LMFDB - Embedded newform 833.2.g.c.344.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [833,2,Mod(344,833)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(833, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("833.344");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.65153848837$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 9 $ x^4 - 5*x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 119)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			344.2
Root			$-1.65831 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	833.344
Dual form			833.2.g.c.540.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.15831 - 1.15831i) q^{3} +1.00000 q^{4} +(1.00000 - 1.00000i) q^{5} +(-1.15831 - 1.15831i) q^{6} -3.00000i q^{8} +0.316625i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.15831 - 1.15831i) q^{3} +1.00000 q^{4} +(1.00000 - 1.00000i) q^{5} +(-1.15831 - 1.15831i) q^{6} -3.00000i q^{8} +0.316625i q^{9} +(-1.00000 - 1.00000i) q^{10} +(-4.15831 - 4.15831i) q^{11} +(1.15831 - 1.15831i) q^{12} +3.31662 q^{13} -2.31662i q^{15} -1.00000 q^{16} +(-4.00000 + 1.00000i) q^{17} +0.316625 q^{18} +2.31662i q^{19} +(1.00000 - 1.00000i) q^{20} +(-4.15831 + 4.15831i) q^{22} +(-3.00000 - 3.00000i) q^{23} +(-3.47494 - 3.47494i) q^{24} +3.00000i q^{25} -3.31662i q^{26} +(3.84169 + 3.84169i) q^{27} +(5.31662 - 5.31662i) q^{29} -2.31662 q^{30} +(-1.31662 + 1.31662i) q^{31} -5.00000i q^{32} -9.63325 q^{33} +(1.00000 + 4.00000i) q^{34} +0.316625i q^{36} +(6.63325 - 6.63325i) q^{37} +2.31662 q^{38} +(3.84169 - 3.84169i) q^{39} +(-3.00000 - 3.00000i) q^{40} +(5.31662 + 5.31662i) q^{41} +4.63325i q^{43} +(-4.15831 - 4.15831i) q^{44} +(0.316625 + 0.316625i) q^{45} +(-3.00000 + 3.00000i) q^{46} +2.31662 q^{47} +(-1.15831 + 1.15831i) q^{48} +3.00000 q^{50} +(-3.47494 + 5.79156i) q^{51} +3.31662 q^{52} +3.63325i q^{53} +(3.84169 - 3.84169i) q^{54} -8.31662 q^{55} +(2.68338 + 2.68338i) q^{57} +(-5.31662 - 5.31662i) q^{58} +2.63325i q^{59} -2.31662i q^{60} +(8.31662 + 8.31662i) q^{61} +(1.31662 + 1.31662i) q^{62} -7.00000 q^{64} +(3.31662 - 3.31662i) q^{65} +9.63325i q^{66} -4.31662 q^{67} +(-4.00000 + 1.00000i) q^{68} -6.94987 q^{69} +(-3.15831 + 3.15831i) q^{71} +0.949874 q^{72} +(5.00000 - 5.00000i) q^{73} +(-6.63325 - 6.63325i) q^{74} +(3.47494 + 3.47494i) q^{75} +2.31662i q^{76} +(-3.84169 - 3.84169i) q^{78} +(-4.47494 - 4.47494i) q^{79} +(-1.00000 + 1.00000i) q^{80} +7.94987 q^{81} +(5.31662 - 5.31662i) q^{82} +8.63325i q^{83} +(-3.00000 + 5.00000i) q^{85} +4.63325 q^{86} -12.3166i q^{87} +(-12.4749 + 12.4749i) q^{88} -10.6834 q^{89} +(0.316625 - 0.316625i) q^{90} +(-3.00000 - 3.00000i) q^{92} +3.05013i q^{93} -2.31662i q^{94} +(2.31662 + 2.31662i) q^{95} +(-5.79156 - 5.79156i) q^{96} +(10.9499 - 10.9499i) q^{97} +(1.31662 - 1.31662i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 4 q^{4} + 4 q^{5} + 2 q^{6}+O(q^{10}) $ 4 * q - 2 * q^3 + 4 * q^4 + 4 * q^5 + 2 * q^6	$ 4 q - 2 q^{3} + 4 q^{4} + 4 q^{5} + 2 q^{6} - 4 q^{10} - 10 q^{11} - 2 q^{12} - 4 q^{16} - 16 q^{17} - 12 q^{18} + 4 q^{20} - 10 q^{22} - 12 q^{23} + 6 q^{24} + 22 q^{27} + 8 q^{29} + 4 q^{30} + 8 q^{31} - 12 q^{33} + 4 q^{34} - 4 q^{38} + 22 q^{39} - 12 q^{40} + 8 q^{41} - 10 q^{44} - 12 q^{45} - 12 q^{46} - 4 q^{47} + 2 q^{48} + 12 q^{50} + 6 q^{51} + 22 q^{54} - 20 q^{55} + 24 q^{57} - 8 q^{58} + 20 q^{61} - 8 q^{62} - 28 q^{64} - 4 q^{67} - 16 q^{68} + 12 q^{69} - 6 q^{71} - 36 q^{72} + 20 q^{73} - 6 q^{75} - 22 q^{78} + 2 q^{79} - 4 q^{80} - 8 q^{81} + 8 q^{82} - 12 q^{85} - 8 q^{86} - 30 q^{88} - 56 q^{89} - 12 q^{90} - 12 q^{92} - 4 q^{95} + 10 q^{96} + 4 q^{97} - 8 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 + 4 * q^4 + 4 * q^5 + 2 * q^6 - 4 * q^10 - 10 * q^11 - 2 * q^12 - 4 * q^16 - 16 * q^17 - 12 * q^18 + 4 * q^20 - 10 * q^22 - 12 * q^23 + 6 * q^24 + 22 * q^27 + 8 * q^29 + 4 * q^30 + 8 * q^31 - 12 * q^33 + 4 * q^34 - 4 * q^38 + 22 * q^39 - 12 * q^40 + 8 * q^41 - 10 * q^44 - 12 * q^45 - 12 * q^46 - 4 * q^47 + 2 * q^48 + 12 * q^50 + 6 * q^51 + 22 * q^54 - 20 * q^55 + 24 * q^57 - 8 * q^58 + 20 * q^61 - 8 * q^62 - 28 * q^64 - 4 * q^67 - 16 * q^68 + 12 * q^69 - 6 * q^71 - 36 * q^72 + 20 * q^73 - 6 * q^75 - 22 * q^78 + 2 * q^79 - 4 * q^80 - 8 * q^81 + 8 * q^82 - 12 * q^85 - 8 * q^86 - 30 * q^88 - 56 * q^89 - 12 * q^90 - 12 * q^92 - 4 * q^95 + 10 * q^96 + 4 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

$n$	$52$	$785$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.00000i		−	0.707107i	−0.935414	−	0.353553i	$-0.884973\pi$
$2$		−	1.00000i		−	0.707107i	0.935414	−	0.353553i	$-0.115027\pi$
$3$	1.15831	−	1.15831i	0.668752	−	0.668752i	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	1.15831	−	1.15831i	0.668752	−	0.668752i	0.957427	+	0.288675i	$0.0932147\pi$
$4$	1.00000			0.500000
$5$	1.00000	−	1.00000i	0.447214	−	0.447214i	−0.447214	−	0.894427i	$-0.647584\pi$
$5$	1.00000	−	1.00000i	0.447214	−	0.447214i	0.894427	+	0.447214i	$0.147584\pi$
$6$	−1.15831	−	1.15831i	−0.472879	−	0.472879i
$7$		0			0
$7$		0			0
$8$		−	3.00000i		−	1.06066i
$9$			0.316625i			0.105542i
$10$	−1.00000	−	1.00000i	−0.316228	−	0.316228i
$11$	−4.15831	−	4.15831i	−1.25378	−	1.25378i	−0.954013	−	0.299765i	$-0.903092\pi$
$11$	−4.15831	−	4.15831i	−1.25378	−	1.25378i	−0.299765	−	0.954013i	$-0.596908\pi$
$12$	1.15831	−	1.15831i	0.334376	−	0.334376i
$13$	3.31662			0.919866			0.459933	−	0.887954i	$-0.347873\pi$
$13$	3.31662			0.919866			0.459933	+	0.887954i	$0.347873\pi$
$14$		0			0
$15$		−	2.31662i		−	0.598150i
$16$	−1.00000			−0.250000
$17$	−4.00000	+	1.00000i	−0.970143	+	0.242536i
$17$	−4.00000	+	1.00000i	−0.970143	+	0.242536i
$18$	0.316625			0.0746292
$19$			2.31662i			0.531470i	0.964046	+	0.265735i	$0.0856146\pi$
$19$			2.31662i			0.531470i	−0.964046	+	0.265735i	$0.914385\pi$
$20$	1.00000	−	1.00000i	0.223607	−	0.223607i
$21$		0			0
$22$	−4.15831	+	4.15831i	−0.886555	+	0.886555i
$23$	−3.00000	−	3.00000i	−0.625543	−	0.625543i	0.321400	−	0.946943i	$-0.395847\pi$
$23$	−3.00000	−	3.00000i	−0.625543	−	0.625543i	−0.946943	+	0.321400i	$0.895847\pi$
$24$	−3.47494	−	3.47494i	−0.709319	−	0.709319i
$25$			3.00000i			0.600000i
$26$		−	3.31662i		−	0.650444i
$27$	3.84169	+	3.84169i	0.739333	+	0.739333i
$28$		0			0
$29$	5.31662	−	5.31662i	0.987272	−	0.987272i	−0.0126476	−	0.999920i	$-0.504026\pi$
$29$	5.31662	−	5.31662i	0.987272	−	0.987272i	0.999920	+	0.0126476i	$0.00402596\pi$
$30$	−2.31662			−0.422956
$31$	−1.31662	+	1.31662i	−0.236473	+	0.236473i	−0.815388	−	0.578915i	$-0.803476\pi$
$31$	−1.31662	+	1.31662i	−0.236473	+	0.236473i	0.578915	+	0.815388i	$0.303476\pi$
$32$		−	5.00000i		−	0.883883i
$33$	−9.63325			−1.67693
$34$	1.00000	+	4.00000i	0.171499	+	0.685994i
$35$		0			0
$36$			0.316625i			0.0527708i
$37$	6.63325	−	6.63325i	1.09050	−	1.09050i	0.0950246	−	0.995475i	$-0.469707\pi$
$37$	6.63325	−	6.63325i	1.09050	−	1.09050i	0.995475	−	0.0950246i	$-0.0302930\pi$
$38$	2.31662			0.375806
$39$	3.84169	−	3.84169i	0.615162	−	0.615162i
$40$	−3.00000	−	3.00000i	−0.474342	−	0.474342i
$41$	5.31662	+	5.31662i	0.830317	+	0.830317i	0.987560	−	0.157243i	$-0.0502605\pi$
$41$	5.31662	+	5.31662i	0.830317	+	0.830317i	−0.157243	+	0.987560i	$0.550260\pi$
$42$		0			0
$43$			4.63325i			0.706564i	0.935517	+	0.353282i	$0.114934\pi$
$43$			4.63325i			0.706564i	−0.935517	+	0.353282i	$0.885066\pi$
$44$	−4.15831	−	4.15831i	−0.626889	−	0.626889i
$45$	0.316625	+	0.316625i	0.0471996	+	0.0471996i
$46$	−3.00000	+	3.00000i	−0.442326	+	0.442326i
$47$	2.31662			0.337914			0.168957	−	0.985623i	$-0.445960\pi$
$47$	2.31662			0.337914			0.168957	+	0.985623i	$0.445960\pi$
$48$	−1.15831	+	1.15831i	−0.167188	+	0.167188i
$49$		0			0
$50$	3.00000			0.424264
$51$	−3.47494	+	5.79156i	−0.486589	+	0.810981i
$52$	3.31662			0.459933
$53$			3.63325i			0.499065i	0.968366	+	0.249533i	$0.0802770\pi$
$53$			3.63325i			0.499065i	−0.968366	+	0.249533i	$0.919723\pi$
$54$	3.84169	−	3.84169i	0.522787	−	0.522787i
$55$	−8.31662			−1.12141
$56$		0			0
$57$	2.68338	+	2.68338i	0.355422	+	0.355422i
$58$	−5.31662	−	5.31662i	−0.698107	−	0.698107i
$59$			2.63325i			0.342820i	0.985200	+	0.171410i	$0.0548323\pi$
$59$			2.63325i			0.342820i	−0.985200	+	0.171410i	$0.945168\pi$
$60$		−	2.31662i		−	0.299075i
$61$	8.31662	+	8.31662i	1.06483	+	1.06483i	0.997747	+	0.0670876i	$0.0213707\pi$
$61$	8.31662	+	8.31662i	1.06483	+	1.06483i	0.0670876	+	0.997747i	$0.478629\pi$
$62$	1.31662	+	1.31662i	0.167212	+	0.167212i
$63$		0			0
$64$	−7.00000			−0.875000
$65$	3.31662	−	3.31662i	0.411377	−	0.411377i
$66$			9.63325i			1.18577i
$67$	−4.31662			−0.527360			−0.263680	−	0.964610i	$-0.584936\pi$
$67$	−4.31662			−0.527360			−0.263680	+	0.964610i	$0.584936\pi$
$68$	−4.00000	+	1.00000i	−0.485071	+	0.121268i
$69$	−6.94987			−0.836667
$70$		0			0
$71$	−3.15831	+	3.15831i	−0.374823	+	0.374823i	−0.869230	−	0.494408i	$-0.835385\pi$
$71$	−3.15831	+	3.15831i	−0.374823	+	0.374823i	0.494408	+	0.869230i	$0.335385\pi$
$72$	0.949874			0.111944
$73$	5.00000	−	5.00000i	0.585206	−	0.585206i	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	5.00000	−	5.00000i	0.585206	−	0.585206i	0.936329	+	0.351123i	$0.114200\pi$
$74$	−6.63325	−	6.63325i	−0.771100	−	0.771100i
$75$	3.47494	+	3.47494i	0.401251	+	0.401251i
$76$			2.31662i			0.265735i
$77$		0			0
$78$	−3.84169	−	3.84169i	−0.434985	−	0.434985i
$79$	−4.47494	−	4.47494i	−0.503470	−	0.503470i	0.409045	−	0.912514i	$-0.365862\pi$
$79$	−4.47494	−	4.47494i	−0.503470	−	0.503470i	−0.912514	+	0.409045i	$0.865862\pi$
$80$	−1.00000	+	1.00000i	−0.111803	+	0.111803i
$81$	7.94987			0.883319
$82$	5.31662	−	5.31662i	0.587123	−	0.587123i
$83$			8.63325i			0.947622i	0.880626	+	0.473811i	$0.157122\pi$
$83$			8.63325i			0.947622i	−0.880626	+	0.473811i	$0.842878\pi$
$84$		0			0
$85$	−3.00000	+	5.00000i	−0.325396	+	0.542326i
$86$	4.63325			0.499616
$87$		−	12.3166i		−	1.32048i
$88$	−12.4749	+	12.4749i	−1.32983	+	1.32983i
$89$	−10.6834			−1.13244			−0.566218	−	0.824256i	$-0.691594\pi$
$89$	−10.6834			−1.13244			−0.566218	+	0.824256i	$0.691594\pi$
$90$	0.316625	−	0.316625i	0.0333752	−	0.0333752i
$91$		0			0
$92$	−3.00000	−	3.00000i	−0.312772	−	0.312772i
$93$			3.05013i			0.316283i
$94$		−	2.31662i		−	0.238942i
$95$	2.31662	+	2.31662i	0.237681	+	0.237681i
$96$	−5.79156	−	5.79156i	−0.591099	−	0.591099i
$97$	10.9499	−	10.9499i	1.11179	−	1.11179i	0.118883	−	0.992908i	$-0.462069\pi$
$97$	10.9499	−	10.9499i	1.11179	−	1.11179i	0.992908	−	0.118883i	$-0.0379314\pi$
$98$		0			0
$99$	1.31662	−	1.31662i	0.132326	−	0.132326i
$100$			3.00000i			0.300000i
$101$	−6.63325			−0.660033			−0.330017	−	0.943975i	$-0.607054\pi$
$101$	−6.63325			−0.660033			−0.330017	+	0.943975i	$0.607054\pi$
$102$	5.79156	+	3.47494i	0.573450	+	0.344070i
$103$	−0.316625			−0.0311980			−0.0155990	−	0.999878i	$-0.504966\pi$
$103$	−0.316625			−0.0311980			−0.0155990	+	0.999878i	$0.504966\pi$
$104$		−	9.94987i		−	0.975665i
$105$		0			0
$106$	3.63325			0.352892
$107$	−7.79156	+	7.79156i	−0.753239	+	0.753239i	−0.975082	−	0.221844i	$-0.928793\pi$
$107$	−7.79156	+	7.79156i	−0.753239	+	0.753239i	0.221844	+	0.975082i	$0.428793\pi$
$108$	3.84169	+	3.84169i	0.369667	+	0.369667i
$109$	−0.316625	−	0.316625i	−0.0303272	−	0.0303272i	0.691781	−	0.722108i	$-0.256827\pi$
$109$	−0.316625	−	0.316625i	−0.0303272	−	0.0303272i	−0.722108	+	0.691781i	$0.756827\pi$
$110$			8.31662i			0.792959i
$111$		−	15.3668i		−	1.45855i
$112$		0			0
$113$	−0.316625	−	0.316625i	−0.0297856	−	0.0297856i	0.692057	−	0.721843i	$-0.256705\pi$
$113$	−0.316625	−	0.316625i	−0.0297856	−	0.0297856i	−0.721843	+	0.692057i	$0.756705\pi$
$114$	2.68338	−	2.68338i	0.251321	−	0.251321i
$115$	−6.00000			−0.559503
$116$	5.31662	−	5.31662i	0.493636	−	0.493636i
$117$			1.05013i			0.0970841i
$118$	2.63325			0.242410
$119$		0			0
$120$	−6.94987			−0.634434
$121$			23.5831i			2.14392i
$122$	8.31662	−	8.31662i	0.752952	−	0.752952i
$123$	12.3166			1.11055
$124$	−1.31662	+	1.31662i	−0.118236	+	0.118236i
$125$	8.00000	+	8.00000i	0.715542	+	0.715542i
$126$		0			0
$127$			3.68338i			0.326847i	0.986556	+	0.163423i	$0.0522536\pi$
$127$			3.68338i			0.326847i	−0.986556	+	0.163423i	$0.947746\pi$
$128$		−	3.00000i		−	0.265165i
$129$	5.36675	+	5.36675i	0.472516	+	0.472516i
$130$	−3.31662	−	3.31662i	−0.290887	−	0.290887i
$131$	−3.63325	+	3.63325i	−0.317438	+	0.317438i	−0.847783	−	0.530344i	$-0.822063\pi$
$131$	−3.63325	+	3.63325i	−0.317438	+	0.317438i	0.530344	+	0.847783i	$0.322063\pi$
$132$	−9.63325			−0.838467
$133$		0			0
$134$			4.31662i			0.372900i
$135$	7.68338			0.661280
$136$	3.00000	+	12.0000i	0.257248	+	1.02899i
$137$	2.68338			0.229256			0.114628	−	0.993408i	$-0.463432\pi$
$137$	2.68338			0.229256			0.114628	+	0.993408i	$0.463432\pi$
$138$			6.94987i			0.591613i
$139$	−10.4749	+	10.4749i	−0.888473	+	0.888473i	−0.994376	−	0.105904i	$-0.966226\pi$
$139$	−10.4749	+	10.4749i	−0.888473	+	0.888473i	0.105904	+	0.994376i	$0.466226\pi$
$140$		0			0
$141$	2.68338	−	2.68338i	0.225981	−	0.225981i
$142$	3.15831	+	3.15831i	0.265040	+	0.265040i
$143$	−13.7916	−	13.7916i	−1.15331	−	1.15331i
$144$		−	0.316625i		−	0.0263854i
$145$		−	10.6332i		−	0.883043i
$146$	−5.00000	−	5.00000i	−0.413803	−	0.413803i
$147$		0			0
$148$	6.63325	−	6.63325i	0.545250	−	0.545250i
$149$	−1.00000			−0.0819232			−0.0409616	−	0.999161i	$-0.513042\pi$
$149$	−1.00000			−0.0819232			−0.0409616	+	0.999161i	$0.513042\pi$
$150$	3.47494	−	3.47494i	0.283727	−	0.283727i
$151$		−	13.5831i		−	1.10538i	−0.833387	−	0.552689i	$-0.813602\pi$
$151$		−	13.5831i		−	1.10538i	0.833387	−	0.552689i	$-0.186398\pi$
$152$	6.94987			0.563709
$153$	−0.316625	−	1.26650i	−0.0255976	−	0.102390i
$154$		0			0
$155$			2.63325i			0.211508i
$156$	3.84169	−	3.84169i	0.307581	−	0.307581i
$157$	10.2665			0.819356			0.409678	−	0.912230i	$-0.365641\pi$
$157$	10.2665			0.819356			0.409678	+	0.912230i	$0.365641\pi$
$158$	−4.47494	+	4.47494i	−0.356007	+	0.356007i
$159$	4.20844	+	4.20844i	0.333751	+	0.333751i
$160$	−5.00000	−	5.00000i	−0.395285	−	0.395285i
$161$		0			0
$162$		−	7.94987i		−	0.624601i
$163$	9.63325	+	9.63325i	0.754534	+	0.754534i	0.975322	−	0.220788i	$-0.0708628\pi$
$163$	9.63325	+	9.63325i	0.754534	+	0.754534i	−0.220788	+	0.975322i	$0.570863\pi$
$164$	5.31662	+	5.31662i	0.415159	+	0.415159i
$165$	−9.63325	+	9.63325i	−0.749947	+	0.749947i
$166$	8.63325			0.670070
$167$	0.158312	−	0.158312i	0.0122506	−	0.0122506i	−0.700955	−	0.713206i	$-0.747243\pi$
$167$	0.158312	−	0.158312i	0.0122506	−	0.0122506i	0.713206	+	0.700955i	$0.247243\pi$
$168$		0			0
$169$	−2.00000			−0.153846
$170$	5.00000	+	3.00000i	0.383482	+	0.230089i
$171$	−0.733501			−0.0560922
$172$			4.63325i			0.353282i
$173$	4.00000	−	4.00000i	0.304114	−	0.304114i	−0.538507	−	0.842621i	$-0.681011\pi$
$173$	4.00000	−	4.00000i	0.304114	−	0.304114i	0.842621	+	0.538507i	$0.181011\pi$
$174$	−12.3166			−0.933721
$175$		0			0
$176$	4.15831	+	4.15831i	0.313445	+	0.313445i
$177$	3.05013	+	3.05013i	0.229261	+	0.229261i
$178$			10.6834i			0.800753i
$179$		−	0.633250i		−	0.0473313i	−0.999720	−	0.0236656i	$-0.992466\pi$
$179$		−	0.633250i		−	0.0473313i	0.999720	−	0.0236656i	$-0.00753371\pi$
$180$	0.316625	+	0.316625i	0.0235998	+	0.0235998i
$181$	−12.3166	−	12.3166i	−0.915488	−	0.915488i	0.0812095	−	0.996697i	$-0.474122\pi$
$181$	−12.3166	−	12.3166i	−0.915488	−	0.915488i	−0.996697	+	0.0812095i	$0.974122\pi$
$182$		0			0
$183$	19.2665			1.42422
$184$	−9.00000	+	9.00000i	−0.663489	+	0.663489i
$185$		−	13.2665i		−	0.975372i
$186$	3.05013			0.223646
$187$	20.7916	+	12.4749i	1.52043	+	0.912258i
$188$	2.31662			0.168957
$189$		0			0
$190$	2.31662	−	2.31662i	0.168066	−	0.168066i
$191$	7.26650			0.525785			0.262893	−	0.964825i	$-0.415323\pi$
$191$	7.26650			0.525785			0.262893	+	0.964825i	$0.415323\pi$
$192$	−8.10819	+	8.10819i	−0.585158	+	0.585158i
$193$	10.9499	+	10.9499i	0.788189	+	0.788189i	0.981197	−	0.193008i	$-0.0618243\pi$
$193$	10.9499	+	10.9499i	0.788189	+	0.788189i	−0.193008	+	0.981197i	$0.561824\pi$
$194$	−10.9499	−	10.9499i	−0.786155	−	0.786155i
$195$		−	7.68338i		−	0.550218i
$196$		0			0
$197$	9.31662	+	9.31662i	0.663782	+	0.663782i	0.956269	−	0.292487i	$-0.0944829\pi$
$197$	9.31662	+	9.31662i	0.663782	+	0.663782i	−0.292487	+	0.956269i	$0.594483\pi$
$198$	−1.31662	−	1.31662i	−0.0935684	−	0.0935684i
$199$	1.52506	−	1.52506i	0.108109	−	0.108109i	−0.650983	−	0.759092i	$-0.725643\pi$
$199$	1.52506	−	1.52506i	0.108109	−	0.108109i	0.759092	+	0.650983i	$0.225643\pi$
$200$	9.00000			0.636396
$201$	−5.00000	+	5.00000i	−0.352673	+	0.352673i
$202$			6.63325i			0.466714i
$203$		0			0
$204$	−3.47494	+	5.79156i	−0.243294	+	0.405490i
$205$	10.6332			0.742658
$206$			0.316625i			0.0220603i
$207$	0.949874	−	0.949874i	0.0660208	−	0.0660208i
$208$	−3.31662			−0.229967
$209$	9.63325	−	9.63325i	0.666346	−	0.666346i
$210$		0			0
$211$	−3.63325	−	3.63325i	−0.250123	−	0.250123i	0.570898	−	0.821021i	$-0.306595\pi$
$211$	−3.63325	−	3.63325i	−0.250123	−	0.250123i	−0.821021	+	0.570898i	$0.806595\pi$
$212$			3.63325i			0.249533i
$213$			7.31662i			0.501327i
$214$	7.79156	+	7.79156i	0.532620	+	0.532620i
$215$	4.63325	+	4.63325i	0.315985	+	0.315985i
$216$	11.5251	−	11.5251i	0.784181	−	0.784181i
$217$		0			0
$218$	−0.316625	+	0.316625i	−0.0214445	+	0.0214445i
$219$		−	11.5831i		−	0.782715i
$220$	−8.31662			−0.560707
$221$	−13.2665	+	3.31662i	−0.892401	+	0.223100i
$222$	−15.3668			−1.03135
$223$		0			0		1.00000			$0$
$223$		0			0		−1.00000			$\pi$
$224$		0			0
$225$	−0.949874			−0.0633250
$226$	−0.316625	+	0.316625i	−0.0210616	+	0.0210616i
$227$	18.7916	+	18.7916i	1.24724	+	1.24724i	0.956934	+	0.290306i	$0.0937570\pi$
$227$	18.7916	+	18.7916i	1.24724	+	1.24724i	0.290306	+	0.956934i	$0.406243\pi$
$228$	2.68338	+	2.68338i	0.177711	+	0.177711i
$229$		−	27.2665i		−	1.80182i	−0.434005	−	0.900910i	$-0.642900\pi$
$229$		−	27.2665i		−	1.80182i	0.434005	−	0.900910i	$-0.357100\pi$
$230$			6.00000i			0.395628i
$231$		0			0
$232$	−15.9499	−	15.9499i	−1.04716	−	1.04716i
$233$	4.31662	−	4.31662i	0.282791	−	0.282791i	−0.551430	−	0.834221i	$-0.685918\pi$
$233$	4.31662	−	4.31662i	0.282791	−	0.282791i	0.834221	+	0.551430i	$0.185918\pi$
$234$	1.05013			0.0686489
$235$	2.31662	−	2.31662i	0.151120	−	0.151120i
$236$			2.63325i			0.171410i
$237$	−10.3668			−0.673393
$238$		0			0
$239$	13.2665			0.858138			0.429069	−	0.903272i	$-0.358842\pi$
$239$	13.2665			0.858138			0.429069	+	0.903272i	$0.358842\pi$
$240$			2.31662i			0.149537i
$241$	−19.3166	+	19.3166i	−1.24429	+	1.24429i	−0.286091	+	0.958203i	$0.592356\pi$
$241$	−19.3166	+	19.3166i	−1.24429	+	1.24429i	−0.958203	+	0.286091i	$0.907644\pi$
$242$	23.5831			1.51598
$243$	−2.31662	+	2.31662i	−0.148612	+	0.148612i
$244$	8.31662	+	8.31662i	0.532417	+	0.532417i
$245$		0			0
$246$		−	12.3166i		−	0.785279i
$247$			7.68338i			0.488881i
$248$	3.94987	+	3.94987i	0.250817	+	0.250817i
$249$	10.0000	+	10.0000i	0.633724	+	0.633724i
$250$	8.00000	−	8.00000i	0.505964	−	0.505964i
$251$	24.3166			1.53485			0.767426	−	0.641138i	$-0.221537\pi$
$251$	24.3166			1.53485			0.767426	+	0.641138i	$0.221537\pi$
$252$		0			0
$253$			24.9499i			1.56859i
$254$	3.68338			0.231116
$255$	2.31662	+	9.26650i	0.145073	+	0.580291i
$256$	−17.0000			−1.06250
$257$			2.68338i			0.167384i	0.996492	+	0.0836922i	$0.0266712\pi$
$257$			2.68338i			0.167384i	−0.996492	+	0.0836922i	$0.973329\pi$
$258$	5.36675	−	5.36675i	0.334119	−	0.334119i
$259$		0			0
$260$	3.31662	−	3.31662i	0.205688	−	0.205688i
$261$	1.68338	+	1.68338i	0.104198	+	0.104198i
$262$	3.63325	+	3.63325i	0.224463	+	0.224463i
$263$			8.31662i			0.512825i	0.966567	+	0.256413i	$0.0825406\pi$
$263$			8.31662i			0.512825i	−0.966567	+	0.256413i	$0.917459\pi$
$264$			28.8997i			1.77866i
$265$	3.63325	+	3.63325i	0.223189	+	0.223189i
$266$		0			0
$267$	−12.3747	+	12.3747i	−0.757318	+	0.757318i
$268$	−4.31662			−0.263680
$269$	3.00000	−	3.00000i	0.182913	−	0.182913i	−0.609711	−	0.792624i	$-0.708714\pi$
$269$	3.00000	−	3.00000i	0.182913	−	0.182913i	0.792624	+	0.609711i	$0.208714\pi$
$270$		−	7.68338i		−	0.467595i
$271$	2.00000			0.121491			0.0607457	−	0.998153i	$-0.480652\pi$
$271$	2.00000			0.121491			0.0607457	+	0.998153i	$0.480652\pi$
$272$	4.00000	−	1.00000i	0.242536	−	0.0606339i
$273$		0			0
$274$		−	2.68338i		−	0.162109i
$275$	12.4749	−	12.4749i	0.752267	−	0.752267i
$276$	−6.94987			−0.418333
$277$	−12.6332	+	12.6332i	−0.759058	+	0.759058i	−0.976151	−	0.217093i	$-0.930343\pi$
$277$	−12.6332	+	12.6332i	−0.759058	+	0.759058i	0.217093	+	0.976151i	$0.430343\pi$
$278$	10.4749	+	10.4749i	0.628245	+	0.628245i
$279$	−0.416876	−	0.416876i	−0.0249577	−	0.0249577i
$280$		0			0
$281$		−	15.0000i		−	0.894825i	−0.894328	−	0.447412i	$-0.852346\pi$
$281$		−	15.0000i		−	0.894825i	0.894328	−	0.447412i	$-0.147654\pi$
$282$	−2.68338	−	2.68338i	−0.159793	−	0.159793i
$283$	−14.4248	−	14.4248i	−0.857466	−	0.857466i	0.133573	−	0.991039i	$-0.457355\pi$
$283$	−14.4248	−	14.4248i	−0.857466	−	0.857466i	−0.991039	+	0.133573i	$0.957355\pi$
$284$	−3.15831	+	3.15831i	−0.187411	+	0.187411i
$285$	5.36675			0.317899
$286$	−13.7916	+	13.7916i	−0.815512	+	0.815512i
$287$		0			0
$288$	1.58312			0.0932865
$289$	15.0000	−	8.00000i	0.882353	−	0.470588i
$290$	−10.6332			−0.624406
$291$		−	25.3668i		−	1.48703i
$292$	5.00000	−	5.00000i	0.292603	−	0.292603i
$293$	−25.5330			−1.49165			−0.745827	−	0.666140i	$-0.767945\pi$
$293$	−25.5330			−1.49165			−0.745827	+	0.666140i	$0.767945\pi$
$294$		0			0
$295$	2.63325	+	2.63325i	0.153314	+	0.153314i
$296$	−19.8997	−	19.8997i	−1.15665	−	1.15665i
$297$		−	31.9499i		−	1.85392i
$298$			1.00000i			0.0579284i
$299$	−9.94987	−	9.94987i	−0.575416	−	0.575416i
$300$	3.47494	+	3.47494i	0.200626	+	0.200626i
$301$		0			0
$302$	−13.5831			−0.781621
$303$	−7.68338	+	7.68338i	−0.441398	+	0.441398i
$304$		−	2.31662i		−	0.132868i
$305$	16.6332			0.952417
$306$	−1.26650	+	0.316625i	−0.0724009	+	0.0181002i
$307$	−26.9499			−1.53811			−0.769055	−	0.639182i	$-0.779273\pi$
$307$	−26.9499			−1.53811			−0.769055	+	0.639182i	$0.779273\pi$
$308$		0			0
$309$	−0.366750	+	0.366750i	−0.0208637	+	0.0208637i
$310$	2.63325			0.149559
$311$	−0.525063	+	0.525063i	−0.0297736	+	0.0297736i	−0.721837	−	0.692063i	$-0.756702\pi$
$311$	−0.525063	+	0.525063i	−0.0297736	+	0.0297736i	0.692063	+	0.721837i	$0.256702\pi$
$312$	−11.5251	−	11.5251i	−0.652478	−	0.652478i
$313$	−13.9499	−	13.9499i	−0.788494	−	0.788494i	0.192754	−	0.981247i	$-0.438258\pi$
$313$	−13.9499	−	13.9499i	−0.788494	−	0.788494i	−0.981247	+	0.192754i	$0.938258\pi$
$314$		−	10.2665i		−	0.579372i
$315$		0			0
$316$	−4.47494	−	4.47494i	−0.251735	−	0.251735i
$317$	−9.68338	−	9.68338i	−0.543873	−	0.543873i	0.380789	−	0.924662i	$-0.375652\pi$
$317$	−9.68338	−	9.68338i	−0.543873	−	0.543873i	−0.924662	+	0.380789i	$0.875652\pi$
$318$	4.20844	−	4.20844i	0.235997	−	0.235997i
$319$	−44.2164			−2.47564
$320$	−7.00000	+	7.00000i	−0.391312	+	0.391312i
$321$			18.0501i			1.00746i
$322$		0			0
$323$	−2.31662	−	9.26650i	−0.128900	−	0.515602i
$324$	7.94987			0.441660
$325$			9.94987i			0.551920i
$326$	9.63325	−	9.63325i	0.533536	−	0.533536i
$327$	−0.733501			−0.0405627
$328$	15.9499	−	15.9499i	0.880684	−	0.880684i
$329$		0			0
$330$	9.63325	+	9.63325i	0.530293	+	0.530293i
$331$		−	20.0000i		−	1.09930i	−0.835395	−	0.549650i	$-0.814761\pi$
$331$		−	20.0000i		−	1.09930i	0.835395	−	0.549650i	$-0.185239\pi$
$332$			8.63325i			0.473811i
$333$	2.10025	+	2.10025i	0.115093	+	0.115093i
$334$	−0.158312	−	0.158312i	−0.00866247	−	0.00866247i
$335$	−4.31662	+	4.31662i	−0.235842	+	0.235842i
$336$		0			0
$337$	−9.36675	+	9.36675i	−0.510239	+	0.510239i	−0.914600	−	0.404360i	$-0.867494\pi$
$337$	−9.36675	+	9.36675i	−0.510239	+	0.510239i	0.404360	+	0.914600i	$0.367494\pi$
$338$			2.00000i			0.108786i
$339$	−0.733501			−0.0398383
$340$	−3.00000	+	5.00000i	−0.162698	+	0.271163i
$341$	10.9499			0.592969
$342$			0.733501i			0.0396632i
$343$		0			0
$344$	13.8997			0.749424
$345$	−6.94987	+	6.94987i	−0.374169	+	0.374169i
$346$	−4.00000	−	4.00000i	−0.215041	−	0.215041i
$347$	−21.6332	−	21.6332i	−1.16133	−	1.16133i	−0.984184	−	0.177150i	$-0.943312\pi$
$347$	−21.6332	−	21.6332i	−1.16133	−	1.16133i	−0.177150	−	0.984184i	$-0.556688\pi$
$348$		−	12.3166i		−	0.660240i
$349$			16.0000i			0.856460i	0.903670	+	0.428230i	$0.140863\pi$
$349$			16.0000i			0.856460i	−0.903670	+	0.428230i	$0.859137\pi$
$350$		0			0
$351$	12.7414	+	12.7414i	0.680088	+	0.680088i
$352$	−20.7916	+	20.7916i	−1.10819	+	1.10819i
$353$	25.0000			1.33062			0.665308	−	0.746569i	$-0.268300\pi$
$353$	25.0000			1.33062			0.665308	+	0.746569i	$0.268300\pi$
$354$	3.05013	−	3.05013i	0.162112	−	0.162112i
$355$			6.31662i			0.335252i
$356$	−10.6834			−0.566218
$357$		0			0
$358$	−0.633250			−0.0334683
$359$			31.8997i			1.68360i	0.539786	+	0.841802i	$0.318505\pi$
$359$			31.8997i			1.68360i	−0.539786	+	0.841802i	$0.681495\pi$
$360$	0.949874	−	0.949874i	0.0500628	−	0.0500628i
$361$	13.6332			0.717539
$362$	−12.3166	+	12.3166i	−0.647347	+	0.647347i
$363$	27.3166	+	27.3166i	1.43375	+	1.43375i
$364$		0			0
$365$		−	10.0000i		−	0.523424i
$366$		−	19.2665i		−	1.00708i
$367$	1.84169	+	1.84169i	0.0961353	+	0.0961353i	0.753539	−	0.657403i	$-0.228345\pi$
$367$	1.84169	+	1.84169i	0.0961353	+	0.0961353i	−0.657403	+	0.753539i	$0.728345\pi$
$368$	3.00000	+	3.00000i	0.156386	+	0.156386i
$369$	−1.68338	+	1.68338i	−0.0876330	+	0.0876330i
$370$	−13.2665			−0.689692
$371$		0			0
$372$			3.05013i			0.158142i
$373$	−30.5831			−1.58353			−0.791767	−	0.610823i	$-0.790839\pi$
$373$	−30.5831			−1.58353			−0.791767	+	0.610823i	$0.790839\pi$
$374$	12.4749	−	20.7916i	0.645064	−	1.07511i
$375$	18.5330			0.957040
$376$		−	6.94987i		−	0.358412i
$377$	17.6332	−	17.6332i	0.908159	−	0.908159i
$378$		0			0
$379$	−0.525063	+	0.525063i	−0.0269707	+	0.0269707i	−0.720464	−	0.693493i	$-0.756071\pi$
$379$	−0.525063	+	0.525063i	−0.0269707	+	0.0269707i	0.693493	+	0.720464i	$0.256071\pi$
$380$	2.31662	+	2.31662i	0.118840	+	0.118840i
$381$	4.26650	+	4.26650i	0.218579	+	0.218579i
$382$		−	7.26650i		−	0.371786i
$383$		−	2.63325i		−	0.134553i	−0.997734	−	0.0672764i	$-0.978569\pi$
$383$		−	2.63325i		−	0.134553i	0.997734	−	0.0672764i	$-0.0214309\pi$
$384$	−3.47494	−	3.47494i	−0.177330	−	0.177330i
$385$		0			0
$386$	10.9499	−	10.9499i	0.557334	−	0.557334i
$387$	−1.46700			−0.0745719
$388$	10.9499	−	10.9499i	0.555896	−	0.555896i
$389$		−	5.41688i		−	0.274647i	−0.990526	−	0.137323i	$-0.956150\pi$
$389$		−	5.41688i		−	0.274647i	0.990526	−	0.137323i	$-0.0438499\pi$
$390$	−7.68338			−0.389063
$391$	15.0000	+	9.00000i	0.758583	+	0.455150i
$392$		0			0
$393$			8.41688i			0.424575i
$394$	9.31662	−	9.31662i	0.469365	−	0.469365i
$395$	−8.94987			−0.450317
$396$	1.31662	−	1.31662i	0.0661629	−	0.0661629i
$397$	21.8997	+	21.8997i	1.09912	+	1.09912i	0.994514	+	0.104603i	$0.0333571\pi$
$397$	21.8997	+	21.8997i	1.09912	+	1.09912i	0.104603	+	0.994514i	$0.466643\pi$
$398$	−1.52506	−	1.52506i	−0.0764445	−	0.0764445i
$399$		0			0
$400$		−	3.00000i		−	0.150000i
$401$	−18.0000	−	18.0000i	−0.898877	−	0.898877i	0.0964598	−	0.995337i	$-0.469248\pi$
$401$	−18.0000	−	18.0000i	−0.898877	−	0.898877i	−0.995337	+	0.0964598i	$0.969248\pi$
$402$	5.00000	+	5.00000i	0.249377	+	0.249377i
$403$	−4.36675	+	4.36675i	−0.217523	+	0.217523i
$404$	−6.63325			−0.330017
$405$	7.94987	−	7.94987i	0.395032	−	0.395032i
$406$		0			0
$407$	−55.1662			−2.73449
$408$	17.3747	+	10.4248i	0.860175	+	0.516105i
$409$	−20.2665			−1.00211			−0.501057	−	0.865414i	$-0.667055\pi$
$409$	−20.2665			−1.00211			−0.501057	+	0.865414i	$0.667055\pi$
$410$		−	10.6332i		−	0.525139i
$411$	3.10819	−	3.10819i	0.153316	−	0.153316i
$412$	−0.316625			−0.0155990
$413$		0			0
$414$	−0.949874	−	0.949874i	−0.0466838	−	0.0466838i
$415$	8.63325	+	8.63325i	0.423790	+	0.423790i
$416$		−	16.5831i		−	0.813055i
$417$			24.2665i			1.18834i
$418$	−9.63325	−	9.63325i	−0.471178	−	0.471178i
$419$	−1.84169	−	1.84169i	−0.0899723	−	0.0899723i	0.660688	−	0.750660i	$-0.270265\pi$
$419$	−1.84169	−	1.84169i	−0.0899723	−	0.0899723i	−0.750660	+	0.660688i	$0.770265\pi$
$420$		0			0
$421$	17.3668			0.846404			0.423202	−	0.906035i	$-0.360906\pi$
$421$	17.3668			0.846404			0.423202	+	0.906035i	$0.360906\pi$
$422$	−3.63325	+	3.63325i	−0.176864	+	0.176864i
$423$			0.733501i			0.0356640i
$424$	10.8997			0.529339
$425$	−3.00000	−	12.0000i	−0.145521	−	0.582086i
$426$	7.31662			0.354492
$427$		0			0
$428$	−7.79156	+	7.79156i	−0.376619	+	0.376619i
$429$	−31.9499			−1.54255
$430$	4.63325	−	4.63325i	0.223435	−	0.223435i
$431$	−15.4749	−	15.4749i	−0.745401	−	0.745401i	0.228210	−	0.973612i	$-0.426713\pi$
$431$	−15.4749	−	15.4749i	−0.745401	−	0.745401i	−0.973612	+	0.228210i	$0.926713\pi$
$432$	−3.84169	−	3.84169i	−0.184833	−	0.184833i
$433$			2.00000i			0.0961139i	0.998845	+	0.0480569i	$0.0153029\pi$
$433$			2.00000i			0.0961139i	−0.998845	+	0.0480569i	$0.984697\pi$
$434$		0			0
$435$	−12.3166	−	12.3166i	−0.590537	−	0.590537i
$436$	−0.316625	−	0.316625i	−0.0151636	−	0.0151636i
$437$	6.94987	−	6.94987i	0.332458	−	0.332458i
$438$	−11.5831			−0.553463
$439$	−4.42481	+	4.42481i	−0.211185	+	0.211185i	−0.804771	−	0.593586i	$-0.797712\pi$
$439$	−4.42481	+	4.42481i	−0.211185	+	0.211185i	0.593586	+	0.804771i	$0.297712\pi$
$440$			24.9499i			1.18944i
$441$		0			0
$442$	3.31662	+	13.2665i	0.157756	+	0.631023i
$443$	−13.8997			−0.660397			−0.330198	−	0.943912i	$-0.607116\pi$
$443$	−13.8997			−0.660397			−0.330198	+	0.943912i	$0.607116\pi$
$444$		−	15.3668i		−	0.729274i
$445$	−10.6834	+	10.6834i	−0.506441	+	0.506441i
$446$		0			0
$447$	−1.15831	+	1.15831i	−0.0547863	+	0.0547863i
$448$		0			0
$449$	−9.00000	−	9.00000i	−0.424736	−	0.424736i	0.462094	−	0.886831i	$-0.347098\pi$
$449$	−9.00000	−	9.00000i	−0.424736	−	0.424736i	−0.886831	+	0.462094i	$0.847098\pi$
$450$			0.949874i			0.0447775i
$451$		−	44.2164i		−	2.08207i
$452$	−0.316625	−	0.316625i	−0.0148928	−	0.0148928i
$453$	−15.7335	−	15.7335i	−0.739224	−	0.739224i
$454$	18.7916	−	18.7916i	0.881932	−	0.881932i
$455$		0			0
$456$	8.05013	−	8.05013i	0.376982	−	0.376982i
$457$			2.63325i			0.123178i	0.998102	+	0.0615891i	$0.0196168\pi$
$457$			2.63325i			0.123178i	−0.998102	+	0.0615891i	$0.980383\pi$
$458$	−27.2665			−1.27408
$459$	−19.2084	−	11.5251i	−0.896573	−	0.537944i
$460$	−6.00000			−0.279751
$461$			19.6332i			0.914412i	0.889361	+	0.457206i	$0.151150\pi$
$461$			19.6332i			0.914412i	−0.889361	+	0.457206i	$0.848850\pi$
$462$		0			0
$463$	−29.5831			−1.37484			−0.687422	−	0.726258i	$-0.741258\pi$
$463$	−29.5831			−1.37484			−0.687422	+	0.726258i	$0.741258\pi$
$464$	−5.31662	+	5.31662i	−0.246818	+	0.246818i
$465$	3.05013	+	3.05013i	0.141446	+	0.141446i
$466$	−4.31662	−	4.31662i	−0.199964	−	0.199964i
$467$			20.3166i			0.940141i	0.882629	+	0.470071i	$0.155772\pi$
$467$			20.3166i			0.940141i	−0.882629	+	0.470071i	$0.844228\pi$
$468$			1.05013i			0.0485421i
$469$		0			0
$470$	−2.31662	−	2.31662i	−0.106858	−	0.106858i
$471$	11.8918	−	11.8918i	0.547946	−	0.547946i
$472$	7.89975			0.363615
$473$	19.2665	−	19.2665i	0.885875	−	0.885875i
$474$			10.3668i			0.476161i
$475$	−6.94987			−0.318882
$476$		0			0
$477$	−1.15038			−0.0526721
$478$		−	13.2665i		−	0.606796i
$479$	−10.2665	+	10.2665i	−0.469088	+	0.469088i	−0.901619	−	0.432531i	$-0.857621\pi$
$479$	−10.2665	+	10.2665i	−0.469088	+	0.469088i	0.432531	+	0.901619i	$0.357621\pi$
$480$	−11.5831			−0.528695
$481$	22.0000	−	22.0000i	1.00311	−	1.00311i
$482$	19.3166	+	19.3166i	0.879848	+	0.879848i
$483$		0			0
$484$			23.5831i			1.07196i
$485$		−	21.8997i		−	0.994416i
$486$	2.31662	+	2.31662i	0.105084	+	0.105084i
$487$	22.4749	+	22.4749i	1.01844	+	1.01844i	0.999827	+	0.0186098i	$0.00592402\pi$
$487$	22.4749	+	22.4749i	1.01844	+	1.01844i	0.0186098	+	0.999827i	$0.494076\pi$
$488$	24.9499	−	24.9499i	1.12943	−	1.12943i
$489$	22.3166			1.00919
$490$		0			0
$491$		−	29.5831i		−	1.33507i	−0.744579	−	0.667534i	$-0.767350\pi$
$491$		−	29.5831i		−	1.33507i	0.744579	−	0.667534i	$-0.232650\pi$
$492$	12.3166			0.555276
$493$	−15.9499	+	26.5831i	−0.718346	+	1.19724i
$494$	7.68338			0.345691
$495$		−	2.63325i		−	0.118356i
$496$	1.31662	−	1.31662i	0.0591182	−	0.0591182i
$497$		0			0
$498$	10.0000	−	10.0000i	0.448111	−	0.448111i
$499$	−13.7916	−	13.7916i	−0.617395	−	0.617395i	0.327467	−	0.944862i	$-0.393805\pi$
$499$	−13.7916	−	13.7916i	−0.617395	−	0.617395i	−0.944862	+	0.327467i	$0.893805\pi$
$500$	8.00000	+	8.00000i	0.357771	+	0.357771i
$501$		−	0.366750i		−	0.0163852i
$502$		−	24.3166i		−	1.08530i
$503$	−26.4248	−	26.4248i	−1.17822	−	1.17822i	−0.980196	−	0.198028i	$-0.936546\pi$
$503$	−26.4248	−	26.4248i	−1.17822	−	1.17822i	−0.198028	−	0.980196i	$-0.563454\pi$
$504$		0			0
$505$	−6.63325	+	6.63325i	−0.295176	+	0.295176i
$506$	24.9499			1.10916
$507$	−2.31662	+	2.31662i	−0.102885	+	0.102885i
$508$			3.68338i			0.163423i
$509$	−35.1662			−1.55872			−0.779358	−	0.626579i	$-0.784455\pi$
$509$	−35.1662			−1.55872			−0.779358	+	0.626579i	$0.784455\pi$
$510$	9.26650	−	2.31662i	0.410327	−	0.102582i
$511$		0			0
$512$			11.0000i			0.486136i
$513$	−8.89975	+	8.89975i	−0.392934	+	0.392934i
$514$	2.68338			0.118359
$515$	−0.316625	+	0.316625i	−0.0139522	+	0.0139522i
$516$	5.36675	+	5.36675i	0.236258	+	0.236258i
$517$	−9.63325	−	9.63325i	−0.423670	−	0.423670i
$518$		0			0
$519$		−	9.26650i		−	0.406754i
$520$	−9.94987	−	9.94987i	−0.436331	−	0.436331i
$521$	−20.2665	−	20.2665i	−0.887891	−	0.887891i	0.106429	−	0.994320i	$-0.466058\pi$
$521$	−20.2665	−	20.2665i	−0.887891	−	0.887891i	−0.994320	+	0.106429i	$0.966058\pi$
$522$	1.68338	−	1.68338i	0.0736793	−	0.0736793i
$523$	−31.8997			−1.39488			−0.697439	−	0.716644i	$-0.745677\pi$
$523$	−31.8997			−1.39488			−0.697439	+	0.716644i	$0.745677\pi$
$524$	−3.63325	+	3.63325i	−0.158719	+	0.158719i
$525$		0			0
$526$	8.31662			0.362622
$527$	3.94987	−	6.58312i	0.172059	−	0.286765i
$528$	9.63325			0.419233
$529$		−	5.00000i		−	0.217391i
$530$	3.63325	−	3.63325i	0.157818	−	0.157818i
$531$	−0.833752			−0.0361818
$532$		0			0
$533$	17.6332	+	17.6332i	0.763781	+	0.763781i
$534$	12.3747	+	12.3747i	0.535505	+	0.535505i
$535$			15.5831i			0.673717i
$536$			12.9499i			0.559349i
$537$	−0.733501	−	0.733501i	−0.0316529	−	0.0316529i
$538$	−3.00000	−	3.00000i	−0.129339	−	0.129339i
$539$		0			0
$540$	7.68338			0.330640
$541$	14.9499	−	14.9499i	0.642745	−	0.642745i	−0.308484	−	0.951229i	$-0.599822\pi$
$541$	14.9499	−	14.9499i	0.642745	−	0.642745i	0.951229	+	0.308484i	$0.0998217\pi$
$542$		−	2.00000i		−	0.0859074i
$543$	−28.5330			−1.22447
$544$	5.00000	+	20.0000i	0.214373	+	0.857493i
$545$	−0.633250			−0.0271254
$546$		0			0
$547$	12.7916	−	12.7916i	0.546928	−	0.546928i	−0.378623	−	0.925551i	$-0.623602\pi$
$547$	12.7916	−	12.7916i	0.546928	−	0.546928i	0.925551	+	0.378623i	$0.123602\pi$
$548$	2.68338			0.114628
$549$	−2.63325	+	2.63325i	−0.112384	+	0.112384i
$550$	−12.4749	−	12.4749i	−0.531933	−	0.531933i
$551$	12.3166	+	12.3166i	0.524706	+	0.524706i
$552$			20.8496i			0.887419i
$553$		0			0
$554$	12.6332	+	12.6332i	0.536735	+	0.536735i
$555$	−15.3668	−	15.3668i	−0.652282	−	0.652282i
$556$	−10.4749	+	10.4749i	−0.444236	+	0.444236i
$557$	30.4829			1.29160			0.645800	−	0.763506i	$-0.276524\pi$
$557$	30.4829			1.29160			0.645800	+	0.763506i	$0.276524\pi$
$558$	−0.416876	+	0.416876i	−0.0176478	+	0.0176478i
$559$			15.3668i			0.649944i
$560$		0			0
$561$	38.5330	−	9.63325i	1.62686	−	0.406716i
$562$	−15.0000			−0.632737
$563$			29.1662i			1.22921i	0.788835	+	0.614605i	$0.210685\pi$
$563$			29.1662i			1.22921i	−0.788835	+	0.614605i	$0.789315\pi$
$564$	2.68338	−	2.68338i	0.112990	−	0.112990i
$565$	−0.633250			−0.0266410
$566$	−14.4248	+	14.4248i	−0.606320	+	0.606320i
$567$		0			0
$568$	9.47494	+	9.47494i	0.397560	+	0.397560i
$569$			19.0000i			0.796521i	0.917272	+	0.398261i	$0.130386\pi$
$569$			19.0000i			0.796521i	−0.917272	+	0.398261i	$0.869614\pi$
$570$		−	5.36675i		−	0.224788i
$571$	6.58312	+	6.58312i	0.275495	+	0.275495i	0.831308	−	0.555813i	$-0.187593\pi$
$571$	6.58312	+	6.58312i	0.275495	+	0.275495i	−0.555813	+	0.831308i	$0.687593\pi$
$572$	−13.7916	−	13.7916i	−0.576654	−	0.576654i
$573$	8.41688	−	8.41688i	0.351620	−	0.351620i
$574$		0			0
$575$	9.00000	−	9.00000i	0.375326	−	0.375326i
$576$		−	2.21637i		−	0.0923489i
$577$	22.5831			0.940148			0.470074	−	0.882627i	$-0.344227\pi$
$577$	22.5831			0.940148			0.470074	+	0.882627i	$0.344227\pi$
$578$	−8.00000	−	15.0000i	−0.332756	−	0.623918i
$579$	25.3668			1.05421
$580$		−	10.6332i		−	0.441522i
$581$		0			0
$582$	−25.3668			−1.05149
$583$	15.1082	−	15.1082i	0.625717	−	0.625717i
$584$	−15.0000	−	15.0000i	−0.620704	−	0.620704i
$585$	1.05013	+	1.05013i	0.0434174	+	0.0434174i
$586$			25.5330i			1.05476i
$587$		−	21.0501i		−	0.868832i	−0.900712	−	0.434416i	$-0.856955\pi$
$587$		−	21.0501i		−	0.868832i	0.900712	−	0.434416i	$-0.143045\pi$
$588$		0			0
$589$	−3.05013	−	3.05013i	−0.125678	−	0.125678i
$590$	2.63325	−	2.63325i	0.108409	−	0.108409i
$591$	21.5831			0.887811
$592$	−6.63325	+	6.63325i	−0.272625	+	0.272625i
$593$			10.2665i			0.421595i	0.977530	+	0.210797i	$0.0676060\pi$
$593$			10.2665i			0.421595i	−0.977530	+	0.210797i	$0.932394\pi$
$594$	−31.9499			−1.31092
$595$		0			0
$596$	−1.00000			−0.0409616
$597$		−	3.53300i		−	0.144596i
$598$	−9.94987	+	9.94987i	−0.406881	+	0.406881i
$599$	9.36675			0.382715			0.191358	−	0.981520i	$-0.438711\pi$
$599$	9.36675			0.382715			0.191358	+	0.981520i	$0.438711\pi$
$600$	10.4248	−	10.4248i	0.425591	−	0.425591i
$601$	4.05013	+	4.05013i	0.165208	+	0.165208i	0.784869	−	0.619661i	$-0.212730\pi$
$601$	4.05013	+	4.05013i	0.165208	+	0.165208i	−0.619661	+	0.784869i	$0.712730\pi$
$602$		0			0
$603$		−	1.36675i		−	0.0556584i
$604$		−	13.5831i		−	0.552689i
$605$	23.5831	+	23.5831i	0.958790	+	0.958790i
$606$	7.68338	+	7.68338i	0.312116	+	0.312116i
$607$	−1.42481	+	1.42481i	−0.0578313	+	0.0578313i	−0.735431	−	0.677600i	$-0.763020\pi$
$607$	−1.42481	+	1.42481i	−0.0578313	+	0.0578313i	0.677600	+	0.735431i	$0.263020\pi$
$608$	11.5831			0.469758
$609$		0			0
$610$		−	16.6332i		−	0.673461i
$611$	7.68338			0.310836
$612$	−0.316625	−	1.26650i	−0.0127988	−	0.0511952i
$613$	5.73350			0.231574			0.115787	−	0.993274i	$-0.463061\pi$
$613$	5.73350			0.231574			0.115787	+	0.993274i	$0.463061\pi$
$614$			26.9499i			1.08761i
$615$	12.3166	−	12.3166i	0.496654	−	0.496654i
$616$		0			0
$617$	−3.94987	+	3.94987i	−0.159016	+	0.159016i	−0.782131	−	0.623115i	$-0.785867\pi$
$617$	−3.94987	+	3.94987i	−0.159016	+	0.159016i	0.623115	+	0.782131i	$0.285867\pi$
$618$	0.366750	+	0.366750i	0.0147529	+	0.0147529i
$619$	−9.15831	−	9.15831i	−0.368104	−	0.368104i	0.498682	−	0.866785i	$-0.333818\pi$
$619$	−9.15831	−	9.15831i	−0.368104	−	0.368104i	−0.866785	+	0.498682i	$0.833818\pi$
$620$			2.63325i			0.105754i
$621$		−	23.0501i		−	0.924970i
$622$	0.525063	+	0.525063i	0.0210531	+	0.0210531i
$623$		0			0
$624$	−3.84169	+	3.84169i	−0.153791	+	0.153791i
$625$	1.00000			0.0400000
$626$	−13.9499	+	13.9499i	−0.557549	+	0.557549i
$627$		−	22.3166i		−	0.891240i
$628$	10.2665			0.409678
$629$	−19.8997	+	33.1662i	−0.793455	+	1.32242i
$630$		0			0
$631$		−	40.6332i		−	1.61758i	−0.588095	−	0.808792i	$-0.700122\pi$
$631$		−	40.6332i		−	1.61758i	0.588095	−	0.808792i	$-0.299878\pi$
$632$	−13.4248	+	13.4248i	−0.534010	+	0.534010i
$633$	−8.41688			−0.334541
$634$	−9.68338	+	9.68338i	−0.384576	+	0.384576i
$635$	3.68338	+	3.68338i	0.146170	+	0.146170i
$636$	4.20844	+	4.20844i	0.166875	+	0.166875i
$637$		0			0
$638$			44.2164i			1.75054i
$639$	−1.00000	−	1.00000i	−0.0395594	−	0.0395594i
$640$	−3.00000	−	3.00000i	−0.118585	−	0.118585i
$641$	−23.3166	+	23.3166i	−0.920951	+	0.920951i	−0.997097	−	0.0761454i	$-0.975739\pi$
$641$	−23.3166	+	23.3166i	−0.920951	+	0.920951i	0.0761454	+	0.997097i	$0.475739\pi$
$642$	18.0501			0.712382
$643$	−33.1082	+	33.1082i	−1.30566	+	1.30566i	−0.381144	+	0.924516i	$0.624470\pi$
$643$	−33.1082	+	33.1082i	−1.30566	+	1.30566i	−0.924516	+	0.381144i	$0.875530\pi$
$644$		0			0
$645$	10.7335			0.422631
$646$	−9.26650	+	2.31662i	−0.364586	+	0.0911464i
$647$	5.36675			0.210989			0.105494	−	0.994420i	$-0.466358\pi$
$647$	5.36675			0.210989			0.105494	+	0.994420i	$0.466358\pi$
$648$		−	23.8496i		−	0.936902i
$649$	10.9499	−	10.9499i	0.429820	−	0.429820i
$650$	9.94987			0.390266
$651$		0			0
$652$	9.63325	+	9.63325i	0.377267	+	0.377267i
$653$	21.5831	+	21.5831i	0.844613	+	0.844613i	0.989455	−	0.144842i	$-0.0462674\pi$
$653$	21.5831	+	21.5831i	0.844613	+	0.844613i	−0.144842	+	0.989455i	$0.546267\pi$
$654$			0.733501i			0.0286822i
$655$			7.26650i			0.283926i
$656$	−5.31662	−	5.31662i	−0.207579	−	0.207579i
$657$	1.58312	+	1.58312i	0.0617635	+	0.0617635i
$658$		0			0
$659$	−6.00000			−0.233727			−0.116863	−	0.993148i	$-0.537284\pi$
$659$	−6.00000			−0.233727			−0.116863	+	0.993148i	$0.537284\pi$
$660$	−9.63325	+	9.63325i	−0.374974	+	0.374974i
$661$			38.5330i			1.49876i	0.662140	+	0.749380i	$0.269648\pi$
$661$			38.5330i			1.49876i	−0.662140	+	0.749380i	$0.730352\pi$
$662$	−20.0000			−0.777322
$663$	−11.5251	+	19.2084i	−0.447596	+	0.745994i
$664$	25.8997			1.00511
$665$		0			0
$666$	2.10025	−	2.10025i	0.0813831	−	0.0813831i
$667$	−31.8997			−1.23516
$668$	0.158312	−	0.158312i	0.00612529	−	0.00612529i
$669$		0			0
$670$	4.31662	+	4.31662i	0.166766	+	0.166766i
$671$		−	69.1662i		−	2.67013i
$672$		0			0
$673$	8.05013	+	8.05013i	0.310310	+	0.310310i	0.845029	−	0.534720i	$-0.179583\pi$
$673$	8.05013	+	8.05013i	0.310310	+	0.310310i	−0.534720	+	0.845029i	$0.679583\pi$
$674$	9.36675	+	9.36675i	0.360794	+	0.360794i
$675$	−11.5251	+	11.5251i	−0.443600	+	0.443600i
$676$	−2.00000			−0.0769231
$677$	−21.6332	+	21.6332i	−0.831433	+	0.831433i	−0.987713	−	0.156280i	$-0.950050\pi$
$677$	−21.6332	+	21.6332i	−0.831433	+	0.831433i	0.156280	+	0.987713i	$0.450050\pi$
$678$			0.733501i			0.0281699i
$679$		0			0
$680$	15.0000	+	9.00000i	0.575224	+	0.345134i
$681$	43.5330			1.66819
$682$		−	10.9499i		−	0.419292i
$683$	−2.47494	+	2.47494i	−0.0947008	+	0.0947008i	−0.752870	−	0.658169i	$-0.771331\pi$
$683$	−2.47494	+	2.47494i	−0.0947008	+	0.0947008i	0.658169	+	0.752870i	$0.271331\pi$
$684$	−0.733501			−0.0280461
$685$	2.68338	−	2.68338i	0.102526	−	0.102526i
$686$		0			0
$687$	−31.5831	−	31.5831i	−1.20497	−	1.20497i
$688$		−	4.63325i		−	0.176641i
$689$			12.0501i			0.459073i
$690$	6.94987	+	6.94987i	0.264577	+	0.264577i
$691$	13.6332	+	13.6332i	0.518633	+	0.518633i	0.917158	−	0.398524i	$-0.130478\pi$
$691$	13.6332	+	13.6332i	0.518633	+	0.518633i	−0.398524	+	0.917158i	$0.630478\pi$
$692$	4.00000	−	4.00000i	0.152057	−	0.152057i
$693$		0			0
$694$	−21.6332	+	21.6332i	−0.821187	+	0.821187i
$695$			20.9499i			0.794674i
$696$	−36.9499			−1.40058
$697$	−26.5831	−	15.9499i	−1.00691	−	0.604145i
$698$	16.0000			0.605609
$699$		−	10.0000i		−	0.378235i
$700$		0			0
$701$	−11.2164			−0.423637			−0.211818	−	0.977309i	$-0.567939\pi$
$701$	−11.2164			−0.423637			−0.211818	+	0.977309i	$0.567939\pi$
$702$	12.7414	−	12.7414i	0.480895	−	0.480895i
$703$	15.3668	+	15.3668i	0.579568	+	0.579568i
$704$	29.1082	+	29.1082i	1.09706	+	1.09706i
$705$		−	5.36675i		−	0.202124i
$706$		−	25.0000i		−	0.940887i
$707$		0			0
$708$	3.05013	+	3.05013i	0.114631	+	0.114631i
$709$	16.6834	−	16.6834i	0.626557	−	0.626557i	−0.320643	−	0.947200i	$-0.603899\pi$
$709$	16.6834	−	16.6834i	0.626557	−	0.626557i	0.947200	+	0.320643i	$0.103899\pi$
$710$	6.31662			0.237059
$711$	1.41688	−	1.41688i	0.0531370	−	0.0531370i
$712$			32.0501i			1.20113i
$713$	7.89975			0.295848
$714$		0			0
$715$	−27.5831			−1.03155
$716$		−	0.633250i		−	0.0236656i
$717$	15.3668	−	15.3668i	0.573882	−	0.573882i
$718$	31.8997			1.19049
$719$	10.7916	−	10.7916i	0.402457	−	0.402457i	−0.476641	−	0.879098i	$-0.658146\pi$
$719$	10.7916	−	10.7916i	0.402457	−	0.402457i	0.879098	+	0.476641i	$0.158146\pi$
$720$	−0.316625	−	0.316625i	−0.0117999	−	0.0117999i
$721$		0			0
$722$		−	13.6332i		−	0.507377i
$723$			44.7494i			1.66425i
$724$	−12.3166	−	12.3166i	−0.457744	−	0.457744i
$725$	15.9499	+	15.9499i	0.592363	+	0.592363i
$726$	27.3166	−	27.3166i	1.01382	−	1.01382i
$727$	−27.3668			−1.01498			−0.507488	−	0.861659i	$-0.669426\pi$
$727$	−27.3668			−1.01498			−0.507488	+	0.861659i	$0.669426\pi$
$728$		0			0
$729$			29.2164i			1.08209i
$730$	−10.0000			−0.370117
$731$	−4.63325	−	18.5330i	−0.171367	−	0.685468i
$732$	19.2665			0.712110
$733$		−	16.2665i		−	0.600817i	−0.953811	−	0.300408i	$-0.902877\pi$
$733$		−	16.2665i		−	0.600817i	0.953811	−	0.300408i	$-0.0971230\pi$
$734$	1.84169	−	1.84169i	0.0679779	−	0.0679779i
$735$		0			0
$736$	−15.0000	+	15.0000i	−0.552907	+	0.552907i
$737$	17.9499	+	17.9499i	0.661192	+	0.661192i
$738$	1.68338	+	1.68338i	0.0619659	+	0.0619659i
$739$		−	10.7335i		−	0.394838i	−0.980319	−	0.197419i	$-0.936744\pi$
$739$		−	10.7335i		−	0.394838i	0.980319	−	0.197419i	$-0.0632560\pi$
$740$		−	13.2665i		−	0.487686i
$741$	8.89975	+	8.89975i	0.326940	+	0.326940i
$742$		0			0
$743$	28.0581	−	28.0581i	1.02935	−	1.02935i	0.0297944	−	0.999556i	$-0.490515\pi$
$743$	28.0581	−	28.0581i	1.02935	−	1.02935i	0.999556	−	0.0297944i	$-0.00948525\pi$
$744$	9.15038			0.335469
$745$	−1.00000	+	1.00000i	−0.0366372	+	0.0366372i
$746$			30.5831i			1.11973i
$747$	−2.73350			−0.100014
$748$	20.7916	+	12.4749i	0.760215	+	0.456129i
$749$		0			0
$750$		−	18.5330i		−	0.676729i
$751$	26.7414	−	26.7414i	0.975809	−	0.975809i	−0.0239054	−	0.999714i	$-0.507610\pi$
$751$	26.7414	−	26.7414i	0.975809	−	0.975809i	0.999714	+	0.0239054i	$0.00761004\pi$
$752$	−2.31662			−0.0844786
$753$	28.1662	−	28.1662i	1.02644	−	1.02644i
$754$	−17.6332	−	17.6332i	−0.642165	−	0.642165i
$755$	−13.5831	−	13.5831i	−0.494340	−	0.494340i
$756$		0			0
$757$		−	4.68338i		−	0.170220i	−0.996372	−	0.0851101i	$-0.972876\pi$
$757$		−	4.68338i		−	0.170220i	0.996372	−	0.0851101i	$-0.0271242\pi$
$758$	0.525063	+	0.525063i	0.0190711	+	0.0190711i
$759$	28.8997	+	28.8997i	1.04899	+	1.04899i
$760$	6.94987	−	6.94987i	0.252098	−	0.252098i
$761$	−1.41688			−0.0513617			−0.0256809	−	0.999670i	$-0.508175\pi$
$761$	−1.41688			−0.0513617			−0.0256809	+	0.999670i	$0.508175\pi$
$762$	4.26650	−	4.26650i	0.154559	−	0.154559i
$763$		0			0
$764$	7.26650			0.262893
$765$	−1.58312	−	0.949874i	−0.0572380	−	0.0343428i
$766$	−2.63325			−0.0951432
$767$			8.73350i			0.315348i
$768$	−19.6913	+	19.6913i	−0.710549	+	0.710549i
$769$	−42.5831			−1.53559			−0.767793	−	0.640698i	$-0.778645\pi$
$769$	−42.5831			−1.53559			−0.767793	+	0.640698i	$0.778645\pi$
$770$		0			0
$771$	3.10819	+	3.10819i	0.111939	+	0.111939i
$772$	10.9499	+	10.9499i	0.394095	+	0.394095i
$773$		−	5.41688i		−	0.194831i	−0.995244	−	0.0974157i	$-0.968942\pi$
$773$		−	5.41688i		−	0.194831i	0.995244	−	0.0974157i	$-0.0310576\pi$
$774$			1.46700i			0.0527303i
$775$	−3.94987	−	3.94987i	−0.141884	−	0.141884i
$776$	−32.8496	−	32.8496i	−1.17923	−	1.17923i
$777$		0			0
$778$	−5.41688			−0.194204
$779$	−12.3166	+	12.3166i	−0.441289	+	0.441289i
$780$		−	7.68338i		−	0.275109i
$781$	26.2665			0.939889
$782$	9.00000	−	15.0000i	0.321839	−	0.536399i
$783$	40.8496			1.45985
$784$		0			0
$785$	10.2665	−	10.2665i	0.366427	−	0.366427i
$786$	8.41688			0.300220
$787$	37.6332	−	37.6332i	1.34148	−	1.34148i	0.446893	−	0.894587i	$-0.352530\pi$
$787$	37.6332	−	37.6332i	1.34148	−	1.34148i	0.894587	−	0.446893i	$-0.147470\pi$
$788$	9.31662	+	9.31662i	0.331891	+	0.331891i
$789$	9.63325	+	9.63325i	0.342953	+	0.342953i
$790$			8.94987i			0.318422i
$791$		0			0
$792$	−3.94987	−	3.94987i	−0.140353	−	0.140353i
$793$	27.5831	+	27.5831i	0.979505	+	0.979505i
$794$	21.8997	−	21.8997i	0.777193	−	0.777193i
$795$	8.41688			0.298516
$796$	1.52506	−	1.52506i	0.0540544	−	0.0540544i
$797$			32.8997i			1.16537i	0.812698	+	0.582684i	$0.197998\pi$
$797$			32.8997i			1.16537i	−0.812698	+	0.582684i	$0.802002\pi$
$798$		0			0
$799$	−9.26650	+	2.31662i	−0.327825	+	0.0819563i
$800$	15.0000			0.530330
$801$		−	3.38262i		−	0.119519i
$802$	−18.0000	+	18.0000i	−0.635602	+	0.635602i
$803$	−41.5831			−1.46744
$804$	−5.00000	+	5.00000i	−0.176336	+	0.176336i
$805$		0			0
$806$	4.36675	+	4.36675i	0.153812	+	0.153812i
$807$		−	6.94987i		−	0.244647i
$808$			19.8997i			0.700071i
$809$	−2.89975	−	2.89975i	−0.101950	−	0.101950i	0.654292	−	0.756242i	$-0.272967\pi$
$809$	−2.89975	−	2.89975i	−0.101950	−	0.101950i	−0.756242	+	0.654292i	$0.772967\pi$
$810$	−7.94987	−	7.94987i	−0.279330	−	0.279330i
$811$	18.1082	−	18.1082i	0.635864	−	0.635864i	−0.313668	−	0.949533i	$-0.601558\pi$
$811$	18.1082	−	18.1082i	0.635864	−	0.635864i	0.949533	+	0.313668i	$0.101558\pi$
$812$		0			0
$813$	2.31662	−	2.31662i	0.0812476	−	0.0812476i
$814$			55.1662i			1.93358i
$815$	19.2665			0.674876
$816$	3.47494	−	5.79156i	0.121647	−	0.202745i
$817$	−10.7335			−0.375518
$818$			20.2665i			0.708602i
$819$		0			0
$820$	10.6332			0.371329
$821$	−7.36675	+	7.36675i	−0.257101	+	0.257101i	−0.823874	−	0.566773i	$-0.808192\pi$
$821$	−7.36675	+	7.36675i	−0.257101	+	0.257101i	0.566773	+	0.823874i	$0.308192\pi$
$822$	−3.10819	−	3.10819i	−0.108410	−	0.108410i
$823$	25.0581	+	25.0581i	0.873469	+	0.873469i	0.992849	−	0.119380i	$-0.0380905\pi$
$823$	25.0581	+	25.0581i	0.873469	+	0.873469i	−0.119380	+	0.992849i	$0.538091\pi$
$824$			0.949874i			0.0330904i
$825$		−	28.8997i		−	1.00616i
$826$		0			0
$827$	28.0581	+	28.0581i	0.975674	+	0.975674i	0.999711	−	0.0240367i	$-0.00765185\pi$
$827$	28.0581	+	28.0581i	0.975674	+	0.975674i	−0.0240367	+	0.999711i	$0.507652\pi$
$828$	0.949874	−	0.949874i	0.0330104	−	0.0330104i
$829$	−22.8997			−0.795341			−0.397671	−	0.917528i	$-0.630181\pi$
$829$	−22.8997			−0.795341			−0.397671	+	0.917528i	$0.630181\pi$
$830$	8.63325	−	8.63325i	0.299664	−	0.299664i
$831$			29.2665i			1.01524i
$832$	−23.2164			−0.804883
$833$		0			0
$834$	24.2665			0.840280
$835$		−	0.316625i		−	0.0109573i
$836$	9.63325	−	9.63325i	0.333173	−	0.333173i
$837$	−10.1161			−0.349664
$838$	−1.84169	+	1.84169i	−0.0636200	+	0.0636200i
$839$	−29.9499	−	29.9499i	−1.03398	−	1.03398i	−0.999402	−	0.0345826i	$-0.988990\pi$
$839$	−29.9499	−	29.9499i	−1.03398	−	1.03398i	−0.0345826	−	0.999402i	$-0.511010\pi$
$840$		0			0
$841$		−	27.5330i		−	0.949414i
$842$		−	17.3668i		−	0.598498i
$843$	−17.3747	−	17.3747i	−0.598416	−	0.598416i
$844$	−3.63325	−	3.63325i	−0.125062	−	0.125062i
$845$	−2.00000	+	2.00000i	−0.0688021	+	0.0688021i
$846$	0.733501			0.0252183
$847$		0			0
$848$		−	3.63325i		−	0.124766i
$849$	−33.4169			−1.14686
$850$	−12.0000	+	3.00000i	−0.411597	+	0.102899i
$851$	−39.7995			−1.36431
$852$			7.31662i			0.250663i
$853$	16.3668	−	16.3668i	0.560387	−	0.560387i	−0.369030	−	0.929417i	$-0.620310\pi$
$853$	16.3668	−	16.3668i	0.560387	−	0.560387i	0.929417	+	0.369030i	$0.120310\pi$
$854$		0			0
$855$	−0.733501	+	0.733501i	−0.0250852	+	0.0250852i
$856$	23.3747	+	23.3747i	0.798930	+	0.798930i
$857$	22.0000	+	22.0000i	0.751506	+	0.751506i	0.974760	−	0.223255i	$-0.0716681\pi$
$857$	22.0000	+	22.0000i	0.751506	+	0.751506i	−0.223255	+	0.974760i	$0.571668\pi$
$858$			31.9499i			1.09075i
$859$			8.31662i			0.283760i	0.989884	+	0.141880i	$0.0453146\pi$
$859$			8.31662i			0.283760i	−0.989884	+	0.141880i	$0.954685\pi$
$860$	4.63325	+	4.63325i	0.157992	+	0.157992i
$861$		0			0
$862$	−15.4749	+	15.4749i	−0.527078	+	0.527078i
$863$	−27.1662			−0.924750			−0.462375	−	0.886685i	$-0.653003\pi$
$863$	−27.1662			−0.924750			−0.462375	+	0.886685i	$0.653003\pi$
$864$	19.2084	−	19.2084i	0.653484	−	0.653484i
$865$		−	8.00000i		−	0.272008i
$866$	2.00000			0.0679628
$867$	8.10819	−	26.6412i	0.275368	−	0.904782i
$868$		0			0
$869$			37.2164i			1.26248i
$870$	−12.3166	+	12.3166i	−0.417573	+	0.417573i
$871$	−14.3166			−0.485100
$872$	−0.949874	+	0.949874i	−0.0321668	+	0.0321668i
$873$	3.46700	+	3.46700i	0.117340	+	0.117340i
$874$	−6.94987	−	6.94987i	−0.235083	−	0.235083i
$875$		0			0
$876$		−	11.5831i		−	0.391357i
$877$	13.3166	+	13.3166i	0.449670	+	0.449670i	0.895245	−	0.445574i	$-0.147001\pi$
$877$	13.3166	+	13.3166i	0.449670	+	0.449670i	−0.445574	+	0.895245i	$0.647001\pi$
$878$	4.42481	+	4.42481i	0.149330	+	0.149330i
$879$	−29.5752	+	29.5752i	−0.997546	+	0.997546i
$880$	8.31662			0.280353
$881$	19.8997	−	19.8997i	0.670440	−	0.670440i	−0.287378	−	0.957817i	$-0.592784\pi$
$881$	19.8997	−	19.8997i	0.670440	−	0.670440i	0.957817	+	0.287378i	$0.0927835\pi$
$882$		0			0
$883$	25.8997			0.871596			0.435798	−	0.900045i	$-0.356466\pi$
$883$	25.8997			0.871596			0.435798	+	0.900045i	$0.356466\pi$
$884$	−13.2665	+	3.31662i	−0.446201	+	0.111550i
$885$	6.10025			0.205058
$886$			13.8997i			0.466971i
$887$	16.1583	−	16.1583i	0.542543	−	0.542543i	−0.381731	−	0.924274i	$-0.624672\pi$
$887$	16.1583	−	16.1583i	0.542543	−	0.542543i	0.924274	+	0.381731i	$0.124672\pi$
$888$	−46.1003			−1.54702
$889$		0			0
$890$	10.6834	+	10.6834i	0.358108	+	0.358108i
$891$	−33.0581	−	33.0581i	−1.10749	−	1.10749i
$892$		0			0
$893$			5.36675i			0.179591i
$894$	1.15831	+	1.15831i	0.0387398	+	0.0387398i
$895$	−0.633250	−	0.633250i	−0.0211672	−	0.0211672i
$896$		0			0
$897$	−23.0501			−0.769621
$898$	−9.00000	+	9.00000i	−0.300334	+	0.300334i
$899$			14.0000i			0.466926i
$900$	−0.949874			−0.0316625
$901$	−3.63325	−	14.5330i	−0.121041	−	0.484164i
$902$	−44.2164			−1.47224
$903$		0			0
$904$	−0.949874	+	0.949874i	−0.0315924	+	0.0315924i
$905$	−24.6332			−0.818837
$906$	−15.7335	+	15.7335i	−0.522711	+	0.522711i
$907$	−28.5831	−	28.5831i	−0.949087	−	0.949087i	0.0496782	−	0.998765i	$-0.484180\pi$
$907$	−28.5831	−	28.5831i	−0.949087	−	0.949087i	−0.998765	+	0.0496782i	$0.984180\pi$
$908$	18.7916	+	18.7916i	0.623620	+	0.623620i
$909$		−	2.10025i		−	0.0696609i
$910$		0			0
$911$	−2.05013	−	2.05013i	−0.0679237	−	0.0679237i	0.672329	−	0.740253i	$-0.265294\pi$
$911$	−2.05013	−	2.05013i	−0.0679237	−	0.0679237i	−0.740253	+	0.672329i	$0.765294\pi$
$912$	−2.68338	−	2.68338i	−0.0888554	−	0.0888554i
$913$	35.8997	−	35.8997i	1.18811	−	1.18811i
$914$	2.63325			0.0871002
$915$	19.2665	−	19.2665i	0.636931	−	0.636931i
$916$		−	27.2665i		−	0.900910i
$917$		0			0
$918$	−11.5251	+	19.2084i	−0.380384	+	0.633973i
$919$	−39.4829			−1.30242			−0.651210	−	0.758898i	$-0.725738\pi$
$919$	−39.4829			−1.30242			−0.651210	+	0.758898i	$0.725738\pi$
$920$			18.0000i			0.593442i
$921$	−31.2164	+	31.2164i	−1.02861	+	1.02861i
$922$	19.6332			0.646587
$923$	−10.4749	+	10.4749i	−0.344787	+	0.344787i
$924$		0			0
$925$	19.8997	+	19.8997i	0.654300	+	0.654300i
$926$			29.5831i			0.972162i
$927$		−	0.100251i		−	0.00329268i
$928$	−26.5831	−	26.5831i	−0.872634	−	0.872634i
$929$	−10.6834	−	10.6834i	−0.350510	−	0.350510i	0.509789	−	0.860299i	$-0.329723\pi$
$929$	−10.6834	−	10.6834i	−0.350510	−	0.350510i	−0.860299	+	0.509789i	$0.829723\pi$
$930$	3.05013	−	3.05013i	0.100018	−	0.100018i
$931$		0			0
$932$	4.31662	−	4.31662i	0.141396	−	0.141396i
$933$			1.21637i			0.0398223i
$934$	20.3166			0.664780
$935$	33.2665	−	8.31662i	1.08793	−	0.271983i
$936$	3.15038			0.102973
$937$			51.7995i			1.69222i	0.533012	+	0.846108i	$0.321060\pi$
$937$			51.7995i			1.69222i	−0.533012	+	0.846108i	$0.678940\pi$
$938$		0			0
$939$	−32.3166			−1.05461
$940$	2.31662	−	2.31662i	0.0755600	−	0.0755600i
$941$	3.63325	+	3.63325i	0.118441	+	0.118441i	0.763843	−	0.645402i	$-0.223310\pi$
$941$	3.63325	+	3.63325i	0.118441	+	0.118441i	−0.645402	+	0.763843i	$0.723310\pi$
$942$	−11.8918	−	11.8918i	−0.387456	−	0.387456i
$943$		−	31.8997i		−	1.03880i
$944$		−	2.63325i		−	0.0857050i
$945$		0			0
$946$	−19.2665	−	19.2665i	−0.626408	−	0.626408i
$947$	24.4248	−	24.4248i	0.793700	−	0.793700i	−0.188394	−	0.982094i	$-0.560328\pi$
$947$	24.4248	−	24.4248i	0.793700	−	0.793700i	0.982094	+	0.188394i	$0.0603281\pi$
$948$	−10.3668			−0.336696
$949$	16.5831	−	16.5831i	0.538311	−	0.538311i
$950$			6.94987i			0.225484i
$951$	−22.4327			−0.727432
$952$		0			0
$953$	−45.7494			−1.48197			−0.740984	−	0.671523i	$-0.765640\pi$
$953$	−45.7494			−1.48197			−0.740984	+	0.671523i	$0.765640\pi$
$954$			1.15038i			0.0372448i
$955$	7.26650	−	7.26650i	0.235138	−	0.235138i
$956$	13.2665			0.429069
$957$	−51.2164	+	51.2164i	−1.65559	+	1.65559i
$958$	10.2665	+	10.2665i	0.331696	+	0.331696i
$959$		0			0
$960$			16.2164i			0.523381i
$961$			27.5330i			0.888161i
$962$	−22.0000	−	22.0000i	−0.709308	−	0.709308i
$963$	−2.46700	−	2.46700i	−0.0794980	−	0.0794980i
$964$	−19.3166	+	19.3166i	−0.622147	+	0.622147i
$965$	21.8997			0.704978
$966$		0			0
$967$			25.5831i			0.822698i	0.911478	+	0.411349i	$0.134942\pi$
$967$			25.5831i			0.822698i	−0.911478	+	0.411349i	$0.865058\pi$
$968$	70.7494			2.27397
$969$	−13.4169	−	8.05013i	−0.431012	−	0.258607i
$970$	−21.8997			−0.703159
$971$			3.78363i			0.121422i	0.998155	+	0.0607112i	$0.0193369\pi$
$971$			3.78363i			0.121422i	−0.998155	+	0.0607112i	$0.980663\pi$
$972$	−2.31662	+	2.31662i	−0.0743058	+	0.0743058i
$973$		0			0
$974$	22.4749	−	22.4749i	0.720143	−	0.720143i
$975$	11.5251	+	11.5251i	0.369097	+	0.369097i
$976$	−8.31662	−	8.31662i	−0.266209	−	0.266209i
$977$		−	11.1662i		−	0.357240i	−0.983918	−	0.178620i	$-0.942837\pi$
$977$		−	11.1662i		−	0.357240i	0.983918	−	0.178620i	$-0.0571633\pi$
$978$		−	22.3166i		−	0.713607i
$979$	44.4248	+	44.4248i	1.41982	+	1.41982i
$980$		0			0
$981$	0.100251	−	0.100251i	0.00320078	−	0.00320078i
$982$	−29.5831			−0.944035
$983$	−13.5752	+	13.5752i	−0.432981	+	0.432981i	−0.889641	−	0.456660i	$-0.849046\pi$
$983$	−13.5752	+	13.5752i	−0.432981	+	0.432981i	0.456660	+	0.889641i	$0.349046\pi$
$984$		−	36.9499i		−	1.17792i
$985$	18.6332			0.593705
$986$	26.5831	+	15.9499i	0.846579	+	0.507947i
$987$		0			0
$988$			7.68338i			0.244441i
$989$	13.8997	−	13.8997i	0.441986	−	0.441986i
$990$	−2.63325			−0.0836902
$991$	33.8417	−	33.8417i	1.07502	−	1.07502i	0.0780687	−	0.996948i	$-0.475125\pi$
$991$	33.8417	−	33.8417i	1.07502	−	1.07502i	0.996948	−	0.0780687i	$-0.0248753\pi$
$992$	6.58312	+	6.58312i	0.209014	+	0.209014i
$993$	−23.1662	−	23.1662i	−0.735159	−	0.735159i
$994$		0			0
$995$		−	3.05013i		−	0.0966955i
$996$	10.0000	+	10.0000i	0.316862	+	0.316862i
$997$	2.68338	+	2.68338i	0.0849833	+	0.0849833i	0.748321	−	0.663337i	$-0.230860\pi$
$997$	2.68338	+	2.68338i	0.0849833	+	0.0849833i	−0.663337	+	0.748321i	$0.730860\pi$
$998$	−13.7916	+	13.7916i	−0.436564	+	0.436564i
$999$	50.9657			1.61248

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.g.c.344.2		4
7.2	even	3		833.2.o.c.361.2		8
7.3	odd	6		119.2.n.a.72.2	yes	8
7.4	even	3		833.2.o.c.667.1		8
7.5	odd	6		119.2.n.a.4.1	✓	8
7.6	odd	2		833.2.g.d.344.1		4
17.13	even	4	inner	833.2.g.c.540.2		4
119.13	odd	4		833.2.g.d.540.1		4
119.30	even	12		833.2.o.c.557.1		8
119.47	odd	12		119.2.n.a.81.2	yes	8
119.81	even	12		833.2.o.c.30.2		8
119.115	odd	12		119.2.n.a.30.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.2.n.a.4.1	✓	8	7.5	odd	6
119.2.n.a.30.1	yes	8	119.115	odd	12
119.2.n.a.72.2	yes	8	7.3	odd	6
119.2.n.a.81.2	yes	8	119.47	odd	12
833.2.g.c.344.2		4	1.1	even	1	trivial
833.2.g.c.540.2		4	17.13	even	4	inner
833.2.g.d.344.1		4	7.6	odd	2
833.2.g.d.540.1		4	119.13	odd	4
833.2.o.c.30.2		8	119.81	even	12
833.2.o.c.361.2		8	7.2	even	3
833.2.o.c.557.1		8	119.30	even	12
833.2.o.c.667.1		8	7.4	even	3

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:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.15831 - 1.15831i) q^{3} +1.00000 q^{4} +(1.00000 - 1.00000i) q^{5} +(-1.15831 - 1.15831i) q^{6} -3.00000i q^{8} +0.316625i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.15831 - 1.15831i) q^{3} +1.00000 q^{4} +(1.00000 - 1.00000i) q^{5} +(-1.15831 - 1.15831i) q^{6} -3.00000i q^{8} +0.316625i q^{9} +(-1.00000 - 1.00000i) q^{10} +(-4.15831 - 4.15831i) q^{11} +(1.15831 - 1.15831i) q^{12} +3.31662 q^{13} -2.31662i q^{15} -1.00000 q^{16} +(-4.00000 + 1.00000i) q^{17} +0.316625 q^{18} +2.31662i q^{19} +(1.00000 - 1.00000i) q^{20} +(-4.15831 + 4.15831i) q^{22} +(-3.00000 - 3.00000i) q^{23} +(-3.47494 - 3.47494i) q^{24} +3.00000i q^{25} -3.31662i q^{26} +(3.84169 + 3.84169i) q^{27} +(5.31662 - 5.31662i) q^{29} -2.31662 q^{30} +(-1.31662 + 1.31662i) q^{31} -5.00000i q^{32} -9.63325 q^{33} +(1.00000 + 4.00000i) q^{34} +0.316625i q^{36} +(6.63325 - 6.63325i) q^{37} +2.31662 q^{38} +(3.84169 - 3.84169i) q^{39} +(-3.00000 - 3.00000i) q^{40} +(5.31662 + 5.31662i) q^{41} +4.63325i q^{43} +(-4.15831 - 4.15831i) q^{44} +(0.316625 + 0.316625i) q^{45} +(-3.00000 + 3.00000i) q^{46} +2.31662 q^{47} +(-1.15831 + 1.15831i) q^{48} +3.00000 q^{50} +(-3.47494 + 5.79156i) q^{51} +3.31662 q^{52} +3.63325i q^{53} +(3.84169 - 3.84169i) q^{54} -8.31662 q^{55} +(2.68338 + 2.68338i) q^{57} +(-5.31662 - 5.31662i) q^{58} +2.63325i q^{59} -2.31662i q^{60} +(8.31662 + 8.31662i) q^{61} +(1.31662 + 1.31662i) q^{62} -7.00000 q^{64} +(3.31662 - 3.31662i) q^{65} +9.63325i q^{66} -4.31662 q^{67} +(-4.00000 + 1.00000i) q^{68} -6.94987 q^{69} +(-3.15831 + 3.15831i) q^{71} +0.949874 q^{72} +(5.00000 - 5.00000i) q^{73} +(-6.63325 - 6.63325i) q^{74} +(3.47494 + 3.47494i) q^{75} +2.31662i q^{76} +(-3.84169 - 3.84169i) q^{78} +(-4.47494 - 4.47494i) q^{79} +(-1.00000 + 1.00000i) q^{80} +7.94987 q^{81} +(5.31662 - 5.31662i) q^{82} +8.63325i q^{83} +(-3.00000 + 5.00000i) q^{85} +4.63325 q^{86} -12.3166i q^{87} +(-12.4749 + 12.4749i) q^{88} -10.6834 q^{89} +(0.316625 - 0.316625i) q^{90} +(-3.00000 - 3.00000i) q^{92} +3.05013i q^{93} -2.31662i q^{94} +(2.31662 + 2.31662i) q^{95} +(-5.79156 - 5.79156i) q^{96} +(10.9499 - 10.9499i) q^{97} +(1.31662 - 1.31662i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 4 q^{4} + 4 q^{5} + 2 q^{6}+O(q^{10}) \) 4 * q - 2 * q^3 + 4 * q^4 + 4 * q^5 + 2 * q^6	\( 4 q - 2 q^{3} + 4 q^{4} + 4 q^{5} + 2 q^{6} - 4 q^{10} - 10 q^{11} - 2 q^{12} - 4 q^{16} - 16 q^{17} - 12 q^{18} + 4 q^{20} - 10 q^{22} - 12 q^{23} + 6 q^{24} + 22 q^{27} + 8 q^{29} + 4 q^{30} + 8 q^{31} - 12 q^{33} + 4 q^{34} - 4 q^{38} + 22 q^{39} - 12 q^{40} + 8 q^{41} - 10 q^{44} - 12 q^{45} - 12 q^{46} - 4 q^{47} + 2 q^{48} + 12 q^{50} + 6 q^{51} + 22 q^{54} - 20 q^{55} + 24 q^{57} - 8 q^{58} + 20 q^{61} - 8 q^{62} - 28 q^{64} - 4 q^{67} - 16 q^{68} + 12 q^{69} - 6 q^{71} - 36 q^{72} + 20 q^{73} - 6 q^{75} - 22 q^{78} + 2 q^{79} - 4 q^{80} - 8 q^{81} + 8 q^{82} - 12 q^{85} - 8 q^{86} - 30 q^{88} - 56 q^{89} - 12 q^{90} - 12 q^{92} - 4 q^{95} + 10 q^{96} + 4 q^{97} - 8 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 + 4 * q^4 + 4 * q^5 + 2 * q^6 - 4 * q^10 - 10 * q^11 - 2 * q^12 - 4 * q^16 - 16 * q^17 - 12 * q^18 + 4 * q^20 - 10 * q^22 - 12 * q^23 + 6 * q^24 + 22 * q^27 + 8 * q^29 + 4 * q^30 + 8 * q^31 - 12 * q^33 + 4 * q^34 - 4 * q^38 + 22 * q^39 - 12 * q^40 + 8 * q^41 - 10 * q^44 - 12 * q^45 - 12 * q^46 - 4 * q^47 + 2 * q^48 + 12 * q^50 + 6 * q^51 + 22 * q^54 - 20 * q^55 + 24 * q^57 - 8 * q^58 + 20 * q^61 - 8 * q^62 - 28 * q^64 - 4 * q^67 - 16 * q^68 + 12 * q^69 - 6 * q^71 - 36 * q^72 + 20 * q^73 - 6 * q^75 - 22 * q^78 + 2 * q^79 - 4 * q^80 - 8 * q^81 + 8 * q^82 - 12 * q^85 - 8 * q^86 - 30 * q^88 - 56 * q^89 - 12 * q^90 - 12 * q^92 - 4 * q^95 + 10 * q^96 + 4 * q^97 - 8 * q^99

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