LMFDB - Embedded newform 6275.2.a.e.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6275,2,Mod(1,6275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6275, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6275.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6275 = 5^{2} \cdot 251 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6275.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:	$50.1061272684$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 2 x^{16} - 28 x^{15} + 54 x^{14} + 317 x^{13} - 582 x^{12} - 1867 x^{11} + 3178 x^{10} + \cdots + 256 $ x^17 - 2x^16 - 28x^15 + 54x^14 + 317x^13 - 582x^12 - 1867x^11 + 3178x^10 + 6186x^9 - 9216x^8 - 11921x^7 + 13680x^6 + 13752x^5 - 9400x^4 - 8800x^3 + 1920x^2 + 2240x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 251)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Root			$-2.32547$ of defining polynomial
Character	$\chi$	$=$	6275.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.32547 q^{2} -3.27059 q^{3} +3.40783 q^{4} -7.60566 q^{6} -1.64874 q^{7} +3.27388 q^{8} +7.69673 q^{9} +O(q^{10})$	\(q+2.32547 q^{2} -3.27059 q^{3} +3.40783 q^{4} -7.60566 q^{6} -1.64874 q^{7} +3.27388 q^{8} +7.69673 q^{9} -3.10982 q^{11} -11.1456 q^{12} -5.70062 q^{13} -3.83409 q^{14} +0.797656 q^{16} -3.66658 q^{17} +17.8985 q^{18} -5.51191 q^{19} +5.39233 q^{21} -7.23182 q^{22} +2.16257 q^{23} -10.7075 q^{24} -13.2566 q^{26} -15.3610 q^{27} -5.61862 q^{28} +8.08572 q^{29} +5.30190 q^{31} -4.69283 q^{32} +10.1709 q^{33} -8.52654 q^{34} +26.2292 q^{36} +2.05773 q^{37} -12.8178 q^{38} +18.6444 q^{39} -2.65933 q^{41} +12.5397 q^{42} +9.01212 q^{43} -10.5978 q^{44} +5.02900 q^{46} -2.30292 q^{47} -2.60880 q^{48} -4.28167 q^{49} +11.9919 q^{51} -19.4267 q^{52} +8.44037 q^{53} -35.7217 q^{54} -5.39776 q^{56} +18.0272 q^{57} +18.8031 q^{58} +1.95895 q^{59} +11.1945 q^{61} +12.3294 q^{62} -12.6899 q^{63} -12.5084 q^{64} +23.6523 q^{66} +1.43672 q^{67} -12.4951 q^{68} -7.07287 q^{69} -15.2173 q^{71} +25.1981 q^{72} +1.27528 q^{73} +4.78520 q^{74} -18.7836 q^{76} +5.12728 q^{77} +43.3570 q^{78} -9.46821 q^{79} +27.1494 q^{81} -6.18421 q^{82} +0.845328 q^{83} +18.3762 q^{84} +20.9575 q^{86} -26.4451 q^{87} -10.1812 q^{88} -6.17322 q^{89} +9.39881 q^{91} +7.36967 q^{92} -17.3403 q^{93} -5.35538 q^{94} +15.3483 q^{96} +9.74063 q^{97} -9.95691 q^{98} -23.9355 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 2 q^{2} + 26 q^{4} + q^{6} - 3 q^{7} - 6 q^{8} + 25 q^{9}+O(q^{10}) $ 17 * q - 2 * q^2 + 26 * q^4 + q^6 - 3 * q^7 - 6 * q^8 + 25 * q^9	$ 17 q - 2 q^{2} + 26 q^{4} + q^{6} - 3 q^{7} - 6 q^{8} + 25 q^{9} - q^{11} + 9 q^{12} - 22 q^{13} - 7 q^{14} + 40 q^{16} + q^{17} + 7 q^{18} + 13 q^{19} + 25 q^{21} - 4 q^{22} + 2 q^{23} - 24 q^{24} - 9 q^{26} + 15 q^{27} + 10 q^{28} + 28 q^{29} + 12 q^{31} - 4 q^{32} + 16 q^{33} - 21 q^{34} + 21 q^{36} - 27 q^{37} + 37 q^{38} + 13 q^{39} - q^{41} + 56 q^{42} - 9 q^{43} - 43 q^{44} + 4 q^{46} + 20 q^{47} + 79 q^{48} + 32 q^{49} - 2 q^{51} + q^{52} - q^{53} - 65 q^{54} - 61 q^{56} + 24 q^{57} + 46 q^{58} - 20 q^{59} + 59 q^{61} + 73 q^{62} + 41 q^{63} + 54 q^{64} - 43 q^{66} - 15 q^{67} + 20 q^{68} + 38 q^{69} - 26 q^{71} + 2 q^{72} - 8 q^{73} + 2 q^{74} + 38 q^{76} + 33 q^{79} + 29 q^{81} - 10 q^{82} + 63 q^{84} + 11 q^{86} + 11 q^{87} - 27 q^{88} + 11 q^{89} - 2 q^{91} - 28 q^{92} - 28 q^{93} + 29 q^{94} - 17 q^{96} + 10 q^{97} - 22 q^{98} - 36 q^{99}+O(q^{100}) $ 17 * q - 2 * q^2 + 26 * q^4 + q^6 - 3 * q^7 - 6 * q^8 + 25 * q^9 - q^11 + 9 * q^12 - 22 * q^13 - 7 * q^14 + 40 * q^16 + q^17 + 7 * q^18 + 13 * q^19 + 25 * q^21 - 4 * q^22 + 2 * q^23 - 24 * q^24 - 9 * q^26 + 15 * q^27 + 10 * q^28 + 28 * q^29 + 12 * q^31 - 4 * q^32 + 16 * q^33 - 21 * q^34 + 21 * q^36 - 27 * q^37 + 37 * q^38 + 13 * q^39 - q^41 + 56 * q^42 - 9 * q^43 - 43 * q^44 + 4 * q^46 + 20 * q^47 + 79 * q^48 + 32 * q^49 - 2 * q^51 + q^52 - q^53 - 65 * q^54 - 61 * q^56 + 24 * q^57 + 46 * q^58 - 20 * q^59 + 59 * q^61 + 73 * q^62 + 41 * q^63 + 54 * q^64 - 43 * q^66 - 15 * q^67 + 20 * q^68 + 38 * q^69 - 26 * q^71 + 2 * q^72 - 8 * q^73 + 2 * q^74 + 38 * q^76 + 33 * q^79 + 29 * q^81 - 10 * q^82 + 63 * q^84 + 11 * q^86 + 11 * q^87 - 27 * q^88 + 11 * q^89 - 2 * q^91 - 28 * q^92 - 28 * q^93 + 29 * q^94 - 17 * q^96 + 10 * q^97 - 22 * q^98 - 36 * 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 $

$2$	2.32547	1.64436	0.822179	−	0.569228i	$-0.192758\pi$
$2$	2.32547	1.64436	0.822179	+	0.569228i	$0.192758\pi$
$3$	−3.27059	−1.88827	−0.944137	−	0.329554i	$-0.893101\pi$
$3$	−3.27059	−1.88827	−0.944137	+	0.329554i	$0.893101\pi$
$4$	3.40783	1.70392
$5$	0	0
$5$	0	0
$6$	−7.60566	−3.10500
$7$	−1.64874	−0.623164	−0.311582	−	0.950219i	$-0.600859\pi$
$7$	−1.64874	−0.623164	−0.311582	+	0.950219i	$0.600859\pi$
$8$	3.27388	1.15749
$9$	7.69673	2.56558
$10$	0	0
$11$	−3.10982	−0.937647	−0.468824	−	0.883292i	$-0.655322\pi$
$11$	−3.10982	−0.937647	−0.468824	+	0.883292i	$0.655322\pi$
$12$	−11.1456	−3.21746
$13$	−5.70062	−1.58107	−0.790533	−	0.612419i	$-0.790197\pi$
$13$	−5.70062	−1.58107	−0.790533	+	0.612419i	$0.790197\pi$
$14$	−3.83409	−1.02470
$15$	0	0
$16$	0.797656	0.199414
$17$	−3.66658	−0.889277	−0.444638	−	0.895710i	$-0.646668\pi$
$17$	−3.66658	−0.889277	−0.444638	+	0.895710i	$0.646668\pi$
$18$	17.8985	4.21873
$19$	−5.51191	−1.26452	−0.632259	−	0.774757i	$-0.717872\pi$
$19$	−5.51191	−1.26452	−0.632259	+	0.774757i	$0.717872\pi$
$20$	0	0
$21$	5.39233	1.17670
$22$	−7.23182	−1.54183
$23$	2.16257	0.450927	0.225463	−	0.974252i	$-0.427610\pi$
$23$	2.16257	0.450927	0.225463	+	0.974252i	$0.427610\pi$
$24$	−10.7075	−2.18566
$25$	0	0
$26$	−13.2566	−2.59984
$27$	−15.3610	−2.95623
$28$	−5.61862	−1.06182
$29$	8.08572	1.50148	0.750741	−	0.660597i	$-0.229697\pi$
$29$	8.08572	1.50148	0.750741	+	0.660597i	$0.229697\pi$
$30$	0	0
$31$	5.30190	0.952249	0.476125	−	0.879378i	$-0.342041\pi$
$31$	5.30190	0.952249	0.476125	+	0.879378i	$0.342041\pi$
$32$	−4.69283	−0.829583
$33$	10.1709	1.77053
$34$	−8.52654	−1.46229
$35$	0	0
$36$	26.2292	4.37153
$37$	2.05773	0.338289	0.169145	−	0.985591i	$-0.445900\pi$
$37$	2.05773	0.338289	0.169145	+	0.985591i	$0.445900\pi$
$38$	−12.8178	−2.07932
$39$	18.6444	2.98549
$40$	0	0
$41$	−2.65933	−0.415318	−0.207659	−	0.978201i	$-0.566584\pi$
$41$	−2.65933	−0.415318	−0.207659	+	0.978201i	$0.566584\pi$
$42$	12.5397	1.93492
$43$	9.01212	1.37434	0.687168	−	0.726499i	$-0.258854\pi$
$43$	9.01212	1.37434	0.687168	+	0.726499i	$0.258854\pi$
$44$	−10.5978	−1.59767
$45$	0	0
$46$	5.02900	0.741485
$47$	−2.30292	−0.335915	−0.167958	−	0.985794i	$-0.553717\pi$
$47$	−2.30292	−0.335915	−0.167958	+	0.985794i	$0.553717\pi$
$48$	−2.60880	−0.376548
$49$	−4.28167	−0.611667
$50$	0	0
$51$	11.9919	1.67920
$52$	−19.4267	−2.69401
$53$	8.44037	1.15937	0.579687	−	0.814839i	$-0.303175\pi$
$53$	8.44037	1.15937	0.579687	+	0.814839i	$0.303175\pi$
$54$	−35.7217	−4.86111
$55$	0	0
$56$	−5.39776	−0.721306
$57$	18.0272	2.38776
$58$	18.8031	2.46897
$59$	1.95895	0.255034	0.127517	−	0.991836i	$-0.459299\pi$
$59$	1.95895	0.255034	0.127517	+	0.991836i	$0.459299\pi$
$60$	0	0
$61$	11.1945	1.43331	0.716655	−	0.697428i	$-0.245672\pi$
$61$	11.1945	1.43331	0.716655	+	0.697428i	$0.245672\pi$
$62$	12.3294	1.56584
$63$	−12.6899	−1.59877
$64$	−12.5084	−1.56355
$65$	0	0
$66$	23.6523	2.91139
$67$	1.43672	0.175523	0.0877615	−	0.996142i	$-0.472029\pi$
$67$	1.43672	0.175523	0.0877615	+	0.996142i	$0.472029\pi$
$68$	−12.4951	−1.51525
$69$	−7.07287	−0.851473
$70$	0	0
$71$	−15.2173	−1.80597	−0.902983	−	0.429677i	$-0.858627\pi$
$71$	−15.2173	−1.80597	−0.902983	+	0.429677i	$0.858627\pi$
$72$	25.1981	2.96963
$73$	1.27528	0.149260	0.0746301	−	0.997211i	$-0.476222\pi$
$73$	1.27528	0.149260	0.0746301	+	0.997211i	$0.476222\pi$
$74$	4.78520	0.556269
$75$	0	0
$76$	−18.7836	−2.15463
$77$	5.12728	0.584308
$78$	43.3570	4.90921
$79$	−9.46821	−1.06526	−0.532628	−	0.846349i	$-0.678796\pi$
$79$	−9.46821	−1.06526	−0.532628	+	0.846349i	$0.678796\pi$
$80$	0	0
$81$	27.1494	3.01660
$82$	−6.18421	−0.682931
$83$	0.845328	0.0927868	0.0463934	−	0.998923i	$-0.485227\pi$
$83$	0.845328	0.0927868	0.0463934	+	0.998923i	$0.485227\pi$
$84$	18.3762	2.00500
$85$	0	0
$86$	20.9575	2.25990
$87$	−26.4451	−2.83521
$88$	−10.1812	−1.08532
$89$	−6.17322	−0.654360	−0.327180	−	0.944962i	$-0.606098\pi$
$89$	−6.17322	−0.654360	−0.327180	+	0.944962i	$0.606098\pi$
$90$	0	0
$91$	9.39881	0.985263
$92$	7.36967	0.768341
$93$	−17.3403	−1.79811
$94$	−5.35538	−0.552365
$95$	0	0
$96$	15.3483	1.56648
$97$	9.74063	0.989012	0.494506	−	0.869174i	$-0.335349\pi$
$97$	9.74063	0.989012	0.494506	+	0.869174i	$0.335349\pi$
$98$	−9.95691	−1.00580
$99$	−23.9355	−2.40560
$100$	0	0
$101$	5.83576	0.580680	0.290340	−	0.956924i	$-0.406232\pi$
$101$	5.83576	0.580680	0.290340	+	0.956924i	$0.406232\pi$
$102$	27.8868	2.76120
$103$	9.73512	0.959229	0.479615	−	0.877479i	$-0.340776\pi$
$103$	9.73512	0.959229	0.479615	+	0.877479i	$0.340776\pi$
$104$	−18.6631	−1.83007
$105$	0	0
$106$	19.6279	1.90643
$107$	7.26599	0.702430	0.351215	−	0.936295i	$-0.385769\pi$
$107$	7.26599	0.702430	0.351215	+	0.936295i	$0.385769\pi$
$108$	−52.3479	−5.03718
$109$	5.18824	0.496943	0.248472	−	0.968639i	$-0.420072\pi$
$109$	5.18824	0.496943	0.248472	+	0.968639i	$0.420072\pi$
$110$	0	0
$111$	−6.72999	−0.638782
$112$	−1.31512	−0.124268
$113$	17.6145	1.65703	0.828516	−	0.559966i	$-0.189186\pi$
$113$	17.6145	1.65703	0.828516	+	0.559966i	$0.189186\pi$
$114$	41.9217	3.92633
$115$	0	0
$116$	27.5548	2.55840
$117$	−43.8761	−4.05635
$118$	4.55550	0.419367
$119$	6.04523	0.554165
$120$	0	0
$121$	−1.32899	−0.120818
$122$	26.0325	2.35688
$123$	8.69757	0.784233
$124$	18.0680	1.62255
$125$	0	0
$126$	−29.5100	−2.62896
$127$	5.45277	0.483855	0.241928	−	0.970294i	$-0.422220\pi$
$127$	5.45277	0.483855	0.241928	+	0.970294i	$0.422220\pi$
$128$	−19.7022	−1.74145
$129$	−29.4749	−2.59512
$130$	0	0
$131$	−13.1350	−1.14761	−0.573805	−	0.818992i	$-0.694533\pi$
$131$	−13.1350	−1.14761	−0.573805	+	0.818992i	$0.694533\pi$
$132$	34.6609	3.01684
$133$	9.08768	0.788002
$134$	3.34105	0.288623
$135$	0	0
$136$	−12.0039	−1.02933
$137$	−5.50982	−0.470736	−0.235368	−	0.971906i	$-0.575630\pi$
$137$	−5.50982	−0.470736	−0.235368	+	0.971906i	$0.575630\pi$
$138$	−16.4478	−1.40013
$139$	18.8534	1.59912	0.799560	−	0.600586i	$-0.205066\pi$
$139$	18.8534	1.59912	0.799560	+	0.600586i	$0.205066\pi$
$140$	0	0
$141$	7.53189	0.634300
$142$	−35.3875	−2.96966
$143$	17.7279	1.48248
$144$	6.13934	0.511612
$145$	0	0
$146$	2.96563	0.245437
$147$	14.0036	1.15499
$148$	7.01241	0.576416
$149$	10.6735	0.874411	0.437206	−	0.899362i	$-0.355968\pi$
$149$	10.6735	0.874411	0.437206	+	0.899362i	$0.355968\pi$
$150$	0	0
$151$	−7.08667	−0.576705	−0.288352	−	0.957524i	$-0.593107\pi$
$151$	−7.08667	−0.576705	−0.288352	+	0.957524i	$0.593107\pi$
$152$	−18.0453	−1.46367
$153$	−28.2207	−2.28151
$154$	11.9234	0.960812
$155$	0	0
$156$	63.5368	5.08702
$157$	4.11273	0.328232	0.164116	−	0.986441i	$-0.447523\pi$
$157$	4.11273	0.328232	0.164116	+	0.986441i	$0.447523\pi$
$158$	−22.0181	−1.75166
$159$	−27.6050	−2.18922
$160$	0	0
$161$	−3.56551	−0.281001
$162$	63.1353	4.96038
$163$	−11.7512	−0.920423	−0.460211	−	0.887809i	$-0.652226\pi$
$163$	−11.7512	−0.920423	−0.460211	+	0.887809i	$0.652226\pi$
$164$	−9.06255	−0.707667
$165$	0	0
$166$	1.96579	0.152575
$167$	−21.6762	−1.67736	−0.838678	−	0.544628i	$-0.816671\pi$
$167$	−21.6762	−1.67736	−0.838678	+	0.544628i	$0.816671\pi$
$168$	17.6538	1.36202
$169$	19.4970	1.49977
$170$	0	0
$171$	−42.4236	−3.24422
$172$	30.7118	2.34175
$173$	−12.4853	−0.949241	−0.474621	−	0.880190i	$-0.657415\pi$
$173$	−12.4853	−0.949241	−0.474621	+	0.880190i	$0.657415\pi$
$174$	−61.4973	−4.66210
$175$	0	0
$176$	−2.48057	−0.186980
$177$	−6.40692	−0.481574
$178$	−14.3557	−1.07600
$179$	20.7357	1.54986	0.774929	−	0.632048i	$-0.217786\pi$
$179$	20.7357	1.54986	0.774929	+	0.632048i	$0.217786\pi$
$180$	0	0
$181$	−9.08366	−0.675183	−0.337591	−	0.941293i	$-0.609612\pi$
$181$	−9.08366	−0.675183	−0.337591	+	0.941293i	$0.609612\pi$
$182$	21.8567	1.62013
$183$	−36.6126	−2.70648
$184$	7.07999	0.521944
$185$	0	0
$186$	−40.3245	−2.95673
$187$	11.4024	0.833828
$188$	−7.84796	−0.572371
$189$	25.3263	1.84222
$190$	0	0
$191$	14.0981	1.02010	0.510051	−	0.860144i	$-0.329627\pi$
$191$	14.0981	1.02010	0.510051	+	0.860144i	$0.329627\pi$
$192$	40.9097	2.95240
$193$	−13.3588	−0.961589	−0.480794	−	0.876833i	$-0.659652\pi$
$193$	−13.3588	−0.961589	−0.480794	+	0.876833i	$0.659652\pi$
$194$	22.6516	1.62629
$195$	0	0
$196$	−14.5912	−1.04223
$197$	9.08734	0.647446	0.323723	−	0.946152i	$-0.395065\pi$
$197$	9.08734	0.647446	0.323723	+	0.946152i	$0.395065\pi$
$198$	−55.6613	−3.95568
$199$	−3.85757	−0.273456	−0.136728	−	0.990609i	$-0.543659\pi$
$199$	−3.85757	−0.273456	−0.136728	+	0.990609i	$0.543659\pi$
$200$	0	0
$201$	−4.69891	−0.331435
$202$	13.5709	0.954846
$203$	−13.3312	−0.935669
$204$	40.8663	2.86121
$205$	0	0
$206$	22.6388	1.57732
$207$	16.6447	1.15689
$208$	−4.54713	−0.315287
$209$	17.1411	1.18567
$210$	0	0
$211$	1.50996	0.103950	0.0519749	−	0.998648i	$-0.483448\pi$
$211$	1.50996	0.103950	0.0519749	+	0.998648i	$0.483448\pi$
$212$	28.7634	1.97548
$213$	49.7696	3.41016
$214$	16.8969	1.15505
$215$	0	0
$216$	−50.2902	−3.42181
$217$	−8.74143	−0.593407
$218$	12.0651	0.817153
$219$	−4.17091	−0.281844
$220$	0	0
$221$	20.9018	1.40601
$222$	−15.6504	−1.05039
$223$	14.9321	0.999926	0.499963	−	0.866047i	$-0.333347\pi$
$223$	14.9321	0.999926	0.499963	+	0.866047i	$0.333347\pi$
$224$	7.73723	0.516966
$225$	0	0
$226$	40.9620	2.72475
$227$	−17.7846	−1.18041	−0.590204	−	0.807254i	$-0.700953\pi$
$227$	−17.7846	−1.18041	−0.590204	+	0.807254i	$0.700953\pi$
$228$	61.4335	4.06853
$229$	20.6901	1.36724	0.683619	−	0.729839i	$-0.260405\pi$
$229$	20.6901	1.36724	0.683619	+	0.729839i	$0.260405\pi$
$230$	0	0
$231$	−16.7692	−1.10333
$232$	26.4717	1.73795
$233$	26.3174	1.72411	0.862055	−	0.506815i	$-0.169177\pi$
$233$	26.3174	1.72411	0.862055	+	0.506815i	$0.169177\pi$
$234$	−102.033	−6.67009
$235$	0	0
$236$	6.67578	0.434557
$237$	30.9666	2.01150
$238$	14.0580	0.911246
$239$	−9.56260	−0.618553	−0.309277	−	0.950972i	$-0.600087\pi$
$239$	−9.56260	−0.618553	−0.309277	+	0.950972i	$0.600087\pi$
$240$	0	0
$241$	3.19451	0.205776	0.102888	−	0.994693i	$-0.467192\pi$
$241$	3.19451	0.205776	0.102888	+	0.994693i	$0.467192\pi$
$242$	−3.09054	−0.198668
$243$	−42.7114	−2.73993
$244$	38.1490	2.44224
$245$	0	0
$246$	20.2260	1.28956
$247$	31.4213	1.99929
$248$	17.3578	1.10222
$249$	−2.76472	−0.175207
$250$	0	0
$251$	1.00000	0.0631194
$251$	1.00000	0.0631194
$252$	−43.2450	−2.72418
$253$	−6.72521	−0.422810
$254$	12.6803	0.795632
$255$	0	0
$256$	−20.8003	−1.30002
$257$	3.41197	0.212833	0.106416	−	0.994322i	$-0.466062\pi$
$257$	3.41197	0.212833	0.106416	+	0.994322i	$0.466062\pi$
$258$	−68.5432	−4.26731
$259$	−3.39266	−0.210809
$260$	0	0
$261$	62.2336	3.85216
$262$	−30.5451	−1.88708
$263$	1.39234	0.0858553	0.0429276	−	0.999078i	$-0.486332\pi$
$263$	1.39234	0.0858553	0.0429276	+	0.999078i	$0.486332\pi$
$264$	33.2984	2.04938
$265$	0	0
$266$	21.1332	1.29576
$267$	20.1900	1.23561
$268$	4.89609	0.299076
$269$	2.68252	0.163556	0.0817782	−	0.996651i	$-0.473940\pi$
$269$	2.68252	0.163556	0.0817782	+	0.996651i	$0.473940\pi$
$270$	0	0
$271$	7.75309	0.470967	0.235483	−	0.971878i	$-0.424333\pi$
$271$	7.75309	0.470967	0.235483	+	0.971878i	$0.424333\pi$
$272$	−2.92467	−0.177334
$273$	−30.7396	−1.86045
$274$	−12.8130	−0.774059
$275$	0	0
$276$	−24.1031	−1.45084
$277$	−12.5977	−0.756922	−0.378461	−	0.925617i	$-0.623547\pi$
$277$	−12.5977	−0.756922	−0.378461	+	0.925617i	$0.623547\pi$
$278$	43.8430	2.62953
$279$	40.8073	2.44307
$280$	0	0
$281$	29.8821	1.78262	0.891308	−	0.453399i	$-0.149789\pi$
$281$	29.8821	1.78262	0.891308	+	0.453399i	$0.149789\pi$
$282$	17.5152	1.04302
$283$	−0.431925	−0.0256753	−0.0128376	−	0.999918i	$-0.504086\pi$
$283$	−0.431925	−0.0256753	−0.0128376	+	0.999918i	$0.504086\pi$
$284$	−51.8581	−3.07721
$285$	0	0
$286$	41.2258	2.43773
$287$	4.38454	0.258811
$288$	−36.1194	−2.12836
$289$	−3.55617	−0.209187
$290$	0	0
$291$	−31.8576	−1.86752
$292$	4.34594	0.254327
$293$	12.7686	0.745949	0.372974	−	0.927842i	$-0.378338\pi$
$293$	12.7686	0.745949	0.372974	+	0.927842i	$0.378338\pi$
$294$	32.5649	1.89923
$295$	0	0
$296$	6.73676	0.391566
$297$	47.7701	2.77190
$298$	24.8211	1.43785
$299$	−12.3280	−0.712945
$300$	0	0
$301$	−14.8586	−0.856436
$302$	−16.4799	−0.948310
$303$	−19.0863	−1.09648
$304$	−4.39660	−0.252162
$305$	0	0
$306$	−65.6265	−3.75162
$307$	11.8932	0.678779	0.339390	−	0.940646i	$-0.389780\pi$
$307$	11.8932	0.678779	0.339390	+	0.940646i	$0.389780\pi$
$308$	17.4729	0.995611
$309$	−31.8395	−1.81129
$310$	0	0
$311$	31.6291	1.79352	0.896760	−	0.442517i	$-0.145914\pi$
$311$	31.6291	1.79352	0.896760	+	0.442517i	$0.145914\pi$
$312$	61.0393	3.45567
$313$	−13.4546	−0.760496	−0.380248	−	0.924884i	$-0.624161\pi$
$313$	−13.4546	−0.760496	−0.380248	+	0.924884i	$0.624161\pi$
$314$	9.56405	0.539731
$315$	0	0
$316$	−32.2661	−1.81511
$317$	7.42754	0.417172	0.208586	−	0.978004i	$-0.433114\pi$
$317$	7.42754	0.417172	0.208586	+	0.978004i	$0.433114\pi$
$318$	−64.1946	−3.59986
$319$	−25.1452	−1.40786
$320$	0	0
$321$	−23.7640	−1.32638
$322$	−8.29149	−0.462067
$323$	20.2099	1.12451
$324$	92.5207	5.14004
$325$	0	0
$326$	−27.3270	−1.51351
$327$	−16.9686	−0.938365
$328$	−8.70632	−0.480726
$329$	3.79690	0.209330
$330$	0	0
$331$	−22.5079	−1.23714	−0.618572	−	0.785728i	$-0.712289\pi$
$331$	−22.5079	−1.23714	−0.618572	+	0.785728i	$0.712289\pi$
$332$	2.88074	0.158101
$333$	15.8378	0.867906
$334$	−50.4075	−2.75817
$335$	0	0
$336$	4.30122	0.234651
$337$	−12.2271	−0.666055	−0.333028	−	0.942917i	$-0.608070\pi$
$337$	−12.2271	−0.666055	−0.333028	+	0.942917i	$0.608070\pi$
$338$	45.3399	2.46616
$339$	−57.6097	−3.12893
$340$	0	0
$341$	−16.4880	−0.892874
$342$	−98.6551	−5.33466
$343$	18.6005	1.00433
$344$	29.5046	1.59078
$345$	0	0
$346$	−29.0343	−1.56089
$347$	20.3626	1.09312	0.546562	−	0.837419i	$-0.315936\pi$
$347$	20.3626	1.09312	0.546562	+	0.837419i	$0.315936\pi$
$348$	−90.1203	−4.83095
$349$	−19.3805	−1.03742	−0.518708	−	0.854951i	$-0.673587\pi$
$349$	−19.3805	−1.03742	−0.518708	+	0.854951i	$0.673587\pi$
$350$	0	0
$351$	87.5674	4.67400
$352$	14.5939	0.777856
$353$	16.3547	0.870472	0.435236	−	0.900316i	$-0.356665\pi$
$353$	16.3547	0.870472	0.435236	+	0.900316i	$0.356665\pi$
$354$	−14.8991	−0.791880
$355$	0	0
$356$	−21.0373	−1.11497
$357$	−19.7714	−1.04642
$358$	48.2203	2.54852
$359$	−10.3782	−0.547740	−0.273870	−	0.961767i	$-0.588304\pi$
$359$	−10.3782	−0.547740	−0.273870	+	0.961767i	$0.588304\pi$
$360$	0	0
$361$	11.3811	0.599005
$362$	−21.1238	−1.11024
$363$	4.34659	0.228137
$364$	32.0296	1.67881
$365$	0	0
$366$	−85.1416	−4.45042
$367$	−27.6014	−1.44078	−0.720390	−	0.693569i	$-0.756037\pi$
$367$	−27.6014	−1.44078	−0.720390	+	0.693569i	$0.756037\pi$
$368$	1.72499	0.0899211
$369$	−20.4681	−1.06553
$370$	0	0
$371$	−13.9159	−0.722480
$372$	−59.0929	−3.06382
$373$	−22.3855	−1.15908	−0.579538	−	0.814945i	$-0.696767\pi$
$373$	−22.3855	−1.15908	−0.579538	+	0.814945i	$0.696767\pi$
$374$	26.5161	1.37111
$375$	0	0
$376$	−7.53947	−0.388819
$377$	−46.0936	−2.37394
$378$	58.8957	3.02927
$379$	13.7898	0.708337	0.354168	−	0.935182i	$-0.384764\pi$
$379$	13.7898	0.708337	0.354168	+	0.935182i	$0.384764\pi$
$380$	0	0
$381$	−17.8338	−0.913651
$382$	32.7847	1.67741
$383$	14.4938	0.740600	0.370300	−	0.928912i	$-0.379255\pi$
$383$	14.4938	0.740600	0.370300	+	0.928912i	$0.379255\pi$
$384$	64.4378	3.28833
$385$	0	0
$386$	−31.0656	−1.58120
$387$	69.3639	3.52596
$388$	33.1944	1.68519
$389$	6.42004	0.325509	0.162755	−	0.986667i	$-0.447962\pi$
$389$	6.42004	0.325509	0.162755	+	0.986667i	$0.447962\pi$
$390$	0	0
$391$	−7.92924	−0.400999
$392$	−14.0177	−0.707999
$393$	42.9591	2.16700
$394$	21.1324	1.06463
$395$	0	0
$396$	−81.5680	−4.09895
$397$	20.9700	1.05245	0.526227	−	0.850344i	$-0.323606\pi$
$397$	20.9700	1.05245	0.526227	+	0.850344i	$0.323606\pi$
$398$	−8.97069	−0.449660
$399$	−29.7220	−1.48796
$400$	0	0
$401$	4.95098	0.247240	0.123620	−	0.992330i	$-0.460550\pi$
$401$	4.95098	0.247240	0.123620	+	0.992330i	$0.460550\pi$
$402$	−10.9272	−0.544998
$403$	−30.2241	−1.50557
$404$	19.8873	0.989430
$405$	0	0
$406$	−31.0014	−1.53858
$407$	−6.39918	−0.317196
$408$	39.2599	1.94366
$409$	27.6111	1.36528	0.682640	−	0.730755i	$-0.260832\pi$
$409$	27.6111	1.36528	0.682640	+	0.730755i	$0.260832\pi$
$410$	0	0
$411$	18.0203	0.888878
$412$	33.1756	1.63445
$413$	−3.22980	−0.158928
$414$	38.7068	1.90234
$415$	0	0
$416$	26.7520	1.31163
$417$	−61.6615	−3.01958
$418$	39.8611	1.94967
$419$	18.0724	0.882894	0.441447	−	0.897287i	$-0.354465\pi$
$419$	18.0724	0.882894	0.441447	+	0.897287i	$0.354465\pi$
$420$	0	0
$421$	30.9507	1.50844	0.754221	−	0.656620i	$-0.228015\pi$
$421$	30.9507	1.50844	0.754221	+	0.656620i	$0.228015\pi$
$422$	3.51137	0.170931
$423$	−17.7249	−0.861816
$424$	27.6328	1.34197
$425$	0	0
$426$	115.738	5.60752
$427$	−18.4568	−0.893186
$428$	24.7613	1.19688
$429$	−57.9807	−2.79933
$430$	0	0
$431$	−11.5470	−0.556200	−0.278100	−	0.960552i	$-0.589705\pi$
$431$	−11.5470	−0.556200	−0.278100	+	0.960552i	$0.589705\pi$
$432$	−12.2528	−0.589514
$433$	−4.80347	−0.230840	−0.115420	−	0.993317i	$-0.536821\pi$
$433$	−4.80347	−0.230840	−0.115420	+	0.993317i	$0.536821\pi$
$434$	−20.3280	−0.975774
$435$	0	0
$436$	17.6807	0.846750
$437$	−11.9199	−0.570205
$438$	−9.69935	−0.463453
$439$	−0.351852	−0.0167930	−0.00839648	−	0.999965i	$-0.502673\pi$
$439$	−0.351852	−0.0167930	−0.00839648	+	0.999965i	$0.502673\pi$
$440$	0	0
$441$	−32.9548	−1.56928
$442$	48.6066	2.31198
$443$	−27.4634	−1.30483	−0.652413	−	0.757864i	$-0.726243\pi$
$443$	−27.4634	−1.30483	−0.652413	+	0.757864i	$0.726243\pi$
$444$	−22.9347	−1.08843
$445$	0	0
$446$	34.7242	1.64424
$447$	−34.9087	−1.65113
$448$	20.6230	0.974345
$449$	−17.3344	−0.818061	−0.409031	−	0.912521i	$-0.634133\pi$
$449$	−17.3344	−0.818061	−0.409031	+	0.912521i	$0.634133\pi$
$450$	0	0
$451$	8.27005	0.389422
$452$	60.0272	2.82344
$453$	23.1776	1.08898
$454$	−41.3577	−1.94101
$455$	0	0
$456$	59.0187	2.76380
$457$	−26.9250	−1.25950	−0.629749	−	0.776799i	$-0.716842\pi$
$457$	−26.9250	−1.25950	−0.629749	+	0.776799i	$0.716842\pi$
$458$	48.1142	2.24823
$459$	56.3225	2.62891
$460$	0	0
$461$	3.38583	0.157694	0.0788468	−	0.996887i	$-0.474876\pi$
$461$	3.38583	0.157694	0.0788468	+	0.996887i	$0.474876\pi$
$462$	−38.9964	−1.81427
$463$	8.86389	0.411940	0.205970	−	0.978558i	$-0.433965\pi$
$463$	8.86389	0.411940	0.205970	+	0.978558i	$0.433965\pi$
$464$	6.44962	0.299416
$465$	0	0
$466$	61.2004	2.83506
$467$	6.12549	0.283454	0.141727	−	0.989906i	$-0.454735\pi$
$467$	6.12549	0.283454	0.141727	+	0.989906i	$0.454735\pi$
$468$	−149.522	−6.91167
$469$	−2.36877	−0.109380
$470$	0	0
$471$	−13.4510	−0.619791
$472$	6.41337	0.295200
$473$	−28.0261	−1.28864
$474$	72.0120	3.30762
$475$	0	0
$476$	20.6011	0.944251
$477$	64.9632	2.97446
$478$	−22.2376	−1.01712
$479$	−2.51387	−0.114862	−0.0574308	−	0.998349i	$-0.518291\pi$
$479$	−2.51387	−0.114862	−0.0574308	+	0.998349i	$0.518291\pi$
$480$	0	0
$481$	−11.7303	−0.534858
$482$	7.42875	0.338370
$483$	11.6613	0.530607
$484$	−4.52899	−0.205863
$485$	0	0
$486$	−99.3242	−4.50544
$487$	−7.32964	−0.332138	−0.166069	−	0.986114i	$-0.553107\pi$
$487$	−7.32964	−0.332138	−0.166069	+	0.986114i	$0.553107\pi$
$488$	36.6494	1.65904
$489$	38.4332	1.73801
$490$	0	0
$491$	−10.2215	−0.461291	−0.230646	−	0.973038i	$-0.574084\pi$
$491$	−10.2215	−0.461291	−0.230646	+	0.973038i	$0.574084\pi$
$492$	29.6399	1.33627
$493$	−29.6470	−1.33523
$494$	73.0694	3.28755
$495$	0	0
$496$	4.22909	0.189892
$497$	25.0894	1.12541
$498$	−6.42928	−0.288103
$499$	−26.3537	−1.17975	−0.589876	−	0.807494i	$-0.700823\pi$
$499$	−26.3537	−1.17975	−0.589876	+	0.807494i	$0.700823\pi$
$500$	0	0
$501$	70.8939	3.16730
$502$	2.32547	0.103791
$503$	−4.42095	−0.197120	−0.0985602	−	0.995131i	$-0.531424\pi$
$503$	−4.42095	−0.197120	−0.0985602	+	0.995131i	$0.531424\pi$
$504$	−41.5451	−1.85057
$505$	0	0
$506$	−15.6393	−0.695252
$507$	−63.7667	−2.83198
$508$	18.5821	0.824449
$509$	19.3043	0.855647	0.427824	−	0.903862i	$-0.359280\pi$
$509$	19.3043	0.855647	0.427824	+	0.903862i	$0.359280\pi$
$510$	0	0
$511$	−2.10260	−0.0930135
$512$	−8.96612	−0.396250
$513$	84.6686	3.73821
$514$	7.93445	0.349974
$515$	0	0
$516$	−100.446	−4.42187
$517$	7.16167	0.314970
$518$	−7.88954	−0.346646
$519$	40.8343	1.79243
$520$	0	0
$521$	16.8838	0.739691	0.369846	−	0.929093i	$-0.379411\pi$
$521$	16.8838	0.739691	0.369846	+	0.929093i	$0.379411\pi$
$522$	144.723	6.33434
$523$	37.7621	1.65122	0.825610	−	0.564241i	$-0.190831\pi$
$523$	37.7621	1.65122	0.825610	+	0.564241i	$0.190831\pi$
$524$	−44.7619	−1.95543
$525$	0	0
$526$	3.23785	0.141177
$527$	−19.4399	−0.846813
$528$	8.11291	0.353069
$529$	−18.3233	−0.796665
$530$	0	0
$531$	15.0775	0.654309
$532$	30.9693	1.34269
$533$	15.1598	0.656645
$534$	46.9514	2.03179
$535$	0	0
$536$	4.70364	0.203166
$537$	−67.8178	−2.92655
$538$	6.23814	0.268945
$539$	13.3152	0.573528
$540$	0	0
$541$	2.51970	0.108330	0.0541652	−	0.998532i	$-0.482750\pi$
$541$	2.51970	0.108330	0.0541652	+	0.998532i	$0.482750\pi$
$542$	18.0296	0.774439
$543$	29.7089	1.27493
$544$	17.2066	0.737729
$545$	0	0
$546$	−71.4842	−3.05924
$547$	14.7422	0.630331	0.315165	−	0.949037i	$-0.397940\pi$
$547$	14.7422	0.630331	0.315165	+	0.949037i	$0.397940\pi$
$548$	−18.7766	−0.802095
$549$	86.1610	3.67726
$550$	0	0
$551$	−44.5678	−1.89865
$552$	−23.1557	−0.985572
$553$	15.6106	0.663829
$554$	−29.2956	−1.24465
$555$	0	0
$556$	64.2491	2.72477
$557$	−2.32712	−0.0986035	−0.0493017	−	0.998784i	$-0.515700\pi$
$557$	−2.32712	−0.0986035	−0.0493017	+	0.998784i	$0.515700\pi$
$558$	94.8963	4.01728
$559$	−51.3747	−2.17292
$560$	0	0
$561$	−37.2926	−1.57450
$562$	69.4900	2.93126
$563$	10.1209	0.426546	0.213273	−	0.976993i	$-0.431588\pi$
$563$	10.1209	0.426546	0.213273	+	0.976993i	$0.431588\pi$
$564$	25.6674	1.08079
$565$	0	0
$566$	−1.00443	−0.0422193
$567$	−44.7622	−1.87984
$568$	−49.8197	−2.09039
$569$	4.70511	0.197249	0.0986243	−	0.995125i	$-0.468556\pi$
$569$	4.70511	0.197249	0.0986243	+	0.995125i	$0.468556\pi$
$570$	0	0
$571$	−19.6052	−0.820454	−0.410227	−	0.911984i	$-0.634550\pi$
$571$	−19.6052	−0.820454	−0.410227	+	0.911984i	$0.634550\pi$
$572$	60.4138	2.52603
$573$	−46.1090	−1.92623
$574$	10.1961	0.425578
$575$	0	0
$576$	−96.2735	−4.01139
$577$	−4.76106	−0.198205	−0.0991027	−	0.995077i	$-0.531597\pi$
$577$	−4.76106	−0.198205	−0.0991027	+	0.995077i	$0.531597\pi$
$578$	−8.26979	−0.343978
$579$	43.6911	1.81574
$580$	0	0
$581$	−1.39372	−0.0578214
$582$	−74.0840	−3.07088
$583$	−26.2481	−1.08708
$584$	4.17511	0.172767
$585$	0	0
$586$	29.6930	1.22661
$587$	−27.5881	−1.13868	−0.569341	−	0.822102i	$-0.692801\pi$
$587$	−27.5881	−1.13868	−0.569341	+	0.822102i	$0.692801\pi$
$588$	47.7218	1.96801
$589$	−29.2236	−1.20414
$590$	0	0
$591$	−29.7209	−1.22256
$592$	1.64136	0.0674596
$593$	35.9409	1.47592	0.737958	−	0.674846i	$-0.235790\pi$
$593$	35.9409	1.47592	0.737958	+	0.674846i	$0.235790\pi$
$594$	111.088	4.55801
$595$	0	0
$596$	36.3737	1.48992
$597$	12.6165	0.516360
$598$	−28.6684	−1.17234
$599$	−45.1866	−1.84627	−0.923137	−	0.384471i	$-0.874384\pi$
$599$	−45.1866	−1.84627	−0.923137	+	0.384471i	$0.874384\pi$
$600$	0	0
$601$	−0.413871	−0.0168822	−0.00844108	−	0.999964i	$-0.502687\pi$
$601$	−0.413871	−0.0168822	−0.00844108	+	0.999964i	$0.502687\pi$
$602$	−34.5533	−1.40829
$603$	11.0580	0.450317
$604$	−24.1502	−0.982657
$605$	0	0
$606$	−44.3848	−1.80301
$607$	−21.6716	−0.879624	−0.439812	−	0.898090i	$-0.644955\pi$
$607$	−21.6716	−0.879624	−0.439812	+	0.898090i	$0.644955\pi$
$608$	25.8664	1.04902
$609$	43.6009	1.76680
$610$	0	0
$611$	13.1281	0.531104
$612$	−96.1713	−3.88750
$613$	−0.169735	−0.00685555	−0.00342777	−	0.999994i	$-0.501091\pi$
$613$	−0.169735	−0.00685555	−0.00342777	+	0.999994i	$0.501091\pi$
$614$	27.6573	1.11616
$615$	0	0
$616$	16.7861	0.676331
$617$	−27.3815	−1.10234	−0.551169	−	0.834394i	$-0.685818\pi$
$617$	−27.3815	−1.10234	−0.551169	+	0.834394i	$0.685818\pi$
$618$	−74.0420	−2.97841
$619$	−34.2960	−1.37847	−0.689237	−	0.724536i	$-0.742054\pi$
$619$	−34.2960	−1.37847	−0.689237	+	0.724536i	$0.742054\pi$
$620$	0	0
$621$	−33.2193	−1.33305
$622$	73.5526	2.94919
$623$	10.1780	0.407773
$624$	14.8718	0.595348
$625$	0	0
$626$	−31.2882	−1.25053
$627$	−56.0613	−2.23887
$628$	14.0155	0.559279
$629$	−7.54484	−0.300833
$630$	0	0
$631$	−13.3011	−0.529509	−0.264755	−	0.964316i	$-0.585291\pi$
$631$	−13.3011	−0.529509	−0.264755	+	0.964316i	$0.585291\pi$
$632$	−30.9978	−1.23302
$633$	−4.93845	−0.196286
$634$	17.2726	0.685981
$635$	0	0
$636$	−94.0731	−3.73024
$637$	24.4082	0.967086
$638$	−58.4745	−2.31503
$639$	−117.124	−4.63334
$640$	0	0
$641$	−29.6261	−1.17016	−0.585080	−	0.810975i	$-0.698937\pi$
$641$	−29.6261	−1.17016	−0.585080	+	0.810975i	$0.698937\pi$
$642$	−55.2627	−2.18104
$643$	−26.9409	−1.06245	−0.531224	−	0.847232i	$-0.678268\pi$
$643$	−26.9409	−1.06245	−0.531224	+	0.847232i	$0.678268\pi$
$644$	−12.1506	−0.478802
$645$	0	0
$646$	46.9975	1.84909
$647$	−16.1051	−0.633157	−0.316579	−	0.948566i	$-0.602534\pi$
$647$	−16.1051	−0.633157	−0.316579	+	0.948566i	$0.602534\pi$
$648$	88.8839	3.49169
$649$	−6.09200	−0.239132
$650$	0	0
$651$	28.5896	1.12051
$652$	−40.0460	−1.56832
$653$	28.4743	1.11429	0.557143	−	0.830417i	$-0.311898\pi$
$653$	28.4743	1.11429	0.557143	+	0.830417i	$0.311898\pi$
$654$	−39.4600	−1.54301
$655$	0	0
$656$	−2.12123	−0.0828201
$657$	9.81548	0.382938
$658$	8.82960	0.344214
$659$	5.65381	0.220241	0.110121	−	0.993918i	$-0.464876\pi$
$659$	5.65381	0.220241	0.110121	+	0.993918i	$0.464876\pi$
$660$	0	0
$661$	−16.9478	−0.659191	−0.329596	−	0.944122i	$-0.606912\pi$
$661$	−16.9478	−0.659191	−0.329596	+	0.944122i	$0.606912\pi$
$662$	−52.3415	−2.03431
$663$	−68.3611	−2.65492
$664$	2.76750	0.107400
$665$	0	0
$666$	36.8304	1.42715
$667$	17.4859	0.677058
$668$	−73.8689	−2.85807
$669$	−48.8367	−1.88813
$670$	0	0
$671$	−34.8129	−1.34394
$672$	−25.3053	−0.976173
$673$	−18.6054	−0.717184	−0.358592	−	0.933494i	$-0.616743\pi$
$673$	−18.6054	−0.717184	−0.358592	+	0.933494i	$0.616743\pi$
$674$	−28.4339	−1.09523
$675$	0	0
$676$	66.4426	2.55549
$677$	−31.7825	−1.22150	−0.610751	−	0.791823i	$-0.709132\pi$
$677$	−31.7825	−1.22150	−0.610751	+	0.791823i	$0.709132\pi$
$678$	−133.970	−5.14508
$679$	−16.0597	−0.616316
$680$	0	0
$681$	58.1661	2.22893
$682$	−38.3424	−1.46821
$683$	23.0817	0.883196	0.441598	−	0.897213i	$-0.354412\pi$
$683$	23.0817	0.883196	0.441598	+	0.897213i	$0.354412\pi$
$684$	−144.573	−5.52787
$685$	0	0
$686$	43.2550	1.65148
$687$	−67.6686	−2.58172
$688$	7.18857	0.274062
$689$	−48.1153	−1.83305
$690$	0	0
$691$	22.4796	0.855164	0.427582	−	0.903976i	$-0.359365\pi$
$691$	22.4796	0.855164	0.427582	+	0.903976i	$0.359365\pi$
$692$	−42.5479	−1.61743
$693$	39.4633	1.49909
$694$	47.3528	1.79749
$695$	0	0
$696$	−86.5779	−3.28173
$697$	9.75066	0.369332
$698$	−45.0689	−1.70588
$699$	−86.0733	−3.25559
$700$	0	0
$701$	30.5570	1.15412	0.577061	−	0.816701i	$-0.304200\pi$
$701$	30.5570	1.15412	0.577061	+	0.816701i	$0.304200\pi$
$702$	203.636	7.68574
$703$	−11.3420	−0.427773
$704$	38.8988	1.46605
$705$	0	0
$706$	38.0324	1.43137
$707$	−9.62163	−0.361859
$708$	−21.8337	−0.820562
$709$	44.9477	1.68805	0.844024	−	0.536306i	$-0.180181\pi$
$709$	44.9477	1.68805	0.844024	+	0.536306i	$0.180181\pi$
$710$	0	0
$711$	−72.8742	−2.73300
$712$	−20.2104	−0.757415
$713$	11.4657	0.429395
$714$	−45.9780	−1.72068
$715$	0	0
$716$	70.6637	2.64083
$717$	31.2753	1.16800
$718$	−24.1342	−0.900681
$719$	−28.4208	−1.05992	−0.529959	−	0.848023i	$-0.677793\pi$
$719$	−28.4208	−1.05992	−0.529959	+	0.848023i	$0.677793\pi$
$720$	0	0
$721$	−16.0506	−0.597757
$722$	26.4665	0.984980
$723$	−10.4479	−0.388562
$724$	−30.9556	−1.15045
$725$	0	0
$726$	10.1079	0.375139
$727$	5.26092	0.195117	0.0975583	−	0.995230i	$-0.468897\pi$
$727$	5.26092	0.195117	0.0975583	+	0.995230i	$0.468897\pi$
$728$	30.7706	1.14043
$729$	58.2429	2.15714
$730$	0	0
$731$	−33.0437	−1.22217
$732$	−124.770	−4.61161
$733$	43.5916	1.61009	0.805046	−	0.593212i	$-0.202140\pi$
$733$	43.5916	1.61009	0.805046	+	0.593212i	$0.202140\pi$
$734$	−64.1863	−2.36916
$735$	0	0
$736$	−10.1486	−0.374081
$737$	−4.46794	−0.164579
$738$	−47.5981	−1.75211
$739$	42.5955	1.56690	0.783450	−	0.621455i	$-0.213458\pi$
$739$	42.5955	1.56690	0.783450	+	0.621455i	$0.213458\pi$
$740$	0	0
$741$	−102.766	−3.77520
$742$	−32.3612	−1.18802
$743$	9.80687	0.359779	0.179890	−	0.983687i	$-0.442426\pi$
$743$	9.80687	0.359779	0.179890	+	0.983687i	$0.442426\pi$
$744$	−56.7701	−2.08129
$745$	0	0
$746$	−52.0569	−1.90594
$747$	6.50626	0.238052
$748$	38.8576	1.42077
$749$	−11.9797	−0.437729
$750$	0	0
$751$	10.5643	0.385498	0.192749	−	0.981248i	$-0.438260\pi$
$751$	10.5643	0.385498	0.192749	+	0.981248i	$0.438260\pi$
$752$	−1.83694	−0.0669862
$753$	−3.27059	−0.119187
$754$	−107.190	−3.90361
$755$	0	0
$756$	86.3078	3.13898
$757$	−20.0840	−0.729967	−0.364983	−	0.931014i	$-0.618925\pi$
$757$	−20.0840	−0.729967	−0.364983	+	0.931014i	$0.618925\pi$
$758$	32.0679	1.16476
$759$	21.9954	0.798381
$760$	0	0
$761$	3.99080	0.144666	0.0723332	−	0.997381i	$-0.476955\pi$
$761$	3.99080	0.144666	0.0723332	+	0.997381i	$0.476955\pi$
$762$	−41.4719	−1.50237
$763$	−8.55404	−0.309677
$764$	48.0439	1.73817
$765$	0	0
$766$	33.7050	1.21781
$767$	−11.1672	−0.403226
$768$	68.0291	2.45479
$769$	36.1597	1.30395	0.651977	−	0.758239i	$-0.273940\pi$
$769$	36.1597	1.30395	0.651977	+	0.758239i	$0.273940\pi$
$770$	0	0
$771$	−11.1591	−0.401887
$772$	−45.5246	−1.63847
$773$	−6.56902	−0.236271	−0.118136	−	0.992997i	$-0.537692\pi$
$773$	−6.56902	−0.236271	−0.118136	+	0.992997i	$0.537692\pi$
$774$	161.304	5.79795
$775$	0	0
$776$	31.8896	1.14477
$777$	11.0960	0.398066
$778$	14.9296	0.535254
$779$	14.6580	0.525177
$780$	0	0
$781$	47.3232	1.69336
$782$	−18.4392	−0.659386
$783$	−124.205	−4.43873
$784$	−3.41530	−0.121975
$785$	0	0
$786$	99.9004	3.56333
$787$	−29.4650	−1.05032	−0.525158	−	0.851005i	$-0.675994\pi$
$787$	−29.4650	−1.05032	−0.525158	+	0.851005i	$0.675994\pi$
$788$	30.9681	1.10319
$789$	−4.55376	−0.162118
$790$	0	0
$791$	−29.0416	−1.03260
$792$	−78.3618	−2.78447
$793$	−63.8156	−2.26616
$794$	48.7652	1.73061
$795$	0	0
$796$	−13.1460	−0.465946
$797$	−6.50783	−0.230519	−0.115260	−	0.993335i	$-0.536770\pi$
$797$	−6.50783	−0.230519	−0.115260	+	0.993335i	$0.536770\pi$
$798$	−69.1178	−2.44674
$799$	8.44384	0.298722
$800$	0	0
$801$	−47.5136	−1.67881
$802$	11.5134	0.406551
$803$	−3.96590	−0.139953
$804$	−16.0131	−0.564738
$805$	0	0
$806$	−70.2854	−2.47570
$807$	−8.77342	−0.308839
$808$	19.1056	0.672131
$809$	−53.0190	−1.86405	−0.932024	−	0.362396i	$-0.881959\pi$
$809$	−53.0190	−1.86405	−0.932024	+	0.362396i	$0.881959\pi$
$810$	0	0
$811$	48.3467	1.69768	0.848841	−	0.528649i	$-0.177301\pi$
$811$	48.3467	1.69768	0.848841	+	0.528649i	$0.177301\pi$
$812$	−45.4306	−1.59430
$813$	−25.3572	−0.889314
$814$	−14.8811	−0.521584
$815$	0	0
$816$	9.56538	0.334855
$817$	−49.6740	−1.73787
$818$	64.2088	2.24501
$819$	72.3401	2.52777
$820$	0	0
$821$	−21.8086	−0.761126	−0.380563	−	0.924755i	$-0.624270\pi$
$821$	−21.8086	−0.761126	−0.380563	+	0.924755i	$0.624270\pi$
$822$	41.9059	1.46163
$823$	−21.5799	−0.752228	−0.376114	−	0.926573i	$-0.622740\pi$
$823$	−21.5799	−0.752228	−0.376114	+	0.926573i	$0.622740\pi$
$824$	31.8716	1.11030
$825$	0	0
$826$	−7.51081	−0.261335
$827$	14.4586	0.502776	0.251388	−	0.967886i	$-0.419113\pi$
$827$	14.4586	0.502776	0.251388	+	0.967886i	$0.419113\pi$
$828$	56.7223	1.97124
$829$	27.7926	0.965278	0.482639	−	0.875819i	$-0.339678\pi$
$829$	27.7926	0.965278	0.482639	+	0.875819i	$0.339678\pi$
$830$	0	0
$831$	41.2018	1.42928
$832$	71.3054	2.47207
$833$	15.6991	0.543941
$834$	−143.392	−4.96527
$835$	0	0
$836$	58.4138	2.02029
$837$	−81.4427	−2.81507
$838$	42.0269	1.45179
$839$	−3.64173	−0.125726	−0.0628632	−	0.998022i	$-0.520023\pi$
$839$	−3.64173	−0.125726	−0.0628632	+	0.998022i	$0.520023\pi$
$840$	0	0
$841$	36.3789	1.25445
$842$	71.9750	2.48042
$843$	−97.7319	−3.36606
$844$	5.14569	0.177122
$845$	0	0
$846$	−41.2189	−1.41713
$847$	2.19116	0.0752892
$848$	6.73251	0.231195
$849$	1.41265	0.0484819
$850$	0	0
$851$	4.44999	0.152544
$852$	169.606	5.81062
$853$	27.1135	0.928348	0.464174	−	0.885744i	$-0.346351\pi$
$853$	27.1135	0.928348	0.464174	+	0.885744i	$0.346351\pi$
$854$	−42.9208	−1.46872
$855$	0	0
$856$	23.7880	0.813056
$857$	27.9166	0.953611	0.476806	−	0.879009i	$-0.341795\pi$
$857$	27.9166	0.953611	0.476806	+	0.879009i	$0.341795\pi$
$858$	−134.833	−4.60311
$859$	−15.0626	−0.513930	−0.256965	−	0.966421i	$-0.582723\pi$
$859$	−15.0626	−0.513930	−0.256965	+	0.966421i	$0.582723\pi$
$860$	0	0
$861$	−14.3400	−0.488706
$862$	−26.8523	−0.914593
$863$	−25.5073	−0.868278	−0.434139	−	0.900846i	$-0.642947\pi$
$863$	−25.5073	−0.868278	−0.434139	+	0.900846i	$0.642947\pi$
$864$	72.0867	2.45244
$865$	0	0
$866$	−11.1704	−0.379584
$867$	11.6308	0.395002
$868$	−29.7893	−1.01112
$869$	29.4445	0.998835
$870$	0	0
$871$	−8.19017	−0.277513
$872$	16.9857	0.575207
$873$	74.9710	2.53738
$874$	−27.7194	−0.937622
$875$	0	0
$876$	−14.2138	−0.480239
$877$	1.61233	0.0544444	0.0272222	−	0.999629i	$-0.491334\pi$
$877$	1.61233	0.0544444	0.0272222	+	0.999629i	$0.491334\pi$
$878$	−0.818222	−0.0276137
$879$	−41.7607	−1.40855
$880$	0	0
$881$	45.6924	1.53942	0.769708	−	0.638396i	$-0.220402\pi$
$881$	45.6924	1.53942	0.769708	+	0.638396i	$0.220402\pi$
$882$	−76.6356	−2.58046
$883$	45.1799	1.52042	0.760212	−	0.649675i	$-0.225095\pi$
$883$	45.1799	1.52042	0.760212	+	0.649675i	$0.225095\pi$
$884$	71.2298	2.39572
$885$	0	0
$886$	−63.8655	−2.14560
$887$	4.42422	0.148551	0.0742754	−	0.997238i	$-0.476336\pi$
$887$	4.42422	0.148551	0.0742754	+	0.997238i	$0.476336\pi$
$888$	−22.0332	−0.739384
$889$	−8.99018	−0.301521
$890$	0	0
$891$	−84.4299	−2.82851
$892$	50.8860	1.70379
$893$	12.6935	0.424771
$894$	−81.1794	−2.71505
$895$	0	0
$896$	32.4838	1.08521
$897$	40.3197	1.34624
$898$	−40.3107	−1.34519
$899$	42.8697	1.42978
$900$	0	0
$901$	−30.9473	−1.03100
$902$	19.2318	0.640349
$903$	48.5964	1.61719
$904$	57.6677	1.91800
$905$	0	0
$906$	53.8988	1.79067
$907$	4.03789	0.134076	0.0670380	−	0.997750i	$-0.478645\pi$
$907$	4.03789	0.134076	0.0670380	+	0.997750i	$0.478645\pi$
$908$	−60.6070	−2.01131
$909$	44.9162	1.48978
$910$	0	0
$911$	17.3439	0.574629	0.287314	−	0.957836i	$-0.407238\pi$
$911$	17.3439	0.574629	0.287314	+	0.957836i	$0.407238\pi$
$912$	14.3795	0.476152
$913$	−2.62882	−0.0870013
$914$	−62.6134	−2.07107
$915$	0	0
$916$	70.5083	2.32966
$917$	21.6561	0.715149
$918$	130.977	4.32287
$919$	−52.7790	−1.74102	−0.870510	−	0.492151i	$-0.836211\pi$
$919$	−52.7790	−1.74102	−0.870510	+	0.492151i	$0.836211\pi$
$920$	0	0
$921$	−38.8976	−1.28172
$922$	7.87365	0.259305
$923$	86.7482	2.85535
$924$	−57.1466	−1.87999
$925$	0	0
$926$	20.6127	0.677377
$927$	74.9285	2.46098
$928$	−37.9449	−1.24560
$929$	3.77741	0.123933	0.0619664	−	0.998078i	$-0.480263\pi$
$929$	3.77741	0.123933	0.0619664	+	0.998078i	$0.480263\pi$
$930$	0	0
$931$	23.6002	0.773464
$932$	89.6853	2.93774
$933$	−103.446	−3.38666
$934$	14.2447	0.466100
$935$	0	0
$936$	−143.645	−4.69518
$937$	−43.9367	−1.43535	−0.717674	−	0.696379i	$-0.754793\pi$
$937$	−43.9367	−1.43535	−0.717674	+	0.696379i	$0.754793\pi$
$938$	−5.50851	−0.179859
$939$	44.0043	1.43603
$940$	0	0
$941$	−18.4606	−0.601799	−0.300900	−	0.953656i	$-0.597287\pi$
$941$	−18.4606	−0.601799	−0.300900	+	0.953656i	$0.597287\pi$
$942$	−31.2800	−1.01916
$943$	−5.75099	−0.187278
$944$	1.56257	0.0508573
$945$	0	0
$946$	−65.1740	−2.11899
$947$	−25.9437	−0.843058	−0.421529	−	0.906815i	$-0.638506\pi$
$947$	−25.9437	−0.843058	−0.421529	+	0.906815i	$0.638506\pi$
$948$	105.529	3.42742
$949$	−7.26988	−0.235990
$950$	0	0
$951$	−24.2924	−0.787736
$952$	19.7913	0.641441
$953$	17.8588	0.578504	0.289252	−	0.957253i	$-0.406593\pi$
$953$	17.8588	0.578504	0.289252	+	0.957253i	$0.406593\pi$
$954$	151.070	4.89108
$955$	0	0
$956$	−32.5877	−1.05396
$957$	82.2395	2.65842
$958$	−5.84594	−0.188874
$959$	9.08425	0.293346
$960$	0	0
$961$	−2.88986	−0.0932212
$962$	−27.2786	−0.879498
$963$	55.9243	1.80214
$964$	10.8864	0.350626
$965$	0	0
$966$	27.1180	0.872508
$967$	−46.3753	−1.49133	−0.745665	−	0.666321i	$-0.767868\pi$
$967$	−46.3753	−1.49133	−0.745665	+	0.666321i	$0.767868\pi$
$968$	−4.35096	−0.139845
$969$	−66.0981	−2.12338
$970$	0	0
$971$	27.0517	0.868130	0.434065	−	0.900882i	$-0.357079\pi$
$971$	27.0517	0.868130	0.434065	+	0.900882i	$0.357079\pi$
$972$	−145.553	−4.66862
$973$	−31.0842	−0.996514
$974$	−17.0449	−0.546153
$975$	0	0
$976$	8.92936	0.285822
$977$	32.7363	1.04733	0.523664	−	0.851925i	$-0.324565\pi$
$977$	32.7363	1.04733	0.523664	+	0.851925i	$0.324565\pi$
$978$	89.3754	2.85791
$979$	19.1976	0.613559
$980$	0	0
$981$	39.9325	1.27495
$982$	−23.7699	−0.758529
$983$	−39.5638	−1.26189	−0.630944	−	0.775828i	$-0.717332\pi$
$983$	−39.5638	−1.26189	−0.630944	+	0.775828i	$0.717332\pi$
$984$	28.4748	0.907743
$985$	0	0
$986$	−68.9433	−2.19560
$987$	−12.4181	−0.395272
$988$	107.078	3.40662
$989$	19.4893	0.619725
$990$	0	0
$991$	9.80219	0.311377	0.155688	−	0.987806i	$-0.450240\pi$
$991$	9.80219	0.311377	0.155688	+	0.987806i	$0.450240\pi$
$992$	−24.8809	−0.789969
$993$	73.6139	2.33607
$994$	58.3447	1.85058
$995$	0	0
$996$	−9.42169	−0.298538
$997$	7.21626	0.228541	0.114271	−	0.993450i	$-0.463547\pi$
$997$	7.21626	0.228541	0.114271	+	0.993450i	$0.463547\pi$
$998$	−61.2848	−1.93993
$999$	−31.6089	−1.00006

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6275.2.a.e.1.15		17
5.4	even	2		251.2.a.b.1.3	✓	17
15.14	odd	2		2259.2.a.k.1.15		17
20.19	odd	2		4016.2.a.k.1.1		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
251.2.a.b.1.3	✓	17	5.4	even	2
2259.2.a.k.1.15		17	15.14	odd	2
4016.2.a.k.1.1		17	20.19	odd	2
6275.2.a.e.1.15		17	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:	\( N \)	\(=\)	\( 6275 = 5^{2} \cdot 251 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6275.a (trivial)

\(f(q)\)	\(=\)	\(q+2.32547 q^{2} -3.27059 q^{3} +3.40783 q^{4} -7.60566 q^{6} -1.64874 q^{7} +3.27388 q^{8} +7.69673 q^{9} +O(q^{10})\)	\(q+2.32547 q^{2} -3.27059 q^{3} +3.40783 q^{4} -7.60566 q^{6} -1.64874 q^{7} +3.27388 q^{8} +7.69673 q^{9} -3.10982 q^{11} -11.1456 q^{12} -5.70062 q^{13} -3.83409 q^{14} +0.797656 q^{16} -3.66658 q^{17} +17.8985 q^{18} -5.51191 q^{19} +5.39233 q^{21} -7.23182 q^{22} +2.16257 q^{23} -10.7075 q^{24} -13.2566 q^{26} -15.3610 q^{27} -5.61862 q^{28} +8.08572 q^{29} +5.30190 q^{31} -4.69283 q^{32} +10.1709 q^{33} -8.52654 q^{34} +26.2292 q^{36} +2.05773 q^{37} -12.8178 q^{38} +18.6444 q^{39} -2.65933 q^{41} +12.5397 q^{42} +9.01212 q^{43} -10.5978 q^{44} +5.02900 q^{46} -2.30292 q^{47} -2.60880 q^{48} -4.28167 q^{49} +11.9919 q^{51} -19.4267 q^{52} +8.44037 q^{53} -35.7217 q^{54} -5.39776 q^{56} +18.0272 q^{57} +18.8031 q^{58} +1.95895 q^{59} +11.1945 q^{61} +12.3294 q^{62} -12.6899 q^{63} -12.5084 q^{64} +23.6523 q^{66} +1.43672 q^{67} -12.4951 q^{68} -7.07287 q^{69} -15.2173 q^{71} +25.1981 q^{72} +1.27528 q^{73} +4.78520 q^{74} -18.7836 q^{76} +5.12728 q^{77} +43.3570 q^{78} -9.46821 q^{79} +27.1494 q^{81} -6.18421 q^{82} +0.845328 q^{83} +18.3762 q^{84} +20.9575 q^{86} -26.4451 q^{87} -10.1812 q^{88} -6.17322 q^{89} +9.39881 q^{91} +7.36967 q^{92} -17.3403 q^{93} -5.35538 q^{94} +15.3483 q^{96} +9.74063 q^{97} -9.95691 q^{98} -23.9355 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 2 q^{2} + 26 q^{4} + q^{6} - 3 q^{7} - 6 q^{8} + 25 q^{9}+O(q^{10}) \) 17 * q - 2 * q^2 + 26 * q^4 + q^6 - 3 * q^7 - 6 * q^8 + 25 * q^9	\( 17 q - 2 q^{2} + 26 q^{4} + q^{6} - 3 q^{7} - 6 q^{8} + 25 q^{9} - q^{11} + 9 q^{12} - 22 q^{13} - 7 q^{14} + 40 q^{16} + q^{17} + 7 q^{18} + 13 q^{19} + 25 q^{21} - 4 q^{22} + 2 q^{23} - 24 q^{24} - 9 q^{26} + 15 q^{27} + 10 q^{28} + 28 q^{29} + 12 q^{31} - 4 q^{32} + 16 q^{33} - 21 q^{34} + 21 q^{36} - 27 q^{37} + 37 q^{38} + 13 q^{39} - q^{41} + 56 q^{42} - 9 q^{43} - 43 q^{44} + 4 q^{46} + 20 q^{47} + 79 q^{48} + 32 q^{49} - 2 q^{51} + q^{52} - q^{53} - 65 q^{54} - 61 q^{56} + 24 q^{57} + 46 q^{58} - 20 q^{59} + 59 q^{61} + 73 q^{62} + 41 q^{63} + 54 q^{64} - 43 q^{66} - 15 q^{67} + 20 q^{68} + 38 q^{69} - 26 q^{71} + 2 q^{72} - 8 q^{73} + 2 q^{74} + 38 q^{76} + 33 q^{79} + 29 q^{81} - 10 q^{82} + 63 q^{84} + 11 q^{86} + 11 q^{87} - 27 q^{88} + 11 q^{89} - 2 q^{91} - 28 q^{92} - 28 q^{93} + 29 q^{94} - 17 q^{96} + 10 q^{97} - 22 q^{98} - 36 q^{99}+O(q^{100}) \) 17 * q - 2 * q^2 + 26 * q^4 + q^6 - 3 * q^7 - 6 * q^8 + 25 * q^9 - q^11 + 9 * q^12 - 22 * q^13 - 7 * q^14 + 40 * q^16 + q^17 + 7 * q^18 + 13 * q^19 + 25 * q^21 - 4 * q^22 + 2 * q^23 - 24 * q^24 - 9 * q^26 + 15 * q^27 + 10 * q^28 + 28 * q^29 + 12 * q^31 - 4 * q^32 + 16 * q^33 - 21 * q^34 + 21 * q^36 - 27 * q^37 + 37 * q^38 + 13 * q^39 - q^41 + 56 * q^42 - 9 * q^43 - 43 * q^44 + 4 * q^46 + 20 * q^47 + 79 * q^48 + 32 * q^49 - 2 * q^51 + q^52 - q^53 - 65 * q^54 - 61 * q^56 + 24 * q^57 + 46 * q^58 - 20 * q^59 + 59 * q^61 + 73 * q^62 + 41 * q^63 + 54 * q^64 - 43 * q^66 - 15 * q^67 + 20 * q^68 + 38 * q^69 - 26 * q^71 + 2 * q^72 - 8 * q^73 + 2 * q^74 + 38 * q^76 + 33 * q^79 + 29 * q^81 - 10 * q^82 + 63 * q^84 + 11 * q^86 + 11 * q^87 - 27 * q^88 + 11 * q^89 - 2 * q^91 - 28 * q^92 - 28 * q^93 + 29 * q^94 - 17 * q^96 + 10 * q^97 - 22 * q^98 - 36 * q^99

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