LMFDB - Embedded newform 525.4.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("525.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	525.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$30.9760027530$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 105)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.236068 q^{2} -3.00000 q^{3} -7.94427 q^{4} +0.708204 q^{6} +7.00000 q^{7} +3.76393 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-0.236068 q^{2} -3.00000 q^{3} -7.94427 q^{4} +0.708204 q^{6} +7.00000 q^{7} +3.76393 q^{8} +9.00000 q^{9} -50.4721 q^{11} +23.8328 q^{12} +80.9706 q^{13} -1.65248 q^{14} +62.6656 q^{16} -76.3870 q^{17} -2.12461 q^{18} +4.13777 q^{19} -21.0000 q^{21} +11.9149 q^{22} +204.721 q^{23} -11.2918 q^{24} -19.1146 q^{26} -27.0000 q^{27} -55.6099 q^{28} -91.1672 q^{29} +198.079 q^{31} -44.9048 q^{32} +151.416 q^{33} +18.0325 q^{34} -71.4984 q^{36} -155.666 q^{37} -0.976794 q^{38} -242.912 q^{39} -156.885 q^{41} +4.95743 q^{42} -354.217 q^{43} +400.964 q^{44} -48.3282 q^{46} +175.659 q^{47} -187.997 q^{48} +49.0000 q^{49} +229.161 q^{51} -643.252 q^{52} -200.302 q^{53} +6.37384 q^{54} +26.3475 q^{56} -12.4133 q^{57} +21.5217 q^{58} -312.498 q^{59} -154.170 q^{61} -46.7601 q^{62} +63.0000 q^{63} -490.724 q^{64} -35.7446 q^{66} -734.715 q^{67} +606.839 q^{68} -614.164 q^{69} -678.577 q^{71} +33.8754 q^{72} +60.8003 q^{73} +36.7477 q^{74} -32.8715 q^{76} -353.305 q^{77} +57.3437 q^{78} -1286.26 q^{79} +81.0000 q^{81} +37.0356 q^{82} -116.170 q^{83} +166.830 q^{84} +83.6192 q^{86} +273.502 q^{87} -189.974 q^{88} -916.440 q^{89} +566.794 q^{91} -1626.36 q^{92} -594.237 q^{93} -41.4676 q^{94} +134.714 q^{96} +1416.30 q^{97} -11.5673 q^{98} -454.249 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} - 6 q^{3} + 2 q^{4} - 12 q^{6} + 14 q^{7} + 12 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q + 4 * q^2 - 6 * q^3 + 2 * q^4 - 12 * q^6 + 14 * q^7 + 12 * q^8 + 18 * q^9	$ 2 q + 4 q^{2} - 6 q^{3} + 2 q^{4} - 12 q^{6} + 14 q^{7} + 12 q^{8} + 18 q^{9} - 92 q^{11} - 6 q^{12} - 8 q^{13} + 28 q^{14} + 18 q^{16} + 44 q^{17} + 36 q^{18} - 108 q^{19} - 42 q^{21} - 164 q^{22} + 320 q^{23} - 36 q^{24} - 396 q^{26} - 54 q^{27} + 14 q^{28} - 236 q^{29} - 60 q^{31} - 300 q^{32} + 276 q^{33} + 528 q^{34} + 18 q^{36} - 204 q^{37} - 476 q^{38} + 24 q^{39} + 44 q^{41} - 84 q^{42} - 136 q^{43} - 12 q^{44} + 440 q^{46} - 400 q^{47} - 54 q^{48} + 98 q^{49} - 132 q^{51} - 1528 q^{52} - 16 q^{53} - 108 q^{54} + 84 q^{56} + 324 q^{57} - 592 q^{58} - 464 q^{59} - 684 q^{61} - 1140 q^{62} + 126 q^{63} - 1214 q^{64} + 492 q^{66} - 736 q^{67} + 1804 q^{68} - 960 q^{69} - 740 q^{71} + 108 q^{72} - 424 q^{73} - 168 q^{74} - 1148 q^{76} - 644 q^{77} + 1188 q^{78} - 408 q^{79} + 162 q^{81} + 888 q^{82} - 608 q^{83} - 42 q^{84} + 1008 q^{86} + 708 q^{87} - 532 q^{88} - 1332 q^{89} - 56 q^{91} - 480 q^{92} + 180 q^{93} - 2480 q^{94} + 900 q^{96} + 2448 q^{97} + 196 q^{98} - 828 q^{99}+O(q^{100}) $ 2 * q + 4 * q^2 - 6 * q^3 + 2 * q^4 - 12 * q^6 + 14 * q^7 + 12 * q^8 + 18 * q^9 - 92 * q^11 - 6 * q^12 - 8 * q^13 + 28 * q^14 + 18 * q^16 + 44 * q^17 + 36 * q^18 - 108 * q^19 - 42 * q^21 - 164 * q^22 + 320 * q^23 - 36 * q^24 - 396 * q^26 - 54 * q^27 + 14 * q^28 - 236 * q^29 - 60 * q^31 - 300 * q^32 + 276 * q^33 + 528 * q^34 + 18 * q^36 - 204 * q^37 - 476 * q^38 + 24 * q^39 + 44 * q^41 - 84 * q^42 - 136 * q^43 - 12 * q^44 + 440 * q^46 - 400 * q^47 - 54 * q^48 + 98 * q^49 - 132 * q^51 - 1528 * q^52 - 16 * q^53 - 108 * q^54 + 84 * q^56 + 324 * q^57 - 592 * q^58 - 464 * q^59 - 684 * q^61 - 1140 * q^62 + 126 * q^63 - 1214 * q^64 + 492 * q^66 - 736 * q^67 + 1804 * q^68 - 960 * q^69 - 740 * q^71 + 108 * q^72 - 424 * q^73 - 168 * q^74 - 1148 * q^76 - 644 * q^77 + 1188 * q^78 - 408 * q^79 + 162 * q^81 + 888 * q^82 - 608 * q^83 - 42 * q^84 + 1008 * q^86 + 708 * q^87 - 532 * q^88 - 1332 * q^89 - 56 * q^91 - 480 * q^92 + 180 * q^93 - 2480 * q^94 + 900 * q^96 + 2448 * q^97 + 196 * q^98 - 828 * 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 $

$2$	−0.236068	−0.0834626	−0.0417313	−	0.999129i	$-0.513287\pi$
$2$	−0.236068	−0.0834626	−0.0417313	+	0.999129i	$0.513287\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−7.94427	−0.993034
$5$	0	0
$5$	0	0
$6$	0.708204	0.0481872
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	3.76393	0.166344
$9$	9.00000	0.333333
$10$	0	0
$11$	−50.4721	−1.38345	−0.691724	−	0.722162i	$-0.743148\pi$
$11$	−50.4721	−1.38345	−0.691724	+	0.722162i	$0.743148\pi$
$12$	23.8328	0.573328
$13$	80.9706	1.72748	0.863738	−	0.503940i	$-0.168117\pi$
$13$	80.9706	1.72748	0.863738	+	0.503940i	$0.168117\pi$
$14$	−1.65248	−0.0315459
$15$	0	0
$16$	62.6656	0.979150
$17$	−76.3870	−1.08980	−0.544899	−	0.838502i	$-0.683432\pi$
$17$	−76.3870	−1.08980	−0.544899	+	0.838502i	$0.683432\pi$
$18$	−2.12461	−0.0278209
$19$	4.13777	0.0499615	0.0249808	−	0.999688i	$-0.492048\pi$
$19$	4.13777	0.0499615	0.0249808	+	0.999688i	$0.492048\pi$
$20$	0	0
$21$	−21.0000	−0.218218
$22$	11.9149	0.115466
$23$	204.721	1.85597	0.927986	−	0.372615i	$-0.121539\pi$
$23$	204.721	1.85597	0.927986	+	0.372615i	$0.121539\pi$
$24$	−11.2918	−0.0960387
$25$	0	0
$26$	−19.1146	−0.144180
$27$	−27.0000	−0.192450
$28$	−55.6099	−0.375332
$29$	−91.1672	−0.583770	−0.291885	−	0.956453i	$-0.594282\pi$
$29$	−91.1672	−0.583770	−0.291885	+	0.956453i	$0.594282\pi$
$30$	0	0
$31$	198.079	1.14761	0.573807	−	0.818991i	$-0.305466\pi$
$31$	198.079	1.14761	0.573807	+	0.818991i	$0.305466\pi$
$32$	−44.9048	−0.248066
$33$	151.416	0.798734
$34$	18.0325	0.0909574
$35$	0	0
$36$	−71.4984	−0.331011
$37$	−155.666	−0.691656	−0.345828	−	0.938298i	$-0.612402\pi$
$37$	−155.666	−0.691656	−0.345828	+	0.938298i	$0.612402\pi$
$38$	−0.976794	−0.00416992
$39$	−242.912	−0.997359
$40$	0	0
$41$	−156.885	−0.597595	−0.298797	−	0.954317i	$-0.596585\pi$
$41$	−156.885	−0.597595	−0.298797	+	0.954317i	$0.596585\pi$
$42$	4.95743	0.0182130
$43$	−354.217	−1.25622	−0.628111	−	0.778124i	$-0.716172\pi$
$43$	−354.217	−1.25622	−0.628111	+	0.778124i	$0.716172\pi$
$44$	400.964	1.37381
$45$	0	0
$46$	−48.3282	−0.154904
$47$	175.659	0.545161	0.272580	−	0.962133i	$-0.412123\pi$
$47$	175.659	0.545161	0.272580	+	0.962133i	$0.412123\pi$
$48$	−187.997	−0.565313
$49$	49.0000	0.142857
$50$	0	0
$51$	229.161	0.629195
$52$	−643.252	−1.71544
$53$	−200.302	−0.519124	−0.259562	−	0.965726i	$-0.583578\pi$
$53$	−200.302	−0.519124	−0.259562	+	0.965726i	$0.583578\pi$
$54$	6.37384	0.0160624
$55$	0	0
$56$	26.3475	0.0628721
$57$	−12.4133	−0.0288453
$58$	21.5217	0.0487230
$59$	−312.498	−0.689556	−0.344778	−	0.938684i	$-0.612046\pi$
$59$	−312.498	−0.689556	−0.344778	+	0.938684i	$0.612046\pi$
$60$	0	0
$61$	−154.170	−0.323598	−0.161799	−	0.986824i	$-0.551730\pi$
$61$	−154.170	−0.323598	−0.161799	+	0.986824i	$0.551730\pi$
$62$	−46.7601	−0.0957829
$63$	63.0000	0.125988
$64$	−490.724	−0.958446
$65$	0	0
$66$	−35.7446	−0.0666644
$67$	−734.715	−1.33970	−0.669849	−	0.742498i	$-0.733641\pi$
$67$	−734.715	−1.33970	−0.669849	+	0.742498i	$0.733641\pi$
$68$	606.839	1.08221
$69$	−614.164	−1.07155
$70$	0	0
$71$	−678.577	−1.13426	−0.567129	−	0.823629i	$-0.691946\pi$
$71$	−678.577	−1.13426	−0.567129	+	0.823629i	$0.691946\pi$
$72$	33.8754	0.0554480
$73$	60.8003	0.0974813	0.0487407	−	0.998811i	$-0.484479\pi$
$73$	60.8003	0.0974813	0.0487407	+	0.998811i	$0.484479\pi$
$74$	36.7477	0.0577274
$75$	0	0
$76$	−32.8715	−0.0496135
$77$	−353.305	−0.522894
$78$	57.3437	0.0832422
$79$	−1286.26	−1.83184	−0.915919	−	0.401363i	$-0.868537\pi$
$79$	−1286.26	−1.83184	−0.915919	+	0.401363i	$0.868537\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	37.0356	0.0498768
$83$	−116.170	−0.153631	−0.0768153	−	0.997045i	$-0.524475\pi$
$83$	−116.170	−0.153631	−0.0768153	+	0.997045i	$0.524475\pi$
$84$	166.830	0.216698
$85$	0	0
$86$	83.6192	0.104848
$87$	273.502	0.337040
$88$	−189.974	−0.230128
$89$	−916.440	−1.09149	−0.545744	−	0.837952i	$-0.683753\pi$
$89$	−916.440	−1.09149	−0.545744	+	0.837952i	$0.683753\pi$
$90$	0	0
$91$	566.794	0.652925
$92$	−1626.36	−1.84304
$93$	−594.237	−0.662575
$94$	−41.4676	−0.0455006
$95$	0	0
$96$	134.714	0.143221
$97$	1416.30	1.48251	0.741256	−	0.671222i	$-0.234230\pi$
$97$	1416.30	1.48251	0.741256	+	0.671222i	$0.234230\pi$
$98$	−11.5673	−0.0119232
$99$	−454.249	−0.461149
$100$	0	0
$101$	−1379.19	−1.35876	−0.679381	−	0.733785i	$-0.737752\pi$
$101$	−1379.19	−1.35876	−0.679381	+	0.733785i	$0.737752\pi$
$102$	−54.0976	−0.0525143
$103$	1308.43	1.25169	0.625844	−	0.779949i	$-0.284755\pi$
$103$	1308.43	1.25169	0.625844	+	0.779949i	$0.284755\pi$
$104$	304.768	0.287355
$105$	0	0
$106$	47.2849	0.0433275
$107$	−1265.65	−1.14351	−0.571754	−	0.820425i	$-0.693737\pi$
$107$	−1265.65	−1.14351	−0.571754	+	0.820425i	$0.693737\pi$
$108$	214.495	0.191109
$109$	2069.32	1.81839	0.909196	−	0.416368i	$-0.136697\pi$
$109$	2069.32	1.81839	0.909196	+	0.416368i	$0.136697\pi$
$110$	0	0
$111$	466.997	0.399328
$112$	438.659	0.370084
$113$	1953.89	1.62661	0.813303	−	0.581840i	$-0.197667\pi$
$113$	1953.89	1.62661	0.813303	+	0.581840i	$0.197667\pi$
$114$	2.93038	0.00240750
$115$	0	0
$116$	724.257	0.579703
$117$	728.735	0.575826
$118$	73.7709	0.0575522
$119$	−534.709	−0.411905
$120$	0	0
$121$	1216.44	0.913927
$122$	36.3947	0.0270083
$123$	470.656	0.345022
$124$	−1573.59	−1.13962
$125$	0	0
$126$	−14.8723	−0.0105153
$127$	−224.251	−0.156685	−0.0783426	−	0.996926i	$-0.524963\pi$
$127$	−224.251	−0.156685	−0.0783426	+	0.996926i	$0.524963\pi$
$128$	475.083	0.328061
$129$	1062.65	0.725280
$130$	0	0
$131$	−490.898	−0.327404	−0.163702	−	0.986510i	$-0.552344\pi$
$131$	−490.898	−0.327404	−0.163702	+	0.986510i	$0.552344\pi$
$132$	−1202.89	−0.793170
$133$	28.9644	0.0188837
$134$	173.443	0.111815
$135$	0	0
$136$	−287.515	−0.181281
$137$	−1831.12	−1.14192	−0.570961	−	0.820977i	$-0.693429\pi$
$137$	−1831.12	−1.14192	−0.570961	+	0.820977i	$0.693429\pi$
$138$	144.984	0.0894340
$139$	−3050.84	−1.86165	−0.930823	−	0.365469i	$-0.880909\pi$
$139$	−3050.84	−1.86165	−0.930823	+	0.365469i	$0.880909\pi$
$140$	0	0
$141$	−526.978	−0.314749
$142$	160.190	0.0946682
$143$	−4086.76	−2.38987
$144$	563.991	0.326383
$145$	0	0
$146$	−14.3530	−0.00813605
$147$	−147.000	−0.0824786
$148$	1236.65	0.686838
$149$	2246.55	1.23520	0.617599	−	0.786493i	$-0.288105\pi$
$149$	2246.55	1.23520	0.617599	+	0.786493i	$0.288105\pi$
$150$	0	0
$151$	−1311.53	−0.706826	−0.353413	−	0.935467i	$-0.614979\pi$
$151$	−1311.53	−0.706826	−0.353413	+	0.935467i	$0.614979\pi$
$152$	15.5743	0.00831079
$153$	−687.483	−0.363266
$154$	83.4040	0.0436421
$155$	0	0
$156$	1929.76	0.990412
$157$	−1790.94	−0.910398	−0.455199	−	0.890390i	$-0.650432\pi$
$157$	−1790.94	−0.910398	−0.455199	+	0.890390i	$0.650432\pi$
$158$	303.644	0.152890
$159$	600.906	0.299716
$160$	0	0
$161$	1433.05	0.701491
$162$	−19.1215	−0.00927363
$163$	491.108	0.235991	0.117996	−	0.993014i	$-0.462353\pi$
$163$	491.108	0.235991	0.117996	+	0.993014i	$0.462353\pi$
$164$	1246.34	0.593432
$165$	0	0
$166$	27.4241	0.0128224
$167$	826.059	0.382769	0.191384	−	0.981515i	$-0.438702\pi$
$167$	826.059	0.382769	0.191384	+	0.981515i	$0.438702\pi$
$168$	−79.0426	−0.0362992
$169$	4359.24	1.98418
$170$	0	0
$171$	37.2399	0.0166538
$172$	2813.99	1.24747
$173$	−2918.00	−1.28238	−0.641190	−	0.767382i	$-0.721559\pi$
$173$	−2918.00	−1.28238	−0.641190	+	0.767382i	$0.721559\pi$
$174$	−64.5650	−0.0281302
$175$	0	0
$176$	−3162.87	−1.35460
$177$	937.495	0.398116
$178$	216.342	0.0910984
$179$	955.745	0.399082	0.199541	−	0.979889i	$-0.436055\pi$
$179$	955.745	0.399082	0.199541	+	0.979889i	$0.436055\pi$
$180$	0	0
$181$	206.080	0.0846289	0.0423145	−	0.999104i	$-0.486527\pi$
$181$	206.080	0.0846289	0.0423145	+	0.999104i	$0.486527\pi$
$182$	−133.802	−0.0544948
$183$	462.511	0.186829
$184$	770.557	0.308730
$185$	0	0
$186$	140.280	0.0553003
$187$	3855.41	1.50768
$188$	−1395.49	−0.541363
$189$	−189.000	−0.0727393
$190$	0	0
$191$	−2018.63	−0.764727	−0.382364	−	0.924012i	$-0.624890\pi$
$191$	−2018.63	−0.764727	−0.382364	+	0.924012i	$0.624890\pi$
$192$	1472.17	0.553359
$193$	−1031.69	−0.384781	−0.192390	−	0.981318i	$-0.561624\pi$
$193$	−1031.69	−0.384781	−0.192390	+	0.981318i	$0.561624\pi$
$194$	−334.344	−0.123734
$195$	0	0
$196$	−389.269	−0.141862
$197$	205.955	0.0744857	0.0372429	−	0.999306i	$-0.488142\pi$
$197$	205.955	0.0744857	0.0372429	+	0.999306i	$0.488142\pi$
$198$	107.234	0.0384887
$199$	−1831.38	−0.652376	−0.326188	−	0.945305i	$-0.605764\pi$
$199$	−1831.38	−0.652376	−0.326188	+	0.945305i	$0.605764\pi$
$200$	0	0
$201$	2204.15	0.773475
$202$	325.584	0.113406
$203$	−638.170	−0.220644
$204$	−1820.52	−0.624812
$205$	0	0
$206$	−308.879	−0.104469
$207$	1842.49	0.618657
$208$	5074.07	1.69146
$209$	−208.842	−0.0691191
$210$	0	0
$211$	1030.19	0.336119	0.168060	−	0.985777i	$-0.446250\pi$
$211$	1030.19	0.336119	0.168060	+	0.985777i	$0.446250\pi$
$212$	1591.25	0.515508
$213$	2035.73	0.654864
$214$	298.780	0.0954402
$215$	0	0
$216$	−101.626	−0.0320129
$217$	1386.55	0.433757
$218$	−488.500	−0.151768
$219$	−182.401	−0.0562809
$220$	0	0
$221$	−6185.10	−1.88260
$222$	−110.243	−0.0333289
$223$	−5368.67	−1.61217	−0.806083	−	0.591803i	$-0.798416\pi$
$223$	−5368.67	−1.61217	−0.806083	+	0.591803i	$0.798416\pi$
$224$	−314.334	−0.0937603
$225$	0	0
$226$	−461.251	−0.135761
$227$	932.121	0.272542	0.136271	−	0.990672i	$-0.456488\pi$
$227$	932.121	0.272542	0.136271	+	0.990672i	$0.456488\pi$
$228$	98.6146	0.0286444
$229$	3163.05	0.912752	0.456376	−	0.889787i	$-0.349147\pi$
$229$	3163.05	0.912752	0.456376	+	0.889787i	$0.349147\pi$
$230$	0	0
$231$	1059.91	0.301893
$232$	−343.147	−0.0971065
$233$	−436.562	−0.122747	−0.0613737	−	0.998115i	$-0.519548\pi$
$233$	−436.562	−0.122747	−0.0613737	+	0.998115i	$0.519548\pi$
$234$	−172.031	−0.0480599
$235$	0	0
$236$	2482.57	0.684753
$237$	3858.77	1.05761
$238$	126.228	0.0343787
$239$	−1980.82	−0.536103	−0.268051	−	0.963405i	$-0.586380\pi$
$239$	−1980.82	−0.536103	−0.268051	+	0.963405i	$0.586380\pi$
$240$	0	0
$241$	5303.55	1.41756	0.708780	−	0.705430i	$-0.249246\pi$
$241$	5303.55	1.41756	0.708780	+	0.705430i	$0.249246\pi$
$242$	−287.162	−0.0762787
$243$	−243.000	−0.0641500
$244$	1224.77	0.321344
$245$	0	0
$246$	−111.107	−0.0287964
$247$	335.037	0.0863074
$248$	745.556	0.190899
$249$	348.511	0.0886987
$250$	0	0
$251$	−2996.04	−0.753420	−0.376710	−	0.926331i	$-0.622945\pi$
$251$	−2996.04	−0.753420	−0.376710	+	0.926331i	$0.622945\pi$
$252$	−500.489	−0.125111
$253$	−10332.7	−2.56764
$254$	52.9384	0.0130774
$255$	0	0
$256$	3813.64	0.931065
$257$	−968.861	−0.235159	−0.117580	−	0.993063i	$-0.537513\pi$
$257$	−968.861	−0.235159	−0.117580	+	0.993063i	$0.537513\pi$
$258$	−250.858	−0.0605338
$259$	−1089.66	−0.261421
$260$	0	0
$261$	−820.505	−0.194590
$262$	115.885	0.0273260
$263$	4830.18	1.13248	0.566239	−	0.824241i	$-0.308398\pi$
$263$	4830.18	1.13248	0.566239	+	0.824241i	$0.308398\pi$
$264$	569.921	0.132864
$265$	0	0
$266$	−6.83756	−0.00157608
$267$	2749.32	0.630171
$268$	5836.78	1.33037
$269$	−4774.97	−1.08229	−0.541143	−	0.840930i	$-0.682008\pi$
$269$	−4774.97	−1.08229	−0.541143	+	0.840930i	$0.682008\pi$
$270$	0	0
$271$	141.909	0.0318094	0.0159047	−	0.999874i	$-0.494937\pi$
$271$	141.909	0.0318094	0.0159047	+	0.999874i	$0.494937\pi$
$272$	−4786.84	−1.06708
$273$	−1700.38	−0.376966
$274$	432.269	0.0953078
$275$	0	0
$276$	4879.09	1.06408
$277$	3621.13	0.785460	0.392730	−	0.919654i	$-0.371531\pi$
$277$	3621.13	0.785460	0.392730	+	0.919654i	$0.371531\pi$
$278$	720.206	0.155378
$279$	1782.71	0.382538
$280$	0	0
$281$	5790.87	1.22937	0.614687	−	0.788771i	$-0.289282\pi$
$281$	5790.87	1.22937	0.614687	+	0.788771i	$0.289282\pi$
$282$	124.403	0.0262698
$283$	−526.043	−0.110495	−0.0552474	−	0.998473i	$-0.517595\pi$
$283$	−526.043	−0.110495	−0.0552474	+	0.998473i	$0.517595\pi$
$284$	5390.80	1.12636
$285$	0	0
$286$	964.753	0.199465
$287$	−1098.20	−0.225870
$288$	−404.143	−0.0826888
$289$	921.972	0.187660
$290$	0	0
$291$	−4248.91	−0.855929
$292$	−483.014	−0.0968023
$293$	−1914.88	−0.381803	−0.190901	−	0.981609i	$-0.561141\pi$
$293$	−1914.88	−0.381803	−0.190901	+	0.981609i	$0.561141\pi$
$294$	34.7020	0.00688388
$295$	0	0
$296$	−585.915	−0.115053
$297$	1362.75	0.266245
$298$	−530.339	−0.103093
$299$	16576.4	3.20615
$300$	0	0
$301$	−2479.52	−0.474807
$302$	309.610	0.0589936
$303$	4137.58	0.784482
$304$	259.296	0.0489199
$305$	0	0
$306$	162.293	0.0303191
$307$	6244.17	1.16083	0.580413	−	0.814322i	$-0.302891\pi$
$307$	6244.17	1.16083	0.580413	+	0.814322i	$0.302891\pi$
$308$	2806.75	0.519251
$309$	−3925.30	−0.722662
$310$	0	0
$311$	−9658.78	−1.76109	−0.880545	−	0.473962i	$-0.842823\pi$
$311$	−9658.78	−1.76109	−0.880545	+	0.473962i	$0.842823\pi$
$312$	−914.303	−0.165905
$313$	−2198.34	−0.396988	−0.198494	−	0.980102i	$-0.563605\pi$
$313$	−2198.34	−0.396988	−0.198494	+	0.980102i	$0.563605\pi$
$314$	422.783	0.0759842
$315$	0	0
$316$	10218.4	1.81908
$317$	−3030.78	−0.536990	−0.268495	−	0.963281i	$-0.586526\pi$
$317$	−3030.78	−0.536990	−0.268495	+	0.963281i	$0.586526\pi$
$318$	−141.855	−0.0250151
$319$	4601.40	0.807615
$320$	0	0
$321$	3796.96	0.660204
$322$	−338.297	−0.0585483
$323$	−316.072	−0.0544480
$324$	−643.486	−0.110337
$325$	0	0
$326$	−115.935	−0.0196965
$327$	−6207.96	−1.04985
$328$	−590.506	−0.0994062
$329$	1229.62	0.206051
$330$	0	0
$331$	4753.74	0.789393	0.394696	−	0.918812i	$-0.370850\pi$
$331$	4753.74	0.789393	0.394696	+	0.918812i	$0.370850\pi$
$332$	922.888	0.152560
$333$	−1400.99	−0.230552
$334$	−195.006	−0.0319469
$335$	0	0
$336$	−1315.98	−0.213668
$337$	−8824.40	−1.42640	−0.713199	−	0.700962i	$-0.752754\pi$
$337$	−8824.40	−1.42640	−0.713199	+	0.700962i	$0.752754\pi$
$338$	−1029.08	−0.165605
$339$	−5861.67	−0.939122
$340$	0	0
$341$	−9997.47	−1.58766
$342$	−8.79115	−0.00138997
$343$	343.000	0.0539949
$344$	−1333.25	−0.208965
$345$	0	0
$346$	688.847	0.107031
$347$	3413.97	0.528160	0.264080	−	0.964501i	$-0.414932\pi$
$347$	3413.97	0.528160	0.264080	+	0.964501i	$0.414932\pi$
$348$	−2172.77	−0.334692
$349$	−5676.32	−0.870621	−0.435310	−	0.900280i	$-0.643361\pi$
$349$	−5676.32	−0.870621	−0.435310	+	0.900280i	$0.643361\pi$
$350$	0	0
$351$	−2186.21	−0.332453
$352$	2266.44	0.343187
$353$	−6225.80	−0.938713	−0.469357	−	0.883009i	$-0.655514\pi$
$353$	−6225.80	−0.938713	−0.469357	+	0.883009i	$0.655514\pi$
$354$	−221.313	−0.0332278
$355$	0	0
$356$	7280.45	1.08388
$357$	1604.13	0.237813
$358$	−225.621	−0.0333084
$359$	−4907.73	−0.721505	−0.360752	−	0.932662i	$-0.617480\pi$
$359$	−4907.73	−0.721505	−0.360752	+	0.932662i	$0.617480\pi$
$360$	0	0
$361$	−6841.88	−0.997504
$362$	−48.6490	−0.00706335
$363$	−3649.31	−0.527656
$364$	−4502.77	−0.648377
$365$	0	0
$366$	−109.184	−0.0155933
$367$	3906.48	0.555631	0.277816	−	0.960634i	$-0.410390\pi$
$367$	3906.48	0.555631	0.277816	+	0.960634i	$0.410390\pi$
$368$	12829.0	1.81728
$369$	−1411.97	−0.199198
$370$	0	0
$371$	−1402.11	−0.196210
$372$	4720.78	0.657960
$373$	2102.52	0.291862	0.145931	−	0.989295i	$-0.453382\pi$
$373$	2102.52	0.291862	0.145931	+	0.989295i	$0.453382\pi$
$374$	−910.140	−0.125835
$375$	0	0
$376$	661.170	0.0906842
$377$	−7381.86	−1.00845
$378$	44.6168	0.00607101
$379$	−6612.76	−0.896239	−0.448120	−	0.893974i	$-0.647906\pi$
$379$	−6612.76	−0.896239	−0.448120	+	0.893974i	$0.647906\pi$
$380$	0	0
$381$	672.752	0.0904623
$382$	476.534	0.0638262
$383$	−2.37457	−0.000316801 0	−0.000158401	−	1.00000i	$-0.500050\pi$
$383$	−2.37457	−0.000316801 0	−0.000158401		1.00000i	$0.500050\pi$
$384$	−1425.25	−0.189406
$385$	0	0
$386$	243.549	0.0321148
$387$	−3187.95	−0.418741
$388$	−11251.5	−1.47218
$389$	7716.98	1.00583	0.502913	−	0.864337i	$-0.332261\pi$
$389$	7716.98	1.00583	0.502913	+	0.864337i	$0.332261\pi$
$390$	0	0
$391$	−15638.0	−2.02263
$392$	184.433	0.0237634
$393$	1472.69	0.189027
$394$	−48.6194	−0.00621678
$395$	0	0
$396$	3608.68	0.457937
$397$	−6403.95	−0.809584	−0.404792	−	0.914409i	$-0.632656\pi$
$397$	−6403.95	−0.809584	−0.404792	+	0.914409i	$0.632656\pi$
$398$	432.329	0.0544490
$399$	−86.8931	−0.0109025
$400$	0	0
$401$	−10969.9	−1.36611	−0.683054	−	0.730368i	$-0.739349\pi$
$401$	−10969.9	−1.36611	−0.683054	+	0.730368i	$0.739349\pi$
$402$	−520.328	−0.0645562
$403$	16038.6	1.98248
$404$	10956.7	1.34930
$405$	0	0
$406$	150.652	0.0184155
$407$	7856.78	0.956870
$408$	862.546	0.104663
$409$	−400.353	−0.0484015	−0.0242007	−	0.999707i	$-0.507704\pi$
$409$	−400.353	−0.0484015	−0.0242007	+	0.999707i	$0.507704\pi$
$410$	0	0
$411$	5493.37	0.659289
$412$	−10394.6	−1.24297
$413$	−2187.49	−0.260628
$414$	−434.953	−0.0516348
$415$	0	0
$416$	−3635.97	−0.428529
$417$	9152.52	1.07482
$418$	49.3009	0.00576887
$419$	−15815.4	−1.84399	−0.921995	−	0.387201i	$-0.873442\pi$
$419$	−15815.4	−1.84399	−0.921995	+	0.387201i	$0.873442\pi$
$420$	0	0
$421$	1936.53	0.224182	0.112091	−	0.993698i	$-0.464245\pi$
$421$	1936.53	0.224182	0.112091	+	0.993698i	$0.464245\pi$
$422$	−243.195	−0.0280534
$423$	1580.93	0.181720
$424$	−753.923	−0.0863531
$425$	0	0
$426$	−480.571	−0.0546567
$427$	−1079.19	−0.122309
$428$	10054.7	1.13554
$429$	12260.3	1.37979
$430$	0	0
$431$	2030.91	0.226973	0.113487	−	0.993540i	$-0.463798\pi$
$431$	2030.91	0.226973	0.113487	+	0.993540i	$0.463798\pi$
$432$	−1691.97	−0.188438
$433$	10784.1	1.19689	0.598443	−	0.801165i	$-0.295786\pi$
$433$	10784.1	1.19689	0.598443	+	0.801165i	$0.295786\pi$
$434$	−327.321	−0.0362025
$435$	0	0
$436$	−16439.2	−1.80573
$437$	847.089	0.0927272
$438$	43.0590	0.00469735
$439$	−6304.19	−0.685382	−0.342691	−	0.939448i	$-0.611338\pi$
$439$	−6304.19	−0.685382	−0.342691	+	0.939448i	$0.611338\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	1460.10	0.157127
$443$	−15494.8	−1.66181	−0.830905	−	0.556414i	$-0.812177\pi$
$443$	−15494.8	−1.66181	−0.830905	+	0.556414i	$0.812177\pi$
$444$	−3709.95	−0.396546
$445$	0	0
$446$	1267.37	0.134556
$447$	−6739.65	−0.713142
$448$	−3435.07	−0.362259
$449$	−242.018	−0.0254377	−0.0127189	−	0.999919i	$-0.504049\pi$
$449$	−242.018	−0.0254377	−0.0127189	+	0.999919i	$0.504049\pi$
$450$	0	0
$451$	7918.34	0.826741
$452$	−15522.2	−1.61528
$453$	3934.59	0.408086
$454$	−220.044	−0.0227471
$455$	0	0
$456$	−46.7228	−0.00479824
$457$	11670.4	1.19457	0.597283	−	0.802030i	$-0.296247\pi$
$457$	11670.4	1.19457	0.597283	+	0.802030i	$0.296247\pi$
$458$	−746.695	−0.0761807
$459$	2062.45	0.209732
$460$	0	0
$461$	12128.1	1.22530	0.612649	−	0.790355i	$-0.290104\pi$
$461$	12128.1	1.22530	0.612649	+	0.790355i	$0.290104\pi$
$462$	−250.212	−0.0251968
$463$	−5161.64	−0.518103	−0.259051	−	0.965864i	$-0.583410\pi$
$463$	−5161.64	−0.518103	−0.259051	+	0.965864i	$0.583410\pi$
$464$	−5713.05	−0.571598
$465$	0	0
$466$	103.058	0.0102448
$467$	−11680.2	−1.15738	−0.578691	−	0.815547i	$-0.696436\pi$
$467$	−11680.2	−1.15738	−0.578691	+	0.815547i	$0.696436\pi$
$468$	−5789.27	−0.571814
$469$	−5143.01	−0.506358
$470$	0	0
$471$	5372.82	0.525619
$472$	−1176.22	−0.114703
$473$	17878.1	1.73792
$474$	−910.932	−0.0882711
$475$	0	0
$476$	4247.87	0.409036
$477$	−1802.72	−0.173041
$478$	467.608	0.0447445
$479$	−18458.7	−1.76075	−0.880373	−	0.474282i	$-0.842708\pi$
$479$	−18458.7	−1.76075	−0.880373	+	0.474282i	$0.842708\pi$
$480$	0	0
$481$	−12604.3	−1.19482
$482$	−1252.00	−0.118313
$483$	−4299.15	−0.405006
$484$	−9663.70	−0.907560
$485$	0	0
$486$	57.3645	0.00535413
$487$	−8630.11	−0.803014	−0.401507	−	0.915856i	$-0.631513\pi$
$487$	−8630.11	−0.803014	−0.401507	+	0.915856i	$0.631513\pi$
$488$	−580.286	−0.0538286
$489$	−1473.33	−0.136250
$490$	0	0
$491$	17801.6	1.63621	0.818103	−	0.575072i	$-0.195026\pi$
$491$	17801.6	1.63621	0.818103	+	0.575072i	$0.195026\pi$
$492$	−3739.02	−0.342618
$493$	6963.99	0.636191
$494$	−79.0916	−0.00720344
$495$	0	0
$496$	12412.7	1.12369
$497$	−4750.04	−0.428709
$498$	−82.2723	−0.00740303
$499$	200.167	0.0179574	0.00897868	−	0.999960i	$-0.497142\pi$
$499$	200.167	0.0179574	0.00897868	+	0.999960i	$0.497142\pi$
$500$	0	0
$501$	−2478.18	−0.220992
$502$	707.269	0.0628824
$503$	−16400.4	−1.45379	−0.726896	−	0.686747i	$-0.759038\pi$
$503$	−16400.4	−1.45379	−0.726896	+	0.686747i	$0.759038\pi$
$504$	237.128	0.0209574
$505$	0	0
$506$	2439.23	0.214302
$507$	−13077.7	−1.14556
$508$	1781.51	0.155594
$509$	−15006.6	−1.30679	−0.653394	−	0.757018i	$-0.726656\pi$
$509$	−15006.6	−1.30679	−0.653394	+	0.757018i	$0.726656\pi$
$510$	0	0
$511$	425.602	0.0368445
$512$	−4700.94	−0.405770
$513$	−111.720	−0.00961510
$514$	228.717	0.0196270
$515$	0	0
$516$	−8441.98	−0.720228
$517$	−8865.91	−0.754201
$518$	257.234	0.0218189
$519$	8754.01	0.740382
$520$	0	0
$521$	7113.18	0.598146	0.299073	−	0.954230i	$-0.403323\pi$
$521$	7113.18	0.598146	0.299073	+	0.954230i	$0.403323\pi$
$522$	193.695	0.0162410
$523$	8888.46	0.743146	0.371573	−	0.928404i	$-0.378819\pi$
$523$	8888.46	0.743146	0.371573	+	0.928404i	$0.378819\pi$
$524$	3899.83	0.325123
$525$	0	0
$526$	−1140.25	−0.0945196
$527$	−15130.7	−1.25067
$528$	9488.60	0.782081
$529$	29743.8	2.44463
$530$	0	0
$531$	−2812.49	−0.229852
$532$	−230.101	−0.0187521
$533$	−12703.1	−1.03233
$534$	−649.026	−0.0525957
$535$	0	0
$536$	−2765.42	−0.222850
$537$	−2867.23	−0.230410
$538$	1127.22	0.0903305
$539$	−2473.13	−0.197635
$540$	0	0
$541$	−653.827	−0.0519597	−0.0259799	−	0.999662i	$-0.508271\pi$
$541$	−653.827	−0.0519597	−0.0259799	+	0.999662i	$0.508271\pi$
$542$	−33.5001	−0.00265489
$543$	−618.241	−0.0488605
$544$	3430.14	0.270342
$545$	0	0
$546$	401.406	0.0314626
$547$	−1138.52	−0.0889940	−0.0444970	−	0.999010i	$-0.514169\pi$
$547$	−1138.52	−0.0889940	−0.0444970	+	0.999010i	$0.514169\pi$
$548$	14546.9	1.13397
$549$	−1387.53	−0.107866
$550$	0	0
$551$	−377.229	−0.0291660
$552$	−2311.67	−0.178245
$553$	−9003.80	−0.692370
$554$	−854.832	−0.0655566
$555$	0	0
$556$	24236.7	1.84868
$557$	19804.8	1.50657	0.753283	−	0.657696i	$-0.228469\pi$
$557$	19804.8	1.50657	0.753283	+	0.657696i	$0.228469\pi$
$558$	−420.841	−0.0319276
$559$	−28681.1	−2.17009
$560$	0	0
$561$	−11566.2	−0.870458
$562$	−1367.04	−0.102607
$563$	−10276.3	−0.769265	−0.384632	−	0.923070i	$-0.625672\pi$
$563$	−10276.3	−0.769265	−0.384632	+	0.923070i	$0.625672\pi$
$564$	4186.46	0.312556
$565$	0	0
$566$	124.182	0.00922219
$567$	567.000	0.0419961
$568$	−2554.12	−0.188677
$569$	4139.03	0.304951	0.152475	−	0.988307i	$-0.451276\pi$
$569$	4139.03	0.304951	0.152475	+	0.988307i	$0.451276\pi$
$570$	0	0
$571$	−4486.81	−0.328839	−0.164420	−	0.986390i	$-0.552575\pi$
$571$	−4486.81	−0.328839	−0.164420	+	0.986390i	$0.552575\pi$
$572$	32466.3	2.37323
$573$	6055.89	0.441516
$574$	259.249	0.0188517
$575$	0	0
$576$	−4416.52	−0.319482
$577$	1104.77	0.0797093	0.0398547	−	0.999205i	$-0.487311\pi$
$577$	1104.77	0.0797093	0.0398547	+	0.999205i	$0.487311\pi$
$578$	−217.648	−0.0156626
$579$	3095.07	0.222153
$580$	0	0
$581$	−813.192	−0.0580669
$582$	1003.03	0.0714381
$583$	10109.7	0.718181
$584$	228.848	0.0162154
$585$	0	0
$586$	452.041	0.0318663
$587$	10413.2	0.732199	0.366100	−	0.930576i	$-0.380693\pi$
$587$	10413.2	0.732199	0.366100	+	0.930576i	$0.380693\pi$
$588$	1167.81	0.0819041
$589$	819.605	0.0573365
$590$	0	0
$591$	−617.865	−0.0430044
$592$	−9754.89	−0.677235
$593$	3235.16	0.224034	0.112017	−	0.993706i	$-0.464269\pi$
$593$	3235.16	0.224034	0.112017	+	0.993706i	$0.464269\pi$
$594$	−321.701	−0.0222215
$595$	0	0
$596$	−17847.2	−1.22659
$597$	5494.13	0.376649
$598$	−3913.16	−0.267594
$599$	569.048	0.0388158	0.0194079	−	0.999812i	$-0.493822\pi$
$599$	569.048	0.0388158	0.0194079	+	0.999812i	$0.493822\pi$
$600$	0	0
$601$	3760.89	0.255258	0.127629	−	0.991822i	$-0.459263\pi$
$601$	3760.89	0.255258	0.127629	+	0.991822i	$0.459263\pi$
$602$	585.335	0.0396287
$603$	−6612.44	−0.446566
$604$	10419.1	0.701902
$605$	0	0
$606$	−976.751	−0.0654749
$607$	2224.05	0.148717	0.0743585	−	0.997232i	$-0.476309\pi$
$607$	2224.05	0.148717	0.0743585	+	0.997232i	$0.476309\pi$
$608$	−185.806	−0.0123938
$609$	1914.51	0.127389
$610$	0	0
$611$	14223.2	0.941753
$612$	5461.55	0.360735
$613$	−5914.50	−0.389697	−0.194849	−	0.980833i	$-0.562422\pi$
$613$	−5914.50	−0.389697	−0.194849	+	0.980833i	$0.562422\pi$
$614$	−1474.05	−0.0968856
$615$	0	0
$616$	−1329.82	−0.0869802
$617$	18591.2	1.21306	0.606528	−	0.795062i	$-0.292562\pi$
$617$	18591.2	1.21306	0.606528	+	0.795062i	$0.292562\pi$
$618$	926.638	0.0603153
$619$	5125.97	0.332844	0.166422	−	0.986055i	$-0.446779\pi$
$619$	5125.97	0.332844	0.166422	+	0.986055i	$0.446779\pi$
$620$	0	0
$621$	−5527.48	−0.357182
$622$	2280.13	0.146985
$623$	−6415.08	−0.412544
$624$	−15222.2	−0.976565
$625$	0	0
$626$	518.957	0.0331337
$627$	626.526	0.0399060
$628$	14227.7	0.904056
$629$	11890.8	0.753765
$630$	0	0
$631$	−10649.0	−0.671839	−0.335919	−	0.941891i	$-0.609047\pi$
$631$	−10649.0	−0.671839	−0.335919	+	0.941891i	$0.609047\pi$
$632$	−4841.38	−0.304715
$633$	−3090.57	−0.194058
$634$	715.471	0.0448186
$635$	0	0
$636$	−4773.76	−0.297629
$637$	3967.56	0.246782
$638$	−1086.24	−0.0674056
$639$	−6107.20	−0.378086
$640$	0	0
$641$	24025.7	1.48044	0.740218	−	0.672367i	$-0.234722\pi$
$641$	24025.7	1.48044	0.740218	+	0.672367i	$0.234722\pi$
$642$	−896.341	−0.0551024
$643$	−14929.3	−0.915638	−0.457819	−	0.889045i	$-0.651369\pi$
$643$	−14929.3	−0.915638	−0.457819	+	0.889045i	$0.651369\pi$
$644$	−11384.5	−0.696605
$645$	0	0
$646$	74.6144	0.00454437
$647$	−14479.1	−0.879801	−0.439901	−	0.898046i	$-0.644986\pi$
$647$	−14479.1	−0.879801	−0.439901	+	0.898046i	$0.644986\pi$
$648$	304.878	0.0184827
$649$	15772.5	0.953965
$650$	0	0
$651$	−4159.66	−0.250430
$652$	−3901.50	−0.234347
$653$	−898.168	−0.0538255	−0.0269127	−	0.999638i	$-0.508568\pi$
$653$	−898.168	−0.0538255	−0.0269127	+	0.999638i	$0.508568\pi$
$654$	1465.50	0.0876232
$655$	0	0
$656$	−9831.33	−0.585135
$657$	547.203	0.0324938
$658$	−290.273	−0.0171976
$659$	−30198.0	−1.78505	−0.892526	−	0.450997i	$-0.851069\pi$
$659$	−30198.0	−1.78505	−0.892526	+	0.450997i	$0.851069\pi$
$660$	0	0
$661$	−19337.8	−1.13790	−0.568952	−	0.822371i	$-0.692651\pi$
$661$	−19337.8	−1.13790	−0.568952	+	0.822371i	$0.692651\pi$
$662$	−1122.20	−0.0658848
$663$	18555.3	1.08692
$664$	−437.257	−0.0255555
$665$	0	0
$666$	330.729	0.0192425
$667$	−18663.9	−1.08346
$668$	−6562.44	−0.380102
$669$	16106.0	0.930784
$670$	0	0
$671$	7781.30	0.447681
$672$	943.001	0.0541325
$673$	−10132.2	−0.580336	−0.290168	−	0.956976i	$-0.593711\pi$
$673$	−10132.2	−0.580336	−0.290168	+	0.956976i	$0.593711\pi$
$674$	2083.16	0.119051
$675$	0	0
$676$	−34631.0	−1.97035
$677$	33177.3	1.88347	0.941733	−	0.336361i	$-0.109196\pi$
$677$	33177.3	1.88347	0.941733	+	0.336361i	$0.109196\pi$
$678$	1383.75	0.0783816
$679$	9914.11	0.560337
$680$	0	0
$681$	−2796.36	−0.157352
$682$	2360.08	0.132511
$683$	11423.6	0.639987	0.319994	−	0.947420i	$-0.396319\pi$
$683$	11423.6	0.639987	0.319994	+	0.947420i	$0.396319\pi$
$684$	−295.844	−0.0165378
$685$	0	0
$686$	−80.9713	−0.00450656
$687$	−9489.15	−0.526978
$688$	−22197.2	−1.23003
$689$	−16218.6	−0.896775
$690$	0	0
$691$	−19737.4	−1.08661	−0.543304	−	0.839536i	$-0.682827\pi$
$691$	−19737.4	−1.08661	−0.543304	+	0.839536i	$0.682827\pi$
$692$	23181.4	1.27345
$693$	−3179.74	−0.174298
$694$	−805.929	−0.0440816
$695$	0	0
$696$	1029.44	0.0560645
$697$	11984.0	0.651258
$698$	1340.00	0.0726643
$699$	1309.69	0.0708682
$700$	0	0
$701$	11307.8	0.609258	0.304629	−	0.952471i	$-0.401468\pi$
$701$	11307.8	0.609258	0.304629	+	0.952471i	$0.401468\pi$
$702$	516.093	0.0277474
$703$	−644.108	−0.0345562
$704$	24767.9	1.32596
$705$	0	0
$706$	1469.71	0.0783475
$707$	−9654.36	−0.513564
$708$	−7447.72	−0.395342
$709$	30859.2	1.63461	0.817307	−	0.576202i	$-0.195466\pi$
$709$	30859.2	1.63461	0.817307	+	0.576202i	$0.195466\pi$
$710$	0	0
$711$	−11576.3	−0.610613
$712$	−3449.42	−0.181562
$713$	40551.0	2.12994
$714$	−378.683	−0.0198485
$715$	0	0
$716$	−7592.69	−0.396302
$717$	5942.46	0.309519
$718$	1158.56	0.0602187
$719$	33152.4	1.71958	0.859789	−	0.510650i	$-0.170595\pi$
$719$	33152.4	1.71958	0.859789	+	0.510650i	$0.170595\pi$
$720$	0	0
$721$	9159.03	0.473093
$722$	1615.15	0.0832543
$723$	−15910.7	−0.818428
$724$	−1637.16	−0.0840394
$725$	0	0
$726$	861.485	0.0440395
$727$	16743.0	0.854146	0.427073	−	0.904217i	$-0.359545\pi$
$727$	16743.0	0.854146	0.427073	+	0.904217i	$0.359545\pi$
$728$	2133.37	0.108610
$729$	729.000	0.0370370
$730$	0	0
$731$	27057.5	1.36903
$732$	−3674.31	−0.185528
$733$	8827.55	0.444820	0.222410	−	0.974953i	$-0.428608\pi$
$733$	8827.55	0.444820	0.222410	+	0.974953i	$0.428608\pi$
$734$	−922.195	−0.0463744
$735$	0	0
$736$	−9192.97	−0.460404
$737$	37082.6	1.85340
$738$	333.321	0.0166256
$739$	36154.0	1.79966	0.899829	−	0.436243i	$-0.143691\pi$
$739$	36154.0	1.79966	0.899829	+	0.436243i	$0.143691\pi$
$740$	0	0
$741$	−1005.11	−0.0498296
$742$	330.994	0.0163762
$743$	1820.69	0.0898987	0.0449494	−	0.998989i	$-0.485687\pi$
$743$	1820.69	0.0898987	0.0449494	+	0.998989i	$0.485687\pi$
$744$	−2236.67	−0.110215
$745$	0	0
$746$	−496.338	−0.0243596
$747$	−1045.53	−0.0512102
$748$	−30628.5	−1.49718
$749$	−8859.57	−0.432205
$750$	0	0
$751$	27764.4	1.34905	0.674526	−	0.738251i	$-0.264348\pi$
$751$	27764.4	1.34905	0.674526	+	0.738251i	$0.264348\pi$
$752$	11007.8	0.533795
$753$	8988.12	0.434987
$754$	1742.62	0.0841678
$755$	0	0
$756$	1501.47	0.0722326
$757$	13518.3	0.649050	0.324525	−	0.945877i	$-0.394795\pi$
$757$	13518.3	0.649050	0.324525	+	0.945877i	$0.394795\pi$
$758$	1561.06	0.0748025
$759$	30998.2	1.48243
$760$	0	0
$761$	30695.2	1.46216	0.731078	−	0.682294i	$-0.239017\pi$
$761$	30695.2	1.46216	0.731078	+	0.682294i	$0.239017\pi$
$762$	−158.815	−0.00755022
$763$	14485.2	0.687288
$764$	16036.5	0.759400
$765$	0	0
$766$	0.560560	2.64410e−5 0
$767$	−25303.2	−1.19119
$768$	−11440.9	−0.537551
$769$	4536.39	0.212726	0.106363	−	0.994327i	$-0.466079\pi$
$769$	4536.39	0.212726	0.106363	+	0.994327i	$0.466079\pi$
$770$	0	0
$771$	2906.58	0.135769
$772$	8196.03	0.382100
$773$	−31238.9	−1.45354	−0.726768	−	0.686883i	$-0.758978\pi$
$773$	−31238.9	−1.45354	−0.726768	+	0.686883i	$0.758978\pi$
$774$	752.573	0.0349492
$775$	0	0
$776$	5330.86	0.246607
$777$	3268.98	0.150932
$778$	−1821.73	−0.0839490
$779$	−649.155	−0.0298567
$780$	0	0
$781$	34249.2	1.56919
$782$	3691.64	0.168814
$783$	2461.51	0.112347
$784$	3070.62	0.139879
$785$	0	0
$786$	−347.656	−0.0157767
$787$	−39597.2	−1.79350	−0.896752	−	0.442534i	$-0.854079\pi$
$787$	−39597.2	−1.79350	−0.896752	+	0.442534i	$0.854079\pi$
$788$	−1636.16	−0.0739669
$789$	−14490.5	−0.653836
$790$	0	0
$791$	13677.2	0.614799
$792$	−1709.76	−0.0767093
$793$	−12483.3	−0.559008
$794$	1511.77	0.0675700
$795$	0	0
$796$	14549.0	0.647832
$797$	16567.0	0.736302	0.368151	−	0.929766i	$-0.379991\pi$
$797$	16567.0	0.736302	0.368151	+	0.929766i	$0.379991\pi$
$798$	20.5127	0.000909951 0
$799$	−13418.1	−0.594115
$800$	0	0
$801$	−8247.96	−0.363829
$802$	2589.63	0.114019
$803$	−3068.72	−0.134860
$804$	−17510.3	−0.768087
$805$	0	0
$806$	−3786.19	−0.165463
$807$	14324.9	0.624859
$808$	−5191.20	−0.226022
$809$	−12141.6	−0.527657	−0.263828	−	0.964570i	$-0.584985\pi$
$809$	−12141.6	−0.527657	−0.263828	+	0.964570i	$0.584985\pi$
$810$	0	0
$811$	30295.6	1.31174	0.655870	−	0.754873i	$-0.272302\pi$
$811$	30295.6	1.31174	0.655870	+	0.754873i	$0.272302\pi$
$812$	5069.80	0.219107
$813$	−425.726	−0.0183651
$814$	−1854.73	−0.0798629
$815$	0	0
$816$	14360.5	0.616077
$817$	−1465.67	−0.0627628
$818$	94.5106	0.00403971
$819$	5101.15	0.217642
$820$	0	0
$821$	−14914.8	−0.634018	−0.317009	−	0.948423i	$-0.602678\pi$
$821$	−14914.8	−0.634018	−0.317009	+	0.948423i	$0.602678\pi$
$822$	−1296.81	−0.0550260
$823$	31077.6	1.31628	0.658138	−	0.752897i	$-0.271344\pi$
$823$	31077.6	1.31628	0.658138	+	0.752897i	$0.271344\pi$
$824$	4924.85	0.208210
$825$	0	0
$826$	516.396	0.0217527
$827$	−15527.8	−0.652908	−0.326454	−	0.945213i	$-0.605854\pi$
$827$	−15527.8	−0.652908	−0.326454	+	0.945213i	$0.605854\pi$
$828$	−14637.3	−0.614348
$829$	−40221.5	−1.68510	−0.842551	−	0.538617i	$-0.818947\pi$
$829$	−40221.5	−1.68510	−0.842551	+	0.538617i	$0.818947\pi$
$830$	0	0
$831$	−10863.4	−0.453486
$832$	−39734.2	−1.65569
$833$	−3742.96	−0.155685
$834$	−2160.62	−0.0897075
$835$	0	0
$836$	1659.10	0.0686377
$837$	−5348.13	−0.220858
$838$	3733.51	0.153904
$839$	−21153.7	−0.870448	−0.435224	−	0.900322i	$-0.643331\pi$
$839$	−21153.7	−0.870448	−0.435224	+	0.900322i	$0.643331\pi$
$840$	0	0
$841$	−16077.5	−0.659213
$842$	−457.152	−0.0187108
$843$	−17372.6	−0.709780
$844$	−8184.10	−0.333778
$845$	0	0
$846$	−373.208	−0.0151669
$847$	8515.06	0.345432
$848$	−12552.0	−0.508301
$849$	1578.13	0.0637942
$850$	0	0
$851$	−31868.1	−1.28369
$852$	−16172.4	−0.650302
$853$	−636.075	−0.0255320	−0.0127660	−	0.999919i	$-0.504064\pi$
$853$	−636.075	−0.0255320	−0.0127660	+	0.999919i	$0.504064\pi$
$854$	254.763	0.0102082
$855$	0	0
$856$	−4763.83	−0.190215
$857$	3941.46	0.157104	0.0785518	−	0.996910i	$-0.474970\pi$
$857$	3941.46	0.157104	0.0785518	+	0.996910i	$0.474970\pi$
$858$	−2894.26	−0.115161
$859$	−21781.6	−0.865165	−0.432583	−	0.901594i	$-0.642398\pi$
$859$	−21781.6	−0.865165	−0.432583	+	0.901594i	$0.642398\pi$
$860$	0	0
$861$	3294.59	0.130406
$862$	−479.432	−0.0189438
$863$	44697.9	1.76308	0.881538	−	0.472112i	$-0.156508\pi$
$863$	44697.9	1.76308	0.881538	+	0.472112i	$0.156508\pi$
$864$	1212.43	0.0477404
$865$	0	0
$866$	−2545.79	−0.0998953
$867$	−2765.92	−0.108345
$868$	−11015.2	−0.430736
$869$	64920.1	2.53425
$870$	0	0
$871$	−59490.3	−2.31430
$872$	7788.78	0.302478
$873$	12746.7	0.494171
$874$	−199.971	−0.00773926
$875$	0	0
$876$	1449.04	0.0558888
$877$	20171.7	0.776682	0.388341	−	0.921516i	$-0.373048\pi$
$877$	20171.7	0.776682	0.388341	+	0.921516i	$0.373048\pi$
$878$	1488.22	0.0572038
$879$	5744.63	0.220434
$880$	0	0
$881$	11577.6	0.442744	0.221372	−	0.975189i	$-0.428946\pi$
$881$	11577.6	0.442744	0.221372	+	0.975189i	$0.428946\pi$
$882$	−104.106	−0.00397441
$883$	35388.3	1.34871	0.674355	−	0.738407i	$-0.264422\pi$
$883$	35388.3	1.34871	0.674355	+	0.738407i	$0.264422\pi$
$884$	49136.1	1.86949
$885$	0	0
$886$	3657.83	0.138699
$887$	41705.0	1.57871	0.789356	−	0.613936i	$-0.210415\pi$
$887$	41705.0	1.57871	0.789356	+	0.613936i	$0.210415\pi$
$888$	1757.74	0.0664257
$889$	−1569.75	−0.0592215
$890$	0	0
$891$	−4088.24	−0.153716
$892$	42650.2	1.60093
$893$	726.838	0.0272371
$894$	1591.02	0.0595207
$895$	0	0
$896$	3325.58	0.123995
$897$	−49729.2	−1.85107
$898$	57.1328	0.00212310
$899$	−18058.3	−0.669942
$900$	0	0
$901$	15300.5	0.565740
$902$	−1869.27	−0.0690020
$903$	7438.55	0.274130
$904$	7354.31	0.270576
$905$	0	0
$906$	−928.830	−0.0340600
$907$	28645.1	1.04867	0.524336	−	0.851511i	$-0.324313\pi$
$907$	28645.1	1.04867	0.524336	+	0.851511i	$0.324313\pi$
$908$	−7405.02	−0.270643
$909$	−12412.8	−0.452921
$910$	0	0
$911$	13337.8	0.485074	0.242537	−	0.970142i	$-0.422020\pi$
$911$	13337.8	0.485074	0.242537	+	0.970142i	$0.422020\pi$
$912$	−777.887	−0.0282439
$913$	5863.36	0.212540
$914$	−2755.00	−0.0997016
$915$	0	0
$916$	−25128.1	−0.906394
$917$	−3436.29	−0.123747
$918$	−486.878	−0.0175048
$919$	−28911.0	−1.03774	−0.518871	−	0.854853i	$-0.673647\pi$
$919$	−28911.0	−1.03774	−0.518871	+	0.854853i	$0.673647\pi$
$920$	0	0
$921$	−18732.5	−0.670203
$922$	−2863.06	−0.102267
$923$	−54944.8	−1.95940
$924$	−8420.25	−0.299790
$925$	0	0
$926$	1218.50	0.0432422
$927$	11775.9	0.417229
$928$	4093.84	0.144814
$929$	7093.88	0.250530	0.125265	−	0.992123i	$-0.460022\pi$
$929$	7093.88	0.250530	0.125265	+	0.992123i	$0.460022\pi$
$930$	0	0
$931$	202.751	0.00713736
$932$	3468.17	0.121892
$933$	28976.3	1.01677
$934$	2757.33	0.0965981
$935$	0	0
$936$	2742.91	0.0957851
$937$	19271.1	0.671888	0.335944	−	0.941882i	$-0.390945\pi$
$937$	19271.1	0.671888	0.335944	+	0.941882i	$0.390945\pi$
$938$	1214.10	0.0422620
$939$	6595.01	0.229201
$940$	0	0
$941$	−18115.2	−0.627563	−0.313782	−	0.949495i	$-0.601596\pi$
$941$	−18115.2	−0.627563	−0.313782	+	0.949495i	$0.601596\pi$
$942$	−1268.35	−0.0438695
$943$	−32117.8	−1.10912
$944$	−19582.9	−0.675180
$945$	0	0
$946$	−4220.44	−0.145051
$947$	2475.55	0.0849468	0.0424734	−	0.999098i	$-0.486476\pi$
$947$	2475.55	0.0849468	0.0424734	+	0.999098i	$0.486476\pi$
$948$	−30655.1	−1.05024
$949$	4923.04	0.168397
$950$	0	0
$951$	9092.35	0.310031
$952$	−2012.61	−0.0685179
$953$	−12866.6	−0.437344	−0.218672	−	0.975798i	$-0.570173\pi$
$953$	−12866.6	−0.437344	−0.218672	+	0.975798i	$0.570173\pi$
$954$	425.564	0.0144425
$955$	0	0
$956$	15736.2	0.532368
$957$	−13804.2	−0.466277
$958$	4357.50	0.146957
$959$	−12817.9	−0.431606
$960$	0	0
$961$	9444.26	0.317017
$962$	2975.48	0.0997228
$963$	−11390.9	−0.381169
$964$	−42132.9	−1.40768
$965$	0	0
$966$	1014.89	0.0338029
$967$	2142.86	0.0712614	0.0356307	−	0.999365i	$-0.488656\pi$
$967$	2142.86	0.0712614	0.0356307	+	0.999365i	$0.488656\pi$
$968$	4578.58	0.152026
$969$	948.215	0.0314356
$970$	0	0
$971$	2879.06	0.0951529	0.0475765	−	0.998868i	$-0.484850\pi$
$971$	2879.06	0.0951529	0.0475765	+	0.998868i	$0.484850\pi$
$972$	1930.46	0.0637032
$973$	−21355.9	−0.703636
$974$	2037.29	0.0670217
$975$	0	0
$976$	−9661.18	−0.316851
$977$	−48741.1	−1.59607	−0.798037	−	0.602608i	$-0.794128\pi$
$977$	−48741.1	−1.59607	−0.798037	+	0.602608i	$0.794128\pi$
$978$	347.805	0.0113718
$979$	46254.7	1.51002
$980$	0	0
$981$	18623.9	0.606131
$982$	−4202.40	−0.136562
$983$	45756.8	1.48466	0.742328	−	0.670037i	$-0.233722\pi$
$983$	45756.8	1.48466	0.742328	+	0.670037i	$0.233722\pi$
$984$	1771.52	0.0573922
$985$	0	0
$986$	−1643.97	−0.0530982
$987$	−3688.85	−0.118964
$988$	−2661.63	−0.0857062
$989$	−72515.7	−2.33151
$990$	0	0
$991$	−51552.1	−1.65248	−0.826240	−	0.563319i	$-0.809524\pi$
$991$	−51552.1	−1.65248	−0.826240	+	0.563319i	$0.809524\pi$
$992$	−8894.70	−0.284684
$993$	−14261.2	−0.455756
$994$	1121.33	0.0357812
$995$	0	0
$996$	−2768.67	−0.0880808
$997$	−25565.3	−0.812097	−0.406048	−	0.913852i	$-0.633094\pi$
$997$	−25565.3	−0.812097	−0.406048	+	0.913852i	$0.633094\pi$
$998$	−47.2531	−0.00149877
$999$	4202.97	0.133109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.4.a.o.1.1		2
3.2	odd	2		1575.4.a.n.1.2		2
5.2	odd	4		525.4.d.k.274.2		4
5.3	odd	4		525.4.d.k.274.3		4
5.4	even	2		105.4.a.d.1.2	✓	2
15.14	odd	2		315.4.a.l.1.1		2
20.19	odd	2		1680.4.a.bd.1.2		2
35.34	odd	2		735.4.a.m.1.2		2
105.104	even	2		2205.4.a.be.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.a.d.1.2	✓	2	5.4	even	2
315.4.a.l.1.1		2	15.14	odd	2
525.4.a.o.1.1		2	1.1	even	1	trivial
525.4.d.k.274.2		4	5.2	odd	4
525.4.d.k.274.3		4	5.3	odd	4
735.4.a.m.1.2		2	35.34	odd	2
1575.4.a.n.1.2		2	3.2	odd	2
1680.4.a.bd.1.2		2	20.19	odd	2
2205.4.a.be.1.1		2	105.104	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	525.a (trivial)

\(f(q)\)	\(=\)	\(q-0.236068 q^{2} -3.00000 q^{3} -7.94427 q^{4} +0.708204 q^{6} +7.00000 q^{7} +3.76393 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-0.236068 q^{2} -3.00000 q^{3} -7.94427 q^{4} +0.708204 q^{6} +7.00000 q^{7} +3.76393 q^{8} +9.00000 q^{9} -50.4721 q^{11} +23.8328 q^{12} +80.9706 q^{13} -1.65248 q^{14} +62.6656 q^{16} -76.3870 q^{17} -2.12461 q^{18} +4.13777 q^{19} -21.0000 q^{21} +11.9149 q^{22} +204.721 q^{23} -11.2918 q^{24} -19.1146 q^{26} -27.0000 q^{27} -55.6099 q^{28} -91.1672 q^{29} +198.079 q^{31} -44.9048 q^{32} +151.416 q^{33} +18.0325 q^{34} -71.4984 q^{36} -155.666 q^{37} -0.976794 q^{38} -242.912 q^{39} -156.885 q^{41} +4.95743 q^{42} -354.217 q^{43} +400.964 q^{44} -48.3282 q^{46} +175.659 q^{47} -187.997 q^{48} +49.0000 q^{49} +229.161 q^{51} -643.252 q^{52} -200.302 q^{53} +6.37384 q^{54} +26.3475 q^{56} -12.4133 q^{57} +21.5217 q^{58} -312.498 q^{59} -154.170 q^{61} -46.7601 q^{62} +63.0000 q^{63} -490.724 q^{64} -35.7446 q^{66} -734.715 q^{67} +606.839 q^{68} -614.164 q^{69} -678.577 q^{71} +33.8754 q^{72} +60.8003 q^{73} +36.7477 q^{74} -32.8715 q^{76} -353.305 q^{77} +57.3437 q^{78} -1286.26 q^{79} +81.0000 q^{81} +37.0356 q^{82} -116.170 q^{83} +166.830 q^{84} +83.6192 q^{86} +273.502 q^{87} -189.974 q^{88} -916.440 q^{89} +566.794 q^{91} -1626.36 q^{92} -594.237 q^{93} -41.4676 q^{94} +134.714 q^{96} +1416.30 q^{97} -11.5673 q^{98} -454.249 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} - 6 q^{3} + 2 q^{4} - 12 q^{6} + 14 q^{7} + 12 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q + 4 * q^2 - 6 * q^3 + 2 * q^4 - 12 * q^6 + 14 * q^7 + 12 * q^8 + 18 * q^9	\( 2 q + 4 q^{2} - 6 q^{3} + 2 q^{4} - 12 q^{6} + 14 q^{7} + 12 q^{8} + 18 q^{9} - 92 q^{11} - 6 q^{12} - 8 q^{13} + 28 q^{14} + 18 q^{16} + 44 q^{17} + 36 q^{18} - 108 q^{19} - 42 q^{21} - 164 q^{22} + 320 q^{23} - 36 q^{24} - 396 q^{26} - 54 q^{27} + 14 q^{28} - 236 q^{29} - 60 q^{31} - 300 q^{32} + 276 q^{33} + 528 q^{34} + 18 q^{36} - 204 q^{37} - 476 q^{38} + 24 q^{39} + 44 q^{41} - 84 q^{42} - 136 q^{43} - 12 q^{44} + 440 q^{46} - 400 q^{47} - 54 q^{48} + 98 q^{49} - 132 q^{51} - 1528 q^{52} - 16 q^{53} - 108 q^{54} + 84 q^{56} + 324 q^{57} - 592 q^{58} - 464 q^{59} - 684 q^{61} - 1140 q^{62} + 126 q^{63} - 1214 q^{64} + 492 q^{66} - 736 q^{67} + 1804 q^{68} - 960 q^{69} - 740 q^{71} + 108 q^{72} - 424 q^{73} - 168 q^{74} - 1148 q^{76} - 644 q^{77} + 1188 q^{78} - 408 q^{79} + 162 q^{81} + 888 q^{82} - 608 q^{83} - 42 q^{84} + 1008 q^{86} + 708 q^{87} - 532 q^{88} - 1332 q^{89} - 56 q^{91} - 480 q^{92} + 180 q^{93} - 2480 q^{94} + 900 q^{96} + 2448 q^{97} + 196 q^{98} - 828 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 - 6 * q^3 + 2 * q^4 - 12 * q^6 + 14 * q^7 + 12 * q^8 + 18 * q^9 - 92 * q^11 - 6 * q^12 - 8 * q^13 + 28 * q^14 + 18 * q^16 + 44 * q^17 + 36 * q^18 - 108 * q^19 - 42 * q^21 - 164 * q^22 + 320 * q^23 - 36 * q^24 - 396 * q^26 - 54 * q^27 + 14 * q^28 - 236 * q^29 - 60 * q^31 - 300 * q^32 + 276 * q^33 + 528 * q^34 + 18 * q^36 - 204 * q^37 - 476 * q^38 + 24 * q^39 + 44 * q^41 - 84 * q^42 - 136 * q^43 - 12 * q^44 + 440 * q^46 - 400 * q^47 - 54 * q^48 + 98 * q^49 - 132 * q^51 - 1528 * q^52 - 16 * q^53 - 108 * q^54 + 84 * q^56 + 324 * q^57 - 592 * q^58 - 464 * q^59 - 684 * q^61 - 1140 * q^62 + 126 * q^63 - 1214 * q^64 + 492 * q^66 - 736 * q^67 + 1804 * q^68 - 960 * q^69 - 740 * q^71 + 108 * q^72 - 424 * q^73 - 168 * q^74 - 1148 * q^76 - 644 * q^77 + 1188 * q^78 - 408 * q^79 + 162 * q^81 + 888 * q^82 - 608 * q^83 - 42 * q^84 + 1008 * q^86 + 708 * q^87 - 532 * q^88 - 1332 * q^89 - 56 * q^91 - 480 * q^92 + 180 * q^93 - 2480 * q^94 + 900 * q^96 + 2448 * q^97 + 196 * q^98 - 828 * q^99

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