LMFDB - Embedded newform 1150.4.a.x.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,4,Mod(1,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1150.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1150.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:	$67.8521965066$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 109x^{4} + 94x^{3} + 2808x^{2} + 81x - 9774 $ x^6 - x^5 - 109x^4 + 94x^3 + 2808x^2 + 81x - 9774
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.16288$ of defining polynomial
Character	$\chi$	$=$	1150.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} -3.16288 q^{3} +4.00000 q^{4} -6.32576 q^{6} +3.52475 q^{7} +8.00000 q^{8} -16.9962 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} -3.16288 q^{3} +4.00000 q^{4} -6.32576 q^{6} +3.52475 q^{7} +8.00000 q^{8} -16.9962 q^{9} -16.9719 q^{11} -12.6515 q^{12} +46.0060 q^{13} +7.04951 q^{14} +16.0000 q^{16} +16.2568 q^{17} -33.9924 q^{18} -31.1330 q^{19} -11.1484 q^{21} -33.9437 q^{22} -23.0000 q^{23} -25.3030 q^{24} +92.0120 q^{26} +139.155 q^{27} +14.0990 q^{28} -11.4072 q^{29} -82.7344 q^{31} +32.0000 q^{32} +53.6800 q^{33} +32.5135 q^{34} -67.9848 q^{36} -296.932 q^{37} -62.2659 q^{38} -145.511 q^{39} +407.814 q^{41} -22.2967 q^{42} -549.918 q^{43} -67.8875 q^{44} -46.0000 q^{46} +503.804 q^{47} -50.6061 q^{48} -330.576 q^{49} -51.4182 q^{51} +184.024 q^{52} -605.711 q^{53} +278.309 q^{54} +28.1980 q^{56} +98.4698 q^{57} -22.8143 q^{58} +522.579 q^{59} +242.576 q^{61} -165.469 q^{62} -59.9074 q^{63} +64.0000 q^{64} +107.360 q^{66} -1014.23 q^{67} +65.0271 q^{68} +72.7462 q^{69} -334.393 q^{71} -135.970 q^{72} -181.460 q^{73} -593.864 q^{74} -124.532 q^{76} -59.8216 q^{77} -291.023 q^{78} -461.511 q^{79} +18.7681 q^{81} +815.628 q^{82} -817.840 q^{83} -44.5935 q^{84} -1099.84 q^{86} +36.0795 q^{87} -135.775 q^{88} -774.536 q^{89} +162.160 q^{91} -92.0000 q^{92} +261.679 q^{93} +1007.61 q^{94} -101.212 q^{96} +1402.97 q^{97} -661.152 q^{98} +288.457 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 12 q^{2} - 5 q^{3} + 24 q^{4} - 10 q^{6} - 42 q^{7} + 48 q^{8} + 61 q^{9}+O(q^{10}) $ 6 * q + 12 * q^2 - 5 * q^3 + 24 * q^4 - 10 * q^6 - 42 * q^7 + 48 * q^8 + 61 * q^9	\( 6 q + 12 q^{2} - 5 q^{3} + 24 q^{4} - 10 q^{6} - 42 q^{7} + 48 q^{8} + 61 q^{9} - 49 q^{11} - 20 q^{12} - 16 q^{13} - 84 q^{14} + 96 q^{16} - 175 q^{17} + 122 q^{18} - 229 q^{19} + 92 q^{21} - 98 q^{22} - 138 q^{23} - 40 q^{24} - 32 q^{26} - 344 q^{27} - 168 q^{28} - 182 q^{29} + 114 q^{31} + 192 q^{32} - 641 q^{33} - 350 q^{34} + 244 q^{36} - 64 q^{37} - 458 q^{38} - 143 q^{39} + 243 q^{41} + 184 q^{42} - 182 q^{43} - 196 q^{44} - 276 q^{46} - 498 q^{47} - 80 q^{48} + 648 q^{49} - 1031 q^{51} - 64 q^{52} - 1290 q^{53} - 688 q^{54} - 336 q^{56} + 353 q^{57} - 364 q^{58} - 559 q^{59} - 688 q^{61} + 228 q^{62} - 3656 q^{63} + 384 q^{64} - 1282 q^{66} + 2069 q^{67} - 700 q^{68} + 115 q^{69} + 584 q^{71} + 488 q^{72} - 2485 q^{73} - 128 q^{74} - 916 q^{76} + 810 q^{77} - 286 q^{78} - 1432 q^{79} + 34 q^{81} + 486 q^{82} - 2089 q^{83} + 368 q^{84} - 364 q^{86} - 527 q^{87} - 392 q^{88} - 591 q^{89} - 2864 q^{91} - 552 q^{92} - 4899 q^{93} - 996 q^{94} - 160 q^{96} + 968 q^{97} + 1296 q^{98} - 142 q^{99}+O(q^{100}) \) 6 * q + 12 * q^2 - 5 * q^3 + 24 * q^4 - 10 * q^6 - 42 * q^7 + 48 * q^8 + 61 * q^9 - 49 * q^11 - 20 * q^12 - 16 * q^13 - 84 * q^14 + 96 * q^16 - 175 * q^17 + 122 * q^18 - 229 * q^19 + 92 * q^21 - 98 * q^22 - 138 * q^23 - 40 * q^24 - 32 * q^26 - 344 * q^27 - 168 * q^28 - 182 * q^29 + 114 * q^31 + 192 * q^32 - 641 * q^33 - 350 * q^34 + 244 * q^36 - 64 * q^37 - 458 * q^38 - 143 * q^39 + 243 * q^41 + 184 * q^42 - 182 * q^43 - 196 * q^44 - 276 * q^46 - 498 * q^47 - 80 * q^48 + 648 * q^49 - 1031 * q^51 - 64 * q^52 - 1290 * q^53 - 688 * q^54 - 336 * q^56 + 353 * q^57 - 364 * q^58 - 559 * q^59 - 688 * q^61 + 228 * q^62 - 3656 * q^63 + 384 * q^64 - 1282 * q^66 + 2069 * q^67 - 700 * q^68 + 115 * q^69 + 584 * q^71 + 488 * q^72 - 2485 * q^73 - 128 * q^74 - 916 * q^76 + 810 * q^77 - 286 * q^78 - 1432 * q^79 + 34 * q^81 + 486 * q^82 - 2089 * q^83 + 368 * q^84 - 364 * q^86 - 527 * q^87 - 392 * q^88 - 591 * q^89 - 2864 * q^91 - 552 * q^92 - 4899 * q^93 - 996 * q^94 - 160 * q^96 + 968 * q^97 + 1296 * q^98 - 142 * 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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−3.16288	−0.608696	−0.304348	−	0.952561i	$-0.598439\pi$
$3$	−3.16288	−0.608696	−0.304348	+	0.952561i	$0.598439\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−6.32576	−0.430413
$7$	3.52475	0.190319	0.0951594	−	0.995462i	$-0.469664\pi$
$7$	3.52475	0.190319	0.0951594	+	0.995462i	$0.469664\pi$
$8$	8.00000	0.353553
$9$	−16.9962	−0.629489
$10$	0	0
$11$	−16.9719	−0.465201	−0.232601	−	0.972572i	$-0.574723\pi$
$11$	−16.9719	−0.465201	−0.232601	+	0.972572i	$0.574723\pi$
$12$	−12.6515	−0.304348
$13$	46.0060	0.981520	0.490760	−	0.871295i	$-0.336719\pi$
$13$	46.0060	0.981520	0.490760	+	0.871295i	$0.336719\pi$
$14$	7.04951	0.134576
$15$	0	0
$16$	16.0000	0.250000
$17$	16.2568	0.231932	0.115966	−	0.993253i	$-0.463004\pi$
$17$	16.2568	0.231932	0.115966	+	0.993253i	$0.463004\pi$
$18$	−33.9924	−0.445116
$19$	−31.1330	−0.375915	−0.187958	−	0.982177i	$-0.560187\pi$
$19$	−31.1330	−0.375915	−0.187958	+	0.982177i	$0.560187\pi$
$20$	0	0
$21$	−11.1484	−0.115846
$22$	−33.9437	−0.328947
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−25.3030	−0.215207
$25$	0	0
$26$	92.0120	0.694040
$27$	139.155	0.991864
$28$	14.0990	0.0951594
$29$	−11.4072	−0.0730433	−0.0365217	−	0.999333i	$-0.511628\pi$
$29$	−11.4072	−0.0730433	−0.0365217	+	0.999333i	$0.511628\pi$
$30$	0	0
$31$	−82.7344	−0.479340	−0.239670	−	0.970854i	$-0.577039\pi$
$31$	−82.7344	−0.479340	−0.239670	+	0.970854i	$0.577039\pi$
$32$	32.0000	0.176777
$33$	53.6800	0.283166
$34$	32.5135	0.164001
$35$	0	0
$36$	−67.9848	−0.314744
$37$	−296.932	−1.31933	−0.659666	−	0.751559i	$-0.729302\pi$
$37$	−296.932	−1.31933	−0.659666	+	0.751559i	$0.729302\pi$
$38$	−62.2659	−0.265812
$39$	−145.511	−0.597448
$40$	0	0
$41$	407.814	1.55341	0.776705	−	0.629864i	$-0.216890\pi$
$41$	407.814	1.55341	0.776705	+	0.629864i	$0.216890\pi$
$42$	−22.2967	−0.0819157
$43$	−549.918	−1.95027	−0.975136	−	0.221609i	$-0.928869\pi$
$43$	−549.918	−1.95027	−0.975136	+	0.221609i	$0.928869\pi$
$44$	−67.8875	−0.232601
$45$	0	0
$46$	−46.0000	−0.147442
$47$	503.804	1.56356	0.781781	−	0.623553i	$-0.214311\pi$
$47$	503.804	1.56356	0.781781	+	0.623553i	$0.214311\pi$
$48$	−50.6061	−0.152174
$49$	−330.576	−0.963779
$50$	0	0
$51$	−51.4182	−0.141176
$52$	184.024	0.490760
$53$	−605.711	−1.56983	−0.784913	−	0.619606i	$-0.787293\pi$
$53$	−605.711	−1.56983	−0.784913	+	0.619606i	$0.787293\pi$
$54$	278.309	0.701354
$55$	0	0
$56$	28.1980	0.0672878
$57$	98.4698	0.228818
$58$	−22.8143	−0.0516494
$59$	522.579	1.15312	0.576559	−	0.817056i	$-0.304395\pi$
$59$	522.579	1.15312	0.576559	+	0.817056i	$0.304395\pi$
$60$	0	0
$61$	242.576	0.509158	0.254579	−	0.967052i	$-0.418063\pi$
$61$	242.576	0.509158	0.254579	+	0.967052i	$0.418063\pi$
$62$	−165.469	−0.338945
$63$	−59.9074	−0.119804
$64$	64.0000	0.125000
$65$	0	0
$66$	107.360	0.200229
$67$	−1014.23	−1.84937	−0.924687	−	0.380728i	$-0.875674\pi$
$67$	−1014.23	−1.84937	−0.924687	+	0.380728i	$0.875674\pi$
$68$	65.0271	0.115966
$69$	72.7462	0.126922
$70$	0	0
$71$	−334.393	−0.558946	−0.279473	−	0.960154i	$-0.590160\pi$
$71$	−334.393	−0.558946	−0.279473	+	0.960154i	$0.590160\pi$
$72$	−135.970	−0.222558
$73$	−181.460	−0.290935	−0.145468	−	0.989363i	$-0.546469\pi$
$73$	−181.460	−0.290935	−0.145468	+	0.989363i	$0.546469\pi$
$74$	−593.864	−0.932909
$75$	0	0
$76$	−124.532	−0.187958
$77$	−59.8216	−0.0885365
$78$	−291.023	−0.422459
$79$	−461.511	−0.657267	−0.328633	−	0.944458i	$-0.606588\pi$
$79$	−461.511	−0.657267	−0.328633	+	0.944458i	$0.606588\pi$
$80$	0	0
$81$	18.7681	0.0257450
$82$	815.628	1.09843
$83$	−817.840	−1.08156	−0.540781	−	0.841164i	$-0.681871\pi$
$83$	−817.840	−1.08156	−0.540781	+	0.841164i	$0.681871\pi$
$84$	−44.5935	−0.0579232
$85$	0	0
$86$	−1099.84	−1.37905
$87$	36.0795	0.0444612
$88$	−135.775	−0.164473
$89$	−774.536	−0.922479	−0.461240	−	0.887276i	$-0.652595\pi$
$89$	−774.536	−0.922479	−0.461240	+	0.887276i	$0.652595\pi$
$90$	0	0
$91$	162.160	0.186802
$92$	−92.0000	−0.104257
$93$	261.679	0.291773
$94$	1007.61	1.10561
$95$	0	0
$96$	−101.212	−0.107603
$97$	1402.97	1.46856	0.734278	−	0.678848i	$-0.237521\pi$
$97$	1402.97	1.46856	0.734278	+	0.678848i	$0.237521\pi$
$98$	−661.152	−0.681495
$99$	288.457	0.292839
$100$	0	0
$101$	−722.988	−0.712278	−0.356139	−	0.934433i	$-0.615907\pi$
$101$	−722.988	−0.712278	−0.356139	+	0.934433i	$0.615907\pi$
$102$	−102.836	−0.0998266
$103$	−1202.82	−1.15066	−0.575328	−	0.817923i	$-0.695126\pi$
$103$	−1202.82	−1.15066	−0.575328	+	0.817923i	$0.695126\pi$
$104$	368.048	0.347020
$105$	0	0
$106$	−1211.42	−1.11004
$107$	−905.720	−0.818311	−0.409155	−	0.912465i	$-0.634177\pi$
$107$	−905.720	−0.818311	−0.409155	+	0.912465i	$0.634177\pi$
$108$	556.619	0.495932
$109$	1447.48	1.27196	0.635978	−	0.771707i	$-0.280597\pi$
$109$	1447.48	1.27196	0.635978	+	0.771707i	$0.280597\pi$
$110$	0	0
$111$	939.159	0.803072
$112$	56.3960	0.0475797
$113$	−977.048	−0.813389	−0.406694	−	0.913564i	$-0.633319\pi$
$113$	−977.048	−0.813389	−0.406694	+	0.913564i	$0.633319\pi$
$114$	196.940	0.161799
$115$	0	0
$116$	−45.6286	−0.0365217
$117$	−781.927	−0.617856
$118$	1045.16	0.815378
$119$	57.3011	0.0441410
$120$	0	0
$121$	−1042.96	−0.783588
$122$	485.152	0.360029
$123$	−1289.87	−0.945555
$124$	−330.938	−0.239670
$125$	0	0
$126$	−119.815	−0.0847139
$127$	1375.77	0.961261	0.480630	−	0.876923i	$-0.340408\pi$
$127$	1375.77	0.961261	0.480630	+	0.876923i	$0.340408\pi$
$128$	128.000	0.0883883
$129$	1739.32	1.18712
$130$	0	0
$131$	−62.3804	−0.0416046	−0.0208023	−	0.999784i	$-0.506622\pi$
$131$	−62.3804	−0.0416046	−0.0208023	+	0.999784i	$0.506622\pi$
$132$	214.720	0.141583
$133$	−109.736	−0.0715437
$134$	−2028.46	−1.30771
$135$	0	0
$136$	130.054	0.0820004
$137$	192.858	0.120270	0.0601349	−	0.998190i	$-0.480847\pi$
$137$	192.858	0.120270	0.0601349	+	0.998190i	$0.480847\pi$
$138$	145.492	0.0897474
$139$	128.503	0.0784136	0.0392068	−	0.999231i	$-0.487517\pi$
$139$	128.503	0.0784136	0.0392068	+	0.999231i	$0.487517\pi$
$140$	0	0
$141$	−1593.47	−0.951734
$142$	−668.786	−0.395234
$143$	−780.807	−0.456604
$144$	−271.939	−0.157372
$145$	0	0
$146$	−362.919	−0.205722
$147$	1045.57	0.586649
$148$	−1187.73	−0.659666
$149$	−1444.01	−0.793945	−0.396973	−	0.917830i	$-0.629939\pi$
$149$	−1444.01	−0.793945	−0.396973	+	0.917830i	$0.629939\pi$
$150$	0	0
$151$	−2402.73	−1.29491	−0.647455	−	0.762104i	$-0.724167\pi$
$151$	−2402.73	−1.29491	−0.647455	+	0.762104i	$0.724167\pi$
$152$	−249.064	−0.132906
$153$	−276.303	−0.145999
$154$	−119.643	−0.0626047
$155$	0	0
$156$	−582.045	−0.298724
$157$	−837.263	−0.425610	−0.212805	−	0.977095i	$-0.568260\pi$
$157$	−837.263	−0.425610	−0.212805	+	0.977095i	$0.568260\pi$
$158$	−923.023	−0.464758
$159$	1915.79	0.955548
$160$	0	0
$161$	−81.0693	−0.0396842
$162$	37.5362	0.0182045
$163$	−1418.97	−0.681854	−0.340927	−	0.940090i	$-0.610741\pi$
$163$	−1418.97	−0.681854	−0.340927	+	0.940090i	$0.610741\pi$
$164$	1631.26	0.776705
$165$	0	0
$166$	−1635.68	−0.764780
$167$	−1786.36	−0.827741	−0.413871	−	0.910336i	$-0.635823\pi$
$167$	−1786.36	−0.827741	−0.413871	+	0.910336i	$0.635823\pi$
$168$	−89.1869	−0.0409579
$169$	−80.4501	−0.0366182
$170$	0	0
$171$	529.142	0.236635
$172$	−2199.67	−0.975136
$173$	−1689.82	−0.742627	−0.371313	−	0.928508i	$-0.621092\pi$
$173$	−1689.82	−0.742627	−0.371313	+	0.928508i	$0.621092\pi$
$174$	72.1589	0.0314388
$175$	0	0
$176$	−271.550	−0.116300
$177$	−1652.85	−0.701899
$178$	−1549.07	−0.652291
$179$	−575.043	−0.240116	−0.120058	−	0.992767i	$-0.538308\pi$
$179$	−575.043	−0.240116	−0.120058	+	0.992767i	$0.538308\pi$
$180$	0	0
$181$	48.4102	0.0198801	0.00994006	−	0.999951i	$-0.496836\pi$
$181$	48.4102	0.0198801	0.00994006	+	0.999951i	$0.496836\pi$
$182$	324.319	0.132089
$183$	−767.238	−0.309923
$184$	−184.000	−0.0737210
$185$	0	0
$186$	523.358	0.206314
$187$	−275.908	−0.107895
$188$	2015.22	0.781781
$189$	490.486	0.188770
$190$	0	0
$191$	−1952.22	−0.739571	−0.369785	−	0.929117i	$-0.620569\pi$
$191$	−1952.22	−0.739571	−0.369785	+	0.929117i	$0.620569\pi$
$192$	−202.424	−0.0760870
$193$	4152.46	1.54871	0.774353	−	0.632754i	$-0.218075\pi$
$193$	4152.46	1.54871	0.774353	+	0.632754i	$0.218075\pi$
$194$	2805.94	1.03843
$195$	0	0
$196$	−1322.30	−0.481889
$197$	−3455.75	−1.24981	−0.624903	−	0.780703i	$-0.714861\pi$
$197$	−3455.75	−1.24981	−0.624903	+	0.780703i	$0.714861\pi$
$198$	576.915	0.207068
$199$	1858.62	0.662081	0.331041	−	0.943617i	$-0.392600\pi$
$199$	1858.62	0.662081	0.331041	+	0.943617i	$0.392600\pi$
$200$	0	0
$201$	3207.89	1.12571
$202$	−1445.98	−0.503656
$203$	−40.2074	−0.0139015
$204$	−205.673	−0.0705881
$205$	0	0
$206$	−2405.64	−0.813637
$207$	390.913	0.131257
$208$	736.096	0.245380
$209$	528.385	0.174876
$210$	0	0
$211$	1247.90	0.407153	0.203576	−	0.979059i	$-0.434744\pi$
$211$	1247.90	0.407153	0.203576	+	0.979059i	$0.434744\pi$
$212$	−2422.84	−0.784913
$213$	1057.64	0.340228
$214$	−1811.44	−0.578633
$215$	0	0
$216$	1113.24	0.350677
$217$	−291.618	−0.0912274
$218$	2894.95	0.899409
$219$	573.935	0.177091
$220$	0	0
$221$	747.908	0.227646
$222$	1878.32	0.567858
$223$	−4469.97	−1.34229	−0.671146	−	0.741325i	$-0.734198\pi$
$223$	−4469.97	−1.34229	−0.671146	+	0.741325i	$0.734198\pi$
$224$	112.792	0.0336439
$225$	0	0
$226$	−1954.10	−0.575153
$227$	1773.90	0.518668	0.259334	−	0.965788i	$-0.416497\pi$
$227$	1773.90	0.518668	0.259334	+	0.965788i	$0.416497\pi$
$228$	393.879	0.114409
$229$	77.0418	0.0222317	0.0111159	−	0.999938i	$-0.496462\pi$
$229$	77.0418	0.0222317	0.0111159	+	0.999938i	$0.496462\pi$
$230$	0	0
$231$	189.209	0.0538918
$232$	−91.2573	−0.0258247
$233$	−5866.47	−1.64946	−0.824732	−	0.565523i	$-0.808674\pi$
$233$	−5866.47	−1.64946	−0.824732	+	0.565523i	$0.808674\pi$
$234$	−1563.85	−0.436890
$235$	0	0
$236$	2090.32	0.576559
$237$	1459.70	0.400076
$238$	114.602	0.0312124
$239$	4724.40	1.27865	0.639323	−	0.768938i	$-0.279215\pi$
$239$	4724.40	1.27865	0.639323	+	0.768938i	$0.279215\pi$
$240$	0	0
$241$	2608.08	0.697100	0.348550	−	0.937290i	$-0.386674\pi$
$241$	2608.08	0.697100	0.348550	+	0.937290i	$0.386674\pi$
$242$	−2085.91	−0.554080
$243$	−3816.54	−1.00753
$244$	970.304	0.254579
$245$	0	0
$246$	−2579.73	−0.668608
$247$	−1432.30	−0.368969
$248$	−661.876	−0.169472
$249$	2586.73	0.658343
$250$	0	0
$251$	−1850.32	−0.465303	−0.232651	−	0.972560i	$-0.574740\pi$
$251$	−1850.32	−0.465303	−0.232651	+	0.972560i	$0.574740\pi$
$252$	−239.630	−0.0599018
$253$	390.353	0.0970011
$254$	2751.55	0.679714
$255$	0	0
$256$	256.000	0.0625000
$257$	−3517.67	−0.853798	−0.426899	−	0.904299i	$-0.640394\pi$
$257$	−3517.67	−0.853798	−0.426899	+	0.904299i	$0.640394\pi$
$258$	3478.65	0.839423
$259$	−1046.61	−0.251094
$260$	0	0
$261$	193.878	0.0459800
$262$	−124.761	−0.0294189
$263$	−3658.06	−0.857665	−0.428832	−	0.903384i	$-0.641075\pi$
$263$	−3658.06	−0.857665	−0.428832	+	0.903384i	$0.641075\pi$
$264$	429.440	0.100114
$265$	0	0
$266$	−219.472	−0.0505891
$267$	2449.76	0.561510
$268$	−4056.93	−0.924687
$269$	6608.58	1.49789	0.748945	−	0.662632i	$-0.230561\pi$
$269$	6608.58	1.49789	0.748945	+	0.662632i	$0.230561\pi$
$270$	0	0
$271$	2221.78	0.498021	0.249010	−	0.968501i	$-0.419895\pi$
$271$	2221.78	0.498021	0.249010	+	0.968501i	$0.419895\pi$
$272$	260.108	0.0579830
$273$	−512.891	−0.113705
$274$	385.716	0.0850436
$275$	0	0
$276$	290.985	0.0634610
$277$	3489.90	0.756995	0.378498	−	0.925602i	$-0.376441\pi$
$277$	3489.90	0.756995	0.378498	+	0.925602i	$0.376441\pi$
$278$	257.006	0.0554468
$279$	1406.17	0.301739
$280$	0	0
$281$	2672.59	0.567378	0.283689	−	0.958916i	$-0.408442\pi$
$281$	2672.59	0.567378	0.283689	+	0.958916i	$0.408442\pi$
$282$	−3186.94	−0.672978
$283$	7336.12	1.54094	0.770471	−	0.637474i	$-0.220021\pi$
$283$	7336.12	1.54094	0.770471	+	0.637474i	$0.220021\pi$
$284$	−1337.57	−0.279473
$285$	0	0
$286$	−1561.61	−0.322868
$287$	1437.44	0.295643
$288$	−543.878	−0.111279
$289$	−4648.72	−0.946208
$290$	0	0
$291$	−4437.42	−0.893905
$292$	−725.839	−0.145468
$293$	−4852.82	−0.967593	−0.483797	−	0.875180i	$-0.660743\pi$
$293$	−4852.82	−0.967593	−0.483797	+	0.875180i	$0.660743\pi$
$294$	2091.14	0.414823
$295$	0	0
$296$	−2375.45	−0.466454
$297$	−2361.71	−0.461416
$298$	−2888.02	−0.561404
$299$	−1058.14	−0.204661
$300$	0	0
$301$	−1938.32	−0.371173
$302$	−4805.46	−0.915639
$303$	2286.72	0.433561
$304$	−498.127	−0.0939788
$305$	0	0
$306$	−552.606	−0.103237
$307$	−2018.34	−0.375222	−0.187611	−	0.982243i	$-0.560074\pi$
$307$	−2018.34	−0.375222	−0.187611	+	0.982243i	$0.560074\pi$
$308$	−239.287	−0.0442682
$309$	3804.38	0.700400
$310$	0	0
$311$	6965.89	1.27009	0.635047	−	0.772473i	$-0.280981\pi$
$311$	6965.89	1.27009	0.635047	+	0.772473i	$0.280981\pi$
$312$	−1164.09	−0.211230
$313$	−2237.01	−0.403972	−0.201986	−	0.979388i	$-0.564739\pi$
$313$	−2237.01	−0.403972	−0.201986	+	0.979388i	$0.564739\pi$
$314$	−1674.53	−0.300952
$315$	0	0
$316$	−1846.05	−0.328633
$317$	6606.75	1.17057	0.585287	−	0.810826i	$-0.300982\pi$
$317$	6606.75	1.17057	0.585287	+	0.810826i	$0.300982\pi$
$318$	3831.58	0.675674
$319$	193.601	0.0339798
$320$	0	0
$321$	2864.68	0.498103
$322$	−162.139	−0.0280610
$323$	−506.121	−0.0871868
$324$	75.0724	0.0128725
$325$	0	0
$326$	−2837.94	−0.482144
$327$	−4578.20	−0.774235
$328$	3262.51	0.549213
$329$	1775.79	0.297575
$330$	0	0
$331$	10788.7	1.79155	0.895773	−	0.444512i	$-0.146623\pi$
$331$	10788.7	1.79155	0.895773	+	0.444512i	$0.146623\pi$
$332$	−3271.36	−0.540781
$333$	5046.71	0.830505
$334$	−3572.72	−0.585301
$335$	0	0
$336$	−178.374	−0.0289616
$337$	2344.43	0.378959	0.189480	−	0.981885i	$-0.439320\pi$
$337$	2344.43	0.378959	0.189480	+	0.981885i	$0.439320\pi$
$338$	−160.900	−0.0258929
$339$	3090.28	0.495107
$340$	0	0
$341$	1404.16	0.222990
$342$	1058.28	0.167326
$343$	−2374.19	−0.373744
$344$	−4399.34	−0.689525
$345$	0	0
$346$	−3379.63	−0.525116
$347$	6153.83	0.952031	0.476016	−	0.879437i	$-0.342081\pi$
$347$	6153.83	0.952031	0.476016	+	0.879437i	$0.342081\pi$
$348$	144.318	0.0222306
$349$	8290.01	1.27150	0.635751	−	0.771894i	$-0.280690\pi$
$349$	8290.01	1.27150	0.635751	+	0.771894i	$0.280690\pi$
$350$	0	0
$351$	6401.95	0.973534
$352$	−543.100	−0.0822367
$353$	−736.002	−0.110973	−0.0554864	−	0.998459i	$-0.517671\pi$
$353$	−736.002	−0.110973	−0.0554864	+	0.998459i	$0.517671\pi$
$354$	−3305.71	−0.496317
$355$	0	0
$356$	−3098.14	−0.461240
$357$	−181.236	−0.0268685
$358$	−1150.09	−0.169788
$359$	2508.91	0.368844	0.184422	−	0.982847i	$-0.440959\pi$
$359$	2508.91	0.368844	0.184422	+	0.982847i	$0.440959\pi$
$360$	0	0
$361$	−5889.74	−0.858688
$362$	96.8204	0.0140574
$363$	3298.74	0.476967
$364$	648.639	0.0934008
$365$	0	0
$366$	−1534.48	−0.219149
$367$	2094.68	0.297932	0.148966	−	0.988842i	$-0.452405\pi$
$367$	2094.68	0.297932	0.148966	+	0.988842i	$0.452405\pi$
$368$	−368.000	−0.0521286
$369$	−6931.28	−0.977854
$370$	0	0
$371$	−2134.98	−0.298767
$372$	1046.72	0.145886
$373$	2809.54	0.390006	0.195003	−	0.980803i	$-0.437528\pi$
$373$	2809.54	0.390006	0.195003	+	0.980803i	$0.437528\pi$
$374$	−551.815	−0.0762933
$375$	0	0
$376$	4030.43	0.552803
$377$	−524.798	−0.0716935
$378$	980.971	0.133481
$379$	−2155.99	−0.292205	−0.146102	−	0.989269i	$-0.546673\pi$
$379$	−2155.99	−0.292205	−0.146102	+	0.989269i	$0.546673\pi$
$380$	0	0
$381$	−4351.40	−0.585116
$382$	−3904.45	−0.522955
$383$	3150.35	0.420302	0.210151	−	0.977669i	$-0.432604\pi$
$383$	3150.35	0.420302	0.210151	+	0.977669i	$0.432604\pi$
$384$	−404.848	−0.0538017
$385$	0	0
$386$	8304.91	1.09510
$387$	9346.51	1.22767
$388$	5611.88	0.734278
$389$	−4603.59	−0.600028	−0.300014	−	0.953935i	$-0.596991\pi$
$389$	−4603.59	−0.600028	−0.300014	+	0.953935i	$0.596991\pi$
$390$	0	0
$391$	−373.906	−0.0483612
$392$	−2644.61	−0.340747
$393$	197.302	0.0253246
$394$	−6911.49	−0.883746
$395$	0	0
$396$	1153.83	0.146419
$397$	10317.2	1.30430	0.652151	−	0.758089i	$-0.273867\pi$
$397$	10317.2	1.30430	0.652151	+	0.758089i	$0.273867\pi$
$398$	3717.24	0.468162
$399$	347.082	0.0435484
$400$	0	0
$401$	12538.6	1.56146	0.780730	−	0.624868i	$-0.214847\pi$
$401$	12538.6	1.56146	0.780730	+	0.624868i	$0.214847\pi$
$402$	6415.78	0.795995
$403$	−3806.28	−0.470482
$404$	−2891.95	−0.356139
$405$	0	0
$406$	−80.4148	−0.00982985
$407$	5039.49	0.613755
$408$	−411.345	−0.0499133
$409$	−321.102	−0.0388202	−0.0194101	−	0.999812i	$-0.506179\pi$
$409$	−321.102	−0.0388202	−0.0194101	+	0.999812i	$0.506179\pi$
$410$	0	0
$411$	−609.986	−0.0732078
$412$	−4811.29	−0.575328
$413$	1841.96	0.219460
$414$	781.825	0.0928131
$415$	0	0
$416$	1472.19	0.173510
$417$	−406.440	−0.0477301
$418$	1056.77	0.123656
$419$	2311.14	0.269467	0.134733	−	0.990882i	$-0.456982\pi$
$419$	2311.14	0.269467	0.134733	+	0.990882i	$0.456982\pi$
$420$	0	0
$421$	14940.8	1.72962	0.864809	−	0.502101i	$-0.167439\pi$
$421$	14940.8	1.72962	0.864809	+	0.502101i	$0.167439\pi$
$422$	2495.81	0.287900
$423$	−8562.76	−0.984245
$424$	−4845.69	−0.555018
$425$	0	0
$426$	2115.29	0.240578
$427$	855.020	0.0969024
$428$	−3622.88	−0.409155
$429$	2469.60	0.277933
$430$	0	0
$431$	−10158.2	−1.13528	−0.567640	−	0.823277i	$-0.692143\pi$
$431$	−10158.2	−1.13528	−0.567640	+	0.823277i	$0.692143\pi$
$432$	2226.47	0.247966
$433$	962.136	0.106784	0.0533918	−	0.998574i	$-0.482997\pi$
$433$	962.136	0.106784	0.0533918	+	0.998574i	$0.482997\pi$
$434$	−583.237	−0.0645075
$435$	0	0
$436$	5789.91	0.635978
$437$	716.058	0.0783838
$438$	1147.87	0.125222
$439$	−694.763	−0.0755335	−0.0377668	−	0.999287i	$-0.512024\pi$
$439$	−694.763	−0.0755335	−0.0377668	+	0.999287i	$0.512024\pi$
$440$	0	0
$441$	5618.54	0.606688
$442$	1495.82	0.160970
$443$	1568.53	0.168224	0.0841121	−	0.996456i	$-0.473195\pi$
$443$	1568.53	0.168224	0.0841121	+	0.996456i	$0.473195\pi$
$444$	3756.64	0.401536
$445$	0	0
$446$	−8939.93	−0.949144
$447$	4567.23	0.483272
$448$	225.584	0.0237898
$449$	−6976.58	−0.733286	−0.366643	−	0.930362i	$-0.619493\pi$
$449$	−6976.58	−0.733286	−0.366643	+	0.930362i	$0.619493\pi$
$450$	0	0
$451$	−6921.36	−0.722648
$452$	−3908.19	−0.406694
$453$	7599.54	0.788207
$454$	3547.79	0.366754
$455$	0	0
$456$	787.758	0.0808995
$457$	11623.4	1.18976	0.594878	−	0.803816i	$-0.297200\pi$
$457$	11623.4	1.18976	0.594878	+	0.803816i	$0.297200\pi$
$458$	154.084	0.0157202
$459$	2262.20	0.230045
$460$	0	0
$461$	17230.4	1.74078	0.870390	−	0.492364i	$-0.163867\pi$
$461$	17230.4	1.74078	0.870390	+	0.492364i	$0.163867\pi$
$462$	378.417	0.0381073
$463$	16831.5	1.68947	0.844735	−	0.535185i	$-0.179758\pi$
$463$	16831.5	1.68947	0.844735	+	0.535185i	$0.179758\pi$
$464$	−182.515	−0.0182608
$465$	0	0
$466$	−11732.9	−1.16635
$467$	−5822.94	−0.576989	−0.288494	−	0.957482i	$-0.593155\pi$
$467$	−5822.94	−0.576989	−0.288494	+	0.957482i	$0.593155\pi$
$468$	−3127.71	−0.308928
$469$	−3574.91	−0.351971
$470$	0	0
$471$	2648.16	0.259068
$472$	4180.63	0.407689
$473$	9333.13	0.907268
$474$	2919.41	0.282896
$475$	0	0
$476$	229.204	0.0220705
$477$	10294.8	0.988188
$478$	9448.81	0.904139
$479$	−17947.6	−1.71199	−0.855997	−	0.516981i	$-0.827056\pi$
$479$	−17947.6	−1.71199	−0.855997	+	0.516981i	$0.827056\pi$
$480$	0	0
$481$	−13660.6	−1.29495
$482$	5216.16	0.492924
$483$	256.412	0.0241556
$484$	−4171.82	−0.391794
$485$	0	0
$486$	−7633.07	−0.712435
$487$	−2599.57	−0.241884	−0.120942	−	0.992660i	$-0.538592\pi$
$487$	−2599.57	−0.241884	−0.120942	+	0.992660i	$0.538592\pi$
$488$	1940.61	0.180015
$489$	4488.03	0.415042
$490$	0	0
$491$	−2667.14	−0.245145	−0.122573	−	0.992460i	$-0.539114\pi$
$491$	−2667.14	−0.245145	−0.122573	+	0.992460i	$0.539114\pi$
$492$	−5159.46	−0.472777
$493$	−185.444	−0.0169411
$494$	−2864.61	−0.260900
$495$	0	0
$496$	−1323.75	−0.119835
$497$	−1178.65	−0.106378
$498$	5173.46	0.465518
$499$	−21768.8	−1.95292	−0.976460	−	0.215700i	$-0.930797\pi$
$499$	−21768.8	−1.95292	−0.976460	+	0.215700i	$0.930797\pi$
$500$	0	0
$501$	5650.04	0.503843
$502$	−3700.64	−0.329019
$503$	−11726.0	−1.03943	−0.519716	−	0.854339i	$-0.673962\pi$
$503$	−11726.0	−1.03943	−0.519716	+	0.854339i	$0.673962\pi$
$504$	−479.259	−0.0423569
$505$	0	0
$506$	780.706	0.0685901
$507$	254.454	0.0222893
$508$	5503.09	0.480630
$509$	−4688.40	−0.408271	−0.204135	−	0.978943i	$-0.565438\pi$
$509$	−4688.40	−0.408271	−0.204135	+	0.978943i	$0.565438\pi$
$510$	0	0
$511$	−639.601	−0.0553704
$512$	512.000	0.0441942
$513$	−4332.30	−0.372857
$514$	−7035.33	−0.603726
$515$	0	0
$516$	6957.29	0.593561
$517$	−8550.50	−0.727371
$518$	−2093.22	−0.177550
$519$	5344.69	0.452034
$520$	0	0
$521$	7292.43	0.613219	0.306609	−	0.951835i	$-0.400805\pi$
$521$	7292.43	0.613219	0.306609	+	0.951835i	$0.400805\pi$
$522$	387.757	0.0325127
$523$	−9892.85	−0.827121	−0.413560	−	0.910477i	$-0.635715\pi$
$523$	−9892.85	−0.827121	−0.413560	+	0.910477i	$0.635715\pi$
$524$	−249.522	−0.0208023
$525$	0	0
$526$	−7316.13	−0.606461
$527$	−1344.99	−0.111174
$528$	858.879	0.0707915
$529$	529.000	0.0434783
$530$	0	0
$531$	−8881.85	−0.725875
$532$	−438.944	−0.0357719
$533$	18761.9	1.52470
$534$	4899.53	0.397047
$535$	0	0
$536$	−8113.85	−0.653853
$537$	1818.79	0.146158
$538$	13217.2	1.05917
$539$	5610.49	0.448351
$540$	0	0
$541$	−3285.06	−0.261065	−0.130532	−	0.991444i	$-0.541669\pi$
$541$	−3285.06	−0.261065	−0.130532	+	0.991444i	$0.541669\pi$
$542$	4443.56	0.352154
$543$	−153.116	−0.0121010
$544$	520.217	0.0410002
$545$	0	0
$546$	−1025.78	−0.0804019
$547$	−9324.56	−0.728866	−0.364433	−	0.931230i	$-0.618737\pi$
$547$	−9324.56	−0.728866	−0.364433	+	0.931230i	$0.618737\pi$
$548$	771.432	0.0601349
$549$	−4122.87	−0.320510
$550$	0	0
$551$	355.139	0.0274581
$552$	581.970	0.0448737
$553$	−1626.71	−0.125090
$554$	6979.80	0.535277
$555$	0	0
$556$	514.012	0.0392068
$557$	24039.6	1.82871	0.914356	−	0.404911i	$-0.132698\pi$
$557$	24039.6	1.82871	0.914356	+	0.404911i	$0.132698\pi$
$558$	2812.34	0.213362
$559$	−25299.5	−1.91423
$560$	0	0
$561$	872.663	0.0656753
$562$	5345.18	0.401197
$563$	−24219.6	−1.81303	−0.906514	−	0.422175i	$-0.861267\pi$
$563$	−24219.6	−1.81303	−0.906514	+	0.422175i	$0.861267\pi$
$564$	−6373.89	−0.475867
$565$	0	0
$566$	14672.2	1.08961
$567$	66.1529	0.00489976
$568$	−2675.15	−0.197617
$569$	−2649.15	−0.195182	−0.0975908	−	0.995227i	$-0.531114\pi$
$569$	−2649.15	−0.195182	−0.0975908	+	0.995227i	$0.531114\pi$
$570$	0	0
$571$	−13031.3	−0.955067	−0.477533	−	0.878614i	$-0.658469\pi$
$571$	−13031.3	−0.955067	−0.477533	+	0.878614i	$0.658469\pi$
$572$	−3123.23	−0.228302
$573$	6174.65	0.450174
$574$	2874.89	0.209051
$575$	0	0
$576$	−1087.76	−0.0786861
$577$	−8479.89	−0.611824	−0.305912	−	0.952060i	$-0.598961\pi$
$577$	−8479.89	−0.611824	−0.305912	+	0.952060i	$0.598961\pi$
$578$	−9297.43	−0.669070
$579$	−13133.7	−0.942692
$580$	0	0
$581$	−2882.68	−0.205841
$582$	−8874.85	−0.632086
$583$	10280.0	0.730285
$584$	−1451.68	−0.102861
$585$	0	0
$586$	−9705.64	−0.684192
$587$	−16516.1	−1.16132	−0.580658	−	0.814148i	$-0.697205\pi$
$587$	−16516.1	−1.16132	−0.580658	+	0.814148i	$0.697205\pi$
$588$	4182.29	0.293324
$589$	2575.77	0.180191
$590$	0	0
$591$	10930.1	0.760752
$592$	−4750.91	−0.329833
$593$	15014.5	1.03975	0.519876	−	0.854242i	$-0.325978\pi$
$593$	15014.5	1.03975	0.519876	+	0.854242i	$0.325978\pi$
$594$	−4723.43	−0.326270
$595$	0	0
$596$	−5776.04	−0.396973
$597$	−5878.59	−0.403006
$598$	−2116.27	−0.144717
$599$	−2916.69	−0.198953	−0.0994765	−	0.995040i	$-0.531717\pi$
$599$	−2916.69	−0.198953	−0.0994765	+	0.995040i	$0.531717\pi$
$600$	0	0
$601$	−1000.67	−0.0679169	−0.0339584	−	0.999423i	$-0.510811\pi$
$601$	−1000.67	−0.0679169	−0.0339584	+	0.999423i	$0.510811\pi$
$602$	−3876.65	−0.262459
$603$	17238.1	1.16416
$604$	−9610.92	−0.647455
$605$	0	0
$606$	4573.45	0.306574
$607$	25010.8	1.67242	0.836210	−	0.548410i	$-0.184767\pi$
$607$	25010.8	1.67242	0.836210	+	0.548410i	$0.184767\pi$
$608$	−996.255	−0.0664531
$609$	127.171	0.00846180
$610$	0	0
$611$	23178.0	1.53467
$612$	−1105.21	−0.0729993
$613$	18681.2	1.23087	0.615437	−	0.788186i	$-0.288980\pi$
$613$	18681.2	1.23087	0.615437	+	0.788186i	$0.288980\pi$
$614$	−4036.69	−0.265322
$615$	0	0
$616$	−478.573	−0.0313024
$617$	−12203.1	−0.796240	−0.398120	−	0.917333i	$-0.630337\pi$
$617$	−12203.1	−0.796240	−0.398120	+	0.917333i	$0.630337\pi$
$618$	7608.76	0.495258
$619$	12011.4	0.779934	0.389967	−	0.920829i	$-0.372486\pi$
$619$	12011.4	0.779934	0.389967	+	0.920829i	$0.372486\pi$
$620$	0	0
$621$	−3200.56	−0.206818
$622$	13931.8	0.898093
$623$	−2730.05	−0.175565
$624$	−2328.18	−0.149362
$625$	0	0
$626$	−4474.01	−0.285651
$627$	−1671.22	−0.106447
$628$	−3349.05	−0.212805
$629$	−4827.15	−0.305995
$630$	0	0
$631$	16773.8	1.05825	0.529124	−	0.848545i	$-0.322521\pi$
$631$	16773.8	1.05825	0.529124	+	0.848545i	$0.322521\pi$
$632$	−3692.09	−0.232379
$633$	−3946.97	−0.247832
$634$	13213.5	0.827721
$635$	0	0
$636$	7663.16	0.477774
$637$	−15208.5	−0.945968
$638$	387.202	0.0240274
$639$	5683.41	0.351850
$640$	0	0
$641$	21518.5	1.32594	0.662972	−	0.748645i	$-0.269295\pi$
$641$	21518.5	1.32594	0.662972	+	0.748645i	$0.269295\pi$
$642$	5729.37	0.352212
$643$	1048.20	0.0642875	0.0321437	−	0.999483i	$-0.489767\pi$
$643$	1048.20	0.0642875	0.0321437	+	0.999483i	$0.489767\pi$
$644$	−324.277	−0.0198421
$645$	0	0
$646$	−1012.24	−0.0616504
$647$	7509.74	0.456319	0.228160	−	0.973624i	$-0.426729\pi$
$647$	7509.74	0.456319	0.228160	+	0.973624i	$0.426729\pi$
$648$	150.145	0.00910223
$649$	−8869.14	−0.536432
$650$	0	0
$651$	922.354	0.0555298
$652$	−5675.87	−0.340927
$653$	−26820.3	−1.60729	−0.803643	−	0.595112i	$-0.797108\pi$
$653$	−26820.3	−1.60729	−0.803643	+	0.595112i	$0.797108\pi$
$654$	−9156.39	−0.547467
$655$	0	0
$656$	6525.02	0.388353
$657$	3084.13	0.183140
$658$	3551.57	0.210417
$659$	−25292.2	−1.49506	−0.747531	−	0.664227i	$-0.768761\pi$
$659$	−25292.2	−1.49506	−0.747531	+	0.664227i	$0.768761\pi$
$660$	0	0
$661$	15985.9	0.940662	0.470331	−	0.882490i	$-0.344134\pi$
$661$	15985.9	0.940662	0.470331	+	0.882490i	$0.344134\pi$
$662$	21577.4	1.26681
$663$	−2365.54	−0.138567
$664$	−6542.72	−0.382390
$665$	0	0
$666$	10093.4	0.587255
$667$	262.365	0.0152306
$668$	−7145.44	−0.413871
$669$	14138.0	0.817048
$670$	0	0
$671$	−4116.97	−0.236861
$672$	−356.748	−0.0204789
$673$	6340.11	0.363140	0.181570	−	0.983378i	$-0.441882\pi$
$673$	6340.11	0.363140	0.181570	+	0.983378i	$0.441882\pi$
$674$	4688.86	0.267965
$675$	0	0
$676$	−321.800	−0.0183091
$677$	−19922.6	−1.13100	−0.565499	−	0.824749i	$-0.691317\pi$
$677$	−19922.6	−1.13100	−0.565499	+	0.824749i	$0.691317\pi$
$678$	6180.57	0.350093
$679$	4945.12	0.279494
$680$	0	0
$681$	−5610.62	−0.315711
$682$	2808.32	0.157677
$683$	−22295.1	−1.24904	−0.624522	−	0.781007i	$-0.714706\pi$
$683$	−22295.1	−1.24904	−0.624522	+	0.781007i	$0.714706\pi$
$684$	2116.57	0.118317
$685$	0	0
$686$	−4748.38	−0.264277
$687$	−243.674	−0.0135324
$688$	−8798.68	−0.487568
$689$	−27866.3	−1.54082
$690$	0	0
$691$	−22591.1	−1.24372	−0.621858	−	0.783130i	$-0.713622\pi$
$691$	−22591.1	−1.24372	−0.621858	+	0.783130i	$0.713622\pi$
$692$	−6759.27	−0.371313
$693$	1016.74	0.0557327
$694$	12307.7	0.673188
$695$	0	0
$696$	288.636	0.0157194
$697$	6629.73	0.360286
$698$	16580.0	0.899088
$699$	18554.9	1.00402
$700$	0	0
$701$	−9628.26	−0.518765	−0.259383	−	0.965775i	$-0.583519\pi$
$701$	−9628.26	−0.518765	−0.259383	+	0.965775i	$0.583519\pi$
$702$	12803.9	0.688393
$703$	9244.37	0.495957
$704$	−1086.20	−0.0581501
$705$	0	0
$706$	−1472.00	−0.0784697
$707$	−2548.36	−0.135560
$708$	−6611.41	−0.350949
$709$	18533.1	0.981699	0.490850	−	0.871244i	$-0.336686\pi$
$709$	18533.1	0.981699	0.490850	+	0.871244i	$0.336686\pi$
$710$	0	0
$711$	7843.94	0.413742
$712$	−6196.29	−0.326146
$713$	1902.89	0.0999493
$714$	−362.473	−0.0189989
$715$	0	0
$716$	−2300.17	−0.120058
$717$	−14942.7	−0.778307
$718$	5017.81	0.260812
$719$	−17752.9	−0.920825	−0.460413	−	0.887705i	$-0.652299\pi$
$719$	−17752.9	−0.920825	−0.460413	+	0.887705i	$0.652299\pi$
$720$	0	0
$721$	−4239.65	−0.218991
$722$	−11779.5	−0.607184
$723$	−8249.04	−0.424322
$724$	193.641	0.00994006
$725$	0	0
$726$	6597.48	0.337267
$727$	31592.5	1.61170	0.805848	−	0.592123i	$-0.201710\pi$
$727$	31592.5	1.61170	0.805848	+	0.592123i	$0.201710\pi$
$728$	1297.28	0.0660444
$729$	11564.5	0.587538
$730$	0	0
$731$	−8939.88	−0.452330
$732$	−3068.95	−0.154961
$733$	30839.9	1.55402	0.777011	−	0.629487i	$-0.216735\pi$
$733$	30839.9	1.55402	0.777011	+	0.629487i	$0.216735\pi$
$734$	4189.35	0.210670
$735$	0	0
$736$	−736.000	−0.0368605
$737$	17213.4	0.860331
$738$	−13862.6	−0.691447
$739$	21675.6	1.07896	0.539480	−	0.841999i	$-0.318621\pi$
$739$	21675.6	1.07896	0.539480	+	0.841999i	$0.318621\pi$
$740$	0	0
$741$	4530.20	0.224590
$742$	−4269.96	−0.211260
$743$	10572.5	0.522031	0.261015	−	0.965335i	$-0.415943\pi$
$743$	10572.5	0.522031	0.261015	+	0.965335i	$0.415943\pi$
$744$	2093.43	0.103157
$745$	0	0
$746$	5619.08	0.275776
$747$	13900.2	0.680831
$748$	−1103.63	−0.0539475
$749$	−3192.44	−0.155740
$750$	0	0
$751$	−11095.7	−0.539132	−0.269566	−	0.962982i	$-0.586880\pi$
$751$	−11095.7	−0.539132	−0.269566	+	0.962982i	$0.586880\pi$
$752$	8060.87	0.390891
$753$	5852.33	0.283228
$754$	−1049.60	−0.0506950
$755$	0	0
$756$	1961.94	0.0943851
$757$	−21207.1	−1.01821	−0.509105	−	0.860704i	$-0.670024\pi$
$757$	−21207.1	−1.01821	−0.509105	+	0.860704i	$0.670024\pi$
$758$	−4311.97	−0.206620
$759$	−1234.64	−0.0590442
$760$	0	0
$761$	17511.2	0.834140	0.417070	−	0.908874i	$-0.363057\pi$
$761$	17511.2	0.834140	0.417070	+	0.908874i	$0.363057\pi$
$762$	−8702.81	−0.413739
$763$	5102.00	0.242077
$764$	−7808.90	−0.369785
$765$	0	0
$766$	6300.71	0.297198
$767$	24041.7	1.13181
$768$	−809.697	−0.0380435
$769$	28707.9	1.34621	0.673104	−	0.739548i	$-0.264961\pi$
$769$	28707.9	1.34621	0.673104	+	0.739548i	$0.264961\pi$
$770$	0	0
$771$	11126.0	0.519704
$772$	16609.8	0.774353
$773$	23514.6	1.09413	0.547065	−	0.837090i	$-0.315745\pi$
$773$	23514.6	1.09413	0.547065	+	0.837090i	$0.315745\pi$
$774$	18693.0	0.868097
$775$	0	0
$776$	11223.8	0.519213
$777$	3310.30	0.152840
$778$	−9207.17	−0.424284
$779$	−12696.5	−0.583951
$780$	0	0
$781$	5675.28	0.260022
$782$	−747.811	−0.0341965
$783$	−1587.36	−0.0724490
$784$	−5289.22	−0.240945
$785$	0	0
$786$	394.603	0.0179072
$787$	−39207.2	−1.77584	−0.887919	−	0.459999i	$-0.847850\pi$
$787$	−39207.2	−1.77584	−0.887919	+	0.459999i	$0.847850\pi$
$788$	−13823.0	−0.624903
$789$	11570.0	0.522057
$790$	0	0
$791$	−3443.85	−0.154803
$792$	2307.66	0.103534
$793$	11159.9	0.499749
$794$	20634.5	0.922281
$795$	0	0
$796$	7434.48	0.331041
$797$	−18802.0	−0.835634	−0.417817	−	0.908531i	$-0.637205\pi$
$797$	−18802.0	−0.835634	−0.417817	+	0.908531i	$0.637205\pi$
$798$	694.163	0.0307934
$799$	8190.23	0.362640
$800$	0	0
$801$	13164.2	0.580690
$802$	25077.1	1.10412
$803$	3079.71	0.135343
$804$	12831.6	0.562854
$805$	0	0
$806$	−7612.56	−0.332681
$807$	−20902.2	−0.911760
$808$	−5783.91	−0.251828
$809$	13206.8	0.573952	0.286976	−	0.957938i	$-0.407350\pi$
$809$	13206.8	0.573952	0.286976	+	0.957938i	$0.407350\pi$
$810$	0	0
$811$	−7558.69	−0.327277	−0.163638	−	0.986520i	$-0.552323\pi$
$811$	−7558.69	−0.327277	−0.163638	+	0.986520i	$0.552323\pi$
$812$	−160.830	−0.00695076
$813$	−7027.23	−0.303143
$814$	10079.0	0.433990
$815$	0	0
$816$	−822.691	−0.0352940
$817$	17120.6	0.733137
$818$	−642.203	−0.0274500
$819$	−2756.10	−0.117590
$820$	0	0
$821$	−22956.9	−0.975884	−0.487942	−	0.872876i	$-0.662252\pi$
$821$	−22956.9	−0.975884	−0.487942	+	0.872876i	$0.662252\pi$
$822$	−1219.97	−0.0517657
$823$	−29077.1	−1.23155	−0.615774	−	0.787923i	$-0.711157\pi$
$823$	−29077.1	−1.23155	−0.615774	+	0.787923i	$0.711157\pi$
$824$	−9622.57	−0.406818
$825$	0	0
$826$	3683.92	0.155182
$827$	−22305.0	−0.937872	−0.468936	−	0.883232i	$-0.655362\pi$
$827$	−22305.0	−0.937872	−0.468936	+	0.883232i	$0.655362\pi$
$828$	1563.65	0.0656287
$829$	32483.1	1.36090	0.680449	−	0.732796i	$-0.261785\pi$
$829$	32483.1	1.36090	0.680449	+	0.732796i	$0.261785\pi$
$830$	0	0
$831$	−11038.1	−0.460780
$832$	2944.38	0.122690
$833$	−5374.10	−0.223531
$834$	−812.879	−0.0337502
$835$	0	0
$836$	2113.54	0.0874381
$837$	−11512.9	−0.475440
$838$	4622.28	0.190542
$839$	34559.6	1.42209	0.711044	−	0.703148i	$-0.248223\pi$
$839$	34559.6	1.42209	0.711044	+	0.703148i	$0.248223\pi$
$840$	0	0
$841$	−24258.9	−0.994665
$842$	29881.6	1.22302
$843$	−8453.08	−0.345361
$844$	4991.61	0.203576
$845$	0	0
$846$	−17125.5	−0.695966
$847$	−3676.16	−0.149131
$848$	−9691.38	−0.392457
$849$	−23203.2	−0.937966
$850$	0	0
$851$	6829.43	0.275100
$852$	4230.58	0.170114
$853$	35437.5	1.42246	0.711229	−	0.702961i	$-0.248139\pi$
$853$	35437.5	1.42246	0.711229	+	0.702961i	$0.248139\pi$
$854$	1710.04	0.0685203
$855$	0	0
$856$	−7245.76	−0.289317
$857$	−18290.2	−0.729032	−0.364516	−	0.931197i	$-0.618766\pi$
$857$	−18290.2	−0.729032	−0.364516	+	0.931197i	$0.618766\pi$
$858$	4939.20	0.196529
$859$	−46209.1	−1.83543	−0.917715	−	0.397240i	$-0.869968\pi$
$859$	−46209.1	−1.83543	−0.917715	+	0.397240i	$0.869968\pi$
$860$	0	0
$861$	−4546.46	−0.179957
$862$	−20316.5	−0.802764
$863$	−26127.8	−1.03059	−0.515297	−	0.857012i	$-0.672318\pi$
$863$	−26127.8	−1.03059	−0.515297	+	0.857012i	$0.672318\pi$
$864$	4452.95	0.175338
$865$	0	0
$866$	1924.27	0.0755074
$867$	14703.3	0.575953
$868$	−1166.47	−0.0456137
$869$	7832.71	0.305761
$870$	0	0
$871$	−46660.7	−1.81520
$872$	11579.8	0.449704
$873$	−23845.2	−0.924440
$874$	1432.12	0.0554257
$875$	0	0
$876$	2295.74	0.0885455
$877$	−15548.8	−0.598685	−0.299342	−	0.954146i	$-0.596767\pi$
$877$	−15548.8	−0.598685	−0.299342	+	0.954146i	$0.596767\pi$
$878$	−1389.53	−0.0534103
$879$	15348.9	0.588970
$880$	0	0
$881$	24798.3	0.948327	0.474164	−	0.880437i	$-0.342750\pi$
$881$	24798.3	0.948327	0.474164	+	0.880437i	$0.342750\pi$
$882$	11237.1	0.428993
$883$	−24110.1	−0.918879	−0.459440	−	0.888209i	$-0.651950\pi$
$883$	−24110.1	−0.918879	−0.459440	+	0.888209i	$0.651950\pi$
$884$	2991.63	0.113823
$885$	0	0
$886$	3137.07	0.118952
$887$	−27257.9	−1.03183	−0.515913	−	0.856641i	$-0.672547\pi$
$887$	−27257.9	−1.03183	−0.515913	+	0.856641i	$0.672547\pi$
$888$	7513.27	0.283929
$889$	4849.26	0.182946
$890$	0	0
$891$	−318.530	−0.0119766
$892$	−17879.9	−0.671146
$893$	−15684.9	−0.587767
$894$	9134.45	0.341725
$895$	0	0
$896$	451.168	0.0168220
$897$	3346.76	0.124576
$898$	−13953.2	−0.518511
$899$	943.765	0.0350126
$900$	0	0
$901$	−9846.90	−0.364093
$902$	−13842.7	−0.510989
$903$	6130.68	0.225932
$904$	−7816.38	−0.287576
$905$	0	0
$906$	15199.1	0.557346
$907$	27771.4	1.01669	0.508343	−	0.861155i	$-0.330258\pi$
$907$	27771.4	1.01669	0.508343	+	0.861155i	$0.330258\pi$
$908$	7095.58	0.259334
$909$	12288.1	0.448371
$910$	0	0
$911$	8300.51	0.301875	0.150937	−	0.988543i	$-0.451771\pi$
$911$	8300.51	0.301875	0.150937	+	0.988543i	$0.451771\pi$
$912$	1575.52	0.0572046
$913$	13880.3	0.503144
$914$	23246.8	0.841285
$915$	0	0
$916$	308.167	0.0111159
$917$	−219.876	−0.00791813
$918$	4524.41	0.162666
$919$	−17134.1	−0.615017	−0.307508	−	0.951545i	$-0.599495\pi$
$919$	−17134.1	−0.615017	−0.307508	+	0.951545i	$0.599495\pi$
$920$	0	0
$921$	6383.78	0.228396
$922$	34460.8	1.23092
$923$	−15384.1	−0.548617
$924$	756.834	0.0269459
$925$	0	0
$926$	33662.9	1.19464
$927$	20443.4	0.724325
$928$	−365.029	−0.0129124
$929$	55698.8	1.96708	0.983541	−	0.180685i	$-0.0578314\pi$
$929$	55698.8	1.96708	0.983541	+	0.180685i	$0.0578314\pi$
$930$	0	0
$931$	10291.8	0.362299
$932$	−23465.9	−0.824732
$933$	−22032.3	−0.773102
$934$	−11645.9	−0.407993
$935$	0	0
$936$	−6255.41	−0.218445
$937$	−47208.1	−1.64591	−0.822957	−	0.568103i	$-0.807678\pi$
$937$	−47208.1	−1.64591	−0.822957	+	0.568103i	$0.807678\pi$
$938$	−7149.83	−0.248881
$939$	7075.38	0.245896
$940$	0	0
$941$	−19051.4	−0.659998	−0.329999	−	0.943981i	$-0.607048\pi$
$941$	−19051.4	−0.659998	−0.329999	+	0.943981i	$0.607048\pi$
$942$	5296.32	0.183188
$943$	−9379.72	−0.323908
$944$	8361.26	0.288280
$945$	0	0
$946$	18666.3	0.641535
$947$	−2632.41	−0.0903294	−0.0451647	−	0.998980i	$-0.514381\pi$
$947$	−2632.41	−0.0903294	−0.0451647	+	0.998980i	$0.514381\pi$
$948$	5838.82	0.200038
$949$	−8348.23	−0.285559
$950$	0	0
$951$	−20896.3	−0.712524
$952$	458.409	0.0156062
$953$	34365.8	1.16812	0.584059	−	0.811711i	$-0.301464\pi$
$953$	34365.8	1.16812	0.584059	+	0.811711i	$0.301464\pi$
$954$	20589.6	0.698755
$955$	0	0
$956$	18897.6	0.639323
$957$	−612.336	−0.0206834
$958$	−35895.1	−1.21056
$959$	679.776	0.0228896
$960$	0	0
$961$	−22946.0	−0.770233
$962$	−27321.3	−0.915669
$963$	15393.8	0.515118
$964$	10432.3	0.348550
$965$	0	0
$966$	512.825	0.0170806
$967$	27010.9	0.898253	0.449126	−	0.893468i	$-0.351735\pi$
$967$	27010.9	0.898253	0.449126	+	0.893468i	$0.351735\pi$
$968$	−8343.65	−0.277040
$969$	1600.80	0.0530703
$970$	0	0
$971$	37382.0	1.23547	0.617737	−	0.786385i	$-0.288050\pi$
$971$	37382.0	1.23547	0.617737	+	0.786385i	$0.288050\pi$
$972$	−15266.1	−0.503767
$973$	452.942	0.0149236
$974$	−5199.13	−0.171038
$975$	0	0
$976$	3881.22	0.127290
$977$	−39469.3	−1.29246	−0.646230	−	0.763143i	$-0.723655\pi$
$977$	−39469.3	−1.29246	−0.646230	+	0.763143i	$0.723655\pi$
$978$	8976.05	0.293479
$979$	13145.3	0.429138
$980$	0	0
$981$	−24601.6	−0.800682
$982$	−5334.27	−0.173344
$983$	11653.4	0.378115	0.189057	−	0.981966i	$-0.439457\pi$
$983$	11653.4	0.378115	0.189057	+	0.981966i	$0.439457\pi$
$984$	−10318.9	−0.334304
$985$	0	0
$986$	−370.887	−0.0119792
$987$	−5616.59	−0.181133
$988$	−5729.21	−0.184484
$989$	12648.1	0.406660
$990$	0	0
$991$	−50841.6	−1.62970	−0.814852	−	0.579669i	$-0.803182\pi$
$991$	−50841.6	−1.62970	−0.814852	+	0.579669i	$0.803182\pi$
$992$	−2647.50	−0.0847362
$993$	−34123.4	−1.09051
$994$	−2357.31	−0.0752205
$995$	0	0
$996$	10346.9	0.329171
$997$	8834.53	0.280634	0.140317	−	0.990107i	$-0.455188\pi$
$997$	8834.53	0.280634	0.140317	+	0.990107i	$0.455188\pi$
$998$	−43537.7	−1.38092
$999$	−41319.4	−1.30860

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.4.a.x.1.3	yes	6
5.2	odd	4		1150.4.b.s.599.10		12
5.3	odd	4		1150.4.b.s.599.3		12
5.4	even	2		1150.4.a.w.1.4	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1150.4.a.w.1.4	✓	6	5.4	even	2
1150.4.a.x.1.3	yes	6	1.1	even	1	trivial
1150.4.b.s.599.3		12	5.3	odd	4
1150.4.b.s.599.10		12	5.2	odd	4

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:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1150.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -3.16288 q^{3} +4.00000 q^{4} -6.32576 q^{6} +3.52475 q^{7} +8.00000 q^{8} -16.9962 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} -3.16288 q^{3} +4.00000 q^{4} -6.32576 q^{6} +3.52475 q^{7} +8.00000 q^{8} -16.9962 q^{9} -16.9719 q^{11} -12.6515 q^{12} +46.0060 q^{13} +7.04951 q^{14} +16.0000 q^{16} +16.2568 q^{17} -33.9924 q^{18} -31.1330 q^{19} -11.1484 q^{21} -33.9437 q^{22} -23.0000 q^{23} -25.3030 q^{24} +92.0120 q^{26} +139.155 q^{27} +14.0990 q^{28} -11.4072 q^{29} -82.7344 q^{31} +32.0000 q^{32} +53.6800 q^{33} +32.5135 q^{34} -67.9848 q^{36} -296.932 q^{37} -62.2659 q^{38} -145.511 q^{39} +407.814 q^{41} -22.2967 q^{42} -549.918 q^{43} -67.8875 q^{44} -46.0000 q^{46} +503.804 q^{47} -50.6061 q^{48} -330.576 q^{49} -51.4182 q^{51} +184.024 q^{52} -605.711 q^{53} +278.309 q^{54} +28.1980 q^{56} +98.4698 q^{57} -22.8143 q^{58} +522.579 q^{59} +242.576 q^{61} -165.469 q^{62} -59.9074 q^{63} +64.0000 q^{64} +107.360 q^{66} -1014.23 q^{67} +65.0271 q^{68} +72.7462 q^{69} -334.393 q^{71} -135.970 q^{72} -181.460 q^{73} -593.864 q^{74} -124.532 q^{76} -59.8216 q^{77} -291.023 q^{78} -461.511 q^{79} +18.7681 q^{81} +815.628 q^{82} -817.840 q^{83} -44.5935 q^{84} -1099.84 q^{86} +36.0795 q^{87} -135.775 q^{88} -774.536 q^{89} +162.160 q^{91} -92.0000 q^{92} +261.679 q^{93} +1007.61 q^{94} -101.212 q^{96} +1402.97 q^{97} -661.152 q^{98} +288.457 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 12 q^{2} - 5 q^{3} + 24 q^{4} - 10 q^{6} - 42 q^{7} + 48 q^{8} + 61 q^{9}+O(q^{10}) \) 6 * q + 12 * q^2 - 5 * q^3 + 24 * q^4 - 10 * q^6 - 42 * q^7 + 48 * q^8 + 61 * q^9	\( 6 q + 12 q^{2} - 5 q^{3} + 24 q^{4} - 10 q^{6} - 42 q^{7} + 48 q^{8} + 61 q^{9} - 49 q^{11} - 20 q^{12} - 16 q^{13} - 84 q^{14} + 96 q^{16} - 175 q^{17} + 122 q^{18} - 229 q^{19} + 92 q^{21} - 98 q^{22} - 138 q^{23} - 40 q^{24} - 32 q^{26} - 344 q^{27} - 168 q^{28} - 182 q^{29} + 114 q^{31} + 192 q^{32} - 641 q^{33} - 350 q^{34} + 244 q^{36} - 64 q^{37} - 458 q^{38} - 143 q^{39} + 243 q^{41} + 184 q^{42} - 182 q^{43} - 196 q^{44} - 276 q^{46} - 498 q^{47} - 80 q^{48} + 648 q^{49} - 1031 q^{51} - 64 q^{52} - 1290 q^{53} - 688 q^{54} - 336 q^{56} + 353 q^{57} - 364 q^{58} - 559 q^{59} - 688 q^{61} + 228 q^{62} - 3656 q^{63} + 384 q^{64} - 1282 q^{66} + 2069 q^{67} - 700 q^{68} + 115 q^{69} + 584 q^{71} + 488 q^{72} - 2485 q^{73} - 128 q^{74} - 916 q^{76} + 810 q^{77} - 286 q^{78} - 1432 q^{79} + 34 q^{81} + 486 q^{82} - 2089 q^{83} + 368 q^{84} - 364 q^{86} - 527 q^{87} - 392 q^{88} - 591 q^{89} - 2864 q^{91} - 552 q^{92} - 4899 q^{93} - 996 q^{94} - 160 q^{96} + 968 q^{97} + 1296 q^{98} - 142 q^{99}+O(q^{100}) \) 6 * q + 12 * q^2 - 5 * q^3 + 24 * q^4 - 10 * q^6 - 42 * q^7 + 48 * q^8 + 61 * q^9 - 49 * q^11 - 20 * q^12 - 16 * q^13 - 84 * q^14 + 96 * q^16 - 175 * q^17 + 122 * q^18 - 229 * q^19 + 92 * q^21 - 98 * q^22 - 138 * q^23 - 40 * q^24 - 32 * q^26 - 344 * q^27 - 168 * q^28 - 182 * q^29 + 114 * q^31 + 192 * q^32 - 641 * q^33 - 350 * q^34 + 244 * q^36 - 64 * q^37 - 458 * q^38 - 143 * q^39 + 243 * q^41 + 184 * q^42 - 182 * q^43 - 196 * q^44 - 276 * q^46 - 498 * q^47 - 80 * q^48 + 648 * q^49 - 1031 * q^51 - 64 * q^52 - 1290 * q^53 - 688 * q^54 - 336 * q^56 + 353 * q^57 - 364 * q^58 - 559 * q^59 - 688 * q^61 + 228 * q^62 - 3656 * q^63 + 384 * q^64 - 1282 * q^66 + 2069 * q^67 - 700 * q^68 + 115 * q^69 + 584 * q^71 + 488 * q^72 - 2485 * q^73 - 128 * q^74 - 916 * q^76 + 810 * q^77 - 286 * q^78 - 1432 * q^79 + 34 * q^81 + 486 * q^82 - 2089 * q^83 + 368 * q^84 - 364 * q^86 - 527 * q^87 - 392 * q^88 - 591 * q^89 - 2864 * q^91 - 552 * q^92 - 4899 * q^93 - 996 * q^94 - 160 * q^96 + 968 * q^97 + 1296 * q^98 - 142 * q^99

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