LMFDB - Embedded newform 1040.2.da.e.881.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1040,2,Mod(641,1040)]

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, 0, 1]))

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

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

chi := DirichletCharacter("1040.641");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.da (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:	12.0.58891012706304.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 520)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			881.1
Root			$-1.12906 + 0.851598i$ of defining polynomial
Character	$\chi$	$=$	1040.881
Dual form			1040.2.da.e.641.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30204 - 2.25519i) q^{3} +1.00000i q^{5} +(-4.29663 - 2.48066i) q^{7} +(-1.89060 + 3.27461i) q^{9} +O(q^{10})$	\(q+(-1.30204 - 2.25519i) q^{3} +1.00000i q^{5} +(-4.29663 - 2.48066i) q^{7} +(-1.89060 + 3.27461i) q^{9} +(-2.16513 + 1.25004i) q^{11} +(-1.78660 - 3.13178i) q^{13} +(2.25519 - 1.30204i) q^{15} +(0.505154 - 0.874953i) q^{17} +(4.03228 + 2.32804i) q^{19} +12.9196i q^{21} +(3.06629 + 5.31097i) q^{23} -1.00000 q^{25} +2.03429 q^{27} +(0.890520 + 1.54243i) q^{29} -1.65817i q^{31} +(5.63816 + 3.25519i) q^{33} +(2.48066 - 4.29663i) q^{35} +(5.54367 - 3.20064i) q^{37} +(-4.73655 + 8.10683i) q^{39} +(-10.4236 + 6.01810i) q^{41} +(1.67120 - 2.89460i) q^{43} +(-3.27461 - 1.89060i) q^{45} +6.68108i q^{47} +(8.80735 + 15.2548i) q^{49} -2.63092 q^{51} -9.78120 q^{53} +(-1.25004 - 2.16513i) q^{55} -12.1248i q^{57} +(10.6859 + 6.16949i) q^{59} +(5.68093 - 9.83965i) q^{61} +(16.2464 - 9.37986i) q^{63} +(3.13178 - 1.78660i) q^{65} +(3.37112 - 1.94632i) q^{67} +(7.98485 - 13.8302i) q^{69} +(-5.68713 - 3.28347i) q^{71} +9.35173i q^{73} +(1.30204 + 2.25519i) q^{75} +12.4037 q^{77} -11.6591 q^{79} +(3.02307 + 5.23611i) q^{81} +12.1910i q^{83} +(0.874953 + 0.505154i) q^{85} +(2.31898 - 4.01659i) q^{87} +(5.51828 - 3.18598i) q^{89} +(-0.0925095 + 17.8881i) q^{91} +(-3.73950 + 2.15900i) q^{93} +(-2.32804 + 4.03228i) q^{95} +(-1.51254 - 0.873267i) q^{97} -9.45329i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{7} + 2 q^{9}+O(q^{10}) $ 12 * q - 6 * q^7 + 2 * q^9	$ 12 q - 6 q^{7} + 2 q^{9} - 2 q^{13} - 8 q^{17} + 24 q^{19} + 2 q^{23} - 12 q^{25} + 12 q^{27} + 12 q^{29} + 4 q^{35} + 24 q^{37} - 28 q^{39} + 24 q^{41} + 18 q^{43} - 12 q^{45} + 24 q^{49} - 68 q^{53} - 2 q^{55} + 48 q^{59} + 18 q^{61} + 36 q^{63} + 16 q^{65} - 18 q^{67} - 8 q^{69} + 64 q^{77} + 12 q^{79} + 14 q^{81} - 18 q^{87} + 30 q^{89} - 76 q^{91} - 12 q^{93} + 10 q^{95} - 84 q^{97}+O(q^{100}) $ 12 * q - 6 * q^7 + 2 * q^9 - 2 * q^13 - 8 * q^17 + 24 * q^19 + 2 * q^23 - 12 * q^25 + 12 * q^27 + 12 * q^29 + 4 * q^35 + 24 * q^37 - 28 * q^39 + 24 * q^41 + 18 * q^43 - 12 * q^45 + 24 * q^49 - 68 * q^53 - 2 * q^55 + 48 * q^59 + 18 * q^61 + 36 * q^63 + 16 * q^65 - 18 * q^67 - 8 * q^69 + 64 * q^77 + 12 * q^79 + 14 * q^81 - 18 * q^87 + 30 * q^89 - 76 * q^91 - 12 * q^93 + 10 * q^95 - 84 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	−1.30204	−	2.25519i	−0.751731	−	1.30204i	−0.946983	−	0.321283i	$-0.895886\pi$
$3$	−1.30204	−	2.25519i	−0.751731	−	1.30204i	0.195252	−	0.980753i	$-0.437448\pi$
$4$		0			0
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$	−4.29663	−	2.48066i	−1.62397	−	0.937601i	−0.985843	−	0.167673i	$-0.946375\pi$
$7$	−4.29663	−	2.48066i	−1.62397	−	0.937601i	−0.638130	−	0.769928i	$-0.720292\pi$
$8$		0			0
$9$	−1.89060	+	3.27461i	−0.630199	+	1.09154i
$10$		0			0
$11$	−2.16513	+	1.25004i	−0.652812	+	0.376901i	−0.789533	−	0.613709i	$-0.789677\pi$
$11$	−2.16513	+	1.25004i	−0.652812	+	0.376901i	0.136721	+	0.990610i	$0.456344\pi$
$12$		0			0
$13$	−1.78660	−	3.13178i	−0.495515	−	0.868600i
$13$	−1.78660	−	3.13178i	−0.495515	−	0.868600i
$14$		0			0
$15$	2.25519	−	1.30204i	0.582288	−	0.336184i
$16$		0			0
$17$	0.505154	−	0.874953i	0.122518	−	0.212207i	−0.798242	−	0.602337i	$-0.794236\pi$
$17$	0.505154	−	0.874953i	0.122518	−	0.212207i	0.920760	+	0.390130i	$0.127570\pi$
$18$		0			0
$19$	4.03228	+	2.32804i	0.925069	+	0.534089i	0.885249	−	0.465118i	$-0.153988\pi$
$19$	4.03228	+	2.32804i	0.925069	+	0.534089i	0.0398203	+	0.999207i	$0.487321\pi$
$20$		0			0
$21$			12.9196i			2.81930i
$22$		0			0
$23$	3.06629	+	5.31097i	0.639366	+	1.10741i	0.985572	+	0.169256i	$0.0541364\pi$
$23$	3.06629	+	5.31097i	0.639366	+	1.10741i	−0.346206	+	0.938158i	$0.612530\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$	2.03429			0.391500
$28$		0			0
$29$	0.890520	+	1.54243i	0.165365	+	0.286421i	0.936785	−	0.349906i	$-0.113786\pi$
$29$	0.890520	+	1.54243i	0.165365	+	0.286421i	−0.771420	+	0.636327i	$0.780453\pi$
$30$		0			0
$31$		−	1.65817i		−	0.297817i	−0.988851	−	0.148908i	$-0.952424\pi$
$31$		−	1.65817i		−	0.297817i	0.988851	−	0.148908i	$-0.0475759\pi$
$32$		0			0
$33$	5.63816	+	3.25519i	0.981478	+	0.566656i
$34$		0			0
$35$	2.48066	−	4.29663i	0.419308	−	0.726263i
$36$		0			0
$37$	5.54367	−	3.20064i	0.911374	−	0.526182i	0.0305011	−	0.999535i	$-0.490290\pi$
$37$	5.54367	−	3.20064i	0.911374	−	0.526182i	0.880873	+	0.473353i	$0.156956\pi$
$38$		0			0
$39$	−4.73655	+	8.10683i	−0.758455	+	1.29813i
$40$		0			0
$41$	−10.4236	+	6.01810i	−1.62790	+	0.939869i	−0.643182	+	0.765713i	$0.722386\pi$
$41$	−10.4236	+	6.01810i	−1.62790	+	0.939869i	−0.984718	+	0.174156i	$0.944280\pi$
$42$		0			0
$43$	1.67120	−	2.89460i	0.254855	−	0.441422i	−0.710001	−	0.704201i	$-0.751306\pi$
$43$	1.67120	−	2.89460i	0.254855	−	0.441422i	0.964856	+	0.262779i	$0.0846389\pi$
$44$		0			0
$45$	−3.27461	−	1.89060i	−0.488150	−	0.281834i
$46$		0			0
$47$			6.68108i			0.974536i	0.873252	+	0.487268i	$0.162007\pi$
$47$			6.68108i			0.974536i	−0.873252	+	0.487268i	$0.837993\pi$
$48$		0			0
$49$	8.80735	+	15.2548i	1.25819	+	2.17925i
$50$		0			0
$51$	−2.63092			−0.368402
$52$		0			0
$53$	−9.78120			−1.34355			−0.671775	−	0.740755i	$-0.734468\pi$
$53$	−9.78120			−1.34355			−0.671775	+	0.740755i	$0.734468\pi$
$54$		0			0
$55$	−1.25004	−	2.16513i	−0.168555	−	0.291946i
$56$		0			0
$57$		−	12.1248i		−	1.60596i
$58$		0			0
$59$	10.6859	+	6.16949i	1.39118	+	0.803199i	0.993446	−	0.114300i	$-0.0364627\pi$
$59$	10.6859	+	6.16949i	1.39118	+	0.803199i	0.397736	+	0.917500i	$0.369796\pi$
$60$		0			0
$61$	5.68093	−	9.83965i	0.727368	−	1.25984i	−0.230624	−	0.973043i	$-0.574077\pi$
$61$	5.68093	−	9.83965i	0.727368	−	1.25984i	0.957992	−	0.286795i	$-0.0925900\pi$
$62$		0			0
$63$	16.2464	−	9.37986i	2.04685	−	1.18175i
$64$		0			0
$65$	3.13178	−	1.78660i	0.388450	−	0.221601i
$66$		0			0
$67$	3.37112	−	1.94632i	0.411848	−	0.237781i	−0.279735	−	0.960077i	$-0.590247\pi$
$67$	3.37112	−	1.94632i	0.411848	−	0.237781i	0.691584	+	0.722296i	$0.256913\pi$
$68$		0			0
$69$	7.98485	−	13.8302i	0.961262	−	1.66496i
$70$		0			0
$71$	−5.68713	−	3.28347i	−0.674939	−	0.389676i	0.123007	−	0.992406i	$-0.460746\pi$
$71$	−5.68713	−	3.28347i	−0.674939	−	0.389676i	−0.797945	+	0.602730i	$0.794080\pi$
$72$		0			0
$73$			9.35173i			1.09454i	0.836957	+	0.547268i	$0.184332\pi$
$73$			9.35173i			1.09454i	−0.836957	+	0.547268i	$0.815668\pi$
$74$		0			0
$75$	1.30204	+	2.25519i	0.150346	+	0.260407i
$76$		0			0
$77$	12.4037			1.41353
$78$		0			0
$79$	−11.6591			−1.31176			−0.655878	−	0.754867i	$-0.727701\pi$
$79$	−11.6591			−1.31176			−0.655878	+	0.754867i	$0.727701\pi$
$80$		0			0
$81$	3.02307	+	5.23611i	0.335897	+	0.581791i
$82$		0			0
$83$			12.1910i			1.33814i	0.743200	+	0.669069i	$0.233307\pi$
$83$			12.1910i			1.33814i	−0.743200	+	0.669069i	$0.766693\pi$
$84$		0			0
$85$	0.874953	+	0.505154i	0.0949019	+	0.0547917i
$86$		0			0
$87$	2.31898	−	4.01659i	0.248621	−	0.430623i
$88$		0			0
$89$	5.51828	−	3.18598i	0.584936	−	0.337713i	−0.178156	−	0.984002i	$-0.557013\pi$
$89$	5.51828	−	3.18598i	0.584936	−	0.337713i	0.763093	+	0.646289i	$0.223680\pi$
$90$		0			0
$91$	−0.0925095	+	17.8881i	−0.00969763	+	1.87518i
$92$		0			0
$93$	−3.73950	+	2.15900i	−0.387768	+	0.223878i
$94$		0			0
$95$	−2.32804	+	4.03228i	−0.238852	+	0.413703i
$96$		0			0
$97$	−1.51254	−	0.873267i	−0.153576	−	0.0886669i	0.421243	−	0.906948i	$-0.361594\pi$
$97$	−1.51254	−	0.873267i	−0.153576	−	0.0886669i	−0.574818	+	0.818281i	$0.694927\pi$
$98$		0			0
$99$		−	9.45329i		−	0.950091i
$100$		0			0
$101$	4.15686	+	7.19990i	0.413623	+	0.716417i	0.995283	−	0.0970156i	$-0.0309297\pi$
$101$	4.15686	+	7.19990i	0.413623	+	0.716417i	−0.581659	+	0.813432i	$0.697596\pi$
$102$		0			0
$103$	−5.65908			−0.557606			−0.278803	−	0.960348i	$-0.589938\pi$
$103$	−5.65908			−0.557606			−0.278803	+	0.960348i	$0.589938\pi$
$104$		0			0
$105$	−12.9196			−1.26083
$106$		0			0
$107$	3.35404	+	5.80937i	0.324247	+	0.561613i	0.981360	−	0.192180i	$-0.0615556\pi$
$107$	3.35404	+	5.80937i	0.324247	+	0.561613i	−0.657112	+	0.753793i	$0.728222\pi$
$108$		0			0
$109$		−	3.10011i		−	0.296937i	−0.988917	−	0.148468i	$-0.952566\pi$
$109$		−	3.10011i		−	0.296937i	0.988917	−	0.148468i	$-0.0474343\pi$
$110$		0			0
$111$	−14.4361	−	8.33470i	−1.37022	−	0.791095i
$112$		0			0
$113$	−1.35041	+	2.33898i	−0.127036	+	0.220033i	−0.922527	−	0.385933i	$-0.873880\pi$
$113$	−1.35041	+	2.33898i	−0.127036	+	0.220033i	0.795491	+	0.605965i	$0.207213\pi$
$114$		0			0
$115$	−5.31097	+	3.06629i	−0.495251	+	0.285933i
$116$		0			0
$117$	13.6331	+	0.0705047i	1.26038	+	0.00651816i
$118$		0			0
$119$	−4.34092	+	2.50623i	−0.397931	+	0.229746i
$120$		0			0
$121$	−2.37480	+	4.11328i	−0.215891	+	0.373935i
$122$		0			0
$123$	27.1439	+	15.6716i	2.44749	+	1.41306i
$124$		0			0
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$	−8.06166	−	13.9632i	−0.715356	−	1.23903i	−0.962822	−	0.270137i	$-0.912931\pi$
$127$	−8.06166	−	13.9632i	−0.715356	−	1.23903i	0.247466	−	0.968897i	$-0.420402\pi$
$128$		0			0
$129$	−8.70384			−0.766330
$130$		0			0
$131$	−3.26372			−0.285152			−0.142576	−	0.989784i	$-0.545539\pi$
$131$	−3.26372			−0.285152			−0.142576	+	0.989784i	$0.545539\pi$
$132$		0			0
$133$	−11.5501	−	20.0054i	−1.00152	−	1.73469i
$134$		0			0
$135$			2.03429i			0.175084i
$136$		0			0
$137$	−3.57387	−	2.06337i	−0.305336	−	0.176286i	0.339501	−	0.940606i	$-0.389742\pi$
$137$	−3.57387	−	2.06337i	−0.305336	−	0.176286i	−0.644838	+	0.764320i	$0.723075\pi$
$138$		0			0
$139$	−0.642059	+	1.11208i	−0.0544587	+	0.0943253i	−0.891970	−	0.452095i	$-0.850677\pi$
$139$	−0.642059	+	1.11208i	−0.0544587	+	0.0943253i	0.837511	+	0.546421i	$0.184010\pi$
$140$		0			0
$141$	15.0671	−	8.69901i	1.26888	−	0.732589i
$142$		0			0
$143$	7.78308	+	4.54739i	0.650854	+	0.380272i
$144$		0			0
$145$	−1.54243	+	0.890520i	−0.128091	+	0.0739536i
$146$		0			0
$147$	22.9350	−	39.7245i	1.89164	−	3.27643i
$148$		0			0
$149$	−9.99223	−	5.76902i	−0.818596	−	0.472616i	0.0313362	−	0.999509i	$-0.490024\pi$
$149$	−9.99223	−	5.76902i	−0.818596	−	0.472616i	−0.849932	+	0.526892i	$0.823357\pi$
$150$		0			0
$151$			22.1588i			1.80326i	0.432511	+	0.901628i	$0.357628\pi$
$151$			22.1588i			1.80326i	−0.432511	+	0.901628i	$0.642372\pi$
$152$		0			0
$153$	1.91009	+	3.30837i	0.154421	+	0.267466i
$154$		0			0
$155$	1.65817			0.133188
$156$		0			0
$157$	1.70661			0.136202			0.0681012	−	0.997678i	$-0.478306\pi$
$157$	1.70661			0.136202			0.0681012	+	0.997678i	$0.478306\pi$
$158$		0			0
$159$	12.7355	+	22.0585i	1.00999	+	1.74935i
$160$		0			0
$161$		−	30.4257i		−	2.39788i
$162$		0			0
$163$	−3.37766	−	1.95009i	−0.264559	−	0.152743i	0.361854	−	0.932235i	$-0.382144\pi$
$163$	−3.37766	−	1.95009i	−0.264559	−	0.152743i	−0.626412	+	0.779492i	$0.715477\pi$
$164$		0			0
$165$	−3.25519	+	5.63816i	−0.253416	+	0.438930i
$166$		0			0
$167$	−6.06780	+	3.50325i	−0.469540	+	0.271089i	−0.716047	−	0.698052i	$-0.754051\pi$
$167$	−6.06780	+	3.50325i	−0.469540	+	0.271089i	0.246507	+	0.969141i	$0.420717\pi$
$168$		0			0
$169$	−6.61610	+	11.1905i	−0.508930	+	0.860808i
$170$		0			0
$171$	−15.2468	+	8.80277i	−1.16596	+	0.673165i
$172$		0			0
$173$	−1.49104	+	2.58256i	−0.113362	+	0.196349i	−0.917124	−	0.398603i	$-0.869495\pi$
$173$	−1.49104	+	2.58256i	−0.113362	+	0.196349i	0.803762	+	0.594951i	$0.202829\pi$
$174$		0			0
$175$	4.29663	+	2.48066i	0.324795	+	0.187520i
$176$		0			0
$177$		−	32.1316i		−	2.41516i
$178$		0			0
$179$	−9.77175	−	16.9252i	−0.730375	−	1.26505i	−0.956723	−	0.291000i	$-0.906012\pi$
$179$	−9.77175	−	16.9252i	−0.730375	−	1.26505i	0.226349	−	0.974046i	$-0.427321\pi$
$180$		0			0
$181$	−2.22811			−0.165614			−0.0828069	−	0.996566i	$-0.526388\pi$
$181$	−2.22811			−0.165614			−0.0828069	+	0.996566i	$0.526388\pi$
$182$		0			0
$183$	−29.5871			−2.18714
$184$		0			0
$185$	3.20064	+	5.54367i	0.235316	+	0.407579i
$186$		0			0
$187$			2.52585i			0.184708i
$188$		0			0
$189$	−8.74060	−	5.04639i	−0.635785	−	0.367071i
$190$		0			0
$191$	−4.63764	+	8.03263i	−0.335568	+	0.581221i	−0.983594	−	0.180398i	$-0.942262\pi$
$191$	−4.63764	+	8.03263i	−0.335568	+	0.581221i	0.648026	+	0.761618i	$0.275595\pi$
$192$		0			0
$193$	−20.5772	+	11.8802i	−1.48118	+	0.855159i	−0.999772	−	0.0213387i	$-0.993207\pi$
$193$	−20.5772	+	11.8802i	−1.48118	+	0.855159i	−0.481406	+	0.876498i	$0.659874\pi$
$194$		0			0
$195$	−8.10683	−	4.73655i	−0.580542	−	0.339191i
$196$		0			0
$197$	−11.8069	+	6.81671i	−0.841206	+	0.485670i	−0.857674	−	0.514194i	$-0.828091\pi$
$197$	−11.8069	+	6.81671i	−0.841206	+	0.485670i	0.0164682	+	0.999864i	$0.494758\pi$
$198$		0			0
$199$	12.5978	−	21.8200i	0.893031	−	1.54678i	0.0568086	−	0.998385i	$-0.481908\pi$
$199$	12.5978	−	21.8200i	0.893031	−	1.54678i	0.836223	−	0.548390i	$-0.184759\pi$
$200$		0			0
$201$	−8.77865	−	5.06836i	−0.619198	−	0.357494i
$202$		0			0
$203$		−	8.83631i		−	0.620187i
$204$		0			0
$205$	−6.01810	−	10.4236i	−0.420322	−	0.728019i
$206$		0			0
$207$	−23.1885			−1.61171
$208$		0			0
$209$	−11.6406			−0.805194
$210$		0			0
$211$	−9.40438	−	16.2889i	−0.647424	−	1.12137i	−0.983736	−	0.179621i	$-0.942513\pi$
$211$	−9.40438	−	16.2889i	−0.647424	−	1.12137i	0.336311	−	0.941751i	$-0.390821\pi$
$212$		0			0
$213$			17.1008i			1.17173i
$214$		0			0
$215$	2.89460	+	1.67120i	0.197410	+	0.113975i
$216$		0			0
$217$	−4.11336	+	7.12455i	−0.279233	+	0.483646i
$218$		0			0
$219$	21.0900	−	12.1763i	1.42513	−	0.822797i
$220$		0			0
$221$	−3.64267	−	0.0188384i	−0.245032	−	0.00126720i
$222$		0			0
$223$	−19.3726	+	11.1848i	−1.29728	+	0.748987i	−0.979934	−	0.199321i	$-0.936126\pi$
$223$	−19.3726	+	11.1848i	−1.29728	+	0.748987i	−0.317350	+	0.948309i	$0.602793\pi$
$224$		0			0
$225$	1.89060	−	3.27461i	0.126040	−	0.218307i
$226$		0			0
$227$	13.5432	+	7.81919i	0.898896	+	0.518978i	0.876842	−	0.480779i	$-0.159646\pi$
$227$	13.5432	+	7.81919i	0.898896	+	0.518978i	0.0220542	+	0.999757i	$0.492979\pi$
$228$		0			0
$229$			29.1681i			1.92748i	0.266839	+	0.963741i	$0.414021\pi$
$229$			29.1681i			1.92748i	−0.266839	+	0.963741i	$0.585979\pi$
$230$		0			0
$231$	−16.1501	−	27.9727i	−1.06260	−	1.84047i
$232$		0			0
$233$	8.60266			0.563579			0.281790	−	0.959476i	$-0.409072\pi$
$233$	8.60266			0.563579			0.281790	+	0.959476i	$0.409072\pi$
$234$		0			0
$235$	−6.68108			−0.435826
$236$		0			0
$237$	15.1806	+	26.2936i	0.986087	+	1.70795i
$238$		0			0
$239$		−	7.78880i		−	0.503816i	−0.967751	−	0.251908i	$-0.918942\pi$
$239$		−	7.78880i		−	0.503816i	0.967751	−	0.251908i	$-0.0810580\pi$
$240$		0			0
$241$	−3.49283	−	2.01659i	−0.224993	−	0.129900i	0.383267	−	0.923638i	$-0.374799\pi$
$241$	−3.49283	−	2.01659i	−0.224993	−	0.129900i	−0.608260	+	0.793738i	$0.708132\pi$
$242$		0			0
$243$	10.9237	−	18.9205i	0.700758	−	1.21375i
$244$		0			0
$245$	−15.2548	+	8.80735i	−0.974592	+	0.562681i
$246$		0			0
$247$	0.0868179	−	16.7875i	0.00552409	−	1.06816i
$248$		0			0
$249$	27.4931	−	15.8731i	1.74230	−	1.00592i
$250$		0			0
$251$	2.17140	−	3.76098i	0.137058	−	0.237391i	−0.789324	−	0.613977i	$-0.789569\pi$
$251$	2.17140	−	3.76098i	0.137058	−	0.237391i	0.926382	+	0.376586i	$0.122902\pi$
$252$		0			0
$253$	−13.2778	−	7.66597i	−0.834771	−	0.481955i
$254$		0			0
$255$		−	2.63092i		−	0.164754i
$256$		0			0
$257$	1.60706	+	2.78351i	0.100246	+	0.173631i	0.911786	−	0.410666i	$-0.134704\pi$
$257$	1.60706	+	2.78351i	0.100246	+	0.173631i	−0.811540	+	0.584297i	$0.801370\pi$
$258$		0			0
$259$	−31.7588			−1.97340
$260$		0			0
$261$	−6.73446			−0.416853
$262$		0			0
$263$	−7.92370	−	13.7242i	−0.488596	−	0.846273i	0.511318	−	0.859392i	$-0.329157\pi$
$263$	−7.92370	−	13.7242i	−0.488596	−	0.846273i	−0.999914	+	0.0131185i	$0.995824\pi$
$264$		0			0
$265$		−	9.78120i		−	0.600854i
$266$		0			0
$267$	−14.3700	−	8.29652i	−0.879430	−	0.507739i
$268$		0			0
$269$	11.1013	−	19.2280i	0.676859	−	1.17235i	−0.299062	−	0.954234i	$-0.596674\pi$
$269$	11.1013	−	19.2280i	0.676859	−	1.17235i	0.975922	−	0.218121i	$-0.0699928\pi$
$270$		0			0
$271$	−26.5941	+	15.3541i	−1.61548	+	0.932697i	−0.627410	+	0.778689i	$0.715885\pi$
$271$	−26.5941	+	15.3541i	−1.61548	+	0.932697i	−0.988070	+	0.154008i	$0.950782\pi$
$272$		0			0
$273$	40.4615	−	23.0823i	2.44884	−	1.39700i
$274$		0			0
$275$	2.16513	−	1.25004i	0.130562	−	0.0753802i
$276$		0			0
$277$	3.48039	−	6.02820i	0.209116	−	0.362200i	−0.742320	−	0.670045i	$-0.766275\pi$
$277$	3.48039	−	6.02820i	0.209116	−	0.362200i	0.951436	+	0.307846i	$0.0996080\pi$
$278$		0			0
$279$	5.42987	+	3.13494i	0.325078	+	0.187684i
$280$		0			0
$281$			26.3835i			1.57391i	0.617011	+	0.786955i	$0.288343\pi$
$281$			26.3835i			1.57391i	−0.617011	+	0.786955i	$0.711657\pi$
$282$		0			0
$283$	8.04295	+	13.9308i	0.478104	+	0.828100i	0.999685	−	0.0251019i	$-0.00799101\pi$
$283$	8.04295	+	13.9308i	0.478104	+	0.828100i	−0.521581	+	0.853202i	$0.674658\pi$
$284$		0			0
$285$	12.1248			0.718209
$286$		0			0
$287$	59.7154			3.52489
$288$		0			0
$289$	7.98964	+	13.8385i	0.469979	+	0.814027i
$290$		0			0
$291$			4.54810i			0.266615i
$292$		0			0
$293$	−27.8527	−	16.0808i	−1.62717	−	0.939448i	−0.984931	−	0.172946i	$-0.944671\pi$
$293$	−27.8527	−	16.0808i	−1.62717	−	0.939448i	−0.642241	−	0.766503i	$-0.721995\pi$
$294$		0			0
$295$	−6.16949	+	10.6859i	−0.359202	+	0.622156i
$296$		0			0
$297$	−4.40451	+	2.54294i	−0.255576	+	0.147557i
$298$		0			0
$299$	11.1546	−	19.0916i	0.645084	−	1.10409i
$300$		0			0
$301$	−14.3610	+	8.29134i	−0.827756	+	0.477905i
$302$		0			0
$303$	10.8248	−	18.7491i	0.621867	−	1.07711i
$304$		0			0
$305$	9.83965	+	5.68093i	0.563417	+	0.325289i
$306$		0			0
$307$			25.8479i			1.47522i	0.675229	+	0.737609i	$0.264045\pi$
$307$			25.8479i			1.47522i	−0.675229	+	0.737609i	$0.735955\pi$
$308$		0			0
$309$	7.36833	+	12.7623i	0.419170	+	0.726023i
$310$		0			0
$311$	24.6116			1.39560			0.697799	−	0.716294i	$-0.254163\pi$
$311$	24.6116			1.39560			0.697799	+	0.716294i	$0.254163\pi$
$312$		0			0
$313$	8.16869			0.461722			0.230861	−	0.972987i	$-0.425846\pi$
$313$	8.16869			0.461722			0.230861	+	0.972987i	$0.425846\pi$
$314$		0			0
$315$	9.37986	+	16.2464i	0.528495	+	0.915381i
$316$		0			0
$317$			15.4583i			0.868226i	0.900858	+	0.434113i	$0.142938\pi$
$317$			15.4583i			0.868226i	−0.900858	+	0.434113i	$0.857062\pi$
$318$		0			0
$319$	−3.85618	−	2.22637i	−0.215905	−	0.124653i
$320$		0			0
$321$	8.73417	−	15.1280i	0.487494	−	0.844364i
$322$		0			0
$323$	4.07385	−	2.35204i	0.226675	−	0.130871i
$324$		0			0
$325$	1.78660	+	3.13178i	0.0991029	+	0.173720i
$326$		0			0
$327$	−6.99135	+	4.03646i	−0.386623	+	0.223217i
$328$		0			0
$329$	16.5735	−	28.7061i	0.913726	−	1.58262i
$330$		0			0
$331$	−1.96841	−	1.13646i	−0.108194	−	0.0624656i	0.444927	−	0.895567i	$-0.353230\pi$
$331$	−1.96841	−	1.13646i	−0.108194	−	0.0624656i	−0.553120	+	0.833101i	$0.686563\pi$
$332$		0			0
$333$			24.2045i			1.32640i
$334$		0			0
$335$	1.94632	+	3.37112i	0.106339	+	0.184184i
$336$		0			0
$337$	3.17735			0.173081			0.0865407	−	0.996248i	$-0.472419\pi$
$337$	3.17735			0.173081			0.0865407	+	0.996248i	$0.472419\pi$
$338$		0			0
$339$	7.03313			0.381987
$340$		0			0
$341$	2.07278	+	3.59016i	0.112247	+	0.194418i
$342$		0			0
$343$		−	52.6629i		−	2.84353i
$344$		0			0
$345$	13.8302	+	7.98485i	0.744591	+	0.429890i
$346$		0			0
$347$	−2.71499	+	4.70249i	−0.145748	+	0.252443i	−0.929652	−	0.368439i	$-0.879892\pi$
$347$	−2.71499	+	4.70249i	−0.145748	+	0.252443i	0.783904	+	0.620882i	$0.213226\pi$
$348$		0			0
$349$	−4.81517	+	2.78004i	−0.257750	+	0.148812i	−0.623308	−	0.781977i	$-0.714212\pi$
$349$	−4.81517	+	2.78004i	−0.257750	+	0.148812i	0.365558	+	0.930789i	$0.380878\pi$
$350$		0			0
$351$	−3.63447	−	6.37095i	−0.193994	−	0.340056i
$352$		0			0
$353$	14.9697	−	8.64276i	0.796756	−	0.460008i	−0.0455793	−	0.998961i	$-0.514513\pi$
$353$	14.9697	−	8.64276i	0.796756	−	0.460008i	0.842336	+	0.538953i	$0.181180\pi$
$354$		0			0
$355$	3.28347	−	5.68713i	0.174268	−	0.301842i
$356$		0			0
$357$	11.3041	+	6.52641i	0.598275	+	0.345414i
$358$		0			0
$359$		−	15.7254i		−	0.829953i	−0.909832	−	0.414976i	$-0.863790\pi$
$359$		−	15.7254i		−	0.829953i	0.909832	−	0.414976i	$-0.136210\pi$
$360$		0			0
$361$	1.33953	+	2.32014i	0.0705017	+	0.122113i
$362$		0			0
$363$	12.3683			0.649169
$364$		0			0
$365$	−9.35173			−0.489492
$366$		0			0
$367$	0.473516	+	0.820153i	0.0247173	+	0.0428117i	0.878119	−	0.478441i	$-0.158798\pi$
$367$	0.473516	+	0.820153i	0.0247173	+	0.0428117i	−0.853402	+	0.521253i	$0.825465\pi$
$368$		0			0
$369$		−	45.5112i		−	2.36922i
$370$		0			0
$371$	42.0262	+	24.2638i	2.18189	+	1.25971i
$372$		0			0
$373$	2.43183	−	4.21206i	0.125916	−	0.218092i	−0.796175	−	0.605067i	$-0.793146\pi$
$373$	2.43183	−	4.21206i	0.125916	−	0.218092i	0.922090	+	0.386974i	$0.126480\pi$
$374$		0			0
$375$	−2.25519	+	1.30204i	−0.116458	+	0.0672369i
$376$		0			0
$377$	3.23953	−	5.54461i	0.166844	−	0.285562i
$378$		0			0
$379$	21.6285	−	12.4872i	1.11098	−	0.641424i	0.171896	−	0.985115i	$-0.445011\pi$
$379$	21.6285	−	12.4872i	1.11098	−	0.641424i	0.939083	+	0.343691i	$0.111677\pi$
$380$		0			0
$381$	−20.9931	+	36.3612i	−1.07551	+	1.86284i
$382$		0			0
$383$	27.7458	+	16.0190i	1.41774	+	0.818535i	0.996100	−	0.0882271i	$-0.0281201\pi$
$383$	27.7458	+	16.0190i	1.41774	+	0.818535i	0.421643	+	0.906762i	$0.361453\pi$
$384$		0			0
$385$			12.4037i			0.632151i
$386$		0			0
$387$	6.31912	+	10.9450i	0.321219	+	0.556368i
$388$		0			0
$389$	11.6811			0.592254			0.296127	−	0.955149i	$-0.404305\pi$
$389$	11.6811			0.592254			0.296127	+	0.955149i	$0.404305\pi$
$390$		0			0
$391$	6.19580			0.313335
$392$		0			0
$393$	4.24948	+	7.36031i	0.214358	+	0.371279i
$394$		0			0
$395$		−	11.6591i		−	0.586635i
$396$		0			0
$397$	−20.4628	−	11.8142i	−1.02700	−	0.592937i	−0.110874	−	0.993834i	$-0.535365\pi$
$397$	−20.4628	−	11.8142i	−1.02700	−	0.592937i	−0.916123	+	0.400897i	$0.868698\pi$
$398$		0			0
$399$	−30.0774	+	52.0956i	−1.50575	+	2.60804i
$400$		0			0
$401$	−22.1437	+	12.7847i	−1.10580	+	0.638436i	−0.937739	−	0.347340i	$-0.887085\pi$
$401$	−22.1437	+	12.7847i	−1.10580	+	0.638436i	−0.168065	+	0.985776i	$0.553752\pi$
$402$		0			0
$403$	−5.19303	+	2.96250i	−0.258683	+	0.147572i
$404$		0			0
$405$	−5.23611	+	3.02307i	−0.260185	+	0.150218i
$406$		0			0
$407$	−8.00185	+	13.8596i	−0.396637	+	0.686996i
$408$		0			0
$409$	−14.0583	−	8.11659i	−0.695141	−	0.401340i	0.110394	−	0.993888i	$-0.464789\pi$
$409$	−14.0583	−	8.11659i	−0.695141	−	0.401340i	−0.805535	+	0.592548i	$0.798122\pi$
$410$		0			0
$411$			10.7464i			0.530078i
$412$		0			0
$413$	−30.6088	−	53.0160i	−1.50616	−	2.60875i
$414$		0			0
$415$	−12.1910			−0.598433
$416$		0			0
$417$	3.34394			0.163753
$418$		0			0
$419$	−3.29602	−	5.70887i	−0.161021	−	0.278897i	0.774214	−	0.632924i	$-0.218145\pi$
$419$	−3.29602	−	5.70887i	−0.161021	−	0.278897i	−0.935235	+	0.354027i	$0.884812\pi$
$420$		0			0
$421$			26.0223i			1.26825i	0.773231	+	0.634125i	$0.218639\pi$
$421$			26.0223i			1.26825i	−0.773231	+	0.634125i	$0.781361\pi$
$422$		0			0
$423$	−21.8780	−	12.6312i	−1.06374	−	0.614152i
$424$		0			0
$425$	−0.505154	+	0.874953i	−0.0245036	+	0.0424414i
$426$		0			0
$427$	−48.8177	+	28.1849i	−2.36245	+	1.36396i
$428$		0			0
$429$	0.121394	−	23.4732i	0.00586094	−	1.13330i
$430$		0			0
$431$	−17.7644	+	10.2563i	−0.855681	+	0.494028i	−0.862564	−	0.505949i	$-0.831142\pi$
$431$	−17.7644	+	10.2563i	−0.855681	+	0.494028i	0.00688275	+	0.999976i	$0.497809\pi$
$432$		0			0
$433$	3.31585	−	5.74322i	0.159350	−	0.276002i	−0.775285	−	0.631612i	$-0.782394\pi$
$433$	3.31585	−	5.74322i	0.159350	−	0.276002i	0.934634	+	0.355610i	$0.115727\pi$
$434$		0			0
$435$	4.01659	+	2.31898i	0.192581	+	0.111186i
$436$		0			0
$437$			28.5538i			1.36591i
$438$		0			0
$439$	9.93221	+	17.2031i	0.474039	+	0.821059i	0.999558	−	0.0297224i	$-0.00946233\pi$
$439$	9.93221	+	17.2031i	0.474039	+	0.821059i	−0.525519	+	0.850782i	$0.676129\pi$
$440$		0			0
$441$	−66.6046			−3.17165
$442$		0			0
$443$	−3.09524			−0.147059			−0.0735297	−	0.997293i	$-0.523426\pi$
$443$	−3.09524			−0.147059			−0.0735297	+	0.997293i	$0.523426\pi$
$444$		0			0
$445$	3.18598	+	5.51828i	0.151030	+	0.261592i
$446$		0			0
$447$			30.0459i			1.42112i
$448$		0			0
$449$	−5.35306	−	3.09059i	−0.252627	−	0.145854i	0.368340	−	0.929691i	$-0.379926\pi$
$449$	−5.35306	−	3.09059i	−0.252627	−	0.145854i	−0.620966	+	0.783837i	$0.713260\pi$
$450$		0			0
$451$	15.0457	−	26.0599i	0.708475	−	1.22711i
$452$		0			0
$453$	49.9724	−	28.8516i	2.34791	−	1.35556i
$454$		0			0
$455$	−17.8881	−	0.0925095i	−0.838605	−	0.00433691i
$456$		0			0
$457$	14.7362	−	8.50794i	0.689330	−	0.397985i	−0.114031	−	0.993477i	$-0.536376\pi$
$457$	14.7362	−	8.50794i	0.689330	−	0.397985i	0.803361	+	0.595493i	$0.203043\pi$
$458$		0			0
$459$	1.02763	−	1.77991i	0.0479657	−	0.0830790i
$460$		0			0
$461$	16.1576	+	9.32857i	0.752533	+	0.434475i	0.826608	−	0.562778i	$-0.190267\pi$
$461$	16.1576	+	9.32857i	0.752533	+	0.434475i	−0.0740756	+	0.997253i	$0.523601\pi$
$462$		0			0
$463$		−	2.58064i		−	0.119933i	−0.998200	−	0.0599663i	$-0.980901\pi$
$463$		−	2.58064i		−	0.119933i	0.998200	−	0.0599663i	$-0.0190993\pi$
$464$		0			0
$465$	−2.15900	−	3.73950i	−0.100121	−	0.173415i
$466$		0			0
$467$	18.1909			0.841773			0.420886	−	0.907113i	$-0.361719\pi$
$467$	18.1909			0.841773			0.420886	+	0.907113i	$0.361719\pi$
$468$		0			0
$469$	−19.3126			−0.891774
$470$		0			0
$471$	−2.22207	−	3.84874i	−0.102388	−	0.177341i
$472$		0			0
$473$			8.35625i			0.384221i
$474$		0			0
$475$	−4.03228	−	2.32804i	−0.185014	−	0.106818i
$476$		0			0
$477$	18.4923	−	32.0296i	0.846705	−	1.46654i
$478$		0			0
$479$	−2.92039	+	1.68609i	−0.133436	+	0.0770393i	−0.565232	−	0.824932i	$-0.691213\pi$
$479$	−2.92039	+	1.68609i	−0.133436	+	0.0770393i	0.431796	+	0.901971i	$0.357880\pi$
$480$		0			0
$481$	−19.9280	−	11.6433i	−0.908641	−	0.530888i
$482$		0			0
$483$	−68.6158	+	39.6154i	−3.12213	+	1.80256i
$484$		0			0
$485$	0.873267	−	1.51254i	0.0396530	−	0.0686811i
$486$		0			0
$487$	22.9900	+	13.2733i	1.04178	+	0.601470i	0.920336	−	0.391129i	$-0.127915\pi$
$487$	22.9900	+	13.2733i	1.04178	+	0.601470i	0.121440	+	0.992599i	$0.461249\pi$
$488$		0			0
$489$			10.1564i			0.459287i
$490$		0			0
$491$	−0.545246	−	0.944393i	−0.0246066	−	0.0426199i	0.853460	−	0.521159i	$-0.174500\pi$
$491$	−0.545246	−	0.944393i	−0.0246066	−	0.0426199i	−0.878066	+	0.478539i	$0.841167\pi$
$492$		0			0
$493$	1.79940			0.0810408
$494$		0			0
$495$	9.45329			0.424894
$496$		0			0
$497$	16.2903	+	28.2157i	0.730722	+	1.26565i
$498$		0			0
$499$			4.89586i			0.219169i	0.993977	+	0.109585i	$0.0349520\pi$
$499$			4.89586i			0.219169i	−0.993977	+	0.109585i	$0.965048\pi$
$500$		0			0
$501$	15.8010	+	9.12271i	0.705936	+	0.407572i
$502$		0			0
$503$	−2.95834	+	5.12399i	−0.131906	+	0.228467i	−0.924411	−	0.381397i	$-0.875443\pi$
$503$	−2.95834	+	5.12399i	−0.131906	+	0.228467i	0.792505	+	0.609865i	$0.208776\pi$
$504$		0			0
$505$	−7.19990	+	4.15686i	−0.320391	+	0.184978i
$506$		0			0
$507$	33.8511	+	0.350137i	1.50338	+	0.0155501i
$508$		0			0
$509$	−11.6527	+	6.72769i	−0.516497	+	0.298200i	−0.735500	−	0.677524i	$-0.763053\pi$
$509$	−11.6527	+	6.72769i	−0.516497	+	0.298200i	0.219003	+	0.975724i	$0.429719\pi$
$510$		0			0
$511$	23.1985	−	40.1809i	1.02624	−	1.77750i
$512$		0			0
$513$	8.20284	+	4.73591i	0.362164	+	0.209096i
$514$		0			0
$515$		−	5.65908i		−	0.249369i
$516$		0			0
$517$	−8.35162	−	14.4654i	−0.367304	−	0.636189i
$518$		0			0
$519$	7.76557			0.340871
$520$		0			0
$521$	−17.5937			−0.770792			−0.385396	−	0.922751i	$-0.625935\pi$
$521$	−17.5937			−0.770792			−0.385396	+	0.922751i	$0.625935\pi$
$522$		0			0
$523$	9.17847	+	15.8976i	0.401346	+	0.695152i	0.993889	−	0.110387i	$-0.0352090\pi$
$523$	9.17847	+	15.8976i	0.401346	+	0.695152i	−0.592542	+	0.805539i	$0.701876\pi$
$524$		0			0
$525$		−	12.9196i		−	0.563859i
$526$		0			0
$527$	−1.45082	−	0.837633i	−0.0631988	−	0.0364878i
$528$		0			0
$529$	−7.30428	+	12.6514i	−0.317577	+	0.550060i
$530$		0			0
$531$	−40.4054	+	23.3281i	−1.75344	+	1.01235i
$532$		0			0
$533$	37.4703	+	21.8926i	1.62302	+	0.948275i
$534$		0			0
$535$	−5.80937	+	3.35404i	−0.251161	+	0.145008i
$536$		0			0
$537$	−25.4463	+	44.0744i	−1.09809	+	1.90195i
$538$		0			0
$539$	−38.1381	−	22.0191i	−1.64273	−	0.948428i
$540$		0			0
$541$		−	15.4282i		−	0.663311i	−0.943401	−	0.331655i	$-0.892393\pi$
$541$		−	15.4282i		−	0.663311i	0.943401	−	0.331655i	$-0.107607\pi$
$542$		0			0
$543$	2.90108	+	5.02481i	0.124497	+	0.215635i
$544$		0			0
$545$	3.10011			0.132794
$546$		0			0
$547$	−12.9215			−0.552486			−0.276243	−	0.961088i	$-0.589089\pi$
$547$	−12.9215			−0.552486			−0.276243	+	0.961088i	$0.589089\pi$
$548$		0			0
$549$	21.4807	+	37.2057i	0.916774	+	1.58790i
$550$		0			0
$551$			8.29266i			0.353279i
$552$		0			0
$553$	50.0950	+	28.9224i	2.13026	+	1.22990i
$554$		0			0
$555$	8.33470	−	14.4361i	0.353788	−	0.612779i
$556$		0			0
$557$	30.5228	−	17.6224i	1.29329	−	0.746684i	0.314058	−	0.949404i	$-0.398312\pi$
$557$	30.5228	−	17.6224i	1.29329	−	0.746684i	0.979237	+	0.202720i	$0.0649782\pi$
$558$		0			0
$559$	−12.0510	−	0.0623227i	−0.509703	−	0.00263597i
$560$		0			0
$561$	5.69628	−	3.28875i	0.240497	−	0.138851i
$562$		0			0
$563$	−20.4923	+	35.4937i	−0.863647	+	1.49588i	0.00473796	+	0.999989i	$0.498492\pi$
$563$	−20.4923	+	35.4937i	−0.863647	+	1.49588i	−0.868385	+	0.495891i	$0.834841\pi$
$564$		0			0
$565$	−2.33898	−	1.35041i	−0.0984015	−	0.0568122i
$566$		0			0
$567$		−	29.9969i		−	1.25975i
$568$		0			0
$569$	−9.91311	−	17.1700i	−0.415579	−	0.719804i	0.579910	−	0.814681i	$-0.303088\pi$
$569$	−9.91311	−	17.1700i	−0.415579	−	0.719804i	−0.995489	+	0.0948766i	$0.969754\pi$
$570$		0			0
$571$	−5.79211			−0.242392			−0.121196	−	0.992629i	$-0.538673\pi$
$571$	−5.79211			−0.242392			−0.121196	+	0.992629i	$0.538673\pi$
$572$		0			0
$573$	24.1535			1.00903
$574$		0			0
$575$	−3.06629	−	5.31097i	−0.127873	−	0.221483i
$576$		0			0
$577$		−	3.33992i		−	0.139043i	−0.997580	−	0.0695214i	$-0.977853\pi$
$577$		−	3.33992i		−	0.139043i	0.997580	−	0.0695214i	$-0.0221472\pi$
$578$		0			0
$579$	53.5845	+	30.9370i	2.22690	+	1.28570i
$580$		0			0
$581$	30.2418	−	52.3803i	1.25464	−	2.17310i
$582$		0			0
$583$	21.1776	−	12.2269i	0.877086	−	0.506386i
$584$		0			0
$585$	−0.0705047	+	13.6331i	−0.00291501	+	0.563660i
$586$		0			0
$587$	−4.41510	+	2.54906i	−0.182231	+	0.105211i	−0.588340	−	0.808613i	$-0.700218\pi$
$587$	−4.41510	+	2.54906i	−0.182231	+	0.105211i	0.406110	+	0.913824i	$0.366885\pi$
$588$		0			0
$589$	3.86029	−	6.68622i	0.159060	−	0.275501i
$590$		0			0
$591$	30.7460	+	17.7512i	1.26472	+	0.730187i
$592$		0			0
$593$		−	0.308347i		−	0.0126623i	−0.999980	−	0.00633114i	$-0.997985\pi$
$593$		−	0.308347i		−	0.0126623i	0.999980	−	0.00633114i	$-0.00201528\pi$
$594$		0			0
$595$	−2.50623	−	4.34092i	−0.102745	−	0.177960i
$596$		0			0
$597$	−65.6109			−2.68528
$598$		0			0
$599$	5.15275			0.210536			0.105268	−	0.994444i	$-0.466430\pi$
$599$	5.15275			0.210536			0.105268	+	0.994444i	$0.466430\pi$
$600$		0			0
$601$	1.79532	+	3.10958i	0.0732325	+	0.126842i	0.900316	−	0.435236i	$-0.143335\pi$
$601$	1.79532	+	3.10958i	0.0732325	+	0.126842i	−0.827084	+	0.562079i	$0.810002\pi$
$602$		0			0
$603$			14.7188i			0.599397i
$604$		0			0
$605$	−4.11328	−	2.37480i	−0.167229	−	0.0965495i
$606$		0			0
$607$	−13.8179	+	23.9333i	−0.560851	+	0.971423i	0.436571	+	0.899670i	$0.356193\pi$
$607$	−13.8179	+	23.9333i	−0.560851	+	0.971423i	−0.997422	+	0.0717534i	$0.977141\pi$
$608$		0			0
$609$	−19.9276	+	11.5052i	−0.807506	+	0.466214i
$610$		0			0
$611$	20.9237	−	11.9364i	0.846482	−	0.482897i
$612$		0			0
$613$	−21.0216	+	12.1368i	−0.849054	+	0.490201i	−0.860331	−	0.509735i	$-0.829743\pi$
$613$	−21.0216	+	12.1368i	−0.849054	+	0.490201i	0.0112778	+	0.999936i	$0.496410\pi$
$614$		0			0
$615$	−15.6716	+	27.1439i	−0.631938	+	1.09455i
$616$		0			0
$617$	11.4091	+	6.58706i	0.459314	+	0.265185i	0.711756	−	0.702427i	$-0.247900\pi$
$617$	11.4091	+	6.58706i	0.459314	+	0.265185i	−0.252442	+	0.967612i	$0.581234\pi$
$618$		0			0
$619$		−	25.3673i		−	1.01960i	−0.860293	−	0.509799i	$-0.829720\pi$
$619$		−	25.3673i		−	1.01960i	0.860293	−	0.509799i	$-0.170280\pi$
$620$		0			0
$621$	6.23773	+	10.8041i	0.250311	+	0.433552i
$622$		0			0
$623$	−31.6133			−1.26656
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	15.1564	+	26.2517i	0.605290	+	1.04839i
$628$		0			0
$629$		−	6.46727i		−	0.257867i
$630$		0			0
$631$	36.3556	+	20.9899i	1.44729	+	0.835596i	0.998320	−	0.0579484i	$-0.0184559\pi$
$631$	36.3556	+	20.9899i	1.44729	+	0.835596i	0.448975	+	0.893544i	$0.351789\pi$
$632$		0			0
$633$	−24.4897	+	42.4174i	−0.973378	+	1.68594i
$634$		0			0
$635$	13.9632	−	8.06166i	0.554113	−	0.319917i
$636$		0			0
$637$	32.0394	−	54.8369i	1.26945	−	2.17272i
$638$		0			0
$639$	21.5042	−	12.4154i	0.850692	−	0.491147i
$640$		0			0
$641$	−2.41274	+	4.17899i	−0.0952975	+	0.165060i	−0.909733	−	0.415194i	$-0.863714\pi$
$641$	−2.41274	+	4.17899i	−0.0952975	+	0.165060i	0.814435	+	0.580254i	$0.197047\pi$
$642$		0			0
$643$	−18.5364	−	10.7020i	−0.731002	−	0.422044i	0.0877864	−	0.996139i	$-0.472021\pi$
$643$	−18.5364	−	10.7020i	−0.731002	−	0.422044i	−0.818789	+	0.574095i	$0.805354\pi$
$644$		0			0
$645$		−	8.70384i		−	0.342713i
$646$		0			0
$647$	−3.69721	−	6.40376i	−0.145353	−	0.251758i	0.784152	−	0.620569i	$-0.213098\pi$
$647$	−3.69721	−	6.40376i	−0.145353	−	0.251758i	−0.929504	+	0.368811i	$0.879765\pi$
$648$		0			0
$649$	−30.8484			−1.21091
$650$		0			0
$651$	21.4230			0.839633
$652$		0			0
$653$	9.46750	+	16.3982i	0.370492	+	0.641711i	0.989641	−	0.143562i	$-0.0458558\pi$
$653$	9.46750	+	16.3982i	0.370492	+	0.641711i	−0.619149	+	0.785273i	$0.712522\pi$
$654$		0			0
$655$		−	3.26372i		−	0.127524i
$656$		0			0
$657$	−30.6233	−	17.6804i	−1.19473	−	0.689776i
$658$		0			0
$659$	1.77854	−	3.08052i	0.0692820	−	0.120000i	−0.829303	−	0.558799i	$-0.811263\pi$
$659$	1.77854	−	3.08052i	0.0692820	−	0.120000i	0.898585	+	0.438799i	$0.144596\pi$
$660$		0			0
$661$	−7.24471	+	4.18274i	−0.281787	+	0.162690i	−0.634232	−	0.773143i	$-0.718684\pi$
$661$	−7.24471	+	4.18274i	−0.281787	+	0.162690i	0.352445	+	0.935832i	$0.385350\pi$
$662$		0			0
$663$	4.70040	+	8.23945i	0.182549	+	0.319994i
$664$		0			0
$665$	20.0054	−	11.5501i	0.775778	−	0.447895i
$666$		0			0
$667$	−5.46118	+	9.45905i	−0.211458	+	0.366256i
$668$		0			0
$669$	50.4476	+	29.1259i	1.95042	+	1.12607i
$670$		0			0
$671$			28.4055i			1.09658i
$672$		0			0
$673$	−22.3414	−	38.6965i	−0.861198	−	1.49164i	−0.870773	−	0.491685i	$-0.836381\pi$
$673$	−22.3414	−	38.6965i	−0.861198	−	1.49164i	0.00957533	−	0.999954i	$-0.496952\pi$
$674$		0			0
$675$	−2.03429			−0.0782999
$676$		0			0
$677$	−21.3684			−0.821253			−0.410627	−	0.911804i	$-0.634690\pi$
$677$	−21.3684			−0.821253			−0.410627	+	0.911804i	$0.634690\pi$
$678$		0			0
$679$	4.33256	+	7.50421i	0.166268	+	0.287985i
$680$		0			0
$681$		−	40.7235i		−	1.56053i
$682$		0			0
$683$	−12.3089	−	7.10654i	−0.470986	−	0.271924i	0.245666	−	0.969355i	$-0.420993\pi$
$683$	−12.3089	−	7.10654i	−0.470986	−	0.271924i	−0.716653	+	0.697430i	$0.754327\pi$
$684$		0			0
$685$	2.06337	−	3.57387i	0.0788374	−	0.136550i
$686$		0			0
$687$	65.7797	−	37.9779i	2.50965	−	1.44895i
$688$		0			0
$689$	17.4751	+	30.6326i	0.665749	+	1.16701i
$690$		0			0
$691$	14.2901	−	8.25038i	0.543620	−	0.313859i	−0.202925	−	0.979194i	$-0.565045\pi$
$691$	14.2901	−	8.25038i	0.543620	−	0.313859i	0.746545	+	0.665335i	$0.231711\pi$
$692$		0			0
$693$	−23.4504	+	40.6173i	−0.890807	+	1.54292i
$694$		0			0
$695$	−1.11208	−	0.642059i	−0.0421836	−	0.0243547i
$696$		0			0
$697$			12.1603i			0.460603i
$698$		0			0
$699$	−11.2010	−	19.4007i	−0.423660	−	0.733801i
$700$		0			0
$701$	34.4980			1.30297			0.651486	−	0.758661i	$-0.274146\pi$
$701$	34.4980			1.30297			0.651486	+	0.758661i	$0.274146\pi$
$702$		0			0
$703$	29.8049			1.12411
$704$		0			0
$705$	8.69901	+	15.0671i	0.327624	+	0.567461i
$706$		0			0
$707$		−	41.2471i		−	1.55126i
$708$		0			0
$709$	−20.8214	−	12.0212i	−0.781964	−	0.451467i	0.0551616	−	0.998477i	$-0.482433\pi$
$709$	−20.8214	−	12.0212i	−0.781964	−	0.451467i	−0.837126	+	0.547010i	$0.815766\pi$
$710$		0			0
$711$	22.0427	−	38.1792i	0.826667	−	1.43183i
$712$		0			0
$713$	8.80651	−	5.08444i	0.329806	−	0.190414i
$714$		0			0
$715$	−4.54739	+	7.78308i	−0.170063	+	0.291071i
$716$		0			0
$717$	−17.5653	+	10.1413i	−0.655986	+	0.378734i
$718$		0			0
$719$	−1.42633	+	2.47048i	−0.0531932	+	0.0921333i	−0.891396	−	0.453225i	$-0.850273\pi$
$719$	−1.42633	+	2.47048i	−0.0531932	+	0.0921333i	0.838203	+	0.545359i	$0.183607\pi$
$720$		0			0
$721$	24.3150	+	14.0383i	0.905537	+	0.522812i
$722$		0			0
$723$			10.5027i			0.390599i
$724$		0			0
$725$	−0.890520	−	1.54243i	−0.0330731	−	0.0572842i
$726$		0			0
$727$	9.88913			0.366768			0.183384	−	0.983041i	$-0.441295\pi$
$727$	9.88913			0.366768			0.183384	+	0.983041i	$0.441295\pi$
$728$		0			0
$729$	−38.7540			−1.43533
$730$		0			0
$731$	−1.68842	−	2.92444i	−0.0624486	−	0.108164i
$732$		0			0
$733$		−	20.0971i		−	0.742303i	−0.928572	−	0.371151i	$-0.878963\pi$
$733$		−	20.0971i		−	0.742303i	0.928572	−	0.371151i	$-0.121037\pi$
$734$		0			0
$735$	39.7245	+	22.9350i	1.46526	+	0.845969i
$736$		0			0
$737$	−4.86595	+	8.42807i	−0.179240	+	0.310452i
$738$		0			0
$739$	−5.38243	+	3.10755i	−0.197996	+	0.114313i	−0.595720	−	0.803192i	$-0.703133\pi$
$739$	−5.38243	+	3.10755i	−0.197996	+	0.114313i	0.397724	+	0.917505i	$0.369800\pi$
$740$		0			0
$741$	−37.9721	+	21.6622i	−1.39494	+	0.795779i
$742$		0			0
$743$	−14.7649	+	8.52453i	−0.541673	+	0.312735i	−0.745757	−	0.666219i	$-0.767912\pi$
$743$	−14.7649	+	8.52453i	−0.541673	+	0.312735i	0.204084	+	0.978953i	$0.434578\pi$
$744$		0			0
$745$	5.76902	−	9.99223i	0.211361	−	0.366087i
$746$		0			0
$747$	−39.9208	−	23.0483i	−1.46063	−	0.843293i
$748$		0			0
$749$		−	33.2809i		−	1.21606i
$750$		0			0
$751$	−12.1516	−	21.0472i	−0.443419	−	0.768024i	0.554522	−	0.832169i	$-0.312901\pi$
$751$	−12.1516	−	21.0472i	−0.443419	−	0.768024i	−0.997941	+	0.0641452i	$0.979568\pi$
$752$		0			0
$753$	−11.3090			−0.412122
$754$		0			0
$755$	−22.1588			−0.806441
$756$		0			0
$757$	−16.0959	−	27.8789i	−0.585015	−	1.01328i	−0.994874	−	0.101127i	$-0.967755\pi$
$757$	−16.0959	−	27.8789i	−0.585015	−	1.01328i	0.409858	−	0.912149i	$-0.365578\pi$
$758$		0			0
$759$			39.9255i			1.44920i
$760$		0			0
$761$	44.3483	+	25.6045i	1.60762	+	0.928162i	0.989900	+	0.141766i	$0.0452781\pi$
$761$	44.3483	+	25.6045i	1.60762	+	0.928162i	0.617723	+	0.786396i	$0.288055\pi$
$762$		0			0
$763$	−7.69033	+	13.3200i	−0.278408	+	0.482218i
$764$		0			0
$765$	−3.30837	+	1.91009i	−0.119614	+	0.0690593i
$766$		0			0
$767$	0.230074	−	44.4882i	0.00830751	−	1.60638i
$768$		0			0
$769$	33.9722	−	19.6138i	1.22507	−	0.707293i	0.259073	−	0.965858i	$-0.416583\pi$
$769$	33.9722	−	19.6138i	1.22507	−	0.707293i	0.965994	+	0.258565i	$0.0832495\pi$
$770$		0			0
$771$	4.18490	−	7.24847i	0.150716	−	0.261047i
$772$		0			0
$773$	−18.5977	−	10.7374i	−0.668914	−	0.386198i	0.126751	−	0.991935i	$-0.459545\pi$
$773$	−18.5977	−	10.7374i	−0.668914	−	0.386198i	−0.795665	+	0.605737i	$0.792878\pi$
$774$		0			0
$775$			1.65817i			0.0595633i
$776$		0			0
$777$	41.3511	+	71.6222i	1.48346	+	2.56943i
$778$		0			0
$779$	−56.0415			−2.00789
$780$		0			0
$781$	16.4179			0.587477
$782$		0			0
$783$	1.81158	+	3.13774i	0.0647405	+	0.112134i
$784$		0			0
$785$			1.70661i			0.0609116i
$786$		0			0
$787$	−23.2583	−	13.4282i	−0.829069	−	0.478663i	0.0244650	−	0.999701i	$-0.492212\pi$
$787$	−23.2583	−	13.4282i	−0.829069	−	0.478663i	−0.853534	+	0.521038i	$0.825545\pi$
$788$		0			0
$789$	−20.6339	+	35.7389i	−0.734586	+	1.27234i
$790$		0			0
$791$	11.6044	−	6.69981i	0.412606	−	0.238218i
$792$		0			0
$793$	−40.9652	−	0.211855i	−1.45472	−	0.00752318i
$794$		0			0
$795$	−22.0585	+	12.7355i	−0.782334	+	0.451681i
$796$		0			0
$797$	−2.71833	+	4.70829i	−0.0962882	+	0.166776i	−0.910146	−	0.414289i	$-0.864030\pi$
$797$	−2.71833	+	4.70829i	−0.0962882	+	0.166776i	0.813857	+	0.581065i	$0.197364\pi$
$798$		0			0
$799$	5.84563	+	3.37498i	0.206804	+	0.119398i
$800$		0			0
$801$			24.0936i			0.851307i
$802$		0			0
$803$	−11.6900	−	20.2477i	−0.412532	−	0.714526i
$804$		0			0
$805$	30.4257			1.07237
$806$		0			0
$807$	−57.8173			−2.03526
$808$		0			0
$809$	13.0787	+	22.6530i	0.459822	+	0.796435i	0.998951	−	0.0457878i	$-0.0145798\pi$
$809$	13.0787	+	22.6530i	0.459822	+	0.796435i	−0.539129	+	0.842223i	$0.681246\pi$
$810$		0			0
$811$		−	26.6986i		−	0.937513i	−0.883327	−	0.468757i	$-0.844702\pi$
$811$		−	26.6986i		−	0.937513i	0.883327	−	0.468757i	$-0.155298\pi$
$812$		0			0
$813$	69.2531	+	39.9833i	2.42881	+	1.40228i
$814$		0			0
$815$	1.95009	−	3.37766i	0.0683088	−	0.118314i
$816$		0			0
$817$	13.4775	−	7.78122i	0.471517	−	0.272231i
$818$		0			0
$819$	−58.4015	−	34.1221i	−2.04071	−	1.19232i
$820$		0			0
$821$	26.8191	−	15.4840i	0.935993	−	0.540396i	0.0472910	−	0.998881i	$-0.484941\pi$
$821$	26.8191	−	15.4840i	0.935993	−	0.540396i	0.888702	+	0.458485i	$0.151608\pi$
$822$		0			0
$823$	2.78771	−	4.82846i	0.0971735	−	0.168309i	−0.813340	−	0.581788i	$-0.802353\pi$
$823$	2.78771	−	4.82846i	0.0971735	−	0.168309i	0.910514	+	0.413479i	$0.135686\pi$
$824$		0			0
$825$	−5.63816	−	3.25519i	−0.196296	−	0.113331i
$826$		0			0
$827$		−	27.1365i		−	0.943627i	−0.881698	−	0.471813i	$-0.843600\pi$
$827$		−	27.1365i		−	0.943627i	0.881698	−	0.471813i	$-0.156400\pi$
$828$		0			0
$829$	25.8390	+	44.7545i	0.897426	+	1.55439i	0.830773	+	0.556611i	$0.187898\pi$
$829$	25.8390	+	44.7545i	0.897426	+	1.55439i	0.0666523	+	0.997776i	$0.478768\pi$
$830$		0			0
$831$	−18.1264			−0.628796
$832$		0			0
$833$	17.7963			0.616604
$834$		0			0
$835$	−3.50325	−	6.06780i	−0.121235	−	0.209985i
$836$		0			0
$837$		−	3.37321i		−	0.116595i
$838$		0			0
$839$	33.1191	+	19.1213i	1.14340	+	0.660142i	0.947270	−	0.320436i	$-0.103830\pi$
$839$	33.1191	+	19.1213i	1.14340	+	0.660142i	0.196129	+	0.980578i	$0.437163\pi$
$840$		0			0
$841$	12.9139	−	22.3676i	0.445309	−	0.771297i
$842$		0			0
$843$	59.5000	−	34.3523i	2.04929	−	1.18316i
$844$		0			0
$845$	−11.1905	−	6.61610i	−0.384965	−	0.227601i
$846$		0			0
$847$	20.4073	−	11.7822i	0.701203	−	0.404840i
$848$		0			0
$849$	20.9444	−	36.2768i	0.718811	−	1.24502i
$850$		0			0
$851$	33.9970	+	19.6282i	1.16540	+	0.672846i
$852$		0			0
$853$			27.8090i			0.952163i	0.879401	+	0.476081i	$0.157943\pi$
$853$			27.8090i			0.952163i	−0.879401	+	0.476081i	$0.842057\pi$
$854$		0			0
$855$	−8.80277	−	15.2468i	−0.301048	−	0.521431i
$856$		0			0
$857$	−52.0465			−1.77788			−0.888938	−	0.458027i	$-0.848556\pi$
$857$	−52.0465			−1.77788			−0.888938	+	0.458027i	$0.848556\pi$
$858$		0			0
$859$	51.2294			1.74793			0.873963	−	0.485993i	$-0.161542\pi$
$859$	51.2294			1.74793			0.873963	+	0.485993i	$0.161542\pi$
$860$		0			0
$861$	−77.7516	−	134.670i	−2.64977	−	4.58953i
$862$		0			0
$863$		−	41.3725i		−	1.40834i	−0.710033	−	0.704168i	$-0.751320\pi$
$863$		−	41.3725i		−	1.40834i	0.710033	−	0.704168i	$-0.248680\pi$
$864$		0			0
$865$	−2.58256	−	1.49104i	−0.0878098	−	0.0506970i
$866$		0			0
$867$	20.8056	−	36.0364i	0.706595	−	1.22386i
$868$		0			0
$869$	25.2436	−	14.5744i	0.856329	−	0.494402i
$870$		0			0
$871$	−12.1183	−	7.08032i	−0.410613	−	0.239907i
$872$		0			0
$873$	5.71922	−	3.30200i	0.193566	−	0.111756i
$874$		0			0
$875$	−2.48066	+	4.29663i	−0.0838616	+	0.145253i
$876$		0			0
$877$	−14.1526	−	8.17103i	−0.477901	−	0.275916i	0.241640	−	0.970366i	$-0.422315\pi$
$877$	−14.1526	−	8.17103i	−0.477901	−	0.275916i	−0.719541	+	0.694450i	$0.755648\pi$
$878$		0			0
$879$			83.7510i			2.82485i
$880$		0			0
$881$	−6.47265	−	11.2110i	−0.218069	−	0.377707i	0.736149	−	0.676820i	$-0.236642\pi$
$881$	−6.47265	−	11.2110i	−0.218069	−	0.377707i	−0.954218	+	0.299113i	$0.903309\pi$
$882$		0			0
$883$	−38.9257			−1.30995			−0.654977	−	0.755649i	$-0.727322\pi$
$883$	−38.9257			−1.30995			−0.654977	+	0.755649i	$0.727322\pi$
$884$		0			0
$885$	32.1316			1.08009
$886$		0			0
$887$	−6.27503	−	10.8687i	−0.210695	−	0.364934i	0.741237	−	0.671243i	$-0.234239\pi$
$887$	−6.27503	−	10.8687i	−0.210695	−	0.364934i	−0.951932	+	0.306309i	$0.900906\pi$
$888$		0			0
$889$			79.9929i			2.68288i
$890$		0			0
$891$	−13.0907	−	7.55792i	−0.438555	−	0.253200i
$892$		0			0
$893$	−15.5538	+	26.9400i	−0.520489	+	0.901513i
$894$		0			0
$895$	16.9252	−	9.77175i	0.565746	−	0.326633i
$896$		0			0
$897$	−57.5788	−	0.297773i	−1.92250	−	0.00994236i
$898$		0			0
$899$	2.55761	−	1.47663i	0.0853010	−	0.0492485i
$900$		0			0
$901$	−4.94101	+	8.55808i	−0.164609	+	0.285111i
$902$		0			0
$903$	37.3972	+	21.5913i	1.24450	+	0.718512i
$904$		0			0
$905$		−	2.22811i		−	0.0740648i
$906$		0			0
$907$	20.3215	+	35.1980i	0.674766	+	1.16873i	0.976537	+	0.215349i	$0.0690888\pi$
$907$	20.3215	+	35.1980i	0.674766	+	1.16873i	−0.301771	+	0.953380i	$0.597578\pi$
$908$		0			0
$909$	−31.4358			−1.04266
$910$		0			0
$911$	−41.5783			−1.37755			−0.688776	−	0.724975i	$-0.741851\pi$
$911$	−41.5783			−1.37755			−0.688776	+	0.724975i	$0.741851\pi$
$912$		0			0
$913$	−15.2392	−	26.3951i	−0.504345	−	0.873552i
$914$		0			0
$915$		−	29.5871i		−	0.978119i
$916$		0			0
$917$	14.0230	+	8.09617i	0.463080	+	0.267359i
$918$		0			0
$919$	13.5620	−	23.4901i	0.447369	−	0.774866i	−0.550845	−	0.834608i	$-0.685694\pi$
$919$	13.5620	−	23.4901i	0.447369	−	0.774866i	0.998214	+	0.0597417i	$0.0190277\pi$
$920$		0			0
$921$	58.2920	−	33.6549i	1.92079	−	1.10897i
$922$		0			0
$923$	−0.122448	+	23.6771i	−0.00403043	+	0.779342i
$924$		0			0
$925$	−5.54367	+	3.20064i	−0.182275	+	0.105236i
$926$		0			0
$927$	10.6990	−	18.5313i	0.351403	−	0.608647i
$928$		0			0
$929$	−27.1844	−	15.6949i	−0.891893	−	0.514935i	−0.0173316	−	0.999850i	$-0.505517\pi$
$929$	−27.1844	−	15.6949i	−0.891893	−	0.514935i	−0.874561	+	0.484915i	$0.838850\pi$
$930$		0			0
$931$			82.0154i			2.68795i
$932$		0			0
$933$	−32.0453	−	55.5040i	−1.04911	−	1.81712i
$934$		0			0
$935$	−2.52585			−0.0826041
$936$		0			0
$937$	36.0313			1.17709			0.588545	−	0.808464i	$-0.299701\pi$
$937$	36.0313			1.17709			0.588545	+	0.808464i	$0.299701\pi$
$938$		0			0
$939$	−10.6359	−	18.4220i	−0.347090	−	0.601178i
$940$		0			0
$941$			56.0340i			1.82666i	0.407226	+	0.913328i	$0.366496\pi$
$941$			56.0340i			1.82666i	−0.407226	+	0.913328i	$0.633504\pi$
$942$		0			0
$943$	−63.9239	−	36.9065i	−2.08165	−	1.20184i
$944$		0			0
$945$	5.04639	−	8.74060i	0.164159	−	0.284332i
$946$		0			0
$947$	21.3836	−	12.3458i	0.694874	−	0.401185i	−0.110562	−	0.993869i	$-0.535265\pi$
$947$	21.3836	−	12.3458i	0.694874	−	0.401185i	0.805435	+	0.592684i	$0.201932\pi$
$948$		0			0
$949$	29.2876	−	16.7078i	0.950714	−	0.542359i
$950$		0			0
$951$	34.8615	−	20.1273i	1.13046	−	0.652672i
$952$		0			0
$953$	−20.4838	+	35.4790i	−0.663536	+	1.14928i	0.316143	+	0.948711i	$0.397612\pi$
$953$	−20.4838	+	35.4790i	−0.663536	+	1.14928i	−0.979680	+	0.200567i	$0.935721\pi$
$954$		0			0
$955$	−8.03263	−	4.63764i	−0.259930	−	0.150071i
$956$		0			0
$957$			11.5953i			0.374821i
$958$		0			0
$959$	10.2371	+	17.7311i	0.330572	+	0.572567i
$960$		0			0
$961$	28.2505			0.911305
$962$		0			0
$963$	−25.3646			−0.817362
$964$		0			0
$965$	−11.8802	−	20.5772i	−0.382439	−	0.662403i
$966$		0			0
$967$			46.7111i			1.50213i	0.660229	+	0.751064i	$0.270459\pi$
$967$			46.7111i			1.50213i	−0.660229	+	0.751064i	$0.729541\pi$
$968$		0			0
$969$	−10.6086	−	6.12488i	−0.340797	−	0.196759i
$970$		0			0
$971$	−11.1530	+	19.3176i	−0.357918	+	0.619932i	−0.987613	−	0.156910i	$-0.949847\pi$
$971$	−11.1530	+	19.3176i	−0.357918	+	0.619932i	0.629695	+	0.776843i	$0.283180\pi$
$972$		0			0
$973$	5.51738	−	3.18546i	0.176879	−	0.102121i
$974$		0			0
$975$	4.73655	−	8.10683i	0.151691	−	0.259626i
$976$		0			0
$977$	19.1058	−	11.0308i	0.611250	−	0.352905i	−0.162205	−	0.986757i	$-0.551860\pi$
$977$	19.1058	−	11.0308i	0.611250	−	0.352905i	0.773454	+	0.633852i	$0.218527\pi$
$978$		0			0
$979$	−7.96520	+	13.7961i	−0.254569	+	0.440926i
$980$		0			0
$981$	10.1517	+	5.86107i	0.324118	+	0.187129i
$982$		0			0
$983$		−	12.1564i		−	0.387729i	−0.981028	−	0.193865i	$-0.937898\pi$
$983$		−	12.1564i		−	0.387729i	0.981028	−	0.193865i	$-0.0621022\pi$
$984$		0			0
$985$	−6.81671	−	11.8069i	−0.217198	−	0.376199i
$986$		0			0
$987$	−86.3172			−2.74751
$988$		0			0
$989$	20.4975			0.651783
$990$		0			0
$991$	−19.6312	−	34.0023i	−0.623607	−	1.08012i	−0.988808	−	0.149190i	$-0.952333\pi$
$991$	−19.6312	−	34.0023i	−0.623607	−	1.08012i	0.365202	−	0.930928i	$-0.381000\pi$
$992$		0			0
$993$			5.91886i			0.187829i
$994$		0			0
$995$	21.8200	+	12.5978i	0.691739	+	0.399376i
$996$		0			0
$997$	−16.2119	+	28.0799i	−0.513437	+	0.889300i	0.486441	+	0.873713i	$0.338295\pi$
$997$	−16.2119	+	28.0799i	−0.513437	+	0.889300i	−0.999879	+	0.0155864i	$0.995039\pi$
$998$		0			0
$999$	11.2774	−	6.51104i	0.356803	−	0.206000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.da.e.881.1		12
4.3	odd	2		520.2.bu.a.361.6	yes	12
13.4	even	6	inner	1040.2.da.e.641.1		12
52.11	even	12		6760.2.a.bg.1.1		6
52.15	even	12		6760.2.a.bj.1.1		6
52.43	odd	6		520.2.bu.a.121.6	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.bu.a.121.6	✓	12	52.43	odd	6
520.2.bu.a.361.6	yes	12	4.3	odd	2
1040.2.da.e.641.1		12	13.4	even	6	inner
1040.2.da.e.881.1		12	1.1	even	1	trivial
6760.2.a.bg.1.1		6	52.11	even	12
6760.2.a.bj.1.1		6	52.15	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.da (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.30204 - 2.25519i) q^{3} +1.00000i q^{5} +(-4.29663 - 2.48066i) q^{7} +(-1.89060 + 3.27461i) q^{9} +O(q^{10})\)	\(q+(-1.30204 - 2.25519i) q^{3} +1.00000i q^{5} +(-4.29663 - 2.48066i) q^{7} +(-1.89060 + 3.27461i) q^{9} +(-2.16513 + 1.25004i) q^{11} +(-1.78660 - 3.13178i) q^{13} +(2.25519 - 1.30204i) q^{15} +(0.505154 - 0.874953i) q^{17} +(4.03228 + 2.32804i) q^{19} +12.9196i q^{21} +(3.06629 + 5.31097i) q^{23} -1.00000 q^{25} +2.03429 q^{27} +(0.890520 + 1.54243i) q^{29} -1.65817i q^{31} +(5.63816 + 3.25519i) q^{33} +(2.48066 - 4.29663i) q^{35} +(5.54367 - 3.20064i) q^{37} +(-4.73655 + 8.10683i) q^{39} +(-10.4236 + 6.01810i) q^{41} +(1.67120 - 2.89460i) q^{43} +(-3.27461 - 1.89060i) q^{45} +6.68108i q^{47} +(8.80735 + 15.2548i) q^{49} -2.63092 q^{51} -9.78120 q^{53} +(-1.25004 - 2.16513i) q^{55} -12.1248i q^{57} +(10.6859 + 6.16949i) q^{59} +(5.68093 - 9.83965i) q^{61} +(16.2464 - 9.37986i) q^{63} +(3.13178 - 1.78660i) q^{65} +(3.37112 - 1.94632i) q^{67} +(7.98485 - 13.8302i) q^{69} +(-5.68713 - 3.28347i) q^{71} +9.35173i q^{73} +(1.30204 + 2.25519i) q^{75} +12.4037 q^{77} -11.6591 q^{79} +(3.02307 + 5.23611i) q^{81} +12.1910i q^{83} +(0.874953 + 0.505154i) q^{85} +(2.31898 - 4.01659i) q^{87} +(5.51828 - 3.18598i) q^{89} +(-0.0925095 + 17.8881i) q^{91} +(-3.73950 + 2.15900i) q^{93} +(-2.32804 + 4.03228i) q^{95} +(-1.51254 - 0.873267i) q^{97} -9.45329i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{7} + 2 q^{9}+O(q^{10}) \) 12 * q - 6 * q^7 + 2 * q^9	\( 12 q - 6 q^{7} + 2 q^{9} - 2 q^{13} - 8 q^{17} + 24 q^{19} + 2 q^{23} - 12 q^{25} + 12 q^{27} + 12 q^{29} + 4 q^{35} + 24 q^{37} - 28 q^{39} + 24 q^{41} + 18 q^{43} - 12 q^{45} + 24 q^{49} - 68 q^{53} - 2 q^{55} + 48 q^{59} + 18 q^{61} + 36 q^{63} + 16 q^{65} - 18 q^{67} - 8 q^{69} + 64 q^{77} + 12 q^{79} + 14 q^{81} - 18 q^{87} + 30 q^{89} - 76 q^{91} - 12 q^{93} + 10 q^{95} - 84 q^{97}+O(q^{100}) \) 12 * q - 6 * q^7 + 2 * q^9 - 2 * q^13 - 8 * q^17 + 24 * q^19 + 2 * q^23 - 12 * q^25 + 12 * q^27 + 12 * q^29 + 4 * q^35 + 24 * q^37 - 28 * q^39 + 24 * q^41 + 18 * q^43 - 12 * q^45 + 24 * q^49 - 68 * q^53 - 2 * q^55 + 48 * q^59 + 18 * q^61 + 36 * q^63 + 16 * q^65 - 18 * q^67 - 8 * q^69 + 64 * q^77 + 12 * q^79 + 14 * q^81 - 18 * q^87 + 30 * q^89 - 76 * q^91 - 12 * q^93 + 10 * q^95 - 84 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more