LMFDB - Embedded newform 1040.2.dh.a.529.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1040,2,Mod(289,1040)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1040, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))

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

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

chi := DirichletCharacter("1040.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.dh (of order $6$, degree $2$, not 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:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 8x^{10} + 54x^{8} - 78x^{6} + 92x^{4} - 10x^{2} + 1 $ x^12 - 8x^10 + 54x^8 - 78x^6 + 92x^4 - 10*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.1
Root			$0.286513 - 0.165418i$ of defining polynomial
Character	$\chi$	$=$	1040.529
Dual form			1040.2.dh.a.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.33117 - 1.34590i) q^{3} +(-2.12291 - 0.702335i) q^{5} +(2.90420 - 1.67674i) q^{7} +(2.12291 + 3.67698i) q^{9} +O(q^{10})$	\(q+(-2.33117 - 1.34590i) q^{3} +(-2.12291 - 0.702335i) q^{5} +(2.90420 - 1.67674i) q^{7} +(2.12291 + 3.67698i) q^{9} +(-1.62291 + 2.81095i) q^{11} +(1.21648 + 3.39414i) q^{13} +(4.00358 + 4.49448i) q^{15} +(1.68772 - 0.974404i) q^{17} +(0.622905 + 1.07890i) q^{19} -9.02690 q^{21} +(2.33117 + 1.34590i) q^{23} +(4.01345 + 2.98198i) q^{25} -3.35348i q^{27} +(1.50000 - 2.59808i) q^{29} -3.78109 q^{31} +(7.56654 - 4.36854i) q^{33} +(-7.34297 + 1.51984i) q^{35} +(1.68772 + 0.974404i) q^{37} +(1.73236 - 9.54958i) q^{39} +(-1.39055 + 2.40850i) q^{41} +(7.56654 - 4.36854i) q^{43} +(-1.92426 - 9.29687i) q^{45} -6.86960i q^{47} +(2.12291 - 3.67698i) q^{49} -5.24581 q^{51} -12.8336i q^{53} +(5.41950 - 4.82757i) q^{55} -3.35348i q^{57} +(1.26764 + 2.19562i) q^{59} +(3.74581 + 6.48793i) q^{61} +(12.3307 + 7.11911i) q^{63} +(-0.198649 - 8.05981i) q^{65} +(3.47722 + 2.00758i) q^{67} +(-3.62291 - 6.27506i) q^{69} +(2.62291 + 4.54300i) q^{71} -5.46493i q^{73} +(-5.34259 - 12.3532i) q^{75} +10.8848i q^{77} +13.7811 q^{79} +(1.85526 - 3.21341i) q^{81} -8.61955i q^{83} +(-4.26722 + 0.883225i) q^{85} +(-6.99351 + 4.03771i) q^{87} +(5.15819 - 8.93425i) q^{89} +(9.22398 + 7.81753i) q^{91} +(8.81438 + 5.08898i) q^{93} +(-0.564617 - 2.72790i) q^{95} +(4.56055 - 2.63304i) q^{97} -13.7811 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{5} + 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^5 + 6 * q^9	$ 12 q - 6 q^{5} + 6 q^{9} + 4 q^{15} - 12 q^{19} - 8 q^{21} - 2 q^{25} + 18 q^{29} + 16 q^{31} - 10 q^{35} + 32 q^{39} + 14 q^{41} - 29 q^{45} + 6 q^{49} - 24 q^{51} + 26 q^{55} + 4 q^{59} + 6 q^{61} + 23 q^{65} - 24 q^{69} + 12 q^{71} - 2 q^{75} + 104 q^{79} + 14 q^{81} + 21 q^{85} + 20 q^{89} + 44 q^{91} - 20 q^{95} - 104 q^{99}+O(q^{100}) $ 12 * q - 6 * q^5 + 6 * q^9 + 4 * q^15 - 12 * q^19 - 8 * q^21 - 2 * q^25 + 18 * q^29 + 16 * q^31 - 10 * q^35 + 32 * q^39 + 14 * q^41 - 29 * q^45 + 6 * q^49 - 24 * q^51 + 26 * q^55 + 4 * q^59 + 6 * q^61 + 23 * q^65 - 24 * q^69 + 12 * q^71 - 2 * q^75 + 104 * q^79 + 14 * q^81 + 21 * q^85 + 20 * q^89 + 44 * q^91 - 20 * q^95 - 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−2.33117	−	1.34590i	−1.34590	−	0.777057i	−0.358236	−	0.933631i	$-0.616622\pi$
$3$	−2.33117	−	1.34590i	−1.34590	−	0.777057i	−0.987666	+	0.156574i	$0.949955\pi$
$4$		0			0
$5$	−2.12291	−	0.702335i	−0.949392	−	0.314094i
$5$	−2.12291	−	0.702335i	−0.949392	−	0.314094i
$6$		0			0
$7$	2.90420	−	1.67674i	1.09768	−	0.633748i	0.162072	−	0.986779i	$-0.448182\pi$
$7$	2.90420	−	1.67674i	1.09768	−	0.633748i	0.935611	+	0.353031i	$0.114849\pi$
$8$		0			0
$9$	2.12291	+	3.67698i	0.707635	+	1.22566i
$10$		0			0
$11$	−1.62291	+	2.81095i	−0.489324	+	0.847535i	−0.999925	−	0.0122837i	$-0.996090\pi$
$11$	−1.62291	+	2.81095i	−0.489324	+	0.847535i	0.510600	+	0.859818i	$0.329423\pi$
$12$		0			0
$13$	1.21648	+	3.39414i	0.337391	+	0.941365i
$13$	1.21648	+	3.39414i	0.337391	+	0.941365i
$14$		0			0
$15$	4.00358	+	4.49448i	1.03372	+	1.16047i
$16$		0			0
$17$	1.68772	−	0.974404i	0.409332	−	0.236328i	−0.281171	−	0.959658i	$-0.590723\pi$
$17$	1.68772	−	0.974404i	0.409332	−	0.236328i	0.690503	+	0.723330i	$0.257389\pi$
$18$		0			0
$19$	0.622905	+	1.07890i	0.142904	+	0.247517i	0.928589	−	0.371110i	$-0.121023\pi$
$19$	0.622905	+	1.07890i	0.142904	+	0.247517i	−0.785685	+	0.618627i	$0.787689\pi$
$20$		0			0
$21$	−9.02690			−1.96983
$22$		0			0
$23$	2.33117	+	1.34590i	0.486083	+	0.280640i	0.722948	−	0.690903i	$-0.242787\pi$
$23$	2.33117	+	1.34590i	0.486083	+	0.280640i	−0.236865	+	0.971543i	$0.576120\pi$
$24$		0			0
$25$	4.01345	+	2.98198i	0.802690	+	0.596396i
$26$		0			0
$27$		−	3.35348i		−	0.645377i
$28$		0			0
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	−0.692480	−	0.721437i	$-0.743482\pi$
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	0.971023	+	0.238987i	$0.0768152\pi$
$30$		0			0
$31$	−3.78109			−0.679105			−0.339552	−	0.940587i	$-0.610276\pi$
$31$	−3.78109			−0.679105			−0.339552	+	0.940587i	$0.610276\pi$
$32$		0			0
$33$	7.56654	−	4.36854i	1.31717	−	0.760466i
$34$		0			0
$35$	−7.34297	+	1.51984i	−1.24119	+	0.256900i
$36$		0			0
$37$	1.68772	+	0.974404i	0.277459	+	0.160191i	0.632273	−	0.774746i	$-0.282122\pi$
$37$	1.68772	+	0.974404i	0.277459	+	0.160191i	−0.354813	+	0.934937i	$0.615456\pi$
$38$		0			0
$39$	1.73236	−	9.54958i	0.277399	−	1.52916i
$40$		0			0
$41$	−1.39055	+	2.40850i	−0.217167	+	0.376144i	−0.953941	−	0.299995i	$-0.903015\pi$
$41$	−1.39055	+	2.40850i	−0.217167	+	0.376144i	0.736774	+	0.676139i	$0.236348\pi$
$42$		0			0
$43$	7.56654	−	4.36854i	1.15389	−	0.666197i	0.204055	−	0.978959i	$-0.434588\pi$
$43$	7.56654	−	4.36854i	1.15389	−	0.666197i	0.949831	+	0.312763i	$0.101255\pi$
$44$		0			0
$45$	−1.92426	−	9.29687i	−0.286851	−	1.38590i
$46$		0			0
$47$		−	6.86960i		−	1.00203i	−0.865437	−	0.501017i	$-0.832959\pi$
$47$		−	6.86960i		−	1.00203i	0.865437	−	0.501017i	$-0.167041\pi$
$48$		0			0
$49$	2.12291	−	3.67698i	0.303272	−	0.525283i
$50$		0			0
$51$	−5.24581			−0.734560
$52$		0			0
$53$		−	12.8336i		−	1.76282i	−0.472347	−	0.881412i	$-0.656593\pi$
$53$		−	12.8336i		−	1.76282i	0.472347	−	0.881412i	$-0.343407\pi$
$54$		0			0
$55$	5.41950	−	4.82757i	0.730766	−	0.650949i
$56$		0			0
$57$		−	3.35348i		−	0.444179i
$58$		0			0
$59$	1.26764	+	2.19562i	0.165033	+	0.285845i	0.936667	−	0.350221i	$-0.113894\pi$
$59$	1.26764	+	2.19562i	0.165033	+	0.285845i	−0.771634	+	0.636067i	$0.780560\pi$
$60$		0			0
$61$	3.74581	+	6.48793i	0.479602	+	0.830695i	0.999726	−	0.0233957i	$-0.00744777\pi$
$61$	3.74581	+	6.48793i	0.479602	+	0.830695i	−0.520124	+	0.854090i	$0.674114\pi$
$62$		0			0
$63$	12.3307	+	7.11911i	1.55352	+	0.896924i
$64$		0			0
$65$	−0.198649	−	8.05981i	−0.0246394	−	0.999696i
$66$		0			0
$67$	3.47722	+	2.00758i	0.424810	+	0.245264i	0.697133	−	0.716942i	$-0.254459\pi$
$67$	3.47722	+	2.00758i	0.424810	+	0.245264i	−0.272323	+	0.962206i	$0.587792\pi$
$68$		0			0
$69$	−3.62291	−	6.27506i	−0.436147	−	0.755428i
$70$		0			0
$71$	2.62291	+	4.54300i	0.311282	+	0.539155i	0.978640	−	0.205581i	$-0.0659084\pi$
$71$	2.62291	+	4.54300i	0.311282	+	0.539155i	−0.667359	+	0.744737i	$0.732575\pi$
$72$		0			0
$73$		−	5.46493i		−	0.639622i	−0.947481	−	0.319811i	$-0.896381\pi$
$73$		−	5.46493i		−	0.639622i	0.947481	−	0.319811i	$-0.103619\pi$
$74$		0			0
$75$	−5.34259	−	12.3532i	−0.616909	−	1.42643i
$76$		0			0
$77$			10.8848i			1.24043i
$78$		0			0
$79$	13.7811			1.55049			0.775247	−	0.631658i	$-0.217625\pi$
$79$	13.7811			1.55049			0.775247	+	0.631658i	$0.217625\pi$
$80$		0			0
$81$	1.85526	−	3.21341i	0.206140	−	0.357046i
$82$		0			0
$83$		−	8.61955i		−	0.946119i	−0.881031	−	0.473059i	$-0.843150\pi$
$83$		−	8.61955i		−	0.946119i	0.881031	−	0.473059i	$-0.156850\pi$
$84$		0			0
$85$	−4.26722	+	0.883225i	−0.462845	+	0.0957992i
$86$		0			0
$87$	−6.99351	+	4.03771i	−0.749783	+	0.432888i
$88$		0			0
$89$	5.15819	−	8.93425i	0.546767	−	0.947028i	−0.451726	−	0.892156i	$-0.649192\pi$
$89$	5.15819	−	8.93425i	0.546767	−	0.947028i	0.998493	−	0.0548717i	$-0.0174750\pi$
$90$		0			0
$91$	9.22398	+	7.81753i	0.966936	+	0.819500i
$92$		0			0
$93$	8.81438	+	5.08898i	0.914008	+	0.527703i
$94$		0			0
$95$	−0.564617	−	2.72790i	−0.0579285	−	0.279876i
$96$		0			0
$97$	4.56055	−	2.63304i	0.463054	−	0.267344i	−0.250273	−	0.968175i	$-0.580521\pi$
$97$	4.56055	−	2.63304i	0.463054	−	0.267344i	0.713328	+	0.700831i	$0.247187\pi$
$98$		0			0
$99$	−13.7811			−1.38505
$100$		0			0
$101$	−2.85526	+	4.94546i	−0.284109	+	0.492092i	−0.972393	−	0.233350i	$-0.925031\pi$
$101$	−2.85526	+	4.94546i	−0.284109	+	0.492092i	0.688283	+	0.725442i	$0.258365\pi$
$102$		0			0
$103$			7.36863i			0.726052i	0.931779	+	0.363026i	$0.118256\pi$
$103$			7.36863i			0.726052i	−0.931779	+	0.363026i	$0.881744\pi$
$104$		0			0
$105$	19.1633	+	6.33991i	1.87014	+	0.618712i
$106$		0			0
$107$	−7.42568	−	4.28722i	−0.717868	−	0.414461i	0.0960996	−	0.995372i	$-0.469363\pi$
$107$	−7.42568	−	4.28722i	−0.717868	−	0.414461i	−0.813967	+	0.580911i	$0.802697\pi$
$108$		0			0
$109$	8.49162			0.813350			0.406675	−	0.913573i	$-0.366688\pi$
$109$	8.49162			0.813350			0.406675	+	0.913573i	$0.366688\pi$
$110$		0			0
$111$	−2.62291	−	4.54300i	−0.248955	−	0.431203i
$112$		0			0
$113$	−6.35006	+	3.66621i	−0.597363	+	0.344888i	−0.768004	−	0.640446i	$-0.778750\pi$
$113$	−6.35006	+	3.66621i	−0.597363	+	0.344888i	0.170640	+	0.985333i	$0.445416\pi$
$114$		0			0
$115$	−4.00358	−	4.49448i	−0.373336	−	0.419113i
$116$		0			0
$117$	−9.89771	+	11.6784i	−0.915044	+	1.07967i
$118$		0			0
$119$	3.26764	−	5.65972i	0.299544	−	0.518826i
$120$		0			0
$121$	0.232358	+	0.402456i	0.0211234	+	0.0365869i
$122$		0			0
$123$	6.48321	−	3.74308i	0.584571	−	0.337502i
$124$		0			0
$125$	−6.42583	−	9.14925i	−0.574744	−	0.818333i
$126$		0			0
$127$	7.93599	+	4.58185i	0.704205	+	0.406573i	0.808912	−	0.587930i	$-0.200057\pi$
$127$	7.93599	+	4.58185i	0.704205	+	0.406573i	−0.104707	+	0.994503i	$0.533390\pi$
$128$		0			0
$129$	−23.5185			−2.07069
$130$		0			0
$131$	−10.0000			−0.873704			−0.436852	−	0.899533i	$-0.643907\pi$
$131$	−10.0000			−0.873704			−0.436852	+	0.899533i	$0.643907\pi$
$132$		0			0
$133$	3.61808	+	2.08890i	0.313727	+	0.181130i
$134$		0			0
$135$	−2.35526	+	7.11911i	−0.202709	+	0.612716i
$136$		0			0
$137$	−14.5914	+	8.42435i	−1.24663	+	0.719741i	−0.970435	−	0.241361i	$-0.922406\pi$
$137$	−14.5914	+	8.42435i	−1.24663	+	0.719741i	−0.276193	+	0.961102i	$0.589073\pi$
$138$		0			0
$139$	0.513452	+	0.889325i	0.0435505	+	0.0754316i	0.886979	−	0.461810i	$-0.152800\pi$
$139$	0.513452	+	0.889325i	0.0435505	+	0.0754316i	−0.843429	+	0.537241i	$0.819466\pi$
$140$		0			0
$141$	−9.24581	+	16.0142i	−0.778638	+	1.34864i
$142$		0			0
$143$	−11.5150	−	2.08890i	−0.962933	−	0.174682i
$144$		0			0
$145$	−5.00908	+	4.46197i	−0.415981	+	0.370546i
$146$		0			0
$147$	−9.89771	+	5.71445i	−0.816349	+	0.471319i
$148$		0			0
$149$	7.92583	+	13.7279i	0.649309	+	1.12464i	0.983288	+	0.182056i	$0.0582753\pi$
$149$	7.92583	+	13.7279i	0.649309	+	1.12464i	−0.333979	+	0.942581i	$0.608391\pi$
$150$		0			0
$151$	−14.5454			−1.18369			−0.591845	−	0.806052i	$-0.701600\pi$
$151$	−14.5454			−1.18369			−0.591845	+	0.806052i	$0.701600\pi$
$152$		0			0
$153$	7.16573	+	4.13713i	0.579315	+	0.334468i
$154$		0			0
$155$	8.02690	+	2.65559i	0.644736	+	0.213302i
$156$		0			0
$157$		−	10.9210i		−	0.871588i	−0.900047	−	0.435794i	$-0.856468\pi$
$157$		−	10.9210i		−	0.871588i	0.900047	−	0.435794i	$-0.143532\pi$
$158$		0			0
$159$	−17.2727	+	29.9172i	−1.36982	+	2.37259i
$160$		0			0
$161$	9.02690			0.711420
$162$		0			0
$163$	3.61808	−	2.08890i	0.283390	−	0.163615i	−0.351567	−	0.936163i	$-0.614351\pi$
$163$	3.61808	−	2.08890i	0.283390	−	0.163615i	0.634957	+	0.772547i	$0.281018\pi$
$164$		0			0
$165$	−19.1312	+	3.95976i	−1.48936	+	0.308267i
$166$		0			0
$167$	2.90420	+	1.67674i	0.224733	+	0.129750i	0.608140	−	0.793830i	$-0.291916\pi$
$167$	2.90420	+	1.67674i	0.224733	+	0.129750i	−0.383407	+	0.923580i	$0.625249\pi$
$168$		0			0
$169$	−10.0404	+	8.25780i	−0.772335	+	0.635215i
$170$		0			0
$171$	−2.64474	+	4.58082i	−0.202248	+	0.350304i
$172$		0			0
$173$	7.56654	−	4.36854i	0.575273	−	0.332134i	−0.183979	−	0.982930i	$-0.558898\pi$
$173$	7.56654	−	4.36854i	0.575273	−	0.332134i	0.759253	+	0.650796i	$0.225565\pi$
$174$		0			0
$175$	16.6559	+	1.93074i	1.25906	+	0.145950i
$176$		0			0
$177$		−	6.82449i		−	0.512960i
$178$		0			0
$179$	9.00507	−	15.5972i	0.673071	−	1.16579i	−0.303958	−	0.952685i	$-0.598308\pi$
$179$	9.00507	−	15.5972i	0.673071	−	1.16579i	0.977029	−	0.213107i	$-0.0683584\pi$
$180$		0			0
$181$	1.04366			0.0775749			0.0387875	−	0.999247i	$-0.487650\pi$
$181$	1.04366			0.0775749			0.0387875	+	0.999247i	$0.487650\pi$
$182$		0			0
$183$		−	20.1660i		−	1.49071i
$184$		0			0
$185$	−2.89851	−	3.25391i	−0.213102	−	0.239232i
$186$		0			0
$187$			6.32546i			0.462564i
$188$		0			0
$189$	−5.62291	−	9.73916i	−0.409006	−	0.708419i
$190$		0			0
$191$	12.7593	+	22.0997i	0.923228	+	1.59908i	0.794387	+	0.607412i	$0.207792\pi$
$191$	12.7593	+	22.0997i	0.923228	+	1.59908i	0.128841	+	0.991665i	$0.458874\pi$
$192$		0			0
$193$	17.1652	+	9.91035i	1.23558	+	0.713362i	0.968188	−	0.250225i	$-0.0805047\pi$
$193$	17.1652	+	9.91035i	1.23558	+	0.713362i	0.267392	+	0.963588i	$0.413838\pi$
$194$		0			0
$195$	−10.3846	+	19.0562i	−0.743659	+	1.36464i
$196$		0			0
$197$	18.7512	+	10.8260i	1.33596	+	0.771319i	0.986206	−	0.165521i	$-0.0529304\pi$
$197$	18.7512	+	10.8260i	1.33596	+	0.771319i	0.349758	+	0.936840i	$0.386264\pi$
$198$		0			0
$199$	−9.11453	−	15.7868i	−0.646112	−	1.11910i	−0.984044	−	0.177928i	$-0.943061\pi$
$199$	−9.11453	−	15.7868i	−0.646112	−	1.11910i	0.337932	−	0.941171i	$-0.390273\pi$
$200$		0			0
$201$	−5.40400	−	9.36000i	−0.381169	−	0.660204i
$202$		0			0
$203$		−	10.0604i		−	0.706104i
$204$		0			0
$205$	4.64357	−	4.13638i	0.324321	−	0.288898i
$206$		0			0
$207$			11.4289i			0.794363i
$208$		0			0
$209$	−4.04366			−0.279706
$210$		0			0
$211$	9.64981	−	16.7140i	0.664320	−	1.15064i	−0.315149	−	0.949042i	$-0.602054\pi$
$211$	9.64981	−	16.7140i	0.664320	−	1.15064i	0.979469	−	0.201594i	$-0.0646122\pi$
$212$		0			0
$213$		−	14.1207i		−	0.967534i
$214$		0			0
$215$	−19.1312	+	3.95976i	−1.30474	+	0.270053i
$216$		0			0
$217$	−10.9810	+	6.33991i	−0.745442	+	0.430381i
$218$		0			0
$219$	−7.35526	+	12.7397i	−0.497023	+	0.860868i
$220$		0			0
$221$	5.36034	+	4.54300i	0.360575	+	0.305596i
$222$		0			0
$223$	10.7134	+	6.18537i	0.717421	+	0.414203i	0.813803	−	0.581141i	$-0.197394\pi$
$223$	10.7134	+	6.18537i	0.717421	+	0.414203i	−0.0963818	+	0.995344i	$0.530727\pi$
$224$		0			0
$225$	−2.44450	+	21.0878i	−0.162967	+	1.40586i
$226$		0			0
$227$	−5.33715	+	3.08141i	−0.354239	+	0.204520i	−0.666551	−	0.745460i	$-0.732230\pi$
$227$	−5.33715	+	3.08141i	−0.354239	+	0.204520i	0.312311	+	0.949980i	$0.398897\pi$
$228$		0			0
$229$	26.9832			1.78310			0.891551	−	0.452920i	$-0.149618\pi$
$229$	26.9832			1.78310			0.891551	+	0.452920i	$0.149618\pi$
$230$		0			0
$231$	14.6498	−	25.3742i	0.963887	−	1.66950i
$232$		0			0
$233$			0.824319i			0.0540029i	0.999635	+	0.0270015i	$0.00859588\pi$
$233$			0.824319i			0.0540029i	−0.999635	+	0.0270015i	$0.991404\pi$
$234$		0			0
$235$	−4.82476	+	14.5835i	−0.314733	+	0.951323i
$236$		0			0
$237$	−32.1261	−	18.5480i	−2.08681	−	1.20482i
$238$		0			0
$239$	4.00000			0.258738			0.129369	−	0.991596i	$-0.458705\pi$
$239$	4.00000			0.258738			0.129369	+	0.991596i	$0.458705\pi$
$240$		0			0
$241$	−11.3469	−	19.6534i	−0.730917	−	1.26599i	−0.956492	−	0.291760i	$-0.905759\pi$
$241$	−11.3469	−	19.6534i	−0.730917	−	1.26599i	0.225575	−	0.974226i	$-0.427574\pi$
$242$		0			0
$243$	−17.3625	+	10.0242i	−1.11380	+	0.643054i
$244$		0			0
$245$	−7.08920	+	6.31489i	−0.452912	+	0.403443i
$246$		0			0
$247$	−2.90420	+	3.42669i	−0.184790	+	0.218035i
$248$		0			0
$249$	−11.6011	+	20.0936i	−0.735188	+	1.27338i
$250$		0			0
$251$	9.51345	+	16.4778i	0.600484	+	1.04007i	0.992748	+	0.120216i	$0.0383586\pi$
$251$	9.51345	+	16.4778i	0.600484	+	1.04007i	−0.392264	+	0.919853i	$0.628308\pi$
$252$		0			0
$253$	−7.56654	+	4.36854i	−0.475704	+	0.274648i
$254$		0			0
$255$	11.1364	+	3.68431i	0.697386	+	0.230721i
$256$		0			0
$257$	−1.82857	−	1.05573i	−0.114063	−	0.0658544i	0.441883	−	0.897073i	$-0.354311\pi$
$257$	−1.82857	−	1.05573i	−0.114063	−	0.0658544i	−0.555946	+	0.831218i	$0.687644\pi$
$258$		0			0
$259$	6.53528			0.406083
$260$		0			0
$261$	12.7374			0.788427
$262$		0			0
$263$	25.9092	+	14.9587i	1.59763	+	0.922391i	0.991943	+	0.126687i	$0.0404343\pi$
$263$	25.9092	+	14.9587i	1.59763	+	0.922391i	0.605685	+	0.795704i	$0.292899\pi$
$264$		0			0
$265$	−9.01345	+	27.2444i	−0.553692	+	1.67361i
$266$		0			0
$267$	−24.0492	+	13.8848i	−1.47179	+	0.849738i
$268$		0			0
$269$	9.29455	+	16.0986i	0.566699	+	0.981551i	0.996889	+	0.0788127i	$0.0251129\pi$
$269$	9.29455	+	16.0986i	0.566699	+	0.981551i	−0.430191	+	0.902738i	$0.641554\pi$
$270$		0			0
$271$	2.91238	−	5.04439i	0.176914	−	0.306425i	−0.763908	−	0.645326i	$-0.776722\pi$
$271$	2.91238	−	5.04439i	0.176914	−	0.306425i	0.940822	+	0.338901i	$0.110055\pi$
$272$		0			0
$273$	−10.9810	−	30.6386i	−0.664603	−	1.85433i
$274$		0			0
$275$	−14.8957	+	6.44216i	−0.898242	+	0.388477i
$276$		0			0
$277$	11.7263	−	6.77017i	0.704564	−	0.406780i	−0.104481	−	0.994527i	$-0.533318\pi$
$277$	11.7263	−	6.77017i	0.704564	−	0.406780i	0.809045	+	0.587747i	$0.199985\pi$
$278$		0			0
$279$	−8.02690	−	13.9030i	−0.480558	−	0.832351i
$280$		0			0
$281$	−0.464716			−0.0277226			−0.0138613	−	0.999904i	$-0.504412\pi$
$281$	−0.464716			−0.0277226			−0.0138613	+	0.999904i	$0.504412\pi$
$282$		0			0
$283$	−8.71259	−	5.03022i	−0.517910	−	0.299015i	0.218169	−	0.975911i	$-0.429991\pi$
$283$	−8.71259	−	5.03022i	−0.517910	−	0.299015i	−0.736079	+	0.676896i	$0.763325\pi$
$284$		0			0
$285$	−2.35526	+	7.11911i	−0.139514	+	0.421700i
$286$		0			0
$287$			9.32634i			0.550516i
$288$		0			0
$289$	−6.60107	+	11.4334i	−0.388298	+	0.672553i
$290$		0			0
$291$	−14.1752			−0.830967
$292$		0			0
$293$	−11.6481	+	6.72506i	−0.680492	+	0.392882i	−0.800040	−	0.599946i	$-0.795189\pi$
$293$	−11.6481	+	6.72506i	−0.680492	+	0.392882i	0.119548	+	0.992828i	$0.461855\pi$
$294$		0			0
$295$	−1.14902	−	5.55140i	−0.0668987	−	0.323215i
$296$		0			0
$297$	9.42647	+	5.44238i	0.546979	+	0.315799i
$298$		0			0
$299$	−1.73236	+	9.54958i	−0.100185	+	0.552266i
$300$		0			0
$301$	14.6498	−	25.3742i	0.844401	−	1.46255i
$302$		0			0
$303$	13.3122	−	7.68581i	0.764767	−	0.441538i
$304$		0			0
$305$	−3.39530	−	16.4041i	−0.194414	−	0.939295i
$306$		0			0
$307$		−	24.6077i		−	1.40444i	−0.711961	−	0.702219i	$-0.752193\pi$
$307$		−	24.6077i		−	1.40444i	0.711961	−	0.702219i	$-0.247807\pi$
$308$		0			0
$309$	9.91745	−	17.1775i	0.564184	−	0.977196i
$310$		0			0
$311$	−2.43781			−0.138236			−0.0691178	−	0.997609i	$-0.522018\pi$
$311$	−2.43781			−0.138236			−0.0691178	+	0.997609i	$0.522018\pi$
$312$		0			0
$313$			19.2965i			1.09071i	0.838207	+	0.545353i	$0.183604\pi$
$313$			19.2965i			1.09071i	−0.838207	+	0.545353i	$0.816396\pi$
$314$		0			0
$315$	−21.1768	−	23.7735i	−1.19318	−	1.33948i
$316$		0			0
$317$		−	28.8217i		−	1.61879i	−0.587265	−	0.809395i	$-0.699795\pi$
$317$		−	28.8217i		−	1.61879i	0.587265	−	0.809395i	$-0.300205\pi$
$318$		0			0
$319$	4.86872	+	8.43286i	0.272596	+	0.472150i
$320$		0			0
$321$	11.5404	+	19.9885i	0.644120	+	1.11565i
$322$		0			0
$323$	2.10258	+	1.21392i	0.116990	+	0.0675445i
$324$		0			0
$325$	−5.23897	+	17.2497i	−0.290606	+	0.956843i
$326$		0			0
$327$	−19.7954	−	11.4289i	−1.09469	−	0.632019i
$328$		0			0
$329$	−11.5185	−	19.9507i	−0.635037	−	1.09992i
$330$		0			0
$331$	−1.48655	−	2.57478i	−0.0817081	−	0.141522i	0.822276	−	0.569089i	$-0.192704\pi$
$331$	−1.48655	−	2.57478i	−0.0817081	−	0.141522i	−0.903984	+	0.427567i	$0.859371\pi$
$332$		0			0
$333$			8.27427i			0.453427i
$334$		0			0
$335$	−5.97182	−	6.70407i	−0.326276	−	0.366282i
$336$		0			0
$337$			1.90370i			0.103701i	0.998655	+	0.0518505i	$0.0165119\pi$
$337$			1.90370i			0.103701i	−0.998655	+	0.0518505i	$0.983488\pi$
$338$		0			0
$339$	19.7374			1.07199
$340$		0			0
$341$	6.13636	−	10.6285i	0.332302	−	0.575565i
$342$		0			0
$343$			9.23611i			0.498703i
$344$		0			0
$345$	3.28390	+	15.8658i	0.176799	+	0.854188i
$346$		0			0
$347$	10.9420	−	6.31735i	0.587396	−	0.339133i	−0.176671	−	0.984270i	$-0.556533\pi$
$347$	10.9420	−	6.31735i	0.587396	−	0.339133i	0.764067	+	0.645137i	$0.223200\pi$
$348$		0			0
$349$	4.48655	−	7.77093i	0.240159	−	0.415968i	−0.720600	−	0.693351i	$-0.756134\pi$
$349$	4.48655	−	7.77093i	0.240159	−	0.415968i	0.960760	+	0.277383i	$0.0894670\pi$
$350$		0			0
$351$	11.3822	−	4.07944i	0.607535	−	0.217744i
$352$		0			0
$353$	−29.6618	−	17.1252i	−1.57874	−	0.911484i	−0.995036	−	0.0995150i	$-0.968271\pi$
$353$	−29.6618	−	17.1252i	−1.57874	−	0.911484i	−0.583701	−	0.811969i	$-0.698396\pi$
$354$		0			0
$355$	−2.37747	−	11.4865i	−0.126183	−	0.609641i
$356$		0			0
$357$	−15.2349	+	8.79585i	−0.806315	+	0.465526i
$358$		0			0
$359$	22.4043			1.18245			0.591227	−	0.806505i	$-0.298644\pi$
$359$	22.4043			1.18245			0.591227	+	0.806505i	$0.298644\pi$
$360$		0			0
$361$	8.72398	−	15.1104i	0.459157	−	0.795283i
$362$		0			0
$363$		−	1.25092i		−	0.0656565i
$364$		0			0
$365$	−3.83821	+	11.6015i	−0.200901	+	0.607252i
$366$		0			0
$367$	−11.4273	−	6.59753i	−0.596498	−	0.344388i	0.171165	−	0.985242i	$-0.445247\pi$
$367$	−11.4273	−	6.59753i	−0.596498	−	0.344388i	−0.767663	+	0.640854i	$0.778580\pi$
$368$		0			0
$369$	−11.8080			−0.614700
$370$		0			0
$371$	−21.5185	−	37.2712i	−1.11719	−	1.93502i
$372$		0			0
$373$	13.2168	−	7.63070i	0.684338	−	0.395103i	−0.117149	−	0.993114i	$-0.537376\pi$
$373$	13.2168	−	7.63070i	0.684338	−	0.395103i	0.801488	+	0.598012i	$0.204042\pi$
$374$		0			0
$375$	2.66572	+	29.9770i	0.137657	+	1.54801i
$376$		0			0
$377$	10.6430	+	1.93070i	0.548140	+	0.0994362i
$378$		0			0
$379$	−9.11453	+	15.7868i	−0.468182	+	0.810915i	−0.999339	−	0.0363588i	$-0.988424\pi$
$379$	−9.11453	+	15.7868i	−0.468182	+	0.810915i	0.531157	+	0.847273i	$0.321757\pi$
$380$		0			0
$381$	−12.3334	−	21.3621i	−0.631861	−	1.09442i
$382$		0			0
$383$	1.24784	−	0.720440i	0.0637616	−	0.0368128i	−0.467780	−	0.883845i	$-0.654946\pi$
$383$	1.24784	−	0.720440i	0.0637616	−	0.0368128i	0.531542	+	0.847032i	$0.321613\pi$
$384$		0			0
$385$	7.64474	−	23.1073i	0.389612	−	1.17766i
$386$		0			0
$387$	32.1261	+	18.5480i	1.63306	+	0.942848i
$388$		0			0
$389$	18.7912			0.952754			0.476377	−	0.879241i	$-0.341950\pi$
$389$	18.7912			0.952754			0.476377	+	0.879241i	$0.341950\pi$
$390$		0			0
$391$	5.24581			0.265292
$392$		0			0
$393$	23.3117	+	13.4590i	1.17592	+	0.678918i
$394$		0			0
$395$	−29.2560	−	9.67894i	−1.47203	−	0.487000i
$396$		0			0
$397$	−14.8027	+	8.54634i	−0.742926	+	0.428928i	−0.823132	−	0.567850i	$-0.807775\pi$
$397$	−14.8027	+	8.54634i	−0.742926	+	0.428928i	0.0802063	+	0.996778i	$0.474442\pi$
$398$		0			0
$399$	−5.62291	−	9.73916i	−0.281497	−	0.487568i
$400$		0			0
$401$	−11.1011	+	19.2276i	−0.554361	+	0.960182i	0.443592	+	0.896229i	$0.353704\pi$
$401$	−11.1011	+	19.2276i	−0.554361	+	0.960182i	−0.997953	+	0.0639527i	$0.979629\pi$
$402$		0			0
$403$	−4.59962	−	12.8336i	−0.229124	−	0.639285i
$404$		0			0
$405$	−6.19544	+	5.51875i	−0.307854	+	0.274229i
$406$		0			0
$407$	−5.47801	+	3.16273i	−0.271535	+	0.156771i
$408$		0			0
$409$	−4.81638	−	8.34221i	−0.238155	−	0.412496i	0.722030	−	0.691862i	$-0.243209\pi$
$409$	−4.81638	−	8.34221i	−0.238155	−	0.412496i	−0.960185	+	0.279366i	$0.909876\pi$
$410$		0			0
$411$	45.3534			2.23712
$412$		0			0
$413$	7.36296	+	4.25101i	0.362308	+	0.209178i
$414$		0			0
$415$	−6.05381	+	18.2985i	−0.297170	+	0.898238i
$416$		0			0
$417$		−	2.76423i		−	0.135365i
$418$		0			0
$419$	0.978168	−	1.69424i	0.0477866	−	0.0827689i	−0.841143	−	0.540813i	$-0.818117\pi$
$419$	0.978168	−	1.69424i	0.0477866	−	0.0827689i	0.888929	+	0.458044i	$0.151450\pi$
$420$		0			0
$421$	−12.0807			−0.588778			−0.294389	−	0.955686i	$-0.595116\pi$
$421$	−12.0807			−0.588778			−0.294389	+	0.955686i	$0.595116\pi$
$422$		0			0
$423$	25.2594	−	14.5835i	1.22815	−	0.709075i
$424$		0			0
$425$	9.67923	+	1.12201i	0.469511	+	0.0544257i
$426$		0			0
$427$	21.7571	+	12.5615i	1.05290	+	0.607893i
$428$		0			0
$429$	24.0320	+	20.3676i	1.16027	+	0.983359i
$430$		0			0
$431$	12.2945	−	21.2948i	0.592207	−	1.02573i	−0.401727	−	0.915759i	$-0.631590\pi$
$431$	12.2945	−	21.2948i	0.592207	−	1.02573i	0.993934	−	0.109974i	$-0.0350767\pi$
$432$		0			0
$433$	31.2400	−	18.0364i	1.50130	−	0.866775i	0.501299	−	0.865274i	$-0.332856\pi$
$433$	31.2400	−	18.0364i	1.50130	−	0.866775i	0.999999	−	0.00150085i	$-0.000477735\pi$
$434$		0			0
$435$	17.6824	−	3.65988i	0.847805	−	0.175478i
$436$		0			0
$437$			3.35348i			0.160419i
$438$		0			0
$439$	−1.26764	+	2.19562i	−0.0605013	+	0.104791i	−0.894690	−	0.446688i	$-0.852603\pi$
$439$	−1.26764	+	2.19562i	−0.0605013	+	0.104791i	0.834188	+	0.551480i	$0.185937\pi$
$440$		0			0
$441$	18.0269			0.858424
$442$		0			0
$443$		−	19.3579i		−	0.919721i	−0.887991	−	0.459860i	$-0.847899\pi$
$443$		−	19.3579i		−	0.919721i	0.887991	−	0.459860i	$-0.152101\pi$
$444$		0			0
$445$	−17.2252	+	15.3438i	−0.816552	+	0.727365i
$446$		0			0
$447$		−	42.6696i		−	2.01820i
$448$		0			0
$449$	−12.4040	−	21.4844i	−0.585381	−	1.01391i	−0.994828	−	0.101576i	$-0.967612\pi$
$449$	−12.4040	−	21.4844i	−0.585381	−	1.01391i	0.409447	−	0.912334i	$-0.365722\pi$
$450$		0			0
$451$	−4.51345	−	7.81753i	−0.212530	−	0.368113i
$452$		0			0
$453$	33.9079	+	19.5767i	1.59313	+	0.919795i
$454$		0			0
$455$	−14.0911	−	23.0742i	−0.660601	−	1.08173i
$456$		0			0
$457$	−6.55363	−	3.78374i	−0.306566	−	0.176996i	0.338823	−	0.940850i	$-0.389971\pi$
$457$	−6.55363	−	3.78374i	−0.306566	−	0.176996i	−0.645389	+	0.763854i	$0.723305\pi$
$458$		0			0
$459$	−3.26764	−	5.65972i	−0.152520	−	0.264173i
$460$		0			0
$461$	6.17164	+	10.6896i	0.287442	+	0.497864i	0.973198	−	0.229967i	$-0.0738618\pi$
$461$	6.17164	+	10.6896i	0.287442	+	0.497864i	−0.685756	+	0.727831i	$0.740528\pi$
$462$		0			0
$463$			22.8578i			1.06229i	0.847281	+	0.531146i	$0.178238\pi$
$463$			22.8578i			1.06229i	−0.847281	+	0.531146i	$0.821762\pi$
$464$		0			0
$465$	−15.1379	−	16.9941i	−0.702004	−	0.788081i
$466$		0			0
$467$			15.2976i			0.707889i	0.935266	+	0.353945i	$0.115160\pi$
$467$			15.2976i			0.707889i	−0.935266	+	0.353945i	$0.884840\pi$
$468$		0			0
$469$	13.4647			0.621743
$470$		0			0
$471$	−14.6985	+	25.4586i	−0.677273	+	1.17307i
$472$		0			0
$473$			28.3589i			1.30394i
$474$		0			0
$475$	−0.717267	+	6.18762i	−0.0329105	+	0.283907i
$476$		0			0
$477$	47.1887	−	27.2444i	2.16062	−	1.24744i
$478$		0			0
$479$	−12.1414	+	21.0296i	−0.554756	+	0.960866i	0.443166	+	0.896439i	$0.353855\pi$
$479$	−12.1414	+	21.0296i	−0.554756	+	0.960866i	−0.997922	+	0.0644264i	$0.979478\pi$
$480$		0			0
$481$	−1.25419	+	6.91369i	−0.0571861	+	0.315237i
$482$		0			0
$483$	−21.0433	−	12.1493i	−0.957501	−	0.552814i
$484$		0			0
$485$	−11.5309	+	2.38665i	−0.523591	+	0.108372i
$486$		0			0
$487$	−31.9462	+	18.4441i	−1.44762	+	0.835783i	−0.998339	−	0.0576081i	$-0.981653\pi$
$487$	−31.9462	+	18.4441i	−1.44762	+	0.835783i	−0.449280	+	0.893391i	$0.648319\pi$
$488$		0			0
$489$	−11.2458			−0.508553
$490$		0			0
$491$	−17.6767	+	30.6170i	−0.797739	+	1.38172i	0.123346	+	0.992364i	$0.460637\pi$
$491$	−17.6767	+	30.6170i	−0.797739	+	1.38172i	−0.921085	+	0.389361i	$0.872696\pi$
$492$		0			0
$493$		−	5.84642i		−	0.263310i
$494$		0			0
$495$	29.2560	+	9.67894i	1.31496	+	0.435036i
$496$		0			0
$497$	15.2349	+	8.79585i	0.683377	+	0.394548i
$498$		0			0
$499$	16.2189			0.726058			0.363029	−	0.931778i	$-0.381743\pi$
$499$	16.2189			0.726058			0.363029	+	0.931778i	$0.381743\pi$
$500$		0			0
$501$	−4.51345	−	7.81753i	−0.201646	−	0.349261i
$502$		0			0
$503$	17.5270	−	10.1192i	0.781489	−	0.451193i	−0.0554688	−	0.998460i	$-0.517665\pi$
$503$	17.5270	−	10.1192i	0.781489	−	0.451193i	0.836958	+	0.547268i	$0.184332\pi$
$504$		0			0
$505$	9.53482	−	8.49339i	0.424294	−	0.377951i
$506$		0			0
$507$	34.5200	−	5.73700i	1.53309	−	0.254789i
$508$		0			0
$509$	−10.0185	+	17.3526i	−0.444063	+	0.769140i	−0.997986	−	0.0634276i	$-0.979797\pi$
$509$	−10.0185	+	17.3526i	−0.444063	+	0.769140i	0.553923	+	0.832568i	$0.313130\pi$
$510$		0			0
$511$	−9.16326	−	15.8712i	−0.405359	−	0.702102i
$512$		0			0
$513$	3.61808	−	2.08890i	0.159742	−	0.0922271i
$514$		0			0
$515$	5.17524	−	15.6429i	0.228048	−	0.689308i
$516$		0			0
$517$	19.3101	+	11.1487i	0.849259	+	0.490320i
$518$		0			0
$519$	−23.5185			−1.03235
$520$		0			0
$521$	16.0269			0.702151			0.351076	−	0.936347i	$-0.385816\pi$
$521$	16.0269			0.702151			0.351076	+	0.936347i	$0.385816\pi$
$522$		0			0
$523$	10.1654	+	5.86898i	0.444501	+	0.256633i	0.705505	−	0.708705i	$-0.250720\pi$
$523$	10.1654	+	5.86898i	0.444501	+	0.256633i	−0.261004	+	0.965338i	$0.584054\pi$
$524$		0			0
$525$	−36.2291	−	26.9180i	−1.58117	−	1.17480i
$526$		0			0
$527$	−6.38142	+	3.68431i	−0.277979	+	0.160491i
$528$		0			0
$529$	−7.87709	−	13.6435i	−0.342482	−	0.593197i
$530$		0			0
$531$	−5.38217	+	9.32219i	−0.233566	+	0.404548i
$532$		0			0
$533$	−9.86635	−	1.78982i	−0.427359	−	0.0775258i
$534$		0			0
$535$	12.7530	+	14.3167i	0.551358	+	0.618964i
$536$		0			0
$537$	−41.9847	+	24.2399i	−1.81177	+	1.04603i
$538$		0			0
$539$	6.89055	+	11.9348i	0.296797	+	0.514067i
$540$		0			0
$541$	−21.8080			−0.937599			−0.468800	−	0.883305i	$-0.655313\pi$
$541$	−21.8080			−0.937599			−0.468800	+	0.883305i	$0.655313\pi$
$542$		0			0
$543$	−2.43296	−	1.40467i	−0.104408	−	0.0602801i
$544$		0			0
$545$	−18.0269	−	5.96396i	−0.772188	−	0.255468i
$546$		0			0
$547$			6.30924i			0.269764i	0.990862	+	0.134882i	$0.0430655\pi$
$547$			6.30924i			0.269764i	−0.990862	+	0.134882i	$0.956935\pi$
$548$		0			0
$549$	−15.9040	+	27.5465i	−0.678766	+	1.17566i
$550$		0			0
$551$	3.73743			0.159220
$552$		0			0
$553$	40.0230	−	23.1073i	1.70195	−	0.982622i
$554$		0			0
$555$	2.37747	+	11.4865i	0.100918	+	0.487576i
$556$		0			0
$557$	−31.0364	−	17.9189i	−1.31506	−	0.759247i	−0.332126	−	0.943235i	$-0.607766\pi$
$557$	−31.0364	−	17.9189i	−1.31506	−	0.759247i	−0.982929	+	0.183987i	$0.941099\pi$
$558$		0			0
$559$	24.0320	+	20.3676i	1.01644	+	0.861459i
$560$		0			0
$561$	8.51345	−	14.7457i	0.359438	−	0.622565i
$562$		0			0
$563$	4.33196	−	2.50106i	0.182570	−	0.105407i	−0.405929	−	0.913904i	$-0.633052\pi$
$563$	4.33196	−	2.50106i	0.182570	−	0.105407i	0.588500	+	0.808497i	$0.299719\pi$
$564$		0			0
$565$	16.0555	−	3.32315i	0.675459	−	0.139806i
$566$		0			0
$567$		−	12.4432i		−	0.522564i
$568$		0			0
$569$	−6.58402	+	11.4039i	−0.276017	+	0.478075i	−0.970391	−	0.241539i	$-0.922348\pi$
$569$	−6.58402	+	11.4039i	−0.276017	+	0.478075i	0.694375	+	0.719614i	$0.255681\pi$
$570$		0			0
$571$	−19.8349			−0.830065			−0.415032	−	0.909807i	$-0.636230\pi$
$571$	−19.8349			−0.830065			−0.415032	+	0.909807i	$0.636230\pi$
$572$		0			0
$573$		−	68.6909i		−	2.86960i
$574$		0			0
$575$	5.34259	+	12.3532i	0.222801	+	0.515165i
$576$		0			0
$577$			10.9210i			0.454646i	0.973819	+	0.227323i	$0.0729972\pi$
$577$			10.9210i			0.454646i	−0.973819	+	0.227323i	$0.927003\pi$
$578$		0			0
$579$	−26.6767	−	46.2054i	−1.10865	−	1.92023i
$580$		0			0
$581$	−14.4527	−	25.0329i	−0.599601	−	1.03854i
$582$		0			0
$583$	36.0745	+	20.8276i	1.49406	+	0.862593i
$584$		0			0
$585$	29.2140	−	17.8406i	1.20785	−	0.737620i
$586$		0			0
$587$	35.0303	+	20.2247i	1.44585	+	0.834764i	0.998231	−	0.0594576i	$-0.0189371\pi$
$587$	35.0303	+	20.2247i	1.44585	+	0.834764i	0.447624	+	0.894222i	$0.352270\pi$
$588$		0			0
$589$	−2.35526	−	4.07944i	−0.0970469	−	0.168090i
$590$		0			0
$591$	−29.1414	−	50.4744i	−1.19872	−	2.07624i
$592$		0			0
$593$		−	1.47709i		−	0.0606569i	−0.999540	−	0.0303284i	$-0.990345\pi$
$593$		−	1.47709i		−	0.0606569i	0.999540	−	0.0303284i	$-0.00965532\pi$
$594$		0			0
$595$	−10.9119	+	9.72008i	−0.447345	+	0.398484i
$596$		0			0
$597$			49.0690i			2.00826i
$598$		0			0
$599$	2.27271			0.0928606			0.0464303	−	0.998922i	$-0.485215\pi$
$599$	2.27271			0.0928606			0.0464303	+	0.998922i	$0.485215\pi$
$600$		0			0
$601$	−3.70215	+	6.41231i	−0.151014	+	0.261563i	−0.931600	−	0.363484i	$-0.881587\pi$
$601$	−3.70215	+	6.41231i	−0.151014	+	0.261563i	0.780587	+	0.625048i	$0.214920\pi$
$602$		0			0
$603$			17.0476i			0.694231i
$604$		0			0
$605$	−0.210615	−	1.01757i	−0.00856273	−	0.0413700i
$606$		0			0
$607$	9.26059	−	5.34661i	0.375876	−	0.217012i	−0.300146	−	0.953893i	$-0.597036\pi$
$607$	9.26059	−	5.34661i	0.375876	−	0.217012i	0.676022	+	0.736881i	$0.263702\pi$
$608$		0			0
$609$	−13.5404	+	23.4526i	−0.548683	+	0.950347i
$610$		0			0
$611$	23.3164	−	8.35673i	0.943280	−	0.338077i
$612$		0			0
$613$	5.26673	+	3.04075i	0.212721	+	0.122815i	0.602575	−	0.798062i	$-0.294141\pi$
$613$	5.26673	+	3.04075i	0.212721	+	0.122815i	−0.389854	+	0.920877i	$0.627475\pi$
$614$		0			0
$615$	−16.3921	+	3.39283i	−0.660994	+	0.136812i
$616$		0			0
$617$	27.5732	−	15.9194i	1.11006	−	0.640892i	0.171213	−	0.985234i	$-0.445231\pi$
$617$	27.5732	−	15.9194i	1.11006	−	0.640892i	0.938844	+	0.344342i	$0.111898\pi$
$618$		0			0
$619$	−26.4043			−1.06128			−0.530639	−	0.847598i	$-0.678048\pi$
$619$	−26.4043			−1.06128			−0.530639	+	0.847598i	$0.678048\pi$
$620$		0			0
$621$	4.51345	−	7.81753i	0.181119	−	0.313707i
$622$		0			0
$623$		−	34.5957i		−	1.38605i
$624$		0			0
$625$	7.21560	+	23.9361i	0.288624	+	0.957443i
$626$		0			0
$627$	9.42647	+	5.44238i	0.376457	+	0.217348i
$628$		0			0
$629$	3.79785			0.151430
$630$		0			0
$631$	17.5840	+	30.4564i	0.700009	+	1.21245i	0.968463	+	0.249158i	$0.0801539\pi$
$631$	17.5840	+	30.4564i	0.700009	+	1.21245i	−0.268454	+	0.963293i	$0.586513\pi$
$632$		0			0
$633$	−44.9907	+	25.9754i	−1.78822	+	1.03243i
$634$		0			0
$635$	−13.6294	−	15.3005i	−0.540865	−	0.607184i
$636$		0			0
$637$	15.0626	+	2.73247i	0.596804	+	0.108264i
$638$		0			0
$639$	−11.1364	+	19.2887i	−0.440547	+	0.763051i
$640$		0			0
$641$	−2.76257	−	4.78491i	−0.109115	−	0.188993i	0.806297	−	0.591511i	$-0.201468\pi$
$641$	−2.76257	−	4.78491i	−0.109115	−	0.188993i	−0.915412	+	0.402518i	$0.868135\pi$
$642$		0			0
$643$	−27.8472	+	16.0776i	−1.09819	+	0.634039i	−0.935744	−	0.352679i	$-0.885271\pi$
$643$	−27.8472	+	16.0776i	−1.09819	+	0.634039i	−0.162444	+	0.986718i	$0.551938\pi$
$644$		0			0
$645$	49.9276	+	16.5179i	1.96590	+	0.650391i
$646$		0			0
$647$	−11.9376	−	6.89216i	−0.469314	−	0.270959i	0.246638	−	0.969108i	$-0.420674\pi$
$647$	−11.9376	−	6.89216i	−0.469314	−	0.270959i	−0.715953	+	0.698149i	$0.754007\pi$
$648$		0			0
$649$	−8.22905			−0.323019
$650$		0			0
$651$	34.1316			1.33772
$652$		0			0
$653$	7.36296	+	4.25101i	0.288135	+	0.166355i	0.637100	−	0.770781i	$-0.280134\pi$
$653$	7.36296	+	4.25101i	0.288135	+	0.166355i	−0.348965	+	0.937136i	$0.613467\pi$
$654$		0			0
$655$	21.2291	+	7.02335i	0.829488	+	0.274425i
$656$		0			0
$657$	20.0944	−	11.6015i	0.783959	−	0.452619i
$658$		0			0
$659$	−2.02183	−	3.50192i	−0.0787594	−	0.136415i	0.823956	−	0.566654i	$-0.191763\pi$
$659$	−2.02183	−	3.50192i	−0.0787594	−	0.136415i	−0.902715	+	0.430239i	$0.858429\pi$
$660$		0			0
$661$	−15.6364	+	27.0830i	−0.608184	+	1.05341i	0.383356	+	0.923601i	$0.374768\pi$
$661$	−15.6364	+	27.0830i	−0.608184	+	1.05341i	−0.991540	+	0.129805i	$0.958565\pi$
$662$		0			0
$663$	−6.38142	−	17.8050i	−0.247834	−	0.691489i
$664$		0			0
$665$	−6.21373	−	6.97563i	−0.240958	−	0.270503i
$666$		0			0
$667$	6.99351	−	4.03771i	0.270790	−	0.156341i
$668$		0			0
$669$	−16.6498	−	28.8383i	−0.643719	−	1.11495i
$670$		0			0
$671$	−24.3164			−0.938723
$672$		0			0
$673$	−27.7768	−	16.0370i	−1.07072	−	0.618179i	−0.142340	−	0.989818i	$-0.545463\pi$
$673$	−27.7768	−	16.0370i	−1.07072	−	0.618179i	−0.928377	+	0.371639i	$0.878796\pi$
$674$		0			0
$675$	10.0000	−	13.4590i	0.384900	−	0.518038i
$676$		0			0
$677$			14.2382i			0.547220i	0.961841	+	0.273610i	$0.0882177\pi$
$677$			14.2382i			0.547220i	−0.961841	+	0.273610i	$0.911782\pi$
$678$		0			0
$679$	8.82983	−	15.2937i	0.338858	−	0.586919i
$680$		0			0
$681$	16.5891			0.635695
$682$		0			0
$683$	−22.3302	+	12.8923i	−0.854440	+	0.493311i	−0.862146	−	0.506659i	$-0.830880\pi$
$683$	−22.3302	+	12.8923i	−0.854440	+	0.493311i	0.00770647	+	0.999970i	$0.497547\pi$
$684$		0			0
$685$	36.8929	−	7.63605i	1.40961	−	0.291759i
$686$		0			0
$687$	−62.9025	−	36.3168i	−2.39988	−	1.38557i
$688$		0			0
$689$	43.5589	−	15.6118i	1.65946	−	0.594761i
$690$		0			0
$691$	−0.0218318	+	0.0378138i	−0.000830522	+	0.00143851i	−0.866440	−	0.499281i	$-0.833598\pi$
$691$	−0.0218318	+	0.0378138i	−0.000830522	+	0.00143851i	0.865610	+	0.500719i	$0.166931\pi$
$692$		0			0
$693$	−40.0230	+	23.1073i	−1.52035	+	0.877774i
$694$		0			0
$695$	−0.465407	−	2.24857i	−0.0176539	−	0.0852931i
$696$		0			0
$697$			5.41982i			0.205290i
$698$		0			0
$699$	1.10945	−	1.92163i	0.0419634	−	0.0726827i
$700$		0			0
$701$	−14.5454			−0.549373			−0.274687	−	0.961534i	$-0.588574\pi$
$701$	−14.5454			−0.549373			−0.274687	+	0.961534i	$0.588574\pi$
$702$		0			0
$703$			2.42785i			0.0915679i
$704$		0			0
$705$	30.8753	−	27.5030i	1.16283	−	1.03582i
$706$		0			0
$707$			19.1501i			0.720214i
$708$		0			0
$709$	9.81638	+	17.0025i	0.368662	+	0.638541i	0.989357	−	0.145511i	$-0.0464827\pi$
$709$	9.81638	+	17.0025i	0.368662	+	0.638541i	−0.620695	+	0.784052i	$0.713149\pi$
$710$		0			0
$711$	29.2560	+	50.6728i	1.09718	+	1.90038i
$712$		0			0
$713$	−8.81438	−	5.08898i	−0.330101	−	0.190584i
$714$		0			0
$715$	22.9781	+	12.5219i	0.859334	+	0.468293i
$716$		0			0
$717$	−9.32468	−	5.38361i	−0.348237	−	0.201055i
$718$		0			0
$719$	−23.7156	−	41.0766i	−0.884443	−	1.53190i	−0.846351	−	0.532625i	$-0.821206\pi$
$719$	−23.7156	−	41.0766i	−0.884443	−	1.53190i	−0.0380914	−	0.999274i	$-0.512128\pi$
$720$		0			0
$721$	12.3553	+	21.3999i	0.460134	+	0.796976i
$722$		0			0
$723$			61.0872i			2.27186i
$724$		0			0
$725$	13.7676	−	5.95429i	0.511315	−	0.221137i
$726$		0			0
$727$		−	34.0951i		−	1.26452i	−0.774757	−	0.632259i	$-0.782128\pi$
$727$		−	34.0951i		−	1.26452i	0.774757	−	0.632259i	$-0.217872\pi$
$728$		0			0
$729$	42.8349			1.58648
$730$		0			0
$731$	8.51345	−	14.7457i	0.314881	−	0.545391i
$732$		0			0
$733$			14.3920i			0.531580i	0.964031	+	0.265790i	$0.0856327\pi$
$733$			14.3920i			0.531580i	−0.964031	+	0.265790i	$0.914367\pi$
$734$		0			0
$735$	25.0253	−	5.17972i	0.923074	−	0.191057i
$736$		0			0
$737$	−11.2864	+	6.51621i	−0.415740	+	0.240028i
$738$		0			0
$739$	17.2240	−	29.8328i	0.633594	−	1.09742i	−0.353217	−	0.935541i	$-0.614912\pi$
$739$	17.2240	−	29.8328i	0.633594	−	1.09742i	0.986811	−	0.161876i	$-0.0517545\pi$
$740$		0			0
$741$	11.3822	−	4.07944i	0.418134	−	0.149862i
$742$		0			0
$743$	−35.2589	−	20.3567i	−1.29352	−	0.746816i	−0.314246	−	0.949342i	$-0.601752\pi$
$743$	−35.2589	−	20.3567i	−1.29352	−	0.746816i	−0.979277	+	0.202526i	$0.935085\pi$
$744$		0			0
$745$	−7.18418	−	34.7097i	−0.263208	−	1.27167i
$746$		0			0
$747$	31.6939	−	18.2985i	1.15962	−	0.669507i
$748$		0			0
$749$	−28.7542			−1.05066
$750$		0			0
$751$	16.2509	−	28.1474i	0.593003	−	1.02711i	−0.400822	−	0.916156i	$-0.631275\pi$
$751$	16.2509	−	28.1474i	0.593003	−	1.02711i	0.993825	−	0.110956i	$-0.0353912\pi$
$752$		0			0
$753$		−	51.2167i		−	1.86644i
$754$		0			0
$755$	30.8786	+	10.2158i	1.12379	+	0.371790i
$756$		0			0
$757$	11.2864	+	6.51621i	0.410211	+	0.236836i	0.690881	−	0.722969i	$-0.257223\pi$
$757$	11.2864	+	6.51621i	0.410211	+	0.236836i	−0.280669	+	0.959805i	$0.590556\pi$
$758$		0			0
$759$	23.5185			0.853668
$760$		0			0
$761$	1.99493	+	3.45532i	0.0723161	+	0.125255i	0.899916	−	0.436063i	$-0.143628\pi$
$761$	1.99493	+	3.45532i	0.0723161	+	0.125255i	−0.827600	+	0.561318i	$0.810294\pi$
$762$		0			0
$763$	24.6613	−	14.2382i	0.892800	−	0.515458i
$764$		0			0
$765$	−12.3065	−	13.8155i	−0.444943	−	0.499500i
$766$		0			0
$767$	−5.91018	+	6.97348i	−0.213404	+	0.251798i
$768$		0			0
$769$	3.33343	−	5.77367i	0.120207	−	0.208204i	−0.799642	−	0.600476i	$-0.794978\pi$
$769$	3.33343	−	5.77367i	0.120207	−	0.208204i	0.919849	+	0.392272i	$0.128311\pi$
$770$		0			0
$771$	2.84181	+	4.92216i	0.102345	+	0.177267i
$772$		0			0
$773$	−41.8593	+	24.1675i	−1.50557	+	0.869244i	−0.505595	+	0.862771i	$0.668727\pi$
$773$	−41.8593	+	24.1675i	−1.50557	+	0.869244i	−0.999979	+	0.00647254i	$0.997940\pi$
$774$		0			0
$775$	−15.1752	−	11.2751i	−0.545111	−	0.405015i
$776$		0			0
$777$	−15.2349	−	8.79585i	−0.546548	−	0.315549i
$778$		0			0
$779$	−3.46472			−0.124136
$780$		0			0
$781$	−17.0269			−0.609271
$782$		0			0
$783$	−8.71259	−	5.03022i	−0.311363	−	0.179765i
$784$		0			0
$785$	−7.67017	+	23.1842i	−0.273760	+	0.827478i
$786$		0			0
$787$	24.2151	−	13.9806i	0.863176	−	0.498355i	−0.00189876	−	0.999998i	$-0.500604\pi$
$787$	24.2151	−	13.9806i	0.863176	−	0.498355i	0.865074	+	0.501643i	$0.167271\pi$
$788$		0			0
$789$	−40.2658	−	69.7424i	−1.43350	−	2.48290i
$790$		0			0
$791$	−12.2945	+	21.2948i	−0.437144	+	0.757155i
$792$		0			0
$793$	−17.4642	+	20.6062i	−0.620174	+	0.731749i
$794$		0			0
$795$	57.6802	−	51.3802i	2.04571	−	1.82227i
$796$		0			0
$797$	32.2529	−	18.6212i	1.14246	−	0.659597i	0.195418	−	0.980720i	$-0.437393\pi$
$797$	32.2529	−	18.6212i	1.14246	−	0.659597i	0.947038	+	0.321123i	$0.104060\pi$
$798$		0			0
$799$	−6.69377	−	11.5939i	−0.236808	−	0.410164i
$800$		0			0
$801$	43.8014			1.54765
$802$		0			0
$803$	15.3617	+	8.86907i	0.542102	+	0.312983i
$804$		0			0
$805$	−19.1633	−	6.33991i	−0.675416	−	0.223452i
$806$		0			0
$807$		−	50.0382i		−	1.76143i
$808$		0			0
$809$	7.26434	−	12.5822i	0.255400	−	0.442367i	−0.709604	−	0.704601i	$-0.751126\pi$
$809$	7.26434	−	12.5822i	0.255400	−	0.442367i	0.965004	+	0.262234i	$0.0844594\pi$
$810$		0			0
$811$	−44.0538			−1.54694			−0.773469	−	0.633834i	$-0.781480\pi$
$811$	−44.0538			−1.54694			−0.773469	+	0.633834i	$0.781480\pi$
$812$		0			0
$813$	−13.5785	+	7.83955i	−0.476219	+	0.274945i
$814$		0			0
$815$	−9.14794	+	1.89343i	−0.320438	+	0.0663240i
$816$		0			0
$817$	9.42647	+	5.44238i	0.329790	+	0.190405i
$818$		0			0
$819$	−9.16326	+	50.5123i	−0.320190	+	1.76504i
$820$		0			0
$821$	−13.5135	+	23.4060i	−0.471623	+	0.816875i	−0.999473	−	0.0324629i	$-0.989665\pi$
$821$	−13.5135	+	23.4060i	−0.471623	+	0.816875i	0.527850	+	0.849337i	$0.322998\pi$
$822$		0			0
$823$	−34.2914	+	19.7981i	−1.19532	+	0.690120i	−0.959509	−	0.281679i	$-0.909109\pi$
$823$	−34.2914	+	19.7981i	−1.19532	+	0.690120i	−0.235814	+	0.971798i	$0.575775\pi$
$824$		0			0
$825$	43.3948	+	5.03032i	1.51081	+	0.175133i
$826$		0			0
$827$			26.5639i			0.923716i	0.886954	+	0.461858i	$0.152817\pi$
$827$			26.5639i			0.923716i	−0.886954	+	0.461858i	$0.847183\pi$
$828$		0			0
$829$	6.99162	−	12.1098i	0.242829	−	0.420592i	−0.718690	−	0.695331i	$-0.755258\pi$
$829$	6.99162	−	12.1098i	0.242829	−	0.420592i	0.961519	+	0.274738i	$0.0885913\pi$
$830$		0			0
$831$	−36.4480			−1.26437
$832$		0			0
$833$		−	8.27427i		−	0.286686i
$834$		0			0
$835$	−4.98770	−	5.59927i	−0.172607	−	0.193771i
$836$		0			0
$837$			12.6798i			0.438278i
$838$		0			0
$839$	−7.19707	−	12.4657i	−0.248471	−	0.430364i	0.714631	−	0.699502i	$-0.246595\pi$
$839$	−7.19707	−	12.4657i	−0.248471	−	0.430364i	−0.963102	+	0.269138i	$0.913261\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$		0			0
$843$	1.08333	+	0.625462i	0.0373119	+	0.0215421i
$844$		0			0
$845$	27.1145	−	10.4788i	0.932766	−	0.360483i
$846$		0			0
$847$	1.34963	+	0.779207i	0.0463737	+	0.0267739i
$848$		0			0
$849$	13.5404	+	23.4526i	0.464704	+	0.804891i
$850$		0			0
$851$	2.62291	+	4.54300i	0.0899120	+	0.155732i
$852$		0			0
$853$			27.2633i			0.933478i	0.884395	+	0.466739i	$0.154571\pi$
$853$			27.2633i			0.933478i	−0.884395	+	0.466739i	$0.845429\pi$
$854$		0			0
$855$	8.83179	−	7.86715i	0.302041	−	0.269051i
$856$		0			0
$857$		−	50.6201i		−	1.72915i	−0.502503	−	0.864575i	$-0.667587\pi$
$857$		−	50.6201i		−	1.72915i	0.502503	−	0.864575i	$-0.332413\pi$
$858$		0			0
$859$	1.27992			0.0436702			0.0218351	−	0.999762i	$-0.493049\pi$
$859$	1.27992			0.0436702			0.0218351	+	0.999762i	$0.493049\pi$
$860$		0			0
$861$	12.5523	−	21.7413i	0.427782	−	0.740941i
$862$		0			0
$863$			8.38448i			0.285411i	0.989765	+	0.142706i	$0.0455802\pi$
$863$			8.38448i			0.285411i	−0.989765	+	0.142706i	$0.954420\pi$
$864$		0			0
$865$	−19.1312	+	3.95976i	−0.650481	+	0.134636i
$866$		0			0
$867$	30.7765	−	17.7688i	1.04522	−	0.603460i
$868$		0			0
$869$	−22.3654	+	38.7380i	−0.758695	+	1.31410i
$870$		0			0
$871$	−2.58402	+	14.2443i	−0.0875562	+	0.482651i
$872$		0			0
$873$	19.3632	+	11.1794i	0.655347	+	0.378365i
$874$		0			0
$875$	−34.0028	−	15.7968i	−1.14950	−	0.534028i
$876$		0			0
$877$	−48.3989	+	27.9431i	−1.63431	+	0.943572i	−0.651573	+	0.758586i	$0.725890\pi$
$877$	−48.3989	+	27.9431i	−1.63431	+	0.943572i	−0.982741	+	0.184985i	$0.940776\pi$
$878$		0			0
$879$	36.2051			1.22117
$880$		0			0
$881$	−12.5975	+	21.8195i	−0.424420	+	0.735116i	−0.996366	−	0.0851746i	$-0.972855\pi$
$881$	−12.5975	+	21.8195i	−0.424420	+	0.735116i	0.571946	+	0.820291i	$0.306189\pi$
$882$		0			0
$883$		−	30.7868i		−	1.03606i	−0.855363	−	0.518029i	$-0.826666\pi$
$883$		−	30.7868i		−	1.03606i	0.855363	−	0.518029i	$-0.173334\pi$
$884$		0			0
$885$	−4.79307	+	14.4877i	−0.161117	+	0.487000i
$886$		0			0
$887$	−10.8011	−	6.23603i	−0.362666	−	0.209385i	0.307584	−	0.951521i	$-0.400480\pi$
$887$	−10.8011	−	6.23603i	−0.362666	−	0.209385i	−0.670250	+	0.742136i	$0.733813\pi$
$888$		0			0
$889$	30.7302			1.03066
$890$		0			0
$891$	6.02183	+	10.4301i	0.201739	+	0.349422i
$892$		0			0
$893$	7.41163	−	4.27911i	0.248021	−	0.143195i
$894$		0			0
$895$	−30.0714	+	26.7869i	−1.00518	+	0.895387i
$896$		0			0
$897$	16.8912	−	19.9301i	0.563981	−	0.665447i
$898$		0			0
$899$	−5.67164	+	9.82357i	−0.189160	+	0.327634i
$900$		0			0
$901$	−12.5051	−	21.6594i	−0.416604	−	0.721580i
$902$		0			0
$903$	−68.3024	+	39.4344i	−2.27296	+	1.31230i
$904$		0			0
$905$	−2.21560	−	0.733001i	−0.0736490	−	0.0243658i
$906$		0			0
$907$	−33.6807	−	19.4455i	−1.11835	−	0.645678i	−0.177369	−	0.984144i	$-0.556759\pi$
$907$	−33.6807	−	19.4455i	−1.11835	−	0.645678i	−0.940979	+	0.338466i	$0.890092\pi$
$908$		0			0
$909$	−24.2458			−0.804183
$910$		0			0
$911$	−0.165096			−0.00546989			−0.00273494	−	0.999996i	$-0.500871\pi$
$911$	−0.165096			−0.00546989			−0.00273494	+	0.999996i	$0.500871\pi$
$912$		0			0
$913$	24.2292	+	13.9887i	0.801868	+	0.462959i
$914$		0			0
$915$	−14.1633	+	42.8105i	−0.468223	+	1.41527i
$916$		0			0
$917$	−29.0420	+	16.7674i	−0.959050	+	0.553708i
$918$		0			0
$919$	−0.447663	−	0.775375i	−0.0147670	−	0.0255773i	0.858547	−	0.512734i	$-0.171367\pi$
$919$	−0.447663	−	0.775375i	−0.0147670	−	0.0255773i	−0.873314	+	0.487157i	$0.838034\pi$
$920$		0			0
$921$	−33.1196	+	57.3648i	−1.09133	+	1.89024i
$922$		0			0
$923$	−12.2289	+	14.4290i	−0.402518	+	0.474935i
$924$		0			0
$925$	3.86792	+	8.94346i	0.127176	+	0.294059i
$926$		0			0
$927$	−27.0943	+	15.6429i	−0.889893	+	0.513780i
$928$		0			0
$929$	−6.14474	−	10.6430i	−0.201602	−	0.349185i	0.747443	−	0.664326i	$-0.231282\pi$
$929$	−6.14474	−	10.6430i	−0.201602	−	0.349185i	−0.949045	+	0.315141i	$0.897948\pi$
$930$		0			0
$931$	5.28947			0.173356
$932$		0			0
$933$	5.68295	+	3.28106i	0.186052	+	0.107417i
$934$		0			0
$935$	4.44259	−	13.4284i	0.145288	−	0.439154i
$936$		0			0
$937$		−	5.77242i		−	0.188577i	−0.995545	−	0.0942884i	$-0.969942\pi$
$937$		−	5.77242i		−	0.188577i	0.995545	−	0.0942884i	$-0.0300576\pi$
$938$		0			0
$939$	25.9713	−	44.9835i	0.847540	−	1.46798i
$940$		0			0
$941$	−55.8887			−1.82192			−0.910960	−	0.412495i	$-0.864658\pi$
$941$	−55.8887			−1.82192			−0.910960	+	0.412495i	$0.864658\pi$
$942$		0			0
$943$	−6.48321	+	3.74308i	−0.211122	+	0.121891i
$944$		0			0
$945$	5.09675	+	24.6245i	0.165797	+	0.801034i
$946$		0			0
$947$	−1.64231	−	0.948188i	−0.0533679	−	0.0308120i	0.473079	−	0.881020i	$-0.343143\pi$
$947$	−1.64231	−	0.948188i	−0.0533679	−	0.0308120i	−0.526447	+	0.850208i	$0.676476\pi$
$948$		0			0
$949$	18.5487	−	6.64798i	0.602117	−	0.215802i
$950$		0			0
$951$	−38.7912	+	67.1884i	−1.25789	+	2.17873i
$952$		0			0
$953$	−29.1438	+	16.8262i	−0.944059	+	0.545053i	−0.891230	−	0.453551i	$-0.850157\pi$
$953$	−29.1438	+	16.8262i	−0.944059	+	0.545053i	−0.0528285	+	0.998604i	$0.516824\pi$
$954$		0			0
$955$	−11.5653	−	55.8768i	−0.374245	−	1.80813i
$956$		0			0
$957$		−	26.2113i		−	0.847290i
$958$		0			0
$959$	−28.2509	+	48.9320i	−0.912269	+	1.58010i
$960$		0			0
$961$	−16.7033			−0.538817
$962$		0			0
$963$		−	36.4054i		−	1.17315i
$964$		0			0
$965$	−29.4798	−	33.0945i	−0.948987	−	1.06535i
$966$		0			0
$967$			23.0493i			0.741216i	0.928789	+	0.370608i	$0.120851\pi$
$967$			23.0493i			0.741216i	−0.928789	+	0.370608i	$0.879149\pi$
$968$		0			0
$969$	−3.26764	−	5.65972i	−0.104972	−	0.181816i
$970$		0			0
$971$	7.45964	+	12.9205i	0.239391	+	0.414638i	0.960540	−	0.278143i	$-0.0897188\pi$
$971$	7.45964	+	12.9205i	0.239391	+	0.414638i	−0.721148	+	0.692781i	$0.756385\pi$
$972$		0			0
$973$	2.98233	+	1.72185i	0.0956092	+	0.0552000i
$974$		0			0
$975$	35.4294	−	33.1609i	1.13465	−	1.06200i
$976$		0			0
$977$	20.2339	+	11.6821i	0.647341	+	0.373742i	0.787437	−	0.616396i	$-0.211408\pi$
$977$	20.2339	+	11.6821i	0.647341	+	0.373742i	−0.140096	+	0.990138i	$0.544741\pi$
$978$		0			0
$979$	16.7425	+	28.9989i	0.535093	+	0.926808i
$980$		0			0
$981$	18.0269	+	31.2235i	0.575555	+	0.996890i
$982$		0			0
$983$			5.31119i			0.169401i	0.996406	+	0.0847003i	$0.0269933\pi$
$983$			5.31119i			0.169401i	−0.996406	+	0.0847003i	$0.973007\pi$
$984$		0			0
$985$	−32.2035	−	36.1521i	−1.02609	−	1.15190i
$986$		0			0
$987$			62.0112i			1.97384i
$988$		0			0
$989$	23.5185			0.747846
$990$		0			0
$991$	−12.0440	+	20.8607i	−0.382589	+	0.662663i	−0.991432	−	0.130628i	$-0.958301\pi$
$991$	−12.0440	+	20.8607i	−0.382589	+	0.662663i	0.608843	+	0.793291i	$0.291634\pi$
$992$		0			0
$993$			8.00299i			0.253967i
$994$		0			0
$995$	8.26164	+	39.9154i	0.261912	+	1.26540i
$996$		0			0
$997$	17.6755	−	10.2050i	0.559790	−	0.323195i	−0.193271	−	0.981145i	$-0.561910\pi$
$997$	17.6755	−	10.2050i	0.559790	−	0.323195i	0.753061	+	0.657951i	$0.228576\pi$
$998$		0			0
$999$	3.26764	−	5.65972i	0.103384	−	0.179066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.dh.a.529.1		12
4.3	odd	2		65.2.n.a.9.4	yes	12
5.4	even	2	inner	1040.2.dh.a.529.6		12
12.11	even	2		585.2.bs.a.334.3		12
13.3	even	3	inner	1040.2.dh.a.289.6		12
20.3	even	4		325.2.e.e.126.4		12
20.7	even	4		325.2.e.e.126.3		12
20.19	odd	2		65.2.n.a.9.3	✓	12
52.3	odd	6		65.2.n.a.29.3	yes	12
52.7	even	12		845.2.d.d.844.7		12
52.11	even	12		845.2.l.f.699.5		24
52.15	even	12		845.2.l.f.699.7		24
52.19	even	12		845.2.d.d.844.5		12
52.23	odd	6		845.2.n.e.484.4		12
52.31	even	4		845.2.l.f.654.8		24
52.35	odd	6		845.2.b.d.339.3		6
52.43	odd	6		845.2.b.e.339.4		6
52.47	even	4		845.2.l.f.654.6		24
52.51	odd	2		845.2.n.e.529.3		12
60.59	even	2		585.2.bs.a.334.4		12
65.29	even	6	inner	1040.2.dh.a.289.1		12
156.107	even	6		585.2.bs.a.289.4		12
260.3	even	12		325.2.e.e.276.4		12
260.19	even	12		845.2.d.d.844.8		12
260.43	even	12		4225.2.a.bq.1.4		6
260.59	even	12		845.2.d.d.844.6		12
260.87	even	12		4225.2.a.br.1.4		6
260.99	even	4		845.2.l.f.654.7		24
260.107	even	12		325.2.e.e.276.3		12
260.119	even	12		845.2.l.f.699.6		24
260.139	odd	6		845.2.b.d.339.4		6
260.147	even	12		4225.2.a.bq.1.3		6
260.159	odd	6		65.2.n.a.29.4	yes	12
260.179	odd	6		845.2.n.e.484.3		12
260.199	odd	6		845.2.b.e.339.3		6
260.219	even	12		845.2.l.f.699.8		24
260.239	even	4		845.2.l.f.654.5		24
260.243	even	12		4225.2.a.br.1.3		6
260.259	odd	2		845.2.n.e.529.4		12
780.419	even	6		585.2.bs.a.289.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.n.a.9.3	✓	12	20.19	odd	2
65.2.n.a.9.4	yes	12	4.3	odd	2
65.2.n.a.29.3	yes	12	52.3	odd	6
65.2.n.a.29.4	yes	12	260.159	odd	6
325.2.e.e.126.3		12	20.7	even	4
325.2.e.e.126.4		12	20.3	even	4
325.2.e.e.276.3		12	260.107	even	12
325.2.e.e.276.4		12	260.3	even	12
585.2.bs.a.289.3		12	780.419	even	6
585.2.bs.a.289.4		12	156.107	even	6
585.2.bs.a.334.3		12	12.11	even	2
585.2.bs.a.334.4		12	60.59	even	2
845.2.b.d.339.3		6	52.35	odd	6
845.2.b.d.339.4		6	260.139	odd	6
845.2.b.e.339.3		6	260.199	odd	6
845.2.b.e.339.4		6	52.43	odd	6
845.2.d.d.844.5		12	52.19	even	12
845.2.d.d.844.6		12	260.59	even	12
845.2.d.d.844.7		12	52.7	even	12
845.2.d.d.844.8		12	260.19	even	12
845.2.l.f.654.5		24	260.239	even	4
845.2.l.f.654.6		24	52.47	even	4
845.2.l.f.654.7		24	260.99	even	4
845.2.l.f.654.8		24	52.31	even	4
845.2.l.f.699.5		24	52.11	even	12
845.2.l.f.699.6		24	260.119	even	12
845.2.l.f.699.7		24	52.15	even	12
845.2.l.f.699.8		24	260.219	even	12
845.2.n.e.484.3		12	260.179	odd	6
845.2.n.e.484.4		12	52.23	odd	6
845.2.n.e.529.3		12	52.51	odd	2
845.2.n.e.529.4		12	260.259	odd	2
1040.2.dh.a.289.1		12	65.29	even	6	inner
1040.2.dh.a.289.6		12	13.3	even	3	inner
1040.2.dh.a.529.1		12	1.1	even	1	trivial
1040.2.dh.a.529.6		12	5.4	even	2	inner
4225.2.a.bq.1.3		6	260.147	even	12
4225.2.a.bq.1.4		6	260.43	even	12
4225.2.a.br.1.3		6	260.243	even	12
4225.2.a.br.1.4		6	260.87	even	12

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:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.dh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.33117 - 1.34590i) q^{3} +(-2.12291 - 0.702335i) q^{5} +(2.90420 - 1.67674i) q^{7} +(2.12291 + 3.67698i) q^{9} +O(q^{10})\)	\(q+(-2.33117 - 1.34590i) q^{3} +(-2.12291 - 0.702335i) q^{5} +(2.90420 - 1.67674i) q^{7} +(2.12291 + 3.67698i) q^{9} +(-1.62291 + 2.81095i) q^{11} +(1.21648 + 3.39414i) q^{13} +(4.00358 + 4.49448i) q^{15} +(1.68772 - 0.974404i) q^{17} +(0.622905 + 1.07890i) q^{19} -9.02690 q^{21} +(2.33117 + 1.34590i) q^{23} +(4.01345 + 2.98198i) q^{25} -3.35348i q^{27} +(1.50000 - 2.59808i) q^{29} -3.78109 q^{31} +(7.56654 - 4.36854i) q^{33} +(-7.34297 + 1.51984i) q^{35} +(1.68772 + 0.974404i) q^{37} +(1.73236 - 9.54958i) q^{39} +(-1.39055 + 2.40850i) q^{41} +(7.56654 - 4.36854i) q^{43} +(-1.92426 - 9.29687i) q^{45} -6.86960i q^{47} +(2.12291 - 3.67698i) q^{49} -5.24581 q^{51} -12.8336i q^{53} +(5.41950 - 4.82757i) q^{55} -3.35348i q^{57} +(1.26764 + 2.19562i) q^{59} +(3.74581 + 6.48793i) q^{61} +(12.3307 + 7.11911i) q^{63} +(-0.198649 - 8.05981i) q^{65} +(3.47722 + 2.00758i) q^{67} +(-3.62291 - 6.27506i) q^{69} +(2.62291 + 4.54300i) q^{71} -5.46493i q^{73} +(-5.34259 - 12.3532i) q^{75} +10.8848i q^{77} +13.7811 q^{79} +(1.85526 - 3.21341i) q^{81} -8.61955i q^{83} +(-4.26722 + 0.883225i) q^{85} +(-6.99351 + 4.03771i) q^{87} +(5.15819 - 8.93425i) q^{89} +(9.22398 + 7.81753i) q^{91} +(8.81438 + 5.08898i) q^{93} +(-0.564617 - 2.72790i) q^{95} +(4.56055 - 2.63304i) q^{97} -13.7811 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{5} + 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^5 + 6 * q^9	\( 12 q - 6 q^{5} + 6 q^{9} + 4 q^{15} - 12 q^{19} - 8 q^{21} - 2 q^{25} + 18 q^{29} + 16 q^{31} - 10 q^{35} + 32 q^{39} + 14 q^{41} - 29 q^{45} + 6 q^{49} - 24 q^{51} + 26 q^{55} + 4 q^{59} + 6 q^{61} + 23 q^{65} - 24 q^{69} + 12 q^{71} - 2 q^{75} + 104 q^{79} + 14 q^{81} + 21 q^{85} + 20 q^{89} + 44 q^{91} - 20 q^{95} - 104 q^{99}+O(q^{100}) \) 12 * q - 6 * q^5 + 6 * q^9 + 4 * q^15 - 12 * q^19 - 8 * q^21 - 2 * q^25 + 18 * q^29 + 16 * q^31 - 10 * q^35 + 32 * q^39 + 14 * q^41 - 29 * q^45 + 6 * q^49 - 24 * q^51 + 26 * q^55 + 4 * q^59 + 6 * q^61 + 23 * q^65 - 24 * q^69 + 12 * q^71 - 2 * q^75 + 104 * q^79 + 14 * q^81 + 21 * q^85 + 20 * q^89 + 44 * q^91 - 20 * q^95 - 104 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more