LMFDB - Embedded newform 1110.2.h.f.961.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(961,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1110.961");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.h (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.279290944.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 26x^{4} + 169x^{2} + 16 $ x^6 + 26x^4 + 169x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{37}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			961.3
Root			$3.75054i$ of defining polynomial
Character	$\chi$	$=$	1110.961
Dual form			1110.2.h.f.961.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} -1.00000i q^{6} +2.75054 q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} -1.00000i q^{6} +2.75054 q^{7} +1.00000i q^{8} +1.00000 q^{9} -1.00000 q^{10} +4.75054 q^{11} -1.00000 q^{12} +6.75054i q^{13} -2.75054i q^{14} -1.00000i q^{15} +1.00000 q^{16} +7.06651i q^{17} -1.00000i q^{18} -6.75054i q^{19} +1.00000i q^{20} +2.75054 q^{21} -4.75054i q^{22} +5.06651i q^{23} +1.00000i q^{24} -1.00000 q^{25} +6.75054 q^{26} +1.00000 q^{27} -2.75054 q^{28} +2.00000i q^{29} -1.00000 q^{30} +0.315979i q^{31} -1.00000i q^{32} +4.75054 q^{33} +7.06651 q^{34} -2.75054i q^{35} -1.00000 q^{36} +(-4.90852 - 3.59255i) q^{37} -6.75054 q^{38} +6.75054i q^{39} +1.00000 q^{40} -2.00000 q^{41} -2.75054i q^{42} -9.81705i q^{43} -4.75054 q^{44} -1.00000i q^{45} +5.06651 q^{46} +3.50107 q^{47} +1.00000 q^{48} +0.565444 q^{49} +1.00000i q^{50} +7.06651i q^{51} -6.75054i q^{52} +4.75054 q^{53} -1.00000i q^{54} -4.75054i q^{55} +2.75054i q^{56} -6.75054i q^{57} +2.00000 q^{58} -11.8170i q^{59} +1.00000i q^{60} +2.00000i q^{61} +0.315979 q^{62} +2.75054 q^{63} -1.00000 q^{64} +6.75054 q^{65} -4.75054i q^{66} +15.0021 q^{67} -7.06651i q^{68} +5.06651i q^{69} -2.75054 q^{70} -14.1330 q^{71} +1.00000i q^{72} -6.43456 q^{73} +(-3.59255 + 4.90852i) q^{74} -1.00000 q^{75} +6.75054i q^{76} +13.0665 q^{77} +6.75054 q^{78} -8.31598i q^{79} -1.00000i q^{80} +1.00000 q^{81} +2.00000i q^{82} +4.43456 q^{83} -2.75054 q^{84} +7.06651 q^{85} -9.81705 q^{86} +2.00000i q^{87} +4.75054i q^{88} +6.25161i q^{89} -1.00000 q^{90} +18.5676i q^{91} -5.06651i q^{92} +0.315979i q^{93} -3.50107i q^{94} -6.75054 q^{95} -1.00000i q^{96} -11.5011i q^{97} -0.565444i q^{98} +4.75054 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{3} - 6 q^{4} - 6 q^{7} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^3 - 6 * q^4 - 6 * q^7 + 6 * q^9	$ 6 q + 6 q^{3} - 6 q^{4} - 6 q^{7} + 6 q^{9} - 6 q^{10} + 6 q^{11} - 6 q^{12} + 6 q^{16} - 6 q^{21} - 6 q^{25} + 18 q^{26} + 6 q^{27} + 6 q^{28} - 6 q^{30} + 6 q^{33} + 10 q^{34} - 6 q^{36} - 2 q^{37} - 18 q^{38} + 6 q^{40} - 12 q^{41} - 6 q^{44} - 2 q^{46} - 24 q^{47} + 6 q^{48} + 16 q^{49} + 6 q^{53} + 12 q^{58} - 8 q^{62} - 6 q^{63} - 6 q^{64} + 18 q^{65} + 6 q^{70} - 20 q^{71} - 26 q^{73} - 4 q^{74} - 6 q^{75} + 46 q^{77} + 18 q^{78} + 6 q^{81} + 14 q^{83} + 6 q^{84} + 10 q^{85} - 4 q^{86} - 6 q^{90} - 18 q^{95} + 6 q^{99}+O(q^{100}) $ 6 * q + 6 * q^3 - 6 * q^4 - 6 * q^7 + 6 * q^9 - 6 * q^10 + 6 * q^11 - 6 * q^12 + 6 * q^16 - 6 * q^21 - 6 * q^25 + 18 * q^26 + 6 * q^27 + 6 * q^28 - 6 * q^30 + 6 * q^33 + 10 * q^34 - 6 * q^36 - 2 * q^37 - 18 * q^38 + 6 * q^40 - 12 * q^41 - 6 * q^44 - 2 * q^46 - 24 * q^47 + 6 * q^48 + 16 * q^49 + 6 * q^53 + 12 * q^58 - 8 * q^62 - 6 * q^63 - 6 * q^64 + 18 * q^65 + 6 * q^70 - 20 * q^71 - 26 * q^73 - 4 * q^74 - 6 * q^75 + 46 * q^77 + 18 * q^78 + 6 * q^81 + 14 * q^83 + 6 * q^84 + 10 * q^85 - 4 * q^86 - 6 * q^90 - 18 * q^95 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−1.00000			−0.500000
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		−	1.00000i		−	0.408248i
$7$	2.75054			1.03960			0.519802	−	0.854287i	$-0.326006\pi$
$7$	2.75054			1.03960			0.519802	+	0.854287i	$0.326006\pi$
$8$			1.00000i			0.353553i
$9$	1.00000			0.333333
$10$	−1.00000			−0.316228
$11$	4.75054			1.43234			0.716170	−	0.697926i	$-0.245893\pi$
$11$	4.75054			1.43234			0.716170	+	0.697926i	$0.245893\pi$
$12$	−1.00000			−0.288675
$13$			6.75054i			1.87226i	0.351652	+	0.936131i	$0.385620\pi$
$13$			6.75054i			1.87226i	−0.351652	+	0.936131i	$0.614380\pi$
$14$		−	2.75054i		−	0.735111i
$15$		−	1.00000i		−	0.258199i
$16$	1.00000			0.250000
$17$			7.06651i			1.71388i	0.515415	+	0.856941i	$0.327638\pi$
$17$			7.06651i			1.71388i	−0.515415	+	0.856941i	$0.672362\pi$
$18$		−	1.00000i		−	0.235702i
$19$		−	6.75054i		−	1.54868i	−0.632770	−	0.774339i	$-0.718082\pi$
$19$		−	6.75054i		−	1.54868i	0.632770	−	0.774339i	$-0.281918\pi$
$20$			1.00000i			0.223607i
$21$	2.75054			0.600216
$22$		−	4.75054i		−	1.01282i
$23$			5.06651i			1.05644i	0.849107	+	0.528221i	$0.177141\pi$
$23$			5.06651i			1.05644i	−0.849107	+	0.528221i	$0.822859\pi$
$24$			1.00000i			0.204124i
$25$	−1.00000			−0.200000
$26$	6.75054			1.32389
$27$	1.00000			0.192450
$28$	−2.75054			−0.519802
$29$			2.00000i			0.371391i	0.982607	+	0.185695i	$0.0594537\pi$
$29$			2.00000i			0.371391i	−0.982607	+	0.185695i	$0.940546\pi$
$30$	−1.00000			−0.182574
$31$			0.315979i			0.0567515i	0.999597	+	0.0283758i	$0.00903350\pi$
$31$			0.315979i			0.0567515i	−0.999597	+	0.0283758i	$0.990966\pi$
$32$		−	1.00000i		−	0.176777i
$33$	4.75054			0.826962
$34$	7.06651			1.21190
$35$		−	2.75054i		−	0.464925i
$36$	−1.00000			−0.166667
$37$	−4.90852	−	3.59255i	−0.806957	−	0.590611i
$37$	−4.90852	−	3.59255i	−0.806957	−	0.590611i
$38$	−6.75054			−1.09508
$39$			6.75054i			1.08095i
$40$	1.00000			0.158114
$41$	−2.00000			−0.312348			−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000			−0.312348			−0.156174	+	0.987730i	$0.549916\pi$
$42$		−	2.75054i		−	0.424417i
$43$		−	9.81705i		−	1.49709i	−0.663086	−	0.748543i	$-0.730754\pi$
$43$		−	9.81705i		−	1.49709i	0.663086	−	0.748543i	$-0.269246\pi$
$44$	−4.75054			−0.716170
$45$		−	1.00000i		−	0.149071i
$46$	5.06651			0.747017
$47$	3.50107			0.510684			0.255342	−	0.966851i	$-0.417812\pi$
$47$	3.50107			0.510684			0.255342	+	0.966851i	$0.417812\pi$
$48$	1.00000			0.144338
$49$	0.565444			0.0807777
$50$			1.00000i			0.141421i
$51$			7.06651i			0.989510i
$52$		−	6.75054i		−	0.936131i
$53$	4.75054			0.652536			0.326268	−	0.945277i	$-0.394209\pi$
$53$	4.75054			0.652536			0.326268	+	0.945277i	$0.394209\pi$
$54$		−	1.00000i		−	0.136083i
$55$		−	4.75054i		−	0.640562i
$56$			2.75054i			0.367556i
$57$		−	6.75054i		−	0.894130i
$58$	2.00000			0.262613
$59$		−	11.8170i		−	1.53845i	−0.638979	−	0.769224i	$-0.720643\pi$
$59$		−	11.8170i		−	1.53845i	0.638979	−	0.769224i	$-0.279357\pi$
$60$			1.00000i			0.129099i
$61$			2.00000i			0.256074i	0.991769	+	0.128037i	$0.0408676\pi$
$61$			2.00000i			0.256074i	−0.991769	+	0.128037i	$0.959132\pi$
$62$	0.315979			0.0401294
$63$	2.75054			0.346535
$64$	−1.00000			−0.125000
$65$	6.75054			0.837301
$66$		−	4.75054i		−	0.584750i
$67$	15.0021			1.83280			0.916402	−	0.400260i	$-0.131080\pi$
$67$	15.0021			1.83280			0.916402	+	0.400260i	$0.131080\pi$
$68$		−	7.06651i		−	0.856941i
$69$			5.06651i			0.609937i
$70$	−2.75054			−0.328752
$71$	−14.1330			−1.67728			−0.838641	−	0.544685i	$-0.816649\pi$
$71$	−14.1330			−1.67728			−0.838641	+	0.544685i	$0.816649\pi$
$72$			1.00000i			0.117851i
$73$	−6.43456			−0.753108			−0.376554	−	0.926395i	$-0.622891\pi$
$73$	−6.43456			−0.753108			−0.376554	+	0.926395i	$0.622891\pi$
$74$	−3.59255	+	4.90852i	−0.417625	+	0.570604i
$75$	−1.00000			−0.115470
$76$			6.75054i			0.774339i
$77$	13.0665			1.48907
$78$	6.75054			0.764348
$79$		−	8.31598i		−	0.935621i	−0.883829	−	0.467810i	$-0.845043\pi$
$79$		−	8.31598i		−	0.935621i	0.883829	−	0.467810i	$-0.154957\pi$
$80$		−	1.00000i		−	0.111803i
$81$	1.00000			0.111111
$82$			2.00000i			0.220863i
$83$	4.43456			0.486756			0.243378	−	0.969932i	$-0.421744\pi$
$83$	4.43456			0.486756			0.243378	+	0.969932i	$0.421744\pi$
$84$	−2.75054			−0.300108
$85$	7.06651			0.766471
$86$	−9.81705			−1.05860
$87$			2.00000i			0.214423i
$88$			4.75054i			0.506409i
$89$			6.25161i			0.662669i	0.943513	+	0.331334i	$0.107499\pi$
$89$			6.25161i			0.662669i	−0.943513	+	0.331334i	$0.892501\pi$
$90$	−1.00000			−0.105409
$91$			18.5676i			1.94641i
$92$		−	5.06651i		−	0.528221i
$93$			0.315979i			0.0327655i
$94$		−	3.50107i		−	0.361108i
$95$	−6.75054			−0.692590
$96$		−	1.00000i		−	0.102062i
$97$		−	11.5011i		−	1.16776i	−0.811841	−	0.583878i	$-0.801534\pi$
$97$		−	11.5011i		−	1.16776i	0.811841	−	0.583878i	$-0.198466\pi$
$98$		−	0.565444i		−	0.0571185i
$99$	4.75054			0.477447
$100$	1.00000			0.100000
$101$	7.18509			0.714943			0.357472	−	0.933924i	$-0.383639\pi$
$101$	7.18509			0.714943			0.357472	+	0.933924i	$0.383639\pi$
$102$	7.06651			0.699689
$103$			0.631958i			0.0622687i	0.999515	+	0.0311344i	$0.00991198\pi$
$103$			0.631958i			0.0622687i	−0.999515	+	0.0311344i	$0.990088\pi$
$104$	−6.75054			−0.661944
$105$		−	2.75054i		−	0.268425i
$106$		−	4.75054i		−	0.461413i
$107$	−12.0687			−1.16672			−0.583360	−	0.812213i	$-0.698262\pi$
$107$	−12.0687			−1.16672			−0.583360	+	0.812213i	$0.698262\pi$
$108$	−1.00000			−0.0962250
$109$		−	4.56758i		−	0.437495i	−0.975781	−	0.218748i	$-0.929803\pi$
$109$		−	4.56758i		−	0.437495i	0.975781	−	0.218748i	$-0.0701971\pi$
$110$	−4.75054			−0.452946
$111$	−4.90852	−	3.59255i	−0.465897	−	0.340989i
$112$	2.75054			0.259901
$113$		−	2.00000i		−	0.188144i	−0.995565	−	0.0940721i	$-0.970012\pi$
$113$		−	2.00000i		−	0.188144i	0.995565	−	0.0940721i	$-0.0299884\pi$
$114$	−6.75054			−0.632246
$115$	5.06651			0.472455
$116$		−	2.00000i		−	0.185695i
$117$			6.75054i			0.624087i
$118$	−11.8170			−1.08785
$119$			19.4367i			1.78176i
$120$	1.00000			0.0912871
$121$	11.5676			1.05160
$122$	2.00000			0.181071
$123$	−2.00000			−0.180334
$124$		−	0.315979i		−	0.0283758i
$125$			1.00000i			0.0894427i
$126$		−	2.75054i		−	0.245037i
$127$	−14.7505			−1.30890			−0.654449	−	0.756106i	$-0.727099\pi$
$127$	−14.7505			−1.30890			−0.654449	+	0.756106i	$0.727099\pi$
$128$			1.00000i			0.0883883i
$129$		−	9.81705i		−	0.864343i
$130$		−	6.75054i		−	0.592061i
$131$			7.18509i			0.627764i	0.949462	+	0.313882i	$0.101630\pi$
$131$			7.18509i			0.627764i	−0.949462	+	0.313882i	$0.898370\pi$
$132$	−4.75054			−0.413481
$133$		−	18.5676i		−	1.61001i
$134$		−	15.0021i		−	1.29599i
$135$		−	1.00000i		−	0.0860663i
$136$	−7.06651			−0.605949
$137$	−1.68402			−0.143876			−0.0719378	−	0.997409i	$-0.522918\pi$
$137$	−1.68402			−0.143876			−0.0719378	+	0.997409i	$0.522918\pi$
$138$	5.06651			0.431290
$139$	−23.0021			−1.95102			−0.975508	−	0.219964i	$-0.929406\pi$
$139$	−23.0021			−1.95102			−0.975508	+	0.219964i	$0.929406\pi$
$140$			2.75054i			0.232463i
$141$	3.50107			0.294843
$142$			14.1330i			1.18602i
$143$			32.0687i			2.68172i
$144$	1.00000			0.0833333
$145$	2.00000			0.166091
$146$			6.43456i			0.532528i
$147$	0.565444			0.0466370
$148$	4.90852	+	3.59255i	0.403478	+	0.295305i
$149$	−7.81705			−0.640398			−0.320199	−	0.947350i	$-0.603750\pi$
$149$	−7.81705			−0.640398			−0.320199	+	0.947350i	$0.603750\pi$
$150$			1.00000i			0.0816497i
$151$	16.4346			1.33743			0.668713	−	0.743521i	$-0.266846\pi$
$151$	16.4346			1.33743			0.668713	+	0.743521i	$0.266846\pi$
$152$	6.75054			0.547541
$153$			7.06651i			0.571294i
$154$		−	13.0665i		−	1.05293i
$155$	0.315979			0.0253801
$156$		−	6.75054i		−	0.540475i
$157$	−5.81705			−0.464251			−0.232126	−	0.972686i	$-0.574568\pi$
$157$	−5.81705			−0.464251			−0.232126	+	0.972686i	$0.574568\pi$
$158$	−8.31598			−0.661584
$159$	4.75054			0.376742
$160$	−1.00000			−0.0790569
$161$			13.9356i			1.09828i
$162$		−	1.00000i		−	0.0785674i
$163$		−	18.2516i		−	1.42958i	−0.699341	−	0.714788i	$-0.746523\pi$
$163$		−	18.2516i		−	1.42958i	0.699341	−	0.714788i	$-0.253477\pi$
$164$	2.00000			0.156174
$165$		−	4.75054i		−	0.369829i
$166$		−	4.43456i		−	0.344188i
$167$		−	5.06651i		−	0.392059i	−0.980598	−	0.196029i	$-0.937195\pi$
$167$		−	5.06651i		−	0.392059i	0.980598	−	0.196029i	$-0.0628048\pi$
$168$			2.75054i			0.212208i
$169$	−32.5697			−2.50536
$170$		−	7.06651i		−	0.541977i
$171$		−	6.75054i		−	0.516226i
$172$			9.81705i			0.748543i
$173$	4.11858			0.313130			0.156565	−	0.987668i	$-0.449958\pi$
$173$	4.11858			0.313130			0.156565	+	0.987668i	$0.449958\pi$
$174$	2.00000			0.151620
$175$	−2.75054			−0.207921
$176$	4.75054			0.358085
$177$		−	11.8170i		−	0.888224i
$178$	6.25161			0.468578
$179$			9.68402i			0.723818i	0.932213	+	0.361909i	$0.117875\pi$
$179$			9.68402i			0.723818i	−0.932213	+	0.361909i	$0.882125\pi$
$180$			1.00000i			0.0745356i
$181$	10.6320			0.790267			0.395134	−	0.918624i	$-0.370698\pi$
$181$	10.6320			0.790267			0.395134	+	0.918624i	$0.370698\pi$
$182$	18.5676			1.37632
$183$			2.00000i			0.147844i
$184$	−5.06651			−0.373508
$185$	−3.59255	+	4.90852i	−0.264129	+	0.360882i
$186$	0.315979			0.0231687
$187$			33.5697i			2.45486i
$188$	−3.50107			−0.255342
$189$	2.75054			0.200072
$190$			6.75054i			0.489735i
$191$		−	6.93349i		−	0.501689i	−0.968027	−	0.250845i	$-0.919292\pi$
$191$		−	6.93349i		−	0.501689i	0.968027	−	0.250845i	$-0.0807084\pi$
$192$	−1.00000			−0.0721688
$193$			0.498930i			0.0359137i	0.999839	+	0.0179569i	$0.00571616\pi$
$193$			0.498930i			0.0359137i	−0.999839	+	0.0179569i	$0.994284\pi$
$194$	−11.5011			−0.825729
$195$	6.75054			0.483416
$196$	−0.565444			−0.0403889
$197$	−16.7505			−1.19343			−0.596713	−	0.802455i	$-0.703527\pi$
$197$	−16.7505			−1.19343			−0.596713	+	0.802455i	$0.703527\pi$
$198$		−	4.75054i		−	0.337606i
$199$		−	3.31812i		−	0.235215i	−0.993060	−	0.117608i	$-0.962477\pi$
$199$		−	3.31812i		−	0.235215i	0.993060	−	0.117608i	$-0.0375225\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	15.0021			1.05817
$202$		−	7.18509i		−	0.505541i
$203$			5.50107i			0.386099i
$204$		−	7.06651i		−	0.494755i
$205$			2.00000i			0.139686i
$206$	0.631958			0.0440306
$207$			5.06651i			0.352147i
$208$			6.75054i			0.468065i
$209$		−	32.0687i		−	2.21824i
$210$	−2.75054			−0.189805
$211$	−13.5011			−0.929452			−0.464726	−	0.885455i	$-0.653847\pi$
$211$	−13.5011			−0.929452			−0.464726	+	0.885455i	$0.653847\pi$
$212$	−4.75054			−0.326268
$213$	−14.1330			−0.968379
$214$			12.0687i			0.824996i
$215$	−9.81705			−0.669517
$216$			1.00000i			0.0680414i
$217$			0.869112i			0.0589992i
$218$	−4.56758			−0.309356
$219$	−6.43456			−0.434807
$220$			4.75054i			0.320281i
$221$	−47.7028			−3.20883
$222$	−3.59255	+	4.90852i	−0.241116	+	0.329439i
$223$	25.3181			1.69543			0.847713	−	0.530455i	$-0.177979\pi$
$223$	25.3181			1.69543			0.847713	+	0.530455i	$0.177979\pi$
$224$		−	2.75054i		−	0.183778i
$225$	−1.00000			−0.0666667
$226$	−2.00000			−0.133038
$227$			4.63196i			0.307434i	0.988115	+	0.153717i	$0.0491244\pi$
$227$			4.63196i			0.307434i	−0.988115	+	0.153717i	$0.950876\pi$
$228$			6.75054i			0.447065i
$229$	20.1330			1.33043			0.665214	−	0.746653i	$-0.268340\pi$
$229$	20.1330			1.33043			0.665214	+	0.746653i	$0.268340\pi$
$230$		−	5.06651i		−	0.334076i
$231$	13.0665			0.859714
$232$	−2.00000			−0.131306
$233$	−6.31598			−0.413774			−0.206887	−	0.978365i	$-0.566333\pi$
$233$	−6.31598			−0.413774			−0.206887	+	0.978365i	$0.566333\pi$
$234$	6.75054			0.441296
$235$		−	3.50107i		−	0.228385i
$236$			11.8170i			0.769224i
$237$		−	8.31598i		−	0.540181i
$238$	19.4367			1.25989
$239$		−	12.6320i		−	0.817093i	−0.912737	−	0.408547i	$-0.866036\pi$
$239$		−	12.6320i		−	0.817093i	0.912737	−	0.408547i	$-0.133964\pi$
$240$		−	1.00000i		−	0.0645497i
$241$		−	16.6320i		−	1.07136i	−0.844422	−	0.535679i	$-0.820056\pi$
$241$		−	16.6320i		−	1.07136i	0.844422	−	0.535679i	$-0.179944\pi$
$242$		−	11.5676i		−	0.743593i
$243$	1.00000			0.0641500
$244$		−	2.00000i		−	0.128037i
$245$		−	0.565444i		−	0.0361249i
$246$			2.00000i			0.127515i
$247$	45.5697			2.89953
$248$	−0.315979			−0.0200647
$249$	4.43456			0.281029
$250$	1.00000			0.0632456
$251$			1.68402i			0.106294i	0.998587	+	0.0531472i	$0.0169253\pi$
$251$			1.68402i			0.106294i	−0.998587	+	0.0531472i	$0.983075\pi$
$252$	−2.75054			−0.173267
$253$			24.0687i			1.51318i
$254$			14.7505i			0.925531i
$255$	7.06651			0.442522
$256$	1.00000			0.0625000
$257$			3.43242i			0.214108i	0.994253	+	0.107054i	$0.0341418\pi$
$257$			3.43242i			0.214108i	−0.994253	+	0.107054i	$0.965858\pi$
$258$	−9.81705			−0.611183
$259$	−13.5011	−	9.88142i	−0.838916	−	0.614002i
$260$	−6.75054			−0.418650
$261$			2.00000i			0.123797i
$262$	7.18509			0.443896
$263$	6.86911			0.423568			0.211784	−	0.977317i	$-0.432073\pi$
$263$	6.86911			0.423568			0.211784	+	0.977317i	$0.432073\pi$
$264$			4.75054i			0.292375i
$265$		−	4.75054i		−	0.291823i
$266$	−18.5676			−1.13845
$267$			6.25161i			0.382592i
$268$	−15.0021			−0.916402
$269$	−9.24946			−0.563950			−0.281975	−	0.959422i	$-0.590989\pi$
$269$	−9.24946			−0.563950			−0.281975	+	0.959422i	$0.590989\pi$
$270$	−1.00000			−0.0608581
$271$	14.3702			0.872926			0.436463	−	0.899722i	$-0.356231\pi$
$271$	14.3702			0.872926			0.436463	+	0.899722i	$0.356231\pi$
$272$			7.06651i			0.428470i
$273$			18.5676i			1.12376i
$274$			1.68402i			0.101735i
$275$	−4.75054			−0.286468
$276$		−	5.06651i		−	0.304968i
$277$			26.3846i			1.58530i	0.609678	+	0.792650i	$0.291299\pi$
$277$			26.3846i			1.58530i	−0.609678	+	0.792650i	$0.708701\pi$
$278$			23.0021i			1.37958i
$279$			0.315979i			0.0189172i
$280$	2.75054			0.164376
$281$			15.7527i			0.939726i	0.882739	+	0.469863i	$0.155697\pi$
$281$			15.7527i			0.939726i	−0.882739	+	0.469863i	$0.844303\pi$
$282$		−	3.50107i		−	0.208486i
$283$			12.3846i			0.736190i	0.929788	+	0.368095i	$0.119990\pi$
$283$			12.3846i			0.736190i	−0.929788	+	0.368095i	$0.880010\pi$
$284$	14.1330			0.838641
$285$	−6.75054			−0.399867
$286$	32.0687			1.89626
$287$	−5.50107			−0.324718
$288$		−	1.00000i		−	0.0589256i
$289$	−32.9356			−1.93739
$290$		−	2.00000i		−	0.117444i
$291$		−	11.5011i		−	0.674205i
$292$	6.43456			0.376554
$293$	0.750535			0.0438467			0.0219234	−	0.999760i	$-0.493021\pi$
$293$	0.750535			0.0438467			0.0219234	+	0.999760i	$0.493021\pi$
$294$		−	0.565444i		−	0.0329774i
$295$	−11.8170			−0.688015
$296$	3.59255	−	4.90852i	0.208812	−	0.285302i
$297$	4.75054			0.275654
$298$			7.81705i			0.452830i
$299$	−34.2017			−1.97793
$300$	1.00000			0.0577350
$301$		−	27.0021i		−	1.55638i
$302$		−	16.4346i		−	0.945702i
$303$	7.18509			0.412773
$304$		−	6.75054i		−	0.387170i
$305$	2.00000			0.114520
$306$	7.06651			0.403966
$307$	18.3702			1.04844			0.524221	−	0.851582i	$-0.324357\pi$
$307$	18.3702			1.04844			0.524221	+	0.851582i	$0.324357\pi$
$308$	−13.0665			−0.744534
$309$			0.631958i			0.0359509i
$310$		−	0.315979i		−	0.0179464i
$311$			35.0021i			1.98479i	0.123097	+	0.992395i	$0.460717\pi$
$311$			35.0021i			1.98479i	−0.123097	+	0.992395i	$0.539283\pi$
$312$	−6.75054			−0.382174
$313$			1.36804i			0.0773263i	0.999252	+	0.0386631i	$0.0123099\pi$
$313$			1.36804i			0.0773263i	−0.999252	+	0.0386631i	$0.987690\pi$
$314$			5.81705i			0.328275i
$315$		−	2.75054i		−	0.154975i
$316$			8.31598i			0.467810i
$317$	10.0542			0.564700			0.282350	−	0.959311i	$-0.408886\pi$
$317$	10.0542			0.564700			0.282350	+	0.959311i	$0.408886\pi$
$318$		−	4.75054i		−	0.266397i
$319$			9.50107i			0.531958i
$320$			1.00000i			0.0559017i
$321$	−12.0687			−0.673607
$322$	13.9356			0.776602
$323$	47.7028			2.65425
$324$	−1.00000			−0.0555556
$325$		−	6.75054i		−	0.374452i
$326$	−18.2516			−1.01086
$327$		−	4.56758i		−	0.252588i
$328$		−	2.00000i		−	0.110432i
$329$	9.62982			0.530909
$330$	−4.75054			−0.261508
$331$			26.3160i			1.44646i	0.690609	+	0.723229i	$0.257343\pi$
$331$			26.3160i			1.44646i	−0.690609	+	0.723229i	$0.742657\pi$
$332$	−4.43456			−0.243378
$333$	−4.90852	−	3.59255i	−0.268986	−	0.196870i
$334$	−5.06651			−0.277227
$335$		−	15.0021i		−	0.819655i
$336$	2.75054			0.150054
$337$	−26.7006			−1.45448			−0.727238	−	0.686386i	$-0.759196\pi$
$337$	−26.7006			−1.45448			−0.727238	+	0.686386i	$0.759196\pi$
$338$			32.5697i			1.77156i
$339$		−	2.00000i		−	0.108625i
$340$	−7.06651			−0.383236
$341$			1.50107i			0.0812875i
$342$	−6.75054			−0.365027
$343$	−17.6985			−0.955628
$344$	9.81705			0.529300
$345$	5.06651			0.272772
$346$		−	4.11858i		−	0.221416i
$347$		−	13.5011i		−	0.724775i	−0.932027	−	0.362388i	$-0.881962\pi$
$347$		−	13.5011i		−	0.724775i	0.932027	−	0.362388i	$-0.118038\pi$
$348$		−	2.00000i		−	0.107211i
$349$	−9.36804			−0.501460			−0.250730	−	0.968057i	$-0.580671\pi$
$349$	−9.36804			−0.501460			−0.250730	+	0.968057i	$0.580671\pi$
$350$			2.75054i			0.147022i
$351$			6.75054i			0.360317i
$352$		−	4.75054i		−	0.253204i
$353$			13.6341i			0.725670i	0.931853	+	0.362835i	$0.118191\pi$
$353$			13.6341i			0.725670i	−0.931853	+	0.362835i	$0.881809\pi$
$354$	−11.8170			−0.628069
$355$			14.1330i			0.750103i
$356$		−	6.25161i		−	0.331334i
$357$			19.4367i			1.02870i
$358$	9.68402			0.511816
$359$	8.86911			0.468094			0.234047	−	0.972225i	$-0.424803\pi$
$359$	8.86911			0.468094			0.234047	+	0.972225i	$0.424803\pi$
$360$	1.00000			0.0527046
$361$	−26.5697			−1.39841
$362$		−	10.6320i		−	0.558803i
$363$	11.5676			0.607141
$364$		−	18.5676i		−	0.973206i
$365$			6.43456i			0.336800i
$366$	2.00000			0.104542
$367$	2.11858			0.110589			0.0552944	−	0.998470i	$-0.482390\pi$
$367$	2.11858			0.110589			0.0552944	+	0.998470i	$0.482390\pi$
$368$			5.06651i			0.264110i
$369$	−2.00000			−0.104116
$370$	4.90852	+	3.59255i	0.255182	+	0.186768i
$371$	13.0665			0.678380
$372$		−	0.315979i		−	0.0163828i
$373$	23.0810			1.19509			0.597544	−	0.801836i	$-0.296143\pi$
$373$	23.0810			1.19509			0.597544	+	0.801836i	$0.296143\pi$
$374$	33.5697			1.73585
$375$			1.00000i			0.0516398i
$376$			3.50107i			0.180554i
$377$	−13.5011			−0.695341
$378$		−	2.75054i		−	0.141472i
$379$	−8.50321			−0.436781			−0.218390	−	0.975862i	$-0.570081\pi$
$379$	−8.50321			−0.436781			−0.218390	+	0.975862i	$0.570081\pi$
$380$	6.75054			0.346295
$381$	−14.7505			−0.755693
$382$	−6.93349			−0.354748
$383$			15.1995i			0.776660i	0.921520	+	0.388330i	$0.126948\pi$
$383$			15.1995i			0.776660i	−0.921520	+	0.388330i	$0.873052\pi$
$384$			1.00000i			0.0510310i
$385$		−	13.0665i		−	0.665931i
$386$	0.498930			0.0253948
$387$		−	9.81705i		−	0.499029i
$388$			11.5011i			0.583878i
$389$			32.1330i			1.62921i	0.580017	+	0.814605i	$0.303046\pi$
$389$			32.1330i			1.62921i	−0.580017	+	0.814605i	$0.696954\pi$
$390$		−	6.75054i		−	0.341827i
$391$	−35.8026			−1.81062
$392$			0.565444i			0.0285592i
$393$			7.18509i			0.362440i
$394$			16.7505i			0.843880i
$395$	−8.31598			−0.418422
$396$	−4.75054			−0.238723
$397$	−28.8192			−1.44639			−0.723197	−	0.690642i	$-0.757328\pi$
$397$	−28.8192			−1.44639			−0.723197	+	0.690642i	$0.757328\pi$
$398$	−3.31812			−0.166322
$399$		−	18.5676i		−	0.929542i
$400$	−1.00000			−0.0500000
$401$			10.6175i			0.530213i	0.964219	+	0.265106i	$0.0854071\pi$
$401$			10.6175i			0.530213i	−0.964219	+	0.265106i	$0.914593\pi$
$402$		−	15.0021i		−	0.748239i
$403$	−2.13303			−0.106254
$404$	−7.18509			−0.357472
$405$		−	1.00000i		−	0.0496904i
$406$	5.50107			0.273014
$407$	−23.3181	−	17.0665i	−1.15584	−	0.845956i
$408$	−7.06651			−0.349845
$409$		−	37.6384i		−	1.86110i	−0.366167	−	0.930549i	$-0.619330\pi$
$409$		−	37.6384i		−	1.86110i	0.366167	−	0.930549i	$-0.380670\pi$
$410$	2.00000			0.0987730
$411$	−1.68402			−0.0830666
$412$		−	0.631958i		−	0.0311344i
$413$		−	32.5032i		−	1.59938i
$414$	5.06651			0.249006
$415$		−	4.43456i		−	0.217684i
$416$	6.75054			0.330972
$417$	−23.0021			−1.12642
$418$	−32.0687			−1.56853
$419$	22.0145			1.07548			0.537738	−	0.843112i	$-0.319279\pi$
$419$	22.0145			1.07548			0.537738	+	0.843112i	$0.319279\pi$
$420$			2.75054i			0.134212i
$421$		−	3.26392i		−	0.159074i	−0.996832	−	0.0795368i	$-0.974656\pi$
$421$		−	3.26392i		−	0.159074i	0.996832	−	0.0795368i	$-0.0253441\pi$
$422$			13.5011i			0.657222i
$423$	3.50107			0.170228
$424$			4.75054i			0.230706i
$425$		−	7.06651i		−	0.342776i
$426$			14.1330i			0.684747i
$427$			5.50107i			0.266215i
$428$	12.0687			0.583360
$429$			32.0687i			1.54829i
$430$			9.81705i			0.473420i
$431$		−	26.5676i		−	1.27972i	−0.768493	−	0.639858i	$-0.778993\pi$
$431$		−	26.5676i		−	1.27972i	0.768493	−	0.639858i	$-0.221007\pi$
$432$	1.00000			0.0481125
$433$	8.56758			0.411732			0.205866	−	0.978580i	$-0.433999\pi$
$433$	8.56758			0.411732			0.205866	+	0.978580i	$0.433999\pi$
$434$	0.869112			0.0417187
$435$	2.00000			0.0958927
$436$			4.56758i			0.218748i
$437$	34.2017			1.63609
$438$			6.43456i			0.307455i
$439$		−	8.31598i		−	0.396900i	−0.980111	−	0.198450i	$-0.936409\pi$
$439$		−	8.31598i		−	0.396900i	0.980111	−	0.198450i	$-0.0635907\pi$
$440$	4.75054			0.226473
$441$	0.565444			0.0269259
$442$			47.7028i			2.26899i
$443$	35.2682			1.67564			0.837821	−	0.545944i	$-0.183829\pi$
$443$	35.2682			1.67564			0.837821	+	0.545944i	$0.183829\pi$
$444$	4.90852	+	3.59255i	0.232948	+	0.170495i
$445$	6.25161			0.296355
$446$		−	25.3181i		−	1.19885i
$447$	−7.81705			−0.369734
$448$	−2.75054			−0.129951
$449$		−	30.3203i		−	1.43090i	−0.698663	−	0.715451i	$-0.746221\pi$
$449$		−	30.3203i		−	1.43090i	0.698663	−	0.715451i	$-0.253779\pi$
$450$			1.00000i			0.0471405i
$451$	−9.50107			−0.447388
$452$			2.00000i			0.0940721i
$453$	16.4346			0.772163
$454$	4.63196			0.217389
$455$	18.5676			0.870462
$456$	6.75054			0.316123
$457$		−	10.6320i		−	0.497342i	−0.968588	−	0.248671i	$-0.920006\pi$
$457$		−	10.6320i		−	0.497342i	0.968588	−	0.248671i	$-0.0799938\pi$
$458$		−	20.1330i		−	0.940755i
$459$			7.06651i			0.329837i
$460$	−5.06651			−0.236227
$461$		−	30.5032i		−	1.42068i	−0.703861	−	0.710338i	$-0.748542\pi$
$461$		−	30.5032i		−	1.42068i	0.703861	−	0.710338i	$-0.251458\pi$
$462$		−	13.0665i		−	0.607909i
$463$		−	39.5054i		−	1.83597i	−0.396616	−	0.917985i	$-0.629815\pi$
$463$		−	39.5054i		−	1.83597i	0.396616	−	0.917985i	$-0.370185\pi$
$464$			2.00000i			0.0928477i
$465$	0.315979			0.0146532
$466$			6.31598i			0.292582i
$467$		−	16.6320i		−	0.769635i	−0.922993	−	0.384818i	$-0.874264\pi$
$467$		−	16.6320i		−	0.769635i	0.922993	−	0.384818i	$-0.125736\pi$
$468$		−	6.75054i		−	0.312044i
$469$	41.2639			1.90539
$470$	−3.50107			−0.161492
$471$	−5.81705			−0.268036
$472$	11.8170			0.543924
$473$		−	46.6362i		−	2.14434i
$474$	−8.31598			−0.381966
$475$			6.75054i			0.309736i
$476$		−	19.4367i		−	0.890880i
$477$	4.75054			0.217512
$478$	−12.6320			−0.577772
$479$			33.2038i			1.51712i	0.651602	+	0.758561i	$0.274097\pi$
$479$			33.2038i			1.51712i	−0.651602	+	0.758561i	$0.725903\pi$
$480$	−1.00000			−0.0456435
$481$	24.2516	−	33.1352i	1.10578	−	1.51083i
$482$	−16.6320			−0.757565
$483$			13.9356i			0.634093i
$484$	−11.5676			−0.525799
$485$	−11.5011			−0.522237
$486$		−	1.00000i		−	0.0453609i
$487$			11.6341i			0.527191i	0.964633	+	0.263596i	$0.0849085\pi$
$487$			11.6341i			0.527191i	−0.964633	+	0.263596i	$0.915092\pi$
$488$	−2.00000			−0.0905357
$489$		−	18.2516i		−	0.825366i
$490$	−0.565444			−0.0255442
$491$	−4.75054			−0.214389			−0.107194	−	0.994238i	$-0.534187\pi$
$491$	−4.75054			−0.214389			−0.107194	+	0.994238i	$0.534187\pi$
$492$	2.00000			0.0901670
$493$	−14.1330			−0.636520
$494$		−	45.5697i		−	2.05028i
$495$		−	4.75054i		−	0.213521i
$496$			0.315979i			0.0141879i
$497$	−38.8734			−1.74371
$498$		−	4.43456i		−	0.198717i
$499$		−	9.12072i		−	0.408299i	−0.978940	−	0.204150i	$-0.934557\pi$
$499$		−	9.12072i		−	0.408299i	0.978940	−	0.204150i	$-0.0654429\pi$
$500$		−	1.00000i		−	0.0447214i
$501$		−	5.06651i		−	0.226355i
$502$	1.68402			0.0751615
$503$			9.26392i			0.413058i	0.978441	+	0.206529i	$0.0662167\pi$
$503$			9.26392i			0.413058i	−0.978441	+	0.206529i	$0.933783\pi$
$504$			2.75054i			0.122519i
$505$		−	7.18509i		−	0.319732i
$506$	24.0687			1.06998
$507$	−32.5697			−1.44647
$508$	14.7505			0.654449
$509$	23.0166			1.02019			0.510096	−	0.860117i	$-0.329610\pi$
$509$	23.0166			1.02019			0.510096	+	0.860117i	$0.329610\pi$
$510$		−	7.06651i		−	0.312911i
$511$	−17.6985			−0.782934
$512$		−	1.00000i		−	0.0441942i
$513$		−	6.75054i		−	0.298043i
$514$	3.43242			0.151397
$515$	0.631958			0.0278474
$516$			9.81705i			0.432172i
$517$	16.6320			0.731473
$518$	−9.88142	+	13.5011i	−0.434165	+	0.593203i
$519$	4.11858			0.180785
$520$			6.75054i			0.296031i
$521$	30.6320			1.34201			0.671005	−	0.741453i	$-0.265863\pi$
$521$	30.6320			1.34201			0.671005	+	0.741453i	$0.265863\pi$
$522$	2.00000			0.0875376
$523$			15.5553i			0.680185i	0.940392	+	0.340092i	$0.110458\pi$
$523$			15.5553i			0.680185i	−0.940392	+	0.340092i	$0.889542\pi$
$524$		−	7.18509i		−	0.313882i
$525$	−2.75054			−0.120043
$526$		−	6.86911i		−	0.299508i
$527$	−2.23287			−0.0972654
$528$	4.75054			0.206741
$529$	−2.66957			−0.116068
$530$	−4.75054			−0.206350
$531$		−	11.8170i		−	0.512816i
$532$			18.5676i			0.805007i
$533$		−	13.5011i		−	0.584796i
$534$	6.25161			0.270533
$535$			12.0687i			0.521773i
$536$			15.0021i			0.647994i
$537$			9.68402i			0.417896i
$538$			9.24946i			0.398773i
$539$	2.68616			0.115701
$540$			1.00000i			0.0430331i
$541$		−	3.43242i		−	0.147571i	−0.997274	−	0.0737855i	$-0.976492\pi$
$541$		−	3.43242i		−	0.147571i	0.997274	−	0.0737855i	$-0.0235080\pi$
$542$		−	14.3702i		−	0.617252i
$543$	10.6320			0.456261
$544$	7.06651			0.302974
$545$	−4.56758			−0.195654
$546$	18.5676			0.794619
$547$			17.3825i			0.743222i	0.928389	+	0.371611i	$0.121194\pi$
$547$			17.3825i			0.743222i	−0.928389	+	0.371611i	$0.878806\pi$
$548$	1.68402			0.0719378
$549$			2.00000i			0.0853579i
$550$			4.75054i			0.202564i
$551$	13.5011			0.575165
$552$	−5.06651			−0.215645
$553$		−	22.8734i		−	0.972676i
$554$	26.3846			1.12098
$555$	−3.59255	+	4.90852i	−0.152495	+	0.208355i
$556$	23.0021			0.975508
$557$		−	17.0021i		−	0.720404i	−0.932874	−	0.360202i	$-0.882708\pi$
$557$		−	17.0021i		−	0.720404i	0.932874	−	0.360202i	$-0.117292\pi$
$558$	0.315979			0.0133765
$559$	66.2703			2.80294
$560$		−	2.75054i		−	0.116231i
$561$			33.5697i			1.41731i
$562$	15.7527			0.664487
$563$		−	38.8734i		−	1.63832i	−0.573566	−	0.819159i	$-0.694441\pi$
$563$		−	38.8734i		−	1.63832i	0.573566	−	0.819159i	$-0.305559\pi$
$564$	−3.50107			−0.147422
$565$	−2.00000			−0.0841406
$566$	12.3846			0.520565
$567$	2.75054			0.115512
$568$		−	14.1330i		−	0.593009i
$569$			10.3804i			0.435167i	0.976042	+	0.217584i	$0.0698174\pi$
$569$			10.3804i			0.435167i	−0.976042	+	0.217584i	$0.930183\pi$
$570$			6.75054i			0.282749i
$571$	−8.99786			−0.376549			−0.188274	−	0.982116i	$-0.560289\pi$
$571$	−8.99786			−0.376549			−0.188274	+	0.982116i	$0.560289\pi$
$572$		−	32.0687i		−	1.34086i
$573$		−	6.93349i		−	0.289651i
$574$			5.50107i			0.229610i
$575$		−	5.06651i		−	0.211288i
$576$	−1.00000			−0.0416667
$577$			26.8691i			1.11858i	0.828973	+	0.559288i	$0.188925\pi$
$577$			26.8691i			1.11858i	−0.828973	+	0.559288i	$0.811075\pi$
$578$			32.9356i			1.36994i
$579$			0.498930i			0.0207348i
$580$	−2.00000			−0.0830455
$581$	12.1974			0.506034
$582$	−11.5011			−0.476735
$583$	22.5676			0.934654
$584$		−	6.43456i		−	0.266264i
$585$	6.75054			0.279100
$586$		−	0.750535i		−	0.0310043i
$587$		−	7.87125i		−	0.324881i	−0.986718	−	0.162441i	$-0.948063\pi$
$587$		−	7.87125i		−	0.324881i	0.986718	−	0.162441i	$-0.0519366\pi$
$588$	−0.565444			−0.0233185
$589$	2.13303			0.0878899
$590$			11.8170i			0.486500i
$591$	−16.7505			−0.689025
$592$	−4.90852	−	3.59255i	−0.201739	−	0.147653i
$593$	33.0810			1.35847			0.679236	−	0.733920i	$-0.262311\pi$
$593$	33.0810			1.35847			0.679236	+	0.733920i	$0.262311\pi$
$594$		−	4.75054i		−	0.194917i
$595$	19.4367			0.796827
$596$	7.81705			0.320199
$597$		−	3.31812i		−	0.135802i
$598$			34.2017i			1.39861i
$599$	−16.5032			−0.674303			−0.337151	−	0.941450i	$-0.609463\pi$
$599$	−16.5032			−0.674303			−0.337151	+	0.941450i	$0.609463\pi$
$600$		−	1.00000i		−	0.0408248i
$601$	−30.0687			−1.22653			−0.613263	−	0.789879i	$-0.710143\pi$
$601$	−30.0687			−1.22653			−0.613263	+	0.789879i	$0.710143\pi$
$602$	−27.0021			−1.10053
$603$	15.0021			0.610934
$604$	−16.4346			−0.668713
$605$		−	11.5676i		−	0.470289i
$606$		−	7.18509i		−	0.291874i
$607$		−	7.36804i		−	0.299060i	−0.988757	−	0.149530i	$-0.952224\pi$
$607$		−	7.36804i		−	0.299060i	0.988757	−	0.149530i	$-0.0477760\pi$
$608$	−6.75054			−0.273770
$609$			5.50107i			0.222915i
$610$		−	2.00000i		−	0.0809776i
$611$			23.6341i			0.956133i
$612$		−	7.06651i		−	0.285647i
$613$	−9.18509			−0.370982			−0.185491	−	0.982646i	$-0.559388\pi$
$613$	−9.18509			−0.370982			−0.185491	+	0.982646i	$0.559388\pi$
$614$		−	18.3702i		−	0.741360i
$615$			2.00000i			0.0806478i
$616$			13.0665i			0.526465i
$617$	7.18509			0.289261			0.144630	−	0.989486i	$-0.453801\pi$
$617$	7.18509			0.289261			0.144630	+	0.989486i	$0.453801\pi$
$618$	0.631958			0.0254211
$619$	−34.0043			−1.36675			−0.683374	−	0.730069i	$-0.739488\pi$
$619$	−34.0043			−1.36675			−0.683374	+	0.730069i	$0.739488\pi$
$620$	−0.315979			−0.0126900
$621$			5.06651i			0.203312i
$622$	35.0021			1.40346
$623$			17.1953i			0.688914i
$624$			6.75054i			0.270238i
$625$	1.00000			0.0400000
$626$	1.36804			0.0546779
$627$		−	32.0687i		−	1.28070i
$628$	5.81705			0.232126
$629$	25.3868	−	34.6862i	1.01224	−	1.38303i
$630$	−2.75054			−0.109584
$631$			5.81705i			0.231573i	0.993274	+	0.115787i	$0.0369389\pi$
$631$			5.81705i			0.231573i	−0.993274	+	0.115787i	$0.963061\pi$
$632$	8.31598			0.330792
$633$	−13.5011			−0.536619
$634$		−	10.0542i		−	0.399303i
$635$			14.7505i			0.585357i
$636$	−4.75054			−0.188371
$637$			3.81705i			0.151237i
$638$	9.50107			0.376151
$639$	−14.1330			−0.559094
$640$	1.00000			0.0395285
$641$	−13.1309			−0.518639			−0.259319	−	0.965792i	$-0.583498\pi$
$641$	−13.1309			−0.518639			−0.259319	+	0.965792i	$0.583498\pi$
$642$			12.0687i			0.476312i
$643$			22.2516i			0.877518i	0.898605	+	0.438759i	$0.144582\pi$
$643$			22.2516i			0.877518i	−0.898605	+	0.438759i	$0.855418\pi$
$644$		−	13.9356i		−	0.549141i
$645$	−9.81705			−0.386546
$646$		−	47.7028i		−	1.87684i
$647$		−	24.0687i		−	0.946236i	−0.880999	−	0.473118i	$-0.843128\pi$
$647$		−	24.0687i		−	0.946236i	0.880999	−	0.473118i	$-0.156872\pi$
$648$			1.00000i			0.0392837i
$649$		−	56.1373i		−	2.20358i
$650$	−6.75054			−0.264778
$651$			0.869112i			0.0340632i
$652$			18.2516i			0.714788i
$653$		−	25.3680i		−	0.992728i	−0.868114	−	0.496364i	$-0.834668\pi$
$653$		−	25.3680i		−	0.992728i	0.868114	−	0.496364i	$-0.165332\pi$
$654$	−4.56758			−0.178607
$655$	7.18509			0.280745
$656$	−2.00000			−0.0780869
$657$	−6.43456			−0.251036
$658$		−	9.62982i		−	0.375409i
$659$	−18.4490			−0.718671			−0.359336	−	0.933208i	$-0.616997\pi$
$659$	−18.4490			−0.718671			−0.359336	+	0.933208i	$0.616997\pi$
$660$			4.75054i			0.184914i
$661$		−	18.9378i		−	0.736594i	−0.929708	−	0.368297i	$-0.879941\pi$
$661$		−	18.9378i		−	0.736594i	0.929708	−	0.368297i	$-0.120059\pi$
$662$	26.3160			1.02280
$663$	−47.7028			−1.85262
$664$			4.43456i			0.172094i
$665$	−18.5676			−0.720020
$666$	−3.59255	+	4.90852i	−0.139208	+	0.190201i
$667$	−10.1330			−0.392352
$668$			5.06651i			0.196029i
$669$	25.3181			0.978855
$670$	−15.0021			−0.579583
$671$			9.50107i			0.366785i
$672$		−	2.75054i		−	0.106104i
$673$	−35.5697			−1.37111			−0.685556	−	0.728020i	$-0.740441\pi$
$673$	−35.5697			−1.37111			−0.685556	+	0.728020i	$0.740441\pi$
$674$			26.7006i			1.02847i
$675$	−1.00000			−0.0384900
$676$	32.5697			1.25268
$677$	−40.8878			−1.57145			−0.785724	−	0.618578i	$-0.787709\pi$
$677$	−40.8878			−1.57145			−0.785724	+	0.618578i	$0.787709\pi$
$678$	−2.00000			−0.0768095
$679$		−	31.6341i		−	1.21401i
$680$			7.06651i			0.270988i
$681$			4.63196i			0.177497i
$682$	1.50107			0.0574790
$683$		−	14.3702i		−	0.549860i	−0.961464	−	0.274930i	$-0.911345\pi$
$683$		−	14.3702i		−	0.549860i	0.961464	−	0.274930i	$-0.0886546\pi$
$684$			6.75054i			0.258113i
$685$			1.68402i			0.0643431i
$686$			17.6985i			0.675731i
$687$	20.1330			0.768123
$688$		−	9.81705i		−	0.374272i
$689$			32.0687i			1.22172i
$690$		−	5.06651i		−	0.192879i
$691$	−17.7671			−0.675893			−0.337947	−	0.941165i	$-0.609732\pi$
$691$	−17.7671			−0.675893			−0.337947	+	0.941165i	$0.609732\pi$
$692$	−4.11858			−0.156565
$693$	13.0665			0.496356
$694$	−13.5011			−0.512494
$695$			23.0021i			0.872521i
$696$	−2.00000			−0.0758098
$697$		−	14.1330i		−	0.535327i
$698$			9.36804i			0.354586i
$699$	−6.31598			−0.238892
$700$	2.75054			0.103960
$701$			28.1330i			1.06257i	0.847193	+	0.531285i	$0.178291\pi$
$701$			28.1330i			1.06257i	−0.847193	+	0.531285i	$0.821709\pi$
$702$	6.75054			0.254783
$703$	−24.2516	+	33.1352i	−0.914667	+	1.24972i
$704$	−4.75054			−0.179043
$705$		−	3.50107i		−	0.131858i
$706$	13.6341			0.513126
$707$	19.7628			0.743258
$708$			11.8170i			0.444112i
$709$		−	34.0687i		−	1.27948i	−0.768593	−	0.639738i	$-0.779043\pi$
$709$		−	34.0687i		−	1.27948i	0.768593	−	0.639738i	$-0.220957\pi$
$710$	14.1330			0.530403
$711$		−	8.31598i		−	0.311874i
$712$	−6.25161			−0.234289
$713$	−1.60091			−0.0599547
$714$	19.4367			0.727400
$715$	32.0687			1.19930
$716$		−	9.68402i		−	0.361909i
$717$		−	12.6320i		−	0.471749i
$718$		−	8.86911i		−	0.330992i
$719$	−40.2661			−1.50167			−0.750835	−	0.660490i	$-0.770349\pi$
$719$	−40.2661			−1.50167			−0.750835	+	0.660490i	$0.770349\pi$
$720$		−	1.00000i		−	0.0372678i
$721$			1.73822i			0.0647348i
$722$			26.5697i			0.988823i
$723$		−	16.6320i		−	0.618549i
$724$	−10.6320			−0.395134
$725$		−	2.00000i		−	0.0742781i
$726$		−	11.5676i		−	0.429313i
$727$		−	13.1352i		−	0.487156i	−0.969881	−	0.243578i	$-0.921679\pi$
$727$		−	13.1352i		−	0.487156i	0.969881	−	0.243578i	$-0.0783213\pi$
$728$	−18.5676			−0.688160
$729$	1.00000			0.0370370
$730$	6.43456			0.238154
$731$	69.3723			2.56583
$732$		−	2.00000i		−	0.0739221i
$733$	−7.05206			−0.260474			−0.130237	−	0.991483i	$-0.541574\pi$
$733$	−7.05206			−0.260474			−0.130237	+	0.991483i	$0.541574\pi$
$734$		−	2.11858i		−	0.0781981i
$735$		−	0.565444i		−	0.0208567i
$736$	5.06651			0.186754
$737$	71.2682			2.62520
$738$			2.00000i			0.0736210i
$739$	24.7404			0.910089			0.455045	−	0.890469i	$-0.349623\pi$
$739$	24.7404			0.910089			0.455045	+	0.890469i	$0.349623\pi$
$740$	3.59255	−	4.90852i	0.132065	−	0.180441i
$741$	45.5697			1.67405
$742$		−	13.0665i		−	0.479687i
$743$	1.36804			0.0501886			0.0250943	−	0.999685i	$-0.492011\pi$
$743$	1.36804			0.0501886			0.0250943	+	0.999685i	$0.492011\pi$
$744$	−0.315979			−0.0115844
$745$			7.81705i			0.286395i
$746$		−	23.0810i		−	0.845054i
$747$	4.43456			0.162252
$748$		−	33.5697i		−	1.22743i
$749$	−33.1953			−1.21293
$750$	1.00000			0.0365148
$751$	16.0000			0.583848			0.291924	−	0.956441i	$-0.405705\pi$
$751$	16.0000			0.583848			0.291924	+	0.956441i	$0.405705\pi$
$752$	3.50107			0.127671
$753$			1.68402i			0.0613691i
$754$			13.5011i			0.491680i
$755$		−	16.4346i		−	0.598115i
$756$	−2.75054			−0.100036
$757$			49.6239i			1.80361i	0.432141	+	0.901806i	$0.357758\pi$
$757$			49.6239i			1.80361i	−0.432141	+	0.901806i	$0.642242\pi$
$758$			8.50321i			0.308851i
$759$			24.0687i			0.873637i
$760$		−	6.75054i		−	0.244868i
$761$	−30.6320			−1.11041			−0.555204	−	0.831714i	$-0.687360\pi$
$761$	−30.6320			−1.11041			−0.555204	+	0.831714i	$0.687360\pi$
$762$			14.7505i			0.534356i
$763$		−	12.5633i		−	0.454822i
$764$			6.93349i			0.250845i
$765$	7.06651			0.255490
$766$	15.1995			0.549182
$767$	79.7714			2.88038
$768$	1.00000			0.0360844
$769$		−	29.1352i		−	1.05064i	−0.850904	−	0.525321i	$-0.823945\pi$
$769$		−	29.1352i		−	1.05064i	0.850904	−	0.525321i	$-0.176055\pi$
$770$	−13.0665			−0.470884
$771$			3.43242i			0.123615i
$772$		−	0.498930i		−	0.0179569i
$773$	46.2516			1.66355			0.831777	−	0.555109i	$-0.187324\pi$
$773$	46.2516			1.66355			0.831777	+	0.555109i	$0.187324\pi$
$774$	−9.81705			−0.352867
$775$		−	0.315979i		−	0.0113503i
$776$	11.5011			0.412864
$777$	−13.5011	−	9.88142i	−0.484348	−	0.354494i
$778$	32.1330			1.15202
$779$			13.5011i			0.483726i
$780$	−6.75054			−0.241708
$781$	−67.1395			−2.40244
$782$			35.8026i			1.28030i
$783$			2.00000i			0.0714742i
$784$	0.565444			0.0201944
$785$			5.81705i			0.207619i
$786$	7.18509			0.256284
$787$	15.8713			0.565749			0.282875	−	0.959157i	$-0.408712\pi$
$787$	15.8713			0.565749			0.282875	+	0.959157i	$0.408712\pi$
$788$	16.7505			0.596713
$789$	6.86911			0.244547
$790$			8.31598i			0.295869i
$791$		−	5.50107i		−	0.195596i
$792$			4.75054i			0.168803i
$793$	−13.5011			−0.479437
$794$			28.8192i			1.02275i
$795$		−	4.75054i		−	0.168484i
$796$			3.31812i			0.117608i
$797$			46.1373i			1.63427i	0.576448	+	0.817134i	$0.304438\pi$
$797$			46.1373i			1.63427i	−0.576448	+	0.817134i	$0.695562\pi$
$798$	−18.5676			−0.657285
$799$			24.7404i			0.875251i
$800$			1.00000i			0.0353553i
$801$			6.25161i			0.220890i
$802$	10.6175			0.374917
$803$	−30.5676			−1.07871
$804$	−15.0021			−0.529085
$805$	13.9356			0.491166
$806$			2.13303i			0.0751327i
$807$	−9.24946			−0.325597
$808$			7.18509i			0.252771i
$809$		−	2.74625i		−	0.0965531i	−0.998834	−	0.0482766i	$-0.984627\pi$
$809$		−	2.74625i		−	0.0965531i	0.998834	−	0.0482766i	$-0.0153729\pi$
$810$	−1.00000			−0.0351364
$811$	−16.5032			−0.579506			−0.289753	−	0.957101i	$-0.593573\pi$
$811$	−16.5032			−0.579506			−0.289753	+	0.957101i	$0.593573\pi$
$812$		−	5.50107i		−	0.193050i
$813$	14.3702			0.503984
$814$	−17.0665	+	23.3181i	−0.598181	+	0.817300i
$815$	−18.2516			−0.639326
$816$			7.06651i			0.247377i
$817$	−66.2703			−2.31851
$818$	−37.6384			−1.31600
$819$			18.5676i			0.648804i
$820$		−	2.00000i		−	0.0698430i
$821$	−39.0166			−1.36169			−0.680844	−	0.732428i	$-0.738387\pi$
$821$	−39.0166			−1.36169			−0.680844	+	0.732428i	$0.738387\pi$
$822$			1.68402i			0.0587370i
$823$	3.14534			0.109640			0.0548198	−	0.998496i	$-0.482542\pi$
$823$	3.14534			0.109640			0.0548198	+	0.998496i	$0.482542\pi$
$824$	−0.631958			−0.0220153
$825$	−4.75054			−0.165392
$826$	−32.5032			−1.13093
$827$		−	14.1330i		−	0.491454i	−0.969339	−	0.245727i	$-0.920973\pi$
$827$		−	14.1330i		−	0.491454i	0.969339	−	0.245727i	$-0.0790266\pi$
$828$		−	5.06651i		−	0.176074i
$829$			4.56758i			0.158639i	0.996849	+	0.0793194i	$0.0252747\pi$
$829$			4.56758i			0.158639i	−0.996849	+	0.0793194i	$0.974725\pi$
$830$	−4.43456			−0.153926
$831$			26.3846i			0.915273i
$832$		−	6.75054i		−	0.234033i
$833$			3.99572i			0.138443i
$834$			23.0021i			0.796499i
$835$	−5.06651			−0.175334
$836$			32.0687i			1.10912i
$837$			0.315979i			0.0109218i
$838$		−	22.0145i		−	0.760477i
$839$	42.3702			1.46278			0.731391	−	0.681959i	$-0.238872\pi$
$839$	42.3702			1.46278			0.731391	+	0.681959i	$0.238872\pi$
$840$	2.75054			0.0949025
$841$	25.0000			0.862069
$842$	−3.26392			−0.112482
$843$			15.7527i			0.542551i
$844$	13.5011			0.464726
$845$			32.5697i			1.12043i
$846$		−	3.50107i		−	0.120369i
$847$	31.8170			1.09325
$848$	4.75054			0.163134
$849$			12.3846i			0.425040i
$850$	−7.06651			−0.242379
$851$	18.2017	−	24.8691i	0.623946	−	0.852502i
$852$	14.1330			0.484190
$853$			20.6175i			0.705930i	0.935637	+	0.352965i	$0.114827\pi$
$853$			20.6175i			0.705930i	−0.935637	+	0.352965i	$0.885173\pi$
$854$	5.50107			0.188243
$855$	−6.75054			−0.230863
$856$		−	12.0687i		−	0.412498i
$857$			3.30367i			0.112851i	0.998407	+	0.0564256i	$0.0179704\pi$
$857$			3.30367i			0.112851i	−0.998407	+	0.0564256i	$0.982030\pi$
$858$	32.0687			1.09481
$859$			41.3868i			1.41210i	0.708163	+	0.706049i	$0.249524\pi$
$859$			41.3868i			1.41210i	−0.708163	+	0.706049i	$0.750476\pi$
$860$	9.81705			0.334759
$861$	−5.50107			−0.187476
$862$	−26.5676			−0.904896
$863$	−46.5032			−1.58299			−0.791494	−	0.611177i	$-0.790696\pi$
$863$	−46.5032			−1.58299			−0.791494	+	0.611177i	$0.790696\pi$
$864$		−	1.00000i		−	0.0340207i
$865$		−	4.11858i		−	0.140036i
$866$		−	8.56758i		−	0.291138i
$867$	−32.9356			−1.11855
$868$		−	0.869112i		−	0.0294996i
$869$		−	39.5054i		−	1.34013i
$870$		−	2.00000i		−	0.0678064i
$871$			101.272i			3.43149i
$872$	4.56758			0.154678
$873$		−	11.5011i		−	0.389252i
$874$		−	34.2017i		−	1.15689i
$875$			2.75054i			0.0929851i
$876$	6.43456			0.217403
$877$	−14.4490			−0.487908			−0.243954	−	0.969787i	$-0.578445\pi$
$877$	−14.4490			−0.487908			−0.243954	+	0.969787i	$0.578445\pi$
$878$	−8.31598			−0.280651
$879$	0.750535			0.0253149
$880$		−	4.75054i		−	0.160141i
$881$	−22.7404			−0.766142			−0.383071	−	0.923719i	$-0.625134\pi$
$881$	−22.7404			−0.766142			−0.383071	+	0.923719i	$0.625134\pi$
$882$		−	0.565444i		−	0.0190395i
$883$		−	47.8900i		−	1.61163i	−0.592170	−	0.805813i	$-0.701729\pi$
$883$		−	47.8900i		−	1.61163i	0.592170	−	0.805813i	$-0.298271\pi$
$884$	47.7028			1.60442
$885$	−11.8170			−0.397226
$886$		−	35.2682i		−	1.18486i
$887$	−40.3991			−1.35647			−0.678234	−	0.734846i	$-0.737255\pi$
$887$	−40.3991			−1.35647			−0.678234	+	0.734846i	$0.737255\pi$
$888$	3.59255	−	4.90852i	0.120558	−	0.164719i
$889$	−40.5719			−1.36074
$890$		−	6.25161i		−	0.209554i
$891$	4.75054			0.159149
$892$	−25.3181			−0.847713
$893$		−	23.6341i		−	0.790885i
$894$			7.81705i			0.261441i
$895$	9.68402			0.323701
$896$			2.75054i			0.0918889i
$897$	−34.2017			−1.14196
$898$	−30.3203			−1.01180
$899$	−0.631958			−0.0210770
$900$	1.00000			0.0333333
$901$			33.5697i			1.11837i
$902$			9.50107i			0.316351i
$903$		−	27.0021i		−	0.898575i
$904$	2.00000			0.0665190
$905$		−	10.6320i		−	0.353418i
$906$		−	16.4346i		−	0.546002i
$907$			42.5177i			1.41178i	0.708324	+	0.705888i	$0.249452\pi$
$907$			42.5177i			1.41178i	−0.708324	+	0.705888i	$0.750548\pi$
$908$		−	4.63196i		−	0.153717i
$909$	7.18509			0.238314
$910$		−	18.5676i		−	0.615509i
$911$		−	24.0000i		−	0.795155i	−0.917568	−	0.397578i	$-0.869851\pi$
$911$		−	24.0000i		−	0.795155i	0.917568	−	0.397578i	$-0.130149\pi$
$912$		−	6.75054i		−	0.223533i
$913$	21.0665			0.697200
$914$	−10.6320			−0.351674
$915$	2.00000			0.0661180
$916$	−20.1330			−0.665214
$917$			19.7628i			0.652627i
$918$	7.06651			0.233230
$919$			43.8213i			1.44553i	0.691093	+	0.722766i	$0.257130\pi$
$919$			43.8213i			1.44553i	−0.691093	+	0.722766i	$0.742870\pi$
$920$			5.06651i			0.167038i
$921$	18.3702			0.605318
$922$	−30.5032			−1.00457
$923$		−	95.4055i		−	3.14031i
$924$	−13.0665			−0.429857
$925$	4.90852	+	3.59255i	0.161391	+	0.118122i
$926$	−39.5054			−1.29823
$927$			0.631958i			0.0207562i
$928$	2.00000			0.0656532
$929$	7.86697			0.258107			0.129053	−	0.991638i	$-0.458806\pi$
$929$	7.86697			0.258107			0.129053	+	0.991638i	$0.458806\pi$
$930$		−	0.315979i		−	0.0103614i
$931$		−	3.81705i		−	0.125099i
$932$	6.31598			0.206887
$933$			35.0021i			1.14592i
$934$	−16.6320			−0.544214
$935$	33.5697			1.09785
$936$	−6.75054			−0.220648
$937$	−53.0021			−1.73150			−0.865752	−	0.500473i	$-0.833160\pi$
$937$	−53.0021			−1.73150			−0.865752	+	0.500473i	$0.833160\pi$
$938$		−	41.2639i		−	1.34731i
$939$			1.36804i			0.0446443i
$940$			3.50107i			0.114192i
$941$	44.5574			1.45253			0.726265	−	0.687415i	$-0.241254\pi$
$941$	44.5574			1.45253			0.726265	+	0.687415i	$0.241254\pi$
$942$			5.81705i			0.189530i
$943$		−	10.1330i		−	0.329977i
$944$		−	11.8170i		−	0.384612i
$945$		−	2.75054i		−	0.0894749i
$946$	−46.6362			−1.51627
$947$			46.0043i			1.49494i	0.664297	+	0.747469i	$0.268731\pi$
$947$			46.0043i			1.49494i	−0.664297	+	0.747469i	$0.731269\pi$
$948$			8.31598i			0.270090i
$949$		−	43.4367i		−	1.41001i
$950$	6.75054			0.219016
$951$	10.0542			0.326030
$952$	−19.4367			−0.629947
$953$	48.9522			1.58572			0.792859	−	0.609405i	$-0.208592\pi$
$953$	48.9522			1.58572			0.792859	+	0.609405i	$0.208592\pi$
$954$		−	4.75054i		−	0.153804i
$955$	−6.93349			−0.224362
$956$			12.6320i			0.408547i
$957$			9.50107i			0.307126i
$958$	33.2038			1.07277
$959$	−4.63196			−0.149574
$960$			1.00000i			0.0322749i
$961$	30.9002			0.996779
$962$	−33.1352	−	24.2516i	−1.06832	−	0.781903i
$963$	−12.0687			−0.388907
$964$			16.6320i			0.535679i
$965$	0.498930			0.0160611
$966$	13.9356			0.448371
$967$			23.2682i			0.748255i	0.927377	+	0.374127i	$0.122058\pi$
$967$			23.2682i			0.748255i	−0.927377	+	0.374127i	$0.877942\pi$
$968$			11.5676i			0.371796i
$969$	47.7028			1.53243
$970$			11.5011i			0.369277i
$971$	−57.8170			−1.85544			−0.927719	−	0.373280i	$-0.878233\pi$
$971$	−57.8170			−1.85544			−0.927719	+	0.373280i	$0.878233\pi$
$972$	−1.00000			−0.0320750
$973$	−63.2682			−2.02829
$974$	11.6341			0.372781
$975$		−	6.75054i		−	0.216190i
$976$			2.00000i			0.0640184i
$977$		−	27.4324i		−	0.877641i	−0.898575	−	0.438820i	$-0.855396\pi$
$977$		−	27.4324i		−	0.877641i	0.898575	−	0.438820i	$-0.144604\pi$
$978$	−18.2516			−0.583622
$979$			29.6985i			0.949167i
$980$			0.565444i			0.0180624i
$981$		−	4.56758i		−	0.145832i
$982$			4.75054i			0.151596i
$983$	23.7671			0.758054			0.379027	−	0.925386i	$-0.376259\pi$
$983$	23.7671			0.758054			0.379027	+	0.925386i	$0.376259\pi$
$984$		−	2.00000i		−	0.0637577i
$985$			16.7505i			0.533716i
$986$			14.1330i			0.450087i
$987$	9.62982			0.306520
$988$	−45.5697			−1.44977
$989$	49.7382			1.58158
$990$	−4.75054			−0.150982
$991$		−	27.5842i		−	0.876240i	−0.898916	−	0.438120i	$-0.855644\pi$
$991$		−	27.5842i		−	0.876240i	0.898916	−	0.438120i	$-0.144356\pi$
$992$	0.315979			0.0100324
$993$			26.3160i			0.835112i
$994$			38.8734i			1.23299i
$995$	−3.31812			−0.105191
$996$	−4.43456			−0.140514
$997$			43.6196i			1.38145i	0.723118	+	0.690724i	$0.242708\pi$
$997$			43.6196i			1.38145i	−0.723118	+	0.690724i	$0.757292\pi$
$998$	−9.12072			−0.288711
$999$	−4.90852	−	3.59255i	−0.155299	−	0.113663i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.h.f.961.3	✓	6
3.2	odd	2		3330.2.h.m.2071.6		6
37.36	even	2	inner	1110.2.h.f.961.6	yes	6
111.110	odd	2		3330.2.h.m.2071.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.h.f.961.3	✓	6	1.1	even	1	trivial
1110.2.h.f.961.6	yes	6	37.36	even	2	inner
3330.2.h.m.2071.3		6	111.110	odd	2
3330.2.h.m.2071.6		6	3.2	odd	2

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} -1.00000i q^{6} +2.75054 q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} -1.00000i q^{6} +2.75054 q^{7} +1.00000i q^{8} +1.00000 q^{9} -1.00000 q^{10} +4.75054 q^{11} -1.00000 q^{12} +6.75054i q^{13} -2.75054i q^{14} -1.00000i q^{15} +1.00000 q^{16} +7.06651i q^{17} -1.00000i q^{18} -6.75054i q^{19} +1.00000i q^{20} +2.75054 q^{21} -4.75054i q^{22} +5.06651i q^{23} +1.00000i q^{24} -1.00000 q^{25} +6.75054 q^{26} +1.00000 q^{27} -2.75054 q^{28} +2.00000i q^{29} -1.00000 q^{30} +0.315979i q^{31} -1.00000i q^{32} +4.75054 q^{33} +7.06651 q^{34} -2.75054i q^{35} -1.00000 q^{36} +(-4.90852 - 3.59255i) q^{37} -6.75054 q^{38} +6.75054i q^{39} +1.00000 q^{40} -2.00000 q^{41} -2.75054i q^{42} -9.81705i q^{43} -4.75054 q^{44} -1.00000i q^{45} +5.06651 q^{46} +3.50107 q^{47} +1.00000 q^{48} +0.565444 q^{49} +1.00000i q^{50} +7.06651i q^{51} -6.75054i q^{52} +4.75054 q^{53} -1.00000i q^{54} -4.75054i q^{55} +2.75054i q^{56} -6.75054i q^{57} +2.00000 q^{58} -11.8170i q^{59} +1.00000i q^{60} +2.00000i q^{61} +0.315979 q^{62} +2.75054 q^{63} -1.00000 q^{64} +6.75054 q^{65} -4.75054i q^{66} +15.0021 q^{67} -7.06651i q^{68} +5.06651i q^{69} -2.75054 q^{70} -14.1330 q^{71} +1.00000i q^{72} -6.43456 q^{73} +(-3.59255 + 4.90852i) q^{74} -1.00000 q^{75} +6.75054i q^{76} +13.0665 q^{77} +6.75054 q^{78} -8.31598i q^{79} -1.00000i q^{80} +1.00000 q^{81} +2.00000i q^{82} +4.43456 q^{83} -2.75054 q^{84} +7.06651 q^{85} -9.81705 q^{86} +2.00000i q^{87} +4.75054i q^{88} +6.25161i q^{89} -1.00000 q^{90} +18.5676i q^{91} -5.06651i q^{92} +0.315979i q^{93} -3.50107i q^{94} -6.75054 q^{95} -1.00000i q^{96} -11.5011i q^{97} -0.565444i q^{98} +4.75054 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{3} - 6 q^{4} - 6 q^{7} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^3 - 6 * q^4 - 6 * q^7 + 6 * q^9	\( 6 q + 6 q^{3} - 6 q^{4} - 6 q^{7} + 6 q^{9} - 6 q^{10} + 6 q^{11} - 6 q^{12} + 6 q^{16} - 6 q^{21} - 6 q^{25} + 18 q^{26} + 6 q^{27} + 6 q^{28} - 6 q^{30} + 6 q^{33} + 10 q^{34} - 6 q^{36} - 2 q^{37} - 18 q^{38} + 6 q^{40} - 12 q^{41} - 6 q^{44} - 2 q^{46} - 24 q^{47} + 6 q^{48} + 16 q^{49} + 6 q^{53} + 12 q^{58} - 8 q^{62} - 6 q^{63} - 6 q^{64} + 18 q^{65} + 6 q^{70} - 20 q^{71} - 26 q^{73} - 4 q^{74} - 6 q^{75} + 46 q^{77} + 18 q^{78} + 6 q^{81} + 14 q^{83} + 6 q^{84} + 10 q^{85} - 4 q^{86} - 6 q^{90} - 18 q^{95} + 6 q^{99}+O(q^{100}) \) 6 * q + 6 * q^3 - 6 * q^4 - 6 * q^7 + 6 * q^9 - 6 * q^10 + 6 * q^11 - 6 * q^12 + 6 * q^16 - 6 * q^21 - 6 * q^25 + 18 * q^26 + 6 * q^27 + 6 * q^28 - 6 * q^30 + 6 * q^33 + 10 * q^34 - 6 * q^36 - 2 * q^37 - 18 * q^38 + 6 * q^40 - 12 * q^41 - 6 * q^44 - 2 * q^46 - 24 * q^47 + 6 * q^48 + 16 * q^49 + 6 * q^53 + 12 * q^58 - 8 * q^62 - 6 * q^63 - 6 * q^64 + 18 * q^65 + 6 * q^70 - 20 * q^71 - 26 * q^73 - 4 * q^74 - 6 * q^75 + 46 * q^77 + 18 * q^78 + 6 * q^81 + 14 * q^83 + 6 * q^84 + 10 * q^85 - 4 * q^86 - 6 * q^90 - 18 * q^95 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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