LMFDB - Embedded newform 2175.4.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2175,4,Mod(1,2175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2175, 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("2175.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2175 = 3 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2175.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:	$128.329154262$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 49x^{4} + 27x^{3} + 692x^{2} - 82x - 2588 $ x^6 - x^5 - 49x^4 + 27x^3 + 692x^2 - 82x - 2588
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 435)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$5.42717$ of defining polynomial
Character	$\chi$	$=$	2175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.42717 q^{2} -3.00000 q^{3} +21.4542 q^{4} +16.2815 q^{6} +10.2400 q^{7} -73.0180 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-5.42717 q^{2} -3.00000 q^{3} +21.4542 q^{4} +16.2815 q^{6} +10.2400 q^{7} -73.0180 q^{8} +9.00000 q^{9} +12.6318 q^{11} -64.3625 q^{12} -84.2342 q^{13} -55.5740 q^{14} +224.647 q^{16} -6.89181 q^{17} -48.8445 q^{18} -79.7045 q^{19} -30.7199 q^{21} -68.5548 q^{22} +73.8181 q^{23} +219.054 q^{24} +457.153 q^{26} -27.0000 q^{27} +219.690 q^{28} +29.0000 q^{29} +0.254654 q^{31} -635.056 q^{32} -37.8953 q^{33} +37.4030 q^{34} +193.087 q^{36} -40.4065 q^{37} +432.570 q^{38} +252.703 q^{39} +208.354 q^{41} +166.722 q^{42} +194.427 q^{43} +271.004 q^{44} -400.623 q^{46} +522.168 q^{47} -673.942 q^{48} -238.143 q^{49} +20.6754 q^{51} -1807.17 q^{52} +294.893 q^{53} +146.534 q^{54} -747.701 q^{56} +239.114 q^{57} -157.388 q^{58} -196.229 q^{59} +189.313 q^{61} -1.38205 q^{62} +92.1597 q^{63} +1649.38 q^{64} +205.664 q^{66} +570.840 q^{67} -147.858 q^{68} -221.454 q^{69} -1126.87 q^{71} -657.162 q^{72} -581.431 q^{73} +219.293 q^{74} -1709.99 q^{76} +129.349 q^{77} -1371.46 q^{78} -255.631 q^{79} +81.0000 q^{81} -1130.77 q^{82} +983.081 q^{83} -659.069 q^{84} -1055.19 q^{86} -87.0000 q^{87} -922.347 q^{88} +678.642 q^{89} -862.555 q^{91} +1583.70 q^{92} -0.763963 q^{93} -2833.89 q^{94} +1905.17 q^{96} +30.8442 q^{97} +1292.44 q^{98} +113.686 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} - 18 q^{3} + 51 q^{4} + 3 q^{6} - 47 q^{7} - 51 q^{8} + 54 q^{9}+O(q^{10}) $ 6 * q - q^2 - 18 * q^3 + 51 * q^4 + 3 * q^6 - 47 * q^7 - 51 * q^8 + 54 * q^9	$ 6 q - q^{2} - 18 q^{3} + 51 q^{4} + 3 q^{6} - 47 q^{7} - 51 q^{8} + 54 q^{9} + 81 q^{11} - 153 q^{12} - 169 q^{13} - 30 q^{14} + 131 q^{16} + q^{17} - 9 q^{18} + 116 q^{19} + 141 q^{21} - 90 q^{22} + 52 q^{23} + 153 q^{24} + 294 q^{26} - 162 q^{27} - 344 q^{28} + 174 q^{29} + 340 q^{31} - 499 q^{32} - 243 q^{33} + 920 q^{34} + 459 q^{36} - 332 q^{37} + 378 q^{38} + 507 q^{39} - 616 q^{41} + 90 q^{42} - 334 q^{43} - 52 q^{44} - 158 q^{46} + 85 q^{47} - 393 q^{48} + 879 q^{49} - 3 q^{51} - 2220 q^{52} + 850 q^{53} + 27 q^{54} - 624 q^{56} - 348 q^{57} - 29 q^{58} - 758 q^{59} - 36 q^{61} + 152 q^{62} - 423 q^{63} + 1795 q^{64} + 270 q^{66} - 939 q^{67} + 186 q^{68} - 156 q^{69} - 1388 q^{71} - 459 q^{72} - 1708 q^{73} - 814 q^{74} + 566 q^{76} - 2585 q^{77} - 882 q^{78} + 1250 q^{79} + 486 q^{81} - 1372 q^{82} + 748 q^{83} + 1032 q^{84} - 800 q^{86} - 522 q^{87} - 536 q^{88} + 1099 q^{89} + 539 q^{91} - 1698 q^{92} - 1020 q^{93} - 4542 q^{94} + 1497 q^{96} + 22 q^{97} + 1433 q^{98} + 729 q^{99}+O(q^{100}) $ 6 * q - q^2 - 18 * q^3 + 51 * q^4 + 3 * q^6 - 47 * q^7 - 51 * q^8 + 54 * q^9 + 81 * q^11 - 153 * q^12 - 169 * q^13 - 30 * q^14 + 131 * q^16 + q^17 - 9 * q^18 + 116 * q^19 + 141 * q^21 - 90 * q^22 + 52 * q^23 + 153 * q^24 + 294 * q^26 - 162 * q^27 - 344 * q^28 + 174 * q^29 + 340 * q^31 - 499 * q^32 - 243 * q^33 + 920 * q^34 + 459 * q^36 - 332 * q^37 + 378 * q^38 + 507 * q^39 - 616 * q^41 + 90 * q^42 - 334 * q^43 - 52 * q^44 - 158 * q^46 + 85 * q^47 - 393 * q^48 + 879 * q^49 - 3 * q^51 - 2220 * q^52 + 850 * q^53 + 27 * q^54 - 624 * q^56 - 348 * q^57 - 29 * q^58 - 758 * q^59 - 36 * q^61 + 152 * q^62 - 423 * q^63 + 1795 * q^64 + 270 * q^66 - 939 * q^67 + 186 * q^68 - 156 * q^69 - 1388 * q^71 - 459 * q^72 - 1708 * q^73 - 814 * q^74 + 566 * q^76 - 2585 * q^77 - 882 * q^78 + 1250 * q^79 + 486 * q^81 - 1372 * q^82 + 748 * q^83 + 1032 * q^84 - 800 * q^86 - 522 * q^87 - 536 * q^88 + 1099 * q^89 + 539 * q^91 - 1698 * q^92 - 1020 * q^93 - 4542 * q^94 + 1497 * q^96 + 22 * q^97 + 1433 * q^98 + 729 * 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 $

$2$	−5.42717	−1.91879	−0.959397	−	0.282060i	$-0.908982\pi$
$2$	−5.42717	−1.91879	−0.959397	+	0.282060i	$0.908982\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	21.4542	2.68177
$5$	0	0
$5$	0	0
$6$	16.2815	1.10782
$7$	10.2400	0.552906	0.276453	−	0.961027i	$-0.410841\pi$
$7$	10.2400	0.552906	0.276453	+	0.961027i	$0.410841\pi$
$8$	−73.0180	−3.22697
$9$	9.00000	0.333333
$10$	0	0
$11$	12.6318	0.346239	0.173119	−	0.984901i	$-0.444615\pi$
$11$	12.6318	0.346239	0.173119	+	0.984901i	$0.444615\pi$
$12$	−64.3625	−1.54832
$13$	−84.2342	−1.79710	−0.898552	−	0.438866i	$-0.855380\pi$
$13$	−84.2342	−1.79710	−0.898552	+	0.438866i	$0.855380\pi$
$14$	−55.5740	−1.06091
$15$	0	0
$16$	224.647	3.51012
$17$	−6.89181	−0.0983241	−0.0491621	−	0.998791i	$-0.515655\pi$
$17$	−6.89181	−0.0983241	−0.0491621	+	0.998791i	$0.515655\pi$
$18$	−48.8445	−0.639598
$19$	−79.7045	−0.962393	−0.481196	−	0.876613i	$-0.659798\pi$
$19$	−79.7045	−0.962393	−0.481196	+	0.876613i	$0.659798\pi$
$20$	0	0
$21$	−30.7199	−0.319220
$22$	−68.5548	−0.664361
$23$	73.8181	0.669223	0.334612	−	0.942356i	$-0.391395\pi$
$23$	73.8181	0.669223	0.334612	+	0.942356i	$0.391395\pi$
$24$	219.054	1.86309
$25$	0	0
$26$	457.153	3.44827
$27$	−27.0000	−0.192450
$28$	219.690	1.48277
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	0	0
$31$	0.254654	0.00147540	0.000737698	−	1.00000i	$-0.499765\pi$
$31$	0.254654	0.00147540	0.000737698		1.00000i	$0.499765\pi$
$32$	−635.056	−3.50822
$33$	−37.8953	−0.199901
$34$	37.4030	0.188664
$35$	0	0
$36$	193.087	0.893923
$37$	−40.4065	−0.179535	−0.0897674	−	0.995963i	$-0.528612\pi$
$37$	−40.4065	−0.179535	−0.0897674	+	0.995963i	$0.528612\pi$
$38$	432.570	1.84663
$39$	252.703	1.03756
$40$	0	0
$41$	208.354	0.793645	0.396822	−	0.917895i	$-0.370113\pi$
$41$	208.354	0.793645	0.396822	+	0.917895i	$0.370113\pi$
$42$	166.722	0.612518
$43$	194.427	0.689531	0.344766	−	0.938689i	$-0.387958\pi$
$43$	194.427	0.689531	0.344766	+	0.938689i	$0.387958\pi$
$44$	271.004	0.928532
$45$	0	0
$46$	−400.623	−1.28410
$47$	522.168	1.62055	0.810277	−	0.586047i	$-0.199317\pi$
$47$	522.168	1.62055	0.810277	+	0.586047i	$0.199317\pi$
$48$	−673.942	−2.02657
$49$	−238.143	−0.694295
$50$	0	0
$51$	20.6754	0.0567675
$52$	−1807.17	−4.81942
$53$	294.893	0.764276	0.382138	−	0.924105i	$-0.375188\pi$
$53$	294.893	0.764276	0.382138	+	0.924105i	$0.375188\pi$
$54$	146.534	0.369272
$55$	0	0
$56$	−747.701	−1.78421
$57$	239.114	0.555638
$58$	−157.388	−0.356311
$59$	−196.229	−0.432997	−0.216498	−	0.976283i	$-0.569464\pi$
$59$	−196.229	−0.432997	−0.216498	+	0.976283i	$0.569464\pi$
$60$	0	0
$61$	189.313	0.397360	0.198680	−	0.980064i	$-0.436334\pi$
$61$	189.313	0.397360	0.198680	+	0.980064i	$0.436334\pi$
$62$	−1.38205	−0.00283098
$63$	92.1597	0.184302
$64$	1649.38	3.22144
$65$	0	0
$66$	205.664	0.383569
$67$	570.840	1.04088	0.520442	−	0.853897i	$-0.325767\pi$
$67$	570.840	1.04088	0.520442	+	0.853897i	$0.325767\pi$
$68$	−147.858	−0.263683
$69$	−221.454	−0.386376
$70$	0	0
$71$	−1126.87	−1.88358	−0.941792	−	0.336196i	$-0.890859\pi$
$71$	−1126.87	−1.88358	−0.941792	+	0.336196i	$0.890859\pi$
$72$	−657.162	−1.07566
$73$	−581.431	−0.932210	−0.466105	−	0.884729i	$-0.654343\pi$
$73$	−581.431	−0.932210	−0.466105	+	0.884729i	$0.654343\pi$
$74$	219.293	0.344490
$75$	0	0
$76$	−1709.99	−2.58092
$77$	129.349	0.191437
$78$	−1371.46	−1.99086
$79$	−255.631	−0.364060	−0.182030	−	0.983293i	$-0.558267\pi$
$79$	−255.631	−0.364060	−0.182030	+	0.983293i	$0.558267\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	−1130.77	−1.52284
$83$	983.081	1.30009	0.650043	−	0.759897i	$-0.274751\pi$
$83$	983.081	1.30009	0.650043	+	0.759897i	$0.274751\pi$
$84$	−659.069	−0.856075
$85$	0	0
$86$	−1055.19	−1.32307
$87$	−87.0000	−0.107211
$88$	−922.347	−1.11730
$89$	678.642	0.808268	0.404134	−	0.914700i	$-0.367573\pi$
$89$	678.642	0.808268	0.404134	+	0.914700i	$0.367573\pi$
$90$	0	0
$91$	−862.555	−0.993630
$92$	1583.70	1.79470
$93$	−0.763963	−0.000851820 0
$94$	−2833.89	−3.10951
$95$	0	0
$96$	1905.17	2.02547
$97$	30.8442	0.0322861	0.0161431	−	0.999870i	$-0.494861\pi$
$97$	30.8442	0.0322861	0.0161431	+	0.999870i	$0.494861\pi$
$98$	1292.44	1.33221
$99$	113.686	0.115413
$100$	0	0
$101$	1749.78	1.72386	0.861930	−	0.507028i	$-0.169256\pi$
$101$	1749.78	1.72386	0.861930	+	0.507028i	$0.169256\pi$
$102$	−112.209	−0.108925
$103$	−1912.26	−1.82933	−0.914663	−	0.404217i	$-0.867544\pi$
$103$	−1912.26	−1.82933	−0.914663	+	0.404217i	$0.867544\pi$
$104$	6150.61	5.79920
$105$	0	0
$106$	−1600.43	−1.46649
$107$	−1719.25	−1.55333	−0.776663	−	0.629916i	$-0.783089\pi$
$107$	−1719.25	−1.55333	−0.776663	+	0.629916i	$0.783089\pi$
$108$	−579.262	−0.516107
$109$	−779.425	−0.684911	−0.342456	−	0.939534i	$-0.611259\pi$
$109$	−779.425	−0.684911	−0.342456	+	0.939534i	$0.611259\pi$
$110$	0	0
$111$	121.220	0.103654
$112$	2300.38	1.94076
$113$	−766.529	−0.638132	−0.319066	−	0.947732i	$-0.603369\pi$
$113$	−766.529	−0.638132	−0.319066	+	0.947732i	$0.603369\pi$
$114$	−1297.71	−1.06615
$115$	0	0
$116$	622.170	0.497992
$117$	−758.108	−0.599035
$118$	1064.97	0.830831
$119$	−70.5719	−0.0543640
$120$	0	0
$121$	−1171.44	−0.880119
$122$	−1027.43	−0.762453
$123$	−625.062	−0.458211
$124$	5.46339	0.00395667
$125$	0	0
$126$	−500.166	−0.353637
$127$	1363.54	0.952715	0.476358	−	0.879252i	$-0.341957\pi$
$127$	1363.54	0.952715	0.476358	+	0.879252i	$0.341957\pi$
$128$	−3870.99	−2.67305
$129$	−583.281	−0.398101
$130$	0	0
$131$	−1346.83	−0.898269	−0.449134	−	0.893464i	$-0.648268\pi$
$131$	−1346.83	−0.898269	−0.449134	+	0.893464i	$0.648268\pi$
$132$	−813.013	−0.536088
$133$	−816.171	−0.532113
$134$	−3098.05	−1.99724
$135$	0	0
$136$	503.226	0.317289
$137$	2508.42	1.56430	0.782148	−	0.623093i	$-0.214124\pi$
$137$	2508.42	1.56430	0.782148	+	0.623093i	$0.214124\pi$
$138$	1201.87	0.741376
$139$	1363.95	0.832292	0.416146	−	0.909298i	$-0.363380\pi$
$139$	1363.95	0.832292	0.416146	+	0.909298i	$0.363380\pi$
$140$	0	0
$141$	−1566.50	−0.935628
$142$	6115.69	3.61421
$143$	−1064.03	−0.622227
$144$	2021.83	1.17004
$145$	0	0
$146$	3155.52	1.78872
$147$	714.430	0.400851
$148$	−866.887	−0.481471
$149$	2792.25	1.53523	0.767617	−	0.640909i	$-0.221442\pi$
$149$	2792.25	1.53523	0.767617	+	0.640909i	$0.221442\pi$
$150$	0	0
$151$	306.493	0.165179	0.0825897	−	0.996584i	$-0.473681\pi$
$151$	306.493	0.165179	0.0825897	+	0.996584i	$0.473681\pi$
$152$	5819.86	3.10561
$153$	−62.0263	−0.0327747
$154$	−701.999	−0.367329
$155$	0	0
$156$	5421.52	2.78249
$157$	1828.15	0.929315	0.464657	−	0.885491i	$-0.346178\pi$
$157$	1828.15	0.929315	0.464657	+	0.885491i	$0.346178\pi$
$158$	1387.35	0.698556
$159$	−884.678	−0.441255
$160$	0	0
$161$	755.894	0.370018
$162$	−439.601	−0.213199
$163$	−2101.15	−1.00966	−0.504830	−	0.863219i	$-0.668445\pi$
$163$	−2101.15	−1.00966	−0.504830	+	0.863219i	$0.668445\pi$
$164$	4470.06	2.12837
$165$	0	0
$166$	−5335.35	−2.49460
$167$	−1564.53	−0.724950	−0.362475	−	0.931994i	$-0.618068\pi$
$167$	−1564.53	−0.724950	−0.362475	+	0.931994i	$0.618068\pi$
$168$	2243.10	1.03011
$169$	4898.40	2.22959
$170$	0	0
$171$	−717.341	−0.320798
$172$	4171.27	1.84916
$173$	2695.23	1.18448	0.592239	−	0.805762i	$-0.298244\pi$
$173$	2695.23	1.18448	0.592239	+	0.805762i	$0.298244\pi$
$174$	472.164	0.205716
$175$	0	0
$176$	2837.70	1.21534
$177$	588.686	0.249991
$178$	−3683.10	−1.55090
$179$	−3604.16	−1.50496	−0.752480	−	0.658615i	$-0.771143\pi$
$179$	−3604.16	−1.50496	−0.752480	+	0.658615i	$0.771143\pi$
$180$	0	0
$181$	−2658.32	−1.09166	−0.545832	−	0.837894i	$-0.683786\pi$
$181$	−2658.32	−1.09166	−0.545832	+	0.837894i	$0.683786\pi$
$182$	4681.23	1.90657
$183$	−567.938	−0.229416
$184$	−5390.05	−2.15956
$185$	0	0
$186$	4.14615	0.00163447
$187$	−87.0559	−0.0340436
$188$	11202.7	4.34595
$189$	−276.479	−0.106407
$190$	0	0
$191$	−145.942	−0.0552877	−0.0276439	−	0.999618i	$-0.508800\pi$
$191$	−145.942	−0.0552877	−0.0276439	+	0.999618i	$0.508800\pi$
$192$	−4948.13	−1.85990
$193$	−1151.46	−0.429451	−0.214725	−	0.976674i	$-0.568886\pi$
$193$	−1151.46	−0.429451	−0.214725	+	0.976674i	$0.568886\pi$
$194$	−167.397	−0.0619504
$195$	0	0
$196$	−5109.16	−1.86194
$197$	−4328.08	−1.56529	−0.782647	−	0.622466i	$-0.786131\pi$
$197$	−4328.08	−1.56529	−0.782647	+	0.622466i	$0.786131\pi$
$198$	−616.993	−0.221454
$199$	1532.72	0.545988	0.272994	−	0.962016i	$-0.411986\pi$
$199$	1532.72	0.545988	0.272994	+	0.962016i	$0.411986\pi$
$200$	0	0
$201$	−1712.52	−0.600955
$202$	−9496.36	−3.30773
$203$	296.959	0.102672
$204$	443.574	0.152237
$205$	0	0
$206$	10378.2	3.51010
$207$	664.363	0.223074
$208$	−18923.0	−6.30805
$209$	−1006.81	−0.333218
$210$	0	0
$211$	5345.39	1.74404	0.872019	−	0.489472i	$-0.162810\pi$
$211$	5345.39	1.74404	0.872019	+	0.489472i	$0.162810\pi$
$212$	6326.67	2.04961
$213$	3380.60	1.08749
$214$	9330.65	2.98051
$215$	0	0
$216$	1971.48	0.621030
$217$	2.60765	0.000815755 0
$218$	4230.07	1.31420
$219$	1744.29	0.538212
$220$	0	0
$221$	580.526	0.176699
$222$	−657.879	−0.198892
$223$	−3783.05	−1.13602	−0.568008	−	0.823023i	$-0.692286\pi$
$223$	−3783.05	−1.13602	−0.568008	+	0.823023i	$0.692286\pi$
$224$	−6502.95	−1.93972
$225$	0	0
$226$	4160.08	1.22444
$227$	4348.46	1.27144	0.635721	−	0.771919i	$-0.280703\pi$
$227$	4348.46	1.27144	0.635721	+	0.771919i	$0.280703\pi$
$228$	5129.98	1.49009
$229$	−3068.67	−0.885517	−0.442759	−	0.896641i	$-0.646000\pi$
$229$	−3068.67	−0.885517	−0.442759	+	0.896641i	$0.646000\pi$
$230$	0	0
$231$	−388.047	−0.110526
$232$	−2117.52	−0.599233
$233$	275.696	0.0775170	0.0387585	−	0.999249i	$-0.487660\pi$
$233$	275.696	0.0775170	0.0387585	+	0.999249i	$0.487660\pi$
$234$	4114.38	1.14942
$235$	0	0
$236$	−4209.92	−1.16120
$237$	766.894	0.210190
$238$	383.006	0.104313
$239$	3132.87	0.847901	0.423950	−	0.905685i	$-0.360643\pi$
$239$	3132.87	0.847901	0.423950	+	0.905685i	$0.360643\pi$
$240$	0	0
$241$	5699.61	1.52342	0.761710	−	0.647918i	$-0.224360\pi$
$241$	5699.61	1.52342	0.761710	+	0.647918i	$0.224360\pi$
$242$	6357.59	1.68877
$243$	−243.000	−0.0641500
$244$	4061.54	1.06563
$245$	0	0
$246$	3392.32	0.879212
$247$	6713.85	1.72952
$248$	−18.5943	−0.00476105
$249$	−2949.24	−0.750605
$250$	0	0
$251$	1714.12	0.431054	0.215527	−	0.976498i	$-0.430853\pi$
$251$	1714.12	0.431054	0.215527	+	0.976498i	$0.430853\pi$
$252$	1977.21	0.494255
$253$	932.454	0.231711
$254$	−7400.17	−1.82806
$255$	0	0
$256$	7813.52	1.90760
$257$	803.085	0.194922	0.0974612	−	0.995239i	$-0.468928\pi$
$257$	803.085	0.194922	0.0974612	+	0.995239i	$0.468928\pi$
$258$	3165.56	0.763874
$259$	−413.761	−0.0992659
$260$	0	0
$261$	261.000	0.0618984
$262$	7309.48	1.72359
$263$	1694.24	0.397230	0.198615	−	0.980078i	$-0.436356\pi$
$263$	1694.24	0.397230	0.198615	+	0.980078i	$0.436356\pi$
$264$	2767.04	0.645074
$265$	0	0
$266$	4429.50	1.02101
$267$	−2035.92	−0.466654
$268$	12246.9	2.79141
$269$	3364.95	0.762693	0.381347	−	0.924432i	$-0.375460\pi$
$269$	3364.95	0.762693	0.381347	+	0.924432i	$0.375460\pi$
$270$	0	0
$271$	8044.10	1.80312	0.901558	−	0.432658i	$-0.142424\pi$
$271$	8044.10	1.80312	0.901558	+	0.432658i	$0.142424\pi$
$272$	−1548.23	−0.345129
$273$	2587.66	0.573673
$274$	−13613.6	−3.00156
$275$	0	0
$276$	−4751.11	−1.03617
$277$	6971.54	1.51220	0.756100	−	0.654456i	$-0.227102\pi$
$277$	6971.54	1.51220	0.756100	+	0.654456i	$0.227102\pi$
$278$	−7402.38	−1.59700
$279$	2.29189	0.000491798 0
$280$	0	0
$281$	−1916.94	−0.406957	−0.203478	−	0.979079i	$-0.565225\pi$
$281$	−1916.94	−0.406957	−0.203478	+	0.979079i	$0.565225\pi$
$282$	8501.68	1.79528
$283$	−2036.63	−0.427792	−0.213896	−	0.976856i	$-0.568615\pi$
$283$	−2036.63	−0.427792	−0.213896	+	0.976856i	$0.568615\pi$
$284$	−24176.0	−5.05134
$285$	0	0
$286$	5774.66	1.19393
$287$	2133.54	0.438811
$288$	−5715.50	−1.16941
$289$	−4865.50	−0.990332
$290$	0	0
$291$	−92.5325	−0.0186404
$292$	−12474.1	−2.49997
$293$	1754.55	0.349836	0.174918	−	0.984583i	$-0.444034\pi$
$293$	1754.55	0.349836	0.174918	+	0.984583i	$0.444034\pi$
$294$	−3877.33	−0.769151
$295$	0	0
$296$	2950.40	0.579353
$297$	−341.058	−0.0666337
$298$	−15154.0	−2.94580
$299$	−6218.01	−1.20266
$300$	0	0
$301$	1990.92	0.381246
$302$	−1663.39	−0.316945
$303$	−5249.35	−0.995271
$304$	−17905.4	−3.37811
$305$	0	0
$306$	336.627	0.0628879
$307$	−8909.41	−1.65631	−0.828154	−	0.560500i	$-0.810609\pi$
$307$	−8909.41	−1.65631	−0.828154	+	0.560500i	$0.810609\pi$
$308$	2775.07	0.513391
$309$	5736.78	1.05616
$310$	0	0
$311$	−7422.88	−1.35342	−0.676709	−	0.736251i	$-0.736595\pi$
$311$	−7422.88	−1.35342	−0.676709	+	0.736251i	$0.736595\pi$
$312$	−18451.8	−3.34817
$313$	1453.62	0.262504	0.131252	−	0.991349i	$-0.458100\pi$
$313$	1453.62	0.262504	0.131252	+	0.991349i	$0.458100\pi$
$314$	−9921.69	−1.78316
$315$	0	0
$316$	−5484.35	−0.976326
$317$	−5203.30	−0.921912	−0.460956	−	0.887423i	$-0.652493\pi$
$317$	−5203.30	−0.921912	−0.460956	+	0.887423i	$0.652493\pi$
$318$	4801.29	0.846677
$319$	366.322	0.0642949
$320$	0	0
$321$	5157.74	0.896813
$322$	−4102.37	−0.709987
$323$	549.309	0.0946264
$324$	1737.79	0.297974
$325$	0	0
$326$	11403.3	1.93733
$327$	2338.27	0.395434
$328$	−15213.6	−2.56107
$329$	5346.98	0.896014
$330$	0	0
$331$	−10985.0	−1.82414	−0.912070	−	0.410035i	$-0.865516\pi$
$331$	−10985.0	−1.82414	−0.912070	+	0.410035i	$0.865516\pi$
$332$	21091.2	3.48653
$333$	−363.659	−0.0598449
$334$	8490.94	1.39103
$335$	0	0
$336$	−6901.14	−1.12050
$337$	−2295.27	−0.371013	−0.185507	−	0.982643i	$-0.559393\pi$
$337$	−2295.27	−0.371013	−0.185507	+	0.982643i	$0.559393\pi$
$338$	−26584.4	−4.27812
$339$	2299.59	0.368426
$340$	0	0
$341$	3.21674	0.000510839 0
$342$	3893.13	0.615545
$343$	−5950.88	−0.936786
$344$	−14196.7	−2.22510
$345$	0	0
$346$	−14627.5	−2.27277
$347$	5313.01	0.821952	0.410976	−	0.911646i	$-0.365188\pi$
$347$	5313.01	0.821952	0.410976	+	0.911646i	$0.365188\pi$
$348$	−1866.51	−0.287516
$349$	2086.08	0.319958	0.159979	−	0.987120i	$-0.448857\pi$
$349$	2086.08	0.319958	0.159979	+	0.987120i	$0.448857\pi$
$350$	0	0
$351$	2274.32	0.345853
$352$	−8021.89	−1.21468
$353$	−5382.37	−0.811543	−0.405772	−	0.913975i	$-0.632997\pi$
$353$	−5382.37	−0.811543	−0.405772	+	0.913975i	$0.632997\pi$
$354$	−3194.90	−0.479681
$355$	0	0
$356$	14559.7	2.16759
$357$	211.716	0.0313871
$358$	19560.4	2.88771
$359$	−7990.36	−1.17469	−0.587347	−	0.809335i	$-0.699827\pi$
$359$	−7990.36	−1.17469	−0.587347	+	0.809335i	$0.699827\pi$
$360$	0	0
$361$	−506.193	−0.0737998
$362$	14427.1	2.09468
$363$	3514.31	0.508137
$364$	−18505.4	−2.66469
$365$	0	0
$366$	3082.29	0.440202
$367$	429.201	0.0610466	0.0305233	−	0.999534i	$-0.490283\pi$
$367$	429.201	0.0610466	0.0305233	+	0.999534i	$0.490283\pi$
$368$	16583.0	2.34905
$369$	1875.19	0.264548
$370$	0	0
$371$	3019.69	0.422572
$372$	−16.3902	−0.00228438
$373$	−6270.80	−0.870482	−0.435241	−	0.900314i	$-0.643337\pi$
$373$	−6270.80	−0.870482	−0.435241	+	0.900314i	$0.643337\pi$
$374$	472.467	0.0653227
$375$	0	0
$376$	−38127.7	−5.22948
$377$	−2442.79	−0.333714
$378$	1500.50	0.204173
$379$	10417.0	1.41183	0.705917	−	0.708294i	$-0.250535\pi$
$379$	10417.0	1.41183	0.705917	+	0.708294i	$0.250535\pi$
$380$	0	0
$381$	−4090.63	−0.550050
$382$	792.049	0.106086
$383$	−10769.3	−1.43677	−0.718387	−	0.695644i	$-0.755119\pi$
$383$	−10769.3	−1.43677	−0.718387	+	0.695644i	$0.755119\pi$
$384$	11613.0	1.54329
$385$	0	0
$386$	6249.18	0.824028
$387$	1749.84	0.229844
$388$	661.736	0.0865839
$389$	−11121.7	−1.44960	−0.724798	−	0.688961i	$-0.758067\pi$
$389$	−11121.7	−1.44960	−0.724798	+	0.688961i	$0.758067\pi$
$390$	0	0
$391$	−508.740	−0.0658008
$392$	17388.7	2.24047
$393$	4040.49	0.518616
$394$	23489.2	3.00348
$395$	0	0
$396$	2439.04	0.309511
$397$	−11286.7	−1.42686	−0.713432	−	0.700724i	$-0.752860\pi$
$397$	−11286.7	−1.42686	−0.713432	+	0.700724i	$0.752860\pi$
$398$	−8318.33	−1.04764
$399$	2448.51	0.307215
$400$	0	0
$401$	−15418.0	−1.92005	−0.960023	−	0.279922i	$-0.909691\pi$
$401$	−15418.0	−1.92005	−0.960023	+	0.279922i	$0.909691\pi$
$402$	9294.14	1.15311
$403$	−21.4506	−0.00265144
$404$	37540.1	4.62299
$405$	0	0
$406$	−1611.65	−0.197006
$407$	−510.406	−0.0621619
$408$	−1509.68	−0.183187
$409$	13849.5	1.67437	0.837183	−	0.546922i	$-0.184201\pi$
$409$	13849.5	1.67437	0.837183	+	0.546922i	$0.184201\pi$
$410$	0	0
$411$	−7525.25	−0.903147
$412$	−41025.9	−4.90583
$413$	−2009.37	−0.239406
$414$	−3605.61	−0.428034
$415$	0	0
$416$	53493.4	6.30464
$417$	−4091.85	−0.480524
$418$	5464.13	0.639376
$419$	−2793.33	−0.325688	−0.162844	−	0.986652i	$-0.552067\pi$
$419$	−2793.33	−0.325688	−0.162844	+	0.986652i	$0.552067\pi$
$420$	0	0
$421$	−3643.79	−0.421823	−0.210911	−	0.977505i	$-0.567643\pi$
$421$	−3643.79	−0.421823	−0.210911	+	0.977505i	$0.567643\pi$
$422$	−29010.4	−3.34645
$423$	4699.51	0.540185
$424$	−21532.4	−2.46629
$425$	0	0
$426$	−18347.1	−2.08666
$427$	1938.55	0.219703
$428$	−36885.0	−4.16566
$429$	3192.08	0.359243
$430$	0	0
$431$	5834.03	0.652007	0.326004	−	0.945369i	$-0.394298\pi$
$431$	5834.03	0.652007	0.326004	+	0.945369i	$0.394298\pi$
$432$	−6065.48	−0.675522
$433$	−7919.15	−0.878915	−0.439457	−	0.898263i	$-0.644829\pi$
$433$	−7919.15	−0.878915	−0.439457	+	0.898263i	$0.644829\pi$
$434$	−14.1522	−0.00156527
$435$	0	0
$436$	−16721.9	−1.83677
$437$	−5883.63	−0.644056
$438$	−9466.57	−1.03272
$439$	11696.0	1.27158	0.635788	−	0.771864i	$-0.280675\pi$
$439$	11696.0	1.27158	0.635788	+	0.771864i	$0.280675\pi$
$440$	0	0
$441$	−2143.29	−0.231432
$442$	−3150.61	−0.339049
$443$	2786.16	0.298814	0.149407	−	0.988776i	$-0.452264\pi$
$443$	2786.16	0.298814	0.149407	+	0.988776i	$0.452264\pi$
$444$	2600.66	0.277977
$445$	0	0
$446$	20531.2	2.17978
$447$	−8376.74	−0.886368
$448$	16889.5	1.78115
$449$	11013.8	1.15762	0.578811	−	0.815462i	$-0.303517\pi$
$449$	11013.8	1.15762	0.578811	+	0.815462i	$0.303517\pi$
$450$	0	0
$451$	2631.88	0.274790
$452$	−16445.2	−1.71132
$453$	−919.480	−0.0953663
$454$	−23599.8	−2.43963
$455$	0	0
$456$	−17459.6	−1.79303
$457$	−12773.5	−1.30748	−0.653739	−	0.756720i	$-0.726801\pi$
$457$	−12773.5	−1.30748	−0.653739	+	0.756720i	$0.726801\pi$
$458$	16654.2	1.69912
$459$	186.079	0.0189225
$460$	0	0
$461$	−13343.4	−1.34808	−0.674039	−	0.738696i	$-0.735442\pi$
$461$	−13343.4	−1.34808	−0.674039	+	0.738696i	$0.735442\pi$
$462$	2106.00	0.212077
$463$	−17265.4	−1.73303	−0.866514	−	0.499153i	$-0.833645\pi$
$463$	−17265.4	−1.73303	−0.866514	+	0.499153i	$0.833645\pi$
$464$	6514.78	0.651812
$465$	0	0
$466$	−1496.25	−0.148739
$467$	16016.7	1.58708	0.793538	−	0.608521i	$-0.208237\pi$
$467$	16016.7	1.58708	0.793538	+	0.608521i	$0.208237\pi$
$468$	−16264.6	−1.60647
$469$	5845.38	0.575511
$470$	0	0
$471$	−5484.46	−0.536540
$472$	14328.2	1.39727
$473$	2455.96	0.238742
$474$	−4162.06	−0.403312
$475$	0	0
$476$	−1514.06	−0.145792
$477$	2654.03	0.254759
$478$	−17002.6	−1.62695
$479$	−5847.01	−0.557738	−0.278869	−	0.960329i	$-0.589960\pi$
$479$	−5847.01	−0.557738	−0.278869	+	0.960329i	$0.589960\pi$
$480$	0	0
$481$	3403.61	0.322643
$482$	−30932.7	−2.92313
$483$	−2267.68	−0.213630
$484$	−25132.2	−2.36028
$485$	0	0
$486$	1318.80	0.123091
$487$	342.662	0.0318840	0.0159420	−	0.999873i	$-0.494925\pi$
$487$	342.662	0.0318840	0.0159420	+	0.999873i	$0.494925\pi$
$488$	−13823.2	−1.28227
$489$	6303.44	0.582927
$490$	0	0
$491$	−1673.48	−0.153815	−0.0769073	−	0.997038i	$-0.524505\pi$
$491$	−1673.48	−0.153815	−0.0769073	+	0.997038i	$0.524505\pi$
$492$	−13410.2	−1.22882
$493$	−199.863	−0.0182583
$494$	−36437.2	−3.31859
$495$	0	0
$496$	57.2074	0.00517881
$497$	−11539.1	−1.04144
$498$	16006.0	1.44026
$499$	10918.2	0.979487	0.489743	−	0.871867i	$-0.337090\pi$
$499$	10918.2	0.979487	0.489743	+	0.871867i	$0.337090\pi$
$500$	0	0
$501$	4693.58	0.418550
$502$	−9302.84	−0.827103
$503$	−16957.6	−1.50319	−0.751595	−	0.659625i	$-0.770715\pi$
$503$	−16957.6	−1.50319	−0.751595	+	0.659625i	$0.770715\pi$
$504$	−6729.31	−0.594737
$505$	0	0
$506$	−5060.58	−0.444606
$507$	−14695.2	−1.28725
$508$	29253.6	2.55496
$509$	−226.179	−0.0196959	−0.00984795	−	0.999952i	$-0.503135\pi$
$509$	−226.179	−0.0196959	−0.00984795	+	0.999952i	$0.503135\pi$
$510$	0	0
$511$	−5953.83	−0.515425
$512$	−11437.3	−0.987234
$513$	2152.02	0.185213
$514$	−4358.48	−0.374016
$515$	0	0
$516$	−12513.8	−1.06762
$517$	6595.91	0.561099
$518$	2245.55	0.190471
$519$	−8085.70	−0.683859
$520$	0	0
$521$	−2051.24	−0.172489	−0.0862443	−	0.996274i	$-0.527487\pi$
$521$	−2051.24	−0.172489	−0.0862443	+	0.996274i	$0.527487\pi$
$522$	−1416.49	−0.118770
$523$	11922.9	0.996852	0.498426	−	0.866932i	$-0.333912\pi$
$523$	11922.9	0.996852	0.498426	+	0.866932i	$0.333912\pi$
$524$	−28895.1	−2.40895
$525$	0	0
$526$	−9194.94	−0.762203
$527$	−1.75503	−0.000145067 0
$528$	−8513.09	−0.701676
$529$	−6717.89	−0.552140
$530$	0	0
$531$	−1766.06	−0.144332
$532$	−17510.3	−1.42700
$533$	−17550.5	−1.42626
$534$	11049.3	0.895412
$535$	0	0
$536$	−41681.6	−3.35890
$537$	10812.5	0.868889
$538$	−18262.1	−1.46345
$539$	−3008.17	−0.240392
$540$	0	0
$541$	12876.2	1.02327	0.511635	−	0.859203i	$-0.329040\pi$
$541$	12876.2	1.02327	0.511635	+	0.859203i	$0.329040\pi$
$542$	−43656.7	−3.45981
$543$	7974.96	0.630273
$544$	4376.69	0.344943
$545$	0	0
$546$	−14043.7	−1.10076
$547$	−9065.39	−0.708607	−0.354304	−	0.935130i	$-0.615282\pi$
$547$	−9065.39	−0.708607	−0.354304	+	0.935130i	$0.615282\pi$
$548$	53816.0	4.19508
$549$	1703.81	0.132453
$550$	0	0
$551$	−2311.43	−0.178712
$552$	16170.1	1.24682
$553$	−2617.65	−0.201291
$554$	−37835.7	−2.90160
$555$	0	0
$556$	29262.4	2.23202
$557$	19520.2	1.48492	0.742458	−	0.669893i	$-0.233660\pi$
$557$	19520.2	1.48492	0.742458	+	0.669893i	$0.233660\pi$
$558$	−12.4385	−0.000943660 0
$559$	−16377.4	−1.23916
$560$	0	0
$561$	261.168	0.0196551
$562$	10403.5	0.780866
$563$	−9786.46	−0.732593	−0.366297	−	0.930498i	$-0.619374\pi$
$563$	−9786.46	−0.732593	−0.366297	+	0.930498i	$0.619374\pi$
$564$	−33608.0	−2.50914
$565$	0	0
$566$	11053.1	0.820844
$567$	829.437	0.0614340
$568$	82281.5	6.07826
$569$	13236.9	0.975257	0.487628	−	0.873051i	$-0.337862\pi$
$569$	13236.9	0.975257	0.487628	+	0.873051i	$0.337862\pi$
$570$	0	0
$571$	−21385.2	−1.56733	−0.783663	−	0.621186i	$-0.786651\pi$
$571$	−21385.2	−1.56733	−0.783663	+	0.621186i	$0.786651\pi$
$572$	−22827.8	−1.66867
$573$	437.825	0.0319204
$574$	−11579.1	−0.841987
$575$	0	0
$576$	14844.4	1.07381
$577$	−1531.13	−0.110471	−0.0552356	−	0.998473i	$-0.517591\pi$
$577$	−1531.13	−0.110471	−0.0552356	+	0.998473i	$0.517591\pi$
$578$	26405.9	1.90024
$579$	3454.39	0.247944
$580$	0	0
$581$	10066.7	0.718825
$582$	502.190	0.0357671
$583$	3725.02	0.264622
$584$	42454.9	3.00821
$585$	0	0
$586$	−9522.25	−0.671263
$587$	−2742.12	−0.192810	−0.0964050	−	0.995342i	$-0.530734\pi$
$587$	−2742.12	−0.192810	−0.0964050	+	0.995342i	$0.530734\pi$
$588$	15327.5	1.07499
$589$	−20.2971	−0.00141991
$590$	0	0
$591$	12984.2	0.903723
$592$	−9077.22	−0.630188
$593$	8476.47	0.586993	0.293497	−	0.955960i	$-0.405181\pi$
$593$	8476.47	0.586993	0.293497	+	0.955960i	$0.405181\pi$
$594$	1850.98	0.127856
$595$	0	0
$596$	59905.3	4.11714
$597$	−4598.16	−0.315226
$598$	33746.2	2.30767
$599$	−14839.1	−1.01220	−0.506100	−	0.862475i	$-0.668913\pi$
$599$	−14839.1	−1.01220	−0.506100	+	0.862475i	$0.668913\pi$
$600$	0	0
$601$	−13198.6	−0.895814	−0.447907	−	0.894080i	$-0.647830\pi$
$601$	−13198.6	−0.895814	−0.447907	+	0.894080i	$0.647830\pi$
$602$	−10805.1	−0.731532
$603$	5137.56	0.346961
$604$	6575.56	0.442973
$605$	0	0
$606$	28489.1	1.90972
$607$	−2310.67	−0.154509	−0.0772547	−	0.997011i	$-0.524615\pi$
$607$	−2310.67	−0.154509	−0.0772547	+	0.997011i	$0.524615\pi$
$608$	50616.8	3.37629
$609$	−890.877	−0.0592777
$610$	0	0
$611$	−43984.4	−2.91231
$612$	−1330.72	−0.0878942
$613$	3944.92	0.259925	0.129962	−	0.991519i	$-0.458514\pi$
$613$	3944.92	0.259925	0.129962	+	0.991519i	$0.458514\pi$
$614$	48352.9	3.17811
$615$	0	0
$616$	−9444.80	−0.617762
$617$	26587.7	1.73482	0.867408	−	0.497598i	$-0.165784\pi$
$617$	26587.7	1.73482	0.867408	+	0.497598i	$0.165784\pi$
$618$	−31134.5	−2.02656
$619$	8691.35	0.564353	0.282177	−	0.959362i	$-0.408944\pi$
$619$	8691.35	0.564353	0.282177	+	0.959362i	$0.408944\pi$
$620$	0	0
$621$	−1993.09	−0.128792
$622$	40285.2	2.59693
$623$	6949.26	0.446896
$624$	56769.0	3.64195
$625$	0	0
$626$	−7889.06	−0.503690
$627$	3020.43	0.192383
$628$	39221.5	2.49221
$629$	278.474	0.0176526
$630$	0	0
$631$	−19396.9	−1.22374	−0.611869	−	0.790959i	$-0.709582\pi$
$631$	−19396.9	−1.22374	−0.611869	+	0.790959i	$0.709582\pi$
$632$	18665.7	1.17481
$633$	−16036.2	−1.00692
$634$	28239.2	1.76896
$635$	0	0
$636$	−18980.0	−1.18334
$637$	20059.8	1.24772
$638$	−1988.09	−0.123369
$639$	−10141.8	−0.627861
$640$	0	0
$641$	−11088.7	−0.683273	−0.341636	−	0.939832i	$-0.610981\pi$
$641$	−11088.7	−0.683273	−0.341636	+	0.939832i	$0.610981\pi$
$642$	−27991.9	−1.72080
$643$	3896.33	0.238968	0.119484	−	0.992836i	$-0.461876\pi$
$643$	3896.33	0.238968	0.119484	+	0.992836i	$0.461876\pi$
$644$	16217.1	0.992302
$645$	0	0
$646$	−2981.19	−0.181569
$647$	−14565.2	−0.885034	−0.442517	−	0.896760i	$-0.645914\pi$
$647$	−14565.2	−0.885034	−0.442517	+	0.896760i	$0.645914\pi$
$648$	−5914.45	−0.358552
$649$	−2478.72	−0.149920
$650$	0	0
$651$	−7.82295	−0.000470976 0
$652$	−45078.3	−2.70767
$653$	−27443.4	−1.64463	−0.822314	−	0.569034i	$-0.807317\pi$
$653$	−27443.4	−1.64463	−0.822314	+	0.569034i	$0.807317\pi$
$654$	−12690.2	−0.758756
$655$	0	0
$656$	46806.2	2.78579
$657$	−5232.88	−0.310737
$658$	−29019.0	−1.71927
$659$	10355.6	0.612135	0.306068	−	0.952010i	$-0.400987\pi$
$659$	10355.6	0.612135	0.306068	+	0.952010i	$0.400987\pi$
$660$	0	0
$661$	9704.01	0.571017	0.285508	−	0.958376i	$-0.407838\pi$
$661$	9704.01	0.571017	0.285508	+	0.958376i	$0.407838\pi$
$662$	59617.4	3.50015
$663$	−1741.58	−0.102017
$664$	−71782.6	−4.19534
$665$	0	0
$666$	1973.64	0.114830
$667$	2140.72	0.124272
$668$	−33565.6	−1.94415
$669$	11349.1	0.655879
$670$	0	0
$671$	2391.35	0.137582
$672$	19508.8	1.11990
$673$	−16876.5	−0.966629	−0.483315	−	0.875447i	$-0.660567\pi$
$673$	−16876.5	−0.966629	−0.483315	+	0.875447i	$0.660567\pi$
$674$	12456.8	0.711898
$675$	0	0
$676$	105091.	5.97924
$677$	1095.44	0.0621880	0.0310940	−	0.999516i	$-0.490101\pi$
$677$	1095.44	0.0621880	0.0310940	+	0.999516i	$0.490101\pi$
$678$	−12480.2	−0.706933
$679$	315.843	0.0178512
$680$	0	0
$681$	−13045.4	−0.734067
$682$	−17.4578	−0.000980195 0
$683$	23004.5	1.28879	0.644394	−	0.764693i	$-0.277110\pi$
$683$	23004.5	1.28879	0.644394	+	0.764693i	$0.277110\pi$
$684$	−15389.9	−0.860305
$685$	0	0
$686$	32296.4	1.79750
$687$	9206.01	0.511254
$688$	43677.5	2.42034
$689$	−24840.0	−1.37348
$690$	0	0
$691$	4973.91	0.273830	0.136915	−	0.990583i	$-0.456281\pi$
$691$	4973.91	0.273830	0.136915	+	0.990583i	$0.456281\pi$
$692$	57824.0	3.17650
$693$	1164.14	0.0638125
$694$	−28834.6	−1.57716
$695$	0	0
$696$	6352.56	0.345967
$697$	−1435.94	−0.0780344
$698$	−11321.5	−0.613933
$699$	−827.089	−0.0447545
$700$	0	0
$701$	19281.6	1.03888	0.519440	−	0.854507i	$-0.326141\pi$
$701$	19281.6	1.03888	0.519440	+	0.854507i	$0.326141\pi$
$702$	−12343.1	−0.663621
$703$	3220.58	0.172783
$704$	20834.6	1.11539
$705$	0	0
$706$	29211.0	1.55718
$707$	17917.7	0.953132
$708$	12629.8	0.670417
$709$	35391.4	1.87468	0.937342	−	0.348412i	$-0.113279\pi$
$709$	35391.4	1.87468	0.937342	+	0.348412i	$0.113279\pi$
$710$	0	0
$711$	−2300.68	−0.121353
$712$	−49553.0	−2.60826
$713$	18.7981	0.000987369 0
$714$	−1149.02	−0.0602253
$715$	0	0
$716$	−77324.3	−4.03596
$717$	−9398.60	−0.489536
$718$	43365.0	2.25399
$719$	−19325.0	−1.00237	−0.501183	−	0.865341i	$-0.667102\pi$
$719$	−19325.0	−1.00237	−0.501183	+	0.865341i	$0.667102\pi$
$720$	0	0
$721$	−19581.5	−1.01145
$722$	2747.19	0.141607
$723$	−17098.8	−0.879547
$724$	−57032.0	−2.92759
$725$	0	0
$726$	−19072.8	−0.975010
$727$	−16887.9	−0.861537	−0.430768	−	0.902462i	$-0.641757\pi$
$727$	−16887.9	−0.861537	−0.430768	+	0.902462i	$0.641757\pi$
$728$	62982.0	3.20641
$729$	729.000	0.0370370
$730$	0	0
$731$	−1339.95	−0.0677975
$732$	−12184.6	−0.615241
$733$	−6698.16	−0.337520	−0.168760	−	0.985657i	$-0.553976\pi$
$733$	−6698.16	−0.337520	−0.168760	+	0.985657i	$0.553976\pi$
$734$	−2329.35	−0.117136
$735$	0	0
$736$	−46878.6	−2.34778
$737$	7210.73	0.360394
$738$	−10176.9	−0.507613
$739$	4934.50	0.245627	0.122814	−	0.992430i	$-0.460808\pi$
$739$	4934.50	0.245627	0.122814	+	0.992430i	$0.460808\pi$
$740$	0	0
$741$	−20141.5	−0.998540
$742$	−16388.4	−0.810829
$743$	5140.65	0.253825	0.126913	−	0.991914i	$-0.459493\pi$
$743$	5140.65	0.253825	0.126913	+	0.991914i	$0.459493\pi$
$744$	55.7830	0.00274880
$745$	0	0
$746$	34032.7	1.67027
$747$	8847.73	0.433362
$748$	−1867.71	−0.0912971
$749$	−17605.0	−0.858843
$750$	0	0
$751$	9625.37	0.467690	0.233845	−	0.972274i	$-0.424869\pi$
$751$	9625.37	0.467690	0.233845	+	0.972274i	$0.424869\pi$
$752$	117304.	5.68834
$753$	−5142.37	−0.248869
$754$	13257.4	0.640328
$755$	0	0
$756$	−5931.62	−0.285358
$757$	5128.83	0.246249	0.123125	−	0.992391i	$-0.460709\pi$
$757$	5128.83	0.246249	0.123125	+	0.992391i	$0.460709\pi$
$758$	−56534.8	−2.70902
$759$	−2797.36	−0.133778
$760$	0	0
$761$	−25024.7	−1.19204	−0.596022	−	0.802968i	$-0.703253\pi$
$761$	−25024.7	−1.19204	−0.596022	+	0.802968i	$0.703253\pi$
$762$	22200.5	1.05543
$763$	−7981.28	−0.378692
$764$	−3131.05	−0.148269
$765$	0	0
$766$	58446.7	2.75687
$767$	16529.2	0.778140
$768$	−23440.6	−1.10135
$769$	−26474.8	−1.24149	−0.620746	−	0.784012i	$-0.713170\pi$
$769$	−26474.8	−1.24149	−0.620746	+	0.784012i	$0.713170\pi$
$770$	0	0
$771$	−2409.26	−0.112539
$772$	−24703.6	−1.15169
$773$	24685.1	1.14859	0.574295	−	0.818648i	$-0.305276\pi$
$773$	24685.1	1.14859	0.574295	+	0.818648i	$0.305276\pi$
$774$	−9496.69	−0.441023
$775$	0	0
$776$	−2252.18	−0.104186
$777$	1241.28	0.0573112
$778$	60359.4	2.78148
$779$	−16606.8	−0.763798
$780$	0	0
$781$	−14234.3	−0.652170
$782$	2761.02	0.126258
$783$	−783.000	−0.0357371
$784$	−53498.3	−2.43706
$785$	0	0
$786$	−21928.4	−0.995116
$787$	35383.4	1.60265	0.801323	−	0.598232i	$-0.204130\pi$
$787$	35383.4	1.60265	0.801323	+	0.598232i	$0.204130\pi$
$788$	−92855.3	−4.19776
$789$	−5082.73	−0.229341
$790$	0	0
$791$	−7849.22	−0.352827
$792$	−8301.12	−0.372434
$793$	−15946.6	−0.714098
$794$	61255.0	2.73786
$795$	0	0
$796$	32883.2	1.46421
$797$	24869.4	1.10529	0.552647	−	0.833415i	$-0.313618\pi$
$797$	24869.4	1.10529	0.552647	+	0.833415i	$0.313618\pi$
$798$	−13288.5	−0.589483
$799$	−3598.69	−0.159340
$800$	0	0
$801$	6107.77	0.269423
$802$	83676.1	3.68417
$803$	−7344.51	−0.322767
$804$	−36740.7	−1.61162
$805$	0	0
$806$	116.416	0.00508757
$807$	−10094.8	−0.440341
$808$	−127765.	−5.56284
$809$	834.568	0.0362693	0.0181346	−	0.999836i	$-0.494227\pi$
$809$	834.568	0.0362693	0.0181346	+	0.999836i	$0.494227\pi$
$810$	0	0
$811$	−17419.5	−0.754232	−0.377116	−	0.926166i	$-0.623084\pi$
$811$	−17419.5	−0.754232	−0.377116	+	0.926166i	$0.623084\pi$
$812$	6371.00	0.275343
$813$	−24132.3	−1.04103
$814$	2770.06	0.119276
$815$	0	0
$816$	4644.69	0.199260
$817$	−15496.7	−0.663600
$818$	−75163.8	−3.21276
$819$	−7762.99	−0.331210
$820$	0	0
$821$	20163.7	0.857148	0.428574	−	0.903507i	$-0.359016\pi$
$821$	20163.7	0.857148	0.428574	+	0.903507i	$0.359016\pi$
$822$	40840.8	1.73295
$823$	−10456.9	−0.442898	−0.221449	−	0.975172i	$-0.571079\pi$
$823$	−10456.9	−0.442898	−0.221449	+	0.975172i	$0.571079\pi$
$824$	139629.	5.90318
$825$	0	0
$826$	10905.2	0.459371
$827$	10943.6	0.460154	0.230077	−	0.973172i	$-0.426102\pi$
$827$	10943.6	0.460154	0.230077	+	0.973172i	$0.426102\pi$
$828$	14253.3	0.598234
$829$	−33775.8	−1.41506	−0.707528	−	0.706685i	$-0.750190\pi$
$829$	−33775.8	−1.41506	−0.707528	+	0.706685i	$0.750190\pi$
$830$	0	0
$831$	−20914.6	−0.873069
$832$	−138934.	−5.78926
$833$	1641.24	0.0682660
$834$	22207.1	0.922027
$835$	0	0
$836$	−21600.3	−0.893613
$837$	−6.87567	−0.000283940 0
$838$	15159.9	0.624927
$839$	39087.3	1.60840	0.804198	−	0.594361i	$-0.202595\pi$
$839$	39087.3	1.60840	0.804198	+	0.594361i	$0.202595\pi$
$840$	0	0
$841$	841.000	0.0344828
$842$	19775.4	0.809391
$843$	5750.81	0.234957
$844$	114681.	4.67711
$845$	0	0
$846$	−25505.1	−1.03650
$847$	−11995.5	−0.486623
$848$	66246.9	2.68270
$849$	6109.89	0.246986
$850$	0	0
$851$	−2982.73	−0.120149
$852$	72527.9	2.91639
$853$	−47274.9	−1.89761	−0.948806	−	0.315859i	$-0.897707\pi$
$853$	−47274.9	−1.89761	−0.948806	+	0.315859i	$0.897707\pi$
$854$	−10520.9	−0.421565
$855$	0	0
$856$	125536.	5.01254
$857$	−15482.0	−0.617099	−0.308550	−	0.951208i	$-0.599844\pi$
$857$	−15482.0	−0.617099	−0.308550	+	0.951208i	$0.599844\pi$
$858$	−17324.0	−0.689313
$859$	−32719.1	−1.29960	−0.649802	−	0.760103i	$-0.725148\pi$
$859$	−32719.1	−1.29960	−0.649802	+	0.760103i	$0.725148\pi$
$860$	0	0
$861$	−6400.61	−0.253348
$862$	−31662.2	−1.25107
$863$	1741.34	0.0686858	0.0343429	−	0.999410i	$-0.489066\pi$
$863$	1741.34	0.0686858	0.0343429	+	0.999410i	$0.489066\pi$
$864$	17146.5	0.675158
$865$	0	0
$866$	42978.6	1.68646
$867$	14596.5	0.571769
$868$	55.9449	0.00218767
$869$	−3229.08	−0.126052
$870$	0	0
$871$	−48084.3	−1.87058
$872$	56912.0	2.21019
$873$	277.598	0.0107620
$874$	31931.5	1.23581
$875$	0	0
$876$	37422.3	1.44336
$877$	−11848.6	−0.456213	−0.228106	−	0.973636i	$-0.573253\pi$
$877$	−11848.6	−0.456213	−0.228106	+	0.973636i	$0.573253\pi$
$878$	−63476.4	−2.43989
$879$	−5263.65	−0.201978
$880$	0	0
$881$	−29332.3	−1.12171	−0.560857	−	0.827913i	$-0.689528\pi$
$881$	−29332.3	−1.12171	−0.560857	+	0.827913i	$0.689528\pi$
$882$	11632.0	0.444070
$883$	25723.3	0.980360	0.490180	−	0.871621i	$-0.336931\pi$
$883$	25723.3	0.980360	0.490180	+	0.871621i	$0.336931\pi$
$884$	12454.7	0.473865
$885$	0	0
$886$	−15121.0	−0.573362
$887$	−10959.8	−0.414875	−0.207437	−	0.978248i	$-0.566512\pi$
$887$	−10959.8	−0.414875	−0.207437	+	0.978248i	$0.566512\pi$
$888$	−8851.20	−0.334490
$889$	13962.6	0.526762
$890$	0	0
$891$	1023.17	0.0384710
$892$	−81162.1	−3.04653
$893$	−41619.2	−1.55961
$894$	45462.0	1.70076
$895$	0	0
$896$	−39638.8	−1.47795
$897$	18654.0	0.694359
$898$	−59773.6	−2.22124
$899$	7.38497	0.000273974 0
$900$	0	0
$901$	−2032.34	−0.0751467
$902$	−14283.7	−0.527266
$903$	−5972.77	−0.220112
$904$	55970.3	2.05923
$905$	0	0
$906$	4990.17	0.182988
$907$	3053.42	0.111783	0.0558915	−	0.998437i	$-0.482200\pi$
$907$	3053.42	0.111783	0.0558915	+	0.998437i	$0.482200\pi$
$908$	93292.4	3.40971
$909$	15748.0	0.574620
$910$	0	0
$911$	−32880.5	−1.19581	−0.597903	−	0.801568i	$-0.703999\pi$
$911$	−32880.5	−1.19581	−0.597903	+	0.801568i	$0.703999\pi$
$912$	53716.2	1.95035
$913$	12418.1	0.450140
$914$	69323.8	2.50878
$915$	0	0
$916$	−65835.7	−2.37475
$917$	−13791.5	−0.496658
$918$	−1009.88	−0.0363083
$919$	−49962.9	−1.79339	−0.896694	−	0.442650i	$-0.854038\pi$
$919$	−49962.9	−1.79339	−0.896694	+	0.442650i	$0.854038\pi$
$920$	0	0
$921$	26728.2	0.956270
$922$	72416.8	2.58668
$923$	94920.7	3.38500
$924$	−8325.22	−0.296406
$925$	0	0
$926$	93702.3	3.32532
$927$	−17210.3	−0.609775
$928$	−18416.6	−0.651460
$929$	−48163.6	−1.70096	−0.850482	−	0.526004i	$-0.823690\pi$
$929$	−48163.6	−1.70096	−0.850482	+	0.526004i	$0.823690\pi$
$930$	0	0
$931$	18981.1	0.668185
$932$	5914.83	0.207883
$933$	22268.6	0.781396
$934$	−86925.3	−3.04527
$935$	0	0
$936$	55355.5	1.93307
$937$	−32244.1	−1.12419	−0.562097	−	0.827071i	$-0.690005\pi$
$937$	−32244.1	−1.12419	−0.562097	+	0.827071i	$0.690005\pi$
$938$	−31723.9	−1.10429
$939$	−4360.87	−0.151557
$940$	0	0
$941$	37391.5	1.29535	0.647677	−	0.761915i	$-0.275740\pi$
$941$	37391.5	1.29535	0.647677	+	0.761915i	$0.275740\pi$
$942$	29765.1	1.02951
$943$	15380.3	0.531125
$944$	−44082.3	−1.51987
$945$	0	0
$946$	−13328.9	−0.458097
$947$	−17887.8	−0.613807	−0.306903	−	0.951741i	$-0.599293\pi$
$947$	−17887.8	−0.613807	−0.306903	+	0.951741i	$0.599293\pi$
$948$	16453.1	0.563682
$949$	48976.4	1.67528
$950$	0	0
$951$	15609.9	0.532266
$952$	5153.02	0.175431
$953$	−20302.3	−0.690090	−0.345045	−	0.938586i	$-0.612136\pi$
$953$	−20302.3	−0.690090	−0.345045	+	0.938586i	$0.612136\pi$
$954$	−14403.9	−0.488829
$955$	0	0
$956$	67213.0	2.27387
$957$	−1098.97	−0.0371207
$958$	31732.7	1.07018
$959$	25686.1	0.864908
$960$	0	0
$961$	−29790.9	−0.999998
$962$	−18472.0	−0.619085
$963$	−15473.2	−0.517776
$964$	122280.	4.08546
$965$	0	0
$966$	12307.1	0.409911
$967$	19313.4	0.642273	0.321137	−	0.947033i	$-0.395935\pi$
$967$	19313.4	0.642273	0.321137	+	0.947033i	$0.395935\pi$
$968$	85536.0	2.84012
$969$	−1647.93	−0.0546326
$970$	0	0
$971$	−25297.3	−0.836077	−0.418038	−	0.908429i	$-0.637282\pi$
$971$	−25297.3	−0.836077	−0.418038	+	0.908429i	$0.637282\pi$
$972$	−5213.36	−0.172036
$973$	13966.8	0.460179
$974$	−1859.68	−0.0611787
$975$	0	0
$976$	42528.6	1.39478
$977$	−21461.4	−0.702776	−0.351388	−	0.936230i	$-0.614290\pi$
$977$	−21461.4	−0.702776	−0.351388	+	0.936230i	$0.614290\pi$
$978$	−34209.8	−1.11852
$979$	8572.45	0.279854
$980$	0	0
$981$	−7014.82	−0.228304
$982$	9082.24	0.295138
$983$	−14059.8	−0.456193	−0.228096	−	0.973639i	$-0.573250\pi$
$983$	−14059.8	−0.456193	−0.228096	+	0.973639i	$0.573250\pi$
$984$	45640.7	1.47863
$985$	0	0
$986$	1084.69	0.0350340
$987$	−16040.9	−0.517314
$988$	144040.	4.63818
$989$	14352.2	0.461450
$990$	0	0
$991$	−60932.3	−1.95316	−0.976578	−	0.215162i	$-0.930972\pi$
$991$	−60932.3	−1.95316	−0.976578	+	0.215162i	$0.930972\pi$
$992$	−161.720	−0.00517601
$993$	32955.0	1.05317
$994$	62624.5	1.99832
$995$	0	0
$996$	−63273.5	−2.01295
$997$	4183.32	0.132886	0.0664428	−	0.997790i	$-0.478835\pi$
$997$	4183.32	0.132886	0.0664428	+	0.997790i	$0.478835\pi$
$998$	−59254.7	−1.87943
$999$	1090.98	0.0345515

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2175.4.a.k.1.1		6
5.4	even	2		435.4.a.h.1.6	✓	6
15.14	odd	2		1305.4.a.h.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.4.a.h.1.6	✓	6	5.4	even	2
1305.4.a.h.1.1		6	15.14	odd	2
2175.4.a.k.1.1		6	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2175 = 3 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2175.a (trivial)

\(f(q)\)	\(=\)	\(q-5.42717 q^{2} -3.00000 q^{3} +21.4542 q^{4} +16.2815 q^{6} +10.2400 q^{7} -73.0180 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-5.42717 q^{2} -3.00000 q^{3} +21.4542 q^{4} +16.2815 q^{6} +10.2400 q^{7} -73.0180 q^{8} +9.00000 q^{9} +12.6318 q^{11} -64.3625 q^{12} -84.2342 q^{13} -55.5740 q^{14} +224.647 q^{16} -6.89181 q^{17} -48.8445 q^{18} -79.7045 q^{19} -30.7199 q^{21} -68.5548 q^{22} +73.8181 q^{23} +219.054 q^{24} +457.153 q^{26} -27.0000 q^{27} +219.690 q^{28} +29.0000 q^{29} +0.254654 q^{31} -635.056 q^{32} -37.8953 q^{33} +37.4030 q^{34} +193.087 q^{36} -40.4065 q^{37} +432.570 q^{38} +252.703 q^{39} +208.354 q^{41} +166.722 q^{42} +194.427 q^{43} +271.004 q^{44} -400.623 q^{46} +522.168 q^{47} -673.942 q^{48} -238.143 q^{49} +20.6754 q^{51} -1807.17 q^{52} +294.893 q^{53} +146.534 q^{54} -747.701 q^{56} +239.114 q^{57} -157.388 q^{58} -196.229 q^{59} +189.313 q^{61} -1.38205 q^{62} +92.1597 q^{63} +1649.38 q^{64} +205.664 q^{66} +570.840 q^{67} -147.858 q^{68} -221.454 q^{69} -1126.87 q^{71} -657.162 q^{72} -581.431 q^{73} +219.293 q^{74} -1709.99 q^{76} +129.349 q^{77} -1371.46 q^{78} -255.631 q^{79} +81.0000 q^{81} -1130.77 q^{82} +983.081 q^{83} -659.069 q^{84} -1055.19 q^{86} -87.0000 q^{87} -922.347 q^{88} +678.642 q^{89} -862.555 q^{91} +1583.70 q^{92} -0.763963 q^{93} -2833.89 q^{94} +1905.17 q^{96} +30.8442 q^{97} +1292.44 q^{98} +113.686 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 18 q^{3} + 51 q^{4} + 3 q^{6} - 47 q^{7} - 51 q^{8} + 54 q^{9}+O(q^{10}) \) 6 * q - q^2 - 18 * q^3 + 51 * q^4 + 3 * q^6 - 47 * q^7 - 51 * q^8 + 54 * q^9	\( 6 q - q^{2} - 18 q^{3} + 51 q^{4} + 3 q^{6} - 47 q^{7} - 51 q^{8} + 54 q^{9} + 81 q^{11} - 153 q^{12} - 169 q^{13} - 30 q^{14} + 131 q^{16} + q^{17} - 9 q^{18} + 116 q^{19} + 141 q^{21} - 90 q^{22} + 52 q^{23} + 153 q^{24} + 294 q^{26} - 162 q^{27} - 344 q^{28} + 174 q^{29} + 340 q^{31} - 499 q^{32} - 243 q^{33} + 920 q^{34} + 459 q^{36} - 332 q^{37} + 378 q^{38} + 507 q^{39} - 616 q^{41} + 90 q^{42} - 334 q^{43} - 52 q^{44} - 158 q^{46} + 85 q^{47} - 393 q^{48} + 879 q^{49} - 3 q^{51} - 2220 q^{52} + 850 q^{53} + 27 q^{54} - 624 q^{56} - 348 q^{57} - 29 q^{58} - 758 q^{59} - 36 q^{61} + 152 q^{62} - 423 q^{63} + 1795 q^{64} + 270 q^{66} - 939 q^{67} + 186 q^{68} - 156 q^{69} - 1388 q^{71} - 459 q^{72} - 1708 q^{73} - 814 q^{74} + 566 q^{76} - 2585 q^{77} - 882 q^{78} + 1250 q^{79} + 486 q^{81} - 1372 q^{82} + 748 q^{83} + 1032 q^{84} - 800 q^{86} - 522 q^{87} - 536 q^{88} + 1099 q^{89} + 539 q^{91} - 1698 q^{92} - 1020 q^{93} - 4542 q^{94} + 1497 q^{96} + 22 q^{97} + 1433 q^{98} + 729 q^{99}+O(q^{100}) \) 6 * q - q^2 - 18 * q^3 + 51 * q^4 + 3 * q^6 - 47 * q^7 - 51 * q^8 + 54 * q^9 + 81 * q^11 - 153 * q^12 - 169 * q^13 - 30 * q^14 + 131 * q^16 + q^17 - 9 * q^18 + 116 * q^19 + 141 * q^21 - 90 * q^22 + 52 * q^23 + 153 * q^24 + 294 * q^26 - 162 * q^27 - 344 * q^28 + 174 * q^29 + 340 * q^31 - 499 * q^32 - 243 * q^33 + 920 * q^34 + 459 * q^36 - 332 * q^37 + 378 * q^38 + 507 * q^39 - 616 * q^41 + 90 * q^42 - 334 * q^43 - 52 * q^44 - 158 * q^46 + 85 * q^47 - 393 * q^48 + 879 * q^49 - 3 * q^51 - 2220 * q^52 + 850 * q^53 + 27 * q^54 - 624 * q^56 - 348 * q^57 - 29 * q^58 - 758 * q^59 - 36 * q^61 + 152 * q^62 - 423 * q^63 + 1795 * q^64 + 270 * q^66 - 939 * q^67 + 186 * q^68 - 156 * q^69 - 1388 * q^71 - 459 * q^72 - 1708 * q^73 - 814 * q^74 + 566 * q^76 - 2585 * q^77 - 882 * q^78 + 1250 * q^79 + 486 * q^81 - 1372 * q^82 + 748 * q^83 + 1032 * q^84 - 800 * q^86 - 522 * q^87 - 536 * q^88 + 1099 * q^89 + 539 * q^91 - 1698 * q^92 - 1020 * q^93 - 4542 * q^94 + 1497 * q^96 + 22 * q^97 + 1433 * q^98 + 729 * q^99

Introduction

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