LMFDB - Embedded newform 825.4.a.bc.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("825.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.6765757547$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 44x^{5} + 118x^{4} + 515x^{3} - 1279x^{2} - 892x + 1840 $ x^7 - 3x^6 - 44x^5 + 118x^4 + 515x^3 - 1279x^2 - 892x + 1840
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 165)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.16334$ of defining polynomial
Character	$\chi$	$=$	825.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.16334 q^{2} +3.00000 q^{3} -6.64664 q^{4} +3.49002 q^{6} +19.4748 q^{7} -17.0390 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+1.16334 q^{2} +3.00000 q^{3} -6.64664 q^{4} +3.49002 q^{6} +19.4748 q^{7} -17.0390 q^{8} +9.00000 q^{9} -11.0000 q^{11} -19.9399 q^{12} -8.26359 q^{13} +22.6558 q^{14} +33.3510 q^{16} +5.66364 q^{17} +10.4701 q^{18} -24.4710 q^{19} +58.4243 q^{21} -12.7967 q^{22} +15.3593 q^{23} -51.1171 q^{24} -9.61336 q^{26} +27.0000 q^{27} -129.442 q^{28} +158.322 q^{29} +302.349 q^{31} +175.111 q^{32} -33.0000 q^{33} +6.58873 q^{34} -59.8198 q^{36} -266.602 q^{37} -28.4681 q^{38} -24.7908 q^{39} +81.4234 q^{41} +67.9673 q^{42} +22.6601 q^{43} +73.1131 q^{44} +17.8681 q^{46} -15.1324 q^{47} +100.053 q^{48} +36.2671 q^{49} +16.9909 q^{51} +54.9251 q^{52} +453.069 q^{53} +31.4102 q^{54} -331.831 q^{56} -73.4131 q^{57} +184.182 q^{58} +292.859 q^{59} +255.185 q^{61} +351.735 q^{62} +175.273 q^{63} -63.0946 q^{64} -38.3902 q^{66} -314.716 q^{67} -37.6442 q^{68} +46.0780 q^{69} -238.686 q^{71} -153.351 q^{72} +744.418 q^{73} -310.148 q^{74} +162.650 q^{76} -214.223 q^{77} -28.8401 q^{78} -177.549 q^{79} +81.0000 q^{81} +94.7231 q^{82} +624.817 q^{83} -388.326 q^{84} +26.3614 q^{86} +474.967 q^{87} +187.429 q^{88} +1521.53 q^{89} -160.932 q^{91} -102.088 q^{92} +907.047 q^{93} -17.6041 q^{94} +525.332 q^{96} +342.953 q^{97} +42.1909 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 3 q^{2} + 21 q^{3} + 41 q^{4} + 9 q^{6} + 50 q^{7} + 21 q^{8} + 63 q^{9}+O(q^{10}) $ 7 * q + 3 * q^2 + 21 * q^3 + 41 * q^4 + 9 * q^6 + 50 * q^7 + 21 * q^8 + 63 * q^9	\( 7 q + 3 q^{2} + 21 q^{3} + 41 q^{4} + 9 q^{6} + 50 q^{7} + 21 q^{8} + 63 q^{9} - 77 q^{11} + 123 q^{12} + 24 q^{13} + 142 q^{14} + 181 q^{16} + 38 q^{17} + 27 q^{18} + 26 q^{19} + 150 q^{21} - 33 q^{22} + 228 q^{23} + 63 q^{24} + 476 q^{26} + 189 q^{27} + 840 q^{28} + 572 q^{29} - 140 q^{31} + 991 q^{32} - 231 q^{33} - 806 q^{34} + 369 q^{36} - 104 q^{37} + 498 q^{38} + 72 q^{39} + 896 q^{41} + 426 q^{42} + 614 q^{43} - 451 q^{44} - 344 q^{46} + 520 q^{47} + 543 q^{48} + 295 q^{49} + 114 q^{51} - 26 q^{52} + 380 q^{53} + 81 q^{54} + 1522 q^{56} + 78 q^{57} + 1600 q^{58} + 1316 q^{59} - 386 q^{61} + 440 q^{62} + 450 q^{63} + 869 q^{64} - 99 q^{66} + 348 q^{67} + 332 q^{68} + 684 q^{69} + 804 q^{71} + 189 q^{72} + 468 q^{73} - 748 q^{74} - 1698 q^{76} - 550 q^{77} + 1428 q^{78} - 374 q^{79} + 567 q^{81} - 620 q^{82} + 3128 q^{83} + 2520 q^{84} - 2534 q^{86} + 1716 q^{87} - 231 q^{88} + 694 q^{89} - 3376 q^{91} - 1184 q^{92} - 420 q^{93} - 2920 q^{94} + 2973 q^{96} - 8 q^{97} + 4211 q^{98} - 693 q^{99}+O(q^{100}) \) 7 * q + 3 * q^2 + 21 * q^3 + 41 * q^4 + 9 * q^6 + 50 * q^7 + 21 * q^8 + 63 * q^9 - 77 * q^11 + 123 * q^12 + 24 * q^13 + 142 * q^14 + 181 * q^16 + 38 * q^17 + 27 * q^18 + 26 * q^19 + 150 * q^21 - 33 * q^22 + 228 * q^23 + 63 * q^24 + 476 * q^26 + 189 * q^27 + 840 * q^28 + 572 * q^29 - 140 * q^31 + 991 * q^32 - 231 * q^33 - 806 * q^34 + 369 * q^36 - 104 * q^37 + 498 * q^38 + 72 * q^39 + 896 * q^41 + 426 * q^42 + 614 * q^43 - 451 * q^44 - 344 * q^46 + 520 * q^47 + 543 * q^48 + 295 * q^49 + 114 * q^51 - 26 * q^52 + 380 * q^53 + 81 * q^54 + 1522 * q^56 + 78 * q^57 + 1600 * q^58 + 1316 * q^59 - 386 * q^61 + 440 * q^62 + 450 * q^63 + 869 * q^64 - 99 * q^66 + 348 * q^67 + 332 * q^68 + 684 * q^69 + 804 * q^71 + 189 * q^72 + 468 * q^73 - 748 * q^74 - 1698 * q^76 - 550 * q^77 + 1428 * q^78 - 374 * q^79 + 567 * q^81 - 620 * q^82 + 3128 * q^83 + 2520 * q^84 - 2534 * q^86 + 1716 * q^87 - 231 * q^88 + 694 * q^89 - 3376 * q^91 - 1184 * q^92 - 420 * q^93 - 2920 * q^94 + 2973 * q^96 - 8 * q^97 + 4211 * q^98 - 693 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.16334	0.411303	0.205651	−	0.978625i	$-0.434069\pi$
$2$	1.16334	0.411303	0.205651	+	0.978625i	$0.434069\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−6.64664	−0.830830
$5$	0	0
$5$	0	0
$6$	3.49002	0.237466
$7$	19.4748	1.05154	0.525770	−	0.850627i	$-0.323777\pi$
$7$	19.4748	1.05154	0.525770	+	0.850627i	$0.323777\pi$
$8$	−17.0390	−0.753025
$9$	9.00000	0.333333
$10$	0	0
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−19.9399	−0.479680
$13$	−8.26359	−0.176300	−0.0881502	−	0.996107i	$-0.528096\pi$
$13$	−8.26359	−0.176300	−0.0881502	+	0.996107i	$0.528096\pi$
$14$	22.6558	0.432501
$15$	0	0
$16$	33.3510	0.521109
$17$	5.66364	0.0808020	0.0404010	−	0.999184i	$-0.487136\pi$
$17$	5.66364	0.0808020	0.0404010	+	0.999184i	$0.487136\pi$
$18$	10.4701	0.137101
$19$	−24.4710	−0.295476	−0.147738	−	0.989027i	$-0.547199\pi$
$19$	−24.4710	−0.295476	−0.147738	+	0.989027i	$0.547199\pi$
$20$	0	0
$21$	58.4243	0.607106
$22$	−12.7967	−0.124012
$23$	15.3593	0.139245	0.0696226	−	0.997573i	$-0.477820\pi$
$23$	15.3593	0.139245	0.0696226	+	0.997573i	$0.477820\pi$
$24$	−51.1171	−0.434759
$25$	0	0
$26$	−9.61336	−0.0725129
$27$	27.0000	0.192450
$28$	−129.442	−0.873651
$29$	158.322	1.01378	0.506891	−	0.862010i	$-0.330795\pi$
$29$	158.322	1.01378	0.506891	+	0.862010i	$0.330795\pi$
$30$	0	0
$31$	302.349	1.75173	0.875863	−	0.482560i	$-0.160293\pi$
$31$	302.349	1.75173	0.875863	+	0.482560i	$0.160293\pi$
$32$	175.111	0.967359
$33$	−33.0000	−0.174078
$34$	6.58873	0.0332341
$35$	0	0
$36$	−59.8198	−0.276943
$37$	−266.602	−1.18457	−0.592285	−	0.805729i	$-0.701774\pi$
$37$	−266.602	−1.18457	−0.592285	+	0.805729i	$0.701774\pi$
$38$	−28.4681	−0.121530
$39$	−24.7908	−0.101787
$40$	0	0
$41$	81.4234	0.310151	0.155076	−	0.987903i	$-0.450438\pi$
$41$	81.4234	0.310151	0.155076	+	0.987903i	$0.450438\pi$
$42$	67.9673	0.249705
$43$	22.6601	0.0803637	0.0401818	−	0.999192i	$-0.487206\pi$
$43$	22.6601	0.0803637	0.0401818	+	0.999192i	$0.487206\pi$
$44$	73.1131	0.250505
$45$	0	0
$46$	17.8681	0.0572720
$47$	−15.1324	−0.0469634	−0.0234817	−	0.999724i	$-0.507475\pi$
$47$	−15.1324	−0.0469634	−0.0234817	+	0.999724i	$0.507475\pi$
$48$	100.053	0.300862
$49$	36.2671	0.105735
$50$	0	0
$51$	16.9909	0.0466510
$52$	54.9251	0.146476
$53$	453.069	1.17422	0.587111	−	0.809506i	$-0.300265\pi$
$53$	453.069	1.17422	0.587111	+	0.809506i	$0.300265\pi$
$54$	31.4102	0.0791552
$55$	0	0
$56$	−331.831	−0.791836
$57$	−73.4131	−0.170593
$58$	184.182	0.416971
$59$	292.859	0.646221	0.323110	−	0.946361i	$-0.395272\pi$
$59$	292.859	0.646221	0.323110	+	0.946361i	$0.395272\pi$
$60$	0	0
$61$	255.185	0.535625	0.267813	−	0.963471i	$-0.413699\pi$
$61$	255.185	0.535625	0.267813	+	0.963471i	$0.413699\pi$
$62$	351.735	0.720490
$63$	175.273	0.350513
$64$	−63.0946	−0.123232
$65$	0	0
$66$	−38.3902	−0.0715986
$67$	−314.716	−0.573860	−0.286930	−	0.957951i	$-0.592635\pi$
$67$	−314.716	−0.573860	−0.286930	+	0.957951i	$0.592635\pi$
$68$	−37.6442	−0.0671327
$69$	46.0780	0.0803933
$70$	0	0
$71$	−238.686	−0.398970	−0.199485	−	0.979901i	$-0.563927\pi$
$71$	−238.686	−0.398970	−0.199485	+	0.979901i	$0.563927\pi$
$72$	−153.351	−0.251008
$73$	744.418	1.19353	0.596764	−	0.802417i	$-0.296453\pi$
$73$	744.418	1.19353	0.596764	+	0.802417i	$0.296453\pi$
$74$	−310.148	−0.487217
$75$	0	0
$76$	162.650	0.245490
$77$	−214.223	−0.317051
$78$	−28.8401	−0.0418653
$79$	−177.549	−0.252858	−0.126429	−	0.991976i	$-0.540352\pi$
$79$	−177.549	−0.252858	−0.126429	+	0.991976i	$0.540352\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	94.7231	0.127566
$83$	624.817	0.826296	0.413148	−	0.910664i	$-0.364429\pi$
$83$	624.817	0.826296	0.413148	+	0.910664i	$0.364429\pi$
$84$	−388.326	−0.504402
$85$	0	0
$86$	26.3614	0.0330538
$87$	474.967	0.585308
$88$	187.429	0.227046
$89$	1521.53	1.81216	0.906078	−	0.423111i	$-0.139062\pi$
$89$	1521.53	1.81216	0.906078	+	0.423111i	$0.139062\pi$
$90$	0	0
$91$	−160.932	−0.185387
$92$	−102.088	−0.115689
$93$	907.047	1.01136
$94$	−17.6041	−0.0193162
$95$	0	0
$96$	525.332	0.558505
$97$	342.953	0.358985	0.179493	−	0.983759i	$-0.442554\pi$
$97$	342.953	0.358985	0.179493	+	0.983759i	$0.442554\pi$
$98$	42.1909	0.0434890
$99$	−99.0000	−0.100504
$100$	0	0
$101$	−1429.06	−1.40789	−0.703944	−	0.710255i	$-0.748580\pi$
$101$	−1429.06	−1.40789	−0.703944	+	0.710255i	$0.748580\pi$
$102$	19.7662	0.0191877
$103$	1688.33	1.61511	0.807556	−	0.589791i	$-0.200790\pi$
$103$	1688.33	1.61511	0.807556	+	0.589791i	$0.200790\pi$
$104$	140.803	0.132759
$105$	0	0
$106$	527.073	0.482961
$107$	1947.81	1.75983	0.879916	−	0.475129i	$-0.157599\pi$
$107$	1947.81	1.75983	0.879916	+	0.475129i	$0.157599\pi$
$108$	−179.459	−0.159893
$109$	2172.13	1.90874	0.954368	−	0.298633i	$-0.0965308\pi$
$109$	2172.13	1.90874	0.954368	+	0.298633i	$0.0965308\pi$
$110$	0	0
$111$	−799.806	−0.683912
$112$	649.503	0.547966
$113$	731.978	0.609369	0.304685	−	0.952453i	$-0.401449\pi$
$113$	731.978	0.609369	0.304685	+	0.952453i	$0.401449\pi$
$114$	−85.4044	−0.0701654
$115$	0	0
$116$	−1052.31	−0.842281
$117$	−74.3723	−0.0587668
$118$	340.695	0.265792
$119$	110.298	0.0849665
$120$	0	0
$121$	121.000	0.0909091
$122$	296.867	0.220304
$123$	244.270	0.179066
$124$	−2009.61	−1.45539
$125$	0	0
$126$	203.902	0.144167
$127$	1072.80	0.749569	0.374785	−	0.927112i	$-0.377717\pi$
$127$	1072.80	0.749569	0.374785	+	0.927112i	$0.377717\pi$
$128$	−1474.29	−1.01804
$129$	67.9804	0.0463980
$130$	0	0
$131$	1287.73	0.858853	0.429426	−	0.903102i	$-0.358716\pi$
$131$	1287.73	0.858853	0.429426	+	0.903102i	$0.358716\pi$
$132$	219.339	0.144629
$133$	−476.568	−0.310705
$134$	−366.121	−0.236030
$135$	0	0
$136$	−96.5028	−0.0608459
$137$	−1759.23	−1.09709	−0.548543	−	0.836122i	$-0.684817\pi$
$137$	−1759.23	−1.09709	−0.548543	+	0.836122i	$0.684817\pi$
$138$	53.6043	0.0330660
$139$	−2634.80	−1.60777	−0.803887	−	0.594782i	$-0.797238\pi$
$139$	−2634.80	−1.60777	−0.803887	+	0.594782i	$0.797238\pi$
$140$	0	0
$141$	−45.3971	−0.0271143
$142$	−277.673	−0.164097
$143$	90.8994	0.0531566
$144$	300.159	0.173703
$145$	0	0
$146$	866.010	0.490901
$147$	108.801	0.0610461
$148$	1772.01	0.984176
$149$	−1557.85	−0.856538	−0.428269	−	0.903651i	$-0.640876\pi$
$149$	−1557.85	−0.856538	−0.428269	+	0.903651i	$0.640876\pi$
$150$	0	0
$151$	−216.999	−0.116948	−0.0584740	−	0.998289i	$-0.518623\pi$
$151$	−216.999	−0.116948	−0.0584740	+	0.998289i	$0.518623\pi$
$152$	416.963	0.222501
$153$	50.9727	0.0269340
$154$	−249.214	−0.130404
$155$	0	0
$156$	164.775	0.0845678
$157$	3003.68	1.52688	0.763439	−	0.645879i	$-0.223509\pi$
$157$	3003.68	1.52688	0.763439	+	0.645879i	$0.223509\pi$
$158$	−206.549	−0.104001
$159$	1359.21	0.677938
$160$	0	0
$161$	299.120	0.146422
$162$	94.2305	0.0457003
$163$	631.007	0.303217	0.151608	−	0.988441i	$-0.451555\pi$
$163$	631.007	0.303217	0.151608	+	0.988441i	$0.451555\pi$
$164$	−541.192	−0.257683
$165$	0	0
$166$	726.875	0.339858
$167$	−2233.32	−1.03485	−0.517423	−	0.855730i	$-0.673109\pi$
$167$	−2233.32	−1.03485	−0.517423	+	0.855730i	$0.673109\pi$
$168$	−995.493	−0.457167
$169$	−2128.71	−0.968918
$170$	0	0
$171$	−220.239	−0.0984920
$172$	−150.614	−0.0667686
$173$	−620.035	−0.272488	−0.136244	−	0.990675i	$-0.543503\pi$
$173$	−620.035	−0.272488	−0.136244	+	0.990675i	$0.543503\pi$
$174$	552.547	0.240739
$175$	0	0
$176$	−366.861	−0.157120
$177$	878.578	0.373096
$178$	1770.06	0.745344
$179$	−1695.52	−0.707983	−0.353991	−	0.935249i	$-0.615176\pi$
$179$	−1695.52	−0.707983	−0.353991	+	0.935249i	$0.615176\pi$
$180$	0	0
$181$	−3003.38	−1.23337	−0.616683	−	0.787211i	$-0.711524\pi$
$181$	−3003.38	−1.23337	−0.616683	+	0.787211i	$0.711524\pi$
$182$	−187.218	−0.0762501
$183$	765.556	0.309243
$184$	−261.708	−0.104855
$185$	0	0
$186$	1055.20	0.415975
$187$	−62.3000	−0.0243627
$188$	100.579	0.0390186
$189$	525.819	0.202369
$190$	0	0
$191$	2399.00	0.908826	0.454413	−	0.890791i	$-0.349849\pi$
$191$	2399.00	0.908826	0.454413	+	0.890791i	$0.349849\pi$
$192$	−189.284	−0.0711478
$193$	−2445.98	−0.912257	−0.456128	−	0.889914i	$-0.650764\pi$
$193$	−2445.98	−0.912257	−0.456128	+	0.889914i	$0.650764\pi$
$194$	398.971	0.147652
$195$	0	0
$196$	−241.054	−0.0878477
$197$	−4223.55	−1.52749	−0.763745	−	0.645519i	$-0.776641\pi$
$197$	−4223.55	−1.52749	−0.763745	+	0.645519i	$0.776641\pi$
$198$	−115.171	−0.0413375
$199$	−3058.60	−1.08954	−0.544771	−	0.838585i	$-0.683383\pi$
$199$	−3058.60	−1.08954	−0.544771	+	0.838585i	$0.683383\pi$
$200$	0	0
$201$	−944.147	−0.331318
$202$	−1662.48	−0.579068
$203$	3083.29	1.06603
$204$	−112.932	−0.0387591
$205$	0	0
$206$	1964.11	0.664300
$207$	138.234	0.0464151
$208$	−275.599	−0.0918717
$209$	269.181	0.0890893
$210$	0	0
$211$	−4391.13	−1.43269	−0.716346	−	0.697746i	$-0.754187\pi$
$211$	−4391.13	−1.43269	−0.716346	+	0.697746i	$0.754187\pi$
$212$	−3011.39	−0.975580
$213$	−716.058	−0.230345
$214$	2265.97	0.723824
$215$	0	0
$216$	−460.053	−0.144920
$217$	5888.18	1.84201
$218$	2526.92	0.785068
$219$	2233.25	0.689083
$220$	0	0
$221$	−46.8019	−0.0142454
$222$	−930.445	−0.281295
$223$	−1965.61	−0.590256	−0.295128	−	0.955458i	$-0.595362\pi$
$223$	−1965.61	−0.590256	−0.295128	+	0.955458i	$0.595362\pi$
$224$	3410.24	1.01722
$225$	0	0
$226$	851.539	0.250635
$227$	3139.70	0.918015	0.459008	−	0.888432i	$-0.348205\pi$
$227$	3139.70	0.918015	0.459008	+	0.888432i	$0.348205\pi$
$228$	487.951	0.141734
$229$	4755.60	1.37231	0.686155	−	0.727455i	$-0.259297\pi$
$229$	4755.60	1.37231	0.686155	+	0.727455i	$0.259297\pi$
$230$	0	0
$231$	−642.668	−0.183049
$232$	−2697.65	−0.763404
$233$	6585.59	1.85166	0.925829	−	0.377944i	$-0.123369\pi$
$233$	6585.59	1.85166	0.925829	+	0.377944i	$0.123369\pi$
$234$	−86.5202	−0.0241710
$235$	0	0
$236$	−1946.53	−0.536900
$237$	−532.646	−0.145988
$238$	128.314	0.0349469
$239$	−486.082	−0.131557	−0.0657784	−	0.997834i	$-0.520953\pi$
$239$	−486.082	−0.131557	−0.0657784	+	0.997834i	$0.520953\pi$
$240$	0	0
$241$	−446.428	−0.119323	−0.0596617	−	0.998219i	$-0.519002\pi$
$241$	−446.428	−0.119323	−0.0596617	+	0.998219i	$0.519002\pi$
$242$	140.764	0.0373912
$243$	243.000	0.0641500
$244$	−1696.13	−0.445014
$245$	0	0
$246$	284.169	0.0736503
$247$	202.219	0.0520925
$248$	−5151.73	−1.31909
$249$	1874.45	0.477062
$250$	0	0
$251$	3060.39	0.769602	0.384801	−	0.922999i	$-0.374270\pi$
$251$	3060.39	0.769602	0.384801	+	0.922999i	$0.374270\pi$
$252$	−1164.98	−0.291217
$253$	−168.953	−0.0419840
$254$	1248.03	0.308300
$255$	0	0
$256$	−1210.34	−0.295493
$257$	−2561.92	−0.621821	−0.310911	−	0.950439i	$-0.600634\pi$
$257$	−2561.92	−0.621821	−0.310911	+	0.950439i	$0.600634\pi$
$258$	79.0843	0.0190836
$259$	−5192.01	−1.24562
$260$	0	0
$261$	1424.90	0.337928
$262$	1498.07	0.353248
$263$	−503.435	−0.118035	−0.0590174	−	0.998257i	$-0.518797\pi$
$263$	−503.435	−0.118035	−0.0590174	+	0.998257i	$0.518797\pi$
$264$	562.288	0.131085
$265$	0	0
$266$	−554.411	−0.127794
$267$	4564.59	1.04625
$268$	2091.80	0.476781
$269$	2395.14	0.542878	0.271439	−	0.962456i	$-0.412500\pi$
$269$	2395.14	0.542878	0.271439	+	0.962456i	$0.412500\pi$
$270$	0	0
$271$	−3339.95	−0.748662	−0.374331	−	0.927295i	$-0.622128\pi$
$271$	−3339.95	−0.748662	−0.374331	+	0.927295i	$0.622128\pi$
$272$	188.888	0.0421066
$273$	−482.795	−0.107033
$274$	−2046.58	−0.451235
$275$	0	0
$276$	−306.264	−0.0667932
$277$	−6951.60	−1.50787	−0.753937	−	0.656946i	$-0.771848\pi$
$277$	−6951.60	−1.50787	−0.753937	+	0.656946i	$0.771848\pi$
$278$	−3065.16	−0.661281
$279$	2721.14	0.583909
$280$	0	0
$281$	9203.01	1.95376	0.976878	−	0.213797i	$-0.0685833\pi$
$281$	9203.01	1.95376	0.976878	+	0.213797i	$0.0685833\pi$
$282$	−52.8122	−0.0111522
$283$	−6159.41	−1.29378	−0.646888	−	0.762585i	$-0.723930\pi$
$283$	−6159.41	−1.29378	−0.646888	+	0.762585i	$0.723930\pi$
$284$	1586.46	0.331476
$285$	0	0
$286$	105.747	0.0218634
$287$	1585.70	0.326136
$288$	1576.00	0.322453
$289$	−4880.92	−0.993471
$290$	0	0
$291$	1028.86	0.207260
$292$	−4947.88	−0.991618
$293$	−657.854	−0.131168	−0.0655840	−	0.997847i	$-0.520891\pi$
$293$	−657.854	−0.131168	−0.0655840	+	0.997847i	$0.520891\pi$
$294$	126.573	0.0251084
$295$	0	0
$296$	4542.63	0.892011
$297$	−297.000	−0.0580259
$298$	−1812.31	−0.352296
$299$	−126.923	−0.0245490
$300$	0	0
$301$	441.301	0.0845056
$302$	−252.444	−0.0481010
$303$	−4287.18	−0.812845
$304$	−816.133	−0.153975
$305$	0	0
$306$	59.2986	0.0110780
$307$	−277.936	−0.0516698	−0.0258349	−	0.999666i	$-0.508224\pi$
$307$	−277.936	−0.0516698	−0.0258349	+	0.999666i	$0.508224\pi$
$308$	1423.86	0.263416
$309$	5065.00	0.932485
$310$	0	0
$311$	−3187.55	−0.581188	−0.290594	−	0.956846i	$-0.593853\pi$
$311$	−3187.55	−0.581188	−0.290594	+	0.956846i	$0.593853\pi$
$312$	422.410	0.0766483
$313$	4947.44	0.893437	0.446719	−	0.894674i	$-0.352592\pi$
$313$	4947.44	0.893437	0.446719	+	0.894674i	$0.352592\pi$
$314$	3494.30	0.628009
$315$	0	0
$316$	1180.10	0.210082
$317$	8717.68	1.54459	0.772293	−	0.635266i	$-0.219110\pi$
$317$	8717.68	1.54459	0.772293	+	0.635266i	$0.219110\pi$
$318$	1581.22	0.278838
$319$	−1741.54	−0.305667
$320$	0	0
$321$	5843.43	1.01604
$322$	347.978	0.0602237
$323$	−138.595	−0.0238750
$324$	−538.378	−0.0923145
$325$	0	0
$326$	734.076	0.124714
$327$	6516.39	1.10201
$328$	−1387.37	−0.233552
$329$	−294.699	−0.0493839
$330$	0	0
$331$	−4666.23	−0.774862	−0.387431	−	0.921899i	$-0.626638\pi$
$331$	−4666.23	−0.774862	−0.387431	+	0.921899i	$0.626638\pi$
$332$	−4152.94	−0.686512
$333$	−2399.42	−0.394857
$334$	−2598.11	−0.425635
$335$	0	0
$336$	1948.51	0.316369
$337$	6034.32	0.975401	0.487701	−	0.873011i	$-0.337836\pi$
$337$	6034.32	0.975401	0.487701	+	0.873011i	$0.337836\pi$
$338$	−2476.42	−0.398519
$339$	2195.93	0.351819
$340$	0	0
$341$	−3325.84	−0.528165
$342$	−256.213	−0.0405100
$343$	−5973.56	−0.940355
$344$	−386.107	−0.0605159
$345$	0	0
$346$	−721.311	−0.112075
$347$	6089.63	0.942099	0.471050	−	0.882107i	$-0.343875\pi$
$347$	6089.63	0.942099	0.471050	+	0.882107i	$0.343875\pi$
$348$	−3156.93	−0.486291
$349$	−8857.56	−1.35855	−0.679276	−	0.733883i	$-0.737706\pi$
$349$	−8857.56	−1.35855	−0.679276	+	0.733883i	$0.737706\pi$
$350$	0	0
$351$	−223.117	−0.0339290
$352$	−1926.22	−0.291670
$353$	−5357.93	−0.807858	−0.403929	−	0.914790i	$-0.632356\pi$
$353$	−5357.93	−0.807858	−0.403929	+	0.914790i	$0.632356\pi$
$354$	1022.08	0.153455
$355$	0	0
$356$	−10113.1	−1.50559
$357$	330.894	0.0490554
$358$	−1972.46	−0.291195
$359$	−6795.15	−0.998981	−0.499491	−	0.866319i	$-0.666479\pi$
$359$	−6795.15	−0.998981	−0.499491	+	0.866319i	$0.666479\pi$
$360$	0	0
$361$	−6260.17	−0.912694
$362$	−3493.95	−0.507287
$363$	363.000	0.0524864
$364$	1069.65	0.154025
$365$	0	0
$366$	890.602	0.127193
$367$	2865.06	0.407507	0.203753	−	0.979022i	$-0.434686\pi$
$367$	2865.06	0.407507	0.203753	+	0.979022i	$0.434686\pi$
$368$	512.248	0.0725619
$369$	732.811	0.103384
$370$	0	0
$371$	8823.42	1.23474
$372$	−6028.82	−0.840268
$373$	−12277.9	−1.70436	−0.852180	−	0.523248i	$-0.824720\pi$
$373$	−12277.9	−1.70436	−0.852180	+	0.523248i	$0.824720\pi$
$374$	−72.4761	−0.0100204
$375$	0	0
$376$	257.840	0.0353646
$377$	−1308.31	−0.178730
$378$	611.706	0.0832348
$379$	−5909.04	−0.800863	−0.400431	−	0.916327i	$-0.631140\pi$
$379$	−5909.04	−0.800863	−0.400431	+	0.916327i	$0.631140\pi$
$380$	0	0
$381$	3218.39	0.432764
$382$	2790.85	0.373802
$383$	−12435.8	−1.65912	−0.829558	−	0.558420i	$-0.811408\pi$
$383$	−12435.8	−1.65912	−0.829558	+	0.558420i	$0.811408\pi$
$384$	−4422.86	−0.587768
$385$	0	0
$386$	−2845.51	−0.375214
$387$	203.941	0.0267879
$388$	−2279.48	−0.298256
$389$	9940.85	1.29568	0.647842	−	0.761775i	$-0.275672\pi$
$389$	9940.85	1.29568	0.647842	+	0.761775i	$0.275672\pi$
$390$	0	0
$391$	86.9897	0.0112513
$392$	−617.955	−0.0796210
$393$	3863.20	0.495859
$394$	−4913.42	−0.628260
$395$	0	0
$396$	658.017	0.0835016
$397$	−9437.35	−1.19307	−0.596533	−	0.802589i	$-0.703455\pi$
$397$	−9437.35	−1.19307	−0.596533	+	0.802589i	$0.703455\pi$
$398$	−3558.19	−0.448131
$399$	−1429.70	−0.179385
$400$	0	0
$401$	923.119	0.114958	0.0574792	−	0.998347i	$-0.481694\pi$
$401$	923.119	0.114958	0.0574792	+	0.998347i	$0.481694\pi$
$402$	−1098.36	−0.136272
$403$	−2498.49	−0.308830
$404$	9498.45	1.16972
$405$	0	0
$406$	3586.91	0.438462
$407$	2932.62	0.357161
$408$	−289.508	−0.0351294
$409$	12437.8	1.50369	0.751847	−	0.659337i	$-0.229163\pi$
$409$	12437.8	1.50369	0.751847	+	0.659337i	$0.229163\pi$
$410$	0	0
$411$	−5277.68	−0.633403
$412$	−11221.8	−1.34188
$413$	5703.37	0.679526
$414$	160.813	0.0190907
$415$	0	0
$416$	−1447.04	−0.170546
$417$	−7904.39	−0.928248
$418$	313.149	0.0366427
$419$	−5835.23	−0.680357	−0.340178	−	0.940361i	$-0.610487\pi$
$419$	−5835.23	−0.680357	−0.340178	+	0.940361i	$0.610487\pi$
$420$	0	0
$421$	3139.66	0.363463	0.181731	−	0.983348i	$-0.441830\pi$
$421$	3139.66	0.363463	0.181731	+	0.983348i	$0.441830\pi$
$422$	−5108.38	−0.589270
$423$	−136.191	−0.0156545
$424$	−7719.85	−0.884220
$425$	0	0
$426$	−833.019	−0.0947416
$427$	4969.68	0.563231
$428$	−12946.4	−1.46212
$429$	272.698	0.0306900
$430$	0	0
$431$	−3956.73	−0.442202	−0.221101	−	0.975251i	$-0.570965\pi$
$431$	−3956.73	−0.442202	−0.221101	+	0.975251i	$0.570965\pi$
$432$	900.476	0.100287
$433$	16363.6	1.81613	0.908067	−	0.418825i	$-0.137558\pi$
$433$	16363.6	1.81613	0.908067	+	0.418825i	$0.137558\pi$
$434$	6849.96	0.757623
$435$	0	0
$436$	−14437.4	−1.58584
$437$	−375.859	−0.0411436
$438$	2598.03	0.283422
$439$	−3948.04	−0.429224	−0.214612	−	0.976699i	$-0.568849\pi$
$439$	−3948.04	−0.429224	−0.214612	+	0.976699i	$0.568849\pi$
$440$	0	0
$441$	326.404	0.0352450
$442$	−54.4466	−0.00585918
$443$	−14702.0	−1.57677	−0.788387	−	0.615179i	$-0.789084\pi$
$443$	−14702.0	−1.57677	−0.788387	+	0.615179i	$0.789084\pi$
$444$	5316.02	0.568214
$445$	0	0
$446$	−2286.67	−0.242774
$447$	−4673.55	−0.494523
$448$	−1228.75	−0.129583
$449$	3715.99	0.390576	0.195288	−	0.980746i	$-0.437436\pi$
$449$	3715.99	0.390576	0.195288	+	0.980746i	$0.437436\pi$
$450$	0	0
$451$	−895.657	−0.0935141
$452$	−4865.19	−0.506282
$453$	−650.998	−0.0675200
$454$	3652.54	0.377582
$455$	0	0
$456$	1250.89	0.128461
$457$	−10215.4	−1.04563	−0.522817	−	0.852445i	$-0.675119\pi$
$457$	−10215.4	−1.04563	−0.522817	+	0.852445i	$0.675119\pi$
$458$	5532.38	0.564435
$459$	152.918	0.0155503
$460$	0	0
$461$	−10460.8	−1.05685	−0.528423	−	0.848981i	$-0.677217\pi$
$461$	−10460.8	−1.05685	−0.528423	+	0.848981i	$0.677217\pi$
$462$	−747.641	−0.0752887
$463$	4244.77	0.426072	0.213036	−	0.977044i	$-0.431665\pi$
$463$	4244.77	0.426072	0.213036	+	0.977044i	$0.431665\pi$
$464$	5280.20	0.528291
$465$	0	0
$466$	7661.27	0.761591
$467$	−964.193	−0.0955408	−0.0477704	−	0.998858i	$-0.515212\pi$
$467$	−964.193	−0.0955408	−0.0477704	+	0.998858i	$0.515212\pi$
$468$	494.326	0.0488252
$469$	−6129.02	−0.603437
$470$	0	0
$471$	9011.05	0.881544
$472$	−4990.03	−0.486620
$473$	−249.262	−0.0242306
$474$	−619.648	−0.0600451
$475$	0	0
$476$	−733.112	−0.0705927
$477$	4077.62	0.391408
$478$	−565.479	−0.0541096
$479$	20956.9	1.99905	0.999526	−	0.0307833i	$-0.00980018\pi$
$479$	20956.9	1.99905	0.999526	+	0.0307833i	$0.00980018\pi$
$480$	0	0
$481$	2203.09	0.208840
$482$	−519.347	−0.0490780
$483$	897.359	0.0845367
$484$	−804.244	−0.0755300
$485$	0	0
$486$	282.692	0.0263851
$487$	1816.63	0.169033	0.0845167	−	0.996422i	$-0.473065\pi$
$487$	1816.63	0.169033	0.0845167	+	0.996422i	$0.473065\pi$
$488$	−4348.11	−0.403339
$489$	1893.02	0.175062
$490$	0	0
$491$	770.176	0.0707893	0.0353947	−	0.999373i	$-0.488731\pi$
$491$	770.176	0.0707893	0.0353947	+	0.999373i	$0.488731\pi$
$492$	−1623.58	−0.148773
$493$	896.679	0.0819156
$494$	235.249	0.0214258
$495$	0	0
$496$	10083.6	0.912840
$497$	−4648.36	−0.419532
$498$	2180.62	0.196217
$499$	−7346.80	−0.659094	−0.329547	−	0.944139i	$-0.606896\pi$
$499$	−7346.80	−0.659094	−0.329547	+	0.944139i	$0.606896\pi$
$500$	0	0
$501$	−6699.96	−0.597469
$502$	3560.27	0.316539
$503$	14710.8	1.30402	0.652010	−	0.758210i	$-0.273926\pi$
$503$	14710.8	1.30402	0.652010	+	0.758210i	$0.273926\pi$
$504$	−2986.48	−0.263945
$505$	0	0
$506$	−196.549	−0.0172681
$507$	−6386.14	−0.559405
$508$	−7130.49	−0.622765
$509$	10845.9	0.944474	0.472237	−	0.881472i	$-0.343447\pi$
$509$	10845.9	0.944474	0.472237	+	0.881472i	$0.343447\pi$
$510$	0	0
$511$	14497.4	1.25504
$512$	10386.2	0.896507
$513$	−660.718	−0.0568644
$514$	−2980.38	−0.255757
$515$	0	0
$516$	−451.841	−0.0385489
$517$	166.456	0.0141600
$518$	−6040.07	−0.512327
$519$	−1860.10	−0.157321
$520$	0	0
$521$	−4527.40	−0.380708	−0.190354	−	0.981716i	$-0.560964\pi$
$521$	−4527.40	−0.380708	−0.190354	+	0.981716i	$0.560964\pi$
$522$	1657.64	0.138990
$523$	9145.34	0.764623	0.382311	−	0.924034i	$-0.375128\pi$
$523$	9145.34	0.764623	0.382311	+	0.924034i	$0.375128\pi$
$524$	−8559.09	−0.713561
$525$	0	0
$526$	−585.666	−0.0485480
$527$	1712.40	0.141543
$528$	−1100.58	−0.0907134
$529$	−11931.1	−0.980611
$530$	0	0
$531$	2635.73	0.215407
$532$	3167.58	0.258143
$533$	−672.849	−0.0546798
$534$	5310.17	0.430325
$535$	0	0
$536$	5362.45	0.432131
$537$	−5086.55	−0.408754
$538$	2786.36	0.223287
$539$	−398.938	−0.0318803
$540$	0	0
$541$	−1476.23	−0.117316	−0.0586579	−	0.998278i	$-0.518682\pi$
$541$	−1476.23	−0.117316	−0.0586579	+	0.998278i	$0.518682\pi$
$542$	−3885.50	−0.307927
$543$	−9010.14	−0.712085
$544$	991.763	0.0781645
$545$	0	0
$546$	−561.654	−0.0440230
$547$	4789.25	0.374358	0.187179	−	0.982326i	$-0.440066\pi$
$547$	4789.25	0.374358	0.187179	+	0.982326i	$0.440066\pi$
$548$	11692.9	0.911492
$549$	2296.67	0.178542
$550$	0	0
$551$	−3874.31	−0.299548
$552$	−785.124	−0.0605382
$553$	−3457.72	−0.265890
$554$	−8087.08	−0.620193
$555$	0	0
$556$	17512.5	1.33579
$557$	3655.56	0.278081	0.139040	−	0.990287i	$-0.455598\pi$
$557$	3655.56	0.278081	0.139040	+	0.990287i	$0.455598\pi$
$558$	3165.61	0.240163
$559$	−187.254	−0.0141682
$560$	0	0
$561$	−186.900	−0.0140658
$562$	10706.2	0.803585
$563$	22937.0	1.71701	0.858507	−	0.512802i	$-0.171393\pi$
$563$	22937.0	1.71701	0.858507	+	0.512802i	$0.171393\pi$
$564$	301.738	0.0225274
$565$	0	0
$566$	−7165.48	−0.532134
$567$	1577.46	0.116838
$568$	4066.98	0.300434
$569$	−1430.04	−0.105361	−0.0526805	−	0.998611i	$-0.516776\pi$
$569$	−1430.04	−0.105361	−0.0526805	+	0.998611i	$0.516776\pi$
$570$	0	0
$571$	−20474.9	−1.50061	−0.750305	−	0.661092i	$-0.770093\pi$
$571$	−20474.9	−1.50061	−0.750305	+	0.661092i	$0.770093\pi$
$572$	−604.176	−0.0441641
$573$	7197.01	0.524711
$574$	1844.71	0.134141
$575$	0	0
$576$	−567.851	−0.0410772
$577$	17471.1	1.26054	0.630270	−	0.776376i	$-0.282944\pi$
$577$	17471.1	1.26054	0.630270	+	0.776376i	$0.282944\pi$
$578$	−5678.17	−0.408617
$579$	−7337.94	−0.526692
$580$	0	0
$581$	12168.2	0.868883
$582$	1196.91	0.0852467
$583$	−4983.76	−0.354042
$584$	−12684.1	−0.898756
$585$	0	0
$586$	−765.307	−0.0539498
$587$	6685.80	0.470107	0.235053	−	0.971982i	$-0.424474\pi$
$587$	6685.80	0.470107	0.235053	+	0.971982i	$0.424474\pi$
$588$	−723.163	−0.0507189
$589$	−7398.80	−0.517593
$590$	0	0
$591$	−12670.6	−0.881896
$592$	−8891.43	−0.617290
$593$	−4310.86	−0.298526	−0.149263	−	0.988798i	$-0.547690\pi$
$593$	−4310.86	−0.298526	−0.149263	+	0.988798i	$0.547690\pi$
$594$	−345.512	−0.0238662
$595$	0	0
$596$	10354.5	0.711638
$597$	−9175.81	−0.629047
$598$	−147.655	−0.0100971
$599$	−25652.9	−1.74983	−0.874916	−	0.484274i	$-0.839084\pi$
$599$	−25652.9	−1.74983	−0.874916	+	0.484274i	$0.839084\pi$
$600$	0	0
$601$	−14398.6	−0.977257	−0.488628	−	0.872492i	$-0.662503\pi$
$601$	−14398.6	−0.977257	−0.488628	+	0.872492i	$0.662503\pi$
$602$	513.383	0.0347574
$603$	−2832.44	−0.191287
$604$	1442.32	0.0971639
$605$	0	0
$606$	−4987.44	−0.334325
$607$	23370.0	1.56270	0.781349	−	0.624094i	$-0.214532\pi$
$607$	23370.0	1.56270	0.781349	+	0.624094i	$0.214532\pi$
$608$	−4285.14	−0.285831
$609$	9249.87	0.615474
$610$	0	0
$611$	125.047	0.00827967
$612$	−338.797	−0.0223776
$613$	16274.5	1.07230	0.536149	−	0.844123i	$-0.319878\pi$
$613$	16274.5	1.07230	0.536149	+	0.844123i	$0.319878\pi$
$614$	−323.334	−0.0212519
$615$	0	0
$616$	3650.14	0.238747
$617$	16851.1	1.09951	0.549757	−	0.835324i	$-0.314720\pi$
$617$	16851.1	1.09951	0.549757	+	0.835324i	$0.314720\pi$
$618$	5892.32	0.383534
$619$	7896.58	0.512747	0.256373	−	0.966578i	$-0.417472\pi$
$619$	7896.58	0.512747	0.256373	+	0.966578i	$0.417472\pi$
$620$	0	0
$621$	414.702	0.0267978
$622$	−3708.21	−0.239044
$623$	29631.5	1.90555
$624$	−826.796	−0.0530422
$625$	0	0
$626$	5755.55	0.367473
$627$	807.544	0.0514358
$628$	−19964.4	−1.26858
$629$	−1509.94	−0.0957156
$630$	0	0
$631$	8006.26	0.505110	0.252555	−	0.967583i	$-0.418729\pi$
$631$	8006.26	0.505110	0.252555	+	0.967583i	$0.418729\pi$
$632$	3025.26	0.190409
$633$	−13173.4	−0.827165
$634$	10141.6	0.635292
$635$	0	0
$636$	−9034.16	−0.563251
$637$	−299.696	−0.0186411
$638$	−2026.01	−0.125722
$639$	−2148.18	−0.132990
$640$	0	0
$641$	17163.6	1.05760	0.528799	−	0.848747i	$-0.322643\pi$
$641$	17163.6	1.05760	0.528799	+	0.848747i	$0.322643\pi$
$642$	6797.90	0.417900
$643$	−11115.5	−0.681731	−0.340865	−	0.940112i	$-0.610720\pi$
$643$	−11115.5	−0.681731	−0.340865	+	0.940112i	$0.610720\pi$
$644$	−1988.14	−0.121652
$645$	0	0
$646$	−161.233	−0.00981987
$647$	17769.6	1.07974	0.539872	−	0.841747i	$-0.318473\pi$
$647$	17769.6	1.07974	0.539872	+	0.841747i	$0.318473\pi$
$648$	−1380.16	−0.0836695
$649$	−3221.45	−0.194843
$650$	0	0
$651$	17664.6	1.06348
$652$	−4194.08	−0.251922
$653$	−9940.57	−0.595719	−0.297859	−	0.954610i	$-0.596273\pi$
$653$	−9940.57	−0.595719	−0.297859	+	0.954610i	$0.596273\pi$
$654$	7580.77	0.453259
$655$	0	0
$656$	2715.55	0.161623
$657$	6699.76	0.397842
$658$	−342.835	−0.0203117
$659$	−12298.0	−0.726955	−0.363478	−	0.931603i	$-0.618411\pi$
$659$	−12298.0	−0.726955	−0.363478	+	0.931603i	$0.618411\pi$
$660$	0	0
$661$	−27922.0	−1.64303	−0.821513	−	0.570190i	$-0.806869\pi$
$661$	−27922.0	−1.64303	−0.821513	+	0.570190i	$0.806869\pi$
$662$	−5428.41	−0.318703
$663$	−140.406	−0.00822460
$664$	−10646.3	−0.622222
$665$	0	0
$666$	−2791.34	−0.162406
$667$	2431.72	0.141164
$668$	14844.1	0.859782
$669$	−5896.84	−0.340785
$670$	0	0
$671$	−2807.04	−0.161497
$672$	10230.7	0.587290
$673$	1088.77	0.0623613	0.0311807	−	0.999514i	$-0.490073\pi$
$673$	1088.77	0.0623613	0.0311807	+	0.999514i	$0.490073\pi$
$674$	7019.96	0.401185
$675$	0	0
$676$	14148.8	0.805006
$677$	15975.8	0.906940	0.453470	−	0.891271i	$-0.350186\pi$
$677$	15975.8	0.906940	0.453470	+	0.891271i	$0.350186\pi$
$678$	2554.62	0.144704
$679$	6678.93	0.377487
$680$	0	0
$681$	9419.11	0.530016
$682$	−3869.08	−0.217236
$683$	19460.4	1.09024	0.545118	−	0.838359i	$-0.316485\pi$
$683$	19460.4	1.09024	0.545118	+	0.838359i	$0.316485\pi$
$684$	1463.85	0.0818301
$685$	0	0
$686$	−6949.27	−0.386770
$687$	14266.8	0.792304
$688$	755.737	0.0418782
$689$	−3743.97	−0.207016
$690$	0	0
$691$	5766.25	0.317451	0.158725	−	0.987323i	$-0.449262\pi$
$691$	5766.25	0.317451	0.158725	+	0.987323i	$0.449262\pi$
$692$	4121.15	0.226391
$693$	−1928.00	−0.105684
$694$	7084.31	0.387488
$695$	0	0
$696$	−8092.96	−0.440751
$697$	461.153	0.0250608
$698$	−10304.4	−0.558776
$699$	19756.8	1.06905
$700$	0	0
$701$	−1217.15	−0.0655791	−0.0327896	−	0.999462i	$-0.510439\pi$
$701$	−1217.15	−0.0655791	−0.0327896	+	0.999462i	$0.510439\pi$
$702$	−259.561	−0.0139551
$703$	6524.03	0.350012
$704$	694.040	0.0371557
$705$	0	0
$706$	−6233.09	−0.332274
$707$	−27830.6	−1.48045
$708$	−5839.59	−0.309979
$709$	−32859.5	−1.74057	−0.870286	−	0.492547i	$-0.836066\pi$
$709$	−32859.5	−1.74057	−0.870286	+	0.492547i	$0.836066\pi$
$710$	0	0
$711$	−1597.94	−0.0842860
$712$	−25925.4	−1.36460
$713$	4643.88	0.243920
$714$	384.942	0.0201766
$715$	0	0
$716$	11269.5	0.588213
$717$	−1458.25	−0.0759543
$718$	−7905.07	−0.410884
$719$	−3283.68	−0.170321	−0.0851604	−	0.996367i	$-0.527140\pi$
$719$	−3283.68	−0.170321	−0.0851604	+	0.996367i	$0.527140\pi$
$720$	0	0
$721$	32879.9	1.69835
$722$	−7282.70	−0.375393
$723$	−1339.28	−0.0688914
$724$	19962.4	1.02472
$725$	0	0
$726$	422.292	0.0215878
$727$	−28198.3	−1.43854	−0.719269	−	0.694731i	$-0.755523\pi$
$727$	−28198.3	−1.43854	−0.719269	+	0.694731i	$0.755523\pi$
$728$	2742.11	0.139601
$729$	729.000	0.0370370
$730$	0	0
$731$	128.339	0.00649355
$732$	−5088.38	−0.256929
$733$	26259.2	1.32320	0.661600	−	0.749857i	$-0.269878\pi$
$733$	26259.2	1.32320	0.661600	+	0.749857i	$0.269878\pi$
$734$	3333.04	0.167609
$735$	0	0
$736$	2689.58	0.134700
$737$	3461.87	0.173025
$738$	852.508	0.0425220
$739$	37945.3	1.88882	0.944412	−	0.328764i	$-0.106632\pi$
$739$	37945.3	1.88882	0.944412	+	0.328764i	$0.106632\pi$
$740$	0	0
$741$	606.656	0.0300756
$742$	10264.6	0.507853
$743$	37735.2	1.86322	0.931608	−	0.363465i	$-0.118406\pi$
$743$	37735.2	1.86322	0.931608	+	0.363465i	$0.118406\pi$
$744$	−15455.2	−0.761579
$745$	0	0
$746$	−14283.4	−0.701008
$747$	5623.35	0.275432
$748$	414.086	0.0202413
$749$	37933.2	1.85053
$750$	0	0
$751$	−23846.1	−1.15866	−0.579332	−	0.815092i	$-0.696687\pi$
$751$	−23846.1	−1.15866	−0.579332	+	0.815092i	$0.696687\pi$
$752$	−504.678	−0.0244730
$753$	9181.17	0.444330
$754$	−1522.01	−0.0735123
$755$	0	0
$756$	−3494.93	−0.168134
$757$	1757.41	0.0843779	0.0421890	−	0.999110i	$-0.486567\pi$
$757$	1757.41	0.0843779	0.0421890	+	0.999110i	$0.486567\pi$
$758$	−6874.22	−0.329397
$759$	−506.858	−0.0242395
$760$	0	0
$761$	−3661.27	−0.174403	−0.0872017	−	0.996191i	$-0.527792\pi$
$761$	−3661.27	−0.174403	−0.0872017	+	0.996191i	$0.527792\pi$
$762$	3744.08	0.177997
$763$	42301.7	2.00711
$764$	−15945.3	−0.755080
$765$	0	0
$766$	−14467.1	−0.682399
$767$	−2420.07	−0.113929
$768$	−3631.01	−0.170603
$769$	16269.5	0.762929	0.381464	−	0.924384i	$-0.375420\pi$
$769$	16269.5	0.762929	0.381464	+	0.924384i	$0.375420\pi$
$770$	0	0
$771$	−7685.75	−0.359009
$772$	16257.6	0.757930
$773$	−9135.30	−0.425063	−0.212532	−	0.977154i	$-0.568171\pi$
$773$	−9135.30	−0.425063	−0.212532	+	0.977154i	$0.568171\pi$
$774$	237.253	0.0110179
$775$	0	0
$776$	−5843.58	−0.270325
$777$	−15576.0	−0.719160
$778$	11564.6	0.532918
$779$	−1992.52	−0.0916422
$780$	0	0
$781$	2625.55	0.120294
$782$	101.199	0.00462769
$783$	4274.70	0.195103
$784$	1209.54	0.0550994
$785$	0	0
$786$	4494.21	0.203948
$787$	−26715.3	−1.21004	−0.605018	−	0.796212i	$-0.706834\pi$
$787$	−26715.3	−1.21004	−0.605018	+	0.796212i	$0.706834\pi$
$788$	28072.4	1.26908
$789$	−1510.31	−0.0681474
$790$	0	0
$791$	14255.1	0.640775
$792$	1686.86	0.0756819
$793$	−2108.75	−0.0944310
$794$	−10978.8	−0.490711
$795$	0	0
$796$	20329.4	0.905224
$797$	5895.59	0.262023	0.131012	−	0.991381i	$-0.458178\pi$
$797$	5895.59	0.262023	0.131012	+	0.991381i	$0.458178\pi$
$798$	−1663.23	−0.0737817
$799$	−85.7041	−0.00379474
$800$	0	0
$801$	13693.8	0.604052
$802$	1073.90	0.0472827
$803$	−8188.59	−0.359862
$804$	6275.41	0.275269
$805$	0	0
$806$	−2906.59	−0.127023
$807$	7185.42	0.313431
$808$	24349.8	1.06018
$809$	−19061.3	−0.828379	−0.414189	−	0.910191i	$-0.635935\pi$
$809$	−19061.3	−0.828379	−0.414189	+	0.910191i	$0.635935\pi$
$810$	0	0
$811$	−39232.1	−1.69867	−0.849337	−	0.527850i	$-0.822998\pi$
$811$	−39232.1	−1.69867	−0.849337	+	0.527850i	$0.822998\pi$
$812$	−20493.5	−0.885692
$813$	−10019.8	−0.432240
$814$	3411.63	0.146901
$815$	0	0
$816$	566.663	0.0243103
$817$	−554.517	−0.0237455
$818$	14469.4	0.618474
$819$	−1448.38	−0.0617956
$820$	0	0
$821$	9139.16	0.388500	0.194250	−	0.980952i	$-0.437773\pi$
$821$	9139.16	0.388500	0.194250	+	0.980952i	$0.437773\pi$
$822$	−6139.73	−0.260520
$823$	−37583.6	−1.59184	−0.795918	−	0.605405i	$-0.793011\pi$
$823$	−37583.6	−1.59184	−0.795918	+	0.605405i	$0.793011\pi$
$824$	−28767.6	−1.21622
$825$	0	0
$826$	6634.95	0.279491
$827$	33269.2	1.39889	0.699445	−	0.714686i	$-0.253430\pi$
$827$	33269.2	1.39889	0.699445	+	0.714686i	$0.253430\pi$
$828$	−918.791	−0.0385631
$829$	−2894.26	−0.121257	−0.0606284	−	0.998160i	$-0.519310\pi$
$829$	−2894.26	−0.121257	−0.0606284	+	0.998160i	$0.519310\pi$
$830$	0	0
$831$	−20854.8	−0.870572
$832$	521.387	0.0217258
$833$	205.403	0.00854359
$834$	−9195.49	−0.381791
$835$	0	0
$836$	−1789.15	−0.0740181
$837$	8163.43	0.337120
$838$	−6788.35	−0.279833
$839$	11124.6	0.457765	0.228882	−	0.973454i	$-0.426493\pi$
$839$	11124.6	0.457765	0.228882	+	0.973454i	$0.426493\pi$
$840$	0	0
$841$	676.918	0.0277551
$842$	3652.50	0.149493
$843$	27609.0	1.12800
$844$	29186.3	1.19032
$845$	0	0
$846$	−158.437	−0.00643873
$847$	2356.45	0.0955945
$848$	15110.3	0.611898
$849$	−18478.2	−0.746962
$850$	0	0
$851$	−4094.83	−0.164946
$852$	4759.38	0.191378
$853$	38057.5	1.52763	0.763813	−	0.645437i	$-0.223325\pi$
$853$	38057.5	1.52763	0.763813	+	0.645437i	$0.223325\pi$
$854$	5781.42	0.231658
$855$	0	0
$856$	−33188.8	−1.32520
$857$	−29926.6	−1.19285	−0.596426	−	0.802668i	$-0.703413\pi$
$857$	−29926.6	−1.19285	−0.596426	+	0.802668i	$0.703413\pi$
$858$	317.241	0.0126229
$859$	−7416.41	−0.294580	−0.147290	−	0.989093i	$-0.547055\pi$
$859$	−7416.41	−0.294580	−0.147290	+	0.989093i	$0.547055\pi$
$860$	0	0
$861$	4757.11	0.188295
$862$	−4603.02	−0.181879
$863$	−27998.3	−1.10437	−0.552185	−	0.833721i	$-0.686206\pi$
$863$	−27998.3	−1.10437	−0.552185	+	0.833721i	$0.686206\pi$
$864$	4727.99	0.186168
$865$	0	0
$866$	19036.5	0.746981
$867$	−14642.8	−0.573581
$868$	−39136.6	−1.53040
$869$	1953.04	0.0762396
$870$	0	0
$871$	2600.68	0.101172
$872$	−37010.9	−1.43733
$873$	3086.58	0.119662
$874$	−437.251	−0.0169225
$875$	0	0
$876$	−14843.6	−0.572511
$877$	14417.3	0.555118	0.277559	−	0.960709i	$-0.410475\pi$
$877$	14417.3	0.555118	0.277559	+	0.960709i	$0.410475\pi$
$878$	−4592.91	−0.176541
$879$	−1973.56	−0.0757299
$880$	0	0
$881$	−23776.9	−0.909266	−0.454633	−	0.890679i	$-0.650229\pi$
$881$	−23776.9	−0.909266	−0.454633	+	0.890679i	$0.650229\pi$
$882$	379.718	0.0144963
$883$	−17079.3	−0.650922	−0.325461	−	0.945556i	$-0.605519\pi$
$883$	−17079.3	−0.650922	−0.325461	+	0.945556i	$0.605519\pi$
$884$	311.076	0.0118355
$885$	0	0
$886$	−17103.4	−0.648532
$887$	25030.3	0.947504	0.473752	−	0.880658i	$-0.342899\pi$
$887$	25030.3	0.947504	0.473752	+	0.880658i	$0.342899\pi$
$888$	13627.9	0.515003
$889$	20892.5	0.788201
$890$	0	0
$891$	−891.000	−0.0335013
$892$	13064.7	0.490403
$893$	370.304	0.0138766
$894$	−5436.93	−0.203398
$895$	0	0
$896$	−28711.4	−1.07051
$897$	−380.769	−0.0141734
$898$	4322.96	0.160645
$899$	47868.6	1.77587
$900$	0	0
$901$	2566.02	0.0948795
$902$	−1041.95	−0.0384626
$903$	1323.90	0.0487893
$904$	−12472.2	−0.458870
$905$	0	0
$906$	−757.331	−0.0277711
$907$	−11688.5	−0.427907	−0.213953	−	0.976844i	$-0.568634\pi$
$907$	−11688.5	−0.427907	−0.213953	+	0.976844i	$0.568634\pi$
$908$	−20868.5	−0.762715
$909$	−12861.5	−0.469296
$910$	0	0
$911$	40671.2	1.47914	0.739570	−	0.673080i	$-0.235029\pi$
$911$	40671.2	1.47914	0.739570	+	0.673080i	$0.235029\pi$
$912$	−2448.40	−0.0888976
$913$	−6872.99	−0.249138
$914$	−11884.0	−0.430072
$915$	0	0
$916$	−31608.8	−1.14016
$917$	25078.3	0.903117
$918$	177.896	0.00639590
$919$	−1094.61	−0.0392905	−0.0196452	−	0.999807i	$-0.506254\pi$
$919$	−1094.61	−0.0392905	−0.0196452	+	0.999807i	$0.506254\pi$
$920$	0	0
$921$	−833.807	−0.0298316
$922$	−12169.4	−0.434684
$923$	1972.40	0.0703385
$924$	4271.58	0.152083
$925$	0	0
$926$	4938.11	0.175245
$927$	15195.0	0.538371
$928$	27723.9	0.980691
$929$	4607.17	0.162709	0.0813544	−	0.996685i	$-0.474075\pi$
$929$	4607.17	0.162709	0.0813544	+	0.996685i	$0.474075\pi$
$930$	0	0
$931$	−887.493	−0.0312421
$932$	−43772.0	−1.53841
$933$	−9562.66	−0.335549
$934$	−1121.68	−0.0392962
$935$	0	0
$936$	1267.23	0.0442529
$937$	40537.0	1.41332	0.706662	−	0.707551i	$-0.250200\pi$
$937$	40537.0	1.41332	0.706662	+	0.707551i	$0.250200\pi$
$938$	−7130.13	−0.248195
$939$	14842.3	0.515826
$940$	0	0
$941$	−23795.5	−0.824349	−0.412174	−	0.911105i	$-0.635231\pi$
$941$	−23795.5	−0.824349	−0.412174	+	0.911105i	$0.635231\pi$
$942$	10482.9	0.362581
$943$	1250.61	0.0431871
$944$	9767.14	0.336751
$945$	0	0
$946$	−289.976	−0.00996610
$947$	−16391.8	−0.562473	−0.281236	−	0.959639i	$-0.590744\pi$
$947$	−16391.8	−0.562473	−0.281236	+	0.959639i	$0.590744\pi$
$948$	3540.31	0.121291
$949$	−6151.56	−0.210419
$950$	0	0
$951$	26153.1	0.891767
$952$	−1879.37	−0.0639819
$953$	−23390.8	−0.795072	−0.397536	−	0.917587i	$-0.630135\pi$
$953$	−23390.8	−0.795072	−0.397536	+	0.917587i	$0.630135\pi$
$954$	4743.66	0.160987
$955$	0	0
$956$	3230.82	0.109301
$957$	−5224.63	−0.176477
$958$	24380.0	0.822215
$959$	−34260.5	−1.15363
$960$	0	0
$961$	61624.0	2.06854
$962$	2562.94	0.0858965
$963$	17530.3	0.586611
$964$	2967.24	0.0991374
$965$	0	0
$966$	1043.93	0.0347702
$967$	45545.1	1.51462	0.757308	−	0.653058i	$-0.226514\pi$
$967$	45545.1	1.51462	0.757308	+	0.653058i	$0.226514\pi$
$968$	−2061.72	−0.0684568
$969$	−415.785	−0.0137843
$970$	0	0
$971$	30755.0	1.01645	0.508225	−	0.861224i	$-0.330302\pi$
$971$	30755.0	1.01645	0.508225	+	0.861224i	$0.330302\pi$
$972$	−1615.13	−0.0532978
$973$	−51312.1	−1.69064
$974$	2113.35	0.0695239
$975$	0	0
$976$	8510.68	0.279119
$977$	−11653.3	−0.381597	−0.190799	−	0.981629i	$-0.561108\pi$
$977$	−11653.3	−0.381597	−0.190799	+	0.981629i	$0.561108\pi$
$978$	2202.23	0.0720036
$979$	−16736.8	−0.546386
$980$	0	0
$981$	19549.2	0.636245
$982$	895.976	0.0291158
$983$	11502.8	0.373227	0.186614	−	0.982433i	$-0.440249\pi$
$983$	11502.8	0.373227	0.186614	+	0.982433i	$0.440249\pi$
$984$	−4162.12	−0.134841
$985$	0	0
$986$	1043.14	0.0336921
$987$	−884.098	−0.0285118
$988$	−1344.07	−0.0432801
$989$	348.045	0.0111903
$990$	0	0
$991$	46171.2	1.48000	0.739998	−	0.672609i	$-0.234826\pi$
$991$	46171.2	1.48000	0.739998	+	0.672609i	$0.234826\pi$
$992$	52944.6	1.69455
$993$	−13998.7	−0.447367
$994$	−5407.62	−0.172555
$995$	0	0
$996$	−12458.8	−0.396358
$997$	25674.8	0.815577	0.407789	−	0.913076i	$-0.366300\pi$
$997$	25674.8	0.815577	0.407789	+	0.913076i	$0.366300\pi$
$998$	−8546.83	−0.271087
$999$	−7198.25	−0.227971

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.a.bc.1.4		7
3.2	odd	2		2475.4.a.bq.1.4		7
5.2	odd	4		165.4.c.a.34.8	yes	14
5.3	odd	4		165.4.c.a.34.7	✓	14
5.4	even	2		825.4.a.bb.1.4		7
15.2	even	4		495.4.c.c.199.7		14
15.8	even	4		495.4.c.c.199.8		14
15.14	odd	2		2475.4.a.br.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.c.a.34.7	✓	14	5.3	odd	4
165.4.c.a.34.8	yes	14	5.2	odd	4
495.4.c.c.199.7		14	15.2	even	4
495.4.c.c.199.8		14	15.8	even	4
825.4.a.bb.1.4		7	5.4	even	2
825.4.a.bc.1.4		7	1.1	even	1	trivial
2475.4.a.bq.1.4		7	3.2	odd	2
2475.4.a.br.1.4		7	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.16334 q^{2} +3.00000 q^{3} -6.64664 q^{4} +3.49002 q^{6} +19.4748 q^{7} -17.0390 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+1.16334 q^{2} +3.00000 q^{3} -6.64664 q^{4} +3.49002 q^{6} +19.4748 q^{7} -17.0390 q^{8} +9.00000 q^{9} -11.0000 q^{11} -19.9399 q^{12} -8.26359 q^{13} +22.6558 q^{14} +33.3510 q^{16} +5.66364 q^{17} +10.4701 q^{18} -24.4710 q^{19} +58.4243 q^{21} -12.7967 q^{22} +15.3593 q^{23} -51.1171 q^{24} -9.61336 q^{26} +27.0000 q^{27} -129.442 q^{28} +158.322 q^{29} +302.349 q^{31} +175.111 q^{32} -33.0000 q^{33} +6.58873 q^{34} -59.8198 q^{36} -266.602 q^{37} -28.4681 q^{38} -24.7908 q^{39} +81.4234 q^{41} +67.9673 q^{42} +22.6601 q^{43} +73.1131 q^{44} +17.8681 q^{46} -15.1324 q^{47} +100.053 q^{48} +36.2671 q^{49} +16.9909 q^{51} +54.9251 q^{52} +453.069 q^{53} +31.4102 q^{54} -331.831 q^{56} -73.4131 q^{57} +184.182 q^{58} +292.859 q^{59} +255.185 q^{61} +351.735 q^{62} +175.273 q^{63} -63.0946 q^{64} -38.3902 q^{66} -314.716 q^{67} -37.6442 q^{68} +46.0780 q^{69} -238.686 q^{71} -153.351 q^{72} +744.418 q^{73} -310.148 q^{74} +162.650 q^{76} -214.223 q^{77} -28.8401 q^{78} -177.549 q^{79} +81.0000 q^{81} +94.7231 q^{82} +624.817 q^{83} -388.326 q^{84} +26.3614 q^{86} +474.967 q^{87} +187.429 q^{88} +1521.53 q^{89} -160.932 q^{91} -102.088 q^{92} +907.047 q^{93} -17.6041 q^{94} +525.332 q^{96} +342.953 q^{97} +42.1909 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 3 q^{2} + 21 q^{3} + 41 q^{4} + 9 q^{6} + 50 q^{7} + 21 q^{8} + 63 q^{9}+O(q^{10}) \) 7 * q + 3 * q^2 + 21 * q^3 + 41 * q^4 + 9 * q^6 + 50 * q^7 + 21 * q^8 + 63 * q^9	\( 7 q + 3 q^{2} + 21 q^{3} + 41 q^{4} + 9 q^{6} + 50 q^{7} + 21 q^{8} + 63 q^{9} - 77 q^{11} + 123 q^{12} + 24 q^{13} + 142 q^{14} + 181 q^{16} + 38 q^{17} + 27 q^{18} + 26 q^{19} + 150 q^{21} - 33 q^{22} + 228 q^{23} + 63 q^{24} + 476 q^{26} + 189 q^{27} + 840 q^{28} + 572 q^{29} - 140 q^{31} + 991 q^{32} - 231 q^{33} - 806 q^{34} + 369 q^{36} - 104 q^{37} + 498 q^{38} + 72 q^{39} + 896 q^{41} + 426 q^{42} + 614 q^{43} - 451 q^{44} - 344 q^{46} + 520 q^{47} + 543 q^{48} + 295 q^{49} + 114 q^{51} - 26 q^{52} + 380 q^{53} + 81 q^{54} + 1522 q^{56} + 78 q^{57} + 1600 q^{58} + 1316 q^{59} - 386 q^{61} + 440 q^{62} + 450 q^{63} + 869 q^{64} - 99 q^{66} + 348 q^{67} + 332 q^{68} + 684 q^{69} + 804 q^{71} + 189 q^{72} + 468 q^{73} - 748 q^{74} - 1698 q^{76} - 550 q^{77} + 1428 q^{78} - 374 q^{79} + 567 q^{81} - 620 q^{82} + 3128 q^{83} + 2520 q^{84} - 2534 q^{86} + 1716 q^{87} - 231 q^{88} + 694 q^{89} - 3376 q^{91} - 1184 q^{92} - 420 q^{93} - 2920 q^{94} + 2973 q^{96} - 8 q^{97} + 4211 q^{98} - 693 q^{99}+O(q^{100}) \) 7 * q + 3 * q^2 + 21 * q^3 + 41 * q^4 + 9 * q^6 + 50 * q^7 + 21 * q^8 + 63 * q^9 - 77 * q^11 + 123 * q^12 + 24 * q^13 + 142 * q^14 + 181 * q^16 + 38 * q^17 + 27 * q^18 + 26 * q^19 + 150 * q^21 - 33 * q^22 + 228 * q^23 + 63 * q^24 + 476 * q^26 + 189 * q^27 + 840 * q^28 + 572 * q^29 - 140 * q^31 + 991 * q^32 - 231 * q^33 - 806 * q^34 + 369 * q^36 - 104 * q^37 + 498 * q^38 + 72 * q^39 + 896 * q^41 + 426 * q^42 + 614 * q^43 - 451 * q^44 - 344 * q^46 + 520 * q^47 + 543 * q^48 + 295 * q^49 + 114 * q^51 - 26 * q^52 + 380 * q^53 + 81 * q^54 + 1522 * q^56 + 78 * q^57 + 1600 * q^58 + 1316 * q^59 - 386 * q^61 + 440 * q^62 + 450 * q^63 + 869 * q^64 - 99 * q^66 + 348 * q^67 + 332 * q^68 + 684 * q^69 + 804 * q^71 + 189 * q^72 + 468 * q^73 - 748 * q^74 - 1698 * q^76 - 550 * q^77 + 1428 * q^78 - 374 * q^79 + 567 * q^81 - 620 * q^82 + 3128 * q^83 + 2520 * q^84 - 2534 * q^86 + 1716 * q^87 - 231 * q^88 + 694 * q^89 - 3376 * q^91 - 1184 * q^92 - 420 * q^93 - 2920 * q^94 + 2973 * q^96 - 8 * q^97 + 4211 * q^98 - 693 * q^99

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