LMFDB - Embedded newform 1470.2.m.a.97.4

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			97.4
Root			$0.382683 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	1470.97
Dual form			1470.2.m.a.1273.4

$q$-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} +1.51594 q^{11} +(0.707107 - 0.707107i) q^{12} +(-3.93015 - 3.93015i) q^{13} +(-0.707107 + 2.12132i) q^{15} -1.00000 q^{16} +(-3.07193 + 3.07193i) q^{17} +(-0.707107 + 0.707107i) q^{18} +0.585786 q^{19} +(2.00000 - 1.00000i) q^{20} +(1.07193 + 1.07193i) q^{22} +(-3.00000 + 3.00000i) q^{23} +1.00000 q^{24} +(-3.00000 + 4.00000i) q^{25} -5.55807i q^{26} +(0.707107 - 0.707107i) q^{27} -4.24558i q^{29} +(-2.00000 + 1.00000i) q^{30} +10.4882i q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.07193 - 1.07193i) q^{33} -4.34436 q^{34} -1.00000 q^{36} +(1.55599 + 1.55599i) q^{37} +(0.414214 + 0.414214i) q^{38} +5.55807i q^{39} +(2.12132 + 0.707107i) q^{40} -6.68873i q^{41} +(-3.83051 + 3.83051i) q^{43} +1.51594i q^{44} +(2.00000 - 1.00000i) q^{45} -4.24264 q^{46} +(-3.97021 + 3.97021i) q^{47} +(0.707107 + 0.707107i) q^{48} +(-4.94975 + 0.707107i) q^{50} +4.34436 q^{51} +(3.93015 - 3.93015i) q^{52} +(-7.02893 + 7.02893i) q^{53} +1.00000 q^{54} +(-1.51594 - 3.03188i) q^{55} +(-0.414214 - 0.414214i) q^{57} +(3.00208 - 3.00208i) q^{58} +0.729646 q^{59} +(-2.12132 - 0.707107i) q^{60} -3.03188i q^{61} +(-7.41629 + 7.41629i) q^{62} -1.00000i q^{64} +(-3.93015 + 11.7905i) q^{65} -1.51594i q^{66} +(-9.93223 - 9.93223i) q^{67} +(-3.07193 - 3.07193i) q^{68} +4.24264 q^{69} -5.70193 q^{71} +(-0.707107 - 0.707107i) q^{72} +(6.48822 + 6.48822i) q^{73} +2.20051i q^{74} +(4.94975 - 0.707107i) q^{75} +0.585786i q^{76} +(-3.93015 + 3.93015i) q^{78} -6.68873i q^{79} +(1.00000 + 2.00000i) q^{80} -1.00000 q^{81} +(4.72965 - 4.72965i) q^{82} +(-10.1029 - 10.1029i) q^{83} +(9.21579 + 3.07193i) q^{85} -5.41716 q^{86} +(-3.00208 + 3.00208i) q^{87} +(-1.07193 + 1.07193i) q^{88} -18.0042 q^{89} +(2.12132 + 0.707107i) q^{90} +(-3.00000 - 3.00000i) q^{92} +(7.41629 - 7.41629i) q^{93} -5.61472 q^{94} +(-0.585786 - 1.17157i) q^{95} +1.00000i q^{96} +(-12.2848 + 12.2848i) q^{97} +1.51594i 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
$11$	1.51594			0.457072			0.228536	−	0.973535i	$-0.426606\pi$
$11$	1.51594			0.457072			0.228536	+	0.973535i	$0.426606\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	−3.93015	−	3.93015i	−1.09003	−	1.09003i	−0.995525	−	0.0945033i	$-0.969874\pi$
$13$	−3.93015	−	3.93015i	−1.09003	−	1.09003i	−0.0945033	−	0.995525i	$-0.530126\pi$
$14$		0			0
$15$	−0.707107	+	2.12132i	−0.182574	+	0.547723i
$16$	−1.00000			−0.250000
$17$	−3.07193	+	3.07193i	−0.745052	+	0.745052i	−0.973546	−	0.228493i	$-0.926620\pi$
$17$	−3.07193	+	3.07193i	−0.745052	+	0.745052i	0.228493	+	0.973546i	$0.426620\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	0.585786			0.134389			0.0671943	−	0.997740i	$-0.478595\pi$
$19$	0.585786			0.134389			0.0671943	+	0.997740i	$0.478595\pi$
$20$	2.00000	−	1.00000i	0.447214	−	0.223607i
$21$		0			0
$22$	1.07193	+	1.07193i	0.228536	+	0.228536i
$23$	−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
$26$		−	5.55807i		−	1.09003i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$		−	4.24558i		−	0.788385i	−0.919028	−	0.394193i	$-0.871024\pi$
$29$		−	4.24558i		−	0.788385i	0.919028	−	0.394193i	$-0.128976\pi$
$30$	−2.00000	+	1.00000i	−0.365148	+	0.182574i
$31$			10.4882i			1.88374i	0.335977	+	0.941870i	$0.390934\pi$
$31$			10.4882i			1.88374i	−0.335977	+	0.941870i	$0.609066\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−1.07193	−	1.07193i	−0.186599	−	0.186599i
$34$	−4.34436			−0.745052
$35$		0			0
$36$	−1.00000			−0.166667
$37$	1.55599	+	1.55599i	0.255804	+	0.255804i	0.823345	−	0.567541i	$-0.192105\pi$
$37$	1.55599	+	1.55599i	0.255804	+	0.255804i	−0.567541	+	0.823345i	$0.692105\pi$
$38$	0.414214	+	0.414214i	0.0671943	+	0.0671943i
$39$			5.55807i			0.890004i
$40$	2.12132	+	0.707107i	0.335410	+	0.111803i
$41$		−	6.68873i		−	1.04460i	−0.852761	−	0.522302i	$-0.825073\pi$
$41$		−	6.68873i		−	1.04460i	0.852761	−	0.522302i	$-0.174927\pi$
$42$		0			0
$43$	−3.83051	+	3.83051i	−0.584147	+	0.584147i	−0.936040	−	0.351893i	$-0.885538\pi$
$43$	−3.83051	+	3.83051i	−0.584147	+	0.584147i	0.351893	+	0.936040i	$0.385538\pi$
$44$			1.51594i			0.228536i
$45$	2.00000	−	1.00000i	0.298142	−	0.149071i
$46$	−4.24264			−0.625543
$47$	−3.97021	+	3.97021i	−0.579114	+	0.579114i	−0.934659	−	0.355545i	$-0.884295\pi$
$47$	−3.97021	+	3.97021i	−0.579114	+	0.579114i	0.355545	+	0.934659i	$0.384295\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$		0			0
$50$	−4.94975	+	0.707107i	−0.700000	+	0.100000i
$51$	4.34436			0.608333
$52$	3.93015	−	3.93015i	0.545014	−	0.545014i
$53$	−7.02893	+	7.02893i	−0.965498	+	0.965498i	−0.999424	−	0.0339262i	$-0.989199\pi$
$53$	−7.02893	+	7.02893i	−0.965498	+	0.965498i	0.0339262	+	0.999424i	$0.489199\pi$
$54$	1.00000			0.136083
$55$	−1.51594	−	3.03188i	−0.204409	−	0.408818i
$56$		0			0
$57$	−0.414214	−	0.414214i	−0.0548639	−	0.0548639i
$58$	3.00208	−	3.00208i	0.394193	−	0.394193i
$59$	0.729646			0.0949918			0.0474959	−	0.998871i	$-0.484876\pi$
$59$	0.729646			0.0949918			0.0474959	+	0.998871i	$0.484876\pi$
$60$	−2.12132	−	0.707107i	−0.273861	−	0.0912871i
$61$		−	3.03188i		−	0.388192i	−0.980983	−	0.194096i	$-0.937823\pi$
$61$		−	3.03188i		−	0.388192i	0.980983	−	0.194096i	$-0.0621773\pi$
$62$	−7.41629	+	7.41629i	−0.941870	+	0.941870i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−3.93015	+	11.7905i	−0.487475	+	1.46243i
$66$		−	1.51594i		−	0.186599i
$67$	−9.93223	−	9.93223i	−1.21342	−	1.21342i	−0.969896	−	0.243519i	$-0.921698\pi$
$67$	−9.93223	−	9.93223i	−1.21342	−	1.21342i	−0.243519	−	0.969896i	$-0.578302\pi$
$68$	−3.07193	−	3.07193i	−0.372526	−	0.372526i
$69$	4.24264			0.510754
$70$		0			0
$71$	−5.70193			−0.676695			−0.338347	−	0.941021i	$-0.609868\pi$
$71$	−5.70193			−0.676695			−0.338347	+	0.941021i	$0.609868\pi$
$72$	−0.707107	−	0.707107i	−0.0833333	−	0.0833333i
$73$	6.48822	+	6.48822i	0.759389	+	0.759389i	0.976211	−	0.216822i	$-0.0695691\pi$
$73$	6.48822	+	6.48822i	0.759389	+	0.759389i	−0.216822	+	0.976211i	$0.569569\pi$
$74$			2.20051i			0.255804i
$75$	4.94975	−	0.707107i	0.571548	−	0.0816497i
$76$			0.585786i			0.0671943i
$77$		0			0
$78$	−3.93015	+	3.93015i	−0.445002	+	0.445002i
$79$		−	6.68873i		−	0.752541i	−0.926510	−	0.376270i	$-0.877206\pi$
$79$		−	6.68873i		−	0.752541i	0.926510	−	0.376270i	$-0.122794\pi$
$80$	1.00000	+	2.00000i	0.111803	+	0.223607i
$81$	−1.00000			−0.111111
$82$	4.72965	−	4.72965i	0.522302	−	0.522302i
$83$	−10.1029	−	10.1029i	−1.10894	−	1.10894i	−0.993290	−	0.115652i	$-0.963104\pi$
$83$	−10.1029	−	10.1029i	−1.10894	−	1.10894i	−0.115652	−	0.993290i	$-0.536896\pi$
$84$		0			0
$85$	9.21579	+	3.07193i	0.999593	+	0.333198i
$86$	−5.41716			−0.584147
$87$	−3.00208	+	3.00208i	−0.321857	+	0.321857i
$88$	−1.07193	+	1.07193i	−0.114268	+	0.114268i
$89$	−18.0042			−1.90844			−0.954219	−	0.299110i	$-0.903310\pi$
$89$	−18.0042			−1.90844			−0.954219	+	0.299110i	$0.903310\pi$
$90$	2.12132	+	0.707107i	0.223607	+	0.0745356i
$91$		0			0
$92$	−3.00000	−	3.00000i	−0.312772	−	0.312772i
$93$	7.41629	−	7.41629i	0.769034	−	0.769034i
$94$	−5.61472			−0.579114
$95$	−0.585786	−	1.17157i	−0.0601004	−	0.120201i
$96$			1.00000i			0.102062i
$97$	−12.2848	+	12.2848i	−1.24733	+	1.24733i	−0.290435	+	0.956895i	$0.593800\pi$
$97$	−12.2848	+	12.2848i	−1.24733	+	1.24733i	−0.956895	+	0.290435i	$0.906200\pi$
$98$		0			0
$99$			1.51594i			0.152357i
$100$	−4.00000	−	3.00000i	−0.400000	−	0.300000i
$101$			7.70193i			0.766371i	0.923671	+	0.383185i	$0.125173\pi$
$101$			7.70193i			0.766371i	−0.923671	+	0.383185i	$0.874827\pi$
$102$	3.07193	+	3.07193i	0.304166	+	0.304166i
$103$	3.17157	+	3.17157i	0.312504	+	0.312504i	0.845879	−	0.533375i	$-0.179076\pi$
$103$	3.17157	+	3.17157i	0.312504	+	0.312504i	−0.533375	+	0.845879i	$0.679076\pi$
$104$	5.55807			0.545014
$105$		0			0
$106$	−9.94041			−0.965498
$107$	0.687511	+	0.687511i	0.0664642	+	0.0664642i	0.739558	−	0.673093i	$-0.235035\pi$
$107$	0.687511	+	0.687511i	0.0664642	+	0.0664642i	−0.673093	+	0.739558i	$0.735035\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$			5.80071i			0.555608i	0.960638	+	0.277804i	$0.0896065\pi$
$109$			5.80071i			0.555608i	−0.960638	+	0.277804i	$0.910393\pi$
$110$	1.07193	−	3.21579i	0.102204	−	0.306613i
$111$		−	2.20051i		−	0.208863i
$112$		0			0
$113$	8.00416	−	8.00416i	0.752968	−	0.752968i	−0.222064	−	0.975032i	$-0.571279\pi$
$113$	8.00416	−	8.00416i	0.752968	−	0.752968i	0.975032	+	0.222064i	$0.0712794\pi$
$114$		−	0.585786i		−	0.0548639i
$115$	9.00000	+	3.00000i	0.839254	+	0.279751i
$116$	4.24558			0.394193
$117$	3.93015	−	3.93015i	0.363343	−	0.363343i
$118$	0.515938	+	0.515938i	0.0474959	+	0.0474959i
$119$		0			0
$120$	−1.00000	−	2.00000i	−0.0912871	−	0.182574i
$121$	−8.70193			−0.791085
$122$	2.14386	−	2.14386i	0.194096	−	0.194096i
$123$	−4.72965	+	4.72965i	−0.426458	+	0.426458i
$124$	−10.4882			−0.941870
$125$	11.0000	+	2.00000i	0.983870	+	0.178885i
$126$		0			0
$127$	11.7019	+	11.7019i	1.03838	+	1.03838i	0.999234	+	0.0391451i	$0.0124635\pi$
$127$	11.7019	+	11.7019i	1.03838	+	1.03838i	0.0391451	+	0.999234i	$0.487537\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	5.41716			0.476954
$130$	−11.1161	+	5.55807i	−0.974951	+	0.487475i
$131$		−	4.92721i		−	0.430492i	−0.976560	−	0.215246i	$-0.930945\pi$
$131$		−	4.92721i		−	0.430492i	0.976560	−	0.215246i	$-0.0690554\pi$
$132$	1.07193	−	1.07193i	0.0932995	−	0.0932995i
$133$		0			0
$134$		−	14.0463i		−	1.21342i
$135$	−2.12132	−	0.707107i	−0.182574	−	0.0608581i
$136$		−	4.34436i		−	0.372526i
$137$	−8.21787	−	8.21787i	−0.702100	−	0.702100i	0.262761	−	0.964861i	$-0.415367\pi$
$137$	−8.21787	−	8.21787i	−0.702100	−	0.702100i	−0.964861	+	0.262761i	$0.915367\pi$
$138$	3.00000	+	3.00000i	0.255377	+	0.255377i
$139$	18.0475			1.53077			0.765385	−	0.643572i	$-0.222548\pi$
$139$	18.0475			1.53077			0.765385	+	0.643572i	$0.222548\pi$
$140$		0			0
$141$	5.61472			0.472845
$142$	−4.03188	−	4.03188i	−0.338347	−	0.338347i
$143$	−5.95786	−	5.95786i	−0.498222	−	0.498222i
$144$		−	1.00000i		−	0.0833333i
$145$	−8.49117	+	4.24558i	−0.705153	+	0.352577i
$146$			9.17574i			0.759389i
$147$		0			0
$148$	−1.55599	+	1.55599i	−0.127902	+	0.127902i
$149$		−	3.20955i		−	0.262936i	−0.991320	−	0.131468i	$-0.958031\pi$
$149$		−	3.20955i		−	0.262936i	0.991320	−	0.131468i	$-0.0419691\pi$
$150$	4.00000	+	3.00000i	0.326599	+	0.244949i
$151$	12.4503			1.01319			0.506594	−	0.862185i	$-0.330904\pi$
$151$	12.4503			1.01319			0.506594	+	0.862185i	$0.330904\pi$
$152$	−0.414214	+	0.414214i	−0.0335972	+	0.0335972i
$153$	−3.07193	−	3.07193i	−0.248351	−	0.248351i
$154$		0			0
$155$	20.9764	−	10.4882i	1.68487	−	0.842434i
$156$	−5.55807			−0.445002
$157$	1.07107	−	1.07107i	0.0854805	−	0.0854805i	−0.663074	−	0.748554i	$-0.730748\pi$
$157$	1.07107	−	1.07107i	0.0854805	−	0.0854805i	0.748554	+	0.663074i	$0.230748\pi$
$158$	4.72965	−	4.72965i	0.376270	−	0.376270i
$159$	9.94041			0.788326
$160$	−0.707107	+	2.12132i	−0.0559017	+	0.167705i
$161$		0			0
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	9.44523	−	9.44523i	0.739807	−	0.739807i	−0.232733	−	0.972541i	$-0.574767\pi$
$163$	9.44523	−	9.44523i	0.739807	−	0.739807i	0.972541	+	0.232733i	$0.0747669\pi$
$164$	6.68873			0.522302
$165$	−1.07193	+	3.21579i	−0.0834496	+	0.250349i
$166$		−	14.2877i		−	1.10894i
$167$	7.59081	−	7.59081i	0.587395	−	0.587395i	−0.349530	−	0.936925i	$-0.613659\pi$
$167$	7.59081	−	7.59081i	0.587395	−	0.587395i	0.936925	+	0.349530i	$0.113659\pi$
$168$		0			0
$169$			17.8922i			1.37632i
$170$	4.34436	+	8.68873i	0.333198	+	0.666395i
$171$			0.585786i			0.0447962i
$172$	−3.83051	−	3.83051i	−0.292074	−	0.292074i
$173$	−15.7875	−	15.7875i	−1.20030	−	1.20030i	−0.974074	−	0.226228i	$-0.927361\pi$
$173$	−15.7875	−	15.7875i	−1.20030	−	1.20030i	−0.226228	−	0.974074i	$-0.572639\pi$
$174$	−4.24558			−0.321857
$175$		0			0
$176$	−1.51594			−0.114268
$177$	−0.515938	−	0.515938i	−0.0387803	−	0.0387803i
$178$	−12.7309	−	12.7309i	−0.954219	−	0.954219i
$179$		−	8.42447i		−	0.629675i	−0.949146	−	0.314837i	$-0.898050\pi$
$179$		−	8.42447i		−	0.629675i	0.949146	−	0.314837i	$-0.101950\pi$
$180$	1.00000	+	2.00000i	0.0745356	+	0.149071i
$181$		−	8.42742i		−	0.626405i	−0.949686	−	0.313202i	$-0.898598\pi$
$181$		−	8.42742i		−	0.626405i	0.949686	−	0.313202i	$-0.101402\pi$
$182$		0			0
$183$	−2.14386	+	2.14386i	−0.158479	+	0.158479i
$184$		−	4.24264i		−	0.312772i
$185$	1.55599	−	4.66798i	0.114399	−	0.343196i
$186$	10.4882			0.769034
$187$	−4.65685	+	4.65685i	−0.340543	+	0.340543i
$188$	−3.97021	−	3.97021i	−0.289557	−	0.289557i
$189$		0			0
$190$	0.414214	−	1.24264i	0.0300502	−	0.0901506i
$191$	22.1029			1.59931			0.799656	−	0.600458i	$-0.205015\pi$
$191$	22.1029			1.59931			0.799656	+	0.600458i	$0.205015\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$	6.55807	−	6.55807i	0.472060	−	0.472060i	−0.430520	−	0.902581i	$-0.641670\pi$
$193$	6.55807	−	6.55807i	0.472060	−	0.472060i	0.902581	+	0.430520i	$0.141670\pi$
$194$	−17.3733			−1.24733
$195$	11.1161	−	5.55807i	0.796044	−	0.398022i
$196$		0			0
$197$	6.52620	+	6.52620i	0.464972	+	0.464972i	0.900281	−	0.435309i	$-0.143361\pi$
$197$	6.52620	+	6.52620i	0.464972	+	0.464972i	−0.435309	+	0.900281i	$0.643361\pi$
$198$	−1.07193	+	1.07193i	−0.0761787	+	0.0761787i
$199$	−13.0373			−0.924187			−0.462093	−	0.886831i	$-0.652901\pi$
$199$	−13.0373			−0.924187			−0.462093	+	0.886831i	$0.652901\pi$
$200$	−0.707107	−	4.94975i	−0.0500000	−	0.350000i
$201$			14.0463i			0.990749i
$202$	−5.44609	+	5.44609i	−0.383185	+	0.383185i
$203$		0			0
$204$			4.34436i			0.304166i
$205$	−13.3775	+	6.68873i	−0.934322	+	0.467161i
$206$			4.48528i			0.312504i
$207$	−3.00000	−	3.00000i	−0.208514	−	0.208514i
$208$	3.93015	+	3.93015i	0.272507	+	0.272507i
$209$	0.888016			0.0614253
$210$		0			0
$211$	−23.6669			−1.62930			−0.814648	−	0.579955i	$-0.803070\pi$
$211$	−23.6669			−1.62930			−0.814648	+	0.579955i	$0.803070\pi$
$212$	−7.02893	−	7.02893i	−0.482749	−	0.482749i
$213$	4.03188	+	4.03188i	0.276260	+	0.276260i
$214$			0.972287i			0.0664642i
$215$	11.4915	+	3.83051i	0.783715	+	0.261238i
$216$			1.00000i			0.0680414i
$217$		0			0
$218$	−4.10172	+	4.10172i	−0.277804	+	0.277804i
$219$		−	9.17574i		−	0.620039i
$220$	3.03188	−	1.51594i	0.204409	−	0.102204i
$221$	24.1463			1.62426
$222$	1.55599	−	1.55599i	0.104431	−	0.104431i
$223$	5.80366	+	5.80366i	0.388642	+	0.388642i	0.874203	−	0.485561i	$-0.161385\pi$
$223$	5.80366	+	5.80366i	0.388642	+	0.388642i	−0.485561	+	0.874203i	$0.661385\pi$
$224$		0			0
$225$	−4.00000	−	3.00000i	−0.266667	−	0.200000i
$226$	11.3196			0.752968
$227$	−3.07279	+	3.07279i	−0.203948	+	0.203948i	−0.801689	−	0.597741i	$-0.796065\pi$
$227$	−3.07279	+	3.07279i	−0.203948	+	0.203948i	0.597741	+	0.801689i	$0.296065\pi$
$228$	0.414214	−	0.414214i	0.0274320	−	0.0274320i
$229$	29.5172			1.95055			0.975274	−	0.220998i	$-0.0709314\pi$
$229$	29.5172			1.95055			0.975274	+	0.220998i	$0.0709314\pi$
$230$	4.24264	+	8.48528i	0.279751	+	0.559503i
$231$		0			0
$232$	3.00208	+	3.00208i	0.197096	+	0.197096i
$233$	−3.16985	+	3.16985i	−0.207664	+	0.207664i	−0.803274	−	0.595610i	$-0.796910\pi$
$233$	−3.16985	+	3.16985i	−0.207664	+	0.207664i	0.595610	+	0.803274i	$0.296910\pi$
$234$	5.55807			0.363343
$235$	11.9106	+	3.97021i	0.776963	+	0.258988i
$236$			0.729646i			0.0474959i
$237$	−4.72965	+	4.72965i	−0.307224	+	0.307224i
$238$		0			0
$239$		−	28.0475i		−	1.81424i	−0.420869	−	0.907122i	$-0.638275\pi$
$239$		−	28.0475i		−	1.81424i	0.420869	−	0.907122i	$-0.361725\pi$
$240$	0.707107	−	2.12132i	0.0456435	−	0.136931i
$241$			16.7846i			1.08119i	0.841283	+	0.540595i	$0.181801\pi$
$241$			16.7846i			1.08119i	−0.841283	+	0.540595i	$0.818199\pi$
$242$	−6.15320	−	6.15320i	−0.395542	−	0.395542i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	3.03188			0.194096
$245$		0			0
$246$	−6.68873			−0.426458
$247$	−2.30223	−	2.30223i	−0.146487	−	0.146487i
$248$	−7.41629	−	7.41629i	−0.470935	−	0.470935i
$249$			14.2877i			0.905447i
$250$	6.36396	+	9.19239i	0.402492	+	0.581378i
$251$		−	1.99411i		−	0.125867i	−0.998018	−	0.0629337i	$-0.979954\pi$
$251$		−	1.99411i		−	0.125867i	0.998018	−	0.0629337i	$-0.0200457\pi$
$252$		0			0
$253$	−4.54781	+	4.54781i	−0.285919	+	0.285919i
$254$			16.5490i			1.03838i
$255$	−4.34436	−	8.68873i	−0.272055	−	0.544109i
$256$	1.00000			0.0625000
$257$	−20.9335	+	20.9335i	−1.30579	+	1.30579i	−0.381371	+	0.924422i	$0.624548\pi$
$257$	−20.9335	+	20.9335i	−1.30579	+	1.30579i	−0.924422	+	0.381371i	$0.875452\pi$
$258$	3.83051	+	3.83051i	0.238477	+	0.238477i
$259$		0			0
$260$	−11.7905	−	3.93015i	−0.731213	−	0.243738i
$261$	4.24558			0.262795
$262$	3.48406	−	3.48406i	0.215246	−	0.215246i
$263$	17.5304	−	17.5304i	1.08097	−	1.08097i	0.0845490	−	0.996419i	$-0.473055\pi$
$263$	17.5304	−	17.5304i	1.08097	−	1.08097i	0.996419	−	0.0845490i	$-0.0269449\pi$
$264$	1.51594			0.0932995
$265$	21.0868	+	7.02893i	1.29535	+	0.431784i
$266$		0			0
$267$	12.7309	+	12.7309i	0.779116	+	0.779116i
$268$	9.93223	−	9.93223i	0.606708	−	0.606708i
$269$	−5.39554			−0.328972			−0.164486	−	0.986379i	$-0.552597\pi$
$269$	−5.39554			−0.328972			−0.164486	+	0.986379i	$0.552597\pi$
$270$	−1.00000	−	2.00000i	−0.0608581	−	0.121716i
$271$			10.6875i			0.649220i	0.945848	+	0.324610i	$0.105233\pi$
$271$			10.6875i			0.649220i	−0.945848	+	0.324610i	$0.894767\pi$
$272$	3.07193	−	3.07193i	0.186263	−	0.186263i
$273$		0			0
$274$		−	11.6218i		−	0.702100i
$275$	−4.54781	+	6.06375i	−0.274243	+	0.365658i
$276$			4.24264i			0.255377i
$277$	11.6168	+	11.6168i	0.697986	+	0.697986i	0.963976	−	0.265990i	$-0.0856988\pi$
$277$	11.6168	+	11.6168i	0.697986	+	0.697986i	−0.265990	+	0.963976i	$0.585699\pi$
$278$	12.7615	+	12.7615i	0.765385	+	0.765385i
$279$	−10.4882			−0.627914
$280$		0			0
$281$	2.40101			0.143232			0.0716161	−	0.997432i	$-0.477184\pi$
$281$	2.40101			0.143232			0.0716161	+	0.997432i	$0.477184\pi$
$282$	3.97021	+	3.97021i	0.236422	+	0.236422i
$283$	−8.66274	−	8.66274i	−0.514946	−	0.514946i	0.401092	−	0.916038i	$-0.368631\pi$
$283$	−8.66274	−	8.66274i	−0.514946	−	0.514946i	−0.916038	+	0.401092i	$0.868631\pi$
$284$		−	5.70193i		−	0.338347i
$285$	−0.414214	+	1.24264i	−0.0245359	+	0.0736077i
$286$		−	8.42569i		−	0.498222i
$287$		0			0
$288$	0.707107	−	0.707107i	0.0416667	−	0.0416667i
$289$		−	1.87351i		−	0.110206i
$290$	−9.00624	−	3.00208i	−0.528865	−	0.176288i
$291$	17.3733			1.01844
$292$	−6.48822	+	6.48822i	−0.379695	+	0.379695i
$293$	−13.9127	−	13.9127i	−0.812789	−	0.812789i	0.172263	−	0.985051i	$-0.444892\pi$
$293$	−13.9127	−	13.9127i	−0.812789	−	0.812789i	−0.985051	+	0.172263i	$0.944892\pi$
$294$		0			0
$295$	−0.729646	−	1.45929i	−0.0424816	−	0.0849633i
$296$	−2.20051			−0.127902
$297$	1.07193	−	1.07193i	0.0621997	−	0.0621997i
$298$	2.26949	−	2.26949i	0.131468	−	0.131468i
$299$	23.5809			1.36372
$300$	0.707107	+	4.94975i	0.0408248	+	0.285774i
$301$		0			0
$302$	8.80366	+	8.80366i	0.506594	+	0.506594i
$303$	5.44609	−	5.44609i	0.312870	−	0.312870i
$304$	−0.585786			−0.0335972
$305$	−6.06375	+	3.03188i	−0.347209	+	0.173605i
$306$		−	4.34436i		−	0.248351i
$307$	−13.5172	+	13.5172i	−0.771465	+	0.771465i	−0.978363	−	0.206898i	$-0.933663\pi$
$307$	−13.5172	+	13.5172i	−0.771465	+	0.771465i	0.206898	+	0.978363i	$0.433663\pi$
$308$		0			0
$309$		−	4.48528i		−	0.255159i
$310$	22.2489	+	7.41629i	1.26365	+	0.421217i
$311$		−	23.5477i		−	1.33527i	−0.744489	−	0.667635i	$-0.767307\pi$
$311$		−	23.5477i		−	1.33527i	0.744489	−	0.667635i	$-0.232693\pi$
$312$	−3.93015	−	3.93015i	−0.222501	−	0.222501i
$313$	8.58995	+	8.58995i	0.485533	+	0.485533i	0.906893	−	0.421361i	$-0.138447\pi$
$313$	8.58995	+	8.58995i	0.485533	+	0.485533i	−0.421361	+	0.906893i	$0.638447\pi$
$314$	1.51472			0.0854805
$315$		0			0
$316$	6.68873			0.376270
$317$	13.4985	+	13.4985i	0.758150	+	0.758150i	0.975986	−	0.217835i	$-0.0698995\pi$
$317$	13.4985	+	13.4985i	0.758150	+	0.758150i	−0.217835	+	0.975986i	$0.569900\pi$
$318$	7.02893	+	7.02893i	0.394163	+	0.394163i
$319$		−	6.43604i		−	0.360349i
$320$	−2.00000	+	1.00000i	−0.111803	+	0.0559017i
$321$		−	0.972287i		−	0.0542678i
$322$		0			0
$323$	−1.79949	+	1.79949i	−0.100127	+	0.100127i
$324$		−	1.00000i		−	0.0555556i
$325$	27.5111	−	3.93015i	1.52604	−	0.218006i
$326$	13.3576			0.739807
$327$	4.10172	−	4.10172i	0.226826	−	0.226826i
$328$	4.72965	+	4.72965i	0.261151	+	0.261151i
$329$		0			0
$330$	−3.03188	+	1.51594i	−0.166899	+	0.0834496i
$331$	−4.42569			−0.243258			−0.121629	−	0.992576i	$-0.538812\pi$
$331$	−4.42569			−0.243258			−0.121629	+	0.992576i	$0.538812\pi$
$332$	10.1029	−	10.1029i	0.554471	−	0.554471i
$333$	−1.55599	+	1.55599i	−0.0852678	+	0.0852678i
$334$	10.7350			0.587395
$335$	−9.93223	+	29.7967i	−0.542656	+	1.62797i
$336$		0			0
$337$	−4.75564	−	4.75564i	−0.259056	−	0.259056i	0.565614	−	0.824670i	$-0.308639\pi$
$337$	−4.75564	−	4.75564i	−0.259056	−	0.259056i	−0.824670	+	0.565614i	$0.808639\pi$
$338$	−12.6517	+	12.6517i	−0.688161	+	0.688161i
$339$	−11.3196			−0.614796
$340$	−3.07193	+	9.21579i	−0.166599	+	0.499796i
$341$			15.8995i			0.861006i
$342$	−0.414214	+	0.414214i	−0.0223981	+	0.0223981i
$343$		0			0
$344$		−	5.41716i		−	0.292074i
$345$	−4.24264	−	8.48528i	−0.228416	−	0.456832i
$346$		−	22.3269i		−	1.20030i
$347$	−21.2600	−	21.2600i	−1.14130	−	1.14130i	−0.988213	−	0.153084i	$-0.951080\pi$
$347$	−21.2600	−	21.2600i	−1.14130	−	1.14130i	−0.153084	−	0.988213i	$-0.548920\pi$
$348$	−3.00208	−	3.00208i	−0.160928	−	0.160928i
$349$	5.85442			0.313380			0.156690	−	0.987648i	$-0.449918\pi$
$349$	5.85442			0.313380			0.156690	+	0.987648i	$0.449918\pi$
$350$		0			0
$351$	−5.55807			−0.296668
$352$	−1.07193	−	1.07193i	−0.0571341	−	0.0571341i
$353$	−23.0165	−	23.0165i	−1.22504	−	1.22504i	−0.965816	−	0.259229i	$-0.916532\pi$
$353$	−23.0165	−	23.0165i	−1.22504	−	1.22504i	−0.259229	−	0.965816i	$-0.583468\pi$
$354$		−	0.729646i		−	0.0387803i
$355$	5.70193	+	11.4039i	0.302627	+	0.605254i
$356$		−	18.0042i		−	0.954219i
$357$		0			0
$358$	5.95700	−	5.95700i	0.314837	−	0.314837i
$359$		−	12.1872i		−	0.643217i	−0.946873	−	0.321608i	$-0.895777\pi$
$359$		−	12.1872i		−	0.643217i	0.946873	−	0.321608i	$-0.104223\pi$
$360$	−0.707107	+	2.12132i	−0.0372678	+	0.111803i
$361$	−18.6569			−0.981940
$362$	5.95908	−	5.95908i	0.313202	−	0.313202i
$363$	6.15320	+	6.15320i	0.322959	+	0.322959i
$364$		0			0
$365$	6.48822	−	19.4647i	0.339609	−	1.01883i
$366$	−3.03188			−0.158479
$367$	−16.9693	+	16.9693i	−0.885793	+	0.885793i	−0.994116	−	0.108323i	$-0.965452\pi$
$367$	−16.9693	+	16.9693i	−0.885793	+	0.885793i	0.108323	+	0.994116i	$0.465452\pi$
$368$	3.00000	−	3.00000i	0.156386	−	0.156386i
$369$	6.68873			0.348201
$370$	4.40101	−	2.20051i	0.228798	−	0.114399i
$371$		0			0
$372$	7.41629	+	7.41629i	0.384517	+	0.384517i
$373$	0.300148	−	0.300148i	0.0155411	−	0.0155411i	−0.699294	−	0.714835i	$-0.746502\pi$
$373$	0.300148	−	0.300148i	0.0155411	−	0.0155411i	0.714835	+	0.699294i	$0.246502\pi$
$374$	−6.58579			−0.340543
$375$	−6.36396	−	9.19239i	−0.328634	−	0.474693i
$376$		−	5.61472i		−	0.289557i
$377$	−16.6858	+	16.6858i	−0.859362	+	0.859362i
$378$		0			0
$379$		−	2.96985i		−	0.152551i	−0.997087	−	0.0762754i	$-0.975697\pi$
$379$		−	2.96985i		−	0.152551i	0.997087	−	0.0762754i	$-0.0243028\pi$
$380$	1.17157	−	0.585786i	0.0601004	−	0.0300502i
$381$		−	16.5490i		−	0.847833i
$382$	15.6291	+	15.6291i	0.799656	+	0.799656i
$383$	−11.3815	−	11.3815i	−0.581566	−	0.581566i	0.353767	−	0.935333i	$-0.384901\pi$
$383$	−11.3815	−	11.3815i	−0.581566	−	0.581566i	−0.935333	+	0.353767i	$0.884901\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	9.27452			0.472060
$387$	−3.83051	−	3.83051i	−0.194716	−	0.194716i
$388$	−12.2848	−	12.2848i	−0.623665	−	0.623665i
$389$			29.3576i			1.48849i	0.667908	+	0.744244i	$0.267190\pi$
$389$			29.3576i			1.48849i	−0.667908	+	0.744244i	$0.732810\pi$
$390$	11.7905	+	3.93015i	0.597033	+	0.199011i
$391$		−	18.4316i		−	0.932125i
$392$		0			0
$393$	−3.48406	+	3.48406i	−0.175748	+	0.175748i
$394$			9.22944i			0.464972i
$395$	−13.3775	+	6.68873i	−0.673093	+	0.336547i
$396$	−1.51594			−0.0761787
$397$	6.24264	−	6.24264i	0.313309	−	0.313309i	−0.532881	−	0.846190i	$-0.678891\pi$
$397$	6.24264	−	6.24264i	0.313309	−	0.313309i	0.846190	+	0.532881i	$0.178891\pi$
$398$	−9.21873	−	9.21873i	−0.462093	−	0.462093i
$399$		0			0
$400$	3.00000	−	4.00000i	0.150000	−	0.200000i
$401$	−7.19209			−0.359156			−0.179578	−	0.983744i	$-0.557473\pi$
$401$	−7.19209			−0.359156			−0.179578	+	0.983744i	$0.557473\pi$
$402$	−9.93223	+	9.93223i	−0.495375	+	0.495375i
$403$	41.2203	−	41.2203i	2.05333	−	2.05333i
$404$	−7.70193			−0.383185
$405$	1.00000	+	2.00000i	0.0496904	+	0.0993808i
$406$		0			0
$407$	2.35879	+	2.35879i	0.116921	+	0.116921i
$408$	−3.07193	+	3.07193i	−0.152083	+	0.152083i
$409$	14.6424			0.724022			0.362011	−	0.932174i	$-0.382090\pi$
$409$	14.6424			0.724022			0.362011	+	0.932174i	$0.382090\pi$
$410$	−14.1889	−	4.72965i	−0.700742	−	0.233581i
$411$			11.6218i			0.573262i
$412$	−3.17157	+	3.17157i	−0.156252	+	0.156252i
$413$		0			0
$414$		−	4.24264i		−	0.208514i
$415$	−10.1029	+	30.3088i	−0.495934	+	1.48780i
$416$			5.55807i			0.272507i
$417$	−12.7615	−	12.7615i	−0.624934	−	0.624934i
$418$	0.627922	+	0.627922i	0.0307127	+	0.0307127i
$419$	13.6569			0.667181			0.333590	−	0.942718i	$-0.391740\pi$
$419$	13.6569			0.667181			0.333590	+	0.942718i	$0.391740\pi$
$420$		0			0
$421$	−20.1497			−0.982039			−0.491019	−	0.871149i	$-0.663376\pi$
$421$	−20.1497			−0.982039			−0.491019	+	0.871149i	$0.663376\pi$
$422$	−16.7350	−	16.7350i	−0.814648	−	0.814648i
$423$	−3.97021	−	3.97021i	−0.193038	−	0.193038i
$424$		−	9.94041i		−	0.482749i
$425$	−3.07193	−	21.5035i	−0.149010	−	1.04307i
$426$			5.70193i			0.276260i
$427$		0			0
$428$	−0.687511	+	0.687511i	−0.0332321	+	0.0332321i
$429$			8.42569i			0.406796i
$430$	5.41716	+	10.8343i	0.261238	+	0.522477i
$431$	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
$433$	−10.6875	−	10.6875i	−0.513609	−	0.513609i	0.402021	−	0.915630i	$-0.368308\pi$
$433$	−10.6875	−	10.6875i	−0.513609	−	0.513609i	−0.915630	+	0.402021i	$0.868308\pi$
$434$		0			0
$435$	9.00624	+	3.00208i	0.431816	+	0.143939i
$436$	−5.80071			−0.277804
$437$	−1.75736	+	1.75736i	−0.0840659	+	0.0840659i
$438$	6.48822	−	6.48822i	0.310019	−	0.310019i
$439$	27.2654			1.30131			0.650653	−	0.759375i	$-0.274495\pi$
$439$	27.2654			1.30131			0.650653	+	0.759375i	$0.274495\pi$
$440$	3.21579	+	1.07193i	0.153307	+	0.0511022i
$441$		0			0
$442$	17.0740	+	17.0740i	0.812128	+	0.812128i
$443$	−12.1439	+	12.1439i	−0.576972	+	0.576972i	−0.934068	−	0.357096i	$-0.883767\pi$
$443$	−12.1439	+	12.1439i	−0.576972	+	0.576972i	0.357096	+	0.934068i	$0.383767\pi$
$444$	2.20051			0.104431
$445$	18.0042	+	36.0083i	0.853479	+	1.70696i
$446$			8.20761i			0.388642i
$447$	−2.26949	+	2.26949i	−0.107343	+	0.107343i
$448$		0			0
$449$			26.8368i			1.26650i	0.773945	+	0.633252i	$0.218280\pi$
$449$			26.8368i			1.26650i	−0.773945	+	0.633252i	$0.781720\pi$
$450$	−0.707107	−	4.94975i	−0.0333333	−	0.233333i
$451$		−	10.1397i		−	0.477460i
$452$	8.00416	+	8.00416i	0.376484	+	0.376484i
$453$	−8.80366	−	8.80366i	−0.413632	−	0.413632i
$454$	−4.34558			−0.203948
$455$		0			0
$456$	0.585786			0.0274320
$457$	−19.1889	−	19.1889i	−0.897621	−	0.897621i	0.0976046	−	0.995225i	$-0.468882\pi$
$457$	−19.1889	−	19.1889i	−0.897621	−	0.897621i	−0.995225	+	0.0976046i	$0.968882\pi$
$458$	20.8718	+	20.8718i	0.975274	+	0.975274i
$459$			4.34436i			0.202778i
$460$	−3.00000	+	9.00000i	−0.139876	+	0.419627i
$461$			32.7813i			1.52678i	0.645939	+	0.763389i	$0.276466\pi$
$461$			32.7813i			1.52678i	−0.645939	+	0.763389i	$0.723534\pi$
$462$		0			0
$463$	26.1480	−	26.1480i	1.21520	−	1.21520i	0.245909	−	0.969293i	$-0.420914\pi$
$463$	26.1480	−	26.1480i	1.21520	−	1.21520i	0.969293	−	0.245909i	$-0.0790863\pi$
$464$			4.24558i			0.197096i
$465$	−22.2489	−	7.41629i	−1.03177	−	0.343922i
$466$	−4.48284			−0.207664
$467$	−1.51299	+	1.51299i	−0.0700130	+	0.0700130i	−0.741246	−	0.671233i	$-0.765765\pi$
$467$	−1.51299	+	1.51299i	−0.0700130	+	0.0700130i	0.671233	+	0.741246i	$0.265765\pi$
$468$	3.93015	+	3.93015i	0.181671	+	0.181671i
$469$		0			0
$470$	5.61472	+	11.2294i	0.258988	+	0.517975i
$471$	−1.51472			−0.0697946
$472$	−0.515938	+	0.515938i	−0.0237480	+	0.0237480i
$473$	−5.80681	+	5.80681i	−0.266997	+	0.266997i
$474$	−6.68873			−0.307224
$475$	−1.75736	+	2.34315i	−0.0806332	+	0.107511i
$476$		0			0
$477$	−7.02893	−	7.02893i	−0.321833	−	0.321833i
$478$	19.8326	−	19.8326i	0.907122	−	0.907122i
$479$	8.54487			0.390425			0.195213	−	0.980761i	$-0.437460\pi$
$479$	8.54487			0.390425			0.195213	+	0.980761i	$0.437460\pi$
$480$	2.00000	−	1.00000i	0.0912871	−	0.0456435i
$481$		−	12.2306i		−	0.557666i
$482$	−11.8685	+	11.8685i	−0.540595	+	0.540595i
$483$		0			0
$484$		−	8.70193i		−	0.395542i
$485$	36.8543	+	12.2848i	1.67347	+	0.557823i
$486$			1.00000i			0.0453609i
$487$	−12.6929	−	12.6929i	−0.575170	−	0.575170i	0.358399	−	0.933569i	$-0.383323\pi$
$487$	−12.6929	−	12.6929i	−0.575170	−	0.575170i	−0.933569	+	0.358399i	$0.883323\pi$
$488$	2.14386	+	2.14386i	0.0970480	+	0.0970480i
$489$	−13.3576			−0.604050
$490$		0			0
$491$	−0.139193			−0.00628167			−0.00314084	−	0.999995i	$-0.501000\pi$
$491$	−0.139193			−0.00628167			−0.00314084	+	0.999995i	$0.501000\pi$
$492$	−4.72965	−	4.72965i	−0.213229	−	0.213229i
$493$	13.0421	+	13.0421i	0.587388	+	0.587388i
$494$		−	3.25584i		−	0.146487i
$495$	3.03188	−	1.51594i	0.136273	−	0.0681363i
$496$		−	10.4882i		−	0.470935i
$497$		0			0
$498$	−10.1029	+	10.1029i	−0.452724	+	0.452724i
$499$			43.2683i			1.93696i	0.249098	+	0.968478i	$0.419866\pi$
$499$			43.2683i			1.93696i	−0.249098	+	0.968478i	$0.580134\pi$
$500$	−2.00000	+	11.0000i	−0.0894427	+	0.491935i
$501$	−10.7350			−0.479606
$502$	1.41005	−	1.41005i	0.0629337	−	0.0629337i
$503$	8.51680	+	8.51680i	0.379745	+	0.379745i	0.871010	−	0.491265i	$-0.163465\pi$
$503$	8.51680	+	8.51680i	0.379745	+	0.379745i	−0.491265	+	0.871010i	$0.663465\pi$
$504$		0			0
$505$	15.4039	−	7.70193i	0.685463	−	0.342732i
$506$	−6.43158			−0.285919
$507$	12.6517	−	12.6517i	0.561881	−	0.561881i
$508$	−11.7019	+	11.7019i	−0.519189	+	0.519189i
$509$	−12.9373			−0.573434			−0.286717	−	0.958015i	$-0.592564\pi$
$509$	−12.9373			−0.573434			−0.286717	+	0.958015i	$0.592564\pi$
$510$	3.07193	−	9.21579i	0.136027	−	0.408082i
$511$		0			0
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	0.414214	−	0.414214i	0.0182880	−	0.0182880i
$514$	−29.6044			−1.30579
$515$	3.17157	−	9.51472i	0.139756	−	0.419269i
$516$			5.41716i			0.238477i
$517$	−6.01858	+	6.01858i	−0.264697	+	0.264697i
$518$		0			0
$519$			22.3269i			0.980043i
$520$	−5.55807	−	11.1161i	−0.243738	−	0.487475i
$521$		−	6.97817i		−	0.305719i	−0.988248	−	0.152860i	$-0.951152\pi$
$521$		−	6.97817i		−	0.305719i	0.988248	−	0.152860i	$-0.0488482\pi$
$522$	3.00208	+	3.00208i	0.131398	+	0.131398i
$523$	0.132380	+	0.132380i	0.00578859	+	0.00578859i	0.709995	−	0.704207i	$-0.248697\pi$
$523$	0.132380	+	0.132380i	0.00578859	+	0.00578859i	−0.704207	+	0.709995i	$0.748697\pi$
$524$	4.92721			0.215246
$525$		0			0
$526$	24.7917			1.08097
$527$	−32.2191	−	32.2191i	−1.40349	−	1.40349i
$528$	1.07193	+	1.07193i	0.0466498	+	0.0466498i
$529$			5.00000i			0.217391i
$530$	9.94041	+	19.8808i	0.431784	+	0.863568i
$531$			0.729646i			0.0316639i
$532$		0			0
$533$	−26.2877	+	26.2877i	−1.13865	+	1.13865i
$534$			18.0042i			0.779116i
$535$	0.687511	−	2.06253i	0.0297237	−	0.0891710i
$536$	14.0463			0.606708
$537$	−5.95700	+	5.95700i	−0.257064	+	0.257064i
$538$	−3.81522	−	3.81522i	−0.164486	−	0.164486i
$539$		0			0
$540$	0.707107	−	2.12132i	0.0304290	−	0.0912871i
$541$	25.4412			1.09380			0.546902	−	0.837197i	$-0.315807\pi$
$541$	25.4412			1.09380			0.546902	+	0.837197i	$0.315807\pi$
$542$	−7.55721	+	7.55721i	−0.324610	+	0.324610i
$543$	−5.95908	+	5.95908i	−0.255729	+	0.255729i
$544$	4.34436			0.186263
$545$	11.6014	−	5.80071i	0.496951	−	0.248475i
$546$		0			0
$547$	−26.7474	−	26.7474i	−1.14363	−	1.14363i	−0.987780	−	0.155855i	$-0.950187\pi$
$547$	−26.7474	−	26.7474i	−1.14363	−	1.14363i	−0.155855	−	0.987780i	$-0.549813\pi$
$548$	8.21787	−	8.21787i	0.351050	−	0.351050i
$549$	3.03188			0.129397
$550$	−7.50351	+	1.07193i	−0.319951	+	0.0457072i
$551$		−	2.48701i		−	0.105950i
$552$	−3.00000	+	3.00000i	−0.127688	+	0.127688i
$553$		0			0
$554$			16.4286i			0.697986i
$555$	−4.40101	+	2.20051i	−0.186812	+	0.0934062i
$556$			18.0475i			0.765385i
$557$	−18.7321	−	18.7321i	−0.793704	−	0.793704i	0.188390	−	0.982094i	$-0.439673\pi$
$557$	−18.7321	−	18.7321i	−0.793704	−	0.793704i	−0.982094	+	0.188390i	$0.939673\pi$
$558$	−7.41629	−	7.41629i	−0.313957	−	0.313957i
$559$	30.1090			1.27347
$560$		0			0
$561$	6.58579			0.278052
$562$	1.69777	+	1.69777i	0.0716161	+	0.0716161i
$563$	3.01320	+	3.01320i	0.126991	+	0.126991i	0.767746	−	0.640754i	$-0.221378\pi$
$563$	3.01320	+	3.01320i	0.126991	+	0.126991i	−0.640754	+	0.767746i	$0.721378\pi$
$564$			5.61472i			0.236422i
$565$	−24.0125	−	8.00416i	−1.01021	−	0.336738i
$566$		−	12.2510i		−	0.514946i
$567$		0			0
$568$	4.03188	−	4.03188i	0.169174	−	0.169174i
$569$		−	17.0956i		−	0.716686i	−0.933590	−	0.358343i	$-0.883342\pi$
$569$		−	17.0956i		−	0.716686i	0.933590	−	0.358343i	$-0.116658\pi$
$570$	−1.17157	+	0.585786i	−0.0490718	+	0.0245359i
$571$	−26.9442			−1.12758			−0.563789	−	0.825919i	$-0.690657\pi$
$571$	−26.9442			−1.12758			−0.563789	+	0.825919i	$0.690657\pi$
$572$	5.95786	−	5.95786i	0.249111	−	0.249111i
$573$	−15.6291	−	15.6291i	−0.652917	−	0.652917i
$574$		0			0
$575$	−3.00000	−	21.0000i	−0.125109	−	0.875761i
$576$	1.00000			0.0416667
$577$	32.1914	−	32.1914i	1.34014	−	1.34014i	0.444233	−	0.895911i	$-0.353476\pi$
$577$	32.1914	−	32.1914i	1.34014	−	1.34014i	0.895911	−	0.444233i	$-0.146524\pi$
$578$	1.32477	−	1.32477i	0.0551031	−	0.0551031i
$579$	−9.27452			−0.385436
$580$	−4.24558	−	8.49117i	−0.176288	−	0.352577i
$581$		0			0
$582$	12.2848	+	12.2848i	0.509220	+	0.509220i
$583$	−10.6554	+	10.6554i	−0.441303	+	0.441303i
$584$	−9.17574			−0.379695
$585$	−11.7905	−	3.93015i	−0.487475	−	0.162492i
$586$		−	19.6755i		−	0.812789i
$587$	1.07695	−	1.07695i	0.0444507	−	0.0444507i	−0.684532	−	0.728983i	$-0.739993\pi$
$587$	1.07695	−	1.07695i	0.0444507	−	0.0444507i	0.728983	+	0.684532i	$0.239993\pi$
$588$		0			0
$589$			6.14386i			0.253153i
$590$	0.515938	−	1.54781i	0.0212408	−	0.0637225i
$591$		−	9.22944i		−	0.379648i
$592$	−1.55599	−	1.55599i	−0.0639509	−	0.0639509i
$593$	10.0371	+	10.0371i	0.412175	+	0.412175i	0.882496	−	0.470321i	$-0.155862\pi$
$593$	10.0371	+	10.0371i	0.412175	+	0.412175i	−0.470321	+	0.882496i	$0.655862\pi$
$594$	1.51594			0.0621997
$595$		0			0
$596$	3.20955			0.131468
$597$	9.21873	+	9.21873i	0.377298	+	0.377298i
$598$	16.6742	+	16.6742i	0.681860	+	0.681860i
$599$			2.76021i			0.112779i	0.998409	+	0.0563897i	$0.0179589\pi$
$599$			2.76021i			0.112779i	−0.998409	+	0.0563897i	$0.982041\pi$
$600$	−3.00000	+	4.00000i	−0.122474	+	0.163299i
$601$		−	26.7656i		−	1.09179i	−0.837853	−	0.545896i	$-0.816189\pi$
$601$		−	26.7656i		−	1.09179i	0.837853	−	0.545896i	$-0.183811\pi$
$602$		0			0
$603$	9.93223	−	9.93223i	0.404472	−	0.404472i
$604$			12.4503i			0.506594i
$605$	8.70193	+	17.4039i	0.353784	+	0.707568i
$606$	7.70193			0.312870
$607$	−26.6858	+	26.6858i	−1.08314	+	1.08314i	−0.0869281	+	0.996215i	$0.527705\pi$
$607$	−26.6858	+	26.6858i	−1.08314	+	1.08314i	−0.996215	+	0.0869281i	$0.972295\pi$
$608$	−0.414214	−	0.414214i	−0.0167986	−	0.0167986i
$609$		0			0
$610$	−6.43158	−	2.14386i	−0.260407	−	0.0868023i
$611$	31.2070			1.26250
$612$	3.07193	−	3.07193i	0.124175	−	0.124175i
$613$	1.98635	−	1.98635i	0.0802280	−	0.0802280i	−0.665854	−	0.746082i	$-0.731933\pi$
$613$	1.98635	−	1.98635i	0.0802280	−	0.0802280i	0.746082	+	0.665854i	$0.231933\pi$
$614$	−19.1161			−0.771465
$615$	14.1889	+	4.72965i	0.572153	+	0.190718i
$616$		0			0
$617$	5.64243	+	5.64243i	0.227156	+	0.227156i	0.811503	−	0.584348i	$-0.198650\pi$
$617$	5.64243	+	5.64243i	0.227156	+	0.227156i	−0.584348	+	0.811503i	$0.698650\pi$
$618$	3.17157	−	3.17157i	0.127579	−	0.127579i
$619$	−17.7393			−0.713002			−0.356501	−	0.934295i	$-0.616030\pi$
$619$	−17.7393			−0.713002			−0.356501	+	0.934295i	$0.616030\pi$
$620$	10.4882	+	20.9764i	0.421217	+	0.842434i
$621$			4.24264i			0.170251i
$622$	16.6508	−	16.6508i	0.667635	−	0.667635i
$623$		0			0
$624$		−	5.55807i		−	0.222501i
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$			12.1480i			0.485533i
$627$	−0.627922	−	0.627922i	−0.0250768	−	0.0250768i
$628$	1.07107	+	1.07107i	0.0427403	+	0.0427403i
$629$	−9.55980			−0.381174
$630$		0			0
$631$	−40.5660			−1.61491			−0.807453	−	0.589932i	$-0.799155\pi$
$631$	−40.5660			−1.61491			−0.807453	+	0.589932i	$0.799155\pi$
$632$	4.72965	+	4.72965i	0.188135	+	0.188135i
$633$	16.7350	+	16.7350i	0.665158	+	0.665158i
$634$			19.0897i			0.758150i
$635$	11.7019	−	35.1058i	0.464377	−	1.39313i
$636$			9.94041i			0.394163i
$637$		0			0
$638$	4.55097	−	4.55097i	0.180175	−	0.180175i
$639$		−	5.70193i		−	0.225565i
$640$	−2.12132	−	0.707107i	−0.0838525	−	0.0279508i
$641$	−39.9529			−1.57804			−0.789022	−	0.614365i	$-0.789412\pi$
$641$	−39.9529			−1.57804			−0.789022	+	0.614365i	$0.789412\pi$
$642$	0.687511	−	0.687511i	0.0271339	−	0.0271339i
$643$	22.1612	+	22.1612i	0.873953	+	0.873953i	0.992901	−	0.118947i	$-0.0379519\pi$
$643$	22.1612	+	22.1612i	0.873953	+	0.873953i	−0.118947	+	0.992901i	$0.537952\pi$
$644$		0			0
$645$	−5.41716	−	10.8343i	−0.213300	−	0.426601i
$646$	−2.54487			−0.100127
$647$	−10.1737	+	10.1737i	−0.399968	+	0.399968i	−0.878222	−	0.478254i	$-0.841270\pi$
$647$	−10.1737	+	10.1737i	−0.399968	+	0.399968i	0.478254	+	0.878222i	$0.341270\pi$
$648$	0.707107	−	0.707107i	0.0277778	−	0.0277778i
$649$	1.10610			0.0434181
$650$	22.2323	+	16.6742i	0.872022	+	0.654017i
$651$		0			0
$652$	9.44523	+	9.44523i	0.369904	+	0.369904i
$653$	−6.28478	+	6.28478i	−0.245942	+	0.245942i	−0.819303	−	0.573361i	$-0.805639\pi$
$653$	−6.28478	+	6.28478i	−0.245942	+	0.245942i	0.573361	+	0.819303i	$0.305639\pi$
$654$	5.80071			0.226826
$655$	−9.85442	+	4.92721i	−0.385044	+	0.192522i
$656$			6.68873i			0.261151i
$657$	−6.48822	+	6.48822i	−0.253130	+	0.253130i
$658$		0			0
$659$			14.7801i			0.575751i	0.957668	+	0.287876i	$0.0929490\pi$
$659$			14.7801i			0.575751i	−0.957668	+	0.287876i	$0.907051\pi$
$660$	−3.21579	−	1.07193i	−0.125174	−	0.0417248i
$661$			20.4995i			0.797338i	0.917095	+	0.398669i	$0.130528\pi$
$661$			20.4995i			0.797338i	−0.917095	+	0.398669i	$0.869472\pi$
$662$	−3.12944	−	3.12944i	−0.121629	−	0.121629i
$663$	−17.0740	−	17.0740i	−0.663100	−	0.663100i
$664$	14.2877			0.554471
$665$		0			0
$666$	−2.20051			−0.0852678
$667$	12.7368	+	12.7368i	0.493169	+	0.493169i
$668$	7.59081	+	7.59081i	0.293697	+	0.293697i
$669$		−	8.20761i		−	0.317325i
$670$	−28.0926	+	14.0463i	−1.08531	+	0.542656i
$671$		−	4.59613i		−	0.177432i
$672$		0			0
$673$	−24.5068	+	24.5068i	−0.944668	+	0.944668i	−0.998547	−	0.0538794i	$-0.982841\pi$
$673$	−24.5068	+	24.5068i	−0.944668	+	0.944668i	0.0538794	+	0.998547i	$0.482841\pi$
$674$		−	6.72548i		−	0.259056i
$675$	0.707107	+	4.94975i	0.0272166	+	0.190516i
$676$	−17.8922			−0.688161
$677$	−2.75564	+	2.75564i	−0.105908	+	0.105908i	−0.758075	−	0.652167i	$-0.773860\pi$
$677$	−2.75564	+	2.75564i	−0.105908	+	0.105908i	0.652167	+	0.758075i	$0.273860\pi$
$678$	−8.00416	−	8.00416i	−0.307398	−	0.307398i
$679$		0			0
$680$	−8.68873	+	4.34436i	−0.333198	+	0.166599i
$681$	4.34558			0.166523
$682$	−11.2426	+	11.2426i	−0.430503	+	0.430503i
$683$	−33.1782	+	33.1782i	−1.26953	+	1.26953i	−0.323195	+	0.946332i	$0.604757\pi$
$683$	−33.1782	+	33.1782i	−1.26953	+	1.26953i	−0.946332	+	0.323195i	$0.895243\pi$
$684$	−0.585786			−0.0223981
$685$	−8.21787	+	24.6536i	−0.313989	+	0.941966i
$686$		0			0
$687$	−20.8718	−	20.8718i	−0.796308	−	0.796308i
$688$	3.83051	−	3.83051i	0.146037	−	0.146037i
$689$	55.2495			2.10484
$690$	3.00000	−	9.00000i	0.114208	−	0.342624i
$691$		−	29.1671i		−	1.10957i	−0.831994	−	0.554785i	$-0.812801\pi$
$691$		−	29.1671i		−	1.10957i	0.831994	−	0.554785i	$-0.187199\pi$
$692$	15.7875	−	15.7875i	0.600151	−	0.600151i
$693$		0			0
$694$		−	30.0662i		−	1.14130i
$695$	−18.0475	−	36.0950i	−0.684581	−	1.36916i
$696$		−	4.24558i		−	0.160928i
$697$	20.5473	+	20.5473i	0.778285	+	0.778285i
$698$	4.13970	+	4.13970i	0.156690	+	0.156690i
$699$	4.48284			0.169557
$700$		0			0
$701$	−51.2203			−1.93456			−0.967282	−	0.253703i	$-0.918351\pi$
$701$	−51.2203			−1.93456			−0.967282	+	0.253703i	$0.918351\pi$
$702$	−3.93015	−	3.93015i	−0.148334	−	0.148334i
$703$	0.911479	+	0.911479i	0.0343771	+	0.0343771i
$704$		−	1.51594i		−	0.0571341i
$705$	−5.61472	−	11.2294i	−0.211463	−	0.422925i
$706$		−	32.5503i		−	1.22504i
$707$		0			0
$708$	0.515938	−	0.515938i	0.0193901	−	0.0193901i
$709$		−	21.4080i		−	0.803995i	−0.915641	−	0.401998i	$-0.868316\pi$
$709$		−	21.4080i		−	0.803995i	0.915641	−	0.401998i	$-0.131684\pi$
$710$	−4.03188	+	12.0956i	−0.151314	+	0.453941i
$711$	6.68873			0.250847
$712$	12.7309	−	12.7309i	0.477109	−	0.477109i
$713$	−31.4647	−	31.4647i	−1.17836	−	1.17836i
$714$		0			0
$715$	−5.95786	+	17.8736i	−0.222811	+	0.668434i
$716$	8.42447			0.314837
$717$	−19.8326	+	19.8326i	−0.740662	+	0.740662i
$718$	8.61766	−	8.61766i	0.321608	−	0.321608i
$719$	28.1380			1.04937			0.524685	−	0.851297i	$-0.324183\pi$
$719$	28.1380			1.04937			0.524685	+	0.851297i	$0.324183\pi$
$720$	−2.00000	+	1.00000i	−0.0745356	+	0.0372678i
$721$		0			0
$722$	−13.1924	−	13.1924i	−0.490970	−	0.490970i
$723$	11.8685	−	11.8685i	0.441394	−	0.441394i
$724$	8.42742			0.313202
$725$	16.9823	+	12.7368i	0.630708	+	0.473031i
$726$			8.70193i			0.322959i
$727$	−14.1426	+	14.1426i	−0.524522	+	0.524522i	−0.918934	−	0.394412i	$-0.870948\pi$
$727$	−14.1426	+	14.1426i	−0.524522	+	0.524522i	0.394412	+	0.918934i	$0.370948\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$	18.3515	−	9.17574i	0.679218	−	0.339609i
$731$		−	23.5341i		−	0.870440i
$732$	−2.14386	−	2.14386i	−0.0792393	−	0.0792393i
$733$	−34.2919	−	34.2919i	−1.26660	−	1.26660i	−0.947833	−	0.318766i	$-0.896732\pi$
$733$	−34.2919	−	34.2919i	−1.26660	−	1.26660i	−0.318766	−	0.947833i	$-0.603268\pi$
$734$	−23.9983			−0.885793
$735$		0			0
$736$	4.24264			0.156386
$737$	−15.0566	−	15.0566i	−0.554619	−	0.554619i
$738$	4.72965	+	4.72965i	0.174101	+	0.174101i
$739$		−	12.9518i		−	0.476438i	−0.971211	−	0.238219i	$-0.923436\pi$
$739$		−	12.9518i		−	0.476438i	0.971211	−	0.238219i	$-0.0765637\pi$
$740$	4.66798	+	1.55599i	0.171598	+	0.0571994i
$741$			3.25584i			0.119606i
$742$		0			0
$743$	−11.2558	+	11.2558i	−0.412937	+	0.412937i	−0.882760	−	0.469824i	$-0.844318\pi$
$743$	−11.2558	+	11.2558i	−0.412937	+	0.412937i	0.469824	+	0.882760i	$0.344318\pi$
$744$			10.4882i			0.384517i
$745$	−6.41909	+	3.20955i	−0.235177	+	0.117589i
$746$	0.424474			0.0155411
$747$	10.1029	−	10.1029i	0.369647	−	0.369647i
$748$	−4.65685	−	4.65685i	−0.170271	−	0.170271i
$749$		0			0
$750$	2.00000	−	11.0000i	0.0730297	−	0.401663i
$751$	4.13351			0.150834			0.0754170	−	0.997152i	$-0.475971\pi$
$751$	4.13351			0.150834			0.0754170	+	0.997152i	$0.475971\pi$
$752$	3.97021	−	3.97021i	0.144779	−	0.144779i
$753$	−1.41005	+	1.41005i	−0.0513851	+	0.0513851i
$754$	−23.5973			−0.859362
$755$	−12.4503	−	24.9005i	−0.453111	−	0.906222i
$756$		0			0
$757$	3.98341	+	3.98341i	0.144779	+	0.144779i	0.775781	−	0.631002i	$-0.217356\pi$
$757$	3.98341	+	3.98341i	0.144779	+	0.144779i	−0.631002	+	0.775781i	$0.717356\pi$
$758$	2.10000	−	2.10000i	0.0762754	−	0.0762754i
$759$	6.43158			0.233452
$760$	1.24264	+	0.414214i	0.0450753	+	0.0150251i
$761$			2.88974i			0.104753i	0.998627	+	0.0523765i	$0.0166796\pi$
$761$			2.88974i			0.104753i	−0.998627	+	0.0523765i	$0.983320\pi$
$762$	11.7019	−	11.7019i	0.423916	−	0.423916i
$763$		0			0
$764$			22.1029i			0.799656i
$765$	−3.07193	+	9.21579i	−0.111066	+	0.333198i
$766$		−	16.0958i		−	0.581566i
$767$	−2.86762	−	2.86762i	−0.103544	−	0.103544i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	−18.3818			−0.662866			−0.331433	−	0.943479i	$-0.607532\pi$
$769$	−18.3818			−0.662866			−0.331433	+	0.943479i	$0.607532\pi$
$770$		0			0
$771$	29.6044			1.06618
$772$	6.55807	+	6.55807i	0.236030	+	0.236030i
$773$	13.6701	+	13.6701i	0.491678	+	0.491678i	0.908835	−	0.417157i	$-0.136973\pi$
$773$	13.6701	+	13.6701i	0.491678	+	0.491678i	−0.417157	+	0.908835i	$0.636973\pi$
$774$		−	5.41716i		−	0.194716i
$775$	−41.9529	−	31.4647i	−1.50699	−	1.13024i
$776$		−	17.3733i		−	0.623665i
$777$		0			0
$778$	−20.7589	+	20.7589i	−0.744244	+	0.744244i
$779$		−	3.91817i		−	0.140383i
$780$	5.55807	+	11.1161i	0.199011	+	0.398022i
$781$	−8.64378			−0.309299
$782$	13.0331	−	13.0331i	0.466063	−	0.466063i
$783$	−3.00208	−	3.00208i	−0.107286	−	0.107286i
$784$		0			0
$785$	−3.21320	−	1.07107i	−0.114684	−	0.0382280i
$786$	−4.92721			−0.175748
$787$	24.0083	−	24.0083i	0.855804	−	0.855804i	−0.135036	−	0.990841i	$-0.543115\pi$
$787$	24.0083	−	24.0083i	0.855804	−	0.855804i	0.990841	+	0.135036i	$0.0431151\pi$
$788$	−6.52620	+	6.52620i	−0.232486	+	0.232486i
$789$	−24.7917			−0.882607
$790$	−14.1889	−	4.72965i	−0.504820	−	0.168273i
$791$		0			0
$792$	−1.07193	−	1.07193i	−0.0380894	−	0.0380894i
$793$	−11.9157	+	11.9157i	−0.423140	+	0.423140i
$794$	8.82843			0.313309
$795$	−9.94041	−	19.8808i	−0.352550	−	0.705100i
$796$		−	13.0373i		−	0.462093i
$797$	21.0825	−	21.0825i	0.746782	−	0.746782i	−0.227091	−	0.973873i	$-0.572922\pi$
$797$	21.0825	−	21.0825i	0.746782	−	0.746782i	0.973873	+	0.227091i	$0.0729216\pi$
$798$		0			0
$799$		−	24.3924i		−	0.862941i
$800$	4.94975	−	0.707107i	0.175000	−	0.0250000i
$801$		−	18.0042i		−	0.636146i
$802$	−5.08558	−	5.08558i	−0.179578	−	0.179578i
$803$	9.83574	+	9.83574i	0.347096	+	0.347096i
$804$	−14.0463			−0.495375
$805$		0			0
$806$	58.2943			2.05333
$807$	3.81522	+	3.81522i	0.134302	+	0.134302i
$808$	−5.44609	−	5.44609i	−0.191593	−	0.191593i
$809$			34.3107i			1.20630i	0.797628	+	0.603150i	$0.206088\pi$
$809$			34.3107i			1.20630i	−0.797628	+	0.603150i	$0.793912\pi$
$810$	−0.707107	+	2.12132i	−0.0248452	+	0.0745356i
$811$		−	23.3563i		−	0.820152i	−0.912051	−	0.410076i	$-0.865502\pi$
$811$		−	23.3563i		−	0.820152i	0.912051	−	0.410076i	$-0.134498\pi$
$812$		0			0
$813$	7.55721	−	7.55721i	0.265043	−	0.265043i
$814$			3.33583i			0.116921i
$815$	−28.3357	−	9.44523i	−0.992556	−	0.330852i
$816$	−4.34436			−0.152083
$817$	−2.24386	+	2.24386i	−0.0785027	+	0.0785027i
$818$	10.3538	+	10.3538i	0.362011	+	0.362011i
$819$		0			0
$820$	−6.68873	−	13.3775i	−0.233581	−	0.467161i
$821$	1.61472			0.0563541			0.0281770	−	0.999603i	$-0.491030\pi$
$821$	1.61472			0.0563541			0.0281770	+	0.999603i	$0.491030\pi$
$822$	−8.21787	+	8.21787i	−0.286631	+	0.286631i
$823$	7.61350	−	7.61350i	0.265390	−	0.265390i	−0.561850	−	0.827239i	$-0.689910\pi$
$823$	7.61350	−	7.61350i	0.265390	−	0.265390i	0.827239	+	0.561850i	$0.189910\pi$
$824$	−4.48528			−0.156252
$825$	7.50351	−	1.07193i	0.261239	−	0.0373198i
$826$		0			0
$827$	−2.62376	−	2.62376i	−0.0912371	−	0.0912371i	0.660015	−	0.751252i	$-0.270550\pi$
$827$	−2.62376	−	2.62376i	−0.0912371	−	0.0912371i	−0.751252	+	0.660015i	$0.770550\pi$
$828$	3.00000	−	3.00000i	0.104257	−	0.104257i
$829$	21.0548			0.731265			0.365632	−	0.930759i	$-0.380853\pi$
$829$	21.0548			0.731265			0.365632	+	0.930759i	$0.380853\pi$
$830$	−28.5754	+	14.2877i	−0.991868	+	0.495934i
$831$		−	16.4286i		−	0.569903i
$832$	−3.93015	+	3.93015i	−0.136253	+	0.136253i
$833$		0			0
$834$		−	18.0475i		−	0.624934i
$835$	−22.7724	−	7.59081i	−0.788073	−	0.262691i
$836$			0.888016i			0.0307127i
$837$	7.41629	+	7.41629i	0.256345	+	0.256345i
$838$	9.65685	+	9.65685i	0.333590	+	0.333590i
$839$	8.08427			0.279100			0.139550	−	0.990215i	$-0.455434\pi$
$839$	8.08427			0.279100			0.139550	+	0.990215i	$0.455434\pi$
$840$		0			0
$841$	10.9750			0.378449
$842$	−14.2480	−	14.2480i	−0.491019	−	0.491019i
$843$	−1.69777	−	1.69777i	−0.0584743	−	0.0584743i
$844$		−	23.6669i		−	0.814648i
$845$	35.7844	−	17.8922i	1.23102	−	0.615510i
$846$		−	5.61472i		−	0.193038i
$847$		0			0
$848$	7.02893	−	7.02893i	0.241375	−	0.241375i
$849$			12.2510i			0.420452i
$850$	13.0331	−	17.3775i	0.447031	−	0.596042i
$851$	−9.33595			−0.320032
$852$	−4.03188	+	4.03188i	−0.138130	+	0.138130i
$853$	21.5189	+	21.5189i	0.736792	+	0.736792i	0.971956	−	0.235163i	$-0.0755625\pi$
$853$	21.5189	+	21.5189i	0.736792	+	0.736792i	−0.235163	+	0.971956i	$0.575563\pi$
$854$		0			0
$855$	1.17157	−	0.585786i	0.0400669	−	0.0200335i
$856$	−0.972287			−0.0332321
$857$	−4.64157	+	4.64157i	−0.158553	+	0.158553i	−0.781925	−	0.623372i	$-0.785762\pi$
$857$	−4.64157	+	4.64157i	−0.158553	+	0.158553i	0.623372	+	0.781925i	$0.285762\pi$
$858$	−5.95786	+	5.95786i	−0.203398	+	0.203398i
$859$	14.6554			0.500037			0.250018	−	0.968241i	$-0.419563\pi$
$859$	14.6554			0.500037			0.250018	+	0.968241i	$0.419563\pi$
$860$	−3.83051	+	11.4915i	−0.130619	+	0.391858i
$861$		0			0
$862$	16.0711	+	16.0711i	0.547383	+	0.547383i
$863$	10.9927	−	10.9927i	0.374195	−	0.374195i	−0.494807	−	0.869003i	$-0.664761\pi$
$863$	10.9927	−	10.9927i	0.374195	−	0.374195i	0.869003	+	0.494807i	$0.164761\pi$
$864$	−1.00000			−0.0340207
$865$	−15.7875	+	47.3625i	−0.536791	+	1.61037i
$866$		−	15.1144i		−	0.513609i
$867$	−1.32477	+	1.32477i	−0.0449915	+	0.0449915i
$868$		0			0
$869$		−	10.1397i		−	0.343966i
$870$	4.24558	+	8.49117i	0.143939	+	0.287878i
$871$			78.0704i			2.64531i
$872$	−4.10172	−	4.10172i	−0.138902	−	0.138902i
$873$	−12.2848	−	12.2848i	−0.415777	−	0.415777i
$874$	−2.48528			−0.0840659
$875$		0			0
$876$	9.17574			0.310019
$877$	25.1269	+	25.1269i	0.848473	+	0.848473i	0.989943	−	0.141469i	$-0.0451826\pi$
$877$	25.1269	+	25.1269i	0.848473	+	0.848473i	−0.141469	+	0.989943i	$0.545183\pi$
$878$	19.2795	+	19.2795i	0.650653	+	0.650653i
$879$			19.6755i			0.663639i
$880$	1.51594	+	3.03188i	0.0511022	+	0.102204i
$881$			4.21981i			0.142169i	0.997470	+	0.0710844i	$0.0226460\pi$
$881$			4.21981i			0.142169i	−0.997470	+	0.0710844i	$0.977354\pi$
$882$		0			0
$883$	9.79426	−	9.79426i	0.329603	−	0.329603i	−0.522832	−	0.852435i	$-0.675125\pi$
$883$	9.79426	−	9.79426i	0.329603	−	0.329603i	0.852435	+	0.522832i	$0.175125\pi$
$884$			24.1463i			0.812128i
$885$	−0.515938	+	1.54781i	−0.0173431	+	0.0520292i
$886$	−17.1740			−0.576972
$887$	16.5513	−	16.5513i	0.555739	−	0.555739i	−0.372352	−	0.928091i	$-0.621449\pi$
$887$	16.5513	−	16.5513i	0.555739	−	0.555739i	0.928091	+	0.372352i	$0.121449\pi$
$888$	1.55599	+	1.55599i	0.0522157	+	0.0522157i
$889$		0			0
$890$	−12.7309	+	38.1926i	−0.426740	+	1.28022i
$891$	−1.51594			−0.0507858
$892$	−5.80366	+	5.80366i	−0.194321	+	0.194321i
$893$	−2.32569	+	2.32569i	−0.0778263	+	0.0778263i
$894$	−3.20955			−0.107343
$895$	−16.8489	+	8.42447i	−0.563198	+	0.281599i
$896$		0			0
$897$	−16.6742	−	16.6742i	−0.556736	−	0.556736i
$898$	−18.9764	+	18.9764i	−0.633252	+	0.633252i
$899$	44.5286			1.48511
$900$	3.00000	−	4.00000i	0.100000	−	0.133333i
$901$		−	43.1848i		−	1.43869i
$902$	7.16985	−	7.16985i	0.238730	−	0.238730i
$903$		0			0
$904$			11.3196i			0.376484i
$905$	−16.8548	+	8.42742i	−0.560274	+	0.280137i
$906$		−	12.4503i		−	0.413632i
$907$	−7.46747	−	7.46747i	−0.247953	−	0.247953i	0.572177	−	0.820130i	$-0.306099\pi$
$907$	−7.46747	−	7.46747i	−0.247953	−	0.247953i	−0.820130	+	0.572177i	$0.806099\pi$
$908$	−3.07279	−	3.07279i	−0.101974	−	0.101974i
$909$	−7.70193			−0.255457
$910$		0			0
$911$	18.8940			0.625987			0.312994	−	0.949755i	$-0.398668\pi$
$911$	18.8940			0.625987			0.312994	+	0.949755i	$0.398668\pi$
$912$	0.414214	+	0.414214i	0.0137160	+	0.0137160i
$913$	−15.3154	−	15.3154i	−0.506867	−	0.506867i
$914$		−	27.1373i		−	0.897621i
$915$	6.43158	+	2.14386i	0.212621	+	0.0708738i
$916$			29.5172i			0.975274i
$917$		0			0
$918$	−3.07193	+	3.07193i	−0.101389	+	0.101389i
$919$			7.16295i			0.236284i	0.992997	+	0.118142i	$0.0376938\pi$
$919$			7.16295i			0.236284i	−0.992997	+	0.118142i	$0.962306\pi$
$920$	−8.48528	+	4.24264i	−0.279751	+	0.139876i
$921$	19.1161			0.629898
$922$	−23.1799	+	23.1799i	−0.763389	+	0.763389i
$923$	22.4095	+	22.4095i	0.737616	+	0.737616i
$924$		0			0
$925$	−10.8919	+	1.55599i	−0.358125	+	0.0511607i
$926$	36.9789			1.21520
$927$	−3.17157	+	3.17157i	−0.104168	+	0.104168i
$928$	−3.00208	+	3.00208i	−0.0985481	+	0.0985481i
$929$	−3.95046			−0.129610			−0.0648052	−	0.997898i	$-0.520643\pi$
$929$	−3.95046			−0.129610			−0.0648052	+	0.997898i	$0.520643\pi$
$930$	−10.4882	−	20.9764i	−0.343922	−	0.687845i
$931$		0			0
$932$	−3.16985	−	3.16985i	−0.103832	−	0.103832i
$933$	−16.6508	+	16.6508i	−0.545121	+	0.545121i
$934$	−2.13970			−0.0700130
$935$	13.9706	+	4.65685i	0.456886	+	0.152295i
$936$			5.55807i			0.181671i
$937$	8.50152	−	8.50152i	0.277732	−	0.277732i	−0.554471	−	0.832203i	$-0.687079\pi$
$937$	8.50152	−	8.50152i	0.277732	−	0.277732i	0.832203	+	0.554471i	$0.187079\pi$
$938$		0			0
$939$		−	12.1480i		−	0.396436i
$940$	−3.97021	+	11.9106i	−0.129494	+	0.388481i
$941$		−	22.7015i		−	0.740048i	−0.929022	−	0.370024i	$-0.879349\pi$
$941$		−	22.7015i		−	0.740048i	0.929022	−	0.370024i	$-0.120651\pi$
$942$	−1.07107	−	1.07107i	−0.0348973	−	0.0348973i
$943$	20.0662	+	20.0662i	0.653445	+	0.653445i
$944$	−0.729646			−0.0237480
$945$		0			0
$946$	−8.21207			−0.266997
$947$	−17.4593	−	17.4593i	−0.567351	−	0.567351i	0.364035	−	0.931385i	$-0.381399\pi$
$947$	−17.4593	−	17.4593i	−0.567351	−	0.567351i	−0.931385	+	0.364035i	$0.881399\pi$
$948$	−4.72965	−	4.72965i	−0.153612	−	0.153612i
$949$		−	50.9994i		−	1.65551i
$950$	−2.89949	+	0.414214i	−0.0940720	+	0.0134389i
$951$		−	19.0897i		−	0.619027i
$952$		0			0
$953$	−9.99390	+	9.99390i	−0.323734	+	0.323734i	−0.850198	−	0.526463i	$-0.823518\pi$
$953$	−9.99390	+	9.99390i	−0.323734	+	0.323734i	0.526463	+	0.850198i	$0.323518\pi$
$954$		−	9.94041i		−	0.321833i
$955$	−22.1029	−	44.2059i	−0.715234	−	1.43047i
$956$	28.0475			0.907122
$957$	−4.55097	+	4.55097i	−0.147112	+	0.147112i
$958$	6.04214	+	6.04214i	0.195213	+	0.195213i
$959$		0			0
$960$	2.12132	+	0.707107i	0.0684653	+	0.0228218i
$961$	−79.0029			−2.54848
$962$	8.64832	−	8.64832i	0.278833	−	0.278833i
$963$	−0.687511	+	0.687511i	−0.0221547	+	0.0221547i
$964$	−16.7846			−0.540595
$965$	−19.6742	−	6.55807i	−0.633336	−	0.211112i
$966$		0			0
$967$	−14.6946	−	14.6946i	−0.472547	−	0.472547i	0.430191	−	0.902738i	$-0.358446\pi$
$967$	−14.6946	−	14.6946i	−0.472547	−	0.472547i	−0.902738	+	0.430191i	$0.858446\pi$
$968$	6.15320	−	6.15320i	0.197771	−	0.197771i
$969$	2.54487			0.0817530
$970$	17.3733	+	34.7466i	0.557823	+	1.11565i
$971$			15.4534i			0.495923i	0.968770	+	0.247962i	$0.0797607\pi$
$971$			15.4534i			0.495923i	−0.968770	+	0.247962i	$0.920239\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$		0			0
$974$		−	17.9505i		−	0.575170i
$975$	−22.2323	−	16.6742i	−0.712003	−	0.534002i
$976$			3.03188i			0.0970480i
$977$	42.9661	+	42.9661i	1.37461	+	1.37461i	0.853477	+	0.521130i	$0.174489\pi$
$977$	42.9661	+	42.9661i	1.37461	+	1.37461i	0.521130	+	0.853477i	$0.325511\pi$
$978$	−9.44523	−	9.44523i	−0.302025	−	0.302025i
$979$	−27.2932			−0.872294
$980$		0			0
$981$	−5.80071			−0.185203
$982$	−0.0984240	−	0.0984240i	−0.00314084	−	0.00314084i
$983$	14.9541	+	14.9541i	0.476960	+	0.476960i	0.904158	−	0.427198i	$-0.140499\pi$
$983$	14.9541	+	14.9541i	0.476960	+	0.476960i	−0.427198	+	0.904158i	$0.640499\pi$
$984$		−	6.68873i		−	0.213229i
$985$	6.52620	−	19.5786i	0.207942	−	0.623826i
$986$			18.4444i			0.587388i
$987$		0			0
$988$	2.30223	−	2.30223i	0.0732437	−	0.0732437i
$989$		−	22.9830i		−	0.730818i
$990$	3.21579	+	1.07193i	0.102204	+	0.0340682i
$991$	−55.6939			−1.76918			−0.884588	−	0.466374i	$-0.845560\pi$
$991$	−55.6939			−1.76918			−0.884588	+	0.466374i	$0.845560\pi$
$992$	7.41629	−	7.41629i	0.235468	−	0.235468i
$993$	3.12944	+	3.12944i	0.0993097	+	0.0993097i
$994$		0			0
$995$	13.0373	+	26.0745i	0.413309	+	0.826618i
$996$	−14.2877			−0.452724
$997$	−39.3443	+	39.3443i	−1.24605	+	1.24605i	−0.288594	+	0.957451i	$0.593188\pi$
$997$	−39.3443	+	39.3443i	−1.24605	+	1.24605i	−0.957451	+	0.288594i	$0.906812\pi$
$998$	−30.5953	+	30.5953i	−0.968478	+	0.968478i
$999$	2.20051			0.0696209

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.m.a.97.4	✓	8
5.3	odd	4		1470.2.m.b.1273.4	yes	8
7.6	odd	2		1470.2.m.b.97.4	yes	8
35.13	even	4	inner	1470.2.m.a.1273.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.m.a.97.4	✓	8	1.1	even	1	trivial
1470.2.m.a.1273.4	yes	8	35.13	even	4	inner
1470.2.m.b.97.4	yes	8	7.6	odd	2
1470.2.m.b.1273.4	yes	8	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
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} +1.51594 q^{11} +(0.707107 - 0.707107i) q^{12} +(-3.93015 - 3.93015i) q^{13} +(-0.707107 + 2.12132i) q^{15} -1.00000 q^{16} +(-3.07193 + 3.07193i) q^{17} +(-0.707107 + 0.707107i) q^{18} +0.585786 q^{19} +(2.00000 - 1.00000i) q^{20} +(1.07193 + 1.07193i) q^{22} +(-3.00000 + 3.00000i) q^{23} +1.00000 q^{24} +(-3.00000 + 4.00000i) q^{25} -5.55807i q^{26} +(0.707107 - 0.707107i) q^{27} -4.24558i q^{29} +(-2.00000 + 1.00000i) q^{30} +10.4882i q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.07193 - 1.07193i) q^{33} -4.34436 q^{34} -1.00000 q^{36} +(1.55599 + 1.55599i) q^{37} +(0.414214 + 0.414214i) q^{38} +5.55807i q^{39} +(2.12132 + 0.707107i) q^{40} -6.68873i q^{41} +(-3.83051 + 3.83051i) q^{43} +1.51594i q^{44} +(2.00000 - 1.00000i) q^{45} -4.24264 q^{46} +(-3.97021 + 3.97021i) q^{47} +(0.707107 + 0.707107i) q^{48} +(-4.94975 + 0.707107i) q^{50} +4.34436 q^{51} +(3.93015 - 3.93015i) q^{52} +(-7.02893 + 7.02893i) q^{53} +1.00000 q^{54} +(-1.51594 - 3.03188i) q^{55} +(-0.414214 - 0.414214i) q^{57} +(3.00208 - 3.00208i) q^{58} +0.729646 q^{59} +(-2.12132 - 0.707107i) q^{60} -3.03188i q^{61} +(-7.41629 + 7.41629i) q^{62} -1.00000i q^{64} +(-3.93015 + 11.7905i) q^{65} -1.51594i q^{66} +(-9.93223 - 9.93223i) q^{67} +(-3.07193 - 3.07193i) q^{68} +4.24264 q^{69} -5.70193 q^{71} +(-0.707107 - 0.707107i) q^{72} +(6.48822 + 6.48822i) q^{73} +2.20051i q^{74} +(4.94975 - 0.707107i) q^{75} +0.585786i q^{76} +(-3.93015 + 3.93015i) q^{78} -6.68873i q^{79} +(1.00000 + 2.00000i) q^{80} -1.00000 q^{81} +(4.72965 - 4.72965i) q^{82} +(-10.1029 - 10.1029i) q^{83} +(9.21579 + 3.07193i) q^{85} -5.41716 q^{86} +(-3.00208 + 3.00208i) q^{87} +(-1.07193 + 1.07193i) q^{88} -18.0042 q^{89} +(2.12132 + 0.707107i) q^{90} +(-3.00000 - 3.00000i) q^{92} +(7.41629 - 7.41629i) q^{93} -5.61472 q^{94} +(-0.585786 - 1.17157i) q^{95} +1.00000i q^{96} +(-12.2848 + 12.2848i) q^{97} +1.51594i 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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