LMFDB - Embedded newform 1470.2.m.b.97.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(97,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("1470.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.m (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:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{16})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.1
Root			$0.923880 - 0.382683i$ of defining polynomial
Character	$\chi$	$=$	1470.97
Dual form			1470.2.m.b.1273.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(1.00000 + 2.00000i) q^{5} +1.00000i q^{6} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(1.00000 + 2.00000i) q^{5} +1.00000i q^{6} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(0.707107 - 2.12132i) q^{10} -1.96428 q^{11} +(0.707107 - 0.707107i) q^{12} +(-2.37849 - 2.37849i) q^{13} +(0.707107 - 2.12132i) q^{15} -1.00000 q^{16} +(3.38896 - 3.38896i) q^{17} +(0.707107 - 0.707107i) q^{18} -3.41421 q^{19} +(-2.00000 + 1.00000i) q^{20} +(1.38896 + 1.38896i) q^{22} +(-3.00000 + 3.00000i) q^{23} -1.00000 q^{24} +(-3.00000 + 4.00000i) q^{25} +3.36370i q^{26} +(0.707107 - 0.707107i) q^{27} -4.22784i q^{29} +(-2.00000 + 1.00000i) q^{30} -1.98520i q^{31} +(0.707107 + 0.707107i) q^{32} +(1.38896 + 1.38896i) q^{33} -4.79271 q^{34} -1.00000 q^{36} +(5.35323 + 5.35323i) q^{37} +(2.41421 + 2.41421i) q^{38} +3.36370i q^{39} +(2.12132 + 0.707107i) q^{40} -11.5854i q^{41} +(7.81796 - 7.81796i) q^{43} -1.96428i q^{44} +(-2.00000 + 1.00000i) q^{45} +4.24264 q^{46} +(4.93902 - 4.93902i) q^{47} +(0.707107 + 0.707107i) q^{48} +(4.94975 - 0.707107i) q^{50} -4.79271 q^{51} +(2.37849 - 2.37849i) q^{52} +(8.39904 - 8.39904i) q^{53} -1.00000 q^{54} +(-1.96428 - 3.92856i) q^{55} +(2.41421 + 2.41421i) q^{57} +(-2.98954 + 2.98954i) q^{58} -4.19212 q^{59} +(2.12132 + 0.707107i) q^{60} -3.92856i q^{61} +(-1.40375 + 1.40375i) q^{62} -1.00000i q^{64} +(2.37849 - 7.13548i) q^{65} -1.96428i q^{66} +(2.36803 + 2.36803i) q^{67} +(3.38896 + 3.38896i) q^{68} +4.24264 q^{69} -4.14161 q^{71} +(0.707107 + 0.707107i) q^{72} +(2.01480 + 2.01480i) q^{73} -7.57062i q^{74} +(4.94975 - 0.707107i) q^{75} -3.41421i q^{76} +(2.37849 - 2.37849i) q^{78} +11.5854i q^{79} +(-1.00000 - 2.00000i) q^{80} -1.00000 q^{81} +(-8.19212 + 8.19212i) q^{82} +(-10.9996 - 10.9996i) q^{83} +(10.1669 + 3.38896i) q^{85} -11.0563 q^{86} +(-2.98954 + 2.98954i) q^{87} +(-1.38896 + 1.38896i) q^{88} +6.02092 q^{89} +(2.12132 + 0.707107i) q^{90} +(-3.00000 - 3.00000i) q^{92} +(-1.40375 + 1.40375i) q^{93} -6.98483 q^{94} +(-3.41421 - 6.82843i) q^{95} -1.00000i q^{96} +(5.08534 - 5.08534i) q^{97} -1.96428i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{5}+O(q^{10}) $ 8 * q + 8 * q^5	$ 8 q + 8 q^{5} + 8 q^{13} - 8 q^{16} + 8 q^{17} - 16 q^{19} - 16 q^{20} - 8 q^{22} - 24 q^{23} - 8 q^{24} - 24 q^{25} - 16 q^{30} - 8 q^{33} - 8 q^{36} + 8 q^{37} + 8 q^{38} + 32 q^{43} - 16 q^{45} + 16 q^{47} - 8 q^{52} - 32 q^{53} - 8 q^{54} + 8 q^{57} - 16 q^{58} + 16 q^{59} + 8 q^{62} - 8 q^{65} - 16 q^{67} + 8 q^{68} + 32 q^{71} + 16 q^{73} - 8 q^{78} - 8 q^{80} - 8 q^{81} - 16 q^{82} + 24 q^{85} - 32 q^{86} - 16 q^{87} + 8 q^{88} + 64 q^{89} - 24 q^{92} + 8 q^{93} + 32 q^{94} - 16 q^{95} + 32 q^{97}+O(q^{100}) $ 8 * q + 8 * q^5 + 8 * q^13 - 8 * q^16 + 8 * q^17 - 16 * q^19 - 16 * q^20 - 8 * q^22 - 24 * q^23 - 8 * q^24 - 24 * q^25 - 16 * q^30 - 8 * q^33 - 8 * q^36 + 8 * q^37 + 8 * q^38 + 32 * q^43 - 16 * q^45 + 16 * q^47 - 8 * q^52 - 32 * q^53 - 8 * q^54 + 8 * q^57 - 16 * q^58 + 16 * q^59 + 8 * q^62 - 8 * q^65 - 16 * q^67 + 8 * q^68 + 32 * q^71 + 16 * q^73 - 8 * q^78 - 8 * q^80 - 8 * q^81 - 16 * q^82 + 24 * q^85 - 32 * q^86 - 16 * q^87 + 8 * q^88 + 64 * q^89 - 24 * q^92 + 8 * q^93 + 32 * q^94 - 16 * q^95 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$			1.00000i			0.500000i
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$6$			1.00000i			0.408248i
$7$		0			0
$7$		0			0
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$			1.00000i			0.333333i
$10$	0.707107	−	2.12132i	0.223607	−	0.670820i
$11$	−1.96428			−0.592252			−0.296126	−	0.955149i	$-0.595695\pi$
$11$	−1.96428			−0.592252			−0.296126	+	0.955149i	$0.595695\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	−2.37849	−	2.37849i	−0.659675	−	0.659675i	0.295628	−	0.955303i	$-0.404471\pi$
$13$	−2.37849	−	2.37849i	−0.659675	−	0.659675i	−0.955303	+	0.295628i	$0.904471\pi$
$14$		0			0
$15$	0.707107	−	2.12132i	0.182574	−	0.547723i
$16$	−1.00000			−0.250000
$17$	3.38896	−	3.38896i	0.821942	−	0.821942i	−0.164444	−	0.986386i	$-0.552583\pi$
$17$	3.38896	−	3.38896i	0.821942	−	0.821942i	0.986386	+	0.164444i	$0.0525830\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	−3.41421			−0.783274			−0.391637	−	0.920120i	$-0.628091\pi$
$19$	−3.41421			−0.783274			−0.391637	+	0.920120i	$0.628091\pi$
$20$	−2.00000	+	1.00000i	−0.447214	+	0.223607i
$21$		0			0
$22$	1.38896	+	1.38896i	0.296126	+	0.296126i
$23$	−3.00000	+	3.00000i	−0.625543	+	0.625543i	−0.946943	−	0.321400i	$-0.895847\pi$
$23$	−3.00000	+	3.00000i	−0.625543	+	0.625543i	0.321400	+	0.946943i	$0.395847\pi$
$24$	−1.00000			−0.204124
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$			3.36370i			0.659675i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$		−	4.22784i		−	0.785091i	−0.919733	−	0.392546i	$-0.871595\pi$
$29$		−	4.22784i		−	0.785091i	0.919733	−	0.392546i	$-0.128405\pi$
$30$	−2.00000	+	1.00000i	−0.365148	+	0.182574i
$31$		−	1.98520i		−	0.356553i	−0.983980	−	0.178277i	$-0.942948\pi$
$31$		−	1.98520i		−	0.356553i	0.983980	−	0.178277i	$-0.0570522\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	1.38896	+	1.38896i	0.241786	+	0.241786i
$34$	−4.79271			−0.821942
$35$		0			0
$36$	−1.00000			−0.166667
$37$	5.35323	+	5.35323i	0.880066	+	0.880066i	0.993541	−	0.113475i	$-0.0361981\pi$
$37$	5.35323	+	5.35323i	0.880066	+	0.880066i	−0.113475	+	0.993541i	$0.536198\pi$
$38$	2.41421	+	2.41421i	0.391637	+	0.391637i
$39$			3.36370i			0.538623i
$40$	2.12132	+	0.707107i	0.335410	+	0.111803i
$41$		−	11.5854i		−	1.80934i	−0.426116	−	0.904669i	$-0.640118\pi$
$41$		−	11.5854i		−	1.80934i	0.426116	−	0.904669i	$-0.359882\pi$
$42$		0			0
$43$	7.81796	−	7.81796i	1.19223	−	1.19223i	0.215788	−	0.976440i	$-0.430768\pi$
$43$	7.81796	−	7.81796i	1.19223	−	1.19223i	0.976440	−	0.215788i	$-0.0692321\pi$
$44$		−	1.96428i		−	0.296126i
$45$	−2.00000	+	1.00000i	−0.298142	+	0.149071i
$46$	4.24264			0.625543
$47$	4.93902	−	4.93902i	0.720430	−	0.720430i	−0.248263	−	0.968693i	$-0.579860\pi$
$47$	4.93902	−	4.93902i	0.720430	−	0.720430i	0.968693	+	0.248263i	$0.0798596\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$		0			0
$50$	4.94975	−	0.707107i	0.700000	−	0.100000i
$51$	−4.79271			−0.671113
$52$	2.37849	−	2.37849i	0.329838	−	0.329838i
$53$	8.39904	−	8.39904i	1.15370	−	1.15370i	0.167892	−	0.985805i	$-0.446304\pi$
$53$	8.39904	−	8.39904i	1.15370	−	1.15370i	0.985805	−	0.167892i	$-0.0536960\pi$
$54$	−1.00000			−0.136083
$55$	−1.96428	−	3.92856i	−0.264863	−	0.529727i
$56$		0			0
$57$	2.41421	+	2.41421i	0.319770	+	0.319770i
$58$	−2.98954	+	2.98954i	−0.392546	+	0.392546i
$59$	−4.19212			−0.545768			−0.272884	−	0.962047i	$-0.587978\pi$
$59$	−4.19212			−0.545768			−0.272884	+	0.962047i	$0.587978\pi$
$60$	2.12132	+	0.707107i	0.273861	+	0.0912871i
$61$		−	3.92856i		−	0.503000i	−0.967857	−	0.251500i	$-0.919076\pi$
$61$		−	3.92856i		−	0.503000i	0.967857	−	0.251500i	$-0.0809239\pi$
$62$	−1.40375	+	1.40375i	−0.178277	+	0.178277i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	2.37849	−	7.13548i	0.295016	−	0.885047i
$66$		−	1.96428i		−	0.241786i
$67$	2.36803	+	2.36803i	0.289301	+	0.289301i	0.836804	−	0.547503i	$-0.184421\pi$
$67$	2.36803	+	2.36803i	0.289301	+	0.289301i	−0.547503	+	0.836804i	$0.684421\pi$
$68$	3.38896	+	3.38896i	0.410971	+	0.410971i
$69$	4.24264			0.510754
$70$		0			0
$71$	−4.14161			−0.491518			−0.245759	−	0.969331i	$-0.579037\pi$
$71$	−4.14161			−0.491518			−0.245759	+	0.969331i	$0.579037\pi$
$72$	0.707107	+	0.707107i	0.0833333	+	0.0833333i
$73$	2.01480	+	2.01480i	0.235814	+	0.235814i	0.815114	−	0.579300i	$-0.196674\pi$
$73$	2.01480	+	2.01480i	0.235814	+	0.235814i	−0.579300	+	0.815114i	$0.696674\pi$
$74$		−	7.57062i		−	0.880066i
$75$	4.94975	−	0.707107i	0.571548	−	0.0816497i
$76$		−	3.41421i		−	0.391637i
$77$		0			0
$78$	2.37849	−	2.37849i	0.269311	−	0.269311i
$79$			11.5854i			1.30346i	0.758451	+	0.651730i	$0.225957\pi$
$79$			11.5854i			1.30346i	−0.758451	+	0.651730i	$0.774043\pi$
$80$	−1.00000	−	2.00000i	−0.111803	−	0.223607i
$81$	−1.00000			−0.111111
$82$	−8.19212	+	8.19212i	−0.904669	+	0.904669i
$83$	−10.9996	−	10.9996i	−1.20737	−	1.20737i	−0.971877	−	0.235489i	$-0.924331\pi$
$83$	−10.9996	−	10.9996i	−1.20737	−	1.20737i	−0.235489	−	0.971877i	$-0.575669\pi$
$84$		0			0
$85$	10.1669	+	3.38896i	1.10275	+	0.367584i
$86$	−11.0563			−1.19223
$87$	−2.98954	+	2.98954i	−0.320512	+	0.320512i
$88$	−1.38896	+	1.38896i	−0.148063	+	0.148063i
$89$	6.02092			0.638217			0.319108	−	0.947718i	$-0.396617\pi$
$89$	6.02092			0.638217			0.319108	+	0.947718i	$0.396617\pi$
$90$	2.12132	+	0.707107i	0.223607	+	0.0745356i
$91$		0			0
$92$	−3.00000	−	3.00000i	−0.312772	−	0.312772i
$93$	−1.40375	+	1.40375i	−0.145562	+	0.145562i
$94$	−6.98483			−0.720430
$95$	−3.41421	−	6.82843i	−0.350291	−	0.700582i
$96$		−	1.00000i		−	0.102062i
$97$	5.08534	−	5.08534i	0.516338	−	0.516338i	−0.400124	−	0.916461i	$-0.631033\pi$
$97$	5.08534	−	5.08534i	0.516338	−	0.516338i	0.916461	+	0.400124i	$0.131033\pi$
$98$		0			0
$99$		−	1.96428i		−	0.197417i
$100$	−4.00000	−	3.00000i	−0.400000	−	0.300000i
$101$		−	6.14161i		−	0.611113i	−0.952174	−	0.305556i	$-0.901158\pi$
$101$		−	6.14161i		−	0.611113i	0.952174	−	0.305556i	$-0.0988424\pi$
$102$	3.38896	+	3.38896i	0.335557	+	0.335557i
$103$	−8.82843	−	8.82843i	−0.869891	−	0.869891i	0.122569	−	0.992460i	$-0.460887\pi$
$103$	−8.82843	−	8.82843i	−0.869891	−	0.869891i	−0.992460	+	0.122569i	$0.960887\pi$
$104$	−3.36370			−0.329838
$105$		0			0
$106$	−11.8780			−1.15370
$107$	2.86415	+	2.86415i	0.276888	+	0.276888i	0.831865	−	0.554978i	$-0.187273\pi$
$107$	2.86415	+	2.86415i	0.276888	+	0.276888i	−0.554978	+	0.831865i	$0.687273\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$		−	4.87894i		−	0.467318i	−0.972319	−	0.233659i	$-0.924930\pi$
$109$		−	4.87894i		−	0.467318i	0.972319	−	0.233659i	$-0.0750699\pi$
$110$	−1.38896	+	4.16687i	−0.132432	+	0.397295i
$111$		−	7.57062i		−	0.718571i
$112$		0			0
$113$	−3.97908	+	3.97908i	−0.374320	+	0.374320i	−0.869048	−	0.494728i	$-0.835268\pi$
$113$	−3.97908	+	3.97908i	−0.374320	+	0.374320i	0.494728	+	0.869048i	$0.335268\pi$
$114$		−	3.41421i		−	0.319770i
$115$	−9.00000	−	3.00000i	−0.839254	−	0.279751i
$116$	4.22784			0.392546
$117$	2.37849	−	2.37849i	0.219892	−	0.219892i
$118$	2.96428	+	2.96428i	0.272884	+	0.272884i
$119$		0			0
$120$	−1.00000	−	2.00000i	−0.0912871	−	0.182574i
$121$	−7.14161			−0.649237
$122$	−2.77791	+	2.77791i	−0.251500	+	0.251500i
$123$	−8.19212	+	8.19212i	−0.738659	+	0.738659i
$124$	1.98520			0.178277
$125$	−11.0000	−	2.00000i	−0.983870	−	0.178885i
$126$		0			0
$127$	10.1416	+	10.1416i	0.899922	+	0.899922i	0.995429	−	0.0955067i	$-0.0304471\pi$
$127$	10.1416	+	10.1416i	0.899922	+	0.899922i	−0.0955067	+	0.995429i	$0.530447\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−11.0563			−0.973450
$130$	−6.72739	+	3.36370i	−0.590031	+	0.295016i
$131$		−	9.84898i		−	0.860509i	−0.902708	−	0.430255i	$-0.858424\pi$
$131$		−	9.84898i		−	0.860509i	0.902708	−	0.430255i	$-0.141576\pi$
$132$	−1.38896	+	1.38896i	−0.120893	+	0.120893i
$133$		0			0
$134$		−	3.34890i		−	0.289301i
$135$	2.12132	+	0.707107i	0.182574	+	0.0608581i
$136$		−	4.79271i		−	0.410971i
$137$	−3.17733	−	3.17733i	−0.271457	−	0.271457i	0.558229	−	0.829687i	$-0.311481\pi$
$137$	−3.17733	−	3.17733i	−0.271457	−	0.271457i	−0.829687	+	0.558229i	$0.811481\pi$
$138$	−3.00000	−	3.00000i	−0.255377	−	0.255377i
$139$	13.1007			1.11118			0.555592	−	0.831455i	$-0.312492\pi$
$139$	13.1007			1.11118			0.555592	+	0.831455i	$0.312492\pi$
$140$		0			0
$141$	−6.98483			−0.588229
$142$	2.92856	+	2.92856i	0.245759	+	0.245759i
$143$	4.67202	+	4.67202i	0.390694	+	0.390694i
$144$		−	1.00000i		−	0.0833333i
$145$	8.45569	−	4.22784i	0.702207	−	0.351103i
$146$		−	2.84935i		−	0.235814i
$147$		0			0
$148$	−5.35323	+	5.35323i	−0.440033	+	0.440033i
$149$		−	22.1355i		−	1.81341i	−0.421766	−	0.906705i	$-0.638590\pi$
$149$		−	22.1355i		−	1.81341i	0.421766	−	0.906705i	$-0.361410\pi$
$150$	−4.00000	−	3.00000i	−0.326599	−	0.244949i
$151$	−9.32185			−0.758601			−0.379301	−	0.925274i	$-0.623835\pi$
$151$	−9.32185			−0.758601			−0.379301	+	0.925274i	$0.623835\pi$
$152$	−2.41421	+	2.41421i	−0.195819	+	0.195819i
$153$	3.38896	+	3.38896i	0.273981	+	0.273981i
$154$		0			0
$155$	3.97041	−	1.98520i	0.318911	−	0.159455i
$156$	−3.36370			−0.269311
$157$	13.0711	−	13.0711i	1.04318	−	1.04318i	0.0441603	−	0.999024i	$-0.485939\pi$
$157$	13.0711	−	13.0711i	1.04318	−	1.04318i	0.999024	−	0.0441603i	$-0.0140612\pi$
$158$	8.19212	−	8.19212i	0.651730	−	0.651730i
$159$	−11.8780			−0.941990
$160$	−0.707107	+	2.12132i	−0.0559017	+	0.167705i
$161$		0			0
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	−14.8028	+	14.8028i	−1.15944	+	1.15944i	−0.174849	+	0.984595i	$0.555944\pi$
$163$	−14.8028	+	14.8028i	−1.15944	+	1.15944i	−0.984595	+	0.174849i	$0.944056\pi$
$164$	11.5854			0.904669
$165$	−1.38896	+	4.16687i	−0.108130	+	0.324390i
$166$			15.5558i			1.20737i
$167$	−12.8952	+	12.8952i	−0.997858	+	0.997858i	−0.999998	−	0.00214017i	$-0.999319\pi$
$167$	−12.8952	+	12.8952i	−0.997858	+	0.997858i	0.00214017	+	0.999998i	$0.499319\pi$
$168$		0			0
$169$		−	1.68554i		−	0.129657i
$170$	−4.79271	−	9.58541i	−0.367584	−	0.735168i
$171$		−	3.41421i		−	0.261091i
$172$	7.81796	+	7.81796i	0.596114	+	0.596114i
$173$	−11.6060	−	11.6060i	−0.882385	−	0.882385i	0.111392	−	0.993777i	$-0.464469\pi$
$173$	−11.6060	−	11.6060i	−0.882385	−	0.882385i	−0.993777	+	0.111392i	$0.964469\pi$
$174$	4.22784			0.320512
$175$		0			0
$176$	1.96428			0.148063
$177$	2.96428	+	2.96428i	0.222809	+	0.222809i
$178$	−4.25744	−	4.25744i	−0.319108	−	0.319108i
$179$		−	13.8423i		−	1.03462i	−0.855797	−	0.517312i	$-0.826933\pi$
$179$		−	13.8423i		−	1.03462i	0.855797	−	0.517312i	$-0.173067\pi$
$180$	−1.00000	−	2.00000i	−0.0745356	−	0.149071i
$181$			22.3128i			1.65850i	0.558879	+	0.829249i	$0.311231\pi$
$181$			22.3128i			1.65850i	−0.558879	+	0.829249i	$0.688769\pi$
$182$		0			0
$183$	−2.77791	+	2.77791i	−0.205349	+	0.205349i
$184$			4.24264i			0.312772i
$185$	−5.35323	+	16.0597i	−0.393578	+	1.18073i
$186$	1.98520			0.145562
$187$	−6.65685	+	6.65685i	−0.486797	+	0.486797i
$188$	4.93902	+	4.93902i	0.360215	+	0.360215i
$189$		0			0
$190$	−2.41421	+	7.24264i	−0.175145	+	0.525436i
$191$	1.00037			0.0723845			0.0361923	−	0.999345i	$-0.488477\pi$
$191$	1.00037			0.0723845			0.0361923	+	0.999345i	$0.488477\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$	4.36370	−	4.36370i	0.314106	−	0.314106i	−0.532392	−	0.846498i	$-0.678707\pi$
$193$	4.36370	−	4.36370i	0.314106	−	0.314106i	0.846498	+	0.532392i	$0.178707\pi$
$194$	−7.19175			−0.516338
$195$	−6.72739	+	3.36370i	−0.481759	+	0.240879i
$196$		0			0
$197$	11.2923	+	11.2923i	0.804540	+	0.804540i	0.983801	−	0.179262i	$-0.0573708\pi$
$197$	11.2923	+	11.2923i	0.804540	+	0.804540i	−0.179262	+	0.983801i	$0.557371\pi$
$198$	−1.38896	+	1.38896i	−0.0987087	+	0.0987087i
$199$	−26.3572			−1.86841			−0.934206	−	0.356734i	$-0.883890\pi$
$199$	−26.3572			−1.86841			−0.934206	+	0.356734i	$0.883890\pi$
$200$	0.707107	+	4.94975i	0.0500000	+	0.350000i
$201$		−	3.34890i		−	0.236213i
$202$	−4.34277	+	4.34277i	−0.305556	+	0.305556i
$203$		0			0
$204$		−	4.79271i		−	0.335557i
$205$	23.1708	−	11.5854i	1.61832	−	0.809160i
$206$			12.4853i			0.869891i
$207$	−3.00000	−	3.00000i	−0.208514	−	0.208514i
$208$	2.37849	+	2.37849i	0.164919	+	0.164919i
$209$	6.70647			0.463896
$210$		0			0
$211$	−17.3050			−1.19133			−0.595664	−	0.803234i	$-0.703111\pi$
$211$	−17.3050			−1.19133			−0.595664	+	0.803234i	$0.703111\pi$
$212$	8.39904	+	8.39904i	0.576849	+	0.576849i
$213$	2.92856	+	2.92856i	0.200662	+	0.200662i
$214$		−	4.05052i		−	0.276888i
$215$	23.4539	+	7.81796i	1.59954	+	0.533181i
$216$		−	1.00000i		−	0.0680414i
$217$		0			0
$218$	−3.44993	+	3.44993i	−0.233659	+	0.233659i
$219$		−	2.84935i		−	0.192541i
$220$	3.92856	−	1.96428i	0.264863	−	0.132432i
$221$	−16.1212			−1.08443
$222$	−5.35323	+	5.35323i	−0.359286	+	0.359286i
$223$	−3.59154	−	3.59154i	−0.240507	−	0.240507i	0.576553	−	0.817060i	$-0.304398\pi$
$223$	−3.59154	−	3.59154i	−0.240507	−	0.240507i	−0.817060	+	0.576553i	$0.804398\pi$
$224$		0			0
$225$	−4.00000	−	3.00000i	−0.266667	−	0.200000i
$226$	5.62726			0.374320
$227$	17.8490	−	17.8490i	1.18468	−	1.18468i	0.206160	−	0.978518i	$-0.433903\pi$
$227$	17.8490	−	17.8490i	1.18468	−	1.18468i	0.978518	−	0.206160i	$-0.0660967\pi$
$228$	−2.41421	+	2.41421i	−0.159885	+	0.159885i
$229$	−5.58616			−0.369144			−0.184572	−	0.982819i	$-0.559090\pi$
$229$	−5.58616			−0.369144			−0.184572	+	0.982819i	$0.559090\pi$
$230$	4.24264	+	8.48528i	0.279751	+	0.559503i
$231$		0			0
$232$	−2.98954	−	2.98954i	−0.196273	−	0.196273i
$233$	20.0916	−	20.0916i	1.31625	−	1.31625i	0.399522	−	0.916724i	$-0.369176\pi$
$233$	20.0916	−	20.0916i	1.31625	−	1.31625i	0.916724	−	0.399522i	$-0.130824\pi$
$234$	−3.36370			−0.219892
$235$	14.8171	+	4.93902i	0.966559	+	0.322186i
$236$		−	4.19212i		−	0.272884i
$237$	8.19212	−	8.19212i	0.532136	−	0.532136i
$238$		0			0
$239$			3.10066i			0.200565i	0.994959	+	0.100283i	$0.0319747\pi$
$239$			3.10066i			0.200565i	−0.994959	+	0.100283i	$0.968025\pi$
$240$	−0.707107	+	2.12132i	−0.0456435	+	0.136931i
$241$			19.0764i			1.22882i	0.788986	+	0.614411i	$0.210606\pi$
$241$			19.0764i			1.22882i	−0.788986	+	0.614411i	$0.789394\pi$
$242$	5.04988	+	5.04988i	0.324619	+	0.324619i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	3.92856			0.251500
$245$		0			0
$246$	11.5854			0.738659
$247$	8.12068	+	8.12068i	0.516707	+	0.516707i
$248$	−1.40375	−	1.40375i	−0.0891383	−	0.0891383i
$249$			15.5558i			0.985810i
$250$	6.36396	+	9.19239i	0.402492	+	0.581378i
$251$		−	14.9410i		−	0.943066i	−0.881848	−	0.471533i	$-0.843701\pi$
$251$		−	14.9410i		−	0.943066i	0.881848	−	0.471533i	$-0.156299\pi$
$252$		0			0
$253$	5.89284	−	5.89284i	0.370480	−	0.370480i
$254$		−	14.3424i		−	0.899922i
$255$	−4.79271	−	9.58541i	−0.300131	−	0.600262i
$256$	1.00000			0.0625000
$257$	−11.8176	+	11.8176i	−0.737161	+	0.737161i	−0.972028	−	0.234867i	$-0.924535\pi$
$257$	−11.8176	+	11.8176i	−0.737161	+	0.737161i	0.234867	+	0.972028i	$0.424535\pi$
$258$	7.81796	+	7.81796i	0.486725	+	0.486725i
$259$		0			0
$260$	7.13548	+	2.37849i	0.442524	+	0.147508i
$261$	4.22784			0.261697
$262$	−6.96428	+	6.96428i	−0.430255	+	0.430255i
$263$	10.3132	−	10.3132i	0.635938	−	0.635938i	−0.313613	−	0.949551i	$-0.601539\pi$
$263$	10.3132	−	10.3132i	0.635938	−	0.635938i	0.949551	+	0.313613i	$0.101539\pi$
$264$	1.96428			0.120893
$265$	25.1971	+	8.39904i	1.54785	+	0.515949i
$266$		0			0
$267$	−4.25744	−	4.25744i	−0.260551	−	0.260551i
$268$	−2.36803	+	2.36803i	−0.144650	+	0.144650i
$269$	26.2414			1.59996			0.799982	−	0.600024i	$-0.204842\pi$
$269$	26.2414			1.59996			0.799982	+	0.600024i	$0.204842\pi$
$270$	−1.00000	−	2.00000i	−0.0608581	−	0.121716i
$271$		−	12.8641i		−	0.781441i	−0.920509	−	0.390721i	$-0.872226\pi$
$271$		−	12.8641i		−	0.781441i	0.920509	−	0.390721i	$-0.127774\pi$
$272$	−3.38896	+	3.38896i	−0.205486	+	0.205486i
$273$		0			0
$274$			4.49342i			0.271457i
$275$	5.89284	−	7.85712i	0.355351	−	0.473802i
$276$			4.24264i			0.255377i
$277$	−6.97437	−	6.97437i	−0.419049	−	0.419049i	0.465827	−	0.884876i	$-0.345757\pi$
$277$	−6.97437	−	6.97437i	−0.419049	−	0.419049i	−0.884876	+	0.465827i	$0.845757\pi$
$278$	−9.26357	−	9.26357i	−0.555592	−	0.555592i
$279$	1.98520			0.118851
$280$		0			0
$281$	−17.1412			−1.02256			−0.511280	−	0.859414i	$-0.670829\pi$
$281$	−17.1412			−1.02256			−0.511280	+	0.859414i	$0.670829\pi$
$282$	4.93902	+	4.93902i	0.294114	+	0.294114i
$283$	14.2841	+	14.2841i	0.849103	+	0.849103i	0.990021	−	0.140919i	$-0.0450056\pi$
$283$	14.2841	+	14.2841i	0.849103	+	0.849103i	−0.140919	+	0.990021i	$0.545006\pi$
$284$		−	4.14161i		−	0.245759i
$285$	−2.41421	+	7.24264i	−0.143006	+	0.429017i
$286$		−	6.60724i		−	0.390694i
$287$		0			0
$288$	−0.707107	+	0.707107i	−0.0416667	+	0.0416667i
$289$		−	5.97003i		−	0.351178i
$290$	−8.96861	−	2.98954i	−0.526655	−	0.175552i
$291$	−7.19175			−0.421588
$292$	−2.01480	+	2.01480i	−0.117907	+	0.117907i
$293$	10.8275	+	10.8275i	0.632551	+	0.632551i	0.948707	−	0.316156i	$-0.102392\pi$
$293$	10.8275	+	10.8275i	0.632551	+	0.632551i	−0.316156	+	0.948707i	$0.602392\pi$
$294$		0			0
$295$	−4.19212	−	8.38425i	−0.244075	−	0.488150i
$296$	7.57062			0.440033
$297$	−1.38896	+	1.38896i	−0.0805954	+	0.0805954i
$298$	−15.6521	+	15.6521i	−0.906705	+	0.906705i
$299$	14.2710			0.825311
$300$	0.707107	+	4.94975i	0.0408248	+	0.285774i
$301$		0			0
$302$	6.59154	+	6.59154i	0.379301	+	0.379301i
$303$	−4.34277	+	4.34277i	−0.249486	+	0.249486i
$304$	3.41421			0.195819
$305$	7.85712	−	3.92856i	0.449897	−	0.224949i
$306$		−	4.79271i		−	0.273981i
$307$	−10.4138	+	10.4138i	−0.594349	+	0.594349i	−0.938803	−	0.344454i	$-0.888064\pi$
$307$	−10.4138	+	10.4138i	−0.594349	+	0.594349i	0.344454	+	0.938803i	$0.388064\pi$
$308$		0			0
$309$			12.4853i			0.710263i
$310$	−4.21125	−	1.40375i	−0.239183	−	0.0797277i
$311$			21.0611i			1.19427i	0.802142	+	0.597133i	$0.203694\pi$
$311$			21.0611i			1.19427i	−0.802142	+	0.597133i	$0.796306\pi$
$312$	2.37849	+	2.37849i	0.134656	+	0.134656i
$313$	0.564862	+	0.564862i	0.0319279	+	0.0319279i	0.722890	−	0.690963i	$-0.242813\pi$
$313$	0.564862	+	0.564862i	0.0319279	+	0.0319279i	−0.690963	+	0.722890i	$0.742813\pi$
$314$	−18.4853			−1.04318
$315$		0			0
$316$	−11.5854			−0.651730
$317$	13.2417	+	13.2417i	0.743730	+	0.743730i	0.973294	−	0.229564i	$-0.0737299\pi$
$317$	13.2417	+	13.2417i	0.743730	+	0.743730i	−0.229564	+	0.973294i	$0.573730\pi$
$318$	8.39904	+	8.39904i	0.470995	+	0.470995i
$319$			8.30467i			0.464972i
$320$	2.00000	−	1.00000i	0.111803	−	0.0559017i
$321$		−	4.05052i		−	0.226078i
$322$		0			0
$323$	−11.5706	+	11.5706i	−0.643806	+	0.643806i
$324$		−	1.00000i		−	0.0555556i
$325$	16.6494	−	2.37849i	0.923545	−	0.131935i
$326$	20.9343			1.15944
$327$	−3.44993	+	3.44993i	−0.190782	+	0.190782i
$328$	−8.19212	−	8.19212i	−0.452334	−	0.452334i
$329$		0			0
$330$	3.92856	−	1.96428i	0.216260	−	0.108130i
$331$	10.6072			0.583027			0.291513	−	0.956567i	$-0.405841\pi$
$331$	10.6072			0.583027			0.291513	+	0.956567i	$0.405841\pi$
$332$	10.9996	−	10.9996i	0.603683	−	0.603683i
$333$	−5.35323	+	5.35323i	−0.293355	+	0.293355i
$334$	18.2365			0.997858
$335$	−2.36803	+	7.10409i	−0.129379	+	0.388138i
$336$		0			0
$337$	15.6774	+	15.6774i	0.854003	+	0.854003i	0.990623	−	0.136621i	$-0.0436242\pi$
$337$	15.6774	+	15.6774i	0.854003	+	0.854003i	−0.136621	+	0.990623i	$0.543624\pi$
$338$	−1.19186	+	1.19186i	−0.0648286	+	0.0648286i
$339$	5.62726			0.305631
$340$	−3.38896	+	10.1669i	−0.183792	+	0.551376i
$341$			3.89949i			0.211169i
$342$	−2.41421	+	2.41421i	−0.130546	+	0.130546i
$343$		0			0
$344$		−	11.0563i		−	0.596114i
$345$	4.24264	+	8.48528i	0.228416	+	0.456832i
$346$			16.4133i			0.882385i
$347$	−17.5053	−	17.5053i	−0.939734	−	0.939734i	0.0585505	−	0.998284i	$-0.481352\pi$
$347$	−17.5053	−	17.5053i	−0.939734	−	0.939734i	−0.998284	+	0.0585505i	$0.981352\pi$
$348$	−2.98954	−	2.98954i	−0.160256	−	0.160256i
$349$	23.6980			1.26852			0.634261	−	0.773119i	$-0.281304\pi$
$349$	23.6980			1.26852			0.634261	+	0.773119i	$0.281304\pi$
$350$		0			0
$351$	−3.36370			−0.179541
$352$	−1.38896	−	1.38896i	−0.0740316	−	0.0740316i
$353$	13.2879	+	13.2879i	0.707245	+	0.707245i	0.965955	−	0.258710i	$-0.0832975\pi$
$353$	13.2879	+	13.2879i	0.707245	+	0.707245i	−0.258710	+	0.965955i	$0.583297\pi$
$354$		−	4.19212i		−	0.222809i
$355$	−4.14161	−	8.28321i	−0.219814	−	0.439627i
$356$			6.02092i			0.319108i
$357$		0			0
$358$	−9.78800	+	9.78800i	−0.517312	+	0.517312i
$359$			6.34367i			0.334806i	0.985889	+	0.167403i	$0.0535382\pi$
$359$			6.34367i			0.334806i	−0.985889	+	0.167403i	$0.946462\pi$
$360$	−0.707107	+	2.12132i	−0.0372678	+	0.111803i
$361$	−7.34315			−0.386481
$362$	15.7775	−	15.7775i	0.829249	−	0.829249i
$363$	5.04988	+	5.04988i	0.265050	+	0.265050i
$364$		0			0
$365$	−2.01480	+	6.04439i	−0.105459	+	0.316378i
$366$	3.92856			0.205349
$367$	3.47900	−	3.47900i	0.181602	−	0.181602i	−0.610451	−	0.792054i	$-0.709012\pi$
$367$	3.47900	−	3.47900i	0.181602	−	0.181602i	0.792054	+	0.610451i	$0.209012\pi$
$368$	3.00000	−	3.00000i	0.156386	−	0.156386i
$369$	11.5854			0.603112
$370$	15.1412	−	7.57062i	0.787155	−	0.393578i
$371$		0			0
$372$	−1.40375	−	1.40375i	−0.0727811	−	0.0727811i
$373$	−4.13114	+	4.13114i	−0.213903	+	0.213903i	−0.805923	−	0.592020i	$-0.798330\pi$
$373$	−4.13114	+	4.13114i	−0.213903	+	0.213903i	0.592020	+	0.805923i	$0.298330\pi$
$374$	9.41421			0.486797
$375$	6.36396	+	9.19239i	0.328634	+	0.474693i
$376$		−	6.98483i		−	0.360215i
$377$	−10.0559	+	10.0559i	−0.517905	+	0.517905i
$378$		0			0
$379$		−	38.8486i		−	1.99552i	−0.0669045	−	0.997759i	$-0.521312\pi$
$379$		−	38.8486i		−	1.99552i	0.0669045	−	0.997759i	$-0.478688\pi$
$380$	6.82843	−	3.41421i	0.350291	−	0.175145i
$381$		−	14.3424i		−	0.734783i
$382$	−0.707371	−	0.707371i	−0.0361923	−	0.0361923i
$383$	1.05432	+	1.05432i	0.0538733	+	0.0538733i	0.733530	−	0.679657i	$-0.237871\pi$
$383$	1.05432	+	1.05432i	0.0538733	+	0.0538733i	−0.679657	+	0.733530i	$0.737871\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−6.17120			−0.314106
$387$	7.81796	+	7.81796i	0.397409	+	0.397409i
$388$	5.08534	+	5.08534i	0.258169	+	0.258169i
$389$			36.9343i			1.87264i	0.351143	+	0.936322i	$0.385793\pi$
$389$			36.9343i			1.87264i	−0.351143	+	0.936322i	$0.614207\pi$
$390$	7.13548	+	2.37849i	0.361319	+	0.120440i
$391$			20.3337i			1.02832i
$392$		0			0
$393$	−6.96428	+	6.96428i	−0.351301	+	0.351301i
$394$		−	15.9697i		−	0.804540i
$395$	−23.1708	+	11.5854i	−1.16585	+	0.582925i
$396$	1.96428			0.0987087
$397$	2.24264	−	2.24264i	0.112555	−	0.112555i	−0.648586	−	0.761141i	$-0.724639\pi$
$397$	2.24264	−	2.24264i	0.112555	−	0.112555i	0.761141	+	0.648586i	$0.224639\pi$
$398$	18.6374	+	18.6374i	0.934206	+	0.934206i
$399$		0			0
$400$	3.00000	−	4.00000i	0.150000	−	0.200000i
$401$	−29.3415			−1.46524			−0.732622	−	0.680636i	$-0.761704\pi$
$401$	−29.3415			−1.46524			−0.732622	+	0.680636i	$0.761704\pi$
$402$	−2.36803	+	2.36803i	−0.118107	+	0.118107i
$403$	−4.72179	+	4.72179i	−0.235209	+	0.235209i
$404$	6.14161			0.305556
$405$	−1.00000	−	2.00000i	−0.0496904	−	0.0993808i
$406$		0			0
$407$	−10.5152	−	10.5152i	−0.521221	−	0.521221i
$408$	−3.38896	+	3.38896i	−0.167778	+	0.167778i
$409$	−7.06569			−0.349376			−0.174688	−	0.984624i	$-0.555892\pi$
$409$	−7.06569			−0.349376			−0.174688	+	0.984624i	$0.555892\pi$
$410$	−24.5764	−	8.19212i	−1.21374	−	0.404580i
$411$			4.49342i			0.221644i
$412$	8.82843	−	8.82843i	0.434945	−	0.434945i
$413$		0			0
$414$			4.24264i			0.208514i
$415$	10.9996	−	32.9989i	0.539950	−	1.61985i
$416$		−	3.36370i		−	0.164919i
$417$	−9.26357	−	9.26357i	−0.453639	−	0.453639i
$418$	−4.74219	−	4.74219i	−0.231948	−	0.231948i
$419$	−2.34315			−0.114470			−0.0572351	−	0.998361i	$-0.518228\pi$
$419$	−2.34315			−0.114470			−0.0572351	+	0.998361i	$0.518228\pi$
$420$		0			0
$421$	−37.7189			−1.83831			−0.919153	−	0.393901i	$-0.871125\pi$
$421$	−37.7189			−1.83831			−0.919153	+	0.393901i	$0.871125\pi$
$422$	12.2365	+	12.2365i	0.595664	+	0.595664i
$423$	4.93902	+	4.93902i	0.240143	+	0.240143i
$424$		−	11.8780i		−	0.576849i
$425$	3.38896	+	23.7227i	0.164388	+	1.15072i
$426$		−	4.14161i		−	0.200662i
$427$		0			0
$428$	−2.86415	+	2.86415i	−0.138444	+	0.138444i
$429$		−	6.60724i		−	0.319001i
$430$	−11.0563	−	22.1125i	−0.533181	−	1.06636i
$431$	−2.72792			−0.131399			−0.0656997	−	0.997839i	$-0.520928\pi$
$431$	−2.72792			−0.131399			−0.0656997	+	0.997839i	$0.520928\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	12.8641	+	12.8641i	0.618211	+	0.618211i	0.945072	−	0.326861i	$-0.105991\pi$
$433$	12.8641	+	12.8641i	0.618211	+	0.618211i	−0.326861	+	0.945072i	$0.605991\pi$
$434$		0			0
$435$	−8.96861	−	2.98954i	−0.430012	−	0.143337i
$436$	4.87894			0.233659
$437$	10.2426	−	10.2426i	0.489972	−	0.489972i
$438$	−2.01480	+	2.01480i	−0.0962707	+	0.0962707i
$439$	8.92333			0.425887			0.212944	−	0.977064i	$-0.431695\pi$
$439$	8.92333			0.425887			0.212944	+	0.977064i	$0.431695\pi$
$440$	−4.16687	−	1.38896i	−0.198648	−	0.0662158i
$441$		0			0
$442$	11.3994	+	11.3994i	0.542215	+	0.542215i
$443$	−12.7779	+	12.7779i	−0.607097	+	0.607097i	−0.942186	−	0.335089i	$-0.891233\pi$
$443$	−12.7779	+	12.7779i	−0.607097	+	0.607097i	0.335089	+	0.942186i	$0.391233\pi$
$444$	7.57062			0.359286
$445$	6.02092	+	12.0418i	0.285419	+	0.570838i
$446$			5.07921i			0.240507i
$447$	−15.6521	+	15.6521i	−0.740321	+	0.740321i
$448$		0			0
$449$		−	2.78658i		−	0.131507i	−0.997836	−	0.0657534i	$-0.979055\pi$
$449$		−	2.78658i		−	0.131507i	0.997836	−	0.0657534i	$-0.0209451\pi$
$450$	0.707107	+	4.94975i	0.0333333	+	0.233333i
$451$			22.7570i			1.07158i
$452$	−3.97908	−	3.97908i	−0.187160	−	0.187160i
$453$	6.59154	+	6.59154i	0.309698	+	0.309698i
$454$	−25.2423			−1.18468
$455$		0			0
$456$	3.41421			0.159885
$457$	−29.5764	−	29.5764i	−1.38352	−	1.38352i	−0.838272	−	0.545252i	$-0.816434\pi$
$457$	−29.5764	−	29.5764i	−1.38352	−	1.38352i	−0.545252	−	0.838272i	$-0.683566\pi$
$458$	3.95001	+	3.95001i	0.184572	+	0.184572i
$459$		−	4.79271i		−	0.223704i
$460$	3.00000	−	9.00000i	0.139876	−	0.419627i
$461$			6.88761i			0.320788i	0.987053	+	0.160394i	$0.0512765\pi$
$461$			6.88761i			0.320788i	−0.987053	+	0.160394i	$0.948724\pi$
$462$		0			0
$463$	14.7988	−	14.7988i	0.687760	−	0.687760i	−0.273976	−	0.961736i	$-0.588339\pi$
$463$	14.7988	−	14.7988i	0.687760	−	0.687760i	0.961736	+	0.273976i	$0.0883390\pi$
$464$			4.22784i			0.196273i
$465$	−4.21125	−	1.40375i	−0.195292	−	0.0650974i
$466$	−28.4138			−1.31625
$467$	−10.4348	+	10.4348i	−0.482863	+	0.482863i	−0.906045	−	0.423182i	$-0.860913\pi$
$467$	−10.4348	+	10.4348i	−0.482863	+	0.482863i	0.423182	+	0.906045i	$0.360913\pi$
$468$	2.37849	+	2.37849i	0.109946	+	0.109946i
$469$		0			0
$470$	−6.98483	−	13.9697i	−0.322186	−	0.644372i
$471$	−18.4853			−0.851757
$472$	−2.96428	+	2.96428i	−0.136442	+	0.136442i
$473$	−15.3567	+	15.3567i	−0.706100	+	0.706100i
$474$	−11.5854			−0.532136
$475$	10.2426	−	13.6569i	0.469965	−	0.626619i
$476$		0			0
$477$	8.39904	+	8.39904i	0.384566	+	0.384566i
$478$	2.19250	−	2.19250i	0.100283	−	0.100283i
$479$	10.3633			0.473512			0.236756	−	0.971569i	$-0.423916\pi$
$479$	10.3633			0.473512			0.236756	+	0.971569i	$0.423916\pi$
$480$	2.00000	−	1.00000i	0.0912871	−	0.0456435i
$481$		−	25.4653i		−	1.16112i
$482$	13.4891	−	13.4891i	0.614411	−	0.614411i
$483$		0			0
$484$		−	7.14161i		−	0.324619i
$485$	15.2560	+	5.08534i	0.692740	+	0.230913i
$486$		−	1.00000i		−	0.0453609i
$487$	17.5645	+	17.5645i	0.795923	+	0.795923i	0.982450	−	0.186527i	$-0.0597232\pi$
$487$	17.5645	+	17.5645i	0.795923	+	0.795923i	−0.186527	+	0.982450i	$0.559723\pi$
$488$	−2.77791	−	2.77791i	−0.125750	−	0.125750i
$489$	20.9343			0.946682
$490$		0			0
$491$	36.6126			1.65230			0.826152	−	0.563447i	$-0.190525\pi$
$491$	36.6126			1.65230			0.826152	+	0.563447i	$0.190525\pi$
$492$	−8.19212	−	8.19212i	−0.369329	−	0.369329i
$493$	−14.3280	−	14.3280i	−0.645300	−	0.645300i
$494$		−	11.4844i		−	0.516707i
$495$	3.92856	−	1.96428i	0.176576	−	0.0882878i
$496$			1.98520i			0.0891383i
$497$		0			0
$498$	10.9996	−	10.9996i	0.492905	−	0.492905i
$499$			15.5472i			0.695986i	0.937497	+	0.347993i	$0.113137\pi$
$499$			15.5472i			0.695986i	−0.937497	+	0.347993i	$0.886863\pi$
$500$	2.00000	−	11.0000i	0.0894427	−	0.491935i
$501$	18.2365			0.814747
$502$	−10.5649	+	10.5649i	−0.471533	+	0.471533i
$503$	−19.4957	−	19.4957i	−0.869272	−	0.869272i	0.123120	−	0.992392i	$-0.460710\pi$
$503$	−19.4957	−	19.4957i	−0.869272	−	0.869272i	−0.992392	+	0.123120i	$0.960710\pi$
$504$		0			0
$505$	12.2832	−	6.14161i	0.546596	−	0.273298i
$506$	−8.33373			−0.370480
$507$	−1.19186	+	1.19186i	−0.0529323	+	0.0529323i
$508$	−10.1416	+	10.1416i	−0.449961	+	0.449961i
$509$	3.11292			0.137978			0.0689888	−	0.997617i	$-0.478023\pi$
$509$	3.11292			0.137978			0.0689888	+	0.997617i	$0.478023\pi$
$510$	−3.38896	+	10.1669i	−0.150065	+	0.450196i
$511$		0			0
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−2.41421	+	2.41421i	−0.106590	+	0.106590i
$514$	16.7126			0.737161
$515$	8.82843	−	26.4853i	0.389027	−	1.16708i
$516$		−	11.0563i		−	0.486725i
$517$	−9.70162	+	9.70162i	−0.426677	+	0.426677i
$518$		0			0
$519$			16.4133i			0.720464i
$520$	−3.36370	−	6.72739i	−0.147508	−	0.295016i
$521$			18.8905i			0.827606i	0.910366	+	0.413803i	$0.135800\pi$
$521$			18.8905i			0.827606i	−0.910366	+	0.413803i	$0.864200\pi$
$522$	−2.98954	−	2.98954i	−0.130849	−	0.130849i
$523$	−12.9709	−	12.9709i	−0.567179	−	0.567179i	0.364158	−	0.931337i	$-0.381357\pi$
$523$	−12.9709	−	12.9709i	−0.567179	−	0.567179i	−0.931337	+	0.364158i	$0.881357\pi$
$524$	9.84898			0.430255
$525$		0			0
$526$	−14.5850			−0.635938
$527$	−6.72777	−	6.72777i	−0.293066	−	0.293066i
$528$	−1.38896	−	1.38896i	−0.0604465	−	0.0604465i
$529$			5.00000i			0.217391i
$530$	−11.8780	−	23.7561i	−0.515949	−	1.03190i
$531$		−	4.19212i		−	0.181923i
$532$		0			0
$533$	−27.5558	+	27.5558i	−1.19358	+	1.19358i
$534$			6.02092i			0.260551i
$535$	−2.86415	+	8.59244i	−0.123828	+	0.371484i
$536$	3.34890			0.144650
$537$	−9.78800	+	9.78800i	−0.422383	+	0.422383i
$538$	−18.5554	−	18.5554i	−0.799982	−	0.799982i
$539$		0			0
$540$	−0.707107	+	2.12132i	−0.0304290	+	0.0912871i
$541$	−25.0279			−1.07604			−0.538018	−	0.842934i	$-0.680827\pi$
$541$	−25.0279			−1.07604			−0.538018	+	0.842934i	$0.680827\pi$
$542$	−9.09633	+	9.09633i	−0.390721	+	0.390721i
$543$	15.7775	−	15.7775i	0.677079	−	0.677079i
$544$	4.79271			0.205486
$545$	9.75789	−	4.87894i	0.417982	−	0.208991i
$546$		0			0
$547$	−0.0304849	−	0.0304849i	−0.00130344	−	0.00130344i	0.706455	−	0.707758i	$-0.250293\pi$
$547$	−0.0304849	−	0.0304849i	−0.00130344	−	0.00130344i	−0.707758	+	0.706455i	$0.750293\pi$
$548$	3.17733	−	3.17733i	0.135729	−	0.135729i
$549$	3.92856			0.167667
$550$	−9.72269	+	1.38896i	−0.414577	+	0.0592252i
$551$			14.4348i			0.614942i
$552$	3.00000	−	3.00000i	0.127688	−	0.127688i
$553$		0			0
$554$			9.86325i			0.419049i
$555$	15.1412	−	7.57062i	0.642710	−	0.321355i
$556$			13.1007i			0.555592i
$557$	18.7070	+	18.7070i	0.792641	+	0.792641i	0.981923	−	0.189282i	$-0.0606160\pi$
$557$	18.7070	+	18.7070i	0.792641	+	0.792641i	−0.189282	+	0.981923i	$0.560616\pi$
$558$	−1.40375	−	1.40375i	−0.0594255	−	0.0594255i
$559$	−37.1899			−1.57297
$560$		0			0
$561$	9.41421			0.397468
$562$	12.1207	+	12.1207i	0.511280	+	0.511280i
$563$	−19.7270	−	19.7270i	−0.831395	−	0.831395i	0.156313	−	0.987708i	$-0.450039\pi$
$563$	−19.7270	−	19.7270i	−0.831395	−	0.831395i	−0.987708	+	0.156313i	$0.950039\pi$
$564$		−	6.98483i		−	0.294114i
$565$	−11.9372	−	3.97908i	−0.502203	−	0.167401i
$566$		−	20.2008i		−	0.849103i
$567$		0			0
$568$	−2.92856	+	2.92856i	−0.122880	+	0.122880i
$569$			3.78568i			0.158704i	0.996847	+	0.0793519i	$0.0252851\pi$
$569$			3.78568i			0.158704i	−0.996847	+	0.0793519i	$0.974715\pi$
$570$	6.82843	−	3.41421i	0.286011	−	0.143006i
$571$	40.4246			1.69172			0.845858	−	0.533407i	$-0.179089\pi$
$571$	40.4246			1.69172			0.845858	+	0.533407i	$0.179089\pi$
$572$	−4.67202	+	4.67202i	−0.195347	+	0.195347i
$573$	−0.707371	−	0.707371i	−0.0295508	−	0.0295508i
$574$		0			0
$575$	−3.00000	−	21.0000i	−0.125109	−	0.875761i
$576$	1.00000			0.0416667
$577$	−1.67725	+	1.67725i	−0.0698249	+	0.0698249i	−0.741157	−	0.671332i	$-0.765723\pi$
$577$	−1.67725	+	1.67725i	−0.0698249	+	0.0698249i	0.671332	+	0.741157i	$0.265723\pi$
$578$	−4.22145	+	4.22145i	−0.175589	+	0.175589i
$579$	−6.17120			−0.256466
$580$	4.22784	+	8.45569i	0.175552	+	0.351103i
$581$		0			0
$582$	5.08534	+	5.08534i	0.210794	+	0.210794i
$583$	−16.4981	+	16.4981i	−0.683280	+	0.683280i
$584$	2.84935			0.117907
$585$	7.13548	+	2.37849i	0.295016	+	0.0983386i
$586$		−	15.3124i		−	0.632551i
$587$	−3.86990	+	3.86990i	−0.159728	+	0.159728i	−0.782446	−	0.622718i	$-0.786028\pi$
$587$	−3.86990	+	3.86990i	−0.159728	+	0.159728i	0.622718	+	0.782446i	$0.286028\pi$
$588$		0			0
$589$			6.77791i			0.279279i
$590$	−2.96428	+	8.89284i	−0.122037	+	0.366112i
$591$		−	15.9697i		−	0.656904i
$592$	−5.35323	−	5.35323i	−0.220017	−	0.220017i
$593$	−8.84703	−	8.84703i	−0.363304	−	0.363304i	0.501724	−	0.865028i	$-0.332699\pi$
$593$	−8.84703	−	8.84703i	−0.363304	−	0.363304i	−0.865028	+	0.501724i	$0.832699\pi$
$594$	1.96428			0.0805954
$595$		0			0
$596$	22.1355			0.906705
$597$	18.6374	+	18.6374i	0.762776	+	0.762776i
$598$	−10.0911	−	10.0911i	−0.412655	−	0.412655i
$599$			27.6671i			1.13045i	0.824938	+	0.565223i	$0.191210\pi$
$599$			27.6671i			1.13045i	−0.824938	+	0.565223i	$0.808790\pi$
$600$	3.00000	−	4.00000i	0.122474	−	0.163299i
$601$			19.2385i			0.784753i	0.919805	+	0.392376i	$0.128347\pi$
$601$			19.2385i			0.784753i	−0.919805	+	0.392376i	$0.871653\pi$
$602$		0			0
$603$	−2.36803	+	2.36803i	−0.0964337	+	0.0964337i
$604$		−	9.32185i		−	0.379301i
$605$	−7.14161	−	14.2832i	−0.290348	−	0.580695i
$606$	6.14161			0.249486
$607$	−0.0558981	+	0.0558981i	−0.00226883	+	0.00226883i	−0.708240	−	0.705971i	$-0.750511\pi$
$607$	−0.0558981	+	0.0558981i	−0.00226883	+	0.00226883i	0.705971	+	0.708240i	$0.250511\pi$
$608$	−2.41421	−	2.41421i	−0.0979093	−	0.0979093i
$609$		0			0
$610$	−8.33373	−	2.77791i	−0.337423	−	0.112474i
$611$	−23.4949			−0.950500
$612$	−3.38896	+	3.38896i	−0.136990	+	0.136990i
$613$	28.1365	−	28.1365i	1.13642	−	1.13642i	0.147337	−	0.989086i	$-0.452930\pi$
$613$	28.1365	−	28.1365i	1.13642	−	1.13642i	0.989086	−	0.147337i	$-0.0470703\pi$
$614$	14.7274			0.594349
$615$	−24.5764	−	8.19212i	−0.991015	−	0.330338i
$616$		0			0
$617$	−1.93431	−	1.93431i	−0.0778725	−	0.0778725i	0.667098	−	0.744970i	$-0.267536\pi$
$617$	−1.93431	−	1.93431i	−0.0778725	−	0.0778725i	−0.744970	+	0.667098i	$0.767536\pi$
$618$	8.82843	−	8.82843i	0.355131	−	0.355131i
$619$	−31.1695			−1.25281			−0.626405	−	0.779498i	$-0.715474\pi$
$619$	−31.1695			−1.25281			−0.626405	+	0.779498i	$0.715474\pi$
$620$	1.98520	+	3.97041i	0.0797277	+	0.159455i
$621$			4.24264i			0.170251i
$622$	14.8925	−	14.8925i	0.597133	−	0.597133i
$623$		0			0
$624$		−	3.36370i		−	0.134656i
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$		−	0.798835i		−	0.0319279i
$627$	−4.74219	−	4.74219i	−0.189385	−	0.189385i
$628$	13.0711	+	13.0711i	0.521592	+	0.521592i
$629$	36.2837			1.44673
$630$		0			0
$631$	42.9180			1.70854			0.854270	−	0.519830i	$-0.174005\pi$
$631$	42.9180			1.70854			0.854270	+	0.519830i	$0.174005\pi$
$632$	8.19212	+	8.19212i	0.325865	+	0.325865i
$633$	12.2365	+	12.2365i	0.486358	+	0.486358i
$634$		−	18.7266i		−	0.743730i
$635$	−10.1416	+	30.4248i	−0.402457	+	1.20737i
$636$		−	11.8780i		−	0.470995i
$637$		0			0
$638$	5.87229	−	5.87229i	0.232486	−	0.232486i
$639$		−	4.14161i		−	0.163839i
$640$	−2.12132	−	0.707107i	−0.0838525	−	0.0279508i
$641$	−5.94082			−0.234648			−0.117324	−	0.993094i	$-0.537432\pi$
$641$	−5.94082			−0.234648			−0.117324	+	0.993094i	$0.537432\pi$
$642$	−2.86415	+	2.86415i	−0.113039	+	0.113039i
$643$	−27.5259	−	27.5259i	−1.08551	−	1.08551i	−0.995984	−	0.0895296i	$-0.971464\pi$
$643$	−27.5259	−	27.5259i	−1.08551	−	1.08551i	−0.0895296	−	0.995984i	$-0.528536\pi$
$644$		0			0
$645$	−11.0563	−	22.1125i	−0.435340	−	0.870681i
$646$	16.3633			0.643806
$647$	9.83889	−	9.83889i	0.386807	−	0.386807i	−0.486740	−	0.873547i	$-0.661814\pi$
$647$	9.83889	−	9.83889i	0.386807	−	0.386807i	0.873547	+	0.486740i	$0.161814\pi$
$648$	−0.707107	+	0.707107i	−0.0277778	+	0.0277778i
$649$	8.23450			0.323232
$650$	−13.4548	−	10.0911i	−0.527740	−	0.395805i
$651$		0			0
$652$	−14.8028	−	14.8028i	−0.579722	−	0.579722i
$653$	0.914665	−	0.914665i	0.0357936	−	0.0357936i	−0.688983	−	0.724777i	$-0.741943\pi$
$653$	0.914665	−	0.914665i	0.0357936	−	0.0357936i	0.724777	+	0.688983i	$0.241943\pi$
$654$	4.87894			0.190782
$655$	19.6980	−	9.84898i	0.769663	−	0.384831i
$656$			11.5854i			0.452334i
$657$	−2.01480	+	2.01480i	−0.0786047	+	0.0786047i
$658$		0			0
$659$		−	4.43805i		−	0.172882i	−0.996257	−	0.0864410i	$-0.972451\pi$
$659$		−	4.43805i		−	0.172882i	0.996257	−	0.0864410i	$-0.0275494\pi$
$660$	−4.16687	−	1.38896i	−0.162195	−	0.0540650i
$661$			3.50246i			0.136230i	0.997677	+	0.0681150i	$0.0216985\pi$
$661$			3.50246i			0.136230i	−0.997677	+	0.0681150i	$0.978302\pi$
$662$	−7.50045	−	7.50045i	−0.291513	−	0.291513i
$663$	11.3994	+	11.3994i	0.442717	+	0.442717i
$664$	−15.5558			−0.603683
$665$		0			0
$666$	7.57062			0.293355
$667$	12.6835	+	12.6835i	0.491108	+	0.491108i
$668$	−12.8952	−	12.8952i	−0.498929	−	0.498929i
$669$			5.07921i			0.196373i
$670$	6.69780	−	3.34890i	0.258759	−	0.129379i
$671$			7.71679i			0.297903i
$672$		0			0
$673$	−0.283588	+	0.283588i	−0.0109315	+	0.0109315i	−0.712551	−	0.701620i	$-0.752460\pi$
$673$	−0.283588	+	0.283588i	−0.0109315	+	0.0109315i	0.701620	+	0.712551i	$0.252460\pi$
$674$		−	22.1712i		−	0.854003i
$675$	0.707107	+	4.94975i	0.0272166	+	0.190516i
$676$	1.68554			0.0648286
$677$	−17.6774	+	17.6774i	−0.679398	+	0.679398i	−0.959864	−	0.280466i	$-0.909511\pi$
$677$	−17.6774	+	17.6774i	−0.679398	+	0.679398i	0.280466	+	0.959864i	$0.409511\pi$
$678$	−3.97908	−	3.97908i	−0.152815	−	0.152815i
$679$		0			0
$680$	9.58541	−	4.79271i	0.367584	−	0.183792i
$681$	−25.2423			−0.967286
$682$	2.75736	−	2.75736i	0.105585	−	0.105585i
$683$	14.0498	−	14.0498i	0.537599	−	0.537599i	−0.385224	−	0.922823i	$-0.625876\pi$
$683$	14.0498	−	14.0498i	0.537599	−	0.537599i	0.922823	+	0.385224i	$0.125876\pi$
$684$	3.41421			0.130546
$685$	3.17733	−	9.53198i	0.121399	−	0.364198i
$686$		0			0
$687$	3.95001	+	3.95001i	0.150702	+	0.150702i
$688$	−7.81796	+	7.81796i	−0.298057	+	0.298057i
$689$	−39.9541			−1.52213
$690$	3.00000	−	9.00000i	0.114208	−	0.342624i
$691$			51.4668i			1.95789i	0.204123	+	0.978945i	$0.434566\pi$
$691$			51.4668i			1.95789i	−0.204123	+	0.978945i	$0.565434\pi$
$692$	11.6060	−	11.6060i	0.441193	−	0.441193i
$693$		0			0
$694$			24.7562i			0.939734i
$695$	13.1007	+	26.2013i	0.496936	+	0.993873i
$696$			4.22784i			0.160256i
$697$	−39.2624	−	39.2624i	−1.48717	−	1.48717i
$698$	−16.7570	−	16.7570i	−0.634261	−	0.634261i
$699$	−28.4138			−1.07471
$700$		0			0
$701$	−5.27821			−0.199355			−0.0996776	−	0.995020i	$-0.531781\pi$
$701$	−5.27821			−0.199355			−0.0996776	+	0.995020i	$0.531781\pi$
$702$	2.37849	+	2.37849i	0.0897704	+	0.0897704i
$703$	−18.2771	−	18.2771i	−0.689333	−	0.689333i
$704$			1.96428i			0.0740316i
$705$	−6.98483	−	13.9697i	−0.263064	−	0.526128i
$706$		−	18.7920i		−	0.707245i
$707$		0			0
$708$	−2.96428	+	2.96428i	−0.111404	+	0.111404i
$709$		−	6.30414i		−	0.236757i	−0.992969	−	0.118378i	$-0.962230\pi$
$709$		−	6.30414i		−	0.236757i	0.992969	−	0.118378i	$-0.0377696\pi$
$710$	−2.92856	+	8.78568i	−0.109907	+	0.329721i
$711$	−11.5854			−0.434487
$712$	4.25744	−	4.25744i	0.159554	−	0.159554i
$713$	5.95561	+	5.95561i	0.223039	+	0.223039i
$714$		0			0
$715$	−4.67202	+	14.0161i	−0.174724	+	0.524171i
$716$	13.8423			0.517312
$717$	2.19250	−	2.19250i	0.0818803	−	0.0818803i
$718$	4.48566	−	4.48566i	0.167403	−	0.167403i
$719$	−11.8369			−0.441443			−0.220722	−	0.975337i	$-0.570841\pi$
$719$	−11.8369			−0.441443			−0.220722	+	0.975337i	$0.570841\pi$
$720$	2.00000	−	1.00000i	0.0745356	−	0.0372678i
$721$		0			0
$722$	5.19239	+	5.19239i	0.193241	+	0.193241i
$723$	13.4891	−	13.4891i	0.501665	−	0.501665i
$724$	−22.3128			−0.829249
$725$	16.9114	+	12.6835i	0.628073	+	0.471055i
$726$		−	7.14161i		−	0.265050i
$727$	35.2275	−	35.2275i	1.30651	−	1.30651i	0.382601	−	0.923914i	$-0.375028\pi$
$727$	35.2275	−	35.2275i	1.30651	−	1.30651i	0.923914	−	0.382601i	$-0.124972\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$	5.69870	−	2.84935i	0.210918	−	0.105459i
$731$		−	52.9895i		−	1.95989i
$732$	−2.77791	−	2.77791i	−0.102675	−	0.102675i
$733$	23.5767	+	23.5767i	0.870827	+	0.870827i	0.992563	−	0.121736i	$-0.0388460\pi$
$733$	23.5767	+	23.5767i	0.870827	+	0.870827i	−0.121736	+	0.992563i	$0.538846\pi$
$734$	−4.92005			−0.181602
$735$		0			0
$736$	−4.24264			−0.156386
$737$	−4.65147	−	4.65147i	−0.171339	−	0.171339i
$738$	−8.19212	−	8.19212i	−0.301556	−	0.301556i
$739$			8.56359i			0.315017i	0.987518	+	0.157508i	$0.0503461\pi$
$739$			8.56359i			0.315017i	−0.987518	+	0.157508i	$0.949654\pi$
$740$	−16.0597	−	5.35323i	−0.590366	−	0.196789i
$741$		−	11.4844i		−	0.421889i
$742$		0			0
$743$	−19.4844	+	19.4844i	−0.714813	+	0.714813i	−0.967538	−	0.252725i	$-0.918673\pi$
$743$	−19.4844	+	19.4844i	−0.714813	+	0.714813i	0.252725	+	0.967538i	$0.418673\pi$
$744$			1.98520i			0.0727811i
$745$	44.2710	−	22.1355i	1.62196	−	0.810981i
$746$	5.84232			0.213903
$747$	10.9996	−	10.9996i	0.402455	−	0.402455i
$748$	−6.65685	−	6.65685i	−0.243399	−	0.243399i
$749$		0			0
$750$	2.00000	−	11.0000i	0.0730297	−	0.401663i
$751$	4.47534			0.163307			0.0816537	−	0.996661i	$-0.473980\pi$
$751$	4.47534			0.163307			0.0816537	+	0.996661i	$0.473980\pi$
$752$	−4.93902	+	4.93902i	−0.180108	+	0.180108i
$753$	−10.5649	+	10.5649i	−0.385005	+	0.385005i
$754$	14.2212			0.517905
$755$	−9.32185	−	18.6437i	−0.339257	−	0.678514i
$756$		0			0
$757$	21.6660	+	21.6660i	0.787466	+	0.787466i	0.981078	−	0.193612i	$-0.0620204\pi$
$757$	21.6660	+	21.6660i	0.787466	+	0.787466i	−0.193612	+	0.981078i	$0.562020\pi$
$758$	−27.4701	+	27.4701i	−0.997759	+	0.997759i
$759$	−8.33373			−0.302495
$760$	−7.24264	−	2.41421i	−0.262718	−	0.0875727i
$761$		−	24.2136i		−	0.877741i	−0.898550	−	0.438871i	$-0.855379\pi$
$761$		−	24.2136i		−	0.877741i	0.898550	−	0.438871i	$-0.144621\pi$
$762$	−10.1416	+	10.1416i	−0.367392	+	0.367392i
$763$		0			0
$764$			1.00037i			0.0361923i
$765$	−3.38896	+	10.1669i	−0.122528	+	0.367584i
$766$		−	1.49104i		−	0.0538733i
$767$	9.97094	+	9.97094i	0.360030	+	0.360030i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	−26.8553			−0.968426			−0.484213	−	0.874950i	$-0.660894\pi$
$769$	−26.8553			−0.968426			−0.484213	+	0.874950i	$0.660894\pi$
$770$		0			0
$771$	16.7126			0.601889
$772$	4.36370	+	4.36370i	0.157053	+	0.157053i
$773$	−19.0702	−	19.0702i	−0.685906	−	0.685906i	0.275418	−	0.961324i	$-0.411184\pi$
$773$	−19.0702	−	19.0702i	−0.685906	−	0.685906i	−0.961324	+	0.275418i	$0.911184\pi$
$774$		−	11.0563i		−	0.397409i
$775$	7.94082	+	5.95561i	0.285243	+	0.213932i
$776$		−	7.19175i		−	0.258169i
$777$		0			0
$778$	26.1165	−	26.1165i	0.936322	−	0.936322i
$779$			39.5551i			1.41721i
$780$	−3.36370	−	6.72739i	−0.120440	−	0.240879i
$781$	8.13527			0.291103
$782$	14.3781	−	14.3781i	0.514160	−	0.514160i
$783$	−2.98954	−	2.98954i	−0.106837	−	0.106837i
$784$		0			0
$785$	39.2132	+	13.0711i	1.39958	+	0.466526i
$786$	9.84898			0.351301
$787$	−0.0418495	+	0.0418495i	−0.00149177	+	0.00149177i	−0.707852	−	0.706361i	$-0.750336\pi$
$787$	−0.0418495	+	0.0418495i	−0.00149177	+	0.00149177i	0.706361	+	0.707852i	$0.250336\pi$
$788$	−11.2923	+	11.2923i	−0.402270	+	0.402270i
$789$	−14.5850			−0.519241
$790$	24.5764	+	8.19212i	0.874388	+	0.291463i
$791$		0			0
$792$	−1.38896	−	1.38896i	−0.0493544	−	0.0493544i
$793$	−9.34405	+	9.34405i	−0.331817	+	0.331817i
$794$	−3.17157			−0.112555
$795$	−11.8780	−	23.7561i	−0.421271	−	0.842541i
$796$		−	26.3572i		−	0.934206i
$797$	5.26409	−	5.26409i	0.186464	−	0.186464i	−0.607702	−	0.794165i	$-0.707908\pi$
$797$	5.26409	−	5.26409i	0.186464	−	0.186464i	0.794165	+	0.607702i	$0.207908\pi$
$798$		0			0
$799$		−	33.4762i		−	1.18430i
$800$	−4.94975	+	0.707107i	−0.175000	+	0.0250000i
$801$			6.02092i			0.212739i
$802$	20.7476	+	20.7476i	0.732622	+	0.732622i
$803$	−3.95762	−	3.95762i	−0.139661	−	0.139661i
$804$	3.34890			0.118107
$805$		0			0
$806$	6.67762			0.235209
$807$	−18.5554	−	18.5554i	−0.653183	−	0.653183i
$808$	−4.34277	−	4.34277i	−0.152778	−	0.152778i
$809$			11.1698i			0.392708i	0.980533	+	0.196354i	$0.0629102\pi$
$809$			11.1698i			0.392708i	−0.980533	+	0.196354i	$0.937090\pi$
$810$	−0.707107	+	2.12132i	−0.0248452	+	0.0745356i
$811$			51.3839i			1.80433i	0.431389	+	0.902166i	$0.358024\pi$
$811$			51.3839i			1.80433i	−0.431389	+	0.902166i	$0.641976\pi$
$812$		0			0
$813$	−9.09633	+	9.09633i	−0.319022	+	0.319022i
$814$			14.8708i			0.521221i
$815$	−44.4084	−	14.8028i	−1.55556	−	0.518519i
$816$	4.79271			0.167778
$817$	−26.6922	+	26.6922i	−0.933842	+	0.933842i
$818$	4.99619	+	4.99619i	0.174688	+	0.174688i
$819$		0			0
$820$	11.5854	+	23.1708i	0.404580	+	0.809160i
$821$	−10.9848			−0.383373			−0.191687	−	0.981456i	$-0.561396\pi$
$821$	−10.9848			−0.383373			−0.191687	+	0.981456i	$0.561396\pi$
$822$	3.17733	−	3.17733i	0.110822	−	0.110822i
$823$	15.4647	−	15.4647i	0.539067	−	0.539067i	−0.384188	−	0.923255i	$-0.625519\pi$
$823$	15.4647	−	15.4647i	0.539067	−	0.539067i	0.923255	+	0.384188i	$0.125519\pi$
$824$	−12.4853			−0.434945
$825$	−9.72269	+	1.38896i	−0.338500	+	0.0483572i
$826$		0			0
$827$	−18.7213	−	18.7213i	−0.651002	−	0.651002i	0.302232	−	0.953234i	$-0.402268\pi$
$827$	−18.7213	−	18.7213i	−0.651002	−	0.651002i	−0.953234	+	0.302232i	$0.902268\pi$
$828$	3.00000	−	3.00000i	0.104257	−	0.104257i
$829$	10.3146			0.358241			0.179121	−	0.983827i	$-0.442675\pi$
$829$	10.3146			0.358241			0.179121	+	0.983827i	$0.442675\pi$
$830$	−31.1116	+	15.5558i	−1.07990	+	0.539950i
$831$			9.86325i			0.342152i
$832$	−2.37849	+	2.37849i	−0.0824594	+	0.0824594i
$833$		0			0
$834$			13.1007i			0.453639i
$835$	−38.6855	−	12.8952i	−1.33877	−	0.446255i
$836$			6.70647i			0.231948i
$837$	−1.40375	−	1.40375i	−0.0485207	−	0.0485207i
$838$	1.65685	+	1.65685i	0.0572351	+	0.0572351i
$839$	−10.6560			−0.367884			−0.183942	−	0.982937i	$-0.558886\pi$
$839$	−10.6560			−0.367884			−0.183942	+	0.982937i	$0.558886\pi$
$840$		0			0
$841$	11.1253			0.383632
$842$	26.6713	+	26.6713i	0.919153	+	0.919153i
$843$	12.1207	+	12.1207i	0.417458	+	0.417458i
$844$		−	17.3050i		−	0.595664i
$845$	3.37109	−	1.68554i	0.115969	−	0.0579845i
$846$		−	6.98483i		−	0.240143i
$847$		0			0
$848$	−8.39904	+	8.39904i	−0.288424	+	0.288424i
$849$		−	20.2008i		−	0.693289i
$850$	14.3781	−	19.1708i	0.493165	−	0.657554i
$851$	−32.1194			−1.10104
$852$	−2.92856	+	2.92856i	−0.100331	+	0.100331i
$853$	−26.5062	−	26.5062i	−0.907555	−	0.907555i	0.0885193	−	0.996074i	$-0.471787\pi$
$853$	−26.5062	−	26.5062i	−0.907555	−	0.907555i	−0.996074	+	0.0885193i	$0.971787\pi$
$854$		0			0
$855$	6.82843	−	3.41421i	0.233527	−	0.116764i
$856$	4.05052			0.138444
$857$	−17.3943	+	17.3943i	−0.594179	+	0.594179i	−0.938758	−	0.344578i	$-0.888022\pi$
$857$	−17.3943	+	17.3943i	−0.594179	+	0.594179i	0.344578	+	0.938758i	$0.388022\pi$
$858$	−4.67202	+	4.67202i	−0.159500	+	0.159500i
$859$	−20.4981			−0.699385			−0.349693	−	0.936865i	$-0.613714\pi$
$859$	−20.4981			−0.699385			−0.349693	+	0.936865i	$0.613714\pi$
$860$	−7.81796	+	23.4539i	−0.266590	+	0.799771i
$861$		0			0
$862$	1.92893	+	1.92893i	0.0656997	+	0.0656997i
$863$	11.2140	−	11.2140i	0.381727	−	0.381727i	−0.489997	−	0.871724i	$-0.663002\pi$
$863$	11.2140	−	11.2140i	0.381727	−	0.381727i	0.871724	+	0.489997i	$0.163002\pi$
$864$	1.00000			0.0340207
$865$	11.6060	−	34.8179i	0.394615	−	1.18384i
$866$		−	18.1927i		−	0.618211i
$867$	−4.22145	+	4.22145i	−0.143368	+	0.143368i
$868$		0			0
$869$		−	22.7570i		−	0.771978i
$870$	4.22784	+	8.45569i	0.143337	+	0.286675i
$871$		−	11.2647i		−	0.381689i
$872$	−3.44993	−	3.44993i	−0.116830	−	0.116830i
$873$	5.08534	+	5.08534i	0.172113	+	0.172113i
$874$	−14.4853			−0.489972
$875$		0			0
$876$	2.84935			0.0962707
$877$	−13.8796	−	13.8796i	−0.468681	−	0.468681i	0.432806	−	0.901487i	$-0.357524\pi$
$877$	−13.8796	−	13.8796i	−0.468681	−	0.468681i	−0.901487	+	0.432806i	$0.857524\pi$
$878$	−6.30975	−	6.30975i	−0.212944	−	0.212944i
$879$		−	15.3124i		−	0.516476i
$880$	1.96428	+	3.92856i	0.0662158	+	0.132432i
$881$		−	31.3920i		−	1.05762i	−0.848739	−	0.528812i	$-0.822638\pi$
$881$		−	31.3920i		−	1.05762i	0.848739	−	0.528812i	$-0.177362\pi$
$882$		0			0
$883$	13.7950	−	13.7950i	0.464240	−	0.464240i	−0.435803	−	0.900042i	$-0.643535\pi$
$883$	13.7950	−	13.7950i	0.464240	−	0.464240i	0.900042	+	0.435803i	$0.143535\pi$
$884$		−	16.1212i		−	0.542215i
$885$	−2.96428	+	8.89284i	−0.0996432	+	0.298929i
$886$	18.0707			0.607097
$887$	17.0373	−	17.0373i	0.572056	−	0.572056i	−0.360646	−	0.932703i	$-0.617444\pi$
$887$	17.0373	−	17.0373i	0.572056	−	0.572056i	0.932703	+	0.360646i	$0.117444\pi$
$888$	−5.35323	−	5.35323i	−0.179643	−	0.179643i
$889$		0			0
$890$	4.25744	−	12.7723i	0.142710	−	0.428129i
$891$	1.96428			0.0658058
$892$	3.59154	−	3.59154i	0.120254	−	0.120254i
$893$	−16.8629	+	16.8629i	−0.564294	+	0.564294i
$894$	22.1355			0.740321
$895$	27.6846	−	13.8423i	0.925396	−	0.462698i
$896$		0			0
$897$	−10.0911	−	10.0911i	−0.336932	−	0.336932i
$898$	−1.97041	+	1.97041i	−0.0657534	+	0.0657534i
$899$	−8.39313			−0.279927
$900$	3.00000	−	4.00000i	0.100000	−	0.133333i
$901$		−	56.9280i		−	1.89655i
$902$	16.0916	−	16.0916i	0.535792	−	0.535792i
$903$		0			0
$904$			5.62726i			0.187160i
$905$	−44.6256	+	22.3128i	−1.48341	+	0.741703i
$906$		−	9.32185i		−	0.309698i
$907$	−28.6303	−	28.6303i	−0.950654	−	0.950654i	0.0481843	−	0.998838i	$-0.484657\pi$
$907$	−28.6303	−	28.6303i	−0.950654	−	0.950654i	−0.998838	+	0.0481843i	$0.984657\pi$
$908$	17.8490	+	17.8490i	0.592339	+	0.592339i
$909$	6.14161			0.203704
$910$		0			0
$911$	39.4831			1.30813			0.654067	−	0.756437i	$-0.273062\pi$
$911$	39.4831			1.30813			0.654067	+	0.756437i	$0.273062\pi$
$912$	−2.41421	−	2.41421i	−0.0799426	−	0.0799426i
$913$	21.6063	+	21.6063i	0.715065	+	0.715065i
$914$			41.8273i			1.38352i
$915$	−8.33373	−	2.77791i	−0.275505	−	0.0918349i
$916$		−	5.58616i		−	0.184572i
$917$		0			0
$918$	−3.38896	+	3.38896i	−0.111852	+	0.111852i
$919$			41.4459i			1.36717i	0.729869	+	0.683587i	$0.239581\pi$
$919$			41.4459i			1.36717i	−0.729869	+	0.683587i	$0.760419\pi$
$920$	−8.48528	+	4.24264i	−0.279751	+	0.139876i
$921$	14.7274			0.485284
$922$	4.87028	−	4.87028i	0.160394	−	0.160394i
$923$	9.85078	+	9.85078i	0.324242	+	0.324242i
$924$		0			0
$925$	−37.4726	+	5.35323i	−1.23209	+	0.176013i
$926$	−20.9287			−0.687760
$927$	8.82843	−	8.82843i	0.289964	−	0.289964i
$928$	2.98954	−	2.98954i	0.0981364	−	0.0981364i
$929$	10.8399			0.355647			0.177823	−	0.984062i	$-0.443094\pi$
$929$	10.8399			0.355647			0.177823	+	0.984062i	$0.443094\pi$
$930$	1.98520	+	3.97041i	0.0650974	+	0.130195i
$931$		0			0
$932$	20.0916	+	20.0916i	0.658123	+	0.658123i
$933$	14.8925	−	14.8925i	0.487557	−	0.487557i
$934$	14.7570			0.482863
$935$	−19.9706	−	6.65685i	−0.653107	−	0.217702i
$936$		−	3.36370i		−	0.109946i
$937$	−8.75826	+	8.75826i	−0.286120	+	0.286120i	−0.835544	−	0.549424i	$-0.814847\pi$
$937$	−8.75826	+	8.75826i	−0.286120	+	0.286120i	0.549424	+	0.835544i	$0.314847\pi$
$938$		0			0
$939$		−	0.798835i		−	0.0260690i
$940$	−4.93902	+	14.8171i	−0.161093	+	0.483279i
$941$		−	36.1820i		−	1.17950i	−0.807587	−	0.589749i	$-0.799227\pi$
$941$		−	36.1820i		−	1.17950i	0.807587	−	0.589749i	$-0.200773\pi$
$942$	13.0711	+	13.0711i	0.425878	+	0.425878i
$943$	34.7562	+	34.7562i	1.13182	+	1.13182i
$944$	4.19212			0.136442
$945$		0			0
$946$	21.7176			0.706100
$947$	−24.3842	−	24.3842i	−0.792382	−	0.792382i	0.189499	−	0.981881i	$-0.439314\pi$
$947$	−24.3842	−	24.3842i	−0.792382	−	0.792382i	−0.981881	+	0.189499i	$0.939314\pi$
$948$	8.19212	+	8.19212i	0.266068	+	0.266068i
$949$		−	9.58436i		−	0.311121i
$950$	−16.8995	+	2.41421i	−0.548292	+	0.0783274i
$951$		−	18.7266i		−	0.607253i
$952$		0			0
$953$	10.2356	−	10.2356i	0.331564	−	0.331564i	−0.521616	−	0.853180i	$-0.674671\pi$
$953$	10.2356	−	10.2356i	0.331564	−	0.331564i	0.853180	+	0.521616i	$0.174671\pi$
$954$		−	11.8780i		−	0.384566i
$955$	1.00037	+	2.00075i	0.0323713	+	0.0647427i
$956$	−3.10066			−0.100283
$957$	5.87229	−	5.87229i	0.189824	−	0.189824i
$958$	−7.32798	−	7.32798i	−0.236756	−	0.236756i
$959$		0			0
$960$	−2.12132	−	0.707107i	−0.0684653	−	0.0228218i
$961$	27.0590			0.872870
$962$	−18.0067	+	18.0067i	−0.580558	+	0.580558i
$963$	−2.86415	+	2.86415i	−0.0922959	+	0.0922959i
$964$	−19.0764			−0.614411
$965$	13.0911	+	4.36370i	0.421417	+	0.140472i
$966$		0			0
$967$	−13.3556	−	13.3556i	−0.429486	−	0.429486i	0.458967	−	0.888453i	$-0.348219\pi$
$967$	−13.3556	−	13.3556i	−0.429486	−	0.429486i	−0.888453	+	0.458967i	$0.848219\pi$
$968$	−5.04988	+	5.04988i	−0.162309	+	0.162309i
$969$	16.3633			0.525666
$970$	−7.19175	−	14.3835i	−0.230913	−	0.461826i
$971$		−	5.44328i		−	0.174683i	−0.996178	−	0.0873415i	$-0.972163\pi$
$971$		−	5.44328i		−	0.174683i	0.996178	−	0.0873415i	$-0.0278371\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$		0			0
$974$		−	24.8399i		−	0.795923i
$975$	−13.4548	−	10.0911i	−0.430898	−	0.323174i
$976$			3.92856i			0.125750i
$977$	25.6678	+	25.6678i	0.821187	+	0.821187i	0.986278	−	0.165091i	$-0.0527919\pi$
$977$	25.6678	+	25.6678i	0.821187	+	0.821187i	−0.165091	+	0.986278i	$0.552792\pi$
$978$	−14.8028	−	14.8028i	−0.473341	−	0.473341i
$979$	−11.8268			−0.377985
$980$		0			0
$981$	4.87894			0.155773
$982$	−25.8890	−	25.8890i	−0.826152	−	0.826152i
$983$	9.25848	+	9.25848i	0.295300	+	0.295300i	0.839170	−	0.543870i	$-0.183041\pi$
$983$	9.25848	+	9.25848i	0.295300	+	0.295300i	−0.543870	+	0.839170i	$0.683041\pi$
$984$			11.5854i			0.369329i
$985$	−11.2923	+	33.8768i	−0.359801	+	1.07940i
$986$			20.2628i			0.645300i
$987$		0			0
$988$	−8.12068	+	8.12068i	−0.258353	+	0.258353i
$989$			46.9078i			1.49158i
$990$	−4.16687	−	1.38896i	−0.132432	−	0.0441439i
$991$	−1.69131			−0.0537263			−0.0268632	−	0.999639i	$-0.508552\pi$
$991$	−1.69131			−0.0537263			−0.0268632	+	0.999639i	$0.508552\pi$
$992$	1.40375	−	1.40375i	0.0445691	−	0.0445691i
$993$	−7.50045	−	7.50045i	−0.238020	−	0.238020i
$994$		0			0
$995$	−26.3572	−	52.7144i	−0.835579	−	1.67116i
$996$	−15.5558			−0.492905
$997$	38.1613	−	38.1613i	1.20858	−	1.20858i	0.237092	−	0.971487i	$-0.423806\pi$
$997$	38.1613	−	38.1613i	1.20858	−	1.20858i	0.971487	−	0.237092i	$-0.0761942\pi$
$998$	10.9935	−	10.9935i	0.347993	−	0.347993i
$999$	7.57062			0.239524

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.m.b.97.1	yes	8
5.3	odd	4		1470.2.m.a.1273.1	yes	8
7.6	odd	2		1470.2.m.a.97.1	✓	8
35.13	even	4	inner	1470.2.m.b.1273.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.m.a.97.1	✓	8	7.6	odd	2
1470.2.m.a.1273.1	yes	8	5.3	odd	4
1470.2.m.b.97.1	yes	8	1.1	even	1	trivial
1470.2.m.b.1273.1	yes	8	35.13	even	4	inner

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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(1.00000 + 2.00000i) q^{5} +1.00000i q^{6} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(1.00000 + 2.00000i) q^{5} +1.00000i q^{6} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(0.707107 - 2.12132i) q^{10} -1.96428 q^{11} +(0.707107 - 0.707107i) q^{12} +(-2.37849 - 2.37849i) q^{13} +(0.707107 - 2.12132i) q^{15} -1.00000 q^{16} +(3.38896 - 3.38896i) q^{17} +(0.707107 - 0.707107i) q^{18} -3.41421 q^{19} +(-2.00000 + 1.00000i) q^{20} +(1.38896 + 1.38896i) q^{22} +(-3.00000 + 3.00000i) q^{23} -1.00000 q^{24} +(-3.00000 + 4.00000i) q^{25} +3.36370i q^{26} +(0.707107 - 0.707107i) q^{27} -4.22784i q^{29} +(-2.00000 + 1.00000i) q^{30} -1.98520i q^{31} +(0.707107 + 0.707107i) q^{32} +(1.38896 + 1.38896i) q^{33} -4.79271 q^{34} -1.00000 q^{36} +(5.35323 + 5.35323i) q^{37} +(2.41421 + 2.41421i) q^{38} +3.36370i q^{39} +(2.12132 + 0.707107i) q^{40} -11.5854i q^{41} +(7.81796 - 7.81796i) q^{43} -1.96428i q^{44} +(-2.00000 + 1.00000i) q^{45} +4.24264 q^{46} +(4.93902 - 4.93902i) q^{47} +(0.707107 + 0.707107i) q^{48} +(4.94975 - 0.707107i) q^{50} -4.79271 q^{51} +(2.37849 - 2.37849i) q^{52} +(8.39904 - 8.39904i) q^{53} -1.00000 q^{54} +(-1.96428 - 3.92856i) q^{55} +(2.41421 + 2.41421i) q^{57} +(-2.98954 + 2.98954i) q^{58} -4.19212 q^{59} +(2.12132 + 0.707107i) q^{60} -3.92856i q^{61} +(-1.40375 + 1.40375i) q^{62} -1.00000i q^{64} +(2.37849 - 7.13548i) q^{65} -1.96428i q^{66} +(2.36803 + 2.36803i) q^{67} +(3.38896 + 3.38896i) q^{68} +4.24264 q^{69} -4.14161 q^{71} +(0.707107 + 0.707107i) q^{72} +(2.01480 + 2.01480i) q^{73} -7.57062i q^{74} +(4.94975 - 0.707107i) q^{75} -3.41421i q^{76} +(2.37849 - 2.37849i) q^{78} +11.5854i q^{79} +(-1.00000 - 2.00000i) q^{80} -1.00000 q^{81} +(-8.19212 + 8.19212i) q^{82} +(-10.9996 - 10.9996i) q^{83} +(10.1669 + 3.38896i) q^{85} -11.0563 q^{86} +(-2.98954 + 2.98954i) q^{87} +(-1.38896 + 1.38896i) q^{88} +6.02092 q^{89} +(2.12132 + 0.707107i) q^{90} +(-3.00000 - 3.00000i) q^{92} +(-1.40375 + 1.40375i) q^{93} -6.98483 q^{94} +(-3.41421 - 6.82843i) q^{95} -1.00000i q^{96} +(5.08534 - 5.08534i) q^{97} -1.96428i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{5}+O(q^{10}) \) 8 * q + 8 * q^5	\( 8 q + 8 q^{5} + 8 q^{13} - 8 q^{16} + 8 q^{17} - 16 q^{19} - 16 q^{20} - 8 q^{22} - 24 q^{23} - 8 q^{24} - 24 q^{25} - 16 q^{30} - 8 q^{33} - 8 q^{36} + 8 q^{37} + 8 q^{38} + 32 q^{43} - 16 q^{45} + 16 q^{47} - 8 q^{52} - 32 q^{53} - 8 q^{54} + 8 q^{57} - 16 q^{58} + 16 q^{59} + 8 q^{62} - 8 q^{65} - 16 q^{67} + 8 q^{68} + 32 q^{71} + 16 q^{73} - 8 q^{78} - 8 q^{80} - 8 q^{81} - 16 q^{82} + 24 q^{85} - 32 q^{86} - 16 q^{87} + 8 q^{88} + 64 q^{89} - 24 q^{92} + 8 q^{93} + 32 q^{94} - 16 q^{95} + 32 q^{97}+O(q^{100}) \) 8 * q + 8 * q^5 + 8 * q^13 - 8 * q^16 + 8 * q^17 - 16 * q^19 - 16 * q^20 - 8 * q^22 - 24 * q^23 - 8 * q^24 - 24 * q^25 - 16 * q^30 - 8 * q^33 - 8 * q^36 + 8 * q^37 + 8 * q^38 + 32 * q^43 - 16 * q^45 + 16 * q^47 - 8 * q^52 - 32 * q^53 - 8 * q^54 + 8 * q^57 - 16 * q^58 + 16 * q^59 + 8 * q^62 - 8 * q^65 - 16 * q^67 + 8 * q^68 + 32 * q^71 + 16 * q^73 - 8 * q^78 - 8 * q^80 - 8 * q^81 - 16 * q^82 + 24 * q^85 - 32 * q^86 - 16 * q^87 + 8 * q^88 + 64 * q^89 - 24 * q^92 + 8 * q^93 + 32 * q^94 - 16 * q^95 + 32 * q^97

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