LMFDB - Embedded newform 725.4.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,4,Mod(1,725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("725.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	725.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:	$42.7763847542$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.13458092.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 14x^{3} + 18x^{2} + 20x - 8 $ x^5 - x^4 - 14x^3 + 18x^2 + 20*x - 8
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 29)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.957567$ of defining polynomial
Character	$\chi$	$=$	725.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.84972 q^{2} -4.64574 q^{3} +0.120922 q^{4} -13.2391 q^{6} -26.0540 q^{7} -22.4532 q^{8} -5.41713 q^{9} +O(q^{10})$	\(q+2.84972 q^{2} -4.64574 q^{3} +0.120922 q^{4} -13.2391 q^{6} -26.0540 q^{7} -22.4532 q^{8} -5.41713 q^{9} -62.8274 q^{11} -0.561770 q^{12} -22.3936 q^{13} -74.2465 q^{14} -64.9528 q^{16} +57.9808 q^{17} -15.4373 q^{18} +71.3143 q^{19} +121.040 q^{21} -179.041 q^{22} +49.5307 q^{23} +104.312 q^{24} -63.8155 q^{26} +150.601 q^{27} -3.15048 q^{28} -29.0000 q^{29} +62.9198 q^{31} -5.47182 q^{32} +291.880 q^{33} +165.229 q^{34} -0.655048 q^{36} -119.123 q^{37} +203.226 q^{38} +104.035 q^{39} -414.916 q^{41} +344.930 q^{42} +348.009 q^{43} -7.59719 q^{44} +141.149 q^{46} -553.259 q^{47} +301.753 q^{48} +335.808 q^{49} -269.364 q^{51} -2.70787 q^{52} +107.308 q^{53} +429.172 q^{54} +584.994 q^{56} -331.308 q^{57} -82.6420 q^{58} +136.881 q^{59} -579.408 q^{61} +179.304 q^{62} +141.138 q^{63} +504.029 q^{64} +831.776 q^{66} -919.959 q^{67} +7.01113 q^{68} -230.106 q^{69} +781.802 q^{71} +121.632 q^{72} +133.237 q^{73} -339.467 q^{74} +8.62344 q^{76} +1636.90 q^{77} +296.470 q^{78} +868.196 q^{79} -553.392 q^{81} -1182.39 q^{82} +83.3560 q^{83} +14.6363 q^{84} +991.730 q^{86} +134.726 q^{87} +1410.68 q^{88} -357.919 q^{89} +583.442 q^{91} +5.98933 q^{92} -292.309 q^{93} -1576.64 q^{94} +25.4206 q^{96} +187.105 q^{97} +956.961 q^{98} +340.344 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 8 q^{3} + 26 q^{4} + 34 q^{6} - 40 q^{7} + 84 q^{8} + 33 q^{9}+O(q^{10}) $ 5 * q - 8 * q^3 + 26 * q^4 + 34 * q^6 - 40 * q^7 + 84 * q^8 + 33 * q^9	$ 5 q - 8 q^{3} + 26 q^{4} + 34 q^{6} - 40 q^{7} + 84 q^{8} + 33 q^{9} + 12 q^{11} + 224 q^{12} - 14 q^{13} - 192 q^{14} + 146 q^{16} - 66 q^{17} + 108 q^{18} + 214 q^{19} + 98 q^{22} - 164 q^{23} + 314 q^{24} + 56 q^{26} - 362 q^{27} - 540 q^{28} - 145 q^{29} + 420 q^{31} + 652 q^{32} + 576 q^{33} + 204 q^{34} - 260 q^{36} - 378 q^{37} + 496 q^{38} - 374 q^{39} - 1158 q^{41} - 348 q^{42} + 204 q^{43} + 784 q^{44} + 580 q^{46} - 248 q^{47} + 1880 q^{48} - 283 q^{49} + 228 q^{51} - 1482 q^{52} + 554 q^{53} + 918 q^{54} - 608 q^{56} - 44 q^{57} + 440 q^{59} + 618 q^{61} - 1250 q^{62} - 804 q^{63} + 2594 q^{64} + 2940 q^{66} - 1164 q^{67} - 356 q^{68} - 1968 q^{69} - 692 q^{71} + 2648 q^{72} + 1950 q^{73} - 1832 q^{74} + 1376 q^{76} + 1616 q^{77} + 1302 q^{78} + 272 q^{79} + 1801 q^{81} - 92 q^{82} - 512 q^{83} - 3208 q^{84} + 2446 q^{86} + 232 q^{87} + 6954 q^{88} + 866 q^{89} + 2580 q^{91} - 3468 q^{92} + 40 q^{93} - 5942 q^{94} + 7386 q^{96} - 1562 q^{97} + 3408 q^{98} - 238 q^{99}+O(q^{100}) $ 5 * q - 8 * q^3 + 26 * q^4 + 34 * q^6 - 40 * q^7 + 84 * q^8 + 33 * q^9 + 12 * q^11 + 224 * q^12 - 14 * q^13 - 192 * q^14 + 146 * q^16 - 66 * q^17 + 108 * q^18 + 214 * q^19 + 98 * q^22 - 164 * q^23 + 314 * q^24 + 56 * q^26 - 362 * q^27 - 540 * q^28 - 145 * q^29 + 420 * q^31 + 652 * q^32 + 576 * q^33 + 204 * q^34 - 260 * q^36 - 378 * q^37 + 496 * q^38 - 374 * q^39 - 1158 * q^41 - 348 * q^42 + 204 * q^43 + 784 * q^44 + 580 * q^46 - 248 * q^47 + 1880 * q^48 - 283 * q^49 + 228 * q^51 - 1482 * q^52 + 554 * q^53 + 918 * q^54 - 608 * q^56 - 44 * q^57 + 440 * q^59 + 618 * q^61 - 1250 * q^62 - 804 * q^63 + 2594 * q^64 + 2940 * q^66 - 1164 * q^67 - 356 * q^68 - 1968 * q^69 - 692 * q^71 + 2648 * q^72 + 1950 * q^73 - 1832 * q^74 + 1376 * q^76 + 1616 * q^77 + 1302 * q^78 + 272 * q^79 + 1801 * q^81 - 92 * q^82 - 512 * q^83 - 3208 * q^84 + 2446 * q^86 + 232 * q^87 + 6954 * q^88 + 866 * q^89 + 2580 * q^91 - 3468 * q^92 + 40 * q^93 - 5942 * q^94 + 7386 * q^96 - 1562 * q^97 + 3408 * q^98 - 238 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.84972	1.00753	0.503765	−	0.863841i	$-0.331948\pi$
$2$	2.84972	1.00753	0.503765	+	0.863841i	$0.331948\pi$
$3$	−4.64574	−0.894072	−0.447036	−	0.894516i	$-0.647520\pi$
$3$	−4.64574	−0.894072	−0.447036	+	0.894516i	$0.647520\pi$
$4$	0.120922	0.0151152
$5$	0	0
$5$	0	0
$6$	−13.2391	−0.900804
$7$	−26.0540	−1.40678	−0.703391	−	0.710804i	$-0.748331\pi$
$7$	−26.0540	−1.40678	−0.703391	+	0.710804i	$0.748331\pi$
$8$	−22.4532	−0.992300
$9$	−5.41713	−0.200635
$10$	0	0
$11$	−62.8274	−1.72211	−0.861053	−	0.508515i	$-0.830195\pi$
$11$	−62.8274	−1.72211	−0.861053	+	0.508515i	$0.830195\pi$
$12$	−0.561770	−0.0135141
$13$	−22.3936	−0.477759	−0.238879	−	0.971049i	$-0.576780\pi$
$13$	−22.3936	−0.477759	−0.238879	+	0.971049i	$0.576780\pi$
$14$	−74.2465	−1.41737
$15$	0	0
$16$	−64.9528	−1.01489
$17$	57.9808	0.827201	0.413601	−	0.910458i	$-0.364271\pi$
$17$	57.9808	0.827201	0.413601	+	0.910458i	$0.364271\pi$
$18$	−15.4373	−0.202145
$19$	71.3143	0.861086	0.430543	−	0.902570i	$-0.358322\pi$
$19$	71.3143	0.861086	0.430543	+	0.902570i	$0.358322\pi$
$20$	0	0
$21$	121.040	1.25776
$22$	−179.041	−1.73507
$23$	49.5307	0.449037	0.224519	−	0.974470i	$-0.427919\pi$
$23$	49.5307	0.449037	0.224519	+	0.974470i	$0.427919\pi$
$24$	104.312	0.887188
$25$	0	0
$26$	−63.8155	−0.481356
$27$	150.601	1.07345
$28$	−3.15048	−0.0212638
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	0	0
$31$	62.9198	0.364540	0.182270	−	0.983249i	$-0.441656\pi$
$31$	62.9198	0.364540	0.182270	+	0.983249i	$0.441656\pi$
$32$	−5.47182	−0.0302278
$33$	291.880	1.53969
$34$	165.229	0.833429
$35$	0	0
$36$	−0.655048	−0.00303263
$37$	−119.123	−0.529288	−0.264644	−	0.964346i	$-0.585254\pi$
$37$	−119.123	−0.529288	−0.264644	+	0.964346i	$0.585254\pi$
$38$	203.226	0.867569
$39$	104.035	0.427151
$40$	0	0
$41$	−414.916	−1.58046	−0.790231	−	0.612810i	$-0.790039\pi$
$41$	−414.916	−1.58046	−0.790231	+	0.612810i	$0.790039\pi$
$42$	344.930	1.26723
$43$	348.009	1.23421	0.617103	−	0.786882i	$-0.288306\pi$
$43$	348.009	1.23421	0.617103	+	0.786882i	$0.288306\pi$
$44$	−7.59719	−0.0260300
$45$	0	0
$46$	141.149	0.452418
$47$	−553.259	−1.71705	−0.858523	−	0.512775i	$-0.828618\pi$
$47$	−553.259	−1.71705	−0.858523	+	0.512775i	$0.828618\pi$
$48$	301.753	0.907382
$49$	335.808	0.979033
$50$	0	0
$51$	−269.364	−0.739578
$52$	−2.70787	−0.00722142
$53$	107.308	0.278111	0.139055	−	0.990285i	$-0.455593\pi$
$53$	107.308	0.278111	0.139055	+	0.990285i	$0.455593\pi$
$54$	429.172	1.08154
$55$	0	0
$56$	584.994	1.39595
$57$	−331.308	−0.769873
$58$	−82.6420	−0.187093
$59$	136.881	0.302041	0.151020	−	0.988531i	$-0.451744\pi$
$59$	136.881	0.302041	0.151020	+	0.988531i	$0.451744\pi$
$60$	0	0
$61$	−579.408	−1.21616	−0.608078	−	0.793877i	$-0.708059\pi$
$61$	−579.408	−1.21616	−0.608078	+	0.793877i	$0.708059\pi$
$62$	179.304	0.367285
$63$	141.138	0.282249
$64$	504.029	0.984431
$65$	0	0
$66$	831.776	1.55128
$67$	−919.959	−1.67748	−0.838738	−	0.544535i	$-0.816706\pi$
$67$	−919.959	−1.67748	−0.838738	+	0.544535i	$0.816706\pi$
$68$	7.01113	0.0125033
$69$	−230.106	−0.401472
$70$	0	0
$71$	781.802	1.30680	0.653400	−	0.757013i	$-0.273342\pi$
$71$	781.802	1.30680	0.653400	+	0.757013i	$0.273342\pi$
$72$	121.632	0.199090
$73$	133.237	0.213619	0.106810	−	0.994279i	$-0.465936\pi$
$73$	133.237	0.213619	0.106810	+	0.994279i	$0.465936\pi$
$74$	−339.467	−0.533273
$75$	0	0
$76$	8.62344	0.0130155
$77$	1636.90	2.42263
$78$	296.470	0.430367
$79$	868.196	1.23645	0.618225	−	0.786001i	$-0.287852\pi$
$79$	868.196	1.23645	0.618225	+	0.786001i	$0.287852\pi$
$80$	0	0
$81$	−553.392	−0.759111
$82$	−1182.39	−1.59236
$83$	83.3560	0.110235	0.0551175	−	0.998480i	$-0.482447\pi$
$83$	83.3560	0.110235	0.0551175	+	0.998480i	$0.482447\pi$
$84$	14.6363	0.0190114
$85$	0	0
$86$	991.730	1.24350
$87$	134.726	0.166025
$88$	1410.68	1.70885
$89$	−357.919	−0.426284	−0.213142	−	0.977021i	$-0.568370\pi$
$89$	−357.919	−0.426284	−0.213142	+	0.977021i	$0.568370\pi$
$90$	0	0
$91$	583.442	0.672102
$92$	5.98933	0.00678729
$93$	−292.309	−0.325925
$94$	−1576.64	−1.72997
$95$	0	0
$96$	25.4206	0.0270259
$97$	187.105	0.195852	0.0979260	−	0.995194i	$-0.468779\pi$
$97$	187.105	0.195852	0.0979260	+	0.995194i	$0.468779\pi$
$98$	956.961	0.986404
$99$	340.344	0.345514
$100$	0	0
$101$	−959.423	−0.945209	−0.472605	−	0.881275i	$-0.656686\pi$
$101$	−959.423	−0.945209	−0.472605	+	0.881275i	$0.656686\pi$
$102$	−767.612	−0.745146
$103$	−78.8738	−0.0754531	−0.0377265	−	0.999288i	$-0.512012\pi$
$103$	−78.8738	−0.0754531	−0.0377265	+	0.999288i	$0.512012\pi$
$104$	502.808	0.474080
$105$	0	0
$106$	305.797	0.280205
$107$	−713.851	−0.644959	−0.322479	−	0.946577i	$-0.604516\pi$
$107$	−713.851	−0.644959	−0.322479	+	0.946577i	$0.604516\pi$
$108$	18.2110	0.0162255
$109$	536.561	0.471497	0.235749	−	0.971814i	$-0.424246\pi$
$109$	536.561	0.471497	0.235749	+	0.971814i	$0.424246\pi$
$110$	0	0
$111$	553.412	0.473222
$112$	1692.28	1.42772
$113$	−1946.36	−1.62034	−0.810170	−	0.586195i	$-0.800625\pi$
$113$	−1946.36	−1.62034	−0.810170	+	0.586195i	$0.800625\pi$
$114$	−944.135	−0.775670
$115$	0	0
$116$	−3.50673	−0.00280682
$117$	121.309	0.0958549
$118$	390.073	0.304315
$119$	−1510.63	−1.16369
$120$	0	0
$121$	2616.28	1.96565
$122$	−1651.15	−1.22531
$123$	1927.59	1.41305
$124$	7.60837	0.00551009
$125$	0	0
$126$	402.203	0.284374
$127$	1995.14	1.39402	0.697009	−	0.717062i	$-0.254514\pi$
$127$	1995.14	1.39402	0.697009	+	0.717062i	$0.254514\pi$
$128$	1480.12	1.02207
$129$	−1616.76	−1.10347
$130$	0	0
$131$	1544.84	1.03033	0.515164	−	0.857092i	$-0.327731\pi$
$131$	1544.84	1.03033	0.515164	+	0.857092i	$0.327731\pi$
$132$	35.2945	0.0232727
$133$	−1858.02	−1.21136
$134$	−2621.63	−1.69011
$135$	0	0
$136$	−1301.85	−0.820832
$137$	1294.93	0.807543	0.403771	−	0.914860i	$-0.367699\pi$
$137$	1294.93	0.807543	0.403771	+	0.914860i	$0.367699\pi$
$138$	−655.740	−0.404495
$139$	1999.66	1.22021	0.610105	−	0.792320i	$-0.291127\pi$
$139$	1999.66	1.22021	0.610105	+	0.792320i	$0.291127\pi$
$140$	0	0
$141$	2570.30	1.53516
$142$	2227.92	1.31664
$143$	1406.93	0.822752
$144$	351.858	0.203621
$145$	0	0
$146$	379.688	0.215228
$147$	−1560.08	−0.875326
$148$	−14.4045	−0.00800029
$149$	1187.63	0.652984	0.326492	−	0.945200i	$-0.394133\pi$
$149$	1187.63	0.652984	0.326492	+	0.945200i	$0.394133\pi$
$150$	0	0
$151$	−2257.61	−1.21670	−0.608350	−	0.793669i	$-0.708168\pi$
$151$	−2257.61	−1.21670	−0.608350	+	0.793669i	$0.708168\pi$
$152$	−1601.23	−0.854456
$153$	−314.090	−0.165965
$154$	4664.72	2.44087
$155$	0	0
$156$	12.5800	0.00645647
$157$	−1188.18	−0.603995	−0.301997	−	0.953309i	$-0.597653\pi$
$157$	−1188.18	−0.603995	−0.301997	+	0.953309i	$0.597653\pi$
$158$	2474.12	1.24576
$159$	−498.524	−0.248651
$160$	0	0
$161$	−1290.47	−0.631697
$162$	−1577.01	−0.764827
$163$	2452.33	1.17841	0.589207	−	0.807982i	$-0.299440\pi$
$163$	2452.33	1.17841	0.589207	+	0.807982i	$0.299440\pi$
$164$	−50.1722	−0.0238890
$165$	0	0
$166$	237.541	0.111065
$167$	2020.14	0.936067	0.468034	−	0.883711i	$-0.344963\pi$
$167$	2020.14	0.936067	0.468034	+	0.883711i	$0.344963\pi$
$168$	−2717.73	−1.24808
$169$	−1695.53	−0.771746
$170$	0	0
$171$	−386.319	−0.172764
$172$	42.0818	0.0186553
$173$	−2862.12	−1.25782	−0.628910	−	0.777478i	$-0.716499\pi$
$173$	−2862.12	−1.25782	−0.628910	+	0.777478i	$0.716499\pi$
$174$	383.933	0.167275
$175$	0	0
$176$	4080.81	1.74774
$177$	−635.914	−0.270046
$178$	−1019.97	−0.429494
$179$	−232.651	−0.0971460	−0.0485730	−	0.998820i	$-0.515467\pi$
$179$	−232.651	−0.0971460	−0.0485730	+	0.998820i	$0.515467\pi$
$180$	0	0
$181$	−2607.67	−1.07086	−0.535432	−	0.844578i	$-0.679851\pi$
$181$	−2607.67	−1.07086	−0.535432	+	0.844578i	$0.679851\pi$
$182$	1662.65	0.677163
$183$	2691.78	1.08733
$184$	−1112.12	−0.445580
$185$	0	0
$186$	−833.000	−0.328379
$187$	−3642.78	−1.42453
$188$	−66.9010	−0.0259535
$189$	−3923.76	−1.51012
$190$	0	0
$191$	1528.90	0.579202	0.289601	−	0.957147i	$-0.406477\pi$
$191$	1528.90	0.579202	0.289601	+	0.957147i	$0.406477\pi$
$192$	−2341.59	−0.880153
$193$	−1017.58	−0.379518	−0.189759	−	0.981831i	$-0.560771\pi$
$193$	−1017.58	−0.379518	−0.189759	+	0.981831i	$0.560771\pi$
$194$	533.197	0.197327
$195$	0	0
$196$	40.6065	0.0147983
$197$	−3290.20	−1.18994	−0.594968	−	0.803749i	$-0.702835\pi$
$197$	−3290.20	−1.18994	−0.594968	+	0.803749i	$0.702835\pi$
$198$	969.887	0.348115
$199$	−29.9190	−0.0106578	−0.00532891	−	0.999986i	$-0.501696\pi$
$199$	−29.9190	−0.0106578	−0.00532891	+	0.999986i	$0.501696\pi$
$200$	0	0
$201$	4273.89	1.49979
$202$	−2734.09	−0.952326
$203$	755.565	0.261233
$204$	−32.5719	−0.0111789
$205$	0	0
$206$	−224.769	−0.0760212
$207$	−268.314	−0.0900924
$208$	1454.53	0.484871
$209$	−4480.49	−1.48288
$210$	0	0
$211$	2267.20	0.739717	0.369859	−	0.929088i	$-0.379406\pi$
$211$	2267.20	0.739717	0.369859	+	0.929088i	$0.379406\pi$
$212$	12.9758	0.00420370
$213$	−3632.05	−1.16837
$214$	−2034.28	−0.649815
$215$	0	0
$216$	−3381.48	−1.06519
$217$	−1639.31	−0.512828
$218$	1529.05	0.475047
$219$	−618.984	−0.190991
$220$	0	0
$221$	−1298.40	−0.395203
$222$	1577.07	0.476785
$223$	−4945.03	−1.48495	−0.742474	−	0.669875i	$-0.766348\pi$
$223$	−4945.03	−1.48495	−0.742474	+	0.669875i	$0.766348\pi$
$224$	142.562	0.0425239
$225$	0	0
$226$	−5546.59	−1.63254
$227$	3559.46	1.04075	0.520374	−	0.853938i	$-0.325792\pi$
$227$	3559.46	1.04075	0.520374	+	0.853938i	$0.325792\pi$
$228$	−40.0622	−0.0116368
$229$	6143.40	1.77278	0.886391	−	0.462937i	$-0.153204\pi$
$229$	6143.40	1.77278	0.886391	+	0.462937i	$0.153204\pi$
$230$	0	0
$231$	−7604.61	−2.16600
$232$	651.143	0.184266
$233$	1087.06	0.305648	0.152824	−	0.988253i	$-0.451163\pi$
$233$	1087.06	0.305648	0.152824	+	0.988253i	$0.451163\pi$
$234$	345.697	0.0965766
$235$	0	0
$236$	16.5519	0.00456540
$237$	−4033.41	−1.10548
$238$	−4304.88	−1.17245
$239$	1079.00	0.292027	0.146013	−	0.989283i	$-0.453356\pi$
$239$	1079.00	0.292027	0.146013	+	0.989283i	$0.453356\pi$
$240$	0	0
$241$	−989.224	−0.264405	−0.132202	−	0.991223i	$-0.542205\pi$
$241$	−989.224	−0.264405	−0.132202	+	0.991223i	$0.542205\pi$
$242$	7455.68	1.98045
$243$	−1495.33	−0.394754
$244$	−70.0629	−0.0183824
$245$	0	0
$246$	5493.09	1.42369
$247$	−1596.98	−0.411391
$248$	−1412.75	−0.361733
$249$	−387.250	−0.0985581
$250$	0	0
$251$	900.246	0.226386	0.113193	−	0.993573i	$-0.463892\pi$
$251$	900.246	0.226386	0.113193	+	0.993573i	$0.463892\pi$
$252$	17.0666	0.00426625
$253$	−3111.88	−0.773290
$254$	5685.61	1.40451
$255$	0	0
$256$	185.693	0.0453353
$257$	3125.18	0.758534	0.379267	−	0.925287i	$-0.376176\pi$
$257$	3125.18	0.758534	0.379267	+	0.925287i	$0.376176\pi$
$258$	−4607.31	−1.11178
$259$	3103.62	0.744592
$260$	0	0
$261$	157.097	0.0372569
$262$	4402.35	1.03808
$263$	−2814.89	−0.659976	−0.329988	−	0.943985i	$-0.607045\pi$
$263$	−2814.89	−0.659976	−0.329988	+	0.943985i	$0.607045\pi$
$264$	−6553.63	−1.52783
$265$	0	0
$266$	−5294.84	−1.22048
$267$	1662.80	0.381129
$268$	−111.243	−0.0253554
$269$	4409.28	0.999400	0.499700	−	0.866199i	$-0.333444\pi$
$269$	4409.28	0.999400	0.499700	+	0.866199i	$0.333444\pi$
$270$	0	0
$271$	−4417.97	−0.990304	−0.495152	−	0.868806i	$-0.664888\pi$
$271$	−4417.97	−0.990304	−0.495152	+	0.868806i	$0.664888\pi$
$272$	−3766.01	−0.839515
$273$	−2710.52	−0.600908
$274$	3690.19	0.813623
$275$	0	0
$276$	−27.8248	−0.00606833
$277$	887.577	0.192525	0.0962624	−	0.995356i	$-0.469311\pi$
$277$	887.577	0.192525	0.0962624	+	0.995356i	$0.469311\pi$
$278$	5698.49	1.22940
$279$	−340.845	−0.0731393
$280$	0	0
$281$	−4286.58	−0.910021	−0.455010	−	0.890486i	$-0.650364\pi$
$281$	−4286.58	−0.910021	−0.455010	+	0.890486i	$0.650364\pi$
$282$	7324.64	1.54672
$283$	1709.59	0.359097	0.179549	−	0.983749i	$-0.442536\pi$
$283$	1709.59	0.359097	0.179549	+	0.983749i	$0.442536\pi$
$284$	94.5367	0.0197525
$285$	0	0
$286$	4009.36	0.828946
$287$	10810.2	2.22336
$288$	29.6416	0.00606474
$289$	−1551.22	−0.315738
$290$	0	0
$291$	−869.241	−0.175106
$292$	16.1112	0.00322890
$293$	−1145.01	−0.228301	−0.114151	−	0.993463i	$-0.536415\pi$
$293$	−1145.01	−0.228301	−0.114151	+	0.993463i	$0.536415\pi$
$294$	−4445.79	−0.881917
$295$	0	0
$296$	2674.68	0.525212
$297$	−9461.90	−1.84860
$298$	3384.42	0.657900
$299$	−1109.17	−0.214532
$300$	0	0
$301$	−9067.01	−1.73626
$302$	−6433.56	−1.22586
$303$	4457.23	0.845086
$304$	−4632.06	−0.873905
$305$	0	0
$306$	−895.069	−0.167215
$307$	−1079.39	−0.200665	−0.100333	−	0.994954i	$-0.531991\pi$
$307$	−1079.39	−0.200665	−0.100333	+	0.994954i	$0.531991\pi$
$308$	197.937	0.0366185
$309$	366.427	0.0674605
$310$	0	0
$311$	2313.90	0.421895	0.210947	−	0.977497i	$-0.432345\pi$
$311$	2313.90	0.421895	0.210947	+	0.977497i	$0.432345\pi$
$312$	−2335.91	−0.423862
$313$	7653.19	1.38206	0.691029	−	0.722827i	$-0.257158\pi$
$313$	7653.19	1.38206	0.691029	+	0.722827i	$0.257158\pi$
$314$	−3385.99	−0.608542
$315$	0	0
$316$	104.984	0.0186892
$317$	3657.23	0.647982	0.323991	−	0.946060i	$-0.394975\pi$
$317$	3657.23	0.647982	0.323991	+	0.946060i	$0.394975\pi$
$318$	−1420.65	−0.250523
$319$	1821.99	0.319787
$320$	0	0
$321$	3316.36	0.576640
$322$	−3677.48	−0.636453
$323$	4134.86	0.712291
$324$	−66.9170	−0.0114741
$325$	0	0
$326$	6988.47	1.18729
$327$	−2492.72	−0.421553
$328$	9316.18	1.56829
$329$	14414.6	2.41551
$330$	0	0
$331$	3237.92	0.537681	0.268841	−	0.963185i	$-0.413360\pi$
$331$	3237.92	0.537681	0.268841	+	0.963185i	$0.413360\pi$
$332$	10.0795	0.00166622
$333$	645.303	0.106193
$334$	5756.84	0.943115
$335$	0	0
$336$	−7861.87	−1.27649
$337$	7976.89	1.28940	0.644702	−	0.764434i	$-0.276982\pi$
$337$	7976.89	1.28940	0.644702	+	0.764434i	$0.276982\pi$
$338$	−4831.78	−0.777557
$339$	9042.29	1.44870
$340$	0	0
$341$	−3953.09	−0.627777
$342$	−1100.90	−0.174064
$343$	187.371	0.0294959
$344$	−7813.92	−1.22470
$345$	0	0
$346$	−8156.25	−1.26729
$347$	8355.93	1.29271	0.646354	−	0.763037i	$-0.276293\pi$
$347$	8355.93	1.29271	0.646354	+	0.763037i	$0.276293\pi$
$348$	16.2913	0.00250950
$349$	5544.56	0.850411	0.425205	−	0.905097i	$-0.360202\pi$
$349$	5544.56	0.850411	0.425205	+	0.905097i	$0.360202\pi$
$350$	0	0
$351$	−3372.51	−0.512852
$352$	343.780	0.0520555
$353$	1682.79	0.253727	0.126864	−	0.991920i	$-0.459509\pi$
$353$	1682.79	0.253727	0.126864	+	0.991920i	$0.459509\pi$
$354$	−1812.18	−0.272080
$355$	0	0
$356$	−43.2801	−0.00644337
$357$	7017.99	1.04042
$358$	−662.990	−0.0978774
$359$	7143.13	1.05014	0.525069	−	0.851059i	$-0.324039\pi$
$359$	7143.13	1.05014	0.525069	+	0.851059i	$0.324039\pi$
$360$	0	0
$361$	−1773.27	−0.258531
$362$	−7431.13	−1.07893
$363$	−12154.6	−1.75743
$364$	70.5507	0.0101590
$365$	0	0
$366$	7670.81	1.09552
$367$	4456.16	0.633814	0.316907	−	0.948457i	$-0.397356\pi$
$367$	4456.16	0.633814	0.316907	+	0.948457i	$0.397356\pi$
$368$	−3217.15	−0.455722
$369$	2247.65	0.317095
$370$	0	0
$371$	−2795.79	−0.391241
$372$	−35.3465	−0.00492642
$373$	−2508.28	−0.348187	−0.174094	−	0.984729i	$-0.555700\pi$
$373$	−2508.28	−0.348187	−0.174094	+	0.984729i	$0.555700\pi$
$374$	−10380.9	−1.43525
$375$	0	0
$376$	12422.4	1.70383
$377$	649.414	0.0887176
$378$	−11181.6	−1.52149
$379$	−12733.9	−1.72585	−0.862926	−	0.505331i	$-0.831371\pi$
$379$	−12733.9	−1.72585	−0.862926	+	0.505331i	$0.831371\pi$
$380$	0	0
$381$	−9268.91	−1.24635
$382$	4356.95	0.583563
$383$	1027.19	0.137042	0.0685209	−	0.997650i	$-0.478172\pi$
$383$	1027.19	0.137042	0.0685209	+	0.997650i	$0.478172\pi$
$384$	−6876.23	−0.913806
$385$	0	0
$386$	−2899.82	−0.382376
$387$	−1885.21	−0.247624
$388$	22.6250	0.00296034
$389$	5153.35	0.671684	0.335842	−	0.941918i	$-0.390979\pi$
$389$	5153.35	0.671684	0.335842	+	0.941918i	$0.390979\pi$
$390$	0	0
$391$	2871.83	0.371444
$392$	−7539.97	−0.971495
$393$	−7176.90	−0.921187
$394$	−9376.17	−1.19890
$395$	0	0
$396$	41.1550	0.00522251
$397$	−6250.95	−0.790242	−0.395121	−	0.918629i	$-0.629297\pi$
$397$	−6250.95	−0.790242	−0.395121	+	0.918629i	$0.629297\pi$
$398$	−85.2610	−0.0107381
$399$	8631.87	1.08304
$400$	0	0
$401$	11083.8	1.38029	0.690145	−	0.723671i	$-0.257547\pi$
$401$	11083.8	1.38029	0.690145	+	0.723671i	$0.257547\pi$
$402$	12179.4	1.51108
$403$	−1409.00	−0.174162
$404$	−116.015	−0.0142870
$405$	0	0
$406$	2153.15	0.263200
$407$	7484.17	0.911490
$408$	6048.07	0.733883
$409$	−3375.43	−0.408079	−0.204039	−	0.978963i	$-0.565407\pi$
$409$	−3375.43	−0.408079	−0.204039	+	0.978963i	$0.565407\pi$
$410$	0	0
$411$	−6015.91	−0.722002
$412$	−9.53754	−0.00114049
$413$	−3566.29	−0.424905
$414$	−764.621	−0.0907707
$415$	0	0
$416$	122.534	0.0144416
$417$	−9289.91	−1.09096
$418$	−12768.2	−1.49405
$419$	6486.50	0.756292	0.378146	−	0.925746i	$-0.376562\pi$
$419$	6486.50	0.756292	0.378146	+	0.925746i	$0.376562\pi$
$420$	0	0
$421$	−10938.6	−1.26631	−0.633153	−	0.774026i	$-0.718240\pi$
$421$	−10938.6	−1.26631	−0.633153	+	0.774026i	$0.718240\pi$
$422$	6460.89	0.745287
$423$	2997.08	0.344499
$424$	−2409.40	−0.275969
$425$	0	0
$426$	−10350.3	−1.17717
$427$	15095.9	1.71087
$428$	−86.3200	−0.00974867
$429$	−6536.23	−0.735600
$430$	0	0
$431$	4124.34	0.460934	0.230467	−	0.973080i	$-0.425975\pi$
$431$	4124.34	0.460934	0.230467	+	0.973080i	$0.425975\pi$
$432$	−9781.98	−1.08943
$433$	1561.41	0.173295	0.0866473	−	0.996239i	$-0.472385\pi$
$433$	1561.41	0.173295	0.0866473	+	0.996239i	$0.472385\pi$
$434$	−4671.58	−0.516689
$435$	0	0
$436$	64.8818	0.00712677
$437$	3532.25	0.386660
$438$	−1763.93	−0.192429
$439$	−15712.7	−1.70826	−0.854130	−	0.520060i	$-0.825909\pi$
$439$	−15712.7	−1.70826	−0.854130	+	0.520060i	$0.825909\pi$
$440$	0	0
$441$	−1819.12	−0.196428
$442$	−3700.08	−0.398178
$443$	−12763.5	−1.36888	−0.684439	−	0.729070i	$-0.739953\pi$
$443$	−12763.5	−1.36888	−0.684439	+	0.729070i	$0.739953\pi$
$444$	66.9195	0.00715284
$445$	0	0
$446$	−14092.0	−1.49613
$447$	−5517.42	−0.583815
$448$	−13131.9	−1.38488
$449$	3117.88	0.327710	0.163855	−	0.986484i	$-0.447607\pi$
$449$	3117.88	0.327710	0.163855	+	0.986484i	$0.447607\pi$
$450$	0	0
$451$	26068.1	2.72172
$452$	−235.357	−0.0244918
$453$	10488.3	1.08782
$454$	10143.5	1.04858
$455$	0	0
$456$	7438.91	0.763945
$457$	8479.41	0.867943	0.433972	−	0.900927i	$-0.357112\pi$
$457$	8479.41	0.867943	0.433972	+	0.900927i	$0.357112\pi$
$458$	17507.0	1.78613
$459$	8732.00	0.887962
$460$	0	0
$461$	9253.32	0.934859	0.467430	−	0.884030i	$-0.345180\pi$
$461$	9253.32	0.934859	0.467430	+	0.884030i	$0.345180\pi$
$462$	−21671.0	−2.18231
$463$	−521.395	−0.0523354	−0.0261677	−	0.999658i	$-0.508330\pi$
$463$	−521.395	−0.0523354	−0.0261677	+	0.999658i	$0.508330\pi$
$464$	1883.63	0.188460
$465$	0	0
$466$	3097.83	0.307949
$467$	−4337.35	−0.429783	−0.214891	−	0.976638i	$-0.568940\pi$
$467$	−4337.35	−0.429783	−0.214891	+	0.976638i	$0.568940\pi$
$468$	14.6689	0.00144887
$469$	23968.6	2.35984
$470$	0	0
$471$	5519.98	0.540015
$472$	−3073.42	−0.299715
$473$	−21864.5	−2.12544
$474$	−11494.1	−1.11380
$475$	0	0
$476$	−182.668	−0.0175894
$477$	−581.300	−0.0557986
$478$	3074.84	0.294226
$479$	−11258.1	−1.07390	−0.536949	−	0.843615i	$-0.680423\pi$
$479$	−11258.1	−1.07390	−0.536949	+	0.843615i	$0.680423\pi$
$480$	0	0
$481$	2667.58	0.252872
$482$	−2819.02	−0.266395
$483$	5995.18	0.564783
$484$	316.365	0.0297112
$485$	0	0
$486$	−4261.26	−0.397726
$487$	−4353.54	−0.405088	−0.202544	−	0.979273i	$-0.564921\pi$
$487$	−4353.54	−0.405088	−0.202544	+	0.979273i	$0.564921\pi$
$488$	13009.6	1.20679
$489$	−11392.9	−1.05359
$490$	0	0
$491$	−8458.77	−0.777472	−0.388736	−	0.921349i	$-0.627088\pi$
$491$	−8458.77	−0.777472	−0.388736	+	0.921349i	$0.627088\pi$
$492$	233.087	0.0213585
$493$	−1681.44	−0.153607
$494$	−4550.96	−0.414489
$495$	0	0
$496$	−4086.82	−0.369967
$497$	−20369.0	−1.83838
$498$	−1103.56	−0.0993002
$499$	14850.9	1.33230	0.666149	−	0.745819i	$-0.267942\pi$
$499$	14850.9	1.33230	0.666149	+	0.745819i	$0.267942\pi$
$500$	0	0
$501$	−9385.04	−0.836912
$502$	2565.45	0.228091
$503$	1686.45	0.149493	0.0747464	−	0.997203i	$-0.476185\pi$
$503$	1686.45	0.149493	0.0747464	+	0.997203i	$0.476185\pi$
$504$	−3168.99	−0.280076
$505$	0	0
$506$	−8868.00	−0.779112
$507$	7876.97	0.689997
$508$	241.256	0.0210709
$509$	−11113.5	−0.967773	−0.483887	−	0.875131i	$-0.660775\pi$
$509$	−11113.5	−0.967773	−0.483887	+	0.875131i	$0.660775\pi$
$510$	0	0
$511$	−3471.35	−0.300516
$512$	−11311.8	−0.976395
$513$	10740.0	0.924336
$514$	8905.90	0.764246
$515$	0	0
$516$	−195.501	−0.0166792
$517$	34759.8	2.95694
$518$	8844.45	0.750198
$519$	13296.7	1.12458
$520$	0	0
$521$	−15931.1	−1.33964	−0.669820	−	0.742523i	$-0.733629\pi$
$521$	−15931.1	−1.33964	−0.669820	+	0.742523i	$0.733629\pi$
$522$	447.682	0.0375374
$523$	7960.43	0.665555	0.332778	−	0.943005i	$-0.392014\pi$
$523$	7960.43	0.665555	0.332778	+	0.943005i	$0.392014\pi$
$524$	186.804	0.0155736
$525$	0	0
$526$	−8021.67	−0.664945
$527$	3648.14	0.301548
$528$	−18958.4	−1.56261
$529$	−9713.71	−0.798366
$530$	0	0
$531$	−741.503	−0.0605998
$532$	−224.675	−0.0183099
$533$	9291.45	0.755079
$534$	4738.51	0.383999
$535$	0	0
$536$	20656.0	1.66456
$537$	1080.83	0.0868555
$538$	12565.2	1.00692
$539$	−21098.0	−1.68600
$540$	0	0
$541$	13818.9	1.09819	0.549096	−	0.835760i	$-0.314972\pi$
$541$	13818.9	1.09819	0.549096	+	0.835760i	$0.314972\pi$
$542$	−12590.0	−0.997760
$543$	12114.5	0.957430
$544$	−317.261	−0.0250045
$545$	0	0
$546$	−7724.22	−0.605432
$547$	−22093.3	−1.72695	−0.863474	−	0.504393i	$-0.831716\pi$
$547$	−22093.3	−1.72695	−0.863474	+	0.504393i	$0.831716\pi$
$548$	156.585	0.0122062
$549$	3138.73	0.244003
$550$	0	0
$551$	−2068.12	−0.159900
$552$	5166.62	0.398381
$553$	−22619.9	−1.73942
$554$	2529.35	0.193974
$555$	0	0
$556$	241.802	0.0184437
$557$	3110.34	0.236606	0.118303	−	0.992978i	$-0.462255\pi$
$557$	3110.34	0.236606	0.118303	+	0.992978i	$0.462255\pi$
$558$	−971.314	−0.0736900
$559$	−7793.17	−0.589653
$560$	0	0
$561$	16923.4	1.27363
$562$	−12215.6	−0.916873
$563$	13284.6	0.994455	0.497227	−	0.867620i	$-0.334351\pi$
$563$	13284.6	0.994455	0.497227	+	0.867620i	$0.334351\pi$
$564$	310.804	0.0232043
$565$	0	0
$566$	4871.86	0.361801
$567$	14418.1	1.06790
$568$	−17553.9	−1.29674
$569$	−6809.18	−0.501680	−0.250840	−	0.968029i	$-0.580707\pi$
$569$	−6809.18	−0.501680	−0.250840	+	0.968029i	$0.580707\pi$
$570$	0	0
$571$	−13471.8	−0.987352	−0.493676	−	0.869646i	$-0.664347\pi$
$571$	−13471.8	−0.987352	−0.493676	+	0.869646i	$0.664347\pi$
$572$	170.128	0.0124361
$573$	−7102.88	−0.517849
$574$	30806.0	2.24010
$575$	0	0
$576$	−2730.39	−0.197511
$577$	−5331.06	−0.384636	−0.192318	−	0.981333i	$-0.561601\pi$
$577$	−5331.06	−0.384636	−0.192318	+	0.981333i	$0.561601\pi$
$578$	−4420.56	−0.318116
$579$	4727.41	0.339317
$580$	0	0
$581$	−2171.75	−0.155077
$582$	−2477.10	−0.176424
$583$	−6741.87	−0.478936
$584$	−2991.59	−0.211974
$585$	0	0
$586$	−3262.96	−0.230020
$587$	−3333.96	−0.234425	−0.117212	−	0.993107i	$-0.537396\pi$
$587$	−3333.96	−0.234425	−0.117212	+	0.993107i	$0.537396\pi$
$588$	−188.647	−0.0132307
$589$	4487.09	0.313900
$590$	0	0
$591$	15285.4	1.06389
$592$	7737.34	0.537167
$593$	23405.3	1.62081	0.810404	−	0.585872i	$-0.199248\pi$
$593$	23405.3	1.62081	0.810404	+	0.585872i	$0.199248\pi$
$594$	−26963.8	−1.86252
$595$	0	0
$596$	143.610	0.00986998
$597$	138.996	0.00952886
$598$	−3160.83	−0.216147
$599$	−10352.1	−0.706133	−0.353067	−	0.935598i	$-0.614861\pi$
$599$	−10352.1	−0.706133	−0.353067	+	0.935598i	$0.614861\pi$
$600$	0	0
$601$	15171.1	1.02969	0.514843	−	0.857285i	$-0.327850\pi$
$601$	15171.1	1.02969	0.514843	+	0.857285i	$0.327850\pi$
$602$	−25838.5	−1.74933
$603$	4983.54	0.336560
$604$	−272.994	−0.0183907
$605$	0	0
$606$	12701.9	0.851449
$607$	20823.0	1.39239	0.696193	−	0.717854i	$-0.254876\pi$
$607$	20823.0	1.39239	0.696193	+	0.717854i	$0.254876\pi$
$608$	−390.219	−0.0260287
$609$	−3510.15	−0.233561
$610$	0	0
$611$	12389.5	0.820334
$612$	−37.9802	−0.00250859
$613$	19071.6	1.25660	0.628299	−	0.777972i	$-0.283751\pi$
$613$	19071.6	1.25660	0.628299	+	0.777972i	$0.283751\pi$
$614$	−3075.97	−0.202176
$615$	0	0
$616$	−36753.7	−2.40397
$617$	−15200.4	−0.991806	−0.495903	−	0.868378i	$-0.665163\pi$
$617$	−15200.4	−0.991806	−0.495903	+	0.868378i	$0.665163\pi$
$618$	1044.22	0.0679684
$619$	4358.76	0.283026	0.141513	−	0.989936i	$-0.454803\pi$
$619$	4358.76	0.283026	0.141513	+	0.989936i	$0.454803\pi$
$620$	0	0
$621$	7459.39	0.482021
$622$	6593.98	0.425071
$623$	9325.20	0.599689
$624$	−6757.34	−0.433510
$625$	0	0
$626$	21809.5	1.39246
$627$	20815.2	1.32580
$628$	−143.677	−0.00912950
$629$	−6906.83	−0.437827
$630$	0	0
$631$	−2580.66	−0.162812	−0.0814062	−	0.996681i	$-0.525941\pi$
$631$	−2580.66	−0.162812	−0.0814062	+	0.996681i	$0.525941\pi$
$632$	−19493.8	−1.22693
$633$	−10532.8	−0.661361
$634$	10422.1	0.652861
$635$	0	0
$636$	−60.2823	−0.00375841
$637$	−7519.96	−0.467742
$638$	5192.18	0.322195
$639$	−4235.12	−0.262189
$640$	0	0
$641$	19858.9	1.22368	0.611840	−	0.790982i	$-0.290430\pi$
$641$	19858.9	1.22368	0.611840	+	0.790982i	$0.290430\pi$
$642$	9450.72	0.580981
$643$	−17371.9	−1.06545	−0.532723	−	0.846290i	$-0.678831\pi$
$643$	−17371.9	−1.06545	−0.532723	+	0.846290i	$0.678831\pi$
$644$	−156.046	−0.00954823
$645$	0	0
$646$	11783.2	0.717654
$647$	−3275.07	−0.199005	−0.0995024	−	0.995037i	$-0.531725\pi$
$647$	−3275.07	−0.199005	−0.0995024	+	0.995037i	$0.531725\pi$
$648$	12425.4	0.753266
$649$	−8599.88	−0.520146
$650$	0	0
$651$	7615.80	0.458505
$652$	296.540	0.0178120
$653$	−20726.5	−1.24210	−0.621049	−	0.783772i	$-0.713293\pi$
$653$	−20726.5	−1.24210	−0.621049	+	0.783772i	$0.713293\pi$
$654$	−7103.56	−0.424727
$655$	0	0
$656$	26949.9	1.60399
$657$	−721.762	−0.0428594
$658$	41077.6	2.43370
$659$	−18404.6	−1.08792	−0.543960	−	0.839111i	$-0.683076\pi$
$659$	−18404.6	−1.08792	−0.543960	+	0.839111i	$0.683076\pi$
$660$	0	0
$661$	−7146.10	−0.420501	−0.210250	−	0.977648i	$-0.567428\pi$
$661$	−7146.10	−0.420501	−0.210250	+	0.977648i	$0.567428\pi$
$662$	9227.19	0.541729
$663$	6032.02	0.353340
$664$	−1871.61	−0.109386
$665$	0	0
$666$	1838.94	0.106993
$667$	−1436.39	−0.0833841
$668$	244.279	0.0141488
$669$	22973.3	1.32765
$670$	0	0
$671$	36402.7	2.09435
$672$	−662.308	−0.0380195
$673$	26819.0	1.53610	0.768051	−	0.640389i	$-0.221227\pi$
$673$	26819.0	1.53610	0.768051	+	0.640389i	$0.221227\pi$
$674$	22731.9	1.29911
$675$	0	0
$676$	−205.026	−0.0116651
$677$	20093.1	1.14068	0.570340	−	0.821408i	$-0.306811\pi$
$677$	20093.1	1.14068	0.570340	+	0.821408i	$0.306811\pi$
$678$	25768.0	1.45961
$679$	−4874.82	−0.275521
$680$	0	0
$681$	−16536.3	−0.930505
$682$	−11265.2	−0.632503
$683$	6876.22	0.385229	0.192614	−	0.981275i	$-0.438303\pi$
$683$	6876.22	0.385229	0.192614	+	0.981275i	$0.438303\pi$
$684$	−46.7143	−0.00261135
$685$	0	0
$686$	533.956	0.0297180
$687$	−28540.6	−1.58500
$688$	−22604.1	−1.25258
$689$	−2403.01	−0.132870
$690$	0	0
$691$	17332.7	0.954224	0.477112	−	0.878842i	$-0.341684\pi$
$691$	17332.7	0.954224	0.477112	+	0.878842i	$0.341684\pi$
$692$	−346.092	−0.0190122
$693$	−8867.31	−0.486063
$694$	23812.1	1.30244
$695$	0	0
$696$	−3025.04	−0.164747
$697$	−24057.1	−1.30736
$698$	15800.5	0.856814
$699$	−5050.21	−0.273271
$700$	0	0
$701$	11127.5	0.599545	0.299772	−	0.954011i	$-0.403089\pi$
$701$	11127.5	0.599545	0.299772	+	0.954011i	$0.403089\pi$
$702$	−9610.71	−0.516714
$703$	−8495.15	−0.455762
$704$	−31666.8	−1.69530
$705$	0	0
$706$	4795.48	0.255638
$707$	24996.8	1.32970
$708$	−76.8957	−0.00408180
$709$	17432.0	0.923374	0.461687	−	0.887043i	$-0.347244\pi$
$709$	17432.0	0.923374	0.461687	+	0.887043i	$0.347244\pi$
$710$	0	0
$711$	−4703.13	−0.248075
$712$	8036.42	0.423002
$713$	3116.46	0.163692
$714$	19999.3	1.04826
$715$	0	0
$716$	−28.1325	−0.00146838
$717$	−5012.73	−0.261093
$718$	20355.9	1.05805
$719$	21082.7	1.09353	0.546767	−	0.837285i	$-0.315858\pi$
$719$	21082.7	1.09353	0.546767	+	0.837285i	$0.315858\pi$
$720$	0	0
$721$	2054.97	0.106146
$722$	−5053.32	−0.260478
$723$	4595.68	0.236397
$724$	−315.323	−0.0161863
$725$	0	0
$726$	−34637.1	−1.77067
$727$	25839.1	1.31818	0.659091	−	0.752063i	$-0.270941\pi$
$727$	25839.1	1.31818	0.659091	+	0.752063i	$0.270941\pi$
$728$	−13100.1	−0.666927
$729$	21888.5	1.11205
$730$	0	0
$731$	20177.9	1.02094
$732$	325.494	0.0164352
$733$	−1278.54	−0.0644256	−0.0322128	−	0.999481i	$-0.510255\pi$
$733$	−1278.54	−0.0644256	−0.0322128	+	0.999481i	$0.510255\pi$
$734$	12698.8	0.638586
$735$	0	0
$736$	−271.023	−0.0135734
$737$	57798.6	2.88879
$738$	6405.19	0.319483
$739$	4224.54	0.210287	0.105144	−	0.994457i	$-0.466470\pi$
$739$	4224.54	0.210287	0.105144	+	0.994457i	$0.466470\pi$
$740$	0	0
$741$	7419.17	0.367814
$742$	−7967.23	−0.394186
$743$	17992.3	0.888390	0.444195	−	0.895930i	$-0.353490\pi$
$743$	17992.3	0.888390	0.444195	+	0.895930i	$0.353490\pi$
$744$	6563.27	0.323416
$745$	0	0
$746$	−7147.91	−0.350809
$747$	−451.550	−0.0221170
$748$	−440.491	−0.0215320
$749$	18598.6	0.907316
$750$	0	0
$751$	−10082.4	−0.489895	−0.244948	−	0.969536i	$-0.578771\pi$
$751$	−10082.4	−0.489895	−0.244948	+	0.969536i	$0.578771\pi$
$752$	35935.7	1.74261
$753$	−4182.30	−0.202406
$754$	1850.65	0.0893856
$755$	0	0
$756$	−474.468	−0.0228257
$757$	−10806.5	−0.518851	−0.259425	−	0.965763i	$-0.583533\pi$
$757$	−10806.5	−0.518851	−0.259425	+	0.965763i	$0.583533\pi$
$758$	−36288.2	−1.73885
$759$	14457.0	0.691377
$760$	0	0
$761$	−30710.4	−1.46288	−0.731439	−	0.681907i	$-0.761151\pi$
$761$	−30710.4	−1.46288	−0.731439	+	0.681907i	$0.761151\pi$
$762$	−26413.8	−1.25574
$763$	−13979.5	−0.663293
$764$	184.877	0.00875475
$765$	0	0
$766$	2927.21	0.138074
$767$	−3065.26	−0.144303
$768$	−862.682	−0.0405330
$769$	10757.1	0.504436	0.252218	−	0.967670i	$-0.418840\pi$
$769$	10757.1	0.504436	0.252218	+	0.967670i	$0.418840\pi$
$770$	0	0
$771$	−14518.8	−0.678185
$772$	−123.047	−0.00573649
$773$	18077.2	0.841125	0.420563	−	0.907263i	$-0.361833\pi$
$773$	18077.2	0.841125	0.420563	+	0.907263i	$0.361833\pi$
$774$	−5372.33	−0.249489
$775$	0	0
$776$	−4201.10	−0.194344
$777$	−14418.6	−0.665719
$778$	14685.6	0.676742
$779$	−29589.4	−1.36091
$780$	0	0
$781$	−49118.6	−2.25045
$782$	8183.92	0.374241
$783$	−4367.44	−0.199335
$784$	−21811.7	−0.993608
$785$	0	0
$786$	−20452.2	−0.928123
$787$	31543.7	1.42873	0.714366	−	0.699773i	$-0.246715\pi$
$787$	31543.7	1.42873	0.714366	+	0.699773i	$0.246715\pi$
$788$	−397.857	−0.0179861
$789$	13077.3	0.590066
$790$	0	0
$791$	50710.4	2.27946
$792$	−7641.81	−0.342854
$793$	12975.0	0.581030
$794$	−17813.5	−0.796192
$795$	0	0
$796$	−3.61786	−0.000161095 0
$797$	−18280.9	−0.812477	−0.406239	−	0.913767i	$-0.633160\pi$
$797$	−18280.9	−0.812477	−0.406239	+	0.913767i	$0.633160\pi$
$798$	24598.4	1.09120
$799$	−32078.4	−1.42034
$800$	0	0
$801$	1938.89	0.0855273
$802$	31585.6	1.39068
$803$	−8370.93	−0.367875
$804$	516.805	0.0226695
$805$	0	0
$806$	−4015.26	−0.175473
$807$	−20484.4	−0.893536
$808$	21542.1	0.937932
$809$	21776.3	0.946372	0.473186	−	0.880963i	$-0.343104\pi$
$809$	21776.3	0.946372	0.473186	+	0.880963i	$0.343104\pi$
$810$	0	0
$811$	17035.7	0.737612	0.368806	−	0.929506i	$-0.379767\pi$
$811$	17035.7	0.737612	0.368806	+	0.929506i	$0.379767\pi$
$812$	91.3640	0.00394858
$813$	20524.7	0.885404
$814$	21327.8	0.918353
$815$	0	0
$816$	17495.9	0.750588
$817$	24818.0	1.06276
$818$	−9619.03	−0.411151
$819$	−3160.58	−0.134847
$820$	0	0
$821$	−45120.7	−1.91805	−0.959027	−	0.283314i	$-0.908566\pi$
$821$	−45120.7	−1.91805	−0.959027	+	0.283314i	$0.908566\pi$
$822$	−17143.7	−0.727438
$823$	−22261.7	−0.942883	−0.471442	−	0.881897i	$-0.656266\pi$
$823$	−22261.7	−0.942883	−0.471442	+	0.881897i	$0.656266\pi$
$824$	1770.97	0.0748721
$825$	0	0
$826$	−10162.9	−0.428104
$827$	−10280.4	−0.432266	−0.216133	−	0.976364i	$-0.569345\pi$
$827$	−10280.4	−0.432266	−0.216133	+	0.976364i	$0.569345\pi$
$828$	−32.4450	−0.00136176
$829$	28509.2	1.19441	0.597206	−	0.802088i	$-0.296278\pi$
$829$	28509.2	1.19441	0.597206	+	0.802088i	$0.296278\pi$
$830$	0	0
$831$	−4123.45	−0.172131
$832$	−11287.0	−0.470321
$833$	19470.4	0.809857
$834$	−26473.7	−1.09917
$835$	0	0
$836$	−541.788	−0.0224140
$837$	9475.82	0.391317
$838$	18484.7	0.761986
$839$	4746.97	0.195332	0.0976661	−	0.995219i	$-0.468862\pi$
$839$	4746.97	0.195332	0.0976661	+	0.995219i	$0.468862\pi$
$840$	0	0
$841$	841.000	0.0344828
$842$	−31172.0	−1.27584
$843$	19914.3	0.813625
$844$	274.153	0.0111810
$845$	0	0
$846$	8540.85	0.347093
$847$	−68164.5	−2.76524
$848$	−6969.94	−0.282251
$849$	−7942.30	−0.321059
$850$	0	0
$851$	−5900.22	−0.237670
$852$	−439.193	−0.0176602
$853$	−35313.3	−1.41747	−0.708736	−	0.705473i	$-0.750734\pi$
$853$	−35313.3	−1.41747	−0.708736	+	0.705473i	$0.750734\pi$
$854$	43019.0	1.72375
$855$	0	0
$856$	16028.2	0.639993
$857$	−32142.8	−1.28119	−0.640594	−	0.767880i	$-0.721312\pi$
$857$	−32142.8	−1.28119	−0.640594	+	0.767880i	$0.721312\pi$
$858$	−18626.4	−0.741138
$859$	37568.2	1.49221	0.746107	−	0.665826i	$-0.231921\pi$
$859$	37568.2	1.49221	0.746107	+	0.665826i	$0.231921\pi$
$860$	0	0
$861$	−50221.3	−1.98785
$862$	11753.2	0.464404
$863$	−3416.95	−0.134779	−0.0673896	−	0.997727i	$-0.521467\pi$
$863$	−3416.95	−0.134779	−0.0673896	+	0.997727i	$0.521467\pi$
$864$	−824.064	−0.0324482
$865$	0	0
$866$	4449.59	0.174599
$867$	7206.57	0.282293
$868$	−198.228	−0.00775149
$869$	−54546.5	−2.12930
$870$	0	0
$871$	20601.2	0.801429
$872$	−12047.5	−0.467867
$873$	−1013.57	−0.0392947
$874$	10065.9	0.389571
$875$	0	0
$876$	−74.8485	−0.00288687
$877$	11891.0	0.457847	0.228923	−	0.973444i	$-0.426479\pi$
$877$	11891.0	0.457847	0.228923	+	0.973444i	$0.426479\pi$
$878$	−44776.8	−1.72112
$879$	5319.42	0.204118
$880$	0	0
$881$	20042.7	0.766464	0.383232	−	0.923652i	$-0.374811\pi$
$881$	20042.7	0.766464	0.383232	+	0.923652i	$0.374811\pi$
$882$	−5183.98	−0.197907
$883$	18042.8	0.687641	0.343821	−	0.939035i	$-0.388279\pi$
$883$	18042.8	0.687641	0.343821	+	0.939035i	$0.388279\pi$
$884$	−157.004	−0.00597356
$885$	0	0
$886$	−36372.5	−1.37919
$887$	−2247.91	−0.0850929	−0.0425464	−	0.999094i	$-0.513547\pi$
$887$	−2247.91	−0.0850929	−0.0425464	+	0.999094i	$0.513547\pi$
$888$	−12425.9	−0.469578
$889$	−51981.4	−1.96108
$890$	0	0
$891$	34768.2	1.30727
$892$	−597.960	−0.0224453
$893$	−39455.3	−1.47852
$894$	−15723.1	−0.588211
$895$	0	0
$896$	−38562.9	−1.43783
$897$	5152.91	0.191807
$898$	8885.09	0.330177
$899$	−1824.68	−0.0676934
$900$	0	0
$901$	6221.80	0.230053
$902$	74286.7	2.74222
$903$	42123.0	1.55234
$904$	43702.1	1.60786
$905$	0	0
$906$	29888.6	1.09601
$907$	1798.34	0.0658354	0.0329177	−	0.999458i	$-0.489520\pi$
$907$	1798.34	0.0658354	0.0329177	+	0.999458i	$0.489520\pi$
$908$	430.416	0.0157311
$909$	5197.32	0.189642
$910$	0	0
$911$	4602.02	0.167367	0.0836837	−	0.996492i	$-0.473331\pi$
$911$	4602.02	0.167367	0.0836837	+	0.996492i	$0.473331\pi$
$912$	21519.3	0.781334
$913$	−5237.04	−0.189836
$914$	24164.0	0.874478
$915$	0	0
$916$	742.869	0.0267960
$917$	−40249.1	−1.44944
$918$	24883.8	0.894648
$919$	20622.0	0.740215	0.370107	−	0.928989i	$-0.379321\pi$
$919$	20622.0	0.740215	0.370107	+	0.928989i	$0.379321\pi$
$920$	0	0
$921$	5014.58	0.179409
$922$	26369.4	0.941898
$923$	−17507.4	−0.624335
$924$	−919.562	−0.0327396
$925$	0	0
$926$	−1485.83	−0.0527294
$927$	427.270	0.0151385
$928$	158.683	0.00561316
$929$	−24061.8	−0.849777	−0.424889	−	0.905246i	$-0.639687\pi$
$929$	−24061.8	−0.849777	−0.424889	+	0.905246i	$0.639687\pi$
$930$	0	0
$931$	23947.9	0.843032
$932$	131.449	0.00461992
$933$	−10749.8	−0.377204
$934$	−12360.2	−0.433019
$935$	0	0
$936$	−2723.78	−0.0951169
$937$	6581.96	0.229481	0.114740	−	0.993396i	$-0.463396\pi$
$937$	6581.96	0.229481	0.114740	+	0.993396i	$0.463396\pi$
$938$	68303.8	2.37761
$939$	−35554.7	−1.23566
$940$	0	0
$941$	23579.7	0.816873	0.408436	−	0.912787i	$-0.366074\pi$
$941$	23579.7	0.816873	0.408436	+	0.912787i	$0.366074\pi$
$942$	15730.4	0.544081
$943$	−20551.0	−0.709686
$944$	−8890.80	−0.306537
$945$	0	0
$946$	−62307.8	−2.14144
$947$	36368.6	1.24796	0.623982	−	0.781439i	$-0.285514\pi$
$947$	36368.6	1.24796	0.623982	+	0.781439i	$0.285514\pi$
$948$	−487.726	−0.0167095
$949$	−2983.65	−0.102058
$950$	0	0
$951$	−16990.5	−0.579343
$952$	33918.5	1.15473
$953$	−44404.3	−1.50933	−0.754667	−	0.656108i	$-0.772202\pi$
$953$	−44404.3	−1.50933	−0.754667	+	0.656108i	$0.772202\pi$
$954$	−1656.55	−0.0562187
$955$	0	0
$956$	130.474	0.00441404
$957$	−8464.51	−0.285913
$958$	−32082.5	−1.08198
$959$	−33738.1	−1.13604
$960$	0	0
$961$	−25832.1	−0.867111
$962$	7601.88	0.254776
$963$	3867.02	0.129401
$964$	−119.619	−0.00399653
$965$	0	0
$966$	17084.6	0.569035
$967$	−21928.3	−0.729230	−0.364615	−	0.931158i	$-0.618799\pi$
$967$	−21928.3	−0.729230	−0.364615	+	0.931158i	$0.618799\pi$
$968$	−58743.9	−1.95052
$969$	−19209.5	−0.636840
$970$	0	0
$971$	−6352.95	−0.209965	−0.104982	−	0.994474i	$-0.533479\pi$
$971$	−6352.95	−0.209965	−0.104982	+	0.994474i	$0.533479\pi$
$972$	−180.817	−0.00596678
$973$	−52099.1	−1.71657
$974$	−12406.4	−0.408138
$975$	0	0
$976$	37634.1	1.23426
$977$	−12792.8	−0.418913	−0.209456	−	0.977818i	$-0.567169\pi$
$977$	−12792.8	−0.418913	−0.209456	+	0.977818i	$0.567169\pi$
$978$	−32466.6	−1.06152
$979$	22487.1	0.734107
$980$	0	0
$981$	−2906.62	−0.0945986
$982$	−24105.1	−0.783326
$983$	−7536.73	−0.244542	−0.122271	−	0.992497i	$-0.539018\pi$
$983$	−7536.73	−0.244542	−0.122271	+	0.992497i	$0.539018\pi$
$984$	−43280.5	−1.40217
$985$	0	0
$986$	−4791.65	−0.154764
$987$	−66966.4	−2.15964
$988$	−193.110	−0.00621826
$989$	17237.1	0.554205
$990$	0	0
$991$	−28088.3	−0.900357	−0.450179	−	0.892938i	$-0.648640\pi$
$991$	−28088.3	−0.900357	−0.450179	+	0.892938i	$0.648640\pi$
$992$	−344.286	−0.0110192
$993$	−15042.5	−0.480726
$994$	−58046.1	−1.85222
$995$	0	0
$996$	−46.8269	−0.00148973
$997$	44951.9	1.42793	0.713963	−	0.700184i	$-0.246899\pi$
$997$	44951.9	1.42793	0.713963	+	0.700184i	$0.246899\pi$
$998$	42320.9	1.34233
$999$	−17940.0	−0.568166

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.4.a.c.1.4		5
5.4	even	2		29.4.a.b.1.2	✓	5
15.14	odd	2		261.4.a.f.1.4		5
20.19	odd	2		464.4.a.l.1.2		5
35.34	odd	2		1421.4.a.e.1.2		5
40.19	odd	2		1856.4.a.bb.1.4		5
40.29	even	2		1856.4.a.y.1.2		5
145.144	even	2		841.4.a.b.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.4.a.b.1.2	✓	5	5.4	even	2
261.4.a.f.1.4		5	15.14	odd	2
464.4.a.l.1.2		5	20.19	odd	2
725.4.a.c.1.4		5	1.1	even	1	trivial
841.4.a.b.1.4		5	145.144	even	2
1421.4.a.e.1.2		5	35.34	odd	2
1856.4.a.y.1.2		5	40.29	even	2
1856.4.a.bb.1.4		5	40.19	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:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	725.a (trivial)

\(f(q)\)	\(=\)	\(q+2.84972 q^{2} -4.64574 q^{3} +0.120922 q^{4} -13.2391 q^{6} -26.0540 q^{7} -22.4532 q^{8} -5.41713 q^{9} +O(q^{10})\)	\(q+2.84972 q^{2} -4.64574 q^{3} +0.120922 q^{4} -13.2391 q^{6} -26.0540 q^{7} -22.4532 q^{8} -5.41713 q^{9} -62.8274 q^{11} -0.561770 q^{12} -22.3936 q^{13} -74.2465 q^{14} -64.9528 q^{16} +57.9808 q^{17} -15.4373 q^{18} +71.3143 q^{19} +121.040 q^{21} -179.041 q^{22} +49.5307 q^{23} +104.312 q^{24} -63.8155 q^{26} +150.601 q^{27} -3.15048 q^{28} -29.0000 q^{29} +62.9198 q^{31} -5.47182 q^{32} +291.880 q^{33} +165.229 q^{34} -0.655048 q^{36} -119.123 q^{37} +203.226 q^{38} +104.035 q^{39} -414.916 q^{41} +344.930 q^{42} +348.009 q^{43} -7.59719 q^{44} +141.149 q^{46} -553.259 q^{47} +301.753 q^{48} +335.808 q^{49} -269.364 q^{51} -2.70787 q^{52} +107.308 q^{53} +429.172 q^{54} +584.994 q^{56} -331.308 q^{57} -82.6420 q^{58} +136.881 q^{59} -579.408 q^{61} +179.304 q^{62} +141.138 q^{63} +504.029 q^{64} +831.776 q^{66} -919.959 q^{67} +7.01113 q^{68} -230.106 q^{69} +781.802 q^{71} +121.632 q^{72} +133.237 q^{73} -339.467 q^{74} +8.62344 q^{76} +1636.90 q^{77} +296.470 q^{78} +868.196 q^{79} -553.392 q^{81} -1182.39 q^{82} +83.3560 q^{83} +14.6363 q^{84} +991.730 q^{86} +134.726 q^{87} +1410.68 q^{88} -357.919 q^{89} +583.442 q^{91} +5.98933 q^{92} -292.309 q^{93} -1576.64 q^{94} +25.4206 q^{96} +187.105 q^{97} +956.961 q^{98} +340.344 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 8 q^{3} + 26 q^{4} + 34 q^{6} - 40 q^{7} + 84 q^{8} + 33 q^{9}+O(q^{10}) \) 5 * q - 8 * q^3 + 26 * q^4 + 34 * q^6 - 40 * q^7 + 84 * q^8 + 33 * q^9	\( 5 q - 8 q^{3} + 26 q^{4} + 34 q^{6} - 40 q^{7} + 84 q^{8} + 33 q^{9} + 12 q^{11} + 224 q^{12} - 14 q^{13} - 192 q^{14} + 146 q^{16} - 66 q^{17} + 108 q^{18} + 214 q^{19} + 98 q^{22} - 164 q^{23} + 314 q^{24} + 56 q^{26} - 362 q^{27} - 540 q^{28} - 145 q^{29} + 420 q^{31} + 652 q^{32} + 576 q^{33} + 204 q^{34} - 260 q^{36} - 378 q^{37} + 496 q^{38} - 374 q^{39} - 1158 q^{41} - 348 q^{42} + 204 q^{43} + 784 q^{44} + 580 q^{46} - 248 q^{47} + 1880 q^{48} - 283 q^{49} + 228 q^{51} - 1482 q^{52} + 554 q^{53} + 918 q^{54} - 608 q^{56} - 44 q^{57} + 440 q^{59} + 618 q^{61} - 1250 q^{62} - 804 q^{63} + 2594 q^{64} + 2940 q^{66} - 1164 q^{67} - 356 q^{68} - 1968 q^{69} - 692 q^{71} + 2648 q^{72} + 1950 q^{73} - 1832 q^{74} + 1376 q^{76} + 1616 q^{77} + 1302 q^{78} + 272 q^{79} + 1801 q^{81} - 92 q^{82} - 512 q^{83} - 3208 q^{84} + 2446 q^{86} + 232 q^{87} + 6954 q^{88} + 866 q^{89} + 2580 q^{91} - 3468 q^{92} + 40 q^{93} - 5942 q^{94} + 7386 q^{96} - 1562 q^{97} + 3408 q^{98} - 238 q^{99}+O(q^{100}) \) 5 * q - 8 * q^3 + 26 * q^4 + 34 * q^6 - 40 * q^7 + 84 * q^8 + 33 * q^9 + 12 * q^11 + 224 * q^12 - 14 * q^13 - 192 * q^14 + 146 * q^16 - 66 * q^17 + 108 * q^18 + 214 * q^19 + 98 * q^22 - 164 * q^23 + 314 * q^24 + 56 * q^26 - 362 * q^27 - 540 * q^28 - 145 * q^29 + 420 * q^31 + 652 * q^32 + 576 * q^33 + 204 * q^34 - 260 * q^36 - 378 * q^37 + 496 * q^38 - 374 * q^39 - 1158 * q^41 - 348 * q^42 + 204 * q^43 + 784 * q^44 + 580 * q^46 - 248 * q^47 + 1880 * q^48 - 283 * q^49 + 228 * q^51 - 1482 * q^52 + 554 * q^53 + 918 * q^54 - 608 * q^56 - 44 * q^57 + 440 * q^59 + 618 * q^61 - 1250 * q^62 - 804 * q^63 + 2594 * q^64 + 2940 * q^66 - 1164 * q^67 - 356 * q^68 - 1968 * q^69 - 692 * q^71 + 2648 * q^72 + 1950 * q^73 - 1832 * q^74 + 1376 * q^76 + 1616 * q^77 + 1302 * q^78 + 272 * q^79 + 1801 * q^81 - 92 * q^82 - 512 * q^83 - 3208 * q^84 + 2446 * q^86 + 232 * q^87 + 6954 * q^88 + 866 * q^89 + 2580 * q^91 - 3468 * q^92 + 40 * q^93 - 5942 * q^94 + 7386 * q^96 - 1562 * q^97 + 3408 * q^98 - 238 * q^99

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