LMFDB - Embedded newform 81.10.c.g.28.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [81,10,Mod(28,81)] 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("81.28"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(81, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	81.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$41.7179027293$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
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} + 119x^{4} - 154x^{3} + 14060x^{2} - 16048x + 18496 $ x^6 - x^5 + 119x^4 - 154x^3 + 14060x^2 - 16048x + 18496
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{8} $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			28.3
Root			$-5.46600 - 9.46739i$ of defining polynomial
Character	$\chi$	$=$	81.28
Dual form			81.10.c.g.55.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(16.3980 + 28.4022i) q^{2} +(-281.788 + 488.072i) q^{4} +(657.691 - 1139.16i) q^{5} +(-2579.27 - 4467.43i) q^{7} -1691.52 q^{8} +43139.3 q^{10} +(-7567.52 - 13107.3i) q^{11} +(-90251.7 + 156321. i) q^{13} +(84589.7 - 146514. i) q^{14} +(116538. + 201850. i) q^{16} -595825. q^{17} -785830. q^{19} +(370660. + 642002. i) q^{20} +(248184. - 429868. i) q^{22} +(-587721. + 1.01796e6i) q^{23} +(111446. + 193031. i) q^{25} -5.91979e6 q^{26} +2.90723e6 q^{28} +(771411. + 1.33612e6i) q^{29} +(1.13524e6 - 1.96630e6i) q^{31} +(-4.25501e6 + 7.36990e6i) q^{32} +(-9.77034e6 - 1.69227e7i) q^{34} -6.78546e6 q^{35} -1.12928e7 q^{37} +(-1.28860e7 - 2.23193e7i) q^{38} +(-1.11250e6 + 1.92690e6i) q^{40} +(-8.36372e6 + 1.44864e7i) q^{41} +(1.55938e7 + 2.70093e7i) q^{43} +8.52976e6 q^{44} -3.85498e7 q^{46} +(9.67768e6 + 1.67622e7i) q^{47} +(6.87153e6 - 1.19018e7i) q^{49} +(-3.65499e6 + 6.33063e6i) q^{50} +(-5.08638e7 - 8.80986e7i) q^{52} +3.77611e7 q^{53} -1.99084e7 q^{55} +(4.36288e6 + 7.55673e6i) q^{56} +(-2.52992e7 + 4.38195e7i) q^{58} +(6.88542e7 - 1.19259e8i) q^{59} +(-9.22233e7 - 1.59735e8i) q^{61} +7.44629e7 q^{62} -1.59760e8 q^{64} +(1.18716e8 + 2.05621e8i) q^{65} +(7.19072e7 - 1.24547e8i) q^{67} +(1.67897e8 - 2.90806e8i) q^{68} +(-1.11268e8 - 1.92722e8i) q^{70} +2.34392e7 q^{71} -1.57666e8 q^{73} +(-1.85179e8 - 3.20739e8i) q^{74} +(2.21438e8 - 3.83541e8i) q^{76} +(-3.90373e7 + 6.76147e7i) q^{77} +(-2.34797e7 - 4.06680e7i) q^{79} +3.06585e8 q^{80} -5.48593e8 q^{82} +(1.22748e8 + 2.12605e8i) q^{83} +(-3.91869e8 + 6.78737e8i) q^{85} +(-5.11415e8 + 8.85797e8i) q^{86} +(1.28006e7 + 2.21713e7i) q^{88} -1.10618e9 q^{89} +9.31134e8 q^{91} +(-3.31226e8 - 5.73700e8i) q^{92} +(-3.17389e8 + 5.49734e8i) q^{94} +(-5.16833e8 + 8.95182e8i) q^{95} +(-1.48493e8 - 2.57197e8i) q^{97} +4.50717e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 597 q^{4} + 1983 q^{5} + 3693 q^{7} - 9006 q^{8} - 37962 q^{10} + 16863 q^{11} - 116916 q^{13} + 503463 q^{14} + 239919 q^{16} - 2028096 q^{17} - 30444 q^{19} + 2548407 q^{20} - 305721 q^{22}+ \cdots + 5184364572 q^{98}+O(q^{100}) $ 6 * q - 3 * q^2 - 597 * q^4 + 1983 * q^5 + 3693 * q^7 - 9006 * q^8 - 37962 * q^10 + 16863 * q^11 - 116916 * q^13 + 503463 * q^14 + 239919 * q^16 - 2028096 * q^17 - 30444 * q^19 + 2548407 * q^20 - 305721 * q^22 + 2927118 * q^23 - 2133732 * q^25 - 9530232 * q^26 - 7071450 * q^28 + 5768790 * q^29 + 6575223 * q^31 - 2687697 * q^32 - 17098128 * q^34 + 34681074 * q^35 - 23372052 * q^37 - 50473374 * q^38 + 4130811 * q^40 - 22213518 * q^41 - 45384414 * q^43 + 114413982 * q^44 - 191277180 * q^46 + 12392034 * q^47 - 18933462 * q^49 - 82984044 * q^50 - 182736492 * q^52 - 161159274 * q^53 - 349470666 * q^55 + 21850521 * q^56 + 102758922 * q^58 + 244026660 * q^59 - 369729960 * q^61 - 332594682 * q^62 - 841384254 * q^64 + 492225684 * q^65 + 252614586 * q^67 + 162270144 * q^68 - 935092377 * q^70 - 806386176 * q^71 - 813253434 * q^73 - 641373558 * q^74 + 39499590 * q^76 + 360443199 * q^77 - 265451856 * q^79 + 2336719674 * q^80 - 1768816332 * q^82 + 121625871 * q^83 - 316251216 * q^85 - 2368956570 * q^86 - 219257739 * q^88 - 755808012 * q^89 + 490118280 * q^91 - 1178754558 * q^92 - 86583438 * q^94 + 536878770 * q^95 + 438907539 * q^97 + 5184364572 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	16.3980	+	28.4022i	0.724696	+	1.25521i	0.959099	+	0.283071i	$0.0913531\pi$
$2$	16.3980	+	28.4022i	0.724696	+	1.25521i	−0.234403	+	0.972139i	$0.575314\pi$
$3$		0			0
$3$		0			0
$4$	−281.788	+	488.072i	−0.550368	+	0.953266i
$5$	657.691	−	1139.16i	0.470606	−	0.815113i	−0.528829	−	0.848728i	$-0.677369\pi$
$5$	657.691	−	1139.16i	0.470606	−	0.815113i	0.999435	+	0.0336153i	$0.0107021\pi$
$6$		0			0
$7$	−2579.27	−	4467.43i	−0.406028	−	0.703261i	0.588413	−	0.808561i	$-0.299753\pi$
$7$	−2579.27	−	4467.43i	−0.406028	−	0.703261i	−0.994440	+	0.105300i	$0.966420\pi$
$8$	−1691.52			−0.146006
$9$		0			0
$10$	43139.3			1.36418
$11$	−7567.52	−	13107.3i	−0.155843	−	0.269927i	0.777523	−	0.628855i	$-0.216476\pi$
$11$	−7567.52	−	13107.3i	−0.155843	−	0.269927i	−0.933366	+	0.358927i	$0.883143\pi$
$12$		0			0
$13$	−90251.7	+	156321.i	−0.876416	+	1.51800i	−0.0211694	+	0.999776i	$0.506739\pi$
$13$	−90251.7	+	156321.i	−0.876416	+	1.51800i	−0.855247	+	0.518221i	$0.826594\pi$
$14$	84589.7	−	146514.i	0.588493	−	1.01930i
$15$		0			0
$16$	116538.	+	201850.i	0.444558	+	0.769997i
$17$	−595825.			−1.73021			−0.865105	−	0.501591i	$-0.832748\pi$
$17$	−595825.			−1.73021			−0.865105	+	0.501591i	$0.832748\pi$
$18$		0			0
$19$	−785830.			−1.38337			−0.691683	−	0.722201i	$-0.743131\pi$
$19$	−785830.			−1.38337			−0.691683	+	0.722201i	$0.743131\pi$
$20$	370660.	+	642002.i	0.518013	+	0.897224i
$21$		0			0
$22$	248184.	−	429868.i	0.225877	−	0.391231i
$23$	−587721.	+	1.01796e6i	−0.437921	+	0.758502i	−0.997529	−	0.0702559i	$-0.977618\pi$
$23$	−587721.	+	1.01796e6i	−0.437921	+	0.758502i	0.559608	+	0.828757i	$0.310952\pi$
$24$		0			0
$25$	111446.	+	193031.i	0.0570605	+	0.0988317i
$26$	−5.91979e6			−2.54054
$27$		0			0
$28$	2.90723e6			0.893859
$29$	771411.	+	1.33612e6i	0.202533	+	0.350797i	0.949344	−	0.314239i	$-0.101749\pi$
$29$	771411.	+	1.33612e6i	0.202533	+	0.350797i	−0.746811	+	0.665036i	$0.768416\pi$
$30$		0			0
$31$	1.13524e6	−	1.96630e6i	0.220781	−	0.382404i	−0.734264	−	0.678864i	$-0.762473\pi$
$31$	1.13524e6	−	1.96630e6i	0.220781	−	0.382404i	0.955045	+	0.296460i	$0.0958061\pi$
$32$	−4.25501e6	+	7.36990e6i	−0.717342	+	1.24247i
$33$		0			0
$34$	−9.77034e6	−	1.69227e7i	−1.25388	−	2.17178i
$35$	−6.78546e6			−0.764316
$36$		0			0
$37$	−1.12928e7			−0.990586			−0.495293	−	0.868726i	$-0.664939\pi$
$37$	−1.12928e7			−0.990586			−0.495293	+	0.868726i	$0.664939\pi$
$38$	−1.28860e7	−	2.23193e7i	−1.00252	−	1.73642i
$39$		0			0
$40$	−1.11250e6	+	1.92690e6i	−0.0687114	+	0.119012i
$41$	−8.36372e6	+	1.44864e7i	−0.462245	+	0.800631i	−0.999072	−	0.0430606i	$-0.986289\pi$
$41$	−8.36372e6	+	1.44864e7i	−0.462245	+	0.800631i	0.536828	+	0.843692i	$0.319622\pi$
$42$		0			0
$43$	1.55938e7	+	2.70093e7i	0.695576	+	1.20477i	0.969986	+	0.243160i	$0.0781841\pi$
$43$	1.55938e7	+	2.70093e7i	0.695576	+	1.20477i	−0.274410	+	0.961613i	$0.588483\pi$
$44$	8.52976e6			0.343083
$45$		0			0
$46$	−3.85498e7			−1.26944
$47$	9.67768e6	+	1.67622e7i	0.289288	+	0.501062i	0.973640	−	0.228090i	$-0.0732480\pi$
$47$	9.67768e6	+	1.67622e7i	0.289288	+	0.501062i	−0.684352	+	0.729152i	$0.739915\pi$
$48$		0			0
$49$	6.87153e6	−	1.19018e7i	0.170283	−	0.294939i
$50$	−3.65499e6	+	6.33063e6i	−0.0827031	+	0.143246i
$51$		0			0
$52$	−5.08638e7	−	8.80986e7i	−0.964703	−	1.67091i
$53$	3.77611e7			0.657360			0.328680	−	0.944441i	$-0.393396\pi$
$53$	3.77611e7			0.657360			0.328680	+	0.944441i	$0.393396\pi$
$54$		0			0
$55$	−1.99084e7			−0.293362
$56$	4.36288e6	+	7.55673e6i	0.0592826	+	0.102680i
$57$		0			0
$58$	−2.52992e7	+	4.38195e7i	−0.293549	+	0.508442i
$59$	6.88542e7	−	1.19259e8i	0.739770	−	1.28132i	−0.212829	−	0.977089i	$-0.568268\pi$
$59$	6.88542e7	−	1.19259e8i	0.739770	−	1.28132i	0.952599	−	0.304229i	$-0.0983989\pi$
$60$		0			0
$61$	−9.22233e7	−	1.59735e8i	−0.852818	−	1.47712i	−0.878655	−	0.477458i	$-0.841558\pi$
$61$	−9.22233e7	−	1.59735e8i	−0.852818	−	1.47712i	0.0258369	−	0.999666i	$-0.491775\pi$
$62$	7.44629e7			0.639996
$63$		0			0
$64$	−1.59760e8			−1.19030
$65$	1.18716e8	+	2.05621e8i	0.824893	+	1.42876i
$66$		0			0
$67$	7.19072e7	−	1.24547e8i	0.435949	−	0.755086i	−0.561423	−	0.827529i	$-0.689746\pi$
$67$	7.19072e7	−	1.24547e8i	0.435949	−	0.755086i	0.997373	+	0.0724426i	$0.0230794\pi$
$68$	1.67897e8	−	2.90806e8i	0.952252	−	1.64935i
$69$		0			0
$70$	−1.11268e8	−	1.92722e8i	−0.553897	−	0.959377i
$71$	2.34392e7			0.109466			0.0547332	−	0.998501i	$-0.482569\pi$
$71$	2.34392e7			0.109466			0.0547332	+	0.998501i	$0.482569\pi$
$72$		0			0
$73$	−1.57666e8			−0.649808			−0.324904	−	0.945747i	$-0.605332\pi$
$73$	−1.57666e8			−0.649808			−0.324904	+	0.945747i	$0.605332\pi$
$74$	−1.85179e8	−	3.20739e8i	−0.717873	−	1.24339i
$75$		0			0
$76$	2.21438e8	−	3.83541e8i	0.761361	−	1.31872i
$77$	−3.90373e7	+	6.76147e7i	−0.126553	+	0.219196i
$78$		0			0
$79$	−2.34797e7	−	4.06680e7i	−0.0678220	−	0.117471i	0.830120	−	0.557584i	$-0.188272\pi$
$79$	−2.34797e7	−	4.06680e7i	−0.0678220	−	0.117471i	−0.897942	+	0.440113i	$0.854938\pi$
$80$	3.06585e8			0.836846
$81$		0			0
$82$	−5.48593e8			−1.33995
$83$	1.22748e8	+	2.12605e8i	0.283898	+	0.491725i	0.972341	−	0.233565i	$-0.0750391\pi$
$83$	1.22748e8	+	2.12605e8i	0.283898	+	0.491725i	−0.688444	+	0.725290i	$0.741706\pi$
$84$		0			0
$85$	−3.91869e8	+	6.78737e8i	−0.814246	+	1.41032i
$86$	−5.11415e8	+	8.85797e8i	−1.00816	+	1.74619i
$87$		0			0
$88$	1.28006e7	+	2.21713e7i	0.0227540	+	0.0394111i
$89$	−1.10618e9			−1.86883			−0.934415	−	0.356185i	$-0.884077\pi$
$89$	−1.10618e9			−1.86883			−0.934415	+	0.356185i	$0.884077\pi$
$90$		0			0
$91$	9.31134e8			1.42340
$92$	−3.31226e8	−	5.73700e8i	−0.482036	−	0.834910i
$93$		0			0
$94$	−3.17389e8	+	5.49734e8i	−0.419292	+	0.726235i
$95$	−5.16833e8	+	8.95182e8i	−0.651020	+	1.12760i
$96$		0			0
$97$	−1.48493e8	−	2.57197e8i	−0.170307	−	0.294980i	0.768220	−	0.640186i	$-0.221143\pi$
$97$	−1.48493e8	−	2.57197e8i	−0.170307	−	0.294980i	−0.938527	+	0.345205i	$0.887809\pi$
$98$	4.50717e8			0.493613
$99$		0			0
$100$	−1.25617e8			−0.125617
$101$	5.02284e7	+	8.69981e7i	0.0480289	+	0.0831886i	0.889040	−	0.457829i	$-0.151373\pi$
$101$	5.02284e7	+	8.69981e7i	0.0480289	+	0.0831886i	−0.841011	+	0.541017i	$0.818039\pi$
$102$		0			0
$103$	4.47262e8	−	7.74681e8i	0.391557	−	0.678196i	−0.601098	−	0.799175i	$-0.705270\pi$
$103$	4.47262e8	−	7.74681e8i	0.391557	−	0.678196i	0.992655	+	0.120979i	$0.0386034\pi$
$104$	1.52662e8	−	2.64419e8i	0.127962	−	0.221637i
$105$		0			0
$106$	6.19207e8	+	1.07250e9i	0.476386	+	0.825125i
$107$	−1.67004e9			−1.23168			−0.615841	−	0.787870i	$-0.711184\pi$
$107$	−1.67004e9			−1.23168			−0.615841	+	0.787870i	$0.711184\pi$
$108$		0			0
$109$	−7.93643e8			−0.538525			−0.269263	−	0.963067i	$-0.586780\pi$
$109$	−7.93643e8			−0.538525			−0.269263	+	0.963067i	$0.586780\pi$
$110$	−3.26457e8	−	5.65441e8i	−0.212598	−	0.368231i
$111$		0			0
$112$	6.01167e8	−	1.04125e9i	0.361006	−	0.625280i
$113$	2.91841e8	−	5.05483e8i	0.168381	−	0.291644i	−0.769470	−	0.638683i	$-0.779479\pi$
$113$	2.91841e8	−	5.05483e8i	0.168381	−	0.291644i	0.937851	+	0.347039i	$0.112813\pi$
$114$		0			0
$115$	7.73078e8	+	1.33901e9i	0.412176	+	0.713910i
$116$	−8.69499e8			−0.445870
$117$		0			0
$118$	4.51629e9			2.14443
$119$	1.53679e9	+	2.66181e9i	0.702513	+	1.21679i
$120$		0			0
$121$	1.06444e9	−	1.84366e9i	0.451426	−	0.781893i
$122$	3.02455e9	−	5.23868e9i	1.23607	−	2.14093i
$123$		0			0
$124$	6.39797e8	+	1.10816e9i	0.243021	+	0.420926i
$125$	2.86230e9			1.04862
$126$		0			0
$127$	1.00303e9			0.342133			0.171067	−	0.985259i	$-0.445279\pi$
$127$	1.00303e9			0.342133			0.171067	+	0.985259i	$0.445279\pi$
$128$	−4.41171e8	−	7.64131e8i	−0.145265	−	0.251607i
$129$		0			0
$130$	−3.89339e9	+	6.74356e9i	−1.19559	+	2.07083i
$131$	−2.33390e9	+	4.04243e9i	−0.692406	+	1.19928i	0.278642	+	0.960395i	$0.410116\pi$
$131$	−2.33390e9	+	4.04243e9i	−0.692406	+	1.19928i	−0.971047	+	0.238887i	$0.923217\pi$
$132$		0			0
$133$	2.02687e9	+	3.51064e9i	0.561685	+	0.972867i
$134$	4.71654e9			1.26372
$135$		0			0
$136$	1.00785e9			0.252621
$137$	1.70061e9	+	2.94555e9i	0.412442	+	0.714370i	0.995156	−	0.0983069i	$-0.0313427\pi$
$137$	1.70061e9	+	2.94555e9i	0.412442	+	0.714370i	−0.582714	+	0.812677i	$0.698009\pi$
$138$		0			0
$139$	−2.30714e9	+	3.99609e9i	−0.524213	+	0.907963i	0.475390	+	0.879775i	$0.342307\pi$
$139$	−2.30714e9	+	3.99609e9i	−0.524213	+	0.907963i	−0.999603	+	0.0281879i	$0.991026\pi$
$140$	1.91206e9	−	3.31179e9i	0.420655	−	0.728596i
$141$		0			0
$142$	3.84357e8	+	6.65725e8i	0.0793299	+	0.137403i
$143$	2.73193e9			0.546332
$144$		0			0
$145$	2.02940e9			0.381252
$146$	−2.58540e9	−	4.47805e9i	−0.470913	−	0.815645i
$147$		0			0
$148$	3.18217e9	−	5.51168e9i	0.545187	−	0.944291i
$149$	−1.13584e9	+	1.96733e9i	−0.188790	+	0.326994i	−0.944847	−	0.327512i	$-0.893790\pi$
$149$	−1.13584e9	+	1.96733e9i	−0.188790	+	0.326994i	0.756057	+	0.654506i	$0.227123\pi$
$150$		0			0
$151$	4.97484e8	+	8.61668e8i	0.0778723	+	0.134879i	0.902332	−	0.431042i	$-0.141854\pi$
$151$	4.97484e8	+	8.61668e8i	0.0778723	+	0.134879i	−0.824459	+	0.565921i	$0.808521\pi$
$152$	1.32924e9			0.201980
$153$		0			0
$154$	−2.56054e9			−0.366849
$155$	−1.49328e9	−	2.58644e9i	−0.207801	−	0.359923i
$156$		0			0
$157$	5.96575e9	−	1.03330e10i	0.783640	−	1.35730i	−0.146169	−	0.989260i	$-0.546694\pi$
$157$	5.96575e9	−	1.03330e10i	0.783640	−	1.35730i	0.929808	−	0.368044i	$-0.119972\pi$
$158$	7.70039e8	−	1.33375e9i	0.0983006	−	0.170262i
$159$		0			0
$160$	5.59697e9	+	9.69424e9i	0.675170	+	1.16943i
$161$	6.06356e9			0.711232
$162$		0			0
$163$	2.02118e9			0.224264			0.112132	−	0.993693i	$-0.464232\pi$
$163$	2.02118e9			0.224264			0.112132	+	0.993693i	$0.464232\pi$
$164$	−4.71360e9	−	8.16419e9i	−0.508809	−	0.881284i
$165$		0			0
$166$	−4.02563e9	+	6.97260e9i	−0.411479	+	0.712702i
$167$	−6.34711e9	+	1.09935e10i	−0.631468	+	1.09374i	0.355783	+	0.934569i	$0.384214\pi$
$167$	−6.34711e9	+	1.09935e10i	−0.631468	+	1.09374i	−0.987252	+	0.159167i	$0.949119\pi$
$168$		0			0
$169$	−1.09885e10	−	1.90326e10i	−1.03621	−	1.79477i
$170$	−2.57035e10			−2.36032
$171$		0			0
$172$	−1.75766e10			−1.53129
$173$	2.86139e9	+	4.95608e9i	0.242868	+	0.420659i	0.961530	−	0.274700i	$-0.0885785\pi$
$173$	2.86139e9	+	4.95608e9i	0.242868	+	0.420659i	−0.718662	+	0.695359i	$0.755245\pi$
$174$		0			0
$175$	5.74901e8	−	9.95757e8i	0.0463363	−	0.0802568i
$176$	1.76381e9	−	3.05501e9i	0.138562	−	0.239997i
$177$		0			0
$178$	−1.81391e10	−	3.14178e10i	−1.35433	−	2.34578i
$179$	−1.53037e10			−1.11419			−0.557093	−	0.830450i	$-0.688083\pi$
$179$	−1.53037e10			−1.11419			−0.557093	+	0.830450i	$0.688083\pi$
$180$		0			0
$181$	1.52538e10			1.05639			0.528197	−	0.849122i	$-0.322868\pi$
$181$	1.52538e10			1.05639			0.528197	+	0.849122i	$0.322868\pi$
$182$	1.52687e10	+	2.64462e10i	1.03153	+	1.78666i
$183$		0			0
$184$	9.94140e8	−	1.72190e9i	0.0639392	−	0.110746i
$185$	−7.42715e9	+	1.28642e10i	−0.466175	+	0.807439i
$186$		0			0
$187$	4.50892e9	+	7.80967e9i	0.269640	+	0.467031i
$188$	−1.09082e10			−0.636860
$189$		0			0
$190$	−3.39001e10			−1.88717
$191$	−9.64613e9	−	1.67076e10i	−0.524448	−	0.908371i	−0.999595	−	0.0284646i	$-0.990938\pi$
$191$	−9.64613e9	−	1.67076e10i	−0.524448	−	0.908371i	0.475146	−	0.879907i	$-0.342395\pi$
$192$		0			0
$193$	−4.40967e9	+	7.63777e9i	−0.228769	+	0.396240i	−0.957444	−	0.288620i	$-0.906803\pi$
$193$	−4.40967e9	+	7.63777e9i	−0.228769	+	0.396240i	0.728674	+	0.684860i	$0.240137\pi$
$194$	4.86996e9	−	8.43503e9i	0.246841	−	0.427542i
$195$		0			0
$196$	3.87264e9	+	6.70760e9i	0.187437	+	0.324650i
$197$	−6.14540e9			−0.290705			−0.145352	−	0.989380i	$-0.546432\pi$
$197$	−6.14540e9			−0.290705			−0.145352	+	0.989380i	$0.546432\pi$
$198$		0			0
$199$	1.32275e10			0.597916			0.298958	−	0.954266i	$-0.403361\pi$
$199$	1.32275e10			0.597916			0.298958	+	0.954266i	$0.403361\pi$
$200$	−1.88513e8	−	3.26515e8i	−0.00833119	−	0.0144300i
$201$		0			0
$202$	−1.64729e9	+	2.85319e9i	−0.0696127	+	0.120573i
$203$	3.97936e9	−	6.89245e9i	0.164468	−	0.284866i
$204$		0			0
$205$	1.10015e10	+	1.90551e10i	0.435070	+	0.753563i
$206$	2.93368e10			1.13504
$207$		0			0
$208$	−4.20711e10			−1.55847
$209$	5.94678e9	+	1.03001e10i	0.215587	+	0.373408i
$210$		0			0
$211$	1.23858e10	−	2.14529e10i	0.430184	−	0.745100i	−0.566705	−	0.823921i	$-0.691782\pi$
$211$	1.23858e10	−	2.14529e10i	0.430184	−	0.745100i	0.996889	+	0.0788207i	$0.0251155\pi$
$212$	−1.06406e10	+	1.84301e10i	−0.361790	+	0.626639i
$213$		0			0
$214$	−2.73852e10	−	4.74326e10i	−0.892596	−	1.54602i
$215$	4.10237e10			1.30937
$216$		0			0
$217$	−1.17124e10			−0.358573
$218$	−1.30142e10	−	2.25412e10i	−0.390267	−	0.675962i
$219$		0			0
$220$	5.60995e9	−	9.71671e9i	0.161457	−	0.279652i
$221$	5.37742e10	−	9.31397e10i	1.51638	−	2.62645i
$222$		0			0
$223$	−6.92407e9	−	1.19928e10i	−0.187495	−	0.324751i	0.756919	−	0.653508i	$-0.226704\pi$
$223$	−6.92407e9	−	1.19928e10i	−0.187495	−	0.324751i	−0.944414	+	0.328757i	$0.893370\pi$
$224$	4.38993e10			1.16504
$225$		0			0
$226$	1.91424e10			0.488100
$227$	−2.77456e10	−	4.80568e10i	−0.693550	−	1.20126i	−0.970667	−	0.240428i	$-0.922712\pi$
$227$	−2.77456e10	−	4.80568e10i	−0.693550	−	1.20126i	0.277117	−	0.960836i	$-0.410621\pi$
$228$		0			0
$229$	−1.60003e9	+	2.77133e9i	−0.0384475	+	0.0665930i	−0.884609	−	0.466334i	$-0.845575\pi$
$229$	−1.60003e9	+	2.77133e9i	−0.0384475	+	0.0665930i	0.846161	+	0.532927i	$0.178908\pi$
$230$	−2.53539e10	+	4.39142e10i	−0.597405	+	1.03474i
$231$		0			0
$232$	−1.30485e9	−	2.26008e9i	−0.0295710	−	0.0512185i
$233$	1.45987e10			0.324498			0.162249	−	0.986750i	$-0.448125\pi$
$233$	1.45987e10			0.324498			0.162249	+	0.986750i	$0.448125\pi$
$234$		0			0
$235$	2.54597e10			0.544563
$236$	3.88047e10	+	6.72116e10i	0.814291	+	1.41039i
$237$		0			0
$238$	−5.04007e10	+	8.72965e10i	−1.01822	+	1.76360i
$239$	−2.28625e10	+	3.95989e10i	−0.453244	+	0.785042i	−0.998585	−	0.0531722i	$-0.983067\pi$
$239$	−2.28625e10	+	3.95989e10i	−0.453244	+	0.785042i	0.545341	+	0.838214i	$0.316400\pi$
$240$		0			0
$241$	−9.31249e8	−	1.61297e9i	−0.0177824	−	0.0307999i	0.856997	−	0.515321i	$-0.172327\pi$
$241$	−9.31249e8	−	1.61297e9i	−0.0177824	−	0.0307999i	−0.874780	+	0.484521i	$0.838994\pi$
$242$	6.98187e10			1.30859
$243$		0			0
$244$	1.03950e11			1.87745
$245$	−9.03870e9	−	1.56555e10i	−0.160272	−	0.277600i
$246$		0			0
$247$	7.09225e10	−	1.22841e11i	1.21240	−	2.09995i
$248$	−1.92028e9	+	3.32603e9i	−0.0322354	+	0.0558333i
$249$		0			0
$250$	4.69359e10	+	8.12954e10i	0.759933	+	1.31624i
$251$	−1.02269e11			−1.62634			−0.813171	−	0.582025i	$-0.802261\pi$
$251$	−1.02269e11			−1.62634			−0.813171	+	0.582025i	$0.802261\pi$
$252$		0			0
$253$	1.77904e10			0.272987
$254$	1.64476e10	+	2.84881e10i	0.247943	+	0.429449i
$255$		0			0
$256$	−2.64298e10	+	4.57778e10i	−0.384605	+	0.666155i
$257$	6.31941e10	−	1.09455e11i	0.903603	−	1.56509i	0.0808220	−	0.996729i	$-0.474245\pi$
$257$	6.31941e10	−	1.09455e11i	0.903603	−	1.56509i	0.822781	−	0.568358i	$-0.192421\pi$
$258$		0			0
$259$	2.91271e10	+	5.04496e10i	0.402205	+	0.696640i
$260$	−1.33811e11			−1.81598
$261$		0			0
$262$	−1.53085e11			−2.00713
$263$	4.57881e10	+	7.93073e10i	0.590135	+	1.02214i	0.994214	+	0.107420i	$0.0342590\pi$
$263$	4.57881e10	+	7.93073e10i	0.590135	+	1.02214i	−0.404078	+	0.914724i	$0.632408\pi$
$264$		0			0
$265$	2.48352e10	−	4.30158e10i	0.309358	−	0.535823i
$266$	−6.64731e10	+	1.15135e11i	−0.814102	+	1.41007i
$267$		0			0
$268$	4.05252e10	+	7.01918e10i	0.479865	+	0.831151i
$269$	−3.86326e9			−0.0449851			−0.0224925	−	0.999747i	$-0.507160\pi$
$269$	−3.86326e9			−0.0449851			−0.0224925	+	0.999747i	$0.507160\pi$
$270$		0			0
$271$	1.26432e11			1.42395			0.711976	−	0.702203i	$-0.247800\pi$
$271$	1.26432e11			1.42395			0.711976	+	0.702203i	$0.247800\pi$
$272$	−6.94364e10	−	1.20267e11i	−0.769178	−	1.33226i
$273$		0			0
$274$	−5.57733e10	+	9.66021e10i	−0.597790	+	1.03540i
$275$	1.68674e9	−	2.92153e9i	0.0177849	−	0.0308044i
$276$		0			0
$277$	6.11376e10	+	1.05893e11i	0.623949	+	1.08071i	0.988743	+	0.149623i	$0.0478061\pi$
$277$	6.11376e10	+	1.05893e11i	0.623949	+	1.08071i	−0.364794	+	0.931088i	$0.618861\pi$
$278$	−1.51330e11			−1.51958
$279$		0			0
$280$	1.14777e10			0.111595
$281$	8.94966e9	+	1.55013e10i	0.0856305	+	0.148316i	0.905660	−	0.424005i	$-0.139376\pi$
$281$	8.94966e9	+	1.55013e10i	0.0856305	+	0.148316i	−0.820029	+	0.572322i	$0.806043\pi$
$282$		0			0
$283$	−9.98248e10	+	1.72902e11i	−0.925123	+	1.60236i	−0.133761	+	0.991014i	$0.542705\pi$
$283$	−9.98248e10	+	1.72902e11i	−0.925123	+	1.60236i	−0.791363	+	0.611347i	$0.790628\pi$
$284$	−6.60491e9	+	1.14400e10i	−0.0602468	+	0.104351i
$285$		0			0
$286$	4.47981e10	+	7.75926e10i	0.395925	+	0.685761i
$287$	8.62891e10			0.750737
$288$		0			0
$289$	2.36420e11			1.99362
$290$	3.32781e10	+	5.76394e10i	0.276292	+	0.478551i
$291$		0			0
$292$	4.44284e10	−	7.69523e10i	0.357634	−	0.619439i
$293$	−2.64701e10	+	4.58476e10i	−0.209822	+	0.363423i	−0.951658	−	0.307158i	$-0.900622\pi$
$293$	−2.64701e10	+	4.58476e10i	−0.209822	+	0.363423i	0.741836	+	0.670581i	$0.233955\pi$
$294$		0			0
$295$	−9.05697e10	−	1.56871e11i	−0.696280	−	1.20599i
$296$	1.91019e10			0.144632
$297$		0			0
$298$	−7.45020e10			−0.547261
$299$	−1.06086e11	−	1.83746e11i	−0.767602	−	1.32953i
$300$		0			0
$301$	8.04414e10	−	1.39329e11i	0.564846	−	0.978343i
$302$	−1.63155e10	+	2.82593e10i	−0.112868	+	0.195492i
$303$		0			0
$304$	−9.15792e10	−	1.58620e11i	−0.614987	−	1.06519i
$305$	−2.42618e11			−1.60536
$306$		0			0
$307$	−6.10366e10			−0.392164			−0.196082	−	0.980587i	$-0.562822\pi$
$307$	−6.10366e10			−0.392164			−0.196082	+	0.980587i	$0.562822\pi$
$308$	−2.20005e10	−	3.81061e10i	−0.139301	−	0.241277i
$309$		0			0
$310$	4.89736e10	−	8.48248e10i	0.301186	−	0.521669i
$311$	−1.87762e10	+	3.25214e10i	−0.113812	+	0.197128i	−0.917304	−	0.398187i	$-0.869639\pi$
$311$	−1.87762e10	+	3.25214e10i	−0.113812	+	0.197128i	0.803492	+	0.595315i	$0.202973\pi$
$312$		0			0
$313$	−4.47739e10	−	7.75506e10i	−0.263679	−	0.456705i	0.703538	−	0.710658i	$-0.251603\pi$
$313$	−4.47739e10	−	7.75506e10i	−0.263679	−	0.456705i	−0.967217	+	0.253953i	$0.918269\pi$
$314$	3.91305e11			2.27160
$315$		0			0
$316$	2.64652e10			0.149308
$317$	1.09931e11	+	1.90407e11i	0.611442	+	1.05905i	0.990998	+	0.133880i	$0.0427437\pi$
$317$	1.09931e11	+	1.90407e11i	0.611442	+	1.05905i	−0.379555	+	0.925169i	$0.623923\pi$
$318$		0			0
$319$	1.16753e10	−	2.02223e10i	0.0631264	−	0.109338i
$320$	−1.05073e11	+	1.81991e11i	−0.560163	+	0.970231i
$321$		0			0
$322$	9.94303e10	+	1.72218e11i	0.515427	+	0.892746i
$323$	4.68217e11			2.39351
$324$		0			0
$325$	−4.02329e10			−0.200035
$326$	3.31432e10	+	5.74058e10i	0.162523	+	0.281499i
$327$		0			0
$328$	1.41474e10	−	2.45040e10i	0.0674906	−	0.116897i
$329$	4.99227e10	−	8.64687e10i	0.234918	−	0.406890i
$330$		0			0
$331$	8.34457e10	+	1.44532e11i	0.382101	+	0.661818i	0.991362	−	0.131151i	$-0.0418674\pi$
$331$	8.34457e10	+	1.44532e11i	0.382101	+	0.661818i	−0.609262	+	0.792969i	$0.708534\pi$
$332$	−1.38356e11			−0.624993
$333$		0			0
$334$	−4.16319e11			−1.83049
$335$	−9.45855e10	−	1.63827e11i	−0.410320	−	0.710696i
$336$		0			0
$337$	1.43012e9	−	2.47704e9i	0.00604000	−	0.0104616i	−0.862990	−	0.505222i	$-0.831411\pi$
$337$	1.43012e9	−	2.47704e9i	0.00604000	−	0.0104616i	0.869030	+	0.494760i	$0.164744\pi$
$338$	3.60378e11	−	6.24194e11i	1.50187	−	2.60132i
$339$		0			0
$340$	−2.20848e11	−	3.82521e11i	−0.896270	−	1.55239i
$341$	−3.43639e10			−0.137628
$342$		0			0
$343$	−2.79060e11			−1.08861
$344$	−2.63772e10	−	4.56867e10i	−0.101558	−	0.175904i
$345$		0			0
$346$	−9.38422e10	+	1.62539e11i	−0.352011	+	0.609700i
$347$	−7.83192e10	+	1.35653e11i	−0.289992	+	0.502280i	−0.973807	−	0.227374i	$-0.926986\pi$
$347$	−7.83192e10	+	1.35653e11i	−0.289992	+	0.502280i	0.683816	+	0.729655i	$0.260319\pi$
$348$		0			0
$349$	1.59376e10	+	2.76047e10i	0.0575054	+	0.0996022i	0.893345	−	0.449371i	$-0.148352\pi$
$349$	1.59376e10	+	2.76047e10i	0.0575054	+	0.0996022i	−0.835840	+	0.548974i	$0.815019\pi$
$350$	3.77089e10			0.134319
$351$		0			0
$352$	1.28800e11			0.447170
$353$	9.98160e10	+	1.72886e11i	0.342148	+	0.592618i	0.984831	−	0.173514i	$-0.0555123\pi$
$353$	9.98160e10	+	1.72886e11i	0.342148	+	0.592618i	−0.642683	+	0.766132i	$0.722179\pi$
$354$		0			0
$355$	1.54158e10	−	2.67009e10i	0.0515155	−	0.0892275i
$356$	3.11708e11	−	5.39894e11i	1.02854	−	1.78149i
$357$		0			0
$358$	−2.50950e11	−	4.34658e11i	−0.807446	−	1.39854i
$359$	4.79288e10			0.152290			0.0761451	−	0.997097i	$-0.475739\pi$
$359$	4.79288e10			0.152290			0.0761451	+	0.997097i	$0.475739\pi$
$360$		0			0
$361$	2.94840e11			0.913702
$362$	2.50133e11	+	4.33242e11i	0.765564	+	1.32600i
$363$		0			0
$364$	−2.62383e11	+	4.54460e11i	−0.783392	+	1.35688i
$365$	−1.03696e11	+	1.79606e11i	−0.305803	+	0.529667i
$366$		0			0
$367$	−9.46312e10	−	1.63906e11i	−0.272293	−	0.471626i	0.697155	−	0.716920i	$-0.254449\pi$
$367$	−9.46312e10	−	1.63906e11i	−0.272293	−	0.471626i	−0.969449	+	0.245294i	$0.921115\pi$
$368$	−2.73968e11			−0.778725
$369$		0			0
$370$	−4.87161e11			−1.35134
$371$	−9.73962e10	−	1.68695e11i	−0.266907	−	0.462296i
$372$		0			0
$373$	4.99125e10	−	8.64509e10i	0.133512	−	0.231249i	−0.791516	−	0.611148i	$-0.790708\pi$
$373$	4.99125e10	−	8.64509e10i	0.133512	−	0.231249i	0.925028	+	0.379899i	$0.124041\pi$
$374$	−1.47874e11	+	2.56126e11i	−0.390815	+	0.676911i
$375$		0			0
$376$	−1.63700e10	−	2.83536e10i	−0.0422379	−	0.0731582i
$377$	−2.78485e11			−0.710011
$378$		0			0
$379$	6.79275e10			0.169110			0.0845550	−	0.996419i	$-0.473053\pi$
$379$	6.79275e10			0.169110			0.0845550	+	0.996419i	$0.473053\pi$
$380$	−2.91275e11	−	5.04504e11i	−0.716601	−	1.24119i
$381$		0			0
$382$	3.16354e11	−	5.47942e11i	0.760131	−	1.31659i
$383$	−2.57757e11	+	4.46448e11i	−0.612091	+	1.06017i	0.378796	+	0.925480i	$0.376338\pi$
$383$	−2.57757e11	+	4.46448e11i	−0.612091	+	1.06017i	−0.990887	+	0.134693i	$0.956995\pi$
$384$		0			0
$385$	5.13491e10	+	8.89392e10i	0.119113	+	0.206310i
$386$	−2.89239e11			−0.663153
$387$		0			0
$388$	1.67374e11			0.374926
$389$	9.85027e10	+	1.70612e11i	0.218110	+	0.377777i	0.954230	−	0.299074i	$-0.0966776\pi$
$389$	9.85027e10	+	1.70612e11i	0.218110	+	0.377777i	−0.736120	+	0.676851i	$0.763344\pi$
$390$		0			0
$391$	3.50179e11	−	6.06528e11i	0.757695	−	1.31237i
$392$	−1.16233e10	+	2.01322e10i	−0.0248624	+	0.0430629i
$393$		0			0
$394$	−1.00772e11	−	1.74543e11i	−0.210672	−	0.364895i
$395$	−6.17696e10			−0.127670
$396$		0			0
$397$	−5.86747e11			−1.18548			−0.592739	−	0.805395i	$-0.701953\pi$
$397$	−5.86747e11			−1.18548			−0.592739	+	0.805395i	$0.701953\pi$
$398$	2.16905e11	+	3.75691e11i	0.433307	+	0.750510i
$399$		0			0
$400$	−2.59755e10	+	4.49909e10i	−0.0507334	+	0.0878729i
$401$	−2.77848e11	+	4.81247e11i	−0.536609	+	0.929434i	0.462475	+	0.886633i	$0.346962\pi$
$401$	−2.77848e11	+	4.81247e11i	−0.536609	+	0.929434i	−0.999084	+	0.0428016i	$0.986372\pi$
$402$		0			0
$403$	2.04915e11	+	3.54924e11i	0.386992	+	0.670289i
$404$	−5.66151e10			−0.105734
$405$		0			0
$406$	2.61014e11			0.476756
$407$	8.54581e10	+	1.48018e11i	0.154376	+	0.267386i
$408$		0			0
$409$	−9.48608e10	+	1.64304e11i	−0.167622	+	0.290330i	−0.937583	−	0.347761i	$-0.886942\pi$
$409$	−9.48608e10	+	1.64304e11i	−0.167622	+	0.290330i	0.769961	+	0.638091i	$0.220276\pi$
$410$	−3.60805e11	+	6.24932e11i	−0.630587	+	1.09221i
$411$		0			0
$412$	2.52067e11	+	4.36592e11i	0.431001	+	0.746515i
$413$	−7.10375e11			−1.20147
$414$		0			0
$415$	3.22920e11			0.534416
$416$	−7.68045e11	−	1.33029e12i	−1.25738	−	2.17785i
$417$		0			0
$418$	−1.95031e11	+	3.37803e11i	−0.312471	+	0.541215i
$419$	−3.62080e11	+	6.27142e11i	−0.573907	+	0.994037i	0.422252	+	0.906479i	$0.361240\pi$
$419$	−3.62080e11	+	6.27142e11i	−0.573907	+	0.994037i	−0.996159	+	0.0875584i	$0.972094\pi$
$420$		0			0
$421$	−5.47488e11	−	9.48278e11i	−0.849387	−	1.47118i	−0.881756	−	0.471705i	$-0.843639\pi$
$421$	−5.47488e11	−	9.48278e11i	−0.849387	−	1.47118i	0.0323695	−	0.999476i	$-0.489695\pi$
$422$	8.12411e11			1.24701
$423$		0			0
$424$	−6.38736e10			−0.0959787
$425$	−6.64025e10	−	1.15013e11i	−0.0987267	−	0.171000i
$426$		0			0
$427$	−4.75738e11	+	8.24002e11i	−0.692535	+	1.19951i
$428$	4.70597e11	−	8.15098e11i	0.677879	−	1.17412i
$429$		0			0
$430$	6.72707e11	+	1.16516e12i	0.948894	+	1.64353i
$431$	5.24483e11			0.732123			0.366061	−	0.930591i	$-0.380706\pi$
$431$	5.24483e11			0.732123			0.366061	+	0.930591i	$0.380706\pi$
$432$		0			0
$433$	−5.33682e11			−0.729604			−0.364802	−	0.931085i	$-0.618863\pi$
$433$	−5.33682e11			−0.729604			−0.364802	+	0.931085i	$0.618863\pi$
$434$	−1.92060e11	−	3.32657e11i	−0.259856	−	0.450084i
$435$		0			0
$436$	2.23639e11	−	3.87355e11i	0.296387	−	0.513357i
$437$	4.61848e11	−	7.99945e11i	0.605805	−	1.04929i
$438$		0			0
$439$	2.71250e11	+	4.69819e11i	0.348562	+	0.603727i	0.985994	−	0.166780i	$-0.0533368\pi$
$439$	2.71250e11	+	4.69819e11i	0.348562	+	0.603727i	−0.637432	+	0.770506i	$0.720004\pi$
$440$	3.36753e10			0.0428326
$441$		0			0
$442$	3.52716e12			4.39567
$443$	5.08428e11	+	8.80622e11i	0.627209	+	1.08636i	0.988109	+	0.153753i	$0.0491362\pi$
$443$	5.08428e11	+	8.80622e11i	0.627209	+	1.08636i	−0.360900	+	0.932604i	$0.617530\pi$
$444$		0			0
$445$	−7.27524e11	+	1.26011e12i	−0.879483	+	1.52331i
$446$	2.27082e11	−	3.93317e11i	0.271754	−	0.470691i
$447$		0			0
$448$	4.12063e11	+	7.13715e11i	0.483296	+	0.837093i
$449$	7.68289e10			0.0892105			0.0446053	−	0.999005i	$-0.485797\pi$
$449$	7.68289e10			0.0892105			0.0446053	+	0.999005i	$0.485797\pi$
$450$		0			0
$451$	2.53170e11			0.288150
$452$	1.64475e11	+	2.84879e11i	0.185343	+	0.321024i
$453$		0			0
$454$	9.09944e11	−	1.57607e12i	1.00523	−	1.74110i
$455$	6.12399e11	−	1.06071e12i	0.669859	−	1.16023i
$456$		0			0
$457$	2.77147e11	+	4.80033e11i	0.297226	+	0.514811i	0.975500	−	0.219998i	$-0.0706050\pi$
$457$	2.77147e11	+	4.80033e11i	0.297226	+	0.514811i	−0.678274	+	0.734809i	$0.737272\pi$
$458$	−1.04949e11			−0.111451
$459$		0			0
$460$	−8.71378e11			−0.907395
$461$	5.46732e11	+	9.46968e11i	0.563794	+	0.976520i	0.997161	+	0.0753023i	$0.0239922\pi$
$461$	5.46732e11	+	9.46968e11i	0.563794	+	0.976520i	−0.433367	+	0.901218i	$0.642674\pi$
$462$		0			0
$463$	−7.00157e11	+	1.21271e12i	−0.708077	+	1.22643i	0.257492	+	0.966280i	$0.417104\pi$
$463$	−7.00157e11	+	1.21271e12i	−0.708077	+	1.22643i	−0.965569	+	0.260145i	$0.916229\pi$
$464$	−1.79798e11	+	3.11419e11i	−0.180075	+	0.311899i
$465$		0			0
$466$	2.39389e11	+	4.14634e11i	0.235163	+	0.407313i
$467$	1.59376e12			1.55059			0.775296	−	0.631599i	$-0.217601\pi$
$467$	1.59376e12			1.55059			0.775296	+	0.631599i	$0.217601\pi$
$468$		0			0
$469$	−7.41873e11			−0.708030
$470$	4.17488e11	+	7.23111e11i	0.394643	+	0.683541i
$471$		0			0
$472$	−1.16468e11	+	2.01729e11i	−0.108011	+	0.187081i
$473$	2.36013e11	−	4.08787e11i	0.216801	−	0.375510i
$474$		0			0
$475$	−8.75778e10	−	1.51689e11i	−0.0789356	−	0.136720i
$476$	−1.73220e12			−1.54656
$477$		0			0
$478$	−1.49959e12			−1.31386
$479$	−4.06062e11	−	7.03319e11i	−0.352438	−	0.610440i	0.634238	−	0.773138i	$-0.281314\pi$
$479$	−4.06062e11	−	7.03319e11i	−0.352438	−	0.610440i	−0.986676	+	0.162698i	$0.947980\pi$
$480$		0			0
$481$	1.01919e12	−	1.76529e12i	0.868165	−	1.50371i
$482$	3.05412e10	−	5.28990e10i	0.0257736	−	0.0446412i
$483$		0			0
$484$	5.99893e11	+	1.03905e12i	0.496901	+	0.860658i
$485$	−3.90650e11			−0.320590
$486$		0			0
$487$	8.95090e11			0.721085			0.360542	−	0.932743i	$-0.382592\pi$
$487$	8.95090e11			0.721085			0.360542	+	0.932743i	$0.382592\pi$
$488$	1.55997e11	+	2.70195e11i	0.124517	+	0.215669i
$489$		0			0
$490$	2.96433e11	−	5.13437e11i	0.232297	−	0.402351i
$491$	7.05747e11	−	1.22239e12i	0.548002	−	0.949168i	−0.450409	−	0.892822i	$-0.648722\pi$
$491$	7.05747e11	−	1.22239e12i	0.548002	−	0.949168i	0.998411	−	0.0563453i	$-0.0179448\pi$
$492$		0			0
$493$	−4.59626e11	−	7.96096e11i	−0.350424	−	0.606952i
$494$	4.65194e12			3.51450
$495$		0			0
$496$	5.29197e11			0.392600
$497$	−6.04562e10	−	1.04713e11i	−0.0444464	−	0.0769834i
$498$		0			0
$499$	9.12138e10	−	1.57987e11i	0.0658580	−	0.114069i	−0.831216	−	0.555949i	$-0.812355\pi$
$499$	9.12138e10	−	1.57987e11i	0.0658580	−	0.114069i	0.897074	+	0.441880i	$0.145688\pi$
$500$	−8.06562e11	+	1.39701e12i	−0.577129	+	0.999617i
$501$		0			0
$502$	−1.67701e12	−	2.90466e12i	−1.17860	−	2.04140i
$503$	−2.33627e12			−1.62730			−0.813649	−	0.581357i	$-0.802522\pi$
$503$	−2.33627e12			−1.62730			−0.813649	+	0.581357i	$0.802522\pi$
$504$		0			0
$505$	1.32139e11			0.0904108
$506$	2.91726e11	+	5.05284e11i	0.197833	+	0.342656i
$507$		0			0
$508$	−2.82641e11	+	4.89549e11i	−0.188299	+	0.326144i
$509$	1.57931e11	−	2.73544e11i	0.104289	−	0.180633i	−0.809159	−	0.587590i	$-0.800077\pi$
$509$	1.57931e11	−	2.73544e11i	0.104289	−	0.180633i	0.913447	+	0.406957i	$0.133410\pi$
$510$		0			0
$511$	4.06663e11	+	7.04361e11i	0.263840	+	0.456984i
$512$	−2.18534e12			−1.40542
$513$		0			0
$514$	4.14503e12			2.61935
$515$	−5.88321e11	−	1.01900e12i	−0.368538	−	0.638326i
$516$		0			0
$517$	1.46472e11	−	2.53697e11i	0.0901669	−	0.156174i
$518$	−9.55251e11	+	1.65454e12i	−0.582953	+	1.00970i
$519$		0			0
$520$	−2.00809e11	−	3.47812e11i	−0.120439	−	0.208607i
$521$	−7.03557e11			−0.418340			−0.209170	−	0.977879i	$-0.567076\pi$
$521$	−7.03557e11			−0.418340			−0.209170	+	0.977879i	$0.567076\pi$
$522$		0			0
$523$	−3.23536e12			−1.89088			−0.945441	−	0.325793i	$-0.894369\pi$
$523$	−3.23536e12			−1.89088			−0.945441	+	0.325793i	$0.894369\pi$
$524$	−1.31533e12	−	2.27822e12i	−0.762156	−	1.32009i
$525$		0			0
$526$	−1.50167e12	+	2.60096e12i	−0.855337	+	1.48149i
$527$	−6.76407e11	+	1.17157e12i	−0.381997	+	0.661638i
$528$		0			0
$529$	2.09745e11	+	3.63288e11i	0.116450	+	0.201698i
$530$	1.62899e12			0.896760
$531$		0			0
$532$	−2.28459e12			−1.23653
$533$	−1.50968e12	−	2.61484e12i	−0.810237	−	1.40337i
$534$		0			0
$535$	−1.09837e12	+	1.90243e12i	−0.579637	+	1.00396i
$536$	−1.21632e11	+	2.10673e11i	−0.0636513	+	0.110247i
$537$		0			0
$538$	−6.33497e10	−	1.09725e11i	−0.0326005	−	0.0564657i
$539$	−2.08002e11			−0.106149
$540$		0			0
$541$	−1.71900e12			−0.862759			−0.431379	−	0.902171i	$-0.641973\pi$
$541$	−1.71900e12			−0.862759			−0.431379	+	0.902171i	$0.641973\pi$
$542$	2.07323e12	+	3.59095e12i	1.03193	+	1.78736i
$543$		0			0
$544$	2.53524e12	−	4.39117e12i	1.24115	−	2.14974i
$545$	−5.21972e11	+	9.04082e11i	−0.253433	+	0.438959i
$546$		0			0
$547$	−6.93110e11	−	1.20050e12i	−0.331024	−	0.573350i	0.651689	−	0.758486i	$-0.274061\pi$
$547$	−6.93110e11	−	1.20050e12i	−0.331024	−	0.573350i	−0.982713	+	0.185136i	$0.940727\pi$
$548$	−1.91685e12			−0.907979
$549$		0			0
$550$	1.10637e11			0.0515547
$551$	−6.06198e11	−	1.04997e12i	−0.280177	−	0.485280i
$552$		0			0
$553$	−1.21121e11	+	2.09788e11i	−0.0550752	+	0.0953930i
$554$	−2.00507e12	+	3.47288e12i	−0.904347	+	1.56637i
$555$		0			0
$556$	−1.30025e12	−	2.25210e12i	−0.577020	−	0.999428i
$557$	1.75428e12			0.772236			0.386118	−	0.922449i	$-0.373816\pi$
$557$	1.75428e12			0.772236			0.386118	+	0.922449i	$0.373816\pi$
$558$		0			0
$559$	−5.62948e12			−2.43846
$560$	−7.90765e11	−	1.36965e12i	−0.339783	−	0.588521i
$561$		0			0
$562$	−2.93513e11	+	5.08380e11i	−0.124112	+	0.214968i
$563$	1.77696e12	−	3.07778e12i	0.745399	−	1.29107i	−0.204609	−	0.978844i	$-0.565592\pi$
$563$	1.77696e12	−	3.07778e12i	0.745399	−	1.29107i	0.950008	−	0.312226i	$-0.101074\pi$
$564$		0			0
$565$	−3.83882e11	−	6.64904e11i	−0.158482	−	0.274499i
$566$	−6.54771e12			−2.68173
$567$		0			0
$568$	−3.96479e10			−0.0159828
$569$	5.74797e11	+	9.95577e11i	0.229884	+	0.398171i	0.957774	−	0.287523i	$-0.0928319\pi$
$569$	5.74797e11	+	9.95577e11i	0.229884	+	0.398171i	−0.727889	+	0.685695i	$0.759499\pi$
$570$		0			0
$571$	8.37800e11	−	1.45111e12i	0.329821	−	0.571266i	−0.652655	−	0.757655i	$-0.726345\pi$
$571$	8.37800e11	−	1.45111e12i	0.329821	−	0.571266i	0.982476	+	0.186389i	$0.0596784\pi$
$572$	−7.69825e11	+	1.33338e12i	−0.300684	+	0.520799i
$573$		0			0
$574$	1.41497e12	+	2.45080e12i	0.544056	+	0.942332i
$575$	−2.61997e11			−0.0999520
$576$		0			0
$577$	2.71422e12			1.01942			0.509712	−	0.860345i	$-0.329752\pi$
$577$	2.71422e12			1.01942			0.509712	+	0.860345i	$0.329752\pi$
$578$	3.87681e12	+	6.71483e12i	1.44477	+	2.50242i
$579$		0			0
$580$	−5.71862e11	+	9.90494e11i	−0.209829	+	0.363434i
$581$	6.33199e11	−	1.09673e12i	0.230541	−	0.399308i
$582$		0			0
$583$	−2.85758e11	−	4.94947e11i	−0.102445	−	0.177440i
$584$	2.66695e11			0.0948760
$585$		0			0
$586$	−1.73623e12			−0.608230
$587$	−2.88822e11	−	5.00254e11i	−0.100406	−	0.173908i	0.811446	−	0.584427i	$-0.198681\pi$
$587$	−2.88822e11	−	5.00254e11i	−0.100406	−	0.173908i	−0.911852	+	0.410519i	$0.865347\pi$
$588$		0			0
$589$	−8.92108e11	+	1.54518e12i	−0.305421	+	0.529004i
$590$	2.97032e12	−	5.14475e12i	1.00918	−	1.74795i
$591$		0			0
$592$	−1.31604e12	−	2.27944e12i	−0.440373	−	0.762748i
$593$	3.92531e12			1.30355			0.651776	−	0.758411i	$-0.274024\pi$
$593$	3.92531e12			1.30355			0.651776	+	0.758411i	$0.274024\pi$
$594$		0			0
$595$	4.04295e12			1.32243
$596$	−6.40133e11	−	1.10874e12i	−0.207808	−	0.359934i
$597$		0			0
$598$	3.47918e12	−	6.02612e12i	1.11256	−	1.92700i
$599$	−1.87955e12	+	3.25548e12i	−0.596532	+	1.03322i	0.396797	+	0.917906i	$0.370122\pi$
$599$	−1.87955e12	+	3.25548e12i	−0.596532	+	1.03322i	−0.993329	+	0.115317i	$0.963212\pi$
$600$		0			0
$601$	−7.16159e11	−	1.24042e12i	−0.223910	−	0.387824i	0.732082	−	0.681217i	$-0.238549\pi$
$601$	−7.16159e11	−	1.24042e12i	−0.223910	−	0.387824i	−0.955992	+	0.293393i	$0.905216\pi$
$602$	5.27631e12			1.63737
$603$		0			0
$604$	−5.60741e11			−0.171434
$605$	−1.40015e12	−	2.42512e12i	−0.424887	−	0.735927i
$606$		0			0
$607$	−1.84111e12	+	3.18889e12i	−0.550465	+	0.953434i	0.447776	+	0.894146i	$0.352216\pi$
$607$	−1.84111e12	+	3.18889e12i	−0.550465	+	0.953434i	−0.998241	+	0.0592880i	$0.981117\pi$
$608$	3.34372e12	−	5.79149e12i	0.992346	−	1.71879i
$609$		0			0
$610$	−3.97845e12	−	6.89087e12i	−1.16340	−	2.01507i
$611$	−3.49371e12			−1.01415
$612$		0			0
$613$	3.14562e12			0.899777			0.449888	−	0.893085i	$-0.351464\pi$
$613$	3.14562e12			0.899777			0.449888	+	0.893085i	$0.351464\pi$
$614$	−1.00088e12	−	1.73357e12i	−0.284200	−	0.492248i
$615$		0			0
$616$	6.60323e10	−	1.14371e11i	0.0184775	−	0.0320040i
$617$	9.20559e11	−	1.59445e12i	0.255722	−	0.442924i	−0.709369	−	0.704837i	$-0.751020\pi$
$617$	9.20559e11	−	1.59445e12i	0.255722	−	0.442924i	0.965091	+	0.261913i	$0.0843534\pi$
$618$		0			0
$619$	1.08436e11	+	1.87817e11i	0.0296870	+	0.0514193i	0.880487	−	0.474070i	$-0.157216\pi$
$619$	1.08436e11	+	1.87817e11i	0.0296870	+	0.0514193i	−0.850800	+	0.525489i	$0.823882\pi$
$620$	1.68316e12			0.457469
$621$		0			0
$622$	−1.23157e12			−0.329915
$623$	2.85313e12	+	4.94177e12i	0.758797	+	1.31428i
$624$		0			0
$625$	1.66484e12	−	2.88359e12i	0.436428	−	0.755915i
$626$	1.46840e12	−	2.54335e12i	0.382174	−	0.661944i
$627$		0			0
$628$	3.36216e12	+	5.82343e12i	0.862581	+	1.49403i
$629$	6.72851e12			1.71392
$630$		0			0
$631$	3.08505e11			0.0774693			0.0387346	−	0.999250i	$-0.487667\pi$
$631$	3.08505e11			0.0774693			0.0387346	+	0.999250i	$0.487667\pi$
$632$	3.97163e10	+	6.87906e10i	0.00990243	+	0.0171515i
$633$		0			0
$634$	−3.60531e12	+	6.24458e12i	−0.886219	+	1.53498i
$635$	6.59682e11	−	1.14260e12i	0.161010	−	0.278877i
$636$		0			0
$637$	1.24033e12	+	2.14832e12i	0.298477	+	0.516978i
$638$	7.65808e11			0.182990
$639$		0			0
$640$	−1.16062e12			−0.273451
$641$	−3.37713e12	−	5.84935e12i	−0.790108	−	1.36851i	−0.925900	−	0.377769i	$-0.876691\pi$
$641$	−3.37713e12	−	5.84935e12i	−0.790108	−	1.36851i	0.135792	−	0.990737i	$-0.456642\pi$
$642$		0			0
$643$	−4.57285e11	+	7.92042e11i	−0.105496	+	0.182725i	−0.913941	−	0.405847i	$-0.866977\pi$
$643$	−4.57285e11	+	7.92042e11i	−0.105496	+	0.182725i	0.808444	+	0.588572i	$0.200310\pi$
$644$	−1.70864e12	+	2.95946e12i	−0.391440	+	0.677993i
$645$		0			0
$646$	7.67782e12	+	1.32984e13i	1.73457	+	3.00436i
$647$	1.29528e12			0.290600			0.145300	−	0.989388i	$-0.453585\pi$
$647$	1.29528e12			0.290600			0.145300	+	0.989388i	$0.453585\pi$
$648$		0			0
$649$	−2.08422e12			−0.461151
$650$	−6.59739e11	−	1.14270e12i	−0.144965	−	0.251086i
$651$		0			0
$652$	−5.69544e11	+	9.86480e11i	−0.123428	+	0.213783i
$653$	−2.61023e12	+	4.52106e12i	−0.561785	+	0.973040i	0.435556	+	0.900162i	$0.356552\pi$
$653$	−2.61023e12	+	4.52106e12i	−0.561785	+	0.973040i	−0.997341	+	0.0728783i	$0.976782\pi$
$654$		0			0
$655$	3.06997e12	+	5.31734e12i	0.651700	+	1.12878i
$656$	−3.89877e12			−0.821978
$657$		0			0
$658$	3.27453e12			0.680977
$659$	2.43495e12	+	4.21746e12i	0.502928	+	0.871098i	0.999994	+	0.00338473i	$0.00107739\pi$
$659$	2.43495e12	+	4.21746e12i	0.502928	+	0.871098i	−0.497066	+	0.867713i	$0.665589\pi$
$660$		0			0
$661$	−8.69844e11	+	1.50661e12i	−0.177229	+	0.306970i	−0.940930	−	0.338600i	$-0.890047\pi$
$661$	−8.69844e11	+	1.50661e12i	−0.177229	+	0.306970i	0.763701	+	0.645570i	$0.223380\pi$
$662$	−2.73668e12	+	4.74007e12i	−0.553814	+	0.959233i
$663$		0			0
$664$	−2.07630e11	−	3.59625e11i	−0.0414508	−	0.0717949i
$665$	5.33221e12			1.05733
$666$		0			0
$667$	−1.81350e12			−0.354773
$668$	−3.57708e12	−	6.19569e12i	−0.695080	−	1.20391i
$669$		0			0
$670$	3.10203e12	−	5.37287e12i	0.594715	−	1.03008i
$671$	−1.39580e12	+	2.41760e12i	−0.265811	+	0.460398i
$672$		0			0
$673$	−2.50421e12	−	4.33741e12i	−0.470546	−	0.815010i	0.528886	−	0.848693i	$-0.322610\pi$
$673$	−2.50421e12	−	4.33741e12i	−0.470546	−	0.815010i	−0.999433	+	0.0336827i	$0.989276\pi$
$674$	9.38042e10			0.0175087
$675$		0			0
$676$	1.23857e13			2.28119
$677$	3.72041e12	+	6.44394e12i	0.680678	+	1.17897i	0.974774	+	0.223194i	$0.0716482\pi$
$677$	3.72041e12	+	6.44394e12i	0.680678	+	1.17897i	−0.294096	+	0.955776i	$0.595018\pi$
$678$		0			0
$679$	−7.66006e11	+	1.32676e12i	−0.138299	+	0.239540i
$680$	6.62853e11	−	1.14810e12i	0.118885	−	0.205915i
$681$		0			0
$682$	−5.63499e11	−	9.76009e11i	−0.0997386	−	0.172752i
$683$	−9.49272e12			−1.66916			−0.834579	−	0.550888i	$-0.814289\pi$
$683$	−9.49272e12			−1.66916			−0.834579	+	0.550888i	$0.814289\pi$
$684$		0			0
$685$	4.47391e12			0.776390
$686$	−4.57602e12	−	7.92590e12i	−0.788914	−	1.36644i
$687$		0			0
$688$	−3.63455e12	+	6.29523e12i	−0.618448	+	1.07118i
$689$	−3.40801e12	+	5.90284e12i	−0.576121	+	0.997871i
$690$		0			0
$691$	−6.51591e11	−	1.12859e12i	−0.108724	−	0.188315i	0.806530	−	0.591193i	$-0.201343\pi$
$691$	−6.51591e11	−	1.12859e12i	−0.108724	−	0.188315i	−0.915253	+	0.402879i	$0.868010\pi$
$692$	−3.22523e12			−0.534667
$693$		0			0
$694$	−5.13711e12			−0.840623
$695$	3.03477e12	+	5.25638e12i	0.493395	+	0.854585i
$696$		0			0
$697$	4.98331e12	−	8.63135e12i	0.799780	−	1.38526i
$698$	−5.22689e11	+	9.05324e11i	−0.0833478	+	0.144363i
$699$		0			0
$700$	3.24001e11	+	5.61186e11i	0.0510041	+	0.0883416i
$701$	−1.24667e13			−1.94993			−0.974966	−	0.222354i	$-0.928626\pi$
$701$	−1.24667e13			−1.94993			−0.974966	+	0.222354i	$0.928626\pi$
$702$		0			0
$703$	8.87418e12			1.37034
$704$	1.20898e12	+	2.09402e12i	0.185500	+	0.321295i
$705$		0			0
$706$	−3.27356e12	+	5.66998e12i	−0.495906	+	0.858935i
$707$	2.59105e11	−	4.48783e11i	0.0390022	−	0.0675537i
$708$		0			0
$709$	−1.49539e12	−	2.59010e12i	−0.222253	−	0.384953i	0.733239	−	0.679971i	$-0.238008\pi$
$709$	−1.49539e12	−	2.59010e12i	−0.222253	−	0.384953i	−0.955492	+	0.295018i	$0.904674\pi$
$710$	1.01115e12			0.149332
$711$		0			0
$712$	1.87112e12			0.272861
$713$	1.33441e12	+	2.31127e12i	0.193369	+	0.334925i
$714$		0			0
$715$	1.79676e12	−	3.11209e12i	0.257107	−	0.445322i
$716$	4.31241e12	−	7.46931e12i	0.613212	−	1.06212i
$717$		0			0
$718$	7.85937e11	+	1.36128e12i	0.110364	+	0.191156i
$719$	−4.07204e12			−0.568240			−0.284120	−	0.958789i	$-0.591701\pi$
$719$	−4.07204e12			−0.568240			−0.284120	+	0.958789i	$0.591701\pi$
$720$		0			0
$721$	−4.61444e12			−0.635931
$722$	4.83479e12	+	8.37411e12i	0.662156	+	1.14689i
$723$		0			0
$724$	−4.29836e12	+	7.44498e12i	−0.581405	+	1.00702i
$725$	−1.71942e11	+	2.97812e11i	−0.0231132	+	0.0400333i
$726$		0			0
$727$	5.16042e12	+	8.93811e12i	0.685141	+	1.18670i	0.973392	+	0.229145i	$0.0735930\pi$
$727$	5.16042e12	+	8.93811e12i	0.685141	+	1.18670i	−0.288251	+	0.957555i	$0.593074\pi$
$728$	−1.57503e12			−0.207825
$729$		0			0
$730$	−6.80159e12			−0.886457
$731$	−9.29119e12	−	1.60928e13i	−1.20349	−	2.08451i
$732$		0			0
$733$	5.46852e12	−	9.47176e12i	0.699684	−	1.21189i	−0.268892	−	0.963170i	$-0.586657\pi$
$733$	5.46852e12	−	9.47176e12i	0.699684	−	1.21189i	0.968576	−	0.248718i	$-0.0800093\pi$
$734$	3.10352e12	−	5.37546e12i	0.394660	−	0.683571i
$735$		0			0
$736$	−5.00152e12	−	8.66289e12i	−0.628278	−	1.08821i
$737$	−2.17664e12			−0.271758
$738$		0			0
$739$	5.74543e12			0.708635			0.354317	−	0.935125i	$-0.384713\pi$
$739$	5.74543e12			0.708635			0.354317	+	0.935125i	$0.384713\pi$
$740$	−4.18577e12	−	7.24997e12i	−0.513136	−	0.888778i
$741$		0			0
$742$	3.19420e12	−	5.53252e12i	0.386852	−	0.670048i
$743$	1.26711e12	−	2.19470e12i	0.152534	−	0.264196i	−0.779625	−	0.626247i	$-0.784590\pi$
$743$	1.26711e12	−	2.19470e12i	0.152534	−	0.264196i	0.932158	+	0.362051i	$0.117923\pi$
$744$		0			0
$745$	1.49406e12	+	2.58780e12i	0.177691	+	0.307770i
$746$	3.27386e12			0.387022
$747$		0			0
$748$	−5.08224e12			−0.593606
$749$	4.30748e12	+	7.46077e12i	0.500097	+	0.866194i
$750$		0			0
$751$	−1.36927e12	+	2.37164e12i	−0.157076	+	0.272063i	−0.933813	−	0.357762i	$-0.883540\pi$
$751$	−1.36927e12	+	2.37164e12i	−0.157076	+	0.272063i	0.776737	+	0.629825i	$0.216873\pi$
$752$	−2.25564e12	+	3.90688e12i	−0.257211	+	0.445502i
$753$		0			0
$754$	−4.56659e12	−	7.90957e12i	−0.514542	−	0.891213i
$755$	1.30876e12			0.146589
$756$		0			0
$757$	−1.27669e13			−1.41304			−0.706519	−	0.707694i	$-0.749736\pi$
$757$	−1.27669e13			−1.41304			−0.706519	+	0.707694i	$0.749736\pi$
$758$	1.11388e12	+	1.92929e12i	0.122553	+	0.212269i
$759$		0			0
$760$	8.74232e11	−	1.51422e12i	0.0950530	−	0.164637i
$761$	−1.98620e12	+	3.44020e12i	−0.214680	+	0.371838i	−0.953174	−	0.302423i	$-0.902204\pi$
$761$	−1.98620e12	+	3.44020e12i	−0.214680	+	0.371838i	0.738493	+	0.674261i	$0.235538\pi$
$762$		0			0
$763$	2.04702e12	+	3.54554e12i	0.218656	+	0.378723i
$764$	1.08727e13			1.15456
$765$		0			0
$766$	−1.69068e13			−1.77432
$767$	1.24284e13	+	2.15267e13i	1.29669	+	2.24594i
$768$		0			0
$769$	2.92820e11	−	5.07180e11i	0.0301948	−	0.0522990i	−0.850533	−	0.525922i	$-0.823721\pi$
$769$	2.92820e11	−	5.07180e11i	0.0301948	−	0.0522990i	0.880728	+	0.473623i	$0.157054\pi$
$770$	−1.68404e12	+	2.91685e12i	−0.172641	+	0.299024i
$771$		0			0
$772$	−2.48519e12	−	4.30447e12i	−0.251815	−	0.436156i
$773$	4.19065e12			0.422157			0.211079	−	0.977469i	$-0.432302\pi$
$773$	4.19065e12			0.422157			0.211079	+	0.977469i	$0.432302\pi$
$774$		0			0
$775$	5.06075e11			0.0503915
$776$	2.51178e11	+	4.35053e11i	0.0248659	+	0.0430689i
$777$		0			0
$778$	−3.23049e12	+	5.59538e12i	−0.316126	+	0.547547i
$779$	6.57246e12	−	1.13838e13i	0.639454	−	1.10757i
$780$		0			0
$781$	−1.77377e11	−	3.07226e11i	−0.0170595	−	0.0295480i
$782$	2.29689e13			2.19639
$783$		0			0
$784$	3.20318e12			0.302803
$785$	−7.84724e12	−	1.35918e13i	−0.737571	−	1.27751i
$786$		0			0
$787$	−4.45343e12	+	7.71357e12i	−0.413817	+	0.716752i	−0.995303	−	0.0968040i	$-0.969138\pi$
$787$	−4.45343e12	+	7.71357e12i	−0.413817	+	0.716752i	0.581486	+	0.813556i	$0.302471\pi$
$788$	1.73170e12	−	2.99940e12i	0.159995	−	0.277119i
$789$		0			0
$790$	−1.01290e12	−	1.75439e12i	−0.0925216	−	0.160252i
$791$	−3.01095e12			−0.273469
$792$		0			0
$793$	3.32932e13			2.98969
$794$	−9.62147e12	−	1.66649e13i	−0.859111	−	1.48802i
$795$		0			0
$796$	−3.72737e12	+	6.45599e12i	−0.329074	+	0.569973i
$797$	7.69801e11	−	1.33333e12i	0.0675797	−	0.117051i	−0.830256	−	0.557383i	$-0.811806\pi$
$797$	7.69801e11	−	1.33333e12i	0.0675797	−	0.117051i	0.897835	+	0.440331i	$0.145139\pi$
$798$		0			0
$799$	−5.76620e12	−	9.98736e12i	−0.500529	−	0.866942i
$800$	−1.89682e12			−0.163728
$801$		0			0
$802$	−1.82246e13			−1.55551
$803$	1.19314e12	+	2.06658e12i	0.101268	+	0.175401i
$804$		0			0
$805$	3.98795e12	−	6.90734e12i	0.334710	−	0.579735i
$806$	−6.72040e12	+	1.16401e13i	−0.560903	+	0.971512i
$807$		0			0
$808$	−8.49621e10	−	1.47159e11i	−0.00701252	−	0.0121460i
$809$	2.05894e13			1.68996			0.844979	−	0.534799i	$-0.179613\pi$
$809$	2.05894e13			1.68996			0.844979	+	0.534799i	$0.179613\pi$
$810$		0			0
$811$	−7.35060e12			−0.596663			−0.298331	−	0.954462i	$-0.596430\pi$
$811$	−7.35060e12			−0.596663			−0.298331	+	0.954462i	$0.596430\pi$
$812$	2.24267e12	+	3.88442e12i	0.181036	+	0.313563i
$813$		0			0
$814$	−2.80268e12	+	4.85439e12i	−0.223751	+	0.387547i
$815$	1.32931e12	−	2.30243e12i	0.105540	−	0.182801i
$816$		0			0
$817$	−1.22541e13	−	2.12247e13i	−0.962236	−	1.66664i
$818$	−6.22210e12			−0.485901
$819$		0			0
$820$	−1.24004e13			−0.957794
$821$	−3.51993e12	−	6.09669e12i	−0.270389	−	0.468328i	0.698572	−	0.715539i	$-0.253819\pi$
$821$	−3.51993e12	−	6.09669e12i	−0.270389	−	0.468328i	−0.968961	+	0.247212i	$0.920486\pi$
$822$		0			0
$823$	−1.69886e11	+	2.94251e11i	−0.0129080	+	0.0223573i	−0.872407	−	0.488780i	$-0.837442\pi$
$823$	−1.69886e11	+	2.94251e11i	−0.0129080	+	0.0223573i	0.859499	+	0.511137i	$0.170776\pi$
$824$	−7.56551e11	+	1.31039e12i	−0.0571697	+	0.0990208i
$825$		0			0
$826$	−1.16487e13	−	2.01762e13i	−0.870699	−	1.50809i
$827$	1.68131e13			1.24989			0.624947	−	0.780668i	$-0.285121\pi$
$827$	1.68131e13			1.24989			0.624947	+	0.780668i	$0.285121\pi$
$828$		0			0
$829$	6.50421e12			0.478299			0.239149	−	0.970983i	$-0.423131\pi$
$829$	6.50421e12			0.478299			0.239149	+	0.970983i	$0.423131\pi$
$830$	5.29525e12	+	9.17164e12i	0.387289	+	0.670804i
$831$		0			0
$832$	1.44186e13	−	2.49737e13i	1.04320	−	1.80688i
$833$	−4.09423e12	+	7.09142e12i	−0.294625	+	0.510306i
$834$		0			0
$835$	8.34888e12	+	1.44607e13i	0.594345	+	1.02944i
$836$	−6.70294e12			−0.474610
$837$		0			0
$838$	−2.37496e13			−1.66363
$839$	−1.05425e12	−	1.82601e12i	−0.0734538	−	0.127226i	0.826959	−	0.562262i	$-0.190069\pi$
$839$	−1.05425e12	−	1.82601e12i	−0.0734538	−	0.127226i	−0.900413	+	0.435036i	$0.856735\pi$
$840$		0			0
$841$	6.06342e12	−	1.05022e13i	0.417961	−	0.723930i
$842$	1.79554e13	−	3.10997e13i	1.23109	−	2.13232i
$843$		0			0
$844$	6.98037e12	+	1.20903e13i	0.473519	+	0.820159i
$845$	−2.89081e13			−1.95059
$846$		0			0
$847$	−1.09819e13			−0.733166
$848$	4.40061e12	+	7.62209e12i	0.292235	+	0.506166i
$849$		0			0
$850$	2.17774e12	−	3.77195e12i	0.143094	−	0.247845i
$851$	6.63699e12	−	1.14956e13i	0.433798	−	0.751361i
$852$		0			0
$853$	−8.71221e12	−	1.50900e13i	−0.563453	−	0.975929i	−0.997192	−	0.0748904i	$-0.976139\pi$
$853$	−8.71221e12	−	1.50900e13i	−0.563453	−	0.975929i	0.433739	−	0.901039i	$-0.357194\pi$
$854$	−3.12046e13			−2.00751
$855$		0			0
$856$	2.82489e12			0.179833
$857$	7.74931e11	+	1.34222e12i	0.0490737	+	0.0849982i	0.889519	−	0.456898i	$-0.151040\pi$
$857$	7.74931e11	+	1.34222e12i	0.0490737	+	0.0849982i	−0.840445	+	0.541897i	$0.817706\pi$
$858$		0			0
$859$	−9.72767e12	+	1.68488e13i	−0.609592	+	1.05584i	0.381715	+	0.924280i	$0.375333\pi$
$859$	−9.72767e12	+	1.68488e13i	−0.609592	+	1.05584i	−0.991308	+	0.131565i	$0.958000\pi$
$860$	−1.15600e13	+	2.00225e13i	−0.720635	+	1.24818i
$861$		0			0
$862$	8.60047e12	+	1.48965e13i	0.530566	+	0.918968i
$863$	1.23365e13			0.757080			0.378540	−	0.925585i	$-0.376426\pi$
$863$	1.23365e13			0.757080			0.378540	+	0.925585i	$0.376426\pi$
$864$		0			0
$865$	7.52765e12			0.457180
$866$	−8.75132e12	−	1.51577e13i	−0.528741	−	0.915806i
$867$		0			0
$868$	3.30042e12	−	5.71649e12i	0.197347	−	0.341815i
$869$	−3.55366e11	+	6.15512e11i	−0.0211391	+	0.0366140i
$870$		0			0
$871$	1.29795e13	+	2.24811e13i	0.764146	+	1.32354i
$872$	1.34246e12			0.0786280
$873$		0			0
$874$	3.02936e13			1.75610
$875$	−7.38264e12	−	1.27871e13i	−0.425770	−	0.737456i
$876$		0			0
$877$	1.18847e13	−	2.05849e13i	0.678406	−	1.17503i	−0.297055	−	0.954860i	$-0.596004\pi$
$877$	1.18847e13	−	2.05849e13i	0.678406	−	1.17503i	0.975461	−	0.220173i	$-0.0706622\pi$
$878$	−8.89592e12	+	1.54082e13i	−0.505202	+	0.875036i
$879$		0			0
$880$	−2.32009e12	−	4.01851e12i	−0.130416	−	0.225888i
$881$	−2.37158e13			−1.32631			−0.663156	−	0.748481i	$-0.730783\pi$
$881$	−2.37158e13			−1.32631			−0.663156	+	0.748481i	$0.730783\pi$
$882$		0			0
$883$	1.17562e13			0.650795			0.325397	−	0.945577i	$-0.394502\pi$
$883$	1.17562e13			0.650795			0.325397	+	0.945577i	$0.394502\pi$
$884$	3.03059e13	+	5.24914e13i	1.66914	+	2.89103i
$885$		0			0
$886$	−1.66744e13	+	2.88809e13i	−0.909072	+	1.57456i
$887$	−1.55671e13	+	2.69630e13i	−0.844406	+	1.46255i	0.0417306	+	0.999129i	$0.486713\pi$
$887$	−1.55671e13	+	2.69630e13i	−0.844406	+	1.46255i	−0.886136	+	0.463425i	$0.846620\pi$
$888$		0			0
$889$	−2.58707e12	−	4.48095e12i	−0.138916	−	0.240609i
$890$	−4.77197e13			−2.54943
$891$		0			0
$892$	7.80449e12			0.412765
$893$	−7.60501e12	−	1.31723e13i	−0.400192	−	0.693152i
$894$		0			0
$895$	−1.00651e13	+	1.74333e13i	−0.524342	+	0.908188i
$896$	−2.27580e12	+	3.94180e12i	−0.117964	+	0.204319i
$897$		0			0
$898$	1.25984e12	+	2.18211e12i	0.0646505	+	0.111978i
$899$	3.50296e12			0.178861
$900$		0			0
$901$	−2.24990e13			−1.13737
$902$	4.15148e12	+	7.19058e12i	0.208821	+	0.361688i
$903$		0			0
$904$	−4.93654e11	+	8.55033e11i	−0.0245847	+	0.0425819i
$905$	1.00323e13	−	1.73765e13i	0.497145	−	0.861080i
$906$		0			0
$907$	1.52208e13	+	2.63632e13i	0.746802	+	1.29350i	0.949348	+	0.314226i	$0.101745\pi$
$907$	1.52208e13	+	2.63632e13i	0.746802	+	1.29350i	−0.202547	+	0.979273i	$0.564922\pi$
$908$	3.12736e13			1.52683
$909$		0			0
$910$	4.01685e13			1.94178
$911$	−8.72437e12	−	1.51110e13i	−0.419664	−	0.726879i	0.576242	−	0.817279i	$-0.304519\pi$
$911$	−8.72437e12	−	1.51110e13i	−0.419664	−	0.726879i	−0.995905	+	0.0904006i	$0.971185\pi$
$912$		0			0
$913$	1.85779e12	−	3.21779e12i	0.0884867	−	0.153264i
$914$	−9.08931e12	+	1.57432e13i	−0.430798	+	0.746163i
$915$		0			0
$916$	−9.01739e11	−	1.56186e12i	−0.0423205	−	0.0733013i
$917$	2.40790e13			1.12454
$918$		0			0
$919$	9.40533e12			0.434965			0.217483	−	0.976064i	$-0.430215\pi$
$919$	9.40533e12			0.434965			0.217483	+	0.976064i	$0.430215\pi$
$920$	−1.30767e12	−	2.26496e12i	−0.0601803	−	0.104235i
$921$		0			0
$922$	−1.79306e13	+	3.10568e13i	−0.817158	+	1.41536i
$923$	−2.11543e12	+	3.66404e12i	−0.0959382	+	0.166170i
$924$		0			0
$925$	−1.25854e12	−	2.17985e12i	−0.0565234	−	0.0979013i
$926$	−4.59247e13			−2.05256
$927$		0			0
$928$	−1.31295e13			−0.581140
$929$	4.21514e12	+	7.30083e12i	0.185670	+	0.321589i	0.943802	−	0.330511i	$-0.107221\pi$
$929$	4.21514e12	+	7.30083e12i	0.185670	+	0.321589i	−0.758132	+	0.652101i	$0.773888\pi$
$930$		0			0
$931$	−5.39985e12	+	9.35282e12i	−0.235564	+	0.408008i
$932$	−4.11374e12	+	7.12521e12i	−0.178594	+	0.309333i
$933$		0			0
$934$	2.61345e13	+	4.52663e13i	1.12371	+	1.94632i
$935$	1.18619e13			0.507577
$936$		0			0
$937$	2.45230e10			0.00103931			0.000519656	−	1.00000i	$-0.499835\pi$
$937$	2.45230e10			0.00103931			0.000519656		1.00000i	$0.499835\pi$
$938$	−1.21652e13	−	2.10708e13i	−0.513106	−	0.888726i
$939$		0			0
$940$	−7.17425e12	+	1.24262e13i	−0.299710	+	0.519113i
$941$	1.76435e13	−	3.05594e13i	0.733553	−	1.27055i	−0.221802	−	0.975092i	$-0.571194\pi$
$941$	1.76435e13	−	3.05594e13i	0.733553	−	1.27055i	0.955355	−	0.295459i	$-0.0954727\pi$
$942$		0			0
$943$	−9.83106e12	−	1.70279e13i	−0.404853	−	0.701227i
$944$	3.20966e13			1.31548
$945$		0			0
$946$	1.54806e13			0.628459
$947$	−8.68390e12	−	1.50410e13i	−0.350865	−	0.607716i	0.635536	−	0.772071i	$-0.280779\pi$
$947$	−8.68390e12	−	1.50410e13i	−0.350865	−	0.607716i	−0.986401	+	0.164355i	$0.947446\pi$
$948$		0			0
$949$	1.42296e13	−	2.46464e13i	0.569502	−	0.986406i
$950$	2.87220e12	−	4.97480e12i	0.114409	−	0.198162i
$951$		0			0
$952$	−2.59951e12	−	4.50249e12i	−0.102571	−	0.177659i
$953$	1.07207e13			0.421024			0.210512	−	0.977591i	$-0.432487\pi$
$953$	1.07207e13			0.421024			0.210512	+	0.977591i	$0.432487\pi$
$954$		0			0
$955$	−2.53767e13			−0.987234
$956$	−1.28848e13	−	2.23170e13i	−0.498902	−	0.864124i
$957$		0			0
$958$	1.33172e13	−	2.30661e13i	0.510820	−	0.884766i
$959$	8.77268e12	−	1.51947e13i	0.334926	−	0.580108i
$960$		0			0
$961$	1.06423e13	+	1.84329e13i	0.402512	+	0.697171i
$962$	6.68507e13			2.51662
$963$		0			0
$964$	1.04966e12			0.0391474
$965$	5.80040e12	+	1.00466e13i	0.215320	+	0.372946i
$966$		0			0
$967$	2.20118e13	−	3.81256e13i	0.809537	−	1.40216i	−0.103648	−	0.994614i	$-0.533051\pi$
$967$	2.20118e13	−	3.81256e13i	0.809537	−	1.40216i	0.913185	−	0.407546i	$-0.133615\pi$
$968$	−1.80052e12	+	3.11859e12i	−0.0659110	+	0.114161i
$969$		0			0
$970$	−6.40587e12	−	1.10953e13i	−0.232330	−	0.402407i
$971$	3.18653e13			1.15035			0.575177	−	0.818029i	$-0.304933\pi$
$971$	3.18653e13			1.15035			0.575177	+	0.818029i	$0.304933\pi$
$972$		0			0
$973$	2.38030e13			0.851380
$974$	1.46777e13	+	2.54225e13i	0.522567	+	0.905113i
$975$		0			0
$976$	2.14951e13	−	3.72306e13i	0.758254	−	1.31333i
$977$	−1.83610e13	+	3.18021e13i	−0.644718	+	1.11669i	0.339648	+	0.940553i	$0.389692\pi$
$977$	−1.83610e13	+	3.18021e13i	−0.644718	+	1.11669i	−0.984366	+	0.176132i	$0.943641\pi$
$978$		0			0
$979$	8.37102e12	+	1.44990e13i	0.291244	+	0.504449i
$980$	1.01880e13			0.352835
$981$		0			0
$982$	4.62913e13			1.58854
$983$	−6.92373e12	−	1.19922e13i	−0.236510	−	0.409647i	0.723201	−	0.690638i	$-0.242670\pi$
$983$	−6.92373e12	−	1.19922e13i	−0.236510	−	0.409647i	−0.959710	+	0.280991i	$0.909337\pi$
$984$		0			0
$985$	−4.04177e12	+	7.00056e12i	−0.136807	+	0.236957i
$986$	1.50739e13	−	2.61087e13i	0.507901	−	0.879711i
$987$		0			0
$988$	3.99703e13	+	6.92305e13i	1.33454	+	2.31149i
$989$	−3.66593e13			−1.21843
$990$		0			0
$991$	4.28865e12			0.141250			0.0706252	−	0.997503i	$-0.477501\pi$
$991$	4.28865e12			0.141250			0.0706252	+	0.997503i	$0.477501\pi$
$992$	9.66095e12	+	1.67333e13i	0.316751	+	0.548628i
$993$		0			0
$994$	1.98272e12	−	3.43417e12i	0.0644203	−	0.111579i
$995$	8.69964e12	−	1.50682e13i	0.281383	−	0.487369i
$996$		0			0
$997$	−2.54518e13	−	4.40837e13i	−0.815811	−	1.41303i	−0.908744	−	0.417354i	$-0.862958\pi$
$997$	−2.54518e13	−	4.40837e13i	−0.815811	−	1.41303i	0.0929331	−	0.995672i	$-0.470376\pi$
$998$	5.98290e12			0.190908
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.10.c.g.28.3		6
3.2	odd	2		81.10.c.h.28.1		6
9.2	odd	6		81.10.c.h.55.1		6
9.4	even	3		27.10.a.c.1.1	yes	3
9.5	odd	6		27.10.a.b.1.3	✓	3
9.7	even	3	inner	81.10.c.g.55.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.a.b.1.3	✓	3	9.5	odd	6
27.10.a.c.1.1	yes	3	9.4	even	3
81.10.c.g.28.3		6	1.1	even	1	trivial
81.10.c.g.55.3		6	9.7	even	3	inner
81.10.c.h.28.1		6	3.2	odd	2
81.10.c.h.55.1		6	9.2	odd	6

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	81.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(16.3980 + 28.4022i) q^{2} +(-281.788 + 488.072i) q^{4} +(657.691 - 1139.16i) q^{5} +(-2579.27 - 4467.43i) q^{7} -1691.52 q^{8} +43139.3 q^{10} +(-7567.52 - 13107.3i) q^{11} +(-90251.7 + 156321. i) q^{13} +(84589.7 - 146514. i) q^{14} +(116538. + 201850. i) q^{16} -595825. q^{17} -785830. q^{19} +(370660. + 642002. i) q^{20} +(248184. - 429868. i) q^{22} +(-587721. + 1.01796e6i) q^{23} +(111446. + 193031. i) q^{25} -5.91979e6 q^{26} +2.90723e6 q^{28} +(771411. + 1.33612e6i) q^{29} +(1.13524e6 - 1.96630e6i) q^{31} +(-4.25501e6 + 7.36990e6i) q^{32} +(-9.77034e6 - 1.69227e7i) q^{34} -6.78546e6 q^{35} -1.12928e7 q^{37} +(-1.28860e7 - 2.23193e7i) q^{38} +(-1.11250e6 + 1.92690e6i) q^{40} +(-8.36372e6 + 1.44864e7i) q^{41} +(1.55938e7 + 2.70093e7i) q^{43} +8.52976e6 q^{44} -3.85498e7 q^{46} +(9.67768e6 + 1.67622e7i) q^{47} +(6.87153e6 - 1.19018e7i) q^{49} +(-3.65499e6 + 6.33063e6i) q^{50} +(-5.08638e7 - 8.80986e7i) q^{52} +3.77611e7 q^{53} -1.99084e7 q^{55} +(4.36288e6 + 7.55673e6i) q^{56} +(-2.52992e7 + 4.38195e7i) q^{58} +(6.88542e7 - 1.19259e8i) q^{59} +(-9.22233e7 - 1.59735e8i) q^{61} +7.44629e7 q^{62} -1.59760e8 q^{64} +(1.18716e8 + 2.05621e8i) q^{65} +(7.19072e7 - 1.24547e8i) q^{67} +(1.67897e8 - 2.90806e8i) q^{68} +(-1.11268e8 - 1.92722e8i) q^{70} +2.34392e7 q^{71} -1.57666e8 q^{73} +(-1.85179e8 - 3.20739e8i) q^{74} +(2.21438e8 - 3.83541e8i) q^{76} +(-3.90373e7 + 6.76147e7i) q^{77} +(-2.34797e7 - 4.06680e7i) q^{79} +3.06585e8 q^{80} -5.48593e8 q^{82} +(1.22748e8 + 2.12605e8i) q^{83} +(-3.91869e8 + 6.78737e8i) q^{85} +(-5.11415e8 + 8.85797e8i) q^{86} +(1.28006e7 + 2.21713e7i) q^{88} -1.10618e9 q^{89} +9.31134e8 q^{91} +(-3.31226e8 - 5.73700e8i) q^{92} +(-3.17389e8 + 5.49734e8i) q^{94} +(-5.16833e8 + 8.95182e8i) q^{95} +(-1.48493e8 - 2.57197e8i) q^{97} +4.50717e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 597 q^{4} + 1983 q^{5} + 3693 q^{7} - 9006 q^{8} - 37962 q^{10} + 16863 q^{11} - 116916 q^{13} + 503463 q^{14} + 239919 q^{16} - 2028096 q^{17} - 30444 q^{19} + 2548407 q^{20} - 305721 q^{22}+ \cdots + 5184364572 q^{98}+O(q^{100}) \) 6 * q - 3 * q^2 - 597 * q^4 + 1983 * q^5 + 3693 * q^7 - 9006 * q^8 - 37962 * q^10 + 16863 * q^11 - 116916 * q^13 + 503463 * q^14 + 239919 * q^16 - 2028096 * q^17 - 30444 * q^19 + 2548407 * q^20 - 305721 * q^22 + 2927118 * q^23 - 2133732 * q^25 - 9530232 * q^26 - 7071450 * q^28 + 5768790 * q^29 + 6575223 * q^31 - 2687697 * q^32 - 17098128 * q^34 + 34681074 * q^35 - 23372052 * q^37 - 50473374 * q^38 + 4130811 * q^40 - 22213518 * q^41 - 45384414 * q^43 + 114413982 * q^44 - 191277180 * q^46 + 12392034 * q^47 - 18933462 * q^49 - 82984044 * q^50 - 182736492 * q^52 - 161159274 * q^53 - 349470666 * q^55 + 21850521 * q^56 + 102758922 * q^58 + 244026660 * q^59 - 369729960 * q^61 - 332594682 * q^62 - 841384254 * q^64 + 492225684 * q^65 + 252614586 * q^67 + 162270144 * q^68 - 935092377 * q^70 - 806386176 * q^71 - 813253434 * q^73 - 641373558 * q^74 + 39499590 * q^76 + 360443199 * q^77 - 265451856 * q^79 + 2336719674 * q^80 - 1768816332 * q^82 + 121625871 * q^83 - 316251216 * q^85 - 2368956570 * q^86 - 219257739 * q^88 - 755808012 * q^89 + 490118280 * q^91 - 1178754558 * q^92 - 86583438 * q^94 + 536878770 * q^95 + 438907539 * q^97 + 5184364572 * q^98

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