LMFDB - Embedded newform 558.2.i.i.343.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [558,2,Mod(109,558)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(558, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("558.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 558 = 2 \cdot 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	558.i (of order $5$, degree $4$, 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:	$4.45565243279$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.511890625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 7x^{6} - 5x^{5} + 16x^{4} + 15x^{3} + 63x^{2} + 81x + 81 $ x^8 - 3x^7 + 7x^6 - 5x^5 + 16x^4 + 15x^3 + 63x^2 + 81*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 62)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			343.2
Root			$0.639176 - 1.96718i$ of defining polynomial
Character	$\chi$	$=$	558.343
Dual form			558.2.i.i.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +3.34677 q^{5} +(0.778353 + 2.39552i) q^{7} +(-0.309017 + 0.951057i) q^{8} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +3.34677 q^{5} +(0.778353 + 2.39552i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.70759 + 1.96718i) q^{10} +(-0.532018 - 1.63738i) q^{11} +(-1.89284 + 1.37523i) q^{13} +(-0.778353 + 2.39552i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(0.244144 - 0.751397i) q^{17} +(-0.326615 - 0.237300i) q^{19} +(1.03421 + 3.18297i) q^{20} +(0.532018 - 1.63738i) q^{22} +(1.56623 - 4.82035i) q^{23} +6.20087 q^{25} -2.33968 q^{26} +(-2.03775 + 1.48051i) q^{28} +(-4.20759 - 3.05700i) q^{29} +(-2.94366 + 4.72598i) q^{31} -1.00000 q^{32} +(0.639176 - 0.464389i) q^{34} +(2.60497 + 8.01727i) q^{35} +5.88930 q^{37} +(-0.124756 - 0.383959i) q^{38} +(-1.03421 + 3.18297i) q^{40} +(6.27601 + 4.55979i) q^{41} +(-6.18645 - 4.49472i) q^{43} +(1.39284 - 1.01196i) q^{44} +(4.10044 - 2.97914i) q^{46} +(-3.91519 + 2.84455i) q^{47} +(0.530422 - 0.385374i) q^{49} +(5.01661 + 3.64478i) q^{50} +(-1.89284 - 1.37523i) q^{52} +(0.812562 - 2.50081i) q^{53} +(-1.78054 - 5.47995i) q^{55} -2.51880 q^{56} +(-1.60716 - 4.94632i) q^{58} +(-3.53202 + 2.56616i) q^{59} +9.60897 q^{61} +(-5.15933 + 2.09315i) q^{62} +(-0.809017 - 0.587785i) q^{64} +(-6.33491 + 4.60258i) q^{65} -8.86119 q^{67} +0.790065 q^{68} +(-2.60497 + 8.01727i) q^{70} +(3.67558 - 11.3123i) q^{71} +(2.42471 + 7.46249i) q^{73} +(4.76454 + 3.46164i) q^{74} +(0.124756 - 0.383959i) q^{76} +(3.50829 - 2.54892i) q^{77} +(-0.647345 + 1.99232i) q^{79} +(-2.70759 + 1.96718i) q^{80} +(2.39722 + 7.37789i) q^{82} +(-9.91519 - 7.20381i) q^{83} +(0.817093 - 2.51475i) q^{85} +(-2.36301 - 7.27261i) q^{86} +1.72165 q^{88} +(-4.52530 - 13.9274i) q^{89} +(-4.76769 - 3.46393i) q^{91} +5.06842 q^{92} -4.83944 q^{94} +(-1.09310 - 0.794187i) q^{95} +(-5.80449 - 17.8644i) q^{97} +0.655638 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{4} + 4 q^{5} + 2 q^{7} + 2 q^{8}+O(q^{10}) $ 8 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 + 2 * q^7 + 2 * q^8	$ 8 q + 2 q^{2} - 2 q^{4} + 4 q^{5} + 2 q^{7} + 2 q^{8} + q^{10} + 2 q^{11} - 11 q^{13} - 2 q^{14} - 2 q^{16} + 7 q^{17} - 14 q^{19} - q^{20} - 2 q^{22} - 3 q^{23} - 14 q^{26} + 2 q^{28} - 13 q^{29} + 15 q^{31} - 8 q^{32} + 3 q^{34} + 28 q^{35} + 52 q^{37} - 21 q^{38} + q^{40} + 11 q^{41} - 22 q^{43} + 7 q^{44} + 8 q^{46} + 10 q^{47} - 10 q^{49} + 15 q^{50} - 11 q^{52} - 7 q^{53} - 7 q^{55} + 8 q^{56} - 17 q^{58} - 22 q^{59} + 4 q^{61} - 5 q^{62} - 2 q^{64} - 26 q^{67} - 8 q^{68} - 28 q^{70} + 15 q^{71} - 29 q^{73} + 23 q^{74} + 21 q^{76} - 34 q^{77} - 2 q^{79} - q^{80} + 9 q^{82} - 38 q^{83} + 25 q^{85} - 18 q^{86} + 18 q^{88} - q^{89} + 38 q^{91} + 22 q^{92} - 20 q^{94} + 12 q^{95} - 10 q^{97} - 60 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 + 2 * q^7 + 2 * q^8 + q^10 + 2 * q^11 - 11 * q^13 - 2 * q^14 - 2 * q^16 + 7 * q^17 - 14 * q^19 - q^20 - 2 * q^22 - 3 * q^23 - 14 * q^26 + 2 * q^28 - 13 * q^29 + 15 * q^31 - 8 * q^32 + 3 * q^34 + 28 * q^35 + 52 * q^37 - 21 * q^38 + q^40 + 11 * q^41 - 22 * q^43 + 7 * q^44 + 8 * q^46 + 10 * q^47 - 10 * q^49 + 15 * q^50 - 11 * q^52 - 7 * q^53 - 7 * q^55 + 8 * q^56 - 17 * q^58 - 22 * q^59 + 4 * q^61 - 5 * q^62 - 2 * q^64 - 26 * q^67 - 8 * q^68 - 28 * q^70 + 15 * q^71 - 29 * q^73 + 23 * q^74 + 21 * q^76 - 34 * q^77 - 2 * q^79 - q^80 + 9 * q^82 - 38 * q^83 + 25 * q^85 - 18 * q^86 + 18 * q^88 - q^89 + 38 * q^91 + 22 * q^92 - 20 * q^94 + 12 * q^95 - 10 * q^97 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/558\mathbb{Z}\right)^\times$.

$n$	$127$	$497$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$		0			0
$3$		0			0
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	3.34677			1.49672			0.748361	−	0.663292i	$-0.230841\pi$
$5$	3.34677			1.49672			0.748361	+	0.663292i	$0.230841\pi$
$6$		0			0
$7$	0.778353	+	2.39552i	0.294190	+	0.905423i	0.983492	+	0.180949i	$0.0579170\pi$
$7$	0.778353	+	2.39552i	0.294190	+	0.905423i	−0.689303	+	0.724473i	$0.742083\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$		0			0
$10$	2.70759	+	1.96718i	0.856216	+	0.622078i
$11$	−0.532018	−	1.63738i	−0.160410	−	0.493690i	0.838259	−	0.545272i	$-0.183574\pi$
$11$	−0.532018	−	1.63738i	−0.160410	−	0.493690i	−0.998669	+	0.0515821i	$0.983574\pi$
$12$		0			0
$13$	−1.89284	+	1.37523i	−0.524980	+	0.381420i	−0.818477	−	0.574540i	$-0.805181\pi$
$13$	−1.89284	+	1.37523i	−0.524980	+	0.381420i	0.293497	+	0.955960i	$0.405181\pi$
$14$	−0.778353	+	2.39552i	−0.208023	+	0.640230i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.244144	−	0.751397i	0.0592135	−	0.182240i	−0.917075	−	0.398716i	$-0.869456\pi$
$17$	0.244144	−	0.751397i	0.0592135	−	0.182240i	0.976288	+	0.216475i	$0.0694560\pi$
$18$		0			0
$19$	−0.326615	−	0.237300i	−0.0749306	−	0.0544402i	0.549689	−	0.835369i	$-0.314746\pi$
$19$	−0.326615	−	0.237300i	−0.0749306	−	0.0544402i	−0.624620	+	0.780929i	$0.714746\pi$
$20$	1.03421	+	3.18297i	0.231256	+	0.711733i
$21$		0			0
$22$	0.532018	−	1.63738i	0.113427	−	0.349091i
$23$	1.56623	−	4.82035i	0.326581	−	1.00511i	−0.644141	−	0.764907i	$-0.722785\pi$
$23$	1.56623	−	4.82035i	0.326581	−	1.00511i	0.970722	−	0.240206i	$-0.0772150\pi$
$24$		0			0
$25$	6.20087			1.24017
$26$	−2.33968			−0.458849
$27$		0			0
$28$	−2.03775	+	1.48051i	−0.385099	+	0.279791i
$29$	−4.20759	−	3.05700i	−0.781331	−	0.567670i	0.124047	−	0.992276i	$-0.460412\pi$
$29$	−4.20759	−	3.05700i	−0.781331	−	0.567670i	−0.905378	+	0.424606i	$0.860412\pi$
$30$		0			0
$31$	−2.94366	+	4.72598i	−0.528697	+	0.848810i
$31$	−2.94366	+	4.72598i	−0.528697	+	0.848810i
$32$	−1.00000			−0.176777
$33$		0			0
$34$	0.639176	−	0.464389i	0.109618	−	0.0796420i
$35$	2.60497	+	8.01727i	0.440320	+	1.35517i
$36$		0			0
$37$	5.88930			0.968195			0.484097	−	0.875014i	$-0.339148\pi$
$37$	5.88930			0.968195			0.484097	+	0.875014i	$0.339148\pi$
$38$	−0.124756	−	0.383959i	−0.0202381	−	0.0622863i
$39$		0			0
$40$	−1.03421	+	3.18297i	−0.163523	+	0.503271i
$41$	6.27601	+	4.55979i	0.980148	+	0.712120i	0.957742	−	0.287629i	$-0.0928671\pi$
$41$	6.27601	+	4.55979i	0.980148	+	0.712120i	0.0224066	+	0.999749i	$0.492867\pi$
$42$		0			0
$43$	−6.18645	−	4.49472i	−0.943425	−	0.685438i	0.00581761	−	0.999983i	$-0.498148\pi$
$43$	−6.18645	−	4.49472i	−0.943425	−	0.685438i	−0.949243	+	0.314545i	$0.898148\pi$
$44$	1.39284	−	1.01196i	0.209979	−	0.152559i
$45$		0			0
$46$	4.10044	−	2.97914i	0.604576	−	0.439250i
$47$	−3.91519	+	2.84455i	−0.571089	+	0.414920i	−0.835501	−	0.549490i	$-0.814822\pi$
$47$	−3.91519	+	2.84455i	−0.571089	+	0.414920i	0.264412	+	0.964410i	$0.414822\pi$
$48$		0			0
$49$	0.530422	−	0.385374i	0.0757746	−	0.0550534i
$50$	5.01661	+	3.64478i	0.709456	+	0.515450i
$51$		0			0
$52$	−1.89284	−	1.37523i	−0.262490	−	0.190710i
$53$	0.812562	−	2.50081i	0.111614	−	0.343512i	−0.879612	−	0.475692i	$-0.842198\pi$
$53$	0.812562	−	2.50081i	0.111614	−	0.343512i	0.991226	+	0.132180i	$0.0421976\pi$
$54$		0			0
$55$	−1.78054	−	5.47995i	−0.240088	−	0.738916i
$56$	−2.51880			−0.336589
$57$		0			0
$58$	−1.60716	−	4.94632i	−0.211030	−	0.649484i
$59$	−3.53202	+	2.56616i	−0.459830	+	0.334086i	−0.793464	−	0.608617i	$-0.791725\pi$
$59$	−3.53202	+	2.56616i	−0.459830	+	0.334086i	0.333635	+	0.942702i	$0.391725\pi$
$60$		0			0
$61$	9.60897			1.23030			0.615151	−	0.788409i	$-0.289095\pi$
$61$	9.60897			1.23030			0.615151	+	0.788409i	$0.289095\pi$
$62$	−5.15933	+	2.09315i	−0.655236	+	0.265831i
$63$		0			0
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−6.33491	+	4.60258i	−0.785749	+	0.570880i
$66$		0			0
$67$	−8.86119			−1.08257			−0.541283	−	0.840840i	$-0.682061\pi$
$67$	−8.86119			−1.08257			−0.541283	+	0.840840i	$0.682061\pi$
$68$	0.790065			0.0958095
$69$		0			0
$70$	−2.60497	+	8.01727i	−0.311353	+	0.958246i
$71$	3.67558	−	11.3123i	0.436211	−	1.34252i	−0.455630	−	0.890169i	$-0.650586\pi$
$71$	3.67558	−	11.3123i	0.436211	−	1.34252i	0.891841	−	0.452349i	$-0.149414\pi$
$72$		0			0
$73$	2.42471	+	7.46249i	0.283791	+	0.873419i	0.986758	+	0.162197i	$0.0518579\pi$
$73$	2.42471	+	7.46249i	0.283791	+	0.873419i	−0.702968	+	0.711222i	$0.748142\pi$
$74$	4.76454	+	3.46164i	0.553867	+	0.402408i
$75$		0			0
$76$	0.124756	−	0.383959i	0.0143105	−	0.0440431i
$77$	3.50829	−	2.54892i	0.399807	−	0.290477i
$78$		0			0
$79$	−0.647345	+	1.99232i	−0.0728320	+	0.224154i	−0.980846	−	0.194787i	$-0.937598\pi$
$79$	−0.647345	+	1.99232i	−0.0728320	+	0.224154i	0.908014	+	0.418941i	$0.137598\pi$
$80$	−2.70759	+	1.96718i	−0.302718	+	0.219938i
$81$		0			0
$82$	2.39722	+	7.37789i	0.264729	+	0.814752i
$83$	−9.91519	−	7.20381i	−1.08833	−	0.790720i	−0.109216	−	0.994018i	$-0.534834\pi$
$83$	−9.91519	−	7.20381i	−1.08833	−	0.790720i	−0.979117	+	0.203298i	$0.934834\pi$
$84$		0			0
$85$	0.817093	−	2.51475i	0.0886261	−	0.272763i
$86$	−2.36301	−	7.27261i	−0.254810	−	0.784226i
$87$		0			0
$88$	1.72165			0.183528
$89$	−4.52530	−	13.9274i	−0.479680	−	1.47630i	−0.839540	−	0.543298i	$-0.817175\pi$
$89$	−4.52530	−	13.9274i	−0.479680	−	1.47630i	0.359859	−	0.933007i	$-0.382825\pi$
$90$		0			0
$91$	−4.76769	−	3.46393i	−0.499790	−	0.363119i
$92$	5.06842			0.528419
$93$		0			0
$94$	−4.83944			−0.499150
$95$	−1.09310	−	0.794187i	−0.112150	−	0.0814819i
$96$		0			0
$97$	−5.80449	−	17.8644i	−0.589356	−	1.81385i	−0.581024	−	0.813887i	$-0.697348\pi$
$97$	−5.80449	−	17.8644i	−0.589356	−	1.81385i	−0.00833268	−	0.999965i	$-0.502652\pi$
$98$	0.655638			0.0662294
$99$		0			0
$100$	1.91617	+	5.89738i	0.191617	+	0.589738i
$101$	2.92191	−	8.99271i	0.290741	−	0.894809i	−0.693878	−	0.720093i	$-0.744099\pi$
$101$	2.92191	−	8.99271i	0.290741	−	0.894809i	0.984619	−	0.174716i	$-0.0559007\pi$
$102$		0			0
$103$	1.05754	+	0.768349i	0.104203	+	0.0757077i	0.638666	−	0.769484i	$-0.279486\pi$
$103$	1.05754	+	0.768349i	0.104203	+	0.0757077i	−0.534464	+	0.845191i	$0.679486\pi$
$104$	−0.723001	−	2.22517i	−0.0708961	−	0.218196i
$105$		0			0
$106$	2.12731	−	1.54558i	0.206623	−	0.150120i
$107$	−4.63903	+	14.2775i	−0.448472	+	1.38025i	0.430160	+	0.902753i	$0.358457\pi$
$107$	−4.63903	+	14.2775i	−0.448472	+	1.38025i	−0.878631	+	0.477501i	$0.841543\pi$
$108$		0			0
$109$	−5.71333	+	4.15098i	−0.547238	+	0.397591i	−0.826766	−	0.562546i	$-0.809822\pi$
$109$	−5.71333	+	4.15098i	−0.547238	+	0.397591i	0.279528	+	0.960137i	$0.409822\pi$
$110$	1.78054	−	5.47995i	0.169768	−	0.522493i
$111$		0			0
$112$	−2.03775	−	1.48051i	−0.192550	−	0.139895i
$113$	−1.67792	−	5.16410i	−0.157845	−	0.485797i	0.840593	−	0.541667i	$-0.182207\pi$
$113$	−1.67792	−	5.16410i	−0.157845	−	0.485797i	−0.998438	+	0.0558701i	$0.982207\pi$
$114$		0			0
$115$	5.24180	−	16.1326i	0.488801	−	1.50437i
$116$	1.60716	−	4.94632i	0.149221	−	0.459255i
$117$		0			0
$118$	−4.36581			−0.401906
$119$	1.99002			0.182425
$120$		0			0
$121$	6.50120	−	4.72340i	0.591019	−	0.429400i
$122$	7.77382	+	5.64801i	0.703809	+	0.511347i
$123$		0			0
$124$	−5.40431	−	1.33918i	−0.485322	−	0.120262i
$125$	4.01904			0.359474
$126$		0			0
$127$	−3.38098	+	2.45643i	−0.300013	+	0.217972i	−0.727600	−	0.686002i	$-0.759364\pi$
$127$	−3.38098	+	2.45643i	−0.300013	+	0.217972i	0.427586	+	0.903975i	$0.359364\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$		0			0
$130$	−7.83038			−0.686769
$131$	−2.13918	−	6.58371i	−0.186901	−	0.575221i	0.813075	−	0.582159i	$-0.197792\pi$
$131$	−2.13918	−	6.58371i	−0.186901	−	0.575221i	−0.999976	+	0.00693742i	$0.997792\pi$
$132$		0			0
$133$	0.314235	−	0.967116i	0.0272476	−	0.0838596i
$134$	−7.16885	−	5.20848i	−0.619295	−	0.449944i
$135$		0			0
$136$	0.639176	+	0.464389i	0.0548089	+	0.0398210i
$137$	−2.87365	+	2.08783i	−0.245512	+	0.178375i	−0.703736	−	0.710462i	$-0.748486\pi$
$137$	−2.87365	+	2.08783i	−0.245512	+	0.178375i	0.458223	+	0.888837i	$0.348486\pi$
$138$		0			0
$139$	1.99646	−	1.45051i	0.169337	−	0.123031i	−0.499889	−	0.866090i	$-0.666626\pi$
$139$	1.99646	−	1.45051i	0.169337	−	0.123031i	0.669226	+	0.743059i	$0.266626\pi$
$140$	−6.81989	+	4.95494i	−0.576386	+	0.418769i
$141$		0			0
$142$	9.62278	−	6.99136i	0.807526	−	0.586702i
$143$	3.25881	+	2.36766i	0.272515	+	0.197994i
$144$		0			0
$145$	−14.0819	−	10.2311i	−1.16943	−	0.849644i
$146$	−2.42471	+	7.46249i	−0.200670	+	0.617600i
$147$		0			0
$148$	1.81989	+	5.60105i	0.149594	+	0.460404i
$149$	14.2287			1.16566			0.582829	−	0.812595i	$-0.301946\pi$
$149$	14.2287			1.16566			0.582829	+	0.812595i	$0.301946\pi$
$150$		0			0
$151$	−1.46345	−	4.50404i	−0.119094	−	0.366533i	0.873685	−	0.486492i	$-0.161724\pi$
$151$	−1.46345	−	4.50404i	−0.119094	−	0.366533i	−0.992779	+	0.119959i	$0.961724\pi$
$152$	0.326615	−	0.237300i	0.0264920	−	0.0192475i
$153$		0			0
$154$	4.33649			0.349444
$155$	−9.85176	+	15.8168i	−0.791313	+	1.27043i
$156$		0			0
$157$	14.8602	+	10.7966i	1.18597	+	0.861660i	0.992833	−	0.119511i	$-0.0381327\pi$
$157$	14.8602	+	10.7966i	1.18597	+	0.861660i	0.193141	+	0.981171i	$0.438133\pi$
$158$	−1.69477	+	1.23132i	−0.134829	+	0.0979588i
$159$		0			0
$160$	−3.34677			−0.264585
$161$	12.7663			1.00613
$162$		0			0
$163$	−3.91753	+	12.0569i	−0.306845	+	0.944370i	0.672138	+	0.740426i	$0.265376\pi$
$163$	−3.91753	+	12.0569i	−0.306845	+	0.944370i	−0.978982	+	0.203944i	$0.934624\pi$
$164$	−2.39722	+	7.37789i	−0.187192	+	0.576117i
$165$		0			0
$166$	−3.78726	−	11.6560i	−0.293949	−	0.904681i
$167$	18.6653	+	13.5611i	1.44436	+	1.04939i	0.987108	+	0.160056i	$0.0511674\pi$
$167$	18.6653	+	13.5611i	1.44436	+	1.04939i	0.457255	+	0.889336i	$0.348833\pi$
$168$		0			0
$169$	−2.32563	+	7.15755i	−0.178894	+	0.550581i
$170$	2.13918	−	1.55420i	0.164067	−	0.119202i
$171$		0			0
$172$	2.36301	−	7.27261i	0.180178	−	0.554531i
$173$	−16.3838	+	11.9035i	−1.24564	+	0.905007i	−0.997960	−	0.0638358i	$-0.979667\pi$
$173$	−16.3838	+	11.9035i	−1.24564	+	0.905007i	−0.247675	+	0.968843i	$0.579667\pi$
$174$		0			0
$175$	4.82646	+	14.8543i	0.364846	+	1.12288i
$176$	1.39284	+	1.01196i	0.104989	+	0.0762793i
$177$		0			0
$178$	4.52530	−	13.9274i	0.339185	−	1.04391i
$179$	2.45235	+	7.54755i	0.183297	+	0.564130i	0.999915	−	0.0130484i	$-0.00415357\pi$
$179$	2.45235	+	7.54755i	0.183297	+	0.564130i	−0.816618	+	0.577179i	$0.804154\pi$
$180$		0			0
$181$	−24.2847			−1.80507			−0.902533	−	0.430620i	$-0.858295\pi$
$181$	−24.2847			−1.80507			−0.902533	+	0.430620i	$0.858295\pi$
$182$	−1.82110	−	5.60476i	−0.134989	−	0.415452i
$183$		0			0
$184$	4.10044	+	2.97914i	0.302288	+	0.219625i
$185$	19.7101			1.44912
$186$		0			0
$187$	−1.36021			−0.0994687
$188$	−3.91519	−	2.84455i	−0.285544	−	0.207460i
$189$		0			0
$190$	−0.417529	−	1.28502i	−0.0302907	−	0.0932253i
$191$	−11.3915			−0.824257			−0.412129	−	0.911126i	$-0.635215\pi$
$191$	−11.3915			−0.824257			−0.412129	+	0.911126i	$0.635215\pi$
$192$		0			0
$193$	−3.13502	−	9.64861i	−0.225664	−	0.694522i	−0.998224	−	0.0595797i	$-0.981024\pi$
$193$	−3.13502	−	9.64861i	−0.225664	−	0.694522i	0.772560	−	0.634942i	$-0.218976\pi$
$194$	5.80449	−	17.8644i	0.416738	−	1.28259i
$195$		0			0
$196$	0.530422	+	0.385374i	0.0378873	+	0.0275267i
$197$	0.723369	+	2.22630i	0.0515379	+	0.158617i	0.973513	−	0.228632i	$-0.0734253\pi$
$197$	0.723369	+	2.22630i	0.0515379	+	0.158617i	−0.921975	+	0.387249i	$0.873425\pi$
$198$		0			0
$199$	9.63624	−	7.00114i	0.683095	−	0.496298i	−0.191288	−	0.981534i	$-0.561266\pi$
$199$	9.63624	−	7.00114i	0.683095	−	0.496298i	0.874383	+	0.485236i	$0.161266\pi$
$200$	−1.91617	+	5.89738i	−0.135494	+	0.417008i
$201$		0			0
$202$	7.64966	−	5.55780i	0.538228	−	0.391046i
$203$	4.04811	−	12.4588i	0.284122	−	0.874437i
$204$		0			0
$205$	21.0044	+	15.2606i	1.46701	+	1.06584i
$206$	0.403945	+	1.24322i	0.0281442	+	0.0866189i
$207$		0			0
$208$	0.723001	−	2.22517i	0.0501311	−	0.154288i
$209$	−0.214785	+	0.661042i	−0.0148570	+	0.0457252i
$210$		0			0
$211$	20.5097			1.41195			0.705974	−	0.708237i	$-0.250509\pi$
$211$	20.5097			1.41195			0.705974	+	0.708237i	$0.250509\pi$
$212$	2.62950			0.180595
$213$		0			0
$214$	−12.1451	+	8.82395i	−0.830224	+	0.603193i
$215$	−20.7046	−	15.0428i	−1.41204	−	1.02591i
$216$		0			0
$217$	−13.6124	−	3.37313i	−0.924069	−	0.228983i
$218$	−7.06206			−0.478303
$219$		0			0
$220$	4.66152	−	3.38679i	0.314280	−	0.228338i
$221$	0.571218	+	1.75803i	0.0384243	+	0.118258i
$222$		0			0
$223$	−3.53346			−0.236618			−0.118309	−	0.992977i	$-0.537747\pi$
$223$	−3.53346			−0.236618			−0.118309	+	0.992977i	$0.537747\pi$
$224$	−0.778353	−	2.39552i	−0.0520059	−	0.160058i
$225$		0			0
$226$	1.67792	−	5.16410i	0.111613	−	0.343511i
$227$	0.453928	+	0.329798i	0.0301283	+	0.0218895i	0.602747	−	0.797932i	$-0.294073\pi$
$227$	0.453928	+	0.329798i	0.0301283	+	0.0218895i	−0.572619	+	0.819821i	$0.694073\pi$
$228$		0			0
$229$	−4.02016	−	2.92081i	−0.265659	−	0.193013i	0.446979	−	0.894544i	$-0.352500\pi$
$229$	−4.02016	−	2.92081i	−0.265659	−	0.193013i	−0.712638	+	0.701532i	$0.752500\pi$
$230$	13.7232	−	9.97050i	0.904882	−	0.657435i
$231$		0			0
$232$	4.20759	−	3.05700i	0.276242	−	0.200702i
$233$	−7.68606	+	5.58425i	−0.503530	+	0.365836i	−0.810364	−	0.585927i	$-0.800731\pi$
$233$	−7.68606	+	5.58425i	−0.503530	+	0.365836i	0.306833	+	0.951763i	$0.400731\pi$
$234$		0			0
$235$	−13.1032	+	9.52006i	−0.854761	+	0.621020i
$236$	−3.53202	−	2.56616i	−0.229915	−	0.167043i
$237$		0			0
$238$	1.60996	+	1.16970i	0.104358	+	0.0758206i
$239$	3.81989	−	11.7564i	0.247088	−	0.760460i	−0.748198	−	0.663476i	$-0.769081\pi$
$239$	3.81989	−	11.7564i	0.247088	−	0.760460i	0.995286	−	0.0969838i	$-0.0309195\pi$
$240$		0			0
$241$	6.15504	+	18.9433i	0.396481	+	1.22024i	0.927802	+	0.373073i	$0.121696\pi$
$241$	6.15504	+	18.9433i	0.396481	+	1.22024i	−0.531321	+	0.847171i	$0.678304\pi$
$242$	8.03593			0.516569
$243$		0			0
$244$	2.96934	+	9.13868i	0.190092	+	0.585044i
$245$	1.77520	−	1.28976i	0.113413	−	0.0823997i
$246$		0			0
$247$	0.944572			0.0601017
$248$	−3.58503	−	4.26000i	−0.227650	−	0.270510i
$249$		0			0
$250$	3.25148	+	2.36233i	0.205641	+	0.149407i
$251$	−19.9146	+	14.4688i	−1.25700	+	0.913261i	−0.998606	−	0.0527792i	$-0.983192\pi$
$251$	−19.9146	+	14.4688i	−1.25700	+	0.913261i	−0.258390	+	0.966041i	$0.583192\pi$
$252$		0			0
$253$	−8.72603			−0.548601
$254$	−4.17912			−0.262221
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−6.33567	+	19.4992i	−0.395208	+	1.21633i	0.533591	+	0.845742i	$0.320842\pi$
$257$	−6.33567	+	19.4992i	−0.395208	+	1.21633i	−0.928799	+	0.370583i	$0.879158\pi$
$258$		0			0
$259$	4.58395	+	14.1079i	0.284833	+	0.876625i
$260$	−6.33491	−	4.60258i	−0.392874	−	0.285440i
$261$		0			0
$262$	2.13918	−	6.58371i	0.132159	−	0.406743i
$263$	4.10167	−	2.98003i	0.252920	−	0.183757i	−0.454100	−	0.890951i	$-0.650039\pi$
$263$	4.10167	−	2.98003i	0.252920	−	0.183757i	0.707020	+	0.707194i	$0.250039\pi$
$264$		0			0
$265$	2.71946	−	8.36963i	0.167055	−	0.514142i
$266$	0.822678	−	0.597710i	0.0504416	−	0.0366480i
$267$		0			0
$268$	−2.73826	−	8.42749i	−0.167266	−	0.514791i
$269$	−4.28568	−	3.11373i	−0.261303	−	0.189848i	0.449418	−	0.893321i	$-0.351631\pi$
$269$	−4.28568	−	3.11373i	−0.261303	−	0.189848i	−0.710721	+	0.703474i	$0.751631\pi$
$270$		0			0
$271$	−2.41473	+	7.43177i	−0.146684	+	0.451448i	−0.997224	−	0.0744634i	$-0.976276\pi$
$271$	−2.41473	+	7.43177i	−0.146684	+	0.451448i	0.850539	+	0.525911i	$0.176276\pi$
$272$	0.244144	+	0.751397i	0.0148034	+	0.0455601i
$273$		0			0
$274$	−3.55202			−0.214586
$275$	−3.29898	−	10.1532i	−0.198936	−	0.612262i
$276$		0			0
$277$	0.833554	+	0.605612i	0.0500834	+	0.0363877i	0.612545	−	0.790435i	$-0.290146\pi$
$277$	0.833554	+	0.605612i	0.0500834	+	0.0363877i	−0.562462	+	0.826823i	$0.690146\pi$
$278$	2.46775			0.148006
$279$		0			0
$280$	−8.42985			−0.503780
$281$	5.71370	+	4.15124i	0.340851	+	0.247642i	0.745021	−	0.667041i	$-0.232440\pi$
$281$	5.71370	+	4.15124i	0.340851	+	0.247642i	−0.404170	+	0.914684i	$0.632440\pi$
$282$		0			0
$283$	6.70026	+	20.6213i	0.398289	+	1.22581i	0.926370	+	0.376614i	$0.122912\pi$
$283$	6.70026	+	20.6213i	0.398289	+	1.22581i	−0.528081	+	0.849194i	$0.677088\pi$
$284$	11.8944			0.705804
$285$		0			0
$286$	1.24475	+	3.83096i	0.0736038	+	0.226529i
$287$	−6.03813	+	18.5835i	−0.356420	+	1.09695i
$288$		0			0
$289$	13.2483	+	9.62545i	0.779312	+	0.566203i
$290$	−5.37879	−	16.5542i	−0.315853	−	0.972097i
$291$		0			0
$292$	−6.34797	+	4.61207i	−0.371487	+	0.269901i
$293$	2.77555	−	8.54227i	0.162149	−	0.499045i	−0.836665	−	0.547714i	$-0.815498\pi$
$293$	2.77555	−	8.54227i	0.162149	−	0.499045i	0.998815	+	0.0486695i	$0.0154981\pi$
$294$		0			0
$295$	−11.8209	+	8.58835i	−0.688237	+	0.500033i
$296$	−1.81989	+	5.60105i	−0.105779	+	0.325555i
$297$		0			0
$298$	11.5112	+	8.36341i	0.666828	+	0.484479i
$299$	3.66447	+	11.2781i	0.211922	+	0.652229i
$300$		0			0
$301$	5.95196	−	18.3183i	0.343066	−	1.05585i
$302$	1.46345	−	4.50404i	0.0842121	−	0.259178i
$303$		0			0
$304$	0.403718			0.0231548
$305$	32.1590			1.84142
$306$		0			0
$307$	11.7641	−	8.54715i	0.671415	−	0.487812i	−0.199083	−	0.979983i	$-0.563796\pi$
$307$	11.7641	−	8.54715i	0.671415	−	0.487812i	0.870499	+	0.492171i	$0.163796\pi$
$308$	3.50829	+	2.54892i	0.199904	+	0.145238i
$309$		0			0
$310$	−17.2671	+	7.00531i	−0.980705	+	0.397875i
$311$	10.6398			0.603327			0.301663	−	0.953414i	$-0.402458\pi$
$311$	10.6398			0.603327			0.301663	+	0.953414i	$0.402458\pi$
$312$		0			0
$313$	−2.73252	+	1.98529i	−0.154451	+	0.112215i	−0.662327	−	0.749215i	$-0.730431\pi$
$313$	−2.73252	+	1.98529i	−0.154451	+	0.112215i	0.507876	+	0.861430i	$0.330431\pi$
$314$	5.67609	+	17.4692i	0.320320	+	0.985845i
$315$		0			0
$316$	−2.09485			−0.117845
$317$	−2.02016	−	6.21740i	−0.113463	−	0.349204i	0.878160	−	0.478367i	$-0.158771\pi$
$317$	−2.02016	−	6.21740i	−0.113463	−	0.349204i	−0.991623	+	0.129163i	$0.958771\pi$
$318$		0			0
$319$	−2.76696	+	8.51583i	−0.154920	+	0.476795i
$320$	−2.70759	−	1.96718i	−0.151359	−	0.109969i
$321$		0			0
$322$	10.3282	+	7.50387i	0.575567	+	0.418174i
$323$	−0.258047	+	0.187482i	−0.0143581	+	0.0104318i
$324$		0			0
$325$	−11.7373	+	8.52763i	−0.651067	+	0.473028i
$326$	−10.2562	+	7.45158i	−0.568040	+	0.412705i
$327$		0			0
$328$	−6.27601	+	4.55979i	−0.346535	+	0.251772i
$329$	−9.86158	−	7.16486i	−0.543687	−	0.395012i
$330$		0			0
$331$	−22.6560	−	16.4606i	−1.24529	−	0.904754i	−0.247348	−	0.968927i	$-0.579559\pi$
$331$	−22.6560	−	16.4606i	−1.24529	−	0.904754i	−0.997939	+	0.0641730i	$0.979559\pi$
$332$	3.78726	−	11.6560i	0.207853	−	0.639706i
$333$		0			0
$334$	7.12950	+	21.9424i	0.390109	+	1.20063i
$335$	−29.6564			−1.62030
$336$		0			0
$337$	9.18116	+	28.2567i	0.500130	+	1.53924i	0.808807	+	0.588074i	$0.200114\pi$
$337$	9.18116	+	28.2567i	0.500130	+	1.53924i	−0.308677	+	0.951167i	$0.599886\pi$
$338$	−6.08857	+	4.42361i	−0.331175	+	0.240613i
$339$		0			0
$340$	2.64417			0.143400
$341$	9.30432	+	2.30560i	0.503857	+	0.124855i
$342$		0			0
$343$	15.6003	+	11.3343i	0.842337	+	0.611994i
$344$	6.18645	−	4.49472i	0.333551	−	0.242339i
$345$		0			0
$346$	−20.2515			−1.08873
$347$	9.82039			0.527186			0.263593	−	0.964634i	$-0.415092\pi$
$347$	9.82039			0.527186			0.263593	+	0.964634i	$0.415092\pi$
$348$		0			0
$349$	0.317093	−	0.975911i	0.0169736	−	0.0522393i	−0.942211	−	0.335020i	$-0.891257\pi$
$349$	0.317093	−	0.975911i	0.0169736	−	0.0522393i	0.959185	+	0.282781i	$0.0912569\pi$
$350$	−4.82646	+	14.8543i	−0.257985	+	0.793997i
$351$		0			0
$352$	0.532018	+	1.63738i	0.0283567	+	0.0872729i
$353$	16.9992	+	12.3507i	0.904778	+	0.657360i	0.939689	−	0.342031i	$-0.111115\pi$
$353$	16.9992	+	12.3507i	0.904778	+	0.657360i	−0.0349109	+	0.999390i	$0.511115\pi$
$354$		0			0
$355$	12.3013	−	37.8595i	0.652886	−	2.00938i
$356$	11.8474	−	8.60763i	0.627910	−	0.456203i
$357$		0			0
$358$	−2.45235	+	7.54755i	−0.129611	+	0.398900i
$359$	−24.6099	+	17.8802i	−1.29886	+	0.943680i	−0.999944	−	0.0105988i	$-0.996626\pi$
$359$	−24.6099	+	17.8802i	−1.29886	+	0.943680i	−0.298920	+	0.954278i	$0.596626\pi$
$360$		0			0
$361$	−5.82096	−	17.9151i	−0.306366	−	0.942898i
$362$	−19.6467	−	14.2742i	−1.03261	−	0.750234i
$363$		0			0
$364$	1.82110	−	5.60476i	0.0954514	−	0.293769i
$365$	8.11495	+	24.9752i	0.424756	+	1.30726i
$366$		0			0
$367$	25.8054			1.34703			0.673516	−	0.739172i	$-0.264783\pi$
$367$	25.8054			1.34703			0.673516	+	0.739172i	$0.264783\pi$
$368$	1.56623	+	4.82035i	0.0816452	+	0.251278i
$369$		0			0
$370$	15.9458	+	11.5853i	0.828984	+	0.602292i
$371$	6.62320			0.343859
$372$		0			0
$373$	12.4846			0.646430			0.323215	−	0.946326i	$-0.395236\pi$
$373$	12.4846			0.646430			0.323215	+	0.946326i	$0.395236\pi$
$374$	−1.10044	−	0.799514i	−0.0569022	−	0.0413419i
$375$		0			0
$376$	−1.49547	−	4.60258i	−0.0771229	−	0.237360i
$377$	12.1684			0.626704
$378$		0			0
$379$	0.582244	+	1.79196i	0.0299079	+	0.0920470i	0.964896	−	0.262631i	$-0.0845903\pi$
$379$	0.582244	+	1.79196i	0.0299079	+	0.0920470i	−0.934988	+	0.354678i	$0.884590\pi$
$380$	0.417529	−	1.28502i	0.0214188	−	0.0659202i
$381$		0			0
$382$	−9.21589	−	6.69573i	−0.471526	−	0.342584i
$383$	−4.02861	−	12.3988i	−0.205852	−	0.633548i	−0.999677	−	0.0254019i	$-0.991913\pi$
$383$	−4.02861	−	12.3988i	−0.205852	−	0.633548i	0.793825	−	0.608146i	$-0.208087\pi$
$384$		0			0
$385$	11.7415	−	8.53066i	0.598400	−	0.434763i
$386$	3.13502	−	9.64861i	0.159568	−	0.491101i
$387$		0			0
$388$	15.1963	−	11.0408i	0.771477	−	0.560511i
$389$	−3.18962	+	9.81664i	−0.161720	+	0.497723i	−0.998780	−	0.0493885i	$-0.984273\pi$
$389$	−3.18962	+	9.81664i	−0.161720	+	0.497723i	0.837060	+	0.547112i	$0.184273\pi$
$390$		0			0
$391$	−3.23961	−	2.35372i	−0.163834	−	0.119033i
$392$	0.202603	+	0.623548i	0.0102330	+	0.0314939i
$393$		0			0
$394$	−0.723369	+	2.22630i	−0.0364428	+	0.112159i
$395$	−2.16651	+	6.66784i	−0.109009	+	0.335496i
$396$		0			0
$397$	14.8604			0.745824			0.372912	−	0.927867i	$-0.378359\pi$
$397$	14.8604			0.745824			0.372912	+	0.927867i	$0.378359\pi$
$398$	11.9110			0.597047
$399$		0			0
$400$	−5.01661	+	3.64478i	−0.250831	+	0.182239i
$401$	9.88612	+	7.18269i	0.493689	+	0.358686i	0.806601	−	0.591096i	$-0.201305\pi$
$401$	9.88612	+	7.18269i	0.493689	+	0.358686i	−0.312912	+	0.949782i	$0.601305\pi$
$402$		0			0
$403$	−0.927418	−	12.9937i	−0.0461980	−	0.647264i
$404$	9.45550			0.470429
$405$		0			0
$406$	10.5981	−	7.69997i	0.525975	−	0.382143i
$407$	−3.13321	−	9.64304i	−0.155308	−	0.477988i
$408$		0			0
$409$	14.9660			0.740021			0.370010	−	0.929028i	$-0.379354\pi$
$409$	14.9660			0.740021			0.370010	+	0.929028i	$0.379354\pi$
$410$	8.02296	+	24.6921i	0.396226	+	1.21946i
$411$		0			0
$412$	−0.403945	+	1.24322i	−0.0199009	+	0.0612488i
$413$	−8.89645	−	6.46365i	−0.437766	−	0.318056i
$414$		0			0
$415$	−33.1839	−	24.1095i	−1.62893	−	1.18349i
$416$	1.89284	−	1.37523i	0.0928042	−	0.0674262i
$417$		0			0
$418$	−0.562315	+	0.408546i	−0.0275037	+	0.0199826i
$419$	12.3701	−	8.98739i	0.604318	−	0.439063i	−0.243091	−	0.970003i	$-0.578161\pi$
$419$	12.3701	−	8.98739i	0.604318	−	0.439063i	0.847409	+	0.530941i	$0.178161\pi$
$420$		0			0
$421$	−17.3497	+	12.6053i	−0.845572	+	0.614344i	−0.923922	−	0.382582i	$-0.875035\pi$
$421$	−17.3497	+	12.6053i	−0.845572	+	0.614344i	0.0783493	+	0.996926i	$0.475035\pi$
$422$	16.5927	+	12.0553i	0.807721	+	0.586844i
$423$		0			0
$424$	2.12731	+	1.54558i	0.103311	+	0.0750602i
$425$	1.51390	−	4.65932i	0.0734351	−	0.226010i
$426$		0			0
$427$	7.47917	+	23.0185i	0.361942	+	1.11394i
$428$	−15.0122			−0.725642
$429$		0			0
$430$	−7.90847	−	24.3398i	−0.381380	−	1.17377i
$431$	7.24276	−	5.26218i	0.348872	−	0.253470i	−0.399524	−	0.916723i	$-0.630825\pi$
$431$	7.24276	−	5.26218i	0.348872	−	0.253470i	0.748396	+	0.663253i	$0.230825\pi$
$432$		0			0
$433$	5.18109			0.248987			0.124494	−	0.992220i	$-0.460269\pi$
$433$	5.18109			0.248987			0.124494	+	0.992220i	$0.460269\pi$
$434$	−9.02998	−	10.7301i	−0.433453	−	0.515061i
$435$		0			0
$436$	−5.71333	−	4.15098i	−0.273619	−	0.198796i
$437$	−1.65542	+	1.20273i	−0.0791895	+	0.0575345i
$438$		0			0
$439$	−2.26810			−0.108251			−0.0541253	−	0.998534i	$-0.517237\pi$
$439$	−2.26810			−0.108251			−0.0541253	+	0.998534i	$0.517237\pi$
$440$	5.76196			0.274691
$441$		0			0
$442$	−0.571218	+	1.75803i	−0.0271701	+	0.0836209i
$443$	6.83506	−	21.0361i	0.324743	−	0.999457i	−0.646813	−	0.762649i	$-0.723899\pi$
$443$	6.83506	−	21.0361i	0.324743	−	0.999457i	0.971556	−	0.236809i	$-0.0761015\pi$
$444$		0			0
$445$	−15.1451	−	46.6119i	−0.717948	−	2.20962i
$446$	−2.85863	−	2.07692i	−0.135360	−	0.0983449i
$447$		0			0
$448$	0.778353	−	2.39552i	0.0367737	−	0.113178i
$449$	−13.4381	+	9.76338i	−0.634185	+	0.460763i	−0.857848	−	0.513904i	$-0.828199\pi$
$449$	−13.4381	+	9.76338i	−0.634185	+	0.460763i	0.223662	+	0.974667i	$0.428199\pi$
$450$		0			0
$451$	4.12717	−	12.7021i	0.194341	−	0.598120i
$452$	4.39284	−	3.19159i	0.206622	−	0.150120i
$453$		0			0
$454$	0.173385	+	0.533625i	0.00813737	+	0.0250443i
$455$	−15.9564	−	11.5930i	−0.748046	−	0.543488i
$456$		0			0
$457$	−11.2417	+	34.5984i	−0.525865	+	1.61845i	0.236734	+	0.971575i	$0.423923\pi$
$457$	−11.2417	+	34.5984i	−0.525865	+	1.61845i	−0.762599	+	0.646872i	$0.776077\pi$
$458$	−1.53556	−	4.72598i	−0.0717521	−	0.220830i
$459$		0			0
$460$	16.9628			0.790896
$461$	−1.07920	−	3.32144i	−0.0502634	−	0.154695i	0.922774	−	0.385341i	$-0.125916\pi$
$461$	−1.07920	−	3.32144i	−0.0502634	−	0.154695i	−0.973038	+	0.230646i	$0.925916\pi$
$462$		0			0
$463$	−4.90751	−	3.56551i	−0.228071	−	0.165703i	0.467881	−	0.883791i	$-0.345018\pi$
$463$	−4.90751	−	3.56551i	−0.228071	−	0.165703i	−0.695952	+	0.718088i	$0.745018\pi$
$464$	5.20087			0.241444
$465$		0			0
$466$	−9.50049			−0.440102
$467$	2.48066	+	1.80230i	0.114791	+	0.0834006i	0.643700	−	0.765278i	$-0.277399\pi$
$467$	2.48066	+	1.80230i	0.114791	+	0.0834006i	−0.528909	+	0.848679i	$0.677399\pi$
$468$		0			0
$469$	−6.89713	−	21.2272i	−0.318480	−	0.980180i
$470$	−16.1965			−0.747088
$471$		0			0
$472$	−1.34911	−	4.15214i	−0.0620979	−	0.191118i
$473$	−4.06828	+	12.5209i	−0.187060	+	0.575710i
$474$		0			0
$475$	−2.02530	−	1.47146i	−0.0929270	−	0.0675154i
$476$	0.614949	+	1.89262i	0.0281862	+	0.0867481i
$477$		0			0
$478$	10.0006	−	7.26587i	0.457417	−	0.332333i
$479$	−1.62355	+	4.99678i	−0.0741820	+	0.228309i	−0.981272	−	0.192629i	$-0.938299\pi$
$479$	−1.62355	+	4.99678i	−0.0741820	+	0.228309i	0.907090	+	0.420937i	$0.138299\pi$
$480$		0			0
$481$	−11.1475	+	8.09914i	−0.508283	+	0.369289i
$482$	−6.15504	+	18.9433i	−0.280355	+	0.862843i
$483$		0			0
$484$	6.50120	+	4.72340i	0.295509	+	0.214700i
$485$	−19.4263	−	59.7879i	−0.882102	−	2.71483i
$486$		0			0
$487$	−2.09983	+	6.46260i	−0.0951522	+	0.292848i	−0.987293	−	0.158908i	$-0.949203\pi$
$487$	−2.09983	+	6.46260i	−0.0951522	+	0.292848i	0.892141	+	0.451757i	$0.149203\pi$
$488$	−2.96934	+	9.13868i	−0.134416	+	0.413688i
$489$		0			0
$490$	2.19427			0.0991269
$491$	−23.1009			−1.04253			−0.521264	−	0.853395i	$-0.674539\pi$
$491$	−23.1009			−1.04253			−0.521264	+	0.853395i	$0.674539\pi$
$492$		0			0
$493$	−3.32427	+	2.41523i	−0.149718	+	0.108776i
$494$	0.764175	+	0.555205i	0.0343818	+	0.0249799i
$495$		0			0
$496$	−0.396387	−	5.55364i	−0.0177983	−	0.249366i
$497$	29.9597			1.34387
$498$		0			0
$499$	−20.3630	+	14.7946i	−0.911573	+	0.662297i	−0.941412	−	0.337258i	$-0.890501\pi$
$499$	−20.3630	+	14.7946i	−0.911573	+	0.662297i	0.0298390	+	0.999555i	$0.490501\pi$
$500$	1.24195	+	3.82234i	0.0555418	+	0.170940i
$501$		0			0
$502$	−24.6158			−1.09866
$503$	2.30850	+	7.10483i	0.102931	+	0.316789i	0.989239	−	0.146307i	$-0.0467387\pi$
$503$	2.30850	+	7.10483i	0.102931	+	0.316789i	−0.886308	+	0.463096i	$0.846739\pi$
$504$		0			0
$505$	9.77896	−	30.0966i	0.435158	−	1.33928i
$506$	−7.05951	−	5.12903i	−0.313833	−	0.228013i
$507$		0			0
$508$	−3.38098	−	2.45643i	−0.150007	−	0.108986i
$509$	27.6648	−	20.0996i	1.22622	−	0.890901i	0.229619	−	0.973281i	$-0.426252\pi$
$509$	27.6648	−	20.0996i	1.22622	−	0.890901i	0.996601	+	0.0823797i	$0.0262520\pi$
$510$		0			0
$511$	−15.9893	+	11.6169i	−0.707325	+	0.513901i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$		0			0
$514$	−16.5870	+	12.0512i	−0.731621	+	0.531554i
$515$	3.53935	+	2.57149i	0.155962	+	0.113313i
$516$		0			0
$517$	6.74057	+	4.89731i	0.296450	+	0.215384i
$518$	−4.58395	+	14.1079i	−0.201407	+	0.619868i
$519$		0			0
$520$	−2.41972	−	7.44713i	−0.106112	−	0.326578i
$521$	6.22092			0.272543			0.136272	−	0.990671i	$-0.456488\pi$
$521$	6.22092			0.272543			0.136272	+	0.990671i	$0.456488\pi$
$522$		0			0
$523$	−5.94426	−	18.2945i	−0.259924	−	0.799964i	−0.992819	−	0.119623i	$-0.961831\pi$
$523$	−5.94426	−	18.2945i	−0.259924	−	0.799964i	0.732895	−	0.680342i	$-0.238169\pi$
$524$	5.60044	−	4.06896i	0.244656	−	0.177753i
$525$		0			0
$526$	5.06994			0.221060
$527$	2.83241	+	3.36568i	0.123382	+	0.146611i
$528$		0			0
$529$	−2.17533	−	1.58047i	−0.0945797	−	0.0687162i
$530$	7.11963	−	5.17271i	0.309257	−	0.224688i
$531$		0			0
$532$	1.01689			0.0440876
$533$	−18.1503			−0.786175
$534$		0			0
$535$	−15.5258	+	47.7834i	−0.671237	+	2.06586i
$536$	2.73826	−	8.42749i	0.118275	−	0.364012i
$537$		0			0
$538$	−1.63699	−	5.03812i	−0.0705755	−	0.217209i
$539$	−0.913200	−	0.663478i	−0.0393343	−	0.0285780i
$540$		0			0
$541$	7.03792	−	21.6605i	0.302584	−	0.931258i	−0.677984	−	0.735077i	$-0.737146\pi$
$541$	7.03792	−	21.6605i	0.302584	−	0.931258i	0.980568	−	0.196181i	$-0.0628539\pi$
$542$	−6.32184	+	4.59309i	−0.271546	+	0.197290i
$543$		0			0
$544$	−0.244144	+	0.751397i	−0.0104676	+	0.0322159i
$545$	−19.1212	+	13.8924i	−0.819062	+	0.595084i
$546$		0			0
$547$	0.683801	+	2.10452i	0.0292372	+	0.0899830i	0.964610	−	0.263680i	$-0.0849361\pi$
$547$	0.683801	+	2.10452i	0.0292372	+	0.0899830i	−0.935373	+	0.353662i	$0.884936\pi$
$548$	−2.87365	−	2.08783i	−0.122756	−	0.0891876i
$549$		0			0
$550$	3.29898	−	10.1532i	0.140669	−	0.432934i
$551$	0.648839	+	1.99692i	0.0276415	+	0.0850717i
$552$		0			0
$553$	−5.27651			−0.224380
$554$	0.318389	+	0.979901i	0.0135271	+	0.0416320i
$555$		0			0
$556$	1.99646	+	1.45051i	0.0846686	+	0.0615153i
$557$	−30.0188			−1.27194			−0.635969	−	0.771715i	$-0.719399\pi$
$557$	−30.0188			−1.27194			−0.635969	+	0.771715i	$0.719399\pi$
$558$		0			0
$559$	17.8913			0.756719
$560$	−6.81989	−	4.95494i	−0.288193	−	0.209385i
$561$		0			0
$562$	2.18244	+	6.71685i	0.0920606	+	0.283333i
$563$	4.60946			0.194265			0.0971327	−	0.995271i	$-0.469033\pi$
$563$	4.60946			0.194265			0.0971327	+	0.995271i	$0.469033\pi$
$564$		0			0
$565$	−5.61560	−	17.2830i	−0.236250	−	0.727103i
$566$	−6.70026	+	20.6213i	−0.281633	+	0.866777i
$567$		0			0
$568$	9.62278	+	6.99136i	0.403763	+	0.293351i
$569$	−4.81521	−	14.8197i	−0.201864	−	0.621274i	−0.999828	−	0.0185682i	$-0.994089\pi$
$569$	−4.81521	−	14.8197i	−0.201864	−	0.621274i	0.797963	−	0.602706i	$-0.205911\pi$
$570$		0			0
$571$	−1.51012	+	1.09716i	−0.0631964	+	0.0459149i	−0.618935	−	0.785442i	$-0.712436\pi$
$571$	−1.51012	+	1.09716i	−0.0631964	+	0.0459149i	0.555739	+	0.831357i	$0.312436\pi$
$572$	−1.24475	+	3.83096i	−0.0520458	+	0.160180i
$573$		0			0
$574$	−15.8080	+	11.4852i	−0.659814	+	0.479383i
$575$	9.71198	−	29.8904i	0.405017	−	1.24652i
$576$		0			0
$577$	24.4672	+	17.7765i	1.01858	+	0.740045i	0.965992	−	0.258571i	$-0.0832518\pi$
$577$	24.4672	+	17.7765i	1.01858	+	0.740045i	0.0525919	+	0.998616i	$0.483252\pi$
$578$	5.06040	+	15.5743i	0.210485	+	0.647806i
$579$		0			0
$580$	5.37879	−	16.5542i	0.223342	−	0.687376i
$581$	9.53937	−	29.3592i	0.395760	−	1.21802i
$582$		0			0
$583$	−4.52708			−0.187492
$584$	−7.84653			−0.324692
$585$		0			0
$586$	7.26649	−	5.27941i	0.300176	−	0.218091i
$587$	17.1362	+	12.4502i	0.707287	+	0.513874i	0.882297	−	0.470692i	$-0.155996\pi$
$587$	17.1362	+	12.4502i	0.707287	+	0.513874i	−0.175010	+	0.984567i	$0.555996\pi$
$588$		0			0
$589$	2.08292	−	0.845044i	0.0858250	−	0.0348194i
$590$	−14.6114			−0.601541
$591$		0			0
$592$	−4.76454	+	3.46164i	−0.195821	+	0.142273i
$593$	−12.9021	−	39.7085i	−0.529824	−	1.63063i	−0.754574	−	0.656215i	$-0.772156\pi$
$593$	−12.9021	−	39.7085i	−0.529824	−	1.63063i	0.224750	−	0.974417i	$-0.427844\pi$
$594$		0			0
$595$	6.66013			0.273039
$596$	4.39690	+	13.5323i	0.180104	+	0.554304i
$597$		0			0
$598$	−3.66447	+	11.2781i	−0.149851	+	0.461195i
$599$	−5.28226	−	3.83779i	−0.215827	−	0.156808i	0.474619	−	0.880191i	$-0.342586\pi$
$599$	−5.28226	−	3.83779i	−0.215827	−	0.156808i	−0.690446	+	0.723384i	$0.742586\pi$
$600$		0			0
$601$	4.23546	+	3.07724i	0.172768	+	0.125523i	0.670809	−	0.741630i	$-0.265947\pi$
$601$	4.23546	+	3.07724i	0.172768	+	0.125523i	−0.498041	+	0.867154i	$0.665947\pi$
$602$	15.5824	−	11.3213i	0.635093	−	0.461422i
$603$		0			0
$604$	3.83136	−	2.78365i	0.155896	−	0.113265i
$605$	21.7580	−	15.8081i	0.884590	−	0.642692i
$606$		0			0
$607$	−16.4180	+	11.9284i	−0.666386	+	0.484157i	−0.868813	−	0.495140i	$-0.835117\pi$
$607$	−16.4180	+	11.9284i	−0.666386	+	0.484157i	0.202428	+	0.979297i	$0.435117\pi$
$608$	0.326615	+	0.237300i	0.0132460	+	0.00962377i
$609$		0			0
$610$	26.0172	+	18.9026i	1.05341	+	0.765344i
$611$	3.49892	−	10.7686i	0.141551	−	0.435650i
$612$		0			0
$613$	−0.456496	−	1.40495i	−0.0184377	−	0.0567454i	0.941414	−	0.337252i	$-0.109497\pi$
$613$	−0.456496	−	1.40495i	−0.0184377	−	0.0567454i	−0.959852	+	0.280507i	$0.909497\pi$
$614$	14.5413			0.586839
$615$		0			0
$616$	1.34005	+	4.12425i	0.0539921	+	0.166171i
$617$	−16.6778	+	12.1171i	−0.671421	+	0.487816i	−0.870501	−	0.492167i	$-0.836205\pi$
$617$	−16.6778	+	12.1171i	−0.671421	+	0.487816i	0.199079	+	0.979983i	$0.436205\pi$
$618$		0			0
$619$	−2.74094			−0.110168			−0.0550839	−	0.998482i	$-0.517543\pi$
$619$	−2.74094			−0.110168			−0.0550839	+	0.998482i	$0.517543\pi$
$620$	−18.0870	−	4.48193i	−0.726391	−	0.179999i
$621$		0			0
$622$	8.60777	+	6.25391i	0.345140	+	0.250759i
$623$	29.8412	−	21.6809i	1.19556	−	0.868627i
$624$		0			0
$625$	−17.5535			−0.702142
$626$	−3.37758			−0.134995
$627$		0			0
$628$	−5.67609	+	17.4692i	−0.226501	+	0.697098i
$629$	1.43783	−	4.42520i	0.0573302	−	0.176444i
$630$		0			0
$631$	−12.8289	−	39.4831i	−0.510709	−	1.57180i	−0.790957	−	0.611872i	$-0.790417\pi$
$631$	−12.8289	−	39.4831i	−0.510709	−	1.57180i	0.280248	−	0.959928i	$-0.409583\pi$
$632$	−1.69477	−	1.23132i	−0.0674143	−	0.0489794i
$633$		0			0
$634$	2.02016	−	6.21740i	0.0802306	−	0.246924i
$635$	−11.3154	+	8.22109i	−0.449036	+	0.326244i
$636$		0			0
$637$	−0.474027	+	1.45890i	−0.0187816	+	0.0578039i
$638$	−7.24399	+	5.26307i	−0.286792	+	0.208367i
$639$		0			0
$640$	−1.03421	−	3.18297i	−0.0408807	−	0.125818i
$641$	−7.93753	−	5.76696i	−0.313514	−	0.227781i	0.419889	−	0.907575i	$-0.362069\pi$
$641$	−7.93753	−	5.76696i	−0.313514	−	0.227781i	−0.733403	+	0.679794i	$0.762069\pi$
$642$		0			0
$643$	11.7291	−	36.0983i	0.462549	−	1.42358i	−0.399490	−	0.916738i	$-0.630813\pi$
$643$	11.7291	−	36.0983i	0.462549	−	1.42358i	0.862039	−	0.506842i	$-0.169187\pi$
$644$	3.94502	+	12.1415i	0.155455	+	0.478443i
$645$		0			0
$646$	−0.318964			−0.0125495
$647$	9.54343	+	29.3717i	0.375191	+	1.15472i	0.943350	+	0.331800i	$0.107656\pi$
$647$	9.54343	+	29.3717i	0.375191	+	1.15472i	−0.568159	+	0.822919i	$0.692344\pi$
$648$		0			0
$649$	6.08089	+	4.41803i	0.238696	+	0.173423i
$650$	−14.5081			−0.569053
$651$		0			0
$652$	−12.6774			−0.496485
$653$	−3.12889	−	2.27327i	−0.122443	−	0.0889601i	0.524878	−	0.851177i	$-0.324111\pi$
$653$	−3.12889	−	2.27327i	−0.122443	−	0.0889601i	−0.647321	+	0.762217i	$0.724111\pi$
$654$		0			0
$655$	−7.15933	−	22.0342i	−0.279738	−	0.860946i
$656$	−7.75758			−0.302883
$657$		0			0
$658$	−3.76679	−	11.5930i	−0.146845	−	0.451942i
$659$	−9.22225	+	28.3832i	−0.359248	+	1.10565i	0.594258	+	0.804275i	$0.297446\pi$
$659$	−9.22225	+	28.3832i	−0.359248	+	1.10565i	−0.953505	+	0.301376i	$0.902554\pi$
$660$		0			0
$661$	−33.3584	−	24.2363i	−1.29749	−	0.942684i	−0.297565	−	0.954701i	$-0.596175\pi$
$661$	−33.3584	−	24.2363i	−1.29749	−	0.942684i	−0.999928	+	0.0120174i	$0.996175\pi$
$662$	−8.65382	−	26.6337i	−0.336340	−	1.03515i
$663$		0			0
$664$	9.91519	−	7.20381i	0.384784	−	0.279562i
$665$	1.05167	−	3.23671i	0.0407821	−	0.125514i
$666$		0			0
$667$	−21.3258	+	15.4941i	−0.825740	+	0.599935i
$668$	−7.12950	+	21.9424i	−0.275849	+	0.848975i
$669$		0			0
$670$	−23.9925	−	17.4316i	−0.926911	−	0.673441i
$671$	−5.11215	−	15.7336i	−0.197352	−	0.607388i
$672$		0			0
$673$	−12.5044	+	38.4845i	−0.482008	+	1.48347i	0.354260	+	0.935147i	$0.384733\pi$
$673$	−12.5044	+	38.4845i	−0.482008	+	1.48347i	−0.836268	+	0.548321i	$0.815267\pi$
$674$	−9.18116	+	28.2567i	−0.353645	+	1.08841i
$675$		0			0
$676$	−7.52589			−0.289457
$677$	−43.9447			−1.68893			−0.844466	−	0.535609i	$-0.820082\pi$
$677$	−43.9447			−1.68893			−0.844466	+	0.535609i	$0.820082\pi$
$678$		0			0
$679$	38.2766	−	27.8096i	1.46892	−	1.06723i
$680$	2.13918	+	1.55420i	0.0820337	+	0.0596009i
$681$		0			0
$682$	6.17216	+	7.33421i	0.236344	+	0.280841i
$683$	4.87945			0.186707			0.0933535	−	0.995633i	$-0.470241\pi$
$683$	4.87945			0.186707			0.0933535	+	0.995633i	$0.470241\pi$
$684$		0			0
$685$	−9.61744	+	6.98748i	−0.367463	+	0.266978i
$686$	5.95879	+	18.3393i	0.227507	+	0.700196i
$687$		0			0
$688$	7.64688			0.291534
$689$	1.90114	+	5.85109i	0.0724275	+	0.222909i
$690$		0			0
$691$	11.0165	−	33.9054i	0.419088	−	1.28982i	−0.489455	−	0.872029i	$-0.662804\pi$
$691$	11.0165	−	33.9054i	0.419088	−	1.28982i	0.908543	−	0.417792i	$-0.137196\pi$
$692$	−16.3838	−	11.9035i	−0.622818	−	0.452504i
$693$		0			0
$694$	7.94487	+	5.77228i	0.301583	+	0.219113i
$695$	6.68168	−	4.85452i	0.253451	−	0.184143i
$696$		0			0
$697$	4.95846	−	3.60253i	0.187815	−	0.136456i
$698$	0.830159	−	0.603146i	0.0314220	−	0.0228294i
$699$		0			0
$700$	−12.6358	+	9.18048i	−0.477590	+	0.346990i
$701$	−16.4492	−	11.9511i	−0.621279	−	0.451386i	0.232089	−	0.972695i	$-0.425444\pi$
$701$	−16.4492	−	11.9511i	−0.621279	−	0.451386i	−0.853368	+	0.521309i	$0.825444\pi$
$702$		0			0
$703$	−1.92353	−	1.39753i	−0.0725474	−	0.0527087i
$704$	−0.532018	+	1.63738i	−0.0200512	+	0.0617112i
$705$		0			0
$706$	6.49313	+	19.9838i	0.244372	+	0.752100i
$707$	23.8165			0.895713
$708$		0			0
$709$	−2.96678	−	9.13080i	−0.111420	−	0.342914i	0.879764	−	0.475411i	$-0.157701\pi$
$709$	−2.96678	−	9.13080i	−0.111420	−	0.342914i	−0.991183	+	0.132497i	$0.957701\pi$
$710$	32.2052	−	23.3985i	1.20864	−	0.878129i
$711$		0			0
$712$	14.6442			0.548813
$713$	18.1704	+	21.5914i	0.680488	+	0.808606i
$714$		0			0
$715$	10.9065	+	7.92402i	0.407879	+	0.296342i
$716$	−6.42033	+	4.66464i	−0.239939	+	0.174326i
$717$		0			0
$718$	−30.4196			−1.13525
$719$	36.7351			1.36999			0.684994	−	0.728549i	$-0.259805\pi$
$719$	36.7351			1.36999			0.684994	+	0.728549i	$0.259805\pi$
$720$		0			0
$721$	−1.01746	+	3.13141i	−0.0378921	+	0.116620i
$722$	5.82096	−	17.9151i	0.216634	−	0.666730i
$723$		0			0
$724$	−7.50438	−	23.0961i	−0.278898	−	0.858360i
$725$	−26.0908	−	18.9560i	−0.968986	−	0.704010i
$726$		0			0
$727$	5.13927	−	15.8170i	0.190605	−	0.586622i	−0.809395	−	0.587265i	$-0.800205\pi$
$727$	5.13927	−	15.8170i	0.190605	−	0.586622i	1.00000		0.000643148i	$0.000204720\pi$
$728$	4.76769	−	3.46393i	0.176702	−	0.128382i
$729$		0			0
$730$	−8.11495	+	24.9752i	−0.300348	+	0.924375i
$731$	−4.88770	+	3.55112i	−0.180778	+	0.131343i
$732$		0			0
$733$	1.09540	+	3.37129i	0.0404594	+	0.124521i	0.969246	−	0.246093i	$-0.0791470\pi$
$733$	1.09540	+	3.37129i	0.0404594	+	0.124521i	−0.928787	+	0.370615i	$0.879147\pi$
$734$	20.8770	+	15.1681i	0.770585	+	0.559863i
$735$		0			0
$736$	−1.56623	+	4.82035i	−0.0577319	+	0.177681i
$737$	4.71432	+	14.5092i	0.173654	+	0.534452i
$738$		0			0
$739$	9.42152			0.346576			0.173288	−	0.984871i	$-0.444561\pi$
$739$	9.42152			0.346576			0.173288	+	0.984871i	$0.444561\pi$
$740$	6.09076	+	18.7454i	0.223901	+	0.689096i
$741$		0			0
$742$	5.35828	+	3.89302i	0.196709	+	0.142917i
$743$	−0.492369			−0.0180633			−0.00903163	−	0.999959i	$-0.502875\pi$
$743$	−0.492369			−0.0180633			−0.00903163	+	0.999959i	$0.502875\pi$
$744$		0			0
$745$	47.6201			1.74467
$746$	10.1003	+	7.33829i	0.369798	+	0.268674i
$747$		0			0
$748$	−0.420329	−	1.29364i	−0.0153688	−	0.0473002i
$749$	−37.8128			−1.38165
$750$		0			0
$751$	12.6383	+	38.8968i	0.461179	+	1.41936i	0.863725	+	0.503964i	$0.168125\pi$
$751$	12.6383	+	38.8968i	0.461179	+	1.41936i	−0.402546	+	0.915400i	$0.631875\pi$
$752$	1.49547	−	4.60258i	0.0545341	−	0.167839i
$753$		0			0
$754$	9.84443	+	7.15240i	0.358513	+	0.260475i
$755$	−4.89783	−	15.0740i	−0.178250	−	0.548598i
$756$		0			0
$757$	11.8157	−	8.58462i	0.429449	−	0.312013i	−0.351979	−	0.936008i	$-0.614491\pi$
$757$	11.8157	−	8.58462i	0.429449	−	0.312013i	0.781429	+	0.623995i	$0.214491\pi$
$758$	−0.582244	+	1.79196i	−0.0211481	+	0.0650870i
$759$		0			0
$760$	1.09310	−	0.794187i	0.0396511	−	0.0288082i
$761$	−16.6393	+	51.2106i	−0.603175	+	1.85638i	−0.0942985	+	0.995544i	$0.530061\pi$
$761$	−16.6393	+	51.2106i	−0.603175	+	1.85638i	−0.508877	+	0.860839i	$0.669939\pi$
$762$		0			0
$763$	−14.3907	−	10.4555i	−0.520980	−	0.378514i
$764$	−3.52016	−	10.8339i	−0.127355	−	0.391958i
$765$		0			0
$766$	4.02861	−	12.3988i	0.145560	−	0.447986i
$767$	3.15649	−	9.71468i	0.113974	−	0.350777i
$768$		0			0
$769$	41.8213			1.50811			0.754057	−	0.656809i	$-0.228094\pi$
$769$	41.8213			1.50811			0.754057	+	0.656809i	$0.228094\pi$
$770$	14.5132			0.523021
$771$		0			0
$772$	8.20759	−	5.96317i	0.295398	−	0.214619i
$773$	15.9544	+	11.5915i	0.573839	+	0.416919i	0.836498	−	0.547970i	$-0.184599\pi$
$773$	15.9544	+	11.5915i	0.573839	+	0.416919i	−0.262658	+	0.964889i	$0.584599\pi$
$774$		0			0
$775$	−18.2533	+	29.3052i	−0.655677	+	1.05267i
$776$	18.7837			0.674296
$777$		0			0
$778$	−8.35053	+	6.06702i	−0.299381	+	0.217513i
$779$	−0.967802	−	2.97859i	−0.0346751	−	0.106719i
$780$		0			0
$781$	−20.4780			−0.732760
$782$	−1.23742	−	3.80839i	−0.0442501	−	0.136188i
$783$		0			0
$784$	−0.202603	+	0.623548i	−0.00723583	+	0.0222696i
$785$	49.7337	+	36.1336i	1.77507	+	1.28967i
$786$		0			0
$787$	−3.06647	−	2.22792i	−0.109308	−	0.0794168i	0.531789	−	0.846877i	$-0.321520\pi$
$787$	−3.06647	−	2.22792i	−0.109308	−	0.0794168i	−0.641096	+	0.767460i	$0.721520\pi$
$788$	−1.89380	+	1.37593i	−0.0674640	+	0.0490154i
$789$		0			0
$790$	−5.67201	+	4.12095i	−0.201801	+	0.146617i
$791$	11.0647	−	8.03897i	0.393415	−	0.285833i
$792$		0			0
$793$	−18.1883	+	13.2145i	−0.645884	+	0.469262i
$794$	12.0223	+	8.73475i	0.426657	+	0.309985i
$795$		0			0
$796$	9.63624	+	7.00114i	0.341548	+	0.248149i
$797$	−3.83584	+	11.8055i	−0.135872	+	0.418172i	−0.995725	−	0.0923708i	$-0.970556\pi$
$797$	−3.83584	+	11.8055i	−0.135872	+	0.418172i	0.859852	+	0.510543i	$0.170556\pi$
$798$		0			0
$799$	1.18152	+	3.63634i	0.0417991	+	0.128644i
$800$	−6.20087			−0.219234
$801$		0			0
$802$	3.77616	+	11.6218i	0.133341	+	0.410381i
$803$	10.9290	−	7.94036i	0.385675	−	0.280209i
$804$		0			0
$805$	42.7260			1.50589
$806$	6.88723	−	11.0573i	0.242592	−	0.389476i
$807$		0			0
$808$	7.64966	+	5.55780i	0.269114	+	0.195523i
$809$	−18.7740	+	13.6401i	−0.660059	+	0.479561i	−0.866683	−	0.498859i	$-0.833752\pi$
$809$	−18.7740	+	13.6401i	−0.660059	+	0.479561i	0.206624	+	0.978420i	$0.433752\pi$
$810$		0			0
$811$	39.4836			1.38646			0.693228	−	0.720718i	$-0.256188\pi$
$811$	39.4836			1.38646			0.693228	+	0.720718i	$0.256188\pi$
$812$	13.1000			0.459719
$813$		0			0
$814$	3.13321	−	9.64304i	0.109819	−	0.337988i
$815$	−13.1111	+	40.3517i	−0.459261	+	1.41346i
$816$		0			0
$817$	0.953992	+	2.93608i	0.0333759	+	0.102721i
$818$	12.1077	+	8.79679i	0.423337	+	0.307573i
$819$		0			0
$820$	−8.02296	+	24.6921i	−0.280174	+	0.862286i
$821$	−14.5456	+	10.5680i	−0.507644	+	0.368825i	−0.811929	−	0.583756i	$-0.801582\pi$
$821$	−14.5456	+	10.5680i	−0.507644	+	0.368825i	0.304285	+	0.952581i	$0.401582\pi$
$822$		0			0
$823$	1.14856	−	3.53490i	0.0400362	−	0.123219i	−0.929041	−	0.369977i	$-0.879365\pi$
$823$	1.14856	−	3.53490i	0.0400362	−	0.123219i	0.969077	+	0.246759i	$0.0793654\pi$
$824$	−1.05754	+	0.768349i	−0.0368412	+	0.0267667i
$825$		0			0
$826$	−3.39814	−	10.4584i	−0.118237	−	0.363895i
$827$	31.4516	+	22.8509i	1.09368	+	0.794605i	0.980017	−	0.198914i	$-0.0637415\pi$
$827$	31.4516	+	22.8509i	1.09368	+	0.794605i	0.113663	+	0.993519i	$0.463741\pi$
$828$		0			0
$829$	6.49478	−	19.9889i	0.225573	−	0.694243i	−0.772660	−	0.634820i	$-0.781074\pi$
$829$	6.49478	−	19.9889i	0.225573	−	0.694243i	0.998233	−	0.0594223i	$-0.0189259\pi$
$830$	−12.6751	−	39.0100i	−0.439959	−	1.35406i
$831$		0			0
$832$	2.33968			0.0811139
$833$	−0.160070	−	0.492644i	−0.00554609	−	0.0170691i
$834$		0			0
$835$	62.4684	+	45.3860i	2.16181	+	1.57065i
$836$	−0.695060			−0.0240392
$837$		0			0
$838$	15.2903			0.528193
$839$	16.9514	+	12.3159i	0.585227	+	0.425192i	0.840605	−	0.541649i	$-0.182200\pi$
$839$	16.9514	+	12.3159i	0.585227	+	0.425192i	−0.255378	+	0.966841i	$0.582200\pi$
$840$		0			0
$841$	−0.602869	−	1.85544i	−0.0207886	−	0.0639807i
$842$	−21.4454			−0.739057
$843$		0			0
$844$	6.33786	+	19.5059i	0.218158	+	0.671422i
$845$	−7.78334	+	23.9547i	−0.267755	+	0.824066i
$846$		0			0
$847$	16.3752	+	11.8973i	0.562660	+	0.408796i
$848$	0.812562	+	2.50081i	0.0279035	+	0.0858781i
$849$		0			0
$850$	3.96345	−	2.87962i	0.135945	−	0.0987700i
$851$	9.22398	−	28.3885i	0.316194	−	0.973145i
$852$		0			0
$853$	−43.0571	+	31.2828i	−1.47425	+	1.07110i	−0.494894	+	0.868954i	$0.664793\pi$
$853$	−43.0571	+	31.2828i	−1.47425	+	1.07110i	−0.979355	+	0.202150i	$0.935207\pi$
$854$	−7.47917	+	23.0185i	−0.255932	+	0.787677i
$855$		0			0
$856$	−12.1451	−	8.82395i	−0.415112	−	0.301596i
$857$	4.36225	+	13.4256i	0.149012	+	0.458611i	0.997505	−	0.0705951i	$-0.0224898\pi$
$857$	4.36225	+	13.4256i	0.149012	+	0.458611i	−0.848493	+	0.529206i	$0.822490\pi$
$858$		0			0
$859$	−6.54750	+	20.1511i	−0.223398	+	0.687548i	0.775052	+	0.631897i	$0.217723\pi$
$859$	−6.54750	+	20.1511i	−0.223398	+	0.687548i	−0.998450	+	0.0556511i	$0.982277\pi$
$860$	7.90847	−	24.3398i	0.269676	−	0.829979i
$861$		0			0
$862$	8.95255			0.304925
$863$	−3.42261			−0.116507			−0.0582535	−	0.998302i	$-0.518553\pi$
$863$	−3.42261			−0.116507			−0.0582535	+	0.998302i	$0.518553\pi$
$864$		0			0
$865$	−54.8327	+	39.8383i	−1.86437	+	1.35454i
$866$	4.19159	+	3.04537i	0.142436	+	0.103486i
$867$		0			0
$868$	−0.998419	−	13.9885i	−0.0338886	−	0.474801i
$869$	3.60659			0.122345
$870$		0			0
$871$	16.7728	−	12.1862i	0.568326	−	0.412913i
$872$	−2.18230	−	6.71642i	−0.0739019	−	0.227447i
$873$		0			0
$874$	−2.04621			−0.0692141
$875$	3.12823	+	9.62771i	0.105754	+	0.325476i
$876$		0			0
$877$	−15.1673	+	46.6803i	−0.512165	+	1.57628i	0.276218	+	0.961095i	$0.410919\pi$
$877$	−15.1673	+	46.6803i	−0.512165	+	1.57628i	−0.788382	+	0.615186i	$0.789081\pi$
$878$	−1.83493	−	1.33316i	−0.0619260	−	0.0449919i
$879$		0			0
$880$	4.66152	+	3.38679i	0.157140	+	0.114169i
$881$	21.4239	−	15.5654i	0.721789	−	0.524411i	−0.165166	−	0.986266i	$-0.552816\pi$
$881$	21.4239	−	15.5654i	0.721789	−	0.524411i	0.886955	+	0.461855i	$0.152816\pi$
$882$		0			0
$883$	−13.4921	+	9.80261i	−0.454047	+	0.329884i	−0.791191	−	0.611569i	$-0.790539\pi$
$883$	−13.4921	+	9.80261i	−0.454047	+	0.329884i	0.337145	+	0.941453i	$0.390539\pi$
$884$	−1.49547	+	1.08652i	−0.0502981	+	0.0365437i
$885$		0			0
$886$	17.8944	−	13.0011i	0.601175	−	0.436779i
$887$	13.8834	+	10.0869i	0.466160	+	0.338685i	0.795943	−	0.605372i	$-0.206976\pi$
$887$	13.8834	+	10.0869i	0.466160	+	0.338685i	−0.329783	+	0.944057i	$0.606976\pi$
$888$		0			0
$889$	−8.51602	−	6.18725i	−0.285618	−	0.207514i
$890$	15.1451	−	46.6119i	0.507666	−	1.56243i
$891$		0			0
$892$	−1.09190	−	3.36052i	−0.0365595	−	0.112519i
$893$	1.95377			0.0653804
$894$		0			0
$895$	8.20744	+	25.2599i	0.274345	+	0.844346i
$896$	2.03775	−	1.48051i	0.0680766	−	0.0494605i
$897$		0			0
$898$	−16.6105			−0.554298
$899$	26.8330	−	10.8862i	0.894932	−	0.363076i
$900$		0			0
$901$	−1.68072	−	1.22111i	−0.0559928	−	0.0406811i
$902$	10.8051	−	7.85035i	0.359770	−	0.261388i
$903$		0			0
$904$	5.42985			0.180594
$905$	−81.2753			−2.70168
$906$		0			0
$907$	−11.5936	+	35.6815i	−0.384960	+	1.18479i	0.551549	+	0.834143i	$0.314037\pi$
$907$	−11.5936	+	35.6815i	−0.384960	+	1.18479i	−0.936509	+	0.350643i	$0.885963\pi$
$908$	−0.173385	+	0.533625i	−0.00575399	+	0.0177090i
$909$		0			0
$910$	−6.09479	−	18.7578i	−0.202040	−	0.621817i
$911$	−21.1009	−	15.3307i	−0.699104	−	0.507929i	0.180536	−	0.983568i	$-0.442217\pi$
$911$	−21.1009	−	15.3307i	−0.699104	−	0.507929i	−0.879640	+	0.475640i	$0.842217\pi$
$912$		0			0
$913$	−6.52033	+	20.0675i	−0.215792	+	0.664138i
$914$	−29.4312	+	21.3830i	−0.973497	+	0.707287i
$915$		0			0
$916$	1.53556	−	4.72598i	0.0507364	−	0.156151i
$917$	14.1064	−	10.2489i	0.465834	−	0.338448i
$918$		0			0
$919$	−15.6792	−	48.2557i	−0.517210	−	1.59181i	−0.779225	−	0.626744i	$-0.784387\pi$
$919$	−15.6792	−	48.2557i	−0.517210	−	1.59181i	0.262016	−	0.965064i	$-0.415613\pi$
$920$	13.7232	+	9.97050i	0.452441	+	0.328718i
$921$		0			0
$922$	1.07920	−	3.32144i	0.0355416	−	0.109386i
$923$	8.59968	+	26.4671i	0.283062	+	0.871175i
$924$		0			0
$925$	36.5188			1.20073
$926$	−1.87450	−	5.76912i	−0.0615999	−	0.189585i
$927$		0			0
$928$	4.20759	+	3.05700i	0.138121	+	0.100351i
$929$	46.0097			1.50953			0.754764	−	0.655996i	$-0.227751\pi$
$929$	46.0097			1.50953			0.754764	+	0.655996i	$0.227751\pi$
$930$		0			0
$931$	−0.264693			−0.00867495
$932$	−7.68606	−	5.58425i	−0.251765	−	0.182918i
$933$		0			0
$934$	0.947526	+	2.91619i	0.0310040	+	0.0954205i
$935$	−4.55232			−0.148877
$936$		0			0
$937$	11.1062	+	34.1815i	0.362825	+	1.11666i	0.951332	+	0.308168i	$0.0997158\pi$
$937$	11.1062	+	34.1815i	0.362825	+	1.11666i	−0.588507	+	0.808492i	$0.700284\pi$
$938$	6.89713	−	21.2272i	0.225199	−	0.693092i
$939$		0			0
$940$	−13.1032	−	9.52006i	−0.427380	−	0.310510i
$941$	−5.65993	−	17.4195i	−0.184509	−	0.567859i	0.815431	−	0.578854i	$-0.196500\pi$
$941$	−5.65993	−	17.4195i	−0.184509	−	0.567859i	−0.999940	+	0.0109954i	$0.996500\pi$
$942$		0			0
$943$	31.8095	−	23.1109i	1.03586	−	0.752595i
$944$	1.34911	−	4.15214i	0.0439098	−	0.135141i
$945$		0			0
$946$	−10.6509	+	7.73832i	−0.346290	+	0.251595i
$947$	16.2732	−	50.0836i	0.528807	−	1.62750i	−0.227857	−	0.973695i	$-0.573172\pi$
$947$	16.2732	−	50.0836i	0.528807	−	1.62750i	0.756663	−	0.653805i	$-0.226828\pi$
$948$		0			0
$949$	−14.8522	−	10.7908i	−0.482124	−	0.350284i
$950$	−0.773594	−	2.38088i	−0.0250987	−	0.0772459i
$951$		0			0
$952$	−0.614949	+	1.89262i	−0.0199306	+	0.0613402i
$953$	−15.3296	+	47.1796i	−0.496574	+	1.52830i	0.317915	+	0.948119i	$0.397017\pi$
$953$	−15.3296	+	47.1796i	−0.496574	+	1.52830i	−0.814489	+	0.580178i	$0.802983\pi$
$954$		0			0
$955$	−38.1246			−1.23368
$956$	12.3614			0.399797
$957$		0			0
$958$	−4.25051	+	3.08818i	−0.137328	+	0.0997745i
$959$	−7.23815	−	5.25882i	−0.233732	−	0.169816i
$960$		0			0
$961$	−13.6697	−	27.8234i	−0.440958	−	0.897528i
$962$	−13.7791			−0.444255
$963$		0			0
$964$	−16.1141	+	11.7076i	−0.519001	+	0.377076i
$965$	−10.4922	−	32.2917i	−0.337756	−	1.03951i
$966$		0			0
$967$	56.5038			1.81704			0.908520	−	0.417841i	$-0.137213\pi$
$967$	56.5038			1.81704			0.908520	+	0.417841i	$0.137213\pi$
$968$	2.48324	+	7.64262i	0.0798143	+	0.245643i
$969$		0			0
$970$	19.4263	−	59.7879i	0.623740	−	1.91968i
$971$	−1.37242	−	0.997121i	−0.0440430	−	0.0319991i	0.565546	−	0.824717i	$-0.308665\pi$
$971$	−1.37242	−	0.997121i	−0.0440430	−	0.0319991i	−0.609589	+	0.792718i	$0.708665\pi$
$972$		0			0
$973$	5.02868	+	3.65355i	0.161212	+	0.117127i
$974$	−5.49742	+	3.99411i	−0.176149	+	0.127979i
$975$		0			0
$976$	−7.77382	+	5.64801i	−0.248834	+	0.180788i
$977$	−16.5809	+	12.0467i	−0.530470	+	0.385409i	−0.820533	−	0.571599i	$-0.806323\pi$
$977$	−16.5809	+	12.0467i	−0.530470	+	0.385409i	0.290064	+	0.957007i	$0.406323\pi$
$978$		0			0
$979$	−20.3970	+	14.8193i	−0.651891	+	0.473627i
$980$	1.77520	+	1.28976i	0.0567067	+	0.0411998i
$981$		0			0
$982$	−18.6890	−	13.5784i	−0.596390	−	0.433303i
$983$	−3.38925	+	10.4310i	−0.108100	+	0.332699i	−0.990446	−	0.137904i	$-0.955963\pi$
$983$	−3.38925	+	10.4310i	−0.108100	+	0.332699i	0.882345	+	0.470603i	$0.155963\pi$
$984$		0			0
$985$	2.42095	+	7.45091i	0.0771378	+	0.237406i
$986$	−4.10903			−0.130858
$987$		0			0
$988$	0.291889	+	0.898341i	0.00928622	+	0.0285800i
$989$	−31.3555	+	22.7811i	−0.997048	+	0.724398i
$990$		0			0
$991$	−32.5863			−1.03514			−0.517569	−	0.855642i	$-0.673163\pi$
$991$	−32.5863			−1.03514			−0.517569	+	0.855642i	$0.673163\pi$
$992$	2.94366	−	4.72598i	0.0934614	−	0.150050i
$993$		0			0
$994$	24.2379	+	17.6099i	0.768779	+	0.558551i
$995$	32.2503	−	23.4312i	1.02240	−	0.742819i
$996$		0			0
$997$	−33.2453			−1.05289			−0.526445	−	0.850209i	$-0.676475\pi$
$997$	−33.2453			−1.05289			−0.526445	+	0.850209i	$0.676475\pi$
$998$	−25.1701			−0.796744
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	558.2.i.i.343.2		8
3.2	odd	2		62.2.d.a.33.1	✓	8
12.11	even	2		496.2.n.e.33.2		8
31.16	even	5	inner	558.2.i.i.109.2		8
93.35	odd	10		1922.2.a.r.1.4		4
93.47	odd	10		62.2.d.a.47.1	yes	8
93.89	even	10		1922.2.a.n.1.1		4
372.47	even	10		496.2.n.e.481.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.2.d.a.33.1	✓	8	3.2	odd	2
62.2.d.a.47.1	yes	8	93.47	odd	10
496.2.n.e.33.2		8	12.11	even	2
496.2.n.e.481.2		8	372.47	even	10
558.2.i.i.109.2		8	31.16	even	5	inner
558.2.i.i.343.2		8	1.1	even	1	trivial
1922.2.a.n.1.1		4	93.89	even	10
1922.2.a.r.1.4		4	93.35	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 558 = 2 \cdot 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	558.i (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +3.34677 q^{5} +(0.778353 + 2.39552i) q^{7} +(-0.309017 + 0.951057i) q^{8} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +3.34677 q^{5} +(0.778353 + 2.39552i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.70759 + 1.96718i) q^{10} +(-0.532018 - 1.63738i) q^{11} +(-1.89284 + 1.37523i) q^{13} +(-0.778353 + 2.39552i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(0.244144 - 0.751397i) q^{17} +(-0.326615 - 0.237300i) q^{19} +(1.03421 + 3.18297i) q^{20} +(0.532018 - 1.63738i) q^{22} +(1.56623 - 4.82035i) q^{23} +6.20087 q^{25} -2.33968 q^{26} +(-2.03775 + 1.48051i) q^{28} +(-4.20759 - 3.05700i) q^{29} +(-2.94366 + 4.72598i) q^{31} -1.00000 q^{32} +(0.639176 - 0.464389i) q^{34} +(2.60497 + 8.01727i) q^{35} +5.88930 q^{37} +(-0.124756 - 0.383959i) q^{38} +(-1.03421 + 3.18297i) q^{40} +(6.27601 + 4.55979i) q^{41} +(-6.18645 - 4.49472i) q^{43} +(1.39284 - 1.01196i) q^{44} +(4.10044 - 2.97914i) q^{46} +(-3.91519 + 2.84455i) q^{47} +(0.530422 - 0.385374i) q^{49} +(5.01661 + 3.64478i) q^{50} +(-1.89284 - 1.37523i) q^{52} +(0.812562 - 2.50081i) q^{53} +(-1.78054 - 5.47995i) q^{55} -2.51880 q^{56} +(-1.60716 - 4.94632i) q^{58} +(-3.53202 + 2.56616i) q^{59} +9.60897 q^{61} +(-5.15933 + 2.09315i) q^{62} +(-0.809017 - 0.587785i) q^{64} +(-6.33491 + 4.60258i) q^{65} -8.86119 q^{67} +0.790065 q^{68} +(-2.60497 + 8.01727i) q^{70} +(3.67558 - 11.3123i) q^{71} +(2.42471 + 7.46249i) q^{73} +(4.76454 + 3.46164i) q^{74} +(0.124756 - 0.383959i) q^{76} +(3.50829 - 2.54892i) q^{77} +(-0.647345 + 1.99232i) q^{79} +(-2.70759 + 1.96718i) q^{80} +(2.39722 + 7.37789i) q^{82} +(-9.91519 - 7.20381i) q^{83} +(0.817093 - 2.51475i) q^{85} +(-2.36301 - 7.27261i) q^{86} +1.72165 q^{88} +(-4.52530 - 13.9274i) q^{89} +(-4.76769 - 3.46393i) q^{91} +5.06842 q^{92} -4.83944 q^{94} +(-1.09310 - 0.794187i) q^{95} +(-5.80449 - 17.8644i) q^{97} +0.655638 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{4} + 4 q^{5} + 2 q^{7} + 2 q^{8}+O(q^{10}) \) 8 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 + 2 * q^7 + 2 * q^8	\( 8 q + 2 q^{2} - 2 q^{4} + 4 q^{5} + 2 q^{7} + 2 q^{8} + q^{10} + 2 q^{11} - 11 q^{13} - 2 q^{14} - 2 q^{16} + 7 q^{17} - 14 q^{19} - q^{20} - 2 q^{22} - 3 q^{23} - 14 q^{26} + 2 q^{28} - 13 q^{29} + 15 q^{31} - 8 q^{32} + 3 q^{34} + 28 q^{35} + 52 q^{37} - 21 q^{38} + q^{40} + 11 q^{41} - 22 q^{43} + 7 q^{44} + 8 q^{46} + 10 q^{47} - 10 q^{49} + 15 q^{50} - 11 q^{52} - 7 q^{53} - 7 q^{55} + 8 q^{56} - 17 q^{58} - 22 q^{59} + 4 q^{61} - 5 q^{62} - 2 q^{64} - 26 q^{67} - 8 q^{68} - 28 q^{70} + 15 q^{71} - 29 q^{73} + 23 q^{74} + 21 q^{76} - 34 q^{77} - 2 q^{79} - q^{80} + 9 q^{82} - 38 q^{83} + 25 q^{85} - 18 q^{86} + 18 q^{88} - q^{89} + 38 q^{91} + 22 q^{92} - 20 q^{94} + 12 q^{95} - 10 q^{97} - 60 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 + 2 * q^7 + 2 * q^8 + q^10 + 2 * q^11 - 11 * q^13 - 2 * q^14 - 2 * q^16 + 7 * q^17 - 14 * q^19 - q^20 - 2 * q^22 - 3 * q^23 - 14 * q^26 + 2 * q^28 - 13 * q^29 + 15 * q^31 - 8 * q^32 + 3 * q^34 + 28 * q^35 + 52 * q^37 - 21 * q^38 + q^40 + 11 * q^41 - 22 * q^43 + 7 * q^44 + 8 * q^46 + 10 * q^47 - 10 * q^49 + 15 * q^50 - 11 * q^52 - 7 * q^53 - 7 * q^55 + 8 * q^56 - 17 * q^58 - 22 * q^59 + 4 * q^61 - 5 * q^62 - 2 * q^64 - 26 * q^67 - 8 * q^68 - 28 * q^70 + 15 * q^71 - 29 * q^73 + 23 * q^74 + 21 * q^76 - 34 * q^77 - 2 * q^79 - q^80 + 9 * q^82 - 38 * q^83 + 25 * q^85 - 18 * q^86 + 18 * q^88 - q^89 + 38 * q^91 + 22 * q^92 - 20 * q^94 + 12 * q^95 - 10 * q^97 - 60 * q^98

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