LMFDB - Embedded newform 1470.2.m.b.97.3

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			97.3
Root			$-0.382683 - 0.923880i$ of defining polynomial
Character	$\chi$	$=$	1470.97
Dual form			1470.2.m.b.1273.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(1.00000 + 2.00000i) q^{5} +1.00000i q^{6} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(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} -4.34436 q^{11} +(-0.707107 + 0.707107i) q^{12} +(-1.93015 - 1.93015i) q^{13} +(-0.707107 + 2.12132i) q^{15} -1.00000 q^{16} +(-1.07193 + 1.07193i) q^{17} +(-0.707107 + 0.707107i) q^{18} -0.585786 q^{19} +(-2.00000 + 1.00000i) q^{20} +(-3.07193 - 3.07193i) q^{22} +(-3.00000 + 3.00000i) q^{23} -1.00000 q^{24} +(-3.00000 + 4.00000i) q^{25} -2.72965i q^{26} +(-0.707107 + 0.707107i) q^{27} +9.90244i q^{29} +(-2.00000 + 1.00000i) q^{30} +3.65980i q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.07193 - 3.07193i) q^{33} -1.51594 q^{34} -1.00000 q^{36} +(3.27243 + 3.27243i) q^{37} +(-0.414214 - 0.414214i) q^{38} -2.72965i q^{39} +(-2.12132 - 0.707107i) q^{40} -5.03188i q^{41} +(6.17365 - 6.17365i) q^{43} -4.34436i q^{44} +(-2.00000 + 1.00000i) q^{45} -4.24264 q^{46} +(5.68665 - 5.68665i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(-4.94975 + 0.707107i) q^{50} -1.51594 q^{51} +(1.93015 - 1.93015i) q^{52} +(-9.45635 + 9.45635i) q^{53} -1.00000 q^{54} +(-4.34436 - 8.68873i) q^{55} +(-0.414214 - 0.414214i) q^{57} +(-7.00208 + 7.00208i) q^{58} +7.55807 q^{59} +(-2.12132 - 0.707107i) q^{60} -8.68873i q^{61} +(-2.58787 + 2.58787i) q^{62} -1.00000i q^{64} +(1.93015 - 5.79045i) q^{65} -4.34436i q^{66} +(5.93223 + 5.93223i) q^{67} +(-1.07193 - 1.07193i) q^{68} -4.24264 q^{69} +10.8735 q^{71} +(-0.707107 - 0.707107i) q^{72} +(7.65980 + 7.65980i) q^{73} +4.62792i q^{74} +(-4.94975 + 0.707107i) q^{75} -0.585786i q^{76} +(1.93015 - 1.93015i) q^{78} +5.03188i q^{79} +(-1.00000 - 2.00000i) q^{80} -1.00000 q^{81} +(3.55807 - 3.55807i) q^{82} +(-1.61766 - 1.61766i) q^{83} +(-3.21579 - 1.07193i) q^{85} +8.73087 q^{86} +(-7.00208 + 7.00208i) q^{87} +(3.07193 - 3.07193i) q^{88} -2.00416 q^{89} +(-2.12132 - 0.707107i) q^{90} +(-3.00000 - 3.00000i) q^{92} +(-2.58787 + 2.58787i) q^{93} +8.04214 q^{94} +(-0.585786 - 1.17157i) q^{95} -1.00000i q^{96} +(9.85736 - 9.85736i) q^{97} -4.34436i 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
$11$	−4.34436			−1.30988			−0.654938	−	0.755683i	$-0.727305\pi$
$11$	−4.34436			−1.30988			−0.654938	+	0.755683i	$0.727305\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	−1.93015	−	1.93015i	−0.535328	−	0.535328i	0.386825	−	0.922153i	$-0.373572\pi$
$13$	−1.93015	−	1.93015i	−0.535328	−	0.535328i	−0.922153	+	0.386825i	$0.873572\pi$
$14$		0			0
$15$	−0.707107	+	2.12132i	−0.182574	+	0.547723i
$16$	−1.00000			−0.250000
$17$	−1.07193	+	1.07193i	−0.259981	+	0.259981i	−0.825046	−	0.565065i	$-0.808851\pi$
$17$	−1.07193	+	1.07193i	−0.259981	+	0.259981i	0.565065	+	0.825046i	$0.308851\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	−0.585786			−0.134389			−0.0671943	−	0.997740i	$-0.521405\pi$
$19$	−0.585786			−0.134389			−0.0671943	+	0.997740i	$0.521405\pi$
$20$	−2.00000	+	1.00000i	−0.447214	+	0.223607i
$21$		0			0
$22$	−3.07193	−	3.07193i	−0.654938	−	0.654938i
$23$	−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
$26$		−	2.72965i		−	0.535328i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$			9.90244i			1.83884i	0.393281	+	0.919418i	$0.371340\pi$
$29$			9.90244i			1.83884i	−0.393281	+	0.919418i	$0.628660\pi$
$30$	−2.00000	+	1.00000i	−0.365148	+	0.182574i
$31$			3.65980i			0.657319i	0.944448	+	0.328660i	$0.106597\pi$
$31$			3.65980i			0.657319i	−0.944448	+	0.328660i	$0.893403\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−3.07193	−	3.07193i	−0.534754	−	0.534754i
$34$	−1.51594			−0.259981
$35$		0			0
$36$	−1.00000			−0.166667
$37$	3.27243	+	3.27243i	0.537985	+	0.537985i	0.922937	−	0.384952i	$-0.125782\pi$
$37$	3.27243	+	3.27243i	0.537985	+	0.537985i	−0.384952	+	0.922937i	$0.625782\pi$
$38$	−0.414214	−	0.414214i	−0.0671943	−	0.0671943i
$39$		−	2.72965i		−	0.437093i
$40$	−2.12132	−	0.707107i	−0.335410	−	0.111803i
$41$		−	5.03188i		−	0.785847i	−0.919571	−	0.392923i	$-0.871464\pi$
$41$		−	5.03188i		−	0.785847i	0.919571	−	0.392923i	$-0.128536\pi$
$42$		0			0
$43$	6.17365	−	6.17365i	0.941473	−	0.941473i	−0.0569061	−	0.998380i	$-0.518124\pi$
$43$	6.17365	−	6.17365i	0.941473	−	0.941473i	0.998380	+	0.0569061i	$0.0181236\pi$
$44$		−	4.34436i		−	0.654938i
$45$	−2.00000	+	1.00000i	−0.298142	+	0.149071i
$46$	−4.24264			−0.625543
$47$	5.68665	−	5.68665i	0.829483	−	0.829483i	−0.157962	−	0.987445i	$-0.550492\pi$
$47$	5.68665	−	5.68665i	0.829483	−	0.829483i	0.987445	+	0.157962i	$0.0504924\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$		0			0
$50$	−4.94975	+	0.707107i	−0.700000	+	0.100000i
$51$	−1.51594			−0.212274
$52$	1.93015	−	1.93015i	0.267664	−	0.267664i
$53$	−9.45635	+	9.45635i	−1.29893	+	1.29893i	−0.369830	+	0.929099i	$0.620584\pi$
$53$	−9.45635	+	9.45635i	−1.29893	+	1.29893i	−0.929099	+	0.369830i	$0.879416\pi$
$54$	−1.00000			−0.136083
$55$	−4.34436	−	8.68873i	−0.585794	−	1.17159i
$56$		0			0
$57$	−0.414214	−	0.414214i	−0.0548639	−	0.0548639i
$58$	−7.00208	+	7.00208i	−0.919418	+	0.919418i
$59$	7.55807			0.983977			0.491989	−	0.870602i	$-0.336270\pi$
$59$	7.55807			0.983977			0.491989	+	0.870602i	$0.336270\pi$
$60$	−2.12132	−	0.707107i	−0.273861	−	0.0912871i
$61$		−	8.68873i		−	1.11248i	−0.831022	−	0.556239i	$-0.812244\pi$
$61$		−	8.68873i		−	1.11248i	0.831022	−	0.556239i	$-0.187756\pi$
$62$	−2.58787	+	2.58787i	−0.328660	+	0.328660i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	1.93015	−	5.79045i	0.239406	−	0.718217i
$66$		−	4.34436i		−	0.534754i
$67$	5.93223	+	5.93223i	0.724738	+	0.724738i	0.969566	−	0.244829i	$-0.0787318\pi$
$67$	5.93223	+	5.93223i	0.724738	+	0.724738i	−0.244829	+	0.969566i	$0.578732\pi$
$68$	−1.07193	−	1.07193i	−0.129991	−	0.129991i
$69$	−4.24264			−0.510754
$70$		0			0
$71$	10.8735			1.29045			0.645224	−	0.763994i	$-0.276764\pi$
$71$	10.8735			1.29045			0.645224	+	0.763994i	$0.276764\pi$
$72$	−0.707107	−	0.707107i	−0.0833333	−	0.0833333i
$73$	7.65980	+	7.65980i	0.896511	+	0.896511i	0.995126	−	0.0986143i	$-0.0314410\pi$
$73$	7.65980	+	7.65980i	0.896511	+	0.896511i	−0.0986143	+	0.995126i	$0.531441\pi$
$74$			4.62792i			0.537985i
$75$	−4.94975	+	0.707107i	−0.571548	+	0.0816497i
$76$		−	0.585786i		−	0.0671943i
$77$		0			0
$78$	1.93015	−	1.93015i	0.218547	−	0.218547i
$79$			5.03188i			0.566130i	0.959101	+	0.283065i	$0.0913513\pi$
$79$			5.03188i			0.566130i	−0.959101	+	0.283065i	$0.908649\pi$
$80$	−1.00000	−	2.00000i	−0.111803	−	0.223607i
$81$	−1.00000			−0.111111
$82$	3.55807	−	3.55807i	0.392923	−	0.392923i
$83$	−1.61766	−	1.61766i	−0.177561	−	0.177561i	0.612730	−	0.790292i	$-0.290071\pi$
$83$	−1.61766	−	1.61766i	−0.177561	−	0.177561i	−0.790292	+	0.612730i	$0.790071\pi$
$84$		0			0
$85$	−3.21579	−	1.07193i	−0.348801	−	0.116267i
$86$	8.73087			0.941473
$87$	−7.00208	+	7.00208i	−0.750702	+	0.750702i
$88$	3.07193	−	3.07193i	0.327469	−	0.327469i
$89$	−2.00416			−0.212441			−0.106220	−	0.994343i	$-0.533875\pi$
$89$	−2.00416			−0.212441			−0.106220	+	0.994343i	$0.533875\pi$
$90$	−2.12132	−	0.707107i	−0.223607	−	0.0745356i
$91$		0			0
$92$	−3.00000	−	3.00000i	−0.312772	−	0.312772i
$93$	−2.58787	+	2.58787i	−0.268349	+	0.268349i
$94$	8.04214			0.829483
$95$	−0.585786	−	1.17157i	−0.0601004	−	0.120201i
$96$		−	1.00000i		−	0.102062i
$97$	9.85736	−	9.85736i	1.00086	−	1.00086i	0.000863581	−	1.00000i	$-0.499725\pi$
$97$	9.85736	−	9.85736i	1.00086	−	1.00086i	1.00000		0.000863581i	$-0.000274886\pi$
$98$		0			0
$99$		−	4.34436i		−	0.436625i
$100$	−4.00000	−	3.00000i	−0.400000	−	0.300000i
$101$			8.87351i			0.882947i	0.897274	+	0.441473i	$0.145544\pi$
$101$			8.87351i			0.882947i	−0.897274	+	0.441473i	$0.854456\pi$
$102$	−1.07193	−	1.07193i	−0.106137	−	0.106137i
$103$	−3.17157	−	3.17157i	−0.312504	−	0.312504i	0.533375	−	0.845879i	$-0.320924\pi$
$103$	−3.17157	−	3.17157i	−0.312504	−	0.312504i	−0.845879	+	0.533375i	$0.820924\pi$
$104$	2.72965			0.267664
$105$		0			0
$106$	−13.3733			−1.29893
$107$	−5.17279	−	5.17279i	−0.500073	−	0.500073i	0.411388	−	0.911460i	$-0.365044\pi$
$107$	−5.17279	−	5.17279i	−0.500073	−	0.500073i	−0.911460	+	0.411388i	$0.865044\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$		−	2.48701i		−	0.238212i	−0.992882	−	0.119106i	$-0.961997\pi$
$109$		−	2.48701i		−	0.238212i	0.992882	−	0.119106i	$-0.0380028\pi$
$110$	3.07193	−	9.21579i	0.292897	−	0.878691i
$111$			4.62792i			0.439263i
$112$		0			0
$113$	−12.0042	+	12.0042i	−1.12926	+	1.12926i	−0.138958	+	0.990298i	$0.544375\pi$
$113$	−12.0042	+	12.0042i	−1.12926	+	1.12926i	−0.990298	+	0.138958i	$0.955625\pi$
$114$		−	0.585786i		−	0.0548639i
$115$	−9.00000	−	3.00000i	−0.839254	−	0.279751i
$116$	−9.90244			−0.919418
$117$	1.93015	−	1.93015i	0.178443	−	0.178443i
$118$	5.34436	+	5.34436i	0.491989	+	0.491989i
$119$		0			0
$120$	−1.00000	−	2.00000i	−0.0912871	−	0.182574i
$121$	7.87351			0.715773
$122$	6.14386	−	6.14386i	0.556239	−	0.556239i
$123$	3.55807	−	3.55807i	0.320821	−	0.320821i
$124$	−3.65980			−0.328660
$125$	−11.0000	−	2.00000i	−0.983870	−	0.178885i
$126$		0			0
$127$	−4.87351	−	4.87351i	−0.432454	−	0.432454i	0.457009	−	0.889462i	$-0.348921\pi$
$127$	−4.87351	−	4.87351i	−0.432454	−	0.432454i	−0.889462	+	0.457009i	$0.848921\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	8.73087			0.768710
$130$	5.45929	−	2.72965i	0.478812	−	0.239406i
$131$			13.2149i			1.15459i	0.816534	+	0.577297i	$0.195892\pi$
$131$			13.2149i			1.15459i	−0.816534	+	0.577297i	$0.804108\pi$
$132$	3.07193	−	3.07193i	0.267377	−	0.267377i
$133$		0			0
$134$			8.38944i			0.724738i
$135$	−2.12132	−	0.707107i	−0.182574	−	0.0608581i
$136$		−	1.51594i		−	0.129991i
$137$	14.2179	+	14.2179i	1.21471	+	1.21471i	0.969458	+	0.245256i	$0.0788722\pi$
$137$	14.2179	+	14.2179i	1.21471	+	1.21471i	0.245256	+	0.969458i	$0.421128\pi$
$138$	−3.00000	−	3.00000i	−0.255377	−	0.255377i
$139$	10.2485			0.869269			0.434634	−	0.900607i	$-0.356878\pi$
$139$	10.2485			0.869269			0.434634	+	0.900607i	$0.356878\pi$
$140$		0			0
$141$	8.04214			0.677270
$142$	7.68873	+	7.68873i	0.645224	+	0.645224i
$143$	8.38528	+	8.38528i	0.701212	+	0.701212i
$144$		−	1.00000i		−	0.0833333i
$145$	−19.8049	+	9.90244i	−1.64471	+	0.822353i
$146$			10.8326i			0.896511i
$147$		0			0
$148$	−3.27243	+	3.27243i	−0.268992	+	0.268992i
$149$		−	20.7905i		−	1.70322i	−0.524176	−	0.851610i	$-0.675626\pi$
$149$		−	20.7905i		−	1.70322i	0.524176	−	0.851610i	$-0.324374\pi$
$150$	−4.00000	−	3.00000i	−0.326599	−	0.244949i
$151$	−19.2787			−1.56888			−0.784438	−	0.620207i	$-0.787049\pi$
$151$	−19.2787			−1.56888			−0.784438	+	0.620207i	$0.787049\pi$
$152$	0.414214	−	0.414214i	0.0335972	−	0.0335972i
$153$	−1.07193	−	1.07193i	−0.0866604	−	0.0866604i
$154$		0			0
$155$	−7.31959	+	3.65980i	−0.587924	+	0.293962i
$156$	2.72965			0.218547
$157$	−1.07107	+	1.07107i	−0.0854805	+	0.0854805i	−0.748554	−	0.663074i	$-0.769252\pi$
$157$	−1.07107	+	1.07107i	−0.0854805	+	0.0854805i	0.663074	+	0.748554i	$0.269252\pi$
$158$	−3.55807	+	3.55807i	−0.283065	+	0.283065i
$159$	−13.3733			−1.06057
$160$	0.707107	−	2.12132i	0.0559017	−	0.167705i
$161$		0			0
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	1.86848	−	1.86848i	0.146351	−	0.146351i	−0.630135	−	0.776486i	$-0.717000\pi$
$163$	1.86848	−	1.86848i	0.146351	−	0.146351i	0.776486	+	0.630135i	$0.217000\pi$
$164$	5.03188			0.392923
$165$	3.07193	−	9.21579i	0.239149	−	0.717448i
$166$		−	2.28772i		−	0.177561i
$167$	16.5614	−	16.5614i	1.28156	−	1.28156i	0.341776	−	0.939781i	$-0.388972\pi$
$167$	16.5614	−	16.5614i	1.28156	−	1.28156i	0.939781	−	0.341776i	$-0.111028\pi$
$168$		0			0
$169$		−	5.54903i		−	0.426849i
$170$	−1.51594	−	3.03188i	−0.116267	−	0.232534i
$171$		−	0.585786i		−	0.0447962i
$172$	6.17365	+	6.17365i	0.470737	+	0.470737i
$173$	12.3546	+	12.3546i	0.939305	+	0.939305i	0.998261	−	0.0589559i	$-0.0187771\pi$
$173$	12.3546	+	12.3546i	0.939305	+	0.939305i	−0.0589559	+	0.998261i	$0.518777\pi$
$174$	−9.90244			−0.750702
$175$		0			0
$176$	4.34436			0.327469
$177$	5.34436	+	5.34436i	0.401707	+	0.401707i
$178$	−1.41716	−	1.41716i	−0.106220	−	0.106220i
$179$		−	17.7177i		−	1.32428i	−0.749380	−	0.662140i	$-0.769648\pi$
$179$		−	17.7177i		−	1.32428i	0.749380	−	0.662140i	$-0.230352\pi$
$180$	−1.00000	−	2.00000i	−0.0745356	−	0.149071i
$181$			3.57258i			0.265548i	0.991146	+	0.132774i	$0.0423885\pi$
$181$			3.57258i			0.265548i	−0.991146	+	0.132774i	$0.957612\pi$
$182$		0			0
$183$	6.14386	−	6.14386i	0.454167	−	0.454167i
$184$		−	4.24264i		−	0.312772i
$185$	−3.27243	+	9.81730i	−0.240594	+	0.721783i
$186$	−3.65980			−0.268349
$187$	4.65685	−	4.65685i	0.340543	−	0.340543i
$188$	5.68665	+	5.68665i	0.414741	+	0.414741i
$189$		0			0
$190$	0.414214	−	1.24264i	0.0300502	−	0.0901506i
$191$	10.3823			0.751240			0.375620	−	0.926774i	$-0.377430\pi$
$191$	10.3823			0.751240			0.375620	+	0.926774i	$0.377430\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	−1.72965	+	1.72965i	−0.124503	+	0.124503i	−0.766613	−	0.642110i	$-0.778059\pi$
$193$	−1.72965	+	1.72965i	−0.124503	+	0.124503i	0.642110	+	0.766613i	$0.278059\pi$
$194$	13.9404			1.00086
$195$	5.45929	−	2.72965i	0.390948	−	0.195474i
$196$		0			0
$197$	9.95908	+	9.95908i	0.709555	+	0.709555i	0.966442	−	0.256886i	$-0.0826966\pi$
$197$	9.95908	+	9.95908i	0.709555	+	0.709555i	−0.256886	+	0.966442i	$0.582697\pi$
$198$	3.07193	−	3.07193i	0.218313	−	0.218313i
$199$	−24.5520			−1.74044			−0.870222	−	0.492660i	$-0.836025\pi$
$199$	−24.5520			−1.74044			−0.870222	+	0.492660i	$0.836025\pi$
$200$	−0.707107	−	4.94975i	−0.0500000	−	0.350000i
$201$			8.38944i			0.591746i
$202$	−6.27452	+	6.27452i	−0.441473	+	0.441473i
$203$		0			0
$204$		−	1.51594i		−	0.106137i
$205$	10.0638	−	5.03188i	0.702883	−	0.351441i
$206$		−	4.48528i		−	0.312504i
$207$	−3.00000	−	3.00000i	−0.208514	−	0.208514i
$208$	1.93015	+	1.93015i	0.133832	+	0.133832i
$209$	2.54487			0.176032
$210$		0			0
$211$	24.6375			1.69611			0.848057	−	0.529906i	$-0.177773\pi$
$211$	24.6375			1.69611			0.848057	+	0.529906i	$0.177773\pi$
$212$	−9.45635	−	9.45635i	−0.649465	−	0.649465i
$213$	7.68873	+	7.68873i	0.526823	+	0.526823i
$214$		−	7.31543i		−	0.500073i
$215$	18.5210	+	6.17365i	1.26312	+	0.421040i
$216$		−	1.00000i		−	0.0680414i
$217$		0			0
$218$	1.75858	−	1.75858i	0.119106	−	0.119106i
$219$			10.8326i			0.731999i
$220$	8.68873	−	4.34436i	0.585794	−	0.292897i
$221$	4.13797			0.278350
$222$	−3.27243	+	3.27243i	−0.219631	+	0.219631i
$223$	16.6321	+	16.6321i	1.11377	+	1.11377i	0.992637	+	0.121130i	$0.0386518\pi$
$223$	16.6321	+	16.6321i	1.11377	+	1.11377i	0.121130	+	0.992637i	$0.461348\pi$
$224$		0			0
$225$	−4.00000	−	3.00000i	−0.266667	−	0.200000i
$226$	−16.9764			−1.12926
$227$	−5.21493	+	5.21493i	−0.346127	+	0.346127i	−0.858665	−	0.512538i	$-0.828705\pi$
$227$	−5.21493	+	5.21493i	−0.346127	+	0.346127i	0.512538	+	0.858665i	$0.328705\pi$
$228$	0.414214	−	0.414214i	0.0274320	−	0.0274320i
$229$	−17.7966			−1.17603			−0.588015	−	0.808850i	$-0.700090\pi$
$229$	−17.7966			−1.17603			−0.588015	+	0.808850i	$0.700090\pi$
$230$	−4.24264	−	8.48528i	−0.279751	−	0.559503i
$231$		0			0
$232$	−7.00208	−	7.00208i	−0.459709	−	0.459709i
$233$	−11.4576	+	11.4576i	−0.750610	+	0.750610i	−0.974593	−	0.223983i	$-0.928094\pi$
$233$	−11.4576	+	11.4576i	−0.750610	+	0.750610i	0.223983	+	0.974593i	$0.428094\pi$
$234$	2.72965			0.178443
$235$	17.0599	+	5.68665i	1.11287	+	0.370956i
$236$			7.55807i			0.491989i
$237$	−3.55807	+	3.55807i	−0.231122	+	0.231122i
$238$		0			0
$239$			0.248527i			0.0160759i	0.999968	+	0.00803793i	$0.00255858\pi$
$239$			0.248527i			0.0160759i	−0.999968	+	0.00803793i	$0.997441\pi$
$240$	0.707107	−	2.12132i	0.0456435	−	0.136931i
$241$		−	27.4997i		−	1.77141i	−0.464247	−	0.885706i	$-0.653675\pi$
$241$		−	27.4997i		−	1.77141i	0.464247	−	0.885706i	$-0.346325\pi$
$242$	5.56741	+	5.56741i	0.357887	+	0.357887i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	8.68873			0.556239
$245$		0			0
$246$	5.03188			0.320821
$247$	1.13066	+	1.13066i	0.0719419	+	0.0719419i
$248$	−2.58787	−	2.58787i	−0.164330	−	0.164330i
$249$		−	2.28772i		−	0.144978i
$250$	−6.36396	−	9.19239i	−0.402492	−	0.581378i
$251$			30.2902i			1.91190i	0.293533	+	0.955949i	$0.405169\pi$
$251$			30.2902i			1.91190i	−0.293533	+	0.955949i	$0.594831\pi$
$252$		0			0
$253$	13.0331	−	13.0331i	0.819384	−	0.819384i
$254$		−	6.89218i		−	0.432454i
$255$	−1.51594	−	3.03188i	−0.0949317	−	0.189863i
$256$	1.00000			0.0625000
$257$	−0.791316	+	0.791316i	−0.0493609	+	0.0493609i	−0.731356	−	0.681995i	$-0.761112\pi$
$257$	−0.791316	+	0.791316i	−0.0493609	+	0.0493609i	0.681995	+	0.731356i	$0.261112\pi$
$258$	6.17365	+	6.17365i	0.384355	+	0.384355i
$259$		0			0
$260$	5.79045	+	1.93015i	0.359109	+	0.119703i
$261$	−9.90244			−0.612946
$262$	−9.34436	+	9.34436i	−0.577297	+	0.577297i
$263$	0.954921	−	0.954921i	0.0588830	−	0.0588830i	−0.677052	−	0.735935i	$-0.736743\pi$
$263$	0.954921	−	0.954921i	0.0588830	−	0.0588830i	0.735935	+	0.677052i	$0.236743\pi$
$264$	4.34436			0.267377
$265$	−28.3690	−	9.45635i	−1.74270	−	0.580899i
$266$		0			0
$267$	−1.41716	−	1.41716i	−0.0867286	−	0.0867286i
$268$	−5.93223	+	5.93223i	−0.362369	+	0.362369i
$269$	12.2613			0.747585			0.373793	−	0.927512i	$-0.378057\pi$
$269$	12.2613			0.747585			0.373793	+	0.927512i	$0.378057\pi$
$270$	−1.00000	−	2.00000i	−0.0608581	−	0.121716i
$271$		−	4.82721i		−	0.293232i	−0.989193	−	0.146616i	$-0.953162\pi$
$271$		−	4.82721i		−	0.293232i	0.989193	−	0.146616i	$-0.0468382\pi$
$272$	1.07193	−	1.07193i	0.0649953	−	0.0649953i
$273$		0			0
$274$			20.1071i			1.21471i
$275$	13.0331	−	17.3775i	0.785925	−	1.04790i
$276$		−	4.24264i		−	0.255377i
$277$	4.04005	+	4.04005i	0.242743	+	0.242743i	0.817984	−	0.575241i	$-0.195092\pi$
$277$	4.04005	+	4.04005i	0.242743	+	0.242743i	−0.575241	+	0.817984i	$0.695092\pi$
$278$	7.24680	+	7.24680i	0.434634	+	0.434634i
$279$	−3.65980			−0.219106
$280$		0			0
$281$	7.25584			0.432847			0.216424	−	0.976300i	$-0.430561\pi$
$281$	7.25584			0.432847			0.216424	+	0.976300i	$0.430561\pi$
$282$	5.68665	+	5.68665i	0.338635	+	0.338635i
$283$	−19.6333	−	19.6333i	−1.16708	−	1.16708i	−0.982891	−	0.184188i	$-0.941035\pi$
$283$	−19.6333	−	19.6333i	−1.16708	−	1.16708i	−0.184188	−	0.982891i	$-0.558965\pi$
$284$			10.8735i			0.645224i
$285$	0.414214	−	1.24264i	0.0245359	−	0.0736077i
$286$			11.8586i			0.701212i
$287$		0			0
$288$	0.707107	−	0.707107i	0.0416667	−	0.0416667i
$289$			14.7019i			0.864820i
$290$	−21.0062	−	7.00208i	−1.23353	−	0.411176i
$291$	13.9404			0.817201
$292$	−7.65980	+	7.65980i	−0.448256	+	0.448256i
$293$	9.05786	+	9.05786i	0.529166	+	0.529166i	0.920324	−	0.391158i	$-0.127925\pi$
$293$	9.05786	+	9.05786i	0.529166	+	0.529166i	−0.391158	+	0.920324i	$0.627925\pi$
$294$		0			0
$295$	7.55807	+	15.1161i	0.440048	+	0.880096i
$296$	−4.62792			−0.268992
$297$	3.07193	−	3.07193i	0.178251	−	0.178251i
$298$	14.7011	−	14.7011i	0.851610	−	0.851610i
$299$	11.5809			0.669741
$300$	−0.707107	−	4.94975i	−0.0408248	−	0.285774i
$301$		0			0
$302$	−13.6321	−	13.6321i	−0.784438	−	0.784438i
$303$	−6.27452	+	6.27452i	−0.360462	+	0.360462i
$304$	0.585786			0.0335972
$305$	17.3775	−	8.68873i	0.995030	−	0.497515i
$306$		−	1.51594i		−	0.0866604i
$307$	1.79655	−	1.79655i	0.102535	−	0.102535i	−0.653979	−	0.756513i	$-0.726901\pi$
$307$	1.79655	−	1.79655i	0.102535	−	0.102535i	0.756513	+	0.653979i	$0.226901\pi$
$308$		0			0
$309$		−	4.48528i		−	0.255159i
$310$	−7.76360	−	2.58787i	−0.440943	−	0.146981i
$311$		−	17.8909i		−	1.01450i	−0.861799	−	0.507249i	$-0.830662\pi$
$311$		−	17.8909i		−	1.01450i	0.861799	−	0.507249i	$-0.169338\pi$
$312$	1.93015	+	1.93015i	0.109273	+	0.109273i
$313$	11.4184	+	11.4184i	0.645405	+	0.645405i	0.951879	−	0.306474i	$-0.0991493\pi$
$313$	11.4184	+	11.4184i	0.645405	+	0.645405i	−0.306474	+	0.951879i	$0.599149\pi$
$314$	−1.51472			−0.0854805
$315$		0			0
$316$	−5.03188			−0.283065
$317$	8.64365	+	8.64365i	0.485476	+	0.485476i	0.906875	−	0.421399i	$-0.138461\pi$
$317$	8.64365	+	8.64365i	0.485476	+	0.485476i	−0.421399	+	0.906875i	$0.638461\pi$
$318$	−9.45635	−	9.45635i	−0.530286	−	0.530286i
$319$		−	43.0198i		−	2.40865i
$320$	2.00000	−	1.00000i	0.111803	−	0.0559017i
$321$		−	7.31543i		−	0.408308i
$322$		0			0
$323$	0.627922	−	0.627922i	0.0349385	−	0.0349385i
$324$		−	1.00000i		−	0.0555556i
$325$	13.5111	−	1.93015i	0.749459	−	0.107066i
$326$	2.64243			0.146351
$327$	1.75858	−	1.75858i	0.0972496	−	0.0972496i
$328$	3.55807	+	3.55807i	0.196462	+	0.196462i
$329$		0			0
$330$	8.68873	−	4.34436i	0.478299	−	0.239149i
$331$	−7.85858			−0.431947			−0.215973	−	0.976399i	$-0.569292\pi$
$331$	−7.85858			−0.431947			−0.215973	+	0.976399i	$0.569292\pi$
$332$	1.61766	−	1.61766i	0.0887807	−	0.0887807i
$333$	−3.27243	+	3.27243i	−0.179328	+	0.179328i
$334$	23.4213			1.28156
$335$	−5.93223	+	17.7967i	−0.324112	+	0.972337i
$336$		0			0
$337$	−13.0434	−	13.0434i	−0.710517	−	0.710517i	0.256126	−	0.966643i	$-0.417554\pi$
$337$	−13.0434	−	13.0434i	−0.710517	−	0.710517i	−0.966643	+	0.256126i	$0.917554\pi$
$338$	3.92376	−	3.92376i	0.213424	−	0.213424i
$339$	−16.9764			−0.922034
$340$	1.07193	−	3.21579i	0.0581336	−	0.174401i
$341$		−	15.8995i		−	0.861006i
$342$	0.414214	−	0.414214i	0.0223981	−	0.0223981i
$343$		0			0
$344$			8.73087i			0.470737i
$345$	−4.24264	−	8.48528i	−0.228416	−	0.456832i
$346$			17.4721i			0.939305i
$347$	3.60315	+	3.60315i	0.193427	+	0.193427i	0.797175	−	0.603748i	$-0.206327\pi$
$347$	3.60315	+	3.60315i	0.193427	+	0.193427i	−0.603748	+	0.797175i	$0.706327\pi$
$348$	−7.00208	−	7.00208i	−0.375351	−	0.375351i
$349$	−22.4299			−1.20064			−0.600321	−	0.799759i	$-0.704961\pi$
$349$	−22.4299			−1.20064			−0.600321	+	0.799759i	$0.704961\pi$
$350$		0			0
$351$	2.72965			0.145698
$352$	3.07193	+	3.07193i	0.163734	+	0.163734i
$353$	2.29721	+	2.29721i	0.122268	+	0.122268i	0.765593	−	0.643325i	$-0.222446\pi$
$353$	2.29721	+	2.29721i	0.122268	+	0.122268i	−0.643325	+	0.765593i	$0.722446\pi$
$354$			7.55807i			0.401707i
$355$	10.8735	+	21.7470i	0.577106	+	1.15421i
$356$		−	2.00416i		−	0.106220i
$357$		0			0
$358$	12.5283	−	12.5283i	0.662140	−	0.662140i
$359$			4.38822i			0.231602i	0.993272	+	0.115801i	$0.0369434\pi$
$359$			4.38822i			0.231602i	−0.993272	+	0.115801i	$0.963057\pi$
$360$	0.707107	−	2.12132i	0.0372678	−	0.111803i
$361$	−18.6569			−0.981940
$362$	−2.52620	+	2.52620i	−0.132774	+	0.132774i
$363$	5.56741	+	5.56741i	0.292213	+	0.292213i
$364$		0			0
$365$	−7.65980	+	22.9794i	−0.400932	+	1.20280i
$366$	8.68873			0.454167
$367$	22.8296	−	22.8296i	1.19170	−	1.19170i	0.215107	−	0.976590i	$-0.430990\pi$
$367$	22.8296	−	22.8296i	1.19170	−	1.19170i	0.976590	−	0.215107i	$-0.0690102\pi$
$368$	3.00000	−	3.00000i	0.156386	−	0.156386i
$369$	5.03188			0.261949
$370$	−9.25584	+	4.62792i	−0.481188	+	0.240594i
$371$		0			0
$372$	−2.58787	−	2.58787i	−0.134175	−	0.134175i
$373$	6.87142	−	6.87142i	0.355789	−	0.355789i	−0.506469	−	0.862258i	$-0.669050\pi$
$373$	6.87142	−	6.87142i	0.355789	−	0.355789i	0.862258	+	0.506469i	$0.169050\pi$
$374$	6.58579			0.340543
$375$	−6.36396	−	9.19239i	−0.328634	−	0.474693i
$376$			8.04214i			0.414741i
$377$	19.1132	−	19.1132i	0.984380	−	0.984380i
$378$		0			0
$379$		−	6.40273i		−	0.328886i	−0.986387	−	0.164443i	$-0.947417\pi$
$379$		−	6.40273i		−	0.328886i	0.986387	−	0.164443i	$-0.0525827\pi$
$380$	1.17157	−	0.585786i	0.0601004	−	0.0300502i
$381$		−	6.89218i		−	0.353097i
$382$	7.34142	+	7.34142i	0.375620	+	0.375620i
$383$	27.2459	+	27.2459i	1.39220	+	1.39220i	0.820371	+	0.571831i	$0.193767\pi$
$383$	27.2459	+	27.2459i	1.39220	+	1.39220i	0.571831	+	0.820371i	$0.306233\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−2.44609			−0.124503
$387$	6.17365	+	6.17365i	0.313824	+	0.313824i
$388$	9.85736	+	9.85736i	0.500432	+	0.500432i
$389$			18.6424i			0.945209i	0.881275	+	0.472604i	$0.156686\pi$
$389$			18.6424i			0.945209i	−0.881275	+	0.472604i	$0.843314\pi$
$390$	5.79045	+	1.93015i	0.293211	+	0.0977370i
$391$		−	6.43158i		−	0.325259i
$392$		0			0
$393$	−9.34436	+	9.34436i	−0.471361	+	0.471361i
$394$			14.0843i			0.709555i
$395$	−10.0638	+	5.03188i	−0.506362	+	0.253181i
$396$	4.34436			0.218313
$397$	−6.24264	+	6.24264i	−0.313309	+	0.313309i	−0.846190	−	0.532881i	$-0.821109\pi$
$397$	−6.24264	+	6.24264i	−0.313309	+	0.313309i	0.532881	+	0.846190i	$0.321109\pi$
$398$	−17.3609	−	17.3609i	−0.870222	−	0.870222i
$399$		0			0
$400$	3.00000	−	4.00000i	0.150000	−	0.200000i
$401$	−25.7785			−1.28732			−0.643658	−	0.765314i	$-0.722584\pi$
$401$	−25.7785			−1.28732			−0.643658	+	0.765314i	$0.722584\pi$
$402$	−5.93223	+	5.93223i	−0.295873	+	0.295873i
$403$	7.06396	−	7.06396i	0.351881	−	0.351881i
$404$	−8.87351			−0.441473
$405$	−1.00000	−	2.00000i	−0.0496904	−	0.0993808i
$406$		0			0
$407$	−14.2167	−	14.2167i	−0.704693	−	0.704693i
$408$	1.07193	−	1.07193i	0.0530684	−	0.0530684i
$409$	−25.3576			−1.25385			−0.626926	−	0.779079i	$-0.715687\pi$
$409$	−25.3576			−1.25385			−0.626926	+	0.779079i	$0.715687\pi$
$410$	10.6742	+	3.55807i	0.527162	+	0.175721i
$411$			20.1071i			0.991810i
$412$	3.17157	−	3.17157i	0.156252	−	0.156252i
$413$		0			0
$414$		−	4.24264i		−	0.208514i
$415$	1.61766	−	4.85299i	0.0794079	−	0.238224i
$416$			2.72965i			0.133832i
$417$	7.24680	+	7.24680i	0.354877	+	0.354877i
$418$	1.79949	+	1.79949i	0.0880162	+	0.0880162i
$419$	−13.6569			−0.667181			−0.333590	−	0.942718i	$-0.608260\pi$
$419$	−13.6569			−0.667181			−0.333590	+	0.942718i	$0.608260\pi$
$420$		0			0
$421$	16.4340			0.800945			0.400472	−	0.916309i	$-0.368846\pi$
$421$	16.4340			0.800945			0.400472	+	0.916309i	$0.368846\pi$
$422$	17.4213	+	17.4213i	0.848057	+	0.848057i
$423$	5.68665	+	5.68665i	0.276494	+	0.276494i
$424$		−	13.3733i		−	0.649465i
$425$	−1.07193	−	7.50351i	−0.0519962	−	0.363974i
$426$			10.8735i			0.526823i
$427$		0			0
$428$	5.17279	−	5.17279i	0.250036	−	0.250036i
$429$			11.8586i			0.572538i
$430$	8.73087	+	17.4617i	0.421040	+	0.842079i
$431$	22.7279			1.09477			0.547383	−	0.836882i	$-0.315624\pi$
$431$	22.7279			1.09477			0.547383	+	0.836882i	$0.315624\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	4.82721	+	4.82721i	0.231981	+	0.231981i	0.813519	−	0.581538i	$-0.197549\pi$
$433$	4.82721	+	4.82721i	0.231981	+	0.231981i	−0.581538	+	0.813519i	$0.697549\pi$
$434$		0			0
$435$	−21.0062	−	7.00208i	−1.00717	−	0.335724i
$436$	2.48701			0.119106
$437$	1.75736	−	1.75736i	0.0840659	−	0.0840659i
$438$	−7.65980	+	7.65980i	−0.365999	+	0.365999i
$439$	23.4664			1.11999			0.559995	−	0.828496i	$-0.310803\pi$
$439$	23.4664			1.11999			0.559995	+	0.828496i	$0.310803\pi$
$440$	9.21579	+	3.07193i	0.439346	+	0.146449i
$441$		0			0
$442$	2.92599	+	2.92599i	0.139175	+	0.139175i
$443$	−3.85614	+	3.85614i	−0.183211	+	0.183211i	−0.792753	−	0.609543i	$-0.791353\pi$
$443$	−3.85614	+	3.85614i	−0.183211	+	0.183211i	0.609543	+	0.792753i	$0.291353\pi$
$444$	−4.62792			−0.219631
$445$	−2.00416	−	4.00832i	−0.0950064	−	0.190013i
$446$			23.5213i			1.11377i
$447$	14.7011	−	14.7011i	0.695337	−	0.695337i
$448$		0			0
$449$		−	13.1799i		−	0.621998i	−0.950410	−	0.310999i	$-0.899336\pi$
$449$		−	13.1799i		−	0.621998i	0.950410	−	0.310999i	$-0.100664\pi$
$450$	−0.707107	−	4.94975i	−0.0333333	−	0.233333i
$451$			21.8603i			1.02936i
$452$	−12.0042	−	12.0042i	−0.564628	−	0.564628i
$453$	−13.6321	−	13.6321i	−0.640491	−	0.640491i
$454$	−7.37502			−0.346127
$455$		0			0
$456$	0.585786			0.0274320
$457$	5.67422	+	5.67422i	0.265429	+	0.265429i	0.827255	−	0.561826i	$-0.189901\pi$
$457$	5.67422	+	5.67422i	0.265429	+	0.265429i	−0.561826	+	0.827255i	$0.689901\pi$
$458$	−12.5841	−	12.5841i	−0.588015	−	0.588015i
$459$		−	1.51594i		−	0.0707579i
$460$	3.00000	−	9.00000i	0.139876	−	0.419627i
$461$			23.8108i			1.10898i	0.832191	+	0.554489i	$0.187086\pi$
$461$			23.8108i			1.10898i	−0.832191	+	0.554489i	$0.812914\pi$
$462$		0			0
$463$	−2.14802	+	2.14802i	−0.0998270	+	0.0998270i	−0.755256	−	0.655429i	$-0.772488\pi$
$463$	−2.14802	+	2.14802i	−0.0998270	+	0.0998270i	0.655429	+	0.755256i	$0.272488\pi$
$464$		−	9.90244i		−	0.459709i
$465$	−7.76360	−	2.58787i	−0.360028	−	0.120009i
$466$	−16.2034			−0.750610
$467$	9.80071	−	9.80071i	0.453523	−	0.453523i	−0.442999	−	0.896522i	$-0.646086\pi$
$467$	9.80071	−	9.80071i	0.453523	−	0.453523i	0.896522	+	0.442999i	$0.146086\pi$
$468$	1.93015	+	1.93015i	0.0892213	+	0.0892213i
$469$		0			0
$470$	8.04214	+	16.0843i	0.370956	+	0.741912i
$471$	−1.51472			−0.0697946
$472$	−5.34436	+	5.34436i	−0.245994	+	0.245994i
$473$	−26.8206	+	26.8206i	−1.23321	+	1.23321i
$474$	−5.03188			−0.231122
$475$	1.75736	−	2.34315i	0.0806332	−	0.107511i
$476$		0			0
$477$	−9.45635	−	9.45635i	−0.432976	−	0.432976i
$478$	−0.175735	+	0.175735i	−0.00803793	+	0.00803793i
$479$	−5.11198			−0.233573			−0.116786	−	0.993157i	$-0.537259\pi$
$479$	−5.11198			−0.233573			−0.116786	+	0.993157i	$0.537259\pi$
$480$	2.00000	−	1.00000i	0.0912871	−	0.0456435i
$481$		−	12.6326i		−	0.575996i
$482$	19.4452	−	19.4452i	0.885706	−	0.885706i
$483$		0			0
$484$			7.87351i			0.357887i
$485$	29.5721	+	9.85736i	1.34280	+	0.447600i
$486$		−	1.00000i		−	0.0453609i
$487$	19.0360	+	19.0360i	0.862605	+	0.862605i	0.991640	−	0.129035i	$-0.0411879\pi$
$487$	19.0360	+	19.0360i	0.862605	+	0.862605i	−0.129035	+	0.991640i	$0.541188\pi$
$488$	6.14386	+	6.14386i	0.278119	+	0.278119i
$489$	2.64243			0.119495
$490$		0			0
$491$	−14.2872			−0.644773			−0.322386	−	0.946608i	$-0.604485\pi$
$491$	−14.2872			−0.644773			−0.322386	+	0.946608i	$0.604485\pi$
$492$	3.55807	+	3.55807i	0.160410	+	0.160410i
$493$	−10.6147	−	10.6147i	−0.478063	−	0.478063i
$494$			1.59899i			0.0719419i
$495$	8.68873	−	4.34436i	0.390529	−	0.195265i
$496$		−	3.65980i		−	0.164330i
$497$		0			0
$498$	1.61766	−	1.61766i	0.0724892	−	0.0724892i
$499$		−	21.6115i		−	0.967463i	−0.875217	−	0.483731i	$-0.839281\pi$
$499$		−	21.6115i		−	0.967463i	0.875217	−	0.483731i	$-0.160719\pi$
$500$	2.00000	−	11.0000i	0.0894427	−	0.491935i
$501$	23.4213			1.04639
$502$	−21.4184	+	21.4184i	−0.955949	+	0.955949i
$503$	1.48736	+	1.48736i	0.0663182	+	0.0663182i	0.739488	−	0.673170i	$-0.235068\pi$
$503$	1.48736	+	1.48736i	0.0663182	+	0.0663182i	−0.673170	+	0.739488i	$0.735068\pi$
$504$		0			0
$505$	−17.7470	+	8.87351i	−0.789732	+	0.394866i
$506$	18.4316			0.819384
$507$	3.92376	−	3.92376i	0.174260	−	0.174260i
$508$	4.87351	−	4.87351i	0.216227	−	0.216227i
$509$	−27.0794			−1.20027			−0.600136	−	0.799898i	$-0.704887\pi$
$509$	−27.0794			−1.20027			−0.600136	+	0.799898i	$0.704887\pi$
$510$	1.07193	−	3.21579i	0.0474659	−	0.142398i
$511$		0			0
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	0.414214	−	0.414214i	0.0182880	−	0.0182880i
$514$	−1.11909			−0.0493609
$515$	3.17157	−	9.51472i	0.139756	−	0.419269i
$516$			8.73087i			0.384355i
$517$	−24.7049	+	24.7049i	−1.08652	+	1.08652i
$518$		0			0
$519$			17.4721i			0.766939i
$520$	2.72965	+	5.45929i	0.119703	+	0.239406i
$521$		−	29.6056i		−	1.29704i	−0.761196	−	0.648522i	$-0.775387\pi$
$521$		−	29.6056i		−	1.29704i	0.761196	−	0.648522i	$-0.224613\pi$
$522$	−7.00208	−	7.00208i	−0.306473	−	0.306473i
$523$	11.5882	+	11.5882i	0.506718	+	0.506718i	0.913517	−	0.406800i	$-0.133355\pi$
$523$	11.5882	+	11.5882i	0.506718	+	0.506718i	−0.406800	+	0.913517i	$0.633355\pi$
$524$	−13.2149			−0.577297
$525$		0			0
$526$	1.35046			0.0588830
$527$	−3.92305	−	3.92305i	−0.170891	−	0.170891i
$528$	3.07193	+	3.07193i	0.133689	+	0.133689i
$529$			5.00000i			0.217391i
$530$	−13.3733	−	26.7466i	−0.580899	−	1.16180i
$531$			7.55807i			0.327992i
$532$		0			0
$533$	−9.71228	+	9.71228i	−0.420686	+	0.420686i
$534$		−	2.00416i		−	0.0867286i
$535$	5.17279	−	15.5184i	0.223639	−	0.670918i
$536$	−8.38944			−0.362369
$537$	12.5283	−	12.5283i	0.540635	−	0.540635i
$538$	8.67006	+	8.67006i	0.373793	+	0.373793i
$539$		0			0
$540$	0.707107	−	2.12132i	0.0304290	−	0.0912871i
$541$	−21.4412			−0.921830			−0.460915	−	0.887444i	$-0.652479\pi$
$541$	−21.4412			−0.921830			−0.460915	+	0.887444i	$0.652479\pi$
$542$	3.41335	−	3.41335i	0.146616	−	0.146616i
$543$	−2.52620	+	2.52620i	−0.108410	+	0.108410i
$544$	1.51594			0.0649953
$545$	4.97401	−	2.48701i	0.213063	−	0.106532i
$546$		0			0
$547$	8.11995	+	8.11995i	0.347184	+	0.347184i	0.859060	−	0.511876i	$-0.171049\pi$
$547$	8.11995	+	8.11995i	0.347184	+	0.347184i	−0.511876	+	0.859060i	$0.671049\pi$
$548$	−14.2179	+	14.2179i	−0.607357	+	0.607357i
$549$	8.68873			0.370826
$550$	21.5035	−	3.07193i	0.916913	−	0.130988i
$551$		−	5.80071i		−	0.247119i
$552$	3.00000	−	3.00000i	0.127688	−	0.127688i
$553$		0			0
$554$			5.71350i			0.242743i
$555$	−9.25584	+	4.62792i	−0.392889	+	0.196444i
$556$			10.2485i			0.434634i
$557$	1.27624	+	1.27624i	0.0540760	+	0.0540760i	0.733628	−	0.679552i	$-0.237826\pi$
$557$	1.27624	+	1.27624i	0.0540760	+	0.0540760i	−0.679552	+	0.733628i	$0.737826\pi$
$558$	−2.58787	−	2.58787i	−0.109553	−	0.109553i
$559$	−23.8322			−1.00799
$560$		0			0
$561$	6.58579			0.278052
$562$	5.13066	+	5.13066i	0.216424	+	0.216424i
$563$	1.84163	+	1.84163i	0.0776155	+	0.0776155i	0.744849	−	0.667233i	$-0.232522\pi$
$563$	1.84163	+	1.84163i	0.0776155	+	0.0776155i	−0.667233	+	0.744849i	$0.732522\pi$
$564$			8.04214i			0.338635i
$565$	−36.0125	−	12.0042i	−1.51506	−	0.505019i
$566$		−	27.7657i		−	1.16708i
$567$		0			0
$568$	−7.68873	+	7.68873i	−0.322612	+	0.322612i
$569$			18.0662i			0.757374i	0.925525	+	0.378687i	$0.123624\pi$
$569$			18.0662i			0.757374i	−0.925525	+	0.378687i	$0.876376\pi$
$570$	1.17157	−	0.585786i	0.0490718	−	0.0245359i
$571$	−36.6538			−1.53391			−0.766957	−	0.641698i	$-0.778230\pi$
$571$	−36.6538			−1.53391			−0.766957	+	0.641698i	$0.778230\pi$
$572$	−8.38528	+	8.38528i	−0.350606	+	0.350606i
$573$	7.34142	+	7.34142i	0.306692	+	0.306692i
$574$		0			0
$575$	−3.00000	−	21.0000i	−0.125109	−	0.875761i
$576$	1.00000			0.0416667
$577$	4.39239	−	4.39239i	0.182857	−	0.182857i	−0.609742	−	0.792600i	$-0.708727\pi$
$577$	4.39239	−	4.39239i	0.182857	−	0.182857i	0.792600	+	0.609742i	$0.208727\pi$
$578$	−10.3958	+	10.3958i	−0.432410	+	0.432410i
$579$	−2.44609			−0.101656
$580$	−9.90244	−	19.8049i	−0.411176	−	0.822353i
$581$		0			0
$582$	9.85736	+	9.85736i	0.408601	+	0.408601i
$583$	41.0818	−	41.0818i	1.70144	−	1.70144i
$584$	−10.8326			−0.448256
$585$	5.79045	+	1.93015i	0.239406	+	0.0798019i
$586$			12.8098i			0.529166i
$587$	27.2191	−	27.2191i	1.12345	−	1.12345i	0.132233	−	0.991219i	$-0.457785\pi$
$587$	27.2191	−	27.2191i	1.12345	−	1.12345i	0.991219	−	0.132233i	$-0.0422149\pi$
$588$		0			0
$589$		−	2.14386i		−	0.0883362i
$590$	−5.34436	+	16.0331i	−0.220024	+	0.660072i
$591$			14.0843i			0.579349i
$592$	−3.27243	−	3.27243i	−0.134496	−	0.134496i
$593$	−31.7619	−	31.7619i	−1.30430	−	1.30430i	−0.925461	−	0.378843i	$-0.876322\pi$
$593$	−31.7619	−	31.7619i	−1.30430	−	1.30430i	−0.378843	−	0.925461i	$-0.623678\pi$
$594$	4.34436			0.178251
$595$		0			0
$596$	20.7905			0.851610
$597$	−17.3609	−	17.3609i	−0.710533	−	0.710533i
$598$	8.18894	+	8.18894i	0.334871	+	0.334871i
$599$		−	35.2455i		−	1.44009i	−0.693926	−	0.720046i	$-0.744121\pi$
$599$		−	35.2455i		−	1.44009i	0.693926	−	0.720046i	$-0.255879\pi$
$600$	3.00000	−	4.00000i	0.122474	−	0.163299i
$601$		−	37.1087i		−	1.51370i	−0.653590	−	0.756849i	$-0.726738\pi$
$601$		−	37.1087i		−	1.51370i	0.653590	−	0.756849i	$-0.273262\pi$
$602$		0			0
$603$	−5.93223	+	5.93223i	−0.241579	+	0.241579i
$604$		−	19.2787i		−	0.784438i
$605$	7.87351	+	15.7470i	0.320104	+	0.640207i
$606$	−8.87351			−0.360462
$607$	29.1132	−	29.1132i	1.18167	−	1.18167i	0.202357	−	0.979312i	$-0.435140\pi$
$607$	29.1132	−	29.1132i	1.18167	−	1.18167i	0.979312	−	0.202357i	$-0.0648600\pi$
$608$	0.414214	+	0.414214i	0.0167986	+	0.0167986i
$609$		0			0
$610$	18.4316	+	6.14386i	0.746273	+	0.248758i
$611$	−21.9522			−0.888090
$612$	1.07193	−	1.07193i	0.0433302	−	0.0433302i
$613$	−15.3001	+	15.3001i	−0.617964	+	0.617964i	−0.945009	−	0.327045i	$-0.893947\pi$
$613$	−15.3001	+	15.3001i	−0.617964	+	0.617964i	0.327045	+	0.945009i	$0.393947\pi$
$614$	2.54071			0.102535
$615$	10.6742	+	3.55807i	0.430426	+	0.143475i
$616$		0			0
$617$	16.3576	+	16.3576i	0.658531	+	0.658531i	0.955032	−	0.296501i	$-0.0958200\pi$
$617$	16.3576	+	16.3576i	0.658531	+	0.658531i	−0.296501	+	0.955032i	$0.595820\pi$
$618$	3.17157	−	3.17157i	0.127579	−	0.127579i
$619$	−12.5677			−0.505139			−0.252569	−	0.967579i	$-0.581276\pi$
$619$	−12.5677			−0.505139			−0.252569	+	0.967579i	$0.581276\pi$
$620$	−3.65980	−	7.31959i	−0.146981	−	0.293962i
$621$		−	4.24264i		−	0.170251i
$622$	12.6508	−	12.6508i	0.507249	−	0.507249i
$623$		0			0
$624$			2.72965i			0.109273i
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$			16.1480i			0.645405i
$627$	1.79949	+	1.79949i	0.0718649	+	0.0718649i
$628$	−1.07107	−	1.07107i	−0.0427403	−	0.0427403i
$629$	−7.01564			−0.279732
$630$		0			0
$631$	−18.5467			−0.738333			−0.369167	−	0.929363i	$-0.620357\pi$
$631$	−18.5467			−0.738333			−0.369167	+	0.929363i	$0.620357\pi$
$632$	−3.55807	−	3.55807i	−0.141533	−	0.141533i
$633$	17.4213	+	17.4213i	0.692435	+	0.692435i
$634$			12.2240i			0.485476i
$635$	4.87351	−	14.6205i	0.193399	−	0.580198i
$636$		−	13.3733i		−	0.530286i
$637$		0			0
$638$	30.4196	−	30.4196i	1.20432	−	1.20432i
$639$			10.8735i			0.430149i
$640$	2.12132	+	0.707107i	0.0838525	+	0.0279508i
$641$	16.6392			0.657208			0.328604	−	0.944468i	$-0.393422\pi$
$641$	16.6392			0.657208			0.328604	+	0.944468i	$0.393422\pi$
$642$	5.17279	−	5.17279i	0.204154	−	0.204154i
$643$	10.9897	+	10.9897i	0.433390	+	0.433390i	0.889780	−	0.456390i	$-0.150858\pi$
$643$	10.9897	+	10.9897i	0.433390	+	0.433390i	−0.456390	+	0.889780i	$0.650858\pi$
$644$		0			0
$645$	8.73087	+	17.4617i	0.343777	+	0.687555i
$646$	0.888016			0.0349385
$647$	0.169492	−	0.169492i	0.00666341	−	0.00666341i	−0.703767	−	0.710431i	$-0.748500\pi$
$647$	0.169492	−	0.169492i	0.00666341	−	0.00666341i	0.710431	+	0.703767i	$0.248500\pi$
$648$	0.707107	−	0.707107i	0.0277778	−	0.0277778i
$649$	−32.8350			−1.28889
$650$	10.9186	+	8.18894i	0.428262	+	0.321197i
$651$		0			0
$652$	1.86848	+	1.86848i	0.0731754	+	0.0731754i
$653$	−3.85736	+	3.85736i	−0.150950	+	0.150950i	−0.778542	−	0.627592i	$-0.784041\pi$
$653$	−3.85736	+	3.85736i	−0.150950	+	0.150950i	0.627592	+	0.778542i	$0.284041\pi$
$654$	2.48701			0.0972496
$655$	−26.4299	+	13.2149i	−1.03270	+	0.516350i
$656$			5.03188i			0.196462i
$657$	−7.65980	+	7.65980i	−0.298837	+	0.298837i
$658$		0			0
$659$		−	35.9517i		−	1.40048i	−0.713908	−	0.700239i	$-0.753077\pi$
$659$		−	35.9517i		−	1.40048i	0.713908	−	0.700239i	$-0.246923\pi$
$660$	9.21579	+	3.07193i	0.358724	+	0.119575i
$661$			47.8132i			1.85972i	0.367916	+	0.929859i	$0.380071\pi$
$661$			47.8132i			1.85972i	−0.367916	+	0.929859i	$0.619929\pi$
$662$	−5.55685	−	5.55685i	−0.215973	−	0.215973i
$663$	2.92599	+	2.92599i	0.113636	+	0.113636i
$664$	2.28772			0.0887807
$665$		0			0
$666$	−4.62792			−0.179328
$667$	−29.7073	−	29.7073i	−1.15027	−	1.15027i
$668$	16.5614	+	16.5614i	0.640779	+	0.640779i
$669$			23.5213i			0.909387i
$670$	−16.7789	+	8.38944i	−0.648225	+	0.324112i
$671$			37.7470i			1.45721i
$672$		0			0
$673$	20.3647	−	20.3647i	0.785000	−	0.785000i	−0.195669	−	0.980670i	$-0.562688\pi$
$673$	20.3647	−	20.3647i	0.785000	−	0.785000i	0.980670	+	0.195669i	$0.0626880\pi$
$674$		−	18.4461i		−	0.710517i
$675$	−0.707107	−	4.94975i	−0.0272166	−	0.190516i
$676$	5.54903			0.213424
$677$	11.0434	−	11.0434i	0.424431	−	0.424431i	−0.462295	−	0.886726i	$-0.652974\pi$
$677$	11.0434	−	11.0434i	0.424431	−	0.424431i	0.886726	+	0.462295i	$0.152974\pi$
$678$	−12.0042	−	12.0042i	−0.461017	−	0.461017i
$679$		0			0
$680$	3.03188	−	1.51594i	0.116267	−	0.0581336i
$681$	−7.37502			−0.282611
$682$	11.2426	−	11.2426i	0.430503	−	0.430503i
$683$	−1.44924	+	1.44924i	−0.0554538	+	0.0554538i	−0.734290	−	0.678836i	$-0.762485\pi$
$683$	−1.44924	+	1.44924i	−0.0554538	+	0.0554538i	0.678836	+	0.734290i	$0.262485\pi$
$684$	0.585786			0.0223981
$685$	−14.2179	+	42.6536i	−0.543237	+	1.62971i
$686$		0			0
$687$	−12.5841	−	12.5841i	−0.480112	−	0.480112i
$688$	−6.17365	+	6.17365i	−0.235368	+	0.235368i
$689$	36.5044			1.39071
$690$	3.00000	−	9.00000i	0.114208	−	0.342624i
$691$		−	32.2798i		−	1.22798i	−0.789313	−	0.613991i	$-0.789563\pi$
$691$		−	32.2798i		−	1.22798i	0.789313	−	0.613991i	$-0.210437\pi$
$692$	−12.3546	+	12.3546i	−0.469652	+	0.469652i
$693$		0			0
$694$			5.09563i			0.193427i
$695$	10.2485	+	20.4971i	0.388749	+	0.777498i
$696$		−	9.90244i		−	0.375351i
$697$	5.39382	+	5.39382i	0.204305	+	0.204305i
$698$	−15.8603	−	15.8603i	−0.600321	−	0.600321i
$699$	−16.2034			−0.612871
$700$		0			0
$701$	−17.0640			−0.644497			−0.322248	−	0.946655i	$-0.604439\pi$
$701$	−17.0640			−0.644497			−0.322248	+	0.946655i	$0.604439\pi$
$702$	1.93015	+	1.93015i	0.0728489	+	0.0728489i
$703$	−1.91695	−	1.91695i	−0.0722991	−	0.0722991i
$704$			4.34436i			0.163734i
$705$	8.04214	+	16.0843i	0.302884	+	0.605769i
$706$			3.24874i			0.122268i
$707$		0			0
$708$	−5.34436	+	5.34436i	−0.200854	+	0.200854i
$709$			31.7512i			1.19244i	0.802821	+	0.596220i	$0.203331\pi$
$709$			31.7512i			1.19244i	−0.802821	+	0.596220i	$0.796669\pi$
$710$	−7.68873	+	23.0662i	−0.288553	+	0.865659i
$711$	−5.03188			−0.188710
$712$	1.41716	−	1.41716i	0.0531102	−	0.0531102i
$713$	−10.9794	−	10.9794i	−0.411181	−	0.411181i
$714$		0			0
$715$	−8.38528	+	25.1558i	−0.313592	+	0.940775i
$716$	17.7177			0.662140
$717$	−0.175735	+	0.175735i	−0.00656295	+	0.00656295i
$718$	−3.10294	+	3.10294i	−0.115801	+	0.115801i
$719$	−48.1463			−1.79555			−0.897777	−	0.440450i	$-0.854819\pi$
$719$	−48.1463			−1.79555			−0.897777	+	0.440450i	$0.854819\pi$
$720$	2.00000	−	1.00000i	0.0745356	−	0.0372678i
$721$		0			0
$722$	−13.1924	−	13.1924i	−0.490970	−	0.490970i
$723$	19.4452	−	19.4452i	0.723176	−	0.723176i
$724$	−3.57258			−0.132774
$725$	−39.6098	−	29.7073i	−1.47107	−	1.10330i
$726$			7.87351i			0.292213i
$727$	11.7152	−	11.7152i	0.434494	−	0.434494i	−0.455660	−	0.890154i	$-0.650597\pi$
$727$	11.7152	−	11.7152i	0.434494	−	0.434494i	0.890154	+	0.455660i	$0.150597\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$	−21.6652	+	10.8326i	−0.801864	+	0.400932i
$731$			13.2354i			0.489531i
$732$	6.14386	+	6.14386i	0.227084	+	0.227084i
$733$	−2.29188	−	2.29188i	−0.0846526	−	0.0846526i	0.663513	−	0.748165i	$-0.269065\pi$
$733$	−2.29188	−	2.29188i	−0.0846526	−	0.0846526i	−0.748165	+	0.663513i	$0.769065\pi$
$734$	32.2860			1.19170
$735$		0			0
$736$	4.24264			0.156386
$737$	−25.7718	−	25.7718i	−0.949316	−	0.949316i
$738$	3.55807	+	3.55807i	0.130974	+	0.130974i
$739$			13.9223i			0.512141i	0.966658	+	0.256071i	$0.0824280\pi$
$739$			13.9223i			0.512141i	−0.966658	+	0.256071i	$0.917572\pi$
$740$	−9.81730	−	3.27243i	−0.360891	−	0.120297i
$741$			1.59899i			0.0587404i
$742$		0			0
$743$	−6.40101	+	6.40101i	−0.234830	+	0.234830i	−0.814705	−	0.579875i	$-0.803101\pi$
$743$	−6.40101	+	6.40101i	−0.234830	+	0.234830i	0.579875	+	0.814705i	$0.303101\pi$
$744$		−	3.65980i		−	0.134175i
$745$	41.5809	−	20.7905i	1.52341	−	0.761703i
$746$	9.71766			0.355789
$747$	1.61766	−	1.61766i	0.0591872	−	0.0591872i
$748$	4.65685	+	4.65685i	0.170271	+	0.170271i
$749$		0			0
$750$	2.00000	−	11.0000i	0.0730297	−	0.401663i
$751$	−37.3051			−1.36128			−0.680641	−	0.732617i	$-0.738299\pi$
$751$	−37.3051			−1.36128			−0.680641	+	0.732617i	$0.738299\pi$
$752$	−5.68665	+	5.68665i	−0.207371	+	0.207371i
$753$	−21.4184	+	21.4184i	−0.780529	+	0.780529i
$754$	27.0302			0.984380
$755$	−19.2787	−	38.5574i	−0.701623	−	1.40325i
$756$		0			0
$757$	0.845018	+	0.845018i	0.0307127	+	0.0307127i	0.722296	−	0.691584i	$-0.243087\pi$
$757$	0.845018	+	0.845018i	0.0307127	+	0.0307127i	−0.691584	+	0.722296i	$0.743087\pi$
$758$	4.52742	−	4.52742i	0.164443	−	0.164443i
$759$	18.4316			0.669024
$760$	1.24264	+	0.414214i	0.0450753	+	0.0150251i
$761$			8.83087i			0.320119i	0.987107	+	0.160059i	$0.0511685\pi$
$761$			8.83087i			0.320119i	−0.987107	+	0.160059i	$0.948831\pi$
$762$	4.87351	−	4.87351i	0.176548	−	0.176548i
$763$		0			0
$764$			10.3823i			0.375620i
$765$	1.07193	−	3.21579i	0.0387557	−	0.116267i
$766$			38.5316i			1.39220i
$767$	−14.5882	−	14.5882i	−0.526750	−	0.526750i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	32.5299			1.17306			0.586528	−	0.809929i	$-0.300494\pi$
$769$	32.5299			1.17306			0.586528	+	0.809929i	$0.300494\pi$
$770$		0			0
$771$	−1.11909			−0.0403030
$772$	−1.72965	−	1.72965i	−0.0622513	−	0.0622513i
$773$	−8.81522	−	8.81522i	−0.317062	−	0.317062i	0.530576	−	0.847637i	$-0.321976\pi$
$773$	−8.81522	−	8.81522i	−0.317062	−	0.317062i	−0.847637	+	0.530576i	$0.821976\pi$
$774$			8.73087i			0.313824i
$775$	−14.6392	−	10.9794i	−0.525855	−	0.394391i
$776$			13.9404i			0.500432i
$777$		0			0
$778$	−13.1822	+	13.1822i	−0.472604	+	0.472604i
$779$			2.94760i			0.105609i
$780$	2.72965	+	5.45929i	0.0977370	+	0.195474i
$781$	−47.2385			−1.69033
$782$	4.54781	−	4.54781i	0.162629	−	0.162629i
$783$	−7.00208	−	7.00208i	−0.250234	−	0.250234i
$784$		0			0
$785$	−3.21320	−	1.07107i	−0.114684	−	0.0382280i
$786$	−13.2149			−0.471361
$787$	16.0083	−	16.0083i	0.570635	−	0.570635i	−0.361671	−	0.932306i	$-0.617794\pi$
$787$	16.0083	−	16.0083i	0.570635	−	0.570635i	0.932306	+	0.361671i	$0.117794\pi$
$788$	−9.95908	+	9.95908i	−0.354778	+	0.354778i
$789$	1.35046			0.0480777
$790$	−10.6742	−	3.55807i	−0.379772	−	0.126591i
$791$		0			0
$792$	3.07193	+	3.07193i	0.109156	+	0.109156i
$793$	−16.7706	+	16.7706i	−0.595540	+	0.595540i
$794$	−8.82843			−0.313309
$795$	−13.3733	−	26.7466i	−0.474302	−	0.948604i
$796$		−	24.5520i		−	0.870222i
$797$	−24.5154	+	24.5154i	−0.868381	+	0.868381i	−0.992293	−	0.123912i	$-0.960456\pi$
$797$	−24.5154	+	24.5154i	−0.868381	+	0.868381i	0.123912	+	0.992293i	$0.460456\pi$
$798$		0			0
$799$			12.1914i			0.431300i
$800$	4.94975	−	0.707107i	0.175000	−	0.0250000i
$801$		−	2.00416i		−	0.0708136i
$802$	−18.2281	−	18.2281i	−0.643658	−	0.643658i
$803$	−33.2770	−	33.2770i	−1.17432	−	1.17432i
$804$	−8.38944			−0.295873
$805$		0			0
$806$	9.98995			0.351881
$807$	8.67006	+	8.67006i	0.305200	+	0.305200i
$808$	−6.27452	−	6.27452i	−0.220737	−	0.220737i
$809$			24.6010i			0.864925i	0.901652	+	0.432463i	$0.142355\pi$
$809$			24.6010i			0.864925i	−0.901652	+	0.432463i	$0.857645\pi$
$810$	0.707107	−	2.12132i	0.0248452	−	0.0745356i
$811$			18.5015i			0.649676i	0.945770	+	0.324838i	$0.105310\pi$
$811$			18.5015i			0.649676i	−0.945770	+	0.324838i	$0.894690\pi$
$812$		0			0
$813$	3.41335	−	3.41335i	0.119711	−	0.119711i
$814$		−	20.1054i		−	0.704693i
$815$	5.60544	+	1.86848i	0.196350	+	0.0654501i
$816$	1.51594			0.0530684
$817$	−3.61644	+	3.61644i	−0.126523	+	0.126523i
$818$	−17.9305	−	17.9305i	−0.626926	−	0.626926i
$819$		0			0
$820$	5.03188	+	10.0638i	0.175721	+	0.351441i
$821$	4.04214			0.141072			0.0705358	−	0.997509i	$-0.477529\pi$
$821$	4.04214			0.141072			0.0705358	+	0.997509i	$0.477529\pi$
$822$	−14.2179	+	14.2179i	−0.495905	+	0.495905i
$823$	15.9012	−	15.9012i	0.554282	−	0.554282i	−0.373392	−	0.927674i	$-0.621805\pi$
$823$	15.9012	−	15.9012i	0.554282	−	0.554282i	0.927674	+	0.373392i	$0.121805\pi$
$824$	4.48528			0.156252
$825$	21.5035	−	3.07193i	0.748656	−	0.106951i
$826$		0			0
$827$	−20.2047	−	20.2047i	−0.702585	−	0.702585i	0.262380	−	0.964965i	$-0.415493\pi$
$827$	−20.2047	−	20.2047i	−0.702585	−	0.702585i	−0.964965	+	0.262380i	$0.915493\pi$
$828$	3.00000	−	3.00000i	0.104257	−	0.104257i
$829$	−16.2000			−0.562649			−0.281325	−	0.959613i	$-0.590774\pi$
$829$	−16.2000			−0.562649			−0.281325	+	0.959613i	$0.590774\pi$
$830$	4.57544	−	2.28772i	0.158816	−	0.0794079i
$831$			5.71350i			0.198199i
$832$	−1.93015	+	1.93015i	−0.0669160	+	0.0669160i
$833$		0			0
$834$			10.2485i			0.354877i
$835$	49.6841	+	16.5614i	1.71939	+	0.573130i
$836$			2.54487i			0.0880162i
$837$	−2.58787	−	2.58787i	−0.0894498	−	0.0894498i
$838$	−9.65685	−	9.65685i	−0.333590	−	0.333590i
$839$	−3.22944			−0.111493			−0.0557463	−	0.998445i	$-0.517754\pi$
$839$	−3.22944			−0.111493			−0.0557463	+	0.998445i	$0.517754\pi$
$840$		0			0
$841$	−69.0583			−2.38132
$842$	11.6206	+	11.6206i	0.400472	+	0.400472i
$843$	5.13066	+	5.13066i	0.176709	+	0.176709i
$844$			24.6375i			0.848057i
$845$	11.0981	−	5.54903i	0.381785	−	0.190893i
$846$			8.04214i			0.276494i
$847$		0			0
$848$	9.45635	−	9.45635i	0.324732	−	0.324732i
$849$		−	27.7657i		−	0.952916i
$850$	4.54781	−	6.06375i	0.155989	−	0.207985i
$851$	−19.6346			−0.673066
$852$	−7.68873	+	7.68873i	−0.263412	+	0.263412i
$853$	−1.51056	−	1.51056i	−0.0517205	−	0.0517205i	0.680774	−	0.732494i	$-0.261644\pi$
$853$	−1.51056	−	1.51056i	−0.0517205	−	0.0517205i	−0.732494	+	0.680774i	$0.761644\pi$
$854$		0			0
$855$	1.17157	−	0.585786i	0.0400669	−	0.0200335i
$856$	7.31543			0.250036
$857$	19.5006	−	19.5006i	0.666127	−	0.666127i	−0.290691	−	0.956817i	$-0.593885\pi$
$857$	19.5006	−	19.5006i	0.666127	−	0.666127i	0.956817	+	0.290691i	$0.0938850\pi$
$858$	−8.38528	+	8.38528i	−0.286269	+	0.286269i
$859$	37.0818			1.26522			0.632608	−	0.774472i	$-0.281985\pi$
$859$	37.0818			1.26522			0.632608	+	0.774472i	$0.281985\pi$
$860$	−6.17365	+	18.5210i	−0.210520	+	0.631560i
$861$		0			0
$862$	16.0711	+	16.0711i	0.547383	+	0.547383i
$863$	−12.4485	+	12.4485i	−0.423753	+	0.423753i	−0.886494	−	0.462741i	$-0.846866\pi$
$863$	−12.4485	+	12.4485i	−0.423753	+	0.423753i	0.462741	+	0.886494i	$0.346866\pi$
$864$	1.00000			0.0340207
$865$	−12.3546	+	37.0639i	−0.420070	+	1.26021i
$866$			6.82670i			0.231981i
$867$	−10.3958	+	10.3958i	−0.353061	+	0.353061i
$868$		0			0
$869$		−	21.8603i		−	0.741560i
$870$	−9.90244	−	19.8049i	−0.335724	−	0.671448i
$871$		−	22.9002i		−	0.775944i
$872$	1.75858	+	1.75858i	0.0595530	+	0.0595530i
$873$	9.85736	+	9.85736i	0.333621	+	0.333621i
$874$	2.48528			0.0840659
$875$		0			0
$876$	−10.8326			−0.365999
$877$	39.9858	+	39.9858i	1.35023	+	1.35023i	0.885404	+	0.464822i	$0.153882\pi$
$877$	39.9858	+	39.9858i	1.35023	+	1.35023i	0.464822	+	0.885404i	$0.346118\pi$
$878$	16.5932	+	16.5932i	0.559995	+	0.559995i
$879$			12.8098i			0.432062i
$880$	4.34436	+	8.68873i	0.146449	+	0.292897i
$881$		−	31.0939i		−	1.04758i	−0.851847	−	0.523790i	$-0.824518\pi$
$881$		−	31.0939i		−	1.04758i	0.851847	−	0.523790i	$-0.175482\pi$
$882$		0			0
$883$	−26.0785	+	26.0785i	−0.877612	+	0.877612i	−0.993287	−	0.115675i	$-0.963097\pi$
$883$	−26.0785	+	26.0785i	−0.877612	+	0.877612i	0.115675	+	0.993287i	$0.463097\pi$
$884$			4.13797i			0.139175i
$885$	−5.34436	+	16.0331i	−0.179649	+	0.538947i
$886$	−5.45341			−0.183211
$887$	−40.7035	+	40.7035i	−1.36669	+	1.36669i	−0.501577	+	0.865113i	$0.667247\pi$
$887$	−40.7035	+	40.7035i	−1.36669	+	1.36669i	−0.865113	+	0.501577i	$0.832753\pi$
$888$	−3.27243	−	3.27243i	−0.109816	−	0.109816i
$889$		0			0
$890$	1.41716	−	4.25147i	0.0475032	−	0.142510i
$891$	4.34436			0.145542
$892$	−16.6321	+	16.6321i	−0.556883	+	0.556883i
$893$	−3.33116	+	3.33116i	−0.111473	+	0.111473i
$894$	20.7905			0.695337
$895$	35.4353	−	17.7177i	1.18447	−	0.592236i
$896$		0			0
$897$	8.18894	+	8.18894i	0.273421	+	0.273421i
$898$	9.31959	−	9.31959i	0.310999	−	0.310999i
$899$	−36.2409			−1.20870
$900$	3.00000	−	4.00000i	0.100000	−	0.133333i
$901$		−	20.2731i		−	0.675394i
$902$	−15.4576	+	15.4576i	−0.514681	+	0.514681i
$903$		0			0
$904$		−	16.9764i		−	0.564628i
$905$	−7.14517	+	3.57258i	−0.237513	+	0.118757i
$906$		−	19.2787i		−	0.640491i
$907$	−10.1894	−	10.1894i	−0.338333	−	0.338333i	0.517407	−	0.855740i	$-0.326897\pi$
$907$	−10.1894	−	10.1894i	−0.338333	−	0.338333i	−0.855740	+	0.517407i	$0.826897\pi$
$908$	−5.21493	−	5.21493i	−0.173063	−	0.173063i
$909$	−8.87351			−0.294316
$910$		0			0
$911$	20.9050			0.692612			0.346306	−	0.938122i	$-0.387436\pi$
$911$	20.9050			0.692612			0.346306	+	0.938122i	$0.387436\pi$
$912$	0.414214	+	0.414214i	0.0137160	+	0.0137160i
$913$	7.02771	+	7.02771i	0.232583	+	0.232583i
$914$			8.02456i			0.265429i
$915$	18.4316	+	6.14386i	0.609329	+	0.203110i
$916$		−	17.7966i		−	0.588015i
$917$		0			0
$918$	1.07193	−	1.07193i	0.0353790	−	0.0353790i
$919$		−	34.2756i		−	1.13065i	−0.824869	−	0.565325i	$-0.808751\pi$
$919$		−	34.2756i		−	1.13065i	0.824869	−	0.565325i	$-0.191249\pi$
$920$	8.48528	−	4.24264i	0.279751	−	0.139876i
$921$	2.54071			0.0837192
$922$	−16.8368	+	16.8368i	−0.554489	+	0.554489i
$923$	−20.9875	−	20.9875i	−0.690812	−	0.690812i
$924$		0			0
$925$	−22.9070	+	3.27243i	−0.753179	+	0.107597i
$926$	−3.03776			−0.0998270
$927$	3.17157	−	3.17157i	0.104168	−	0.104168i
$928$	7.00208	−	7.00208i	0.229855	−	0.229855i
$929$	−40.9210			−1.34258			−0.671288	−	0.741197i	$-0.734258\pi$
$929$	−40.9210			−1.34258			−0.671288	+	0.741197i	$0.734258\pi$
$930$	−3.65980	−	7.31959i	−0.120009	−	0.240019i
$931$		0			0
$932$	−11.4576	−	11.4576i	−0.375305	−	0.375305i
$933$	12.6508	−	12.6508i	0.414167	−	0.414167i
$934$	13.8603			0.453523
$935$	13.9706	+	4.65685i	0.456886	+	0.152295i
$936$			2.72965i			0.0892213i
$937$	−13.3563	+	13.3563i	−0.436333	+	0.436333i	−0.890776	−	0.454443i	$-0.849838\pi$
$937$	−13.3563	+	13.3563i	−0.436333	+	0.436333i	0.454443	+	0.890776i	$0.349838\pi$
$938$		0			0
$939$			16.1480i			0.526971i
$940$	−5.68665	+	17.0599i	−0.185478	+	0.556434i
$941$			32.4112i			1.05657i	0.849066	+	0.528287i	$0.177166\pi$
$941$			32.4112i			1.05657i	−0.849066	+	0.528287i	$0.822834\pi$
$942$	−1.07107	−	1.07107i	−0.0348973	−	0.0348973i
$943$	15.0956	+	15.0956i	0.491581	+	0.491581i
$944$	−7.55807			−0.245994
$945$		0			0
$946$	−37.9301			−1.23321
$947$	−0.883854	−	0.883854i	−0.0287214	−	0.0287214i	0.692600	−	0.721322i	$-0.256465\pi$
$947$	−0.883854	−	0.883854i	−0.0287214	−	0.0287214i	−0.721322	+	0.692600i	$0.756465\pi$
$948$	−3.55807	−	3.55807i	−0.115561	−	0.115561i
$949$		−	29.5691i		−	0.959855i
$950$	2.89949	−	0.414214i	0.0940720	−	0.0134389i
$951$			12.2240i			0.396389i
$952$		0			0
$953$	19.3076	−	19.3076i	0.625435	−	0.625435i	−0.321481	−	0.946916i	$-0.604181\pi$
$953$	19.3076	−	19.3076i	0.625435	−	0.625435i	0.946916	+	0.321481i	$0.104181\pi$
$954$		−	13.3733i		−	0.432976i
$955$	10.3823	+	20.7647i	0.335965	+	0.671929i
$956$	−0.248527			−0.00803793
$957$	30.4196	−	30.4196i	0.983326	−	0.983326i
$958$	−3.61472	−	3.61472i	−0.116786	−	0.116786i
$959$		0			0
$960$	2.12132	+	0.707107i	0.0684653	+	0.0228218i
$961$	17.6059			0.567932
$962$	8.93259	−	8.93259i	0.287998	−	0.287998i
$963$	5.17279	−	5.17279i	0.166691	−	0.166691i
$964$	27.4997			0.885706
$965$	−5.18894	−	1.72965i	−0.167038	−	0.0556793i
$966$		0			0
$967$	25.3220	+	25.3220i	0.814302	+	0.814302i	0.985276	−	0.170974i	$-0.0546914\pi$
$967$	25.3220	+	25.3220i	0.814302	+	0.814302i	−0.170974	+	0.985276i	$0.554691\pi$
$968$	−5.56741	+	5.56741i	−0.178943	+	0.178943i
$969$	0.888016			0.0285272
$970$	13.9404	+	27.8808i	0.447600	+	0.895199i
$971$		−	27.1740i		−	0.872056i	−0.899933	−	0.436028i	$-0.856385\pi$
$971$		−	27.1740i		−	0.872056i	0.899933	−	0.436028i	$-0.143615\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$		0			0
$974$			26.9210i			0.862605i
$975$	10.9186	+	8.18894i	0.349675	+	0.262256i
$976$			8.68873i			0.278119i
$977$	−18.4808	−	18.4808i	−0.591254	−	0.591254i	0.346716	−	0.937970i	$-0.387297\pi$
$977$	−18.4808	−	18.4808i	−0.591254	−	0.591254i	−0.937970	+	0.346716i	$0.887297\pi$
$978$	1.86848	+	1.86848i	0.0597475	+	0.0597475i
$979$	8.70681			0.278271
$980$		0			0
$981$	2.48701			0.0794040
$982$	−10.1026	−	10.1026i	−0.322386	−	0.322386i
$983$	−35.6734	−	35.6734i	−1.13780	−	1.13780i	−0.988843	−	0.148960i	$-0.952407\pi$
$983$	−35.6734	−	35.6734i	−1.13780	−	1.13780i	−0.148960	−	0.988843i	$-0.547593\pi$
$984$			5.03188i			0.160410i
$985$	−9.95908	+	29.8773i	−0.317323	+	0.951968i
$986$		−	15.0115i		−	0.478063i
$987$		0			0
$988$	−1.13066	+	1.13066i	−0.0359710	+	0.0359710i
$989$			37.0419i			1.17786i
$990$	9.21579	+	3.07193i	0.292897	+	0.0976323i
$991$	39.4929			1.25453			0.627266	−	0.778805i	$-0.284174\pi$
$991$	39.4929			1.25453			0.627266	+	0.778805i	$0.284174\pi$
$992$	2.58787	−	2.58787i	0.0821649	−	0.0821649i
$993$	−5.55685	−	5.55685i	−0.176341	−	0.176341i
$994$		0			0
$995$	−24.5520	−	49.1040i	−0.778350	−	1.55670i
$996$	2.28772			0.0724892
$997$	9.62629	−	9.62629i	0.304868	−	0.304868i	−0.538047	−	0.842915i	$-0.680838\pi$
$997$	9.62629	−	9.62629i	0.304868	−	0.304868i	0.842915	+	0.538047i	$0.180838\pi$
$998$	15.2816	−	15.2816i	0.483731	−	0.483731i
$999$	−4.62792			−0.146421

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.m.b.97.3	yes	8
5.3	odd	4		1470.2.m.a.1273.3	yes	8
7.6	odd	2		1470.2.m.a.97.3	✓	8
35.13	even	4	inner	1470.2.m.b.1273.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.m.a.97.3	✓	8	7.6	odd	2
1470.2.m.a.1273.3	yes	8	5.3	odd	4
1470.2.m.b.97.3	yes	8	1.1	even	1	trivial
1470.2.m.b.1273.3	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} -4.34436 q^{11} +(-0.707107 + 0.707107i) q^{12} +(-1.93015 - 1.93015i) q^{13} +(-0.707107 + 2.12132i) q^{15} -1.00000 q^{16} +(-1.07193 + 1.07193i) q^{17} +(-0.707107 + 0.707107i) q^{18} -0.585786 q^{19} +(-2.00000 + 1.00000i) q^{20} +(-3.07193 - 3.07193i) q^{22} +(-3.00000 + 3.00000i) q^{23} -1.00000 q^{24} +(-3.00000 + 4.00000i) q^{25} -2.72965i q^{26} +(-0.707107 + 0.707107i) q^{27} +9.90244i q^{29} +(-2.00000 + 1.00000i) q^{30} +3.65980i q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.07193 - 3.07193i) q^{33} -1.51594 q^{34} -1.00000 q^{36} +(3.27243 + 3.27243i) q^{37} +(-0.414214 - 0.414214i) q^{38} -2.72965i q^{39} +(-2.12132 - 0.707107i) q^{40} -5.03188i q^{41} +(6.17365 - 6.17365i) q^{43} -4.34436i q^{44} +(-2.00000 + 1.00000i) q^{45} -4.24264 q^{46} +(5.68665 - 5.68665i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(-4.94975 + 0.707107i) q^{50} -1.51594 q^{51} +(1.93015 - 1.93015i) q^{52} +(-9.45635 + 9.45635i) q^{53} -1.00000 q^{54} +(-4.34436 - 8.68873i) q^{55} +(-0.414214 - 0.414214i) q^{57} +(-7.00208 + 7.00208i) q^{58} +7.55807 q^{59} +(-2.12132 - 0.707107i) q^{60} -8.68873i q^{61} +(-2.58787 + 2.58787i) q^{62} -1.00000i q^{64} +(1.93015 - 5.79045i) q^{65} -4.34436i q^{66} +(5.93223 + 5.93223i) q^{67} +(-1.07193 - 1.07193i) q^{68} -4.24264 q^{69} +10.8735 q^{71} +(-0.707107 - 0.707107i) q^{72} +(7.65980 + 7.65980i) q^{73} +4.62792i q^{74} +(-4.94975 + 0.707107i) q^{75} -0.585786i q^{76} +(1.93015 - 1.93015i) q^{78} +5.03188i q^{79} +(-1.00000 - 2.00000i) q^{80} -1.00000 q^{81} +(3.55807 - 3.55807i) q^{82} +(-1.61766 - 1.61766i) q^{83} +(-3.21579 - 1.07193i) q^{85} +8.73087 q^{86} +(-7.00208 + 7.00208i) q^{87} +(3.07193 - 3.07193i) q^{88} -2.00416 q^{89} +(-2.12132 - 0.707107i) q^{90} +(-3.00000 - 3.00000i) q^{92} +(-2.58787 + 2.58787i) q^{93} +8.04214 q^{94} +(-0.585786 - 1.17157i) q^{95} -1.00000i q^{96} +(9.85736 - 9.85736i) q^{97} -4.34436i 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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