LMFDB - Embedded newform 833.2.g.c.540.2

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			540.2
Root			$-1.65831 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	833.540
Dual form			833.2.g.c.344.2

$q$-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 $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

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

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 $

$2$			1.00000i			0.707107i	0.935414	+	0.353553i	$0.115027\pi$
$2$			1.00000i			0.707107i	−0.935414	+	0.353553i	$0.884973\pi$
$3$	1.15831	+	1.15831i	0.668752	+	0.668752i	0.957427	−	0.288675i	$-0.0932147\pi$
$3$	1.15831	+	1.15831i	0.668752	+	0.668752i	−0.288675	+	0.957427i	$0.593215\pi$
$4$	1.00000			0.500000
$5$	1.00000	+	1.00000i	0.447214	+	0.447214i	0.894427	−	0.447214i	$-0.147584\pi$
$5$	1.00000	+	1.00000i	0.447214	+	0.447214i	−0.447214	+	0.894427i	$0.647584\pi$
$6$	−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	−0.299765	+	0.954013i	$0.596908\pi$
$11$	−4.15831	+	4.15831i	−1.25378	+	1.25378i	−0.954013	+	0.299765i	$0.903092\pi$
$12$	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	$-0.914385\pi$
$19$		−	2.31662i		−	0.531470i	0.964046	−	0.265735i	$-0.0856146\pi$
$20$	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	−0.946943	−	0.321400i	$-0.895847\pi$
$23$	−3.00000	+	3.00000i	−0.625543	+	0.625543i	0.321400	+	0.946943i	$0.395847\pi$
$24$	−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	0.999920	−	0.0126476i	$-0.00402596\pi$
$29$	5.31662	+	5.31662i	0.987272	+	0.987272i	−0.0126476	+	0.999920i	$0.504026\pi$
$30$	−2.31662			−0.422956
$31$	−1.31662	−	1.31662i	−0.236473	−	0.236473i	0.578915	−	0.815388i	$-0.303476\pi$
$31$	−1.31662	−	1.31662i	−0.236473	−	0.236473i	−0.815388	+	0.578915i	$0.803476\pi$
$32$			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	0.995475	+	0.0950246i	$0.0302930\pi$
$37$	6.63325	+	6.63325i	1.09050	+	1.09050i	0.0950246	+	0.995475i	$0.469707\pi$
$38$	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	−0.157243	−	0.987560i	$-0.550260\pi$
$41$	5.31662	−	5.31662i	0.830317	−	0.830317i	0.987560	+	0.157243i	$0.0502605\pi$
$42$		0			0
$43$		−	4.63325i		−	0.706564i	−0.935517	−	0.353282i	$-0.885066\pi$
$43$		−	4.63325i		−	0.706564i	0.935517	−	0.353282i	$-0.114934\pi$
$44$	−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	$-0.919723\pi$
$53$		−	3.63325i		−	0.499065i	0.968366	−	0.249533i	$-0.0802770\pi$
$54$	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	$-0.945168\pi$
$59$		−	2.63325i		−	0.342820i	0.985200	−	0.171410i	$-0.0548323\pi$
$60$			2.31662i			0.299075i
$61$	8.31662	−	8.31662i	1.06483	−	1.06483i	0.0670876	−	0.997747i	$-0.478629\pi$
$61$	8.31662	−	8.31662i	1.06483	−	1.06483i	0.997747	−	0.0670876i	$-0.0213707\pi$
$62$	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	0.494408	−	0.869230i	$-0.335385\pi$
$71$	−3.15831	−	3.15831i	−0.374823	−	0.374823i	−0.869230	+	0.494408i	$0.835385\pi$
$72$	0.949874			0.111944
$73$	5.00000	+	5.00000i	0.585206	+	0.585206i	0.936329	−	0.351123i	$-0.114200\pi$
$73$	5.00000	+	5.00000i	0.585206	+	0.585206i	−0.351123	+	0.936329i	$0.614200\pi$
$74$	−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	−0.912514	−	0.409045i	$-0.865862\pi$
$79$	−4.47494	+	4.47494i	−0.503470	+	0.503470i	0.409045	+	0.912514i	$0.365862\pi$
$80$	−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	$-0.842878\pi$
$83$		−	8.63325i		−	0.947622i	0.880626	−	0.473811i	$-0.157122\pi$
$84$		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	0.992908	+	0.118883i	$0.0379314\pi$
$97$	10.9499	+	10.9499i	1.11179	+	1.11179i	0.118883	+	0.992908i	$0.462069\pi$
$98$		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	0.221844	−	0.975082i	$-0.428793\pi$
$107$	−7.79156	−	7.79156i	−0.753239	−	0.753239i	−0.975082	+	0.221844i	$0.928793\pi$
$108$	3.84169	−	3.84169i	0.369667	−	0.369667i
$109$	−0.316625	+	0.316625i	−0.0303272	+	0.0303272i	−0.722108	−	0.691781i	$-0.756827\pi$
$109$	−0.316625	+	0.316625i	−0.0303272	+	0.0303272i	0.691781	+	0.722108i	$0.256827\pi$
$110$		−	8.31662i		−	0.792959i
$111$			15.3668i			1.45855i
$112$		0			0
$113$	−0.316625	+	0.316625i	−0.0297856	+	0.0297856i	−0.721843	−	0.692057i	$-0.756705\pi$
$113$	−0.316625	+	0.316625i	−0.0297856	+	0.0297856i	0.692057	+	0.721843i	$0.256705\pi$
$114$	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	$-0.947746\pi$
$127$		−	3.68338i		−	0.326847i	0.986556	−	0.163423i	$-0.0522536\pi$
$128$			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	0.530344	−	0.847783i	$-0.322063\pi$
$131$	−3.63325	−	3.63325i	−0.317438	−	0.317438i	−0.847783	+	0.530344i	$0.822063\pi$
$132$	−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	0.105904	−	0.994376i	$-0.466226\pi$
$139$	−10.4749	−	10.4749i	−0.888473	−	0.888473i	−0.994376	+	0.105904i	$0.966226\pi$
$140$		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	$0.186398\pi$
$151$			13.5831i			1.10538i	−0.833387	+	0.552689i	$0.813602\pi$
$152$	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	−0.220788	−	0.975322i	$-0.570863\pi$
$163$	9.63325	−	9.63325i	0.754534	−	0.754534i	0.975322	+	0.220788i	$0.0708628\pi$
$164$	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	0.713206	−	0.700955i	$-0.247243\pi$
$167$	0.158312	+	0.158312i	0.0122506	+	0.0122506i	−0.700955	+	0.713206i	$0.747243\pi$
$168$		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	0.842621	−	0.538507i	$-0.181011\pi$
$173$	4.00000	+	4.00000i	0.304114	+	0.304114i	−0.538507	+	0.842621i	$0.681011\pi$
$174$	−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	$0.00753371\pi$
$179$			0.633250i			0.0473313i	−0.999720	+	0.0236656i	$0.992466\pi$
$180$	0.316625	−	0.316625i	0.0235998	−	0.0235998i
$181$	−12.3166	+	12.3166i	−0.915488	+	0.915488i	−0.996697	−	0.0812095i	$-0.974122\pi$
$181$	−12.3166	+	12.3166i	−0.915488	+	0.915488i	0.0812095	+	0.996697i	$0.474122\pi$
$182$		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	−0.193008	−	0.981197i	$-0.561824\pi$
$193$	10.9499	−	10.9499i	0.788189	−	0.788189i	0.981197	+	0.193008i	$0.0618243\pi$
$194$	−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	−0.292487	−	0.956269i	$-0.594483\pi$
$197$	9.31662	−	9.31662i	0.663782	−	0.663782i	0.956269	+	0.292487i	$0.0944829\pi$
$198$	−1.31662	+	1.31662i	−0.0935684	+	0.0935684i
$199$	1.52506	+	1.52506i	0.108109	+	0.108109i	0.759092	−	0.650983i	$-0.225643\pi$
$199$	1.52506	+	1.52506i	0.108109	+	0.108109i	−0.650983	+	0.759092i	$0.725643\pi$
$200$	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	−0.821021	−	0.570898i	$-0.806595\pi$
$211$	−3.63325	+	3.63325i	−0.250123	+	0.250123i	0.570898	+	0.821021i	$0.306595\pi$
$212$		−	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	0.290306	−	0.956934i	$-0.406243\pi$
$227$	18.7916	−	18.7916i	1.24724	−	1.24724i	0.956934	−	0.290306i	$-0.0937570\pi$
$228$	2.68338	−	2.68338i	0.177711	−	0.177711i
$229$			27.2665i			1.80182i	0.434005	+	0.900910i	$0.357100\pi$
$229$			27.2665i			1.80182i	−0.434005	+	0.900910i	$0.642900\pi$
$230$		−	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	0.834221	−	0.551430i	$-0.185918\pi$
$233$	4.31662	+	4.31662i	0.282791	+	0.282791i	−0.551430	+	0.834221i	$0.685918\pi$
$234$	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	−0.958203	−	0.286091i	$-0.907644\pi$
$241$	−19.3166	−	19.3166i	−1.24429	−	1.24429i	−0.286091	−	0.958203i	$-0.592356\pi$
$242$	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	$-0.973329\pi$
$257$		−	2.68338i		−	0.167384i	0.996492	−	0.0836922i	$-0.0266712\pi$
$258$	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	$-0.917459\pi$
$263$		−	8.31662i		−	0.512825i	0.966567	−	0.256413i	$-0.0825406\pi$
$264$		−	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	0.792624	−	0.609711i	$-0.208714\pi$
$269$	3.00000	+	3.00000i	0.182913	+	0.182913i	−0.609711	+	0.792624i	$0.708714\pi$
$270$			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	0.217093	−	0.976151i	$-0.430343\pi$
$277$	−12.6332	−	12.6332i	−0.759058	−	0.759058i	−0.976151	+	0.217093i	$0.930343\pi$
$278$	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	$0.147654\pi$
$281$			15.0000i			0.894825i	−0.894328	+	0.447412i	$0.852346\pi$
$282$	−2.68338	+	2.68338i	−0.159793	+	0.159793i
$283$	−14.4248	+	14.4248i	−0.857466	+	0.857466i	−0.991039	−	0.133573i	$-0.957355\pi$
$283$	−14.4248	+	14.4248i	−0.857466	+	0.857466i	0.133573	+	0.991039i	$0.457355\pi$
$284$	−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	0.692063	−	0.721837i	$-0.256702\pi$
$311$	−0.525063	−	0.525063i	−0.0297736	−	0.0297736i	−0.721837	+	0.692063i	$0.756702\pi$
$312$	−11.5251	+	11.5251i	−0.652478	+	0.652478i
$313$	−13.9499	+	13.9499i	−0.788494	+	0.788494i	−0.981247	−	0.192754i	$-0.938258\pi$
$313$	−13.9499	+	13.9499i	−0.788494	+	0.788494i	0.192754	+	0.981247i	$0.438258\pi$
$314$			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	−0.924662	−	0.380789i	$-0.875652\pi$
$317$	−9.68338	+	9.68338i	−0.543873	+	0.543873i	0.380789	+	0.924662i	$0.375652\pi$
$318$	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	$0.185239\pi$
$331$			20.0000i			1.09930i	−0.835395	+	0.549650i	$0.814761\pi$
$332$		−	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	0.404360	−	0.914600i	$-0.367494\pi$
$337$	−9.36675	−	9.36675i	−0.510239	−	0.510239i	−0.914600	+	0.404360i	$0.867494\pi$
$338$		−	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	−0.177150	+	0.984184i	$0.556688\pi$
$347$	−21.6332	+	21.6332i	−1.16133	+	1.16133i	−0.984184	+	0.177150i	$0.943312\pi$
$348$			12.3166i			0.660240i
$349$		−	16.0000i		−	0.856460i	−0.903670	−	0.428230i	$-0.859137\pi$
$349$		−	16.0000i		−	0.856460i	0.903670	−	0.428230i	$-0.140863\pi$
$350$		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	$-0.681495\pi$
$359$		−	31.8997i		−	1.68360i	0.539786	−	0.841802i	$-0.318505\pi$
$360$	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	−0.657403	−	0.753539i	$-0.728345\pi$
$367$	1.84169	−	1.84169i	0.0961353	−	0.0961353i	0.753539	+	0.657403i	$0.228345\pi$
$368$	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	0.693493	−	0.720464i	$-0.256071\pi$
$379$	−0.525063	−	0.525063i	−0.0269707	−	0.0269707i	−0.720464	+	0.693493i	$0.756071\pi$
$380$	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	$0.0214309\pi$
$383$			2.63325i			0.134553i	−0.997734	+	0.0672764i	$0.978569\pi$
$384$	−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	$0.0438499\pi$
$389$			5.41688i			0.274647i	−0.990526	+	0.137323i	$0.956150\pi$
$390$	−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	0.104603	−	0.994514i	$-0.466643\pi$
$397$	21.8997	−	21.8997i	1.09912	−	1.09912i	0.994514	−	0.104603i	$-0.0333571\pi$
$398$	−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	−0.995337	−	0.0964598i	$-0.969248\pi$
$401$	−18.0000	+	18.0000i	−0.898877	+	0.898877i	0.0964598	+	0.995337i	$0.469248\pi$
$402$	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	−0.750660	−	0.660688i	$-0.770265\pi$
$419$	−1.84169	+	1.84169i	−0.0899723	+	0.0899723i	0.660688	+	0.750660i	$0.270265\pi$
$420$		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	−0.973612	−	0.228210i	$-0.926713\pi$
$431$	−15.4749	+	15.4749i	−0.745401	+	0.745401i	0.228210	+	0.973612i	$0.426713\pi$
$432$	−3.84169	+	3.84169i	−0.184833	+	0.184833i
$433$		−	2.00000i		−	0.0961139i	−0.998845	−	0.0480569i	$-0.984697\pi$
$433$		−	2.00000i		−	0.0961139i	0.998845	−	0.0480569i	$-0.0153029\pi$
$434$		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	0.593586	−	0.804771i	$-0.297712\pi$
$439$	−4.42481	−	4.42481i	−0.211185	−	0.211185i	−0.804771	+	0.593586i	$0.797712\pi$
$440$		−	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	−0.886831	−	0.462094i	$-0.847098\pi$
$449$	−9.00000	+	9.00000i	−0.424736	+	0.424736i	0.462094	+	0.886831i	$0.347098\pi$
$450$		−	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	$-0.980383\pi$
$457$		−	2.63325i		−	0.123178i	0.998102	−	0.0615891i	$-0.0196168\pi$
$458$	−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	$-0.848850\pi$
$461$		−	19.6332i		−	0.914412i	0.889361	−	0.457206i	$-0.151150\pi$
$462$		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	$-0.844228\pi$
$467$		−	20.3166i		−	0.940141i	0.882629	−	0.470071i	$-0.155772\pi$
$468$		−	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	0.432531	−	0.901619i	$-0.357621\pi$
$479$	−10.2665	−	10.2665i	−0.469088	−	0.469088i	−0.901619	+	0.432531i	$0.857621\pi$
$480$	−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	0.0186098	−	0.999827i	$-0.494076\pi$
$487$	22.4749	−	22.4749i	1.01844	−	1.01844i	0.999827	−	0.0186098i	$-0.00592402\pi$
$488$	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	$0.232650\pi$
$491$			29.5831i			1.33507i	−0.744579	+	0.667534i	$0.767350\pi$
$492$	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	−0.944862	−	0.327467i	$-0.893805\pi$
$499$	−13.7916	+	13.7916i	−0.617395	+	0.617395i	0.327467	+	0.944862i	$0.393805\pi$
$500$	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	−0.198028	+	0.980196i	$0.563454\pi$
$503$	−26.4248	+	26.4248i	−1.17822	+	1.17822i	−0.980196	+	0.198028i	$0.936546\pi$
$504$		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	−0.994320	−	0.106429i	$-0.966058\pi$
$521$	−20.2665	+	20.2665i	−0.887891	+	0.887891i	0.106429	+	0.994320i	$0.466058\pi$
$522$	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	0.951229	−	0.308484i	$-0.0998217\pi$
$541$	14.9499	+	14.9499i	0.642745	+	0.642745i	−0.308484	+	0.951229i	$0.599822\pi$
$542$			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	0.925551	−	0.378623i	$-0.123602\pi$
$547$	12.7916	+	12.7916i	0.546928	+	0.546928i	−0.378623	+	0.925551i	$0.623602\pi$
$548$	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	$-0.789315\pi$
$563$		−	29.1662i		−	1.22921i	0.788835	−	0.614605i	$-0.210685\pi$
$564$	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	$-0.869614\pi$
$569$		−	19.0000i		−	0.796521i	0.917272	−	0.398261i	$-0.130386\pi$
$570$			5.36675i			0.224788i
$571$	6.58312	−	6.58312i	0.275495	−	0.275495i	−0.555813	−	0.831308i	$-0.687593\pi$
$571$	6.58312	−	6.58312i	0.275495	−	0.275495i	0.831308	+	0.555813i	$0.187593\pi$
$572$	−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	$0.143045\pi$
$587$			21.0501i			0.868832i	−0.900712	+	0.434416i	$0.856955\pi$
$588$		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	$-0.932394\pi$
$593$		−	10.2665i		−	0.421595i	0.977530	−	0.210797i	$-0.0676060\pi$
$594$	−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	−0.619661	−	0.784869i	$-0.712730\pi$
$601$	4.05013	−	4.05013i	0.165208	−	0.165208i	0.784869	+	0.619661i	$0.212730\pi$
$602$		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	0.677600	−	0.735431i	$-0.263020\pi$
$607$	−1.42481	−	1.42481i	−0.0578313	−	0.0578313i	−0.735431	+	0.677600i	$0.763020\pi$
$608$	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	0.623115	−	0.782131i	$-0.285867\pi$
$617$	−3.94987	−	3.94987i	−0.159016	−	0.159016i	−0.782131	+	0.623115i	$0.785867\pi$
$618$	0.366750	−	0.366750i	0.0147529	−	0.0147529i
$619$	−9.15831	+	9.15831i	−0.368104	+	0.368104i	−0.866785	−	0.498682i	$-0.833818\pi$
$619$	−9.15831	+	9.15831i	−0.368104	+	0.368104i	0.498682	+	0.866785i	$0.333818\pi$
$620$		−	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	$0.299878\pi$
$631$			40.6332i			1.61758i	−0.588095	+	0.808792i	$0.700122\pi$
$632$	−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	0.0761454	−	0.997097i	$-0.475739\pi$
$641$	−23.3166	−	23.3166i	−0.920951	−	0.920951i	−0.997097	+	0.0761454i	$0.975739\pi$
$642$	18.0501			0.712382
$643$	−33.1082	−	33.1082i	−1.30566	−	1.30566i	−0.924516	−	0.381144i	$-0.875530\pi$
$643$	−33.1082	−	33.1082i	−1.30566	−	1.30566i	−0.381144	−	0.924516i	$-0.624470\pi$
$644$		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	−0.144842	−	0.989455i	$-0.546267\pi$
$653$	21.5831	−	21.5831i	0.844613	−	0.844613i	0.989455	+	0.144842i	$0.0462674\pi$
$654$		−	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	$-0.730352\pi$
$661$		−	38.5330i		−	1.49876i	0.662140	−	0.749380i	$-0.269648\pi$
$662$	−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	−0.534720	−	0.845029i	$-0.679583\pi$
$673$	8.05013	−	8.05013i	0.310310	−	0.310310i	0.845029	+	0.534720i	$0.179583\pi$
$674$	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	0.156280	−	0.987713i	$-0.450050\pi$
$677$	−21.6332	−	21.6332i	−0.831433	−	0.831433i	−0.987713	+	0.156280i	$0.950050\pi$
$678$		−	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	0.658169	−	0.752870i	$-0.271331\pi$
$683$	−2.47494	−	2.47494i	−0.0947008	−	0.0947008i	−0.752870	+	0.658169i	$0.771331\pi$
$684$	−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	−0.398524	−	0.917158i	$-0.630478\pi$
$691$	13.6332	−	13.6332i	0.518633	−	0.518633i	0.917158	+	0.398524i	$0.130478\pi$
$692$	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	0.947200	−	0.320643i	$-0.103899\pi$
$709$	16.6834	+	16.6834i	0.626557	+	0.626557i	−0.320643	+	0.947200i	$0.603899\pi$
$710$	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	0.879098	−	0.476641i	$-0.158146\pi$
$719$	10.7916	+	10.7916i	0.402457	+	0.402457i	−0.476641	+	0.879098i	$0.658146\pi$
$720$	−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	$0.0971230\pi$
$733$			16.2665i			0.600817i	−0.953811	+	0.300408i	$0.902877\pi$
$734$	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	$0.0632560\pi$
$739$			10.7335i			0.394838i	−0.980319	+	0.197419i	$0.936744\pi$
$740$			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	0.999556	+	0.0297944i	$0.00948525\pi$
$743$	28.0581	+	28.0581i	1.02935	+	1.02935i	0.0297944	+	0.999556i	$0.490515\pi$
$744$	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	0.999714	−	0.0239054i	$-0.00761004\pi$
$751$	26.7414	+	26.7414i	0.975809	+	0.975809i	−0.0239054	+	0.999714i	$0.507610\pi$
$752$	−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	$0.0271242\pi$
$757$			4.68338i			0.170220i	−0.996372	+	0.0851101i	$0.972876\pi$
$758$	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	$0.0310576\pi$
$773$			5.41688i			0.194831i	−0.995244	+	0.0974157i	$0.968942\pi$
$774$		−	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	0.894587	+	0.446893i	$0.147470\pi$
$787$	37.6332	+	37.6332i	1.34148	+	1.34148i	0.446893	+	0.894587i	$0.352530\pi$
$788$	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	$-0.802002\pi$
$797$		−	32.8997i		−	1.16537i	0.812698	−	0.582684i	$-0.197998\pi$
$798$		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	−0.756242	−	0.654292i	$-0.772967\pi$
$809$	−2.89975	+	2.89975i	−0.101950	+	0.101950i	0.654292	+	0.756242i	$0.272967\pi$
$810$	−7.94987	+	7.94987i	−0.279330	+	0.279330i
$811$	18.1082	+	18.1082i	0.635864	+	0.635864i	0.949533	−	0.313668i	$-0.101558\pi$
$811$	18.1082	+	18.1082i	0.635864	+	0.635864i	−0.313668	+	0.949533i	$0.601558\pi$
$812$		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	0.566773	−	0.823874i	$-0.308192\pi$
$821$	−7.36675	−	7.36675i	−0.257101	−	0.257101i	−0.823874	+	0.566773i	$0.808192\pi$
$822$	−3.10819	+	3.10819i	−0.108410	+	0.108410i
$823$	25.0581	−	25.0581i	0.873469	−	0.873469i	−0.119380	−	0.992849i	$-0.538091\pi$
$823$	25.0581	−	25.0581i	0.873469	−	0.873469i	0.992849	+	0.119380i	$0.0380905\pi$
$824$		−	0.949874i		−	0.0330904i
$825$			28.8997i			1.00616i
$826$		0			0
$827$	28.0581	−	28.0581i	0.975674	−	0.975674i	−0.0240367	−	0.999711i	$-0.507652\pi$
$827$	28.0581	−	28.0581i	0.975674	−	0.975674i	0.999711	+	0.0240367i	$0.00765185\pi$
$828$	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	−0.0345826	+	0.999402i	$0.511010\pi$
$839$	−29.9499	+	29.9499i	−1.03398	+	1.03398i	−0.999402	+	0.0345826i	$0.988990\pi$
$840$		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	0.929417	−	0.369030i	$-0.120310\pi$
$853$	16.3668	+	16.3668i	0.560387	+	0.560387i	−0.369030	+	0.929417i	$0.620310\pi$
$854$		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	−0.223255	−	0.974760i	$-0.571668\pi$
$857$	22.0000	−	22.0000i	0.751506	−	0.751506i	0.974760	+	0.223255i	$0.0716681\pi$
$858$		−	31.9499i		−	1.09075i
$859$		−	8.31662i		−	0.283760i	−0.989884	−	0.141880i	$-0.954685\pi$
$859$		−	8.31662i		−	0.283760i	0.989884	−	0.141880i	$-0.0453146\pi$
$860$	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	−0.445574	−	0.895245i	$-0.647001\pi$
$877$	13.3166	−	13.3166i	0.449670	−	0.449670i	0.895245	+	0.445574i	$0.147001\pi$
$878$	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	0.957817	−	0.287378i	$-0.0927835\pi$
$881$	19.8997	+	19.8997i	0.670440	+	0.670440i	−0.287378	+	0.957817i	$0.592784\pi$
$882$		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	0.924274	−	0.381731i	$-0.124672\pi$
$887$	16.1583	+	16.1583i	0.542543	+	0.542543i	−0.381731	+	0.924274i	$0.624672\pi$
$888$	−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	−0.998765	−	0.0496782i	$-0.984180\pi$
$907$	−28.5831	+	28.5831i	−0.949087	+	0.949087i	0.0496782	+	0.998765i	$0.484180\pi$
$908$	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	−0.740253	−	0.672329i	$-0.765294\pi$
$911$	−2.05013	+	2.05013i	−0.0679237	+	0.0679237i	0.672329	+	0.740253i	$0.265294\pi$
$912$	−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	−0.860299	−	0.509789i	$-0.829723\pi$
$929$	−10.6834	+	10.6834i	−0.350510	+	0.350510i	0.509789	+	0.860299i	$0.329723\pi$
$930$	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	$-0.678940\pi$
$937$		−	51.7995i		−	1.69222i	0.533012	−	0.846108i	$-0.321060\pi$
$938$		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	−0.645402	−	0.763843i	$-0.723310\pi$
$941$	3.63325	−	3.63325i	0.118441	−	0.118441i	0.763843	+	0.645402i	$0.223310\pi$
$942$	−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	0.982094	−	0.188394i	$-0.0603281\pi$
$947$	24.4248	+	24.4248i	0.793700	+	0.793700i	−0.188394	+	0.982094i	$0.560328\pi$
$948$	−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	$-0.865058\pi$
$967$		−	25.5831i		−	0.822698i	0.911478	−	0.411349i	$-0.134942\pi$
$968$	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	$-0.980663\pi$
$971$		−	3.78363i		−	0.121422i	0.998155	−	0.0607112i	$-0.0193369\pi$
$972$	−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	$0.0571633\pi$
$977$			11.1662i			0.357240i	−0.983918	+	0.178620i	$0.942837\pi$
$978$			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	0.456660	−	0.889641i	$-0.349046\pi$
$983$	−13.5752	−	13.5752i	−0.432981	−	0.432981i	−0.889641	+	0.456660i	$0.849046\pi$
$984$			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	0.996948	+	0.0780687i	$0.0248753\pi$
$991$	33.8417	+	33.8417i	1.07502	+	1.07502i	0.0780687	+	0.996948i	$0.475125\pi$
$992$	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	−0.663337	−	0.748321i	$-0.730860\pi$
$997$	2.68338	−	2.68338i	0.0849833	−	0.0849833i	0.748321	+	0.663337i	$0.230860\pi$
$998$	−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.540.2		4
7.2	even	3		833.2.o.c.557.1		8
7.3	odd	6		119.2.n.a.30.1	yes	8
7.4	even	3		833.2.o.c.30.2		8
7.5	odd	6		119.2.n.a.81.2	yes	8
7.6	odd	2		833.2.g.d.540.1		4
17.4	even	4	inner	833.2.g.c.344.2		4
119.4	even	12		833.2.o.c.667.1		8
119.38	odd	12		119.2.n.a.72.2	yes	8
119.55	odd	4		833.2.g.d.344.1		4
119.72	even	12		833.2.o.c.361.2		8
119.89	odd	12		119.2.n.a.4.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.2.n.a.4.1	✓	8	119.89	odd	12
119.2.n.a.30.1	yes	8	7.3	odd	6
119.2.n.a.72.2	yes	8	119.38	odd	12
119.2.n.a.81.2	yes	8	7.5	odd	6
833.2.g.c.344.2		4	17.4	even	4	inner
833.2.g.c.540.2		4	1.1	even	1	trivial
833.2.g.d.344.1		4	119.55	odd	4
833.2.g.d.540.1		4	7.6	odd	2
833.2.o.c.30.2		8	7.4	even	3
833.2.o.c.361.2		8	119.72	even	12
833.2.o.c.557.1		8	7.2	even	3
833.2.o.c.667.1		8	119.4	even	12

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more