LMFDB - Embedded newform 1040.2.da.e.641.1

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			641.1
Root			$-1.12906 - 0.851598i$ of defining polynomial
Character	$\chi$	$=$	1040.641
Dual form			1040.2.da.e.881.1

$q$-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 $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

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

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	0.195252	+	0.980753i	$0.437448\pi$
$3$	−1.30204	+	2.25519i	−0.751731	+	1.30204i	−0.946983	+	0.321283i	$0.895886\pi$
$4$		0			0
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	−4.29663	+	2.48066i	−1.62397	+	0.937601i	−0.638130	+	0.769928i	$0.720292\pi$
$7$	−4.29663	+	2.48066i	−1.62397	+	0.937601i	−0.985843	+	0.167673i	$0.946375\pi$
$8$		0			0
$9$	−1.89060	−	3.27461i	−0.630199	−	1.09154i
$10$		0			0
$11$	−2.16513	−	1.25004i	−0.652812	−	0.376901i	0.136721	−	0.990610i	$-0.456344\pi$
$11$	−2.16513	−	1.25004i	−0.652812	−	0.376901i	−0.789533	+	0.613709i	$0.789677\pi$
$12$		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	0.920760	−	0.390130i	$-0.127570\pi$
$17$	0.505154	+	0.874953i	0.122518	+	0.212207i	−0.798242	+	0.602337i	$0.794236\pi$
$18$		0			0
$19$	4.03228	−	2.32804i	0.925069	−	0.534089i	0.0398203	−	0.999207i	$-0.487321\pi$
$19$	4.03228	−	2.32804i	0.925069	−	0.534089i	0.885249	+	0.465118i	$0.153988\pi$
$20$		0			0
$21$		−	12.9196i		−	2.81930i
$22$		0			0
$23$	3.06629	−	5.31097i	0.639366	−	1.10741i	−0.346206	−	0.938158i	$-0.612530\pi$
$23$	3.06629	−	5.31097i	0.639366	−	1.10741i	0.985572	−	0.169256i	$-0.0541364\pi$
$24$		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	−0.771420	−	0.636327i	$-0.780453\pi$
$29$	0.890520	−	1.54243i	0.165365	−	0.286421i	0.936785	+	0.349906i	$0.113786\pi$
$30$		0			0
$31$			1.65817i			0.297817i	0.988851	+	0.148908i	$0.0475759\pi$
$31$			1.65817i			0.297817i	−0.988851	+	0.148908i	$0.952424\pi$
$32$		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	0.880873	−	0.473353i	$-0.156956\pi$
$37$	5.54367	+	3.20064i	0.911374	+	0.526182i	0.0305011	+	0.999535i	$0.490290\pi$
$38$		0			0
$39$	−4.73655	−	8.10683i	−0.758455	−	1.29813i
$40$		0			0
$41$	−10.4236	−	6.01810i	−1.62790	−	0.939869i	−0.984718	−	0.174156i	$-0.944280\pi$
$41$	−10.4236	−	6.01810i	−1.62790	−	0.939869i	−0.643182	−	0.765713i	$-0.722386\pi$
$42$		0			0
$43$	1.67120	+	2.89460i	0.254855	+	0.441422i	0.964856	−	0.262779i	$-0.0846389\pi$
$43$	1.67120	+	2.89460i	0.254855	+	0.441422i	−0.710001	+	0.704201i	$0.751306\pi$
$44$		0			0
$45$	−3.27461	+	1.89060i	−0.488150	+	0.281834i
$46$		0			0
$47$		−	6.68108i		−	0.974536i	−0.873252	−	0.487268i	$-0.837993\pi$
$47$		−	6.68108i		−	0.974536i	0.873252	−	0.487268i	$-0.162007\pi$
$48$		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	0.397736	−	0.917500i	$-0.369796\pi$
$59$	10.6859	−	6.16949i	1.39118	−	0.803199i	0.993446	+	0.114300i	$0.0364627\pi$
$60$		0			0
$61$	5.68093	+	9.83965i	0.727368	+	1.25984i	0.957992	+	0.286795i	$0.0925900\pi$
$61$	5.68093	+	9.83965i	0.727368	+	1.25984i	−0.230624	+	0.973043i	$0.574077\pi$
$62$		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	0.691584	−	0.722296i	$-0.256913\pi$
$67$	3.37112	+	1.94632i	0.411848	+	0.237781i	−0.279735	+	0.960077i	$0.590247\pi$
$68$		0			0
$69$	7.98485	+	13.8302i	0.961262	+	1.66496i
$70$		0			0
$71$	−5.68713	+	3.28347i	−0.674939	+	0.389676i	−0.797945	−	0.602730i	$-0.794080\pi$
$71$	−5.68713	+	3.28347i	−0.674939	+	0.389676i	0.123007	+	0.992406i	$0.460746\pi$
$72$		0			0
$73$		−	9.35173i		−	1.09454i	−0.836957	−	0.547268i	$-0.815668\pi$
$73$		−	9.35173i		−	1.09454i	0.836957	−	0.547268i	$-0.184332\pi$
$74$		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	$-0.766693\pi$
$83$		−	12.1910i		−	1.33814i	0.743200	−	0.669069i	$-0.233307\pi$
$84$		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	0.763093	−	0.646289i	$-0.223680\pi$
$89$	5.51828	+	3.18598i	0.584936	+	0.337713i	−0.178156	+	0.984002i	$0.557013\pi$
$90$		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	−0.574818	−	0.818281i	$-0.694927\pi$
$97$	−1.51254	+	0.873267i	−0.153576	+	0.0886669i	0.421243	+	0.906948i	$0.361594\pi$
$98$		0			0
$99$			9.45329i			0.950091i
$100$		0			0
$101$	4.15686	−	7.19990i	0.413623	−	0.716417i	−0.581659	−	0.813432i	$-0.697596\pi$
$101$	4.15686	−	7.19990i	0.413623	−	0.716417i	0.995283	+	0.0970156i	$0.0309297\pi$
$102$		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	−0.657112	−	0.753793i	$-0.728222\pi$
$107$	3.35404	−	5.80937i	0.324247	−	0.561613i	0.981360	+	0.192180i	$0.0615556\pi$
$108$		0			0
$109$			3.10011i			0.296937i	0.988917	+	0.148468i	$0.0474343\pi$
$109$			3.10011i			0.296937i	−0.988917	+	0.148468i	$0.952566\pi$
$110$		0			0
$111$	−14.4361	+	8.33470i	−1.37022	+	0.791095i
$112$		0			0
$113$	−1.35041	−	2.33898i	−0.127036	−	0.220033i	0.795491	−	0.605965i	$-0.207213\pi$
$113$	−1.35041	−	2.33898i	−0.127036	−	0.220033i	−0.922527	+	0.385933i	$0.873880\pi$
$114$		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	0.247466	+	0.968897i	$0.420402\pi$
$127$	−8.06166	+	13.9632i	−0.715356	+	1.23903i	−0.962822	+	0.270137i	$0.912931\pi$
$128$		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	−0.644838	−	0.764320i	$-0.723075\pi$
$137$	−3.57387	+	2.06337i	−0.305336	+	0.176286i	0.339501	+	0.940606i	$0.389742\pi$
$138$		0			0
$139$	−0.642059	−	1.11208i	−0.0544587	−	0.0943253i	0.837511	−	0.546421i	$-0.184010\pi$
$139$	−0.642059	−	1.11208i	−0.0544587	−	0.0943253i	−0.891970	+	0.452095i	$0.850677\pi$
$140$		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	−0.849932	−	0.526892i	$-0.823357\pi$
$149$	−9.99223	+	5.76902i	−0.818596	+	0.472616i	0.0313362	+	0.999509i	$0.490024\pi$
$150$		0			0
$151$		−	22.1588i		−	1.80326i	−0.432511	−	0.901628i	$-0.642372\pi$
$151$		−	22.1588i		−	1.80326i	0.432511	−	0.901628i	$-0.357628\pi$
$152$		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	−0.626412	−	0.779492i	$-0.715477\pi$
$163$	−3.37766	+	1.95009i	−0.264559	+	0.152743i	0.361854	+	0.932235i	$0.382144\pi$
$164$		0			0
$165$	−3.25519	−	5.63816i	−0.253416	−	0.438930i
$166$		0			0
$167$	−6.06780	−	3.50325i	−0.469540	−	0.271089i	0.246507	−	0.969141i	$-0.420717\pi$
$167$	−6.06780	−	3.50325i	−0.469540	−	0.271089i	−0.716047	+	0.698052i	$0.754051\pi$
$168$		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	0.803762	−	0.594951i	$-0.202829\pi$
$173$	−1.49104	−	2.58256i	−0.113362	−	0.196349i	−0.917124	+	0.398603i	$0.869495\pi$
$174$		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	0.226349	+	0.974046i	$0.427321\pi$
$179$	−9.77175	+	16.9252i	−0.730375	+	1.26505i	−0.956723	+	0.291000i	$0.906012\pi$
$180$		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	0.648026	−	0.761618i	$-0.275595\pi$
$191$	−4.63764	−	8.03263i	−0.335568	−	0.581221i	−0.983594	+	0.180398i	$0.942262\pi$
$192$		0			0
$193$	−20.5772	−	11.8802i	−1.48118	−	0.855159i	−0.481406	−	0.876498i	$-0.659874\pi$
$193$	−20.5772	−	11.8802i	−1.48118	−	0.855159i	−0.999772	+	0.0213387i	$0.993207\pi$
$194$		0			0
$195$	−8.10683	+	4.73655i	−0.580542	+	0.339191i
$196$		0			0
$197$	−11.8069	−	6.81671i	−0.841206	−	0.485670i	0.0164682	−	0.999864i	$-0.494758\pi$
$197$	−11.8069	−	6.81671i	−0.841206	−	0.485670i	−0.857674	+	0.514194i	$0.828091\pi$
$198$		0			0
$199$	12.5978	+	21.8200i	0.893031	+	1.54678i	0.836223	+	0.548390i	$0.184759\pi$
$199$	12.5978	+	21.8200i	0.893031	+	1.54678i	0.0568086	+	0.998385i	$0.481908\pi$
$200$		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	0.336311	+	0.941751i	$0.390821\pi$
$211$	−9.40438	+	16.2889i	−0.647424	+	1.12137i	−0.983736	+	0.179621i	$0.942513\pi$
$212$		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	−0.317350	−	0.948309i	$-0.602793\pi$
$223$	−19.3726	−	11.1848i	−1.29728	−	0.748987i	−0.979934	+	0.199321i	$0.936126\pi$
$224$		0			0
$225$	1.89060	+	3.27461i	0.126040	+	0.218307i
$226$		0			0
$227$	13.5432	−	7.81919i	0.898896	−	0.518978i	0.0220542	−	0.999757i	$-0.492979\pi$
$227$	13.5432	−	7.81919i	0.898896	−	0.518978i	0.876842	+	0.480779i	$0.159646\pi$
$228$		0			0
$229$		−	29.1681i		−	1.92748i	−0.266839	−	0.963741i	$-0.585979\pi$
$229$		−	29.1681i		−	1.92748i	0.266839	−	0.963741i	$-0.414021\pi$
$230$		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	$0.0810580\pi$
$239$			7.78880i			0.503816i	−0.967751	+	0.251908i	$0.918942\pi$
$240$		0			0
$241$	−3.49283	+	2.01659i	−0.224993	+	0.129900i	−0.608260	−	0.793738i	$-0.708132\pi$
$241$	−3.49283	+	2.01659i	−0.224993	+	0.129900i	0.383267	+	0.923638i	$0.374799\pi$
$242$		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	0.926382	−	0.376586i	$-0.122902\pi$
$251$	2.17140	+	3.76098i	0.137058	+	0.237391i	−0.789324	+	0.613977i	$0.789569\pi$
$252$		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	−0.811540	−	0.584297i	$-0.801370\pi$
$257$	1.60706	−	2.78351i	0.100246	−	0.173631i	0.911786	+	0.410666i	$0.134704\pi$
$258$		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	−0.999914	−	0.0131185i	$-0.995824\pi$
$263$	−7.92370	+	13.7242i	−0.488596	+	0.846273i	0.511318	+	0.859392i	$0.329157\pi$
$264$		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	0.975922	+	0.218121i	$0.0699928\pi$
$269$	11.1013	+	19.2280i	0.676859	+	1.17235i	−0.299062	+	0.954234i	$0.596674\pi$
$270$		0			0
$271$	−26.5941	−	15.3541i	−1.61548	−	0.932697i	−0.988070	−	0.154008i	$-0.950782\pi$
$271$	−26.5941	−	15.3541i	−1.61548	−	0.932697i	−0.627410	−	0.778689i	$-0.715885\pi$
$272$		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	0.951436	−	0.307846i	$-0.0996080\pi$
$277$	3.48039	+	6.02820i	0.209116	+	0.362200i	−0.742320	+	0.670045i	$0.766275\pi$
$278$		0			0
$279$	5.42987	−	3.13494i	0.325078	−	0.187684i
$280$		0			0
$281$		−	26.3835i		−	1.57391i	−0.617011	−	0.786955i	$-0.711657\pi$
$281$		−	26.3835i		−	1.57391i	0.617011	−	0.786955i	$-0.288343\pi$
$282$		0			0
$283$	8.04295	−	13.9308i	0.478104	−	0.828100i	−0.521581	−	0.853202i	$-0.674658\pi$
$283$	8.04295	−	13.9308i	0.478104	−	0.828100i	0.999685	+	0.0251019i	$0.00799101\pi$
$284$		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	−0.642241	+	0.766503i	$0.721995\pi$
$293$	−27.8527	+	16.0808i	−1.62717	+	0.939448i	−0.984931	+	0.172946i	$0.944671\pi$
$294$		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	$-0.735955\pi$
$307$		−	25.8479i		−	1.47522i	0.675229	−	0.737609i	$-0.264045\pi$
$308$		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	$-0.857062\pi$
$317$		−	15.4583i		−	0.868226i	0.900858	−	0.434113i	$-0.142938\pi$
$318$		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	−0.553120	−	0.833101i	$-0.686563\pi$
$331$	−1.96841	+	1.13646i	−0.108194	+	0.0624656i	0.444927	+	0.895567i	$0.353230\pi$
$332$		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	0.783904	−	0.620882i	$-0.213226\pi$
$347$	−2.71499	−	4.70249i	−0.145748	−	0.252443i	−0.929652	+	0.368439i	$0.879892\pi$
$348$		0			0
$349$	−4.81517	−	2.78004i	−0.257750	−	0.148812i	0.365558	−	0.930789i	$-0.380878\pi$
$349$	−4.81517	−	2.78004i	−0.257750	−	0.148812i	−0.623308	+	0.781977i	$0.714212\pi$
$350$		0			0
$351$	−3.63447	+	6.37095i	−0.193994	+	0.340056i
$352$		0			0
$353$	14.9697	+	8.64276i	0.796756	+	0.460008i	0.842336	−	0.538953i	$-0.181180\pi$
$353$	14.9697	+	8.64276i	0.796756	+	0.460008i	−0.0455793	+	0.998961i	$0.514513\pi$
$354$		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	$0.136210\pi$
$359$			15.7254i			0.829953i	−0.909832	+	0.414976i	$0.863790\pi$
$360$		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	−0.853402	−	0.521253i	$-0.825465\pi$
$367$	0.473516	−	0.820153i	0.0247173	−	0.0428117i	0.878119	+	0.478441i	$0.158798\pi$
$368$		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	0.922090	−	0.386974i	$-0.126480\pi$
$373$	2.43183	+	4.21206i	0.125916	+	0.218092i	−0.796175	+	0.605067i	$0.793146\pi$
$374$		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	0.939083	−	0.343691i	$-0.111677\pi$
$379$	21.6285	+	12.4872i	1.11098	+	0.641424i	0.171896	+	0.985115i	$0.445011\pi$
$380$		0			0
$381$	−20.9931	−	36.3612i	−1.07551	−	1.86284i
$382$		0			0
$383$	27.7458	−	16.0190i	1.41774	−	0.818535i	0.421643	−	0.906762i	$-0.361453\pi$
$383$	27.7458	−	16.0190i	1.41774	−	0.818535i	0.996100	+	0.0882271i	$0.0281201\pi$
$384$		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	−0.916123	−	0.400897i	$-0.868698\pi$
$397$	−20.4628	+	11.8142i	−1.02700	+	0.592937i	−0.110874	+	0.993834i	$0.535365\pi$
$398$		0			0
$399$	−30.0774	−	52.0956i	−1.50575	−	2.60804i
$400$		0			0
$401$	−22.1437	−	12.7847i	−1.10580	−	0.638436i	−0.168065	−	0.985776i	$-0.553752\pi$
$401$	−22.1437	−	12.7847i	−1.10580	−	0.638436i	−0.937739	+	0.347340i	$0.887085\pi$
$402$		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	−0.805535	−	0.592548i	$-0.798122\pi$
$409$	−14.0583	+	8.11659i	−0.695141	+	0.401340i	0.110394	+	0.993888i	$0.464789\pi$
$410$		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	−0.935235	−	0.354027i	$-0.884812\pi$
$419$	−3.29602	+	5.70887i	−0.161021	+	0.278897i	0.774214	+	0.632924i	$0.218145\pi$
$420$		0			0
$421$		−	26.0223i		−	1.26825i	−0.773231	−	0.634125i	$-0.781361\pi$
$421$		−	26.0223i		−	1.26825i	0.773231	−	0.634125i	$-0.218639\pi$
$422$		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	0.00688275	−	0.999976i	$-0.497809\pi$
$431$	−17.7644	−	10.2563i	−0.855681	−	0.494028i	−0.862564	+	0.505949i	$0.831142\pi$
$432$		0			0
$433$	3.31585	+	5.74322i	0.159350	+	0.276002i	0.934634	−	0.355610i	$-0.115727\pi$
$433$	3.31585	+	5.74322i	0.159350	+	0.276002i	−0.775285	+	0.631612i	$0.782394\pi$
$434$		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	−0.525519	−	0.850782i	$-0.676129\pi$
$439$	9.93221	−	17.2031i	0.474039	−	0.821059i	0.999558	+	0.0297224i	$0.00946233\pi$
$440$		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	−0.620966	−	0.783837i	$-0.713260\pi$
$449$	−5.35306	+	3.09059i	−0.252627	+	0.145854i	0.368340	+	0.929691i	$0.379926\pi$
$450$		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	0.803361	−	0.595493i	$-0.203043\pi$
$457$	14.7362	+	8.50794i	0.689330	+	0.397985i	−0.114031	+	0.993477i	$0.536376\pi$
$458$		0			0
$459$	1.02763	+	1.77991i	0.0479657	+	0.0830790i
$460$		0			0
$461$	16.1576	−	9.32857i	0.752533	−	0.434475i	−0.0740756	−	0.997253i	$-0.523601\pi$
$461$	16.1576	−	9.32857i	0.752533	−	0.434475i	0.826608	+	0.562778i	$0.190267\pi$
$462$		0			0
$463$			2.58064i			0.119933i	0.998200	+	0.0599663i	$0.0190993\pi$
$463$			2.58064i			0.119933i	−0.998200	+	0.0599663i	$0.980901\pi$
$464$		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	0.431796	−	0.901971i	$-0.357880\pi$
$479$	−2.92039	−	1.68609i	−0.133436	−	0.0770393i	−0.565232	+	0.824932i	$0.691213\pi$
$480$		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	0.121440	−	0.992599i	$-0.461249\pi$
$487$	22.9900	−	13.2733i	1.04178	−	0.601470i	0.920336	+	0.391129i	$0.127915\pi$
$488$		0			0
$489$		−	10.1564i		−	0.459287i
$490$		0			0
$491$	−0.545246	+	0.944393i	−0.0246066	+	0.0426199i	−0.878066	−	0.478539i	$-0.841167\pi$
$491$	−0.545246	+	0.944393i	−0.0246066	+	0.0426199i	0.853460	+	0.521159i	$0.174500\pi$
$492$		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	$-0.965048\pi$
$499$		−	4.89586i		−	0.219169i	0.993977	−	0.109585i	$-0.0349520\pi$
$500$		0			0
$501$	15.8010	−	9.12271i	0.705936	−	0.407572i
$502$		0			0
$503$	−2.95834	−	5.12399i	−0.131906	−	0.228467i	0.792505	−	0.609865i	$-0.208776\pi$
$503$	−2.95834	−	5.12399i	−0.131906	−	0.228467i	−0.924411	+	0.381397i	$0.875443\pi$
$504$		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	0.219003	−	0.975724i	$-0.429719\pi$
$509$	−11.6527	−	6.72769i	−0.516497	−	0.298200i	−0.735500	+	0.677524i	$0.763053\pi$
$510$		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	−0.592542	−	0.805539i	$-0.701876\pi$
$523$	9.17847	−	15.8976i	0.401346	−	0.695152i	0.993889	+	0.110387i	$0.0352090\pi$
$524$		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	$0.107607\pi$
$541$			15.4282i			0.663311i	−0.943401	+	0.331655i	$0.892393\pi$
$542$		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	0.979237	−	0.202720i	$-0.0649782\pi$
$557$	30.5228	+	17.6224i	1.29329	+	0.746684i	0.314058	+	0.949404i	$0.398312\pi$
$558$		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	−0.868385	−	0.495891i	$-0.834841\pi$
$563$	−20.4923	−	35.4937i	−0.863647	−	1.49588i	0.00473796	−	0.999989i	$-0.498492\pi$
$564$		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	−0.995489	−	0.0948766i	$-0.969754\pi$
$569$	−9.91311	+	17.1700i	−0.415579	+	0.719804i	0.579910	+	0.814681i	$0.303088\pi$
$570$		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	$0.0221472\pi$
$577$			3.33992i			0.139043i	−0.997580	+	0.0695214i	$0.977853\pi$
$578$		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	0.406110	−	0.913824i	$-0.366885\pi$
$587$	−4.41510	−	2.54906i	−0.182231	−	0.105211i	−0.588340	+	0.808613i	$0.700218\pi$
$588$		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	$0.00201528\pi$
$593$			0.308347i			0.0126623i	−0.999980	+	0.00633114i	$0.997985\pi$
$594$		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	−0.827084	−	0.562079i	$-0.810002\pi$
$601$	1.79532	−	3.10958i	0.0732325	−	0.126842i	0.900316	+	0.435236i	$0.143335\pi$
$602$		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	−0.997422	−	0.0717534i	$-0.977141\pi$
$607$	−13.8179	−	23.9333i	−0.560851	−	0.971423i	0.436571	−	0.899670i	$-0.356193\pi$
$608$		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	0.0112778	−	0.999936i	$-0.496410\pi$
$613$	−21.0216	−	12.1368i	−0.849054	−	0.490201i	−0.860331	+	0.509735i	$0.829743\pi$
$614$		0			0
$615$	−15.6716	−	27.1439i	−0.631938	−	1.09455i
$616$		0			0
$617$	11.4091	−	6.58706i	0.459314	−	0.265185i	−0.252442	−	0.967612i	$-0.581234\pi$
$617$	11.4091	−	6.58706i	0.459314	−	0.265185i	0.711756	+	0.702427i	$0.247900\pi$
$618$		0			0
$619$			25.3673i			1.01960i	0.860293	+	0.509799i	$0.170280\pi$
$619$			25.3673i			1.01960i	−0.860293	+	0.509799i	$0.829720\pi$
$620$		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	0.448975	−	0.893544i	$-0.351789\pi$
$631$	36.3556	−	20.9899i	1.44729	−	0.835596i	0.998320	+	0.0579484i	$0.0184559\pi$
$632$		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	0.814435	−	0.580254i	$-0.197047\pi$
$641$	−2.41274	−	4.17899i	−0.0952975	−	0.165060i	−0.909733	+	0.415194i	$0.863714\pi$
$642$		0			0
$643$	−18.5364	+	10.7020i	−0.731002	+	0.422044i	−0.818789	−	0.574095i	$-0.805354\pi$
$643$	−18.5364	+	10.7020i	−0.731002	+	0.422044i	0.0877864	+	0.996139i	$0.472021\pi$
$644$		0			0
$645$			8.70384i			0.342713i
$646$		0			0
$647$	−3.69721	+	6.40376i	−0.145353	+	0.251758i	−0.929504	−	0.368811i	$-0.879765\pi$
$647$	−3.69721	+	6.40376i	−0.145353	+	0.251758i	0.784152	+	0.620569i	$0.213098\pi$
$648$		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	−0.619149	−	0.785273i	$-0.712522\pi$
$653$	9.46750	−	16.3982i	0.370492	−	0.641711i	0.989641	+	0.143562i	$0.0458558\pi$
$654$		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	0.898585	−	0.438799i	$-0.144596\pi$
$659$	1.77854	+	3.08052i	0.0692820	+	0.120000i	−0.829303	+	0.558799i	$0.811263\pi$
$660$		0			0
$661$	−7.24471	−	4.18274i	−0.281787	−	0.162690i	0.352445	−	0.935832i	$-0.385350\pi$
$661$	−7.24471	−	4.18274i	−0.281787	−	0.162690i	−0.634232	+	0.773143i	$0.718684\pi$
$662$		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	0.00957533	+	0.999954i	$0.496952\pi$
$673$	−22.3414	+	38.6965i	−0.861198	+	1.49164i	−0.870773	+	0.491685i	$0.836381\pi$
$674$		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	−0.716653	−	0.697430i	$-0.754327\pi$
$683$	−12.3089	+	7.10654i	−0.470986	+	0.271924i	0.245666	+	0.969355i	$0.420993\pi$
$684$		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	0.746545	−	0.665335i	$-0.231711\pi$
$691$	14.2901	+	8.25038i	0.543620	+	0.313859i	−0.202925	+	0.979194i	$0.565045\pi$
$692$		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	−0.837126	−	0.547010i	$-0.815766\pi$
$709$	−20.8214	+	12.0212i	−0.781964	+	0.451467i	0.0551616	+	0.998477i	$0.482433\pi$
$710$		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	0.838203	−	0.545359i	$-0.183607\pi$
$719$	−1.42633	−	2.47048i	−0.0531932	−	0.0921333i	−0.891396	+	0.453225i	$0.850273\pi$
$720$		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	$0.121037\pi$
$733$			20.0971i			0.742303i	−0.928572	+	0.371151i	$0.878963\pi$
$734$		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	0.397724	−	0.917505i	$-0.369800\pi$
$739$	−5.38243	−	3.10755i	−0.197996	−	0.114313i	−0.595720	+	0.803192i	$0.703133\pi$
$740$		0			0
$741$	−37.9721	−	21.6622i	−1.39494	−	0.795779i
$742$		0			0
$743$	−14.7649	−	8.52453i	−0.541673	−	0.312735i	0.204084	−	0.978953i	$-0.434578\pi$
$743$	−14.7649	−	8.52453i	−0.541673	−	0.312735i	−0.745757	+	0.666219i	$0.767912\pi$
$744$		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	−0.997941	−	0.0641452i	$-0.979568\pi$
$751$	−12.1516	+	21.0472i	−0.443419	+	0.768024i	0.554522	+	0.832169i	$0.312901\pi$
$752$		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	0.409858	+	0.912149i	$0.365578\pi$
$757$	−16.0959	+	27.8789i	−0.585015	+	1.01328i	−0.994874	+	0.101127i	$0.967755\pi$
$758$		0			0
$759$		−	39.9255i		−	1.44920i
$760$		0			0
$761$	44.3483	−	25.6045i	1.60762	−	0.928162i	0.617723	−	0.786396i	$-0.288055\pi$
$761$	44.3483	−	25.6045i	1.60762	−	0.928162i	0.989900	−	0.141766i	$-0.0452781\pi$
$762$		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	0.965994	−	0.258565i	$-0.0832495\pi$
$769$	33.9722	+	19.6138i	1.22507	+	0.707293i	0.259073	+	0.965858i	$0.416583\pi$
$770$		0			0
$771$	4.18490	+	7.24847i	0.150716	+	0.261047i
$772$		0			0
$773$	−18.5977	+	10.7374i	−0.668914	+	0.386198i	−0.795665	−	0.605737i	$-0.792878\pi$
$773$	−18.5977	+	10.7374i	−0.668914	+	0.386198i	0.126751	+	0.991935i	$0.459545\pi$
$774$		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	−0.853534	−	0.521038i	$-0.825545\pi$
$787$	−23.2583	+	13.4282i	−0.829069	+	0.478663i	0.0244650	+	0.999701i	$0.492212\pi$
$788$		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	0.813857	−	0.581065i	$-0.197364\pi$
$797$	−2.71833	−	4.70829i	−0.0962882	−	0.166776i	−0.910146	+	0.414289i	$0.864030\pi$
$798$		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	−0.539129	−	0.842223i	$-0.681246\pi$
$809$	13.0787	−	22.6530i	0.459822	−	0.796435i	0.998951	+	0.0457878i	$0.0145798\pi$
$810$		0			0
$811$			26.6986i			0.937513i	0.883327	+	0.468757i	$0.155298\pi$
$811$			26.6986i			0.937513i	−0.883327	+	0.468757i	$0.844702\pi$
$812$		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	0.888702	−	0.458485i	$-0.151608\pi$
$821$	26.8191	+	15.4840i	0.935993	+	0.540396i	0.0472910	+	0.998881i	$0.484941\pi$
$822$		0			0
$823$	2.78771	+	4.82846i	0.0971735	+	0.168309i	0.910514	−	0.413479i	$-0.135686\pi$
$823$	2.78771	+	4.82846i	0.0971735	+	0.168309i	−0.813340	+	0.581788i	$0.802353\pi$
$824$		0			0
$825$	−5.63816	+	3.25519i	−0.196296	+	0.113331i
$826$		0			0
$827$			27.1365i			0.943627i	0.881698	+	0.471813i	$0.156400\pi$
$827$			27.1365i			0.943627i	−0.881698	+	0.471813i	$0.843600\pi$
$828$		0			0
$829$	25.8390	−	44.7545i	0.897426	−	1.55439i	0.0666523	−	0.997776i	$-0.478768\pi$
$829$	25.8390	−	44.7545i	0.897426	−	1.55439i	0.830773	−	0.556611i	$-0.187898\pi$
$830$		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	0.196129	−	0.980578i	$-0.437163\pi$
$839$	33.1191	−	19.1213i	1.14340	−	0.660142i	0.947270	+	0.320436i	$0.103830\pi$
$840$		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	$-0.842057\pi$
$853$		−	27.8090i		−	0.952163i	0.879401	−	0.476081i	$-0.157943\pi$
$854$		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	$0.248680\pi$
$863$			41.3725i			1.40834i	−0.710033	+	0.704168i	$0.751320\pi$
$864$		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	−0.719541	−	0.694450i	$-0.755648\pi$
$877$	−14.1526	+	8.17103i	−0.477901	+	0.275916i	0.241640	+	0.970366i	$0.422315\pi$
$878$		0			0
$879$		−	83.7510i		−	2.82485i
$880$		0			0
$881$	−6.47265	+	11.2110i	−0.218069	+	0.377707i	−0.954218	−	0.299113i	$-0.903309\pi$
$881$	−6.47265	+	11.2110i	−0.218069	+	0.377707i	0.736149	+	0.676820i	$0.236642\pi$
$882$		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	−0.951932	−	0.306309i	$-0.900906\pi$
$887$	−6.27503	+	10.8687i	−0.210695	+	0.364934i	0.741237	+	0.671243i	$0.234239\pi$
$888$		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	−0.301771	−	0.953380i	$-0.597578\pi$
$907$	20.3215	−	35.1980i	0.674766	−	1.16873i	0.976537	−	0.215349i	$-0.0690888\pi$
$908$		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	0.998214	−	0.0597417i	$-0.0190277\pi$
$919$	13.5620	+	23.4901i	0.447369	+	0.774866i	−0.550845	+	0.834608i	$0.685694\pi$
$920$		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	−0.874561	−	0.484915i	$-0.838850\pi$
$929$	−27.1844	+	15.6949i	−0.891893	+	0.514935i	−0.0173316	+	0.999850i	$0.505517\pi$
$930$		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	$-0.633504\pi$
$941$		−	56.0340i		−	1.82666i	0.407226	−	0.913328i	$-0.366496\pi$
$942$		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	0.805435	−	0.592684i	$-0.201932\pi$
$947$	21.3836	+	12.3458i	0.694874	+	0.401185i	−0.110562	+	0.993869i	$0.535265\pi$
$948$		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	−0.979680	−	0.200567i	$-0.935721\pi$
$953$	−20.4838	−	35.4790i	−0.663536	−	1.14928i	0.316143	−	0.948711i	$-0.397612\pi$
$954$		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	$-0.729541\pi$
$967$		−	46.7111i		−	1.50213i	0.660229	−	0.751064i	$-0.270459\pi$
$968$		0			0
$969$	−10.6086	+	6.12488i	−0.340797	+	0.196759i
$970$		0			0
$971$	−11.1530	−	19.3176i	−0.357918	−	0.619932i	0.629695	−	0.776843i	$-0.283180\pi$
$971$	−11.1530	−	19.3176i	−0.357918	−	0.619932i	−0.987613	+	0.156910i	$0.949847\pi$
$972$		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	0.773454	−	0.633852i	$-0.218527\pi$
$977$	19.1058	+	11.0308i	0.611250	+	0.352905i	−0.162205	+	0.986757i	$0.551860\pi$
$978$		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	$0.0621022\pi$
$983$			12.1564i			0.387729i	−0.981028	+	0.193865i	$0.937898\pi$
$984$		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	0.365202	+	0.930928i	$0.381000\pi$
$991$	−19.6312	+	34.0023i	−0.623607	+	1.08012i	−0.988808	+	0.149190i	$0.952333\pi$
$992$		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	−0.999879	−	0.0155864i	$-0.995039\pi$
$997$	−16.2119	−	28.0799i	−0.513437	−	0.889300i	0.486441	−	0.873713i	$-0.338295\pi$
$998$		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.641.1		12
4.3	odd	2		520.2.bu.a.121.6	✓	12
13.10	even	6	inner	1040.2.da.e.881.1		12
52.7	even	12		6760.2.a.bj.1.1		6
52.19	even	12		6760.2.a.bg.1.1		6
52.23	odd	6		520.2.bu.a.361.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.bu.a.121.6	✓	12	4.3	odd	2
520.2.bu.a.361.6	yes	12	52.23	odd	6
1040.2.da.e.641.1		12	1.1	even	1	trivial
1040.2.da.e.881.1		12	13.10	even	6	inner
6760.2.a.bg.1.1		6	52.19	even	12
6760.2.a.bj.1.1		6	52.7	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

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