LMFDB - Embedded newform 825.2.k.g.518.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(518,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("825.518");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			518.1
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	825.518
Dual form			825.2.k.g.782.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.292893 + 0.292893i) q^{2} +(0.292893 - 1.70711i) q^{3} -1.82843i q^{4} +(0.585786 - 0.414214i) q^{6} +(-0.585786 + 0.585786i) q^{7} +(1.12132 - 1.12132i) q^{8} +(-2.82843 - 1.00000i) q^{9} +O(q^{10})$	\(q+(0.292893 + 0.292893i) q^{2} +(0.292893 - 1.70711i) q^{3} -1.82843i q^{4} +(0.585786 - 0.414214i) q^{6} +(-0.585786 + 0.585786i) q^{7} +(1.12132 - 1.12132i) q^{8} +(-2.82843 - 1.00000i) q^{9} +1.00000i q^{11} +(-3.12132 - 0.535534i) q^{12} +(-3.41421 - 3.41421i) q^{13} -0.343146 q^{14} -3.00000 q^{16} +(-2.00000 - 2.00000i) q^{17} +(-0.535534 - 1.12132i) q^{18} -0.828427i q^{19} +(0.828427 + 1.17157i) q^{21} +(-0.292893 + 0.292893i) q^{22} +(-0.828427 + 0.828427i) q^{23} +(-1.58579 - 2.24264i) q^{24} -2.00000i q^{26} +(-2.53553 + 4.53553i) q^{27} +(1.07107 + 1.07107i) q^{28} +8.82843 q^{29} +4.00000 q^{31} +(-3.12132 - 3.12132i) q^{32} +(1.70711 + 0.292893i) q^{33} -1.17157i q^{34} +(-1.82843 + 5.17157i) q^{36} +(-5.65685 + 5.65685i) q^{37} +(0.242641 - 0.242641i) q^{38} +(-6.82843 + 4.82843i) q^{39} -4.82843i q^{41} +(-0.100505 + 0.585786i) q^{42} +(-4.58579 - 4.58579i) q^{43} +1.82843 q^{44} -0.485281 q^{46} +(-4.82843 - 4.82843i) q^{47} +(-0.878680 + 5.12132i) q^{48} +6.31371i q^{49} +(-4.00000 + 2.82843i) q^{51} +(-6.24264 + 6.24264i) q^{52} +(8.48528 - 8.48528i) q^{53} +(-2.07107 + 0.585786i) q^{54} +1.31371i q^{56} +(-1.41421 - 0.242641i) q^{57} +(2.58579 + 2.58579i) q^{58} +2.34315 q^{59} -6.00000 q^{61} +(1.17157 + 1.17157i) q^{62} +(2.24264 - 1.07107i) q^{63} +4.17157i q^{64} +(0.414214 + 0.585786i) q^{66} +(2.58579 - 2.58579i) q^{67} +(-3.65685 + 3.65685i) q^{68} +(1.17157 + 1.65685i) q^{69} -9.65685i q^{71} +(-4.29289 + 2.05025i) q^{72} +(-4.58579 - 4.58579i) q^{73} -3.31371 q^{74} -1.51472 q^{76} +(-0.585786 - 0.585786i) q^{77} +(-3.41421 - 0.585786i) q^{78} +4.82843i q^{79} +(7.00000 + 5.65685i) q^{81} +(1.41421 - 1.41421i) q^{82} +(-4.24264 + 4.24264i) q^{83} +(2.14214 - 1.51472i) q^{84} -2.68629i q^{86} +(2.58579 - 15.0711i) q^{87} +(1.12132 + 1.12132i) q^{88} +15.3137 q^{89} +4.00000 q^{91} +(1.51472 + 1.51472i) q^{92} +(1.17157 - 6.82843i) q^{93} -2.82843i q^{94} +(-6.24264 + 4.41421i) q^{96} +(1.65685 - 1.65685i) q^{97} +(-1.84924 + 1.84924i) q^{98} +(1.00000 - 2.82843i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 8 q^{6} - 8 q^{7} - 4 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^3 + 8 * q^6 - 8 * q^7 - 4 * q^8	$ 4 q + 4 q^{2} + 4 q^{3} + 8 q^{6} - 8 q^{7} - 4 q^{8} - 4 q^{12} - 8 q^{13} - 24 q^{14} - 12 q^{16} - 8 q^{17} + 12 q^{18} - 8 q^{21} - 4 q^{22} + 8 q^{23} - 12 q^{24} + 4 q^{27} - 24 q^{28} + 24 q^{29} + 16 q^{31} - 4 q^{32} + 4 q^{33} + 4 q^{36} - 16 q^{38} - 16 q^{39} - 40 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} - 8 q^{47} - 12 q^{48} - 16 q^{51} - 8 q^{52} + 20 q^{54} + 16 q^{58} + 32 q^{59} - 24 q^{61} + 16 q^{62} - 8 q^{63} - 4 q^{66} + 16 q^{67} + 8 q^{68} + 16 q^{69} - 20 q^{72} - 24 q^{73} + 32 q^{74} - 40 q^{76} - 8 q^{77} - 8 q^{78} + 28 q^{81} - 48 q^{84} + 16 q^{87} - 4 q^{88} + 16 q^{89} + 16 q^{91} + 40 q^{92} + 16 q^{93} - 8 q^{96} - 16 q^{97} + 52 q^{98} + 4 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^3 + 8 * q^6 - 8 * q^7 - 4 * q^8 - 4 * q^12 - 8 * q^13 - 24 * q^14 - 12 * q^16 - 8 * q^17 + 12 * q^18 - 8 * q^21 - 4 * q^22 + 8 * q^23 - 12 * q^24 + 4 * q^27 - 24 * q^28 + 24 * q^29 + 16 * q^31 - 4 * q^32 + 4 * q^33 + 4 * q^36 - 16 * q^38 - 16 * q^39 - 40 * q^42 - 24 * q^43 - 4 * q^44 + 32 * q^46 - 8 * q^47 - 12 * q^48 - 16 * q^51 - 8 * q^52 + 20 * q^54 + 16 * q^58 + 32 * q^59 - 24 * q^61 + 16 * q^62 - 8 * q^63 - 4 * q^66 + 16 * q^67 + 8 * q^68 + 16 * q^69 - 20 * q^72 - 24 * q^73 + 32 * q^74 - 40 * q^76 - 8 * q^77 - 8 * q^78 + 28 * q^81 - 48 * q^84 + 16 * q^87 - 4 * q^88 + 16 * q^89 + 16 * q^91 + 40 * q^92 + 16 * q^93 - 8 * q^96 - 16 * q^97 + 52 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.292893	+	0.292893i	0.207107	+	0.207107i	0.803037	−	0.595930i	$-0.203216\pi$
$2$	0.292893	+	0.292893i	0.207107	+	0.207107i	−0.595930	+	0.803037i	$0.703216\pi$
$3$	0.292893	−	1.70711i	0.169102	−	0.985599i
$3$	0.292893	−	1.70711i	0.169102	−	0.985599i
$4$		−	1.82843i		−	0.914214i
$5$		0			0
$5$		0			0
$6$	0.585786	−	0.414214i	0.239146	−	0.169102i
$7$	−0.585786	+	0.585786i	−0.221406	+	0.221406i	−0.809091	−	0.587684i	$-0.800040\pi$
$7$	−0.585786	+	0.585786i	−0.221406	+	0.221406i	0.587684	+	0.809091i	$0.300040\pi$
$8$	1.12132	−	1.12132i	0.396447	−	0.396447i
$9$	−2.82843	−	1.00000i	−0.942809	−	0.333333i
$10$		0			0
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$	−3.12132	−	0.535534i	−0.901048	−	0.154595i
$13$	−3.41421	−	3.41421i	−0.946932	−	0.946932i	0.0517287	−	0.998661i	$-0.483527\pi$
$13$	−3.41421	−	3.41421i	−0.946932	−	0.946932i	−0.998661	+	0.0517287i	$0.983527\pi$
$14$	−0.343146			−0.0917096
$15$		0			0
$16$	−3.00000			−0.750000
$17$	−2.00000	−	2.00000i	−0.485071	−	0.485071i	0.421676	−	0.906747i	$-0.361442\pi$
$17$	−2.00000	−	2.00000i	−0.485071	−	0.485071i	−0.906747	+	0.421676i	$0.861442\pi$
$18$	−0.535534	−	1.12132i	−0.126227	−	0.264298i
$19$		−	0.828427i		−	0.190054i	−0.995475	−	0.0950271i	$-0.969706\pi$
$19$		−	0.828427i		−	0.190054i	0.995475	−	0.0950271i	$-0.0302938\pi$
$20$		0			0
$21$	0.828427	+	1.17157i	0.180778	+	0.255658i
$22$	−0.292893	+	0.292893i	−0.0624450	+	0.0624450i
$23$	−0.828427	+	0.828427i	−0.172739	+	0.172739i	−0.788182	−	0.615443i	$-0.788977\pi$
$23$	−0.828427	+	0.828427i	−0.172739	+	0.172739i	0.615443	+	0.788182i	$0.288977\pi$
$24$	−1.58579	−	2.24264i	−0.323697	−	0.457777i
$25$		0			0
$26$		−	2.00000i		−	0.392232i
$27$	−2.53553	+	4.53553i	−0.487964	+	0.872864i
$28$	1.07107	+	1.07107i	0.202413	+	0.202413i
$29$	8.82843			1.63940			0.819699	−	0.572795i	$-0.194141\pi$
$29$	8.82843			1.63940			0.819699	+	0.572795i	$0.194141\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	−3.12132	−	3.12132i	−0.551777	−	0.551777i
$33$	1.70711	+	0.292893i	0.297169	+	0.0509862i
$34$		−	1.17157i		−	0.200923i
$35$		0			0
$36$	−1.82843	+	5.17157i	−0.304738	+	0.861929i
$37$	−5.65685	+	5.65685i	−0.929981	+	0.929981i	−0.997704	−	0.0677230i	$-0.978427\pi$
$37$	−5.65685	+	5.65685i	−0.929981	+	0.929981i	0.0677230	+	0.997704i	$0.478427\pi$
$38$	0.242641	−	0.242641i	0.0393615	−	0.0393615i
$39$	−6.82843	+	4.82843i	−1.09342	+	0.773167i
$40$		0			0
$41$		−	4.82843i		−	0.754074i	−0.926198	−	0.377037i	$-0.876943\pi$
$41$		−	4.82843i		−	0.754074i	0.926198	−	0.377037i	$-0.123057\pi$
$42$	−0.100505	+	0.585786i	−0.0155083	+	0.0903888i
$43$	−4.58579	−	4.58579i	−0.699326	−	0.699326i	0.264939	−	0.964265i	$-0.414648\pi$
$43$	−4.58579	−	4.58579i	−0.699326	−	0.699326i	−0.964265	+	0.264939i	$0.914648\pi$
$44$	1.82843			0.275646
$45$		0			0
$46$	−0.485281			−0.0715508
$47$	−4.82843	−	4.82843i	−0.704298	−	0.704298i	0.261032	−	0.965330i	$-0.415937\pi$
$47$	−4.82843	−	4.82843i	−0.704298	−	0.704298i	−0.965330	+	0.261032i	$0.915937\pi$
$48$	−0.878680	+	5.12132i	−0.126826	+	0.739199i
$49$			6.31371i			0.901958i
$50$		0			0
$51$	−4.00000	+	2.82843i	−0.560112	+	0.396059i
$52$	−6.24264	+	6.24264i	−0.865699	+	0.865699i
$53$	8.48528	−	8.48528i	1.16554	−	1.16554i	0.182300	−	0.983243i	$-0.441646\pi$
$53$	8.48528	−	8.48528i	1.16554	−	1.16554i	0.983243	−	0.182300i	$-0.0583542\pi$
$54$	−2.07107	+	0.585786i	−0.281837	+	0.0797154i
$55$		0			0
$56$			1.31371i			0.175552i
$57$	−1.41421	−	0.242641i	−0.187317	−	0.0321385i
$58$	2.58579	+	2.58579i	0.339530	+	0.339530i
$59$	2.34315			0.305052			0.152526	−	0.988299i	$-0.451259\pi$
$59$	2.34315			0.305052			0.152526	+	0.988299i	$0.451259\pi$
$60$		0			0
$61$	−6.00000			−0.768221			−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000			−0.768221			−0.384111	+	0.923287i	$0.625492\pi$
$62$	1.17157	+	1.17157i	0.148790	+	0.148790i
$63$	2.24264	−	1.07107i	0.282546	−	0.134942i
$64$			4.17157i			0.521447i
$65$		0			0
$66$	0.414214	+	0.585786i	0.0509862	+	0.0721053i
$67$	2.58579	−	2.58579i	0.315904	−	0.315904i	−0.531287	−	0.847192i	$-0.678292\pi$
$67$	2.58579	−	2.58579i	0.315904	−	0.315904i	0.847192	+	0.531287i	$0.178292\pi$
$68$	−3.65685	+	3.65685i	−0.443459	+	0.443459i
$69$	1.17157	+	1.65685i	0.141041	+	0.199462i
$70$		0			0
$71$		−	9.65685i		−	1.14606i	−0.819535	−	0.573029i	$-0.805768\pi$
$71$		−	9.65685i		−	1.14606i	0.819535	−	0.573029i	$-0.194232\pi$
$72$	−4.29289	+	2.05025i	−0.505922	+	0.241625i
$73$	−4.58579	−	4.58579i	−0.536726	−	0.536726i	0.385840	−	0.922566i	$-0.373912\pi$
$73$	−4.58579	−	4.58579i	−0.536726	−	0.536726i	−0.922566	+	0.385840i	$0.873912\pi$
$74$	−3.31371			−0.385211
$75$		0			0
$76$	−1.51472			−0.173750
$77$	−0.585786	−	0.585786i	−0.0667566	−	0.0667566i
$78$	−3.41421	−	0.585786i	−0.386584	−	0.0663273i
$79$			4.82843i			0.543240i	0.962405	+	0.271620i	$0.0875595\pi$
$79$			4.82843i			0.543240i	−0.962405	+	0.271620i	$0.912441\pi$
$80$		0			0
$81$	7.00000	+	5.65685i	0.777778	+	0.628539i
$82$	1.41421	−	1.41421i	0.156174	−	0.156174i
$83$	−4.24264	+	4.24264i	−0.465690	+	0.465690i	−0.900515	−	0.434825i	$-0.856810\pi$
$83$	−4.24264	+	4.24264i	−0.465690	+	0.465690i	0.434825	+	0.900515i	$0.356810\pi$
$84$	2.14214	−	1.51472i	0.233726	−	0.165269i
$85$		0			0
$86$		−	2.68629i		−	0.289670i
$87$	2.58579	−	15.0711i	0.277225	−	1.61579i
$88$	1.12132	+	1.12132i	0.119533	+	0.119533i
$89$	15.3137			1.62325			0.811625	−	0.584179i	$-0.198583\pi$
$89$	15.3137			1.62325			0.811625	+	0.584179i	$0.198583\pi$
$90$		0			0
$91$	4.00000			0.419314
$92$	1.51472	+	1.51472i	0.157920	+	0.157920i
$93$	1.17157	−	6.82843i	0.121486	−	0.708075i
$94$		−	2.82843i		−	0.291730i
$95$		0			0
$96$	−6.24264	+	4.41421i	−0.637137	+	0.450524i
$97$	1.65685	−	1.65685i	0.168228	−	0.168228i	−0.617972	−	0.786200i	$-0.712046\pi$
$97$	1.65685	−	1.65685i	0.168228	−	0.168228i	0.786200	+	0.617972i	$0.212046\pi$
$98$	−1.84924	+	1.84924i	−0.186802	+	0.186802i
$99$	1.00000	−	2.82843i	0.100504	−	0.284268i
$100$		0			0
$101$		−	0.828427i		−	0.0824316i	−0.999150	−	0.0412158i	$-0.986877\pi$
$101$		−	0.828427i		−	0.0824316i	0.999150	−	0.0412158i	$-0.0131231\pi$
$102$	−2.00000	−	0.343146i	−0.198030	−	0.0339765i
$103$	−4.24264	−	4.24264i	−0.418040	−	0.418040i	0.466488	−	0.884528i	$-0.345519\pi$
$103$	−4.24264	−	4.24264i	−0.418040	−	0.418040i	−0.884528	+	0.466488i	$0.845519\pi$
$104$	−7.65685			−0.750816
$105$		0			0
$106$	4.97056			0.482784
$107$	13.8995	+	13.8995i	1.34371	+	1.34371i	0.892329	+	0.451386i	$0.149070\pi$
$107$	13.8995	+	13.8995i	1.34371	+	1.34371i	0.451386	+	0.892329i	$0.350930\pi$
$108$	8.29289	+	4.63604i	0.797984	+	0.446103i
$109$		−	2.00000i		−	0.191565i	−0.995402	−	0.0957826i	$-0.969465\pi$
$109$		−	2.00000i		−	0.191565i	0.995402	−	0.0957826i	$-0.0305354\pi$
$110$		0			0
$111$	8.00000	+	11.3137i	0.759326	+	1.07385i
$112$	1.75736	−	1.75736i	0.166055	−	0.166055i
$113$	8.48528	−	8.48528i	0.798228	−	0.798228i	−0.184588	−	0.982816i	$-0.559095\pi$
$113$	8.48528	−	8.48528i	0.798228	−	0.798228i	0.982816	+	0.184588i	$0.0590950\pi$
$114$	−0.343146	−	0.485281i	−0.0321385	−	0.0454508i
$115$		0			0
$116$		−	16.1421i		−	1.49876i
$117$	6.24264	+	13.0711i	0.577132	+	1.20842i
$118$	0.686292	+	0.686292i	0.0631783	+	0.0631783i
$119$	2.34315			0.214796
$120$		0			0
$121$	−1.00000			−0.0909091
$122$	−1.75736	−	1.75736i	−0.159104	−	0.159104i
$123$	−8.24264	−	1.41421i	−0.743214	−	0.127515i
$124$		−	7.31371i		−	0.656790i
$125$		0			0
$126$	0.970563	+	0.343146i	0.0864646	+	0.0305699i
$127$	10.2426	−	10.2426i	0.908887	−	0.908887i	−0.0872951	−	0.996182i	$-0.527822\pi$
$127$	10.2426	−	10.2426i	0.908887	−	0.908887i	0.996182	+	0.0872951i	$0.0278223\pi$
$128$	−7.46447	+	7.46447i	−0.659772	+	0.659772i
$129$	−9.17157	+	6.48528i	−0.807512	+	0.570997i
$130$		0			0
$131$		−	17.6569i		−	1.54269i	−0.636419	−	0.771343i	$-0.719585\pi$
$131$		−	17.6569i		−	1.54269i	0.636419	−	0.771343i	$-0.280415\pi$
$132$	0.535534	−	3.12132i	0.0466122	−	0.271676i
$133$	0.485281	+	0.485281i	0.0420792	+	0.0420792i
$134$	1.51472			0.130852
$135$		0			0
$136$	−4.48528			−0.384610
$137$	1.65685	+	1.65685i	0.141555	+	0.141555i	0.774333	−	0.632778i	$-0.218086\pi$
$137$	1.65685	+	1.65685i	0.141555	+	0.141555i	−0.632778	+	0.774333i	$0.718086\pi$
$138$	−0.142136	+	0.828427i	−0.0120994	+	0.0705204i
$139$		−	16.8284i		−	1.42737i	−0.700468	−	0.713684i	$-0.747025\pi$
$139$		−	16.8284i		−	1.42737i	0.700468	−	0.713684i	$-0.252975\pi$
$140$		0			0
$141$	−9.65685	+	6.82843i	−0.813254	+	0.575057i
$142$	2.82843	−	2.82843i	0.237356	−	0.237356i
$143$	3.41421	−	3.41421i	0.285511	−	0.285511i
$144$	8.48528	+	3.00000i	0.707107	+	0.250000i
$145$		0			0
$146$		−	2.68629i		−	0.222319i
$147$	10.7782	+	1.84924i	0.888969	+	0.152523i
$148$	10.3431	+	10.3431i	0.850201	+	0.850201i
$149$	−17.7990			−1.45815			−0.729075	−	0.684434i	$-0.760049\pi$
$149$	−17.7990			−1.45815			−0.729075	+	0.684434i	$0.760049\pi$
$150$		0			0
$151$	14.4853			1.17880			0.589398	−	0.807843i	$-0.299365\pi$
$151$	14.4853			1.17880			0.589398	+	0.807843i	$0.299365\pi$
$152$	−0.928932	−	0.928932i	−0.0753463	−	0.0753463i
$153$	3.65685	+	7.65685i	0.295639	+	0.619020i
$154$		−	0.343146i		−	0.0276515i
$155$		0			0
$156$	8.82843	+	12.4853i	0.706840	+	0.999623i
$157$	15.3137	−	15.3137i	1.22217	−	1.22217i	0.255307	−	0.966860i	$-0.417823\pi$
$157$	15.3137	−	15.3137i	1.22217	−	1.22217i	0.966860	−	0.255307i	$-0.0821765\pi$
$158$	−1.41421	+	1.41421i	−0.112509	+	0.112509i
$159$	−12.0000	−	16.9706i	−0.951662	−	1.34585i
$160$		0			0
$161$		−	0.970563i		−	0.0764911i
$162$	0.393398	+	3.70711i	0.0309083	+	0.291258i
$163$	9.89949	+	9.89949i	0.775388	+	0.775388i	0.979043	−	0.203655i	$-0.0652819\pi$
$163$	9.89949	+	9.89949i	0.775388	+	0.775388i	−0.203655	+	0.979043i	$0.565282\pi$
$164$	−8.82843			−0.689384
$165$		0			0
$166$	−2.48528			−0.192895
$167$	8.24264	+	8.24264i	0.637835	+	0.637835i	0.950021	−	0.312186i	$-0.101061\pi$
$167$	8.24264	+	8.24264i	0.637835	+	0.637835i	−0.312186	+	0.950021i	$0.601061\pi$
$168$	2.24264	+	0.384776i	0.173023	+	0.0296861i
$169$			10.3137i			0.793362i
$170$		0			0
$171$	−0.828427	+	2.34315i	−0.0633514	+	0.179185i
$172$	−8.38478	+	8.38478i	−0.639333	+	0.639333i
$173$	−4.82843	+	4.82843i	−0.367099	+	0.367099i	−0.866418	−	0.499319i	$-0.833583\pi$
$173$	−4.82843	+	4.82843i	−0.367099	+	0.367099i	0.499319	+	0.866418i	$0.333583\pi$
$174$	5.17157	−	3.65685i	0.392056	−	0.277225i
$175$		0			0
$176$		−	3.00000i		−	0.226134i
$177$	0.686292	−	4.00000i	0.0515848	−	0.300658i
$178$	4.48528	+	4.48528i	0.336186	+	0.336186i
$179$	19.3137			1.44357			0.721787	−	0.692115i	$-0.243321\pi$
$179$	19.3137			1.44357			0.721787	+	0.692115i	$0.243321\pi$
$180$		0			0
$181$	−6.00000			−0.445976			−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000			−0.445976			−0.222988	+	0.974821i	$0.571581\pi$
$182$	1.17157	+	1.17157i	0.0868428	+	0.0868428i
$183$	−1.75736	+	10.2426i	−0.129908	+	0.757158i
$184$			1.85786i			0.136964i
$185$		0			0
$186$	2.34315	−	1.65685i	0.171808	−	0.121486i
$187$	2.00000	−	2.00000i	0.146254	−	0.146254i
$188$	−8.82843	+	8.82843i	−0.643879	+	0.643879i
$189$	−1.17157	−	4.14214i	−0.0852194	−	0.301296i
$190$		0			0
$191$			11.3137i			0.818631i	0.912393	+	0.409316i	$0.134232\pi$
$191$			11.3137i			0.818631i	−0.912393	+	0.409316i	$0.865768\pi$
$192$	7.12132	+	1.22183i	0.513937	+	0.0881777i
$193$	−9.07107	−	9.07107i	−0.652950	−	0.652950i	0.300752	−	0.953702i	$-0.402762\pi$
$193$	−9.07107	−	9.07107i	−0.652950	−	0.652950i	−0.953702	+	0.300752i	$0.902762\pi$
$194$	0.970563			0.0696823
$195$		0			0
$196$	11.5442			0.824583
$197$	−14.4853	−	14.4853i	−1.03203	−	1.03203i	−0.999470	−	0.0325639i	$-0.989633\pi$
$197$	−14.4853	−	14.4853i	−1.03203	−	1.03203i	−0.0325639	−	0.999470i	$-0.510367\pi$
$198$	1.12132	−	0.535534i	0.0796888	−	0.0380587i
$199$		−	12.9706i		−	0.919459i	−0.888059	−	0.459729i	$-0.847946\pi$
$199$		−	12.9706i		−	0.919459i	0.888059	−	0.459729i	$-0.152054\pi$
$200$		0			0
$201$	−3.65685	−	5.17157i	−0.257935	−	0.364775i
$202$	0.242641	−	0.242641i	0.0170721	−	0.0170721i
$203$	−5.17157	+	5.17157i	−0.362973	+	0.362973i
$204$	5.17157	+	7.31371i	0.362083	+	0.512062i
$205$		0			0
$206$		−	2.48528i		−	0.173158i
$207$	3.17157	−	1.51472i	0.220440	−	0.105280i
$208$	10.2426	+	10.2426i	0.710199	+	0.710199i
$209$	0.828427			0.0573035
$210$		0			0
$211$	−10.4853			−0.721837			−0.360918	−	0.932597i	$-0.617537\pi$
$211$	−10.4853			−0.721837			−0.360918	+	0.932597i	$0.617537\pi$
$212$	−15.5147	−	15.5147i	−1.06556	−	1.06556i
$213$	−16.4853	−	2.82843i	−1.12955	−	0.193801i
$214$			8.14214i			0.556585i
$215$		0			0
$216$	2.24264	+	7.92893i	0.152592	+	0.539496i
$217$	−2.34315	+	2.34315i	−0.159063	+	0.159063i
$218$	0.585786	−	0.585786i	0.0396745	−	0.0396745i
$219$	−9.17157	+	6.48528i	−0.619757	+	0.438235i
$220$		0			0
$221$			13.6569i			0.918659i
$222$	−0.970563	+	5.65685i	−0.0651399	+	0.379663i
$223$	16.2426	+	16.2426i	1.08769	+	1.08769i	0.995766	+	0.0919214i	$0.0293009\pi$
$223$	16.2426	+	16.2426i	1.08769	+	1.08769i	0.0919214	+	0.995766i	$0.470699\pi$
$224$	3.65685			0.244334
$225$		0			0
$226$	4.97056			0.330637
$227$	20.2426	+	20.2426i	1.34355	+	1.34355i	0.892496	+	0.451055i	$0.148952\pi$
$227$	20.2426	+	20.2426i	1.34355	+	1.34355i	0.451055	+	0.892496i	$0.351048\pi$
$228$	−0.443651	+	2.58579i	−0.0293815	+	0.171248i
$229$			18.0000i			1.18947i	0.803921	+	0.594737i	$0.202744\pi$
$229$			18.0000i			1.18947i	−0.803921	+	0.594737i	$0.797256\pi$
$230$		0			0
$231$	−1.17157	+	0.828427i	−0.0770838	+	0.0545065i
$232$	9.89949	−	9.89949i	0.649934	−	0.649934i
$233$	−10.0000	+	10.0000i	−0.655122	+	0.655122i	−0.954222	−	0.299100i	$-0.903314\pi$
$233$	−10.0000	+	10.0000i	−0.655122	+	0.655122i	0.299100	+	0.954222i	$0.403314\pi$
$234$	−2.00000	+	5.65685i	−0.130744	+	0.369800i
$235$		0			0
$236$		−	4.28427i		−	0.278882i
$237$	8.24264	+	1.41421i	0.535417	+	0.0918630i
$238$	0.686292	+	0.686292i	0.0444857	+	0.0444857i
$239$	−2.34315			−0.151565			−0.0757827	−	0.997124i	$-0.524146\pi$
$239$	−2.34315			−0.151565			−0.0757827	+	0.997124i	$0.524146\pi$
$240$		0			0
$241$	−26.9706			−1.73733			−0.868663	−	0.495403i	$-0.835020\pi$
$241$	−26.9706			−1.73733			−0.868663	+	0.495403i	$0.835020\pi$
$242$	−0.292893	−	0.292893i	−0.0188279	−	0.0188279i
$243$	11.7071	−	10.2929i	0.751011	−	0.660289i
$244$			10.9706i			0.702318i
$245$		0			0
$246$	−2.00000	−	2.82843i	−0.127515	−	0.180334i
$247$	−2.82843	+	2.82843i	−0.179969	+	0.179969i
$248$	4.48528	−	4.48528i	0.284816	−	0.284816i
$249$	6.00000	+	8.48528i	0.380235	+	0.537733i
$250$		0			0
$251$		−	1.65685i		−	0.104580i	−0.998632	−	0.0522899i	$-0.983348\pi$
$251$		−	1.65685i		−	0.104580i	0.998632	−	0.0522899i	$-0.0166520\pi$
$252$	−1.95837	−	4.10051i	−0.123366	−	0.258308i
$253$	−0.828427	−	0.828427i	−0.0520828	−	0.0520828i
$254$	6.00000			0.376473
$255$		0			0
$256$	3.97056			0.248160
$257$	16.0000	+	16.0000i	0.998053	+	0.998053i	0.999998	−	0.00194553i	$-0.000619281\pi$
$257$	16.0000	+	16.0000i	0.998053	+	0.998053i	−0.00194553	+	0.999998i	$0.500619\pi$
$258$	−4.58579	−	0.786797i	−0.285499	−	0.0489838i
$259$		−	6.62742i		−	0.411808i
$260$		0			0
$261$	−24.9706	−	8.82843i	−1.54564	−	0.546466i
$262$	5.17157	−	5.17157i	0.319501	−	0.319501i
$263$	16.2426	−	16.2426i	1.00156	−	1.00156i	0.00156536	−	0.999999i	$-0.499502\pi$
$263$	16.2426	−	16.2426i	1.00156	−	1.00156i	0.999999	−	0.00156536i	$-0.000498269\pi$
$264$	2.24264	−	1.58579i	0.138025	−	0.0975984i
$265$		0			0
$266$			0.284271i			0.0174298i
$267$	4.48528	−	26.1421i	0.274495	−	1.59987i
$268$	−4.72792	−	4.72792i	−0.288804	−	0.288804i
$269$	13.6569			0.832673			0.416337	−	0.909211i	$-0.363314\pi$
$269$	13.6569			0.832673			0.416337	+	0.909211i	$0.363314\pi$
$270$		0			0
$271$	−9.51472			−0.577978			−0.288989	−	0.957332i	$-0.593319\pi$
$271$	−9.51472			−0.577978			−0.288989	+	0.957332i	$0.593319\pi$
$272$	6.00000	+	6.00000i	0.363803	+	0.363803i
$273$	1.17157	−	6.82843i	0.0709068	−	0.413275i
$274$			0.970563i			0.0586338i
$275$		0			0
$276$	3.02944	−	2.14214i	0.182351	−	0.128941i
$277$	−17.0711	+	17.0711i	−1.02570	+	1.02570i	−0.0260402	+	0.999661i	$0.508290\pi$
$277$	−17.0711	+	17.0711i	−1.02570	+	1.02570i	−0.999661	+	0.0260402i	$0.991710\pi$
$278$	4.92893	−	4.92893i	0.295618	−	0.295618i
$279$	−11.3137	−	4.00000i	−0.677334	−	0.239474i
$280$		0			0
$281$			8.14214i			0.485719i	0.970061	+	0.242860i	$0.0780854\pi$
$281$			8.14214i			0.485719i	−0.970061	+	0.242860i	$0.921915\pi$
$282$	−4.82843	−	0.828427i	−0.287529	−	0.0493321i
$283$	−4.58579	−	4.58579i	−0.272597	−	0.272597i	0.557548	−	0.830145i	$-0.311742\pi$
$283$	−4.58579	−	4.58579i	−0.272597	−	0.272597i	−0.830145	+	0.557548i	$0.811742\pi$
$284$	−17.6569			−1.04774
$285$		0			0
$286$	2.00000			0.118262
$287$	2.82843	+	2.82843i	0.166957	+	0.166957i
$288$	5.70711	+	11.9497i	0.336294	+	0.704146i
$289$		−	9.00000i		−	0.529412i
$290$		0			0
$291$	−2.34315	−	3.31371i	−0.137358	−	0.194253i
$292$	−8.38478	+	8.38478i	−0.490682	+	0.490682i
$293$	−2.48528	+	2.48528i	−0.145192	+	0.145192i	−0.775966	−	0.630775i	$-0.782737\pi$
$293$	−2.48528	+	2.48528i	−0.145192	+	0.145192i	0.630775	+	0.775966i	$0.282737\pi$
$294$	2.61522	+	3.69848i	0.152523	+	0.215700i
$295$		0			0
$296$			12.6863i			0.737376i
$297$	−4.53553	−	2.53553i	−0.263178	−	0.147127i
$298$	−5.21320	−	5.21320i	−0.301993	−	0.301993i
$299$	5.65685			0.327144
$300$		0			0
$301$	5.37258			0.309671
$302$	4.24264	+	4.24264i	0.244137	+	0.244137i
$303$	−1.41421	−	0.242641i	−0.0812444	−	0.0139393i
$304$			2.48528i			0.142541i
$305$		0			0
$306$	−1.17157	+	3.31371i	−0.0669744	+	0.189432i
$307$	18.7279	−	18.7279i	1.06886	−	1.06886i	0.0714121	−	0.997447i	$-0.477249\pi$
$307$	18.7279	−	18.7279i	1.06886	−	1.06886i	0.997447	−	0.0714121i	$-0.0227505\pi$
$308$	−1.07107	+	1.07107i	−0.0610298	+	0.0610298i
$309$	−8.48528	+	6.00000i	−0.482711	+	0.341328i
$310$		0			0
$311$			10.3431i			0.586506i	0.956035	+	0.293253i	$0.0947378\pi$
$311$			10.3431i			0.586506i	−0.956035	+	0.293253i	$0.905262\pi$
$312$	−2.24264	+	13.0711i	−0.126965	+	0.740003i
$313$	−18.8284	−	18.8284i	−1.06425	−	1.06425i	−0.997789	−	0.0664563i	$-0.978831\pi$
$313$	−18.8284	−	18.8284i	−1.06425	−	1.06425i	−0.0664563	−	0.997789i	$-0.521169\pi$
$314$	8.97056			0.506238
$315$		0			0
$316$	8.82843			0.496638
$317$	−18.1421	−	18.1421i	−1.01896	−	1.01896i	−0.999817	−	0.0191472i	$-0.993905\pi$
$317$	−18.1421	−	18.1421i	−1.01896	−	1.01896i	−0.0191472	−	0.999817i	$-0.506095\pi$
$318$	1.45584	−	8.48528i	0.0816397	−	0.475831i
$319$			8.82843i			0.494297i
$320$		0			0
$321$	27.7990	−	19.6569i	1.55159	−	1.09714i
$322$	0.284271	−	0.284271i	0.0158418	−	0.0158418i
$323$	−1.65685	+	1.65685i	−0.0921898	+	0.0921898i
$324$	10.3431	−	12.7990i	0.574619	−	0.711055i
$325$		0			0
$326$			5.79899i			0.321176i
$327$	−3.41421	−	0.585786i	−0.188806	−	0.0323941i
$328$	−5.41421	−	5.41421i	−0.298950	−	0.298950i
$329$	5.65685			0.311872
$330$		0			0
$331$	1.65685			0.0910689			0.0455345	−	0.998963i	$-0.485501\pi$
$331$	1.65685			0.0910689			0.0455345	+	0.998963i	$0.485501\pi$
$332$	7.75736	+	7.75736i	0.425740	+	0.425740i
$333$	21.6569	−	10.3431i	1.18679	−	0.566801i
$334$			4.82843i			0.264200i
$335$		0			0
$336$	−2.48528	−	3.51472i	−0.135583	−	0.191744i
$337$	−15.8995	+	15.8995i	−0.866101	+	0.866101i	−0.992038	−	0.125938i	$-0.959806\pi$
$337$	−15.8995	+	15.8995i	−0.866101	+	0.866101i	0.125938	+	0.992038i	$0.459806\pi$
$338$	−3.02082	+	3.02082i	−0.164311	+	0.164311i
$339$	−12.0000	−	16.9706i	−0.651751	−	0.921714i
$340$		0			0
$341$			4.00000i			0.216612i
$342$	−0.928932	+	0.443651i	−0.0502309	+	0.0239899i
$343$	−7.79899	−	7.79899i	−0.421106	−	0.421106i
$344$	−10.2843			−0.554491
$345$		0			0
$346$	−2.82843			−0.152057
$347$	−7.75736	−	7.75736i	−0.416437	−	0.416437i	0.467537	−	0.883974i	$-0.345142\pi$
$347$	−7.75736	−	7.75736i	−0.416437	−	0.416437i	−0.883974	+	0.467537i	$0.845142\pi$
$348$	−27.5563	−	4.72792i	−1.47718	−	0.253443i
$349$		−	10.9706i		−	0.587241i	−0.955922	−	0.293620i	$-0.905140\pi$
$349$		−	10.9706i		−	0.587241i	0.955922	−	0.293620i	$-0.0948602\pi$
$350$		0			0
$351$	24.1421	−	6.82843i	1.28861	−	0.364474i
$352$	3.12132	−	3.12132i	0.166367	−	0.166367i
$353$	12.4853	−	12.4853i	0.664524	−	0.664524i	−0.291919	−	0.956443i	$-0.594294\pi$
$353$	12.4853	−	12.4853i	0.664524	−	0.664524i	0.956443	+	0.291919i	$0.0942937\pi$
$354$	1.37258	−	0.970563i	0.0729520	−	0.0515848i
$355$		0			0
$356$		−	28.0000i		−	1.48400i
$357$	0.686292	−	4.00000i	0.0363224	−	0.211702i
$358$	5.65685	+	5.65685i	0.298974	+	0.298974i
$359$	16.9706			0.895672			0.447836	−	0.894116i	$-0.352195\pi$
$359$	16.9706			0.895672			0.447836	+	0.894116i	$0.352195\pi$
$360$		0			0
$361$	18.3137			0.963879
$362$	−1.75736	−	1.75736i	−0.0923648	−	0.0923648i
$363$	−0.292893	+	1.70711i	−0.0153729	+	0.0895999i
$364$		−	7.31371i		−	0.383342i
$365$		0			0
$366$	−3.51472	+	2.48528i	−0.183717	+	0.129908i
$367$	−7.75736	+	7.75736i	−0.404931	+	0.404931i	−0.879967	−	0.475036i	$-0.842435\pi$
$367$	−7.75736	+	7.75736i	−0.404931	+	0.404931i	0.475036	+	0.879967i	$0.342435\pi$
$368$	2.48528	−	2.48528i	0.129554	−	0.129554i
$369$	−4.82843	+	13.6569i	−0.251358	+	0.710947i
$370$		0			0
$371$			9.94113i			0.516118i
$372$	−12.4853	−	2.14214i	−0.647332	−	0.111065i
$373$	15.8995	+	15.8995i	0.823245	+	0.823245i	0.986572	−	0.163327i	$-0.0522227\pi$
$373$	15.8995	+	15.8995i	0.823245	+	0.823245i	−0.163327	+	0.986572i	$0.552223\pi$
$374$	1.17157			0.0605806
$375$		0			0
$376$	−10.8284			−0.558433
$377$	−30.1421	−	30.1421i	−1.55240	−	1.55240i
$378$	0.870058	−	1.55635i	0.0447509	−	0.0800500i
$379$			18.6274i			0.956826i	0.878135	+	0.478413i	$0.158788\pi$
$379$			18.6274i			0.956826i	−0.878135	+	0.478413i	$0.841212\pi$
$380$		0			0
$381$	−14.4853	−	20.4853i	−0.742103	−	1.04949i
$382$	−3.31371	+	3.31371i	−0.169544	+	0.169544i
$383$	−9.31371	+	9.31371i	−0.475908	+	0.475908i	−0.903820	−	0.427912i	$-0.859249\pi$
$383$	−9.31371	+	9.31371i	−0.475908	+	0.475908i	0.427912	+	0.903820i	$0.359249\pi$
$384$	10.5563	+	14.9289i	0.538701	+	0.761839i
$385$		0			0
$386$		−	5.31371i		−	0.270461i
$387$	8.38478	+	17.5563i	0.426222	+	0.892439i
$388$	−3.02944	−	3.02944i	−0.153796	−	0.153796i
$389$	−12.0000			−0.608424			−0.304212	−	0.952604i	$-0.598393\pi$
$389$	−12.0000			−0.608424			−0.304212	+	0.952604i	$0.598393\pi$
$390$		0			0
$391$	3.31371			0.167581
$392$	7.07969	+	7.07969i	0.357578	+	0.357578i
$393$	−30.1421	−	5.17157i	−1.52047	−	0.260871i
$394$		−	8.48528i		−	0.427482i
$395$		0			0
$396$	−5.17157	−	1.82843i	−0.259881	−	0.0918819i
$397$	−22.8284	+	22.8284i	−1.14573	+	1.14573i	−0.158342	+	0.987384i	$0.550615\pi$
$397$	−22.8284	+	22.8284i	−1.14573	+	1.14573i	−0.987384	+	0.158342i	$0.949385\pi$
$398$	3.79899	−	3.79899i	0.190426	−	0.190426i
$399$	0.970563	−	0.686292i	0.0485889	−	0.0343575i
$400$		0			0
$401$			20.2843i			1.01295i	0.862255	+	0.506474i	$0.169051\pi$
$401$			20.2843i			1.01295i	−0.862255	+	0.506474i	$0.830949\pi$
$402$	0.443651	−	2.58579i	0.0221273	−	0.128967i
$403$	−13.6569	−	13.6569i	−0.680296	−	0.680296i
$404$	−1.51472			−0.0753601
$405$		0			0
$406$	−3.02944			−0.150348
$407$	−5.65685	−	5.65685i	−0.280400	−	0.280400i
$408$	−1.31371	+	7.65685i	−0.0650383	+	0.379071i
$409$		−	16.3431i		−	0.808117i	−0.914733	−	0.404058i	$-0.867599\pi$
$409$		−	16.3431i		−	0.808117i	0.914733	−	0.404058i	$-0.132401\pi$
$410$		0			0
$411$	3.31371	−	2.34315i	0.163453	−	0.115579i
$412$	−7.75736	+	7.75736i	−0.382178	+	0.382178i
$413$	−1.37258	+	1.37258i	−0.0675404	+	0.0675404i
$414$	1.37258	+	0.485281i	0.0674588	+	0.0238503i
$415$		0			0
$416$			21.3137i			1.04499i
$417$	−28.7279	−	4.92893i	−1.40681	−	0.241371i
$418$	0.242641	+	0.242641i	0.0118679	+	0.0118679i
$419$	−35.3137			−1.72519			−0.862594	−	0.505897i	$-0.831162\pi$
$419$	−35.3137			−1.72519			−0.862594	+	0.505897i	$0.831162\pi$
$420$		0			0
$421$	13.3137			0.648870			0.324435	−	0.945908i	$-0.394826\pi$
$421$	13.3137			0.648870			0.324435	+	0.945908i	$0.394826\pi$
$422$	−3.07107	−	3.07107i	−0.149497	−	0.149497i
$423$	8.82843	+	18.4853i	0.429253	+	0.898785i
$424$		−	19.0294i		−	0.924151i
$425$		0			0
$426$	−4.00000	−	5.65685i	−0.193801	−	0.274075i
$427$	3.51472	−	3.51472i	0.170089	−	0.170089i
$428$	25.4142	−	25.4142i	1.22844	−	1.22844i
$429$	−4.82843	−	6.82843i	−0.233119	−	0.329680i
$430$		0			0
$431$		−	5.65685i		−	0.272481i	−0.990676	−	0.136241i	$-0.956498\pi$
$431$		−	5.65685i		−	0.272481i	0.990676	−	0.136241i	$-0.0435020\pi$
$432$	7.60660	−	13.6066i	0.365973	−	0.654648i
$433$	7.31371	+	7.31371i	0.351474	+	0.351474i	0.860658	−	0.509184i	$-0.170053\pi$
$433$	7.31371	+	7.31371i	0.351474	+	0.351474i	−0.509184	+	0.860658i	$0.670053\pi$
$434$	−1.37258			−0.0658861
$435$		0			0
$436$	−3.65685			−0.175132
$437$	0.686292	+	0.686292i	0.0328298	+	0.0328298i
$438$	−4.58579	−	0.786797i	−0.219117	−	0.0375946i
$439$		−	24.1421i		−	1.15224i	−0.817365	−	0.576121i	$-0.804566\pi$
$439$		−	24.1421i		−	1.15224i	0.817365	−	0.576121i	$-0.195434\pi$
$440$		0			0
$441$	6.31371	−	17.8579i	0.300653	−	0.850374i
$442$	−4.00000	+	4.00000i	−0.190261	+	0.190261i
$443$	13.3137	−	13.3137i	0.632553	−	0.632553i	−0.316154	−	0.948708i	$-0.602392\pi$
$443$	13.3137	−	13.3137i	0.632553	−	0.632553i	0.948708	+	0.316154i	$0.102392\pi$
$444$	20.6863	−	14.6274i	0.981728	−	0.694186i
$445$		0			0
$446$			9.51472i			0.450535i
$447$	−5.21320	+	30.3848i	−0.246576	+	1.43715i
$448$	−2.44365	−	2.44365i	−0.115452	−	0.115452i
$449$	14.3431			0.676895			0.338447	−	0.940985i	$-0.390098\pi$
$449$	14.3431			0.676895			0.338447	+	0.940985i	$0.390098\pi$
$450$		0			0
$451$	4.82843			0.227362
$452$	−15.5147	−	15.5147i	−0.729751	−	0.729751i
$453$	4.24264	−	24.7279i	0.199337	−	1.16182i
$454$			11.8579i			0.556517i
$455$		0			0
$456$	−1.85786	+	1.31371i	−0.0870025	+	0.0615200i
$457$	−19.4142	+	19.4142i	−0.908159	+	0.908159i	−0.996124	−	0.0879650i	$-0.971964\pi$
$457$	−19.4142	+	19.4142i	−0.908159	+	0.908159i	0.0879650	+	0.996124i	$0.471964\pi$
$458$	−5.27208	+	5.27208i	−0.246348	+	0.246348i
$459$	14.1421	−	4.00000i	0.660098	−	0.186704i
$460$		0			0
$461$			23.1716i			1.07921i	0.841919	+	0.539604i	$0.181426\pi$
$461$			23.1716i			1.07921i	−0.841919	+	0.539604i	$0.818574\pi$
$462$	−0.585786	−	0.100505i	−0.0272533	−	0.00467592i
$463$	22.3848	+	22.3848i	1.04031	+	1.04031i	0.999153	+	0.0411560i	$0.0131041\pi$
$463$	22.3848	+	22.3848i	1.04031	+	1.04031i	0.0411560	+	0.999153i	$0.486896\pi$
$464$	−26.4853			−1.22955
$465$		0			0
$466$	−5.85786			−0.271360
$467$	−12.8284	−	12.8284i	−0.593629	−	0.593629i	0.344981	−	0.938610i	$-0.387885\pi$
$467$	−12.8284	−	12.8284i	−0.593629	−	0.593629i	−0.938610	+	0.344981i	$0.887885\pi$
$468$	23.8995	−	11.4142i	1.10475	−	0.527622i
$469$			3.02944i			0.139886i
$470$		0			0
$471$	−21.6569	−	30.6274i	−0.997895	−	1.41124i
$472$	2.62742	−	2.62742i	0.120937	−	0.120937i
$473$	4.58579	−	4.58579i	0.210855	−	0.210855i
$474$	2.00000	+	2.82843i	0.0918630	+	0.129914i
$475$		0			0
$476$		−	4.28427i		−	0.196369i
$477$	−32.4853	+	15.5147i	−1.48740	+	0.710370i
$478$	−0.686292	−	0.686292i	−0.0313902	−	0.0313902i
$479$	26.3431			1.20365			0.601825	−	0.798628i	$-0.294441\pi$
$479$	26.3431			1.20365			0.601825	+	0.798628i	$0.294441\pi$
$480$		0			0
$481$	38.6274			1.76126
$482$	−7.89949	−	7.89949i	−0.359812	−	0.359812i
$483$	−1.65685	−	0.284271i	−0.0753895	−	0.0129348i
$484$			1.82843i			0.0831103i
$485$		0			0
$486$	6.44365	+	0.414214i	0.292290	+	0.0187891i
$487$	10.5858	−	10.5858i	0.479688	−	0.479688i	−0.425344	−	0.905032i	$-0.639847\pi$
$487$	10.5858	−	10.5858i	0.479688	−	0.479688i	0.905032	+	0.425344i	$0.139847\pi$
$488$	−6.72792	+	6.72792i	−0.304559	+	0.304559i
$489$	19.7990	−	14.0000i	0.895341	−	0.633102i
$490$		0			0
$491$		−	18.6274i		−	0.840644i	−0.907375	−	0.420322i	$-0.861917\pi$
$491$		−	18.6274i		−	0.840644i	0.907375	−	0.420322i	$-0.138083\pi$
$492$	−2.58579	+	15.0711i	−0.116576	+	0.679456i
$493$	−17.6569	−	17.6569i	−0.795225	−	0.795225i
$494$	−1.65685			−0.0745454
$495$		0			0
$496$	−12.0000			−0.538816
$497$	5.65685	+	5.65685i	0.253745	+	0.253745i
$498$	−0.727922	+	4.24264i	−0.0326190	+	0.190117i
$499$		−	2.34315i		−	0.104894i	−0.998624	−	0.0524468i	$-0.983298\pi$
$499$		−	2.34315i		−	0.104894i	0.998624	−	0.0524468i	$-0.0167020\pi$
$500$		0			0
$501$	16.4853	−	11.6569i	0.736508	−	0.520790i
$502$	0.485281	−	0.485281i	0.0216592	−	0.0216592i
$503$	−26.3848	+	26.3848i	−1.17644	+	1.17644i	−0.195794	+	0.980645i	$0.562728\pi$
$503$	−26.3848	+	26.3848i	−1.17644	+	1.17644i	−0.980645	+	0.195794i	$0.937272\pi$
$504$	1.31371	−	3.71573i	0.0585172	−	0.165512i
$505$		0			0
$506$		−	0.485281i		−	0.0215734i
$507$	17.6066	+	3.02082i	0.781937	+	0.134159i
$508$	−18.7279	−	18.7279i	−0.830917	−	0.830917i
$509$	−35.3137			−1.56525			−0.782626	−	0.622492i	$-0.786120\pi$
$509$	−35.3137			−1.56525			−0.782626	+	0.622492i	$0.786120\pi$
$510$		0			0
$511$	5.37258			0.237669
$512$	16.0919	+	16.0919i	0.711167	+	0.711167i
$513$	3.75736	+	2.10051i	0.165891	+	0.0927396i
$514$			9.37258i			0.413407i
$515$		0			0
$516$	11.8579	+	16.7696i	0.522013	+	0.738238i
$517$	4.82843	−	4.82843i	0.212354	−	0.212354i
$518$	1.94113	−	1.94113i	0.0852882	−	0.0852882i
$519$	6.82843	+	9.65685i	0.299735	+	0.423889i
$520$		0			0
$521$			40.9706i			1.79495i	0.441062	+	0.897476i	$0.354602\pi$
$521$			40.9706i			1.79495i	−0.441062	+	0.897476i	$0.645398\pi$
$522$	−4.72792	−	9.89949i	−0.206936	−	0.433289i
$523$	2.92893	+	2.92893i	0.128073	+	0.128073i	0.768238	−	0.640165i	$-0.221134\pi$
$523$	2.92893	+	2.92893i	0.128073	+	0.128073i	−0.640165	+	0.768238i	$0.721134\pi$
$524$	−32.2843			−1.41034
$525$		0			0
$526$	9.51472			0.414861
$527$	−8.00000	−	8.00000i	−0.348485	−	0.348485i
$528$	−5.12132	−	0.878680i	−0.222877	−	0.0382396i
$529$			21.6274i			0.940322i
$530$		0			0
$531$	−6.62742	−	2.34315i	−0.287605	−	0.101684i
$532$	0.887302	−	0.887302i	0.0384694	−	0.0384694i
$533$	−16.4853	+	16.4853i	−0.714057	+	0.714057i
$534$	8.97056	−	6.34315i	0.388194	−	0.274495i
$535$		0			0
$536$		−	5.79899i		−	0.250478i
$537$	5.65685	−	32.9706i	0.244111	−	1.42278i
$538$	4.00000	+	4.00000i	0.172452	+	0.172452i
$539$	−6.31371			−0.271951
$540$		0			0
$541$	−34.9706			−1.50350			−0.751751	−	0.659447i	$-0.770790\pi$
$541$	−34.9706			−1.50350			−0.751751	+	0.659447i	$0.770790\pi$
$542$	−2.78680	−	2.78680i	−0.119703	−	0.119703i
$543$	−1.75736	+	10.2426i	−0.0754155	+	0.439554i
$544$			12.4853i			0.535302i
$545$		0			0
$546$	2.34315	−	1.65685i	0.100277	−	0.0709068i
$547$	−6.72792	+	6.72792i	−0.287665	+	0.287665i	−0.836156	−	0.548491i	$-0.815202\pi$
$547$	−6.72792	+	6.72792i	−0.287665	+	0.287665i	0.548491	+	0.836156i	$0.315202\pi$
$548$	3.02944	−	3.02944i	0.129411	−	0.129411i
$549$	16.9706	+	6.00000i	0.724286	+	0.256074i
$550$		0			0
$551$		−	7.31371i		−	0.311574i
$552$	3.17157	+	0.544156i	0.134991	+	0.0231608i
$553$	−2.82843	−	2.82843i	−0.120277	−	0.120277i
$554$	−10.0000			−0.424859
$555$		0			0
$556$	−30.7696			−1.30492
$557$	19.4558	+	19.4558i	0.824371	+	0.824371i	0.986731	−	0.162361i	$-0.0519109\pi$
$557$	19.4558	+	19.4558i	0.824371	+	0.824371i	−0.162361	+	0.986731i	$0.551911\pi$
$558$	−2.14214	−	4.48528i	−0.0906838	−	0.189877i
$559$			31.3137i			1.32443i
$560$		0			0
$561$	−2.82843	−	4.00000i	−0.119416	−	0.168880i
$562$	−2.38478	+	2.38478i	−0.100596	+	0.100596i
$563$	−0.242641	+	0.242641i	−0.0102261	+	0.0102261i	−0.712201	−	0.701975i	$-0.752302\pi$
$563$	−0.242641	+	0.242641i	−0.0102261	+	0.0102261i	0.701975	+	0.712201i	$0.252302\pi$
$564$	12.4853	+	17.6569i	0.525725	+	0.743488i
$565$		0			0
$566$		−	2.68629i		−	0.112913i
$567$	−7.41421	+	0.786797i	−0.311368	+	0.0330423i
$568$	−10.8284	−	10.8284i	−0.454351	−	0.454351i
$569$	12.8284			0.537796			0.268898	−	0.963169i	$-0.413341\pi$
$569$	12.8284			0.537796			0.268898	+	0.963169i	$0.413341\pi$
$570$		0			0
$571$	−21.5147			−0.900363			−0.450181	−	0.892937i	$-0.648641\pi$
$571$	−21.5147			−0.900363			−0.450181	+	0.892937i	$0.648641\pi$
$572$	−6.24264	−	6.24264i	−0.261018	−	0.261018i
$573$	19.3137	+	3.31371i	0.806842	+	0.138432i
$574$			1.65685i			0.0691558i
$575$		0			0
$576$	4.17157	−	11.7990i	0.173816	−	0.491625i
$577$	−3.51472	+	3.51472i	−0.146320	+	0.146320i	−0.776472	−	0.630152i	$-0.782993\pi$
$577$	−3.51472	+	3.51472i	−0.146320	+	0.146320i	0.630152	+	0.776472i	$0.282993\pi$
$578$	2.63604	−	2.63604i	0.109645	−	0.109645i
$579$	−18.1421	+	12.8284i	−0.753961	+	0.533131i
$580$		0			0
$581$		−	4.97056i		−	0.206214i
$582$	0.284271	−	1.65685i	0.0117834	−	0.0686788i
$583$	8.48528	+	8.48528i	0.351424	+	0.351424i
$584$	−10.2843			−0.425566
$585$		0			0
$586$	−1.45584			−0.0601404
$587$	22.4853	+	22.4853i	0.928067	+	0.928067i	0.997581	−	0.0695141i	$-0.0221449\pi$
$587$	22.4853	+	22.4853i	0.928067	+	0.928067i	−0.0695141	+	0.997581i	$0.522145\pi$
$588$	3.38120	−	19.7071i	0.139439	−	0.812707i
$589$		−	3.31371i		−	0.136539i
$590$		0			0
$591$	−28.9706	+	20.4853i	−1.19169	+	0.842652i
$592$	16.9706	−	16.9706i	0.697486	−	0.697486i
$593$	19.6569	−	19.6569i	0.807210	−	0.807210i	−0.177001	−	0.984211i	$-0.556639\pi$
$593$	19.6569	−	19.6569i	0.807210	−	0.807210i	0.984211	+	0.177001i	$0.0566394\pi$
$594$	−0.585786	−	2.07107i	−0.0240351	−	0.0849769i
$595$		0			0
$596$			32.5442i			1.33306i
$597$	−22.1421	−	3.79899i	−0.906217	−	0.155482i
$598$	1.65685	+	1.65685i	0.0677538	+	0.0677538i
$599$	−23.3137			−0.952572			−0.476286	−	0.879290i	$-0.658017\pi$
$599$	−23.3137			−0.952572			−0.476286	+	0.879290i	$0.658017\pi$
$600$		0			0
$601$	22.9706			0.936989			0.468494	−	0.883466i	$-0.344797\pi$
$601$	22.9706			0.936989			0.468494	+	0.883466i	$0.344797\pi$
$602$	1.57359	+	1.57359i	0.0641349	+	0.0641349i
$603$	−9.89949	+	4.72792i	−0.403139	+	0.192536i
$604$		−	26.4853i		−	1.07767i
$605$		0			0
$606$	−0.343146	−	0.485281i	−0.0139393	−	0.0197132i
$607$	8.10051	−	8.10051i	0.328789	−	0.328789i	−0.523337	−	0.852126i	$-0.675313\pi$
$607$	8.10051	−	8.10051i	0.328789	−	0.328789i	0.852126	+	0.523337i	$0.175313\pi$
$608$	−2.58579	+	2.58579i	−0.104867	+	0.104867i
$609$	7.31371	+	10.3431i	0.296366	+	0.419125i
$610$		0			0
$611$			32.9706i			1.33385i
$612$	14.0000	−	6.68629i	0.565916	−	0.270277i
$613$	−18.0416	−	18.0416i	−0.728695	−	0.728695i	0.241665	−	0.970360i	$-0.422306\pi$
$613$	−18.0416	−	18.0416i	−0.728695	−	0.728695i	−0.970360	+	0.241665i	$0.922306\pi$
$614$	10.9706			0.442736
$615$		0			0
$616$	−1.31371			−0.0529308
$617$	7.51472	+	7.51472i	0.302531	+	0.302531i	0.842003	−	0.539472i	$-0.181376\pi$
$617$	7.51472	+	7.51472i	0.302531	+	0.302531i	−0.539472	+	0.842003i	$0.681376\pi$
$618$	−4.24264	−	0.727922i	−0.170664	−	0.0292813i
$619$			4.97056i			0.199784i	0.994998	+	0.0998919i	$0.0318497\pi$
$619$			4.97056i			0.199784i	−0.994998	+	0.0998919i	$0.968150\pi$
$620$		0			0
$621$	−1.65685	−	5.85786i	−0.0664873	−	0.235068i
$622$	−3.02944	+	3.02944i	−0.121469	+	0.121469i
$623$	−8.97056	+	8.97056i	−0.359398	+	0.359398i
$624$	20.4853	−	14.4853i	0.820068	−	0.579875i
$625$		0			0
$626$		−	11.0294i		−	0.440825i
$627$	0.242641	−	1.41421i	0.00969014	−	0.0564782i
$628$	−28.0000	−	28.0000i	−1.11732	−	1.11732i
$629$	22.6274			0.902214
$630$		0			0
$631$	1.65685			0.0659583			0.0329792	−	0.999456i	$-0.489501\pi$
$631$	1.65685			0.0659583			0.0329792	+	0.999456i	$0.489501\pi$
$632$	5.41421	+	5.41421i	0.215366	+	0.215366i
$633$	−3.07107	+	17.8995i	−0.122064	+	0.711441i
$634$		−	10.6274i		−	0.422069i
$635$		0			0
$636$	−31.0294	+	21.9411i	−1.23040	+	0.870022i
$637$	21.5563	−	21.5563i	0.854094	−	0.854094i
$638$	−2.58579	+	2.58579i	−0.102372	+	0.102372i
$639$	−9.65685	+	27.3137i	−0.382019	+	1.08051i
$640$		0			0
$641$		−	6.34315i		−	0.250539i	−0.992123	−	0.125270i	$-0.960020\pi$
$641$		−	6.34315i		−	0.250539i	0.992123	−	0.125270i	$-0.0399796\pi$
$642$	13.8995	+	2.38478i	0.548569	+	0.0941196i
$643$	−1.41421	−	1.41421i	−0.0557711	−	0.0557711i	0.678671	−	0.734442i	$-0.262556\pi$
$643$	−1.41421	−	1.41421i	−0.0557711	−	0.0557711i	−0.734442	+	0.678671i	$0.762556\pi$
$644$	−1.77460			−0.0699292
$645$		0			0
$646$	−0.970563			−0.0381863
$647$	−6.00000	−	6.00000i	−0.235884	−	0.235884i	0.579259	−	0.815143i	$-0.303342\pi$
$647$	−6.00000	−	6.00000i	−0.235884	−	0.235884i	−0.815143	+	0.579259i	$0.803342\pi$
$648$	14.1924	−	1.50610i	0.557530	−	0.0591651i
$649$			2.34315i			0.0919765i
$650$		0			0
$651$	3.31371	+	4.68629i	0.129874	+	0.183670i
$652$	18.1005	−	18.1005i	0.708870	−	0.708870i
$653$	−4.00000	+	4.00000i	−0.156532	+	0.156532i	−0.781028	−	0.624496i	$-0.785304\pi$
$653$	−4.00000	+	4.00000i	−0.156532	+	0.156532i	0.624496	+	0.781028i	$0.285304\pi$
$654$	−0.828427	−	1.17157i	−0.0323941	−	0.0458121i
$655$		0			0
$656$			14.4853i			0.565555i
$657$	8.38478	+	17.5563i	0.327121	+	0.684938i
$658$	1.65685	+	1.65685i	0.0645909	+	0.0645909i
$659$	30.3431			1.18200			0.591001	−	0.806671i	$-0.298733\pi$
$659$	30.3431			1.18200			0.591001	+	0.806671i	$0.298733\pi$
$660$		0			0
$661$	−44.6274			−1.73581			−0.867903	−	0.496734i	$-0.834532\pi$
$661$	−44.6274			−1.73581			−0.867903	+	0.496734i	$0.834532\pi$
$662$	0.485281	+	0.485281i	0.0188610	+	0.0188610i
$663$	23.3137	+	4.00000i	0.905429	+	0.155347i
$664$			9.51472i			0.369243i
$665$		0			0
$666$	9.37258	+	3.31371i	0.363180	+	0.128404i
$667$	−7.31371	+	7.31371i	−0.283188	+	0.283188i
$668$	15.0711	−	15.0711i	0.583117	−	0.583117i
$669$	32.4853	−	22.9706i	1.25595	−	0.888093i
$670$		0			0
$671$		−	6.00000i		−	0.231627i
$672$	1.07107	−	6.24264i	0.0413173	−	0.240815i
$673$	30.7279	+	30.7279i	1.18447	+	1.18447i	0.978573	+	0.205902i	$0.0660127\pi$
$673$	30.7279	+	30.7279i	1.18447	+	1.18447i	0.205902	+	0.978573i	$0.433987\pi$
$674$	−9.31371			−0.358751
$675$		0			0
$676$	18.8579			0.725302
$677$	−14.4853	−	14.4853i	−0.556715	−	0.556715i	0.371656	−	0.928371i	$-0.378790\pi$
$677$	−14.4853	−	14.4853i	−0.556715	−	0.556715i	−0.928371	+	0.371656i	$0.878790\pi$
$678$	1.45584	−	8.48528i	0.0559114	−	0.325875i
$679$			1.94113i			0.0744936i
$680$		0			0
$681$	40.4853	−	28.6274i	1.55140	−	1.09701i
$682$	−1.17157	+	1.17157i	−0.0448618	+	0.0448618i
$683$	10.4853	−	10.4853i	0.401208	−	0.401208i	−0.477451	−	0.878659i	$-0.658439\pi$
$683$	10.4853	−	10.4853i	0.401208	−	0.401208i	0.878659	+	0.477451i	$0.158439\pi$
$684$	4.28427	+	1.51472i	0.163813	+	0.0579167i
$685$		0			0
$686$		−	4.56854i		−	0.174428i
$687$	30.7279	+	5.27208i	1.17234	+	0.201142i
$688$	13.7574	+	13.7574i	0.524494	+	0.524494i
$689$	−57.9411			−2.20738
$690$		0			0
$691$	29.9411			1.13901			0.569507	−	0.821986i	$-0.307134\pi$
$691$	29.9411			1.13901			0.569507	+	0.821986i	$0.307134\pi$
$692$	8.82843	+	8.82843i	0.335606	+	0.335606i
$693$	1.07107	+	2.24264i	0.0406865	+	0.0851909i
$694$		−	4.54416i		−	0.172494i
$695$		0			0
$696$	−14.0000	−	19.7990i	−0.530669	−	0.750479i
$697$	−9.65685	+	9.65685i	−0.365779	+	0.365779i
$698$	3.21320	−	3.21320i	0.121622	−	0.121622i
$699$	14.1421	+	20.0000i	0.534905	+	0.756469i
$700$		0			0
$701$			33.5147i			1.26583i	0.774220	+	0.632917i	$0.218142\pi$
$701$			33.5147i			1.26583i	−0.774220	+	0.632917i	$0.781858\pi$
$702$	9.07107	+	5.07107i	0.342365	+	0.191395i
$703$	4.68629	+	4.68629i	0.176747	+	0.176747i
$704$	−4.17157			−0.157222
$705$		0			0
$706$	7.31371			0.275255
$707$	0.485281	+	0.485281i	0.0182509	+	0.0182509i
$708$	−7.31371	−	1.25483i	−0.274866	−	0.0471595i
$709$		−	10.0000i		−	0.375558i	−0.982211	−	0.187779i	$-0.939871\pi$
$709$		−	10.0000i		−	0.375558i	0.982211	−	0.187779i	$-0.0601289\pi$
$710$		0			0
$711$	4.82843	−	13.6569i	0.181080	−	0.512172i
$712$	17.1716	−	17.1716i	0.643532	−	0.643532i
$713$	−3.31371	+	3.31371i	−0.124099	+	0.124099i
$714$	1.37258	−	0.970563i	0.0513676	−	0.0363224i
$715$		0			0
$716$		−	35.3137i		−	1.31974i
$717$	−0.686292	+	4.00000i	−0.0256300	+	0.149383i
$718$	4.97056	+	4.97056i	0.185500	+	0.185500i
$719$	4.68629			0.174769			0.0873846	−	0.996175i	$-0.472149\pi$
$719$	4.68629			0.174769			0.0873846	+	0.996175i	$0.472149\pi$
$720$		0			0
$721$	4.97056			0.185113
$722$	5.36396	+	5.36396i	0.199626	+	0.199626i
$723$	−7.89949	+	46.0416i	−0.293785	+	1.71231i
$724$			10.9706i			0.407718i
$725$		0			0
$726$	−0.585786	+	0.414214i	−0.0217406	+	0.0153729i
$727$	9.89949	−	9.89949i	0.367152	−	0.367152i	−0.499286	−	0.866437i	$-0.666404\pi$
$727$	9.89949	−	9.89949i	0.367152	−	0.367152i	0.866437	+	0.499286i	$0.166404\pi$
$728$	4.48528	−	4.48528i	0.166236	−	0.166236i
$729$	−14.1421	−	23.0000i	−0.523783	−	0.851852i
$730$		0			0
$731$			18.3431i			0.678446i
$732$	18.7279	+	3.21320i	0.692204	+	0.118763i
$733$	7.89949	+	7.89949i	0.291775	+	0.291775i	0.837781	−	0.546006i	$-0.183853\pi$
$733$	7.89949	+	7.89949i	0.291775	+	0.291775i	−0.546006	+	0.837781i	$0.683853\pi$
$734$	−4.54416			−0.167728
$735$		0			0
$736$	5.17157			0.190627
$737$	2.58579	+	2.58579i	0.0952487	+	0.0952487i
$738$	−5.41421	+	2.58579i	−0.199300	+	0.0951841i
$739$			5.51472i			0.202862i	0.994843	+	0.101431i	$0.0323421\pi$
$739$			5.51472i			0.202862i	−0.994843	+	0.101431i	$0.967658\pi$
$740$		0			0
$741$	4.00000	+	5.65685i	0.146944	+	0.207810i
$742$	−2.91169	+	2.91169i	−0.106891	+	0.106891i
$743$	−16.7279	+	16.7279i	−0.613688	+	0.613688i	−0.943905	−	0.330217i	$-0.892878\pi$
$743$	−16.7279	+	16.7279i	−0.613688	+	0.613688i	0.330217	+	0.943905i	$0.392878\pi$
$744$	−6.34315	−	8.97056i	−0.232551	−	0.328877i
$745$		0			0
$746$			9.31371i			0.340999i
$747$	16.2426	−	7.75736i	0.594287	−	0.283827i
$748$	−3.65685	−	3.65685i	−0.133708	−	0.133708i
$749$	−16.2843			−0.595014
$750$		0			0
$751$	−32.2843			−1.17807			−0.589035	−	0.808108i	$-0.700492\pi$
$751$	−32.2843			−1.17807			−0.589035	+	0.808108i	$0.700492\pi$
$752$	14.4853	+	14.4853i	0.528224	+	0.528224i
$753$	−2.82843	−	0.485281i	−0.103074	−	0.0176846i
$754$		−	17.6569i		−	0.643025i
$755$		0			0
$756$	−7.57359	+	2.14214i	−0.275449	+	0.0779087i
$757$	−0.686292	+	0.686292i	−0.0249437	+	0.0249437i	−0.719469	−	0.694525i	$-0.755615\pi$
$757$	−0.686292	+	0.686292i	−0.0249437	+	0.0249437i	0.694525	+	0.719469i	$0.255615\pi$
$758$	−5.45584	+	5.45584i	−0.198165	+	0.198165i
$759$	−1.65685	+	1.17157i	−0.0601400	+	0.0425254i
$760$		0			0
$761$		−	13.7990i		−	0.500213i	−0.968218	−	0.250106i	$-0.919534\pi$
$761$		−	13.7990i		−	0.500213i	0.968218	−	0.250106i	$-0.0804656\pi$
$762$	1.75736	−	10.2426i	0.0636624	−	0.371052i
$763$	1.17157	+	1.17157i	0.0424138	+	0.0424138i
$764$	20.6863			0.748404
$765$		0			0
$766$	−5.45584			−0.197128
$767$	−8.00000	−	8.00000i	−0.288863	−	0.288863i
$768$	1.16295	−	6.77817i	0.0419644	−	0.244586i
$769$		−	1.31371i		−	0.0473735i	−0.999719	−	0.0236868i	$-0.992460\pi$
$769$		−	1.31371i		−	0.0473735i	0.999719	−	0.0236868i	$-0.00754044\pi$
$770$		0			0
$771$	32.0000	−	22.6274i	1.15245	−	0.814907i
$772$	−16.5858	+	16.5858i	−0.596936	+	0.596936i
$773$	−4.97056	+	4.97056i	−0.178779	+	0.178779i	−0.790823	−	0.612045i	$-0.790347\pi$
$773$	−4.97056	+	4.97056i	−0.178779	+	0.178779i	0.612045	+	0.790823i	$0.290347\pi$
$774$	−2.68629	+	7.59798i	−0.0965568	+	0.273104i
$775$		0			0
$776$		−	3.71573i		−	0.133387i
$777$	−11.3137	−	1.94113i	−0.405877	−	0.0696375i
$778$	−3.51472	−	3.51472i	−0.126009	−	0.126009i
$779$	−4.00000			−0.143315
$780$		0			0
$781$	9.65685			0.345549
$782$	0.970563	+	0.970563i	0.0347073	+	0.0347073i
$783$	−22.3848	+	40.0416i	−0.799967	+	1.43097i
$784$		−	18.9411i		−	0.676469i
$785$		0			0
$786$	−7.31371	−	10.3431i	−0.260871	−	0.368928i
$787$	39.2132	−	39.2132i	1.39780	−	1.39780i	0.591480	−	0.806319i	$-0.298544\pi$
$787$	39.2132	−	39.2132i	1.39780	−	1.39780i	0.806319	−	0.591480i	$-0.201456\pi$
$788$	−26.4853	+	26.4853i	−0.943499	+	0.943499i
$789$	−22.9706	−	32.4853i	−0.817774	−	1.15651i
$790$		0			0
$791$			9.94113i			0.353466i
$792$	−2.05025	−	4.29289i	−0.0728526	−	0.152541i
$793$	20.4853	+	20.4853i	0.727454	+	0.727454i
$794$	−13.3726			−0.474575
$795$		0			0
$796$	−23.7157			−0.840582
$797$	−6.82843	−	6.82843i	−0.241875	−	0.241875i	0.575750	−	0.817626i	$-0.304710\pi$
$797$	−6.82843	−	6.82843i	−0.241875	−	0.241875i	−0.817626	+	0.575750i	$0.804710\pi$
$798$	0.485281	+	0.0832611i	0.0171788	+	0.00294741i
$799$			19.3137i			0.683270i
$800$		0			0
$801$	−43.3137	−	15.3137i	−1.53041	−	0.541083i
$802$	−5.94113	+	5.94113i	−0.209788	+	0.209788i
$803$	4.58579	−	4.58579i	0.161829	−	0.161829i
$804$	−9.45584	+	6.68629i	−0.333482	+	0.235807i
$805$		0			0
$806$		−	8.00000i		−	0.281788i
$807$	4.00000	−	23.3137i	0.140807	−	0.820681i
$808$	−0.928932	−	0.928932i	−0.0326797	−	0.0326797i
$809$	2.20101			0.0773834			0.0386917	−	0.999251i	$-0.487681\pi$
$809$	2.20101			0.0773834			0.0386917	+	0.999251i	$0.487681\pi$
$810$		0			0
$811$	31.1716			1.09458			0.547291	−	0.836942i	$-0.315659\pi$
$811$	31.1716			1.09458			0.547291	+	0.836942i	$0.315659\pi$
$812$	9.45584	+	9.45584i	0.331835	+	0.331835i
$813$	−2.78680	+	16.2426i	−0.0977372	+	0.569654i
$814$		−	3.31371i		−	0.116145i
$815$		0			0
$816$	12.0000	−	8.48528i	0.420084	−	0.297044i
$817$	−3.79899	+	3.79899i	−0.132910	+	0.132910i
$818$	4.78680	−	4.78680i	0.167366	−	0.167366i
$819$	−11.3137	−	4.00000i	−0.395333	−	0.139771i
$820$		0			0
$821$		−	3.17157i		−	0.110689i	−0.998467	−	0.0553443i	$-0.982374\pi$
$821$		−	3.17157i		−	0.110689i	0.998467	−	0.0553443i	$-0.0176257\pi$
$822$	1.65685	+	0.284271i	0.0577894	+	0.00991510i
$823$	39.5563	+	39.5563i	1.37885	+	1.37885i	0.846570	+	0.532278i	$0.178664\pi$
$823$	39.5563	+	39.5563i	1.37885	+	1.37885i	0.532278	+	0.846570i	$0.321336\pi$
$824$	−9.51472			−0.331461
$825$		0			0
$826$	−0.804041			−0.0279761
$827$	23.7574	+	23.7574i	0.826124	+	0.826124i	0.986978	−	0.160854i	$-0.0514248\pi$
$827$	23.7574	+	23.7574i	0.826124	+	0.826124i	−0.160854	+	0.986978i	$0.551425\pi$
$828$	−2.76955	−	5.79899i	−0.0962486	−	0.201529i
$829$		−	45.3137i		−	1.57381i	−0.617074	−	0.786905i	$-0.711682\pi$
$829$		−	45.3137i		−	1.57381i	0.617074	−	0.786905i	$-0.288318\pi$
$830$		0			0
$831$	24.1421	+	34.1421i	0.837481	+	1.18438i
$832$	14.2426	−	14.2426i	0.493775	−	0.493775i
$833$	12.6274	−	12.6274i	0.437514	−	0.437514i
$834$	−6.97056	−	9.85786i	−0.241371	−	0.341350i
$835$		0			0
$836$		−	1.51472i		−	0.0523876i
$837$	−10.1421	+	18.1421i	−0.350563	+	0.627084i
$838$	−10.3431	−	10.3431i	−0.357298	−	0.357298i
$839$	39.5980			1.36707			0.683537	−	0.729916i	$-0.260441\pi$
$839$	39.5980			1.36707			0.683537	+	0.729916i	$0.260441\pi$
$840$		0			0
$841$	48.9411			1.68763
$842$	3.89949	+	3.89949i	0.134385	+	0.134385i
$843$	13.8995	+	2.38478i	0.478724	+	0.0821361i
$844$			19.1716i			0.659913i
$845$		0			0
$846$	−2.82843	+	8.00000i	−0.0972433	+	0.275046i
$847$	0.585786	−	0.585786i	0.0201279	−	0.0201279i
$848$	−25.4558	+	25.4558i	−0.874157	+	0.874157i
$849$	−9.17157	+	6.48528i	−0.314768	+	0.222574i
$850$		0			0
$851$		−	9.37258i		−	0.321288i
$852$	−5.17157	+	30.1421i	−0.177175	+	1.03265i
$853$	−4.58579	−	4.58579i	−0.157014	−	0.157014i	0.624228	−	0.781242i	$-0.285414\pi$
$853$	−4.58579	−	4.58579i	−0.157014	−	0.157014i	−0.781242	+	0.624228i	$0.785414\pi$
$854$	2.05887			0.0704532
$855$		0			0
$856$	31.1716			1.06542
$857$	−19.6569	−	19.6569i	−0.671465	−	0.671465i	0.286588	−	0.958054i	$-0.407479\pi$
$857$	−19.6569	−	19.6569i	−0.671465	−	0.671465i	−0.958054	+	0.286588i	$0.907479\pi$
$858$	0.585786	−	3.41421i	0.0199984	−	0.116559i
$859$		−	28.9706i		−	0.988463i	−0.869330	−	0.494231i	$-0.835450\pi$
$859$		−	28.9706i		−	0.988463i	0.869330	−	0.494231i	$-0.164550\pi$
$860$		0			0
$861$	5.65685	−	4.00000i	0.192785	−	0.136320i
$862$	1.65685	−	1.65685i	0.0564327	−	0.0564327i
$863$	−30.9706	+	30.9706i	−1.05425	+	1.05425i	−0.0558087	+	0.998441i	$0.517774\pi$
$863$	−30.9706	+	30.9706i	−1.05425	+	1.05425i	−0.998441	+	0.0558087i	$0.982226\pi$
$864$	22.0711	−	6.24264i	0.750873	−	0.212379i
$865$		0			0
$866$			4.28427i			0.145585i
$867$	−15.3640	−	2.63604i	−0.521787	−	0.0895246i
$868$	4.28427	+	4.28427i	0.145418	+	0.145418i
$869$	−4.82843			−0.163793
$870$		0			0
$871$	−17.6569			−0.598280
$872$	−2.24264	−	2.24264i	−0.0759454	−	0.0759454i
$873$	−6.34315	+	3.02944i	−0.214683	+	0.102531i
$874$			0.402020i			0.0135985i
$875$		0			0
$876$	11.8579	+	16.7696i	0.400640	+	0.566591i
$877$	−9.07107	+	9.07107i	−0.306308	+	0.306308i	−0.843476	−	0.537167i	$-0.819494\pi$
$877$	−9.07107	+	9.07107i	−0.306308	+	0.306308i	0.537167	+	0.843476i	$0.319494\pi$
$878$	7.07107	−	7.07107i	0.238637	−	0.238637i
$879$	3.51472	+	4.97056i	0.118549	+	0.167653i
$880$		0			0
$881$			12.0000i			0.404290i	0.979356	+	0.202145i	$0.0647913\pi$
$881$			12.0000i			0.404290i	−0.979356	+	0.202145i	$0.935209\pi$
$882$	7.07969	−	3.38120i	0.238386	−	0.113851i
$883$	6.58579	+	6.58579i	0.221629	+	0.221629i	0.809184	−	0.587555i	$-0.199909\pi$
$883$	6.58579	+	6.58579i	0.221629	+	0.221629i	−0.587555	+	0.809184i	$0.699909\pi$
$884$	24.9706			0.839851
$885$		0			0
$886$	7.79899			0.262012
$887$	8.72792	+	8.72792i	0.293055	+	0.293055i	0.838286	−	0.545231i	$-0.183558\pi$
$887$	8.72792	+	8.72792i	0.293055	+	0.293055i	−0.545231	+	0.838286i	$0.683558\pi$
$888$	21.6569	+	3.71573i	0.726756	+	0.124692i
$889$			12.0000i			0.402467i
$890$		0			0
$891$	−5.65685	+	7.00000i	−0.189512	+	0.234509i
$892$	29.6985	−	29.6985i	0.994379	−	0.994379i
$893$	−4.00000	+	4.00000i	−0.133855	+	0.133855i
$894$	−10.4264	+	7.37258i	−0.348711	+	0.246576i
$895$		0			0
$896$		−	8.74517i		−	0.292155i
$897$	1.65685	−	9.65685i	0.0553208	−	0.322433i
$898$	4.20101	+	4.20101i	0.140190	+	0.140190i
$899$	35.3137			1.17778
$900$		0			0
$901$	−33.9411			−1.13074
$902$	1.41421	+	1.41421i	0.0470882	+	0.0470882i
$903$	1.57359	−	9.17157i	0.0523659	−	0.305211i
$904$		−	19.0294i		−	0.632910i
$905$		0			0
$906$	8.48528	−	6.00000i	0.281905	−	0.199337i
$907$	24.7279	−	24.7279i	0.821077	−	0.821077i	−0.165185	−	0.986263i	$-0.552822\pi$
$907$	24.7279	−	24.7279i	0.821077	−	0.821077i	0.986263	+	0.165185i	$0.0528222\pi$
$908$	37.0122	−	37.0122i	1.22829	−	1.22829i
$909$	−0.828427	+	2.34315i	−0.0274772	+	0.0777172i
$910$		0			0
$911$		−	30.6274i		−	1.01473i	−0.861731	−	0.507366i	$-0.830619\pi$
$911$		−	30.6274i		−	1.01473i	0.861731	−	0.507366i	$-0.169381\pi$
$912$	4.24264	+	0.727922i	0.140488	+	0.0241039i
$913$	−4.24264	−	4.24264i	−0.140411	−	0.140411i
$914$	−11.3726			−0.376172
$915$		0			0
$916$	32.9117			1.08743
$917$	10.3431	+	10.3431i	0.341561	+	0.341561i
$918$	5.31371	+	2.97056i	0.175379	+	0.0980432i
$919$		−	14.4853i		−	0.477825i	−0.971041	−	0.238913i	$-0.923209\pi$
$919$		−	14.4853i		−	0.477825i	0.971041	−	0.238913i	$-0.0767910\pi$
$920$		0			0
$921$	−26.4853	−	37.4558i	−0.872720	−	1.23421i
$922$	−6.78680	+	6.78680i	−0.223511	+	0.223511i
$923$	−32.9706	+	32.9706i	−1.08524	+	1.08524i
$924$	1.51472	+	2.14214i	0.0498306	+	0.0704711i
$925$		0			0
$926$			13.1127i			0.430910i
$927$	7.75736	+	16.2426i	0.254785	+	0.533478i
$928$	−27.5563	−	27.5563i	−0.904581	−	0.904581i
$929$	45.9411			1.50728			0.753640	−	0.657288i	$-0.228296\pi$
$929$	45.9411			1.50728			0.753640	+	0.657288i	$0.228296\pi$
$930$		0			0
$931$	5.23045			0.171421
$932$	18.2843	+	18.2843i	0.598921	+	0.598921i
$933$	17.6569	+	3.02944i	0.578059	+	0.0991793i
$934$		−	7.51472i		−	0.245889i
$935$		0			0
$936$	21.6569	+	7.65685i	0.707876	+	0.250272i
$937$	10.2426	−	10.2426i	0.334612	−	0.334612i	−0.519723	−	0.854335i	$-0.673965\pi$
$937$	10.2426	−	10.2426i	0.334612	−	0.334612i	0.854335	+	0.519723i	$0.173965\pi$
$938$	−0.887302	+	0.887302i	−0.0289714	+	0.0289714i
$939$	−37.6569	+	26.6274i	−1.22888	+	0.868953i
$940$		0			0
$941$		−	13.7990i		−	0.449834i	−0.974378	−	0.224917i	$-0.927789\pi$
$941$		−	13.7990i		−	0.449834i	0.974378	−	0.224917i	$-0.0722111\pi$
$942$	2.62742	−	15.3137i	0.0856059	−	0.498948i
$943$	4.00000	+	4.00000i	0.130258	+	0.130258i
$944$	−7.02944			−0.228789
$945$		0			0
$946$	2.68629			0.0873389
$947$	−11.4558	−	11.4558i	−0.372265	−	0.372265i	0.496037	−	0.868302i	$-0.334788\pi$
$947$	−11.4558	−	11.4558i	−0.372265	−	0.372265i	−0.868302	+	0.496037i	$0.834788\pi$
$948$	2.58579	−	15.0711i	0.0839824	−	0.489486i
$949$			31.3137i			1.01649i
$950$		0			0
$951$	−36.2843	+	25.6569i	−1.17660	+	0.831981i
$952$	2.62742	−	2.62742i	0.0851551	−	0.0851551i
$953$	26.0000	−	26.0000i	0.842223	−	0.842223i	−0.146925	−	0.989148i	$-0.546938\pi$
$953$	26.0000	−	26.0000i	0.842223	−	0.842223i	0.989148	+	0.146925i	$0.0469376\pi$
$954$	−14.0589	−	4.97056i	−0.455173	−	0.160928i
$955$		0			0
$956$			4.28427i			0.138563i
$957$	15.0711	+	2.58579i	0.487178	+	0.0835866i
$958$	7.71573	+	7.71573i	0.249284	+	0.249284i
$959$	−1.94113			−0.0626822
$960$		0			0
$961$	−15.0000			−0.483871
$962$	11.3137	+	11.3137i	0.364769	+	0.364769i
$963$	−25.4142	−	53.2132i	−0.818962	−	1.71477i
$964$			49.3137i			1.58829i
$965$		0			0
$966$	−0.402020	−	0.568542i	−0.0129348	−	0.0182926i
$967$	−25.0711	+	25.0711i	−0.806231	+	0.806231i	−0.984061	−	0.177830i	$-0.943092\pi$
$967$	−25.0711	+	25.0711i	−0.806231	+	0.806231i	0.177830	+	0.984061i	$0.443092\pi$
$968$	−1.12132	+	1.12132i	−0.0360406	+	0.0360406i
$969$	2.34315	+	3.31371i	0.0752727	+	0.106452i
$970$		0			0
$971$			10.6274i			0.341050i	0.985353	+	0.170525i	$0.0545464\pi$
$971$			10.6274i			0.341050i	−0.985353	+	0.170525i	$0.945454\pi$
$972$	−18.8198	−	21.4056i	−0.603646	−	0.686585i
$973$	9.85786	+	9.85786i	0.316029	+	0.316029i
$974$	6.20101			0.198693
$975$		0			0
$976$	18.0000			0.576166
$977$	20.0000	+	20.0000i	0.639857	+	0.639857i	0.950520	−	0.310663i	$-0.100551\pi$
$977$	20.0000	+	20.0000i	0.639857	+	0.639857i	−0.310663	+	0.950520i	$0.600551\pi$
$978$	9.89949	+	1.69848i	0.316551	+	0.0543116i
$979$			15.3137i			0.489428i
$980$		0			0
$981$	−2.00000	+	5.65685i	−0.0638551	+	0.180609i
$982$	5.45584	−	5.45584i	0.174103	−	0.174103i
$983$	8.34315	−	8.34315i	0.266105	−	0.266105i	−0.561424	−	0.827529i	$-0.689746\pi$
$983$	8.34315	−	8.34315i	0.266105	−	0.266105i	0.827529	+	0.561424i	$0.189746\pi$
$984$	−10.8284	+	7.65685i	−0.345198	+	0.244092i
$985$		0			0
$986$		−	10.3431i		−	0.329393i
$987$	1.65685	−	9.65685i	0.0527383	−	0.307381i
$988$	5.17157	+	5.17157i	0.164530	+	0.164530i
$989$	7.59798			0.241602
$990$		0			0
$991$	−37.9411			−1.20524			−0.602620	−	0.798028i	$-0.705876\pi$
$991$	−37.9411			−1.20524			−0.602620	+	0.798028i	$0.705876\pi$
$992$	−12.4853	−	12.4853i	−0.396408	−	0.396408i
$993$	0.485281	−	2.82843i	0.0153999	−	0.0897574i
$994$			3.31371i			0.105104i
$995$		0			0
$996$	15.5147	−	10.9706i	0.491603	−	0.347616i
$997$	−21.5563	+	21.5563i	−0.682696	+	0.682696i	−0.960607	−	0.277911i	$-0.910358\pi$
$997$	−21.5563	+	21.5563i	−0.682696	+	0.682696i	0.277911	+	0.960607i	$0.410358\pi$
$998$	0.686292	−	0.686292i	0.0217242	−	0.0217242i
$999$	−11.3137	−	40.0000i	−0.357950	−	1.26554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.k.g.518.1	yes	4
3.2	odd	2		825.2.k.a.518.2	✓	4
5.2	odd	4		825.2.k.a.782.2	yes	4
5.3	odd	4		825.2.k.h.782.1	yes	4
5.4	even	2		825.2.k.b.518.2	yes	4
15.2	even	4	inner	825.2.k.g.782.1	yes	4
15.8	even	4		825.2.k.b.782.2	yes	4
15.14	odd	2		825.2.k.h.518.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.k.a.518.2	✓	4	3.2	odd	2
825.2.k.a.782.2	yes	4	5.2	odd	4
825.2.k.b.518.2	yes	4	5.4	even	2
825.2.k.b.782.2	yes	4	15.8	even	4
825.2.k.g.518.1	yes	4	1.1	even	1	trivial
825.2.k.g.782.1	yes	4	15.2	even	4	inner
825.2.k.h.518.1	yes	4	15.14	odd	2
825.2.k.h.782.1	yes	4	5.3	odd	4

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.292893 + 0.292893i) q^{2} +(0.292893 - 1.70711i) q^{3} -1.82843i q^{4} +(0.585786 - 0.414214i) q^{6} +(-0.585786 + 0.585786i) q^{7} +(1.12132 - 1.12132i) q^{8} +(-2.82843 - 1.00000i) q^{9} +O(q^{10})\)	\(q+(0.292893 + 0.292893i) q^{2} +(0.292893 - 1.70711i) q^{3} -1.82843i q^{4} +(0.585786 - 0.414214i) q^{6} +(-0.585786 + 0.585786i) q^{7} +(1.12132 - 1.12132i) q^{8} +(-2.82843 - 1.00000i) q^{9} +1.00000i q^{11} +(-3.12132 - 0.535534i) q^{12} +(-3.41421 - 3.41421i) q^{13} -0.343146 q^{14} -3.00000 q^{16} +(-2.00000 - 2.00000i) q^{17} +(-0.535534 - 1.12132i) q^{18} -0.828427i q^{19} +(0.828427 + 1.17157i) q^{21} +(-0.292893 + 0.292893i) q^{22} +(-0.828427 + 0.828427i) q^{23} +(-1.58579 - 2.24264i) q^{24} -2.00000i q^{26} +(-2.53553 + 4.53553i) q^{27} +(1.07107 + 1.07107i) q^{28} +8.82843 q^{29} +4.00000 q^{31} +(-3.12132 - 3.12132i) q^{32} +(1.70711 + 0.292893i) q^{33} -1.17157i q^{34} +(-1.82843 + 5.17157i) q^{36} +(-5.65685 + 5.65685i) q^{37} +(0.242641 - 0.242641i) q^{38} +(-6.82843 + 4.82843i) q^{39} -4.82843i q^{41} +(-0.100505 + 0.585786i) q^{42} +(-4.58579 - 4.58579i) q^{43} +1.82843 q^{44} -0.485281 q^{46} +(-4.82843 - 4.82843i) q^{47} +(-0.878680 + 5.12132i) q^{48} +6.31371i q^{49} +(-4.00000 + 2.82843i) q^{51} +(-6.24264 + 6.24264i) q^{52} +(8.48528 - 8.48528i) q^{53} +(-2.07107 + 0.585786i) q^{54} +1.31371i q^{56} +(-1.41421 - 0.242641i) q^{57} +(2.58579 + 2.58579i) q^{58} +2.34315 q^{59} -6.00000 q^{61} +(1.17157 + 1.17157i) q^{62} +(2.24264 - 1.07107i) q^{63} +4.17157i q^{64} +(0.414214 + 0.585786i) q^{66} +(2.58579 - 2.58579i) q^{67} +(-3.65685 + 3.65685i) q^{68} +(1.17157 + 1.65685i) q^{69} -9.65685i q^{71} +(-4.29289 + 2.05025i) q^{72} +(-4.58579 - 4.58579i) q^{73} -3.31371 q^{74} -1.51472 q^{76} +(-0.585786 - 0.585786i) q^{77} +(-3.41421 - 0.585786i) q^{78} +4.82843i q^{79} +(7.00000 + 5.65685i) q^{81} +(1.41421 - 1.41421i) q^{82} +(-4.24264 + 4.24264i) q^{83} +(2.14214 - 1.51472i) q^{84} -2.68629i q^{86} +(2.58579 - 15.0711i) q^{87} +(1.12132 + 1.12132i) q^{88} +15.3137 q^{89} +4.00000 q^{91} +(1.51472 + 1.51472i) q^{92} +(1.17157 - 6.82843i) q^{93} -2.82843i q^{94} +(-6.24264 + 4.41421i) q^{96} +(1.65685 - 1.65685i) q^{97} +(-1.84924 + 1.84924i) q^{98} +(1.00000 - 2.82843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 8 q^{6} - 8 q^{7} - 4 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^3 + 8 * q^6 - 8 * q^7 - 4 * q^8	\( 4 q + 4 q^{2} + 4 q^{3} + 8 q^{6} - 8 q^{7} - 4 q^{8} - 4 q^{12} - 8 q^{13} - 24 q^{14} - 12 q^{16} - 8 q^{17} + 12 q^{18} - 8 q^{21} - 4 q^{22} + 8 q^{23} - 12 q^{24} + 4 q^{27} - 24 q^{28} + 24 q^{29} + 16 q^{31} - 4 q^{32} + 4 q^{33} + 4 q^{36} - 16 q^{38} - 16 q^{39} - 40 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} - 8 q^{47} - 12 q^{48} - 16 q^{51} - 8 q^{52} + 20 q^{54} + 16 q^{58} + 32 q^{59} - 24 q^{61} + 16 q^{62} - 8 q^{63} - 4 q^{66} + 16 q^{67} + 8 q^{68} + 16 q^{69} - 20 q^{72} - 24 q^{73} + 32 q^{74} - 40 q^{76} - 8 q^{77} - 8 q^{78} + 28 q^{81} - 48 q^{84} + 16 q^{87} - 4 q^{88} + 16 q^{89} + 16 q^{91} + 40 q^{92} + 16 q^{93} - 8 q^{96} - 16 q^{97} + 52 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 8 * q^6 - 8 * q^7 - 4 * q^8 - 4 * q^12 - 8 * q^13 - 24 * q^14 - 12 * q^16 - 8 * q^17 + 12 * q^18 - 8 * q^21 - 4 * q^22 + 8 * q^23 - 12 * q^24 + 4 * q^27 - 24 * q^28 + 24 * q^29 + 16 * q^31 - 4 * q^32 + 4 * q^33 + 4 * q^36 - 16 * q^38 - 16 * q^39 - 40 * q^42 - 24 * q^43 - 4 * q^44 + 32 * q^46 - 8 * q^47 - 12 * q^48 - 16 * q^51 - 8 * q^52 + 20 * q^54 + 16 * q^58 + 32 * q^59 - 24 * q^61 + 16 * q^62 - 8 * q^63 - 4 * q^66 + 16 * q^67 + 8 * q^68 + 16 * q^69 - 20 * q^72 - 24 * q^73 + 32 * q^74 - 40 * q^76 - 8 * q^77 - 8 * q^78 + 28 * q^81 - 48 * q^84 + 16 * q^87 - 4 * q^88 + 16 * q^89 + 16 * q^91 + 40 * q^92 + 16 * q^93 - 8 * q^96 - 16 * q^97 + 52 * q^98 + 4 * q^99

Introduction

L-functions

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