LMFDB - Embedded newform 525.4.a.v.1.3

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:	$0$
Dimension:	$4$
Coefficient field:	4.4.26729725.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 18x^{2} + 19x + 44 $ x^4 - 2x^3 - 18x^2 + 19*x + 44
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.21734$ 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)

$f(q)$	$=$	$q+3.21734 q^{2} +3.00000 q^{3} +2.35129 q^{4} +9.65203 q^{6} -7.00000 q^{7} -18.1738 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+3.21734 q^{2} +3.00000 q^{3} +2.35129 q^{4} +9.65203 q^{6} -7.00000 q^{7} -18.1738 q^{8} +9.00000 q^{9} -2.09810 q^{11} +7.05388 q^{12} +80.8215 q^{13} -22.5214 q^{14} -77.2818 q^{16} +101.965 q^{17} +28.9561 q^{18} +143.319 q^{19} -21.0000 q^{21} -6.75032 q^{22} -116.258 q^{23} -54.5215 q^{24} +260.030 q^{26} +27.0000 q^{27} -16.4590 q^{28} +181.194 q^{29} +303.614 q^{31} -103.251 q^{32} -6.29431 q^{33} +328.058 q^{34} +21.1616 q^{36} +158.336 q^{37} +461.106 q^{38} +242.465 q^{39} -379.372 q^{41} -67.5642 q^{42} -238.980 q^{43} -4.93326 q^{44} -374.041 q^{46} +125.956 q^{47} -231.845 q^{48} +49.0000 q^{49} +305.896 q^{51} +190.035 q^{52} -43.4805 q^{53} +86.8682 q^{54} +127.217 q^{56} +429.956 q^{57} +582.964 q^{58} +31.0944 q^{59} -812.675 q^{61} +976.830 q^{62} -63.0000 q^{63} +286.059 q^{64} -20.2510 q^{66} -426.225 q^{67} +239.750 q^{68} -348.774 q^{69} -1034.51 q^{71} -163.564 q^{72} -471.741 q^{73} +509.422 q^{74} +336.984 q^{76} +14.6867 q^{77} +780.091 q^{78} +1201.92 q^{79} +81.0000 q^{81} -1220.57 q^{82} +1325.72 q^{83} -49.3771 q^{84} -768.880 q^{86} +543.582 q^{87} +38.1306 q^{88} -886.226 q^{89} -565.751 q^{91} -273.356 q^{92} +910.841 q^{93} +405.245 q^{94} -309.754 q^{96} -134.908 q^{97} +157.650 q^{98} -18.8829 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{2} + 12 q^{3} + 16 q^{4} + 18 q^{6} - 28 q^{7} + 93 q^{8} + 36 q^{9}+O(q^{10}) $ 4 * q + 6 * q^2 + 12 * q^3 + 16 * q^4 + 18 * q^6 - 28 * q^7 + 93 * q^8 + 36 * q^9	\( 4 q + 6 q^{2} + 12 q^{3} + 16 q^{4} + 18 q^{6} - 28 q^{7} + 93 q^{8} + 36 q^{9} + 57 q^{11} + 48 q^{12} + 43 q^{13} - 42 q^{14} + 216 q^{16} + 99 q^{17} + 54 q^{18} - 12 q^{19} - 84 q^{21} - 41 q^{22} + 156 q^{23} + 279 q^{24} - 81 q^{26} + 108 q^{27} - 112 q^{28} + 378 q^{29} - 93 q^{31} + 690 q^{32} + 171 q^{33} + 783 q^{34} + 144 q^{36} + 81 q^{37} + 216 q^{38} + 129 q^{39} - 465 q^{41} - 126 q^{42} - 64 q^{43} + 681 q^{44} + 310 q^{46} + 744 q^{47} + 648 q^{48} + 196 q^{49} + 297 q^{51} - 727 q^{52} + 729 q^{53} + 162 q^{54} - 651 q^{56} - 36 q^{57} + 1172 q^{58} + 231 q^{59} - 1353 q^{61} - 165 q^{62} - 252 q^{63} + 3107 q^{64} - 123 q^{66} + 1487 q^{67} + 2577 q^{68} + 468 q^{69} - 1725 q^{71} + 837 q^{72} + 512 q^{73} - 1953 q^{74} - 3046 q^{76} - 399 q^{77} - 243 q^{78} + 1629 q^{79} + 324 q^{81} - 693 q^{82} + 321 q^{83} - 336 q^{84} - 4542 q^{86} + 1134 q^{87} + 3482 q^{88} - 978 q^{89} - 301 q^{91} + 852 q^{92} - 279 q^{93} + 2480 q^{94} + 2070 q^{96} + 2616 q^{97} + 294 q^{98} + 513 q^{99}+O(q^{100}) \) 4 * q + 6 * q^2 + 12 * q^3 + 16 * q^4 + 18 * q^6 - 28 * q^7 + 93 * q^8 + 36 * q^9 + 57 * q^11 + 48 * q^12 + 43 * q^13 - 42 * q^14 + 216 * q^16 + 99 * q^17 + 54 * q^18 - 12 * q^19 - 84 * q^21 - 41 * q^22 + 156 * q^23 + 279 * q^24 - 81 * q^26 + 108 * q^27 - 112 * q^28 + 378 * q^29 - 93 * q^31 + 690 * q^32 + 171 * q^33 + 783 * q^34 + 144 * q^36 + 81 * q^37 + 216 * q^38 + 129 * q^39 - 465 * q^41 - 126 * q^42 - 64 * q^43 + 681 * q^44 + 310 * q^46 + 744 * q^47 + 648 * q^48 + 196 * q^49 + 297 * q^51 - 727 * q^52 + 729 * q^53 + 162 * q^54 - 651 * q^56 - 36 * q^57 + 1172 * q^58 + 231 * q^59 - 1353 * q^61 - 165 * q^62 - 252 * q^63 + 3107 * q^64 - 123 * q^66 + 1487 * q^67 + 2577 * q^68 + 468 * q^69 - 1725 * q^71 + 837 * q^72 + 512 * q^73 - 1953 * q^74 - 3046 * q^76 - 399 * q^77 - 243 * q^78 + 1629 * q^79 + 324 * q^81 - 693 * q^82 + 321 * q^83 - 336 * q^84 - 4542 * q^86 + 1134 * q^87 + 3482 * q^88 - 978 * q^89 - 301 * q^91 + 852 * q^92 - 279 * q^93 + 2480 * q^94 + 2070 * q^96 + 2616 * q^97 + 294 * q^98 + 513 * 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 $

$2$	3.21734	1.13750	0.568751	−	0.822510i	$-0.307427\pi$
$2$	3.21734	1.13750	0.568751	+	0.822510i	$0.307427\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	2.35129	0.293911
$5$	0	0
$5$	0	0
$6$	9.65203	0.656737
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−18.1738	−0.803177
$9$	9.00000	0.333333
$10$	0	0
$11$	−2.09810	−0.0575093	−0.0287546	−	0.999586i	$-0.509154\pi$
$11$	−2.09810	−0.0575093	−0.0287546	+	0.999586i	$0.509154\pi$
$12$	7.05388	0.169690
$13$	80.8215	1.72430	0.862148	−	0.506656i	$-0.169119\pi$
$13$	80.8215	1.72430	0.862148	+	0.506656i	$0.169119\pi$
$14$	−22.5214	−0.429935
$15$	0	0
$16$	−77.2818	−1.20753
$17$	101.965	1.45472	0.727360	−	0.686256i	$-0.240747\pi$
$17$	101.965	1.45472	0.727360	+	0.686256i	$0.240747\pi$
$18$	28.9561	0.379167
$19$	143.319	1.73050	0.865252	−	0.501337i	$-0.167158\pi$
$19$	143.319	1.73050	0.865252	+	0.501337i	$0.167158\pi$
$20$	0	0
$21$	−21.0000	−0.218218
$22$	−6.75032	−0.0654170
$23$	−116.258	−1.05398	−0.526988	−	0.849873i	$-0.676679\pi$
$23$	−116.258	−1.05398	−0.526988	+	0.849873i	$0.676679\pi$
$24$	−54.5215	−0.463715
$25$	0	0
$26$	260.030	1.96139
$27$	27.0000	0.192450
$28$	−16.4590	−0.111088
$29$	181.194	1.16024	0.580119	−	0.814532i	$-0.303006\pi$
$29$	181.194	1.16024	0.580119	+	0.814532i	$0.303006\pi$
$30$	0	0
$31$	303.614	1.75905	0.879527	−	0.475850i	$-0.157859\pi$
$31$	303.614	1.75905	0.879527	+	0.475850i	$0.157859\pi$
$32$	−103.251	−0.570388
$33$	−6.29431	−0.0332030
$34$	328.058	1.65475
$35$	0	0
$36$	21.1616	0.0979705
$37$	158.336	0.703522	0.351761	−	0.936090i	$-0.385583\pi$
$37$	158.336	0.703522	0.351761	+	0.936090i	$0.385583\pi$
$38$	461.106	1.96845
$39$	242.465	0.995523
$40$	0	0
$41$	−379.372	−1.44507	−0.722536	−	0.691333i	$-0.757024\pi$
$41$	−379.372	−1.44507	−0.722536	+	0.691333i	$0.757024\pi$
$42$	−67.5642	−0.248223
$43$	−238.980	−0.847537	−0.423769	−	0.905770i	$-0.639293\pi$
$43$	−238.980	−0.847537	−0.423769	+	0.905770i	$0.639293\pi$
$44$	−4.93326	−0.0169026
$45$	0	0
$46$	−374.041	−1.19890
$47$	125.956	0.390907	0.195453	−	0.980713i	$-0.437382\pi$
$47$	125.956	0.390907	0.195453	+	0.980713i	$0.437382\pi$
$48$	−231.845	−0.697166
$49$	49.0000	0.142857
$50$	0	0
$51$	305.896	0.839883
$52$	190.035	0.506790
$53$	−43.4805	−0.112689	−0.0563443	−	0.998411i	$-0.517944\pi$
$53$	−43.4805	−0.112689	−0.0563443	+	0.998411i	$0.517944\pi$
$54$	86.8682	0.218912
$55$	0	0
$56$	127.217	0.303572
$57$	429.956	0.999107
$58$	582.964	1.31977
$59$	31.0944	0.0686127	0.0343063	−	0.999411i	$-0.489078\pi$
$59$	31.0944	0.0686127	0.0343063	+	0.999411i	$0.489078\pi$
$60$	0	0
$61$	−812.675	−1.70578	−0.852889	−	0.522093i	$-0.825151\pi$
$61$	−812.675	−1.70578	−0.852889	+	0.522093i	$0.825151\pi$
$62$	976.830	2.00093
$63$	−63.0000	−0.125988
$64$	286.059	0.558710
$65$	0	0
$66$	−20.2510	−0.0377685
$67$	−426.225	−0.777189	−0.388595	−	0.921409i	$-0.627039\pi$
$67$	−426.225	−0.777189	−0.388595	+	0.921409i	$0.627039\pi$
$68$	239.750	0.427559
$69$	−348.774	−0.608513
$70$	0	0
$71$	−1034.51	−1.72921	−0.864603	−	0.502455i	$-0.832430\pi$
$71$	−1034.51	−1.72921	−0.864603	+	0.502455i	$0.832430\pi$
$72$	−163.564	−0.267726
$73$	−471.741	−0.756344	−0.378172	−	0.925735i	$-0.623447\pi$
$73$	−471.741	−0.756344	−0.378172	+	0.925735i	$0.623447\pi$
$74$	509.422	0.800257
$75$	0	0
$76$	336.984	0.508615
$77$	14.6867	0.0217365
$78$	780.091	1.13241
$79$	1201.92	1.71172	0.855861	−	0.517205i	$-0.173028\pi$
$79$	1201.92	1.71172	0.855861	+	0.517205i	$0.173028\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	−1220.57	−1.64377
$83$	1325.72	1.75321	0.876606	−	0.481209i	$-0.159802\pi$
$83$	1325.72	1.75321	0.876606	+	0.481209i	$0.159802\pi$
$84$	−49.3771	−0.0641367
$85$	0	0
$86$	−768.880	−0.964076
$87$	543.582	0.669864
$88$	38.1306	0.0461902
$89$	−886.226	−1.05550	−0.527751	−	0.849399i	$-0.676965\pi$
$89$	−886.226	−1.05550	−0.527751	+	0.849399i	$0.676965\pi$
$90$	0	0
$91$	−565.751	−0.651723
$92$	−273.356	−0.309776
$93$	910.841	1.01559
$94$	405.245	0.444657
$95$	0	0
$96$	−309.754	−0.329314
$97$	−134.908	−0.141215	−0.0706076	−	0.997504i	$-0.522494\pi$
$97$	−134.908	−0.141215	−0.0706076	+	0.997504i	$0.522494\pi$
$98$	157.650	0.162500
$99$	−18.8829	−0.0191698
$100$	0	0
$101$	585.617	0.576941	0.288471	−	0.957489i	$-0.406853\pi$
$101$	585.617	0.576941	0.288471	+	0.957489i	$0.406853\pi$
$102$	984.173	0.955369
$103$	850.822	0.813923	0.406961	−	0.913445i	$-0.366588\pi$
$103$	850.822	0.813923	0.406961	+	0.913445i	$0.366588\pi$
$104$	−1468.84	−1.38492
$105$	0	0
$106$	−139.892	−0.128184
$107$	566.799	0.512099	0.256049	−	0.966664i	$-0.417579\pi$
$107$	566.799	0.512099	0.256049	+	0.966664i	$0.417579\pi$
$108$	63.4849	0.0565633
$109$	−1111.49	−0.976714	−0.488357	−	0.872644i	$-0.662404\pi$
$109$	−1111.49	−0.976714	−0.488357	+	0.872644i	$0.662404\pi$
$110$	0	0
$111$	475.008	0.406178
$112$	540.972	0.456403
$113$	192.740	0.160455	0.0802275	−	0.996777i	$-0.474435\pi$
$113$	192.740	0.160455	0.0802275	+	0.996777i	$0.474435\pi$
$114$	1383.32	1.13649
$115$	0	0
$116$	426.040	0.341007
$117$	727.394	0.574765
$118$	100.041	0.0780471
$119$	−713.758	−0.549833
$120$	0	0
$121$	−1326.60	−0.996693
$122$	−2614.65	−1.94033
$123$	−1138.12	−0.834313
$124$	713.885	0.517006
$125$	0	0
$126$	−202.693	−0.143312
$127$	937.870	0.655296	0.327648	−	0.944800i	$-0.393744\pi$
$127$	937.870	0.655296	0.327648	+	0.944800i	$0.393744\pi$
$128$	1746.36	1.20592
$129$	−716.940	−0.489326
$130$	0	0
$131$	746.316	0.497755	0.248878	−	0.968535i	$-0.419938\pi$
$131$	746.316	0.497755	0.248878	+	0.968535i	$0.419938\pi$
$132$	−14.7998	−0.00975875
$133$	−1003.23	−0.654069
$134$	−1371.31	−0.884054
$135$	0	0
$136$	−1853.10	−1.16840
$137$	492.514	0.307141	0.153570	−	0.988138i	$-0.450923\pi$
$137$	492.514	0.307141	0.153570	+	0.988138i	$0.450923\pi$
$138$	−1122.12	−0.692185
$139$	−152.482	−0.0930456	−0.0465228	−	0.998917i	$-0.514814\pi$
$139$	−152.482	−0.0930456	−0.0465228	+	0.998917i	$0.514814\pi$
$140$	0	0
$141$	377.869	0.225690
$142$	−3328.37	−1.96698
$143$	−169.572	−0.0991631
$144$	−695.536	−0.402509
$145$	0	0
$146$	−1517.75	−0.860343
$147$	147.000	0.0824786
$148$	372.294	0.206773
$149$	−1433.18	−0.787989	−0.393994	−	0.919113i	$-0.628907\pi$
$149$	−1433.18	−0.787989	−0.393994	+	0.919113i	$0.628907\pi$
$150$	0	0
$151$	916.243	0.493794	0.246897	−	0.969042i	$-0.420589\pi$
$151$	916.243	0.493794	0.246897	+	0.969042i	$0.420589\pi$
$152$	−2604.65	−1.38990
$153$	917.689	0.484907
$154$	47.2522	0.0247253
$155$	0	0
$156$	570.105	0.292596
$157$	169.765	0.0862978	0.0431489	−	0.999069i	$-0.486261\pi$
$157$	169.765	0.0862978	0.0431489	+	0.999069i	$0.486261\pi$
$158$	3866.98	1.94709
$159$	−130.441	−0.0650608
$160$	0	0
$161$	813.805	0.398365
$162$	260.605	0.126389
$163$	1051.63	0.505338	0.252669	−	0.967553i	$-0.418692\pi$
$163$	1051.63	0.505338	0.252669	+	0.967553i	$0.418692\pi$
$164$	−892.014	−0.424723
$165$	0	0
$166$	4265.29	1.99428
$167$	2891.32	1.33974	0.669870	−	0.742478i	$-0.266350\pi$
$167$	2891.32	1.33974	0.669870	+	0.742478i	$0.266350\pi$
$168$	381.650	0.175268
$169$	4335.12	1.97320
$170$	0	0
$171$	1289.87	0.576835
$172$	−561.912	−0.249101
$173$	−868.785	−0.381806	−0.190903	−	0.981609i	$-0.561142\pi$
$173$	−868.785	−0.381806	−0.190903	+	0.981609i	$0.561142\pi$
$174$	1748.89	0.761972
$175$	0	0
$176$	162.145	0.0694441
$177$	93.2833	0.0396136
$178$	−2851.29	−1.20064
$179$	−2073.48	−0.865804	−0.432902	−	0.901441i	$-0.642510\pi$
$179$	−2073.48	−0.865804	−0.432902	+	0.901441i	$0.642510\pi$
$180$	0	0
$181$	−2152.24	−0.883839	−0.441919	−	0.897055i	$-0.645702\pi$
$181$	−2152.24	−0.883839	−0.441919	+	0.897055i	$0.645702\pi$
$182$	−1820.21	−0.741336
$183$	−2438.03	−0.984831
$184$	2112.85	0.846529
$185$	0	0
$186$	2930.49	1.15524
$187$	−213.934	−0.0836599
$188$	296.160	0.114892
$189$	−189.000	−0.0727393
$190$	0	0
$191$	−4149.19	−1.57186	−0.785929	−	0.618316i	$-0.787815\pi$
$191$	−4149.19	−1.57186	−0.785929	+	0.618316i	$0.787815\pi$
$192$	858.178	0.322571
$193$	−1860.51	−0.693899	−0.346949	−	0.937884i	$-0.612782\pi$
$193$	−1860.51	−0.693899	−0.346949	+	0.937884i	$0.612782\pi$
$194$	−434.047	−0.160633
$195$	0	0
$196$	115.213	0.0419874
$197$	−97.0507	−0.0350994	−0.0175497	−	0.999846i	$-0.505587\pi$
$197$	−97.0507	−0.0350994	−0.0175497	+	0.999846i	$0.505587\pi$
$198$	−60.7529	−0.0218057
$199$	−936.970	−0.333769	−0.166885	−	0.985976i	$-0.553371\pi$
$199$	−936.970	−0.333769	−0.166885	+	0.985976i	$0.553371\pi$
$200$	0	0
$201$	−1278.67	−0.448710
$202$	1884.13	0.656272
$203$	−1268.36	−0.438529
$204$	719.251	0.246851
$205$	0	0
$206$	2737.39	0.925839
$207$	−1046.32	−0.351325
$208$	−6246.03	−2.08214
$209$	−300.698	−0.0995201
$210$	0	0
$211$	−1342.19	−0.437915	−0.218958	−	0.975734i	$-0.570266\pi$
$211$	−1342.19	−0.437915	−0.218958	+	0.975734i	$0.570266\pi$
$212$	−102.235	−0.0331205
$213$	−3103.53	−0.998358
$214$	1823.59	0.582513
$215$	0	0
$216$	−490.693	−0.154572
$217$	−2125.30	−0.664860
$218$	−3576.06	−1.11101
$219$	−1415.22	−0.436675
$220$	0	0
$221$	8241.00	2.50837
$222$	1528.26	0.462029
$223$	810.794	0.243474	0.121737	−	0.992562i	$-0.461153\pi$
$223$	810.794	0.243474	0.121737	+	0.992562i	$0.461153\pi$
$224$	722.759	0.215586
$225$	0	0
$226$	620.109	0.182518
$227$	2584.59	0.755707	0.377853	−	0.925865i	$-0.376662\pi$
$227$	2584.59	0.755707	0.377853	+	0.925865i	$0.376662\pi$
$228$	1010.95	0.293649
$229$	−1637.36	−0.472489	−0.236244	−	0.971694i	$-0.575917\pi$
$229$	−1637.36	−0.472489	−0.236244	+	0.971694i	$0.575917\pi$
$230$	0	0
$231$	44.0602	0.0125496
$232$	−3292.99	−0.931877
$233$	3336.49	0.938115	0.469057	−	0.883168i	$-0.344594\pi$
$233$	3336.49	0.938115	0.469057	+	0.883168i	$0.344594\pi$
$234$	2340.27	0.653797
$235$	0	0
$236$	73.1121	0.0201661
$237$	3605.75	0.988264
$238$	−2296.40	−0.625436
$239$	−3983.20	−1.07804	−0.539020	−	0.842293i	$-0.681205\pi$
$239$	−3983.20	−1.07804	−0.539020	+	0.842293i	$0.681205\pi$
$240$	0	0
$241$	2282.78	0.610152	0.305076	−	0.952328i	$-0.401318\pi$
$241$	2282.78	0.610152	0.305076	+	0.952328i	$0.401318\pi$
$242$	−4268.12	−1.13374
$243$	243.000	0.0641500
$244$	−1910.84	−0.501347
$245$	0	0
$246$	−3661.71	−0.949033
$247$	11583.2	2.98390
$248$	−5517.83	−1.41283
$249$	3977.16	1.01222
$250$	0	0
$251$	−855.255	−0.215073	−0.107536	−	0.994201i	$-0.534296\pi$
$251$	−855.255	−0.215073	−0.107536	+	0.994201i	$0.534296\pi$
$252$	−148.131	−0.0370294
$253$	243.921	0.0606134
$254$	3017.45	0.745400
$255$	0	0
$256$	3330.17	0.813029
$257$	−2892.91	−0.702158	−0.351079	−	0.936346i	$-0.614185\pi$
$257$	−2892.91	−0.702158	−0.351079	+	0.936346i	$0.614185\pi$
$258$	−2306.64	−0.556609
$259$	−1108.35	−0.265906
$260$	0	0
$261$	1630.75	0.386746
$262$	2401.15	0.566198
$263$	−4167.10	−0.977014	−0.488507	−	0.872560i	$-0.662458\pi$
$263$	−4167.10	−0.977014	−0.488507	+	0.872560i	$0.662458\pi$
$264$	114.392	0.0266679
$265$	0	0
$266$	−3227.74	−0.744005
$267$	−2658.68	−0.609395
$268$	−1002.18	−0.228425
$269$	−7519.40	−1.70433	−0.852167	−	0.523270i	$-0.824712\pi$
$269$	−7519.40	−1.70433	−0.852167	+	0.523270i	$0.824712\pi$
$270$	0	0
$271$	7793.64	1.74697	0.873487	−	0.486848i	$-0.161853\pi$
$271$	7793.64	1.74697	0.873487	+	0.486848i	$0.161853\pi$
$272$	−7880.07	−1.75661
$273$	−1697.25	−0.376272
$274$	1584.59	0.349373
$275$	0	0
$276$	−820.068	−0.178849
$277$	3192.46	0.692477	0.346238	−	0.938147i	$-0.387459\pi$
$277$	3192.46	0.692477	0.346238	+	0.938147i	$0.387459\pi$
$278$	−490.586	−0.105840
$279$	2732.52	0.586351
$280$	0	0
$281$	−2566.33	−0.544819	−0.272410	−	0.962181i	$-0.587821\pi$
$281$	−2566.33	−0.544819	−0.272410	+	0.962181i	$0.587821\pi$
$282$	1215.73	0.256723
$283$	−6114.58	−1.28436	−0.642181	−	0.766553i	$-0.721970\pi$
$283$	−6114.58	−1.28436	−0.642181	+	0.766553i	$0.721970\pi$
$284$	−2432.43	−0.508234
$285$	0	0
$286$	−545.571	−0.112798
$287$	2655.60	0.546186
$288$	−929.261	−0.190129
$289$	5483.94	1.11621
$290$	0	0
$291$	−404.725	−0.0815307
$292$	−1109.20	−0.222298
$293$	−3546.49	−0.707127	−0.353563	−	0.935411i	$-0.615030\pi$
$293$	−3546.49	−0.707127	−0.353563	+	0.935411i	$0.615030\pi$
$294$	472.949	0.0938196
$295$	0	0
$296$	−2877.57	−0.565053
$297$	−56.6488	−0.0110677
$298$	−4611.02	−0.896339
$299$	−9396.13	−1.81737
$300$	0	0
$301$	1672.86	0.320339
$302$	2947.87	0.561691
$303$	1756.85	0.333097
$304$	−11075.9	−2.08963
$305$	0	0
$306$	2952.52	0.551583
$307$	1705.97	0.317150	0.158575	−	0.987347i	$-0.449310\pi$
$307$	1705.97	0.317150	0.158575	+	0.987347i	$0.449310\pi$
$308$	34.5328	0.00638860
$309$	2552.47	0.469918
$310$	0	0
$311$	−10323.6	−1.88230	−0.941152	−	0.337983i	$-0.890255\pi$
$311$	−10323.6	−1.88230	−0.941152	+	0.337983i	$0.890255\pi$
$312$	−4406.51	−0.799581
$313$	7118.85	1.28556	0.642781	−	0.766050i	$-0.277780\pi$
$313$	7118.85	1.28556	0.642781	+	0.766050i	$0.277780\pi$
$314$	546.193	0.0981640
$315$	0	0
$316$	2826.06	0.503095
$317$	−10755.2	−1.90559	−0.952797	−	0.303607i	$-0.901809\pi$
$317$	−10755.2	−1.90559	−0.952797	+	0.303607i	$0.901809\pi$
$318$	−419.675	−0.0740069
$319$	−380.164	−0.0667245
$320$	0	0
$321$	1700.40	0.295660
$322$	2618.29	0.453141
$323$	14613.6	2.51740
$324$	190.455	0.0326568
$325$	0	0
$326$	3383.46	0.574823
$327$	−3334.48	−0.563906
$328$	6894.64	1.16065
$329$	−881.694	−0.147749
$330$	0	0
$331$	−494.875	−0.0821776	−0.0410888	−	0.999155i	$-0.513083\pi$
$331$	−494.875	−0.0821776	−0.0410888	+	0.999155i	$0.513083\pi$
$332$	3117.15	0.515289
$333$	1425.03	0.234507
$334$	9302.35	1.52396
$335$	0	0
$336$	1622.92	0.263504
$337$	409.916	0.0662598	0.0331299	−	0.999451i	$-0.489452\pi$
$337$	409.916	0.0662598	0.0331299	+	0.999451i	$0.489452\pi$
$338$	13947.6	2.24452
$339$	578.219	0.0926387
$340$	0	0
$341$	−637.013	−0.101162
$342$	4149.95	0.656151
$343$	−343.000	−0.0539949
$344$	4343.18	0.680723
$345$	0	0
$346$	−2795.18	−0.434306
$347$	−7377.44	−1.14133	−0.570666	−	0.821182i	$-0.693315\pi$
$347$	−7377.44	−1.14133	−0.570666	+	0.821182i	$0.693315\pi$
$348$	1278.12	0.196881
$349$	−11284.7	−1.73083	−0.865413	−	0.501059i	$-0.832944\pi$
$349$	−11284.7	−1.73083	−0.865413	+	0.501059i	$0.832944\pi$
$350$	0	0
$351$	2182.18	0.331841
$352$	216.632	0.0328026
$353$	−3910.15	−0.589565	−0.294783	−	0.955564i	$-0.595247\pi$
$353$	−3910.15	−0.589565	−0.294783	+	0.955564i	$0.595247\pi$
$354$	300.124	0.0450605
$355$	0	0
$356$	−2083.78	−0.310224
$357$	−2141.27	−0.317446
$358$	−6671.08	−0.984854
$359$	12865.9	1.89147	0.945733	−	0.324945i	$-0.105346\pi$
$359$	12865.9	1.89147	0.945733	+	0.324945i	$0.105346\pi$
$360$	0	0
$361$	13681.3	1.99464
$362$	−6924.50	−1.00537
$363$	−3979.79	−0.575441
$364$	−1330.24	−0.191549
$365$	0	0
$366$	−7843.96	−1.12025
$367$	892.357	0.126923	0.0634614	−	0.997984i	$-0.479786\pi$
$367$	892.357	0.126923	0.0634614	+	0.997984i	$0.479786\pi$
$368$	8984.61	1.27270
$369$	−3414.35	−0.481691
$370$	0	0
$371$	304.363	0.0425923
$372$	2141.65	0.298494
$373$	8666.00	1.20297	0.601486	−	0.798884i	$-0.294576\pi$
$373$	8666.00	1.20297	0.601486	+	0.798884i	$0.294576\pi$
$374$	−688.299	−0.0951634
$375$	0	0
$376$	−2289.11	−0.313967
$377$	14644.4	2.00059
$378$	−608.078	−0.0827411
$379$	−7111.00	−0.963767	−0.481883	−	0.876235i	$-0.660047\pi$
$379$	−7111.00	−0.963767	−0.481883	+	0.876235i	$0.660047\pi$
$380$	0	0
$381$	2813.61	0.378335
$382$	−13349.4	−1.78799
$383$	−14017.9	−1.87019	−0.935094	−	0.354401i	$-0.884685\pi$
$383$	−14017.9	−1.87019	−0.935094	+	0.354401i	$0.884685\pi$
$384$	5239.08	0.696239
$385$	0	0
$386$	−5985.90	−0.789312
$387$	−2150.82	−0.282512
$388$	−317.209	−0.0415048
$389$	−4848.24	−0.631917	−0.315959	−	0.948773i	$-0.602326\pi$
$389$	−4848.24	−0.631917	−0.315959	+	0.948773i	$0.602326\pi$
$390$	0	0
$391$	−11854.3	−1.53324
$392$	−890.518	−0.114740
$393$	2238.95	0.287379
$394$	−312.245	−0.0399256
$395$	0	0
$396$	−44.3993	−0.00563421
$397$	4088.76	0.516899	0.258449	−	0.966025i	$-0.416788\pi$
$397$	4088.76	0.516899	0.258449	+	0.966025i	$0.416788\pi$
$398$	−3014.55	−0.379663
$399$	−3009.69	−0.377627
$400$	0	0
$401$	7187.01	0.895018	0.447509	−	0.894279i	$-0.352311\pi$
$401$	7187.01	0.895018	0.447509	+	0.894279i	$0.352311\pi$
$402$	−4113.93	−0.510409
$403$	24538.5	3.03313
$404$	1376.96	0.169570
$405$	0	0
$406$	−4080.75	−0.498828
$407$	−332.206	−0.0404590
$408$	−5559.31	−0.674575
$409$	924.965	0.111825	0.0559127	−	0.998436i	$-0.482193\pi$
$409$	924.965	0.111825	0.0559127	+	0.998436i	$0.482193\pi$
$410$	0	0
$411$	1477.54	0.177328
$412$	2000.53	0.239221
$413$	−217.661	−0.0259332
$414$	−3366.37	−0.399633
$415$	0	0
$416$	−8344.92	−0.983518
$417$	−457.445	−0.0537199
$418$	−967.448	−0.113204
$419$	4460.85	0.520112	0.260056	−	0.965594i	$-0.416259\pi$
$419$	4460.85	0.520112	0.260056	+	0.965594i	$0.416259\pi$
$420$	0	0
$421$	−3443.27	−0.398610	−0.199305	−	0.979938i	$-0.563868\pi$
$421$	−3443.27	−0.398610	−0.199305	+	0.979938i	$0.563868\pi$
$422$	−4318.28	−0.498130
$423$	1133.61	0.130302
$424$	790.206	0.0905090
$425$	0	0
$426$	−9985.11	−1.13563
$427$	5688.73	0.644723
$428$	1332.71	0.150512
$429$	−508.716	−0.0572518
$430$	0	0
$431$	−6214.55	−0.694535	−0.347267	−	0.937766i	$-0.612890\pi$
$431$	−6214.55	−0.694535	−0.347267	+	0.937766i	$0.612890\pi$
$432$	−2086.61	−0.232389
$433$	13129.1	1.45714	0.728571	−	0.684970i	$-0.240185\pi$
$433$	13129.1	1.45714	0.728571	+	0.684970i	$0.240185\pi$
$434$	−6837.81	−0.756279
$435$	0	0
$436$	−2613.45	−0.287067
$437$	−16661.9	−1.82391
$438$	−4553.26	−0.496719
$439$	6830.51	0.742602	0.371301	−	0.928512i	$-0.378912\pi$
$439$	6830.51	0.742602	0.371301	+	0.928512i	$0.378912\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	26514.1	2.85328
$443$	12837.6	1.37682	0.688410	−	0.725322i	$-0.258309\pi$
$443$	12837.6	1.37682	0.688410	+	0.725322i	$0.258309\pi$
$444$	1116.88	0.119380
$445$	0	0
$446$	2608.60	0.276953
$447$	−4299.53	−0.454945
$448$	−2002.42	−0.211172
$449$	−16800.5	−1.76585	−0.882923	−	0.469518i	$-0.844428\pi$
$449$	−16800.5	−1.76585	−0.882923	+	0.469518i	$0.844428\pi$
$450$	0	0
$451$	795.962	0.0831051
$452$	453.187	0.0471596
$453$	2748.73	0.285092
$454$	8315.52	0.859618
$455$	0	0
$456$	−7813.95	−0.802460
$457$	9601.60	0.982809	0.491405	−	0.870931i	$-0.336484\pi$
$457$	9601.60	0.982809	0.491405	+	0.870931i	$0.336484\pi$
$458$	−5267.96	−0.537457
$459$	2753.07	0.279961
$460$	0	0
$461$	3506.77	0.354287	0.177144	−	0.984185i	$-0.443314\pi$
$461$	3506.77	0.354287	0.177144	+	0.984185i	$0.443314\pi$
$462$	141.757	0.0142752
$463$	−4212.28	−0.422810	−0.211405	−	0.977399i	$-0.567804\pi$
$463$	−4212.28	−0.422810	−0.211405	+	0.977399i	$0.567804\pi$
$464$	−14003.0	−1.40102
$465$	0	0
$466$	10734.6	1.06711
$467$	560.881	0.0555771	0.0277885	−	0.999614i	$-0.491153\pi$
$467$	560.881	0.0555771	0.0277885	+	0.999614i	$0.491153\pi$
$468$	1710.31	0.168930
$469$	2983.57	0.293750
$470$	0	0
$471$	509.296	0.0498241
$472$	−565.105	−0.0551082
$473$	501.405	0.0487413
$474$	11600.9	1.12415
$475$	0	0
$476$	−1678.25	−0.161602
$477$	−391.324	−0.0375629
$478$	−12815.3	−1.22627
$479$	13267.8	1.26559	0.632796	−	0.774318i	$-0.281907\pi$
$479$	13267.8	1.26559	0.632796	+	0.774318i	$0.281907\pi$
$480$	0	0
$481$	12797.0	1.21308
$482$	7344.48	0.694049
$483$	2441.41	0.229996
$484$	−3119.22	−0.292939
$485$	0	0
$486$	781.814	0.0729708
$487$	−16137.0	−1.50151	−0.750755	−	0.660581i	$-0.770310\pi$
$487$	−16137.0	−1.50151	−0.750755	+	0.660581i	$0.770310\pi$
$488$	14769.4	1.37004
$489$	3154.89	0.291757
$490$	0	0
$491$	5186.66	0.476722	0.238361	−	0.971177i	$-0.423390\pi$
$491$	5186.66	0.476722	0.238361	+	0.971177i	$0.423390\pi$
$492$	−2676.04	−0.245214
$493$	18475.5	1.68782
$494$	37267.2	3.39420
$495$	0	0
$496$	−23463.8	−2.12411
$497$	7241.56	0.653579
$498$	12795.9	1.15140
$499$	14822.5	1.32975	0.664877	−	0.746953i	$-0.268484\pi$
$499$	14822.5	1.32975	0.664877	+	0.746953i	$0.268484\pi$
$500$	0	0
$501$	8673.95	0.773500
$502$	−2751.65	−0.244646
$503$	−1690.53	−0.149855	−0.0749273	−	0.997189i	$-0.523872\pi$
$503$	−1690.53	−0.149855	−0.0749273	+	0.997189i	$0.523872\pi$
$504$	1144.95	0.101191
$505$	0	0
$506$	784.778	0.0689479
$507$	13005.3	1.13923
$508$	2205.21	0.192599
$509$	5355.09	0.466326	0.233163	−	0.972438i	$-0.425092\pi$
$509$	5355.09	0.466326	0.233163	+	0.972438i	$0.425092\pi$
$510$	0	0
$511$	3302.19	0.285871
$512$	−3256.60	−0.281100
$513$	3869.61	0.333036
$514$	−9307.47	−0.798706
$515$	0	0
$516$	−1685.73	−0.143818
$517$	−264.269	−0.0224808
$518$	−3565.95	−0.302469
$519$	−2606.35	−0.220436
$520$	0	0
$521$	−15355.6	−1.29125	−0.645624	−	0.763655i	$-0.723403\pi$
$521$	−15355.6	−1.29125	−0.645624	+	0.763655i	$0.723403\pi$
$522$	5246.67	0.439925
$523$	6142.95	0.513599	0.256800	−	0.966465i	$-0.417332\pi$
$523$	6142.95	0.513599	0.256800	+	0.966465i	$0.417332\pi$
$524$	1754.81	0.146296
$525$	0	0
$526$	−13407.0	−1.11136
$527$	30958.1	2.55893
$528$	486.436	0.0400935
$529$	1348.89	0.110864
$530$	0	0
$531$	279.850	0.0228709
$532$	−2358.89	−0.192238
$533$	−30661.4	−2.49173
$534$	−8553.88	−0.693188
$535$	0	0
$536$	7746.14	0.624221
$537$	−6220.43	−0.499872
$538$	−24192.5	−1.93868
$539$	−102.807	−0.00821561
$540$	0	0
$541$	4877.07	0.387582	0.193791	−	0.981043i	$-0.437922\pi$
$541$	4877.07	0.387582	0.193791	+	0.981043i	$0.437922\pi$
$542$	25074.8	1.98719
$543$	−6456.72	−0.510285
$544$	−10528.1	−0.829755
$545$	0	0
$546$	−5460.64	−0.428011
$547$	3823.80	0.298892	0.149446	−	0.988770i	$-0.452251\pi$
$547$	3823.80	0.298892	0.149446	+	0.988770i	$0.452251\pi$
$548$	1158.04	0.0902722
$549$	−7314.08	−0.568592
$550$	0	0
$551$	25968.5	2.00780
$552$	6338.55	0.488744
$553$	−8413.41	−0.646970
$554$	10271.2	0.787694
$555$	0	0
$556$	−358.529	−0.0273472
$557$	10514.6	0.799849	0.399925	−	0.916548i	$-0.369036\pi$
$557$	10514.6	0.799849	0.399925	+	0.916548i	$0.369036\pi$
$558$	8791.47	0.666976
$559$	−19314.7	−1.46141
$560$	0	0
$561$	−641.802	−0.0483011
$562$	−8256.75	−0.619733
$563$	1679.55	0.125728	0.0628639	−	0.998022i	$-0.479977\pi$
$563$	1679.55	0.125728	0.0628639	+	0.998022i	$0.479977\pi$
$564$	888.480	0.0663329
$565$	0	0
$566$	−19672.7	−1.46096
$567$	−567.000	−0.0419961
$568$	18801.0	1.38886
$569$	7067.14	0.520686	0.260343	−	0.965516i	$-0.416164\pi$
$569$	7067.14	0.520686	0.260343	+	0.965516i	$0.416164\pi$
$570$	0	0
$571$	−10609.6	−0.777577	−0.388788	−	0.921327i	$-0.627106\pi$
$571$	−10609.6	−0.777577	−0.388788	+	0.921327i	$0.627106\pi$
$572$	−398.713	−0.0291452
$573$	−12447.6	−0.907513
$574$	8543.99	0.621288
$575$	0	0
$576$	2574.53	0.186237
$577$	4002.39	0.288773	0.144386	−	0.989521i	$-0.453879\pi$
$577$	4002.39	0.288773	0.144386	+	0.989521i	$0.453879\pi$
$578$	17643.7	1.26969
$579$	−5581.53	−0.400623
$580$	0	0
$581$	−9280.03	−0.662652
$582$	−1302.14	−0.0927413
$583$	91.2266	0.00648065
$584$	8573.34	0.607478
$585$	0	0
$586$	−11410.3	−0.804358
$587$	2334.57	0.164154	0.0820768	−	0.996626i	$-0.473845\pi$
$587$	2334.57	0.164154	0.0820768	+	0.996626i	$0.473845\pi$
$588$	345.640	0.0242414
$589$	43513.6	3.04405
$590$	0	0
$591$	−291.152	−0.0202646
$592$	−12236.5	−0.849522
$593$	12401.0	0.858768	0.429384	−	0.903122i	$-0.358731\pi$
$593$	12401.0	0.858768	0.429384	+	0.903122i	$0.358731\pi$
$594$	−182.259	−0.0125895
$595$	0	0
$596$	−3369.81	−0.231599
$597$	−2810.91	−0.192702
$598$	−30230.6	−2.06726
$599$	15848.8	1.08108	0.540538	−	0.841320i	$-0.318221\pi$
$599$	15848.8	1.08108	0.540538	+	0.841320i	$0.318221\pi$
$600$	0	0
$601$	298.912	0.0202877	0.0101438	−	0.999949i	$-0.496771\pi$
$601$	298.912	0.0202877	0.0101438	+	0.999949i	$0.496771\pi$
$602$	5382.16	0.364386
$603$	−3836.02	−0.259063
$604$	2154.36	0.145132
$605$	0	0
$606$	5652.39	0.378899
$607$	8731.31	0.583843	0.291922	−	0.956442i	$-0.405705\pi$
$607$	8731.31	0.583843	0.291922	+	0.956442i	$0.405705\pi$
$608$	−14797.8	−0.987059
$609$	−3805.08	−0.253185
$610$	0	0
$611$	10180.0	0.674039
$612$	2157.75	0.142520
$613$	−10037.7	−0.661368	−0.330684	−	0.943742i	$-0.607279\pi$
$613$	−10037.7	−0.661368	−0.330684	+	0.943742i	$0.607279\pi$
$614$	5488.70	0.360759
$615$	0	0
$616$	−266.914	−0.0174582
$617$	−20567.7	−1.34202	−0.671008	−	0.741450i	$-0.734138\pi$
$617$	−20567.7	−1.34202	−0.671008	+	0.741450i	$0.734138\pi$
$618$	8212.16	0.534533
$619$	15714.5	1.02039	0.510193	−	0.860060i	$-0.329574\pi$
$619$	15714.5	1.02039	0.510193	+	0.860060i	$0.329574\pi$
$620$	0	0
$621$	−3138.96	−0.202838
$622$	−33214.5	−2.14113
$623$	6203.58	0.398943
$624$	−18738.1	−1.20212
$625$	0	0
$626$	22903.8	1.46233
$627$	−902.093	−0.0574579
$628$	399.168	0.0253639
$629$	16144.8	1.02343
$630$	0	0
$631$	−8962.39	−0.565431	−0.282716	−	0.959204i	$-0.591235\pi$
$631$	−8962.39	−0.565431	−0.282716	+	0.959204i	$0.591235\pi$
$632$	−21843.4	−1.37482
$633$	−4026.57	−0.252831
$634$	−34603.2	−2.16762
$635$	0	0
$636$	−306.706	−0.0191221
$637$	3960.25	0.246328
$638$	−1223.12	−0.0758993
$639$	−9310.58	−0.576402
$640$	0	0
$641$	26919.8	1.65877	0.829383	−	0.558681i	$-0.188692\pi$
$641$	26919.8	1.65877	0.829383	+	0.558681i	$0.188692\pi$
$642$	5470.76	0.336314
$643$	−5675.19	−0.348068	−0.174034	−	0.984740i	$-0.555680\pi$
$643$	−5675.19	−0.348068	−0.174034	+	0.984740i	$0.555680\pi$
$644$	1913.49	0.117084
$645$	0	0
$646$	47016.8	2.86355
$647$	8444.54	0.513121	0.256560	−	0.966528i	$-0.417411\pi$
$647$	8444.54	0.513121	0.256560	+	0.966528i	$0.417411\pi$
$648$	−1472.08	−0.0892419
$649$	−65.2393	−0.00394587
$650$	0	0
$651$	−6375.89	−0.383857
$652$	2472.69	0.148525
$653$	−25968.1	−1.55622	−0.778108	−	0.628130i	$-0.783820\pi$
$653$	−25968.1	−1.55622	−0.778108	+	0.628130i	$0.783820\pi$
$654$	−10728.2	−0.641444
$655$	0	0
$656$	29318.5	1.74496
$657$	−4245.67	−0.252115
$658$	−2836.71	−0.168065
$659$	−21195.4	−1.25289	−0.626446	−	0.779465i	$-0.715491\pi$
$659$	−21195.4	−1.25289	−0.626446	+	0.779465i	$0.715491\pi$
$660$	0	0
$661$	−9283.40	−0.546267	−0.273134	−	0.961976i	$-0.588060\pi$
$661$	−9283.40	−0.546267	−0.273134	+	0.961976i	$0.588060\pi$
$662$	−1592.18	−0.0934773
$663$	24723.0	1.44821
$664$	−24093.4	−1.40814
$665$	0	0
$666$	4584.79	0.266752
$667$	−21065.2	−1.22286
$668$	6798.33	0.393765
$669$	2432.38	0.140570
$670$	0	0
$671$	1705.08	0.0980980
$672$	2168.28	0.124469
$673$	−25358.3	−1.45244	−0.726219	−	0.687463i	$-0.758724\pi$
$673$	−25358.3	−1.45244	−0.726219	+	0.687463i	$0.758724\pi$
$674$	1318.84	0.0753707
$675$	0	0
$676$	10193.1	0.579945
$677$	7140.67	0.405374	0.202687	−	0.979244i	$-0.435033\pi$
$677$	7140.67	0.405374	0.202687	+	0.979244i	$0.435033\pi$
$678$	1860.33	0.105377
$679$	944.359	0.0533743
$680$	0	0
$681$	7753.78	0.436308
$682$	−2049.49	−0.115072
$683$	10666.3	0.597561	0.298780	−	0.954322i	$-0.403420\pi$
$683$	10666.3	0.597561	0.298780	+	0.954322i	$0.403420\pi$
$684$	3032.86	0.169538
$685$	0	0
$686$	−1103.55	−0.0614194
$687$	−4912.09	−0.272792
$688$	18468.8	1.02342
$689$	−3514.16	−0.194309
$690$	0	0
$691$	−19360.0	−1.06583	−0.532915	−	0.846169i	$-0.678903\pi$
$691$	−19360.0	−1.06583	−0.532915	+	0.846169i	$0.678903\pi$
$692$	−2042.77	−0.112217
$693$	132.181	0.00724549
$694$	−23735.8	−1.29827
$695$	0	0
$696$	−9878.97	−0.538019
$697$	−38682.8	−2.10218
$698$	−36306.9	−1.96882
$699$	10009.5	0.541621
$700$	0	0
$701$	−19252.3	−1.03730	−0.518651	−	0.854986i	$-0.673566\pi$
$701$	−19252.3	−1.03730	−0.518651	+	0.854986i	$0.673566\pi$
$702$	7020.82	0.377470
$703$	22692.5	1.21745
$704$	−600.183	−0.0321310
$705$	0	0
$706$	−12580.3	−0.670632
$707$	−4099.32	−0.218063
$708$	219.336	0.0116429
$709$	−19553.0	−1.03572	−0.517861	−	0.855465i	$-0.673272\pi$
$709$	−19553.0	−1.03572	−0.517861	+	0.855465i	$0.673272\pi$
$710$	0	0
$711$	10817.2	0.570574
$712$	16106.1	0.847756
$713$	−35297.5	−1.85400
$714$	−6889.21	−0.361096
$715$	0	0
$716$	−4875.35	−0.254470
$717$	−11949.6	−0.622407
$718$	41394.0	2.15155
$719$	−16334.8	−0.847265	−0.423633	−	0.905834i	$-0.639245\pi$
$719$	−16334.8	−0.847265	−0.423633	+	0.905834i	$0.639245\pi$
$720$	0	0
$721$	−5955.76	−0.307634
$722$	44017.3	2.26891
$723$	6848.33	0.352272
$724$	−5060.55	−0.259770
$725$	0	0
$726$	−12804.4	−0.654565
$727$	−30698.8	−1.56610	−0.783051	−	0.621957i	$-0.786338\pi$
$727$	−30698.8	−1.56610	−0.783051	+	0.621957i	$0.786338\pi$
$728$	10281.9	0.523449
$729$	729.000	0.0370370
$730$	0	0
$731$	−24367.7	−1.23293
$732$	−5732.51	−0.289453
$733$	7388.56	0.372309	0.186155	−	0.982520i	$-0.440397\pi$
$733$	7388.56	0.372309	0.186155	+	0.982520i	$0.440397\pi$
$734$	2871.02	0.144375
$735$	0	0
$736$	12003.8	0.601175
$737$	894.264	0.0446956
$738$	−10985.1	−0.547924
$739$	22650.8	1.12750	0.563751	−	0.825945i	$-0.309358\pi$
$739$	22650.8	1.12750	0.563751	+	0.825945i	$0.309358\pi$
$740$	0	0
$741$	34749.7	1.72276
$742$	979.241	0.0484489
$743$	−17656.4	−0.871806	−0.435903	−	0.899994i	$-0.643571\pi$
$743$	−17656.4	−0.871806	−0.435903	+	0.899994i	$0.643571\pi$
$744$	−16553.5	−0.815699
$745$	0	0
$746$	27881.5	1.36838
$747$	11931.5	0.584404
$748$	−503.021	−0.0245886
$749$	−3967.59	−0.193555
$750$	0	0
$751$	22109.0	1.07426	0.537130	−	0.843500i	$-0.319508\pi$
$751$	22109.0	1.07426	0.537130	+	0.843500i	$0.319508\pi$
$752$	−9734.12	−0.472031
$753$	−2565.77	−0.124172
$754$	47116.0	2.27568
$755$	0	0
$756$	−444.394	−0.0213789
$757$	−11034.2	−0.529784	−0.264892	−	0.964278i	$-0.585336\pi$
$757$	−11034.2	−0.529784	−0.264892	+	0.964278i	$0.585336\pi$
$758$	−22878.5	−1.09629
$759$	731.763	0.0349952
$760$	0	0
$761$	−6357.12	−0.302819	−0.151410	−	0.988471i	$-0.548381\pi$
$761$	−6357.12	−0.302819	−0.151410	+	0.988471i	$0.548381\pi$
$762$	9052.35	0.430357
$763$	7780.46	0.369163
$764$	−9755.96	−0.461987
$765$	0	0
$766$	−45100.4	−2.12734
$767$	2513.10	0.118309
$768$	9990.50	0.469402
$769$	−35810.1	−1.67925	−0.839627	−	0.543163i	$-0.817226\pi$
$769$	−35810.1	−1.67925	−0.839627	+	0.543163i	$0.817226\pi$
$770$	0	0
$771$	−8678.72	−0.405391
$772$	−4374.60	−0.203945
$773$	3158.57	0.146967	0.0734837	−	0.997296i	$-0.476588\pi$
$773$	3158.57	0.146967	0.0734837	+	0.997296i	$0.476588\pi$
$774$	−6919.92	−0.321359
$775$	0	0
$776$	2451.80	0.113421
$777$	−3325.06	−0.153521
$778$	−15598.5	−0.718807
$779$	−54371.1	−2.50070
$780$	0	0
$781$	2170.51	0.0994455
$782$	−38139.3	−1.74406
$783$	4892.24	0.223288
$784$	−3786.81	−0.172504
$785$	0	0
$786$	7203.46	0.326894
$787$	−20371.2	−0.922687	−0.461344	−	0.887222i	$-0.652632\pi$
$787$	−20371.2	−0.922687	−0.461344	+	0.887222i	$0.652632\pi$
$788$	−228.195	−0.0103161
$789$	−12501.3	−0.564079
$790$	0	0
$791$	−1349.18	−0.0606463
$792$	343.175	0.0153967
$793$	−65681.6	−2.94127
$794$	13154.9	0.587973
$795$	0	0
$796$	−2203.09	−0.0980986
$797$	31056.5	1.38027	0.690136	−	0.723680i	$-0.257551\pi$
$797$	31056.5	1.38027	0.690136	+	0.723680i	$0.257551\pi$
$798$	−9683.22	−0.429552
$799$	12843.2	0.568660
$800$	0	0
$801$	−7976.03	−0.351834
$802$	23123.1	1.01809
$803$	989.761	0.0434968
$804$	−3006.54	−0.131881
$805$	0	0
$806$	78948.8	3.45019
$807$	−22558.2	−0.983998
$808$	−10642.9	−0.463386
$809$	9549.52	0.415010	0.207505	−	0.978234i	$-0.433466\pi$
$809$	9549.52	0.415010	0.207505	+	0.978234i	$0.433466\pi$
$810$	0	0
$811$	−26730.9	−1.15740	−0.578698	−	0.815542i	$-0.696439\pi$
$811$	−26730.9	−1.15740	−0.578698	+	0.815542i	$0.696439\pi$
$812$	−2982.28	−0.128889
$813$	23380.9	1.00862
$814$	−1068.82	−0.0460222
$815$	0	0
$816$	−23640.2	−1.01418
$817$	−34250.3	−1.46667
$818$	2975.93	0.127202
$819$	−5091.75	−0.217241
$820$	0	0
$821$	−30878.1	−1.31261	−0.656305	−	0.754496i	$-0.727882\pi$
$821$	−30878.1	−1.31261	−0.656305	+	0.754496i	$0.727882\pi$
$822$	4753.76	0.201711
$823$	20618.3	0.873280	0.436640	−	0.899636i	$-0.356168\pi$
$823$	20618.3	0.873280	0.436640	+	0.899636i	$0.356168\pi$
$824$	−15462.7	−0.653724
$825$	0	0
$826$	−700.290	−0.0294990
$827$	12493.2	0.525311	0.262656	−	0.964890i	$-0.415402\pi$
$827$	12493.2	0.525311	0.262656	+	0.964890i	$0.415402\pi$
$828$	−2460.21	−0.103259
$829$	−36795.9	−1.54158	−0.770792	−	0.637087i	$-0.780139\pi$
$829$	−36795.9	−1.54158	−0.770792	+	0.637087i	$0.780139\pi$
$830$	0	0
$831$	9577.37	0.399802
$832$	23119.8	0.963381
$833$	4996.31	0.207817
$834$	−1471.76	−0.0611065
$835$	0	0
$836$	−707.028	−0.0292501
$837$	8197.57	0.338530
$838$	14352.1	0.591628
$839$	6904.41	0.284108	0.142054	−	0.989859i	$-0.454629\pi$
$839$	6904.41	0.284108	0.142054	+	0.989859i	$0.454629\pi$
$840$	0	0
$841$	8442.32	0.346153
$842$	−11078.2	−0.453419
$843$	−7698.98	−0.314552
$844$	−3155.88	−0.128708
$845$	0	0
$846$	3647.20	0.148219
$847$	9286.19	0.376714
$848$	3360.25	0.136075
$849$	−18343.8	−0.741527
$850$	0	0
$851$	−18407.8	−0.741495
$852$	−7297.30	−0.293429
$853$	34285.8	1.37623	0.688115	−	0.725602i	$-0.258439\pi$
$853$	34285.8	1.37623	0.688115	+	0.725602i	$0.258439\pi$
$854$	18302.6	0.733374
$855$	0	0
$856$	−10300.9	−0.411306
$857$	34301.1	1.36722	0.683608	−	0.729849i	$-0.260410\pi$
$857$	34301.1	1.36722	0.683608	+	0.729849i	$0.260410\pi$
$858$	−1636.71	−0.0651241
$859$	6823.12	0.271015	0.135507	−	0.990776i	$-0.456734\pi$
$859$	6823.12	0.271015	0.135507	+	0.990776i	$0.456734\pi$
$860$	0	0
$861$	7966.81	0.315341
$862$	−19994.3	−0.790035
$863$	−8059.34	−0.317895	−0.158947	−	0.987287i	$-0.550810\pi$
$863$	−8059.34	−0.317895	−0.158947	+	0.987287i	$0.550810\pi$
$864$	−2787.78	−0.109771
$865$	0	0
$866$	42240.7	1.65750
$867$	16451.8	0.644445
$868$	−4997.19	−0.195410
$869$	−2521.75	−0.0984400
$870$	0	0
$871$	−34448.1	−1.34010
$872$	20200.1	0.784474
$873$	−1214.18	−0.0470717
$874$	−53607.1	−2.07470
$875$	0	0
$876$	−3327.60	−0.128344
$877$	−162.992	−0.00627577	−0.00313789	−	0.999995i	$-0.500999\pi$
$877$	−162.992	−0.00627577	−0.00313789	+	0.999995i	$0.500999\pi$
$878$	21976.1	0.844712
$879$	−10639.5	−0.408260
$880$	0	0
$881$	10633.9	0.406658	0.203329	−	0.979110i	$-0.434824\pi$
$881$	10633.9	0.406658	0.203329	+	0.979110i	$0.434824\pi$
$882$	1418.85	0.0541668
$883$	−42208.3	−1.60863	−0.804317	−	0.594201i	$-0.797468\pi$
$883$	−42208.3	−1.60863	−0.804317	+	0.594201i	$0.797468\pi$
$884$	19377.0	0.737238
$885$	0	0
$886$	41302.8	1.56614
$887$	−15696.0	−0.594161	−0.297080	−	0.954852i	$-0.596013\pi$
$887$	−15696.0	−0.594161	−0.297080	+	0.954852i	$0.596013\pi$
$888$	−8632.72	−0.326233
$889$	−6565.09	−0.247678
$890$	0	0
$891$	−169.946	−0.00638992
$892$	1906.41	0.0715599
$893$	18051.9	0.676466
$894$	−13833.0	−0.517501
$895$	0	0
$896$	−12224.5	−0.455796
$897$	−28188.4	−1.04926
$898$	−54053.0	−2.00865
$899$	55013.0	2.04092
$900$	0	0
$901$	−4433.50	−0.163931
$902$	2560.88	0.0945322
$903$	5018.58	0.184948
$904$	−3502.82	−0.128874
$905$	0	0
$906$	8843.61	0.324293
$907$	−24251.5	−0.887827	−0.443913	−	0.896070i	$-0.646410\pi$
$907$	−24251.5	−0.887827	−0.443913	+	0.896070i	$0.646410\pi$
$908$	6077.13	0.222111
$909$	5270.55	0.192314
$910$	0	0
$911$	−34110.8	−1.24055	−0.620276	−	0.784384i	$-0.712979\pi$
$911$	−34110.8	−1.24055	−0.620276	+	0.784384i	$0.712979\pi$
$912$	−33227.8	−1.20645
$913$	−2781.50	−0.100826
$914$	30891.6	1.11795
$915$	0	0
$916$	−3849.92	−0.138870
$917$	−5224.21	−0.188134
$918$	8857.56	0.318456
$919$	55153.2	1.97969	0.989846	−	0.142146i	$-0.0454002\pi$
$919$	55153.2	1.97969	0.989846	+	0.142146i	$0.0454002\pi$
$920$	0	0
$921$	5117.92	0.183107
$922$	11282.5	0.403003
$923$	−83610.6	−2.98166
$924$	103.598	0.00368846
$925$	0	0
$926$	−13552.3	−0.480947
$927$	7657.40	0.271308
$928$	−18708.5	−0.661786
$929$	14429.8	0.509607	0.254804	−	0.966993i	$-0.417989\pi$
$929$	14429.8	0.509607	0.254804	+	0.966993i	$0.417989\pi$
$930$	0	0
$931$	7022.62	0.247215
$932$	7845.06	0.275723
$933$	−30970.7	−1.08675
$934$	1804.55	0.0632190
$935$	0	0
$936$	−13219.5	−0.461639
$937$	3625.32	0.126397	0.0631985	−	0.998001i	$-0.479870\pi$
$937$	3625.32	0.126397	0.0631985	+	0.998001i	$0.479870\pi$
$938$	9599.18	0.334141
$939$	21356.5	0.742220
$940$	0	0
$941$	−15634.7	−0.541632	−0.270816	−	0.962631i	$-0.587293\pi$
$941$	−15634.7	−0.541632	−0.270816	+	0.962631i	$0.587293\pi$
$942$	1638.58	0.0566750
$943$	44105.0	1.52307
$944$	−2403.03	−0.0828517
$945$	0	0
$946$	1613.19	0.0554433
$947$	32438.0	1.11309	0.556544	−	0.830818i	$-0.312127\pi$
$947$	32438.0	1.11309	0.556544	+	0.830818i	$0.312127\pi$
$948$	8478.17	0.290462
$949$	−38126.8	−1.30416
$950$	0	0
$951$	−32265.7	−1.10020
$952$	12971.7	0.441613
$953$	−10940.1	−0.371862	−0.185931	−	0.982563i	$-0.559530\pi$
$953$	−10940.1	−0.371862	−0.185931	+	0.982563i	$0.559530\pi$
$954$	−1259.02	−0.0427279
$955$	0	0
$956$	−9365.66	−0.316849
$957$	−1140.49	−0.0385234
$958$	42686.9	1.43961
$959$	−3447.60	−0.116088
$960$	0	0
$961$	62390.3	2.09427
$962$	41172.2	1.37988
$963$	5101.19	0.170700
$964$	5367.48	0.179331
$965$	0	0
$966$	7854.87	0.261621
$967$	27827.5	0.925412	0.462706	−	0.886512i	$-0.346879\pi$
$967$	27827.5	0.925412	0.462706	+	0.886512i	$0.346879\pi$
$968$	24109.4	0.800521
$969$	43840.7	1.45342
$970$	0	0
$971$	−58041.1	−1.91826	−0.959129	−	0.282970i	$-0.908680\pi$
$971$	−58041.1	−1.91826	−0.959129	+	0.282970i	$0.908680\pi$
$972$	571.364	0.0188544
$973$	1067.37	0.0351679
$974$	−51918.1	−1.70797
$975$	0	0
$976$	62805.0	2.05977
$977$	−28430.6	−0.930988	−0.465494	−	0.885051i	$-0.654123\pi$
$977$	−28430.6	−0.930988	−0.465494	+	0.885051i	$0.654123\pi$
$978$	10150.4	0.331874
$979$	1859.39	0.0607012
$980$	0	0
$981$	−10003.4	−0.325571
$982$	16687.2	0.542272
$983$	−9356.47	−0.303586	−0.151793	−	0.988412i	$-0.548505\pi$
$983$	−9356.47	−0.303586	−0.151793	+	0.988412i	$0.548505\pi$
$984$	20683.9	0.670101
$985$	0	0
$986$	59442.1	1.91990
$987$	−2645.08	−0.0853028
$988$	27235.6	0.877003
$989$	27783.3	0.893284
$990$	0	0
$991$	−9199.90	−0.294898	−0.147449	−	0.989070i	$-0.547106\pi$
$991$	−9199.90	−0.294898	−0.147449	+	0.989070i	$0.547106\pi$
$992$	−31348.5	−1.00334
$993$	−1484.63	−0.0474453
$994$	23298.6	0.743447
$995$	0	0
$996$	9351.46	0.297502
$997$	5396.25	0.171415	0.0857076	−	0.996320i	$-0.472685\pi$
$997$	5396.25	0.171415	0.0857076	+	0.996320i	$0.472685\pi$
$998$	47689.1	1.51260
$999$	4275.08	0.135393

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.4.a.v.1.3	yes	4
3.2	odd	2		1575.4.a.bf.1.2		4
5.2	odd	4		525.4.d.o.274.7		8
5.3	odd	4		525.4.d.o.274.2		8
5.4	even	2		525.4.a.s.1.2	✓	4
15.14	odd	2		1575.4.a.bm.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.4.a.s.1.2	✓	4	5.4	even	2
525.4.a.v.1.3	yes	4	1.1	even	1	trivial
525.4.d.o.274.2		8	5.3	odd	4
525.4.d.o.274.7		8	5.2	odd	4
1575.4.a.bf.1.2		4	3.2	odd	2
1575.4.a.bm.1.3		4	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+3.21734 q^{2} +3.00000 q^{3} +2.35129 q^{4} +9.65203 q^{6} -7.00000 q^{7} -18.1738 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+3.21734 q^{2} +3.00000 q^{3} +2.35129 q^{4} +9.65203 q^{6} -7.00000 q^{7} -18.1738 q^{8} +9.00000 q^{9} -2.09810 q^{11} +7.05388 q^{12} +80.8215 q^{13} -22.5214 q^{14} -77.2818 q^{16} +101.965 q^{17} +28.9561 q^{18} +143.319 q^{19} -21.0000 q^{21} -6.75032 q^{22} -116.258 q^{23} -54.5215 q^{24} +260.030 q^{26} +27.0000 q^{27} -16.4590 q^{28} +181.194 q^{29} +303.614 q^{31} -103.251 q^{32} -6.29431 q^{33} +328.058 q^{34} +21.1616 q^{36} +158.336 q^{37} +461.106 q^{38} +242.465 q^{39} -379.372 q^{41} -67.5642 q^{42} -238.980 q^{43} -4.93326 q^{44} -374.041 q^{46} +125.956 q^{47} -231.845 q^{48} +49.0000 q^{49} +305.896 q^{51} +190.035 q^{52} -43.4805 q^{53} +86.8682 q^{54} +127.217 q^{56} +429.956 q^{57} +582.964 q^{58} +31.0944 q^{59} -812.675 q^{61} +976.830 q^{62} -63.0000 q^{63} +286.059 q^{64} -20.2510 q^{66} -426.225 q^{67} +239.750 q^{68} -348.774 q^{69} -1034.51 q^{71} -163.564 q^{72} -471.741 q^{73} +509.422 q^{74} +336.984 q^{76} +14.6867 q^{77} +780.091 q^{78} +1201.92 q^{79} +81.0000 q^{81} -1220.57 q^{82} +1325.72 q^{83} -49.3771 q^{84} -768.880 q^{86} +543.582 q^{87} +38.1306 q^{88} -886.226 q^{89} -565.751 q^{91} -273.356 q^{92} +910.841 q^{93} +405.245 q^{94} -309.754 q^{96} -134.908 q^{97} +157.650 q^{98} -18.8829 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{2} + 12 q^{3} + 16 q^{4} + 18 q^{6} - 28 q^{7} + 93 q^{8} + 36 q^{9}+O(q^{10}) \) 4 * q + 6 * q^2 + 12 * q^3 + 16 * q^4 + 18 * q^6 - 28 * q^7 + 93 * q^8 + 36 * q^9	\( 4 q + 6 q^{2} + 12 q^{3} + 16 q^{4} + 18 q^{6} - 28 q^{7} + 93 q^{8} + 36 q^{9} + 57 q^{11} + 48 q^{12} + 43 q^{13} - 42 q^{14} + 216 q^{16} + 99 q^{17} + 54 q^{18} - 12 q^{19} - 84 q^{21} - 41 q^{22} + 156 q^{23} + 279 q^{24} - 81 q^{26} + 108 q^{27} - 112 q^{28} + 378 q^{29} - 93 q^{31} + 690 q^{32} + 171 q^{33} + 783 q^{34} + 144 q^{36} + 81 q^{37} + 216 q^{38} + 129 q^{39} - 465 q^{41} - 126 q^{42} - 64 q^{43} + 681 q^{44} + 310 q^{46} + 744 q^{47} + 648 q^{48} + 196 q^{49} + 297 q^{51} - 727 q^{52} + 729 q^{53} + 162 q^{54} - 651 q^{56} - 36 q^{57} + 1172 q^{58} + 231 q^{59} - 1353 q^{61} - 165 q^{62} - 252 q^{63} + 3107 q^{64} - 123 q^{66} + 1487 q^{67} + 2577 q^{68} + 468 q^{69} - 1725 q^{71} + 837 q^{72} + 512 q^{73} - 1953 q^{74} - 3046 q^{76} - 399 q^{77} - 243 q^{78} + 1629 q^{79} + 324 q^{81} - 693 q^{82} + 321 q^{83} - 336 q^{84} - 4542 q^{86} + 1134 q^{87} + 3482 q^{88} - 978 q^{89} - 301 q^{91} + 852 q^{92} - 279 q^{93} + 2480 q^{94} + 2070 q^{96} + 2616 q^{97} + 294 q^{98} + 513 q^{99}+O(q^{100}) \) 4 * q + 6 * q^2 + 12 * q^3 + 16 * q^4 + 18 * q^6 - 28 * q^7 + 93 * q^8 + 36 * q^9 + 57 * q^11 + 48 * q^12 + 43 * q^13 - 42 * q^14 + 216 * q^16 + 99 * q^17 + 54 * q^18 - 12 * q^19 - 84 * q^21 - 41 * q^22 + 156 * q^23 + 279 * q^24 - 81 * q^26 + 108 * q^27 - 112 * q^28 + 378 * q^29 - 93 * q^31 + 690 * q^32 + 171 * q^33 + 783 * q^34 + 144 * q^36 + 81 * q^37 + 216 * q^38 + 129 * q^39 - 465 * q^41 - 126 * q^42 - 64 * q^43 + 681 * q^44 + 310 * q^46 + 744 * q^47 + 648 * q^48 + 196 * q^49 + 297 * q^51 - 727 * q^52 + 729 * q^53 + 162 * q^54 - 651 * q^56 - 36 * q^57 + 1172 * q^58 + 231 * q^59 - 1353 * q^61 - 165 * q^62 - 252 * q^63 + 3107 * q^64 - 123 * q^66 + 1487 * q^67 + 2577 * q^68 + 468 * q^69 - 1725 * q^71 + 837 * q^72 + 512 * q^73 - 1953 * q^74 - 3046 * q^76 - 399 * q^77 - 243 * q^78 + 1629 * q^79 + 324 * q^81 - 693 * q^82 + 321 * q^83 - 336 * q^84 - 4542 * q^86 + 1134 * q^87 + 3482 * q^88 - 978 * q^89 - 301 * q^91 + 852 * q^92 - 279 * q^93 + 2480 * q^94 + 2070 * q^96 + 2616 * q^97 + 294 * q^98 + 513 * q^99

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