LMFDB - Embedded newform 525.4.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,4,Mod(1,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, 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("525.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	525.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:	$30.9760027530$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{65}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 16 $ x^2 - x - 16
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$4.53113$ of defining polynomial
Character	$\chi$	$=$	525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.53113 q^{2} -3.00000 q^{3} +12.5311 q^{4} +13.5934 q^{6} +7.00000 q^{7} -20.5311 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-4.53113 q^{2} -3.00000 q^{3} +12.5311 q^{4} +13.5934 q^{6} +7.00000 q^{7} -20.5311 q^{8} +9.00000 q^{9} -19.0623 q^{11} -37.5934 q^{12} +2.93774 q^{13} -31.7179 q^{14} -7.21984 q^{16} +6.49806 q^{17} -40.7802 q^{18} -5.43580 q^{19} -21.0000 q^{21} +86.3735 q^{22} -49.3774 q^{23} +61.5934 q^{24} -13.3113 q^{26} -27.0000 q^{27} +87.7179 q^{28} -291.494 q^{29} +244.307 q^{31} +196.963 q^{32} +57.1868 q^{33} -29.4436 q^{34} +112.780 q^{36} +193.121 q^{37} +24.6303 q^{38} -8.81323 q^{39} +315.113 q^{41} +95.1537 q^{42} +300.996 q^{43} -238.872 q^{44} +223.735 q^{46} -86.5058 q^{47} +21.6595 q^{48} +49.0000 q^{49} -19.4942 q^{51} +36.8132 q^{52} -509.677 q^{53} +122.340 q^{54} -143.718 q^{56} +16.3074 q^{57} +1320.80 q^{58} -83.3852 q^{59} -5.25291 q^{61} -1106.99 q^{62} +63.0000 q^{63} -834.706 q^{64} -259.121 q^{66} -205.992 q^{67} +81.4281 q^{68} +148.132 q^{69} +1004.31 q^{71} -184.780 q^{72} +1007.29 q^{73} -875.055 q^{74} -68.1168 q^{76} -133.436 q^{77} +39.9339 q^{78} -863.237 q^{79} +81.0000 q^{81} -1427.82 q^{82} -1334.72 q^{83} -263.154 q^{84} -1363.85 q^{86} +874.483 q^{87} +391.370 q^{88} +326.249 q^{89} +20.5642 q^{91} -618.755 q^{92} -732.922 q^{93} +391.969 q^{94} -590.889 q^{96} -1526.77 q^{97} -222.025 q^{98} -171.560 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 6 q^{3} + 17 q^{4} + 3 q^{6} + 14 q^{7} - 33 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q - q^2 - 6 * q^3 + 17 * q^4 + 3 * q^6 + 14 * q^7 - 33 * q^8 + 18 * q^9	$ 2 q - q^{2} - 6 q^{3} + 17 q^{4} + 3 q^{6} + 14 q^{7} - 33 q^{8} + 18 q^{9} - 22 q^{11} - 51 q^{12} + 22 q^{13} - 7 q^{14} - 87 q^{16} - 116 q^{17} - 9 q^{18} + 102 q^{19} - 42 q^{21} + 76 q^{22} - 260 q^{23} + 99 q^{24} + 54 q^{26} - 54 q^{27} + 119 q^{28} - 196 q^{29} + 150 q^{31} + 15 q^{32} + 66 q^{33} - 462 q^{34} + 153 q^{36} + 96 q^{37} + 404 q^{38} - 66 q^{39} - 176 q^{41} + 21 q^{42} + 344 q^{43} - 252 q^{44} - 520 q^{46} - 560 q^{47} + 261 q^{48} + 98 q^{49} + 348 q^{51} + 122 q^{52} - 326 q^{53} + 27 q^{54} - 231 q^{56} - 306 q^{57} + 1658 q^{58} - 844 q^{59} - 204 q^{61} - 1440 q^{62} + 126 q^{63} - 839 q^{64} - 228 q^{66} + 104 q^{67} - 466 q^{68} + 780 q^{69} + 1670 q^{71} - 297 q^{72} + 386 q^{73} - 1218 q^{74} + 412 q^{76} - 154 q^{77} - 162 q^{78} - 888 q^{79} + 162 q^{81} - 3162 q^{82} - 928 q^{83} - 357 q^{84} - 1212 q^{86} + 588 q^{87} + 428 q^{88} + 588 q^{89} + 154 q^{91} - 1560 q^{92} - 450 q^{93} - 1280 q^{94} - 45 q^{96} - 522 q^{97} - 49 q^{98} - 198 q^{99}+O(q^{100}) $ 2 * q - q^2 - 6 * q^3 + 17 * q^4 + 3 * q^6 + 14 * q^7 - 33 * q^8 + 18 * q^9 - 22 * q^11 - 51 * q^12 + 22 * q^13 - 7 * q^14 - 87 * q^16 - 116 * q^17 - 9 * q^18 + 102 * q^19 - 42 * q^21 + 76 * q^22 - 260 * q^23 + 99 * q^24 + 54 * q^26 - 54 * q^27 + 119 * q^28 - 196 * q^29 + 150 * q^31 + 15 * q^32 + 66 * q^33 - 462 * q^34 + 153 * q^36 + 96 * q^37 + 404 * q^38 - 66 * q^39 - 176 * q^41 + 21 * q^42 + 344 * q^43 - 252 * q^44 - 520 * q^46 - 560 * q^47 + 261 * q^48 + 98 * q^49 + 348 * q^51 + 122 * q^52 - 326 * q^53 + 27 * q^54 - 231 * q^56 - 306 * q^57 + 1658 * q^58 - 844 * q^59 - 204 * q^61 - 1440 * q^62 + 126 * q^63 - 839 * q^64 - 228 * q^66 + 104 * q^67 - 466 * q^68 + 780 * q^69 + 1670 * q^71 - 297 * q^72 + 386 * q^73 - 1218 * q^74 + 412 * q^76 - 154 * q^77 - 162 * q^78 - 888 * q^79 + 162 * q^81 - 3162 * q^82 - 928 * q^83 - 357 * q^84 - 1212 * q^86 + 588 * q^87 + 428 * q^88 + 588 * q^89 + 154 * q^91 - 1560 * q^92 - 450 * q^93 - 1280 * q^94 - 45 * q^96 - 522 * q^97 - 49 * q^98 - 198 * 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 $

$2$	−4.53113	−1.60200	−0.800998	−	0.598667i	$-0.795697\pi$
$2$	−4.53113	−1.60200	−0.800998	+	0.598667i	$0.795697\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	12.5311	1.56639
$5$	0	0
$5$	0	0
$6$	13.5934	0.924913
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−20.5311	−0.907356
$9$	9.00000	0.333333
$10$	0	0
$11$	−19.0623	−0.522499	−0.261249	−	0.965271i	$-0.584135\pi$
$11$	−19.0623	−0.522499	−0.261249	+	0.965271i	$0.584135\pi$
$12$	−37.5934	−0.904356
$13$	2.93774	0.0626756	0.0313378	−	0.999509i	$-0.490023\pi$
$13$	2.93774	0.0626756	0.0313378	+	0.999509i	$0.490023\pi$
$14$	−31.7179	−0.605498
$15$	0	0
$16$	−7.21984	−0.112810
$17$	6.49806	0.0927066	0.0463533	−	0.998925i	$-0.485240\pi$
$17$	6.49806	0.0927066	0.0463533	+	0.998925i	$0.485240\pi$
$18$	−40.7802	−0.533999
$19$	−5.43580	−0.0656347	−0.0328173	−	0.999461i	$-0.510448\pi$
$19$	−5.43580	−0.0656347	−0.0328173	+	0.999461i	$0.510448\pi$
$20$	0	0
$21$	−21.0000	−0.218218
$22$	86.3735	0.837041
$23$	−49.3774	−0.447648	−0.223824	−	0.974630i	$-0.571854\pi$
$23$	−49.3774	−0.447648	−0.223824	+	0.974630i	$0.571854\pi$
$24$	61.5934	0.523862
$25$	0	0
$26$	−13.3113	−0.100406
$27$	−27.0000	−0.192450
$28$	87.7179	0.592040
$29$	−291.494	−1.86652	−0.933261	−	0.359200i	$-0.883050\pi$
$29$	−291.494	−1.86652	−0.933261	+	0.359200i	$0.883050\pi$
$30$	0	0
$31$	244.307	1.41545	0.707724	−	0.706489i	$-0.249722\pi$
$31$	244.307	1.41545	0.707724	+	0.706489i	$0.249722\pi$
$32$	196.963	1.08808
$33$	57.1868	0.301665
$34$	−29.4436	−0.148516
$35$	0	0
$36$	112.780	0.522130
$37$	193.121	0.858077	0.429038	−	0.903286i	$-0.358853\pi$
$37$	193.121	0.858077	0.429038	+	0.903286i	$0.358853\pi$
$38$	24.6303	0.105147
$39$	−8.81323	−0.0361858
$40$	0	0
$41$	315.113	1.20030	0.600151	−	0.799887i	$-0.295107\pi$
$41$	315.113	1.20030	0.600151	+	0.799887i	$0.295107\pi$
$42$	95.1537	0.349584
$43$	300.996	1.06748	0.533738	−	0.845650i	$-0.320787\pi$
$43$	300.996	1.06748	0.533738	+	0.845650i	$0.320787\pi$
$44$	−238.872	−0.818437
$45$	0	0
$46$	223.735	0.717130
$47$	−86.5058	−0.268472	−0.134236	−	0.990949i	$-0.542858\pi$
$47$	−86.5058	−0.268472	−0.134236	+	0.990949i	$0.542858\pi$
$48$	21.6595	0.0651309
$49$	49.0000	0.142857
$50$	0	0
$51$	−19.4942	−0.0535242
$52$	36.8132	0.0981745
$53$	−509.677	−1.32093	−0.660467	−	0.750855i	$-0.729642\pi$
$53$	−509.677	−1.32093	−0.660467	+	0.750855i	$0.729642\pi$
$54$	122.340	0.308304
$55$	0	0
$56$	−143.718	−0.342948
$57$	16.3074	0.0378942
$58$	1320.80	2.99016
$59$	−83.3852	−0.183997	−0.0919985	−	0.995759i	$-0.529326\pi$
$59$	−83.3852	−0.183997	−0.0919985	+	0.995759i	$0.529326\pi$
$60$	0	0
$61$	−5.25291	−0.0110257	−0.00551283	−	0.999985i	$-0.501755\pi$
$61$	−5.25291	−0.0110257	−0.00551283	+	0.999985i	$0.501755\pi$
$62$	−1106.99	−2.26754
$63$	63.0000	0.125988
$64$	−834.706	−1.63029
$65$	0	0
$66$	−259.121	−0.483266
$67$	−205.992	−0.375611	−0.187806	−	0.982206i	$-0.560138\pi$
$67$	−205.992	−0.375611	−0.187806	+	0.982206i	$0.560138\pi$
$68$	81.4281	0.145215
$69$	148.132	0.258450
$70$	0	0
$71$	1004.31	1.67872	0.839362	−	0.543573i	$-0.182929\pi$
$71$	1004.31	1.67872	0.839362	+	0.543573i	$0.182929\pi$
$72$	−184.780	−0.302452
$73$	1007.29	1.61499	0.807494	−	0.589876i	$-0.200823\pi$
$73$	1007.29	1.61499	0.807494	+	0.589876i	$0.200823\pi$
$74$	−875.055	−1.37464
$75$	0	0
$76$	−68.1168	−0.102810
$77$	−133.436	−0.197486
$78$	39.9339	0.0579695
$79$	−863.237	−1.22939	−0.614695	−	0.788765i	$-0.710721\pi$
$79$	−863.237	−1.22939	−0.614695	+	0.788765i	$0.710721\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	−1427.82	−1.92288
$83$	−1334.72	−1.76512	−0.882560	−	0.470200i	$-0.844182\pi$
$83$	−1334.72	−1.76512	−0.882560	+	0.470200i	$0.844182\pi$
$84$	−263.154	−0.341815
$85$	0	0
$86$	−1363.85	−1.71009
$87$	874.483	1.07764
$88$	391.370	0.474093
$89$	326.249	0.388565	0.194283	−	0.980946i	$-0.437762\pi$
$89$	326.249	0.388565	0.194283	+	0.980946i	$0.437762\pi$
$90$	0	0
$91$	20.5642	0.0236892
$92$	−618.755	−0.701192
$93$	−732.922	−0.817210
$94$	391.969	0.430091
$95$	0	0
$96$	−590.889	−0.628202
$97$	−1526.77	−1.59815	−0.799075	−	0.601232i	$-0.794677\pi$
$97$	−1526.77	−1.59815	−0.799075	+	0.601232i	$0.794677\pi$
$98$	−222.025	−0.228857
$99$	−171.560	−0.174166
$100$	0	0
$101$	96.8716	0.0954365	0.0477182	−	0.998861i	$-0.484805\pi$
$101$	96.8716	0.0954365	0.0477182	+	0.998861i	$0.484805\pi$
$102$	88.3307	0.0857455
$103$	−1321.99	−1.26466	−0.632329	−	0.774700i	$-0.717901\pi$
$103$	−1321.99	−1.26466	−0.632329	+	0.774700i	$0.717901\pi$
$104$	−60.3152	−0.0568691
$105$	0	0
$106$	2309.41	2.11613
$107$	−1745.71	−1.57724	−0.788619	−	0.614883i	$-0.789203\pi$
$107$	−1745.71	−1.57724	−0.788619	+	0.614883i	$0.789203\pi$
$108$	−338.340	−0.301452
$109$	476.856	0.419032	0.209516	−	0.977805i	$-0.432811\pi$
$109$	476.856	0.419032	0.209516	+	0.977805i	$0.432811\pi$
$110$	0	0
$111$	−579.362	−0.495411
$112$	−50.5389	−0.0426382
$113$	−1641.65	−1.36666	−0.683332	−	0.730108i	$-0.739470\pi$
$113$	−1641.65	−1.36666	−0.683332	+	0.730108i	$0.739470\pi$
$114$	−73.8910	−0.0607064
$115$	0	0
$116$	−3652.75	−2.92370
$117$	26.4397	0.0208919
$118$	377.829	0.294763
$119$	45.4864	0.0350398
$120$	0	0
$121$	−967.630	−0.726995
$122$	23.8016	0.0176631
$123$	−945.339	−0.692994
$124$	3061.45	2.21715
$125$	0	0
$126$	−285.461	−0.201833
$127$	844.016	0.589719	0.294859	−	0.955541i	$-0.404727\pi$
$127$	844.016	0.589719	0.294859	+	0.955541i	$0.404727\pi$
$128$	2206.46	1.52363
$129$	−902.988	−0.616308
$130$	0	0
$131$	−2796.20	−1.86493	−0.932463	−	0.361265i	$-0.882345\pi$
$131$	−2796.20	−1.86493	−0.932463	+	0.361265i	$0.882345\pi$
$132$	716.615	0.472525
$133$	−38.0506	−0.0248076
$134$	933.377	0.601728
$135$	0	0
$136$	−133.413	−0.0841179
$137$	2057.13	1.28287	0.641433	−	0.767179i	$-0.278340\pi$
$137$	2057.13	1.28287	0.641433	+	0.767179i	$0.278340\pi$
$138$	−671.206	−0.414035
$139$	−1745.12	−1.06489	−0.532444	−	0.846465i	$-0.678726\pi$
$139$	−1745.12	−1.06489	−0.532444	+	0.846465i	$0.678726\pi$
$140$	0	0
$141$	259.517	0.155002
$142$	−4550.65	−2.68931
$143$	−56.0000	−0.0327479
$144$	−64.9786	−0.0376033
$145$	0	0
$146$	−4564.15	−2.58720
$147$	−147.000	−0.0824786
$148$	2420.02	1.34408
$149$	−1173.57	−0.645254	−0.322627	−	0.946526i	$-0.604566\pi$
$149$	−1173.57	−0.645254	−0.322627	+	0.946526i	$0.604566\pi$
$150$	0	0
$151$	1540.07	0.829994	0.414997	−	0.909823i	$-0.363783\pi$
$151$	1540.07	0.829994	0.414997	+	0.909823i	$0.363783\pi$
$152$	111.603	0.0595540
$153$	58.4826	0.0309022
$154$	604.615	0.316372
$155$	0	0
$156$	−110.440	−0.0566811
$157$	2544.53	1.29348	0.646738	−	0.762712i	$-0.276133\pi$
$157$	2544.53	1.29348	0.646738	+	0.762712i	$0.276133\pi$
$158$	3911.44	1.96948
$159$	1529.03	0.762642
$160$	0	0
$161$	−345.642	−0.169195
$162$	−367.021	−0.178000
$163$	594.708	0.285774	0.142887	−	0.989739i	$-0.454361\pi$
$163$	594.708	0.285774	0.142887	+	0.989739i	$0.454361\pi$
$164$	3948.72	1.88014
$165$	0	0
$166$	6047.81	2.82772
$167$	−928.498	−0.430236	−0.215118	−	0.976588i	$-0.569014\pi$
$167$	−928.498	−0.430236	−0.215118	+	0.976588i	$0.569014\pi$
$168$	431.154	0.198001
$169$	−2188.37	−0.996072
$170$	0	0
$171$	−48.9222	−0.0218782
$172$	3771.82	1.67209
$173$	315.642	0.138716	0.0693578	−	0.997592i	$-0.477905\pi$
$173$	315.642	0.138716	0.0693578	+	0.997592i	$0.477905\pi$
$174$	−3962.39	−1.72637
$175$	0	0
$176$	137.626	0.0589431
$177$	250.156	0.106231
$178$	−1478.28	−0.622480
$179$	−1445.49	−0.603581	−0.301791	−	0.953374i	$-0.597584\pi$
$179$	−1445.49	−0.603581	−0.301791	+	0.953374i	$0.597584\pi$
$180$	0	0
$181$	−1843.81	−0.757180	−0.378590	−	0.925564i	$-0.623591\pi$
$181$	−1843.81	−0.757180	−0.378590	+	0.925564i	$0.623591\pi$
$182$	−93.1790	−0.0379499
$183$	15.7587	0.00636567
$184$	1013.77	0.406176
$185$	0	0
$186$	3320.97	1.30917
$187$	−123.868	−0.0484391
$188$	−1084.02	−0.420532
$189$	−189.000	−0.0727393
$190$	0	0
$191$	−244.074	−0.0924637	−0.0462318	−	0.998931i	$-0.514721\pi$
$191$	−244.074	−0.0924637	−0.0462318	+	0.998931i	$0.514721\pi$
$192$	2504.12	0.941246
$193$	1733.03	0.646355	0.323178	−	0.946338i	$-0.395249\pi$
$193$	1733.03	0.646355	0.323178	+	0.946338i	$0.395249\pi$
$194$	6918.01	2.56023
$195$	0	0
$196$	614.025	0.223770
$197$	−358.230	−0.129557	−0.0647787	−	0.997900i	$-0.520634\pi$
$197$	−358.230	−0.129557	−0.0647787	+	0.997900i	$0.520634\pi$
$198$	777.362	0.279014
$199$	−3203.63	−1.14120	−0.570601	−	0.821227i	$-0.693290\pi$
$199$	−3203.63	−1.14120	−0.570601	+	0.821227i	$0.693290\pi$
$200$	0	0
$201$	617.977	0.216859
$202$	−438.938	−0.152889
$203$	−2040.46	−0.705479
$204$	−244.284	−0.0838398
$205$	0	0
$206$	5990.12	2.02598
$207$	−444.397	−0.149216
$208$	−21.2100	−0.00707044
$209$	103.619	0.0342940
$210$	0	0
$211$	4943.16	1.61280	0.806401	−	0.591369i	$-0.201412\pi$
$211$	4943.16	1.61280	0.806401	+	0.591369i	$0.201412\pi$
$212$	−6386.83	−2.06910
$213$	−3012.92	−0.969211
$214$	7910.05	2.52673
$215$	0	0
$216$	554.340	0.174621
$217$	1710.15	0.534989
$218$	−2160.70	−0.671288
$219$	−3021.86	−0.932414
$220$	0	0
$221$	19.0896	0.00581044
$222$	2625.16	0.793646
$223$	−3160.15	−0.948965	−0.474482	−	0.880265i	$-0.657365\pi$
$223$	−3160.15	−0.948965	−0.474482	+	0.880265i	$0.657365\pi$
$224$	1378.74	0.411255
$225$	0	0
$226$	7438.51	2.18939
$227$	3651.11	1.06755	0.533773	−	0.845628i	$-0.320774\pi$
$227$	3651.11	1.06755	0.533773	+	0.845628i	$0.320774\pi$
$228$	204.350	0.0593571
$229$	−4083.70	−1.17842	−0.589210	−	0.807980i	$-0.700561\pi$
$229$	−4083.70	−1.17842	−0.589210	+	0.807980i	$0.700561\pi$
$230$	0	0
$231$	400.307	0.114019
$232$	5984.70	1.69360
$233$	3682.51	1.03540	0.517702	−	0.855561i	$-0.326788\pi$
$233$	3682.51	1.03540	0.517702	+	0.855561i	$0.326788\pi$
$234$	−119.802	−0.0334687
$235$	0	0
$236$	−1044.91	−0.288211
$237$	2589.71	0.709789
$238$	−206.105	−0.0561336
$239$	2658.78	0.719591	0.359796	−	0.933031i	$-0.382846\pi$
$239$	2658.78	0.719591	0.359796	+	0.933031i	$0.382846\pi$
$240$	0	0
$241$	−4820.39	−1.28842	−0.644209	−	0.764850i	$-0.722813\pi$
$241$	−4820.39	−1.28842	−0.644209	+	0.764850i	$0.722813\pi$
$242$	4384.46	1.16464
$243$	−243.000	−0.0641500
$244$	−65.8249	−0.0172705
$245$	0	0
$246$	4283.45	1.11017
$247$	−15.9690	−0.00411369
$248$	−5015.91	−1.28432
$249$	4004.17	1.01909
$250$	0	0
$251$	1672.27	0.420530	0.210265	−	0.977644i	$-0.432567\pi$
$251$	1672.27	0.420530	0.210265	+	0.977644i	$0.432567\pi$
$252$	789.461	0.197347
$253$	941.245	0.233896
$254$	−3824.34	−0.944727
$255$	0	0
$256$	−3320.09	−0.810569
$257$	3697.74	0.897506	0.448753	−	0.893656i	$-0.351868\pi$
$257$	3697.74	0.897506	0.448753	+	0.893656i	$0.351868\pi$
$258$	4091.56	0.987322
$259$	1351.84	0.324323
$260$	0	0
$261$	−2623.45	−0.622174
$262$	12670.0	2.98760
$263$	−7319.00	−1.71600	−0.858002	−	0.513646i	$-0.828294\pi$
$263$	−7319.00	−1.71600	−0.858002	+	0.513646i	$0.828294\pi$
$264$	−1174.11	−0.273717
$265$	0	0
$266$	172.412	0.0397416
$267$	−978.747	−0.224338
$268$	−2581.32	−0.588354
$269$	−815.097	−0.184749	−0.0923743	−	0.995724i	$-0.529446\pi$
$269$	−815.097	−0.184749	−0.0923743	+	0.995724i	$0.529446\pi$
$270$	0	0
$271$	−5106.02	−1.14453	−0.572267	−	0.820068i	$-0.693936\pi$
$271$	−5106.02	−1.14453	−0.572267	+	0.820068i	$0.693936\pi$
$272$	−46.9150	−0.0104582
$273$	−61.6926	−0.0136769
$274$	−9321.13	−2.05515
$275$	0	0
$276$	1856.26	0.404833
$277$	−1398.72	−0.303398	−0.151699	−	0.988427i	$-0.548474\pi$
$277$	−1398.72	−0.303398	−0.151699	+	0.988427i	$0.548474\pi$
$278$	7907.39	1.70595
$279$	2198.77	0.471816
$280$	0	0
$281$	−7102.38	−1.50780	−0.753901	−	0.656988i	$-0.771830\pi$
$281$	−7102.38	−1.50780	−0.753901	+	0.656988i	$0.771830\pi$
$282$	−1175.91	−0.248313
$283$	−4465.18	−0.937907	−0.468953	−	0.883223i	$-0.655369\pi$
$283$	−4465.18	−0.937907	−0.468953	+	0.883223i	$0.655369\pi$
$284$	12585.1	2.62954
$285$	0	0
$286$	253.743	0.0524621
$287$	2205.79	0.453671
$288$	1772.67	0.362692
$289$	−4870.78	−0.991405
$290$	0	0
$291$	4580.32	0.922692
$292$	12622.5	2.52970
$293$	−7590.61	−1.51348	−0.756738	−	0.653718i	$-0.773208\pi$
$293$	−7590.61	−1.51348	−0.756738	+	0.653718i	$0.773208\pi$
$294$	666.076	0.132130
$295$	0	0
$296$	−3964.98	−0.778581
$297$	514.681	0.100555
$298$	5317.61	1.03369
$299$	−145.058	−0.0280566
$300$	0	0
$301$	2106.97	0.403468
$302$	−6978.26	−1.32965
$303$	−290.615	−0.0551003
$304$	39.2456	0.00740425
$305$	0	0
$306$	−264.992	−0.0495052
$307$	−9480.12	−1.76241	−0.881203	−	0.472737i	$-0.843266\pi$
$307$	−9480.12	−1.76241	−0.881203	+	0.472737i	$0.843266\pi$
$308$	−1672.10	−0.309340
$309$	3965.98	0.730151
$310$	0	0
$311$	7078.01	1.29054	0.645268	−	0.763956i	$-0.276746\pi$
$311$	7078.01	1.29054	0.645268	+	0.763956i	$0.276746\pi$
$312$	180.945	0.0328334
$313$	−5593.84	−1.01017	−0.505084	−	0.863070i	$-0.668539\pi$
$313$	−5593.84	−1.01017	−0.505084	+	0.863070i	$0.668539\pi$
$314$	−11529.6	−2.07214
$315$	0	0
$316$	−10817.3	−1.92571
$317$	−3567.81	−0.632139	−0.316070	−	0.948736i	$-0.602363\pi$
$317$	−3567.81	−0.632139	−0.316070	+	0.948736i	$0.602363\pi$
$318$	−6928.24	−1.22175
$319$	5556.54	0.975255
$320$	0	0
$321$	5237.14	0.910618
$322$	1566.15	0.271050
$323$	−35.3222	−0.00608477
$324$	1015.02	0.174043
$325$	0	0
$326$	−2694.70	−0.457809
$327$	−1430.57	−0.241928
$328$	−6469.62	−1.08910
$329$	−605.541	−0.101473
$330$	0	0
$331$	−4389.67	−0.728936	−0.364468	−	0.931216i	$-0.618749\pi$
$331$	−4389.67	−0.728936	−0.364468	+	0.931216i	$0.618749\pi$
$332$	−16725.6	−2.76487
$333$	1738.09	0.286026
$334$	4207.14	0.689236
$335$	0	0
$336$	151.617	0.0246172
$337$	−2348.83	−0.379671	−0.189835	−	0.981816i	$-0.560795\pi$
$337$	−2348.83	−0.379671	−0.189835	+	0.981816i	$0.560795\pi$
$338$	9915.79	1.59570
$339$	4924.94	0.789044
$340$	0	0
$341$	−4657.05	−0.739570
$342$	221.673	0.0350488
$343$	343.000	0.0539949
$344$	−6179.79	−0.968581
$345$	0	0
$346$	−1430.21	−0.222222
$347$	−558.436	−0.0863931	−0.0431965	−	0.999067i	$-0.513754\pi$
$347$	−558.436	−0.0863931	−0.0431965	+	0.999067i	$0.513754\pi$
$348$	10958.3	1.68800
$349$	3233.89	0.496006	0.248003	−	0.968759i	$-0.420226\pi$
$349$	3233.89	0.496006	0.248003	+	0.968759i	$0.420226\pi$
$350$	0	0
$351$	−79.3190	−0.0120619
$352$	−3754.56	−0.568519
$353$	7516.35	1.13330	0.566650	−	0.823959i	$-0.308239\pi$
$353$	7516.35	1.13330	0.566650	+	0.823959i	$0.308239\pi$
$354$	−1133.49	−0.170181
$355$	0	0
$356$	4088.27	0.608646
$357$	−136.459	−0.0202302
$358$	6549.70	0.966935
$359$	−6577.76	−0.967021	−0.483511	−	0.875338i	$-0.660639\pi$
$359$	−6577.76	−0.967021	−0.483511	+	0.875338i	$0.660639\pi$
$360$	0	0
$361$	−6829.45	−0.995692
$362$	8354.56	1.21300
$363$	2902.89	0.419731
$364$	257.693	0.0371065
$365$	0	0
$366$	−71.4048	−0.0101978
$367$	−8307.17	−1.18155	−0.590777	−	0.806835i	$-0.701179\pi$
$367$	−8307.17	−1.18155	−0.590777	+	0.806835i	$0.701179\pi$
$368$	356.497	0.0504992
$369$	2836.02	0.400101
$370$	0	0
$371$	−3567.74	−0.499266
$372$	−9184.34	−1.28007
$373$	4551.09	0.631760	0.315880	−	0.948799i	$-0.397700\pi$
$373$	4551.09	0.631760	0.315880	+	0.948799i	$0.397700\pi$
$374$	561.261	0.0775992
$375$	0	0
$376$	1776.06	0.243599
$377$	−856.335	−0.116985
$378$	856.383	0.116528
$379$	−1788.29	−0.242370	−0.121185	−	0.992630i	$-0.538669\pi$
$379$	−1788.29	−0.242370	−0.121185	+	0.992630i	$0.538669\pi$
$380$	0	0
$381$	−2532.05	−0.340474
$382$	1105.93	0.148126
$383$	1358.47	0.181240	0.0906199	−	0.995886i	$-0.471115\pi$
$383$	1358.47	0.181240	0.0906199	+	0.995886i	$0.471115\pi$
$384$	−6619.37	−0.879670
$385$	0	0
$386$	−7852.60	−1.03546
$387$	2708.97	0.355825
$388$	−19132.2	−2.50333
$389$	9722.54	1.26723	0.633615	−	0.773649i	$-0.281570\pi$
$389$	9722.54	1.26723	0.633615	+	0.773649i	$0.281570\pi$
$390$	0	0
$391$	−320.858	−0.0414999
$392$	−1006.03	−0.129622
$393$	8388.61	1.07672
$394$	1623.19	0.207551
$395$	0	0
$396$	−2149.84	−0.272812
$397$	4788.04	0.605302	0.302651	−	0.953101i	$-0.402128\pi$
$397$	4788.04	0.605302	0.302651	+	0.953101i	$0.402128\pi$
$398$	14516.1	1.82820
$399$	114.152	0.0143227
$400$	0	0
$401$	9681.41	1.20565	0.602826	−	0.797873i	$-0.294041\pi$
$401$	9681.41	1.20565	0.602826	+	0.797873i	$0.294041\pi$
$402$	−2800.13	−0.347408
$403$	717.712	0.0887141
$404$	1213.91	0.149491
$405$	0	0
$406$	9245.58	1.13017
$407$	−3681.32	−0.448344
$408$	400.238	0.0485655
$409$	11113.1	1.34353	0.671767	−	0.740763i	$-0.265536\pi$
$409$	11113.1	1.34353	0.671767	+	0.740763i	$0.265536\pi$
$410$	0	0
$411$	−6171.40	−0.740663
$412$	−16566.1	−1.98095
$413$	−583.696	−0.0695443
$414$	2013.62	0.239043
$415$	0	0
$416$	578.627	0.0681959
$417$	5235.37	0.614814
$418$	−469.510	−0.0549389
$419$	−1230.09	−0.143421	−0.0717107	−	0.997425i	$-0.522846\pi$
$419$	−1230.09	−0.143421	−0.0717107	+	0.997425i	$0.522846\pi$
$420$	0	0
$421$	−12356.5	−1.43044	−0.715222	−	0.698897i	$-0.753674\pi$
$421$	−12356.5	−1.43044	−0.715222	+	0.698897i	$0.753674\pi$
$422$	−22398.1	−2.58370
$423$	−778.552	−0.0894906
$424$	10464.2	1.19856
$425$	0	0
$426$	13651.9	1.55267
$427$	−36.7703	−0.00416731
$428$	−21875.7	−2.47057
$429$	168.000	0.0189070
$430$	0	0
$431$	−7375.27	−0.824256	−0.412128	−	0.911126i	$-0.635214\pi$
$431$	−7375.27	−0.824256	−0.412128	+	0.911126i	$0.635214\pi$
$432$	194.936	0.0217103
$433$	690.067	0.0765877	0.0382939	−	0.999267i	$-0.487808\pi$
$433$	690.067	0.0765877	0.0382939	+	0.999267i	$0.487808\pi$
$434$	−7748.92	−0.857051
$435$	0	0
$436$	5975.55	0.656369
$437$	268.406	0.0293812
$438$	13692.5	1.49372
$439$	8408.79	0.914191	0.457095	−	0.889418i	$-0.348890\pi$
$439$	8408.79	0.914191	0.457095	+	0.889418i	$0.348890\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	−86.4976	−0.00930830
$443$	−6568.55	−0.704473	−0.352236	−	0.935911i	$-0.614579\pi$
$443$	−6568.55	−0.704473	−0.352236	+	0.935911i	$0.614579\pi$
$444$	−7260.06	−0.776007
$445$	0	0
$446$	14319.0	1.52024
$447$	3520.72	0.372537
$448$	−5842.94	−0.616190
$449$	2954.55	0.310543	0.155271	−	0.987872i	$-0.450375\pi$
$449$	2954.55	0.310543	0.155271	+	0.987872i	$0.450375\pi$
$450$	0	0
$451$	−6006.76	−0.627156
$452$	−20571.7	−2.14073
$453$	−4620.21	−0.479197
$454$	−16543.7	−1.71020
$455$	0	0
$456$	−334.810	−0.0343835
$457$	8144.84	0.833697	0.416849	−	0.908976i	$-0.363135\pi$
$457$	8144.84	0.833697	0.416849	+	0.908976i	$0.363135\pi$
$458$	18503.8	1.88782
$459$	−175.448	−0.0178414
$460$	0	0
$461$	2495.26	0.252095	0.126048	−	0.992024i	$-0.459771\pi$
$461$	2495.26	0.252095	0.126048	+	0.992024i	$0.459771\pi$
$462$	−1813.84	−0.182657
$463$	5755.66	0.577728	0.288864	−	0.957370i	$-0.406722\pi$
$463$	5755.66	0.577728	0.288864	+	0.957370i	$0.406722\pi$
$464$	2104.54	0.210562
$465$	0	0
$466$	−16685.9	−1.65871
$467$	4143.73	0.410598	0.205299	−	0.978699i	$-0.434183\pi$
$467$	4143.73	0.410598	0.205299	+	0.978699i	$0.434183\pi$
$468$	331.319	0.0327248
$469$	−1441.95	−0.141968
$470$	0	0
$471$	−7633.60	−0.746789
$472$	1711.99	0.166951
$473$	−5737.67	−0.557755
$474$	−11734.3	−1.13708
$475$	0	0
$476$	569.996	0.0548860
$477$	−4587.09	−0.440312
$478$	−12047.3	−1.15278
$479$	−6765.96	−0.645396	−0.322698	−	0.946502i	$-0.604590\pi$
$479$	−6765.96	−0.645396	−0.322698	+	0.946502i	$0.604590\pi$
$480$	0	0
$481$	567.339	0.0537805
$482$	21841.8	2.06404
$483$	1036.93	0.0976848
$484$	−12125.5	−1.13876
$485$	0	0
$486$	1101.06	0.102768
$487$	−6360.42	−0.591824	−0.295912	−	0.955215i	$-0.595623\pi$
$487$	−6360.42	−0.591824	−0.295912	+	0.955215i	$0.595623\pi$
$488$	107.848	0.0100042
$489$	−1784.12	−0.164992
$490$	0	0
$491$	−7072.54	−0.650060	−0.325030	−	0.945704i	$-0.605374\pi$
$491$	−7072.54	−0.650060	−0.325030	+	0.945704i	$0.605374\pi$
$492$	−11846.2	−1.08550
$493$	−1894.15	−0.173039
$494$	72.3576	0.00659012
$495$	0	0
$496$	−1763.86	−0.159677
$497$	7030.15	0.634498
$498$	−18143.4	−1.63258
$499$	−18473.9	−1.65732	−0.828661	−	0.559751i	$-0.810897\pi$
$499$	−18473.9	−1.65732	−0.828661	+	0.559751i	$0.810897\pi$
$500$	0	0
$501$	2785.49	0.248397
$502$	−7577.28	−0.673687
$503$	−11379.2	−1.00869	−0.504347	−	0.863501i	$-0.668267\pi$
$503$	−11379.2	−1.00869	−0.504347	+	0.863501i	$0.668267\pi$
$504$	−1293.46	−0.114316
$505$	0	0
$506$	−4264.90	−0.374700
$507$	6565.11	0.575082
$508$	10576.5	0.923730
$509$	6064.48	0.528101	0.264051	−	0.964509i	$-0.414941\pi$
$509$	6064.48	0.528101	0.264051	+	0.964509i	$0.414941\pi$
$510$	0	0
$511$	7051.02	0.610408
$512$	−2607.89	−0.225105
$513$	146.767	0.0126314
$514$	−16755.0	−1.43780
$515$	0	0
$516$	−11315.5	−0.965379
$517$	1649.00	0.140276
$518$	−6125.38	−0.519563
$519$	−946.926	−0.0800875
$520$	0	0
$521$	2682.88	0.225603	0.112801	−	0.993618i	$-0.464018\pi$
$521$	2682.88	0.225603	0.112801	+	0.993618i	$0.464018\pi$
$522$	11887.2	0.996720
$523$	4309.02	0.360268	0.180134	−	0.983642i	$-0.442347\pi$
$523$	4309.02	0.360268	0.180134	+	0.983642i	$0.442347\pi$
$524$	−35039.6	−2.92120
$525$	0	0
$526$	33163.3	2.74903
$527$	1587.52	0.131221
$528$	−412.879	−0.0340308
$529$	−9728.87	−0.799611
$530$	0	0
$531$	−750.467	−0.0613323
$532$	−476.817	−0.0388584
$533$	925.720	0.0752296
$534$	4434.83	0.359389
$535$	0	0
$536$	4229.25	0.340813
$537$	4336.47	0.348478
$538$	3693.31	0.295966
$539$	−934.051	−0.0746427
$540$	0	0
$541$	4081.47	0.324355	0.162178	−	0.986762i	$-0.448148\pi$
$541$	4081.47	0.324355	0.162178	+	0.986762i	$0.448148\pi$
$542$	23136.0	1.83354
$543$	5531.44	0.437158
$544$	1279.88	0.100872
$545$	0	0
$546$	279.537	0.0219104
$547$	−8844.82	−0.691366	−0.345683	−	0.938351i	$-0.612353\pi$
$547$	−8844.82	−0.691366	−0.345683	+	0.938351i	$0.612353\pi$
$548$	25778.2	2.00947
$549$	−47.2762	−0.00367522
$550$	0	0
$551$	1584.51	0.122509
$552$	−3041.32	−0.234506
$553$	−6042.66	−0.464666
$554$	6337.80	0.486042
$555$	0	0
$556$	−21868.4	−1.66803
$557$	11144.7	0.847787	0.423894	−	0.905712i	$-0.360663\pi$
$557$	11144.7	0.847787	0.423894	+	0.905712i	$0.360663\pi$
$558$	−9962.90	−0.755848
$559$	884.249	0.0669047
$560$	0	0
$561$	371.603	0.0279663
$562$	32181.8	2.41549
$563$	21857.5	1.63621	0.818104	−	0.575071i	$-0.195025\pi$
$563$	21857.5	1.63621	0.818104	+	0.575071i	$0.195025\pi$
$564$	3252.05	0.242794
$565$	0	0
$566$	20232.3	1.50252
$567$	567.000	0.0419961
$568$	−20619.6	−1.52320
$569$	23496.4	1.73115	0.865573	−	0.500783i	$-0.166954\pi$
$569$	23496.4	1.73115	0.865573	+	0.500783i	$0.166954\pi$
$570$	0	0
$571$	11067.8	0.811164	0.405582	−	0.914059i	$-0.367069\pi$
$571$	11067.8	0.811164	0.405582	+	0.914059i	$0.367069\pi$
$572$	−701.743	−0.0512961
$573$	732.222	0.0533839
$574$	−9994.72	−0.726780
$575$	0	0
$576$	−7512.36	−0.543429
$577$	−20482.9	−1.47784	−0.738922	−	0.673791i	$-0.764665\pi$
$577$	−20482.9	−1.47784	−0.738922	+	0.673791i	$0.764665\pi$
$578$	22070.1	1.58823
$579$	−5199.10	−0.373173
$580$	0	0
$581$	−9343.07	−0.667153
$582$	−20754.0	−1.47815
$583$	9715.60	0.690187
$584$	−20680.8	−1.46537
$585$	0	0
$586$	34394.1	2.42458
$587$	23444.3	1.64847	0.824235	−	0.566248i	$-0.191606\pi$
$587$	23444.3	1.64847	0.824235	+	0.566248i	$0.191606\pi$
$588$	−1842.08	−0.129194
$589$	−1328.01	−0.0929025
$590$	0	0
$591$	1074.69	0.0748000
$592$	−1394.30	−0.0967996
$593$	−4404.69	−0.305024	−0.152512	−	0.988302i	$-0.548736\pi$
$593$	−4404.69	−0.305024	−0.152512	+	0.988302i	$0.548736\pi$
$594$	−2332.09	−0.161089
$595$	0	0
$596$	−14706.2	−1.01072
$597$	9610.89	0.658874
$598$	657.277	0.0449466
$599$	3327.05	0.226945	0.113472	−	0.993541i	$-0.463803\pi$
$599$	3327.05	0.226945	0.113472	+	0.993541i	$0.463803\pi$
$600$	0	0
$601$	−14244.8	−0.966818	−0.483409	−	0.875395i	$-0.660602\pi$
$601$	−14244.8	−0.966818	−0.483409	+	0.875395i	$0.660602\pi$
$602$	−9546.97	−0.646354
$603$	−1853.93	−0.125204
$604$	19298.8	1.30010
$605$	0	0
$606$	1316.81	0.0882704
$607$	−11446.5	−0.765402	−0.382701	−	0.923872i	$-0.625006\pi$
$607$	−11446.5	−0.765402	−0.382701	+	0.923872i	$0.625006\pi$
$608$	−1070.65	−0.0714156
$609$	6121.38	0.407308
$610$	0	0
$611$	−254.132	−0.0168266
$612$	732.852	0.0484049
$613$	19436.4	1.28063	0.640316	−	0.768111i	$-0.278803\pi$
$613$	19436.4	1.28063	0.640316	+	0.768111i	$0.278803\pi$
$614$	42955.6	2.82337
$615$	0	0
$616$	2739.59	0.179190
$617$	20530.1	1.33956	0.669781	−	0.742558i	$-0.266388\pi$
$617$	20530.1	1.33956	0.669781	+	0.742558i	$0.266388\pi$
$618$	−17970.4	−1.16970
$619$	5833.35	0.378776	0.189388	−	0.981902i	$-0.439350\pi$
$619$	5833.35	0.378776	0.189388	+	0.981902i	$0.439350\pi$
$620$	0	0
$621$	1333.19	0.0861499
$622$	−32071.4	−2.06744
$623$	2283.74	0.146864
$624$	63.6301	0.00408212
$625$	0	0
$626$	25346.4	1.61829
$627$	−310.856	−0.0197997
$628$	31885.9	2.02609
$629$	1254.91	0.0795493
$630$	0	0
$631$	24776.6	1.56314	0.781568	−	0.623820i	$-0.214420\pi$
$631$	24776.6	1.56314	0.781568	+	0.623820i	$0.214420\pi$
$632$	17723.2	1.11549
$633$	−14829.5	−0.931152
$634$	16166.2	1.01268
$635$	0	0
$636$	19160.5	1.19460
$637$	143.949	0.00895366
$638$	−25177.4	−1.56235
$639$	9038.77	0.559574
$640$	0	0
$641$	27219.4	1.67723	0.838613	−	0.544728i	$-0.183367\pi$
$641$	27219.4	1.67723	0.838613	+	0.544728i	$0.183367\pi$
$642$	−23730.1	−1.45881
$643$	−7091.79	−0.434950	−0.217475	−	0.976066i	$-0.569782\pi$
$643$	−7091.79	−0.434950	−0.217475	+	0.976066i	$0.569782\pi$
$644$	−4331.28	−0.265026
$645$	0	0
$646$	160.049	0.00974777
$647$	−27773.0	−1.68758	−0.843792	−	0.536670i	$-0.819682\pi$
$647$	−27773.0	−1.68758	−0.843792	+	0.536670i	$0.819682\pi$
$648$	−1663.02	−0.100817
$649$	1589.51	0.0961382
$650$	0	0
$651$	−5130.46	−0.308876
$652$	7452.37	0.447634
$653$	−21380.4	−1.28129	−0.640643	−	0.767839i	$-0.721332\pi$
$653$	−21380.4	−1.28129	−0.640643	+	0.767839i	$0.721332\pi$
$654$	6482.09	0.387568
$655$	0	0
$656$	−2275.06	−0.135406
$657$	9065.59	0.538329
$658$	2743.78	0.162559
$659$	−17232.3	−1.01863	−0.509315	−	0.860580i	$-0.670101\pi$
$659$	−17232.3	−1.01863	−0.509315	+	0.860580i	$0.670101\pi$
$660$	0	0
$661$	26577.7	1.56392	0.781962	−	0.623326i	$-0.214219\pi$
$661$	26577.7	1.56392	0.781962	+	0.623326i	$0.214219\pi$
$662$	19890.1	1.16775
$663$	−57.2689	−0.00335466
$664$	27403.4	1.60159
$665$	0	0
$666$	−7875.49	−0.458212
$667$	14393.2	0.835544
$668$	−11635.1	−0.673917
$669$	9480.44	0.547885
$670$	0	0
$671$	100.132	0.00576090
$672$	−4136.22	−0.237438
$673$	31695.2	1.81540	0.907698	−	0.419624i	$-0.137838\pi$
$673$	31695.2	1.81540	0.907698	+	0.419624i	$0.137838\pi$
$674$	10642.9	0.608231
$675$	0	0
$676$	−27422.7	−1.56024
$677$	−20440.3	−1.16039	−0.580195	−	0.814477i	$-0.697024\pi$
$677$	−20440.3	−1.16039	−0.580195	+	0.814477i	$0.697024\pi$
$678$	−22315.5	−1.26405
$679$	−10687.4	−0.604044
$680$	0	0
$681$	−10953.3	−0.616348
$682$	21101.7	1.18479
$683$	22896.9	1.28276	0.641381	−	0.767223i	$-0.278362\pi$
$683$	22896.9	1.28276	0.641381	+	0.767223i	$0.278362\pi$
$684$	−613.051	−0.0342699
$685$	0	0
$686$	−1554.18	−0.0864997
$687$	12251.1	0.680361
$688$	−2173.14	−0.120422
$689$	−1497.30	−0.0827904
$690$	0	0
$691$	−23764.0	−1.30829	−0.654143	−	0.756371i	$-0.726971\pi$
$691$	−23764.0	−1.30829	−0.654143	+	0.756371i	$0.726971\pi$
$692$	3955.35	0.217283
$693$	−1200.92	−0.0658287
$694$	2530.34	0.138401
$695$	0	0
$696$	−17954.1	−0.977800
$697$	2047.62	0.111276
$698$	−14653.2	−0.794600
$699$	−11047.5	−0.597791
$700$	0	0
$701$	26259.5	1.41485	0.707423	−	0.706791i	$-0.249858\pi$
$701$	26259.5	1.41485	0.707423	+	0.706791i	$0.249858\pi$
$702$	359.405	0.0193232
$703$	−1049.77	−0.0563196
$704$	15911.4	0.851822
$705$	0	0
$706$	−34057.6	−1.81554
$707$	678.101	0.0360716
$708$	3134.73	0.166399
$709$	12783.0	0.677116	0.338558	−	0.940945i	$-0.390061\pi$
$709$	12783.0	0.677116	0.338558	+	0.940945i	$0.390061\pi$
$710$	0	0
$711$	−7769.14	−0.409797
$712$	−6698.26	−0.352567
$713$	−12063.3	−0.633623
$714$	618.315	0.0324087
$715$	0	0
$716$	−18113.6	−0.945444
$717$	−7976.35	−0.415456
$718$	29804.7	1.54916
$719$	−27609.0	−1.43205	−0.716025	−	0.698075i	$-0.754040\pi$
$719$	−27609.0	−1.43205	−0.716025	+	0.698075i	$0.754040\pi$
$720$	0	0
$721$	−9253.95	−0.477996
$722$	30945.1	1.59509
$723$	14461.2	0.743868
$724$	−23105.1	−1.18604
$725$	0	0
$726$	−13153.4	−0.672407
$727$	−31306.2	−1.59709	−0.798544	−	0.601937i	$-0.794396\pi$
$727$	−31306.2	−1.59709	−0.798544	+	0.601937i	$0.794396\pi$
$728$	−422.206	−0.0214945
$729$	729.000	0.0370370
$730$	0	0
$731$	1955.89	0.0989621
$732$	197.475	0.00997113
$733$	15765.8	0.794441	0.397220	−	0.917723i	$-0.369975\pi$
$733$	15765.8	0.794441	0.397220	+	0.917723i	$0.369975\pi$
$734$	37640.8	1.89285
$735$	0	0
$736$	−9725.53	−0.487076
$737$	3926.68	0.196256
$738$	−12850.4	−0.640959
$739$	3966.51	0.197443	0.0987216	−	0.995115i	$-0.468525\pi$
$739$	3966.51	0.197443	0.0987216	+	0.995115i	$0.468525\pi$
$740$	0	0
$741$	47.9070	0.00237504
$742$	16165.9	0.799823
$743$	−8224.50	−0.406094	−0.203047	−	0.979169i	$-0.565084\pi$
$743$	−8224.50	−0.406094	−0.203047	+	0.979169i	$0.565084\pi$
$744$	15047.7	0.741500
$745$	0	0
$746$	−20621.6	−1.01208
$747$	−12012.5	−0.588373
$748$	−1552.20	−0.0758745
$749$	−12220.0	−0.596140
$750$	0	0
$751$	18929.2	0.919754	0.459877	−	0.887983i	$-0.347894\pi$
$751$	18929.2	0.919754	0.459877	+	0.887983i	$0.347894\pi$
$752$	624.558	0.0302863
$753$	−5016.82	−0.242793
$754$	3880.16	0.187410
$755$	0	0
$756$	−2368.38	−0.113938
$757$	34906.8	1.67597	0.837984	−	0.545695i	$-0.183734\pi$
$757$	34906.8	1.67597	0.837984	+	0.545695i	$0.183734\pi$
$758$	8102.96	0.388276
$759$	−2823.74	−0.135040
$760$	0	0
$761$	−13683.4	−0.651803	−0.325902	−	0.945404i	$-0.605668\pi$
$761$	−13683.4	−0.651803	−0.325902	+	0.945404i	$0.605668\pi$
$762$	11473.0	0.545438
$763$	3337.99	0.158379
$764$	−3058.52	−0.144834
$765$	0	0
$766$	−6155.42	−0.290345
$767$	−244.964	−0.0115321
$768$	9960.28	0.467982
$769$	41837.3	1.96189	0.980943	−	0.194294i	$-0.0622416\pi$
$769$	41837.3	1.96189	0.980943	+	0.194294i	$0.0622416\pi$
$770$	0	0
$771$	−11093.2	−0.518175
$772$	21716.9	1.01245
$773$	−19640.0	−0.913843	−0.456921	−	0.889507i	$-0.651048\pi$
$773$	−19640.0	−0.913843	−0.456921	+	0.889507i	$0.651048\pi$
$774$	−12274.7	−0.570031
$775$	0	0
$776$	31346.4	1.45009
$777$	−4055.53	−0.187248
$778$	−44054.1	−2.03010
$779$	−1712.89	−0.0787814
$780$	0	0
$781$	−19144.4	−0.877131
$782$	1453.85	0.0664827
$783$	7870.34	0.359212
$784$	−353.772	−0.0161157
$785$	0	0
$786$	−38009.9	−1.72489
$787$	−24935.3	−1.12941	−0.564705	−	0.825293i	$-0.691010\pi$
$787$	−24935.3	−1.12941	−0.564705	+	0.825293i	$0.691010\pi$
$788$	−4489.02	−0.202938
$789$	21957.0	0.990736
$790$	0	0
$791$	−11491.5	−0.516551
$792$	3522.33	0.158031
$793$	−15.4317	−0.000691041 0
$794$	−21695.2	−0.969692
$795$	0	0
$796$	−40145.1	−1.78757
$797$	1168.33	0.0519251	0.0259625	−	0.999663i	$-0.491735\pi$
$797$	1168.33	0.0519251	0.0259625	+	0.999663i	$0.491735\pi$
$798$	−517.237	−0.0229448
$799$	−562.120	−0.0248891
$800$	0	0
$801$	2936.24	0.129522
$802$	−43867.7	−1.93145
$803$	−19201.2	−0.843829
$804$	7743.95	0.339686
$805$	0	0
$806$	−3252.05	−0.142120
$807$	2445.29	0.106665
$808$	−1988.88	−0.0865949
$809$	−35175.7	−1.52869	−0.764345	−	0.644807i	$-0.776938\pi$
$809$	−35175.7	−1.52869	−0.764345	+	0.644807i	$0.776938\pi$
$810$	0	0
$811$	−15256.5	−0.660577	−0.330288	−	0.943880i	$-0.607146\pi$
$811$	−15256.5	−0.660577	−0.330288	+	0.943880i	$0.607146\pi$
$812$	−25569.3	−1.10506
$813$	15318.1	0.660797
$814$	16680.5	0.718245
$815$	0	0
$816$	140.745	0.00603806
$817$	−1636.16	−0.0700635
$818$	−50354.7	−2.15233
$819$	185.078	0.00789639
$820$	0	0
$821$	−15971.9	−0.678956	−0.339478	−	0.940614i	$-0.610250\pi$
$821$	−15971.9	−0.678956	−0.339478	+	0.940614i	$0.610250\pi$
$822$	27963.4	1.18654
$823$	−2312.41	−0.0979409	−0.0489705	−	0.998800i	$-0.515594\pi$
$823$	−2312.41	−0.0979409	−0.0489705	+	0.998800i	$0.515594\pi$
$824$	27142.0	1.14750
$825$	0	0
$826$	2644.80	0.111410
$827$	−10422.4	−0.438238	−0.219119	−	0.975698i	$-0.570318\pi$
$827$	−10422.4	−0.438238	−0.219119	+	0.975698i	$0.570318\pi$
$828$	−5568.79	−0.233731
$829$	−13213.4	−0.553584	−0.276792	−	0.960930i	$-0.589271\pi$
$829$	−13213.4	−0.553584	−0.276792	+	0.960930i	$0.589271\pi$
$830$	0	0
$831$	4196.17	0.175167
$832$	−2452.15	−0.102179
$833$	318.405	0.0132438
$834$	−23722.2	−0.984929
$835$	0	0
$836$	1298.46	0.0537179
$837$	−6596.30	−0.272403
$838$	5573.67	0.229761
$839$	−10119.6	−0.416409	−0.208205	−	0.978085i	$-0.566762\pi$
$839$	−10119.6	−0.416409	−0.208205	+	0.978085i	$0.566762\pi$
$840$	0	0
$841$	60579.9	2.48390
$842$	55988.7	2.29157
$843$	21307.1	0.870530
$844$	61943.4	2.52628
$845$	0	0
$846$	3527.72	0.143364
$847$	−6773.41	−0.274778
$848$	3679.79	0.149015
$849$	13395.5	0.541501
$850$	0	0
$851$	−9535.80	−0.384116
$852$	−37755.3	−1.51816
$853$	−35378.1	−1.42007	−0.710037	−	0.704165i	$-0.751322\pi$
$853$	−35378.1	−1.42007	−0.710037	+	0.704165i	$0.751322\pi$
$854$	166.611	0.00667602
$855$	0	0
$856$	35841.4	1.43112
$857$	−6697.57	−0.266960	−0.133480	−	0.991052i	$-0.542615\pi$
$857$	−6697.57	−0.266960	−0.133480	+	0.991052i	$0.542615\pi$
$858$	−761.230	−0.0302890
$859$	−24298.4	−0.965135	−0.482568	−	0.875859i	$-0.660296\pi$
$859$	−24298.4	−0.965135	−0.482568	+	0.875859i	$0.660296\pi$
$860$	0	0
$861$	−6617.37	−0.261927
$862$	33418.3	1.32045
$863$	−24942.9	−0.983853	−0.491926	−	0.870637i	$-0.663707\pi$
$863$	−24942.9	−0.983853	−0.491926	+	0.870637i	$0.663707\pi$
$864$	−5318.00	−0.209401
$865$	0	0
$866$	−3126.78	−0.122693
$867$	14612.3	0.572388
$868$	21430.1	0.838002
$869$	16455.3	0.642355
$870$	0	0
$871$	−605.152	−0.0235417
$872$	−9790.39	−0.380212
$873$	−13741.0	−0.532716
$874$	−1216.18	−0.0470686
$875$	0	0
$876$	−37867.4	−1.46052
$877$	16276.6	0.626705	0.313353	−	0.949637i	$-0.398548\pi$
$877$	16276.6	0.626705	0.313353	+	0.949637i	$0.398548\pi$
$878$	−38101.3	−1.46453
$879$	22771.8	0.873806
$880$	0	0
$881$	26636.5	1.01862	0.509311	−	0.860582i	$-0.329900\pi$
$881$	26636.5	1.01862	0.509311	+	0.860582i	$0.329900\pi$
$882$	−1998.23	−0.0762855
$883$	21788.3	0.830392	0.415196	−	0.909732i	$-0.363713\pi$
$883$	21788.3	0.830392	0.415196	+	0.909732i	$0.363713\pi$
$884$	239.215	0.00910142
$885$	0	0
$886$	29763.0	1.12856
$887$	26813.2	1.01499	0.507496	−	0.861654i	$-0.330571\pi$
$887$	26813.2	1.01499	0.507496	+	0.861654i	$0.330571\pi$
$888$	11895.0	0.449514
$889$	5908.11	0.222893
$890$	0	0
$891$	−1544.04	−0.0580554
$892$	−39600.2	−1.48645
$893$	470.229	0.0176211
$894$	−15952.8	−0.596803
$895$	0	0
$896$	15445.2	0.575879
$897$	435.174	0.0161985
$898$	−13387.4	−0.497488
$899$	−71214.2	−2.64196
$900$	0	0
$901$	−3311.91	−0.122459
$902$	27217.4	1.00470
$903$	−6320.92	−0.232942
$904$	33704.8	1.24005
$905$	0	0
$906$	20934.8	0.767672
$907$	−15543.0	−0.569014	−0.284507	−	0.958674i	$-0.591830\pi$
$907$	−15543.0	−0.569014	−0.284507	+	0.958674i	$0.591830\pi$
$908$	45752.6	1.67219
$909$	871.844	0.0318122
$910$	0	0
$911$	48711.1	1.77154	0.885768	−	0.464128i	$-0.153632\pi$
$911$	48711.1	1.77154	0.885768	+	0.464128i	$0.153632\pi$
$912$	−117.737	−0.00427485
$913$	25442.8	0.922273
$914$	−36905.3	−1.33558
$915$	0	0
$916$	−51173.3	−1.84587
$917$	−19573.4	−0.704876
$918$	794.976	0.0285818
$919$	1030.47	0.0369883	0.0184941	−	0.999829i	$-0.494113\pi$
$919$	1030.47	0.0369883	0.0184941	+	0.999829i	$0.494113\pi$
$920$	0	0
$921$	28440.4	1.01753
$922$	−11306.3	−0.403855
$923$	2950.40	0.105215
$924$	5016.30	0.178598
$925$	0	0
$926$	−26079.6	−0.925518
$927$	−11897.9	−0.421553
$928$	−57413.6	−2.03092
$929$	879.756	0.0310698	0.0155349	−	0.999879i	$-0.495055\pi$
$929$	879.756	0.0310698	0.0155349	+	0.999879i	$0.495055\pi$
$930$	0	0
$931$	−266.354	−0.00937638
$932$	46146.0	1.62185
$933$	−21234.0	−0.745092
$934$	−18775.8	−0.657776
$935$	0	0
$936$	−542.836	−0.0189564
$937$	18668.1	0.650864	0.325432	−	0.945565i	$-0.394490\pi$
$937$	18668.1	0.650864	0.325432	+	0.945565i	$0.394490\pi$
$938$	6533.64	0.227432
$939$	16781.5	0.583221
$940$	0	0
$941$	29613.4	1.02590	0.512948	−	0.858420i	$-0.328553\pi$
$941$	29613.4	1.02590	0.512948	+	0.858420i	$0.328553\pi$
$942$	34588.8	1.19635
$943$	−15559.5	−0.537313
$944$	602.028	0.0207567
$945$	0	0
$946$	25998.1	0.893521
$947$	−20738.9	−0.711640	−0.355820	−	0.934554i	$-0.615798\pi$
$947$	−20738.9	−0.711640	−0.355820	+	0.934554i	$0.615798\pi$
$948$	32452.0	1.11181
$949$	2959.15	0.101220
$950$	0	0
$951$	10703.4	0.364966
$952$	−933.888	−0.0317936
$953$	45776.5	1.55598	0.777988	−	0.628279i	$-0.216240\pi$
$953$	45776.5	1.55598	0.777988	+	0.628279i	$0.216240\pi$
$954$	20784.7	0.705377
$955$	0	0
$956$	33317.5	1.12716
$957$	−16669.6	−0.563064
$958$	30657.4	1.03392
$959$	14399.9	0.484878
$960$	0	0
$961$	29895.1	1.00349
$962$	−2570.68	−0.0861561
$963$	−15711.4	−0.525746
$964$	−60404.9	−2.01817
$965$	0	0
$966$	−4698.44	−0.156491
$967$	−34461.0	−1.14601	−0.573005	−	0.819552i	$-0.694222\pi$
$967$	−34461.0	−1.14601	−0.573005	+	0.819552i	$0.694222\pi$
$968$	19866.5	0.659643
$969$	105.967	0.00351304
$970$	0	0
$971$	−22762.8	−0.752309	−0.376154	−	0.926557i	$-0.622754\pi$
$971$	−22762.8	−0.752309	−0.376154	+	0.926557i	$0.622754\pi$
$972$	−3045.06	−0.100484
$973$	−12215.9	−0.402490
$974$	28819.9	0.948099
$975$	0	0
$976$	37.9251	0.00124381
$977$	−4809.57	−0.157494	−0.0787470	−	0.996895i	$-0.525092\pi$
$977$	−4809.57	−0.157494	−0.0787470	+	0.996895i	$0.525092\pi$
$978$	8084.10	0.264316
$979$	−6219.04	−0.203025
$980$	0	0
$981$	4291.70	0.139677
$982$	32046.6	1.04139
$983$	27591.6	0.895256	0.447628	−	0.894220i	$-0.352269\pi$
$983$	27591.6	0.895256	0.447628	+	0.894220i	$0.352269\pi$
$984$	19408.9	0.628793
$985$	0	0
$986$	8582.63	0.277207
$987$	1816.62	0.0585853
$988$	−200.109	−0.00644365
$989$	−14862.4	−0.477854
$990$	0	0
$991$	−22263.4	−0.713643	−0.356822	−	0.934173i	$-0.616140\pi$
$991$	−22263.4	−0.713643	−0.356822	+	0.934173i	$0.616140\pi$
$992$	48119.5	1.54012
$993$	13169.0	0.420851
$994$	−31854.5	−1.01646
$995$	0	0
$996$	50176.8	1.59630
$997$	−30378.2	−0.964983	−0.482491	−	0.875901i	$-0.660268\pi$
$997$	−30378.2	−0.964983	−0.482491	+	0.875901i	$0.660268\pi$
$998$	83707.4	2.65502
$999$	−5214.26	−0.165137

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.4.a.k.1.1		2
3.2	odd	2		1575.4.a.w.1.2		2
5.2	odd	4		525.4.d.h.274.1		4
5.3	odd	4		525.4.d.h.274.4		4
5.4	even	2		105.4.a.f.1.2	✓	2
15.14	odd	2		315.4.a.i.1.1		2
20.19	odd	2		1680.4.a.bg.1.2		2
35.34	odd	2		735.4.a.p.1.2		2
105.104	even	2		2205.4.a.z.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.a.f.1.2	✓	2	5.4	even	2
315.4.a.i.1.1		2	15.14	odd	2
525.4.a.k.1.1		2	1.1	even	1	trivial
525.4.d.h.274.1		4	5.2	odd	4
525.4.d.h.274.4		4	5.3	odd	4
735.4.a.p.1.2		2	35.34	odd	2
1575.4.a.w.1.2		2	3.2	odd	2
1680.4.a.bg.1.2		2	20.19	odd	2
2205.4.a.z.1.1		2	105.104	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	525.a (trivial)

\(f(q)\)	\(=\)	\(q-4.53113 q^{2} -3.00000 q^{3} +12.5311 q^{4} +13.5934 q^{6} +7.00000 q^{7} -20.5311 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-4.53113 q^{2} -3.00000 q^{3} +12.5311 q^{4} +13.5934 q^{6} +7.00000 q^{7} -20.5311 q^{8} +9.00000 q^{9} -19.0623 q^{11} -37.5934 q^{12} +2.93774 q^{13} -31.7179 q^{14} -7.21984 q^{16} +6.49806 q^{17} -40.7802 q^{18} -5.43580 q^{19} -21.0000 q^{21} +86.3735 q^{22} -49.3774 q^{23} +61.5934 q^{24} -13.3113 q^{26} -27.0000 q^{27} +87.7179 q^{28} -291.494 q^{29} +244.307 q^{31} +196.963 q^{32} +57.1868 q^{33} -29.4436 q^{34} +112.780 q^{36} +193.121 q^{37} +24.6303 q^{38} -8.81323 q^{39} +315.113 q^{41} +95.1537 q^{42} +300.996 q^{43} -238.872 q^{44} +223.735 q^{46} -86.5058 q^{47} +21.6595 q^{48} +49.0000 q^{49} -19.4942 q^{51} +36.8132 q^{52} -509.677 q^{53} +122.340 q^{54} -143.718 q^{56} +16.3074 q^{57} +1320.80 q^{58} -83.3852 q^{59} -5.25291 q^{61} -1106.99 q^{62} +63.0000 q^{63} -834.706 q^{64} -259.121 q^{66} -205.992 q^{67} +81.4281 q^{68} +148.132 q^{69} +1004.31 q^{71} -184.780 q^{72} +1007.29 q^{73} -875.055 q^{74} -68.1168 q^{76} -133.436 q^{77} +39.9339 q^{78} -863.237 q^{79} +81.0000 q^{81} -1427.82 q^{82} -1334.72 q^{83} -263.154 q^{84} -1363.85 q^{86} +874.483 q^{87} +391.370 q^{88} +326.249 q^{89} +20.5642 q^{91} -618.755 q^{92} -732.922 q^{93} +391.969 q^{94} -590.889 q^{96} -1526.77 q^{97} -222.025 q^{98} -171.560 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 6 q^{3} + 17 q^{4} + 3 q^{6} + 14 q^{7} - 33 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q - q^2 - 6 * q^3 + 17 * q^4 + 3 * q^6 + 14 * q^7 - 33 * q^8 + 18 * q^9	\( 2 q - q^{2} - 6 q^{3} + 17 q^{4} + 3 q^{6} + 14 q^{7} - 33 q^{8} + 18 q^{9} - 22 q^{11} - 51 q^{12} + 22 q^{13} - 7 q^{14} - 87 q^{16} - 116 q^{17} - 9 q^{18} + 102 q^{19} - 42 q^{21} + 76 q^{22} - 260 q^{23} + 99 q^{24} + 54 q^{26} - 54 q^{27} + 119 q^{28} - 196 q^{29} + 150 q^{31} + 15 q^{32} + 66 q^{33} - 462 q^{34} + 153 q^{36} + 96 q^{37} + 404 q^{38} - 66 q^{39} - 176 q^{41} + 21 q^{42} + 344 q^{43} - 252 q^{44} - 520 q^{46} - 560 q^{47} + 261 q^{48} + 98 q^{49} + 348 q^{51} + 122 q^{52} - 326 q^{53} + 27 q^{54} - 231 q^{56} - 306 q^{57} + 1658 q^{58} - 844 q^{59} - 204 q^{61} - 1440 q^{62} + 126 q^{63} - 839 q^{64} - 228 q^{66} + 104 q^{67} - 466 q^{68} + 780 q^{69} + 1670 q^{71} - 297 q^{72} + 386 q^{73} - 1218 q^{74} + 412 q^{76} - 154 q^{77} - 162 q^{78} - 888 q^{79} + 162 q^{81} - 3162 q^{82} - 928 q^{83} - 357 q^{84} - 1212 q^{86} + 588 q^{87} + 428 q^{88} + 588 q^{89} + 154 q^{91} - 1560 q^{92} - 450 q^{93} - 1280 q^{94} - 45 q^{96} - 522 q^{97} - 49 q^{98} - 198 q^{99}+O(q^{100}) \) 2 * q - q^2 - 6 * q^3 + 17 * q^4 + 3 * q^6 + 14 * q^7 - 33 * q^8 + 18 * q^9 - 22 * q^11 - 51 * q^12 + 22 * q^13 - 7 * q^14 - 87 * q^16 - 116 * q^17 - 9 * q^18 + 102 * q^19 - 42 * q^21 + 76 * q^22 - 260 * q^23 + 99 * q^24 + 54 * q^26 - 54 * q^27 + 119 * q^28 - 196 * q^29 + 150 * q^31 + 15 * q^32 + 66 * q^33 - 462 * q^34 + 153 * q^36 + 96 * q^37 + 404 * q^38 - 66 * q^39 - 176 * q^41 + 21 * q^42 + 344 * q^43 - 252 * q^44 - 520 * q^46 - 560 * q^47 + 261 * q^48 + 98 * q^49 + 348 * q^51 + 122 * q^52 - 326 * q^53 + 27 * q^54 - 231 * q^56 - 306 * q^57 + 1658 * q^58 - 844 * q^59 - 204 * q^61 - 1440 * q^62 + 126 * q^63 - 839 * q^64 - 228 * q^66 + 104 * q^67 - 466 * q^68 + 780 * q^69 + 1670 * q^71 - 297 * q^72 + 386 * q^73 - 1218 * q^74 + 412 * q^76 - 154 * q^77 - 162 * q^78 - 888 * q^79 + 162 * q^81 - 3162 * q^82 - 928 * q^83 - 357 * q^84 - 1212 * q^86 + 588 * q^87 + 428 * q^88 + 588 * q^89 + 154 * q^91 - 1560 * q^92 - 450 * q^93 - 1280 * q^94 - 45 * q^96 - 522 * q^97 - 49 * q^98 - 198 * q^99

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