LMFDB - Embedded newform 1150.4.a.x.1.2

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			1.2
Root			$-4.90184$ 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)

$f(q)$	$=$	$q+2.00000 q^{2} -5.90184 q^{3} +4.00000 q^{4} -11.8037 q^{6} -1.63515 q^{7} +8.00000 q^{8} +7.83172 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} -5.90184 q^{3} +4.00000 q^{4} -11.8037 q^{6} -1.63515 q^{7} +8.00000 q^{8} +7.83172 q^{9} +42.3658 q^{11} -23.6074 q^{12} -18.1952 q^{13} -3.27031 q^{14} +16.0000 q^{16} -122.548 q^{17} +15.6634 q^{18} +87.0852 q^{19} +9.65041 q^{21} +84.7316 q^{22} -23.0000 q^{23} -47.2147 q^{24} -36.3904 q^{26} +113.128 q^{27} -6.54061 q^{28} -187.490 q^{29} +167.702 q^{31} +32.0000 q^{32} -250.036 q^{33} -245.096 q^{34} +31.3269 q^{36} +405.079 q^{37} +174.170 q^{38} +107.385 q^{39} -111.070 q^{41} +19.3008 q^{42} -192.424 q^{43} +169.463 q^{44} -46.0000 q^{46} -245.437 q^{47} -94.4294 q^{48} -340.326 q^{49} +723.258 q^{51} -72.7809 q^{52} +52.0761 q^{53} +226.256 q^{54} -13.0812 q^{56} -513.963 q^{57} -374.979 q^{58} -425.068 q^{59} +669.437 q^{61} +335.404 q^{62} -12.8061 q^{63} +64.0000 q^{64} -500.072 q^{66} +661.392 q^{67} -490.191 q^{68} +135.742 q^{69} -425.237 q^{71} +62.6537 q^{72} -1109.13 q^{73} +810.158 q^{74} +348.341 q^{76} -69.2745 q^{77} +214.771 q^{78} +1195.16 q^{79} -879.121 q^{81} -222.139 q^{82} -1475.59 q^{83} +38.6016 q^{84} -384.849 q^{86} +1106.53 q^{87} +338.926 q^{88} -74.2100 q^{89} +29.7520 q^{91} -92.0000 q^{92} -989.750 q^{93} -490.874 q^{94} -188.859 q^{96} -937.166 q^{97} -680.653 q^{98} +331.797 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−5.90184	−1.13581	−0.567905	−	0.823094i	$-0.692246\pi$
$3$	−5.90184	−1.13581	−0.567905	+	0.823094i	$0.692246\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−11.8037	−0.803139
$7$	−1.63515	−0.0882900	−0.0441450	−	0.999025i	$-0.514056\pi$
$7$	−1.63515	−0.0882900	−0.0441450	+	0.999025i	$0.514056\pi$
$8$	8.00000	0.353553
$9$	7.83172	0.290064
$10$	0	0
$11$	42.3658	1.16125	0.580626	−	0.814171i	$-0.302808\pi$
$11$	42.3658	1.16125	0.580626	+	0.814171i	$0.302808\pi$
$12$	−23.6074	−0.567905
$13$	−18.1952	−0.388188	−0.194094	−	0.980983i	$-0.562177\pi$
$13$	−18.1952	−0.388188	−0.194094	+	0.980983i	$0.562177\pi$
$14$	−3.27031	−0.0624304
$15$	0	0
$16$	16.0000	0.250000
$17$	−122.548	−1.74837	−0.874183	−	0.485597i	$-0.838602\pi$
$17$	−122.548	−1.74837	−0.874183	+	0.485597i	$0.838602\pi$
$18$	15.6634	0.205106
$19$	87.0852	1.05151	0.525756	−	0.850636i	$-0.323783\pi$
$19$	87.0852	1.05151	0.525756	+	0.850636i	$0.323783\pi$
$20$	0	0
$21$	9.65041	0.100281
$22$	84.7316	0.821129
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−47.2147	−0.401569
$25$	0	0
$26$	−36.3904	−0.274490
$27$	113.128	0.806353
$28$	−6.54061	−0.0441450
$29$	−187.490	−1.20055	−0.600275	−	0.799793i	$-0.704942\pi$
$29$	−187.490	−1.20055	−0.600275	+	0.799793i	$0.704942\pi$
$30$	0	0
$31$	167.702	0.971618	0.485809	−	0.874065i	$-0.338525\pi$
$31$	167.702	0.971618	0.485809	+	0.874065i	$0.338525\pi$
$32$	32.0000	0.176777
$33$	−250.036	−1.31896
$34$	−245.096	−1.23628
$35$	0	0
$36$	31.3269	0.145032
$37$	405.079	1.79985	0.899926	−	0.436042i	$-0.143620\pi$
$37$	405.079	1.79985	0.899926	+	0.436042i	$0.143620\pi$
$38$	174.170	0.743531
$39$	107.385	0.440908
$40$	0	0
$41$	−111.070	−0.423078	−0.211539	−	0.977370i	$-0.567847\pi$
$41$	−111.070	−0.423078	−0.211539	+	0.977370i	$0.567847\pi$
$42$	19.3008	0.0709091
$43$	−192.424	−0.682429	−0.341214	−	0.939986i	$-0.610838\pi$
$43$	−192.424	−0.682429	−0.341214	+	0.939986i	$0.610838\pi$
$44$	169.463	0.580626
$45$	0	0
$46$	−46.0000	−0.147442
$47$	−245.437	−0.761716	−0.380858	−	0.924634i	$-0.624371\pi$
$47$	−245.437	−0.761716	−0.380858	+	0.924634i	$0.624371\pi$
$48$	−94.4294	−0.283952
$49$	−340.326	−0.992205
$50$	0	0
$51$	723.258	1.98581
$52$	−72.7809	−0.194094
$53$	52.0761	0.134966	0.0674831	−	0.997720i	$-0.478503\pi$
$53$	52.0761	0.134966	0.0674831	+	0.997720i	$0.478503\pi$
$54$	226.256	0.570177
$55$	0	0
$56$	−13.0812	−0.0312152
$57$	−513.963	−1.19432
$58$	−374.979	−0.848918
$59$	−425.068	−0.937952	−0.468976	−	0.883211i	$-0.655377\pi$
$59$	−425.068	−0.937952	−0.468976	+	0.883211i	$0.655377\pi$
$60$	0	0
$61$	669.437	1.40513	0.702563	−	0.711622i	$-0.252039\pi$
$61$	669.437	1.40513	0.702563	+	0.711622i	$0.252039\pi$
$62$	335.404	0.687037
$63$	−12.8061	−0.0256097
$64$	64.0000	0.125000
$65$	0	0
$66$	−500.072	−0.932646
$67$	661.392	1.20600	0.602999	−	0.797742i	$-0.293972\pi$
$67$	661.392	1.20600	0.602999	+	0.797742i	$0.293972\pi$
$68$	−490.191	−0.874183
$69$	135.742	0.236833
$70$	0	0
$71$	−425.237	−0.710793	−0.355396	−	0.934716i	$-0.615654\pi$
$71$	−425.237	−0.710793	−0.355396	+	0.934716i	$0.615654\pi$
$72$	62.6537	0.102553
$73$	−1109.13	−1.77827	−0.889133	−	0.457649i	$-0.848692\pi$
$73$	−1109.13	−1.77827	−0.889133	+	0.457649i	$0.848692\pi$
$74$	810.158	1.27269
$75$	0	0
$76$	348.341	0.525756
$77$	−69.2745	−0.102527
$78$	214.771	0.311769
$79$	1195.16	1.70210	0.851052	−	0.525082i	$-0.175965\pi$
$79$	1195.16	1.70210	0.851052	+	0.525082i	$0.175965\pi$
$80$	0	0
$81$	−879.121	−1.20593
$82$	−222.139	−0.299161
$83$	−1475.59	−1.95141	−0.975704	−	0.219095i	$-0.929690\pi$
$83$	−1475.59	−1.95141	−0.975704	+	0.219095i	$0.929690\pi$
$84$	38.6016	0.0501403
$85$	0	0
$86$	−384.849	−0.482550
$87$	1106.53	1.36360
$88$	338.926	0.410564
$89$	−74.2100	−0.0883847	−0.0441924	−	0.999023i	$-0.514071\pi$
$89$	−74.2100	−0.0883847	−0.0441924	+	0.999023i	$0.514071\pi$
$90$	0	0
$91$	29.7520	0.0342731
$92$	−92.0000	−0.104257
$93$	−989.750	−1.10357
$94$	−490.874	−0.538614
$95$	0	0
$96$	−188.859	−0.200785
$97$	−937.166	−0.980977	−0.490489	−	0.871448i	$-0.663182\pi$
$97$	−937.166	−0.980977	−0.490489	+	0.871448i	$0.663182\pi$
$98$	−680.653	−0.701595
$99$	331.797	0.336837
$100$	0	0
$101$	21.6198	0.0212995	0.0106497	−	0.999943i	$-0.496610\pi$
$101$	21.6198	0.0212995	0.0106497	+	0.999943i	$0.496610\pi$
$102$	1446.52	1.40418
$103$	−509.165	−0.487083	−0.243541	−	0.969890i	$-0.578309\pi$
$103$	−509.165	−0.487083	−0.243541	+	0.969890i	$0.578309\pi$
$104$	−145.562	−0.137245
$105$	0	0
$106$	104.152	0.0954355
$107$	−1269.28	−1.14678	−0.573391	−	0.819282i	$-0.694372\pi$
$107$	−1269.28	−1.14678	−0.573391	+	0.819282i	$0.694372\pi$
$108$	452.513	0.403176
$109$	−1827.07	−1.60552	−0.802762	−	0.596300i	$-0.796637\pi$
$109$	−1827.07	−1.60552	−0.802762	+	0.596300i	$0.796637\pi$
$110$	0	0
$111$	−2390.71	−2.04429
$112$	−26.1624	−0.0220725
$113$	−1175.67	−0.978744	−0.489372	−	0.872075i	$-0.662774\pi$
$113$	−1175.67	−0.978744	−0.489372	+	0.872075i	$0.662774\pi$
$114$	−1027.93	−0.844510
$115$	0	0
$116$	−749.959	−0.600275
$117$	−142.500	−0.112599
$118$	−850.137	−0.663232
$119$	200.384	0.154363
$120$	0	0
$121$	463.860	0.348505
$122$	1338.87	0.993574
$123$	655.516	0.480536
$124$	670.808	0.485809
$125$	0	0
$126$	−25.6121	−0.0181088
$127$	−1657.04	−1.15778	−0.578890	−	0.815405i	$-0.696514\pi$
$127$	−1657.04	−1.15778	−0.578890	+	0.815405i	$0.696514\pi$
$128$	128.000	0.0883883
$129$	1135.66	0.775109
$130$	0	0
$131$	−1206.22	−0.804488	−0.402244	−	0.915532i	$-0.631770\pi$
$131$	−1206.22	−0.804488	−0.402244	+	0.915532i	$0.631770\pi$
$132$	−1000.14	−0.659480
$133$	−142.398	−0.0928379
$134$	1322.78	0.852770
$135$	0	0
$136$	−980.383	−0.618141
$137$	−2091.57	−1.30434	−0.652171	−	0.758072i	$-0.726142\pi$
$137$	−2091.57	−1.30434	−0.652171	+	0.758072i	$0.726142\pi$
$138$	271.485	0.167466
$139$	−41.5499	−0.0253541	−0.0126770	−	0.999920i	$-0.504035\pi$
$139$	−41.5499	−0.0253541	−0.0126770	+	0.999920i	$0.504035\pi$
$140$	0	0
$141$	1448.53	0.865164
$142$	−850.473	−0.502606
$143$	−770.855	−0.450784
$144$	125.307	0.0725159
$145$	0	0
$146$	−2218.25	−1.25742
$147$	2008.55	1.12696
$148$	1620.32	0.899926
$149$	1494.41	0.821659	0.410829	−	0.911712i	$-0.365239\pi$
$149$	1494.41	0.821659	0.410829	+	0.911712i	$0.365239\pi$
$150$	0	0
$151$	−401.577	−0.216423	−0.108211	−	0.994128i	$-0.534512\pi$
$151$	−401.577	−0.216423	−0.108211	+	0.994128i	$0.534512\pi$
$152$	696.682	0.371766
$153$	−959.760	−0.507137
$154$	−138.549	−0.0724974
$155$	0	0
$156$	429.541	0.220454
$157$	2631.01	1.33744	0.668719	−	0.743515i	$-0.266843\pi$
$157$	2631.01	1.33744	0.668719	+	0.743515i	$0.266843\pi$
$158$	2390.32	1.20357
$159$	−307.345	−0.153296
$160$	0	0
$161$	37.6085	0.0184097
$162$	−1758.24	−0.852719
$163$	627.170	0.301373	0.150686	−	0.988582i	$-0.451852\pi$
$163$	627.170	0.301373	0.150686	+	0.988582i	$0.451852\pi$
$164$	−444.279	−0.211539
$165$	0	0
$166$	−2951.18	−1.37985
$167$	−2495.88	−1.15651	−0.578255	−	0.815856i	$-0.696266\pi$
$167$	−2495.88	−1.15651	−0.578255	+	0.815856i	$0.696266\pi$
$168$	77.2033	0.0354545
$169$	−1865.93	−0.849310
$170$	0	0
$171$	682.027	0.305005
$172$	−769.697	−0.341214
$173$	2853.58	1.25407	0.627034	−	0.778992i	$-0.284269\pi$
$173$	2853.58	1.25407	0.627034	+	0.778992i	$0.284269\pi$
$174$	2213.07	0.964209
$175$	0	0
$176$	677.853	0.290313
$177$	2508.68	1.06534
$178$	−148.420	−0.0624974
$179$	−307.069	−0.128220	−0.0641101	−	0.997943i	$-0.520421\pi$
$179$	−307.069	−0.128220	−0.0641101	+	0.997943i	$0.520421\pi$
$180$	0	0
$181$	−1733.53	−0.711889	−0.355945	−	0.934507i	$-0.615841\pi$
$181$	−1733.53	−0.711889	−0.355945	+	0.934507i	$0.615841\pi$
$182$	59.5039	0.0242347
$183$	−3950.91	−1.59596
$184$	−184.000	−0.0737210
$185$	0	0
$186$	−1979.50	−0.780344
$187$	−5191.83	−2.03029
$188$	−981.747	−0.380858
$189$	−184.982	−0.0711928
$190$	0	0
$191$	2160.38	0.818427	0.409213	−	0.912439i	$-0.365803\pi$
$191$	2160.38	0.818427	0.409213	+	0.912439i	$0.365803\pi$
$192$	−377.718	−0.141976
$193$	−3725.78	−1.38957	−0.694785	−	0.719217i	$-0.744501\pi$
$193$	−3725.78	−1.38957	−0.694785	+	0.719217i	$0.744501\pi$
$194$	−1874.33	−0.693656
$195$	0	0
$196$	−1361.31	−0.496102
$197$	5267.32	1.90498	0.952491	−	0.304568i	$-0.0985121\pi$
$197$	5267.32	1.90498	0.952491	+	0.304568i	$0.0985121\pi$
$198$	663.594	0.238179
$199$	−190.118	−0.0677241	−0.0338620	−	0.999427i	$-0.510781\pi$
$199$	−190.118	−0.0677241	−0.0338620	+	0.999427i	$0.510781\pi$
$200$	0	0
$201$	−3903.43	−1.36978
$202$	43.2396	0.0150610
$203$	306.574	0.105997
$204$	2893.03	0.992905
$205$	0	0
$206$	−1018.33	−0.344420
$207$	−180.129	−0.0604824
$208$	−291.123	−0.0970470
$209$	3689.43	1.22107
$210$	0	0
$211$	677.866	0.221167	0.110583	−	0.993867i	$-0.464728\pi$
$211$	677.866	0.221167	0.110583	+	0.993867i	$0.464728\pi$
$212$	208.305	0.0674831
$213$	2509.68	0.807325
$214$	−2538.55	−0.810897
$215$	0	0
$216$	905.025	0.285089
$217$	−274.218	−0.0857841
$218$	−3654.15	−1.13528
$219$	6545.89	2.01977
$220$	0	0
$221$	2229.78	0.678695
$222$	−4781.42	−1.44553
$223$	−4214.82	−1.26567	−0.632837	−	0.774285i	$-0.718110\pi$
$223$	−4214.82	−1.26567	−0.632837	+	0.774285i	$0.718110\pi$
$224$	−52.3249	−0.0156076
$225$	0	0
$226$	−2351.35	−0.692076
$227$	−3368.29	−0.984850	−0.492425	−	0.870355i	$-0.663889\pi$
$227$	−3368.29	−0.984850	−0.492425	+	0.870355i	$0.663889\pi$
$228$	−2055.85	−0.597159
$229$	−1138.51	−0.328536	−0.164268	−	0.986416i	$-0.552526\pi$
$229$	−1138.51	−0.328536	−0.164268	+	0.986416i	$0.552526\pi$
$230$	0	0
$231$	408.847	0.116451
$232$	−1499.92	−0.424459
$233$	−659.376	−0.185396	−0.0926978	−	0.995694i	$-0.529549\pi$
$233$	−659.376	−0.185396	−0.0926978	+	0.995694i	$0.529549\pi$
$234$	−285.000	−0.0796197
$235$	0	0
$236$	−1700.27	−0.468976
$237$	−7053.65	−1.93327
$238$	400.769	0.109151
$239$	1401.18	0.379224	0.189612	−	0.981859i	$-0.439277\pi$
$239$	1401.18	0.379224	0.189612	+	0.981859i	$0.439277\pi$
$240$	0	0
$241$	3668.16	0.980443	0.490221	−	0.871598i	$-0.336916\pi$
$241$	3668.16	0.980443	0.490221	+	0.871598i	$0.336916\pi$
$242$	927.719	0.246430
$243$	2133.97	0.563350
$244$	2677.75	0.702563
$245$	0	0
$246$	1311.03	0.339790
$247$	−1584.53	−0.408184
$248$	1341.62	0.343519
$249$	8708.68	2.21643
$250$	0	0
$251$	591.784	0.148817	0.0744085	−	0.997228i	$-0.476293\pi$
$251$	591.784	0.148817	0.0744085	+	0.997228i	$0.476293\pi$
$252$	−51.2242	−0.0128048
$253$	−974.413	−0.242138
$254$	−3314.07	−0.818675
$255$	0	0
$256$	256.000	0.0625000
$257$	−2144.75	−0.520566	−0.260283	−	0.965532i	$-0.583816\pi$
$257$	−2144.75	−0.520566	−0.260283	+	0.965532i	$0.583816\pi$
$258$	2271.31	0.548085
$259$	−662.366	−0.158909
$260$	0	0
$261$	−1468.37	−0.348236
$262$	−2412.44	−0.568859
$263$	−3895.49	−0.913333	−0.456666	−	0.889638i	$-0.650957\pi$
$263$	−3895.49	−0.913333	−0.456666	+	0.889638i	$0.650957\pi$
$264$	−2000.29	−0.466323
$265$	0	0
$266$	−284.795	−0.0656463
$267$	437.975	0.100388
$268$	2645.57	0.602999
$269$	−3225.65	−0.731119	−0.365560	−	0.930788i	$-0.619122\pi$
$269$	−3225.65	−0.731119	−0.365560	+	0.930788i	$0.619122\pi$
$270$	0	0
$271$	−6791.74	−1.52239	−0.761197	−	0.648521i	$-0.775388\pi$
$271$	−6791.74	−1.52239	−0.761197	+	0.648521i	$0.775388\pi$
$272$	−1960.77	−0.437091
$273$	−175.591	−0.0389277
$274$	−4183.14	−0.922309
$275$	0	0
$276$	542.969	0.118416
$277$	4155.88	0.901454	0.450727	−	0.892662i	$-0.351165\pi$
$277$	4155.88	0.901454	0.450727	+	0.892662i	$0.351165\pi$
$278$	−83.0998	−0.0179280
$279$	1313.39	0.281831
$280$	0	0
$281$	1420.05	0.301471	0.150735	−	0.988574i	$-0.451836\pi$
$281$	1420.05	0.301471	0.150735	+	0.988574i	$0.451836\pi$
$282$	2897.06	0.611763
$283$	−3809.86	−0.800256	−0.400128	−	0.916459i	$-0.631034\pi$
$283$	−3809.86	−0.800256	−0.400128	+	0.916459i	$0.631034\pi$
$284$	−1700.95	−0.355396
$285$	0	0
$286$	−1541.71	−0.318752
$287$	181.616	0.0373535
$288$	250.615	0.0512765
$289$	10105.0	2.05678
$290$	0	0
$291$	5531.00	1.11420
$292$	−4436.50	−0.889133
$293$	−4958.44	−0.988652	−0.494326	−	0.869277i	$-0.664585\pi$
$293$	−4958.44	−0.988652	−0.494326	+	0.869277i	$0.664585\pi$
$294$	4017.10	0.796878
$295$	0	0
$296$	3240.63	0.636344
$297$	4792.76	0.936378
$298$	2988.83	0.581001
$299$	418.490	0.0809428
$300$	0	0
$301$	314.643	0.0602516
$302$	−803.153	−0.153034
$303$	−127.597	−0.0241922
$304$	1393.36	0.262878
$305$	0	0
$306$	−1919.52	−0.358600
$307$	6103.13	1.13461	0.567303	−	0.823509i	$-0.307987\pi$
$307$	6103.13	1.13461	0.567303	+	0.823509i	$0.307987\pi$
$308$	−277.098	−0.0512634
$309$	3005.01	0.553234
$310$	0	0
$311$	5156.67	0.940219	0.470110	−	0.882608i	$-0.344214\pi$
$311$	5156.67	0.940219	0.470110	+	0.882608i	$0.344214\pi$
$312$	859.082	0.155884
$313$	8640.79	1.56040	0.780202	−	0.625528i	$-0.215116\pi$
$313$	8640.79	1.56040	0.780202	+	0.625528i	$0.215116\pi$
$314$	5262.03	0.945711
$315$	0	0
$316$	4780.65	0.851052
$317$	88.2506	0.0156361	0.00781806	−	0.999969i	$-0.497511\pi$
$317$	88.2506	0.0156361	0.00781806	+	0.999969i	$0.497511\pi$
$318$	−614.690	−0.108397
$319$	−7943.15	−1.39414
$320$	0	0
$321$	7491.07	1.30253
$322$	75.2170	0.0130176
$323$	−10672.1	−1.83843
$324$	−3516.48	−0.602963
$325$	0	0
$326$	1254.34	0.213103
$327$	10783.1	1.82357
$328$	−888.558	−0.149580
$329$	401.327	0.0672518
$330$	0	0
$331$	−9121.75	−1.51473	−0.757367	−	0.652990i	$-0.773515\pi$
$331$	−9121.75	−1.51473	−0.757367	+	0.652990i	$0.773515\pi$
$332$	−5902.35	−0.975704
$333$	3172.46	0.522072
$334$	−4991.77	−0.817776
$335$	0	0
$336$	154.407	0.0250701
$337$	−2934.28	−0.474303	−0.237152	−	0.971473i	$-0.576214\pi$
$337$	−2934.28	−0.474303	−0.237152	+	0.971473i	$0.576214\pi$
$338$	−3731.87	−0.600553
$339$	6938.64	1.11167
$340$	0	0
$341$	7104.82	1.12829
$342$	1364.05	0.215671
$343$	1117.34	0.175892
$344$	−1539.39	−0.241275
$345$	0	0
$346$	5707.16	0.886760
$347$	3445.57	0.533049	0.266524	−	0.963828i	$-0.414125\pi$
$347$	3445.57	0.533049	0.266524	+	0.963828i	$0.414125\pi$
$348$	4426.14	0.681799
$349$	−10884.1	−1.66938	−0.834688	−	0.550722i	$-0.814352\pi$
$349$	−10884.1	−1.66938	−0.834688	+	0.550722i	$0.814352\pi$
$350$	0	0
$351$	−2058.39	−0.313016
$352$	1355.71	0.205282
$353$	−408.637	−0.0616135	−0.0308067	−	0.999525i	$-0.509808\pi$
$353$	−408.637	−0.0616135	−0.0308067	+	0.999525i	$0.509808\pi$
$354$	5017.37	0.753306
$355$	0	0
$356$	−296.840	−0.0441924
$357$	−1182.64	−0.175327
$358$	−614.138	−0.0906653
$359$	−779.667	−0.114622	−0.0573109	−	0.998356i	$-0.518253\pi$
$359$	−779.667	−0.114622	−0.0573109	+	0.998356i	$0.518253\pi$
$360$	0	0
$361$	724.837	0.105677
$362$	−3467.05	−0.503382
$363$	−2737.63	−0.395835
$364$	119.008	0.0171366
$365$	0	0
$366$	−7901.82	−1.12851
$367$	3815.03	0.542624	0.271312	−	0.962491i	$-0.412543\pi$
$367$	3815.03	0.542624	0.271312	+	0.962491i	$0.412543\pi$
$368$	−368.000	−0.0521286
$369$	−869.867	−0.122719
$370$	0	0
$371$	−85.1524	−0.0119162
$372$	−3959.00	−0.551786
$373$	10833.2	1.50381	0.751904	−	0.659272i	$-0.229136\pi$
$373$	10833.2	1.50381	0.751904	+	0.659272i	$0.229136\pi$
$374$	−10383.7	−1.43563
$375$	0	0
$376$	−1963.49	−0.269307
$377$	3411.42	0.466039
$378$	−369.964	−0.0503409
$379$	12700.8	1.72136	0.860679	−	0.509148i	$-0.170039\pi$
$379$	12700.8	1.72136	0.860679	+	0.509148i	$0.170039\pi$
$380$	0	0
$381$	9779.56	1.31502
$382$	4320.76	0.578715
$383$	3332.12	0.444553	0.222276	−	0.974984i	$-0.428651\pi$
$383$	3332.12	0.444553	0.222276	+	0.974984i	$0.428651\pi$
$384$	−755.436	−0.100392
$385$	0	0
$386$	−7451.55	−0.982575
$387$	−1507.01	−0.197948
$388$	−3748.66	−0.490489
$389$	4267.28	0.556195	0.278097	−	0.960553i	$-0.410296\pi$
$389$	4267.28	0.556195	0.278097	+	0.960553i	$0.410296\pi$
$390$	0	0
$391$	2818.60	0.364559
$392$	−2722.61	−0.350797
$393$	7118.92	0.913746
$394$	10534.6	1.34703
$395$	0	0
$396$	1327.19	0.168418
$397$	10684.1	1.35068	0.675342	−	0.737505i	$-0.263996\pi$
$397$	10684.1	1.35068	0.675342	+	0.737505i	$0.263996\pi$
$398$	−380.236	−0.0478882
$399$	840.408	0.105446
$400$	0	0
$401$	10178.2	1.26752	0.633760	−	0.773530i	$-0.281511\pi$
$401$	10178.2	1.26752	0.633760	+	0.773530i	$0.281511\pi$
$402$	−7806.86	−0.968584
$403$	−3051.37	−0.377170
$404$	86.4791	0.0106497
$405$	0	0
$406$	613.149	0.0749509
$407$	17161.5	2.09008
$408$	5786.06	0.702090
$409$	−13759.6	−1.66349	−0.831744	−	0.555160i	$-0.812657\pi$
$409$	−13759.6	−1.66349	−0.831744	+	0.555160i	$0.812657\pi$
$410$	0	0
$411$	12344.1	1.48148
$412$	−2036.66	−0.243541
$413$	695.052	0.0828118
$414$	−360.259	−0.0427675
$415$	0	0
$416$	−582.247	−0.0686226
$417$	245.221	0.0287974
$418$	7378.87	0.863426
$419$	−737.389	−0.0859757	−0.0429878	−	0.999076i	$-0.513688\pi$
$419$	−737.389	−0.0859757	−0.0429878	+	0.999076i	$0.513688\pi$
$420$	0	0
$421$	9700.13	1.12294	0.561468	−	0.827499i	$-0.310237\pi$
$421$	9700.13	1.12294	0.561468	+	0.827499i	$0.310237\pi$
$422$	1355.73	0.156389
$423$	−1922.19	−0.220946
$424$	416.609	0.0477177
$425$	0	0
$426$	5019.36	0.570865
$427$	−1094.63	−0.124058
$428$	−5077.11	−0.573391
$429$	4549.46	0.512005
$430$	0	0
$431$	−1036.16	−0.115800	−0.0579001	−	0.998322i	$-0.518440\pi$
$431$	−1036.16	−0.115800	−0.0579001	+	0.998322i	$0.518440\pi$
$432$	1810.05	0.201588
$433$	12256.9	1.36034	0.680171	−	0.733053i	$-0.261905\pi$
$433$	12256.9	1.36034	0.680171	+	0.733053i	$0.261905\pi$
$434$	−548.436	−0.0606585
$435$	0	0
$436$	−7308.30	−0.802762
$437$	−2002.96	−0.219255
$438$	13091.8	1.42819
$439$	11855.5	1.28891	0.644455	−	0.764642i	$-0.277084\pi$
$439$	11855.5	1.28891	0.644455	+	0.764642i	$0.277084\pi$
$440$	0	0
$441$	−2665.34	−0.287802
$442$	4459.57	0.479910
$443$	−9475.12	−1.01620	−0.508100	−	0.861298i	$-0.669652\pi$
$443$	−9475.12	−1.01620	−0.508100	+	0.861298i	$0.669652\pi$
$444$	−9562.84	−1.02215
$445$	0	0
$446$	−8429.64	−0.894967
$447$	−8819.79	−0.933248
$448$	−104.650	−0.0110362
$449$	−501.444	−0.0527052	−0.0263526	−	0.999653i	$-0.508389\pi$
$449$	−501.444	−0.0527052	−0.0263526	+	0.999653i	$0.508389\pi$
$450$	0	0
$451$	−4705.56	−0.491299
$452$	−4702.69	−0.489372
$453$	2370.04	0.245815
$454$	−6736.57	−0.696394
$455$	0	0
$456$	−4111.70	−0.422255
$457$	12951.1	1.32566	0.662829	−	0.748770i	$-0.269355\pi$
$457$	12951.1	1.32566	0.662829	+	0.748770i	$0.269355\pi$
$458$	−2277.01	−0.232310
$459$	−13863.6	−1.40980
$460$	0	0
$461$	−10829.4	−1.09409	−0.547044	−	0.837104i	$-0.684247\pi$
$461$	−10829.4	−1.09409	−0.547044	+	0.837104i	$0.684247\pi$
$462$	817.694	0.0823433
$463$	−14228.9	−1.42823	−0.714117	−	0.700026i	$-0.753172\pi$
$463$	−14228.9	−1.42823	−0.714117	+	0.700026i	$0.753172\pi$
$464$	−2999.84	−0.300138
$465$	0	0
$466$	−1318.75	−0.131095
$467$	11724.0	1.16172	0.580860	−	0.814003i	$-0.302716\pi$
$467$	11724.0	1.16172	0.580860	+	0.814003i	$0.302716\pi$
$468$	−569.999	−0.0562996
$469$	−1081.48	−0.106478
$470$	0	0
$471$	−15527.8	−1.51907
$472$	−3400.55	−0.331616
$473$	−8152.20	−0.792471
$474$	−14107.3	−1.36703
$475$	0	0
$476$	801.538	0.0771816
$477$	407.845	0.0391488
$478$	2802.35	0.268152
$479$	−8686.62	−0.828605	−0.414302	−	0.910139i	$-0.635974\pi$
$479$	−8686.62	−0.828605	−0.414302	+	0.910139i	$0.635974\pi$
$480$	0	0
$481$	−7370.50	−0.698681
$482$	7336.31	0.693278
$483$	−221.959	−0.0209099
$484$	1855.44	0.174252
$485$	0	0
$486$	4267.94	0.398349
$487$	7556.93	0.703156	0.351578	−	0.936159i	$-0.385645\pi$
$487$	7556.93	0.703156	0.351578	+	0.936159i	$0.385645\pi$
$488$	5355.50	0.496787
$489$	−3701.46	−0.342302
$490$	0	0
$491$	20466.9	1.88118	0.940591	−	0.339542i	$-0.110272\pi$
$491$	20466.9	1.88118	0.940591	+	0.339542i	$0.110272\pi$
$492$	2622.06	0.240268
$493$	22976.5	2.09900
$494$	−3169.07	−0.288630
$495$	0	0
$496$	2683.23	0.242904
$497$	695.327	0.0627559
$498$	17417.4	1.56725
$499$	−21514.4	−1.93009	−0.965046	−	0.262080i	$-0.915592\pi$
$499$	−21514.4	−1.93009	−0.965046	+	0.262080i	$0.915592\pi$
$500$	0	0
$501$	14730.3	1.31358
$502$	1183.57	0.105229
$503$	10975.0	0.972862	0.486431	−	0.873719i	$-0.338298\pi$
$503$	10975.0	0.972862	0.486431	+	0.873719i	$0.338298\pi$
$504$	−102.448	−0.00905440
$505$	0	0
$506$	−1948.83	−0.171217
$507$	11012.4	0.964655
$508$	−6628.14	−0.578890
$509$	−6282.97	−0.547127	−0.273563	−	0.961854i	$-0.588202\pi$
$509$	−6282.97	−0.547127	−0.273563	+	0.961854i	$0.588202\pi$
$510$	0	0
$511$	1813.59	0.157003
$512$	512.000	0.0441942
$513$	9851.79	0.847889
$514$	−4289.49	−0.368096
$515$	0	0
$516$	4542.63	0.387554
$517$	−10398.1	−0.884543
$518$	−1324.73	−0.112366
$519$	−16841.4	−1.42438
$520$	0	0
$521$	−16517.6	−1.38896	−0.694481	−	0.719511i	$-0.744366\pi$
$521$	−16517.6	−1.38896	−0.694481	+	0.719511i	$0.744366\pi$
$522$	−2936.73	−0.246240
$523$	−8149.95	−0.681400	−0.340700	−	0.940172i	$-0.610664\pi$
$523$	−8149.95	−0.681400	−0.340700	+	0.940172i	$0.610664\pi$
$524$	−4824.88	−0.402244
$525$	0	0
$526$	−7790.99	−0.645824
$527$	−20551.5	−1.69874
$528$	−4000.58	−0.329740
$529$	529.000	0.0434783
$530$	0	0
$531$	−3329.01	−0.272066
$532$	−569.591	−0.0464190
$533$	2020.94	0.164234
$534$	875.951	0.0709852
$535$	0	0
$536$	5291.14	0.426385
$537$	1812.27	0.145634
$538$	−6451.29	−0.516979
$539$	−14418.2	−1.15220
$540$	0	0
$541$	6661.54	0.529394	0.264697	−	0.964332i	$-0.414728\pi$
$541$	6661.54	0.529394	0.264697	+	0.964332i	$0.414728\pi$
$542$	−13583.5	−1.07650
$543$	10231.0	0.808571
$544$	−3921.53	−0.309070
$545$	0	0
$546$	−351.183	−0.0275261
$547$	16232.2	1.26881	0.634403	−	0.773002i	$-0.281246\pi$
$547$	16232.2	1.26881	0.634403	+	0.773002i	$0.281246\pi$
$548$	−8366.28	−0.652171
$549$	5242.84	0.407576
$550$	0	0
$551$	−16327.6	−1.26239
$552$	1085.94	0.0837330
$553$	−1954.27	−0.150279
$554$	8311.76	0.637424
$555$	0	0
$556$	−166.200	−0.0126770
$557$	−21238.0	−1.61559	−0.807796	−	0.589462i	$-0.799340\pi$
$557$	−21238.0	−1.61559	−0.807796	+	0.589462i	$0.799340\pi$
$558$	2626.79	0.199285
$559$	3501.20	0.264911
$560$	0	0
$561$	30641.4	2.30602
$562$	2840.10	0.213172
$563$	15600.2	1.16780	0.583898	−	0.811827i	$-0.301527\pi$
$563$	15600.2	1.16780	0.583898	+	0.811827i	$0.301527\pi$
$564$	5794.11	0.432582
$565$	0	0
$566$	−7619.71	−0.565866
$567$	1437.50	0.106471
$568$	−3401.89	−0.251303
$569$	678.547	0.0499932	0.0249966	−	0.999688i	$-0.492043\pi$
$569$	678.547	0.0499932	0.0249966	+	0.999688i	$0.492043\pi$
$570$	0	0
$571$	7228.40	0.529771	0.264885	−	0.964280i	$-0.414666\pi$
$571$	7228.40	0.529771	0.264885	+	0.964280i	$0.414666\pi$
$572$	−3083.42	−0.225392
$573$	−12750.2	−0.929577
$574$	363.232	0.0264129
$575$	0	0
$576$	501.230	0.0362579
$577$	−6170.01	−0.445166	−0.222583	−	0.974914i	$-0.571449\pi$
$577$	−6170.01	−0.445166	−0.222583	+	0.974914i	$0.571449\pi$
$578$	20209.9	1.45436
$579$	21988.9	1.57829
$580$	0	0
$581$	2412.81	0.172290
$582$	11062.0	0.787861
$583$	2206.25	0.156730
$584$	−8873.01	−0.628712
$585$	0	0
$586$	−9916.88	−0.699082
$587$	−5074.72	−0.356825	−0.178412	−	0.983956i	$-0.557096\pi$
$587$	−5074.72	−0.356825	−0.178412	+	0.983956i	$0.557096\pi$
$588$	8034.20	0.563478
$589$	14604.4	1.02167
$590$	0	0
$591$	−31086.9	−2.16370
$592$	6481.26	0.449963
$593$	1668.31	0.115530	0.0577649	−	0.998330i	$-0.481603\pi$
$593$	1668.31	0.115530	0.0577649	+	0.998330i	$0.481603\pi$
$594$	9585.53	0.662119
$595$	0	0
$596$	5977.66	0.410829
$597$	1122.04	0.0769217
$598$	836.980	0.0572352
$599$	−3896.54	−0.265790	−0.132895	−	0.991130i	$-0.542427\pi$
$599$	−3896.54	−0.265790	−0.132895	+	0.991130i	$0.542427\pi$
$600$	0	0
$601$	−6319.03	−0.428883	−0.214441	−	0.976737i	$-0.568793\pi$
$601$	−6319.03	−0.428883	−0.214441	+	0.976737i	$0.568793\pi$
$602$	629.286	0.0426043
$603$	5179.84	0.349816
$604$	−1606.31	−0.108211
$605$	0	0
$606$	−255.193	−0.0171064
$607$	−26623.5	−1.78025	−0.890126	−	0.455714i	$-0.849384\pi$
$607$	−26623.5	−1.78025	−0.890126	+	0.455714i	$0.849384\pi$
$608$	2786.73	0.185883
$609$	−1809.35	−0.120392
$610$	0	0
$611$	4465.77	0.295689
$612$	−3839.04	−0.253569
$613$	5819.80	0.383458	0.191729	−	0.981448i	$-0.438591\pi$
$613$	5819.80	0.383458	0.191729	+	0.981448i	$0.438591\pi$
$614$	12206.3	0.802287
$615$	0	0
$616$	−554.196	−0.0362487
$617$	−9816.46	−0.640512	−0.320256	−	0.947331i	$-0.603769\pi$
$617$	−9816.46	−0.640512	−0.320256	+	0.947331i	$0.603769\pi$
$618$	6010.02	0.391195
$619$	−14246.0	−0.925029	−0.462515	−	0.886612i	$-0.653053\pi$
$619$	−14246.0	−0.925029	−0.462515	+	0.886612i	$0.653053\pi$
$620$	0	0
$621$	−2601.95	−0.168136
$622$	10313.3	0.664835
$623$	121.345	0.00780348
$624$	1718.16	0.110227
$625$	0	0
$626$	17281.6	1.10337
$627$	−21774.4	−1.38690
$628$	10524.1	0.668719
$629$	−49641.5	−3.14680
$630$	0	0
$631$	−7637.96	−0.481874	−0.240937	−	0.970541i	$-0.577455\pi$
$631$	−7637.96	−0.481874	−0.240937	+	0.970541i	$0.577455\pi$
$632$	9561.29	0.601785
$633$	−4000.66	−0.251204
$634$	176.501	0.0110564
$635$	0	0
$636$	−1229.38	−0.0766479
$637$	6192.31	0.385162
$638$	−15886.3	−0.985807
$639$	−3330.33	−0.206175
$640$	0	0
$641$	−15541.7	−0.957663	−0.478831	−	0.877907i	$-0.658940\pi$
$641$	−15541.7	−0.957663	−0.478831	+	0.877907i	$0.658940\pi$
$642$	14982.1	0.921025
$643$	−7899.02	−0.484459	−0.242229	−	0.970219i	$-0.577879\pi$
$643$	−7899.02	−0.484459	−0.242229	+	0.970219i	$0.577879\pi$
$644$	150.434	0.00920486
$645$	0	0
$646$	−21344.2	−1.29996
$647$	23848.3	1.44911	0.724553	−	0.689219i	$-0.242046\pi$
$647$	23848.3	1.44911	0.724553	+	0.689219i	$0.242046\pi$
$648$	−7032.96	−0.426359
$649$	−18008.4	−1.08920
$650$	0	0
$651$	1618.39	0.0974344
$652$	2508.68	0.150686
$653$	−6308.32	−0.378046	−0.189023	−	0.981973i	$-0.560532\pi$
$653$	−6308.32	−0.378046	−0.189023	+	0.981973i	$0.560532\pi$
$654$	21566.2	1.28946
$655$	0	0
$656$	−1777.12	−0.105769
$657$	−8686.36	−0.515810
$658$	802.653	0.0475542
$659$	16683.7	0.986196	0.493098	−	0.869974i	$-0.335864\pi$
$659$	16683.7	0.986196	0.493098	+	0.869974i	$0.335864\pi$
$660$	0	0
$661$	1994.62	0.117370	0.0586850	−	0.998277i	$-0.481309\pi$
$661$	1994.62	0.117370	0.0586850	+	0.998277i	$0.481309\pi$
$662$	−18243.5	−1.07108
$663$	−13159.8	−0.770868
$664$	−11804.7	−0.689927
$665$	0	0
$666$	6344.92	0.369160
$667$	4312.26	0.250332
$668$	−9983.53	−0.578255
$669$	24875.2	1.43756
$670$	0	0
$671$	28361.2	1.63170
$672$	308.813	0.0177273
$673$	19202.9	1.09988	0.549939	−	0.835205i	$-0.314651\pi$
$673$	19202.9	1.09988	0.549939	+	0.835205i	$0.314651\pi$
$674$	−5868.55	−0.335383
$675$	0	0
$676$	−7463.74	−0.424655
$677$	9478.33	0.538083	0.269041	−	0.963129i	$-0.413293\pi$
$677$	9478.33	0.538083	0.269041	+	0.963129i	$0.413293\pi$
$678$	13877.3	0.786067
$679$	1532.41	0.0866104
$680$	0	0
$681$	19879.1	1.11860
$682$	14209.6	0.797823
$683$	−12019.1	−0.673348	−0.336674	−	0.941621i	$-0.609302\pi$
$683$	−12019.1	−0.673348	−0.336674	+	0.941621i	$0.609302\pi$
$684$	2728.11	0.152503
$685$	0	0
$686$	2234.69	0.124374
$687$	6719.29	0.373154
$688$	−3078.79	−0.170607
$689$	−947.536	−0.0523923
$690$	0	0
$691$	9605.96	0.528839	0.264420	−	0.964408i	$-0.414820\pi$
$691$	9605.96	0.528839	0.264420	+	0.964408i	$0.414820\pi$
$692$	11414.3	0.627034
$693$	−542.538	−0.0297393
$694$	6891.14	0.376922
$695$	0	0
$696$	8852.28	0.482104
$697$	13611.4	0.739694
$698$	−21768.2	−1.18043
$699$	3891.53	0.210574
$700$	0	0
$701$	1557.50	0.0839170	0.0419585	−	0.999119i	$-0.486640\pi$
$701$	1557.50	0.0839170	0.0419585	+	0.999119i	$0.486640\pi$
$702$	−4116.78	−0.221336
$703$	35276.4	1.89257
$704$	2711.41	0.145156
$705$	0	0
$706$	−817.274	−0.0435673
$707$	−35.3517	−0.00188053
$708$	10034.7	0.532668
$709$	−29539.5	−1.56471	−0.782354	−	0.622834i	$-0.785981\pi$
$709$	−29539.5	−1.56471	−0.782354	+	0.622834i	$0.785981\pi$
$710$	0	0
$711$	9360.17	0.493718
$712$	−593.680	−0.0312487
$713$	−3857.14	−0.202596
$714$	−2365.27	−0.123975
$715$	0	0
$716$	−1228.28	−0.0641101
$717$	−8269.52	−0.430727
$718$	−1559.33	−0.0810499
$719$	−20393.6	−1.05780	−0.528898	−	0.848686i	$-0.677394\pi$
$719$	−20393.6	−1.05780	−0.528898	+	0.848686i	$0.677394\pi$
$720$	0	0
$721$	832.563	0.0430045
$722$	1449.67	0.0747248
$723$	−21648.9	−1.11360
$724$	−6934.10	−0.355945
$725$	0	0
$726$	−5475.25	−0.279898
$727$	−27602.9	−1.40816	−0.704082	−	0.710119i	$-0.748641\pi$
$727$	−27602.9	−1.40816	−0.704082	+	0.710119i	$0.748641\pi$
$728$	238.016	0.0121174
$729$	11141.9	0.566068
$730$	0	0
$731$	23581.2	1.19313
$732$	−15803.6	−0.797978
$733$	28300.4	1.42606	0.713028	−	0.701136i	$-0.247323\pi$
$733$	28300.4	1.42606	0.713028	+	0.701136i	$0.247323\pi$
$734$	7630.06	0.383693
$735$	0	0
$736$	−736.000	−0.0368605
$737$	28020.4	1.40047
$738$	−1739.73	−0.0867757
$739$	−643.235	−0.0320187	−0.0160093	−	0.999872i	$-0.505096\pi$
$739$	−643.235	−0.0320187	−0.0160093	+	0.999872i	$0.505096\pi$
$740$	0	0
$741$	9351.67	0.463620
$742$	−170.305	−0.00842600
$743$	27212.6	1.34365	0.671826	−	0.740709i	$-0.265510\pi$
$743$	27212.6	1.34365	0.671826	+	0.740709i	$0.265510\pi$
$744$	−7918.00	−0.390172
$745$	0	0
$746$	21666.4	1.06335
$747$	−11556.4	−0.566032
$748$	−20767.3	−1.01515
$749$	2075.46	0.101249
$750$	0	0
$751$	−6331.75	−0.307655	−0.153827	−	0.988098i	$-0.549160\pi$
$751$	−6331.75	−0.307655	−0.153827	+	0.988098i	$0.549160\pi$
$752$	−3926.99	−0.190429
$753$	−3492.61	−0.169028
$754$	6822.83	0.329540
$755$	0	0
$756$	−739.927	−0.0355964
$757$	−13949.1	−0.669734	−0.334867	−	0.942265i	$-0.608691\pi$
$757$	−13949.1	−0.669734	−0.334867	+	0.942265i	$0.608691\pi$
$758$	25401.5	1.21718
$759$	5750.83	0.275022
$760$	0	0
$761$	16217.5	0.772517	0.386258	−	0.922391i	$-0.373767\pi$
$761$	16217.5	0.772517	0.386258	+	0.922391i	$0.373767\pi$
$762$	19559.1	0.929859
$763$	2987.55	0.141752
$764$	8641.52	0.409213
$765$	0	0
$766$	6664.25	0.314346
$767$	7734.21	0.364102
$768$	−1510.87	−0.0709881
$769$	2419.50	0.113458	0.0567291	−	0.998390i	$-0.481933\pi$
$769$	2419.50	0.113458	0.0567291	+	0.998390i	$0.481933\pi$
$770$	0	0
$771$	12657.9	0.591264
$772$	−14903.1	−0.694785
$773$	−20853.3	−0.970299	−0.485150	−	0.874431i	$-0.661235\pi$
$773$	−20853.3	−0.970299	−0.485150	+	0.874431i	$0.661235\pi$
$774$	−3014.02	−0.139970
$775$	0	0
$776$	−7497.33	−0.346828
$777$	3909.18	0.180490
$778$	8534.56	0.393289
$779$	−9672.53	−0.444871
$780$	0	0
$781$	−18015.5	−0.825409
$782$	5637.20	0.257782
$783$	−21210.4	−0.968067
$784$	−5445.22	−0.248051
$785$	0	0
$786$	14237.8	0.646116
$787$	9499.10	0.430249	0.215125	−	0.976587i	$-0.430984\pi$
$787$	9499.10	0.430249	0.215125	+	0.976587i	$0.430984\pi$
$788$	21069.3	0.952491
$789$	22990.6	1.03737
$790$	0	0
$791$	1922.41	0.0864132
$792$	2654.37	0.119090
$793$	−12180.6	−0.545453
$794$	21368.3	0.955078
$795$	0	0
$796$	−760.471	−0.0338620
$797$	−19087.7	−0.848334	−0.424167	−	0.905584i	$-0.639433\pi$
$797$	−19087.7	−0.848334	−0.424167	+	0.905584i	$0.639433\pi$
$798$	1680.82	0.0745617
$799$	30077.7	1.33176
$800$	0	0
$801$	−581.191	−0.0256372
$802$	20356.4	0.896272
$803$	−46989.0	−2.06501
$804$	−15613.7	−0.684892
$805$	0	0
$806$	−6102.74	−0.266700
$807$	19037.2	0.830412
$808$	172.958	0.00753051
$809$	34482.0	1.49855	0.749273	−	0.662262i	$-0.230403\pi$
$809$	34482.0	1.49855	0.749273	+	0.662262i	$0.230403\pi$
$810$	0	0
$811$	−17807.0	−0.771009	−0.385505	−	0.922706i	$-0.625973\pi$
$811$	−17807.0	−0.771009	−0.385505	+	0.922706i	$0.625973\pi$
$812$	1226.30	0.0529983
$813$	40083.8	1.72915
$814$	34323.0	1.47791
$815$	0	0
$816$	11572.1	0.496453
$817$	−16757.3	−0.717582
$818$	−27519.1	−1.17626
$819$	233.009	0.00994138
$820$	0	0
$821$	15030.8	0.638950	0.319475	−	0.947595i	$-0.396493\pi$
$821$	15030.8	0.638950	0.319475	+	0.947595i	$0.396493\pi$
$822$	24688.2	1.04757
$823$	21668.9	0.917775	0.458888	−	0.888494i	$-0.348248\pi$
$823$	21668.9	0.917775	0.458888	+	0.888494i	$0.348248\pi$
$824$	−4073.32	−0.172210
$825$	0	0
$826$	1390.10	0.0585568
$827$	−8174.05	−0.343699	−0.171850	−	0.985123i	$-0.554974\pi$
$827$	−8174.05	−0.343699	−0.171850	+	0.985123i	$0.554974\pi$
$828$	−720.518	−0.0302412
$829$	22775.9	0.954211	0.477106	−	0.878846i	$-0.341686\pi$
$829$	22775.9	0.954211	0.477106	+	0.878846i	$0.341686\pi$
$830$	0	0
$831$	−24527.3	−1.02388
$832$	−1164.49	−0.0485235
$833$	41706.2	1.73474
$834$	490.442	0.0203628
$835$	0	0
$836$	14757.7	0.610535
$837$	18971.8	0.783467
$838$	−1474.78	−0.0607940
$839$	−4543.66	−0.186966	−0.0934831	−	0.995621i	$-0.529800\pi$
$839$	−4543.66	−0.186966	−0.0934831	+	0.995621i	$0.529800\pi$
$840$	0	0
$841$	10763.4	0.441322
$842$	19400.3	0.794035
$843$	−8380.92	−0.342413
$844$	2711.46	0.110583
$845$	0	0
$846$	−3844.38	−0.156232
$847$	−758.481	−0.0307695
$848$	833.218	0.0337415
$849$	22485.2	0.908938
$850$	0	0
$851$	−9316.81	−0.375295
$852$	10038.7	0.403663
$853$	−13198.5	−0.529785	−0.264892	−	0.964278i	$-0.585336\pi$
$853$	−13198.5	−0.529785	−0.264892	+	0.964278i	$0.585336\pi$
$854$	−2189.26	−0.0877226
$855$	0	0
$856$	−10154.2	−0.405449
$857$	8209.19	0.327212	0.163606	−	0.986526i	$-0.447687\pi$
$857$	8209.19	0.327212	0.163606	+	0.986526i	$0.447687\pi$
$858$	9098.92	0.362042
$859$	−2296.20	−0.0912055	−0.0456027	−	0.998960i	$-0.514521\pi$
$859$	−2296.20	−0.0912055	−0.0456027	+	0.998960i	$0.514521\pi$
$860$	0	0
$861$	−1071.87	−0.0424265
$862$	−2072.31	−0.0818831
$863$	−35083.8	−1.38385	−0.691927	−	0.721967i	$-0.743238\pi$
$863$	−35083.8	−1.38385	−0.691927	+	0.721967i	$0.743238\pi$
$864$	3620.10	0.142544
$865$	0	0
$866$	24513.8	0.961908
$867$	−59637.9	−2.33611
$868$	−1096.87	−0.0428920
$869$	50634.0	1.97657
$870$	0	0
$871$	−12034.2	−0.468154
$872$	−14616.6	−0.567638
$873$	−7339.62	−0.284546
$874$	−4005.92	−0.155037
$875$	0	0
$876$	26183.5	1.00989
$877$	−13761.2	−0.529854	−0.264927	−	0.964268i	$-0.585348\pi$
$877$	−13761.2	−0.529854	−0.264927	+	0.964268i	$0.585348\pi$
$878$	23711.0	0.911397
$879$	29263.9	1.12292
$880$	0	0
$881$	35260.1	1.34840	0.674202	−	0.738547i	$-0.264488\pi$
$881$	35260.1	1.34840	0.674202	+	0.738547i	$0.264488\pi$
$882$	−5330.68	−0.203507
$883$	−21770.3	−0.829704	−0.414852	−	0.909889i	$-0.636167\pi$
$883$	−21770.3	−0.829704	−0.414852	+	0.909889i	$0.636167\pi$
$884$	8919.14	0.339347
$885$	0	0
$886$	−18950.2	−0.718562
$887$	6289.26	0.238075	0.119038	−	0.992890i	$-0.462019\pi$
$887$	6289.26	0.238075	0.119038	+	0.992890i	$0.462019\pi$
$888$	−19125.7	−0.722766
$889$	2709.51	0.102220
$890$	0	0
$891$	−37244.6	−1.40038
$892$	−16859.3	−0.632837
$893$	−21373.9	−0.800953
$894$	−17639.6	−0.659906
$895$	0	0
$896$	−209.300	−0.00780380
$897$	−2469.86	−0.0919356
$898$	−1002.89	−0.0372682
$899$	−31442.4	−1.16648
$900$	0	0
$901$	−6381.82	−0.235970
$902$	−9411.11	−0.347401
$903$	−1856.97	−0.0684343
$904$	−9405.39	−0.346038
$905$	0	0
$906$	4740.08	0.173818
$907$	19725.0	0.722115	0.361058	−	0.932543i	$-0.382416\pi$
$907$	19725.0	0.722115	0.361058	+	0.932543i	$0.382416\pi$
$908$	−13473.1	−0.492425
$909$	169.320	0.00617821
$910$	0	0
$911$	−13617.4	−0.495241	−0.247620	−	0.968857i	$-0.579649\pi$
$911$	−13617.4	−0.495241	−0.247620	+	0.968857i	$0.579649\pi$
$912$	−8223.41	−0.298579
$913$	−62514.4	−2.26607
$914$	25902.2	0.937382
$915$	0	0
$916$	−4554.03	−0.164268
$917$	1972.35	0.0710282
$918$	−27727.2	−0.996878
$919$	−12440.7	−0.446553	−0.223276	−	0.974755i	$-0.571675\pi$
$919$	−12440.7	−0.446553	−0.223276	+	0.974755i	$0.571675\pi$
$920$	0	0
$921$	−36019.7	−1.28870
$922$	−21658.7	−0.773636
$923$	7737.27	0.275921
$924$	1635.39	0.0582255
$925$	0	0
$926$	−28457.8	−1.00991
$927$	−3987.64	−0.141285
$928$	−5999.67	−0.212229
$929$	−6881.48	−0.243029	−0.121515	−	0.992590i	$-0.538775\pi$
$929$	−6881.48	−0.243029	−0.121515	+	0.992590i	$0.538775\pi$
$930$	0	0
$931$	−29637.4	−1.04332
$932$	−2637.51	−0.0926978
$933$	−30433.9	−1.06791
$934$	23448.1	0.821461
$935$	0	0
$936$	−1140.00	−0.0398098
$937$	−44549.4	−1.55322	−0.776609	−	0.629983i	$-0.783062\pi$
$937$	−44549.4	−1.55322	−0.776609	+	0.629983i	$0.783062\pi$
$938$	−2162.95	−0.0752910
$939$	−50996.5	−1.77232
$940$	0	0
$941$	−53673.0	−1.85939	−0.929697	−	0.368324i	$-0.879932\pi$
$941$	−53673.0	−1.85939	−0.929697	+	0.368324i	$0.879932\pi$
$942$	−31055.6	−1.07415
$943$	2554.60	0.0882178
$944$	−6801.09	−0.234488
$945$	0	0
$946$	−16304.4	−0.560362
$947$	−15772.6	−0.541226	−0.270613	−	0.962688i	$-0.587226\pi$
$947$	−15772.6	−0.541226	−0.270613	+	0.962688i	$0.587226\pi$
$948$	−28214.6	−0.966633
$949$	20180.8	0.690302
$950$	0	0
$951$	−520.841	−0.0177596
$952$	1603.08	0.0545756
$953$	33796.2	1.14876	0.574379	−	0.818589i	$-0.305244\pi$
$953$	33796.2	1.14876	0.574379	+	0.818589i	$0.305244\pi$
$954$	815.691	0.0276824
$955$	0	0
$956$	5604.71	0.189612
$957$	46879.2	1.58348
$958$	−17373.2	−0.585912
$959$	3420.04	0.115160
$960$	0	0
$961$	−1667.08	−0.0559591
$962$	−14741.0	−0.494042
$963$	−9940.62	−0.332640
$964$	14672.6	0.490221
$965$	0	0
$966$	−443.919	−0.0147856
$967$	36502.1	1.21389	0.606944	−	0.794745i	$-0.292395\pi$
$967$	36502.1	1.21389	0.606944	+	0.794745i	$0.292395\pi$
$968$	3710.88	0.123215
$969$	62985.1	2.08810
$970$	0	0
$971$	−23238.4	−0.768029	−0.384014	−	0.923327i	$-0.625459\pi$
$971$	−23238.4	−0.768029	−0.384014	+	0.923327i	$0.625459\pi$
$972$	8535.88	0.281675
$973$	67.9404	0.00223851
$974$	15113.9	0.497207
$975$	0	0
$976$	10711.0	0.351281
$977$	−4074.86	−0.133435	−0.0667177	−	0.997772i	$-0.521253\pi$
$977$	−4074.86	−0.133435	−0.0667177	+	0.997772i	$0.521253\pi$
$978$	−7402.91	−0.242044
$979$	−3143.96	−0.102637
$980$	0	0
$981$	−14309.1	−0.465704
$982$	40933.9	1.33020
$983$	−41839.4	−1.35755	−0.678775	−	0.734347i	$-0.737489\pi$
$983$	−41839.4	−1.35755	−0.678775	+	0.734347i	$0.737489\pi$
$984$	5244.13	0.169895
$985$	0	0
$986$	45952.9	1.48422
$987$	−2368.57	−0.0763853
$988$	−6338.14	−0.204092
$989$	4425.76	0.142296
$990$	0	0
$991$	−30214.8	−0.968521	−0.484260	−	0.874924i	$-0.660911\pi$
$991$	−30214.8	−0.968521	−0.484260	+	0.874924i	$0.660911\pi$
$992$	5366.46	0.171759
$993$	53835.1	1.72045
$994$	1390.65	0.0443751
$995$	0	0
$996$	34834.7	1.10821
$997$	−23509.3	−0.746788	−0.373394	−	0.927673i	$-0.621806\pi$
$997$	−23509.3	−0.746788	−0.373394	+	0.927673i	$0.621806\pi$
$998$	−43028.8	−1.36478
$999$	45825.8	1.45132

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.4.a.x.1.2	yes	6
5.2	odd	4		1150.4.b.s.599.11		12
5.3	odd	4		1150.4.b.s.599.2		12
5.4	even	2		1150.4.a.w.1.5	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1150.4.a.w.1.5	✓	6	5.4	even	2
1150.4.a.x.1.2	yes	6	1.1	even	1	trivial
1150.4.b.s.599.2		12	5.3	odd	4
1150.4.b.s.599.11		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)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -5.90184 q^{3} +4.00000 q^{4} -11.8037 q^{6} -1.63515 q^{7} +8.00000 q^{8} +7.83172 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} -5.90184 q^{3} +4.00000 q^{4} -11.8037 q^{6} -1.63515 q^{7} +8.00000 q^{8} +7.83172 q^{9} +42.3658 q^{11} -23.6074 q^{12} -18.1952 q^{13} -3.27031 q^{14} +16.0000 q^{16} -122.548 q^{17} +15.6634 q^{18} +87.0852 q^{19} +9.65041 q^{21} +84.7316 q^{22} -23.0000 q^{23} -47.2147 q^{24} -36.3904 q^{26} +113.128 q^{27} -6.54061 q^{28} -187.490 q^{29} +167.702 q^{31} +32.0000 q^{32} -250.036 q^{33} -245.096 q^{34} +31.3269 q^{36} +405.079 q^{37} +174.170 q^{38} +107.385 q^{39} -111.070 q^{41} +19.3008 q^{42} -192.424 q^{43} +169.463 q^{44} -46.0000 q^{46} -245.437 q^{47} -94.4294 q^{48} -340.326 q^{49} +723.258 q^{51} -72.7809 q^{52} +52.0761 q^{53} +226.256 q^{54} -13.0812 q^{56} -513.963 q^{57} -374.979 q^{58} -425.068 q^{59} +669.437 q^{61} +335.404 q^{62} -12.8061 q^{63} +64.0000 q^{64} -500.072 q^{66} +661.392 q^{67} -490.191 q^{68} +135.742 q^{69} -425.237 q^{71} +62.6537 q^{72} -1109.13 q^{73} +810.158 q^{74} +348.341 q^{76} -69.2745 q^{77} +214.771 q^{78} +1195.16 q^{79} -879.121 q^{81} -222.139 q^{82} -1475.59 q^{83} +38.6016 q^{84} -384.849 q^{86} +1106.53 q^{87} +338.926 q^{88} -74.2100 q^{89} +29.7520 q^{91} -92.0000 q^{92} -989.750 q^{93} -490.874 q^{94} -188.859 q^{96} -937.166 q^{97} -680.653 q^{98} +331.797 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 12 q^{2} - 5 q^{3} + 24 q^{4} - 10 q^{6} - 42 q^{7} + 48 q^{8} + 61 q^{9}+O(q^{10}) \) 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

Introduction

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