−	13.9365i	0.136539	−	0.509569i
$749$	10.7765	−	18.6655i	0.393766	−	0.682022i
$750$		0			0
$751$	3.83062	+	4.56515i	0.139781	+	0.166585i	0.831393	−	0.555684i	$-0.187544\pi$
$751$	3.83062	+	4.56515i	0.139781	+	0.166585i	−0.691612	+	0.722269i	$0.743099\pi$
$752$	3.31823	+	12.3838i	0.121003	+	0.451591i
$753$	37.9872	+	10.1786i	1.38433	+	0.370930i
$754$	21.1392	+	7.69405i	0.769846	+	0.280201i
$755$		0			0
$756$	35.8548	−	6.32218i	1.30403	−	0.229935i
$757$	6.60826	−	14.1715i	0.240181	−	0.515070i	−0.748857	−	0.662732i	$-0.769397\pi$
$757$	6.60826	−	14.1715i	0.240181	−	0.515070i	0.989038	+	0.147662i	$0.0471747\pi$
$758$	−2.04872	−	23.4170i	−0.0744130	−	0.850545i
$759$	20.0825			0.728947
$760$		0			0
$761$	47.0910			1.70705			0.853523	−	0.521055i	$-0.174461\pi$
$761$	47.0910			1.70705			0.853523	+	0.521055i	$0.174461\pi$
$762$	−0.847330	−	9.68503i	−0.0306955	−	0.350852i
$763$	−7.61464	+	16.3297i	−0.275669	+	0.591173i
$764$	−2.66698	+	0.470261i	−0.0964881	+	0.0170135i
$765$		0			0
$766$	−4.99895	−	1.81947i	−0.180619	−	0.0657400i
$767$	35.5100	+	9.51487i	1.28219	+	0.343562i
$768$	−0.836508	−	3.12189i	−0.0301849	−	0.112652i
$769$	31.2892	+	37.2890i	1.12832	+	1.34468i	0.931290	+	0.364278i	$0.118684\pi$
$769$	31.2892	+	37.2890i	1.12832	+	1.34468i	0.197027	+	0.980398i	$0.436871\pi$
$770$		0			0
$771$	36.6470	−	63.4744i	1.31981	−	2.28598i
$772$	3.13532	−	11.7012i	0.112843	−	0.421135i
$773$	27.1557	−	12.6629i	0.976722	−	0.455453i	0.132346	−	0.991204i	$-0.457749\pi$
$773$	27.1557	−	12.6629i	0.976722	−	0.455453i	0.844376	+	0.535751i	$0.179971\pi$
$774$	−7.93788	+	45.0180i	−0.285321	+	1.61814i
$775$		0			0
$776$	7.34493	−	2.67334i	0.263668	−	0.0959672i
$777$	56.7859	−	4.96813i	2.03718	−	0.178231i
$778$	−17.3323	+	17.3323i	−0.621393	+	0.621393i
$779$	−14.2731	−	34.5801i	−0.511386	−	1.23896i
$780$		0			0
$781$	−13.9896	+	16.6722i	−0.500588	+	0.596577i
$782$	−5.22796	−	2.43784i	−0.186951	−	0.0871768i
$783$	50.1702	−	71.6505i	1.79294	−	2.56058i
$784$	−0.571446	−	0.100761i	−0.0204088	−	0.00359862i
$785$		0			0
$786$	29.3027	+	50.7537i	1.04519	+	1.81032i
$787$	−32.6623	+	8.75182i	−1.16428	+	0.311969i	−0.788675	−	0.614810i	$-0.789233\pi$
$787$	−32.6623	+	8.75182i	−1.16428	+	0.311969i	−0.375608	+	0.926779i	$0.622566\pi$
$788$	−20.8522	−	1.82433i	−0.742829	−	0.0649891i
$789$	−26.6788	+	22.3861i	−0.949789	+	0.796968i
$790$		0			0
$791$	12.5546	−	7.24841i	0.446391	−	0.257724i
$792$	−12.4056	−	26.6038i	−0.440813	−	0.945326i
$793$	−5.35437	−	7.64684i	−0.190139	−	0.271547i
$794$	5.65934	+	32.0957i	0.200842	+	1.13903i
$795$		0			0
$796$	12.7472	+	10.6962i	0.451812	+	0.379116i
$797$	8.46761	+	8.46761i	0.299938	+	0.299938i	0.840989	−	0.541051i	$-0.181974\pi$
$797$	8.46761	+	8.46761i	0.299938	+	0.299938i	−0.541051	+	0.840989i	$0.681974\pi$
$798$	−30.0811	−	19.2165i	−1.06486	−	0.680257i
$799$		−	46.9215i		−	1.65996i
$800$		0			0
$801$	5.83417	+	16.0293i	0.206140	+	0.566366i
$802$	14.2329	+	9.96597i	0.502581	+	0.351911i
$803$	18.8252	−	13.1815i	0.664327	−	0.465167i
$804$	12.7533	−	35.0395i	0.449776	−	1.23575i
$805$		0			0
$806$	13.7283	+	7.92605i	0.483559	+	0.279183i
$807$	1.50645	−	17.2188i	0.0530297	−	0.606132i
$808$	−1.34184	+	15.3374i	−0.0472059	+	0.539566i
$809$	−2.66522	−	1.53877i	−0.0937041	−	0.0541001i	0.452416	−	0.891807i	$-0.350562\pi$
$809$	−2.66522	−	1.53877i	−0.0937041	−	0.0541001i	−0.546120	+	0.837707i	$0.683896\pi$
$810$		0			0
$811$	15.4853	−	42.5455i	0.543762	−	1.49398i	−0.298234	−	0.954493i	$-0.596398\pi$
$811$	15.4853	−	42.5455i	0.543762	−	1.49398i	0.841997	−	0.539482i	$-0.181380\pi$
$812$	12.6340	−	8.84640i	0.443366	−	0.310448i
$813$	81.7636	+	57.2515i	2.86757	+	2.00790i
$814$	−9.38565	−	25.7869i	−0.328967	−	0.903829i
$815$		0			0
$816$			11.8287i			0.414086i
$817$	21.2507	−	16.2642i	0.743467	−	0.569012i
$818$	9.36094	+	9.36094i	0.327297	+	0.327297i
$819$	−53.4096	−	44.8160i	−1.86628	−	1.56600i
$820$		0			0
$821$	2.49565	+	14.1535i	0.0870987	+	0.493962i	0.996884	+	0.0788822i	$0.0251351\pi$
$821$	2.49565	+	14.1535i	0.0870987	+	0.493962i	−0.909785	+	0.415079i	$0.863754\pi$
$822$	5.75473	+	8.21860i	0.200719	+	0.286657i
$823$	−15.4765	−	33.1894i	−0.539476	−	1.15691i	−0.967437	−	0.253113i	$-0.918546\pi$
$823$	−15.4765	−	33.1894i	−0.539476	−	1.15691i	0.427961	−	0.903797i	$-0.359232\pi$
$824$	−9.00634	+	5.19981i	−0.313751	+	0.181144i
$825$		0			0
$826$	19.3078	−	16.2012i	0.671804	−	0.563710i
$827$	−6.42486	−	0.562102i	−0.223414	−	0.0195462i	−0.0251010	−	0.999685i	$-0.507991\pi$
$827$	−6.42486	−	0.562102i	−0.223414	−	0.0195462i	−0.198313	+	0.980139i	$0.563546\pi$
$828$	−11.3360	+	3.03746i	−0.393952	+	0.105559i
$829$	0.793407	+	1.37422i	0.0275562	+	0.0477287i	0.879475	−	0.475946i	$-0.157894\pi$
$829$	0.793407	+	1.37422i	0.0275562	+	0.0477287i	−0.851918	+	0.523674i	$0.824561\pi$
$830$		0			0
$831$	34.3184	+	6.05127i	1.19049	+	0.209916i
$832$	−2.11972	+	3.02727i	−0.0734880	+	0.104952i
$833$	1.92469	+	0.897498i	0.0666866	+	0.0310965i
$834$	−31.8747	+	37.9868i	−1.10373	+	1.31537i
$835$		0			0
$836$	−5.18777	+	16.3823i	−0.179423	+	0.566592i
$837$	43.5836	−	43.5836i	1.50647	−	1.50647i
$838$	−5.49460	+	0.480715i	−0.189808	+	0.0166060i
$839$	−38.8710	+	14.1479i	−1.34198	+	0.488440i	−0.910435	−	0.413653i	$-0.864253\pi$
$839$	−38.8710	+	14.1479i	−1.34198	+	0.488440i	−0.431543	+	0.902092i	$0.642031\pi$
$840$		0			0
$841$	1.39854	−	7.93150i	0.0482255	−	0.273500i
$842$	−11.5376	+	5.38009i	−0.397613	+	0.185410i
$843$	−10.0480	+	37.4996i	−0.346071	+	1.29156i
$844$	−6.67994	+	11.5700i	−0.229933	+	0.398255i
$845$		0			0
$846$	−61.3617	−	73.1280i	−2.10966	−	2.51419i
$847$	−2.97831	−	11.1152i	−0.102336	−	0.381922i
$848$	0.912928	+	0.244618i	0.0313501	+	0.00840022i
$849$	46.6346	+	16.9736i	1.60050	+	0.582533i
$850$		0			0
$851$	−10.8046	+	1.90515i	−0.370378	+	0.0653077i
$852$	7.54070	−	16.1711i	0.258340	−	0.554012i
$853$	−1.04460	−	11.9398i	−0.0357664	−	0.408812i	−0.992882	−	0.119105i	$-0.961998\pi$
$853$	−1.04460	−	11.9398i	−0.0357664	−	0.408812i	0.957115	−	0.289707i	$-0.0935579\pi$
$854$	−6.40013			−0.219008
$855$		0			0
$856$	8.50648			0.290746
$857$	3.10606	+	35.5024i	0.106101	+	1.21274i	0.843443	+	0.537219i	$0.180525\pi$
$857$	3.10606	+	35.5024i	0.106101	+	1.21274i	−0.737342	+	0.675520i	$0.763919\pi$
$858$	−19.9002	+	42.6761i	−0.679382	+	1.45694i
$859$	−42.8794	+	7.56079i	−1.46303	+	0.257971i	−0.847773	−	0.530359i	$-0.822057\pi$
$859$	−42.8794	+	7.56079i	−1.46303	+	0.257971i	−0.615252	+	0.788330i	$0.710946\pi$
$860$		0			0
$861$	−66.0433	−	24.0378i	−2.25075	−	0.819206i
$862$	22.9742	+	6.15591i	0.782503	+	0.209671i
$863$	−5.41950	−	20.2259i	−0.184482	−	0.688496i	−0.994741	−	0.102424i	$-0.967340\pi$
$863$	−5.41950	−	20.2259i	−0.184482	−	0.688496i	0.810259	−	0.586072i	$-0.199326\pi$
$864$	9.23645	+	11.0076i	0.314231	+	0.374485i
$865$		0			0
$866$	6.97222	−	12.0762i	0.236926	−	0.410367i
$867$	−3.01611	+	11.2563i	−0.102433	+	0.382284i
$868$	9.84996	−	4.59311i	0.334329	−	0.155900i
$869$	10.3148	−	58.4983i	0.349906	−	1.98442i
$870$		0			0
$871$	−40.0656	+	14.5827i	−1.35757	+	0.494115i
$872$	−7.08414	+	0.619782i	−0.239899	+	0.0209885i
$873$	−41.1535	+	41.1535i	−1.39283	+	1.39283i
$874$	6.09001	+	3.17991i	0.205998	+	0.107562i
$875$		0			0
$876$	−12.1107	+	14.4329i	−0.409181	+	0.487643i
$877$	−27.9030	−	13.0114i	−0.942218	−	0.439363i	−0.110074	−	0.993923i	$-0.535109\pi$
$877$	−27.9030	−	13.0114i	−0.942218	−	0.439363i	−0.832144	+	0.554560i	$0.812887\pi$
$878$	−8.37873	+	11.9661i	−0.282768	+	0.403835i
$879$	−9.23648	−	1.62864i	−0.311539	−	0.0549327i
$880$		0			0
$881$	−12.2260	−	21.1761i	−0.411906	−	0.713442i	0.583192	−	0.812334i	$-0.301803\pi$
$881$	−12.2260	−	21.1761i	−0.411906	−	0.713442i	−0.995098	+	0.0988924i	$0.968470\pi$
$882$	4.17337	−	1.11825i	0.140525	−	0.0376535i
$883$	−6.08198	−	0.532104i	−0.204675	−	0.0179067i	−0.0156428	−	0.999878i	$-0.504979\pi$
$883$	−6.08198	−	0.532104i	−0.204675	−	0.0179067i	−0.189032	+	0.981971i	$0.560535\pi$
$884$	10.3610	−	8.69393i	0.348479	−	0.292408i
$885$		0			0
$886$	8.86450	−	5.11792i	0.297809	−	0.171940i
$887$	−18.7865	−	40.2877i	−0.630787	−	1.35273i	−0.918656	−	0.395058i	$-0.870724\pi$
$887$	−18.7865	−	40.2877i	−0.630787	−	1.35273i	0.287869	−	0.957670i	$-0.407053\pi$
$888$	12.9041	+	18.4290i	0.433035	+	0.618438i
$889$	1.32346	+	7.50573i	0.0443875	+	0.251734i
$890$		0			0
$891$	72.7941	+	61.0815i	2.43869	+	2.04631i
$892$	−8.28829	−	8.28829i	−0.277512	−	0.277512i
$893$	−2.50722	+	55.8277i	−0.0839009	+	1.86820i
$894$		−	11.8152i		−	0.395158i
$895$		0			0
$896$	0.866583	+	2.38092i	0.0289505	+	0.0795409i
$897$	15.4213	+	10.7981i	0.514901	+	0.360537i
$898$	−10.3143	+	7.22218i	−0.344194	+	0.241007i
$899$	8.93035	−	24.5359i	0.297844	−	0.818319i
$900$		0			0
$901$	−2.99561	−	1.72951i	−0.0997981	−	0.0576185i
$902$	−2.94887	+	33.7057i	−0.0981865	+	1.12228i
$903$	4.38170	−	50.0831i	0.145814	−	1.66666i
$904$	4.95501	+	2.86078i	0.164801	+	0.0951480i
$905$		0			0
$906$	−18.6928	+	51.3579i	−0.621025	+	1.70625i
$907$	−38.1001	+	26.6780i	−1.26509	+	0.885828i	−0.996988	−	0.0775610i	$-0.975287\pi$
$907$	−38.1001	+	26.6780i	−1.26509	+	0.885828i	−0.268106	+	0.963389i	$0.586398\pi$
$908$	8.43244	+	5.90446i	0.279840	+	0.195946i
$909$	−39.2083	−	107.724i	−1.30046	−	3.57297i
$910$		0			0
$911$			5.31610i			0.176130i	0.996115	+	0.0880651i	$0.0280684\pi$
$911$			5.31610i			0.176130i	−0.996115	+	0.0880651i	$0.971932\pi$
$912$	0.632056	−	14.0739i	0.0209295	−	0.466032i
$913$	50.4374	+	50.4374i	1.66923	+	1.66923i
$914$	19.3033	+	16.1974i	0.638497	+	0.535763i
$915$		0			0
$916$	0.289406	+	1.64130i	0.00956225	+	0.0542302i
$917$	−26.3520	−	37.6345i	−0.870219	−	1.24280i
$918$	−22.2253	−	47.6623i	−0.733544	−	1.57309i
$919$	−50.4140	+	29.1066i	−1.66301	+	0.960137i	−0.691737	+	0.722150i	$0.743154\pi$
$919$	−50.4140	+	29.1066i	−1.66301	+	0.960137i	−0.971268	+	0.237987i	$0.923512\pi$
$920$		0			0
$921$	58.6968	−	49.2525i	1.93413	−	1.62292i
$922$	−13.8281	−	1.20980i	−0.455403	−	0.0398426i
$923$	−19.7070	+	5.28047i	−0.648663	+	0.173809i
$924$	16.1418	+	27.9584i	0.531025	+	0.919763i
$925$		0			0
$926$	2.48159	+	0.437571i	0.0815501	+	0.0143795i
$927$	44.4149	−	63.4311i	1.45878	−	2.08335i
$928$	5.51687	+	2.57256i	0.181100	+	0.0844483i
$929$	23.9686	−	28.5646i	0.786383	−	0.937175i	−0.212820	−	0.977091i	$-0.568265\pi$
$929$	23.9686	−	28.5646i	0.786383	−	0.937175i	0.999203	+	0.0399164i	$0.0127092\pi$
$930$		0			0
$931$	−2.24206	−	1.17070i	−0.0734805	−	0.0383680i
$932$	−1.89792	+	1.89792i	−0.0621685	+	0.0621685i
$933$	−72.0460	+	6.30321i	−2.35868	+	0.206358i
$934$	−37.4120	+	13.6169i	−1.22416	+	0.445557i
$935$		0			0
$936$	4.77834	−	27.0993i	0.156185	−	0.885768i
$937$	−3.59828	+	1.67790i	−0.117551	+	0.0548147i	−0.480504	−	0.876993i	$-0.659546\pi$
$937$	−3.59828	+	1.67790i	−0.117551	+	0.0548147i	0.362953	+	0.931807i	$0.381768\pi$
$938$	−7.56578	+	28.2359i	−0.247031	+	0.921934i
$939$	13.9234	−	24.1160i	0.454372	−	0.786995i
$940$		0			0
$941$	31.8602	+	37.9696i	1.03861	+	1.23777i	0.970754	+	0.240077i	$0.0771728\pi$
$941$	31.8602	+	37.9696i	1.03861	+	1.23777i	0.0678605	+	0.997695i	$0.478383\pi$
$942$	−7.51343	−	28.0405i	−0.244801	−	0.913608i
$943$	13.0662	+	3.50107i	0.425494	+	0.114011i
$944$	9.34772	+	3.40229i	0.304242	+	0.110735i
$945$		0			0
$946$	−23.8350	+	4.20275i	−0.774942	+	0.136643i
$947$	−15.8773	+	34.0490i	−0.515944	+	1.10644i	0.459899	+	0.887971i	$0.347885\pi$
$947$	−15.8773	+	34.0490i	−0.515944	+	1.10644i	−0.975843	+	0.218473i	$0.929892\pi$
$948$	4.24437	+	48.5133i	0.137851	+	1.57564i
$949$	21.5433			0.699326
$950$		0			0
$951$	56.4569			1.83074
$952$	−0.808195	−	9.23771i	−0.0261938	−	0.299396i
$953$	4.74708	−	10.1801i	0.153773	−	0.329767i	−0.814297	−	0.580449i	$-0.802877\pi$
$953$	4.74708	−	10.1801i	0.153773	−	0.329767i	0.968070	+	0.250682i	$0.0806548\pi$
$954$	−6.93049	+	1.22203i	−0.224383	+	0.0395647i
$955$		0			0
$956$	3.20654	+	1.16709i	0.103707	+	0.0377462i
$957$	74.9175	+	20.0741i	2.42174	+	0.648903i
$958$	−0.794334	−	2.96450i	−0.0256638	−	0.0957785i
$959$	−5.05575	−	6.02521i	−0.163259	−	0.194564i
$960$		0			0
$961$	−6.30038	+	10.9126i	−0.203238	+	0.352019i
$962$	6.65805	−	24.8482i	0.214664	−	0.801138i
$963$	−57.4044	+	26.7681i	−1.84983	+	0.862591i
$964$	−0.847999	+	4.80924i	−0.0273122	+	0.154895i
$965$		0			0
$966$	12.1287	−	4.41447i	0.390233	−	0.142033i
$967$	−29.3776	+	2.57021i	−0.944721	+	0.0826524i	−0.549095	−	0.835760i	$-0.685028\pi$
$967$	−29.3776	+	2.57021i	−0.944721	+	0.0826524i	−0.395625	+	0.918412i	$0.629472\pi$
$968$	3.21144	−	3.21144i	0.103219	−	0.103219i
$969$	−15.5657	+	49.1542i	−0.500041	+	1.57906i
$970$		0			0
$971$	−23.8812	+	28.4605i	−0.766385	+	0.913342i	−0.998234	−	0.0594102i	$-0.981078\pi$
$971$	−23.8812	+	28.4605i	−0.766385	+	0.913342i	0.231849	+	0.972752i	$0.425522\pi$
$972$	−31.5370	−	14.7060i	−1.01155	−	0.471694i
$973$	22.2974	−	31.8440i	0.714822	−	1.02087i
$974$	14.2942	+	2.52045i	0.458015	+	0.0807604i
$975$		0			0
$976$	−1.26299	−	2.18757i	−0.0404274	−	0.0700223i
$977$	−7.63544	+	2.04591i	−0.244279	+	0.0654544i	−0.378881	−	0.925445i	$-0.623691\pi$
$977$	−7.63544	+	2.04591i	−0.244279	+	0.0654544i	0.134602	+	0.990900i	$0.457024\pi$
$978$	−20.9986	−	1.83714i	−0.671460	−	0.0587451i
$979$	−6.91848	+	5.80529i	−0.221115	+	0.185538i
$980$		0			0
$981$	45.8557	−	26.4748i	1.46406	−	0.845275i
$982$	−5.24529	−	11.2486i	−0.167384	−	0.358956i
$983$	−5.02927	−	7.18255i	−0.160409	−	0.229088i	0.730900	−	0.682485i	$-0.239101\pi$
$983$	−5.02927	−	7.18255i	−0.160409	−	0.229088i	−0.891309	+	0.453397i	$0.850212\pi$
$984$	−4.81676	−	27.3172i	−0.153553	−	0.870840i
$985$		0			0
$986$	−17.0660	−	14.3201i	−0.543493	−	0.456045i
$987$	74.2383	+	74.2383i	2.36303	+	2.36303i
$988$	−12.7922	+	9.79049i	−0.406974	+	0.311477i
$989$			9.67630i			0.307688i
$990$		0			0
$991$	−9.03655	−	24.8277i	−0.287055	−	0.788678i	−0.996475	−	0.0838918i	$-0.973265\pi$
$991$	−9.03655	−	24.8277i	−0.287055	−	0.788678i	0.709419	−	0.704787i	$-0.248957\pi$
$992$	3.51370	+	2.46032i	0.111560	+	0.0781152i
$993$	81.1269	−	56.8057i	2.57448	−	1.80267i
$994$	−4.78410	+	13.1442i	−0.151742	+	0.416909i
$995$		0			0
$996$	−50.6434	−	29.2390i	−1.60470	−	0.926473i
$997$	−5.05084	+	57.7314i	−0.159962	+	1.82837i	0.315832	+	0.948815i	$0.397716\pi$
$997$	−5.05084	+	57.7314i	−0.159962	+	1.82837i	−0.475794	+	0.879557i	$0.657839\pi$
$998$	−2.13176	+	24.3661i	−0.0674797	+	0.771297i
$999$	−86.6229	−	50.0117i	−2.74063	−	1.58230i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.d.193.4	✓	96
5.2	odd	4	inner	950.2.bb.d.307.5	yes	96
5.3	odd	4	inner	950.2.bb.d.307.4	yes	96
5.4	even	2	inner	950.2.bb.d.193.5	yes	96
19.13	odd	18	inner	950.2.bb.d.393.5	yes	96
95.13	even	36	inner	950.2.bb.d.507.5	yes	96
95.32	even	36	inner	950.2.bb.d.507.4	yes	96
95.89	odd	18	inner	950.2.bb.d.393.4	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.bb.d.193.4	✓	96	1.1	even	1	trivial
950.2.bb.d.193.5	yes	96	5.4	even	2	inner
950.2.bb.d.307.4	yes	96	5.3	odd	4	inner
950.2.bb.d.307.5	yes	96	5.2	odd	4	inner
950.2.bb.d.393.4	yes	96	95.89	odd	18	inner
950.2.bb.d.393.5	yes	96	19.13	odd	18	inner
950.2.bb.d.507.4	yes	96	95.32	even	36	inner
950.2.bb.d.507.5	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)

\(f(q)\)	\(=\)	\(q+(-0.0871557 - 0.996195i) q^{2} +(1.36591 - 2.92920i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-3.03710 - 1.10542i) q^{6} +(2.44739 + 0.655775i) q^{7} +(0.258819 + 0.965926i) q^{8} +(-4.78616 - 5.70392i) q^{9} +O(q^{10})\)	\(q+(-0.0871557 - 0.996195i) q^{2} +(1.36591 - 2.92920i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-3.03710 - 1.10542i) q^{6} +(2.44739 + 0.655775i) q^{7} +(0.258819 + 0.965926i) q^{8} +(-4.78616 - 5.70392i) q^{9} +(1.97115 - 3.41412i) q^{11} +(-0.836508 + 3.12189i) q^{12} +(3.34937 - 1.56183i) q^{13} +(0.439976 - 2.49523i) q^{14} +(0.939693 - 0.342020i) q^{16} +(-3.64591 + 0.318976i) q^{17} +(-5.26508 + 5.26508i) q^{18} +(4.35498 - 0.184704i) q^{19} +(5.26381 - 6.27316i) q^{21} +(-3.57293 - 1.66608i) q^{22} +(-0.904036 + 1.29110i) q^{23} +(3.18292 + 0.561234i) q^{24} +(-1.84781 - 3.20050i) q^{26} +(-13.8797 + 3.71907i) q^{27} +(-2.52408 - 0.220828i) q^{28} +(-4.66306 + 3.91277i) q^{29} +(-3.71476 + 2.14472i) q^{31} +(-0.422618 - 0.906308i) q^{32} +(-7.30826 - 10.4373i) q^{33} +(0.635524 + 3.60423i) q^{34} +(5.70392 + 4.78616i) q^{36} +(4.92208 + 4.92208i) q^{37} +(-0.563563 - 4.32231i) q^{38} -11.9443i q^{39} +(-2.93537 - 8.06485i) q^{41} +(-6.70806 - 4.69704i) q^{42} +(5.02897 - 3.52132i) q^{43} +(-1.34834 + 3.70454i) q^{44} +(1.36498 + 0.788070i) q^{46} +(-1.11739 + 12.7719i) q^{47} +(0.281689 - 3.21972i) q^{48} +(-0.502521 - 0.290131i) q^{49} +(-4.04564 + 11.1153i) q^{51} +(-3.02727 + 2.11972i) q^{52} +(0.774207 + 0.542106i) q^{53} +(4.91461 + 13.5028i) q^{54} +2.53372i q^{56} +(5.40748 - 13.0089i) q^{57} +(4.30429 + 4.30429i) q^{58} +(7.62033 + 6.39421i) q^{59} +(-0.438632 - 2.48761i) q^{61} +(2.46032 + 3.51370i) q^{62} +(-7.97309 - 17.0983i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(-9.76060 + 8.19011i) q^{66} +(-11.4932 - 1.00553i) q^{67} +(3.53513 - 0.947235i) q^{68} +(2.54706 + 4.41163i) q^{69} +(-5.43677 - 0.958650i) q^{71} +(4.27082 - 6.09936i) q^{72} +(5.28326 + 2.46362i) q^{73} +(4.47437 - 5.33234i) q^{74} +(-4.25675 + 0.938133i) q^{76} +(7.06305 - 7.06305i) q^{77} +(-11.8988 + 1.04101i) q^{78} +(14.1589 - 5.15341i) q^{79} +(-4.18566 + 23.7380i) q^{81} +(-7.77833 + 3.62709i) q^{82} +(-4.68290 + 17.4768i) q^{83} +(-4.09452 + 7.09191i) q^{84} +(-3.94623 - 4.70293i) q^{86} +(5.09198 + 19.0035i) q^{87} +(3.80796 + 1.02034i) q^{88} +(-2.15275 - 0.783537i) q^{89} +(9.22140 - 1.62598i) q^{91} +(0.666105 - 1.42847i) q^{92} +(1.20829 + 13.8108i) q^{93} +12.8207 q^{94} -3.23202 q^{96} +(-0.681237 - 7.78657i) q^{97} +(-0.245229 + 0.525895i) q^{98} +(-28.9081 + 5.09728i) 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

Related objects

Downloads

Learn more