LMFDB - Embedded newform 1014.3.f.h.775.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,3,Mod(577,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1014.577");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1014.f (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:	$27.6294988061$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 82x^{5} + 5053x^{4} - 6736x^{3} + 6728x^{2} + 275384x + 5635876 $ x^8 - 2x^7 + 2x^6 + 82x^5 + 5053x^4 - 6736x^3 + 6728x^2 + 275384*x + 5635876
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			775.1
Root			$5.02578 + 5.02578i$ of defining polynomial
Character	$\chi$	$=$	1014.775
Dual form			1014.3.f.h.577.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} -1.73205 q^{3} +2.00000i q^{4} +(-6.39181 - 6.39181i) q^{5} +(1.73205 + 1.73205i) q^{6} +(-6.75784 + 6.75784i) q^{7} +(2.00000 - 2.00000i) q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} -1.73205 q^{3} +2.00000i q^{4} +(-6.39181 - 6.39181i) q^{5} +(1.73205 + 1.73205i) q^{6} +(-6.75784 + 6.75784i) q^{7} +(2.00000 - 2.00000i) q^{8} +3.00000 q^{9} +12.7836i q^{10} +(11.5157 - 11.5157i) q^{11} -3.46410i q^{12} +13.5157 q^{14} +(11.0709 + 11.0709i) q^{15} -4.00000 q^{16} +9.60634i q^{17} +(-3.00000 - 3.00000i) q^{18} +(6.99865 + 6.99865i) q^{19} +(12.7836 - 12.7836i) q^{20} +(11.7049 - 11.7049i) q^{21} -23.0313 q^{22} +27.3583i q^{23} +(-3.46410 + 3.46410i) q^{24} +56.7105i q^{25} -5.19615 q^{27} +(-13.5157 - 13.5157i) q^{28} +27.6046 q^{29} -22.1419i q^{30} +(11.5613 + 11.5613i) q^{31} +(4.00000 + 4.00000i) q^{32} +(-19.9457 + 19.9457i) q^{33} +(9.60634 - 9.60634i) q^{34} +86.3896 q^{35} +6.00000i q^{36} +(-14.9065 + 14.9065i) q^{37} -13.9973i q^{38} -25.5672 q^{40} +(-28.6254 - 28.6254i) q^{41} -23.4098 q^{42} -35.6912i q^{43} +(23.0313 + 23.0313i) q^{44} +(-19.1754 - 19.1754i) q^{45} +(27.3583 - 27.3583i) q^{46} +(25.5184 - 25.5184i) q^{47} +6.92820 q^{48} -42.3367i q^{49} +(56.7105 - 56.7105i) q^{50} -16.6387i q^{51} -39.0697 q^{53} +(5.19615 + 5.19615i) q^{54} -147.212 q^{55} +27.0313i q^{56} +(-12.1220 - 12.1220i) q^{57} +(-27.6046 - 27.6046i) q^{58} +(33.6963 - 33.6963i) q^{59} +(-22.1419 + 22.1419i) q^{60} +70.5433 q^{61} -23.1226i q^{62} +(-20.2735 + 20.2735i) q^{63} -8.00000i q^{64} +39.8915 q^{66} +(-28.3486 - 28.3486i) q^{67} -19.2127 q^{68} -47.3859i q^{69} +(-86.3896 - 86.3896i) q^{70} +(-22.6245 - 22.6245i) q^{71} +(6.00000 - 6.00000i) q^{72} +(-9.68320 + 9.68320i) q^{73} +29.8130 q^{74} -98.2254i q^{75} +(-13.9973 + 13.9973i) q^{76} +155.642i q^{77} -56.1543 q^{79} +(25.5672 + 25.5672i) q^{80} +9.00000 q^{81} +57.2507i q^{82} +(4.59931 + 4.59931i) q^{83} +(23.4098 + 23.4098i) q^{84} +(61.4019 - 61.4019i) q^{85} +(-35.6912 + 35.6912i) q^{86} -47.8126 q^{87} -46.0627i q^{88} +(81.8193 - 81.8193i) q^{89} +38.3509i q^{90} -54.7165 q^{92} +(-20.0248 - 20.0248i) q^{93} -51.0367 q^{94} -89.4681i q^{95} +(-6.92820 - 6.92820i) q^{96} +(-24.7045 - 24.7045i) q^{97} +(-42.3367 + 42.3367i) q^{98} +(34.5470 - 34.5470i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 6 q^{5} - 2 q^{7} + 16 q^{8} + 24 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 - 6 * q^5 - 2 * q^7 + 16 * q^8 + 24 * q^9	$ 8 q - 8 q^{2} - 6 q^{5} - 2 q^{7} + 16 q^{8} + 24 q^{9} - 12 q^{11} + 4 q^{14} + 6 q^{15} - 32 q^{16} - 24 q^{18} - 44 q^{19} + 12 q^{20} + 18 q^{21} + 24 q^{22} - 4 q^{28} - 72 q^{29} - 94 q^{31} + 32 q^{32} - 36 q^{33} + 60 q^{34} + 408 q^{35} - 46 q^{37} - 24 q^{40} - 30 q^{41} - 36 q^{42} - 24 q^{44} - 18 q^{45} + 144 q^{46} + 300 q^{47} + 208 q^{50} + 84 q^{53} - 792 q^{55} + 24 q^{57} + 72 q^{58} - 12 q^{59} - 12 q^{60} + 180 q^{61} - 6 q^{63} + 72 q^{66} - 74 q^{67} - 120 q^{68} - 408 q^{70} + 156 q^{71} + 48 q^{72} + 16 q^{73} + 92 q^{74} + 88 q^{76} - 96 q^{79} + 24 q^{80} + 72 q^{81} + 36 q^{84} + 234 q^{85} + 168 q^{86} - 60 q^{87} + 228 q^{89} - 288 q^{92} - 198 q^{93} - 600 q^{94} + 2 q^{97} - 32 q^{98} - 36 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 - 6 * q^5 - 2 * q^7 + 16 * q^8 + 24 * q^9 - 12 * q^11 + 4 * q^14 + 6 * q^15 - 32 * q^16 - 24 * q^18 - 44 * q^19 + 12 * q^20 + 18 * q^21 + 24 * q^22 - 4 * q^28 - 72 * q^29 - 94 * q^31 + 32 * q^32 - 36 * q^33 + 60 * q^34 + 408 * q^35 - 46 * q^37 - 24 * q^40 - 30 * q^41 - 36 * q^42 - 24 * q^44 - 18 * q^45 + 144 * q^46 + 300 * q^47 + 208 * q^50 + 84 * q^53 - 792 * q^55 + 24 * q^57 + 72 * q^58 - 12 * q^59 - 12 * q^60 + 180 * q^61 - 6 * q^63 + 72 * q^66 - 74 * q^67 - 120 * q^68 - 408 * q^70 + 156 * q^71 + 48 * q^72 + 16 * q^73 + 92 * q^74 + 88 * q^76 - 96 * q^79 + 24 * q^80 + 72 * q^81 + 36 * q^84 + 234 * q^85 + 168 * q^86 - 60 * q^87 + 228 * q^89 - 288 * q^92 - 198 * q^93 - 600 * q^94 + 2 * q^97 - 32 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$			2.00000i			0.500000i
$5$	−6.39181	−	6.39181i	−1.27836	−	1.27836i	−0.941584	−	0.336778i	$-0.890663\pi$
$5$	−6.39181	−	6.39181i	−1.27836	−	1.27836i	−0.336778	−	0.941584i	$-0.609337\pi$
$6$	1.73205	+	1.73205i	0.288675	+	0.288675i
$7$	−6.75784	+	6.75784i	−0.965405	+	0.965405i	−0.999421	−	0.0340162i	$-0.989170\pi$
$7$	−6.75784	+	6.75784i	−0.965405	+	0.965405i	0.0340162	+	0.999421i	$0.489170\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$	3.00000			0.333333
$10$			12.7836i			1.27836i
$11$	11.5157	−	11.5157i	1.04688	−	1.04688i	0.0480334	−	0.998846i	$-0.484705\pi$
$11$	11.5157	−	11.5157i	1.04688	−	1.04688i	0.998846	−	0.0480334i	$-0.0152954\pi$
$12$		−	3.46410i		−	0.288675i
$13$		0			0
$13$		0			0
$14$	13.5157			0.965405
$15$	11.0709	+	11.0709i	0.738063	+	0.738063i
$16$	−4.00000			−0.250000
$17$			9.60634i			0.565079i	0.959256	+	0.282540i	$0.0911768\pi$
$17$			9.60634i			0.565079i	−0.959256	+	0.282540i	$0.908823\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$	6.99865	+	6.99865i	0.368350	+	0.368350i	0.866875	−	0.498525i	$-0.166125\pi$
$19$	6.99865	+	6.99865i	0.368350	+	0.368350i	−0.498525	+	0.866875i	$0.666125\pi$
$20$	12.7836	−	12.7836i	0.639181	−	0.639181i
$21$	11.7049	−	11.7049i	0.557377	−	0.557377i
$22$	−23.0313			−1.04688
$23$			27.3583i			1.18949i	0.803915	+	0.594745i	$0.202747\pi$
$23$			27.3583i			1.18949i	−0.803915	+	0.594745i	$0.797253\pi$
$24$	−3.46410	+	3.46410i	−0.144338	+	0.144338i
$25$			56.7105i			2.26842i
$26$		0			0
$27$	−5.19615			−0.192450
$28$	−13.5157	−	13.5157i	−0.482703	−	0.482703i
$29$	27.6046			0.951884			0.475942	−	0.879477i	$-0.342107\pi$
$29$	27.6046			0.951884			0.475942	+	0.879477i	$0.342107\pi$
$30$		−	22.1419i		−	0.738063i
$31$	11.5613	+	11.5613i	0.372946	+	0.372946i	0.868549	−	0.495603i	$-0.165053\pi$
$31$	11.5613	+	11.5613i	0.372946	+	0.372946i	−0.495603	+	0.868549i	$0.665053\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	−19.9457	+	19.9457i	−0.604416	+	0.604416i
$34$	9.60634	−	9.60634i	0.282540	−	0.282540i
$35$	86.3896			2.46827
$36$			6.00000i			0.166667i
$37$	−14.9065	+	14.9065i	−0.402878	+	0.402878i	−0.879246	−	0.476368i	$-0.841953\pi$
$37$	−14.9065	+	14.9065i	−0.402878	+	0.402878i	0.476368	+	0.879246i	$0.341953\pi$
$38$		−	13.9973i		−	0.368350i
$39$		0			0
$40$	−25.5672			−0.639181
$41$	−28.6254	−	28.6254i	−0.698179	−	0.698179i	0.265838	−	0.964018i	$-0.414351\pi$
$41$	−28.6254	−	28.6254i	−0.698179	−	0.698179i	−0.964018	+	0.265838i	$0.914351\pi$
$42$	−23.4098			−0.557377
$43$		−	35.6912i		−	0.830029i	−0.909815	−	0.415014i	$-0.863777\pi$
$43$		−	35.6912i		−	0.830029i	0.909815	−	0.415014i	$-0.136223\pi$
$44$	23.0313	+	23.0313i	0.523440	+	0.523440i
$45$	−19.1754	−	19.1754i	−0.426121	−	0.426121i
$46$	27.3583	−	27.3583i	0.594745	−	0.594745i
$47$	25.5184	−	25.5184i	0.542944	−	0.542944i	−0.381447	−	0.924391i	$-0.624574\pi$
$47$	25.5184	−	25.5184i	0.542944	−	0.542944i	0.924391	+	0.381447i	$0.124574\pi$
$48$	6.92820			0.144338
$49$		−	42.3367i		−	0.864014i
$50$	56.7105	−	56.7105i	1.13421	−	1.13421i
$51$		−	16.6387i		−	0.326249i
$52$		0			0
$53$	−39.0697			−0.737165			−0.368582	−	0.929595i	$-0.620157\pi$
$53$	−39.0697			−0.737165			−0.368582	+	0.929595i	$0.620157\pi$
$54$	5.19615	+	5.19615i	0.0962250	+	0.0962250i
$55$	−147.212			−2.67658
$56$			27.0313i			0.482703i
$57$	−12.1220	−	12.1220i	−0.212667	−	0.212667i
$58$	−27.6046	−	27.6046i	−0.475942	−	0.475942i
$59$	33.6963	−	33.6963i	0.571124	−	0.571124i	−0.361319	−	0.932442i	$-0.617673\pi$
$59$	33.6963	−	33.6963i	0.571124	−	0.571124i	0.932442	+	0.361319i	$0.117673\pi$
$60$	−22.1419	+	22.1419i	−0.369031	+	0.369031i
$61$	70.5433			1.15645			0.578224	−	0.815878i	$-0.303746\pi$
$61$	70.5433			1.15645			0.578224	+	0.815878i	$0.303746\pi$
$62$		−	23.1226i		−	0.372946i
$63$	−20.2735	+	20.2735i	−0.321802	+	0.321802i
$64$		−	8.00000i		−	0.125000i
$65$		0			0
$66$	39.8915			0.604416
$67$	−28.3486	−	28.3486i	−0.423114	−	0.423114i	0.463160	−	0.886274i	$-0.346715\pi$
$67$	−28.3486	−	28.3486i	−0.423114	−	0.423114i	−0.886274	+	0.463160i	$0.846715\pi$
$68$	−19.2127			−0.282540
$69$		−	47.3859i		−	0.686752i
$70$	−86.3896	−	86.3896i	−1.23414	−	1.23414i
$71$	−22.6245	−	22.6245i	−0.318655	−	0.318655i	0.529595	−	0.848250i	$-0.322344\pi$
$71$	−22.6245	−	22.6245i	−0.318655	−	0.318655i	−0.848250	+	0.529595i	$0.822344\pi$
$72$	6.00000	−	6.00000i	0.0833333	−	0.0833333i
$73$	−9.68320	+	9.68320i	−0.132647	+	0.132647i	−0.770313	−	0.637666i	$-0.779900\pi$
$73$	−9.68320	+	9.68320i	−0.132647	+	0.132647i	0.637666	+	0.770313i	$0.279900\pi$
$74$	29.8130			0.402878
$75$		−	98.2254i		−	1.30967i
$76$	−13.9973	+	13.9973i	−0.184175	+	0.184175i
$77$			155.642i			2.02132i
$78$		0			0
$79$	−56.1543			−0.710814			−0.355407	−	0.934712i	$-0.615658\pi$
$79$	−56.1543			−0.710814			−0.355407	+	0.934712i	$0.615658\pi$
$80$	25.5672	+	25.5672i	0.319591	+	0.319591i
$81$	9.00000			0.111111
$82$			57.2507i			0.698179i
$83$	4.59931	+	4.59931i	0.0554133	+	0.0554133i	0.734270	−	0.678857i	$-0.237524\pi$
$83$	4.59931	+	4.59931i	0.0554133	+	0.0554133i	−0.678857	+	0.734270i	$0.737524\pi$
$84$	23.4098	+	23.4098i	0.278688	+	0.278688i
$85$	61.4019	−	61.4019i	0.722376	−	0.722376i
$86$	−35.6912	+	35.6912i	−0.415014	+	0.415014i
$87$	−47.8126			−0.549570
$88$		−	46.0627i		−	0.523440i
$89$	81.8193	−	81.8193i	0.919318	−	0.919318i	−0.0776620	−	0.996980i	$-0.524745\pi$
$89$	81.8193	−	81.8193i	0.919318	−	0.919318i	0.996980	+	0.0776620i	$0.0247455\pi$
$90$			38.3509i			0.426121i
$91$		0			0
$92$	−54.7165			−0.594745
$93$	−20.0248	−	20.0248i	−0.215320	−	0.215320i
$94$	−51.0367			−0.542944
$95$		−	89.4681i		−	0.941769i
$96$	−6.92820	−	6.92820i	−0.0721688	−	0.0721688i
$97$	−24.7045	−	24.7045i	−0.254686	−	0.254686i	0.568203	−	0.822889i	$-0.307639\pi$
$97$	−24.7045	−	24.7045i	−0.254686	−	0.254686i	−0.822889	+	0.568203i	$0.807639\pi$
$98$	−42.3367	+	42.3367i	−0.432007	+	0.432007i
$99$	34.5470	−	34.5470i	0.348960	−	0.348960i
$100$	−113.421			−1.13421
$101$			117.169i			1.16009i	0.814584	+	0.580045i	$0.196965\pi$
$101$			117.169i			1.16009i	−0.814584	+	0.580045i	$0.803035\pi$
$102$	−16.6387	+	16.6387i	−0.163124	+	0.163124i
$103$		−	184.178i		−	1.78813i	−0.447933	−	0.894067i	$-0.647840\pi$
$103$		−	184.178i		−	1.78813i	0.447933	−	0.894067i	$-0.352160\pi$
$104$		0			0
$105$	−149.631			−1.42506
$106$	39.0697	+	39.0697i	0.368582	+	0.368582i
$107$	7.15198			0.0668410			0.0334205	−	0.999441i	$-0.489360\pi$
$107$	7.15198			0.0668410			0.0334205	+	0.999441i	$0.489360\pi$
$108$		−	10.3923i		−	0.0962250i
$109$	8.07627	+	8.07627i	0.0740942	+	0.0740942i	0.743183	−	0.669089i	$-0.233315\pi$
$109$	8.07627	+	8.07627i	0.0740942	+	0.0740942i	−0.669089	+	0.743183i	$0.733315\pi$
$110$	147.212	+	147.212i	1.33829	+	1.33829i
$111$	25.8188	−	25.8188i	0.232602	−	0.232602i
$112$	27.0313	−	27.0313i	0.241351	−	0.241351i
$113$	−116.408			−1.03015			−0.515077	−	0.857144i	$-0.672237\pi$
$113$	−116.408			−1.03015			−0.515077	+	0.857144i	$0.672237\pi$
$114$			24.2440i			0.212667i
$115$	174.869	−	174.869i	1.52060	−	1.52060i
$116$			55.2093i			0.475942i
$117$		0			0
$118$	−67.3926			−0.571124
$119$	−64.9181	−	64.9181i	−0.545530	−	0.545530i
$120$	44.2838			0.369031
$121$		−	144.221i		−	1.19191i
$122$	−70.5433	−	70.5433i	−0.578224	−	0.578224i
$123$	49.5806	+	49.5806i	0.403094	+	0.403094i
$124$	−23.1226	+	23.1226i	−0.186473	+	0.186473i
$125$	202.687	−	202.687i	1.62150	−	1.62150i
$126$	40.5470			0.321802
$127$			27.0182i			0.212742i	0.994327	+	0.106371i	$0.0339230\pi$
$127$			27.0182i			0.212742i	−0.994327	+	0.106371i	$0.966077\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$			61.8190i			0.479217i
$130$		0			0
$131$	−64.5682			−0.492887			−0.246444	−	0.969157i	$-0.579262\pi$
$131$	−64.5682			−0.492887			−0.246444	+	0.969157i	$0.579262\pi$
$132$	−39.8915	−	39.8915i	−0.302208	−	0.302208i
$133$	−94.5914			−0.711214
$134$			56.6973i			0.423114i
$135$	33.2128	+	33.2128i	0.246021	+	0.246021i
$136$	19.2127	+	19.2127i	0.141270	+	0.141270i
$137$	−144.369	+	144.369i	−1.05379	+	1.05379i	−0.0553206	+	0.998469i	$0.517618\pi$
$137$	−144.369	+	144.369i	−1.05379	+	1.05379i	−0.998469	+	0.0553206i	$0.982382\pi$
$138$	−47.3859	+	47.3859i	−0.343376	+	0.343376i
$139$	63.6113			0.457635			0.228818	−	0.973469i	$-0.426514\pi$
$139$	63.6113			0.457635			0.228818	+	0.973469i	$0.426514\pi$
$140$			172.779i			1.23414i
$141$	−44.1991	+	44.1991i	−0.313469	+	0.313469i
$142$			45.2490i			0.318655i
$143$		0			0
$144$	−12.0000			−0.0833333
$145$	−176.444	−	176.444i	−1.21685	−	1.21685i
$146$	19.3664			0.132647
$147$			73.3293i			0.498839i
$148$	−29.8130	−	29.8130i	−0.201439	−	0.201439i
$149$	20.5202	+	20.5202i	0.137720	+	0.137720i	0.772606	−	0.634886i	$-0.218953\pi$
$149$	20.5202	+	20.5202i	0.137720	+	0.137720i	−0.634886	+	0.772606i	$0.718953\pi$
$150$	−98.2254	+	98.2254i	−0.654836	+	0.654836i
$151$	31.6350	−	31.6350i	0.209503	−	0.209503i	−0.594553	−	0.804056i	$-0.702671\pi$
$151$	31.6350	−	31.6350i	0.209503	−	0.209503i	0.804056	+	0.594553i	$0.202671\pi$
$152$	27.9946			0.184175
$153$			28.8190i			0.188360i
$154$	155.642	−	155.642i	1.01066	−	1.01066i
$155$		−	147.796i		−	0.953520i
$156$		0			0
$157$	242.423			1.54409			0.772047	−	0.635566i	$-0.219233\pi$
$157$	242.423			1.54409			0.772047	+	0.635566i	$0.219233\pi$
$158$	56.1543	+	56.1543i	0.355407	+	0.355407i
$159$	67.6707			0.425602
$160$		−	51.1345i		−	0.319591i
$161$	−184.883	−	184.883i	−1.14834	−	1.14834i
$162$	−9.00000	−	9.00000i	−0.0555556	−	0.0555556i
$163$	11.0402	−	11.0402i	0.0677314	−	0.0677314i	−0.672430	−	0.740161i	$-0.734749\pi$
$163$	11.0402	−	11.0402i	0.0677314	−	0.0677314i	0.740161	+	0.672430i	$0.234749\pi$
$164$	57.2507	−	57.2507i	0.349090	−	0.349090i
$165$	254.979			1.54532
$166$		−	9.19861i		−	0.0554133i
$167$	35.0077	−	35.0077i	0.209627	−	0.209627i	−0.594482	−	0.804109i	$-0.702643\pi$
$167$	35.0077	−	35.0077i	0.209627	−	0.209627i	0.804109	+	0.594482i	$0.202643\pi$
$168$		−	46.8197i		−	0.278688i
$169$		0			0
$170$	−122.804			−0.722376
$171$	20.9959	+	20.9959i	0.122783	+	0.122783i
$172$	71.3825			0.415014
$173$		−	168.425i		−	0.973553i	−0.873527	−	0.486776i	$-0.838173\pi$
$173$		−	168.425i		−	0.973553i	0.873527	−	0.486776i	$-0.161827\pi$
$174$	47.8126	+	47.8126i	0.274785	+	0.274785i
$175$	−383.240	−	383.240i	−2.18994	−	2.18994i
$176$	−46.0627	+	46.0627i	−0.261720	+	0.261720i
$177$	−58.3637	+	58.3637i	−0.329738	+	0.329738i
$178$	−163.639			−0.919318
$179$		−	313.047i		−	1.74886i	−0.485148	−	0.874432i	$-0.661234\pi$
$179$		−	313.047i		−	1.74886i	0.485148	−	0.874432i	$-0.338766\pi$
$180$	38.3509	−	38.3509i	0.213060	−	0.213060i
$181$		−	19.4795i		−	0.107622i	−0.998551	−	0.0538108i	$-0.982863\pi$
$181$		−	19.4795i		−	0.107622i	0.998551	−	0.0538108i	$-0.0171368\pi$
$182$		0			0
$183$	−122.185			−0.667675
$184$	54.7165	+	54.7165i	0.297372	+	0.297372i
$185$	190.559			1.03005
$186$			40.0496i			0.215320i
$187$	110.623	+	110.623i	0.591569	+	0.591569i
$188$	51.0367	+	51.0367i	0.271472	+	0.271472i
$189$	35.1147	−	35.1147i	0.185792	−	0.185792i
$190$	−89.4681	+	89.4681i	−0.470885	+	0.470885i
$191$	142.951			0.748435			0.374218	−	0.927341i	$-0.377911\pi$
$191$	142.951			0.748435			0.374218	+	0.927341i	$0.377911\pi$
$192$			13.8564i			0.0721688i
$193$	−118.662	+	118.662i	−0.614830	+	0.614830i	−0.944201	−	0.329370i	$-0.893164\pi$
$193$	−118.662	+	118.662i	−0.614830	+	0.614830i	0.329370	+	0.944201i	$0.393164\pi$
$194$			49.4091i			0.254686i
$195$		0			0
$196$	84.6734			0.432007
$197$	−120.481	−	120.481i	−0.611580	−	0.611580i	0.331778	−	0.943358i	$-0.392352\pi$
$197$	−120.481	−	120.481i	−0.611580	−	0.611580i	−0.943358	+	0.331778i	$0.892352\pi$
$198$	−69.0940			−0.348960
$199$			161.726i			0.812693i	0.913719	+	0.406346i	$0.133197\pi$
$199$			161.726i			0.812693i	−0.913719	+	0.406346i	$0.866803\pi$
$200$	113.421	+	113.421i	0.567105	+	0.567105i
$201$	49.1013	+	49.1013i	0.244285	+	0.244285i
$202$	117.169	−	117.169i	0.580045	−	0.580045i
$203$	−186.548	+	186.548i	−0.918953	+	0.918953i
$204$	33.2773			0.163124
$205$			365.936i			1.78505i
$206$	−184.178	+	184.178i	−0.894067	+	0.894067i
$207$			82.0748i			0.396497i
$208$		0			0
$209$	161.188			0.771236
$210$	149.631	+	149.631i	0.712529	+	0.712529i
$211$	−179.875			−0.852490			−0.426245	−	0.904608i	$-0.640164\pi$
$211$	−179.875			−0.852490			−0.426245	+	0.904608i	$0.640164\pi$
$212$		−	78.1394i		−	0.368582i
$213$	39.1868	+	39.1868i	0.183975	+	0.183975i
$214$	−7.15198	−	7.15198i	−0.0334205	−	0.0334205i
$215$	−228.132	+	228.132i	−1.06108	+	1.06108i
$216$	−10.3923	+	10.3923i	−0.0481125	+	0.0481125i
$217$	−156.259			−0.720088
$218$		−	16.1525i		−	0.0740942i
$219$	16.7718	−	16.7718i	0.0765836	−	0.0765836i
$220$		−	294.424i		−	1.33829i
$221$		0			0
$222$	−51.6376			−0.232602
$223$	−275.631	−	275.631i	−1.23602	−	1.23602i	−0.961616	−	0.274399i	$-0.911521\pi$
$223$	−275.631	−	275.631i	−1.23602	−	1.23602i	−0.274399	−	0.961616i	$-0.588479\pi$
$224$	−54.0627			−0.241351
$225$			170.131i			0.756140i
$226$	116.408	+	116.408i	0.515077	+	0.515077i
$227$	94.2749	+	94.2749i	0.415308	+	0.415308i	0.883583	−	0.468275i	$-0.155124\pi$
$227$	94.2749	+	94.2749i	0.415308	+	0.415308i	−0.468275	+	0.883583i	$0.655124\pi$
$228$	24.2440	−	24.2440i	0.106333	−	0.106333i
$229$	−304.866	+	304.866i	−1.33129	+	1.33129i	−0.427077	+	0.904215i	$0.640457\pi$
$229$	−304.866	+	304.866i	−1.33129	+	1.33129i	−0.904215	+	0.427077i	$0.859543\pi$
$230$	−349.738			−1.52060
$231$		−	269.580i		−	1.16701i
$232$	55.2093	−	55.2093i	0.237971	−	0.237971i
$233$			44.1414i			0.189448i	0.995504	+	0.0947240i	$0.0301969\pi$
$233$			44.1414i			0.189448i	−0.995504	+	0.0947240i	$0.969803\pi$
$234$		0			0
$235$	−326.217			−1.38816
$236$	67.3926	+	67.3926i	0.285562	+	0.285562i
$237$	97.2622			0.410389
$238$			129.836i			0.545530i
$239$	−15.8448	−	15.8448i	−0.0662964	−	0.0662964i	0.673181	−	0.739478i	$-0.264927\pi$
$239$	−15.8448	−	15.8448i	−0.0662964	−	0.0662964i	−0.739478	+	0.673181i	$0.764927\pi$
$240$	−44.2838	−	44.2838i	−0.184516	−	0.184516i
$241$	340.106	−	340.106i	1.41123	−	1.41123i	0.659686	−	0.751541i	$-0.270689\pi$
$241$	340.106	−	340.106i	1.41123	−	1.41123i	0.751541	−	0.659686i	$-0.229311\pi$
$242$	−144.221	+	144.221i	−0.595956	+	0.595956i
$243$	−15.5885			−0.0641500
$244$			141.087i			0.578224i
$245$	−270.608	+	270.608i	−1.10452	+	1.10452i
$246$		−	99.1611i		−	0.403094i
$247$		0			0
$248$	46.2453			0.186473
$249$	−7.96623	−	7.96623i	−0.0319929	−	0.0319929i
$250$	−405.375			−1.62150
$251$		−	211.776i		−	0.843729i	−0.906659	−	0.421865i	$-0.861376\pi$
$251$		−	211.776i		−	0.843729i	0.906659	−	0.421865i	$-0.138624\pi$
$252$	−40.5470	−	40.5470i	−0.160901	−	0.160901i
$253$	315.049	+	315.049i	1.24525	+	1.24525i
$254$	27.0182	−	27.0182i	0.106371	−	0.106371i
$255$	−106.351	+	106.351i	−0.417064	+	0.417064i
$256$	16.0000			0.0625000
$257$		−	272.421i		−	1.06000i	−0.847997	−	0.530002i	$-0.822191\pi$
$257$		−	272.421i		−	1.06000i	0.847997	−	0.530002i	$-0.177809\pi$
$258$	61.8190	−	61.8190i	0.239609	−	0.239609i
$259$		−	201.471i		−	0.777881i
$260$		0			0
$261$	82.8139			0.317295
$262$	64.5682	+	64.5682i	0.246444	+	0.246444i
$263$	236.343			0.898643			0.449321	−	0.893370i	$-0.351666\pi$
$263$	236.343			0.898643			0.449321	+	0.893370i	$0.351666\pi$
$264$			79.7829i			0.302208i
$265$	249.726	+	249.726i	0.942363	+	0.942363i
$266$	94.5914	+	94.5914i	0.355607	+	0.355607i
$267$	−141.715	+	141.715i	−0.530768	+	0.530768i
$268$	56.6973	−	56.6973i	0.211557	−	0.211557i
$269$	466.361			1.73368			0.866842	−	0.498583i	$-0.166146\pi$
$269$	466.361			1.73368			0.866842	+	0.498583i	$0.166146\pi$
$270$		−	66.4256i		−	0.246021i
$271$	−326.130	+	326.130i	−1.20343	+	1.20343i	−0.230315	+	0.973116i	$0.573976\pi$
$271$	−326.130	+	326.130i	−1.20343	+	1.20343i	−0.973116	+	0.230315i	$0.926024\pi$
$272$		−	38.4254i		−	0.141270i
$273$		0			0
$274$	288.738			1.05379
$275$	653.059	+	653.059i	2.37476	+	2.37476i
$276$	94.7718			0.343376
$277$		−	24.5533i		−	0.0886400i	−0.999017	−	0.0443200i	$-0.985888\pi$
$277$		−	24.5533i		−	0.0886400i	0.999017	−	0.0443200i	$-0.0141121\pi$
$278$	−63.6113	−	63.6113i	−0.228818	−	0.228818i
$279$	34.6840	+	34.6840i	0.124315	+	0.124315i
$280$	172.779	−	172.779i	0.617069	−	0.617069i
$281$	276.591	−	276.591i	0.984311	−	0.984311i	−0.0155674	−	0.999879i	$-0.504955\pi$
$281$	276.591	−	276.591i	0.984311	−	0.984311i	0.999879	+	0.0155674i	$0.00495547\pi$
$282$	88.3982			0.313469
$283$		−	391.711i		−	1.38414i	−0.721832	−	0.692068i	$-0.756700\pi$
$283$		−	391.711i		−	1.38414i	0.721832	−	0.692068i	$-0.243300\pi$
$284$	45.2490	−	45.2490i	0.159327	−	0.159327i
$285$			154.963i			0.543731i
$286$		0			0
$287$	386.891			1.34805
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$	196.718			0.680686
$290$			352.887i			1.21685i
$291$	42.7895	+	42.7895i	0.147043	+	0.147043i
$292$	−19.3664	−	19.3664i	−0.0663233	−	0.0663233i
$293$	−209.571	+	209.571i	−0.715261	+	0.715261i	−0.967631	−	0.252370i	$-0.918790\pi$
$293$	−209.571	+	209.571i	−0.715261	+	0.715261i	0.252370	+	0.967631i	$0.418790\pi$
$294$	73.3293	−	73.3293i	0.249419	−	0.249419i
$295$	−430.761			−1.46021
$296$			59.6260i			0.201439i
$297$	−59.8372	+	59.8372i	−0.201472	+	0.201472i
$298$		−	41.0405i		−	0.137720i
$299$		0			0
$300$	196.451			0.654836
$301$	241.195	+	241.195i	0.801314	+	0.801314i
$302$	−63.2700			−0.209503
$303$		−	202.943i		−	0.669779i
$304$	−27.9946	−	27.9946i	−0.0920875	−	0.0920875i
$305$	−450.899	−	450.899i	−1.47836	−	1.47836i
$306$	28.8190	−	28.8190i	0.0941798	−	0.0941798i
$307$	221.215	−	221.215i	0.720571	−	0.720571i	−0.248150	−	0.968722i	$-0.579823\pi$
$307$	221.215	−	221.215i	0.720571	−	0.720571i	0.968722	+	0.248150i	$0.0798227\pi$
$308$	−311.284			−1.01066
$309$			319.005i			1.03238i
$310$	−147.796	+	147.796i	−0.476760	+	0.476760i
$311$		−	12.5556i		−	0.0403716i	−0.999796	−	0.0201858i	$-0.993574\pi$
$311$		−	12.5556i		−	0.0403716i	0.999796	−	0.0201858i	$-0.00642578\pi$
$312$		0			0
$313$	590.956			1.88804			0.944018	−	0.329893i	$-0.107013\pi$
$313$	590.956			1.88804			0.944018	+	0.329893i	$0.107013\pi$
$314$	−242.423	−	242.423i	−0.772047	−	0.772047i
$315$	259.169			0.822758
$316$		−	112.309i		−	0.355407i
$317$	54.7137	+	54.7137i	0.172598	+	0.172598i	0.788120	−	0.615522i	$-0.211055\pi$
$317$	54.7137	+	54.7137i	0.172598	+	0.172598i	−0.615522	+	0.788120i	$0.711055\pi$
$318$	−67.6707	−	67.6707i	−0.212801	−	0.212801i
$319$	317.886	−	317.886i	0.996507	−	0.996507i
$320$	−51.1345	+	51.1345i	−0.159795	+	0.159795i
$321$	−12.3876			−0.0385906
$322$			369.765i			1.14834i
$323$	−67.2314	+	67.2314i	−0.208147	+	0.208147i
$324$			18.0000i			0.0555556i
$325$		0			0
$326$	−22.0804			−0.0677314
$327$	−13.9885	−	13.9885i	−0.0427783	−	0.0427783i
$328$	−114.501			−0.349090
$329$			344.898i			1.04832i
$330$	−254.979	−	254.979i	−0.772662	−	0.772662i
$331$	−14.4546	−	14.4546i	−0.0436693	−	0.0436693i	0.684935	−	0.728604i	$-0.259831\pi$
$331$	−14.4546	−	14.4546i	−0.0436693	−	0.0436693i	−0.728604	+	0.684935i	$0.759831\pi$
$332$	−9.19861	+	9.19861i	−0.0277067	+	0.0277067i
$333$	−44.7195	+	44.7195i	−0.134293	+	0.134293i
$334$	−70.0153			−0.209627
$335$			362.398i			1.08179i
$336$	−46.8197	+	46.8197i	−0.139344	+	0.139344i
$337$			202.326i			0.600375i	0.953880	+	0.300188i	$0.0970493\pi$
$337$			202.326i			0.600375i	−0.953880	+	0.300188i	$0.902951\pi$
$338$		0			0
$339$	201.624			0.594760
$340$	122.804	+	122.804i	0.361188	+	0.361188i
$341$	266.273			0.780858
$342$		−	41.9919i		−	0.122783i
$343$	−45.0296	−	45.0296i	−0.131282	−	0.131282i
$344$	−71.3825	−	71.3825i	−0.207507	−	0.207507i
$345$	−302.882	+	302.882i	−0.877918	+	0.877918i
$346$	−168.425	+	168.425i	−0.486776	+	0.486776i
$347$	556.526			1.60382			0.801911	−	0.597444i	$-0.203817\pi$
$347$	556.526			1.60382			0.801911	+	0.597444i	$0.203817\pi$
$348$		−	95.6252i		−	0.274785i
$349$	327.786	−	327.786i	0.939216	−	0.939216i	−0.0590400	−	0.998256i	$-0.518804\pi$
$349$	327.786	−	327.786i	0.939216	−	0.939216i	0.998256	+	0.0590400i	$0.0188040\pi$
$350$			766.480i			2.18994i
$351$		0			0
$352$	92.1254			0.261720
$353$	199.807	+	199.807i	0.566025	+	0.566025i	0.931012	−	0.364987i	$-0.118927\pi$
$353$	199.807	+	199.807i	0.566025	+	0.566025i	−0.364987	+	0.931012i	$0.618927\pi$
$354$	116.727			0.329738
$355$			289.223i			0.814713i
$356$	163.639	+	163.639i	0.459659	+	0.459659i
$357$	112.441	+	112.441i	0.314962	+	0.314962i
$358$	−313.047	+	313.047i	−0.874432	+	0.874432i
$359$	−280.398	+	280.398i	−0.781054	+	0.781054i	−0.980009	−	0.198955i	$-0.936245\pi$
$359$	−280.398	+	280.398i	−0.781054	+	0.781054i	0.198955	+	0.980009i	$0.436245\pi$
$360$	−76.7017			−0.213060
$361$		−	263.038i		−	0.728637i
$362$	−19.4795	+	19.4795i	−0.0538108	+	0.0538108i
$363$			249.799i			0.688151i
$364$		0			0
$365$	123.786			0.339141
$366$	122.185	+	122.185i	0.333838	+	0.333838i
$367$	591.886			1.61277			0.806384	−	0.591392i	$-0.201421\pi$
$367$	591.886			1.61277			0.806384	+	0.591392i	$0.201421\pi$
$368$		−	109.433i		−	0.297372i
$369$	−85.8761	−	85.8761i	−0.232726	−	0.232726i
$370$	−190.559	−	190.559i	−0.515024	−	0.515024i
$371$	264.027	−	264.027i	0.711662	−	0.711662i
$372$	40.0496	−	40.0496i	0.107660	−	0.107660i
$373$	−511.886			−1.37235			−0.686174	−	0.727437i	$-0.740711\pi$
$373$	−511.886			−1.37235			−0.686174	+	0.727437i	$0.740711\pi$
$374$		−	221.247i		−	0.591569i
$375$	−351.065	+	351.065i	−0.936173	+	0.936173i
$376$		−	102.073i		−	0.271472i
$377$		0			0
$378$	−70.2295			−0.185792
$379$	−144.716	−	144.716i	−0.381837	−	0.381837i	0.489926	−	0.871764i	$-0.337024\pi$
$379$	−144.716	−	144.716i	−0.381837	−	0.381837i	−0.871764	+	0.489926i	$0.837024\pi$
$380$	178.936			0.470885
$381$		−	46.7968i		−	0.122826i
$382$	−142.951	−	142.951i	−0.374218	−	0.374218i
$383$	232.211	+	232.211i	0.606295	+	0.606295i	0.941976	−	0.335681i	$-0.108966\pi$
$383$	232.211	+	232.211i	0.606295	+	0.606295i	−0.335681	+	0.941976i	$0.608966\pi$
$384$	13.8564	−	13.8564i	0.0360844	−	0.0360844i
$385$	994.834	−	994.834i	2.58398	−	2.58398i
$386$	237.325			0.614830
$387$		−	107.074i		−	0.276676i
$388$	49.4091	−	49.4091i	0.127343	−	0.127343i
$389$		−	393.984i		−	1.01281i	−0.862295	−	0.506406i	$-0.830974\pi$
$389$		−	393.984i		−	1.01281i	0.862295	−	0.506406i	$-0.169026\pi$
$390$		0			0
$391$	−262.813			−0.672156
$392$	−84.6734	−	84.6734i	−0.216003	−	0.216003i
$393$	111.835			0.284569
$394$			240.963i			0.611580i
$395$	358.928	+	358.928i	0.908678	+	0.908678i
$396$	69.0940	+	69.0940i	0.174480	+	0.174480i
$397$	84.9000	−	84.9000i	0.213854	−	0.213854i	−0.592048	−	0.805902i	$-0.701681\pi$
$397$	84.9000	−	84.9000i	0.213854	−	0.213854i	0.805902	+	0.592048i	$0.201681\pi$
$398$	161.726	−	161.726i	0.406346	−	0.406346i
$399$	163.837			0.410619
$400$		−	226.842i		−	0.567105i
$401$	234.950	−	234.950i	0.585910	−	0.585910i	−0.350611	−	0.936521i	$-0.614026\pi$
$401$	234.950	−	234.950i	0.585910	−	0.585910i	0.936521	+	0.350611i	$0.114026\pi$
$402$		−	98.2025i		−	0.244285i
$403$		0			0
$404$	−234.338			−0.580045
$405$	−57.5263	−	57.5263i	−0.142040	−	0.142040i
$406$	373.095			0.918953
$407$			343.316i			0.843529i
$408$	−33.2773	−	33.2773i	−0.0815621	−	0.0815621i
$409$	−311.016	−	311.016i	−0.760431	−	0.760431i	0.215970	−	0.976400i	$-0.430709\pi$
$409$	−311.016	−	311.016i	−0.760431	−	0.760431i	−0.976400	+	0.215970i	$0.930709\pi$
$410$	365.936	−	365.936i	0.892526	−	0.892526i
$411$	250.055	−	250.055i	0.608406	−	0.608406i
$412$	368.356			0.894067
$413$			455.428i			1.10273i
$414$	82.0748	−	82.0748i	0.198248	−	0.198248i
$415$		−	58.7958i		−	0.141677i
$416$		0			0
$417$	−110.178			−0.264216
$418$	−161.188	−	161.188i	−0.385618	−	0.385618i
$419$	−124.953			−0.298217			−0.149108	−	0.988821i	$-0.547640\pi$
$419$	−124.953			−0.298217			−0.149108	+	0.988821i	$0.547640\pi$
$420$		−	299.262i		−	0.712529i
$421$	9.46318	+	9.46318i	0.0224779	+	0.0224779i	0.718256	−	0.695779i	$-0.244940\pi$
$421$	9.46318	+	9.46318i	0.0224779	+	0.0224779i	−0.695779	+	0.718256i	$0.744940\pi$
$422$	179.875	+	179.875i	0.426245	+	0.426245i
$423$	76.5551	−	76.5551i	0.180981	−	0.180981i
$424$	−78.1394	+	78.1394i	−0.184291	+	0.184291i
$425$	−544.780			−1.28184
$426$		−	78.3735i		−	0.183975i
$427$	−476.720	+	476.720i	−1.11644	+	1.11644i
$428$			14.3040i			0.0334205i
$429$		0			0
$430$	456.263			1.06108
$431$	−511.221	−	511.221i	−1.18613	−	1.18613i	−0.978129	−	0.207999i	$-0.933305\pi$
$431$	−511.221	−	511.221i	−1.18613	−	1.18613i	−0.207999	−	0.978129i	$-0.566695\pi$
$432$	20.7846			0.0481125
$433$			40.9607i			0.0945973i	0.998881	+	0.0472987i	$0.0150613\pi$
$433$			40.9607i			0.0945973i	−0.998881	+	0.0472987i	$0.984939\pi$
$434$	156.259	+	156.259i	0.360044	+	0.360044i
$435$	305.609	+	305.609i	0.702550	+	0.702550i
$436$	−16.1525	+	16.1525i	−0.0370471	+	0.0370471i
$437$	−191.471	+	191.471i	−0.438148	+	0.438148i
$438$	−33.5436			−0.0765836
$439$			665.355i			1.51562i	0.652478	+	0.757808i	$0.273729\pi$
$439$			665.355i			1.51562i	−0.652478	+	0.757808i	$0.726271\pi$
$440$	−294.424	+	294.424i	−0.669145	+	0.669145i
$441$		−	127.010i		−	0.288005i
$442$		0			0
$443$	267.578			0.604013			0.302006	−	0.953306i	$-0.402344\pi$
$443$	267.578			0.604013			0.302006	+	0.953306i	$0.402344\pi$
$444$	51.6376	+	51.6376i	0.116301	+	0.116301i
$445$	−1045.95			−2.35044
$446$			551.263i			1.23602i
$447$	−35.5421	−	35.5421i	−0.0795125	−	0.0795125i
$448$	54.0627	+	54.0627i	0.120676	+	0.120676i
$449$	398.196	−	398.196i	0.886850	−	0.886850i	−0.107369	−	0.994219i	$-0.534243\pi$
$449$	398.196	−	398.196i	0.886850	−	0.886850i	0.994219	+	0.107369i	$0.0342427\pi$
$450$	170.131	−	170.131i	0.378070	−	0.378070i
$451$	−659.280			−1.46182
$452$		−	232.815i		−	0.515077i
$453$	−54.7934	+	54.7934i	−0.120957	+	0.120957i
$454$		−	188.550i		−	0.415308i
$455$		0			0
$456$	−48.4881			−0.106333
$457$	471.131	+	471.131i	1.03092	+	1.03092i	0.999506	+	0.0314138i	$0.0100010\pi$
$457$	471.131	+	471.131i	1.03092	+	1.03092i	0.0314138	+	0.999506i	$0.489999\pi$
$458$	609.732			1.33129
$459$		−	49.9160i		−	0.108750i
$460$	349.738	+	349.738i	0.760299	+	0.760299i
$461$	−253.308	−	253.308i	−0.549475	−	0.549475i	0.376814	−	0.926289i	$-0.377020\pi$
$461$	−253.308	−	253.308i	−0.549475	−	0.549475i	−0.926289	+	0.376814i	$0.877020\pi$
$462$	−269.580	+	269.580i	−0.583506	+	0.583506i
$463$	−630.292	+	630.292i	−1.36132	+	1.36132i	−0.489084	+	0.872236i	$0.662669\pi$
$463$	−630.292	+	630.292i	−1.36132	+	1.36132i	−0.872236	+	0.489084i	$0.837331\pi$
$464$	−110.419			−0.237971
$465$			255.989i			0.550515i
$466$	44.1414	−	44.1414i	0.0947240	−	0.0947240i
$467$		−	425.264i		−	0.910630i	−0.890331	−	0.455315i	$-0.849527\pi$
$467$		−	425.264i		−	0.910630i	0.890331	−	0.455315i	$-0.150473\pi$
$468$		0			0
$469$	383.151			0.816953
$470$	326.217	+	326.217i	0.694079	+	0.694079i
$471$	−419.888			−0.891483
$472$		−	134.785i		−	0.285562i
$473$	−411.009	−	411.009i	−0.868940	−	0.868940i
$474$	−97.2622	−	97.2622i	−0.205194	−	0.205194i
$475$	−396.897	+	396.897i	−0.835572	+	0.835572i
$476$	129.836	−	129.836i	0.272765	−	0.272765i
$477$	−117.209			−0.245722
$478$			31.6897i			0.0662964i
$479$	−194.811	+	194.811i	−0.406704	+	0.406704i	−0.880588	−	0.473883i	$-0.842852\pi$
$479$	−194.811	+	194.811i	−0.406704	+	0.406704i	0.473883	+	0.880588i	$0.342852\pi$
$480$			88.5675i			0.184516i
$481$		0			0
$482$	−680.212			−1.41123
$483$	320.226	+	320.226i	0.662994	+	0.662994i
$484$	288.443			0.595956
$485$			315.813i			0.651162i
$486$	15.5885	+	15.5885i	0.0320750	+	0.0320750i
$487$	−452.708	−	452.708i	−0.929585	−	0.929585i	0.0680942	−	0.997679i	$-0.478308\pi$
$487$	−452.708	−	452.708i	−0.929585	−	0.929585i	−0.997679	+	0.0680942i	$0.978308\pi$
$488$	141.087	−	141.087i	0.289112	−	0.289112i
$489$	−19.1222	+	19.1222i	−0.0391048	+	0.0391048i
$490$	541.216			1.10452
$491$		−	566.666i		−	1.15411i	−0.816706	−	0.577053i	$-0.804202\pi$
$491$		−	566.666i		−	1.15411i	0.816706	−	0.577053i	$-0.195798\pi$
$492$	−99.1611	+	99.1611i	−0.201547	+	0.201547i
$493$			265.180i			0.537890i
$494$		0			0
$495$	−441.636			−0.892194
$496$	−46.2453	−	46.2453i	−0.0932365	−	0.0932365i
$497$	305.785			0.615262
$498$			15.9325i			0.0319929i
$499$	−409.292	−	409.292i	−0.820224	−	0.820224i	0.165916	−	0.986140i	$-0.446942\pi$
$499$	−409.292	−	409.292i	−0.820224	−	0.820224i	−0.986140	+	0.165916i	$0.946942\pi$
$500$	405.375	+	405.375i	0.810749	+	0.810749i
$501$	−60.6351	+	60.6351i	−0.121028	+	0.121028i
$502$	−211.776	+	211.776i	−0.421865	+	0.421865i
$503$	223.242			0.443821			0.221910	−	0.975067i	$-0.428771\pi$
$503$	223.242			0.443821			0.221910	+	0.975067i	$0.428771\pi$
$504$			81.0940i			0.160901i
$505$	748.923	−	748.923i	1.48302	−	1.48302i
$506$		−	630.097i		−	1.24525i
$507$		0			0
$508$	−54.0363			−0.106371
$509$	303.312	+	303.312i	0.595898	+	0.595898i	0.939218	−	0.343320i	$-0.111552\pi$
$509$	303.312	+	303.312i	0.595898	+	0.595898i	−0.343320	+	0.939218i	$0.611552\pi$
$510$	212.702			0.417064
$511$		−	130.875i		−	0.256115i
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	−36.3660	−	36.3660i	−0.0708890	−	0.0708890i
$514$	−272.421	+	272.421i	−0.530002	+	0.530002i
$515$	−1177.23	+	1177.23i	−2.28588	+	2.28588i
$516$	−123.638			−0.239609
$517$		−	587.722i		−	1.13679i
$518$	−201.471	+	201.471i	−0.388941	+	0.388941i
$519$			291.720i			0.562081i
$520$		0			0
$521$	−470.908			−0.903854			−0.451927	−	0.892055i	$-0.649263\pi$
$521$	−470.908			−0.903854			−0.451927	+	0.892055i	$0.649263\pi$
$522$	−82.8139	−	82.8139i	−0.158647	−	0.158647i
$523$	−911.570			−1.74296			−0.871481	−	0.490428i	$-0.836840\pi$
$523$	−911.570			−1.74296			−0.871481	+	0.490428i	$0.836840\pi$
$524$		−	129.136i		−	0.246444i
$525$	663.791	+	663.791i	1.26436	+	1.26436i
$526$	−236.343	−	236.343i	−0.449321	−	0.449321i
$527$	−111.062	+	111.062i	−0.210744	+	0.210744i
$528$	79.7829	−	79.7829i	0.151104	−	0.151104i
$529$	−219.474			−0.414885
$530$		−	499.452i		−	0.942363i
$531$	101.089	−	101.089i	0.190375	−	0.190375i
$532$		−	189.183i		−	0.355607i
$533$		0			0
$534$	283.430			0.530768
$535$	−45.7141	−	45.7141i	−0.0854469	−	0.0854469i
$536$	−113.395			−0.211557
$537$			542.213i			1.00971i
$538$	−466.361	−	466.361i	−0.866842	−	0.866842i
$539$	−487.535	−	487.535i	−0.904518	−	0.904518i
$540$	−66.4256	+	66.4256i	−0.123010	+	0.123010i
$541$	−393.572	+	393.572i	−0.727490	+	0.727490i	−0.970119	−	0.242629i	$-0.921990\pi$
$541$	−393.572	+	393.572i	−0.727490	+	0.727490i	0.242629	+	0.970119i	$0.421990\pi$
$542$	652.260			1.20343
$543$			33.7395i			0.0621353i
$544$	−38.4254	+	38.4254i	−0.0706349	+	0.0706349i
$545$		−	103.244i		−	0.189438i
$546$		0			0
$547$	−388.679			−0.710565			−0.355283	−	0.934759i	$-0.615615\pi$
$547$	−388.679			−0.710565			−0.355283	+	0.934759i	$0.615615\pi$
$548$	−288.738	−	288.738i	−0.526895	−	0.526895i
$549$	211.630			0.385483
$550$		−	1306.12i		−	2.37476i
$551$	193.195	+	193.195i	0.350626	+	0.350626i
$552$	−94.7718	−	94.7718i	−0.171688	−	0.171688i
$553$	379.482	−	379.482i	0.686224	−	0.686224i
$554$	−24.5533	+	24.5533i	−0.0443200	+	0.0443200i
$555$	−330.058			−0.594699
$556$			127.223i			0.228818i
$557$	500.081	−	500.081i	0.897811	−	0.897811i	−0.0974309	−	0.995242i	$-0.531062\pi$
$557$	500.081	−	500.081i	0.897811	−	0.897811i	0.995242	+	0.0974309i	$0.0310625\pi$
$558$		−	69.3679i		−	0.124315i
$559$		0			0
$560$	−345.558			−0.617069
$561$	−191.606	−	191.606i	−0.341543	−	0.341543i
$562$	−553.183			−0.984311
$563$		−	594.275i		−	1.05555i	−0.849384	−	0.527776i	$-0.823026\pi$
$563$		−	594.275i		−	1.05555i	0.849384	−	0.527776i	$-0.176974\pi$
$564$	−88.3982	−	88.3982i	−0.156734	−	0.156734i
$565$	744.055	+	744.055i	1.31691	+	1.31691i
$566$	−391.711	+	391.711i	−0.692068	+	0.692068i
$567$	−60.8205	+	60.8205i	−0.107267	+	0.107267i
$568$	−90.4980			−0.159327
$569$		−	116.935i		−	0.205509i	−0.994707	−	0.102754i	$-0.967234\pi$
$569$		−	116.935i		−	0.205509i	0.994707	−	0.102754i	$-0.0327656\pi$
$570$	154.963	−	154.963i	0.271865	−	0.271865i
$571$		−	137.505i		−	0.240815i	−0.992725	−	0.120408i	$-0.961580\pi$
$571$		−	137.505i		−	0.240815i	0.992725	−	0.120408i	$-0.0384201\pi$
$572$		0			0
$573$	−247.599			−0.432109
$574$	−386.891	−	386.891i	−0.674026	−	0.674026i
$575$	−1551.50			−2.69826
$576$		−	24.0000i		−	0.0416667i
$577$	−617.016	−	617.016i	−1.06935	−	1.06935i	−0.997409	−	0.0719422i	$-0.977080\pi$
$577$	−617.016	−	617.016i	−1.06935	−	1.06935i	−0.0719422	−	0.997409i	$-0.522920\pi$
$578$	−196.718	−	196.718i	−0.340343	−	0.340343i
$579$	205.529	−	205.529i	0.354972	−	0.354972i
$580$	352.887	−	352.887i	0.608426	−	0.608426i
$581$	−62.1627			−0.106993
$582$		−	85.5790i		−	0.147043i
$583$	−449.914	+	449.914i	−0.771722	+	0.771722i
$584$			38.7328i			0.0663233i
$585$		0			0
$586$	419.143			0.715261
$587$	−273.246	−	273.246i	−0.465495	−	0.465495i	0.434956	−	0.900452i	$-0.356764\pi$
$587$	−273.246	−	273.246i	−0.465495	−	0.465495i	−0.900452	+	0.434956i	$0.856764\pi$
$588$	−146.659			−0.249419
$589$			161.827i			0.274749i
$590$	430.761	+	430.761i	0.730103	+	0.730103i
$591$	208.680	+	208.680i	0.353096	+	0.353096i
$592$	59.6260	−	59.6260i	0.100720	−	0.100720i
$593$	536.353	−	536.353i	0.904473	−	0.904473i	−0.0913459	−	0.995819i	$-0.529117\pi$
$593$	536.353	−	536.353i	0.904473	−	0.904473i	0.995819	+	0.0913459i	$0.0291169\pi$
$594$	119.674			0.201472
$595$			829.888i			1.39477i
$596$	−41.0405	+	41.0405i	−0.0688598	+	0.0688598i
$597$		−	280.117i		−	0.469208i
$598$		0			0
$599$	344.623			0.575331			0.287666	−	0.957731i	$-0.407121\pi$
$599$	344.623			0.575331			0.287666	+	0.957731i	$0.407121\pi$
$600$	−196.451	−	196.451i	−0.327418	−	0.327418i
$601$	891.739			1.48376			0.741879	−	0.670533i	$-0.233935\pi$
$601$	891.739			1.48376			0.741879	+	0.670533i	$0.233935\pi$
$602$		−	482.391i		−	0.801314i
$603$	−85.0459	−	85.0459i	−0.141038	−	0.141038i
$604$	63.2700	+	63.2700i	0.104752	+	0.104752i
$605$	−921.835	+	921.835i	−1.52370	+	1.52370i
$606$	−202.943	+	202.943i	−0.334889	+	0.334889i
$607$	465.467			0.766832			0.383416	−	0.923576i	$-0.374748\pi$
$607$	465.467			0.766832			0.383416	+	0.923576i	$0.374748\pi$
$608$			55.9892i			0.0920875i
$609$	323.110	−	323.110i	0.530558	−	0.530558i
$610$			901.799i			1.47836i
$611$		0			0
$612$	−57.6381			−0.0941798
$613$	−623.188	−	623.188i	−1.01662	−	1.01662i	−0.999860	−	0.0167601i	$-0.994665\pi$
$613$	−623.188	−	623.188i	−1.01662	−	1.01662i	−0.0167601	−	0.999860i	$-0.505335\pi$
$614$	−442.431			−0.720571
$615$		−	633.819i		−	1.03060i
$616$	311.284	+	311.284i	0.505331	+	0.505331i
$617$	802.642	+	802.642i	1.30088	+	1.30088i	0.927800	+	0.373078i	$0.121697\pi$
$617$	802.642	+	802.642i	1.30088	+	1.30088i	0.373078	+	0.927800i	$0.378303\pi$
$618$	319.005	−	319.005i	0.516190	−	0.516190i
$619$	69.6384	−	69.6384i	0.112501	−	0.112501i	−0.648615	−	0.761117i	$-0.724651\pi$
$619$	69.6384	−	69.6384i	0.112501	−	0.112501i	0.761117	+	0.648615i	$0.224651\pi$
$620$	295.591			0.476760
$621$		−	142.158i		−	0.228917i
$622$	−12.5556	+	12.5556i	−0.0201858	+	0.0201858i
$623$			1105.84i			1.77503i
$624$		0			0
$625$	−1173.32			−1.87731
$626$	−590.956	−	590.956i	−0.944018	−	0.944018i
$627$	−279.186			−0.445273
$628$			484.845i			0.772047i
$629$	−143.197	−	143.197i	−0.227658	−	0.227658i
$630$	−259.169	−	259.169i	−0.411379	−	0.411379i
$631$	−451.647	+	451.647i	−0.715764	+	0.715764i	−0.967735	−	0.251971i	$-0.918921\pi$
$631$	−451.647	+	451.647i	−0.715764	+	0.715764i	0.251971	+	0.967735i	$0.418921\pi$
$632$	−112.309	+	112.309i	−0.177704	+	0.177704i
$633$	311.553			0.492185
$634$		−	109.427i		−	0.172598i
$635$	172.695	−	172.695i	0.271961	−	0.271961i
$636$			135.341i			0.212801i
$637$		0			0
$638$	−635.772			−0.996507
$639$	−67.8735	−	67.8735i	−0.106218	−	0.106218i
$640$	102.269			0.159795
$641$		−	915.621i		−	1.42843i	−0.699928	−	0.714213i	$-0.746785\pi$
$641$		−	915.621i		−	1.42843i	0.699928	−	0.714213i	$-0.253215\pi$
$642$	12.3876	+	12.3876i	0.0192953	+	0.0192953i
$643$	298.879	+	298.879i	0.464819	+	0.464819i	0.900231	−	0.435412i	$-0.143397\pi$
$643$	298.879	+	298.879i	0.464819	+	0.464819i	−0.435412	+	0.900231i	$0.643397\pi$
$644$	369.765	−	369.765i	0.574170	−	0.574170i
$645$	395.135	−	395.135i	0.612613	−	0.612613i
$646$	134.463			0.208147
$647$		−	643.609i		−	0.994760i	−0.867533	−	0.497380i	$-0.834296\pi$
$647$		−	643.609i		−	0.994760i	0.867533	−	0.497380i	$-0.165704\pi$
$648$	18.0000	−	18.0000i	0.0277778	−	0.0277778i
$649$		−	776.071i		−	1.19579i
$650$		0			0
$651$	270.649			0.415743
$652$	22.0804	+	22.0804i	0.0338657	+	0.0338657i
$653$	−298.247			−0.456733			−0.228366	−	0.973575i	$-0.573338\pi$
$653$	−298.247			−0.456733			−0.228366	+	0.973575i	$0.573338\pi$
$654$			27.9770i			0.0427783i
$655$	412.708	+	412.708i	0.630088	+	0.630088i
$656$	114.501	+	114.501i	0.174545	+	0.174545i
$657$	−29.0496	+	29.0496i	−0.0442155	+	0.0442155i
$658$	344.898	−	344.898i	0.524161	−	0.524161i
$659$	−645.888			−0.980103			−0.490052	−	0.871693i	$-0.663022\pi$
$659$	−645.888			−0.980103			−0.490052	+	0.871693i	$0.663022\pi$
$660$			509.957i			0.772662i
$661$	686.907	−	686.907i	1.03919	−	1.03919i	0.0399930	−	0.999200i	$-0.487266\pi$
$661$	686.907	−	686.907i	1.03919	−	1.03919i	0.999200	−	0.0399930i	$-0.0127336\pi$
$662$			28.9091i			0.0436693i
$663$		0			0
$664$	18.3972			0.0277067
$665$	604.610	+	604.610i	0.909189	+	0.909189i
$666$	89.4389			0.134293
$667$			755.215i			1.13226i
$668$	70.0153	+	70.0153i	0.104813	+	0.104813i
$669$	477.408	+	477.408i	0.713614	+	0.713614i
$670$	362.398	−	362.398i	0.540893	−	0.540893i
$671$	812.354	−	812.354i	1.21066	−	1.21066i
$672$	93.6393			0.139344
$673$			822.616i			1.22231i	0.791510	+	0.611156i	$0.209295\pi$
$673$			822.616i			1.22231i	−0.791510	+	0.611156i	$0.790705\pi$
$674$	202.326	−	202.326i	0.300188	−	0.300188i
$675$		−	294.676i		−	0.436557i
$676$		0			0
$677$	195.713			0.289089			0.144544	−	0.989498i	$-0.453828\pi$
$677$	195.713			0.289089			0.144544	+	0.989498i	$0.453828\pi$
$678$	−201.624	−	201.624i	−0.297380	−	0.297380i
$679$	333.898			0.491750
$680$		−	245.608i		−	0.361188i
$681$	−163.289	−	163.289i	−0.239778	−	0.239778i
$682$	−266.273	−	266.273i	−0.390429	−	0.390429i
$683$	460.017	−	460.017i	0.673525	−	0.673525i	−0.285002	−	0.958527i	$-0.591994\pi$
$683$	460.017	−	460.017i	0.673525	−	0.673525i	0.958527	+	0.285002i	$0.0919944\pi$
$684$	−41.9919	+	41.9919i	−0.0613917	+	0.0613917i
$685$	1845.56			2.69425
$686$			90.0592i			0.131282i
$687$	528.043	−	528.043i	0.768622	−	0.768622i
$688$			142.765i			0.207507i
$689$		0			0
$690$	605.763			0.877918
$691$	222.362	+	222.362i	0.321797	+	0.321797i	0.849456	−	0.527659i	$-0.176930\pi$
$691$	222.362	+	222.362i	0.321797	+	0.321797i	−0.527659	+	0.849456i	$0.676930\pi$
$692$	336.849			0.486776
$693$			466.926i			0.673775i
$694$	−556.526	−	556.526i	−0.801911	−	0.801911i
$695$	−406.592	−	406.592i	−0.585024	−	0.585024i
$696$	−95.6252	+	95.6252i	−0.137393	+	0.137393i
$697$	274.985	−	274.985i	0.394526	−	0.394526i
$698$	−655.572			−0.939216
$699$		−	76.4552i		−	0.109378i
$700$	766.480	−	766.480i	1.09497	−	1.09497i
$701$		−	769.901i		−	1.09829i	−0.835727	−	0.549145i	$-0.814954\pi$
$701$		−	769.901i		−	1.09829i	0.835727	−	0.549145i	$-0.185046\pi$
$702$		0			0
$703$	−208.651			−0.296800
$704$	−92.1254	−	92.1254i	−0.130860	−	0.130860i
$705$	565.025			0.801454
$706$		−	399.614i		−	0.566025i
$707$	−791.810	−	791.810i	−1.11996	−	1.11996i
$708$	−116.727	−	116.727i	−0.164869	−	0.164869i
$709$	−672.423	+	672.423i	−0.948411	+	0.948411i	−0.998733	−	0.0503224i	$-0.983975\pi$
$709$	−672.423	+	672.423i	−0.948411	+	0.948411i	0.0503224	+	0.998733i	$0.483975\pi$
$710$	289.223	−	289.223i	0.407356	−	0.407356i
$711$	−168.463			−0.236938
$712$		−	327.277i		−	0.459659i
$713$	−316.298	+	316.298i	−0.443615	+	0.443615i
$714$		−	224.883i		−	0.314962i
$715$		0			0
$716$	626.093			0.874432
$717$	27.4441	+	27.4441i	0.0382763	+	0.0382763i
$718$	560.797			0.781054
$719$		−	1345.47i		−	1.87130i	−0.352926	−	0.935651i	$-0.614813\pi$
$719$		−	1345.47i		−	1.87130i	0.352926	−	0.935651i	$-0.385187\pi$
$720$	76.7017	+	76.7017i	0.106530	+	0.106530i
$721$	1244.64	+	1244.64i	1.72627	+	1.72627i
$722$	−263.038	+	263.038i	−0.364318	+	0.364318i
$723$	−589.081	+	589.081i	−0.814773	+	0.814773i
$724$	38.9590			0.0538108
$725$			1565.47i			2.15927i
$726$	249.799	−	249.799i	0.344075	−	0.344075i
$727$			681.807i			0.937837i	0.883241	+	0.468918i	$0.155356\pi$
$727$			681.807i			0.937837i	−0.883241	+	0.468918i	$0.844644\pi$
$728$		0			0
$729$	27.0000			0.0370370
$730$	−123.786	−	123.786i	−0.169570	−	0.169570i
$731$	342.862			0.469032
$732$		−	244.369i		−	0.333838i
$733$	760.545	+	760.545i	1.03758	+	1.03758i	0.999266	+	0.0383126i	$0.0121983\pi$
$733$	760.545	+	760.545i	1.03758	+	1.03758i	0.0383126	+	0.999266i	$0.487802\pi$
$734$	−591.886	−	591.886i	−0.806384	−	0.806384i
$735$	468.707	−	468.707i	0.637696	−	0.637696i
$736$	−109.433	+	109.433i	−0.148686	+	0.148686i
$737$	−652.907			−0.885898
$738$			171.752i			0.232726i
$739$	553.955	−	553.955i	0.749601	−	0.749601i	−0.224803	−	0.974404i	$-0.572174\pi$
$739$	553.955	−	553.955i	0.749601	−	0.749601i	0.974404	+	0.224803i	$0.0721740\pi$
$740$			381.118i			0.515024i
$741$		0			0
$742$	−528.053			−0.711662
$743$	−570.731	−	570.731i	−0.768144	−	0.768144i	0.209636	−	0.977780i	$-0.432772\pi$
$743$	−570.731	−	570.731i	−0.768144	−	0.768144i	−0.977780	+	0.209636i	$0.932772\pi$
$744$	−80.0992			−0.107660
$745$		−	262.323i		−	0.352111i
$746$	511.886	+	511.886i	0.686174	+	0.686174i
$747$	13.7979	+	13.7979i	0.0184711	+	0.0184711i
$748$	−221.247	+	221.247i	−0.295785	+	0.295785i
$749$	−48.3319	+	48.3319i	−0.0645286	+	0.0645286i
$750$	702.129			0.936173
$751$		−	991.338i		−	1.32002i	−0.751255	−	0.660012i	$-0.770551\pi$
$751$		−	991.338i		−	1.32002i	0.751255	−	0.660012i	$-0.229449\pi$
$752$	−102.073	+	102.073i	−0.135736	+	0.135736i
$753$			366.807i			0.487127i
$754$		0			0
$755$	−404.410			−0.535642
$756$	70.2295	+	70.2295i	0.0928961	+	0.0928961i
$757$	740.328			0.977976			0.488988	−	0.872290i	$-0.337366\pi$
$757$	740.328			0.977976			0.488988	+	0.872290i	$0.337366\pi$
$758$			289.433i			0.381837i
$759$	−545.680	−	545.680i	−0.718946	−	0.718946i
$760$	−178.936	−	178.936i	−0.235442	−	0.235442i
$761$	−558.497	+	558.497i	−0.733898	+	0.733898i	−0.971390	−	0.237491i	$-0.923675\pi$
$761$	−558.497	+	558.497i	−0.733898	+	0.733898i	0.237491	+	0.971390i	$0.423675\pi$
$762$	−46.7968	+	46.7968i	−0.0614132	+	0.0614132i
$763$	−109.156			−0.143062
$764$			285.902i			0.374218i
$765$	184.206	−	184.206i	0.240792	−	0.240792i
$766$		−	464.422i		−	0.606295i
$767$		0			0
$768$	−27.7128			−0.0360844
$769$	−9.05118	−	9.05118i	−0.0117701	−	0.0117701i	0.701197	−	0.712967i	$-0.252649\pi$
$769$	−9.05118	−	9.05118i	−0.0117701	−	0.0117701i	−0.712967	+	0.701197i	$0.752649\pi$
$770$	−1989.67			−2.58398
$771$			471.847i			0.611993i
$772$	−237.325	−	237.325i	−0.307415	−	0.307415i
$773$	67.3318	+	67.3318i	0.0871045	+	0.0871045i	0.749317	−	0.662212i	$-0.230382\pi$
$773$	67.3318	+	67.3318i	0.0871045	+	0.0871045i	−0.662212	+	0.749317i	$0.730382\pi$
$774$	−107.074	+	107.074i	−0.138338	+	0.138338i
$775$	−655.648	+	655.648i	−0.845997	+	0.845997i
$776$	−98.8182			−0.127343
$777$			348.958i			0.449110i
$778$	−393.984	+	393.984i	−0.506406	+	0.506406i
$779$		−	400.678i		−	0.514349i
$780$		0			0
$781$	−521.072			−0.667186
$782$	262.813	+	262.813i	0.336078	+	0.336078i
$783$	−143.438			−0.183190
$784$			169.347i			0.216003i
$785$	−1549.52	−	1549.52i	−1.97391	−	1.97391i
$786$	−111.835	−	111.835i	−0.142284	−	0.142284i
$787$	636.463	−	636.463i	0.808721	−	0.808721i	−0.175720	−	0.984440i	$-0.556225\pi$
$787$	636.463	−	636.463i	0.808721	−	0.808721i	0.984440	+	0.175720i	$0.0562252\pi$
$788$	240.963	−	240.963i	0.305790	−	0.305790i
$789$	−409.358			−0.518832
$790$		−	717.856i		−	0.908678i
$791$	786.663	−	786.663i	0.994517	−	0.994517i
$792$		−	138.188i		−	0.174480i
$793$		0			0
$794$	−169.800			−0.213854
$795$	−432.539	−	432.539i	−0.544074	−	0.544074i
$796$	−323.452			−0.406346
$797$		−	646.448i		−	0.811102i	−0.914072	−	0.405551i	$-0.867080\pi$
$797$		−	646.448i		−	0.811102i	0.914072	−	0.405551i	$-0.132920\pi$
$798$	−163.837	−	163.837i	−0.205310	−	0.205310i
$799$	245.138	+	245.138i	0.306806	+	0.306806i
$800$	−226.842	+	226.842i	−0.283552	+	0.283552i
$801$	245.458	−	245.458i	0.306439	−	0.306439i
$802$	−469.900			−0.585910
$803$			223.017i			0.277730i
$804$	−98.2025	+	98.2025i	−0.122142	+	0.122142i
$805$			2363.47i			2.93599i
$806$		0			0
$807$	−807.761			−1.00094
$808$	234.338	+	234.338i	0.290023	+	0.290023i
$809$	−1145.39			−1.41581			−0.707903	−	0.706310i	$-0.750358\pi$
$809$	−1145.39			−1.41581			−0.707903	+	0.706310i	$0.750358\pi$
$810$			115.053i			0.142040i
$811$	394.302	+	394.302i	0.486192	+	0.486192i	0.907102	−	0.420910i	$-0.138289\pi$
$811$	394.302	+	394.302i	0.486192	+	0.486192i	−0.420910	+	0.907102i	$0.638289\pi$
$812$	−373.095	−	373.095i	−0.459477	−	0.459477i
$813$	564.873	−	564.873i	0.694801	−	0.694801i
$814$	343.316	−	343.316i	0.421765	−	0.421765i
$815$	−141.134			−0.173171
$816$			66.5547i			0.0815621i
$817$	249.790	−	249.790i	0.305741	−	0.305741i
$818$			622.032i			0.760431i
$819$		0			0
$820$	−731.871			−0.892526
$821$	501.342	+	501.342i	0.610648	+	0.610648i	0.943115	−	0.332467i	$-0.107881\pi$
$821$	501.342	+	501.342i	0.610648	+	0.610648i	−0.332467	+	0.943115i	$0.607881\pi$
$822$	−500.109			−0.608406
$823$			554.185i			0.673372i	0.941617	+	0.336686i	$0.109306\pi$
$823$			554.185i			0.673372i	−0.941617	+	0.336686i	$0.890694\pi$
$824$	−368.356	−	368.356i	−0.447034	−	0.447034i
$825$	−1131.13	−	1131.13i	−1.37107	−	1.37107i
$826$	455.428	−	455.428i	0.551366	−	0.551366i
$827$	140.395	−	140.395i	0.169764	−	0.169764i	−0.617112	−	0.786876i	$-0.711697\pi$
$827$	140.395	−	140.395i	0.169764	−	0.169764i	0.786876	+	0.617112i	$0.211697\pi$
$828$	−164.150			−0.198248
$829$		−	515.600i		−	0.621955i	−0.950417	−	0.310977i	$-0.899344\pi$
$829$		−	515.600i		−	0.621955i	0.950417	−	0.310977i	$-0.100656\pi$
$830$	−58.7958	+	58.7958i	−0.0708383	+	0.0708383i
$831$			42.5275i			0.0511763i
$832$		0			0
$833$	406.701			0.488236
$834$	110.178	+	110.178i	0.132108	+	0.132108i
$835$	−447.525			−0.535958
$836$			322.377i			0.385618i
$837$	−60.0744	−	60.0744i	−0.0717735	−	0.0717735i
$838$	124.953	+	124.953i	0.149108	+	0.149108i
$839$	615.379	−	615.379i	0.733467	−	0.733467i	−0.237838	−	0.971305i	$-0.576439\pi$
$839$	615.379	−	615.379i	0.733467	−	0.733467i	0.971305	+	0.237838i	$0.0764386\pi$
$840$	−299.262	+	299.262i	−0.356265	+	0.356265i
$841$	−78.9844			−0.0939173
$842$		−	18.9264i		−	0.0224779i
$843$	−479.071	+	479.071i	−0.568292	+	0.568292i
$844$		−	359.751i		−	0.426245i
$845$		0			0
$846$	−153.110			−0.180981
$847$	974.624	+	974.624i	1.15068	+	1.15068i
$848$	156.279			0.184291
$849$			678.463i			0.799131i
$850$	544.780	+	544.780i	0.640918	+	0.640918i
$851$	−407.816	−	407.816i	−0.479219	−	0.479219i
$852$	−78.3735	+	78.3735i	−0.0919877	+	0.0919877i
$853$	−42.9256	+	42.9256i	−0.0503230	+	0.0503230i	−0.731820	−	0.681497i	$-0.761329\pi$
$853$	−42.9256	+	42.9256i	−0.0503230	+	0.0503230i	0.681497	+	0.731820i	$0.261329\pi$
$854$	953.440			1.11644
$855$		−	268.404i		−	0.313923i
$856$	14.3040	−	14.3040i	0.0167102	−	0.0167102i
$857$		−	236.541i		−	0.276011i	−0.990431	−	0.138005i	$-0.955931\pi$
$857$		−	236.541i		−	0.276011i	0.990431	−	0.138005i	$-0.0440692\pi$
$858$		0			0
$859$	−646.957			−0.753151			−0.376575	−	0.926386i	$-0.622898\pi$
$859$	−646.957			−0.753151			−0.376575	+	0.926386i	$0.622898\pi$
$860$	−456.263	−	456.263i	−0.530539	−	0.530539i
$861$	−670.115			−0.778298
$862$			1022.44i			1.18613i
$863$	−344.605	−	344.605i	−0.399310	−	0.399310i	0.478680	−	0.877990i	$-0.341116\pi$
$863$	−344.605	−	344.605i	−0.399310	−	0.399310i	−0.877990	+	0.478680i	$0.841116\pi$
$864$	−20.7846	−	20.7846i	−0.0240563	−	0.0240563i
$865$	−1076.54	+	1076.54i	−1.24455	+	1.24455i
$866$	40.9607	−	40.9607i	0.0472987	−	0.0472987i
$867$	−340.726			−0.392994
$868$		−	312.518i		−	0.360044i
$869$	−646.655	+	646.655i	−0.744137	+	0.744137i
$870$		−	611.218i		−	0.702550i
$871$		0			0
$872$	32.3051			0.0370471
$873$	−74.1136	−	74.1136i	−0.0848953	−	0.0848953i
$874$	382.942			0.438148
$875$			2739.45i			3.13081i
$876$	33.5436	+	33.5436i	0.0382918	+	0.0382918i
$877$	622.004	+	622.004i	0.709240	+	0.709240i	0.966375	−	0.257135i	$-0.0827786\pi$
$877$	622.004	+	622.004i	0.709240	+	0.709240i	−0.257135	+	0.966375i	$0.582779\pi$
$878$	665.355	−	665.355i	0.757808	−	0.757808i
$879$	362.988	−	362.988i	0.412956	−	0.412956i
$880$	588.848			0.669145
$881$		−	41.4598i		−	0.0470599i	−0.999723	−	0.0235299i	$-0.992509\pi$
$881$		−	41.4598i		−	0.0470599i	0.999723	−	0.0235299i	$-0.00749050\pi$
$882$	−127.010	+	127.010i	−0.144002	+	0.144002i
$883$			28.0736i			0.0317934i	0.999874	+	0.0158967i	$0.00506029\pi$
$883$			28.0736i			0.0317934i	−0.999874	+	0.0158967i	$0.994940\pi$
$884$		0			0
$885$	746.099			0.843050
$886$	−267.578	−	267.578i	−0.302006	−	0.302006i
$887$	137.864			0.155427			0.0777135	−	0.996976i	$-0.475238\pi$
$887$	137.864			0.155427			0.0777135	+	0.996976i	$0.475238\pi$
$888$		−	103.275i		−	0.116301i
$889$	−182.584	−	182.584i	−0.205382	−	0.205382i
$890$	1045.95	+	1045.95i	1.17522	+	1.17522i
$891$	103.641	−	103.641i	0.116320	−	0.116320i
$892$	551.263	−	551.263i	0.618008	−	0.618008i
$893$	357.188			0.399987
$894$			71.0842i			0.0795125i
$895$	−2000.94	+	2000.94i	−2.23568	+	2.23568i
$896$		−	108.125i		−	0.120676i
$897$		0			0
$898$	−796.391			−0.886850
$899$	319.146	+	319.146i	0.355001	+	0.355001i
$900$	−340.263			−0.378070
$901$		−	375.317i		−	0.416556i
$902$	659.280	+	659.280i	0.730909	+	0.730909i
$903$	−417.763	−	417.763i	−0.462639	−	0.462639i
$904$	−232.815	+	232.815i	−0.257539	+	0.257539i
$905$	−124.509	+	124.509i	−0.137579	+	0.137579i
$906$	109.587			0.120957
$907$		−	896.456i		−	0.988375i	−0.869355	−	0.494187i	$-0.835466\pi$
$907$		−	896.456i		−	0.988375i	0.869355	−	0.494187i	$-0.164534\pi$
$908$	−188.550	+	188.550i	−0.207654	+	0.207654i
$909$			351.507i			0.386697i
$910$		0			0
$911$	−318.659			−0.349791			−0.174895	−	0.984587i	$-0.555959\pi$
$911$	−318.659			−0.349791			−0.174895	+	0.984587i	$0.555959\pi$
$912$	48.4881	+	48.4881i	0.0531667	+	0.0531667i
$913$	105.928			0.116022
$914$		−	942.261i		−	1.03092i
$915$	780.981	+	780.981i	0.853531	+	0.853531i
$916$	−609.732	−	609.732i	−0.665646	−	0.665646i
$917$	436.341	−	436.341i	0.475836	−	0.475836i
$918$	−49.9160	+	49.9160i	−0.0543748	+	0.0543748i
$919$	−100.528			−0.109389			−0.0546944	−	0.998503i	$-0.517418\pi$
$919$	−100.528			−0.109389			−0.0546944	+	0.998503i	$0.517418\pi$
$920$		−	699.475i		−	0.760299i
$921$	−383.156	+	383.156i	−0.416022	+	0.416022i
$922$			506.616i			0.549475i
$923$		0			0
$924$	539.160			0.583506
$925$	−845.354	−	845.354i	−0.913896	−	0.913896i
$926$	1260.58			1.36132
$927$		−	552.534i		−	0.596045i
$928$	110.419	+	110.419i	0.118985	+	0.118985i
$929$	−786.064	−	786.064i	−0.846140	−	0.846140i	0.143509	−	0.989649i	$-0.454161\pi$
$929$	−786.064	−	786.064i	−0.846140	−	0.846140i	−0.989649	+	0.143509i	$0.954161\pi$
$930$	255.989	−	255.989i	0.275257	−	0.275257i
$931$	296.300	−	296.300i	0.318259	−	0.318259i
$932$	−88.2828			−0.0947240
$933$			21.7469i			0.0233086i
$934$	−425.264	+	425.264i	−0.455315	+	0.455315i
$935$		−	1414.17i		−	1.51248i
$936$		0			0
$937$	−99.5793			−0.106275			−0.0531373	−	0.998587i	$-0.516922\pi$
$937$	−99.5793			−0.106275			−0.0531373	+	0.998587i	$0.516922\pi$
$938$	−383.151	−	383.151i	−0.408476	−	0.408476i
$939$	−1023.57			−1.09006
$940$		−	652.434i		−	0.694079i
$941$	795.092	+	795.092i	0.844943	+	0.844943i	0.989497	−	0.144554i	$-0.0461746\pi$
$941$	795.092	+	795.092i	0.844943	+	0.844943i	−0.144554	+	0.989497i	$0.546175\pi$
$942$	419.888	+	419.888i	0.445741	+	0.445741i
$943$	783.140	−	783.140i	0.830477	−	0.830477i
$944$	−134.785	+	134.785i	−0.142781	+	0.142781i
$945$	−448.894			−0.475020
$946$			822.017i			0.868940i
$947$	258.294	−	258.294i	0.272750	−	0.272750i	−0.557456	−	0.830206i	$-0.688223\pi$
$947$	258.294	−	258.294i	0.272750	−	0.272750i	0.830206	+	0.557456i	$0.188223\pi$
$948$			194.524i			0.205194i
$949$		0			0
$950$	793.793			0.835572
$951$	−94.7669	−	94.7669i	−0.0996497	−	0.0996497i
$952$	−259.672			−0.272765
$953$		−	302.820i		−	0.317755i	−0.987298	−	0.158877i	$-0.949213\pi$
$953$		−	302.820i		−	0.317755i	0.987298	−	0.158877i	$-0.0507875\pi$
$954$	117.209	+	117.209i	0.122861	+	0.122861i
$955$	−913.716	−	913.716i	−0.956771	−	0.956771i
$956$	31.6897	−	31.6897i	0.0331482	−	0.0331482i
$957$	−550.594	+	550.594i	−0.575334	+	0.575334i
$958$	389.623			0.406704
$959$		−	1951.25i		−	2.03467i
$960$	88.5675	−	88.5675i	0.0922578	−	0.0922578i
$961$		−	693.672i		−	0.721823i
$962$		0			0
$963$	21.4559			0.0222803
$964$	680.212	+	680.212i	0.705614	+	0.705614i
$965$	1516.93			1.57195
$966$		−	640.452i		−	0.662994i
$967$	228.726	+	228.726i	0.236532	+	0.236532i	0.815412	−	0.578881i	$-0.196510\pi$
$967$	228.726	+	228.726i	0.236532	+	0.236532i	−0.578881	+	0.815412i	$0.696510\pi$
$968$	−288.443	−	288.443i	−0.297978	−	0.297978i
$969$	116.448	−	116.448i	0.120174	−	0.120174i
$970$	315.813	−	315.813i	0.325581	−	0.325581i
$971$	−595.549			−0.613335			−0.306668	−	0.951817i	$-0.599214\pi$
$971$	−595.549			−0.613335			−0.306668	+	0.951817i	$0.599214\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	−429.875	+	429.875i	−0.441804	+	0.441804i
$974$			905.415i			0.929585i
$975$		0			0
$976$	−282.173			−0.289112
$977$	−675.329	−	675.329i	−0.691227	−	0.691227i	0.271275	−	0.962502i	$-0.412555\pi$
$977$	−675.329	−	675.329i	−0.691227	−	0.691227i	−0.962502	+	0.271275i	$0.912555\pi$
$978$	38.2444			0.0391048
$979$		−	1884.41i		−	1.92483i
$980$	−541.216	−	541.216i	−0.552261	−	0.552261i
$981$	24.2288	+	24.2288i	0.0246981	+	0.0246981i
$982$	−566.666	+	566.666i	−0.577053	+	0.577053i
$983$	265.546	−	265.546i	0.270138	−	0.270138i	−0.559018	−	0.829156i	$-0.688822\pi$
$983$	265.546	−	265.546i	0.270138	−	0.270138i	0.829156	+	0.559018i	$0.188822\pi$
$984$	198.322			0.201547
$985$			1540.19i			1.56364i
$986$	265.180	−	265.180i	0.268945	−	0.268945i
$987$		−	597.381i		−	0.605249i
$988$		0			0
$989$	976.450			0.987310
$990$	441.636	+	441.636i	0.446097	+	0.446097i
$991$	145.155			0.146473			0.0732366	−	0.997315i	$-0.476667\pi$
$991$	145.155			0.146473			0.0732366	+	0.997315i	$0.476667\pi$
$992$			92.4906i			0.0932365i
$993$	25.0360	+	25.0360i	0.0252125	+	0.0252125i
$994$	−305.785	−	305.785i	−0.307631	−	0.307631i
$995$	1033.72	−	1033.72i	1.03892	−	1.03892i
$996$	15.9325	−	15.9325i	0.0159965	−	0.0159965i
$997$	584.322			0.586081			0.293040	−	0.956100i	$-0.405333\pi$
$997$	584.322			0.586081			0.293040	+	0.956100i	$0.405333\pi$
$998$			818.583i			0.820224i
$999$	77.4564	−	77.4564i	0.0775339	−	0.0775339i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.3.f.h.775.1		8
13.3	even	3		78.3.l.c.7.1	✓	8
13.5	odd	4	inner	1014.3.f.h.577.1		8
13.6	odd	12		78.3.l.c.67.1	yes	8
13.8	odd	4		1014.3.f.j.577.2		8
13.12	even	2		1014.3.f.j.775.2		8
39.29	odd	6		234.3.bb.d.163.2		8
39.32	even	12		234.3.bb.d.145.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.3.l.c.7.1	✓	8	13.3	even	3
78.3.l.c.67.1	yes	8	13.6	odd	12
234.3.bb.d.145.2		8	39.32	even	12
234.3.bb.d.163.2		8	39.29	odd	6
1014.3.f.h.577.1		8	13.5	odd	4	inner
1014.3.f.h.775.1		8	1.1	even	1	trivial
1014.3.f.j.577.2		8	13.8	odd	4
1014.3.f.j.775.2		8	13.12	even	2

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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1014.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} -1.73205 q^{3} +2.00000i q^{4} +(-6.39181 - 6.39181i) q^{5} +(1.73205 + 1.73205i) q^{6} +(-6.75784 + 6.75784i) q^{7} +(2.00000 - 2.00000i) q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} -1.73205 q^{3} +2.00000i q^{4} +(-6.39181 - 6.39181i) q^{5} +(1.73205 + 1.73205i) q^{6} +(-6.75784 + 6.75784i) q^{7} +(2.00000 - 2.00000i) q^{8} +3.00000 q^{9} +12.7836i q^{10} +(11.5157 - 11.5157i) q^{11} -3.46410i q^{12} +13.5157 q^{14} +(11.0709 + 11.0709i) q^{15} -4.00000 q^{16} +9.60634i q^{17} +(-3.00000 - 3.00000i) q^{18} +(6.99865 + 6.99865i) q^{19} +(12.7836 - 12.7836i) q^{20} +(11.7049 - 11.7049i) q^{21} -23.0313 q^{22} +27.3583i q^{23} +(-3.46410 + 3.46410i) q^{24} +56.7105i q^{25} -5.19615 q^{27} +(-13.5157 - 13.5157i) q^{28} +27.6046 q^{29} -22.1419i q^{30} +(11.5613 + 11.5613i) q^{31} +(4.00000 + 4.00000i) q^{32} +(-19.9457 + 19.9457i) q^{33} +(9.60634 - 9.60634i) q^{34} +86.3896 q^{35} +6.00000i q^{36} +(-14.9065 + 14.9065i) q^{37} -13.9973i q^{38} -25.5672 q^{40} +(-28.6254 - 28.6254i) q^{41} -23.4098 q^{42} -35.6912i q^{43} +(23.0313 + 23.0313i) q^{44} +(-19.1754 - 19.1754i) q^{45} +(27.3583 - 27.3583i) q^{46} +(25.5184 - 25.5184i) q^{47} +6.92820 q^{48} -42.3367i q^{49} +(56.7105 - 56.7105i) q^{50} -16.6387i q^{51} -39.0697 q^{53} +(5.19615 + 5.19615i) q^{54} -147.212 q^{55} +27.0313i q^{56} +(-12.1220 - 12.1220i) q^{57} +(-27.6046 - 27.6046i) q^{58} +(33.6963 - 33.6963i) q^{59} +(-22.1419 + 22.1419i) q^{60} +70.5433 q^{61} -23.1226i q^{62} +(-20.2735 + 20.2735i) q^{63} -8.00000i q^{64} +39.8915 q^{66} +(-28.3486 - 28.3486i) q^{67} -19.2127 q^{68} -47.3859i q^{69} +(-86.3896 - 86.3896i) q^{70} +(-22.6245 - 22.6245i) q^{71} +(6.00000 - 6.00000i) q^{72} +(-9.68320 + 9.68320i) q^{73} +29.8130 q^{74} -98.2254i q^{75} +(-13.9973 + 13.9973i) q^{76} +155.642i q^{77} -56.1543 q^{79} +(25.5672 + 25.5672i) q^{80} +9.00000 q^{81} +57.2507i q^{82} +(4.59931 + 4.59931i) q^{83} +(23.4098 + 23.4098i) q^{84} +(61.4019 - 61.4019i) q^{85} +(-35.6912 + 35.6912i) q^{86} -47.8126 q^{87} -46.0627i q^{88} +(81.8193 - 81.8193i) q^{89} +38.3509i q^{90} -54.7165 q^{92} +(-20.0248 - 20.0248i) q^{93} -51.0367 q^{94} -89.4681i q^{95} +(-6.92820 - 6.92820i) q^{96} +(-24.7045 - 24.7045i) q^{97} +(-42.3367 + 42.3367i) q^{98} +(34.5470 - 34.5470i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 6 q^{5} - 2 q^{7} + 16 q^{8} + 24 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - 6 * q^5 - 2 * q^7 + 16 * q^8 + 24 * q^9	\( 8 q - 8 q^{2} - 6 q^{5} - 2 q^{7} + 16 q^{8} + 24 q^{9} - 12 q^{11} + 4 q^{14} + 6 q^{15} - 32 q^{16} - 24 q^{18} - 44 q^{19} + 12 q^{20} + 18 q^{21} + 24 q^{22} - 4 q^{28} - 72 q^{29} - 94 q^{31} + 32 q^{32} - 36 q^{33} + 60 q^{34} + 408 q^{35} - 46 q^{37} - 24 q^{40} - 30 q^{41} - 36 q^{42} - 24 q^{44} - 18 q^{45} + 144 q^{46} + 300 q^{47} + 208 q^{50} + 84 q^{53} - 792 q^{55} + 24 q^{57} + 72 q^{58} - 12 q^{59} - 12 q^{60} + 180 q^{61} - 6 q^{63} + 72 q^{66} - 74 q^{67} - 120 q^{68} - 408 q^{70} + 156 q^{71} + 48 q^{72} + 16 q^{73} + 92 q^{74} + 88 q^{76} - 96 q^{79} + 24 q^{80} + 72 q^{81} + 36 q^{84} + 234 q^{85} + 168 q^{86} - 60 q^{87} + 228 q^{89} - 288 q^{92} - 198 q^{93} - 600 q^{94} + 2 q^{97} - 32 q^{98} - 36 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 6 * q^5 - 2 * q^7 + 16 * q^8 + 24 * q^9 - 12 * q^11 + 4 * q^14 + 6 * q^15 - 32 * q^16 - 24 * q^18 - 44 * q^19 + 12 * q^20 + 18 * q^21 + 24 * q^22 - 4 * q^28 - 72 * q^29 - 94 * q^31 + 32 * q^32 - 36 * q^33 + 60 * q^34 + 408 * q^35 - 46 * q^37 - 24 * q^40 - 30 * q^41 - 36 * q^42 - 24 * q^44 - 18 * q^45 + 144 * q^46 + 300 * q^47 + 208 * q^50 + 84 * q^53 - 792 * q^55 + 24 * q^57 + 72 * q^58 - 12 * q^59 - 12 * q^60 + 180 * q^61 - 6 * q^63 + 72 * q^66 - 74 * q^67 - 120 * q^68 - 408 * q^70 + 156 * q^71 + 48 * q^72 + 16 * q^73 + 92 * q^74 + 88 * q^76 - 96 * q^79 + 24 * q^80 + 72 * q^81 + 36 * q^84 + 234 * q^85 + 168 * q^86 - 60 * q^87 + 228 * q^89 - 288 * q^92 - 198 * q^93 - 600 * q^94 + 2 * q^97 - 32 * q^98 - 36 * q^99

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