LMFDB - Embedded newform 567.2.p.c.404.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(80,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("567.80");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.288778218147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			404.5
Root			$1.07065 - 1.85442i$ of defining polynomial
Character	$\chi$	$=$	567.404
Dual form			567.2.p.c.80.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.24607 + 1.29677i) q^{2} +(2.36322 + 4.09323i) q^{4} +(-0.626493 + 1.08512i) q^{5} +(2.54556 - 0.721191i) q^{7} +7.07116i q^{8} +O(q^{10})$	\(q+(2.24607 + 1.29677i) q^{2} +(2.36322 + 4.09323i) q^{4} +(-0.626493 + 1.08512i) q^{5} +(2.54556 - 0.721191i) q^{7} +7.07116i q^{8} +(-2.81429 + 1.62483i) q^{10} +(-0.534126 + 0.308378i) q^{11} -1.22795i q^{13} +(6.65273 + 1.68116i) q^{14} +(-4.44321 + 7.69587i) q^{16} +(-2.21501 - 3.83652i) q^{17} +(-1.64679 - 0.950775i) q^{19} -5.92217 q^{20} -1.59958 q^{22} +(-4.11267 - 2.37445i) q^{23} +(1.71501 + 2.97049i) q^{25} +(1.59237 - 2.75806i) q^{26} +(8.96773 + 8.71522i) q^{28} +5.86159i q^{29} +(2.14851 - 1.24044i) q^{31} +(-7.71195 + 4.45249i) q^{32} -11.4895i q^{34} +(-0.812198 + 3.21405i) q^{35} +(1.33217 - 2.30738i) q^{37} +(-2.46587 - 4.27102i) q^{38} +(-7.67303 - 4.43003i) q^{40} -4.19931 q^{41} +4.49274 q^{43} +(-2.52452 - 1.45753i) q^{44} +(-6.15823 - 10.6664i) q^{46} +(3.80738 - 6.59458i) q^{47} +(5.95977 - 3.67167i) q^{49} +8.89591i q^{50} +(5.02627 - 2.90192i) q^{52} +(2.67782 - 1.54604i) q^{53} -0.772786i q^{55} +(5.09966 + 18.0001i) q^{56} +(-7.60114 + 13.1656i) q^{58} +(1.78229 + 3.08702i) q^{59} +(-12.5136 - 7.22473i) q^{61} +6.43428 q^{62} -5.32259 q^{64} +(1.33247 + 0.769301i) q^{65} +(-6.80644 - 11.7891i) q^{67} +(10.4692 - 18.1331i) q^{68} +(-5.99214 + 6.16576i) q^{70} +10.4095i q^{71} +(9.95016 - 5.74473i) q^{73} +(5.98429 - 3.45503i) q^{74} -8.98758i q^{76} +(-1.13725 + 1.17020i) q^{77} +(2.01592 - 3.49168i) q^{79} +(-5.56728 - 9.64281i) q^{80} +(-9.43196 - 5.44554i) q^{82} -8.73549 q^{83} +5.55076 q^{85} +(10.0910 + 5.82605i) q^{86} +(-2.18059 - 3.77689i) q^{88} +(-0.811226 + 1.40508i) q^{89} +(-0.885586 - 3.12582i) q^{91} -22.4454i q^{92} +(17.1033 - 9.87459i) q^{94} +(2.06341 - 1.19131i) q^{95} +10.1213i q^{97} +(18.1474 - 0.518397i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{4} + 3 q^{7}+O(q^{10}) $ 10 * q + 4 * q^4 + 3 * q^7	$ 10 q + 4 q^{4} + 3 q^{7} - 15 q^{10} - 12 q^{11} + 18 q^{14} - 6 q^{16} - 12 q^{17} + 3 q^{19} + 6 q^{20} - 10 q^{22} - 15 q^{23} + 7 q^{25} + 3 q^{26} + 2 q^{28} + 9 q^{31} - 48 q^{32} - 15 q^{35} + 6 q^{37} - 18 q^{38} - 15 q^{40} + 18 q^{41} - 6 q^{43} + 24 q^{44} - 13 q^{46} + 15 q^{47} + 19 q^{49} + 12 q^{52} - 9 q^{53} + 21 q^{56} + 8 q^{58} - 18 q^{59} - 12 q^{61} + 12 q^{62} + 6 q^{64} + 3 q^{65} - 10 q^{67} + 27 q^{68} - 15 q^{70} + 3 q^{73} - 30 q^{74} - 6 q^{77} + 20 q^{79} - 30 q^{80} + 9 q^{82} + 30 q^{83} - 36 q^{85} + 54 q^{86} - 8 q^{88} + 24 q^{89} - 24 q^{91} + 3 q^{94} + 45 q^{98}+O(q^{100}) $ 10 * q + 4 * q^4 + 3 * q^7 - 15 * q^10 - 12 * q^11 + 18 * q^14 - 6 * q^16 - 12 * q^17 + 3 * q^19 + 6 * q^20 - 10 * q^22 - 15 * q^23 + 7 * q^25 + 3 * q^26 + 2 * q^28 + 9 * q^31 - 48 * q^32 - 15 * q^35 + 6 * q^37 - 18 * q^38 - 15 * q^40 + 18 * q^41 - 6 * q^43 + 24 * q^44 - 13 * q^46 + 15 * q^47 + 19 * q^49 + 12 * q^52 - 9 * q^53 + 21 * q^56 + 8 * q^58 - 18 * q^59 - 12 * q^61 + 12 * q^62 + 6 * q^64 + 3 * q^65 - 10 * q^67 + 27 * q^68 - 15 * q^70 + 3 * q^73 - 30 * q^74 - 6 * q^77 + 20 * q^79 - 30 * q^80 + 9 * q^82 + 30 * q^83 - 36 * q^85 + 54 * q^86 - 8 * q^88 + 24 * q^89 - 24 * q^91 + 3 * q^94 + 45 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	2.24607	+	1.29677i	1.58821	+	0.916955i	0.993602	+	0.112941i	$0.0360271\pi$
$2$	2.24607	+	1.29677i	1.58821	+	0.916955i	0.594611	+	0.804014i	$0.297306\pi$
$3$		0			0
$3$		0			0
$4$	2.36322	+	4.09323i	1.18161	+	2.04661i
$5$	−0.626493	+	1.08512i	−0.280176	+	0.485279i	−0.971428	−	0.237335i	$-0.923726\pi$
$5$	−0.626493	+	1.08512i	−0.280176	+	0.485279i	0.691252	+	0.722614i	$0.257059\pi$
$6$		0			0
$7$	2.54556	−	0.721191i	0.962132	−	0.272585i
$7$	2.54556	−	0.721191i	0.962132	−	0.272585i
$8$			7.07116i			2.50003i
$9$		0			0
$10$	−2.81429	+	1.62483i	−0.889958	+	0.513817i
$11$	−0.534126	+	0.308378i	−0.161045	+	0.0929794i	−0.578357	−	0.815784i	$-0.696306\pi$
$11$	−0.534126	+	0.308378i	−0.161045	+	0.0929794i	0.417311	+	0.908764i	$0.362972\pi$
$12$		0			0
$13$		−	1.22795i		−	0.340572i	−0.985395	−	0.170286i	$-0.945531\pi$
$13$		−	1.22795i		−	0.340572i	0.985395	−	0.170286i	$-0.0544691\pi$
$14$	6.65273	+	1.68116i	1.77802	+	0.449309i
$15$		0			0
$16$	−4.44321	+	7.69587i	−1.11080	+	1.92397i
$17$	−2.21501	−	3.83652i	−0.537220	−	0.930492i	−0.999052	−	0.0435249i	$-0.986141\pi$
$17$	−2.21501	−	3.83652i	−0.537220	−	0.930492i	0.461833	−	0.886967i	$-0.347192\pi$
$18$		0			0
$19$	−1.64679	−	0.950775i	−0.377800	−	0.218123i	0.299061	−	0.954234i	$-0.403327\pi$
$19$	−1.64679	−	0.950775i	−0.377800	−	0.218123i	−0.676861	+	0.736111i	$0.736660\pi$
$20$	−5.92217			−1.32424
$21$		0			0
$22$	−1.59958			−0.341032
$23$	−4.11267	−	2.37445i	−0.857550	−	0.495107i	0.00564111	−	0.999984i	$-0.498204\pi$
$23$	−4.11267	−	2.37445i	−0.857550	−	0.495107i	−0.863191	+	0.504877i	$0.831538\pi$
$24$		0			0
$25$	1.71501	+	2.97049i	0.343003	+	0.594098i
$26$	1.59237	−	2.75806i	0.312289	−	0.540900i
$27$		0			0
$28$	8.96773	+	8.71522i	1.69474	+	1.64702i
$29$			5.86159i			1.08847i	0.838933	+	0.544235i	$0.183180\pi$
$29$			5.86159i			1.08847i	−0.838933	+	0.544235i	$0.816820\pi$
$30$		0			0
$31$	2.14851	−	1.24044i	0.385884	−	0.222790i	−0.294491	−	0.955654i	$-0.595150\pi$
$31$	2.14851	−	1.24044i	0.385884	−	0.222790i	0.680375	+	0.732864i	$0.261817\pi$
$32$	−7.71195	+	4.45249i	−1.36329	+	0.787097i
$33$		0			0
$34$		−	11.4895i		−	1.97043i
$35$	−0.812198	+	3.21405i	−0.137287	+	0.543274i
$36$		0			0
$37$	1.33217	−	2.30738i	0.219007	−	0.379331i	−0.735498	−	0.677527i	$-0.763052\pi$
$37$	1.33217	−	2.30738i	0.219007	−	0.379331i	0.954505	+	0.298196i	$0.0963849\pi$
$38$	−2.46587	−	4.27102i	−0.400018	−	0.692851i
$39$		0			0
$40$	−7.67303	−	4.43003i	−1.21321	−	0.700449i
$41$	−4.19931			−0.655823			−0.327911	−	0.944709i	$-0.606345\pi$
$41$	−4.19931			−0.655823			−0.327911	+	0.944709i	$0.606345\pi$
$42$		0			0
$43$	4.49274			0.685137			0.342568	−	0.939493i	$-0.388703\pi$
$43$	4.49274			0.685137			0.342568	+	0.939493i	$0.388703\pi$
$44$	−2.52452	−	1.45753i	−0.380586	−	0.219731i
$45$		0			0
$46$	−6.15823	−	10.6664i	−0.907981	−	1.57267i
$47$	3.80738	−	6.59458i	0.555364	−	0.961918i	−0.442512	−	0.896763i	$-0.645912\pi$
$47$	3.80738	−	6.59458i	0.555364	−	0.961918i	0.997875	−	0.0651551i	$-0.0207542\pi$
$48$		0			0
$49$	5.95977	−	3.67167i	0.851395	−	0.524525i
$50$			8.89591i			1.25807i
$51$		0			0
$52$	5.02627	−	2.90192i	0.697018	−	0.402424i
$53$	2.67782	−	1.54604i	0.367827	−	0.212365i	−0.304682	−	0.952454i	$-0.598550\pi$
$53$	2.67782	−	1.54604i	0.367827	−	0.212365i	0.672509	+	0.740089i	$0.265217\pi$
$54$		0			0
$55$		−	0.772786i		−	0.104202i
$56$	5.09966	+	18.0001i	0.681470	+	2.40536i
$57$		0			0
$58$	−7.60114	+	13.1656i	−0.998078	+	1.72872i
$59$	1.78229	+	3.08702i	0.232035	+	0.401896i	0.958407	−	0.285406i	$-0.0921283\pi$
$59$	1.78229	+	3.08702i	0.232035	+	0.401896i	−0.726372	+	0.687302i	$0.758795\pi$
$60$		0			0
$61$	−12.5136	−	7.22473i	−1.60220	−	0.925032i	−0.991046	−	0.133521i	$-0.957372\pi$
$61$	−12.5136	−	7.22473i	−1.60220	−	0.925032i	−0.611156	−	0.791510i	$-0.709295\pi$
$62$	6.43428			0.817154
$63$		0			0
$64$	−5.32259			−0.665324
$65$	1.33247	+	0.769301i	0.165272	+	0.0954200i
$66$		0			0
$67$	−6.80644	−	11.7891i	−0.831539	−	1.44027i	−0.896818	−	0.442400i	$-0.854127\pi$
$67$	−6.80644	−	11.7891i	−0.831539	−	1.44027i	0.0652791	−	0.997867i	$-0.479206\pi$
$68$	10.4692	−	18.1331i	1.26957	−	2.19896i
$69$		0			0
$70$	−5.99214	+	6.16576i	−0.716198	+	0.736949i
$71$			10.4095i			1.23538i	0.786420	+	0.617692i	$0.211932\pi$
$71$			10.4095i			1.23538i	−0.786420	+	0.617692i	$0.788068\pi$
$72$		0			0
$73$	9.95016	−	5.74473i	1.16458	−	0.672369i	0.212181	−	0.977230i	$-0.431943\pi$
$73$	9.95016	−	5.74473i	1.16458	−	0.672369i	0.952397	+	0.304861i	$0.0986100\pi$
$74$	5.98429	−	3.45503i	0.695659	−	0.401639i
$75$		0			0
$76$		−	8.98758i		−	1.03095i
$77$	−1.13725	+	1.17020i	−0.129602	+	0.133357i
$78$		0			0
$79$	2.01592	−	3.49168i	0.226809	−	0.392845i	−0.730052	−	0.683392i	$-0.760504\pi$
$79$	2.01592	−	3.49168i	0.226809	−	0.392845i	0.956861	+	0.290547i	$0.0938373\pi$
$80$	−5.56728	−	9.64281i	−0.622441	−	1.07810i
$81$		0			0
$82$	−9.43196	−	5.44554i	−1.04159	−	0.601360i
$83$	−8.73549			−0.958845			−0.479422	−	0.877584i	$-0.659154\pi$
$83$	−8.73549			−0.958845			−0.479422	+	0.877584i	$0.659154\pi$
$84$		0			0
$85$	5.55076			0.602064
$86$	10.0910	+	5.82605i	1.08814	+	0.628240i
$87$		0			0
$88$	−2.18059	−	3.77689i	−0.232451	−	0.402618i
$89$	−0.811226	+	1.40508i	−0.0859897	+	0.148939i	−0.905813	−	0.423679i	$-0.860739\pi$
$89$	−0.811226	+	1.40508i	−0.0859897	+	0.148939i	0.819823	+	0.572617i	$0.194072\pi$
$90$		0			0
$91$	−0.885586	−	3.12582i	−0.0928346	−	0.327675i
$92$		−	22.4454i		−	2.34010i
$93$		0			0
$94$	17.1033	−	9.87459i	1.76407	−	1.01849i
$95$	2.06341	−	1.19131i	0.211701	−	0.122226i
$96$		0			0
$97$			10.1213i			1.02766i	0.857892	+	0.513829i	$0.171774\pi$
$97$			10.1213i			1.02766i	−0.857892	+	0.513829i	$0.828226\pi$
$98$	18.1474	−	0.518397i	1.83316	−	0.0523660i
$99$		0			0
$100$	−8.10593	+	14.0399i	−0.810593	+	1.40399i
$101$	0.856611	+	1.48369i	0.0852360	+	0.147633i	0.905492	−	0.424364i	$-0.139502\pi$
$101$	0.856611	+	1.48369i	0.0852360	+	0.147633i	−0.820256	+	0.571997i	$0.806169\pi$
$102$		0			0
$103$	6.41315	+	3.70263i	0.631906	+	0.364831i	0.781490	−	0.623918i	$-0.214460\pi$
$103$	6.41315	+	3.70263i	0.631906	+	0.364831i	−0.149584	+	0.988749i	$0.547793\pi$
$104$	8.68301			0.851440
$105$		0			0
$106$	8.01943			0.778916
$107$	−0.131657	−	0.0760123i	−0.0127278	−	0.00734839i	0.493623	−	0.869676i	$-0.335672\pi$
$107$	−0.131657	−	0.0760123i	−0.0127278	−	0.00734839i	−0.506350	+	0.862328i	$0.669006\pi$
$108$		0			0
$109$	2.70051	+	4.67742i	0.258662	+	0.448016i	0.965884	−	0.258976i	$-0.0833851\pi$
$109$	2.70051	+	4.67742i	0.258662	+	0.448016i	−0.707222	+	0.706992i	$0.750052\pi$
$110$	1.00213	−	1.73573i	0.0955489	−	0.165496i
$111$		0			0
$112$	−5.76028	+	22.7947i	−0.544295	+	2.15390i
$113$		−	6.47083i		−	0.608725i	−0.952556	−	0.304362i	$-0.901557\pi$
$113$		−	6.47083i		−	0.608725i	0.952556	−	0.304362i	$-0.0984434\pi$
$114$		0			0
$115$	5.15311	−	2.97515i	0.480530	−	0.277434i
$116$	−23.9928	+	13.8523i	−2.22768	+	1.28615i
$117$		0			0
$118$			9.24490i			0.851062i
$119$	−8.40532	−	8.16864i	−0.770514	−	0.748818i
$120$		0			0
$121$	−5.30981	+	9.19685i	−0.482710	+	0.836078i
$122$	−18.7376	−	32.4545i	−1.69642	−	2.93829i
$123$		0			0
$124$	10.1548	+	5.86289i	0.911930	+	0.526503i
$125$	−10.5627			−0.944757
$126$		0			0
$127$	−2.93175			−0.260151			−0.130075	−	0.991504i	$-0.541522\pi$
$127$	−2.93175			−0.260151			−0.130075	+	0.991504i	$0.541522\pi$
$128$	3.46897	+	2.00281i	0.306617	+	0.177025i
$129$		0			0
$130$	1.99521	+	3.45581i	0.174992	+	0.303094i
$131$	−8.11382	+	14.0535i	−0.708908	+	1.22786i	0.256355	+	0.966583i	$0.417478\pi$
$131$	−8.11382	+	14.0535i	−0.708908	+	1.22786i	−0.965263	+	0.261281i	$0.915855\pi$
$132$		0			0
$133$	−4.87770	−	1.23261i	−0.422950	−	0.106880i
$134$		−	35.3055i		−	3.04993i
$135$		0			0
$136$	27.1286	−	15.6627i	2.32626	−	1.34307i
$137$	−15.0711	+	8.70129i	−1.28761	+	0.743402i	−0.978227	−	0.207536i	$-0.933456\pi$
$137$	−15.0711	+	8.70129i	−1.28761	+	0.743402i	−0.309382	+	0.950938i	$0.600122\pi$
$138$		0			0
$139$			6.29627i			0.534042i	0.963691	+	0.267021i	$0.0860394\pi$
$139$			6.29627i			0.534042i	−0.963691	+	0.267021i	$0.913961\pi$
$140$	−15.0753	+	4.27102i	−1.27409	+	0.360967i
$141$		0			0
$142$	−13.4988	+	23.3805i	−1.13279	+	1.96205i
$143$	0.378672	+	0.655879i	0.0316661	+	0.0548474i
$144$		0			0
$145$	−6.36052	−	3.67225i	−0.528212	−	0.304963i
$146$	29.7984			2.46613
$147$		0			0
$148$	12.5928			1.03513
$149$	−9.20319	−	5.31346i	−0.753954	−	0.435296i	0.0731665	−	0.997320i	$-0.476690\pi$
$149$	−9.20319	−	5.31346i	−0.753954	−	0.435296i	−0.827121	+	0.562024i	$0.810023\pi$
$150$		0			0
$151$	−4.74465	−	8.21798i	−0.386114	−	0.668770i	0.605809	−	0.795610i	$-0.292850\pi$
$151$	−4.74465	−	8.21798i	−0.386114	−	0.668770i	−0.991923	+	0.126841i	$0.959516\pi$
$152$	6.72308	−	11.6447i	0.545314	−	0.944511i
$153$		0			0
$154$	−4.07183	+	1.15360i	−0.328117	+	0.0929600i
$155$			3.10851i			0.249682i
$156$		0			0
$157$	−20.6214	+	11.9058i	−1.64577	+	0.950185i	−0.667040	+	0.745022i	$0.732439\pi$
$157$	−20.6214	+	11.9058i	−1.64577	+	0.950185i	−0.978728	+	0.205163i	$0.934228\pi$
$158$	9.05582	−	5.22838i	0.720442	−	0.415947i
$159$		0			0
$160$		−	11.1578i		−	0.882103i
$161$	−12.1815	−	3.07829i	−0.960035	−	0.242603i
$162$		0			0
$163$	−4.41101	+	7.64009i	−0.345497	+	0.598418i	−0.985444	−	0.170001i	$-0.945623\pi$
$163$	−4.41101	+	7.64009i	−0.345497	+	0.598418i	0.639947	+	0.768419i	$0.278956\pi$
$164$	−9.92392	−	17.1887i	−0.774928	−	1.34221i
$165$		0			0
$166$	−19.6205	−	11.3279i	−1.52285	−	0.879217i
$167$	22.0671			1.70760			0.853800	−	0.520601i	$-0.174292\pi$
$167$	22.0671			1.70760			0.853800	+	0.520601i	$0.174292\pi$
$168$		0			0
$169$	11.4921			0.884011
$170$	12.4674	+	7.19806i	0.956206	+	0.552066i
$171$		0			0
$172$	10.6174	+	18.3898i	0.809566	+	1.40221i
$173$	2.03375	−	3.52256i	0.154623	−	0.267815i	−0.778299	−	0.627894i	$-0.783917\pi$
$173$	2.03375	−	3.52256i	0.154623	−	0.267815i	0.932922	+	0.360079i	$0.117250\pi$
$174$		0			0
$175$	6.50797	+	6.32472i	0.491956	+	0.478104i
$176$		−	5.48075i		−	0.413127i
$177$		0			0
$178$	−3.64414	+	2.10395i	−0.273140	+	0.157697i
$179$	7.20787	−	4.16146i	0.538741	−	0.311042i	−0.205827	−	0.978588i	$-0.565989\pi$
$179$	7.20787	−	4.16146i	0.538741	−	0.311042i	0.744569	+	0.667546i	$0.232655\pi$
$180$		0			0
$181$			12.6701i			0.941763i	0.882196	+	0.470881i	$0.156064\pi$
$181$			12.6701i			0.941763i	−0.882196	+	0.470881i	$0.843936\pi$
$182$	2.06438	−	8.16921i	0.153022	−	0.605542i
$183$		0			0
$184$	16.7901	−	29.0813i	1.23778	−	2.14390i
$185$	1.66919	+	2.89111i	0.122721	+	0.212559i
$186$		0			0
$187$	2.36619	+	1.36612i	0.173033	+	0.0999008i
$188$	35.9908			2.62490
$189$		0			0
$190$	6.17941			0.448301
$191$	3.29133	+	1.90025i	0.238152	+	0.137497i	0.614327	−	0.789051i	$-0.289427\pi$
$191$	3.29133	+	1.90025i	0.238152	+	0.137497i	−0.376175	+	0.926549i	$0.622761\pi$
$192$		0			0
$193$	−3.39448	−	5.87942i	−0.244340	−	0.423210i	0.717606	−	0.696450i	$-0.245238\pi$
$193$	−3.39448	−	5.87942i	−0.244340	−	0.423210i	−0.961946	+	0.273240i	$0.911905\pi$
$194$	−13.1250	+	22.7331i	−0.942317	+	1.63214i
$195$		0			0
$196$	29.1133	+	15.7177i	2.07952	+	1.12269i
$197$		−	6.41453i		−	0.457017i	−0.973542	−	0.228508i	$-0.926615\pi$
$197$		−	6.41453i		−	0.457017i	0.973542	−	0.228508i	$-0.0733848\pi$
$198$		0			0
$199$	−13.8921	+	8.02063i	−0.984788	+	0.568568i	−0.903712	−	0.428140i	$-0.859169\pi$
$199$	−13.8921	+	8.02063i	−0.984788	+	0.568568i	−0.0810756	+	0.996708i	$0.525836\pi$
$200$	−21.0048	+	12.1271i	−1.48526	+	0.857518i
$201$		0			0
$202$			4.44331i			0.312630i
$203$	4.22733	+	14.9210i	0.296700	+	1.04725i
$204$		0			0
$205$	2.63084	−	4.55675i	0.183746	−	0.318257i
$206$	9.60292	+	16.6327i	0.669067	+	1.15886i
$207$		0			0
$208$	9.45013	+	5.45604i	0.655249	+	0.378308i
$209$	1.17279			0.0811237
$210$		0			0
$211$	8.12139			0.559100			0.279550	−	0.960131i	$-0.409815\pi$
$211$	8.12139			0.559100			0.279550	+	0.960131i	$0.409815\pi$
$212$	12.6566	+	7.30728i	0.869257	+	0.501866i
$213$		0			0
$214$	−0.197141	−	0.341458i	−0.0134763	−	0.0233416i
$215$	−2.81467	+	4.87515i	−0.191959	+	0.332483i
$216$		0			0
$217$	4.57457	−	4.70711i	0.310542	−	0.319540i
$218$			14.0078i			0.948725i
$219$		0			0
$220$	3.16319	−	1.82627i	0.213262	−	0.123127i
$221$	−4.71104	+	2.71992i	−0.316899	+	0.182962i
$222$		0			0
$223$			8.03908i			0.538336i	0.963093	+	0.269168i	$0.0867488\pi$
$223$			8.03908i			0.538336i	−0.963093	+	0.269168i	$0.913251\pi$
$224$	−16.4201	+	16.8959i	−1.09712	+	1.12890i
$225$		0			0
$226$	8.39118	−	14.5340i	0.558173	−	0.966784i
$227$	10.4117	+	18.0336i	0.691048	+	1.19693i	0.971495	+	0.237061i	$0.0761840\pi$
$227$	10.4117	+	18.0336i	0.691048	+	1.19693i	−0.280447	+	0.959870i	$0.590483\pi$
$228$		0			0
$229$	−5.21276	−	3.00959i	−0.344469	−	0.198879i	0.317777	−	0.948165i	$-0.397064\pi$
$229$	−5.21276	−	3.00959i	−0.344469	−	0.198879i	−0.662247	+	0.749286i	$0.730397\pi$
$230$	15.4323			1.01758
$231$		0			0
$232$	−41.4482			−2.72121
$233$	−18.2156	−	10.5168i	−1.19335	−	0.688978i	−0.234282	−	0.972169i	$-0.575274\pi$
$233$	−18.2156	−	10.5168i	−1.19335	−	0.688978i	−0.959064	+	0.283191i	$0.908607\pi$
$234$		0			0
$235$	4.77059	+	8.26291i	0.311199	+	0.539013i
$236$	−8.42392	+	14.5907i	−0.548350	+	0.949771i
$237$		0			0
$238$	−8.28610	−	29.2471i	−0.537108	−	1.89581i
$239$		−	8.67271i		−	0.560991i	−0.959855	−	0.280496i	$-0.909501\pi$
$239$		−	8.67271i		−	0.560991i	0.959855	−	0.280496i	$-0.0904988\pi$
$240$		0			0
$241$	−7.33797	+	4.23658i	−0.472680	+	0.272902i	−0.717361	−	0.696702i	$-0.754650\pi$
$241$	−7.33797	+	4.23658i	−0.472680	+	0.272902i	0.244681	+	0.969604i	$0.421317\pi$
$242$	−23.8524	+	13.7712i	−1.53329	+	0.885246i
$243$		0			0
$244$		−	68.2946i		−	4.37211i
$245$	0.250447	+	8.76732i	0.0160005	+	0.560124i
$246$		0			0
$247$	−1.16750	+	2.02217i	−0.0742864	+	0.128668i
$248$	8.77137	+	15.1925i	0.556982	+	0.964722i
$249$		0			0
$250$	−23.7246	−	13.6974i	−1.50047	−	0.866299i
$251$	23.4435			1.47974			0.739871	−	0.672749i	$-0.234887\pi$
$251$	23.4435			1.47974			0.739871	+	0.672749i	$0.234887\pi$
$252$		0			0
$253$	2.92891			0.184139
$254$	−6.58492	−	3.80180i	−0.413174	−	0.238546i
$255$		0			0
$256$	10.5170	+	18.2159i	0.657310	+	1.13849i
$257$	12.2585	−	21.2324i	0.764665	−	1.32444i	−0.175758	−	0.984433i	$-0.556238\pi$
$257$	12.2585	−	21.2324i	0.764665	−	1.32444i	0.940423	−	0.340005i	$-0.110429\pi$
$258$		0			0
$259$	1.72705	−	6.83433i	0.107314	−	0.424665i
$260$			7.27212i			0.450998i
$261$		0			0
$262$	−36.4484	+	21.0435i	−2.25179	+	1.30007i
$263$	9.14036	−	5.27719i	0.563619	−	0.325406i	−0.190978	−	0.981594i	$-0.561166\pi$
$263$	9.14036	−	5.27719i	0.563619	−	0.325406i	0.754597	+	0.656189i	$0.227833\pi$
$264$		0			0
$265$			3.87433i			0.237998i
$266$	−9.35726	−	9.09377i	−0.573730	−	0.557575i
$267$		0			0
$268$	32.1703	−	55.7206i	1.96511	−	3.40367i
$269$	1.14451	+	1.98235i	0.0697821	+	0.120866i	0.898805	−	0.438348i	$-0.144436\pi$
$269$	1.14451	+	1.98235i	0.0697821	+	0.120866i	−0.829023	+	0.559214i	$0.811103\pi$
$270$		0			0
$271$	−20.9239	−	12.0804i	−1.27103	−	0.733831i	−0.295851	−	0.955234i	$-0.595603\pi$
$271$	−20.9239	−	12.0804i	−1.27103	−	0.733831i	−0.975182	+	0.221403i	$0.928936\pi$
$272$	39.3671			2.38698
$273$		0			0
$274$	−45.1343			−2.72666
$275$	−1.83207	−	1.05774i	−0.110478	−	0.0637844i
$276$		0			0
$277$	5.68551	+	9.84760i	0.341609	+	0.591685i	0.984732	−	0.174079i	$-0.0556947\pi$
$277$	5.68551	+	9.84760i	0.341609	+	0.591685i	−0.643122	+	0.765763i	$0.722361\pi$
$278$	−8.16481	+	14.1419i	−0.489693	+	0.848173i
$279$		0			0
$280$	−22.7271	−	5.74318i	−1.35820	−	0.343221i
$281$		−	20.3669i		−	1.21498i	−0.794326	−	0.607492i	$-0.792176\pi$
$281$		−	20.3669i		−	1.21498i	0.794326	−	0.607492i	$-0.207824\pi$
$282$		0			0
$283$	−10.5318	+	6.08055i	−0.626052	+	0.361451i	−0.779222	−	0.626749i	$-0.784385\pi$
$283$	−10.5318	+	6.08055i	−0.626052	+	0.361451i	0.153169	+	0.988200i	$0.451052\pi$
$284$	−42.6085	+	24.6000i	−2.52835	+	1.45974i
$285$		0			0
$286$			1.96420i			0.116146i
$287$	−10.6896	+	3.02851i	−0.630988	+	0.178767i
$288$		0			0
$289$	−1.31257	+	2.27345i	−0.0772103	+	0.133732i
$290$	−9.52411	−	16.4962i	−0.559275	−	0.968693i
$291$		0			0
$292$	47.0289	+	27.1522i	2.75216	+	1.58896i
$293$	−26.9348			−1.57355			−0.786773	−	0.617242i	$-0.788250\pi$
$293$	−26.9348			−1.57355			−0.786773	+	0.617242i	$0.788250\pi$
$294$		0			0
$295$	−4.46637			−0.260042
$296$	16.3159	+	9.41996i	0.948340	+	0.547524i
$297$		0			0
$298$	−13.7807	−	23.8688i	−0.798293	−	1.38268i
$299$	−2.91570	+	5.05014i	−0.168619	+	0.292057i
$300$		0			0
$301$	11.4366	−	3.24013i	0.659192	−	0.186758i
$302$		−	24.6109i		−	1.41620i
$303$		0			0
$304$	14.6341	−	8.44899i	0.839322	−	0.484583i
$305$	15.6793	−	9.05248i	0.897797	−	0.518343i
$306$		0			0
$307$			21.3700i			1.21965i	0.792536	+	0.609825i	$0.208760\pi$
$307$			21.3700i			1.21965i	−0.792536	+	0.609825i	$0.791240\pi$
$308$	−7.47748	−	1.88958i	−0.426069	−	0.107669i
$309$		0			0
$310$	−4.03103	+	6.98195i	−0.228947	+	0.396548i
$311$	8.11558	+	14.0566i	0.460192	+	0.797076i	0.998970	−	0.0453714i	$-0.0144471\pi$
$311$	8.11558	+	14.0566i	0.460192	+	0.797076i	−0.538778	+	0.842448i	$0.681114\pi$
$312$		0			0
$313$	−12.1941	−	7.04027i	−0.689252	−	0.397940i	0.114080	−	0.993472i	$-0.463608\pi$
$313$	−12.1941	−	7.04027i	−0.689252	−	0.397940i	−0.803332	+	0.595532i	$0.796941\pi$
$314$	−61.7562			−3.48511
$315$		0			0
$316$	19.0563			1.07200
$317$	−17.5776	−	10.1484i	−0.987254	−	0.569991i	−0.0828017	−	0.996566i	$-0.526387\pi$
$317$	−17.5776	−	10.1484i	−0.987254	−	0.569991i	−0.904452	+	0.426575i	$0.859720\pi$
$318$		0			0
$319$	−1.80759	−	3.13083i	−0.101205	−	0.175293i
$320$	3.33456	−	5.77563i	0.186408	−	0.322868i
$321$		0			0
$322$	−23.3686	−	22.7106i	−1.30228	−	1.26561i
$323$			8.42392i			0.468720i
$324$		0			0
$325$	3.64761	−	2.10595i	0.202333	−	0.116817i
$326$	−19.8149	+	11.4401i	−1.09744	+	0.633610i
$327$		0			0
$328$		−	29.6940i		−	1.63958i
$329$	4.93597	−	19.5327i	0.272129	−	1.07688i
$330$		0			0
$331$	−13.2341	+	22.9221i	−0.727411	+	1.25991i	0.230563	+	0.973057i	$0.425943\pi$
$331$	−13.2341	+	22.9221i	−0.727411	+	1.25991i	−0.957974	+	0.286856i	$0.907390\pi$
$332$	−20.6439	−	35.7563i	−1.13298	−	1.96238i
$333$		0			0
$334$	49.5642	+	28.6159i	2.71203	+	1.56579i
$335$	17.0567			0.931909
$336$		0			0
$337$	3.47317			0.189196			0.0945979	−	0.995516i	$-0.469843\pi$
$337$	3.47317			0.189196			0.0945979	+	0.995516i	$0.469843\pi$
$338$	25.8122	+	14.9027i	1.40400	+	0.810598i
$339$		0			0
$340$	13.1177	+	22.7205i	0.711407	+	1.23219i
$341$	−0.765051	+	1.32511i	−0.0414298	+	0.0717585i
$342$		0			0
$343$	12.5230	−	13.6446i	0.676177	−	0.736739i
$344$			31.7689i			1.71286i
$345$		0			0
$346$	9.13589	−	5.27461i	0.491149	−	0.283565i
$347$	−8.14765	+	4.70405i	−0.437389	+	0.252527i	−0.702489	−	0.711694i	$-0.747928\pi$
$347$	−8.14765	+	4.70405i	−0.437389	+	0.252527i	0.265101	+	0.964221i	$0.414595\pi$
$348$		0			0
$349$			14.2321i			0.761824i	0.924611	+	0.380912i	$0.124390\pi$
$349$			14.2321i			0.761824i	−0.924611	+	0.380912i	$0.875610\pi$
$350$	6.41566	+	22.6451i	0.342931	+	1.21043i
$351$		0			0
$352$	2.74610	−	4.75639i	0.146368	−	0.253516i
$353$	−8.58262	−	14.8655i	−0.456807	−	0.791213i	0.541983	−	0.840389i	$-0.317674\pi$
$353$	−8.58262	−	14.8655i	−0.456807	−	0.791213i	−0.998790	+	0.0491765i	$0.984340\pi$
$354$		0			0
$355$	−11.2956	−	6.52149i	−0.599506	−	0.346125i
$356$	−7.66843			−0.406426
$357$		0			0
$358$	21.5858			1.14085
$359$	24.4705	+	14.1281i	1.29150	+	0.745650i	0.978921	−	0.204241i	$-0.0654725\pi$
$359$	24.4705	+	14.1281i	1.29150	+	0.745650i	0.312583	+	0.949890i	$0.398806\pi$
$360$		0			0
$361$	−7.69205	−	13.3230i	−0.404845	−	0.701212i
$362$	−16.4302	+	28.4580i	−0.863554	+	1.49572i
$363$		0			0
$364$	10.7018	−	11.0119i	0.560929	−	0.577181i
$365$			14.3961i			0.753527i
$366$		0			0
$367$	−19.9796	+	11.5352i	−1.04293	+	0.602133i	−0.920661	−	0.390364i	$-0.872349\pi$
$367$	−19.9796	+	11.5352i	−1.04293	+	0.602133i	−0.122265	+	0.992498i	$0.539016\pi$
$368$	36.5469	−	21.1004i	1.90514	−	1.09993i
$369$		0			0
$370$			8.65820i			0.450118i
$371$	5.70156	−	5.86676i	0.296010	−	0.304587i
$372$		0			0
$373$	6.93635	−	12.0141i	0.359150	−	0.622067i	−0.628669	−	0.777673i	$-0.716400\pi$
$373$	6.93635	−	12.0141i	0.359150	−	0.622067i	0.987819	+	0.155607i	$0.0497332\pi$
$374$	3.54309	+	6.13682i	0.183209	+	0.317327i
$375$		0			0
$376$	46.6313	+	26.9226i	2.40482	+	1.38843i
$377$	7.19773			0.370702
$378$		0			0
$379$	22.7814			1.17020			0.585101	−	0.810961i	$-0.301055\pi$
$379$	22.7814			1.17020			0.585101	+	0.810961i	$0.301055\pi$
$380$	9.75258	+	5.63065i	0.500297	+	0.288846i
$381$		0			0
$382$	4.92838	+	8.53620i	0.252158	+	0.436750i
$383$	7.61598	−	13.1913i	0.389158	−	0.674042i	−0.603178	−	0.797606i	$-0.706099\pi$
$383$	7.61598	−	13.1913i	0.389158	−	0.674042i	0.992337	+	0.123564i	$0.0394325\pi$
$384$		0			0
$385$	−0.557326	−	1.96717i	−0.0284040	−	0.100256i
$386$		−	17.6075i		−	0.896196i
$387$		0			0
$388$	−41.4286	+	23.9188i	−2.10322	+	1.21429i
$389$	12.2525	−	7.07396i	0.621224	−	0.358664i	−0.156121	−	0.987738i	$-0.549899\pi$
$389$	12.2525	−	7.07396i	0.621224	−	0.358664i	0.777346	+	0.629074i	$0.216566\pi$
$390$		0			0
$391$			21.0377i			1.06392i
$392$	25.9630	+	42.1424i	1.31133	+	2.12851i
$393$		0			0
$394$	8.31817	−	14.4075i	0.419063	−	0.725839i
$395$	2.52592	+	4.37503i	0.127093	+	0.220131i
$396$		0			0
$397$	8.40688	+	4.85371i	0.421929	+	0.243601i	0.695902	−	0.718136i	$-0.255005\pi$
$397$	8.40688	+	4.85371i	0.421929	+	0.243601i	−0.273973	+	0.961737i	$0.588338\pi$
$398$	−41.6037			−2.08540
$399$		0			0
$400$	−30.4807			−1.52403
$401$	−7.56156	−	4.36567i	−0.377606	−	0.218011i	0.299170	−	0.954200i	$-0.403290\pi$
$401$	−7.56156	−	4.36567i	−0.377606	−	0.218011i	−0.676776	+	0.736189i	$0.736624\pi$
$402$		0			0
$403$	−1.52320	−	2.63826i	−0.0758760	−	0.131421i
$404$	−4.04873	+	7.01261i	−0.201432	+	0.348890i
$405$		0			0
$406$	−9.85428	+	38.9956i	−0.489060	+	1.93532i
$407$			1.64324i			0.0814526i
$408$		0			0
$409$	12.8967	−	7.44591i	0.637700	−	0.368176i	−0.146028	−	0.989280i	$-0.546649\pi$
$409$	12.8967	−	7.44591i	0.637700	−	0.368176i	0.783728	+	0.621104i	$0.213316\pi$
$410$	11.8181	−	6.82318i	0.583654	−	0.336973i
$411$		0			0
$412$			35.0006i			1.72436i
$413$	6.76327	+	6.57283i	0.332799	+	0.323428i
$414$		0			0
$415$	5.47272	−	9.47903i	0.268645	−	0.465307i
$416$	5.46743	+	9.46987i	0.268063	+	0.464299i
$417$		0			0
$418$	2.63418	+	1.52084i	0.128842	+	0.0743868i
$419$	4.27717			0.208954			0.104477	−	0.994527i	$-0.466683\pi$
$419$	4.27717			0.208954			0.104477	+	0.994527i	$0.466683\pi$
$420$		0			0
$421$	−11.5336			−0.562114			−0.281057	−	0.959691i	$-0.590685\pi$
$421$	−11.5336			−0.562114			−0.281057	+	0.959691i	$0.590685\pi$
$422$	18.2412	+	10.5316i	0.887969	+	0.512669i
$423$		0			0
$424$	10.9323	+	18.9353i	0.530919	+	0.919578i
$425$	7.59756	−	13.1594i	0.368536	−	0.638323i
$426$		0			0
$427$	−37.0645	−	9.36629i	−1.79368	−	0.453267i
$428$		−	0.718537i		−	0.0347318i
$429$		0			0
$430$	−12.6439	+	7.29996i	−0.609743	+	0.352035i
$431$	−14.4497	+	8.34254i	−0.696018	+	0.401846i	−0.805863	−	0.592103i	$-0.798298\pi$
$431$	−14.4497	+	8.34254i	−0.696018	+	0.401846i	0.109845	+	0.993949i	$0.464965\pi$
$432$		0			0
$433$			12.3503i			0.593516i	0.954953	+	0.296758i	$0.0959055\pi$
$433$			12.3503i			0.593516i	−0.954953	+	0.296758i	$0.904094\pi$
$434$	16.3789	−	4.64035i	0.786210	−	0.222744i
$435$		0			0
$436$	−12.7638	+	22.1076i	−0.611276	+	1.05876i
$437$	4.51513	+	7.82044i	0.215988	+	0.374102i
$438$		0			0
$439$	19.1691	+	11.0673i	0.914892	+	0.528213i	0.882002	−	0.471246i	$-0.156195\pi$
$439$	19.1691	+	11.0673i	0.914892	+	0.528213i	0.0328902	+	0.999459i	$0.489529\pi$
$440$	5.46449			0.260509
$441$		0			0
$442$	−14.1085			−0.671071
$443$	4.22906	+	2.44165i	0.200929	+	0.116006i	0.597089	−	0.802175i	$-0.296324\pi$
$443$	4.22906	+	2.44165i	0.200929	+	0.116006i	−0.396160	+	0.918182i	$0.629657\pi$
$444$		0			0
$445$	−1.01645	−	1.76055i	−0.0481845	−	0.0834580i
$446$	−10.4248	+	18.0563i	−0.493630	+	0.854993i
$447$		0			0
$448$	−13.5490	+	3.83861i	−0.640129	+	0.181357i
$449$			12.4409i			0.587121i	0.955941	+	0.293560i	$0.0948401\pi$
$449$			12.4409i			0.587121i	−0.955941	+	0.293560i	$0.905160\pi$
$450$		0			0
$451$	2.24296	−	1.29498i	0.105617	−	0.0609780i
$452$	26.4866	−	15.2920i	1.24582	−	0.719277i
$453$		0			0
$454$			54.0063i			2.53464i
$455$	3.94669	+	0.997338i	0.185024	+	0.0467559i
$456$		0			0
$457$	5.38774	−	9.33185i	0.252028	−	0.436525i	−0.712056	−	0.702123i	$-0.752236\pi$
$457$	5.38774	−	9.33185i	0.252028	−	0.436525i	0.964084	+	0.265597i	$0.0855691\pi$
$458$	−7.80549	−	13.5195i	−0.364727	−	0.631725i
$459$		0			0
$460$	24.3559	+	14.0619i	1.13560	+	0.655639i
$461$	0.666605			0.0310469			0.0155235	−	0.999880i	$-0.495059\pi$
$461$	0.666605			0.0310469			0.0155235	+	0.999880i	$0.495059\pi$
$462$		0			0
$463$	41.5784			1.93231			0.966155	−	0.257961i	$-0.0830507\pi$
$463$	41.5784			1.93231			0.966155	+	0.257961i	$0.0830507\pi$
$464$	−45.1101	−	26.0443i	−2.09418	−	1.20908i
$465$		0			0
$466$	−27.2757	−	47.2429i	−1.26352	−	2.18849i
$467$	19.6568	−	34.0465i	0.909606	−	1.57548i	0.0949943	−	0.995478i	$-0.469717\pi$
$467$	19.6568	−	34.0465i	0.909606	−	1.57548i	0.814612	−	0.580006i	$-0.196950\pi$
$468$		0			0
$469$	−25.8284	−	25.1011i	−1.19264	−	1.15906i
$470$			24.7454i			1.14142i
$471$		0			0
$472$	−21.8288	+	12.6029i	−1.00475	+	0.580094i
$473$	−2.39969	+	1.38546i	−0.110338	+	0.0637036i
$474$		0			0
$475$		−	6.52237i		−	0.299267i
$476$	13.5724	−	53.7092i	0.622091	−	2.46176i
$477$		0			0
$478$	11.2465	−	19.4795i	0.514403	−	0.890973i
$479$	19.0577	+	33.0088i	0.870767	+	1.50821i	0.861205	+	0.508258i	$0.169710\pi$
$479$	19.0577	+	33.0088i	0.870767	+	1.50821i	0.00956182	+	0.999954i	$0.496956\pi$
$480$		0			0
$481$	−2.83335	−	1.63583i	−0.129189	−	0.0745875i
$482$	−21.9755			−1.00095
$483$		0			0
$484$	−50.1931			−2.28150
$485$	−10.9828	−	6.34090i	−0.498701	−	0.287925i
$486$		0			0
$487$	−3.80277	−	6.58659i	−0.172320	−	0.298467i	0.766911	−	0.641754i	$-0.221793\pi$
$487$	−3.80277	−	6.58659i	−0.172320	−	0.298467i	−0.939231	+	0.343287i	$0.888460\pi$
$488$	51.0872	−	88.4856i	2.31261	−	4.00555i
$489$		0			0
$490$	−10.8067	+	20.0168i	−0.488196	+	0.904267i
$491$			3.84858i			0.173684i	0.996222	+	0.0868420i	$0.0276775\pi$
$491$			3.84858i			0.173684i	−0.996222	+	0.0868420i	$0.972322\pi$
$492$		0			0
$493$	22.4881	−	12.9835i	1.01281	−	0.584748i
$494$	−5.24459	+	3.02797i	−0.235965	+	0.136235i
$495$		0			0
$496$			22.0462i			0.989904i
$497$	7.50726	+	26.4981i	0.336747	+	1.18860i
$498$		0			0
$499$	16.0794	−	27.8503i	0.719812	−	1.24675i	−0.241262	−	0.970460i	$-0.577561\pi$
$499$	16.0794	−	27.8503i	0.719812	−	1.24675i	0.961074	−	0.276291i	$-0.0891053\pi$
$500$	−24.9620	−	43.2355i	−1.11634	−	1.93355i
$501$		0			0
$502$	52.6558	+	30.4009i	2.35014	+	1.35686i
$503$	−0.425693			−0.0189807			−0.00949035	−	0.999955i	$-0.503021\pi$
$503$	−0.425693			−0.0189807			−0.00949035	+	0.999955i	$0.503021\pi$
$504$		0			0
$505$	−2.14664			−0.0955243
$506$	6.57854	+	3.79812i	0.292452	+	0.168847i
$507$		0			0
$508$	−6.92838	−	12.0003i	−0.307397	−	0.532427i
$509$	12.8963	−	22.3370i	0.571617	−	0.990071i	−0.424783	−	0.905295i	$-0.639649\pi$
$509$	12.8963	−	22.3370i	0.571617	−	0.990071i	0.996400	−	0.0847751i	$-0.0270172\pi$
$510$		0			0
$511$	21.1857	−	21.7995i	0.937200	−	0.964354i
$512$			46.5411i			2.05684i
$513$		0			0
$514$	55.0670	−	31.7929i	2.42890	−	1.40233i
$515$	−8.03558	+	4.63934i	−0.354090	+	0.204434i
$516$		0			0
$517$			4.69645i			0.206550i
$518$	12.7416	−	13.1108i	0.559835	−	0.576056i
$519$		0			0
$520$	−5.43984	+	9.42209i	−0.238553	+	0.413186i
$521$	−9.07174	−	15.7127i	−0.397440	−	0.688386i	0.595969	−	0.803007i	$-0.296768\pi$
$521$	−9.07174	−	15.7127i	−0.397440	−	0.688386i	−0.993409	+	0.114621i	$0.963435\pi$
$522$		0			0
$523$	12.0723	+	6.96997i	0.527887	+	0.304776i	0.740155	−	0.672436i	$-0.234752\pi$
$523$	12.0723	+	6.96997i	0.527887	+	0.304776i	−0.212269	+	0.977211i	$0.568085\pi$
$524$	−76.6991			−3.35062
$525$		0			0
$526$	27.3732			1.19353
$527$	−9.51796	−	5.49520i	−0.414609	−	0.239375i
$528$		0			0
$529$	−0.223990	−	0.387962i	−0.00973870	−	0.0168679i
$530$	−5.02411	+	8.70202i	−0.218234	+	0.377992i
$531$		0			0
$532$	−6.48177	−	22.8784i	−0.281020	−	0.991906i
$533$			5.15654i			0.223355i
$534$		0			0
$535$	0.164965	−	0.0952423i	0.00713204	−	0.00411769i
$536$	83.3625	−	48.1294i	3.60071	−	2.07887i
$537$		0			0
$538$			5.93667i			0.255948i
$539$	−2.05100	+	3.79900i	−0.0883430	+	0.163634i
$540$		0			0
$541$	−14.8576	+	25.7341i	−0.638779	+	1.10640i	0.346922	+	0.937894i	$0.387227\pi$
$541$	−14.8576	+	25.7341i	−0.638779	+	1.10640i	−0.985701	+	0.168503i	$0.946107\pi$
$542$	−31.3310	−	54.2668i	−1.34578	−	2.33096i
$543$		0			0
$544$	34.1641	+	19.7247i	1.46478	+	0.845688i
$545$	−6.76740			−0.289883
$546$		0			0
$547$	18.2703			0.781182			0.390591	−	0.920564i	$-0.372271\pi$
$547$	18.2703			0.781182			0.390591	+	0.920564i	$0.372271\pi$
$548$	−71.2327	−	41.1262i	−3.04291	−	1.75683i
$549$		0			0
$550$	−2.74330	−	4.75154i	−0.116975	−	0.202606i
$551$	5.57306	−	9.65282i	0.237420	−	0.411224i
$552$		0			0
$553$	2.61349	−	10.3422i	0.111137	−	0.439793i
$554$			29.4912i			1.25296i
$555$		0			0
$556$	−25.7720	+	14.8795i	−1.09298	+	0.631031i
$557$	−0.359456	+	0.207532i	−0.0152307	+	0.00879343i	−0.507596	−	0.861595i	$-0.669466\pi$
$557$	−0.359456	+	0.207532i	−0.0152307	+	0.00879343i	0.492365	+	0.870389i	$0.336132\pi$
$558$		0			0
$559$		−	5.51686i		−	0.233338i
$560$	−21.1262	−	20.5313i	−0.892743	−	0.867605i
$561$		0			0
$562$	26.4111	−	45.7454i	1.11409	−	1.92965i
$563$	1.82962	+	3.16900i	0.0771095	+	0.133558i	0.902002	−	0.431733i	$-0.142098\pi$
$563$	1.82962	+	3.16900i	0.0771095	+	0.133558i	−0.824892	+	0.565290i	$0.808764\pi$
$564$		0			0
$565$	7.02161	+	4.05393i	0.295401	+	0.170550i
$566$	−31.5403			−1.32574
$567$		0			0
$568$	−73.6074			−3.08850
$569$	−30.4692	−	17.5914i	−1.27733	−	0.737470i	−0.300977	−	0.953631i	$-0.597313\pi$
$569$	−30.4692	−	17.5914i	−1.27733	−	0.737470i	−0.976358	+	0.216162i	$0.930646\pi$
$570$		0			0
$571$	5.02680	+	8.70667i	0.210365	+	0.364363i	0.951829	−	0.306630i	$-0.0992014\pi$
$571$	5.02680	+	8.70667i	0.210365	+	0.364363i	−0.741464	+	0.670993i	$0.765868\pi$
$572$	−1.78977	+	3.09998i	−0.0748342	+	0.129617i
$573$		0			0
$574$	−27.9369	−	7.05972i	−1.16606	−	0.294667i
$575$		−	16.2888i		−	0.679292i
$576$		0			0
$577$	0.0597672	−	0.0345066i	0.00248814	−	0.00143653i	−0.498755	−	0.866743i	$-0.666209\pi$
$577$	0.0597672	−	0.0345066i	0.00248814	−	0.00143653i	0.501244	+	0.865306i	$0.332876\pi$
$578$	−5.89627	+	3.40421i	−0.245253	+	0.141597i
$579$		0			0
$580$		−	34.7134i		−	1.44139i
$581$	−22.2367	+	6.29996i	−0.922535	+	0.261366i
$582$		0			0
$583$	−0.953529	+	1.65156i	−0.0394911	+	0.0684006i
$584$	40.6219	+	70.3591i	1.68094	+	2.91148i
$585$		0			0
$586$	−60.4974	−	34.9282i	−2.49913	−	1.44287i
$587$	22.9598			0.947654			0.473827	−	0.880618i	$-0.342872\pi$
$587$	22.9598			0.947654			0.473827	+	0.880618i	$0.342872\pi$
$588$		0			0
$589$	−4.71753			−0.194383
$590$	−10.0318	−	5.79186i	−0.413003	−	0.238447i
$591$		0			0
$592$	11.8382	+	20.5044i	0.486547	+	0.842725i
$593$	14.3970	−	24.9363i	0.591213	−	1.02401i	−0.402856	−	0.915263i	$-0.631982\pi$
$593$	14.3970	−	24.9363i	0.591213	−	1.02401i	0.994069	−	0.108748i	$-0.0346843\pi$
$594$		0			0
$595$	14.1298	−	4.00316i	0.579265	−	0.164114i
$596$		−	50.2276i		−	2.05740i
$597$		0			0
$598$	−13.0977	+	7.56198i	−0.535606	+	0.309233i
$599$	33.1588	−	19.1442i	1.35483	−	0.782212i	0.365910	−	0.930650i	$-0.380758\pi$
$599$	33.1588	−	19.1442i	1.35483	−	0.782212i	0.988922	+	0.148438i	$0.0474246\pi$
$600$		0			0
$601$		−	30.9019i		−	1.26051i	−0.776387	−	0.630257i	$-0.782949\pi$
$601$		−	30.9019i		−	1.26051i	0.776387	−	0.630257i	$-0.217051\pi$
$602$	29.8890	+	7.55302i	1.21819	+	0.307838i
$603$		0			0
$604$	22.4254	−	38.8419i	0.912475	−	1.58045i
$605$	−6.65311	−	11.5235i	−0.270487	−	0.468498i
$606$		0			0
$607$	−28.7339	−	16.5895i	−1.16627	−	0.673349i	−0.213475	−	0.976949i	$-0.568478\pi$
$607$	−28.7339	−	16.5895i	−1.16627	−	0.673349i	−0.952800	+	0.303600i	$0.901811\pi$
$608$	16.9333			0.686735
$609$		0			0
$610$	46.9559			1.90119
$611$	−8.09780	−	4.67527i	−0.327602	−	0.189141i
$612$		0			0
$613$	−2.01164	−	3.48426i	−0.0812492	−	0.140728i	0.822538	−	0.568711i	$-0.192558\pi$
$613$	−2.01164	−	3.48426i	−0.0812492	−	0.140728i	−0.903787	+	0.427983i	$0.859224\pi$
$614$	−27.7120	+	47.9985i	−1.11836	+	1.93706i
$615$		0			0
$616$	−8.27468	−	8.04168i	−0.333396	−	0.324009i
$617$			31.3144i			1.26067i	0.776323	+	0.630336i	$0.217083\pi$
$617$			31.3144i			1.26067i	−0.776323	+	0.630336i	$0.782917\pi$
$618$		0			0
$619$	−12.0646	+	6.96550i	−0.484917	+	0.279967i	−0.722463	−	0.691409i	$-0.756990\pi$
$619$	−12.0646	+	6.96550i	−0.484917	+	0.279967i	0.237546	+	0.971376i	$0.423657\pi$
$620$	−12.7238	+	7.34612i	−0.511002	+	0.295027i
$621$		0			0
$622$			42.0962i			1.68790i
$623$	−1.05169	+	4.16178i	−0.0421351	+	0.166738i
$624$		0			0
$625$	−1.95762	+	3.39069i	−0.0783047	+	0.135628i
$626$	−18.2592	−	31.6259i	−0.729786	−	1.26403i
$627$		0			0
$628$	−97.4661	−	56.2721i	−3.88932	−	2.24550i
$629$	−11.8031			−0.470620
$630$		0			0
$631$	−4.61815			−0.183846			−0.0919229	−	0.995766i	$-0.529301\pi$
$631$	−4.61815			−0.183846			−0.0919229	+	0.995766i	$0.529301\pi$
$632$	24.6902	+	14.2549i	0.982124	+	0.567030i
$633$		0			0
$634$	−26.3203	−	45.5881i	−1.04531	−	1.81053i
$635$	1.83672	−	3.18129i	0.0728879	−	0.126246i
$636$		0			0
$637$	−4.50863	−	7.31828i	−0.178638	−	0.289961i
$638$		−	9.37609i		−	0.371203i
$639$		0			0
$640$	−4.34657	+	2.50949i	−0.171813	+	0.0991964i
$641$	36.7821	−	21.2362i	1.45281	−	0.838779i	0.454167	−	0.890917i	$-0.349937\pi$
$641$	36.7821	−	21.2362i	1.45281	−	0.838779i	0.998640	+	0.0521380i	$0.0166036\pi$
$642$		0			0
$643$		−	3.62015i		−	0.142765i	−0.997449	−	0.0713825i	$-0.977259\pi$
$643$		−	3.62015i		−	0.142765i	0.997449	−	0.0713825i	$-0.0227411\pi$
$644$	−16.1874	−	57.1362i	−0.637875	−	2.25148i
$645$		0			0
$646$	−10.9239	+	18.9207i	−0.429795	+	0.744426i
$647$	6.00617	+	10.4030i	0.236127	+	0.408984i	0.959600	−	0.281369i	$-0.0907886\pi$
$647$	6.00617	+	10.4030i	0.236127	+	0.408984i	−0.723473	+	0.690353i	$0.757455\pi$
$648$		0			0
$649$	−1.90394	−	1.09924i	−0.0747361	−	0.0431489i
$650$	10.9237			0.428464
$651$		0			0
$652$	−41.6968			−1.63297
$653$	39.9950	+	23.0911i	1.56512	+	0.903625i	0.996724	+	0.0808728i	$0.0257707\pi$
$653$	39.9950	+	23.0911i	1.56512	+	0.903625i	0.568400	+	0.822752i	$0.307563\pi$
$654$		0			0
$655$	−10.1665	−	17.6089i	−0.397238	−	0.688036i
$656$	18.6584	−	32.3174i	0.728490	−	1.26178i
$657$		0			0
$658$	36.4160	−	37.4711i	1.41964	−	1.46078i
$659$			18.8769i			0.735341i	0.929956	+	0.367671i	$0.119845\pi$
$659$			18.8769i			0.735341i	−0.929956	+	0.367671i	$0.880155\pi$
$660$		0			0
$661$	−2.88202	+	1.66393i	−0.112097	+	0.0647195i	−0.555000	−	0.831850i	$-0.687282\pi$
$661$	−2.88202	+	1.66393i	−0.112097	+	0.0647195i	0.442903	+	0.896570i	$0.353949\pi$
$662$	−59.4494	+	34.3231i	−2.31057	+	1.33401i
$663$		0			0
$664$		−	61.7700i		−	2.39714i
$665$	4.39336	−	4.52066i	0.170367	−	0.175304i
$666$		0			0
$667$	13.9181	−	24.1068i	0.538909	−	0.933418i
$668$	52.1494	+	90.3254i	2.01772	+	3.49480i
$669$		0			0
$670$	38.3106	+	22.1187i	1.48007	+	0.854518i
$671$	8.91178			0.344036
$672$		0			0
$673$	32.7357			1.26187			0.630934	−	0.775837i	$-0.282672\pi$
$673$	32.7357			1.26187			0.630934	+	0.775837i	$0.282672\pi$
$674$	7.80099	+	4.50390i	0.300483	+	0.173484i
$675$		0			0
$676$	27.1585	+	47.0399i	1.04456	+	1.80923i
$677$	−16.9228	+	29.3111i	−0.650396	+	1.12652i	0.332631	+	0.943057i	$0.392063\pi$
$677$	−16.9228	+	29.3111i	−0.650396	+	1.12652i	−0.983027	+	0.183461i	$0.941270\pi$
$678$		0			0
$679$	7.29937	+	25.7643i	0.280124	+	0.988743i
$680$			39.2503i			1.50518i
$681$		0			0
$682$	−3.43672	+	1.98419i	−0.131599	+	0.0759785i
$683$	4.79617	−	2.76907i	0.183520	−	0.105956i	−0.405425	−	0.914128i	$-0.632877\pi$
$683$	4.79617	−	2.76907i	0.183520	−	0.105956i	0.588946	+	0.808173i	$0.299543\pi$
$684$		0			0
$685$		−	21.8052i		−	0.833133i
$686$	45.8214	−	14.4073i	1.74947	−	0.550075i
$687$		0			0
$688$	−19.9622	+	34.5756i	−0.761052	+	1.31818i
$689$	−1.89846	−	3.28822i	−0.0723254	−	0.125271i
$690$		0			0
$691$	−12.3417	−	7.12550i	−0.469502	−	0.271067i	0.246530	−	0.969135i	$-0.420710\pi$
$691$	−12.3417	−	7.12550i	−0.469502	−	0.271067i	−0.716031	+	0.698068i	$0.754043\pi$
$692$	19.2248			0.730818
$693$		0			0
$694$	−24.4003			−0.926222
$695$	−6.83219	−	3.94456i	−0.259160	−	0.149626i
$696$		0			0
$697$	9.30154	+	16.1107i	0.352321	+	0.610238i
$698$	−18.4557	+	31.9662i	−0.698559	+	1.20994i
$699$		0			0
$700$	−10.5087	+	41.5853i	−0.397191	+	1.57178i
$701$			18.6105i			0.702908i	0.936205	+	0.351454i	$0.114313\pi$
$701$			18.6105i			0.702908i	−0.936205	+	0.351454i	$0.885687\pi$
$702$		0			0
$703$	−4.38760	+	2.53318i	−0.165482	+	0.0955408i
$704$	2.84293	−	1.64137i	0.107147	−	0.0618614i
$705$		0			0
$706$		−	44.5187i		−	1.67549i
$707$	3.25058	+	3.15905i	0.122251	+	0.118808i
$708$		0			0
$709$	6.74733	−	11.6867i	0.253401	−	0.438904i	−0.711059	−	0.703133i	$-0.751784\pi$
$709$	6.74733	−	11.6867i	0.253401	−	0.438904i	0.964460	+	0.264229i	$0.0851174\pi$
$710$	−16.9137	−	29.2955i	−0.634762	−	1.09944i
$711$		0			0
$712$	−9.93557	−	5.73630i	−0.372351	−	0.214977i
$713$	−11.7815			−0.441220
$714$		0			0
$715$	−0.948941			−0.0354884
$716$	34.0676	+	19.6689i	1.27317	+	0.735063i
$717$		0			0
$718$	36.6417	+	63.4652i	1.36745	+	2.36850i
$719$	−18.8692	+	32.6824i	−0.703702	+	1.21885i	0.263456	+	0.964671i	$0.415137\pi$
$719$	−18.8692	+	32.6824i	−0.703702	+	1.21885i	−0.967158	+	0.254176i	$0.918196\pi$
$720$		0			0
$721$	18.9954	+	4.80017i	0.707424	+	0.178768i
$722$		−	39.8993i		−	1.48490i
$723$		0			0
$724$	−51.8617	+	29.9424i	−1.92742	+	1.11280i
$725$	−17.4118	+	10.0527i	−0.646659	+	0.373348i
$726$		0			0
$727$		−	2.29185i		−	0.0849999i	−0.999096	−	0.0424999i	$-0.986468\pi$
$727$		−	2.29185i		−	0.0849999i	0.999096	−	0.0424999i	$-0.0135322\pi$
$728$	22.1031	−	6.26211i	0.819197	−	0.232089i
$729$		0			0
$730$	−18.6685	+	32.3347i	−0.690950	+	1.19676i
$731$	−9.95149	−	17.2365i	−0.368069	−	0.637514i
$732$		0			0
$733$	21.4678	+	12.3944i	0.792930	+	0.457798i	0.840993	−	0.541046i	$-0.181972\pi$
$733$	21.4678	+	12.3944i	0.792930	+	0.457798i	−0.0480633	+	0.998844i	$0.515305\pi$
$734$	−59.8341			−2.20852
$735$		0			0
$736$	42.2889			1.55879
$737$	7.27099	+	4.19791i	0.267830	+	0.154632i
$738$		0			0
$739$	8.10081	+	14.0310i	0.297993	+	0.516139i	0.975677	−	0.219214i	$-0.0703494\pi$
$739$	8.10081	+	14.0310i	0.297993	+	0.516139i	−0.677684	+	0.735354i	$0.737016\pi$
$740$	−7.88932	+	13.6647i	−0.290017	+	0.502325i
$741$		0			0
$742$	20.4140	−	5.78354i	0.749420	−	0.212321i
$743$		−	21.7444i		−	0.797723i	−0.917011	−	0.398862i	$-0.869405\pi$
$743$		−	21.7444i		−	0.797723i	0.917011	−	0.398862i	$-0.130595\pi$
$744$		0			0
$745$	11.5315	−	6.65769i	0.422480	−	0.243919i
$746$	31.1591	−	17.9897i	1.14081	−	0.658649i
$747$		0			0
$748$			12.9138i			0.472176i
$749$	−0.389961	−	0.0985440i	−0.0142489	−	0.00360072i
$750$		0			0
$751$	3.78997	−	6.56443i	0.138298	−	0.239539i	−0.788554	−	0.614965i	$-0.789170\pi$
$751$	3.78997	−	6.56443i	0.138298	−	0.239539i	0.926853	+	0.375426i	$0.122503\pi$
$752$	33.8340	+	58.6022i	1.23380	+	2.13700i
$753$		0			0
$754$	16.1666	+	9.33381i	0.588754	+	0.339917i
$755$	11.8900			0.432720
$756$		0			0
$757$	10.3436			0.375944			0.187972	−	0.982174i	$-0.439809\pi$
$757$	10.3436			0.375944			0.187972	+	0.982174i	$0.439809\pi$
$758$	51.1686	+	29.5422i	1.85853	+	1.07302i
$759$		0			0
$760$	8.42392	+	14.5907i	0.305568	+	0.529259i
$761$	17.2169	−	29.8206i	0.624114	−	1.08100i	−0.364598	−	0.931165i	$-0.618793\pi$
$761$	17.2169	−	29.8206i	0.624114	−	1.08100i	0.988711	−	0.149832i	$-0.0478732\pi$
$762$		0			0
$763$	10.2476	+	9.95908i	0.370989	+	0.360543i
$764$			17.9629i			0.649874i
$765$		0			0
$766$	34.2121	−	19.7523i	1.23613	−	0.713681i
$767$	3.79070	−	2.18856i	0.136874	−	0.0790245i
$768$		0			0
$769$		−	14.9353i		−	0.538581i	−0.963059	−	0.269290i	$-0.913211\pi$
$769$		−	14.9353i		−	0.538581i	0.963059	−	0.269290i	$-0.0867892\pi$
$770$	1.29918	−	5.14114i	0.0468191	−	0.185274i
$771$		0			0
$772$	16.0439	−	27.7888i	0.577431	−	1.00014i
$773$	19.9924	+	34.6278i	0.719076	+	1.24548i	0.961366	+	0.275272i	$0.0887680\pi$
$773$	19.9924	+	34.6278i	0.719076	+	1.24548i	−0.242290	+	0.970204i	$0.577899\pi$
$774$		0			0
$775$	7.36945	+	4.25476i	0.264719	+	0.152835i
$776$	−71.5690			−2.56918
$777$		0			0
$778$	36.6932			1.31552
$779$	6.91539	+	3.99260i	0.247770	+	0.143050i
$780$		0			0
$781$	−3.21007	−	5.56000i	−0.114865	−	0.198952i
$782$	−27.2811	+	47.2523i	−0.975571	+	1.68974i
$783$		0			0
$784$	1.77622	+	62.1796i	0.0634364	+	2.22070i
$785$		−	29.8355i		−	1.06488i
$786$		0			0
$787$	1.94091	−	1.12059i	0.0691860	−	0.0399446i	−0.465008	−	0.885307i	$-0.653949\pi$
$787$	1.94091	−	1.12059i	0.0691860	−	0.0399446i	0.534194	+	0.845362i	$0.320615\pi$
$788$	26.2561	−	15.1590i	0.935336	−	0.540016i
$789$		0			0
$790$			13.1022i			0.466154i
$791$	−4.66671	−	16.4719i	−0.165929	−	0.585674i
$792$		0			0
$793$	−8.87159	+	15.3660i	−0.315039	+	0.545664i
$794$	12.5883	+	21.8036i	0.446742	+	0.773780i
$795$		0			0
$796$	−65.6605	−	37.9091i	−2.32727	−	1.34365i
$797$	44.2153			1.56619			0.783094	−	0.621904i	$-0.213640\pi$
$797$	44.2153			1.56619			0.783094	+	0.621904i	$0.213640\pi$
$798$		0			0
$799$	−33.7336			−1.19341
$800$	−26.4522	−	15.2722i	−0.935226	−	0.539953i
$801$		0			0
$802$	−11.3225	−	19.6112i	−0.399812	−	0.692495i
$803$	−3.54309	+	6.13682i	−0.125033	+	0.216564i
$804$		0			0
$805$	10.9719	−	11.2898i	0.386709	−	0.397913i
$806$		−	7.90096i		−	0.278300i
$807$		0			0
$808$	−10.4914	+	6.05723i	−0.369087	+	0.213093i
$809$	4.31478	−	2.49114i	0.151699	−	0.0875837i	−0.422229	−	0.906489i	$-0.638752\pi$
$809$	4.31478	−	2.49114i	0.151699	−	0.0875837i	0.573928	+	0.818906i	$0.305419\pi$
$810$		0			0
$811$		−	36.5749i		−	1.28432i	−0.766571	−	0.642160i	$-0.778039\pi$
$811$		−	36.5749i		−	1.28432i	0.766571	−	0.642160i	$-0.221961\pi$
$812$	−51.0851	+	52.5652i	−1.79273	+	1.84468i
$813$		0			0
$814$	−2.13091	+	3.69084i	−0.0746883	+	0.129364i
$815$	−5.52693	−	9.57292i	−0.193600	−	0.335325i
$816$		0			0
$817$	−7.39861	−	4.27159i	−0.258845	−	0.149444i
$818$	38.6225			1.35040
$819$		0			0
$820$	24.8690			0.868465
$821$	−34.8397	−	20.1147i	−1.21591	−	0.702008i	−0.251872	−	0.967761i	$-0.581046\pi$
$821$	−34.8397	−	20.1147i	−1.21591	−	0.702008i	−0.964041	+	0.265753i	$0.914379\pi$
$822$		0			0
$823$	17.9016	+	31.0065i	0.624011	+	1.08082i	0.988731	+	0.149701i	$0.0478313\pi$
$823$	17.9016	+	31.0065i	0.624011	+	1.08082i	−0.364720	+	0.931117i	$0.618835\pi$
$824$	−26.1819	+	45.3483i	−0.912089	+	1.57978i
$825$		0			0
$826$	6.66734	+	23.5335i	0.231986	+	0.818834i
$827$		−	32.0733i		−	1.11530i	−0.830077	−	0.557648i	$-0.811704\pi$
$827$		−	32.0733i		−	1.11530i	0.830077	−	0.557648i	$-0.188296\pi$
$828$		0			0
$829$	−14.0640	+	8.11986i	−0.488463	+	0.282014i	−0.723937	−	0.689866i	$-0.757669\pi$
$829$	−14.0640	+	8.11986i	−0.488463	+	0.282014i	0.235474	+	0.971881i	$0.424336\pi$
$830$	24.5842	−	14.1937i	0.853332	−	0.492671i
$831$		0			0
$832$			6.53587i			0.226590i
$833$	−27.2874	−	14.7319i	−0.945453	−	0.510431i
$834$		0			0
$835$	−13.8248	+	23.9453i	−0.478429	+	0.828663i
$836$	2.77157	+	4.80050i	0.0958568	+	0.166029i
$837$		0			0
$838$	9.60684	+	5.54651i	0.331863	+	0.191601i
$839$	2.70289			0.0933142			0.0466571	−	0.998911i	$-0.485143\pi$
$839$	2.70289			0.0933142			0.0466571	+	0.998911i	$0.485143\pi$
$840$		0			0
$841$	−5.35828			−0.184768
$842$	−25.9053	−	14.9565i	−0.892757	−	0.515434i
$843$		0			0
$844$	19.1927	+	33.2427i	0.660639	+	1.14426i
$845$	−7.19974	+	12.4703i	−0.247679	+	0.428992i
$846$		0			0
$847$	−6.88375	+	27.2405i	−0.236528	+	0.935996i
$848$			27.4775i			0.943582i
$849$		0			0
$850$	34.1293	−	19.7046i	1.17063	−	0.675861i
$851$	−10.9575	+	6.32632i	−0.375619	+	0.216864i
$852$		0			0
$853$			47.7108i			1.63359i	0.576931	+	0.816793i	$0.304250\pi$
$853$			47.7108i			1.63359i	−0.576931	+	0.816793i	$0.695750\pi$
$854$	−71.1037	−	69.1015i	−2.43312	−	2.36461i
$855$		0			0
$856$	0.537495	−	0.930969i	0.0183712	−	0.0318199i
$857$	−8.93973	−	15.4841i	−0.305375	−	0.528926i	0.671969	−	0.740579i	$-0.265449\pi$
$857$	−8.93973	−	15.4841i	−0.305375	−	0.528926i	−0.977345	+	0.211653i	$0.932115\pi$
$858$		0			0
$859$	−29.1901	−	16.8529i	−0.995953	−	0.575014i	−0.0889047	−	0.996040i	$-0.528337\pi$
$859$	−29.1901	−	16.8529i	−0.995953	−	0.575014i	−0.907048	+	0.421026i	$0.861670\pi$
$860$	−26.6068			−0.907284
$861$		0			0
$862$	−43.2734			−1.47390
$863$	−16.4318	−	9.48693i	−0.559347	−	0.322939i	0.193537	−	0.981093i	$-0.438004\pi$
$863$	−16.4318	−	9.48693i	−0.559347	−	0.322939i	−0.752883	+	0.658154i	$0.771338\pi$
$864$		0			0
$865$	2.54826	+	4.41371i	0.0866434	+	0.150071i
$866$	−16.0155	+	27.7396i	−0.544228	+	0.942630i
$867$		0			0
$868$	30.0780	+	7.60078i	1.02091	+	0.257987i
$869$			2.48666i			0.0843543i
$870$		0			0
$871$	−14.4764	+	8.35795i	−0.490514	+	0.283198i
$872$	−33.0748	+	19.0957i	−1.12005	+	0.646663i
$873$		0			0
$874$			23.4204i			0.792206i
$875$	−26.8880	+	7.61773i	−0.908980	+	0.257526i
$876$		0			0
$877$	−18.6188	+	32.2487i	−0.628712	+	1.08896i	0.359098	+	0.933300i	$0.383084\pi$
$877$	−18.6188	+	32.2487i	−0.628712	+	1.08896i	−0.987810	+	0.155662i	$0.950249\pi$
$878$	28.7035	+	49.7159i	0.968695	+	1.67783i
$879$		0			0
$880$	5.94726	+	3.43365i	0.200482	+	0.115748i
$881$	−4.71527			−0.158862			−0.0794308	−	0.996840i	$-0.525310\pi$
$881$	−4.71527			−0.158862			−0.0794308	+	0.996840i	$0.525310\pi$
$882$		0			0
$883$	30.1766			1.01552			0.507762	−	0.861497i	$-0.330473\pi$
$883$	30.1766			1.01552			0.507762	+	0.861497i	$0.330473\pi$
$884$	−22.2665	−	12.8556i	−0.748904	−	0.432380i
$885$		0			0
$886$	6.33251	+	10.9682i	0.212745	+	0.368485i
$887$	−19.2217	+	33.2930i	−0.645402	+	1.11787i	0.338806	+	0.940856i	$0.389977\pi$
$887$	−19.2217	+	33.2930i	−0.645402	+	1.11787i	−0.984208	+	0.177013i	$0.943356\pi$
$888$		0			0
$889$	−7.46294	+	2.11435i	−0.250299	+	0.0709131i
$890$		−	5.27243i		−	0.176732i
$891$		0			0
$892$	−32.9058	+	18.9981i	−1.10177	+	0.636105i
$893$	−12.5399	+	7.23993i	−0.419632	+	0.242275i
$894$		0			0
$895$			10.4285i			0.348586i
$896$	10.2749	+	2.59649i	0.343260	+	0.0867426i
$897$		0			0
$898$	−16.1329	+	27.9431i	−0.538363	+	0.932472i
$899$	7.27098	+	12.5937i	0.242501	+	0.420023i
$900$		0			0
$901$	−11.8628	−	6.84900i	−0.395208	−	0.228173i
$902$	6.71714			0.223656
$903$		0			0
$904$	45.7563			1.52183
$905$	−13.7486	−	7.93774i	−0.457018	−	0.263859i
$906$		0			0
$907$	−21.7951	−	37.7503i	−0.723695	−	1.25348i	−0.959509	−	0.281678i	$-0.909109\pi$
$907$	−21.7951	−	37.7503i	−0.723695	−	1.25348i	0.235814	−	0.971798i	$-0.424224\pi$
$908$	−49.2103	+	85.2348i	−1.63310	+	2.82862i
$909$		0			0
$910$	7.57123	+	7.35804i	0.250984	+	0.243917i
$911$			1.93685i			0.0641706i	0.999485	+	0.0320853i	$0.0102148\pi$
$911$			1.93685i			0.0641706i	−0.999485	+	0.0320853i	$0.989785\pi$
$912$		0			0
$913$	4.66585	−	2.69383i	0.154417	−	0.0891528i
$914$	24.2025	−	13.9733i	0.800548	−	0.462197i
$915$		0			0
$916$		−	28.4494i		−	0.939993i
$917$	−10.5189	+	41.6258i	−0.347366	+	1.37460i
$918$		0			0
$919$	4.61421	−	7.99205i	0.152209	−	0.263634i	−0.779830	−	0.625991i	$-0.784695\pi$
$919$	4.61421	−	7.99205i	0.152209	−	0.263634i	0.932039	+	0.362357i	$0.118028\pi$
$920$	21.0377	+	36.4384i	0.693594	+	1.20134i
$921$		0			0
$922$	1.49724	+	0.864434i	0.0493091	+	0.0284686i
$923$	12.7824			0.420736
$924$		0			0
$925$	9.13874			0.300480
$926$	93.3880	+	53.9176i	3.06892	+	1.77184i
$927$		0			0
$928$	−26.0987	−	45.2043i	−0.856732	−	1.48390i
$929$	26.6849	−	46.2197i	0.875504	−	1.51642i	0.0192794	−	0.999814i	$-0.493863\pi$
$929$	26.6849	−	46.2197i	0.875504	−	1.51642i	0.856225	−	0.516603i	$-0.172804\pi$
$930$		0			0
$931$	−13.3054	+	0.380082i	−0.436068	+	0.0124567i
$932$		−	99.4142i		−	3.25642i
$933$		0			0
$934$	88.3010	−	50.9806i	2.88930	−	1.66814i
$935$	−2.96481	+	1.71173i	−0.0969595	+	0.0559796i
$936$		0			0
$937$			28.6378i			0.935555i	0.883846	+	0.467778i	$0.154945\pi$
$937$			28.6378i			0.935555i	−0.883846	+	0.467778i	$0.845055\pi$
$938$	−25.4620	−	89.8724i	−0.831365	−	2.93444i
$939$		0			0
$940$	−22.5480	+	39.0542i	−0.735433	+	1.27381i
$941$	−0.688308	−	1.19218i	−0.0224382	−	0.0388641i	0.854588	−	0.519306i	$-0.173810\pi$
$941$	−0.688308	−	1.19218i	−0.0224382	−	0.0388641i	−0.877026	+	0.480442i	$0.840476\pi$
$942$		0			0
$943$	17.2704	+	9.97105i	0.562401	+	0.324702i
$944$	−31.6764			−1.03098
$945$		0			0
$946$	−7.18651			−0.233653
$947$	47.0080	+	27.1401i	1.52755	+	0.881933i	0.999464	+	0.0327450i	$0.0104249\pi$
$947$	47.0080	+	27.1401i	1.52755	+	0.881933i	0.528090	+	0.849188i	$0.322908\pi$
$948$		0			0
$949$	−7.05423	−	12.2183i	−0.228990	−	0.396622i
$950$	8.45802	−	14.6497i	0.274414	−	0.475300i
$951$		0			0
$952$	57.7617	−	59.4353i	1.87207	−	1.92631i
$953$			11.2998i			0.366036i	0.983110	+	0.183018i	$0.0585867\pi$
$953$			11.2998i			0.366036i	−0.983110	+	0.183018i	$0.941413\pi$
$954$		0			0
$955$	−4.12399	+	2.38099i	−0.133449	+	0.0770469i
$956$	35.4994	−	20.4956i	1.14813	−	0.662874i
$957$		0			0
$958$			98.8536i			3.19382i
$959$	−32.0891	+	33.0188i	−1.03621	+	1.06623i
$960$		0			0
$961$	−12.4226	+	21.5166i	−0.400729	+	0.694083i
$962$	−4.24260	−	7.34839i	−0.136787	−	0.236922i
$963$		0			0
$964$	−34.6825	−	20.0240i	−1.11705	−	0.644928i
$965$	8.50647			0.273833
$966$		0			0
$967$	−11.8682			−0.381657			−0.190829	−	0.981623i	$-0.561117\pi$
$967$	−11.8682			−0.381657			−0.190829	+	0.981623i	$0.561117\pi$
$968$	−65.0324	−	37.5465i	−2.09022	−	1.20679i
$969$		0			0
$970$	−16.4454	−	28.4842i	−0.528029	−	0.914573i
$971$	28.0837	−	48.6424i	0.901249	−	1.56101i	0.0753736	−	0.997155i	$-0.475985\pi$
$971$	28.0837	−	48.6424i	0.901249	−	1.56101i	0.825875	−	0.563853i	$-0.190682\pi$
$972$		0			0
$973$	4.54081	+	16.0275i	0.145572	+	0.513819i
$974$		−	19.7253i		−	0.632038i
$975$		0			0
$976$	111.201	−	64.2020i	3.55946	−	2.05506i
$977$	−18.7626	+	10.8326i	−0.600268	+	0.346565i	−0.769147	−	0.639072i	$-0.779319\pi$
$977$	−18.7626	+	10.8326i	−0.600268	+	0.346565i	0.168879	+	0.985637i	$0.445985\pi$
$978$		0			0
$979$		−	1.00066i		−	0.0319811i
$980$	−35.2948	+	21.7443i	−1.12745	+	0.694596i
$981$		0			0
$982$	−4.99072	+	8.64419i	−0.159260	+	0.275847i
$983$	9.70006	+	16.8010i	0.309384	+	0.535869i	0.978228	−	0.207534i	$-0.0665438\pi$
$983$	9.70006	+	16.8010i	0.309384	+	0.535869i	−0.668844	+	0.743403i	$0.733211\pi$
$984$		0			0
$985$	6.96052	+	4.01866i	0.221781	+	0.128045i
$986$	67.3465			2.14475
$987$		0			0
$988$	−11.0363			−0.351111
$989$	−18.4771	−	10.6678i	−0.587539	−	0.339216i
$990$		0			0
$991$	−12.6630	−	21.9330i	−0.402254	−	0.696725i	0.591743	−	0.806126i	$-0.298440\pi$
$991$	−12.6630	−	21.9330i	−0.402254	−	0.696725i	−0.993998	+	0.109402i	$0.965107\pi$
$992$	−11.0461	+	19.1325i	−0.350715	+	0.607456i
$993$		0			0
$994$	−17.5001	+	69.2518i	−0.555069	+	2.19653i
$995$		−	20.0995i		−	0.637196i
$996$		0			0
$997$	−4.82016	+	2.78292i	−0.152656	+	0.0881360i	−0.574382	−	0.818587i	$-0.694758\pi$
$997$	−4.82016	+	2.78292i	−0.152656	+	0.0881360i	0.421726	+	0.906723i	$0.361424\pi$
$998$	72.2309	−	41.7025i	2.28643	−	1.32007i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.p.c.404.5		10
3.2	odd	2		567.2.p.d.404.1		10
7.3	odd	6		567.2.p.d.80.1		10
9.2	odd	6		63.2.i.b.5.5	✓	10
9.4	even	3		63.2.s.b.47.1	yes	10
9.5	odd	6		189.2.s.b.89.5		10
9.7	even	3		189.2.i.b.152.1		10
21.17	even	6	inner	567.2.p.c.80.5		10
36.7	odd	6		3024.2.ca.b.2609.2		10
36.11	even	6		1008.2.ca.b.257.1		10
36.23	even	6		3024.2.df.b.1601.2		10
36.31	odd	6		1008.2.df.b.929.1		10
63.2	odd	6		441.2.o.d.293.5		10
63.4	even	3		441.2.i.b.227.1		10
63.5	even	6		1323.2.o.c.440.1		10
63.11	odd	6		441.2.s.b.374.1		10
63.13	odd	6		441.2.s.b.362.1		10
63.16	even	3		1323.2.o.c.881.1		10
63.20	even	6		441.2.i.b.68.5		10
63.23	odd	6		1323.2.o.d.440.1		10
63.25	even	3		1323.2.s.b.962.5		10
63.31	odd	6		63.2.i.b.38.1	yes	10
63.32	odd	6		1323.2.i.b.521.5		10
63.34	odd	6		1323.2.i.b.1097.1		10
63.38	even	6		63.2.s.b.59.1	yes	10
63.40	odd	6		441.2.o.d.146.5		10
63.41	even	6		1323.2.s.b.656.5		10
63.47	even	6		441.2.o.c.293.5		10
63.52	odd	6		189.2.s.b.17.5		10
63.58	even	3		441.2.o.c.146.5		10
63.59	even	6		189.2.i.b.143.5		10
63.61	odd	6		1323.2.o.d.881.1		10
252.31	even	6		1008.2.ca.b.353.1		10
252.59	odd	6		3024.2.ca.b.2033.2		10
252.115	even	6		3024.2.df.b.17.2		10
252.227	odd	6		1008.2.df.b.689.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.5	✓	10	9.2	odd	6
63.2.i.b.38.1	yes	10	63.31	odd	6
63.2.s.b.47.1	yes	10	9.4	even	3
63.2.s.b.59.1	yes	10	63.38	even	6
189.2.i.b.143.5		10	63.59	even	6
189.2.i.b.152.1		10	9.7	even	3
189.2.s.b.17.5		10	63.52	odd	6
189.2.s.b.89.5		10	9.5	odd	6
441.2.i.b.68.5		10	63.20	even	6
441.2.i.b.227.1		10	63.4	even	3
441.2.o.c.146.5		10	63.58	even	3
441.2.o.c.293.5		10	63.47	even	6
441.2.o.d.146.5		10	63.40	odd	6
441.2.o.d.293.5		10	63.2	odd	6
441.2.s.b.362.1		10	63.13	odd	6
441.2.s.b.374.1		10	63.11	odd	6
567.2.p.c.80.5		10	21.17	even	6	inner
567.2.p.c.404.5		10	1.1	even	1	trivial
567.2.p.d.80.1		10	7.3	odd	6
567.2.p.d.404.1		10	3.2	odd	2
1008.2.ca.b.257.1		10	36.11	even	6
1008.2.ca.b.353.1		10	252.31	even	6
1008.2.df.b.689.1		10	252.227	odd	6
1008.2.df.b.929.1		10	36.31	odd	6
1323.2.i.b.521.5		10	63.32	odd	6
1323.2.i.b.1097.1		10	63.34	odd	6
1323.2.o.c.440.1		10	63.5	even	6
1323.2.o.c.881.1		10	63.16	even	3
1323.2.o.d.440.1		10	63.23	odd	6
1323.2.o.d.881.1		10	63.61	odd	6
1323.2.s.b.656.5		10	63.41	even	6
1323.2.s.b.962.5		10	63.25	even	3
3024.2.ca.b.2033.2		10	252.59	odd	6
3024.2.ca.b.2609.2		10	36.7	odd	6
3024.2.df.b.17.2		10	252.115	even	6
3024.2.df.b.1601.2		10	36.23	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.24607 + 1.29677i) q^{2} +(2.36322 + 4.09323i) q^{4} +(-0.626493 + 1.08512i) q^{5} +(2.54556 - 0.721191i) q^{7} +7.07116i q^{8} +O(q^{10})\)	\(q+(2.24607 + 1.29677i) q^{2} +(2.36322 + 4.09323i) q^{4} +(-0.626493 + 1.08512i) q^{5} +(2.54556 - 0.721191i) q^{7} +7.07116i q^{8} +(-2.81429 + 1.62483i) q^{10} +(-0.534126 + 0.308378i) q^{11} -1.22795i q^{13} +(6.65273 + 1.68116i) q^{14} +(-4.44321 + 7.69587i) q^{16} +(-2.21501 - 3.83652i) q^{17} +(-1.64679 - 0.950775i) q^{19} -5.92217 q^{20} -1.59958 q^{22} +(-4.11267 - 2.37445i) q^{23} +(1.71501 + 2.97049i) q^{25} +(1.59237 - 2.75806i) q^{26} +(8.96773 + 8.71522i) q^{28} +5.86159i q^{29} +(2.14851 - 1.24044i) q^{31} +(-7.71195 + 4.45249i) q^{32} -11.4895i q^{34} +(-0.812198 + 3.21405i) q^{35} +(1.33217 - 2.30738i) q^{37} +(-2.46587 - 4.27102i) q^{38} +(-7.67303 - 4.43003i) q^{40} -4.19931 q^{41} +4.49274 q^{43} +(-2.52452 - 1.45753i) q^{44} +(-6.15823 - 10.6664i) q^{46} +(3.80738 - 6.59458i) q^{47} +(5.95977 - 3.67167i) q^{49} +8.89591i q^{50} +(5.02627 - 2.90192i) q^{52} +(2.67782 - 1.54604i) q^{53} -0.772786i q^{55} +(5.09966 + 18.0001i) q^{56} +(-7.60114 + 13.1656i) q^{58} +(1.78229 + 3.08702i) q^{59} +(-12.5136 - 7.22473i) q^{61} +6.43428 q^{62} -5.32259 q^{64} +(1.33247 + 0.769301i) q^{65} +(-6.80644 - 11.7891i) q^{67} +(10.4692 - 18.1331i) q^{68} +(-5.99214 + 6.16576i) q^{70} +10.4095i q^{71} +(9.95016 - 5.74473i) q^{73} +(5.98429 - 3.45503i) q^{74} -8.98758i q^{76} +(-1.13725 + 1.17020i) q^{77} +(2.01592 - 3.49168i) q^{79} +(-5.56728 - 9.64281i) q^{80} +(-9.43196 - 5.44554i) q^{82} -8.73549 q^{83} +5.55076 q^{85} +(10.0910 + 5.82605i) q^{86} +(-2.18059 - 3.77689i) q^{88} +(-0.811226 + 1.40508i) q^{89} +(-0.885586 - 3.12582i) q^{91} -22.4454i q^{92} +(17.1033 - 9.87459i) q^{94} +(2.06341 - 1.19131i) q^{95} +10.1213i q^{97} +(18.1474 - 0.518397i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{4} + 3 q^{7}+O(q^{10}) \) 10 * q + 4 * q^4 + 3 * q^7	\( 10 q + 4 q^{4} + 3 q^{7} - 15 q^{10} - 12 q^{11} + 18 q^{14} - 6 q^{16} - 12 q^{17} + 3 q^{19} + 6 q^{20} - 10 q^{22} - 15 q^{23} + 7 q^{25} + 3 q^{26} + 2 q^{28} + 9 q^{31} - 48 q^{32} - 15 q^{35} + 6 q^{37} - 18 q^{38} - 15 q^{40} + 18 q^{41} - 6 q^{43} + 24 q^{44} - 13 q^{46} + 15 q^{47} + 19 q^{49} + 12 q^{52} - 9 q^{53} + 21 q^{56} + 8 q^{58} - 18 q^{59} - 12 q^{61} + 12 q^{62} + 6 q^{64} + 3 q^{65} - 10 q^{67} + 27 q^{68} - 15 q^{70} + 3 q^{73} - 30 q^{74} - 6 q^{77} + 20 q^{79} - 30 q^{80} + 9 q^{82} + 30 q^{83} - 36 q^{85} + 54 q^{86} - 8 q^{88} + 24 q^{89} - 24 q^{91} + 3 q^{94} + 45 q^{98}+O(q^{100}) \) 10 * q + 4 * q^4 + 3 * q^7 - 15 * q^10 - 12 * q^11 + 18 * q^14 - 6 * q^16 - 12 * q^17 + 3 * q^19 + 6 * q^20 - 10 * q^22 - 15 * q^23 + 7 * q^25 + 3 * q^26 + 2 * q^28 + 9 * q^31 - 48 * q^32 - 15 * q^35 + 6 * q^37 - 18 * q^38 - 15 * q^40 + 18 * q^41 - 6 * q^43 + 24 * q^44 - 13 * q^46 + 15 * q^47 + 19 * q^49 + 12 * q^52 - 9 * q^53 + 21 * q^56 + 8 * q^58 - 18 * q^59 - 12 * q^61 + 12 * q^62 + 6 * q^64 + 3 * q^65 - 10 * q^67 + 27 * q^68 - 15 * q^70 + 3 * q^73 - 30 * q^74 - 6 * q^77 + 20 * q^79 - 30 * q^80 + 9 * q^82 + 30 * q^83 - 36 * q^85 + 54 * q^86 - 8 * q^88 + 24 * q^89 - 24 * q^91 + 3 * q^94 + 45 * q^98

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