LMFDB - Embedded newform 760.2.q.f.121.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [760,2,Mod(121,760)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(760, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("760.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 760 = 2^{3} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	760.q (of order $3$, degree $2$, 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:	$6.06863055362$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.4601315889.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 3x^{5} + 26x^{4} - 14x^{3} + 31x^{2} + 12x + 9 $ x^8 - x^7 + 6x^6 - 3x^5 + 26x^4 - 14x^3 + 31x^2 + 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.4
Root			$-0.245959 - 0.426014i$ of defining polynomial
Character	$\chi$	$=$	760.121
Dual form			760.2.q.f.201.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37901 + 2.38851i) q^{3} +(-0.500000 - 0.866025i) q^{5} +4.11474 q^{7} +(-2.30333 + 3.98948i) q^{9} +O(q^{10})$	\(q+(1.37901 + 2.38851i) q^{3} +(-0.500000 - 0.866025i) q^{5} +4.11474 q^{7} +(-2.30333 + 3.98948i) q^{9} -6.09857 q^{11} +(-1.17028 + 2.02698i) q^{13} +(1.37901 - 2.38851i) q^{15} +(3.80333 + 6.58756i) q^{17} +(1.46155 + 4.10657i) q^{19} +(5.67425 + 9.82810i) q^{21} +(2.98977 - 5.17843i) q^{23} +(-0.500000 + 0.866025i) q^{25} -4.43118 q^{27} +(-0.969629 + 1.67945i) q^{29} -1.43118 q^{31} +(-8.40998 - 14.5665i) q^{33} +(-2.05737 - 3.56347i) q^{35} +8.91733 q^{37} -6.45529 q^{39} +(-1.70065 - 2.94561i) q^{41} +(0.655338 + 1.13508i) q^{43} +4.60665 q^{45} +(-0.192567 + 0.333536i) q^{47} +9.93105 q^{49} +(-10.4896 + 18.1686i) q^{51} +(-0.597970 + 1.03572i) q^{53} +(3.04929 + 5.28152i) q^{55} +(-7.79309 + 9.15391i) q^{57} +(-5.48566 - 9.50145i) q^{59} +(-0.0825396 + 0.142963i) q^{61} +(-9.47758 + 16.4157i) q^{63} +2.34056 q^{65} +(0.848637 - 1.46988i) q^{67} +16.4917 q^{69} +(-4.75679 - 8.23901i) q^{71} +(-5.97360 - 10.3466i) q^{73} -2.75802 q^{75} -25.0940 q^{77} +(3.87563 + 6.71280i) q^{79} +(0.799351 + 1.38452i) q^{81} -3.25570 q^{83} +(3.80333 - 6.58756i) q^{85} -5.34851 q^{87} +(9.26077 - 16.0401i) q^{89} +(-4.81538 + 8.34049i) q^{91} +(-1.97360 - 3.41838i) q^{93} +(2.82562 - 3.31902i) q^{95} +(0.203531 + 0.352527i) q^{97} +(14.0470 - 24.3301i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{3} - 4 q^{5} + 4 q^{7} - q^{9}+O(q^{10}) $ 8 * q + q^3 - 4 * q^5 + 4 * q^7 - q^9	$ 8 q + q^{3} - 4 q^{5} + 4 q^{7} - q^{9} - 8 q^{11} + q^{13} + q^{15} + 13 q^{17} + q^{19} + 12 q^{21} + 8 q^{23} - 4 q^{25} - 20 q^{27} - 3 q^{29} + 4 q^{31} - 15 q^{33} - 2 q^{35} + 20 q^{37} - 2 q^{39} - 8 q^{41} - 3 q^{43} + 2 q^{45} + 10 q^{47} + 12 q^{49} - 16 q^{51} - 11 q^{53} + 4 q^{55} - 29 q^{57} + q^{59} - 25 q^{63} - 2 q^{65} - 8 q^{67} + 22 q^{69} - 4 q^{71} - 20 q^{73} - 2 q^{75} - 36 q^{77} - 3 q^{79} + 12 q^{81} - 30 q^{83} + 13 q^{85} + 24 q^{87} + 17 q^{89} - 4 q^{91} + 12 q^{93} + 4 q^{95} + 11 q^{97} + 30 q^{99}+O(q^{100}) $ 8 * q + q^3 - 4 * q^5 + 4 * q^7 - q^9 - 8 * q^11 + q^13 + q^15 + 13 * q^17 + q^19 + 12 * q^21 + 8 * q^23 - 4 * q^25 - 20 * q^27 - 3 * q^29 + 4 * q^31 - 15 * q^33 - 2 * q^35 + 20 * q^37 - 2 * q^39 - 8 * q^41 - 3 * q^43 + 2 * q^45 + 10 * q^47 + 12 * q^49 - 16 * q^51 - 11 * q^53 + 4 * q^55 - 29 * q^57 + q^59 - 25 * q^63 - 2 * q^65 - 8 * q^67 + 22 * q^69 - 4 * q^71 - 20 * q^73 - 2 * q^75 - 36 * q^77 - 3 * q^79 + 12 * q^81 - 30 * q^83 + 13 * q^85 + 24 * q^87 + 17 * q^89 - 4 * q^91 + 12 * q^93 + 4 * q^95 + 11 * q^97 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/760\mathbb{Z}\right)^\times$.

$n$	$191$	$381$	$401$	$457$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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			0
$2$		0			0
$3$	1.37901	+	2.38851i	0.796171	+	1.37901i	0.922093	+	0.386968i	$0.126478\pi$
$3$	1.37901	+	2.38851i	0.796171	+	1.37901i	−0.125922	+	0.992040i	$0.540189\pi$
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	4.11474			1.55522			0.777612	−	0.628745i	$-0.216431\pi$
$7$	4.11474			1.55522			0.777612	+	0.628745i	$0.216431\pi$
$8$		0			0
$9$	−2.30333	+	3.98948i	−0.767776	+	1.32983i
$10$		0			0
$11$	−6.09857			−1.83879			−0.919394	−	0.393337i	$-0.871321\pi$
$11$	−6.09857			−1.83879			−0.919394	+	0.393337i	$0.871321\pi$
$12$		0			0
$13$	−1.17028	+	2.02698i	−0.324577	+	0.562183i	−0.981427	−	0.191838i	$-0.938555\pi$
$13$	−1.17028	+	2.02698i	−0.324577	+	0.562183i	0.656850	+	0.754021i	$0.271889\pi$
$14$		0			0
$15$	1.37901	−	2.38851i	0.356058	−	0.616711i
$16$		0			0
$17$	3.80333	+	6.58756i	0.922442	+	1.59772i	0.795624	+	0.605791i	$0.207143\pi$
$17$	3.80333	+	6.58756i	0.922442	+	1.59772i	0.126818	+	0.991926i	$0.459523\pi$
$18$		0			0
$19$	1.46155	+	4.10657i	0.335302	+	0.942111i
$19$	1.46155	+	4.10657i	0.335302	+	0.942111i
$20$		0			0
$21$	5.67425	+	9.82810i	1.23822	+	2.14467i
$22$		0			0
$23$	2.98977	−	5.17843i	0.623410	−	1.07978i	−0.365436	−	0.930836i	$-0.619080\pi$
$23$	2.98977	−	5.17843i	0.623410	−	1.07978i	0.988846	−	0.148941i	$-0.0475864\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−4.43118			−0.852780
$28$		0			0
$29$	−0.969629	+	1.67945i	−0.180056	+	0.311866i	−0.941899	−	0.335895i	$-0.890961\pi$
$29$	−0.969629	+	1.67945i	−0.180056	+	0.311866i	0.761844	+	0.647761i	$0.224294\pi$
$30$		0			0
$31$	−1.43118			−0.257047			−0.128523	−	0.991706i	$-0.541024\pi$
$31$	−1.43118			−0.257047			−0.128523	+	0.991706i	$0.541024\pi$
$32$		0			0
$33$	−8.40998	−	14.5665i	−1.46399	−	2.53570i
$34$		0			0
$35$	−2.05737	−	3.56347i	−0.347759	−	0.602336i
$36$		0			0
$37$	8.91733			1.46600			0.733000	−	0.680229i	$-0.238120\pi$
$37$	8.91733			1.46600			0.733000	+	0.680229i	$0.238120\pi$
$38$		0			0
$39$	−6.45529			−1.03367
$40$		0			0
$41$	−1.70065	−	2.94561i	−0.265597	−	0.460027i	0.702123	−	0.712056i	$-0.252236\pi$
$41$	−1.70065	−	2.94561i	−0.265597	−	0.460027i	−0.967720	+	0.252029i	$0.918902\pi$
$42$		0			0
$43$	0.655338	+	1.13508i	0.0999381	+	0.173098i	0.911659	−	0.410948i	$-0.134802\pi$
$43$	0.655338	+	1.13508i	0.0999381	+	0.173098i	−0.811721	+	0.584046i	$0.801469\pi$
$44$		0			0
$45$	4.60665			0.686719
$46$		0			0
$47$	−0.192567	+	0.333536i	−0.0280888	+	0.0486512i	−0.879728	−	0.475477i	$-0.842275\pi$
$47$	−0.192567	+	0.333536i	−0.0280888	+	0.0486512i	0.851639	+	0.524128i	$0.175609\pi$
$48$		0			0
$49$	9.93105			1.41872
$50$		0			0
$51$	−10.4896	+	18.1686i	−1.46884	+	2.54411i
$52$		0			0
$53$	−0.597970	+	1.03572i	−0.0821376	+	0.142266i	−0.904168	−	0.427177i	$-0.859508\pi$
$53$	−0.597970	+	1.03572i	−0.0821376	+	0.142266i	0.822030	+	0.569444i	$0.192841\pi$
$54$		0			0
$55$	3.04929	+	5.28152i	0.411166	+	0.712160i
$56$		0			0
$57$	−7.79309	+	9.15391i	−1.03222	+	1.21247i
$58$		0			0
$59$	−5.48566	−	9.50145i	−0.714172	−	1.23698i	−0.963278	−	0.268506i	$-0.913470\pi$
$59$	−5.48566	−	9.50145i	−0.714172	−	1.23698i	0.249106	−	0.968476i	$-0.419863\pi$
$60$		0			0
$61$	−0.0825396	+	0.142963i	−0.0105681	+	0.0183045i	−0.871261	−	0.490820i	$-0.836697\pi$
$61$	−0.0825396	+	0.142963i	−0.0105681	+	0.0183045i	0.860693	+	0.509124i	$0.170031\pi$
$62$		0			0
$63$	−9.47758	+	16.4157i	−1.19406	+	2.06818i
$64$		0			0
$65$	2.34056			0.290310
$66$		0			0
$67$	0.848637	−	1.46988i	0.103678	−	0.179575i	−0.809520	−	0.587093i	$-0.800272\pi$
$67$	0.848637	−	1.46988i	0.103678	−	0.179575i	0.913197	+	0.407518i	$0.133606\pi$
$68$		0			0
$69$	16.4917			1.98536
$70$		0			0
$71$	−4.75679	−	8.23901i	−0.564527	−	0.977790i	−0.997093	−	0.0761880i	$-0.975725\pi$
$71$	−4.75679	−	8.23901i	−0.564527	−	0.977790i	0.432566	−	0.901602i	$-0.357608\pi$
$72$		0			0
$73$	−5.97360	−	10.3466i	−0.699158	−	1.21098i	−0.968759	−	0.248004i	$-0.920225\pi$
$73$	−5.97360	−	10.3466i	−0.699158	−	1.21098i	0.269601	−	0.962972i	$-0.413108\pi$
$74$		0			0
$75$	−2.75802			−0.318468
$76$		0			0
$77$	−25.0940			−2.85973
$78$		0			0
$79$	3.87563	+	6.71280i	0.436043	+	0.755249i	0.997380	−	0.0723387i	$-0.0230462\pi$
$79$	3.87563	+	6.71280i	0.436043	+	0.755249i	−0.561337	+	0.827587i	$0.689713\pi$
$80$		0			0
$81$	0.799351	+	1.38452i	0.0888168	+	0.153835i
$82$		0			0
$83$	−3.25570			−0.357360			−0.178680	−	0.983907i	$-0.557183\pi$
$83$	−3.25570			−0.357360			−0.178680	+	0.983907i	$0.557183\pi$
$84$		0			0
$85$	3.80333	−	6.58756i	0.412529	−	0.714521i
$86$		0			0
$87$	−5.34851			−0.573420
$88$		0			0
$89$	9.26077	−	16.0401i	0.981639	−	1.70025i	0.325629	−	0.945498i	$-0.394424\pi$
$89$	9.26077	−	16.0401i	0.981639	−	1.70025i	0.656010	−	0.754752i	$-0.272243\pi$
$90$		0			0
$91$	−4.81538	+	8.34049i	−0.504789	+	0.874321i
$92$		0			0
$93$	−1.97360	−	3.41838i	−0.204653	−	0.354470i
$94$		0			0
$95$	2.82562	−	3.31902i	0.289902	−	0.340524i
$96$		0			0
$97$	0.203531	+	0.352527i	0.0206655	+	0.0357937i	0.876173	−	0.481996i	$-0.160088\pi$
$97$	0.203531	+	0.352527i	0.0206655	+	0.0357937i	−0.855508	+	0.517790i	$0.826755\pi$
$98$		0			0
$99$	14.0470	−	24.3301i	1.41178	−	2.44527i
$100$		0			0
$101$	−1.02626	+	1.77754i	−0.102117	+	0.176872i	−0.912557	−	0.408950i	$-0.865895\pi$
$101$	−1.02626	+	1.77754i	−0.102117	+	0.176872i	0.810440	+	0.585822i	$0.199228\pi$
$102$		0			0
$103$	−0.0204641			−0.00201639			−0.00100820	−	0.999999i	$-0.500321\pi$
$103$	−0.0204641			−0.00201639			−0.00100820	+	0.999999i	$0.500321\pi$
$104$		0			0
$105$	5.67425	−	9.82810i	0.553750	−	0.959124i
$106$		0			0
$107$	0.463503			0.0448086			0.0224043	−	0.999749i	$-0.492868\pi$
$107$	0.463503			0.0448086			0.0224043	+	0.999749i	$0.492868\pi$
$108$		0			0
$109$	−7.36589	−	12.7581i	−0.705525	−	1.22200i	−0.966502	−	0.256660i	$-0.917378\pi$
$109$	−7.36589	−	12.7581i	−0.705525	−	1.22200i	0.260977	−	0.965345i	$-0.415955\pi$
$110$		0			0
$111$	12.2971	+	21.2992i	1.16719	+	2.02163i
$112$		0			0
$113$	8.36613			0.787020			0.393510	−	0.919320i	$-0.371261\pi$
$113$	8.36613			0.787020			0.393510	+	0.919320i	$0.371261\pi$
$114$		0			0
$115$	−5.97954			−0.557595
$116$		0			0
$117$	−5.39107	−	9.33760i	−0.498404	−	0.863261i
$118$		0			0
$119$	15.6497	+	27.1060i	1.43460	+	2.48481i
$120$		0			0
$121$	26.1926			2.38114
$122$		0			0
$123$	4.69042	−	8.12404i	0.422921	−	0.732520i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	9.23377	−	15.9934i	0.819365	−	1.41918i	−0.0867862	−	0.996227i	$-0.527660\pi$
$127$	9.23377	−	15.9934i	0.819365	−	1.41918i	0.906151	−	0.422954i	$-0.139007\pi$
$128$		0			0
$129$	−1.80743	+	3.13057i	−0.159136	+	0.275631i
$130$		0			0
$131$	−8.13978	−	14.0985i	−0.711176	−	1.23179i	−0.964416	−	0.264389i	$-0.914830\pi$
$131$	−8.13978	−	14.0985i	−0.711176	−	1.23179i	0.253241	−	0.967403i	$-0.418504\pi$
$132$		0			0
$133$	6.01388	+	16.8974i	0.521470	+	1.46519i
$134$		0			0
$135$	2.21559	+	3.83751i	0.190687	+	0.330280i
$136$		0			0
$137$	−2.02822	+	3.51298i	−0.173283	+	0.300134i	−0.939566	−	0.342369i	$-0.888771\pi$
$137$	−2.02822	+	3.51298i	−0.173283	+	0.300134i	0.766283	+	0.642503i	$0.222104\pi$
$138$		0			0
$139$	5.42021	−	9.38808i	0.459736	−	0.796287i	−0.539210	−	0.842171i	$-0.681277\pi$
$139$	5.42021	−	9.38808i	0.459736	−	0.796287i	0.998947	+	0.0458843i	$0.0146105\pi$
$140$		0			0
$141$	−1.06221			−0.0894539
$142$		0			0
$143$	7.13702	−	12.3617i	0.596828	−	1.03374i
$144$		0			0
$145$	1.93926			0.161047
$146$		0			0
$147$	13.6950	+	23.7204i	1.12954	+	1.95643i
$148$		0			0
$149$	11.4721	+	19.8702i	0.939827	+	1.62783i	0.765791	+	0.643090i	$0.222348\pi$
$149$	11.4721	+	19.8702i	0.939827	+	1.62783i	0.174037	+	0.984739i	$0.444319\pi$
$150$		0			0
$151$	−16.3025			−1.32668			−0.663338	−	0.748320i	$-0.730861\pi$
$151$	−16.3025			−1.32668			−0.663338	+	0.748320i	$0.730861\pi$
$152$		0			0
$153$	−35.0412			−2.83291
$154$		0			0
$155$	0.715589	+	1.23944i	0.0574775	+	0.0995539i
$156$		0			0
$157$	4.46890	+	7.74036i	0.356657	+	0.617748i	0.987400	−	0.158244i	$-0.0505832\pi$
$157$	4.46890	+	7.74036i	0.356657	+	0.617748i	−0.630743	+	0.775992i	$0.717250\pi$
$158$		0			0
$159$	−3.29842			−0.261582
$160$		0			0
$161$	12.3021	−	21.3079i	0.969542	−	1.67930i
$162$		0			0
$163$	−5.65488			−0.442925			−0.221462	−	0.975169i	$-0.571083\pi$
$163$	−5.65488			−0.442925			−0.221462	+	0.975169i	$0.571083\pi$
$164$		0			0
$165$	−8.40998	+	14.5665i	−0.654716	+	1.13400i
$166$		0			0
$167$	−6.63414	+	11.4907i	−0.513365	+	0.889175i	0.486515	+	0.873672i	$0.338268\pi$
$167$	−6.63414	+	11.4907i	−0.513365	+	0.889175i	−0.999880	+	0.0155023i	$0.995065\pi$
$168$		0			0
$169$	3.76090	+	6.51407i	0.289300	+	0.501082i
$170$		0			0
$171$	−19.7495	−	3.62795i	−1.51028	−	0.277436i
$172$		0			0
$173$	0.642354	+	1.11259i	0.0488373	+	0.0845886i	0.889411	−	0.457109i	$-0.151115\pi$
$173$	0.642354	+	1.11259i	0.0488373	+	0.0845886i	−0.840573	+	0.541698i	$0.817782\pi$
$174$		0			0
$175$	−2.05737	+	3.56347i	−0.155522	+	0.269373i
$176$		0			0
$177$	15.1295	−	26.2051i	1.13721	−	1.96970i
$178$		0			0
$179$	4.27160			0.319275			0.159637	−	0.987176i	$-0.448968\pi$
$179$	4.27160			0.319275			0.159637	+	0.987176i	$0.448968\pi$
$180$		0			0
$181$	0.869999	−	1.50688i	0.0646665	−	0.112006i	−0.831879	−	0.554956i	$-0.812735\pi$
$181$	0.869999	−	1.50688i	0.0646665	−	0.112006i	0.896546	+	0.442951i	$0.146068\pi$
$182$		0			0
$183$	−0.455291			−0.0336561
$184$		0			0
$185$	−4.45866	−	7.72263i	−0.327808	−	0.567779i
$186$		0			0
$187$	−23.1949	−	40.1747i	−1.69618	−	2.93786i
$188$		0			0
$189$	−18.2331			−1.32626
$190$		0			0
$191$	22.4806			1.62664			0.813320	−	0.581817i	$-0.197658\pi$
$191$	22.4806			1.62664			0.813320	+	0.581817i	$0.197658\pi$
$192$		0			0
$193$	4.08559	+	7.07645i	0.294087	+	0.509374i	0.974772	−	0.223202i	$-0.0716511\pi$
$193$	4.08559	+	7.07645i	0.294087	+	0.509374i	−0.680685	+	0.732576i	$0.738318\pi$
$194$		0			0
$195$	3.22765	+	5.59045i	0.231137	+	0.400340i
$196$		0			0
$197$	14.6952			1.04699			0.523493	−	0.852030i	$-0.324628\pi$
$197$	14.6952			1.04699			0.523493	+	0.852030i	$0.324628\pi$
$198$		0			0
$199$	7.80137	−	13.5124i	0.553025	−	0.957867i	−0.445030	−	0.895516i	$-0.646807\pi$
$199$	7.80137	−	13.5124i	0.553025	−	0.957867i	0.998054	−	0.0623508i	$-0.0198598\pi$
$200$		0			0
$201$	4.68111			0.330180
$202$		0			0
$203$	−3.98977	+	6.91048i	−0.280027	+	0.485021i
$204$		0			0
$205$	−1.70065	+	2.94561i	−0.118778	+	0.205730i
$206$		0			0
$207$	13.7728	+	23.8552i	0.957278	+	1.65805i
$208$		0			0
$209$	−8.91335	−	25.0442i	−0.616550	−	1.73234i
$210$		0			0
$211$	−7.14968	−	12.3836i	−0.492204	−	0.852523i	0.507755	−	0.861501i	$-0.330475\pi$
$211$	−7.14968	−	12.3836i	−0.492204	−	0.852523i	−0.999960	+	0.00897821i	$0.997142\pi$
$212$		0			0
$213$	13.1193	−	22.7233i	0.898920	−	1.55698i
$214$		0			0
$215$	0.655338	−	1.13508i	0.0446937	−	0.0774117i
$216$		0			0
$217$	−5.88891			−0.399766
$218$		0			0
$219$	16.4753	−	28.5361i	1.11330	−	1.92829i
$220$		0			0
$221$	−17.8038			−1.19761
$222$		0			0
$223$	−0.145237	−	0.251557i	−0.00972576	−	0.0168455i	0.861122	−	0.508399i	$-0.169763\pi$
$223$	−0.145237	−	0.251557i	−0.00972576	−	0.0168455i	−0.870847	+	0.491554i	$0.836429\pi$
$224$		0			0
$225$	−2.30333	−	3.98948i	−0.153555	−	0.265965i
$226$		0			0
$227$	−22.6811			−1.50540			−0.752699	−	0.658365i	$-0.771248\pi$
$227$	−22.6811			−1.50540			−0.752699	+	0.658365i	$0.771248\pi$
$228$		0			0
$229$	7.08241			0.468019			0.234009	−	0.972234i	$-0.424815\pi$
$229$	7.08241			0.468019			0.234009	+	0.972234i	$0.424815\pi$
$230$		0			0
$231$	−34.6048	−	59.9373i	−2.27683	−	3.94359i
$232$		0			0
$233$	4.98884	+	8.64093i	0.326830	+	0.566086i	0.981881	−	0.189499i	$-0.0606863\pi$
$233$	4.98884	+	8.64093i	0.326830	+	0.566086i	−0.655051	+	0.755585i	$0.727353\pi$
$234$		0			0
$235$	0.385134			0.0251234
$236$		0			0
$237$	−10.6891	+	18.5140i	−0.694329	+	1.20261i
$238$		0			0
$239$	−28.3785			−1.83565			−0.917825	−	0.396986i	$-0.870056\pi$
$239$	−28.3785			−1.83565			−0.917825	+	0.396986i	$0.870056\pi$
$240$		0			0
$241$	−2.87994	+	4.98819i	−0.185513	+	0.321318i	−0.943749	−	0.330662i	$-0.892728\pi$
$241$	−2.87994	+	4.98819i	−0.185513	+	0.321318i	0.758236	+	0.651980i	$0.226061\pi$
$242$		0			0
$243$	−8.85139	+	15.3311i	−0.567817	+	0.983488i
$244$		0			0
$245$	−4.96552	−	8.60054i	−0.317236	−	0.549468i
$246$		0			0
$247$	−10.0343	−	1.84329i	−0.638470	−	0.117286i
$248$		0			0
$249$	−4.48964	−	7.77628i	−0.284519	−	0.492802i
$250$		0			0
$251$	3.29127	−	5.70065i	0.207743	−	0.359822i	−0.743260	−	0.669003i	$-0.766722\pi$
$251$	3.29127	−	5.70065i	0.207743	−	0.359822i	0.951003	+	0.309181i	$0.100055\pi$
$252$		0			0
$253$	−18.2333	+	31.5810i	−1.14632	+	1.98548i
$254$		0			0
$255$	20.9793			1.31377
$256$		0			0
$257$	11.4694	−	19.8655i	0.715440	−	1.23918i	−0.247350	−	0.968926i	$-0.579560\pi$
$257$	11.4694	−	19.8655i	0.715440	−	1.23918i	0.962790	−	0.270251i	$-0.0871068\pi$
$258$		0			0
$259$	36.6925			2.27996
$260$		0			0
$261$	−4.46675	−	7.73663i	−0.276485	−	0.478885i
$262$		0			0
$263$	3.04458	+	5.27336i	0.187737	+	0.325170i	0.944495	−	0.328525i	$-0.106551\pi$
$263$	3.04458	+	5.27336i	0.187737	+	0.325170i	−0.756759	+	0.653694i	$0.773218\pi$
$264$		0			0
$265$	1.19594			0.0734661
$266$		0			0
$267$	51.0827			3.12621
$268$		0			0
$269$	−3.06208	−	5.30367i	−0.186698	−	0.323370i	0.757449	−	0.652894i	$-0.226445\pi$
$269$	−3.06208	−	5.30367i	−0.186698	−	0.323370i	−0.944147	+	0.329523i	$0.893112\pi$
$270$		0			0
$271$	4.74920	+	8.22586i	0.288493	+	0.499685i	0.973450	−	0.228898i	$-0.0735123\pi$
$271$	4.74920	+	8.22586i	0.288493	+	0.499685i	−0.684957	+	0.728584i	$0.740179\pi$
$272$		0			0
$273$	−26.5618			−1.60759
$274$		0			0
$275$	3.04929	−	5.28152i	0.183879	−	0.318488i
$276$		0			0
$277$	−8.79770			−0.528603			−0.264301	−	0.964440i	$-0.585141\pi$
$277$	−8.79770			−0.528603			−0.264301	+	0.964440i	$0.585141\pi$
$278$		0			0
$279$	3.29647	−	5.70965i	0.197354	−	0.341828i
$280$		0			0
$281$	−12.9565	+	22.4413i	−0.772921	+	1.33874i	0.163035	+	0.986620i	$0.447872\pi$
$281$	−12.9565	+	22.4413i	−0.772921	+	1.33874i	−0.935956	+	0.352118i	$0.885462\pi$
$282$		0			0
$283$	10.3636	+	17.9502i	0.616051	+	1.06703i	0.990199	+	0.139662i	$0.0446017\pi$
$283$	10.3636	+	17.9502i	0.616051	+	1.06703i	−0.374148	+	0.927369i	$0.622065\pi$
$284$		0			0
$285$	11.8241	+	2.17206i	0.700397	+	0.128662i
$286$		0			0
$287$	−6.99772	−	12.1204i	−0.413062	−	0.715445i
$288$		0			0
$289$	−20.4306	+	35.3868i	−1.20180	+	2.08158i
$290$		0			0
$291$	−0.561343	+	0.972275i	−0.0329065	+	0.0569958i
$292$		0			0
$293$	−14.7175			−0.859804			−0.429902	−	0.902876i	$-0.641452\pi$
$293$	−14.7175			−0.859804			−0.429902	+	0.902876i	$0.641452\pi$
$294$		0			0
$295$	−5.48566	+	9.50145i	−0.319388	+	0.553196i
$296$		0			0
$297$	27.0239			1.56808
$298$		0			0
$299$	6.99772	+	12.1204i	0.404689	+	0.700941i
$300$		0			0
$301$	2.69654	+	4.67055i	0.155426	+	0.269206i
$302$		0			0
$303$	−5.66091			−0.325211
$304$		0			0
$305$	0.165079			0.00945241
$306$		0			0
$307$	−0.213929	−	0.370536i	−0.0122096	−	0.0211476i	0.859856	−	0.510537i	$-0.170553\pi$
$307$	−0.213929	−	0.370536i	−0.0122096	−	0.0211476i	−0.872066	+	0.489389i	$0.837220\pi$
$308$		0			0
$309$	−0.0282202	−	0.0488788i	−0.00160539	−	0.00278062i
$310$		0			0
$311$	−9.35307			−0.530364			−0.265182	−	0.964198i	$-0.585432\pi$
$311$	−9.35307			−0.530364			−0.265182	+	0.964198i	$0.585432\pi$
$312$		0			0
$313$	−13.2718	+	22.9874i	−0.750165	+	1.29932i	0.197578	+	0.980287i	$0.436692\pi$
$313$	−13.2718	+	22.9874i	−0.750165	+	1.29932i	−0.947743	+	0.319036i	$0.896641\pi$
$314$		0			0
$315$	18.9552			1.06800
$316$		0			0
$317$	2.47556	−	4.28780i	0.139041	−	0.240827i	−0.788093	−	0.615557i	$-0.788931\pi$
$317$	2.47556	−	4.28780i	0.139041	−	0.240827i	0.927134	+	0.374730i	$0.122265\pi$
$318$		0			0
$319$	5.91335	−	10.2422i	0.331084	−	0.573455i
$320$		0			0
$321$	0.639175	+	1.10708i	0.0356753	+	0.0617914i
$322$		0			0
$323$	−21.4935	+	25.2466i	−1.19593	+	1.40476i
$324$		0			0
$325$	−1.17028	−	2.02698i	−0.0649153	−	0.112437i
$326$		0			0
$327$	20.3153	−	35.1871i	1.12344	−	1.94585i
$328$		0			0
$329$	−0.792362	+	1.37241i	−0.0436844	+	0.0756635i
$330$		0			0
$331$	3.47145			0.190808			0.0954042	−	0.995439i	$-0.469586\pi$
$331$	3.47145			0.190808			0.0954042	+	0.995439i	$0.469586\pi$
$332$		0			0
$333$	−20.5395	+	35.5755i	−1.12556	+	1.94953i
$334$		0			0
$335$	−1.69727			−0.0927320
$336$		0			0
$337$	−5.16753	−	8.95042i	−0.281493	−	0.487560i	0.690260	−	0.723562i	$-0.257496\pi$
$337$	−5.16753	−	8.95042i	−0.281493	−	0.487560i	−0.971753	+	0.236001i	$0.924163\pi$
$338$		0			0
$339$	11.5370	+	19.9826i	0.626602	+	1.08531i
$340$		0			0
$341$	8.72814			0.472655
$342$		0			0
$343$	12.0605			0.651205
$344$		0			0
$345$	−8.24583	−	14.2822i	−0.443940	−	0.768927i
$346$		0			0
$347$	−0.775839	−	1.34379i	−0.0416492	−	0.0721386i	0.844449	−	0.535635i	$-0.179928\pi$
$347$	−0.775839	−	1.34379i	−0.0416492	−	0.0721386i	−0.886099	+	0.463497i	$0.846595\pi$
$348$		0			0
$349$	8.03451			0.430078			0.215039	−	0.976606i	$-0.431012\pi$
$349$	8.03451			0.430078			0.215039	+	0.976606i	$0.431012\pi$
$350$		0			0
$351$	5.18571	−	8.98191i	0.276793	−	0.479419i
$352$		0			0
$353$	−17.2875			−0.920121			−0.460061	−	0.887888i	$-0.652172\pi$
$353$	−17.2875			−0.920121			−0.460061	+	0.887888i	$0.652172\pi$
$354$		0			0
$355$	−4.75679	+	8.23901i	−0.252464	+	0.437281i
$356$		0			0
$357$	−43.1621	+	74.7589i	−2.28438	+	3.95666i
$358$		0			0
$359$	8.40203	+	14.5527i	0.443442	+	0.768064i	0.997942	−	0.0641193i	$-0.0204238\pi$
$359$	8.40203	+	14.5527i	0.443442	+	0.768064i	−0.554500	+	0.832184i	$0.687090\pi$
$360$		0			0
$361$	−14.7278	+	12.0039i	−0.775145	+	0.631783i
$362$		0			0
$363$	36.1198	+	62.5613i	1.89580	+	3.28362i
$364$		0			0
$365$	−5.97360	+	10.3466i	−0.312673	+	0.541565i
$366$		0			0
$367$	16.0589	−	27.8149i	0.838269	−	1.45193i	−0.0530711	−	0.998591i	$-0.516901\pi$
$367$	16.0589	−	27.8149i	0.838269	−	1.45193i	0.891340	−	0.453334i	$-0.149766\pi$
$368$		0			0
$369$	15.6686			0.815675
$370$		0			0
$371$	−2.46049	+	4.26169i	−0.127742	+	0.221256i
$372$		0			0
$373$	28.4233			1.47170			0.735851	−	0.677143i	$-0.236782\pi$
$373$	28.4233			1.47170			0.735851	+	0.677143i	$0.236782\pi$
$374$		0			0
$375$	1.37901	+	2.38851i	0.0712117	+	0.123342i
$376$		0			0
$377$	−2.26947	−	3.93084i	−0.116884	−	0.202449i
$378$		0			0
$379$	−31.0504			−1.59495			−0.797476	−	0.603350i	$-0.793832\pi$
$379$	−31.0504			−1.59495			−0.797476	+	0.603350i	$0.793832\pi$
$380$		0			0
$381$	50.9338			2.60942
$382$		0			0
$383$	−14.6428	−	25.3621i	−0.748213	−	1.29594i	−0.948678	−	0.316243i	$-0.897579\pi$
$383$	−14.6428	−	25.3621i	−0.748213	−	1.29594i	0.200465	−	0.979701i	$-0.435755\pi$
$384$		0			0
$385$	12.5470	+	21.7321i	0.639455	+	1.10757i
$386$		0			0
$387$	−6.03783			−0.306920
$388$		0			0
$389$	5.66415	−	9.81060i	0.287184	−	0.497417i	−0.685953	−	0.727646i	$-0.740614\pi$
$389$	5.66415	−	9.81060i	0.287184	−	0.497417i	0.973136	+	0.230229i	$0.0739476\pi$
$390$		0			0
$391$	45.4843			2.30024
$392$		0			0
$393$	22.4496	−	38.8839i	1.13243	−	1.96143i
$394$		0			0
$395$	3.87563	−	6.71280i	0.195004	−	0.337757i
$396$		0			0
$397$	−1.84526	−	3.19609i	−0.0926111	−	0.160407i	0.815998	−	0.578055i	$-0.196188\pi$
$397$	−1.84526	−	3.19609i	−0.0926111	−	0.160407i	−0.908609	+	0.417648i	$0.862855\pi$
$398$		0			0
$399$	−32.0665	+	37.6659i	−1.60533	+	1.88565i
$400$		0			0
$401$	6.63776	+	11.4969i	0.331474	+	0.574129i	0.982801	−	0.184668i	$-0.0591208\pi$
$401$	6.63776	+	11.4969i	0.331474	+	0.574129i	−0.651327	+	0.758797i	$0.725787\pi$
$402$		0			0
$403$	1.67487	−	2.90097i	0.0834315	−	0.144508i
$404$		0			0
$405$	0.799351	−	1.38452i	0.0397201	−	0.0687972i
$406$		0			0
$407$	−54.3830			−2.69566
$408$		0			0
$409$	2.01100	−	3.48315i	0.0994375	−	0.172231i	−0.812014	−	0.583637i	$-0.801629\pi$
$409$	2.01100	−	3.48315i	0.0994375	−	0.172231i	0.911452	+	0.411406i	$0.134962\pi$
$410$		0			0
$411$	−11.1877			−0.551850
$412$		0			0
$413$	−22.5720	−	39.0959i	−1.11070	−	1.92378i
$414$		0			0
$415$	1.62785	+	2.81952i	0.0799080	+	0.138405i
$416$		0			0
$417$	29.8981			1.46411
$418$		0			0
$419$	4.41991			0.215927			0.107963	−	0.994155i	$-0.465567\pi$
$419$	4.41991			0.215927			0.107963	+	0.994155i	$0.465567\pi$
$420$		0			0
$421$	6.58578	+	11.4069i	0.320971	+	0.555939i	0.980689	−	0.195575i	$-0.0626573\pi$
$421$	6.58578	+	11.4069i	0.320971	+	0.555939i	−0.659717	+	0.751514i	$0.729324\pi$
$422$		0			0
$423$	−0.887090	−	1.53648i	−0.0431318	−	0.0747064i
$424$		0			0
$425$	−7.60665			−0.368977
$426$		0			0
$427$	−0.339629	+	0.588254i	−0.0164358	+	0.0284676i
$428$		0			0
$429$	39.3681			1.90071
$430$		0			0
$431$	14.4124	−	24.9630i	0.694221	−	1.20243i	−0.276221	−	0.961094i	$-0.589082\pi$
$431$	14.4124	−	24.9630i	0.694221	−	1.20243i	0.970443	−	0.241332i	$-0.0775844\pi$
$432$		0			0
$433$	6.30575	−	10.9219i	0.303035	−	0.524872i	−0.673787	−	0.738926i	$-0.735333\pi$
$433$	6.30575	−	10.9219i	0.303035	−	0.524872i	0.976822	+	0.214054i	$0.0686667\pi$
$434$		0			0
$435$	2.67425	+	4.63194i	0.128221	+	0.222085i
$436$		0			0
$437$	25.6352	+	4.70915i	1.22630	+	0.225269i
$438$		0			0
$439$	4.78563	+	8.28896i	0.228406	+	0.395611i	0.957336	−	0.288978i	$-0.0933153\pi$
$439$	4.78563	+	8.28896i	0.228406	+	0.395611i	−0.728930	+	0.684588i	$0.759982\pi$
$440$		0			0
$441$	−22.8744	+	39.6197i	−1.08926	+	1.88665i
$442$		0			0
$443$	−0.885541	+	1.53380i	−0.0420733	+	0.0728731i	−0.886295	−	0.463121i	$-0.846730\pi$
$443$	−0.885541	+	1.53380i	−0.0420733	+	0.0728731i	0.844222	+	0.535994i	$0.180063\pi$
$444$		0			0
$445$	−18.5215			−0.878005
$446$		0			0
$447$	−31.6401	+	54.8023i	−1.49653	+	2.59206i
$448$		0			0
$449$	5.20350			0.245568			0.122784	−	0.992433i	$-0.460818\pi$
$449$	5.20350			0.245568			0.122784	+	0.992433i	$0.460818\pi$
$450$		0			0
$451$	10.3715	+	17.9640i	0.488376	+	0.845892i
$452$		0			0
$453$	−22.4812	−	38.9386i	−1.05626	−	1.82950i
$454$		0			0
$455$	9.63077			0.451497
$456$		0			0
$457$	6.45311			0.301864			0.150932	−	0.988544i	$-0.451773\pi$
$457$	6.45311			0.301864			0.150932	+	0.988544i	$0.451773\pi$
$458$		0			0
$459$	−16.8532	−	29.1906i	−0.786641	−	1.36250i
$460$		0			0
$461$	−1.12464	−	1.94794i	−0.0523798	−	0.0907245i	0.838647	−	0.544676i	$-0.183347\pi$
$461$	−1.12464	−	1.94794i	−0.0523798	−	0.0907245i	−0.891026	+	0.453951i	$0.850014\pi$
$462$		0			0
$463$	33.8252			1.57199			0.785995	−	0.618232i	$-0.212151\pi$
$463$	33.8252			1.57199			0.785995	+	0.618232i	$0.212151\pi$
$464$		0			0
$465$	−1.97360	+	3.41838i	−0.0915237	+	0.158524i
$466$		0			0
$467$	7.01926			0.324813			0.162406	−	0.986724i	$-0.448074\pi$
$467$	7.01926			0.324813			0.162406	+	0.986724i	$0.448074\pi$
$468$		0			0
$469$	3.49192	−	6.04818i	0.161242	−	0.279279i
$470$		0			0
$471$	−12.3253	+	21.3480i	−0.567919	+	0.983665i
$472$		0			0
$473$	−3.99663	−	6.92236i	−0.183765	−	0.318290i
$474$		0			0
$475$	−4.28716	−	0.787545i	−0.196709	−	0.0361351i
$476$		0			0
$477$	−2.75464	−	4.77118i	−0.126126	−	0.218457i
$478$		0			0
$479$	−11.0213	+	19.0895i	−0.503578	+	0.872223i	0.496413	+	0.868086i	$0.334650\pi$
$479$	−11.0213	+	19.0895i	−0.503578	+	0.872223i	−0.999991	+	0.00413643i	$0.998683\pi$
$480$		0			0
$481$	−10.4358	+	18.0753i	−0.475829	+	0.824161i
$482$		0			0
$483$	67.8588			3.08768
$484$		0			0
$485$	0.203531	−	0.352527i	0.00924189	−	0.0160074i
$486$		0			0
$487$	−18.1596			−0.822892			−0.411446	−	0.911434i	$-0.634976\pi$
$487$	−18.1596			−0.822892			−0.411446	+	0.911434i	$0.634976\pi$
$488$		0			0
$489$	−7.79813	−	13.5068i	−0.352644	−	0.610797i
$490$		0			0
$491$	17.0204	+	29.4802i	0.768121	+	1.33042i	0.938581	+	0.345059i	$0.112141\pi$
$491$	17.0204	+	29.4802i	0.768121	+	1.33042i	−0.170460	+	0.985365i	$0.554525\pi$
$492$		0			0
$493$	−14.7513			−0.664364
$494$		0			0
$495$	−28.0940			−1.26273
$496$		0			0
$497$	−19.5729	−	33.9013i	−0.877967	−	1.52068i
$498$		0			0
$499$	−10.1552	−	17.5893i	−0.454610	−	0.787407i	0.544056	−	0.839049i	$-0.316888\pi$
$499$	−10.1552	−	17.5893i	−0.454610	−	0.787407i	−0.998666	+	0.0516420i	$0.983555\pi$
$500$		0			0
$501$	−36.5941			−1.63491
$502$		0			0
$503$	−0.231947	+	0.401743i	−0.0103420	+	0.0179128i	−0.871150	−	0.491017i	$-0.836625\pi$
$503$	−0.231947	+	0.401743i	−0.0103420	+	0.0179128i	0.860808	+	0.508930i	$0.169959\pi$
$504$		0			0
$505$	2.05253			0.0913363
$506$		0			0
$507$	−10.3726	+	17.9659i	−0.460664	+	0.797894i
$508$		0			0
$509$	6.08533	−	10.5401i	0.269727	−	0.467181i	−0.699064	−	0.715059i	$-0.746400\pi$
$509$	6.08533	−	10.5401i	0.269727	−	0.467181i	0.968791	+	0.247878i	$0.0797331\pi$
$510$		0			0
$511$	−24.5798	−	42.5735i	−1.08735	−	1.88334i
$512$		0			0
$513$	−6.47638	−	18.1969i	−0.285939	−	0.803414i
$514$		0			0
$515$	0.0102321	+	0.0177225i	0.000450879	+	0.000780945i
$516$		0			0
$517$	1.17438	−	2.03409i	0.0516494	−	0.0894593i
$518$		0			0
$519$	−1.77162	+	3.06854i	−0.0777656	+	0.134694i
$520$		0			0
$521$	−41.4580			−1.81631			−0.908155	−	0.418635i	$-0.862509\pi$
$521$	−41.4580			−1.81631			−0.908155	+	0.418635i	$0.862509\pi$
$522$		0			0
$523$	1.09675	−	1.89962i	0.0479574	−	0.0830647i	−0.841050	−	0.540957i	$-0.818062\pi$
$523$	1.09675	−	1.89962i	0.0479574	−	0.0830647i	0.889008	+	0.457892i	$0.151395\pi$
$524$		0			0
$525$	−11.3485			−0.495289
$526$		0			0
$527$	−5.44323	−	9.42796i	−0.237111	−	0.410688i
$528$		0			0
$529$	−6.37742	−	11.0460i	−0.277279	−	0.480262i
$530$		0			0
$531$	50.5411			2.19330
$532$		0			0
$533$	7.96093			0.344826
$534$		0			0
$535$	−0.231752	−	0.401406i	−0.0100195	−	0.0173543i
$536$		0			0
$537$	5.89057	+	10.2028i	0.254197	+	0.440282i
$538$		0			0
$539$	−60.5652			−2.60873
$540$		0			0
$541$	−3.83490	+	6.64224i	−0.164875	+	0.285572i	−0.936611	−	0.350371i	$-0.886055\pi$
$541$	−3.83490	+	6.64224i	−0.164875	+	0.285572i	0.771736	+	0.635943i	$0.219389\pi$
$542$		0			0
$543$	4.79894			0.205942
$544$		0			0
$545$	−7.36589	+	12.7581i	−0.315520	+	0.546497i
$546$		0			0
$547$	−19.0123	+	32.9303i	−0.812909	+	1.40800i	0.0979112	+	0.995195i	$0.468784\pi$
$547$	−19.0123	+	32.9303i	−0.812909	+	1.40800i	−0.910820	+	0.412804i	$0.864549\pi$
$548$		0			0
$549$	−0.380231	−	0.658580i	−0.0162279	−	0.0281075i
$550$		0			0
$551$	−8.31392	−	1.52725i	−0.354185	−	0.0650632i
$552$		0			0
$553$	15.9472	+	27.6214i	0.678144	+	1.17458i
$554$		0			0
$555$	12.2971	−	21.2992i	0.521982	−	0.904099i
$556$		0			0
$557$	−11.6565	+	20.1897i	−0.493904	+	0.855466i	−0.999975	−	0.00702537i	$-0.997764\pi$
$557$	−11.6565	+	20.1897i	−0.493904	+	0.855466i	0.506072	+	0.862491i	$0.331097\pi$
$558$		0			0
$559$	−3.06771			−0.129750
$560$		0			0
$561$	63.9718	−	110.802i	2.70089	−	4.67808i
$562$		0			0
$563$	−18.1507			−0.764961			−0.382481	−	0.923964i	$-0.624930\pi$
$563$	−18.1507			−0.764961			−0.382481	+	0.923964i	$0.624930\pi$
$564$		0			0
$565$	−4.18307	−	7.24529i	−0.175983	−	0.304811i
$566$		0			0
$567$	3.28912	+	5.69692i	0.138130	+	0.239248i
$568$		0			0
$569$	−41.6104			−1.74440			−0.872200	−	0.489149i	$-0.837307\pi$
$569$	−41.6104			−1.74440			−0.872200	+	0.489149i	$0.837307\pi$
$570$		0			0
$571$	−25.5273			−1.06828			−0.534142	−	0.845395i	$-0.679365\pi$
$571$	−25.5273			−1.06828			−0.534142	+	0.845395i	$0.679365\pi$
$572$		0			0
$573$	31.0009	+	53.6952i	1.29508	+	2.24315i
$574$		0			0
$575$	2.98977	+	5.17843i	0.124682	+	0.215955i
$576$		0			0
$577$	−12.7680			−0.531540			−0.265770	−	0.964036i	$-0.585626\pi$
$577$	−12.7680			−0.531540			−0.265770	+	0.964036i	$0.585626\pi$
$578$		0			0
$579$	−11.2681	+	19.5170i	−0.468287	+	0.811097i
$580$		0			0
$581$	−13.3963			−0.555774
$582$		0			0
$583$	3.64677	−	6.31638i	0.151034	−	0.261598i
$584$		0			0
$585$	−5.39107	+	9.33760i	−0.222893	+	0.386062i
$586$		0			0
$587$	12.1686	+	21.0767i	0.502253	+	0.869927i	0.999997	+	0.00260307i	$0.000828583\pi$
$587$	12.1686	+	21.0767i	0.502253	+	0.869927i	−0.497744	+	0.867324i	$0.665838\pi$
$588$		0			0
$589$	−2.09173	−	5.87722i	−0.0861884	−	0.242167i
$590$		0			0
$591$	20.2647	+	35.0996i	0.833580	+	1.44380i
$592$		0			0
$593$	10.4025	−	18.0177i	0.427180	−	0.739897i	−0.569442	−	0.822032i	$-0.692841\pi$
$593$	10.4025	−	18.0177i	0.427180	−	0.739897i	0.996621	+	0.0821351i	$0.0261739\pi$
$594$		0			0
$595$	15.6497	−	27.1060i	0.641574	−	1.11124i
$596$		0			0
$597$	43.0326			1.76121
$598$		0			0
$599$	15.7162	−	27.2212i	0.642146	−	1.11223i	−0.342807	−	0.939406i	$-0.611378\pi$
$599$	15.7162	−	27.2212i	0.642146	−	1.11223i	0.984953	−	0.172824i	$-0.0552891\pi$
$600$		0			0
$601$	4.41844			0.180232			0.0901160	−	0.995931i	$-0.471276\pi$
$601$	4.41844			0.180232			0.0901160	+	0.995931i	$0.471276\pi$
$602$		0			0
$603$	3.90938	+	6.77124i	0.159202	+	0.275746i
$604$		0			0
$605$	−13.0963	−	22.6834i	−0.532440	−	0.922213i
$606$		0			0
$607$	−26.2340			−1.06481			−0.532403	−	0.846491i	$-0.678711\pi$
$607$	−26.2340			−1.06481			−0.532403	+	0.846491i	$0.678711\pi$
$608$		0			0
$609$	−22.0077			−0.891797
$610$		0			0
$611$	−0.450714	−	0.780659i	−0.0182339	−	0.0315821i
$612$		0			0
$613$	−21.6066	−	37.4237i	−0.872681	−	1.51153i	−0.859213	−	0.511618i	$-0.829046\pi$
$613$	−21.6066	−	37.4237i	−0.872681	−	1.51153i	−0.0134676	−	0.999909i	$-0.504287\pi$
$614$		0			0
$615$	−9.38083			−0.378272
$616$		0			0
$617$	8.62914	−	14.9461i	0.347396	−	0.601708i	−0.638390	−	0.769713i	$-0.720399\pi$
$617$	8.62914	−	14.9461i	0.347396	−	0.601708i	0.985786	+	0.168005i	$0.0537326\pi$
$618$		0			0
$619$	−12.4548			−0.500599			−0.250300	−	0.968168i	$-0.580529\pi$
$619$	−12.4548			−0.500599			−0.250300	+	0.968168i	$0.580529\pi$
$620$		0			0
$621$	−13.2482	+	22.9465i	−0.531632	+	0.920813i
$622$		0			0
$623$	38.1056	−	66.0009i	1.52667	−	2.64427i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	47.5268	−	55.8258i	1.89804	−	2.22947i
$628$		0			0
$629$	33.9155	+	58.7434i	1.35230	+	2.34225i
$630$		0			0
$631$	3.02335	−	5.23659i	0.120358	−	0.208465i	−0.799551	−	0.600598i	$-0.794929\pi$
$631$	3.02335	−	5.23659i	0.120358	−	0.208465i	0.919909	+	0.392133i	$0.128263\pi$
$632$		0			0
$633$	19.7189	−	34.1542i	0.783758	−	1.35751i
$634$		0			0
$635$	−18.4675			−0.732862
$636$		0			0
$637$	−11.6221	+	20.1300i	−0.460484	+	0.797581i
$638$		0			0
$639$	43.8258			1.73372
$640$		0			0
$641$	14.8639	+	25.7449i	0.587087	+	1.01686i	0.994612	+	0.103670i	$0.0330587\pi$
$641$	14.8639	+	25.7449i	0.587087	+	1.01686i	−0.407525	+	0.913194i	$0.633608\pi$
$642$		0			0
$643$	−14.7949	−	25.6256i	−0.583455	−	1.01057i	−0.995066	−	0.0992137i	$-0.968367\pi$
$643$	−14.7949	−	25.6256i	−0.583455	−	1.01057i	0.411611	−	0.911359i	$-0.364966\pi$
$644$		0			0
$645$	3.61487			0.142335
$646$		0			0
$647$	−35.2808			−1.38703			−0.693515	−	0.720442i	$-0.743939\pi$
$647$	−35.2808			−1.38703			−0.693515	+	0.720442i	$0.743939\pi$
$648$		0			0
$649$	33.4547	+	57.9452i	1.31321	+	2.27455i
$650$		0			0
$651$	−8.12086	−	14.0657i	−0.318282	−	0.551280i
$652$		0			0
$653$	6.40217			0.250536			0.125268	−	0.992123i	$-0.460021\pi$
$653$	6.40217			0.250536			0.125268	+	0.992123i	$0.460021\pi$
$654$		0			0
$655$	−8.13978	+	14.0985i	−0.318047	+	0.550874i
$656$		0			0
$657$	55.0367			2.14718
$658$		0			0
$659$	20.0539	−	34.7344i	0.781189	−	1.35306i	−0.150061	−	0.988677i	$-0.547947\pi$
$659$	20.0539	−	34.7344i	0.781189	−	1.35306i	0.931250	−	0.364382i	$-0.118720\pi$
$660$		0			0
$661$	−11.9089	+	20.6268i	−0.463202	+	0.802289i	−0.999118	−	0.0419816i	$-0.986633\pi$
$661$	−11.9089	+	20.6268i	−0.463202	+	0.802289i	0.535916	+	0.844271i	$0.319966\pi$
$662$		0			0
$663$	−24.5516	−	42.5246i	−0.953504	−	1.65152i
$664$		0			0
$665$	11.6267	−	13.6569i	0.450863	−	0.529591i
$666$		0			0
$667$	5.79793	+	10.0423i	0.224497	+	0.388840i
$668$		0			0
$669$	0.400565	−	0.693799i	0.0154867	−	0.0268238i
$670$		0			0
$671$	0.503374	−	0.871869i	0.0194325	−	0.0336581i
$672$		0			0
$673$	−2.45529			−0.0946445			−0.0473223	−	0.998880i	$-0.515069\pi$
$673$	−2.45529			−0.0946445			−0.0473223	+	0.998880i	$0.515069\pi$
$674$		0			0
$675$	2.21559	−	3.83751i	0.0852780	−	0.147706i
$676$		0			0
$677$	11.1525			0.428625			0.214313	−	0.976765i	$-0.431249\pi$
$677$	11.1525			0.428625			0.214313	+	0.976765i	$0.431249\pi$
$678$		0			0
$679$	0.837478	+	1.45055i	0.0321395	+	0.0556672i
$680$		0			0
$681$	−31.2774	−	54.1741i	−1.19855	−	2.07596i
$682$		0			0
$683$	−18.0171			−0.689407			−0.344703	−	0.938712i	$-0.612021\pi$
$683$	−18.0171			−0.689407			−0.344703	+	0.938712i	$0.612021\pi$
$684$		0			0
$685$	4.05644			0.154989
$686$		0			0
$687$	9.76670	+	16.9164i	0.372623	+	0.645402i
$688$		0			0
$689$	−1.39958	−	2.42415i	−0.0533199	−	0.0923527i
$690$		0			0
$691$	0.184631			0.00702370			0.00351185	−	0.999994i	$-0.498882\pi$
$691$	0.184631			0.00702370			0.00351185	+	0.999994i	$0.498882\pi$
$692$		0			0
$693$	57.7997	−	100.112i	2.19563	−	3.80294i
$694$		0			0
$695$	−10.8404			−0.411201
$696$		0			0
$697$	12.9362	−	22.4062i	0.489995	−	0.848697i
$698$		0			0
$699$	−13.7593	+	23.8318i	−0.520425	+	0.901402i
$700$		0			0
$701$	16.8233	+	29.1387i	0.635405	+	1.10055i	0.986429	+	0.164188i	$0.0525003\pi$
$701$	16.8233	+	29.1387i	0.635405	+	1.10055i	−0.351024	+	0.936367i	$0.614166\pi$
$702$		0			0
$703$	13.0331	+	36.6196i	0.491553	+	1.38113i
$704$		0			0
$705$	0.531103	+	0.919897i	0.0200025	+	0.0346453i
$706$		0			0
$707$	−4.22281	+	7.31412i	−0.158815	+	0.275076i
$708$		0			0
$709$	−11.5040	+	19.9255i	−0.432042	+	0.748319i	−0.997049	−	0.0767672i	$-0.975540\pi$
$709$	−11.5040	+	19.9255i	−0.432042	+	0.748319i	0.565007	+	0.825086i	$0.308874\pi$
$710$		0			0
$711$	−35.7074			−1.33913
$712$		0			0
$713$	−4.27889	+	7.41125i	−0.160246	+	0.277553i
$714$		0			0
$715$	−14.2740			−0.533819
$716$		0			0
$717$	−39.1341	−	67.7823i	−1.46149	−	2.53138i
$718$		0			0
$719$	11.4576	+	19.8452i	0.427297	+	0.740099i	0.996632	−	0.0820060i	$-0.0261327\pi$
$719$	11.4576	+	19.8452i	0.427297	+	0.740099i	−0.569335	+	0.822105i	$0.692799\pi$
$720$		0			0
$721$	−0.0842045			−0.00313594
$722$		0			0
$723$	−15.8858			−0.590800
$724$		0			0
$725$	−0.969629	−	1.67945i	−0.0360111	−	0.0623731i
$726$		0			0
$727$	−7.94740	−	13.7653i	−0.294753	−	0.510527i	0.680174	−	0.733050i	$-0.261904\pi$
$727$	−7.94740	−	13.7653i	−0.294753	−	0.510527i	−0.974927	+	0.222523i	$0.928571\pi$
$728$		0			0
$729$	−44.0284			−1.63068
$730$		0			0
$731$	−4.98493	+	8.63415i	−0.184374	+	0.319346i
$732$		0			0
$733$	18.5670			0.685787			0.342894	−	0.939374i	$-0.388593\pi$
$733$	18.5670			0.685787			0.342894	+	0.939374i	$0.388593\pi$
$734$		0			0
$735$	13.6950	−	23.7204i	0.505147	−	0.874941i
$736$		0			0
$737$	−5.17548	+	8.96419i	−0.190641	+	0.330200i
$738$		0			0
$739$	−1.70308	−	2.94981i	−0.0626486	−	0.108511i	0.833000	−	0.553273i	$-0.186621\pi$
$739$	−1.70308	−	2.94981i	−0.0626486	−	0.108511i	−0.895649	+	0.444763i	$0.853288\pi$
$740$		0			0
$741$	−9.43472	−	26.5091i	−0.346593	−	0.973835i
$742$		0			0
$743$	2.08221	+	3.60650i	0.0763890	+	0.132310i	0.901689	−	0.432384i	$-0.142328\pi$
$743$	2.08221	+	3.60650i	0.0763890	+	0.132310i	−0.825300	+	0.564694i	$0.808994\pi$
$744$		0			0
$745$	11.4721	−	19.8702i	0.420304	−	0.727987i
$746$		0			0
$747$	7.49894	−	12.9885i	0.274372	−	0.475226i
$748$		0			0
$749$	1.90719			0.0696873
$750$		0			0
$751$	−8.92844	+	15.4645i	−0.325803	+	0.564308i	−0.981675	−	0.190565i	$-0.938968\pi$
$751$	−8.92844	+	15.4645i	−0.325803	+	0.564308i	0.655871	+	0.754873i	$0.272301\pi$
$752$		0			0
$753$	18.1548			0.661596
$754$		0			0
$755$	8.15123	+	14.1183i	0.296654	+	0.513819i
$756$		0			0
$757$	−17.7593	−	30.7600i	−0.645473	−	1.11799i	−0.984192	−	0.177104i	$-0.943327\pi$
$757$	−17.7593	−	30.7600i	−0.645473	−	1.11799i	0.338719	−	0.940888i	$-0.390006\pi$
$758$		0			0
$759$	−100.576			−3.65066
$760$		0			0
$761$	−46.6528			−1.69116			−0.845581	−	0.533848i	$-0.820746\pi$
$761$	−46.6528			−1.69116			−0.845581	+	0.533848i	$0.820746\pi$
$762$		0			0
$763$	−30.3087	−	52.4962i	−1.09725	−	1.90049i
$764$		0			0
$765$	17.5206	+	30.3466i	0.633459	+	1.09718i
$766$		0			0
$767$	25.6790			0.927215
$768$		0			0
$769$	17.5585	−	30.4121i	0.633174	−	1.09669i	−0.353725	−	0.935350i	$-0.615085\pi$
$769$	17.5585	−	30.4121i	0.633174	−	1.09669i	0.986899	−	0.161340i	$-0.0515817\pi$
$770$		0			0
$771$	63.2654			2.27845
$772$		0			0
$773$	−5.99581	+	10.3850i	−0.215654	+	0.373524i	−0.953475	−	0.301473i	$-0.902522\pi$
$773$	−5.99581	+	10.3850i	−0.215654	+	0.373524i	0.737820	+	0.674997i	$0.235855\pi$
$774$		0			0
$775$	0.715589	−	1.23944i	0.0257047	−	0.0445218i
$776$		0			0
$777$	50.5992	+	87.6404i	1.81524	+	3.14408i
$778$		0			0
$779$	9.61076	−	11.2890i	0.344341	−	0.404469i
$780$		0			0
$781$	29.0096	+	50.2462i	1.03805	+	1.79795i
$782$		0			0
$783$	4.29660	−	7.44193i	0.153548	−	0.265953i
$784$		0			0
$785$	4.46890	−	7.74036i	0.159502	−	0.276265i
$786$		0			0
$787$	16.9481			0.604134			0.302067	−	0.953287i	$-0.402323\pi$
$787$	16.9481			0.604134			0.302067	+	0.953287i	$0.402323\pi$
$788$		0			0
$789$	−8.39700	+	14.5440i	−0.298941	+	0.517781i
$790$		0			0
$791$	34.4244			1.22399
$792$		0			0
$793$	−0.193189	−	0.334612i	−0.00686033	−	0.0118824i
$794$		0			0
$795$	1.64921	+	2.85652i	0.0584915	+	0.101310i
$796$		0			0
$797$	37.2372			1.31901			0.659505	−	0.751700i	$-0.270766\pi$
$797$	37.2372			1.31901			0.659505	+	0.751700i	$0.270766\pi$
$798$		0			0
$799$	−2.92958			−0.103641
$800$		0			0
$801$	42.6612	+	73.8913i	1.50736	+	2.61082i
$802$		0			0
$803$	36.4305	+	63.0994i	1.28560	+	2.22673i
$804$		0			0
$805$	−24.6042			−0.867184
$806$		0			0
$807$	8.44525	−	14.6276i	0.297287	−	0.514916i
$808$		0			0
$809$	5.51662			0.193954			0.0969771	−	0.995287i	$-0.469083\pi$
$809$	5.51662			0.193954			0.0969771	+	0.995287i	$0.469083\pi$
$810$		0			0
$811$	−9.93118	+	17.2013i	−0.348731	+	0.604019i	−0.986024	−	0.166602i	$-0.946721\pi$
$811$	−9.93118	+	17.2013i	−0.348731	+	0.604019i	0.637293	+	0.770621i	$0.280054\pi$
$812$		0			0
$813$	−13.0984	+	22.6871i	−0.459380	+	0.795670i
$814$		0			0
$815$	2.82744	+	4.89727i	0.0990409	+	0.171544i
$816$		0			0
$817$	−3.70347	+	4.35016i	−0.129568	+	0.152193i
$818$		0			0
$819$	−22.1828	−	38.4217i	−0.775130	−	1.34256i
$820$		0			0
$821$	15.0415	−	26.0527i	0.524954	−	0.909246i	−0.474624	−	0.880189i	$-0.657416\pi$
$821$	15.0415	−	26.0527i	0.524954	−	0.909246i	0.999578	−	0.0290577i	$-0.00925064\pi$
$822$		0			0
$823$	8.94291	−	15.4896i	0.311730	−	0.539933i	−0.667007	−	0.745052i	$-0.732425\pi$
$823$	8.94291	−	15.4896i	0.311730	−	0.539933i	0.978737	+	0.205119i	$0.0657582\pi$
$824$		0			0
$825$	16.8200			0.585596
$826$		0			0
$827$	−13.8490	+	23.9872i	−0.481577	+	0.834116i	−0.999776	−	0.0211442i	$-0.993269\pi$
$827$	−13.8490	+	23.9872i	−0.481577	+	0.834116i	0.518200	+	0.855260i	$0.326602\pi$
$828$		0			0
$829$	−17.4963			−0.607671			−0.303836	−	0.952724i	$-0.598267\pi$
$829$	−17.4963			−0.607671			−0.303836	+	0.952724i	$0.598267\pi$
$830$		0			0
$831$	−12.1321	−	21.0134i	−0.420858	−	0.728947i
$832$		0			0
$833$	37.7710	+	65.4213i	1.30869	+	2.26671i
$834$		0			0
$835$	13.2683			0.459168
$836$		0			0
$837$	6.34180			0.219205
$838$		0			0
$839$	25.3835	+	43.9655i	0.876335	+	1.51786i	0.855333	+	0.518078i	$0.173352\pi$
$839$	25.3835	+	43.9655i	0.876335	+	1.51786i	0.0210020	+	0.999779i	$0.493314\pi$
$840$		0			0
$841$	12.6196	+	21.8579i	0.435160	+	0.753719i
$842$		0			0
$843$	−71.4686			−2.46151
$844$		0			0
$845$	3.76090	−	6.51407i	0.129379	−	0.224091i
$846$		0			0
$847$	107.776			3.70321
$848$		0			0
$849$	−28.5829	+	49.5071i	−0.980963	+	1.69908i
$850$		0			0
$851$	26.6607	−	46.1778i	0.913919	−	1.58295i
$852$		0			0
$853$	−4.80853	−	8.32861i	−0.164641	−	0.285166i	0.771887	−	0.635760i	$-0.219313\pi$
$853$	−4.80853	−	8.32861i	−0.164641	−	0.285166i	−0.936528	+	0.350594i	$0.885980\pi$
$854$		0			0
$855$	6.73284	+	18.9175i	0.230258	+	0.646966i
$856$		0			0
$857$	−17.5932	−	30.4723i	−0.600973	−	1.04092i	−0.992674	−	0.120823i	$-0.961447\pi$
$857$	−17.5932	−	30.4723i	−0.600973	−	1.04092i	0.391701	−	0.920092i	$-0.371887\pi$
$858$		0			0
$859$	3.86934	−	6.70190i	0.132020	−	0.228666i	−0.792435	−	0.609956i	$-0.791187\pi$
$859$	3.86934	−	6.70190i	0.132020	−	0.228666i	0.924455	+	0.381291i	$0.124520\pi$
$860$		0			0
$861$	19.2998	−	33.4283i	0.657736	−	1.13923i
$862$		0			0
$863$	−8.56120			−0.291427			−0.145713	−	0.989327i	$-0.546548\pi$
$863$	−8.56120			−0.291427			−0.145713	+	0.989327i	$0.546548\pi$
$864$		0			0
$865$	0.642354	−	1.11259i	0.0218407	−	0.0378292i
$866$		0			0
$867$	−112.696			−3.82735
$868$		0			0
$869$	−23.6358	−	40.9385i	−0.801791	−	1.38874i
$870$		0			0
$871$	1.98628	+	3.44034i	0.0673026	+	0.116572i
$872$		0			0
$873$	−1.87520			−0.0634658
$874$		0			0
$875$	4.11474			0.139103
$876$		0			0
$877$	−15.0547	−	26.0754i	−0.508360	−	0.880505i	−0.999953	−	0.00968005i	$-0.996919\pi$
$877$	−15.0547	−	26.0754i	−0.508360	−	0.880505i	0.491593	−	0.870825i	$-0.336415\pi$
$878$		0			0
$879$	−20.2955	−	35.1529i	−0.684551	−	1.18568i
$880$		0			0
$881$	−33.2485			−1.12017			−0.560085	−	0.828435i	$-0.689231\pi$
$881$	−33.2485			−1.12017			−0.560085	+	0.828435i	$0.689231\pi$
$882$		0			0
$883$	26.8385	−	46.4857i	0.903188	−	1.56437i	0.0798558	−	0.996806i	$-0.474554\pi$
$883$	26.8385	−	46.4857i	0.903188	−	1.56437i	0.823332	−	0.567560i	$-0.192113\pi$
$884$		0			0
$885$	−30.2591			−1.01715
$886$		0			0
$887$	−19.3414	+	33.5003i	−0.649420	+	1.12483i	0.333841	+	0.942629i	$0.391655\pi$
$887$	−19.3414	+	33.5003i	−0.649420	+	1.12483i	−0.983262	+	0.182200i	$0.941678\pi$
$888$		0			0
$889$	37.9945	−	65.8084i	1.27430	−	2.20714i
$890$		0			0
$891$	−4.87490	−	8.44358i	−0.163315	−	0.282871i
$892$		0			0
$893$	−1.65113	−	0.303310i	−0.0552531	−	0.0101499i
$894$		0			0
$895$	−2.13580	−	3.69932i	−0.0713920	−	0.123654i
$896$		0			0
$897$	−19.2998	+	33.4283i	−0.644402	+	1.11614i
$898$		0			0
$899$	1.38771	−	2.40359i	0.0462828	−	0.0801641i
$900$		0			0
$901$	−9.09711			−0.303069
$902$		0			0
$903$	−7.43711	+	12.8814i	−0.247491	+	0.428668i
$904$		0			0
$905$	−1.74000			−0.0578395
$906$		0			0
$907$	−3.23524	−	5.60359i	−0.107424	−	0.186064i	0.807302	−	0.590139i	$-0.200927\pi$
$907$	−3.23524	−	5.60359i	−0.107424	−	0.186064i	−0.914726	+	0.404075i	$0.867594\pi$
$908$		0			0
$909$	−4.72765	−	8.18852i	−0.156806	−	0.271596i
$910$		0			0
$911$	−8.50013			−0.281622			−0.140811	−	0.990037i	$-0.544971\pi$
$911$	−8.50013			−0.281622			−0.140811	+	0.990037i	$0.544971\pi$
$912$		0			0
$913$	19.8551			0.657109
$914$		0			0
$915$	0.227646	+	0.394294i	0.00752573	+	0.0130349i
$916$		0			0
$917$	−33.4930	−	58.0116i	−1.10604	−	1.91571i
$918$		0			0
$919$	52.9504			1.74667			0.873337	−	0.487117i	$-0.161951\pi$
$919$	52.9504			1.74667			0.873337	+	0.487117i	$0.161951\pi$
$920$		0			0
$921$	0.590019	−	1.02194i	0.0194418	−	0.0336742i
$922$		0			0
$923$	22.2671			0.732930
$924$		0			0
$925$	−4.45866	+	7.72263i	−0.146600	+	0.253919i
$926$		0			0
$927$	0.0471356	−	0.0816412i	0.00154814	−	0.00268145i
$928$		0			0
$929$	−7.00673	−	12.1360i	−0.229883	−	0.398170i	0.727890	−	0.685694i	$-0.240501\pi$
$929$	−7.00673	−	12.1360i	−0.229883	−	0.398170i	−0.957773	+	0.287524i	$0.907168\pi$
$930$		0			0
$931$	14.5147	+	40.7825i	0.475700	+	1.33659i
$932$		0			0
$933$	−12.8980	−	22.3399i	−0.422260	−	0.731376i
$934$		0			0
$935$	−23.1949	+	40.1747i	−0.758553	+	1.31385i
$936$		0			0
$937$	19.0274	−	32.9564i	0.621598	−	1.07664i	−0.367590	−	0.929988i	$-0.619817\pi$
$937$	19.0274	−	32.9564i	0.621598	−	1.07664i	0.989188	−	0.146651i	$-0.0468495\pi$
$938$		0			0
$939$	−73.2075			−2.38904
$940$		0			0
$941$	5.99493	−	10.3835i	0.195429	−	0.338493i	−0.751612	−	0.659606i	$-0.770723\pi$
$941$	5.99493	−	10.3835i	0.195429	−	0.338493i	0.947041	+	0.321112i	$0.104057\pi$
$942$		0			0
$943$	−20.3382			−0.662302
$944$		0			0
$945$	9.11656	+	15.7903i	0.296562	+	0.513660i
$946$		0			0
$947$	−12.3157	−	21.3314i	−0.400206	−	0.693177i	0.593545	−	0.804801i	$-0.297728\pi$
$947$	−12.3157	−	21.3314i	−0.400206	−	0.693177i	−0.993750	+	0.111624i	$0.964395\pi$
$948$		0			0
$949$	27.9631			0.907721
$950$		0			0
$951$	13.6553			0.442803
$952$		0			0
$953$	20.8042	+	36.0339i	0.673913	+	1.16725i	0.976785	+	0.214220i	$0.0687210\pi$
$953$	20.8042	+	36.0339i	0.673913	+	1.16725i	−0.302873	+	0.953031i	$0.597946\pi$
$954$		0			0
$955$	−11.2403	−	19.4688i	−0.363728	−	0.629995i
$956$		0			0
$957$	32.6183			1.05440
$958$		0			0
$959$	−8.34559	+	14.4550i	−0.269493	+	0.466776i
$960$		0			0
$961$	−28.9517			−0.933927
$962$		0			0
$963$	−1.06760	+	1.84914i	−0.0344029	+	0.0595876i
$964$		0			0
$965$	4.08559	−	7.07645i	0.131520	−	0.227799i
$966$		0			0
$967$	6.72960	+	11.6560i	0.216409	+	0.374832i	0.953708	−	0.300735i	$-0.0972321\pi$
$967$	6.72960	+	11.6560i	0.216409	+	0.374832i	−0.737298	+	0.675567i	$0.763899\pi$
$968$		0			0
$969$	−89.9416	−	16.5221i	−2.88934	−	0.530767i
$970$		0			0
$971$	−23.5036	−	40.7095i	−0.754267	−	1.30643i	−0.945738	−	0.324931i	$-0.894659\pi$
$971$	−23.5036	−	40.7095i	−0.754267	−	1.30643i	0.191470	−	0.981498i	$-0.438674\pi$
$972$		0			0
$973$	22.3027	−	38.6295i	0.714993	−	1.23840i
$974$		0			0
$975$	3.22765	−	5.59045i	0.103367	−	0.179038i
$976$		0			0
$977$	50.5955			1.61869			0.809346	−	0.587332i	$-0.199822\pi$
$977$	50.5955			1.61869			0.809346	+	0.587332i	$0.199822\pi$
$978$		0			0
$979$	−56.4775	+	97.8218i	−1.80503	+	3.12640i
$980$		0			0
$981$	67.8642			2.16674
$982$		0			0
$983$	−4.92144	−	8.52418i	−0.156969	−	0.271879i	0.776805	−	0.629741i	$-0.216839\pi$
$983$	−4.92144	−	8.52418i	−0.156969	−	0.271879i	−0.933774	+	0.357862i	$0.883506\pi$
$984$		0			0
$985$	−7.34758	−	12.7264i	−0.234113	−	0.405496i
$986$		0			0
$987$	−4.37070			−0.139121
$988$		0			0
$989$	7.83723			0.249210
$990$		0			0
$991$	8.27955	+	14.3406i	0.263009	+	0.455544i	0.967040	−	0.254625i	$-0.0819519\pi$
$991$	8.27955	+	14.3406i	0.263009	+	0.455544i	−0.704031	+	0.710169i	$0.748619\pi$
$992$		0			0
$993$	4.78716	+	8.29161i	0.151916	+	0.263126i
$994$		0			0
$995$	−15.6027			−0.494640
$996$		0			0
$997$	−3.51612	+	6.09009i	−0.111357	+	0.192875i	−0.916317	−	0.400453i	$-0.868853\pi$
$997$	−3.51612	+	6.09009i	−0.111357	+	0.192875i	0.804961	+	0.593328i	$0.202186\pi$
$998$		0			0
$999$	−39.5143			−1.25018

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	760.2.q.f.121.4	✓	8
4.3	odd	2		1520.2.q.k.881.1		8
19.11	even	3	inner	760.2.q.f.201.4	yes	8
76.11	odd	6		1520.2.q.k.961.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
760.2.q.f.121.4	✓	8	1.1	even	1	trivial
760.2.q.f.201.4	yes	8	19.11	even	3	inner
1520.2.q.k.881.1		8	4.3	odd	2
1520.2.q.k.961.1		8	76.11	odd	6

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:	\( N \)	\(=\)	\( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	760.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37901 + 2.38851i) q^{3} +(-0.500000 - 0.866025i) q^{5} +4.11474 q^{7} +(-2.30333 + 3.98948i) q^{9} +O(q^{10})\)	\(q+(1.37901 + 2.38851i) q^{3} +(-0.500000 - 0.866025i) q^{5} +4.11474 q^{7} +(-2.30333 + 3.98948i) q^{9} -6.09857 q^{11} +(-1.17028 + 2.02698i) q^{13} +(1.37901 - 2.38851i) q^{15} +(3.80333 + 6.58756i) q^{17} +(1.46155 + 4.10657i) q^{19} +(5.67425 + 9.82810i) q^{21} +(2.98977 - 5.17843i) q^{23} +(-0.500000 + 0.866025i) q^{25} -4.43118 q^{27} +(-0.969629 + 1.67945i) q^{29} -1.43118 q^{31} +(-8.40998 - 14.5665i) q^{33} +(-2.05737 - 3.56347i) q^{35} +8.91733 q^{37} -6.45529 q^{39} +(-1.70065 - 2.94561i) q^{41} +(0.655338 + 1.13508i) q^{43} +4.60665 q^{45} +(-0.192567 + 0.333536i) q^{47} +9.93105 q^{49} +(-10.4896 + 18.1686i) q^{51} +(-0.597970 + 1.03572i) q^{53} +(3.04929 + 5.28152i) q^{55} +(-7.79309 + 9.15391i) q^{57} +(-5.48566 - 9.50145i) q^{59} +(-0.0825396 + 0.142963i) q^{61} +(-9.47758 + 16.4157i) q^{63} +2.34056 q^{65} +(0.848637 - 1.46988i) q^{67} +16.4917 q^{69} +(-4.75679 - 8.23901i) q^{71} +(-5.97360 - 10.3466i) q^{73} -2.75802 q^{75} -25.0940 q^{77} +(3.87563 + 6.71280i) q^{79} +(0.799351 + 1.38452i) q^{81} -3.25570 q^{83} +(3.80333 - 6.58756i) q^{85} -5.34851 q^{87} +(9.26077 - 16.0401i) q^{89} +(-4.81538 + 8.34049i) q^{91} +(-1.97360 - 3.41838i) q^{93} +(2.82562 - 3.31902i) q^{95} +(0.203531 + 0.352527i) q^{97} +(14.0470 - 24.3301i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{3} - 4 q^{5} + 4 q^{7} - q^{9}+O(q^{10}) \) 8 * q + q^3 - 4 * q^5 + 4 * q^7 - q^9	\( 8 q + q^{3} - 4 q^{5} + 4 q^{7} - q^{9} - 8 q^{11} + q^{13} + q^{15} + 13 q^{17} + q^{19} + 12 q^{21} + 8 q^{23} - 4 q^{25} - 20 q^{27} - 3 q^{29} + 4 q^{31} - 15 q^{33} - 2 q^{35} + 20 q^{37} - 2 q^{39} - 8 q^{41} - 3 q^{43} + 2 q^{45} + 10 q^{47} + 12 q^{49} - 16 q^{51} - 11 q^{53} + 4 q^{55} - 29 q^{57} + q^{59} - 25 q^{63} - 2 q^{65} - 8 q^{67} + 22 q^{69} - 4 q^{71} - 20 q^{73} - 2 q^{75} - 36 q^{77} - 3 q^{79} + 12 q^{81} - 30 q^{83} + 13 q^{85} + 24 q^{87} + 17 q^{89} - 4 q^{91} + 12 q^{93} + 4 q^{95} + 11 q^{97} + 30 q^{99}+O(q^{100}) \) 8 * q + q^3 - 4 * q^5 + 4 * q^7 - q^9 - 8 * q^11 + q^13 + q^15 + 13 * q^17 + q^19 + 12 * q^21 + 8 * q^23 - 4 * q^25 - 20 * q^27 - 3 * q^29 + 4 * q^31 - 15 * q^33 - 2 * q^35 + 20 * q^37 - 2 * q^39 - 8 * q^41 - 3 * q^43 + 2 * q^45 + 10 * q^47 + 12 * q^49 - 16 * q^51 - 11 * q^53 + 4 * q^55 - 29 * q^57 + q^59 - 25 * q^63 - 2 * q^65 - 8 * q^67 + 22 * q^69 - 4 * q^71 - 20 * q^73 - 2 * q^75 - 36 * q^77 - 3 * q^79 + 12 * q^81 - 30 * q^83 + 13 * q^85 + 24 * q^87 + 17 * q^89 - 4 * q^91 + 12 * q^93 + 4 * q^95 + 11 * q^97 + 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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