LMFDB - Embedded newform 833.2.g.c.344.1

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			344.1
Root			$1.65831 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	833.344
Dual form			833.2.g.c.540.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-2.15831 + 2.15831i) q^{3} +1.00000 q^{4} +(1.00000 - 1.00000i) q^{5} +(2.15831 + 2.15831i) q^{6} -3.00000i q^{8} -6.31662i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-2.15831 + 2.15831i) q^{3} +1.00000 q^{4} +(1.00000 - 1.00000i) q^{5} +(2.15831 + 2.15831i) q^{6} -3.00000i q^{8} -6.31662i q^{9} +(-1.00000 - 1.00000i) q^{10} +(-0.841688 - 0.841688i) q^{11} +(-2.15831 + 2.15831i) q^{12} -3.31662 q^{13} +4.31662i q^{15} -1.00000 q^{16} +(-4.00000 + 1.00000i) q^{17} -6.31662 q^{18} -4.31662i q^{19} +(1.00000 - 1.00000i) q^{20} +(-0.841688 + 0.841688i) q^{22} +(-3.00000 - 3.00000i) q^{23} +(6.47494 + 6.47494i) q^{24} +3.00000i q^{25} +3.31662i q^{26} +(7.15831 + 7.15831i) q^{27} +(-1.31662 + 1.31662i) q^{29} +4.31662 q^{30} +(5.31662 - 5.31662i) q^{31} -5.00000i q^{32} +3.63325 q^{33} +(1.00000 + 4.00000i) q^{34} -6.31662i q^{36} +(-6.63325 + 6.63325i) q^{37} -4.31662 q^{38} +(7.15831 - 7.15831i) q^{39} +(-3.00000 - 3.00000i) q^{40} +(-1.31662 - 1.31662i) q^{41} -8.63325i q^{43} +(-0.841688 - 0.841688i) q^{44} +(-6.31662 - 6.31662i) q^{45} +(-3.00000 + 3.00000i) q^{46} -4.31662 q^{47} +(2.15831 - 2.15831i) q^{48} +3.00000 q^{50} +(6.47494 - 10.7916i) q^{51} -3.31662 q^{52} -9.63325i q^{53} +(7.15831 - 7.15831i) q^{54} -1.68338 q^{55} +(9.31662 + 9.31662i) q^{57} +(1.31662 + 1.31662i) q^{58} -10.6332i q^{59} +4.31662i q^{60} +(1.68338 + 1.68338i) q^{61} +(-5.31662 - 5.31662i) q^{62} -7.00000 q^{64} +(-3.31662 + 3.31662i) q^{65} -3.63325i q^{66} +2.31662 q^{67} +(-4.00000 + 1.00000i) q^{68} +12.9499 q^{69} +(0.158312 - 0.158312i) q^{71} -18.9499 q^{72} +(5.00000 - 5.00000i) q^{73} +(6.63325 + 6.63325i) q^{74} +(-6.47494 - 6.47494i) q^{75} -4.31662i q^{76} +(-7.15831 - 7.15831i) q^{78} +(5.47494 + 5.47494i) q^{79} +(-1.00000 + 1.00000i) q^{80} -11.9499 q^{81} +(-1.31662 + 1.31662i) q^{82} -4.63325i q^{83} +(-3.00000 + 5.00000i) q^{85} -8.63325 q^{86} -5.68338i q^{87} +(-2.52506 + 2.52506i) q^{88} -17.3166 q^{89} +(-6.31662 + 6.31662i) q^{90} +(-3.00000 - 3.00000i) q^{92} +22.9499i q^{93} +4.31662i q^{94} +(-4.31662 - 4.31662i) q^{95} +(10.7916 + 10.7916i) q^{96} +(-8.94987 + 8.94987i) q^{97} +(-5.31662 + 5.31662i) 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	$-0.115027\pi$
$3$	−2.15831	+	2.15831i	−1.24610	+	1.24610i	−0.288675	+	0.957427i	$0.593215\pi$
$3$	−2.15831	+	2.15831i	−1.24610	+	1.24610i	−0.957427	+	0.288675i	$0.906785\pi$
$4$	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	$0.147584\pi$
$6$	2.15831	+	2.15831i	0.881127	+	0.881127i
$7$		0			0
$7$		0			0
$8$		−	3.00000i		−	1.06066i
$9$		−	6.31662i		−	2.10554i
$10$	−1.00000	−	1.00000i	−0.316228	−	0.316228i
$11$	−0.841688	−	0.841688i	−0.253778	−	0.253778i	0.568739	−	0.822518i	$-0.307431\pi$
$11$	−0.841688	−	0.841688i	−0.253778	−	0.253778i	−0.822518	+	0.568739i	$0.807431\pi$
$12$	−2.15831	+	2.15831i	−0.623051	+	0.623051i
$13$	−3.31662			−0.919866			−0.459933	−	0.887954i	$-0.652127\pi$
$13$	−3.31662			−0.919866			−0.459933	+	0.887954i	$0.652127\pi$
$14$		0			0
$15$			4.31662i			1.11455i
$16$	−1.00000			−0.250000
$17$	−4.00000	+	1.00000i	−0.970143	+	0.242536i
$17$	−4.00000	+	1.00000i	−0.970143	+	0.242536i
$18$	−6.31662			−1.48884
$19$		−	4.31662i		−	0.990302i	−0.868807	−	0.495151i	$-0.835113\pi$
$19$		−	4.31662i		−	0.990302i	0.868807	−	0.495151i	$-0.164887\pi$
$20$	1.00000	−	1.00000i	0.223607	−	0.223607i
$21$		0			0
$22$	−0.841688	+	0.841688i	−0.179448	+	0.179448i
$23$	−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	$0.895847\pi$
$24$	6.47494	+	6.47494i	1.32169	+	1.32169i
$25$			3.00000i			0.600000i
$26$			3.31662i			0.650444i
$27$	7.15831	+	7.15831i	1.37762	+	1.37762i
$28$		0			0
$29$	−1.31662	+	1.31662i	−0.244491	+	0.244491i	−0.818705	−	0.574214i	$-0.805308\pi$
$29$	−1.31662	+	1.31662i	−0.244491	+	0.244491i	0.574214	+	0.818705i	$0.305308\pi$
$30$	4.31662			0.788104
$31$	5.31662	−	5.31662i	0.954894	−	0.954894i	−0.0441317	−	0.999026i	$-0.514052\pi$
$31$	5.31662	−	5.31662i	0.954894	−	0.954894i	0.999026	+	0.0441317i	$0.0140521\pi$
$32$		−	5.00000i		−	0.883883i
$33$	3.63325			0.632468
$34$	1.00000	+	4.00000i	0.171499	+	0.685994i
$35$		0			0
$36$		−	6.31662i		−	1.05277i
$37$	−6.63325	+	6.63325i	−1.09050	+	1.09050i	−0.0950246	+	0.995475i	$0.530293\pi$
$37$	−6.63325	+	6.63325i	−1.09050	+	1.09050i	−0.995475	+	0.0950246i	$0.969707\pi$
$38$	−4.31662			−0.700249
$39$	7.15831	−	7.15831i	1.14625	−	1.14625i
$40$	−3.00000	−	3.00000i	−0.474342	−	0.474342i
$41$	−1.31662	−	1.31662i	−0.205622	−	0.205622i	0.596782	−	0.802404i	$-0.296446\pi$
$41$	−1.31662	−	1.31662i	−0.205622	−	0.205622i	−0.802404	+	0.596782i	$0.796446\pi$
$42$		0			0
$43$		−	8.63325i		−	1.31656i	−0.752774	−	0.658279i	$-0.771285\pi$
$43$		−	8.63325i		−	1.31656i	0.752774	−	0.658279i	$-0.228715\pi$
$44$	−0.841688	−	0.841688i	−0.126889	−	0.126889i
$45$	−6.31662	−	6.31662i	−0.941627	−	0.941627i
$46$	−3.00000	+	3.00000i	−0.442326	+	0.442326i
$47$	−4.31662			−0.629644			−0.314822	−	0.949151i	$-0.601945\pi$
$47$	−4.31662			−0.629644			−0.314822	+	0.949151i	$0.601945\pi$
$48$	2.15831	−	2.15831i	0.311526	−	0.311526i
$49$		0			0
$50$	3.00000			0.424264
$51$	6.47494	−	10.7916i	0.906673	−	1.51112i
$52$	−3.31662			−0.459933
$53$		−	9.63325i		−	1.32323i	−0.749844	−	0.661614i	$-0.769872\pi$
$53$		−	9.63325i		−	1.32323i	0.749844	−	0.661614i	$-0.230128\pi$
$54$	7.15831	−	7.15831i	0.974123	−	0.974123i
$55$	−1.68338			−0.226986
$56$		0			0
$57$	9.31662	+	9.31662i	1.23402	+	1.23402i
$58$	1.31662	+	1.31662i	0.172881	+	0.172881i
$59$		−	10.6332i		−	1.38433i	−0.721739	−	0.692166i	$-0.756657\pi$
$59$		−	10.6332i		−	1.38433i	0.721739	−	0.692166i	$-0.243343\pi$
$60$			4.31662i			0.557274i
$61$	1.68338	+	1.68338i	0.215534	+	0.215534i	0.806613	−	0.591079i	$-0.201298\pi$
$61$	1.68338	+	1.68338i	0.215534	+	0.215534i	−0.591079	+	0.806613i	$0.701298\pi$
$62$	−5.31662	−	5.31662i	−0.675212	−	0.675212i
$63$		0			0
$64$	−7.00000			−0.875000
$65$	−3.31662	+	3.31662i	−0.411377	+	0.411377i
$66$		−	3.63325i		−	0.447222i
$67$	2.31662			0.283021			0.141510	−	0.989937i	$-0.454804\pi$
$67$	2.31662			0.283021			0.141510	+	0.989937i	$0.454804\pi$
$68$	−4.00000	+	1.00000i	−0.485071	+	0.121268i
$69$	12.9499			1.55898
$70$		0			0
$71$	0.158312	−	0.158312i	0.0187882	−	0.0187882i	−0.697650	−	0.716438i	$-0.745771\pi$
$71$	0.158312	−	0.158312i	0.0187882	−	0.0187882i	0.716438	+	0.697650i	$0.245771\pi$
$72$	−18.9499			−2.23326
$73$	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
$75$	−6.47494	−	6.47494i	−0.747661	−	0.747661i
$76$		−	4.31662i		−	0.495151i
$77$		0			0
$78$	−7.15831	−	7.15831i	−0.810519	−	0.810519i
$79$	5.47494	+	5.47494i	0.615979	+	0.615979i	0.944497	−	0.328519i	$-0.106549\pi$
$79$	5.47494	+	5.47494i	0.615979	+	0.615979i	−0.328519	+	0.944497i	$0.606549\pi$
$80$	−1.00000	+	1.00000i	−0.111803	+	0.111803i
$81$	−11.9499			−1.32776
$82$	−1.31662	+	1.31662i	−0.145397	+	0.145397i
$83$		−	4.63325i		−	0.508565i	−0.967130	−	0.254283i	$-0.918161\pi$
$83$		−	4.63325i		−	0.508565i	0.967130	−	0.254283i	$-0.0818393\pi$
$84$		0			0
$85$	−3.00000	+	5.00000i	−0.325396	+	0.542326i
$86$	−8.63325			−0.930947
$87$		−	5.68338i		−	0.609322i
$88$	−2.52506	+	2.52506i	−0.269173	+	0.269173i
$89$	−17.3166			−1.83556			−0.917779	−	0.397091i	$-0.870020\pi$
$89$	−17.3166			−1.83556			−0.917779	+	0.397091i	$0.870020\pi$
$90$	−6.31662	+	6.31662i	−0.665831	+	0.665831i
$91$		0			0
$92$	−3.00000	−	3.00000i	−0.312772	−	0.312772i
$93$			22.9499i			2.37979i
$94$			4.31662i			0.445226i
$95$	−4.31662	−	4.31662i	−0.442876	−	0.442876i
$96$	10.7916	+	10.7916i	1.10141	+	1.10141i
$97$	−8.94987	+	8.94987i	−0.908722	+	0.908722i	−0.996169	−	0.0874471i	$-0.972129\pi$
$97$	−8.94987	+	8.94987i	−0.908722	+	0.908722i	0.0874471	+	0.996169i	$0.472129\pi$
$98$		0			0
$99$	−5.31662	+	5.31662i	−0.534341	+	0.534341i
$100$			3.00000i			0.300000i
$101$	6.63325			0.660033			0.330017	−	0.943975i	$-0.392946\pi$
$101$	6.63325			0.660033			0.330017	+	0.943975i	$0.392946\pi$
$102$	−10.7916	−	6.47494i	−1.06852	−	0.641114i
$103$	6.31662			0.622396			0.311198	−	0.950345i	$-0.399270\pi$
$103$	6.31662			0.622396			0.311198	+	0.950345i	$0.399270\pi$
$104$			9.94987i			0.975665i
$105$		0			0
$106$	−9.63325			−0.935664
$107$	8.79156	−	8.79156i	0.849912	−	0.849912i	−0.140209	−	0.990122i	$-0.544778\pi$
$107$	8.79156	−	8.79156i	0.849912	−	0.849912i	0.990122	+	0.140209i	$0.0447776\pi$
$108$	7.15831	+	7.15831i	0.688809	+	0.688809i
$109$	6.31662	+	6.31662i	0.605023	+	0.605023i	0.941641	−	0.336618i	$-0.109283\pi$
$109$	6.31662	+	6.31662i	0.605023	+	0.605023i	−0.336618	+	0.941641i	$0.609283\pi$
$110$			1.68338i			0.160504i
$111$		−	28.6332i		−	2.71775i
$112$		0			0
$113$	6.31662	+	6.31662i	0.594218	+	0.594218i	0.938768	−	0.344550i	$-0.111968\pi$
$113$	6.31662	+	6.31662i	0.594218	+	0.594218i	−0.344550	+	0.938768i	$0.611968\pi$
$114$	9.31662	−	9.31662i	0.872582	−	0.872582i
$115$	−6.00000			−0.559503
$116$	−1.31662	+	1.31662i	−0.122246	+	0.122246i
$117$			20.9499i			1.93682i
$118$	−10.6332			−0.978870
$119$		0			0
$120$	12.9499			1.18216
$121$		−	9.58312i		−	0.871193i
$122$	1.68338	−	1.68338i	0.152406	−	0.152406i
$123$	5.68338			0.512453
$124$	5.31662	−	5.31662i	0.477447	−	0.477447i
$125$	8.00000	+	8.00000i	0.715542	+	0.715542i
$126$		0			0
$127$			10.3166i			0.915452i	0.889093	+	0.457726i	$0.151336\pi$
$127$			10.3166i			0.915452i	−0.889093	+	0.457726i	$0.848664\pi$
$128$		−	3.00000i		−	0.265165i
$129$	18.6332	+	18.6332i	1.64057	+	1.64057i
$130$	3.31662	+	3.31662i	0.290887	+	0.290887i
$131$	9.63325	−	9.63325i	0.841661	−	0.841661i	−0.147414	−	0.989075i	$-0.547095\pi$
$131$	9.63325	−	9.63325i	0.841661	−	0.841661i	0.989075	+	0.147414i	$0.0470950\pi$
$132$	3.63325			0.316234
$133$		0			0
$134$		−	2.31662i		−	0.200126i
$135$	14.3166			1.23218
$136$	3.00000	+	12.0000i	0.257248	+	1.02899i
$137$	9.31662			0.795973			0.397986	−	0.917391i	$-0.369709\pi$
$137$	9.31662			0.795973			0.397986	+	0.917391i	$0.369709\pi$
$138$		−	12.9499i		−	1.10237i
$139$	−0.525063	+	0.525063i	−0.0445352	+	0.0445352i	−0.729024	−	0.684488i	$-0.760026\pi$
$139$	−0.525063	+	0.525063i	−0.0445352	+	0.0445352i	0.684488	+	0.729024i	$0.260026\pi$
$140$		0			0
$141$	9.31662	−	9.31662i	0.784601	−	0.784601i
$142$	−0.158312	−	0.158312i	−0.0132853	−	0.0132853i
$143$	2.79156	+	2.79156i	0.233442	+	0.233442i
$144$			6.31662i			0.526385i
$145$			2.63325i			0.218679i
$146$	−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	$0.513042\pi$
$150$	−6.47494	+	6.47494i	−0.528676	+	0.528676i
$151$			19.5831i			1.59365i	0.604209	+	0.796826i	$0.293489\pi$
$151$			19.5831i			1.59365i	−0.604209	+	0.796826i	$0.706511\pi$
$152$	−12.9499			−1.05037
$153$	6.31662	+	25.2665i	0.510669	+	2.04268i
$154$		0			0
$155$		−	10.6332i		−	0.854083i
$156$	7.15831	−	7.15831i	0.573124	−	0.573124i
$157$	−16.2665			−1.29821			−0.649104	−	0.760700i	$-0.724856\pi$
$157$	−16.2665			−1.29821			−0.649104	+	0.760700i	$0.724856\pi$
$158$	5.47494	−	5.47494i	0.435563	−	0.435563i
$159$	20.7916	+	20.7916i	1.64888	+	1.64888i
$160$	−5.00000	−	5.00000i	−0.395285	−	0.395285i
$161$		0			0
$162$			11.9499i			0.938871i
$163$	−3.63325	−	3.63325i	−0.284578	−	0.284578i	0.550354	−	0.834932i	$-0.314493\pi$
$163$	−3.63325	−	3.63325i	−0.284578	−	0.284578i	−0.834932	+	0.550354i	$0.814493\pi$
$164$	−1.31662	−	1.31662i	−0.102811	−	0.102811i
$165$	3.63325	−	3.63325i	0.282848	−	0.282848i
$166$	−4.63325			−0.359610
$167$	−3.15831	+	3.15831i	−0.244398	+	0.244398i	−0.818667	−	0.574269i	$-0.805286\pi$
$167$	−3.15831	+	3.15831i	−0.244398	+	0.244398i	0.574269	+	0.818667i	$0.305286\pi$
$168$		0			0
$169$	−2.00000			−0.153846
$170$	5.00000	+	3.00000i	0.383482	+	0.230089i
$171$	−27.2665			−2.08512
$172$		−	8.63325i		−	0.658279i
$173$	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	$0.181011\pi$
$174$	−5.68338			−0.430856
$175$		0			0
$176$	0.841688	+	0.841688i	0.0634446	+	0.0634446i
$177$	22.9499	+	22.9499i	1.72502	+	1.72502i
$178$			17.3166i			1.29794i
$179$			12.6332i			0.944253i	0.881531	+	0.472127i	$0.156514\pi$
$179$			12.6332i			0.944253i	−0.881531	+	0.472127i	$0.843486\pi$
$180$	−6.31662	−	6.31662i	−0.470813	−	0.470813i
$181$	−5.68338	−	5.68338i	−0.422442	−	0.422442i	0.463602	−	0.886044i	$-0.346557\pi$
$181$	−5.68338	−	5.68338i	−0.422442	−	0.422442i	−0.886044	+	0.463602i	$0.846557\pi$
$182$		0			0
$183$	−7.26650			−0.537155
$184$	−9.00000	+	9.00000i	−0.663489	+	0.663489i
$185$			13.2665i			0.975372i
$186$	22.9499			1.68277
$187$	4.20844	+	2.52506i	0.307751	+	0.184651i
$188$	−4.31662			−0.314822
$189$		0			0
$190$	−4.31662	+	4.31662i	−0.313161	+	0.313161i
$191$	−19.2665			−1.39407			−0.697037	−	0.717035i	$-0.745499\pi$
$191$	−19.2665			−1.39407			−0.697037	+	0.717035i	$0.745499\pi$
$192$	15.1082	−	15.1082i	1.09034	−	1.09034i
$193$	−8.94987	−	8.94987i	−0.644226	−	0.644226i	0.307365	−	0.951592i	$-0.400553\pi$
$193$	−8.94987	−	8.94987i	−0.644226	−	0.644226i	−0.951592	+	0.307365i	$0.900553\pi$
$194$	8.94987	+	8.94987i	0.642564	+	0.642564i
$195$		−	14.3166i		−	1.02523i
$196$		0			0
$197$	2.68338	+	2.68338i	0.191183	+	0.191183i	0.796207	−	0.605024i	$-0.206837\pi$
$197$	2.68338	+	2.68338i	0.191183	+	0.191183i	−0.605024	+	0.796207i	$0.706837\pi$
$198$	5.31662	+	5.31662i	0.377836	+	0.377836i
$199$	11.4749	−	11.4749i	0.813437	−	0.813437i	−0.171711	−	0.985147i	$-0.554929\pi$
$199$	11.4749	−	11.4749i	0.813437	−	0.813437i	0.985147	+	0.171711i	$0.0549294\pi$
$200$	9.00000			0.636396
$201$	−5.00000	+	5.00000i	−0.352673	+	0.352673i
$202$		−	6.63325i		−	0.466714i
$203$		0			0
$204$	6.47494	−	10.7916i	0.453336	−	0.755560i
$205$	−2.63325			−0.183914
$206$		−	6.31662i		−	0.440100i
$207$	−18.9499	+	18.9499i	−1.31711	+	1.31711i
$208$	3.31662			0.229967
$209$	−3.63325	+	3.63325i	−0.251317	+	0.251317i
$210$		0			0
$211$	9.63325	+	9.63325i	0.663180	+	0.663180i	0.956128	−	0.292948i	$-0.0946363\pi$
$211$	9.63325	+	9.63325i	0.663180	+	0.663180i	−0.292948	+	0.956128i	$0.594636\pi$
$212$		−	9.63325i		−	0.661614i
$213$			0.683375i			0.0468241i
$214$	−8.79156	−	8.79156i	−0.600979	−	0.600979i
$215$	−8.63325	−	8.63325i	−0.588783	−	0.588783i
$216$	21.4749	−	21.4749i	1.46118	−	1.46118i
$217$		0			0
$218$	6.31662	−	6.31662i	0.427816	−	0.427816i
$219$			21.5831i			1.45845i
$220$	−1.68338			−0.113493
$221$	13.2665	−	3.31662i	0.892401	−	0.223100i
$222$	−28.6332			−1.92174
$223$		0			0		1.00000			$0$
$223$		0			0		−1.00000			$\pi$
$224$		0			0
$225$	18.9499			1.26332
$226$	6.31662	−	6.31662i	0.420176	−	0.420176i
$227$	2.20844	+	2.20844i	0.146579	+	0.146579i	0.776588	−	0.630009i	$-0.216949\pi$
$227$	2.20844	+	2.20844i	0.146579	+	0.146579i	−0.630009	+	0.776588i	$0.716949\pi$
$228$	9.31662	+	9.31662i	0.617009	+	0.617009i
$229$		−	0.733501i		−	0.0484711i	−0.999706	−	0.0242355i	$-0.992285\pi$
$229$		−	0.733501i		−	0.0484711i	0.999706	−	0.0242355i	$-0.00771517\pi$
$230$			6.00000i			0.395628i
$231$		0			0
$232$	3.94987	+	3.94987i	0.259322	+	0.259322i
$233$	−2.31662	+	2.31662i	−0.151767	+	0.151767i	−0.778907	−	0.627140i	$-0.784226\pi$
$233$	−2.31662	+	2.31662i	−0.151767	+	0.151767i	0.627140	+	0.778907i	$0.284226\pi$
$234$	20.9499			1.36954
$235$	−4.31662	+	4.31662i	−0.281586	+	0.281586i
$236$		−	10.6332i		−	0.692166i
$237$	−23.6332			−1.53514
$238$		0			0
$239$	−13.2665			−0.858138			−0.429069	−	0.903272i	$-0.641158\pi$
$239$	−13.2665			−0.858138			−0.429069	+	0.903272i	$0.641158\pi$
$240$		−	4.31662i		−	0.278637i
$241$	−12.6834	+	12.6834i	−0.817008	+	0.817008i	−0.985673	−	0.168665i	$-0.946054\pi$
$241$	−12.6834	+	12.6834i	−0.817008	+	0.817008i	0.168665	+	0.985673i	$0.446054\pi$
$242$	−9.58312			−0.616027
$243$	4.31662	−	4.31662i	0.276912	−	0.276912i
$244$	1.68338	+	1.68338i	0.107767	+	0.107767i
$245$		0			0
$246$		−	5.68338i		−	0.362359i
$247$			14.3166i			0.910945i
$248$	−15.9499	−	15.9499i	−1.01282	−	1.01282i
$249$	10.0000	+	10.0000i	0.633724	+	0.633724i
$250$	8.00000	−	8.00000i	0.505964	−	0.505964i
$251$	17.6834			1.11616			0.558082	−	0.829786i	$-0.311537\pi$
$251$	17.6834			1.11616			0.558082	+	0.829786i	$0.311537\pi$
$252$		0			0
$253$			5.05013i			0.317499i
$254$	10.3166			0.647323
$255$	−4.31662	−	17.2665i	−0.270318	−	1.08127i
$256$	−17.0000			−1.06250
$257$			9.31662i			0.581155i	0.956851	+	0.290578i	$0.0938474\pi$
$257$			9.31662i			0.581155i	−0.956851	+	0.290578i	$0.906153\pi$
$258$	18.6332	−	18.6332i	1.16006	−	1.16006i
$259$		0			0
$260$	−3.31662	+	3.31662i	−0.205688	+	0.205688i
$261$	8.31662	+	8.31662i	0.514786	+	0.514786i
$262$	−9.63325	−	9.63325i	−0.595144	−	0.595144i
$263$			1.68338i			0.103801i	0.998652	+	0.0519007i	$0.0165279\pi$
$263$			1.68338i			0.103801i	−0.998652	+	0.0519007i	$0.983472\pi$
$264$		−	10.8997i		−	0.670833i
$265$	−9.63325	−	9.63325i	−0.591766	−	0.591766i
$266$		0			0
$267$	37.3747	−	37.3747i	2.28729	−	2.28729i
$268$	2.31662			0.141510
$269$	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	$0.208714\pi$
$270$		−	14.3166i		−	0.871282i
$271$	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
$274$		−	9.31662i		−	0.562838i
$275$	2.52506	−	2.52506i	0.152267	−	0.152267i
$276$	12.9499			0.779491
$277$	0.633250	−	0.633250i	0.0380483	−	0.0380483i	−0.687827	−	0.725875i	$-0.741435\pi$
$277$	0.633250	−	0.633250i	0.0380483	−	0.0380483i	0.725875	+	0.687827i	$0.241435\pi$
$278$	0.525063	+	0.525063i	0.0314912	+	0.0314912i
$279$	−33.5831	−	33.5831i	−2.01057	−	2.01057i
$280$		0			0
$281$		−	15.0000i		−	0.894825i	−0.894328	−	0.447412i	$-0.852346\pi$
$281$		−	15.0000i		−	0.894825i	0.894328	−	0.447412i	$-0.147654\pi$
$282$	−9.31662	−	9.31662i	−0.554797	−	0.554797i
$283$	15.4248	+	15.4248i	0.916910	+	0.916910i	0.996803	−	0.0798935i	$-0.0254580\pi$
$283$	15.4248	+	15.4248i	0.916910	+	0.916910i	−0.0798935	+	0.996803i	$0.525458\pi$
$284$	0.158312	−	0.158312i	0.00939411	−	0.00939411i
$285$	18.6332			1.10374
$286$	2.79156	−	2.79156i	0.165069	−	0.165069i
$287$		0			0
$288$	−31.5831			−1.86105
$289$	15.0000	−	8.00000i	0.882353	−	0.470588i
$290$	2.63325			0.154630
$291$		−	38.6332i		−	2.26472i
$292$	5.00000	−	5.00000i	0.292603	−	0.292603i
$293$	27.5330			1.60849			0.804247	−	0.594295i	$-0.202569\pi$
$293$	27.5330			1.60849			0.804247	+	0.594295i	$0.202569\pi$
$294$		0			0
$295$	−10.6332	−	10.6332i	−0.619092	−	0.619092i
$296$	19.8997	+	19.8997i	1.15665	+	1.15665i
$297$		−	12.0501i		−	0.699219i
$298$			1.00000i			0.0579284i
$299$	9.94987	+	9.94987i	0.575416	+	0.575416i
$300$	−6.47494	−	6.47494i	−0.373831	−	0.373831i
$301$		0			0
$302$	19.5831			1.12688
$303$	−14.3166	+	14.3166i	−0.822469	+	0.822469i
$304$			4.31662i			0.247575i
$305$	3.36675			0.192780
$306$	25.2665	−	6.31662i	1.44439	−	0.361097i
$307$	−7.05013			−0.402372			−0.201186	−	0.979553i	$-0.564480\pi$
$307$	−7.05013			−0.402372			−0.201186	+	0.979553i	$0.564480\pi$
$308$		0			0
$309$	−13.6332	+	13.6332i	−0.775568	+	0.775568i
$310$	−10.6332			−0.603928
$311$	−10.4749	+	10.4749i	−0.593979	+	0.593979i	−0.938704	−	0.344725i	$-0.887972\pi$
$311$	−10.4749	+	10.4749i	−0.593979	+	0.593979i	0.344725	+	0.938704i	$0.387972\pi$
$312$	−21.4749	−	21.4749i	−1.21578	−	1.21578i
$313$	5.94987	+	5.94987i	0.336307	+	0.336307i	0.854975	−	0.518669i	$-0.173572\pi$
$313$	5.94987	+	5.94987i	0.336307	+	0.336307i	−0.518669	+	0.854975i	$0.673572\pi$
$314$			16.2665i			0.917972i
$315$		0			0
$316$	5.47494	+	5.47494i	0.307989	+	0.307989i
$317$	−16.3166	−	16.3166i	−0.916433	−	0.916433i	0.0803350	−	0.996768i	$-0.474401\pi$
$317$	−16.3166	−	16.3166i	−0.916433	−	0.916433i	−0.996768	+	0.0803350i	$0.974401\pi$
$318$	20.7916	−	20.7916i	1.16593	−	1.16593i
$319$	2.21637			0.124093
$320$	−7.00000	+	7.00000i	−0.391312	+	0.391312i
$321$			37.9499i			2.11816i
$322$		0			0
$323$	4.31662	+	17.2665i	0.240183	+	0.960734i
$324$	−11.9499			−0.663882
$325$		−	9.94987i		−	0.551920i
$326$	−3.63325	+	3.63325i	−0.201227	+	0.201227i
$327$	−27.2665			−1.50784
$328$	−3.94987	+	3.94987i	−0.218095	+	0.218095i
$329$		0			0
$330$	−3.63325	−	3.63325i	−0.200004	−	0.200004i
$331$		−	20.0000i		−	1.09930i	−0.835395	−	0.549650i	$-0.814761\pi$
$331$		−	20.0000i		−	1.09930i	0.835395	−	0.549650i	$-0.185239\pi$
$332$		−	4.63325i		−	0.254283i
$333$	41.8997	+	41.8997i	2.29609	+	2.29609i
$334$	3.15831	+	3.15831i	0.172815	+	0.172815i
$335$	2.31662	−	2.31662i	0.126571	−	0.126571i
$336$		0			0
$337$	−22.6332	+	22.6332i	−1.23291	+	1.23291i	−0.270071	+	0.962840i	$0.587047\pi$
$337$	−22.6332	+	22.6332i	−1.23291	+	1.23291i	−0.962840	+	0.270071i	$0.912953\pi$
$338$			2.00000i			0.108786i
$339$	−27.2665			−1.48091
$340$	−3.00000	+	5.00000i	−0.162698	+	0.271163i
$341$	−8.94987			−0.484663
$342$			27.2665i			1.47440i
$343$		0			0
$344$	−25.8997			−1.39642
$345$	12.9499	−	12.9499i	0.697198	−	0.697198i
$346$	−4.00000	−	4.00000i	−0.215041	−	0.215041i
$347$	−8.36675	−	8.36675i	−0.449151	−	0.449151i	0.445921	−	0.895072i	$-0.352876\pi$
$347$	−8.36675	−	8.36675i	−0.449151	−	0.449151i	−0.895072	+	0.445921i	$0.852876\pi$
$348$		−	5.68338i		−	0.304661i
$349$			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
$351$	−23.7414	−	23.7414i	−1.26722	−	1.26722i
$352$	−4.20844	+	4.20844i	−0.224311	+	0.224311i
$353$	25.0000			1.33062			0.665308	−	0.746569i	$-0.268300\pi$
$353$	25.0000			1.33062			0.665308	+	0.746569i	$0.268300\pi$
$354$	22.9499	−	22.9499i	1.21977	−	1.21977i
$355$		−	0.316625i		−	0.0168047i
$356$	−17.3166			−0.917779
$357$		0			0
$358$	12.6332			0.667688
$359$		−	7.89975i		−	0.416933i	−0.978030	−	0.208466i	$-0.933153\pi$
$359$		−	7.89975i		−	0.416933i	0.978030	−	0.208466i	$-0.0668472\pi$
$360$	−18.9499	+	18.9499i	−0.998746	+	0.998746i
$361$	0.366750			0.0193027
$362$	−5.68338	+	5.68338i	−0.298712	+	0.298712i
$363$	20.6834	+	20.6834i	1.08560	+	1.08560i
$364$		0			0
$365$		−	10.0000i		−	0.523424i
$366$			7.26650i			0.379826i
$367$	5.15831	+	5.15831i	0.269262	+	0.269262i	0.828803	−	0.559541i	$-0.189023\pi$
$367$	5.15831	+	5.15831i	0.269262	+	0.269262i	−0.559541	+	0.828803i	$0.689023\pi$
$368$	3.00000	+	3.00000i	0.156386	+	0.156386i
$369$	−8.31662	+	8.31662i	−0.432946	+	0.432946i
$370$	13.2665			0.689692
$371$		0			0
$372$			22.9499i			1.18990i
$373$	2.58312			0.133749			0.0668745	−	0.997761i	$-0.478697\pi$
$373$	2.58312			0.133749			0.0668745	+	0.997761i	$0.478697\pi$
$374$	2.52506	−	4.20844i	0.130568	−	0.217613i
$375$	−34.5330			−1.78328
$376$			12.9499i			0.667839i
$377$	4.36675	−	4.36675i	0.224899	−	0.224899i
$378$		0			0
$379$	−10.4749	+	10.4749i	−0.538061	+	0.538061i	−0.922959	−	0.384898i	$-0.874237\pi$
$379$	−10.4749	+	10.4749i	−0.538061	+	0.538061i	0.384898	+	0.922959i	$0.374237\pi$
$380$	−4.31662	−	4.31662i	−0.221438	−	0.221438i
$381$	−22.2665	−	22.2665i	−1.14075	−	1.14075i
$382$			19.2665i			0.985760i
$383$			10.6332i			0.543334i	0.962391	+	0.271667i	$0.0875749\pi$
$383$			10.6332i			0.543334i	−0.962391	+	0.271667i	$0.912425\pi$
$384$	6.47494	+	6.47494i	0.330423	+	0.330423i
$385$		0			0
$386$	−8.94987	+	8.94987i	−0.455537	+	0.455537i
$387$	−54.5330			−2.77207
$388$	−8.94987	+	8.94987i	−0.454361	+	0.454361i
$389$		−	38.5831i		−	1.95624i	−0.208037	−	0.978121i	$-0.566707\pi$
$389$		−	38.5831i		−	1.95624i	0.208037	−	0.978121i	$-0.433293\pi$
$390$	−14.3166			−0.724950
$391$	15.0000	+	9.00000i	0.758583	+	0.455150i
$392$		0			0
$393$			41.5831i			2.09759i
$394$	2.68338	−	2.68338i	0.135186	−	0.135186i
$395$	10.9499			0.550948
$396$	−5.31662	+	5.31662i	−0.267170	+	0.267170i
$397$	−17.8997	−	17.8997i	−0.898363	−	0.898363i	0.0969287	−	0.995291i	$-0.469098\pi$
$397$	−17.8997	−	17.8997i	−0.898363	−	0.898363i	−0.995291	+	0.0969287i	$0.969098\pi$
$398$	−11.4749	−	11.4749i	−0.575187	−	0.575187i
$399$		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
$403$	−17.6332	+	17.6332i	−0.878375	+	0.878375i
$404$	6.63325			0.330017
$405$	−11.9499	+	11.9499i	−0.593794	+	0.593794i
$406$		0			0
$407$	11.1662			0.553490
$408$	−32.3747	−	19.4248i	−1.60279	−	0.961671i
$409$	6.26650			0.309858			0.154929	−	0.987926i	$-0.450485\pi$
$409$	6.26650			0.309858			0.154929	+	0.987926i	$0.450485\pi$
$410$			2.63325i			0.130047i
$411$	−20.1082	+	20.1082i	−0.991864	+	0.991864i
$412$	6.31662			0.311198
$413$		0			0
$414$	18.9499	+	18.9499i	0.931336	+	0.931336i
$415$	−4.63325	−	4.63325i	−0.227437	−	0.227437i
$416$			16.5831i			0.813055i
$417$		−	2.26650i		−	0.110991i
$418$	3.63325	+	3.63325i	0.177708	+	0.177708i
$419$	−5.15831	−	5.15831i	−0.252000	−	0.252000i	0.569790	−	0.821790i	$-0.307024\pi$
$419$	−5.15831	−	5.15831i	−0.252000	−	0.252000i	−0.821790	+	0.569790i	$0.807024\pi$
$420$		0			0
$421$	30.6332			1.49297			0.746487	−	0.665400i	$-0.231739\pi$
$421$	30.6332			1.49297			0.746487	+	0.665400i	$0.231739\pi$
$422$	9.63325	−	9.63325i	0.468939	−	0.468939i
$423$			27.2665i			1.32574i
$424$	−28.8997			−1.40350
$425$	−3.00000	−	12.0000i	−0.145521	−	0.582086i
$426$	0.683375			0.0331096
$427$		0			0
$428$	8.79156	−	8.79156i	0.424956	−	0.424956i
$429$	−12.0501			−0.581786
$430$	−8.63325	+	8.63325i	−0.416332	+	0.416332i
$431$	−5.52506	−	5.52506i	−0.266133	−	0.266133i	0.561407	−	0.827540i	$-0.310260\pi$
$431$	−5.52506	−	5.52506i	−0.266133	−	0.266133i	−0.827540	+	0.561407i	$0.810260\pi$
$432$	−7.15831	−	7.15831i	−0.344404	−	0.344404i
$433$			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
$435$	−5.68338	−	5.68338i	−0.272497	−	0.272497i
$436$	6.31662	+	6.31662i	0.302511	+	0.302511i
$437$	−12.9499	+	12.9499i	−0.619477	+	0.619477i
$438$	21.5831			1.03128
$439$	25.4248	−	25.4248i	1.21346	−	1.21346i	0.243579	−	0.969881i	$-0.421678\pi$
$439$	25.4248	−	25.4248i	1.21346	−	1.21346i	0.969881	−	0.243579i	$-0.0783215\pi$
$440$			5.05013i			0.240755i
$441$		0			0
$442$	−3.31662	−	13.2665i	−0.157756	−	0.631023i
$443$	25.8997			1.23053			0.615267	−	0.788319i	$-0.289048\pi$
$443$	25.8997			1.23053			0.615267	+	0.788319i	$0.289048\pi$
$444$		−	28.6332i		−	1.35887i
$445$	−17.3166	+	17.3166i	−0.820887	+	0.820887i
$446$		0			0
$447$	2.15831	−	2.15831i	0.102085	−	0.102085i
$448$		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	$0.847098\pi$
$450$		−	18.9499i		−	0.893306i
$451$			2.21637i			0.104365i
$452$	6.31662	+	6.31662i	0.297109	+	0.297109i
$453$	−42.2665	−	42.2665i	−1.98585	−	1.98585i
$454$	2.20844	−	2.20844i	0.103647	−	0.103647i
$455$		0			0
$456$	27.9499	−	27.9499i	1.30887	−	1.30887i
$457$		−	10.6332i		−	0.497402i	−0.968580	−	0.248701i	$-0.919996\pi$
$457$		−	10.6332i		−	0.497402i	0.968580	−	0.248701i	$-0.0800037\pi$
$458$	−0.733501			−0.0342742
$459$	−35.7916	−	21.4749i	−1.67061	−	1.00236i
$460$	−6.00000			−0.279751
$461$			6.36675i			0.296529i	0.988948	+	0.148265i	$0.0473687\pi$
$461$			6.36675i			0.296529i	−0.988948	+	0.148265i	$0.952631\pi$
$462$		0			0
$463$	3.58312			0.166522			0.0832609	−	0.996528i	$-0.473467\pi$
$463$	3.58312			0.166522			0.0832609	+	0.996528i	$0.473467\pi$
$464$	1.31662	−	1.31662i	0.0611228	−	0.0611228i
$465$	22.9499	+	22.9499i	1.06427	+	1.06427i
$466$	2.31662	+	2.31662i	0.107316	+	0.107316i
$467$			13.6834i			0.633191i	0.948561	+	0.316596i	$0.102540\pi$
$467$			13.6834i			0.633191i	−0.948561	+	0.316596i	$0.897460\pi$
$468$			20.9499i			0.968408i
$469$		0			0
$470$	4.31662	+	4.31662i	0.199111	+	0.199111i
$471$	35.1082	−	35.1082i	1.61770	−	1.61770i
$472$	−31.8997			−1.46830
$473$	−7.26650	+	7.26650i	−0.334114	+	0.334114i
$474$			23.6332i			1.08551i
$475$	12.9499			0.594181
$476$		0			0
$477$	−60.8496			−2.78611
$478$			13.2665i			0.606796i
$479$	16.2665	−	16.2665i	0.743235	−	0.743235i	−0.229964	−	0.973199i	$-0.573861\pi$
$479$	16.2665	−	16.2665i	0.743235	−	0.743235i	0.973199	+	0.229964i	$0.0738608\pi$
$480$	21.5831			0.985130
$481$	22.0000	−	22.0000i	1.00311	−	1.00311i
$482$	12.6834	+	12.6834i	0.577712	+	0.577712i
$483$		0			0
$484$		−	9.58312i		−	0.435597i
$485$			17.8997i			0.812786i
$486$	−4.31662	−	4.31662i	−0.195806	−	0.195806i
$487$	12.5251	+	12.5251i	0.567565	+	0.567565i	0.931446	−	0.363881i	$-0.118548\pi$
$487$	12.5251	+	12.5251i	0.567565	+	0.567565i	−0.363881	+	0.931446i	$0.618548\pi$
$488$	5.05013	−	5.05013i	0.228608	−	0.228608i
$489$	15.6834			0.709227
$490$		0			0
$491$			3.58312i			0.161704i	0.996726	+	0.0808521i	$0.0257641\pi$
$491$			3.58312i			0.161704i	−0.996726	+	0.0808521i	$0.974236\pi$
$492$	5.68338			0.256226
$493$	3.94987	−	6.58312i	0.177893	−	0.296489i
$494$	14.3166			0.644135
$495$			10.6332i			0.477929i
$496$	−5.31662	+	5.31662i	−0.238724	+	0.238724i
$497$		0			0
$498$	10.0000	−	10.0000i	0.448111	−	0.448111i
$499$	2.79156	+	2.79156i	0.124967	+	0.124967i	0.766824	−	0.641857i	$-0.221836\pi$
$499$	2.79156	+	2.79156i	0.124967	+	0.124967i	−0.641857	+	0.766824i	$0.721836\pi$
$500$	8.00000	+	8.00000i	0.357771	+	0.357771i
$501$		−	13.6332i		−	0.609089i
$502$		−	17.6834i		−	0.789248i
$503$	3.42481	+	3.42481i	0.152705	+	0.152705i	0.779325	−	0.626620i	$-0.215562\pi$
$503$	3.42481	+	3.42481i	0.152705	+	0.152705i	−0.626620	+	0.779325i	$0.715562\pi$
$504$		0			0
$505$	6.63325	−	6.63325i	0.295176	−	0.295176i
$506$	5.05013			0.224505
$507$	4.31662	−	4.31662i	0.191708	−	0.191708i
$508$			10.3166i			0.457726i
$509$	31.1662			1.38142			0.690710	−	0.723132i	$-0.257298\pi$
$509$	31.1662			1.38142			0.690710	+	0.723132i	$0.257298\pi$
$510$	−17.2665	+	4.31662i	−0.764573	+	0.191143i
$511$		0			0
$512$			11.0000i			0.486136i
$513$	30.8997	−	30.8997i	1.36426	−	1.36426i
$514$	9.31662			0.410939
$515$	6.31662	−	6.31662i	0.278344	−	0.278344i
$516$	18.6332	+	18.6332i	0.820283	+	0.820283i
$517$	3.63325	+	3.63325i	0.159790	+	0.159790i
$518$		0			0
$519$			17.2665i			0.757915i
$520$	9.94987	+	9.94987i	0.436331	+	0.436331i
$521$	6.26650	+	6.26650i	0.274540	+	0.274540i	0.830925	−	0.556385i	$-0.187812\pi$
$521$	6.26650	+	6.26650i	0.274540	+	0.274540i	−0.556385	+	0.830925i	$0.687812\pi$
$522$	8.31662	−	8.31662i	0.364009	−	0.364009i
$523$	7.89975			0.345432			0.172716	−	0.984972i	$-0.444746\pi$
$523$	7.89975			0.345432			0.172716	+	0.984972i	$0.444746\pi$
$524$	9.63325	−	9.63325i	0.420830	−	0.420830i
$525$		0			0
$526$	1.68338			0.0733986
$527$	−15.9499	+	26.5831i	−0.694787	+	1.15798i
$528$	−3.63325			−0.158117
$529$		−	5.00000i		−	0.217391i
$530$	−9.63325	+	9.63325i	−0.418442	+	0.418442i
$531$	−67.1662			−2.91477
$532$		0			0
$533$	4.36675	+	4.36675i	0.189145	+	0.189145i
$534$	−37.3747	−	37.3747i	−1.61736	−	1.61736i
$535$		−	17.5831i		−	0.760185i
$536$		−	6.94987i		−	0.300189i
$537$	−27.2665	−	27.2665i	−1.17664	−	1.17664i
$538$	−3.00000	−	3.00000i	−0.129339	−	0.129339i
$539$		0			0
$540$	14.3166			0.616089
$541$	−4.94987	+	4.94987i	−0.212812	+	0.212812i	−0.805461	−	0.592649i	$-0.798082\pi$
$541$	−4.94987	+	4.94987i	−0.212812	+	0.212812i	0.592649	+	0.805461i	$0.298082\pi$
$542$		−	2.00000i		−	0.0859074i
$543$	24.5330			1.05281
$544$	5.00000	+	20.0000i	0.214373	+	0.857493i
$545$	12.6332			0.541149
$546$		0			0
$547$	−3.79156	+	3.79156i	−0.162115	+	0.162115i	−0.783503	−	0.621388i	$-0.786569\pi$
$547$	−3.79156	+	3.79156i	−0.162115	+	0.162115i	0.621388	+	0.783503i	$0.286569\pi$
$548$	9.31662			0.397986
$549$	10.6332	−	10.6332i	0.453816	−	0.453816i
$550$	−2.52506	−	2.52506i	−0.107669	−	0.107669i
$551$	5.68338	+	5.68338i	0.242120	+	0.242120i
$552$		−	38.8496i		−	1.65355i
$553$		0			0
$554$	−0.633250	−	0.633250i	−0.0269042	−	0.0269042i
$555$	−28.6332	−	28.6332i	−1.21541	−	1.21541i
$556$	−0.525063	+	0.525063i	−0.0222676	+	0.0222676i
$557$	−42.4829			−1.80006			−0.900029	−	0.435831i	$-0.856455\pi$
$557$	−42.4829			−1.80006			−0.900029	+	0.435831i	$0.856455\pi$
$558$	−33.5831	+	33.5831i	−1.42169	+	1.42169i
$559$			28.6332i			1.21106i
$560$		0			0
$561$	−14.5330	+	3.63325i	−0.613584	+	0.153396i
$562$	−15.0000			−0.632737
$563$		−	37.1662i		−	1.56637i	−0.621788	−	0.783185i	$-0.713594\pi$
$563$		−	37.1662i		−	1.56637i	0.621788	−	0.783185i	$-0.286406\pi$
$564$	9.31662	−	9.31662i	0.392301	−	0.392301i
$565$	12.6332			0.531485
$566$	15.4248	−	15.4248i	0.648353	−	0.648353i
$567$		0			0
$568$	−0.474937	−	0.474937i	−0.0199279	−	0.0199279i
$569$			19.0000i			0.796521i	0.917272	+	0.398261i	$0.130386\pi$
$569$			19.0000i			0.796521i	−0.917272	+	0.398261i	$0.869614\pi$
$570$		−	18.6332i		−	0.780461i
$571$	−26.5831	−	26.5831i	−1.11247	−	1.11247i	−0.992816	−	0.119653i	$-0.961822\pi$
$571$	−26.5831	−	26.5831i	−1.11247	−	1.11247i	−0.119653	−	0.992816i	$-0.538178\pi$
$572$	2.79156	+	2.79156i	0.116721	+	0.116721i
$573$	41.5831	−	41.5831i	1.73716	−	1.73716i
$574$		0			0
$575$	9.00000	−	9.00000i	0.375326	−	0.375326i
$576$			44.2164i			1.84235i
$577$	−10.5831			−0.440581			−0.220291	−	0.975434i	$-0.570701\pi$
$577$	−10.5831			−0.440581			−0.220291	+	0.975434i	$0.570701\pi$
$578$	−8.00000	−	15.0000i	−0.332756	−	0.623918i
$579$	38.6332			1.60554
$580$			2.63325i			0.109340i
$581$		0			0
$582$	−38.6332			−1.60140
$583$	−8.10819	+	8.10819i	−0.335807	+	0.335807i
$584$	−15.0000	−	15.0000i	−0.620704	−	0.620704i
$585$	20.9499	+	20.9499i	0.866171	+	0.866171i
$586$		−	27.5330i		−	1.13738i
$587$		−	40.9499i		−	1.69018i	−0.534622	−	0.845091i	$-0.679546\pi$
$587$		−	40.9499i		−	1.69018i	0.534622	−	0.845091i	$-0.320454\pi$
$588$		0			0
$589$	−22.9499	−	22.9499i	−0.945633	−	0.945633i
$590$	−10.6332	+	10.6332i	−0.437764	+	0.437764i
$591$	−11.5831			−0.476466
$592$	6.63325	−	6.63325i	0.272625	−	0.272625i
$593$		−	16.2665i		−	0.667985i	−0.942576	−	0.333993i	$-0.891604\pi$
$593$		−	16.2665i		−	0.667985i	0.942576	−	0.333993i	$-0.108396\pi$
$594$	−12.0501			−0.494423
$595$		0			0
$596$	−1.00000			−0.0409616
$597$			49.5330i			2.02725i
$598$	9.94987	−	9.94987i	0.406881	−	0.406881i
$599$	22.6332			0.924770			0.462385	−	0.886679i	$-0.346994\pi$
$599$	22.6332			0.924770			0.462385	+	0.886679i	$0.346994\pi$
$600$	−19.4248	+	19.4248i	−0.793015	+	0.793015i
$601$	23.9499	+	23.9499i	0.976936	+	0.976936i	0.999740	−	0.0228042i	$-0.00725943\pi$
$601$	23.9499	+	23.9499i	0.976936	+	0.976936i	−0.0228042	+	0.999740i	$0.507259\pi$
$602$		0			0
$603$		−	14.6332i		−	0.595912i
$604$			19.5831i			0.796826i
$605$	−9.58312	−	9.58312i	−0.389609	−	0.389609i
$606$	14.3166	+	14.3166i	0.581573	+	0.581573i
$607$	28.4248	−	28.4248i	1.15373	−	1.15373i	0.167928	−	0.985799i	$-0.446292\pi$
$607$	28.4248	−	28.4248i	1.15373	−	1.15373i	0.985799	−	0.167928i	$-0.0537077\pi$
$608$	−21.5831			−0.875311
$609$		0			0
$610$		−	3.36675i		−	0.136316i
$611$	14.3166			0.579189
$612$	6.31662	+	25.2665i	0.255334	+	1.02134i
$613$	32.2665			1.30323			0.651616	−	0.758549i	$-0.274091\pi$
$613$	32.2665			1.30323			0.651616	+	0.758549i	$0.274091\pi$
$614$			7.05013i			0.284520i
$615$	5.68338	−	5.68338i	0.229176	−	0.229176i
$616$		0			0
$617$	15.9499	−	15.9499i	0.642118	−	0.642118i	−0.308958	−	0.951076i	$-0.599980\pi$
$617$	15.9499	−	15.9499i	0.642118	−	0.642118i	0.951076	+	0.308958i	$0.0999802\pi$
$618$	13.6332	+	13.6332i	0.548410	+	0.548410i
$619$	−5.84169	−	5.84169i	−0.234797	−	0.234797i	0.579894	−	0.814692i	$-0.303094\pi$
$619$	−5.84169	−	5.84169i	−0.234797	−	0.234797i	−0.814692	+	0.579894i	$0.803094\pi$
$620$		−	10.6332i		−	0.427042i
$621$		−	42.9499i		−	1.72352i
$622$	10.4749	+	10.4749i	0.420007	+	0.420007i
$623$		0			0
$624$	−7.15831	+	7.15831i	−0.286562	+	0.286562i
$625$	1.00000			0.0400000
$626$	5.94987	−	5.94987i	0.237805	−	0.237805i
$627$		−	15.6834i		−	0.626334i
$628$	−16.2665			−0.649104
$629$	19.8997	−	33.1662i	0.793455	−	1.32242i
$630$		0			0
$631$		−	27.3668i		−	1.08945i	−0.838614	−	0.544727i	$-0.816633\pi$
$631$		−	27.3668i		−	1.08945i	0.838614	−	0.544727i	$-0.183367\pi$
$632$	16.4248	−	16.4248i	0.653344	−	0.653344i
$633$	−41.5831			−1.65278
$634$	−16.3166	+	16.3166i	−0.648016	+	0.648016i
$635$	10.3166	+	10.3166i	0.409403	+	0.409403i
$636$	20.7916	+	20.7916i	0.824439	+	0.824439i
$637$		0			0
$638$		−	2.21637i		−	0.0877471i
$639$	−1.00000	−	1.00000i	−0.0395594	−	0.0395594i
$640$	−3.00000	−	3.00000i	−0.118585	−	0.118585i
$641$	−16.6834	+	16.6834i	−0.658954	+	0.658954i	−0.955133	−	0.296179i	$-0.904288\pi$
$641$	−16.6834	+	16.6834i	−0.658954	+	0.658954i	0.296179	+	0.955133i	$0.404288\pi$
$642$	37.9499			1.49776
$643$	−9.89181	+	9.89181i	−0.390095	+	0.390095i	−0.874721	−	0.484626i	$-0.838956\pi$
$643$	−9.89181	+	9.89181i	−0.390095	+	0.390095i	0.484626	+	0.874721i	$0.338956\pi$
$644$		0			0
$645$	37.2665			1.46737
$646$	17.2665	−	4.31662i	0.679341	−	0.169835i
$647$	18.6332			0.732549			0.366274	−	0.930507i	$-0.380633\pi$
$647$	18.6332			0.732549			0.366274	+	0.930507i	$0.380633\pi$
$648$			35.8496i			1.40831i
$649$	−8.94987	+	8.94987i	−0.351313	+	0.351313i
$650$	−9.94987			−0.390266
$651$		0			0
$652$	−3.63325	−	3.63325i	−0.142289	−	0.142289i
$653$	−11.5831	−	11.5831i	−0.453283	−	0.453283i	0.443160	−	0.896443i	$-0.353857\pi$
$653$	−11.5831	−	11.5831i	−0.453283	−	0.453283i	−0.896443	+	0.443160i	$0.853857\pi$
$654$			27.2665i			1.06620i
$655$		−	19.2665i		−	0.752804i
$656$	1.31662	+	1.31662i	0.0514056	+	0.0514056i
$657$	−31.5831	−	31.5831i	−1.23218	−	1.23218i
$658$		0			0
$659$	−6.00000			−0.233727			−0.116863	−	0.993148i	$-0.537284\pi$
$659$	−6.00000			−0.233727			−0.116863	+	0.993148i	$0.537284\pi$
$660$	3.63325	−	3.63325i	0.141424	−	0.141424i
$661$		−	14.5330i		−	0.565268i	−0.959228	−	0.282634i	$-0.908792\pi$
$661$		−	14.5330i		−	0.565268i	0.959228	−	0.282634i	$-0.0912082\pi$
$662$	−20.0000			−0.777322
$663$	−21.4749	+	35.7916i	−0.834017	+	1.39003i
$664$	−13.8997			−0.539415
$665$		0			0
$666$	41.8997	−	41.8997i	1.62358	−	1.62358i
$667$	7.89975			0.305879
$668$	−3.15831	+	3.15831i	−0.122199	+	0.122199i
$669$		0			0
$670$	−2.31662	−	2.31662i	−0.0894990	−	0.0894990i
$671$		−	2.83375i		−	0.109396i
$672$		0			0
$673$	27.9499	+	27.9499i	1.07739	+	1.07739i	0.996743	+	0.0806456i	$0.0256982\pi$
$673$	27.9499	+	27.9499i	1.07739	+	1.07739i	0.0806456	+	0.996743i	$0.474302\pi$
$674$	22.6332	+	22.6332i	0.871800	+	0.871800i
$675$	−21.4749	+	21.4749i	−0.826571	+	0.826571i
$676$	−2.00000			−0.0769231
$677$	−8.36675	+	8.36675i	−0.321560	+	0.321560i	−0.849365	−	0.527805i	$-0.823015\pi$
$677$	−8.36675	+	8.36675i	−0.321560	+	0.321560i	0.527805	+	0.849365i	$0.323015\pi$
$678$			27.2665i			1.04716i
$679$		0			0
$680$	15.0000	+	9.00000i	0.575224	+	0.345134i
$681$	−9.53300			−0.365305
$682$			8.94987i			0.342708i
$683$	7.47494	−	7.47494i	0.286021	−	0.286021i	−0.549484	−	0.835504i	$-0.685176\pi$
$683$	7.47494	−	7.47494i	0.286021	−	0.286021i	0.835504	+	0.549484i	$0.185176\pi$
$684$	−27.2665			−1.04256
$685$	9.31662	−	9.31662i	0.355970	−	0.355970i
$686$		0			0
$687$	1.58312	+	1.58312i	0.0603999	+	0.0603999i
$688$			8.63325i			0.329140i
$689$			31.9499i			1.21719i
$690$	−12.9499	−	12.9499i	−0.492993	−	0.492993i
$691$	0.366750	+	0.366750i	0.0139518	+	0.0139518i	0.714048	−	0.700096i	$-0.246860\pi$
$691$	0.366750	+	0.366750i	0.0139518	+	0.0139518i	−0.700096	+	0.714048i	$0.746860\pi$
$692$	4.00000	−	4.00000i	0.152057	−	0.152057i
$693$		0			0
$694$	−8.36675	+	8.36675i	−0.317598	+	0.317598i
$695$			1.05013i			0.0398335i
$696$	−17.0501			−0.646283
$697$	6.58312	+	3.94987i	0.249354	+	0.149612i
$698$	16.0000			0.605609
$699$		−	10.0000i		−	0.378235i
$700$		0			0
$701$	35.2164			1.33010			0.665052	−	0.746797i	$-0.268409\pi$
$701$	35.2164			1.33010			0.665052	+	0.746797i	$0.268409\pi$
$702$	−23.7414	+	23.7414i	−0.896063	+	0.896063i
$703$	28.6332	+	28.6332i	1.07992	+	1.07992i
$704$	5.89181	+	5.89181i	0.222056	+	0.222056i
$705$		−	18.6332i		−	0.701769i
$706$		−	25.0000i		−	0.940887i
$707$		0			0
$708$	22.9499	+	22.9499i	0.862509	+	0.862509i
$709$	23.3166	−	23.3166i	0.875674	−	0.875674i	−0.117409	−	0.993084i	$-0.537459\pi$
$709$	23.3166	−	23.3166i	0.875674	−	0.875674i	0.993084	+	0.117409i	$0.0374590\pi$
$710$	−0.316625			−0.0118827
$711$	34.5831	−	34.5831i	1.29697	−	1.29697i
$712$			51.9499i			1.94690i
$713$	−31.8997			−1.19465
$714$		0			0
$715$	5.58312			0.208797
$716$			12.6332i			0.472127i
$717$	28.6332	−	28.6332i	1.06933	−	1.06933i
$718$	−7.89975			−0.294816
$719$	−5.79156	+	5.79156i	−0.215989	+	0.215989i	−0.806806	−	0.590817i	$-0.798806\pi$
$719$	−5.79156	+	5.79156i	−0.215989	+	0.215989i	0.590817	+	0.806806i	$0.298806\pi$
$720$	6.31662	+	6.31662i	0.235407	+	0.235407i
$721$		0			0
$722$		−	0.366750i		−	0.0136490i
$723$		−	54.7494i		−	2.03615i
$724$	−5.68338	−	5.68338i	−0.211221	−	0.211221i
$725$	−3.94987	−	3.94987i	−0.146695	−	0.146695i
$726$	20.6834	−	20.6834i	0.767632	−	0.767632i
$727$	−40.6332			−1.50700			−0.753502	−	0.657446i	$-0.771637\pi$
$727$	−40.6332			−1.50700			−0.753502	+	0.657446i	$0.771637\pi$
$728$		0			0
$729$		−	17.2164i		−	0.637643i
$730$	−10.0000			−0.370117
$731$	8.63325	+	34.5330i	0.319312	+	1.27725i
$732$	−7.26650			−0.268578
$733$			10.2665i			0.379202i	0.981861	+	0.189601i	$0.0607194\pi$
$733$			10.2665i			0.379202i	−0.981861	+	0.189601i	$0.939281\pi$
$734$	5.15831	−	5.15831i	0.190397	−	0.190397i
$735$		0			0
$736$	−15.0000	+	15.0000i	−0.552907	+	0.552907i
$737$	−1.94987	−	1.94987i	−0.0718245	−	0.0718245i
$738$	8.31662	+	8.31662i	0.306139	+	0.306139i
$739$		−	37.2665i		−	1.37087i	−0.728134	−	0.685435i	$-0.759612\pi$
$739$		−	37.2665i		−	1.37087i	0.728134	−	0.685435i	$-0.240388\pi$
$740$			13.2665i			0.487686i
$741$	−30.8997	−	30.8997i	−1.13513	−	1.13513i
$742$		0			0
$743$	−15.0581	+	15.0581i	−0.552427	+	0.552427i	−0.927141	−	0.374714i	$-0.877741\pi$
$743$	−15.0581	+	15.0581i	−0.552427	+	0.552427i	0.374714	+	0.927141i	$0.377741\pi$
$744$	68.8496			2.52415
$745$	−1.00000	+	1.00000i	−0.0366372	+	0.0366372i
$746$		−	2.58312i		−	0.0945749i
$747$	−29.2665			−1.07081
$748$	4.20844	+	2.52506i	0.153876	+	0.0923254i
$749$		0			0
$750$			34.5330i			1.26097i
$751$	−9.74144	+	9.74144i	−0.355470	+	0.355470i	−0.862140	−	0.506670i	$-0.830876\pi$
$751$	−9.74144	+	9.74144i	−0.355470	+	0.355470i	0.506670	+	0.862140i	$0.330876\pi$
$752$	4.31662			0.157411
$753$	−38.1662	+	38.1662i	−1.39086	+	1.39086i
$754$	−4.36675	−	4.36675i	−0.159028	−	0.159028i
$755$	19.5831	+	19.5831i	0.712703	+	0.712703i
$756$		0			0
$757$		−	11.3166i		−	0.411310i	−0.978625	−	0.205655i	$-0.934068\pi$
$757$		−	11.3166i		−	0.411310i	0.978625	−	0.205655i	$-0.0659324\pi$
$758$	10.4749	+	10.4749i	0.380467	+	0.380467i
$759$	−10.8997	−	10.8997i	−0.395636	−	0.395636i
$760$	−12.9499	+	12.9499i	−0.469741	+	0.469741i
$761$	−34.5831			−1.25364			−0.626819	−	0.779165i	$-0.715643\pi$
$761$	−34.5831			−1.25364			−0.626819	+	0.779165i	$0.715643\pi$
$762$	−22.2665	+	22.2665i	−0.806630	+	0.806630i
$763$		0			0
$764$	−19.2665			−0.697037
$765$	31.5831	+	18.9499i	1.14189	+	0.685134i
$766$	10.6332			0.384195
$767$			35.2665i			1.27340i
$768$	36.6913	−	36.6913i	1.32398	−	1.32398i
$769$	−9.41688			−0.339581			−0.169791	−	0.985480i	$-0.554309\pi$
$769$	−9.41688			−0.339581			−0.169791	+	0.985480i	$0.554309\pi$
$770$		0			0
$771$	−20.1082	−	20.1082i	−0.724179	−	0.724179i
$772$	−8.94987	−	8.94987i	−0.322113	−	0.322113i
$773$		−	38.5831i		−	1.38774i	−0.720101	−	0.693869i	$-0.755905\pi$
$773$		−	38.5831i		−	1.38774i	0.720101	−	0.693869i	$-0.244095\pi$
$774$			54.5330i			1.96015i
$775$	15.9499	+	15.9499i	0.572936	+	0.572936i
$776$	26.8496	+	26.8496i	0.963845	+	0.963845i
$777$		0			0
$778$	−38.5831			−1.38327
$779$	−5.68338	+	5.68338i	−0.203628	+	0.203628i
$780$		−	14.3166i		−	0.512617i
$781$	−0.266499			−0.00953609
$782$	9.00000	−	15.0000i	0.321839	−	0.536399i
$783$	−18.8496			−0.673631
$784$		0			0
$785$	−16.2665	+	16.2665i	−0.580576	+	0.580576i
$786$	41.5831			1.48322
$787$	24.3668	−	24.3668i	0.868581	−	0.868581i	−0.123735	−	0.992315i	$-0.539487\pi$
$787$	24.3668	−	24.3668i	0.868581	−	0.868581i	0.992315	+	0.123735i	$0.0394871\pi$
$788$	2.68338	+	2.68338i	0.0955913	+	0.0955913i
$789$	−3.63325	−	3.63325i	−0.129347	−	0.129347i
$790$		−	10.9499i		−	0.389579i
$791$		0			0
$792$	15.9499	+	15.9499i	0.566754	+	0.566754i
$793$	−5.58312	−	5.58312i	−0.198263	−	0.198263i
$794$	−17.8997	+	17.8997i	−0.635238	+	0.635238i
$795$	41.5831			1.47480
$796$	11.4749	−	11.4749i	0.406718	−	0.406718i
$797$		−	6.89975i		−	0.244402i	−0.992505	−	0.122201i	$-0.961005\pi$
$797$		−	6.89975i		−	0.244402i	0.992505	−	0.122201i	$-0.0389952\pi$
$798$		0			0
$799$	17.2665	−	4.31662i	0.610845	−	0.152711i
$800$	15.0000			0.530330
$801$			109.383i			3.86484i
$802$	−18.0000	+	18.0000i	−0.635602	+	0.635602i
$803$	−8.41688			−0.297025
$804$	−5.00000	+	5.00000i	−0.176336	+	0.176336i
$805$		0			0
$806$	17.6332	+	17.6332i	0.621105	+	0.621105i
$807$			12.9499i			0.455857i
$808$		−	19.8997i		−	0.700071i
$809$	36.8997	+	36.8997i	1.29733	+	1.29733i	0.930152	+	0.367174i	$0.119675\pi$
$809$	36.8997	+	36.8997i	1.29733	+	1.29733i	0.367174	+	0.930152i	$0.380325\pi$
$810$	11.9499	+	11.9499i	0.419876	+	0.419876i
$811$	−5.10819	+	5.10819i	−0.179373	+	0.179373i	−0.791082	−	0.611710i	$-0.790482\pi$
$811$	−5.10819	+	5.10819i	−0.179373	+	0.179373i	0.611710	+	0.791082i	$0.290482\pi$
$812$		0			0
$813$	−4.31662	+	4.31662i	−0.151391	+	0.151391i
$814$		−	11.1662i		−	0.391377i
$815$	−7.26650			−0.254534
$816$	−6.47494	+	10.7916i	−0.226668	+	0.377780i
$817$	−37.2665			−1.30379
$818$		−	6.26650i		−	0.219103i
$819$		0			0
$820$	−2.63325			−0.0919571
$821$	−20.6332	+	20.6332i	−0.720105	+	0.720105i	−0.968626	−	0.248521i	$-0.920055\pi$
$821$	−20.6332	+	20.6332i	−0.720105	+	0.720105i	0.248521	+	0.968626i	$0.420055\pi$
$822$	20.1082	+	20.1082i	0.701354	+	0.701354i
$823$	−18.0581	−	18.0581i	−0.629464	−	0.629464i	0.318469	−	0.947933i	$-0.396831\pi$
$823$	−18.0581	−	18.0581i	−0.629464	−	0.629464i	−0.947933	+	0.318469i	$0.896831\pi$
$824$		−	18.9499i		−	0.660150i
$825$			10.8997i			0.379481i
$826$		0			0
$827$	−15.0581	−	15.0581i	−0.523620	−	0.523620i	0.395043	−	0.918663i	$-0.370730\pi$
$827$	−15.0581	−	15.0581i	−0.523620	−	0.523620i	−0.918663	+	0.395043i	$0.870730\pi$
$828$	−18.9499	+	18.9499i	−0.658554	+	0.658554i
$829$	16.8997			0.586953			0.293476	−	0.955966i	$-0.405188\pi$
$829$	16.8997			0.586953			0.293476	+	0.955966i	$0.405188\pi$
$830$	−4.63325	+	4.63325i	−0.160822	+	0.160822i
$831$			2.73350i			0.0948241i
$832$	23.2164			0.804883
$833$		0			0
$834$	−2.26650			−0.0784824
$835$			6.31662i			0.218596i
$836$	−3.63325	+	3.63325i	−0.125659	+	0.125659i
$837$	76.1161			2.63096
$838$	−5.15831	+	5.15831i	−0.178191	+	0.178191i
$839$	−10.0501	−	10.0501i	−0.346969	−	0.346969i	0.512010	−	0.858979i	$-0.328901\pi$
$839$	−10.0501	−	10.0501i	−0.346969	−	0.346969i	−0.858979	+	0.512010i	$0.828901\pi$
$840$		0			0
$841$			25.5330i			0.880448i
$842$		−	30.6332i		−	1.05569i
$843$	32.3747	+	32.3747i	1.11504	+	1.11504i
$844$	9.63325	+	9.63325i	0.331590	+	0.331590i
$845$	−2.00000	+	2.00000i	−0.0688021	+	0.0688021i
$846$	27.2665			0.937442
$847$		0			0
$848$			9.63325i			0.330807i
$849$	−66.5831			−2.28513
$850$	−12.0000	+	3.00000i	−0.411597	+	0.102899i
$851$	39.7995			1.36431
$852$			0.683375i			0.0234120i
$853$	29.6332	−	29.6332i	1.01462	−	1.01462i	0.0147317	−	0.999891i	$-0.495311\pi$
$853$	29.6332	−	29.6332i	1.01462	−	1.01462i	0.999891	−	0.0147317i	$-0.00468940\pi$
$854$		0			0
$855$	−27.2665	+	27.2665i	−0.932495	+	0.932495i
$856$	−26.3747	−	26.3747i	−0.901468	−	0.901468i
$857$	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	$0.571668\pi$
$858$			12.0501i			0.411385i
$859$			1.68338i			0.0574360i	0.999588	+	0.0287180i	$0.00914248\pi$
$859$			1.68338i			0.0574360i	−0.999588	+	0.0287180i	$0.990858\pi$
$860$	−8.63325	−	8.63325i	−0.294391	−	0.294391i
$861$		0			0
$862$	−5.52506	+	5.52506i	−0.188184	+	0.188184i
$863$	39.1662			1.33323			0.666617	−	0.745400i	$-0.267742\pi$
$863$	39.1662			1.33323			0.666617	+	0.745400i	$0.267742\pi$
$864$	35.7916	−	35.7916i	1.21765	−	1.21765i
$865$		−	8.00000i		−	0.272008i
$866$	2.00000			0.0679628
$867$	−15.1082	+	49.6412i	−0.513101	+	1.68590i
$868$		0			0
$869$		−	9.21637i		−	0.312644i
$870$	−5.68338	+	5.68338i	−0.192684	+	0.192684i
$871$	−7.68338			−0.260341
$872$	18.9499	−	18.9499i	0.641724	−	0.641724i
$873$	56.5330	+	56.5330i	1.91335	+	1.91335i
$874$	12.9499	+	12.9499i	0.438036	+	0.438036i
$875$		0			0
$876$			21.5831i			0.729226i
$877$	6.68338	+	6.68338i	0.225682	+	0.225682i	0.810886	−	0.585204i	$-0.198986\pi$
$877$	6.68338	+	6.68338i	0.225682	+	0.225682i	−0.585204	+	0.810886i	$0.698986\pi$
$878$	−25.4248	−	25.4248i	−0.858046	−	0.858046i
$879$	−59.4248	+	59.4248i	−2.00435	+	2.00435i
$880$	1.68338			0.0567466
$881$	−19.8997	+	19.8997i	−0.670440	+	0.670440i	−0.957817	−	0.287378i	$-0.907216\pi$
$881$	−19.8997	+	19.8997i	−0.670440	+	0.670440i	0.287378	+	0.957817i	$0.407216\pi$
$882$		0			0
$883$	−13.8997			−0.467764			−0.233882	−	0.972265i	$-0.575143\pi$
$883$	−13.8997			−0.467764			−0.233882	+	0.972265i	$0.575143\pi$
$884$	13.2665	−	3.31662i	0.446201	−	0.111550i
$885$	45.8997			1.54290
$886$		−	25.8997i		−	0.870119i
$887$	12.8417	−	12.8417i	0.431182	−	0.431182i	−0.457849	−	0.889030i	$-0.651380\pi$
$887$	12.8417	−	12.8417i	0.431182	−	0.431182i	0.889030	+	0.457849i	$0.151380\pi$
$888$	−85.8997			−2.88261
$889$		0			0
$890$	17.3166	+	17.3166i	0.580455	+	0.580455i
$891$	10.0581	+	10.0581i	0.336958	+	0.336958i
$892$		0			0
$893$			18.6332i			0.623538i
$894$	−2.15831	−	2.15831i	−0.0721848	−	0.0721848i
$895$	12.6332	+	12.6332i	0.422283	+	0.422283i
$896$		0			0
$897$	−42.9499			−1.43405
$898$	−9.00000	+	9.00000i	−0.300334	+	0.300334i
$899$			14.0000i			0.466926i
$900$	18.9499			0.631662
$901$	9.63325	+	38.5330i	0.320930	+	1.28372i
$902$	2.21637			0.0737972
$903$		0			0
$904$	18.9499	−	18.9499i	0.630263	−	0.630263i
$905$	−11.3668			−0.377844
$906$	−42.2665	+	42.2665i	−1.40421	+	1.40421i
$907$	4.58312	+	4.58312i	0.152180	+	0.152180i	0.779091	−	0.626911i	$-0.215681\pi$
$907$	4.58312	+	4.58312i	0.152180	+	0.152180i	−0.626911	+	0.779091i	$0.715681\pi$
$908$	2.20844	+	2.20844i	0.0732896	+	0.0732896i
$909$		−	41.8997i		−	1.38973i
$910$		0			0
$911$	−21.9499	−	21.9499i	−0.727232	−	0.727232i	0.242836	−	0.970067i	$-0.421922\pi$
$911$	−21.9499	−	21.9499i	−0.727232	−	0.727232i	−0.970067	+	0.242836i	$0.921922\pi$
$912$	−9.31662	−	9.31662i	−0.308504	−	0.308504i
$913$	−3.89975	+	3.89975i	−0.129063	+	0.129063i
$914$	−10.6332			−0.351717
$915$	−7.26650	+	7.26650i	−0.240223	+	0.240223i
$916$		−	0.733501i		−	0.0242355i
$917$		0			0
$918$	−21.4749	+	35.7916i	−0.708779	+	1.18130i
$919$	33.4829			1.10450			0.552249	−	0.833679i	$-0.313770\pi$
$919$	33.4829			1.10450			0.552249	+	0.833679i	$0.313770\pi$
$920$			18.0000i			0.593442i
$921$	15.2164	−	15.2164i	0.501397	−	0.501397i
$922$	6.36675			0.209678
$923$	−0.525063	+	0.525063i	−0.0172827	+	0.0172827i
$924$		0			0
$925$	−19.8997	−	19.8997i	−0.654300	−	0.654300i
$926$		−	3.58312i		−	0.117749i
$927$		−	39.8997i		−	1.31048i
$928$	6.58312	+	6.58312i	0.216102	+	0.216102i
$929$	−17.3166	−	17.3166i	−0.568140	−	0.568140i	0.363467	−	0.931607i	$-0.381593\pi$
$929$	−17.3166	−	17.3166i	−0.568140	−	0.568140i	−0.931607	+	0.363467i	$0.881593\pi$
$930$	22.9499	−	22.9499i	0.752556	−	0.752556i
$931$		0			0
$932$	−2.31662	+	2.31662i	−0.0758836	+	0.0758836i
$933$		−	45.2164i		−	1.48032i
$934$	13.6834			0.447734
$935$	6.73350	−	1.68338i	0.220209	−	0.0550523i
$936$	62.8496			2.05430
$937$		−	27.7995i		−	0.908170i	−0.890958	−	0.454085i	$-0.849966\pi$
$937$		−	27.7995i		−	0.908170i	0.890958	−	0.454085i	$-0.150034\pi$
$938$		0			0
$939$	−25.6834			−0.838145
$940$	−4.31662	+	4.31662i	−0.140793	+	0.140793i
$941$	−9.63325	−	9.63325i	−0.314035	−	0.314035i	0.532436	−	0.846471i	$-0.321277\pi$
$941$	−9.63325	−	9.63325i	−0.314035	−	0.314035i	−0.846471	+	0.532436i	$0.821277\pi$
$942$	−35.1082	−	35.1082i	−1.14389	−	1.14389i
$943$			7.89975i			0.257251i
$944$			10.6332i			0.346083i
$945$		0			0
$946$	7.26650	+	7.26650i	0.236254	+	0.236254i
$947$	−5.42481	+	5.42481i	−0.176283	+	0.176283i	−0.789733	−	0.613450i	$-0.789781\pi$
$947$	−5.42481	+	5.42481i	−0.176283	+	0.176283i	0.613450	+	0.789733i	$0.289781\pi$
$948$	−23.6332			−0.767572
$949$	−16.5831	+	16.5831i	−0.538311	+	0.538311i
$950$		−	12.9499i		−	0.420149i
$951$	70.4327			2.28394
$952$		0			0
$953$	53.7494			1.74111			0.870556	−	0.492069i	$-0.163759\pi$
$953$	53.7494			1.74111			0.870556	+	0.492069i	$0.163759\pi$
$954$			60.8496i			1.97008i
$955$	−19.2665	+	19.2665i	−0.623449	+	0.623449i
$956$	−13.2665			−0.429069
$957$	−4.78363	+	4.78363i	−0.154633	+	0.154633i
$958$	−16.2665	−	16.2665i	−0.525547	−	0.525547i
$959$		0			0
$960$		−	30.2164i		−	0.975229i
$961$		−	25.5330i		−	0.823645i
$962$	−22.0000	−	22.0000i	−0.709308	−	0.709308i
$963$	−55.5330	−	55.5330i	−1.78953	−	1.78953i
$964$	−12.6834	+	12.6834i	−0.408504	+	0.408504i
$965$	−17.8997			−0.576213
$966$		0			0
$967$		−	7.58312i		−	0.243857i	−0.992539	−	0.121928i	$-0.961092\pi$
$967$		−	7.58312i		−	0.243857i	0.992539	−	0.121928i	$-0.0389078\pi$
$968$	−28.7494			−0.924040
$969$	−46.5831	−	27.9499i	−1.49647	−	0.897879i
$970$	17.8997			0.574726
$971$			50.2164i			1.61152i	0.592242	+	0.805760i	$0.298243\pi$
$971$			50.2164i			1.61152i	−0.592242	+	0.805760i	$0.701757\pi$
$972$	4.31662	−	4.31662i	0.138456	−	0.138456i
$973$		0			0
$974$	12.5251	−	12.5251i	0.401329	−	0.401329i
$975$	21.4749	+	21.4749i	0.687748	+	0.687748i
$976$	−1.68338	−	1.68338i	−0.0538835	−	0.0538835i
$977$			55.1662i			1.76492i	0.470383	+	0.882462i	$0.344116\pi$
$977$			55.1662i			1.76492i	−0.470383	+	0.882462i	$0.655884\pi$
$978$		−	15.6834i		−	0.501499i
$979$	14.5752	+	14.5752i	0.465825	+	0.465825i
$980$		0			0
$981$	39.8997	−	39.8997i	1.27390	−	1.27390i
$982$	3.58312			0.114342
$983$	−43.4248	+	43.4248i	−1.38504	+	1.38504i	−0.549625	+	0.835412i	$0.685229\pi$
$983$	−43.4248	+	43.4248i	−1.38504	+	1.38504i	−0.835412	+	0.549625i	$0.814771\pi$
$984$		−	17.0501i		−	0.543538i
$985$	5.36675			0.170999
$986$	−6.58312	−	3.94987i	−0.209649	−	0.125790i
$987$		0			0
$988$			14.3166i			0.455473i
$989$	−25.8997	+	25.8997i	−0.823564	+	0.823564i
$990$	10.6332			0.337947
$991$	37.1583	−	37.1583i	1.18037	−	1.18037i	0.200725	−	0.979648i	$-0.435670\pi$
$991$	37.1583	−	37.1583i	1.18037	−	1.18037i	0.979648	−	0.200725i	$-0.0643298\pi$
$992$	−26.5831	−	26.5831i	−0.844015	−	0.844015i
$993$	43.1662	+	43.1662i	1.36984	+	1.36984i
$994$		0			0
$995$		−	22.9499i		−	0.727560i
$996$	10.0000	+	10.0000i	0.316862	+	0.316862i
$997$	9.31662	+	9.31662i	0.295060	+	0.295060i	0.839075	−	0.544015i	$-0.183097\pi$
$997$	9.31662	+	9.31662i	0.295060	+	0.295060i	−0.544015	+	0.839075i	$0.683097\pi$
$998$	2.79156	−	2.79156i	0.0883654	−	0.0883654i
$999$	−94.9657			−3.00458

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.g.c.344.1		4
7.2	even	3		833.2.o.c.361.1		8
7.3	odd	6		119.2.n.a.72.1	yes	8
7.4	even	3		833.2.o.c.667.2		8
7.5	odd	6		119.2.n.a.4.2	✓	8
7.6	odd	2		833.2.g.d.344.2		4
17.13	even	4	inner	833.2.g.c.540.1		4
119.13	odd	4		833.2.g.d.540.2		4
119.30	even	12		833.2.o.c.557.2		8
119.47	odd	12		119.2.n.a.81.1	yes	8
119.81	even	12		833.2.o.c.30.1		8
119.115	odd	12		119.2.n.a.30.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.2.n.a.4.2	✓	8	7.5	odd	6
119.2.n.a.30.2	yes	8	119.115	odd	12
119.2.n.a.72.1	yes	8	7.3	odd	6
119.2.n.a.81.1	yes	8	119.47	odd	12
833.2.g.c.344.1		4	1.1	even	1	trivial
833.2.g.c.540.1		4	17.13	even	4	inner
833.2.g.d.344.2		4	7.6	odd	2
833.2.g.d.540.2		4	119.13	odd	4
833.2.o.c.30.1		8	119.81	even	12
833.2.o.c.361.1		8	7.2	even	3
833.2.o.c.557.2		8	119.30	even	12
833.2.o.c.667.2		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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-2.15831 + 2.15831i) q^{3} +1.00000 q^{4} +(1.00000 - 1.00000i) q^{5} +(2.15831 + 2.15831i) q^{6} -3.00000i q^{8} -6.31662i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-2.15831 + 2.15831i) q^{3} +1.00000 q^{4} +(1.00000 - 1.00000i) q^{5} +(2.15831 + 2.15831i) q^{6} -3.00000i q^{8} -6.31662i q^{9} +(-1.00000 - 1.00000i) q^{10} +(-0.841688 - 0.841688i) q^{11} +(-2.15831 + 2.15831i) q^{12} -3.31662 q^{13} +4.31662i q^{15} -1.00000 q^{16} +(-4.00000 + 1.00000i) q^{17} -6.31662 q^{18} -4.31662i q^{19} +(1.00000 - 1.00000i) q^{20} +(-0.841688 + 0.841688i) q^{22} +(-3.00000 - 3.00000i) q^{23} +(6.47494 + 6.47494i) q^{24} +3.00000i q^{25} +3.31662i q^{26} +(7.15831 + 7.15831i) q^{27} +(-1.31662 + 1.31662i) q^{29} +4.31662 q^{30} +(5.31662 - 5.31662i) q^{31} -5.00000i q^{32} +3.63325 q^{33} +(1.00000 + 4.00000i) q^{34} -6.31662i q^{36} +(-6.63325 + 6.63325i) q^{37} -4.31662 q^{38} +(7.15831 - 7.15831i) q^{39} +(-3.00000 - 3.00000i) q^{40} +(-1.31662 - 1.31662i) q^{41} -8.63325i q^{43} +(-0.841688 - 0.841688i) q^{44} +(-6.31662 - 6.31662i) q^{45} +(-3.00000 + 3.00000i) q^{46} -4.31662 q^{47} +(2.15831 - 2.15831i) q^{48} +3.00000 q^{50} +(6.47494 - 10.7916i) q^{51} -3.31662 q^{52} -9.63325i q^{53} +(7.15831 - 7.15831i) q^{54} -1.68338 q^{55} +(9.31662 + 9.31662i) q^{57} +(1.31662 + 1.31662i) q^{58} -10.6332i q^{59} +4.31662i q^{60} +(1.68338 + 1.68338i) q^{61} +(-5.31662 - 5.31662i) q^{62} -7.00000 q^{64} +(-3.31662 + 3.31662i) q^{65} -3.63325i q^{66} +2.31662 q^{67} +(-4.00000 + 1.00000i) q^{68} +12.9499 q^{69} +(0.158312 - 0.158312i) q^{71} -18.9499 q^{72} +(5.00000 - 5.00000i) q^{73} +(6.63325 + 6.63325i) q^{74} +(-6.47494 - 6.47494i) q^{75} -4.31662i q^{76} +(-7.15831 - 7.15831i) q^{78} +(5.47494 + 5.47494i) q^{79} +(-1.00000 + 1.00000i) q^{80} -11.9499 q^{81} +(-1.31662 + 1.31662i) q^{82} -4.63325i q^{83} +(-3.00000 + 5.00000i) q^{85} -8.63325 q^{86} -5.68338i q^{87} +(-2.52506 + 2.52506i) q^{88} -17.3166 q^{89} +(-6.31662 + 6.31662i) q^{90} +(-3.00000 - 3.00000i) q^{92} +22.9499i q^{93} +4.31662i q^{94} +(-4.31662 - 4.31662i) q^{95} +(10.7916 + 10.7916i) q^{96} +(-8.94987 + 8.94987i) q^{97} +(-5.31662 + 5.31662i) 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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