LMFDB - Embedded newform 177.2.d.a.176.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,2,Mod(176,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("177.176");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	177.d (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:	$1.41335211578$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.19298288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} - 2x^{3} + 9x^{2} - 9x + 27 $ x^6 - x^5 + 3x^4 - 2x^3 + 9x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			176.6
Root			$1.34067 - 1.09664i$ of defining polynomial
Character	$\chi$	$=$	177.176
Dual form			177.2.d.a.176.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.93543 q^{2} +(-1.34067 + 1.09664i) q^{3} +1.74590 q^{4} +3.21911i q^{5} +(-2.59477 + 2.12247i) q^{6} +0.254102 q^{7} -0.491797 q^{8} +(0.594767 - 2.94045i) q^{9} +O(q^{10})$	\(q+1.93543 q^{2} +(-1.34067 + 1.09664i) q^{3} +1.74590 q^{4} +3.21911i q^{5} +(-2.59477 + 2.12247i) q^{6} +0.254102 q^{7} -0.491797 q^{8} +(0.594767 - 2.94045i) q^{9} +6.23037i q^{10} +5.68133 q^{11} +(-2.34067 + 1.91462i) q^{12} -2.66179i q^{13} +0.491797 q^{14} +(-3.53020 - 4.31575i) q^{15} -4.44364 q^{16} -4.03709i q^{17} +(1.15113 - 5.69104i) q^{18} -2.44364 q^{19} +5.62024i q^{20} +(-0.340665 + 0.278658i) q^{21} +10.9958 q^{22} +3.25410 q^{23} +(0.659335 - 0.539323i) q^{24} -5.36266 q^{25} -5.15172i q^{26} +(2.42723 + 4.59441i) q^{27} +0.443636 q^{28} -3.56857i q^{29} +(-6.83246 - 8.35284i) q^{30} +7.81351i q^{31} -7.61676 q^{32} +(-7.61676 + 6.23037i) q^{33} -7.81351i q^{34} +0.817981i q^{35} +(1.03840 - 5.13373i) q^{36} -5.15172i q^{37} -4.72949 q^{38} +(2.91903 + 3.56857i) q^{39} -1.58315i q^{40} +7.25620i q^{41} +(-0.659335 + 0.539323i) q^{42} -9.79894i q^{43} +9.91903 q^{44} +(9.46563 + 1.91462i) q^{45} +6.29809 q^{46} -5.06457 q^{47} +(5.95743 - 4.87306i) q^{48} -6.93543 q^{49} -10.3791 q^{50} +(4.42723 + 5.41239i) q^{51} -4.64722i q^{52} -1.16745i q^{53} +(4.69774 + 8.89216i) q^{54} +18.2888i q^{55} -0.124966 q^{56} +(3.27610 - 2.67979i) q^{57} -6.90673i q^{58} +(7.12497 - 2.86964i) q^{59} +(-6.16337 - 7.53486i) q^{60} +0.676366i q^{61} +15.1225i q^{62} +(0.151131 - 0.747174i) q^{63} -5.85446 q^{64} +8.56860 q^{65} +(-14.7417 + 12.0585i) q^{66} +2.66179i q^{67} -7.04835i q^{68} +(-4.36266 + 3.56857i) q^{69} +1.58315i q^{70} +16.2372i q^{71} +(-0.292504 + 1.44610i) q^{72} -13.1371i q^{73} -9.97081i q^{74} +(7.18953 - 5.88090i) q^{75} -4.26634 q^{76} +1.44364 q^{77} +(5.64958 + 6.90673i) q^{78} -11.7253 q^{79} -14.3045i q^{80} +(-8.29250 - 3.49777i) q^{81} +14.0439i q^{82} +9.91903 q^{83} +(-0.594767 + 0.486508i) q^{84} +12.9958 q^{85} -18.9652i q^{86} +(3.91344 + 4.78426i) q^{87} -2.79406 q^{88} -7.95184 q^{89} +(18.3201 + 3.70562i) q^{90} -0.676366i q^{91} +5.68133 q^{92} +(-8.56860 - 10.4753i) q^{93} -9.80213 q^{94} -7.86633i q^{95} +(10.2115 - 8.35284i) q^{96} -4.47535i q^{97} -13.4231 q^{98} +(3.37907 - 16.7057i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 4 q^{2} - q^{3} + 12 q^{4} - 7 q^{6} - 6 q^{8} - 5 q^{9}+O(q^{10}) $ 6 * q - 4 * q^2 - q^3 + 12 * q^4 - 7 * q^6 - 6 * q^8 - 5 * q^9	$ 6 q - 4 q^{2} - q^{3} + 12 q^{4} - 7 q^{6} - 6 q^{8} - 5 q^{9} + 20 q^{11} - 7 q^{12} + 6 q^{14} + 3 q^{15} - 8 q^{16} + 17 q^{18} + 4 q^{19} + 5 q^{21} + 2 q^{22} + 18 q^{23} + 11 q^{24} - 4 q^{25} + 2 q^{27} - 16 q^{28} - 37 q^{30} - 16 q^{32} - 16 q^{33} - 21 q^{36} - 36 q^{38} + 8 q^{39} - 11 q^{42} + 50 q^{44} + 17 q^{45} - 6 q^{46} - 46 q^{47} - q^{48} - 26 q^{49} - 28 q^{50} + 14 q^{51} + 8 q^{54} + 32 q^{56} - 3 q^{57} + 10 q^{59} + 23 q^{60} + 11 q^{63} - 10 q^{64} - 26 q^{66} + 2 q^{69} + 27 q^{72} + 26 q^{75} + 46 q^{76} - 10 q^{77} - 8 q^{78} - 14 q^{79} - 21 q^{81} + 50 q^{83} + 5 q^{84} + 14 q^{85} + 29 q^{87} - 40 q^{88} - 26 q^{89} + 45 q^{90} + 20 q^{92} + 52 q^{94} + 23 q^{96} - 4 q^{98} - 14 q^{99}+O(q^{100}) $ 6 * q - 4 * q^2 - q^3 + 12 * q^4 - 7 * q^6 - 6 * q^8 - 5 * q^9 + 20 * q^11 - 7 * q^12 + 6 * q^14 + 3 * q^15 - 8 * q^16 + 17 * q^18 + 4 * q^19 + 5 * q^21 + 2 * q^22 + 18 * q^23 + 11 * q^24 - 4 * q^25 + 2 * q^27 - 16 * q^28 - 37 * q^30 - 16 * q^32 - 16 * q^33 - 21 * q^36 - 36 * q^38 + 8 * q^39 - 11 * q^42 + 50 * q^44 + 17 * q^45 - 6 * q^46 - 46 * q^47 - q^48 - 26 * q^49 - 28 * q^50 + 14 * q^51 + 8 * q^54 + 32 * q^56 - 3 * q^57 + 10 * q^59 + 23 * q^60 + 11 * q^63 - 10 * q^64 - 26 * q^66 + 2 * q^69 + 27 * q^72 + 26 * q^75 + 46 * q^76 - 10 * q^77 - 8 * q^78 - 14 * q^79 - 21 * q^81 + 50 * q^83 + 5 * q^84 + 14 * q^85 + 29 * q^87 - 40 * q^88 - 26 * q^89 + 45 * q^90 + 20 * q^92 + 52 * q^94 + 23 * q^96 - 4 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$-1$

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 $

$2$	1.93543			1.36856			0.684279	−	0.729221i	$-0.260117\pi$
$2$	1.93543			1.36856			0.684279	+	0.729221i	$0.260117\pi$
$3$	−1.34067	+	1.09664i	−0.774033	+	0.633145i
$3$	−1.34067	+	1.09664i	−0.774033	+	0.633145i
$4$	1.74590			0.872949
$5$			3.21911i			1.43963i	0.694166	+	0.719815i	$0.255773\pi$
$5$			3.21911i			1.43963i	−0.694166	+	0.719815i	$0.744227\pi$
$6$	−2.59477	+	2.12247i	−1.05931	+	0.866495i
$7$	0.254102			0.0960414			0.0480207	−	0.998846i	$-0.484709\pi$
$7$	0.254102			0.0960414			0.0480207	+	0.998846i	$0.484709\pi$
$8$	−0.491797			−0.173876
$9$	0.594767	−	2.94045i	0.198256	−	0.980150i
$10$			6.23037i			1.97022i
$11$	5.68133			1.71299			0.856493	−	0.516159i	$-0.172639\pi$
$11$	5.68133			1.71299			0.856493	+	0.516159i	$0.172639\pi$
$12$	−2.34067	+	1.91462i	−0.675692	+	0.552703i
$13$		−	2.66179i		−	0.738249i	−0.929380	−	0.369124i	$-0.879658\pi$
$13$		−	2.66179i		−	0.738249i	0.929380	−	0.369124i	$-0.120342\pi$
$14$	0.491797			0.131438
$15$	−3.53020	−	4.31575i	−0.911494	−	1.11432i
$16$	−4.44364			−1.11091
$17$		−	4.03709i		−	0.979138i	−0.871965	−	0.489569i	$-0.837154\pi$
$17$		−	4.03709i		−	0.979138i	0.871965	−	0.489569i	$-0.162846\pi$
$18$	1.15113	−	5.69104i	0.271324	−	1.34139i
$19$	−2.44364			−0.560608			−0.280304	−	0.959911i	$-0.590435\pi$
$19$	−2.44364			−0.560608			−0.280304	+	0.959911i	$0.590435\pi$
$20$			5.62024i			1.25672i
$21$	−0.340665	+	0.278658i	−0.0743393	+	0.0608081i
$22$	10.9958			2.34432
$23$	3.25410			0.678527			0.339264	−	0.940691i	$-0.389822\pi$
$23$	3.25410			0.678527			0.339264	+	0.940691i	$0.389822\pi$
$24$	0.659335	−	0.539323i	0.134586	−	0.110089i
$25$	−5.36266			−1.07253
$26$		−	5.15172i		−	1.01034i
$27$	2.42723	+	4.59441i	0.467120	+	0.884194i
$28$	0.443636			0.0838393
$29$		−	3.56857i		−	0.662668i	−0.943514	−	0.331334i	$-0.892501\pi$
$29$		−	3.56857i		−	0.662668i	0.943514	−	0.331334i	$-0.107499\pi$
$30$	−6.83246	−	8.35284i	−1.24743	−	1.52501i
$31$			7.81351i			1.40335i	0.712498	+	0.701674i	$0.247564\pi$
$31$			7.81351i			1.40335i	−0.712498	+	0.701674i	$0.752436\pi$
$32$	−7.61676			−1.34647
$33$	−7.61676	+	6.23037i	−1.32591	+	1.08457i
$34$		−	7.81351i		−	1.34001i
$35$			0.817981i			0.138264i
$36$	1.03840	−	5.13373i	0.173067	−	0.855621i
$37$		−	5.15172i		−	0.846938i	−0.905911	−	0.423469i	$-0.860812\pi$
$37$		−	5.15172i		−	0.846938i	0.905911	−	0.423469i	$-0.139188\pi$
$38$	−4.72949			−0.767225
$39$	2.91903	+	3.56857i	0.467418	+	0.571429i
$40$		−	1.58315i		−	0.250317i
$41$			7.25620i			1.13323i	0.823983	+	0.566614i	$0.191747\pi$
$41$			7.25620i			1.13323i	−0.823983	+	0.566614i	$0.808253\pi$
$42$	−0.659335	+	0.539323i	−0.101738	+	0.0832194i
$43$		−	9.79894i		−	1.49432i	−0.664642	−	0.747162i	$-0.731416\pi$
$43$		−	9.79894i		−	1.49432i	0.664642	−	0.747162i	$-0.268584\pi$
$44$	9.91903			1.49535
$45$	9.46563	+	1.91462i	1.41105	+	0.285415i
$46$	6.29809			0.928603
$47$	−5.06457			−0.738743			−0.369372	−	0.929282i	$-0.620427\pi$
$47$	−5.06457			−0.738743			−0.369372	+	0.929282i	$0.620427\pi$
$48$	5.95743	−	4.87306i	0.859881	−	0.703366i
$49$	−6.93543			−0.990776
$50$	−10.3791			−1.46782
$51$	4.42723	+	5.41239i	0.619936	+	0.757886i
$52$		−	4.64722i		−	0.644454i
$53$		−	1.16745i		−	0.160361i	−0.996780	−	0.0801805i	$-0.974450\pi$
$53$		−	1.16745i		−	0.160361i	0.996780	−	0.0801805i	$-0.0255497\pi$
$54$	4.69774	+	8.89216i	0.639281	+	1.21007i
$55$			18.2888i			2.46606i
$56$	−0.124966			−0.0166993
$57$	3.27610	−	2.67979i	0.433930	−	0.354946i
$58$		−	6.90673i		−	0.906899i
$59$	7.12497	−	2.86964i	0.927592	−	0.373596i
$59$	7.12497	−	2.86964i	0.927592	−	0.373596i
$60$	−6.16337	−	7.53486i	−0.795688	−	0.972746i
$61$			0.676366i			0.0865998i	0.999062	+	0.0432999i	$0.0137871\pi$
$61$			0.676366i			0.0865998i	−0.999062	+	0.0432999i	$0.986213\pi$
$62$			15.1225i			1.92056i
$63$	0.151131	−	0.747174i	0.0190408	−	0.0941350i
$64$	−5.85446			−0.731807
$65$	8.56860			1.06280
$66$	−14.7417	+	12.0585i	−1.81458	+	1.48429i
$67$			2.66179i			0.325190i	0.986693	+	0.162595i	$0.0519864\pi$
$67$			2.66179i			0.325190i	−0.986693	+	0.162595i	$0.948014\pi$
$68$		−	7.04835i		−	0.854738i
$69$	−4.36266	+	3.56857i	−0.525203	+	0.429606i
$70$			1.58315i			0.189222i
$71$			16.2372i			1.92700i	0.267715	+	0.963498i	$0.413731\pi$
$71$			16.2372i			1.92700i	−0.267715	+	0.963498i	$0.586269\pi$
$72$	−0.292504	+	1.44610i	−0.0344720	+	0.170425i
$73$		−	13.1371i		−	1.53758i	−0.639501	−	0.768791i	$-0.720859\pi$
$73$		−	13.1371i		−	1.53758i	0.639501	−	0.768791i	$-0.279141\pi$
$74$		−	9.97081i		−	1.15908i
$75$	7.18953	−	5.88090i	0.830176	−	0.679068i
$76$	−4.26634			−0.489383
$77$	1.44364			0.164518
$78$	5.64958	+	6.90673i	0.639689	+	0.782034i
$79$	−11.7253			−1.31920			−0.659601	−	0.751616i	$-0.729275\pi$
$79$	−11.7253			−1.31920			−0.659601	+	0.751616i	$0.729275\pi$
$80$		−	14.3045i		−	1.59930i
$81$	−8.29250	−	3.49777i	−0.921389	−	0.388641i
$82$			14.0439i			1.55089i
$83$	9.91903			1.08875			0.544377	−	0.838841i	$-0.316766\pi$
$83$	9.91903			1.08875			0.544377	+	0.838841i	$0.316766\pi$
$84$	−0.594767	+	0.486508i	−0.0648944	+	0.0530824i
$85$	12.9958			1.40960
$86$		−	18.9652i		−	2.04507i
$87$	3.91344	+	4.78426i	0.419564	+	0.512927i
$88$	−2.79406			−0.297848
$89$	−7.95184			−0.842893			−0.421447	−	0.906853i	$-0.638478\pi$
$89$	−7.95184			−0.842893			−0.421447	+	0.906853i	$0.638478\pi$
$90$	18.3201	+	3.70562i	1.93111	+	0.390606i
$91$		−	0.676366i		−	0.0709024i
$92$	5.68133			0.592320
$93$	−8.56860	−	10.4753i	−0.888523	−	1.08624i
$94$	−9.80213			−1.01101
$95$		−	7.86633i		−	0.807068i
$96$	10.2115	−	8.35284i	1.04221	−	0.852508i
$97$		−	4.47535i		−	0.454403i	−0.973848	−	0.227202i	$-0.927042\pi$
$97$		−	4.47535i		−	0.454403i	0.973848	−	0.227202i	$-0.0729577\pi$
$98$	−13.4231			−1.35593
$99$	3.37907	−	16.7057i	0.339609	−	1.67898i
$100$	−9.36266			−0.936266
$101$	−4.85446			−0.483037			−0.241518	−	0.970396i	$-0.577645\pi$
$101$	−4.85446			−0.483037			−0.241518	+	0.970396i	$0.577645\pi$
$102$	8.56860	+	10.4753i	0.848418	+	1.03721i
$103$			12.4607i			1.22779i	0.789387	+	0.613896i	$0.210399\pi$
$103$			12.4607i			1.22779i	−0.789387	+	0.613896i	$0.789601\pi$
$104$			1.30906i			0.128364i
$105$	−0.897030	−	1.09664i	−0.0875411	−	0.107021i
$106$		−	2.25951i		−	0.219463i
$107$			9.91799i			0.958808i	0.877594	+	0.479404i	$0.159147\pi$
$107$			9.91799i			0.958808i	−0.877594	+	0.479404i	$0.840853\pi$
$108$	4.23769	+	8.02136i	0.407772	+	0.771856i
$109$		−	3.33816i		−	0.319738i	−0.987138	−	0.159869i	$-0.948893\pi$
$109$		−	3.33816i		−	0.319738i	0.987138	−	0.159869i	$-0.0511071\pi$
$110$			35.3968i			3.37495i
$111$	5.64958	+	6.90673i	0.536234	+	0.655558i
$112$	−1.12914			−0.106693
$113$	−4.69774			−0.441926			−0.220963	−	0.975282i	$-0.570920\pi$
$113$	−4.69774			−0.441926			−0.220963	+	0.975282i	$0.570920\pi$
$114$	6.34067	−	5.18654i	0.593858	−	0.485764i
$115$			10.4753i			0.976827i
$116$		−	6.23037i		−	0.578475i
$117$	−7.82687	−	1.58315i	−0.723595	−	0.146362i
$118$	13.7899	−	5.55400i	1.26946	−	0.511287i
$119$		−	1.02583i		−	0.0940378i
$120$	1.73614	+	2.12247i	0.158487	+	0.193754i
$121$	21.2775			1.93432
$122$			1.30906i			0.118517i
$123$	−7.95743	−	9.72813i	−0.717497	−	0.877156i
$124$			13.6416i			1.22505i
$125$		−	1.16745i		−	0.104420i
$126$	0.292504	−	1.44610i	0.0260584	−	0.128829i
$127$	2.62093			0.232570			0.116285	−	0.993216i	$-0.462901\pi$
$127$	2.62093			0.232570			0.116285	+	0.993216i	$0.462901\pi$
$128$	3.90262			0.344946
$129$	10.7459	+	13.1371i	0.946124	+	1.15666i
$130$	16.5839			1.45451
$131$	−16.8873			−1.47545			−0.737724	−	0.675103i	$-0.764099\pi$
$131$	−16.8873			−1.47545			−0.737724	+	0.675103i	$0.764099\pi$
$132$	−13.2981	+	10.8776i	−1.15745	+	0.946772i
$133$	−0.620932			−0.0538416
$134$			5.15172i			0.445041i
$135$	−14.7899	+	7.81351i	−1.27291	+	0.672480i
$136$			1.98543i			0.170249i
$137$		−	0.646115i		−	0.0552013i	−0.999619	−	0.0276007i	$-0.991213\pi$
$137$		−	0.646115i		−	0.0552013i	0.999619	−	0.0276007i	$-0.00878668\pi$
$138$	−8.44364	+	6.90673i	−0.718770	+	0.587940i
$139$	−12.5358			−1.06327			−0.531636	−	0.846973i	$-0.678422\pi$
$139$	−12.5358			−1.06327			−0.531636	+	0.846973i	$0.678422\pi$
$140$			1.42811i			0.120697i
$141$	6.78989	−	5.55400i	0.571812	−	0.467731i
$142$			31.4259i			2.63720i
$143$		−	15.1225i		−	1.26461i
$144$	−2.64293	+	13.0663i	−0.220244	+	1.08886i
$145$	11.4876			0.953996
$146$		−	25.4260i		−	2.10427i
$147$	9.29809	−	7.60566i	0.766894	−	0.627305i
$148$		−	8.99438i		−	0.739334i
$149$	−6.45481			−0.528799			−0.264399	−	0.964413i	$-0.585174\pi$
$149$	−6.45481			−0.528799			−0.264399	+	0.964413i	$0.585174\pi$
$150$	13.9149	−	11.3821i	1.13614	−	0.929344i
$151$		−	13.1371i		−	1.06908i	−0.845143	−	0.534541i	$-0.820484\pi$
$151$		−	13.1371i		−	1.06908i	0.845143	−	0.534541i	$-0.179516\pi$
$152$	1.20177			0.0974766
$153$	−11.8709	−	2.40113i	−0.959703	−	0.194120i
$154$	2.79406			0.225152
$155$	−25.1526			−2.02030
$156$	5.09632	+	6.23037i	0.408032	+	0.498829i
$157$		−	11.1517i		−	0.890000i	−0.895530	−	0.445000i	$-0.853204\pi$
$157$		−	11.1517i		−	0.890000i	0.895530	−	0.445000i	$-0.146796\pi$
$158$	−22.6936			−1.80540
$159$	1.28027	+	1.56515i	0.101532	+	0.124125i
$160$		−	24.5192i		−	1.93841i
$161$	0.826873			0.0651667
$162$	−16.0496	−	6.76969i	−1.26097	−	0.531877i
$163$	7.66075			0.600037			0.300018	−	0.953933i	$-0.403007\pi$
$163$	7.66075			0.600037			0.300018	+	0.953933i	$0.403007\pi$
$164$			12.6686i			0.989250i
$165$	−20.0562	−	24.5192i	−1.56138	−	1.90882i
$166$	19.1976			1.49002
$167$		−	12.5798i		−	0.973453i	−0.873554	−	0.486726i	$-0.838191\pi$
$167$		−	12.5798i		−	0.973453i	0.873554	−	0.486726i	$-0.161809\pi$
$168$	0.167538	−	0.137043i	0.0129258	−	0.0105731i
$169$	5.91486			0.454989
$170$	25.1526			1.92911
$171$	−1.45339	+	7.18539i	−0.111144	+	0.549481i
$172$		−	17.1080i		−	1.30447i
$173$	23.1854			1.76275			0.881375	−	0.472417i	$-0.156618\pi$
$173$	23.1854			1.76275			0.881375	+	0.472417i	$0.156618\pi$
$174$	7.57419	+	9.25962i	0.574198	+	0.701970i
$175$	−1.36266			−0.103008
$176$	−25.2458			−1.90297
$177$	−6.40523	+	11.6607i	−0.481447	+	0.876475i
$178$	−15.3902			−1.15355
$179$	14.8269			1.10821			0.554106	−	0.832446i	$-0.313060\pi$
$179$	14.8269			1.10821			0.554106	+	0.832446i	$0.313060\pi$
$180$	16.5260	+	3.34273i	1.23178	+	0.249152i
$181$	−2.76231			−0.205321			−0.102660	−	0.994716i	$-0.532735\pi$
$181$	−2.76231			−0.205321			−0.102660	+	0.994716i	$0.532735\pi$
$182$		−	1.30906i		−	0.0970341i
$183$	−0.741729	−	0.906781i	−0.0548302	−	0.0670312i
$184$	−1.60036			−0.117980
$185$	16.5839			1.21928
$186$	−16.5839	−	20.2742i	−1.21599	−	1.48658i
$187$		−	22.9360i		−	1.67725i
$188$	−8.84222			−0.644885
$189$	0.616763	+	1.16745i	0.0448629	+	0.0849192i
$190$		−	15.2247i		−	1.10452i
$191$	−4.69774			−0.339916			−0.169958	−	0.985451i	$-0.554363\pi$
$191$	−4.69774			−0.339916			−0.169958	+	0.985451i	$0.554363\pi$
$192$	7.84887	−	6.42023i	0.566443	−	0.463340i
$193$	−13.5686			−0.976689			−0.488345	−	0.872651i	$-0.662399\pi$
$193$	−13.5686			−0.976689			−0.488345	+	0.872651i	$0.662399\pi$
$194$		−	8.66175i		−	0.621877i
$195$	−11.4876	+	9.39666i	−0.822646	+	0.672909i
$196$	−12.1086			−0.864897
$197$			4.62466i			0.329493i	0.986336	+	0.164747i	$0.0526806\pi$
$197$			4.62466i			0.329493i	−0.986336	+	0.164747i	$0.947319\pi$
$198$	6.53996	−	32.3327i	0.464775	−	2.29779i
$199$	10.2541			0.726894			0.363447	−	0.931615i	$-0.381600\pi$
$199$	10.2541			0.726894			0.363447	+	0.931615i	$0.381600\pi$
$200$	2.63734			0.186488
$201$	−2.91903	−	3.56857i	−0.205892	−	0.251708i
$202$	−9.39547			−0.661063
$203$		−	0.906781i		−	0.0636435i
$204$	7.72949	+	9.44948i	0.541173	+	0.661596i
$205$	−23.3585			−1.63143
$206$			24.1169i			1.68030i
$207$	1.93543	−	9.56853i	0.134522	−	0.665059i
$208$			11.8280i			0.820127i
$209$	−13.8831			−0.960314
$210$	−1.73614	−	2.12247i	−0.119805	−	0.146464i
$211$			9.12257i			0.628024i	0.949419	+	0.314012i	$0.101673\pi$
$211$			9.12257i			0.628024i	−0.949419	+	0.314012i	$0.898327\pi$
$212$		−	2.03824i		−	0.139987i
$213$	−17.8063	−	21.7686i	−1.22007	−	1.49156i
$214$			19.1956i			1.31218i
$215$	31.5439			2.15127
$216$	−1.19370	−	2.25951i	−0.0812212	−	0.153740i
$217$			1.98543i			0.134780i
$218$		−	6.46078i		−	0.437579i
$219$	14.4067	+	17.6125i	0.973511	+	1.19014i
$220$			31.9304i			2.15275i
$221$	−10.7459			−0.722847
$222$	10.9344	+	13.3675i	0.733867	+	0.897169i
$223$	−11.2663			−0.754450			−0.377225	−	0.926122i	$-0.623122\pi$
$223$	−11.2663			−0.754450			−0.377225	+	0.926122i	$0.623122\pi$
$224$	−1.93543			−0.129317
$225$	−3.18953	+	15.7686i	−0.212636	+	1.05124i
$226$	−9.09215			−0.604801
$227$	−1.28692			−0.0854156			−0.0427078	−	0.999088i	$-0.513598\pi$
$227$	−1.28692			−0.0854156			−0.0427078	+	0.999088i	$0.513598\pi$
$228$	5.71973	−	4.67863i	0.378799	−	0.309850i
$229$			26.9506i			1.78094i	0.455038	+	0.890472i	$0.349626\pi$
$229$			26.9506i			1.78094i	−0.455038	+	0.890472i	$0.650374\pi$
$230$			20.2742i			1.33684i
$231$	−1.93543	+	1.58315i	−0.127342	+	0.104163i
$232$			1.75501i			0.115222i
$233$	5.52461			0.361929			0.180965	−	0.983490i	$-0.442078\pi$
$233$	5.52461			0.361929			0.180965	+	0.983490i	$0.442078\pi$
$234$	−15.1484	−	3.06407i	−0.990281	−	0.200305i
$235$		−	16.3034i		−	1.06352i
$236$	12.4395	−	5.01011i	0.809740	−	0.326130i
$237$	15.7197	−	12.8584i	1.02111	−	0.835246i
$238$		−	1.98543i		−	0.128696i
$239$			14.7428i			0.953633i	0.879003	+	0.476817i	$0.158209\pi$
$239$			14.7428i			0.953633i	−0.879003	+	0.476817i	$0.841791\pi$
$240$	15.6869	+	19.1776i	1.01259	+	1.23791i
$241$	0.777652			0.0500930			0.0250465	−	0.999686i	$-0.492027\pi$
$241$	0.777652			0.0500930			0.0250465	+	0.999686i	$0.492027\pi$
$242$	41.1812			2.64723
$243$	14.9533	−	4.40455i	0.959252	−	0.282552i
$244$			1.18087i			0.0755972i
$245$		−	22.3259i		−	1.42635i
$246$	−15.4011	−	18.8281i	−0.981936	−	1.20044i
$247$			6.50445i			0.413868i
$248$		−	3.84266i		−	0.244009i
$249$	−13.2981	+	10.8776i	−0.842732	+	0.689339i
$250$		−	2.25951i		−	0.142904i
$251$		−	13.5226i		−	0.853536i	−0.904361	−	0.426768i	$-0.859652\pi$
$251$		−	13.5226i		−	0.853536i	0.904361	−	0.426768i	$-0.140348\pi$
$252$	0.263860	−	1.30449i	0.0166216	−	0.0821751i
$253$	18.4876			1.16231
$254$	5.07264			0.318286
$255$	−17.4231	+	14.2517i	−1.09107	+	0.892478i
$256$	19.2622			1.20389
$257$			17.1214i			1.06800i	0.845484	+	0.534001i	$0.179312\pi$
$257$			17.1214i			1.06800i	−0.845484	+	0.534001i	$0.820688\pi$
$258$	20.7980	+	25.4260i	1.29482	+	1.58295i
$259$		−	1.30906i		−	0.0813411i
$260$	14.9599			0.927774
$261$	−10.4932	−	2.12247i	−0.649514	−	0.131378i
$262$	−32.6842			−2.01923
$263$			26.3327i			1.62375i	0.583833	+	0.811873i	$0.301552\pi$
$263$			26.3327i			1.62375i	−0.583833	+	0.811873i	$0.698448\pi$
$264$	3.74590	−	3.06407i	0.230544	−	0.188581i
$265$	3.75814			0.230860
$266$	−1.20177			−0.0736854
$267$	10.6608	−	8.72029i	0.652428	−	0.533673i
$268$			4.64722i			0.283874i
$269$	15.6402			0.953599			0.476799	−	0.879012i	$-0.341797\pi$
$269$	15.6402			0.953599			0.476799	+	0.879012i	$0.341797\pi$
$270$	−28.6248	+	15.1225i	−1.74205	+	0.920328i
$271$	26.2663			1.59557			0.797783	−	0.602944i	$-0.206006\pi$
$271$	26.2663			1.59557			0.797783	+	0.602944i	$0.206006\pi$
$272$			17.9394i			1.08773i
$273$	0.741729	+	0.906781i	0.0448915	+	0.0548809i
$274$		−	1.25051i		−	0.0755462i
$275$	−30.4671			−1.83723
$276$	−7.61676	+	6.23037i	−0.458475	+	0.375024i
$277$	−19.0552			−1.14491			−0.572457	−	0.819935i	$-0.694010\pi$
$277$	−19.0552			−1.14491			−0.572457	+	0.819935i	$0.694010\pi$
$278$	−24.2622			−1.45515
$279$	22.9753	+	4.64722i	1.37549	+	0.278222i
$280$		−	0.402280i		−	0.0240408i
$281$		−	13.4338i		−	0.801390i	−0.916211	−	0.400695i	$-0.868769\pi$
$281$		−	13.4338i		−	0.801390i	0.916211	−	0.400695i	$-0.131231\pi$
$282$	13.1414	−	10.7494i	0.782557	−	0.640117i
$283$		−	18.9652i		−	1.12736i	−0.825992	−	0.563682i	$-0.809384\pi$
$283$		−	18.9652i		−	1.12736i	0.825992	−	0.563682i	$-0.190616\pi$
$284$			28.3484i			1.68217i
$285$	8.62652	+	10.5461i	0.510991	+	0.624698i
$286$		−	29.2686i		−	1.73069i
$287$			1.84381i			0.108837i
$288$	−4.53020	+	22.3967i	−0.266945	+	1.31974i
$289$	0.701906			0.0412886
$290$	22.2335			1.30560
$291$	4.90785	+	5.99995i	0.287703	+	0.351723i
$292$		−	22.9360i		−	1.34223i
$293$		−	6.40797i		−	0.374357i	−0.982326	−	0.187179i	$-0.940066\pi$
$293$		−	6.40797i		−	0.374357i	0.982326	−	0.187179i	$-0.0599343\pi$
$294$	17.9958	−	14.7202i	1.04954	−	0.858502i
$295$	9.23769	+	22.9360i	0.537839	+	1.33539i
$296$			2.53360i			0.147262i
$297$	13.7899	+	26.1023i	0.800171	+	1.51461i
$298$	−12.4929			−0.723692
$299$		−	8.66175i		−	0.500922i
$300$	12.5522	−	10.2675i	0.724701	−	0.592792i
$301$		−	2.48993i		−	0.143517i
$302$		−	25.4260i		−	1.46310i
$303$	6.50820	−	5.32359i	0.373887	−	0.305832i
$304$	10.8586			0.622785
$305$	−2.17730			−0.124672
$306$	−22.9753	−	4.64722i	−1.31341	−	0.265664i
$307$	13.9149			0.794163			0.397081	−	0.917783i	$-0.370023\pi$
$307$	13.9149			0.794163			0.397081	+	0.917783i	$0.370023\pi$
$308$	2.52044			0.143615
$309$	−13.6649	−	16.7057i	−0.777370	−	0.950353i
$310$	−48.6811			−2.76490
$311$			1.60571i			0.0910515i	0.998963	+	0.0455258i	$0.0144963\pi$
$311$			1.60571i			0.0910515i	−0.998963	+	0.0455258i	$0.985504\pi$
$312$	−1.43557	−	1.75501i	−0.0812730	−	0.0993580i
$313$			26.1023i			1.47539i	0.675133	+	0.737696i	$0.264086\pi$
$313$			26.1023i			1.47539i	−0.675133	+	0.737696i	$0.735914\pi$
$314$		−	21.5833i		−	1.21802i
$315$	2.40523	+	0.486508i	0.135520	+	0.0274116i
$316$	−20.4712			−1.15160
$317$			9.27761i			0.521083i	0.965463	+	0.260541i	$0.0839010\pi$
$317$			9.27761i			0.521083i	−0.965463	+	0.260541i	$0.916099\pi$
$318$	2.47787	+	3.02925i	0.138952	+	0.169872i
$319$		−	20.2742i		−	1.13514i
$320$		−	18.8461i		−	1.05353i
$321$	−10.8765	−	13.2967i	−0.607064	−	0.742150i
$322$	1.60036			0.0891844
$323$			9.86518i			0.548913i
$324$	−14.4779	−	6.10674i	−0.804326	−	0.339264i
$325$			14.2743i			0.791795i
$326$	14.8269			0.821185
$327$	3.66075	+	4.47535i	0.202440	+	0.247488i
$328$		−	3.56857i		−	0.197042i
$329$	−1.28692			−0.0709499
$330$	−38.8175	−	47.4552i	−2.13683	−	2.61232i
$331$	25.0932			1.37925			0.689624	−	0.724168i	$-0.257776\pi$
$331$	25.0932			1.37925			0.689624	+	0.724168i	$0.257776\pi$
$332$	17.3176			0.950427
$333$	−15.1484	−	3.06407i	−0.830126	−	0.167910i
$334$		−	24.3473i		−	1.33223i
$335$	−8.56860			−0.468153
$336$	1.51379	−	1.23825i	0.0825842	−	0.0675523i
$337$			20.7787i			1.13189i	0.824443	+	0.565945i	$0.191489\pi$
$337$			20.7787i			1.13189i	−0.824443	+	0.565945i	$0.808511\pi$
$338$	11.4478			0.622678
$339$	6.29809	−	5.15172i	0.342065	−	0.279803i
$340$	22.6894			1.23051
$341$			44.3912i			2.40392i
$342$	−2.81295	+	13.9068i	−0.152107	+	0.751996i
$343$	−3.54102			−0.191197
$344$			4.81909i			0.259828i
$345$	−11.4876	−	14.0439i	−0.618473	−	0.756097i
$346$	44.8737			2.41243
$347$	−1.75708			−0.0943248			−0.0471624	−	0.998887i	$-0.515018\pi$
$347$	−1.75708			−0.0943248			−0.0471624	+	0.998887i	$0.515018\pi$
$348$	6.83246	+	8.35284i	0.366258	+	0.447759i
$349$			9.79894i			0.524525i	0.964997	+	0.262263i	$0.0844687\pi$
$349$			9.79894i			0.524525i	−0.964997	+	0.262263i	$0.915531\pi$
$350$	−2.63734			−0.140972
$351$	12.2294	−	6.46078i	0.652755	−	0.344851i
$352$	−43.2733			−2.30648
$353$	−27.2130			−1.44840			−0.724200	−	0.689590i	$-0.757791\pi$
$353$	−27.2130			−1.44840			−0.724200	+	0.689590i	$0.757791\pi$
$354$	−12.3969	+	22.5686i	−0.658888	+	1.19951i
$355$	−52.2692			−2.77416
$356$	−13.8831			−0.735803
$357$	1.12497	+	1.37530i	0.0595395	+	0.0727884i
$358$	28.6964			1.51665
$359$		−	4.24494i		−	0.224039i	−0.993706	−	0.112020i	$-0.964268\pi$
$359$		−	4.24494i		−	0.224039i	0.993706	−	0.112020i	$-0.0357320\pi$
$360$	−4.65517	−	0.941604i	−0.245349	−	0.0496269i
$361$	−13.0286			−0.685718
$362$	−5.34625			−0.280993
$363$	−28.5260	+	23.3338i	−1.49723	+	1.22470i
$364$		−	1.18087i		−	0.0618942i
$365$	42.2898			2.21355
$366$	−1.43557	−	1.75501i	−0.0750383	−	0.0917360i
$367$		−	23.6124i		−	1.23256i	−0.787528	−	0.616279i	$-0.788639\pi$
$367$		−	23.6124i		−	1.23256i	0.787528	−	0.616279i	$-0.211361\pi$
$368$	−14.4600			−0.753782
$369$	21.3365	+	4.31575i	1.11073	+	0.224669i
$370$	32.0971			1.66865
$371$		−	0.296650i		−	0.0154013i
$372$	−14.9599	−	18.2888i	−0.775635	−	0.948231i
$373$	21.5040			1.11344			0.556718	−	0.830701i	$-0.312060\pi$
$373$	21.5040			1.11344			0.556718	+	0.830701i	$0.312060\pi$
$374$		−	44.3912i		−	2.29541i
$375$	1.28027	+	1.56515i	0.0661127	+	0.0808242i
$376$	2.49074			0.128450
$377$	−9.49881			−0.489213
$378$	1.19370	+	2.25951i	0.0613975	+	0.116217i
$379$	14.9588			0.768384			0.384192	−	0.923253i	$-0.374480\pi$
$379$	14.9588			0.768384			0.384192	+	0.923253i	$0.374480\pi$
$380$		−	13.7338i		−	0.704530i
$381$	−3.51379	+	2.87422i	−0.180017	+	0.147251i
$382$	−9.09215			−0.465195
$383$			9.38324i			0.479461i	0.970839	+	0.239731i	$0.0770591\pi$
$383$			9.38324i			0.479461i	−0.970839	+	0.239731i	$0.922941\pi$
$384$	−5.23211	+	4.27976i	−0.267000	+	0.218401i
$385$			4.64722i			0.236844i
$386$	−26.2611			−1.33666
$387$	−28.8133	−	5.82809i	−1.46466	−	0.296258i
$388$		−	7.81351i		−	0.396671i
$389$		−	1.39786i		−	0.0708743i	−0.999372	−	0.0354372i	$-0.988718\pi$
$389$		−	1.39786i		−	0.0708743i	0.999372	−	0.0354372i	$-0.0112824\pi$
$390$	−22.2335	+	18.1866i	−1.12584	+	0.920914i
$391$		−	13.1371i		−	0.664372i
$392$	3.41082			0.172273
$393$	22.6402	−	18.5192i	1.14205	−	0.934172i
$394$			8.95071i			0.450930i
$395$		−	37.7451i		−	1.89916i
$396$	5.89951	−	29.1664i	0.296461	−	1.46567i
$397$		−	12.9652i		−	0.650706i	−0.945593	−	0.325353i	$-0.894517\pi$
$397$		−	12.9652i		−	0.650706i	0.945593	−	0.325353i	$-0.105483\pi$
$398$	19.8461			0.994796
$399$	0.832462	−	0.680938i	0.0416752	−	0.0340895i
$400$	23.8297			1.19149
$401$	19.9711			0.997308			0.498654	−	0.866801i	$-0.333828\pi$
$401$	19.9711			0.997308			0.498654	+	0.866801i	$0.333828\pi$
$402$	−5.64958	−	6.90673i	−0.281775	−	0.344477i
$403$	20.7980			1.03602
$404$	−8.47539			−0.421666
$405$	11.2597	−	26.6945i	0.559499	−	1.32646i
$406$		−	1.75501i		−	0.0870998i
$407$		−	29.2686i		−	1.45079i
$408$	−2.17730	−	2.66179i	−0.107792	−	0.131778i
$409$		−	11.1080i		−	0.549255i	−0.961551	−	0.274628i	$-0.911445\pi$
$409$		−	11.1080i		−	0.549255i	0.961551	−	0.274628i	$-0.0885546\pi$
$410$	−45.2088			−2.23270
$411$	0.708555	+	0.866224i	0.0349504	+	0.0427277i
$412$			21.7552i			1.07180i
$413$	1.81047	−	0.729181i	0.0890872	−	0.0358807i
$414$	3.74590	−	18.5192i	0.184101	−	0.910171i
$415$			31.9304i			1.56740i
$416$			20.2742i			0.994027i
$417$	16.8063	−	13.7472i	0.823008	−	0.673205i
$418$	−26.8698			−1.31425
$419$	−7.91202			−0.386527			−0.193264	−	0.981147i	$-0.561907\pi$
$419$	−7.91202			−0.386527			−0.193264	+	0.981147i	$0.561907\pi$
$420$	−1.56612	−	1.91462i	−0.0764190	−	0.0934239i
$421$			29.3968i			1.43271i	0.697734	+	0.716357i	$0.254192\pi$
$421$			29.3968i			1.43271i	−0.697734	+	0.716357i	$0.745808\pi$
$422$			17.6561i			0.859487i
$423$	−3.01224	+	14.8921i	−0.146460	+	0.724079i
$424$			0.574146i			0.0278830i
$425$			21.6495i			1.05016i
$426$	−34.4629	−	42.1316i	−1.66973	−	2.04128i
$427$			0.171866i			0.00831717i
$428$			17.3158i			0.836991i
$429$	16.5839	+	20.2742i	0.800681	+	0.978850i
$430$	61.0510			2.94414
$431$	23.4988			1.13190			0.565949	−	0.824440i	$-0.308510\pi$
$431$	23.4988			1.13190			0.565949	+	0.824440i	$0.308510\pi$
$432$	−10.7857	−	20.4159i	−0.518928	−	0.982259i
$433$	−5.16896			−0.248404			−0.124202	−	0.992257i	$-0.539637\pi$
$433$	−5.16896			−0.248404			−0.124202	+	0.992257i	$0.539637\pi$
$434$			3.84266i			0.184454i
$435$	−15.4011	+	12.5978i	−0.738424	+	0.604017i
$436$		−	5.82809i		−	0.279115i
$437$	−7.95184			−0.380388
$438$	27.8831	+	34.0877i	1.33231	+	1.62877i
$439$	−22.6084			−1.07904			−0.539521	−	0.841972i	$-0.681395\pi$
$439$	−22.6084			−1.07904			−0.539521	+	0.841972i	$0.681395\pi$
$440$		−	8.99438i		−	0.428790i
$441$	−4.12497	+	20.3933i	−0.196427	+	0.971109i
$442$	−20.7980			−0.989258
$443$	−29.1166			−1.38337			−0.691686	−	0.722198i	$-0.743132\pi$
$443$	−29.1166			−1.38337			−0.691686	+	0.722198i	$0.743132\pi$
$444$	9.86359	+	12.0585i	0.468105	+	0.572269i
$445$		−	25.5978i		−	1.21345i
$446$	−21.8052			−1.03251
$447$	8.65375	−	7.07860i	0.409308	−	0.334806i
$448$	−1.48763			−0.0702838
$449$			20.0664i			0.946992i	0.880796	+	0.473496i	$0.157008\pi$
$449$			20.0664i			0.946992i	−0.880796	+	0.473496i	$0.842992\pi$
$450$	−6.17313	+	30.5191i	−0.291004	+	1.43869i
$451$			41.2249i			1.94120i
$452$	−8.20177			−0.385779
$453$	14.4067	+	17.6125i	0.676884	+	0.827505i
$454$	−2.49074			−0.116896
$455$	2.17730			0.102073
$456$	−1.61117	+	1.31791i	−0.0754501	+	0.0617168i
$457$		−	41.2249i		−	1.92842i	−0.265144	−	0.964209i	$-0.585419\pi$
$457$		−	41.2249i		−	1.92842i	0.265144	−	0.964209i	$-0.414581\pi$
$458$			52.1610i			2.43732i
$459$	18.5480	−	9.79894i	0.865748	−	0.457375i
$460$			18.2888i			0.852721i
$461$			15.7384i			0.733010i	0.930416	+	0.366505i	$0.119446\pi$
$461$			15.7384i			0.733010i	−0.930416	+	0.366505i	$0.880554\pi$
$462$	−3.74590	+	3.06407i	−0.174275	+	0.142554i
$463$			15.7989i			0.734237i	0.930174	+	0.367118i	$0.119656\pi$
$463$			15.7989i			0.734237i	−0.930174	+	0.367118i	$0.880344\pi$
$464$			15.8574i			0.736163i
$465$	33.7212	−	27.5833i	1.56378	−	1.27914i
$466$	10.6925			0.495321
$467$	−16.2171			−0.750439			−0.375219	−	0.926936i	$-0.622433\pi$
$467$	−16.2171			−0.750439			−0.375219	+	0.926936i	$0.622433\pi$
$468$	−13.6649	−	2.76401i	−0.631661	−	0.127767i
$469$			0.676366i			0.0312317i
$470$		−	31.5541i		−	1.45548i
$471$	12.2294	+	14.9507i	0.563499	+	0.688890i
$472$	−3.50403	+	1.41128i	−0.161286	+	0.0649595i
$473$		−	55.6710i		−	2.55976i
$474$	30.4245	−	24.8866i	1.39744	−	1.14308i
$475$	13.1044			0.601271
$476$		−	1.79100i		−	0.0820902i
$477$	−3.43282	−	0.694358i	−0.157178	−	0.0317925i
$478$			28.5337i			1.30510i
$479$			6.37198i			0.291143i	0.989348	+	0.145572i	$0.0465021\pi$
$479$			6.37198i			0.291143i	−0.989348	+	0.145572i	$0.953498\pi$
$480$	26.8887	+	32.8720i	1.22730	+	1.50040i
$481$	−13.7128			−0.625251
$482$	1.50509			0.0685551
$483$	−1.10856	+	0.906781i	−0.0504412	+	0.0412599i
$484$	37.1484			1.68856
$485$	14.4067			0.654172
$486$	28.9410	−	8.52470i	1.31279	−	0.386688i
$487$	29.6688			1.34442			0.672211	−	0.740359i	$-0.265345\pi$
$487$	29.6688			1.34442			0.672211	+	0.740359i	$0.265345\pi$
$488$		−	0.332635i		−	0.0150577i
$489$	−10.2705	+	8.40108i	−0.464448	+	0.379910i
$490$		−	43.2103i		−	1.95204i
$491$		−	28.7281i		−	1.29648i	−0.761435	−	0.648241i	$-0.775505\pi$
$491$		−	28.7281i		−	1.29648i	0.761435	−	0.648241i	$-0.224495\pi$
$492$	−13.8929	−	16.9843i	−0.626339	−	0.765713i
$493$	−14.4067			−0.648843
$494$			12.5889i			0.566403i
$495$	53.7774	+	10.8776i	2.41711	+	0.488911i
$496$		−	34.7204i		−	1.55899i
$497$			4.12589i			0.185071i
$498$	−25.7376	+	21.0528i	−1.15333	+	0.943400i
$499$	−23.0328			−1.03109			−0.515545	−	0.856862i	$-0.672411\pi$
$499$	−23.0328			−1.03109			−0.515545	+	0.856862i	$0.672411\pi$
$500$		−	2.03824i		−	0.0911530i
$501$	13.7955	+	16.8653i	0.616337	+	0.753485i
$502$		−	26.1720i		−	1.16811i
$503$	−22.4517			−1.00107			−0.500536	−	0.865716i	$-0.666864\pi$
$503$	−22.4517			−1.00107			−0.500536	+	0.865716i	$0.666864\pi$
$504$	−0.0743259	+	0.367457i	−0.00331074	+	0.0163679i
$505$		−	15.6270i		−	0.695394i
$506$	35.7816			1.59068
$507$	−7.92984	+	6.48646i	−0.352177	+	0.288074i
$508$	4.57588			0.203022
$509$	3.16089			0.140104			0.0700520	−	0.997543i	$-0.477683\pi$
$509$	3.16089			0.140104			0.0700520	+	0.997543i	$0.477683\pi$
$510$	−33.7212	+	27.5833i	−1.49320	+	1.22141i
$511$		−	3.33816i		−	0.147671i
$512$	29.4754			1.30264
$513$	−5.93126	−	11.2271i	−0.261872	−	0.495686i
$514$			33.1373i			1.46162i
$515$	−40.1125			−1.76757
$516$	18.7612	+	22.9360i	0.825918	+	1.00970i
$517$	−28.7735			−1.26546
$518$		−	2.53360i		−	0.111320i
$519$	−31.0838	+	25.4260i	−1.36443	+	1.11608i
$520$	−4.21401			−0.184797
$521$		−	16.5415i		−	0.724696i	−0.932043	−	0.362348i	$-0.881975\pi$
$521$		−	16.5415i		−	0.724696i	0.932043	−	0.362348i	$-0.118025\pi$
$522$	−20.3089	−	4.10790i	−0.888897	−	0.179798i
$523$	−28.0716			−1.22748			−0.613742	−	0.789507i	$-0.710337\pi$
$523$	−28.0716			−1.22748			−0.613742	+	0.789507i	$0.710337\pi$
$524$	−29.4835			−1.28799
$525$	1.82687	−	1.49435i	0.0797313	−	0.0652187i
$526$			50.9653i			2.22219i
$527$	31.5439			1.37407
$528$	33.8461	−	27.6855i	1.47296	−	1.20486i
$529$	−12.4108			−0.539601
$530$	7.27362			0.315946
$531$	−4.20035	−	22.6574i	−0.182280	−	0.983247i
$532$	−1.08408			−0.0470010
$533$	19.3145			0.836604
$534$	20.6332	−	16.8775i	0.892885	−	0.730363i
$535$	−31.9271			−1.38033
$536$		−	1.30906i		−	0.0565428i
$537$	−19.8779	+	16.2597i	−0.857794	+	0.701659i
$538$	30.2705			1.30505
$539$	−39.4025			−1.69719
$540$	−25.8216	+	13.6416i	−1.11119	+	0.587041i
$541$			12.9652i			0.557419i	0.960375	+	0.278709i	$0.0899067\pi$
$541$			12.9652i			0.557419i	−0.960375	+	0.278709i	$0.910093\pi$
$542$	50.8367			2.18362
$543$	3.70333	−	3.02925i	0.158925	−	0.129998i
$544$			30.7496i			1.31838i
$545$	10.7459			0.460304
$546$	1.43557	+	1.75501i	0.0614366	+	0.0751076i
$547$	5.30927			0.227008			0.113504	−	0.993538i	$-0.463793\pi$
$547$	5.30927			0.227008			0.113504	+	0.993538i	$0.463793\pi$
$548$		−	1.12805i		−	0.0481880i
$549$	1.98882	+	0.402280i	0.0848808	+	0.0171689i
$550$	−58.9669			−2.51436
$551$			8.72029i			0.371497i
$552$	2.14554	−	1.75501i	0.0913203	−	0.0746983i
$553$	−2.97942			−0.126698
$554$	−36.8800			−1.56688
$555$	−22.2335	+	18.1866i	−0.943761	+	0.771978i
$556$	−21.8862			−0.928182
$557$		−	39.0541i		−	1.65478i	−0.561630	−	0.827389i	$-0.689825\pi$
$557$		−	39.0541i		−	1.65478i	0.561630	−	0.827389i	$-0.310175\pi$
$558$	44.4671	+	8.99438i	1.88244	+	0.380762i
$559$	−26.0828			−1.10318
$560$		−	3.63481i		−	0.153599i
$561$	25.1526	+	30.7496i	1.06194	+	1.29825i
$562$		−	26.0001i		−	1.09675i
$563$	−5.26111			−0.221729			−0.110865	−	0.993836i	$-0.535362\pi$
$563$	−5.26111			−0.221729			−0.110865	+	0.993836i	$0.535362\pi$
$564$	11.8545	−	9.69672i	0.499163	−	0.408306i
$565$		−	15.1225i		−	0.636210i
$566$		−	36.7058i		−	1.54286i
$567$	−2.10714	−	0.888788i	−0.0884915	−	0.0373256i
$568$		−	7.98538i		−	0.335059i
$569$	9.43530			0.395548			0.197774	−	0.980248i	$-0.436629\pi$
$569$	9.43530			0.395548			0.197774	+	0.980248i	$0.436629\pi$
$570$	16.6960	+	20.4113i	0.699320	+	0.854935i
$571$		−	24.0732i		−	1.00743i	−0.863869	−	0.503717i	$-0.831966\pi$
$571$		−	24.0732i		−	1.00743i	0.863869	−	0.503717i	$-0.168034\pi$
$572$		−	26.4024i		−	1.10394i
$573$	6.29809	−	5.15172i	0.263107	−	0.215216i
$574$			3.56857i			0.148949i
$575$	−17.4506			−0.727742
$576$	−3.48204	+	17.2147i	−0.145085	+	0.717281i
$577$	−7.00000			−0.291414			−0.145707	−	0.989328i	$-0.546546\pi$
$577$	−7.00000			−0.291414			−0.145707	+	0.989328i	$0.546546\pi$
$578$	1.35849			0.0565058
$579$	18.1910	−	14.8799i	0.755990	−	0.618386i
$580$	20.0562			0.832790
$581$	2.52044			0.104566
$582$	9.49881	+	11.6125i	0.393738	+	0.481354i
$583$		−	6.63265i		−	0.274696i
$584$			6.46078i			0.267349i
$585$	5.09632	−	25.1956i	0.210707	−	1.04171i
$586$		−	12.4022i		−	0.512330i
$587$	−25.2856			−1.04365			−0.521824	−	0.853053i	$-0.674748\pi$
$587$	−25.2856			−1.04365			−0.521824	+	0.853053i	$0.674748\pi$
$588$	16.2335	−	13.2787i	0.669459	−	0.547605i
$589$		−	19.0934i		−	0.786729i
$590$	17.8789	+	44.3912i	0.736064	+	1.82755i
$591$	−5.07158	−	6.20012i	−0.208617	−	0.255039i
$592$			22.8924i			0.940871i
$593$		−	40.9056i		−	1.67979i	−0.542746	−	0.839897i	$-0.682615\pi$
$593$		−	40.9056i		−	1.67979i	0.542746	−	0.839897i	$-0.317385\pi$
$594$	26.6894	+	50.5193i	1.09508	+	2.07283i
$595$	3.30226			0.135380
$596$	−11.2694			−0.461615
$597$	−13.7473	+	11.2450i	−0.562640	+	0.460229i
$598$		−	16.7642i		−	0.685540i
$599$			5.46520i			0.223302i	0.993747	+	0.111651i	$0.0356139\pi$
$599$			5.46520i			0.223302i	−0.993747	+	0.111651i	$0.964386\pi$
$600$	−3.53579	+	2.89221i	−0.144348	+	0.118074i
$601$			13.6416i			0.556453i	0.960516	+	0.278226i	$0.0897465\pi$
$601$			13.6416i			0.556453i	−0.960516	+	0.278226i	$0.910253\pi$
$602$		−	4.81909i		−	0.196411i
$603$	7.82687	+	1.58315i	0.318735	+	0.0644707i
$604$		−	22.9360i		−	0.933254i
$605$			68.4946i			2.78470i
$606$	12.5962	−	10.3034i	0.511685	−	0.418549i
$607$	13.7581			0.558426			0.279213	−	0.960229i	$-0.409927\pi$
$607$	13.7581			0.558426			0.279213	+	0.960229i	$0.409927\pi$
$608$	18.6126			0.754840
$609$	0.994411	+	1.21569i	0.0402956	+	0.0492622i
$610$	−4.21401			−0.170620
$611$			13.4808i			0.545376i
$612$	−20.7253	−	4.19212i	−0.837772	−	0.169457i
$613$			13.8135i			0.557921i	0.960303	+	0.278960i	$0.0899898\pi$
$613$			13.8135i			0.557921i	−0.960303	+	0.278960i	$0.910010\pi$
$614$	26.9313			1.08686
$615$	31.3159	−	25.6158i	1.26278	−	1.03293i
$616$	−0.709975			−0.0286057
$617$			31.3899i			1.26371i	0.775086	+	0.631856i	$0.217706\pi$
$617$			31.3899i			1.26371i	−0.775086	+	0.631856i	$0.782294\pi$
$618$	−26.4475	−	32.3327i	−1.06388	−	1.30061i
$619$	26.4835			1.06446			0.532230	−	0.846600i	$-0.321354\pi$
$619$	26.4835			1.06446			0.532230	+	0.846600i	$0.321354\pi$
$620$	−43.9138			−1.76362
$621$	7.89845	+	14.9507i	0.316954	+	0.599949i
$622$			3.10774i			0.124609i
$623$	−2.02058			−0.0809527
$624$	−12.9711	−	15.8574i	−0.519259	−	0.634806i
$625$	−23.0552			−0.922207
$626$			50.5193i			2.01916i
$627$	18.6126	−	15.2247i	0.743315	−	0.608018i
$628$		−	19.4697i		−	0.776925i
$629$	−20.7980			−0.829269
$630$	4.65517	+	0.941604i	0.185466	+	0.0375144i
$631$	−18.4723			−0.735370			−0.367685	−	0.929950i	$-0.619850\pi$
$631$	−18.4723			−0.735370			−0.367685	+	0.929950i	$0.619850\pi$
$632$	5.76647			0.229378
$633$	−10.0042	−	12.2303i	−0.397630	−	0.486112i
$634$			17.9562i			0.713131i
$635$			8.43707i			0.334815i
$636$	2.23522	+	2.73260i	0.0886321	+	0.108355i
$637$			18.4607i			0.731439i
$638$		−	39.2394i		−	1.55350i
$639$	47.7446	+	9.65733i	1.88875	+	0.382038i
$640$			12.5630i			0.496594i
$641$		−	33.8439i		−	1.33675i	−0.743823	−	0.668376i	$-0.766990\pi$
$641$		−	33.8439i		−	1.33675i	0.743823	−	0.668376i	$-0.233010\pi$
$642$	−21.0506	−	25.7349i	−0.830803	−	1.01567i
$643$	10.2405			0.403847			0.201924	−	0.979401i	$-0.435281\pi$
$643$	10.2405			0.403847			0.201924	+	0.979401i	$0.435281\pi$
$644$	1.44364			0.0568872
$645$	−42.2898	+	34.5922i	−1.66516	+	1.36207i
$646$			19.0934i			0.751219i
$647$			14.7865i			0.581317i	0.956827	+	0.290658i	$0.0938743\pi$
$647$			14.7865i			0.581317i	−0.956827	+	0.290658i	$0.906126\pi$
$648$	4.07823	+	1.72019i	0.160208	+	0.0675754i
$649$	40.4793	−	16.3034i	1.58895	−	0.639964i
$650$			27.6269i			1.08362i
$651$	−2.17730	−	2.66179i	−0.0853350	−	0.104324i
$652$	13.3749			0.523801
$653$			18.7348i			0.733148i	0.930389	+	0.366574i	$0.119469\pi$
$653$			18.7348i			0.733148i	−0.930389	+	0.366574i	$0.880531\pi$
$654$	7.08514	+	8.66175i	0.277051	+	0.338701i
$655$		−	54.3620i		−	2.12410i
$656$		−	32.2439i		−	1.25891i
$657$	−38.6290	−	7.81351i	−1.50706	−	0.304834i
$658$	−2.49074			−0.0970990
$659$	25.8091			1.00538			0.502691	−	0.864466i	$-0.332343\pi$
$659$	25.8091			1.00538			0.502691	+	0.864466i	$0.332343\pi$
$660$	−35.0161	−	42.8080i	−1.36300	−	1.66630i
$661$	37.9547			1.47627			0.738133	−	0.674655i	$-0.235708\pi$
$661$	37.9547			1.47627			0.738133	+	0.674655i	$0.235708\pi$
$662$	48.5662			1.88758
$663$	14.4067	−	11.7844i	0.559508	−	0.457667i
$664$	−4.87814			−0.189309
$665$		−	1.99885i		−	0.0775120i
$666$	−29.3187	−	5.93031i	−1.13608	−	0.229795i
$667$		−	11.6125i		−	0.449638i
$668$		−	21.9630i		−	0.849775i
$669$	15.1044	−	12.3551i	0.583969	−	0.477676i
$670$	−16.5839			−0.640694
$671$			3.84266i			0.148344i
$672$	2.59477	−	2.12247i	0.100095	−	0.0818761i
$673$		−	15.1662i		−	0.584614i	−0.956325	−	0.292307i	$-0.905577\pi$
$673$		−	15.1662i		−	0.584614i	0.956325	−	0.292307i	$-0.0944229\pi$
$674$			40.2159i			1.54906i
$675$	−13.0164	−	24.6382i	−0.501002	−	0.948326i
$676$	10.3267			0.397182
$677$		−	36.7552i		−	1.41262i	−0.707903	−	0.706309i	$-0.750359\pi$
$677$		−	36.7552i		−	1.41262i	0.707903	−	0.706309i	$-0.249641\pi$
$678$	12.1895	−	9.97081i	0.468136	−	0.382927i
$679$		−	1.13720i		−	0.0436415i
$680$	−6.39131			−0.245095
$681$	1.72532	−	1.41128i	0.0661145	−	0.0540804i
$682$			85.9161i			3.28990i
$683$	−16.4806			−0.630613			−0.315307	−	0.948990i	$-0.602107\pi$
$683$	−16.4806			−0.630613			−0.315307	+	0.948990i	$0.602107\pi$
$684$	−2.53748	+	12.5450i	−0.0970229	+	0.479669i
$685$	2.07992			0.0794695
$686$	−6.85340			−0.261664
$687$	−29.5550	−	36.1317i	−1.12759	−	1.37851i
$688$			43.5429i			1.66006i
$689$	−3.10750			−0.118386
$690$	−22.2335	−	27.1810i	−0.846416	−	1.03476i
$691$		−	16.0879i		−	0.612011i	−0.952030	−	0.306005i	$-0.901007\pi$
$691$		−	16.0879i		−	0.612011i	0.952030	−	0.306005i	$-0.0989926\pi$
$692$	40.4793			1.53879
$693$	0.858627	−	4.24494i	0.0326165	−	0.161252i
$694$	−3.40070			−0.129089
$695$		−	40.3541i		−	1.53072i
$696$	−1.92461	−	2.35288i	−0.0729523	−	0.0891859i
$697$	29.2939			1.10959
$698$			18.9652i			0.717843i
$699$	−7.40665	+	6.05850i	−0.280145	+	0.229154i
$700$	−2.37907			−0.0899203
$701$	26.3861			0.996588			0.498294	−	0.867008i	$-0.333960\pi$
$701$	26.3861			0.996588			0.498294	+	0.867008i	$0.333960\pi$
$702$	23.6691	−	12.5044i	0.893332	−	0.471948i
$703$			12.5889i			0.474800i
$704$	−33.2611			−1.25358
$705$	17.8789	+	21.8574i	0.673360	+	0.823197i
$706$	−52.6688			−1.98222
$707$	−1.23353			−0.0463915
$708$	−11.1829	+	20.3585i	−0.420279	+	0.765118i
$709$	32.8901			1.23521			0.617607	−	0.786487i	$-0.288102\pi$
$709$	32.8901			1.23521			0.617607	+	0.786487i	$0.288102\pi$
$710$	−101.163			−3.79660
$711$	−6.97384	+	34.4777i	−0.261539	+	1.29302i
$712$	3.91069			0.146559
$713$			25.4260i			0.952210i
$714$	2.17730	+	2.66179i	0.0814833	+	0.0996151i
$715$	48.6811			1.82057
$716$	25.8862			0.967413
$717$	−16.1675	−	19.7652i	−0.603788	−	0.738144i
$718$		−	8.21579i		−	0.306611i
$719$	−33.0510			−1.23259			−0.616297	−	0.787514i	$-0.711368\pi$
$719$	−33.0510			−1.23259			−0.616297	+	0.787514i	$0.711368\pi$
$720$	−42.0618	−	8.50787i	−1.56755	−	0.317070i
$721$			3.16629i			0.117919i
$722$	−25.2161			−0.938445
$723$	−1.04257	+	0.852804i	−0.0387737	+	0.0317161i
$724$	−4.82270			−0.179234
$725$			19.1371i			0.710732i
$726$	−55.2102	+	45.1609i	−2.04904	+	1.67608i
$727$	−47.6043			−1.76554			−0.882772	−	0.469802i	$-0.844325\pi$
$727$	−47.6043			−1.76554			−0.882772	+	0.469802i	$0.844325\pi$
$728$			0.332635i			0.0123283i
$729$	−15.2171	+	22.3033i	−0.563597	+	0.826050i
$730$	81.8490			3.02937
$731$	−39.5592			−1.46315
$732$	−1.29498	−	1.58315i	−0.0478640	−	0.0585148i
$733$	−44.3900			−1.63958			−0.819791	−	0.572663i	$-0.805910\pi$
$733$	−44.3900			−1.63958			−0.819791	+	0.572663i	$0.805910\pi$
$734$		−	45.7002i		−	1.68683i
$735$	24.4835	+	29.9316i	0.903086	+	1.10404i
$736$	−24.7857			−0.913614
$737$			15.1225i			0.557045i
$738$	41.2953	+	8.35284i	1.52010	+	0.307472i
$739$		−	27.4551i		−	1.00995i	−0.863134	−	0.504975i	$-0.831502\pi$
$739$		−	27.4551i		−	1.00995i	0.863134	−	0.504975i	$-0.168498\pi$
$740$	28.9539			1.06437
$741$	−7.13304	−	8.72029i	−0.262039	−	0.320348i
$742$		−	0.574146i		−	0.0210776i
$743$			5.49545i			0.201609i	0.994906	+	0.100804i	$0.0321416\pi$
$743$			5.49545i			0.201609i	−0.994906	+	0.100804i	$0.967858\pi$
$744$	4.21401	+	5.15172i	0.154493	+	0.188871i
$745$		−	20.7787i		−	0.761274i
$746$	41.6196			1.52380
$747$	5.89951	−	29.1664i	0.215852	−	1.06714i
$748$		−	40.0440i		−	1.46415i
$749$			2.52018i			0.0920853i
$750$	2.47787	+	3.02925i	0.0904790	+	0.110613i
$751$			2.61812i			0.0955366i	0.998858	+	0.0477683i	$0.0152109\pi$
$751$			2.61812i			0.0955366i	−0.998858	+	0.0477683i	$0.984789\pi$
$752$	22.5051			0.820676
$753$	14.8294	+	18.1292i	0.540412	+	0.660665i
$754$	−18.3843			−0.669517
$755$	42.2898			1.53908
$756$	1.07681	+	2.03824i	0.0391630	+	0.0741302i
$757$	−1.36372			−0.0495653			−0.0247826	−	0.999693i	$-0.507889\pi$
$757$	−1.36372			−0.0495653			−0.0247826	+	0.999693i	$0.507889\pi$
$758$	28.9518			1.05158
$759$	−24.7857	+	20.2742i	−0.899665	+	0.735909i
$760$			3.86863i			0.140330i
$761$			9.13600i			0.331180i	0.986195	+	0.165590i	$0.0529528\pi$
$761$			9.13600i			0.331180i	−0.986195	+	0.165590i	$0.947047\pi$
$762$	−6.80071	+	5.56285i	−0.246364	+	0.201521i
$763$		−	0.848232i		−	0.0307081i
$764$	−8.20177			−0.296730
$765$	7.72949	−	38.2136i	0.279460	−	1.38162i
$766$			18.1606i			0.656170i
$767$	−7.63840	−	18.9652i	−0.275807	−	0.684793i
$768$	−25.8241	+	21.1236i	−0.931848	+	0.762234i
$769$		−	30.0732i		−	1.08447i	−0.840228	−	0.542233i	$-0.817579\pi$
$769$		−	30.0732i		−	1.08447i	0.840228	−	0.542233i	$-0.182421\pi$
$770$			8.99438i			0.324135i
$771$	−18.7760	−	22.9540i	−0.676200	−	0.826669i
$772$	−23.6894			−0.852600
$773$	5.41783			0.194866			0.0974329	−	0.995242i	$-0.468937\pi$
$773$	5.41783			0.194866			0.0974329	+	0.995242i	$0.468937\pi$
$774$	−55.7662	−	11.2799i	−2.00447	−	0.405446i
$775$		−	41.9012i		−	1.50514i
$776$			2.20096i			0.0790100i
$777$	1.43557	+	1.75501i	0.0515007	+	0.0629607i
$778$		−	2.70546i		−	0.0969956i
$779$		−	17.7315i		−	0.635297i
$780$	−20.0562	+	16.4056i	−0.718128	+	0.587415i
$781$			92.2487i			3.30092i
$782$		−	25.4260i		−	0.909231i
$783$	16.3955	−	8.66175i	0.585926	−	0.309546i
$784$	30.8185			1.10066
$785$	35.8984			1.28127
$786$	43.8185	−	35.8427i	1.56296	−	1.27847i
$787$	−3.55530			−0.126733			−0.0633665	−	0.997990i	$-0.520184\pi$
$787$	−3.55530			−0.126733			−0.0633665	+	0.997990i	$0.520184\pi$
$788$			8.07418i			0.287631i
$789$	−28.8775	−	35.3034i	−1.02807	−	1.25683i
$790$		−	73.0531i		−	2.59911i
$791$	−1.19370			−0.0424432
$792$	−1.66181	+	8.21579i	−0.0590500	+	0.291936i
$793$	1.80035			0.0639322
$794$		−	25.0933i		−	0.890529i
$795$	−5.03840	+	4.12132i	−0.178694	+	0.146168i
$796$	17.9026			0.634542
$797$	28.1864			0.998414			0.499207	−	0.866483i	$-0.333625\pi$
$797$	28.1864			0.998414			0.499207	+	0.866483i	$0.333625\pi$
$798$	1.61117	−	1.31791i	0.0570349	−	0.0466535i
$799$			20.4461i			0.723332i
$800$	40.8461			1.44413
$801$	−4.72949	+	23.3820i	−0.167108	+	0.826162i
$802$	38.6527			1.36487
$803$		−	74.6362i		−	2.63385i
$804$	−5.09632	−	6.23037i	−0.179733	−	0.219728i
$805$			2.66179i			0.0938159i
$806$	40.2530			1.41785
$807$	−20.9682	+	17.1516i	−0.738117	+	0.603766i
$808$	2.38741			0.0839887
$809$	−29.4301			−1.03471			−0.517353	−	0.855772i	$-0.673083\pi$
$809$	−29.4301			−1.03471			−0.517353	+	0.855772i	$0.673083\pi$
$810$	21.7924	−	51.6653i	0.765706	−	1.81534i
$811$			0.460829i			0.0161819i	0.999967	+	0.00809095i	$0.00257546\pi$
$811$			0.460829i			0.0161819i	−0.999967	+	0.00809095i	$0.997425\pi$
$812$		−	1.58315i		−	0.0555576i
$813$	−35.2144	+	28.8047i	−1.23502	+	1.01022i
$814$		−	56.6475i		−	1.98549i
$815$			24.6608i			0.863830i
$816$	−19.6730	−	24.0507i	−0.688692	−	0.841942i
$817$			23.9450i			0.837731i
$818$		−	21.4988i		−	0.751687i
$819$	−1.98882	−	0.402280i	−0.0694951	−	0.0140568i
$820$	−40.7816			−1.42415
$821$	16.9271			0.590760			0.295380	−	0.955380i	$-0.404554\pi$
$821$	16.9271			0.590760			0.295380	+	0.955380i	$0.404554\pi$
$822$	1.37136	+	1.67652i	0.0478317	+	0.0584753i
$823$			2.31806i			0.0808026i	0.999184	+	0.0404013i	$0.0128636\pi$
$823$			2.31806i			0.0808026i	−0.999184	+	0.0404013i	$0.987136\pi$
$824$		−	6.12815i		−	0.213484i
$825$	40.8461	−	33.4113i	1.42208	−	1.16323i
$826$	3.50403	−	1.41128i	0.121921	−	0.0491047i
$827$			43.8641i			1.52530i	0.646809	+	0.762652i	$0.276103\pi$
$827$			43.8641i			1.52530i	−0.646809	+	0.762652i	$0.723897\pi$
$828$	3.37907	−	16.7057i	0.117431	−	0.580562i
$829$	−24.1906			−0.840174			−0.420087	−	0.907484i	$-0.638000\pi$
$829$	−24.1906			−0.840174			−0.420087	+	0.907484i	$0.638000\pi$
$830$			61.7992i			2.14508i
$831$	25.5466	−	20.8966i	0.886202	−	0.724896i
$832$			15.5834i			0.540256i
$833$			27.9990i			0.970107i
$834$	32.5275	−	26.6068i	1.12633	−	0.921319i
$835$	40.4957			1.40141
$836$	−24.2385			−0.838306
$837$	−35.8984	+	18.9652i	−1.24083	+	0.655533i
$838$	−15.3132			−0.528985
$839$	23.2388			0.802291			0.401145	−	0.916014i	$-0.368612\pi$
$839$	23.2388			0.802291			0.401145	+	0.916014i	$0.368612\pi$
$840$	0.441156	+	0.539323i	0.0152213	+	0.0186084i
$841$	16.2653			0.560872
$842$			56.8956i			1.96075i
$843$	14.7320	+	18.0102i	0.507396	+	0.620303i
$844$			15.9271i			0.548233i
$845$			19.0406i			0.655015i
$846$	−5.82998	+	28.8227i	−0.200439	+	0.990944i
$847$	5.40665			0.185775
$848$			5.18771i			0.178147i
$849$	20.7980	+	25.4260i	0.713784	+	0.872617i
$850$			41.9012i			1.43720i
$851$		−	16.7642i		−	0.574670i
$852$	−31.0880	−	38.0058i	−1.06506	−	1.30206i
$853$	24.3369			0.833278			0.416639	−	0.909072i	$-0.363208\pi$
$853$	24.3369			0.833278			0.416639	+	0.909072i	$0.363208\pi$
$854$			0.332635i			0.0113825i
$855$	−23.1306	−	4.67863i	−0.791048	−	0.160006i
$856$		−	4.87763i		−	0.166714i
$857$	−34.8513			−1.19050			−0.595250	−	0.803541i	$-0.702947\pi$
$857$	−34.8513			−1.19050			−0.595250	+	0.803541i	$0.702947\pi$
$858$	32.0971	+	39.2394i	1.09578	+	1.33961i
$859$		−	17.7843i		−	0.606793i	−0.952864	−	0.303397i	$-0.901879\pi$
$859$		−	17.7843i		−	0.606793i	0.952864	−	0.303397i	$-0.0981207\pi$
$860$	55.0724			1.87795
$861$	−2.02200	−	2.47194i	−0.0689094	−	0.0842433i
$862$	45.4803			1.54907
$863$	−8.35849			−0.284526			−0.142263	−	0.989829i	$-0.545438\pi$
$863$	−8.35849			−0.284526			−0.142263	+	0.989829i	$0.545438\pi$
$864$	−18.4876	−	34.9945i	−0.628962	−	1.19054i
$865$			74.6362i			2.53771i
$866$	−10.0042			−0.339956
$867$	−0.941022	+	0.769738i	−0.0319588	+	0.0261417i
$868$			3.46635i			0.117656i
$869$	−66.6154			−2.25977
$870$	−29.8077	+	24.3821i	−1.01058	+	0.826632i
$871$	7.08514			0.240071
$872$			1.64170i			0.0555948i
$873$	−13.1596	−	2.66179i	−0.445384	−	0.0900881i
$874$	−15.3902			−0.520583
$875$		−	0.296650i		−	0.0100286i
$876$	25.1526	+	30.7496i	0.849826	+	1.03893i
$877$	16.1731			0.546128			0.273064	−	0.961996i	$-0.411963\pi$
$877$	16.1731			0.546128			0.273064	+	0.961996i	$0.411963\pi$
$878$	−43.7571			−1.47673
$879$	7.02722	+	8.59094i	0.237022	+	0.289765i
$880$		−	81.2689i		−	2.73957i
$881$	22.0552			0.743058			0.371529	−	0.928421i	$-0.378834\pi$
$881$	22.0552			0.743058			0.371529	+	0.928421i	$0.378834\pi$
$882$	−7.98359	+	39.4699i	−0.268822	+	1.32902i
$883$	−6.68133			−0.224845			−0.112422	−	0.993661i	$-0.535861\pi$
$883$	−6.68133			−0.224845			−0.112422	+	0.993661i	$0.535861\pi$
$884$	−18.7612			−0.631009
$885$	−37.5372	−	20.6191i	−1.26180	−	0.693105i
$886$	−56.3533			−1.89322
$887$	1.07681			0.0361556			0.0180778	−	0.999837i	$-0.494245\pi$
$887$	1.07681			0.0361556			0.0180778	+	0.999837i	$0.494245\pi$
$888$	−2.77844	−	3.39671i	−0.0932384	−	0.113986i
$889$	0.665983			0.0223364
$890$		−	49.5429i		−	1.66068i
$891$	−47.1125	−	19.8720i	−1.57833	−	0.665736i
$892$	−19.6699			−0.658596
$893$	12.3760			0.414146
$894$	16.7487	−	13.7001i	0.560162	−	0.458202i
$895$			47.7293i			1.59542i
$896$	0.991662			0.0331291
$897$	9.49881	+	11.6125i	0.317156	+	0.387730i
$898$			38.8372i			1.29601i
$899$	27.8831			0.929954
$900$	−5.56860	+	27.5304i	−0.185620	+	0.917682i
$901$	−4.71308			−0.157016
$902$			79.7879i			2.65665i
$903$	2.73055	+	3.33816i	0.0908670	+	0.111087i
$904$	2.31033			0.0768405
$905$		−	8.89216i		−	0.295585i
$906$	27.8831	+	34.0877i	0.926354	+	1.13249i
$907$	−2.36266			−0.0784509			−0.0392254	−	0.999230i	$-0.512489\pi$
$907$	−2.36266			−0.0784509			−0.0392254	+	0.999230i	$0.512489\pi$
$908$	−2.24682			−0.0745634
$909$	−2.88727	+	14.2743i	−0.0957647	+	0.473449i
$910$	4.21401			0.139693
$911$			21.0092i			0.696065i	0.937483	+	0.348032i	$0.113150\pi$
$911$			21.0092i			0.696065i	−0.937483	+	0.348032i	$0.886850\pi$
$912$	−14.5578	+	11.9080i	−0.482056	+	0.394313i
$913$	56.3533			1.86502
$914$		−	79.7879i		−	2.63915i
$915$	2.91903	−	2.38771i	0.0965000	−	0.0789352i
$916$			47.0529i			1.55467i
$917$	−4.29108			−0.141704
$918$	35.8984	−	18.9652i	1.18483	−	0.625944i
$919$			39.0787i			1.28909i	0.764568	+	0.644543i	$0.222952\pi$
$919$			39.0787i			1.28909i	−0.764568	+	0.644543i	$0.777048\pi$
$920$		−	5.15172i		−	0.169847i
$921$	−18.6552	+	15.2596i	−0.614709	+	0.502820i
$922$			30.4606i			1.00317i
$923$	43.2200			1.42260
$924$	−3.37907	+	2.76401i	−0.111163	+	0.0909294i
$925$			27.6269i			0.908368i
$926$			30.5777i			1.00485i
$927$	36.6402	+	7.41123i	1.20342	+	0.243417i
$928$			27.1810i			0.892259i
$929$	−38.7222			−1.27043			−0.635217	−	0.772333i	$-0.719089\pi$
$929$	−38.7222			−1.27043			−0.635217	+	0.772333i	$0.719089\pi$
$930$	65.2650	−	53.3855i	2.14012	−	1.75058i
$931$	16.9477			0.555437
$932$	9.64541			0.315946
$933$	−1.76088	−	2.15272i	−0.0576488	−	0.0704769i
$934$	−31.3871			−1.02702
$935$	73.8336			2.41462
$936$	3.84923	+	0.778586i	0.125816	+	0.0254489i
$937$			6.63265i			0.216679i	0.994114	+	0.108340i	$0.0345534\pi$
$937$			6.63265i			0.216679i	−0.994114	+	0.108340i	$0.965447\pi$
$938$			1.30906i			0.0427424i
$939$	−28.6248	−	34.9945i	−0.934136	−	1.14200i
$940$		−	28.4641i		−	0.928396i
$941$	35.6485			1.16211			0.581054	−	0.813865i	$-0.302640\pi$
$941$	35.6485			1.16211			0.581054	+	0.813865i	$0.302640\pi$
$942$	23.6691	+	28.9360i	0.771181	+	0.942786i
$943$			23.6124i			0.768926i
$944$	−31.6608	+	12.7517i	−1.03047	+	0.415031i
$945$	−3.75814	+	1.98543i	−0.122252	+	0.0645859i
$946$		−	107.748i		−	3.50317i
$947$			25.3237i			0.822911i	0.911430	+	0.411456i	$0.134979\pi$
$947$			25.3237i			0.822911i	−0.911430	+	0.411456i	$0.865021\pi$
$948$	27.4451	−	22.4495i	0.891374	−	0.729127i
$949$	−34.9682			−1.13512
$950$	25.3627			0.822873
$951$	−10.1742	−	12.4382i	−0.329921	−	0.403335i
$952$			0.504500i			0.0163510i
$953$			22.6585i			0.733982i	0.930224	+	0.366991i	$0.119612\pi$
$953$			22.6585i			0.733982i	−0.930224	+	0.366991i	$0.880388\pi$
$954$	−6.64399	−	1.34388i	−0.215107	−	0.0435098i
$955$		−	15.1225i		−	0.489354i
$956$			25.7394i			0.832473i
$957$	22.2335	+	27.1810i	0.718708	+	0.878636i
$958$			12.3325i			0.398446i
$959$		−	0.164179i		−	0.00530162i
$960$	20.6674	+	25.2664i	0.667038	+	0.815468i
$961$	−30.0510			−0.969387
$962$	−26.5402			−0.855691
$963$	29.1634	+	5.89889i	0.939776	+	0.190089i
$964$	1.35770			0.0437286
$965$		−	43.6788i		−	1.40607i
$966$	−2.14554	+	1.75501i	−0.0690317	+	0.0564666i
$967$			26.5632i			0.854214i	0.904201	+	0.427107i	$0.140467\pi$
$967$			26.5632i			0.854214i	−0.904201	+	0.427107i	$0.859533\pi$
$968$	−10.4642			−0.336332
$969$	−10.8185	−	13.2259i	−0.347541	−	0.424877i
$970$	27.8831			0.895272
$971$			49.5295i			1.58948i	0.606953	+	0.794738i	$0.292392\pi$
$971$			49.5295i			1.58948i	−0.606953	+	0.794738i	$0.707608\pi$
$972$	26.1069	−	7.68989i	0.837378	−	0.246653i
$973$	−3.18537			−0.102118
$974$	57.4220			1.83992
$975$	−15.6537	−	19.1371i	−0.501321	−	0.612876i
$976$		−	3.00552i		−	0.0962045i
$977$	37.1320			1.18796			0.593979	−	0.804481i	$-0.297556\pi$
$977$	37.1320			1.18796			0.593979	+	0.804481i	$0.297556\pi$
$978$	−19.8779	+	16.2597i	−0.635624	+	0.519929i
$979$	−45.1770			−1.44386
$980$		−	38.9788i		−	1.24513i
$981$	−9.81569	−	1.98543i	−0.313391	−	0.0633898i
$982$		−	55.6014i		−	1.77431i
$983$	−6.24470			−0.199175			−0.0995876	−	0.995029i	$-0.531752\pi$
$983$	−6.24470			−0.199175			−0.0995876	+	0.995029i	$0.531752\pi$
$984$	3.91344	+	4.78426i	0.124756	+	0.152517i
$985$	−14.8873			−0.474348
$986$	−27.8831			−0.887979
$987$	1.72532	−	1.41128i	0.0549176	−	0.0449216i
$988$			11.3561i			0.361286i
$989$		−	31.8868i		−	1.01394i
$990$	104.082	+	21.0528i	3.30796	+	0.669103i
$991$		−	16.2597i		−	0.516507i	−0.966077	−	0.258254i	$-0.916853\pi$
$991$		−	16.2597i		−	0.516507i	0.966077	−	0.258254i	$-0.0831470\pi$
$992$		−	59.5137i		−	1.88956i
$993$	−33.6416	+	27.5182i	−1.06758	+	0.873263i
$994$			7.98538i			0.253281i
$995$			33.0091i			1.04646i
$996$	−23.2171	+	18.9912i	−0.735663	+	0.601758i
$997$	−42.4957			−1.34585			−0.672926	−	0.739710i	$-0.734963\pi$
$997$	−42.4957			−1.34585			−0.672926	+	0.739710i	$0.734963\pi$
$998$	−44.5785			−1.41111
$999$	23.6691	−	12.5044i	0.748857	−	0.395622i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.2.d.a.176.6	yes	6
3.2	odd	2		177.2.d.c.176.1	yes	6
59.58	odd	2		177.2.d.c.176.2	yes	6
177.176	even	2	inner	177.2.d.a.176.5	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.2.d.a.176.5	✓	6	177.176	even	2	inner
177.2.d.a.176.6	yes	6	1.1	even	1	trivial
177.2.d.c.176.1	yes	6	3.2	odd	2
177.2.d.c.176.2	yes	6	59.58	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	177.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.93543 q^{2} +(-1.34067 + 1.09664i) q^{3} +1.74590 q^{4} +3.21911i q^{5} +(-2.59477 + 2.12247i) q^{6} +0.254102 q^{7} -0.491797 q^{8} +(0.594767 - 2.94045i) q^{9} +O(q^{10})\)	\(q+1.93543 q^{2} +(-1.34067 + 1.09664i) q^{3} +1.74590 q^{4} +3.21911i q^{5} +(-2.59477 + 2.12247i) q^{6} +0.254102 q^{7} -0.491797 q^{8} +(0.594767 - 2.94045i) q^{9} +6.23037i q^{10} +5.68133 q^{11} +(-2.34067 + 1.91462i) q^{12} -2.66179i q^{13} +0.491797 q^{14} +(-3.53020 - 4.31575i) q^{15} -4.44364 q^{16} -4.03709i q^{17} +(1.15113 - 5.69104i) q^{18} -2.44364 q^{19} +5.62024i q^{20} +(-0.340665 + 0.278658i) q^{21} +10.9958 q^{22} +3.25410 q^{23} +(0.659335 - 0.539323i) q^{24} -5.36266 q^{25} -5.15172i q^{26} +(2.42723 + 4.59441i) q^{27} +0.443636 q^{28} -3.56857i q^{29} +(-6.83246 - 8.35284i) q^{30} +7.81351i q^{31} -7.61676 q^{32} +(-7.61676 + 6.23037i) q^{33} -7.81351i q^{34} +0.817981i q^{35} +(1.03840 - 5.13373i) q^{36} -5.15172i q^{37} -4.72949 q^{38} +(2.91903 + 3.56857i) q^{39} -1.58315i q^{40} +7.25620i q^{41} +(-0.659335 + 0.539323i) q^{42} -9.79894i q^{43} +9.91903 q^{44} +(9.46563 + 1.91462i) q^{45} +6.29809 q^{46} -5.06457 q^{47} +(5.95743 - 4.87306i) q^{48} -6.93543 q^{49} -10.3791 q^{50} +(4.42723 + 5.41239i) q^{51} -4.64722i q^{52} -1.16745i q^{53} +(4.69774 + 8.89216i) q^{54} +18.2888i q^{55} -0.124966 q^{56} +(3.27610 - 2.67979i) q^{57} -6.90673i q^{58} +(7.12497 - 2.86964i) q^{59} +(-6.16337 - 7.53486i) q^{60} +0.676366i q^{61} +15.1225i q^{62} +(0.151131 - 0.747174i) q^{63} -5.85446 q^{64} +8.56860 q^{65} +(-14.7417 + 12.0585i) q^{66} +2.66179i q^{67} -7.04835i q^{68} +(-4.36266 + 3.56857i) q^{69} +1.58315i q^{70} +16.2372i q^{71} +(-0.292504 + 1.44610i) q^{72} -13.1371i q^{73} -9.97081i q^{74} +(7.18953 - 5.88090i) q^{75} -4.26634 q^{76} +1.44364 q^{77} +(5.64958 + 6.90673i) q^{78} -11.7253 q^{79} -14.3045i q^{80} +(-8.29250 - 3.49777i) q^{81} +14.0439i q^{82} +9.91903 q^{83} +(-0.594767 + 0.486508i) q^{84} +12.9958 q^{85} -18.9652i q^{86} +(3.91344 + 4.78426i) q^{87} -2.79406 q^{88} -7.95184 q^{89} +(18.3201 + 3.70562i) q^{90} -0.676366i q^{91} +5.68133 q^{92} +(-8.56860 - 10.4753i) q^{93} -9.80213 q^{94} -7.86633i q^{95} +(10.2115 - 8.35284i) q^{96} -4.47535i q^{97} -13.4231 q^{98} +(3.37907 - 16.7057i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4 q^{2} - q^{3} + 12 q^{4} - 7 q^{6} - 6 q^{8} - 5 q^{9}+O(q^{10}) \) 6 * q - 4 * q^2 - q^3 + 12 * q^4 - 7 * q^6 - 6 * q^8 - 5 * q^9	\( 6 q - 4 q^{2} - q^{3} + 12 q^{4} - 7 q^{6} - 6 q^{8} - 5 q^{9} + 20 q^{11} - 7 q^{12} + 6 q^{14} + 3 q^{15} - 8 q^{16} + 17 q^{18} + 4 q^{19} + 5 q^{21} + 2 q^{22} + 18 q^{23} + 11 q^{24} - 4 q^{25} + 2 q^{27} - 16 q^{28} - 37 q^{30} - 16 q^{32} - 16 q^{33} - 21 q^{36} - 36 q^{38} + 8 q^{39} - 11 q^{42} + 50 q^{44} + 17 q^{45} - 6 q^{46} - 46 q^{47} - q^{48} - 26 q^{49} - 28 q^{50} + 14 q^{51} + 8 q^{54} + 32 q^{56} - 3 q^{57} + 10 q^{59} + 23 q^{60} + 11 q^{63} - 10 q^{64} - 26 q^{66} + 2 q^{69} + 27 q^{72} + 26 q^{75} + 46 q^{76} - 10 q^{77} - 8 q^{78} - 14 q^{79} - 21 q^{81} + 50 q^{83} + 5 q^{84} + 14 q^{85} + 29 q^{87} - 40 q^{88} - 26 q^{89} + 45 q^{90} + 20 q^{92} + 52 q^{94} + 23 q^{96} - 4 q^{98} - 14 q^{99}+O(q^{100}) \) 6 * q - 4 * q^2 - q^3 + 12 * q^4 - 7 * q^6 - 6 * q^8 - 5 * q^9 + 20 * q^11 - 7 * q^12 + 6 * q^14 + 3 * q^15 - 8 * q^16 + 17 * q^18 + 4 * q^19 + 5 * q^21 + 2 * q^22 + 18 * q^23 + 11 * q^24 - 4 * q^25 + 2 * q^27 - 16 * q^28 - 37 * q^30 - 16 * q^32 - 16 * q^33 - 21 * q^36 - 36 * q^38 + 8 * q^39 - 11 * q^42 + 50 * q^44 + 17 * q^45 - 6 * q^46 - 46 * q^47 - q^48 - 26 * q^49 - 28 * q^50 + 14 * q^51 + 8 * q^54 + 32 * q^56 - 3 * q^57 + 10 * q^59 + 23 * q^60 + 11 * q^63 - 10 * q^64 - 26 * q^66 + 2 * q^69 + 27 * q^72 + 26 * q^75 + 46 * q^76 - 10 * q^77 - 8 * q^78 - 14 * q^79 - 21 * q^81 + 50 * q^83 + 5 * q^84 + 14 * q^85 + 29 * q^87 - 40 * q^88 - 26 * q^89 + 45 * q^90 + 20 * q^92 + 52 * q^94 + 23 * q^96 - 4 * q^98 - 14 * q^99

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