LMFDB - Embedded newform 1045.2.b.e.419.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,2,Mod(419,1045)]

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([1, 0, 0]))

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

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

chi := DirichletCharacter("1045.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1045.b (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:	$30$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			419.20
Character	$\chi$	$=$	1045.419
Dual form			1045.2.b.e.419.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.961626i q^{2} -0.510054i q^{3} +1.07528 q^{4} +(1.58322 - 1.57905i) q^{5} +0.490481 q^{6} +0.688271i q^{7} +2.95726i q^{8} +2.73984 q^{9} +O(q^{10})$	\(q+0.961626i q^{2} -0.510054i q^{3} +1.07528 q^{4} +(1.58322 - 1.57905i) q^{5} +0.490481 q^{6} +0.688271i q^{7} +2.95726i q^{8} +2.73984 q^{9} +(1.51846 + 1.52247i) q^{10} +1.00000 q^{11} -0.548449i q^{12} +6.48283i q^{13} -0.661859 q^{14} +(-0.805402 - 0.807529i) q^{15} -0.693232 q^{16} -4.14033i q^{17} +2.63471i q^{18} -1.00000 q^{19} +(1.70240 - 1.69792i) q^{20} +0.351055 q^{21} +0.961626i q^{22} +5.52434i q^{23} +1.50836 q^{24} +(0.0131852 - 4.99998i) q^{25} -6.23406 q^{26} -2.92763i q^{27} +0.740081i q^{28} -10.4774 q^{29} +(0.776541 - 0.774496i) q^{30} +6.18325 q^{31} +5.24790i q^{32} -0.510054i q^{33} +3.98145 q^{34} +(1.08682 + 1.08969i) q^{35} +2.94609 q^{36} +0.887957i q^{37} -0.961626i q^{38} +3.30659 q^{39} +(4.66968 + 4.68201i) q^{40} +1.87732 q^{41} +0.337584i q^{42} -10.6567i q^{43} +1.07528 q^{44} +(4.33778 - 4.32636i) q^{45} -5.31235 q^{46} +2.89795i q^{47} +0.353586i q^{48} +6.52628 q^{49} +(4.80811 + 0.0126793i) q^{50} -2.11179 q^{51} +6.97083i q^{52} -9.37705i q^{53} +2.81529 q^{54} +(1.58322 - 1.57905i) q^{55} -2.03540 q^{56} +0.510054i q^{57} -10.0753i q^{58} -1.00087 q^{59} +(-0.866029 - 0.868316i) q^{60} -4.33844 q^{61} +5.94598i q^{62} +1.88576i q^{63} -6.43298 q^{64} +(10.2367 + 10.2638i) q^{65} +0.490481 q^{66} +1.18194i q^{67} -4.45200i q^{68} +2.81771 q^{69} +(-1.04787 + 1.04511i) q^{70} +12.1904 q^{71} +8.10245i q^{72} -1.17954i q^{73} -0.853882 q^{74} +(-2.55026 - 0.00672518i) q^{75} -1.07528 q^{76} +0.688271i q^{77} +3.17971i q^{78} -1.99189 q^{79} +(-1.09754 + 1.09465i) q^{80} +6.72628 q^{81} +1.80528i q^{82} -0.103936i q^{83} +0.377481 q^{84} +(-6.53780 - 6.55507i) q^{85} +10.2478 q^{86} +5.34405i q^{87} +2.95726i q^{88} -9.70208 q^{89} +(4.16034 + 4.17133i) q^{90} -4.46194 q^{91} +5.94019i q^{92} -3.15379i q^{93} -2.78674 q^{94} +(-1.58322 + 1.57905i) q^{95} +2.67671 q^{96} -0.708659i q^{97} +6.27584i q^{98} +2.73984 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9}+O(q^{10}) $ 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9	$ 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9} + 10 q^{10} + 30 q^{11} + 4 q^{14} + 4 q^{15} + 66 q^{16} - 30 q^{19} + 10 q^{20} + 14 q^{21} - 22 q^{24} - 6 q^{25} - 30 q^{29} + 14 q^{30} + 26 q^{31} - 12 q^{34} + 6 q^{35} + 78 q^{36} - 64 q^{39} - 20 q^{40} + 22 q^{41} - 42 q^{44} + 6 q^{45} + 28 q^{46} - 60 q^{49} + 64 q^{51} - 62 q^{54} - 32 q^{56} + 14 q^{59} - 28 q^{60} + 78 q^{61} - 90 q^{64} + 40 q^{65} + 12 q^{66} + 28 q^{69} + 12 q^{70} + 20 q^{71} - 42 q^{74} + 50 q^{75} + 42 q^{76} - 102 q^{79} - 40 q^{80} + 42 q^{81} - 98 q^{84} - 2 q^{85} - 52 q^{86} + 8 q^{89} + 22 q^{90} + 56 q^{91} - 40 q^{94} - 74 q^{96} - 40 q^{99}+O(q^{100}) $ 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9 + 10 * q^10 + 30 * q^11 + 4 * q^14 + 4 * q^15 + 66 * q^16 - 30 * q^19 + 10 * q^20 + 14 * q^21 - 22 * q^24 - 6 * q^25 - 30 * q^29 + 14 * q^30 + 26 * q^31 - 12 * q^34 + 6 * q^35 + 78 * q^36 - 64 * q^39 - 20 * q^40 + 22 * q^41 - 42 * q^44 + 6 * q^45 + 28 * q^46 - 60 * q^49 + 64 * q^51 - 62 * q^54 - 32 * q^56 + 14 * q^59 - 28 * q^60 + 78 * q^61 - 90 * q^64 + 40 * q^65 + 12 * q^66 + 28 * q^69 + 12 * q^70 + 20 * q^71 - 42 * q^74 + 50 * q^75 + 42 * q^76 - 102 * q^79 - 40 * q^80 + 42 * q^81 - 98 * q^84 - 2 * q^85 - 52 * q^86 + 8 * q^89 + 22 * q^90 + 56 * q^91 - 40 * q^94 - 74 * q^96 - 40 * 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 $

$2$			0.961626i			0.679972i	0.940430	+	0.339986i	$0.110422\pi$
$2$			0.961626i			0.679972i	−0.940430	+	0.339986i	$0.889578\pi$
$3$		−	0.510054i		−	0.294480i	−0.989101	−	0.147240i	$-0.952961\pi$
$3$		−	0.510054i		−	0.294480i	0.989101	−	0.147240i	$-0.0470389\pi$
$4$	1.07528			0.537638
$5$	1.58322	−	1.57905i	0.708039	−	0.706174i
$5$	1.58322	−	1.57905i	0.708039	−	0.706174i
$6$	0.490481			0.200238
$7$			0.688271i			0.260142i	0.991505	+	0.130071i	$0.0415205\pi$
$7$			0.688271i			0.260142i	−0.991505	+	0.130071i	$0.958479\pi$
$8$			2.95726i			1.04555i
$9$	2.73984			0.913282
$10$	1.51846	+	1.52247i	0.480179	+	0.481447i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$		−	0.548449i		−	0.158323i
$13$			6.48283i			1.79801i	0.437934	+	0.899007i	$0.355710\pi$
$13$			6.48283i			1.79801i	−0.437934	+	0.899007i	$0.644290\pi$
$14$	−0.661859			−0.176889
$15$	−0.805402	−	0.807529i	−0.207954	−	0.208503i
$16$	−0.693232			−0.173308
$17$		−	4.14033i		−	1.00418i	−0.864816	−	0.502089i	$-0.832565\pi$
$17$		−	4.14033i		−	1.00418i	0.864816	−	0.502089i	$-0.167435\pi$
$18$			2.63471i			0.621006i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	1.70240	−	1.69792i	0.380668	−	0.379666i
$21$	0.351055			0.0766066
$22$			0.961626i			0.205019i
$23$			5.52434i			1.15191i	0.817483	+	0.575953i	$0.195369\pi$
$23$			5.52434i			1.15191i	−0.817483	+	0.575953i	$0.804631\pi$
$24$	1.50836			0.307894
$25$	0.0131852	−	4.99998i	0.00263705	−	0.999997i
$26$	−6.23406			−1.22260
$27$		−	2.92763i		−	0.563423i
$28$			0.740081i			0.139862i
$29$	−10.4774			−1.94561			−0.972803	−	0.231634i	$-0.925593\pi$
$29$	−10.4774			−1.94561			−0.972803	+	0.231634i	$0.925593\pi$
$30$	0.776541	−	0.774496i	0.141776	−	0.141403i
$31$	6.18325			1.11055			0.555273	−	0.831668i	$-0.312614\pi$
$31$	6.18325			1.11055			0.555273	+	0.831668i	$0.312614\pi$
$32$			5.24790i			0.927706i
$33$		−	0.510054i		−	0.0887890i
$34$	3.98145			0.682813
$35$	1.08682	+	1.08969i	0.183705	+	0.184190i
$36$	2.94609			0.491015
$37$			0.887957i			0.145979i	0.997333	+	0.0729896i	$0.0232540\pi$
$37$			0.887957i			0.145979i	−0.997333	+	0.0729896i	$0.976746\pi$
$38$		−	0.961626i		−	0.155996i
$39$	3.30659			0.529479
$40$	4.66968	+	4.68201i	0.738341	+	0.740290i
$41$	1.87732			0.293189			0.146594	−	0.989197i	$-0.453169\pi$
$41$	1.87732			0.293189			0.146594	+	0.989197i	$0.453169\pi$
$42$			0.337584i			0.0520903i
$43$		−	10.6567i		−	1.62514i	−0.582867	−	0.812568i	$-0.698069\pi$
$43$		−	10.6567i		−	1.62514i	0.582867	−	0.812568i	$-0.301931\pi$
$44$	1.07528			0.162104
$45$	4.33778	−	4.32636i	0.646639	−	0.644936i
$46$	−5.31235			−0.783263
$47$			2.89795i			0.422710i	0.977409	+	0.211355i	$0.0677875\pi$
$47$			2.89795i			0.422710i	−0.977409	+	0.211355i	$0.932212\pi$
$48$			0.353586i			0.0510357i
$49$	6.52628			0.932326
$50$	4.80811	+	0.0126793i	0.679970	+	0.00179312i
$51$	−2.11179			−0.295710
$52$			6.97083i			0.966680i
$53$		−	9.37705i		−	1.28804i	−0.765010	−	0.644018i	$-0.777266\pi$
$53$		−	9.37705i		−	1.28804i	0.765010	−	0.644018i	$-0.222734\pi$
$54$	2.81529			0.383112
$55$	1.58322	−	1.57905i	0.213482	−	0.212919i
$56$	−2.03540			−0.271992
$57$			0.510054i			0.0675583i
$58$		−	10.0753i		−	1.32296i
$59$	−1.00087			−0.130302			−0.0651509	−	0.997875i	$-0.520753\pi$
$59$	−1.00087			−0.130302			−0.0651509	+	0.997875i	$0.520753\pi$
$60$	−0.866029	−	0.868316i	−0.111804	−	0.112099i
$61$	−4.33844			−0.555481			−0.277740	−	0.960656i	$-0.589585\pi$
$61$	−4.33844			−0.555481			−0.277740	+	0.960656i	$0.589585\pi$
$62$			5.94598i			0.755140i
$63$			1.88576i			0.237583i
$64$	−6.43298			−0.804123
$65$	10.2367	+	10.2638i	1.26971	+	1.27306i
$66$	0.490481			0.0603741
$67$			1.18194i			0.144397i	0.997390	+	0.0721984i	$0.0230015\pi$
$67$			1.18194i			0.144397i	−0.997390	+	0.0721984i	$0.976999\pi$
$68$		−	4.45200i		−	0.539884i
$69$	2.81771			0.339213
$70$	−1.04787	+	1.04511i	−0.125244	+	0.124915i
$71$	12.1904			1.44674			0.723369	−	0.690462i	$-0.242593\pi$
$71$	12.1904			1.44674			0.723369	+	0.690462i	$0.242593\pi$
$72$			8.10245i			0.954883i
$73$		−	1.17954i		−	0.138055i	−0.997615	−	0.0690275i	$-0.978010\pi$
$73$		−	1.17954i		−	0.138055i	0.997615	−	0.0690275i	$-0.0219896\pi$
$74$	−0.853882			−0.0992618
$75$	−2.55026	−	0.00672518i	−0.294479	−	0.000776557i
$76$	−1.07528			−0.123343
$77$			0.688271i			0.0784357i
$78$			3.17971i			0.360031i
$79$	−1.99189			−0.224106			−0.112053	−	0.993702i	$-0.535743\pi$
$79$	−1.99189			−0.224106			−0.112053	+	0.993702i	$0.535743\pi$
$80$	−1.09754	+	1.09465i	−0.122709	+	0.122386i
$81$	6.72628			0.747365
$82$			1.80528i			0.199360i
$83$		−	0.103936i		−	0.0114085i	−0.999984	−	0.00570423i	$-0.998184\pi$
$83$		−	0.103936i		−	0.0114085i	0.999984	−	0.00570423i	$-0.00181572\pi$
$84$	0.377481			0.0411866
$85$	−6.53780	−	6.55507i	−0.709124	−	0.710997i
$86$	10.2478			1.10505
$87$			5.34405i			0.572942i
$88$			2.95726i			0.315245i
$89$	−9.70208			−1.02842			−0.514209	−	0.857665i	$-0.671914\pi$
$89$	−9.70208			−1.02842			−0.514209	+	0.857665i	$0.671914\pi$
$90$	4.16034	+	4.17133i	0.438538	+	0.439696i
$91$	−4.46194			−0.467739
$92$			5.94019i			0.619308i
$93$		−	3.15379i		−	0.327033i
$94$	−2.78674			−0.287431
$95$	−1.58322	+	1.57905i	−0.162435	+	0.162007i
$96$	2.67671			0.273191
$97$		−	0.708659i		−	0.0719534i	−0.999353	−	0.0359767i	$-0.988546\pi$
$97$		−	0.708659i		−	0.0719534i	0.999353	−	0.0359767i	$-0.0114542\pi$
$98$			6.27584i			0.633956i
$99$	2.73984			0.275365
$100$	0.0141778	−	5.37636i	0.00141778	−	0.537636i
$101$	−10.4808			−1.04288			−0.521440	−	0.853288i	$-0.674605\pi$
$101$	−10.4808			−1.04288			−0.521440	+	0.853288i	$0.674605\pi$
$102$		−	2.03076i		−	0.201075i
$103$			14.5420i			1.43287i	0.697656	+	0.716433i	$0.254226\pi$
$103$			14.5420i			1.43287i	−0.697656	+	0.716433i	$0.745774\pi$
$104$	−19.1714			−1.87992
$105$	0.555799	−	0.554335i	0.0542404	−	0.0540975i
$106$	9.01721			0.875829
$107$		−	6.29379i		−	0.608443i	−0.952601	−	0.304222i	$-0.901604\pi$
$107$		−	6.29379i		−	0.608443i	0.952601	−	0.304222i	$-0.0983964\pi$
$108$		−	3.14801i		−	0.302917i
$109$	−17.6134			−1.68706			−0.843531	−	0.537081i	$-0.819527\pi$
$109$	−17.6134			−1.68706			−0.843531	+	0.537081i	$0.819527\pi$
$110$	1.51846	+	1.52247i	0.144779	+	0.145162i
$111$	0.452906			0.0429879
$112$		−	0.477131i		−	0.0450847i
$113$		−	18.6566i		−	1.75506i	−0.479519	−	0.877531i	$-0.659189\pi$
$113$		−	18.6566i		−	1.75506i	0.479519	−	0.877531i	$-0.340811\pi$
$114$	−0.490481			−0.0459378
$115$	8.72323	+	8.74626i	0.813445	+	0.815593i
$116$	−11.2661			−1.04603
$117$			17.7620i			1.64209i
$118$		−	0.962460i		−	0.0886016i
$119$	2.84967			0.261229
$120$	2.38808	−	2.38179i	0.218001	−	0.217426i
$121$	1.00000			0.0909091
$122$		−	4.17196i		−	0.377711i
$123$		−	0.957536i		−	0.0863382i
$124$	6.64870			0.597071
$125$	−7.87436	−	7.93690i	−0.704304	−	0.709898i
$126$	−1.81339			−0.161550
$127$			13.0789i			1.16056i	0.814416	+	0.580282i	$0.197058\pi$
$127$			13.0789i			1.16056i	−0.814416	+	0.580282i	$0.802942\pi$
$128$			4.30968i			0.380925i
$129$	−5.43551			−0.478570
$130$	−9.86990	+	9.84391i	−0.865648	+	0.863368i
$131$	−3.52128			−0.307655			−0.153828	−	0.988098i	$-0.549160\pi$
$131$	−3.52128			−0.307655			−0.153828	+	0.988098i	$0.549160\pi$
$132$		−	0.548449i		−	0.0477363i
$133$		−	0.688271i		−	0.0596806i
$134$	−1.13658			−0.0981858
$135$	−4.62288	−	4.63509i	−0.397874	−	0.398925i
$136$	12.2441			1.04992
$137$		−	17.8977i		−	1.52910i	−0.644562	−	0.764552i	$-0.722960\pi$
$137$		−	17.8977i		−	1.52910i	0.644562	−	0.764552i	$-0.277040\pi$
$138$			2.70959i			0.230655i
$139$	17.3265			1.46962			0.734808	−	0.678275i	$-0.237272\pi$
$139$	17.3265			1.46962			0.734808	+	0.678275i	$0.237272\pi$
$140$	1.16863	+	1.17171i	0.0987670	+	0.0990278i
$141$	1.47811			0.124479
$142$			11.7226i			0.983742i
$143$			6.48283i			0.542122i
$144$	−1.89935			−0.158279
$145$	−16.5881	+	16.5444i	−1.37756	+	1.37394i
$146$	1.13428			0.0938736
$147$		−	3.32876i		−	0.274551i
$148$			0.954798i			0.0784839i
$149$	18.3865			1.50628			0.753139	−	0.657862i	$-0.228539\pi$
$149$	18.3865			1.50628			0.753139	+	0.657862i	$0.228539\pi$
$150$	0.00646711	−	2.45240i	0.000528037	−	0.200237i
$151$	12.9787			1.05619			0.528095	−	0.849185i	$-0.322906\pi$
$151$	12.9787			1.05619			0.528095	+	0.849185i	$0.322906\pi$
$152$		−	2.95726i		−	0.239866i
$153$		−	11.3439i		−	0.917098i
$154$	−0.661859			−0.0533341
$155$	9.78947	−	9.76368i	0.786309	−	0.784238i
$156$	3.55550			0.284668
$157$			6.62321i			0.528590i	0.964442	+	0.264295i	$0.0851392\pi$
$157$			6.62321i			0.528590i	−0.964442	+	0.264295i	$0.914861\pi$
$158$		−	1.91546i		−	0.152386i
$159$	−4.78280			−0.379301
$160$	8.28671	+	8.30859i	0.655122	+	0.656852i
$161$	−3.80224			−0.299659
$162$			6.46817i			0.508187i
$163$			11.9647i			0.937149i	0.883424	+	0.468575i	$0.155232\pi$
$163$			11.9647i			0.937149i	−0.883424	+	0.468575i	$0.844768\pi$
$164$	2.01864			0.157629
$165$	−0.805402	−	0.807529i	−0.0627005	−	0.0628660i
$166$	0.0999476			0.00775744
$167$		−	8.93784i		−	0.691631i	−0.938303	−	0.345816i	$-0.887602\pi$
$167$		−	8.93784i		−	0.691631i	0.938303	−	0.345816i	$-0.112398\pi$
$168$			1.03816i			0.0800961i
$169$	−29.0271			−2.23285
$170$	6.30352	−	6.28692i	0.483458	−	0.482185i
$171$	−2.73984			−0.209521
$172$		−	11.4589i		−	0.873734i
$173$		−	1.87770i		−	0.142759i	−0.997449	−	0.0713795i	$-0.977260\pi$
$173$		−	1.87770i		−	0.142759i	0.997449	−	0.0713795i	$-0.0227401\pi$
$174$	−5.13897			−0.389585
$175$	3.44134	+	0.00907501i	0.260141	+	0.000686007i
$176$	−0.693232			−0.0522543
$177$			0.510496i			0.0383713i
$178$		−	9.32977i		−	0.699296i
$179$	−14.0693			−1.05159			−0.525795	−	0.850611i	$-0.676232\pi$
$179$	−14.0693			−1.05159			−0.525795	+	0.850611i	$0.676232\pi$
$180$	4.66431	−	4.65203i	0.347657	−	0.346742i
$181$	−25.0694			−1.86340			−0.931699	−	0.363232i	$-0.881673\pi$
$181$	−25.0694			−1.86340			−0.931699	+	0.363232i	$0.881673\pi$
$182$		−	4.29072i		−	0.318049i
$183$			2.21284i			0.163578i
$184$	−16.3369			−1.20438
$185$	1.40213	+	1.40583i	0.103087	+	0.103359i
$186$	3.03277			0.222374
$187$		−	4.14033i		−	0.302771i
$188$			3.11610i			0.227265i
$189$	2.01500			0.146570
$190$	−1.51846	−	1.52247i	−0.110161	−	0.110451i
$191$	−23.8766			−1.72765			−0.863827	−	0.503789i	$-0.831939\pi$
$191$	−23.8766			−1.72765			−0.863827	+	0.503789i	$0.831939\pi$
$192$			3.28117i			0.236798i
$193$		−	6.83212i		−	0.491786i	−0.969297	−	0.245893i	$-0.920919\pi$
$193$		−	6.83212i		−	0.491786i	0.969297	−	0.245893i	$-0.0790813\pi$
$194$	0.681465			0.0489263
$195$	5.23507	−	5.22129i	0.374891	−	0.373904i
$196$	7.01755			0.501254
$197$		−	11.3000i		−	0.805090i	−0.915400	−	0.402545i	$-0.868126\pi$
$197$		−	11.3000i		−	0.805090i	0.915400	−	0.402545i	$-0.131874\pi$
$198$			2.63471i			0.187240i
$199$	−12.2584			−0.868978			−0.434489	−	0.900677i	$-0.643071\pi$
$199$	−12.2584			−0.868978			−0.434489	+	0.900677i	$0.643071\pi$
$200$	14.7863	+	0.0389922i	1.04555	+	0.00275717i
$201$	0.602852			0.0425219
$202$		−	10.0786i		−	0.709130i
$203$		−	7.21130i		−	0.506134i
$204$	−2.27076			−0.158985
$205$	2.97222	−	2.96439i	0.207589	−	0.207042i
$206$	−13.9840			−0.974309
$207$			15.1358i			1.05201i
$208$		−	4.49410i		−	0.311610i
$209$	−1.00000			−0.0691714
$210$	0.533063	+	0.534470i	0.0367848	+	0.0368820i
$211$	11.4229			0.786382			0.393191	−	0.919457i	$-0.371371\pi$
$211$	11.4229			0.786382			0.393191	+	0.919457i	$0.371371\pi$
$212$		−	10.0829i		−	0.692497i
$213$		−	6.21778i		−	0.426035i
$214$	6.05227			0.413725
$215$	−16.8275	−	16.8720i	−1.14763	−	1.15066i
$216$	8.65778			0.589087
$217$			4.25575i			0.288899i
$218$		−	16.9375i		−	1.14715i
$219$	−0.601631			−0.0406544
$220$	1.70240	−	1.69792i	0.114776	−	0.114474i
$221$	26.8411			1.80553
$222$			0.435526i			0.0292306i
$223$			9.56130i			0.640272i	0.947372	+	0.320136i	$0.103729\pi$
$223$			9.56130i			0.640272i	−0.947372	+	0.320136i	$0.896271\pi$
$224$	−3.61198			−0.241335
$225$	0.0361255	−	13.6992i	0.00240837	−	0.913278i
$226$	17.9406			1.19339
$227$		−	9.62721i		−	0.638980i	−0.947590	−	0.319490i	$-0.896488\pi$
$227$		−	9.62721i		−	0.638980i	0.947590	−	0.319490i	$-0.103512\pi$
$228$			0.548449i			0.0363219i
$229$	−1.62508			−0.107389			−0.0536943	−	0.998557i	$-0.517100\pi$
$229$	−1.62508			−0.107389			−0.0536943	+	0.998557i	$0.517100\pi$
$230$	−8.41063	+	8.38848i	−0.554581	+	0.553120i
$231$	0.351055			0.0230977
$232$		−	30.9845i		−	2.03423i
$233$		−	20.3861i		−	1.33554i	−0.744369	−	0.667769i	$-0.767249\pi$
$233$		−	20.3861i		−	1.33554i	0.744369	−	0.667769i	$-0.232751\pi$
$234$	−17.0804			−1.11658
$235$	4.57602	+	4.58810i	0.298506	+	0.299295i
$236$	−1.07621			−0.0700552
$237$			1.01597i			0.0659946i
$238$			2.74032i			0.177628i
$239$	−17.7150			−1.14589			−0.572944	−	0.819595i	$-0.694199\pi$
$239$	−17.7150			−1.14589			−0.572944	+	0.819595i	$0.694199\pi$
$240$	0.558330	+	0.559805i	0.0360401	+	0.0361352i
$241$	12.6034			0.811854			0.405927	−	0.913905i	$-0.366949\pi$
$241$	12.6034			0.811854			0.405927	+	0.913905i	$0.366949\pi$
$242$			0.961626i			0.0618157i
$243$		−	12.2137i		−	0.783507i
$244$	−4.66502			−0.298647
$245$	10.3326	−	10.3053i	0.660123	−	0.658384i
$246$	0.920792			0.0587075
$247$		−	6.48283i		−	0.412493i
$248$			18.2855i			1.16113i
$249$	−0.0530130			−0.00335956
$250$	7.63233	−	7.57219i	0.482711	−	0.478907i
$251$	24.4686			1.54444			0.772221	−	0.635354i	$-0.219146\pi$
$251$	24.4686			1.54444			0.772221	+	0.635354i	$0.219146\pi$
$252$			2.02771i			0.127733i
$253$			5.52434i			0.347312i
$254$	−12.5770			−0.789151
$255$	−3.34344	+	3.33463i	−0.209374	+	0.208823i
$256$	−17.0103			−1.06314
$257$			1.56488i			0.0976144i	0.998808	+	0.0488072i	$0.0155420\pi$
$257$			1.56488i			0.0976144i	−0.998808	+	0.0488072i	$0.984458\pi$
$258$		−	5.22693i		−	0.325414i
$259$	−0.611155			−0.0379753
$260$	11.0073	+	11.0364i	0.682644	+	0.684447i
$261$	−28.7065			−1.77689
$262$		−	3.38615i		−	0.209197i
$263$		−	4.18552i		−	0.258090i	−0.991639	−	0.129045i	$-0.958809\pi$
$263$		−	4.18552i		−	0.258090i	0.991639	−	0.129045i	$-0.0411912\pi$
$264$	1.50836			0.0928334
$265$	−14.8069	−	14.8459i	−0.909578	−	0.911979i
$266$	0.661859			0.0405812
$267$			4.94858i			0.302848i
$268$			1.27091i			0.0776332i
$269$	−20.3877			−1.24306			−0.621530	−	0.783391i	$-0.713488\pi$
$269$	−20.3877			−1.24306			−0.621530	+	0.783391i	$0.713488\pi$
$270$	4.45722	−	4.44549i	0.271258	−	0.270544i
$271$	−25.9150			−1.57423			−0.787113	−	0.616809i	$-0.788425\pi$
$271$	−25.9150			−1.57423			−0.787113	+	0.616809i	$0.788425\pi$
$272$			2.87021i			0.174032i
$273$			2.27583i			0.137740i
$274$	17.2109			1.03975
$275$	0.0131852	−	4.99998i	0.000795100	−	0.301510i
$276$	3.02982			0.182374
$277$			8.65460i			0.520004i	0.965608	+	0.260002i	$0.0837233\pi$
$277$			8.65460i			0.520004i	−0.965608	+	0.260002i	$0.916277\pi$
$278$			16.6616i			0.999298i
$279$	16.9412			1.01424
$280$	−3.22249	+	3.21400i	−0.192581	+	0.192073i
$281$	25.5928			1.52674			0.763370	−	0.645962i	$-0.223543\pi$
$281$	25.5928			1.52674			0.763370	+	0.645962i	$0.223543\pi$
$282$			1.42139i			0.0846426i
$283$		−	11.7449i		−	0.698162i	−0.937093	−	0.349081i	$-0.886494\pi$
$283$		−	11.7449i		−	0.698162i	0.937093	−	0.349081i	$-0.113506\pi$
$284$	13.1081			0.777821
$285$	0.805402	+	0.807529i	0.0477079	+	0.0478339i
$286$	−6.23406			−0.368628
$287$			1.29211i			0.0762707i
$288$			14.3784i			0.847257i
$289$	−0.142359			−0.00837405
$290$	−15.9095	−	15.9515i	−0.934238	−	0.936705i
$291$	−0.361455			−0.0211888
$292$		−	1.26833i		−	0.0742236i
$293$		−	12.3537i		−	0.721713i	−0.932621	−	0.360857i	$-0.882484\pi$
$293$		−	12.3537i		−	0.721713i	0.932621	−	0.360857i	$-0.117516\pi$
$294$	3.20102			0.186687
$295$	−1.58459	+	1.58042i	−0.0922587	+	0.0920157i
$296$	−2.62592			−0.152629
$297$		−	2.92763i		−	0.169878i
$298$			17.6809i			1.02423i
$299$	−35.8134			−2.07114
$300$	−2.74223	−	0.00723142i	−0.158323	−	0.000417506i
$301$	7.33472			0.422766
$302$			12.4806i			0.718180i
$303$			5.34578i			0.307107i
$304$	0.693232			0.0397596
$305$	−6.86872	+	6.85063i	−0.393302	+	0.392266i
$306$	10.9086			0.623601
$307$		−	27.2713i		−	1.55646i	−0.627981	−	0.778229i	$-0.716118\pi$
$307$		−	27.2713i		−	1.55646i	0.627981	−	0.778229i	$-0.283882\pi$
$308$			0.740081i			0.0421700i
$309$	7.41720			0.421950
$310$	9.38901	+	9.41380i	0.533260	+	0.534668i
$311$	−19.0990			−1.08301			−0.541504	−	0.840698i	$-0.682145\pi$
$311$	−19.0990			−1.08301			−0.541504	+	0.840698i	$0.682145\pi$
$312$			9.77848i			0.553597i
$313$			8.05315i			0.455191i	0.973756	+	0.227596i	$0.0730864\pi$
$313$			8.05315i			0.455191i	−0.973756	+	0.227596i	$0.926914\pi$
$314$	−6.36905			−0.359426
$315$	2.97771	+	2.98557i	0.167775	+	0.168218i
$316$	−2.14183			−0.120488
$317$			13.0280i			0.731727i	0.930669	+	0.365863i	$0.119226\pi$
$317$			13.0280i			0.731727i	−0.930669	+	0.365863i	$0.880774\pi$
$318$		−	4.59927i		−	0.257914i
$319$	−10.4774			−0.586622
$320$	−10.1848	+	10.1580i	−0.569350	+	0.567850i
$321$	−3.21017			−0.179174
$322$		−	3.65634i		−	0.203760i
$323$			4.14033i			0.230374i
$324$	7.23261			0.401812
$325$	32.4140	+	0.0854777i	1.79801	+	0.00474145i
$326$	−11.5056			−0.637236
$327$			8.98380i			0.496806i
$328$			5.55174i			0.306544i
$329$	−1.99458			−0.109964
$330$	0.776541	−	0.774496i	0.0427472	−	0.0426346i
$331$	8.27303			0.454727			0.227363	−	0.973810i	$-0.426990\pi$
$331$	8.27303			0.454727			0.227363	+	0.973810i	$0.426990\pi$
$332$		−	0.111760i		−	0.00613362i
$333$			2.43286i			0.133320i
$334$	8.59486			0.470290
$335$	1.86634	+	1.87127i	0.101969	+	0.102238i
$336$	−0.243363			−0.0132765
$337$			13.0966i			0.713420i	0.934215	+	0.356710i	$0.116102\pi$
$337$			13.0966i			0.713420i	−0.934215	+	0.356710i	$0.883898\pi$
$338$		−	27.9132i		−	1.51828i
$339$	−9.51586			−0.516831
$340$	−7.02994	−	7.04850i	−0.381252	−	0.382259i
$341$	6.18325			0.334842
$342$		−	2.63471i		−	0.142469i
$343$			9.30975i			0.502679i
$344$	31.5148			1.69916
$345$	4.46107	−	4.44932i	0.240176	−	0.239543i
$346$	1.80565			0.0970721
$347$			35.8019i			1.92195i	0.276638	+	0.960974i	$0.410780\pi$
$347$			35.8019i			1.92195i	−0.276638	+	0.960974i	$0.589220\pi$
$348$			5.74632i			0.308035i
$349$	−9.71708			−0.520143			−0.260072	−	0.965589i	$-0.583746\pi$
$349$	−9.71708			−0.520143			−0.260072	+	0.965589i	$0.583746\pi$
$350$	−0.00872677	+	3.30928i	−0.000466465	+	0.176889i
$351$	18.9793			1.01304
$352$			5.24790i			0.279714i
$353$			27.2287i			1.44923i	0.689151	+	0.724617i	$0.257984\pi$
$353$			27.2287i			1.44923i	−0.689151	+	0.724617i	$0.742016\pi$
$354$	−0.490906			−0.0260914
$355$	19.3002	−	19.2493i	1.02435	−	1.02165i
$356$	−10.4324			−0.552916
$357$		−	1.45349i		−	0.0769266i
$358$		−	13.5294i		−	0.715053i
$359$	27.7019			1.46205			0.731026	−	0.682350i	$-0.239042\pi$
$359$	27.7019			1.46205			0.731026	+	0.682350i	$0.239042\pi$
$360$	12.7942	+	12.8280i	0.674313	+	0.676094i
$361$	1.00000			0.0526316
$362$		−	24.1074i		−	1.26706i
$363$		−	0.510054i		−	0.0267709i
$364$	−4.79782			−0.251474
$365$	−1.86256	−	1.86748i	−0.0974909	−	0.0977483i
$366$	−2.12792			−0.111228
$367$			2.20229i			0.114959i	0.998347	+	0.0574794i	$0.0183063\pi$
$367$			2.20229i			0.114959i	−0.998347	+	0.0574794i	$0.981694\pi$
$368$		−	3.82965i		−	0.199634i
$369$	5.14358			0.267764
$370$	−1.35189	+	1.34833i	−0.0702812	+	0.0700961i
$371$	6.45395			0.335072
$372$		−	3.39120i		−	0.175825i
$373$		−	22.7342i		−	1.17713i	−0.808450	−	0.588565i	$-0.799693\pi$
$373$		−	22.7342i		−	1.17713i	0.808450	−	0.588565i	$-0.200307\pi$
$374$	3.98145			0.205876
$375$	−4.04825	+	4.01635i	−0.209051	+	0.207403i
$376$	−8.57001			−0.441964
$377$		−	67.9233i		−	3.49823i
$378$			1.93768i			0.0996635i
$379$	−19.7067			−1.01226			−0.506132	−	0.862456i	$-0.668925\pi$
$379$	−19.7067			−1.01226			−0.506132	+	0.862456i	$0.668925\pi$
$380$	−1.70240	+	1.69792i	−0.0873313	+	0.0871013i
$381$	6.67094			0.341763
$382$		−	22.9604i		−	1.17476i
$383$			13.2847i			0.678816i	0.940639	+	0.339408i	$0.110227\pi$
$383$			13.2847i			0.678816i	−0.940639	+	0.339408i	$0.889773\pi$
$384$	2.19817			0.112175
$385$	1.08682	+	1.08969i	0.0553893	+	0.0555355i
$386$	6.56994			0.334401
$387$		−	29.1978i		−	1.48421i
$388$		−	0.762004i		−	0.0386849i
$389$	−4.39062			−0.222613			−0.111307	−	0.993786i	$-0.535504\pi$
$389$	−4.39062			−0.222613			−0.111307	+	0.993786i	$0.535504\pi$
$390$	5.02093	+	5.03418i	0.254244	+	0.254916i
$391$	22.8726			1.15672
$392$			19.2999i			0.974795i
$393$			1.79604i			0.0905983i
$394$	10.8664			0.547439
$395$	−3.15361	+	3.14531i	−0.158675	+	0.158257i
$396$	2.94609			0.148046
$397$			27.3568i			1.37300i	0.727129	+	0.686500i	$0.240854\pi$
$397$			27.3568i			1.37300i	−0.727129	+	0.686500i	$0.759146\pi$
$398$		−	11.7880i		−	0.590881i
$399$	−0.351055			−0.0175747
$400$	−0.00914042	+	3.46615i	−0.000457021	+	0.173307i
$401$	−13.6063			−0.679465			−0.339733	−	0.940522i	$-0.610337\pi$
$401$	−13.6063			−0.679465			−0.339733	+	0.940522i	$0.610337\pi$
$402$			0.579719i			0.0289137i
$403$			40.0850i			1.99678i
$404$	−11.2698			−0.560692
$405$	10.6492	−	10.6212i	0.529163	−	0.527770i
$406$	6.93457			0.344157
$407$			0.887957i			0.0440144i
$408$		−	6.24513i		−	0.309180i
$409$	−17.5087			−0.865749			−0.432874	−	0.901454i	$-0.642501\pi$
$409$	−17.5087			−0.865749			−0.432874	+	0.901454i	$0.642501\pi$
$410$	2.85064	+	2.85816i	0.140783	+	0.141155i
$411$	−9.12879			−0.450290
$412$			15.6367i			0.770363i
$413$		−	0.688868i		−	0.0338970i
$414$	−14.5550			−0.715340
$415$	−0.164121	−	0.164554i	−0.00805636	−	0.00807763i
$416$	−34.0213			−1.66803
$417$		−	8.83746i		−	0.432772i
$418$		−	0.961626i		−	0.0470347i
$419$	−19.7012			−0.962468			−0.481234	−	0.876592i	$-0.659811\pi$
$419$	−19.7012			−0.962468			−0.481234	+	0.876592i	$0.659811\pi$
$420$	0.597637	−	0.596063i	0.0291617	−	0.0290849i
$421$	5.31579			0.259076			0.129538	−	0.991574i	$-0.458651\pi$
$421$	5.31579			0.259076			0.129538	+	0.991574i	$0.458651\pi$
$422$			10.9845i			0.534718i
$423$			7.93994i			0.386053i
$424$	27.7304			1.34671
$425$	−20.7016	−	0.0545913i	−1.00417	−	0.00264807i
$426$	5.97918			0.289692
$427$		−	2.98602i		−	0.144504i
$428$		−	6.76756i		−	0.327122i
$429$	3.30659			0.159644
$430$	16.2245	−	16.1818i	0.782416	−	0.780355i
$431$	27.2369			1.31195			0.655977	−	0.754781i	$-0.272257\pi$
$431$	27.2369			1.31195			0.655977	+	0.754781i	$0.272257\pi$
$432$			2.02953i			0.0976456i
$433$		−	3.89064i		−	0.186972i	−0.995621	−	0.0934861i	$-0.970199\pi$
$433$		−	3.89064i		−	0.186972i	0.995621	−	0.0934861i	$-0.0298011\pi$
$434$	−4.09244			−0.196444
$435$	8.43853	+	8.46081i	0.404597	+	0.405665i
$436$	−18.9393			−0.907028
$437$		−	5.52434i		−	0.264265i
$438$		−	0.578544i		−	0.0276439i
$439$	1.25080			0.0596974			0.0298487	−	0.999554i	$-0.490497\pi$
$439$	1.25080			0.0596974			0.0298487	+	0.999554i	$0.490497\pi$
$440$	4.66968	+	4.68201i	0.222618	+	0.223206i
$441$	17.8810			0.851476
$442$			25.8111i			1.22771i
$443$		−	10.5989i		−	0.503570i	−0.967783	−	0.251785i	$-0.918982\pi$
$443$		−	10.5989i		−	0.503570i	0.967783	−	0.251785i	$-0.0810175\pi$
$444$	0.486999			0.0231119
$445$	−15.3605	+	15.3201i	−0.728160	+	0.726242i
$446$	−9.19440			−0.435367
$447$		−	9.37809i		−	0.443568i
$448$		−	4.42763i		−	0.209186i
$449$	−0.989895			−0.0467160			−0.0233580	−	0.999727i	$-0.507436\pi$
$449$	−0.989895			−0.0467160			−0.0233580	+	0.999727i	$0.507436\pi$
$450$	13.1735	+	0.0347392i	0.621004	+	0.00163762i
$451$	1.87732			0.0883997
$452$		−	20.0610i		−	0.943588i
$453$		−	6.61983i		−	0.311027i
$454$	9.25777			0.434489
$455$	−7.06425	+	7.04564i	−0.331177	+	0.330305i
$456$	−1.50836			−0.0706357
$457$			29.4742i			1.37875i	0.724407	+	0.689373i	$0.242114\pi$
$457$			29.4742i			1.37875i	−0.724407	+	0.689373i	$0.757886\pi$
$458$		−	1.56272i		−	0.0730213i
$459$	−12.1214			−0.565777
$460$	9.37987	+	9.40464i	0.437339	+	0.438494i
$461$	7.22200			0.336362			0.168181	−	0.985756i	$-0.446211\pi$
$461$	7.22200			0.336362			0.168181	+	0.985756i	$0.446211\pi$
$462$			0.337584i			0.0157058i
$463$			12.7588i			0.592953i	0.955040	+	0.296477i	$0.0958117\pi$
$463$			12.7588i			0.592953i	−0.955040	+	0.296477i	$0.904188\pi$
$464$	7.26327			0.337189
$465$	−4.98001	−	4.99316i	−0.230942	−	0.231552i
$466$	19.6038			0.908129
$467$			13.7424i			0.635923i	0.948104	+	0.317961i	$0.102998\pi$
$467$			13.7424i			0.635923i	−0.948104	+	0.317961i	$0.897002\pi$
$468$			19.0990i			0.882851i
$469$	−0.813494			−0.0375637
$470$	−4.41204	+	4.40042i	−0.203512	+	0.202976i
$471$	3.37820			0.155659
$472$		−	2.95983i		−	0.136237i
$473$		−	10.6567i		−	0.489997i
$474$	−0.976986			−0.0448745
$475$	−0.0131852	+	4.99998i	−0.000604980	+	0.229415i
$476$	3.06418			0.140446
$477$		−	25.6917i		−	1.17634i
$478$		−	17.0352i		−	0.779172i
$479$	−15.6305			−0.714175			−0.357087	−	0.934071i	$-0.616230\pi$
$479$	−15.6305			−0.714175			−0.357087	+	0.934071i	$0.616230\pi$
$480$	4.23783	−	4.22667i	0.193430	−	0.192920i
$481$	−5.75647			−0.262473
$482$			12.1197i			0.552038i
$483$			1.93935i			0.0882435i
$484$	1.07528			0.0488762
$485$	−1.11901	−	1.12197i	−0.0508116	−	0.0509458i
$486$	11.7450			0.532763
$487$		−	1.70560i		−	0.0772881i	−0.999253	−	0.0386440i	$-0.987696\pi$
$487$		−	1.70560i		−	0.0772881i	0.999253	−	0.0386440i	$-0.0123038\pi$
$488$		−	12.8299i		−	0.580783i
$489$	6.10266			0.275972
$490$	9.90989	+	9.93605i	0.447683	+	0.448865i
$491$	−2.66160			−0.120117			−0.0600583	−	0.998195i	$-0.519129\pi$
$491$	−2.66160			−0.120117			−0.0600583	+	0.998195i	$0.519129\pi$
$492$		−	1.02962i		−	0.0464187i
$493$			43.3800i			1.95374i
$494$	6.23406			0.280484
$495$	4.33778	−	4.32636i	0.194969	−	0.194455i
$496$	−4.28643			−0.192466
$497$			8.39032i			0.376357i
$498$		−	0.0509787i		−	0.00228441i
$499$	−20.6389			−0.923924			−0.461962	−	0.886900i	$-0.652854\pi$
$499$	−20.6389			−0.923924			−0.461962	+	0.886900i	$0.652854\pi$
$500$	−8.46711	−	8.53436i	−0.378661	−	0.381668i
$501$	−4.55878			−0.203671
$502$			23.5296i			1.05018i
$503$		−	1.73353i		−	0.0772944i	−0.999253	−	0.0386472i	$-0.987695\pi$
$503$		−	1.73353i		−	0.0772944i	0.999253	−	0.0386472i	$-0.0123048\pi$
$504$	−5.57668			−0.248405
$505$	−16.5935	+	16.5498i	−0.738399	+	0.736455i
$506$	−5.31235			−0.236163
$507$			14.8054i			0.657531i
$508$			14.0634i			0.623963i
$509$	−25.6006			−1.13473			−0.567363	−	0.823468i	$-0.692036\pi$
$509$	−25.6006			−1.13473			−0.567363	+	0.823468i	$0.692036\pi$
$510$	−3.20667	−	3.21514i	−0.141994	−	0.142369i
$511$	0.811845			0.0359139
$512$		−	7.73815i		−	0.341981i
$513$			2.92763i			0.129258i
$514$	−1.50483			−0.0663751
$515$	22.9626	+	23.0232i	1.01185	+	1.01452i
$516$	−5.84467			−0.257297
$517$			2.89795i			0.127452i
$518$		−	0.587702i		−	0.0258222i
$519$	−0.957729			−0.0420396
$520$	−30.3527	+	30.2727i	−1.33105	+	1.32755i
$521$	9.00899			0.394691			0.197346	−	0.980334i	$-0.436768\pi$
$521$	9.00899			0.394691			0.197346	+	0.980334i	$0.436768\pi$
$522$		−	27.6049i		−	1.20823i
$523$			43.1934i			1.88872i	0.328920	+	0.944358i	$0.393316\pi$
$523$			43.1934i			1.88872i	−0.328920	+	0.944358i	$0.606684\pi$
$524$	−3.78634			−0.165407
$525$	0.00462875	−	1.75527i	0.000202015	−	0.0766063i
$526$	4.02490			0.175494
$527$		−	25.6007i		−	1.11519i
$528$			0.353586i			0.0153878i
$529$	−7.51836			−0.326885
$530$	14.2762	−	14.2387i	0.620121	−	0.618488i
$531$	−2.74222			−0.119002
$532$		−	0.740081i		−	0.0320866i
$533$			12.1704i			0.527157i
$534$	−4.75869			−0.205928
$535$	−9.93822	−	9.96446i	−0.429667	−	0.430801i
$536$	−3.49530			−0.150974
$537$			7.17612i			0.309672i
$538$		−	19.6053i		−	0.845246i
$539$	6.52628			0.281107
$540$	−4.97087	−	4.98400i	−0.213912	−	0.214477i
$541$	1.31951			0.0567303			0.0283651	−	0.999598i	$-0.490970\pi$
$541$	1.31951			0.0567303			0.0283651	+	0.999598i	$0.490970\pi$
$542$		−	24.9206i		−	1.07043i
$543$			12.7868i			0.548733i
$544$	21.7281			0.931583
$545$	−27.8860	+	27.8125i	−1.19450	+	1.19136i
$546$	−2.18850			−0.0936591
$547$			18.9294i			0.809365i	0.914457	+	0.404682i	$0.132618\pi$
$547$			18.9294i			0.809365i	−0.914457	+	0.404682i	$0.867382\pi$
$548$		−	19.2450i		−	0.822104i
$549$	−11.8867			−0.507310
$550$	4.80811	+	0.0126793i	0.205019	+	0.000540646i
$551$	10.4774			0.446353
$552$			8.33272i			0.354664i
$553$		−	1.37096i		−	0.0582992i
$554$	−8.32249			−0.353589
$555$	0.717051	−	0.715162i	0.0304371	−	0.0303570i
$556$	18.6308			0.790121
$557$		−	24.5765i		−	1.04134i	−0.853759	−	0.520669i	$-0.825683\pi$
$557$		−	24.5765i		−	1.04134i	0.853759	−	0.520669i	$-0.174317\pi$
$558$			16.2911i			0.689655i
$559$	69.0858			2.92202
$560$	−0.753415	−	0.755405i	−0.0318376	−	0.0319217i
$561$	−2.11179			−0.0891600
$562$			24.6107i			1.03814i
$563$			33.6044i			1.41626i	0.706083	+	0.708129i	$0.250461\pi$
$563$			33.6044i			1.41626i	−0.706083	+	0.708129i	$0.749539\pi$
$564$	1.58938			0.0669249
$565$	−29.4597	−	29.5375i	−1.23938	−	1.24265i
$566$	11.2942			0.474731
$567$			4.62951i			0.194421i
$568$			36.0503i			1.51264i
$569$	−4.03120			−0.168997			−0.0844984	−	0.996424i	$-0.526929\pi$
$569$	−4.03120			−0.168997			−0.0844984	+	0.996424i	$0.526929\pi$
$570$	−0.776541	+	0.774496i	−0.0325257	+	0.0324401i
$571$	11.9017			0.498070			0.249035	−	0.968494i	$-0.419887\pi$
$571$	11.9017			0.498070			0.249035	+	0.968494i	$0.419887\pi$
$572$			6.97083i			0.291465i
$573$			12.1784i			0.508759i
$574$	−1.24252			−0.0518619
$575$	27.6216	+	0.0728398i	1.15190	+	0.00303763i
$576$	−17.6254			−0.734390
$577$			0.789644i			0.0328733i	0.999865	+	0.0164366i	$0.00523218\pi$
$577$			0.789644i			0.0328733i	−0.999865	+	0.0164366i	$0.994768\pi$
$578$		−	0.136896i		−	0.00569412i
$579$	−3.48475			−0.144821
$580$	−17.8367	+	17.7898i	−0.740630	+	0.738680i
$581$	0.0715362			0.00296782
$582$		−	0.347584i		−	0.0144078i
$583$		−	9.37705i		−	0.388358i
$584$	3.48822			0.144344
$585$	28.0471	+	28.1211i	1.15960	+	1.16267i
$586$	11.8797			0.490745
$587$			33.5657i			1.38540i	0.721224	+	0.692702i	$0.243580\pi$
$587$			33.5657i			1.38540i	−0.721224	+	0.692702i	$0.756420\pi$
$588$		−	3.57933i		−	0.147609i
$589$	−6.18325			−0.254777
$590$	−1.51977	−	1.52379i	−0.0625681	−	0.0627333i
$591$	−5.76360			−0.237083
$592$		−	0.615560i		−	0.0252993i
$593$		−	2.99002i		−	0.122786i	−0.998114	−	0.0613928i	$-0.980446\pi$
$593$		−	2.99002i		−	0.122786i	0.998114	−	0.0613928i	$-0.0195542\pi$
$594$	2.81529			0.115513
$595$	4.51166	−	4.49978i	0.184960	−	0.184473i
$596$	19.7705			0.809832
$597$			6.25247i			0.255896i
$598$		−	34.4391i		−	1.40832i
$599$	38.4498			1.57102			0.785509	−	0.618851i	$-0.212401\pi$
$599$	38.4498			1.57102			0.785509	+	0.618851i	$0.212401\pi$
$600$	0.0198881	−	7.54180i	0.000811930	−	0.307893i
$601$	11.8755			0.484413			0.242207	−	0.970225i	$-0.422129\pi$
$601$	11.8755			0.484413			0.242207	+	0.970225i	$0.422129\pi$
$602$			7.05325i			0.287469i
$603$			3.23833i			0.131875i
$604$	13.9557			0.567848
$605$	1.58322	−	1.57905i	0.0643671	−	0.0641976i
$606$	−5.14064			−0.208824
$607$		−	39.1905i		−	1.59069i	−0.606155	−	0.795346i	$-0.707289\pi$
$607$		−	39.1905i		−	1.59069i	0.606155	−	0.795346i	$-0.292711\pi$
$608$		−	5.24790i		−	0.212830i
$609$	−3.67815			−0.149046
$610$	−6.58774	−	6.60514i	−0.266730	−	0.267434i
$611$	−18.7869			−0.760038
$612$		−	12.1978i		−	0.493066i
$613$		−	24.8651i		−	1.00429i	−0.864783	−	0.502147i	$-0.832544\pi$
$613$		−	24.8651i		−	1.00429i	0.864783	−	0.502147i	$-0.167456\pi$
$614$	26.2248			1.05835
$615$	−1.51200	−	1.51599i	−0.0609697	−	0.0611307i
$616$	−2.03540			−0.0820086
$617$		−	8.14880i		−	0.328058i	−0.986455	−	0.164029i	$-0.947551\pi$
$617$		−	8.14880i		−	0.328058i	0.986455	−	0.164029i	$-0.0524491\pi$
$618$			7.13258i			0.286914i
$619$	5.57832			0.224212			0.112106	−	0.993696i	$-0.464240\pi$
$619$	5.57832			0.224212			0.112106	+	0.993696i	$0.464240\pi$
$620$	10.5264	−	10.4987i	0.422749	−	0.421636i
$621$	16.1732			0.649010
$622$		−	18.3661i		−	0.736415i
$623$		−	6.67766i		−	0.267535i
$624$	−2.29224			−0.0917629
$625$	−24.9997	−	0.131852i	−0.999986	−	0.00527408i
$626$	−7.74412			−0.309517
$627$			0.510054i			0.0203696i
$628$			7.12178i			0.284190i
$629$	3.67644			0.146589
$630$	−2.87100	+	2.86344i	−0.114383	+	0.114082i
$631$	−3.90071			−0.155285			−0.0776423	−	0.996981i	$-0.524739\pi$
$631$	−3.90071			−0.155285			−0.0776423	+	0.996981i	$0.524739\pi$
$632$		−	5.89056i		−	0.234314i
$633$		−	5.82627i		−	0.231574i
$634$	−12.5281			−0.497554
$635$	20.6523	+	20.7068i	0.819560	+	0.821724i
$636$	−5.14283			−0.203926
$637$			42.3088i			1.67634i
$638$		−	10.0753i		−	0.398887i
$639$	33.3999			1.32128
$640$	6.80521	+	6.82318i	0.269000	+	0.269710i
$641$	−37.4881			−1.48069			−0.740345	−	0.672227i	$-0.765338\pi$
$641$	−37.4881			−1.48069			−0.740345	+	0.672227i	$0.765338\pi$
$642$		−	3.08698i		−	0.121834i
$643$			4.50786i			0.177773i	0.996042	+	0.0888864i	$0.0283308\pi$
$643$			4.50786i			0.177773i	−0.996042	+	0.0888864i	$0.971669\pi$
$644$	−4.08846			−0.161108
$645$	−8.60562	+	8.58295i	−0.338846	+	0.337953i
$646$	−3.98145			−0.156648
$647$		−	17.4372i		−	0.685528i	−0.939421	−	0.342764i	$-0.888637\pi$
$647$		−	17.4372i		−	0.685528i	0.939421	−	0.342764i	$-0.111363\pi$
$648$			19.8914i			0.781408i
$649$	−1.00087			−0.0392875
$650$	−0.0821975	+	31.1702i	−0.00322405	+	1.22260i
$651$	2.17066			0.0850750
$652$			12.8654i			0.503847i
$653$		−	2.40659i		−	0.0941772i	−0.998891	−	0.0470886i	$-0.985006\pi$
$653$		−	2.40659i		−	0.0941772i	0.998891	−	0.0470886i	$-0.0149943\pi$
$654$	−8.63906			−0.337814
$655$	−5.57496	+	5.56028i	−0.217832	+	0.217258i
$656$	−1.30142			−0.0508119
$657$		−	3.23176i		−	0.126083i
$658$		−	1.91804i		−	0.0747728i
$659$	−10.8154			−0.421308			−0.210654	−	0.977561i	$-0.567559\pi$
$659$	−10.8154			−0.421308			−0.210654	+	0.977561i	$0.567559\pi$
$660$	−0.866029	−	0.868316i	−0.0337101	−	0.0337992i
$661$	30.3121			1.17900			0.589502	−	0.807767i	$-0.299324\pi$
$661$	30.3121			1.17900			0.589502	+	0.807767i	$0.299324\pi$
$662$			7.95556i			0.309201i
$663$		−	13.6904i		−	0.531691i
$664$	0.307367			0.0119281
$665$	−1.08682	−	1.08969i	−0.0421449	−	0.0422562i
$666$	−2.33951			−0.0906540
$667$		−	57.8808i		−	2.24115i
$668$		−	9.61064i		−	0.371847i
$669$	4.87678			0.188547
$670$	−1.79946	+	1.79472i	−0.0695193	+	0.0693362i
$671$	−4.33844			−0.167484
$672$			1.84230i			0.0710684i
$673$			39.0409i			1.50491i	0.658641	+	0.752457i	$0.271132\pi$
$673$			39.0409i			1.50491i	−0.658641	+	0.752457i	$0.728868\pi$
$674$	−12.5941			−0.485106
$675$	−14.6381	−	0.0386015i	−0.563421	−	0.00148577i
$676$	−31.2121			−1.20047
$677$			16.5727i			0.636939i	0.947933	+	0.318470i	$0.103169\pi$
$677$			16.5727i			0.636939i	−0.947933	+	0.318470i	$0.896831\pi$
$678$		−	9.15070i		−	0.351431i
$679$	0.487749			0.0187181
$680$	19.3851	−	19.3340i	0.743384	−	0.741426i
$681$	−4.91040			−0.188167
$682$			5.94598i			0.227683i
$683$		−	4.49305i		−	0.171922i	−0.996299	−	0.0859608i	$-0.972604\pi$
$683$		−	4.49305i		−	0.171922i	0.996299	−	0.0859608i	$-0.0273960\pi$
$684$	−2.94609			−0.112646
$685$	−28.2614	−	28.3360i	−1.07981	−	1.08266i
$686$	−8.95249			−0.341808
$687$			0.828881i			0.0316238i
$688$			7.38758i			0.281649i
$689$	60.7898			2.31591
$690$	4.27858	+	4.28988i	0.162883	+	0.163313i
$691$	48.0343			1.82731			0.913656	−	0.406489i	$-0.133247\pi$
$691$	48.0343			1.82731			0.913656	+	0.406489i	$0.133247\pi$
$692$		−	2.01905i		−	0.0767526i
$693$			1.88576i			0.0716339i
$694$	−34.4281			−1.30687
$695$	27.4317	−	27.3595i	1.04054	−	1.03780i
$696$	−15.8038			−0.599040
$697$		−	7.77274i		−	0.294414i
$698$		−	9.34419i		−	0.353683i
$699$	−10.3980			−0.393289
$700$	3.70039	+	0.00975814i	0.139862	+	0.000368823i
$701$	26.4660			0.999607			0.499804	−	0.866139i	$-0.333405\pi$
$701$	26.4660			0.999607			0.499804	+	0.866139i	$0.333405\pi$
$702$			18.2510i			0.688841i
$703$		−	0.887957i		−	0.0334899i
$704$	−6.43298			−0.242452
$705$	2.34018	−	2.33402i	0.0881362	−	0.0879041i
$706$	−26.1838			−0.985439
$707$		−	7.21364i		−	0.271297i
$708$			0.548924i			0.0206298i
$709$	−27.4893			−1.03238			−0.516191	−	0.856473i	$-0.672651\pi$
$709$	−27.4893			−1.03238			−0.516191	+	0.856473i	$0.672651\pi$
$710$	18.5107	+	18.5595i	0.694693	+	0.696527i
$711$	−5.45748			−0.204671
$712$		−	28.6916i		−	1.07526i
$713$			34.1584i			1.27924i
$714$	1.39771			0.0523080
$715$	10.2367	+	10.2638i	0.382832	+	0.383843i
$716$	−15.1284			−0.565375
$717$			9.03561i			0.337441i
$718$			26.6389i			0.994154i
$719$	34.0349			1.26929			0.634644	−	0.772805i	$-0.281147\pi$
$719$	34.0349			1.26929			0.634644	+	0.772805i	$0.281147\pi$
$720$	−3.00709	+	2.99917i	−0.112068	+	0.111772i
$721$	−10.0088			−0.372748
$722$			0.961626i			0.0357880i
$723$		−	6.42840i		−	0.239075i
$724$	−26.9566			−1.00183
$725$	−0.138147	+	52.3869i	−0.00513066	+	1.94560i
$726$	0.490481			0.0182035
$727$		−	1.03554i		−	0.0384061i	−0.999816	−	0.0192031i	$-0.993887\pi$
$727$		−	1.03554i		−	0.0384061i	0.999816	−	0.0192031i	$-0.00611290\pi$
$728$		−	13.1951i		−	0.489045i
$729$	13.9492			0.516638
$730$	1.79582	−	1.79109i	0.0664661	−	0.0662911i
$731$	−44.1224			−1.63193
$732$			2.37941i			0.0879456i
$733$			2.04726i			0.0756171i	0.999285	+	0.0378086i	$0.0120377\pi$
$733$			2.04726i			0.0756171i	−0.999285	+	0.0378086i	$0.987962\pi$
$734$	−2.11778			−0.0781688
$735$	−5.25628	−	5.27016i	−0.193881	−	0.194393i
$736$	−28.9912			−1.06863
$737$			1.18194i			0.0435373i
$738$			4.94620i			0.182072i
$739$	40.5443			1.49145			0.745724	−	0.666255i	$-0.232104\pi$
$739$	40.5443			1.49145			0.745724	+	0.666255i	$0.232104\pi$
$740$	1.50768	+	1.51166i	0.0554233	+	0.0555696i
$741$	−3.30659			−0.121471
$742$			6.20628i			0.227840i
$743$		−	35.9460i		−	1.31873i	−0.751823	−	0.659365i	$-0.770825\pi$
$743$		−	35.9460i		−	1.31873i	0.751823	−	0.659365i	$-0.229175\pi$
$744$	9.32660			0.341930
$745$	29.1099	−	29.0332i	1.06650	−	1.06369i
$746$	21.8618			0.800416
$747$		−	0.284769i		−	0.0104191i
$748$		−	4.45200i		−	0.162781i
$749$	4.33183			0.158282
$750$	−3.86223	−	3.89290i	−0.141029	−	0.142149i
$751$	14.1516			0.516400			0.258200	−	0.966091i	$-0.416871\pi$
$751$	14.1516			0.516400			0.258200	+	0.966091i	$0.416871\pi$
$752$		−	2.00895i		−	0.0732589i
$753$		−	12.4803i		−	0.454807i
$754$	65.3168			2.37870
$755$	20.5481	−	20.4940i	0.747823	−	0.745854i
$756$	2.16668			0.0788015
$757$		−	9.23939i		−	0.335811i	−0.985803	−	0.167906i	$-0.946300\pi$
$757$		−	9.23939i		−	0.335811i	0.985803	−	0.167906i	$-0.0537004\pi$
$758$		−	18.9505i		−	0.688312i
$759$	2.81771			0.102277
$760$	−4.66968	−	4.68201i	−0.169387	−	0.169834i
$761$	−28.6410			−1.03824			−0.519118	−	0.854702i	$-0.673740\pi$
$761$	−28.6410			−1.03824			−0.519118	+	0.854702i	$0.673740\pi$
$762$			6.41495i			0.232389i
$763$		−	12.1228i		−	0.438875i
$764$	−25.6740			−0.928852
$765$	−17.9126	−	17.9599i	−0.647630	−	0.649340i
$766$	−12.7749			−0.461576
$767$		−	6.48845i		−	0.234284i
$768$			8.67615i			0.313074i
$769$	−28.4609			−1.02633			−0.513163	−	0.858291i	$-0.671526\pi$
$769$	−28.4609			−1.02633			−0.513163	+	0.858291i	$0.671526\pi$
$770$	−1.04787	+	1.04511i	−0.0377626	+	0.0376632i
$771$	0.798172			0.0287455
$772$		−	7.34641i		−	0.264403i
$773$		−	30.7310i		−	1.10532i	−0.833408	−	0.552659i	$-0.813613\pi$
$773$		−	30.7310i		−	1.10532i	0.833408	−	0.552659i	$-0.186387\pi$
$774$	28.0773			1.00922
$775$	0.0815277	−	30.9162i	0.00292856	−	1.11054i
$776$	2.09569			0.0752310
$777$			0.311722i			0.0111830i
$778$		−	4.22213i		−	0.151371i
$779$	−1.87732			−0.0672621
$780$	5.62915	−	5.61432i	0.201556	−	0.201025i
$781$	12.1904			0.436208
$782$			21.9949i			0.786536i
$783$			30.6740i			1.09620i
$784$	−4.52423			−0.161579
$785$	10.4584	+	10.4860i	0.373276	+	0.374262i
$786$	−1.72712			−0.0616043
$787$			11.2677i			0.401650i	0.979627	+	0.200825i	$0.0643623\pi$
$787$			11.2677i			0.401650i	−0.979627	+	0.200825i	$0.935638\pi$
$788$		−	12.1506i		−	0.432847i
$789$	−2.13484			−0.0760024
$790$	−3.02461	−	3.03259i	−0.107611	−	0.107895i
$791$	12.8408			0.456565
$792$			8.10245i			0.287908i
$793$		−	28.1254i		−	0.998762i
$794$	−26.3071			−0.933602
$795$	−7.57224	+	7.55229i	−0.268560	+	0.267852i
$796$	−13.1812			−0.467195
$797$			42.5707i			1.50793i	0.656914	+	0.753965i	$0.271861\pi$
$797$			42.5707i			1.50793i	−0.656914	+	0.753965i	$0.728139\pi$
$798$		−	0.337584i		−	0.0119503i
$799$	11.9985			0.424476
$800$	26.2394	+	0.0691948i	0.927703	+	0.00244641i
$801$	−26.5822			−0.939235
$802$		−	13.0842i		−	0.462018i
$803$		−	1.17954i		−	0.0416252i
$804$	0.648233			0.0228614
$805$	−6.01980	+	6.00394i	−0.212170	+	0.211611i
$806$	−38.5468			−1.35775
$807$			10.3988i			0.366056i
$808$		−	30.9946i		−	1.09038i
$809$	41.8290			1.47063			0.735314	−	0.677726i	$-0.237035\pi$
$809$	41.8290			1.47063			0.735314	+	0.677726i	$0.237035\pi$
$810$	10.2136	+	10.2406i	0.358869	+	0.359816i
$811$	10.3669			0.364030			0.182015	−	0.983296i	$-0.441738\pi$
$811$	10.3669			0.364030			0.182015	+	0.983296i	$0.441738\pi$
$812$		−	7.75413i		−	0.272117i
$813$			13.2181i			0.463578i
$814$	−0.853882			−0.0299286
$815$	18.8929	+	18.9428i	0.661790	+	0.663538i
$816$	1.46396			0.0512489
$817$			10.6567i			0.372832i
$818$		−	16.8368i		−	0.588685i
$819$	−12.2250			−0.427177
$820$	3.19596	−	3.18754i	0.111608	−	0.111314i
$821$	43.8682			1.53101			0.765505	−	0.643430i	$-0.222489\pi$
$821$	43.8682			1.53101			0.765505	+	0.643430i	$0.222489\pi$
$822$		−	8.77848i		−	0.306185i
$823$		−	37.9861i		−	1.32411i	−0.749454	−	0.662057i	$-0.769684\pi$
$823$		−	37.9861i		−	1.32411i	0.749454	−	0.662057i	$-0.230316\pi$
$824$	−43.0045			−1.49813
$825$	−2.55026	−	0.00672518i	−0.0887887	−	0.000234141i
$826$	0.662433			0.0230490
$827$		−	55.5822i		−	1.93278i	−0.257078	−	0.966391i	$-0.582760\pi$
$827$		−	55.5822i		−	1.93278i	0.257078	−	0.966391i	$-0.417240\pi$
$828$			16.2752i			0.565602i
$829$	39.8530			1.38415			0.692076	−	0.721824i	$-0.256696\pi$
$829$	39.8530			1.38415			0.692076	+	0.721824i	$0.256696\pi$
$830$	0.158239	−	0.157823i	0.00549257	−	0.00547810i
$831$	4.41431			0.153131
$832$		−	41.7039i		−	1.44582i
$833$		−	27.0210i		−	0.936222i
$834$	8.49833			0.294273
$835$	−14.1133	−	14.1506i	−0.488412	−	0.489701i
$836$	−1.07528			−0.0371892
$837$		−	18.1023i		−	0.625707i
$838$		−	18.9452i		−	0.654451i
$839$	−8.01006			−0.276538			−0.138269	−	0.990395i	$-0.544154\pi$
$839$	−8.01006			−0.276538			−0.138269	+	0.990395i	$0.544154\pi$
$840$	1.63931	+	1.64364i	0.0565617	+	0.0567111i
$841$	80.7761			2.78538
$842$			5.11180i			0.176164i
$843$		−	13.0537i		−	0.449594i
$844$	12.2827			0.422789
$845$	−45.9564	+	45.8353i	−1.58095	+	1.57678i
$846$	−7.63525			−0.262505
$847$			0.688271i			0.0236493i
$848$			6.50047i			0.223227i
$849$	−5.99054			−0.205595
$850$	0.0524964	−	19.9072i	0.00180061	−	0.682811i
$851$	−4.90538			−0.168154
$852$		−	6.68582i		−	0.229053i
$853$			7.12627i			0.243999i	0.992530	+	0.121999i	$0.0389306\pi$
$853$			7.12627i			0.243999i	−0.992530	+	0.121999i	$0.961069\pi$
$854$	2.87144			0.0982586
$855$	−4.33778	+	4.32636i	−0.148349	+	0.147958i
$856$	18.6124			0.636159
$857$		−	9.13446i		−	0.312027i	−0.987755	−	0.156014i	$-0.950136\pi$
$857$		−	9.13446i		−	0.312027i	0.987755	−	0.156014i	$-0.0498644\pi$
$858$			3.17971i			0.108553i
$859$	7.34788			0.250707			0.125353	−	0.992112i	$-0.459994\pi$
$859$	7.34788			0.250707			0.125353	+	0.992112i	$0.459994\pi$
$860$	−18.0942	−	18.1420i	−0.617008	−	0.618638i
$861$	0.659044			0.0224602
$862$			26.1917i			0.892093i
$863$			9.34871i			0.318234i	0.987260	+	0.159117i	$0.0508647\pi$
$863$			9.34871i			0.318234i	−0.987260	+	0.159117i	$0.949135\pi$
$864$	15.3639			0.522691
$865$	−2.96499	−	2.97282i	−0.100813	−	0.101079i
$866$	3.74134			0.127136
$867$			0.0726107i			0.00246599i
$868$			4.57611i			0.155323i
$869$	−1.99189			−0.0675704
$870$	−8.13614	+	8.11471i	−0.275841	+	0.275114i
$871$	−7.66231			−0.259627
$872$		−	52.0876i		−	1.76391i
$873$		−	1.94162i		−	0.0657138i
$874$	5.31235			0.179693
$875$	5.46274	−	5.41969i	0.184674	−	0.183219i
$876$	−0.646919			−0.0218574
$877$		−	28.6524i		−	0.967523i	−0.875200	−	0.483762i	$-0.839270\pi$
$877$		−	28.6524i		−	0.967523i	0.875200	−	0.483762i	$-0.160730\pi$
$878$			1.20280i			0.0405926i
$879$	−6.30108			−0.212530
$880$	−1.09754	+	1.09465i	−0.0369981	+	0.0369006i
$881$	−6.31902			−0.212893			−0.106447	−	0.994318i	$-0.533947\pi$
$881$	−6.31902			−0.212893			−0.106447	+	0.994318i	$0.533947\pi$
$882$			17.1948i			0.578980i
$883$			22.9395i			0.771977i	0.922504	+	0.385988i	$0.126140\pi$
$883$			22.9395i			0.771977i	−0.922504	+	0.385988i	$0.873860\pi$
$884$	28.8616			0.970719
$885$	0.806101	+	0.808229i	0.0270968	+	0.0271683i
$886$	10.1922			0.342413
$887$			21.8308i			0.733006i	0.930417	+	0.366503i	$0.119445\pi$
$887$			21.8308i			0.733006i	−0.930417	+	0.366503i	$0.880555\pi$
$888$			1.33936i			0.0449461i
$889$	−9.00182			−0.301911
$890$	−14.7322	−	14.7711i	−0.493824	−	0.495128i
$891$	6.72628			0.225339
$892$			10.2810i			0.344235i
$893$		−	2.89795i		−	0.0969762i
$894$	9.01821			0.301614
$895$	−22.2749	+	22.2162i	−0.744567	+	0.742606i
$896$	−2.96623			−0.0990947
$897$			18.2668i			0.609909i
$898$		−	0.951909i		−	0.0317656i
$899$	−64.7845			−2.16068
$900$	0.0388449	−	14.7304i	0.00129483	−	0.491013i
$901$	−38.8241			−1.29342
$902$			1.80528i			0.0601093i
$903$		−	3.74110i		−	0.124496i
$904$	55.1724			1.83501
$905$	−39.6905	+	39.5860i	−1.31936	+	1.31588i
$906$	6.36580			0.211490
$907$		−	37.9585i		−	1.26039i	−0.776437	−	0.630195i	$-0.782975\pi$
$907$		−	37.9585i		−	1.26039i	0.776437	−	0.630195i	$-0.217025\pi$
$908$		−	10.3519i		−	0.343540i
$909$	−28.7158			−0.952443
$910$	−6.77527	−	6.79316i	−0.224598	−	0.225191i
$911$	−10.3855			−0.344086			−0.172043	−	0.985089i	$-0.555037\pi$
$911$	−10.3855			−0.344086			−0.172043	+	0.985089i	$0.555037\pi$
$912$		−	0.353586i		−	0.0117084i
$913$		−	0.103936i		−	0.00343978i
$914$	−28.3432			−0.937509
$915$	3.49419	+	3.50342i	0.115514	+	0.115819i
$916$	−1.74741			−0.0577362
$917$		−	2.42359i		−	0.0800341i
$918$		−	11.6562i		−	0.384713i
$919$	13.6145			0.449099			0.224550	−	0.974463i	$-0.427909\pi$
$919$	13.6145			0.449099			0.224550	+	0.974463i	$0.427909\pi$
$920$	−25.8650	+	25.7969i	−0.852744	+	0.850498i
$921$	−13.9099			−0.458345
$922$			6.94487i			0.228717i
$923$			79.0285i			2.60125i
$924$	0.377481			0.0124182
$925$	4.43977	+	0.0117079i	0.145979	+	0.000384954i
$926$	−12.2692			−0.403192
$927$			39.8428i			1.30861i
$928$		−	54.9844i		−	1.80495i
$929$	−6.48395			−0.212732			−0.106366	−	0.994327i	$-0.533921\pi$
$929$	−6.48395			−0.212732			−0.106366	+	0.994327i	$0.533921\pi$
$930$	4.80155	−	4.78890i	0.157449	−	0.157034i
$931$	−6.52628			−0.213890
$932$		−	21.9207i		−	0.718036i
$933$			9.74154i			0.318924i
$934$	−13.2151			−0.432410
$935$	−6.53780	−	6.55507i	−0.213809	−	0.214374i
$936$	−52.5268			−1.71689
$937$		−	42.0810i		−	1.37473i	−0.726314	−	0.687364i	$-0.758768\pi$
$937$		−	42.0810i		−	1.37473i	0.726314	−	0.687364i	$-0.241232\pi$
$938$		−	0.782277i		−	0.0255422i
$939$	4.10754			0.134045
$940$	4.92048	+	4.93347i	0.160488	+	0.160912i
$941$	−4.06486			−0.132511			−0.0662554	−	0.997803i	$-0.521105\pi$
$941$	−4.06486			−0.132511			−0.0662554	+	0.997803i	$0.521105\pi$
$942$			3.24856i			0.105844i
$943$			10.3710i			0.337726i
$944$	0.693833			0.0225823
$945$	3.19020	−	3.18180i	0.103777	−	0.103504i
$946$	10.2478			0.333184
$947$			19.1584i			0.622565i	0.950317	+	0.311282i	$0.100759\pi$
$947$			19.1584i			0.622565i	−0.950317	+	0.311282i	$0.899241\pi$
$948$			1.09245i			0.0354812i
$949$	7.64678			0.248225
$950$	−4.80811	−	0.0126793i	−0.155996	−	0.000411370i
$951$	6.64500			0.215479
$952$			8.42723i			0.273128i
$953$			3.66509i			0.118724i	0.998237	+	0.0593619i	$0.0189066\pi$
$953$			3.66509i			0.118724i	−0.998237	+	0.0593619i	$0.981093\pi$
$954$	24.7058			0.799879
$955$	−37.8020	+	37.7025i	−1.22324	+	1.22002i
$956$	−19.0485			−0.616073
$957$			5.34405i			0.172748i
$958$		−	15.0307i		−	0.485619i
$959$	12.3185			0.397784
$960$	5.18114	+	5.19482i	0.167220	+	0.167662i
$961$	7.23264			0.233311
$962$		−	5.53558i		−	0.178474i
$963$		−	17.2440i		−	0.555680i
$964$	13.5521			0.436484
$965$	−10.7883	−	10.8168i	−0.347287	−	0.348204i
$966$	−1.86493			−0.0600031
$967$			56.3847i			1.81321i	0.421981	+	0.906605i	$0.361335\pi$
$967$			56.3847i			1.81321i	−0.421981	+	0.906605i	$0.638665\pi$
$968$			2.95726i			0.0950501i
$969$	2.11179			0.0678406
$970$	1.07891	−	1.07607i	0.0346417	−	0.0345505i
$971$	−46.1812			−1.48203			−0.741013	−	0.671490i	$-0.765655\pi$
$971$	−46.1812			−1.48203			−0.741013	+	0.671490i	$0.765655\pi$
$972$		−	13.1331i		−	0.421243i
$973$			11.9253i			0.382309i
$974$	1.64015			0.0525537
$975$	0.0435982	−	16.5329i	0.00139626	−	0.529477i
$976$	3.00755			0.0962692
$977$		−	25.6738i		−	0.821378i	−0.911776	−	0.410689i	$-0.865288\pi$
$977$		−	25.6738i		−	0.821378i	0.911776	−	0.410689i	$-0.134712\pi$
$978$			5.86847i			0.187653i
$979$	−9.70208			−0.310080
$980$	11.1103	−	11.0811i	0.354907	−	0.353972i
$981$	−48.2581			−1.54076
$982$		−	2.55947i		−	0.0816759i
$983$		−	30.0311i		−	0.957842i	−0.877858	−	0.478921i	$-0.841028\pi$
$983$		−	30.0311i		−	0.957842i	0.877858	−	0.478921i	$-0.158972\pi$
$984$	2.83169			0.0902709
$985$	−17.8433	−	17.8904i	−0.568533	−	0.570035i
$986$	−41.7153			−1.32849
$987$			1.01734i			0.0323823i
$988$		−	6.97083i		−	0.221772i
$989$	58.8714			1.87200
$990$	4.16034	+	4.17133i	0.132224	+	0.132573i
$991$	27.5780			0.876044			0.438022	−	0.898964i	$-0.355679\pi$
$991$	27.5780			0.876044			0.438022	+	0.898964i	$0.355679\pi$
$992$			32.4491i			1.03026i
$993$		−	4.21969i		−	0.133908i
$994$	−8.06835			−0.255912
$995$	−19.4078	+	19.3567i	−0.615270	+	0.613649i
$996$	−0.0570036			−0.00180623
$997$		−	37.6537i		−	1.19251i	−0.802797	−	0.596253i	$-0.796656\pi$
$997$		−	37.6537i		−	1.19251i	0.802797	−	0.596253i	$-0.203344\pi$
$998$		−	19.8469i		−	0.628243i
$999$	2.59961			0.0822480

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.b.e.419.20	yes	30
5.2	odd	4		5225.2.a.bc.1.11		30
5.3	odd	4		5225.2.a.bc.1.20		30
5.4	even	2	inner	1045.2.b.e.419.11	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.b.e.419.11	✓	30	5.4	even	2	inner
1045.2.b.e.419.20	yes	30	1.1	even	1	trivial
5225.2.a.bc.1.11		30	5.2	odd	4
5225.2.a.bc.1.20		30	5.3	odd	4

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.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.961626i q^{2} -0.510054i q^{3} +1.07528 q^{4} +(1.58322 - 1.57905i) q^{5} +0.490481 q^{6} +0.688271i q^{7} +2.95726i q^{8} +2.73984 q^{9} +O(q^{10})\)	\(q+0.961626i q^{2} -0.510054i q^{3} +1.07528 q^{4} +(1.58322 - 1.57905i) q^{5} +0.490481 q^{6} +0.688271i q^{7} +2.95726i q^{8} +2.73984 q^{9} +(1.51846 + 1.52247i) q^{10} +1.00000 q^{11} -0.548449i q^{12} +6.48283i q^{13} -0.661859 q^{14} +(-0.805402 - 0.807529i) q^{15} -0.693232 q^{16} -4.14033i q^{17} +2.63471i q^{18} -1.00000 q^{19} +(1.70240 - 1.69792i) q^{20} +0.351055 q^{21} +0.961626i q^{22} +5.52434i q^{23} +1.50836 q^{24} +(0.0131852 - 4.99998i) q^{25} -6.23406 q^{26} -2.92763i q^{27} +0.740081i q^{28} -10.4774 q^{29} +(0.776541 - 0.774496i) q^{30} +6.18325 q^{31} +5.24790i q^{32} -0.510054i q^{33} +3.98145 q^{34} +(1.08682 + 1.08969i) q^{35} +2.94609 q^{36} +0.887957i q^{37} -0.961626i q^{38} +3.30659 q^{39} +(4.66968 + 4.68201i) q^{40} +1.87732 q^{41} +0.337584i q^{42} -10.6567i q^{43} +1.07528 q^{44} +(4.33778 - 4.32636i) q^{45} -5.31235 q^{46} +2.89795i q^{47} +0.353586i q^{48} +6.52628 q^{49} +(4.80811 + 0.0126793i) q^{50} -2.11179 q^{51} +6.97083i q^{52} -9.37705i q^{53} +2.81529 q^{54} +(1.58322 - 1.57905i) q^{55} -2.03540 q^{56} +0.510054i q^{57} -10.0753i q^{58} -1.00087 q^{59} +(-0.866029 - 0.868316i) q^{60} -4.33844 q^{61} +5.94598i q^{62} +1.88576i q^{63} -6.43298 q^{64} +(10.2367 + 10.2638i) q^{65} +0.490481 q^{66} +1.18194i q^{67} -4.45200i q^{68} +2.81771 q^{69} +(-1.04787 + 1.04511i) q^{70} +12.1904 q^{71} +8.10245i q^{72} -1.17954i q^{73} -0.853882 q^{74} +(-2.55026 - 0.00672518i) q^{75} -1.07528 q^{76} +0.688271i q^{77} +3.17971i q^{78} -1.99189 q^{79} +(-1.09754 + 1.09465i) q^{80} +6.72628 q^{81} +1.80528i q^{82} -0.103936i q^{83} +0.377481 q^{84} +(-6.53780 - 6.55507i) q^{85} +10.2478 q^{86} +5.34405i q^{87} +2.95726i q^{88} -9.70208 q^{89} +(4.16034 + 4.17133i) q^{90} -4.46194 q^{91} +5.94019i q^{92} -3.15379i q^{93} -2.78674 q^{94} +(-1.58322 + 1.57905i) q^{95} +2.67671 q^{96} -0.708659i q^{97} +6.27584i q^{98} +2.73984 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9}+O(q^{10}) \) 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9	\( 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9} + 10 q^{10} + 30 q^{11} + 4 q^{14} + 4 q^{15} + 66 q^{16} - 30 q^{19} + 10 q^{20} + 14 q^{21} - 22 q^{24} - 6 q^{25} - 30 q^{29} + 14 q^{30} + 26 q^{31} - 12 q^{34} + 6 q^{35} + 78 q^{36} - 64 q^{39} - 20 q^{40} + 22 q^{41} - 42 q^{44} + 6 q^{45} + 28 q^{46} - 60 q^{49} + 64 q^{51} - 62 q^{54} - 32 q^{56} + 14 q^{59} - 28 q^{60} + 78 q^{61} - 90 q^{64} + 40 q^{65} + 12 q^{66} + 28 q^{69} + 12 q^{70} + 20 q^{71} - 42 q^{74} + 50 q^{75} + 42 q^{76} - 102 q^{79} - 40 q^{80} + 42 q^{81} - 98 q^{84} - 2 q^{85} - 52 q^{86} + 8 q^{89} + 22 q^{90} + 56 q^{91} - 40 q^{94} - 74 q^{96} - 40 q^{99}+O(q^{100}) \) 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9 + 10 * q^10 + 30 * q^11 + 4 * q^14 + 4 * q^15 + 66 * q^16 - 30 * q^19 + 10 * q^20 + 14 * q^21 - 22 * q^24 - 6 * q^25 - 30 * q^29 + 14 * q^30 + 26 * q^31 - 12 * q^34 + 6 * q^35 + 78 * q^36 - 64 * q^39 - 20 * q^40 + 22 * q^41 - 42 * q^44 + 6 * q^45 + 28 * q^46 - 60 * q^49 + 64 * q^51 - 62 * q^54 - 32 * q^56 + 14 * q^59 - 28 * q^60 + 78 * q^61 - 90 * q^64 + 40 * q^65 + 12 * q^66 + 28 * q^69 + 12 * q^70 + 20 * q^71 - 42 * q^74 + 50 * q^75 + 42 * q^76 - 102 * q^79 - 40 * q^80 + 42 * q^81 - 98 * q^84 - 2 * q^85 - 52 * q^86 + 8 * q^89 + 22 * q^90 + 56 * q^91 - 40 * q^94 - 74 * q^96 - 40 * q^99

Introduction

L-functions

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Database

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