LMFDB - Embedded newform 243.4.e.d.55.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [243,4,Mod(28,243)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("243.28"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(243, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	243.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,3,0,3,15] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$14.3374641314$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			55.2
Character	$\chi$	$=$	243.55
Dual form			243.4.e.d.190.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.46620 + 1.26159i) q^{2} +(4.29454 - 3.60355i) q^{4} +(-0.280549 - 1.59107i) q^{5} +(26.0189 + 21.8324i) q^{7} +(4.41508 - 7.64714i) q^{8} +(2.97972 + 5.16102i) q^{10} +(4.27839 - 24.2640i) q^{11} +(-28.9704 - 10.5444i) q^{13} +(-117.730 - 42.8503i) q^{14} +(-13.4439 + 76.2442i) q^{16} +(-18.2417 - 31.5955i) q^{17} +(36.5170 - 63.2494i) q^{19} +(-6.93833 - 5.82195i) q^{20} +(15.7815 + 89.5013i) q^{22} +(51.3192 - 43.0619i) q^{23} +(115.009 - 41.8598i) q^{25} +113.720 q^{26} +190.413 q^{28} +(-222.243 + 80.8897i) q^{29} +(124.249 - 104.257i) q^{31} +(-37.3231 - 211.670i) q^{32} +(103.090 + 86.5026i) q^{34} +(27.4374 - 47.5229i) q^{35} +(93.1046 + 161.262i) q^{37} +(-46.7803 + 265.304i) q^{38} +(-13.4058 - 4.87930i) q^{40} +(205.238 + 74.7005i) q^{41} +(35.5866 - 201.821i) q^{43} +(-69.0627 - 119.620i) q^{44} +(-123.556 + 214.005i) q^{46} +(366.994 + 307.945i) q^{47} +(140.766 + 798.323i) q^{49} +(-345.833 + 290.188i) q^{50} +(-162.412 + 59.1130i) q^{52} +736.254 q^{53} -39.8060 q^{55} +(281.831 - 102.578i) q^{56} +(668.287 - 560.759i) q^{58} +(8.89301 + 50.4348i) q^{59} +(-88.6017 - 74.3457i) q^{61} +(-299.141 + 518.127i) q^{62} +(86.7288 + 150.219i) q^{64} +(-8.64921 + 49.0521i) q^{65} +(-109.443 - 39.8339i) q^{67} +(-192.195 - 69.9534i) q^{68} +(-35.1488 + 199.339i) q^{70} +(118.488 + 205.227i) q^{71} +(-23.0477 + 39.9198i) q^{73} +(-526.165 - 441.505i) q^{74} +(-71.0982 - 403.218i) q^{76} +(641.061 - 537.914i) q^{77} +(707.704 - 257.583i) q^{79} +125.081 q^{80} -805.637 q^{82} +(321.016 - 116.840i) q^{83} +(-45.1529 + 37.8878i) q^{85} +(131.266 + 744.448i) q^{86} +(-166.661 - 139.845i) q^{88} +(-455.636 + 789.185i) q^{89} +(-523.568 - 906.847i) q^{91} +(65.2167 - 369.863i) q^{92} +(-1660.57 - 604.399i) q^{94} +(-110.879 - 40.3566i) q^{95} +(-8.54286 + 48.4489i) q^{97} +(-1495.08 - 2589.55i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 3 q^{2} + 3 q^{4} + 15 q^{5} + 3 q^{7} - 75 q^{8} - 3 q^{10} + 102 q^{11} + 3 q^{13} + 285 q^{14} + 27 q^{16} - 207 q^{17} - 3 q^{19} - 84 q^{20} - 51 q^{22} - 435 q^{23} - 213 q^{25} + 1914 q^{26}+ \cdots - 4392 q^{98}+O(q^{100}) $ 48 * q + 3 * q^2 + 3 * q^4 + 15 * q^5 + 3 * q^7 - 75 * q^8 - 3 * q^10 + 102 * q^11 + 3 * q^13 + 285 * q^14 + 27 * q^16 - 207 * q^17 - 3 * q^19 - 84 * q^20 - 51 * q^22 - 435 * q^23 - 213 * q^25 + 1914 * q^26 - 12 * q^28 - 429 * q^29 - 51 * q^31 - 999 * q^32 + 225 * q^34 - 1257 * q^35 - 3 * q^37 + 2049 * q^38 - 555 * q^40 + 1284 * q^41 - 1023 * q^43 - 2211 * q^44 - 3 * q^46 - 3093 * q^47 + 1191 * q^49 + 579 * q^50 + 2781 * q^52 + 2736 * q^53 - 12 * q^55 + 1866 * q^56 + 1785 * q^58 - 5286 * q^59 - 105 * q^61 - 2118 * q^62 - 195 * q^64 + 3693 * q^65 - 1401 * q^67 + 7596 * q^68 - 1491 * q^70 - 3105 * q^71 - 219 * q^73 - 12549 * q^74 - 2001 * q^76 + 4263 * q^77 - 1401 * q^79 + 9870 * q^80 - 12 * q^82 + 5043 * q^83 - 702 * q^85 - 16131 * q^86 + 843 * q^88 - 5202 * q^89 + 267 * q^91 + 13335 * q^92 + 3864 * q^94 + 4935 * q^95 + 1812 * q^97 - 4392 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−3.46620	+	1.26159i	−1.22549	+	0.446040i	−0.872049	−	0.489419i	$-0.837209\pi$
$2$	−3.46620	+	1.26159i	−1.22549	+	0.446040i	−0.353436	+	0.935459i	$0.614987\pi$
$3$		0			0
$3$		0			0
$4$	4.29454	−	3.60355i	0.536818	−	0.450444i
$5$	−0.280549	−	1.59107i	−0.0250930	−	0.142310i	0.969687	−	0.244349i	$-0.0785743\pi$
$5$	−0.280549	−	1.59107i	−0.0250930	−	0.142310i	−0.994780	+	0.102040i	$0.967463\pi$
$6$		0			0
$7$	26.0189	+	21.8324i	1.40489	+	1.17884i	0.958880	+	0.283812i	$0.0915992\pi$
$7$	26.0189	+	21.8324i	1.40489	+	1.17884i	0.446008	+	0.895029i	$0.352845\pi$
$8$	4.41508	−	7.64714i	0.195121	−	0.337959i
$9$		0			0
$10$	2.97972	+	5.16102i	0.0942269	+	0.163206i
$11$	4.27839	−	24.2640i	0.117271	−	0.665078i	−0.868329	−	0.495988i	$-0.834806\pi$
$11$	4.27839	−	24.2640i	0.117271	−	0.665078i	0.985601	−	0.169090i	$-0.0540830\pi$
$12$		0			0
$13$	−28.9704	−	10.5444i	−0.618072	−	0.224960i	0.0139592	−	0.999903i	$-0.495557\pi$
$13$	−28.9704	−	10.5444i	−0.618072	−	0.224960i	−0.632032	+	0.774943i	$0.717779\pi$
$14$	−117.730	−	42.8503i	−2.24748	−	0.818016i
$15$		0			0
$16$	−13.4439	+	76.2442i	−0.210061	+	1.19132i
$17$	−18.2417	−	31.5955i	−0.260250	−	0.450766i	0.706058	−	0.708154i	$-0.250472\pi$
$17$	−18.2417	−	31.5955i	−0.260250	−	0.450766i	−0.966308	+	0.257387i	$0.917138\pi$
$18$		0			0
$19$	36.5170	−	63.2494i	0.440925	−	0.763705i	−0.556833	−	0.830625i	$-0.687984\pi$
$19$	36.5170	−	63.2494i	0.440925	−	0.763705i	0.997758	+	0.0669192i	$0.0213170\pi$
$20$	−6.93833	−	5.82195i	−0.0775728	−	0.0650913i
$21$		0			0
$22$	15.7815	+	89.5013i	0.152937	+	0.867352i
$23$	51.3192	−	43.0619i	0.465252	−	0.390393i	−0.379807	−	0.925066i	$-0.624010\pi$
$23$	51.3192	−	43.0619i	0.465252	−	0.390393i	0.845059	+	0.534673i	$0.179565\pi$
$24$		0			0
$25$	115.009	−	41.8598i	0.920070	−	0.334878i
$26$	113.720			0.857780
$27$		0			0
$28$	190.413			1.28517
$29$	−222.243	+	80.8897i	−1.42308	+	0.517960i	−0.934941	−	0.354803i	$-0.884548\pi$
$29$	−222.243	+	80.8897i	−1.42308	+	0.517960i	−0.488143	+	0.872764i	$0.662326\pi$
$30$		0			0
$31$	124.249	−	104.257i	0.719862	−	0.604036i	−0.207485	−	0.978238i	$-0.566528\pi$
$31$	124.249	−	104.257i	0.719862	−	0.604036i	0.927347	+	0.374202i	$0.122083\pi$
$32$	−37.3231	−	211.670i	−0.206183	−	1.16932i
$33$		0			0
$34$	103.090	+	86.5026i	0.519993	+	0.436326i
$35$	27.4374	−	47.5229i	0.132508	−	0.229510i
$36$		0			0
$37$	93.1046	+	161.262i	0.413684	+	0.716521i	0.995289	−	0.0969496i	$-0.0309086\pi$
$37$	93.1046	+	161.262i	0.413684	+	0.716521i	−0.581605	+	0.813471i	$0.697575\pi$
$38$	−46.7803	+	265.304i	−0.199704	+	1.13258i
$39$		0			0
$40$	−13.4058	−	4.87930i	−0.0529910	−	0.0192871i
$41$	205.238	+	74.7005i	0.781776	+	0.284543i	0.701913	−	0.712263i	$-0.252330\pi$
$41$	205.238	+	74.7005i	0.781776	+	0.284543i	0.0798627	+	0.996806i	$0.474552\pi$
$42$		0			0
$43$	35.5866	−	201.821i	0.126207	−	0.715755i	−0.854377	−	0.519654i	$-0.826061\pi$
$43$	35.5866	−	201.821i	0.126207	−	0.715755i	0.980584	−	0.196101i	$-0.0628281\pi$
$44$	−69.0627	−	119.620i	−0.236627	−	0.409850i
$45$		0			0
$46$	−123.556	+	214.005i	−0.396029	+	0.685942i
$47$	366.994	+	307.945i	1.13897	+	0.955709i	0.999405	−	0.0345036i	$-0.0109850\pi$
$47$	366.994	+	307.945i	1.13897	+	0.955709i	0.139565	+	0.990213i	$0.455429\pi$
$48$		0			0
$49$	140.766	+	798.323i	0.410396	+	2.32747i
$50$	−345.833	+	290.188i	−0.978163	+	0.820777i
$51$		0			0
$52$	−162.412	+	59.1130i	−0.433124	+	0.157644i
$53$	736.254			1.90816			0.954078	−	0.299559i	$-0.0968396\pi$
$53$	736.254			1.90816			0.954078	+	0.299559i	$0.0968396\pi$
$54$		0			0
$55$	−39.8060			−0.0975898
$56$	281.831	−	102.578i	0.672523	−	0.244778i
$57$		0			0
$58$	668.287	−	560.759i	1.51294	−	1.26951i
$59$	8.89301	+	50.4348i	0.0196232	+	0.111289i	0.993046	−	0.117726i	$-0.0375605\pi$
$59$	8.89301	+	50.4348i	0.0196232	+	0.111289i	−0.973423	+	0.229015i	$0.926449\pi$
$60$		0			0
$61$	−88.6017	−	74.3457i	−0.185972	−	0.156049i	0.545049	−	0.838404i	$-0.316511\pi$
$61$	−88.6017	−	74.3457i	−0.185972	−	0.156049i	−0.731021	+	0.682355i	$0.760956\pi$
$62$	−299.141	+	518.127i	−0.612756	+	1.06133i
$63$		0			0
$64$	86.7288	+	150.219i	0.169392	+	0.293396i
$65$	−8.64921	+	49.0521i	−0.0165047	+	0.0936026i
$66$		0			0
$67$	−109.443	−	39.8339i	−0.199561	−	0.0726341i	0.240306	−	0.970697i	$-0.422752\pi$
$67$	−109.443	−	39.8339i	−0.199561	−	0.0726341i	−0.439867	+	0.898063i	$0.644974\pi$
$68$	−192.195	−	69.9534i	−0.342752	−	0.124751i
$69$		0			0
$70$	−35.1488	+	199.339i	−0.0600154	+	0.340364i
$71$	118.488	+	205.227i	0.198055	+	0.343042i	0.947898	−	0.318575i	$-0.103204\pi$
$71$	118.488	+	205.227i	0.198055	+	0.343042i	−0.749843	+	0.661616i	$0.769871\pi$
$72$		0			0
$73$	−23.0477	+	39.9198i	−0.0369524	+	0.0640035i	−0.883910	−	0.467657i	$-0.845098\pi$
$73$	−23.0477	+	39.9198i	−0.0369524	+	0.0640035i	0.846958	+	0.531660i	$0.178432\pi$
$74$	−526.165	−	441.505i	−0.826561	−	0.693567i
$75$		0			0
$76$	−71.0982	−	403.218i	−0.107310	−	0.608583i
$77$	641.061	−	537.914i	0.948775	−	0.796117i
$78$		0			0
$79$	707.704	−	257.583i	1.00789	−	0.366840i	0.215265	−	0.976556i	$-0.430939\pi$
$79$	707.704	−	257.583i	1.00789	−	0.366840i	0.792620	+	0.609716i	$0.208716\pi$
$80$	125.081			0.174807
$81$		0			0
$82$	−805.637			−1.08497
$83$	321.016	−	116.840i	0.424531	−	0.154517i	−0.120915	−	0.992663i	$-0.538583\pi$
$83$	321.016	−	116.840i	0.424531	−	0.154517i	0.545445	+	0.838146i	$0.316361\pi$
$84$		0			0
$85$	−45.1529	+	37.8878i	−0.0576179	+	0.0483472i
$86$	131.266	+	744.448i	0.164591	+	0.933441i
$87$		0			0
$88$	−166.661	−	139.845i	−0.201887	−	0.169404i
$89$	−455.636	+	789.185i	−0.542667	+	0.939926i	0.456083	+	0.889937i	$0.349252\pi$
$89$	−455.636	+	789.185i	−0.542667	+	0.939926i	−0.998750	+	0.0499890i	$0.984081\pi$
$90$		0			0
$91$	−523.568	−	906.847i	−0.603131	−	1.04465i
$92$	65.2167	−	369.863i	0.0739056	−	0.419140i
$93$		0			0
$94$	−1660.57	−	604.399i	−1.82208	−	0.663181i
$95$	−110.879	−	40.3566i	−0.119747	−	0.0435843i
$96$		0			0
$97$	−8.54286	+	48.4489i	−0.00894222	+	0.0507139i	−0.988952	−	0.148234i	$-0.952641\pi$
$97$	−8.54286	+	48.4489i	−0.00894222	+	0.0507139i	0.980010	+	0.198948i	$0.0637523\pi$
$98$	−1495.08	−	2589.55i	−1.54108	−	2.66923i
$99$		0			0
$100$	343.066	−	594.208i	0.343066	−	0.594208i
$101$	−831.496	−	697.708i	−0.819178	−	0.687372i	0.133602	−	0.991035i	$-0.457346\pi$
$101$	−831.496	−	697.708i	−0.819178	−	0.687372i	−0.952779	+	0.303663i	$0.901790\pi$
$102$		0			0
$103$	−99.0327	−	561.642i	−0.0947377	−	0.537284i	−0.994827	−	0.101579i	$-0.967610\pi$
$103$	−99.0327	−	561.642i	−0.0947377	−	0.537284i	0.900090	−	0.435704i	$-0.143501\pi$
$104$	−208.541	+	174.987i	−0.196626	+	0.164989i
$105$		0			0
$106$	−2552.00	+	928.852i	−2.33842	+	0.851114i
$107$	−360.258			−0.325490			−0.162745	−	0.986668i	$-0.552035\pi$
$107$	−360.258			−0.325490			−0.162745	+	0.986668i	$0.552035\pi$
$108$		0			0
$109$	895.448			0.786866			0.393433	−	0.919353i	$-0.371287\pi$
$109$	895.448			0.786866			0.393433	+	0.919353i	$0.371287\pi$
$110$	137.975	−	50.2189i	0.119595	−	0.0435289i
$111$		0			0
$112$	−2014.39	+	1690.28i	−1.69948	+	1.42604i
$113$	−9.31309	−	52.8172i	−0.00775312	−	0.0439701i	0.980686	−	0.195590i	$-0.0626622\pi$
$113$	−9.31309	−	52.8172i	−0.00775312	−	0.0439701i	−0.988439	+	0.151620i	$0.951551\pi$
$114$		0			0
$115$	−82.9121	−	69.5715i	−0.0672312	−	0.0564137i
$116$	−662.941	+	1148.25i	−0.530625	+	0.919069i
$117$		0			0
$118$	−94.4530	−	163.597i	−0.0736874	−	0.127630i
$119$	215.179	−	1220.34i	0.165760	−	0.940070i
$120$		0			0
$121$	680.295	+	247.607i	0.511116	+	0.186031i
$122$	400.905	+	145.917i	0.297510	+	0.108285i
$123$		0			0
$124$	157.896	−	895.473i	0.114351	−	0.648515i
$125$	−199.843	−	346.139i	−0.142996	−	0.247677i
$126$		0			0
$127$	432.376	−	748.897i	0.302104	−	0.523259i	−0.674509	−	0.738267i	$-0.735644\pi$
$127$	432.376	−	748.897i	0.302104	−	0.523259i	0.976612	+	0.215008i	$0.0689778\pi$
$128$	827.066	+	693.991i	0.571117	+	0.479224i
$129$		0			0
$130$	−31.9039	−	180.936i	−0.0215243	−	0.122070i
$131$	426.126	−	357.562i	0.284205	−	0.238476i	−0.489529	−	0.871987i	$-0.662831\pi$
$131$	426.126	−	357.562i	0.284205	−	0.238476i	0.773734	+	0.633511i	$0.218387\pi$
$132$		0			0
$133$	2331.02	−	848.422i	1.51974	−	0.553139i
$134$	429.604			0.276956
$135$		0			0
$136$	−322.153			−0.203121
$137$	−816.605	+	297.220i	−0.509250	+	0.185352i	−0.583850	−	0.811862i	$-0.698454\pi$
$137$	−816.605	+	297.220i	−0.509250	+	0.185352i	0.0745996	+	0.997214i	$0.476232\pi$
$138$		0			0
$139$	710.568	−	596.237i	0.433594	−	0.363829i	−0.399712	−	0.916641i	$-0.630890\pi$
$139$	710.568	−	596.237i	0.433594	−	0.363829i	0.833306	+	0.552812i	$0.186445\pi$
$140$	−53.4202	−	302.961i	−0.0322488	−	0.182892i
$141$		0			0
$142$	−669.614	−	561.873i	−0.395724	−	0.332052i
$143$	−379.795	+	657.824i	−0.222098	+	0.384685i
$144$		0			0
$145$	191.051	+	330.910i	0.109420	+	0.189521i
$146$	29.5253	−	167.446i	0.0167365	−	0.0949176i
$147$		0			0
$148$	980.957	+	357.039i	0.544825	+	0.198300i
$149$	1577.08	+	574.009i	0.867109	+	0.315602i	0.736996	−	0.675897i	$-0.236244\pi$
$149$	1577.08	+	574.009i	0.867109	+	0.315602i	0.130113	+	0.991499i	$0.458466\pi$
$150$		0			0
$151$	−427.510	+	2424.53i	−0.230399	+	1.30666i	0.621690	+	0.783263i	$0.286446\pi$
$151$	−427.510	+	2424.53i	−0.230399	+	1.30666i	−0.852090	+	0.523396i	$0.824665\pi$
$152$	−322.451	−	558.502i	−0.172067	−	0.298030i
$153$		0			0
$154$	−1543.41	+	2673.27i	−0.807609	+	1.39882i
$155$	−200.738	−	168.439i	−0.104024	−	0.0872863i
$156$		0			0
$157$	−483.749	−	2743.48i	−0.245907	−	1.39461i	−0.818377	−	0.574681i	$-0.805126\pi$
$157$	−483.749	−	2743.48i	−0.245907	−	1.39461i	0.572471	−	0.819925i	$-0.305985\pi$
$158$	−2128.08	+	1785.67i	−1.07152	+	0.899114i
$159$		0			0
$160$	−326.311	+	118.767i	−0.161232	+	0.0586836i
$161$	2275.42			1.11384
$162$		0			0
$163$	−2058.86			−0.989337			−0.494669	−	0.869082i	$-0.664711\pi$
$163$	−2058.86			−0.989337			−0.494669	+	0.869082i	$0.664711\pi$
$164$	1150.59	−	418.781i	0.547842	−	0.199398i
$165$		0			0
$166$	−965.298	+	809.981i	−0.451335	+	0.378715i
$167$	−64.6444	−	366.617i	−0.0299541	−	0.169878i	0.966161	−	0.257940i	$-0.0830437\pi$
$167$	−64.6444	−	366.617i	−0.0299541	−	0.169878i	−0.996115	+	0.0880620i	$0.971933\pi$
$168$		0			0
$169$	−954.899	−	801.256i	−0.434638	−	0.364704i
$170$	108.710	−	188.291i	0.0490451	−	0.0849487i
$171$		0			0
$172$	−574.445	−	994.968i	−0.254657	−	0.441079i
$173$	−297.266	+	1685.88i	−0.130640	+	0.740897i	0.847157	+	0.531343i	$0.178312\pi$
$173$	−297.266	+	1685.88i	−0.130640	+	0.740897i	−0.977797	+	0.209554i	$0.932799\pi$
$174$		0			0
$175$	3906.30	+	1421.78i	1.68736	+	0.614150i
$176$	1792.47	+	652.405i	0.767684	+	0.279414i
$177$		0			0
$178$	583.695	−	3310.30i	0.245785	−	1.39392i
$179$	1512.45	+	2619.64i	0.631540	+	1.09386i	0.987237	+	0.159258i	$0.0509100\pi$
$179$	1512.45	+	2619.64i	0.631540	+	1.09386i	−0.355697	+	0.934601i	$0.615757\pi$
$180$		0			0
$181$	33.5721	−	58.1486i	0.0137867	−	0.0238793i	−0.859050	−	0.511892i	$-0.828945\pi$
$181$	33.5721	−	58.1486i	0.0137867	−	0.0238793i	0.872836	+	0.488013i	$0.162278\pi$
$182$	2958.86	+	2482.78i	1.20508	+	1.01119i
$183$		0			0
$184$	−102.722	−	582.567i	−0.0411565	−	0.233410i
$185$	230.459	−	193.378i	0.0915873	−	0.0768509i
$186$		0			0
$187$	−844.677	+	307.437i	−0.330315	+	0.120225i
$188$	2685.76			1.04191
$189$		0			0
$190$	435.242			0.166188
$191$	−950.341	+	345.896i	−0.360022	+	0.131037i	−0.515697	−	0.856771i	$-0.672467\pi$
$191$	−950.341	+	345.896i	−0.360022	+	0.131037i	0.155675	+	0.987808i	$0.450245\pi$
$192$		0			0
$193$	153.570	−	128.860i	0.0572757	−	0.0480600i	−0.613700	−	0.789539i	$-0.710320\pi$
$193$	153.570	−	128.860i	0.0572757	−	0.0480600i	0.670976	+	0.741479i	$0.265875\pi$
$194$	−31.5116	−	178.711i	−0.0116619	−	0.0661377i
$195$		0			0
$196$	3481.32	+	2921.17i	1.26870	+	1.06457i
$197$	−1376.86	+	2384.79i	−0.497954	+	0.862482i	−0.999997	−	0.00236077i	$-0.999249\pi$
$197$	−1376.86	+	2384.79i	−0.497954	+	0.862482i	0.502043	+	0.864843i	$0.332582\pi$
$198$		0			0
$199$	2395.21	+	4148.63i	0.853227	+	1.47783i	0.878280	+	0.478146i	$0.158691\pi$
$199$	2395.21	+	4148.63i	0.853227	+	1.47783i	−0.0250538	+	0.999686i	$0.507976\pi$
$200$	187.665	−	1064.30i	0.0663497	−	0.376288i
$201$		0			0
$202$	3762.35	+	1369.38i	1.31049	+	0.476978i
$203$	−7548.53	−	2747.44i	−2.60987	−	0.949914i
$204$		0			0
$205$	61.2745	−	347.505i	0.0208761	−	0.118394i
$206$	1051.83	+	1821.82i	0.355750	+	0.616177i
$207$		0			0
$208$	1193.42	−	2067.07i	0.397831	−	0.689064i
$209$	−1378.45	−	1156.65i	−0.456216	−	0.382811i
$210$		0			0
$211$	170.318	+	965.919i	0.0555694	+	0.315150i	0.999904	−	0.0138360i	$-0.00440428\pi$
$211$	170.318	+	965.919i	0.0555694	+	0.315150i	−0.944335	+	0.328986i	$0.893293\pi$
$212$	3161.87	−	2653.13i	1.02433	−	0.859516i
$213$		0			0
$214$	1248.72	−	454.499i	0.398883	−	0.145182i
$215$	−331.096			−0.105026
$216$		0			0
$217$	5509.00			1.72339
$218$	−3103.80	+	1129.69i	−0.964293	+	0.350974i
$219$		0			0
$220$	−170.948	+	143.443i	−0.0523879	+	0.0439587i
$221$	195.314	+	1107.68i	0.0594490	+	0.337152i
$222$		0			0
$223$	356.556	+	299.186i	0.107071	+	0.0898429i	0.694751	−	0.719250i	$-0.255514\pi$
$223$	356.556	+	299.186i	0.107071	+	0.0898429i	−0.587681	+	0.809093i	$0.699959\pi$
$224$	3650.16	−	6322.27i	1.08878	−	1.88582i
$225$		0			0
$226$	98.9147	+	171.325i	0.0291138	+	0.0504265i
$227$	−816.851	+	4632.59i	−0.238838	+	1.35452i	0.595539	+	0.803326i	$0.296938\pi$
$227$	−816.851	+	4632.59i	−0.238838	+	1.35452i	−0.834378	+	0.551193i	$0.814173\pi$
$228$		0			0
$229$	−1473.51	−	536.315i	−0.425207	−	0.154763i	0.120548	−	0.992708i	$-0.461535\pi$
$229$	−1473.51	−	536.315i	−0.425207	−	0.154763i	−0.545755	+	0.837945i	$0.683757\pi$
$230$	375.160	+	136.547i	0.107554	+	0.0391463i
$231$		0			0
$232$	−362.644	+	2056.66i	−0.102624	+	0.582009i
$233$	−2879.03	−	4986.62i	−0.809491	−	1.40208i	−0.913217	−	0.407473i	$-0.866410\pi$
$233$	−2879.03	−	4986.62i	−0.809491	−	1.40208i	0.103727	−	0.994606i	$-0.466923\pi$
$234$		0			0
$235$	387.002	−	670.307i	0.107426	−	0.186068i
$236$	219.936	+	184.548i	0.0606635	+	0.0509027i
$237$		0			0
$238$	793.719	+	4501.40i	0.216173	+	1.22598i
$239$	2467.38	−	2070.38i	0.667788	−	0.560341i	−0.244622	−	0.969619i	$-0.578664\pi$
$239$	2467.38	−	2070.38i	0.667788	−	0.560341i	0.912410	+	0.409278i	$0.134219\pi$
$240$		0			0
$241$	2555.58	−	930.155i	0.683068	−	0.248616i	0.0229036	−	0.999738i	$-0.492709\pi$
$241$	2555.58	−	930.155i	0.683068	−	0.248616i	0.660164	+	0.751121i	$0.270487\pi$
$242$	−2670.42			−0.709342
$243$		0			0
$244$	−648.412			−0.170124
$245$	1230.70	−	447.937i	0.320923	−	0.116807i
$246$		0			0
$247$	−1724.84	+	1447.31i	−0.444327	+	0.372835i
$248$	−248.701	−	1410.45i	−0.0636794	−	0.361144i
$249$		0			0
$250$	1129.38	+	947.664i	0.285714	+	0.239742i
$251$	2711.14	−	4695.84i	0.681777	−	1.18087i	−0.292661	−	0.956216i	$-0.594541\pi$
$251$	2711.14	−	4695.84i	0.681777	−	1.18087i	0.974438	−	0.224656i	$-0.0721258\pi$
$252$		0			0
$253$	−825.290	−	1429.44i	−0.205081	−	0.355211i
$254$	−553.897	+	3141.31i	−0.136829	+	0.775996i
$255$		0			0
$256$	−5046.28	−	1836.70i	−1.23200	−	0.448412i
$257$	−993.871	−	361.739i	−0.241229	−	0.0878003i	0.218576	−	0.975820i	$-0.429859\pi$
$257$	−993.871	−	361.739i	−0.241229	−	0.0878003i	−0.459806	+	0.888020i	$0.652081\pi$
$258$		0			0
$259$	−1098.26	+	6228.56i	−0.263485	+	1.49430i
$260$	139.617	+	241.824i	0.0333027	+	0.0576819i
$261$		0			0
$262$	−1025.94	+	1776.98i	−0.241919	+	0.419016i
$263$	−4050.88	−	3399.09i	−0.949764	−	0.796947i	0.0294937	−	0.999565i	$-0.490610\pi$
$263$	−4050.88	−	3399.09i	−0.949764	−	0.796947i	−0.979258	+	0.202618i	$0.935055\pi$
$264$		0			0
$265$	−206.555	−	1171.43i	−0.0478814	−	0.271549i
$266$	−7009.41	+	5881.60i	−1.61569	+	1.35573i
$267$		0			0
$268$	−613.550	+	223.314i	−0.139845	+	0.0508995i
$269$	−7352.28			−1.66646			−0.833228	−	0.552930i	$-0.813510\pi$
$269$	−7352.28			−1.66646			−0.833228	+	0.552930i	$0.813510\pi$
$270$		0			0
$271$	3845.21			0.861917			0.430959	−	0.902372i	$-0.358175\pi$
$271$	3845.21			0.861917			0.430959	+	0.902372i	$0.358175\pi$
$272$	2654.21	−	966.053i	0.591673	−	0.215351i
$273$		0			0
$274$	2455.54	−	2060.45i	0.541404	−	0.454292i
$275$	−523.632	−	2969.66i	−0.114822	−	0.651191i
$276$		0			0
$277$	−2913.16	−	2444.43i	−0.631894	−	0.530222i	0.269623	−	0.962966i	$-0.413101\pi$
$277$	−2913.16	−	2444.43i	−0.631894	−	0.530222i	−0.901517	+	0.432744i	$0.857545\pi$
$278$	−1710.76	+	2963.12i	−0.369081	+	0.639267i
$279$		0			0
$280$	−242.276	−	419.635i	−0.0517099	−	0.0895642i
$281$	950.077	−	5388.15i	0.201697	−	1.14388i	−0.700856	−	0.713302i	$-0.747199\pi$
$281$	950.077	−	5388.15i	0.201697	−	1.14388i	0.902553	−	0.430578i	$-0.141690\pi$
$282$		0			0
$283$	−5798.32	−	2110.42i	−1.21793	−	0.443290i	−0.348482	−	0.937315i	$-0.613303\pi$
$283$	−5798.32	−	2110.42i	−1.21793	−	0.443290i	−0.869448	+	0.494025i	$0.835525\pi$
$284$	1248.40	+	454.379i	0.260840	+	0.0949381i
$285$		0			0
$286$	486.538	−	2759.29i	0.100593	−	0.570491i
$287$	3709.17	+	6424.47i	0.762876	+	1.32134i
$288$		0			0
$289$	1790.98	−	3102.08i	0.364540	−	0.631401i
$290$	−1079.69	−	905.971i	−0.218627	−	0.183450i
$291$		0			0
$292$	44.8736	+	254.491i	0.00899324	+	0.0510032i
$293$	1208.96	−	1014.44i	0.241052	−	0.202267i	−0.514256	−	0.857637i	$-0.671932\pi$
$293$	1208.96	−	1014.44i	0.241052	−	0.202267i	0.755308	+	0.655370i	$0.227487\pi$
$294$		0			0
$295$	77.7503	−	28.2988i	0.0153451	−	0.00558515i
$296$	1644.26			0.322873
$297$		0			0
$298$	−6190.63			−1.20340
$299$	−1940.80	+	706.393i	−0.375382	+	0.136628i
$300$		0			0
$301$	5332.18	−	4474.23i	1.02107	−	0.856778i
$302$	−1576.93	−	8943.24i	−0.300471	−	1.70406i
$303$		0			0
$304$	4331.46	+	3634.53i	0.817192	+	0.685706i
$305$	−93.4321	+	161.829i	−0.0175407	+	0.0303813i
$306$		0			0
$307$	−2688.23	−	4656.16i	−0.499758	−	0.865606i	0.500242	−	0.865886i	$-0.333244\pi$
$307$	−2688.23	−	4656.16i	−0.499758	−	0.865606i	−1.00000		0.000279643i	$0.999911\pi$
$308$	814.664	−	4620.19i	0.150714	−	0.854739i
$309$		0			0
$310$	908.299	+	330.594i	0.166413	+	0.0605693i
$311$	5781.99	+	2104.47i	1.05423	+	0.383710i	0.810259	−	0.586072i	$-0.199326\pi$
$311$	5781.99	+	2104.47i	1.05423	+	0.383710i	0.243974	+	0.969782i	$0.421549\pi$
$312$		0			0
$313$	1275.33	−	7232.74i	0.230306	−	1.30613i	−0.621971	−	0.783040i	$-0.713668\pi$
$313$	1275.33	−	7232.74i	0.230306	−	1.30613i	0.852277	−	0.523090i	$-0.175221\pi$
$314$	5137.91	+	8899.13i	0.923405	+	1.59939i
$315$		0			0
$316$	2111.05	−	3656.45i	0.375810	−	0.650922i
$317$	785.913	+	659.459i	0.139247	+	0.116842i	0.709751	−	0.704453i	$-0.248808\pi$
$317$	785.913	+	659.459i	0.139247	+	0.116842i	−0.570504	+	0.821295i	$0.693252\pi$
$318$		0			0
$319$	1011.86	+	5738.57i	0.177597	+	1.00720i
$320$	214.677	−	180.135i	0.0375025	−	0.0314683i
$321$		0			0
$322$	−7887.04	+	2870.65i	−1.36499	+	0.496816i
$323$	−2664.53			−0.459004
$324$		0			0
$325$	−3773.23			−0.644004
$326$	7136.39	−	2597.44i	1.21242	−	0.441284i
$327$		0			0
$328$	1477.39	−	1239.68i	0.248705	−	0.208688i
$329$	2825.60	+	16024.8i	0.473496	+	2.68533i
$330$		0			0
$331$	−4414.18	−	3703.94i	−0.733008	−	0.615066i	0.197942	−	0.980214i	$-0.436574\pi$
$331$	−4414.18	−	3703.94i	−0.733008	−	0.615066i	−0.930950	+	0.365147i	$0.881019\pi$
$332$	957.576	−	1658.57i	0.158295	−	0.274174i
$333$		0			0
$334$	686.591	+	1189.21i	0.112481	+	0.194822i
$335$	−32.6745	+	185.306i	−0.00532895	+	0.0302220i
$336$		0			0
$337$	−3018.97	−	1098.81i	−0.487993	−	0.177615i	0.0862929	−	0.996270i	$-0.472498\pi$
$337$	−3018.97	−	1098.81i	−0.487993	−	0.177615i	−0.574286	+	0.818655i	$0.694720\pi$
$338$	4320.73	+	1572.62i	0.695315	+	0.253074i
$339$		0			0
$340$	−57.3806	+	325.422i	−0.00915265	+	0.0519073i
$341$	−1998.11	−	3460.82i	−0.317312	−	0.549601i
$342$		0			0
$343$	−7941.72	+	13755.5i	−1.25018	+	2.16538i
$344$	−1386.24	−	1163.19i	−0.217270	−	0.182311i
$345$		0			0
$346$	−1096.51	−	6218.62i	−0.170372	−	0.966229i
$347$	−2758.50	+	2314.66i	−0.426756	+	0.358091i	−0.830726	−	0.556681i	$-0.812074\pi$
$347$	−2758.50	+	2314.66i	−0.426756	+	0.358091i	0.403970	+	0.914772i	$0.367630\pi$
$348$		0			0
$349$	1738.30	−	632.689i	0.266616	−	0.0970403i	−0.205253	−	0.978709i	$-0.565802\pi$
$349$	1738.30	−	632.689i	0.266616	−	0.0970403i	0.471869	+	0.881669i	$0.343580\pi$
$350$	−15333.7			−2.34177
$351$		0			0
$352$	−5295.63			−0.801870
$353$	−2923.41	+	1064.03i	−0.440785	+	0.160433i	−0.552873	−	0.833266i	$-0.686468\pi$
$353$	−2923.41	+	1064.03i	−0.440785	+	0.160433i	0.112088	+	0.993698i	$0.464246\pi$
$354$		0			0
$355$	293.289	−	246.098i	0.0438483	−	0.0367931i
$356$	887.118	+	5031.09i	0.132071	+	0.749010i
$357$		0			0
$358$	−8547.35	−	7172.08i	−1.26185	−	1.05882i
$359$	3228.43	−	5591.80i	0.474624	−	0.822072i	−0.524954	−	0.851131i	$-0.675918\pi$
$359$	3228.43	−	5591.80i	0.474624	−	0.822072i	0.999578	+	0.0290584i	$0.00925087\pi$
$360$		0			0
$361$	762.511	+	1320.71i	0.111169	+	0.192551i
$362$	−43.0077	+	243.909i	−0.00624429	+	0.0354131i
$363$		0			0
$364$	−5516.35	−	2007.79i	−0.794328	−	0.289112i
$365$	69.9811	+	25.4710i	0.0100356	+	0.00365265i
$366$		0			0
$367$	−906.412	+	5140.52i	−0.128922	+	0.731152i	0.849979	+	0.526816i	$0.176614\pi$
$367$	−906.412	+	5140.52i	−0.128922	+	0.731152i	−0.978901	+	0.204336i	$0.934497\pi$
$368$	2593.29	+	4491.71i	0.367350	+	0.636268i
$369$		0			0
$370$	−554.851	+	961.030i	−0.0779603	+	0.135031i
$371$	19156.5	+	16074.2i	2.68074	+	2.24941i
$372$		0			0
$373$	1006.75	+	5709.58i	0.139753	+	0.792576i	0.971432	+	0.237319i	$0.0762688\pi$
$373$	1006.75	+	5709.58i	0.139753	+	0.792576i	−0.831679	+	0.555257i	$0.812620\pi$
$374$	2539.95	−	2131.27i	0.351171	−	0.294667i
$375$		0			0
$376$	3975.20	−	1446.86i	0.545227	−	0.198447i
$377$	7291.39			0.996089
$378$		0			0
$379$	−12786.6			−1.73299			−0.866495	−	0.499185i	$-0.833633\pi$
$379$	−12786.6			−1.73299			−0.866495	+	0.499185i	$0.833633\pi$
$380$	−621.602	+	226.244i	−0.0839144	+	0.0305424i
$381$		0			0
$382$	2857.69	−	2397.89i	0.382754	−	0.321169i
$383$	649.225	+	3681.94i	0.0866158	+	0.491222i	0.996996	+	0.0774502i	$0.0246779\pi$
$383$	649.225	+	3681.94i	0.0866158	+	0.491222i	−0.910380	+	0.413772i	$0.864211\pi$
$384$		0			0
$385$	−1035.71	−	869.062i	−0.137103	−	0.115043i
$386$	−369.734	+	640.398i	−0.0487538	+	0.0844441i
$387$		0			0
$388$	137.900	+	238.851i	0.0180434	+	0.0312521i
$389$	986.228	−	5593.17i	0.128544	−	0.729011i	−0.850595	−	0.525821i	$-0.823758\pi$
$389$	986.228	−	5593.17i	0.128544	−	0.729011i	0.979139	−	0.203190i	$-0.0651308\pi$
$390$		0			0
$391$	−2296.71	−	835.934i	−0.297058	−	0.108120i
$392$	6726.38	+	2448.20i	0.866667	+	0.315441i
$393$		0			0
$394$	1763.83	−	10003.2i	0.225534	−	1.27907i
$395$	−608.378	−	1053.74i	−0.0774958	−	0.134227i
$396$		0			0
$397$	3935.17	−	6815.91i	0.497482	−	0.861664i	−0.502514	−	0.864569i	$-0.667591\pi$
$397$	3935.17	−	6815.91i	0.497482	−	0.861664i	0.999996	+	0.00290500i	$0.000924692\pi$
$398$	−13536.2	−	11358.2i	−1.70479	−	1.43049i
$399$		0			0
$400$	1645.40	+	9331.51i	0.205675	+	1.16644i
$401$	9608.42	−	8062.42i	1.19656	−	1.00403i	0.196841	−	0.980436i	$-0.436932\pi$
$401$	9608.42	−	8062.42i	1.19656	−	1.00403i	0.999721	−	0.0235993i	$-0.00751258\pi$
$402$		0			0
$403$	−4698.86	+	1710.25i	−0.580811	+	0.211398i
$404$	−6085.12			−0.749371
$405$		0			0
$406$	29630.8			3.62205
$407$	4311.19	−	1569.15i	0.525056	−	0.191105i
$408$		0			0
$409$	−6143.31	+	5154.85i	−0.742707	+	0.623205i	−0.933563	−	0.358413i	$-0.883318\pi$
$409$	−6143.31	+	5154.85i	−0.742707	+	0.623205i	0.190856	+	0.981618i	$0.438874\pi$
$410$	226.020	+	1281.82i	0.0272252	+	0.154402i
$411$		0			0
$412$	−2449.20	−	2055.13i	−0.292873	−	0.245750i
$413$	−869.728	+	1506.41i	−0.103624	+	0.179481i
$414$		0			0
$415$	−275.961	−	477.979i	−0.0326419	−	0.0565375i
$416$	−1150.66	+	6525.71i	−0.135615	+	0.769109i
$417$		0			0
$418$	6237.19	+	2270.15i	0.729835	+	0.265638i
$419$	−14549.0	−	5295.41i	−1.69634	−	0.617417i	−0.700938	−	0.713222i	$-0.747235\pi$
$419$	−14549.0	−	5295.41i	−1.69634	−	0.617417i	−0.995400	+	0.0958055i	$0.969457\pi$
$420$		0			0
$421$	−666.717	+	3781.14i	−0.0771824	+	0.437723i	0.921589	+	0.388167i	$0.126892\pi$
$421$	−666.717	+	3781.14i	−0.0771824	+	0.437723i	−0.998771	+	0.0495559i	$0.984219\pi$
$422$	−1808.95	−	3133.19i	−0.208669	−	0.361425i
$423$		0			0
$424$	3250.62	−	5630.24i	0.372321	−	0.644878i
$425$	−3420.53	−	2870.17i	−0.390400	−	0.327585i
$426$		0			0
$427$	−682.171	−	3868.78i	−0.0773128	−	0.438463i
$428$	−1547.14	+	1298.21i	−0.174729	+	0.146615i
$429$		0			0
$430$	1147.64	−	417.708i	0.128708	−	0.0468457i
$431$	−4322.86			−0.483121			−0.241560	−	0.970386i	$-0.577659\pi$
$431$	−4322.86			−0.483121			−0.241560	+	0.970386i	$0.577659\pi$
$432$		0			0
$433$	−8167.34			−0.906460			−0.453230	−	0.891394i	$-0.649728\pi$
$433$	−8167.34			−0.906460			−0.453230	+	0.891394i	$0.649728\pi$
$434$	−19095.3	+	6950.11i	−2.11199	+	0.768701i
$435$		0			0
$436$	3845.54	−	3226.79i	0.422404	−	0.354439i
$437$	−849.614	−	4818.40i	−0.0930036	−	0.527450i
$438$		0			0
$439$	5677.63	+	4764.10i	0.617263	+	0.517945i	0.896942	−	0.442149i	$-0.145784\pi$
$439$	5677.63	+	4764.10i	0.617263	+	0.517945i	−0.279679	+	0.960094i	$0.590228\pi$
$440$	−175.747	+	304.402i	−0.0190418	+	0.0329813i
$441$		0			0
$442$	−2074.44	−	3593.03i	−0.223237	−	0.386658i
$443$	1230.62	−	6979.18i	0.131983	−	0.748512i	−0.844931	−	0.534876i	$-0.820358\pi$
$443$	1230.62	−	6979.18i	0.131983	−	0.748512i	0.976913	−	0.213636i	$-0.0685306\pi$
$444$		0			0
$445$	1383.48	+	503.544i	0.147378	+	0.0536411i
$446$	−1613.34	−	587.209i	−0.171287	−	0.0623433i
$447$		0			0
$448$	−1023.05	+	5802.02i	−0.107890	+	0.611875i
$449$	5632.70	+	9756.13i	0.592035	+	1.02543i	0.993958	+	0.109761i	$0.0350085\pi$
$449$	5632.70	+	9756.13i	0.592035	+	1.02543i	−0.401923	+	0.915673i	$0.631658\pi$
$450$		0			0
$451$	2690.62	−	4660.29i	0.280923	−	0.486573i
$452$	−230.325	−	193.265i	−0.0239681	−	0.0201116i
$453$		0			0
$454$	−3013.08	−	17088.0i	−0.311477	−	1.76647i
$455$	−1295.97	+	1087.45i	−0.133530	+	0.112045i
$456$		0			0
$457$	−1891.59	+	688.481i	−0.193621	+	0.0704722i	−0.437011	−	0.899456i	$-0.643963\pi$
$457$	−1891.59	+	688.481i	−0.193621	+	0.0704722i	0.243390	+	0.969929i	$0.421741\pi$
$458$	5784.10			0.590116
$459$		0			0
$460$	−606.774			−0.0615021
$461$	12501.4	−	4550.13i	1.26301	−	0.459698i	0.378231	−	0.925711i	$-0.376532\pi$
$461$	12501.4	−	4550.13i	1.26301	−	0.459698i	0.884778	+	0.466013i	$0.154310\pi$
$462$		0			0
$463$	−13672.5	+	11472.6i	−1.37238	+	1.15157i	−0.400447	+	0.916320i	$0.631145\pi$
$463$	−13672.5	+	11472.6i	−1.37238	+	1.15157i	−0.971936	+	0.235246i	$0.924411\pi$
$464$	−3179.56	−	18032.2i	−0.318119	−	1.80414i
$465$		0			0
$466$	16270.4	+	13652.4i	1.61740	+	1.35716i
$467$	5090.74	−	8817.42i	0.504435	−	0.873708i	−0.495551	−	0.868579i	$-0.665034\pi$
$467$	5090.74	−	8817.42i	0.504435	−	0.873708i	0.999987	−	0.00512926i	$-0.00163270\pi$
$468$		0			0
$469$	−1977.91	−	3425.84i	−0.194736	−	0.337293i
$470$	−495.770	+	2811.65i	−0.0486557	+	0.275940i
$471$		0			0
$472$	424.945	+	154.667i	0.0414400	+	0.0150829i
$473$	−4744.74	−	1726.94i	−0.461233	−	0.167875i
$474$		0			0
$475$	1552.18	−	8802.83i	0.149934	−	0.850319i
$476$	−3473.46	−	6016.20i	−0.334466	−	0.579311i
$477$		0			0
$478$	−5940.44	+	10289.2i	−0.568430	+	0.984550i
$479$	−2361.56	−	1981.59i	−0.225266	−	0.189021i	0.523168	−	0.852229i	$-0.324750\pi$
$479$	−2361.56	−	1981.59i	−0.225266	−	0.189021i	−0.748435	+	0.663208i	$0.769194\pi$
$480$		0			0
$481$	−996.873	−	5653.55i	−0.0944979	−	0.535924i
$482$	−7684.66	+	6448.20i	−0.726197	+	0.609351i
$483$		0			0
$484$	3813.82	−	1388.12i	0.358172	−	0.130364i
$485$	79.4823			0.00744146
$486$		0			0
$487$	1482.64			0.137956			0.0689782	−	0.997618i	$-0.478026\pi$
$487$	1482.64			0.137956			0.0689782	+	0.997618i	$0.478026\pi$
$488$	−959.716	+	349.308i	−0.0890252	+	0.0324025i
$489$		0			0
$490$	−3700.72	+	3105.27i	−0.341187	+	0.286289i
$491$	1375.17	+	7799.00i	0.126397	+	0.716831i	0.980469	+	0.196676i	$0.0630147\pi$
$491$	1375.17	+	7799.00i	0.126397	+	0.716831i	−0.854072	+	0.520155i	$0.825874\pi$
$492$		0			0
$493$	6609.83	+	5546.30i	0.603837	+	0.506679i
$494$	4152.71	−	7192.70i	0.378217	−	0.655091i
$495$		0			0
$496$	6278.61	+	10874.9i	0.568383	+	0.984468i
$497$	−1397.68	+	7926.65i	−0.126146	+	0.715410i
$498$		0			0
$499$	7668.09	+	2790.96i	0.687918	+	0.250382i	0.662243	−	0.749289i	$-0.269605\pi$
$499$	7668.09	+	2790.96i	0.687918	+	0.250382i	0.0256742	+	0.999670i	$0.491827\pi$
$500$	−2105.56	−	766.362i	−0.188327	−	0.0685455i
$501$		0			0
$502$	−3473.12	+	19697.1i	−0.308791	+	1.75124i
$503$	−8812.36	−	15263.5i	−0.781161	−	1.35301i	−0.931266	−	0.364340i	$-0.881295\pi$
$503$	−8812.36	−	15263.5i	−0.781161	−	1.35301i	0.150105	−	0.988670i	$-0.452039\pi$
$504$		0			0
$505$	−876.827	+	1518.71i	−0.0772640	+	0.133825i
$506$	4663.99	+	3913.55i	0.409762	+	0.343831i
$507$		0			0
$508$	−841.830	−	4774.26i	−0.0735240	−	0.416975i
$509$	−6816.30	+	5719.56i	−0.593571	+	0.498065i	−0.889372	−	0.457185i	$-0.848858\pi$
$509$	−6816.30	+	5719.56i	−0.593571	+	0.498065i	0.295801	+	0.955250i	$0.404413\pi$
$510$		0			0
$511$	−1471.22	+	535.481i	−0.127364	+	0.0463567i
$512$	11171.3			0.964269
$513$		0			0
$514$	3901.32			0.334786
$515$	−865.829	+	315.136i	−0.0740834	+	0.0269642i
$516$		0			0
$517$	9042.10	−	7587.23i	0.769190	−	0.645427i
$518$	−4051.10	−	22975.0i	−0.343620	−	1.94877i
$519$		0			0
$520$	336.922	+	282.711i	0.0284134	+	0.0238417i
$521$	−9964.97	+	17259.8i	−0.837953	+	1.45138i	0.0536508	+	0.998560i	$0.482914\pi$
$521$	−9964.97	+	17259.8i	−0.837953	+	1.45138i	−0.891604	+	0.452817i	$0.850419\pi$
$522$		0			0
$523$	894.732	+	1549.72i	0.0748067	+	0.129569i	0.901002	−	0.433815i	$-0.142833\pi$
$523$	894.732	+	1549.72i	0.0748067	+	0.129569i	−0.826195	+	0.563384i	$0.809499\pi$
$524$	541.524	−	3071.13i	0.0451461	−	0.256036i
$525$		0			0
$526$	18329.4	+	6671.36i	1.51939	+	0.553013i
$527$	−5560.56	−	2023.88i	−0.459624	−	0.167289i
$528$		0			0
$529$	−1333.45	+	7562.35i	−0.109595	+	0.621546i
$530$	2193.83	+	3799.82i	0.179800	+	0.311422i
$531$		0			0
$532$	6953.34	−	12043.5i	0.566664	−	0.981491i
$533$	−5158.16	−	4328.21i	−0.419183	−	0.351736i
$534$		0			0
$535$	101.070	+	573.196i	0.00816753	+	0.0463204i
$536$	−787.814	+	661.054i	−0.0634858	+	0.0532709i
$537$		0			0
$538$	25484.5	−	9275.58i	2.04222	−	0.743306i
$539$	19972.7			1.59608
$540$		0			0
$541$	9074.21			0.721129			0.360564	−	0.932734i	$-0.382584\pi$
$541$	9074.21			0.721129			0.360564	+	0.932734i	$0.382584\pi$
$542$	−13328.2	+	4851.08i	−1.05627	+	0.384450i
$543$		0			0
$544$	−6006.97	+	5040.45i	−0.473432	+	0.397256i
$545$	−251.217	−	1424.72i	−0.0197449	−	0.111979i
$546$		0			0
$547$	−6139.27	−	5151.46i	−0.479883	−	0.402670i	0.370501	−	0.928832i	$-0.379186\pi$
$547$	−6139.27	−	5151.46i	−0.479883	−	0.402670i	−0.850384	+	0.526162i	$0.823630\pi$
$548$	−2435.90	+	4219.10i	−0.189884	+	0.328889i
$549$		0			0
$550$	5561.51	+	9632.82i	0.431170	+	0.746809i
$551$	−2999.42	+	17010.6i	−0.231905	+	1.31520i
$552$		0			0
$553$	24037.3	+	8748.88i	1.84841	+	0.672767i
$554$	13181.4	+	4797.65i	1.01088	+	0.367929i
$555$		0			0
$556$	902.994	−	5121.13i	0.0688767	−	0.390619i
$557$	3679.68	+	6373.39i	0.279915	+	0.484828i	0.971363	−	0.237598i	$-0.0763602\pi$
$557$	3679.68	+	6373.39i	0.279915	+	0.484828i	−0.691448	+	0.722426i	$0.743027\pi$
$558$		0			0
$559$	−3159.03	+	5471.61i	−0.239021	+	0.413997i
$560$	3254.48	+	2730.83i	0.245584	+	0.206069i
$561$		0			0
$562$	3504.50	+	19875.0i	0.263040	+	1.49177i
$563$	1446.33	−	1213.61i	0.108269	−	0.0908485i	−0.587046	−	0.809554i	$-0.699709\pi$
$563$	1446.33	−	1213.61i	0.108269	−	0.0908485i	0.695315	+	0.718705i	$0.255265\pi$
$564$		0			0
$565$	−81.4231	+	29.6356i	−0.00606282	+	0.00220669i
$566$	22760.6			1.69028
$567$		0			0
$568$	2092.53			0.154579
$569$	23332.6	−	8492.37i	1.71907	−	0.625692i	0.721316	−	0.692606i	$-0.243538\pi$
$569$	23332.6	−	8492.37i	1.71907	−	0.625692i	0.997759	+	0.0669139i	$0.0213153\pi$
$570$		0			0
$571$	−10810.9	+	9071.41i	−0.792332	+	0.664845i	−0.946321	−	0.323227i	$-0.895232\pi$
$571$	−10810.9	+	9071.41i	−0.792332	+	0.664845i	0.153990	+	0.988072i	$0.450788\pi$
$572$	739.456	+	4193.66i	0.0540528	+	0.306549i
$573$		0			0
$574$	−20961.8	−	17589.0i	−1.52426	−	1.27901i
$575$	4099.60	−	7100.71i	0.297330	−	0.514992i
$576$		0			0
$577$	−4690.34	−	8123.90i	−0.338408	−	0.586140i	0.645726	−	0.763570i	$-0.276555\pi$
$577$	−4690.34	−	8123.90i	−0.338408	−	0.586140i	−0.984133	+	0.177430i	$0.943222\pi$
$578$	−2294.35	+	13011.9i	−0.165108	+	0.936372i
$579$		0			0
$580$	2012.93	+	732.646i	0.144107	+	0.0524508i
$581$	10903.4	+	3968.50i	0.778568	+	0.283376i
$582$		0			0
$583$	3149.98	−	17864.4i	0.223772	−	1.26907i
$584$	203.515	+	352.498i	0.0144204	+	0.0249768i
$585$		0			0
$586$	−2910.69	+	5041.46i	−0.205187	+	0.355394i
$587$	2803.87	+	2352.73i	0.197152	+	0.165430i	0.736019	−	0.676960i	$-0.236703\pi$
$587$	2803.87	+	2352.73i	0.197152	+	0.165430i	−0.538867	+	0.842391i	$0.681148\pi$
$588$		0			0
$589$	−2057.00	−	11665.8i	−0.143900	−	0.816098i
$590$	−233.796	+	196.178i	−0.0163140	+	0.0136890i
$591$		0			0
$592$	−13547.0	+	4930.69i	−0.940502	+	0.342315i
$593$	−21034.0			−1.45660			−0.728299	−	0.685260i	$-0.759689\pi$
$593$	−21034.0			−1.45660			−0.728299	+	0.685260i	$0.759689\pi$
$594$		0			0
$595$	−2002.01			−0.137940
$596$	8841.30	−	3217.97i	0.607640	−	0.221163i
$597$		0			0
$598$	5836.01	−	4896.99i	0.399084	−	0.334871i
$599$	3124.47	+	17719.7i	0.213126	+	1.20870i	0.884129	+	0.467242i	$0.154752\pi$
$599$	3124.47	+	17719.7i	0.213126	+	1.20870i	−0.671003	+	0.741454i	$0.734136\pi$
$600$		0			0
$601$	15058.7	+	12635.7i	1.02206	+	0.857608i	0.989885	−	0.141875i	$-0.0453130\pi$
$601$	15058.7	+	12635.7i	1.02206	+	0.857608i	0.0321724	+	0.999482i	$0.489757\pi$
$602$	−12837.7	+	22235.6i	−0.869147	+	1.50541i
$603$		0			0
$604$	6900.95	+	11952.8i	0.464894	+	0.805220i
$605$	203.105	−	1151.86i	0.0136486	−	0.0774048i
$606$		0			0
$607$	−18969.8	−	6904.46i	−1.26847	−	0.461686i	−0.381868	−	0.924217i	$-0.624719\pi$
$607$	−18969.8	−	6904.46i	−1.26847	−	0.461686i	−0.886603	+	0.462531i	$0.846941\pi$
$608$	−14750.9	−	5368.89i	−0.983929	−	0.358121i
$609$		0			0
$610$	119.692	−	678.805i	0.00794454	−	0.0450557i
$611$	−7384.88	−	12791.0i	−0.488970	−	0.846920i
$612$		0			0
$613$	−2360.70	+	4088.85i	−0.155543	+	0.269408i	−0.933257	−	0.359210i	$-0.883046\pi$
$613$	−2360.70	+	4088.85i	−0.155543	+	0.269408i	0.777714	+	0.628619i	$0.216379\pi$
$614$	15192.1	+	12747.7i	0.998541	+	0.837875i
$615$		0			0
$616$	−1283.17	−	7277.21i	−0.0839292	−	0.475986i
$617$	20520.4	−	17218.6i	1.33893	−	1.12349i	0.357028	−	0.934094i	$-0.383790\pi$
$617$	20520.4	−	17218.6i	1.33893	−	1.12349i	0.981900	−	0.189401i	$-0.0606545\pi$
$618$		0			0
$619$	−25061.7	+	9121.70i	−1.62732	+	0.592297i	−0.984757	−	0.173934i	$-0.944352\pi$
$619$	−25061.7	+	9121.70i	−1.62732	+	0.592297i	−0.642566	+	0.766231i	$0.722130\pi$
$620$	−1469.06			−0.0951593
$621$		0			0
$622$	−22696.5			−1.46310
$623$	−29085.0	+	10586.1i	−1.87041	+	0.680773i
$624$		0			0
$625$	11224.8	−	9418.76i	0.718390	−	0.602800i
$626$	4704.23	+	26679.0i	0.300350	+	1.70337i
$627$		0			0
$628$	−11963.7	−	10038.8i	−0.760199	−	0.637882i
$629$	3396.76	−	5883.37i	0.215323	−	0.372950i
$630$		0			0
$631$	8435.45	+	14610.6i	0.532187	+	0.921775i	0.999294	+	0.0375740i	$0.0119630\pi$
$631$	8435.45	+	14610.6i	0.532187	+	0.921775i	−0.467107	+	0.884201i	$0.654704\pi$
$632$	1154.79	−	6549.16i	0.0726823	−	0.412202i
$633$		0			0
$634$	−3556.10	−	1294.31i	−0.222761	−	0.0810784i
$635$	−1312.85	−	477.838i	−0.0820455	−	0.0298621i
$636$		0			0
$637$	4339.76	−	24612.0i	0.269933	−	1.53087i
$638$	−10747.1	−	18614.4i	−0.666897	−	1.15510i
$639$		0			0
$640$	872.156	−	1510.62i	0.0538671	−	0.0933006i
$641$	−10763.3	−	9031.52i	−0.663224	−	0.556511i	0.247827	−	0.968804i	$-0.420283\pi$
$641$	−10763.3	−	9031.52i	−0.663224	−	0.556511i	−0.911051	+	0.412293i	$0.864728\pi$
$642$		0			0
$643$	790.815	+	4484.94i	0.0485019	+	0.275068i	0.999408	−	0.0344125i	$-0.0109560\pi$
$643$	790.815	+	4484.94i	0.0485019	+	0.275068i	−0.950906	+	0.309480i	$0.899845\pi$
$644$	9771.87	−	8199.57i	0.597928	−	0.501721i
$645$		0			0
$646$	9235.77	−	3361.54i	0.562502	−	0.204734i
$647$	23937.2			1.45451			0.727257	−	0.686366i	$-0.240795\pi$
$647$	23937.2			1.45451			0.727257	+	0.686366i	$0.240795\pi$
$648$		0			0
$649$	1261.80			0.0763171
$650$	13078.8	−	4760.28i	0.789218	−	0.287252i
$651$		0			0
$652$	−8841.84	+	7419.18i	−0.531094	+	0.445641i
$653$	2089.01	+	11847.4i	0.125191	+	0.709991i	0.981194	+	0.193022i	$0.0618288\pi$
$653$	2089.01	+	11847.4i	0.125191	+	0.709991i	−0.856004	+	0.516969i	$0.827060\pi$
$654$		0			0
$655$	−688.456	−	577.683i	−0.0410690	−	0.0344610i
$656$	−8454.68	+	14643.9i	−0.503201	+	0.871570i
$657$		0			0
$658$	−30010.8	−	51980.2i	−1.77803	−	3.07963i
$659$	−627.504	+	3558.75i	−0.0370927	+	0.210363i	−0.997721	−	0.0674734i	$-0.978506\pi$
$659$	−627.504	+	3558.75i	−0.0370927	+	0.210363i	0.960628	+	0.277836i	$0.0896173\pi$
$660$		0			0
$661$	−21121.7	−	7687.68i	−1.24287	−	0.452369i	−0.364886	−	0.931052i	$-0.618892\pi$
$661$	−21121.7	−	7687.68i	−1.24287	−	0.452369i	−0.877988	+	0.478683i	$0.841114\pi$
$662$	19973.3	+	7269.68i	1.17263	+	0.426804i
$663$		0			0
$664$	523.816	−	2970.71i	0.0306145	−	0.173623i
$665$	−2003.86	−	3470.79i	−0.116852	−	0.202393i
$666$		0			0
$667$	−7922.05	+	13721.4i	−0.459885	+	0.796544i
$668$	−1598.74	−	1341.50i	−0.0926004	−	0.0777010i
$669$		0			0
$670$	−120.525	−	683.530i	−0.00694967	−	0.0394135i
$671$	−2182.99	+	1831.75i	−0.125594	+	0.105386i
$672$		0			0
$673$	−4417.94	+	1608.00i	−0.253045	+	0.0921007i	−0.465428	−	0.885086i	$-0.654100\pi$
$673$	−4417.94	+	1608.00i	−0.253045	+	0.0921007i	0.212383	+	0.977186i	$0.431877\pi$
$674$	11850.6			0.677251
$675$		0			0
$676$	−6988.22			−0.397600
$677$	−8198.22	+	2983.91i	−0.465411	+	0.169396i	−0.564072	−	0.825725i	$-0.690766\pi$
$677$	−8198.22	+	2983.91i	−0.465411	+	0.169396i	0.0986615	+	0.995121i	$0.468544\pi$
$678$		0			0
$679$	−1280.03	+	1074.08i	−0.0723464	+	0.0607058i
$680$	90.3797	+	512.569i	0.00509691	+	0.0289060i
$681$		0			0
$682$	11292.0	+	9475.09i	0.634006	+	0.531994i
$683$	−12790.4	+	22153.6i	−0.716559	+	1.24112i	0.245796	+	0.969322i	$0.420951\pi$
$683$	−12790.4	+	22153.6i	−0.716559	+	1.24112i	−0.962355	+	0.271795i	$0.912383\pi$
$684$		0			0
$685$	701.995	+	1215.89i	0.0391560	+	0.0678202i
$686$	10173.8	−	57698.3i	0.566234	−	3.21127i
$687$		0			0
$688$	14909.3	+	5426.53i	0.826179	+	0.300705i
$689$	−21329.6	−	7763.33i	−1.17938	−	0.429259i
$690$		0			0
$691$	−5710.63	+	32386.6i	−0.314389	+	1.78299i	0.261239	+	0.965274i	$0.415869\pi$
$691$	−5710.63	+	32386.6i	−0.314389	+	1.78299i	−0.575628	+	0.817712i	$0.695242\pi$
$692$	4798.53	+	8311.30i	0.263602	+	0.456573i
$693$		0			0
$694$	6641.36	−	11503.2i	0.363260	−	0.629185i
$695$	−1148.00	−	963.289i	−0.0626565	−	0.0525750i
$696$		0			0
$697$	−1383.68	−	7847.26i	−0.0751947	−	0.426451i
$698$	−5227.09	+	4386.05i	−0.283450	+	0.237843i
$699$		0			0
$700$	21899.2	−	7970.66i	1.18245	−	0.430375i
$701$	−27261.0			−1.46881			−0.734404	−	0.678713i	$-0.762538\pi$
$701$	−27261.0			−1.46881			−0.734404	+	0.678713i	$0.762538\pi$
$702$		0			0
$703$	13599.6			0.729615
$704$	4015.96	−	1461.69i	0.214996	−	0.0782522i
$705$		0			0
$706$	8790.72	−	7376.29i	0.468616	−	0.393216i
$707$	−6401.94	−	36307.2i	−0.340551	−	1.93136i
$708$		0			0
$709$	−12883.2	−	10810.3i	−0.682422	−	0.572620i	0.234291	−	0.972167i	$-0.424723\pi$
$709$	−12883.2	−	10810.3i	−0.682422	−	0.572620i	−0.916713	+	0.399546i	$0.869168\pi$
$710$	−706.120	+	1223.04i	−0.0373243	+	0.0646475i
$711$		0			0
$712$	4023.34	+	6968.63i	0.211771	+	0.366798i
$713$	1886.84	−	10700.8i	0.0991060	−	0.562058i
$714$		0			0
$715$	1153.19	+	419.729i	0.0603175	+	0.0219538i
$716$	15935.2	+	5799.96i	0.831743	+	0.302730i
$717$		0			0
$718$	−4135.79	+	23455.2i	−0.214967	+	1.21914i
$719$	−8119.01	−	14062.5i	−0.421124	−	0.729408i	0.574926	−	0.818206i	$-0.305031\pi$
$719$	−8119.01	−	14062.5i	−0.421124	−	0.729408i	−0.996050	+	0.0887976i	$0.971698\pi$
$720$		0			0
$721$	9685.30	−	16775.4i	0.500277	−	0.866504i
$722$	−4309.21	−	3615.85i	−0.222122	−	0.186383i
$723$		0			0
$724$	−65.3644	−	370.700i	−0.00335532	−	0.0190289i
$725$	−22173.8	+	18606.1i	−1.13588	+	0.953120i
$726$		0			0
$727$	−5121.72	+	1864.15i	−0.261285	+	0.0950999i	−0.469341	−	0.883017i	$-0.655509\pi$
$727$	−5121.72	+	1864.15i	−0.261285	+	0.0950999i	0.208056	+	0.978117i	$0.433286\pi$
$728$	−9246.38			−0.470733
$729$		0			0
$730$	−274.702			−0.0139277
$731$	−7025.80	+	2557.18i	−0.355484	+	0.129386i
$732$		0			0
$733$	7753.54	−	6506.00i	0.390701	−	0.327837i	−0.426185	−	0.904636i	$-0.640143\pi$
$733$	7753.54	−	6506.00i	0.390701	−	0.327837i	0.816886	+	0.576799i	$0.195698\pi$
$734$	−3343.43	−	18961.6i	−0.168131	−	0.953520i
$735$		0			0
$736$	−11030.3	−	9255.53i	−0.552422	−	0.463537i
$737$	−1434.77	+	2485.09i	−0.0717101	+	0.124206i
$738$		0			0
$739$	458.883	+	794.808i	0.0228421	+	0.0395636i	0.877220	−	0.480088i	$-0.159395\pi$
$739$	458.883	+	794.808i	0.0228421	+	0.0395636i	−0.854378	+	0.519651i	$0.826062\pi$
$740$	292.868	−	1660.94i	0.0145487	−	0.0825098i
$741$		0			0
$742$	−86679.3	−	31548.7i	−4.28854	−	1.56090i
$743$	−12922.2	−	4703.29i	−0.638047	−	0.232230i	0.00268319	−	0.999996i	$-0.499146\pi$
$743$	−12922.2	−	4703.29i	−0.638047	−	0.232230i	−0.640730	+	0.767766i	$0.721368\pi$
$744$		0			0
$745$	470.842	−	2670.28i	0.0231548	−	0.131317i
$746$	−10692.8	−	18520.4i	−0.524785	−	0.908955i
$747$		0			0
$748$	−2519.63	+	4364.14i	−0.123164	+	0.213327i
$749$	−9373.51	−	7865.31i	−0.457277	−	0.383701i
$750$		0			0
$751$	3894.15	+	22084.8i	0.189214	+	1.07309i	0.920421	+	0.390930i	$0.127846\pi$
$751$	3894.15	+	22084.8i	0.189214	+	1.07309i	−0.731207	+	0.682156i	$0.761042\pi$
$752$	−28412.8	+	23841.2i	−1.37780	+	1.15611i
$753$		0			0
$754$	−25273.4	+	9198.76i	−1.22069	+	0.444296i
$755$	3977.53			0.191732
$756$		0			0
$757$	5900.33			0.283291			0.141645	−	0.989917i	$-0.454761\pi$
$757$	5900.33			0.283291			0.141645	+	0.989917i	$0.454761\pi$
$758$	44320.9	−	16131.5i	2.12375	−	0.772984i
$759$		0			0
$760$	−798.152	+	669.729i	−0.0380948	+	0.0319653i
$761$	1929.72	+	10944.0i	0.0919214	+	0.521312i	0.995647	+	0.0932006i	$0.0297098\pi$
$761$	1929.72	+	10944.0i	0.0919214	+	0.521312i	−0.903726	+	0.428111i	$0.859179\pi$
$762$		0			0
$763$	23298.6	+	19549.8i	1.10546	+	0.927590i
$764$	−2834.83	+	4910.06i	−0.134241	+	0.232513i
$765$		0			0
$766$	−6895.44	−	11943.3i	−0.325251	−	0.563352i
$767$	274.169	−	1554.89i	0.0129070	−	0.0731991i
$768$		0			0
$769$	−7544.46	−	2745.96i	−0.353784	−	0.128767i	0.159013	−	0.987276i	$-0.449169\pi$
$769$	−7544.46	−	2745.96i	−0.353784	−	0.128767i	−0.512798	+	0.858509i	$0.671391\pi$
$770$	4686.36	+	1705.70i	0.219331	+	0.0798300i
$771$		0			0
$772$	195.158	−	1106.79i	0.00909828	−	0.0515989i
$773$	661.004	+	1144.89i	0.0307564	+	0.0532716i	0.880994	−	0.473128i	$-0.156875\pi$
$773$	661.004	+	1144.89i	0.0307564	+	0.0532716i	−0.850238	+	0.526399i	$0.823542\pi$
$774$		0			0
$775$	9925.52	−	17191.5i	0.460045	−	0.796822i
$776$	332.779	+	279.234i	0.0153944	+	0.0129174i
$777$		0			0
$778$	3637.85	+	20631.3i	0.167639	+	0.950728i
$779$	12219.4	−	10253.3i	0.562012	−	0.471584i
$780$		0			0
$781$	5486.56	−	1996.94i	0.251376	−	0.0914933i
$782$	9015.45			0.412266
$783$		0			0
$784$	−62759.9			−2.85896
$785$	−4229.35	+	1539.36i	−0.192295	+	0.0699898i
$786$		0			0
$787$	8902.73	−	7470.28i	0.403238	−	0.338357i	−0.418506	−	0.908214i	$-0.637446\pi$
$787$	8902.73	−	7470.28i	0.403238	−	0.338357i	0.821744	+	0.569857i	$0.193002\pi$
$788$	2680.72	+	15203.1i	0.121189	+	0.687296i
$789$		0			0
$790$	3438.15	+	2884.95i	0.154840	+	0.129926i
$791$	910.812	−	1577.57i	0.0409415	−	0.0709128i
$792$		0			0
$793$	1782.90	+	3088.07i	0.0798394	+	0.138286i
$794$	−5041.16	+	28589.9i	−0.225320	+	1.27785i
$795$		0			0
$796$	25236.1	+	9185.20i	1.12371	+	0.408996i
$797$	30888.7	+	11242.6i	1.37282	+	0.499664i	0.919992	−	0.391937i	$-0.128195\pi$
$797$	30888.7	+	11242.6i	1.37282	+	0.499664i	0.452823	+	0.891600i	$0.350417\pi$
$798$		0			0
$799$	3035.08	−	17212.8i	0.134385	−	0.762133i
$800$	−13152.9	−	22781.6i	−0.581283	−	1.00681i
$801$		0			0
$802$	−23133.2	+	40067.8i	−1.01853	+	1.76414i
$803$	870.005	+	730.021i	0.0382339	+	0.0320820i
$804$		0			0
$805$	−638.365	−	3620.35i	−0.0279496	−	0.158510i
$806$	14129.5	−	11856.1i	0.617484	−	0.518130i
$807$		0			0
$808$	−9006.59	+	3278.13i	−0.392142	+	0.142728i
$809$	−19325.6			−0.839865			−0.419932	−	0.907555i	$-0.637946\pi$
$809$	−19325.6			−0.839865			−0.419932	+	0.907555i	$0.637946\pi$
$810$		0			0
$811$	20360.2			0.881556			0.440778	−	0.897616i	$-0.354703\pi$
$811$	20360.2			0.881556			0.440778	+	0.897616i	$0.354703\pi$
$812$	−42318.0	+	15402.5i	−1.82891	+	0.665667i
$813$		0			0
$814$	−12963.8	+	10877.9i	−0.558208	+	0.468392i
$815$	577.609	+	3275.78i	0.0248255	+	0.140792i
$816$		0			0
$817$	−11465.6	−	9620.75i	−0.490978	−	0.411980i
$818$	14790.6	−	25618.1i	0.632202	−	1.09501i
$819$		0			0
$820$	−989.106	−	1713.18i	−0.0421233	−	0.0729596i
$821$	3434.47	−	19477.8i	0.145997	−	0.827992i	−0.820564	−	0.571555i	$-0.806340\pi$
$821$	3434.47	−	19477.8i	0.145997	−	0.827992i	0.966561	−	0.256437i	$-0.0825486\pi$
$822$		0			0
$823$	−24904.1	−	9064.36i	−1.05480	−	0.383917i	−0.244329	−	0.969692i	$-0.578568\pi$
$823$	−24904.1	−	9064.36i	−1.05480	−	0.383917i	−0.810473	+	0.585775i	$0.800790\pi$
$824$	−4732.19	−	1722.38i	−0.200065	−	0.0728178i
$825$		0			0
$826$	1114.17	−	6318.76i	0.0469333	−	0.266172i
$827$	9829.63	+	17025.4i	0.413313	+	0.715879i	0.995250	−	0.0973550i	$-0.0310382\pi$
$827$	9829.63	+	17025.4i	0.413313	+	0.715879i	−0.581937	+	0.813234i	$0.697705\pi$
$828$		0			0
$829$	23296.2	−	40350.2i	0.976007	−	1.69049i	0.299436	−	0.954116i	$-0.403201\pi$
$829$	23296.2	−	40350.2i	0.976007	−	1.69049i	0.676571	−	0.736378i	$-0.263465\pi$
$830$	1559.55	+	1308.62i	0.0652202	+	0.0547263i
$831$		0			0
$832$	−928.607	−	5266.39i	−0.0386943	−	0.219446i
$833$	22655.6	−	19010.3i	0.942340	−	0.790717i
$834$		0			0
$835$	−565.177	+	205.708i	−0.0234237	+	0.00852551i
$836$	−10087.9			−0.417340
$837$		0			0
$838$	57110.4			2.35423
$839$	−28759.2	+	10467.5i	−1.18341	+	0.430724i	−0.857403	−	0.514645i	$-0.827924\pi$
$839$	−28759.2	+	10467.5i	−1.18341	+	0.430724i	−0.326002	+	0.945369i	$0.605702\pi$
$840$		0			0
$841$	24165.6	−	20277.4i	0.990841	−	0.831414i
$842$	−2459.28	−	13947.3i	−0.100656	−	0.570850i
$843$		0			0
$844$	4212.17	+	3534.43i	0.171788	+	0.144147i
$845$	−1006.96	+	1744.10i	−0.0409946	+	0.0710047i
$846$		0			0
$847$	12294.7	+	21295.0i	0.498760	+	0.863877i
$848$	−9898.13	+	56135.1i	−0.400829	+	2.27321i
$849$		0			0
$850$	15477.2	+	5633.24i	0.624546	+	0.227316i
$851$	11722.3	+	4266.57i	0.472192	+	0.171864i
$852$		0			0
$853$	6164.68	−	34961.7i	0.247450	−	1.40336i	−0.567284	−	0.823522i	$-0.692006\pi$
$853$	6164.68	−	34961.7i	0.247450	−	1.40336i	0.814734	−	0.579835i	$-0.196883\pi$
$854$	7245.37	+	12549.3i	0.290318	+	0.502845i
$855$		0			0
$856$	−1590.57	+	2754.94i	−0.0635099	+	0.110002i
$857$	−4073.86	−	3418.37i	−0.162381	−	0.136254i	0.557977	−	0.829857i	$-0.311578\pi$
$857$	−4073.86	−	3418.37i	−0.162381	−	0.136254i	−0.720358	+	0.693603i	$0.756022\pi$
$858$		0			0
$859$	4089.33	+	23191.7i	0.162428	+	0.921178i	0.951676	+	0.307103i	$0.0993596\pi$
$859$	4089.33	+	23191.7i	0.162428	+	0.921178i	−0.789248	+	0.614075i	$0.789529\pi$
$860$	−1421.90	+	1193.12i	−0.0563797	+	0.0473082i
$861$		0			0
$862$	14983.9	−	5453.69i	0.592057	−	0.215491i
$863$	41574.3			1.63987			0.819934	−	0.572459i	$-0.194010\pi$
$863$	41574.3			1.63987			0.819934	+	0.572459i	$0.194010\pi$
$864$		0			0
$865$	2765.75			0.108715
$866$	28309.6	−	10303.8i	1.11085	−	0.404317i
$867$		0			0
$868$	23658.6	−	19852.0i	0.925146	−	0.776289i
$869$	−3222.16	−	18273.8i	−0.125782	−	0.713342i
$870$		0			0
$871$	2750.58	+	2308.01i	0.107003	+	0.0897863i
$872$	3953.48	−	6847.62i	0.153534	−	0.265929i
$873$		0			0
$874$	9023.79	+	15629.7i	0.349238	+	0.604898i
$875$	2357.35	−	13369.2i	0.0910778	−	0.516528i
$876$		0			0
$877$	42371.4	+	15421.9i	1.63145	+	0.593799i	0.985514	−	0.169593i	$-0.0542453\pi$
$877$	42371.4	+	15421.9i	1.63145	+	0.593799i	0.645935	+	0.763392i	$0.276468\pi$
$878$	−25690.1	−	9350.44i	−0.987471	−	0.359410i
$879$		0			0
$880$	535.148	−	3034.97i	0.0204998	−	0.116260i
$881$	24958.3	+	43229.1i	0.954446	+	1.65315i	0.735631	+	0.677382i	$0.236886\pi$
$881$	24958.3	+	43229.1i	0.954446	+	1.65315i	0.218815	+	0.975766i	$0.429781\pi$
$882$		0			0
$883$	−17926.2	+	31049.0i	−0.683197	+	1.18333i	0.290803	+	0.956783i	$0.406078\pi$
$883$	−17926.2	+	31049.0i	−0.683197	+	1.18333i	−0.974000	+	0.226549i	$0.927256\pi$
$884$	4830.36	+	4053.16i	0.183781	+	0.154211i
$885$		0			0
$886$	4539.32	+	25743.7i	0.172123	+	0.976160i
$887$	6619.16	−	5554.14i	0.250563	−	0.210248i	−0.508852	−	0.860854i	$-0.669930\pi$
$887$	6619.16	−	5554.14i	0.250563	−	0.210248i	0.759415	+	0.650607i	$0.225485\pi$
$888$		0			0
$889$	27600.2	−	10045.6i	1.04126	−	0.378988i
$890$	−5430.67			−0.204535
$891$		0			0
$892$	2609.37			0.0979465
$893$	32878.8	−	11966.9i	1.23208	−	0.448441i
$894$		0			0
$895$	3743.71	−	3141.34i	0.139819	−	0.117322i
$896$	6367.83	+	36113.7i	0.237426	+	1.34651i
$897$		0			0
$898$	−31832.3	−	26710.5i	−1.18291	−	0.992583i
$899$	−19180.1	+	33220.8i	−0.711558	+	1.23245i
$900$		0			0
$901$	−13430.5	−	23262.3i	−0.496598	−	0.860132i
$902$	−3446.83	+	19548.0i	−0.127236	+	0.721592i
$903$		0			0
$904$	−445.018	−	161.973i	−0.0163729	−	0.00595925i
$905$	−101.937	−	37.1020i	−0.00374420	−	0.00136278i
$906$		0			0
$907$	−3863.48	+	21910.9i	−0.141439	+	0.802139i	0.828719	+	0.559665i	$0.189070\pi$
$907$	−3863.48	+	21910.9i	−0.141439	+	0.802139i	−0.970158	+	0.242474i	$0.922041\pi$
$908$	13185.8	+	22838.4i	0.481922	+	0.834713i
$909$		0			0
$910$	3120.17	−	5404.30i	0.113662	−	0.196869i
$911$	24282.5	+	20375.5i	0.883114	+	0.741020i	0.966817	−	0.255470i	$-0.0822303\pi$
$911$	24282.5	+	20375.5i	0.883114	+	0.741020i	−0.0837031	+	0.996491i	$0.526675\pi$
$912$		0			0
$913$	−1461.57	−	8289.00i	−0.0529804	−	0.300467i
$914$	5688.03	−	4772.82i	0.205846	−	0.172725i
$915$		0			0
$916$	−8260.70	+	3006.65i	−0.297971	+	0.108453i
$917$	18893.8			0.680401
$918$		0			0
$919$	−47605.4			−1.70877			−0.854384	−	0.519642i	$-0.826065\pi$
$919$	−47605.4			−1.70877			−0.854384	+	0.519642i	$0.826065\pi$
$920$	−898.086	+	326.877i	−0.0321837	+	0.0117139i
$921$		0			0
$922$	−37591.8	+	31543.3i	−1.34276	+	1.12671i
$923$	−1268.65	−	7194.88i	−0.0452418	−	0.256579i
$924$		0			0
$925$	17458.2	+	14649.2i	0.620566	+	0.520716i
$926$	32917.7	−	57015.2i	1.16819	−	2.02336i
$927$		0			0
$928$	25416.7	+	44023.0i	0.899078	+	1.55725i
$929$	−7601.26	+	43108.9i	−0.268449	+	1.52245i	0.490581	+	0.871395i	$0.336785\pi$
$929$	−7601.26	+	43108.9i	−0.268449	+	1.52245i	−0.759030	+	0.651055i	$0.774327\pi$
$930$		0			0
$931$	55633.8	+	20249.0i	1.95846	+	0.712820i
$932$	−30333.6	−	11040.5i	−1.06611	−	0.388031i
$933$		0			0
$934$	−6521.51	+	36985.3i	−0.228469	+	1.29571i
$935$	726.127	+	1257.69i	0.0253977	+	0.0439902i
$936$		0			0
$937$	−14470.7	+	25064.0i	−0.504522	+	0.873857i	0.495465	+	0.868628i	$0.334998\pi$
$937$	−14470.7	+	25064.0i	−0.504522	+	0.873857i	−0.999986	+	0.00522921i	$0.998335\pi$
$938$	11177.8	+	9379.31i	0.389093	+	0.326487i
$939$		0			0
$940$	−753.487	−	4273.24i	−0.0261447	−	0.148274i
$941$	−33382.2	+	28011.0i	−1.15646	+	0.970386i	−0.999851	−	0.0172745i	$-0.994501\pi$
$941$	−33382.2	+	28011.0i	−1.15646	+	0.970386i	−0.156610	+	0.987660i	$0.550057\pi$
$942$		0			0
$943$	13749.4	−	5004.37i	0.474806	−	0.172815i
$944$	−3964.92			−0.136702
$945$		0			0
$946$	18624.9			0.640113
$947$	3634.77	−	1322.95i	0.124724	−	0.0453960i	−0.278904	−	0.960319i	$-0.589971\pi$
$947$	3634.77	−	1322.95i	0.124724	−	0.0453960i	0.403628	+	0.914923i	$0.367749\pi$
$948$		0			0
$949$	1088.63	−	913.468i	0.0372375	−	0.0312460i
$950$	5725.43	+	32470.5i	0.195534	+	1.10893i
$951$		0			0
$952$	−8382.07	−	7033.39i	−0.285362	−	0.239447i
$953$	15695.5	−	27185.4i	0.533502	−	0.924053i	−0.465732	−	0.884926i	$-0.654209\pi$
$953$	15695.5	−	27185.4i	0.533502	−	0.924053i	0.999234	−	0.0391271i	$-0.0124577\pi$
$954$		0			0
$955$	816.961	+	1415.02i	0.0276819	+	0.0479465i
$956$	3135.56	−	17782.6i	0.106079	−	0.601602i
$957$		0			0
$958$	10685.6	+	3889.24i	0.360372	+	0.131165i
$959$	−27736.2	−	10095.2i	−0.933940	−	0.339926i
$960$		0			0
$961$	−604.939	+	3430.78i	−0.0203061	+	0.115162i
$962$	10587.8	+	18338.7i	0.354850	+	0.614618i
$963$		0			0
$964$	7623.18	−	13203.7i	0.254695	−	0.441145i
$965$	−248.110	−	208.189i	−0.00827662	−	0.00694491i
$966$		0			0
$967$	−4471.30	−	25358.0i	−0.148694	−	0.843287i	−0.964326	−	0.264716i	$-0.914722\pi$
$967$	−4471.30	−	25358.0i	−0.148694	−	0.843287i	0.815632	−	0.578571i	$-0.196389\pi$
$968$	4897.04	−	4109.11i	0.162600	−	0.136438i
$969$		0			0
$970$	−275.501	+	100.274i	−0.00911940	+	0.00331919i
$971$	−28752.1			−0.950258			−0.475129	−	0.879916i	$-0.657599\pi$
$971$	−28752.1			−0.950258			−0.475129	+	0.879916i	$0.657599\pi$
$972$		0			0
$973$	31505.5			1.03805
$974$	−5139.12	+	1870.49i	−0.169064	+	0.0615341i
$975$		0			0
$976$	6859.58	−	5755.87i	0.224969	−	0.188771i
$977$	−717.456	−	4068.90i	−0.0234938	−	0.133240i	0.970805	−	0.239870i	$-0.0771050\pi$
$977$	−717.456	−	4068.90i	−0.0234938	−	0.133240i	−0.994299	+	0.106630i	$0.965994\pi$
$978$		0			0
$979$	17199.4	+	14432.0i	0.561485	+	0.471142i
$980$	3671.11	−	6358.55i	0.119663	−	0.207262i
$981$		0			0
$982$	−14605.8	−	25298.0i	−0.474633	−	0.822088i
$983$	1213.45	−	6881.81i	0.0393723	−	0.223292i	−0.958773	−	0.284175i	$-0.908280\pi$
$983$	1213.45	−	6881.81i	0.0393723	−	0.223292i	0.998145	+	0.0608828i	$0.0193916\pi$
$984$		0			0
$985$	4180.64	+	1521.63i	0.135235	+	0.0492214i
$986$	−29908.1	−	10885.7i	−0.965992	−	0.351592i
$987$		0			0
$988$	−2191.93	+	12431.1i	−0.0705817	+	0.400289i
$989$	−6864.55	−	11889.7i	−0.220708	−	0.382277i
$990$		0			0
$991$	−11482.3	+	19888.0i	−0.368060	+	0.637499i	−0.989262	−	0.146151i	$-0.953311\pi$
$991$	−11482.3	+	19888.0i	−0.368060	+	0.637499i	0.621202	+	0.783651i	$0.286645\pi$
$992$	−26705.4	−	22408.5i	−0.854736	−	0.717209i
$993$		0			0
$994$	−5155.56	−	29238.6i	−0.164512	−	0.932991i
$995$	5928.79	−	4974.84i	0.188900	−	0.158506i
$996$		0			0
$997$	−1669.34	+	607.590i	−0.0530276	+	0.0193005i	−0.368398	−	0.929668i	$-0.620094\pi$
$997$	−1669.34	+	607.590i	−0.0530276	+	0.0193005i	0.315370	+	0.948969i	$0.397871\pi$
$998$	−30100.1			−0.954713
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.4.e.d.55.2		48
3.2	odd	2		243.4.e.a.55.7		48
9.2	odd	6		243.4.e.b.136.2		48
9.4	even	3		27.4.e.a.25.7	yes	48
9.5	odd	6		81.4.e.a.73.2		48
9.7	even	3		243.4.e.c.136.7		48
27.2	odd	18		729.4.a.c.1.5		24
27.4	even	9	inner	243.4.e.d.190.2		48
27.5	odd	18		81.4.e.a.10.2		48
27.13	even	9		243.4.e.c.109.7		48
27.14	odd	18		243.4.e.b.109.2		48
27.22	even	9		27.4.e.a.13.7	✓	48
27.23	odd	18		243.4.e.a.190.7		48
27.25	even	9		729.4.a.d.1.20		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.4.e.a.13.7	✓	48	27.22	even	9
27.4.e.a.25.7	yes	48	9.4	even	3
81.4.e.a.10.2		48	27.5	odd	18
81.4.e.a.73.2		48	9.5	odd	6
243.4.e.a.55.7		48	3.2	odd	2
243.4.e.a.190.7		48	27.23	odd	18
243.4.e.b.109.2		48	27.14	odd	18
243.4.e.b.136.2		48	9.2	odd	6
243.4.e.c.109.7		48	27.13	even	9
243.4.e.c.136.7		48	9.7	even	3
243.4.e.d.55.2		48	1.1	even	1	trivial
243.4.e.d.190.2		48	27.4	even	9	inner
729.4.a.c.1.5		24	27.2	odd	18
729.4.a.d.1.20		24	27.25	even	9

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	243.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.46620 + 1.26159i) q^{2} +(4.29454 - 3.60355i) q^{4} +(-0.280549 - 1.59107i) q^{5} +(26.0189 + 21.8324i) q^{7} +(4.41508 - 7.64714i) q^{8} +(2.97972 + 5.16102i) q^{10} +(4.27839 - 24.2640i) q^{11} +(-28.9704 - 10.5444i) q^{13} +(-117.730 - 42.8503i) q^{14} +(-13.4439 + 76.2442i) q^{16} +(-18.2417 - 31.5955i) q^{17} +(36.5170 - 63.2494i) q^{19} +(-6.93833 - 5.82195i) q^{20} +(15.7815 + 89.5013i) q^{22} +(51.3192 - 43.0619i) q^{23} +(115.009 - 41.8598i) q^{25} +113.720 q^{26} +190.413 q^{28} +(-222.243 + 80.8897i) q^{29} +(124.249 - 104.257i) q^{31} +(-37.3231 - 211.670i) q^{32} +(103.090 + 86.5026i) q^{34} +(27.4374 - 47.5229i) q^{35} +(93.1046 + 161.262i) q^{37} +(-46.7803 + 265.304i) q^{38} +(-13.4058 - 4.87930i) q^{40} +(205.238 + 74.7005i) q^{41} +(35.5866 - 201.821i) q^{43} +(-69.0627 - 119.620i) q^{44} +(-123.556 + 214.005i) q^{46} +(366.994 + 307.945i) q^{47} +(140.766 + 798.323i) q^{49} +(-345.833 + 290.188i) q^{50} +(-162.412 + 59.1130i) q^{52} +736.254 q^{53} -39.8060 q^{55} +(281.831 - 102.578i) q^{56} +(668.287 - 560.759i) q^{58} +(8.89301 + 50.4348i) q^{59} +(-88.6017 - 74.3457i) q^{61} +(-299.141 + 518.127i) q^{62} +(86.7288 + 150.219i) q^{64} +(-8.64921 + 49.0521i) q^{65} +(-109.443 - 39.8339i) q^{67} +(-192.195 - 69.9534i) q^{68} +(-35.1488 + 199.339i) q^{70} +(118.488 + 205.227i) q^{71} +(-23.0477 + 39.9198i) q^{73} +(-526.165 - 441.505i) q^{74} +(-71.0982 - 403.218i) q^{76} +(641.061 - 537.914i) q^{77} +(707.704 - 257.583i) q^{79} +125.081 q^{80} -805.637 q^{82} +(321.016 - 116.840i) q^{83} +(-45.1529 + 37.8878i) q^{85} +(131.266 + 744.448i) q^{86} +(-166.661 - 139.845i) q^{88} +(-455.636 + 789.185i) q^{89} +(-523.568 - 906.847i) q^{91} +(65.2167 - 369.863i) q^{92} +(-1660.57 - 604.399i) q^{94} +(-110.879 - 40.3566i) q^{95} +(-8.54286 + 48.4489i) q^{97} +(-1495.08 - 2589.55i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 3 q^{2} + 3 q^{4} + 15 q^{5} + 3 q^{7} - 75 q^{8} - 3 q^{10} + 102 q^{11} + 3 q^{13} + 285 q^{14} + 27 q^{16} - 207 q^{17} - 3 q^{19} - 84 q^{20} - 51 q^{22} - 435 q^{23} - 213 q^{25} + 1914 q^{26}+ \cdots - 4392 q^{98}+O(q^{100}) \) 48 * q + 3 * q^2 + 3 * q^4 + 15 * q^5 + 3 * q^7 - 75 * q^8 - 3 * q^10 + 102 * q^11 + 3 * q^13 + 285 * q^14 + 27 * q^16 - 207 * q^17 - 3 * q^19 - 84 * q^20 - 51 * q^22 - 435 * q^23 - 213 * q^25 + 1914 * q^26 - 12 * q^28 - 429 * q^29 - 51 * q^31 - 999 * q^32 + 225 * q^34 - 1257 * q^35 - 3 * q^37 + 2049 * q^38 - 555 * q^40 + 1284 * q^41 - 1023 * q^43 - 2211 * q^44 - 3 * q^46 - 3093 * q^47 + 1191 * q^49 + 579 * q^50 + 2781 * q^52 + 2736 * q^53 - 12 * q^55 + 1866 * q^56 + 1785 * q^58 - 5286 * q^59 - 105 * q^61 - 2118 * q^62 - 195 * q^64 + 3693 * q^65 - 1401 * q^67 + 7596 * q^68 - 1491 * q^70 - 3105 * q^71 - 219 * q^73 - 12549 * q^74 - 2001 * q^76 + 4263 * q^77 - 1401 * q^79 + 9870 * q^80 - 12 * q^82 + 5043 * q^83 - 702 * q^85 - 16131 * q^86 + 843 * q^88 - 5202 * q^89 + 267 * q^91 + 13335 * q^92 + 3864 * q^94 + 4935 * q^95 + 1812 * q^97 - 4392 * q^98

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