LMFDB - Embedded newform 825.4.a.y.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("825.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.6765757547$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 21x^{3} + 17x^{2} + 78x - 30 $ x^5 - x^4 - 21x^3 + 17x^2 + 78*x - 30
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.368634$ of defining polynomial
Character	$\chi$	$=$	825.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.368634 q^{2} -3.00000 q^{3} -7.86411 q^{4} -1.10590 q^{6} -26.5824 q^{7} -5.84806 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+0.368634 q^{2} -3.00000 q^{3} -7.86411 q^{4} -1.10590 q^{6} -26.5824 q^{7} -5.84806 q^{8} +9.00000 q^{9} -11.0000 q^{11} +23.5923 q^{12} +50.4402 q^{13} -9.79918 q^{14} +60.7571 q^{16} +108.843 q^{17} +3.31771 q^{18} +19.1278 q^{19} +79.7471 q^{21} -4.05498 q^{22} +60.4434 q^{23} +17.5442 q^{24} +18.5940 q^{26} -27.0000 q^{27} +209.047 q^{28} -39.2097 q^{29} -22.4715 q^{31} +69.1816 q^{32} +33.0000 q^{33} +40.1234 q^{34} -70.7770 q^{36} -345.619 q^{37} +7.05117 q^{38} -151.321 q^{39} -96.3091 q^{41} +29.3975 q^{42} +335.088 q^{43} +86.5052 q^{44} +22.2815 q^{46} -514.880 q^{47} -182.271 q^{48} +363.623 q^{49} -326.530 q^{51} -396.667 q^{52} +131.589 q^{53} -9.95313 q^{54} +155.455 q^{56} -57.3834 q^{57} -14.4541 q^{58} -210.728 q^{59} -68.9791 q^{61} -8.28378 q^{62} -239.241 q^{63} -460.554 q^{64} +12.1649 q^{66} +202.618 q^{67} -855.955 q^{68} -181.330 q^{69} -645.234 q^{71} -52.6325 q^{72} +1021.75 q^{73} -127.407 q^{74} -150.423 q^{76} +292.406 q^{77} -55.7820 q^{78} +321.381 q^{79} +81.0000 q^{81} -35.5029 q^{82} +840.583 q^{83} -627.140 q^{84} +123.525 q^{86} +117.629 q^{87} +64.3286 q^{88} -1449.66 q^{89} -1340.82 q^{91} -475.333 q^{92} +67.4146 q^{93} -189.803 q^{94} -207.545 q^{96} +1602.70 q^{97} +134.044 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} - 15 q^{3} + 3 q^{4} - 3 q^{6} + 18 q^{7} - 3 q^{8} + 45 q^{9}+O(q^{10}) $ 5 * q + q^2 - 15 * q^3 + 3 * q^4 - 3 * q^6 + 18 * q^7 - 3 * q^8 + 45 * q^9	$ 5 q + q^{2} - 15 q^{3} + 3 q^{4} - 3 q^{6} + 18 q^{7} - 3 q^{8} + 45 q^{9} - 55 q^{11} - 9 q^{12} + 31 q^{13} + 8 q^{14} - 125 q^{16} + 38 q^{17} + 9 q^{18} - 57 q^{19} - 54 q^{21} - 11 q^{22} + 161 q^{23} + 9 q^{24} - 125 q^{26} - 135 q^{27} + 324 q^{28} - 107 q^{29} - 295 q^{31} - 23 q^{32} + 165 q^{33} + 34 q^{34} + 27 q^{36} - 260 q^{37} + 619 q^{38} - 93 q^{39} - 128 q^{41} - 24 q^{42} + 377 q^{43} - 33 q^{44} - 577 q^{46} - 114 q^{47} + 375 q^{48} - 415 q^{49} - 114 q^{51} - 395 q^{52} + 812 q^{53} - 27 q^{54} - 132 q^{56} + 171 q^{57} + 339 q^{58} - 1152 q^{59} - 344 q^{61} - 235 q^{62} + 162 q^{63} - 545 q^{64} + 33 q^{66} - 928 q^{67} + 654 q^{68} - 483 q^{69} - 707 q^{71} - 27 q^{72} + 322 q^{73} - 1176 q^{74} - 1699 q^{76} - 198 q^{77} + 375 q^{78} - 2494 q^{79} + 405 q^{81} - 2776 q^{82} + 1657 q^{83} - 972 q^{84} - 799 q^{86} + 321 q^{87} + 33 q^{88} - 2435 q^{89} - 804 q^{91} - 2775 q^{92} + 885 q^{93} - 502 q^{94} + 69 q^{96} - 1901 q^{97} + 343 q^{98} - 495 q^{99}+O(q^{100}) $ 5 * q + q^2 - 15 * q^3 + 3 * q^4 - 3 * q^6 + 18 * q^7 - 3 * q^8 + 45 * q^9 - 55 * q^11 - 9 * q^12 + 31 * q^13 + 8 * q^14 - 125 * q^16 + 38 * q^17 + 9 * q^18 - 57 * q^19 - 54 * q^21 - 11 * q^22 + 161 * q^23 + 9 * q^24 - 125 * q^26 - 135 * q^27 + 324 * q^28 - 107 * q^29 - 295 * q^31 - 23 * q^32 + 165 * q^33 + 34 * q^34 + 27 * q^36 - 260 * q^37 + 619 * q^38 - 93 * q^39 - 128 * q^41 - 24 * q^42 + 377 * q^43 - 33 * q^44 - 577 * q^46 - 114 * q^47 + 375 * q^48 - 415 * q^49 - 114 * q^51 - 395 * q^52 + 812 * q^53 - 27 * q^54 - 132 * q^56 + 171 * q^57 + 339 * q^58 - 1152 * q^59 - 344 * q^61 - 235 * q^62 + 162 * q^63 - 545 * q^64 + 33 * q^66 - 928 * q^67 + 654 * q^68 - 483 * q^69 - 707 * q^71 - 27 * q^72 + 322 * q^73 - 1176 * q^74 - 1699 * q^76 - 198 * q^77 + 375 * q^78 - 2494 * q^79 + 405 * q^81 - 2776 * q^82 + 1657 * q^83 - 972 * q^84 - 799 * q^86 + 321 * q^87 + 33 * q^88 - 2435 * q^89 - 804 * q^91 - 2775 * q^92 + 885 * q^93 - 502 * q^94 + 69 * q^96 - 1901 * q^97 + 343 * q^98 - 495 * 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 $

$2$	0.368634	0.130332	0.0651660	−	0.997874i	$-0.479242\pi$
$2$	0.368634	0.130332	0.0651660	+	0.997874i	$0.479242\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−7.86411	−0.983014
$5$	0	0
$5$	0	0
$6$	−1.10590	−0.0752472
$7$	−26.5824	−1.43531	−0.717657	−	0.696397i	$-0.754785\pi$
$7$	−26.5824	−1.43531	−0.717657	+	0.696397i	$0.754785\pi$
$8$	−5.84806	−0.258450
$9$	9.00000	0.333333
$10$	0	0
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	23.5923	0.567543
$13$	50.4402	1.07612	0.538061	−	0.842906i	$-0.319157\pi$
$13$	50.4402	1.07612	0.538061	+	0.842906i	$0.319157\pi$
$14$	−9.79918	−0.187067
$15$	0	0
$16$	60.7571	0.949329
$17$	108.843	1.55284	0.776422	−	0.630213i	$-0.217032\pi$
$17$	108.843	1.55284	0.776422	+	0.630213i	$0.217032\pi$
$18$	3.31771	0.0434440
$19$	19.1278	0.230959	0.115479	−	0.993310i	$-0.463160\pi$
$19$	19.1278	0.230959	0.115479	+	0.993310i	$0.463160\pi$
$20$	0	0
$21$	79.7471	0.828679
$22$	−4.05498	−0.0392966
$23$	60.4434	0.547970	0.273985	−	0.961734i	$-0.411658\pi$
$23$	60.4434	0.547970	0.273985	+	0.961734i	$0.411658\pi$
$24$	17.5442	0.149216
$25$	0	0
$26$	18.5940	0.140253
$27$	−27.0000	−0.192450
$28$	209.047	1.41093
$29$	−39.2097	−0.251071	−0.125536	−	0.992089i	$-0.540065\pi$
$29$	−39.2097	−0.251071	−0.125536	+	0.992089i	$0.540065\pi$
$30$	0	0
$31$	−22.4715	−0.130194	−0.0650969	−	0.997879i	$-0.520736\pi$
$31$	−22.4715	−0.130194	−0.0650969	+	0.997879i	$0.520736\pi$
$32$	69.1816	0.382178
$33$	33.0000	0.174078
$34$	40.1234	0.202385
$35$	0	0
$36$	−70.7770	−0.327671
$37$	−345.619	−1.53566	−0.767830	−	0.640654i	$-0.778663\pi$
$37$	−345.619	−1.53566	−0.767830	+	0.640654i	$0.778663\pi$
$38$	7.05117	0.0301013
$39$	−151.321	−0.621300
$40$	0	0
$41$	−96.3091	−0.366853	−0.183426	−	0.983033i	$-0.558719\pi$
$41$	−96.3091	−0.366853	−0.183426	+	0.983033i	$0.558719\pi$
$42$	29.3975	0.108003
$43$	335.088	1.18838	0.594191	−	0.804324i	$-0.297472\pi$
$43$	335.088	1.18838	0.594191	+	0.804324i	$0.297472\pi$
$44$	86.5052	0.296390
$45$	0	0
$46$	22.2815	0.0714180
$47$	−514.880	−1.59794	−0.798968	−	0.601373i	$-0.794621\pi$
$47$	−514.880	−1.59794	−0.798968	+	0.601373i	$0.794621\pi$
$48$	−182.271	−0.548096
$49$	363.623	1.06012
$50$	0	0
$51$	−326.530	−0.896535
$52$	−396.667	−1.05784
$53$	131.589	0.341041	0.170521	−	0.985354i	$-0.445455\pi$
$53$	131.589	0.341041	0.170521	+	0.985354i	$0.445455\pi$
$54$	−9.95313	−0.0250824
$55$	0	0
$56$	155.455	0.370957
$57$	−57.3834	−0.133344
$58$	−14.4541	−0.0327226
$59$	−210.728	−0.464991	−0.232495	−	0.972598i	$-0.574689\pi$
$59$	−210.728	−0.464991	−0.232495	+	0.972598i	$0.574689\pi$
$60$	0	0
$61$	−68.9791	−0.144785	−0.0723924	−	0.997376i	$-0.523063\pi$
$61$	−68.9791	−0.144785	−0.0723924	+	0.997376i	$0.523063\pi$
$62$	−8.28378	−0.0169684
$63$	−239.241	−0.478438
$64$	−460.554	−0.899519
$65$	0	0
$66$	12.1649	0.0226879
$67$	202.618	0.369459	0.184729	−	0.982789i	$-0.440859\pi$
$67$	202.618	0.369459	0.184729	+	0.982789i	$0.440859\pi$
$68$	−855.955	−1.52647
$69$	−181.330	−0.316371
$70$	0	0
$71$	−645.234	−1.07852	−0.539262	−	0.842138i	$-0.681297\pi$
$71$	−645.234	−1.07852	−0.539262	+	0.842138i	$0.681297\pi$
$72$	−52.6325	−0.0861500
$73$	1021.75	1.63818	0.819089	−	0.573666i	$-0.194479\pi$
$73$	1021.75	1.63818	0.819089	+	0.573666i	$0.194479\pi$
$74$	−127.407	−0.200145
$75$	0	0
$76$	−150.423	−0.227036
$77$	292.406	0.432763
$78$	−55.7820	−0.0809752
$79$	321.381	0.457699	0.228849	−	0.973462i	$-0.426504\pi$
$79$	321.381	0.457699	0.228849	+	0.973462i	$0.426504\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	−35.5029	−0.0478126
$83$	840.583	1.11164	0.555819	−	0.831303i	$-0.312405\pi$
$83$	840.583	1.11164	0.555819	+	0.831303i	$0.312405\pi$
$84$	−627.140	−0.814602
$85$	0	0
$86$	123.525	0.154884
$87$	117.629	0.144956
$88$	64.3286	0.0779256
$89$	−1449.66	−1.72655	−0.863277	−	0.504731i	$-0.831592\pi$
$89$	−1449.66	−1.72655	−0.863277	+	0.504731i	$0.831592\pi$
$90$	0	0
$91$	−1340.82	−1.54457
$92$	−475.333	−0.538662
$93$	67.4146	0.0751674
$94$	−189.803	−0.208262
$95$	0	0
$96$	−207.545	−0.220651
$97$	1602.70	1.67762	0.838811	−	0.544422i	$-0.183251\pi$
$97$	1602.70	1.67762	0.838811	+	0.544422i	$0.183251\pi$
$98$	134.044	0.138168
$99$	−99.0000	−0.100504
$100$	0	0
$101$	−970.653	−0.956273	−0.478136	−	0.878286i	$-0.658688\pi$
$101$	−970.653	−0.956273	−0.478136	+	0.878286i	$0.658688\pi$
$102$	−120.370	−0.116847
$103$	−185.474	−0.177430	−0.0887152	−	0.996057i	$-0.528276\pi$
$103$	−185.474	−0.177430	−0.0887152	+	0.996057i	$0.528276\pi$
$104$	−294.977	−0.278124
$105$	0	0
$106$	48.5084	0.0444486
$107$	−652.518	−0.589545	−0.294773	−	0.955567i	$-0.595244\pi$
$107$	−652.518	−0.589545	−0.294773	+	0.955567i	$0.595244\pi$
$108$	212.331	0.189181
$109$	−915.109	−0.804143	−0.402071	−	0.915608i	$-0.631710\pi$
$109$	−915.109	−0.804143	−0.402071	+	0.915608i	$0.631710\pi$
$110$	0	0
$111$	1036.86	0.886613
$112$	−1615.07	−1.36258
$113$	327.063	0.272279	0.136139	−	0.990690i	$-0.456530\pi$
$113$	327.063	0.272279	0.136139	+	0.990690i	$0.456530\pi$
$114$	−21.1535	−0.0173790
$115$	0	0
$116$	308.349	0.246806
$117$	453.962	0.358708
$118$	−77.6816	−0.0606031
$119$	−2893.31	−2.22882
$120$	0	0
$121$	121.000	0.0909091
$122$	−25.4281	−0.0188701
$123$	288.927	0.211802
$124$	176.719	0.127982
$125$	0	0
$126$	−88.1926	−0.0623557
$127$	−1739.39	−1.21532	−0.607661	−	0.794196i	$-0.707892\pi$
$127$	−1739.39	−1.21532	−0.607661	+	0.794196i	$0.707892\pi$
$128$	−723.229	−0.499414
$129$	−1005.26	−0.686112
$130$	0	0
$131$	1537.93	1.02572	0.512860	−	0.858472i	$-0.328586\pi$
$131$	1537.93	1.02572	0.512860	+	0.858472i	$0.328586\pi$
$132$	−259.516	−0.171121
$133$	−508.463	−0.331498
$134$	74.6920	0.0481523
$135$	0	0
$136$	−636.521	−0.401333
$137$	1885.08	1.17557	0.587787	−	0.809016i	$-0.299999\pi$
$137$	1885.08	1.17557	0.587787	+	0.809016i	$0.299999\pi$
$138$	−66.8445	−0.0412332
$139$	−482.323	−0.294317	−0.147159	−	0.989113i	$-0.547013\pi$
$139$	−482.323	−0.294317	−0.147159	+	0.989113i	$0.547013\pi$
$140$	0	0
$141$	1544.64	0.922569
$142$	−237.855	−0.140566
$143$	−554.842	−0.324463
$144$	546.814	0.316443
$145$	0	0
$146$	376.653	0.213507
$147$	−1090.87	−0.612063
$148$	2717.98	1.50957
$149$	−757.043	−0.416237	−0.208119	−	0.978104i	$-0.566734\pi$
$149$	−757.043	−0.416237	−0.208119	+	0.978104i	$0.566734\pi$
$150$	0	0
$151$	−2919.01	−1.57315	−0.786576	−	0.617494i	$-0.788148\pi$
$151$	−2919.01	−1.57315	−0.786576	+	0.617494i	$0.788148\pi$
$152$	−111.861	−0.0596914
$153$	979.589	0.517615
$154$	107.791	0.0564029
$155$	0	0
$156$	1190.00	0.610746
$157$	−1352.65	−0.687599	−0.343799	−	0.939043i	$-0.611714\pi$
$157$	−1352.65	−0.687599	−0.343799	+	0.939043i	$0.611714\pi$
$158$	118.472	0.0596527
$159$	−394.768	−0.196900
$160$	0	0
$161$	−1606.73	−0.786509
$162$	29.8594	0.0144813
$163$	−3027.63	−1.45486	−0.727431	−	0.686181i	$-0.759286\pi$
$163$	−3027.63	−1.45486	−0.727431	+	0.686181i	$0.759286\pi$
$164$	757.385	0.360621
$165$	0	0
$166$	309.868	0.144882
$167$	−4225.69	−1.95805	−0.979023	−	0.203749i	$-0.934687\pi$
$167$	−4225.69	−1.95805	−0.979023	+	0.203749i	$0.934687\pi$
$168$	−466.366	−0.214172
$169$	347.214	0.158040
$170$	0	0
$171$	172.150	0.0769863
$172$	−2635.17	−1.16820
$173$	1515.20	0.665886	0.332943	−	0.942947i	$-0.391958\pi$
$173$	1515.20	0.665886	0.332943	+	0.942947i	$0.391958\pi$
$174$	43.3622	0.0188924
$175$	0	0
$176$	−668.328	−0.286234
$177$	632.184	0.268462
$178$	−534.393	−0.225025
$179$	1087.42	0.454066	0.227033	−	0.973887i	$-0.427098\pi$
$179$	1087.42	0.454066	0.227033	+	0.973887i	$0.427098\pi$
$180$	0	0
$181$	−145.994	−0.0599538	−0.0299769	−	0.999551i	$-0.509543\pi$
$181$	−145.994	−0.0599538	−0.0299769	+	0.999551i	$0.509543\pi$
$182$	−494.273	−0.201307
$183$	206.937	0.0835915
$184$	−353.476	−0.141623
$185$	0	0
$186$	24.8514	0.00979672
$187$	−1197.28	−0.468200
$188$	4049.08	1.57079
$189$	717.724	0.276226
$190$	0	0
$191$	3586.76	1.35879	0.679395	−	0.733773i	$-0.262243\pi$
$191$	3586.76	1.35879	0.679395	+	0.733773i	$0.262243\pi$
$192$	1381.66	0.519338
$193$	1015.55	0.378762	0.189381	−	0.981904i	$-0.439352\pi$
$193$	1015.55	0.378762	0.189381	+	0.981904i	$0.439352\pi$
$194$	590.810	0.218648
$195$	0	0
$196$	−2859.57	−1.04212
$197$	2992.63	1.08231	0.541157	−	0.840921i	$-0.317986\pi$
$197$	2992.63	1.08231	0.541157	+	0.840921i	$0.317986\pi$
$198$	−36.4948	−0.0130989
$199$	−3267.57	−1.16398	−0.581989	−	0.813196i	$-0.697725\pi$
$199$	−3267.57	−1.16398	−0.581989	+	0.813196i	$0.697725\pi$
$200$	0	0
$201$	−607.854	−0.213307
$202$	−357.816	−0.124633
$203$	1042.29	0.360366
$204$	2567.86	0.881306
$205$	0	0
$206$	−68.3722	−0.0231248
$207$	543.990	0.182657
$208$	3064.60	1.02159
$209$	−210.406	−0.0696368
$210$	0	0
$211$	−4275.02	−1.39481	−0.697403	−	0.716679i	$-0.745661\pi$
$211$	−4275.02	−1.39481	−0.697403	+	0.716679i	$0.745661\pi$
$212$	−1034.83	−0.335248
$213$	1935.70	0.622686
$214$	−240.541	−0.0768366
$215$	0	0
$216$	157.898	0.0497387
$217$	597.347	0.186869
$218$	−337.341	−0.104805
$219$	−3065.26	−0.945803
$220$	0	0
$221$	5490.07	1.67105
$222$	382.221	0.115554
$223$	−3771.24	−1.13247	−0.566235	−	0.824244i	$-0.691601\pi$
$223$	−3771.24	−1.13247	−0.566235	+	0.824244i	$0.691601\pi$
$224$	−1839.01	−0.548545
$225$	0	0
$226$	120.567	0.0354866
$227$	2891.58	0.845467	0.422733	−	0.906254i	$-0.361071\pi$
$227$	2891.58	0.845467	0.422733	+	0.906254i	$0.361071\pi$
$228$	451.270	0.131079
$229$	921.309	0.265859	0.132930	−	0.991125i	$-0.457562\pi$
$229$	921.309	0.265859	0.132930	+	0.991125i	$0.457562\pi$
$230$	0	0
$231$	−877.218	−0.249856
$232$	229.301	0.0648893
$233$	2818.65	0.792516	0.396258	−	0.918139i	$-0.370309\pi$
$233$	2818.65	0.792516	0.396258	+	0.918139i	$0.370309\pi$
$234$	167.346	0.0467511
$235$	0	0
$236$	1657.19	0.457092
$237$	−964.143	−0.264252
$238$	−1066.57	−0.290486
$239$	783.622	0.212085	0.106042	−	0.994362i	$-0.466182\pi$
$239$	783.622	0.212085	0.106042	+	0.994362i	$0.466182\pi$
$240$	0	0
$241$	5891.99	1.57484	0.787420	−	0.616417i	$-0.211417\pi$
$241$	5891.99	1.57484	0.787420	+	0.616417i	$0.211417\pi$
$242$	44.6048	0.0118484
$243$	−243.000	−0.0641500
$244$	542.459	0.142325
$245$	0	0
$246$	106.509	0.0276046
$247$	964.811	0.248540
$248$	131.415	0.0336486
$249$	−2521.75	−0.641805
$250$	0	0
$251$	−7892.69	−1.98479	−0.992394	−	0.123101i	$-0.960716\pi$
$251$	−7892.69	−1.98479	−0.992394	+	0.123101i	$0.960716\pi$
$252$	1881.42	0.470311
$253$	−664.877	−0.165219
$254$	−641.199	−0.158395
$255$	0	0
$256$	3417.82	0.834430
$257$	3375.73	0.819348	0.409674	−	0.912232i	$-0.365643\pi$
$257$	3375.73	0.819348	0.409674	+	0.912232i	$0.365643\pi$
$258$	−370.575	−0.0894224
$259$	9187.37	2.20415
$260$	0	0
$261$	−352.887	−0.0836904
$262$	566.933	0.133684
$263$	−1823.12	−0.427447	−0.213724	−	0.976894i	$-0.568559\pi$
$263$	−1823.12	−0.427447	−0.213724	+	0.976894i	$0.568559\pi$
$264$	−192.986	−0.0449904
$265$	0	0
$266$	−187.437	−0.0432048
$267$	4348.97	0.996826
$268$	−1593.41	−0.363183
$269$	−7312.95	−1.65754	−0.828770	−	0.559590i	$-0.810959\pi$
$269$	−7312.95	−1.65754	−0.828770	+	0.559590i	$0.810959\pi$
$270$	0	0
$271$	6168.14	1.38261	0.691306	−	0.722562i	$-0.257036\pi$
$271$	6168.14	1.38261	0.691306	+	0.722562i	$0.257036\pi$
$272$	6612.99	1.47416
$273$	4022.46	0.891760
$274$	694.907	0.153215
$275$	0	0
$276$	1426.00	0.310997
$277$	−1858.13	−0.403048	−0.201524	−	0.979484i	$-0.564589\pi$
$277$	−1858.13	−0.403048	−0.201524	+	0.979484i	$0.564589\pi$
$278$	−177.801	−0.0383589
$279$	−202.244	−0.0433979
$280$	0	0
$281$	−7716.88	−1.63826	−0.819129	−	0.573609i	$-0.805543\pi$
$281$	−7716.88	−1.63826	−0.819129	+	0.573609i	$0.805543\pi$
$282$	569.408	0.120240
$283$	−6582.51	−1.38265	−0.691324	−	0.722545i	$-0.742972\pi$
$283$	−6582.51	−1.38265	−0.691324	+	0.722545i	$0.742972\pi$
$284$	5074.19	1.06020
$285$	0	0
$286$	−204.534	−0.0422879
$287$	2560.12	0.526548
$288$	622.634	0.127393
$289$	6933.84	1.41133
$290$	0	0
$291$	−4808.10	−0.968576
$292$	−8035.17	−1.61035
$293$	−4788.12	−0.954692	−0.477346	−	0.878715i	$-0.658401\pi$
$293$	−4788.12	−0.954692	−0.477346	+	0.878715i	$0.658401\pi$
$294$	−402.131	−0.0797714
$295$	0	0
$296$	2021.20	0.396891
$297$	297.000	0.0580259
$298$	−279.072	−0.0542490
$299$	3048.78	0.589683
$300$	0	0
$301$	−8907.43	−1.70570
$302$	−1076.05	−0.205032
$303$	2911.96	0.552104
$304$	1162.15	0.219256
$305$	0	0
$306$	361.110	0.0674617
$307$	−6612.72	−1.22934	−0.614671	−	0.788784i	$-0.710711\pi$
$307$	−6612.72	−1.22934	−0.614671	+	0.788784i	$0.710711\pi$
$308$	−2299.51	−0.425412
$309$	556.423	0.102439
$310$	0	0
$311$	−1915.55	−0.349264	−0.174632	−	0.984634i	$-0.555874\pi$
$311$	−1915.55	−0.349264	−0.174632	+	0.984634i	$0.555874\pi$
$312$	884.931	0.160575
$313$	−6383.65	−1.15280	−0.576398	−	0.817169i	$-0.695542\pi$
$313$	−6383.65	−1.15280	−0.576398	+	0.817169i	$0.695542\pi$
$314$	−498.632	−0.0896161
$315$	0	0
$316$	−2527.38	−0.449924
$317$	10128.7	1.79459	0.897293	−	0.441434i	$-0.145530\pi$
$317$	10128.7	1.79459	0.897293	+	0.441434i	$0.145530\pi$
$318$	−145.525	−0.0256624
$319$	431.307	0.0757008
$320$	0	0
$321$	1957.56	0.340374
$322$	−592.295	−0.102507
$323$	2081.93	0.358643
$324$	−636.993	−0.109224
$325$	0	0
$326$	−1116.09	−0.189615
$327$	2745.33	0.464272
$328$	563.221	0.0948131
$329$	13686.7	2.29354
$330$	0	0
$331$	3453.52	0.573483	0.286741	−	0.958008i	$-0.407428\pi$
$331$	3453.52	0.573483	0.286741	+	0.958008i	$0.407428\pi$
$332$	−6610.44	−1.09276
$333$	−3110.57	−0.511886
$334$	−1557.73	−0.255196
$335$	0	0
$336$	4845.20	0.786689
$337$	−4246.90	−0.686480	−0.343240	−	0.939248i	$-0.611524\pi$
$337$	−4246.90	−0.686480	−0.343240	+	0.939248i	$0.611524\pi$
$338$	127.995	0.0205977
$339$	−981.190	−0.157200
$340$	0	0
$341$	247.187	0.0392549
$342$	63.4605	0.0100338
$343$	−548.198	−0.0862971
$344$	−1959.61	−0.307137
$345$	0	0
$346$	558.554	0.0867863
$347$	10332.8	1.59854	0.799268	−	0.600975i	$-0.205221\pi$
$347$	10332.8	1.59854	0.799268	+	0.600975i	$0.205221\pi$
$348$	−925.048	−0.142494
$349$	−3899.90	−0.598156	−0.299078	−	0.954229i	$-0.596679\pi$
$349$	−3899.90	−0.598156	−0.299078	+	0.954229i	$0.596679\pi$
$350$	0	0
$351$	−1361.89	−0.207100
$352$	−760.998	−0.115231
$353$	−7564.03	−1.14049	−0.570245	−	0.821475i	$-0.693152\pi$
$353$	−7564.03	−1.14049	−0.570245	+	0.821475i	$0.693152\pi$
$354$	233.045	0.0349892
$355$	0	0
$356$	11400.3	1.69723
$357$	8679.93	1.28681
$358$	400.861	0.0591793
$359$	−11198.7	−1.64637	−0.823185	−	0.567773i	$-0.807805\pi$
$359$	−11198.7	−1.64637	−0.823185	+	0.567773i	$0.807805\pi$
$360$	0	0
$361$	−6493.13	−0.946658
$362$	−53.8183	−0.00781389
$363$	−363.000	−0.0524864
$364$	10544.4	1.51834
$365$	0	0
$366$	76.2842	0.0108946
$367$	−5939.65	−0.844816	−0.422408	−	0.906406i	$-0.638815\pi$
$367$	−5939.65	−0.844816	−0.422408	+	0.906406i	$0.638815\pi$
$368$	3672.36	0.520204
$369$	−866.782	−0.122284
$370$	0	0
$371$	−3497.96	−0.489501
$372$	−530.156	−0.0738906
$373$	−20.1820	−0.00280157	−0.00140078	−	0.999999i	$-0.500446\pi$
$373$	−20.1820	−0.00280157	−0.00140078	+	0.999999i	$0.500446\pi$
$374$	−441.357	−0.0610214
$375$	0	0
$376$	3011.05	0.412987
$377$	−1977.75	−0.270183
$378$	264.578	0.0360011
$379$	8241.81	1.11703	0.558514	−	0.829495i	$-0.311372\pi$
$379$	8241.81	1.11703	0.558514	+	0.829495i	$0.311372\pi$
$380$	0	0
$381$	5218.17	0.701667
$382$	1322.20	0.177094
$383$	−9971.48	−1.33034	−0.665168	−	0.746694i	$-0.731640\pi$
$383$	−9971.48	−1.33034	−0.665168	+	0.746694i	$0.731640\pi$
$384$	2169.69	0.288337
$385$	0	0
$386$	374.367	0.0493647
$387$	3015.79	0.396127
$388$	−12603.8	−1.64913
$389$	6897.31	0.898991	0.449496	−	0.893283i	$-0.351604\pi$
$389$	6897.31	0.898991	0.449496	+	0.893283i	$0.351604\pi$
$390$	0	0
$391$	6578.85	0.850913
$392$	−2126.49	−0.273989
$393$	−4613.78	−0.592200
$394$	1103.19	0.141060
$395$	0	0
$396$	778.547	0.0987966
$397$	−10587.7	−1.33849	−0.669243	−	0.743043i	$-0.733382\pi$
$397$	−10587.7	−1.33849	−0.669243	+	0.743043i	$0.733382\pi$
$398$	−1204.54	−0.151704
$399$	1525.39	0.191391
$400$	0	0
$401$	5700.87	0.709944	0.354972	−	0.934877i	$-0.384490\pi$
$401$	5700.87	0.709944	0.354972	+	0.934877i	$0.384490\pi$
$402$	−224.076	−0.0278007
$403$	−1133.47	−0.140105
$404$	7633.32	0.940029
$405$	0	0
$406$	384.223	0.0469672
$407$	3801.81	0.463019
$408$	1909.56	0.231710
$409$	2389.92	0.288934	0.144467	−	0.989510i	$-0.453853\pi$
$409$	2389.92	0.288934	0.144467	+	0.989510i	$0.453853\pi$
$410$	0	0
$411$	−5655.25	−0.678718
$412$	1458.59	0.174416
$413$	5601.65	0.667407
$414$	200.534	0.0238060
$415$	0	0
$416$	3489.53	0.411270
$417$	1446.97	0.169924
$418$	−77.5629	−0.00907589
$419$	2338.30	0.272633	0.136316	−	0.990665i	$-0.456474\pi$
$419$	2338.30	0.272633	0.136316	+	0.990665i	$0.456474\pi$
$420$	0	0
$421$	−9848.22	−1.14008	−0.570039	−	0.821618i	$-0.693072\pi$
$421$	−9848.22	−1.14008	−0.570039	+	0.821618i	$0.693072\pi$
$422$	−1575.92	−0.181788
$423$	−4633.92	−0.532646
$424$	−769.542	−0.0881422
$425$	0	0
$426$	713.566	0.0811559
$427$	1833.63	0.207811
$428$	5131.48	0.579531
$429$	1664.53	0.187329
$430$	0	0
$431$	13734.9	1.53501	0.767504	−	0.641045i	$-0.221499\pi$
$431$	13734.9	1.53501	0.767504	+	0.641045i	$0.221499\pi$
$432$	−1640.44	−0.182699
$433$	−300.831	−0.0333881	−0.0166940	−	0.999861i	$-0.505314\pi$
$433$	−300.831	−0.0333881	−0.0166940	+	0.999861i	$0.505314\pi$
$434$	220.203	0.0243550
$435$	0	0
$436$	7196.52	0.790483
$437$	1156.15	0.126559
$438$	−1129.96	−0.123268
$439$	12002.9	1.30494	0.652468	−	0.757816i	$-0.273734\pi$
$439$	12002.9	1.30494	0.652468	+	0.757816i	$0.273734\pi$
$440$	0	0
$441$	3272.60	0.353375
$442$	2023.83	0.217791
$443$	9448.03	1.01329	0.506647	−	0.862153i	$-0.330885\pi$
$443$	9448.03	1.01329	0.506647	+	0.862153i	$0.330885\pi$
$444$	−8153.95	−0.871553
$445$	0	0
$446$	−1390.21	−0.147597
$447$	2271.13	0.240315
$448$	12242.6	1.29109
$449$	−5412.07	−0.568845	−0.284422	−	0.958699i	$-0.591802\pi$
$449$	−5412.07	−0.568845	−0.284422	+	0.958699i	$0.591802\pi$
$450$	0	0
$451$	1059.40	0.110610
$452$	−2572.06	−0.267654
$453$	8757.04	0.908259
$454$	1065.94	0.110191
$455$	0	0
$456$	335.582	0.0344628
$457$	10009.7	1.02458	0.512291	−	0.858812i	$-0.328797\pi$
$457$	10009.7	1.02458	0.512291	+	0.858812i	$0.328797\pi$
$458$	339.626	0.0346500
$459$	−2938.77	−0.298845
$460$	0	0
$461$	9058.72	0.915199	0.457599	−	0.889159i	$-0.348709\pi$
$461$	9058.72	0.915199	0.457599	+	0.889159i	$0.348709\pi$
$462$	−323.373	−0.0325642
$463$	−16017.2	−1.60774	−0.803871	−	0.594804i	$-0.797230\pi$
$463$	−16017.2	−1.60774	−0.803871	+	0.594804i	$0.797230\pi$
$464$	−2382.27	−0.238349
$465$	0	0
$466$	1039.05	0.103290
$467$	−10318.0	−1.02240	−0.511201	−	0.859461i	$-0.670799\pi$
$467$	−10318.0	−1.02240	−0.511201	+	0.859461i	$0.670799\pi$
$468$	−3570.00	−0.352614
$469$	−5386.07	−0.530289
$470$	0	0
$471$	4057.94	0.396985
$472$	1232.35	0.120177
$473$	−3685.97	−0.358311
$474$	−355.416	−0.0344405
$475$	0	0
$476$	22753.3	2.19096
$477$	1184.30	0.113680
$478$	288.870	0.0276414
$479$	−9810.96	−0.935854	−0.467927	−	0.883767i	$-0.654999\pi$
$479$	−9810.96	−0.935854	−0.467927	+	0.883767i	$0.654999\pi$
$480$	0	0
$481$	−17433.1	−1.65256
$482$	2171.99	0.205252
$483$	4820.19	0.454091
$484$	−951.557	−0.0893649
$485$	0	0
$486$	−89.5782	−0.00836080
$487$	8081.87	0.752001	0.376001	−	0.926619i	$-0.377299\pi$
$487$	8081.87	0.752001	0.376001	+	0.926619i	$0.377299\pi$
$488$	403.394	0.0374196
$489$	9082.90	0.839965
$490$	0	0
$491$	−5645.54	−0.518900	−0.259450	−	0.965757i	$-0.583541\pi$
$491$	−5645.54	−0.518900	−0.259450	+	0.965757i	$0.583541\pi$
$492$	−2272.16	−0.208205
$493$	−4267.71	−0.389874
$494$	355.662	0.0323927
$495$	0	0
$496$	−1365.31	−0.123597
$497$	17151.8	1.54802
$498$	−929.604	−0.0836477
$499$	4176.04	0.374640	0.187320	−	0.982299i	$-0.440020\pi$
$499$	4176.04	0.374640	0.187320	+	0.982299i	$0.440020\pi$
$500$	0	0
$501$	12677.1	1.13048
$502$	−2909.52	−0.258681
$503$	9131.76	0.809473	0.404737	−	0.914433i	$-0.367363\pi$
$503$	9131.76	0.809473	0.404737	+	0.914433i	$0.367363\pi$
$504$	1399.10	0.123652
$505$	0	0
$506$	−245.097	−0.0215333
$507$	−1041.64	−0.0912444
$508$	13678.8	1.19468
$509$	21062.6	1.83415	0.917076	−	0.398712i	$-0.130543\pi$
$509$	21062.6	1.83415	0.917076	+	0.398712i	$0.130543\pi$
$510$	0	0
$511$	−27160.6	−2.35130
$512$	7045.76	0.608167
$513$	−516.451	−0.0444481
$514$	1244.41	0.106787
$515$	0	0
$516$	7905.50	0.674458
$517$	5663.68	0.481796
$518$	3386.78	0.287271
$519$	−4545.59	−0.384450
$520$	0	0
$521$	−6858.67	−0.576744	−0.288372	−	0.957518i	$-0.593114\pi$
$521$	−6858.67	−0.576744	−0.288372	+	0.957518i	$0.593114\pi$
$522$	−130.086	−0.0109075
$523$	5752.51	0.480956	0.240478	−	0.970655i	$-0.422696\pi$
$523$	5752.51	0.480956	0.240478	+	0.970655i	$0.422696\pi$
$524$	−12094.4	−1.00830
$525$	0	0
$526$	−672.067	−0.0557101
$527$	−2445.87	−0.202171
$528$	2004.98	0.165257
$529$	−8513.60	−0.699729
$530$	0	0
$531$	−1896.55	−0.154997
$532$	3998.61	0.325868
$533$	−4857.85	−0.394778
$534$	1603.18	0.129918
$535$	0	0
$536$	−1184.92	−0.0954866
$537$	−3262.27	−0.262155
$538$	−2695.80	−0.216030
$539$	−3999.85	−0.319639
$540$	0	0
$541$	4957.66	0.393986	0.196993	−	0.980405i	$-0.436882\pi$
$541$	4957.66	0.393986	0.196993	+	0.980405i	$0.436882\pi$
$542$	2273.79	0.180199
$543$	437.981	0.0346143
$544$	7529.95	0.593463
$545$	0	0
$546$	1482.82	0.116225
$547$	−19515.0	−1.52542	−0.762709	−	0.646742i	$-0.776131\pi$
$547$	−19515.0	−1.52542	−0.762709	+	0.646742i	$0.776131\pi$
$548$	−14824.5	−1.15560
$549$	−620.812	−0.0482616
$550$	0	0
$551$	−749.996	−0.0579871
$552$	1060.43	0.0817660
$553$	−8543.07	−0.656941
$554$	−684.971	−0.0525301
$555$	0	0
$556$	3793.04	0.289318
$557$	−227.163	−0.0172804	−0.00864022	−	0.999963i	$-0.502750\pi$
$557$	−227.163	−0.0172804	−0.00864022	+	0.999963i	$0.502750\pi$
$558$	−74.5541	−0.00565614
$559$	16901.9	1.27884
$560$	0	0
$561$	3591.83	0.270316
$562$	−2844.71	−0.213517
$563$	−18313.6	−1.37092	−0.685460	−	0.728110i	$-0.740399\pi$
$563$	−18313.6	−1.37092	−0.685460	+	0.728110i	$0.740399\pi$
$564$	−12147.2	−0.906898
$565$	0	0
$566$	−2426.54	−0.180203
$567$	−2153.17	−0.159479
$568$	3773.36	0.278744
$569$	−5703.35	−0.420206	−0.210103	−	0.977679i	$-0.567380\pi$
$569$	−5703.35	−0.420206	−0.210103	+	0.977679i	$0.567380\pi$
$570$	0	0
$571$	−14797.1	−1.08448	−0.542241	−	0.840223i	$-0.682424\pi$
$571$	−14797.1	−1.08448	−0.542241	+	0.840223i	$0.682424\pi$
$572$	4363.34	0.318952
$573$	−10760.3	−0.784497
$574$	943.750	0.0686261
$575$	0	0
$576$	−4144.98	−0.299840
$577$	2045.44	0.147578	0.0737891	−	0.997274i	$-0.476491\pi$
$577$	2045.44	0.147578	0.0737891	+	0.997274i	$0.476491\pi$
$578$	2556.05	0.183941
$579$	−3046.65	−0.218678
$580$	0	0
$581$	−22344.7	−1.59555
$582$	−1772.43	−0.126236
$583$	−1447.48	−0.102828
$584$	−5975.27	−0.423387
$585$	0	0
$586$	−1765.06	−0.124427
$587$	−10482.6	−0.737075	−0.368537	−	0.929613i	$-0.620141\pi$
$587$	−10482.6	−0.737075	−0.368537	+	0.929613i	$0.620141\pi$
$588$	8578.70	0.601666
$589$	−429.831	−0.0300694
$590$	0	0
$591$	−8977.89	−0.624875
$592$	−20998.8	−1.45785
$593$	−938.019	−0.0649575	−0.0324788	−	0.999472i	$-0.510340\pi$
$593$	−938.019	−0.0649575	−0.0324788	+	0.999472i	$0.510340\pi$
$594$	109.484	0.00756263
$595$	0	0
$596$	5953.47	0.409167
$597$	9802.70	0.672023
$598$	1123.88	0.0768546
$599$	2885.83	0.196848	0.0984239	−	0.995145i	$-0.468620\pi$
$599$	2885.83	0.196848	0.0984239	+	0.995145i	$0.468620\pi$
$600$	0	0
$601$	−25636.7	−1.74000	−0.870001	−	0.493049i	$-0.835882\pi$
$601$	−25636.7	−1.74000	−0.870001	+	0.493049i	$0.835882\pi$
$602$	−3283.59	−0.222307
$603$	1823.56	0.123153
$604$	22955.4	1.54643
$605$	0	0
$606$	1073.45	0.0719568
$607$	−9924.91	−0.663657	−0.331828	−	0.943340i	$-0.607665\pi$
$607$	−9924.91	−0.663657	−0.331828	+	0.943340i	$0.607665\pi$
$608$	1323.29	0.0882674
$609$	−3126.86	−0.208057
$610$	0	0
$611$	−25970.7	−1.71958
$612$	−7703.59	−0.508822
$613$	−9514.05	−0.626866	−0.313433	−	0.949610i	$-0.601479\pi$
$613$	−9514.05	−0.626866	−0.313433	+	0.949610i	$0.601479\pi$
$614$	−2437.68	−0.160222
$615$	0	0
$616$	−1710.01	−0.111848
$617$	−25714.5	−1.67784	−0.838920	−	0.544255i	$-0.816812\pi$
$617$	−25714.5	−1.67784	−0.838920	+	0.544255i	$0.816812\pi$
$618$	205.117	0.0133511
$619$	−17933.5	−1.16447	−0.582235	−	0.813020i	$-0.697822\pi$
$619$	−17933.5	−1.16447	−0.582235	+	0.813020i	$0.697822\pi$
$620$	0	0
$621$	−1631.97	−0.105457
$622$	−706.139	−0.0455203
$623$	38535.3	2.47815
$624$	−9193.80	−0.589818
$625$	0	0
$626$	−2353.23	−0.150246
$627$	631.218	0.0402048
$628$	10637.4	0.675919
$629$	−37618.3	−2.38464
$630$	0	0
$631$	−3836.00	−0.242011	−0.121005	−	0.992652i	$-0.538612\pi$
$631$	−3836.00	−0.242011	−0.121005	+	0.992652i	$0.538612\pi$
$632$	−1879.45	−0.118292
$633$	12825.0	0.805292
$634$	3733.78	0.233892
$635$	0	0
$636$	3104.50	0.193556
$637$	18341.2	1.14082
$638$	158.995	0.00986623
$639$	−5807.10	−0.359508
$640$	0	0
$641$	20430.4	1.25890	0.629449	−	0.777042i	$-0.283281\pi$
$641$	20430.4	1.25890	0.629449	+	0.777042i	$0.283281\pi$
$642$	721.622	0.0443616
$643$	14252.9	0.874152	0.437076	−	0.899424i	$-0.356014\pi$
$643$	14252.9	0.874152	0.437076	+	0.899424i	$0.356014\pi$
$644$	12635.5	0.773149
$645$	0	0
$646$	767.472	0.0467427
$647$	18729.4	1.13807	0.569033	−	0.822315i	$-0.307318\pi$
$647$	18729.4	1.13807	0.569033	+	0.822315i	$0.307318\pi$
$648$	−473.693	−0.0287167
$649$	2318.01	0.140200
$650$	0	0
$651$	−1792.04	−0.107889
$652$	23809.6	1.43015
$653$	−4415.88	−0.264635	−0.132318	−	0.991207i	$-0.542242\pi$
$653$	−4415.88	−0.264635	−0.132318	+	0.991207i	$0.542242\pi$
$654$	1012.02	0.0605095
$655$	0	0
$656$	−5851.46	−0.348264
$657$	9195.77	0.546060
$658$	5045.40	0.298922
$659$	7391.89	0.436946	0.218473	−	0.975843i	$-0.429893\pi$
$659$	7391.89	0.436946	0.218473	+	0.975843i	$0.429893\pi$
$660$	0	0
$661$	−640.842	−0.0377093	−0.0188547	−	0.999822i	$-0.506002\pi$
$661$	−640.842	−0.0377093	−0.0188547	+	0.999822i	$0.506002\pi$
$662$	1273.09	0.0747431
$663$	−16470.2	−0.964782
$664$	−4915.78	−0.287303
$665$	0	0
$666$	−1146.66	−0.0667152
$667$	−2369.97	−0.137579
$668$	33231.3	1.92479
$669$	11313.7	0.653832
$670$	0	0
$671$	758.770	0.0436542
$672$	5517.03	0.316703
$673$	19129.0	1.09564	0.547822	−	0.836595i	$-0.315457\pi$
$673$	19129.0	1.09564	0.547822	+	0.836595i	$0.315457\pi$
$674$	−1565.56	−0.0894702
$675$	0	0
$676$	−2730.53	−0.155355
$677$	4043.27	0.229536	0.114768	−	0.993392i	$-0.463388\pi$
$677$	4043.27	0.229536	0.114768	+	0.993392i	$0.463388\pi$
$678$	−361.700	−0.0204882
$679$	−42603.5	−2.40791
$680$	0	0
$681$	−8674.74	−0.488130
$682$	91.1216	0.00511617
$683$	−26633.3	−1.49209	−0.746044	−	0.665897i	$-0.768049\pi$
$683$	−26633.3	−1.49209	−0.746044	+	0.665897i	$0.768049\pi$
$684$	−1353.81	−0.0756786
$685$	0	0
$686$	−202.085	−0.0112473
$687$	−2763.93	−0.153494
$688$	20359.0	1.12817
$689$	6637.40	0.367002
$690$	0	0
$691$	30662.4	1.68806	0.844032	−	0.536293i	$-0.180176\pi$
$691$	30662.4	1.68806	0.844032	+	0.536293i	$0.180176\pi$
$692$	−11915.7	−0.654575
$693$	2631.66	0.144254
$694$	3809.01	0.208340
$695$	0	0
$696$	−687.902	−0.0374639
$697$	−10482.6	−0.569665
$698$	−1437.64	−0.0779589
$699$	−8455.96	−0.457559
$700$	0	0
$701$	18443.3	0.993717	0.496858	−	0.867832i	$-0.334487\pi$
$701$	18443.3	0.993717	0.496858	+	0.867832i	$0.334487\pi$
$702$	−502.038	−0.0269917
$703$	−6610.93	−0.354674
$704$	5066.09	0.271215
$705$	0	0
$706$	−2788.36	−0.148642
$707$	25802.3	1.37255
$708$	−4971.56	−0.263902
$709$	−21693.3	−1.14910	−0.574548	−	0.818471i	$-0.694822\pi$
$709$	−21693.3	−1.14910	−0.574548	+	0.818471i	$0.694822\pi$
$710$	0	0
$711$	2892.43	0.152566
$712$	8477.67	0.446228
$713$	−1358.26	−0.0713423
$714$	3199.72	0.167712
$715$	0	0
$716$	−8551.61	−0.446353
$717$	−2350.87	−0.122447
$718$	−4128.24	−0.214575
$719$	−28555.1	−1.48112	−0.740560	−	0.671990i	$-0.765440\pi$
$719$	−28555.1	−1.48112	−0.740560	+	0.671990i	$0.765440\pi$
$720$	0	0
$721$	4930.35	0.254668
$722$	−2393.59	−0.123380
$723$	−17676.0	−0.909234
$724$	1148.11	0.0589354
$725$	0	0
$726$	−133.814	−0.00684065
$727$	−21629.1	−1.10341	−0.551704	−	0.834040i	$-0.686022\pi$
$727$	−21629.1	−1.10341	−0.551704	+	0.834040i	$0.686022\pi$
$728$	7841.19	0.399195
$729$	729.000	0.0370370
$730$	0	0
$731$	36472.0	1.84537
$732$	−1627.38	−0.0821716
$733$	−13081.1	−0.659157	−0.329579	−	0.944128i	$-0.606907\pi$
$733$	−13081.1	−0.659157	−0.329579	+	0.944128i	$0.606907\pi$
$734$	−2189.56	−0.110106
$735$	0	0
$736$	4181.57	0.209422
$737$	−2228.80	−0.111396
$738$	−319.526	−0.0159375
$739$	−24296.5	−1.20942	−0.604710	−	0.796446i	$-0.706711\pi$
$739$	−24296.5	−1.20942	−0.604710	+	0.796446i	$0.706711\pi$
$740$	0	0
$741$	−2894.43	−0.143495
$742$	−1289.47	−0.0637977
$743$	−7572.81	−0.373916	−0.186958	−	0.982368i	$-0.559863\pi$
$743$	−7572.81	−0.373916	−0.186958	+	0.982368i	$0.559863\pi$
$744$	−394.245	−0.0194270
$745$	0	0
$746$	−7.43978	−0.000365134 0
$747$	7565.25	0.370546
$748$	9415.50	0.460247
$749$	17345.5	0.846182
$750$	0	0
$751$	38506.1	1.87098	0.935492	−	0.353347i	$-0.114957\pi$
$751$	38506.1	1.87098	0.935492	+	0.353347i	$0.114957\pi$
$752$	−31282.6	−1.51697
$753$	23678.1	1.14592
$754$	−729.065	−0.0352135
$755$	0	0
$756$	−5644.26	−0.271534
$757$	−22513.0	−1.08091	−0.540455	−	0.841373i	$-0.681748\pi$
$757$	−22513.0	−1.08091	−0.540455	+	0.841373i	$0.681748\pi$
$758$	3038.21	0.145584
$759$	1994.63	0.0953894
$760$	0	0
$761$	−29062.0	−1.38436	−0.692179	−	0.721726i	$-0.743349\pi$
$761$	−29062.0	−1.38436	−0.692179	+	0.721726i	$0.743349\pi$
$762$	1923.60	0.0914496
$763$	24325.8	1.15420
$764$	−28206.7	−1.33571
$765$	0	0
$766$	−3675.83	−0.173385
$767$	−10629.2	−0.500387
$768$	−10253.5	−0.481758
$769$	−17769.2	−0.833257	−0.416628	−	0.909077i	$-0.636788\pi$
$769$	−17769.2	−0.833257	−0.416628	+	0.909077i	$0.636788\pi$
$770$	0	0
$771$	−10127.2	−0.473051
$772$	−7986.41	−0.372328
$773$	15074.0	0.701391	0.350695	−	0.936490i	$-0.385945\pi$
$773$	15074.0	0.701391	0.350695	+	0.936490i	$0.385945\pi$
$774$	1111.72	0.0516280
$775$	0	0
$776$	−9372.67	−0.433582
$777$	−27562.1	−1.27257
$778$	2542.59	0.117167
$779$	−1842.18	−0.0847279
$780$	0	0
$781$	7097.57	0.325187
$782$	2425.19	0.110901
$783$	1058.66	0.0483187
$784$	22092.6	1.00641
$785$	0	0
$786$	−1700.80	−0.0771826
$787$	−15445.3	−0.699573	−0.349787	−	0.936829i	$-0.613746\pi$
$787$	−15445.3	−0.699573	−0.349787	+	0.936829i	$0.613746\pi$
$788$	−23534.4	−1.06393
$789$	5469.37	0.246787
$790$	0	0
$791$	−8694.12	−0.390806
$792$	578.958	0.0259752
$793$	−3479.32	−0.155806
$794$	−3902.97	−0.174448
$795$	0	0
$796$	25696.5	1.14421
$797$	−14902.8	−0.662337	−0.331169	−	0.943572i	$-0.607443\pi$
$797$	−14902.8	−0.662337	−0.331169	+	0.943572i	$0.607443\pi$
$798$	562.310	0.0249443
$799$	−56041.2	−2.48135
$800$	0	0
$801$	−13046.9	−0.575518
$802$	2101.54	0.0925284
$803$	−11239.3	−0.493930
$804$	4780.23	0.209684
$805$	0	0
$806$	−417.836	−0.0182601
$807$	21938.8	0.956981
$808$	5676.43	0.247149
$809$	19642.4	0.853633	0.426816	−	0.904338i	$-0.359635\pi$
$809$	19642.4	0.853633	0.426816	+	0.904338i	$0.359635\pi$
$810$	0	0
$811$	16729.7	0.724365	0.362182	−	0.932107i	$-0.382032\pi$
$811$	16729.7	0.724365	0.362182	+	0.932107i	$0.382032\pi$
$812$	−8196.66	−0.354244
$813$	−18504.4	−0.798252
$814$	1401.48	0.0603461
$815$	0	0
$816$	−19839.0	−0.851107
$817$	6409.50	0.274467
$818$	881.007	0.0376573
$819$	−12067.4	−0.514858
$820$	0	0
$821$	−10838.2	−0.460726	−0.230363	−	0.973105i	$-0.573991\pi$
$821$	−10838.2	−0.460726	−0.230363	+	0.973105i	$0.573991\pi$
$822$	−2084.72	−0.0884586
$823$	12375.6	0.524164	0.262082	−	0.965046i	$-0.415591\pi$
$823$	12375.6	0.524164	0.262082	+	0.965046i	$0.415591\pi$
$824$	1084.66	0.0458569
$825$	0	0
$826$	2064.96	0.0869845
$827$	−30336.4	−1.27558	−0.637788	−	0.770212i	$-0.720150\pi$
$827$	−30336.4	−1.27558	−0.637788	+	0.770212i	$0.720150\pi$
$828$	−4278.00	−0.179554
$829$	−26159.0	−1.09595	−0.547973	−	0.836496i	$-0.684600\pi$
$829$	−26159.0	−1.09595	−0.547973	+	0.836496i	$0.684600\pi$
$830$	0	0
$831$	5574.40	0.232700
$832$	−23230.4	−0.967993
$833$	39577.9	1.64621
$834$	533.402	0.0221465
$835$	0	0
$836$	1654.65	0.0684539
$837$	606.732	0.0250558
$838$	861.976	0.0355328
$839$	22058.7	0.907690	0.453845	−	0.891081i	$-0.350052\pi$
$839$	22058.7	0.907690	0.453845	+	0.891081i	$0.350052\pi$
$840$	0	0
$841$	−22851.6	−0.936963
$842$	−3630.39	−0.148589
$843$	23150.6	0.945849
$844$	33619.2	1.37111
$845$	0	0
$846$	−1708.22	−0.0694207
$847$	−3216.47	−0.130483
$848$	7994.99	0.323761
$849$	19747.5	0.798272
$850$	0	0
$851$	−20890.4	−0.841496
$852$	−15222.6	−0.612109
$853$	−41626.5	−1.67088	−0.835442	−	0.549578i	$-0.814788\pi$
$853$	−41626.5	−1.67088	−0.835442	+	0.549578i	$0.814788\pi$
$854$	675.938	0.0270845
$855$	0	0
$856$	3815.96	0.152368
$857$	44478.1	1.77286	0.886431	−	0.462860i	$-0.153177\pi$
$857$	44478.1	1.77286	0.886431	+	0.462860i	$0.153177\pi$
$858$	613.602	0.0244149
$859$	−5250.15	−0.208537	−0.104268	−	0.994549i	$-0.533250\pi$
$859$	−5250.15	−0.208537	−0.104268	+	0.994549i	$0.533250\pi$
$860$	0	0
$861$	−7680.37	−0.304003
$862$	5063.17	0.200061
$863$	−8110.49	−0.319912	−0.159956	−	0.987124i	$-0.551135\pi$
$863$	−8110.49	−0.319912	−0.159956	+	0.987124i	$0.551135\pi$
$864$	−1867.90	−0.0735502
$865$	0	0
$866$	−110.897	−0.00435153
$867$	−20801.5	−0.814829
$868$	−4697.60	−0.183695
$869$	−3535.19	−0.138001
$870$	0	0
$871$	10220.1	0.397583
$872$	5351.61	0.207831
$873$	14424.3	0.559208
$874$	426.196	0.0164946
$875$	0	0
$876$	24105.5	0.929737
$877$	−11508.7	−0.443126	−0.221563	−	0.975146i	$-0.571116\pi$
$877$	−11508.7	−0.443126	−0.221563	+	0.975146i	$0.571116\pi$
$878$	4424.68	0.170075
$879$	14364.4	0.551192
$880$	0	0
$881$	−15689.1	−0.599978	−0.299989	−	0.953943i	$-0.596983\pi$
$881$	−15689.1	−0.599978	−0.299989	+	0.953943i	$0.596983\pi$
$882$	1206.39	0.0460560
$883$	−12353.4	−0.470809	−0.235405	−	0.971897i	$-0.575642\pi$
$883$	−12353.4	−0.470809	−0.235405	+	0.971897i	$0.575642\pi$
$884$	−43174.5	−1.64267
$885$	0	0
$886$	3482.87	0.132065
$887$	−5146.08	−0.194801	−0.0974005	−	0.995245i	$-0.531053\pi$
$887$	−5146.08	−0.194801	−0.0974005	+	0.995245i	$0.531053\pi$
$888$	−6063.60	−0.229145
$889$	46237.1	1.74437
$890$	0	0
$891$	−891.000	−0.0335013
$892$	29657.4	1.11323
$893$	−9848.53	−0.369058
$894$	837.216	0.0313207
$895$	0	0
$896$	19225.1	0.716816
$897$	−9146.33	−0.340454
$898$	−1995.07	−0.0741386
$899$	881.103	0.0326879
$900$	0	0
$901$	14322.6	0.529584
$902$	390.531	0.0144160
$903$	26722.3	0.984786
$904$	−1912.68	−0.0703705
$905$	0	0
$906$	3228.15	0.118375
$907$	19902.0	0.728594	0.364297	−	0.931283i	$-0.381309\pi$
$907$	19902.0	0.728594	0.364297	+	0.931283i	$0.381309\pi$
$908$	−22739.7	−0.831105
$909$	−8735.88	−0.318758
$910$	0	0
$911$	−6980.14	−0.253856	−0.126928	−	0.991912i	$-0.540512\pi$
$911$	−6980.14	−0.253856	−0.126928	+	0.991912i	$0.540512\pi$
$912$	−3486.45	−0.126588
$913$	−9246.42	−0.335172
$914$	3689.92	0.133536
$915$	0	0
$916$	−7245.27	−0.261343
$917$	−40881.8	−1.47223
$918$	−1083.33	−0.0389491
$919$	−13632.2	−0.489320	−0.244660	−	0.969609i	$-0.578676\pi$
$919$	−13632.2	−0.489320	−0.244660	+	0.969609i	$0.578676\pi$
$920$	0	0
$921$	19838.2	0.709760
$922$	3339.36	0.119280
$923$	−32545.7	−1.16062
$924$	6898.54	0.245612
$925$	0	0
$926$	−5904.50	−0.209540
$927$	−1669.27	−0.0591435
$928$	−2712.59	−0.0959538
$929$	48008.6	1.69549	0.847746	−	0.530403i	$-0.177959\pi$
$929$	48008.6	1.69549	0.847746	+	0.530403i	$0.177959\pi$
$930$	0	0
$931$	6955.30	0.244845
$932$	−22166.2	−0.779054
$933$	5746.66	0.201648
$934$	−3803.58	−0.133252
$935$	0	0
$936$	−2654.79	−0.0927080
$937$	19708.7	0.687144	0.343572	−	0.939126i	$-0.388363\pi$
$937$	19708.7	0.687144	0.343572	+	0.939126i	$0.388363\pi$
$938$	−1985.49	−0.0691136
$939$	19150.9	0.665567
$940$	0	0
$941$	−40078.3	−1.38843	−0.694216	−	0.719767i	$-0.744249\pi$
$941$	−40078.3	−1.38843	−0.694216	+	0.719767i	$0.744249\pi$
$942$	1495.90	0.0517399
$943$	−5821.25	−0.201024
$944$	−12803.2	−0.441429
$945$	0	0
$946$	−1358.77	−0.0466993
$947$	34849.6	1.19584	0.597919	−	0.801556i	$-0.295994\pi$
$947$	34849.6	1.19584	0.597919	+	0.801556i	$0.295994\pi$
$948$	7582.13	0.259764
$949$	51537.4	1.76288
$950$	0	0
$951$	−30386.1	−1.03611
$952$	16920.2	0.576038
$953$	40133.0	1.36415	0.682076	−	0.731282i	$-0.261077\pi$
$953$	40133.0	1.36415	0.682076	+	0.731282i	$0.261077\pi$
$954$	436.575	0.0148162
$955$	0	0
$956$	−6162.49	−0.208482
$957$	−1293.92	−0.0437059
$958$	−3616.66	−0.121972
$959$	−50110.0	−1.68732
$960$	0	0
$961$	−29286.0	−0.983050
$962$	−6426.43	−0.215381
$963$	−5872.67	−0.196515
$964$	−46335.2	−1.54809
$965$	0	0
$966$	1776.89	0.0591826
$967$	36825.4	1.22464	0.612320	−	0.790610i	$-0.290237\pi$
$967$	36825.4	1.22464	0.612320	+	0.790610i	$0.290237\pi$
$968$	−707.615	−0.0234955
$969$	−6245.80	−0.207063
$970$	0	0
$971$	72.3675	0.00239174	0.00119587	−	0.999999i	$-0.499619\pi$
$971$	72.3675	0.00239174	0.00119587	+	0.999999i	$0.499619\pi$
$972$	1910.98	0.0630604
$973$	12821.3	0.422437
$974$	2979.26	0.0980098
$975$	0	0
$976$	−4190.97	−0.137448
$977$	25134.8	0.823065	0.411533	−	0.911395i	$-0.364994\pi$
$977$	25134.8	0.823065	0.411533	+	0.911395i	$0.364994\pi$
$978$	3348.27	0.109474
$979$	15946.2	0.520576
$980$	0	0
$981$	−8235.98	−0.268048
$982$	−2081.14	−0.0676292
$983$	43144.8	1.39990	0.699952	−	0.714190i	$-0.253205\pi$
$983$	43144.8	1.39990	0.699952	+	0.714190i	$0.253205\pi$
$984$	−1689.66	−0.0547403
$985$	0	0
$986$	−1573.23	−0.0508131
$987$	−41060.2	−1.32418
$988$	−7587.38	−0.244318
$989$	20253.8	0.651198
$990$	0	0
$991$	28318.0	0.907721	0.453860	−	0.891073i	$-0.350046\pi$
$991$	28318.0	0.907721	0.453860	+	0.891073i	$0.350046\pi$
$992$	−1554.62	−0.0497572
$993$	−10360.6	−0.331100
$994$	6322.76	0.201756
$995$	0	0
$996$	19831.3	0.630903
$997$	17969.5	0.570811	0.285405	−	0.958407i	$-0.407872\pi$
$997$	17969.5	0.570811	0.285405	+	0.958407i	$0.407872\pi$
$998$	1539.43	0.0488275
$999$	9331.71	0.295538

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.a.y.1.3	yes	5
3.2	odd	2		2475.4.a.bi.1.3		5
5.2	odd	4		825.4.c.s.199.6		10
5.3	odd	4		825.4.c.s.199.5		10
5.4	even	2		825.4.a.x.1.3	✓	5
15.14	odd	2		2475.4.a.bj.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.4.a.x.1.3	✓	5	5.4	even	2
825.4.a.y.1.3	yes	5	1.1	even	1	trivial
825.4.c.s.199.5		10	5.3	odd	4
825.4.c.s.199.6		10	5.2	odd	4
2475.4.a.bi.1.3		5	3.2	odd	2
2475.4.a.bj.1.3		5	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+0.368634 q^{2} -3.00000 q^{3} -7.86411 q^{4} -1.10590 q^{6} -26.5824 q^{7} -5.84806 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+0.368634 q^{2} -3.00000 q^{3} -7.86411 q^{4} -1.10590 q^{6} -26.5824 q^{7} -5.84806 q^{8} +9.00000 q^{9} -11.0000 q^{11} +23.5923 q^{12} +50.4402 q^{13} -9.79918 q^{14} +60.7571 q^{16} +108.843 q^{17} +3.31771 q^{18} +19.1278 q^{19} +79.7471 q^{21} -4.05498 q^{22} +60.4434 q^{23} +17.5442 q^{24} +18.5940 q^{26} -27.0000 q^{27} +209.047 q^{28} -39.2097 q^{29} -22.4715 q^{31} +69.1816 q^{32} +33.0000 q^{33} +40.1234 q^{34} -70.7770 q^{36} -345.619 q^{37} +7.05117 q^{38} -151.321 q^{39} -96.3091 q^{41} +29.3975 q^{42} +335.088 q^{43} +86.5052 q^{44} +22.2815 q^{46} -514.880 q^{47} -182.271 q^{48} +363.623 q^{49} -326.530 q^{51} -396.667 q^{52} +131.589 q^{53} -9.95313 q^{54} +155.455 q^{56} -57.3834 q^{57} -14.4541 q^{58} -210.728 q^{59} -68.9791 q^{61} -8.28378 q^{62} -239.241 q^{63} -460.554 q^{64} +12.1649 q^{66} +202.618 q^{67} -855.955 q^{68} -181.330 q^{69} -645.234 q^{71} -52.6325 q^{72} +1021.75 q^{73} -127.407 q^{74} -150.423 q^{76} +292.406 q^{77} -55.7820 q^{78} +321.381 q^{79} +81.0000 q^{81} -35.5029 q^{82} +840.583 q^{83} -627.140 q^{84} +123.525 q^{86} +117.629 q^{87} +64.3286 q^{88} -1449.66 q^{89} -1340.82 q^{91} -475.333 q^{92} +67.4146 q^{93} -189.803 q^{94} -207.545 q^{96} +1602.70 q^{97} +134.044 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} - 15 q^{3} + 3 q^{4} - 3 q^{6} + 18 q^{7} - 3 q^{8} + 45 q^{9}+O(q^{10}) \) 5 * q + q^2 - 15 * q^3 + 3 * q^4 - 3 * q^6 + 18 * q^7 - 3 * q^8 + 45 * q^9	\( 5 q + q^{2} - 15 q^{3} + 3 q^{4} - 3 q^{6} + 18 q^{7} - 3 q^{8} + 45 q^{9} - 55 q^{11} - 9 q^{12} + 31 q^{13} + 8 q^{14} - 125 q^{16} + 38 q^{17} + 9 q^{18} - 57 q^{19} - 54 q^{21} - 11 q^{22} + 161 q^{23} + 9 q^{24} - 125 q^{26} - 135 q^{27} + 324 q^{28} - 107 q^{29} - 295 q^{31} - 23 q^{32} + 165 q^{33} + 34 q^{34} + 27 q^{36} - 260 q^{37} + 619 q^{38} - 93 q^{39} - 128 q^{41} - 24 q^{42} + 377 q^{43} - 33 q^{44} - 577 q^{46} - 114 q^{47} + 375 q^{48} - 415 q^{49} - 114 q^{51} - 395 q^{52} + 812 q^{53} - 27 q^{54} - 132 q^{56} + 171 q^{57} + 339 q^{58} - 1152 q^{59} - 344 q^{61} - 235 q^{62} + 162 q^{63} - 545 q^{64} + 33 q^{66} - 928 q^{67} + 654 q^{68} - 483 q^{69} - 707 q^{71} - 27 q^{72} + 322 q^{73} - 1176 q^{74} - 1699 q^{76} - 198 q^{77} + 375 q^{78} - 2494 q^{79} + 405 q^{81} - 2776 q^{82} + 1657 q^{83} - 972 q^{84} - 799 q^{86} + 321 q^{87} + 33 q^{88} - 2435 q^{89} - 804 q^{91} - 2775 q^{92} + 885 q^{93} - 502 q^{94} + 69 q^{96} - 1901 q^{97} + 343 q^{98} - 495 q^{99}+O(q^{100}) \) 5 * q + q^2 - 15 * q^3 + 3 * q^4 - 3 * q^6 + 18 * q^7 - 3 * q^8 + 45 * q^9 - 55 * q^11 - 9 * q^12 + 31 * q^13 + 8 * q^14 - 125 * q^16 + 38 * q^17 + 9 * q^18 - 57 * q^19 - 54 * q^21 - 11 * q^22 + 161 * q^23 + 9 * q^24 - 125 * q^26 - 135 * q^27 + 324 * q^28 - 107 * q^29 - 295 * q^31 - 23 * q^32 + 165 * q^33 + 34 * q^34 + 27 * q^36 - 260 * q^37 + 619 * q^38 - 93 * q^39 - 128 * q^41 - 24 * q^42 + 377 * q^43 - 33 * q^44 - 577 * q^46 - 114 * q^47 + 375 * q^48 - 415 * q^49 - 114 * q^51 - 395 * q^52 + 812 * q^53 - 27 * q^54 - 132 * q^56 + 171 * q^57 + 339 * q^58 - 1152 * q^59 - 344 * q^61 - 235 * q^62 + 162 * q^63 - 545 * q^64 + 33 * q^66 - 928 * q^67 + 654 * q^68 - 483 * q^69 - 707 * q^71 - 27 * q^72 + 322 * q^73 - 1176 * q^74 - 1699 * q^76 - 198 * q^77 + 375 * q^78 - 2494 * q^79 + 405 * q^81 - 2776 * q^82 + 1657 * q^83 - 972 * q^84 - 799 * q^86 + 321 * q^87 + 33 * q^88 - 2435 * q^89 - 804 * q^91 - 2775 * q^92 + 885 * q^93 - 502 * q^94 + 69 * q^96 - 1901 * q^97 + 343 * q^98 - 495 * q^99

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