LMFDB - Embedded newform 225.2.h.d.181.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [225,2,Mod(46,225)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(225, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 6])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("225.46"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.h (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0] 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 3x^{10} - 2x^{9} + 34x^{8} - 22x^{7} + 236x^{6} - 179x^{5} + 877x^{4} - 409x^{3} + 96x^{2} - 11x + 1 $ x^12 + 3x^10 - 2x^9 + 34x^8 - 22x^7 + 236x^6 - 179x^5 + 877x^4 - 409x^3 + 96x^2 - 11x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			181.2
Root			$0.199632 - 0.145041i$ of defining polynomial
Character	$\chi$	$=$	225.181
Dual form			225.2.h.d.46.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0762527 - 0.234682i) q^{2} +(1.56877 - 1.13978i) q^{4} +(2.09387 - 0.784664i) q^{5} -1.24676 q^{7} +(-0.786373 - 0.571334i) q^{8} +(-0.343810 - 0.431561i) q^{10} +(-0.794084 - 2.44394i) q^{11} +(-1.44659 + 4.45215i) q^{13} +(0.0950687 + 0.292592i) q^{14} +(1.12432 - 3.46029i) q^{16} +(4.72397 + 3.43216i) q^{17} +(-3.37244 - 2.45022i) q^{19} +(2.39047 - 3.61751i) q^{20} +(-0.512997 + 0.372714i) q^{22} +(-0.496117 - 1.52689i) q^{23} +(3.76860 - 3.28597i) q^{25} +1.15514 q^{26} +(-1.95588 + 1.42103i) q^{28} +(-2.60158 + 1.89016i) q^{29} +(7.43739 + 5.40358i) q^{31} -2.84182 q^{32} +(0.445250 - 1.37034i) q^{34} +(-2.61055 + 0.978287i) q^{35} +(-0.394857 + 1.21524i) q^{37} +(-0.317865 + 0.978287i) q^{38} +(-2.09487 - 0.579261i) q^{40} +(-2.68719 + 8.27031i) q^{41} -3.88086 q^{43} +(-4.03129 - 2.92891i) q^{44} +(-0.320503 + 0.232859i) q^{46} +(-2.59656 + 1.88651i) q^{47} -5.44559 q^{49} +(-1.05852 - 0.633858i) q^{50} +(2.80510 + 8.63320i) q^{52} +(-10.7877 + 7.83770i) q^{53} +(-3.58038 - 4.49421i) q^{55} +(0.980418 + 0.712315i) q^{56} +(0.641964 + 0.466414i) q^{58} +(1.97548 - 6.07990i) q^{59} +(1.18258 + 3.63961i) q^{61} +(0.701000 - 2.15746i) q^{62} +(-2.03194 - 6.25366i) q^{64} +(0.464465 + 10.4573i) q^{65} +(8.19034 + 5.95063i) q^{67} +11.3227 q^{68} +(0.428648 + 0.538052i) q^{70} +(11.2284 - 8.15794i) q^{71} +(-3.51704 - 10.8243i) q^{73} +0.315305 q^{74} -8.08332 q^{76} +(0.990032 + 3.04700i) q^{77} +(-9.29008 + 6.74964i) q^{79} +(-0.360991 - 8.12762i) q^{80} +2.14580 q^{82} +(-2.29137 - 1.66478i) q^{83} +(12.5845 + 3.47978i) q^{85} +(0.295926 + 0.910766i) q^{86} +(-0.771858 + 2.37554i) q^{88} +(0.426682 + 1.31319i) q^{89} +(1.80355 - 5.55075i) q^{91} +(-2.51861 - 1.82988i) q^{92} +(0.640724 + 0.465513i) q^{94} +(-8.98407 - 2.48422i) q^{95} +(-0.0246815 + 0.0179322i) q^{97} +(0.415241 + 1.27798i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 10 q^{4} + 6 q^{5} - 12 q^{7} - 9 q^{8} - 9 q^{10} + 4 q^{11} - 2 q^{13} - 6 q^{14} + 16 q^{16} + q^{17} + 7 q^{19} - 26 q^{20} + 13 q^{22} - 19 q^{23} + 4 q^{25} + 56 q^{26} + q^{28} + q^{29}+ \cdots + 18 q^{98}+O(q^{100}) $ 12 * q - 10 * q^4 + 6 * q^5 - 12 * q^7 - 9 * q^8 - 9 * q^10 + 4 * q^11 - 2 * q^13 - 6 * q^14 + 16 * q^16 + q^17 + 7 * q^19 - 26 * q^20 + 13 * q^22 - 19 * q^23 + 4 * q^25 + 56 * q^26 + q^28 + q^29 + 13 * q^31 + 32 * q^32 - 25 * q^34 + 10 * q^35 + 8 * q^37 + 22 * q^38 - 28 * q^40 - 8 * q^41 - 4 * q^43 - 33 * q^44 - 22 * q^46 + 13 * q^47 - 28 * q^49 - 81 * q^50 + 44 * q^52 - 44 * q^53 + 9 * q^55 - 45 * q^56 + 41 * q^58 + 22 * q^59 - 8 * q^61 - 41 * q^62 + 49 * q^64 + 38 * q^65 - 6 * q^67 + 100 * q^68 - 45 * q^70 + 21 * q^71 - 16 * q^73 + 44 * q^74 - 52 * q^76 - q^77 + 10 * q^79 + 99 * q^80 + 26 * q^82 + 10 * q^83 + 23 * q^85 - 56 * q^86 - 16 * q^88 - 57 * q^89 - 7 * q^91 - 3 * q^92 - 23 * q^94 - 21 * q^95 + 4 * q^97 + 18 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.0762527	−	0.234682i	−0.0539188	−	0.165945i	0.920471	−	0.390811i	$-0.127805\pi$
$2$	−0.0762527	−	0.234682i	−0.0539188	−	0.165945i	−0.974390	+	0.224866i	$0.927805\pi$
$3$		0			0
$3$		0			0
$4$	1.56877	−	1.13978i	0.784386	−	0.569890i
$5$	2.09387	−	0.784664i	0.936408	−	0.350913i
$5$	2.09387	−	0.784664i	0.936408	−	0.350913i
$6$		0			0
$7$	−1.24676			−0.471231			−0.235615	−	0.971846i	$-0.575711\pi$
$7$	−1.24676			−0.471231			−0.235615	+	0.971846i	$0.575711\pi$
$8$	−0.786373	−	0.571334i	−0.278025	−	0.201997i
$9$		0			0
$10$	−0.343810	−	0.431561i	−0.108722	−	0.136472i
$11$	−0.794084	−	2.44394i	−0.239425	−	0.736876i	−0.996503	−	0.0835513i	$-0.973374\pi$
$11$	−0.794084	−	2.44394i	−0.239425	−	0.736876i	0.757078	−	0.653324i	$-0.226626\pi$
$12$		0			0
$13$	−1.44659	+	4.45215i	−0.401212	+	1.23480i	0.522805	+	0.852452i	$0.324885\pi$
$13$	−1.44659	+	4.45215i	−0.401212	+	1.23480i	−0.924017	+	0.382351i	$0.875115\pi$
$14$	0.0950687	+	0.292592i	0.0254082	+	0.0781984i
$15$		0			0
$16$	1.12432	−	3.46029i	0.281079	−	0.865073i
$17$	4.72397	+	3.43216i	1.14573	+	0.832422i	0.987907	−	0.155046i	$-0.0495526\pi$
$17$	4.72397	+	3.43216i	1.14573	+	0.832422i	0.157823	+	0.987467i	$0.449553\pi$
$18$		0			0
$19$	−3.37244	−	2.45022i	−0.773692	−	0.562120i	0.129387	−	0.991594i	$-0.458699\pi$
$19$	−3.37244	−	2.45022i	−0.773692	−	0.562120i	−0.903079	+	0.429474i	$0.858699\pi$
$20$	2.39047	−	3.61751i	0.534524	−	0.808901i
$21$		0			0
$22$	−0.512997	+	0.372714i	−0.109371	+	0.0794629i
$23$	−0.496117	−	1.52689i	−0.103447	−	0.318379i	0.885915	−	0.463847i	$-0.153531\pi$
$23$	−0.496117	−	1.52689i	−0.103447	−	0.318379i	−0.989363	+	0.145468i	$0.953531\pi$
$24$		0			0
$25$	3.76860	−	3.28597i	0.753721	−	0.657195i
$26$	1.15514			0.226542
$27$		0			0
$28$	−1.95588	+	1.42103i	−0.369627	+	0.268550i
$29$	−2.60158	+	1.89016i	−0.483102	+	0.350994i	−0.802525	−	0.596618i	$-0.796511\pi$
$29$	−2.60158	+	1.89016i	−0.483102	+	0.350994i	0.319423	+	0.947612i	$0.396511\pi$
$30$		0			0
$31$	7.43739	+	5.40358i	1.33579	+	0.970512i	0.999587	+	0.0287236i	$0.00914425\pi$
$31$	7.43739	+	5.40358i	1.33579	+	0.970512i	0.336207	+	0.941788i	$0.390856\pi$
$32$	−2.84182			−0.502368
$33$		0			0
$34$	0.445250	−	1.37034i	0.0763598	−	0.235011i
$35$	−2.61055	+	0.978287i	−0.441264	+	0.165361i
$36$		0			0
$37$	−0.394857	+	1.21524i	−0.0649141	+	0.199785i	−0.978253	−	0.207415i	$-0.933495\pi$
$37$	−0.394857	+	1.21524i	−0.0649141	+	0.199785i	0.913339	+	0.407200i	$0.133495\pi$
$38$	−0.317865	+	0.978287i	−0.0515645	+	0.158699i
$39$		0			0
$40$	−2.09487	−	0.579261i	−0.331228	−	0.0915891i
$41$	−2.68719	+	8.27031i	−0.419668	+	1.29161i	0.488340	+	0.872654i	$0.337603\pi$
$41$	−2.68719	+	8.27031i	−0.419668	+	1.29161i	−0.908008	+	0.418953i	$0.862397\pi$
$42$		0			0
$43$	−3.88086			−0.591825			−0.295913	−	0.955215i	$-0.595624\pi$
$43$	−3.88086			−0.591825			−0.295913	+	0.955215i	$0.595624\pi$
$44$	−4.03129	−	2.92891i	−0.607740	−	0.441549i
$45$		0			0
$46$	−0.320503	+	0.232859i	−0.0472556	+	0.0343332i
$47$	−2.59656	+	1.88651i	−0.378747	+	0.275176i	−0.760829	−	0.648953i	$-0.775207\pi$
$47$	−2.59656	+	1.88651i	−0.378747	+	0.275176i	0.382082	+	0.924129i	$0.375207\pi$
$48$		0			0
$49$	−5.44559			−0.777942
$50$	−1.05852	−	0.633858i	−0.149698	−	0.0896411i
$51$		0			0
$52$	2.80510	+	8.63320i	0.388997	+	1.19721i
$53$	−10.7877	+	7.83770i	−1.48180	+	1.07659i	−0.504829	+	0.863219i	$0.668444\pi$
$53$	−10.7877	+	7.83770i	−1.48180	+	1.07659i	−0.976971	+	0.213371i	$0.931556\pi$
$54$		0			0
$55$	−3.58038	−	4.49421i	−0.482779	−	0.605999i
$56$	0.980418	+	0.712315i	0.131014	+	0.0951871i
$57$		0			0
$58$	0.641964	+	0.466414i	0.0842940	+	0.0612432i
$59$	1.97548	−	6.07990i	0.257186	−	0.791536i	−0.736206	−	0.676758i	$-0.763384\pi$
$59$	1.97548	−	6.07990i	0.257186	−	0.791536i	0.993391	−	0.114778i	$-0.0366157\pi$
$60$		0			0
$61$	1.18258	+	3.63961i	0.151414	+	0.466005i	0.997780	−	0.0665973i	$-0.0212143\pi$
$61$	1.18258	+	3.63961i	0.151414	+	0.466005i	−0.846366	+	0.532602i	$0.821214\pi$
$62$	0.701000	−	2.15746i	0.0890271	−	0.273997i
$63$		0			0
$64$	−2.03194	−	6.25366i	−0.253992	−	0.781708i
$65$	0.464465	+	10.4573i	0.0576098	+	1.29707i
$66$		0			0
$67$	8.19034	+	5.95063i	1.00061	+	0.726985i	0.962219	−	0.272277i	$-0.0877768\pi$
$67$	8.19034	+	5.95063i	1.00061	+	0.726985i	0.0383907	+	0.999263i	$0.487777\pi$
$68$	11.3227			1.37308
$69$		0			0
$70$	0.428648	+	0.538052i	0.0512332	+	0.0643095i
$71$	11.2284	−	8.15794i	1.33257	−	0.968169i	0.332888	−	0.942966i	$-0.391977\pi$
$71$	11.2284	−	8.15794i	1.33257	−	0.968169i	0.999682	−	0.0252028i	$-0.00802316\pi$
$72$		0			0
$73$	−3.51704	−	10.8243i	−0.411638	−	1.26689i	−0.915223	−	0.402947i	$-0.867986\pi$
$73$	−3.51704	−	10.8243i	−0.411638	−	1.26689i	0.503585	−	0.863946i	$-0.332014\pi$
$74$	0.315305			0.0366534
$75$		0			0
$76$	−8.08332			−0.927220
$77$	0.990032	+	3.04700i	0.112825	+	0.347238i
$78$		0			0
$79$	−9.29008	+	6.74964i	−1.04522	+	0.759394i	−0.971297	−	0.237871i	$-0.923551\pi$
$79$	−9.29008	+	6.74964i	−1.04522	+	0.759394i	−0.0739188	+	0.997264i	$0.523551\pi$
$80$	−0.360991	−	8.12762i	−0.0403601	−	0.908696i
$81$		0			0
$82$	2.14580			0.236964
$83$	−2.29137	−	1.66478i	−0.251511	−	0.182733i	0.454885	−	0.890550i	$-0.349680\pi$
$83$	−2.29137	−	1.66478i	−0.251511	−	0.182733i	−0.706396	+	0.707817i	$0.749680\pi$
$84$		0			0
$85$	12.5845	+	3.47978i	1.36498	+	0.377435i
$86$	0.295926	+	0.910766i	0.0319105	+	0.0982105i
$87$		0			0
$88$	−0.771858	+	2.37554i	−0.0822804	+	0.253233i
$89$	0.426682	+	1.31319i	0.0452282	+	0.139198i	0.971121	−	0.238589i	$-0.0766850\pi$
$89$	0.426682	+	1.31319i	0.0452282	+	0.139198i	−0.925892	+	0.377788i	$0.876685\pi$
$90$		0			0
$91$	1.80355	−	5.55075i	0.189063	−	0.581877i
$92$	−2.51861	−	1.82988i	−0.262584	−	0.190778i
$93$		0			0
$94$	0.640724	+	0.465513i	0.0660857	+	0.0480140i
$95$	−8.98407	−	2.48422i	−0.921746	−	0.254876i
$96$		0			0
$97$	−0.0246815	+	0.0179322i	−0.00250603	+	0.00182074i	−0.589038	−	0.808106i	$-0.700493\pi$
$97$	−0.0246815	+	0.0179322i	−0.00250603	+	0.00182074i	0.586532	+	0.809926i	$0.300493\pi$
$98$	0.415241	+	1.27798i	0.0419457	+	0.129096i
$99$		0			0
$100$	2.16680	−	9.45033i	0.216680	−	0.945033i
$101$	11.2308			1.11750			0.558751	−	0.829336i	$-0.311281\pi$
$101$	11.2308			1.11750			0.558751	+	0.829336i	$0.311281\pi$
$102$		0			0
$103$	0.583288	−	0.423783i	0.0574730	−	0.0417566i	−0.558678	−	0.829385i	$-0.688691\pi$
$103$	0.583288	−	0.423783i	0.0574730	−	0.0417566i	0.616151	+	0.787628i	$0.288691\pi$
$104$	3.68122	−	2.67456i	0.360973	−	0.262262i
$105$		0			0
$106$	2.66195	+	1.93402i	0.258552	+	0.187849i
$107$	−2.11668			−0.204627			−0.102313	−	0.994752i	$-0.532624\pi$
$107$	−2.11668			−0.204627			−0.102313	+	0.994752i	$0.532624\pi$
$108$		0			0
$109$	0.690602	−	2.12545i	0.0661477	−	0.203582i	−0.912520	−	0.409033i	$-0.865866\pi$
$109$	0.690602	−	2.12545i	0.0661477	−	0.203582i	0.978667	+	0.205451i	$0.0658662\pi$
$110$	−0.781695	+	1.18295i	−0.0745317	+	0.112790i
$111$		0			0
$112$	−1.40175	+	4.31415i	−0.132453	+	0.407649i
$113$	0.973217	−	2.99525i	0.0915526	−	0.281770i	−0.894787	−	0.446493i	$-0.852673\pi$
$113$	0.973217	−	2.99525i	0.0915526	−	0.281770i	0.986340	+	0.164723i	$0.0526729\pi$
$114$		0			0
$115$	−2.23690	−	2.80783i	−0.208592	−	0.261831i
$116$	−1.92693	+	5.93047i	−0.178911	+	0.550630i
$117$		0			0
$118$	−1.57748			−0.145219
$119$	−5.88965	−	4.27908i	−0.539903	−	0.392262i
$120$		0			0
$121$	3.55691	−	2.58425i	0.323356	−	0.234932i
$122$	0.763975	−	0.555061i	0.0691671	−	0.0502528i
$123$		0			0
$124$	17.8265			1.60086
$125$	5.31259	−	9.83750i	0.475172	−	0.879893i
$126$		0			0
$127$	−4.83929	−	14.8938i	−0.429418	−	1.32161i	−0.898700	−	0.438564i	$-0.855487\pi$
$127$	−4.83929	−	14.8938i	−0.429418	−	1.32161i	0.469282	−	0.883048i	$-0.344513\pi$
$128$	−5.91084	+	4.29448i	−0.522450	+	0.379582i
$129$		0			0
$130$	2.41872	−	0.906400i	0.212136	−	0.0794965i
$131$	−12.1000	−	8.79116i	−1.05718	−	0.768087i	−0.0836161	−	0.996498i	$-0.526647\pi$
$131$	−12.1000	−	8.79116i	−1.05718	−	0.768087i	−0.973565	+	0.228411i	$0.926647\pi$
$132$		0			0
$133$	4.20463	+	3.05484i	0.364587	+	0.264888i
$134$	0.771969	−	2.37588i	0.0666879	−	0.205244i
$135$		0			0
$136$	−1.75389	−	5.39792i	−0.150395	−	0.462868i
$137$	3.24300	−	9.98092i	0.277068	−	0.852727i	−0.711597	−	0.702588i	$-0.752028\pi$
$137$	3.24300	−	9.98092i	0.277068	−	0.852727i	0.988665	−	0.150139i	$-0.0479723\pi$
$138$		0			0
$139$	3.84749	+	11.8414i	0.326340	+	1.00437i	0.970832	+	0.239761i	$0.0770690\pi$
$139$	3.84749	+	11.8414i	0.326340	+	1.00437i	−0.644492	+	0.764611i	$0.722931\pi$
$140$	−2.98033	+	4.51017i	−0.251884	+	0.381179i
$141$		0			0
$142$	−2.77072	−	2.01304i	−0.232513	−	0.168931i
$143$	12.0295			1.00596
$144$		0			0
$145$	−3.96424	+	5.99913i	−0.329212	+	0.498200i
$146$	−2.27209	+	1.65077i	−0.188039	+	0.136619i
$147$		0			0
$148$	0.765671	+	2.35649i	0.0629378	+	0.193703i
$149$	17.0680			1.39826			0.699131	−	0.714994i	$-0.253570\pi$
$149$	17.0680			1.39826			0.699131	+	0.714994i	$0.253570\pi$
$150$		0			0
$151$	−1.57516			−0.128185			−0.0640923	−	0.997944i	$-0.520415\pi$
$151$	−1.57516			−0.128185			−0.0640923	+	0.997944i	$0.520415\pi$
$152$	1.25210	+	3.85358i	0.101559	+	0.312567i
$153$		0			0
$154$	0.639584	−	0.464685i	0.0515391	−	0.0374454i
$155$	19.8129	+	5.47855i	1.59141	+	0.440048i
$156$		0			0
$157$	−9.20058			−0.734286			−0.367143	−	0.930164i	$-0.619664\pi$
$157$	−9.20058			−0.734286			−0.367143	+	0.930164i	$0.619664\pi$
$158$	2.29241	+	1.66553i	0.182374	+	0.132503i
$159$		0			0
$160$	−5.95041	+	2.22988i	−0.470421	+	0.176287i
$161$	0.618538	+	1.90366i	0.0487476	+	0.150030i
$162$		0			0
$163$	−1.41553	+	4.35656i	−0.110873	+	0.341232i	−0.991064	−	0.133388i	$-0.957414\pi$
$163$	−1.41553	+	4.35656i	−0.110873	+	0.341232i	0.880191	+	0.474620i	$0.157414\pi$
$164$	5.21075	+	16.0370i	0.406891	+	1.25228i
$165$		0			0
$166$	−0.215970	+	0.664687i	−0.0167625	+	0.0515897i
$167$	0.115310	+	0.0837776i	0.00892296	+	0.00648291i	0.592238	−	0.805763i	$-0.298245\pi$
$167$	0.115310	+	0.0837776i	0.00892296	+	0.00648291i	−0.583315	+	0.812246i	$0.698245\pi$
$168$		0			0
$169$	−7.21176	−	5.23965i	−0.554751	−	0.403050i
$170$	−0.142959	−	3.21869i	−0.0109645	−	0.246862i
$171$		0			0
$172$	−6.08819	+	4.42333i	−0.464220	+	0.337275i
$173$	−7.60885	−	23.4176i	−0.578490	−	1.78041i	−0.623974	−	0.781445i	$-0.714483\pi$
$173$	−7.60885	−	23.4176i	−0.578490	−	1.78041i	0.0454831	−	0.998965i	$-0.485517\pi$
$174$		0			0
$175$	−4.69854	+	4.09682i	−0.355176	+	0.309690i
$176$	−9.34955			−0.704749
$177$		0			0
$178$	0.275647	−	0.200269i	0.0206606	−	0.0150108i
$179$	−19.5420	+	14.1981i	−1.46064	+	1.06122i	−0.477446	+	0.878661i	$0.658437\pi$
$179$	−19.5420	+	14.1981i	−1.46064	+	1.06122i	−0.983195	+	0.182557i	$0.941563\pi$
$180$		0			0
$181$	−1.59218	−	1.15679i	−0.118346	−	0.0859834i	0.527038	−	0.849842i	$-0.323303\pi$
$181$	−1.59218	−	1.15679i	−0.118346	−	0.0859834i	−0.645384	+	0.763858i	$0.723303\pi$
$182$	−1.44019			−0.106754
$183$		0			0
$184$	−0.482231	+	1.48415i	−0.0355505	+	0.109413i
$185$	0.126779	+	2.85440i	0.00932098	+	0.209859i
$186$		0			0
$187$	4.63677	−	14.2705i	0.339074	−	1.04356i
$188$	−1.92320	+	5.91901i	−0.140264	+	0.431689i
$189$		0			0
$190$	0.102059	+	2.29783i	0.00740412	+	0.166702i
$191$	2.40061	−	7.38832i	0.173702	−	0.534600i	−0.825870	−	0.563861i	$-0.809315\pi$
$191$	2.40061	−	7.38832i	0.173702	−	0.534600i	0.999572	+	0.0292607i	$0.00931531\pi$
$192$		0			0
$193$	14.3458			1.03264			0.516318	−	0.856397i	$-0.327302\pi$
$193$	14.3458			1.03264			0.516318	+	0.856397i	$0.327302\pi$
$194$	0.00609039	+	0.00442493i	0.000437265	+	0.000317691i
$195$		0			0
$196$	−8.54290	+	6.20678i	−0.610207	+	0.443341i
$197$	0.132307	−	0.0961264i	0.00942645	−	0.00684872i	−0.583062	−	0.812428i	$-0.698146\pi$
$197$	0.132307	−	0.0961264i	0.00942645	−	0.00684872i	0.592489	+	0.805579i	$0.298146\pi$
$198$		0			0
$199$	4.96974			0.352295			0.176148	−	0.984364i	$-0.443636\pi$
$199$	4.96974			0.352295			0.176148	+	0.984364i	$0.443636\pi$
$200$	−4.84092	+	0.430872i	−0.342304	+	0.0304673i
$201$		0			0
$202$	−0.856375	−	2.63565i	−0.0602543	−	0.185444i
$203$	3.24355	−	2.35658i	0.227652	−	0.165399i
$204$		0			0
$205$	0.862792	+	19.4255i	0.0602600	+	1.35674i
$206$	−0.143931	−	0.104572i	−0.0100282	−	0.00728590i
$207$		0			0
$208$	13.7793	+	10.0112i	0.955423	+	0.694155i
$209$	−3.31020	+	10.1877i	−0.228971	+	0.704701i
$210$		0			0
$211$	1.01784	+	3.13260i	0.0700713	+	0.215657i	0.979960	−	0.199196i	$-0.0638330\pi$
$211$	1.01784	+	3.13260i	0.0700713	+	0.215657i	−0.909888	+	0.414853i	$0.863833\pi$
$212$	−7.99015	+	24.5911i	−0.548766	+	1.68893i
$213$		0			0
$214$	0.161402	+	0.496745i	0.0110332	+	0.0339568i
$215$	−8.12602	+	3.04517i	−0.554190	+	0.207679i
$216$		0			0
$217$	−9.27263	−	6.73696i	−0.629467	−	0.457335i
$218$	−0.551465			−0.0373500
$219$		0			0
$220$	−10.7392	−	2.96954i	−0.724038	−	0.200207i
$221$	−22.1141	+	16.0669i	−1.48756	+	1.08077i
$222$		0			0
$223$	−4.87419	−	15.0012i	−0.326400	−	1.00456i	−0.970805	−	0.239872i	$-0.922895\pi$
$223$	−4.87419	−	15.0012i	−0.326400	−	1.00456i	0.644404	−	0.764685i	$-0.277105\pi$
$224$	3.54307			0.236731
$225$		0			0
$226$	−0.777142			−0.0516947
$227$	−4.18427	−	12.8779i	−0.277720	−	0.854734i	−0.988487	−	0.151307i	$-0.951652\pi$
$227$	−4.18427	−	12.8779i	−0.277720	−	0.854734i	0.710767	−	0.703428i	$-0.248348\pi$
$228$		0			0
$229$	11.9596	−	8.68915i	0.790312	−	0.574195i	−0.117744	−	0.993044i	$-0.537566\pi$
$229$	11.9596	−	8.68915i	0.790312	−	0.574195i	0.908056	+	0.418849i	$0.137566\pi$
$230$	−0.488376	+	0.739064i	−0.0322026	+	0.0487325i
$231$		0			0
$232$	3.12573			0.205214
$233$	0.419864	+	0.305049i	0.0275062	+	0.0199844i	0.601453	−	0.798908i	$-0.294589\pi$
$233$	0.419864	+	0.305049i	0.0275062	+	0.0199844i	−0.573947	+	0.818892i	$0.694589\pi$
$234$		0			0
$235$	−3.95659	+	5.98754i	−0.258099	+	0.390584i
$236$	−3.83067	−	11.7896i	−0.249356	−	0.767438i
$237$		0			0
$238$	−0.555120	+	1.70848i	−0.0359831	+	0.110745i
$239$	−2.54331	−	7.82750i	−0.164513	−	0.506319i	0.834487	−	0.551027i	$-0.185764\pi$
$239$	−2.54331	−	7.82750i	−0.164513	−	0.506319i	−0.999000	+	0.0447086i	$0.985764\pi$
$240$		0			0
$241$	−0.395906	+	1.21847i	−0.0255025	+	0.0784888i	−0.962998	−	0.269509i	$-0.913138\pi$
$241$	−0.395906	+	1.21847i	−0.0255025	+	0.0784888i	0.937495	+	0.347998i	$0.113138\pi$
$242$	−0.877700	−	0.637686i	−0.0564207	−	0.0409920i
$243$		0			0
$244$	6.00356	+	4.36184i	0.384339	+	0.279238i
$245$	−11.4024	+	4.27296i	−0.728471	+	0.272990i
$246$		0			0
$247$	15.7873	−	11.4701i	1.00452	−	0.729828i
$248$	−2.76132	−	8.49846i	−0.175344	−	0.539653i
$249$		0			0
$250$	−2.71378	−	0.496631i	−0.171635	−	0.0314097i
$251$	−4.63494			−0.292555			−0.146277	−	0.989244i	$-0.546729\pi$
$251$	−4.63494			−0.292555			−0.146277	+	0.989244i	$0.546729\pi$
$252$		0			0
$253$	−3.33767	+	2.42496i	−0.209837	+	0.152456i
$254$	−3.12630	+	2.27139i	−0.196161	+	0.142519i
$255$		0			0
$256$	−9.18081	−	6.67025i	−0.573801	−	0.416891i
$257$	18.3001			1.14153			0.570766	−	0.821113i	$-0.306647\pi$
$257$	18.3001			1.14153			0.570766	+	0.821113i	$0.306647\pi$
$258$		0			0
$259$	0.492291	−	1.51512i	0.0305895	−	0.0941448i
$260$	12.6477	+	15.8758i	0.784376	+	0.984573i
$261$		0			0
$262$	−1.14047	+	3.51000i	−0.0704583	+	0.216848i
$263$	−5.15027	+	15.8509i	−0.317579	+	0.977409i	0.657100	+	0.753803i	$0.271783\pi$
$263$	−5.15027	+	15.8509i	−0.317579	+	0.977409i	−0.974680	+	0.223606i	$0.928217\pi$
$264$		0			0
$265$	−16.4380	+	24.8758i	−1.00978	+	1.52811i
$266$	0.396301	−	1.21969i	0.0242988	−	0.0747839i
$267$		0			0
$268$	19.6312			1.19917
$269$	2.12942	+	1.54712i	0.129833	+	0.0943294i	0.650807	−	0.759244i	$-0.274431\pi$
$269$	2.12942	+	1.54712i	0.129833	+	0.0943294i	−0.520973	+	0.853573i	$0.674431\pi$
$270$		0			0
$271$	−3.69192	+	2.68233i	−0.224268	+	0.162940i	−0.694246	−	0.719738i	$-0.744262\pi$
$271$	−3.69192	+	2.68233i	−0.224268	+	0.162940i	0.469978	+	0.882678i	$0.344262\pi$
$272$	17.1875	−	12.4875i	1.04215	−	0.757164i
$273$		0			0
$274$	−2.58963			−0.156445
$275$	−11.0233	−	6.60090i	−0.664731	−	0.398049i
$276$		0			0
$277$	0.389132	+	1.19762i	0.0233807	+	0.0719583i	0.962066	−	0.272817i	$-0.0879552\pi$
$277$	0.389132	+	1.19762i	0.0233807	+	0.0719583i	−0.938685	+	0.344775i	$0.887955\pi$
$278$	2.48557	−	1.80587i	0.149075	−	0.108309i
$279$		0			0
$280$	2.61180	+	0.722198i	0.156085	+	0.0431596i
$281$	10.8543	+	7.88611i	0.647513	+	0.470446i	0.862423	−	0.506188i	$-0.168946\pi$
$281$	10.8543	+	7.88611i	0.647513	+	0.470446i	−0.214910	+	0.976634i	$0.568946\pi$
$282$		0			0
$283$	−19.4884	−	14.1591i	−1.15846	−	0.841674i	−0.168882	−	0.985636i	$-0.554016\pi$
$283$	−19.4884	−	14.1591i	−1.15846	−	0.841674i	−0.989583	+	0.143962i	$0.954016\pi$
$284$	8.31661	−	25.5959i	0.493500	−	1.51884i
$285$		0			0
$286$	−0.917281	−	2.82310i	−0.0542400	−	0.166934i
$287$	3.35028	−	10.3111i	0.197761	−	0.608644i
$288$		0			0
$289$	5.28283	+	16.2589i	0.310754	+	0.956404i
$290$	1.71017	+	0.472886i	0.100425	+	0.0277688i
$291$		0			0
$292$	−17.8548	−	12.9723i	−1.04487	−	0.759145i
$293$	32.1727			1.87955			0.939776	−	0.341792i	$-0.111034\pi$
$293$	32.1727			1.87955			0.939776	+	0.341792i	$0.111034\pi$
$294$		0			0
$295$	−0.634279	−	14.2806i	−0.0369292	−	0.831450i
$296$	1.00481	−	0.730041i	0.0584037	−	0.0424328i
$297$		0			0
$298$	−1.30148	−	4.00554i	−0.0753926	−	0.232035i
$299$	7.51561			0.434639
$300$		0			0
$301$	4.83849			0.278886
$302$	0.120110	+	0.369661i	0.00691156	+	0.0212716i
$303$		0			0
$304$	−12.2702	+	8.91482i	−0.703744	+	0.511300i
$305$	5.33205	+	6.69296i	0.305312	+	0.383237i
$306$		0			0
$307$	20.2962			1.15837			0.579183	−	0.815198i	$-0.303372\pi$
$307$	20.2962			1.15837			0.579183	+	0.815198i	$0.303372\pi$
$308$	5.02605	+	3.65164i	0.286386	+	0.208071i
$309$		0			0
$310$	−0.225074	−	5.06749i	−0.0127834	−	0.287814i
$311$	5.78554	+	17.8061i	0.328068	+	1.00969i	0.970037	+	0.242959i	$0.0781180\pi$
$311$	5.78554	+	17.8061i	0.328068	+	1.00969i	−0.641969	+	0.766731i	$0.721882\pi$
$312$		0			0
$313$	7.68955	−	23.6660i	0.434639	−	1.33768i	−0.458817	−	0.888531i	$-0.651726\pi$
$313$	7.68955	−	23.6660i	0.434639	−	1.33768i	0.893456	−	0.449151i	$-0.148274\pi$
$314$	0.701569	+	2.15921i	0.0395919	+	0.121851i
$315$		0			0
$316$	−6.88092	+	21.1773i	−0.387082	+	1.19132i
$317$	−20.3775	−	14.8052i	−1.14452	−	0.831540i	−0.156775	−	0.987634i	$-0.550110\pi$
$317$	−20.3775	−	14.8052i	−1.14452	−	0.831540i	−0.987742	+	0.156094i	$0.950110\pi$
$318$		0			0
$319$	6.68532	+	4.85717i	0.374306	+	0.271949i
$320$	−9.16165	−	11.5000i	−0.512152	−	0.642869i
$321$		0			0
$322$	0.399590	−	0.290319i	0.0222683	−	0.0161788i
$323$	−7.52174	−	23.1496i	−0.418521	−	1.28808i
$324$		0			0
$325$	9.17801	+	21.5318i	0.509104	+	1.19437i
$326$	1.13034			0.0626039
$327$		0			0
$328$	6.83824	−	4.96827i	0.377579	−	0.274327i
$329$	3.23728	−	2.35202i	0.178477	−	0.129671i
$330$		0			0
$331$	−24.6097	−	17.8800i	−1.35267	−	0.982773i	−0.998874	−	0.0474508i	$-0.984890\pi$
$331$	−24.6097	−	17.8800i	−1.35267	−	0.982773i	−0.353797	−	0.935322i	$-0.615110\pi$
$332$	−5.49212			−0.301419
$333$		0			0
$334$	0.0108684	−	0.0334494i	0.000594691	−	0.00183027i
$335$	21.8188	+	6.03319i	1.19209	+	0.329629i
$336$		0			0
$337$	−1.41361	+	4.35066i	−0.0770045	+	0.236995i	−0.982148	−	0.188111i	$-0.939763\pi$
$337$	−1.41361	+	4.35066i	−0.0770045	+	0.236995i	0.905143	+	0.425107i	$0.139763\pi$
$338$	−0.679734	+	2.09200i	−0.0369726	+	0.113790i
$339$		0			0
$340$	23.7084	−	8.88455i	1.28577	−	0.481832i
$341$	7.30011	−	22.4674i	0.395323	−	1.21668i
$342$		0			0
$343$	15.5167			0.837821
$344$	3.05180	+	2.21726i	0.164542	+	0.119547i
$345$		0			0
$346$	−4.91550	+	3.57132i	−0.264259	+	0.191995i
$347$	−13.6038	+	9.88377i	−0.730293	+	0.530589i	−0.889656	−	0.456631i	$-0.849056\pi$
$347$	−13.6038	+	9.88377i	−0.730293	+	0.530589i	0.159363	+	0.987220i	$0.449056\pi$
$348$		0			0
$349$	0.373581			0.0199973			0.00999866	−	0.999950i	$-0.496817\pi$
$349$	0.373581			0.0199973			0.00999866	+	0.999950i	$0.496817\pi$
$350$	1.31972	+	0.790268i	0.0705422	+	0.0422416i
$351$		0			0
$352$	2.25665	+	6.94524i	0.120280	+	0.370183i
$353$	−19.3909	+	14.0883i	−1.03208	+	0.749847i	−0.968723	−	0.248144i	$-0.920179\pi$
$353$	−19.3909	+	14.0883i	−1.03208	+	0.749847i	−0.0633526	+	0.997991i	$0.520179\pi$
$354$		0			0
$355$	17.1097	−	25.8922i	0.908087	−	1.37422i
$356$	2.16612	+	1.57378i	0.114804	+	0.0834101i
$357$		0			0
$358$	4.82218	+	3.50352i	0.254860	+	0.185167i
$359$	1.46789	−	4.51771i	0.0774724	−	0.238435i	−0.904819	−	0.425797i	$-0.859994\pi$
$359$	1.46789	−	4.51771i	0.0774724	−	0.238435i	0.982291	+	0.187362i	$0.0599937\pi$
$360$		0			0
$361$	−0.501540	−	1.54358i	−0.0263969	−	0.0812412i
$362$	−0.150069	+	0.461865i	−0.00788744	+	0.0242751i
$363$		0			0
$364$	−3.49728	−	10.7635i	−0.183307	−	0.564162i
$365$	−15.8577	−	19.9051i	−0.830030	−	1.04188i
$366$		0			0
$367$	14.0526	+	10.2098i	0.733540	+	0.532948i	0.890681	−	0.454628i	$-0.150228\pi$
$367$	14.0526	+	10.2098i	0.733540	+	0.532948i	−0.157141	+	0.987576i	$0.550228\pi$
$368$	−5.84128			−0.304498
$369$		0			0
$370$	0.660208	−	0.247408i	0.0343226	−	0.0128621i
$371$	13.4496	−	9.77172i	0.698270	−	0.507323i
$372$		0			0
$373$	0.651645	+	2.00556i	0.0337409	+	0.103844i	0.966509	−	0.256634i	$-0.0826136\pi$
$373$	0.651645	+	2.00556i	0.0337409	+	0.103844i	−0.932768	+	0.360478i	$0.882614\pi$
$374$	−3.70260			−0.191457
$375$		0			0
$376$	3.11969			0.160886
$377$	−4.65185	−	14.3169i	−0.239582	−	0.737359i
$378$		0			0
$379$	−10.0391	+	7.29380i	−0.515671	+	0.374657i	−0.814971	−	0.579502i	$-0.803247\pi$
$379$	−10.0391	+	7.29380i	−0.515671	+	0.374657i	0.299299	+	0.954159i	$0.403247\pi$
$380$	−16.9254	+	6.34269i	−0.868256	+	0.325373i
$381$		0			0
$382$	−1.91696			−0.0980801
$383$	26.9448	+	19.5766i	1.37682	+	1.00032i	0.997170	+	0.0751836i	$0.0239543\pi$
$383$	26.9448	+	19.5766i	1.37682	+	1.00032i	0.379646	+	0.925132i	$0.376046\pi$
$384$		0			0
$385$	4.46388	+	5.60320i	0.227500	+	0.285565i
$386$	−1.09391	−	3.36671i	−0.0556785	−	0.171361i
$387$		0			0
$388$	−0.0182810	+	0.0562631i	−0.000928076	+	0.00285633i
$389$	5.24639	+	16.1467i	0.266002	+	0.818671i	0.991461	+	0.130405i	$0.0416278\pi$
$389$	5.24639	+	16.1467i	0.266002	+	0.818671i	−0.725459	+	0.688266i	$0.758372\pi$
$390$		0			0
$391$	2.89690	−	8.91573i	0.146502	−	0.450888i
$392$	4.28227	+	3.11125i	0.216287	+	0.157142i
$393$		0			0
$394$	−0.0326478	−	0.0237200i	−0.00164477	−	0.00119500i
$395$	−14.1560	+	21.4225i	−0.712268	+	1.07788i
$396$		0			0
$397$	0.701070	−	0.509357i	0.0351857	−	0.0255639i	−0.570053	−	0.821608i	$-0.693078\pi$
$397$	0.701070	−	0.509357i	0.0351857	−	0.0255639i	0.605239	+	0.796044i	$0.293078\pi$
$398$	−0.378956	−	1.16631i	−0.0189953	−	0.0584617i
$399$		0			0
$400$	−7.13333	−	16.7350i	−0.356666	−	0.836748i
$401$	−9.68680			−0.483736			−0.241868	−	0.970309i	$-0.577760\pi$
$401$	−9.68680			−0.483736			−0.241868	+	0.970309i	$0.577760\pi$
$402$		0			0
$403$	−34.8164	+	25.2956i	−1.73433	+	1.26006i
$404$	17.6185	−	12.8006i	0.876553	−	0.636853i
$405$		0			0
$406$	−0.800374	−	0.581506i	−0.0397219	−	0.0288597i
$407$	3.28353			0.162759
$408$		0			0
$409$	0.469043	−	1.44357i	0.0231927	−	0.0713797i	−0.938790	−	0.344489i	$-0.888052\pi$
$409$	0.469043	−	1.44357i	0.0231927	−	0.0713797i	0.961983	+	0.273109i	$0.0880521\pi$
$410$	4.49302	−	1.68373i	0.221895	−	0.0831535i
$411$		0			0
$412$	0.432026	−	1.32964i	0.0212844	−	0.0655066i
$413$	−2.46295	+	7.58017i	−0.121194	+	0.372996i
$414$		0			0
$415$	−6.10413	−	1.68788i	−0.299640	−	0.0828546i
$416$	4.11095	−	12.6522i	0.201556	−	0.620325i
$417$		0			0
$418$	2.64329			0.129287
$419$	−24.7252	−	17.9639i	−1.20790	−	0.877594i	−0.212866	−	0.977081i	$-0.568280\pi$
$419$	−24.7252	−	17.9639i	−1.20790	−	0.877594i	−0.995039	+	0.0994875i	$0.968280\pi$
$420$		0			0
$421$	5.64016	−	4.09782i	0.274885	−	0.199715i	−0.441799	−	0.897114i	$-0.645659\pi$
$421$	5.64016	−	4.09782i	0.274885	−	0.199715i	0.716683	+	0.697399i	$0.245659\pi$
$422$	0.657551	−	0.477739i	0.0320091	−	0.0232560i
$423$		0			0
$424$	12.9611			0.629445
$425$	29.0807	−	2.58837i	1.41062	−	0.125554i
$426$		0			0
$427$	−1.47439	−	4.53772i	−0.0713510	−	0.219596i
$428$	−3.32058	+	2.41255i	−0.160506	+	0.116615i
$429$		0			0
$430$	1.33428	+	1.67483i	0.0643446	+	0.0807673i
$431$	8.85650	+	6.43463i	0.426603	+	0.309945i	0.780289	−	0.625419i	$-0.215072\pi$
$431$	8.85650	+	6.43463i	0.426603	+	0.309945i	−0.353686	+	0.935364i	$0.615072\pi$
$432$		0			0
$433$	−8.44561	−	6.13609i	−0.405870	−	0.294882i	0.366058	−	0.930592i	$-0.380707\pi$
$433$	−8.44561	−	6.13609i	−0.405870	−	0.294882i	−0.771928	+	0.635710i	$0.780707\pi$
$434$	−0.873978	+	2.68983i	−0.0419523	+	0.129116i
$435$		0			0
$436$	−1.33915	−	4.12149i	−0.0641338	−	0.197384i
$437$	−2.06810	+	6.36495i	−0.0989305	+	0.304477i
$438$		0			0
$439$	4.76917	+	14.6780i	0.227620	+	0.700543i	0.998015	+	0.0629758i	$0.0200591\pi$
$439$	4.76917	+	14.6780i	0.227620	+	0.700543i	−0.770395	+	0.637567i	$0.779941\pi$
$440$	0.247825	+	5.57972i	0.0118146	+	0.266003i
$441$		0			0
$442$	5.45686	+	3.96464i	0.259556	+	0.188579i
$443$	−18.9105			−0.898463			−0.449231	−	0.893415i	$-0.648302\pi$
$443$	−18.9105			−0.898463			−0.449231	+	0.893415i	$0.648302\pi$
$444$		0			0
$445$	1.92383	+	2.41486i	0.0911985	+	0.114475i
$446$	−3.14884	+	2.28777i	−0.149102	+	0.108329i
$447$		0			0
$448$	2.53334	+	7.79681i	0.119689	+	0.368365i
$449$	11.4152			0.538714			0.269357	−	0.963040i	$-0.413189\pi$
$449$	11.4152			0.538714			0.269357	+	0.963040i	$0.413189\pi$
$450$		0			0
$451$	22.3460			1.05223
$452$	−1.88717	−	5.80813i	−0.0887652	−	0.273191i
$453$		0			0
$454$	−2.70314	+	1.96395i	−0.126865	+	0.0921725i
$455$	−0.579076	−	13.0377i	−0.0271475	−	0.611219i
$456$		0			0
$457$	−33.9739			−1.58923			−0.794616	−	0.607112i	$-0.792328\pi$
$457$	−33.9739			−1.58923			−0.794616	+	0.607112i	$0.792328\pi$
$458$	−2.95114	−	2.14413i	−0.137898	−	0.100188i
$459$		0			0
$460$	−6.70950	−	1.85527i	−0.312832	−	0.0865023i
$461$	7.62985	+	23.4823i	0.355358	+	1.09368i	0.955802	+	0.294012i	$0.0949905\pi$
$461$	7.62985	+	23.4823i	0.355358	+	1.09368i	−0.600444	+	0.799667i	$0.705009\pi$
$462$		0			0
$463$	−4.21237	+	12.9643i	−0.195765	+	0.602504i	0.804202	+	0.594357i	$0.202593\pi$
$463$	−4.21237	+	12.9643i	−0.195765	+	0.602504i	−0.999967	+	0.00814689i	$0.997407\pi$
$464$	3.61551	+	11.1274i	0.167846	+	0.516576i
$465$		0			0
$466$	0.0395737	−	0.121795i	0.00183321	−	0.00564205i
$467$	7.66232	+	5.56700i	0.354570	+	0.257610i	0.750784	−	0.660548i	$-0.229676\pi$
$467$	7.66232	+	5.56700i	0.354570	+	0.257610i	−0.396214	+	0.918158i	$0.629676\pi$
$468$		0			0
$469$	−10.2114	−	7.41900i	−0.471518	−	0.342578i
$470$	1.70687	+	0.471972i	0.0787319	+	0.0217705i
$471$		0			0
$472$	−5.02712	+	3.65241i	−0.231392	+	0.168116i
$473$	3.08173	+	9.48459i	0.141698	+	0.436102i
$474$		0			0
$475$	−20.7608	+	1.84784i	−0.952570	+	0.0847847i
$476$	−14.1167			−0.647039
$477$		0			0
$478$	−1.64304	+	1.19374i	−0.0751508	+	0.0546002i
$479$	−20.8149	+	15.1229i	−0.951055	+	0.690982i	−0.951056	−	0.309018i	$-0.900000\pi$
$479$	−20.8149	+	15.1229i	−0.951055	+	0.690982i	1.08775e−6		1.00000i	$0.500000\pi$
$480$		0			0
$481$	−4.83925	−	3.51592i	−0.220651	−	0.160312i
$482$	0.316142			0.0143999
$483$		0			0
$484$	2.63451	−	8.10820i	0.119751	−	0.368554i
$485$	−0.0376093	+	0.0569145i	−0.00170775	+	0.00258435i
$486$		0			0
$487$	−8.77751	+	27.0144i	−0.397747	+	1.22414i	0.529055	+	0.848588i	$0.322547\pi$
$487$	−8.77751	+	27.0144i	−0.397747	+	1.22414i	−0.926802	+	0.375551i	$0.877453\pi$
$488$	1.14948	−	3.53774i	0.0520346	−	0.160146i
$489$		0			0
$490$	1.87225	+	2.35010i	0.0845795	+	0.106167i
$491$	1.88593	−	5.80429i	0.0851107	−	0.261944i	−0.899440	−	0.437045i	$-0.856025\pi$
$491$	1.88593	−	5.80429i	0.0851107	−	0.261944i	0.984551	+	0.175101i	$0.0560251\pi$
$492$		0			0
$493$	−18.7771			−0.845679
$494$	−3.89566	−	2.83036i	−0.175274	−	0.127344i
$495$		0			0
$496$	27.0600	−	19.6602i	1.21503	−	0.882770i
$497$	−13.9992	+	10.1710i	−0.627948	+	0.456231i
$498$		0			0
$499$	−20.3163			−0.909481			−0.454740	−	0.890624i	$-0.650268\pi$
$499$	−20.3163			−0.909481			−0.454740	+	0.890624i	$0.650268\pi$
$500$	−2.87834	−	21.4880i	−0.128723	−	0.960972i
$501$		0			0
$502$	0.353426	+	1.08773i	0.0157742	+	0.0485480i
$503$	11.8332	−	8.59734i	0.527617	−	0.383336i	−0.291848	−	0.956465i	$-0.594270\pi$
$503$	11.8332	−	8.59734i	0.527617	−	0.383336i	0.819466	+	0.573128i	$0.194270\pi$
$504$		0			0
$505$	23.5158	−	8.81237i	1.04644	−	0.392145i
$506$	0.823600	+	0.598380i	0.0366135	+	0.0266012i
$507$		0			0
$508$	−24.5674	−	17.8493i	−1.09000	−	0.791934i
$509$	1.33058	−	4.09510i	0.0589768	−	0.181512i	−0.917228	−	0.398363i	$-0.869578\pi$
$509$	1.33058	−	4.09510i	0.0589768	−	0.181512i	0.976205	+	0.216851i	$0.0695785\pi$
$510$		0			0
$511$	4.38490	+	13.4953i	0.193977	+	0.596999i
$512$	−5.38081	+	16.5604i	−0.237800	+	0.731874i
$513$		0			0
$514$	−1.39543	−	4.29471i	−0.0615500	−	0.189431i
$515$	0.888802	−	1.34503i	0.0391653	−	0.0592692i
$516$		0			0
$517$	6.67241	+	4.84779i	0.293452	+	0.213205i
$518$	−0.393109			−0.0172722
$519$		0			0
$520$	5.60937	−	8.48871i	0.245987	−	0.372255i
$521$	−32.0705	+	23.3006i	−1.40503	+	1.02082i	−0.411011	+	0.911630i	$0.634824\pi$
$521$	−32.0705	+	23.3006i	−1.40503	+	1.02082i	−0.994021	+	0.109186i	$0.965176\pi$
$522$		0			0
$523$	11.2134	+	34.5114i	0.490329	+	1.50908i	0.824111	+	0.566428i	$0.191675\pi$
$523$	11.2134	+	34.5114i	0.490329	+	1.50908i	−0.333782	+	0.942650i	$0.608325\pi$
$524$	−29.0021			−1.26696
$525$		0			0
$526$	4.11264			0.179320
$527$	16.5880	+	51.0526i	0.722585	+	2.22389i
$528$		0			0
$529$	16.5221	−	12.0040i	0.718353	−	0.521914i
$530$	7.09135	+	1.96086i	0.308029	+	0.0851742i
$531$		0			0
$532$	10.0779			0.436934
$533$	−32.9334	−	23.9275i	−1.42650	−	1.03642i
$534$		0			0
$535$	−4.43205	+	1.66088i	−0.191614	+	0.0718061i
$536$	−3.04087	−	9.35883i	−0.131346	−	0.404240i
$537$		0			0
$538$	0.200706	−	0.617709i	0.00865304	−	0.0266313i
$539$	4.32426	+	13.3087i	0.186259	+	0.573246i
$540$		0			0
$541$	−11.9294	+	36.7150i	−0.512886	+	1.57850i	0.274211	+	0.961670i	$0.411583\pi$
$541$	−11.9294	+	36.7150i	−0.512886	+	1.57850i	−0.787096	+	0.616830i	$0.788417\pi$
$542$	0.911014	+	0.661890i	0.0391314	+	0.0284306i
$543$		0			0
$544$	−13.4247	−	9.75359i	−0.575578	−	0.418182i
$545$	−0.221736	−	4.99232i	−0.00949812	−	0.213848i
$546$		0			0
$547$	−8.38303	+	6.09063i	−0.358433	+	0.260416i	−0.752398	−	0.658709i	$-0.771103\pi$
$547$	−8.38303	+	6.09063i	−0.358433	+	0.260416i	0.393965	+	0.919125i	$0.371103\pi$
$548$	−6.28853	−	19.3541i	−0.268633	−	0.826766i
$549$		0			0
$550$	−0.708553	+	3.09031i	−0.0302128	+	0.131771i
$551$	13.4050			0.571073
$552$		0			0
$553$	11.5825	−	8.41517i	0.492538	−	0.357850i
$554$	0.251388	−	0.182644i	0.0106805	−	0.00775981i
$555$		0			0
$556$	19.5324	+	14.1911i	0.828359	+	0.601838i
$557$	−12.6830			−0.537398			−0.268699	−	0.963224i	$-0.586594\pi$
$557$	−12.6830			−0.537398			−0.268699	+	0.963224i	$0.586594\pi$
$558$		0			0
$559$	5.61401	−	17.2781i	0.237447	−	0.730788i
$560$	0.450069	+	10.1332i	0.0190189	+	0.428205i
$561$		0			0
$562$	1.02306	−	3.14864i	0.0431550	−	0.132817i
$563$	−4.04480	+	12.4486i	−0.170468	+	0.524646i	−0.999398	−	0.0347068i	$-0.988950\pi$
$563$	−4.04480	+	12.4486i	−0.170468	+	0.524646i	0.828930	+	0.559353i	$0.188950\pi$
$564$		0			0
$565$	−0.312477	−	7.03533i	−0.0131460	−	0.295978i
$566$	−1.83685	+	5.65324i	−0.0772086	+	0.237624i
$567$		0			0
$568$	−13.4906			−0.566055
$569$	−2.09376	−	1.52120i	−0.0877748	−	0.0637721i	0.543032	−	0.839712i	$-0.317276\pi$
$569$	−2.09376	−	1.52120i	−0.0877748	−	0.0637721i	−0.630807	+	0.775940i	$0.717276\pi$
$570$		0			0
$571$	8.55571	−	6.21609i	0.358045	−	0.260135i	−0.394191	−	0.919029i	$-0.628975\pi$
$571$	8.55571	−	6.21609i	0.358045	−	0.260135i	0.752236	+	0.658893i	$0.228975\pi$
$572$	18.8715	−	13.7110i	0.789059	−	0.573285i
$573$		0			0
$574$	−2.67529			−0.111665
$575$	−6.88699	−	4.12402i	−0.287207	−	0.171983i
$576$		0			0
$577$	−0.00441597	−	0.0135910i	−0.000183839	−	0.000565800i	0.950965	−	0.309300i	$-0.100095\pi$
$577$	−0.00441597	−	0.0135910i	−0.000183839	−	0.000565800i	−0.951148	+	0.308734i	$0.900095\pi$
$578$	3.41283	−	2.47957i	0.141955	−	0.103136i
$579$		0			0
$580$	0.618690	+	13.9296i	0.0256897	+	0.578397i
$581$	2.85679	+	2.07558i	0.118519	+	0.0861094i
$582$		0			0
$583$	27.7212	+	20.1406i	1.14809	+	0.834139i
$584$	−3.41860	+	10.5214i	−0.141463	+	0.435377i
$585$		0			0
$586$	−2.45326	−	7.55035i	−0.101343	−	0.311902i
$587$	6.99581	−	21.5309i	0.288748	−	0.888675i	−0.696502	−	0.717555i	$-0.745261\pi$
$587$	6.99581	−	21.5309i	0.288748	−	0.888675i	0.985250	−	0.171120i	$-0.0547387\pi$
$588$		0			0
$589$	−11.8422	−	36.4465i	−0.487949	−	1.50175i
$590$	−3.30304	+	1.23779i	−0.135984	+	0.0509590i
$591$		0			0
$592$	3.76116	+	2.73264i	0.154583	+	0.112311i
$593$	−12.7423			−0.523264			−0.261632	−	0.965168i	$-0.584261\pi$
$593$	−12.7423			−0.523264			−0.261632	+	0.965168i	$0.584261\pi$
$594$		0			0
$595$	−15.6898	−	4.33845i	−0.643219	−	0.177859i
$596$	26.7758	−	19.4537i	1.09678	−	0.796856i
$597$		0			0
$598$	−0.573086	−	1.76378i	−0.0234352	−	0.0721262i
$599$	6.83599			0.279311			0.139656	−	0.990200i	$-0.455400\pi$
$599$	6.83599			0.279311			0.139656	+	0.990200i	$0.455400\pi$
$600$		0			0
$601$	31.8422			1.29887			0.649435	−	0.760417i	$-0.275005\pi$
$601$	31.8422			1.29887			0.649435	+	0.760417i	$0.275005\pi$
$602$	−0.368948	−	1.13551i	−0.0150372	−	0.0462798i
$603$		0			0
$604$	−2.47107	+	1.79534i	−0.100546	+	0.0730511i
$605$	5.41995	−	8.20207i	0.220352	−	0.333462i
$606$		0			0
$607$	27.7763			1.12741			0.563703	−	0.825977i	$-0.309376\pi$
$607$	27.7763			1.12741			0.563703	+	0.825977i	$0.309376\pi$
$608$	9.58388	+	6.96310i	0.388678	+	0.282391i
$609$		0			0
$610$	1.16413	−	1.76169i	0.0471343	−	0.0713288i
$611$	−4.64286	−	14.2893i	−0.187830	−	0.578082i
$612$		0			0
$613$	−1.11769	+	3.43991i	−0.0451433	+	0.138937i	−0.971088	−	0.238723i	$-0.923271\pi$
$613$	−1.11769	+	3.43991i	−0.0451433	+	0.138937i	0.925944	+	0.377660i	$0.123271\pi$
$614$	−1.54764	−	4.76315i	−0.0624577	−	0.192225i
$615$		0			0
$616$	0.962321	−	2.96172i	0.0387730	−	0.119331i
$617$	36.1166	+	26.2402i	1.45400	+	1.05639i	0.984876	+	0.173259i	$0.0554297\pi$
$617$	36.1166	+	26.2402i	1.45400	+	1.05639i	0.469122	+	0.883133i	$0.344570\pi$
$618$		0			0
$619$	−16.5917	−	12.0546i	−0.666878	−	0.484515i	0.202101	−	0.979365i	$-0.435223\pi$
$619$	−16.5917	−	12.0546i	−0.666878	−	0.484515i	−0.868979	+	0.494850i	$0.835223\pi$
$620$	37.3264	−	13.9878i	1.49906	−	0.561763i
$621$		0			0
$622$	3.73760	−	2.71552i	0.149864	−	0.108883i
$623$	−0.531970	−	1.63724i	−0.0213129	−	0.0655945i
$624$		0			0
$625$	3.40475	−	24.7671i	0.136190	−	0.990683i
$626$	−6.14033			−0.245417
$627$		0			0
$628$	−14.4336	+	10.4866i	−0.575964	+	0.418463i
$629$	−6.03621	+	4.38556i	−0.240679	+	0.174864i
$630$		0			0
$631$	30.5288	+	22.1805i	1.21533	+	0.882991i	0.995704	−	0.0925923i	$-0.0295153\pi$
$631$	30.5288	+	22.1805i	1.21533	+	0.882991i	0.219629	+	0.975583i	$0.429515\pi$
$632$	11.1618			0.443991
$633$		0			0
$634$	−1.92066	+	5.91117i	−0.0762790	+	0.234763i
$635$	−21.8195	−	27.3885i	−0.865881	−	1.08688i
$636$		0			0
$637$	7.87754	−	24.2446i	0.312119	−	0.960605i
$638$	0.630115	−	1.93929i	0.0249465	−	0.0767774i
$639$		0			0
$640$	−9.00683	+	13.6301i	−0.356026	+	0.538778i
$641$	2.83865	−	8.73646i	0.112120	−	0.345070i	−0.879216	−	0.476424i	$-0.841933\pi$
$641$	2.83865	−	8.73646i	0.112120	−	0.345070i	0.991335	+	0.131355i	$0.0419327\pi$
$642$		0			0
$643$	3.42111			0.134915			0.0674577	−	0.997722i	$-0.478511\pi$
$643$	3.42111			0.134915			0.0674577	+	0.997722i	$0.478511\pi$
$644$	3.14010	+	2.28142i	0.123737	+	0.0899005i
$645$		0			0
$646$	−4.85922	+	3.53043i	−0.191184	+	0.138903i
$647$	2.64334	−	1.92050i	0.103920	−	0.0755027i	−0.534611	−	0.845098i	$-0.679542\pi$
$647$	2.64334	−	1.92050i	0.103920	−	0.0755027i	0.638532	+	0.769595i	$0.279542\pi$
$648$		0			0
$649$	−16.4276			−0.644840
$650$	4.35328	−	3.79577i	0.170750	−	0.148882i
$651$		0			0
$652$	2.74487	+	8.44785i	0.107498	+	0.330843i
$653$	10.2229	−	7.42740i	0.400054	−	0.290656i	−0.369509	−	0.929227i	$-0.620474\pi$
$653$	10.2229	−	7.42740i	0.400054	−	0.290656i	0.769563	+	0.638571i	$0.220474\pi$
$654$		0			0
$655$	−32.2339	−	8.91313i	−1.25948	−	0.348265i
$656$	25.5965	+	18.5969i	0.999374	+	0.726088i
$657$		0			0
$658$	−0.798829	−	0.580383i	−0.0311416	−	0.0226257i
$659$	2.82719	−	8.70118i	0.110131	−	0.338950i	−0.880769	−	0.473546i	$-0.842974\pi$
$659$	2.82719	−	8.70118i	0.110131	−	0.338950i	0.990901	+	0.134596i	$0.0429737\pi$
$660$		0			0
$661$	1.97487	+	6.07804i	0.0768137	+	0.236408i	0.982089	−	0.188417i	$-0.0603356\pi$
$661$	1.97487	+	6.07804i	0.0768137	+	0.236408i	−0.905275	+	0.424825i	$0.860336\pi$
$662$	−2.31955	+	7.13884i	−0.0901519	+	0.277459i
$663$		0			0
$664$	0.850729	+	2.61827i	0.0330147	+	0.101609i
$665$	11.2010	+	3.09722i	0.434355	+	0.120105i
$666$		0			0
$667$	4.17676	+	3.03459i	0.161725	+	0.117500i
$668$	0.276383			0.0106936
$669$		0			0
$670$	−0.247861	−	5.58052i	−0.00957569	−	0.215594i
$671$	7.95593	−	5.78032i	0.307135	−	0.223147i
$672$		0			0
$673$	−10.4158	−	32.0566i	−0.401500	−	1.23569i	−0.923782	−	0.382918i	$-0.874919\pi$
$673$	−10.4158	−	32.0566i	−0.401500	−	1.23569i	0.522282	−	0.852773i	$-0.325081\pi$
$674$	1.12881			0.0434802
$675$		0			0
$676$	−17.2857			−0.664833
$677$	−2.84401	−	8.75295i	−0.109304	−	0.336403i	0.881412	−	0.472347i	$-0.156593\pi$
$677$	−2.84401	−	8.75295i	−0.109304	−	0.336403i	−0.990716	+	0.135944i	$0.956593\pi$
$678$		0			0
$679$	0.0307719	−	0.0223571i	0.00118092	−	0.000857988i
$680$	−7.90798	−	9.92634i	−0.303257	−	0.380658i
$681$		0			0
$682$	−5.82935			−0.223217
$683$	22.0227	+	16.0005i	0.842677	+	0.612241i	0.923117	−	0.384519i	$-0.125633\pi$
$683$	22.0227	+	16.0005i	0.842677	+	0.612241i	−0.0804402	+	0.996759i	$0.525633\pi$
$684$		0			0
$685$	−1.04125	−	23.4434i	−0.0397841	−	0.895728i
$686$	−1.18319	−	3.64147i	−0.0451743	−	0.139032i
$687$		0			0
$688$	−4.36332	+	13.4289i	−0.166350	+	0.511972i
$689$	−19.2892	−	59.3662i	−0.734862	−	2.26167i
$690$		0			0
$691$	9.21607	−	28.3642i	0.350596	−	1.07902i	−0.607923	−	0.793996i	$-0.707997\pi$
$691$	9.21607	−	28.3642i	0.350596	−	1.07902i	0.958519	−	0.285028i	$-0.0920028\pi$
$692$	−38.6275	−	28.0645i	−1.46840	−	1.06685i
$693$		0			0
$694$	3.35687	+	2.43891i	0.127425	+	0.0925797i
$695$	17.3477	+	21.7753i	0.658034	+	0.825985i
$696$		0			0
$697$	−41.0792	+	29.8458i	−1.55599	+	1.13049i
$698$	−0.0284865	−	0.0876726i	−0.00107823	−	0.00331846i
$699$		0			0
$700$	−2.70147	+	11.7823i	−0.102106	+	0.445328i
$701$	19.1081			0.721704			0.360852	−	0.932623i	$-0.382486\pi$
$701$	19.1081			0.721704			0.360852	+	0.932623i	$0.382486\pi$
$702$		0			0
$703$	4.30925	−	3.13086i	0.162527	−	0.118082i
$704$	−13.6700	+	9.93187i	−0.515209	+	0.374322i
$705$		0			0
$706$	4.78489	+	3.47642i	0.180082	+	0.130837i
$707$	−14.0020			−0.526601
$708$		0			0
$709$	4.48525	−	13.8042i	0.168447	−	0.518427i	−0.830827	−	0.556531i	$-0.812132\pi$
$709$	4.48525	−	13.8042i	0.168447	−	0.518427i	0.999274	+	0.0381042i	$0.0121319\pi$
$710$	−7.38109	−	2.04097i	−0.277008	−	0.0765964i
$711$		0			0
$712$	0.414740	−	1.27644i	0.0155430	−	0.0478365i
$713$	4.56086	−	14.0369i	0.170806	−	0.525685i
$714$		0			0
$715$	25.1882	−	9.43911i	0.941986	−	0.353003i
$716$	−14.4743	+	44.5473i	−0.540930	+	1.66481i
$717$		0			0
$718$	−1.17215			−0.0437444
$719$	28.1139	+	20.4260i	1.04847	+	0.761760i	0.971921	−	0.235306i	$-0.0756091\pi$
$719$	28.1139	+	20.4260i	1.04847	+	0.761760i	0.0765512	+	0.997066i	$0.475609\pi$
$720$		0			0
$721$	−0.727219	+	0.528356i	−0.0270831	+	0.0196770i
$722$	−0.324007	+	0.235405i	−0.0120583	+	0.00876086i
$723$		0			0
$724$	−3.81626			−0.141830
$725$	−3.59332	+	15.6720i	−0.133452	+	0.582044i
$726$		0			0
$727$	13.1727	+	40.5415i	0.488550	+	1.50360i	0.826773	+	0.562536i	$0.190174\pi$
$727$	13.1727	+	40.5415i	0.488550	+	1.50360i	−0.338223	+	0.941066i	$0.609826\pi$
$728$	−4.58959	+	3.33453i	−0.170102	+	0.123586i
$729$		0			0
$730$	−3.46217	+	5.23933i	−0.128141	+	0.193916i
$731$	−18.3330	−	13.3197i	−0.678072	−	0.492648i
$732$		0			0
$733$	−1.58754	−	1.15341i	−0.0586370	−	0.0426023i	0.558081	−	0.829787i	$-0.311538\pi$
$733$	−1.58754	−	1.15341i	−0.0586370	−	0.0426023i	−0.616718	+	0.787184i	$0.711538\pi$
$734$	1.32451	−	4.07642i	0.0488885	−	0.150463i
$735$		0			0
$736$	1.40987	+	4.33915i	0.0519687	+	0.159943i
$737$	8.03917	−	24.7420i	0.296127	−	0.911384i
$738$		0			0
$739$	3.81947	+	11.7551i	0.140501	+	0.432419i	0.996405	−	0.0847164i	$-0.0269984\pi$
$739$	3.81947	+	11.7551i	0.140501	+	0.432419i	−0.855904	+	0.517135i	$0.826998\pi$
$740$	3.45227	+	4.33340i	0.126908	+	0.159299i
$741$		0			0
$742$	−3.31881	−	2.41126i	−0.121838	−	0.0885201i
$743$	−8.63742			−0.316876			−0.158438	−	0.987369i	$-0.550646\pi$
$743$	−8.63742			−0.316876			−0.158438	+	0.987369i	$0.550646\pi$
$744$		0			0
$745$	35.7381	−	13.3926i	1.30934	−	0.490668i
$746$	0.420978	−	0.305858i	0.0154131	−	0.0111983i
$747$		0			0
$748$	−8.99121	−	27.6721i	−0.328751	−	1.01179i
$749$	2.63898			0.0964264
$750$		0			0
$751$	−24.3654			−0.889105			−0.444552	−	0.895753i	$-0.646637\pi$
$751$	−24.3654			−0.889105			−0.444552	+	0.895753i	$0.646637\pi$
$752$	3.60852	+	11.1059i	0.131589	+	0.404990i
$753$		0			0
$754$	−3.00520	+	2.18341i	−0.109443	+	0.0795150i
$755$	−3.29818	+	1.23597i	−0.120033	+	0.0449816i
$756$		0			0
$757$	−5.18352			−0.188398			−0.0941991	−	0.995553i	$-0.530029\pi$
$757$	−5.18352			−0.188398			−0.0941991	+	0.995553i	$0.530029\pi$
$758$	2.47723	+	1.79981i	0.0899769	+	0.0653720i
$759$		0			0
$760$	5.64551	+	7.08643i	0.204784	+	0.257052i
$761$	−9.66099	−	29.7335i	−0.350211	−	1.07784i	−0.958735	−	0.284302i	$-0.908238\pi$
$761$	−9.66099	−	29.7335i	−0.350211	−	1.07784i	0.608524	−	0.793535i	$-0.291762\pi$
$762$		0			0
$763$	−0.861014	+	2.64993i	−0.0311708	+	0.0959339i
$764$	−4.65505	−	14.3268i	−0.168414	−	0.518324i
$765$		0			0
$766$	2.53964	−	7.81622i	0.0917611	−	0.282412i
$767$	24.2109	+	17.5903i	0.874205	+	0.635147i
$768$		0			0
$769$	35.7497	+	25.9737i	1.28917	+	0.936636i	0.999788	−	0.0205786i	$-0.00655083\pi$
$769$	35.7497	+	25.9737i	1.28917	+	0.936636i	0.289380	+	0.957214i	$0.406551\pi$
$770$	0.974585	−	1.47485i	0.0351216	−	0.0531499i
$771$		0			0
$772$	22.5054	−	16.3511i	0.809986	−	0.588489i
$773$	6.67110	+	20.5315i	0.239943	+	0.738468i	0.996427	+	0.0844563i	$0.0269153\pi$
$773$	6.67110	+	20.5315i	0.239943	+	0.738468i	−0.756484	+	0.654012i	$0.773085\pi$
$774$		0			0
$775$	45.7846	−	4.07512i	1.64463	−	0.146383i
$776$	0.0296542			0.00106452
$777$		0			0
$778$	3.38929	−	2.46246i	0.121512	−	0.0882835i
$779$	29.3265	−	21.3070i	1.05073	−	0.763401i
$780$		0			0
$781$	−28.8538	−	20.9635i	−1.03247	−	0.750135i
$782$	−2.31325			−0.0827218
$783$		0			0
$784$	−6.12257	+	18.8433i	−0.218663	+	0.672977i
$785$	−19.2648	+	7.21937i	−0.687592	+	0.257670i
$786$		0			0
$787$	4.45638	−	13.7153i	0.158853	−	0.488899i	−0.839678	−	0.543085i	$-0.817256\pi$
$787$	4.45638	−	13.7153i	0.158853	−	0.488899i	0.998531	+	0.0541857i	$0.0172563\pi$
$788$	0.0979961	−	0.301601i	0.00349097	−	0.0107441i
$789$		0			0
$790$	6.10690	+	1.68864i	0.217274	+	0.0600792i
$791$	−1.21337	+	3.73436i	−0.0431424	+	0.132779i
$792$		0			0
$793$	−17.9148			−0.636173
$794$	−0.172995	−	0.125688i	−0.00613937	−	0.00446052i
$795$		0			0
$796$	7.79639	−	5.66441i	0.276336	−	0.200770i
$797$	−31.9211	+	23.1921i	−1.13070	+	0.821505i	−0.985797	−	0.167941i	$-0.946288\pi$
$797$	−31.9211	+	23.1921i	−1.13070	+	0.821505i	−0.144907	+	0.989445i	$0.546288\pi$
$798$		0			0
$799$	−18.7409			−0.663004
$800$	−10.7097	+	9.33815i	−0.378645	+	0.330153i
$801$		0			0
$802$	0.738645	+	2.27332i	0.0260825	+	0.0802736i
$803$	−23.6612	+	17.1909i	−0.834986	+	0.606653i
$804$		0			0
$805$	2.78888	+	3.50068i	0.0982950	+	0.123383i
$806$	8.59125	+	6.24191i	0.302614	+	0.219862i
$807$		0			0
$808$	−8.83156	−	6.41650i	−0.310693	−	0.225732i
$809$	1.84237	−	5.67024i	0.0647744	−	0.199355i	−0.913431	−	0.406993i	$-0.866577\pi$
$809$	1.84237	−	5.67024i	0.0647744	−	0.199355i	0.978206	+	0.207638i	$0.0665775\pi$
$810$		0			0
$811$	−12.1062	−	37.2590i	−0.425105	−	1.30834i	−0.902893	−	0.429865i	$-0.858561\pi$
$811$	−12.1062	−	37.2590i	−0.425105	−	1.30834i	0.477788	−	0.878475i	$-0.341439\pi$
$812$	2.40241	−	7.39386i	0.0843081	−	0.259474i
$813$		0			0
$814$	−0.250378	−	0.770586i	−0.00877576	−	0.0270090i
$815$	0.454493	+	10.2328i	0.0159202	+	0.358439i
$816$		0			0
$817$	13.0880	+	9.50897i	0.457890	+	0.332677i
$818$	−0.374544			−0.0130956
$819$		0			0
$820$	23.4944	+	29.4908i	0.820458	+	1.02986i
$821$	16.6923	−	12.1277i	0.582567	−	0.423260i	−0.257082	−	0.966390i	$-0.582761\pi$
$821$	16.6923	−	12.1277i	0.582567	−	0.423260i	0.839649	+	0.543130i	$0.182761\pi$
$822$		0			0
$823$	12.0567	+	37.1066i	0.420269	+	1.29345i	0.907452	+	0.420155i	$0.138024\pi$
$823$	12.0567	+	37.1066i	0.420269	+	1.29345i	−0.487183	+	0.873300i	$0.661976\pi$
$824$	−0.700803			−0.0244136
$825$		0			0
$826$	1.96673			0.0684314
$827$	−6.05598	−	18.6384i	−0.210587	−	0.648120i	−0.999438	−	0.0335352i	$-0.989323\pi$
$827$	−6.05598	−	18.6384i	−0.210587	−	0.648120i	0.788850	−	0.614585i	$-0.210677\pi$
$828$		0			0
$829$	7.01831	−	5.09910i	0.243756	−	0.177099i	−0.459199	−	0.888333i	$-0.651864\pi$
$829$	7.01831	−	5.09910i	0.243756	−	0.177099i	0.702955	+	0.711234i	$0.251864\pi$
$830$	0.0693427	+	1.56123i	0.00240692	+	0.0541912i
$831$		0			0
$832$	30.7816			1.06716
$833$	−25.7248	−	18.6902i	−0.891311	−	0.647575i
$834$		0			0
$835$	0.307182	+	0.0849400i	0.0106305	+	0.00293947i
$836$	6.41884	+	19.7551i	0.222000	+	0.683246i
$837$		0			0
$838$	−2.33044	+	7.17235i	−0.0805036	+	0.247765i
$839$	1.19256	+	3.67033i	0.0411718	+	0.126714i	0.969530	−	0.244974i	$-0.0787793\pi$
$839$	1.19256	+	3.67033i	0.0411718	+	0.126714i	−0.928358	+	0.371687i	$0.878779\pi$
$840$		0			0
$841$	−5.76596	+	17.7458i	−0.198826	+	0.611925i
$842$	−1.39176	−	1.01117i	−0.0479632	−	0.0348473i
$843$		0			0
$844$	5.16724	+	3.75422i	0.177864	+	0.129226i
$845$	−19.2119	−	5.31235i	−0.660908	−	0.182750i
$846$		0			0
$847$	−4.43461	+	3.22193i	−0.152375	+	0.110707i
$848$	14.9920	+	46.1406i	0.514827	+	1.58447i
$849$		0			0
$850$	−2.82493	−	6.62735i	−0.0968943	−	0.227316i
$851$	2.05144			0.0703224
$852$		0			0
$853$	24.1004	−	17.5100i	0.825183	−	0.599531i	−0.0930093	−	0.995665i	$-0.529649\pi$
$853$	24.1004	−	17.5100i	0.825183	−	0.599531i	0.918192	+	0.396135i	$0.129649\pi$
$854$	−0.952493	+	0.692027i	−0.0325936	+	0.0236807i
$855$		0			0
$856$	1.66450	+	1.20933i	0.0568913	+	0.0413340i
$857$	−36.2041			−1.23671			−0.618354	−	0.785899i	$-0.712200\pi$
$857$	−36.2041			−1.23671			−0.618354	+	0.785899i	$0.712200\pi$
$858$		0			0
$859$	−11.6355	+	35.8104i	−0.396998	+	1.22184i	0.530396	+	0.847750i	$0.322043\pi$
$859$	−11.6355	+	35.8104i	−0.396998	+	1.22184i	−0.927394	+	0.374086i	$0.877957\pi$
$860$	−9.27706	+	14.0391i	−0.316345	+	0.478728i
$861$		0			0
$862$	0.834757	−	2.56912i	0.0284319	−	0.0875045i
$863$	0.772275	−	2.37682i	0.0262885	−	0.0809078i	−0.937051	−	0.349191i	$-0.886456\pi$
$863$	0.772275	−	2.37682i	0.0262885	−	0.0809078i	0.963340	+	0.268283i	$0.0864564\pi$
$864$		0			0
$865$	−34.3070	−	43.0632i	−1.16647	−	1.46419i
$866$	−0.796028	+	2.44992i	−0.0270501	+	0.0832518i
$867$		0			0
$868$	−22.2253			−0.754376
$869$	23.8728	+	17.3446i	0.809830	+	0.588376i
$870$		0			0
$871$	−38.3411	+	27.8565i	−1.29914	+	0.943881i
$872$	−1.75741	+	1.27684i	−0.0595136	+	0.0432391i
$873$		0			0
$874$	1.65143			0.0558606
$875$	−6.62352	+	12.2650i	−0.223916	+	0.414632i
$876$		0			0
$877$	−10.0273	−	30.8609i	−0.338599	−	1.04210i	−0.964922	−	0.262537i	$-0.915441\pi$
$877$	−10.0273	−	30.8609i	−0.338599	−	1.04210i	0.626323	−	0.779563i	$-0.284559\pi$
$878$	3.08100	−	2.23847i	0.103979	−	0.0755449i
$879$		0			0
$880$	−19.5768	+	7.33626i	−0.659933	+	0.247305i
$881$	−26.9099	−	19.5512i	−0.906619	−	0.658697i	0.0335388	−	0.999437i	$-0.489322\pi$
$881$	−26.9099	−	19.5512i	−0.906619	−	0.658697i	−0.940157	+	0.340740i	$0.889322\pi$
$882$		0			0
$883$	8.87730	+	6.44974i	0.298745	+	0.217051i	0.727052	−	0.686582i	$-0.240890\pi$
$883$	8.87730	+	6.44974i	0.298745	+	0.217051i	−0.428307	+	0.903633i	$0.640890\pi$
$884$	−16.3794	+	50.4105i	−0.550897	+	1.69549i
$885$		0			0
$886$	1.44197	+	4.43794i	0.0484440	+	0.149095i
$887$	8.03604	−	24.7324i	0.269824	−	0.830432i	−0.720719	−	0.693227i	$-0.756188\pi$
$887$	8.03604	−	24.7324i	0.269824	−	0.830432i	0.990543	−	0.137205i	$-0.0438118\pi$
$888$		0			0
$889$	6.03343	+	18.5690i	0.202355	+	0.622784i
$890$	0.420025	−	0.635628i	0.0140793	−	0.0213063i
$891$		0			0
$892$	−24.7446	−	17.9780i	−0.828511	−	0.601948i
$893$	13.3791			0.447715
$894$		0			0
$895$	−29.7778	+	45.0630i	−0.995362	+	1.50629i
$896$	7.36940	−	5.35418i	0.246194	−	0.178871i
$897$		0			0
$898$	−0.870436	−	2.67893i	−0.0290468	−	0.0893970i
$899$	−29.5626			−0.985969
$900$		0			0
$901$	−77.8608			−2.59392
$902$	−1.70394	−	5.24420i	−0.0567351	−	0.174613i
$903$		0			0
$904$	−2.47660	+	1.79936i	−0.0823705	+	0.0598457i
$905$	−4.24152	−	1.17284i	−0.140993	−	0.0389865i
$906$		0			0
$907$	−55.0108			−1.82660			−0.913302	−	0.407283i	$-0.866476\pi$
$907$	−55.0108			−1.82660			−0.913302	+	0.407283i	$0.866476\pi$
$908$	−21.2421	−	15.4333i	−0.704944	−	0.512172i
$909$		0			0
$910$	−3.01556	+	1.13006i	−0.0999650	+	0.0374612i
$911$	3.74142	+	11.5149i	0.123959	+	0.381506i	0.993710	−	0.111985i	$-0.0357208\pi$
$911$	3.74142	+	11.5149i	0.123959	+	0.381506i	−0.869751	+	0.493490i	$0.835721\pi$
$912$		0			0
$913$	−2.24908	+	6.92195i	−0.0744336	+	0.229083i
$914$	2.59060	+	7.97306i	0.0856895	+	0.263725i
$915$		0			0
$916$	8.85816	−	27.2626i	0.292682	−	0.900782i
$917$	15.0858	+	10.9605i	0.498176	+	0.361946i
$918$		0			0
$919$	−4.83138	−	3.51020i	−0.159372	−	0.115791i	0.505241	−	0.862978i	$-0.331404\pi$
$919$	−4.83138	−	3.51020i	−0.159372	−	0.115791i	−0.664613	+	0.747188i	$0.731404\pi$
$920$	0.154833	+	3.48602i	0.00510468	+	0.114931i
$921$		0			0
$922$	4.92906	−	3.58117i	0.162330	−	0.117940i
$923$	20.0774	+	61.7918i	0.660855	+	2.03390i
$924$		0			0
$925$	2.50520	+	5.87726i	0.0823706	+	0.193243i
$926$	3.36370			0.110538
$927$		0			0
$928$	7.39324	−	5.37150i	0.242695	−	0.176328i
$929$	37.9232	−	27.5528i	1.24422	−	0.903979i	0.246348	−	0.969182i	$-0.420770\pi$
$929$	37.9232	−	27.5528i	1.24422	−	0.903979i	0.997872	+	0.0652030i	$0.0207695\pi$
$930$		0			0
$931$	18.3650	+	13.3429i	0.601887	+	0.437297i
$932$	1.00636			0.0329644
$933$		0			0
$934$	0.722201	−	2.22271i	0.0236311	−	0.0727291i
$935$	−1.48876	−	33.5189i	−0.0486875	−	1.09619i
$936$		0			0
$937$	−6.00528	+	18.4823i	−0.196184	+	0.603792i	0.803777	+	0.594931i	$0.202821\pi$
$937$	−6.00528	+	18.4823i	−0.196184	+	0.603792i	−0.999961	+	0.00886093i	$0.997179\pi$
$938$	−0.962459	+	2.96214i	−0.0314254	+	0.0967174i
$939$		0			0
$940$	0.617495	+	13.9027i	0.0201405	+	0.453457i
$941$	−6.70867	+	20.6472i	−0.218696	+	0.673078i	0.780174	+	0.625563i	$0.215130\pi$
$941$	−6.70867	+	20.6472i	−0.218696	+	0.673078i	−0.998870	+	0.0475159i	$0.984870\pi$
$942$		0			0
$943$	13.9610			0.454633
$944$	−18.8172	−	13.6715i	−0.612447	−	0.444969i
$945$		0			0
$946$	1.99087	−	1.44645i	0.0647287	−	0.0470282i
$947$	−5.10943	+	3.71222i	−0.166034	+	0.120631i	−0.667699	−	0.744431i	$-0.732721\pi$
$947$	−5.10943	+	3.71222i	−0.166034	+	0.120631i	0.501665	+	0.865062i	$0.332721\pi$
$948$		0			0
$949$	53.2792			1.72952
$950$	2.01672	+	4.73127i	0.0654310	+	0.153503i
$951$		0			0
$952$	2.18668	+	6.72990i	0.0708707	+	0.218117i
$953$	17.6380	−	12.8147i	0.571350	−	0.415110i	−0.264245	−	0.964455i	$-0.585123\pi$
$953$	17.6380	−	12.8147i	0.571350	−	0.415110i	0.835595	+	0.549345i	$0.185123\pi$
$954$		0			0
$955$	−0.770779	−	17.3539i	−0.0249418	−	0.561558i
$956$	−12.9115	−	9.38076i	−0.417588	−	0.303395i
$957$		0			0
$958$	5.13625	+	3.73171i	0.165945	+	0.120566i
$959$	−4.04324	+	12.4438i	−0.130563	+	0.401831i
$960$		0			0
$961$	16.5366	+	50.8943i	0.533437	+	1.64175i
$962$	−0.456116	+	1.40378i	−0.0147058	+	0.0452597i
$963$		0			0
$964$	0.767705	+	2.36275i	0.0247261	+	0.0760992i
$965$	30.0384	−	11.2567i	0.966969	−	0.362365i
$966$		0			0
$967$	5.67338	+	4.12195i	0.182444	+	0.132553i	0.675259	−	0.737581i	$-0.264032\pi$
$967$	5.67338	+	4.12195i	0.182444	+	0.132553i	−0.492815	+	0.870134i	$0.664032\pi$
$968$	−4.27353			−0.137356
$969$		0			0
$970$	0.0162246	+	0.00448632i	0.000520940	+	0.000144047i
$971$	5.99504	−	4.35565i	0.192390	−	0.139779i	−0.487420	−	0.873167i	$-0.662062\pi$
$971$	5.99504	−	4.35565i	0.192390	−	0.139779i	0.679810	+	0.733388i	$0.262062\pi$
$972$		0			0
$973$	−4.79690	−	14.7633i	−0.153781	−	0.473291i
$974$	7.00909			0.224586
$975$		0			0
$976$	13.9237			0.445688
$977$	−12.1315	−	37.3370i	−0.388122	−	1.19452i	−0.934190	−	0.356776i	$-0.883876\pi$
$977$	−12.1315	−	37.3370i	−0.388122	−	1.19452i	0.546068	−	0.837741i	$-0.316124\pi$
$978$		0			0
$979$	2.87054	−	2.08557i	0.0917430	−	0.0666552i
$980$	−13.0175	+	19.6995i	−0.415829	+	0.629278i
$981$		0			0
$982$	−1.50597			−0.0480573
$983$	−14.8719	−	10.8051i	−0.474341	−	0.344629i	0.324790	−	0.945786i	$-0.394706\pi$
$983$	−14.8719	−	10.8051i	−0.474341	−	0.344629i	−0.799131	+	0.601158i	$0.794706\pi$
$984$		0			0
$985$	0.201606	−	0.305093i	0.00642371	−	0.00972106i
$986$	1.43181	+	4.40665i	0.0455980	+	0.140336i
$987$		0			0
$988$	11.6932	−	35.9881i	0.372012	−	1.14493i
$989$	1.92536	+	5.92564i	0.0612228	+	0.188424i
$990$		0			0
$991$	16.2128	−	49.8980i	0.515018	−	1.58506i	−0.268233	−	0.963354i	$-0.586440\pi$
$991$	16.2128	−	49.8980i	0.515018	−	1.58506i	0.783250	−	0.621707i	$-0.213560\pi$
$992$	−21.1357	−	15.3560i	−0.671060	−	0.487554i
$993$		0			0
$994$	3.45442	+	2.50978i	0.109567	+	0.0796054i
$995$	10.4060	−	3.89958i	0.329892	−	0.123625i
$996$		0			0
$997$	29.4256	−	21.3789i	0.931917	−	0.677077i	−0.0145444	−	0.999894i	$-0.504630\pi$
$997$	29.4256	−	21.3789i	0.931917	−	0.677077i	0.946461	+	0.322817i	$0.104630\pi$
$998$	1.54917	+	4.76785i	0.0490381	+	0.150924i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.h.d.181.2		12
3.2	odd	2		75.2.g.c.31.2	✓	12
15.2	even	4		375.2.i.d.349.3		24
15.8	even	4		375.2.i.d.349.4		24
15.14	odd	2		375.2.g.c.151.2		12
25.11	even	5		5625.2.a.p.1.3		6
25.14	even	10		5625.2.a.q.1.4		6
25.21	even	5	inner	225.2.h.d.46.2		12
75.2	even	20		1875.2.b.f.1249.8		12
75.11	odd	10		1875.2.a.j.1.4		6
75.14	odd	10		1875.2.a.k.1.3		6
75.23	even	20		1875.2.b.f.1249.5		12
75.29	odd	10		375.2.g.c.226.2		12
75.47	even	20		375.2.i.d.274.4		24
75.53	even	20		375.2.i.d.274.3		24
75.71	odd	10		75.2.g.c.46.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.c.31.2	✓	12	3.2	odd	2
75.2.g.c.46.2	yes	12	75.71	odd	10
225.2.h.d.46.2		12	25.21	even	5	inner
225.2.h.d.181.2		12	1.1	even	1	trivial
375.2.g.c.151.2		12	15.14	odd	2
375.2.g.c.226.2		12	75.29	odd	10
375.2.i.d.274.3		24	75.53	even	20
375.2.i.d.274.4		24	75.47	even	20
375.2.i.d.349.3		24	15.2	even	4
375.2.i.d.349.4		24	15.8	even	4
1875.2.a.j.1.4		6	75.11	odd	10
1875.2.a.k.1.3		6	75.14	odd	10
1875.2.b.f.1249.5		12	75.23	even	20
1875.2.b.f.1249.8		12	75.2	even	20
5625.2.a.p.1.3		6	25.11	even	5
5625.2.a.q.1.4		6	25.14	even	10

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0762527 - 0.234682i) q^{2} +(1.56877 - 1.13978i) q^{4} +(2.09387 - 0.784664i) q^{5} -1.24676 q^{7} +(-0.786373 - 0.571334i) q^{8} +(-0.343810 - 0.431561i) q^{10} +(-0.794084 - 2.44394i) q^{11} +(-1.44659 + 4.45215i) q^{13} +(0.0950687 + 0.292592i) q^{14} +(1.12432 - 3.46029i) q^{16} +(4.72397 + 3.43216i) q^{17} +(-3.37244 - 2.45022i) q^{19} +(2.39047 - 3.61751i) q^{20} +(-0.512997 + 0.372714i) q^{22} +(-0.496117 - 1.52689i) q^{23} +(3.76860 - 3.28597i) q^{25} +1.15514 q^{26} +(-1.95588 + 1.42103i) q^{28} +(-2.60158 + 1.89016i) q^{29} +(7.43739 + 5.40358i) q^{31} -2.84182 q^{32} +(0.445250 - 1.37034i) q^{34} +(-2.61055 + 0.978287i) q^{35} +(-0.394857 + 1.21524i) q^{37} +(-0.317865 + 0.978287i) q^{38} +(-2.09487 - 0.579261i) q^{40} +(-2.68719 + 8.27031i) q^{41} -3.88086 q^{43} +(-4.03129 - 2.92891i) q^{44} +(-0.320503 + 0.232859i) q^{46} +(-2.59656 + 1.88651i) q^{47} -5.44559 q^{49} +(-1.05852 - 0.633858i) q^{50} +(2.80510 + 8.63320i) q^{52} +(-10.7877 + 7.83770i) q^{53} +(-3.58038 - 4.49421i) q^{55} +(0.980418 + 0.712315i) q^{56} +(0.641964 + 0.466414i) q^{58} +(1.97548 - 6.07990i) q^{59} +(1.18258 + 3.63961i) q^{61} +(0.701000 - 2.15746i) q^{62} +(-2.03194 - 6.25366i) q^{64} +(0.464465 + 10.4573i) q^{65} +(8.19034 + 5.95063i) q^{67} +11.3227 q^{68} +(0.428648 + 0.538052i) q^{70} +(11.2284 - 8.15794i) q^{71} +(-3.51704 - 10.8243i) q^{73} +0.315305 q^{74} -8.08332 q^{76} +(0.990032 + 3.04700i) q^{77} +(-9.29008 + 6.74964i) q^{79} +(-0.360991 - 8.12762i) q^{80} +2.14580 q^{82} +(-2.29137 - 1.66478i) q^{83} +(12.5845 + 3.47978i) q^{85} +(0.295926 + 0.910766i) q^{86} +(-0.771858 + 2.37554i) q^{88} +(0.426682 + 1.31319i) q^{89} +(1.80355 - 5.55075i) q^{91} +(-2.51861 - 1.82988i) q^{92} +(0.640724 + 0.465513i) q^{94} +(-8.98407 - 2.48422i) q^{95} +(-0.0246815 + 0.0179322i) q^{97} +(0.415241 + 1.27798i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 10 q^{4} + 6 q^{5} - 12 q^{7} - 9 q^{8} - 9 q^{10} + 4 q^{11} - 2 q^{13} - 6 q^{14} + 16 q^{16} + q^{17} + 7 q^{19} - 26 q^{20} + 13 q^{22} - 19 q^{23} + 4 q^{25} + 56 q^{26} + q^{28} + q^{29}+ \cdots + 18 q^{98}+O(q^{100}) \) 12 * q - 10 * q^4 + 6 * q^5 - 12 * q^7 - 9 * q^8 - 9 * q^10 + 4 * q^11 - 2 * q^13 - 6 * q^14 + 16 * q^16 + q^17 + 7 * q^19 - 26 * q^20 + 13 * q^22 - 19 * q^23 + 4 * q^25 + 56 * q^26 + q^28 + q^29 + 13 * q^31 + 32 * q^32 - 25 * q^34 + 10 * q^35 + 8 * q^37 + 22 * q^38 - 28 * q^40 - 8 * q^41 - 4 * q^43 - 33 * q^44 - 22 * q^46 + 13 * q^47 - 28 * q^49 - 81 * q^50 + 44 * q^52 - 44 * q^53 + 9 * q^55 - 45 * q^56 + 41 * q^58 + 22 * q^59 - 8 * q^61 - 41 * q^62 + 49 * q^64 + 38 * q^65 - 6 * q^67 + 100 * q^68 - 45 * q^70 + 21 * q^71 - 16 * q^73 + 44 * q^74 - 52 * q^76 - q^77 + 10 * q^79 + 99 * q^80 + 26 * q^82 + 10 * q^83 + 23 * q^85 - 56 * q^86 - 16 * q^88 - 57 * q^89 - 7 * q^91 - 3 * q^92 - 23 * q^94 - 21 * q^95 + 4 * q^97 + 18 * q^98

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