LMFDB - Embedded newform 390.2.p.g.281.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(161,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("390.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.p (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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.40960000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 7x^{4} + 1 $ x^8 + 7*x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			281.3
Root			$1.14412 + 1.14412i$ of defining polynomial
Character	$\chi$	$=$	390.281
Dual form			390.2.p.g.161.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{2} +(-1.58114 + 0.707107i) q^{3} -1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.618034 + 1.61803i) q^{6} +(-0.707107 - 0.707107i) q^{8} +(2.00000 - 2.23607i) q^{9} -1.00000i q^{10} +(-1.41421 - 1.41421i) q^{11} +(0.707107 + 1.58114i) q^{12} +(0.418861 - 3.58114i) q^{13} +(-0.618034 + 1.61803i) q^{15} -1.00000 q^{16} +7.30056 q^{17} +(-0.166925 - 2.99535i) q^{18} +(-5.16228 - 5.16228i) q^{19} +(-0.707107 - 0.707107i) q^{20} -2.00000 q^{22} +4.47214 q^{23} +(1.61803 + 0.618034i) q^{24} -1.00000i q^{25} +(-2.23607 - 2.82843i) q^{26} +(-1.58114 + 4.94975i) q^{27} -4.47214i q^{29} +(0.707107 + 1.58114i) q^{30} +(-3.00000 - 3.00000i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(3.23607 + 1.23607i) q^{33} +(5.16228 - 5.16228i) q^{34} +(-2.23607 - 2.00000i) q^{36} +(-4.00000 + 4.00000i) q^{37} -7.30056 q^{38} +(1.86997 + 5.95846i) q^{39} -1.00000 q^{40} +(-2.23607 + 2.23607i) q^{41} -7.16228i q^{43} +(-1.41421 + 1.41421i) q^{44} +(-0.166925 - 2.99535i) q^{45} +(3.16228 - 3.16228i) q^{46} +(7.30056 + 7.30056i) q^{47} +(1.58114 - 0.707107i) q^{48} +7.00000i q^{49} +(-0.707107 - 0.707107i) q^{50} +(-11.5432 + 5.16228i) q^{51} +(-3.58114 - 0.418861i) q^{52} +1.41421i q^{53} +(2.38197 + 4.61803i) q^{54} -2.00000 q^{55} +(11.8126 + 4.51200i) q^{57} +(-3.16228 - 3.16228i) q^{58} +(5.88635 + 5.88635i) q^{59} +(1.61803 + 0.618034i) q^{60} +10.6491 q^{61} -4.24264 q^{62} +1.00000i q^{64} +(-2.23607 - 2.82843i) q^{65} +(3.16228 - 1.41421i) q^{66} +(7.16228 + 7.16228i) q^{67} -7.30056i q^{68} +(-7.07107 + 3.16228i) q^{69} +(-3.87978 + 3.87978i) q^{71} +(-2.99535 + 0.166925i) q^{72} +(-5.16228 + 5.16228i) q^{73} +5.65685i q^{74} +(0.707107 + 1.58114i) q^{75} +(-5.16228 + 5.16228i) q^{76} +(5.53553 + 2.89100i) q^{78} -10.0000 q^{79} +(-0.707107 + 0.707107i) q^{80} +(-1.00000 - 8.94427i) q^{81} +3.16228i q^{82} +(-5.65685 + 5.65685i) q^{83} +(5.16228 - 5.16228i) q^{85} +(-5.06450 - 5.06450i) q^{86} +(3.16228 + 7.07107i) q^{87} +2.00000i q^{88} +(0.592359 + 0.592359i) q^{89} +(-2.23607 - 2.00000i) q^{90} -4.47214i q^{92} +(6.86474 + 2.62210i) q^{93} +10.3246 q^{94} -7.30056 q^{95} +(0.618034 - 1.61803i) q^{96} +(-1.16228 - 1.16228i) q^{97} +(4.94975 + 4.94975i) q^{98} +(-5.99070 + 0.333851i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{6} + 16 q^{9} + 16 q^{13} + 4 q^{15} - 8 q^{16} - 16 q^{19} - 16 q^{22} + 4 q^{24} - 24 q^{31} + 8 q^{33} + 16 q^{34} - 32 q^{37} + 20 q^{39} - 8 q^{40} - 16 q^{52} + 28 q^{54} - 16 q^{55} + 40 q^{57}+ \cdots + 16 q^{97}+O(q^{100}) $ 8 * q + 4 * q^6 + 16 * q^9 + 16 * q^13 + 4 * q^15 - 8 * q^16 - 16 * q^19 - 16 * q^22 + 4 * q^24 - 24 * q^31 + 8 * q^33 + 16 * q^34 - 32 * q^37 + 20 * q^39 - 8 * q^40 - 16 * q^52 + 28 * q^54 - 16 * q^55 + 40 * q^57 + 4 * q^60 - 16 * q^61 + 32 * q^67 - 16 * q^73 - 16 * q^76 + 16 * q^78 - 80 * q^79 - 8 * q^81 + 16 * q^85 + 32 * q^94 - 4 * q^96 + 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−1.58114	+	0.707107i	−0.912871	+	0.408248i
$3$	−1.58114	+	0.707107i	−0.912871	+	0.408248i
$4$		−	1.00000i		−	0.500000i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	−0.618034	+	1.61803i	−0.252311	+	0.660560i
$7$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$7$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	2.00000	−	2.23607i	0.666667	−	0.745356i
$10$		−	1.00000i		−	0.316228i
$11$	−1.41421	−	1.41421i	−0.426401	−	0.426401i	0.460999	−	0.887401i	$-0.347491\pi$
$11$	−1.41421	−	1.41421i	−0.426401	−	0.426401i	−0.887401	+	0.460999i	$0.847491\pi$
$12$	0.707107	+	1.58114i	0.204124	+	0.456435i
$13$	0.418861	−	3.58114i	0.116171	−	0.993229i
$13$	0.418861	−	3.58114i	0.116171	−	0.993229i
$14$		0			0
$15$	−0.618034	+	1.61803i	−0.159576	+	0.417775i
$16$	−1.00000			−0.250000
$17$	7.30056			1.77065			0.885323	−	0.464976i	$-0.153937\pi$
$17$	7.30056			1.77065			0.885323	+	0.464976i	$0.153937\pi$
$18$	−0.166925	−	2.99535i	−0.0393447	−	0.706011i
$19$	−5.16228	−	5.16228i	−1.18431	−	1.18431i	−0.978617	−	0.205691i	$-0.934056\pi$
$19$	−5.16228	−	5.16228i	−1.18431	−	1.18431i	−0.205691	−	0.978617i	$-0.565944\pi$
$20$	−0.707107	−	0.707107i	−0.158114	−	0.158114i
$21$		0			0
$22$	−2.00000			−0.426401
$23$	4.47214			0.932505			0.466252	−	0.884652i	$-0.345604\pi$
$23$	4.47214			0.932505			0.466252	+	0.884652i	$0.345604\pi$
$24$	1.61803	+	0.618034i	0.330280	+	0.126156i
$25$		−	1.00000i		−	0.200000i
$26$	−2.23607	−	2.82843i	−0.438529	−	0.554700i
$27$	−1.58114	+	4.94975i	−0.304290	+	0.952579i
$28$		0			0
$29$		−	4.47214i		−	0.830455i	−0.909718	−	0.415227i	$-0.863702\pi$
$29$		−	4.47214i		−	0.830455i	0.909718	−	0.415227i	$-0.136298\pi$
$30$	0.707107	+	1.58114i	0.129099	+	0.288675i
$31$	−3.00000	−	3.00000i	−0.538816	−	0.538816i	0.384365	−	0.923181i	$-0.374420\pi$
$31$	−3.00000	−	3.00000i	−0.538816	−	0.538816i	−0.923181	+	0.384365i	$0.874420\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	3.23607	+	1.23607i	0.563327	+	0.215172i
$34$	5.16228	−	5.16228i	0.885323	−	0.885323i
$35$		0			0
$36$	−2.23607	−	2.00000i	−0.372678	−	0.333333i
$37$	−4.00000	+	4.00000i	−0.657596	+	0.657596i	−0.954811	−	0.297215i	$-0.903942\pi$
$37$	−4.00000	+	4.00000i	−0.657596	+	0.657596i	0.297215	+	0.954811i	$0.403942\pi$
$38$	−7.30056			−1.18431
$39$	1.86997	+	5.95846i	0.299435	+	0.954117i
$40$	−1.00000			−0.158114
$41$	−2.23607	+	2.23607i	−0.349215	+	0.349215i	−0.859817	−	0.510602i	$-0.829423\pi$
$41$	−2.23607	+	2.23607i	−0.349215	+	0.349215i	0.510602	+	0.859817i	$0.329423\pi$
$42$		0			0
$43$		−	7.16228i		−	1.09224i	−0.837708	−	0.546119i	$-0.816105\pi$
$43$		−	7.16228i		−	1.09224i	0.837708	−	0.546119i	$-0.183895\pi$
$44$	−1.41421	+	1.41421i	−0.213201	+	0.213201i
$45$	−0.166925	−	2.99535i	−0.0248837	−	0.446521i
$46$	3.16228	−	3.16228i	0.466252	−	0.466252i
$47$	7.30056	+	7.30056i	1.06490	+	1.06490i	0.997743	+	0.0671539i	$0.0213919\pi$
$47$	7.30056	+	7.30056i	1.06490	+	1.06490i	0.0671539	+	0.997743i	$0.478608\pi$
$48$	1.58114	−	0.707107i	0.228218	−	0.102062i
$49$			7.00000i			1.00000i
$50$	−0.707107	−	0.707107i	−0.100000	−	0.100000i
$51$	−11.5432	+	5.16228i	−1.61637	+	0.722863i
$52$	−3.58114	−	0.418861i	−0.496615	−	0.0580856i
$53$			1.41421i			0.194257i	0.995272	+	0.0971286i	$0.0309658\pi$
$53$			1.41421i			0.194257i	−0.995272	+	0.0971286i	$0.969034\pi$
$54$	2.38197	+	4.61803i	0.324145	+	0.628435i
$55$	−2.00000			−0.269680
$56$		0			0
$57$	11.8126	+	4.51200i	1.56461	+	0.597628i
$58$	−3.16228	−	3.16228i	−0.415227	−	0.415227i
$59$	5.88635	+	5.88635i	0.766337	+	0.766337i	0.977460	−	0.211122i	$-0.0677118\pi$
$59$	5.88635	+	5.88635i	0.766337	+	0.766337i	−0.211122	+	0.977460i	$0.567712\pi$
$60$	1.61803	+	0.618034i	0.208887	+	0.0797878i
$61$	10.6491			1.36348			0.681739	−	0.731595i	$-0.261224\pi$
$61$	10.6491			1.36348			0.681739	+	0.731595i	$0.261224\pi$
$62$	−4.24264			−0.538816
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−2.23607	−	2.82843i	−0.277350	−	0.350823i
$66$	3.16228	−	1.41421i	0.389249	−	0.174078i
$67$	7.16228	+	7.16228i	0.875011	+	0.875011i	0.993013	−	0.118002i	$-0.0376489\pi$
$67$	7.16228	+	7.16228i	0.875011	+	0.875011i	−0.118002	+	0.993013i	$0.537649\pi$
$68$		−	7.30056i		−	0.885323i
$69$	−7.07107	+	3.16228i	−0.851257	+	0.380693i
$70$		0			0
$71$	−3.87978	+	3.87978i	−0.460445	+	0.460445i	−0.898801	−	0.438356i	$-0.855561\pi$
$71$	−3.87978	+	3.87978i	−0.460445	+	0.460445i	0.438356	+	0.898801i	$0.355561\pi$
$72$	−2.99535	+	0.166925i	−0.353006	+	0.0196723i
$73$	−5.16228	+	5.16228i	−0.604199	+	0.604199i	−0.941424	−	0.337225i	$-0.890512\pi$
$73$	−5.16228	+	5.16228i	−0.604199	+	0.604199i	0.337225	+	0.941424i	$0.390512\pi$
$74$			5.65685i			0.657596i
$75$	0.707107	+	1.58114i	0.0816497	+	0.182574i
$76$	−5.16228	+	5.16228i	−0.592154	+	0.592154i
$77$		0			0
$78$	5.53553	+	2.89100i	0.626776	+	0.327341i
$79$	−10.0000			−1.12509			−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000			−1.12509			−0.562544	+	0.826767i	$0.690177\pi$
$80$	−0.707107	+	0.707107i	−0.0790569	+	0.0790569i
$81$	−1.00000	−	8.94427i	−0.111111	−	0.993808i
$82$			3.16228i			0.349215i
$83$	−5.65685	+	5.65685i	−0.620920	+	0.620920i	−0.945767	−	0.324846i	$-0.894687\pi$
$83$	−5.65685	+	5.65685i	−0.620920	+	0.620920i	0.324846	+	0.945767i	$0.394687\pi$
$84$		0			0
$85$	5.16228	−	5.16228i	0.559928	−	0.559928i
$86$	−5.06450	−	5.06450i	−0.546119	−	0.546119i
$87$	3.16228	+	7.07107i	0.339032	+	0.758098i
$88$			2.00000i			0.213201i
$89$	0.592359	+	0.592359i	0.0627899	+	0.0627899i	0.737804	−	0.675015i	$-0.235863\pi$
$89$	0.592359	+	0.592359i	0.0627899	+	0.0627899i	−0.675015	+	0.737804i	$0.735863\pi$
$90$	−2.23607	−	2.00000i	−0.235702	−	0.210819i
$91$		0			0
$92$		−	4.47214i		−	0.466252i
$93$	6.86474	+	2.62210i	0.711840	+	0.271899i
$94$	10.3246			1.06490
$95$	−7.30056			−0.749022
$96$	0.618034	−	1.61803i	0.0630778	−	0.165140i
$97$	−1.16228	−	1.16228i	−0.118011	−	0.118011i	0.645635	−	0.763646i	$-0.276593\pi$
$97$	−1.16228	−	1.16228i	−0.118011	−	0.118011i	−0.763646	+	0.645635i	$0.776593\pi$
$98$	4.94975	+	4.94975i	0.500000	+	0.500000i
$99$	−5.99070	+	0.333851i	−0.602088	+	0.0335532i
$100$	−1.00000			−0.100000
$101$	6.84157			0.680762			0.340381	−	0.940288i	$-0.389444\pi$
$101$	6.84157			0.680762			0.340381	+	0.940288i	$0.389444\pi$
$102$	−4.51200	+	11.8126i	−0.446754	+	1.16962i
$103$			18.6491i			1.83755i	0.394780	+	0.918776i	$0.370821\pi$
$103$			18.6491i			1.83755i	−0.394780	+	0.918776i	$0.629179\pi$
$104$	−2.82843	+	2.23607i	−0.277350	+	0.219265i
$105$		0			0
$106$	1.00000	+	1.00000i	0.0971286	+	0.0971286i
$107$		−	7.53006i		−	0.727958i	−0.931407	−	0.363979i	$-0.881418\pi$
$107$		−	7.53006i		−	0.727958i	0.931407	−	0.363979i	$-0.118582\pi$
$108$	4.94975	+	1.58114i	0.476290	+	0.152145i
$109$	−4.83772	−	4.83772i	−0.463370	−	0.463370i	0.436389	−	0.899758i	$-0.356257\pi$
$109$	−4.83772	−	4.83772i	−0.463370	−	0.463370i	−0.899758	+	0.436389i	$0.856257\pi$
$110$	−1.41421	+	1.41421i	−0.134840	+	0.134840i
$111$	3.49613	−	9.15298i	0.331838	−	0.868763i
$112$		0			0
$113$		−	16.2448i		−	1.52819i	−0.645106	−	0.764093i	$-0.723187\pi$
$113$		−	16.2448i		−	1.52819i	0.645106	−	0.764093i	$-0.276813\pi$
$114$	11.5432	−	5.16228i	1.08112	−	0.483492i
$115$	3.16228	−	3.16228i	0.294884	−	0.294884i
$116$	−4.47214			−0.415227
$117$	−7.16995	−	8.09888i	−0.662862	−	0.748742i
$118$	8.32456			0.766337
$119$		0			0
$120$	1.58114	−	0.707107i	0.144338	−	0.0645497i
$121$		−	7.00000i		−	0.636364i
$122$	7.53006	−	7.53006i	0.681739	−	0.681739i
$123$	1.95440	−	5.11667i	0.176222	−	0.461355i
$124$	−3.00000	+	3.00000i	−0.269408	+	0.269408i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$		0			0
$127$		−	16.9737i		−	1.50617i	−0.657924	−	0.753085i	$-0.728565\pi$
$127$		−	16.9737i		−	1.50617i	0.657924	−	0.753085i	$-0.271435\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	5.06450	+	11.3246i	0.445904	+	0.997071i
$130$	−3.58114	−	0.418861i	−0.314087	−	0.0367366i
$131$			0.458991i			0.0401022i	0.999799	+	0.0200511i	$0.00638289\pi$
$131$			0.458991i			0.0401022i	−0.999799	+	0.0200511i	$0.993617\pi$
$132$	1.23607	−	3.23607i	0.107586	−	0.281664i
$133$		0			0
$134$	10.1290			0.875011
$135$	2.38197	+	4.61803i	0.205007	+	0.397457i
$136$	−5.16228	−	5.16228i	−0.442662	−	0.442662i
$137$	14.3716	+	14.3716i	1.22785	+	1.22785i	0.964775	+	0.263076i	$0.0847371\pi$
$137$	14.3716	+	14.3716i	1.22785	+	1.22785i	0.263076	+	0.964775i	$0.415263\pi$
$138$	−2.76393	+	7.23607i	−0.235282	+	0.615975i
$139$	6.32456			0.536442			0.268221	−	0.963357i	$-0.413564\pi$
$139$	6.32456			0.536442			0.268221	+	0.963357i	$0.413564\pi$
$140$		0			0
$141$	−16.7055	−	6.38093i	−1.40686	−	0.537371i
$142$			5.48683i			0.460445i
$143$	−5.65685	+	4.47214i	−0.473050	+	0.373979i
$144$	−2.00000	+	2.23607i	−0.166667	+	0.186339i
$145$	−3.16228	−	3.16228i	−0.262613	−	0.262613i
$146$			7.30056i			0.604199i
$147$	−4.94975	−	11.0680i	−0.408248	−	0.912871i
$148$	4.00000	+	4.00000i	0.328798	+	0.328798i
$149$	2.59893	−	2.59893i	0.212913	−	0.212913i	−0.592591	−	0.805504i	$-0.701895\pi$
$149$	2.59893	−	2.59893i	0.212913	−	0.212913i	0.805504	+	0.592591i	$0.201895\pi$
$150$	1.61803	+	0.618034i	0.132112	+	0.0504623i
$151$	0.675445	−	0.675445i	0.0549669	−	0.0549669i	−0.679089	−	0.734056i	$-0.737625\pi$
$151$	0.675445	−	0.675445i	0.0549669	−	0.0549669i	0.734056	+	0.679089i	$0.237625\pi$
$152$			7.30056i			0.592154i
$153$	14.6011	−	16.3246i	1.18043	−	1.31976i
$154$		0			0
$155$	−4.24264			−0.340777
$156$	5.95846	−	1.86997i	0.477058	−	0.149717i
$157$	23.1623			1.84855			0.924276	−	0.381726i	$-0.124670\pi$
$157$	23.1623			1.84855			0.924276	+	0.381726i	$0.124670\pi$
$158$	−7.07107	+	7.07107i	−0.562544	+	0.562544i
$159$	−1.00000	−	2.23607i	−0.0793052	−	0.177332i
$160$			1.00000i			0.0790569i
$161$		0			0
$162$	−7.03166	−	5.61745i	−0.552460	−	0.441348i
$163$	2.32456	−	2.32456i	0.182073	−	0.182073i	−0.610185	−	0.792259i	$-0.708905\pi$
$163$	2.32456	−	2.32456i	0.182073	−	0.182073i	0.792259	+	0.610185i	$0.208905\pi$
$164$	2.23607	+	2.23607i	0.174608	+	0.174608i
$165$	3.16228	−	1.41421i	0.246183	−	0.110096i
$166$			8.00000i			0.620920i
$167$	1.64371	+	1.64371i	0.127194	+	0.127194i	0.767838	−	0.640644i	$-0.221333\pi$
$167$	1.64371	+	1.64371i	0.127194	+	0.127194i	−0.640644	+	0.767838i	$0.721333\pi$
$168$		0			0
$169$	−12.6491	−	3.00000i	−0.973009	−	0.230769i
$170$		−	7.30056i		−	0.559928i
$171$	−21.8678	+	1.21865i	−1.67227	+	0.0931924i
$172$	−7.16228			−0.546119
$173$	−22.1312			−1.68260			−0.841301	−	0.540566i	$-0.818210\pi$
$173$	−22.1312			−1.68260			−0.841301	+	0.540566i	$0.818210\pi$
$174$	7.23607	+	2.76393i	0.548565	+	0.209533i
$175$		0			0
$176$	1.41421	+	1.41421i	0.106600	+	0.106600i
$177$	−13.4694	−	5.14486i	−1.01242	−	0.386711i
$178$	0.837722			0.0627899
$179$	0.458991			0.0343066			0.0171533	−	0.999853i	$-0.494540\pi$
$179$	0.458991			0.0343066			0.0171533	+	0.999853i	$0.494540\pi$
$180$	−2.99535	+	0.166925i	−0.223260	+	0.0124419i
$181$			4.32456i			0.321442i	0.987000	+	0.160721i	$0.0513819\pi$
$181$			4.32456i			0.321442i	−0.987000	+	0.160721i	$0.948618\pi$
$182$		0			0
$183$	−16.8377	+	7.53006i	−1.24468	+	0.556638i
$184$	−3.16228	−	3.16228i	−0.233126	−	0.233126i
$185$			5.65685i			0.415900i
$186$	6.70820	−	3.00000i	0.491869	−	0.219971i
$187$	−10.3246	−	10.3246i	−0.755006	−	0.755006i
$188$	7.30056	−	7.30056i	0.532448	−	0.532448i
$189$		0			0
$190$	−5.16228	+	5.16228i	−0.374511	+	0.374511i
$191$			2.10270i			0.152146i	0.997102	+	0.0760730i	$0.0242382\pi$
$191$			2.10270i			0.152146i	−0.997102	+	0.0760730i	$0.975762\pi$
$192$	−0.707107	−	1.58114i	−0.0510310	−	0.114109i
$193$	−3.48683	+	3.48683i	−0.250988	+	0.250988i	−0.821376	−	0.570388i	$-0.806793\pi$
$193$	−3.48683	+	3.48683i	−0.250988	+	0.250988i	0.570388	+	0.821376i	$0.306793\pi$
$194$	−1.64371			−0.118011
$195$	5.53553	+	2.89100i	0.396408	+	0.207029i
$196$	7.00000			0.500000
$197$	−8.94427	+	8.94427i	−0.637253	+	0.637253i	−0.949877	−	0.312624i	$-0.898792\pi$
$197$	−8.94427	+	8.94427i	−0.637253	+	0.637253i	0.312624	+	0.949877i	$0.398792\pi$
$198$	−4.00000	+	4.47214i	−0.284268	+	0.317821i
$199$		−	2.00000i		−	0.141776i	−0.997484	−	0.0708881i	$-0.977417\pi$
$199$		−	2.00000i		−	0.141776i	0.997484	−	0.0708881i	$-0.0225833\pi$
$200$	−0.707107	+	0.707107i	−0.0500000	+	0.0500000i
$201$	−16.3891	−	6.26006i	−1.15599	−	0.441551i
$202$	4.83772	−	4.83772i	0.340381	−	0.340381i
$203$		0			0
$204$	5.16228	+	11.5432i	0.361432	+	0.808186i
$205$			3.16228i			0.220863i
$206$	13.1869	+	13.1869i	0.918776	+	0.918776i
$207$	8.94427	−	10.0000i	0.621670	−	0.695048i
$208$	−0.418861	+	3.58114i	−0.0290428	+	0.248307i
$209$			14.6011i			1.00998i
$210$		0			0
$211$	3.35089			0.230685			0.115342	−	0.993326i	$-0.463203\pi$
$211$	3.35089			0.230685			0.115342	+	0.993326i	$0.463203\pi$
$212$	1.41421			0.0971286
$213$	3.39105	−	8.87788i	0.232351	−	0.608302i
$214$	−5.32456	−	5.32456i	−0.363979	−	0.363979i
$215$	−5.06450	−	5.06450i	−0.345396	−	0.345396i
$216$	4.61803	−	2.38197i	0.314217	−	0.162072i
$217$		0			0
$218$	−6.84157			−0.463370
$219$	4.51200	−	11.8126i	0.304892	−	0.798219i
$220$			2.00000i			0.134840i
$221$	3.05792	−	26.1443i	0.205698	−	1.75866i
$222$	−4.00000	−	8.94427i	−0.268462	−	0.600300i
$223$	16.6491	+	16.6491i	1.11491	+	1.11491i	0.992477	+	0.122430i	$0.0390686\pi$
$223$	16.6491	+	16.6491i	1.11491	+	1.11491i	0.122430	+	0.992477i	$0.460931\pi$
$224$		0			0
$225$	−2.23607	−	2.00000i	−0.149071	−	0.133333i
$226$	−11.4868	−	11.4868i	−0.764093	−	0.764093i
$227$	12.7279	−	12.7279i	0.844782	−	0.844782i	−0.144695	−	0.989476i	$-0.546220\pi$
$227$	12.7279	−	12.7279i	0.844782	−	0.844782i	0.989476	+	0.144695i	$0.0462199\pi$
$228$	4.51200	−	11.8126i	0.298814	−	0.782306i
$229$	−13.8114	+	13.8114i	−0.912682	+	0.912682i	−0.996483	−	0.0838003i	$-0.973294\pi$
$229$	−13.8114	+	13.8114i	−0.912682	+	0.912682i	0.0838003	+	0.996483i	$0.473294\pi$
$230$		−	4.47214i		−	0.294884i
$231$		0			0
$232$	−3.16228	+	3.16228i	−0.207614	+	0.207614i
$233$	−4.01315			−0.262910			−0.131455	−	0.991322i	$-0.541965\pi$
$233$	−4.01315			−0.262910			−0.131455	+	0.991322i	$0.541965\pi$
$234$	−10.7967	−	0.656854i	−0.705802	−	0.0429399i
$235$	10.3246			0.673500
$236$	5.88635	−	5.88635i	0.383169	−	0.383169i
$237$	15.8114	−	7.07107i	1.02706	−	0.459315i
$238$		0			0
$239$	7.89292	−	7.89292i	0.510551	−	0.510551i	−0.404144	−	0.914695i	$-0.632431\pi$
$239$	7.89292	−	7.89292i	0.510551	−	0.510551i	0.914695	+	0.404144i	$0.132431\pi$
$240$	0.618034	−	1.61803i	0.0398939	−	0.104444i
$241$	7.64911	−	7.64911i	0.492723	−	0.492723i	−0.416440	−	0.909163i	$-0.636723\pi$
$241$	7.64911	−	7.64911i	0.492723	−	0.492723i	0.909163	+	0.416440i	$0.136723\pi$
$242$	−4.94975	−	4.94975i	−0.318182	−	0.318182i
$243$	7.90569	+	13.4350i	0.507151	+	0.861858i
$244$		−	10.6491i		−	0.681739i
$245$	4.94975	+	4.94975i	0.316228	+	0.316228i
$246$	−2.23607	−	5.00000i	−0.142566	−	0.318788i
$247$	−20.6491	+	16.3246i	−1.31387	+	1.03871i
$248$			4.24264i			0.269408i
$249$	4.94427	−	12.9443i	0.313331	−	0.820310i
$250$	−1.00000			−0.0632456
$251$	14.6011			0.921615			0.460807	−	0.887500i	$-0.347560\pi$
$251$	14.6011			0.921615			0.460807	+	0.887500i	$0.347560\pi$
$252$		0			0
$253$	−6.32456	−	6.32456i	−0.397621	−	0.397621i
$254$	−12.0022	−	12.0022i	−0.753085	−	0.753085i
$255$	−4.51200	+	11.8126i	−0.282552	+	0.739731i
$256$	1.00000			0.0625000
$257$	−1.64371			−0.102532			−0.0512659	−	0.998685i	$-0.516326\pi$
$257$	−1.64371			−0.102532			−0.0512659	+	0.998685i	$0.516326\pi$
$258$	11.5888	+	4.42653i	0.721488	+	0.275584i
$259$		0			0
$260$	−2.82843	+	2.23607i	−0.175412	+	0.138675i
$261$	−10.0000	−	8.94427i	−0.618984	−	0.553637i
$262$	0.324555	+	0.324555i	0.0200511	+	0.0200511i
$263$			1.18472i			0.0730529i	0.999333	+	0.0365264i	$0.0116293\pi$
$263$			1.18472i			0.0730529i	−0.999333	+	0.0365264i	$0.988371\pi$
$264$	−1.41421	−	3.16228i	−0.0870388	−	0.194625i
$265$	1.00000	+	1.00000i	0.0614295	+	0.0614295i
$266$		0			0
$267$	−1.35546	−	0.517741i	−0.0829530	−	0.0316852i
$268$	7.16228	−	7.16228i	0.437506	−	0.437506i
$269$		−	4.47214i		−	0.272671i	−0.990663	−	0.136335i	$-0.956467\pi$
$269$		−	4.47214i		−	0.272671i	0.990663	−	0.136335i	$-0.0435325\pi$
$270$	4.94975	+	1.58114i	0.301232	+	0.0962250i
$271$	−7.32456	+	7.32456i	−0.444935	+	0.444935i	−0.893667	−	0.448732i	$-0.851876\pi$
$271$	−7.32456	+	7.32456i	−0.444935	+	0.444935i	0.448732	+	0.893667i	$0.351876\pi$
$272$	−7.30056			−0.442662
$273$		0			0
$274$	20.3246			1.22785
$275$	−1.41421	+	1.41421i	−0.0852803	+	0.0852803i
$276$	3.16228	+	7.07107i	0.190347	+	0.425628i
$277$		−	3.16228i		−	0.190003i	−0.995477	−	0.0950014i	$-0.969714\pi$
$277$		−	3.16228i		−	0.190003i	0.995477	−	0.0950014i	$-0.0302856\pi$
$278$	4.47214	−	4.47214i	0.268221	−	0.268221i
$279$	−12.7082	+	0.708204i	−0.760820	+	0.0423991i
$280$		0			0
$281$	17.5629	+	17.5629i	1.04772	+	1.04772i	0.998803	+	0.0489130i	$0.0155757\pi$
$281$	17.5629	+	17.5629i	1.04772	+	1.04772i	0.0489130	+	0.998803i	$0.484424\pi$
$282$	−16.3246	+	7.30056i	−0.972113	+	0.434742i
$283$			12.8377i			0.763123i	0.924343	+	0.381562i	$0.124614\pi$
$283$			12.8377i			0.763123i	−0.924343	+	0.381562i	$0.875386\pi$
$284$	3.87978	+	3.87978i	0.230222	+	0.230222i
$285$	11.5432	−	5.16228i	0.683760	−	0.305787i
$286$	−0.837722	+	7.16228i	−0.0495356	+	0.423514i
$287$		0			0
$288$	0.166925	+	2.99535i	0.00983617	+	0.176503i
$289$	36.2982			2.13519
$290$	−4.47214			−0.262613
$291$	2.65958	+	1.01587i	0.155907	+	0.0595512i
$292$	5.16228	+	5.16228i	0.302099	+	0.302099i
$293$	2.82843	+	2.82843i	0.165238	+	0.165238i	0.784883	−	0.619644i	$-0.212723\pi$
$293$	2.82843	+	2.82843i	0.165238	+	0.165238i	−0.619644	+	0.784883i	$0.712723\pi$
$294$	−11.3262	−	4.32624i	−0.660560	−	0.252311i
$295$	8.32456			0.484674
$296$	5.65685			0.328798
$297$	9.23607	−	4.76393i	0.535931	−	0.276431i
$298$		−	3.67544i		−	0.212913i
$299$	1.87320	−	16.0153i	0.108330	−	0.926191i
$300$	1.58114	−	0.707107i	0.0912871	−	0.0408248i
$301$		0			0
$302$		−	0.955223i		−	0.0549669i
$303$	−10.8175	+	4.83772i	−0.621448	+	0.277920i
$304$	5.16228	+	5.16228i	0.296077	+	0.296077i
$305$	7.53006	−	7.53006i	0.431170	−	0.431170i
$306$	−1.21865	−	21.8678i	−0.0696655	−	1.25010i
$307$	7.16228	−	7.16228i	0.408773	−	0.408773i	−0.472538	−	0.881310i	$-0.656662\pi$
$307$	7.16228	−	7.16228i	0.408773	−	0.408773i	0.881310	+	0.472538i	$0.156662\pi$
$308$		0			0
$309$	−13.1869	−	29.4868i	−0.750177	−	1.67745i
$310$	−3.00000	+	3.00000i	−0.170389	+	0.170389i
$311$	21.1760			1.20078			0.600389	−	0.799708i	$-0.295012\pi$
$311$	21.1760			1.20078			0.600389	+	0.799708i	$0.295012\pi$
$312$	2.89100	−	5.53553i	0.163670	−	0.313388i
$313$	−18.6491			−1.05411			−0.527055	−	0.849831i	$-0.676704\pi$
$313$	−18.6491			−1.05411			−0.527055	+	0.849831i	$0.676704\pi$
$314$	16.3782	−	16.3782i	0.924276	−	0.924276i
$315$		0			0
$316$			10.0000i			0.562544i
$317$	−17.8885	+	17.8885i	−1.00472	+	1.00472i	−0.00473191	+	0.999989i	$0.501506\pi$
$317$	−17.8885	+	17.8885i	−1.00472	+	1.00472i	−0.999989	+	0.00473191i	$0.998494\pi$
$318$	−2.28825	−	0.874032i	−0.128318	−	0.0490133i
$319$	−6.32456	+	6.32456i	−0.354107	+	0.354107i
$320$	0.707107	+	0.707107i	0.0395285	+	0.0395285i
$321$	5.32456	+	11.9061i	0.297188	+	0.664532i
$322$		0			0
$323$	−37.6875	−	37.6875i	−2.09699	−	2.09699i
$324$	−8.94427	+	1.00000i	−0.496904	+	0.0555556i
$325$	−3.58114	−	0.418861i	−0.198646	−	0.0232342i
$326$		−	3.28742i		−	0.182073i
$327$	11.0699	+	4.22832i	0.612167	+	0.233827i
$328$	3.16228			0.174608
$329$		0			0
$330$	1.23607	−	3.23607i	0.0680433	−	0.178140i
$331$	−9.48683	−	9.48683i	−0.521443	−	0.521443i	0.396564	−	0.918007i	$-0.370203\pi$
$331$	−9.48683	−	9.48683i	−0.521443	−	0.521443i	−0.918007	+	0.396564i	$0.870203\pi$
$332$	5.65685	+	5.65685i	0.310460	+	0.310460i
$333$	0.944272	+	16.9443i	0.0517458	+	0.928540i
$334$	2.32456			0.127194
$335$	10.1290			0.553406
$336$		0			0
$337$			30.6491i			1.66956i	0.550581	+	0.834782i	$0.314406\pi$
$337$			30.6491i			1.66956i	−0.550581	+	0.834782i	$0.685594\pi$
$338$	−11.0656	+	6.82295i	−0.601889	+	0.371120i
$339$	11.4868	+	25.6853i	0.623879	+	1.39504i
$340$	−5.16228	−	5.16228i	−0.279964	−	0.279964i
$341$			8.48528i			0.459504i
$342$	−14.6011	+	16.3246i	−0.789538	+	0.882731i
$343$		0			0
$344$	−5.06450	+	5.06450i	−0.273059	+	0.273059i
$345$	−2.76393	+	7.23607i	−0.148805	+	0.389577i
$346$	−15.6491	+	15.6491i	−0.841301	+	0.841301i
$347$			7.53006i			0.404235i	0.979361	+	0.202117i	$0.0647822\pi$
$347$			7.53006i			0.404235i	−0.979361	+	0.202117i	$0.935218\pi$
$348$	7.07107	−	3.16228i	0.379049	−	0.169516i
$349$	−0.837722	+	0.837722i	−0.0448422	+	0.0448422i	−0.729172	−	0.684330i	$-0.760095\pi$
$349$	−0.837722	+	0.837722i	−0.0448422	+	0.0448422i	0.684330	+	0.729172i	$0.260095\pi$
$350$		0			0
$351$	17.0635	+	7.73553i	0.910780	+	0.412892i
$352$	2.00000			0.106600
$353$	9.17377	−	9.17377i	0.488270	−	0.488270i	−0.419490	−	0.907760i	$-0.637791\pi$
$353$	9.17377	−	9.17377i	0.488270	−	0.488270i	0.907760	+	0.419490i	$0.137791\pi$
$354$	−13.1623	+	5.88635i	−0.699567	+	0.312856i
$355$			5.48683i			0.291211i
$356$	0.592359	−	0.592359i	0.0313950	−	0.0313950i
$357$		0			0
$358$	0.324555	−	0.324555i	0.0171533	−	0.0171533i
$359$	−22.4940	−	22.4940i	−1.18719	−	1.18719i	−0.977841	−	0.209350i	$-0.932865\pi$
$359$	−22.4940	−	22.4940i	−1.18719	−	1.18719i	−0.209350	−	0.977841i	$-0.567135\pi$
$360$	−2.00000	+	2.23607i	−0.105409	+	0.117851i
$361$			34.2982i			1.80517i
$362$	3.05792	+	3.05792i	0.160721	+	0.160721i
$363$	4.94975	+	11.0680i	0.259794	+	0.580918i
$364$		0			0
$365$			7.30056i			0.382129i
$366$	−6.58151	+	17.2306i	−0.344021	+	0.900659i
$367$	18.6491			0.973476			0.486738	−	0.873548i	$-0.338187\pi$
$367$	18.6491			0.973476			0.486738	+	0.873548i	$0.338187\pi$
$368$	−4.47214			−0.233126
$369$	0.527864	+	9.47214i	0.0274795	+	0.493100i
$370$	4.00000	+	4.00000i	0.207950	+	0.207950i
$371$		0			0
$372$	2.62210	−	6.86474i	0.135949	−	0.355920i
$373$	15.1623			0.785073			0.392536	−	0.919736i	$-0.371598\pi$
$373$	15.1623			0.785073			0.392536	+	0.919736i	$0.371598\pi$
$374$	−14.6011			−0.755006
$375$	1.61803	+	0.618034i	0.0835549	+	0.0319151i
$376$		−	10.3246i		−	0.532448i
$377$	−16.0153	−	1.87320i	−0.824832	−	0.0964749i
$378$		0			0
$379$	−13.1623	−	13.1623i	−0.676101	−	0.676101i	0.283015	−	0.959116i	$-0.408665\pi$
$379$	−13.1623	−	13.1623i	−0.676101	−	0.676101i	−0.959116	+	0.283015i	$0.908665\pi$
$380$			7.30056i			0.374511i
$381$	12.0022	+	26.8377i	0.614891	+	1.37494i
$382$	1.48683	+	1.48683i	0.0760730	+	0.0760730i
$383$	4.93113	−	4.93113i	0.251969	−	0.251969i	−0.569809	−	0.821777i	$-0.692983\pi$
$383$	4.93113	−	4.93113i	0.251969	−	0.251969i	0.821777	+	0.569809i	$0.192983\pi$
$384$	−1.61803	−	0.618034i	−0.0825700	−	0.0315389i
$385$		0			0
$386$			4.93113i			0.250988i
$387$	−16.0153	−	14.3246i	−0.814105	−	0.728158i
$388$	−1.16228	+	1.16228i	−0.0590057	+	0.0590057i
$389$	−29.9280			−1.51741			−0.758704	−	0.651435i	$-0.774167\pi$
$389$	−29.9280			−1.51741			−0.758704	+	0.651435i	$0.774167\pi$
$390$	5.95846	−	1.86997i	0.301718	−	0.0946896i
$391$	32.6491			1.65114
$392$	4.94975	−	4.94975i	0.250000	−	0.250000i
$393$	−0.324555	−	0.725728i	−0.0163717	−	0.0366081i
$394$			12.6491i			0.637253i
$395$	−7.07107	+	7.07107i	−0.355784	+	0.355784i
$396$	0.333851	+	5.99070i	0.0167766	+	0.301044i
$397$	−12.8377	+	12.8377i	−0.644307	+	0.644307i	−0.951611	−	0.307304i	$-0.900573\pi$
$397$	−12.8377	+	12.8377i	−0.644307	+	0.644307i	0.307304	+	0.951611i	$0.400573\pi$
$398$	−1.41421	−	1.41421i	−0.0708881	−	0.0708881i
$399$		0			0
$400$			1.00000i			0.0500000i
$401$	15.1935	+	15.1935i	0.758726	+	0.758726i	0.976091	−	0.217364i	$-0.0697459\pi$
$401$	15.1935	+	15.1935i	0.758726	+	0.758726i	−0.217364	+	0.976091i	$0.569746\pi$
$402$	−16.0153	+	7.16228i	−0.798773	+	0.357222i
$403$	−12.0000	+	9.48683i	−0.597763	+	0.472573i
$404$		−	6.84157i		−	0.340381i
$405$	−7.03166	−	5.61745i	−0.349406	−	0.279133i
$406$		0			0
$407$	11.3137			0.560800
$408$	11.8126	+	4.51200i	0.584809	+	0.223377i
$409$	10.6754	+	10.6754i	0.527867	+	0.527867i	0.919936	−	0.392069i	$-0.128241\pi$
$409$	10.6754	+	10.6754i	0.527867	+	0.527867i	−0.392069	+	0.919936i	$0.628241\pi$
$410$	2.23607	+	2.23607i	0.110432	+	0.110432i
$411$	−32.8858	−	12.5613i	−1.62214	−	0.619602i
$412$	18.6491			0.918776
$413$		0			0
$414$	−0.746512	−	13.3956i	−0.0366891	−	0.658359i
$415$			8.00000i			0.392705i
$416$	2.23607	+	2.82843i	0.109632	+	0.138675i
$417$	−10.0000	+	4.47214i	−0.489702	+	0.219001i
$418$	10.3246	+	10.3246i	0.504991	+	0.504991i
$419$			40.5160i			1.97933i	0.143384	+	0.989667i	$0.454202\pi$
$419$			40.5160i			1.97933i	−0.143384	+	0.989667i	$0.545798\pi$
$420$		0			0
$421$	−12.8377	−	12.8377i	−0.625672	−	0.625672i	0.321304	−	0.946976i	$-0.395879\pi$
$421$	−12.8377	−	12.8377i	−0.625672	−	0.625672i	−0.946976	+	0.321304i	$0.895879\pi$
$422$	2.36944	−	2.36944i	0.115342	−	0.115342i
$423$	30.9257	−	1.72343i	1.50366	−	0.0837960i
$424$	1.00000	−	1.00000i	0.0485643	−	0.0485643i
$425$		−	7.30056i		−	0.354129i
$426$	−3.87978	−	8.67544i	−0.187976	−	0.420327i
$427$		0			0
$428$	−7.53006			−0.363979
$429$	5.78199	−	11.0711i	0.279157	−	0.534516i
$430$	−7.16228			−0.345396
$431$	−1.77708	+	1.77708i	−0.0855988	+	0.0855988i	−0.748610	−	0.663011i	$-0.769278\pi$
$431$	−1.77708	+	1.77708i	−0.0855988	+	0.0855988i	0.663011	+	0.748610i	$0.269278\pi$
$432$	1.58114	−	4.94975i	0.0760726	−	0.238145i
$433$		−	39.2982i		−	1.88855i	−0.329155	−	0.944276i	$-0.606764\pi$
$433$		−	39.2982i		−	1.88855i	0.329155	−	0.944276i	$-0.393236\pi$
$434$		0			0
$435$	7.23607	+	2.76393i	0.346943	+	0.132520i
$436$	−4.83772	+	4.83772i	−0.231685	+	0.231685i
$437$	−23.0864	−	23.0864i	−1.10437	−	1.10437i
$438$	−5.16228	−	11.5432i	−0.246663	−	0.551556i
$439$			3.35089i			0.159929i	0.996798	+	0.0799646i	$0.0254807\pi$
$439$			3.35089i			0.159929i	−0.996798	+	0.0799646i	$0.974519\pi$
$440$	1.41421	+	1.41421i	0.0674200	+	0.0674200i
$441$	15.6525	+	14.0000i	0.745356	+	0.666667i
$442$	−16.3246	−	20.6491i	−0.776480	−	0.982178i
$443$			10.3585i			0.492146i	0.969251	+	0.246073i	$0.0791404\pi$
$443$			10.3585i			0.492146i	−0.969251	+	0.246073i	$0.920860\pi$
$444$	−9.15298	−	3.49613i	−0.434381	−	0.165919i
$445$	0.837722			0.0397118
$446$	23.5454			1.11491
$447$	−2.27155	+	5.94699i	−0.107441	+	0.281283i
$448$		0			0
$449$	14.0088	+	14.0088i	0.661115	+	0.661115i	0.955643	−	0.294528i	$-0.0951625\pi$
$449$	14.0088	+	14.0088i	0.661115	+	0.661115i	−0.294528	+	0.955643i	$0.595162\pi$
$450$	−2.99535	+	0.166925i	−0.141202	+	0.00786893i
$451$	6.32456			0.297812
$452$	−16.2448			−0.764093
$453$	−0.590360	+	1.54558i	−0.0277375	+	0.0726178i
$454$		−	18.0000i		−	0.844782i
$455$		0			0
$456$	−5.16228	−	11.5432i	−0.241746	−	0.540560i
$457$	3.48683	+	3.48683i	0.163107	+	0.163107i	0.783942	−	0.620834i	$-0.213206\pi$
$457$	3.48683	+	3.48683i	0.163107	+	0.163107i	−0.620834	+	0.783942i	$0.713206\pi$
$458$			19.5323i			0.912682i
$459$	−11.5432	+	36.1359i	−0.538791	+	1.68668i
$460$	−3.16228	−	3.16228i	−0.147442	−	0.147442i
$461$	−21.6722	+	21.6722i	−1.00937	+	1.00937i	−0.00941906	+	0.999956i	$0.502998\pi$
$461$	−21.6722	+	21.6722i	−1.00937	+	1.00937i	−0.999956	+	0.00941906i	$0.997002\pi$
$462$		0			0
$463$	8.32456	−	8.32456i	0.386875	−	0.386875i	−0.486696	−	0.873571i	$-0.661798\pi$
$463$	8.32456	−	8.32456i	0.386875	−	0.386875i	0.873571	+	0.486696i	$0.161798\pi$
$464$			4.47214i			0.207614i
$465$	6.70820	−	3.00000i	0.311086	−	0.139122i
$466$	−2.83772	+	2.83772i	−0.131455	+	0.131455i
$467$	33.9039			1.56888			0.784442	−	0.620202i	$-0.212949\pi$
$467$	33.9039			1.56888			0.784442	+	0.620202i	$0.212949\pi$
$468$	−8.09888	+	7.16995i	−0.374371	+	0.331431i
$469$		0			0
$470$	7.30056	−	7.30056i	0.336750	−	0.336750i
$471$	−36.6228	+	16.3782i	−1.68749	+	0.754668i
$472$		−	8.32456i		−	0.383169i
$473$	−10.1290	+	10.1290i	−0.465731	+	0.465731i
$474$	6.18034	−	16.1803i	0.283872	−	0.743188i
$475$	−5.16228	+	5.16228i	−0.236862	+	0.236862i
$476$		0			0
$477$	3.16228	+	2.82843i	0.144791	+	0.129505i
$478$		−	11.1623i		−	0.510551i
$479$	0.133369	+	0.133369i	0.00609377	+	0.00609377i	0.710147	−	0.704053i	$-0.248628\pi$
$479$	0.133369	+	0.133369i	0.00609377	+	0.00609377i	−0.704053	+	0.710147i	$0.748628\pi$
$480$	−0.707107	−	1.58114i	−0.0322749	−	0.0721688i
$481$	12.6491	+	16.0000i	0.576750	+	0.729537i
$482$		−	10.8175i		−	0.492723i
$483$		0			0
$484$	−7.00000			−0.318182
$485$	−1.64371			−0.0746370
$486$	15.0902	+	3.90983i	0.684504	+	0.177353i
$487$	−18.0000	−	18.0000i	−0.815658	−	0.815658i	0.169818	−	0.985476i	$-0.445682\pi$
$487$	−18.0000	−	18.0000i	−0.815658	−	0.815658i	−0.985476	+	0.169818i	$0.945682\pi$
$488$	−7.53006	−	7.53006i	−0.340870	−	0.340870i
$489$	−2.03174	+	5.31915i	−0.0918783	+	0.240540i
$490$	7.00000			0.316228
$491$	28.2843			1.27645			0.638226	−	0.769849i	$-0.279669\pi$
$491$	28.2843			1.27645			0.638226	+	0.769849i	$0.279669\pi$
$492$	−5.11667	−	1.95440i	−0.230677	−	0.0881109i
$493$		−	32.6491i		−	1.47044i
$494$	−3.05792	+	26.1443i	−0.137582	+	1.17629i
$495$	−4.00000	+	4.47214i	−0.179787	+	0.201008i
$496$	3.00000	+	3.00000i	0.134704	+	0.134704i
$497$		0			0
$498$	−5.65685	−	12.6491i	−0.253490	−	0.566820i
$499$	−11.1623	−	11.1623i	−0.499692	−	0.499692i	0.411650	−	0.911342i	$-0.364953\pi$
$499$	−11.1623	−	11.1623i	−0.499692	−	0.499692i	−0.911342	+	0.411650i	$0.864953\pi$
$500$	−0.707107	+	0.707107i	−0.0316228	+	0.0316228i
$501$	−3.76121	−	1.43665i	−0.168038	−	0.0641850i
$502$	10.3246	−	10.3246i	0.460807	−	0.460807i
$503$		−	25.1891i		−	1.12313i	−0.827434	−	0.561563i	$-0.810200\pi$
$503$		−	25.1891i		−	1.12313i	0.827434	−	0.561563i	$-0.189800\pi$
$504$		0			0
$505$	4.83772	−	4.83772i	0.215276	−	0.215276i
$506$	−8.94427			−0.397621
$507$	22.1213	−	4.20086i	0.982442	−	0.186567i
$508$	−16.9737			−0.753085
$509$	14.3716	−	14.3716i	0.637011	−	0.637011i	−0.312806	−	0.949817i	$-0.601269\pi$
$509$	14.3716	−	14.3716i	0.637011	−	0.637011i	0.949817	+	0.312806i	$0.101269\pi$
$510$	5.16228	+	11.5432i	0.228589	+	0.511142i
$511$		0			0
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	33.7142	−	17.3897i	1.48852	−	0.767774i
$514$	−1.16228	+	1.16228i	−0.0512659	+	0.0512659i
$515$	13.1869	+	13.1869i	0.581085	+	0.581085i
$516$	11.3246	−	5.06450i	0.498536	−	0.222952i
$517$		−	20.6491i		−	0.908147i
$518$		0			0
$519$	34.9925	−	15.6491i	1.53600	−	0.686920i
$520$	−0.418861	+	3.58114i	−0.0183683	+	0.157043i
$521$		−	2.10270i		−	0.0921209i	−0.998939	−	0.0460605i	$-0.985333\pi$
$521$		−	2.10270i		−	0.0921209i	0.998939	−	0.0460605i	$-0.0146667\pi$
$522$	−13.3956	+	0.746512i	−0.586310	+	0.0326740i
$523$	−35.8114			−1.56592			−0.782961	−	0.622070i	$-0.786292\pi$
$523$	−35.8114			−1.56592			−0.782961	+	0.622070i	$0.786292\pi$
$524$	0.458991			0.0200511
$525$		0			0
$526$	0.837722	+	0.837722i	0.0365264	+	0.0365264i
$527$	−21.9017	−	21.9017i	−0.954053	−	0.954053i
$528$	−3.23607	−	1.23607i	−0.140832	−	0.0537930i
$529$	−3.00000			−0.130435
$530$	1.41421			0.0614295
$531$	24.9350	−	1.38958i	1.08209	−	0.0603026i
$532$		0			0
$533$	7.07107	+	8.94427i	0.306282	+	0.387419i
$534$	−1.32456	+	0.592359i	−0.0573191	+	0.0256339i
$535$	−5.32456	−	5.32456i	−0.230201	−	0.230201i
$536$		−	10.1290i		−	0.437506i
$537$	−0.725728	+	0.324555i	−0.0313175	+	0.0140056i
$538$	−3.16228	−	3.16228i	−0.136335	−	0.136335i
$539$	9.89949	−	9.89949i	0.426401	−	0.426401i
$540$	4.61803	−	2.38197i	0.198729	−	0.102503i
$541$	29.8114	−	29.8114i	1.28169	−	1.28169i	0.341987	−	0.939705i	$-0.388900\pi$
$541$	29.8114	−	29.8114i	1.28169	−	1.28169i	0.939705	−	0.341987i	$-0.111100\pi$
$542$			10.3585i			0.444935i
$543$	−3.05792	−	6.83772i	−0.131228	−	0.293435i
$544$	−5.16228	+	5.16228i	−0.221331	+	0.221331i
$545$	−6.84157			−0.293061
$546$		0			0
$547$	−9.48683			−0.405628			−0.202814	−	0.979217i	$-0.565009\pi$
$547$	−9.48683			−0.405628			−0.202814	+	0.979217i	$0.565009\pi$
$548$	14.3716	−	14.3716i	0.613926	−	0.613926i
$549$	21.2982	−	23.8121i	0.908986	−	1.01628i
$550$			2.00000i			0.0852803i
$551$	−23.0864	+	23.0864i	−0.983514	+	0.983514i
$552$	7.23607	+	2.76393i	0.307988	+	0.117641i
$553$		0			0
$554$	−2.23607	−	2.23607i	−0.0950014	−	0.0950014i
$555$	−4.00000	−	8.94427i	−0.169791	−	0.379663i
$556$		−	6.32456i		−	0.268221i
$557$	−11.7727	−	11.7727i	−0.498825	−	0.498825i	0.412247	−	0.911072i	$-0.364744\pi$
$557$	−11.7727	−	11.7727i	−0.498825	−	0.498825i	−0.911072	+	0.412247i	$0.864744\pi$
$558$	−8.48528	+	9.48683i	−0.359211	+	0.401610i
$559$	−25.6491	−	3.00000i	−1.08484	−	0.126886i
$560$		0			0
$561$	23.6251	+	9.02399i	0.997453	+	0.380993i
$562$	24.8377			1.04772
$563$	−11.2765			−0.475246			−0.237623	−	0.971357i	$-0.576368\pi$
$563$	−11.2765			−0.475246			−0.237623	+	0.971357i	$0.576368\pi$
$564$	−6.38093	+	16.7055i	−0.268685	+	0.703428i
$565$	−11.4868	−	11.4868i	−0.483255	−	0.483255i
$566$	9.07764	+	9.07764i	0.381562	+	0.381562i
$567$		0			0
$568$	5.48683			0.230222
$569$	−2.10270			−0.0881497			−0.0440749	−	0.999028i	$-0.514034\pi$
$569$	−2.10270			−0.0881497			−0.0440749	+	0.999028i	$0.514034\pi$
$570$	4.51200	−	11.8126i	0.188987	−	0.494774i
$571$			18.9737i			0.794023i	0.917814	+	0.397012i	$0.129953\pi$
$571$			18.9737i			0.794023i	−0.917814	+	0.397012i	$0.870047\pi$
$572$	4.47214	+	5.65685i	0.186989	+	0.236525i
$573$	−1.48683	−	3.32466i	−0.0621133	−	0.138890i
$574$		0			0
$575$		−	4.47214i		−	0.186501i
$576$	2.23607	+	2.00000i	0.0931695	+	0.0833333i
$577$	−21.1623	−	21.1623i	−0.880997	−	0.880997i	0.112639	−	0.993636i	$-0.464070\pi$
$577$	−21.1623	−	21.1623i	−0.880997	−	0.880997i	−0.993636	+	0.112639i	$0.964070\pi$
$578$	25.6667	−	25.6667i	1.06759	−	1.06759i
$579$	3.04760	−	7.97873i	0.126654	−	0.331585i
$580$	−3.16228	+	3.16228i	−0.131306	+	0.131306i
$581$		0			0
$582$	2.59893	−	1.16228i	0.107729	−	0.0481780i
$583$	2.00000	−	2.00000i	0.0828315	−	0.0828315i
$584$	7.30056			0.302099
$585$	−10.7967	−	0.656854i	−0.446388	−	0.0271576i
$586$	4.00000			0.165238
$587$	−0.458991	+	0.458991i	−0.0189446	+	0.0189446i	−0.716516	−	0.697571i	$-0.754264\pi$
$587$	−0.458991	+	0.458991i	−0.0189446	+	0.0189446i	0.697571	+	0.716516i	$0.254264\pi$
$588$	−11.0680	+	4.94975i	−0.456435	+	0.204124i
$589$			30.9737i			1.27625i
$590$	5.88635	−	5.88635i	0.242337	−	0.242337i
$591$	7.81758	−	20.4667i	0.321572	−	0.841887i
$592$	4.00000	−	4.00000i	0.164399	−	0.164399i
$593$	31.0755	+	31.0755i	1.27612	+	1.27612i	0.942823	+	0.333293i	$0.108160\pi$
$593$	31.0755	+	31.0755i	1.27612	+	1.27612i	0.333293	+	0.942823i	$0.391840\pi$
$594$	3.16228	−	9.89949i	0.129750	−	0.406181i
$595$		0			0
$596$	−2.59893	−	2.59893i	−0.106456	−	0.106456i
$597$	1.41421	+	3.16228i	0.0578799	+	0.129423i
$598$	−10.0000	−	12.6491i	−0.408930	−	0.517261i
$599$		−	41.7007i		−	1.70384i	−0.523669	−	0.851922i	$-0.675437\pi$
$599$		−	41.7007i		−	1.70384i	0.523669	−	0.851922i	$-0.324563\pi$
$600$	0.618034	−	1.61803i	0.0252311	−	0.0660560i
$601$	−24.6491			−1.00546			−0.502729	−	0.864444i	$-0.667671\pi$
$601$	−24.6491			−1.00546			−0.502729	+	0.864444i	$0.667671\pi$
$602$		0			0
$603$	30.3399	−	1.69078i	1.23554	−	0.0688541i
$604$	−0.675445	−	0.675445i	−0.0274835	−	0.0274835i
$605$	−4.94975	−	4.94975i	−0.201236	−	0.201236i
$606$	−4.22832	+	11.0699i	−0.171764	+	0.449684i
$607$	−21.6228			−0.877641			−0.438821	−	0.898575i	$-0.644604\pi$
$607$	−21.6228			−0.877641			−0.438821	+	0.898575i	$0.644604\pi$
$608$	7.30056			0.296077
$609$		0			0
$610$		−	10.6491i		−	0.431170i
$611$	29.2023	−	23.0864i	1.18140	−	0.933976i
$612$	−16.3246	−	14.6011i	−0.659881	−	0.590216i
$613$	−22.3246	−	22.3246i	−0.901680	−	0.901680i	0.0939012	−	0.995582i	$-0.470066\pi$
$613$	−22.3246	−	22.3246i	−0.901680	−	0.901680i	−0.995582	+	0.0939012i	$0.970066\pi$
$614$		−	10.1290i		−	0.408773i
$615$	−2.23607	−	5.00000i	−0.0901670	−	0.201619i
$616$		0			0
$617$	−18.3848	+	18.3848i	−0.740143	+	0.740143i	−0.972605	−	0.232462i	$-0.925322\pi$
$617$	−18.3848	+	18.3848i	−0.740143	+	0.740143i	0.232462	+	0.972605i	$0.425322\pi$
$618$	−30.1749	−	11.5258i	−1.21381	−	0.463635i
$619$	29.4868	−	29.4868i	1.18518	−	1.18518i	0.206791	−	0.978385i	$-0.433698\pi$
$619$	29.4868	−	29.4868i	1.18518	−	1.18518i	0.978385	−	0.206791i	$-0.0663019\pi$
$620$			4.24264i			0.170389i
$621$	−7.07107	+	22.1359i	−0.283752	+	0.888285i
$622$	14.9737	−	14.9737i	0.600389	−	0.600389i
$623$		0			0
$624$	−1.86997	−	5.95846i	−0.0748587	−	0.238529i
$625$	−1.00000			−0.0400000
$626$	−13.1869	+	13.1869i	−0.527055	+	0.527055i
$627$	−10.3246	−	23.0864i	−0.412323	−	0.921982i
$628$		−	23.1623i		−	0.924276i
$629$	−29.2023	+	29.2023i	−1.16437	+	1.16437i
$630$		0			0
$631$	13.3246	−	13.3246i	0.530442	−	0.530442i	−0.390262	−	0.920704i	$-0.627615\pi$
$631$	13.3246	−	13.3246i	0.530442	−	0.530442i	0.920704	+	0.390262i	$0.127615\pi$
$632$	7.07107	+	7.07107i	0.281272	+	0.281272i
$633$	−5.29822	+	2.36944i	−0.210585	+	0.0941766i
$634$			25.2982i			1.00472i
$635$	−12.0022	−	12.0022i	−0.476293	−	0.476293i
$636$	−2.23607	+	1.00000i	−0.0886659	+	0.0396526i
$637$	25.0680	+	2.93203i	0.993229	+	0.116171i
$638$			8.94427i			0.354107i
$639$	0.915891	+	16.4350i	0.0362321	+	0.650158i
$640$	1.00000			0.0395285
$641$	35.7771			1.41311			0.706555	−	0.707658i	$-0.250248\pi$
$641$	35.7771			1.41311			0.706555	+	0.707658i	$0.250248\pi$
$642$	12.1839	+	4.65383i	0.480860	+	0.183672i
$643$	32.6491	+	32.6491i	1.28756	+	1.28756i	0.936268	+	0.351288i	$0.114256\pi$
$643$	32.6491	+	32.6491i	1.28756	+	1.28756i	0.351288	+	0.936268i	$0.385744\pi$
$644$		0			0
$645$	11.5888	+	4.42653i	0.456309	+	0.174294i
$646$	−53.2982			−2.09699
$647$	−46.8985			−1.84377			−0.921886	−	0.387461i	$-0.873352\pi$
$647$	−46.8985			−1.84377			−0.921886	+	0.387461i	$0.873352\pi$
$648$	−5.61745	+	7.03166i	−0.220674	+	0.276230i
$649$		−	16.6491i		−	0.653535i
$650$	−2.82843	+	2.23607i	−0.110940	+	0.0877058i
$651$		0			0
$652$	−2.32456	−	2.32456i	−0.0910366	−	0.0910366i
$653$			5.61961i			0.219912i	0.993936	+	0.109956i	$0.0350711\pi$
$653$			5.61961i			0.219912i	−0.993936	+	0.109956i	$0.964929\pi$
$654$	10.8175	−	4.83772i	0.422997	−	0.189170i
$655$	0.324555	+	0.324555i	0.0126814	+	0.0126814i
$656$	2.23607	−	2.23607i	0.0873038	−	0.0873038i
$657$	1.21865	+	21.8678i	0.0475440	+	0.853143i
$658$		0			0
$659$			8.94427i			0.348419i	0.984709	+	0.174210i	$0.0557371\pi$
$659$			8.94427i			0.348419i	−0.984709	+	0.174210i	$0.944263\pi$
$660$	−1.41421	−	3.16228i	−0.0550482	−	0.123091i
$661$	−10.8377	+	10.8377i	−0.421539	+	0.421539i	−0.885733	−	0.464195i	$-0.846344\pi$
$661$	−10.8377	+	10.8377i	−0.421539	+	0.421539i	0.464195	+	0.885733i	$0.346344\pi$
$662$	−13.4164			−0.521443
$663$	13.6518	+	43.5001i	0.530193	+	1.68940i
$664$	8.00000			0.310460
$665$		0			0
$666$	12.6491	+	11.3137i	0.490143	+	0.438397i
$667$		−	20.0000i		−	0.774403i
$668$	1.64371	−	1.64371i	0.0635970	−	0.0635970i
$669$	−38.0973	−	14.5519i	−1.47292	−	0.562607i
$670$	7.16228	−	7.16228i	0.276703	−	0.276703i
$671$	−15.0601	−	15.0601i	−0.581389	−	0.581389i
$672$		0			0
$673$			19.6754i			0.758433i	0.925308	+	0.379216i	$0.123806\pi$
$673$			19.6754i			0.758433i	−0.925308	+	0.379216i	$0.876194\pi$
$674$	21.6722	+	21.6722i	0.834782	+	0.834782i
$675$	4.94975	+	1.58114i	0.190516	+	0.0608581i
$676$	−3.00000	+	12.6491i	−0.115385	+	0.486504i
$677$			4.70163i			0.180698i	0.995910	+	0.0903492i	$0.0287983\pi$
$677$			4.70163i			0.180698i	−0.995910	+	0.0903492i	$0.971202\pi$
$678$	26.2847	+	10.0399i	1.00946	+	0.385579i
$679$		0			0
$680$	−7.30056			−0.279964
$681$	−11.1246	+	29.1246i	−0.426296	+	1.11606i
$682$	6.00000	+	6.00000i	0.229752	+	0.229752i
$683$	4.24264	+	4.24264i	0.162340	+	0.162340i	0.783603	−	0.621262i	$-0.213380\pi$
$683$	4.24264	+	4.24264i	0.162340	+	0.162340i	−0.621262	+	0.783603i	$0.713380\pi$
$684$	1.21865	+	21.8678i	0.0465962	+	0.836135i
$685$	20.3246			0.776561
$686$		0			0
$687$	12.0716	−	31.6038i	0.460560	−	1.20576i
$688$			7.16228i			0.273059i
$689$	5.06450	+	0.592359i	0.192942	+	0.0225671i
$690$	3.16228	+	7.07107i	0.120386	+	0.269191i
$691$	−35.8114	−	35.8114i	−1.36233	−	1.36233i	−0.870940	−	0.491389i	$-0.836489\pi$
$691$	−35.8114	−	35.8114i	−1.36233	−	1.36233i	−0.491389	−	0.870940i	$-0.663511\pi$
$692$			22.1312i			0.841301i
$693$		0			0
$694$	5.32456	+	5.32456i	0.202117	+	0.202117i
$695$	4.47214	−	4.47214i	0.169638	−	0.169638i
$696$	2.76393	−	7.23607i	0.104767	−	0.274282i
$697$	−16.3246	+	16.3246i	−0.618337	+	0.618337i
$698$			1.18472i			0.0448422i
$699$	6.34534	−	2.83772i	0.240003	−	0.107333i
$700$		0			0
$701$	−39.3312			−1.48552			−0.742760	−	0.669557i	$-0.766484\pi$
$701$	−39.3312			−1.48552			−0.742760	+	0.669557i	$0.766484\pi$
$702$	17.5355	−	6.59584i	0.661836	−	0.248944i
$703$	41.2982			1.55759
$704$	1.41421	−	1.41421i	0.0533002	−	0.0533002i
$705$	−16.3246	+	7.30056i	−0.614818	+	0.274955i
$706$		−	12.9737i		−	0.488270i
$707$		0			0
$708$	−5.14486	+	13.4694i	−0.193356	+	0.506212i
$709$	−15.4868	+	15.4868i	−0.581620	+	0.581620i	−0.935348	−	0.353728i	$-0.884914\pi$
$709$	−15.4868	+	15.4868i	−0.581620	+	0.581620i	0.353728	+	0.935348i	$0.384914\pi$
$710$	3.87978	+	3.87978i	0.145605	+	0.145605i
$711$	−20.0000	+	22.3607i	−0.750059	+	0.838591i
$712$		−	0.837722i		−	0.0313950i
$713$	−13.4164	−	13.4164i	−0.502448	−	0.502448i
$714$		0			0
$715$	−0.837722	+	7.16228i	−0.0313290	+	0.267854i
$716$		−	0.458991i		−	0.0171533i
$717$	−6.89867	+	18.0609i	−0.257635	+	0.674498i
$718$	−31.8114			−1.18719
$719$	−2.10270			−0.0784175			−0.0392087	−	0.999231i	$-0.512484\pi$
$719$	−2.10270			−0.0784175			−0.0392087	+	0.999231i	$0.512484\pi$
$720$	0.166925	+	2.99535i	0.00622094	+	0.111630i
$721$		0			0
$722$	24.2525	+	24.2525i	0.902585	+	0.902585i
$723$	−6.68557	+	17.5030i	−0.248639	+	0.650945i
$724$	4.32456			0.160721
$725$	−4.47214			−0.166091
$726$	11.3262	+	4.32624i	0.420356	+	0.160562i
$727$		−	4.97367i		−	0.184463i	−0.995738	−	0.0922315i	$-0.970600\pi$
$727$		−	4.97367i		−	0.184463i	0.995738	−	0.0922315i	$-0.0294000\pi$
$728$		0			0
$729$	−22.0000	−	15.6525i	−0.814815	−	0.579721i
$730$	5.16228	+	5.16228i	0.191064	+	0.191064i
$731$		−	52.2887i		−	1.93397i
$732$	7.53006	+	16.8377i	0.278319	+	0.622340i
$733$	−33.4868	−	33.4868i	−1.23686	−	1.23686i	−0.961276	−	0.275589i	$-0.911127\pi$
$733$	−33.4868	−	33.4868i	−1.23686	−	1.23686i	−0.275589	−	0.961276i	$-0.588873\pi$
$734$	13.1869	−	13.1869i	0.486738	−	0.486738i
$735$	−11.3262	−	4.32624i	−0.417775	−	0.159576i
$736$	−3.16228	+	3.16228i	−0.116563	+	0.116563i
$737$		−	20.2580i		−	0.746212i
$738$	7.07107	+	6.32456i	0.260290	+	0.232810i
$739$	12.1359	−	12.1359i	0.446428	−	0.446428i	−0.447737	−	0.894165i	$-0.647770\pi$
$739$	12.1359	−	12.1359i	0.446428	−	0.446428i	0.894165	+	0.447737i	$0.147770\pi$
$740$	5.65685			0.207950
$741$	21.1059	−	40.4125i	0.775345	−	1.48459i
$742$		0			0
$743$	−27.5585	+	27.5585i	−1.01102	+	1.01102i	−0.0110864	+	0.999939i	$0.503529\pi$
$743$	−27.5585	+	27.5585i	−1.01102	+	1.01102i	−0.999939	+	0.0110864i	$0.996471\pi$
$744$	−3.00000	−	6.70820i	−0.109985	−	0.245935i
$745$		−	3.67544i		−	0.134658i
$746$	10.7213	−	10.7213i	0.392536	−	0.392536i
$747$	1.33540	+	23.9628i	0.0488598	+	0.876754i
$748$	−10.3246	+	10.3246i	−0.377503	+	0.377503i
$749$		0			0
$750$	1.58114	−	0.707107i	0.0577350	−	0.0258199i
$751$		−	28.0000i		−	1.02173i	−0.859660	−	0.510867i	$-0.829324\pi$
$751$		−	28.0000i		−	1.02173i	0.859660	−	0.510867i	$-0.170676\pi$
$752$	−7.30056	−	7.30056i	−0.266224	−	0.266224i
$753$	−23.0864	+	10.3246i	−0.841315	+	0.376248i
$754$	−12.6491	+	10.0000i	−0.460653	+	0.364179i
$755$		−	0.955223i		−	0.0347641i
$756$		0			0
$757$	7.81139			0.283910			0.141955	−	0.989873i	$-0.454661\pi$
$757$	7.81139			0.283910			0.141955	+	0.989873i	$0.454661\pi$
$758$	−18.6143			−0.676101
$759$	14.4721	+	5.52786i	0.525305	+	0.200649i
$760$	5.16228	+	5.16228i	0.187255	+	0.187255i
$761$	1.51034	+	1.51034i	0.0547498	+	0.0547498i	0.733952	−	0.679202i	$-0.237674\pi$
$761$	1.51034	+	1.51034i	0.0547498	+	0.0547498i	−0.679202	+	0.733952i	$0.737674\pi$
$762$	27.4640	+	10.4903i	0.994915	+	0.380024i
$763$		0			0
$764$	2.10270			0.0760730
$765$	−1.21865	−	21.8678i	−0.0440603	−	0.790630i
$766$		−	6.97367i		−	0.251969i
$767$	23.5454	−	18.6143i	0.850175	−	0.672122i
$768$	−1.58114	+	0.707107i	−0.0570544	+	0.0255155i
$769$	6.35089	+	6.35089i	0.229019	+	0.229019i	0.812283	−	0.583264i	$-0.198225\pi$
$769$	6.35089	+	6.35089i	0.229019	+	0.229019i	−0.583264	+	0.812283i	$0.698225\pi$
$770$		0			0
$771$	2.59893	−	1.16228i	0.0935982	−	0.0418584i
$772$	3.48683	+	3.48683i	0.125494	+	0.125494i
$773$	−16.9706	+	16.9706i	−0.610389	+	0.610389i	−0.943047	−	0.332659i	$-0.892054\pi$
$773$	−16.9706	+	16.9706i	−0.610389	+	0.610389i	0.332659	+	0.943047i	$0.392054\pi$
$774$	−21.4535	+	1.19557i	−0.771132	+	0.0429737i
$775$	−3.00000	+	3.00000i	−0.107763	+	0.107763i
$776$			1.64371i			0.0590057i
$777$		0			0
$778$	−21.1623	+	21.1623i	−0.758704	+	0.758704i
$779$	23.0864			0.827156
$780$	2.89100	−	5.53553i	0.103514	−	0.198204i
$781$	10.9737			0.392669
$782$	23.0864	−	23.0864i	0.825568	−	0.825568i
$783$	22.1359	+	7.07107i	0.791074	+	0.252699i
$784$		−	7.00000i		−	0.250000i
$785$	16.3782	−	16.3782i	0.584563	−	0.584563i
$786$	−0.742662	−	0.283672i	−0.0264899	−	0.0101182i
$787$	−9.48683	+	9.48683i	−0.338169	+	0.338169i	−0.855678	−	0.517509i	$-0.826859\pi$
$787$	−9.48683	+	9.48683i	−0.338169	+	0.338169i	0.517509	+	0.855678i	$0.326859\pi$
$788$	8.94427	+	8.94427i	0.318626	+	0.318626i
$789$	−0.837722	−	1.87320i	−0.0298237	−	0.0666878i
$790$			10.0000i			0.355784i
$791$		0			0
$792$	4.47214	+	4.00000i	0.158910	+	0.142134i
$793$	4.46050	−	38.1359i	0.158397	−	1.35425i
$794$			18.1553i			0.644307i
$795$	−2.28825	−	0.874032i	−0.0811557	−	0.0309987i
$796$	−2.00000			−0.0708881
$797$	31.5344			1.11701			0.558504	−	0.829502i	$-0.311376\pi$
$797$	31.5344			1.11701			0.558504	+	0.829502i	$0.311376\pi$
$798$		0			0
$799$	53.2982	+	53.2982i	1.88556	+	1.88556i
$800$	0.707107	+	0.707107i	0.0250000	+	0.0250000i
$801$	2.50927	−	0.139837i	0.0886608	−	0.00494090i
$802$	21.4868			0.758726
$803$	14.6011			0.515263
$804$	−6.26006	+	16.3891i	−0.220775	+	0.577997i
$805$		0			0
$806$	−1.77708	+	15.1935i	−0.0625949	+	0.535168i
$807$	3.16228	+	7.07107i	0.111317	+	0.248913i
$808$	−4.83772	−	4.83772i	−0.170190	−	0.170190i
$809$			19.3400i			0.679958i	0.940433	+	0.339979i	$0.110420\pi$
$809$			19.3400i			0.679958i	−0.940433	+	0.339979i	$0.889580\pi$
$810$	−8.94427	+	1.00000i	−0.314270	+	0.0351364i
$811$	7.48683	+	7.48683i	0.262898	+	0.262898i	0.826230	−	0.563332i	$-0.190481\pi$
$811$	7.48683	+	7.48683i	0.262898	+	0.262898i	−0.563332	+	0.826230i	$0.690481\pi$
$812$		0			0
$813$	6.40190	−	16.7604i	0.224524	−	0.587812i
$814$	8.00000	−	8.00000i	0.280400	−	0.280400i
$815$		−	3.28742i		−	0.115153i
$816$	11.5432	−	5.16228i	0.404093	−	0.180716i
$817$	−36.9737	+	36.9737i	−1.29354	+	1.29354i
$818$	15.0974			0.527867
$819$		0			0
$820$	3.16228			0.110432
$821$	−39.5607	+	39.5607i	−1.38068	+	1.38068i	−0.537267	+	0.843412i	$0.680543\pi$
$821$	−39.5607	+	39.5607i	−1.38068	+	1.38068i	−0.843412	+	0.537267i	$0.819457\pi$
$822$	−32.1359	+	14.3716i	−1.12087	+	0.501268i
$823$		−	7.02633i		−	0.244923i	−0.992473	−	0.122461i	$-0.960921\pi$
$823$		−	7.02633i		−	0.244923i	0.992473	−	0.122461i	$-0.0390787\pi$
$824$	13.1869	−	13.1869i	0.459388	−	0.459388i
$825$	1.23607	−	3.23607i	0.0430344	−	0.112665i
$826$		0			0
$827$	−10.8175	−	10.8175i	−0.376160	−	0.376160i	0.493554	−	0.869715i	$-0.335697\pi$
$827$	−10.8175	−	10.8175i	−0.376160	−	0.376160i	−0.869715	+	0.493554i	$0.835697\pi$
$828$	−10.0000	−	8.94427i	−0.347524	−	0.310835i
$829$			14.0000i			0.486240i	0.969996	+	0.243120i	$0.0781709\pi$
$829$			14.0000i			0.486240i	−0.969996	+	0.243120i	$0.921829\pi$
$830$	5.65685	+	5.65685i	0.196352	+	0.196352i
$831$	2.23607	+	5.00000i	0.0775683	+	0.173448i
$832$	3.58114	+	0.418861i	0.124154	+	0.0145214i
$833$			51.1039i			1.77065i
$834$	−3.90879	+	10.2333i	−0.135350	+	0.354352i
$835$	2.32456			0.0804446
$836$	14.6011			0.504991
$837$	19.5927	−	10.1058i	0.677221	−	0.349308i
$838$	28.6491	+	28.6491i	0.989667	+	0.989667i
$839$	−27.6919	−	27.6919i	−0.956031	−	0.956031i	0.0430423	−	0.999073i	$-0.486295\pi$
$839$	−27.6919	−	27.6919i	−0.956031	−	0.956031i	−0.999073	+	0.0430423i	$0.986295\pi$
$840$		0			0
$841$	9.00000			0.310345
$842$	−18.1553			−0.625672
$843$	−40.1883	−	15.3506i	−1.38416	−	0.528701i
$844$		−	3.35089i		−	0.115342i
$845$	−11.0656	+	6.82295i	−0.380668	+	0.234717i
$846$	20.6491	−	23.0864i	0.709931	−	0.793727i
$847$		0			0
$848$		−	1.41421i		−	0.0485643i
$849$	−9.07764	−	20.2982i	−0.311544	−	0.696633i
$850$	−5.16228	−	5.16228i	−0.177065	−	0.177065i
$851$	−17.8885	+	17.8885i	−0.613211	+	0.613211i
$852$	−8.87788	−	3.39105i	−0.304151	−	0.116175i
$853$	20.6491	−	20.6491i	0.707012	−	0.707012i	−0.258894	−	0.965906i	$-0.583358\pi$
$853$	20.6491	−	20.6491i	0.707012	−	0.707012i	0.965906	+	0.258894i	$0.0833579\pi$
$854$		0			0
$855$	−14.6011	+	16.3246i	−0.499348	+	0.558288i
$856$	−5.32456	+	5.32456i	−0.181990	+	0.181990i
$857$	36.0438			1.23123			0.615617	−	0.788046i	$-0.288907\pi$
$857$	36.0438			1.23123			0.615617	+	0.788046i	$0.288907\pi$
$858$	−3.73994	−	11.9169i	−0.127679	−	0.406837i
$859$	1.67544			0.0571654			0.0285827	−	0.999591i	$-0.490901\pi$
$859$	1.67544			0.0571654			0.0285827	+	0.999591i	$0.490901\pi$
$860$	−5.06450	+	5.06450i	−0.172698	+	0.172698i
$861$		0			0
$862$			2.51317i			0.0855988i
$863$	25.6481	−	25.6481i	0.873071	−	0.873071i	−0.119735	−	0.992806i	$-0.538204\pi$
$863$	25.6481	−	25.6481i	0.873071	−	0.873071i	0.992806	+	0.119735i	$0.0382044\pi$
$864$	−2.38197	−	4.61803i	−0.0810361	−	0.157109i
$865$	−15.6491	+	15.6491i	−0.532086	+	0.532086i
$866$	−27.7880	−	27.7880i	−0.944276	−	0.944276i
$867$	−57.3925	+	25.6667i	−1.94915	+	0.871687i
$868$		0			0
$869$	14.1421	+	14.1421i	0.479739	+	0.479739i
$870$	7.07107	−	3.16228i	0.239732	−	0.107211i
$871$	28.6491	−	22.6491i	0.970738	−	0.767436i
$872$			6.84157i			0.231685i
$873$	−4.92349	+	0.274377i	−0.166635	+	0.00928624i
$874$	−32.6491			−1.10437
$875$		0			0
$876$	−11.8126	−	4.51200i	−0.399109	−	0.152446i
$877$	−4.18861	−	4.18861i	−0.141439	−	0.141439i	0.632842	−	0.774281i	$-0.281888\pi$
$877$	−4.18861	−	4.18861i	−0.141439	−	0.141439i	−0.774281	+	0.632842i	$0.781888\pi$
$878$	2.36944	+	2.36944i	0.0799646	+	0.0799646i
$879$	−6.47214	−	2.47214i	−0.218300	−	0.0833831i
$880$	2.00000			0.0674200
$881$	−53.9324			−1.81703			−0.908514	−	0.417855i	$-0.862782\pi$
$881$	−53.9324			−1.81703			−0.908514	+	0.417855i	$0.862782\pi$
$882$	20.9675	−	1.16848i	0.706011	−	0.0393447i
$883$			51.8114i			1.74359i	0.489869	+	0.871796i	$0.337045\pi$
$883$			51.8114i			1.74359i	−0.489869	+	0.871796i	$0.662955\pi$
$884$	−26.1443	−	3.05792i	−0.879329	−	0.102849i
$885$	−13.1623	+	5.88635i	−0.442445	+	0.197867i
$886$	7.32456	+	7.32456i	0.246073	+	0.246073i
$887$		−	8.67753i		−	0.291363i	−0.989332	−	0.145682i	$-0.953463\pi$
$887$		−	8.67753i		−	0.291363i	0.989332	−	0.145682i	$-0.0465375\pi$
$888$	−8.94427	+	4.00000i	−0.300150	+	0.134231i
$889$		0			0
$890$	0.592359	−	0.592359i	0.0198559	−	0.0198559i
$891$	−11.2349	+	14.0633i	−0.376383	+	0.471139i
$892$	16.6491	−	16.6491i	0.557453	−	0.557453i
$893$		−	75.3751i		−	2.52233i
$894$	2.59893	+	5.81139i	0.0869213	+	0.194362i
$895$	0.324555	−	0.324555i	0.0108487	−	0.0108487i
$896$		0			0
$897$	8.36276	+	26.6470i	0.279224	+	0.889718i
$898$	19.8114			0.661115
$899$	−13.4164	+	13.4164i	−0.447462	+	0.447462i
$900$	−2.00000	+	2.23607i	−0.0666667	+	0.0745356i
$901$			10.3246i			0.343961i
$902$	4.47214	−	4.47214i	0.148906	−	0.148906i
$903$		0			0
$904$	−11.4868	+	11.4868i	−0.382046	+	0.382046i
$905$	3.05792	+	3.05792i	0.101649	+	0.101649i
$906$	0.675445	+	1.51034i	0.0224401	+	0.0501777i
$907$			46.7851i			1.55347i	0.629826	+	0.776736i	$0.283126\pi$
$907$			46.7851i			1.55347i	−0.629826	+	0.776736i	$0.716874\pi$
$908$	−12.7279	−	12.7279i	−0.422391	−	0.422391i
$909$	13.6831	−	15.2982i	0.453841	−	0.507410i
$910$		0			0
$911$		−	53.9324i		−	1.78686i	−0.449203	−	0.893430i	$-0.648292\pi$
$911$		−	53.9324i		−	1.78686i	0.449203	−	0.893430i	$-0.351708\pi$
$912$	−11.8126	−	4.51200i	−0.391153	−	0.149407i
$913$	16.0000			0.529523
$914$	4.93113			0.163107
$915$	−6.58151	+	17.2306i	−0.217578	+	0.569627i
$916$	13.8114	+	13.8114i	0.456341	+	0.456341i
$917$		0			0
$918$	17.3897	+	33.7142i	0.573945	+	1.11274i
$919$	−29.2982			−0.966459			−0.483230	−	0.875494i	$-0.660536\pi$
$919$	−29.2982			−0.966459			−0.483230	+	0.875494i	$0.660536\pi$
$920$	−4.47214			−0.147442
$921$	−6.26006	+	16.3891i	−0.206276	+	0.540038i
$922$			30.6491i			1.00937i
$923$	12.2689	+	15.5191i	0.403837	+	0.510818i
$924$		0			0
$925$	4.00000	+	4.00000i	0.131519	+	0.131519i
$926$		−	11.7727i		−	0.386875i
$927$	41.7007	+	37.2982i	1.36963	+	1.22503i
$928$	3.16228	+	3.16228i	0.103807	+	0.103807i
$929$	−17.5629	+	17.5629i	−0.576221	+	0.576221i	−0.933860	−	0.357639i	$-0.883582\pi$
$929$	−17.5629	+	17.5629i	−0.576221	+	0.576221i	0.357639	+	0.933860i	$0.383582\pi$
$930$	2.62210	−	6.86474i	0.0859819	−	0.225104i
$931$	36.1359	−	36.1359i	1.18431	−	1.18431i
$932$			4.01315i			0.131455i
$933$	−33.4821	+	14.9737i	−1.09616	+	0.490216i
$934$	23.9737	−	23.9737i	0.784442	−	0.784442i
$935$	−14.6011			−0.477508
$936$	−0.656854	+	10.7967i	−0.0214700	+	0.352901i
$937$	−27.2982			−0.891794			−0.445897	−	0.895084i	$-0.647115\pi$
$937$	−27.2982			−0.891794			−0.445897	+	0.895084i	$0.647115\pi$
$938$		0			0
$939$	29.4868	−	13.1869i	0.962266	−	0.430339i
$940$		−	10.3246i		−	0.336750i
$941$	−12.4612	+	12.4612i	−0.406223	+	0.406223i	−0.880419	−	0.474196i	$-0.842739\pi$
$941$	−12.4612	+	12.4612i	−0.406223	+	0.406223i	0.474196	+	0.880419i	$0.342739\pi$
$942$	−14.3151	+	37.4774i	−0.466410	+	1.22108i
$943$	−10.0000	+	10.0000i	−0.325645	+	0.325645i
$944$	−5.88635	−	5.88635i	−0.191584	−	0.191584i
$945$		0			0
$946$			14.3246i			0.465731i
$947$	25.4186	+	25.4186i	0.825994	+	0.825994i	0.986960	−	0.160966i	$-0.0514611\pi$
$947$	25.4186	+	25.4186i	0.825994	+	0.825994i	−0.160966	+	0.986960i	$0.551461\pi$
$948$	−7.07107	−	15.8114i	−0.229658	−	0.513530i
$949$	16.3246	+	20.6491i	0.529917	+	0.670298i
$950$			7.30056i			0.236862i
$951$	15.6352	−	40.9334i	0.507005	−	1.32736i
$952$		0			0
$953$	−8.67753			−0.281093			−0.140546	−	0.990074i	$-0.544886\pi$
$953$	−8.67753			−0.281093			−0.140546	+	0.990074i	$0.544886\pi$
$954$	4.23607	−	0.236068i	0.137148	−	0.00764298i
$955$	1.48683	+	1.48683i	0.0481128	+	0.0481128i
$956$	−7.89292	−	7.89292i	−0.255275	−	0.255275i
$957$	5.52786	−	14.4721i	0.178690	−	0.467818i
$958$	0.188612			0.00609377
$959$		0			0
$960$	−1.61803	−	0.618034i	−0.0522218	−	0.0199470i
$961$		−	13.0000i		−	0.419355i
$962$	20.2580	+	2.36944i	0.653144	+	0.0763937i
$963$	−16.8377	−	15.0601i	−0.542588	−	0.485305i
$964$	−7.64911	−	7.64911i	−0.246361	−	0.246361i
$965$			4.93113i			0.158739i
$966$		0			0
$967$	−0.324555	−	0.324555i	−0.0104370	−	0.0104370i	0.701869	−	0.712306i	$-0.252349\pi$
$967$	−0.324555	−	0.324555i	−0.0104370	−	0.0104370i	−0.712306	+	0.701869i	$0.752349\pi$
$968$	−4.94975	+	4.94975i	−0.159091	+	0.159091i
$969$	86.2383	+	32.9401i	2.77037	+	1.05819i
$970$	−1.16228	+	1.16228i	−0.0373185	+	0.0373185i
$971$			18.3475i			0.588800i	0.955682	+	0.294400i	$0.0951199\pi$
$971$			18.3475i			0.588800i	−0.955682	+	0.294400i	$0.904880\pi$
$972$	13.4350	−	7.90569i	0.430929	−	0.253575i
$973$		0			0
$974$	−25.4558			−0.815658
$975$	5.95846	−	1.86997i	0.190823	−	0.0598870i
$976$	−10.6491			−0.340870
$977$	5.16062	−	5.16062i	0.165103	−	0.165103i	−0.619720	−	0.784823i	$-0.712754\pi$
$977$	5.16062	−	5.16062i	0.165103	−	0.165103i	0.784823	+	0.619720i	$0.212754\pi$
$978$	2.32456	+	5.19786i	0.0743311	+	0.166209i
$979$		−	1.67544i		−	0.0535474i
$980$	4.94975	−	4.94975i	0.158114	−	0.158114i
$981$	−20.4929	+	1.14203i	−0.654289	+	0.0364623i
$982$	20.0000	−	20.0000i	0.638226	−	0.638226i
$983$	29.6612	+	29.6612i	0.946047	+	0.946047i	0.998617	−	0.0525705i	$-0.0167414\pi$
$983$	29.6612	+	29.6612i	0.946047	+	0.946047i	−0.0525705	+	0.998617i	$0.516741\pi$
$984$	−5.00000	+	2.23607i	−0.159394	+	0.0712832i
$985$			12.6491i			0.403034i
$986$	−23.0864	−	23.0864i	−0.735221	−	0.735221i
$987$		0			0
$988$	16.3246	+	20.6491i	0.519353	+	0.656936i
$989$		−	32.0307i		−	1.01852i
$990$	0.333851	+	5.99070i	0.0106105	+	0.190397i
$991$	4.70178			0.149357			0.0746785	−	0.997208i	$-0.476207\pi$
$991$	4.70178			0.149357			0.0746785	+	0.997208i	$0.476207\pi$
$992$	4.24264			0.134704
$993$	21.7082	+	8.29180i	0.688889	+	0.263132i
$994$		0			0
$995$	−1.41421	−	1.41421i	−0.0448336	−	0.0448336i
$996$	−12.9443	−	4.94427i	−0.410155	−	0.156665i
$997$	−24.4605			−0.774672			−0.387336	−	0.921939i	$-0.626605\pi$
$997$	−24.4605			−0.774672			−0.387336	+	0.921939i	$0.626605\pi$
$998$	−15.7858			−0.499692
$999$	−13.4744	−	26.1235i	−0.426312	−	0.826512i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.p.g.281.3	yes	8
3.2	odd	2	inner	390.2.p.g.281.1	yes	8
13.5	odd	4	inner	390.2.p.g.161.1	✓	8
39.5	even	4	inner	390.2.p.g.161.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.p.g.161.1	✓	8	13.5	odd	4	inner
390.2.p.g.161.3	yes	8	39.5	even	4	inner
390.2.p.g.281.1	yes	8	3.2	odd	2	inner
390.2.p.g.281.3	yes	8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.58114 + 0.707107i) q^{3} -1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.618034 + 1.61803i) q^{6} +(-0.707107 - 0.707107i) q^{8} +(2.00000 - 2.23607i) q^{9} -1.00000i q^{10} +(-1.41421 - 1.41421i) q^{11} +(0.707107 + 1.58114i) q^{12} +(0.418861 - 3.58114i) q^{13} +(-0.618034 + 1.61803i) q^{15} -1.00000 q^{16} +7.30056 q^{17} +(-0.166925 - 2.99535i) q^{18} +(-5.16228 - 5.16228i) q^{19} +(-0.707107 - 0.707107i) q^{20} -2.00000 q^{22} +4.47214 q^{23} +(1.61803 + 0.618034i) q^{24} -1.00000i q^{25} +(-2.23607 - 2.82843i) q^{26} +(-1.58114 + 4.94975i) q^{27} -4.47214i q^{29} +(0.707107 + 1.58114i) q^{30} +(-3.00000 - 3.00000i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(3.23607 + 1.23607i) q^{33} +(5.16228 - 5.16228i) q^{34} +(-2.23607 - 2.00000i) q^{36} +(-4.00000 + 4.00000i) q^{37} -7.30056 q^{38} +(1.86997 + 5.95846i) q^{39} -1.00000 q^{40} +(-2.23607 + 2.23607i) q^{41} -7.16228i q^{43} +(-1.41421 + 1.41421i) q^{44} +(-0.166925 - 2.99535i) q^{45} +(3.16228 - 3.16228i) q^{46} +(7.30056 + 7.30056i) q^{47} +(1.58114 - 0.707107i) q^{48} +7.00000i q^{49} +(-0.707107 - 0.707107i) q^{50} +(-11.5432 + 5.16228i) q^{51} +(-3.58114 - 0.418861i) q^{52} +1.41421i q^{53} +(2.38197 + 4.61803i) q^{54} -2.00000 q^{55} +(11.8126 + 4.51200i) q^{57} +(-3.16228 - 3.16228i) q^{58} +(5.88635 + 5.88635i) q^{59} +(1.61803 + 0.618034i) q^{60} +10.6491 q^{61} -4.24264 q^{62} +1.00000i q^{64} +(-2.23607 - 2.82843i) q^{65} +(3.16228 - 1.41421i) q^{66} +(7.16228 + 7.16228i) q^{67} -7.30056i q^{68} +(-7.07107 + 3.16228i) q^{69} +(-3.87978 + 3.87978i) q^{71} +(-2.99535 + 0.166925i) q^{72} +(-5.16228 + 5.16228i) q^{73} +5.65685i q^{74} +(0.707107 + 1.58114i) q^{75} +(-5.16228 + 5.16228i) q^{76} +(5.53553 + 2.89100i) q^{78} -10.0000 q^{79} +(-0.707107 + 0.707107i) q^{80} +(-1.00000 - 8.94427i) q^{81} +3.16228i q^{82} +(-5.65685 + 5.65685i) q^{83} +(5.16228 - 5.16228i) q^{85} +(-5.06450 - 5.06450i) q^{86} +(3.16228 + 7.07107i) q^{87} +2.00000i q^{88} +(0.592359 + 0.592359i) q^{89} +(-2.23607 - 2.00000i) q^{90} -4.47214i q^{92} +(6.86474 + 2.62210i) q^{93} +10.3246 q^{94} -7.30056 q^{95} +(0.618034 - 1.61803i) q^{96} +(-1.16228 - 1.16228i) q^{97} +(4.94975 + 4.94975i) q^{98} +(-5.99070 + 0.333851i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{6} + 16 q^{9} + 16 q^{13} + 4 q^{15} - 8 q^{16} - 16 q^{19} - 16 q^{22} + 4 q^{24} - 24 q^{31} + 8 q^{33} + 16 q^{34} - 32 q^{37} + 20 q^{39} - 8 q^{40} - 16 q^{52} + 28 q^{54} - 16 q^{55} + 40 q^{57}+ \cdots + 16 q^{97}+O(q^{100}) \) 8 * q + 4 * q^6 + 16 * q^9 + 16 * q^13 + 4 * q^15 - 8 * q^16 - 16 * q^19 - 16 * q^22 + 4 * q^24 - 24 * q^31 + 8 * q^33 + 16 * q^34 - 32 * q^37 + 20 * q^39 - 8 * q^40 - 16 * q^52 + 28 * q^54 - 16 * q^55 + 40 * q^57 + 4 * q^60 - 16 * q^61 + 32 * q^67 - 16 * q^73 - 16 * q^76 + 16 * q^78 - 80 * q^79 - 8 * q^81 + 16 * q^85 + 32 * q^94 - 4 * q^96 + 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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