LMFDB - Embedded newform 750.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(1,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("750.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.a (trivial)

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:	yes
Analytic conductor:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	750.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +0.763932 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +0.763932 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.85410 q^{11} +1.00000 q^{12} +2.61803 q^{13} +0.763932 q^{14} +1.00000 q^{16} -3.38197 q^{17} +1.00000 q^{18} -4.47214 q^{19} +0.763932 q^{21} +2.85410 q^{22} -2.38197 q^{23} +1.00000 q^{24} +2.61803 q^{26} +1.00000 q^{27} +0.763932 q^{28} +1.38197 q^{29} +7.32624 q^{31} +1.00000 q^{32} +2.85410 q^{33} -3.38197 q^{34} +1.00000 q^{36} -2.85410 q^{37} -4.47214 q^{38} +2.61803 q^{39} +9.23607 q^{41} +0.763932 q^{42} +9.32624 q^{43} +2.85410 q^{44} -2.38197 q^{46} -7.85410 q^{47} +1.00000 q^{48} -6.41641 q^{49} -3.38197 q^{51} +2.61803 q^{52} -13.2361 q^{53} +1.00000 q^{54} +0.763932 q^{56} -4.47214 q^{57} +1.38197 q^{58} -3.09017 q^{59} +10.9443 q^{61} +7.32624 q^{62} +0.763932 q^{63} +1.00000 q^{64} +2.85410 q^{66} -12.3262 q^{67} -3.38197 q^{68} -2.38197 q^{69} -11.4164 q^{71} +1.00000 q^{72} -10.4721 q^{73} -2.85410 q^{74} -4.47214 q^{76} +2.18034 q^{77} +2.61803 q^{78} +7.56231 q^{79} +1.00000 q^{81} +9.23607 q^{82} -7.70820 q^{83} +0.763932 q^{84} +9.32624 q^{86} +1.38197 q^{87} +2.85410 q^{88} +16.1803 q^{89} +2.00000 q^{91} -2.38197 q^{92} +7.32624 q^{93} -7.85410 q^{94} +1.00000 q^{96} -4.76393 q^{97} -6.41641 q^{98} +2.85410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + 6 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + 6 * q^7 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + 6 q^{7} + 2 q^{8} + 2 q^{9} - q^{11} + 2 q^{12} + 3 q^{13} + 6 q^{14} + 2 q^{16} - 9 q^{17} + 2 q^{18} + 6 q^{21} - q^{22} - 7 q^{23} + 2 q^{24} + 3 q^{26} + 2 q^{27} + 6 q^{28} + 5 q^{29} - q^{31} + 2 q^{32} - q^{33} - 9 q^{34} + 2 q^{36} + q^{37} + 3 q^{39} + 14 q^{41} + 6 q^{42} + 3 q^{43} - q^{44} - 7 q^{46} - 9 q^{47} + 2 q^{48} + 14 q^{49} - 9 q^{51} + 3 q^{52} - 22 q^{53} + 2 q^{54} + 6 q^{56} + 5 q^{58} + 5 q^{59} + 4 q^{61} - q^{62} + 6 q^{63} + 2 q^{64} - q^{66} - 9 q^{67} - 9 q^{68} - 7 q^{69} + 4 q^{71} + 2 q^{72} - 12 q^{73} + q^{74} - 18 q^{77} + 3 q^{78} - 5 q^{79} + 2 q^{81} + 14 q^{82} - 2 q^{83} + 6 q^{84} + 3 q^{86} + 5 q^{87} - q^{88} + 10 q^{89} + 4 q^{91} - 7 q^{92} - q^{93} - 9 q^{94} + 2 q^{96} - 14 q^{97} + 14 q^{98} - q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + 6 * q^7 + 2 * q^8 + 2 * q^9 - q^11 + 2 * q^12 + 3 * q^13 + 6 * q^14 + 2 * q^16 - 9 * q^17 + 2 * q^18 + 6 * q^21 - q^22 - 7 * q^23 + 2 * q^24 + 3 * q^26 + 2 * q^27 + 6 * q^28 + 5 * q^29 - q^31 + 2 * q^32 - q^33 - 9 * q^34 + 2 * q^36 + q^37 + 3 * q^39 + 14 * q^41 + 6 * q^42 + 3 * q^43 - q^44 - 7 * q^46 - 9 * q^47 + 2 * q^48 + 14 * q^49 - 9 * q^51 + 3 * q^52 - 22 * q^53 + 2 * q^54 + 6 * q^56 + 5 * q^58 + 5 * q^59 + 4 * q^61 - q^62 + 6 * q^63 + 2 * q^64 - q^66 - 9 * q^67 - 9 * q^68 - 7 * q^69 + 4 * q^71 + 2 * q^72 - 12 * q^73 + q^74 - 18 * q^77 + 3 * q^78 - 5 * q^79 + 2 * q^81 + 14 * q^82 - 2 * q^83 + 6 * q^84 + 3 * q^86 + 5 * q^87 - q^88 + 10 * q^89 + 4 * q^91 - 7 * q^92 - q^93 - 9 * q^94 + 2 * q^96 - 14 * q^97 + 14 * q^98 - q^99

Display 100 coefficients 10 coefficients

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	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	0.763932	0.288739	0.144370	−	0.989524i	$-0.453885\pi$
$7$	0.763932	0.288739	0.144370	+	0.989524i	$0.453885\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	2.85410	0.860544	0.430272	−	0.902699i	$-0.358418\pi$
$11$	2.85410	0.860544	0.430272	+	0.902699i	$0.358418\pi$
$12$	1.00000	0.288675
$13$	2.61803	0.726112	0.363056	−	0.931767i	$-0.381733\pi$
$13$	2.61803	0.726112	0.363056	+	0.931767i	$0.381733\pi$
$14$	0.763932	0.204169
$15$	0	0
$16$	1.00000	0.250000
$17$	−3.38197	−0.820247	−0.410124	−	0.912030i	$-0.634514\pi$
$17$	−3.38197	−0.820247	−0.410124	+	0.912030i	$0.634514\pi$
$18$	1.00000	0.235702
$19$	−4.47214	−1.02598	−0.512989	−	0.858395i	$-0.671462\pi$
$19$	−4.47214	−1.02598	−0.512989	+	0.858395i	$0.671462\pi$
$20$	0	0
$21$	0.763932	0.166704
$22$	2.85410	0.608497
$23$	−2.38197	−0.496674	−0.248337	−	0.968674i	$-0.579884\pi$
$23$	−2.38197	−0.496674	−0.248337	+	0.968674i	$0.579884\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	2.61803	0.513439
$27$	1.00000	0.192450
$28$	0.763932	0.144370
$29$	1.38197	0.256625	0.128312	−	0.991734i	$-0.459044\pi$
$29$	1.38197	0.256625	0.128312	+	0.991734i	$0.459044\pi$
$30$	0	0
$31$	7.32624	1.31583	0.657916	−	0.753092i	$-0.271438\pi$
$31$	7.32624	1.31583	0.657916	+	0.753092i	$0.271438\pi$
$32$	1.00000	0.176777
$33$	2.85410	0.496835
$34$	−3.38197	−0.580002
$35$	0	0
$36$	1.00000	0.166667
$37$	−2.85410	−0.469211	−0.234606	−	0.972091i	$-0.575380\pi$
$37$	−2.85410	−0.469211	−0.234606	+	0.972091i	$0.575380\pi$
$38$	−4.47214	−0.725476
$39$	2.61803	0.419221
$40$	0	0
$41$	9.23607	1.44243	0.721216	−	0.692711i	$-0.243584\pi$
$41$	9.23607	1.44243	0.721216	+	0.692711i	$0.243584\pi$
$42$	0.763932	0.117877
$43$	9.32624	1.42224	0.711119	−	0.703072i	$-0.248189\pi$
$43$	9.32624	1.42224	0.711119	+	0.703072i	$0.248189\pi$
$44$	2.85410	0.430272
$45$	0	0
$46$	−2.38197	−0.351202
$47$	−7.85410	−1.14564	−0.572819	−	0.819682i	$-0.694150\pi$
$47$	−7.85410	−1.14564	−0.572819	+	0.819682i	$0.694150\pi$
$48$	1.00000	0.144338
$49$	−6.41641	−0.916630
$50$	0	0
$51$	−3.38197	−0.473570
$52$	2.61803	0.363056
$53$	−13.2361	−1.81811	−0.909057	−	0.416672i	$-0.863196\pi$
$53$	−13.2361	−1.81811	−0.909057	+	0.416672i	$0.863196\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	0.763932	0.102085
$57$	−4.47214	−0.592349
$58$	1.38197	0.181461
$59$	−3.09017	−0.402306	−0.201153	−	0.979560i	$-0.564469\pi$
$59$	−3.09017	−0.402306	−0.201153	+	0.979560i	$0.564469\pi$
$60$	0	0
$61$	10.9443	1.40127	0.700635	−	0.713520i	$-0.252900\pi$
$61$	10.9443	1.40127	0.700635	+	0.713520i	$0.252900\pi$
$62$	7.32624	0.930433
$63$	0.763932	0.0962464
$64$	1.00000	0.125000
$65$	0	0
$66$	2.85410	0.351316
$67$	−12.3262	−1.50589	−0.752945	−	0.658084i	$-0.771367\pi$
$67$	−12.3262	−1.50589	−0.752945	+	0.658084i	$0.771367\pi$
$68$	−3.38197	−0.410124
$69$	−2.38197	−0.286755
$70$	0	0
$71$	−11.4164	−1.35488	−0.677439	−	0.735579i	$-0.736910\pi$
$71$	−11.4164	−1.35488	−0.677439	+	0.735579i	$0.736910\pi$
$72$	1.00000	0.117851
$73$	−10.4721	−1.22567	−0.612835	−	0.790211i	$-0.709971\pi$
$73$	−10.4721	−1.22567	−0.612835	+	0.790211i	$0.709971\pi$
$74$	−2.85410	−0.331783
$75$	0	0
$76$	−4.47214	−0.512989
$77$	2.18034	0.248473
$78$	2.61803	0.296434
$79$	7.56231	0.850826	0.425413	−	0.904999i	$-0.360129\pi$
$79$	7.56231	0.850826	0.425413	+	0.904999i	$0.360129\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	9.23607	1.01995
$83$	−7.70820	−0.846085	−0.423043	−	0.906110i	$-0.639038\pi$
$83$	−7.70820	−0.846085	−0.423043	+	0.906110i	$0.639038\pi$
$84$	0.763932	0.0833518
$85$	0	0
$86$	9.32624	1.00567
$87$	1.38197	0.148162
$88$	2.85410	0.304248
$89$	16.1803	1.71511	0.857556	−	0.514390i	$-0.171982\pi$
$89$	16.1803	1.71511	0.857556	+	0.514390i	$0.171982\pi$
$90$	0	0
$91$	2.00000	0.209657
$92$	−2.38197	−0.248337
$93$	7.32624	0.759695
$94$	−7.85410	−0.810089
$95$	0	0
$96$	1.00000	0.102062
$97$	−4.76393	−0.483704	−0.241852	−	0.970313i	$-0.577755\pi$
$97$	−4.76393	−0.483704	−0.241852	+	0.970313i	$0.577755\pi$
$98$	−6.41641	−0.648155
$99$	2.85410	0.286848
$100$	0	0
$101$	−13.3262	−1.32601	−0.663005	−	0.748615i	$-0.730719\pi$
$101$	−13.3262	−1.32601	−0.663005	+	0.748615i	$0.730719\pi$
$102$	−3.38197	−0.334865
$103$	7.41641	0.730760	0.365380	−	0.930858i	$-0.380939\pi$
$103$	7.41641	0.730760	0.365380	+	0.930858i	$0.380939\pi$
$104$	2.61803	0.256719
$105$	0	0
$106$	−13.2361	−1.28560
$107$	−0.291796	−0.0282090	−0.0141045	−	0.999901i	$-0.504490\pi$
$107$	−0.291796	−0.0282090	−0.0141045	+	0.999901i	$0.504490\pi$
$108$	1.00000	0.0962250
$109$	−10.0000	−0.957826	−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000	−0.957826	−0.478913	+	0.877862i	$0.658969\pi$
$110$	0	0
$111$	−2.85410	−0.270899
$112$	0.763932	0.0721848
$113$	−18.5623	−1.74619	−0.873097	−	0.487546i	$-0.837892\pi$
$113$	−18.5623	−1.74619	−0.873097	+	0.487546i	$0.837892\pi$
$114$	−4.47214	−0.418854
$115$	0	0
$116$	1.38197	0.128312
$117$	2.61803	0.242037
$118$	−3.09017	−0.284473
$119$	−2.58359	−0.236838
$120$	0	0
$121$	−2.85410	−0.259464
$122$	10.9443	0.990848
$123$	9.23607	0.832788
$124$	7.32624	0.657916
$125$	0	0
$126$	0.763932	0.0680565
$127$	12.4721	1.10672	0.553362	−	0.832941i	$-0.313345\pi$
$127$	12.4721	1.10672	0.553362	+	0.832941i	$0.313345\pi$
$128$	1.00000	0.0883883
$129$	9.32624	0.821129
$130$	0	0
$131$	−8.00000	−0.698963	−0.349482	−	0.936943i	$-0.613642\pi$
$131$	−8.00000	−0.698963	−0.349482	+	0.936943i	$0.613642\pi$
$132$	2.85410	0.248418
$133$	−3.41641	−0.296240
$134$	−12.3262	−1.06482
$135$	0	0
$136$	−3.38197	−0.290001
$137$	1.61803	0.138238	0.0691190	−	0.997608i	$-0.477981\pi$
$137$	1.61803	0.138238	0.0691190	+	0.997608i	$0.477981\pi$
$138$	−2.38197	−0.202766
$139$	12.7639	1.08262	0.541311	−	0.840822i	$-0.317928\pi$
$139$	12.7639	1.08262	0.541311	+	0.840822i	$0.317928\pi$
$140$	0	0
$141$	−7.85410	−0.661435
$142$	−11.4164	−0.958044
$143$	7.47214	0.624851
$144$	1.00000	0.0833333
$145$	0	0
$146$	−10.4721	−0.866680
$147$	−6.41641	−0.529216
$148$	−2.85410	−0.234606
$149$	−4.47214	−0.366372	−0.183186	−	0.983078i	$-0.558641\pi$
$149$	−4.47214	−0.366372	−0.183186	+	0.983078i	$0.558641\pi$
$150$	0	0
$151$	−19.5066	−1.58742	−0.793711	−	0.608295i	$-0.791854\pi$
$151$	−19.5066	−1.58742	−0.793711	+	0.608295i	$0.791854\pi$
$152$	−4.47214	−0.362738
$153$	−3.38197	−0.273416
$154$	2.18034	0.175697
$155$	0	0
$156$	2.61803	0.209610
$157$	4.38197	0.349719	0.174859	−	0.984593i	$-0.444053\pi$
$157$	4.38197	0.349719	0.174859	+	0.984593i	$0.444053\pi$
$158$	7.56231	0.601625
$159$	−13.2361	−1.04969
$160$	0	0
$161$	−1.81966	−0.143409
$162$	1.00000	0.0785674
$163$	21.5623	1.68889	0.844445	−	0.535642i	$-0.179930\pi$
$163$	21.5623	1.68889	0.844445	+	0.535642i	$0.179930\pi$
$164$	9.23607	0.721216
$165$	0	0
$166$	−7.70820	−0.598273
$167$	14.3820	1.11291	0.556455	−	0.830878i	$-0.312161\pi$
$167$	14.3820	1.11291	0.556455	+	0.830878i	$0.312161\pi$
$168$	0.763932	0.0589386
$169$	−6.14590	−0.472761
$170$	0	0
$171$	−4.47214	−0.341993
$172$	9.32624	0.711119
$173$	−3.23607	−0.246034	−0.123017	−	0.992405i	$-0.539257\pi$
$173$	−3.23607	−0.246034	−0.123017	+	0.992405i	$0.539257\pi$
$174$	1.38197	0.104767
$175$	0	0
$176$	2.85410	0.215136
$177$	−3.09017	−0.232271
$178$	16.1803	1.21277
$179$	−14.4721	−1.08170	−0.540849	−	0.841120i	$-0.681897\pi$
$179$	−14.4721	−1.08170	−0.540849	+	0.841120i	$0.681897\pi$
$180$	0	0
$181$	6.47214	0.481070	0.240535	−	0.970640i	$-0.422677\pi$
$181$	6.47214	0.481070	0.240535	+	0.970640i	$0.422677\pi$
$182$	2.00000	0.148250
$183$	10.9443	0.809024
$184$	−2.38197	−0.175601
$185$	0	0
$186$	7.32624	0.537186
$187$	−9.65248	−0.705859
$188$	−7.85410	−0.572819
$189$	0.763932	0.0555679
$190$	0	0
$191$	−3.52786	−0.255267	−0.127634	−	0.991821i	$-0.540738\pi$
$191$	−3.52786	−0.255267	−0.127634	+	0.991821i	$0.540738\pi$
$192$	1.00000	0.0721688
$193$	1.23607	0.0889741	0.0444871	−	0.999010i	$-0.485835\pi$
$193$	1.23607	0.0889741	0.0444871	+	0.999010i	$0.485835\pi$
$194$	−4.76393	−0.342030
$195$	0	0
$196$	−6.41641	−0.458315
$197$	−6.47214	−0.461121	−0.230560	−	0.973058i	$-0.574056\pi$
$197$	−6.47214	−0.461121	−0.230560	+	0.973058i	$0.574056\pi$
$198$	2.85410	0.202832
$199$	13.0902	0.927938	0.463969	−	0.885852i	$-0.346425\pi$
$199$	13.0902	0.927938	0.463969	+	0.885852i	$0.346425\pi$
$200$	0	0
$201$	−12.3262	−0.869426
$202$	−13.3262	−0.937631
$203$	1.05573	0.0740976
$204$	−3.38197	−0.236785
$205$	0	0
$206$	7.41641	0.516726
$207$	−2.38197	−0.165558
$208$	2.61803	0.181528
$209$	−12.7639	−0.882900
$210$	0	0
$211$	12.0000	0.826114	0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000	0.826114	0.413057	+	0.910705i	$0.364461\pi$
$212$	−13.2361	−0.909057
$213$	−11.4164	−0.782239
$214$	−0.291796	−0.0199468
$215$	0	0
$216$	1.00000	0.0680414
$217$	5.59675	0.379932
$218$	−10.0000	−0.677285
$219$	−10.4721	−0.707641
$220$	0	0
$221$	−8.85410	−0.595591
$222$	−2.85410	−0.191555
$223$	10.1803	0.681726	0.340863	−	0.940113i	$-0.389281\pi$
$223$	10.1803	0.681726	0.340863	+	0.940113i	$0.389281\pi$
$224$	0.763932	0.0510424
$225$	0	0
$226$	−18.5623	−1.23475
$227$	−2.00000	−0.132745	−0.0663723	−	0.997795i	$-0.521143\pi$
$227$	−2.00000	−0.132745	−0.0663723	+	0.997795i	$0.521143\pi$
$228$	−4.47214	−0.296174
$229$	17.2361	1.13899	0.569496	−	0.821994i	$-0.307139\pi$
$229$	17.2361	1.13899	0.569496	+	0.821994i	$0.307139\pi$
$230$	0	0
$231$	2.18034	0.143456
$232$	1.38197	0.0907305
$233$	−1.20163	−0.0787211	−0.0393606	−	0.999225i	$-0.512532\pi$
$233$	−1.20163	−0.0787211	−0.0393606	+	0.999225i	$0.512532\pi$
$234$	2.61803	0.171146
$235$	0	0
$236$	−3.09017	−0.201153
$237$	7.56231	0.491225
$238$	−2.58359	−0.167469
$239$	11.7082	0.757341	0.378670	−	0.925532i	$-0.376381\pi$
$239$	11.7082	0.757341	0.378670	+	0.925532i	$0.376381\pi$
$240$	0	0
$241$	6.79837	0.437922	0.218961	−	0.975734i	$-0.429733\pi$
$241$	6.79837	0.437922	0.218961	+	0.975734i	$0.429733\pi$
$242$	−2.85410	−0.183469
$243$	1.00000	0.0641500
$244$	10.9443	0.700635
$245$	0	0
$246$	9.23607	0.588870
$247$	−11.7082	−0.744975
$248$	7.32624	0.465217
$249$	−7.70820	−0.488488
$250$	0	0
$251$	−5.56231	−0.351090	−0.175545	−	0.984471i	$-0.556169\pi$
$251$	−5.56231	−0.351090	−0.175545	+	0.984471i	$0.556169\pi$
$252$	0.763932	0.0481232
$253$	−6.79837	−0.427410
$254$	12.4721	0.782571
$255$	0	0
$256$	1.00000	0.0625000
$257$	−17.8541	−1.11371	−0.556854	−	0.830610i	$-0.687992\pi$
$257$	−17.8541	−1.11371	−0.556854	+	0.830610i	$0.687992\pi$
$258$	9.32624	0.580626
$259$	−2.18034	−0.135480
$260$	0	0
$261$	1.38197	0.0855415
$262$	−8.00000	−0.494242
$263$	19.8541	1.22426	0.612128	−	0.790759i	$-0.290314\pi$
$263$	19.8541	1.22426	0.612128	+	0.790759i	$0.290314\pi$
$264$	2.85410	0.175658
$265$	0	0
$266$	−3.41641	−0.209473
$267$	16.1803	0.990221
$268$	−12.3262	−0.752945
$269$	3.61803	0.220595	0.110298	−	0.993899i	$-0.464820\pi$
$269$	3.61803	0.220595	0.110298	+	0.993899i	$0.464820\pi$
$270$	0	0
$271$	7.20163	0.437468	0.218734	−	0.975785i	$-0.429807\pi$
$271$	7.20163	0.437468	0.218734	+	0.975785i	$0.429807\pi$
$272$	−3.38197	−0.205062
$273$	2.00000	0.121046
$274$	1.61803	0.0977490
$275$	0	0
$276$	−2.38197	−0.143378
$277$	32.4721	1.95106	0.975531	−	0.219863i	$-0.0705610\pi$
$277$	32.4721	1.95106	0.975531	+	0.219863i	$0.0705610\pi$
$278$	12.7639	0.765530
$279$	7.32624	0.438610
$280$	0	0
$281$	−20.3607	−1.21462	−0.607308	−	0.794466i	$-0.707751\pi$
$281$	−20.3607	−1.21462	−0.607308	+	0.794466i	$0.707751\pi$
$282$	−7.85410	−0.467705
$283$	−30.2705	−1.79940	−0.899698	−	0.436514i	$-0.856213\pi$
$283$	−30.2705	−1.79940	−0.899698	+	0.436514i	$0.856213\pi$
$284$	−11.4164	−0.677439
$285$	0	0
$286$	7.47214	0.441837
$287$	7.05573	0.416486
$288$	1.00000	0.0589256
$289$	−5.56231	−0.327194
$290$	0	0
$291$	−4.76393	−0.279267
$292$	−10.4721	−0.612835
$293$	−2.18034	−0.127377	−0.0636884	−	0.997970i	$-0.520286\pi$
$293$	−2.18034	−0.127377	−0.0636884	+	0.997970i	$0.520286\pi$
$294$	−6.41641	−0.374213
$295$	0	0
$296$	−2.85410	−0.165891
$297$	2.85410	0.165612
$298$	−4.47214	−0.259064
$299$	−6.23607	−0.360641
$300$	0	0
$301$	7.12461	0.410656
$302$	−19.5066	−1.12248
$303$	−13.3262	−0.765572
$304$	−4.47214	−0.256495
$305$	0	0
$306$	−3.38197	−0.193334
$307$	31.6180	1.80454	0.902268	−	0.431175i	$-0.141901\pi$
$307$	31.6180	1.80454	0.902268	+	0.431175i	$0.141901\pi$
$308$	2.18034	0.124236
$309$	7.41641	0.421905
$310$	0	0
$311$	34.3607	1.94842	0.974208	−	0.225653i	$-0.0724516\pi$
$311$	34.3607	1.94842	0.974208	+	0.225653i	$0.0724516\pi$
$312$	2.61803	0.148217
$313$	2.94427	0.166420	0.0832100	−	0.996532i	$-0.473483\pi$
$313$	2.94427	0.166420	0.0832100	+	0.996532i	$0.473483\pi$
$314$	4.38197	0.247289
$315$	0	0
$316$	7.56231	0.425413
$317$	32.0689	1.80117	0.900584	−	0.434682i	$-0.143139\pi$
$317$	32.0689	1.80117	0.900584	+	0.434682i	$0.143139\pi$
$318$	−13.2361	−0.742242
$319$	3.94427	0.220837
$320$	0	0
$321$	−0.291796	−0.0162865
$322$	−1.81966	−0.101406
$323$	15.1246	0.841556
$324$	1.00000	0.0555556
$325$	0	0
$326$	21.5623	1.19423
$327$	−10.0000	−0.553001
$328$	9.23607	0.509977
$329$	−6.00000	−0.330791
$330$	0	0
$331$	25.4164	1.39701	0.698506	−	0.715604i	$-0.253849\pi$
$331$	25.4164	1.39701	0.698506	+	0.715604i	$0.253849\pi$
$332$	−7.70820	−0.423043
$333$	−2.85410	−0.156404
$334$	14.3820	0.786946
$335$	0	0
$336$	0.763932	0.0416759
$337$	−35.4164	−1.92925	−0.964627	−	0.263617i	$-0.915084\pi$
$337$	−35.4164	−1.92925	−0.964627	+	0.263617i	$0.915084\pi$
$338$	−6.14590	−0.334293
$339$	−18.5623	−1.00817
$340$	0	0
$341$	20.9098	1.13233
$342$	−4.47214	−0.241825
$343$	−10.2492	−0.553406
$344$	9.32624	0.502837
$345$	0	0
$346$	−3.23607	−0.173972
$347$	4.58359	0.246060	0.123030	−	0.992403i	$-0.460739\pi$
$347$	4.58359	0.246060	0.123030	+	0.992403i	$0.460739\pi$
$348$	1.38197	0.0740812
$349$	−8.94427	−0.478776	−0.239388	−	0.970924i	$-0.576947\pi$
$349$	−8.94427	−0.478776	−0.239388	+	0.970924i	$0.576947\pi$
$350$	0	0
$351$	2.61803	0.139740
$352$	2.85410	0.152124
$353$	−16.8541	−0.897053	−0.448527	−	0.893769i	$-0.648051\pi$
$353$	−16.8541	−0.897053	−0.448527	+	0.893769i	$0.648051\pi$
$354$	−3.09017	−0.164241
$355$	0	0
$356$	16.1803	0.857556
$357$	−2.58359	−0.136738
$358$	−14.4721	−0.764876
$359$	6.58359	0.347469	0.173734	−	0.984793i	$-0.444417\pi$
$359$	6.58359	0.347469	0.173734	+	0.984793i	$0.444417\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	6.47214	0.340168
$363$	−2.85410	−0.149802
$364$	2.00000	0.104828
$365$	0	0
$366$	10.9443	0.572066
$367$	−0.291796	−0.0152316	−0.00761582	−	0.999971i	$-0.502424\pi$
$367$	−0.291796	−0.0152316	−0.00761582	+	0.999971i	$0.502424\pi$
$368$	−2.38197	−0.124169
$369$	9.23607	0.480810
$370$	0	0
$371$	−10.1115	−0.524961
$372$	7.32624	0.379848
$373$	−14.6180	−0.756893	−0.378447	−	0.925623i	$-0.623542\pi$
$373$	−14.6180	−0.756893	−0.378447	+	0.925623i	$0.623542\pi$
$374$	−9.65248	−0.499118
$375$	0	0
$376$	−7.85410	−0.405044
$377$	3.61803	0.186338
$378$	0.763932	0.0392924
$379$	12.7639	0.655639	0.327820	−	0.944740i	$-0.393686\pi$
$379$	12.7639	0.655639	0.327820	+	0.944740i	$0.393686\pi$
$380$	0	0
$381$	12.4721	0.638967
$382$	−3.52786	−0.180501
$383$	24.0000	1.22634	0.613171	−	0.789950i	$-0.289894\pi$
$383$	24.0000	1.22634	0.613171	+	0.789950i	$0.289894\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	1.23607	0.0629142
$387$	9.32624	0.474079
$388$	−4.76393	−0.241852
$389$	−7.56231	−0.383424	−0.191712	−	0.981451i	$-0.561404\pi$
$389$	−7.56231	−0.383424	−0.191712	+	0.981451i	$0.561404\pi$
$390$	0	0
$391$	8.05573	0.407396
$392$	−6.41641	−0.324078
$393$	−8.00000	−0.403547
$394$	−6.47214	−0.326061
$395$	0	0
$396$	2.85410	0.143424
$397$	30.3607	1.52376	0.761879	−	0.647719i	$-0.224277\pi$
$397$	30.3607	1.52376	0.761879	+	0.647719i	$0.224277\pi$
$398$	13.0902	0.656151
$399$	−3.41641	−0.171034
$400$	0	0
$401$	26.4721	1.32196	0.660978	−	0.750406i	$-0.270142\pi$
$401$	26.4721	1.32196	0.660978	+	0.750406i	$0.270142\pi$
$402$	−12.3262	−0.614777
$403$	19.1803	0.955441
$404$	−13.3262	−0.663005
$405$	0	0
$406$	1.05573	0.0523949
$407$	−8.14590	−0.403777
$408$	−3.38197	−0.167432
$409$	−22.5623	−1.11563	−0.557817	−	0.829964i	$-0.688361\pi$
$409$	−22.5623	−1.11563	−0.557817	+	0.829964i	$0.688361\pi$
$410$	0	0
$411$	1.61803	0.0798117
$412$	7.41641	0.365380
$413$	−2.36068	−0.116161
$414$	−2.38197	−0.117067
$415$	0	0
$416$	2.61803	0.128360
$417$	12.7639	0.625052
$418$	−12.7639	−0.624304
$419$	2.11146	0.103151	0.0515757	−	0.998669i	$-0.483576\pi$
$419$	2.11146	0.103151	0.0515757	+	0.998669i	$0.483576\pi$
$420$	0	0
$421$	12.0000	0.584844	0.292422	−	0.956289i	$-0.405539\pi$
$421$	12.0000	0.584844	0.292422	+	0.956289i	$0.405539\pi$
$422$	12.0000	0.584151
$423$	−7.85410	−0.381880
$424$	−13.2361	−0.642800
$425$	0	0
$426$	−11.4164	−0.553127
$427$	8.36068	0.404602
$428$	−0.291796	−0.0141045
$429$	7.47214	0.360758
$430$	0	0
$431$	−1.81966	−0.0876499	−0.0438250	−	0.999039i	$-0.513954\pi$
$431$	−1.81966	−0.0876499	−0.0438250	+	0.999039i	$0.513954\pi$
$432$	1.00000	0.0481125
$433$	−40.0689	−1.92559	−0.962794	−	0.270237i	$-0.912898\pi$
$433$	−40.0689	−1.92559	−0.962794	+	0.270237i	$0.912898\pi$
$434$	5.59675	0.268652
$435$	0	0
$436$	−10.0000	−0.478913
$437$	10.6525	0.509577
$438$	−10.4721	−0.500378
$439$	19.1459	0.913784	0.456892	−	0.889522i	$-0.348963\pi$
$439$	19.1459	0.913784	0.456892	+	0.889522i	$0.348963\pi$
$440$	0	0
$441$	−6.41641	−0.305543
$442$	−8.85410	−0.421147
$443$	14.6525	0.696160	0.348080	−	0.937465i	$-0.386834\pi$
$443$	14.6525	0.696160	0.348080	+	0.937465i	$0.386834\pi$
$444$	−2.85410	−0.135450
$445$	0	0
$446$	10.1803	0.482053
$447$	−4.47214	−0.211525
$448$	0.763932	0.0360924
$449$	27.8885	1.31614	0.658071	−	0.752956i	$-0.271373\pi$
$449$	27.8885	1.31614	0.658071	+	0.752956i	$0.271373\pi$
$450$	0	0
$451$	26.3607	1.24128
$452$	−18.5623	−0.873097
$453$	−19.5066	−0.916499
$454$	−2.00000	−0.0938647
$455$	0	0
$456$	−4.47214	−0.209427
$457$	−30.9443	−1.44751	−0.723756	−	0.690056i	$-0.757586\pi$
$457$	−30.9443	−1.44751	−0.723756	+	0.690056i	$0.757586\pi$
$458$	17.2361	0.805389
$459$	−3.38197	−0.157857
$460$	0	0
$461$	−21.0902	−0.982267	−0.491134	−	0.871084i	$-0.663417\pi$
$461$	−21.0902	−0.982267	−0.491134	+	0.871084i	$0.663417\pi$
$462$	2.18034	0.101439
$463$	28.0689	1.30447	0.652236	−	0.758016i	$-0.273831\pi$
$463$	28.0689	1.30447	0.652236	+	0.758016i	$0.273831\pi$
$464$	1.38197	0.0641562
$465$	0	0
$466$	−1.20163	−0.0556643
$467$	16.2918	0.753894	0.376947	−	0.926235i	$-0.376974\pi$
$467$	16.2918	0.753894	0.376947	+	0.926235i	$0.376974\pi$
$468$	2.61803	0.121019
$469$	−9.41641	−0.434809
$470$	0	0
$471$	4.38197	0.201910
$472$	−3.09017	−0.142237
$473$	26.6180	1.22390
$474$	7.56231	0.347348
$475$	0	0
$476$	−2.58359	−0.118419
$477$	−13.2361	−0.606038
$478$	11.7082	0.535521
$479$	−29.5967	−1.35231	−0.676155	−	0.736759i	$-0.736355\pi$
$479$	−29.5967	−1.35231	−0.676155	+	0.736759i	$0.736355\pi$
$480$	0	0
$481$	−7.47214	−0.340700
$482$	6.79837	0.309657
$483$	−1.81966	−0.0827974
$484$	−2.85410	−0.129732
$485$	0	0
$486$	1.00000	0.0453609
$487$	29.7082	1.34621	0.673104	−	0.739548i	$-0.264961\pi$
$487$	29.7082	1.34621	0.673104	+	0.739548i	$0.264961\pi$
$488$	10.9443	0.495424
$489$	21.5623	0.975081
$490$	0	0
$491$	19.0344	0.859012	0.429506	−	0.903064i	$-0.358688\pi$
$491$	19.0344	0.859012	0.429506	+	0.903064i	$0.358688\pi$
$492$	9.23607	0.416394
$493$	−4.67376	−0.210496
$494$	−11.7082	−0.526777
$495$	0	0
$496$	7.32624	0.328958
$497$	−8.72136	−0.391206
$498$	−7.70820	−0.345413
$499$	−3.81966	−0.170991	−0.0854957	−	0.996339i	$-0.527247\pi$
$499$	−3.81966	−0.170991	−0.0854957	+	0.996339i	$0.527247\pi$
$500$	0	0
$501$	14.3820	0.642539
$502$	−5.56231	−0.248258
$503$	−1.52786	−0.0681241	−0.0340620	−	0.999420i	$-0.510844\pi$
$503$	−1.52786	−0.0681241	−0.0340620	+	0.999420i	$0.510844\pi$
$504$	0.763932	0.0340282
$505$	0	0
$506$	−6.79837	−0.302225
$507$	−6.14590	−0.272949
$508$	12.4721	0.553362
$509$	38.9443	1.72617	0.863087	−	0.505055i	$-0.168528\pi$
$509$	38.9443	1.72617	0.863087	+	0.505055i	$0.168528\pi$
$510$	0	0
$511$	−8.00000	−0.353899
$512$	1.00000	0.0441942
$513$	−4.47214	−0.197450
$514$	−17.8541	−0.787511
$515$	0	0
$516$	9.32624	0.410565
$517$	−22.4164	−0.985872
$518$	−2.18034	−0.0957986
$519$	−3.23607	−0.142048
$520$	0	0
$521$	5.81966	0.254964	0.127482	−	0.991841i	$-0.459311\pi$
$521$	5.81966	0.254964	0.127482	+	0.991841i	$0.459311\pi$
$522$	1.38197	0.0604870
$523$	−1.85410	−0.0810742	−0.0405371	−	0.999178i	$-0.512907\pi$
$523$	−1.85410	−0.0810742	−0.0405371	+	0.999178i	$0.512907\pi$
$524$	−8.00000	−0.349482
$525$	0	0
$526$	19.8541	0.865680
$527$	−24.7771	−1.07931
$528$	2.85410	0.124209
$529$	−17.3262	−0.753315
$530$	0	0
$531$	−3.09017	−0.134102
$532$	−3.41641	−0.148120
$533$	24.1803	1.04737
$534$	16.1803	0.700192
$535$	0	0
$536$	−12.3262	−0.532412
$537$	−14.4721	−0.624519
$538$	3.61803	0.155985
$539$	−18.3131	−0.788800
$540$	0	0
$541$	−29.7082	−1.27726	−0.638628	−	0.769516i	$-0.720498\pi$
$541$	−29.7082	−1.27726	−0.638628	+	0.769516i	$0.720498\pi$
$542$	7.20163	0.309336
$543$	6.47214	0.277746
$544$	−3.38197	−0.145001
$545$	0	0
$546$	2.00000	0.0855921
$547$	−29.5623	−1.26399	−0.631996	−	0.774971i	$-0.717764\pi$
$547$	−29.5623	−1.26399	−0.631996	+	0.774971i	$0.717764\pi$
$548$	1.61803	0.0691190
$549$	10.9443	0.467090
$550$	0	0
$551$	−6.18034	−0.263291
$552$	−2.38197	−0.101383
$553$	5.77709	0.245667
$554$	32.4721	1.37961
$555$	0	0
$556$	12.7639	0.541311
$557$	9.05573	0.383704	0.191852	−	0.981424i	$-0.438551\pi$
$557$	9.05573	0.383704	0.191852	+	0.981424i	$0.438551\pi$
$558$	7.32624	0.310144
$559$	24.4164	1.03270
$560$	0	0
$561$	−9.65248	−0.407528
$562$	−20.3607	−0.858863
$563$	38.0689	1.60441	0.802206	−	0.597047i	$-0.203660\pi$
$563$	38.0689	1.60441	0.802206	+	0.597047i	$0.203660\pi$
$564$	−7.85410	−0.330717
$565$	0	0
$566$	−30.2705	−1.27236
$567$	0.763932	0.0320821
$568$	−11.4164	−0.479022
$569$	4.47214	0.187482	0.0937408	−	0.995597i	$-0.470117\pi$
$569$	4.47214	0.187482	0.0937408	+	0.995597i	$0.470117\pi$
$570$	0	0
$571$	−13.5279	−0.566123	−0.283062	−	0.959102i	$-0.591350\pi$
$571$	−13.5279	−0.566123	−0.283062	+	0.959102i	$0.591350\pi$
$572$	7.47214	0.312426
$573$	−3.52786	−0.147379
$574$	7.05573	0.294500
$575$	0	0
$576$	1.00000	0.0416667
$577$	39.3050	1.63629	0.818143	−	0.575014i	$-0.195004\pi$
$577$	39.3050	1.63629	0.818143	+	0.575014i	$0.195004\pi$
$578$	−5.56231	−0.231361
$579$	1.23607	0.0513692
$580$	0	0
$581$	−5.88854	−0.244298
$582$	−4.76393	−0.197471
$583$	−37.7771	−1.56457
$584$	−10.4721	−0.433340
$585$	0	0
$586$	−2.18034	−0.0900690
$587$	14.1803	0.585285	0.292643	−	0.956222i	$-0.405465\pi$
$587$	14.1803	0.585285	0.292643	+	0.956222i	$0.405465\pi$
$588$	−6.41641	−0.264608
$589$	−32.7639	−1.35001
$590$	0	0
$591$	−6.47214	−0.266228
$592$	−2.85410	−0.117303
$593$	40.6312	1.66852	0.834261	−	0.551369i	$-0.185894\pi$
$593$	40.6312	1.66852	0.834261	+	0.551369i	$0.185894\pi$
$594$	2.85410	0.117105
$595$	0	0
$596$	−4.47214	−0.183186
$597$	13.0902	0.535745
$598$	−6.23607	−0.255012
$599$	10.0000	0.408589	0.204294	−	0.978909i	$-0.434510\pi$
$599$	10.0000	0.408589	0.204294	+	0.978909i	$0.434510\pi$
$600$	0	0
$601$	0.0901699	0.00367811	0.00183905	−	0.999998i	$-0.499415\pi$
$601$	0.0901699	0.00367811	0.00183905	+	0.999998i	$0.499415\pi$
$602$	7.12461	0.290377
$603$	−12.3262	−0.501963
$604$	−19.5066	−0.793711
$605$	0	0
$606$	−13.3262	−0.541341
$607$	−29.8885	−1.21314	−0.606569	−	0.795031i	$-0.707455\pi$
$607$	−29.8885	−1.21314	−0.606569	+	0.795031i	$0.707455\pi$
$608$	−4.47214	−0.181369
$609$	1.05573	0.0427803
$610$	0	0
$611$	−20.5623	−0.831862
$612$	−3.38197	−0.136708
$613$	5.05573	0.204199	0.102099	−	0.994774i	$-0.467444\pi$
$613$	5.05573	0.204199	0.102099	+	0.994774i	$0.467444\pi$
$614$	31.6180	1.27600
$615$	0	0
$616$	2.18034	0.0878484
$617$	−16.4721	−0.663143	−0.331572	−	0.943430i	$-0.607579\pi$
$617$	−16.4721	−0.663143	−0.331572	+	0.943430i	$0.607579\pi$
$618$	7.41641	0.298332
$619$	3.81966	0.153525	0.0767626	−	0.997049i	$-0.475542\pi$
$619$	3.81966	0.153525	0.0767626	+	0.997049i	$0.475542\pi$
$620$	0	0
$621$	−2.38197	−0.0955850
$622$	34.3607	1.37774
$623$	12.3607	0.495220
$624$	2.61803	0.104805
$625$	0	0
$626$	2.94427	0.117677
$627$	−12.7639	−0.509742
$628$	4.38197	0.174859
$629$	9.65248	0.384869
$630$	0	0
$631$	−27.2705	−1.08562	−0.542811	−	0.839855i	$-0.682640\pi$
$631$	−27.2705	−1.08562	−0.542811	+	0.839855i	$0.682640\pi$
$632$	7.56231	0.300812
$633$	12.0000	0.476957
$634$	32.0689	1.27362
$635$	0	0
$636$	−13.2361	−0.524844
$637$	−16.7984	−0.665576
$638$	3.94427	0.156155
$639$	−11.4164	−0.451626
$640$	0	0
$641$	1.59675	0.0630677	0.0315339	−	0.999503i	$-0.489961\pi$
$641$	1.59675	0.0630677	0.0315339	+	0.999503i	$0.489961\pi$
$642$	−0.291796	−0.0115163
$643$	−4.74265	−0.187032	−0.0935158	−	0.995618i	$-0.529811\pi$
$643$	−4.74265	−0.187032	−0.0935158	+	0.995618i	$0.529811\pi$
$644$	−1.81966	−0.0717047
$645$	0	0
$646$	15.1246	0.595070
$647$	−23.9098	−0.939992	−0.469996	−	0.882668i	$-0.655745\pi$
$647$	−23.9098	−0.939992	−0.469996	+	0.882668i	$0.655745\pi$
$648$	1.00000	0.0392837
$649$	−8.81966	−0.346202
$650$	0	0
$651$	5.59675	0.219354
$652$	21.5623	0.844445
$653$	−13.8885	−0.543501	−0.271750	−	0.962368i	$-0.587603\pi$
$653$	−13.8885	−0.543501	−0.271750	+	0.962368i	$0.587603\pi$
$654$	−10.0000	−0.391031
$655$	0	0
$656$	9.23607	0.360608
$657$	−10.4721	−0.408557
$658$	−6.00000	−0.233904
$659$	18.2148	0.709547	0.354774	−	0.934952i	$-0.384558\pi$
$659$	18.2148	0.709547	0.354774	+	0.934952i	$0.384558\pi$
$660$	0	0
$661$	−37.5967	−1.46234	−0.731172	−	0.682193i	$-0.761026\pi$
$661$	−37.5967	−1.46234	−0.731172	+	0.682193i	$0.761026\pi$
$662$	25.4164	0.987837
$663$	−8.85410	−0.343865
$664$	−7.70820	−0.299136
$665$	0	0
$666$	−2.85410	−0.110594
$667$	−3.29180	−0.127459
$668$	14.3820	0.556455
$669$	10.1803	0.393595
$670$	0	0
$671$	31.2361	1.20586
$672$	0.763932	0.0294693
$673$	−17.0557	−0.657450	−0.328725	−	0.944426i	$-0.606619\pi$
$673$	−17.0557	−0.657450	−0.328725	+	0.944426i	$0.606619\pi$
$674$	−35.4164	−1.36419
$675$	0	0
$676$	−6.14590	−0.236381
$677$	16.2918	0.626145	0.313072	−	0.949729i	$-0.398642\pi$
$677$	16.2918	0.626145	0.313072	+	0.949729i	$0.398642\pi$
$678$	−18.5623	−0.712881
$679$	−3.63932	−0.139664
$680$	0	0
$681$	−2.00000	−0.0766402
$682$	20.9098	0.800679
$683$	2.29180	0.0876931	0.0438466	−	0.999038i	$-0.486039\pi$
$683$	2.29180	0.0876931	0.0438466	+	0.999038i	$0.486039\pi$
$684$	−4.47214	−0.170996
$685$	0	0
$686$	−10.2492	−0.391317
$687$	17.2361	0.657597
$688$	9.32624	0.355559
$689$	−34.6525	−1.32015
$690$	0	0
$691$	−16.5410	−0.629250	−0.314625	−	0.949216i	$-0.601879\pi$
$691$	−16.5410	−0.629250	−0.314625	+	0.949216i	$0.601879\pi$
$692$	−3.23607	−0.123017
$693$	2.18034	0.0828243
$694$	4.58359	0.173991
$695$	0	0
$696$	1.38197	0.0523833
$697$	−31.2361	−1.18315
$698$	−8.94427	−0.338546
$699$	−1.20163	−0.0454497
$700$	0	0
$701$	−20.5623	−0.776628	−0.388314	−	0.921527i	$-0.626942\pi$
$701$	−20.5623	−0.776628	−0.388314	+	0.921527i	$0.626942\pi$
$702$	2.61803	0.0988113
$703$	12.7639	0.481401
$704$	2.85410	0.107568
$705$	0	0
$706$	−16.8541	−0.634312
$707$	−10.1803	−0.382871
$708$	−3.09017	−0.116136
$709$	−31.7082	−1.19083	−0.595413	−	0.803420i	$-0.703012\pi$
$709$	−31.7082	−1.19083	−0.595413	+	0.803420i	$0.703012\pi$
$710$	0	0
$711$	7.56231	0.283609
$712$	16.1803	0.606384
$713$	−17.4508	−0.653539
$714$	−2.58359	−0.0966885
$715$	0	0
$716$	−14.4721	−0.540849
$717$	11.7082	0.437251
$718$	6.58359	0.245697
$719$	22.7639	0.848951	0.424476	−	0.905439i	$-0.360458\pi$
$719$	22.7639	0.848951	0.424476	+	0.905439i	$0.360458\pi$
$720$	0	0
$721$	5.66563	0.210999
$722$	1.00000	0.0372161
$723$	6.79837	0.252834
$724$	6.47214	0.240535
$725$	0	0
$726$	−2.85410	−0.105926
$727$	13.1246	0.486765	0.243382	−	0.969930i	$-0.421743\pi$
$727$	13.1246	0.486765	0.243382	+	0.969930i	$0.421743\pi$
$728$	2.00000	0.0741249
$729$	1.00000	0.0370370
$730$	0	0
$731$	−31.5410	−1.16659
$732$	10.9443	0.404512
$733$	3.79837	0.140296	0.0701481	−	0.997537i	$-0.477653\pi$
$733$	3.79837	0.140296	0.0701481	+	0.997537i	$0.477653\pi$
$734$	−0.291796	−0.0107704
$735$	0	0
$736$	−2.38197	−0.0878004
$737$	−35.1803	−1.29588
$738$	9.23607	0.339984
$739$	−23.8197	−0.876220	−0.438110	−	0.898921i	$-0.644352\pi$
$739$	−23.8197	−0.876220	−0.438110	+	0.898921i	$0.644352\pi$
$740$	0	0
$741$	−11.7082	−0.430112
$742$	−10.1115	−0.371203
$743$	−37.3820	−1.37141	−0.685706	−	0.727879i	$-0.740506\pi$
$743$	−37.3820	−1.37141	−0.685706	+	0.727879i	$0.740506\pi$
$744$	7.32624	0.268593
$745$	0	0
$746$	−14.6180	−0.535204
$747$	−7.70820	−0.282028
$748$	−9.65248	−0.352929
$749$	−0.222912	−0.00814504
$750$	0	0
$751$	−2.47214	−0.0902095	−0.0451048	−	0.998982i	$-0.514362\pi$
$751$	−2.47214	−0.0902095	−0.0451048	+	0.998982i	$0.514362\pi$
$752$	−7.85410	−0.286410
$753$	−5.56231	−0.202702
$754$	3.61803	0.131761
$755$	0	0
$756$	0.763932	0.0277839
$757$	46.9443	1.70622	0.853109	−	0.521732i	$-0.174714\pi$
$757$	46.9443	1.70622	0.853109	+	0.521732i	$0.174714\pi$
$758$	12.7639	0.463607
$759$	−6.79837	−0.246765
$760$	0	0
$761$	−22.0689	−0.799996	−0.399998	−	0.916516i	$-0.630989\pi$
$761$	−22.0689	−0.799996	−0.399998	+	0.916516i	$0.630989\pi$
$762$	12.4721	0.451818
$763$	−7.63932	−0.276562
$764$	−3.52786	−0.127634
$765$	0	0
$766$	24.0000	0.867155
$767$	−8.09017	−0.292119
$768$	1.00000	0.0360844
$769$	3.09017	0.111434	0.0557172	−	0.998447i	$-0.482255\pi$
$769$	3.09017	0.111434	0.0557172	+	0.998447i	$0.482255\pi$
$770$	0	0
$771$	−17.8541	−0.643000
$772$	1.23607	0.0444871
$773$	−22.8328	−0.821239	−0.410620	−	0.911807i	$-0.634688\pi$
$773$	−22.8328	−0.821239	−0.410620	+	0.911807i	$0.634688\pi$
$774$	9.32624	0.335225
$775$	0	0
$776$	−4.76393	−0.171015
$777$	−2.18034	−0.0782193
$778$	−7.56231	−0.271122
$779$	−41.3050	−1.47990
$780$	0	0
$781$	−32.5836	−1.16593
$782$	8.05573	0.288072
$783$	1.38197	0.0493874
$784$	−6.41641	−0.229157
$785$	0	0
$786$	−8.00000	−0.285351
$787$	−9.56231	−0.340859	−0.170430	−	0.985370i	$-0.554516\pi$
$787$	−9.56231	−0.340859	−0.170430	+	0.985370i	$0.554516\pi$
$788$	−6.47214	−0.230560
$789$	19.8541	0.706825
$790$	0	0
$791$	−14.1803	−0.504195
$792$	2.85410	0.101416
$793$	28.6525	1.01748
$794$	30.3607	1.07746
$795$	0	0
$796$	13.0902	0.463969
$797$	52.7214	1.86749	0.933743	−	0.357944i	$-0.116522\pi$
$797$	52.7214	1.86749	0.933743	+	0.357944i	$0.116522\pi$
$798$	−3.41641	−0.120940
$799$	26.5623	0.939707
$800$	0	0
$801$	16.1803	0.571704
$802$	26.4721	0.934764
$803$	−29.8885	−1.05474
$804$	−12.3262	−0.434713
$805$	0	0
$806$	19.1803	0.675599
$807$	3.61803	0.127361
$808$	−13.3262	−0.468815
$809$	31.0557	1.09186	0.545931	−	0.837830i	$-0.316176\pi$
$809$	31.0557	1.09186	0.545931	+	0.837830i	$0.316176\pi$
$810$	0	0
$811$	−33.7771	−1.18607	−0.593037	−	0.805175i	$-0.702071\pi$
$811$	−33.7771	−1.18607	−0.593037	+	0.805175i	$0.702071\pi$
$812$	1.05573	0.0370488
$813$	7.20163	0.252572
$814$	−8.14590	−0.285514
$815$	0	0
$816$	−3.38197	−0.118392
$817$	−41.7082	−1.45919
$818$	−22.5623	−0.788873
$819$	2.00000	0.0698857
$820$	0	0
$821$	33.1033	1.15531	0.577657	−	0.816280i	$-0.303967\pi$
$821$	33.1033	1.15531	0.577657	+	0.816280i	$0.303967\pi$
$822$	1.61803	0.0564354
$823$	−5.34752	−0.186403	−0.0932015	−	0.995647i	$-0.529710\pi$
$823$	−5.34752	−0.186403	−0.0932015	+	0.995647i	$0.529710\pi$
$824$	7.41641	0.258363
$825$	0	0
$826$	−2.36068	−0.0821386
$827$	−22.0000	−0.765015	−0.382507	−	0.923952i	$-0.624939\pi$
$827$	−22.0000	−0.765015	−0.382507	+	0.923952i	$0.624939\pi$
$828$	−2.38197	−0.0827790
$829$	−39.5967	−1.37525	−0.687626	−	0.726065i	$-0.741347\pi$
$829$	−39.5967	−1.37525	−0.687626	+	0.726065i	$0.741347\pi$
$830$	0	0
$831$	32.4721	1.12645
$832$	2.61803	0.0907640
$833$	21.7001	0.751863
$834$	12.7639	0.441979
$835$	0	0
$836$	−12.7639	−0.441450
$837$	7.32624	0.253232
$838$	2.11146	0.0729390
$839$	−48.5410	−1.67582	−0.837911	−	0.545807i	$-0.816223\pi$
$839$	−48.5410	−1.67582	−0.837911	+	0.545807i	$0.816223\pi$
$840$	0	0
$841$	−27.0902	−0.934144
$842$	12.0000	0.413547
$843$	−20.3607	−0.701259
$844$	12.0000	0.413057
$845$	0	0
$846$	−7.85410	−0.270030
$847$	−2.18034	−0.0749174
$848$	−13.2361	−0.454528
$849$	−30.2705	−1.03888
$850$	0	0
$851$	6.79837	0.233045
$852$	−11.4164	−0.391120
$853$	13.1459	0.450107	0.225053	−	0.974346i	$-0.427744\pi$
$853$	13.1459	0.450107	0.225053	+	0.974346i	$0.427744\pi$
$854$	8.36068	0.286097
$855$	0	0
$856$	−0.291796	−0.00997338
$857$	−52.4508	−1.79169	−0.895843	−	0.444370i	$-0.853428\pi$
$857$	−52.4508	−1.79169	−0.895843	+	0.444370i	$0.853428\pi$
$858$	7.47214	0.255095
$859$	51.9574	1.77276	0.886382	−	0.462954i	$-0.153211\pi$
$859$	51.9574	1.77276	0.886382	+	0.462954i	$0.153211\pi$
$860$	0	0
$861$	7.05573	0.240459
$862$	−1.81966	−0.0619779
$863$	−41.4508	−1.41100	−0.705502	−	0.708708i	$-0.749278\pi$
$863$	−41.4508	−1.41100	−0.705502	+	0.708708i	$0.749278\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	−40.0689	−1.36160
$867$	−5.56231	−0.188906
$868$	5.59675	0.189966
$869$	21.5836	0.732173
$870$	0	0
$871$	−32.2705	−1.09344
$872$	−10.0000	−0.338643
$873$	−4.76393	−0.161235
$874$	10.6525	0.360325
$875$	0	0
$876$	−10.4721	−0.353821
$877$	−22.4508	−0.758111	−0.379056	−	0.925374i	$-0.623751\pi$
$877$	−22.4508	−0.758111	−0.379056	+	0.925374i	$0.623751\pi$
$878$	19.1459	0.646143
$879$	−2.18034	−0.0735410
$880$	0	0
$881$	2.00000	0.0673817	0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000	0.0673817	0.0336909	+	0.999432i	$0.489274\pi$
$882$	−6.41641	−0.216052
$883$	2.49342	0.0839103	0.0419552	−	0.999119i	$-0.486641\pi$
$883$	2.49342	0.0839103	0.0419552	+	0.999119i	$0.486641\pi$
$884$	−8.85410	−0.297796
$885$	0	0
$886$	14.6525	0.492260
$887$	20.3607	0.683645	0.341822	−	0.939765i	$-0.388956\pi$
$887$	20.3607	0.683645	0.341822	+	0.939765i	$0.388956\pi$
$888$	−2.85410	−0.0957774
$889$	9.52786	0.319554
$890$	0	0
$891$	2.85410	0.0956160
$892$	10.1803	0.340863
$893$	35.1246	1.17540
$894$	−4.47214	−0.149571
$895$	0	0
$896$	0.763932	0.0255212
$897$	−6.23607	−0.208216
$898$	27.8885	0.930653
$899$	10.1246	0.337675
$900$	0	0
$901$	44.7639	1.49130
$902$	26.3607	0.877715
$903$	7.12461	0.237092
$904$	−18.5623	−0.617373
$905$	0	0
$906$	−19.5066	−0.648063
$907$	22.7984	0.757008	0.378504	−	0.925600i	$-0.376439\pi$
$907$	22.7984	0.757008	0.378504	+	0.925600i	$0.376439\pi$
$908$	−2.00000	−0.0663723
$909$	−13.3262	−0.442003
$910$	0	0
$911$	0.944272	0.0312851	0.0156426	−	0.999878i	$-0.495021\pi$
$911$	0.944272	0.0312851	0.0156426	+	0.999878i	$0.495021\pi$
$912$	−4.47214	−0.148087
$913$	−22.0000	−0.728094
$914$	−30.9443	−1.02355
$915$	0	0
$916$	17.2361	0.569496
$917$	−6.11146	−0.201818
$918$	−3.38197	−0.111622
$919$	37.8885	1.24983	0.624914	−	0.780694i	$-0.285134\pi$
$919$	37.8885	1.24983	0.624914	+	0.780694i	$0.285134\pi$
$920$	0	0
$921$	31.6180	1.04185
$922$	−21.0902	−0.694568
$923$	−29.8885	−0.983793
$924$	2.18034	0.0717279
$925$	0	0
$926$	28.0689	0.922401
$927$	7.41641	0.243587
$928$	1.38197	0.0453653
$929$	13.8197	0.453408	0.226704	−	0.973964i	$-0.427205\pi$
$929$	13.8197	0.453408	0.226704	+	0.973964i	$0.427205\pi$
$930$	0	0
$931$	28.6950	0.940442
$932$	−1.20163	−0.0393606
$933$	34.3607	1.12492
$934$	16.2918	0.533084
$935$	0	0
$936$	2.61803	0.0855731
$937$	−9.88854	−0.323045	−0.161522	−	0.986869i	$-0.551640\pi$
$937$	−9.88854	−0.323045	−0.161522	+	0.986869i	$0.551640\pi$
$938$	−9.41641	−0.307457
$939$	2.94427	0.0960827
$940$	0	0
$941$	9.15905	0.298577	0.149288	−	0.988794i	$-0.452302\pi$
$941$	9.15905	0.298577	0.149288	+	0.988794i	$0.452302\pi$
$942$	4.38197	0.142772
$943$	−22.0000	−0.716419
$944$	−3.09017	−0.100576
$945$	0	0
$946$	26.6180	0.865427
$947$	−33.0557	−1.07417	−0.537083	−	0.843529i	$-0.680474\pi$
$947$	−33.0557	−1.07417	−0.537083	+	0.843529i	$0.680474\pi$
$948$	7.56231	0.245612
$949$	−27.4164	−0.889974
$950$	0	0
$951$	32.0689	1.03990
$952$	−2.58359	−0.0837347
$953$	6.36068	0.206043	0.103021	−	0.994679i	$-0.467149\pi$
$953$	6.36068	0.206043	0.103021	+	0.994679i	$0.467149\pi$
$954$	−13.2361	−0.428534
$955$	0	0
$956$	11.7082	0.378670
$957$	3.94427	0.127500
$958$	−29.5967	−0.956228
$959$	1.23607	0.0399147
$960$	0	0
$961$	22.6738	0.731412
$962$	−7.47214	−0.240911
$963$	−0.291796	−0.00940300
$964$	6.79837	0.218961
$965$	0	0
$966$	−1.81966	−0.0585466
$967$	−36.0689	−1.15990	−0.579949	−	0.814653i	$-0.696927\pi$
$967$	−36.0689	−1.15990	−0.579949	+	0.814653i	$0.696927\pi$
$968$	−2.85410	−0.0917343
$969$	15.1246	0.485873
$970$	0	0
$971$	38.5066	1.23573	0.617867	−	0.786282i	$-0.287997\pi$
$971$	38.5066	1.23573	0.617867	+	0.786282i	$0.287997\pi$
$972$	1.00000	0.0320750
$973$	9.75078	0.312596
$974$	29.7082	0.951912
$975$	0	0
$976$	10.9443	0.350318
$977$	−34.5623	−1.10575	−0.552873	−	0.833265i	$-0.686469\pi$
$977$	−34.5623	−1.10575	−0.552873	+	0.833265i	$0.686469\pi$
$978$	21.5623	0.689487
$979$	46.1803	1.47593
$980$	0	0
$981$	−10.0000	−0.319275
$982$	19.0344	0.607413
$983$	−56.4508	−1.80050	−0.900251	−	0.435371i	$-0.856617\pi$
$983$	−56.4508	−1.80050	−0.900251	+	0.435371i	$0.856617\pi$
$984$	9.23607	0.294435
$985$	0	0
$986$	−4.67376	−0.148843
$987$	−6.00000	−0.190982
$988$	−11.7082	−0.372488
$989$	−22.2148	−0.706389
$990$	0	0
$991$	−48.4508	−1.53909	−0.769546	−	0.638591i	$-0.779517\pi$
$991$	−48.4508	−1.53909	−0.769546	+	0.638591i	$0.779517\pi$
$992$	7.32624	0.232608
$993$	25.4164	0.806565
$994$	−8.72136	−0.276625
$995$	0	0
$996$	−7.70820	−0.244244
$997$	41.7426	1.32200	0.661001	−	0.750385i	$-0.270132\pi$
$997$	41.7426	1.32200	0.661001	+	0.750385i	$0.270132\pi$
$998$	−3.81966	−0.120909
$999$	−2.85410	−0.0902998

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.a.h.1.1	yes	2
3.2	odd	2		2250.2.a.h.1.1		2
4.3	odd	2		6000.2.a.b.1.2		2
5.2	odd	4		750.2.c.c.499.3		4
5.3	odd	4		750.2.c.c.499.2		4
5.4	even	2		750.2.a.a.1.2	✓	2
15.2	even	4		2250.2.c.e.1999.1		4
15.8	even	4		2250.2.c.e.1999.4		4
15.14	odd	2		2250.2.a.i.1.2		2
20.3	even	4		6000.2.f.g.1249.1		4
20.7	even	4		6000.2.f.g.1249.4		4
20.19	odd	2		6000.2.a.ba.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.a.a.1.2	✓	2	5.4	even	2
750.2.a.h.1.1	yes	2	1.1	even	1	trivial
750.2.c.c.499.2		4	5.3	odd	4
750.2.c.c.499.3		4	5.2	odd	4
2250.2.a.h.1.1		2	3.2	odd	2
2250.2.a.i.1.2		2	15.14	odd	2
2250.2.c.e.1999.1		4	15.2	even	4
2250.2.c.e.1999.4		4	15.8	even	4
6000.2.a.b.1.2		2	4.3	odd	2
6000.2.a.ba.1.1		2	20.19	odd	2
6000.2.f.g.1249.1		4	20.3	even	4
6000.2.f.g.1249.4		4	20.7	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +0.763932 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +0.763932 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.85410 q^{11} +1.00000 q^{12} +2.61803 q^{13} +0.763932 q^{14} +1.00000 q^{16} -3.38197 q^{17} +1.00000 q^{18} -4.47214 q^{19} +0.763932 q^{21} +2.85410 q^{22} -2.38197 q^{23} +1.00000 q^{24} +2.61803 q^{26} +1.00000 q^{27} +0.763932 q^{28} +1.38197 q^{29} +7.32624 q^{31} +1.00000 q^{32} +2.85410 q^{33} -3.38197 q^{34} +1.00000 q^{36} -2.85410 q^{37} -4.47214 q^{38} +2.61803 q^{39} +9.23607 q^{41} +0.763932 q^{42} +9.32624 q^{43} +2.85410 q^{44} -2.38197 q^{46} -7.85410 q^{47} +1.00000 q^{48} -6.41641 q^{49} -3.38197 q^{51} +2.61803 q^{52} -13.2361 q^{53} +1.00000 q^{54} +0.763932 q^{56} -4.47214 q^{57} +1.38197 q^{58} -3.09017 q^{59} +10.9443 q^{61} +7.32624 q^{62} +0.763932 q^{63} +1.00000 q^{64} +2.85410 q^{66} -12.3262 q^{67} -3.38197 q^{68} -2.38197 q^{69} -11.4164 q^{71} +1.00000 q^{72} -10.4721 q^{73} -2.85410 q^{74} -4.47214 q^{76} +2.18034 q^{77} +2.61803 q^{78} +7.56231 q^{79} +1.00000 q^{81} +9.23607 q^{82} -7.70820 q^{83} +0.763932 q^{84} +9.32624 q^{86} +1.38197 q^{87} +2.85410 q^{88} +16.1803 q^{89} +2.00000 q^{91} -2.38197 q^{92} +7.32624 q^{93} -7.85410 q^{94} +1.00000 q^{96} -4.76393 q^{97} -6.41641 q^{98} +2.85410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + 6 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + 6 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + 6 q^{7} + 2 q^{8} + 2 q^{9} - q^{11} + 2 q^{12} + 3 q^{13} + 6 q^{14} + 2 q^{16} - 9 q^{17} + 2 q^{18} + 6 q^{21} - q^{22} - 7 q^{23} + 2 q^{24} + 3 q^{26} + 2 q^{27} + 6 q^{28} + 5 q^{29} - q^{31} + 2 q^{32} - q^{33} - 9 q^{34} + 2 q^{36} + q^{37} + 3 q^{39} + 14 q^{41} + 6 q^{42} + 3 q^{43} - q^{44} - 7 q^{46} - 9 q^{47} + 2 q^{48} + 14 q^{49} - 9 q^{51} + 3 q^{52} - 22 q^{53} + 2 q^{54} + 6 q^{56} + 5 q^{58} + 5 q^{59} + 4 q^{61} - q^{62} + 6 q^{63} + 2 q^{64} - q^{66} - 9 q^{67} - 9 q^{68} - 7 q^{69} + 4 q^{71} + 2 q^{72} - 12 q^{73} + q^{74} - 18 q^{77} + 3 q^{78} - 5 q^{79} + 2 q^{81} + 14 q^{82} - 2 q^{83} + 6 q^{84} + 3 q^{86} + 5 q^{87} - q^{88} + 10 q^{89} + 4 q^{91} - 7 q^{92} - q^{93} - 9 q^{94} + 2 q^{96} - 14 q^{97} + 14 q^{98} - q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + 6 * q^7 + 2 * q^8 + 2 * q^9 - q^11 + 2 * q^12 + 3 * q^13 + 6 * q^14 + 2 * q^16 - 9 * q^17 + 2 * q^18 + 6 * q^21 - q^22 - 7 * q^23 + 2 * q^24 + 3 * q^26 + 2 * q^27 + 6 * q^28 + 5 * q^29 - q^31 + 2 * q^32 - q^33 - 9 * q^34 + 2 * q^36 + q^37 + 3 * q^39 + 14 * q^41 + 6 * q^42 + 3 * q^43 - q^44 - 7 * q^46 - 9 * q^47 + 2 * q^48 + 14 * q^49 - 9 * q^51 + 3 * q^52 - 22 * q^53 + 2 * q^54 + 6 * q^56 + 5 * q^58 + 5 * q^59 + 4 * q^61 - q^62 + 6 * q^63 + 2 * q^64 - q^66 - 9 * q^67 - 9 * q^68 - 7 * q^69 + 4 * q^71 + 2 * q^72 - 12 * q^73 + q^74 - 18 * q^77 + 3 * q^78 - 5 * q^79 + 2 * q^81 + 14 * q^82 - 2 * q^83 + 6 * q^84 + 3 * q^86 + 5 * q^87 - q^88 + 10 * q^89 + 4 * q^91 - 7 * q^92 - q^93 - 9 * q^94 + 2 * q^96 - 14 * q^97 + 14 * q^98 - q^99

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