LMFDB - Embedded newform 1450.2.a.p.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1450,2,Mod(1,1450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1450, 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("1450.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1450 = 2 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1450.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:	$11.5783082931$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.621.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 6x - 3 $ x^3 - 6*x - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 290)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.66908$ of defining polynomial
Character	$\chi$	$=$	1450.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.66908 q^{3} +1.00000 q^{4} -1.66908 q^{6} -3.21417 q^{7} -1.00000 q^{8} -0.214175 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.66908 q^{3} +1.00000 q^{4} -1.66908 q^{6} -3.21417 q^{7} -1.00000 q^{8} -0.214175 q^{9} +5.33816 q^{11} +1.66908 q^{12} -4.57889 q^{13} +3.21417 q^{14} +1.00000 q^{16} -4.12398 q^{17} +0.214175 q^{18} -6.24797 q^{19} -5.36471 q^{21} -5.33816 q^{22} +8.57889 q^{23} -1.66908 q^{24} +4.57889 q^{26} -5.36471 q^{27} -3.21417 q^{28} -1.00000 q^{29} +0.123983 q^{31} -1.00000 q^{32} +8.90981 q^{33} +4.12398 q^{34} -0.214175 q^{36} -4.42835 q^{37} +6.24797 q^{38} -7.64252 q^{39} -8.42835 q^{41} +5.36471 q^{42} -6.12398 q^{43} +5.33816 q^{44} -8.57889 q^{46} +10.6763 q^{47} +1.66908 q^{48} +3.33092 q^{49} -6.88325 q^{51} -4.57889 q^{52} -12.3719 q^{53} +5.36471 q^{54} +3.21417 q^{56} -10.4283 q^{57} +1.00000 q^{58} -13.9170 q^{59} -3.00724 q^{61} -0.123983 q^{62} +0.688396 q^{63} +1.00000 q^{64} -8.90981 q^{66} +5.58612 q^{67} -4.12398 q^{68} +14.3188 q^{69} -12.0000 q^{71} +0.214175 q^{72} -0.123983 q^{73} +4.42835 q^{74} -6.24797 q^{76} -17.1578 q^{77} +7.64252 q^{78} +12.8269 q^{79} -8.31160 q^{81} +8.42835 q^{82} +2.24797 q^{83} -5.36471 q^{84} +6.12398 q^{86} -1.66908 q^{87} -5.33816 q^{88} +5.33816 q^{89} +14.7173 q^{91} +8.57889 q^{92} +0.206938 q^{93} -10.6763 q^{94} -1.66908 q^{96} +0.578887 q^{97} -3.33092 q^{98} -1.14330 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{6} - 3 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^6 - 3 * q^7 - 3 * q^8 + 6 * q^9	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{6} - 3 q^{7} - 3 q^{8} + 6 q^{9} - 3 q^{12} - 3 q^{13} + 3 q^{14} + 3 q^{16} - 3 q^{17} - 6 q^{18} - 12 q^{21} + 15 q^{23} + 3 q^{24} + 3 q^{26} - 12 q^{27} - 3 q^{28} - 3 q^{29} - 9 q^{31} - 3 q^{32} + 24 q^{33} + 3 q^{34} + 6 q^{36} - 3 q^{39} - 12 q^{41} + 12 q^{42} - 9 q^{43} - 15 q^{46} - 3 q^{48} + 18 q^{49} - 6 q^{51} - 3 q^{52} - 9 q^{53} + 12 q^{54} + 3 q^{56} - 18 q^{57} + 3 q^{58} - 15 q^{59} + 15 q^{61} + 9 q^{62} + 30 q^{63} + 3 q^{64} - 24 q^{66} - 18 q^{67} - 3 q^{68} - 9 q^{69} - 36 q^{71} - 6 q^{72} + 9 q^{73} - 30 q^{77} + 3 q^{78} + 9 q^{79} + 3 q^{81} + 12 q^{82} - 12 q^{83} - 12 q^{84} + 9 q^{86} + 3 q^{87} - 24 q^{91} + 15 q^{92} + 18 q^{93} + 3 q^{96} - 9 q^{97} - 18 q^{98} - 30 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^6 - 3 * q^7 - 3 * q^8 + 6 * q^9 - 3 * q^12 - 3 * q^13 + 3 * q^14 + 3 * q^16 - 3 * q^17 - 6 * q^18 - 12 * q^21 + 15 * q^23 + 3 * q^24 + 3 * q^26 - 12 * q^27 - 3 * q^28 - 3 * q^29 - 9 * q^31 - 3 * q^32 + 24 * q^33 + 3 * q^34 + 6 * q^36 - 3 * q^39 - 12 * q^41 + 12 * q^42 - 9 * q^43 - 15 * q^46 - 3 * q^48 + 18 * q^49 - 6 * q^51 - 3 * q^52 - 9 * q^53 + 12 * q^54 + 3 * q^56 - 18 * q^57 + 3 * q^58 - 15 * q^59 + 15 * q^61 + 9 * q^62 + 30 * q^63 + 3 * q^64 - 24 * q^66 - 18 * q^67 - 3 * q^68 - 9 * q^69 - 36 * q^71 - 6 * q^72 + 9 * q^73 - 30 * q^77 + 3 * q^78 + 9 * q^79 + 3 * q^81 + 12 * q^82 - 12 * q^83 - 12 * q^84 + 9 * q^86 + 3 * q^87 - 24 * q^91 + 15 * q^92 + 18 * q^93 + 3 * q^96 - 9 * q^97 - 18 * q^98 - 30 * 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
$3$	1.66908	0.963643	0.481822	−	0.876269i	$-0.339975\pi$
$3$	1.66908	0.963643	0.481822	+	0.876269i	$0.339975\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−1.66908	−0.681399
$7$	−3.21417	−1.21484	−0.607422	−	0.794379i	$-0.707796\pi$
$7$	−3.21417	−1.21484	−0.607422	+	0.794379i	$0.707796\pi$
$8$	−1.00000	−0.353553
$9$	−0.214175	−0.0713917
$10$	0	0
$11$	5.33816	1.60952	0.804758	−	0.593604i	$-0.202295\pi$
$11$	5.33816	1.60952	0.804758	+	0.593604i	$0.202295\pi$
$12$	1.66908	0.481822
$13$	−4.57889	−1.26995	−0.634977	−	0.772531i	$-0.718991\pi$
$13$	−4.57889	−1.26995	−0.634977	+	0.772531i	$0.718991\pi$
$14$	3.21417	0.859024
$15$	0	0
$16$	1.00000	0.250000
$17$	−4.12398	−1.00021	−0.500106	−	0.865964i	$-0.666706\pi$
$17$	−4.12398	−1.00021	−0.500106	+	0.865964i	$0.666706\pi$
$18$	0.214175	0.0504815
$19$	−6.24797	−1.43338	−0.716691	−	0.697391i	$-0.754344\pi$
$19$	−6.24797	−1.43338	−0.716691	+	0.697391i	$0.754344\pi$
$20$	0	0
$21$	−5.36471	−1.17068
$22$	−5.33816	−1.13810
$23$	8.57889	1.78882	0.894411	−	0.447246i	$-0.147595\pi$
$23$	8.57889	1.78882	0.894411	+	0.447246i	$0.147595\pi$
$24$	−1.66908	−0.340699
$25$	0	0
$26$	4.57889	0.897994
$27$	−5.36471	−1.03244
$28$	−3.21417	−0.607422
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0	0
$31$	0.123983	0.0222680	0.0111340	−	0.999938i	$-0.496456\pi$
$31$	0.123983	0.0222680	0.0111340	+	0.999938i	$0.496456\pi$
$32$	−1.00000	−0.176777
$33$	8.90981	1.55100
$34$	4.12398	0.707257
$35$	0	0
$36$	−0.214175	−0.0356958
$37$	−4.42835	−0.728016	−0.364008	−	0.931396i	$-0.618592\pi$
$37$	−4.42835	−0.728016	−0.364008	+	0.931396i	$0.618592\pi$
$38$	6.24797	1.01355
$39$	−7.64252	−1.22378
$40$	0	0
$41$	−8.42835	−1.31629	−0.658144	−	0.752892i	$-0.728658\pi$
$41$	−8.42835	−1.31629	−0.658144	+	0.752892i	$0.728658\pi$
$42$	5.36471	0.827793
$43$	−6.12398	−0.933899	−0.466949	−	0.884284i	$-0.654647\pi$
$43$	−6.12398	−0.933899	−0.466949	+	0.884284i	$0.654647\pi$
$44$	5.33816	0.804758
$45$	0	0
$46$	−8.57889	−1.26489
$47$	10.6763	1.55730	0.778650	−	0.627458i	$-0.215905\pi$
$47$	10.6763	1.55730	0.778650	+	0.627458i	$0.215905\pi$
$48$	1.66908	0.240911
$49$	3.33092	0.475846
$50$	0	0
$51$	−6.88325	−0.963848
$52$	−4.57889	−0.634977
$53$	−12.3719	−1.69942	−0.849709	−	0.527252i	$-0.823222\pi$
$53$	−12.3719	−1.69942	−0.849709	+	0.527252i	$0.823222\pi$
$54$	5.36471	0.730045
$55$	0	0
$56$	3.21417	0.429512
$57$	−10.4283	−1.38127
$58$	1.00000	0.131306
$59$	−13.9170	−1.81184	−0.905922	−	0.423444i	$-0.860821\pi$
$59$	−13.9170	−1.81184	−0.905922	+	0.423444i	$0.860821\pi$
$60$	0	0
$61$	−3.00724	−0.385037	−0.192519	−	0.981293i	$-0.561666\pi$
$61$	−3.00724	−0.385037	−0.192519	+	0.981293i	$0.561666\pi$
$62$	−0.123983	−0.0157459
$63$	0.688396	0.0867297
$64$	1.00000	0.125000
$65$	0	0
$66$	−8.90981	−1.09672
$67$	5.58612	0.682454	0.341227	−	0.939981i	$-0.389158\pi$
$67$	5.58612	0.682454	0.341227	+	0.939981i	$0.389158\pi$
$68$	−4.12398	−0.500106
$69$	14.3188	1.72379
$70$	0	0
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	0.214175	0.0252408
$73$	−0.123983	−0.0145111	−0.00725557	−	0.999974i	$-0.502310\pi$
$73$	−0.123983	−0.0145111	−0.00725557	+	0.999974i	$0.502310\pi$
$74$	4.42835	0.514785
$75$	0	0
$76$	−6.24797	−0.716691
$77$	−17.1578	−1.95531
$78$	7.64252	0.865346
$79$	12.8269	1.44313	0.721567	−	0.692345i	$-0.243422\pi$
$79$	12.8269	1.44313	0.721567	+	0.692345i	$0.243422\pi$
$80$	0	0
$81$	−8.31160	−0.923512
$82$	8.42835	0.930756
$83$	2.24797	0.246746	0.123373	−	0.992360i	$-0.460629\pi$
$83$	2.24797	0.246746	0.123373	+	0.992360i	$0.460629\pi$
$84$	−5.36471	−0.585338
$85$	0	0
$86$	6.12398	0.660366
$87$	−1.66908	−0.178944
$88$	−5.33816	−0.569050
$89$	5.33816	0.565844	0.282922	−	0.959143i	$-0.408696\pi$
$89$	5.33816	0.565844	0.282922	+	0.959143i	$0.408696\pi$
$90$	0	0
$91$	14.7173	1.54280
$92$	8.57889	0.894411
$93$	0.206938	0.0214584
$94$	−10.6763	−1.10118
$95$	0	0
$96$	−1.66908	−0.170350
$97$	0.578887	0.0587771	0.0293885	−	0.999568i	$-0.490644\pi$
$97$	0.578887	0.0587771	0.0293885	+	0.999568i	$0.490644\pi$
$98$	−3.33092	−0.336474
$99$	−1.14330	−0.114906
$100$	0	0
$101$	5.18762	0.516188	0.258094	−	0.966120i	$-0.416906\pi$
$101$	5.18762	0.516188	0.258094	+	0.966120i	$0.416906\pi$
$102$	6.88325	0.681544
$103$	11.7665	1.15939	0.579694	−	0.814834i	$-0.303172\pi$
$103$	11.7665	1.15939	0.579694	+	0.814834i	$0.303172\pi$
$104$	4.57889	0.448997
$105$	0	0
$106$	12.3719	1.20167
$107$	−8.42835	−0.814799	−0.407400	−	0.913250i	$-0.633564\pi$
$107$	−8.42835	−0.814799	−0.407400	+	0.913250i	$0.633564\pi$
$108$	−5.36471	−0.516220
$109$	5.75203	0.550945	0.275472	−	0.961309i	$-0.411166\pi$
$109$	5.75203	0.550945	0.275472	+	0.961309i	$0.411166\pi$
$110$	0	0
$111$	−7.39127	−0.701548
$112$	−3.21417	−0.303711
$113$	7.25520	0.682512	0.341256	−	0.939970i	$-0.389148\pi$
$113$	7.25520	0.682512	0.341256	+	0.939970i	$0.389148\pi$
$114$	10.4283	0.976704
$115$	0	0
$116$	−1.00000	−0.0928477
$117$	0.980683	0.0906642
$118$	13.9170	1.28117
$119$	13.2552	1.21510
$120$	0	0
$121$	17.4959	1.59054
$122$	3.00724	0.272262
$123$	−14.0676	−1.26843
$124$	0.123983	0.0111340
$125$	0	0
$126$	−0.688396	−0.0613272
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	−1.00000	−0.0883883
$129$	−10.2214	−0.899945
$130$	0	0
$131$	−11.8196	−1.03268	−0.516342	−	0.856382i	$-0.672707\pi$
$131$	−11.8196	−1.03268	−0.516342	+	0.856382i	$0.672707\pi$
$132$	8.90981	0.775499
$133$	20.0821	1.74134
$134$	−5.58612	−0.482568
$135$	0	0
$136$	4.12398	0.353629
$137$	−3.42111	−0.292285	−0.146143	−	0.989264i	$-0.546686\pi$
$137$	−3.42111	−0.292285	−0.146143	+	0.989264i	$0.546686\pi$
$138$	−14.3188	−1.21890
$139$	−7.64252	−0.648231	−0.324115	−	0.946018i	$-0.605067\pi$
$139$	−7.64252	−0.648231	−0.324115	+	0.946018i	$0.605067\pi$
$140$	0	0
$141$	17.8196	1.50068
$142$	12.0000	1.00702
$143$	−24.4428	−2.04401
$144$	−0.214175	−0.0178479
$145$	0	0
$146$	0.123983	0.0102609
$147$	5.55957	0.458546
$148$	−4.42835	−0.364008
$149$	−11.5185	−0.943636	−0.471818	−	0.881696i	$-0.656402\pi$
$149$	−11.5185	−0.943636	−0.471818	+	0.881696i	$0.656402\pi$
$150$	0	0
$151$	−9.15777	−0.745249	−0.372625	−	0.927982i	$-0.621542\pi$
$151$	−9.15777	−0.745249	−0.372625	+	0.927982i	$0.621542\pi$
$152$	6.24797	0.506777
$153$	0.883254	0.0714069
$154$	17.1578	1.38261
$155$	0	0
$156$	−7.64252	−0.611892
$157$	10.0000	0.798087	0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000	0.798087	0.399043	+	0.916932i	$0.369342\pi$
$158$	−12.8269	−1.02045
$159$	−20.6498	−1.63763
$160$	0	0
$161$	−27.5740	−2.17314
$162$	8.31160	0.653021
$163$	−18.6763	−1.46284	−0.731421	−	0.681926i	$-0.761143\pi$
$163$	−18.6763	−1.46284	−0.731421	+	0.681926i	$0.761143\pi$
$164$	−8.42835	−0.658144
$165$	0	0
$166$	−2.24797	−0.174476
$167$	20.3188	1.57232	0.786160	−	0.618024i	$-0.212066\pi$
$167$	20.3188	1.57232	0.786160	+	0.618024i	$0.212066\pi$
$168$	5.36471	0.413897
$169$	7.96621	0.612785
$170$	0	0
$171$	1.33816	0.102332
$172$	−6.12398	−0.466949
$173$	−7.91705	−0.601922	−0.300961	−	0.953636i	$-0.597307\pi$
$173$	−7.91705	−0.601922	−0.300961	+	0.953636i	$0.597307\pi$
$174$	1.66908	0.126533
$175$	0	0
$176$	5.33816	0.402379
$177$	−23.2286	−1.74597
$178$	−5.33816	−0.400112
$179$	8.09743	0.605230	0.302615	−	0.953113i	$-0.402140\pi$
$179$	8.09743	0.605230	0.302615	+	0.953113i	$0.402140\pi$
$180$	0	0
$181$	−6.24797	−0.464408	−0.232204	−	0.972667i	$-0.574594\pi$
$181$	−6.24797	−0.464408	−0.232204	+	0.972667i	$0.574594\pi$
$182$	−14.7173	−1.09092
$183$	−5.01932	−0.371039
$184$	−8.57889	−0.632444
$185$	0	0
$186$	−0.206938	−0.0151734
$187$	−22.0145	−1.60986
$188$	10.6763	0.778650
$189$	17.2431	1.25425
$190$	0	0
$191$	11.0483	0.799424	0.399712	−	0.916641i	$-0.369110\pi$
$191$	11.0483	0.799424	0.399712	+	0.916641i	$0.369110\pi$
$192$	1.66908	0.120455
$193$	−0.0829546	−0.00597120	−0.00298560	−	0.999996i	$-0.500950\pi$
$193$	−0.0829546	−0.00597120	−0.00298560	+	0.999996i	$0.500950\pi$
$194$	−0.578887	−0.0415617
$195$	0	0
$196$	3.33092	0.237923
$197$	−0.732717	−0.0522039	−0.0261020	−	0.999659i	$-0.508309\pi$
$197$	−0.732717	−0.0522039	−0.0261020	+	0.999659i	$0.508309\pi$
$198$	1.14330	0.0812508
$199$	4.60873	0.326704	0.163352	−	0.986568i	$-0.447769\pi$
$199$	4.60873	0.326704	0.163352	+	0.986568i	$0.447769\pi$
$200$	0	0
$201$	9.32368	0.657642
$202$	−5.18762	−0.365000
$203$	3.21417	0.225591
$204$	−6.88325	−0.481924
$205$	0	0
$206$	−11.7665	−0.819811
$207$	−1.83738	−0.127707
$208$	−4.57889	−0.317489
$209$	−33.3526	−2.30705
$210$	0	0
$211$	2.66184	0.183249	0.0916244	−	0.995794i	$-0.470794\pi$
$211$	2.66184	0.183249	0.0916244	+	0.995794i	$0.470794\pi$
$212$	−12.3719	−0.849709
$213$	−20.0289	−1.37236
$214$	8.42835	0.576150
$215$	0	0
$216$	5.36471	0.365022
$217$	−0.398504	−0.0270522
$218$	−5.75203	−0.389577
$219$	−0.206938	−0.0139836
$220$	0	0
$221$	18.8833	1.27023
$222$	7.39127	0.496069
$223$	−0.744796	−0.0498753	−0.0249376	−	0.999689i	$-0.507939\pi$
$223$	−0.744796	−0.0498753	−0.0249376	+	0.999689i	$0.507939\pi$
$224$	3.21417	0.214756
$225$	0	0
$226$	−7.25520	−0.482609
$227$	0.180384	0.0119725	0.00598624	−	0.999982i	$-0.498095\pi$
$227$	0.180384	0.0119725	0.00598624	+	0.999982i	$0.498095\pi$
$228$	−10.4283	−0.690634
$229$	10.1385	0.669968	0.334984	−	0.942224i	$-0.391269\pi$
$229$	10.1385	0.669968	0.334984	+	0.942224i	$0.391269\pi$
$230$	0	0
$231$	−28.6377	−1.88422
$232$	1.00000	0.0656532
$233$	27.3526	1.79193	0.895965	−	0.444124i	$-0.146485\pi$
$233$	27.3526	1.79193	0.895965	+	0.444124i	$0.146485\pi$
$234$	−0.980683	−0.0641093
$235$	0	0
$236$	−13.9170	−0.905922
$237$	21.4090	1.39067
$238$	−13.2552	−0.859207
$239$	−25.7665	−1.66670	−0.833348	−	0.552748i	$-0.813579\pi$
$239$	−25.7665	−1.66670	−0.833348	+	0.552748i	$0.813579\pi$
$240$	0	0
$241$	6.34540	0.408743	0.204371	−	0.978893i	$-0.434485\pi$
$241$	6.34540	0.408743	0.204371	+	0.978893i	$0.434485\pi$
$242$	−17.4959	−1.12468
$243$	2.22141	0.142504
$244$	−3.00724	−0.192519
$245$	0	0
$246$	14.0676	0.896916
$247$	28.6087	1.82033
$248$	−0.123983	−0.00787294
$249$	3.75203	0.237775
$250$	0	0
$251$	19.1047	1.20588	0.602938	−	0.797788i	$-0.293997\pi$
$251$	19.1047	1.20588	0.602938	+	0.797788i	$0.293997\pi$
$252$	0.688396	0.0433649
$253$	45.7955	2.87914
$254$	8.00000	0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	−19.1047	−1.19172	−0.595858	−	0.803090i	$-0.703188\pi$
$257$	−19.1047	−1.19172	−0.595858	+	0.803090i	$0.703188\pi$
$258$	10.2214	0.636357
$259$	14.2335	0.884426
$260$	0	0
$261$	0.214175	0.0132571
$262$	11.8196	0.730218
$263$	12.0000	0.739952	0.369976	−	0.929041i	$-0.379366\pi$
$263$	12.0000	0.739952	0.369976	+	0.929041i	$0.379366\pi$
$264$	−8.90981	−0.548361
$265$	0	0
$266$	−20.0821	−1.23131
$267$	8.90981	0.545271
$268$	5.58612	0.341227
$269$	−19.2142	−1.17151	−0.585754	−	0.810489i	$-0.699202\pi$
$269$	−19.2142	−1.17151	−0.585754	+	0.810489i	$0.699202\pi$
$270$	0	0
$271$	−1.09019	−0.0662244	−0.0331122	−	0.999452i	$-0.510542\pi$
$271$	−1.09019	−0.0662244	−0.0331122	+	0.999452i	$0.510542\pi$
$272$	−4.12398	−0.250053
$273$	24.5644	1.48671
$274$	3.42111	0.206677
$275$	0	0
$276$	14.3188	0.861893
$277$	25.5330	1.53413	0.767065	−	0.641569i	$-0.221716\pi$
$277$	25.5330	1.53413	0.767065	+	0.641569i	$0.221716\pi$
$278$	7.64252	0.458368
$279$	−0.0265541	−0.00158975
$280$	0	0
$281$	1.39456	0.0831924	0.0415962	−	0.999135i	$-0.486756\pi$
$281$	1.39456	0.0831924	0.0415962	+	0.999135i	$0.486756\pi$
$282$	−17.8196	−1.06114
$283$	−10.2480	−0.609178	−0.304589	−	0.952484i	$-0.598519\pi$
$283$	−10.2480	−0.609178	−0.304589	+	0.952484i	$0.598519\pi$
$284$	−12.0000	−0.712069
$285$	0	0
$286$	24.4428	1.44533
$287$	27.0902	1.59908
$288$	0.214175	0.0126204
$289$	0.00723726	0.000425721 0
$290$	0	0
$291$	0.966209	0.0566402
$292$	−0.123983	−0.00725557
$293$	−3.57165	−0.208658	−0.104329	−	0.994543i	$-0.533269\pi$
$293$	−3.57165	−0.208658	−0.104329	+	0.994543i	$0.533269\pi$
$294$	−5.55957	−0.324241
$295$	0	0
$296$	4.42835	0.257393
$297$	−28.6377	−1.66173
$298$	11.5185	0.667251
$299$	−39.2818	−2.27172
$300$	0	0
$301$	19.6836	1.13454
$302$	9.15777	0.526971
$303$	8.65855	0.497421
$304$	−6.24797	−0.358345
$305$	0	0
$306$	−0.883254	−0.0504923
$307$	−12.4959	−0.713181	−0.356590	−	0.934261i	$-0.616061\pi$
$307$	−12.4959	−0.713181	−0.356590	+	0.934261i	$0.616061\pi$
$308$	−17.1578	−0.977655
$309$	19.6392	1.11724
$310$	0	0
$311$	21.9846	1.24663	0.623317	−	0.781969i	$-0.285785\pi$
$311$	21.9846	1.24663	0.623317	+	0.781969i	$0.285785\pi$
$312$	7.64252	0.432673
$313$	−17.1722	−0.970633	−0.485316	−	0.874339i	$-0.661296\pi$
$313$	−17.1722	−0.970633	−0.485316	+	0.874339i	$0.661296\pi$
$314$	−10.0000	−0.564333
$315$	0	0
$316$	12.8269	0.721567
$317$	4.97739	0.279558	0.139779	−	0.990183i	$-0.455361\pi$
$317$	4.97739	0.279558	0.139779	+	0.990183i	$0.455361\pi$
$318$	20.6498	1.15798
$319$	−5.33816	−0.298879
$320$	0	0
$321$	−14.0676	−0.785176
$322$	27.5740	1.53664
$323$	25.7665	1.43369
$324$	−8.31160	−0.461756
$325$	0	0
$326$	18.6763	1.03439
$327$	9.60060	0.530914
$328$	8.42835	0.465378
$329$	−34.3155	−1.89188
$330$	0	0
$331$	−20.0145	−1.10010	−0.550048	−	0.835133i	$-0.685390\pi$
$331$	−20.0145	−1.10010	−0.550048	+	0.835133i	$0.685390\pi$
$332$	2.24797	0.123373
$333$	0.948442	0.0519743
$334$	−20.3188	−1.11180
$335$	0	0
$336$	−5.36471	−0.292669
$337$	−2.55233	−0.139034	−0.0695172	−	0.997581i	$-0.522146\pi$
$337$	−2.55233	−0.139034	−0.0695172	+	0.997581i	$0.522146\pi$
$338$	−7.96621	−0.433305
$339$	12.1095	0.657698
$340$	0	0
$341$	0.661842	0.0358407
$342$	−1.33816	−0.0723593
$343$	11.7931	0.636766
$344$	6.12398	0.330183
$345$	0	0
$346$	7.91705	0.425623
$347$	13.8872	0.745504	0.372752	−	0.927931i	$-0.378414\pi$
$347$	13.8872	0.745504	0.372752	+	0.927931i	$0.378414\pi$
$348$	−1.66908	−0.0894720
$349$	26.0821	1.39614	0.698070	−	0.716029i	$-0.254042\pi$
$349$	26.0821	1.39614	0.698070	+	0.716029i	$0.254042\pi$
$350$	0	0
$351$	24.5644	1.31115
$352$	−5.33816	−0.284525
$353$	−19.4057	−1.03286	−0.516432	−	0.856328i	$-0.672740\pi$
$353$	−19.4057	−1.03286	−0.516432	+	0.856328i	$0.672740\pi$
$354$	23.2286	1.23459
$355$	0	0
$356$	5.33816	0.282922
$357$	22.1240	1.17093
$358$	−8.09743	−0.427962
$359$	16.1650	0.853157	0.426578	−	0.904451i	$-0.359719\pi$
$359$	16.1650	0.853157	0.426578	+	0.904451i	$0.359719\pi$
$360$	0	0
$361$	20.0371	1.05458
$362$	6.24797	0.328386
$363$	29.2021	1.53271
$364$	14.7173	0.771398
$365$	0	0
$366$	5.01932	0.262364
$367$	−1.51854	−0.0792672	−0.0396336	−	0.999214i	$-0.512619\pi$
$367$	−1.51854	−0.0792672	−0.0396336	+	0.999214i	$0.512619\pi$
$368$	8.57889	0.447205
$369$	1.80514	0.0939719
$370$	0	0
$371$	39.7656	2.06453
$372$	0.206938	0.0107292
$373$	7.16107	0.370786	0.185393	−	0.982664i	$-0.440644\pi$
$373$	7.16107	0.370786	0.185393	+	0.982664i	$0.440644\pi$
$374$	22.0145	1.13834
$375$	0	0
$376$	−10.6763	−0.550589
$377$	4.57889	0.235825
$378$	−17.2431	−0.886891
$379$	24.0145	1.23354	0.616770	−	0.787143i	$-0.288441\pi$
$379$	24.0145	1.23354	0.616770	+	0.787143i	$0.288441\pi$
$380$	0	0
$381$	−13.3526	−0.684076
$382$	−11.0483	−0.565278
$383$	−34.3864	−1.75706	−0.878532	−	0.477683i	$-0.841477\pi$
$383$	−34.3864	−1.75706	−0.878532	+	0.477683i	$0.841477\pi$
$384$	−1.66908	−0.0851748
$385$	0	0
$386$	0.0829546	0.00422228
$387$	1.31160	0.0666726
$388$	0.578887	0.0293885
$389$	5.63923	0.285920	0.142960	−	0.989728i	$-0.454338\pi$
$389$	5.63923	0.285920	0.142960	+	0.989728i	$0.454338\pi$
$390$	0	0
$391$	−35.3792	−1.78920
$392$	−3.33092	−0.168237
$393$	−19.7279	−0.995140
$394$	0.732717	0.0369137
$395$	0	0
$396$	−1.14330	−0.0574530
$397$	10.9131	0.547713	0.273856	−	0.961771i	$-0.411701\pi$
$397$	10.9131	0.547713	0.273856	+	0.961771i	$0.411701\pi$
$398$	−4.60873	−0.231015
$399$	33.5185	1.67803
$400$	0	0
$401$	21.9846	1.09786	0.548930	−	0.835868i	$-0.315035\pi$
$401$	21.9846	1.09786	0.548930	+	0.835868i	$0.315035\pi$
$402$	−9.32368	−0.465023
$403$	−0.567705	−0.0282794
$404$	5.18762	0.258094
$405$	0	0
$406$	−3.21417	−0.159517
$407$	−23.6392	−1.17175
$408$	6.88325	0.340772
$409$	−5.58612	−0.276216	−0.138108	−	0.990417i	$-0.544102\pi$
$409$	−5.58612	−0.276216	−0.138108	+	0.990417i	$0.544102\pi$
$410$	0	0
$411$	−5.71011	−0.281659
$412$	11.7665	0.579694
$413$	44.7318	2.20111
$414$	1.83738	0.0903025
$415$	0	0
$416$	4.57889	0.224498
$417$	−12.7560	−0.624663
$418$	33.3526	1.63133
$419$	−12.2513	−0.598513	−0.299257	−	0.954173i	$-0.596739\pi$
$419$	−12.2513	−0.598513	−0.299257	+	0.954173i	$0.596739\pi$
$420$	0	0
$421$	−2.85670	−0.139227	−0.0696135	−	0.997574i	$-0.522177\pi$
$421$	−2.85670	−0.139227	−0.0696135	+	0.997574i	$0.522177\pi$
$422$	−2.66184	−0.129576
$423$	−2.28660	−0.111178
$424$	12.3719	0.600835
$425$	0	0
$426$	20.0289	0.970406
$427$	9.66579	0.467760
$428$	−8.42835	−0.407400
$429$	−40.7970	−1.96970
$430$	0	0
$431$	−11.3382	−0.546140	−0.273070	−	0.961994i	$-0.588039\pi$
$431$	−11.3382	−0.546140	−0.273070	+	0.961994i	$0.588039\pi$
$432$	−5.36471	−0.258110
$433$	−34.0289	−1.63533	−0.817663	−	0.575696i	$-0.804731\pi$
$433$	−34.0289	−1.63533	−0.817663	+	0.575696i	$0.804731\pi$
$434$	0.398504	0.0191288
$435$	0	0
$436$	5.75203	0.275472
$437$	−53.6006	−2.56406
$438$	0.206938	0.00988787
$439$	5.27058	0.251551	0.125775	−	0.992059i	$-0.459858\pi$
$439$	5.27058	0.251551	0.125775	+	0.992059i	$0.459858\pi$
$440$	0	0
$441$	−0.713400	−0.0339714
$442$	−18.8833	−0.898185
$443$	−13.1731	−0.625875	−0.312938	−	0.949774i	$-0.601313\pi$
$443$	−13.1731	−0.625875	−0.312938	+	0.949774i	$0.601313\pi$
$444$	−7.39127	−0.350774
$445$	0	0
$446$	0.744796	0.0352671
$447$	−19.2254	−0.909328
$448$	−3.21417	−0.151855
$449$	12.9243	0.609935	0.304967	−	0.952363i	$-0.401354\pi$
$449$	12.9243	0.609935	0.304967	+	0.952363i	$0.401354\pi$
$450$	0	0
$451$	−44.9919	−2.11858
$452$	7.25520	0.341256
$453$	−15.2850	−0.718154
$454$	−0.180384	−0.00846582
$455$	0	0
$456$	10.4283	0.488352
$457$	14.4959	0.678091	0.339046	−	0.940770i	$-0.389896\pi$
$457$	14.4959	0.678091	0.339046	+	0.940770i	$0.389896\pi$
$458$	−10.1385	−0.473739
$459$	22.1240	1.03266
$460$	0	0
$461$	27.4621	1.27904	0.639520	−	0.768775i	$-0.279133\pi$
$461$	27.4621	1.27904	0.639520	+	0.768775i	$0.279133\pi$
$462$	28.6377	1.33235
$463$	2.41388	0.112182	0.0560912	−	0.998426i	$-0.482136\pi$
$463$	2.41388	0.112182	0.0560912	+	0.998426i	$0.482136\pi$
$464$	−1.00000	−0.0464238
$465$	0	0
$466$	−27.3526	−1.26709
$467$	1.51525	0.0701174	0.0350587	−	0.999385i	$-0.488838\pi$
$467$	1.51525	0.0701174	0.0350587	+	0.999385i	$0.488838\pi$
$468$	0.980683	0.0453321
$469$	−17.9548	−0.829075
$470$	0	0
$471$	16.6908	0.769071
$472$	13.9170	0.640584
$473$	−32.6908	−1.50312
$474$	−21.4090	−0.983349
$475$	0	0
$476$	13.2552	0.607551
$477$	2.64976	0.121324
$478$	25.7665	1.17853
$479$	−20.6199	−0.942148	−0.471074	−	0.882094i	$-0.656134\pi$
$479$	−20.6199	−0.942148	−0.471074	+	0.882094i	$0.656134\pi$
$480$	0	0
$481$	20.2769	0.924548
$482$	−6.34540	−0.289025
$483$	−46.0233	−2.09413
$484$	17.4959	0.795270
$485$	0	0
$486$	−2.22141	−0.100765
$487$	17.7367	0.803725	0.401862	−	0.915700i	$-0.368363\pi$
$487$	17.7367	0.803725	0.401862	+	0.915700i	$0.368363\pi$
$488$	3.00724	0.136131
$489$	−31.1722	−1.40966
$490$	0	0
$491$	22.4139	1.01152	0.505762	−	0.862673i	$-0.331211\pi$
$491$	22.4139	1.01152	0.505762	+	0.862673i	$0.331211\pi$
$492$	−14.0676	−0.634216
$493$	4.12398	0.185735
$494$	−28.6087	−1.28717
$495$	0	0
$496$	0.123983	0.00556701
$497$	38.5701	1.73011
$498$	−3.75203	−0.168133
$499$	14.7737	0.661364	0.330682	−	0.943742i	$-0.392721\pi$
$499$	14.7737	0.661364	0.330682	+	0.943742i	$0.392721\pi$
$500$	0	0
$501$	33.9138	1.51515
$502$	−19.1047	−0.852683
$503$	21.3526	0.952067	0.476033	−	0.879427i	$-0.342074\pi$
$503$	21.3526	0.952067	0.476033	+	0.879427i	$0.342074\pi$
$504$	−0.688396	−0.0306636
$505$	0	0
$506$	−45.7955	−2.03586
$507$	13.2962	0.590506
$508$	−8.00000	−0.354943
$509$	19.1047	0.846799	0.423400	−	0.905943i	$-0.360837\pi$
$509$	19.1047	0.846799	0.423400	+	0.905943i	$0.360837\pi$
$510$	0	0
$511$	0.398504	0.0176288
$512$	−1.00000	−0.0441942
$513$	33.5185	1.47988
$514$	19.1047	0.842671
$515$	0	0
$516$	−10.2214	−0.449973
$517$	56.9919	2.50650
$518$	−14.2335	−0.625384
$519$	−13.2142	−0.580038
$520$	0	0
$521$	22.7472	0.996573	0.498286	−	0.867013i	$-0.333963\pi$
$521$	22.7472	0.996573	0.498286	+	0.867013i	$0.333963\pi$
$522$	−0.214175	−0.00937418
$523$	−25.7810	−1.12732	−0.563662	−	0.826006i	$-0.690608\pi$
$523$	−25.7810	−1.12732	−0.563662	+	0.826006i	$0.690608\pi$
$524$	−11.8196	−0.516342
$525$	0	0
$526$	−12.0000	−0.523225
$527$	−0.511305	−0.0222728
$528$	8.90981	0.387750
$529$	50.5973	2.19988
$530$	0	0
$531$	2.98068	0.129351
$532$	20.0821	0.870668
$533$	38.5925	1.67163
$534$	−8.90981	−0.385565
$535$	0	0
$536$	−5.58612	−0.241284
$537$	13.5152	0.583226
$538$	19.2142	0.828382
$539$	17.7810	0.765881
$540$	0	0
$541$	−21.5297	−0.925635	−0.462818	−	0.886454i	$-0.653161\pi$
$541$	−21.5297	−0.925635	−0.462818	+	0.886454i	$0.653161\pi$
$542$	1.09019	0.0468277
$543$	−10.4283	−0.447523
$544$	4.12398	0.176814
$545$	0	0
$546$	−24.5644	−1.05126
$547$	−21.8872	−0.935829	−0.467915	−	0.883774i	$-0.654994\pi$
$547$	−21.8872	−0.935829	−0.467915	+	0.883774i	$0.654994\pi$
$548$	−3.42111	−0.146143
$549$	0.644075	0.0274885
$550$	0	0
$551$	6.24797	0.266172
$552$	−14.3188	−0.609450
$553$	−41.2278	−1.75318
$554$	−25.5330	−1.08479
$555$	0	0
$556$	−7.64252	−0.324115
$557$	−9.24073	−0.391542	−0.195771	−	0.980650i	$-0.562721\pi$
$557$	−9.24073	−0.391542	−0.195771	+	0.980650i	$0.562721\pi$
$558$	0.0265541	0.00112412
$559$	28.0410	1.18601
$560$	0	0
$561$	−36.7439	−1.55133
$562$	−1.39456	−0.0588259
$563$	−23.1876	−0.977242	−0.488621	−	0.872496i	$-0.662500\pi$
$563$	−23.1876	−0.977242	−0.488621	+	0.872496i	$0.662500\pi$
$564$	17.8196	0.750341
$565$	0	0
$566$	10.2480	0.430754
$567$	26.7150	1.12192
$568$	12.0000	0.503509
$569$	2.90981	0.121986	0.0609928	−	0.998138i	$-0.480573\pi$
$569$	2.90981	0.121986	0.0609928	+	0.998138i	$0.480573\pi$
$570$	0	0
$571$	26.4130	1.10535	0.552674	−	0.833397i	$-0.313607\pi$
$571$	26.4130	1.10535	0.552674	+	0.833397i	$0.313607\pi$
$572$	−24.4428	−1.02201
$573$	18.4404	0.770360
$574$	−27.0902	−1.13072
$575$	0	0
$576$	−0.214175	−0.00892396
$577$	−9.47662	−0.394517	−0.197258	−	0.980352i	$-0.563204\pi$
$577$	−9.47662	−0.394517	−0.197258	+	0.980352i	$0.563204\pi$
$578$	−0.00723726	−0.000301031 0
$579$	−0.138458	−0.00575411
$580$	0	0
$581$	−7.22536	−0.299758
$582$	−0.966209	−0.0400506
$583$	−66.0434	−2.73524
$584$	0.123983	0.00513046
$585$	0	0
$586$	3.57165	0.147544
$587$	1.50407	0.0620795	0.0310398	−	0.999518i	$-0.490118\pi$
$587$	1.50407	0.0620795	0.0310398	+	0.999518i	$0.490118\pi$
$588$	5.55957	0.229273
$589$	−0.774643	−0.0319186
$590$	0	0
$591$	−1.22296	−0.0503059
$592$	−4.42835	−0.182004
$593$	−20.5104	−0.842261	−0.421131	−	0.907000i	$-0.638367\pi$
$593$	−20.5104	−0.842261	−0.421131	+	0.907000i	$0.638367\pi$
$594$	28.6377	1.17502
$595$	0	0
$596$	−11.5185	−0.471818
$597$	7.69234	0.314827
$598$	39.2818	1.60635
$599$	−7.51525	−0.307065	−0.153532	−	0.988144i	$-0.549065\pi$
$599$	−7.51525	−0.307065	−0.153532	+	0.988144i	$0.549065\pi$
$600$	0	0
$601$	4.51041	0.183983	0.0919917	−	0.995760i	$-0.470677\pi$
$601$	4.51041	0.183983	0.0919917	+	0.995760i	$0.470677\pi$
$602$	−19.6836	−0.802242
$603$	−1.19641	−0.0487215
$604$	−9.15777	−0.372625
$605$	0	0
$606$	−8.65855	−0.351730
$607$	30.2093	1.22616	0.613079	−	0.790021i	$-0.289931\pi$
$607$	30.2093	1.22616	0.613079	+	0.790021i	$0.289931\pi$
$608$	6.24797	0.253388
$609$	5.36471	0.217389
$610$	0	0
$611$	−48.8856	−1.97770
$612$	0.883254	0.0357034
$613$	31.1611	1.25858	0.629292	−	0.777169i	$-0.283345\pi$
$613$	31.1611	1.25858	0.629292	+	0.777169i	$0.283345\pi$
$614$	12.4959	0.504295
$615$	0	0
$616$	17.1578	0.691306
$617$	−19.8760	−0.800178	−0.400089	−	0.916476i	$-0.631021\pi$
$617$	−19.8760	−0.800178	−0.400089	+	0.916476i	$0.631021\pi$
$618$	−19.6392	−0.790006
$619$	−15.2175	−0.611642	−0.305821	−	0.952089i	$-0.598931\pi$
$619$	−15.2175	−0.611642	−0.305821	+	0.952089i	$0.598931\pi$
$620$	0	0
$621$	−46.0233	−1.84685
$622$	−21.9846	−0.881503
$623$	−17.1578	−0.687412
$624$	−7.64252	−0.305946
$625$	0	0
$626$	17.1722	0.686341
$627$	−55.6682	−2.22317
$628$	10.0000	0.399043
$629$	18.2624	0.728171
$630$	0	0
$631$	−8.05311	−0.320589	−0.160295	−	0.987069i	$-0.551244\pi$
$631$	−8.05311	−0.320589	−0.160295	+	0.987069i	$0.551244\pi$
$632$	−12.8269	−0.510225
$633$	4.44282	0.176586
$634$	−4.97739	−0.197677
$635$	0	0
$636$	−20.6498	−0.818816
$637$	−15.2519	−0.604303
$638$	5.33816	0.211340
$639$	2.57010	0.101672
$640$	0	0
$641$	−22.2769	−0.879885	−0.439943	−	0.898026i	$-0.645001\pi$
$641$	−22.2769	−0.879885	−0.439943	+	0.898026i	$0.645001\pi$
$642$	14.0676	0.555203
$643$	16.4815	0.649965	0.324983	−	0.945720i	$-0.394642\pi$
$643$	16.4815	0.649965	0.324983	+	0.945720i	$0.394642\pi$
$644$	−27.5740	−1.08657
$645$	0	0
$646$	−25.7665	−1.01377
$647$	−11.9017	−0.467903	−0.233952	−	0.972248i	$-0.575166\pi$
$647$	−11.9017	−0.467903	−0.233952	+	0.972248i	$0.575166\pi$
$648$	8.31160	0.326511
$649$	−74.2914	−2.91619
$650$	0	0
$651$	−0.665134	−0.0260687
$652$	−18.6763	−0.731421
$653$	38.3300	1.49997	0.749985	−	0.661455i	$-0.230061\pi$
$653$	38.3300	1.49997	0.749985	+	0.661455i	$0.230061\pi$
$654$	−9.60060	−0.375413
$655$	0	0
$656$	−8.42835	−0.329072
$657$	0.0265541	0.00103597
$658$	34.3155	1.33776
$659$	−15.6537	−0.609782	−0.304891	−	0.952387i	$-0.598620\pi$
$659$	−15.6537	−0.609782	−0.304891	+	0.952387i	$0.598620\pi$
$660$	0	0
$661$	−15.1578	−0.589569	−0.294785	−	0.955564i	$-0.595248\pi$
$661$	−15.1578	−0.589569	−0.294785	+	0.955564i	$0.595248\pi$
$662$	20.0145	0.777885
$663$	31.5176	1.22404
$664$	−2.24797	−0.0872380
$665$	0	0
$666$	−0.948442	−0.0367514
$667$	−8.57889	−0.332176
$668$	20.3188	0.786160
$669$	−1.24312	−0.0480620
$670$	0	0
$671$	−16.0531	−0.619723
$672$	5.36471	0.206948
$673$	22.3831	0.862806	0.431403	−	0.902159i	$-0.358019\pi$
$673$	22.3831	0.862806	0.431403	+	0.902159i	$0.358019\pi$
$674$	2.55233	0.0983122
$675$	0	0
$676$	7.96621	0.306393
$677$	−41.1191	−1.58034	−0.790168	−	0.612890i	$-0.790007\pi$
$677$	−41.1191	−1.58034	−0.790168	+	0.612890i	$0.790007\pi$
$678$	−12.1095	−0.465063
$679$	−1.86064	−0.0714050
$680$	0	0
$681$	0.301075	0.0115372
$682$	−0.661842	−0.0253432
$683$	−50.7728	−1.94277	−0.971385	−	0.237512i	$-0.923668\pi$
$683$	−50.7728	−1.94277	−0.971385	+	0.237512i	$0.923668\pi$
$684$	1.33816	0.0511658
$685$	0	0
$686$	−11.7931	−0.450261
$687$	16.9219	0.645610
$688$	−6.12398	−0.233475
$689$	56.6498	2.15818
$690$	0	0
$691$	−3.14659	−0.119702	−0.0598510	−	0.998207i	$-0.519063\pi$
$691$	−3.14659	−0.119702	−0.0598510	+	0.998207i	$0.519063\pi$
$692$	−7.91705	−0.300961
$693$	3.67477	0.139593
$694$	−13.8872	−0.527151
$695$	0	0
$696$	1.66908	0.0632663
$697$	34.7584	1.31657
$698$	−26.0821	−0.987220
$699$	45.6537	1.72678
$700$	0	0
$701$	18.6618	0.704848	0.352424	−	0.935840i	$-0.385357\pi$
$701$	18.6618	0.704848	0.352424	+	0.935840i	$0.385357\pi$
$702$	−24.5644	−0.927124
$703$	27.6682	1.04353
$704$	5.33816	0.201189
$705$	0	0
$706$	19.4057	0.730345
$707$	−16.6739	−0.627087
$708$	−23.2286	−0.872986
$709$	−44.5394	−1.67271	−0.836355	−	0.548188i	$-0.815318\pi$
$709$	−44.5394	−1.67271	−0.836355	+	0.548188i	$0.815318\pi$
$710$	0	0
$711$	−2.74719	−0.103028
$712$	−5.33816	−0.200056
$713$	1.06364	0.0398335
$714$	−22.1240	−0.827969
$715$	0	0
$716$	8.09743	0.302615
$717$	−43.0063	−1.60610
$718$	−16.1650	−0.603273
$719$	−49.5475	−1.84781	−0.923905	−	0.382622i	$-0.875021\pi$
$719$	−49.5475	−1.84781	−0.923905	+	0.382622i	$0.875021\pi$
$720$	0	0
$721$	−37.8196	−1.40848
$722$	−20.0371	−0.745703
$723$	10.5910	0.393882
$724$	−6.24797	−0.232204
$725$	0	0
$726$	−29.2021	−1.08379
$727$	1.21088	0.0449092	0.0224546	−	0.999748i	$-0.492852\pi$
$727$	1.21088	0.0449092	0.0224546	+	0.999748i	$0.492852\pi$
$728$	−14.7173	−0.545461
$729$	28.6425	1.06083
$730$	0	0
$731$	25.2552	0.934097
$732$	−5.01932	−0.185519
$733$	−23.2706	−0.859518	−0.429759	−	0.902944i	$-0.641402\pi$
$733$	−23.2706	−0.859518	−0.429759	+	0.902944i	$0.641402\pi$
$734$	1.51854	0.0560504
$735$	0	0
$736$	−8.57889	−0.316222
$737$	29.8196	1.09842
$738$	−1.80514	−0.0664482
$739$	−23.7665	−0.874265	−0.437133	−	0.899397i	$-0.644006\pi$
$739$	−23.7665	−0.874265	−0.437133	+	0.899397i	$0.644006\pi$
$740$	0	0
$741$	47.7502	1.75415
$742$	−39.7656	−1.45984
$743$	−46.6763	−1.71239	−0.856194	−	0.516654i	$-0.827177\pi$
$743$	−46.6763	−1.71239	−0.856194	+	0.516654i	$0.827177\pi$
$744$	−0.206938	−0.00758671
$745$	0	0
$746$	−7.16107	−0.262185
$747$	−0.481458	−0.0176156
$748$	−22.0145	−0.804929
$749$	27.0902	0.989854
$750$	0	0
$751$	−2.41388	−0.0880836	−0.0440418	−	0.999030i	$-0.514023\pi$
$751$	−2.41388	−0.0880836	−0.0440418	+	0.999030i	$0.514023\pi$
$752$	10.6763	0.389325
$753$	31.8872	1.16203
$754$	−4.57889	−0.166753
$755$	0	0
$756$	17.2431	0.627126
$757$	−11.5717	−0.420579	−0.210289	−	0.977639i	$-0.567441\pi$
$757$	−11.5717	−0.420579	−0.210289	+	0.977639i	$0.567441\pi$
$758$	−24.0145	−0.872245
$759$	76.4362	2.77446
$760$	0	0
$761$	3.10137	0.112425	0.0562124	−	0.998419i	$-0.482098\pi$
$761$	3.10137	0.112425	0.0562124	+	0.998419i	$0.482098\pi$
$762$	13.3526	0.483715
$763$	−18.4880	−0.669312
$764$	11.0483	0.399712
$765$	0	0
$766$	34.3864	1.24243
$767$	63.7246	2.30096
$768$	1.66908	0.0602277
$769$	−43.6537	−1.57419	−0.787096	−	0.616830i	$-0.788417\pi$
$769$	−43.6537	−1.57419	−0.787096	+	0.616830i	$0.788417\pi$
$770$	0	0
$771$	−31.8872	−1.14839
$772$	−0.0829546	−0.00298560
$773$	13.6682	0.491610	0.245805	−	0.969319i	$-0.420948\pi$
$773$	13.6682	0.491610	0.245805	+	0.969319i	$0.420948\pi$
$774$	−1.31160	−0.0471446
$775$	0	0
$776$	−0.578887	−0.0207808
$777$	23.7568	0.852271
$778$	−5.63923	−0.202176
$779$	52.6600	1.88674
$780$	0	0
$781$	−64.0579	−2.29217
$782$	35.3792	1.26516
$783$	5.36471	0.191719
$784$	3.33092	0.118961
$785$	0	0
$786$	19.7279	0.703670
$787$	−9.28505	−0.330976	−0.165488	−	0.986212i	$-0.552920\pi$
$787$	−9.28505	−0.330976	−0.165488	+	0.986212i	$0.552920\pi$
$788$	−0.732717	−0.0261020
$789$	20.0289	0.713049
$790$	0	0
$791$	−23.3195	−0.829146
$792$	1.14330	0.0406254
$793$	13.7698	0.488980
$794$	−10.9131	−0.387291
$795$	0	0
$796$	4.60873	0.163352
$797$	−25.9469	−0.919086	−0.459543	−	0.888156i	$-0.651987\pi$
$797$	−25.9469	−0.919086	−0.459543	+	0.888156i	$0.651987\pi$
$798$	−33.5185	−1.18654
$799$	−44.0289	−1.55763
$800$	0	0
$801$	−1.14330	−0.0403965
$802$	−21.9846	−0.776304
$803$	−0.661842	−0.0233559
$804$	9.32368	0.328821
$805$	0	0
$806$	0.567705	0.0199966
$807$	−32.0700	−1.12892
$808$	−5.18762	−0.182500
$809$	−6.08206	−0.213834	−0.106917	−	0.994268i	$-0.534098\pi$
$809$	−6.08206	−0.213834	−0.106917	+	0.994268i	$0.534098\pi$
$810$	0	0
$811$	−47.9194	−1.68268	−0.841340	−	0.540507i	$-0.818232\pi$
$811$	−47.9194	−1.68268	−0.841340	+	0.540507i	$0.818232\pi$
$812$	3.21417	0.112795
$813$	−1.81962	−0.0638167
$814$	23.6392	0.828555
$815$	0	0
$816$	−6.88325	−0.240962
$817$	38.2624	1.33863
$818$	5.58612	0.195314
$819$	−3.15209	−0.110143
$820$	0	0
$821$	−7.98553	−0.278697	−0.139348	−	0.990243i	$-0.544501\pi$
$821$	−7.98553	−0.278697	−0.139348	+	0.990243i	$0.544501\pi$
$822$	5.71011	0.199163
$823$	12.3077	0.429018	0.214509	−	0.976722i	$-0.431185\pi$
$823$	12.3077	0.429018	0.214509	+	0.976722i	$0.431185\pi$
$824$	−11.7665	−0.409906
$825$	0	0
$826$	−44.7318	−1.55642
$827$	−34.8679	−1.21248	−0.606238	−	0.795284i	$-0.707322\pi$
$827$	−34.8679	−1.21248	−0.606238	+	0.795284i	$0.707322\pi$
$828$	−1.83738	−0.0638535
$829$	45.7777	1.58992	0.794962	−	0.606659i	$-0.207491\pi$
$829$	45.7777	1.58992	0.794962	+	0.606659i	$0.207491\pi$
$830$	0	0
$831$	42.6166	1.47835
$832$	−4.57889	−0.158744
$833$	−13.7367	−0.475947
$834$	12.7560	0.441703
$835$	0	0
$836$	−33.3526	−1.15352
$837$	−0.665134	−0.0229904
$838$	12.2513	0.423213
$839$	−47.9017	−1.65375	−0.826875	−	0.562386i	$-0.809883\pi$
$839$	−47.9017	−1.65375	−0.826875	+	0.562386i	$0.809883\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	2.85670	0.0984484
$843$	2.32763	0.0801678
$844$	2.66184	0.0916244
$845$	0	0
$846$	2.28660	0.0786149
$847$	−56.2350	−1.93226
$848$	−12.3719	−0.424854
$849$	−17.1047	−0.587031
$850$	0	0
$851$	−37.9903	−1.30229
$852$	−20.0289	−0.686180
$853$	−5.03050	−0.172241	−0.0861205	−	0.996285i	$-0.527447\pi$
$853$	−5.03050	−0.172241	−0.0861205	+	0.996285i	$0.527447\pi$
$854$	−9.66579	−0.330756
$855$	0	0
$856$	8.42835	0.288075
$857$	8.51041	0.290710	0.145355	−	0.989380i	$-0.453568\pi$
$857$	8.51041	0.290710	0.145355	+	0.989380i	$0.453568\pi$
$858$	40.7970	1.39279
$859$	−25.7520	−0.878648	−0.439324	−	0.898329i	$-0.644782\pi$
$859$	−25.7520	−0.878648	−0.439324	+	0.898329i	$0.644782\pi$
$860$	0	0
$861$	45.2157	1.54095
$862$	11.3382	0.386179
$863$	2.45820	0.0836780	0.0418390	−	0.999124i	$-0.486678\pi$
$863$	2.45820	0.0836780	0.0418390	+	0.999124i	$0.486678\pi$
$864$	5.36471	0.182511
$865$	0	0
$866$	34.0289	1.15635
$867$	0.0120796	0.000410244 0
$868$	−0.398504	−0.0135261
$869$	68.4718	2.32275
$870$	0	0
$871$	−25.5782	−0.866685
$872$	−5.75203	−0.194788
$873$	−0.123983	−0.00419619
$874$	53.6006	1.81307
$875$	0	0
$876$	−0.206938	−0.00699178
$877$	49.4645	1.67030	0.835149	−	0.550023i	$-0.185381\pi$
$877$	49.4645	1.67030	0.835149	+	0.550023i	$0.185381\pi$
$878$	−5.27058	−0.177873
$879$	−5.96137	−0.201072
$880$	0	0
$881$	41.0594	1.38333	0.691664	−	0.722219i	$-0.256878\pi$
$881$	41.0594	1.38333	0.691664	+	0.722219i	$0.256878\pi$
$882$	0.713400	0.0240214
$883$	−29.3913	−0.989095	−0.494547	−	0.869151i	$-0.664666\pi$
$883$	−29.3913	−0.989095	−0.494547	+	0.869151i	$0.664666\pi$
$884$	18.8833	0.635113
$885$	0	0
$886$	13.1731	0.442561
$887$	−4.85670	−0.163072	−0.0815360	−	0.996670i	$-0.525983\pi$
$887$	−4.85670	−0.163072	−0.0815360	+	0.996670i	$0.525983\pi$
$888$	7.39127	0.248035
$889$	25.7134	0.862400
$890$	0	0
$891$	−44.3687	−1.48641
$892$	−0.744796	−0.0249376
$893$	−66.7053	−2.23221
$894$	19.2254	0.642992
$895$	0	0
$896$	3.21417	0.107378
$897$	−65.5644	−2.18913
$898$	−12.9243	−0.431289
$899$	−0.123983	−0.00413507
$900$	0	0
$901$	51.0217	1.69978
$902$	44.9919	1.49807
$903$	32.8534	1.09329
$904$	−7.25520	−0.241304
$905$	0	0
$906$	15.2850	0.507812
$907$	−42.8679	−1.42340	−0.711702	−	0.702481i	$-0.752076\pi$
$907$	−42.8679	−1.42340	−0.711702	+	0.702481i	$0.752076\pi$
$908$	0.180384	0.00598624
$909$	−1.11106	−0.0368515
$910$	0	0
$911$	−20.3599	−0.674553	−0.337276	−	0.941406i	$-0.609506\pi$
$911$	−20.3599	−0.674553	−0.337276	+	0.941406i	$0.609506\pi$
$912$	−10.4283	−0.345317
$913$	12.0000	0.397142
$914$	−14.4959	−0.479483
$915$	0	0
$916$	10.1385	0.334984
$917$	37.9903	1.25455
$918$	−22.1240	−0.730200
$919$	44.0000	1.45143	0.725713	−	0.687998i	$-0.241510\pi$
$919$	44.0000	1.45143	0.725713	+	0.687998i	$0.241510\pi$
$920$	0	0
$921$	−20.8567	−0.687252
$922$	−27.4621	−0.904417
$923$	54.9466	1.80859
$924$	−28.6377	−0.942111
$925$	0	0
$926$	−2.41388	−0.0793249
$927$	−2.52009	−0.0827707
$928$	1.00000	0.0328266
$929$	−40.5668	−1.33095	−0.665477	−	0.746418i	$-0.731772\pi$
$929$	−40.5668	−1.33095	−0.665477	+	0.746418i	$0.731772\pi$
$930$	0	0
$931$	−20.8115	−0.682069
$932$	27.3526	0.895965
$933$	36.6941	1.20131
$934$	−1.51525	−0.0495805
$935$	0	0
$936$	−0.980683	−0.0320546
$937$	34.7439	1.13503	0.567517	−	0.823362i	$-0.307904\pi$
$937$	34.7439	1.13503	0.567517	+	0.823362i	$0.307904\pi$
$938$	17.9548	0.586244
$939$	−28.6618	−0.935344
$940$	0	0
$941$	−18.0821	−0.589458	−0.294729	−	0.955581i	$-0.595229\pi$
$941$	−18.0821	−0.589458	−0.294729	+	0.955581i	$0.595229\pi$
$942$	−16.6908	−0.543815
$943$	−72.3059	−2.35460
$944$	−13.9170	−0.452961
$945$	0	0
$946$	32.6908	1.06287
$947$	48.3743	1.57195	0.785977	−	0.618255i	$-0.212160\pi$
$947$	48.3743	1.57195	0.785977	+	0.618255i	$0.212160\pi$
$948$	21.4090	0.695333
$949$	0.567705	0.0184285
$950$	0	0
$951$	8.30766	0.269394
$952$	−13.2552	−0.429604
$953$	−14.0289	−0.454442	−0.227221	−	0.973843i	$-0.572964\pi$
$953$	−14.0289	−0.454442	−0.227221	+	0.973843i	$0.572964\pi$
$954$	−2.64976	−0.0857892
$955$	0	0
$956$	−25.7665	−0.833348
$957$	−8.90981	−0.288013
$958$	20.6199	0.666199
$959$	10.9961	0.355081
$960$	0	0
$961$	−30.9846	−0.999504
$962$	−20.2769	−0.653754
$963$	1.80514	0.0581699
$964$	6.34540	0.204371
$965$	0	0
$966$	46.0233	1.48077
$967$	−25.9614	−0.834861	−0.417431	−	0.908709i	$-0.637069\pi$
$967$	−25.9614	−0.834861	−0.417431	+	0.908709i	$0.637069\pi$
$968$	−17.4959	−0.562341
$969$	43.0063	1.38156
$970$	0	0
$971$	21.7520	0.698056	0.349028	−	0.937112i	$-0.386512\pi$
$971$	21.7520	0.698056	0.349028	+	0.937112i	$0.386512\pi$
$972$	2.22141	0.0712518
$973$	24.5644	0.787499
$974$	−17.7367	−0.568319
$975$	0	0
$976$	−3.00724	−0.0962593
$977$	−26.6908	−0.853914	−0.426957	−	0.904272i	$-0.640414\pi$
$977$	−26.6908	−0.853914	−0.426957	+	0.904272i	$0.640414\pi$
$978$	31.1722	0.996779
$979$	28.4959	0.910734
$980$	0	0
$981$	−1.23194	−0.0393329
$982$	−22.4139	−0.715256
$983$	−37.0450	−1.18155	−0.590776	−	0.806836i	$-0.701178\pi$
$983$	−37.0450	−1.18155	−0.590776	+	0.806836i	$0.701178\pi$
$984$	14.0676	0.448458
$985$	0	0
$986$	−4.12398	−0.131334
$987$	−57.2754	−1.82309
$988$	28.6087	0.910165
$989$	−52.5370	−1.67058
$990$	0	0
$991$	−30.4283	−0.966588	−0.483294	−	0.875458i	$-0.660560\pi$
$991$	−30.4283	−0.966588	−0.483294	+	0.875458i	$0.660560\pi$
$992$	−0.123983	−0.00393647
$993$	−33.4057	−1.06010
$994$	−38.5701	−1.22337
$995$	0	0
$996$	3.75203	0.118888
$997$	−15.0226	−0.475771	−0.237885	−	0.971293i	$-0.576454\pi$
$997$	−15.0226	−0.475771	−0.237885	+	0.971293i	$0.576454\pi$
$998$	−14.7737	−0.467655
$999$	23.7568	0.751633

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.2.a.p.1.3		3
5.2	odd	4		1450.2.b.l.349.1		6
5.3	odd	4		1450.2.b.l.349.6		6
5.4	even	2		290.2.a.e.1.1	✓	3
15.14	odd	2		2610.2.a.x.1.2		3
20.19	odd	2		2320.2.a.l.1.3		3
40.19	odd	2		9280.2.a.by.1.1		3
40.29	even	2		9280.2.a.bf.1.3		3
145.144	even	2		8410.2.a.v.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
290.2.a.e.1.1	✓	3	5.4	even	2
1450.2.a.p.1.3		3	1.1	even	1	trivial
1450.2.b.l.349.1		6	5.2	odd	4
1450.2.b.l.349.6		6	5.3	odd	4
2320.2.a.l.1.3		3	20.19	odd	2
2610.2.a.x.1.2		3	15.14	odd	2
8410.2.a.v.1.3		3	145.144	even	2
9280.2.a.bf.1.3		3	40.29	even	2
9280.2.a.by.1.1		3	40.19	odd	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:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1450.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.66908 q^{3} +1.00000 q^{4} -1.66908 q^{6} -3.21417 q^{7} -1.00000 q^{8} -0.214175 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.66908 q^{3} +1.00000 q^{4} -1.66908 q^{6} -3.21417 q^{7} -1.00000 q^{8} -0.214175 q^{9} +5.33816 q^{11} +1.66908 q^{12} -4.57889 q^{13} +3.21417 q^{14} +1.00000 q^{16} -4.12398 q^{17} +0.214175 q^{18} -6.24797 q^{19} -5.36471 q^{21} -5.33816 q^{22} +8.57889 q^{23} -1.66908 q^{24} +4.57889 q^{26} -5.36471 q^{27} -3.21417 q^{28} -1.00000 q^{29} +0.123983 q^{31} -1.00000 q^{32} +8.90981 q^{33} +4.12398 q^{34} -0.214175 q^{36} -4.42835 q^{37} +6.24797 q^{38} -7.64252 q^{39} -8.42835 q^{41} +5.36471 q^{42} -6.12398 q^{43} +5.33816 q^{44} -8.57889 q^{46} +10.6763 q^{47} +1.66908 q^{48} +3.33092 q^{49} -6.88325 q^{51} -4.57889 q^{52} -12.3719 q^{53} +5.36471 q^{54} +3.21417 q^{56} -10.4283 q^{57} +1.00000 q^{58} -13.9170 q^{59} -3.00724 q^{61} -0.123983 q^{62} +0.688396 q^{63} +1.00000 q^{64} -8.90981 q^{66} +5.58612 q^{67} -4.12398 q^{68} +14.3188 q^{69} -12.0000 q^{71} +0.214175 q^{72} -0.123983 q^{73} +4.42835 q^{74} -6.24797 q^{76} -17.1578 q^{77} +7.64252 q^{78} +12.8269 q^{79} -8.31160 q^{81} +8.42835 q^{82} +2.24797 q^{83} -5.36471 q^{84} +6.12398 q^{86} -1.66908 q^{87} -5.33816 q^{88} +5.33816 q^{89} +14.7173 q^{91} +8.57889 q^{92} +0.206938 q^{93} -10.6763 q^{94} -1.66908 q^{96} +0.578887 q^{97} -3.33092 q^{98} -1.14330 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{6} - 3 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^6 - 3 * q^7 - 3 * q^8 + 6 * q^9	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{6} - 3 q^{7} - 3 q^{8} + 6 q^{9} - 3 q^{12} - 3 q^{13} + 3 q^{14} + 3 q^{16} - 3 q^{17} - 6 q^{18} - 12 q^{21} + 15 q^{23} + 3 q^{24} + 3 q^{26} - 12 q^{27} - 3 q^{28} - 3 q^{29} - 9 q^{31} - 3 q^{32} + 24 q^{33} + 3 q^{34} + 6 q^{36} - 3 q^{39} - 12 q^{41} + 12 q^{42} - 9 q^{43} - 15 q^{46} - 3 q^{48} + 18 q^{49} - 6 q^{51} - 3 q^{52} - 9 q^{53} + 12 q^{54} + 3 q^{56} - 18 q^{57} + 3 q^{58} - 15 q^{59} + 15 q^{61} + 9 q^{62} + 30 q^{63} + 3 q^{64} - 24 q^{66} - 18 q^{67} - 3 q^{68} - 9 q^{69} - 36 q^{71} - 6 q^{72} + 9 q^{73} - 30 q^{77} + 3 q^{78} + 9 q^{79} + 3 q^{81} + 12 q^{82} - 12 q^{83} - 12 q^{84} + 9 q^{86} + 3 q^{87} - 24 q^{91} + 15 q^{92} + 18 q^{93} + 3 q^{96} - 9 q^{97} - 18 q^{98} - 30 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^6 - 3 * q^7 - 3 * q^8 + 6 * q^9 - 3 * q^12 - 3 * q^13 + 3 * q^14 + 3 * q^16 - 3 * q^17 - 6 * q^18 - 12 * q^21 + 15 * q^23 + 3 * q^24 + 3 * q^26 - 12 * q^27 - 3 * q^28 - 3 * q^29 - 9 * q^31 - 3 * q^32 + 24 * q^33 + 3 * q^34 + 6 * q^36 - 3 * q^39 - 12 * q^41 + 12 * q^42 - 9 * q^43 - 15 * q^46 - 3 * q^48 + 18 * q^49 - 6 * q^51 - 3 * q^52 - 9 * q^53 + 12 * q^54 + 3 * q^56 - 18 * q^57 + 3 * q^58 - 15 * q^59 + 15 * q^61 + 9 * q^62 + 30 * q^63 + 3 * q^64 - 24 * q^66 - 18 * q^67 - 3 * q^68 - 9 * q^69 - 36 * q^71 - 6 * q^72 + 9 * q^73 - 30 * q^77 + 3 * q^78 + 9 * q^79 + 3 * q^81 + 12 * q^82 - 12 * q^83 - 12 * q^84 + 9 * q^86 + 3 * q^87 - 24 * q^91 + 15 * q^92 + 18 * q^93 + 3 * q^96 - 9 * q^97 - 18 * q^98 - 30 * q^99

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