LMFDB - Embedded newform 1122.2.b.a.1055.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1122,2,Mod(1055,1122)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1122, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("1122.1055");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1122 = 2 \cdot 3 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1122.b (of order $2$, degree $1$, 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:	$8.95921510679$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 18x^{14} + 124x^{12} + 420x^{10} + 746x^{8} + 681x^{6} + 288x^{4} + 42x^{2} + 1 $ x^16 + 18x^14 + 124x^12 + 420x^10 + 746x^8 + 681x^6 + 288x^4 + 42*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1055.7
Root			$-0.469643i$ of defining polynomial
Character	$\chi$	$=$	1122.1055
Dual form			1122.2.b.a.1055.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.240909 - 1.71522i) q^{3} +1.00000 q^{4} +2.17582i q^{5} +(0.240909 + 1.71522i) q^{6} -0.914768i q^{7} -1.00000 q^{8} +(-2.88393 + 0.826423i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.240909 - 1.71522i) q^{3} +1.00000 q^{4} +2.17582i q^{5} +(0.240909 + 1.71522i) q^{6} -0.914768i q^{7} -1.00000 q^{8} +(-2.88393 + 0.826423i) q^{9} -2.17582i q^{10} +(-1.74515 + 2.82036i) q^{11} +(-0.240909 - 1.71522i) q^{12} -1.44014i q^{13} +0.914768i q^{14} +(3.73201 - 0.524177i) q^{15} +1.00000 q^{16} +1.00000 q^{17} +(2.88393 - 0.826423i) q^{18} -5.07185i q^{19} +2.17582i q^{20} +(-1.56902 + 0.220376i) q^{21} +(1.74515 - 2.82036i) q^{22} +0.247175i q^{23} +(0.240909 + 1.71522i) q^{24} +0.265786 q^{25} +1.44014i q^{26} +(2.11226 + 4.74746i) q^{27} -0.914768i q^{28} +4.33115 q^{29} +(-3.73201 + 0.524177i) q^{30} +2.84085 q^{31} -1.00000 q^{32} +(5.25795 + 2.31386i) q^{33} -1.00000 q^{34} +1.99037 q^{35} +(-2.88393 + 0.826423i) q^{36} +8.89109 q^{37} +5.07185i q^{38} +(-2.47015 + 0.346944i) q^{39} -2.17582i q^{40} +5.87226 q^{41} +(1.56902 - 0.220376i) q^{42} -0.252147i q^{43} +(-1.74515 + 2.82036i) q^{44} +(-1.79815 - 6.27492i) q^{45} -0.247175i q^{46} +3.78349i q^{47} +(-0.240909 - 1.71522i) q^{48} +6.16320 q^{49} -0.265786 q^{50} +(-0.240909 - 1.71522i) q^{51} -1.44014i q^{52} +8.41459i q^{53} +(-2.11226 - 4.74746i) q^{54} +(-6.13662 - 3.79714i) q^{55} +0.914768i q^{56} +(-8.69932 + 1.22186i) q^{57} -4.33115 q^{58} -8.62391i q^{59} +(3.73201 - 0.524177i) q^{60} +8.16742i q^{61} -2.84085 q^{62} +(0.755985 + 2.63812i) q^{63} +1.00000 q^{64} +3.13350 q^{65} +(-5.25795 - 2.31386i) q^{66} +1.06805 q^{67} +1.00000 q^{68} +(0.423958 - 0.0595467i) q^{69} -1.99037 q^{70} -8.84578i q^{71} +(2.88393 - 0.826423i) q^{72} +10.2675i q^{73} -8.89109 q^{74} +(-0.0640304 - 0.455881i) q^{75} -5.07185i q^{76} +(2.57998 + 1.59641i) q^{77} +(2.47015 - 0.346944i) q^{78} -7.27791i q^{79} +2.17582i q^{80} +(7.63405 - 4.76668i) q^{81} -5.87226 q^{82} +10.4725 q^{83} +(-1.56902 + 0.220376i) q^{84} +2.17582i q^{85} +0.252147i q^{86} +(-1.04341 - 7.42885i) q^{87} +(1.74515 - 2.82036i) q^{88} -6.43234i q^{89} +(1.79815 + 6.27492i) q^{90} -1.31740 q^{91} +0.247175i q^{92} +(-0.684387 - 4.87266i) q^{93} -3.78349i q^{94} +11.0355 q^{95} +(0.240909 + 1.71522i) q^{96} +8.67647 q^{97} -6.16320 q^{98} +(2.70207 - 9.57595i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{2} + q^{3} + 16 q^{4} - q^{6} - 16 q^{8} - 3 q^{9}+O(q^{10}) $ 16 * q - 16 * q^2 + q^3 + 16 * q^4 - q^6 - 16 * q^8 - 3 * q^9	$ 16 q - 16 q^{2} + q^{3} + 16 q^{4} - q^{6} - 16 q^{8} - 3 q^{9} + 6 q^{11} + q^{12} + 16 q^{16} + 16 q^{17} + 3 q^{18} + 24 q^{21} - 6 q^{22} - q^{24} - 22 q^{25} + 13 q^{27} - 20 q^{29} + 24 q^{31} - 16 q^{32} - 3 q^{33} - 16 q^{34} + 12 q^{35} - 3 q^{36} + 6 q^{37} - q^{39} + 22 q^{41} - 24 q^{42} + 6 q^{44} - 15 q^{45} + q^{48} - 54 q^{49} + 22 q^{50} + q^{51} - 13 q^{54} - 10 q^{55} + 8 q^{57} + 20 q^{58} - 24 q^{62} - 36 q^{63} + 16 q^{64} - 68 q^{65} + 3 q^{66} + 12 q^{67} + 16 q^{68} - 40 q^{69} - 12 q^{70} + 3 q^{72} - 6 q^{74} + q^{75} + 10 q^{77} + q^{78} + 17 q^{81} - 22 q^{82} - 10 q^{83} + 24 q^{84} + 12 q^{87} - 6 q^{88} + 15 q^{90} + 4 q^{91} + 6 q^{93} - 48 q^{95} - q^{96} + 54 q^{98} + 31 q^{99}+O(q^{100}) $ 16 * q - 16 * q^2 + q^3 + 16 * q^4 - q^6 - 16 * q^8 - 3 * q^9 + 6 * q^11 + q^12 + 16 * q^16 + 16 * q^17 + 3 * q^18 + 24 * q^21 - 6 * q^22 - q^24 - 22 * q^25 + 13 * q^27 - 20 * q^29 + 24 * q^31 - 16 * q^32 - 3 * q^33 - 16 * q^34 + 12 * q^35 - 3 * q^36 + 6 * q^37 - q^39 + 22 * q^41 - 24 * q^42 + 6 * q^44 - 15 * q^45 + q^48 - 54 * q^49 + 22 * q^50 + q^51 - 13 * q^54 - 10 * q^55 + 8 * q^57 + 20 * q^58 - 24 * q^62 - 36 * q^63 + 16 * q^64 - 68 * q^65 + 3 * q^66 + 12 * q^67 + 16 * q^68 - 40 * q^69 - 12 * q^70 + 3 * q^72 - 6 * q^74 + q^75 + 10 * q^77 + q^78 + 17 * q^81 - 22 * q^82 - 10 * q^83 + 24 * q^84 + 12 * q^87 - 6 * q^88 + 15 * q^90 + 4 * q^91 + 6 * q^93 - 48 * q^95 - q^96 + 54 * q^98 + 31 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1122\mathbb{Z}\right)^\times$.

$n$	$409$	$749$	$1057$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.240909	−	1.71522i	−0.139089	−	0.990280i
$3$	−0.240909	−	1.71522i	−0.139089	−	0.990280i
$4$	1.00000			0.500000
$5$			2.17582i			0.973058i	0.873664	+	0.486529i	$0.161737\pi$
$5$			2.17582i			0.973058i	−0.873664	+	0.486529i	$0.838263\pi$
$6$	0.240909	+	1.71522i	0.0983509	+	0.700234i
$7$		−	0.914768i		−	0.345750i	−0.984944	−	0.172875i	$-0.944694\pi$
$7$		−	0.914768i		−	0.345750i	0.984944	−	0.172875i	$-0.0553056\pi$
$8$	−1.00000			−0.353553
$9$	−2.88393	+	0.826423i	−0.961308	+	0.275474i
$10$		−	2.17582i		−	0.688056i
$11$	−1.74515	+	2.82036i	−0.526183	+	0.850371i
$11$	−1.74515	+	2.82036i	−0.526183	+	0.850371i
$12$	−0.240909	−	1.71522i	−0.0695446	−	0.495140i
$13$		−	1.44014i		−	0.399424i	−0.979855	−	0.199712i	$-0.935999\pi$
$13$		−	1.44014i		−	0.399424i	0.979855	−	0.199712i	$-0.0640006\pi$
$14$			0.914768i			0.244482i
$15$	3.73201	−	0.524177i	0.963600	−	0.135342i
$16$	1.00000			0.250000
$17$	1.00000			0.242536
$17$	1.00000			0.242536
$18$	2.88393	−	0.826423i	0.679748	−	0.194790i
$19$		−	5.07185i		−	1.16356i	−0.813345	−	0.581781i	$-0.802356\pi$
$19$		−	5.07185i		−	1.16356i	0.813345	−	0.581781i	$-0.197644\pi$
$20$			2.17582i			0.486529i
$21$	−1.56902	+	0.220376i	−0.342389	+	0.0480900i
$22$	1.74515	−	2.82036i	0.372067	−	0.601303i
$23$			0.247175i			0.0515395i	0.999668	+	0.0257697i	$0.00820367\pi$
$23$			0.247175i			0.0515395i	−0.999668	+	0.0257697i	$0.991796\pi$
$24$	0.240909	+	1.71522i	0.0491754	+	0.350117i
$25$	0.265786			0.0531573
$26$			1.44014i			0.282435i
$27$	2.11226	+	4.74746i	0.406504	+	0.913649i
$28$		−	0.914768i		−	0.172875i
$29$	4.33115			0.804274			0.402137	−	0.915579i	$-0.368268\pi$
$29$	4.33115			0.804274			0.402137	+	0.915579i	$0.368268\pi$
$30$	−3.73201	+	0.524177i	−0.681368	+	0.0957011i
$31$	2.84085			0.510231			0.255116	−	0.966911i	$-0.417886\pi$
$31$	2.84085			0.510231			0.255116	+	0.966911i	$0.417886\pi$
$32$	−1.00000			−0.176777
$33$	5.25795	+	2.31386i	0.915292	+	0.402791i
$34$	−1.00000			−0.171499
$35$	1.99037			0.336435
$36$	−2.88393	+	0.826423i	−0.480654	+	0.137737i
$37$	8.89109			1.46169			0.730843	−	0.682545i	$-0.239127\pi$
$37$	8.89109			1.46169			0.730843	+	0.682545i	$0.239127\pi$
$38$			5.07185i			0.822763i
$39$	−2.47015	+	0.346944i	−0.395541	+	0.0555555i
$40$		−	2.17582i		−	0.344028i
$41$	5.87226			0.917093			0.458546	−	0.888670i	$-0.348370\pi$
$41$	5.87226			0.917093			0.458546	+	0.888670i	$0.348370\pi$
$42$	1.56902	−	0.220376i	0.242106	−	0.0340048i
$43$		−	0.252147i		−	0.0384521i	−0.999815	−	0.0192261i	$-0.993880\pi$
$43$		−	0.252147i		−	0.0384521i	0.999815	−	0.0192261i	$-0.00612022\pi$
$44$	−1.74515	+	2.82036i	−0.263091	+	0.425186i
$45$	−1.79815	−	6.27492i	−0.268053	−	0.935409i
$46$		−	0.247175i		−	0.0364439i
$47$			3.78349i			0.551879i	0.961175	+	0.275940i	$0.0889890\pi$
$47$			3.78349i			0.551879i	−0.961175	+	0.275940i	$0.911011\pi$
$48$	−0.240909	−	1.71522i	−0.0347723	−	0.247570i
$49$	6.16320			0.880457
$50$	−0.265786			−0.0375879
$51$	−0.240909	−	1.71522i	−0.0337341	−	0.240178i
$52$		−	1.44014i		−	0.199712i
$53$			8.41459i			1.15583i	0.816096	+	0.577917i	$0.196134\pi$
$53$			8.41459i			1.15583i	−0.816096	+	0.577917i	$0.803866\pi$
$54$	−2.11226	−	4.74746i	−0.287442	−	0.646047i
$55$	−6.13662	−	3.79714i	−0.827461	−	0.512007i
$56$			0.914768i			0.122241i
$57$	−8.69932	+	1.22186i	−1.15225	+	0.161839i
$58$	−4.33115			−0.568708
$59$		−	8.62391i		−	1.12274i	−0.827566	−	0.561369i	$-0.810275\pi$
$59$		−	8.62391i		−	1.12274i	0.827566	−	0.561369i	$-0.189725\pi$
$60$	3.73201	−	0.524177i	0.481800	−	0.0676709i
$61$			8.16742i			1.04573i	0.852415	+	0.522865i	$0.175137\pi$
$61$			8.16742i			1.04573i	−0.852415	+	0.522865i	$0.824863\pi$
$62$	−2.84085			−0.360788
$63$	0.755985	+	2.63812i	0.0952452	+	0.332372i
$64$	1.00000			0.125000
$65$	3.13350			0.388663
$66$	−5.25795	−	2.31386i	−0.647209	−	0.284816i
$67$	1.06805			0.130483			0.0652414	−	0.997870i	$-0.479218\pi$
$67$	1.06805			0.130483			0.0652414	+	0.997870i	$0.479218\pi$
$68$	1.00000			0.121268
$69$	0.423958	−	0.0595467i	0.0510385	−	0.00716858i
$70$	−1.99037			−0.237895
$71$		−	8.84578i		−	1.04980i	−0.851164	−	0.524900i	$-0.824103\pi$
$71$		−	8.84578i		−	1.04980i	0.851164	−	0.524900i	$-0.175897\pi$
$72$	2.88393	−	0.826423i	0.339874	−	0.0973949i
$73$			10.2675i			1.20172i	0.799356	+	0.600858i	$0.205174\pi$
$73$			10.2675i			1.20172i	−0.799356	+	0.600858i	$0.794826\pi$
$74$	−8.89109			−1.03357
$75$	−0.0640304	−	0.455881i	−0.00739360	−	0.0526406i
$76$		−	5.07185i		−	0.581781i
$77$	2.57998	+	1.59641i	0.294016	+	0.181928i
$78$	2.47015	−	0.346944i	0.279690	−	0.0392837i
$79$		−	7.27791i		−	0.818829i	−0.912349	−	0.409414i	$-0.865733\pi$
$79$		−	7.27791i		−	0.818829i	0.912349	−	0.409414i	$-0.134267\pi$
$80$			2.17582i			0.243265i
$81$	7.63405	−	4.76668i	0.848228	−	0.529632i
$82$	−5.87226			−0.648483
$83$	10.4725			1.14951			0.574753	−	0.818327i	$-0.305098\pi$
$83$	10.4725			1.14951			0.574753	+	0.818327i	$0.305098\pi$
$84$	−1.56902	+	0.220376i	−0.171194	+	0.0240450i
$85$			2.17582i			0.236001i
$86$			0.252147i			0.0271898i
$87$	−1.04341	−	7.42885i	−0.111866	−	0.796457i
$88$	1.74515	−	2.82036i	0.186034	−	0.300652i
$89$		−	6.43234i		−	0.681827i	−0.940095	−	0.340914i	$-0.889264\pi$
$89$		−	6.43234i		−	0.681827i	0.940095	−	0.340914i	$-0.110736\pi$
$90$	1.79815	+	6.27492i	0.189542	+	0.661434i
$91$	−1.31740			−0.138101
$92$			0.247175i			0.0257697i
$93$	−0.684387	−	4.87266i	−0.0709676	−	0.505272i
$94$		−	3.78349i		−	0.390237i
$95$	11.0355			1.13221
$96$	0.240909	+	1.71522i	0.0245877	+	0.175058i
$97$	8.67647			0.880962			0.440481	−	0.897762i	$-0.354808\pi$
$97$	8.67647			0.880962			0.440481	+	0.897762i	$0.354808\pi$
$98$	−6.16320			−0.622577
$99$	2.70207	−	9.57595i	0.271569	−	0.962419i
$100$	0.265786			0.0265786
$101$	−12.4477			−1.23860			−0.619298	−	0.785156i	$-0.712583\pi$
$101$	−12.4477			−1.23860			−0.619298	+	0.785156i	$0.712583\pi$
$102$	0.240909	+	1.71522i	0.0238536	+	0.169832i
$103$	9.54941			0.940931			0.470465	−	0.882418i	$-0.344086\pi$
$103$	9.54941			0.940931			0.470465	+	0.882418i	$0.344086\pi$
$104$			1.44014i			0.141218i
$105$	−0.479500	−	3.41392i	−0.0467944	−	0.333164i
$106$		−	8.41459i		−	0.817297i
$107$	10.2480			0.990710			0.495355	−	0.868691i	$-0.335038\pi$
$107$	10.2480			0.990710			0.495355	+	0.868691i	$0.335038\pi$
$108$	2.11226	+	4.74746i	0.203252	+	0.456824i
$109$		−	6.33788i		−	0.607059i	−0.952822	−	0.303529i	$-0.901835\pi$
$109$		−	6.33788i		−	0.607059i	0.952822	−	0.303529i	$-0.0981651\pi$
$110$	6.13662	+	3.79714i	0.585103	+	0.362043i
$111$	−2.14195	−	15.2501i	−0.203305	−	1.44748i
$112$		−	0.914768i		−	0.0864374i
$113$		−	3.26821i		−	0.307448i	−0.988114	−	0.153724i	$-0.950873\pi$
$113$		−	3.26821i		−	0.307448i	0.988114	−	0.153724i	$-0.0491266\pi$
$114$	8.69932	−	1.22186i	0.814766	−	0.114437i
$115$	−0.537809			−0.0501509
$116$	4.33115			0.402137
$117$	1.19017	+	4.15326i	0.110031	+	0.383969i
$118$			8.62391i			0.793895i
$119$		−	0.914768i		−	0.0838566i
$120$	−3.73201	+	0.524177i	−0.340684	+	0.0478506i
$121$	−4.90889	−	9.84392i	−0.446263	−	0.894902i
$122$		−	8.16742i		−	0.739443i
$123$	−1.41468	−	10.0722i	−0.127558	−	0.908179i
$124$	2.84085			0.255116
$125$			11.4574i			1.02478i
$126$	−0.755985	−	2.63812i	−0.0673485	−	0.235023i
$127$		−	6.39050i		−	0.567066i	−0.958963	−	0.283533i	$-0.908494\pi$
$127$		−	6.39050i		−	0.567066i	0.958963	−	0.283533i	$-0.0915065\pi$
$128$	−1.00000			−0.0883883
$129$	−0.432487	+	0.0607447i	−0.0380784	+	0.00534827i
$130$	−3.13350			−0.274826
$131$	10.0658			0.879451			0.439725	−	0.898132i	$-0.355076\pi$
$131$	10.0658			0.879451			0.439725	+	0.898132i	$0.355076\pi$
$132$	5.25795	+	2.31386i	0.457646	+	0.201395i
$133$	−4.63957			−0.402301
$134$	−1.06805			−0.0922653
$135$	−10.3296	+	4.59590i	−0.889034	+	0.395552i
$136$	−1.00000			−0.0857493
$137$		−	1.76610i		−	0.150888i	−0.997150	−	0.0754440i	$-0.975963\pi$
$137$		−	1.76610i		−	0.150888i	0.997150	−	0.0754440i	$-0.0240374\pi$
$138$	−0.423958	+	0.0595467i	−0.0360897	+	0.00506895i
$139$		−	7.00740i		−	0.594360i	−0.954822	−	0.297180i	$-0.903954\pi$
$139$		−	7.00740i		−	0.594360i	0.954822	−	0.297180i	$-0.0960461\pi$
$140$	1.99037			0.168217
$141$	6.48950	−	0.911479i	0.546515	−	0.0767604i
$142$			8.84578i			0.742321i
$143$	4.06172	+	2.51327i	0.339658	+	0.210170i
$144$	−2.88393	+	0.826423i	−0.240327	+	0.0688686i
$145$			9.42382i			0.782606i
$146$		−	10.2675i		−	0.849742i
$147$	−1.48477	−	10.5712i	−0.122462	−	0.871899i
$148$	8.89109			0.730843
$149$	−18.1425			−1.48629			−0.743145	−	0.669131i	$-0.766667\pi$
$149$	−18.1425			−1.48629			−0.743145	+	0.669131i	$0.766667\pi$
$150$	0.0640304	+	0.455881i	0.00522806	+	0.0372225i
$151$			21.0005i			1.70900i	0.519454	+	0.854498i	$0.326135\pi$
$151$			21.0005i			1.70900i	−0.519454	+	0.854498i	$0.673865\pi$
$152$			5.07185i			0.411381i
$153$	−2.88393	+	0.826423i	−0.233152	+	0.0668123i
$154$	−2.57998	−	1.59641i	−0.207900	−	0.128642i
$155$			6.18119i			0.496485i
$156$	−2.47015	+	0.346944i	−0.197771	+	0.0277777i
$157$	−11.2519			−0.898003			−0.449001	−	0.893531i	$-0.648220\pi$
$157$	−11.2519			−0.898003			−0.449001	+	0.893531i	$0.648220\pi$
$158$			7.27791i			0.578999i
$159$	14.4328	−	2.02715i	1.14460	−	0.160764i
$160$		−	2.17582i		−	0.172014i
$161$	0.226107			0.0178198
$162$	−7.63405	+	4.76668i	−0.599788	+	0.374506i
$163$	−19.5363			−1.53020			−0.765101	−	0.643910i	$-0.777311\pi$
$163$	−19.5363			−1.53020			−0.765101	+	0.643910i	$0.777311\pi$
$164$	5.87226			0.458546
$165$	−5.03455	+	11.4404i	−0.391939	+	0.890633i
$166$	−10.4725			−0.812824
$167$	4.85714			0.375857			0.187928	−	0.982183i	$-0.439823\pi$
$167$	4.85714			0.375857			0.187928	+	0.982183i	$0.439823\pi$
$168$	1.56902	−	0.220376i	0.121053	−	0.0170024i
$169$	10.9260			0.840461
$170$		−	2.17582i		−	0.166878i
$171$	4.19149	+	14.6268i	0.320532	+	1.11854i
$172$		−	0.252147i		−	0.0192261i
$173$	18.2437			1.38704			0.693522	−	0.720436i	$-0.256058\pi$
$173$	18.2437			1.38704			0.693522	+	0.720436i	$0.256058\pi$
$174$	1.04341	+	7.42885i	0.0791011	+	0.563180i
$175$		−	0.243133i		−	0.0183791i
$176$	−1.74515	+	2.82036i	−0.131546	+	0.212593i
$177$	−14.7919	+	2.07758i	−1.11182	+	0.156161i
$178$			6.43234i			0.482125i
$179$		−	6.50862i		−	0.486477i	−0.969966	−	0.243239i	$-0.921790\pi$
$179$		−	6.50862i		−	0.486477i	0.969966	−	0.243239i	$-0.0782098\pi$
$180$	−1.79815	−	6.27492i	−0.134026	−	0.467705i
$181$	−1.17436			−0.0872895			−0.0436447	−	0.999047i	$-0.513897\pi$
$181$	−1.17436			−0.0872895			−0.0436447	+	0.999047i	$0.513897\pi$
$182$	1.31740			0.0976519
$183$	14.0089	−	1.96761i	1.03557	−	0.145450i
$184$		−	0.247175i		−	0.0182220i
$185$			19.3455i			1.42231i
$186$	0.684387	+	4.87266i	0.0501817	+	0.357281i
$187$	−1.74515	+	2.82036i	−0.127618	+	0.206245i
$188$			3.78349i			0.275940i
$189$	4.34282	−	1.93223i	0.315894	−	0.140549i
$190$	−11.0355			−0.800596
$191$		−	0.442002i		−	0.0319821i	−0.999872	−	0.0159911i	$-0.994910\pi$
$191$		−	0.442002i		−	0.0319821i	0.999872	−	0.0159911i	$-0.00509033\pi$
$192$	−0.240909	−	1.71522i	−0.0173861	−	0.123785i
$193$			19.1245i			1.37661i	0.725420	+	0.688307i	$0.241646\pi$
$193$			19.1245i			1.37661i	−0.725420	+	0.688307i	$0.758354\pi$
$194$	−8.67647			−0.622934
$195$	−0.754889	−	5.37462i	−0.0540587	−	0.384885i
$196$	6.16320			0.440229
$197$	−6.19505			−0.441379			−0.220690	−	0.975344i	$-0.570831\pi$
$197$	−6.19505			−0.441379			−0.220690	+	0.975344i	$0.570831\pi$
$198$	−2.70207	+	9.57595i	−0.192028	+	0.680533i
$199$	−18.0962			−1.28281			−0.641403	−	0.767204i	$-0.721647\pi$
$199$	−18.0962			−1.28281			−0.641403	+	0.767204i	$0.721647\pi$
$200$	−0.265786			−0.0187939
$201$	−0.257303	−	1.83193i	−0.0181487	−	0.129214i
$202$	12.4477			0.875819
$203$		−	3.96200i		−	0.278078i
$204$	−0.240909	−	1.71522i	−0.0168670	−	0.120089i
$205$			12.7770i			0.892385i
$206$	−9.54941			−0.665339
$207$	−0.204271	−	0.712833i	−0.0141978	−	0.0495453i
$208$		−	1.44014i		−	0.0998559i
$209$	14.3045	+	8.85115i	0.989460	+	0.612247i
$210$	0.479500	+	3.41392i	0.0330886	+	0.235583i
$211$		−	11.1612i		−	0.768366i	−0.923257	−	0.384183i	$-0.874483\pi$
$211$		−	11.1612i		−	0.768366i	0.923257	−	0.384183i	$-0.125517\pi$
$212$			8.41459i			0.577917i
$213$	−15.1724	+	2.13103i	−1.03960	+	0.146016i
$214$	−10.2480			−0.700538
$215$	0.548629			0.0374162
$216$	−2.11226	−	4.74746i	−0.143721	−	0.323024i
$217$		−	2.59871i		−	0.176412i
$218$			6.33788i			0.429255i
$219$	17.6109	−	2.47353i	1.19004	−	0.167146i
$220$	−6.13662	−	3.79714i	−0.413731	−	0.256003i
$221$		−	1.44014i		−	0.0968745i
$222$	2.14195	+	15.2501i	0.143758	+	1.02352i
$223$	−7.13541			−0.477822			−0.238911	−	0.971041i	$-0.576790\pi$
$223$	−7.13541			−0.477822			−0.238911	+	0.971041i	$0.576790\pi$
$224$			0.914768i			0.0611205i
$225$	−0.766508	+	0.219652i	−0.0511005	+	0.0146435i
$226$			3.26821i			0.217398i
$227$	−9.84285			−0.653293			−0.326646	−	0.945147i	$-0.605919\pi$
$227$	−9.84285			−0.653293			−0.326646	+	0.945147i	$0.605919\pi$
$228$	−8.69932	+	1.22186i	−0.576126	+	0.0809195i
$229$	16.3616			1.08120			0.540602	−	0.841278i	$-0.318196\pi$
$229$	16.3616			1.08120			0.540602	+	0.841278i	$0.318196\pi$
$230$	0.537809			0.0354621
$231$	2.11664	−	4.80981i	0.139265	−	0.316462i
$232$	−4.33115			−0.284354
$233$	3.47357			0.227561			0.113780	−	0.993506i	$-0.463704\pi$
$233$	3.47357			0.227561			0.113780	+	0.993506i	$0.463704\pi$
$234$	−1.19017	−	4.15326i	−0.0778036	−	0.271507i
$235$	−8.23222			−0.537011
$236$		−	8.62391i		−	0.561369i
$237$	−12.4832	+	1.75332i	−0.810870	+	0.113890i
$238$			0.914768i			0.0592956i
$239$	11.1467			0.721023			0.360512	−	0.932755i	$-0.382602\pi$
$239$	11.1467			0.721023			0.360512	+	0.932755i	$0.382602\pi$
$240$	3.73201	−	0.524177i	0.240900	−	0.0338355i
$241$		−	7.68610i		−	0.495105i	−0.968874	−	0.247553i	$-0.920374\pi$
$241$		−	7.68610i		−	0.495105i	0.968874	−	0.247553i	$-0.0796263\pi$
$242$	4.90889	+	9.84392i	0.315556	+	0.632791i
$243$	−10.0150	−	11.9457i	−0.642463	−	0.766317i
$244$			8.16742i			0.522865i
$245$			13.4100i			0.856736i
$246$	1.41468	+	10.0722i	0.0901969	+	0.642179i
$247$	−7.30419			−0.464754
$248$	−2.84085			−0.180394
$249$	−2.52292	−	17.9626i	−0.159884	−	1.13833i
$250$		−	11.4574i		−	0.724631i
$251$			28.0273i			1.76907i	0.466475	+	0.884534i	$0.345524\pi$
$251$			28.0273i			1.76907i	−0.466475	+	0.884534i	$0.654476\pi$
$252$	0.755985	+	2.63812i	0.0476226	+	0.166186i
$253$	−0.697122	−	0.431357i	−0.0438277	−	0.0271192i
$254$			6.39050i			0.400976i
$255$	3.73201	−	0.524177i	0.233707	−	0.0328252i
$256$	1.00000			0.0625000
$257$			12.8291i			0.800258i	0.916459	+	0.400129i	$0.131035\pi$
$257$			12.8291i			0.800258i	−0.916459	+	0.400129i	$0.868965\pi$
$258$	0.432487	−	0.0607447i	0.0269255	−	0.00378180i
$259$		−	8.13328i		−	0.505378i
$260$	3.13350			0.194331
$261$	−12.4907	+	3.57936i	−0.773156	+	0.221557i
$262$	−10.0658			−0.621865
$263$	−13.4262			−0.827896			−0.413948	−	0.910301i	$-0.635850\pi$
$263$	−13.4262			−0.827896			−0.413948	+	0.910301i	$0.635850\pi$
$264$	−5.25795	−	2.31386i	−0.323605	−	0.142408i
$265$	−18.3087			−1.12469
$266$	4.63957			0.284470
$267$	−11.0329	+	1.54961i	−0.675200	+	0.0948347i
$268$	1.06805			0.0652414
$269$		−	26.8511i		−	1.63714i	−0.574406	−	0.818571i	$-0.694767\pi$
$269$		−	26.8511i		−	1.63714i	0.574406	−	0.818571i	$-0.305233\pi$
$270$	10.3296	−	4.59590i	0.628642	−	0.279698i
$271$			23.4452i			1.42420i	0.702080	+	0.712098i	$0.252255\pi$
$271$			23.4452i			1.42420i	−0.702080	+	0.712098i	$0.747745\pi$
$272$	1.00000			0.0606339
$273$	0.317373	+	2.25962i	0.0192083	+	0.136758i
$274$			1.76610i			0.106694i
$275$	−0.463837	+	0.749614i	−0.0279704	+	0.0452034i
$276$	0.423958	−	0.0595467i	0.0255192	−	0.00358429i
$277$			23.8841i			1.43506i	0.696529	+	0.717528i	$0.254727\pi$
$277$			23.8841i			1.43506i	−0.696529	+	0.717528i	$0.745273\pi$
$278$			7.00740i			0.420276i
$279$	−8.19279	+	2.34774i	−0.490490	+	0.140556i
$280$	−1.99037			−0.118948
$281$	−18.7644			−1.11939			−0.559696	−	0.828698i	$-0.689082\pi$
$281$	−18.7644			−1.11939			−0.559696	+	0.828698i	$0.689082\pi$
$282$	−6.48950	+	0.911479i	−0.386444	+	0.0542778i
$283$			17.2516i			1.02550i	0.858537	+	0.512751i	$0.171374\pi$
$283$			17.2516i			1.02550i	−0.858537	+	0.512751i	$0.828626\pi$
$284$		−	8.84578i		−	0.524900i
$285$	−2.65855	−	18.9282i	−0.157479	−	1.12121i
$286$	−4.06172	−	2.51327i	−0.240175	−	0.148613i
$287$		−	5.37175i		−	0.317085i
$288$	2.88393	−	0.826423i	0.169937	−	0.0486974i
$289$	1.00000			0.0588235
$290$		−	9.42382i		−	0.553386i
$291$	−2.09024	−	14.8820i	−0.122532	−	0.872399i
$292$			10.2675i			0.600858i
$293$	−14.5425			−0.849582			−0.424791	−	0.905292i	$-0.639652\pi$
$293$	−14.5425			−0.849582			−0.424791	+	0.905292i	$0.639652\pi$
$294$	1.48477	+	10.5712i	0.0865937	+	0.616526i
$295$	18.7641			1.09249
$296$	−8.89109			−0.516784
$297$	−17.0758	−	2.32770i	−0.990836	−	0.135067i
$298$	18.1425			1.05097
$299$	0.355967			0.0205861
$300$	−0.0640304	−	0.455881i	−0.00369680	−	0.0263203i
$301$	−0.230656			−0.0132948
$302$		−	21.0005i		−	1.20844i
$303$	2.99878	+	21.3505i	0.172275	+	1.22656i
$304$		−	5.07185i		−	0.290891i
$305$	−17.7709			−1.01756
$306$	2.88393	−	0.826423i	0.164863	−	0.0472435i
$307$		−	8.39034i		−	0.478862i	−0.970913	−	0.239431i	$-0.923039\pi$
$307$		−	8.39034i		−	0.478862i	0.970913	−	0.239431i	$-0.0769609\pi$
$308$	2.57998	+	1.59641i	0.147008	+	0.0909638i
$309$	−2.30054	−	16.3793i	−0.130873	−	0.931785i
$310$		−	6.18119i		−	0.351068i
$311$		−	27.3529i		−	1.55104i	−0.631321	−	0.775522i	$-0.717487\pi$
$311$		−	27.3529i		−	1.55104i	0.631321	−	0.775522i	$-0.282513\pi$
$312$	2.47015	−	0.346944i	0.139845	−	0.0196418i
$313$	−8.44224			−0.477183			−0.238592	−	0.971120i	$-0.576686\pi$
$313$	−8.44224			−0.477183			−0.238592	+	0.971120i	$0.576686\pi$
$314$	11.2519			0.634984
$315$	−5.74009	+	1.64489i	−0.323417	+	0.0926791i
$316$		−	7.27791i		−	0.409414i
$317$		−	4.13694i		−	0.232354i	−0.993229	−	0.116177i	$-0.962936\pi$
$317$		−	4.13694i		−	0.232354i	0.993229	−	0.116177i	$-0.0370639\pi$
$318$	−14.4328	+	2.02715i	−0.809353	+	0.113677i
$319$	−7.55851	+	12.2154i	−0.423195	+	0.683932i
$320$			2.17582i			0.121632i
$321$	−2.46884	−	17.5775i	−0.137797	−	0.981080i
$322$	−0.226107			−0.0126005
$323$		−	5.07185i		−	0.282205i
$324$	7.63405	−	4.76668i	0.424114	−	0.264816i
$325$		−	0.382770i		−	0.0212323i
$326$	19.5363			1.08202
$327$	−10.8708	+	1.52686i	−0.601158	+	0.0844353i
$328$	−5.87226			−0.324241
$329$	3.46102			0.190812
$330$	5.03455	−	11.4404i	0.277143	−	0.629772i
$331$	24.6779			1.35642			0.678209	−	0.734869i	$-0.262757\pi$
$331$	24.6779			1.35642			0.678209	+	0.734869i	$0.262757\pi$
$332$	10.4725			0.574753
$333$	−25.6412	+	7.34780i	−1.40513	+	0.402657i
$334$	−4.85714			−0.265771
$335$			2.32388i			0.126967i
$336$	−1.56902	+	0.220376i	−0.0855972	+	0.0120225i
$337$		−	22.5600i		−	1.22892i	−0.788948	−	0.614460i	$-0.789374\pi$
$337$		−	22.5600i		−	1.22892i	0.788948	−	0.614460i	$-0.210626\pi$
$338$	−10.9260			−0.594295
$339$	−5.60569	+	0.787344i	−0.304459	+	0.0427626i
$340$			2.17582i			0.118001i
$341$	−4.95771	+	8.01222i	−0.268475	+	0.433886i
$342$	−4.19149	−	14.6268i	−0.226650	−	0.790929i
$343$		−	12.0413i		−	0.650167i
$344$			0.252147i			0.0135949i
$345$	0.129563	+	0.922457i	0.00697545	+	0.0496634i
$346$	−18.2437			−0.980788
$347$	−30.3795			−1.63086			−0.815429	−	0.578857i	$-0.803499\pi$
$347$	−30.3795			−1.63086			−0.815429	+	0.578857i	$0.803499\pi$
$348$	−1.04341	−	7.42885i	−0.0559329	−	0.398228i
$349$			31.2072i			1.67048i	0.549883	+	0.835242i	$0.314672\pi$
$349$			31.2072i			1.67048i	−0.549883	+	0.835242i	$0.685328\pi$
$350$			0.243133i			0.0129960i
$351$	6.83702	−	3.04195i	0.364933	−	0.162367i
$352$	1.74515	−	2.82036i	0.0930169	−	0.150326i
$353$			3.09718i			0.164846i	0.996597	+	0.0824231i	$0.0262659\pi$
$353$			3.09718i			0.164846i	−0.996597	+	0.0824231i	$0.973734\pi$
$354$	14.7919	−	2.07758i	0.786179	−	0.110422i
$355$	19.2469			1.02152
$356$		−	6.43234i		−	0.340914i
$357$	−1.56902	+	0.220376i	−0.0830415	+	0.0116635i
$358$			6.50862i			0.343991i
$359$	13.3438			0.704261			0.352131	−	0.935951i	$-0.385457\pi$
$359$	13.3438			0.704261			0.352131	+	0.935951i	$0.385457\pi$
$360$	1.79815	+	6.27492i	0.0947709	+	0.330717i
$361$	−6.72368			−0.353878
$362$	1.17436			0.0617230
$363$	−15.7018	+	10.7913i	−0.824133	+	0.566397i
$364$	−1.31740			−0.0690503
$365$	−22.3402			−1.16934
$366$	−14.0089	+	1.96761i	−0.732256	+	0.102849i
$367$	13.4260			0.700830			0.350415	−	0.936595i	$-0.386041\pi$
$367$	13.4260			0.700830			0.350415	+	0.936595i	$0.386041\pi$
$368$			0.247175i			0.0128849i
$369$	−16.9352	+	4.85297i	−0.881609	+	0.252636i
$370$		−	19.3455i		−	1.00572i
$371$	7.69740			0.399629
$372$	−0.684387	−	4.87266i	−0.0354838	−	0.252636i
$373$			3.95141i			0.204596i	0.994754	+	0.102298i	$0.0326196\pi$
$373$			3.95141i			0.204596i	−0.994754	+	0.102298i	$0.967380\pi$
$374$	1.74515	−	2.82036i	0.0902396	−	0.145837i
$375$	19.6520	−	2.76020i	1.01482	−	0.142536i
$376$		−	3.78349i		−	0.195119i
$377$		−	6.23747i		−	0.321246i
$378$	−4.34282	+	1.93223i	−0.223371	+	0.0993830i
$379$	10.6928			0.549255			0.274627	−	0.961551i	$-0.411445\pi$
$379$	10.6928			0.549255			0.274627	+	0.961551i	$0.411445\pi$
$380$	11.0355			0.566107
$381$	−10.9611	+	1.53953i	−0.561554	+	0.0788727i
$382$			0.442002i			0.0226148i
$383$			9.17107i			0.468620i	0.972162	+	0.234310i	$0.0752830\pi$
$383$			9.17107i			0.468620i	−0.972162	+	0.234310i	$0.924717\pi$
$384$	0.240909	+	1.71522i	0.0122939	+	0.0875292i
$385$	−3.47350	+	5.61358i	−0.177026	+	0.286094i
$386$		−	19.1245i		−	0.973412i
$387$	0.208380	+	0.727174i	0.0105926	+	0.0369643i
$388$	8.67647			0.440481
$389$		−	6.84500i		−	0.347055i	−0.984829	−	0.173528i	$-0.944483\pi$
$389$		−	6.84500i		−	0.347055i	0.984829	−	0.173528i	$-0.0555166\pi$
$390$	0.754889	+	5.37462i	0.0382253	+	0.272155i
$391$			0.247175i			0.0125002i
$392$	−6.16320			−0.311289
$393$	−2.42494	−	17.2650i	−0.122322	−	0.870902i
$394$	6.19505			0.312102
$395$	15.8355			0.796768
$396$	2.70207	−	9.57595i	0.135784	−	0.481210i
$397$	26.3151			1.32072			0.660359	−	0.750950i	$-0.270404\pi$
$397$	26.3151			1.32072			0.660359	+	0.750950i	$0.270404\pi$
$398$	18.0962			0.907081
$399$	1.11772	+	7.95785i	0.0559558	+	0.398391i
$400$	0.265786			0.0132893
$401$		−	27.8316i		−	1.38984i	−0.719086	−	0.694921i	$-0.755439\pi$
$401$		−	27.8316i		−	1.38984i	0.719086	−	0.694921i	$-0.244561\pi$
$402$	0.257303	+	1.83193i	0.0128331	+	0.0913684i
$403$		−	4.09122i		−	0.203798i
$404$	−12.4477			−0.619298
$405$	10.3715	+	16.6104i	0.515363	+	0.825375i
$406$			3.96200i			0.196631i
$407$	−15.5163	+	25.0761i	−0.769114	+	1.24298i
$408$	0.240909	+	1.71522i	0.0119268	+	0.0849158i
$409$			9.00961i			0.445497i	0.974876	+	0.222748i	$0.0715028\pi$
$409$			9.00961i			0.445497i	−0.974876	+	0.222748i	$0.928497\pi$
$410$		−	12.7770i		−	0.631012i
$411$	−3.02924	+	0.425470i	−0.149421	+	0.0209869i
$412$	9.54941			0.470465
$413$	−7.88888			−0.388186
$414$	0.204271	+	0.712833i	0.0100394	+	0.0350338i
$415$			22.7863i			1.11854i
$416$			1.44014i			0.0706088i
$417$	−12.0192	+	1.68815i	−0.588582	+	0.0826690i
$418$	−14.3045	−	8.85115i	−0.699654	−	0.432924i
$419$			3.93679i			0.192325i	0.995366	+	0.0961623i	$0.0306568\pi$
$419$			3.93679i			0.192325i	−0.995366	+	0.0961623i	$0.969343\pi$
$420$	−0.479500	−	3.41392i	−0.0233972	−	0.166582i
$421$	25.6268			1.24898			0.624488	−	0.781035i	$-0.285308\pi$
$421$	25.6268			1.24898			0.624488	+	0.781035i	$0.285308\pi$
$422$			11.1612i			0.543317i
$423$	−3.12677	−	10.9113i	−0.152029	−	0.530526i
$424$		−	8.41459i		−	0.408649i
$425$	0.265786			0.0128925
$426$	15.1724	−	2.13103i	0.735106	−	0.103249i
$427$	7.47129			0.361561
$428$	10.2480			0.495355
$429$	3.33228	−	7.57220i	0.160884	−	0.365589i
$430$	−0.548629			−0.0264572
$431$	−13.5935			−0.654775			−0.327387	−	0.944890i	$-0.606168\pi$
$431$	−13.5935			−0.654775			−0.327387	+	0.944890i	$0.606168\pi$
$432$	2.11226	+	4.74746i	0.101626	+	0.228412i
$433$	−11.5534			−0.555223			−0.277611	−	0.960693i	$-0.589543\pi$
$433$	−11.5534			−0.555223			−0.277611	+	0.960693i	$0.589543\pi$
$434$			2.59871i			0.124742i
$435$	16.1639	−	2.27029i	0.774999	−	0.108852i
$436$		−	6.33788i		−	0.303529i
$437$	1.25363			0.0599694
$438$	−17.6109	+	2.47353i	−0.841482	+	0.118190i
$439$		−	7.64064i		−	0.364668i	−0.983237	−	0.182334i	$-0.941635\pi$
$439$		−	7.64064i		−	0.364668i	0.983237	−	0.182334i	$-0.0583652\pi$
$440$	6.13662	+	3.79714i	0.292552	+	0.181022i
$441$	−17.7742	+	5.09341i	−0.846391	+	0.242543i
$442$			1.44014i			0.0685006i
$443$			12.5318i			0.595405i	0.954659	+	0.297702i	$0.0962203\pi$
$443$			12.5318i			0.595405i	−0.954659	+	0.297702i	$0.903780\pi$
$444$	−2.14195	−	15.2501i	−0.101652	−	0.723739i
$445$	13.9957			0.663458
$446$	7.13541			0.337871
$447$	4.37069	+	31.1182i	0.206727	+	1.47184i
$448$		−	0.914768i		−	0.0432187i
$449$			19.8841i			0.938389i	0.883095	+	0.469194i	$0.155456\pi$
$449$			19.8841i			0.938389i	−0.883095	+	0.469194i	$0.844544\pi$
$450$	0.766508	−	0.219652i	0.0361335	−	0.0103545i
$451$	−10.2480	+	16.5619i	−0.482559	+	0.779870i
$452$		−	3.26821i		−	0.153724i
$453$	36.0204	−	5.05922i	1.69238	−	0.237703i
$454$	9.84285			0.461948
$455$		−	2.86642i		−	0.134380i
$456$	8.69932	−	1.22186i	0.407383	−	0.0572187i
$457$		−	10.3076i		−	0.482170i	−0.970504	−	0.241085i	$-0.922497\pi$
$457$		−	10.3076i		−	0.482170i	0.970504	−	0.241085i	$-0.0775033\pi$
$458$	−16.3616			−0.764527
$459$	2.11226	+	4.74746i	0.0985918	+	0.221592i
$460$	−0.537809			−0.0250755
$461$	8.43677			0.392940			0.196470	−	0.980510i	$-0.437052\pi$
$461$	8.43677			0.392940			0.196470	+	0.980510i	$0.437052\pi$
$462$	−2.11664	+	4.80981i	−0.0984751	+	0.223772i
$463$	37.6708			1.75071			0.875356	−	0.483479i	$-0.160627\pi$
$463$	37.6708			1.75071			0.875356	+	0.483479i	$0.160627\pi$
$464$	4.33115			0.201069
$465$	10.6021	−	1.48911i	0.491659	−	0.0690556i
$466$	−3.47357			−0.160910
$467$		−	19.0628i		−	0.882121i	−0.897477	−	0.441060i	$-0.854602\pi$
$467$		−	19.0628i		−	0.882121i	0.897477	−	0.441060i	$-0.145398\pi$
$468$	1.19017	+	4.15326i	0.0550155	+	0.191985i
$469$		−	0.977016i		−	0.0451144i
$470$	8.23222			0.379724
$471$	2.71070	+	19.2995i	0.124902	+	0.889274i
$472$			8.62391i			0.396948i
$473$	0.711147	+	0.440035i	0.0326986	+	0.0202328i
$474$	12.4832	−	1.75332i	0.573372	−	0.0805325i
$475$		−	1.34803i		−	0.0618518i
$476$		−	0.914768i		−	0.0419283i
$477$	−6.95401	−	24.2671i	−0.318402	−	1.11111i
$478$	−11.1467			−0.509840
$479$	39.7520			1.81631			0.908157	−	0.418631i	$-0.137490\pi$
$479$	39.7520			1.81631			0.908157	+	0.418631i	$0.137490\pi$
$480$	−3.73201	+	0.524177i	−0.170342	+	0.0239253i
$481$		−	12.8044i		−	0.583832i
$482$			7.68610i			0.350092i
$483$	−0.0544714	−	0.387823i	−0.00247853	−	0.0176465i
$484$	−4.90889	−	9.84392i	−0.223132	−	0.447451i
$485$			18.8785i			0.857228i
$486$	10.0150	+	11.9457i	0.454290	+	0.541868i
$487$	−0.937948			−0.0425025			−0.0212512	−	0.999774i	$-0.506765\pi$
$487$	−0.937948			−0.0425025			−0.0212512	+	0.999774i	$0.506765\pi$
$488$		−	8.16742i		−	0.369722i
$489$	4.70648	+	33.5090i	0.212835	+	1.51533i
$490$		−	13.4100i		−	0.605804i
$491$	−31.4122			−1.41761			−0.708806	−	0.705404i	$-0.750766\pi$
$491$	−31.4122			−1.41761			−0.708806	+	0.705404i	$0.750766\pi$
$492$	−1.41468	−	10.0722i	−0.0637788	−	0.454089i
$493$	4.33115			0.195065
$494$	7.30419			0.328631
$495$	20.8356	+	5.87924i	0.936490	+	0.264252i
$496$	2.84085			0.127558
$497$	−8.09183			−0.362968
$498$	2.52292	+	17.9626i	0.113055	+	0.804923i
$499$	−0.818503			−0.0366412			−0.0183206	−	0.999832i	$-0.505832\pi$
$499$	−0.818503			−0.0366412			−0.0183206	+	0.999832i	$0.505832\pi$
$500$			11.4574i			0.512392i
$501$	−1.17013	−	8.33104i	−0.0522776	−	0.372203i
$502$		−	28.0273i		−	1.25092i
$503$	39.9957			1.78332			0.891660	−	0.452705i	$-0.149541\pi$
$503$	39.9957			1.78332			0.891660	+	0.452705i	$0.149541\pi$
$504$	−0.755985	−	2.63812i	−0.0336743	−	0.117511i
$505$		−	27.0841i		−	1.20523i
$506$	0.697122	+	0.431357i	0.0309909	+	0.0191762i
$507$	−2.63217	−	18.7404i	−0.116899	−	0.832291i
$508$		−	6.39050i		−	0.283533i
$509$			11.7713i			0.521755i	0.965372	+	0.260877i	$0.0840118\pi$
$509$			11.7713i			0.521755i	−0.965372	+	0.260877i	$0.915988\pi$
$510$	−3.73201	+	0.524177i	−0.165256	+	0.0232109i
$511$	9.39235			0.415493
$512$	−1.00000			−0.0441942
$513$	24.0784	−	10.7131i	1.06309	−	0.472993i
$514$		−	12.8291i		−	0.565868i
$515$			20.7778i			0.915581i
$516$	−0.432487	+	0.0607447i	−0.0190392	+	0.00267414i
$517$	−10.6708	−	6.60277i	−0.469302	−	0.290389i
$518$			8.13328i			0.357356i
$519$	−4.39508	−	31.2919i	−0.192923	−	1.37356i
$520$	−3.13350			−0.137413
$521$			11.7587i			0.515160i	0.966257	+	0.257580i	$0.0829250\pi$
$521$			11.7587i			0.515160i	−0.966257	+	0.257580i	$0.917075\pi$
$522$	12.4907	−	3.57936i	0.546704	−	0.156664i
$523$			9.37409i			0.409900i	0.978772	+	0.204950i	$0.0657032\pi$
$523$			9.37409i			0.409900i	−0.978772	+	0.204950i	$0.934297\pi$
$524$	10.0658			0.439725
$525$	−0.417025	+	0.0585730i	−0.0182005	+	0.00255633i
$526$	13.4262			0.585411
$527$	2.84085			0.123749
$528$	5.25795	+	2.31386i	0.228823	+	0.100698i
$529$	22.9389			0.997344
$530$	18.3087			0.795278
$531$	7.12700	+	24.8707i	0.309285	+	1.07930i
$532$	−4.63957			−0.201151
$533$		−	8.45689i		−	0.366309i
$534$	11.0329	−	1.54961i	0.477438	−	0.0670583i
$535$			22.2978i			0.964019i
$536$	−1.06805			−0.0461326
$537$	−11.1637	+	1.56799i	−0.481749	+	0.0676637i
$538$			26.8511i			1.15763i
$539$	−10.7557	+	17.3825i	−0.463281	+	0.748716i
$540$	−10.3296	+	4.59590i	−0.444517	+	0.197776i
$541$			21.9117i			0.942056i	0.882118	+	0.471028i	$0.156117\pi$
$541$			21.9117i			0.942056i	−0.882118	+	0.471028i	$0.843883\pi$
$542$		−	23.4452i		−	1.00706i
$543$	0.282914	+	2.01428i	0.0121410	+	0.0864410i
$544$	−1.00000			−0.0428746
$545$	13.7901			0.590704
$546$	−0.317373	−	2.25962i	−0.0135823	−	0.0967027i
$547$			14.4587i			0.618208i	0.951028	+	0.309104i	$0.100029\pi$
$547$			14.4587i			0.618208i	−0.951028	+	0.309104i	$0.899971\pi$
$548$		−	1.76610i		−	0.0754440i
$549$	−6.74974	−	23.5542i	−0.288072	−	1.00527i
$550$	0.463837	−	0.749614i	0.0197781	−	0.0319636i
$551$		−	21.9669i		−	0.935823i
$552$	−0.423958	+	0.0595467i	−0.0180448	+	0.00253448i
$553$	−6.65760			−0.283110
$554$		−	23.8841i		−	1.01474i
$555$	33.1816	−	4.66050i	1.40848	−	0.197827i
$556$		−	7.00740i		−	0.297180i
$557$	−25.5109			−1.08093			−0.540465	−	0.841366i	$-0.681752\pi$
$557$	−25.5109			−1.08093			−0.540465	+	0.841366i	$0.681752\pi$
$558$	8.19279	−	2.34774i	0.346828	−	0.0993878i
$559$	−0.363128			−0.0153587
$560$	1.99037			0.0841087
$561$	5.25795	+	2.31386i	0.221991	+	0.0976911i
$562$	18.7644			0.791530
$563$	−33.9687			−1.43161			−0.715805	−	0.698300i	$-0.753940\pi$
$563$	−33.9687			−1.43161			−0.715805	+	0.698300i	$0.753940\pi$
$564$	6.48950	−	0.911479i	0.273257	−	0.0383802i
$565$	7.11106			0.299165
$566$		−	17.2516i		−	0.725139i
$567$	−4.36041	−	6.98338i	−0.183120	−	0.293274i
$568$			8.84578i			0.371161i
$569$	−2.85245			−0.119581			−0.0597904	−	0.998211i	$-0.519043\pi$
$569$	−2.85245			−0.119581			−0.0597904	+	0.998211i	$0.519043\pi$
$570$	2.65855	+	18.9282i	0.111354	+	0.792815i
$571$		−	22.6869i		−	0.949418i	−0.880143	−	0.474709i	$-0.842553\pi$
$571$		−	22.6869i		−	0.949418i	0.880143	−	0.474709i	$-0.157447\pi$
$572$	4.06172	+	2.51327i	0.169829	+	0.105085i
$573$	−0.758128	+	0.106482i	−0.0316712	+	0.00444837i
$574$			5.37175i			0.224213i
$575$			0.0656956i			0.00273970i
$576$	−2.88393	+	0.826423i	−0.120164	+	0.0344343i
$577$	−46.7935			−1.94804			−0.974020	−	0.226462i	$-0.927284\pi$
$577$	−46.7935			−1.94804			−0.974020	+	0.226462i	$0.927284\pi$
$578$	−1.00000			−0.0415945
$579$	32.8027	−	4.60728i	1.36323	−	0.191472i
$580$			9.42382i			0.391303i
$581$		−	9.57990i		−	0.397441i
$582$	2.09024	+	14.8820i	0.0866434	+	0.616879i
$583$	−23.7322	−	14.6847i	−0.982887	−	0.608180i
$584$		−	10.2675i		−	0.424871i
$585$	−9.03677	+	2.58959i	−0.373625	+	0.107067i
$586$	14.5425			0.600745
$587$			26.0340i			1.07454i	0.843411	+	0.537268i	$0.180544\pi$
$587$			26.0340i			1.07454i	−0.843411	+	0.537268i	$0.819456\pi$
$588$	−1.48477	−	10.5712i	−0.0612310	−	0.435949i
$589$		−	14.4084i		−	0.593686i
$590$	−18.7641			−0.772507
$591$	1.49245	+	10.6258i	0.0613911	+	0.437089i
$592$	8.89109			0.365422
$593$	37.3886			1.53536			0.767682	−	0.640831i	$-0.221410\pi$
$593$	37.3886			1.53536			0.767682	+	0.640831i	$0.221410\pi$
$594$	17.0758	+	2.32770i	0.700627	+	0.0955067i
$595$	1.99037			0.0815974
$596$	−18.1425			−0.743145
$597$	4.35955	+	31.0389i	0.178424	+	1.27034i
$598$	−0.355967			−0.0145566
$599$		−	36.5393i		−	1.49296i	−0.665410	−	0.746478i	$-0.731743\pi$
$599$		−	36.5393i		−	1.49296i	0.665410	−	0.746478i	$-0.268257\pi$
$600$	0.0640304	+	0.455881i	0.00261403	+	0.0186112i
$601$		−	26.9639i		−	1.09988i	−0.835204	−	0.549940i	$-0.814651\pi$
$601$		−	26.9639i		−	1.09988i	0.835204	−	0.549940i	$-0.185349\pi$
$602$	0.230656			0.00940085
$603$	−3.08017	+	0.882659i	−0.125434	+	0.0359447i
$604$			21.0005i			0.854498i
$605$	21.4186	−	10.6809i	0.870792	−	0.434240i
$606$	−2.99878	−	21.3505i	−0.121817	−	0.867306i
$607$			1.76705i			0.0717224i	0.999357	+	0.0358612i	$0.0114174\pi$
$607$			1.76705i			0.0717224i	−0.999357	+	0.0358612i	$0.988583\pi$
$608$			5.07185i			0.205691i
$609$	−6.79567	+	0.954482i	−0.275375	+	0.0386776i
$610$	17.7709			0.719521
$611$	5.44877			0.220434
$612$	−2.88393	+	0.826423i	−0.116576	+	0.0334062i
$613$		−	9.53800i		−	0.385236i	−0.981274	−	0.192618i	$-0.938302\pi$
$613$		−	9.53800i		−	0.385236i	0.981274	−	0.192618i	$-0.0616979\pi$
$614$			8.39034i			0.338606i
$615$	21.9153	−	3.07810i	0.883711	−	0.124121i
$616$	−2.57998	−	1.59641i	−0.103950	−	0.0643211i
$617$		−	24.2686i		−	0.977016i	−0.872559	−	0.488508i	$-0.837541\pi$
$617$		−	24.2686i		−	0.977016i	0.872559	−	0.488508i	$-0.162459\pi$
$618$	2.30054	+	16.3793i	0.0925414	+	0.658871i
$619$	16.6083			0.667543			0.333771	−	0.942654i	$-0.391679\pi$
$619$	16.6083			0.667543			0.333771	+	0.942654i	$0.391679\pi$
$620$			6.18119i			0.248242i
$621$	−1.17345	+	0.522097i	−0.0470890	+	0.0209510i
$622$			27.3529i			1.09675i
$623$	−5.88410			−0.235742
$624$	−2.47015	+	0.346944i	−0.0988853	+	0.0138889i
$625$	−23.6004			−0.944017
$626$	8.44224			0.337420
$627$	11.7355	−	26.6676i	0.468672	−	1.06500i
$628$	−11.2519			−0.449001
$629$	8.89109			0.354511
$630$	5.74009	−	1.64489i	0.228691	−	0.0655340i
$631$	−13.6751			−0.544396			−0.272198	−	0.962241i	$-0.587750\pi$
$631$	−13.6751			−0.544396			−0.272198	+	0.962241i	$0.587750\pi$
$632$			7.27791i			0.289500i
$633$	−19.1438	+	2.68883i	−0.760897	+	0.106871i
$634$			4.13694i			0.164299i
$635$	13.9046			0.551788
$636$	14.4328	−	2.02715i	0.572299	−	0.0803819i
$637$		−	8.87589i		−	0.351675i
$638$	7.55851	−	12.2154i	0.299244	−	0.483613i
$639$	7.31036	+	25.5106i	0.289193	+	1.00918i
$640$		−	2.17582i		−	0.0860070i
$641$			5.65893i			0.223514i	0.993736	+	0.111757i	$0.0356479\pi$
$641$			5.65893i			0.223514i	−0.993736	+	0.111757i	$0.964352\pi$
$642$	2.46884	+	17.5775i	0.0974372	+	0.693728i
$643$	−48.7903			−1.92410			−0.962050	−	0.272872i	$-0.912027\pi$
$643$	−48.7903			−1.92410			−0.962050	+	0.272872i	$0.912027\pi$
$644$	0.226107			0.00890988
$645$	−0.132170	−	0.941016i	−0.00520418	−	0.0370525i
$646$			5.07185i			0.199549i
$647$		−	19.6385i		−	0.772067i	−0.922485	−	0.386034i	$-0.873845\pi$
$647$		−	19.6385i		−	0.772067i	0.922485	−	0.386034i	$-0.126155\pi$
$648$	−7.63405	+	4.76668i	−0.299894	+	0.187253i
$649$	24.3226	+	15.0500i	0.954744	+	0.590765i
$650$			0.382770i			0.0150135i
$651$	−4.45736	+	0.626055i	−0.174698	+	0.0245370i
$652$	−19.5363			−0.765101
$653$			8.06608i			0.315650i	0.987467	+	0.157825i	$0.0504482\pi$
$653$			8.06608i			0.315650i	−0.987467	+	0.157825i	$0.949552\pi$
$654$	10.8708	−	1.52686i	0.425083	−	0.0597048i
$655$			21.9014i			0.855757i
$656$	5.87226			0.229273
$657$	−8.48527	−	29.6106i	−0.331042	−	1.15522i
$658$	−3.46102			−0.134924
$659$	−19.7601			−0.769744			−0.384872	−	0.922970i	$-0.625754\pi$
$659$	−19.7601			−0.769744			−0.384872	+	0.922970i	$0.625754\pi$
$660$	−5.03455	+	11.4404i	−0.195970	+	0.445316i
$661$	10.2861			0.400082			0.200041	−	0.979788i	$-0.435892\pi$
$661$	10.2861			0.400082			0.200041	+	0.979788i	$0.435892\pi$
$662$	−24.6779			−0.959132
$663$	−2.47015	+	0.346944i	−0.0959328	+	0.0134742i
$664$	−10.4725			−0.406412
$665$		−	10.0949i		−	0.391463i
$666$	25.6412	−	7.34780i	0.993578	−	0.284722i
$667$			1.07055i			0.0414519i
$668$	4.85714			0.187928
$669$	1.71899	+	12.2388i	0.0664599	+	0.473178i
$670$		−	2.32388i		−	0.0897795i
$671$	−23.0351	−	14.2534i	−0.889259	−	0.550246i
$672$	1.56902	−	0.220376i	0.0605264	−	0.00850120i
$673$			8.16424i			0.314708i	0.987542	+	0.157354i	$0.0502964\pi$
$673$			8.16424i			0.314708i	−0.987542	+	0.157354i	$0.949704\pi$
$674$			22.5600i			0.868978i
$675$	0.561409	+	1.26181i	0.0216087	+	0.0485671i
$676$	10.9260			0.420230
$677$	−39.2910			−1.51008			−0.755039	−	0.655680i	$-0.772382\pi$
$677$	−39.2910			−1.51008			−0.755039	+	0.655680i	$0.772382\pi$
$678$	5.60569	−	0.787344i	0.215285	−	0.0302378i
$679$		−	7.93696i		−	0.304592i
$680$		−	2.17582i		−	0.0834391i
$681$	2.37123	+	16.8826i	0.0908659	+	0.646943i
$682$	4.95771	−	8.01222i	0.189840	−	0.306804i
$683$		−	27.0737i		−	1.03595i	−0.855397	−	0.517974i	$-0.826687\pi$
$683$		−	27.0737i		−	1.03595i	0.855397	−	0.517974i	$-0.173313\pi$
$684$	4.19149	+	14.6268i	0.160266	+	0.559271i
$685$	3.84272			0.146823
$686$			12.0413i			0.459738i
$687$	−3.94166	−	28.0636i	−0.150384	−	1.07069i
$688$		−	0.252147i		−	0.00961303i
$689$	12.1182			0.461667
$690$	−0.129563	−	0.922457i	−0.00493239	−	0.0351174i
$691$	−19.7932			−0.752970			−0.376485	−	0.926423i	$-0.622867\pi$
$691$	−19.7932			−0.752970			−0.376485	+	0.926423i	$0.622867\pi$
$692$	18.2437			0.693522
$693$	−8.75977	−	2.47177i	−0.332756	−	0.0938947i
$694$	30.3795			1.15319
$695$	15.2469			0.578347
$696$	1.04341	+	7.42885i	0.0395505	+	0.281590i
$697$	5.87226			0.222428
$698$		−	31.2072i		−	1.18121i
$699$	−0.836815	−	5.95792i	−0.0316513	−	0.225349i
$700$		−	0.243133i		−	0.00918955i
$701$	−16.3389			−0.617113			−0.308557	−	0.951206i	$-0.599846\pi$
$701$	−16.3389			−0.617113			−0.308557	+	0.951206i	$0.599846\pi$
$702$	−6.83702	+	3.04195i	−0.258047	+	0.114811i
$703$		−	45.0943i		−	1.70076i
$704$	−1.74515	+	2.82036i	−0.0657729	+	0.106296i
$705$	1.98322	+	14.1200i	0.0746923	+	0.531791i
$706$		−	3.09718i		−	0.116564i
$707$			11.3868i			0.428244i
$708$	−14.7919	+	2.07758i	−0.555912	+	0.0780803i
$709$	12.0220			0.451494			0.225747	−	0.974186i	$-0.427518\pi$
$709$	12.0220			0.451494			0.225747	+	0.974186i	$0.427518\pi$
$710$	−19.2469			−0.722322
$711$	6.01463	+	20.9889i	0.225566	+	0.787147i
$712$			6.43234i			0.241062i
$713$			0.702185i			0.0262970i
$714$	1.56902	−	0.220376i	0.0587192	−	0.00824737i
$715$	−5.46843	+	8.83760i	−0.204508	+	0.330508i
$716$		−	6.50862i		−	0.243239i
$717$	−2.68536	−	19.1191i	−0.100286	−	0.714015i
$718$	−13.3438			−0.497988
$719$		−	20.7975i		−	0.775615i	−0.921740	−	0.387808i	$-0.873233\pi$
$719$		−	20.7975i		−	0.775615i	0.921740	−	0.387808i	$-0.126767\pi$
$720$	−1.79815	−	6.27492i	−0.0670132	−	0.233852i
$721$		−	8.73549i		−	0.325327i
$722$	6.72368			0.250229
$723$	−13.1833	+	1.85165i	−0.490293	+	0.0688637i
$724$	−1.17436			−0.0436447
$725$	1.15116			0.0427530
$726$	15.7018	−	10.7913i	0.582750	−	0.400503i
$727$	10.6506			0.395007			0.197504	−	0.980302i	$-0.436717\pi$
$727$	10.6506			0.395007			0.197504	+	0.980302i	$0.436717\pi$
$728$	1.31740			0.0488259
$729$	−18.0767	+	20.0557i	−0.669509	+	0.742804i
$730$	22.3402			0.826848
$731$		−	0.252147i		−	0.00932601i
$732$	14.0089	−	1.96761i	0.517783	−	0.0727249i
$733$			20.6340i			0.762136i	0.924547	+	0.381068i	$0.124444\pi$
$733$			20.6340i			0.762136i	−0.924547	+	0.381068i	$0.875556\pi$
$734$	−13.4260			−0.495562
$735$	23.0011	−	3.23061i	0.848409	−	0.119163i
$736$		−	0.247175i		−	0.00911098i
$737$	−1.86390	+	3.01228i	−0.0686578	+	0.110959i
$738$	16.9352	−	4.85297i	0.623392	−	0.178640i
$739$		−	51.1652i		−	1.88214i	−0.338206	−	0.941072i	$-0.609820\pi$
$739$		−	51.1652i		−	1.88214i	0.338206	−	0.941072i	$-0.390180\pi$
$740$			19.3455i			0.711153i
$741$	1.75965	+	12.5283i	0.0646423	+	0.460237i
$742$	−7.69740			−0.282580
$743$	41.6655			1.52856			0.764279	−	0.644886i	$-0.223095\pi$
$743$	41.6655			1.52856			0.764279	+	0.644886i	$0.223095\pi$
$744$	0.684387	+	4.87266i	0.0250908	+	0.178641i
$745$		−	39.4748i		−	1.44625i
$746$		−	3.95141i		−	0.144671i
$747$	−30.2019	+	8.65471i	−1.10503	+	0.316659i
$748$	−1.74515	+	2.82036i	−0.0638090	+	0.103123i
$749$		−	9.37452i		−	0.342538i
$750$	−19.6520	+	2.76020i	−0.717588	+	0.100788i
$751$	32.2271			1.17598			0.587991	−	0.808867i	$-0.299919\pi$
$751$	32.2271			1.17598			0.587991	+	0.808867i	$0.299919\pi$
$752$			3.78349i			0.137970i
$753$	48.0729	−	6.75204i	1.75187	−	0.246058i
$754$			6.23747i			0.227155i
$755$	−45.6934			−1.66295
$756$	4.34282	−	1.93223i	0.157947	−	0.0702744i
$757$	−15.9581			−0.580007			−0.290004	−	0.957026i	$-0.593657\pi$
$757$	−15.9581			−0.580007			−0.290004	+	0.957026i	$0.593657\pi$
$758$	−10.6928			−0.388382
$759$	−0.571927	+	1.29963i	−0.0207596	+	0.0471737i
$760$	−11.0355			−0.400298
$761$	−42.3618			−1.53561			−0.767807	−	0.640681i	$-0.778652\pi$
$761$	−42.3618			−1.53561			−0.767807	+	0.640681i	$0.778652\pi$
$762$	10.9611	−	1.53953i	0.397078	−	0.0557714i
$763$	−5.79769			−0.209890
$764$		−	0.442002i		−	0.0159911i
$765$	−1.79815	−	6.27492i	−0.0650123	−	0.226870i
$766$		−	9.17107i		−	0.331364i
$767$	−12.4197			−0.448448
$768$	−0.240909	−	1.71522i	−0.00869307	−	0.0618925i
$769$		−	3.54522i		−	0.127844i	−0.997955	−	0.0639220i	$-0.979639\pi$
$769$		−	3.54522i		−	0.127844i	0.997955	−	0.0639220i	$-0.0203609\pi$
$770$	3.47350	−	5.61358i	0.125176	−	0.202299i
$771$	22.0047	−	3.09066i	0.792480	−	0.111307i
$772$			19.1245i			0.688307i
$773$			36.1807i			1.30133i	0.759365	+	0.650665i	$0.225510\pi$
$773$			36.1807i			1.30133i	−0.759365	+	0.650665i	$0.774490\pi$
$774$	−0.208380	−	0.727174i	−0.00749008	−	0.0261377i
$775$	0.755058			0.0271225
$776$	−8.67647			−0.311467
$777$	−13.9503	+	1.95938i	−0.500465	+	0.0702925i
$778$			6.84500i			0.245405i
$779$		−	29.7832i		−	1.06710i
$780$	−0.754889	−	5.37462i	−0.0270294	−	0.192442i
$781$	24.9483	+	15.4372i	0.892721	+	0.552387i
$782$		−	0.247175i		−	0.00883895i
$783$	9.14850	+	20.5620i	0.326941	+	0.734824i
$784$	6.16320			0.220114
$785$		−	24.4823i		−	0.873809i
$786$	2.42494	+	17.2650i	0.0864947	+	0.615821i
$787$		−	37.1678i		−	1.32489i	−0.749111	−	0.662444i	$-0.769519\pi$
$787$		−	37.1678i		−	1.32489i	0.749111	−	0.662444i	$-0.230481\pi$
$788$	−6.19505			−0.220690
$789$	3.23450	+	23.0288i	0.115151	+	0.819849i
$790$	−15.8355			−0.563400
$791$	−2.98966			−0.106300
$792$	−2.70207	+	9.57595i	−0.0960140	+	0.340267i
$793$	11.7622			0.417690
$794$	−26.3151			−0.933888
$795$	4.41073	+	31.4033i	0.156433	+	1.11376i
$796$	−18.0962			−0.641403
$797$		−	15.0101i		−	0.531686i	−0.964016	−	0.265843i	$-0.914350\pi$
$797$		−	15.0101i		−	0.531686i	0.964016	−	0.265843i	$-0.0856503\pi$
$798$	−1.11772	−	7.95785i	−0.0395667	−	0.281705i
$799$			3.78349i			0.133850i
$800$	−0.265786			−0.00939696
$801$	5.31584	+	18.5504i	0.187826	+	0.655446i
$802$			27.8316i			0.982767i
$803$	−28.9580	−	17.9183i	−1.02191	−	0.632322i
$804$	−0.257303	−	1.83193i	−0.00907437	−	0.0646072i
$805$			0.491970i			0.0173397i
$806$			4.09122i			0.144107i
$807$	−46.0554	+	6.46869i	−1.62123	+	0.227709i
$808$	12.4477			0.437910
$809$	−39.6860			−1.39529			−0.697643	−	0.716446i	$-0.745768\pi$
$809$	−39.6860			−1.39529			−0.697643	+	0.716446i	$0.745768\pi$
$810$	−10.3715	−	16.6104i	−0.364416	−	0.583628i
$811$		−	28.6519i		−	1.00610i	−0.864256	−	0.503052i	$-0.832210\pi$
$811$		−	28.6519i		−	1.00610i	0.864256	−	0.503052i	$-0.167790\pi$
$812$		−	3.96200i		−	0.139039i
$813$	40.2136	−	5.64817i	1.41035	−	0.198090i
$814$	15.5163	−	25.0761i	0.543846	−	0.878917i
$815$		−	42.5076i		−	1.48898i
$816$	−0.240909	−	1.71522i	−0.00843352	−	0.0600445i
$817$	−1.27885			−0.0447414
$818$		−	9.00961i		−	0.315014i
$819$	3.79927	−	1.08873i	0.132757	−	0.0380432i
$820$			12.7770i			0.446193i
$821$	5.69112			0.198621			0.0993107	−	0.995056i	$-0.468336\pi$
$821$	5.69112			0.198621			0.0993107	+	0.995056i	$0.468336\pi$
$822$	3.02924	−	0.425470i	0.105657	−	0.0148400i
$823$	−17.2088			−0.599863			−0.299931	−	0.953961i	$-0.596964\pi$
$823$	−17.2088			−0.599863			−0.299931	+	0.953961i	$0.596964\pi$
$824$	−9.54941			−0.332669
$825$	1.39749	+	0.614992i	0.0486544	+	0.0214113i
$826$	7.88888			0.274489
$827$	24.9576			0.867861			0.433930	−	0.900946i	$-0.357126\pi$
$827$	24.9576			0.867861			0.433930	+	0.900946i	$0.357126\pi$
$828$	−0.204271	−	0.712833i	−0.00709890	−	0.0247727i
$829$	35.8769			1.24606			0.623028	−	0.782199i	$-0.285902\pi$
$829$	35.8769			1.24606			0.623028	+	0.782199i	$0.285902\pi$
$830$		−	22.7863i		−	0.790925i
$831$	40.9664	−	5.75391i	1.42111	−	0.199601i
$832$		−	1.44014i		−	0.0499280i
$833$	6.16320			0.213542
$834$	12.0192	−	1.68815i	0.416191	−	0.0584558i
$835$			10.5683i			0.365731i
$836$	14.3045	+	8.85115i	0.494730	+	0.306123i
$837$	6.00060	+	13.4868i	0.207411	+	0.466172i
$838$		−	3.93679i		−	0.135994i
$839$			7.56333i			0.261115i	0.991441	+	0.130558i	$0.0416767\pi$
$839$			7.56333i			0.261115i	−0.991441	+	0.130558i	$0.958323\pi$
$840$	0.479500	+	3.41392i	0.0165443	+	0.117791i
$841$	−10.2411			−0.353143
$842$	−25.6268			−0.883159
$843$	4.52053	+	32.1850i	0.155695	+	1.10851i
$844$		−	11.1612i		−	0.384183i
$845$			23.7730i			0.817817i
$846$	3.12677	+	10.9113i	0.107500	+	0.375139i
$847$	−9.00490	+	4.49050i	−0.309412	+	0.154295i
$848$			8.41459i			0.288958i
$849$	29.5902	−	4.15608i	1.01553	−	0.142636i
$850$	−0.265786			−0.00911639
$851$			2.19765i			0.0753345i
$852$	−15.1724	+	2.13103i	−0.519798	+	0.0730079i
$853$			42.7805i			1.46478i	0.680887	+	0.732388i	$0.261594\pi$
$853$			42.7805i			1.46478i	−0.680887	+	0.732388i	$0.738406\pi$
$854$	−7.47129			−0.255662
$855$	−31.8254	+	9.11996i	−1.08841	+	0.311896i
$856$	−10.2480			−0.350269
$857$	−47.4820			−1.62195			−0.810977	−	0.585079i	$-0.801064\pi$
$857$	−47.4820			−1.62195			−0.810977	+	0.585079i	$0.801064\pi$
$858$	−3.33228	+	7.57220i	−0.113762	+	0.258511i
$859$	−12.5704			−0.428896			−0.214448	−	0.976735i	$-0.568795\pi$
$859$	−12.5704			−0.428896			−0.214448	+	0.976735i	$0.568795\pi$
$860$	0.548629			0.0187081
$861$	−9.21371	+	1.29411i	−0.314003	+	0.0441030i
$862$	13.5935			0.462996
$863$			19.5049i			0.663955i	0.943287	+	0.331978i	$0.107716\pi$
$863$			19.5049i			0.663955i	−0.943287	+	0.331978i	$0.892284\pi$
$864$	−2.11226	−	4.74746i	−0.0718605	−	0.161512i
$865$			39.6951i			1.34967i
$866$	11.5534			0.392602
$867$	−0.240909	−	1.71522i	−0.00818171	−	0.0582518i
$868$		−	2.59871i		−	0.0882061i
$869$	20.5263	+	12.7011i	0.696309	+	0.430854i
$870$	−16.1639	+	2.27029i	−0.548007	+	0.0769700i
$871$		−	1.53814i		−	0.0521179i
$872$			6.33788i			0.214628i
$873$	−25.0223	+	7.17044i	−0.846877	+	0.242683i
$874$	−1.25363			−0.0424048
$875$	10.4809			0.354319
$876$	17.6109	−	2.47353i	0.595018	−	0.0835728i
$877$		−	9.70412i		−	0.327685i	−0.986487	−	0.163842i	$-0.947611\pi$
$877$		−	9.70412i		−	0.327685i	0.986487	−	0.163842i	$-0.0523889\pi$
$878$			7.64064i			0.257859i
$879$	3.50343	+	24.9435i	0.118168	+	0.841324i
$880$	−6.13662	−	3.79714i	−0.206865	−	0.128002i
$881$		−	24.4424i		−	0.823484i	−0.911300	−	0.411742i	$-0.864920\pi$
$881$		−	24.4424i		−	0.823484i	0.911300	−	0.411742i	$-0.135080\pi$
$882$	17.7742	−	5.09341i	0.598489	−	0.171504i
$883$	−6.26852			−0.210953			−0.105476	−	0.994422i	$-0.533637\pi$
$883$	−6.26852			−0.210953			−0.105476	+	0.994422i	$0.533637\pi$
$884$		−	1.44014i		−	0.0484372i
$885$	−4.52045	−	32.1845i	−0.151953	−	1.08187i
$886$		−	12.5318i		−	0.421015i
$887$	51.1575			1.71770			0.858850	−	0.512227i	$-0.171179\pi$
$887$	51.1575			1.71770			0.858850	+	0.512227i	$0.171179\pi$
$888$	2.14195	+	15.2501i	0.0718791	+	0.511761i
$889$	−5.84583			−0.196063
$890$	−13.9957			−0.469135
$891$	0.121209	+	29.8494i	0.00406065	+	0.999992i
$892$	−7.13541			−0.238911
$893$	19.1893			0.642146
$894$	−4.37069	−	31.1182i	−0.146178	−	1.04075i
$895$	14.1616			0.473371
$896$			0.914768i			0.0305602i
$897$	−0.0857557	−	0.610559i	−0.00286330	−	0.0203860i
$898$		−	19.8841i		−	0.663541i
$899$	12.3041			0.410366
$900$	−0.766508	+	0.219652i	−0.0255503	+	0.00732173i
$901$			8.41459i			0.280331i
$902$	10.2480	−	16.5619i	0.341220	−	0.551451i
$903$	0.0555673	+	0.395625i	0.00184916	+	0.0131656i
$904$			3.26821i			0.108699i
$905$		−	2.55520i		−	0.0849377i
$906$	−36.0204	+	5.05922i	−1.19670	+	0.168081i
$907$	−32.1052			−1.06604			−0.533019	−	0.846104i	$-0.678942\pi$
$907$	−32.1052			−1.06604			−0.533019	+	0.846104i	$0.678942\pi$
$908$	−9.84285			−0.326646
$909$	35.8983	−	10.2871i	1.19067	−	0.341201i
$910$			2.86642i			0.0950210i
$911$		−	4.08946i		−	0.135490i	−0.997703	−	0.0677449i	$-0.978420\pi$
$911$		−	4.08946i		−	0.135490i	0.997703	−	0.0677449i	$-0.0215804\pi$
$912$	−8.69932	+	1.22186i	−0.288063	+	0.0404597i
$913$	−18.2761	+	29.5362i	−0.604850	+	0.977507i
$914$			10.3076i			0.340946i
$915$	4.28117	+	30.4809i	0.141531	+	1.00767i
$916$	16.3616			0.540602
$917$		−	9.20784i		−	0.304070i
$918$	−2.11226	−	4.74746i	−0.0697149	−	0.156689i
$919$		−	31.7709i		−	1.04802i	−0.851711	−	0.524012i	$-0.824435\pi$
$919$		−	31.7709i		−	1.04802i	0.851711	−	0.524012i	$-0.175565\pi$
$920$	0.537809			0.0177310
$921$	−14.3912	+	2.02131i	−0.474207	+	0.0666045i
$922$	−8.43677			−0.277850
$923$	−12.7392			−0.419315
$924$	2.11664	−	4.80981i	0.0696324	−	0.158231i
$925$	2.36313			0.0776992
$926$	−37.6708			−1.23794
$927$	−27.5398	+	7.89185i	−0.904525	+	0.259202i
$928$	−4.33115			−0.142177
$929$		−	19.5749i		−	0.642232i	−0.947040	−	0.321116i	$-0.895942\pi$
$929$		−	19.5749i		−	0.642232i	0.947040	−	0.321116i	$-0.104058\pi$
$930$	−10.6021	+	1.48911i	−0.347655	+	0.0488297i
$931$		−	31.2588i		−	1.02447i
$932$	3.47357			0.113780
$933$	−46.9162	+	6.58958i	−1.53597	+	0.215733i
$934$			19.0628i			0.623753i
$935$	−6.13662	−	3.79714i	−0.200689	−	0.124180i
$936$	−1.19017	−	4.15326i	−0.0389018	−	0.135754i
$937$		−	44.0152i		−	1.43791i	−0.695055	−	0.718956i	$-0.744620\pi$
$937$		−	44.0152i		−	1.43791i	0.695055	−	0.718956i	$-0.255380\pi$
$938$			0.977016i			0.0319007i
$939$	2.03381	+	14.4802i	0.0663710	+	0.472545i
$940$	−8.23222			−0.268505
$941$	−30.0760			−0.980450			−0.490225	−	0.871596i	$-0.663085\pi$
$941$	−30.0760			−0.980450			−0.490225	+	0.871596i	$0.663085\pi$
$942$	−2.71070	−	19.2995i	−0.0883194	−	0.628812i
$943$			1.45147i			0.0472665i
$944$		−	8.62391i		−	0.280684i
$945$	4.20418	+	9.44922i	0.136762	+	0.307383i
$946$	−0.711147	−	0.440035i	−0.0231214	−	0.0143068i
$947$			56.0844i			1.82250i	0.411858	+	0.911248i	$0.364880\pi$
$947$			56.0844i			1.82250i	−0.411858	+	0.911248i	$0.635120\pi$
$948$	−12.4832	+	1.75332i	−0.405435	+	0.0569451i
$949$	14.7866			0.479994
$950$			1.34803i			0.0437358i
$951$	−7.09574	+	0.996628i	−0.230095	+	0.0323179i
$952$			0.914768i			0.0296478i
$953$	50.0518			1.62134			0.810668	−	0.585506i	$-0.199104\pi$
$953$	50.0518			1.62134			0.810668	+	0.585506i	$0.199104\pi$
$954$	6.95401	+	24.2671i	0.225144	+	0.785675i
$955$	0.961718			0.0311205
$956$	11.1467			0.360512
$957$	22.7730	+	10.0217i	0.736146	+	0.323954i
$958$	−39.7520			−1.28433
$959$	−1.61557			−0.0521695
$960$	3.73201	−	0.524177i	0.120450	−	0.0169177i
$961$	−22.9296			−0.739664
$962$			12.8044i			0.412832i
$963$	−29.5544	+	8.46917i	−0.952378	+	0.272915i
$964$		−	7.68610i		−	0.247553i
$965$	−41.6116			−1.33953
$966$	0.0544714	+	0.387823i	0.00175259	+	0.0124780i
$967$			12.7298i			0.409362i	0.978829	+	0.204681i	$0.0656157\pi$
$967$			12.7298i			0.409362i	−0.978829	+	0.204681i	$0.934384\pi$
$968$	4.90889	+	9.84392i	0.157778	+	0.316396i
$969$	−8.69932	+	1.22186i	−0.279462	+	0.0392517i
$970$		−	18.8785i		−	0.606152i
$971$			4.13395i			0.132665i	0.997798	+	0.0663324i	$0.0211298\pi$
$971$			4.13395i			0.132665i	−0.997798	+	0.0663324i	$0.978870\pi$
$972$	−10.0150	−	11.9457i	−0.321231	−	0.383158i
$973$	−6.41014			−0.205500
$974$	0.937948			0.0300538
$975$	−0.656533	+	0.0922129i	−0.0210259	+	0.00295318i
$976$			8.16742i			0.261433i
$977$			4.49115i			0.143685i	0.997416	+	0.0718423i	$0.0228878\pi$
$977$			4.49115i			0.143685i	−0.997416	+	0.0718423i	$0.977112\pi$
$978$	−4.70648	−	33.5090i	−0.150497	−	1.07150i
$979$	18.1415	+	11.2254i	0.579806	+	0.358766i
$980$			13.4100i			0.428368i
$981$	5.23777	+	18.2780i	0.167229	+	0.583571i
$982$	31.4122			1.00240
$983$		−	16.2947i		−	0.519720i	−0.965646	−	0.259860i	$-0.916324\pi$
$983$		−	16.2947i		−	0.519720i	0.965646	−	0.259860i	$-0.0836765\pi$
$984$	1.41468	+	10.0722i	0.0450984	+	0.321090i
$985$		−	13.4794i		−	0.429488i
$986$	−4.33115			−0.137932
$987$	−0.833792	−	5.93639i	−0.0265399	−	0.188957i
$988$	−7.30419			−0.232377
$989$	0.0623244			0.00198180
$990$	−20.8356	−	5.87924i	−0.662198	−	0.186854i
$991$	−35.1812			−1.11757			−0.558784	−	0.829313i	$-0.688732\pi$
$991$	−35.1812			−1.11757			−0.558784	+	0.829313i	$0.688732\pi$
$992$	−2.84085			−0.0901970
$993$	−5.94513	−	42.3278i	−0.188663	−	1.34323i
$994$	8.09183			0.256657
$995$		−	39.3742i		−	1.24825i
$996$	−2.52292	−	17.9626i	−0.0799419	−	0.569166i
$997$			42.9151i			1.35913i	0.733614	+	0.679567i	$0.237832\pi$
$997$			42.9151i			1.35913i	−0.733614	+	0.679567i	$0.762168\pi$
$998$	0.818503			0.0259093
$999$	18.7803	+	42.2101i	0.594182	+	1.33547i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1122.2.b.a.1055.7	✓	16
3.2	odd	2		1122.2.b.c.1055.8	yes	16
11.10	odd	2		1122.2.b.c.1055.7	yes	16
33.32	even	2	inner	1122.2.b.a.1055.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1122.2.b.a.1055.7	✓	16	1.1	even	1	trivial
1122.2.b.a.1055.8	yes	16	33.32	even	2	inner
1122.2.b.c.1055.7	yes	16	11.10	odd	2
1122.2.b.c.1055.8	yes	16	3.2	odd	2

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:	\( N \)	\(=\)	\( 1122 = 2 \cdot 3 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1122.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.240909 - 1.71522i) q^{3} +1.00000 q^{4} +2.17582i q^{5} +(0.240909 + 1.71522i) q^{6} -0.914768i q^{7} -1.00000 q^{8} +(-2.88393 + 0.826423i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.240909 - 1.71522i) q^{3} +1.00000 q^{4} +2.17582i q^{5} +(0.240909 + 1.71522i) q^{6} -0.914768i q^{7} -1.00000 q^{8} +(-2.88393 + 0.826423i) q^{9} -2.17582i q^{10} +(-1.74515 + 2.82036i) q^{11} +(-0.240909 - 1.71522i) q^{12} -1.44014i q^{13} +0.914768i q^{14} +(3.73201 - 0.524177i) q^{15} +1.00000 q^{16} +1.00000 q^{17} +(2.88393 - 0.826423i) q^{18} -5.07185i q^{19} +2.17582i q^{20} +(-1.56902 + 0.220376i) q^{21} +(1.74515 - 2.82036i) q^{22} +0.247175i q^{23} +(0.240909 + 1.71522i) q^{24} +0.265786 q^{25} +1.44014i q^{26} +(2.11226 + 4.74746i) q^{27} -0.914768i q^{28} +4.33115 q^{29} +(-3.73201 + 0.524177i) q^{30} +2.84085 q^{31} -1.00000 q^{32} +(5.25795 + 2.31386i) q^{33} -1.00000 q^{34} +1.99037 q^{35} +(-2.88393 + 0.826423i) q^{36} +8.89109 q^{37} +5.07185i q^{38} +(-2.47015 + 0.346944i) q^{39} -2.17582i q^{40} +5.87226 q^{41} +(1.56902 - 0.220376i) q^{42} -0.252147i q^{43} +(-1.74515 + 2.82036i) q^{44} +(-1.79815 - 6.27492i) q^{45} -0.247175i q^{46} +3.78349i q^{47} +(-0.240909 - 1.71522i) q^{48} +6.16320 q^{49} -0.265786 q^{50} +(-0.240909 - 1.71522i) q^{51} -1.44014i q^{52} +8.41459i q^{53} +(-2.11226 - 4.74746i) q^{54} +(-6.13662 - 3.79714i) q^{55} +0.914768i q^{56} +(-8.69932 + 1.22186i) q^{57} -4.33115 q^{58} -8.62391i q^{59} +(3.73201 - 0.524177i) q^{60} +8.16742i q^{61} -2.84085 q^{62} +(0.755985 + 2.63812i) q^{63} +1.00000 q^{64} +3.13350 q^{65} +(-5.25795 - 2.31386i) q^{66} +1.06805 q^{67} +1.00000 q^{68} +(0.423958 - 0.0595467i) q^{69} -1.99037 q^{70} -8.84578i q^{71} +(2.88393 - 0.826423i) q^{72} +10.2675i q^{73} -8.89109 q^{74} +(-0.0640304 - 0.455881i) q^{75} -5.07185i q^{76} +(2.57998 + 1.59641i) q^{77} +(2.47015 - 0.346944i) q^{78} -7.27791i q^{79} +2.17582i q^{80} +(7.63405 - 4.76668i) q^{81} -5.87226 q^{82} +10.4725 q^{83} +(-1.56902 + 0.220376i) q^{84} +2.17582i q^{85} +0.252147i q^{86} +(-1.04341 - 7.42885i) q^{87} +(1.74515 - 2.82036i) q^{88} -6.43234i q^{89} +(1.79815 + 6.27492i) q^{90} -1.31740 q^{91} +0.247175i q^{92} +(-0.684387 - 4.87266i) q^{93} -3.78349i q^{94} +11.0355 q^{95} +(0.240909 + 1.71522i) q^{96} +8.67647 q^{97} -6.16320 q^{98} +(2.70207 - 9.57595i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{2} + q^{3} + 16 q^{4} - q^{6} - 16 q^{8} - 3 q^{9}+O(q^{10}) \) 16 * q - 16 * q^2 + q^3 + 16 * q^4 - q^6 - 16 * q^8 - 3 * q^9	\( 16 q - 16 q^{2} + q^{3} + 16 q^{4} - q^{6} - 16 q^{8} - 3 q^{9} + 6 q^{11} + q^{12} + 16 q^{16} + 16 q^{17} + 3 q^{18} + 24 q^{21} - 6 q^{22} - q^{24} - 22 q^{25} + 13 q^{27} - 20 q^{29} + 24 q^{31} - 16 q^{32} - 3 q^{33} - 16 q^{34} + 12 q^{35} - 3 q^{36} + 6 q^{37} - q^{39} + 22 q^{41} - 24 q^{42} + 6 q^{44} - 15 q^{45} + q^{48} - 54 q^{49} + 22 q^{50} + q^{51} - 13 q^{54} - 10 q^{55} + 8 q^{57} + 20 q^{58} - 24 q^{62} - 36 q^{63} + 16 q^{64} - 68 q^{65} + 3 q^{66} + 12 q^{67} + 16 q^{68} - 40 q^{69} - 12 q^{70} + 3 q^{72} - 6 q^{74} + q^{75} + 10 q^{77} + q^{78} + 17 q^{81} - 22 q^{82} - 10 q^{83} + 24 q^{84} + 12 q^{87} - 6 q^{88} + 15 q^{90} + 4 q^{91} + 6 q^{93} - 48 q^{95} - q^{96} + 54 q^{98} + 31 q^{99}+O(q^{100}) \) 16 * q - 16 * q^2 + q^3 + 16 * q^4 - q^6 - 16 * q^8 - 3 * q^9 + 6 * q^11 + q^12 + 16 * q^16 + 16 * q^17 + 3 * q^18 + 24 * q^21 - 6 * q^22 - q^24 - 22 * q^25 + 13 * q^27 - 20 * q^29 + 24 * q^31 - 16 * q^32 - 3 * q^33 - 16 * q^34 + 12 * q^35 - 3 * q^36 + 6 * q^37 - q^39 + 22 * q^41 - 24 * q^42 + 6 * q^44 - 15 * q^45 + q^48 - 54 * q^49 + 22 * q^50 + q^51 - 13 * q^54 - 10 * q^55 + 8 * q^57 + 20 * q^58 - 24 * q^62 - 36 * q^63 + 16 * q^64 - 68 * q^65 + 3 * q^66 + 12 * q^67 + 16 * q^68 - 40 * q^69 - 12 * q^70 + 3 * q^72 - 6 * q^74 + q^75 + 10 * q^77 + q^78 + 17 * q^81 - 22 * q^82 - 10 * q^83 + 24 * q^84 + 12 * q^87 - 6 * q^88 + 15 * q^90 + 4 * q^91 + 6 * q^93 - 48 * q^95 - q^96 + 54 * q^98 + 31 * q^99

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