LMFDB - Embedded newform 825.4.a.m.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,4,Mod(1,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("825.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	825.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:	$48.6765757547$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.56155$ of defining polynomial
Character	$\chi$	$=$	825.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.56155 q^{2} -3.00000 q^{3} -5.56155 q^{4} +4.68466 q^{6} +10.2462 q^{7} +21.1771 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-1.56155 q^{2} -3.00000 q^{3} -5.56155 q^{4} +4.68466 q^{6} +10.2462 q^{7} +21.1771 q^{8} +9.00000 q^{9} -11.0000 q^{11} +16.6847 q^{12} +40.8769 q^{13} -16.0000 q^{14} +11.4233 q^{16} +98.7083 q^{17} -14.0540 q^{18} -39.6458 q^{19} -30.7386 q^{21} +17.1771 q^{22} -61.6932 q^{23} -63.5312 q^{24} -63.8314 q^{26} -27.0000 q^{27} -56.9848 q^{28} -149.093 q^{29} +54.7386 q^{31} -187.255 q^{32} +33.0000 q^{33} -154.138 q^{34} -50.0540 q^{36} -44.8939 q^{37} +61.9091 q^{38} -122.631 q^{39} +336.479 q^{41} +48.0000 q^{42} +2.36745 q^{43} +61.1771 q^{44} +96.3371 q^{46} +333.295 q^{47} -34.2699 q^{48} -238.015 q^{49} -296.125 q^{51} -227.339 q^{52} -640.064 q^{53} +42.1619 q^{54} +216.985 q^{56} +118.938 q^{57} +232.816 q^{58} -370.773 q^{59} -714.405 q^{61} -85.4773 q^{62} +92.2159 q^{63} +201.022 q^{64} -51.5312 q^{66} +404.985 q^{67} -548.972 q^{68} +185.080 q^{69} +939.292 q^{71} +190.594 q^{72} +362.570 q^{73} +70.1042 q^{74} +220.492 q^{76} -112.708 q^{77} +191.494 q^{78} +951.835 q^{79} +81.0000 q^{81} -525.430 q^{82} -735.221 q^{83} +170.955 q^{84} -3.69690 q^{86} +447.278 q^{87} -232.948 q^{88} +385.879 q^{89} +418.833 q^{91} +343.110 q^{92} -164.216 q^{93} -520.458 q^{94} +561.764 q^{96} +966.345 q^{97} +371.673 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 6 q^{3} - 7 q^{4} - 3 q^{6} + 4 q^{7} - 3 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q + q^2 - 6 * q^3 - 7 * q^4 - 3 * q^6 + 4 * q^7 - 3 * q^8 + 18 * q^9	$ 2 q + q^{2} - 6 q^{3} - 7 q^{4} - 3 q^{6} + 4 q^{7} - 3 q^{8} + 18 q^{9} - 22 q^{11} + 21 q^{12} + 90 q^{13} - 32 q^{14} - 39 q^{16} + 16 q^{17} + 9 q^{18} - 170 q^{19} - 12 q^{21} - 11 q^{22} + 124 q^{23} + 9 q^{24} + 62 q^{26} - 54 q^{27} - 48 q^{28} - 158 q^{29} + 60 q^{31} - 123 q^{32} + 66 q^{33} - 366 q^{34} - 63 q^{36} + 372 q^{37} - 272 q^{38} - 270 q^{39} + 38 q^{41} + 96 q^{42} + 516 q^{43} + 77 q^{44} + 572 q^{46} - 224 q^{47} + 117 q^{48} - 542 q^{49} - 48 q^{51} - 298 q^{52} - 472 q^{53} - 27 q^{54} + 368 q^{56} + 510 q^{57} + 210 q^{58} + 248 q^{59} + 72 q^{61} - 72 q^{62} + 36 q^{63} + 769 q^{64} + 33 q^{66} + 744 q^{67} - 430 q^{68} - 372 q^{69} + 2060 q^{71} - 27 q^{72} + 486 q^{73} + 1138 q^{74} + 408 q^{76} - 44 q^{77} - 186 q^{78} + 642 q^{79} + 162 q^{81} - 1290 q^{82} + 286 q^{83} + 144 q^{84} + 1312 q^{86} + 474 q^{87} + 33 q^{88} + 244 q^{89} + 112 q^{91} + 76 q^{92} - 180 q^{93} - 1948 q^{94} + 369 q^{96} + 168 q^{97} - 407 q^{98} - 198 q^{99}+O(q^{100}) $ 2 * q + q^2 - 6 * q^3 - 7 * q^4 - 3 * q^6 + 4 * q^7 - 3 * q^8 + 18 * q^9 - 22 * q^11 + 21 * q^12 + 90 * q^13 - 32 * q^14 - 39 * q^16 + 16 * q^17 + 9 * q^18 - 170 * q^19 - 12 * q^21 - 11 * q^22 + 124 * q^23 + 9 * q^24 + 62 * q^26 - 54 * q^27 - 48 * q^28 - 158 * q^29 + 60 * q^31 - 123 * q^32 + 66 * q^33 - 366 * q^34 - 63 * q^36 + 372 * q^37 - 272 * q^38 - 270 * q^39 + 38 * q^41 + 96 * q^42 + 516 * q^43 + 77 * q^44 + 572 * q^46 - 224 * q^47 + 117 * q^48 - 542 * q^49 - 48 * q^51 - 298 * q^52 - 472 * q^53 - 27 * q^54 + 368 * q^56 + 510 * q^57 + 210 * q^58 + 248 * q^59 + 72 * q^61 - 72 * q^62 + 36 * q^63 + 769 * q^64 + 33 * q^66 + 744 * q^67 - 430 * q^68 - 372 * q^69 + 2060 * q^71 - 27 * q^72 + 486 * q^73 + 1138 * q^74 + 408 * q^76 - 44 * q^77 - 186 * q^78 + 642 * q^79 + 162 * q^81 - 1290 * q^82 + 286 * q^83 + 144 * q^84 + 1312 * q^86 + 474 * q^87 + 33 * q^88 + 244 * q^89 + 112 * q^91 + 76 * q^92 - 180 * q^93 - 1948 * q^94 + 369 * q^96 + 168 * q^97 - 407 * q^98 - 198 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.56155	−0.552092	−0.276046	−	0.961144i	$-0.589024\pi$
$2$	−1.56155	−0.552092	−0.276046	+	0.961144i	$0.589024\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−5.56155	−0.695194
$5$	0	0
$5$	0	0
$6$	4.68466	0.318751
$7$	10.2462	0.553243	0.276622	−	0.960979i	$-0.410785\pi$
$7$	10.2462	0.553243	0.276622	+	0.960979i	$0.410785\pi$
$8$	21.1771	0.935904
$9$	9.00000	0.333333
$10$	0	0
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	16.6847	0.401371
$13$	40.8769	0.872093	0.436047	−	0.899924i	$-0.356378\pi$
$13$	40.8769	0.872093	0.436047	+	0.899924i	$0.356378\pi$
$14$	−16.0000	−0.305441
$15$	0	0
$16$	11.4233	0.178489
$17$	98.7083	1.40825	0.704126	−	0.710075i	$-0.251339\pi$
$17$	98.7083	1.40825	0.704126	+	0.710075i	$0.251339\pi$
$18$	−14.0540	−0.184031
$19$	−39.6458	−0.478704	−0.239352	−	0.970933i	$-0.576935\pi$
$19$	−39.6458	−0.478704	−0.239352	+	0.970933i	$0.576935\pi$
$20$	0	0
$21$	−30.7386	−0.319415
$22$	17.1771	0.166462
$23$	−61.6932	−0.559301	−0.279650	−	0.960102i	$-0.590219\pi$
$23$	−61.6932	−0.559301	−0.279650	+	0.960102i	$0.590219\pi$
$24$	−63.5312	−0.540344
$25$	0	0
$26$	−63.8314	−0.481476
$27$	−27.0000	−0.192450
$28$	−56.9848	−0.384612
$29$	−149.093	−0.954684	−0.477342	−	0.878718i	$-0.658400\pi$
$29$	−149.093	−0.954684	−0.477342	+	0.878718i	$0.658400\pi$
$30$	0	0
$31$	54.7386	0.317140	0.158570	−	0.987348i	$-0.449312\pi$
$31$	54.7386	0.317140	0.158570	+	0.987348i	$0.449312\pi$
$32$	−187.255	−1.03445
$33$	33.0000	0.174078
$34$	−154.138	−0.777485
$35$	0	0
$36$	−50.0540	−0.231731
$37$	−44.8939	−0.199473	−0.0997367	−	0.995014i	$-0.531800\pi$
$37$	−44.8939	−0.199473	−0.0997367	+	0.995014i	$0.531800\pi$
$38$	61.9091	0.264289
$39$	−122.631	−0.503503
$40$	0	0
$41$	336.479	1.28169	0.640844	−	0.767671i	$-0.278585\pi$
$41$	336.479	1.28169	0.640844	+	0.767671i	$0.278585\pi$
$42$	48.0000	0.176347
$43$	2.36745	0.00839611	0.00419806	−	0.999991i	$-0.498664\pi$
$43$	2.36745	0.00839611	0.00419806	+	0.999991i	$0.498664\pi$
$44$	61.1771	0.209609
$45$	0	0
$46$	96.3371	0.308786
$47$	333.295	1.03439	0.517193	−	0.855869i	$-0.326977\pi$
$47$	333.295	1.03439	0.517193	+	0.855869i	$0.326977\pi$
$48$	−34.2699	−0.103051
$49$	−238.015	−0.693922
$50$	0	0
$51$	−296.125	−0.813055
$52$	−227.339	−0.606274
$53$	−640.064	−1.65886	−0.829430	−	0.558610i	$-0.811335\pi$
$53$	−640.064	−1.65886	−0.829430	+	0.558610i	$0.811335\pi$
$54$	42.1619	0.106250
$55$	0	0
$56$	216.985	0.517782
$57$	118.938	0.276380
$58$	232.816	0.527074
$59$	−370.773	−0.818144	−0.409072	−	0.912502i	$-0.634147\pi$
$59$	−370.773	−0.818144	−0.409072	+	0.912502i	$0.634147\pi$
$60$	0	0
$61$	−714.405	−1.49951	−0.749756	−	0.661715i	$-0.769829\pi$
$61$	−714.405	−1.49951	−0.749756	+	0.661715i	$0.769829\pi$
$62$	−85.4773	−0.175091
$63$	92.2159	0.184414
$64$	201.022	0.392621
$65$	0	0
$66$	−51.5312	−0.0961069
$67$	404.985	0.738459	0.369230	−	0.929338i	$-0.379622\pi$
$67$	404.985	0.738459	0.369230	+	0.929338i	$0.379622\pi$
$68$	−548.972	−0.979009
$69$	185.080	0.322912
$70$	0	0
$71$	939.292	1.57005	0.785024	−	0.619465i	$-0.212651\pi$
$71$	939.292	1.57005	0.785024	+	0.619465i	$0.212651\pi$
$72$	190.594	0.311968
$73$	362.570	0.581310	0.290655	−	0.956828i	$-0.406127\pi$
$73$	362.570	0.581310	0.290655	+	0.956828i	$0.406127\pi$
$74$	70.1042	0.110128
$75$	0	0
$76$	220.492	0.332792
$77$	−112.708	−0.166809
$78$	191.494	0.277980
$79$	951.835	1.35557	0.677784	−	0.735261i	$-0.262941\pi$
$79$	951.835	1.35557	0.677784	+	0.735261i	$0.262941\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	−525.430	−0.707610
$83$	−735.221	−0.972302	−0.486151	−	0.873875i	$-0.661599\pi$
$83$	−735.221	−0.972302	−0.486151	+	0.873875i	$0.661599\pi$
$84$	170.955	0.222056
$85$	0	0
$86$	−3.69690	−0.00463543
$87$	447.278	0.551187
$88$	−232.948	−0.282186
$89$	385.879	0.459585	0.229793	−	0.973240i	$-0.426195\pi$
$89$	385.879	0.459585	0.229793	+	0.973240i	$0.426195\pi$
$90$	0	0
$91$	418.833	0.482480
$92$	343.110	0.388823
$93$	−164.216	−0.183101
$94$	−520.458	−0.571076
$95$	0	0
$96$	561.764	0.597238
$97$	966.345	1.01152	0.505760	−	0.862674i	$-0.331212\pi$
$97$	966.345	1.01152	0.505760	+	0.862674i	$0.331212\pi$
$98$	371.673	0.383109
$99$	−99.0000	−0.100504
$100$	0	0
$101$	348.600	0.343436	0.171718	−	0.985146i	$-0.445068\pi$
$101$	348.600	0.343436	0.171718	+	0.985146i	$0.445068\pi$
$102$	462.415	0.448881
$103$	1536.38	1.46975	0.734873	−	0.678204i	$-0.237242\pi$
$103$	1536.38	1.46975	0.734873	+	0.678204i	$0.237242\pi$
$104$	865.653	0.816195
$105$	0	0
$106$	999.494	0.915844
$107$	779.180	0.703983	0.351991	−	0.936003i	$-0.385505\pi$
$107$	779.180	0.703983	0.351991	+	0.936003i	$0.385505\pi$
$108$	150.162	0.133790
$109$	−1501.79	−1.31968	−0.659842	−	0.751404i	$-0.729377\pi$
$109$	−1501.79	−1.31968	−0.659842	+	0.751404i	$0.729377\pi$
$110$	0	0
$111$	134.682	0.115166
$112$	117.045	0.0987478
$113$	−170.000	−0.141524	−0.0707622	−	0.997493i	$-0.522543\pi$
$113$	−170.000	−0.141524	−0.0707622	+	0.997493i	$0.522543\pi$
$114$	−185.727	−0.152587
$115$	0	0
$116$	829.187	0.663691
$117$	367.892	0.290698
$118$	578.981	0.451691
$119$	1011.39	0.779106
$120$	0	0
$121$	121.000	0.0909091
$122$	1115.58	0.827869
$123$	−1009.44	−0.739983
$124$	−304.432	−0.220474
$125$	0	0
$126$	−144.000	−0.101814
$127$	1739.82	1.21562	0.607811	−	0.794082i	$-0.292048\pi$
$127$	1739.82	1.21562	0.607811	+	0.794082i	$0.292048\pi$
$128$	1184.13	0.817683
$129$	−7.10235	−0.00484750
$130$	0	0
$131$	312.837	0.208647	0.104323	−	0.994543i	$-0.466732\pi$
$131$	312.837	0.208647	0.104323	+	0.994543i	$0.466732\pi$
$132$	−183.531	−0.121018
$133$	−406.220	−0.264840
$134$	−632.405	−0.407698
$135$	0	0
$136$	2090.35	1.31799
$137$	716.928	0.447090	0.223545	−	0.974694i	$-0.428237\pi$
$137$	716.928	0.447090	0.223545	+	0.974694i	$0.428237\pi$
$138$	−289.011	−0.178277
$139$	−876.483	−0.534837	−0.267418	−	0.963581i	$-0.586171\pi$
$139$	−876.483	−0.534837	−0.267418	+	0.963581i	$0.586171\pi$
$140$	0	0
$141$	−999.886	−0.597203
$142$	−1466.75	−0.866811
$143$	−449.646	−0.262946
$144$	102.810	0.0594963
$145$	0	0
$146$	−566.172	−0.320937
$147$	714.045	0.400636
$148$	249.680	0.138673
$149$	−2376.36	−1.30657	−0.653285	−	0.757112i	$-0.726610\pi$
$149$	−2376.36	−1.30657	−0.653285	+	0.757112i	$0.726610\pi$
$150$	0	0
$151$	−92.8466	−0.0500381	−0.0250190	−	0.999687i	$-0.507965\pi$
$151$	−92.8466	−0.0500381	−0.0250190	+	0.999687i	$0.507965\pi$
$152$	−839.583	−0.448021
$153$	888.375	0.469417
$154$	176.000	0.0920941
$155$	0	0
$156$	682.017	0.350032
$157$	1881.24	0.956301	0.478150	−	0.878278i	$-0.341307\pi$
$157$	1881.24	0.956301	0.478150	+	0.878278i	$0.341307\pi$
$158$	−1486.34	−0.748398
$159$	1920.19	0.957743
$160$	0	0
$161$	−632.121	−0.309429
$162$	−126.486	−0.0613436
$163$	2465.49	1.18474	0.592369	−	0.805667i	$-0.298193\pi$
$163$	2465.49	1.18474	0.592369	+	0.805667i	$0.298193\pi$
$164$	−1871.35	−0.891022
$165$	0	0
$166$	1148.09	0.536800
$167$	1254.30	0.581200	0.290600	−	0.956845i	$-0.406145\pi$
$167$	1254.30	0.581200	0.290600	+	0.956845i	$0.406145\pi$
$168$	−650.955	−0.298942
$169$	−526.080	−0.239454
$170$	0	0
$171$	−356.813	−0.159568
$172$	−13.1667	−0.00583693
$173$	1206.71	0.530314	0.265157	−	0.964205i	$-0.414576\pi$
$173$	1206.71	0.530314	0.265157	+	0.964205i	$0.414576\pi$
$174$	−698.449	−0.304306
$175$	0	0
$176$	−125.656	−0.0538164
$177$	1112.32	0.472356
$178$	−602.570	−0.253733
$179$	−1442.29	−0.602244	−0.301122	−	0.953586i	$-0.597361\pi$
$179$	−1442.29	−0.602244	−0.301122	+	0.953586i	$0.597361\pi$
$180$	0	0
$181$	4261.81	1.75015	0.875076	−	0.483985i	$-0.160811\pi$
$181$	4261.81	1.75015	0.875076	+	0.483985i	$0.160811\pi$
$182$	−654.030	−0.266373
$183$	2143.22	0.865744
$184$	−1306.48	−0.523451
$185$	0	0
$186$	256.432	0.101089
$187$	−1085.79	−0.424604
$188$	−1853.64	−0.719099
$189$	−276.648	−0.106472
$190$	0	0
$191$	−852.223	−0.322852	−0.161426	−	0.986885i	$-0.551609\pi$
$191$	−852.223	−0.322852	−0.161426	+	0.986885i	$0.551609\pi$
$192$	−603.065	−0.226680
$193$	2459.95	0.917468	0.458734	−	0.888574i	$-0.348303\pi$
$193$	2459.95	0.917468	0.458734	+	0.888574i	$0.348303\pi$
$194$	−1509.00	−0.558452
$195$	0	0
$196$	1323.73	0.482410
$197$	−3477.06	−1.25751	−0.628756	−	0.777602i	$-0.716436\pi$
$197$	−3477.06	−1.25751	−0.628756	+	0.777602i	$0.716436\pi$
$198$	154.594	0.0554874
$199$	3995.04	1.42312	0.711560	−	0.702626i	$-0.247989\pi$
$199$	3995.04	1.42312	0.711560	+	0.702626i	$0.247989\pi$
$200$	0	0
$201$	−1214.95	−0.426350
$202$	−544.358	−0.189608
$203$	−1527.64	−0.528173
$204$	1646.91	0.565231
$205$	0	0
$206$	−2399.14	−0.811436
$207$	−555.239	−0.186434
$208$	466.949	0.155659
$209$	436.104	0.144335
$210$	0	0
$211$	1046.13	0.341319	0.170660	−	0.985330i	$-0.445410\pi$
$211$	1046.13	0.341319	0.170660	+	0.985330i	$0.445410\pi$
$212$	3559.75	1.15323
$213$	−2817.88	−0.906468
$214$	−1216.73	−0.388664
$215$	0	0
$216$	−571.781	−0.180115
$217$	560.864	0.175456
$218$	2345.13	0.728587
$219$	−1087.71	−0.335619
$220$	0	0
$221$	4034.89	1.22813
$222$	−210.313	−0.0635823
$223$	506.265	0.152027	0.0760135	−	0.997107i	$-0.475781\pi$
$223$	506.265	0.152027	0.0760135	+	0.997107i	$0.475781\pi$
$224$	−1918.65	−0.572300
$225$	0	0
$226$	265.464	0.0781345
$227$	4286.29	1.25326	0.626632	−	0.779315i	$-0.284433\pi$
$227$	4286.29	1.25326	0.626632	+	0.779315i	$0.284433\pi$
$228$	−661.477	−0.192138
$229$	5709.37	1.64754	0.823769	−	0.566926i	$-0.191867\pi$
$229$	5709.37	1.64754	0.823769	+	0.566926i	$0.191867\pi$
$230$	0	0
$231$	338.125	0.0963073
$232$	−3157.35	−0.893492
$233$	−2946.09	−0.828348	−0.414174	−	0.910198i	$-0.635929\pi$
$233$	−2946.09	−0.828348	−0.414174	+	0.910198i	$0.635929\pi$
$234$	−574.483	−0.160492
$235$	0	0
$236$	2062.07	0.568769
$237$	−2855.51	−0.782637
$238$	−1579.33	−0.430139
$239$	−2078.89	−0.562646	−0.281323	−	0.959613i	$-0.590773\pi$
$239$	−2078.89	−0.562646	−0.281323	+	0.959613i	$0.590773\pi$
$240$	0	0
$241$	1853.37	0.495378	0.247689	−	0.968840i	$-0.420329\pi$
$241$	1853.37	0.495378	0.247689	+	0.968840i	$0.420329\pi$
$242$	−188.948	−0.0501902
$243$	−243.000	−0.0641500
$244$	3973.20	1.04245
$245$	0	0
$246$	1576.29	0.408539
$247$	−1620.60	−0.417475
$248$	1159.20	0.296813
$249$	2205.66	0.561359
$250$	0	0
$251$	−2358.39	−0.593068	−0.296534	−	0.955022i	$-0.595831\pi$
$251$	−2358.39	−0.593068	−0.296534	+	0.955022i	$0.595831\pi$
$252$	−512.864	−0.128204
$253$	678.625	0.168635
$254$	−2716.82	−0.671135
$255$	0	0
$256$	−3457.26	−0.844057
$257$	−5519.25	−1.33962	−0.669809	−	0.742534i	$-0.733624\pi$
$257$	−5519.25	−1.33962	−0.669809	+	0.742534i	$0.733624\pi$
$258$	11.0907	0.00267627
$259$	−459.993	−0.110357
$260$	0	0
$261$	−1341.84	−0.318228
$262$	−488.512	−0.115192
$263$	−2259.65	−0.529795	−0.264898	−	0.964277i	$-0.585338\pi$
$263$	−2259.65	−0.529795	−0.264898	+	0.964277i	$0.585338\pi$
$264$	698.844	0.162920
$265$	0	0
$266$	634.333	0.146216
$267$	−1157.64	−0.265342
$268$	−2252.34	−0.513373
$269$	7039.53	1.59557	0.797783	−	0.602944i	$-0.206006\pi$
$269$	7039.53	1.59557	0.797783	+	0.602944i	$0.206006\pi$
$270$	0	0
$271$	5155.08	1.15553	0.577765	−	0.816203i	$-0.303925\pi$
$271$	5155.08	1.15553	0.577765	+	0.816203i	$0.303925\pi$
$272$	1127.57	0.251357
$273$	−1256.50	−0.278560
$274$	−1119.52	−0.246835
$275$	0	0
$276$	−1029.33	−0.224487
$277$	−9074.52	−1.96836	−0.984179	−	0.177175i	$-0.943304\pi$
$277$	−9074.52	−1.96836	−0.984179	+	0.177175i	$0.943304\pi$
$278$	1368.67	0.295279
$279$	492.648	0.105713
$280$	0	0
$281$	−3407.79	−0.723459	−0.361729	−	0.932283i	$-0.617814\pi$
$281$	−3407.79	−0.723459	−0.361729	+	0.932283i	$0.617814\pi$
$282$	1561.38	0.329711
$283$	8827.73	1.85425	0.927127	−	0.374746i	$-0.122270\pi$
$283$	8827.73	1.85425	0.927127	+	0.374746i	$0.122270\pi$
$284$	−5223.92	−1.09149
$285$	0	0
$286$	702.146	0.145170
$287$	3447.64	0.709085
$288$	−1685.29	−0.344815
$289$	4830.33	0.983174
$290$	0	0
$291$	−2899.03	−0.584001
$292$	−2016.45	−0.404123
$293$	4528.29	0.902886	0.451443	−	0.892300i	$-0.350909\pi$
$293$	4528.29	0.902886	0.451443	+	0.892300i	$0.350909\pi$
$294$	−1115.02	−0.221188
$295$	0	0
$296$	−950.722	−0.186688
$297$	297.000	0.0580259
$298$	3710.81	0.721347
$299$	−2521.83	−0.487762
$300$	0	0
$301$	24.2574	0.00464509
$302$	144.985	0.0276256
$303$	−1045.80	−0.198283
$304$	−452.886	−0.0854434
$305$	0	0
$306$	−1387.24	−0.259162
$307$	−568.106	−0.105614	−0.0528071	−	0.998605i	$-0.516817\pi$
$307$	−568.106	−0.105614	−0.0528071	+	0.998605i	$0.516817\pi$
$308$	626.833	0.115965
$309$	−4609.14	−0.848559
$310$	0	0
$311$	−6853.59	−1.24962	−0.624809	−	0.780778i	$-0.714823\pi$
$311$	−6853.59	−1.24962	−0.624809	+	0.780778i	$0.714823\pi$
$312$	−2596.96	−0.471230
$313$	1138.92	0.205673	0.102837	−	0.994698i	$-0.467208\pi$
$313$	1138.92	0.205673	0.102837	+	0.994698i	$0.467208\pi$
$314$	−2937.65	−0.527966
$315$	0	0
$316$	−5293.68	−0.942382
$317$	−3207.48	−0.568297	−0.284148	−	0.958780i	$-0.591711\pi$
$317$	−3207.48	−0.568297	−0.284148	+	0.958780i	$0.591711\pi$
$318$	−2998.48	−0.528763
$319$	1640.02	0.287848
$320$	0	0
$321$	−2337.54	−0.406445
$322$	987.091	0.170834
$323$	−3913.37	−0.674136
$324$	−450.486	−0.0772438
$325$	0	0
$326$	−3850.00	−0.654085
$327$	4505.37	0.761920
$328$	7125.65	1.19954
$329$	3415.02	0.572267
$330$	0	0
$331$	−9135.12	−1.51695	−0.758477	−	0.651700i	$-0.774056\pi$
$331$	−9135.12	−1.51695	−0.758477	+	0.651700i	$0.774056\pi$
$332$	4088.97	0.675938
$333$	−404.045	−0.0664911
$334$	−1958.65	−0.320876
$335$	0	0
$336$	−351.136	−0.0570121
$337$	3470.05	0.560907	0.280453	−	0.959868i	$-0.409515\pi$
$337$	3470.05	0.560907	0.280453	+	0.959868i	$0.409515\pi$
$338$	821.501	0.132200
$339$	510.000	0.0817091
$340$	0	0
$341$	−602.125	−0.0956214
$342$	557.182	0.0880963
$343$	−5953.20	−0.937151
$344$	50.1357	0.00785795
$345$	0	0
$346$	−1884.34	−0.292782
$347$	89.3315	0.0138201	0.00691004	−	0.999976i	$-0.497800\pi$
$347$	89.3315	0.0138201	0.00691004	+	0.999976i	$0.497800\pi$
$348$	−2487.56	−0.383182
$349$	−149.375	−0.0229107	−0.0114554	−	0.999934i	$-0.503646\pi$
$349$	−149.375	−0.0229107	−0.0114554	+	0.999934i	$0.503646\pi$
$350$	0	0
$351$	−1103.68	−0.167834
$352$	2059.80	0.311897
$353$	−7867.64	−1.18627	−0.593133	−	0.805104i	$-0.702109\pi$
$353$	−7867.64	−1.18627	−0.593133	+	0.805104i	$0.702109\pi$
$354$	−1736.94	−0.260784
$355$	0	0
$356$	−2146.09	−0.319501
$357$	−3034.16	−0.449817
$358$	2252.21	0.332494
$359$	4974.22	0.731279	0.365639	−	0.930757i	$-0.380850\pi$
$359$	4974.22	0.731279	0.365639	+	0.930757i	$0.380850\pi$
$360$	0	0
$361$	−5287.21	−0.770842
$362$	−6655.04	−0.966246
$363$	−363.000	−0.0524864
$364$	−2329.36	−0.335417
$365$	0	0
$366$	−3346.74	−0.477970
$367$	13266.7	1.88696	0.943479	−	0.331433i	$-0.107532\pi$
$367$	13266.7	1.88696	0.943479	+	0.331433i	$0.107532\pi$
$368$	−704.739	−0.0998290
$369$	3028.31	0.427229
$370$	0	0
$371$	−6558.23	−0.917754
$372$	913.295	0.127291
$373$	4632.77	0.643099	0.321549	−	0.946893i	$-0.395796\pi$
$373$	4632.77	0.643099	0.321549	+	0.946893i	$0.395796\pi$
$374$	1695.52	0.234421
$375$	0	0
$376$	7058.22	0.968085
$377$	−6094.45	−0.832573
$378$	432.000	0.0587822
$379$	6503.31	0.881406	0.440703	−	0.897653i	$-0.354729\pi$
$379$	6503.31	0.881406	0.440703	+	0.897653i	$0.354729\pi$
$380$	0	0
$381$	−5219.45	−0.701839
$382$	1330.79	0.178244
$383$	−12734.5	−1.69897	−0.849484	−	0.527614i	$-0.823087\pi$
$383$	−12734.5	−1.69897	−0.849484	+	0.527614i	$0.823087\pi$
$384$	−3552.39	−0.472090
$385$	0	0
$386$	−3841.35	−0.506527
$387$	21.3071	0.00279870
$388$	−5374.38	−0.703203
$389$	12024.6	1.56728	0.783639	−	0.621216i	$-0.213361\pi$
$389$	12024.6	1.56728	0.783639	+	0.621216i	$0.213361\pi$
$390$	0	0
$391$	−6089.63	−0.787636
$392$	−5040.47	−0.649444
$393$	−938.511	−0.120462
$394$	5429.61	0.694263
$395$	0	0
$396$	550.594	0.0698696
$397$	5223.65	0.660371	0.330186	−	0.943916i	$-0.392889\pi$
$397$	5223.65	0.660371	0.330186	+	0.943916i	$0.392889\pi$
$398$	−6238.46	−0.785693
$399$	1218.66	0.152905
$400$	0	0
$401$	9648.18	1.20151	0.600757	−	0.799432i	$-0.294866\pi$
$401$	9648.18	1.20151	0.600757	+	0.799432i	$0.294866\pi$
$402$	1897.22	0.235384
$403$	2237.55	0.276576
$404$	−1938.76	−0.238755
$405$	0	0
$406$	2385.48	0.291600
$407$	493.833	0.0601435
$408$	−6271.06	−0.760941
$409$	−2010.47	−0.243060	−0.121530	−	0.992588i	$-0.538780\pi$
$409$	−2010.47	−0.243060	−0.121530	+	0.992588i	$0.538780\pi$
$410$	0	0
$411$	−2150.78	−0.258127
$412$	−8544.65	−1.02176
$413$	−3799.02	−0.452633
$414$	867.034	0.102929
$415$	0	0
$416$	−7654.39	−0.902133
$417$	2629.45	0.308788
$418$	−681.000	−0.0796861
$419$	4435.27	0.517129	0.258565	−	0.965994i	$-0.416750\pi$
$419$	4435.27	0.517129	0.258565	+	0.965994i	$0.416750\pi$
$420$	0	0
$421$	15217.9	1.76170	0.880852	−	0.473392i	$-0.156971\pi$
$421$	15217.9	1.76170	0.880852	+	0.473392i	$0.156971\pi$
$422$	−1633.58	−0.188440
$423$	2999.66	0.344795
$424$	−13554.7	−1.55253
$425$	0	0
$426$	4400.26	0.500454
$427$	−7319.95	−0.829595
$428$	−4333.45	−0.489405
$429$	1348.94	0.151812
$430$	0	0
$431$	−5622.11	−0.628324	−0.314162	−	0.949369i	$-0.601723\pi$
$431$	−5622.11	−0.628324	−0.314162	+	0.949369i	$0.601723\pi$
$432$	−308.429	−0.0343502
$433$	14306.3	1.58780	0.793898	−	0.608051i	$-0.208049\pi$
$433$	14306.3	1.58780	0.793898	+	0.608051i	$0.208049\pi$
$434$	−875.818	−0.0968678
$435$	0	0
$436$	8352.29	0.917436
$437$	2445.88	0.267740
$438$	1698.52	0.185293
$439$	4384.20	0.476643	0.238322	−	0.971186i	$-0.423403\pi$
$439$	4384.20	0.476643	0.238322	+	0.971186i	$0.423403\pi$
$440$	0	0
$441$	−2142.14	−0.231307
$442$	−6300.69	−0.678039
$443$	10090.0	1.08214	0.541071	−	0.840977i	$-0.318019\pi$
$443$	10090.0	1.08214	0.541071	+	0.840977i	$0.318019\pi$
$444$	−749.040	−0.0800627
$445$	0	0
$446$	−790.560	−0.0839330
$447$	7129.07	0.754348
$448$	2059.71	0.217215
$449$	9582.52	1.00719	0.503594	−	0.863941i	$-0.332011\pi$
$449$	9582.52	1.00719	0.503594	+	0.863941i	$0.332011\pi$
$450$	0	0
$451$	−3701.27	−0.386444
$452$	945.464	0.0983869
$453$	278.540	0.0288895
$454$	−6693.27	−0.691918
$455$	0	0
$456$	2518.75	0.258665
$457$	−9999.34	−1.02352	−0.511761	−	0.859128i	$-0.671007\pi$
$457$	−9999.34	−1.02352	−0.511761	+	0.859128i	$0.671007\pi$
$458$	−8915.49	−0.909593
$459$	−2665.12	−0.271018
$460$	0	0
$461$	−11115.8	−1.12302	−0.561512	−	0.827468i	$-0.689780\pi$
$461$	−11115.8	−1.12302	−0.561512	+	0.827468i	$0.689780\pi$
$462$	−528.000	−0.0531705
$463$	1567.16	0.157305	0.0786524	−	0.996902i	$-0.474938\pi$
$463$	1567.16	0.157305	0.0786524	+	0.996902i	$0.474938\pi$
$464$	−1703.13	−0.170401
$465$	0	0
$466$	4600.48	0.457325
$467$	−12648.8	−1.25335	−0.626675	−	0.779281i	$-0.715585\pi$
$467$	−12648.8	−1.25335	−0.626675	+	0.779281i	$0.715585\pi$
$468$	−2046.05	−0.202091
$469$	4149.56	0.408548
$470$	0	0
$471$	−5643.72	−0.552120
$472$	−7851.88	−0.765704
$473$	−26.0420	−0.00253152
$474$	4459.02	0.432088
$475$	0	0
$476$	−5624.88	−0.541630
$477$	−5760.58	−0.552953
$478$	3246.30	0.310633
$479$	−10719.2	−1.02249	−0.511247	−	0.859434i	$-0.670816\pi$
$479$	−10719.2	−1.02249	−0.511247	+	0.859434i	$0.670816\pi$
$480$	0	0
$481$	−1835.12	−0.173959
$482$	−2894.14	−0.273494
$483$	1896.36	0.178649
$484$	−672.948	−0.0631995
$485$	0	0
$486$	379.457	0.0354167
$487$	−7161.20	−0.666335	−0.333167	−	0.942868i	$-0.608117\pi$
$487$	−7161.20	−0.666335	−0.333167	+	0.942868i	$0.608117\pi$
$488$	−15129.0	−1.40340
$489$	−7396.48	−0.684009
$490$	0	0
$491$	14567.3	1.33893	0.669463	−	0.742845i	$-0.266524\pi$
$491$	14567.3	1.33893	0.669463	+	0.742845i	$0.266524\pi$
$492$	5614.04	0.514432
$493$	−14716.7	−1.34444
$494$	2530.65	0.230485
$495$	0	0
$496$	625.295	0.0566060
$497$	9624.18	0.868619
$498$	−3444.26	−0.309922
$499$	−4638.99	−0.416172	−0.208086	−	0.978111i	$-0.566723\pi$
$499$	−4638.99	−0.416172	−0.208086	+	0.978111i	$0.566723\pi$
$500$	0	0
$501$	−3762.89	−0.335556
$502$	3682.75	0.327428
$503$	12206.3	1.08201	0.541006	−	0.841019i	$-0.318044\pi$
$503$	12206.3	1.08201	0.541006	+	0.841019i	$0.318044\pi$
$504$	1952.86	0.172594
$505$	0	0
$506$	−1059.71	−0.0931024
$507$	1578.24	0.138249
$508$	−9676.09	−0.845093
$509$	10018.6	0.872427	0.436214	−	0.899843i	$-0.356319\pi$
$509$	10018.6	0.872427	0.436214	+	0.899843i	$0.356319\pi$
$510$	0	0
$511$	3714.97	0.321606
$512$	−4074.36	−0.351686
$513$	1070.44	0.0921267
$514$	8618.61	0.739592
$515$	0	0
$516$	39.5001	0.00336995
$517$	−3666.25	−0.311879
$518$	718.303	0.0609274
$519$	−3620.12	−0.306177
$520$	0	0
$521$	1054.72	0.0886916	0.0443458	−	0.999016i	$-0.485880\pi$
$521$	1054.72	0.0886916	0.0443458	+	0.999016i	$0.485880\pi$
$522$	2095.35	0.175691
$523$	16234.2	1.35730	0.678652	−	0.734460i	$-0.262564\pi$
$523$	16234.2	1.35730	0.678652	+	0.734460i	$0.262564\pi$
$524$	−1739.86	−0.145050
$525$	0	0
$526$	3528.57	0.292496
$527$	5403.16	0.446613
$528$	376.969	0.0310709
$529$	−8360.95	−0.687183
$530$	0	0
$531$	−3336.95	−0.272715
$532$	2259.21	0.184115
$533$	13754.2	1.11775
$534$	1807.71	0.146493
$535$	0	0
$536$	8576.40	0.691127
$537$	4326.86	0.347706
$538$	−10992.6	−0.880900
$539$	2618.17	0.209225
$540$	0	0
$541$	675.936	0.0537167	0.0268584	−	0.999639i	$-0.491450\pi$
$541$	675.936	0.0537167	0.0268584	+	0.999639i	$0.491450\pi$
$542$	−8049.93	−0.637960
$543$	−12785.4	−1.01045
$544$	−18483.6	−1.45676
$545$	0	0
$546$	1962.09	0.153791
$547$	−13058.2	−1.02071	−0.510355	−	0.859964i	$-0.670486\pi$
$547$	−13058.2	−1.02071	−0.510355	+	0.859964i	$0.670486\pi$
$548$	−3987.23	−0.310814
$549$	−6429.65	−0.499837
$550$	0	0
$551$	5910.91	0.457011
$552$	3919.44	0.302215
$553$	9752.70	0.749959
$554$	14170.3	1.08672
$555$	0	0
$556$	4874.61	0.371815
$557$	6710.48	0.510471	0.255236	−	0.966879i	$-0.417847\pi$
$557$	6710.48	0.510471	0.255236	+	0.966879i	$0.417847\pi$
$558$	−769.295	−0.0583636
$559$	96.7741	0.00732219
$560$	0	0
$561$	3257.37	0.245145
$562$	5321.45	0.399416
$563$	20820.5	1.55858	0.779288	−	0.626666i	$-0.215581\pi$
$563$	20820.5	1.55858	0.779288	+	0.626666i	$0.215581\pi$
$564$	5560.92	0.415172
$565$	0	0
$566$	−13785.0	−1.02372
$567$	829.943	0.0614715
$568$	19891.5	1.46941
$569$	3251.08	0.239530	0.119765	−	0.992802i	$-0.461786\pi$
$569$	3251.08	0.239530	0.119765	+	0.992802i	$0.461786\pi$
$570$	0	0
$571$	−4637.50	−0.339883	−0.169941	−	0.985454i	$-0.554358\pi$
$571$	−4637.50	−0.339883	−0.169941	+	0.985454i	$0.554358\pi$
$572$	2500.73	0.182798
$573$	2556.67	0.186399
$574$	−5383.67	−0.391481
$575$	0	0
$576$	1809.20	0.130874
$577$	−14462.4	−1.04346	−0.521730	−	0.853111i	$-0.674713\pi$
$577$	−14462.4	−1.04346	−0.521730	+	0.853111i	$0.674713\pi$
$578$	−7542.82	−0.542803
$579$	−7379.86	−0.529700
$580$	0	0
$581$	−7533.23	−0.537920
$582$	4526.99	0.322423
$583$	7040.71	0.500165
$584$	7678.18	0.544050
$585$	0	0
$586$	−7071.17	−0.498476
$587$	22759.7	1.60033	0.800166	−	0.599779i	$-0.204745\pi$
$587$	22759.7	1.60033	0.800166	+	0.599779i	$0.204745\pi$
$588$	−3971.20	−0.278520
$589$	−2170.16	−0.151816
$590$	0	0
$591$	10431.2	0.726025
$592$	−512.836	−0.0356038
$593$	14956.4	1.03573	0.517864	−	0.855463i	$-0.326727\pi$
$593$	14956.4	1.03573	0.517864	+	0.855463i	$0.326727\pi$
$594$	−463.781	−0.0320356
$595$	0	0
$596$	13216.2	0.908319
$597$	−11985.1	−0.821638
$598$	3937.96	0.269290
$599$	2150.77	0.146708	0.0733539	−	0.997306i	$-0.476630\pi$
$599$	2150.77	0.146708	0.0733539	+	0.997306i	$0.476630\pi$
$600$	0	0
$601$	27759.8	1.88410	0.942050	−	0.335472i	$-0.108896\pi$
$601$	27759.8	1.88410	0.942050	+	0.335472i	$0.108896\pi$
$602$	−37.8792	−0.00256452
$603$	3644.86	0.246153
$604$	516.371	0.0347862
$605$	0	0
$606$	1633.07	0.109470
$607$	10991.5	0.734974	0.367487	−	0.930029i	$-0.380218\pi$
$607$	10991.5	0.734974	0.367487	+	0.930029i	$0.380218\pi$
$608$	7423.87	0.495194
$609$	4582.91	0.304941
$610$	0	0
$611$	13624.1	0.902081
$612$	−4940.74	−0.326336
$613$	−10646.1	−0.701457	−0.350728	−	0.936477i	$-0.614066\pi$
$613$	−10646.1	−0.701457	−0.350728	+	0.936477i	$0.614066\pi$
$614$	887.128	0.0583088
$615$	0	0
$616$	−2386.83	−0.156117
$617$	−7199.92	−0.469786	−0.234893	−	0.972021i	$-0.575474\pi$
$617$	−7199.92	−0.469786	−0.234893	+	0.972021i	$0.575474\pi$
$618$	7197.41	0.468483
$619$	12186.9	0.791332	0.395666	−	0.918395i	$-0.370514\pi$
$619$	12186.9	0.791332	0.395666	+	0.918395i	$0.370514\pi$
$620$	0	0
$621$	1665.72	0.107637
$622$	10702.2	0.689905
$623$	3953.80	0.254262
$624$	−1400.85	−0.0898698
$625$	0	0
$626$	−1778.49	−0.113551
$627$	−1308.31	−0.0833317
$628$	−10462.6	−0.664814
$629$	−4431.40	−0.280909
$630$	0	0
$631$	7370.64	0.465009	0.232505	−	0.972595i	$-0.425308\pi$
$631$	7370.64	0.465009	0.232505	+	0.972595i	$0.425308\pi$
$632$	20157.1	1.26868
$633$	−3138.38	−0.197061
$634$	5008.65	0.313752
$635$	0	0
$636$	−10679.3	−0.665818
$637$	−9729.32	−0.605164
$638$	−2560.98	−0.158919
$639$	8453.63	0.523349
$640$	0	0
$641$	−25014.9	−1.54139	−0.770693	−	0.637207i	$-0.780090\pi$
$641$	−25014.9	−1.54139	−0.770693	+	0.637207i	$0.780090\pi$
$642$	3650.19	0.224395
$643$	21668.2	1.32894	0.664472	−	0.747313i	$-0.268657\pi$
$643$	21668.2	1.32894	0.664472	+	0.747313i	$0.268657\pi$
$644$	3515.58	0.215113
$645$	0	0
$646$	6110.94	0.372185
$647$	27625.3	1.67861	0.839305	−	0.543661i	$-0.182962\pi$
$647$	27625.3	1.67861	0.839305	+	0.543661i	$0.182962\pi$
$648$	1715.34	0.103989
$649$	4078.50	0.246680
$650$	0	0
$651$	−1682.59	−0.101299
$652$	−13712.0	−0.823623
$653$	14314.0	0.857810	0.428905	−	0.903350i	$-0.358899\pi$
$653$	14314.0	0.857810	0.428905	+	0.903350i	$0.358899\pi$
$654$	−7035.38	−0.420650
$655$	0	0
$656$	3843.70	0.228767
$657$	3263.13	0.193770
$658$	−5332.73	−0.315944
$659$	−28327.8	−1.67450	−0.837249	−	0.546822i	$-0.815837\pi$
$659$	−28327.8	−1.67450	−0.837249	+	0.546822i	$0.815837\pi$
$660$	0	0
$661$	−32190.9	−1.89422	−0.947112	−	0.320905i	$-0.896013\pi$
$661$	−32190.9	−1.89422	−0.947112	+	0.320905i	$0.896013\pi$
$662$	14265.0	0.837498
$663$	−12104.7	−0.709059
$664$	−15569.8	−0.909981
$665$	0	0
$666$	630.938	0.0367092
$667$	9198.01	0.533955
$668$	−6975.84	−0.404047
$669$	−1518.80	−0.0877729
$670$	0	0
$671$	7858.46	0.452120
$672$	5755.95	0.330418
$673$	6207.38	0.355538	0.177769	−	0.984072i	$-0.443112\pi$
$673$	6207.38	0.355538	0.177769	+	0.984072i	$0.443112\pi$
$674$	−5418.66	−0.309672
$675$	0	0
$676$	2925.82	0.166467
$677$	−28831.1	−1.63674	−0.818368	−	0.574695i	$-0.805121\pi$
$677$	−28831.1	−1.63674	−0.818368	+	0.574695i	$0.805121\pi$
$678$	−796.392	−0.0451110
$679$	9901.37	0.559617
$680$	0	0
$681$	−12858.9	−0.723573
$682$	940.250	0.0527918
$683$	−3193.10	−0.178888	−0.0894441	−	0.995992i	$-0.528509\pi$
$683$	−3193.10	−0.178888	−0.0894441	+	0.995992i	$0.528509\pi$
$684$	1984.43	0.110931
$685$	0	0
$686$	9296.24	0.517394
$687$	−17128.1	−0.951206
$688$	27.0441	0.00149861
$689$	−26163.8	−1.44668
$690$	0	0
$691$	7682.49	0.422946	0.211473	−	0.977384i	$-0.432174\pi$
$691$	7682.49	0.422946	0.211473	+	0.977384i	$0.432174\pi$
$692$	−6711.17	−0.368671
$693$	−1014.37	−0.0556031
$694$	−139.496	−0.00762996
$695$	0	0
$696$	9472.05	0.515858
$697$	33213.3	1.80494
$698$	233.256	0.0126488
$699$	8838.28	0.478247
$700$	0	0
$701$	26551.6	1.43058	0.715292	−	0.698825i	$-0.246293\pi$
$701$	26551.6	1.43058	0.715292	+	0.698825i	$0.246293\pi$
$702$	1723.45	0.0926601
$703$	1779.86	0.0954887
$704$	−2211.24	−0.118380
$705$	0	0
$706$	12285.7	0.654928
$707$	3571.83	0.190004
$708$	−6186.22	−0.328379
$709$	−16304.6	−0.863655	−0.431828	−	0.901956i	$-0.642131\pi$
$709$	−16304.6	−0.863655	−0.431828	+	0.901956i	$0.642131\pi$
$710$	0	0
$711$	8566.52	0.451856
$712$	8171.79	0.430127
$713$	−3377.00	−0.177377
$714$	4738.00	0.248341
$715$	0	0
$716$	8021.36	0.418676
$717$	6236.68	0.324844
$718$	−7767.50	−0.403733
$719$	−3973.62	−0.206107	−0.103053	−	0.994676i	$-0.532861\pi$
$719$	−3973.62	−0.206107	−0.103053	+	0.994676i	$0.532861\pi$
$720$	0	0
$721$	15742.1	0.813128
$722$	8256.25	0.425576
$723$	−5560.11	−0.286007
$724$	−23702.3	−1.21670
$725$	0	0
$726$	566.844	0.0289773
$727$	10780.4	0.549961	0.274980	−	0.961450i	$-0.411329\pi$
$727$	10780.4	0.549961	0.274980	+	0.961450i	$0.411329\pi$
$728$	8869.67	0.451555
$729$	729.000	0.0370370
$730$	0	0
$731$	233.687	0.0118238
$732$	−11919.6	−0.601860
$733$	9211.46	0.464165	0.232083	−	0.972696i	$-0.425446\pi$
$733$	9211.46	0.464165	0.232083	+	0.972696i	$0.425446\pi$
$734$	−20716.6	−1.04177
$735$	0	0
$736$	11552.3	0.578566
$737$	−4454.83	−0.222654
$738$	−4728.87	−0.235870
$739$	11084.7	0.551768	0.275884	−	0.961191i	$-0.411029\pi$
$739$	11084.7	0.551768	0.275884	+	0.961191i	$0.411029\pi$
$740$	0	0
$741$	4861.80	0.241029
$742$	10241.0	0.506685
$743$	27420.4	1.35391	0.676955	−	0.736024i	$-0.263299\pi$
$743$	27420.4	1.35391	0.676955	+	0.736024i	$0.263299\pi$
$744$	−3477.61	−0.171365
$745$	0	0
$746$	−7234.32	−0.355050
$747$	−6616.99	−0.324101
$748$	6038.69	0.295182
$749$	7983.64	0.389474
$750$	0	0
$751$	−11290.8	−0.548614	−0.274307	−	0.961642i	$-0.588448\pi$
$751$	−11290.8	−0.548614	−0.274307	+	0.961642i	$0.588448\pi$
$752$	3807.33	0.184626
$753$	7075.16	0.342408
$754$	9516.81	0.459657
$755$	0	0
$756$	1538.59	0.0740185
$757$	−3739.19	−0.179528	−0.0897642	−	0.995963i	$-0.528611\pi$
$757$	−3739.19	−0.179528	−0.0897642	+	0.995963i	$0.528611\pi$
$758$	−10155.3	−0.486617
$759$	−2035.87	−0.0973617
$760$	0	0
$761$	−15621.1	−0.744107	−0.372053	−	0.928211i	$-0.621346\pi$
$761$	−15621.1	−0.744107	−0.372053	+	0.928211i	$0.621346\pi$
$762$	8150.45	0.387480
$763$	−15387.7	−0.730106
$764$	4739.69	0.224445
$765$	0	0
$766$	19885.7	0.937987
$767$	−15156.0	−0.713498
$768$	10371.8	0.487317
$769$	40241.7	1.88706	0.943531	−	0.331284i	$-0.107482\pi$
$769$	40241.7	1.88706	0.943531	+	0.331284i	$0.107482\pi$
$770$	0	0
$771$	16557.8	0.773428
$772$	−13681.2	−0.637818
$773$	−22821.4	−1.06187	−0.530936	−	0.847412i	$-0.678160\pi$
$773$	−22821.4	−1.06187	−0.530936	+	0.847412i	$0.678160\pi$
$774$	−33.2721	−0.00154514
$775$	0	0
$776$	20464.4	0.946685
$777$	1379.98	0.0637148
$778$	−18777.0	−0.865282
$779$	−13340.0	−0.613549
$780$	0	0
$781$	−10332.2	−0.473387
$782$	9509.28	0.434848
$783$	4025.51	0.183729
$784$	−2718.92	−0.123857
$785$	0	0
$786$	1465.53	0.0665062
$787$	29454.3	1.33410	0.667048	−	0.745015i	$-0.267558\pi$
$787$	29454.3	1.33410	0.667048	+	0.745015i	$0.267558\pi$
$788$	19337.8	0.874216
$789$	6778.96	0.305878
$790$	0	0
$791$	−1741.86	−0.0782974
$792$	−2096.53	−0.0940619
$793$	−29202.7	−1.30771
$794$	−8157.00	−0.364586
$795$	0	0
$796$	−22218.6	−0.989344
$797$	27440.3	1.21955	0.609777	−	0.792573i	$-0.291259\pi$
$797$	27440.3	1.21955	0.609777	+	0.792573i	$0.291259\pi$
$798$	−1903.00	−0.0844179
$799$	32899.0	1.45668
$800$	0	0
$801$	3472.91	0.153195
$802$	−15066.1	−0.663346
$803$	−3988.27	−0.175272
$804$	6757.03	0.296396
$805$	0	0
$806$	−3494.05	−0.152695
$807$	−21118.6	−0.921201
$808$	7382.34	0.321423
$809$	−5060.18	−0.219909	−0.109954	−	0.993937i	$-0.535070\pi$
$809$	−5060.18	−0.219909	−0.109954	+	0.993937i	$0.535070\pi$
$810$	0	0
$811$	30480.1	1.31973	0.659865	−	0.751384i	$-0.270613\pi$
$811$	30480.1	1.31973	0.659865	+	0.751384i	$0.270613\pi$
$812$	8496.03	0.367183
$813$	−15465.2	−0.667146
$814$	−771.146	−0.0332048
$815$	0	0
$816$	−3382.72	−0.145121
$817$	−93.8596	−0.00401925
$818$	3139.46	0.134192
$819$	3769.50	0.160827
$820$	0	0
$821$	37909.0	1.61149	0.805745	−	0.592263i	$-0.201765\pi$
$821$	37909.0	1.61149	0.805745	+	0.592263i	$0.201765\pi$
$822$	3358.56	0.142510
$823$	−23636.0	−1.00109	−0.500546	−	0.865710i	$-0.666867\pi$
$823$	−23636.0	−1.00109	−0.500546	+	0.865710i	$0.666867\pi$
$824$	32536.0	1.37554
$825$	0	0
$826$	5932.36	0.249895
$827$	42634.3	1.79267	0.896336	−	0.443376i	$-0.146219\pi$
$827$	42634.3	1.79267	0.896336	+	0.443376i	$0.146219\pi$
$828$	3087.99	0.129608
$829$	−45152.5	−1.89169	−0.945845	−	0.324619i	$-0.894764\pi$
$829$	−45152.5	−1.89169	−0.945845	+	0.324619i	$0.894764\pi$
$830$	0	0
$831$	27223.6	1.13643
$832$	8217.15	0.342402
$833$	−23494.1	−0.977217
$834$	−4106.02	−0.170480
$835$	0	0
$836$	−2425.42	−0.100341
$837$	−1477.94	−0.0610337
$838$	−6925.91	−0.285503
$839$	30431.5	1.25222	0.626110	−	0.779734i	$-0.284646\pi$
$839$	30431.5	1.25222	0.626110	+	0.779734i	$0.284646\pi$
$840$	0	0
$841$	−2160.34	−0.0885784
$842$	−23763.6	−0.972623
$843$	10223.4	0.417689
$844$	−5818.09	−0.237283
$845$	0	0
$846$	−4684.13	−0.190359
$847$	1239.79	0.0502949
$848$	−7311.64	−0.296088
$849$	−26483.2	−1.07055
$850$	0	0
$851$	2769.65	0.111566
$852$	15671.8	0.630171
$853$	−10367.2	−0.416139	−0.208070	−	0.978114i	$-0.566718\pi$
$853$	−10367.2	−0.416139	−0.208070	+	0.978114i	$0.566718\pi$
$854$	11430.5	0.458013
$855$	0	0
$856$	16500.8	0.658860
$857$	−12947.1	−0.516063	−0.258032	−	0.966136i	$-0.583074\pi$
$857$	−12947.1	−0.516063	−0.258032	+	0.966136i	$0.583074\pi$
$858$	−2106.44	−0.0838142
$859$	−20383.5	−0.809636	−0.404818	−	0.914397i	$-0.632665\pi$
$859$	−20383.5	−0.809636	−0.404818	+	0.914397i	$0.632665\pi$
$860$	0	0
$861$	−10342.9	−0.409391
$862$	8779.22	0.346893
$863$	−9056.42	−0.357224	−0.178612	−	0.983920i	$-0.557161\pi$
$863$	−9056.42	−0.357224	−0.178612	+	0.983920i	$0.557161\pi$
$864$	5055.88	0.199079
$865$	0	0
$866$	−22340.0	−0.876610
$867$	−14491.0	−0.567636
$868$	−3119.27	−0.121976
$869$	−10470.2	−0.408719
$870$	0	0
$871$	16554.5	0.644005
$872$	−31803.6	−1.23510
$873$	8697.10	0.337173
$874$	−3819.37	−0.147817
$875$	0	0
$876$	6049.36	0.233321
$877$	2867.88	0.110424	0.0552118	−	0.998475i	$-0.482417\pi$
$877$	2867.88	0.110424	0.0552118	+	0.998475i	$0.482417\pi$
$878$	−6846.16	−0.263151
$879$	−13584.9	−0.521281
$880$	0	0
$881$	−11862.5	−0.453640	−0.226820	−	0.973937i	$-0.572833\pi$
$881$	−11862.5	−0.453640	−0.226820	+	0.973937i	$0.572833\pi$
$882$	3345.06	0.127703
$883$	−33463.8	−1.27537	−0.637683	−	0.770299i	$-0.720107\pi$
$883$	−33463.8	−1.27537	−0.637683	+	0.770299i	$0.720107\pi$
$884$	−22440.3	−0.853787
$885$	0	0
$886$	−15756.0	−0.597442
$887$	−2420.75	−0.0916357	−0.0458178	−	0.998950i	$-0.514589\pi$
$887$	−2420.75	−0.0916357	−0.0458178	+	0.998950i	$0.514589\pi$
$888$	2852.17	0.107784
$889$	17826.5	0.672534
$890$	0	0
$891$	−891.000	−0.0335013
$892$	−2815.62	−0.105688
$893$	−13213.8	−0.495165
$894$	−11132.4	−0.416470
$895$	0	0
$896$	12132.9	0.452378
$897$	7565.48	0.281610
$898$	−14963.6	−0.556060
$899$	−8161.14	−0.302769
$900$	0	0
$901$	−63179.7	−2.33609
$902$	5779.73	0.213352
$903$	−72.7722	−0.00268185
$904$	−3600.10	−0.132453
$905$	0	0
$906$	−434.955	−0.0159497
$907$	38154.1	1.39679	0.698393	−	0.715714i	$-0.253899\pi$
$907$	38154.1	1.39679	0.698393	+	0.715714i	$0.253899\pi$
$908$	−23838.4	−0.871262
$909$	3137.40	0.114479
$910$	0	0
$911$	−35758.0	−1.30045	−0.650227	−	0.759740i	$-0.725326\pi$
$911$	−35758.0	−1.30045	−0.650227	+	0.759740i	$0.725326\pi$
$912$	1358.66	0.0493308
$913$	8087.44	0.293160
$914$	15614.5	0.565079
$915$	0	0
$916$	−31753.0	−1.14536
$917$	3205.39	0.115432
$918$	4161.73	0.149627
$919$	17387.5	0.624115	0.312058	−	0.950063i	$-0.398982\pi$
$919$	17387.5	0.624115	0.312058	+	0.950063i	$0.398982\pi$
$920$	0	0
$921$	1704.32	0.0609764
$922$	17357.9	0.620013
$923$	38395.3	1.36923
$924$	−1880.50	−0.0669523
$925$	0	0
$926$	−2447.20	−0.0868467
$927$	13827.4	0.489915
$928$	27918.3	0.987569
$929$	6955.93	0.245658	0.122829	−	0.992428i	$-0.460803\pi$
$929$	6955.93	0.245658	0.122829	+	0.992428i	$0.460803\pi$
$930$	0	0
$931$	9436.31	0.332183
$932$	16384.9	0.575863
$933$	20560.8	0.721467
$934$	19751.7	0.691965
$935$	0	0
$936$	7790.88	0.272065
$937$	16074.5	0.560438	0.280219	−	0.959936i	$-0.409593\pi$
$937$	16074.5	0.560438	0.280219	+	0.959936i	$0.409593\pi$
$938$	−6479.76	−0.225556
$939$	−3416.77	−0.118746
$940$	0	0
$941$	−687.126	−0.0238041	−0.0119021	−	0.999929i	$-0.503789\pi$
$941$	−687.126	−0.0238041	−0.0119021	+	0.999929i	$0.503789\pi$
$942$	8812.96	0.304821
$943$	−20758.5	−0.716849
$944$	−4235.44	−0.146030
$945$	0	0
$946$	40.6659	0.00139763
$947$	−35352.0	−1.21308	−0.606540	−	0.795053i	$-0.707443\pi$
$947$	−35352.0	−1.21308	−0.606540	+	0.795053i	$0.707443\pi$
$948$	15881.0	0.544085
$949$	14820.7	0.506956
$950$	0	0
$951$	9622.44	0.328106
$952$	21418.2	0.729168
$953$	19390.7	0.659103	0.329552	−	0.944138i	$-0.393102\pi$
$953$	19390.7	0.659103	0.329552	+	0.944138i	$0.393102\pi$
$954$	8995.45	0.305281
$955$	0	0
$956$	11561.9	0.391148
$957$	−4920.06	−0.166189
$958$	16738.7	0.564511
$959$	7345.80	0.247349
$960$	0	0
$961$	−26794.7	−0.899422
$962$	2865.64	0.0960416
$963$	7012.62	0.234661
$964$	−10307.6	−0.344384
$965$	0	0
$966$	−2961.27	−0.0986308
$967$	−28643.6	−0.952551	−0.476275	−	0.879296i	$-0.658013\pi$
$967$	−28643.6	−0.952551	−0.476275	+	0.879296i	$0.658013\pi$
$968$	2562.43	0.0850821
$969$	11740.1	0.389213
$970$	0	0
$971$	−19574.8	−0.646946	−0.323473	−	0.946237i	$-0.604851\pi$
$971$	−19574.8	−0.646946	−0.323473	+	0.946237i	$0.604851\pi$
$972$	1351.46	0.0445967
$973$	−8980.63	−0.295895
$974$	11182.6	0.367878
$975$	0	0
$976$	−8160.86	−0.267646
$977$	−50095.5	−1.64043	−0.820213	−	0.572058i	$-0.806145\pi$
$977$	−50095.5	−1.64043	−0.820213	+	0.572058i	$0.806145\pi$
$978$	11550.0	0.377636
$979$	−4244.67	−0.138570
$980$	0	0
$981$	−13516.1	−0.439895
$982$	−22747.6	−0.739211
$983$	−14445.4	−0.468706	−0.234353	−	0.972152i	$-0.575297\pi$
$983$	−14445.4	−0.468706	−0.234353	+	0.972152i	$0.575297\pi$
$984$	−21376.9	−0.692553
$985$	0	0
$986$	22980.9	0.742253
$987$	−10245.0	−0.330399
$988$	9013.05	0.290226
$989$	−146.056	−0.00469595
$990$	0	0
$991$	29120.1	0.933430	0.466715	−	0.884408i	$-0.345437\pi$
$991$	29120.1	0.933430	0.466715	+	0.884408i	$0.345437\pi$
$992$	−10250.1	−0.328064
$993$	27405.4	0.875814
$994$	−15028.7	−0.479558
$995$	0	0
$996$	−12266.9	−0.390253
$997$	9137.45	0.290257	0.145128	−	0.989413i	$-0.453640\pi$
$997$	9137.45	0.290257	0.145128	+	0.989413i	$0.453640\pi$
$998$	7244.03	0.229765
$999$	1212.14	0.0383887

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.a.m.1.1		2
3.2	odd	2		2475.4.a.n.1.2		2
5.2	odd	4		825.4.c.j.199.2		4
5.3	odd	4		825.4.c.j.199.3		4
5.4	even	2		165.4.a.c.1.2	✓	2
15.14	odd	2		495.4.a.d.1.1		2
55.54	odd	2		1815.4.a.n.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.a.c.1.2	✓	2	5.4	even	2
495.4.a.d.1.1		2	15.14	odd	2
825.4.a.m.1.1		2	1.1	even	1	trivial
825.4.c.j.199.2		4	5.2	odd	4
825.4.c.j.199.3		4	5.3	odd	4
1815.4.a.n.1.1		2	55.54	odd	2
2475.4.a.n.1.2		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	825.a (trivial)

\(f(q)\)	\(=\)	\(q-1.56155 q^{2} -3.00000 q^{3} -5.56155 q^{4} +4.68466 q^{6} +10.2462 q^{7} +21.1771 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-1.56155 q^{2} -3.00000 q^{3} -5.56155 q^{4} +4.68466 q^{6} +10.2462 q^{7} +21.1771 q^{8} +9.00000 q^{9} -11.0000 q^{11} +16.6847 q^{12} +40.8769 q^{13} -16.0000 q^{14} +11.4233 q^{16} +98.7083 q^{17} -14.0540 q^{18} -39.6458 q^{19} -30.7386 q^{21} +17.1771 q^{22} -61.6932 q^{23} -63.5312 q^{24} -63.8314 q^{26} -27.0000 q^{27} -56.9848 q^{28} -149.093 q^{29} +54.7386 q^{31} -187.255 q^{32} +33.0000 q^{33} -154.138 q^{34} -50.0540 q^{36} -44.8939 q^{37} +61.9091 q^{38} -122.631 q^{39} +336.479 q^{41} +48.0000 q^{42} +2.36745 q^{43} +61.1771 q^{44} +96.3371 q^{46} +333.295 q^{47} -34.2699 q^{48} -238.015 q^{49} -296.125 q^{51} -227.339 q^{52} -640.064 q^{53} +42.1619 q^{54} +216.985 q^{56} +118.938 q^{57} +232.816 q^{58} -370.773 q^{59} -714.405 q^{61} -85.4773 q^{62} +92.2159 q^{63} +201.022 q^{64} -51.5312 q^{66} +404.985 q^{67} -548.972 q^{68} +185.080 q^{69} +939.292 q^{71} +190.594 q^{72} +362.570 q^{73} +70.1042 q^{74} +220.492 q^{76} -112.708 q^{77} +191.494 q^{78} +951.835 q^{79} +81.0000 q^{81} -525.430 q^{82} -735.221 q^{83} +170.955 q^{84} -3.69690 q^{86} +447.278 q^{87} -232.948 q^{88} +385.879 q^{89} +418.833 q^{91} +343.110 q^{92} -164.216 q^{93} -520.458 q^{94} +561.764 q^{96} +966.345 q^{97} +371.673 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 6 q^{3} - 7 q^{4} - 3 q^{6} + 4 q^{7} - 3 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q + q^2 - 6 * q^3 - 7 * q^4 - 3 * q^6 + 4 * q^7 - 3 * q^8 + 18 * q^9	\( 2 q + q^{2} - 6 q^{3} - 7 q^{4} - 3 q^{6} + 4 q^{7} - 3 q^{8} + 18 q^{9} - 22 q^{11} + 21 q^{12} + 90 q^{13} - 32 q^{14} - 39 q^{16} + 16 q^{17} + 9 q^{18} - 170 q^{19} - 12 q^{21} - 11 q^{22} + 124 q^{23} + 9 q^{24} + 62 q^{26} - 54 q^{27} - 48 q^{28} - 158 q^{29} + 60 q^{31} - 123 q^{32} + 66 q^{33} - 366 q^{34} - 63 q^{36} + 372 q^{37} - 272 q^{38} - 270 q^{39} + 38 q^{41} + 96 q^{42} + 516 q^{43} + 77 q^{44} + 572 q^{46} - 224 q^{47} + 117 q^{48} - 542 q^{49} - 48 q^{51} - 298 q^{52} - 472 q^{53} - 27 q^{54} + 368 q^{56} + 510 q^{57} + 210 q^{58} + 248 q^{59} + 72 q^{61} - 72 q^{62} + 36 q^{63} + 769 q^{64} + 33 q^{66} + 744 q^{67} - 430 q^{68} - 372 q^{69} + 2060 q^{71} - 27 q^{72} + 486 q^{73} + 1138 q^{74} + 408 q^{76} - 44 q^{77} - 186 q^{78} + 642 q^{79} + 162 q^{81} - 1290 q^{82} + 286 q^{83} + 144 q^{84} + 1312 q^{86} + 474 q^{87} + 33 q^{88} + 244 q^{89} + 112 q^{91} + 76 q^{92} - 180 q^{93} - 1948 q^{94} + 369 q^{96} + 168 q^{97} - 407 q^{98} - 198 q^{99}+O(q^{100}) \) 2 * q + q^2 - 6 * q^3 - 7 * q^4 - 3 * q^6 + 4 * q^7 - 3 * q^8 + 18 * q^9 - 22 * q^11 + 21 * q^12 + 90 * q^13 - 32 * q^14 - 39 * q^16 + 16 * q^17 + 9 * q^18 - 170 * q^19 - 12 * q^21 - 11 * q^22 + 124 * q^23 + 9 * q^24 + 62 * q^26 - 54 * q^27 - 48 * q^28 - 158 * q^29 + 60 * q^31 - 123 * q^32 + 66 * q^33 - 366 * q^34 - 63 * q^36 + 372 * q^37 - 272 * q^38 - 270 * q^39 + 38 * q^41 + 96 * q^42 + 516 * q^43 + 77 * q^44 + 572 * q^46 - 224 * q^47 + 117 * q^48 - 542 * q^49 - 48 * q^51 - 298 * q^52 - 472 * q^53 - 27 * q^54 + 368 * q^56 + 510 * q^57 + 210 * q^58 + 248 * q^59 + 72 * q^61 - 72 * q^62 + 36 * q^63 + 769 * q^64 + 33 * q^66 + 744 * q^67 - 430 * q^68 - 372 * q^69 + 2060 * q^71 - 27 * q^72 + 486 * q^73 + 1138 * q^74 + 408 * q^76 - 44 * q^77 - 186 * q^78 + 642 * q^79 + 162 * q^81 - 1290 * q^82 + 286 * q^83 + 144 * q^84 + 1312 * q^86 + 474 * q^87 + 33 * q^88 + 244 * q^89 + 112 * q^91 + 76 * q^92 - 180 * q^93 - 1948 * q^94 + 369 * q^96 + 168 * q^97 - 407 * q^98 - 198 * q^99

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