LMFDB - Embedded newform 975.4.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,4,Mod(1,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, 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("975.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	975.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:	$57.5268622556$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{14}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 14 $ x^2 - 14
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-3.74166$ of defining polynomial
Character	$\chi$	$=$	975.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.74166 q^{2} +3.00000 q^{3} +14.4833 q^{4} -14.2250 q^{6} +7.48331 q^{7} -30.7417 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-4.74166 q^{2} +3.00000 q^{3} +14.4833 q^{4} -14.2250 q^{6} +7.48331 q^{7} -30.7417 q^{8} +9.00000 q^{9} -66.8999 q^{11} +43.4499 q^{12} +13.0000 q^{13} -35.4833 q^{14} +29.8999 q^{16} -96.9666 q^{17} -42.6749 q^{18} +31.4833 q^{19} +22.4499 q^{21} +317.216 q^{22} -183.600 q^{23} -92.2250 q^{24} -61.6415 q^{26} +27.0000 q^{27} +108.383 q^{28} +112.200 q^{29} -77.2831 q^{31} +104.158 q^{32} -200.700 q^{33} +459.783 q^{34} +130.350 q^{36} -54.7664 q^{37} -149.283 q^{38} +39.0000 q^{39} +451.716 q^{41} -106.450 q^{42} +113.434 q^{43} -968.932 q^{44} +870.566 q^{46} +42.2670 q^{47} +89.6997 q^{48} -287.000 q^{49} -290.900 q^{51} +188.283 q^{52} +530.999 q^{53} -128.025 q^{54} -230.049 q^{56} +94.4499 q^{57} -532.015 q^{58} +219.666 q^{59} +822.865 q^{61} +366.450 q^{62} +67.3498 q^{63} -733.082 q^{64} +951.649 q^{66} +872.082 q^{67} -1404.40 q^{68} -550.799 q^{69} -100.299 q^{71} -276.675 q^{72} +165.634 q^{73} +259.684 q^{74} +455.983 q^{76} -500.633 q^{77} -184.925 q^{78} -545.266 q^{79} +81.0000 q^{81} -2141.88 q^{82} +454.534 q^{83} +325.150 q^{84} -537.864 q^{86} +336.601 q^{87} +2056.61 q^{88} -230.915 q^{89} +97.2831 q^{91} -2659.13 q^{92} -231.849 q^{93} -200.415 q^{94} +312.475 q^{96} +1089.16 q^{97} +1360.86 q^{98} -602.099 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 6 q^{3} + 14 q^{4} - 6 q^{6} - 54 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 6 * q^3 + 14 * q^4 - 6 * q^6 - 54 * q^8 + 18 * q^9	$ 2 q - 2 q^{2} + 6 q^{3} + 14 q^{4} - 6 q^{6} - 54 q^{8} + 18 q^{9} - 44 q^{11} + 42 q^{12} + 26 q^{13} - 56 q^{14} - 30 q^{16} - 164 q^{17} - 18 q^{18} + 48 q^{19} + 380 q^{22} - 8 q^{23} - 162 q^{24} - 26 q^{26} + 54 q^{27} + 112 q^{28} + 404 q^{29} + 40 q^{31} + 126 q^{32} - 132 q^{33} + 276 q^{34} + 126 q^{36} + 100 q^{37} - 104 q^{38} + 78 q^{39} + 200 q^{41} - 168 q^{42} + 616 q^{43} - 980 q^{44} + 1352 q^{46} + 324 q^{47} - 90 q^{48} - 574 q^{49} - 492 q^{51} + 182 q^{52} + 164 q^{53} - 54 q^{54} - 56 q^{56} + 144 q^{57} + 268 q^{58} + 140 q^{59} + 628 q^{61} + 688 q^{62} - 194 q^{64} + 1140 q^{66} + 472 q^{67} - 1372 q^{68} - 24 q^{69} + 428 q^{71} - 486 q^{72} + 900 q^{73} + 684 q^{74} + 448 q^{76} - 672 q^{77} - 78 q^{78} - 432 q^{79} + 162 q^{81} - 2832 q^{82} + 1388 q^{83} + 336 q^{84} + 840 q^{86} + 1212 q^{87} + 1524 q^{88} + 960 q^{89} - 2744 q^{92} + 120 q^{93} + 572 q^{94} + 378 q^{96} + 532 q^{97} + 574 q^{98} - 396 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 6 * q^3 + 14 * q^4 - 6 * q^6 - 54 * q^8 + 18 * q^9 - 44 * q^11 + 42 * q^12 + 26 * q^13 - 56 * q^14 - 30 * q^16 - 164 * q^17 - 18 * q^18 + 48 * q^19 + 380 * q^22 - 8 * q^23 - 162 * q^24 - 26 * q^26 + 54 * q^27 + 112 * q^28 + 404 * q^29 + 40 * q^31 + 126 * q^32 - 132 * q^33 + 276 * q^34 + 126 * q^36 + 100 * q^37 - 104 * q^38 + 78 * q^39 + 200 * q^41 - 168 * q^42 + 616 * q^43 - 980 * q^44 + 1352 * q^46 + 324 * q^47 - 90 * q^48 - 574 * q^49 - 492 * q^51 + 182 * q^52 + 164 * q^53 - 54 * q^54 - 56 * q^56 + 144 * q^57 + 268 * q^58 + 140 * q^59 + 628 * q^61 + 688 * q^62 - 194 * q^64 + 1140 * q^66 + 472 * q^67 - 1372 * q^68 - 24 * q^69 + 428 * q^71 - 486 * q^72 + 900 * q^73 + 684 * q^74 + 448 * q^76 - 672 * q^77 - 78 * q^78 - 432 * q^79 + 162 * q^81 - 2832 * q^82 + 1388 * q^83 + 336 * q^84 + 840 * q^86 + 1212 * q^87 + 1524 * q^88 + 960 * q^89 - 2744 * q^92 + 120 * q^93 + 572 * q^94 + 378 * q^96 + 532 * q^97 + 574 * q^98 - 396 * 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 $

$2$	−4.74166	−1.67643	−0.838215	−	0.545341i	$-0.816400\pi$
$2$	−4.74166	−1.67643	−0.838215	+	0.545341i	$0.816400\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	14.4833	1.81041
$5$	0	0
$5$	0	0
$6$	−14.2250	−0.967887
$7$	7.48331	0.404061	0.202031	−	0.979379i	$-0.435246\pi$
$7$	7.48331	0.404061	0.202031	+	0.979379i	$0.435246\pi$
$8$	−30.7417	−1.35860
$9$	9.00000	0.333333
$10$	0	0
$11$	−66.8999	−1.83373	−0.916867	−	0.399193i	$-0.869290\pi$
$11$	−66.8999	−1.83373	−0.916867	+	0.399193i	$0.869290\pi$
$12$	43.4499	1.04524
$13$	13.0000	0.277350
$13$	13.0000	0.277350
$14$	−35.4833	−0.677380
$15$	0	0
$16$	29.8999	0.467186
$17$	−96.9666	−1.38340	−0.691702	−	0.722183i	$-0.743139\pi$
$17$	−96.9666	−1.38340	−0.691702	+	0.722183i	$0.743139\pi$
$18$	−42.6749	−0.558810
$19$	31.4833	0.380146	0.190073	−	0.981770i	$-0.439128\pi$
$19$	31.4833	0.380146	0.190073	+	0.981770i	$0.439128\pi$
$20$	0	0
$21$	22.4499	0.233285
$22$	317.216	3.07413
$23$	−183.600	−1.66448	−0.832242	−	0.554412i	$-0.812943\pi$
$23$	−183.600	−1.66448	−0.832242	+	0.554412i	$0.812943\pi$
$24$	−92.2250	−0.784389
$25$	0	0
$26$	−61.6415	−0.464958
$27$	27.0000	0.192450
$28$	108.383	0.731518
$29$	112.200	0.718450	0.359225	−	0.933251i	$-0.383041\pi$
$29$	112.200	0.718450	0.359225	+	0.933251i	$0.383041\pi$
$30$	0	0
$31$	−77.2831	−0.447757	−0.223878	−	0.974617i	$-0.571872\pi$
$31$	−77.2831	−0.447757	−0.223878	+	0.974617i	$0.571872\pi$
$32$	104.158	0.575398
$33$	−200.700	−1.05871
$34$	459.783	2.31918
$35$	0	0
$36$	130.350	0.603471
$37$	−54.7664	−0.243339	−0.121669	−	0.992571i	$-0.538825\pi$
$37$	−54.7664	−0.243339	−0.121669	+	0.992571i	$0.538825\pi$
$38$	−149.283	−0.637287
$39$	39.0000	0.160128
$40$	0	0
$41$	451.716	1.72064	0.860319	−	0.509756i	$-0.170264\pi$
$41$	451.716	1.72064	0.860319	+	0.509756i	$0.170264\pi$
$42$	−106.450	−0.391085
$43$	113.434	0.402291	0.201145	−	0.979561i	$-0.435534\pi$
$43$	113.434	0.402291	0.201145	+	0.979561i	$0.435534\pi$
$44$	−968.932	−3.31982
$45$	0	0
$46$	870.566	2.79039
$47$	42.2670	0.131176	0.0655880	−	0.997847i	$-0.479108\pi$
$47$	42.2670	0.131176	0.0655880	+	0.997847i	$0.479108\pi$
$48$	89.6997	0.269730
$49$	−287.000	−0.836735
$50$	0	0
$51$	−290.900	−0.798708
$52$	188.283	0.502119
$53$	530.999	1.37619	0.688097	−	0.725618i	$-0.258446\pi$
$53$	530.999	1.37619	0.688097	+	0.725618i	$0.258446\pi$
$54$	−128.025	−0.322629
$55$	0	0
$56$	−230.049	−0.548958
$57$	94.4499	0.219477
$58$	−532.015	−1.20443
$59$	219.666	0.484714	0.242357	−	0.970187i	$-0.422080\pi$
$59$	219.666	0.484714	0.242357	+	0.970187i	$0.422080\pi$
$60$	0	0
$61$	822.865	1.72717	0.863583	−	0.504207i	$-0.168215\pi$
$61$	822.865	1.72717	0.863583	+	0.504207i	$0.168215\pi$
$62$	366.450	0.750632
$63$	67.3498	0.134687
$64$	−733.082	−1.43180
$65$	0	0
$66$	951.649	1.77485
$67$	872.082	1.59018	0.795088	−	0.606495i	$-0.207425\pi$
$67$	872.082	1.59018	0.795088	+	0.606495i	$0.207425\pi$
$68$	−1404.40	−2.50453
$69$	−550.799	−0.960991
$70$	0	0
$71$	−100.299	−0.167653	−0.0838263	−	0.996480i	$-0.526714\pi$
$71$	−100.299	−0.167653	−0.0838263	+	0.996480i	$0.526714\pi$
$72$	−276.675	−0.452867
$73$	165.634	0.265562	0.132781	−	0.991145i	$-0.457609\pi$
$73$	165.634	0.265562	0.132781	+	0.991145i	$0.457609\pi$
$74$	259.684	0.407941
$75$	0	0
$76$	455.983	0.688221
$77$	−500.633	−0.740940
$78$	−184.925	−0.268443
$79$	−545.266	−0.776547	−0.388273	−	0.921544i	$-0.626928\pi$
$79$	−545.266	−0.776547	−0.388273	+	0.921544i	$0.626928\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	−2141.88	−2.88453
$83$	454.534	0.601103	0.300552	−	0.953766i	$-0.402829\pi$
$83$	454.534	0.601103	0.300552	+	0.953766i	$0.402829\pi$
$84$	325.150	0.422342
$85$	0	0
$86$	−537.864	−0.674412
$87$	336.601	0.414797
$88$	2056.61	2.49132
$89$	−230.915	−0.275022	−0.137511	−	0.990500i	$-0.543910\pi$
$89$	−230.915	−0.275022	−0.137511	+	0.990500i	$0.543910\pi$
$90$	0	0
$91$	97.2831	0.112066
$92$	−2659.13	−3.01341
$93$	−231.849	−0.258512
$94$	−200.415	−0.219907
$95$	0	0
$96$	312.475	0.332206
$97$	1089.16	1.14008	0.570041	−	0.821616i	$-0.306927\pi$
$97$	1089.16	1.14008	0.570041	+	0.821616i	$0.306927\pi$
$98$	1360.86	1.40273
$99$	−602.099	−0.611245
$100$	0	0
$101$	−77.2336	−0.0760894	−0.0380447	−	0.999276i	$-0.512113\pi$
$101$	−77.2336	−0.0760894	−0.0380447	+	0.999276i	$0.512113\pi$
$102$	1379.35	1.33898
$103$	−1351.36	−1.29275	−0.646377	−	0.763018i	$-0.723717\pi$
$103$	−1351.36	−1.29275	−0.646377	+	0.763018i	$0.723717\pi$
$104$	−399.642	−0.376808
$105$	0	0
$106$	−2517.81	−2.30709
$107$	−1133.67	−1.02426	−0.512129	−	0.858908i	$-0.671143\pi$
$107$	−1133.67	−1.02426	−0.512129	+	0.858908i	$0.671143\pi$
$108$	391.049	0.348414
$109$	1017.66	0.894262	0.447131	−	0.894469i	$-0.352446\pi$
$109$	1017.66	0.894262	0.447131	+	0.894469i	$0.352446\pi$
$110$	0	0
$111$	−164.299	−0.140492
$112$	223.750	0.188772
$113$	−1570.06	−1.30707	−0.653536	−	0.756895i	$-0.726715\pi$
$113$	−1570.06	−1.30707	−0.653536	+	0.756895i	$0.726715\pi$
$114$	−447.849	−0.367938
$115$	0	0
$116$	1625.03	1.30069
$117$	117.000	0.0924500
$118$	−1041.58	−0.812588
$119$	−725.632	−0.558979
$120$	0	0
$121$	3144.60	2.36258
$122$	−3901.75	−2.89547
$123$	1355.15	0.993411
$124$	−1119.32	−0.810625
$125$	0	0
$126$	−319.350	−0.225793
$127$	1248.16	0.872099	0.436050	−	0.899923i	$-0.356377\pi$
$127$	1248.16	0.872099	0.436050	+	0.899923i	$0.356377\pi$
$128$	2642.76	1.82491
$129$	340.301	0.232263
$130$	0	0
$131$	−1274.80	−0.850227	−0.425113	−	0.905140i	$-0.639766\pi$
$131$	−1274.80	−0.850227	−0.425113	+	0.905140i	$0.639766\pi$
$132$	−2906.80	−1.91670
$133$	235.600	0.153602
$134$	−4135.11	−2.66582
$135$	0	0
$136$	2980.91	1.87950
$137$	−874.915	−0.545613	−0.272807	−	0.962069i	$-0.587952\pi$
$137$	−874.915	−0.545613	−0.272807	+	0.962069i	$0.587952\pi$
$138$	2611.70	1.61103
$139$	310.334	0.189368	0.0946840	−	0.995507i	$-0.469816\pi$
$139$	310.334	0.189368	0.0946840	+	0.995507i	$0.469816\pi$
$140$	0	0
$141$	126.801	0.0757345
$142$	475.585	0.281058
$143$	−869.699	−0.508586
$144$	269.099	0.155729
$145$	0	0
$146$	−785.380	−0.445195
$147$	−861.000	−0.483089
$148$	−793.199	−0.440544
$149$	5.08064	0.00279344	0.00139672	−	0.999999i	$-0.499555\pi$
$149$	5.08064	0.00279344	0.00139672	+	0.999999i	$0.499555\pi$
$150$	0	0
$151$	6.54894	0.00352944	0.00176472	−	0.999998i	$-0.499438\pi$
$151$	6.54894	0.00352944	0.00176472	+	0.999998i	$0.499438\pi$
$152$	−967.849	−0.516467
$153$	−872.700	−0.461135
$154$	2373.83	1.24213
$155$	0	0
$156$	564.849	0.289898
$157$	2297.60	1.16795	0.583975	−	0.811772i	$-0.301497\pi$
$157$	2297.60	1.16795	0.583975	+	0.811772i	$0.301497\pi$
$158$	2585.46	1.30183
$159$	1593.00	0.794546
$160$	0	0
$161$	−1373.93	−0.672553
$162$	−384.074	−0.186270
$163$	1085.49	0.521606	0.260803	−	0.965392i	$-0.416013\pi$
$163$	1085.49	0.521606	0.260803	+	0.965392i	$0.416013\pi$
$164$	6542.34	3.11507
$165$	0	0
$166$	−2155.24	−1.00771
$167$	109.066	0.0505374	0.0252687	−	0.999681i	$-0.491956\pi$
$167$	109.066	0.0505374	0.0252687	+	0.999681i	$0.491956\pi$
$168$	−690.148	−0.316941
$169$	169.000	0.0769231
$170$	0	0
$171$	283.350	0.126715
$172$	1642.90	0.728313
$173$	1889.17	0.830236	0.415118	−	0.909768i	$-0.363740\pi$
$173$	1889.17	0.830236	0.415118	+	0.909768i	$0.363740\pi$
$174$	−1596.05	−0.695379
$175$	0	0
$176$	−2000.30	−0.856694
$177$	658.999	0.279850
$178$	1094.92	0.461054
$179$	3427.86	1.43134	0.715672	−	0.698437i	$-0.246121\pi$
$179$	3427.86	1.43134	0.715672	+	0.698437i	$0.246121\pi$
$180$	0	0
$181$	208.403	0.0855826	0.0427913	−	0.999084i	$-0.486375\pi$
$181$	208.403	0.0855826	0.0427913	+	0.999084i	$0.486375\pi$
$182$	−461.283	−0.187871
$183$	2468.60	0.997180
$184$	5644.15	2.26137
$185$	0	0
$186$	1099.35	0.433378
$187$	6487.06	2.53679
$188$	612.166	0.237483
$189$	202.049	0.0777616
$190$	0	0
$191$	957.735	0.362824	0.181412	−	0.983407i	$-0.441933\pi$
$191$	957.735	0.362824	0.181412	+	0.983407i	$0.441933\pi$
$192$	−2199.25	−0.826650
$193$	512.730	0.191228	0.0956142	−	0.995418i	$-0.469518\pi$
$193$	512.730	0.191228	0.0956142	+	0.995418i	$0.469518\pi$
$194$	−5164.45	−1.91127
$195$	0	0
$196$	−4156.71	−1.51484
$197$	3870.35	1.39975	0.699876	−	0.714265i	$-0.253239\pi$
$197$	3870.35	1.39975	0.699876	+	0.714265i	$0.253239\pi$
$198$	2854.95	1.02471
$199$	2305.83	0.821388	0.410694	−	0.911773i	$-0.365286\pi$
$199$	2305.83	0.821388	0.410694	+	0.911773i	$0.365286\pi$
$200$	0	0
$201$	2616.25	0.918088
$202$	366.215	0.127558
$203$	839.630	0.290298
$204$	−4213.19	−1.44599
$205$	0	0
$206$	6407.70	2.16721
$207$	−1652.40	−0.554828
$208$	388.699	0.129574
$209$	−2106.23	−0.697086
$210$	0	0
$211$	−3672.40	−1.19819	−0.599096	−	0.800677i	$-0.704473\pi$
$211$	−3672.40	−1.19819	−0.599096	+	0.800677i	$0.704473\pi$
$212$	7690.62	2.49148
$213$	−300.898	−0.0967942
$214$	5375.46	1.71710
$215$	0	0
$216$	−830.025	−0.261463
$217$	−578.334	−0.180921
$218$	−4825.41	−1.49917
$219$	496.902	0.153322
$220$	0	0
$221$	−1260.57	−0.383687
$222$	779.051	0.235525
$223$	−5087.05	−1.52760	−0.763798	−	0.645455i	$-0.776668\pi$
$223$	−5087.05	−1.52760	−0.763798	+	0.645455i	$0.776668\pi$
$224$	779.449	0.232496
$225$	0	0
$226$	7444.71	2.19122
$227$	2625.83	0.767763	0.383882	−	0.923382i	$-0.374587\pi$
$227$	2625.83	0.767763	0.383882	+	0.923382i	$0.374587\pi$
$228$	1367.95	0.397345
$229$	1678.73	0.484425	0.242213	−	0.970223i	$-0.422127\pi$
$229$	1678.73	0.484425	0.242213	+	0.970223i	$0.422127\pi$
$230$	0	0
$231$	−1501.90	−0.427782
$232$	−3449.22	−0.976088
$233$	−648.506	−0.182339	−0.0911696	−	0.995835i	$-0.529061\pi$
$233$	−648.506	−0.182339	−0.0911696	+	0.995835i	$0.529061\pi$
$234$	−554.774	−0.154986
$235$	0	0
$236$	3181.50	0.877533
$237$	−1635.80	−0.448340
$238$	3440.70	0.937089
$239$	5219.69	1.41269	0.706347	−	0.707866i	$-0.250342\pi$
$239$	5219.69	1.41269	0.706347	+	0.707866i	$0.250342\pi$
$240$	0	0
$241$	6103.56	1.63139	0.815695	−	0.578483i	$-0.196355\pi$
$241$	6103.56	1.63139	0.815695	+	0.578483i	$0.196355\pi$
$242$	−14910.6	−3.96070
$243$	243.000	0.0641500
$244$	11917.8	3.12689
$245$	0	0
$246$	−6425.64	−1.66538
$247$	409.283	0.105433
$248$	2375.81	0.608323
$249$	1363.60	0.347047
$250$	0	0
$251$	6423.40	1.61530	0.807652	−	0.589660i	$-0.200738\pi$
$251$	6423.40	1.61530	0.807652	+	0.589660i	$0.200738\pi$
$252$	975.449	0.243839
$253$	12282.8	3.05222
$254$	−5918.36	−1.46201
$255$	0	0
$256$	−6666.39	−1.62754
$257$	1230.23	0.298597	0.149299	−	0.988792i	$-0.452298\pi$
$257$	1230.23	0.298597	0.149299	+	0.988792i	$0.452298\pi$
$258$	−1613.59	−0.389372
$259$	−409.834	−0.0983238
$260$	0	0
$261$	1009.80	0.239483
$262$	6044.66	1.42534
$263$	514.992	0.120744	0.0603722	−	0.998176i	$-0.480771\pi$
$263$	514.992	0.120744	0.0603722	+	0.998176i	$0.480771\pi$
$264$	6169.84	1.43836
$265$	0	0
$266$	−1117.13	−0.257503
$267$	−692.745	−0.158784
$268$	12630.6	2.87888
$269$	−5132.60	−1.16335	−0.581673	−	0.813423i	$-0.697602\pi$
$269$	−5132.60	−1.16335	−0.581673	+	0.813423i	$0.697602\pi$
$270$	0	0
$271$	−4300.00	−0.963862	−0.481931	−	0.876209i	$-0.660064\pi$
$271$	−4300.00	−0.963862	−0.481931	+	0.876209i	$0.660064\pi$
$272$	−2899.29	−0.646306
$273$	291.849	0.0647015
$274$	4148.55	0.914682
$275$	0	0
$276$	−7977.39	−1.73979
$277$	1812.80	0.393215	0.196607	−	0.980482i	$-0.437008\pi$
$277$	1812.80	0.393215	0.196607	+	0.980482i	$0.437008\pi$
$278$	−1471.50	−0.317462
$279$	−695.548	−0.149252
$280$	0	0
$281$	−4073.08	−0.864696	−0.432348	−	0.901707i	$-0.642315\pi$
$281$	−4073.08	−0.864696	−0.432348	+	0.901707i	$0.642315\pi$
$282$	−601.246	−0.126963
$283$	−6346.29	−1.33303	−0.666516	−	0.745491i	$-0.732215\pi$
$283$	−6346.29	−1.33303	−0.666516	+	0.745491i	$0.732215\pi$
$284$	−1452.67	−0.303520
$285$	0	0
$286$	4123.81	0.852609
$287$	3380.33	0.695243
$288$	937.424	0.191799
$289$	4489.53	0.913806
$290$	0	0
$291$	3267.49	0.658226
$292$	2398.93	0.480777
$293$	8390.97	1.67306	0.836529	−	0.547923i	$-0.184581\pi$
$293$	8390.97	1.67306	0.836529	+	0.547923i	$0.184581\pi$
$294$	4082.57	0.809864
$295$	0	0
$296$	1683.61	0.330601
$297$	−1806.30	−0.352902
$298$	−24.0907	−0.00468300
$299$	−2386.79	−0.461645
$300$	0	0
$301$	848.861	0.162550
$302$	−31.0528	−0.00591685
$303$	−231.701	−0.0439302
$304$	941.348	0.177599
$305$	0	0
$306$	4138.04	0.773059
$307$	−4005.27	−0.744603	−0.372301	−	0.928112i	$-0.621431\pi$
$307$	−4005.27	−0.744603	−0.372301	+	0.928112i	$0.621431\pi$
$308$	−7250.82	−1.34141
$309$	−4054.09	−0.746372
$310$	0	0
$311$	5836.53	1.06418	0.532088	−	0.846689i	$-0.321407\pi$
$311$	5836.53	1.06418	0.532088	+	0.846689i	$0.321407\pi$
$312$	−1198.92	−0.217550
$313$	−1763.19	−0.318407	−0.159204	−	0.987246i	$-0.550893\pi$
$313$	−1763.19	−0.318407	−0.159204	+	0.987246i	$0.550893\pi$
$314$	−10894.4	−1.95798
$315$	0	0
$316$	−7897.26	−1.40587
$317$	6106.35	1.08191	0.540957	−	0.841050i	$-0.318062\pi$
$317$	6106.35	1.08191	0.540957	+	0.841050i	$0.318062\pi$
$318$	−7553.44	−1.33200
$319$	−7506.18	−1.31745
$320$	0	0
$321$	−3401.00	−0.591356
$322$	6514.72	1.12749
$323$	−3052.83	−0.525895
$324$	1173.15	0.201157
$325$	0	0
$326$	−5147.00	−0.874436
$327$	3052.99	0.516302
$328$	−13886.5	−2.33766
$329$	316.297	0.0530031
$330$	0	0
$331$	7490.38	1.24383	0.621916	−	0.783084i	$-0.286354\pi$
$331$	7490.38	1.24383	0.621916	+	0.783084i	$0.286354\pi$
$332$	6583.16	1.08825
$333$	−492.898	−0.0811130
$334$	−517.152	−0.0847224
$335$	0	0
$336$	671.251	0.108987
$337$	−9462.46	−1.52953	−0.764767	−	0.644307i	$-0.777146\pi$
$337$	−9462.46	−1.52953	−0.764767	+	0.644307i	$0.777146\pi$
$338$	−801.340	−0.128956
$339$	−4710.19	−0.754639
$340$	0	0
$341$	5170.23	0.821066
$342$	−1343.55	−0.212429
$343$	−4714.49	−0.742153
$344$	−3487.14	−0.546553
$345$	0	0
$346$	−8957.79	−1.39183
$347$	−11460.3	−1.77297	−0.886487	−	0.462753i	$-0.846862\pi$
$347$	−11460.3	−1.77297	−0.886487	+	0.462753i	$0.846862\pi$
$348$	4875.09	0.750955
$349$	−3673.96	−0.563503	−0.281751	−	0.959487i	$-0.590915\pi$
$349$	−3673.96	−0.563503	−0.281751	+	0.959487i	$0.590915\pi$
$350$	0	0
$351$	351.000	0.0533761
$352$	−6968.17	−1.05513
$353$	−3388.65	−0.510935	−0.255467	−	0.966818i	$-0.582229\pi$
$353$	−3388.65	−0.510935	−0.255467	+	0.966818i	$0.582229\pi$
$354$	−3124.75	−0.469148
$355$	0	0
$356$	−3344.41	−0.497903
$357$	−2176.90	−0.322727
$358$	−16253.7	−2.39955
$359$	−9673.98	−1.42221	−0.711105	−	0.703086i	$-0.751805\pi$
$359$	−9673.98	−1.42221	−0.711105	+	0.703086i	$0.751805\pi$
$360$	0	0
$361$	−5867.80	−0.855489
$362$	−988.174	−0.143473
$363$	9433.79	1.36404
$364$	1408.98	0.202887
$365$	0	0
$366$	−11705.2	−1.67170
$367$	8715.98	1.23970	0.619851	−	0.784720i	$-0.287193\pi$
$367$	8715.98	1.23970	0.619851	+	0.784720i	$0.287193\pi$
$368$	−5489.61	−0.777624
$369$	4065.44	0.573546
$370$	0	0
$371$	3973.63	0.556067
$372$	−3357.95	−0.468014
$373$	−4667.99	−0.647987	−0.323994	−	0.946059i	$-0.605026\pi$
$373$	−4667.99	−0.647987	−0.323994	+	0.946059i	$0.605026\pi$
$374$	−30759.4	−4.25276
$375$	0	0
$376$	−1299.36	−0.178216
$377$	1458.60	0.199262
$378$	−958.049	−0.130362
$379$	10862.7	1.47225	0.736123	−	0.676848i	$-0.236655\pi$
$379$	10862.7	1.47225	0.736123	+	0.676848i	$0.236655\pi$
$380$	0	0
$381$	3744.49	0.503507
$382$	−4541.25	−0.608248
$383$	−10054.2	−1.34137	−0.670686	−	0.741742i	$-0.734000\pi$
$383$	−10054.2	−1.34137	−0.670686	+	0.741742i	$0.734000\pi$
$384$	7928.27	1.05361
$385$	0	0
$386$	−2431.19	−0.320581
$387$	1020.90	0.134097
$388$	15774.7	2.06402
$389$	6418.50	0.836584	0.418292	−	0.908313i	$-0.362629\pi$
$389$	6418.50	0.836584	0.418292	+	0.908313i	$0.362629\pi$
$390$	0	0
$391$	17803.0	2.30265
$392$	8822.86	1.13679
$393$	−3824.40	−0.490879
$394$	−18351.9	−2.34658
$395$	0	0
$396$	−8720.39	−1.10661
$397$	12019.9	1.51955	0.759775	−	0.650186i	$-0.225309\pi$
$397$	12019.9	1.51955	0.759775	+	0.650186i	$0.225309\pi$
$398$	−10933.5	−1.37700
$399$	706.799	0.0886822
$400$	0	0
$401$	3599.80	0.448293	0.224147	−	0.974555i	$-0.428041\pi$
$401$	3599.80	0.448293	0.224147	+	0.974555i	$0.428041\pi$
$402$	−12405.3	−1.53911
$403$	−1004.68	−0.124185
$404$	−1118.60	−0.137753
$405$	0	0
$406$	−3981.24	−0.486664
$407$	3663.87	0.446219
$408$	8942.74	1.08513
$409$	−48.0968	−0.00581475	−0.00290737	−	0.999996i	$-0.500925\pi$
$409$	−48.0968	−0.00581475	−0.00290737	+	0.999996i	$0.500925\pi$
$410$	0	0
$411$	−2624.74	−0.315010
$412$	−19572.2	−2.34042
$413$	1643.83	0.195854
$414$	7835.10	0.930130
$415$	0	0
$416$	1354.06	0.159587
$417$	931.001	0.109332
$418$	9987.02	1.16862
$419$	723.462	0.0843518	0.0421759	−	0.999110i	$-0.486571\pi$
$419$	723.462	0.0843518	0.0421759	+	0.999110i	$0.486571\pi$
$420$	0	0
$421$	−14845.5	−1.71859	−0.859295	−	0.511481i	$-0.829097\pi$
$421$	−14845.5	−1.71859	−0.859295	+	0.511481i	$0.829097\pi$
$422$	17413.3	2.00868
$423$	380.403	0.0437253
$424$	−16323.8	−1.86970
$425$	0	0
$426$	1426.75	0.162269
$427$	6157.76	0.697880
$428$	−16419.2	−1.85433
$429$	−2609.10	−0.293632
$430$	0	0
$431$	1103.11	0.123283	0.0616417	−	0.998098i	$-0.480366\pi$
$431$	1103.11	0.123283	0.0616417	+	0.998098i	$0.480366\pi$
$432$	807.297	0.0899099
$433$	−8893.53	−0.987057	−0.493528	−	0.869730i	$-0.664293\pi$
$433$	−8893.53	−0.987057	−0.493528	+	0.869730i	$0.664293\pi$
$434$	2742.26	0.303301
$435$	0	0
$436$	14739.1	1.61898
$437$	−5780.32	−0.632747
$438$	−2356.14	−0.257034
$439$	−10901.7	−1.18521	−0.592607	−	0.805492i	$-0.701901\pi$
$439$	−10901.7	−1.18521	−0.592607	+	0.805492i	$0.701901\pi$
$440$	0	0
$441$	−2583.00	−0.278912
$442$	5977.17	0.643224
$443$	3781.37	0.405550	0.202775	−	0.979225i	$-0.435004\pi$
$443$	3781.37	0.405550	0.202775	+	0.979225i	$0.435004\pi$
$444$	−2379.60	−0.254348
$445$	0	0
$446$	24121.0	2.56091
$447$	15.2419	0.00161279
$448$	−5485.88	−0.578535
$449$	106.834	0.0112289	0.00561447	−	0.999984i	$-0.498213\pi$
$449$	106.834	0.0112289	0.00561447	+	0.999984i	$0.498213\pi$
$450$	0	0
$451$	−30219.7	−3.15519
$452$	−22739.7	−2.36634
$453$	19.6468	0.00203772
$454$	−12450.8	−1.28710
$455$	0	0
$456$	−2903.55	−0.298182
$457$	1237.64	0.126684	0.0633419	−	0.997992i	$-0.479824\pi$
$457$	1237.64	0.126684	0.0633419	+	0.997992i	$0.479824\pi$
$458$	−7959.95	−0.812105
$459$	−2618.10	−0.266236
$460$	0	0
$461$	8790.90	0.888141	0.444071	−	0.895992i	$-0.353534\pi$
$461$	8790.90	0.888141	0.444071	+	0.895992i	$0.353534\pi$
$462$	7121.49	0.717146
$463$	3861.55	0.387606	0.193803	−	0.981040i	$-0.437918\pi$
$463$	3861.55	0.387606	0.193803	+	0.981040i	$0.437918\pi$
$464$	3354.77	0.335650
$465$	0	0
$466$	3074.99	0.305679
$467$	8991.38	0.890945	0.445473	−	0.895296i	$-0.353036\pi$
$467$	8991.38	0.890945	0.445473	+	0.895296i	$0.353036\pi$
$468$	1694.55	0.167373
$469$	6526.06	0.642528
$470$	0	0
$471$	6892.79	0.674316
$472$	−6752.91	−0.658533
$473$	−7588.71	−0.737694
$474$	7756.39	0.751609
$475$	0	0
$476$	−10509.6	−1.01198
$477$	4778.99	0.458731
$478$	−24750.0	−2.36828
$479$	4179.82	0.398707	0.199354	−	0.979928i	$-0.436116\pi$
$479$	4179.82	0.398707	0.199354	+	0.979928i	$0.436116\pi$
$480$	0	0
$481$	−711.963	−0.0674901
$482$	−28941.0	−2.73491
$483$	−4121.80	−0.388299
$484$	45544.2	4.27725
$485$	0	0
$486$	−1152.22	−0.107543
$487$	18443.8	1.71616	0.858078	−	0.513519i	$-0.171658\pi$
$487$	18443.8	1.71616	0.858078	+	0.513519i	$0.171658\pi$
$488$	−25296.2	−2.34653
$489$	3256.46	0.301149
$490$	0	0
$491$	8093.26	0.743877	0.371939	−	0.928257i	$-0.378693\pi$
$491$	8093.26	0.743877	0.371939	+	0.928257i	$0.378693\pi$
$492$	19627.0	1.79849
$493$	−10879.7	−0.993907
$494$	−1940.68	−0.176752
$495$	0	0
$496$	−2310.76	−0.209185
$497$	−750.571	−0.0677418
$498$	−6465.73	−0.581800
$499$	−10941.6	−0.981591	−0.490796	−	0.871275i	$-0.663294\pi$
$499$	−10941.6	−0.981591	−0.490796	+	0.871275i	$0.663294\pi$
$500$	0	0
$501$	327.197	0.0291778
$502$	−30457.5	−2.70794
$503$	9260.11	0.820851	0.410425	−	0.911894i	$-0.365380\pi$
$503$	9260.11	0.820851	0.410425	+	0.911894i	$0.365380\pi$
$504$	−2070.45	−0.182986
$505$	0	0
$506$	−58240.8	−5.11684
$507$	507.000	0.0444116
$508$	18077.5	1.57886
$509$	−9996.40	−0.870497	−0.435248	−	0.900310i	$-0.643339\pi$
$509$	−9996.40	−0.870497	−0.435248	+	0.900310i	$0.643339\pi$
$510$	0	0
$511$	1239.49	0.107303
$512$	10467.7	0.903538
$513$	850.049	0.0731591
$514$	−5833.32	−0.500577
$515$	0	0
$516$	4928.69	0.420491
$517$	−2827.66	−0.240542
$518$	1943.29	0.164833
$519$	5667.51	0.479337
$520$	0	0
$521$	11427.9	0.960973	0.480486	−	0.877002i	$-0.340460\pi$
$521$	11427.9	0.960973	0.480486	+	0.877002i	$0.340460\pi$
$522$	−4788.14	−0.401477
$523$	4810.47	0.402193	0.201097	−	0.979571i	$-0.435549\pi$
$523$	4810.47	0.402193	0.201097	+	0.979571i	$0.435549\pi$
$524$	−18463.3	−1.53926
$525$	0	0
$526$	−2441.92	−0.202419
$527$	7493.88	0.619428
$528$	−6000.90	−0.494613
$529$	21541.8	1.77051
$530$	0	0
$531$	1977.00	0.161571
$532$	3412.26	0.278083
$533$	5872.31	0.477219
$534$	3284.76	0.266190
$535$	0	0
$536$	−26809.2	−2.16042
$537$	10283.6	0.826386
$538$	24337.0	1.95027
$539$	19200.3	1.53435
$540$	0	0
$541$	2411.99	0.191681	0.0958406	−	0.995397i	$-0.469446\pi$
$541$	2411.99	0.191681	0.0958406	+	0.995397i	$0.469446\pi$
$542$	20389.1	1.61585
$543$	625.208	0.0494111
$544$	−10099.9	−0.796008
$545$	0	0
$546$	−1383.85	−0.108468
$547$	4396.34	0.343646	0.171823	−	0.985128i	$-0.445034\pi$
$547$	4396.34	0.343646	0.171823	+	0.985128i	$0.445034\pi$
$548$	−12671.7	−0.987786
$549$	7405.79	0.575722
$550$	0	0
$551$	3532.43	0.273116
$552$	16932.5	1.30560
$553$	−4080.40	−0.313772
$554$	−8595.67	−0.659197
$555$	0	0
$556$	4494.66	0.342835
$557$	17488.0	1.33032	0.665160	−	0.746701i	$-0.268363\pi$
$557$	17488.0	1.33032	0.665160	+	0.746701i	$0.268363\pi$
$558$	3298.05	0.250211
$559$	1474.64	0.111575
$560$	0	0
$561$	19461.2	1.46462
$562$	19313.2	1.44960
$563$	6881.77	0.515154	0.257577	−	0.966258i	$-0.417076\pi$
$563$	6881.77	0.515154	0.257577	+	0.966258i	$0.417076\pi$
$564$	1836.50	0.137111
$565$	0	0
$566$	30092.0	2.23473
$567$	606.148	0.0448957
$568$	3083.36	0.227773
$569$	14733.5	1.08552	0.542758	−	0.839889i	$-0.317380\pi$
$569$	14733.5	1.08552	0.542758	+	0.839889i	$0.317380\pi$
$570$	0	0
$571$	4488.51	0.328964	0.164482	−	0.986380i	$-0.447405\pi$
$571$	4488.51	0.328964	0.164482	+	0.986380i	$0.447405\pi$
$572$	−12596.1	−0.920752
$573$	2873.21	0.209476
$574$	−16028.4	−1.16553
$575$	0	0
$576$	−6597.74	−0.477267
$577$	10552.2	0.761338	0.380669	−	0.924711i	$-0.375694\pi$
$577$	10552.2	0.761338	0.380669	+	0.924711i	$0.375694\pi$
$578$	−21287.8	−1.53193
$579$	1538.19	0.110406
$580$	0	0
$581$	3401.42	0.242882
$582$	−15493.3	−1.10347
$583$	−35523.8	−2.52357
$584$	−5091.86	−0.360793
$585$	0	0
$586$	−39787.1	−2.80476
$587$	1637.20	0.115118	0.0575591	−	0.998342i	$-0.481668\pi$
$587$	1637.20	0.115118	0.0575591	+	0.998342i	$0.481668\pi$
$588$	−12470.1	−0.874591
$589$	−2433.13	−0.170213
$590$	0	0
$591$	11611.1	0.808147
$592$	−1637.51	−0.113685
$593$	−14024.0	−0.971155	−0.485577	−	0.874194i	$-0.661391\pi$
$593$	−14024.0	−0.971155	−0.485577	+	0.874194i	$0.661391\pi$
$594$	8564.84	0.591616
$595$	0	0
$596$	73.5845	0.00505728
$597$	6917.50	0.474229
$598$	11317.4	0.773915
$599$	365.860	0.0249560	0.0124780	−	0.999922i	$-0.496028\pi$
$599$	365.860	0.0249560	0.0124780	+	0.999922i	$0.496028\pi$
$600$	0	0
$601$	−10128.9	−0.687465	−0.343733	−	0.939068i	$-0.611691\pi$
$601$	−10128.9	−0.687465	−0.343733	+	0.939068i	$0.611691\pi$
$602$	−4025.01	−0.272503
$603$	7848.74	0.530058
$604$	94.8504	0.00638975
$605$	0	0
$606$	1098.65	0.0736459
$607$	−2324.97	−0.155465	−0.0777327	−	0.996974i	$-0.524768\pi$
$607$	−2324.97	−0.155465	−0.0777327	+	0.996974i	$0.524768\pi$
$608$	3279.25	0.218735
$609$	2518.89	0.167603
$610$	0	0
$611$	549.471	0.0363817
$612$	−12639.6	−0.834845
$613$	−633.133	−0.0417162	−0.0208581	−	0.999782i	$-0.506640\pi$
$613$	−633.133	−0.0417162	−0.0208581	+	0.999782i	$0.506640\pi$
$614$	18991.6	1.24827
$615$	0	0
$616$	15390.3	1.00664
$617$	2981.85	0.194562	0.0972810	−	0.995257i	$-0.468985\pi$
$617$	2981.85	0.194562	0.0972810	+	0.995257i	$0.468985\pi$
$618$	19223.1	1.25124
$619$	15158.6	0.984292	0.492146	−	0.870513i	$-0.336213\pi$
$619$	15158.6	0.984292	0.492146	+	0.870513i	$0.336213\pi$
$620$	0	0
$621$	−4957.19	−0.320330
$622$	−27674.8	−1.78402
$623$	−1728.01	−0.111126
$624$	1166.10	0.0748096
$625$	0	0
$626$	8360.45	0.533787
$627$	−6318.69	−0.402463
$628$	33276.8	2.11447
$629$	5310.51	0.336636
$630$	0	0
$631$	5562.30	0.350922	0.175461	−	0.984486i	$-0.443858\pi$
$631$	5562.30	0.350922	0.175461	+	0.984486i	$0.443858\pi$
$632$	16762.4	1.05502
$633$	−11017.2	−0.691776
$634$	−28954.2	−1.81375
$635$	0	0
$636$	23071.9	1.43846
$637$	−3731.00	−0.232068
$638$	35591.7	2.20861
$639$	−902.693	−0.0558842
$640$	0	0
$641$	−24140.7	−1.48752	−0.743761	−	0.668446i	$-0.766960\pi$
$641$	−24140.7	−1.48752	−0.743761	+	0.668446i	$0.766960\pi$
$642$	16126.4	0.991366
$643$	1749.69	0.107311	0.0536555	−	0.998560i	$-0.482913\pi$
$643$	1749.69	0.107311	0.0536555	+	0.998560i	$0.482913\pi$
$644$	−19899.1	−1.21760
$645$	0	0
$646$	14475.5	0.881626
$647$	−1489.51	−0.0905083	−0.0452542	−	0.998976i	$-0.514410\pi$
$647$	−1489.51	−0.0905083	−0.0452542	+	0.998976i	$0.514410\pi$
$648$	−2490.07	−0.150956
$649$	−14695.7	−0.888836
$650$	0	0
$651$	−1735.00	−0.104455
$652$	15721.4	0.944323
$653$	−10668.2	−0.639327	−0.319663	−	0.947531i	$-0.603570\pi$
$653$	−10668.2	−0.639327	−0.319663	+	0.947531i	$0.603570\pi$
$654$	−14476.2	−0.865544
$655$	0	0
$656$	13506.3	0.803858
$657$	1490.71	0.0885205
$658$	−1499.77	−0.0888559
$659$	−13933.1	−0.823608	−0.411804	−	0.911272i	$-0.635101\pi$
$659$	−13933.1	−0.823608	−0.411804	+	0.911272i	$0.635101\pi$
$660$	0	0
$661$	−2349.69	−0.138264	−0.0691320	−	0.997608i	$-0.522023\pi$
$661$	−2349.69	−0.138264	−0.0691320	+	0.997608i	$0.522023\pi$
$662$	−35516.8	−2.08520
$663$	−3781.70	−0.221522
$664$	−13973.1	−0.816660
$665$	0	0
$666$	2337.15	0.135980
$667$	−20599.9	−1.19585
$668$	1579.63	0.0914937
$669$	−15261.1	−0.881958
$670$	0	0
$671$	−55049.6	−3.16716
$672$	2338.35	0.134232
$673$	32421.0	1.85697	0.928483	−	0.371374i	$-0.121113\pi$
$673$	32421.0	1.85697	0.928483	+	0.371374i	$0.121113\pi$
$674$	44867.7	2.56415
$675$	0	0
$676$	2447.68	0.139263
$677$	1071.74	0.0608421	0.0304211	−	0.999537i	$-0.490315\pi$
$677$	1071.74	0.0608421	0.0304211	+	0.999537i	$0.490315\pi$
$678$	22334.1	1.26510
$679$	8150.56	0.460663
$680$	0	0
$681$	7877.48	0.443268
$682$	−24515.5	−1.37646
$683$	305.487	0.0171144	0.00855721	−	0.999963i	$-0.497276\pi$
$683$	305.487	0.0171144	0.00855721	+	0.999963i	$0.497276\pi$
$684$	4103.84	0.229407
$685$	0	0
$686$	22354.5	1.24417
$687$	5036.18	0.279683
$688$	3391.66	0.187944
$689$	6902.99	0.381688
$690$	0	0
$691$	2180.81	0.120061	0.0600303	−	0.998197i	$-0.480880\pi$
$691$	2180.81	0.120061	0.0600303	+	0.998197i	$0.480880\pi$
$692$	27361.4	1.50307
$693$	−4505.70	−0.246980
$694$	54340.9	2.97227
$695$	0	0
$696$	−10347.7	−0.563545
$697$	−43801.4	−2.38034
$698$	17420.6	0.944672
$699$	−1945.52	−0.105274
$700$	0	0
$701$	−15168.3	−0.817259	−0.408629	−	0.912700i	$-0.633993\pi$
$701$	−15168.3	−0.817259	−0.408629	+	0.912700i	$0.633993\pi$
$702$	−1664.32	−0.0894812
$703$	−1724.23	−0.0925043
$704$	49043.1	2.62554
$705$	0	0
$706$	16067.8	0.856545
$707$	−577.963	−0.0307448
$708$	9544.49	0.506644
$709$	−8988.17	−0.476104	−0.238052	−	0.971252i	$-0.576509\pi$
$709$	−8988.17	−0.476104	−0.238052	+	0.971252i	$0.576509\pi$
$710$	0	0
$711$	−4907.39	−0.258849
$712$	7098.71	0.373645
$713$	14189.1	0.745284
$714$	10322.1	0.541029
$715$	0	0
$716$	49646.8	2.59132
$717$	15659.1	0.815619
$718$	45870.7	2.38423
$719$	8448.18	0.438198	0.219099	−	0.975703i	$-0.429688\pi$
$719$	8448.18	0.438198	0.219099	+	0.975703i	$0.429688\pi$
$720$	0	0
$721$	−10112.7	−0.522352
$722$	27823.1	1.43417
$723$	18310.7	0.941883
$724$	3018.36	0.154940
$725$	0	0
$726$	−44731.8	−2.28671
$727$	8624.18	0.439963	0.219982	−	0.975504i	$-0.429400\pi$
$727$	8624.18	0.439963	0.219982	+	0.975504i	$0.429400\pi$
$728$	−2990.64	−0.152254
$729$	729.000	0.0370370
$730$	0	0
$731$	−10999.3	−0.556530
$732$	35753.5	1.80531
$733$	−31124.2	−1.56835	−0.784174	−	0.620541i	$-0.786913\pi$
$733$	−31124.2	−1.56835	−0.784174	+	0.620541i	$0.786913\pi$
$734$	−41328.2	−2.07827
$735$	0	0
$736$	−19123.4	−0.957742
$737$	−58342.2	−2.91596
$738$	−19276.9	−0.961509
$739$	−17671.1	−0.879626	−0.439813	−	0.898089i	$-0.644955\pi$
$739$	−17671.1	−0.879626	−0.439813	+	0.898089i	$0.644955\pi$
$740$	0	0
$741$	1227.85	0.0608720
$742$	−18841.6	−0.932206
$743$	21331.1	1.05325	0.526623	−	0.850099i	$-0.323458\pi$
$743$	21331.1	1.05325	0.526623	+	0.850099i	$0.323458\pi$
$744$	7127.43	0.351215
$745$	0	0
$746$	22134.0	1.08630
$747$	4090.81	0.200368
$748$	93954.1	4.59265
$749$	−8483.58	−0.413863
$750$	0	0
$751$	11712.9	0.569122	0.284561	−	0.958658i	$-0.408152\pi$
$751$	11712.9	0.569122	0.284561	+	0.958658i	$0.408152\pi$
$752$	1263.78	0.0612835
$753$	19270.2	0.932596
$754$	−6916.20	−0.334049
$755$	0	0
$756$	2926.35	0.140781
$757$	16610.9	0.797537	0.398768	−	0.917052i	$-0.369438\pi$
$757$	16610.9	0.797537	0.398768	+	0.917052i	$0.369438\pi$
$758$	−51507.4	−2.46812
$759$	36848.4	1.76220
$760$	0	0
$761$	−29365.5	−1.39882	−0.699408	−	0.714723i	$-0.746553\pi$
$761$	−29365.5	−1.39882	−0.699408	+	0.714723i	$0.746553\pi$
$762$	−17755.1	−0.844093
$763$	7615.50	0.361336
$764$	13871.2	0.656861
$765$	0	0
$766$	47673.5	2.24871
$767$	2855.66	0.134435
$768$	−19999.2	−0.939659
$769$	−28599.9	−1.34114	−0.670572	−	0.741844i	$-0.733951\pi$
$769$	−28599.9	−1.34114	−0.670572	+	0.741844i	$0.733951\pi$
$770$	0	0
$771$	3690.68	0.172395
$772$	7426.03	0.346203
$773$	−13491.8	−0.627772	−0.313886	−	0.949461i	$-0.601631\pi$
$773$	−13491.8	−0.627772	−0.313886	+	0.949461i	$0.601631\pi$
$774$	−4840.78	−0.224804
$775$	0	0
$776$	−33482.7	−1.54892
$777$	−1229.50	−0.0567673
$778$	−30434.3	−1.40247
$779$	14221.5	0.654093
$780$	0	0
$781$	6710.01	0.307430
$782$	−84415.9	−3.86024
$783$	3029.41	0.138266
$784$	−8581.27	−0.390911
$785$	0	0
$786$	18134.0	0.822923
$787$	−25876.7	−1.17205	−0.586025	−	0.810293i	$-0.699308\pi$
$787$	−25876.7	−1.17205	−0.586025	+	0.810293i	$0.699308\pi$
$788$	56055.5	2.53413
$789$	1544.98	0.0697118
$790$	0	0
$791$	−11749.3	−0.528137
$792$	18509.5	0.830438
$793$	10697.3	0.479030
$794$	−56994.2	−2.54742
$795$	0	0
$796$	33396.1	1.48705
$797$	−21936.4	−0.974938	−0.487469	−	0.873140i	$-0.662080\pi$
$797$	−21936.4	−0.974938	−0.487469	+	0.873140i	$0.662080\pi$
$798$	−3351.40	−0.148669
$799$	−4098.49	−0.181469
$800$	0	0
$801$	−2078.23	−0.0916739
$802$	−17069.0	−0.751531
$803$	−11080.9	−0.486969
$804$	37891.9	1.66212
$805$	0	0
$806$	4763.85	0.208188
$807$	−15397.8	−0.671658
$808$	2374.29	0.103375
$809$	5583.23	0.242640	0.121320	−	0.992613i	$-0.461287\pi$
$809$	5583.23	0.242640	0.121320	+	0.992613i	$0.461287\pi$
$810$	0	0
$811$	12925.4	0.559647	0.279823	−	0.960052i	$-0.409724\pi$
$811$	12925.4	0.559647	0.279823	+	0.960052i	$0.409724\pi$
$812$	12160.6	0.525559
$813$	−12900.0	−0.556486
$814$	−17372.8	−0.748054
$815$	0	0
$816$	−8697.87	−0.373145
$817$	3571.27	0.152929
$818$	228.058	0.00974801
$819$	875.548	0.0373555
$820$	0	0
$821$	−10153.2	−0.431608	−0.215804	−	0.976437i	$-0.569237\pi$
$821$	−10153.2	−0.431608	−0.215804	+	0.976437i	$0.569237\pi$
$822$	12445.6	0.528092
$823$	−3282.93	−0.139047	−0.0695235	−	0.997580i	$-0.522148\pi$
$823$	−3282.93	−0.139047	−0.0695235	+	0.997580i	$0.522148\pi$
$824$	41543.1	1.75634
$825$	0	0
$826$	−7794.49	−0.328335
$827$	17689.3	0.743795	0.371897	−	0.928274i	$-0.378707\pi$
$827$	17689.3	0.743795	0.371897	+	0.928274i	$0.378707\pi$
$828$	−23932.2	−1.00447
$829$	38181.5	1.59964	0.799818	−	0.600243i	$-0.204930\pi$
$829$	38181.5	1.59964	0.799818	+	0.600243i	$0.204930\pi$
$830$	0	0
$831$	5438.40	0.227023
$832$	−9530.06	−0.397110
$833$	27829.4	1.15754
$834$	−4414.49	−0.183287
$835$	0	0
$836$	−30505.2	−1.26201
$837$	−2086.64	−0.0861708
$838$	−3430.41	−0.141410
$839$	43895.2	1.80623	0.903117	−	0.429395i	$-0.141273\pi$
$839$	43895.2	1.80623	0.903117	+	0.429395i	$0.141273\pi$
$840$	0	0
$841$	−11800.1	−0.483829
$842$	70392.4	2.88109
$843$	−12219.2	−0.499233
$844$	−53188.5	−2.16922
$845$	0	0
$846$	−1803.74	−0.0733024
$847$	23532.0	0.954627
$848$	15876.8	0.642938
$849$	−19038.9	−0.769626
$850$	0	0
$851$	10055.1	0.405034
$852$	−4358.00	−0.175238
$853$	19955.2	0.800998	0.400499	−	0.916297i	$-0.368837\pi$
$853$	19955.2	0.800998	0.400499	+	0.916297i	$0.368837\pi$
$854$	−29198.0	−1.16995
$855$	0	0
$856$	34850.8	1.39156
$857$	−26030.4	−1.03755	−0.518776	−	0.854910i	$-0.673612\pi$
$857$	−26030.4	−1.03755	−0.518776	+	0.854910i	$0.673612\pi$
$858$	12371.4	0.492254
$859$	−45617.4	−1.81193	−0.905964	−	0.423354i	$-0.860853\pi$
$859$	−45617.4	−1.81193	−0.905964	+	0.423354i	$0.860853\pi$
$860$	0	0
$861$	10141.0	0.401399
$862$	−5230.59	−0.206676
$863$	2010.93	0.0793195	0.0396597	−	0.999213i	$-0.487373\pi$
$863$	2010.93	0.0793195	0.0396597	+	0.999213i	$0.487373\pi$
$864$	2812.27	0.110735
$865$	0	0
$866$	42170.1	1.65473
$867$	13468.6	0.527586
$868$	−8376.19	−0.327542
$869$	36478.2	1.42398
$870$	0	0
$871$	11337.1	0.441035
$872$	−31284.7	−1.21495
$873$	9802.48	0.380027
$874$	27408.3	1.06076
$875$	0	0
$876$	7196.79	0.277576
$877$	36767.3	1.41567	0.707836	−	0.706376i	$-0.249671\pi$
$877$	36767.3	1.41567	0.707836	+	0.706376i	$0.249671\pi$
$878$	51692.0	1.98693
$879$	25172.9	0.965940
$880$	0	0
$881$	35401.2	1.35380	0.676899	−	0.736076i	$-0.263323\pi$
$881$	35401.2	1.35380	0.676899	+	0.736076i	$0.263323\pi$
$882$	12247.7	0.467575
$883$	11928.0	0.454596	0.227298	−	0.973825i	$-0.427011\pi$
$883$	11928.0	0.454596	0.227298	+	0.973825i	$0.427011\pi$
$884$	−18257.2	−0.694633
$885$	0	0
$886$	−17930.0	−0.679875
$887$	32939.3	1.24689	0.623447	−	0.781866i	$-0.285732\pi$
$887$	32939.3	1.24689	0.623447	+	0.781866i	$0.285732\pi$
$888$	5050.83	0.190872
$889$	9340.40	0.352381
$890$	0	0
$891$	−5418.89	−0.203748
$892$	−73677.3	−2.76558
$893$	1330.70	0.0498660
$894$	−72.2720	−0.00270373
$895$	0	0
$896$	19776.6	0.737376
$897$	−7160.38	−0.266531
$898$	−506.569	−0.0188245
$899$	−8671.18	−0.321691
$900$	0	0
$901$	−51489.2	−1.90383
$902$	143292.	5.28946
$903$	2546.58	0.0938483
$904$	48266.4	1.77579
$905$	0	0
$906$	−93.1585	−0.00341610
$907$	−1500.89	−0.0549461	−0.0274731	−	0.999623i	$-0.508746\pi$
$907$	−1500.89	−0.0549461	−0.0274731	+	0.999623i	$0.508746\pi$
$908$	38030.7	1.38997
$909$	−695.102	−0.0253631
$910$	0	0
$911$	19728.2	0.717481	0.358740	−	0.933437i	$-0.383206\pi$
$911$	19728.2	0.717481	0.358740	+	0.933437i	$0.383206\pi$
$912$	2824.04	0.102537
$913$	−30408.3	−1.10226
$914$	−5868.48	−0.212376
$915$	0	0
$916$	24313.5	0.877011
$917$	−9539.72	−0.343543
$918$	12414.1	0.446326
$919$	19992.0	0.717602	0.358801	−	0.933414i	$-0.383186\pi$
$919$	19992.0	0.717602	0.358801	+	0.933414i	$0.383186\pi$
$920$	0	0
$921$	−12015.8	−0.429897
$922$	−41683.4	−1.48891
$923$	−1303.89	−0.0464984
$924$	−21752.5	−0.774463
$925$	0	0
$926$	−18310.2	−0.649794
$927$	−12162.3	−0.430918
$928$	11686.6	0.413395
$929$	−1923.62	−0.0679354	−0.0339677	−	0.999423i	$-0.510814\pi$
$929$	−1923.62	−0.0679354	−0.0339677	+	0.999423i	$0.510814\pi$
$930$	0	0
$931$	−9035.71	−0.318081
$932$	−9392.52	−0.330110
$933$	17509.6	0.614403
$934$	−42634.0	−1.49361
$935$	0	0
$936$	−3596.77	−0.125603
$937$	10252.9	0.357468	0.178734	−	0.983897i	$-0.442800\pi$
$937$	10252.9	0.357468	0.178734	+	0.983897i	$0.442800\pi$
$938$	−30944.4	−1.07715
$939$	−5289.58	−0.183833
$940$	0	0
$941$	11043.0	0.382563	0.191282	−	0.981535i	$-0.438736\pi$
$941$	11043.0	0.382563	0.191282	+	0.981535i	$0.438736\pi$
$942$	−32683.2	−1.13044
$943$	−82934.8	−2.86398
$944$	6568.00	0.226451
$945$	0	0
$946$	35983.1	1.23669
$947$	−32105.2	−1.10167	−0.550833	−	0.834615i	$-0.685690\pi$
$947$	−32105.2	−1.10167	−0.550833	+	0.834615i	$0.685690\pi$
$948$	−23691.8	−0.811680
$949$	2153.24	0.0736535
$950$	0	0
$951$	18319.0	0.624643
$952$	22307.1	0.759431
$953$	9473.37	0.322007	0.161003	−	0.986954i	$-0.448527\pi$
$953$	9473.37	0.322007	0.161003	+	0.986954i	$0.448527\pi$
$954$	−22660.3	−0.769031
$955$	0	0
$956$	75598.4	2.55756
$957$	−22518.5	−0.760628
$958$	−19819.3	−0.668404
$959$	−6547.26	−0.220461
$960$	0	0
$961$	−23818.3	−0.799514
$962$	3375.89	0.113142
$963$	−10203.0	−0.341419
$964$	88399.8	2.95349
$965$	0	0
$966$	19544.2	0.650956
$967$	5310.75	0.176610	0.0883052	−	0.996093i	$-0.471855\pi$
$967$	5310.75	0.176610	0.0883052	+	0.996093i	$0.471855\pi$
$968$	−96670.1	−3.20981
$969$	−9158.49	−0.303626
$970$	0	0
$971$	24271.2	0.802164	0.401082	−	0.916042i	$-0.368634\pi$
$971$	24271.2	0.802164	0.401082	+	0.916042i	$0.368634\pi$
$972$	3519.45	0.116138
$973$	2322.32	0.0765163
$974$	−87454.2	−2.87702
$975$	0	0
$976$	24603.6	0.806907
$977$	49602.5	1.62428	0.812142	−	0.583460i	$-0.198301\pi$
$977$	49602.5	1.62428	0.812142	+	0.583460i	$0.198301\pi$
$978$	−15441.0	−0.504856
$979$	15448.2	0.504317
$980$	0	0
$981$	9158.98	0.298087
$982$	−38375.5	−1.24706
$983$	−47385.7	−1.53751	−0.768753	−	0.639545i	$-0.779123\pi$
$983$	−47385.7	−1.53751	−0.768753	+	0.639545i	$0.779123\pi$
$984$	−41659.5	−1.34965
$985$	0	0
$986$	51587.7	1.66621
$987$	948.891	0.0306014
$988$	5927.78	0.190878
$989$	−20826.4	−0.669607
$990$	0	0
$991$	−8947.33	−0.286802	−0.143401	−	0.989665i	$-0.545804\pi$
$991$	−8947.33	−0.286802	−0.143401	+	0.989665i	$0.545804\pi$
$992$	−8049.67	−0.257638
$993$	22471.1	0.718127
$994$	3558.95	0.113564
$995$	0	0
$996$	19749.5	0.628299
$997$	14908.6	0.473582	0.236791	−	0.971561i	$-0.423904\pi$
$997$	14908.6	0.473582	0.236791	+	0.971561i	$0.423904\pi$
$998$	51881.4	1.64557
$999$	−1478.69	−0.0468306

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.4.a.j.1.1		2
5.4	even	2		39.4.a.b.1.2	✓	2
15.14	odd	2		117.4.a.c.1.1		2
20.19	odd	2		624.4.a.r.1.1		2
35.34	odd	2		1911.4.a.h.1.2		2
40.19	odd	2		2496.4.a.s.1.2		2
40.29	even	2		2496.4.a.bc.1.2		2
60.59	even	2		1872.4.a.t.1.2		2
65.34	odd	4		507.4.b.f.337.4		4
65.44	odd	4		507.4.b.f.337.1		4
65.64	even	2		507.4.a.f.1.1		2
195.194	odd	2		1521.4.a.s.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.a.b.1.2	✓	2	5.4	even	2
117.4.a.c.1.1		2	15.14	odd	2
507.4.a.f.1.1		2	65.64	even	2
507.4.b.f.337.1		4	65.44	odd	4
507.4.b.f.337.4		4	65.34	odd	4
624.4.a.r.1.1		2	20.19	odd	2
975.4.a.j.1.1		2	1.1	even	1	trivial
1521.4.a.s.1.2		2	195.194	odd	2
1872.4.a.t.1.2		2	60.59	even	2
1911.4.a.h.1.2		2	35.34	odd	2
2496.4.a.s.1.2		2	40.19	odd	2
2496.4.a.bc.1.2		2	40.29	even	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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	975.a (trivial)

\(f(q)\)	\(=\)	\(q-4.74166 q^{2} +3.00000 q^{3} +14.4833 q^{4} -14.2250 q^{6} +7.48331 q^{7} -30.7417 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-4.74166 q^{2} +3.00000 q^{3} +14.4833 q^{4} -14.2250 q^{6} +7.48331 q^{7} -30.7417 q^{8} +9.00000 q^{9} -66.8999 q^{11} +43.4499 q^{12} +13.0000 q^{13} -35.4833 q^{14} +29.8999 q^{16} -96.9666 q^{17} -42.6749 q^{18} +31.4833 q^{19} +22.4499 q^{21} +317.216 q^{22} -183.600 q^{23} -92.2250 q^{24} -61.6415 q^{26} +27.0000 q^{27} +108.383 q^{28} +112.200 q^{29} -77.2831 q^{31} +104.158 q^{32} -200.700 q^{33} +459.783 q^{34} +130.350 q^{36} -54.7664 q^{37} -149.283 q^{38} +39.0000 q^{39} +451.716 q^{41} -106.450 q^{42} +113.434 q^{43} -968.932 q^{44} +870.566 q^{46} +42.2670 q^{47} +89.6997 q^{48} -287.000 q^{49} -290.900 q^{51} +188.283 q^{52} +530.999 q^{53} -128.025 q^{54} -230.049 q^{56} +94.4499 q^{57} -532.015 q^{58} +219.666 q^{59} +822.865 q^{61} +366.450 q^{62} +67.3498 q^{63} -733.082 q^{64} +951.649 q^{66} +872.082 q^{67} -1404.40 q^{68} -550.799 q^{69} -100.299 q^{71} -276.675 q^{72} +165.634 q^{73} +259.684 q^{74} +455.983 q^{76} -500.633 q^{77} -184.925 q^{78} -545.266 q^{79} +81.0000 q^{81} -2141.88 q^{82} +454.534 q^{83} +325.150 q^{84} -537.864 q^{86} +336.601 q^{87} +2056.61 q^{88} -230.915 q^{89} +97.2831 q^{91} -2659.13 q^{92} -231.849 q^{93} -200.415 q^{94} +312.475 q^{96} +1089.16 q^{97} +1360.86 q^{98} -602.099 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 6 q^{3} + 14 q^{4} - 6 q^{6} - 54 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 6 * q^3 + 14 * q^4 - 6 * q^6 - 54 * q^8 + 18 * q^9	\( 2 q - 2 q^{2} + 6 q^{3} + 14 q^{4} - 6 q^{6} - 54 q^{8} + 18 q^{9} - 44 q^{11} + 42 q^{12} + 26 q^{13} - 56 q^{14} - 30 q^{16} - 164 q^{17} - 18 q^{18} + 48 q^{19} + 380 q^{22} - 8 q^{23} - 162 q^{24} - 26 q^{26} + 54 q^{27} + 112 q^{28} + 404 q^{29} + 40 q^{31} + 126 q^{32} - 132 q^{33} + 276 q^{34} + 126 q^{36} + 100 q^{37} - 104 q^{38} + 78 q^{39} + 200 q^{41} - 168 q^{42} + 616 q^{43} - 980 q^{44} + 1352 q^{46} + 324 q^{47} - 90 q^{48} - 574 q^{49} - 492 q^{51} + 182 q^{52} + 164 q^{53} - 54 q^{54} - 56 q^{56} + 144 q^{57} + 268 q^{58} + 140 q^{59} + 628 q^{61} + 688 q^{62} - 194 q^{64} + 1140 q^{66} + 472 q^{67} - 1372 q^{68} - 24 q^{69} + 428 q^{71} - 486 q^{72} + 900 q^{73} + 684 q^{74} + 448 q^{76} - 672 q^{77} - 78 q^{78} - 432 q^{79} + 162 q^{81} - 2832 q^{82} + 1388 q^{83} + 336 q^{84} + 840 q^{86} + 1212 q^{87} + 1524 q^{88} + 960 q^{89} - 2744 q^{92} + 120 q^{93} + 572 q^{94} + 378 q^{96} + 532 q^{97} + 574 q^{98} - 396 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 6 * q^3 + 14 * q^4 - 6 * q^6 - 54 * q^8 + 18 * q^9 - 44 * q^11 + 42 * q^12 + 26 * q^13 - 56 * q^14 - 30 * q^16 - 164 * q^17 - 18 * q^18 + 48 * q^19 + 380 * q^22 - 8 * q^23 - 162 * q^24 - 26 * q^26 + 54 * q^27 + 112 * q^28 + 404 * q^29 + 40 * q^31 + 126 * q^32 - 132 * q^33 + 276 * q^34 + 126 * q^36 + 100 * q^37 - 104 * q^38 + 78 * q^39 + 200 * q^41 - 168 * q^42 + 616 * q^43 - 980 * q^44 + 1352 * q^46 + 324 * q^47 - 90 * q^48 - 574 * q^49 - 492 * q^51 + 182 * q^52 + 164 * q^53 - 54 * q^54 - 56 * q^56 + 144 * q^57 + 268 * q^58 + 140 * q^59 + 628 * q^61 + 688 * q^62 - 194 * q^64 + 1140 * q^66 + 472 * q^67 - 1372 * q^68 - 24 * q^69 + 428 * q^71 - 486 * q^72 + 900 * q^73 + 684 * q^74 + 448 * q^76 - 672 * q^77 - 78 * q^78 - 432 * q^79 + 162 * q^81 - 2832 * q^82 + 1388 * q^83 + 336 * q^84 + 840 * q^86 + 1212 * q^87 + 1524 * q^88 + 960 * q^89 - 2744 * q^92 + 120 * q^93 + 572 * q^94 + 378 * q^96 + 532 * q^97 + 574 * q^98 - 396 * q^99

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