LMFDB - Embedded newform 975.4.a.j.1.2

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			1.2
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)

$f(q)$	$=$	$q+2.74166 q^{2} +3.00000 q^{3} -0.483315 q^{4} +8.22497 q^{6} -7.48331 q^{7} -23.2583 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.74166 q^{2} +3.00000 q^{3} -0.483315 q^{4} +8.22497 q^{6} -7.48331 q^{7} -23.2583 q^{8} +9.00000 q^{9} +22.8999 q^{11} -1.44994 q^{12} +13.0000 q^{13} -20.5167 q^{14} -59.8999 q^{16} -67.0334 q^{17} +24.6749 q^{18} +16.5167 q^{19} -22.4499 q^{21} +62.7836 q^{22} +175.600 q^{23} -69.7750 q^{24} +35.6415 q^{26} +27.0000 q^{27} +3.61680 q^{28} +291.800 q^{29} +117.283 q^{31} +21.8418 q^{32} +68.6997 q^{33} -183.783 q^{34} -4.34983 q^{36} +154.766 q^{37} +45.2831 q^{38} +39.0000 q^{39} -251.716 q^{41} -61.5501 q^{42} +502.566 q^{43} -11.0679 q^{44} +481.434 q^{46} +281.733 q^{47} -179.700 q^{48} -287.000 q^{49} -201.100 q^{51} -6.28309 q^{52} -366.999 q^{53} +74.0247 q^{54} +174.049 q^{56} +49.5501 q^{57} +800.015 q^{58} -79.6663 q^{59} -194.865 q^{61} +321.550 q^{62} -67.3498 q^{63} +539.082 q^{64} +188.351 q^{66} -400.082 q^{67} +32.3982 q^{68} +526.799 q^{69} +528.299 q^{71} -209.325 q^{72} +734.366 q^{73} +424.316 q^{74} -7.98276 q^{76} -171.367 q^{77} +106.925 q^{78} +113.266 q^{79} +81.0000 q^{81} -690.118 q^{82} +933.466 q^{83} +10.8504 q^{84} +1377.86 q^{86} +875.399 q^{87} -532.613 q^{88} +1190.91 q^{89} -97.2831 q^{91} -84.8699 q^{92} +351.849 q^{93} +772.415 q^{94} +65.5253 q^{96} -557.165 q^{97} -786.856 q^{98} +206.099 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.74166	0.969322	0.484661	−	0.874702i	$-0.338943\pi$
$2$	2.74166	0.969322	0.484661	+	0.874702i	$0.338943\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−0.483315	−0.0604143
$5$	0	0
$5$	0	0
$6$	8.22497	0.559638
$7$	−7.48331	−0.404061	−0.202031	−	0.979379i	$-0.564754\pi$
$7$	−7.48331	−0.404061	−0.202031	+	0.979379i	$0.564754\pi$
$8$	−23.2583	−1.02788
$9$	9.00000	0.333333
$10$	0	0
$11$	22.8999	0.627689	0.313844	−	0.949474i	$-0.398383\pi$
$11$	22.8999	0.627689	0.313844	+	0.949474i	$0.398383\pi$
$12$	−1.44994	−0.0348802
$13$	13.0000	0.277350
$13$	13.0000	0.277350
$14$	−20.5167	−0.391665
$15$	0	0
$16$	−59.8999	−0.935936
$17$	−67.0334	−0.956352	−0.478176	−	0.878264i	$-0.658702\pi$
$17$	−67.0334	−0.956352	−0.478176	+	0.878264i	$0.658702\pi$
$18$	24.6749	0.323107
$19$	16.5167	0.199431	0.0997155	−	0.995016i	$-0.468207\pi$
$19$	16.5167	0.199431	0.0997155	+	0.995016i	$0.468207\pi$
$20$	0	0
$21$	−22.4499	−0.233285
$22$	62.7836	0.608433
$23$	175.600	1.59196	0.795979	−	0.605324i	$-0.206956\pi$
$23$	175.600	1.59196	0.795979	+	0.605324i	$0.206956\pi$
$24$	−69.7750	−0.593449
$25$	0	0
$26$	35.6415	0.268842
$27$	27.0000	0.192450
$28$	3.61680	0.0244111
$29$	291.800	1.86848	0.934239	−	0.356648i	$-0.116080\pi$
$29$	291.800	1.86848	0.934239	+	0.356648i	$0.116080\pi$
$30$	0	0
$31$	117.283	0.679505	0.339753	−	0.940515i	$-0.389657\pi$
$31$	117.283	0.679505	0.339753	+	0.940515i	$0.389657\pi$
$32$	21.8418	0.120660
$33$	68.6997	0.362396
$34$	−183.783	−0.927013
$35$	0	0
$36$	−4.34983	−0.0201381
$37$	154.766	0.687661	0.343830	−	0.939032i	$-0.388276\pi$
$37$	154.766	0.687661	0.343830	+	0.939032i	$0.388276\pi$
$38$	45.2831	0.193313
$39$	39.0000	0.160128
$40$	0	0
$41$	−251.716	−0.958815	−0.479407	−	0.877592i	$-0.659148\pi$
$41$	−251.716	−0.958815	−0.479407	+	0.877592i	$0.659148\pi$
$42$	−61.5501	−0.226128
$43$	502.566	1.78234	0.891170	−	0.453669i	$-0.149885\pi$
$43$	502.566	1.78234	0.891170	+	0.453669i	$0.149885\pi$
$44$	−11.0679	−0.0379214
$45$	0	0
$46$	481.434	1.54312
$47$	281.733	0.874361	0.437181	−	0.899374i	$-0.355977\pi$
$47$	281.733	0.874361	0.437181	+	0.899374i	$0.355977\pi$
$48$	−179.700	−0.540363
$49$	−287.000	−0.836735
$50$	0	0
$51$	−201.100	−0.552150
$52$	−6.28309	−0.0167559
$53$	−366.999	−0.951154	−0.475577	−	0.879674i	$-0.657761\pi$
$53$	−366.999	−0.951154	−0.475577	+	0.879674i	$0.657761\pi$
$54$	74.0247	0.186546
$55$	0	0
$56$	174.049	0.415328
$57$	49.5501	0.115141
$58$	800.015	1.81116
$59$	−79.6663	−0.175791	−0.0878955	−	0.996130i	$-0.528014\pi$
$59$	−79.6663	−0.175791	−0.0878955	+	0.996130i	$0.528014\pi$
$60$	0	0
$61$	−194.865	−0.409016	−0.204508	−	0.978865i	$-0.565559\pi$
$61$	−194.865	−0.409016	−0.204508	+	0.978865i	$0.565559\pi$
$62$	321.550	0.658660
$63$	−67.3498	−0.134687
$64$	539.082	1.05289
$65$	0	0
$66$	188.351	0.351279
$67$	−400.082	−0.729519	−0.364759	−	0.931102i	$-0.618849\pi$
$67$	−400.082	−0.729519	−0.364759	+	0.931102i	$0.618849\pi$
$68$	32.3982	0.0577774
$69$	526.799	0.919117
$70$	0	0
$71$	528.299	0.883065	0.441532	−	0.897245i	$-0.354435\pi$
$71$	528.299	0.883065	0.441532	+	0.897245i	$0.354435\pi$
$72$	−209.325	−0.342628
$73$	734.366	1.17741	0.588706	−	0.808347i	$-0.299638\pi$
$73$	734.366	1.17741	0.588706	+	0.808347i	$0.299638\pi$
$74$	424.316	0.666565
$75$	0	0
$76$	−7.98276	−0.0120485
$77$	−171.367	−0.253625
$78$	106.925	0.155216
$79$	113.266	0.161309	0.0806545	−	0.996742i	$-0.474299\pi$
$79$	113.266	0.161309	0.0806545	+	0.996742i	$0.474299\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	−690.118	−0.929400
$83$	933.466	1.23447	0.617236	−	0.786778i	$-0.288252\pi$
$83$	933.466	1.23447	0.617236	+	0.786778i	$0.288252\pi$
$84$	10.8504	0.0140937
$85$	0	0
$86$	1377.86	1.72766
$87$	875.399	1.07877
$88$	−532.613	−0.645191
$89$	1190.91	1.41839	0.709195	−	0.705012i	$-0.249059\pi$
$89$	1190.91	1.41839	0.709195	+	0.705012i	$0.249059\pi$
$90$	0	0
$91$	−97.2831	−0.112066
$92$	−84.8699	−0.0961771
$93$	351.849	0.392313
$94$	772.415	0.847538
$95$	0	0
$96$	65.5253	0.0696630
$97$	−557.165	−0.583211	−0.291606	−	0.956539i	$-0.594189\pi$
$97$	−557.165	−0.583211	−0.291606	+	0.956539i	$0.594189\pi$
$98$	−786.856	−0.811066
$99$	206.099	0.209230
$100$	0	0
$101$	−286.766	−0.282518	−0.141259	−	0.989973i	$-0.545115\pi$
$101$	−286.766	−0.282518	−0.141259	+	0.989973i	$0.545115\pi$
$102$	−551.348	−0.535211
$103$	1911.36	1.82847	0.914234	−	0.405187i	$-0.132794\pi$
$103$	1911.36	1.82847	0.914234	+	0.405187i	$0.132794\pi$
$104$	−302.358	−0.285084
$105$	0	0
$106$	−1006.19	−0.921975
$107$	−834.334	−0.753814	−0.376907	−	0.926251i	$-0.623012\pi$
$107$	−834.334	−0.753814	−0.376907	+	0.926251i	$0.623012\pi$
$108$	−13.0495	−0.0116267
$109$	−1077.66	−0.946986	−0.473493	−	0.880798i	$-0.657007\pi$
$109$	−1077.66	−0.946986	−0.473493	+	0.880798i	$0.657007\pi$
$110$	0	0
$111$	464.299	0.397021
$112$	448.250	0.378175
$113$	166.065	0.138248	0.0691241	−	0.997608i	$-0.477980\pi$
$113$	166.065	0.138248	0.0691241	+	0.997608i	$0.477980\pi$
$114$	135.849	0.111609
$115$	0	0
$116$	−141.031	−0.112883
$117$	117.000	0.0924500
$118$	−218.418	−0.170398
$119$	501.632	0.386424
$120$	0	0
$121$	−806.595	−0.606007
$122$	−534.254	−0.396468
$123$	−755.147	−0.553572
$124$	−56.6847	−0.0410519
$125$	0	0
$126$	−184.650	−0.130555
$127$	−1296.16	−0.905637	−0.452819	−	0.891603i	$-0.649581\pi$
$127$	−1296.16	−0.905637	−0.452819	+	0.891603i	$0.649581\pi$
$128$	1303.24	0.899934
$129$	1507.70	1.02903
$130$	0	0
$131$	−197.201	−0.131523	−0.0657617	−	0.997835i	$-0.520948\pi$
$131$	−197.201	−0.131523	−0.0657617	+	0.997835i	$0.520948\pi$
$132$	−33.2036	−0.0218939
$133$	−123.600	−0.0805823
$134$	−1096.89	−0.707139
$135$	0	0
$136$	1559.09	0.983018
$137$	546.915	0.341066	0.170533	−	0.985352i	$-0.445451\pi$
$137$	546.915	0.341066	0.170533	+	0.985352i	$0.445451\pi$
$138$	1444.30	0.890921
$139$	609.666	0.372023	0.186012	−	0.982548i	$-0.440444\pi$
$139$	609.666	0.372023	0.186012	+	0.982548i	$0.440444\pi$
$140$	0	0
$141$	845.199	0.504813
$142$	1448.42	0.855974
$143$	297.699	0.174090
$144$	−539.099	−0.311979
$145$	0	0
$146$	2013.38	1.14129
$147$	−861.000	−0.483089
$148$	−74.8009	−0.0415446
$149$	−2165.08	−1.19040	−0.595202	−	0.803576i	$-0.702928\pi$
$149$	−2165.08	−1.19040	−0.595202	+	0.803576i	$0.702928\pi$
$150$	0	0
$151$	−846.549	−0.456233	−0.228116	−	0.973634i	$-0.573257\pi$
$151$	−846.549	−0.456233	−0.228116	+	0.973634i	$0.573257\pi$
$152$	−384.151	−0.204992
$153$	−603.300	−0.318784
$154$	−469.830	−0.245844
$155$	0	0
$156$	−18.8493	−0.00967404
$157$	−1653.60	−0.840581	−0.420291	−	0.907390i	$-0.638072\pi$
$157$	−1653.60	−0.840581	−0.420291	+	0.907390i	$0.638072\pi$
$158$	310.536	0.156360
$159$	−1101.00	−0.549149
$160$	0	0
$161$	−1314.07	−0.643248
$162$	222.074	0.107702
$163$	2866.51	1.37744	0.688720	−	0.725027i	$-0.258173\pi$
$163$	2866.51	1.37744	0.688720	+	0.725027i	$0.258173\pi$
$164$	121.658	0.0579262
$165$	0	0
$166$	2559.24	1.19660
$167$	−729.066	−0.337825	−0.168913	−	0.985631i	$-0.554026\pi$
$167$	−729.066	−0.337825	−0.168913	+	0.985631i	$0.554026\pi$
$168$	522.148	0.239789
$169$	169.000	0.0769231
$170$	0	0
$171$	148.650	0.0664770
$172$	−242.898	−0.107679
$173$	3834.83	1.68530	0.842650	−	0.538462i	$-0.180995\pi$
$173$	3834.83	1.68530	0.842650	+	0.538462i	$0.180995\pi$
$174$	2400.05	1.04567
$175$	0	0
$176$	−1371.70	−0.587476
$177$	−238.999	−0.101493
$178$	3265.08	1.37488
$179$	−283.862	−0.118530	−0.0592649	−	0.998242i	$-0.518876\pi$
$179$	−283.862	−0.118530	−0.0592649	+	0.998242i	$0.518876\pi$
$180$	0	0
$181$	2363.60	0.970634	0.485317	−	0.874338i	$-0.338704\pi$
$181$	2363.60	0.970634	0.485317	+	0.874338i	$0.338704\pi$
$182$	−266.717	−0.108628
$183$	−584.596	−0.236145
$184$	−4084.15	−1.63635
$185$	0	0
$186$	964.650	0.380277
$187$	−1535.06	−0.600291
$188$	−136.166	−0.0528240
$189$	−202.049	−0.0777616
$190$	0	0
$191$	2514.26	0.952491	0.476246	−	0.879312i	$-0.341997\pi$
$191$	2514.26	0.952491	0.476246	+	0.879312i	$0.341997\pi$
$192$	1617.25	0.607889
$193$	−2420.73	−0.902839	−0.451420	−	0.892312i	$-0.649082\pi$
$193$	−2420.73	−0.902839	−0.451420	+	0.892312i	$0.649082\pi$
$194$	−1527.55	−0.565320
$195$	0	0
$196$	138.711	0.0505508
$197$	4633.65	1.67581	0.837903	−	0.545819i	$-0.183781\pi$
$197$	4633.65	1.67581	0.837903	+	0.545819i	$0.183781\pi$
$198$	565.053	0.202811
$199$	3054.17	1.08796	0.543980	−	0.839098i	$-0.316917\pi$
$199$	3054.17	1.08796	0.543980	+	0.839098i	$0.316917\pi$
$200$	0	0
$201$	−1200.25	−0.421188
$202$	−786.215	−0.273851
$203$	−2183.63	−0.754979
$204$	97.1947	0.0333578
$205$	0	0
$206$	5240.30	1.77237
$207$	1580.40	0.530653
$208$	−778.699	−0.259582
$209$	378.230	0.125181
$210$	0	0
$211$	−4031.60	−1.31539	−0.657694	−	0.753285i	$-0.728468\pi$
$211$	−4031.60	−1.31539	−0.657694	+	0.753285i	$0.728468\pi$
$212$	177.376	0.0574634
$213$	1584.90	0.509838
$214$	−2287.46	−0.730689
$215$	0	0
$216$	−627.975	−0.197816
$217$	−877.666	−0.274562
$218$	−2954.59	−0.917935
$219$	2203.10	0.679779
$220$	0	0
$221$	−871.434	−0.265244
$222$	1272.95	0.384841
$223$	−3784.95	−1.13659	−0.568294	−	0.822826i	$-0.692396\pi$
$223$	−3784.95	−1.13659	−0.568294	+	0.822826i	$0.692396\pi$
$224$	−163.449	−0.0487539
$225$	0	0
$226$	455.292	0.134007
$227$	−2013.83	−0.588821	−0.294411	−	0.955679i	$-0.595123\pi$
$227$	−2013.83	−0.588821	−0.294411	+	0.955679i	$0.595123\pi$
$228$	−23.9483	−0.00695620
$229$	−3050.73	−0.880340	−0.440170	−	0.897915i	$-0.645082\pi$
$229$	−3050.73	−0.880340	−0.440170	+	0.897915i	$0.645082\pi$
$230$	0	0
$231$	−514.101	−0.146430
$232$	−6786.78	−1.92058
$233$	−5587.49	−1.57103	−0.785513	−	0.618846i	$-0.787601\pi$
$233$	−5587.49	−1.57103	−0.785513	+	0.618846i	$0.787601\pi$
$234$	320.774	0.0896139
$235$	0	0
$236$	38.5039	0.0106203
$237$	339.798	0.0931317
$238$	1375.30	0.374570
$239$	−1335.69	−0.361501	−0.180750	−	0.983529i	$-0.557853\pi$
$239$	−1335.69	−0.361501	−0.180750	+	0.983529i	$0.557853\pi$
$240$	0	0
$241$	−571.558	−0.152769	−0.0763845	−	0.997078i	$-0.524338\pi$
$241$	−571.558	−0.152769	−0.0763845	+	0.997078i	$0.524338\pi$
$242$	−2211.41	−0.587416
$243$	243.000	0.0641500
$244$	94.1813	0.0247104
$245$	0	0
$246$	−2070.36	−0.536590
$247$	214.717	0.0553122
$248$	−2727.81	−0.698452
$249$	2800.40	0.712723
$250$	0	0
$251$	4088.60	1.02817	0.514084	−	0.857740i	$-0.328132\pi$
$251$	4088.60	1.02817	0.514084	+	0.857740i	$0.328132\pi$
$252$	32.5512	0.00813703
$253$	4021.21	0.999254
$254$	−3553.64	−0.877854
$255$	0	0
$256$	−739.607	−0.180568
$257$	−3050.23	−0.740342	−0.370171	−	0.928964i	$-0.620701\pi$
$257$	−3050.23	−0.740342	−0.370171	+	0.928964i	$0.620701\pi$
$258$	4133.59	0.997466
$259$	−1158.17	−0.277857
$260$	0	0
$261$	2626.20	0.622826
$262$	−540.659	−0.127489
$263$	−5770.99	−1.35306	−0.676530	−	0.736415i	$-0.736517\pi$
$263$	−5770.99	−1.35306	−0.676530	+	0.736415i	$0.736517\pi$
$264$	−1597.84	−0.372501
$265$	0	0
$266$	−338.868	−0.0781102
$267$	3572.74	0.818908
$268$	193.365	0.0440734
$269$	−2079.40	−0.471314	−0.235657	−	0.971836i	$-0.575724\pi$
$269$	−2079.40	−0.471314	−0.235657	+	0.971836i	$0.575724\pi$
$270$	0	0
$271$	6012.00	1.34761	0.673807	−	0.738908i	$-0.264658\pi$
$271$	6012.00	1.34761	0.673807	+	0.738908i	$0.264658\pi$
$272$	4015.29	0.895084
$273$	−291.849	−0.0647015
$274$	1499.45	0.330603
$275$	0	0
$276$	−254.610	−0.0555279
$277$	735.201	0.159473	0.0797364	−	0.996816i	$-0.474592\pi$
$277$	735.201	0.159473	0.0797364	+	0.996816i	$0.474592\pi$
$278$	1671.50	0.360610
$279$	1055.55	0.226502
$280$	0	0
$281$	−1902.92	−0.403981	−0.201990	−	0.979387i	$-0.564741\pi$
$281$	−1902.92	−0.403981	−0.201990	+	0.979387i	$0.564741\pi$
$282$	2317.25	0.489326
$283$	−2125.71	−0.446502	−0.223251	−	0.974761i	$-0.571667\pi$
$283$	−2125.71	−0.446502	−0.223251	+	0.974761i	$0.571667\pi$
$284$	−255.335	−0.0533498
$285$	0	0
$286$	816.187	0.168749
$287$	1883.67	0.387420
$288$	196.576	0.0402200
$289$	−419.527	−0.0853913
$290$	0	0
$291$	−1671.49	−0.336717
$292$	−354.930	−0.0711325
$293$	1641.03	0.327200	0.163600	−	0.986527i	$-0.447689\pi$
$293$	1641.03	0.327200	0.163600	+	0.986527i	$0.447689\pi$
$294$	−2360.57	−0.468269
$295$	0	0
$296$	−3599.61	−0.706835
$297$	618.297	0.120799
$298$	−5935.91	−1.15389
$299$	2282.79	0.441530
$300$	0	0
$301$	−3760.86	−0.720174
$302$	−2320.95	−0.442237
$303$	−860.299	−0.163112
$304$	−989.348	−0.186655
$305$	0	0
$306$	−1654.04	−0.309004
$307$	3373.27	0.627111	0.313555	−	0.949570i	$-0.398480\pi$
$307$	3373.27	0.627111	0.313555	+	0.949570i	$0.398480\pi$
$308$	82.8242	0.0153226
$309$	5734.09	1.05567
$310$	0	0
$311$	−868.525	−0.158359	−0.0791793	−	0.996860i	$-0.525230\pi$
$311$	−868.525	−0.158359	−0.0791793	+	0.996860i	$0.525230\pi$
$312$	−907.075	−0.164593
$313$	4343.19	0.784319	0.392159	−	0.919897i	$-0.371728\pi$
$313$	4343.19	0.784319	0.392159	+	0.919897i	$0.371728\pi$
$314$	−4533.59	−0.814794
$315$	0	0
$316$	−54.7431	−0.00974537
$317$	3277.65	0.580730	0.290365	−	0.956916i	$-0.406223\pi$
$317$	3277.65	0.580730	0.290365	+	0.956916i	$0.406223\pi$
$318$	−3018.56	−0.532302
$319$	6682.18	1.17282
$320$	0	0
$321$	−2503.00	−0.435215
$322$	−3602.72	−0.623515
$323$	−1107.17	−0.190726
$324$	−39.1485	−0.00671271
$325$	0	0
$326$	7859.00	1.33518
$327$	−3232.99	−0.546743
$328$	5854.49	0.985550
$329$	−2108.30	−0.353295
$330$	0	0
$331$	5589.62	0.928197	0.464099	−	0.885784i	$-0.346378\pi$
$331$	5589.62	0.928197	0.464099	+	0.885784i	$0.346378\pi$
$332$	−451.158	−0.0745798
$333$	1392.90	0.229220
$334$	−1998.85	−0.327461
$335$	0	0
$336$	1344.75	0.218340
$337$	−901.544	−0.145728	−0.0728638	−	0.997342i	$-0.523214\pi$
$337$	−901.544	−0.145728	−0.0728638	+	0.997342i	$0.523214\pi$
$338$	463.340	0.0745633
$339$	498.194	0.0798176
$340$	0	0
$341$	2685.77	0.426518
$342$	407.548	0.0644376
$343$	4714.49	0.742153
$344$	−11688.9	−1.83204
$345$	0	0
$346$	10513.8	1.63360
$347$	812.318	0.125670	0.0628350	−	0.998024i	$-0.479986\pi$
$347$	812.318	0.125670	0.0628350	+	0.998024i	$0.479986\pi$
$348$	−423.093	−0.0651730
$349$	4437.96	0.680683	0.340342	−	0.940302i	$-0.389457\pi$
$349$	4437.96	0.680683	0.340342	+	0.940302i	$0.389457\pi$
$350$	0	0
$351$	351.000	0.0533761
$352$	500.174	0.0757368
$353$	−7115.35	−1.07284	−0.536419	−	0.843952i	$-0.680223\pi$
$353$	−7115.35	−1.07284	−0.536419	+	0.843952i	$0.680223\pi$
$354$	−655.253	−0.0983794
$355$	0	0
$356$	−575.587	−0.0856911
$357$	1504.90	0.223102
$358$	−778.253	−0.114894
$359$	4693.98	0.690081	0.345040	−	0.938588i	$-0.387865\pi$
$359$	4693.98	0.690081	0.345040	+	0.938588i	$0.387865\pi$
$360$	0	0
$361$	−6586.20	−0.960227
$362$	6480.17	0.940857
$363$	−2419.79	−0.349878
$364$	47.0184	0.00677042
$365$	0	0
$366$	−1602.76	−0.228901
$367$	−9243.98	−1.31480	−0.657400	−	0.753542i	$-0.728344\pi$
$367$	−9243.98	−1.31480	−0.657400	+	0.753542i	$0.728344\pi$
$368$	−10518.4	−1.48997
$369$	−2265.44	−0.319605
$370$	0	0
$371$	2746.37	0.384324
$372$	−170.054	−0.0237013
$373$	4311.99	0.598569	0.299285	−	0.954164i	$-0.403252\pi$
$373$	4311.99	0.598569	0.299285	+	0.954164i	$0.403252\pi$
$374$	−4208.60	−0.581876
$375$	0	0
$376$	−6552.64	−0.898741
$377$	3793.40	0.518223
$378$	−553.951	−0.0753760
$379$	−2382.73	−0.322936	−0.161468	−	0.986878i	$-0.551623\pi$
$379$	−2382.73	−0.322936	−0.161468	+	0.986878i	$0.551623\pi$
$380$	0	0
$381$	−3888.49	−0.522870
$382$	6893.25	0.923271
$383$	−4845.81	−0.646499	−0.323250	−	0.946314i	$-0.604775\pi$
$383$	−4845.81	−0.646499	−0.323250	+	0.946314i	$0.604775\pi$
$384$	3909.73	0.519577
$385$	0	0
$386$	−6636.81	−0.875142
$387$	4523.10	0.594113
$388$	269.286	0.0352343
$389$	9561.50	1.24624	0.623120	−	0.782127i	$-0.285865\pi$
$389$	9561.50	1.24624	0.623120	+	0.782127i	$0.285865\pi$
$390$	0	0
$391$	−11771.0	−1.52247
$392$	6675.14	0.860066
$393$	−591.604	−0.0759350
$394$	12703.9	1.62440
$395$	0	0
$396$	−99.6107	−0.0126405
$397$	7440.11	0.940575	0.470287	−	0.882513i	$-0.344150\pi$
$397$	7440.11	0.940575	0.470287	+	0.882513i	$0.344150\pi$
$398$	8373.48	1.05458
$399$	−370.799	−0.0465242
$400$	0	0
$401$	−8687.80	−1.08192	−0.540958	−	0.841050i	$-0.681938\pi$
$401$	−8687.80	−1.08192	−0.540958	+	0.841050i	$0.681938\pi$
$402$	−3290.66	−0.408267
$403$	1524.68	0.188461
$404$	138.598	0.0170681
$405$	0	0
$406$	−5986.76	−0.731818
$407$	3544.13	0.431637
$408$	4677.26	0.567546
$409$	2556.10	0.309024	0.154512	−	0.987991i	$-0.450619\pi$
$409$	2556.10	0.309024	0.154512	+	0.987991i	$0.450619\pi$
$410$	0	0
$411$	1640.74	0.196915
$412$	−923.790	−0.110466
$413$	596.168	0.0710303
$414$	4332.90	0.514374
$415$	0	0
$416$	283.943	0.0334650
$417$	1829.00	0.214788
$418$	1036.98	0.121340
$419$	−3347.46	−0.390296	−0.195148	−	0.980774i	$-0.562519\pi$
$419$	−3347.46	−0.390296	−0.195148	+	0.980774i	$0.562519\pi$
$420$	0	0
$421$	−1854.48	−0.214684	−0.107342	−	0.994222i	$-0.534234\pi$
$421$	−1854.48	−0.214684	−0.107342	+	0.994222i	$0.534234\pi$
$422$	−11053.3	−1.27503
$423$	2535.60	0.291454
$424$	8535.79	0.977675
$425$	0	0
$426$	4345.25	0.494197
$427$	1458.24	0.165267
$428$	403.246	0.0455412
$429$	893.096	0.100511
$430$	0	0
$431$	−14043.1	−1.56945	−0.784725	−	0.619844i	$-0.787196\pi$
$431$	−14043.1	−1.56945	−0.784725	+	0.619844i	$0.787196\pi$
$432$	−1617.30	−0.180121
$433$	−3086.47	−0.342555	−0.171278	−	0.985223i	$-0.554790\pi$
$433$	−3086.47	−0.342555	−0.171278	+	0.985223i	$0.554790\pi$
$434$	−2406.26	−0.266139
$435$	0	0
$436$	520.851	0.0572116
$437$	2900.32	0.317486
$438$	6040.14	0.658925
$439$	2837.68	0.308508	0.154254	−	0.988031i	$-0.450703\pi$
$439$	2837.68	0.308508	0.154254	+	0.988031i	$0.450703\pi$
$440$	0	0
$441$	−2583.00	−0.278912
$442$	−2389.17	−0.257107
$443$	−18309.4	−1.96367	−0.981834	−	0.189744i	$-0.939234\pi$
$443$	−18309.4	−1.96367	−0.981834	+	0.189744i	$0.939234\pi$
$444$	−224.403	−0.0239858
$445$	0	0
$446$	−10377.0	−1.10172
$447$	−6495.24	−0.687281
$448$	−4034.12	−0.425433
$449$	13861.2	1.45690	0.728451	−	0.685098i	$-0.240241\pi$
$449$	13861.2	1.45690	0.728451	+	0.685098i	$0.240241\pi$
$450$	0	0
$451$	−5764.26	−0.601837
$452$	−80.2614	−0.00835217
$453$	−2539.65	−0.263406
$454$	−5521.23	−0.570758
$455$	0	0
$456$	−1152.45	−0.118352
$457$	8990.36	0.920243	0.460122	−	0.887856i	$-0.347806\pi$
$457$	8990.36	0.920243	0.460122	+	0.887856i	$0.347806\pi$
$458$	−8364.05	−0.853333
$459$	−1809.90	−0.184050
$460$	0	0
$461$	−3406.90	−0.344198	−0.172099	−	0.985080i	$-0.555055\pi$
$461$	−3406.90	−0.344198	−0.172099	+	0.985080i	$0.555055\pi$
$462$	−1409.49	−0.141938
$463$	7498.45	0.752662	0.376331	−	0.926485i	$-0.377186\pi$
$463$	7498.45	0.752662	0.376331	+	0.926485i	$0.377186\pi$
$464$	−17478.8	−1.74878
$465$	0	0
$466$	−15319.0	−1.52283
$467$	−7711.38	−0.764112	−0.382056	−	0.924139i	$-0.624784\pi$
$467$	−7711.38	−0.764112	−0.382056	+	0.924139i	$0.624784\pi$
$468$	−56.5478	−0.00558531
$469$	2993.94	0.294770
$470$	0	0
$471$	−4960.79	−0.485310
$472$	1852.91	0.180693
$473$	11508.7	1.11875
$474$	931.608	0.0902747
$475$	0	0
$476$	−242.446	−0.0233456
$477$	−3302.99	−0.317051
$478$	−3662.01	−0.350411
$479$	−9439.82	−0.900451	−0.450226	−	0.892915i	$-0.648656\pi$
$479$	−9439.82	−0.900451	−0.450226	+	0.892915i	$0.648656\pi$
$480$	0	0
$481$	2011.96	0.190723
$482$	−1567.02	−0.148082
$483$	−3942.20	−0.371380
$484$	389.839	0.0366115
$485$	0	0
$486$	666.223	0.0621821
$487$	6156.20	0.572821	0.286411	−	0.958107i	$-0.407538\pi$
$487$	6156.20	0.572821	0.286411	+	0.958107i	$0.407538\pi$
$488$	4532.25	0.420420
$489$	8599.54	0.795265
$490$	0	0
$491$	3842.74	0.353198	0.176599	−	0.984283i	$-0.443490\pi$
$491$	3842.74	0.353198	0.176599	+	0.984283i	$0.443490\pi$
$492$	364.974	0.0334437
$493$	−19560.3	−1.78692
$494$	588.680	0.0536153
$495$	0	0
$496$	−7025.24	−0.635973
$497$	−3953.43	−0.356812
$498$	7677.73	0.690858
$499$	−12842.4	−1.15211	−0.576056	−	0.817410i	$-0.695409\pi$
$499$	−12842.4	−1.15211	−0.576056	+	0.817410i	$0.695409\pi$
$500$	0	0
$501$	−2187.20	−0.195043
$502$	11209.5	0.996627
$503$	−8580.11	−0.760573	−0.380287	−	0.924869i	$-0.624175\pi$
$503$	−8580.11	−0.760573	−0.380287	+	0.924869i	$0.624175\pi$
$504$	1566.45	0.138443
$505$	0	0
$506$	11024.8	0.968599
$507$	507.000	0.0444116
$508$	626.455	0.0547135
$509$	−43.5957	−0.00379635	−0.00189818	−	0.999998i	$-0.500604\pi$
$509$	−43.5957	−0.00379635	−0.00189818	+	0.999998i	$0.500604\pi$
$510$	0	0
$511$	−5495.49	−0.475746
$512$	−12453.7	−1.07496
$513$	445.951	0.0383805
$514$	−8362.68	−0.717630
$515$	0	0
$516$	−728.693	−0.0621684
$517$	6451.66	0.548827
$518$	−3175.29	−0.269333
$519$	11504.5	0.973008
$520$	0	0
$521$	11368.1	0.955939	0.477969	−	0.878377i	$-0.341373\pi$
$521$	11368.1	0.955939	0.477969	+	0.878377i	$0.341373\pi$
$522$	7200.14	0.603719
$523$	5229.53	0.437230	0.218615	−	0.975811i	$-0.429846\pi$
$523$	5229.53	0.437230	0.218615	+	0.975811i	$0.429846\pi$
$524$	95.3103	0.00794590
$525$	0	0
$526$	−15822.1	−1.31155
$527$	−7861.88	−0.649846
$528$	−4115.10	−0.339180
$529$	18668.2	1.53433
$530$	0	0
$531$	−716.997	−0.0585970
$532$	59.7375	0.00486832
$533$	−3272.31	−0.265927
$534$	9795.24	0.793786
$535$	0	0
$536$	9305.24	0.749860
$537$	−851.586	−0.0684333
$538$	−5701.01	−0.456855
$539$	−6572.27	−0.525209
$540$	0	0
$541$	−6567.99	−0.521959	−0.260980	−	0.965344i	$-0.584046\pi$
$541$	−6567.99	−0.521959	−0.260980	+	0.965344i	$0.584046\pi$
$542$	16482.9	1.30627
$543$	7090.79	0.560396
$544$	−1464.13	−0.115393
$545$	0	0
$546$	−800.151	−0.0627166
$547$	13675.7	1.06897	0.534487	−	0.845177i	$-0.320505\pi$
$547$	13675.7	1.06897	0.534487	+	0.845177i	$0.320505\pi$
$548$	−264.332	−0.0206053
$549$	−1753.79	−0.136339
$550$	0	0
$551$	4819.57	0.372632
$552$	−12252.5	−0.944745
$553$	−847.604	−0.0651786
$554$	2015.67	0.154581
$555$	0	0
$556$	−294.661	−0.0224755
$557$	−4527.96	−0.344445	−0.172222	−	0.985058i	$-0.555095\pi$
$557$	−4527.96	−0.344445	−0.172222	+	0.985058i	$0.555095\pi$
$558$	2893.95	0.219553
$559$	6533.36	0.494332
$560$	0	0
$561$	−4605.17	−0.346578
$562$	−5217.15	−0.391588
$563$	−18441.8	−1.38051	−0.690256	−	0.723566i	$-0.742502\pi$
$563$	−18441.8	−1.38051	−0.690256	+	0.723566i	$0.742502\pi$
$564$	−408.497	−0.0304979
$565$	0	0
$566$	−5827.96	−0.432804
$567$	−606.148	−0.0448957
$568$	−12287.4	−0.907687
$569$	−13553.5	−0.998578	−0.499289	−	0.866436i	$-0.666405\pi$
$569$	−13553.5	−0.998578	−0.499289	+	0.866436i	$0.666405\pi$
$570$	0	0
$571$	14815.5	1.08583	0.542915	−	0.839788i	$-0.317321\pi$
$571$	14815.5	1.08583	0.542915	+	0.839788i	$0.317321\pi$
$572$	−143.882	−0.0105175
$573$	7542.79	0.549921
$574$	5164.37	0.375534
$575$	0	0
$576$	4851.74	0.350965
$577$	−21596.2	−1.55816	−0.779081	−	0.626923i	$-0.784314\pi$
$577$	−21596.2	−1.55816	−0.779081	+	0.626923i	$0.784314\pi$
$578$	−1150.20	−0.0827716
$579$	−7262.19	−0.521254
$580$	0	0
$581$	−6985.42	−0.498802
$582$	−4582.66	−0.326387
$583$	−8404.23	−0.597029
$584$	−17080.1	−1.21024
$585$	0	0
$586$	4499.13	0.317163
$587$	918.801	0.0646047	0.0323024	−	0.999478i	$-0.489716\pi$
$587$	918.801	0.0646047	0.0323024	+	0.999478i	$0.489716\pi$
$588$	416.134	0.0291855
$589$	1937.13	0.135514
$590$	0	0
$591$	13900.9	0.967527
$592$	−9270.49	−0.643606
$593$	−19816.0	−1.37226	−0.686128	−	0.727481i	$-0.740691\pi$
$593$	−19816.0	−1.37226	−0.686128	+	0.727481i	$0.740691\pi$
$594$	1695.16	0.117093
$595$	0	0
$596$	1046.42	0.0719175
$597$	9162.50	0.628134
$598$	6258.64	0.427985
$599$	−5141.86	−0.350736	−0.175368	−	0.984503i	$-0.556111\pi$
$599$	−5141.86	−0.350736	−0.175368	+	0.984503i	$0.556111\pi$
$600$	0	0
$601$	12380.9	0.840312	0.420156	−	0.907452i	$-0.361975\pi$
$601$	12380.9	0.840312	0.420156	+	0.907452i	$0.361975\pi$
$602$	−10311.0	−0.698081
$603$	−3600.74	−0.243173
$604$	409.150	0.0275630
$605$	0	0
$606$	−2358.65	−0.158108
$607$	23717.0	1.58590	0.792951	−	0.609286i	$-0.208544\pi$
$607$	23717.0	1.58590	0.792951	+	0.609286i	$0.208544\pi$
$608$	360.754	0.0240633
$609$	−6550.89	−0.435887
$610$	0	0
$611$	3662.53	0.242504
$612$	291.584	0.0192591
$613$	26157.1	1.72345	0.861726	−	0.507373i	$-0.169383\pi$
$613$	26157.1	1.72345	0.861726	+	0.507373i	$0.169383\pi$
$614$	9248.36	0.607872
$615$	0	0
$616$	3985.71	0.260696
$617$	−23613.9	−1.54077	−0.770387	−	0.637576i	$-0.779937\pi$
$617$	−23613.9	−1.54077	−0.770387	+	0.637576i	$0.779937\pi$
$618$	15720.9	1.02328
$619$	23345.4	1.51588	0.757940	−	0.652324i	$-0.226206\pi$
$619$	23345.4	1.51588	0.757940	+	0.652324i	$0.226206\pi$
$620$	0	0
$621$	4741.19	0.306372
$622$	−2381.20	−0.153501
$623$	−8911.99	−0.573116
$624$	−2336.10	−0.149870
$625$	0	0
$626$	11907.5	0.760258
$627$	1134.69	0.0722730
$628$	799.207	0.0507832
$629$	−10374.5	−0.657645
$630$	0	0
$631$	15245.7	0.961841	0.480921	−	0.876764i	$-0.340302\pi$
$631$	15245.7	0.961841	0.480921	+	0.876764i	$0.340302\pi$
$632$	−2634.38	−0.165807
$633$	−12094.8	−0.759439
$634$	8986.20	0.562914
$635$	0	0
$636$	532.128	0.0331765
$637$	−3731.00	−0.232068
$638$	18320.3	1.13684
$639$	4754.69	0.294355
$640$	0	0
$641$	10192.7	0.628063	0.314032	−	0.949413i	$-0.398320\pi$
$641$	10192.7	0.628063	0.314032	+	0.949413i	$0.398320\pi$
$642$	−6862.37	−0.421863
$643$	5506.31	0.337710	0.168855	−	0.985641i	$-0.445993\pi$
$643$	5506.31	0.337710	0.168855	+	0.985641i	$0.445993\pi$
$644$	635.108	0.0388614
$645$	0	0
$646$	−3035.48	−0.184875
$647$	13297.5	0.808005	0.404003	−	0.914758i	$-0.367619\pi$
$647$	13297.5	0.808005	0.404003	+	0.914758i	$0.367619\pi$
$648$	−1883.93	−0.114209
$649$	−1824.35	−0.110342
$650$	0	0
$651$	−2633.00	−0.158518
$652$	−1385.43	−0.0832171
$653$	12440.2	0.745519	0.372760	−	0.927928i	$-0.378412\pi$
$653$	12440.2	0.745519	0.372760	+	0.927928i	$0.378412\pi$
$654$	−8863.76	−0.529970
$655$	0	0
$656$	15077.7	0.897389
$657$	6609.29	0.392470
$658$	−5780.23	−0.342457
$659$	−9562.87	−0.565276	−0.282638	−	0.959227i	$-0.591209\pi$
$659$	−9562.87	−0.565276	−0.282638	+	0.959227i	$0.591209\pi$
$660$	0	0
$661$	2409.69	0.141795	0.0708973	−	0.997484i	$-0.477414\pi$
$661$	2409.69	0.141795	0.0708973	+	0.997484i	$0.477414\pi$
$662$	15324.8	0.899722
$663$	−2614.30	−0.153139
$664$	−21710.9	−1.26889
$665$	0	0
$666$	3818.85	0.222188
$667$	51239.9	2.97454
$668$	352.368	0.0204095
$669$	−11354.9	−0.656209
$670$	0	0
$671$	−4462.40	−0.256735
$672$	−490.346	−0.0281481
$673$	−7929.02	−0.454147	−0.227074	−	0.973878i	$-0.572916\pi$
$673$	−7929.02	−0.454147	−0.227074	+	0.973878i	$0.572916\pi$
$674$	−2471.72	−0.141257
$675$	0	0
$676$	−81.6802	−0.00464726
$677$	2628.26	0.149206	0.0746030	−	0.997213i	$-0.476231\pi$
$677$	2628.26	0.149206	0.0746030	+	0.997213i	$0.476231\pi$
$678$	1365.88	0.0773690
$679$	4169.44	0.235653
$680$	0	0
$681$	−6041.48	−0.339956
$682$	7363.46	0.413433
$683$	−10021.5	−0.561437	−0.280719	−	0.959790i	$-0.590573\pi$
$683$	−10021.5	−0.561437	−0.280719	+	0.959790i	$0.590573\pi$
$684$	−71.8448	−0.00401616
$685$	0	0
$686$	12925.5	0.719385
$687$	−9152.18	−0.508264
$688$	−30103.7	−1.66816
$689$	−4770.99	−0.263803
$690$	0	0
$691$	23987.2	1.32057	0.660286	−	0.751014i	$-0.270435\pi$
$691$	23987.2	1.32057	0.660286	+	0.751014i	$0.270435\pi$
$692$	−1853.43	−0.101816
$693$	−1542.30	−0.0845415
$694$	2227.10	0.121815
$695$	0	0
$696$	−20360.3	−1.10885
$697$	16873.4	0.916964
$698$	12167.4	0.659801
$699$	−16762.5	−0.907032
$700$	0	0
$701$	−3763.71	−0.202787	−0.101393	−	0.994846i	$-0.532330\pi$
$701$	−3763.71	−0.202787	−0.101393	+	0.994846i	$0.532330\pi$
$702$	962.322	0.0517386
$703$	2556.23	0.137141
$704$	12344.9	0.660890
$705$	0	0
$706$	−19507.8	−1.03993
$707$	2145.96	0.114155
$708$	115.512	0.00613163
$709$	−36047.8	−1.90946	−0.954728	−	0.297479i	$-0.903854\pi$
$709$	−36047.8	−1.90946	−0.954728	+	0.297479i	$0.903854\pi$
$710$	0	0
$711$	1019.39	0.0537696
$712$	−27698.7	−1.45794
$713$	20594.9	1.08174
$714$	4125.91	0.216258
$715$	0	0
$716$	137.195	0.00716090
$717$	−4007.08	−0.208713
$718$	12869.3	0.668910
$719$	−3944.18	−0.204580	−0.102290	−	0.994755i	$-0.532617\pi$
$719$	−3944.18	−0.204580	−0.102290	+	0.994755i	$0.532617\pi$
$720$	0	0
$721$	−14303.3	−0.738812
$722$	−18057.1	−0.930770
$723$	−1714.68	−0.0882012
$724$	−1142.36	−0.0586402
$725$	0	0
$726$	−6634.22	−0.339145
$727$	20447.8	1.04315	0.521573	−	0.853206i	$-0.325345\pi$
$727$	20447.8	1.04315	0.521573	+	0.853206i	$0.325345\pi$
$728$	2262.64	0.115191
$729$	729.000	0.0370370
$730$	0	0
$731$	−33688.7	−1.70454
$732$	282.544	0.0142666
$733$	13536.2	0.682089	0.341045	−	0.940047i	$-0.389219\pi$
$733$	13536.2	0.682089	0.341045	+	0.940047i	$0.389219\pi$
$734$	−25343.8	−1.27447
$735$	0	0
$736$	3835.40	0.192085
$737$	−9161.83	−0.457911
$738$	−6211.07	−0.309800
$739$	15839.1	0.788433	0.394217	−	0.919018i	$-0.371016\pi$
$739$	15839.1	0.788433	0.394217	+	0.919018i	$0.371016\pi$
$740$	0	0
$741$	644.151	0.0319345
$742$	7529.60	0.372534
$743$	1664.92	0.0822075	0.0411037	−	0.999155i	$-0.486913\pi$
$743$	1664.92	0.0822075	0.0411037	+	0.999155i	$0.486913\pi$
$744$	−8183.43	−0.403252
$745$	0	0
$746$	11822.0	0.580206
$747$	8401.19	0.411491
$748$	741.916	0.0362662
$749$	6243.58	0.304587
$750$	0	0
$751$	22399.1	1.08835	0.544177	−	0.838970i	$-0.316842\pi$
$751$	22399.1	1.08835	0.544177	+	0.838970i	$0.316842\pi$
$752$	−16875.8	−0.818346
$753$	12265.8	0.593613
$754$	10400.2	0.502325
$755$	0	0
$756$	97.6535	0.00469792
$757$	−23798.9	−1.14265	−0.571326	−	0.820723i	$-0.693571\pi$
$757$	−23798.9	−1.14265	−0.571326	+	0.820723i	$0.693571\pi$
$758$	−6532.64	−0.313029
$759$	12063.6	0.576920
$760$	0	0
$761$	13693.5	0.652285	0.326142	−	0.945321i	$-0.394251\pi$
$761$	13693.5	0.652285	0.326142	+	0.945321i	$0.394251\pi$
$762$	−10660.9	−0.506829
$763$	8064.50	0.382640
$764$	−1215.18	−0.0575441
$765$	0	0
$766$	−13285.5	−0.626666
$767$	−1035.66	−0.0487556
$768$	−2218.82	−0.104251
$769$	16299.9	0.764358	0.382179	−	0.924088i	$-0.375174\pi$
$769$	16299.9	0.764358	0.382179	+	0.924088i	$0.375174\pi$
$770$	0	0
$771$	−9150.68	−0.427437
$772$	1169.97	0.0545444
$773$	−33532.2	−1.56024	−0.780122	−	0.625628i	$-0.784843\pi$
$773$	−33532.2	−1.56024	−0.780122	+	0.625628i	$0.784843\pi$
$774$	12400.8	0.575887
$775$	0	0
$776$	12958.7	0.599473
$777$	−3474.50	−0.160421
$778$	26214.3	1.20801
$779$	−4157.51	−0.191217
$780$	0	0
$781$	12098.0	0.554290
$782$	−32272.1	−1.47577
$783$	7878.59	0.359589
$784$	17191.3	0.783130
$785$	0	0
$786$	−1621.98	−0.0736055
$787$	−16163.3	−0.732097	−0.366049	−	0.930596i	$-0.619290\pi$
$787$	−16163.3	−0.732097	−0.366049	+	0.930596i	$0.619290\pi$
$788$	−2239.51	−0.101243
$789$	−17313.0	−0.781189
$790$	0	0
$791$	−1242.71	−0.0558607
$792$	−4793.52	−0.215064
$793$	−2533.25	−0.113441
$794$	20398.2	0.911720
$795$	0	0
$796$	−1476.12	−0.0657284
$797$	39636.4	1.76160	0.880798	−	0.473492i	$-0.157007\pi$
$797$	39636.4	1.76160	0.880798	+	0.473492i	$0.157007\pi$
$798$	−1016.60	−0.0450969
$799$	−18885.5	−0.836197
$800$	0	0
$801$	10718.2	0.472797
$802$	−23819.0	−1.04872
$803$	16816.9	0.739048
$804$	580.096	0.0254458
$805$	0	0
$806$	4180.15	0.182679
$807$	−6238.21	−0.272113
$808$	6669.71	0.290396
$809$	−23811.2	−1.03481	−0.517403	−	0.855742i	$-0.673101\pi$
$809$	−23811.2	−1.03481	−0.517403	+	0.855742i	$0.673101\pi$
$810$	0	0
$811$	27218.6	1.17851	0.589256	−	0.807946i	$-0.299421\pi$
$811$	27218.6	1.17851	0.589256	+	0.807946i	$0.299421\pi$
$812$	1055.38	0.0456116
$813$	18036.0	0.778045
$814$	9716.80	0.418395
$815$	0	0
$816$	12045.9	0.516777
$817$	8300.73	0.355454
$818$	7007.94	0.299544
$819$	−875.548	−0.0373555
$820$	0	0
$821$	−43094.8	−1.83193	−0.915967	−	0.401253i	$-0.868575\pi$
$821$	−43094.8	−1.83193	−0.915967	+	0.401253i	$0.868575\pi$
$822$	4498.36	0.190874
$823$	−26541.1	−1.12414	−0.562068	−	0.827091i	$-0.689994\pi$
$823$	−26541.1	−1.12414	−0.562068	+	0.827091i	$0.689994\pi$
$824$	−44455.1	−1.87945
$825$	0	0
$826$	1634.49	0.0688512
$827$	44898.7	1.88788	0.943942	−	0.330112i	$-0.107087\pi$
$827$	44898.7	1.88788	0.943942	+	0.330112i	$0.107087\pi$
$828$	−763.829	−0.0320590
$829$	−7137.48	−0.299029	−0.149514	−	0.988760i	$-0.547771\pi$
$829$	−7137.48	−0.299029	−0.149514	+	0.988760i	$0.547771\pi$
$830$	0	0
$831$	2205.60	0.0920717
$832$	7008.06	0.292020
$833$	19238.6	0.800213
$834$	5014.49	0.208198
$835$	0	0
$836$	−182.804	−0.00756270
$837$	3166.64	0.130771
$838$	−9177.59	−0.378323
$839$	−4387.17	−0.180527	−0.0902634	−	0.995918i	$-0.528771\pi$
$839$	−4387.17	−0.180527	−0.0902634	+	0.995918i	$0.528771\pi$
$840$	0	0
$841$	60758.1	2.49121
$842$	−5084.36	−0.208098
$843$	−5708.76	−0.233239
$844$	1948.53	0.0794683
$845$	0	0
$846$	6951.74	0.282513
$847$	6036.01	0.244864
$848$	21983.2	0.890219
$849$	−6377.12	−0.257788
$850$	0	0
$851$	27176.9	1.09473
$852$	−766.004	−0.0308015
$853$	9328.85	0.374459	0.187230	−	0.982316i	$-0.440049\pi$
$853$	9328.85	0.374459	0.187230	+	0.982316i	$0.440049\pi$
$854$	3997.99	0.160197
$855$	0	0
$856$	19405.2	0.774833
$857$	5010.39	0.199710	0.0998552	−	0.995002i	$-0.468162\pi$
$857$	5010.39	0.199710	0.0998552	+	0.995002i	$0.468162\pi$
$858$	2448.56	0.0974272
$859$	30233.4	1.20088	0.600438	−	0.799672i	$-0.294993\pi$
$859$	30233.4	1.20088	0.600438	+	0.799672i	$0.294993\pi$
$860$	0	0
$861$	5651.01	0.223677
$862$	−38501.4	−1.52130
$863$	−4334.93	−0.170988	−0.0854940	−	0.996339i	$-0.527247\pi$
$863$	−4334.93	−0.170988	−0.0854940	+	0.996339i	$0.527247\pi$
$864$	589.728	0.0232210
$865$	0	0
$866$	−8462.05	−0.332047
$867$	−1258.58	−0.0493007
$868$	424.189	0.0165875
$869$	2593.78	0.101252
$870$	0	0
$871$	−5201.06	−0.202332
$872$	25064.7	0.973391
$873$	−5014.48	−0.194404
$874$	7951.69	0.307746
$875$	0	0
$876$	−1064.79	−0.0410684
$877$	−34683.3	−1.33543	−0.667716	−	0.744416i	$-0.732728\pi$
$877$	−34683.3	−1.33543	−0.667716	+	0.744416i	$0.732728\pi$
$878$	7779.95	0.299044
$879$	4923.08	0.188909
$880$	0	0
$881$	−18269.2	−0.698642	−0.349321	−	0.937003i	$-0.613588\pi$
$881$	−18269.2	−0.698642	−0.349321	+	0.937003i	$0.613588\pi$
$882$	−7081.70	−0.270355
$883$	14592.0	0.556128	0.278064	−	0.960563i	$-0.410307\pi$
$883$	14592.0	0.556128	0.278064	+	0.960563i	$0.410307\pi$
$884$	421.177	0.0160246
$885$	0	0
$886$	−50198.0	−1.90343
$887$	−30459.3	−1.15301	−0.576507	−	0.817092i	$-0.695585\pi$
$887$	−30459.3	−1.15301	−0.576507	+	0.817092i	$0.695585\pi$
$888$	−10798.8	−0.408091
$889$	9699.60	0.365933
$890$	0	0
$891$	1854.89	0.0697432
$892$	1829.32	0.0686662
$893$	4653.30	0.174375
$894$	−17807.7	−0.666196
$895$	0	0
$896$	−9752.58	−0.363628
$897$	6848.38	0.254917
$898$	38002.6	1.41221
$899$	34223.2	1.26964
$900$	0	0
$901$	24601.2	0.909638
$902$	−15803.6	−0.583374
$903$	−11282.6	−0.415793
$904$	−3862.39	−0.142103
$905$	0	0
$906$	−6962.84	−0.255326
$907$	9364.89	0.342840	0.171420	−	0.985198i	$-0.445164\pi$
$907$	9364.89	0.342840	0.171420	+	0.985198i	$0.445164\pi$
$908$	973.313	0.0355733
$909$	−2580.90	−0.0941727
$910$	0	0
$911$	32479.8	1.18123	0.590616	−	0.806952i	$-0.298885\pi$
$911$	32479.8	1.18123	0.590616	+	0.806952i	$0.298885\pi$
$912$	−2968.04	−0.107765
$913$	21376.3	0.774864
$914$	24648.5	0.892012
$915$	0	0
$916$	1474.46	0.0531851
$917$	1475.72	0.0531435
$918$	−4962.13	−0.178404
$919$	295.958	0.0106232	0.00531161	−	0.999986i	$-0.498309\pi$
$919$	295.958	0.0106232	0.00531161	+	0.999986i	$0.498309\pi$
$920$	0	0
$921$	10119.8	0.362062
$922$	−9340.56	−0.333639
$923$	6867.89	0.244918
$924$	248.473	0.00884649
$925$	0	0
$926$	20558.2	0.729572
$927$	17202.3	0.609489
$928$	6373.42	0.225450
$929$	−5620.38	−0.198492	−0.0992458	−	0.995063i	$-0.531643\pi$
$929$	−5620.38	−0.198492	−0.0992458	+	0.995063i	$0.531643\pi$
$930$	0	0
$931$	−4740.29	−0.166871
$932$	2700.52	0.0949125
$933$	−2605.58	−0.0914284
$934$	−21142.0	−0.740670
$935$	0	0
$936$	−2721.23	−0.0950278
$937$	32583.1	1.13601	0.568006	−	0.823024i	$-0.307715\pi$
$937$	32583.1	1.13601	0.568006	+	0.823024i	$0.307715\pi$
$938$	8208.35	0.285727
$939$	13029.6	0.452827
$940$	0	0
$941$	8812.99	0.305308	0.152654	−	0.988280i	$-0.451218\pi$
$941$	8812.99	0.305308	0.152654	+	0.988280i	$0.451218\pi$
$942$	−13600.8	−0.470422
$943$	−44201.2	−1.52639
$944$	4772.00	0.164529
$945$	0	0
$946$	31552.9	1.08443
$947$	−13426.8	−0.460732	−0.230366	−	0.973104i	$-0.573992\pi$
$947$	−13426.8	−0.460732	−0.230366	+	0.973104i	$0.573992\pi$
$948$	−164.229	−0.00562649
$949$	9546.76	0.326555
$950$	0	0
$951$	9832.96	0.335285
$952$	−11667.1	−0.397199
$953$	13394.6	0.455293	0.227647	−	0.973744i	$-0.426897\pi$
$953$	13394.6	0.455293	0.227647	+	0.973744i	$0.426897\pi$
$954$	−9055.67	−0.307325
$955$	0	0
$956$	645.560	0.0218398
$957$	20046.5	0.677129
$958$	−25880.7	−0.872828
$959$	−4092.74	−0.137812
$960$	0	0
$961$	−16035.7	−0.538273
$962$	5516.11	0.184872
$963$	−7509.00	−0.251271
$964$	276.243	0.00922944
$965$	0	0
$966$	−10808.2	−0.359986
$967$	−45590.8	−1.51613	−0.758066	−	0.652178i	$-0.773856\pi$
$967$	−45590.8	−1.51613	−0.758066	+	0.652178i	$0.773856\pi$
$968$	18760.1	0.622904
$969$	−3321.51	−0.110116
$970$	0	0
$971$	264.763	0.00875041	0.00437521	−	0.999990i	$-0.498607\pi$
$971$	264.763	0.00875041	0.00437521	+	0.999990i	$0.498607\pi$
$972$	−117.445	−0.00387558
$973$	−4562.32	−0.150320
$974$	16878.2	0.555248
$975$	0	0
$976$	11672.4	0.382812
$977$	−610.521	−0.0199921	−0.00999606	−	0.999950i	$-0.503182\pi$
$977$	−610.521	−0.0199921	−0.00999606	+	0.999950i	$0.503182\pi$
$978$	23577.0	0.770868
$979$	27271.8	0.890308
$980$	0	0
$981$	−9698.98	−0.315662
$982$	10535.5	0.342363
$983$	57829.7	1.87638	0.938190	−	0.346121i	$-0.112501\pi$
$983$	57829.7	1.87638	0.938190	+	0.346121i	$0.112501\pi$
$984$	17563.5	0.569007
$985$	0	0
$986$	−53627.7	−1.73210
$987$	−6324.89	−0.203975
$988$	−103.776	−0.00334165
$989$	88250.4	2.83741
$990$	0	0
$991$	−56780.7	−1.82008	−0.910039	−	0.414522i	$-0.863949\pi$
$991$	−56780.7	−1.82008	−0.910039	+	0.414522i	$0.863949\pi$
$992$	2561.67	0.0819890
$993$	16768.9	0.535895
$994$	−10838.9	−0.345866
$995$	0	0
$996$	−1353.47	−0.0430587
$997$	−18616.6	−0.591369	−0.295684	−	0.955286i	$-0.595548\pi$
$997$	−18616.6	−0.591369	−0.295684	+	0.955286i	$0.595548\pi$
$998$	−35209.4	−1.11677
$999$	4178.69	0.132340

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.4.a.j.1.2		2
5.4	even	2		39.4.a.b.1.1	✓	2
15.14	odd	2		117.4.a.c.1.2		2
20.19	odd	2		624.4.a.r.1.2		2
35.34	odd	2		1911.4.a.h.1.1		2
40.19	odd	2		2496.4.a.s.1.1		2
40.29	even	2		2496.4.a.bc.1.1		2
60.59	even	2		1872.4.a.t.1.1		2
65.34	odd	4		507.4.b.f.337.2		4
65.44	odd	4		507.4.b.f.337.3		4
65.64	even	2		507.4.a.f.1.2		2
195.194	odd	2		1521.4.a.s.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.a.b.1.1	✓	2	5.4	even	2
117.4.a.c.1.2		2	15.14	odd	2
507.4.a.f.1.2		2	65.64	even	2
507.4.b.f.337.2		4	65.34	odd	4
507.4.b.f.337.3		4	65.44	odd	4
624.4.a.r.1.2		2	20.19	odd	2
975.4.a.j.1.2		2	1.1	even	1	trivial
1521.4.a.s.1.1		2	195.194	odd	2
1872.4.a.t.1.1		2	60.59	even	2
1911.4.a.h.1.1		2	35.34	odd	2
2496.4.a.s.1.1		2	40.19	odd	2
2496.4.a.bc.1.1		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)

\(f(q)\)	\(=\)	\(q+2.74166 q^{2} +3.00000 q^{3} -0.483315 q^{4} +8.22497 q^{6} -7.48331 q^{7} -23.2583 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.74166 q^{2} +3.00000 q^{3} -0.483315 q^{4} +8.22497 q^{6} -7.48331 q^{7} -23.2583 q^{8} +9.00000 q^{9} +22.8999 q^{11} -1.44994 q^{12} +13.0000 q^{13} -20.5167 q^{14} -59.8999 q^{16} -67.0334 q^{17} +24.6749 q^{18} +16.5167 q^{19} -22.4499 q^{21} +62.7836 q^{22} +175.600 q^{23} -69.7750 q^{24} +35.6415 q^{26} +27.0000 q^{27} +3.61680 q^{28} +291.800 q^{29} +117.283 q^{31} +21.8418 q^{32} +68.6997 q^{33} -183.783 q^{34} -4.34983 q^{36} +154.766 q^{37} +45.2831 q^{38} +39.0000 q^{39} -251.716 q^{41} -61.5501 q^{42} +502.566 q^{43} -11.0679 q^{44} +481.434 q^{46} +281.733 q^{47} -179.700 q^{48} -287.000 q^{49} -201.100 q^{51} -6.28309 q^{52} -366.999 q^{53} +74.0247 q^{54} +174.049 q^{56} +49.5501 q^{57} +800.015 q^{58} -79.6663 q^{59} -194.865 q^{61} +321.550 q^{62} -67.3498 q^{63} +539.082 q^{64} +188.351 q^{66} -400.082 q^{67} +32.3982 q^{68} +526.799 q^{69} +528.299 q^{71} -209.325 q^{72} +734.366 q^{73} +424.316 q^{74} -7.98276 q^{76} -171.367 q^{77} +106.925 q^{78} +113.266 q^{79} +81.0000 q^{81} -690.118 q^{82} +933.466 q^{83} +10.8504 q^{84} +1377.86 q^{86} +875.399 q^{87} -532.613 q^{88} +1190.91 q^{89} -97.2831 q^{91} -84.8699 q^{92} +351.849 q^{93} +772.415 q^{94} +65.5253 q^{96} -557.165 q^{97} -786.856 q^{98} +206.099 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 6 q^{3} + 14 q^{4} - 6 q^{6} - 54 q^{8} + 18 q^{9}+O(q^{10}) \) 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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