LMFDB - Embedded newform 8025.2.a.ba.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8025,2,Mod(1,8025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8025, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8025 = 3 \cdot 5^{2} \cdot 107 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8025.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:	$64.0799476221$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.13231312.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 8x^{4} + 9x^{3} + 8x^{2} - 9x + 1 $ x^6 - x^5 - 8x^4 + 9x^3 + 8x^2 - 9x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 321)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.759615$ of defining polynomial
Character	$\chi$	$=$	8025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.40654 q^{2} -1.00000 q^{3} -0.0216539 q^{4} +1.40654 q^{6} -1.09008 q^{7} +2.84353 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.40654 q^{2} -1.00000 q^{3} -0.0216539 q^{4} +1.40654 q^{6} -1.09008 q^{7} +2.84353 q^{8} +1.00000 q^{9} -4.25771 q^{11} +0.0216539 q^{12} +4.58149 q^{13} +1.53324 q^{14} -3.95622 q^{16} +0.619105 q^{17} -1.40654 q^{18} +3.09156 q^{19} +1.09008 q^{21} +5.98863 q^{22} -4.02930 q^{23} -2.84353 q^{24} -6.44404 q^{26} -1.00000 q^{27} +0.0236045 q^{28} -6.40851 q^{29} +6.89024 q^{31} -0.122488 q^{32} +4.25771 q^{33} -0.870793 q^{34} -0.0216539 q^{36} +4.32314 q^{37} -4.34840 q^{38} -4.58149 q^{39} -1.43070 q^{41} -1.53324 q^{42} +11.2506 q^{43} +0.0921961 q^{44} +5.66736 q^{46} -8.48310 q^{47} +3.95622 q^{48} -5.81173 q^{49} -0.619105 q^{51} -0.0992072 q^{52} +7.06944 q^{53} +1.40654 q^{54} -3.09968 q^{56} -3.09156 q^{57} +9.01380 q^{58} +11.6571 q^{59} -13.7744 q^{61} -9.69137 q^{62} -1.09008 q^{63} +8.08473 q^{64} -5.98863 q^{66} +8.41892 q^{67} -0.0134060 q^{68} +4.02930 q^{69} +5.80273 q^{71} +2.84353 q^{72} -9.35652 q^{73} -6.08066 q^{74} -0.0669444 q^{76} +4.64125 q^{77} +6.44404 q^{78} +6.51246 q^{79} +1.00000 q^{81} +2.01233 q^{82} -13.3601 q^{83} -0.0236045 q^{84} -15.8243 q^{86} +6.40851 q^{87} -12.1069 q^{88} +15.6784 q^{89} -4.99419 q^{91} +0.0872501 q^{92} -6.89024 q^{93} +11.9318 q^{94} +0.122488 q^{96} -8.69559 q^{97} +8.17441 q^{98} -4.25771 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 6 q^{3} + 7 q^{4} + 3 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 6 * q^3 + 7 * q^4 + 3 * q^6 - 6 * q^8 + 6 * q^9	$ 6 q - 3 q^{2} - 6 q^{3} + 7 q^{4} + 3 q^{6} - 6 q^{8} + 6 q^{9} + 6 q^{11} - 7 q^{12} + 8 q^{13} - 2 q^{14} + q^{16} - 4 q^{17} - 3 q^{18} - 4 q^{19} + 22 q^{22} - 14 q^{23} + 6 q^{24} - 7 q^{26} - 6 q^{27} + 16 q^{28} + 10 q^{29} + 12 q^{31} - 5 q^{32} - 6 q^{33} - q^{34} + 7 q^{36} + 12 q^{37} + q^{38} - 8 q^{39} - 6 q^{41} + 2 q^{42} + 12 q^{43} + 4 q^{44} + 18 q^{46} - 16 q^{47} - q^{48} - 12 q^{49} + 4 q^{51} + 25 q^{52} - 12 q^{53} + 3 q^{54} - 32 q^{56} + 4 q^{57} - 12 q^{58} + 8 q^{59} - 24 q^{61} + 8 q^{62} - 12 q^{64} - 22 q^{66} + 4 q^{67} + 15 q^{68} + 14 q^{69} + 36 q^{71} - 6 q^{72} + 26 q^{73} - 39 q^{74} - 17 q^{76} - 14 q^{77} + 7 q^{78} + 8 q^{79} + 6 q^{81} + 38 q^{82} + 8 q^{83} - 16 q^{84} + 16 q^{86} - 10 q^{87} + 8 q^{88} - 8 q^{89} - 18 q^{91} - 2 q^{92} - 12 q^{93} + 24 q^{94} + 5 q^{96} + 24 q^{97} - 43 q^{98} + 6 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 6 * q^3 + 7 * q^4 + 3 * q^6 - 6 * q^8 + 6 * q^9 + 6 * q^11 - 7 * q^12 + 8 * q^13 - 2 * q^14 + q^16 - 4 * q^17 - 3 * q^18 - 4 * q^19 + 22 * q^22 - 14 * q^23 + 6 * q^24 - 7 * q^26 - 6 * q^27 + 16 * q^28 + 10 * q^29 + 12 * q^31 - 5 * q^32 - 6 * q^33 - q^34 + 7 * q^36 + 12 * q^37 + q^38 - 8 * q^39 - 6 * q^41 + 2 * q^42 + 12 * q^43 + 4 * q^44 + 18 * q^46 - 16 * q^47 - q^48 - 12 * q^49 + 4 * q^51 + 25 * q^52 - 12 * q^53 + 3 * q^54 - 32 * q^56 + 4 * q^57 - 12 * q^58 + 8 * q^59 - 24 * q^61 + 8 * q^62 - 12 * q^64 - 22 * q^66 + 4 * q^67 + 15 * q^68 + 14 * q^69 + 36 * q^71 - 6 * q^72 + 26 * q^73 - 39 * q^74 - 17 * q^76 - 14 * q^77 + 7 * q^78 + 8 * q^79 + 6 * q^81 + 38 * q^82 + 8 * q^83 - 16 * q^84 + 16 * q^86 - 10 * q^87 + 8 * q^88 - 8 * q^89 - 18 * q^91 - 2 * q^92 - 12 * q^93 + 24 * q^94 + 5 * q^96 + 24 * q^97 - 43 * q^98 + 6 * 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 $

$2$	−1.40654	−0.994572	−0.497286	−	0.867587i	$-0.665670\pi$
$2$	−1.40654	−0.994572	−0.497286	+	0.867587i	$0.665670\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.0216539	−0.0108270
$5$	0	0
$5$	0	0
$6$	1.40654	0.574216
$7$	−1.09008	−0.412012	−0.206006	−	0.978551i	$-0.566047\pi$
$7$	−1.09008	−0.412012	−0.206006	+	0.978551i	$0.566047\pi$
$8$	2.84353	1.00534
$9$	1.00000	0.333333
$10$	0	0
$11$	−4.25771	−1.28375	−0.641874	−	0.766810i	$-0.721843\pi$
$11$	−4.25771	−1.28375	−0.641874	+	0.766810i	$0.721843\pi$
$12$	0.0216539	0.00625094
$13$	4.58149	1.27068	0.635339	−	0.772234i	$-0.280861\pi$
$13$	4.58149	1.27068	0.635339	+	0.772234i	$0.280861\pi$
$14$	1.53324	0.409775
$15$	0	0
$16$	−3.95622	−0.989056
$17$	0.619105	0.150155	0.0750774	−	0.997178i	$-0.476080\pi$
$17$	0.619105	0.150155	0.0750774	+	0.997178i	$0.476080\pi$
$18$	−1.40654	−0.331524
$19$	3.09156	0.709253	0.354626	−	0.935008i	$-0.384608\pi$
$19$	3.09156	0.709253	0.354626	+	0.935008i	$0.384608\pi$
$20$	0	0
$21$	1.09008	0.237875
$22$	5.98863	1.27678
$23$	−4.02930	−0.840167	−0.420084	−	0.907485i	$-0.637999\pi$
$23$	−4.02930	−0.840167	−0.420084	+	0.907485i	$0.637999\pi$
$24$	−2.84353	−0.580433
$25$	0	0
$26$	−6.44404	−1.26378
$27$	−1.00000	−0.192450
$28$	0.0236045	0.00446083
$29$	−6.40851	−1.19003	−0.595015	−	0.803715i	$-0.702854\pi$
$29$	−6.40851	−1.19003	−0.595015	+	0.803715i	$0.702854\pi$
$30$	0	0
$31$	6.89024	1.23752	0.618762	−	0.785579i	$-0.287635\pi$
$31$	6.89024	1.23752	0.618762	+	0.785579i	$0.287635\pi$
$32$	−0.122488	−0.0216530
$33$	4.25771	0.741173
$34$	−0.870793	−0.149340
$35$	0	0
$36$	−0.0216539	−0.00360898
$37$	4.32314	0.710720	0.355360	−	0.934729i	$-0.384358\pi$
$37$	4.32314	0.710720	0.355360	+	0.934729i	$0.384358\pi$
$38$	−4.34840	−0.705403
$39$	−4.58149	−0.733626
$40$	0	0
$41$	−1.43070	−0.223437	−0.111719	−	0.993740i	$-0.535636\pi$
$41$	−1.43070	−0.223437	−0.111719	+	0.993740i	$0.535636\pi$
$42$	−1.53324	−0.236584
$43$	11.2506	1.71569	0.857847	−	0.513905i	$-0.171802\pi$
$43$	11.2506	1.71569	0.857847	+	0.513905i	$0.171802\pi$
$44$	0.0921961	0.0138991
$45$	0	0
$46$	5.66736	0.835606
$47$	−8.48310	−1.23739	−0.618694	−	0.785632i	$-0.712338\pi$
$47$	−8.48310	−1.23739	−0.618694	+	0.785632i	$0.712338\pi$
$48$	3.95622	0.571032
$49$	−5.81173	−0.830247
$50$	0	0
$51$	−0.619105	−0.0866920
$52$	−0.0992072	−0.0137576
$53$	7.06944	0.971062	0.485531	−	0.874219i	$-0.338626\pi$
$53$	7.06944	0.971062	0.485531	+	0.874219i	$0.338626\pi$
$54$	1.40654	0.191405
$55$	0	0
$56$	−3.09968	−0.414212
$57$	−3.09156	−0.409487
$58$	9.01380	1.18357
$59$	11.6571	1.51763	0.758814	−	0.651307i	$-0.225779\pi$
$59$	11.6571	1.51763	0.758814	+	0.651307i	$0.225779\pi$
$60$	0	0
$61$	−13.7744	−1.76363	−0.881816	−	0.471593i	$-0.843679\pi$
$61$	−13.7744	−1.76363	−0.881816	+	0.471593i	$0.843679\pi$
$62$	−9.69137	−1.23081
$63$	−1.09008	−0.137337
$64$	8.08473	1.01059
$65$	0	0
$66$	−5.98863	−0.737150
$67$	8.41892	1.02853	0.514267	−	0.857630i	$-0.328064\pi$
$67$	8.41892	1.02853	0.514267	+	0.857630i	$0.328064\pi$
$68$	−0.0134060	−0.00162572
$69$	4.02930	0.485071
$70$	0	0
$71$	5.80273	0.688657	0.344329	−	0.938849i	$-0.388107\pi$
$71$	5.80273	0.688657	0.344329	+	0.938849i	$0.388107\pi$
$72$	2.84353	0.335113
$73$	−9.35652	−1.09510	−0.547549	−	0.836774i	$-0.684439\pi$
$73$	−9.35652	−1.09510	−0.547549	+	0.836774i	$0.684439\pi$
$74$	−6.08066	−0.706863
$75$	0	0
$76$	−0.0669444	−0.00767905
$77$	4.64125	0.528919
$78$	6.44404	0.729644
$79$	6.51246	0.732709	0.366355	−	0.930475i	$-0.380606\pi$
$79$	6.51246	0.732709	0.366355	+	0.930475i	$0.380606\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	2.01233	0.222224
$83$	−13.3601	−1.46646	−0.733232	−	0.679979i	$-0.761989\pi$
$83$	−13.3601	−1.46646	−0.733232	+	0.679979i	$0.761989\pi$
$84$	−0.0236045	−0.00257546
$85$	0	0
$86$	−15.8243	−1.70638
$87$	6.40851	0.687064
$88$	−12.1069	−1.29060
$89$	15.6784	1.66191	0.830954	−	0.556341i	$-0.187795\pi$
$89$	15.6784	1.66191	0.830954	+	0.556341i	$0.187795\pi$
$90$	0	0
$91$	−4.99419	−0.523534
$92$	0.0872501	0.00909645
$93$	−6.89024	−0.714484
$94$	11.9318	1.23067
$95$	0	0
$96$	0.122488	0.0125013
$97$	−8.69559	−0.882903	−0.441452	−	0.897285i	$-0.645536\pi$
$97$	−8.69559	−0.882903	−0.441452	+	0.897285i	$0.645536\pi$
$98$	8.17441	0.825740
$99$	−4.25771	−0.427916
$100$	0	0
$101$	2.62059	0.260758	0.130379	−	0.991464i	$-0.458381\pi$
$101$	2.62059	0.260758	0.130379	+	0.991464i	$0.458381\pi$
$102$	0.870793	0.0862214
$103$	−1.18902	−0.117158	−0.0585790	−	0.998283i	$-0.518657\pi$
$103$	−1.18902	−0.117158	−0.0585790	+	0.998283i	$0.518657\pi$
$104$	13.0276	1.27746
$105$	0	0
$106$	−9.94343	−0.965791
$107$	1.00000	0.0966736
$107$	1.00000	0.0966736
$108$	0.0216539	0.00208365
$109$	−9.14346	−0.875785	−0.437892	−	0.899027i	$-0.644275\pi$
$109$	−9.14346	−0.875785	−0.437892	+	0.899027i	$0.644275\pi$
$110$	0	0
$111$	−4.32314	−0.410335
$112$	4.31260	0.407502
$113$	2.15594	0.202814	0.101407	−	0.994845i	$-0.467666\pi$
$113$	2.15594	0.202814	0.101407	+	0.994845i	$0.467666\pi$
$114$	4.34840	0.407265
$115$	0	0
$116$	0.138769	0.0128844
$117$	4.58149	0.423559
$118$	−16.3962	−1.50939
$119$	−0.674873	−0.0618655
$120$	0	0
$121$	7.12812	0.648011
$122$	19.3742	1.75406
$123$	1.43070	0.129002
$124$	−0.149201	−0.0133986
$125$	0	0
$126$	1.53324	0.136592
$127$	8.55873	0.759465	0.379732	−	0.925096i	$-0.376016\pi$
$127$	8.55873	0.759465	0.379732	+	0.925096i	$0.376016\pi$
$128$	−11.1265	−0.983453
$129$	−11.2506	−0.990556
$130$	0	0
$131$	−20.8566	−1.82225	−0.911124	−	0.412132i	$-0.864784\pi$
$131$	−20.8566	−1.82225	−0.911124	+	0.412132i	$0.864784\pi$
$132$	−0.0921961	−0.00802464
$133$	−3.37005	−0.292220
$134$	−11.8415	−1.02295
$135$	0	0
$136$	1.76044	0.150957
$137$	5.39998	0.461352	0.230676	−	0.973031i	$-0.425906\pi$
$137$	5.39998	0.461352	0.230676	+	0.973031i	$0.425906\pi$
$138$	−5.66736	−0.482438
$139$	0.595963	0.0505490	0.0252745	−	0.999681i	$-0.491954\pi$
$139$	0.595963	0.0505490	0.0252745	+	0.999681i	$0.491954\pi$
$140$	0	0
$141$	8.48310	0.714406
$142$	−8.16175	−0.684919
$143$	−19.5067	−1.63123
$144$	−3.95622	−0.329685
$145$	0	0
$146$	13.1603	1.08915
$147$	5.81173	0.479343
$148$	−0.0936130	−0.00769494
$149$	7.24361	0.593419	0.296710	−	0.954968i	$-0.404111\pi$
$149$	7.24361	0.593419	0.296710	+	0.954968i	$0.404111\pi$
$150$	0	0
$151$	−3.12446	−0.254265	−0.127132	−	0.991886i	$-0.540577\pi$
$151$	−3.12446	−0.254265	−0.127132	+	0.991886i	$0.540577\pi$
$152$	8.79095	0.713040
$153$	0.619105	0.0500516
$154$	−6.52809	−0.526048
$155$	0	0
$156$	0.0992072	0.00794293
$157$	−7.61190	−0.607496	−0.303748	−	0.952752i	$-0.598238\pi$
$157$	−7.61190	−0.607496	−0.303748	+	0.952752i	$0.598238\pi$
$158$	−9.16002	−0.728732
$159$	−7.06944	−0.560643
$160$	0	0
$161$	4.39226	0.346158
$162$	−1.40654	−0.110508
$163$	−3.11099	−0.243671	−0.121836	−	0.992550i	$-0.538878\pi$
$163$	−3.11099	−0.243671	−0.121836	+	0.992550i	$0.538878\pi$
$164$	0.0309802	0.00241915
$165$	0	0
$166$	18.7915	1.45850
$167$	−2.19535	−0.169882	−0.0849408	−	0.996386i	$-0.527070\pi$
$167$	−2.19535	−0.169882	−0.0849408	+	0.996386i	$0.527070\pi$
$168$	3.09968	0.239145
$169$	7.99007	0.614620
$170$	0	0
$171$	3.09156	0.236418
$172$	−0.243619	−0.0185757
$173$	−21.8703	−1.66277	−0.831383	−	0.555699i	$-0.812451\pi$
$173$	−21.8703	−1.66277	−0.831383	+	0.555699i	$0.812451\pi$
$174$	−9.01380	−0.683335
$175$	0	0
$176$	16.8445	1.26970
$177$	−11.6571	−0.876203
$178$	−22.0523	−1.65289
$179$	11.1245	0.831481	0.415741	−	0.909483i	$-0.363522\pi$
$179$	11.1245	0.831481	0.415741	+	0.909483i	$0.363522\pi$
$180$	0	0
$181$	−10.9436	−0.813431	−0.406715	−	0.913555i	$-0.633326\pi$
$181$	−10.9436	−0.813431	−0.406715	+	0.913555i	$0.633326\pi$
$182$	7.02452	0.520692
$183$	13.7744	1.01823
$184$	−11.4574	−0.844653
$185$	0	0
$186$	9.69137	0.710606
$187$	−2.63597	−0.192761
$188$	0.183692	0.0133971
$189$	1.09008	0.0792917
$190$	0	0
$191$	−8.29665	−0.600324	−0.300162	−	0.953888i	$-0.597041\pi$
$191$	−8.29665	−0.600324	−0.300162	+	0.953888i	$0.597041\pi$
$192$	−8.08473	−0.583465
$193$	−3.15939	−0.227418	−0.113709	−	0.993514i	$-0.536273\pi$
$193$	−3.15939	−0.227418	−0.113709	+	0.993514i	$0.536273\pi$
$194$	12.2307	0.878110
$195$	0	0
$196$	0.125847	0.00898904
$197$	10.5703	0.753106	0.376553	−	0.926395i	$-0.377109\pi$
$197$	10.5703	0.753106	0.376553	+	0.926395i	$0.377109\pi$
$198$	5.98863	0.425593
$199$	−0.266160	−0.0188676	−0.00943380	−	0.999956i	$-0.503003\pi$
$199$	−0.266160	−0.0188676	−0.00943380	+	0.999956i	$0.503003\pi$
$200$	0	0
$201$	−8.41892	−0.593825
$202$	−3.68595	−0.259343
$203$	6.98579	0.490306
$204$	0.0134060	0.000938610 0
$205$	0	0
$206$	1.67241	0.116522
$207$	−4.02930	−0.280056
$208$	−18.1254	−1.25677
$209$	−13.1630	−0.910503
$210$	0	0
$211$	16.6134	1.14371	0.571856	−	0.820354i	$-0.306224\pi$
$211$	16.6134	1.14371	0.571856	+	0.820354i	$0.306224\pi$
$212$	−0.153081	−0.0105136
$213$	−5.80273	−0.397596
$214$	−1.40654	−0.0961489
$215$	0	0
$216$	−2.84353	−0.193478
$217$	−7.51091	−0.509874
$218$	12.8606	0.871031
$219$	9.35652	0.632255
$220$	0	0
$221$	2.83642	0.190798
$222$	6.08066	0.408107
$223$	20.0301	1.34132	0.670659	−	0.741766i	$-0.266012\pi$
$223$	20.0301	1.34132	0.670659	+	0.741766i	$0.266012\pi$
$224$	0.133521	0.00892127
$225$	0	0
$226$	−3.03241	−0.201713
$227$	−14.2513	−0.945893	−0.472946	−	0.881091i	$-0.656810\pi$
$227$	−14.2513	−0.945893	−0.472946	+	0.881091i	$0.656810\pi$
$228$	0.0669444	0.00443350
$229$	20.3626	1.34560	0.672799	−	0.739825i	$-0.265092\pi$
$229$	20.3626	1.34560	0.672799	+	0.739825i	$0.265092\pi$
$230$	0	0
$231$	−4.64125	−0.305372
$232$	−18.2228	−1.19638
$233$	−13.0126	−0.852484	−0.426242	−	0.904609i	$-0.640163\pi$
$233$	−13.0126	−0.852484	−0.426242	+	0.904609i	$0.640163\pi$
$234$	−6.44404	−0.421260
$235$	0	0
$236$	−0.252422	−0.0164313
$237$	−6.51246	−0.423030
$238$	0.949234	0.0615297
$239$	17.1324	1.10820	0.554102	−	0.832449i	$-0.313062\pi$
$239$	17.1324	1.10820	0.554102	+	0.832449i	$0.313062\pi$
$240$	0	0
$241$	11.9276	0.768324	0.384162	−	0.923266i	$-0.374490\pi$
$241$	11.9276	0.768324	0.384162	+	0.923266i	$0.374490\pi$
$242$	−10.0260	−0.644494
$243$	−1.00000	−0.0641500
$244$	0.298270	0.0190948
$245$	0	0
$246$	−2.01233	−0.128301
$247$	14.1640	0.901231
$248$	19.5926	1.24413
$249$	13.3601	0.846663
$250$	0	0
$251$	−24.2349	−1.52969	−0.764847	−	0.644212i	$-0.777185\pi$
$251$	−24.2349	−1.52969	−0.764847	+	0.644212i	$0.777185\pi$
$252$	0.0236045	0.00148694
$253$	17.1556	1.07856
$254$	−12.0382	−0.755342
$255$	0	0
$256$	−0.519633	−0.0324770
$257$	2.12990	0.132860	0.0664298	−	0.997791i	$-0.478839\pi$
$257$	2.12990	0.132860	0.0664298	+	0.997791i	$0.478839\pi$
$258$	15.8243	0.985179
$259$	−4.71257	−0.292825
$260$	0	0
$261$	−6.40851	−0.396677
$262$	29.3356	1.81236
$263$	−14.3736	−0.886313	−0.443157	−	0.896444i	$-0.646141\pi$
$263$	−14.3736	−0.886313	−0.443157	+	0.896444i	$0.646141\pi$
$264$	12.1069	0.745131
$265$	0	0
$266$	4.74010	0.290634
$267$	−15.6784	−0.959503
$268$	−0.182302	−0.0111359
$269$	16.0831	0.980601	0.490301	−	0.871553i	$-0.336887\pi$
$269$	16.0831	0.980601	0.490301	+	0.871553i	$0.336887\pi$
$270$	0	0
$271$	−6.22356	−0.378055	−0.189027	−	0.981972i	$-0.560533\pi$
$271$	−6.22356	−0.378055	−0.189027	+	0.981972i	$0.560533\pi$
$272$	−2.44932	−0.148512
$273$	4.99419	0.302262
$274$	−7.59528	−0.458847
$275$	0	0
$276$	−0.0872501	−0.00525184
$277$	13.3951	0.804834	0.402417	−	0.915457i	$-0.368170\pi$
$277$	13.3951	0.804834	0.402417	+	0.915457i	$0.368170\pi$
$278$	−0.838245	−0.0502746
$279$	6.89024	0.412508
$280$	0	0
$281$	−30.4196	−1.81468	−0.907341	−	0.420396i	$-0.861891\pi$
$281$	−30.4196	−1.81468	−0.907341	+	0.420396i	$0.861891\pi$
$282$	−11.9318	−0.710528
$283$	−12.0754	−0.717810	−0.358905	−	0.933374i	$-0.616850\pi$
$283$	−12.0754	−0.717810	−0.358905	+	0.933374i	$0.616850\pi$
$284$	−0.125652	−0.00745606
$285$	0	0
$286$	27.4369	1.62238
$287$	1.55957	0.0920587
$288$	−0.122488	−0.00721765
$289$	−16.6167	−0.977454
$290$	0	0
$291$	8.69559	0.509744
$292$	0.202605	0.0118566
$293$	−33.9285	−1.98212	−0.991062	−	0.133400i	$-0.957410\pi$
$293$	−33.9285	−1.98212	−0.991062	+	0.133400i	$0.957410\pi$
$294$	−8.17441	−0.476741
$295$	0	0
$296$	12.2930	0.714516
$297$	4.25771	0.247058
$298$	−10.1884	−0.590198
$299$	−18.4602	−1.06758
$300$	0	0
$301$	−12.2640	−0.706886
$302$	4.39467	0.252885
$303$	−2.62059	−0.150549
$304$	−12.2309	−0.701491
$305$	0	0
$306$	−0.870793	−0.0497799
$307$	30.9929	1.76886	0.884430	−	0.466672i	$-0.154547\pi$
$307$	30.9929	1.76886	0.884430	+	0.466672i	$0.154547\pi$
$308$	−0.100501	−0.00572659
$309$	1.18902	0.0676412
$310$	0	0
$311$	8.04809	0.456365	0.228183	−	0.973618i	$-0.426722\pi$
$311$	8.04809	0.456365	0.228183	+	0.973618i	$0.426722\pi$
$312$	−13.0276	−0.737543
$313$	22.7384	1.28525	0.642626	−	0.766180i	$-0.277845\pi$
$313$	22.7384	1.28525	0.642626	+	0.766180i	$0.277845\pi$
$314$	10.7064	0.604198
$315$	0	0
$316$	−0.141020	−0.00793301
$317$	10.7199	0.602090	0.301045	−	0.953610i	$-0.402665\pi$
$317$	10.7199	0.602090	0.301045	+	0.953610i	$0.402665\pi$
$318$	9.94343	0.557600
$319$	27.2856	1.52770
$320$	0	0
$321$	−1.00000	−0.0558146
$322$	−6.17787	−0.344279
$323$	1.91400	0.106498
$324$	−0.0216539	−0.00120299
$325$	0	0
$326$	4.37572	0.242349
$327$	9.14346	0.505634
$328$	−4.06823	−0.224630
$329$	9.24726	0.509818
$330$	0	0
$331$	16.4750	0.905547	0.452774	−	0.891626i	$-0.350435\pi$
$331$	16.4750	0.905547	0.452774	+	0.891626i	$0.350435\pi$
$332$	0.289299	0.0158773
$333$	4.32314	0.236907
$334$	3.08785	0.168959
$335$	0	0
$336$	−4.31260	−0.235272
$337$	−26.8779	−1.46413	−0.732067	−	0.681232i	$-0.761444\pi$
$337$	−26.8779	−1.46413	−0.732067	+	0.681232i	$0.761444\pi$
$338$	−11.2383	−0.611284
$339$	−2.15594	−0.117095
$340$	0	0
$341$	−29.3367	−1.58867
$342$	−4.34840	−0.235134
$343$	13.9658	0.754083
$344$	31.9913	1.72486
$345$	0	0
$346$	30.7614	1.65374
$347$	17.9888	0.965690	0.482845	−	0.875706i	$-0.339603\pi$
$347$	17.9888	0.965690	0.482845	+	0.875706i	$0.339603\pi$
$348$	−0.138769	−0.00743881
$349$	−34.9353	−1.87005	−0.935023	−	0.354588i	$-0.884621\pi$
$349$	−34.9353	−1.87005	−0.935023	+	0.354588i	$0.884621\pi$
$350$	0	0
$351$	−4.58149	−0.244542
$352$	0.521517	0.0277970
$353$	27.6834	1.47344	0.736719	−	0.676199i	$-0.236374\pi$
$353$	27.6834	1.47344	0.736719	+	0.676199i	$0.236374\pi$
$354$	16.3962	0.871447
$355$	0	0
$356$	−0.339499	−0.0179934
$357$	0.674873	0.0357181
$358$	−15.6470	−0.826968
$359$	3.96990	0.209523	0.104762	−	0.994497i	$-0.466592\pi$
$359$	3.96990	0.209523	0.104762	+	0.994497i	$0.466592\pi$
$360$	0	0
$361$	−9.44225	−0.496960
$362$	15.3926	0.809015
$363$	−7.12812	−0.374129
$364$	0.108144	0.00566827
$365$	0	0
$366$	−19.3742	−1.01271
$367$	21.2998	1.11184	0.555920	−	0.831236i	$-0.312366\pi$
$367$	21.2998	1.11184	0.555920	+	0.831236i	$0.312366\pi$
$368$	15.9408	0.830972
$369$	−1.43070	−0.0744791
$370$	0	0
$371$	−7.70625	−0.400089
$372$	0.149201	0.00773569
$373$	13.2661	0.686895	0.343447	−	0.939172i	$-0.388405\pi$
$373$	13.2661	0.686895	0.343447	+	0.939172i	$0.388405\pi$
$374$	3.70759	0.191715
$375$	0	0
$376$	−24.1220	−1.24399
$377$	−29.3605	−1.51214
$378$	−1.53324	−0.0788612
$379$	19.6374	1.00870	0.504352	−	0.863498i	$-0.331732\pi$
$379$	19.6374	1.00870	0.504352	+	0.863498i	$0.331732\pi$
$380$	0	0
$381$	−8.55873	−0.438477
$382$	11.6695	0.597066
$383$	−16.6742	−0.852012	−0.426006	−	0.904720i	$-0.640080\pi$
$383$	−16.6742	−0.852012	−0.426006	+	0.904720i	$0.640080\pi$
$384$	11.1265	0.567797
$385$	0	0
$386$	4.44379	0.226183
$387$	11.2506	0.571898
$388$	0.188293	0.00955915
$389$	−3.83723	−0.194555	−0.0972776	−	0.995257i	$-0.531013\pi$
$389$	−3.83723	−0.194555	−0.0972776	+	0.995257i	$0.531013\pi$
$390$	0	0
$391$	−2.49456	−0.126155
$392$	−16.5258	−0.834680
$393$	20.8566	1.05208
$394$	−14.8676	−0.749018
$395$	0	0
$396$	0.0921961	0.00463303
$397$	−8.74006	−0.438651	−0.219325	−	0.975652i	$-0.570386\pi$
$397$	−8.74006	−0.438651	−0.219325	+	0.975652i	$0.570386\pi$
$398$	0.374364	0.0187652
$399$	3.37005	0.168714
$400$	0	0
$401$	9.13827	0.456343	0.228172	−	0.973621i	$-0.426725\pi$
$401$	9.13827	0.456343	0.228172	+	0.973621i	$0.426725\pi$
$402$	11.8415	0.590601
$403$	31.5676	1.57249
$404$	−0.0567459	−0.00282322
$405$	0	0
$406$	−9.82577	−0.487645
$407$	−18.4067	−0.912387
$408$	−1.76044	−0.0871549
$409$	−19.0675	−0.942825	−0.471412	−	0.881913i	$-0.656256\pi$
$409$	−19.0675	−0.942825	−0.471412	+	0.881913i	$0.656256\pi$
$410$	0	0
$411$	−5.39998	−0.266362
$412$	0.0257470	0.00126846
$413$	−12.7072	−0.625281
$414$	5.66736	0.278535
$415$	0	0
$416$	−0.561176	−0.0275139
$417$	−0.595963	−0.0291845
$418$	18.5142	0.905560
$419$	3.72395	0.181927	0.0909634	−	0.995854i	$-0.471005\pi$
$419$	3.72395	0.181927	0.0909634	+	0.995854i	$0.471005\pi$
$420$	0	0
$421$	1.02004	0.0497139	0.0248569	−	0.999691i	$-0.492087\pi$
$421$	1.02004	0.0497139	0.0248569	+	0.999691i	$0.492087\pi$
$422$	−23.3673	−1.13750
$423$	−8.48310	−0.412462
$424$	20.1022	0.976248
$425$	0	0
$426$	8.16175	0.395438
$427$	15.0152	0.726637
$428$	−0.0216539	−0.00104668
$429$	19.5067	0.941791
$430$	0	0
$431$	−9.08177	−0.437453	−0.218727	−	0.975786i	$-0.570190\pi$
$431$	−9.08177	−0.437453	−0.218727	+	0.975786i	$0.570190\pi$
$432$	3.95622	0.190344
$433$	37.6226	1.80803	0.904014	−	0.427503i	$-0.140607\pi$
$433$	37.6226	1.80803	0.904014	+	0.427503i	$0.140607\pi$
$434$	10.5644	0.507106
$435$	0	0
$436$	0.197992	0.00948208
$437$	−12.4568	−0.595891
$438$	−13.1603	−0.628823
$439$	11.7037	0.558587	0.279293	−	0.960206i	$-0.409900\pi$
$439$	11.7037	0.558587	0.279293	+	0.960206i	$0.409900\pi$
$440$	0	0
$441$	−5.81173	−0.276749
$442$	−3.98953	−0.189763
$443$	0.552095	0.0262308	0.0131154	−	0.999914i	$-0.495825\pi$
$443$	0.552095	0.0262308	0.0131154	+	0.999914i	$0.495825\pi$
$444$	0.0936130	0.00444267
$445$	0	0
$446$	−28.1731	−1.33404
$447$	−7.24361	−0.342611
$448$	−8.81300	−0.416375
$449$	−32.4240	−1.53018	−0.765092	−	0.643921i	$-0.777307\pi$
$449$	−32.4240	−1.53018	−0.765092	+	0.643921i	$0.777307\pi$
$450$	0	0
$451$	6.09150	0.286837
$452$	−0.0466845	−0.00219586
$453$	3.12446	0.146800
$454$	20.0450	0.940758
$455$	0	0
$456$	−8.79095	−0.411674
$457$	−27.0290	−1.26436	−0.632182	−	0.774820i	$-0.717841\pi$
$457$	−27.0290	−1.26436	−0.632182	+	0.774820i	$0.717841\pi$
$458$	−28.6408	−1.33829
$459$	−0.619105	−0.0288973
$460$	0	0
$461$	41.3115	1.92407	0.962033	−	0.272932i	$-0.0879934\pi$
$461$	41.3115	1.92407	0.962033	+	0.272932i	$0.0879934\pi$
$462$	6.52809	0.303714
$463$	20.4227	0.949125	0.474563	−	0.880222i	$-0.342606\pi$
$463$	20.4227	0.949125	0.474563	+	0.880222i	$0.342606\pi$
$464$	25.3535	1.17701
$465$	0	0
$466$	18.3027	0.847856
$467$	21.5202	0.995838	0.497919	−	0.867224i	$-0.334098\pi$
$467$	21.5202	0.995838	0.497919	+	0.867224i	$0.334098\pi$
$468$	−0.0992072	−0.00458585
$469$	−9.17729	−0.423768
$470$	0	0
$471$	7.61190	0.350738
$472$	33.1474	1.52573
$473$	−47.9016	−2.20252
$474$	9.16002	0.420734
$475$	0	0
$476$	0.0146136	0.000669815 0
$477$	7.06944	0.323687
$478$	−24.0974	−1.10219
$479$	7.34463	0.335585	0.167792	−	0.985822i	$-0.446336\pi$
$479$	7.34463	0.335585	0.167792	+	0.985822i	$0.446336\pi$
$480$	0	0
$481$	19.8064	0.903096
$482$	−16.7766	−0.764154
$483$	−4.39226	−0.199855
$484$	−0.154352	−0.00701599
$485$	0	0
$486$	1.40654	0.0638018
$487$	−18.0944	−0.819937	−0.409968	−	0.912100i	$-0.634460\pi$
$487$	−18.0944	−0.819937	−0.409968	+	0.912100i	$0.634460\pi$
$488$	−39.1680	−1.77305
$489$	3.11099	0.140684
$490$	0	0
$491$	18.4378	0.832086	0.416043	−	0.909345i	$-0.363417\pi$
$491$	18.4378	0.832086	0.416043	+	0.909345i	$0.363417\pi$
$492$	−0.0309802	−0.00139669
$493$	−3.96754	−0.178689
$494$	−19.9221	−0.896339
$495$	0	0
$496$	−27.2593	−1.22398
$497$	−6.32544	−0.283735
$498$	−18.7915	−0.842067
$499$	17.4968	0.783264	0.391632	−	0.920122i	$-0.371911\pi$
$499$	17.4968	0.783264	0.391632	+	0.920122i	$0.371911\pi$
$500$	0	0
$501$	2.19535	0.0980812
$502$	34.0873	1.52139
$503$	15.5818	0.694757	0.347378	−	0.937725i	$-0.387072\pi$
$503$	15.5818	0.694757	0.347378	+	0.937725i	$0.387072\pi$
$504$	−3.09968	−0.138071
$505$	0	0
$506$	−24.1300	−1.07271
$507$	−7.99007	−0.354851
$508$	−0.185330	−0.00822269
$509$	11.0080	0.487921	0.243960	−	0.969785i	$-0.421553\pi$
$509$	11.0080	0.487921	0.243960	+	0.969785i	$0.421553\pi$
$510$	0	0
$511$	10.1994	0.451193
$512$	22.9839	1.01575
$513$	−3.09156	−0.136496
$514$	−2.99579	−0.132138
$515$	0	0
$516$	0.243619	0.0107247
$517$	36.1186	1.58849
$518$	6.62841	0.291236
$519$	21.8703	0.959999
$520$	0	0
$521$	−17.9139	−0.784822	−0.392411	−	0.919790i	$-0.628359\pi$
$521$	−17.9139	−0.784822	−0.392411	+	0.919790i	$0.628359\pi$
$522$	9.01380	0.394523
$523$	42.2335	1.84674	0.923372	−	0.383908i	$-0.125422\pi$
$523$	42.2335	1.84674	0.923372	+	0.383908i	$0.125422\pi$
$524$	0.451627	0.0197294
$525$	0	0
$526$	20.2170	0.881502
$527$	4.26578	0.185820
$528$	−16.8445	−0.733061
$529$	−6.76475	−0.294119
$530$	0	0
$531$	11.6571	0.505876
$532$	0.0729747	0.00316386
$533$	−6.55472	−0.283917
$534$	22.0523	0.954295
$535$	0	0
$536$	23.9395	1.03403
$537$	−11.1245	−0.480056
$538$	−22.6214	−0.975278
$539$	24.7447	1.06583
$540$	0	0
$541$	0.938008	0.0403281	0.0201641	−	0.999797i	$-0.493581\pi$
$541$	0.938008	0.0403281	0.0201641	+	0.999797i	$0.493581\pi$
$542$	8.75367	0.376002
$543$	10.9436	0.469634
$544$	−0.0758326	−0.00325130
$545$	0	0
$546$	−7.02452	−0.300622
$547$	0.332496	0.0142165	0.00710825	−	0.999975i	$-0.497737\pi$
$547$	0.332496	0.0142165	0.00710825	+	0.999975i	$0.497737\pi$
$548$	−0.116931	−0.00499503
$549$	−13.7744	−0.587877
$550$	0	0
$551$	−19.8123	−0.844032
$552$	11.4574	0.487661
$553$	−7.09911	−0.301885
$554$	−18.8407	−0.800465
$555$	0	0
$556$	−0.0129049	−0.000547291 0
$557$	29.9349	1.26838	0.634192	−	0.773176i	$-0.281333\pi$
$557$	29.9349	1.26838	0.634192	+	0.773176i	$0.281333\pi$
$558$	−9.69137	−0.410269
$559$	51.5443	2.18009
$560$	0	0
$561$	2.63597	0.111291
$562$	42.7863	1.80483
$563$	−8.38177	−0.353249	−0.176625	−	0.984278i	$-0.556518\pi$
$563$	−8.38177	−0.353249	−0.176625	+	0.984278i	$0.556518\pi$
$564$	−0.183692	−0.00773484
$565$	0	0
$566$	16.9845	0.713913
$567$	−1.09008	−0.0457791
$568$	16.5002	0.692335
$569$	−33.8828	−1.42044	−0.710221	−	0.703979i	$-0.751405\pi$
$569$	−33.8828	−1.42044	−0.710221	+	0.703979i	$0.751405\pi$
$570$	0	0
$571$	−34.7966	−1.45619	−0.728096	−	0.685475i	$-0.759594\pi$
$571$	−34.7966	−1.45619	−0.728096	+	0.685475i	$0.759594\pi$
$572$	0.422396	0.0176613
$573$	8.29665	0.346597
$574$	−2.19360	−0.0915590
$575$	0	0
$576$	8.08473	0.336864
$577$	−10.5402	−0.438793	−0.219397	−	0.975636i	$-0.570409\pi$
$577$	−10.5402	−0.438793	−0.219397	+	0.975636i	$0.570409\pi$
$578$	23.3720	0.972148
$579$	3.15939	0.131300
$580$	0	0
$581$	14.5636	0.604200
$582$	−12.2307	−0.506977
$583$	−30.0996	−1.24660
$584$	−26.6055	−1.10095
$585$	0	0
$586$	47.7217	1.97137
$587$	9.01330	0.372019	0.186009	−	0.982548i	$-0.440445\pi$
$587$	9.01330	0.372019	0.186009	+	0.982548i	$0.440445\pi$
$588$	−0.125847	−0.00518983
$589$	21.3016	0.877717
$590$	0	0
$591$	−10.5703	−0.434806
$592$	−17.1033	−0.702942
$593$	28.3355	1.16360	0.581799	−	0.813333i	$-0.302349\pi$
$593$	28.3355	1.16360	0.581799	+	0.813333i	$0.302349\pi$
$594$	−5.98863	−0.245717
$595$	0	0
$596$	−0.156852	−0.00642493
$597$	0.266160	0.0108932
$598$	25.9650	1.06179
$599$	35.7252	1.45969	0.729847	−	0.683610i	$-0.239591\pi$
$599$	35.7252	1.45969	0.729847	+	0.683610i	$0.239591\pi$
$600$	0	0
$601$	19.6055	0.799723	0.399862	−	0.916576i	$-0.369058\pi$
$601$	19.6055	0.799723	0.399862	+	0.916576i	$0.369058\pi$
$602$	17.2498	0.703049
$603$	8.41892	0.342845
$604$	0.0676567	0.00275291
$605$	0	0
$606$	3.68595	0.149732
$607$	−38.5301	−1.56389	−0.781944	−	0.623349i	$-0.785772\pi$
$607$	−38.5301	−1.56389	−0.781944	+	0.623349i	$0.785772\pi$
$608$	−0.378678	−0.0153574
$609$	−6.98579	−0.283078
$610$	0	0
$611$	−38.8652	−1.57232
$612$	−0.0134060	−0.000541907 0
$613$	18.2623	0.737606	0.368803	−	0.929508i	$-0.379768\pi$
$613$	18.2623	0.737606	0.368803	+	0.929508i	$0.379768\pi$
$614$	−43.5927	−1.75926
$615$	0	0
$616$	13.1975	0.531744
$617$	32.2617	1.29881	0.649404	−	0.760444i	$-0.275018\pi$
$617$	32.2617	1.29881	0.649404	+	0.760444i	$0.275018\pi$
$618$	−1.67241	−0.0672740
$619$	12.4397	0.499994	0.249997	−	0.968247i	$-0.419570\pi$
$619$	12.4397	0.499994	0.249997	+	0.968247i	$0.419570\pi$
$620$	0	0
$621$	4.02930	0.161690
$622$	−11.3199	−0.453888
$623$	−17.0907	−0.684725
$624$	18.1254	0.725597
$625$	0	0
$626$	−31.9824	−1.27828
$627$	13.1630	0.525679
$628$	0.164827	0.00657733
$629$	2.67648	0.106718
$630$	0	0
$631$	30.5394	1.21576	0.607878	−	0.794031i	$-0.292021\pi$
$631$	30.5394	1.21576	0.607878	+	0.794031i	$0.292021\pi$
$632$	18.5184	0.736622
$633$	−16.6134	−0.660323
$634$	−15.0779	−0.598821
$635$	0	0
$636$	0.153081	0.00607006
$637$	−26.6264	−1.05498
$638$	−38.3782	−1.51941
$639$	5.80273	0.229552
$640$	0	0
$641$	7.19734	0.284278	0.142139	−	0.989847i	$-0.454602\pi$
$641$	7.19734	0.284278	0.142139	+	0.989847i	$0.454602\pi$
$642$	1.40654	0.0555116
$643$	27.9136	1.10080	0.550402	−	0.834900i	$-0.314474\pi$
$643$	27.9136	1.10080	0.550402	+	0.834900i	$0.314474\pi$
$644$	−0.0951096	−0.00374784
$645$	0	0
$646$	−2.69211	−0.105920
$647$	44.5143	1.75004	0.875019	−	0.484088i	$-0.160848\pi$
$647$	44.5143	1.75004	0.875019	+	0.484088i	$0.160848\pi$
$648$	2.84353	0.111704
$649$	−49.6327	−1.94825
$650$	0	0
$651$	7.51091	0.294376
$652$	0.0673650	0.00263822
$653$	16.3644	0.640390	0.320195	−	0.947352i	$-0.396252\pi$
$653$	16.3644	0.640390	0.320195	+	0.947352i	$0.396252\pi$
$654$	−12.8606	−0.502890
$655$	0	0
$656$	5.66016	0.220992
$657$	−9.35652	−0.365033
$658$	−13.0066	−0.507050
$659$	37.8355	1.47386	0.736930	−	0.675969i	$-0.236275\pi$
$659$	37.8355	1.47386	0.736930	+	0.675969i	$0.236275\pi$
$660$	0	0
$661$	−11.1022	−0.431825	−0.215913	−	0.976413i	$-0.569273\pi$
$661$	−11.1022	−0.431825	−0.215913	+	0.976413i	$0.569273\pi$
$662$	−23.1727	−0.900632
$663$	−2.83642	−0.110158
$664$	−37.9899	−1.47429
$665$	0	0
$666$	−6.08066	−0.235621
$667$	25.8218	0.999824
$668$	0.0475380	0.00183930
$669$	−20.0301	−0.774410
$670$	0	0
$671$	58.6475	2.26406
$672$	−0.133521	−0.00515070
$673$	38.3181	1.47706	0.738528	−	0.674223i	$-0.235521\pi$
$673$	38.3181	1.47706	0.738528	+	0.674223i	$0.235521\pi$
$674$	37.8048	1.45619
$675$	0	0
$676$	−0.173016	−0.00665447
$677$	−20.9207	−0.804046	−0.402023	−	0.915630i	$-0.631693\pi$
$677$	−20.9207	−0.804046	−0.402023	+	0.915630i	$0.631693\pi$
$678$	3.03241	0.116459
$679$	9.47888	0.363766
$680$	0	0
$681$	14.2513	0.546111
$682$	41.2631	1.58005
$683$	49.2684	1.88520	0.942601	−	0.333920i	$-0.108372\pi$
$683$	49.2684	1.88520	0.942601	+	0.333920i	$0.108372\pi$
$684$	−0.0669444	−0.00255968
$685$	0	0
$686$	−19.6434	−0.749989
$687$	−20.3626	−0.776882
$688$	−44.5097	−1.69692
$689$	32.3886	1.23391
$690$	0	0
$691$	42.6108	1.62099	0.810496	−	0.585744i	$-0.199198\pi$
$691$	42.6108	1.62099	0.810496	+	0.585744i	$0.199198\pi$
$692$	0.473577	0.0180027
$693$	4.64125	0.176306
$694$	−25.3019	−0.960448
$695$	0	0
$696$	18.2228	0.690733
$697$	−0.885751	−0.0335502
$698$	49.1378	1.85989
$699$	13.0126	0.492182
$700$	0	0
$701$	2.80014	0.105760	0.0528798	−	0.998601i	$-0.483160\pi$
$701$	2.80014	0.105760	0.0528798	+	0.998601i	$0.483160\pi$
$702$	6.44404	0.243215
$703$	13.3653	0.504081
$704$	−34.4225	−1.29735
$705$	0	0
$706$	−38.9377	−1.46544
$707$	−2.85665	−0.107435
$708$	0.252422	0.00948661
$709$	39.9851	1.50167	0.750836	−	0.660488i	$-0.229651\pi$
$709$	39.9851	1.50167	0.750836	+	0.660488i	$0.229651\pi$
$710$	0	0
$711$	6.51246	0.244236
$712$	44.5820	1.67078
$713$	−27.7628	−1.03973
$714$	−0.949234	−0.0355242
$715$	0	0
$716$	−0.240888	−0.00900241
$717$	−17.1324	−0.639822
$718$	−5.58381	−0.208386
$719$	26.6855	0.995203	0.497601	−	0.867406i	$-0.334214\pi$
$719$	26.6855	0.995203	0.497601	+	0.867406i	$0.334214\pi$
$720$	0	0
$721$	1.29613	0.0482704
$722$	13.2809	0.494263
$723$	−11.9276	−0.443592
$724$	0.236971	0.00880698
$725$	0	0
$726$	10.0260	0.372099
$727$	25.6294	0.950544	0.475272	−	0.879839i	$-0.342350\pi$
$727$	25.6294	0.950544	0.475272	+	0.879839i	$0.342350\pi$
$728$	−14.2011	−0.526329
$729$	1.00000	0.0370370
$730$	0	0
$731$	6.96527	0.257620
$732$	−0.298270	−0.0110244
$733$	−5.22470	−0.192979	−0.0964894	−	0.995334i	$-0.530761\pi$
$733$	−5.22470	−0.192979	−0.0964894	+	0.995334i	$0.530761\pi$
$734$	−29.9589	−1.10580
$735$	0	0
$736$	0.493539	0.0181921
$737$	−35.8453	−1.32038
$738$	2.01233	0.0740748
$739$	−7.43720	−0.273582	−0.136791	−	0.990600i	$-0.543679\pi$
$739$	−7.43720	−0.273582	−0.136791	+	0.990600i	$0.543679\pi$
$740$	0	0
$741$	−14.1640	−0.520326
$742$	10.8391	0.397917
$743$	1.99627	0.0732360	0.0366180	−	0.999329i	$-0.488342\pi$
$743$	1.99627	0.0732360	0.0366180	+	0.999329i	$0.488342\pi$
$744$	−19.5926	−0.718300
$745$	0	0
$746$	−18.6593	−0.683166
$747$	−13.3601	−0.488821
$748$	0.0570790	0.00208702
$749$	−1.09008	−0.0398307
$750$	0	0
$751$	11.0892	0.404651	0.202326	−	0.979318i	$-0.435150\pi$
$751$	11.0892	0.404651	0.202326	+	0.979318i	$0.435150\pi$
$752$	33.5610	1.22384
$753$	24.2349	0.883169
$754$	41.2967	1.50394
$755$	0	0
$756$	−0.0236045	−0.000858487 0
$757$	13.9295	0.506277	0.253138	−	0.967430i	$-0.418537\pi$
$757$	13.9295	0.506277	0.253138	+	0.967430i	$0.418537\pi$
$758$	−27.6207	−1.00323
$759$	−17.1556	−0.622709
$760$	0	0
$761$	−30.5684	−1.10810	−0.554051	−	0.832483i	$-0.686919\pi$
$761$	−30.5684	−1.10810	−0.554051	+	0.832483i	$0.686919\pi$
$762$	12.0382	0.436097
$763$	9.96710	0.360833
$764$	0.179655	0.00649968
$765$	0	0
$766$	23.4529	0.847387
$767$	53.4070	1.92842
$768$	0.519633	0.0187506
$769$	21.5666	0.777713	0.388857	−	0.921298i	$-0.372870\pi$
$769$	21.5666	0.777713	0.388857	+	0.921298i	$0.372870\pi$
$770$	0	0
$771$	−2.12990	−0.0767066
$772$	0.0684130	0.00246224
$773$	−11.3659	−0.408802	−0.204401	−	0.978887i	$-0.565525\pi$
$773$	−11.3659	−0.408802	−0.204401	+	0.978887i	$0.565525\pi$
$774$	−15.8243	−0.568794
$775$	0	0
$776$	−24.7262	−0.887618
$777$	4.71257	0.169063
$778$	5.39720	0.193499
$779$	−4.42309	−0.158474
$780$	0	0
$781$	−24.7064	−0.884063
$782$	3.50869	0.125470
$783$	6.40851	0.229021
$784$	22.9925	0.821160
$785$	0	0
$786$	−29.3356	−1.04636
$787$	10.9593	0.390656	0.195328	−	0.980738i	$-0.437423\pi$
$787$	10.9593	0.390656	0.195328	+	0.980738i	$0.437423\pi$
$788$	−0.228889	−0.00815385
$789$	14.3736	0.511713
$790$	0	0
$791$	−2.35015	−0.0835616
$792$	−12.1069	−0.430201
$793$	−63.1073	−2.24101
$794$	12.2932	0.436270
$795$	0	0
$796$	0.00576341	0.000204279 0
$797$	−16.9163	−0.599207	−0.299603	−	0.954064i	$-0.596854\pi$
$797$	−16.9163	−0.599207	−0.299603	+	0.954064i	$0.596854\pi$
$798$	−4.74010	−0.167798
$799$	−5.25192	−0.185800
$800$	0	0
$801$	15.6784	0.553969
$802$	−12.8533	−0.453866
$803$	39.8374	1.40583
$804$	0.182302	0.00642931
$805$	0	0
$806$	−44.4009	−1.56396
$807$	−16.0831	−0.566150
$808$	7.45172	0.262151
$809$	31.9598	1.12365	0.561824	−	0.827257i	$-0.310100\pi$
$809$	31.9598	1.12365	0.561824	+	0.827257i	$0.310100\pi$
$810$	0	0
$811$	−31.5712	−1.10861	−0.554307	−	0.832312i	$-0.687017\pi$
$811$	−31.5712	−1.10861	−0.554307	+	0.832312i	$0.687017\pi$
$812$	−0.151270	−0.00530852
$813$	6.22356	0.218270
$814$	25.8897	0.907434
$815$	0	0
$816$	2.44932	0.0857432
$817$	34.7818	1.21686
$818$	26.8191	0.937707
$819$	−4.99419	−0.174511
$820$	0	0
$821$	24.7129	0.862485	0.431243	−	0.902236i	$-0.358075\pi$
$821$	24.7129	0.862485	0.431243	+	0.902236i	$0.358075\pi$
$822$	7.59528	0.264916
$823$	−21.6128	−0.753374	−0.376687	−	0.926341i	$-0.622937\pi$
$823$	−21.6128	−0.753374	−0.376687	+	0.926341i	$0.622937\pi$
$824$	−3.38102	−0.117784
$825$	0	0
$826$	17.8731	0.621886
$827$	4.10071	0.142596	0.0712978	−	0.997455i	$-0.477286\pi$
$827$	4.10071	0.142596	0.0712978	+	0.997455i	$0.477286\pi$
$828$	0.0872501	0.00303215
$829$	31.6076	1.09778	0.548888	−	0.835896i	$-0.315051\pi$
$829$	31.6076	1.09778	0.548888	+	0.835896i	$0.315051\pi$
$830$	0	0
$831$	−13.3951	−0.464671
$832$	37.0401	1.28414
$833$	−3.59807	−0.124666
$834$	0.838245	0.0290260
$835$	0	0
$836$	0.285030	0.00985797
$837$	−6.89024	−0.238161
$838$	−5.23787	−0.180939
$839$	−18.3396	−0.633155	−0.316578	−	0.948567i	$-0.602534\pi$
$839$	−18.3396	−0.633155	−0.316578	+	0.948567i	$0.602534\pi$
$840$	0	0
$841$	12.0690	0.416172
$842$	−1.43473	−0.0494440
$843$	30.4196	1.04771
$844$	−0.359745	−0.0123829
$845$	0	0
$846$	11.9318	0.410223
$847$	−7.77022	−0.266988
$848$	−27.9683	−0.960435
$849$	12.0754	0.414428
$850$	0	0
$851$	−17.4192	−0.597124
$852$	0.125652	0.00430476
$853$	−1.96607	−0.0673170	−0.0336585	−	0.999433i	$-0.510716\pi$
$853$	−1.96607	−0.0673170	−0.0336585	+	0.999433i	$0.510716\pi$
$854$	−21.1194	−0.722693
$855$	0	0
$856$	2.84353	0.0971899
$857$	−44.1692	−1.50879	−0.754396	−	0.656420i	$-0.772070\pi$
$857$	−44.1692	−1.50879	−0.754396	+	0.656420i	$0.772070\pi$
$858$	−27.4369	−0.936679
$859$	−52.4182	−1.78849	−0.894243	−	0.447581i	$-0.852286\pi$
$859$	−52.4182	−1.78849	−0.894243	+	0.447581i	$0.852286\pi$
$860$	0	0
$861$	−1.55957	−0.0531501
$862$	12.7738	0.435079
$863$	0.252455	0.00859367	0.00429684	−	0.999991i	$-0.498632\pi$
$863$	0.252455	0.00859367	0.00429684	+	0.999991i	$0.498632\pi$
$864$	0.122488	0.00416711
$865$	0	0
$866$	−52.9176	−1.79821
$867$	16.6167	0.564333
$868$	0.162641	0.00552038
$869$	−27.7282	−0.940615
$870$	0	0
$871$	38.5712	1.30694
$872$	−25.9997	−0.880461
$873$	−8.69559	−0.294301
$874$	17.5210	0.592656
$875$	0	0
$876$	−0.202605	−0.00684539
$877$	22.2879	0.752608	0.376304	−	0.926496i	$-0.377195\pi$
$877$	22.2879	0.752608	0.376304	+	0.926496i	$0.377195\pi$
$878$	−16.4617	−0.555554
$879$	33.9285	1.14438
$880$	0	0
$881$	55.1343	1.85752	0.928761	−	0.370678i	$-0.120875\pi$
$881$	55.1343	1.85752	0.928761	+	0.370678i	$0.120875\pi$
$882$	8.17441	0.275247
$883$	−45.8201	−1.54197	−0.770984	−	0.636854i	$-0.780235\pi$
$883$	−45.8201	−1.54197	−0.770984	+	0.636854i	$0.780235\pi$
$884$	−0.0614196	−0.00206577
$885$	0	0
$886$	−0.776542	−0.0260885
$887$	−23.4786	−0.788333	−0.394167	−	0.919039i	$-0.628967\pi$
$887$	−23.4786	−0.788333	−0.394167	+	0.919039i	$0.628967\pi$
$888$	−12.2930	−0.412526
$889$	−9.32971	−0.312908
$890$	0	0
$891$	−4.25771	−0.142639
$892$	−0.433731	−0.0145224
$893$	−26.2260	−0.877620
$894$	10.1884	0.340751
$895$	0	0
$896$	12.1288	0.405194
$897$	18.4602	0.616368
$898$	45.6056	1.52188
$899$	−44.1561	−1.47269
$900$	0	0
$901$	4.37672	0.145810
$902$	−8.56791	−0.285280
$903$	12.2640	0.408121
$904$	6.13048	0.203897
$905$	0	0
$906$	−4.39467	−0.146003
$907$	21.1130	0.701047	0.350523	−	0.936554i	$-0.386004\pi$
$907$	21.1130	0.701047	0.350523	+	0.936554i	$0.386004\pi$
$908$	0.308597	0.0102411
$909$	2.62059	0.0869194
$910$	0	0
$911$	−25.9371	−0.859335	−0.429668	−	0.902987i	$-0.641369\pi$
$911$	−25.9371	−0.859335	−0.429668	+	0.902987i	$0.641369\pi$
$912$	12.2309	0.405006
$913$	56.8835	1.88257
$914$	38.0173	1.25750
$915$	0	0
$916$	−0.440930	−0.0145687
$917$	22.7353	0.750787
$918$	0.870793	0.0287405
$919$	−7.13398	−0.235328	−0.117664	−	0.993053i	$-0.537541\pi$
$919$	−7.13398	−0.235328	−0.117664	+	0.993053i	$0.537541\pi$
$920$	0	0
$921$	−30.9929	−1.02125
$922$	−58.1061	−1.91362
$923$	26.5852	0.875061
$924$	0.100501	0.00330625
$925$	0	0
$926$	−28.7253	−0.943973
$927$	−1.18902	−0.0390526
$928$	0.784963	0.0257677
$929$	−24.9802	−0.819575	−0.409788	−	0.912181i	$-0.634397\pi$
$929$	−24.9802	−0.819575	−0.409788	+	0.912181i	$0.634397\pi$
$930$	0	0
$931$	−17.9673	−0.588855
$932$	0.281774	0.00922980
$933$	−8.04809	−0.263483
$934$	−30.2690	−0.990432
$935$	0	0
$936$	13.0276	0.425821
$937$	−16.5948	−0.542130	−0.271065	−	0.962561i	$-0.587376\pi$
$937$	−16.5948	−0.542130	−0.271065	+	0.962561i	$0.587376\pi$
$938$	12.9082	0.421468
$939$	−22.7384	−0.742040
$940$	0	0
$941$	26.6519	0.868827	0.434414	−	0.900714i	$-0.356956\pi$
$941$	26.6519	0.868827	0.434414	+	0.900714i	$0.356956\pi$
$942$	−10.7064	−0.348834
$943$	5.76471	0.187725
$944$	−46.1182	−1.50102
$945$	0	0
$946$	67.3754	2.19056
$947$	−15.2730	−0.496305	−0.248152	−	0.968721i	$-0.579823\pi$
$947$	−15.2730	−0.496305	−0.248152	+	0.968721i	$0.579823\pi$
$948$	0.141020	0.00458013
$949$	−42.8668	−1.39152
$950$	0	0
$951$	−10.7199	−0.347617
$952$	−1.91902	−0.0621959
$953$	32.5875	1.05561	0.527806	−	0.849365i	$-0.323015\pi$
$953$	32.5875	1.05561	0.527806	+	0.849365i	$0.323015\pi$
$954$	−9.94343	−0.321930
$955$	0	0
$956$	−0.370984	−0.0119985
$957$	−27.2856	−0.882018
$958$	−10.3305	−0.333763
$959$	−5.88641	−0.190082
$960$	0	0
$961$	16.4754	0.531464
$962$	−27.8585	−0.898194
$963$	1.00000	0.0322245
$964$	−0.258279	−0.00831861
$965$	0	0
$966$	6.17787	0.198770
$967$	−28.1254	−0.904452	−0.452226	−	0.891903i	$-0.649370\pi$
$967$	−28.1254	−0.904452	−0.452226	+	0.891903i	$0.649370\pi$
$968$	20.2690	0.651471
$969$	−1.91400	−0.0614865
$970$	0	0
$971$	−25.2454	−0.810164	−0.405082	−	0.914280i	$-0.632757\pi$
$971$	−25.2454	−0.810164	−0.405082	+	0.914280i	$0.632757\pi$
$972$	0.0216539	0.000694549 0
$973$	−0.649648	−0.0208268
$974$	25.4505	0.815486
$975$	0	0
$976$	54.4946	1.74433
$977$	0.0350767	0.00112220	0.000561101	−	1.00000i	$-0.499821\pi$
$977$	0.0350767	0.00112220	0.000561101		1.00000i	$0.499821\pi$
$978$	−4.37572	−0.139920
$979$	−66.7542	−2.13347
$980$	0	0
$981$	−9.14346	−0.291928
$982$	−25.9334	−0.827570
$983$	55.8520	1.78140	0.890702	−	0.454588i	$-0.150214\pi$
$983$	55.8520	1.78140	0.890702	+	0.454588i	$0.150214\pi$
$984$	4.06823	0.129690
$985$	0	0
$986$	5.58049	0.177719
$987$	−9.24726	−0.294343
$988$	−0.306705	−0.00975759
$989$	−45.3319	−1.44147
$990$	0	0
$991$	35.4259	1.12534	0.562671	−	0.826681i	$-0.309774\pi$
$991$	35.4259	1.12534	0.562671	+	0.826681i	$0.309774\pi$
$992$	−0.843969	−0.0267960
$993$	−16.4750	−0.522818
$994$	8.89696	0.282195
$995$	0	0
$996$	−0.289299	−0.00916678
$997$	11.4942	0.364026	0.182013	−	0.983296i	$-0.441739\pi$
$997$	11.4942	0.364026	0.182013	+	0.983296i	$0.441739\pi$
$998$	−24.6099	−0.779013
$999$	−4.32314	−0.136778

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8025.2.a.ba.1.3		6
5.4	even	2		321.2.a.c.1.4	✓	6
15.14	odd	2		963.2.a.d.1.3		6
20.19	odd	2		5136.2.a.bg.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
321.2.a.c.1.4	✓	6	5.4	even	2
963.2.a.d.1.3		6	15.14	odd	2
5136.2.a.bg.1.6		6	20.19	odd	2
8025.2.a.ba.1.3		6	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 8025 = 3 \cdot 5^{2} \cdot 107 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8025.a (trivial)

\(f(q)\)	\(=\)	\(q-1.40654 q^{2} -1.00000 q^{3} -0.0216539 q^{4} +1.40654 q^{6} -1.09008 q^{7} +2.84353 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.40654 q^{2} -1.00000 q^{3} -0.0216539 q^{4} +1.40654 q^{6} -1.09008 q^{7} +2.84353 q^{8} +1.00000 q^{9} -4.25771 q^{11} +0.0216539 q^{12} +4.58149 q^{13} +1.53324 q^{14} -3.95622 q^{16} +0.619105 q^{17} -1.40654 q^{18} +3.09156 q^{19} +1.09008 q^{21} +5.98863 q^{22} -4.02930 q^{23} -2.84353 q^{24} -6.44404 q^{26} -1.00000 q^{27} +0.0236045 q^{28} -6.40851 q^{29} +6.89024 q^{31} -0.122488 q^{32} +4.25771 q^{33} -0.870793 q^{34} -0.0216539 q^{36} +4.32314 q^{37} -4.34840 q^{38} -4.58149 q^{39} -1.43070 q^{41} -1.53324 q^{42} +11.2506 q^{43} +0.0921961 q^{44} +5.66736 q^{46} -8.48310 q^{47} +3.95622 q^{48} -5.81173 q^{49} -0.619105 q^{51} -0.0992072 q^{52} +7.06944 q^{53} +1.40654 q^{54} -3.09968 q^{56} -3.09156 q^{57} +9.01380 q^{58} +11.6571 q^{59} -13.7744 q^{61} -9.69137 q^{62} -1.09008 q^{63} +8.08473 q^{64} -5.98863 q^{66} +8.41892 q^{67} -0.0134060 q^{68} +4.02930 q^{69} +5.80273 q^{71} +2.84353 q^{72} -9.35652 q^{73} -6.08066 q^{74} -0.0669444 q^{76} +4.64125 q^{77} +6.44404 q^{78} +6.51246 q^{79} +1.00000 q^{81} +2.01233 q^{82} -13.3601 q^{83} -0.0236045 q^{84} -15.8243 q^{86} +6.40851 q^{87} -12.1069 q^{88} +15.6784 q^{89} -4.99419 q^{91} +0.0872501 q^{92} -6.89024 q^{93} +11.9318 q^{94} +0.122488 q^{96} -8.69559 q^{97} +8.17441 q^{98} -4.25771 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 6 q^{3} + 7 q^{4} + 3 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 6 * q^3 + 7 * q^4 + 3 * q^6 - 6 * q^8 + 6 * q^9	\( 6 q - 3 q^{2} - 6 q^{3} + 7 q^{4} + 3 q^{6} - 6 q^{8} + 6 q^{9} + 6 q^{11} - 7 q^{12} + 8 q^{13} - 2 q^{14} + q^{16} - 4 q^{17} - 3 q^{18} - 4 q^{19} + 22 q^{22} - 14 q^{23} + 6 q^{24} - 7 q^{26} - 6 q^{27} + 16 q^{28} + 10 q^{29} + 12 q^{31} - 5 q^{32} - 6 q^{33} - q^{34} + 7 q^{36} + 12 q^{37} + q^{38} - 8 q^{39} - 6 q^{41} + 2 q^{42} + 12 q^{43} + 4 q^{44} + 18 q^{46} - 16 q^{47} - q^{48} - 12 q^{49} + 4 q^{51} + 25 q^{52} - 12 q^{53} + 3 q^{54} - 32 q^{56} + 4 q^{57} - 12 q^{58} + 8 q^{59} - 24 q^{61} + 8 q^{62} - 12 q^{64} - 22 q^{66} + 4 q^{67} + 15 q^{68} + 14 q^{69} + 36 q^{71} - 6 q^{72} + 26 q^{73} - 39 q^{74} - 17 q^{76} - 14 q^{77} + 7 q^{78} + 8 q^{79} + 6 q^{81} + 38 q^{82} + 8 q^{83} - 16 q^{84} + 16 q^{86} - 10 q^{87} + 8 q^{88} - 8 q^{89} - 18 q^{91} - 2 q^{92} - 12 q^{93} + 24 q^{94} + 5 q^{96} + 24 q^{97} - 43 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 6 * q^3 + 7 * q^4 + 3 * q^6 - 6 * q^8 + 6 * q^9 + 6 * q^11 - 7 * q^12 + 8 * q^13 - 2 * q^14 + q^16 - 4 * q^17 - 3 * q^18 - 4 * q^19 + 22 * q^22 - 14 * q^23 + 6 * q^24 - 7 * q^26 - 6 * q^27 + 16 * q^28 + 10 * q^29 + 12 * q^31 - 5 * q^32 - 6 * q^33 - q^34 + 7 * q^36 + 12 * q^37 + q^38 - 8 * q^39 - 6 * q^41 + 2 * q^42 + 12 * q^43 + 4 * q^44 + 18 * q^46 - 16 * q^47 - q^48 - 12 * q^49 + 4 * q^51 + 25 * q^52 - 12 * q^53 + 3 * q^54 - 32 * q^56 + 4 * q^57 - 12 * q^58 + 8 * q^59 - 24 * q^61 + 8 * q^62 - 12 * q^64 - 22 * q^66 + 4 * q^67 + 15 * q^68 + 14 * q^69 + 36 * q^71 - 6 * q^72 + 26 * q^73 - 39 * q^74 - 17 * q^76 - 14 * q^77 + 7 * q^78 + 8 * q^79 + 6 * q^81 + 38 * q^82 + 8 * q^83 - 16 * q^84 + 16 * q^86 - 10 * q^87 + 8 * q^88 - 8 * q^89 - 18 * q^91 - 2 * q^92 - 12 * q^93 + 24 * q^94 + 5 * q^96 + 24 * q^97 - 43 * q^98 + 6 * q^99

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