LMFDB - Embedded newform 6825.2.a.bg.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6825,2,Mod(1,6825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6825, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6825.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6825 = 3 \cdot 5^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6825.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:	$54.4978993795$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.17428.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 6x^{2} + 4x + 6 $ x^4 - x^3 - 6x^2 + 4x + 6
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 273)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.36865$ of defining polynomial
Character	$\chi$	$=$	6825.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61050 q^{2} -1.00000 q^{3} +4.81471 q^{4} +2.61050 q^{6} -1.00000 q^{7} -7.34780 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.61050 q^{2} -1.00000 q^{3} +4.81471 q^{4} +2.61050 q^{6} -1.00000 q^{7} -7.34780 q^{8} +1.00000 q^{9} -4.73730 q^{11} -4.81471 q^{12} -1.00000 q^{13} +2.61050 q^{14} +9.55201 q^{16} +5.22100 q^{17} -2.61050 q^{18} +2.92259 q^{19} +1.00000 q^{21} +12.3667 q^{22} -3.33101 q^{23} +7.34780 q^{24} +2.61050 q^{26} -1.00000 q^{27} -4.81471 q^{28} -0.922589 q^{29} -7.51941 q^{31} -10.2399 q^{32} +4.73730 q^{33} -13.6294 q^{34} +4.81471 q^{36} -0.154821 q^{37} -7.62942 q^{38} +1.00000 q^{39} +6.36672 q^{41} -2.61050 q^{42} +6.55201 q^{43} -22.8087 q^{44} +8.69560 q^{46} -9.03571 q^{47} -9.55201 q^{48} +1.00000 q^{49} -5.22100 q^{51} -4.81471 q^{52} -8.55201 q^{53} +2.61050 q^{54} +7.34780 q^{56} -2.92259 q^{57} +2.40842 q^{58} +3.95830 q^{59} +12.4420 q^{61} +19.6294 q^{62} -1.00000 q^{63} +7.62729 q^{64} -12.3667 q^{66} +10.6620 q^{67} +25.1376 q^{68} +3.33101 q^{69} -6.58248 q^{71} -7.34780 q^{72} +7.73517 q^{73} +0.404161 q^{74} +14.0714 q^{76} +4.73730 q^{77} -2.61050 q^{78} +13.3646 q^{79} +1.00000 q^{81} -16.6203 q^{82} +1.40629 q^{83} +4.81471 q^{84} -17.1040 q^{86} +0.922589 q^{87} +34.8087 q^{88} -1.96953 q^{89} +1.00000 q^{91} -16.0378 q^{92} +7.51941 q^{93} +23.5877 q^{94} +10.2399 q^{96} +2.11001 q^{97} -2.61050 q^{98} -4.73730 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - 4 q^{3} + 7 q^{4} + q^{6} - 4 q^{7} - 3 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - q^2 - 4 * q^3 + 7 * q^4 + q^6 - 4 * q^7 - 3 * q^8 + 4 * q^9	$ 4 q - q^{2} - 4 q^{3} + 7 q^{4} + q^{6} - 4 q^{7} - 3 q^{8} + 4 q^{9} - 2 q^{11} - 7 q^{12} - 4 q^{13} + q^{14} + 9 q^{16} + 2 q^{17} - q^{18} + 7 q^{19} + 4 q^{21} + 8 q^{22} - 3 q^{23} + 3 q^{24} + q^{26} - 4 q^{27} - 7 q^{28} + q^{29} + 3 q^{31} - 7 q^{32} + 2 q^{33} - 30 q^{34} + 7 q^{36} - 10 q^{37} - 6 q^{38} + 4 q^{39} - 16 q^{41} - q^{42} - 3 q^{43} - 12 q^{44} - 18 q^{46} - 5 q^{47} - 9 q^{48} + 4 q^{49} - 2 q^{51} - 7 q^{52} - 5 q^{53} + q^{54} + 3 q^{56} - 7 q^{57} + 4 q^{58} - 20 q^{59} + 12 q^{61} + 54 q^{62} - 4 q^{63} + 5 q^{64} - 8 q^{66} + 22 q^{67} + 10 q^{68} + 3 q^{69} - 3 q^{72} + 13 q^{73} - 6 q^{74} - 6 q^{76} + 2 q^{77} - q^{78} + 11 q^{79} + 4 q^{81} - 10 q^{82} - q^{83} + 7 q^{84} - 10 q^{86} - q^{87} + 60 q^{88} - 5 q^{89} + 4 q^{91} - 34 q^{92} - 3 q^{93} + 34 q^{94} + 7 q^{96} + 17 q^{97} - q^{98} - 2 q^{99}+O(q^{100}) $ 4 * q - q^2 - 4 * q^3 + 7 * q^4 + q^6 - 4 * q^7 - 3 * q^8 + 4 * q^9 - 2 * q^11 - 7 * q^12 - 4 * q^13 + q^14 + 9 * q^16 + 2 * q^17 - q^18 + 7 * q^19 + 4 * q^21 + 8 * q^22 - 3 * q^23 + 3 * q^24 + q^26 - 4 * q^27 - 7 * q^28 + q^29 + 3 * q^31 - 7 * q^32 + 2 * q^33 - 30 * q^34 + 7 * q^36 - 10 * q^37 - 6 * q^38 + 4 * q^39 - 16 * q^41 - q^42 - 3 * q^43 - 12 * q^44 - 18 * q^46 - 5 * q^47 - 9 * q^48 + 4 * q^49 - 2 * q^51 - 7 * q^52 - 5 * q^53 + q^54 + 3 * q^56 - 7 * q^57 + 4 * q^58 - 20 * q^59 + 12 * q^61 + 54 * q^62 - 4 * q^63 + 5 * q^64 - 8 * q^66 + 22 * q^67 + 10 * q^68 + 3 * q^69 - 3 * q^72 + 13 * q^73 - 6 * q^74 - 6 * q^76 + 2 * q^77 - q^78 + 11 * q^79 + 4 * q^81 - 10 * q^82 - q^83 + 7 * q^84 - 10 * q^86 - q^87 + 60 * q^88 - 5 * q^89 + 4 * q^91 - 34 * q^92 - 3 * q^93 + 34 * q^94 + 7 * q^96 + 17 * q^97 - q^98 - 2 * 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 $

$2$	−2.61050	−1.84590	−0.922951	−	0.384917i	$-0.874230\pi$
$2$	−2.61050	−1.84590	−0.922951	+	0.384917i	$0.874230\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.81471	2.40735
$5$	0	0
$5$	0	0
$6$	2.61050	1.06573
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−7.34780	−2.59784
$9$	1.00000	0.333333
$10$	0	0
$11$	−4.73730	−1.42835	−0.714175	−	0.699968i	$-0.753198\pi$
$11$	−4.73730	−1.42835	−0.714175	+	0.699968i	$0.753198\pi$
$12$	−4.81471	−1.38989
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	2.61050	0.697685
$15$	0	0
$16$	9.55201	2.38800
$17$	5.22100	1.26628	0.633139	−	0.774038i	$-0.281766\pi$
$17$	5.22100	1.26628	0.633139	+	0.774038i	$0.281766\pi$
$18$	−2.61050	−0.615301
$19$	2.92259	0.670488	0.335244	−	0.942131i	$-0.391181\pi$
$19$	2.92259	0.670488	0.335244	+	0.942131i	$0.391181\pi$
$20$	0	0
$21$	1.00000	0.218218
$22$	12.3667	2.63659
$23$	−3.33101	−0.694563	−0.347282	−	0.937761i	$-0.612895\pi$
$23$	−3.33101	−0.694563	−0.347282	+	0.937761i	$0.612895\pi$
$24$	7.34780	1.49986
$25$	0	0
$26$	2.61050	0.511961
$27$	−1.00000	−0.192450
$28$	−4.81471	−0.909895
$29$	−0.922589	−0.171321	−0.0856603	−	0.996324i	$-0.527300\pi$
$29$	−0.922589	−0.171321	−0.0856603	+	0.996324i	$0.527300\pi$
$30$	0	0
$31$	−7.51941	−1.35053	−0.675263	−	0.737577i	$-0.735970\pi$
$31$	−7.51941	−1.35053	−0.675263	+	0.737577i	$0.735970\pi$
$32$	−10.2399	−1.81018
$33$	4.73730	0.824658
$34$	−13.6294	−2.33743
$35$	0	0
$36$	4.81471	0.802452
$37$	−0.154821	−0.0254525	−0.0127262	−	0.999919i	$-0.504051\pi$
$37$	−0.154821	−0.0254525	−0.0127262	+	0.999919i	$0.504051\pi$
$38$	−7.62942	−1.23766
$39$	1.00000	0.160128
$40$	0	0
$41$	6.36672	0.994314	0.497157	−	0.867661i	$-0.334377\pi$
$41$	6.36672	0.994314	0.497157	+	0.867661i	$0.334377\pi$
$42$	−2.61050	−0.402809
$43$	6.55201	0.999172	0.499586	−	0.866264i	$-0.333486\pi$
$43$	6.55201	0.999172	0.499586	+	0.866264i	$0.333486\pi$
$44$	−22.8087	−3.43854
$45$	0	0
$46$	8.69560	1.28210
$47$	−9.03571	−1.31799	−0.658997	−	0.752146i	$-0.729019\pi$
$47$	−9.03571	−1.31799	−0.658997	+	0.752146i	$0.729019\pi$
$48$	−9.55201	−1.37871
$49$	1.00000	0.142857
$50$	0	0
$51$	−5.22100	−0.731086
$52$	−4.81471	−0.667680
$53$	−8.55201	−1.17471	−0.587354	−	0.809330i	$-0.699830\pi$
$53$	−8.55201	−1.17471	−0.587354	+	0.809330i	$0.699830\pi$
$54$	2.61050	0.355244
$55$	0	0
$56$	7.34780	0.981891
$57$	−2.92259	−0.387106
$58$	2.40842	0.316241
$59$	3.95830	0.515327	0.257663	−	0.966235i	$-0.417047\pi$
$59$	3.95830	0.515327	0.257663	+	0.966235i	$0.417047\pi$
$60$	0	0
$61$	12.4420	1.59303	0.796517	−	0.604616i	$-0.206673\pi$
$61$	12.4420	1.59303	0.796517	+	0.604616i	$0.206673\pi$
$62$	19.6294	2.49294
$63$	−1.00000	−0.125988
$64$	7.62729	0.953411
$65$	0	0
$66$	−12.3667	−1.52224
$67$	10.6620	1.30257	0.651286	−	0.758832i	$-0.274230\pi$
$67$	10.6620	1.30257	0.651286	+	0.758832i	$0.274230\pi$
$68$	25.1376	3.04838
$69$	3.33101	0.401006
$70$	0	0
$71$	−6.58248	−0.781196	−0.390598	−	0.920561i	$-0.627732\pi$
$71$	−6.58248	−0.781196	−0.390598	+	0.920561i	$0.627732\pi$
$72$	−7.34780	−0.865946
$73$	7.73517	0.905333	0.452667	−	0.891680i	$-0.350473\pi$
$73$	7.73517	0.905333	0.452667	+	0.891680i	$0.350473\pi$
$74$	0.404161	0.0469828
$75$	0	0
$76$	14.0714	1.61410
$77$	4.73730	0.539865
$78$	−2.61050	−0.295581
$79$	13.3646	1.50363	0.751817	−	0.659372i	$-0.229178\pi$
$79$	13.3646	1.50363	0.751817	+	0.659372i	$0.229178\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−16.6203	−1.83541
$83$	1.40629	0.154360	0.0771802	−	0.997017i	$-0.475408\pi$
$83$	1.40629	0.154360	0.0771802	+	0.997017i	$0.475408\pi$
$84$	4.81471	0.525328
$85$	0	0
$86$	−17.1040	−1.84437
$87$	0.922589	0.0989120
$88$	34.8087	3.71062
$89$	−1.96953	−0.208770	−0.104385	−	0.994537i	$-0.533287\pi$
$89$	−1.96953	−0.208770	−0.104385	+	0.994537i	$0.533287\pi$
$90$	0	0
$91$	1.00000	0.104828
$92$	−16.0378	−1.67206
$93$	7.51941	0.779727
$94$	23.5877	2.43289
$95$	0	0
$96$	10.2399	1.04511
$97$	2.11001	0.214239	0.107119	−	0.994246i	$-0.465837\pi$
$97$	2.11001	0.214239	0.107119	+	0.994246i	$0.465837\pi$
$98$	−2.61050	−0.263700
$99$	−4.73730	−0.476116
$100$	0	0
$101$	0.850419	0.0846198	0.0423099	−	0.999105i	$-0.486528\pi$
$101$	0.850419	0.0846198	0.0423099	+	0.999105i	$0.486528\pi$
$102$	13.6294	1.34951
$103$	1.47460	0.145296	0.0726482	−	0.997358i	$-0.476855\pi$
$103$	1.47460	0.145296	0.0726482	+	0.997358i	$0.476855\pi$
$104$	7.34780	0.720511
$105$	0	0
$106$	22.3250	2.16840
$107$	−2.62418	−0.253689	−0.126844	−	0.991923i	$-0.540485\pi$
$107$	−2.62418	−0.253689	−0.126844	+	0.991923i	$0.540485\pi$
$108$	−4.81471	−0.463296
$109$	−17.9166	−1.71610	−0.858049	−	0.513567i	$-0.828324\pi$
$109$	−17.9166	−1.71610	−0.858049	+	0.513567i	$0.828324\pi$
$110$	0	0
$111$	0.154821	0.0146950
$112$	−9.55201	−0.902580
$113$	−0.922589	−0.0867899	−0.0433950	−	0.999058i	$-0.513817\pi$
$113$	−0.922589	−0.0867899	−0.0433950	+	0.999058i	$0.513817\pi$
$114$	7.62942	0.714561
$115$	0	0
$116$	−4.44200	−0.412429
$117$	−1.00000	−0.0924500
$118$	−10.3331	−0.951242
$119$	−5.22100	−0.478608
$120$	0	0
$121$	11.4420	1.04018
$122$	−32.4798	−2.94059
$123$	−6.36672	−0.574068
$124$	−36.2038	−3.25119
$125$	0	0
$126$	2.61050	0.232562
$127$	−17.4746	−1.55062	−0.775310	−	0.631581i	$-0.782406\pi$
$127$	−17.4746	−1.55062	−0.775310	+	0.631581i	$0.782406\pi$
$128$	0.568798	0.0502751
$129$	−6.55201	−0.576872
$130$	0	0
$131$	0.967402	0.0845223	0.0422611	−	0.999107i	$-0.486544\pi$
$131$	0.967402	0.0845223	0.0422611	+	0.999107i	$0.486544\pi$
$132$	22.8087	1.98524
$133$	−2.92259	−0.253421
$134$	−27.8332	−2.40442
$135$	0	0
$136$	−38.3629	−3.28959
$137$	−3.29628	−0.281620	−0.140810	−	0.990037i	$-0.544971\pi$
$137$	−3.29628	−0.281620	−0.140810	+	0.990037i	$0.544971\pi$
$138$	−8.69560	−0.740218
$139$	0.370581	0.0314323	0.0157161	−	0.999876i	$-0.494997\pi$
$139$	0.370581	0.0314323	0.0157161	+	0.999876i	$0.494997\pi$
$140$	0	0
$141$	9.03571	0.760944
$142$	17.1836	1.44201
$143$	4.73730	0.396153
$144$	9.55201	0.796001
$145$	0	0
$146$	−20.1927	−1.67116
$147$	−1.00000	−0.0824786
$148$	−0.745420	−0.0612732
$149$	−15.7425	−1.28968	−0.644840	−	0.764318i	$-0.723076\pi$
$149$	−15.7425	−1.28968	−0.644840	+	0.764318i	$0.723076\pi$
$150$	0	0
$151$	10.2914	0.837505	0.418753	−	0.908100i	$-0.362467\pi$
$151$	10.2914	0.837505	0.418753	+	0.908100i	$0.362467\pi$
$152$	−21.4746	−1.74182
$153$	5.22100	0.422093
$154$	−12.3667	−0.996539
$155$	0	0
$156$	4.81471	0.385485
$157$	11.4137	0.910909	0.455455	−	0.890259i	$-0.349477\pi$
$157$	11.4137	0.910909	0.455455	+	0.890259i	$0.349477\pi$
$158$	−34.8883	−2.77556
$159$	8.55201	0.678218
$160$	0	0
$161$	3.33101	0.262520
$162$	−2.61050	−0.205100
$163$	13.4746	1.05541	0.527706	−	0.849427i	$-0.323052\pi$
$163$	13.4746	1.05541	0.527706	+	0.849427i	$0.323052\pi$
$164$	30.6539	2.39367
$165$	0	0
$166$	−3.67112	−0.284934
$167$	−19.1905	−1.48501	−0.742504	−	0.669842i	$-0.766362\pi$
$167$	−19.1905	−1.48501	−0.742504	+	0.669842i	$0.766362\pi$
$168$	−7.34780	−0.566895
$169$	1.00000	0.0769231
$170$	0	0
$171$	2.92259	0.223496
$172$	31.5460	2.40536
$173$	19.5124	1.48350	0.741752	−	0.670675i	$-0.233995\pi$
$173$	19.5124	1.48350	0.741752	+	0.670675i	$0.233995\pi$
$174$	−2.40842	−0.182582
$175$	0	0
$176$	−45.2507	−3.41090
$177$	−3.95830	−0.297524
$178$	5.14146	0.385369
$179$	−16.5856	−1.23967	−0.619833	−	0.784734i	$-0.712799\pi$
$179$	−16.5856	−1.23967	−0.619833	+	0.784734i	$0.712799\pi$
$180$	0	0
$181$	−2.81684	−0.209374	−0.104687	−	0.994505i	$-0.533384\pi$
$181$	−2.81684	−0.209374	−0.104687	+	0.994505i	$0.533384\pi$
$182$	−2.61050	−0.193503
$183$	−12.4420	−0.919739
$184$	24.4756	1.80436
$185$	0	0
$186$	−19.6294	−1.43930
$187$	−24.7334	−1.80869
$188$	−43.5043	−3.17288
$189$	1.00000	0.0727393
$190$	0	0
$191$	15.1601	1.09694	0.548472	−	0.836169i	$-0.315210\pi$
$191$	15.1601	1.09694	0.548472	+	0.836169i	$0.315210\pi$
$192$	−7.62729	−0.550452
$193$	−0.0651962	−0.00469293	−0.00234646	−	0.999997i	$-0.500747\pi$
$193$	−0.0651962	−0.00469293	−0.00234646	+	0.999997i	$0.500747\pi$
$194$	−5.50818	−0.395464
$195$	0	0
$196$	4.81471	0.343908
$197$	17.1415	1.22128	0.610639	−	0.791909i	$-0.290913\pi$
$197$	17.1415	1.22128	0.610639	+	0.791909i	$0.290913\pi$
$198$	12.3667	0.878864
$199$	6.44200	0.456661	0.228331	−	0.973584i	$-0.426673\pi$
$199$	6.44200	0.456661	0.228331	+	0.973584i	$0.426673\pi$
$200$	0	0
$201$	−10.6620	−0.752041
$202$	−2.22002	−0.156200
$203$	0.922589	0.0647531
$204$	−25.1376	−1.75998
$205$	0	0
$206$	−3.84944	−0.268203
$207$	−3.33101	−0.231521
$208$	−9.55201	−0.662313
$209$	−13.8452	−0.957691
$210$	0	0
$211$	−16.0266	−1.10332	−0.551659	−	0.834070i	$-0.686005\pi$
$211$	−16.0266	−1.10332	−0.551659	+	0.834070i	$0.686005\pi$
$212$	−41.1754	−2.82794
$213$	6.58248	0.451024
$214$	6.85042	0.468285
$215$	0	0
$216$	7.34780	0.499954
$217$	7.51941	0.510451
$218$	46.7713	3.16775
$219$	−7.73517	−0.522694
$220$	0	0
$221$	−5.22100	−0.351202
$222$	−0.404161	−0.0271255
$223$	−20.0266	−1.34108	−0.670540	−	0.741873i	$-0.733938\pi$
$223$	−20.0266	−1.34108	−0.670540	+	0.741873i	$0.733938\pi$
$224$	10.2399	0.684183
$225$	0	0
$226$	2.40842	0.160206
$227$	−19.2171	−1.27549	−0.637743	−	0.770249i	$-0.720132\pi$
$227$	−19.2171	−1.27549	−0.637743	+	0.770249i	$0.720132\pi$
$228$	−14.0714	−0.931902
$229$	5.25884	0.347514	0.173757	−	0.984789i	$-0.444409\pi$
$229$	5.25884	0.347514	0.173757	+	0.984789i	$0.444409\pi$
$230$	0	0
$231$	−4.73730	−0.311691
$232$	6.77900	0.445063
$233$	26.6234	1.74416	0.872079	−	0.489365i	$-0.162771\pi$
$233$	26.6234	1.74416	0.872079	+	0.489365i	$0.162771\pi$
$234$	2.61050	0.170654
$235$	0	0
$236$	19.0581	1.24057
$237$	−13.3646	−0.868123
$238$	13.6294	0.883464
$239$	4.29104	0.277564	0.138782	−	0.990323i	$-0.455681\pi$
$239$	4.29104	0.277564	0.138782	+	0.990323i	$0.455681\pi$
$240$	0	0
$241$	7.52367	0.484642	0.242321	−	0.970196i	$-0.422091\pi$
$241$	7.52367	0.484642	0.242321	+	0.970196i	$0.422091\pi$
$242$	−29.8693	−1.92007
$243$	−1.00000	−0.0641500
$244$	59.9046	3.83500
$245$	0	0
$246$	16.6203	1.05967
$247$	−2.92259	−0.185960
$248$	55.2511	3.50845
$249$	−1.40629	−0.0891200
$250$	0	0
$251$	11.3198	0.714498	0.357249	−	0.934009i	$-0.383715\pi$
$251$	11.3198	0.714498	0.357249	+	0.934009i	$0.383715\pi$
$252$	−4.81471	−0.303298
$253$	15.7800	0.992079
$254$	45.6174	2.86229
$255$	0	0
$256$	−16.7394	−1.04621
$257$	24.8504	1.55013	0.775063	−	0.631884i	$-0.217718\pi$
$257$	24.8504	1.55013	0.775063	+	0.631884i	$0.217718\pi$
$258$	17.1040	1.06485
$259$	0.154821	0.00962013
$260$	0	0
$261$	−0.922589	−0.0571068
$262$	−2.52540	−0.156020
$263$	−17.1762	−1.05913	−0.529565	−	0.848270i	$-0.677645\pi$
$263$	−17.1762	−1.05913	−0.529565	+	0.848270i	$0.677645\pi$
$264$	−34.8087	−2.14233
$265$	0	0
$266$	7.62942	0.467790
$267$	1.96953	0.120533
$268$	51.3345	3.13575
$269$	−7.74640	−0.472306	−0.236153	−	0.971716i	$-0.575887\pi$
$269$	−7.74640	−0.472306	−0.236153	+	0.971716i	$0.575887\pi$
$270$	0	0
$271$	−29.7008	−1.80420	−0.902099	−	0.431530i	$-0.857974\pi$
$271$	−29.7008	−1.80420	−0.902099	+	0.431530i	$0.857974\pi$
$272$	49.8710	3.02388
$273$	−1.00000	−0.0605228
$274$	8.60494	0.519844
$275$	0	0
$276$	16.0378	0.965364
$277$	−25.1488	−1.51105	−0.755523	−	0.655122i	$-0.772617\pi$
$277$	−25.1488	−1.51105	−0.755523	+	0.655122i	$0.772617\pi$
$278$	−0.967402	−0.0580209
$279$	−7.51941	−0.450175
$280$	0	0
$281$	8.40030	0.501120	0.250560	−	0.968101i	$-0.419385\pi$
$281$	8.40030	0.501120	0.250560	+	0.968101i	$0.419385\pi$
$282$	−23.5877	−1.40463
$283$	21.3912	1.27157	0.635787	−	0.771864i	$-0.280676\pi$
$283$	21.3912	1.27157	0.635787	+	0.771864i	$0.280676\pi$
$284$	−31.6927	−1.88062
$285$	0	0
$286$	−12.3667	−0.731259
$287$	−6.36672	−0.375815
$288$	−10.2399	−0.603393
$289$	10.2588	0.603461
$290$	0	0
$291$	−2.11001	−0.123691
$292$	37.2426	2.17946
$293$	9.59895	0.560777	0.280388	−	0.959887i	$-0.409537\pi$
$293$	9.59895	0.560777	0.280388	+	0.959887i	$0.409537\pi$
$294$	2.61050	0.152247
$295$	0	0
$296$	1.13760	0.0661215
$297$	4.73730	0.274886
$298$	41.0959	2.38062
$299$	3.33101	0.192637
$300$	0	0
$301$	−6.55201	−0.377651
$302$	−26.8658	−1.54595
$303$	−0.850419	−0.0488553
$304$	27.9166	1.60113
$305$	0	0
$306$	−13.6294	−0.779142
$307$	15.1488	0.864589	0.432295	−	0.901732i	$-0.357704\pi$
$307$	15.1488	0.864589	0.432295	+	0.901732i	$0.357704\pi$
$308$	22.8087	1.29965
$309$	−1.47460	−0.0838869
$310$	0	0
$311$	−4.37058	−0.247833	−0.123916	−	0.992293i	$-0.539545\pi$
$311$	−4.37058	−0.247833	−0.123916	+	0.992293i	$0.539545\pi$
$312$	−7.34780	−0.415987
$313$	1.49280	0.0843783	0.0421891	−	0.999110i	$-0.486567\pi$
$313$	1.49280	0.0843783	0.0421891	+	0.999110i	$0.486567\pi$
$314$	−29.7954	−1.68145
$315$	0	0
$316$	64.3466	3.61978
$317$	−23.2129	−1.30377	−0.651883	−	0.758320i	$-0.726021\pi$
$317$	−23.2129	−1.30377	−0.651883	+	0.758320i	$0.726021\pi$
$318$	−22.3250	−1.25192
$319$	4.37058	0.244706
$320$	0	0
$321$	2.62418	0.146467
$322$	−8.69560	−0.484587
$323$	15.2588	0.849024
$324$	4.81471	0.267484
$325$	0	0
$326$	−35.1754	−1.94819
$327$	17.9166	0.990790
$328$	−46.7814	−2.58307
$329$	9.03571	0.498155
$330$	0	0
$331$	1.10402	0.0606822	0.0303411	−	0.999540i	$-0.490341\pi$
$331$	1.10402	0.0606822	0.0303411	+	0.999540i	$0.490341\pi$
$332$	6.77088	0.371600
$333$	−0.154821	−0.00848416
$334$	50.0969	2.74118
$335$	0	0
$336$	9.55201	0.521105
$337$	4.24237	0.231096	0.115548	−	0.993302i	$-0.463138\pi$
$337$	4.24237	0.231096	0.115548	+	0.993302i	$0.463138\pi$
$338$	−2.61050	−0.141992
$339$	0.922589	0.0501082
$340$	0	0
$341$	35.6217	1.92902
$342$	−7.62942	−0.412552
$343$	−1.00000	−0.0539949
$344$	−48.1428	−2.59569
$345$	0	0
$346$	−50.9372	−2.73840
$347$	−14.0336	−0.753362	−0.376681	−	0.926343i	$-0.622935\pi$
$347$	−14.0336	−0.753362	−0.376681	+	0.926343i	$0.622935\pi$
$348$	4.44200	0.238116
$349$	4.10575	0.219776	0.109888	−	0.993944i	$-0.464951\pi$
$349$	4.10575	0.219776	0.109888	+	0.993944i	$0.464951\pi$
$350$	0	0
$351$	1.00000	0.0533761
$352$	48.5096	2.58557
$353$	16.0753	0.855601	0.427800	−	0.903873i	$-0.359289\pi$
$353$	16.0753	0.855601	0.427800	+	0.903873i	$0.359289\pi$
$354$	10.3331	0.549200
$355$	0	0
$356$	−9.48272	−0.502583
$357$	5.22100	0.276325
$358$	43.2967	2.28830
$359$	−18.1510	−0.957971	−0.478985	−	0.877823i	$-0.658995\pi$
$359$	−18.1510	−0.957971	−0.478985	+	0.877823i	$0.658995\pi$
$360$	0	0
$361$	−10.4585	−0.550446
$362$	7.35336	0.386484
$363$	−11.4420	−0.600549
$364$	4.81471	0.252359
$365$	0	0
$366$	32.4798	1.69775
$367$	23.3955	1.22123	0.610616	−	0.791927i	$-0.290922\pi$
$367$	23.3955	1.22123	0.610616	+	0.791927i	$0.290922\pi$
$368$	−31.8178	−1.65862
$369$	6.36672	0.331438
$370$	0	0
$371$	8.55201	0.443998
$372$	36.2038	1.87708
$373$	4.75164	0.246031	0.123015	−	0.992405i	$-0.460744\pi$
$373$	4.75164	0.246031	0.123015	+	0.992405i	$0.460744\pi$
$374$	64.5666	3.33866
$375$	0	0
$376$	66.3926	3.42394
$377$	0.922589	0.0475158
$378$	−2.61050	−0.134270
$379$	−6.81258	−0.349939	−0.174969	−	0.984574i	$-0.555983\pi$
$379$	−6.81258	−0.349939	−0.174969	+	0.984574i	$0.555983\pi$
$380$	0	0
$381$	17.4746	0.895251
$382$	−39.5753	−2.02485
$383$	−2.25746	−0.115351	−0.0576754	−	0.998335i	$-0.518369\pi$
$383$	−2.25746	−0.115351	−0.0576754	+	0.998335i	$0.518369\pi$
$384$	−0.568798	−0.0290264
$385$	0	0
$386$	0.170195	0.00866268
$387$	6.55201	0.333057
$388$	10.1591	0.515749
$389$	6.00000	0.304212	0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000	0.304212	0.152106	+	0.988364i	$0.451394\pi$
$390$	0	0
$391$	−17.3912	−0.879511
$392$	−7.34780	−0.371120
$393$	−0.967402	−0.0487990
$394$	−44.7478	−2.25436
$395$	0	0
$396$	−22.8087	−1.14618
$397$	−24.9897	−1.25420	−0.627100	−	0.778939i	$-0.715758\pi$
$397$	−24.9897	−1.25420	−0.627100	+	0.778939i	$0.715758\pi$
$398$	−16.8168	−0.842952
$399$	2.92259	0.146312
$400$	0	0
$401$	27.6529	1.38092	0.690460	−	0.723370i	$-0.257408\pi$
$401$	27.6529	1.38092	0.690460	+	0.723370i	$0.257408\pi$
$402$	27.8332	1.38819
$403$	7.51941	0.374568
$404$	4.09452	0.203710
$405$	0	0
$406$	−2.40842	−0.119528
$407$	0.733435	0.0363550
$408$	38.3629	1.89924
$409$	13.1488	0.650168	0.325084	−	0.945685i	$-0.394607\pi$
$409$	13.1488	0.650168	0.325084	+	0.945685i	$0.394607\pi$
$410$	0	0
$411$	3.29628	0.162594
$412$	7.09976	0.349780
$413$	−3.95830	−0.194775
$414$	8.69560	0.427365
$415$	0	0
$416$	10.2399	0.502053
$417$	−0.370581	−0.0181474
$418$	36.1428	1.76780
$419$	−5.69462	−0.278200	−0.139100	−	0.990278i	$-0.544421\pi$
$419$	−5.69462	−0.278200	−0.139100	+	0.990278i	$0.544421\pi$
$420$	0	0
$421$	−23.0206	−1.12196	−0.560978	−	0.827831i	$-0.689575\pi$
$421$	−23.0206	−1.12196	−0.560978	+	0.827831i	$0.689575\pi$
$422$	41.8375	2.03662
$423$	−9.03571	−0.439331
$424$	62.8384	3.05170
$425$	0	0
$426$	−17.1836	−0.832546
$427$	−12.4420	−0.602111
$428$	−12.6347	−0.610719
$429$	−4.73730	−0.228719
$430$	0	0
$431$	20.8045	1.00212	0.501058	−	0.865414i	$-0.332944\pi$
$431$	20.8045	1.00212	0.501058	+	0.865414i	$0.332944\pi$
$432$	−9.55201	−0.459571
$433$	−31.4808	−1.51287	−0.756436	−	0.654068i	$-0.773061\pi$
$433$	−31.4808	−1.51287	−0.756436	+	0.654068i	$0.773061\pi$
$434$	−19.6294	−0.942242
$435$	0	0
$436$	−86.2632	−4.13126
$437$	−9.73517	−0.465696
$438$	20.1927	0.964843
$439$	22.3811	1.06819	0.534095	−	0.845425i	$-0.320653\pi$
$439$	22.3811	1.06819	0.534095	+	0.845425i	$0.320653\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	13.6294	0.648285
$443$	−8.52465	−0.405018	−0.202509	−	0.979280i	$-0.564910\pi$
$443$	−8.52465	−0.405018	−0.202509	+	0.979280i	$0.564910\pi$
$444$	0.745420	0.0353761
$445$	0	0
$446$	52.2795	2.47550
$447$	15.7425	0.744597
$448$	−7.62729	−0.360356
$449$	18.7142	0.883178	0.441589	−	0.897218i	$-0.354415\pi$
$449$	18.7142	0.883178	0.441589	+	0.897218i	$0.354415\pi$
$450$	0	0
$451$	−30.1610	−1.42023
$452$	−4.44200	−0.208934
$453$	−10.2914	−0.483534
$454$	50.1663	2.35442
$455$	0	0
$456$	21.4746	1.00564
$457$	14.1366	0.661283	0.330641	−	0.943756i	$-0.392735\pi$
$457$	14.1366	0.661283	0.330641	+	0.943756i	$0.392735\pi$
$458$	−13.7282	−0.641476
$459$	−5.22100	−0.243695
$460$	0	0
$461$	−2.67636	−0.124651	−0.0623253	−	0.998056i	$-0.519852\pi$
$461$	−2.67636	−0.124651	−0.0623253	+	0.998056i	$0.519852\pi$
$462$	12.3667	0.575352
$463$	2.53162	0.117655	0.0588273	−	0.998268i	$-0.481264\pi$
$463$	2.53162	0.117655	0.0588273	+	0.998268i	$0.481264\pi$
$464$	−8.81258	−0.409114
$465$	0	0
$466$	−69.5005	−3.21955
$467$	−2.00426	−0.0927460	−0.0463730	−	0.998924i	$-0.514766\pi$
$467$	−2.00426	−0.0927460	−0.0463730	+	0.998924i	$0.514766\pi$
$468$	−4.81471	−0.222560
$469$	−10.6620	−0.492326
$470$	0	0
$471$	−11.4137	−0.525914
$472$	−29.0848	−1.33874
$473$	−31.0388	−1.42717
$474$	34.8883	1.60247
$475$	0	0
$476$	−25.1376	−1.15218
$477$	−8.55201	−0.391570
$478$	−11.2018	−0.512357
$479$	−14.6609	−0.669872	−0.334936	−	0.942241i	$-0.608715\pi$
$479$	−14.6609	−0.669872	−0.334936	+	0.942241i	$0.608715\pi$
$480$	0	0
$481$	0.154821	0.00705925
$482$	−19.6405	−0.894602
$483$	−3.33101	−0.151566
$484$	55.0899	2.50409
$485$	0	0
$486$	2.61050	0.118415
$487$	−38.2143	−1.73165	−0.865827	−	0.500344i	$-0.833207\pi$
$487$	−38.2143	−1.73165	−0.865827	+	0.500344i	$0.833207\pi$
$488$	−91.4213	−4.13845
$489$	−13.4746	−0.609342
$490$	0	0
$491$	21.3758	0.964677	0.482339	−	0.875985i	$-0.339787\pi$
$491$	21.3758	0.964677	0.482339	+	0.875985i	$0.339787\pi$
$492$	−30.6539	−1.38198
$493$	−4.81684	−0.216939
$494$	7.62942	0.343264
$495$	0	0
$496$	−71.8255	−3.22506
$497$	6.58248	0.295264
$498$	3.67112	0.164507
$499$	27.0920	1.21281	0.606403	−	0.795158i	$-0.292612\pi$
$499$	27.0920	1.21281	0.606403	+	0.795158i	$0.292612\pi$
$500$	0	0
$501$	19.1905	0.857370
$502$	−29.5503	−1.31889
$503$	−24.8778	−1.10925	−0.554623	−	0.832102i	$-0.687137\pi$
$503$	−24.8778	−1.10925	−0.554623	+	0.832102i	$0.687137\pi$
$504$	7.34780	0.327297
$505$	0	0
$506$	−41.1936	−1.83128
$507$	−1.00000	−0.0444116
$508$	−84.1351	−3.73289
$509$	2.70297	0.119807	0.0599034	−	0.998204i	$-0.480921\pi$
$509$	2.70297	0.119807	0.0599034	+	0.998204i	$0.480921\pi$
$510$	0	0
$511$	−7.73517	−0.342184
$512$	42.5607	1.88093
$513$	−2.92259	−0.129035
$514$	−64.8720	−2.86138
$515$	0	0
$516$	−31.5460	−1.38874
$517$	42.8049	1.88256
$518$	−0.404161	−0.0177578
$519$	−19.5124	−0.856501
$520$	0	0
$521$	−33.4472	−1.46535	−0.732675	−	0.680579i	$-0.761728\pi$
$521$	−33.4472	−1.46535	−0.732675	+	0.680579i	$0.761728\pi$
$522$	2.40842	0.105414
$523$	−19.3198	−0.844795	−0.422397	−	0.906411i	$-0.638811\pi$
$523$	−19.3198	−0.844795	−0.422397	+	0.906411i	$0.638811\pi$
$524$	4.65776	0.203475
$525$	0	0
$526$	44.8384	1.95505
$527$	−39.2588	−1.71014
$528$	45.2507	1.96928
$529$	−11.9044	−0.517582
$530$	0	0
$531$	3.95830	0.171776
$532$	−14.0714	−0.610073
$533$	−6.36672	−0.275773
$534$	−5.14146	−0.222493
$535$	0	0
$536$	−78.3424	−3.38387
$537$	16.5856	0.715721
$538$	20.2220	0.871832
$539$	−4.73730	−0.204050
$540$	0	0
$541$	−24.9554	−1.07292	−0.536459	−	0.843927i	$-0.680238\pi$
$541$	−24.9554	−1.07292	−0.536459	+	0.843927i	$0.680238\pi$
$542$	77.5340	3.33037
$543$	2.81684	0.120882
$544$	−53.4626	−2.29219
$545$	0	0
$546$	2.61050	0.111719
$547$	−3.80037	−0.162492	−0.0812460	−	0.996694i	$-0.525890\pi$
$547$	−3.80037	−0.162492	−0.0812460	+	0.996694i	$0.525890\pi$
$548$	−15.8706	−0.677960
$549$	12.4420	0.531012
$550$	0	0
$551$	−2.69635	−0.114868
$552$	−24.4756	−1.04175
$553$	−13.3646	−0.568320
$554$	65.6510	2.78924
$555$	0	0
$556$	1.78424	0.0756686
$557$	−43.8792	−1.85922	−0.929610	−	0.368546i	$-0.879856\pi$
$557$	−43.8792	−1.85922	−0.929610	+	0.368546i	$0.879856\pi$
$558$	19.6294	0.830980
$559$	−6.55201	−0.277120
$560$	0	0
$561$	24.7334	1.04425
$562$	−21.9290	−0.925018
$563$	−12.3768	−0.521620	−0.260810	−	0.965390i	$-0.583990\pi$
$563$	−12.3768	−0.521620	−0.260810	+	0.965390i	$0.583990\pi$
$564$	43.5043	1.83186
$565$	0	0
$566$	−55.8417	−2.34720
$567$	−1.00000	−0.0419961
$568$	48.3667	2.02942
$569$	−26.6234	−1.11611	−0.558056	−	0.829803i	$-0.688453\pi$
$569$	−26.6234	−1.11611	−0.558056	+	0.829803i	$0.688453\pi$
$570$	0	0
$571$	10.9983	0.460263	0.230132	−	0.973160i	$-0.426084\pi$
$571$	10.9983	0.460263	0.230132	+	0.973160i	$0.426084\pi$
$572$	22.8087	0.953680
$573$	−15.1601	−0.633321
$574$	16.6203	0.693719
$575$	0	0
$576$	7.62729	0.317804
$577$	−30.4238	−1.26656	−0.633280	−	0.773923i	$-0.718292\pi$
$577$	−30.4238	−1.26656	−0.633280	+	0.773923i	$0.718292\pi$
$578$	−26.7807	−1.11393
$579$	0.0651962	0.00270946
$580$	0	0
$581$	−1.40629	−0.0583428
$582$	5.50818	0.228321
$583$	40.5134	1.67789
$584$	−56.8365	−2.35191
$585$	0	0
$586$	−25.0581	−1.03514
$587$	−3.84207	−0.158579	−0.0792895	−	0.996852i	$-0.525265\pi$
$587$	−3.84207	−0.158579	−0.0792895	+	0.996852i	$0.525265\pi$
$588$	−4.81471	−0.198555
$589$	−21.9761	−0.905511
$590$	0	0
$591$	−17.1415	−0.705105
$592$	−1.47886	−0.0607806
$593$	23.8904	0.981061	0.490530	−	0.871424i	$-0.336803\pi$
$593$	23.8904	0.981061	0.490530	+	0.871424i	$0.336803\pi$
$594$	−12.3667	−0.507413
$595$	0	0
$596$	−75.7958	−3.10471
$597$	−6.44200	−0.263653
$598$	−8.69560	−0.355589
$599$	−15.4206	−0.630070	−0.315035	−	0.949080i	$-0.602016\pi$
$599$	−15.4206	−0.630070	−0.315035	+	0.949080i	$0.602016\pi$
$600$	0	0
$601$	−1.49280	−0.0608928	−0.0304464	−	0.999536i	$-0.509693\pi$
$601$	−1.49280	−0.0608928	−0.0304464	+	0.999536i	$0.509693\pi$
$602$	17.1040	0.697108
$603$	10.6620	0.434191
$604$	49.5503	2.01617
$605$	0	0
$606$	2.22002	0.0901821
$607$	4.44626	0.180468	0.0902340	−	0.995921i	$-0.471239\pi$
$607$	4.44626	0.180468	0.0902340	+	0.995921i	$0.471239\pi$
$608$	−29.9271	−1.21370
$609$	−0.922589	−0.0373852
$610$	0	0
$611$	9.03571	0.365546
$612$	25.1376	1.01613
$613$	−26.6640	−1.07695	−0.538474	−	0.842642i	$-0.680999\pi$
$613$	−26.6640	−1.07695	−0.538474	+	0.842642i	$0.680999\pi$
$614$	−39.5460	−1.59595
$615$	0	0
$616$	−34.8087	−1.40248
$617$	−27.3495	−1.10105	−0.550525	−	0.834819i	$-0.685572\pi$
$617$	−27.3495	−1.10105	−0.550525	+	0.834819i	$0.685572\pi$
$618$	3.84944	0.154847
$619$	−9.24836	−0.371723	−0.185861	−	0.982576i	$-0.559508\pi$
$619$	−9.24836	−0.371723	−0.185861	+	0.982576i	$0.559508\pi$
$620$	0	0
$621$	3.33101	0.133669
$622$	11.4094	0.457475
$623$	1.96953	0.0789076
$624$	9.55201	0.382386
$625$	0	0
$626$	−3.89697	−0.155754
$627$	13.8452	0.552923
$628$	54.9535	2.19288
$629$	−0.808323	−0.0322299
$630$	0	0
$631$	24.5134	0.975864	0.487932	−	0.872882i	$-0.337751\pi$
$631$	24.5134	0.975864	0.487932	+	0.872882i	$0.337751\pi$
$632$	−98.2003	−3.90620
$633$	16.0266	0.637000
$634$	60.5972	2.40662
$635$	0	0
$636$	41.1754	1.63271
$637$	−1.00000	−0.0396214
$638$	−11.4094	−0.451703
$639$	−6.58248	−0.260399
$640$	0	0
$641$	34.3972	1.35861	0.679304	−	0.733857i	$-0.262282\pi$
$641$	34.3972	1.35861	0.679304	+	0.733857i	$0.262282\pi$
$642$	−6.85042	−0.270364
$643$	7.69036	0.303278	0.151639	−	0.988436i	$-0.451545\pi$
$643$	7.69036	0.303278	0.151639	+	0.988436i	$0.451545\pi$
$644$	16.0378	0.631979
$645$	0	0
$646$	−39.8332	−1.56722
$647$	−41.9123	−1.64774	−0.823872	−	0.566776i	$-0.808191\pi$
$647$	−41.9123	−1.64774	−0.823872	+	0.566776i	$0.808191\pi$
$648$	−7.34780	−0.288649
$649$	−18.7516	−0.736066
$650$	0	0
$651$	−7.51941	−0.294709
$652$	64.8763	2.54075
$653$	−34.2262	−1.33938	−0.669688	−	0.742642i	$-0.733572\pi$
$653$	−34.2262	−1.33938	−0.669688	+	0.742642i	$0.733572\pi$
$654$	−46.7713	−1.82890
$655$	0	0
$656$	60.8149	2.37442
$657$	7.73517	0.301778
$658$	−23.5877	−0.919545
$659$	45.1685	1.75951	0.879757	−	0.475424i	$-0.157705\pi$
$659$	45.1685	1.75951	0.879757	+	0.475424i	$0.157705\pi$
$660$	0	0
$661$	11.9839	0.466119	0.233059	−	0.972463i	$-0.425126\pi$
$661$	11.9839	0.466119	0.233059	+	0.972463i	$0.425126\pi$
$662$	−2.88203	−0.112013
$663$	5.22100	0.202767
$664$	−10.3331	−0.401004
$665$	0	0
$666$	0.404161	0.0156609
$667$	3.07315	0.118993
$668$	−92.3968	−3.57494
$669$	20.0266	0.774273
$670$	0	0
$671$	−58.9415	−2.27541
$672$	−10.2399	−0.395013
$673$	29.5117	1.13759	0.568796	−	0.822479i	$-0.307409\pi$
$673$	29.5117	1.13759	0.568796	+	0.822479i	$0.307409\pi$
$674$	−11.0747	−0.426581
$675$	0	0
$676$	4.81471	0.185181
$677$	31.0662	1.19397	0.596985	−	0.802252i	$-0.296365\pi$
$677$	31.0662	1.19397	0.596985	+	0.802252i	$0.296365\pi$
$678$	−2.40842	−0.0924948
$679$	−2.11001	−0.0809747
$680$	0	0
$681$	19.2171	0.736402
$682$	−92.9904	−3.56079
$683$	−5.79433	−0.221714	−0.110857	−	0.993836i	$-0.535360\pi$
$683$	−5.79433	−0.221714	−0.110857	+	0.993836i	$0.535360\pi$
$684$	14.0714	0.538034
$685$	0	0
$686$	2.61050	0.0996693
$687$	−5.25884	−0.200637
$688$	62.5848	2.38602
$689$	8.55201	0.325806
$690$	0	0
$691$	18.8617	0.717531	0.358766	−	0.933428i	$-0.383198\pi$
$691$	18.8617	0.717531	0.358766	+	0.933428i	$0.383198\pi$
$692$	93.9467	3.57132
$693$	4.73730	0.179955
$694$	36.6347	1.39063
$695$	0	0
$696$	−6.77900	−0.256957
$697$	33.2406	1.25908
$698$	−10.7181	−0.405685
$699$	−26.6234	−1.00699
$700$	0	0
$701$	−32.3180	−1.22064	−0.610318	−	0.792157i	$-0.708958\pi$
$701$	−32.3180	−1.22064	−0.610318	+	0.792157i	$0.708958\pi$
$702$	−2.61050	−0.0985270
$703$	−0.452479	−0.0170656
$704$	−36.1328	−1.36180
$705$	0	0
$706$	−41.9645	−1.57936
$707$	−0.850419	−0.0319833
$708$	−19.0581	−0.716246
$709$	4.72296	0.177374	0.0886872	−	0.996060i	$-0.471733\pi$
$709$	4.72296	0.177374	0.0886872	+	0.996060i	$0.471733\pi$
$710$	0	0
$711$	13.3646	0.501211
$712$	14.4717	0.542350
$713$	25.0472	0.938026
$714$	−13.6294	−0.510068
$715$	0	0
$716$	−79.8548	−2.98431
$717$	−4.29104	−0.160252
$718$	47.3831	1.76832
$719$	−40.8902	−1.52495	−0.762474	−	0.647019i	$-0.776015\pi$
$719$	−40.8902	−1.52495	−0.762474	+	0.647019i	$0.776015\pi$
$720$	0	0
$721$	−1.47460	−0.0549169
$722$	27.3018	1.01607
$723$	−7.52367	−0.279808
$724$	−13.5623	−0.504037
$725$	0	0
$726$	29.8693	1.10856
$727$	−18.7292	−0.694627	−0.347313	−	0.937749i	$-0.612906\pi$
$727$	−18.7292	−0.694627	−0.347313	+	0.937749i	$0.612906\pi$
$728$	−7.34780	−0.272328
$729$	1.00000	0.0370370
$730$	0	0
$731$	34.2080	1.26523
$732$	−59.9046	−2.21414
$733$	14.1100	0.521165	0.260583	−	0.965452i	$-0.416085\pi$
$733$	14.1100	0.521165	0.260583	+	0.965452i	$0.416085\pi$
$734$	−61.0738	−2.25428
$735$	0	0
$736$	34.1093	1.25728
$737$	−50.5092	−1.86053
$738$	−16.6203	−0.611802
$739$	−49.9209	−1.83637	−0.918184	−	0.396154i	$-0.870345\pi$
$739$	−49.9209	−1.83637	−0.918184	+	0.396154i	$0.870345\pi$
$740$	0	0
$741$	2.92259	0.107364
$742$	−22.3250	−0.819577
$743$	−2.15868	−0.0791945	−0.0395972	−	0.999216i	$-0.512607\pi$
$743$	−2.15868	−0.0791945	−0.0395972	+	0.999216i	$0.512607\pi$
$744$	−55.2511	−2.02560
$745$	0	0
$746$	−12.4042	−0.454149
$747$	1.40629	0.0514535
$748$	−119.084	−4.35415
$749$	2.62418	0.0958854
$750$	0	0
$751$	16.8372	0.614399	0.307199	−	0.951645i	$-0.400608\pi$
$751$	16.8372	0.614399	0.307199	+	0.951645i	$0.400608\pi$
$752$	−86.3092	−3.14737
$753$	−11.3198	−0.412516
$754$	−2.40842	−0.0877095
$755$	0	0
$756$	4.81471	0.175109
$757$	17.6028	0.639785	0.319893	−	0.947454i	$-0.396353\pi$
$757$	17.6028	0.639785	0.319893	+	0.947454i	$0.396353\pi$
$758$	17.7842	0.645953
$759$	−15.7800	−0.572777
$760$	0	0
$761$	19.2179	0.696648	0.348324	−	0.937374i	$-0.386751\pi$
$761$	19.2179	0.696648	0.348324	+	0.937374i	$0.386751\pi$
$762$	−45.6174	−1.65255
$763$	17.9166	0.648624
$764$	72.9913	2.64073
$765$	0	0
$766$	5.89310	0.212926
$767$	−3.95830	−0.142926
$768$	16.7394	0.604032
$769$	−14.0406	−0.506315	−0.253158	−	0.967425i	$-0.581469\pi$
$769$	−14.0406	−0.506315	−0.253158	+	0.967425i	$0.581469\pi$
$770$	0	0
$771$	−24.8504	−0.894966
$772$	−0.313901	−0.0112975
$773$	−22.4339	−0.806891	−0.403445	−	0.915004i	$-0.632187\pi$
$773$	−22.4339	−0.806891	−0.403445	+	0.915004i	$0.632187\pi$
$774$	−17.1040	−0.614791
$775$	0	0
$776$	−15.5039	−0.556558
$777$	−0.154821	−0.00555419
$778$	−15.6630	−0.561546
$779$	18.6073	0.666676
$780$	0	0
$781$	31.1832	1.11582
$782$	45.3997	1.62349
$783$	0.922589	0.0329707
$784$	9.55201	0.341143
$785$	0	0
$786$	2.52540	0.0900781
$787$	0.926847	0.0330385	0.0165193	−	0.999864i	$-0.494742\pi$
$787$	0.926847	0.0330385	0.0165193	+	0.999864i	$0.494742\pi$
$788$	82.5311	2.94005
$789$	17.1762	0.611488
$790$	0	0
$791$	0.922589	0.0328035
$792$	34.8087	1.23687
$793$	−12.4420	−0.441828
$794$	65.2357	2.31513
$795$	0	0
$796$	31.0164	1.09935
$797$	26.0154	0.921512	0.460756	−	0.887527i	$-0.347578\pi$
$797$	26.0154	0.921512	0.460756	+	0.887527i	$0.347578\pi$
$798$	−7.62942	−0.270079
$799$	−47.1754	−1.66895
$800$	0	0
$801$	−1.96953	−0.0695900
$802$	−72.1879	−2.54904
$803$	−36.6438	−1.29313
$804$	−51.3345	−1.81043
$805$	0	0
$806$	−19.6294	−0.691417
$807$	7.74640	0.272686
$808$	−6.24870	−0.219829
$809$	−44.8539	−1.57698	−0.788490	−	0.615048i	$-0.789137\pi$
$809$	−44.8539	−1.57698	−0.788490	+	0.615048i	$0.789137\pi$
$810$	0	0
$811$	27.2511	0.956916	0.478458	−	0.878110i	$-0.341196\pi$
$811$	27.2511	0.956916	0.478458	+	0.878110i	$0.341196\pi$
$812$	4.44200	0.155884
$813$	29.7008	1.04165
$814$	−1.91463	−0.0671078
$815$	0	0
$816$	−49.8710	−1.74584
$817$	19.1488	0.669933
$818$	−34.3250	−1.20015
$819$	1.00000	0.0349428
$820$	0	0
$821$	20.4003	0.711975	0.355988	−	0.934491i	$-0.384145\pi$
$821$	20.4003	0.711975	0.355988	+	0.934491i	$0.384145\pi$
$822$	−8.60494	−0.300132
$823$	−54.3509	−1.89455	−0.947276	−	0.320418i	$-0.896176\pi$
$823$	−54.3509	−1.89455	−0.947276	+	0.320418i	$0.896176\pi$
$824$	−10.8350	−0.377457
$825$	0	0
$826$	10.3331	0.359536
$827$	−3.48272	−0.121106	−0.0605530	−	0.998165i	$-0.519286\pi$
$827$	−3.48272	−0.121106	−0.0605530	+	0.998165i	$0.519286\pi$
$828$	−16.0378	−0.557353
$829$	−29.8417	−1.03645	−0.518223	−	0.855246i	$-0.673406\pi$
$829$	−29.8417	−1.03645	−0.518223	+	0.855246i	$0.673406\pi$
$830$	0	0
$831$	25.1488	0.872403
$832$	−7.62729	−0.264429
$833$	5.22100	0.180897
$834$	0.967402	0.0334984
$835$	0	0
$836$	−66.6605	−2.30550
$837$	7.51941	0.259909
$838$	14.8658	0.513530
$839$	−43.0033	−1.48464	−0.742320	−	0.670045i	$-0.766275\pi$
$839$	−43.0033	−1.48464	−0.742320	+	0.670045i	$0.766275\pi$
$840$	0	0
$841$	−28.1488	−0.970649
$842$	60.0953	2.07102
$843$	−8.40030	−0.289322
$844$	−77.1634	−2.65608
$845$	0	0
$846$	23.5877	0.810962
$847$	−11.4420	−0.393152
$848$	−81.6889	−2.80521
$849$	−21.3912	−0.734144
$850$	0	0
$851$	0.515711	0.0176784
$852$	31.6927	1.08577
$853$	−34.1023	−1.16764	−0.583820	−	0.811883i	$-0.698443\pi$
$853$	−34.1023	−1.16764	−0.583820	+	0.811883i	$0.698443\pi$
$854$	32.4798	1.11144
$855$	0	0
$856$	19.2819	0.659043
$857$	45.7344	1.56226	0.781129	−	0.624370i	$-0.214644\pi$
$857$	45.7344	1.56226	0.781129	+	0.624370i	$0.214644\pi$
$858$	12.3667	0.422193
$859$	15.9861	0.545437	0.272719	−	0.962094i	$-0.412077\pi$
$859$	15.9861	0.545437	0.272719	+	0.962094i	$0.412077\pi$
$860$	0	0
$861$	6.36672	0.216977
$862$	−54.3100	−1.84981
$863$	24.5096	0.834315	0.417157	−	0.908834i	$-0.363026\pi$
$863$	24.5096	0.834315	0.417157	+	0.908834i	$0.363026\pi$
$864$	10.2399	0.348369
$865$	0	0
$866$	82.1807	2.79261
$867$	−10.2588	−0.348408
$868$	36.2038	1.22884
$869$	−63.3120	−2.14771
$870$	0	0
$871$	−10.6620	−0.361269
$872$	131.648	4.45815
$873$	2.11001	0.0714130
$874$	25.4137	0.859630
$875$	0	0
$876$	−37.2426	−1.25831
$877$	−53.4913	−1.80627	−0.903136	−	0.429354i	$-0.858741\pi$
$877$	−53.4913	−1.80627	−0.903136	+	0.429354i	$0.858741\pi$
$878$	−58.4258	−1.97177
$879$	−9.59895	−0.323765
$880$	0	0
$881$	26.1745	0.881840	0.440920	−	0.897546i	$-0.354652\pi$
$881$	26.1745	0.881840	0.440920	+	0.897546i	$0.354652\pi$
$882$	−2.61050	−0.0879001
$883$	−23.1840	−0.780202	−0.390101	−	0.920772i	$-0.627560\pi$
$883$	−23.1840	−0.780202	−0.390101	+	0.920772i	$0.627560\pi$
$884$	−25.1376	−0.845469
$885$	0	0
$886$	22.2536	0.747624
$887$	13.7008	0.460029	0.230015	−	0.973187i	$-0.426123\pi$
$887$	13.7008	0.460029	0.230015	+	0.973187i	$0.426123\pi$
$888$	−1.13760	−0.0381752
$889$	17.4746	0.586079
$890$	0	0
$891$	−4.73730	−0.158705
$892$	−96.4223	−3.22846
$893$	−26.4077	−0.883699
$894$	−41.0959	−1.37445
$895$	0	0
$896$	−0.568798	−0.0190022
$897$	−3.33101	−0.111219
$898$	−48.8534	−1.63026
$899$	6.93733	0.231373
$900$	0	0
$901$	−44.6500	−1.48751
$902$	78.7354	2.62160
$903$	6.55201	0.218037
$904$	6.77900	0.225466
$905$	0	0
$906$	26.8658	0.892556
$907$	−25.5621	−0.848777	−0.424388	−	0.905480i	$-0.639511\pi$
$907$	−25.5621	−0.848777	−0.424388	+	0.905480i	$0.639511\pi$
$908$	−92.5249	−3.07055
$909$	0.850419	0.0282066
$910$	0	0
$911$	2.07643	0.0687951	0.0343976	−	0.999408i	$-0.489049\pi$
$911$	2.07643	0.0687951	0.0343976	+	0.999408i	$0.489049\pi$
$912$	−27.9166	−0.924411
$913$	−6.66202	−0.220481
$914$	−36.9036	−1.22066
$915$	0	0
$916$	25.3198	0.836589
$917$	−0.967402	−0.0319464
$918$	13.6294	0.449838
$919$	17.8514	0.588863	0.294432	−	0.955673i	$-0.404870\pi$
$919$	17.8514	0.588863	0.294432	+	0.955673i	$0.404870\pi$
$920$	0	0
$921$	−15.1488	−0.499171
$922$	6.98664	0.230093
$923$	6.58248	0.216665
$924$	−22.8087	−0.750352
$925$	0	0
$926$	−6.60881	−0.217179
$927$	1.47460	0.0484321
$928$	9.44724	0.310121
$929$	−37.0553	−1.21575	−0.607873	−	0.794034i	$-0.707977\pi$
$929$	−37.0553	−1.21575	−0.607873	+	0.794034i	$0.707977\pi$
$930$	0	0
$931$	2.92259	0.0957840
$932$	128.184	4.19881
$933$	4.37058	0.143086
$934$	5.23212	0.171200
$935$	0	0
$936$	7.34780	0.240170
$937$	−39.7540	−1.29871	−0.649354	−	0.760486i	$-0.724961\pi$
$937$	−39.7540	−1.29871	−0.649354	+	0.760486i	$0.724961\pi$
$938$	27.8332	0.908786
$939$	−1.49280	−0.0487158
$940$	0	0
$941$	−47.3530	−1.54366	−0.771832	−	0.635827i	$-0.780659\pi$
$941$	−47.3530	−1.54366	−0.771832	+	0.635827i	$0.780659\pi$
$942$	29.7954	0.970785
$943$	−21.2076	−0.690614
$944$	37.8097	1.23060
$945$	0	0
$946$	81.0268	2.63441
$947$	−8.80446	−0.286106	−0.143053	−	0.989715i	$-0.545692\pi$
$947$	−8.80446	−0.286106	−0.143053	+	0.989715i	$0.545692\pi$
$948$	−64.3466	−2.08988
$949$	−7.73517	−0.251094
$950$	0	0
$951$	23.2129	0.752729
$952$	38.3629	1.24335
$953$	−7.72895	−0.250365	−0.125183	−	0.992134i	$-0.539952\pi$
$953$	−7.72895	−0.250365	−0.125183	+	0.992134i	$0.539952\pi$
$954$	22.3250	0.722799
$955$	0	0
$956$	20.6601	0.668196
$957$	−4.37058	−0.141281
$958$	38.2722	1.23652
$959$	3.29628	0.106442
$960$	0	0
$961$	25.5415	0.823920
$962$	−0.404161	−0.0130307
$963$	−2.62418	−0.0845630
$964$	36.2243	1.16671
$965$	0	0
$966$	8.69560	0.279776
$967$	−14.3054	−0.460030	−0.230015	−	0.973187i	$-0.573878\pi$
$967$	−14.3054	−0.460030	−0.230015	+	0.973187i	$0.573878\pi$
$968$	−84.0735	−2.70222
$969$	−15.2588	−0.490184
$970$	0	0
$971$	−15.1692	−0.486803	−0.243402	−	0.969926i	$-0.578263\pi$
$971$	−15.1692	−0.486803	−0.243402	+	0.969926i	$0.578263\pi$
$972$	−4.81471	−0.154432
$973$	−0.370581	−0.0118803
$974$	99.7583	3.19646
$975$	0	0
$976$	118.846	3.80417
$977$	8.25746	0.264180	0.132090	−	0.991238i	$-0.457831\pi$
$977$	8.25746	0.264180	0.132090	+	0.991238i	$0.457831\pi$
$978$	35.1754	1.12479
$979$	9.33026	0.298196
$980$	0	0
$981$	−17.9166	−0.572033
$982$	−55.8016	−1.78070
$983$	25.8525	0.824568	0.412284	−	0.911055i	$-0.364731\pi$
$983$	25.8525	0.824568	0.412284	+	0.911055i	$0.364731\pi$
$984$	46.7814	1.49134
$985$	0	0
$986$	12.5744	0.400449
$987$	−9.03571	−0.287610
$988$	−14.0714	−0.447671
$989$	−21.8248	−0.693988
$990$	0	0
$991$	−56.2100	−1.78557	−0.892785	−	0.450484i	$-0.851252\pi$
$991$	−56.2100	−1.78557	−0.892785	+	0.450484i	$0.851252\pi$
$992$	76.9981	2.44469
$993$	−1.10402	−0.0350349
$994$	−17.1836	−0.545029
$995$	0	0
$996$	−6.77088	−0.214544
$997$	−37.4789	−1.18697	−0.593484	−	0.804846i	$-0.702248\pi$
$997$	−37.4789	−1.18697	−0.593484	+	0.804846i	$0.702248\pi$
$998$	−70.7237	−2.23872
$999$	0.154821	0.00489833

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6825.2.a.bg.1.1		4
5.4	even	2		273.2.a.e.1.4	✓	4
15.14	odd	2		819.2.a.k.1.1		4
20.19	odd	2		4368.2.a.br.1.1		4
35.34	odd	2		1911.2.a.s.1.4		4
65.64	even	2		3549.2.a.w.1.1		4
105.104	even	2		5733.2.a.bf.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.a.e.1.4	✓	4	5.4	even	2
819.2.a.k.1.1		4	15.14	odd	2
1911.2.a.s.1.4		4	35.34	odd	2
3549.2.a.w.1.1		4	65.64	even	2
4368.2.a.br.1.1		4	20.19	odd	2
5733.2.a.bf.1.1		4	105.104	even	2
6825.2.a.bg.1.1		4	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:	\( N \)	\(=\)	\( 6825 = 3 \cdot 5^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6825.a (trivial)

\(f(q)\)	\(=\)	\(q-2.61050 q^{2} -1.00000 q^{3} +4.81471 q^{4} +2.61050 q^{6} -1.00000 q^{7} -7.34780 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.61050 q^{2} -1.00000 q^{3} +4.81471 q^{4} +2.61050 q^{6} -1.00000 q^{7} -7.34780 q^{8} +1.00000 q^{9} -4.73730 q^{11} -4.81471 q^{12} -1.00000 q^{13} +2.61050 q^{14} +9.55201 q^{16} +5.22100 q^{17} -2.61050 q^{18} +2.92259 q^{19} +1.00000 q^{21} +12.3667 q^{22} -3.33101 q^{23} +7.34780 q^{24} +2.61050 q^{26} -1.00000 q^{27} -4.81471 q^{28} -0.922589 q^{29} -7.51941 q^{31} -10.2399 q^{32} +4.73730 q^{33} -13.6294 q^{34} +4.81471 q^{36} -0.154821 q^{37} -7.62942 q^{38} +1.00000 q^{39} +6.36672 q^{41} -2.61050 q^{42} +6.55201 q^{43} -22.8087 q^{44} +8.69560 q^{46} -9.03571 q^{47} -9.55201 q^{48} +1.00000 q^{49} -5.22100 q^{51} -4.81471 q^{52} -8.55201 q^{53} +2.61050 q^{54} +7.34780 q^{56} -2.92259 q^{57} +2.40842 q^{58} +3.95830 q^{59} +12.4420 q^{61} +19.6294 q^{62} -1.00000 q^{63} +7.62729 q^{64} -12.3667 q^{66} +10.6620 q^{67} +25.1376 q^{68} +3.33101 q^{69} -6.58248 q^{71} -7.34780 q^{72} +7.73517 q^{73} +0.404161 q^{74} +14.0714 q^{76} +4.73730 q^{77} -2.61050 q^{78} +13.3646 q^{79} +1.00000 q^{81} -16.6203 q^{82} +1.40629 q^{83} +4.81471 q^{84} -17.1040 q^{86} +0.922589 q^{87} +34.8087 q^{88} -1.96953 q^{89} +1.00000 q^{91} -16.0378 q^{92} +7.51941 q^{93} +23.5877 q^{94} +10.2399 q^{96} +2.11001 q^{97} -2.61050 q^{98} -4.73730 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 4 q^{3} + 7 q^{4} + q^{6} - 4 q^{7} - 3 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - q^2 - 4 * q^3 + 7 * q^4 + q^6 - 4 * q^7 - 3 * q^8 + 4 * q^9	\( 4 q - q^{2} - 4 q^{3} + 7 q^{4} + q^{6} - 4 q^{7} - 3 q^{8} + 4 q^{9} - 2 q^{11} - 7 q^{12} - 4 q^{13} + q^{14} + 9 q^{16} + 2 q^{17} - q^{18} + 7 q^{19} + 4 q^{21} + 8 q^{22} - 3 q^{23} + 3 q^{24} + q^{26} - 4 q^{27} - 7 q^{28} + q^{29} + 3 q^{31} - 7 q^{32} + 2 q^{33} - 30 q^{34} + 7 q^{36} - 10 q^{37} - 6 q^{38} + 4 q^{39} - 16 q^{41} - q^{42} - 3 q^{43} - 12 q^{44} - 18 q^{46} - 5 q^{47} - 9 q^{48} + 4 q^{49} - 2 q^{51} - 7 q^{52} - 5 q^{53} + q^{54} + 3 q^{56} - 7 q^{57} + 4 q^{58} - 20 q^{59} + 12 q^{61} + 54 q^{62} - 4 q^{63} + 5 q^{64} - 8 q^{66} + 22 q^{67} + 10 q^{68} + 3 q^{69} - 3 q^{72} + 13 q^{73} - 6 q^{74} - 6 q^{76} + 2 q^{77} - q^{78} + 11 q^{79} + 4 q^{81} - 10 q^{82} - q^{83} + 7 q^{84} - 10 q^{86} - q^{87} + 60 q^{88} - 5 q^{89} + 4 q^{91} - 34 q^{92} - 3 q^{93} + 34 q^{94} + 7 q^{96} + 17 q^{97} - q^{98} - 2 q^{99}+O(q^{100}) \) 4 * q - q^2 - 4 * q^3 + 7 * q^4 + q^6 - 4 * q^7 - 3 * q^8 + 4 * q^9 - 2 * q^11 - 7 * q^12 - 4 * q^13 + q^14 + 9 * q^16 + 2 * q^17 - q^18 + 7 * q^19 + 4 * q^21 + 8 * q^22 - 3 * q^23 + 3 * q^24 + q^26 - 4 * q^27 - 7 * q^28 + q^29 + 3 * q^31 - 7 * q^32 + 2 * q^33 - 30 * q^34 + 7 * q^36 - 10 * q^37 - 6 * q^38 + 4 * q^39 - 16 * q^41 - q^42 - 3 * q^43 - 12 * q^44 - 18 * q^46 - 5 * q^47 - 9 * q^48 + 4 * q^49 - 2 * q^51 - 7 * q^52 - 5 * q^53 + q^54 + 3 * q^56 - 7 * q^57 + 4 * q^58 - 20 * q^59 + 12 * q^61 + 54 * q^62 - 4 * q^63 + 5 * q^64 - 8 * q^66 + 22 * q^67 + 10 * q^68 + 3 * q^69 - 3 * q^72 + 13 * q^73 - 6 * q^74 - 6 * q^76 + 2 * q^77 - q^78 + 11 * q^79 + 4 * q^81 - 10 * q^82 - q^83 + 7 * q^84 - 10 * q^86 - q^87 + 60 * q^88 - 5 * q^89 + 4 * q^91 - 34 * q^92 - 3 * q^93 + 34 * q^94 + 7 * q^96 + 17 * q^97 - q^98 - 2 * q^99

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