LMFDB - Embedded newform 1045.2.f.b.626.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,2,Mod(626,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("1045.626");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1045.f (of order $2$, degree $1$, 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:	$8.34436701122$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			626.13
Character	$\chi$	$=$	1045.626
Dual form			1045.2.f.b.626.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.10652 q^{2} -0.279240i q^{3} -0.775612 q^{4} +1.00000 q^{5} +0.308985i q^{6} +2.99424i q^{7} +3.07127 q^{8} +2.92202 q^{9} +O(q^{10})$	\(q-1.10652 q^{2} -0.279240i q^{3} -0.775612 q^{4} +1.00000 q^{5} +0.308985i q^{6} +2.99424i q^{7} +3.07127 q^{8} +2.92202 q^{9} -1.10652 q^{10} +(-3.17739 + 0.950891i) q^{11} +0.216582i q^{12} -0.947201 q^{13} -3.31319i q^{14} -0.279240i q^{15} -1.84720 q^{16} +0.958737i q^{17} -3.23328 q^{18} +(0.265527 + 4.35080i) q^{19} -0.775612 q^{20} +0.836113 q^{21} +(3.51585 - 1.05218i) q^{22} -4.10617 q^{23} -0.857622i q^{24} +1.00000 q^{25} +1.04810 q^{26} -1.65367i q^{27} -2.32237i q^{28} +5.40885 q^{29} +0.308985i q^{30} -1.45728i q^{31} -4.09858 q^{32} +(0.265527 + 0.887255i) q^{33} -1.06086i q^{34} +2.99424i q^{35} -2.26636 q^{36} -9.06487i q^{37} +(-0.293811 - 4.81425i) q^{38} +0.264497i q^{39} +3.07127 q^{40} -10.1734 q^{41} -0.925177 q^{42} +8.70825i q^{43} +(2.46442 - 0.737523i) q^{44} +2.92202 q^{45} +4.54356 q^{46} -6.30093 q^{47} +0.515813i q^{48} -1.96550 q^{49} -1.10652 q^{50} +0.267718 q^{51} +0.734661 q^{52} +10.8908i q^{53} +1.82982i q^{54} +(-3.17739 + 0.950891i) q^{55} +9.19614i q^{56} +(1.21492 - 0.0741458i) q^{57} -5.98501 q^{58} -11.8666i q^{59} +0.216582i q^{60} +3.81467i q^{61} +1.61251i q^{62} +8.74926i q^{63} +8.22956 q^{64} -0.947201 q^{65} +(-0.293811 - 0.981766i) q^{66} +11.2124i q^{67} -0.743608i q^{68} +1.14661i q^{69} -3.31319i q^{70} +16.1413i q^{71} +8.97433 q^{72} +8.49095i q^{73} +10.0305i q^{74} -0.279240i q^{75} +(-0.205946 - 3.37454i) q^{76} +(-2.84720 - 9.51388i) q^{77} -0.292671i q^{78} -9.49398 q^{79} -1.84720 q^{80} +8.30430 q^{81} +11.2571 q^{82} +11.6621i q^{83} -0.648500 q^{84} +0.958737i q^{85} -9.63586i q^{86} -1.51037i q^{87} +(-9.75863 + 2.92045i) q^{88} -4.52922i q^{89} -3.23328 q^{90} -2.83615i q^{91} +3.18479 q^{92} -0.406931 q^{93} +6.97211 q^{94} +(0.265527 + 4.35080i) q^{95} +1.14449i q^{96} +12.4604i q^{97} +2.17487 q^{98} +(-9.28441 + 2.77853i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{4} + 40 q^{5} - 28 q^{9}+O(q^{10}) $ 40 * q + 40 * q^4 + 40 * q^5 - 28 * q^9	$ 40 q + 40 q^{4} + 40 q^{5} - 28 q^{9} - 4 q^{11} + 48 q^{16} + 40 q^{20} + 24 q^{23} + 40 q^{25} - 24 q^{26} + 24 q^{36} - 28 q^{38} - 60 q^{42} - 48 q^{44} - 28 q^{45} - 36 q^{49} - 4 q^{55} - 36 q^{58} - 40 q^{64} - 28 q^{66} + 8 q^{77} + 48 q^{80} + 80 q^{81} + 8 q^{82} + 4 q^{92} + 56 q^{93} - 16 q^{99}+O(q^{100}) $ 40 * q + 40 * q^4 + 40 * q^5 - 28 * q^9 - 4 * q^11 + 48 * q^16 + 40 * q^20 + 24 * q^23 + 40 * q^25 - 24 * q^26 + 24 * q^36 - 28 * q^38 - 60 * q^42 - 48 * q^44 - 28 * q^45 - 36 * q^49 - 4 * q^55 - 36 * q^58 - 40 * q^64 - 28 * q^66 + 8 * q^77 + 48 * q^80 + 80 * q^81 + 8 * q^82 + 4 * q^92 + 56 * q^93 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times$.

$n$	$496$	$761$	$837$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.10652			−0.782428			−0.391214	−	0.920300i	$-0.627945\pi$
$2$	−1.10652			−0.782428			−0.391214	+	0.920300i	$0.627945\pi$
$3$		−	0.279240i		−	0.161219i	−0.996746	−	0.0806097i	$-0.974313\pi$
$3$		−	0.279240i		−	0.161219i	0.996746	−	0.0806097i	$-0.0256867\pi$
$4$	−0.775612			−0.387806
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$			0.308985i			0.126143i
$7$			2.99424i			1.13172i	0.824502	+	0.565859i	$0.191455\pi$
$7$			2.99424i			1.13172i	−0.824502	+	0.565859i	$0.808545\pi$
$8$	3.07127			1.08586
$9$	2.92202			0.974008
$10$	−1.10652			−0.349913
$11$	−3.17739	+	0.950891i	−0.958019	+	0.286705i
$11$	−3.17739	+	0.950891i	−0.958019	+	0.286705i
$12$			0.216582i			0.0625219i
$13$	−0.947201			−0.262706			−0.131353	−	0.991336i	$-0.541932\pi$
$13$	−0.947201			−0.262706			−0.131353	+	0.991336i	$0.541932\pi$
$14$		−	3.31319i		−	0.885488i
$15$		−	0.279240i		−	0.0720995i
$16$	−1.84720			−0.461800
$17$			0.958737i			0.232528i	0.993218	+	0.116264i	$0.0370918\pi$
$17$			0.958737i			0.232528i	−0.993218	+	0.116264i	$0.962908\pi$
$18$	−3.23328			−0.762092
$19$	0.265527	+	4.35080i	0.0609161	+	0.998143i
$19$	0.265527	+	4.35080i	0.0609161	+	0.998143i
$20$	−0.775612			−0.173432
$21$	0.836113			0.182455
$22$	3.51585	−	1.05218i	0.749581	−	0.224326i
$23$	−4.10617			−0.856195			−0.428097	−	0.903733i	$-0.640816\pi$
$23$	−4.10617			−0.856195			−0.428097	+	0.903733i	$0.640816\pi$
$24$		−	0.857622i		−	0.175061i
$25$	1.00000			0.200000
$26$	1.04810			0.205549
$27$		−	1.65367i		−	0.318248i
$28$		−	2.32237i		−	0.438887i
$29$	5.40885			1.00440			0.502199	−	0.864752i	$-0.332524\pi$
$29$	5.40885			1.00440			0.502199	+	0.864752i	$0.332524\pi$
$30$			0.308985i			0.0564127i
$31$		−	1.45728i		−	0.261735i	−0.991400	−	0.130867i	$-0.958224\pi$
$31$		−	1.45728i		−	0.261735i	0.991400	−	0.130867i	$-0.0417762\pi$
$32$	−4.09858			−0.724533
$33$	0.265527	+	0.887255i	0.0462223	+	0.154451i
$34$		−	1.06086i		−	0.181936i
$35$			2.99424i			0.506120i
$36$	−2.26636			−0.377726
$37$		−	9.06487i		−	1.49026i	−0.666922	−	0.745128i	$-0.732389\pi$
$37$		−	9.06487i		−	1.49026i	0.666922	−	0.745128i	$-0.267611\pi$
$38$	−0.293811	−	4.81425i	−0.0476625	−	0.780975i
$39$			0.264497i			0.0423534i
$40$	3.07127			0.485611
$41$	−10.1734			−1.58882			−0.794409	−	0.607383i	$-0.792219\pi$
$41$	−10.1734			−1.58882			−0.794409	+	0.607383i	$0.792219\pi$
$42$	−0.925177			−0.142758
$43$			8.70825i			1.32800i	0.747734	+	0.663998i	$0.231142\pi$
$43$			8.70825i			1.32800i	−0.747734	+	0.663998i	$0.768858\pi$
$44$	2.46442	−	0.737523i	0.371526	−	0.111186i
$45$	2.92202			0.435590
$46$	4.54356			0.669911
$47$	−6.30093			−0.919086			−0.459543	−	0.888156i	$-0.651987\pi$
$47$	−6.30093			−0.919086			−0.459543	+	0.888156i	$0.651987\pi$
$48$			0.515813i			0.0744512i
$49$	−1.96550			−0.280786
$50$	−1.10652			−0.156486
$51$	0.267718			0.0374880
$52$	0.734661			0.101879
$53$			10.8908i			1.49597i	0.663718	+	0.747983i	$0.268978\pi$
$53$			10.8908i			1.49597i	−0.663718	+	0.747983i	$0.731022\pi$
$54$			1.82982i			0.249007i
$55$	−3.17739	+	0.950891i	−0.428439	+	0.128218i
$56$			9.19614i			1.22889i
$57$	1.21492	−	0.0741458i	0.160920	−	0.00982085i
$58$	−5.98501			−0.785870
$59$		−	11.8666i		−	1.54490i	−0.635076	−	0.772450i	$-0.719031\pi$
$59$		−	11.8666i		−	1.54490i	0.635076	−	0.772450i	$-0.280969\pi$
$60$			0.216582i			0.0279606i
$61$			3.81467i			0.488418i	0.969723	+	0.244209i	$0.0785283\pi$
$61$			3.81467i			0.488418i	−0.969723	+	0.244209i	$0.921472\pi$
$62$			1.61251i			0.204789i
$63$			8.74926i			1.10230i
$64$	8.22956			1.02870
$65$	−0.947201			−0.117486
$66$	−0.293811	−	0.981766i	−0.0361657	−	0.120847i
$67$			11.2124i			1.36981i	0.728632	+	0.684905i	$0.240156\pi$
$67$			11.2124i			1.36981i	−0.728632	+	0.684905i	$0.759844\pi$
$68$		−	0.743608i		−	0.0901757i
$69$			1.14661i			0.138035i
$70$		−	3.31319i		−	0.396002i
$71$			16.1413i			1.91561i	0.287412	+	0.957807i	$0.407205\pi$
$71$			16.1413i			1.91561i	−0.287412	+	0.957807i	$0.592795\pi$
$72$	8.97433			1.05764
$73$			8.49095i			0.993790i	0.867811	+	0.496895i	$0.165527\pi$
$73$			8.49095i			0.993790i	−0.867811	+	0.496895i	$0.834473\pi$
$74$			10.0305i			1.16602i
$75$		−	0.279240i		−	0.0322439i
$76$	−0.205946	−	3.37454i	−0.0236236	−	0.387086i
$77$	−2.84720	−	9.51388i	−0.324469	−	1.08421i
$78$		−	0.292671i		−	0.0331385i
$79$	−9.49398			−1.06816			−0.534078	−	0.845435i	$-0.679341\pi$
$79$	−9.49398			−1.06816			−0.534078	+	0.845435i	$0.679341\pi$
$80$	−1.84720			−0.206523
$81$	8.30430			0.922701
$82$	11.2571			1.24314
$83$			11.6621i			1.28008i	0.768342	+	0.640040i	$0.221082\pi$
$83$			11.6621i			1.28008i	−0.768342	+	0.640040i	$0.778918\pi$
$84$	−0.648500			−0.0707571
$85$			0.958737i			0.103990i
$86$		−	9.63586i		−	1.03906i
$87$		−	1.51037i		−	0.161929i
$88$	−9.75863	+	2.92045i	−1.04027	+	0.311321i
$89$		−	4.52922i		−	0.480096i	−0.970761	−	0.240048i	$-0.922837\pi$
$89$		−	4.52922i		−	0.480096i	0.970761	−	0.240048i	$-0.0771632\pi$
$90$	−3.23328			−0.340818
$91$		−	2.83615i		−	0.297310i
$92$	3.18479			0.332037
$93$	−0.406931			−0.0421967
$94$	6.97211			0.719119
$95$	0.265527	+	4.35080i	0.0272425	+	0.446383i
$96$			1.14449i			0.116809i
$97$			12.4604i			1.26516i	0.774495	+	0.632580i	$0.218004\pi$
$97$			12.4604i			1.26516i	−0.774495	+	0.632580i	$0.781996\pi$
$98$	2.17487			0.219695
$99$	−9.28441	+	2.77853i	−0.933119	+	0.279253i
$100$	−0.775612			−0.0775612
$101$		−	8.77704i		−	0.873348i	−0.899620	−	0.436674i	$-0.856156\pi$
$101$		−	8.77704i		−	0.873348i	0.899620	−	0.436674i	$-0.143844\pi$
$102$	−0.296235			−0.0293317
$103$			5.61007i			0.552777i	0.961046	+	0.276388i	$0.0891376\pi$
$103$			5.61007i			0.552777i	−0.961046	+	0.276388i	$0.910862\pi$
$104$	−2.90911			−0.285262
$105$	0.836113			0.0815963
$106$		−	12.0509i		−	1.17049i
$107$	8.96726			0.866898			0.433449	−	0.901178i	$-0.357296\pi$
$107$	8.96726			0.866898			0.433449	+	0.901178i	$0.357296\pi$
$108$			1.28260i			0.123419i
$109$	−2.12415			−0.203457			−0.101728	−	0.994812i	$-0.532437\pi$
$109$	−2.12415			−0.203457			−0.101728	+	0.994812i	$0.532437\pi$
$110$	3.51585	−	1.05218i	0.335223	−	0.100322i
$111$	−2.53128			−0.240258
$112$		−	5.53097i		−	0.522628i
$113$			2.88598i			0.271491i	0.990744	+	0.135745i	$0.0433429\pi$
$113$			2.88598i			0.271491i	−0.990744	+	0.135745i	$0.956657\pi$
$114$	−1.34433	+	0.0820439i	−0.125908	+	0.00768411i
$115$	−4.10617			−0.382902
$116$	−4.19517			−0.389512
$117$	−2.76775			−0.255878
$118$			13.1306i			1.20877i
$119$	−2.87069			−0.263156
$120$		−	0.857622i		−	0.0782899i
$121$	9.19161	−	6.04271i	0.835601	−	0.549337i
$122$		−	4.22101i		−	0.382152i
$123$			2.84082i			0.256148i
$124$			1.13028i			0.101502i
$125$	1.00000			0.0894427
$126$		−	9.68123i		−	0.862473i
$127$	−20.8264			−1.84804			−0.924021	−	0.382342i	$-0.875118\pi$
$127$	−20.8264			−1.84804			−0.924021	+	0.382342i	$0.875118\pi$
$128$	−0.909027			−0.0803474
$129$	2.43169			0.214099
$130$	1.04810			0.0919243
$131$		−	10.9978i		−	0.960882i	−0.877027	−	0.480441i	$-0.840477\pi$
$131$		−	10.9978i		−	0.960882i	0.877027	−	0.480441i	$-0.159523\pi$
$132$	−0.205946	−	0.688166i	−0.0179253	−	0.0598971i
$133$	−13.0274	+	0.795053i	−1.12962	+	0.0689398i
$134$		−	12.4067i		−	1.07178i
$135$		−	1.65367i		−	0.142325i
$136$			2.94454i			0.252492i
$137$	3.54890			0.303203			0.151601	−	0.988442i	$-0.451557\pi$
$137$	3.54890			0.303203			0.151601	+	0.988442i	$0.451557\pi$
$138$		−	1.26874i		−	0.108003i
$139$		−	3.74807i		−	0.317907i	−0.987286	−	0.158954i	$-0.949188\pi$
$139$		−	3.74807i		−	0.317907i	0.987286	−	0.158954i	$-0.0508120\pi$
$140$		−	2.32237i		−	0.196276i
$141$			1.75947i			0.148174i
$142$		−	17.8606i		−	1.49883i
$143$	3.00963	−	0.900686i	0.251678	−	0.0753191i
$144$	−5.39757			−0.449797
$145$	5.40885			0.449181
$146$		−	9.39541i		−	0.777569i
$147$			0.548847i			0.0452681i
$148$			7.03082i			0.577930i
$149$			2.62253i			0.214846i	0.994213	+	0.107423i	$0.0342600\pi$
$149$			2.62253i			0.214846i	−0.994213	+	0.107423i	$0.965740\pi$
$150$			0.308985i			0.0252285i
$151$	15.7431			1.28116			0.640579	−	0.767892i	$-0.278694\pi$
$151$	15.7431			1.28116			0.640579	+	0.767892i	$0.278694\pi$
$152$	0.815506	+	13.3625i	0.0661463	+	1.08384i
$153$			2.80145i			0.226484i
$154$	3.15049	+	10.5273i	0.253873	+	0.848315i
$155$		−	1.45728i		−	0.117051i
$156$		−	0.205147i		−	0.0164249i
$157$	10.6474			0.849756			0.424878	−	0.905251i	$-0.360317\pi$
$157$	10.6474			0.849756			0.424878	+	0.905251i	$0.360317\pi$
$158$	10.5053			0.835755
$159$	3.04115			0.241179
$160$	−4.09858			−0.324021
$161$		−	12.2949i		−	0.968971i
$162$	−9.18888			−0.721947
$163$	−5.24498			−0.410818			−0.205409	−	0.978676i	$-0.565853\pi$
$163$	−5.24498			−0.410818			−0.205409	+	0.978676i	$0.565853\pi$
$164$	7.89061			0.616153
$165$	0.265527	+	0.887255i	0.0206713	+	0.0690727i
$166$		−	12.9043i		−	1.00157i
$167$	12.0022			0.928755			0.464378	−	0.885637i	$-0.346278\pi$
$167$	12.0022			0.928755			0.464378	+	0.885637i	$0.346278\pi$
$168$	2.56793			0.198120
$169$	−12.1028			−0.930985
$170$		−	1.06086i		−	0.0813644i
$171$	0.775877	+	12.7132i	0.0593328	+	0.972199i
$172$		−	6.75423i		−	0.515005i
$173$	−16.6985			−1.26956			−0.634781	−	0.772692i	$-0.718910\pi$
$173$	−16.6985			−1.26956			−0.634781	+	0.772692i	$0.718910\pi$
$174$			1.67125i			0.126697i
$175$			2.99424i			0.226344i
$176$	5.86928	−	1.75649i	0.442414	−	0.132400i
$177$	−3.31363			−0.249068
$178$			5.01167i			0.375641i
$179$		−	7.91163i		−	0.591343i	−0.955290	−	0.295672i	$-0.904457\pi$
$179$		−	7.91163i		−	0.591343i	0.955290	−	0.295672i	$-0.0955434\pi$
$180$	−2.26636			−0.168924
$181$			18.2419i			1.35591i	0.735104	+	0.677954i	$0.237133\pi$
$181$			18.2419i			1.35591i	−0.735104	+	0.677954i	$0.762867\pi$
$182$			3.13826i			0.232623i
$183$	1.06521			0.0787425
$184$	−12.6112			−0.929706
$185$		−	9.06487i		−	0.666462i
$186$	0.450277			0.0330159
$187$	−0.911655	−	3.04628i	−0.0666668	−	0.222766i
$188$	4.88708			0.356427
$189$	4.95148			0.360167
$190$	−0.293811	−	4.81425i	−0.0213153	−	0.349263i
$191$	11.4711			0.830021			0.415011	−	0.909817i	$-0.363778\pi$
$191$	11.4711			0.830021			0.415011	+	0.909817i	$0.363778\pi$
$192$		−	2.29802i		−	0.165846i
$193$	1.99534			0.143628			0.0718139	−	0.997418i	$-0.477121\pi$
$193$	1.99534			0.143628			0.0718139	+	0.997418i	$0.477121\pi$
$194$		−	13.7877i		−	0.989896i
$195$			0.264497i			0.0189410i
$196$	1.52447			0.108890
$197$		−	5.26729i		−	0.375279i	−0.982238	−	0.187640i	$-0.939916\pi$
$197$		−	5.26729i		−	0.375279i	0.982238	−	0.187640i	$-0.0600837\pi$
$198$	10.2734	−	3.07450i	0.730098	−	0.218495i
$199$	5.14197			0.364504			0.182252	−	0.983252i	$-0.441661\pi$
$199$	5.14197			0.364504			0.182252	+	0.983252i	$0.441661\pi$
$200$	3.07127			0.217172
$201$	3.13095			0.220840
$202$			9.71198i			0.683332i
$203$			16.1954i			1.13670i
$204$	−0.207645			−0.0145381
$205$	−10.1734			−0.710541
$206$		−	6.20766i		−	0.432508i
$207$	−11.9983			−0.833941
$208$	1.74967			0.121318
$209$	−4.98083	−	13.5717i	−0.344531	−	0.938775i
$210$	−0.925177			−0.0638432
$211$	−21.3141			−1.46733			−0.733663	−	0.679513i	$-0.762191\pi$
$211$	−21.3141			−1.46733			−0.733663	+	0.679513i	$0.762191\pi$
$212$		−	8.44703i		−	0.580145i
$213$	4.50729			0.308834
$214$	−9.92246			−0.678285
$215$			8.70825i			0.593898i
$216$		−	5.07886i		−	0.345573i
$217$	4.36345			0.296210
$218$	2.35042			0.159190
$219$	2.37101			0.160218
$220$	2.46442	−	0.737523i	0.166151	−	0.0497238i
$221$		−	0.908117i		−	0.0610866i
$222$	2.80091			0.187985
$223$		−	4.88317i		−	0.327002i	−0.986543	−	0.163501i	$-0.947721\pi$
$223$		−	4.88317i		−	0.327002i	0.986543	−	0.163501i	$-0.0522786\pi$
$224$		−	12.2721i		−	0.819967i
$225$	2.92202			0.194802
$226$		−	3.19340i		−	0.212422i
$227$	−5.63748			−0.374173			−0.187086	−	0.982343i	$-0.559904\pi$
$227$	−5.63748			−0.374173			−0.187086	+	0.982343i	$0.559904\pi$
$228$	−0.942306	+	0.0575084i	−0.0624057	+	0.00380859i
$229$	14.2907			0.944356			0.472178	−	0.881503i	$-0.343468\pi$
$229$	14.2907			0.944356			0.472178	+	0.881503i	$0.343468\pi$
$230$	4.54356			0.299593
$231$	−2.65666	+	0.795053i	−0.174795	+	0.0523106i
$232$	16.6121			1.09064
$233$		−	10.5089i		−	0.688462i	−0.938885	−	0.344231i	$-0.888140\pi$
$233$		−	10.5089i		−	0.688462i	0.938885	−	0.344231i	$-0.111860\pi$
$234$	3.06257			0.200206
$235$	−6.30093			−0.411028
$236$			9.20388i			0.599122i
$237$			2.65110i			0.172207i
$238$	3.17648			0.205901
$239$		−	8.73438i		−	0.564980i	−0.959270	−	0.282490i	$-0.908840\pi$
$239$		−	8.73438i		−	0.564980i	0.959270	−	0.282490i	$-0.0911604\pi$
$240$			0.515813i			0.0332956i
$241$	−5.13198			−0.330580			−0.165290	−	0.986245i	$-0.552856\pi$
$241$	−5.13198			−0.330580			−0.165290	+	0.986245i	$0.552856\pi$
$242$	−10.1707	+	6.68638i	−0.653798	+	0.429817i
$243$		−	7.27990i		−	0.467006i
$244$		−	2.95870i		−	0.189412i
$245$	−1.96550			−0.125571
$246$		−	3.14343i		−	0.200418i
$247$	−0.251508	−	4.12109i	−0.0160030	−	0.262218i
$248$		−	4.47570i		−	0.284207i
$249$	3.25652			0.206374
$250$	−1.10652			−0.0699825
$251$	9.12443			0.575929			0.287964	−	0.957641i	$-0.407021\pi$
$251$	9.12443			0.575929			0.287964	+	0.957641i	$0.407021\pi$
$252$		−	6.78603i		−	0.427480i
$253$	13.0469	−	3.90452i	0.820251	−	0.245475i
$254$	23.0448			1.44596
$255$	0.267718			0.0167651
$256$	−15.4533			−0.965829
$257$		−	25.2129i		−	1.57274i	−0.617758	−	0.786368i	$-0.711959\pi$
$257$		−	25.2129i		−	1.57274i	0.617758	−	0.786368i	$-0.288041\pi$
$258$	−2.69072			−0.167517
$259$	27.1424			1.68655
$260$	0.734661			0.0455617
$261$	15.8048			0.978293
$262$			12.1693i			0.751821i
$263$		−	0.846345i		−	0.0521879i	−0.999659	−	0.0260939i	$-0.991693\pi$
$263$		−	0.846345i		−	0.0521879i	0.999659	−	0.0260939i	$-0.00830690\pi$
$264$	0.815506	+	2.72500i	0.0501909	+	0.167712i
$265$			10.8908i			0.669016i
$266$	14.4151	−	0.879743i	0.883844	−	0.0539405i
$267$	−1.26474			−0.0774008
$268$		−	8.69646i		−	0.531221i
$269$		−	21.0063i		−	1.28078i	−0.768051	−	0.640389i	$-0.778773\pi$
$269$		−	21.0063i		−	1.28078i	0.768051	−	0.640389i	$-0.221227\pi$
$270$			1.82982i			0.111359i
$271$		−	25.7316i		−	1.56308i	−0.623853	−	0.781542i	$-0.714434\pi$
$271$		−	25.7316i		−	1.56308i	0.623853	−	0.781542i	$-0.285566\pi$
$272$		−	1.77098i		−	0.107381i
$273$	−0.791968			−0.0479321
$274$	−3.92693			−0.237234
$275$	−3.17739	+	0.950891i	−0.191604	+	0.0573409i
$276$		−	0.889322i		−	0.0535309i
$277$			20.1887i			1.21302i	0.795076	+	0.606510i	$0.207431\pi$
$277$			20.1887i			1.21302i	−0.795076	+	0.606510i	$0.792569\pi$
$278$			4.14732i			0.248740i
$279$		−	4.25820i		−	0.254932i
$280$			9.19614i			0.549574i
$281$	4.12999			0.246374			0.123187	−	0.992383i	$-0.460688\pi$
$281$	4.12999			0.246374			0.123187	+	0.992383i	$0.460688\pi$
$282$		−	1.94689i		−	0.115936i
$283$			19.8787i			1.18167i	0.806794	+	0.590833i	$0.201201\pi$
$283$			19.8787i			1.18167i	−0.806794	+	0.590833i	$0.798799\pi$
$284$		−	12.5193i		−	0.742887i
$285$	1.21492	−	0.0741458i	0.0719656	−	0.00439202i
$286$	−3.33021	+	0.996627i	−0.196920	+	0.0589318i
$287$		−	30.4616i		−	1.79809i
$288$	−11.9761			−0.705701
$289$	16.0808			0.945931
$290$	−5.98501			−0.351452
$291$	3.47944			0.203968
$292$		−	6.58568i		−	0.385398i
$293$	7.90615			0.461882			0.230941	−	0.972968i	$-0.425820\pi$
$293$	7.90615			0.461882			0.230941	+	0.972968i	$0.425820\pi$
$294$		−	0.607310i		−	0.0354190i
$295$		−	11.8666i		−	0.690900i
$296$		−	27.8407i		−	1.61821i
$297$	1.57246	+	5.25434i	0.0912433	+	0.304888i
$298$		−	2.90189i		−	0.168102i
$299$	3.88937			0.224928
$300$			0.216582i			0.0125044i
$301$	−26.0746			−1.50292
$302$	−17.4201			−1.00241
$303$	−2.45090			−0.140801
$304$	−0.490482	−	8.03681i	−0.0281311	−	0.460943i
$305$			3.81467i			0.218427i
$306$		−	3.09987i		−	0.177208i
$307$	3.65169			0.208413			0.104206	−	0.994556i	$-0.466770\pi$
$307$	3.65169			0.208413			0.104206	+	0.994556i	$0.466770\pi$
$308$	2.20832	+	7.37908i	0.125831	+	0.420462i
$309$	1.56656			0.0891183
$310$			1.61251i			0.0915843i
$311$	24.9537			1.41500			0.707498	−	0.706716i	$-0.249824\pi$
$311$	24.9537			1.41500			0.707498	+	0.706716i	$0.249824\pi$
$312$			0.812341i			0.0459898i
$313$	5.23379			0.295831			0.147916	−	0.989000i	$-0.452744\pi$
$313$	5.23379			0.295831			0.147916	+	0.989000i	$0.452744\pi$
$314$	−11.7816			−0.664873
$315$			8.74926i			0.492965i
$316$	7.36365			0.414237
$317$		−	16.0133i		−	0.899395i	−0.893181	−	0.449697i	$-0.851532\pi$
$317$		−	16.0133i		−	0.899395i	0.893181	−	0.449697i	$-0.148468\pi$
$318$	−3.36509			−0.188705
$319$	−17.1860	+	5.14323i	−0.962233	+	0.287966i
$320$	8.22956			0.460047
$321$		−	2.50402i		−	0.139761i
$322$			13.6045i			0.758150i
$323$	−4.17128	+	0.254571i	−0.232096	+	0.0141647i
$324$	−6.44092			−0.357829
$325$	−0.947201			−0.0525413
$326$	5.80368			0.321436
$327$			0.593148i			0.0328012i
$328$	−31.2453			−1.72523
$329$		−	18.8665i		−	1.04015i
$330$	−0.293811	−	0.981766i	−0.0161738	−	0.0540444i
$331$			7.45374i			0.409695i	0.978794	+	0.204847i	$0.0656698\pi$
$331$			7.45374i			0.409695i	−0.978794	+	0.204847i	$0.934330\pi$
$332$		−	9.04525i		−	0.496423i
$333$		−	26.4878i		−	1.45152i
$334$	−13.2806			−0.726684
$335$			11.2124i			0.612598i
$336$	−1.54447			−0.0842577
$337$	27.3744			1.49118			0.745589	−	0.666406i	$-0.232168\pi$
$337$	27.3744			1.49118			0.745589	+	0.666406i	$0.232168\pi$
$338$	13.3920			0.728429
$339$	0.805883			0.0437695
$340$		−	0.743608i		−	0.0403278i
$341$	1.38571	+	4.63034i	0.0750406	+	0.250747i
$342$	−0.858524	−	14.0674i	−0.0464236	−	0.760676i
$343$			15.0745i			0.813948i
$344$			26.7454i			1.44202i
$345$			1.14661i			0.0617312i
$346$	18.4772			0.993341
$347$			30.6961i			1.64786i	0.566695	+	0.823928i	$0.308222\pi$
$347$			30.6961i			1.64786i	−0.566695	+	0.823928i	$0.691778\pi$
$348$			1.17146i			0.0627969i
$349$			31.0582i			1.66251i	0.555894	+	0.831253i	$0.312376\pi$
$349$			31.0582i			1.66251i	−0.555894	+	0.831253i	$0.687624\pi$
$350$		−	3.31319i		−	0.177098i
$351$			1.56636i			0.0836059i
$352$	13.0228	−	3.89730i	0.694116	−	0.207727i
$353$	−27.4987			−1.46361			−0.731805	−	0.681514i	$-0.761322\pi$
$353$	−27.4987			−1.46361			−0.731805	+	0.681514i	$0.761322\pi$
$354$	3.66660			0.194878
$355$			16.1413i			0.856689i
$356$			3.51292i			0.186184i
$357$			0.801613i			0.0424258i
$358$			8.75438i			0.462683i
$359$		−	33.9515i		−	1.79189i	−0.444165	−	0.895945i	$-0.646500\pi$
$359$		−	33.9515i		−	1.79189i	0.444165	−	0.895945i	$-0.353500\pi$
$360$	8.97433			0.472989
$361$	−18.8590	+	2.31051i	−0.992578	+	0.121606i
$362$		−	20.1850i		−	1.06090i
$363$	−1.68737	−	2.56667i	−0.0885637	−	0.134715i
$364$			2.19975i			0.115298i
$365$			8.49095i			0.444436i
$366$	−1.17867			−0.0616103
$367$	−1.89400			−0.0988662			−0.0494331	−	0.998777i	$-0.515741\pi$
$367$	−1.89400			−0.0988662			−0.0494331	+	0.998777i	$0.515741\pi$
$368$	7.58491			0.395391
$369$	−29.7269			−1.54752
$370$			10.0305i			0.521459i
$371$	−32.6097			−1.69301
$372$	0.315620			0.0163641
$373$	−11.7231			−0.606997			−0.303498	−	0.952832i	$-0.598155\pi$
$373$	−11.7231			−0.606997			−0.303498	+	0.952832i	$0.598155\pi$
$374$	1.00876	+	3.37077i	0.0521620	+	0.174299i
$375$		−	0.279240i		−	0.0144199i
$376$	−19.3519			−0.997997
$377$	−5.12327			−0.263862
$378$	−5.47892			−0.281805
$379$			23.3336i			1.19857i	0.800537	+	0.599283i	$0.204548\pi$
$379$			23.3336i			1.19857i	−0.800537	+	0.599283i	$0.795452\pi$
$380$	−0.205946	−	3.37454i	−0.0105648	−	0.173110i
$381$			5.81556i			0.297940i
$382$	−12.6930			−0.649432
$383$		−	1.96917i		−	0.100620i	−0.998734	−	0.0503100i	$-0.983979\pi$
$383$		−	1.96917i		−	0.100620i	0.998734	−	0.0503100i	$-0.0160209\pi$
$384$			0.253837i			0.0129536i
$385$	−2.84720	−	9.51388i	−0.145107	−	0.484872i
$386$	−2.20789			−0.112378
$387$			25.4457i			1.29348i
$388$		−	9.66442i		−	0.490636i
$389$	9.42561			0.477897			0.238949	−	0.971032i	$-0.423197\pi$
$389$	9.42561			0.477897			0.238949	+	0.971032i	$0.423197\pi$
$390$		−	0.292671i		−	0.0148200i
$391$		−	3.93673i		−	0.199089i
$392$	−6.03659			−0.304894
$393$	−3.07103			−0.154913
$394$			5.82837i			0.293629i
$395$	−9.49398			−0.477694
$396$	7.20110	−	2.15506i	0.361869	−	0.108296i
$397$	0.925140			0.0464314			0.0232157	−	0.999730i	$-0.492610\pi$
$397$	0.925140			0.0464314			0.0232157	+	0.999730i	$0.492610\pi$
$398$	−5.68969			−0.285198
$399$	0.222011	+	3.63777i	0.0111144	+	0.182116i
$400$	−1.84720			−0.0923601
$401$			21.1881i			1.05808i	0.848596	+	0.529041i	$0.177448\pi$
$401$			21.1881i			1.05808i	−0.848596	+	0.529041i	$0.822552\pi$
$402$	−3.46446			−0.172791
$403$			1.38034i			0.0687594i
$404$			6.80758i			0.338690i
$405$	8.30430			0.412644
$406$		−	17.9206i		−	0.889383i
$407$	8.61971	+	28.8026i	0.427263	+	1.42769i
$408$	0.822234			0.0407067
$409$	−6.78814			−0.335652			−0.167826	−	0.985817i	$-0.553675\pi$
$409$	−6.78814			−0.335652			−0.167826	+	0.985817i	$0.553675\pi$
$410$	11.2571			0.555947
$411$		−	0.990994i		−	0.0488822i
$412$		−	4.35124i		−	0.214370i
$413$	35.5315			1.74839
$414$	13.2764			0.652499
$415$			11.6621i			0.572469i
$416$	3.88218			0.190339
$417$	−1.04661			−0.0512528
$418$	5.51139	+	15.0174i	0.269571	+	0.734524i
$419$	28.3012			1.38260			0.691302	−	0.722566i	$-0.257038\pi$
$419$	28.3012			1.38260			0.691302	+	0.722566i	$0.257038\pi$
$420$	−0.648500			−0.0316435
$421$		−	15.2141i		−	0.741491i	−0.928735	−	0.370745i	$-0.879102\pi$
$421$		−	15.2141i		−	0.741491i	0.928735	−	0.370745i	$-0.120898\pi$
$422$	23.5845			1.14808
$423$	−18.4115			−0.895197
$424$			33.4486i			1.62441i
$425$			0.958737i			0.0465056i
$426$	−4.98740			−0.241641
$427$	−11.4220			−0.552752
$428$	−6.95512			−0.336188
$429$	−0.251508	−	0.840409i	−0.0121429	−	0.0405753i
$430$		−	9.63586i		−	0.464683i
$431$	29.3893			1.41563			0.707815	−	0.706398i	$-0.249681\pi$
$431$	29.3893			1.41563			0.707815	+	0.706398i	$0.249681\pi$
$432$			3.05466i			0.146967i
$433$		−	11.5536i		−	0.555232i	−0.960692	−	0.277616i	$-0.910456\pi$
$433$		−	11.5536i		−	0.555232i	0.960692	−	0.277616i	$-0.0895444\pi$
$434$	−4.82824			−0.231763
$435$		−	1.51037i		−	0.0724167i
$436$	1.64752			0.0789018
$437$	−1.09030	−	17.8651i	−0.0521560	−	0.854605i
$438$	−2.62357			−0.125359
$439$	27.0257			1.28986			0.644932	−	0.764240i	$-0.276886\pi$
$439$	27.0257			1.28986			0.644932	+	0.764240i	$0.276886\pi$
$440$	−9.75863	+	2.92045i	−0.465224	+	0.139227i
$441$	−5.74324			−0.273488
$442$			1.00485i			0.0477958i
$443$	10.5342			0.500494			0.250247	−	0.968182i	$-0.419488\pi$
$443$	10.5342			0.500494			0.250247	+	0.968182i	$0.419488\pi$
$444$	1.96329			0.0931735
$445$		−	4.52922i		−	0.214706i
$446$			5.40333i			0.255855i
$447$	0.732317			0.0346374
$448$			24.6413i			1.16419i
$449$		−	7.41007i		−	0.349703i	−0.984595	−	0.174851i	$-0.944055\pi$
$449$		−	7.41007i		−	0.349703i	0.984595	−	0.174851i	$-0.0559445\pi$
$450$	−3.23328			−0.152418
$451$	32.3248	−	9.67380i	1.52212	−	0.455521i
$452$		−	2.23840i		−	0.105286i
$453$		−	4.39612i		−	0.206548i
$454$	6.23799			0.292763
$455$		−	2.83615i		−	0.132961i
$456$	3.73135	−	0.227722i	0.174736	−	0.0106641i
$457$			7.85744i			0.367556i	0.982968	+	0.183778i	$0.0588327\pi$
$457$			7.85744i			0.367556i	−0.982968	+	0.183778i	$0.941167\pi$
$458$	−15.8130			−0.738891
$459$	1.58543			0.0740016
$460$	3.18479			0.148492
$461$		−	8.02143i		−	0.373595i	−0.982398	−	0.186798i	$-0.940189\pi$
$461$		−	8.02143i		−	0.373595i	0.982398	−	0.186798i	$-0.0598108\pi$
$462$	2.93965	−	0.879743i	0.136765	−	0.0409293i
$463$	14.8831			0.691674			0.345837	−	0.938295i	$-0.387595\pi$
$463$	14.8831			0.691674			0.345837	+	0.938295i	$0.387595\pi$
$464$	−9.99124			−0.463832
$465$	−0.406931			−0.0188710
$466$			11.6283i			0.538672i
$467$	21.4287			0.991604			0.495802	−	0.868436i	$-0.334874\pi$
$467$	21.4287			0.991604			0.495802	+	0.868436i	$0.334874\pi$
$468$	2.14670			0.0992311
$469$	−33.5726			−1.55024
$470$	6.97211			0.321600
$471$		−	2.97319i		−	0.136997i
$472$		−	36.4456i		−	1.67754i
$473$	−8.28061	−	27.6695i	−0.380743	−	1.27225i
$474$		−	2.93350i		−	0.134740i
$475$	0.265527	+	4.35080i	0.0121832	+	0.199629i
$476$	2.22654			0.102053
$477$			31.8232i			1.45708i
$478$			9.66477i			0.442056i
$479$		−	16.5403i		−	0.755745i	−0.925858	−	0.377873i	$-0.876656\pi$
$479$		−	16.5403i		−	0.755745i	0.925858	−	0.377873i	$-0.123344\pi$
$480$			1.14449i			0.0522385i
$481$			8.58625i			0.391500i
$482$	5.67865			0.258655
$483$	−3.43322			−0.156217
$484$	−7.12913	+	4.68680i	−0.324051	+	0.213036i
$485$			12.4604i			0.565796i
$486$			8.05536i			0.365398i
$487$		−	41.4208i		−	1.87696i	−0.345338	−	0.938478i	$-0.612236\pi$
$487$		−	41.4208i		−	1.87696i	0.345338	−	0.938478i	$-0.387764\pi$
$488$			11.7159i			0.530353i
$489$			1.46461i			0.0662319i
$490$	2.17487			0.0982505
$491$		−	9.64620i		−	0.435327i	−0.976024	−	0.217664i	$-0.930156\pi$
$491$		−	9.64620i		−	0.435327i	0.976024	−	0.217664i	$-0.0698435\pi$
$492$		−	2.20338i		−	0.0993358i
$493$			5.18567i			0.233551i
$494$	0.278298	+	4.56007i	0.0125212	+	0.205167i
$495$	−9.28441	+	2.77853i	−0.417303	+	0.124886i
$496$			2.69189i			0.120869i
$497$	−48.3309			−2.16793
$498$	−3.60341			−0.161473
$499$	−25.9537			−1.16185			−0.580924	−	0.813958i	$-0.697308\pi$
$499$	−25.9537			−1.16185			−0.580924	+	0.813958i	$0.697308\pi$
$500$	−0.775612			−0.0346864
$501$		−	3.35149i		−	0.149733i
$502$	−10.0964			−0.450623
$503$			39.3068i			1.75260i	0.481762	+	0.876302i	$0.339997\pi$
$503$			39.3068i			1.75260i	−0.481762	+	0.876302i	$0.660003\pi$
$504$			26.8713i			1.19695i
$505$		−	8.77704i		−	0.390573i
$506$	−14.4367	+	4.32043i	−0.641787	+	0.192067i
$507$			3.37959i			0.150093i
$508$	16.1532			0.716682
$509$			28.9070i			1.28128i	0.767842	+	0.640640i	$0.221331\pi$
$509$			28.9070i			1.28128i	−0.767842	+	0.640640i	$0.778669\pi$
$510$	−0.296235			−0.0131175
$511$	−25.4240			−1.12469
$512$	18.9174			0.836040
$513$	7.19478	−	0.439093i	0.317657	−	0.0193864i
$514$			27.8986i			1.23055i
$515$			5.61007i			0.247209i
$516$	−1.88605			−0.0830288
$517$	20.0205	−	5.99150i	0.880502	−	0.263506i
$518$	−30.0337			−1.31960
$519$			4.66288i			0.204678i
$520$	−2.90911			−0.127573
$521$		−	24.0376i		−	1.05310i	−0.850143	−	0.526552i	$-0.823484\pi$
$521$		−	24.0376i		−	1.05310i	0.850143	−	0.526552i	$-0.176516\pi$
$522$	−17.4883			−0.765444
$523$	−19.7372			−0.863047			−0.431524	−	0.902102i	$-0.642024\pi$
$523$	−19.7372			−0.863047			−0.431524	+	0.902102i	$0.642024\pi$
$524$			8.53003i			0.372636i
$525$	0.836113			0.0364910
$526$			0.936498i			0.0408333i
$527$	1.39715			0.0608607
$528$	−0.490482	−	1.63894i	−0.0213455	−	0.0713256i
$529$	−6.13941			−0.266931
$530$		−	12.0509i		−	0.523457i
$531$		−	34.6745i		−	1.50475i
$532$	10.1042	−	0.616653i	0.438072	−	0.0267353i
$533$	9.63625			0.417392
$534$	1.39946			0.0605606
$535$	8.96726			0.387689
$536$			34.4363i			1.48742i
$537$	−2.20924			−0.0953360
$538$			23.2439i			1.00212i
$539$	6.24516	−	1.86898i	0.268998	−	0.0805026i
$540$			1.28260i			0.0551945i
$541$			30.9340i			1.32995i	0.746864	+	0.664977i	$0.231559\pi$
$541$			30.9340i			1.32995i	−0.746864	+	0.664977i	$0.768441\pi$
$542$			28.4725i			1.22300i
$543$	5.09386			0.218599
$544$		−	3.92946i		−	0.168474i
$545$	−2.12415			−0.0909887
$546$	0.876328			0.0375034
$547$	−12.1167			−0.518073			−0.259037	−	0.965867i	$-0.583405\pi$
$547$	−12.1167			−0.518073			−0.259037	+	0.965867i	$0.583405\pi$
$548$	−2.75257			−0.117584
$549$			11.1466i			0.475723i
$550$	3.51585	−	1.05218i	0.149916	−	0.0448651i
$551$	1.43620	+	23.5329i	0.0611840	+	1.00253i
$552$			3.52154i			0.149887i
$553$		−	28.4273i		−	1.20885i
$554$		−	22.3392i		−	0.949101i
$555$	−2.53128			−0.107447
$556$			2.90705i			0.123286i
$557$			2.18544i			0.0926000i	0.998928	+	0.0463000i	$0.0147430\pi$
$557$			2.18544i			0.0926000i	−0.998928	+	0.0463000i	$0.985257\pi$
$558$			4.71179i			0.199466i
$559$		−	8.24847i		−	0.348873i
$560$		−	5.53097i		−	0.233726i
$561$	−0.850644	+	0.254571i	−0.0359142	+	0.0107480i
$562$	−4.56991			−0.192770
$563$	−3.28052			−0.138257			−0.0691287	−	0.997608i	$-0.522022\pi$
$563$	−3.28052			−0.138257			−0.0691287	+	0.997608i	$0.522022\pi$
$564$		−	1.36467i		−	0.0574629i
$565$			2.88598i			0.121414i
$566$		−	21.9962i		−	0.924569i
$567$			24.8651i			1.04424i
$568$			49.5742i			2.08009i
$569$	30.7606			1.28955			0.644775	−	0.764372i	$-0.276951\pi$
$569$	30.7606			1.28955			0.644775	+	0.764372i	$0.276951\pi$
$570$	−1.34433	+	0.0820439i	−0.0563079	+	0.00343644i
$571$			25.9514i			1.08603i	0.839722	+	0.543017i	$0.182718\pi$
$571$			25.9514i			1.08603i	−0.839722	+	0.543017i	$0.817282\pi$
$572$	−2.33430	+	0.698583i	−0.0976021	+	0.0292092i
$573$		−	3.20320i		−	0.133816i
$574$			33.7064i			1.40688i
$575$	−4.10617			−0.171239
$576$	24.0470			1.00196
$577$	−11.0226			−0.458877			−0.229439	−	0.973323i	$-0.573689\pi$
$577$	−11.0226			−0.458877			−0.229439	+	0.973323i	$0.573689\pi$
$578$	−17.7938			−0.740123
$579$		−	0.557179i		−	0.0231556i
$580$	−4.19517			−0.174195
$581$	−34.9191			−1.44869
$582$	−3.85007			−0.159590
$583$	−10.3560	−	34.6043i	−0.428900	−	1.43316i
$584$			26.0780i			1.07912i
$585$	−2.76775			−0.114432
$586$	−8.74832			−0.361390
$587$	−43.7642			−1.80634			−0.903170	−	0.429283i	$-0.858766\pi$
$587$	−43.7642			−1.80634			−0.903170	+	0.429283i	$0.858766\pi$
$588$		−	0.425692i		−	0.0175552i
$589$	6.34033	−	0.386947i	0.261249	−	0.0159439i
$590$			13.1306i			0.540580i
$591$	−1.47084			−0.0605023
$592$			16.7446i			0.688200i
$593$		−	41.1778i		−	1.69097i	−0.534000	−	0.845485i	$-0.679312\pi$
$593$		−	41.1778i		−	1.69097i	0.534000	−	0.845485i	$-0.320688\pi$
$594$	−1.73996	−	5.81404i	−0.0713913	−	0.238553i
$595$	−2.87069			−0.117687
$596$		−	2.03407i		−	0.0833187i
$597$		−	1.43584i		−	0.0587652i
$598$	−4.30366			−0.175990
$599$		−	9.27307i		−	0.378887i	−0.981892	−	0.189444i	$-0.939332\pi$
$599$		−	9.27307i		−	0.378887i	0.981892	−	0.189444i	$-0.0606685\pi$
$600$		−	0.857622i		−	0.0350123i
$601$	−6.89631			−0.281306			−0.140653	−	0.990059i	$-0.544920\pi$
$601$	−6.89631			−0.281306			−0.140653	+	0.990059i	$0.544920\pi$
$602$	28.8521			1.17593
$603$			32.7629i			1.33421i
$604$	−12.2106			−0.496841
$605$	9.19161	−	6.04271i	0.373692	−	0.245671i
$606$	2.71197			0.110166
$607$	8.14177			0.330464			0.165232	−	0.986255i	$-0.447163\pi$
$607$	8.14177			0.330464			0.165232	+	0.986255i	$0.447163\pi$
$608$	−1.08828	−	17.8321i	−0.0441357	−	0.723187i
$609$	4.52241			0.183257
$610$		−	4.22101i		−	0.170904i
$611$	5.96825			0.241450
$612$		−	2.17284i		−	0.0878319i
$613$			11.0047i			0.444475i	0.974993	+	0.222237i	$0.0713360\pi$
$613$			11.0047i			0.444475i	−0.974993	+	0.222237i	$0.928664\pi$
$614$	−4.04067			−0.163068
$615$			2.84082i			0.114553i
$616$	−8.74453	−	29.2197i	−0.352327	−	1.17730i
$617$	−32.9712			−1.32737			−0.663685	−	0.748012i	$-0.731009\pi$
$617$	−32.9712			−1.32737			−0.663685	+	0.748012i	$0.731009\pi$
$618$	−1.73343			−0.0697287
$619$	−41.1794			−1.65514			−0.827571	−	0.561361i	$-0.810278\pi$
$619$	−41.1794			−1.65514			−0.827571	+	0.561361i	$0.810278\pi$
$620$			1.13028i			0.0453932i
$621$			6.79023i			0.272483i
$622$	−27.6118			−1.10713
$623$	13.5616			0.543334
$624$		−	0.488579i		−	0.0195588i
$625$	1.00000			0.0400000
$626$	−5.79130			−0.231467
$627$	−3.78977	+	1.39085i	−0.151349	+	0.0555451i
$628$	−8.25826			−0.329541
$629$	8.69083			0.346526
$630$		−	9.68123i		−	0.385710i
$631$	24.6494			0.981276			0.490638	−	0.871363i	$-0.336764\pi$
$631$	24.6494			0.981276			0.490638	+	0.871363i	$0.336764\pi$
$632$	−29.1586			−1.15987
$633$			5.95177i			0.236561i
$634$			17.7190i			0.703712i
$635$	−20.8264			−0.826469
$636$	−2.35875			−0.0935306
$637$	1.86172			0.0737642
$638$	19.0167	−	5.69109i	0.752878	−	0.225313i
$639$			47.1651i			1.86582i
$640$	−0.909027			−0.0359324
$641$			35.3510i			1.39628i	0.715961	+	0.698140i	$0.245989\pi$
$641$			35.3510i			1.39628i	−0.715961	+	0.698140i	$0.754011\pi$
$642$			2.77075i			0.109353i
$643$	38.8221			1.53099			0.765497	−	0.643440i	$-0.222493\pi$
$643$	38.8221			1.53099			0.765497	+	0.643440i	$0.222493\pi$
$644$			9.53605i			0.375773i
$645$	2.43169			0.0957479
$646$	4.61560	−	0.281688i	0.181599	−	0.0110829i
$647$	35.1723			1.38277			0.691383	−	0.722489i	$-0.257002\pi$
$647$	35.1723			1.38277			0.691383	+	0.722489i	$0.257002\pi$
$648$	25.5048			1.00192
$649$	11.2838	+	37.7048i	0.442930	+	1.48004i
$650$	1.04810			0.0411098
$651$		−	1.21845i		−	0.0477548i
$652$	4.06807			0.159318
$653$	30.2689			1.18452			0.592258	−	0.805749i	$-0.298237\pi$
$653$	30.2689			1.18452			0.592258	+	0.805749i	$0.298237\pi$
$654$		−	0.656331i		−	0.0256646i
$655$		−	10.9978i		−	0.429720i
$656$	18.7923			0.733717
$657$			24.8108i			0.967960i
$658$			20.8762i			0.813839i
$659$	−34.3229			−1.33703			−0.668514	−	0.743699i	$-0.733069\pi$
$659$	−34.3229			−1.33703			−0.668514	+	0.743699i	$0.733069\pi$
$660$	−0.205946	−	0.688166i	−0.00801644	−	0.0267868i
$661$		−	4.95687i		−	0.192800i	−0.995343	−	0.0963999i	$-0.969267\pi$
$661$		−	4.95687i		−	0.192800i	0.995343	−	0.0963999i	$-0.0307328\pi$
$662$		−	8.24772i		−	0.320557i
$663$	−0.253583			−0.00984834
$664$			35.8174i			1.38999i
$665$	−13.0274	+	0.795053i	−0.505180	+	0.0308308i
$666$			29.3093i			1.13571i
$667$	−22.2096			−0.859961
$668$	−9.30902			−0.360177
$669$	−1.36358			−0.0527190
$670$		−	12.4067i		−	0.479314i
$671$	−3.62733	−	12.1207i	−0.140032	−	0.467914i
$672$	−3.42688			−0.132195
$673$	38.5349			1.48541			0.742705	−	0.669619i	$-0.233543\pi$
$673$	38.5349			1.48541			0.742705	+	0.669619i	$0.233543\pi$
$674$	−30.2903			−1.16674
$675$		−	1.65367i		−	0.0636497i
$676$	9.38709			0.361042
$677$	25.7887			0.991141			0.495570	−	0.868568i	$-0.334959\pi$
$677$	25.7887			0.991141			0.495570	+	0.868568i	$0.334959\pi$
$678$	−0.891726			−0.0342465
$679$	−37.3094			−1.43180
$680$			2.94454i			0.112918i
$681$			1.57421i			0.0603239i
$682$	−1.53332	−	5.12357i	−0.0587139	−	0.196192i
$683$		−	39.5689i		−	1.51406i	−0.653378	−	0.757032i	$-0.726649\pi$
$683$		−	39.5689i		−	1.51406i	0.653378	−	0.757032i	$-0.273351\pi$
$684$	−0.601779	−	9.86048i	−0.0230096	−	0.377025i
$685$	3.54890			0.135596
$686$		−	16.6803i		−	0.636856i
$687$		−	3.99054i		−	0.152248i
$688$		−	16.0859i		−	0.613269i
$689$		−	10.3158i		−	0.393000i
$690$		−	1.26874i		−	0.0483002i
$691$	9.08769			0.345712			0.172856	−	0.984947i	$-0.444700\pi$
$691$	9.08769			0.345712			0.172856	+	0.984947i	$0.444700\pi$
$692$	12.9515			0.492344
$693$	−8.31959	−	27.7998i	−0.316035	−	1.05603i
$694$		−	33.9659i		−	1.28933i
$695$		−	3.74807i		−	0.142172i
$696$		−	4.63875i		−	0.175832i
$697$		−	9.75361i		−	0.369444i
$698$		−	34.3665i		−	1.30079i
$699$	−2.93451			−0.110993
$700$		−	2.32237i		−	0.0877774i
$701$		−	28.4499i		−	1.07454i	−0.843411	−	0.537268i	$-0.819456\pi$
$701$		−	28.4499i		−	1.07454i	0.843411	−	0.537268i	$-0.180544\pi$
$702$		−	1.73320i		−	0.0654156i
$703$	39.4395	−	2.40697i	1.48749	−	0.0907805i
$704$	−26.1485	+	7.82542i	−0.985510	+	0.294932i
$705$			1.75947i			0.0662656i
$706$	30.4279			1.14517
$707$	26.2806			0.988384
$708$	2.57009			0.0965900
$709$	28.3604			1.06510			0.532548	−	0.846400i	$-0.321234\pi$
$709$	28.3604			1.06510			0.532548	+	0.846400i	$0.321234\pi$
$710$		−	17.8606i		−	0.670297i
$711$	−27.7416			−1.04039
$712$		−	13.9105i		−	0.521317i
$713$			5.98382i			0.224096i
$714$		−	0.887001i		−	0.0331952i
$715$	3.00963	−	0.900686i	0.112554	−	0.0336837i
$716$			6.13636i			0.229326i
$717$	−2.43899			−0.0910857
$718$			37.5680i			1.40203i
$719$	−19.8307			−0.739562			−0.369781	−	0.929119i	$-0.620567\pi$
$719$	−19.8307			−0.739562			−0.369781	+	0.929119i	$0.620567\pi$
$720$	−5.39757			−0.201156
$721$	−16.7979			−0.625588
$722$	20.8679	−	2.55663i	0.776621	−	0.0951479i
$723$			1.43306i			0.0532959i
$724$		−	14.1486i		−	0.525829i
$725$	5.40885			0.200880
$726$	1.86711	+	2.84007i	0.0692948	+	0.105405i
$727$	1.46979			0.0545114			0.0272557	−	0.999628i	$-0.491323\pi$
$727$	1.46979			0.0545114			0.0272557	+	0.999628i	$0.491323\pi$
$728$		−	8.71060i		−	0.322836i
$729$	22.8801			0.847410
$730$		−	9.39541i		−	0.347740i
$731$	−8.34893			−0.308796
$732$	−0.826189			−0.0305368
$733$		−	15.3222i		−	0.565937i	−0.959129	−	0.282969i	$-0.908681\pi$
$733$		−	15.3222i		−	0.565937i	0.959129	−	0.282969i	$-0.0913192\pi$
$734$	2.09575			0.0773557
$735$			0.548847i			0.0202445i
$736$	16.8294			0.620341
$737$	−10.6618	−	35.6261i	−0.392731	−	1.31230i
$738$	32.8934			1.21082
$739$			13.6088i			0.500609i	0.968167	+	0.250305i	$0.0805308\pi$
$739$			13.6088i			0.500609i	−0.968167	+	0.250305i	$0.919469\pi$
$740$			7.03082i			0.258458i
$741$	−1.15077	+	0.0702310i	−0.0422747	+	0.00258000i
$742$	36.0833			1.32466
$743$	−32.2115			−1.18173			−0.590863	−	0.806772i	$-0.701213\pi$
$743$	−32.2115			−1.18173			−0.590863	+	0.806772i	$0.701213\pi$
$744$	−1.24979			−0.0458197
$745$			2.62253i			0.0960822i
$746$	12.9718			0.474931
$747$			34.0769i			1.24681i
$748$	0.707091	+	2.36273i	0.0258538	+	0.0863901i
$749$			26.8502i			0.981084i
$750$			0.308985i			0.0112825i
$751$		−	27.0831i		−	0.988277i	−0.869383	−	0.494138i	$-0.835484\pi$
$751$		−	27.0831i		−	0.988277i	0.869383	−	0.494138i	$-0.164516\pi$
$752$	11.6391			0.424434
$753$		−	2.54791i		−	0.0928509i
$754$	5.66901			0.206453
$755$	15.7431			0.572951
$756$	−3.84043			−0.139675
$757$	31.0889			1.12995			0.564973	−	0.825109i	$-0.308887\pi$
$757$	31.0889			1.12995			0.564973	+	0.825109i	$0.308887\pi$
$758$		−	25.8191i		−	0.937792i
$759$	−1.09030	−	3.64321i	−0.0395753	−	0.132240i
$760$	0.815506	+	13.3625i	0.0295815	+	0.484709i
$761$			25.0470i			0.907953i	0.891014	+	0.453977i	$0.149995\pi$
$761$			25.0470i			0.907953i	−0.891014	+	0.453977i	$0.850005\pi$
$762$		−	6.43504i		−	0.233117i
$763$		−	6.36023i		−	0.230256i
$764$	−8.89714			−0.321887
$765$			2.80145i			0.101287i
$766$			2.17893i			0.0787279i
$767$			11.2401i			0.405855i
$768$			4.31517i			0.155710i
$769$		−	37.7274i		−	1.36048i	−0.732988	−	0.680242i	$-0.761875\pi$
$769$		−	37.7274i		−	1.36048i	0.732988	−	0.680242i	$-0.238125\pi$
$770$	3.15049	+	10.5273i	0.113536	+	0.379378i
$771$	−7.04045			−0.253556
$772$	−1.54761			−0.0556997
$773$			0.677275i			0.0243599i	0.999926	+	0.0121799i	$0.00387709\pi$
$773$			0.677275i			0.0243599i	−0.999926	+	0.0121799i	$0.996123\pi$
$774$		−	28.1562i		−	1.01205i
$775$		−	1.45728i		−	0.0523470i
$776$			38.2692i			1.37378i
$777$		−	7.57926i		−	0.271904i
$778$	−10.4296			−0.373920
$779$	−2.70131	−	44.2625i	−0.0967846	−	1.58587i
$780$		−	0.205147i		−	0.00734543i
$781$	−15.3486	−	51.2870i	−0.549215	−	1.83519i
$782$			4.35608i			0.155773i
$783$		−	8.94444i		−	0.319648i
$784$	3.63068			0.129667
$785$	10.6474			0.380022
$786$	3.39815			0.121208
$787$	48.3488			1.72345			0.861725	−	0.507376i	$-0.169384\pi$
$787$	48.3488			1.72345			0.861725	+	0.507376i	$0.169384\pi$
$788$			4.08538i			0.145536i
$789$	−0.236333			−0.00841369
$790$	10.5053			0.373761
$791$	−8.64134			−0.307251
$792$	−28.5150	+	8.53362i	−1.01323	+	0.303229i
$793$		−	3.61326i		−	0.128311i
$794$	−1.02369			−0.0363293
$795$	3.04115			0.107858
$796$	−3.98817			−0.141357
$797$			7.73336i			0.273930i	0.990576	+	0.136965i	$0.0437347\pi$
$797$			7.73336i			0.273930i	−0.990576	+	0.136965i	$0.956265\pi$
$798$	−0.245659	−	4.02526i	−0.00869625	−	0.142493i
$799$		−	6.04094i		−	0.213713i
$800$	−4.09858			−0.144907
$801$		−	13.2345i		−	0.467618i
$802$		−	23.4451i		−	0.827874i
$803$	−8.07397	−	26.9790i	−0.284924	−	0.952070i
$804$	−2.42840			−0.0856431
$805$		−	12.2949i		−	0.433337i
$806$		−	1.52737i		−	0.0537993i
$807$	−5.86581			−0.206486
$808$		−	26.9567i		−	0.948333i
$809$		−	31.6709i		−	1.11349i	−0.830683	−	0.556745i	$-0.812050\pi$
$809$		−	31.6709i		−	1.11349i	0.830683	−	0.556745i	$-0.187950\pi$
$810$	−9.18888			−0.322864
$811$	27.8656			0.978495			0.489247	−	0.872145i	$-0.337272\pi$
$811$	27.8656			0.978495			0.489247	+	0.872145i	$0.337272\pi$
$812$		−	12.5614i		−	0.440818i
$813$	−7.18529			−0.251999
$814$	−9.53788	−	31.8707i	−0.334303	−	1.11707i
$815$	−5.24498			−0.183724
$816$	−0.494529			−0.0173120
$817$	−37.8879	+	2.31228i	−1.32553	+	0.0808963i
$818$	7.51122			0.262624
$819$		−	8.28731i		−	0.289582i
$820$	7.89061			0.275552
$821$		−	3.24327i		−	0.113191i	−0.998397	−	0.0565955i	$-0.981975\pi$
$821$		−	3.24327i		−	0.113191i	0.998397	−	0.0565955i	$-0.0180245\pi$
$822$			1.09656i			0.0382468i
$823$	46.4828			1.62029			0.810145	−	0.586230i	$-0.199389\pi$
$823$	46.4828			1.62029			0.810145	+	0.586230i	$0.199389\pi$
$824$			17.2301i			0.600238i
$825$	0.265527	+	0.887255i	0.00924447	+	0.0308902i
$826$	−39.3163			−1.36799
$827$	16.7341			0.581903			0.290952	−	0.956738i	$-0.406028\pi$
$827$	16.7341			0.581903			0.290952	+	0.956738i	$0.406028\pi$
$828$	9.30604			0.323407
$829$		−	19.4673i		−	0.676126i	−0.941124	−	0.338063i	$-0.890228\pi$
$829$		−	19.4673i		−	0.676126i	0.941124	−	0.338063i	$-0.109772\pi$
$830$		−	12.9043i		−	0.447916i
$831$	5.63749			0.195562
$832$	−7.79505			−0.270245
$833$		−	1.88440i		−	0.0652905i
$834$	1.15810			0.0401017
$835$	12.0022			0.415352
$836$	3.86319	+	10.5264i	0.133611	+	0.364063i
$837$	−2.40985			−0.0832967
$838$	−31.3158			−1.08179
$839$			36.9638i			1.27613i	0.769981	+	0.638067i	$0.220266\pi$
$839$			36.9638i			1.27613i	−0.769981	+	0.638067i	$0.779734\pi$
$840$	2.56793			0.0886020
$841$	0.255694			0.00881705
$842$			16.8347i			0.580163i
$843$		−	1.15326i		−	0.0397203i
$844$	16.5315			0.569038
$845$	−12.1028			−0.416349
$846$	20.3727			0.700427
$847$	18.0933	+	27.5219i	0.621694	+	0.945665i
$848$		−	20.1175i		−	0.690838i
$849$	5.55093			0.190508
$850$		−	1.06086i		−	0.0363873i
$851$			37.2218i			1.27595i
$852$	−3.49591			−0.119768
$853$		−	45.4214i		−	1.55520i	−0.628761	−	0.777599i	$-0.716438\pi$
$853$		−	45.4214i		−	1.55520i	0.628761	−	0.777599i	$-0.283562\pi$
$854$	12.6387			0.432488
$855$	0.775877	+	12.7132i	0.0265344	+	0.434781i
$856$	27.5409			0.941329
$857$	26.7416			0.913477			0.456738	−	0.889601i	$-0.349018\pi$
$857$	26.7416			0.913477			0.456738	+	0.889601i	$0.349018\pi$
$858$	0.278298	+	0.929930i	0.00950095	+	0.0317473i
$859$	18.7187			0.638673			0.319337	−	0.947641i	$-0.396540\pi$
$859$	18.7187			0.638673			0.319337	+	0.947641i	$0.396540\pi$
$860$		−	6.75423i		−	0.230317i
$861$	−8.50611			−0.289888
$862$	−32.5198			−1.10763
$863$		−	3.03093i		−	0.103174i	−0.998669	−	0.0515870i	$-0.983572\pi$
$863$		−	3.03093i		−	0.103174i	0.998669	−	0.0515870i	$-0.0164280\pi$
$864$			6.77768i			0.230581i
$865$	−16.6985			−0.567765
$866$			12.7843i			0.434430i
$867$		−	4.49041i		−	0.152502i
$868$	−3.38434			−0.114872
$869$	30.1661	−	9.02774i	1.02331	−	0.306245i
$870$			1.67125i			0.0566608i
$871$		−	10.6204i		−	0.359858i
$872$	−6.52385			−0.220925
$873$			36.4095i			1.23228i
$874$	1.20644	+	19.7681i	0.0408083	+	0.668667i
$875$			2.99424i			0.101224i
$876$	−1.83899			−0.0621336
$877$	1.71461			0.0578984			0.0289492	−	0.999581i	$-0.490784\pi$
$877$	1.71461			0.0578984			0.0289492	+	0.999581i	$0.490784\pi$
$878$	−29.9044			−1.00923
$879$		−	2.20771i		−	0.0744643i
$880$	5.86928	−	1.75649i	0.197853	−	0.0592112i
$881$	33.0583			1.11376			0.556881	−	0.830593i	$-0.311998\pi$
$881$	33.0583			1.11376			0.556881	+	0.830593i	$0.311998\pi$
$882$	6.35501			0.213984
$883$	−42.8695			−1.44267			−0.721336	−	0.692585i	$-0.756472\pi$
$883$	−42.8695			−1.44267			−0.721336	+	0.692585i	$0.756472\pi$
$884$			0.704347i			0.0236897i
$885$	−3.31363			−0.111387
$886$	−11.6563			−0.391600
$887$	−9.09299			−0.305313			−0.152656	−	0.988279i	$-0.548783\pi$
$887$	−9.09299			−0.305313			−0.152656	+	0.988279i	$0.548783\pi$
$888$	−7.77423			−0.260886
$889$		−	62.3593i		−	2.09146i
$890$			5.01167i			0.167992i
$891$	−26.3860	+	7.89649i	−0.883965	+	0.264542i
$892$			3.78745i			0.126813i
$893$	−1.67307	−	27.4141i	−0.0559871	−	0.917379i
$894$	−0.810323			−0.0271013
$895$		−	7.91163i		−	0.264457i
$896$		−	2.72185i		−	0.0909306i
$897$		−	1.08607i		−	0.0362627i
$898$			8.19939i			0.273617i
$899$		−	7.88220i		−	0.262886i
$900$	−2.26636			−0.0755453
$901$	−10.4414			−0.347854
$902$	−35.7681	+	10.7043i	−1.19095	+	0.356413i
$903$			7.28109i			0.242299i
$904$			8.86364i			0.294800i
$905$			18.2419i			0.606380i
$906$			4.86439i			0.161609i
$907$		−	5.29258i		−	0.175737i	−0.996132	−	0.0878686i	$-0.971994\pi$
$907$		−	5.29258i		−	0.175737i	0.996132	−	0.0878686i	$-0.0280056\pi$
$908$	4.37250			0.145106
$909$		−	25.6467i		−	0.850649i
$910$			3.13826i			0.104032i
$911$			36.2340i			1.20049i	0.799817	+	0.600244i	$0.204930\pi$
$911$			36.2340i			1.20049i	−0.799817	+	0.600244i	$0.795070\pi$
$912$	−2.24420	+	0.136962i	−0.0743129	+	0.00453527i
$913$	−11.0894	−	37.0550i	−0.367005	−	1.22634i
$914$		−	8.69442i		−	0.287586i
$915$	1.06521			0.0352147
$916$	−11.0840			−0.366227
$917$	32.9301			1.08745
$918$	−1.75431			−0.0579010
$919$		−	7.84814i		−	0.258886i	−0.991587	−	0.129443i	$-0.958681\pi$
$919$		−	7.84814i		−	0.258886i	0.991587	−	0.129443i	$-0.0413190\pi$
$920$	−12.6112			−0.415777
$921$		−	1.01970i		−	0.0336002i
$922$			8.87587i			0.292311i
$923$		−	15.2890i		−	0.503244i
$924$	2.06054	−	0.616653i	0.0677867	−	0.0202864i
$925$		−	9.06487i		−	0.298051i
$926$	−16.4684			−0.541185
$927$			16.3928i			0.538409i
$928$	−22.1686			−0.727720
$929$	2.37661			0.0779742			0.0389871	−	0.999240i	$-0.487587\pi$
$929$	2.37661			0.0779742			0.0389871	+	0.999240i	$0.487587\pi$
$930$	0.450277			0.0147652
$931$	−0.521894	−	8.55151i	−0.0171044	−	0.280264i
$932$			8.15085i			0.266990i
$933$		−	6.96808i		−	0.228125i
$934$	−23.7113			−0.775859
$935$	−0.911655	−	3.04628i	−0.0298143	−	0.0996240i
$936$	−8.50050			−0.277848
$937$		−	22.0686i		−	0.720950i	−0.932769	−	0.360475i	$-0.882615\pi$
$937$		−	22.0686i		−	0.720950i	0.932769	−	0.360475i	$-0.117385\pi$
$938$	37.1488			1.21295
$939$		−	1.46149i		−	0.0476938i
$940$	4.88708			0.159399
$941$	−50.1080			−1.63348			−0.816738	−	0.577009i	$-0.804220\pi$
$941$	−50.1080			−1.63348			−0.816738	+	0.577009i	$0.804220\pi$
$942$			3.28989i			0.107190i
$943$	41.7736			1.36034
$944$			21.9200i			0.713435i
$945$	4.95148			0.161072
$946$	9.16266	+	30.6169i	0.297904	+	0.995441i
$947$	22.7643			0.739739			0.369870	−	0.929084i	$-0.379402\pi$
$947$	22.7643			0.739739			0.369870	+	0.929084i	$0.379402\pi$
$948$		−	2.05623i		−	0.0667831i
$949$		−	8.04264i		−	0.261075i
$950$	−0.293811	−	4.81425i	−0.00953249	−	0.156195i
$951$	−4.47155			−0.145000
$952$	−8.81668			−0.285750
$953$	−41.6403			−1.34886			−0.674431	−	0.738338i	$-0.735611\pi$
$953$	−41.6403			−1.34886			−0.674431	+	0.738338i	$0.735611\pi$
$954$		−	35.2130i		−	1.14006i
$955$	11.4711			0.371197
$956$			6.77449i			0.219103i
$957$	1.43620	+	4.79903i	0.0464257	+	0.155131i
$958$			18.3022i			0.591316i
$959$			10.6263i			0.343140i
$960$		−	2.29802i		−	0.0741684i
$961$	28.8763			0.931495
$962$		−	9.50087i		−	0.306320i
$963$	26.2026			0.844366
$964$	3.98043			0.128201
$965$	1.99534			0.0642323
$966$	3.79893			0.122229
$967$		−	16.3135i		−	0.524607i	−0.964985	−	0.262303i	$-0.915518\pi$
$967$		−	16.3135i		−	0.524607i	0.964985	−	0.262303i	$-0.0844821\pi$
$968$	28.2299	−	18.5588i	0.907345	−	0.596502i
$969$	0.0710863	+	1.16479i	0.00228362	+	0.0374184i
$970$		−	13.7877i		−	0.442695i
$971$			53.7010i			1.72335i	0.507464	+	0.861673i	$0.330583\pi$
$971$			53.7010i			1.72335i	−0.507464	+	0.861673i	$0.669417\pi$
$972$			5.64638i			0.181108i
$973$	11.2226			0.359781
$974$			45.8330i			1.46858i
$975$			0.264497i			0.00847067i
$976$		−	7.04646i		−	0.225552i
$977$		−	25.2197i		−	0.806850i	−0.915013	−	0.403425i	$-0.867820\pi$
$977$		−	25.2197i		−	0.806850i	0.915013	−	0.403425i	$-0.132180\pi$
$978$		−	1.62062i		−	0.0518217i
$979$	4.30680	+	14.3911i	0.137646	+	0.459941i
$980$	1.52447			0.0486973
$981$	−6.20682			−0.198169
$982$			10.6737i			0.340612i
$983$			10.3167i			0.329050i	0.986373	+	0.164525i	$0.0526092\pi$
$983$			10.3167i			0.329050i	−0.986373	+	0.164525i	$0.947391\pi$
$984$			8.72493i			0.278141i
$985$		−	5.26729i		−	0.167830i
$986$		−	5.73805i		−	0.182737i
$987$	−5.26829			−0.167692
$988$	0.195072	+	3.19637i	0.00620608	+	0.101690i
$989$		−	35.7575i		−	1.13702i
$990$	10.2734	−	3.07450i	0.326510	−	0.0977140i
$991$			11.4321i			0.363152i	0.983377	+	0.181576i	$0.0581198\pi$
$991$			11.4321i			0.363152i	−0.983377	+	0.181576i	$0.941880\pi$
$992$			5.97277i			0.189636i
$993$	2.08138			0.0660508
$994$	53.4791			1.69625
$995$	5.14197			0.163011
$996$	−2.52580			−0.0800330
$997$		−	46.3192i		−	1.46694i	−0.679721	−	0.733471i	$-0.737899\pi$
$997$		−	46.3192i		−	1.46694i	0.679721	−	0.733471i	$-0.262101\pi$
$998$	28.7183			0.909062
$999$	−14.9903			−0.474271

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.f.b.626.13	✓	40
11.10	odd	2	inner	1045.2.f.b.626.27	yes	40
19.18	odd	2	inner	1045.2.f.b.626.28	yes	40
209.208	even	2	inner	1045.2.f.b.626.14	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.f.b.626.13	✓	40	1.1	even	1	trivial
1045.2.f.b.626.14	yes	40	209.208	even	2	inner
1045.2.f.b.626.27	yes	40	11.10	odd	2	inner
1045.2.f.b.626.28	yes	40	19.18	odd	2	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.10652 q^{2} -0.279240i q^{3} -0.775612 q^{4} +1.00000 q^{5} +0.308985i q^{6} +2.99424i q^{7} +3.07127 q^{8} +2.92202 q^{9} +O(q^{10})\)	\(q-1.10652 q^{2} -0.279240i q^{3} -0.775612 q^{4} +1.00000 q^{5} +0.308985i q^{6} +2.99424i q^{7} +3.07127 q^{8} +2.92202 q^{9} -1.10652 q^{10} +(-3.17739 + 0.950891i) q^{11} +0.216582i q^{12} -0.947201 q^{13} -3.31319i q^{14} -0.279240i q^{15} -1.84720 q^{16} +0.958737i q^{17} -3.23328 q^{18} +(0.265527 + 4.35080i) q^{19} -0.775612 q^{20} +0.836113 q^{21} +(3.51585 - 1.05218i) q^{22} -4.10617 q^{23} -0.857622i q^{24} +1.00000 q^{25} +1.04810 q^{26} -1.65367i q^{27} -2.32237i q^{28} +5.40885 q^{29} +0.308985i q^{30} -1.45728i q^{31} -4.09858 q^{32} +(0.265527 + 0.887255i) q^{33} -1.06086i q^{34} +2.99424i q^{35} -2.26636 q^{36} -9.06487i q^{37} +(-0.293811 - 4.81425i) q^{38} +0.264497i q^{39} +3.07127 q^{40} -10.1734 q^{41} -0.925177 q^{42} +8.70825i q^{43} +(2.46442 - 0.737523i) q^{44} +2.92202 q^{45} +4.54356 q^{46} -6.30093 q^{47} +0.515813i q^{48} -1.96550 q^{49} -1.10652 q^{50} +0.267718 q^{51} +0.734661 q^{52} +10.8908i q^{53} +1.82982i q^{54} +(-3.17739 + 0.950891i) q^{55} +9.19614i q^{56} +(1.21492 - 0.0741458i) q^{57} -5.98501 q^{58} -11.8666i q^{59} +0.216582i q^{60} +3.81467i q^{61} +1.61251i q^{62} +8.74926i q^{63} +8.22956 q^{64} -0.947201 q^{65} +(-0.293811 - 0.981766i) q^{66} +11.2124i q^{67} -0.743608i q^{68} +1.14661i q^{69} -3.31319i q^{70} +16.1413i q^{71} +8.97433 q^{72} +8.49095i q^{73} +10.0305i q^{74} -0.279240i q^{75} +(-0.205946 - 3.37454i) q^{76} +(-2.84720 - 9.51388i) q^{77} -0.292671i q^{78} -9.49398 q^{79} -1.84720 q^{80} +8.30430 q^{81} +11.2571 q^{82} +11.6621i q^{83} -0.648500 q^{84} +0.958737i q^{85} -9.63586i q^{86} -1.51037i q^{87} +(-9.75863 + 2.92045i) q^{88} -4.52922i q^{89} -3.23328 q^{90} -2.83615i q^{91} +3.18479 q^{92} -0.406931 q^{93} +6.97211 q^{94} +(0.265527 + 4.35080i) q^{95} +1.14449i q^{96} +12.4604i q^{97} +2.17487 q^{98} +(-9.28441 + 2.77853i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{4} + 40 q^{5} - 28 q^{9}+O(q^{10}) \) 40 * q + 40 * q^4 + 40 * q^5 - 28 * q^9	\( 40 q + 40 q^{4} + 40 q^{5} - 28 q^{9} - 4 q^{11} + 48 q^{16} + 40 q^{20} + 24 q^{23} + 40 q^{25} - 24 q^{26} + 24 q^{36} - 28 q^{38} - 60 q^{42} - 48 q^{44} - 28 q^{45} - 36 q^{49} - 4 q^{55} - 36 q^{58} - 40 q^{64} - 28 q^{66} + 8 q^{77} + 48 q^{80} + 80 q^{81} + 8 q^{82} + 4 q^{92} + 56 q^{93} - 16 q^{99}+O(q^{100}) \) 40 * q + 40 * q^4 + 40 * q^5 - 28 * q^9 - 4 * q^11 + 48 * q^16 + 40 * q^20 + 24 * q^23 + 40 * q^25 - 24 * q^26 + 24 * q^36 - 28 * q^38 - 60 * q^42 - 48 * q^44 - 28 * q^45 - 36 * q^49 - 4 * q^55 - 36 * q^58 - 40 * q^64 - 28 * q^66 + 8 * q^77 + 48 * q^80 + 80 * q^81 + 8 * q^82 + 4 * q^92 + 56 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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