LMFDB - Embedded newform 261.2.k.a.82.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,2,Mod(82,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("261.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.k (of order $7$, degree $6$, 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:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			82.1
Root			$0.222521 - 0.974928i$ of defining polynomial
Character	$\chi$	$=$	261.82
Dual form			261.2.k.a.226.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.12349 + 1.40881i) q^{2} +(-0.277479 + 1.21572i) q^{4} +(-0.222521 - 0.279032i) q^{5} +(0.900969 + 3.94740i) q^{7} +(1.22252 - 0.588735i) q^{8} +(0.143104 - 0.626980i) q^{10} +(2.62349 + 1.26341i) q^{11} +(-4.67241 - 2.25011i) q^{13} +(-4.54892 + 5.70416i) q^{14} +(4.44989 + 2.14295i) q^{16} -1.10992 q^{17} +(-0.455927 + 1.99755i) q^{19} +(0.400969 - 0.193096i) q^{20} +(1.16756 + 5.11543i) q^{22} +(2.57942 - 3.23449i) q^{23} +(1.08426 - 4.75046i) q^{25} +(-2.07942 - 9.11052i) q^{26} -5.04892 q^{28} +(-4.38404 - 3.12733i) q^{29} +(-3.96346 - 4.97002i) q^{31} +(1.37651 + 6.03089i) q^{32} +(-1.24698 - 1.56366i) q^{34} +(0.900969 - 1.12978i) q^{35} +(2.62349 - 1.26341i) q^{37} +(-3.32640 + 1.60191i) q^{38} +(-0.436313 - 0.210117i) q^{40} -0.396125 q^{41} +(3.57942 - 4.48845i) q^{43} +(-2.26391 + 2.83885i) q^{44} +7.45473 q^{46} +(-7.02930 - 3.38513i) q^{47} +(-8.46346 + 4.07579i) q^{49} +(7.91066 - 3.80957i) q^{50} +(4.03199 - 5.05596i) q^{52} +(2.71648 + 3.40636i) q^{53} +(-0.231250 - 1.01317i) q^{55} +(3.42543 + 4.29535i) q^{56} +(-0.519614 - 9.68981i) q^{58} +9.10992 q^{59} +(1.34601 + 5.89726i) q^{61} +(2.54892 - 11.1675i) q^{62} +(-0.791053 + 0.991949i) q^{64} +(0.411854 + 1.80445i) q^{65} +(-0.337282 + 0.162426i) q^{67} +(0.307979 - 1.34934i) q^{68} +2.60388 q^{70} +(-10.2763 - 4.94880i) q^{71} +(-5.57942 + 6.99637i) q^{73} +(4.72737 + 2.27658i) q^{74} +(-2.30194 - 1.10855i) q^{76} +(-2.62349 + 11.4943i) q^{77} +(0.535344 - 0.257808i) q^{79} +(-0.392240 - 1.71851i) q^{80} +(-0.445042 - 0.558065i) q^{82} +(-2.09903 + 9.19646i) q^{83} +(0.246980 + 0.309703i) q^{85} +10.3448 q^{86} +3.95108 q^{88} +(-0.887395 - 1.11276i) q^{89} +(4.67241 - 20.4712i) q^{91} +(3.21648 + 4.03334i) q^{92} +(-3.12833 - 13.7061i) q^{94} +(0.658834 - 0.317278i) q^{95} +(-3.50484 + 15.3557i) q^{97} +(-15.2506 - 7.34432i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - 2 q^{4} - q^{5} + q^{7} + 7 q^{8} + 9 q^{10} + 11 q^{11} - 5 q^{13} - 9 q^{14} + 4 q^{16} - 8 q^{17} + q^{19} - 2 q^{20} + 6 q^{22} + 7 q^{23} - 24 q^{25} - 4 q^{26} - 12 q^{28} - 6 q^{29}+ \cdots - 19 q^{98}+O(q^{100}) $ 6 * q + 2 * q^2 - 2 * q^4 - q^5 + q^7 + 7 * q^8 + 9 * q^10 + 11 * q^11 - 5 * q^13 - 9 * q^14 + 4 * q^16 - 8 * q^17 + q^19 - 2 * q^20 + 6 * q^22 + 7 * q^23 - 24 * q^25 - 4 * q^26 - 12 * q^28 - 6 * q^29 + 5 * q^31 + 13 * q^32 + 2 * q^34 + q^35 + 11 * q^37 - 2 * q^38 + 14 * q^40 - 20 * q^41 + 13 * q^43 - 20 * q^44 - 11 * q^47 - 22 * q^49 - q^50 - 10 * q^52 - 3 * q^53 - 17 * q^55 + 7 * q^56 - 16 * q^58 + 56 * q^59 + 3 * q^61 - 3 * q^62 + q^64 - 5 * q^65 + 19 * q^67 + 12 * q^68 - 2 * q^70 - 21 * q^71 - 25 * q^73 + 6 * q^74 - 5 * q^76 - 11 * q^77 - 9 * q^79 + 18 * q^80 - 2 * q^82 - 17 * q^83 - 8 * q^85 + 16 * q^86 + 42 * q^88 - 7 * q^89 + 5 * q^91 + 8 * q^94 - 13 * q^95 + q^97 - 19 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{2}{7}\right)$	$1$

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 $

$2$	1.12349	+	1.40881i	0.794427	+	0.996180i	0.999847	+	0.0175063i	$0.00557270\pi$
$2$	1.12349	+	1.40881i	0.794427	+	0.996180i	−0.205419	+	0.978674i	$0.565856\pi$
$3$		0			0
$3$		0			0
$4$	−0.277479	+	1.21572i	−0.138740	+	0.607858i
$5$	−0.222521	−	0.279032i	−0.0995144	−	0.124787i	0.729581	−	0.683895i	$-0.239715\pi$
$5$	−0.222521	−	0.279032i	−0.0995144	−	0.124787i	−0.829095	+	0.559108i	$0.811144\pi$
$6$		0			0
$7$	0.900969	+	3.94740i	0.340534	+	1.49198i	0.797949	+	0.602725i	$0.205918\pi$
$7$	0.900969	+	3.94740i	0.340534	+	1.49198i	−0.457415	+	0.889253i	$0.651225\pi$
$8$	1.22252	−	0.588735i	0.432226	−	0.208149i
$9$		0			0
$10$	0.143104	−	0.626980i	0.0452535	−	0.198269i
$11$	2.62349	+	1.26341i	0.791012	+	0.380931i	0.785349	−	0.619053i	$-0.212483\pi$
$11$	2.62349	+	1.26341i	0.791012	+	0.380931i	0.00566249	+	0.999984i	$0.498198\pi$
$12$		0			0
$13$	−4.67241	−	2.25011i	−1.29589	−	0.624069i	−0.346467	−	0.938062i	$-0.612619\pi$
$13$	−4.67241	−	2.25011i	−1.29589	−	0.624069i	−0.949425	+	0.313993i	$0.898333\pi$
$14$	−4.54892	+	5.70416i	−1.21575	+	1.52450i
$15$		0			0
$16$	4.44989	+	2.14295i	1.11247	+	0.535738i
$17$	−1.10992			−0.269194			−0.134597	−	0.990900i	$-0.542974\pi$
$17$	−1.10992			−0.269194			−0.134597	+	0.990900i	$0.542974\pi$
$18$		0			0
$19$	−0.455927	+	1.99755i	−0.104597	+	0.458269i	0.895321	+	0.445422i	$0.146946\pi$
$19$	−0.455927	+	1.99755i	−0.104597	+	0.458269i	−0.999917	+	0.0128465i	$0.995911\pi$
$20$	0.400969	−	0.193096i	0.0896594	−	0.0431777i
$21$		0			0
$22$	1.16756	+	5.11543i	0.248925	+	1.09061i
$23$	2.57942	−	3.23449i	0.537846	−	0.674437i	−0.436445	−	0.899731i	$-0.643763\pi$
$23$	2.57942	−	3.23449i	0.537846	−	0.674437i	0.974291	+	0.225294i	$0.0723342\pi$
$24$		0			0
$25$	1.08426	−	4.75046i	0.216852	−	0.950092i
$26$	−2.07942	−	9.11052i	−0.407807	−	1.78672i
$27$		0			0
$28$	−5.04892			−0.954156
$29$	−4.38404	−	3.12733i	−0.814096	−	0.580730i
$29$	−4.38404	−	3.12733i	−0.814096	−	0.580730i
$30$		0			0
$31$	−3.96346	−	4.97002i	−0.711858	−	0.892642i	0.285988	−	0.958233i	$-0.407678\pi$
$31$	−3.96346	−	4.97002i	−0.711858	−	0.892642i	−0.997847	+	0.0655910i	$0.979107\pi$
$32$	1.37651	+	6.03089i	0.243335	+	1.06612i
$33$		0			0
$34$	−1.24698	−	1.56366i	−0.213855	−	0.268166i
$35$	0.900969	−	1.12978i	0.152292	−	0.190968i
$36$		0			0
$37$	2.62349	−	1.26341i	0.431299	−	0.207703i	−0.205622	−	0.978631i	$-0.565922\pi$
$37$	2.62349	−	1.26341i	0.431299	−	0.207703i	0.636921	+	0.770929i	$0.280208\pi$
$38$	−3.32640	+	1.60191i	−0.539613	+	0.259864i
$39$		0			0
$40$	−0.436313	−	0.210117i	−0.0689871	−	0.0332224i
$41$	−0.396125			−0.0618643			−0.0309321	−	0.999521i	$-0.509848\pi$
$41$	−0.396125			−0.0618643			−0.0309321	+	0.999521i	$0.509848\pi$
$42$		0			0
$43$	3.57942	−	4.48845i	0.545856	−	0.684482i	−0.430017	−	0.902821i	$-0.641492\pi$
$43$	3.57942	−	4.48845i	0.545856	−	0.684482i	0.975873	+	0.218339i	$0.0700639\pi$
$44$	−2.26391	+	2.83885i	−0.341297	+	0.427972i
$45$		0			0
$46$	7.45473			1.09914
$47$	−7.02930	−	3.38513i	−1.02533	−	0.493773i	−0.155870	−	0.987778i	$-0.549818\pi$
$47$	−7.02930	−	3.38513i	−1.02533	−	0.493773i	−0.869459	+	0.494005i	$0.835532\pi$
$48$		0			0
$49$	−8.46346	+	4.07579i	−1.20907	+	0.582255i
$50$	7.91066	−	3.80957i	1.11874	−	0.538755i
$51$		0			0
$52$	4.03199	−	5.05596i	0.559137	−	0.701135i
$53$	2.71648	+	3.40636i	0.373137	+	0.467899i	0.932577	−	0.360972i	$-0.117555\pi$
$53$	2.71648	+	3.40636i	0.373137	+	0.467899i	−0.559439	+	0.828871i	$0.688984\pi$
$54$		0			0
$55$	−0.231250	−	1.01317i	−0.0311818	−	0.136616i
$56$	3.42543	+	4.29535i	0.457742	+	0.573990i
$57$		0			0
$58$	−0.519614	−	9.68981i	−0.0682287	−	1.27233i
$59$	9.10992			1.18601			0.593005	−	0.805199i	$-0.297941\pi$
$59$	9.10992			1.18601			0.593005	+	0.805199i	$0.297941\pi$
$60$		0			0
$61$	1.34601	+	5.89726i	0.172339	+	0.755067i	0.985032	+	0.172374i	$0.0551437\pi$
$61$	1.34601	+	5.89726i	0.172339	+	0.755067i	−0.812693	+	0.582693i	$0.801999\pi$
$62$	2.54892	−	11.1675i	0.323713	−	1.41828i
$63$		0			0
$64$	−0.791053	+	0.991949i	−0.0988816	+	0.123994i
$65$	0.411854	+	1.80445i	0.0510842	+	0.223815i
$66$		0			0
$67$	−0.337282	+	0.162426i	−0.0412055	+	0.0198435i	−0.454373	−	0.890812i	$-0.650137\pi$
$67$	−0.337282	+	0.162426i	−0.0412055	+	0.0198435i	0.413168	+	0.910655i	$0.364422\pi$
$68$	0.307979	−	1.34934i	0.0373479	−	0.163632i
$69$		0			0
$70$	2.60388			0.311223
$71$	−10.2763	−	4.94880i	−1.21957	−	0.587314i	−0.290379	−	0.956912i	$-0.593781\pi$
$71$	−10.2763	−	4.94880i	−1.21957	−	0.587314i	−0.929192	+	0.369598i	$0.879495\pi$
$72$		0			0
$73$	−5.57942	+	6.99637i	−0.653021	+	0.818863i	−0.992563	−	0.121728i	$-0.961156\pi$
$73$	−5.57942	+	6.99637i	−0.653021	+	0.818863i	0.339542	+	0.940591i	$0.389728\pi$
$74$	4.72737	+	2.27658i	0.549545	+	0.264647i
$75$		0			0
$76$	−2.30194	−	1.10855i	−0.264050	−	0.127160i
$77$	−2.62349	+	11.4943i	−0.298974	+	1.30989i
$78$		0			0
$79$	0.535344	−	0.257808i	0.0602309	−	0.0290057i	−0.403526	−	0.914968i	$-0.632215\pi$
$79$	0.535344	−	0.257808i	0.0602309	−	0.0290057i	0.463757	+	0.885963i	$0.346501\pi$
$80$	−0.392240	−	1.71851i	−0.0438537	−	0.192136i
$81$		0			0
$82$	−0.445042	−	0.558065i	−0.0491467	−	0.0616280i
$83$	−2.09903	+	9.19646i	−0.230399	+	1.00944i	0.718912	+	0.695101i	$0.244641\pi$
$83$	−2.09903	+	9.19646i	−0.230399	+	1.00944i	−0.949310	+	0.314341i	$0.898217\pi$
$84$		0			0
$85$	0.246980	+	0.309703i	0.0267887	+	0.0335920i
$86$	10.3448			1.11551
$87$		0			0
$88$	3.95108			0.421187
$89$	−0.887395	−	1.11276i	−0.0940637	−	0.117952i	0.732572	−	0.680689i	$-0.238320\pi$
$89$	−0.887395	−	1.11276i	−0.0940637	−	0.117952i	−0.826636	+	0.562737i	$0.809748\pi$
$90$		0			0
$91$	4.67241	−	20.4712i	0.489801	−	2.14596i
$92$	3.21648	+	4.03334i	0.335341	+	0.420505i
$93$		0			0
$94$	−3.12833	−	13.7061i	−0.322663	−	1.41368i
$95$	0.658834	−	0.317278i	0.0675949	−	0.0325520i
$96$		0			0
$97$	−3.50484	+	15.3557i	−0.355863	+	1.55914i	0.407523	+	0.913195i	$0.366393\pi$
$97$	−3.50484	+	15.3557i	−0.355863	+	1.55914i	−0.763386	+	0.645943i	$0.776464\pi$
$98$	−15.2506	−	7.34432i	−1.54055	−	0.741888i
$99$		0			0
$100$	5.47434	+	2.63631i	0.547434	+	0.263631i
$101$	10.8753	−	13.6372i	1.08213	−	1.35695i	0.152570	−	0.988293i	$-0.451245\pi$
$101$	10.8753	−	13.6372i	1.08213	−	1.35695i	0.929564	−	0.368661i	$-0.120184\pi$
$102$		0			0
$103$	2.53534	+	1.22096i	0.249815	+	0.120304i	0.554601	−	0.832116i	$-0.312871\pi$
$103$	2.53534	+	1.22096i	0.249815	+	0.120304i	−0.304786	+	0.952421i	$0.598585\pi$
$104$	−7.03684			−0.690019
$105$		0			0
$106$	−1.74698	+	7.65402i	−0.169682	+	0.743424i
$107$	−6.72132	+	3.23682i	−0.649775	+	0.312915i	−0.729580	−	0.683895i	$-0.760284\pi$
$107$	−6.72132	+	3.23682i	−0.649775	+	0.312915i	0.0798052	+	0.996810i	$0.474570\pi$
$108$		0			0
$109$	0.367781	+	1.61135i	0.0352270	+	0.154340i	0.989482	−	0.144653i	$-0.0462066\pi$
$109$	0.367781	+	1.61135i	0.0352270	+	0.154340i	−0.954255	+	0.298993i	$0.903349\pi$
$110$	1.16756	−	1.46408i	0.111323	−	0.139594i
$111$		0			0
$112$	−4.44989	+	19.4962i	−0.420475	+	1.84222i
$113$	1.92274	+	8.42407i	0.180876	+	0.792470i	0.981214	+	0.192921i	$0.0617961\pi$
$113$	1.92274	+	8.42407i	0.180876	+	0.792470i	−0.800338	+	0.599549i	$0.795347\pi$
$114$		0			0
$115$	−1.47650			−0.137684
$116$	5.01842	−	4.46198i	0.465948	−	0.414284i
$117$		0			0
$118$	10.2349	+	12.8342i	0.942199	+	1.18148i
$119$	−1.00000	−	4.38129i	−0.0916698	−	0.401632i
$120$		0			0
$121$	−1.57188	−	1.97108i	−0.142899	−	0.179189i
$122$	−6.79590	+	8.52179i	−0.615272	+	0.771526i
$123$		0			0
$124$	7.14191	−	3.43936i	0.641362	−	0.308864i
$125$	−3.17456	+	1.52879i	−0.283942	+	0.136739i
$126$		0			0
$127$	−9.43512	−	4.54371i	−0.837231	−	0.403189i	−0.0344090	−	0.999408i	$-0.510955\pi$
$127$	−9.43512	−	4.54371i	−0.837231	−	0.403189i	−0.802822	+	0.596219i	$0.796669\pi$
$128$	10.0858			0.891463
$129$		0			0
$130$	−2.07942	+	2.60751i	−0.182377	+	0.228693i
$131$	0.283520	−	0.355523i	0.0247712	−	0.0310622i	−0.769292	−	0.638898i	$-0.779391\pi$
$131$	0.283520	−	0.355523i	0.0247712	−	0.0310622i	0.794063	+	0.607836i	$0.207962\pi$
$132$		0			0
$133$	−8.29590			−0.719345
$134$	−0.607760	−	0.292682i	−0.0525025	−	0.0252839i
$135$		0			0
$136$	−1.35690	+	0.653447i	−0.116353	+	0.0560326i
$137$	−11.9291	+	5.74474i	−1.01917	+	0.490806i	−0.867401	−	0.497610i	$-0.834211\pi$
$137$	−11.9291	+	5.74474i	−1.01917	+	0.490806i	−0.151769	+	0.988416i	$0.548497\pi$
$138$		0			0
$139$	−1.74363	+	2.18644i	−0.147893	+	0.185451i	−0.850260	−	0.526364i	$-0.823555\pi$
$139$	−1.74363	+	2.18644i	−0.147893	+	0.185451i	0.702367	+	0.711815i	$0.252127\pi$
$140$	1.12349	+	1.40881i	0.0949522	+	0.119066i
$141$		0			0
$142$	−4.57338	−	20.0373i	−0.383789	−	1.68149i
$143$	−9.41521	−	11.8063i	−0.787339	−	0.987292i
$144$		0			0
$145$	0.102916	+	1.91919i	0.00854671	+	0.159380i
$146$	−16.1250			−1.33451
$147$		0			0
$148$	0.807979	+	3.53999i	0.0664154	+	0.290985i
$149$	0.602679	−	2.64051i	0.0493734	−	0.216319i	−0.944223	−	0.329307i	$-0.893185\pi$
$149$	0.602679	−	2.64051i	0.0493734	−	0.216319i	0.993596	+	0.112988i	$0.0360421\pi$
$150$		0			0
$151$	−1.51842	+	1.90404i	−0.123567	+	0.154948i	−0.839767	−	0.542947i	$-0.817308\pi$
$151$	−1.51842	+	1.90404i	−0.123567	+	0.154948i	0.716200	+	0.697895i	$0.245880\pi$
$152$	0.618645	+	2.71046i	0.0501788	+	0.219848i
$153$		0			0
$154$	−19.1407	+	9.21768i	−1.54240	+	0.742782i
$155$	−0.504844	+	2.21187i	−0.0405501	+	0.177661i
$156$		0			0
$157$	17.6775			1.41082			0.705411	−	0.708799i	$-0.250762\pi$
$157$	17.6775			1.41082			0.705411	+	0.708799i	$0.250762\pi$
$158$	0.964656	+	0.464554i	0.0767439	+	0.0369579i
$159$		0			0
$160$	1.37651	−	1.72609i	0.108823	−	0.136459i
$161$	15.0918	+	7.26782i	1.18940	+	0.572785i
$162$		0			0
$163$	4.47434	+	2.15473i	0.350458	+	0.168772i	0.600827	−	0.799379i	$-0.294838\pi$
$163$	4.47434	+	2.15473i	0.350458	+	0.168772i	−0.250370	+	0.968150i	$0.580552\pi$
$164$	0.109916	−	0.481575i	0.00858302	−	0.0376047i
$165$		0			0
$166$	−15.3143	+	7.37499i	−1.18862	+	0.572410i
$167$	3.21864	+	14.1018i	0.249066	+	1.09123i	0.932487	+	0.361203i	$0.117634\pi$
$167$	3.21864	+	14.1018i	0.249066	+	1.09123i	−0.683422	+	0.730024i	$0.739509\pi$
$168$		0			0
$169$	8.66301	+	10.8631i	0.666386	+	0.835621i
$170$	−0.158834	+	0.695895i	−0.0121820	+	0.0533727i
$171$		0			0
$172$	4.46346	+	5.59700i	0.340336	+	0.426767i
$173$	−10.5133			−0.799314			−0.399657	−	0.916665i	$-0.630871\pi$
$173$	−10.5133			−0.799314			−0.399657	+	0.916665i	$0.630871\pi$
$174$		0			0
$175$	19.7289			1.49136
$176$	8.96681	+	11.2440i	0.675899	+	0.847550i
$177$		0			0
$178$	0.570688	−	2.50035i	0.0427748	−	0.187409i
$179$	3.57942	+	4.48845i	0.267538	+	0.335482i	0.897394	−	0.441230i	$-0.145458\pi$
$179$	3.57942	+	4.48845i	0.267538	+	0.335482i	−0.629856	+	0.776712i	$0.716886\pi$
$180$		0			0
$181$	1.47770	+	6.47421i	0.109836	+	0.481225i	0.999688	+	0.0249747i	$0.00795053\pi$
$181$	1.47770	+	6.47421i	0.109836	+	0.481225i	−0.889852	+	0.456250i	$0.849192\pi$
$182$	34.0894	−	16.4166i	2.52687	−	1.21688i
$183$		0			0
$184$	1.24914	−	5.47282i	0.0920875	−	0.403462i
$185$	−0.936313	−	0.450904i	−0.0688391	−	0.0331512i
$186$		0			0
$187$	−2.91185	−	1.40227i	−0.212936	−	0.102545i
$188$	6.06584	−	7.60633i	0.442397	−	0.554748i
$189$		0			0
$190$	1.18718	+	0.571714i	0.0861269	+	0.0414765i
$191$	18.8116			1.36116			0.680581	−	0.732673i	$-0.261728\pi$
$191$	18.8116			1.36116			0.680581	+	0.732673i	$0.261728\pi$
$192$		0			0
$193$	−2.42208	+	10.6118i	−0.174345	+	0.763854i	0.809832	+	0.586662i	$0.199558\pi$
$193$	−2.42208	+	10.6118i	−0.174345	+	0.763854i	−0.984176	+	0.177192i	$0.943299\pi$
$194$	−25.5710	+	12.3143i	−1.83589	+	0.884118i
$195$		0			0
$196$	−2.60656	−	11.4201i	−0.186183	−	0.815722i
$197$	5.23759	−	6.56773i	0.373163	−	0.467931i	−0.559422	−	0.828883i	$-0.688977\pi$
$197$	5.23759	−	6.56773i	0.373163	−	0.467931i	0.932584	+	0.360952i	$0.117548\pi$
$198$		0			0
$199$	1.47339	−	6.45532i	0.104446	−	0.457606i	−0.895476	−	0.445109i	$-0.853165\pi$
$199$	1.47339	−	6.45532i	0.104446	−	0.457606i	0.999922	−	0.0124967i	$-0.00397793\pi$
$200$	−1.47123	−	6.44588i	−0.104032	−	0.455792i
$201$		0			0
$202$	31.4306			2.21145
$203$	8.39493	−	20.1232i	0.589208	−	1.41237i
$204$		0			0
$205$	0.0881460	+	0.110532i	0.00615638	+	0.00771986i
$206$	1.12833	+	4.94355i	0.0786148	+	0.344434i
$207$		0			0
$208$	−15.9698	−	20.0255i	−1.10731	−	1.38852i
$209$	−3.71983	+	4.66452i	−0.257306	+	0.322652i
$210$		0			0
$211$	7.29805	−	3.51456i	0.502419	−	0.241952i	−0.165468	−	0.986215i	$-0.552913\pi$
$211$	7.29805	−	3.51456i	0.502419	−	0.241952i	0.667887	+	0.744263i	$0.267199\pi$
$212$	−4.89493	+	2.35727i	−0.336185	+	0.161898i
$213$		0			0
$214$	−12.1114	−	5.83255i	−0.827919	−	0.398705i
$215$	−2.04892			−0.139735
$216$		0			0
$217$	16.0477	−	20.1232i	1.08939	−	1.36605i
$218$	−1.85690	+	2.32847i	−0.125765	+	0.157704i
$219$		0			0
$220$	1.29590			0.0873694
$221$	5.18598	+	2.49744i	0.348847	+	0.167996i
$222$		0			0
$223$	−19.7485	+	9.51036i	−1.32246	+	0.636861i	−0.955943	−	0.293552i	$-0.905163\pi$
$223$	−19.7485	+	9.51036i	−1.32246	+	0.636861i	−0.366512	+	0.930413i	$0.619448\pi$
$224$	−22.5661	+	10.8673i	−1.50776	+	0.726101i
$225$		0			0
$226$	−9.70775	+	12.1731i	−0.645750	+	0.809745i
$227$	11.3964	+	14.2907i	0.756407	+	0.948504i	0.999770	−	0.0214309i	$-0.00682218\pi$
$227$	11.3964	+	14.2907i	0.756407	+	0.948504i	−0.243363	+	0.969935i	$0.578251\pi$
$228$		0			0
$229$	−3.56584	−	15.6230i	−0.235638	−	1.03240i	−0.944876	−	0.327427i	$-0.893818\pi$
$229$	−3.56584	−	15.6230i	−0.235638	−	1.03240i	0.709239	−	0.704968i	$-0.249039\pi$
$230$	−1.65883	−	2.08011i	−0.109380	−	0.137158i
$231$		0			0
$232$	−7.20075	−	1.24218i	−0.472752	−	0.0815532i
$233$	−1.95646			−0.128172			−0.0640860	−	0.997944i	$-0.520413\pi$
$233$	−1.95646			−0.128172			−0.0640860	+	0.997944i	$0.520413\pi$
$234$		0			0
$235$	0.619605	+	2.71467i	0.0404186	+	0.177085i
$236$	−2.52781	+	11.0751i	−0.164546	+	0.720925i
$237$		0			0
$238$	5.04892	−	6.33114i	0.327273	−	0.410387i
$239$	−1.99449	−	8.73844i	−0.129013	−	0.565243i	−0.997571	−	0.0696554i	$-0.977810\pi$
$239$	−1.99449	−	8.73844i	−0.129013	−	0.565243i	0.868558	−	0.495587i	$-0.165047\pi$
$240$		0			0
$241$	−17.9291	+	8.63419i	−1.15491	+	0.556177i	−0.910506	−	0.413496i	$-0.864308\pi$
$241$	−17.9291	+	8.63419i	−1.15491	+	0.556177i	−0.244407	+	0.969673i	$0.578593\pi$
$242$	1.01089	−	4.42898i	0.0649822	−	0.284705i
$243$		0			0
$244$	−7.54288			−0.482883
$245$	3.02057	+	1.45463i	0.192977	+	0.0929330i
$246$		0			0
$247$	6.62498	−	8.30746i	0.421537	−	0.528591i
$248$	−7.77144	−	3.74253i	−0.493487	−	0.237651i
$249$		0			0
$250$	−5.72037	−	2.75478i	−0.361788	−	0.174228i
$251$	5.74214	−	25.1579i	0.362440	−	1.58795i	−0.384540	−	0.923108i	$-0.625640\pi$
$251$	5.74214	−	25.1579i	0.362440	−	1.58795i	0.746980	−	0.664847i	$-0.231503\pi$
$252$		0			0
$253$	10.8535	−	5.22679i	0.682356	−	0.328606i
$254$	−4.19902	−	18.3971i	−0.263470	−	1.15434i
$255$		0			0
$256$	12.9133	+	16.1928i	0.807084	+	1.01205i
$257$	2.65937	−	11.6514i	0.165887	−	0.726797i	−0.821726	−	0.569883i	$-0.806988\pi$
$257$	2.65937	−	11.6514i	0.165887	−	0.726797i	0.987612	−	0.156914i	$-0.0501545\pi$
$258$		0			0
$259$	7.35086	+	9.21768i	0.456760	+	0.572759i
$260$	−2.30798			−0.143135
$261$		0			0
$262$	0.819396			0.0506225
$263$	0.207455	+	0.260141i	0.0127923	+	0.0160410i	0.788186	−	0.615437i	$-0.211020\pi$
$263$	0.207455	+	0.260141i	0.0127923	+	0.0160410i	−0.775394	+	0.631477i	$0.782449\pi$
$264$		0			0
$265$	0.346011	−	1.51597i	0.0212553	−	0.0931254i
$266$	−9.32036	−	11.6874i	−0.571468	−	0.716598i
$267$		0			0
$268$	−0.103875	−	0.455108i	−0.00634520	−	0.0278002i
$269$	−0.958615	+	0.461645i	−0.0584478	+	0.0281470i	−0.462879	−	0.886421i	$-0.653184\pi$
$269$	−0.958615	+	0.461645i	−0.0584478	+	0.0281470i	0.404432	+	0.914568i	$0.367469\pi$
$270$		0			0
$271$	3.66368	−	16.0516i	0.222553	−	0.975067i	−0.732996	−	0.680233i	$-0.761879\pi$
$271$	3.66368	−	16.0516i	0.222553	−	0.975067i	0.955549	−	0.294834i	$-0.0952642\pi$
$272$	−4.93900	−	2.37850i	−0.299471	−	0.144218i
$273$		0			0
$274$	−21.4955	−	10.3517i	−1.29859	−	0.625367i
$275$	8.84631	−	11.0929i	0.533452	−	0.668928i
$276$		0			0
$277$	−5.94116	−	2.86111i	−0.356970	−	0.171907i	0.246800	−	0.969066i	$-0.420621\pi$
$277$	−5.94116	−	2.86111i	−0.356970	−	0.171907i	−0.603769	+	0.797159i	$0.706335\pi$
$278$	−5.03923			−0.302233
$279$		0			0
$280$	0.436313	−	1.91161i	0.0260747	−	0.114241i
$281$	−27.5112	+	13.2487i	−1.64118	+	0.790350i	−0.641448	+	0.767166i	$0.721666\pi$
$281$	−27.5112	+	13.2487i	−1.64118	+	0.790350i	−0.999731	+	0.0231840i	$0.992620\pi$
$282$		0			0
$283$	0.791053	+	3.46583i	0.0470232	+	0.206022i	0.992982	−	0.118264i	$-0.0377330\pi$
$283$	0.791053	+	3.46583i	0.0470232	+	0.206022i	−0.945959	+	0.324286i	$0.894876\pi$
$284$	8.86778	−	11.1198i	0.526206	−	0.659841i
$285$		0			0
$286$	6.05496	−	26.5285i	0.358037	−	1.56866i
$287$	−0.356896	−	1.56366i	−0.0210669	−	0.0923001i
$288$		0			0
$289$	−15.7681			−0.927534
$290$	−2.58815	+	2.30117i	−0.151981	+	0.135130i
$291$		0			0
$292$	−6.95742	−	8.72433i	−0.407152	−	0.510553i
$293$	7.31647	+	32.0556i	0.427433	+	1.87271i	0.485246	+	0.874378i	$0.338730\pi$
$293$	7.31647	+	32.0556i	0.427433	+	1.87271i	−0.0578127	+	0.998327i	$0.518413\pi$
$294$		0			0
$295$	−2.02715	−	2.54196i	−0.118025	−	0.147999i
$296$	2.46346	−	3.08908i	0.143186	−	0.179549i
$297$		0			0
$298$	4.39708	−	2.11752i	0.254716	−	0.122665i
$299$	−19.3300	+	9.30886i	−1.11789	+	0.538345i
$300$		0			0
$301$	20.9426	+	10.0854i	1.20711	+	0.581316i
$302$	−4.38835			−0.252521
$303$		0			0
$304$	−6.30947	+	7.91183i	−0.361873	+	0.453774i
$305$	1.34601	−	1.68784i	0.0770724	−	0.0966457i
$306$		0			0
$307$	14.6703			0.837275			0.418638	−	0.908153i	$-0.362508\pi$
$307$	14.6703			0.837275			0.418638	+	0.908153i	$0.362508\pi$
$308$	−13.2458	−	6.37883i	−0.754749	−	0.363468i
$309$		0			0
$310$	−3.68329	+	1.77378i	−0.209197	+	0.100744i
$311$	16.6918	−	8.03834i	0.946504	−	0.455812i	0.104045	−	0.994573i	$-0.466821\pi$
$311$	16.6918	−	8.03834i	0.946504	−	0.455812i	0.842459	+	0.538760i	$0.181107\pi$
$312$		0			0
$313$	14.3354	−	17.9760i	0.810286	−	1.01607i	−0.189132	−	0.981952i	$-0.560567\pi$
$313$	14.3354	−	17.9760i	0.810286	−	1.01607i	0.999418	−	0.0341147i	$-0.0108612\pi$
$314$	19.8605	+	24.9043i	1.12080	+	1.40543i
$315$		0			0
$316$	0.164874	+	0.722362i	0.00927491	+	0.0406360i
$317$	−8.76540	−	10.9915i	−0.492314	−	0.617342i	0.472162	−	0.881512i	$-0.343474\pi$
$317$	−8.76540	−	10.9915i	−0.492314	−	0.617342i	−0.964476	+	0.264170i	$0.914902\pi$
$318$		0			0
$319$	−7.55041	−	13.7433i	−0.422742	−	0.769479i
$320$	0.452812			0.0253129
$321$		0			0
$322$	6.71648	+	29.4268i	0.374295	+	1.63989i
$323$	0.506041	−	2.21711i	0.0281569	−	0.123363i
$324$		0			0
$325$	−15.7552	+	19.7564i	−0.873940	+	1.09589i
$326$	1.99127	+	8.72433i	0.110286	+	0.483196i
$327$		0			0
$328$	−0.484271	+	0.233212i	−0.0267394	+	0.0128770i
$329$	7.02930	−	30.7974i	0.387538	−	1.69792i
$330$		0			0
$331$	13.9565			0.767116			0.383558	−	0.923517i	$-0.374699\pi$
$331$	13.9565			0.767116			0.383558	+	0.923517i	$0.374699\pi$
$332$	−10.5978	−	5.10365i	−0.581632	−	0.280099i
$333$		0			0
$334$	−16.2506	+	20.3776i	−0.889195	+	1.11501i
$335$	0.120374	+	0.0579692i	0.00657676	+	0.00316720i
$336$		0			0
$337$	12.6114	+	6.07333i	0.686987	+	0.330836i	0.744607	−	0.667503i	$-0.232637\pi$
$337$	12.6114	+	6.07333i	0.686987	+	0.330836i	−0.0576199	+	0.998339i	$0.518351\pi$
$338$	−5.57122	+	24.4091i	−0.303034	+	1.32768i
$339$		0			0
$340$	−0.445042	+	0.214321i	−0.0241358	+	0.0116232i
$341$	−4.11894	−	18.0463i	−0.223053	−	0.977260i
$342$		0			0
$343$	−6.04288	−	7.57753i	−0.326285	−	0.409148i
$344$	1.73341	−	7.59455i	0.0934590	−	0.409471i
$345$		0			0
$346$	−11.8116	−	14.8113i	−0.634997	−	0.796261i
$347$	19.8538			1.06581			0.532905	−	0.846175i	$-0.321100\pi$
$347$	19.8538			1.06581			0.532905	+	0.846175i	$0.321100\pi$
$348$		0			0
$349$	−26.9202			−1.44101			−0.720503	−	0.693452i	$-0.756089\pi$
$349$	−26.9202			−1.44101			−0.720503	+	0.693452i	$0.756089\pi$
$350$	22.1652	+	27.7942i	1.18478	+	1.48566i
$351$		0			0
$352$	−4.00820	+	17.5611i	−0.213638	+	0.936007i
$353$	2.50335	+	3.13910i	0.133240	+	0.167078i	0.843976	−	0.536382i	$-0.180209\pi$
$353$	2.50335	+	3.13910i	0.133240	+	0.167078i	−0.710736	+	0.703459i	$0.751638\pi$
$354$		0			0
$355$	0.905813	+	3.96863i	0.0480756	+	0.210633i
$356$	1.59903	−	0.770053i	0.0847485	−	0.0408127i
$357$		0			0
$358$	−2.30194	+	10.0854i	−0.121661	+	0.533032i
$359$	−0.672407	−	0.323814i	−0.0354883	−	0.0170903i	0.416055	−	0.909339i	$-0.363412\pi$
$359$	−0.672407	−	0.323814i	−0.0354883	−	0.0170903i	−0.451544	+	0.892249i	$0.649127\pi$
$360$		0			0
$361$	13.3361	+	6.42232i	0.701899	+	0.338017i
$362$	−7.46077	+	9.35551i	−0.392129	+	0.491715i
$363$		0			0
$364$	23.5906	+	11.3606i	1.23648	+	0.595459i
$365$	3.19375			0.167169
$366$		0			0
$367$	7.57660	−	33.1952i	0.395495	−	1.73278i	−0.249304	−	0.968425i	$-0.580202\pi$
$367$	7.57660	−	33.1952i	0.395495	−	1.73278i	0.644799	−	0.764352i	$-0.276941\pi$
$368$	18.4095	−	8.86553i	0.959659	−	0.462148i
$369$		0			0
$370$	−0.416698	−	1.82567i	−0.0216631	−	0.0949123i
$371$	−10.9988	+	13.7921i	−0.571029	+	0.716048i
$372$		0			0
$373$	−6.23072	+	27.2986i	−0.322614	+	1.41347i	0.510268	+	0.860015i	$0.329546\pi$
$373$	−6.23072	+	27.2986i	−0.322614	+	1.41347i	−0.832882	+	0.553450i	$0.813311\pi$
$374$	−1.29590	−	5.67770i	−0.0670092	−	0.293587i
$375$		0			0
$376$	−10.5864			−0.545953
$377$	13.4472	+	24.4767i	0.692566	+	1.26062i
$378$		0			0
$379$	14.2661	+	17.8891i	0.732798	+	0.918900i	0.998986	−	0.0450211i	$-0.0143355\pi$
$379$	14.2661	+	17.8891i	0.732798	+	0.918900i	−0.266188	+	0.963921i	$0.585764\pi$
$380$	0.202907	+	0.888992i	0.0104089	+	0.0456043i
$381$		0			0
$382$	21.1347	+	26.5020i	1.08134	+	1.35596i
$383$	−7.39344	+	9.27108i	−0.377787	+	0.473730i	−0.933981	−	0.357323i	$-0.883690\pi$
$383$	−7.39344	+	9.27108i	−0.377787	+	0.473730i	0.556194	+	0.831052i	$0.312261\pi$
$384$		0			0
$385$	3.79105	−	1.82567i	0.193210	−	0.0930450i
$386$	−17.6712	+	8.51001i	−0.899441	+	0.433148i
$387$		0			0
$388$	−17.6957	−	8.52179i	−0.898362	−	0.432628i
$389$	10.3913			0.526862			0.263431	−	0.964678i	$-0.415146\pi$
$389$	10.3913			0.526862			0.263431	+	0.964678i	$0.415146\pi$
$390$		0			0
$391$	−2.86294	+	3.59001i	−0.144785	+	0.181555i
$392$	−7.94720	+	9.96547i	−0.401394	+	0.503332i
$393$		0			0
$394$	15.1371			0.762594
$395$	−0.191062	−	0.0920106i	−0.00961337	−	0.00462956i
$396$		0			0
$397$	−7.40366	+	3.56541i	−0.371579	+	0.178943i	−0.610348	−	0.792133i	$-0.708970\pi$
$397$	−7.40366	+	3.56541i	−0.371579	+	0.178943i	0.238769	+	0.971076i	$0.423256\pi$
$398$	10.7497	−	5.17677i	0.538832	−	0.259488i
$399$		0			0
$400$	15.0048	−	18.8155i	0.750242	−	0.940774i
$401$	−15.5130	−	19.4527i	−0.774684	−	0.971423i	0.225312	−	0.974287i	$-0.427660\pi$
$401$	−15.5130	−	19.4527i	−0.774684	−	0.971423i	−0.999996	+	0.00286337i	$0.999089\pi$
$402$		0			0
$403$	7.33579	+	32.1402i	0.365422	+	1.60102i
$404$	13.5613	+	17.0053i	0.674700	+	0.846047i
$405$		0			0
$406$	37.7814	−	10.7813i	1.87506	−	0.535069i
$407$	8.47889			0.420283
$408$		0			0
$409$	−4.20464	−	18.4217i	−0.207906	−	0.910895i	−0.965958	−	0.258701i	$-0.916706\pi$
$409$	−4.20464	−	18.4217i	−0.207906	−	0.910895i	0.758052	−	0.652194i	$-0.226151\pi$
$410$	−0.0566871	+	0.248362i	−0.00279957	+	0.0122657i
$411$		0			0
$412$	−2.18784	+	2.74347i	−0.107787	+	0.135161i
$413$	8.20775	+	35.9605i	0.403877	+	1.76950i
$414$		0			0
$415$	3.03319	−	1.46071i	0.148893	−	0.0717033i
$416$	7.13856	−	31.2761i	0.349996	−	1.53343i
$417$		0			0
$418$	−10.7506			−0.525830
$419$	−9.81378	−	4.72607i	−0.479435	−	0.230884i	0.178527	−	0.983935i	$-0.442867\pi$
$419$	−9.81378	−	4.72607i	−0.479435	−	0.230884i	−0.657962	+	0.753051i	$0.728581\pi$
$420$		0			0
$421$	−12.4453	+	15.6060i	−0.606549	+	0.760588i	−0.986383	−	0.164467i	$-0.947410\pi$
$421$	−12.4453	+	15.6060i	−0.606549	+	0.760588i	0.379834	+	0.925055i	$0.375981\pi$
$422$	13.1506	+	6.33301i	0.640163	+	0.308286i
$423$		0			0
$424$	5.32640	+	2.56506i	0.258673	+	0.124570i
$425$	−1.20344	+	5.27261i	−0.0583754	+	0.255759i
$426$		0			0
$427$	−22.0661	+	10.6265i	−1.06786	+	0.514252i
$428$	−2.07002	−	9.06937i	−0.100058	−	0.438384i
$429$		0			0
$430$	−2.30194	−	2.88654i	−0.111009	−	0.139201i
$431$	−6.71797	+	29.4334i	−0.323593	+	1.41776i	0.507514	+	0.861643i	$0.330564\pi$
$431$	−6.71797	+	29.4334i	−0.323593	+	1.41776i	−0.831108	+	0.556112i	$0.812293\pi$
$432$		0			0
$433$	−12.5891	−	15.7862i	−0.604994	−	0.758638i	0.381153	−	0.924512i	$-0.375527\pi$
$433$	−12.5891	−	15.7862i	−0.604994	−	0.758638i	−0.986147	+	0.165874i	$0.946956\pi$
$434$	46.3793			2.22628
$435$		0			0
$436$	−2.06100			−0.0987039
$437$	5.28501	+	6.62720i	0.252816	+	0.317022i
$438$		0			0
$439$	2.37316	−	10.3975i	0.113265	−	0.496245i	−0.886193	−	0.463316i	$-0.846659\pi$
$439$	2.37316	−	10.3975i	0.113265	−	0.496245i	0.999458	−	0.0329287i	$-0.0104834\pi$
$440$	−0.879199	−	1.10248i	−0.0419141	−	0.0525587i
$441$		0			0
$442$	2.30798	+	10.1119i	0.109779	+	0.480975i
$443$	−18.3349	+	8.82962i	−0.871117	+	0.419508i	−0.815372	−	0.578937i	$-0.803468\pi$
$443$	−18.3349	+	8.82962i	−0.871117	+	0.419508i	−0.0557448	+	0.998445i	$0.517753\pi$
$444$		0			0
$445$	−0.113032	+	0.495224i	−0.00535822	+	0.0234759i
$446$	−35.5855	−	17.1371i	−1.68502	−	0.811464i
$447$		0			0
$448$	−4.62833	−	2.22889i	−0.218668	−	0.105305i
$449$	−12.1102	+	15.1857i	−0.571516	+	0.716659i	−0.980640	−	0.195820i	$-0.937263\pi$
$449$	−12.1102	+	15.1857i	−0.571516	+	0.716659i	0.409124	+	0.912479i	$0.365834\pi$
$450$		0			0
$451$	−1.03923	−	0.500466i	−0.0489354	−	0.0235660i
$452$	−10.7748			−0.506804
$453$		0			0
$454$	−7.32908	+	32.1108i	−0.343971	+	1.50704i
$455$	−6.75182	+	3.25151i	−0.316530	+	0.152433i
$456$		0			0
$457$	2.76391	+	12.1095i	0.129290	+	0.566457i	0.997526	+	0.0703045i	$0.0223971\pi$
$457$	2.76391	+	12.1095i	0.129290	+	0.566457i	−0.868236	+	0.496152i	$0.834746\pi$
$458$	18.0036	−	22.5759i	0.841255	−	1.05490i
$459$		0			0
$460$	0.409698	−	1.79500i	0.0191023	−	0.0836925i
$461$	−4.88351	−	21.3961i	−0.227448	−	0.996514i	−0.951712	−	0.306991i	$-0.900678\pi$
$461$	−4.88351	−	21.3961i	−0.227448	−	0.996514i	0.724265	−	0.689522i	$-0.242179\pi$
$462$		0			0
$463$	−33.0073			−1.53398			−0.766990	−	0.641660i	$-0.778246\pi$
$463$	−33.0073			−1.53398			−0.766990	+	0.641660i	$0.778246\pi$
$464$	−12.8068	−	23.3110i	−0.594540	−	1.08219i
$465$		0			0
$466$	−2.19806	−	2.75628i	−0.101823	−	0.127682i
$467$	−5.80851	−	25.4487i	−0.268786	−	1.17763i	−0.911427	−	0.411461i	$-0.865019\pi$
$467$	−5.80851	−	25.4487i	−0.268786	−	1.17763i	0.642642	−	0.766167i	$-0.277838\pi$
$468$		0			0
$469$	−0.945042	−	1.18505i	−0.0436380	−	0.0547203i
$470$	−3.12833	+	3.92281i	−0.144299	+	0.180946i
$471$		0			0
$472$	11.1371	−	5.36333i	0.512625	−	0.246867i
$473$	15.0613	−	7.25314i	0.692519	−	0.333500i
$474$		0			0
$475$	8.99492	+	4.33172i	0.412715	+	0.198753i
$476$	5.60388			0.256853
$477$		0			0
$478$	10.0700	−	12.6274i	0.460592	−	0.577564i
$479$	−20.6163	+	25.8520i	−0.941981	+	1.18121i	0.0413068	+	0.999147i	$0.486848\pi$
$479$	−20.6163	+	25.8520i	−0.941981	+	1.18121i	−0.983287	+	0.182060i	$0.941724\pi$
$480$		0			0
$481$	−15.1008			−0.688538
$482$	−32.3071	−	15.5583i	−1.47155	−	0.708660i
$483$		0			0
$484$	2.83244	−	1.36403i	0.128747	−	0.0620014i
$485$	5.06465	−	2.43901i	0.229974	−	0.110750i
$486$		0			0
$487$	−6.33244	+	7.94063i	−0.286950	+	0.359824i	−0.904325	−	0.426845i	$-0.859625\pi$
$487$	−6.33244	+	7.94063i	−0.286950	+	0.359824i	0.617375	+	0.786669i	$0.288196\pi$
$488$	5.11745	+	6.41708i	0.231656	+	0.290487i
$489$		0			0
$490$	1.34428	+	5.88968i	0.0607285	+	0.266069i
$491$	12.2714	+	15.3879i	0.553802	+	0.694446i	0.977399	−	0.211405i	$-0.0678039\pi$
$491$	12.2714	+	15.3879i	0.553802	+	0.694446i	−0.423596	+	0.905851i	$0.639232\pi$
$492$		0			0
$493$	4.86592	+	3.47107i	0.219150	+	0.156329i
$494$	19.1468			0.861453
$495$		0			0
$496$	−6.98643	−	30.6095i	−0.313700	−	1.37441i
$497$	10.2763	−	45.0233i	0.460954	−	2.01957i
$498$		0			0
$499$	17.3639	−	21.7736i	0.777315	−	0.974722i	−0.222685	−	0.974890i	$-0.571482\pi$
$499$	17.3639	−	21.7736i	0.777315	−	0.974722i	1.00000		0.000168534i	$5.36461e-5\pi$
$500$	−0.977697	−	4.28357i	−0.0437240	−	0.191567i
$501$		0			0
$502$	41.8940	−	20.1751i	1.86982	−	0.900459i
$503$	−0.0501138	+	0.219563i	−0.00223446	+	0.00978982i	−0.976033	−	0.217623i	$-0.930170\pi$
$503$	−0.0501138	+	0.219563i	−0.00223446	+	0.00978982i	0.973798	+	0.227413i	$0.0730267\pi$
$504$		0			0
$505$	−6.22521			−0.277018
$506$	19.5574	+	9.41835i	0.869433	+	0.418697i
$507$		0			0
$508$	8.14191	−	10.2096i	0.361239	−	0.452979i
$509$	−22.7974	−	10.9786i	−1.01048	−	0.486620i	−0.145995	−	0.989285i	$-0.546638\pi$
$509$	−22.7974	−	10.9786i	−1.01048	−	0.486620i	−0.864481	+	0.502665i	$0.832353\pi$
$510$		0			0
$511$	−32.6444	−	15.7207i	−1.44410	−	0.695443i
$512$	−3.81604	+	16.7192i	−0.168647	+	0.738890i
$513$		0			0
$514$	19.4025	−	9.34373i	0.855806	−	0.412134i
$515$	−0.223480	−	0.979132i	−0.00984772	−	0.0431457i
$516$		0			0
$517$	−14.1645	−	17.7617i	−0.622954	−	0.781160i
$518$	−4.72737	+	20.7119i	−0.207709	+	0.910030i
$519$		0			0
$520$	1.56584	+	1.96351i	0.0686668	+	0.0861054i
$521$	−23.5797			−1.03305			−0.516523	−	0.856273i	$-0.672774\pi$
$521$	−23.5797			−1.03305			−0.516523	+	0.856273i	$0.672774\pi$
$522$		0			0
$523$	3.96508			0.173381			0.0866905	−	0.996235i	$-0.472371\pi$
$523$	3.96508			0.173381			0.0866905	+	0.996235i	$0.472371\pi$
$524$	0.353543	+	0.443330i	0.0154446	+	0.0193669i
$525$		0			0
$526$	−0.133415	+	0.584531i	−0.00581719	+	0.0254868i
$527$	4.39911	+	5.51631i	0.191628	+	0.240294i
$528$		0			0
$529$	1.30947	+	5.73717i	0.0569335	+	0.249442i
$530$	2.52446	−	1.21572i	0.109655	−	0.0528073i
$531$		0			0
$532$	2.30194	−	10.0854i	0.0998017	−	0.437260i
$533$	1.85086	+	0.891325i	0.0801694	+	0.0386076i
$534$		0			0
$535$	2.39881	+	1.15521i	0.103710	+	0.0499440i
$536$	−0.316708	+	0.397139i	−0.0136797	+	0.0171538i
$537$		0			0
$538$	−1.72737	−	0.831855i	−0.0744720	−	0.0358638i
$539$	−27.3532			−1.17818
$540$		0			0
$541$	5.48739	−	24.0418i	0.235921	−	1.03364i	−0.708709	−	0.705501i	$-0.750722\pi$
$541$	5.48739	−	24.0418i	0.235921	−	1.03364i	0.944630	−	0.328137i	$-0.106421\pi$
$542$	26.7298	−	12.8724i	1.14814	−	0.552917i
$543$		0			0
$544$	−1.52781	−	6.69378i	−0.0655044	−	0.286993i
$545$	0.367781	−	0.461183i	0.0157540	−	0.0197549i
$546$		0			0
$547$	−5.52768	+	24.2183i	−0.236347	+	1.03550i	0.707913	+	0.706300i	$0.249637\pi$
$547$	−5.52768	+	24.2183i	−0.236347	+	1.03550i	−0.944259	+	0.329202i	$0.893220\pi$
$548$	−3.67390	−	16.0964i	−0.156941	−	0.687604i
$549$		0			0
$550$	25.5666			1.09016
$551$	8.24578	−	7.33150i	0.351282	−	0.312332i
$552$		0			0
$553$	1.50000	+	1.88094i	0.0637865	+	0.0799857i
$554$	−2.64406	−	11.5844i	−0.112335	−	0.492174i
$555$		0			0
$556$	−2.17427	−	2.72645i	−0.0922095	−	0.115627i
$557$	−4.84146	+	6.07100i	−0.205139	+	0.257237i	−0.873749	−	0.486377i	$-0.838318\pi$
$557$	−4.84146	+	6.07100i	−0.205139	+	0.257237i	0.668610	+	0.743613i	$0.266890\pi$
$558$		0			0
$559$	−26.8240	+	12.9178i	−1.13453	+	0.546363i
$560$	6.43027	−	3.09666i	0.271729	−	0.130858i
$561$		0			0
$562$	−49.5734	−	23.8733i	−2.09113	−	1.00703i
$563$	−20.8009			−0.876652			−0.438326	−	0.898816i	$-0.644429\pi$
$563$	−20.8009			−0.876652			−0.438326	+	0.898816i	$0.644429\pi$
$564$		0			0
$565$	1.92274	−	2.41104i	0.0808902	−	0.101433i
$566$	−3.99396	+	5.00827i	−0.167879	+	0.210513i
$567$		0			0
$568$	−15.4765			−0.649380
$569$	2.53103	+	1.21888i	0.106106	+	0.0510981i	0.486184	−	0.873856i	$-0.338388\pi$
$569$	2.53103	+	1.21888i	0.106106	+	0.0510981i	−0.380078	+	0.924955i	$0.624103\pi$
$570$		0			0
$571$	−2.60603	+	1.25500i	−0.109059	+	0.0525201i	−0.487618	−	0.873057i	$-0.662134\pi$
$571$	−2.60603	+	1.25500i	−0.109059	+	0.0525201i	0.378559	+	0.925577i	$0.376420\pi$
$572$	16.9656	−	8.17021i	0.709368	−	0.341614i
$573$		0			0
$574$	1.80194	−	2.25956i	0.0752114	−	0.0943121i
$575$	−12.5685	−	15.7604i	−0.524144	−	0.657256i
$576$		0			0
$577$	−1.59970	−	7.00872i	−0.0665962	−	0.291777i	0.930653	−	0.365904i	$-0.119240\pi$
$577$	−1.59970	−	7.00872i	−0.0665962	−	0.291777i	−0.997249	+	0.0741270i	$0.976383\pi$
$578$	−17.7153	−	22.2143i	−0.736859	−	0.923992i
$579$		0			0
$580$	−2.36174	−	0.407417i	−0.0980659	−	0.0169171i
$581$	−38.1933			−1.58452
$582$		0			0
$583$	2.82304	+	12.3686i	0.116919	+	0.512254i
$584$	−2.70195	+	11.8380i	−0.111807	+	0.489860i
$585$		0			0
$586$	−36.9403	+	46.3216i	−1.52599	+	1.91353i
$587$	−6.90635	−	30.2587i	−0.285055	−	1.24891i	−0.891220	−	0.453570i	$-0.850150\pi$
$587$	−6.90635	−	30.2587i	−0.285055	−	1.24891i	0.606165	−	0.795339i	$-0.292707\pi$
$588$		0			0
$589$	11.7349	−	5.65123i	0.483528	−	0.232855i
$590$	1.30367	−	5.71174i	0.0536711	−	0.235148i
$591$		0			0
$592$	14.3817			0.591082
$593$	32.8560	+	15.8226i	1.34923	+	0.649757i	0.962209	−	0.272312i	$-0.0877884\pi$
$593$	32.8560	+	15.8226i	1.34923	+	0.649757i	0.387025	+	0.922069i	$0.373503\pi$
$594$		0			0
$595$	−1.00000	+	1.25396i	−0.0409960	+	0.0514074i
$596$	3.04288	+	1.46537i	0.124641	+	0.0600240i
$597$		0			0
$598$	−34.8315	−	16.7740i	−1.42437	−	0.685939i
$599$	6.69083	−	29.3144i	0.273380	−	1.19775i	−0.632615	−	0.774466i	$-0.718019\pi$
$599$	6.69083	−	29.3144i	0.273380	−	1.19775i	0.905995	−	0.423288i	$-0.139124\pi$
$600$		0			0
$601$	29.8995	−	14.3989i	1.21963	−	0.587342i	0.290420	−	0.956899i	$-0.406205\pi$
$601$	29.8995	−	14.3989i	1.21963	−	0.587342i	0.929208	+	0.369558i	$0.120491\pi$
$602$	9.32036	+	40.8351i	0.379869	+	1.66432i
$603$		0			0
$604$	−1.89344	−	2.37429i	−0.0770428	−	0.0966086i
$605$	−0.200218	+	0.877213i	−0.00814003	+	0.0356638i
$606$		0			0
$607$	−9.42729	−	11.8214i	−0.382642	−	0.479818i	0.552792	−	0.833319i	$-0.313562\pi$
$607$	−9.42729	−	11.8214i	−0.382642	−	0.479818i	−0.935434	+	0.353502i	$0.884991\pi$
$608$	−12.6746			−0.514021
$609$		0			0
$610$	3.89008			0.157505
$611$	25.2268	+	31.6334i	1.02057	+	1.27975i
$612$		0			0
$613$	−0.835658	+	3.66126i	−0.0337519	+	0.147877i	−0.988996	−	0.147942i	$-0.952735\pi$
$613$	−0.835658	+	3.66126i	−0.0337519	+	0.147877i	0.955244	+	0.295818i	$0.0955923\pi$
$614$	16.4819	+	20.6676i	0.665154	+	0.834077i
$615$		0			0
$616$	3.55980	+	15.5965i	0.143429	+	0.628401i
$617$	26.8995	−	12.9541i	1.08293	−	0.521514i	0.194681	−	0.980867i	$-0.437633\pi$
$617$	26.8995	−	12.9541i	1.08293	−	0.521514i	0.888254	+	0.459353i	$0.151919\pi$
$618$		0			0
$619$	10.2622	−	44.9615i	0.412472	−	1.80716i	−0.159866	−	0.987139i	$-0.551106\pi$
$619$	10.2622	−	44.9615i	0.412472	−	1.80716i	0.572338	−	0.820018i	$-0.306037\pi$
$620$	−2.54892	−	1.22749i	−0.102367	−	0.0492973i
$621$		0			0
$622$	30.0776	+	14.4846i	1.20600	+	0.580779i
$623$	3.59299	−	4.50547i	0.143950	−	0.180508i
$624$		0			0
$625$	−20.8174	−	10.0251i	−0.832697	−	0.401006i
$626$	41.4306			1.65590
$627$		0			0
$628$	−4.90515	+	21.4909i	−0.195737	+	0.857579i
$629$	−2.91185	+	1.40227i	−0.116103	+	0.0559124i
$630$		0			0
$631$	−2.81043	−	12.3133i	−0.111881	−	0.490185i	−0.999558	−	0.0297178i	$-0.990539\pi$
$631$	−2.81043	−	12.3133i	−0.111881	−	0.490185i	0.887677	−	0.460467i	$-0.152318\pi$
$632$	0.502688	−	0.630351i	0.0199959	−	0.0250740i
$633$		0			0
$634$	5.63706	−	24.6976i	0.223876	−	0.980867i
$635$	0.831668	+	3.64377i	0.0330037	+	0.144599i
$636$		0			0
$637$	48.7157			1.93019
$638$	10.8790	−	26.0776i	0.430702	−	1.03242i
$639$		0			0
$640$	−2.24429	−	2.81425i	−0.0887134	−	0.111243i
$641$	8.67874	+	38.0241i	0.342790	+	1.50186i	0.793157	+	0.609017i	$0.208436\pi$
$641$	8.67874	+	38.0241i	0.342790	+	1.50186i	−0.450368	+	0.892843i	$0.648707\pi$
$642$		0			0
$643$	25.7479	+	32.2869i	1.01540	+	1.27327i	0.961523	+	0.274723i	$0.0885862\pi$
$643$	25.7479	+	32.2869i	1.01540	+	1.27327i	0.0538762	+	0.998548i	$0.482842\pi$
$644$	−13.0233	+	16.3307i	−0.513188	+	0.643518i
$645$		0			0
$646$	3.69202	−	1.77798i	0.145261	−	0.0699538i
$647$	−16.1368	+	7.77109i	−0.634404	+	0.305513i	−0.723306	−	0.690527i	$-0.757378\pi$
$647$	−16.1368	+	7.77109i	−0.634404	+	0.305513i	0.0889021	+	0.996040i	$0.471664\pi$
$648$		0			0
$649$	23.8998	+	11.5095i	0.938148	+	0.451788i
$650$	−45.5338			−1.78598
$651$		0			0
$652$	−3.86108	+	4.84164i	−0.151211	+	0.189613i
$653$	8.30529	−	10.4145i	0.325011	−	0.407551i	−0.592303	−	0.805715i	$-0.701781\pi$
$653$	8.30529	−	10.4145i	0.325011	−	0.407551i	0.917314	+	0.398164i	$0.130353\pi$
$654$		0			0
$655$	−0.162291			−0.00634125
$656$	−1.76271	−	0.848876i	−0.0688222	−	0.0331430i
$657$		0			0
$658$	51.2851	−	24.6976i	1.99930	−	0.962812i
$659$	16.9073	−	8.14213i	0.658615	−	0.317172i	−0.0745557	−	0.997217i	$-0.523754\pi$
$659$	16.9073	−	8.14213i	0.658615	−	0.317172i	0.733171	+	0.680045i	$0.238040\pi$
$660$		0			0
$661$	−15.4182	+	19.3338i	−0.599698	+	0.751998i	−0.985331	−	0.170655i	$-0.945412\pi$
$661$	−15.4182	+	19.3338i	−0.599698	+	0.751998i	0.385633	+	0.922652i	$0.373983\pi$
$662$	15.6799	+	19.6620i	0.609418	+	0.764186i
$663$		0			0
$664$	2.84817	+	12.4786i	0.110530	+	0.484265i
$665$	1.84601	+	2.31482i	0.0715852	+	0.0897650i
$666$		0			0
$667$	−21.4236	+	6.11345i	−0.829524	+	0.236714i
$668$	−18.0368			−0.697866
$669$		0			0
$670$	0.0535716	+	0.234713i	0.00206965	+	0.00906774i
$671$	−3.91939	+	17.1720i	−0.151306	+	0.662916i
$672$		0			0
$673$	15.8632	−	19.8919i	0.611483	−	0.766775i	−0.375636	−	0.926767i	$-0.622576\pi$
$673$	15.8632	−	19.8919i	0.611483	−	0.766775i	0.987118	+	0.159992i	$0.0511470\pi$
$674$	5.61260	+	24.5904i	0.216189	+	0.947188i
$675$		0			0
$676$	−15.6102	+	7.51748i	−0.600393	+	0.289134i
$677$	0.137195	−	0.601090i	0.00527283	−	0.0231018i	−0.972223	−	0.234056i	$-0.924800\pi$
$677$	0.137195	−	0.601090i	0.00527283	−	0.0231018i	0.977496	+	0.210954i	$0.0676572\pi$
$678$		0			0
$679$	−63.7730			−2.44738
$680$	0.484271	+	0.233212i	0.0185709	+	0.00894329i
$681$		0			0
$682$	20.7962	−	26.0776i	0.796327	−	0.998563i
$683$	16.2371	+	7.81935i	0.621294	+	0.299199i	0.717924	−	0.696121i	$-0.245092\pi$
$683$	16.2371	+	7.81935i	0.621294	+	0.299199i	−0.0966308	+	0.995320i	$0.530807\pi$
$684$		0			0
$685$	4.25744	+	2.05027i	0.162668	+	0.0783369i
$686$	3.88620	−	17.0265i	0.148376	−	0.650077i
$687$		0			0
$688$	25.5465	−	12.3026i	0.973952	−	0.469031i
$689$	−5.02781	−	22.0283i	−0.191544	−	0.839211i
$690$		0			0
$691$	7.69769	+	9.65260i	0.292834	+	0.367202i	0.906385	−	0.422453i	$-0.138831\pi$
$691$	7.69769	+	9.65260i	0.292834	+	0.367202i	−0.613551	+	0.789655i	$0.710259\pi$
$692$	2.91723	−	12.7812i	0.110896	−	0.485869i
$693$		0			0
$694$	22.3056	+	27.9703i	0.846708	+	1.06174i
$695$	0.998081			0.0378594
$696$		0			0
$697$	0.439665			0.0166535
$698$	−30.2446	−	37.9255i	−1.14477	−	1.43550i
$699$		0			0
$700$	−5.47434	+	23.9847i	−0.206911	+	0.906535i
$701$	21.2594	+	26.6584i	0.802955	+	1.00687i	0.999651	+	0.0264091i	$0.00840724\pi$
$701$	21.2594	+	26.6584i	0.802955	+	1.00687i	−0.196696	+	0.980464i	$0.563021\pi$
$702$		0			0
$703$	1.32759	+	5.81656i	0.0500711	+	0.219376i
$704$	−3.32855	+	1.60295i	−0.125450	+	0.0604133i
$705$		0			0
$706$	−1.60992	+	7.05350i	−0.0605900	+	0.265462i
$707$	63.6299	+	30.6425i	2.39305	+	1.15243i
$708$		0			0
$709$	−37.9267	−	18.2645i	−1.42437	−	0.685939i	−0.446426	−	0.894821i	$-0.647303\pi$
$709$	−37.9267	−	18.2645i	−1.42437	−	0.685939i	−0.977941	+	0.208882i	$0.933018\pi$
$710$	−4.57338	+	5.73483i	−0.171636	+	0.215224i
$711$		0			0
$712$	−1.73998	−	0.837930i	−0.0652085	−	0.0314028i
$713$	−26.2989			−0.984901
$714$		0			0
$715$	−1.19926	+	5.25430i	−0.0448497	+	0.196500i
$716$	−6.44989	+	3.10610i	−0.241044	+	0.116080i
$717$		0			0
$718$	−0.299249	−	1.31110i	−0.0111679	−	0.0489297i
$719$	32.5800	−	40.8540i	1.21503	−	1.52360i	0.431667	−	0.902033i	$-0.357926\pi$
$719$	32.5800	−	40.8540i	1.21503	−	1.52360i	0.783362	−	0.621566i	$-0.213503\pi$
$720$		0			0
$721$	−2.53534	+	11.1081i	−0.0944211	+	0.413686i
$722$	5.93512	+	26.0034i	0.220882	+	0.967748i
$723$		0			0
$724$	−8.28083			−0.307755
$725$	−19.6097	+	17.4354i	−0.728285	+	0.647534i
$726$		0			0
$727$	18.6953	+	23.4432i	0.693370	+	0.869459i	0.996509	−	0.0834876i	$-0.0266059\pi$
$727$	18.6953	+	23.4432i	0.693370	+	0.869459i	−0.303138	+	0.952947i	$0.598034\pi$
$728$	−6.33997	−	27.7772i	−0.234975	−	1.02949i
$729$		0			0
$730$	3.58815	+	4.49939i	0.132803	+	0.166530i
$731$	−3.97285	+	4.98180i	−0.146941	+	0.184259i
$732$		0			0
$733$	−2.71595	+	1.30793i	−0.100316	+	0.0483096i	−0.483369	−	0.875417i	$-0.660587\pi$
$733$	−2.71595	+	1.30793i	−0.100316	+	0.0483096i	0.383053	+	0.923726i	$0.374873\pi$
$734$	55.2781	−	26.6205i	2.04035	−	0.982581i
$735$		0			0
$736$	23.0574	+	11.1039i	0.849907	+	0.409294i
$737$	−1.09006			−0.0401531
$738$		0			0
$739$	−12.9919	+	16.2914i	−0.477916	+	0.599288i	−0.961090	−	0.276237i	$-0.910913\pi$
$739$	−12.9919	+	16.2914i	−0.477916	+	0.599288i	0.483174	+	0.875525i	$0.339484\pi$
$740$	0.807979	−	1.01317i	0.0297019	−	0.0372450i
$741$		0			0
$742$	−31.7875			−1.16695
$743$	−27.7189	−	13.3487i	−1.01691	−	0.489718i	−0.150266	−	0.988646i	$-0.548013\pi$
$743$	−27.7189	−	13.3487i	−1.01691	−	0.489718i	−0.866643	+	0.498928i	$0.833727\pi$
$744$		0			0
$745$	−0.870896	+	0.419402i	−0.0319072	+	0.0153657i
$746$	−45.4587	+	21.8917i	−1.66436	+	0.801514i
$747$		0			0
$748$	2.51275	−	3.15088i	0.0918751	−	0.115208i
$749$	−18.8327	−	23.6155i	−0.688133	−	0.862892i
$750$		0			0
$751$	0.994492	+	4.35715i	0.0362895	+	0.158995i	0.989826	−	0.142283i	$-0.0454442\pi$
$751$	0.994492	+	4.35715i	0.0362895	+	0.158995i	−0.953537	+	0.301277i	$0.902587\pi$
$752$	−24.0254	−	30.1269i	−0.876117	−	1.09862i
$753$		0			0
$754$	−19.3753	+	46.4439i	−0.705607	+	1.69139i
$755$	0.869167			0.0316322
$756$		0			0
$757$	1.88159	+	8.24379i	0.0683876	+	0.299626i	0.997542	−	0.0700652i	$-0.0223207\pi$
$757$	1.88159	+	8.24379i	0.0683876	+	0.299626i	−0.929155	+	0.369691i	$0.879464\pi$
$758$	−9.17456	+	40.1964i	−0.333235	+	1.46000i
$759$		0			0
$760$	0.618645	−	0.775757i	0.0224406	−	0.0281397i
$761$	5.49516	+	24.0759i	0.199199	+	0.872749i	0.971415	+	0.237388i	$0.0762914\pi$
$761$	5.49516	+	24.0759i	0.199199	+	0.872749i	−0.772216	+	0.635361i	$0.780851\pi$
$762$		0			0
$763$	−6.02930	+	2.90356i	−0.218275	+	0.105116i
$764$	−5.21983	+	22.8696i	−0.188847	+	0.827392i
$765$		0			0
$766$	−21.3676			−0.772045
$767$	−42.5652	−	20.4983i	−1.53694	−	0.740152i
$768$		0			0
$769$	18.7939	−	23.5668i	0.677724	−	0.849839i	−0.317418	−	0.948286i	$-0.602816\pi$
$769$	18.7939	−	23.5668i	0.677724	−	0.849839i	0.995142	+	0.0984462i	$0.0313872\pi$
$770$	6.83124	+	3.28975i	0.246181	+	0.118554i
$771$		0			0
$772$	−12.2289	−	5.88911i	−0.440126	−	0.211954i
$773$	1.26324	−	5.53462i	0.0454356	−	0.199067i	−0.947116	−	0.320892i	$-0.896018\pi$
$773$	1.26324	−	5.53462i	0.0454356	−	0.199067i	0.992552	+	0.121825i	$0.0388747\pi$
$774$		0			0
$775$	−27.9073	+	13.4394i	−1.00246	+	0.482759i
$776$	4.75571	+	20.8361i	0.170720	+	0.747973i
$777$		0			0
$778$	11.6746	+	14.6394i	0.418553	+	0.524849i
$779$	0.180604	−	0.791277i	0.00647081	−	0.0283504i
$780$		0			0
$781$	−20.7074	−	25.9662i	−0.740968	−	0.929145i
$782$	−8.27413			−0.295882
$783$		0			0
$784$	−46.3957			−1.65699
$785$	−3.93362	−	4.93261i	−0.140397	−	0.176052i
$786$		0			0
$787$	0.803134	−	3.51876i	0.0286286	−	0.125430i	−0.958594	−	0.284775i	$-0.908081\pi$
$787$	0.803134	−	3.51876i	0.0286286	−	0.125430i	0.987223	+	0.159345i	$0.0509382\pi$
$788$	6.53116	+	8.18982i	0.232663	+	0.291750i
$789$		0			0
$790$	−0.0850306	−	0.372543i	−0.00302525	−	0.0132545i
$791$	−31.5209	+	15.1797i	−1.12075	+	0.539726i
$792$		0			0
$793$	6.98039	−	30.5831i	0.247881	−	1.08604i
$794$	−13.3409	−	6.42465i	−0.473452	−	0.228002i
$795$		0			0
$796$	7.43900	+	3.58243i	0.263668	+	0.126976i
$797$	19.1930	−	24.0672i	0.679850	−	0.852505i	−0.315490	−	0.948929i	$-0.602169\pi$
$797$	19.1930	−	24.0672i	0.679850	−	0.852505i	0.995340	+	0.0964236i	$0.0307403\pi$
$798$		0			0
$799$	7.80194	+	3.75722i	0.276013	+	0.132921i
$800$	30.1420			1.06568
$801$		0			0
$802$	9.97650	−	43.7099i	0.352282	−	1.54345i
$803$	−23.4768	+	11.3058i	−0.828478	+	0.398974i
$804$		0			0
$805$	−1.33028	−	5.82834i	−0.0468863	−	0.205422i
$806$	−37.0378	+	46.4439i	−1.30460	+	1.63592i
$807$		0			0
$808$	5.26659	−	23.0745i	0.185278	−	0.811757i
$809$	1.16541	+	5.10598i	0.0409735	+	0.179517i	0.991274	−	0.131817i	$-0.0420813\pi$
$809$	1.16541	+	5.10598i	0.0409735	+	0.179517i	−0.950300	+	0.311334i	$0.899224\pi$
$810$		0			0
$811$	41.8646			1.47006			0.735032	−	0.678032i	$-0.237167\pi$
$811$	41.8646			1.47006			0.735032	+	0.678032i	$0.237167\pi$
$812$	22.1347	+	15.7896i	0.776775	+	0.554107i
$813$		0			0
$814$	9.52595	+	11.9452i	0.333884	+	0.418678i
$815$	−0.394396	−	1.72796i	−0.0138151	−	0.0605278i
$816$		0			0
$817$	7.33393	+	9.19646i	0.256582	+	0.321743i
$818$	21.2289	−	26.6201i	0.742250	−	0.930752i
$819$		0			0
$820$	−0.158834	+	0.0764902i	−0.00554671	+	0.00267115i
$821$	13.8802	−	6.68433i	0.484421	−	0.233285i	−0.175701	−	0.984444i	$-0.556219\pi$
$821$	13.8802	−	6.68433i	0.484421	−	0.233285i	0.660121	+	0.751159i	$0.270505\pi$
$822$		0			0
$823$	32.1247	+	15.4705i	1.11980	+	0.539266i	0.899830	−	0.436241i	$-0.143690\pi$
$823$	32.1247	+	15.4705i	1.11980	+	0.539266i	0.219968	+	0.975507i	$0.429405\pi$
$824$	3.81833			0.133018
$825$		0			0
$826$	−41.4403	+	51.9644i	−1.44189	+	1.80807i
$827$	32.4550	−	40.6973i	1.12857	−	1.41518i	0.231760	−	0.972773i	$-0.425552\pi$
$827$	32.4550	−	40.6973i	1.12857	−	1.41518i	0.896812	−	0.442411i	$-0.145877\pi$
$828$		0			0
$829$	−13.4168			−0.465986			−0.232993	−	0.972478i	$-0.574852\pi$
$829$	−13.4168			−0.465986			−0.232993	+	0.972478i	$0.574852\pi$
$830$	5.46562	+	2.63210i	0.189714	+	0.0913616i
$831$		0			0
$832$	5.92812	−	2.85483i	0.205520	−	0.0989734i
$833$	9.39373	−	4.52378i	0.325474	−	0.156740i
$834$		0			0
$835$	3.21864	−	4.03604i	0.111385	−	0.139673i
$836$	−4.63856	−	5.81656i	−0.160428	−	0.201170i
$837$		0			0
$838$	−4.36754	−	19.1355i	−0.150874	−	0.661024i
$839$	19.3602	+	24.2769i	0.668387	+	0.838131i	0.994227	−	0.107294i	$-0.0342185\pi$
$839$	19.3602	+	24.2769i	0.668387	+	0.838131i	−0.325840	+	0.945425i	$0.605647\pi$
$840$		0			0
$841$	9.43967	+	27.4207i	0.325506	+	0.945540i
$842$	−35.9681			−1.23954
$843$		0			0
$844$	2.24764	+	9.84757i	0.0773671	+	0.338967i
$845$	1.10345	−	4.83452i	0.0379598	−	0.166313i
$846$		0			0
$847$	6.36443	−	7.98074i	0.218684	−	0.274222i
$848$	4.78836	+	20.9792i	0.164433	+	0.720428i
$849$		0			0
$850$	−8.78017	+	4.22831i	−0.301157	+	0.145030i
$851$	2.68060	−	11.7445i	0.0918899	−	0.402596i
$852$		0			0
$853$	21.3357			0.730521			0.365261	−	0.930905i	$-0.380980\pi$
$853$	21.3357			0.730521			0.365261	+	0.930905i	$0.380980\pi$
$854$	−39.7618	−	19.1483i	−1.36062	−	0.655241i
$855$		0			0
$856$	−6.31133	+	7.91416i	−0.215717	+	0.270500i
$857$	−8.85839	−	4.26597i	−0.302597	−	0.145723i	0.276424	−	0.961036i	$-0.410851\pi$
$857$	−8.85839	−	4.26597i	−0.302597	−	0.145723i	−0.579021	+	0.815313i	$0.696565\pi$
$858$		0			0
$859$	46.6555	+	22.4681i	1.59187	+	0.766602i	0.999244	−	0.0388778i	$-0.0123783\pi$
$859$	46.6555	+	22.4681i	1.59187	+	0.766602i	0.592623	+	0.805480i	$0.298093\pi$
$860$	0.568532	−	2.49090i	0.0193868	−	0.0849390i
$861$		0			0
$862$	−49.0136	+	23.6037i	−1.66941	+	0.803946i
$863$	−3.62147	−	15.8667i	−0.123276	−	0.540108i	−0.998417	−	0.0562402i	$-0.982089\pi$
$863$	−3.62147	−	15.8667i	−0.123276	−	0.540108i	0.875141	−	0.483868i	$-0.160768\pi$
$864$		0			0
$865$	2.33944	+	2.93356i	0.0795433	+	0.0997441i
$866$	8.09611	−	35.4714i	0.275117	−	1.20537i
$867$		0			0
$868$	20.0112	+	25.0932i	0.679224	+	0.851720i
$869$	1.73019			0.0586925
$870$		0			0
$871$	1.94139			0.0657816
$872$	1.39828	+	1.75339i	0.0473518	+	0.0593772i
$873$		0			0
$874$	−3.39881	+	14.8912i	−0.114967	+	0.503701i
$875$	−8.89493	−	11.1539i	−0.300703	−	0.377070i
$876$		0			0
$877$	−3.29470	−	14.4350i	−0.111254	−	0.487436i	−0.999601	−	0.0282623i	$-0.991003\pi$
$877$	−3.29470	−	14.4350i	−0.111254	−	0.487436i	0.888346	−	0.459174i	$-0.151855\pi$
$878$	17.3143	−	8.33813i	0.584330	−	0.281398i
$879$		0			0
$880$	1.14214	−	5.00406i	0.0385017	−	0.168687i
$881$	−16.7920	−	8.08661i	−0.565737	−	0.272445i	0.129076	−	0.991635i	$-0.458799\pi$
$881$	−16.7920	−	8.08661i	−0.565737	−	0.272445i	−0.694813	+	0.719190i	$0.744513\pi$
$882$		0			0
$883$	29.1857	+	14.0551i	0.982178	+	0.472992i	0.854854	−	0.518869i	$-0.173647\pi$
$883$	29.1857	+	14.0551i	0.982178	+	0.472992i	0.127325	+	0.991861i	$0.459361\pi$
$884$	−4.47517	+	5.61169i	−0.150516	+	0.188742i
$885$		0			0
$886$	−33.0383	−	15.9104i	−1.10994	−	0.534521i
$887$	6.16288			0.206929			0.103465	−	0.994633i	$-0.467007\pi$
$887$	6.16288			0.206929			0.103465	+	0.994633i	$0.467007\pi$
$888$		0			0
$889$	9.43512	−	41.3379i	0.316444	−	1.38643i
$890$	−0.824667	+	0.397139i	−0.0276429	+	0.0133121i
$891$		0			0
$892$	−6.08211	−	26.6474i	−0.203644	−	0.892222i
$893$	9.96681	−	12.4980i	0.333527	−	0.418229i
$894$		0			0
$895$	0.455927	−	1.99755i	0.0152400	−	0.0667706i
$896$	9.08695	+	39.8125i	0.303574	+	1.33004i
$897$		0			0
$898$	−34.9995			−1.16795
$899$	1.83310	+	34.1838i	0.0611373	+	1.14009i
$900$		0			0
$901$	−3.01507	−	3.78077i	−0.100446	−	0.125956i
$902$	−0.462500	−	2.02635i	−0.0153996	−	0.0674699i
$903$		0			0
$904$	7.31013	+	9.16662i	0.243131	+	0.304877i
$905$	1.47770	−	1.85297i	0.0491203	−	0.0615949i
$906$		0			0
$907$	−39.6284	+	19.0840i	−1.31584	+	0.633675i	−0.954347	−	0.298700i	$-0.903447\pi$
$907$	−39.6284	+	19.0840i	−1.31584	+	0.633675i	−0.361492	+	0.932375i	$0.617733\pi$
$908$	−20.5356	+	9.88944i	−0.681499	+	0.328193i
$909$		0			0
$910$	−12.1664	−	5.85901i	−0.403311	−	0.194224i
$911$	25.6233			0.848936			0.424468	−	0.905443i	$-0.360461\pi$
$911$	25.6233			0.848936			0.424468	+	0.905443i	$0.360461\pi$
$912$		0			0
$913$	−17.1256	+	21.4749i	−0.566776	+	0.710715i
$914$	−13.9547	+	17.4987i	−0.461581	+	0.578805i
$915$		0			0
$916$	19.9825			0.660242
$917$	1.65883	+	0.798852i	0.0547795	+	0.0263804i
$918$		0			0
$919$	5.62349	−	2.70813i	0.185502	−	0.0893330i	−0.338828	−	0.940848i	$-0.610030\pi$
$919$	5.62349	−	2.70813i	0.185502	−	0.0893330i	0.524329	+	0.851516i	$0.324316\pi$
$920$	−1.80505	+	0.869268i	−0.0595108	+	0.0286589i
$921$		0			0
$922$	24.6564	−	30.9182i	0.812017	−	1.01824i
$923$	36.8796	+	46.2456i	1.21391	+	1.52219i
$924$		0			0
$925$	−3.15721	−	13.8326i	−0.103808	−	0.454814i
$926$	−37.0834	−	46.5011i	−1.21863	−	1.52812i
$927$		0			0
$928$	12.8259	−	30.7445i	0.421030	−	1.00924i
$929$	24.5133			0.804256			0.402128	−	0.915583i	$-0.368271\pi$
$929$	24.5133			0.804256			0.402128	+	0.915583i	$0.368271\pi$
$930$		0			0
$931$	−4.28286	−	18.7644i	−0.140365	−	0.614979i
$932$	0.542877	−	2.37850i	0.0177825	−	0.0779103i
$933$		0			0
$934$	29.3267	−	36.7745i	0.959599	−	1.20330i
$935$	0.256668	+	1.12454i	0.00839395	+	0.0367763i
$936$		0			0
$937$	3.68449	−	1.77436i	0.120367	−	0.0579657i	−0.372731	−	0.927939i	$-0.621579\pi$
$937$	3.68449	−	1.77436i	0.120367	−	0.0579657i	0.493098	+	0.869974i	$0.335864\pi$
$938$	0.607760	−	2.66277i	0.0198441	−	0.0869426i
$939$		0			0
$940$	−3.47219			−0.113250
$941$	5.55280	+	2.67409i	0.181016	+	0.0871728i	0.522197	−	0.852825i	$-0.325113\pi$
$941$	5.55280	+	2.67409i	0.181016	+	0.0871728i	−0.341181	+	0.939998i	$0.610827\pi$
$942$		0			0
$943$	−1.02177	+	1.28126i	−0.0332734	+	0.0417235i
$944$	40.5381	+	19.5221i	1.31940	+	0.635391i
$945$		0			0
$946$	27.1395	+	13.0697i	0.882382	+	0.424933i
$947$	−11.0598	+	48.4562i	−0.359395	+	1.57461i	0.395309	+	0.918548i	$0.370638\pi$
$947$	−11.0598	+	48.4562i	−0.359395	+	1.57461i	−0.754704	+	0.656065i	$0.772220\pi$
$948$		0			0
$949$	41.8119	−	20.1356i	1.35727	−	0.653628i
$950$	4.00312	+	17.5388i	0.129878	+	0.569034i
$951$		0			0
$952$	−3.80194	−	4.76748i	−0.123222	−	0.154515i
$953$	3.93541	−	17.2422i	0.127480	−	0.558529i	−0.870335	−	0.492461i	$-0.836098\pi$
$953$	3.93541	−	17.2422i	0.127480	−	0.558529i	0.997815	−	0.0660678i	$-0.0210454\pi$
$954$		0			0
$955$	−4.18598	−	5.24905i	−0.135455	−	0.169855i
$956$	11.1769			0.361486
$957$		0			0
$958$	−59.5827			−1.92503
$959$	−33.4245	−	41.9130i	−1.07933	−	1.35344i
$960$		0			0
$961$	−2.09395	+	9.17419i	−0.0675468	+	0.295942i
$962$	−16.9656	−	21.2742i	−0.546993	−	0.685908i
$963$		0			0
$964$	−5.52177	−	24.1925i	−0.177844	−	0.779187i
$965$	3.50000	−	1.68551i	0.112669	−	0.0542585i
$966$		0			0
$967$	2.86904	−	12.5701i	0.0922620	−	0.404226i	−0.907617	−	0.419800i	$-0.862100\pi$
$967$	2.86904	−	12.5701i	0.0922620	−	0.404226i	0.999879	+	0.0155736i	$0.00495744\pi$
$968$	−3.08211	−	1.48426i	−0.0990626	−	0.0477060i
$969$		0			0
$970$	9.12618	+	4.39494i	0.293024	+	0.141113i
$971$	−3.01610	+	3.78207i	−0.0967912	+	0.121372i	−0.827868	−	0.560923i	$-0.810447\pi$
$971$	−3.01610	+	3.78207i	−0.0967912	+	0.121372i	0.731077	+	0.682295i	$0.239018\pi$
$972$		0			0
$973$	−10.2017	−	4.91288i	−0.327052	−	0.157500i
$974$	−18.3013			−0.586411
$975$		0			0
$976$	−6.64795	+	29.1266i	−0.212796	+	0.932319i
$977$	14.8138	−	7.13394i	0.473935	−	0.228235i	−0.181640	−	0.983365i	$-0.558141\pi$
$977$	14.8138	−	7.13394i	0.473935	−	0.228235i	0.655575	+	0.755130i	$0.272426\pi$
$978$		0			0
$979$	−0.922207	−	4.04045i	−0.0294739	−	0.129133i
$980$	−2.60656	+	3.26853i	−0.0832636	+	0.104409i
$981$		0			0
$982$	−7.89181	+	34.5763i	−0.251838	+	1.10337i
$983$	5.89666	+	25.8349i	0.188074	+	0.824007i	0.977631	+	0.210329i	$0.0674535\pi$
$983$	5.89666	+	25.8349i	0.188074	+	0.824007i	−0.789557	+	0.613678i	$0.789689\pi$
$984$		0			0
$985$	−2.99808			−0.0955268
$986$	0.576728	+	10.7549i	0.0183668	+	0.342505i
$987$		0			0
$988$	8.26122	+	10.3592i	0.262824	+	0.329571i
$989$	−5.28501	−	23.1551i	−0.168054	−	0.736291i
$990$		0			0
$991$	25.1930	+	31.5910i	0.800281	+	1.00352i	0.999721	+	0.0236111i	$0.00751634\pi$
$991$	25.1930	+	31.5910i	0.800281	+	1.00352i	−0.199440	+	0.979910i	$0.563912\pi$
$992$	24.5179	−	30.7445i	0.778444	−	0.976137i
$993$		0			0
$994$	74.9747	−	36.1059i	2.37805	−	1.14521i
$995$	−2.12910	+	1.02532i	−0.0674971	+	0.0325049i
$996$		0			0
$997$	21.1325	+	10.1769i	0.669273	+	0.322305i	0.737483	−	0.675366i	$-0.236014\pi$
$997$	21.1325	+	10.1769i	0.669273	+	0.322305i	−0.0682093	+	0.997671i	$0.521729\pi$
$998$	50.1831			1.58852
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.k.a.82.1		6
3.2	odd	2		29.2.d.a.24.1	yes	6
12.11	even	2		464.2.u.f.401.1		6
15.2	even	4		725.2.r.b.24.2		12
15.8	even	4		725.2.r.b.24.1		12
15.14	odd	2		725.2.l.b.401.1		6
29.9	even	14		7569.2.a.p.1.1		3
29.20	even	7		7569.2.a.r.1.3		3
29.23	even	7	inner	261.2.k.a.226.1		6
87.2	even	28		841.2.e.b.270.1		12
87.5	odd	14		841.2.d.a.571.1		6
87.8	even	28		841.2.b.c.840.1		6
87.11	even	28		841.2.e.c.236.1		12
87.14	even	28		841.2.e.d.267.2		12
87.17	even	4		841.2.e.d.63.1		12
87.20	odd	14		841.2.a.e.1.1		3
87.23	odd	14		29.2.d.a.23.1	✓	6
87.26	even	28		841.2.e.b.651.1		12
87.32	even	28		841.2.e.b.651.2		12
87.35	odd	14		841.2.d.d.574.1		6
87.38	odd	14		841.2.a.f.1.3		3
87.41	even	4		841.2.e.d.63.2		12
87.44	even	28		841.2.e.d.267.1		12
87.47	even	28		841.2.e.c.236.2		12
87.50	even	28		841.2.b.c.840.6		6
87.53	odd	14		841.2.d.e.571.1		6
87.56	even	28		841.2.e.b.270.2		12
87.62	odd	14		841.2.d.c.645.1		6
87.65	odd	14		841.2.d.e.190.1		6
87.68	even	28		841.2.e.c.196.1		12
87.71	odd	14		841.2.d.c.605.1		6
87.74	odd	14		841.2.d.b.605.1		6
87.77	even	28		841.2.e.c.196.2		12
87.80	odd	14		841.2.d.a.190.1		6
87.83	odd	14		841.2.d.b.645.1		6
87.86	odd	2		841.2.d.d.778.1		6
348.23	even	14		464.2.u.f.81.1		6
435.23	even	28		725.2.r.b.574.2		12
435.197	even	28		725.2.r.b.574.1		12
435.284	odd	14		725.2.l.b.226.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.d.a.23.1	✓	6	87.23	odd	14
29.2.d.a.24.1	yes	6	3.2	odd	2
261.2.k.a.82.1		6	1.1	even	1	trivial
261.2.k.a.226.1		6	29.23	even	7	inner
464.2.u.f.81.1		6	348.23	even	14
464.2.u.f.401.1		6	12.11	even	2
725.2.l.b.226.1		6	435.284	odd	14
725.2.l.b.401.1		6	15.14	odd	2
725.2.r.b.24.1		12	15.8	even	4
725.2.r.b.24.2		12	15.2	even	4
725.2.r.b.574.1		12	435.197	even	28
725.2.r.b.574.2		12	435.23	even	28
841.2.a.e.1.1		3	87.20	odd	14
841.2.a.f.1.3		3	87.38	odd	14
841.2.b.c.840.1		6	87.8	even	28
841.2.b.c.840.6		6	87.50	even	28
841.2.d.a.190.1		6	87.80	odd	14
841.2.d.a.571.1		6	87.5	odd	14
841.2.d.b.605.1		6	87.74	odd	14
841.2.d.b.645.1		6	87.83	odd	14
841.2.d.c.605.1		6	87.71	odd	14
841.2.d.c.645.1		6	87.62	odd	14
841.2.d.d.574.1		6	87.35	odd	14
841.2.d.d.778.1		6	87.86	odd	2
841.2.d.e.190.1		6	87.65	odd	14
841.2.d.e.571.1		6	87.53	odd	14
841.2.e.b.270.1		12	87.2	even	28
841.2.e.b.270.2		12	87.56	even	28
841.2.e.b.651.1		12	87.26	even	28
841.2.e.b.651.2		12	87.32	even	28
841.2.e.c.196.1		12	87.68	even	28
841.2.e.c.196.2		12	87.77	even	28
841.2.e.c.236.1		12	87.11	even	28
841.2.e.c.236.2		12	87.47	even	28
841.2.e.d.63.1		12	87.17	even	4
841.2.e.d.63.2		12	87.41	even	4
841.2.e.d.267.1		12	87.44	even	28
841.2.e.d.267.2		12	87.14	even	28
7569.2.a.p.1.1		3	29.9	even	14
7569.2.a.r.1.3		3	29.20	even	7

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.12349 + 1.40881i) q^{2} +(-0.277479 + 1.21572i) q^{4} +(-0.222521 - 0.279032i) q^{5} +(0.900969 + 3.94740i) q^{7} +(1.22252 - 0.588735i) q^{8} +(0.143104 - 0.626980i) q^{10} +(2.62349 + 1.26341i) q^{11} +(-4.67241 - 2.25011i) q^{13} +(-4.54892 + 5.70416i) q^{14} +(4.44989 + 2.14295i) q^{16} -1.10992 q^{17} +(-0.455927 + 1.99755i) q^{19} +(0.400969 - 0.193096i) q^{20} +(1.16756 + 5.11543i) q^{22} +(2.57942 - 3.23449i) q^{23} +(1.08426 - 4.75046i) q^{25} +(-2.07942 - 9.11052i) q^{26} -5.04892 q^{28} +(-4.38404 - 3.12733i) q^{29} +(-3.96346 - 4.97002i) q^{31} +(1.37651 + 6.03089i) q^{32} +(-1.24698 - 1.56366i) q^{34} +(0.900969 - 1.12978i) q^{35} +(2.62349 - 1.26341i) q^{37} +(-3.32640 + 1.60191i) q^{38} +(-0.436313 - 0.210117i) q^{40} -0.396125 q^{41} +(3.57942 - 4.48845i) q^{43} +(-2.26391 + 2.83885i) q^{44} +7.45473 q^{46} +(-7.02930 - 3.38513i) q^{47} +(-8.46346 + 4.07579i) q^{49} +(7.91066 - 3.80957i) q^{50} +(4.03199 - 5.05596i) q^{52} +(2.71648 + 3.40636i) q^{53} +(-0.231250 - 1.01317i) q^{55} +(3.42543 + 4.29535i) q^{56} +(-0.519614 - 9.68981i) q^{58} +9.10992 q^{59} +(1.34601 + 5.89726i) q^{61} +(2.54892 - 11.1675i) q^{62} +(-0.791053 + 0.991949i) q^{64} +(0.411854 + 1.80445i) q^{65} +(-0.337282 + 0.162426i) q^{67} +(0.307979 - 1.34934i) q^{68} +2.60388 q^{70} +(-10.2763 - 4.94880i) q^{71} +(-5.57942 + 6.99637i) q^{73} +(4.72737 + 2.27658i) q^{74} +(-2.30194 - 1.10855i) q^{76} +(-2.62349 + 11.4943i) q^{77} +(0.535344 - 0.257808i) q^{79} +(-0.392240 - 1.71851i) q^{80} +(-0.445042 - 0.558065i) q^{82} +(-2.09903 + 9.19646i) q^{83} +(0.246980 + 0.309703i) q^{85} +10.3448 q^{86} +3.95108 q^{88} +(-0.887395 - 1.11276i) q^{89} +(4.67241 - 20.4712i) q^{91} +(3.21648 + 4.03334i) q^{92} +(-3.12833 - 13.7061i) q^{94} +(0.658834 - 0.317278i) q^{95} +(-3.50484 + 15.3557i) q^{97} +(-15.2506 - 7.34432i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 2 q^{4} - q^{5} + q^{7} + 7 q^{8} + 9 q^{10} + 11 q^{11} - 5 q^{13} - 9 q^{14} + 4 q^{16} - 8 q^{17} + q^{19} - 2 q^{20} + 6 q^{22} + 7 q^{23} - 24 q^{25} - 4 q^{26} - 12 q^{28} - 6 q^{29}+ \cdots - 19 q^{98}+O(q^{100}) \) 6 * q + 2 * q^2 - 2 * q^4 - q^5 + q^7 + 7 * q^8 + 9 * q^10 + 11 * q^11 - 5 * q^13 - 9 * q^14 + 4 * q^16 - 8 * q^17 + q^19 - 2 * q^20 + 6 * q^22 + 7 * q^23 - 24 * q^25 - 4 * q^26 - 12 * q^28 - 6 * q^29 + 5 * q^31 + 13 * q^32 + 2 * q^34 + q^35 + 11 * q^37 - 2 * q^38 + 14 * q^40 - 20 * q^41 + 13 * q^43 - 20 * q^44 - 11 * q^47 - 22 * q^49 - q^50 - 10 * q^52 - 3 * q^53 - 17 * q^55 + 7 * q^56 - 16 * q^58 + 56 * q^59 + 3 * q^61 - 3 * q^62 + q^64 - 5 * q^65 + 19 * q^67 + 12 * q^68 - 2 * q^70 - 21 * q^71 - 25 * q^73 + 6 * q^74 - 5 * q^76 - 11 * q^77 - 9 * q^79 + 18 * q^80 - 2 * q^82 - 17 * q^83 - 8 * q^85 + 16 * q^86 + 42 * q^88 - 7 * q^89 + 5 * q^91 + 8 * q^94 - 13 * q^95 + q^97 - 19 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more