LMFDB - Embedded newform 177.2.d.c.176.5

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			176.5
Root			$0.321037 + 1.70204i$ of defining polynomial
Character	$\chi$	$=$	177.176
Dual form			177.2.d.c.176.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.47283 q^{2} +(-0.321037 - 1.70204i) q^{3} +4.11491 q^{4} +2.50682i q^{5} +(-0.793871 - 4.20886i) q^{6} -2.11491 q^{7} +5.22982 q^{8} +(-2.79387 + 1.09283i) q^{9} +O(q^{10})$	\(q+2.47283 q^{2} +(-0.321037 - 1.70204i) q^{3} +4.11491 q^{4} +2.50682i q^{5} +(-0.793871 - 4.20886i) q^{6} -2.11491 q^{7} +5.22982 q^{8} +(-2.79387 + 1.09283i) q^{9} +6.19895i q^{10} -3.64207 q^{11} +(-1.32104 - 7.00373i) q^{12} -4.69249i q^{13} -5.22982 q^{14} +(4.26670 - 0.804782i) q^{15} +4.70265 q^{16} +2.79487i q^{17} +(-6.90878 + 2.70240i) q^{18} +6.70265 q^{19} +10.3153i q^{20} +(0.678963 + 3.59965i) q^{21} -9.00624 q^{22} -0.885092 q^{23} +(-1.67896 - 8.90135i) q^{24} -1.28415 q^{25} -11.6037i q^{26} +(2.75698 + 4.40444i) q^{27} -8.70265 q^{28} +1.50646i q^{29} +(10.5509 - 1.99009i) q^{30} -6.91126i q^{31} +1.16924 q^{32} +(1.16924 + 6.19895i) q^{33} +6.91126i q^{34} -5.30169i q^{35} +(-11.4965 + 4.49691i) q^{36} +11.6037i q^{37} +16.5745 q^{38} +(-7.98680 + 1.50646i) q^{39} +13.1102i q^{40} -0.288053i q^{41} +(1.67896 + 8.90135i) q^{42} -7.70541i q^{43} -14.9868 q^{44} +(-2.73954 - 7.00373i) q^{45} -2.18869 q^{46} +9.47283 q^{47} +(-1.50972 - 8.00409i) q^{48} -2.52717 q^{49} -3.17548 q^{50} +(4.75698 - 0.897257i) q^{51} -19.3092i q^{52} +9.31497i q^{53} +(6.81756 + 10.8914i) q^{54} -9.13002i q^{55} -11.0606 q^{56} +(-2.15180 - 11.4082i) q^{57} +3.72523i q^{58} +(4.06058 - 6.52010i) q^{59} +(17.5571 - 3.31160i) q^{60} -9.92418i q^{61} -17.0904i q^{62} +(5.90878 - 2.31124i) q^{63} -6.51396 q^{64} +11.7632 q^{65} +(2.89134 + 15.3290i) q^{66} +4.69249i q^{67} +11.5006i q^{68} +(0.284147 + 1.50646i) q^{69} -13.1102i q^{70} -2.69177i q^{71} +(-14.6114 + 5.71532i) q^{72} -2.47372i q^{73} +28.6941i q^{74} +(0.412259 + 2.18567i) q^{75} +27.5808 q^{76} +7.70265 q^{77} +(-19.7500 + 3.72523i) q^{78} -3.56829 q^{79} +11.7887i q^{80} +(6.61143 - 6.10647i) q^{81} -0.712306i q^{82} -14.9868 q^{83} +(2.79387 + 14.8122i) q^{84} -7.00624 q^{85} -19.0542i q^{86} +(2.56406 - 0.483630i) q^{87} -19.0474 q^{88} -5.93246 q^{89} +(-6.77442 - 17.3191i) q^{90} +9.92418i q^{91} -3.64207 q^{92} +(-11.7632 + 2.21877i) q^{93} +23.4247 q^{94} +16.8023i q^{95} +(-0.375369 - 1.99009i) q^{96} +1.67957i q^{97} -6.24926 q^{98} +(10.1755 - 3.98018i) 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 $

$2$	2.47283			1.74856			0.874279	−	0.485424i	$-0.161335\pi$
$2$	2.47283			1.74856			0.874279	+	0.485424i	$0.161335\pi$
$3$	−0.321037	−	1.70204i	−0.185351	−	0.982672i
$3$	−0.321037	−	1.70204i	−0.185351	−	0.982672i
$4$	4.11491			2.05745
$5$			2.50682i			1.12108i	0.828126	+	0.560542i	$0.189407\pi$
$5$			2.50682i			1.12108i	−0.828126	+	0.560542i	$0.810593\pi$
$6$	−0.793871	−	4.20886i	−0.324096	−	1.71826i
$7$	−2.11491			−0.799360			−0.399680	−	0.916655i	$-0.630879\pi$
$7$	−2.11491			−0.799360			−0.399680	+	0.916655i	$0.630879\pi$
$8$	5.22982			1.84902
$9$	−2.79387	+	1.09283i	−0.931290	+	0.364278i
$10$			6.19895i			1.96028i
$11$	−3.64207			−1.09813			−0.549063	−	0.835781i	$-0.685015\pi$
$11$	−3.64207			−1.09813			−0.549063	+	0.835781i	$0.685015\pi$
$12$	−1.32104	−	7.00373i	−0.381350	−	2.02180i
$13$		−	4.69249i		−	1.30146i	−0.759308	−	0.650731i	$-0.774463\pi$
$13$		−	4.69249i		−	1.30146i	0.759308	−	0.650731i	$-0.225537\pi$
$14$	−5.22982			−1.39773
$15$	4.26670	−	0.804782i	1.10166	−	0.207794i
$16$	4.70265			1.17566
$17$			2.79487i			0.677856i	0.940812	+	0.338928i	$0.110064\pi$
$17$			2.79487i			0.677856i	−0.940812	+	0.338928i	$0.889936\pi$
$18$	−6.90878	+	2.70240i	−1.62841	+	0.636961i
$19$	6.70265			1.53769			0.768847	−	0.639433i	$-0.220831\pi$
$19$	6.70265			1.53769			0.768847	+	0.639433i	$0.220831\pi$
$20$			10.3153i			2.30658i
$21$	0.678963	+	3.59965i	0.148162	+	0.785509i
$22$	−9.00624			−1.92014
$23$	−0.885092			−0.184555			−0.0922773	−	0.995733i	$-0.529415\pi$
$23$	−0.885092			−0.184555			−0.0922773	+	0.995733i	$0.529415\pi$
$24$	−1.67896	−	8.90135i	−0.342717	−	1.81698i
$25$	−1.28415			−0.256829
$26$		−	11.6037i		−	2.27568i
$27$	2.75698	+	4.40444i	0.530581	+	0.847634i
$28$	−8.70265			−1.64465
$29$			1.50646i			0.279743i	0.990170	+	0.139871i	$0.0446689\pi$
$29$			1.50646i			0.279743i	−0.990170	+	0.139871i	$0.955331\pi$
$30$	10.5509	−	1.99009i	1.92631	−	0.363339i
$31$		−	6.91126i		−	1.24130i	−0.784088	−	0.620649i	$-0.786869\pi$
$31$		−	6.91126i		−	1.24130i	0.784088	−	0.620649i	$-0.213131\pi$
$32$	1.16924			0.206694
$33$	1.16924	+	6.19895i	0.203539	+	1.07910i
$34$			6.91126i			1.18527i
$35$		−	5.30169i		−	0.896150i
$36$	−11.4965	+	4.49691i	−1.91609	+	0.749485i
$37$			11.6037i			1.90764i	0.300373	+	0.953822i	$0.402889\pi$
$37$			11.6037i			1.90764i	−0.300373	+	0.953822i	$0.597111\pi$
$38$	16.5745			2.68875
$39$	−7.98680	+	1.50646i	−1.27891	+	0.241227i
$40$			13.1102i			2.07291i
$41$		−	0.288053i		−	0.0449862i	−0.999747	−	0.0224931i	$-0.992840\pi$
$41$		−	0.288053i		−	0.0449862i	0.999747	−	0.0224931i	$-0.00716039\pi$
$42$	1.67896	+	8.90135i	0.259070	+	1.37351i
$43$		−	7.70541i		−	1.17506i	−0.809201	−	0.587532i	$-0.800100\pi$
$43$		−	7.70541i		−	1.17506i	0.809201	−	0.587532i	$-0.199900\pi$
$44$	−14.9868			−2.25934
$45$	−2.73954	−	7.00373i	−0.408386	−	1.04405i
$46$	−2.18869			−0.322704
$47$	9.47283			1.38175			0.690877	−	0.722972i	$-0.257224\pi$
$47$	9.47283			1.38175			0.690877	+	0.722972i	$0.257224\pi$
$48$	−1.50972	−	8.00409i	−0.217910	−	1.15529i
$49$	−2.52717			−0.361024
$50$	−3.17548			−0.449081
$51$	4.75698	−	0.897257i	0.666111	−	0.125641i
$52$		−	19.3092i		−	2.67770i
$53$			9.31497i			1.27951i	0.768579	+	0.639755i	$0.220964\pi$
$53$			9.31497i			1.27951i	−0.768579	+	0.639755i	$0.779036\pi$
$54$	6.81756	+	10.8914i	0.927752	+	1.48214i
$55$		−	9.13002i		−	1.23109i
$56$	−11.0606			−1.47803
$57$	−2.15180	−	11.4082i	−0.285012	−	1.51105i
$58$			3.72523i			0.489147i
$59$	4.06058	−	6.52010i	0.528642	−	0.848845i
$59$	4.06058	−	6.52010i	0.528642	−	0.848845i
$60$	17.5571	−	3.31160i	2.26661	−	0.427526i
$61$		−	9.92418i		−	1.27066i	−0.772240	−	0.635330i	$-0.780864\pi$
$61$		−	9.92418i		−	1.27066i	0.772240	−	0.635330i	$-0.219136\pi$
$62$		−	17.0904i		−	2.17048i
$63$	5.90878	−	2.31124i	0.744436	−	0.291189i
$64$	−6.51396			−0.814245
$65$	11.7632			1.45905
$66$	2.89134	+	15.3290i	0.355899	+	1.88687i
$67$			4.69249i			0.573279i	0.958039	+	0.286639i	$0.0925381\pi$
$67$			4.69249i			0.573279i	−0.958039	+	0.286639i	$0.907462\pi$
$68$			11.5006i			1.39466i
$69$	0.284147	+	1.50646i	0.0342073	+	0.181357i
$70$		−	13.1102i		−	1.56697i
$71$		−	2.69177i		−	0.319454i	−0.987161	−	0.159727i	$-0.948939\pi$
$71$		−	2.69177i		−	0.319454i	0.987161	−	0.159727i	$-0.0510615\pi$
$72$	−14.6114	+	5.71532i	−1.72197	+	0.673557i
$73$		−	2.47372i		−	0.289527i	−0.989466	−	0.144764i	$-0.953758\pi$
$73$		−	2.47372i		−	0.289527i	0.989466	−	0.144764i	$-0.0462422\pi$
$74$			28.6941i			3.33563i
$75$	0.412259	+	2.18567i	0.0476035	+	0.252379i
$76$	27.5808			3.16373
$77$	7.70265			0.877798
$78$	−19.7500	+	3.72523i	−2.23625	+	0.421799i
$79$	−3.56829			−0.401465			−0.200732	−	0.979646i	$-0.564332\pi$
$79$	−3.56829			−0.401465			−0.200732	+	0.979646i	$0.564332\pi$
$80$			11.7887i			1.31802i
$81$	6.61143	−	6.10647i	0.734603	−	0.678497i
$82$		−	0.712306i		−	0.0786610i
$83$	−14.9868			−1.64501			−0.822507	−	0.568755i	$-0.807425\pi$
$83$	−14.9868			−1.64501			−0.822507	+	0.568755i	$0.807425\pi$
$84$	2.79387	+	14.8122i	0.304836	+	1.61615i
$85$	−7.00624			−0.759934
$86$		−	19.0542i		−	2.05467i
$87$	2.56406	−	0.483630i	0.274896	−	0.0518505i
$88$	−19.0474			−2.03046
$89$	−5.93246			−0.628840			−0.314420	−	0.949284i	$-0.601810\pi$
$89$	−5.93246			−0.628840			−0.314420	+	0.949284i	$0.601810\pi$
$90$	−6.77442	−	17.3191i	−0.714087	−	1.82559i
$91$			9.92418i			1.04034i
$92$	−3.64207			−0.379712
$93$	−11.7632	+	2.21877i	−1.21979	+	0.230075i
$94$	23.4247			2.41608
$95$			16.8023i			1.72388i
$96$	−0.375369	−	1.99009i	−0.0383109	−	0.203113i
$97$			1.67957i			0.170534i	0.996358	+	0.0852670i	$0.0271743\pi$
$97$			1.67957i			0.170534i	−0.996358	+	0.0852670i	$0.972826\pi$
$98$	−6.24926			−0.631271
$99$	10.1755	−	3.98018i	1.02267	−	0.400023i
$100$	−5.28415			−0.528415
$101$	5.51396			0.548660			0.274330	−	0.961636i	$-0.411544\pi$
$101$	5.51396			0.548660			0.274330	+	0.961636i	$0.411544\pi$
$102$	11.7632	−	2.21877i	1.16473	−	0.219691i
$103$			12.3979i			1.22160i	0.791784	+	0.610801i	$0.209152\pi$
$103$			12.3979i			1.22160i	−0.791784	+	0.610801i	$0.790848\pi$
$104$		−	24.5408i		−	2.40643i
$105$	−9.02369	+	1.70204i	−0.880622	+	0.166102i
$106$			23.0344i			2.23730i
$107$		−	4.98054i		−	0.481487i	−0.970589	−	0.240744i	$-0.922609\pi$
$107$		−	4.98054i		−	0.481487i	0.970589	−	0.240744i	$-0.0773913\pi$
$108$	11.3447	+	18.1238i	1.09165	+	1.74397i
$109$			5.23169i			0.501105i	0.968103	+	0.250553i	$0.0806123\pi$
$109$			5.23169i			0.501105i	−0.968103	+	0.250553i	$0.919388\pi$
$110$		−	22.5770i		−	2.15264i
$111$	19.7500	−	3.72523i	1.87459	−	0.353583i
$112$	−9.94567			−0.939777
$113$	−6.81756			−0.641342			−0.320671	−	0.947191i	$-0.603908\pi$
$113$	−6.81756			−0.641342			−0.320671	+	0.947191i	$0.603908\pi$
$114$	−5.32104	−	28.2105i	−0.498361	−	2.64216i
$115$		−	2.21877i		−	0.206901i
$116$			6.19895i			0.575558i
$117$	5.12811	+	13.1102i	0.474094	+	1.21204i
$118$	10.0411	−	16.1231i	0.924361	−	1.48425i
$119$		−	5.91090i		−	0.541851i
$120$	22.3141	−	4.20886i	2.03699	−	0.384214i
$121$	2.26470			0.205882
$122$		−	24.5408i		−	2.22182i
$123$	−0.490277	+	0.0924755i	−0.0442067	+	0.00833823i
$124$		−	28.4392i		−	2.55391i
$125$			9.31497i			0.833157i
$126$	14.6114	−	5.71532i	1.30169	−	0.509161i
$127$	16.1755			1.43534			0.717671	−	0.696382i	$-0.245208\pi$
$127$	16.1755			1.43534			0.717671	+	0.696382i	$0.245208\pi$
$128$	−18.4464			−1.63045
$129$	−13.1149	+	2.47372i	−1.15470	+	0.217799i
$130$	29.0885			2.55123
$131$	−1.40530			−0.122781			−0.0613907	−	0.998114i	$-0.519554\pi$
$131$	−1.40530			−0.122781			−0.0613907	+	0.998114i	$0.519554\pi$
$132$	4.81131	+	25.5081i	0.418771	+	2.22020i
$133$	−14.1755			−1.22917
$134$			11.6037i			1.00241i
$135$	−11.0411	+	6.91126i	−0.950269	+	0.594826i
$136$			14.6167i			1.25337i
$137$		−	15.6870i		−	1.34023i	−0.742256	−	0.670117i	$-0.766244\pi$
$137$		−	15.6870i		−	1.34023i	0.742256	−	0.670117i	$-0.233756\pi$
$138$	0.702649	+	3.72523i	0.0598135	+	0.317113i
$139$	−11.1560			−0.946243			−0.473121	−	0.880997i	$-0.656873\pi$
$139$	−11.1560			−0.946243			−0.473121	+	0.880997i	$0.656873\pi$
$140$		−	21.8160i		−	1.84379i
$141$	−3.04113	−	16.1231i	−0.256109	−	1.35781i
$142$		−	6.65630i		−	0.558585i
$143$			17.0904i			1.42917i
$144$	−13.1386	+	5.13922i	−1.09488	+	0.428268i
$145$	−3.77643			−0.313615
$146$		−	6.11710i		−	0.506255i
$147$	0.811313	+	4.30133i	0.0669160	+	0.354768i
$148$			47.7483i			3.92489i
$149$	10.1428			0.830933			0.415467	−	0.909608i	$-0.363618\pi$
$149$	10.1428			0.830933			0.415467	+	0.909608i	$0.363618\pi$
$150$	1.01945	+	5.40479i	0.0832375	+	0.441300i
$151$		−	2.47372i		−	0.201309i	−0.994921	−	0.100654i	$-0.967906\pi$
$151$		−	2.47372i		−	0.201309i	0.994921	−	0.100654i	$-0.0320936\pi$
$152$	35.0536			2.84322
$153$	−3.05433	−	7.80851i	−0.246928	−	0.631281i
$154$	19.0474			1.53488
$155$	17.3253			1.39160
$156$	−32.8649	+	6.19895i	−2.63130	+	0.496313i
$157$			12.1429i			0.969113i	0.874760	+	0.484556i	$0.161019\pi$
$157$			12.1429i			0.969113i	−0.874760	+	0.484556i	$0.838981\pi$
$158$	−8.82380			−0.701984
$159$	15.8544	−	2.99045i	1.25734	−	0.237158i
$160$			2.93107i			0.231722i
$161$	1.87189			0.147525
$162$	16.3490	−	15.1003i	1.28450	−	1.18639i
$163$	−4.90454			−0.384153			−0.192077	−	0.981380i	$-0.561522\pi$
$163$	−4.90454			−0.384153			−0.192077	+	0.981380i	$0.561522\pi$
$164$		−	1.18531i		−	0.0925571i
$165$	−15.5397	+	2.93107i	−1.20976	+	0.228184i
$166$	−37.0599			−2.87640
$167$			9.67303i			0.748521i	0.927324	+	0.374261i	$0.122103\pi$
$167$			9.67303i			0.748521i	−0.927324	+	0.374261i	$0.877897\pi$
$168$	3.55085	+	18.8255i	0.273954	+	1.45242i
$169$	−9.01945			−0.693804
$170$	−17.3253			−1.32879
$171$	−18.7263	+	7.32488i	−1.43204	+	0.560148i
$172$		−	31.7071i		−	2.41764i
$173$	3.59398			0.273246			0.136623	−	0.990623i	$-0.456375\pi$
$173$	3.59398			0.273246			0.136623	+	0.990623i	$0.456375\pi$
$174$	6.34048	−	1.19594i	0.480671	−	0.0906637i
$175$	2.71585			0.205299
$176$	−17.1274			−1.29103
$177$	−12.4011	−	4.81806i	−0.932121	−	0.362148i
$178$	−14.6700			−1.09956
$179$	−12.1281			−0.906498			−0.453249	−	0.891384i	$-0.649735\pi$
$179$	−12.1281			−0.906498			−0.453249	+	0.891384i	$0.649735\pi$
$180$	−11.2729	−	28.8197i	−0.840236	−	2.14809i
$181$	4.34472			0.322941			0.161470	−	0.986878i	$-0.448376\pi$
$181$	4.34472			0.322941			0.161470	+	0.986878i	$0.448376\pi$
$182$			24.5408i			1.81909i
$183$	−16.8913	+	3.18603i	−1.24864	+	0.235518i
$184$	−4.62887			−0.341245
$185$	−29.0885			−2.13863
$186$	−29.0885	+	5.48664i	−2.13287	+	0.402300i
$187$		−	10.1791i		−	0.744372i
$188$	38.9798			2.84290
$189$	−5.83076	−	9.31497i	−0.424125	−	0.677565i
$190$			41.5494i			3.01431i
$191$	−6.81756			−0.493301			−0.246651	−	0.969104i	$-0.579330\pi$
$191$	−6.81756			−0.493301			−0.246651	+	0.969104i	$0.579330\pi$
$192$	2.09122	+	11.0870i	0.150921	+	0.800136i
$193$	6.76322			0.486828			0.243414	−	0.969923i	$-0.421733\pi$
$193$	6.76322			0.486828			0.243414	+	0.969923i	$0.421733\pi$
$194$			4.15329i			0.298189i
$195$	−3.77643	−	20.0215i	−0.270436	−	1.43377i
$196$	−10.3991			−0.742790
$197$		−	1.35841i		−	0.0967829i	−0.998828	−	0.0483915i	$-0.984590\pi$
$197$		−	1.35841i		−	0.0967829i	0.998828	−	0.0483915i	$-0.0154095\pi$
$198$	25.1623	−	9.84233i	1.78821	−	0.699464i
$199$	7.88509			0.558959			0.279480	−	0.960152i	$-0.409838\pi$
$199$	7.88509			0.558959			0.279480	+	0.960152i	$0.409838\pi$
$200$	−6.71585			−0.474883
$201$	7.98680	−	1.50646i	0.563345	−	0.106258i
$202$	13.6351			0.959363
$203$		−	3.18603i		−	0.223615i
$204$	19.5745	−	3.69213i	1.37049	−	0.258501i
$205$	0.722096			0.0504334
$206$			30.6579i			2.13604i
$207$	2.47283	−	0.967259i	0.171874	−	0.0672292i
$208$		−	22.0671i		−	1.53008i
$209$	−24.4115			−1.68858
$210$	−22.3141	+	4.20886i	−1.53982	+	0.290439i
$211$			17.6296i			1.21367i	0.794827	+	0.606836i	$0.207561\pi$
$211$			17.6296i			1.21367i	−0.794827	+	0.606836i	$0.792439\pi$
$212$			38.3303i			2.63253i
$213$	−4.58150	+	0.864158i	−0.313919	+	0.0592111i
$214$		−	12.3161i		−	0.841908i
$215$	19.3161			1.31735
$216$	14.4185	+	23.0344i	0.981055	+	1.56729i
$217$			14.6167i			0.992244i
$218$			12.9371i			0.876211i
$219$	−4.21037	+	0.794155i	−0.284510	+	0.0536641i
$220$		−	37.5692i		−	2.53292i
$221$	13.1149			0.882204
$222$	48.8385	−	9.21187i	3.27783	−	0.618260i
$223$	20.5808			1.37819			0.689096	−	0.724671i	$-0.258008\pi$
$223$	20.5808			1.37819			0.689096	+	0.724671i	$0.258008\pi$
$224$	−2.47283			−0.165223
$225$	3.58774	−	1.40336i	0.239183	−	0.0935573i
$226$	−16.8587			−1.12142
$227$	−20.0342			−1.32971			−0.664857	−	0.746970i	$-0.731508\pi$
$227$	−20.0342			−1.32971			−0.664857	+	0.746970i	$0.731508\pi$
$228$	−8.85445	−	46.9436i	−0.586400	−	3.10891i
$229$		−	4.97674i		−	0.328872i	−0.986388	−	0.164436i	$-0.947420\pi$
$229$		−	4.97674i		−	0.328872i	0.986388	−	0.164436i	$-0.0525804\pi$
$230$		−	5.48664i		−	0.361779i
$231$	−2.47283	−	13.1102i	−0.162701	−	0.862588i
$232$			7.87852i			0.517250i
$233$	8.68945			0.569264			0.284632	−	0.958637i	$-0.408129\pi$
$233$	8.68945			0.569264			0.284632	+	0.958637i	$0.408129\pi$
$234$	12.6810	+	32.4194i	0.828981	+	2.11932i
$235$			23.7467i			1.54906i
$236$	16.7089	−	26.8296i	1.08766	−	1.74646i
$237$	1.14555	+	6.07337i	0.0744117	+	0.394508i
$238$		−	14.6167i		−	0.947458i
$239$		−	7.31426i		−	0.473120i	−0.971617	−	0.236560i	$-0.923980\pi$
$239$		−	7.31426i		−	0.473120i	0.971617	−	0.236560i	$-0.0760200\pi$
$240$	20.0648	−	3.78461i	1.29518	−	0.244295i
$241$	26.5070			1.70747			0.853733	−	0.520711i	$-0.174333\pi$
$241$	26.5070			1.70747			0.853733	+	0.520711i	$0.174333\pi$
$242$	5.60023			0.359996
$243$	−12.5160	−	9.29250i	−0.802900	−	0.596114i
$244$		−	40.8371i		−	2.61433i
$245$		−	6.33515i		−	0.404738i
$246$	−1.21237	+	0.228676i	−0.0772980	+	0.0145799i
$247$		−	31.4521i		−	2.00125i
$248$		−	36.1446i		−	2.29518i
$249$	4.81131	+	25.5081i	0.304905	+	1.61651i
$250$			23.0344i			1.45682i
$251$		−	25.7143i		−	1.62307i	−0.584302	−	0.811536i	$-0.698632\pi$
$251$		−	25.7143i		−	1.62307i	0.584302	−	0.811536i	$-0.301368\pi$
$252$	24.3141	−	9.51055i	1.53164	−	0.599108i
$253$	3.22357			0.202664
$254$	39.9993			2.50978
$255$	2.24926	+	11.9249i	0.140854	+	0.746766i
$256$	−32.5870			−2.03669
$257$			18.4450i			1.15057i	0.817954	+	0.575284i	$0.195108\pi$
$257$			18.4450i			1.15057i	−0.817954	+	0.575284i	$0.804892\pi$
$258$	−32.4310	+	6.11710i	−2.01907	+	0.380834i
$259$		−	24.5408i		−	1.52489i
$260$	48.4046			3.00192
$261$	−1.64631	−	4.20886i	−0.101904	−	0.260522i
$262$	−3.47507			−0.214690
$263$			9.30313i			0.573655i	0.957982	+	0.286828i	$0.0926007\pi$
$263$			9.30313i			0.573655i	−0.957982	+	0.286828i	$0.907399\pi$
$264$	6.11491	+	32.4194i	0.376347	+	1.99527i
$265$	−23.3510			−1.43444
$266$	−35.0536			−2.14928
$267$	1.90454	+	10.0973i	0.116556	+	0.617944i
$268$			19.3092i			1.17949i
$269$	7.45115			0.454305			0.227152	−	0.973859i	$-0.427058\pi$
$269$	7.45115			0.454305			0.227152	+	0.973859i	$0.427058\pi$
$270$	−27.3029	+	17.0904i	−1.66160	+	1.04009i
$271$	−5.58078			−0.339008			−0.169504	−	0.985529i	$-0.554217\pi$
$271$	−5.58078			−0.339008			−0.169504	+	0.985529i	$0.554217\pi$
$272$			13.1433i			0.796930i
$273$	16.8913	−	3.18603i	1.02231	−	0.192827i
$274$		−	38.7914i		−	2.34348i
$275$	4.67696			0.282031
$276$	1.16924	+	6.19895i	0.0703800	+	0.373133i
$277$	−25.7717			−1.54847			−0.774236	−	0.632897i	$-0.781866\pi$
$277$	−25.7717			−1.54847			−0.774236	+	0.632897i	$0.781866\pi$
$278$	−27.5870			−1.65456
$279$	7.55286	+	19.3092i	0.452178	+	1.15601i
$280$		−	27.7269i		−	1.65700i
$281$		−	17.2266i		−	1.02765i	−0.857894	−	0.513826i	$-0.828228\pi$
$281$		−	17.2266i		−	1.02765i	0.857894	−	0.513826i	$-0.171772\pi$
$282$	−7.52021	−	39.8698i	−0.447822	−	2.37421i
$283$			19.0542i			1.13265i	0.824180	+	0.566327i	$0.191636\pi$
$283$			19.0542i			1.13265i	−0.824180	+	0.566327i	$0.808364\pi$
$284$		−	11.0764i		−	0.657263i
$285$	28.5982	−	5.39417i	1.69401	−	0.319523i
$286$			42.2617i			2.49899i
$287$			0.609204i			0.0359602i
$288$	−3.26670	+	1.27779i	−0.192492	+	0.0752942i
$289$	9.18869			0.540511
$290$	−9.33848			−0.548374
$291$	2.85868	−	0.539202i	0.167579	−	0.0316086i
$292$		−	10.1791i		−	0.595689i
$293$		−	10.7765i		−	0.629569i	−0.949163	−	0.314785i	$-0.898068\pi$
$293$		−	10.7765i		−	0.629569i	0.949163	−	0.314785i	$-0.101932\pi$
$294$	2.00624	+	10.6365i	0.117006	+	0.620332i
$295$	16.3447	+	10.1791i	0.951627	+	0.592652i
$296$			60.6854i			3.52727i
$297$	−10.0411	−	16.0413i	−0.582645	−	0.930809i
$298$	25.0815			1.45293
$299$			4.15329i			0.240191i
$300$	1.69641	+	8.99382i	0.0979420	+	0.519259i
$301$			16.2962i			0.939299i
$302$		−	6.11710i		−	0.352000i
$303$	−1.77018	−	9.38498i	−0.101694	−	0.539153i
$304$	31.5202			1.80781
$305$	24.8781			1.42452
$306$	−7.55286	−	19.3092i	−0.431768	−	1.10383i
$307$	−1.01945			−0.0581829			−0.0290915	−	0.999577i	$-0.509261\pi$
$307$	−1.01945			−0.0581829			−0.0290915	+	0.999577i	$0.509261\pi$
$308$	31.6957			1.80603
$309$	21.1017	−	3.98018i	1.20043	−	0.226425i
$310$	42.8425			2.43329
$311$		−	4.84054i		−	0.274482i	−0.990538	−	0.137241i	$-0.956177\pi$
$311$		−	4.84054i		−	0.274482i	0.990538	−	0.137241i	$-0.0438234\pi$
$312$	−41.7695	+	7.87852i	−2.36473	+	0.446033i
$313$		−	16.0413i		−	0.906707i	−0.891331	−	0.453353i	$-0.850228\pi$
$313$		−	16.0413i		−	0.906707i	0.891331	−	0.453353i	$-0.149772\pi$
$314$			30.0275i			1.69455i
$315$	5.79387	+	14.8122i	0.326448	+	0.834575i
$316$	−14.6832			−0.825995
$317$			17.2966i			0.971473i	0.874105	+	0.485737i	$0.161449\pi$
$317$			17.2966i			0.971473i	−0.874105	+	0.485737i	$0.838551\pi$
$318$	39.2054	−	7.39489i	2.19853	−	0.414685i
$319$		−	5.48664i		−	0.307193i
$320$		−	16.3293i		−	0.912837i
$321$	−8.47707	+	1.59894i	−0.473144	+	0.0892440i
$322$	4.62887			0.257957
$323$			18.7331i			1.04233i
$324$	27.2054	−	25.1276i	1.51141	−	1.39598i
$325$			6.02585i			0.334254i
$326$	−12.1281			−0.671714
$327$	8.90454	−	1.67957i	0.492422	−	0.0928802i
$328$		−	1.50646i		−	0.0831804i
$329$	−20.0342			−1.10452
$330$	−38.4270	+	7.24806i	−2.11534	+	0.398992i
$331$	−9.45267			−0.519566			−0.259783	−	0.965667i	$-0.583651\pi$
$331$	−9.45267			−0.519566			−0.259783	+	0.965667i	$0.583651\pi$
$332$	−61.6693			−3.38454
$333$	−12.6810	−	32.4194i	−0.694913	−	1.77657i
$334$			23.9198i			1.30883i
$335$	−11.7632			−0.642694
$336$	3.19293	+	16.9279i	0.174188	+	0.923493i
$337$		−	25.4263i		−	1.38506i	−0.721391	−	0.692528i	$-0.756497\pi$
$337$		−	25.4263i		−	1.38506i	0.721391	−	0.692528i	$-0.243503\pi$
$338$	−22.3036			−1.21316
$339$	2.18869	+	11.6037i	0.118873	+	0.630229i
$340$	−28.8300			−1.56353
$341$			25.1713i			1.36310i
$342$	−46.3071	+	18.1132i	−2.50400	+	0.979451i
$343$	20.1491			1.08795
$344$		−	40.2979i		−	2.17272i
$345$	−3.77643	+	0.712306i	−0.203316	+	0.0383493i
$346$	8.88733			0.477786
$347$	16.9604			0.910481			0.455241	−	0.890368i	$-0.349553\pi$
$347$	16.9604			0.910481			0.455241	+	0.890368i	$0.349553\pi$
$348$	10.5509	−	1.99009i	0.565585	−	0.106680i
$349$			7.70541i			0.412461i	0.978503	+	0.206231i	$0.0661197\pi$
$349$			7.70541i			0.412461i	−0.978503	+	0.206231i	$0.933880\pi$
$350$	6.71585			0.358977
$351$	20.6678	−	12.9371i	1.10316	−	0.690531i
$352$	−4.25846			−0.226977
$353$	3.79187			0.201821			0.100910	−	0.994896i	$-0.467824\pi$
$353$	3.79187			0.201821			0.100910	+	0.994896i	$0.467824\pi$
$354$	−30.6658	−	11.9143i	−1.62987	−	0.633236i
$355$	6.74779			0.358135
$356$	−24.4115			−1.29381
$357$	−10.0606	+	1.89762i	−0.532462	+	0.100432i
$358$	−29.9908			−1.58506
$359$		−	8.41772i		−	0.444270i	−0.975016	−	0.222135i	$-0.928697\pi$
$359$		−	8.41772i		−	0.444270i	0.975016	−	0.222135i	$-0.0713026\pi$
$360$	−14.3273	−	36.6282i	−0.755114	−	1.93048i
$361$	25.9255			1.36450
$362$	10.7438			0.564680
$363$	−0.727052	−	3.85461i	−0.0381603	−	0.202314i
$364$			40.8371i			2.14044i
$365$	6.20117			0.324584
$366$	−41.7695	+	7.87852i	−2.18333	+	0.411817i
$367$		−	0.254953i		−	0.0133084i	−0.999978	−	0.00665422i	$-0.997882\pi$
$367$		−	0.254953i		−	0.0133084i	0.999978	−	0.00665422i	$-0.00211812\pi$
$368$	−4.16228			−0.216974
$369$	0.314794	+	0.804782i	0.0163875	+	0.0418953i
$370$	−71.9310			−3.73952
$371$		−	19.7003i		−	1.02279i
$372$	−48.4046	+	9.13002i	−2.50966	+	0.473370i
$373$	−3.23606			−0.167557			−0.0837784	−	0.996484i	$-0.526699\pi$
$373$	−3.23606			−0.167557			−0.0837784	+	0.996484i	$0.526699\pi$
$374$		−	25.1713i		−	1.30158i
$375$	15.8544	−	2.99045i	0.818720	−	0.154426i
$376$	49.5412			2.55489
$377$	7.06905			0.364075
$378$	−14.4185	−	23.0344i	−0.741608	−	1.18476i
$379$	−6.09323			−0.312988			−0.156494	−	0.987679i	$-0.550019\pi$
$379$	−6.09323			−0.312988			−0.156494	+	0.987679i	$0.550019\pi$
$380$			69.1401i			3.54681i
$381$	−5.19293	−	27.5313i	−0.266042	−	1.41047i
$382$	−16.8587			−0.862565
$383$		−	30.1306i		−	1.53960i	−0.638284	−	0.769801i	$-0.720356\pi$
$383$		−	30.1306i		−	1.53960i	0.638284	−	0.769801i	$-0.279644\pi$
$384$	5.92198	+	31.3965i	0.302205	+	1.60220i
$385$			19.3092i			0.984086i
$386$	16.7243			0.851246
$387$	8.42074	+	21.5279i	0.428050	+	1.09433i
$388$			6.91126i			0.350866i
$389$			16.0531i			0.813926i	0.913445	+	0.406963i	$0.133412\pi$
$389$			16.0531i			0.813926i	−0.913445	+	0.406963i	$0.866588\pi$
$390$	−9.33848	−	49.5097i	−0.472872	−	2.50702i
$391$		−	2.47372i		−	0.125101i
$392$	−13.2166			−0.667540
$393$	0.451152	+	2.39187i	0.0227576	+	0.120654i
$394$		−	3.35913i		−	0.169231i
$395$		−	8.94507i		−	0.450075i
$396$	41.8712	−	16.3781i	2.10411	−	0.823030i
$397$			18.5150i			0.929241i	0.885510	+	0.464621i	$0.153809\pi$
$397$			18.5150i			0.929241i	−0.885510	+	0.464621i	$0.846191\pi$
$398$	19.4985			0.977373
$399$	4.55085	+	24.1272i	0.227828	+	1.20787i
$400$	−6.03889			−0.301945
$401$	30.5591			1.52605			0.763024	−	0.646370i	$-0.223714\pi$
$401$	30.5591			1.52605			0.763024	+	0.646370i	$0.223714\pi$
$402$	19.7500	−	3.72523i	0.985041	−	0.185798i
$403$	−32.4310			−1.61550
$404$	22.6894			1.12884
$405$	15.3078	+	16.5737i	0.760652	+	0.823552i
$406$		−	7.87852i		−	0.391004i
$407$		−	42.2617i		−	2.09483i
$408$	24.8781	−	4.69249i	1.23165	−	0.232313i
$409$		−	32.2463i		−	1.59447i	−0.603666	−	0.797237i	$-0.706294\pi$
$409$		−	32.2463i		−	1.59447i	0.603666	−	0.797237i	$-0.293706\pi$
$410$	1.78562			0.0881856
$411$	−26.6999	+	5.03611i	−1.31701	+	0.248413i
$412$			51.0162i			2.51339i
$413$	−8.58774	+	13.7894i	−0.422575	+	0.678533i
$414$	6.11491	−	2.39187i	0.300531	−	0.117554i
$415$		−	37.5692i		−	1.84420i
$416$		−	5.48664i		−	0.269005i
$417$	3.58150	+	18.9880i	0.175387	+	0.929847i
$418$	−60.3657			−2.95258
$419$	20.1476			0.984273			0.492136	−	0.870518i	$-0.336216\pi$
$419$	20.1476			0.984273			0.492136	+	0.870518i	$0.336216\pi$
$420$	−37.1316	+	7.00373i	−1.81184	+	0.341747i
$421$			23.1162i			1.12662i	0.826247	+	0.563308i	$0.190472\pi$
$421$			23.1162i			1.12662i	−0.826247	+	0.563308i	$0.809528\pi$
$422$			43.5950i			2.12217i
$423$	−26.4659	+	10.3522i	−1.28681	+	0.503343i
$424$			48.7156i			2.36584i
$425$		−	3.58903i		−	0.174093i
$426$	−11.3293	+	2.13692i	−0.548906	+	0.103534i
$427$			20.9887i			1.01572i
$428$		−	20.4945i		−	0.990637i
$429$	29.0885	−	5.48664i	1.40441	−	0.264898i
$430$	47.7655			2.30345
$431$	−21.0691			−1.01486			−0.507430	−	0.861693i	$-0.669405\pi$
$431$	−21.0691			−1.01486			−0.507430	+	0.861693i	$0.669405\pi$
$432$	12.9651	+	20.7125i	0.623784	+	0.996531i
$433$	12.1344			0.583140			0.291570	−	0.956550i	$-0.405822\pi$
$433$	12.1344			0.583140			0.291570	+	0.956550i	$0.405822\pi$
$434$			36.1446i			1.73500i
$435$	1.21237	+	6.42763i	0.0581288	+	0.308181i
$436$			21.5279i			1.03100i
$437$	−5.93246			−0.283788
$438$	−10.4115	+	1.96381i	−0.497483	+	0.0938347i
$439$	23.8432			1.13798			0.568988	−	0.822346i	$-0.307335\pi$
$439$	23.8432			1.13798			0.568988	+	0.822346i	$0.307335\pi$
$440$		−	47.7483i		−	2.27631i
$441$	7.06058	−	2.76177i	0.336218	−	0.131513i
$442$	32.4310			1.54258
$443$	−22.0731			−1.04872			−0.524361	−	0.851496i	$-0.675696\pi$
$443$	−22.0731			−1.04872			−0.524361	+	0.851496i	$0.675696\pi$
$444$	81.2695	−	15.3290i	3.85688	−	0.727481i
$445$		−	14.8716i		−	0.704982i
$446$	50.8929			2.40985
$447$	−3.25622	−	17.2635i	−0.154014	−	0.816535i
$448$	13.7764			0.650875
$449$		−	16.6992i		−	0.788086i	−0.919092	−	0.394043i	$-0.871076\pi$
$449$		−	16.6992i		−	0.788086i	0.919092	−	0.394043i	$-0.128924\pi$
$450$	8.87189	−	3.47028i	0.418225	−	0.163590i
$451$			1.04911i			0.0494006i
$452$	−28.0536			−1.31953
$453$	−4.21037	+	0.794155i	−0.197820	+	0.0373127i
$454$	−49.5412			−2.32508
$455$	−24.8781			−1.16630
$456$	−11.2535	−	59.6626i	−0.526993	−	2.79396i
$457$		−	1.04911i		−	0.0490752i	−0.999699	−	0.0245376i	$-0.992189\pi$
$457$		−	1.04911i		−	0.0490752i	0.999699	−	0.0245376i	$-0.00781135\pi$
$458$		−	12.3066i		−	0.575052i
$459$	−12.3098	+	7.70541i	−0.574574	+	0.359658i
$460$		−	9.13002i		−	0.425690i
$461$			4.35949i			0.203042i	0.994833	+	0.101521i	$0.0323709\pi$
$461$			4.35949i			0.203042i	−0.994833	+	0.101521i	$0.967629\pi$
$462$	−6.11491	−	32.4194i	−0.284491	−	1.50829i
$463$			7.16621i			0.333042i	0.986038	+	0.166521i	$0.0532534\pi$
$463$			7.16621i			0.333042i	−0.986038	+	0.166521i	$0.946747\pi$
$464$			7.08436i			0.328883i
$465$	−5.56205	−	29.4883i	−0.257934	−	1.36749i
$466$	21.4876			0.995392
$467$	12.7981			0.592226			0.296113	−	0.955153i	$-0.404310\pi$
$467$	12.7981			0.592226			0.296113	+	0.955153i	$0.404310\pi$
$468$	21.1017	+	53.9473i	0.975427	+	2.49371i
$469$		−	9.92418i		−	0.458256i
$470$			58.7216i			2.70863i
$471$	20.6678	−	3.89833i	0.952320	−	0.179626i
$472$	21.2361	−	34.0989i	0.977469	−	1.56953i
$473$			28.0637i			1.29037i
$474$	2.83276	+	15.0184i	0.130113	+	0.689820i
$475$	−8.60719			−0.394925
$476$		−	24.3228i		−	1.11483i
$477$	−10.1797	−	26.0248i	−0.466097	−	1.19160i
$478$		−	18.0869i		−	0.827278i
$479$		−	21.4248i		−	0.978925i	−0.872024	−	0.489463i	$-0.837193\pi$
$479$		−	21.4248i		−	0.978925i	0.872024	−	0.489463i	$-0.162807\pi$
$480$	4.98880	−	0.940983i	0.227707	−	0.0429498i
$481$	54.4504			2.48273
$482$	65.5474			2.98560
$483$	−0.600945	−	3.18603i	−0.0273440	−	0.144969i
$484$	9.31903			0.423592
$485$	−4.21037			−0.191183
$486$	−30.9499	−	22.9788i	−1.40392	−	1.04234i
$487$	−32.3767			−1.46713			−0.733563	−	0.679621i	$-0.762144\pi$
$487$	−32.3767			−1.46713			−0.733563	+	0.679621i	$0.762144\pi$
$488$		−	51.9016i		−	2.34948i
$489$	1.57454	+	8.34772i	0.0712031	+	0.377497i
$490$		−	15.6658i		−	0.707708i
$491$			20.8525i			0.941061i	0.882384	+	0.470531i	$0.155937\pi$
$491$			20.8525i			0.941061i	−0.882384	+	0.470531i	$0.844063\pi$
$492$	−2.01744	+	0.380528i	−0.0909533	+	0.0171555i
$493$	−4.21037			−0.189625
$494$		−	77.7758i		−	3.49930i
$495$	9.97760	+	25.5081i	0.448460	+	1.14650i
$496$		−	32.5012i		−	1.45935i
$497$			5.69285i			0.255359i
$498$	11.8976	+	63.0773i	0.533143	+	2.82656i
$499$	−4.08074			−0.182679			−0.0913395	−	0.995820i	$-0.529115\pi$
$499$	−4.08074			−0.182679			−0.0913395	+	0.995820i	$0.529115\pi$
$500$			38.3303i			1.71418i
$501$	16.4639	−	3.10540i	0.735551	−	0.138739i
$502$		−	63.5872i		−	2.83804i
$503$	−36.1748			−1.61295			−0.806477	−	0.591266i	$-0.798628\pi$
$503$	−36.1748			−1.61295			−0.806477	+	0.591266i	$0.798628\pi$
$504$	30.9018	−	12.0874i	1.37648	−	0.538414i
$505$			13.8225i			0.615094i
$506$	7.97136			0.354370
$507$	2.89557	+	15.3514i	0.128597	+	0.681782i
$508$	66.5606			2.95315
$509$	−35.3378			−1.56632			−0.783159	−	0.621821i	$-0.786393\pi$
$509$	−35.3378			−1.56632			−0.783159	+	0.621821i	$0.786393\pi$
$510$	5.56205	+	29.4883i	0.246292	+	1.30576i
$511$			5.23169i			0.231436i
$512$	−43.6894			−1.93082
$513$	18.4791	+	29.5214i	0.815871	+	1.30340i
$514$			45.6114i			2.01183i
$515$	−31.0793			−1.36952
$516$	−53.9666	+	10.1791i	−2.37575	+	0.448111i
$517$	−34.5008			−1.51734
$518$		−	60.6854i		−	2.66637i
$519$	−1.15380	−	6.11710i	−0.0506463	−	0.268511i
$520$	61.5195			2.69781
$521$		−	29.1964i		−	1.27912i	−0.768742	−	0.639559i	$-0.779117\pi$
$521$		−	29.1964i		−	1.27912i	0.768742	−	0.639559i	$-0.220883\pi$
$522$	−4.07106	−	10.4078i	−0.178185	−	0.455537i
$523$	−25.3121			−1.10682			−0.553410	−	0.832909i	$-0.686674\pi$
$523$	−25.3121			−1.10682			−0.553410	+	0.832909i	$0.686674\pi$
$524$	−5.78267			−0.252617
$525$	−0.871889	−	4.62249i	−0.0380523	−	0.201742i
$526$			23.0051i			1.00307i
$527$	19.3161			0.841422
$528$	5.49852	+	29.1515i	0.239293	+	1.26866i
$529$	−22.2166			−0.965940
$530$	−57.7431			−2.50820
$531$	−4.21933	+	22.6539i	−0.183103	+	0.983094i
$532$	−58.3308			−2.52896
$533$	−1.35168			−0.0585479
$534$	4.70961	+	24.9689i	0.203805	+	1.08051i
$535$	12.4853			0.539787
$536$			24.5408i			1.06000i
$537$	3.89357	+	20.6425i	0.168020	+	0.890790i
$538$	18.4255			0.794378
$539$	9.20412			0.396450
$540$	−45.4332	+	28.4392i	−1.95513	+	1.22383i
$541$		−	18.5150i		−	0.796022i	−0.917381	−	0.398011i	$-0.869701\pi$
$541$		−	18.5150i		−	0.796022i	0.917381	−	0.398011i	$-0.130299\pi$
$542$	−13.8003			−0.592776
$543$	−1.39482	−	7.39489i	−0.0598573	−	0.317345i
$544$			3.26788i			0.140109i
$545$	−13.1149			−0.561781
$546$	41.7695	−	7.87852i	1.78757	−	0.337169i
$547$	9.65679			0.412895			0.206447	−	0.978458i	$-0.433810\pi$
$547$	9.65679			0.412895			0.206447	+	0.978458i	$0.433810\pi$
$548$		−	64.5507i		−	2.75747i
$549$	10.8455	+	27.7269i	0.462874	+	1.18335i
$550$	11.5653			0.493148
$551$			10.0973i			0.430159i
$552$	1.48604	+	7.87852i	0.0632500	+	0.335332i
$553$	7.54661			0.320915
$554$	−63.7291			−2.70759
$555$	9.33848	+	49.5097i	0.396396	+	2.10157i
$556$	−45.9061			−1.94685
$557$			15.5958i			0.660814i	0.943839	+	0.330407i	$0.107186\pi$
$557$			15.5958i			0.660814i	−0.943839	+	0.330407i	$0.892814\pi$
$558$	18.6770	+	47.7483i	0.790659	+	2.02135i
$559$	−36.1576			−1.52930
$560$		−	24.9320i		−	1.05357i
$561$	−17.3253	+	3.26788i	−0.731474	+	0.137970i
$562$		−	42.5985i		−	1.79691i
$563$	−4.27567			−0.180198			−0.0900990	−	0.995933i	$-0.528718\pi$
$563$	−4.27567			−0.180198			−0.0900990	+	0.995933i	$0.528718\pi$
$564$	−12.5140	−	66.3452i	−0.526933	−	2.79364i
$565$		−	17.0904i		−	0.718998i
$566$			47.1179i			1.98051i
$567$	−13.9826	+	12.9146i	−0.587212	+	0.542363i
$568$		−	14.0775i		−	0.590677i
$569$	39.7151			1.66495			0.832473	−	0.554066i	$-0.186925\pi$
$569$	39.7151			1.66495			0.832473	+	0.554066i	$0.186925\pi$
$570$	70.7187	−	13.3389i	2.96208	−	0.558704i
$571$		−	13.7313i		−	0.574635i	−0.957835	−	0.287318i	$-0.907236\pi$
$571$		−	13.7313i		−	0.574635i	0.957835	−	0.287318i	$-0.0927635\pi$
$572$			70.3254i			2.94045i
$573$	2.18869	+	11.6037i	0.0914337	+	0.484753i
$574$			1.50646i			0.0628785i
$575$	1.13659			0.0473990
$576$	18.1992	−	7.11868i	0.758299	−	0.296612i
$577$	−7.00000			−0.291414			−0.145707	−	0.989328i	$-0.546546\pi$
$577$	−7.00000			−0.291414			−0.145707	+	0.989328i	$0.546546\pi$
$578$	22.7221			0.945115
$579$	−2.17124	−	11.5113i	−0.0902338	−	0.478392i
$580$	−15.5397			−0.645249
$581$	31.6957			1.31496
$582$	7.06905	−	1.33336i	0.293022	−	0.0552695i
$583$		−	33.9258i		−	1.40506i
$584$		−	12.9371i		−	0.535341i
$585$	−32.8649	+	12.8553i	−1.35880	+	0.531499i
$586$		−	26.6485i		−	1.10084i
$587$	−43.2074			−1.78336			−0.891680	−	0.452665i	$-0.850473\pi$
$587$	−43.2074			−1.78336			−0.891680	+	0.452665i	$0.850473\pi$
$588$	3.33848	+	17.6996i	0.137677	+	0.729919i
$589$		−	46.3237i		−	1.90874i
$590$	40.4178	+	25.1713i	1.66397	+	1.03629i
$591$	−2.31207	+	0.436101i	−0.0951059	+	0.0179388i
$592$			54.5683i			2.24274i
$593$			2.79868i			0.114928i	0.998348	+	0.0574639i	$0.0183014\pi$
$593$			2.79868i			0.114928i	−0.998348	+	0.0574639i	$0.981699\pi$
$594$	−24.8300	−	39.6674i	−1.01879	−	1.62757i
$595$	14.8176			0.607461
$596$	41.7368			1.70961
$597$	−2.53140	−	13.4207i	−0.103604	−	0.549274i
$598$			10.2704i			0.419987i
$599$		−	24.6108i		−	1.00557i	−0.864411	−	0.502786i	$-0.832308\pi$
$599$		−	24.6108i		−	1.00557i	0.864411	−	0.502786i	$-0.167692\pi$
$600$	2.15604	+	11.4306i	0.0880198	+	0.466654i
$601$		−	28.4392i		−	1.16006i	−0.814596	−	0.580029i	$-0.803041\pi$
$601$		−	28.4392i		−	1.16006i	0.814596	−	0.580029i	$-0.196959\pi$
$602$			40.2979i			1.64242i
$603$	−5.12811	−	13.1102i	−0.208833	−	0.533889i
$604$		−	10.1791i		−	0.414183i
$605$			5.67720i			0.230811i
$606$	−4.37737	−	23.2075i	−0.177819	−	0.942740i
$607$	−13.3510			−0.541899			−0.270949	−	0.962594i	$-0.587338\pi$
$607$	−13.3510			−0.541899			−0.270949	+	0.962594i	$0.587338\pi$
$608$	7.83700			0.317832
$609$	−5.42274	+	1.02283i	−0.219741	+	0.0414472i
$610$	61.5195			2.49085
$611$		−	44.4512i		−	1.79830i
$612$	−12.5683	−	32.1313i	−0.508043	−	1.29883i
$613$		−	7.45046i		−	0.300921i	−0.988616	−	0.150461i	$-0.951924\pi$
$613$		−	7.45046i		−	0.300921i	0.988616	−	0.150461i	$-0.0480757\pi$
$614$	−2.52092			−0.101736
$615$	−0.231819	−	1.22904i	−0.00934786	−	0.0495595i
$616$	40.2834			1.62307
$617$		−	25.5450i		−	1.02840i	−0.857669	−	0.514202i	$-0.828088\pi$
$617$		−	25.5450i		−	1.02840i	0.857669	−	0.514202i	$-0.171912\pi$
$618$	52.1810	−	9.84233i	2.09903	−	0.395917i
$619$	−8.78267			−0.353005			−0.176503	−	0.984300i	$-0.556478\pi$
$619$	−8.78267			−0.353005			−0.176503	+	0.984300i	$0.556478\pi$
$620$	71.2919			2.86315
$621$	−2.44018	−	3.89833i	−0.0979212	−	0.156435i
$622$		−	11.9698i		−	0.479947i
$623$	12.5466			0.502669
$624$	−37.5591	+	7.08436i	−1.50357	+	0.283601i
$625$	−29.7717			−1.19087
$626$		−	39.6674i		−	1.58543i
$627$	7.83700	+	41.5494i	0.312980	+	1.65932i
$628$			49.9671i			1.99390i
$629$	−32.4310			−1.29311
$630$	14.3273	+	36.6282i	0.570812	+	1.45930i
$631$	29.6282			1.17948			0.589739	−	0.807594i	$-0.299231\pi$
$631$	29.6282			1.17948			0.589739	+	0.807594i	$0.299231\pi$
$632$	−18.6615			−0.742315
$633$	30.0062	−	5.65975i	1.19264	−	0.224955i
$634$			42.7716i			1.69868i
$635$			40.5490i			1.60914i
$636$	65.2396	−	12.3054i	2.58692	−	0.487942i
$637$			11.8587i			0.469859i
$638$		−	13.5676i		−	0.537145i
$639$	2.94166	+	7.52046i	0.116370	+	0.297505i
$640$		−	46.2419i		−	1.82787i
$641$			41.4501i			1.63718i	0.574378	+	0.818590i	$0.305244\pi$
$641$			41.4501i			1.63718i	−0.574378	+	0.818590i	$0.694756\pi$
$642$	−20.9624	+	3.95391i	−0.827320	+	0.156048i
$643$	−9.82228			−0.387353			−0.193677	−	0.981065i	$-0.562041\pi$
$643$	−9.82228			−0.387353			−0.193677	+	0.981065i	$0.562041\pi$
$644$	7.70265			0.303527
$645$	−6.20117	−	32.8767i	−0.244171	−	1.29452i
$646$			46.3237i			1.82258i
$647$			37.0749i			1.45757i	0.684744	+	0.728783i	$0.259914\pi$
$647$			37.0749i			1.45757i	−0.684744	+	0.728783i	$0.740086\pi$
$648$	34.5765	−	31.9357i	1.35829	−	1.25455i
$649$	−14.7889	+	23.7467i	−0.580516	+	0.932139i
$650$			14.9009i			0.584462i
$651$	24.8781	−	4.69249i	0.975051	−	0.183913i
$652$	−20.1817			−0.790377
$653$			25.7924i			1.00933i	0.863314	+	0.504666i	$0.168385\pi$
$653$			25.7924i			1.00933i	−0.863314	+	0.504666i	$0.831615\pi$
$654$	22.0194	−	4.15329i	0.861029	−	0.162406i
$655$		−	3.52283i		−	0.137648i
$656$		−	1.35461i		−	0.0528886i
$657$	2.70337	+	6.91126i	0.105468	+	0.269634i
$658$	−49.5412			−1.93132
$659$	14.5855			0.568171			0.284085	−	0.958799i	$-0.408310\pi$
$659$	14.5855			0.568171			0.284085	+	0.958799i	$0.408310\pi$
$660$	−63.9442	+	12.0611i	−2.48903	+	0.469478i
$661$	−3.09947			−0.120555			−0.0602777	−	0.998182i	$-0.519199\pi$
$661$	−3.09947			−0.120555			−0.0602777	+	0.998182i	$0.519199\pi$
$662$	−23.3749			−0.908491
$663$	−4.21037	−	22.3221i	−0.163517	−	0.866918i
$664$	−78.3782			−3.04166
$665$		−	35.5354i		−	1.37800i
$666$	−31.3579	−	80.1677i	−1.21509	−	3.10644i
$667$		−	1.33336i		−	0.0516278i
$668$			39.8036i			1.54005i
$669$	−6.60719	−	35.0293i	−0.255449	−	1.35431i
$670$	−29.0885			−1.12379
$671$			36.1446i			1.39535i
$672$	0.793871	+	4.20886i	0.0306242	+	0.162360i
$673$			27.2988i			1.05229i	0.850394	+	0.526146i	$0.176363\pi$
$673$			27.2988i			1.05229i	−0.850394	+	0.526146i	$0.823637\pi$
$674$		−	62.8749i		−	2.42185i
$675$	−3.54037	−	5.65594i	−0.136269	−	0.217697i
$676$	−37.1142			−1.42747
$677$		−	35.2355i		−	1.35421i	−0.735887	−	0.677105i	$-0.763234\pi$
$677$		−	35.2355i		−	1.35421i	0.735887	−	0.677105i	$-0.236766\pi$
$678$	5.41226	+	28.6941i	0.207857	+	1.10199i
$679$		−	3.55213i		−	0.136318i
$680$	−36.6414			−1.40513
$681$	6.43171	+	34.0989i	0.246463	+	1.30667i
$682$			62.2445i			2.38346i
$683$	8.38433			0.320818			0.160409	−	0.987051i	$-0.448719\pi$
$683$	8.38433			0.320818			0.160409	+	0.987051i	$0.448719\pi$
$684$	−77.0571	+	30.1412i	−2.94635	+	1.15248i
$685$	39.3246			1.50251
$686$	49.8253			1.90234
$687$	−8.47060	+	1.59772i	−0.323174	+	0.0609567i
$688$		−	36.2358i		−	1.38148i
$689$	43.7104			1.66523
$690$	−9.33848	+	1.76141i	−0.355510	+	0.0670559i
$691$			0.346208i			0.0131704i	0.999978	+	0.00658518i	$0.00209614\pi$
$691$			0.346208i			0.0131704i	−0.999978	+	0.00658518i	$0.997904\pi$
$692$	14.7889			0.562190
$693$	−21.5202	+	8.41772i	−0.817485	+	0.319763i
$694$	41.9402			1.59203
$695$		−	27.9662i		−	1.06082i
$696$	13.4095	−	2.52929i	0.508287	−	0.0958726i
$697$	0.805070			0.0304942
$698$			19.0542i			0.721212i
$699$	−2.78963	−	14.7898i	−0.105514	−	0.559401i
$700$	11.1755			0.422394
$701$	−5.66376			−0.213917			−0.106959	−	0.994263i	$-0.534111\pi$
$701$	−5.66376			−0.213917			−0.106959	+	0.994263i	$0.534111\pi$
$702$	51.1079	−	31.9913i	1.92895	−	1.20743i
$703$			77.7758i			2.93337i
$704$	23.7243			0.894144
$705$	40.4178	−	7.62356i	1.52222	−	0.287120i
$706$	9.37666			0.352895
$707$	−11.6615			−0.438577
$708$	−51.0292	−	19.8259i	−1.91780	−	0.745102i
$709$	−12.5723			−0.472163			−0.236081	−	0.971733i	$-0.575863\pi$
$709$	−12.5723			−0.472163			−0.236081	+	0.971733i	$0.575863\pi$
$710$	16.6862			0.626220
$711$	9.96935	−	3.89955i	0.373880	−	0.146245i
$712$	−31.0257			−1.16274
$713$			6.11710i			0.229087i
$714$	−24.8781	+	4.69249i	−0.931041	+	0.175612i
$715$	−42.8425			−1.60222
$716$	−49.9061			−1.86508
$717$	−12.4491	+	2.34815i	−0.464922	+	0.0876931i
$718$		−	20.8156i		−	0.776832i
$719$	19.7655			0.737127			0.368564	−	0.929603i	$-0.379850\pi$
$719$	19.7655			0.737127			0.368564	+	0.929603i	$0.379850\pi$
$720$	−12.8831	−	32.9361i	−0.480124	−	1.22746i
$721$		−	26.2204i		−	0.976499i
$722$	64.1095			2.38591
$723$	−8.50972	−	45.1159i	−0.316480	−	1.67788i
$724$	17.8781			0.664436
$725$		−	1.93452i		−	0.0718462i
$726$	−1.79788	−	9.53180i	−0.0667256	−	0.353758i
$727$	18.8495			0.699089			0.349544	−	0.936920i	$-0.386336\pi$
$727$	18.8495			0.699089			0.349544	+	0.936920i	$0.386336\pi$
$728$			51.9016i			1.92360i
$729$	−11.7981	+	24.2859i	−0.436967	+	0.899478i
$730$	15.3345			0.567554
$731$	21.5356			0.796525
$732$	−69.5063	+	13.1102i	−2.56903	+	0.484567i
$733$	45.8146			1.69220			0.846101	−	0.533023i	$-0.178944\pi$
$733$	45.8146			1.69220			0.846101	+	0.533023i	$0.178944\pi$
$734$		−	0.630457i		−	0.0232706i
$735$	−10.7827	+	2.03382i	−0.397725	+	0.0750185i
$736$	−1.03489			−0.0381464
$737$		−	17.0904i		−	0.629533i
$738$	0.778432	+	1.99009i	0.0286545	+	0.0732563i
$739$			35.8896i			1.32022i	0.751168	+	0.660111i	$0.229491\pi$
$739$			35.8896i			1.32022i	−0.751168	+	0.660111i	$0.770509\pi$
$740$	−119.696			−4.40013
$741$	−53.5327	+	10.0973i	−1.96657	+	0.370933i
$742$		−	48.7156i		−	1.78841i
$743$		−	30.3737i		−	1.11430i	−0.830411	−	0.557151i	$-0.811894\pi$
$743$		−	30.3737i		−	1.11430i	0.830411	−	0.557151i	$-0.188106\pi$
$744$	−61.5195	+	11.6037i	−2.25541	+	0.425414i
$745$			25.4263i			0.931546i
$746$	−8.00223			−0.292983
$747$	41.8712	−	16.3781i	1.53199	−	0.599243i
$748$		−	41.8862i		−	1.53151i
$749$			10.5334i			0.384881i
$750$	39.2054	−	7.39489i	1.43158	−	0.270023i
$751$			49.0817i			1.79102i	0.445045	+	0.895508i	$0.353188\pi$
$751$			49.0817i			1.79102i	−0.445045	+	0.895508i	$0.646812\pi$
$752$	44.5474			1.62448
$753$	−43.7667	+	8.25524i	−1.59495	+	0.300838i
$754$	17.4806			0.636606
$755$	6.20117			0.225684
$756$	−23.9930	−	38.3303i	−0.872618	−	1.39406i
$757$	45.0272			1.63654			0.818271	−	0.574833i	$-0.194933\pi$
$757$	45.0272			1.63654			0.818271	+	0.574833i	$0.194933\pi$
$758$	−15.0675			−0.547278
$759$	−1.03489	−	5.48664i	−0.0375640	−	0.199153i
$760$			87.8731i			3.18749i
$761$			32.5225i			1.17894i	0.807791	+	0.589469i	$0.200663\pi$
$761$			32.5225i			1.17894i	−0.807791	+	0.589469i	$0.799337\pi$
$762$	−12.8412	−	68.0803i	−0.465189	−	2.46629i
$763$		−	11.0645i		−	0.400563i
$764$	−28.0536			−1.01494
$765$	19.5745	−	7.65666i	0.707719	−	0.276827i
$766$		−	74.5079i		−	2.69208i
$767$	−30.5955	−	19.0542i	−1.10474	−	0.688007i
$768$	10.4616	+	55.4644i	0.377502	+	2.00140i
$769$		−	13.1921i		−	0.475718i	−0.971300	−	0.237859i	$-0.923554\pi$
$769$		−	13.1921i		−	0.475718i	0.971300	−	0.237859i	$-0.0764456\pi$
$770$			47.7483i			1.72073i
$771$	31.3941	−	5.92152i	1.13063	−	0.213258i
$772$	27.8300			1.00163
$773$	−8.05585			−0.289749			−0.144874	−	0.989450i	$-0.546278\pi$
$773$	−8.05585			−0.289749			−0.144874	+	0.989450i	$0.546278\pi$
$774$	20.8231	+	53.2350i	0.748470	+	1.91349i
$775$			8.87507i			0.318802i
$776$			8.78382i			0.315321i
$777$	−41.7695	+	7.87852i	−1.49847	+	0.282640i
$778$			39.6967i			1.42320i
$779$		−	1.93072i		−	0.0691750i
$780$	−15.5397	−	82.3865i	−0.556409	−	2.94991i
$781$			9.80363i			0.350801i
$782$		−	6.11710i		−	0.218747i
$783$	−6.63511	+	4.15329i	−0.237120	+	0.148426i
$784$	−11.8844			−0.424442
$785$	−30.4402			−1.08646
$786$	1.11562	+	5.91470i	0.0397930	+	0.210970i
$787$	−55.0140			−1.96104			−0.980519	−	0.196426i	$-0.937067\pi$
$787$	−55.0140			−1.96104			−0.980519	+	0.196426i	$0.937067\pi$
$788$		−	5.58975i		−	0.199126i
$789$	15.8343	−	2.98665i	0.563715	−	0.106327i
$790$		−	22.1197i		−	0.786983i
$791$	14.4185			0.512663
$792$	53.2159	−	20.8156i	1.89094	−	0.739651i
$793$	−46.5691			−1.65372
$794$			45.7845i			1.62483i
$795$	7.49652	+	39.7442i	0.265874	+	1.40958i
$796$	32.4464			1.15003
$797$	40.9053			1.44894			0.724471	−	0.689306i	$-0.242084\pi$
$797$	40.9053			1.44894			0.724471	+	0.689306i	$0.242084\pi$
$798$	11.2535	+	59.6626i	0.398370	+	2.11203i
$799$			26.4754i			0.936631i
$800$	−1.50148			−0.0530852
$801$	16.5745	−	6.48320i	0.585632	−	0.229073i
$802$	75.5676			2.66838
$803$			9.00947i			0.317937i
$804$	32.8649	−	6.19895i	1.15906	−	0.218620i
$805$			4.69249i			0.165388i
$806$	−80.1964			−2.82480
$807$	−2.39209	−	12.6821i	−0.0842057	−	0.446433i
$808$	28.8370			1.01448
$809$	2.58998			0.0910587			0.0455294	−	0.998963i	$-0.485503\pi$
$809$	2.58998			0.0910587			0.0455294	+	0.998963i	$0.485503\pi$
$810$	37.8537	+	40.9839i	1.33004	+	1.44003i
$811$			13.4763i			0.473217i	0.971605	+	0.236609i	$0.0760359\pi$
$811$			13.4763i			0.473217i	−0.971605	+	0.236609i	$0.923964\pi$
$812$		−	13.1102i		−	0.460078i
$813$	1.79164	+	9.49870i	0.0628354	+	0.333134i
$814$		−	104.506i		−	3.66294i
$815$		−	12.2948i		−	0.430668i
$816$	22.3704	−	4.21948i	0.783121	−	0.147712i
$817$		−	51.6467i		−	1.80689i
$818$		−	79.7396i		−	2.78803i
$819$	−10.8455	−	27.7269i	−0.378972	−	0.968855i
$820$	2.97136			0.103764
$821$	27.4853			0.959244			0.479622	−	0.877475i	$-0.340774\pi$
$821$	27.4853			0.959244			0.479622	+	0.877475i	$0.340774\pi$
$822$	−66.0245	+	12.4535i	−2.30287	+	0.434365i
$823$		−	37.2850i		−	1.29967i	−0.760075	−	0.649836i	$-0.774838\pi$
$823$		−	37.2850i		−	1.29967i	0.760075	−	0.649836i	$-0.225162\pi$
$824$			64.8387i			2.25876i
$825$	−1.50148	−	7.96036i	−0.0522747	−	0.277144i
$826$	−21.2361	+	34.0989i	−0.738897	+	1.18645i
$827$			12.2091i			0.424554i	0.977210	+	0.212277i	$0.0680878\pi$
$827$			12.2091i			0.424554i	−0.977210	+	0.212277i	$0.931912\pi$
$828$	10.1755	−	3.98018i	0.353622	−	0.138321i
$829$	24.8991			0.864781			0.432391	−	0.901686i	$-0.357670\pi$
$829$	24.8991			0.864781			0.432391	+	0.901686i	$0.357670\pi$
$830$		−	92.9024i		−	3.22469i
$831$	8.27367	+	43.8644i	0.287010	+	1.52164i
$832$			30.5667i			1.05971i
$833$		−	7.06311i		−	0.244722i
$834$	8.85645	+	46.9542i	0.306674	+	1.62589i
$835$	−24.2485			−0.839155
$836$	−100.451			−3.47418
$837$	30.4402	−	19.0542i	1.05217	−	0.658610i
$838$	49.8216			1.72106
$839$	11.9666			0.413134			0.206567	−	0.978432i	$-0.433771\pi$
$839$	11.9666			0.413134			0.206567	+	0.978432i	$0.433771\pi$
$840$	−47.1922	+	8.90135i	−1.62829	+	0.307126i
$841$	26.7306			0.921744
$842$			57.1626i			1.96995i
$843$	−29.3203	+	5.53037i	−1.00985	+	0.190476i
$844$			72.5441i			2.49707i
$845$		−	22.6101i		−	0.777812i
$846$	−65.4457	+	25.5994i	−2.25007	+	0.880124i
$847$	−4.78963			−0.164574
$848$			43.8051i			1.50427i
$849$	32.4310	−	6.11710i	1.11303	−	0.209938i
$850$		−	8.87507i		−	0.304412i
$851$		−	10.2704i		−	0.352064i
$852$	−18.8524	+	3.55593i	−0.645874	+	0.121824i
$853$	32.0426			1.09712			0.548560	−	0.836111i	$-0.315176\pi$
$853$	32.0426			1.09712			0.548560	+	0.836111i	$0.315176\pi$
$854$			51.9016i			1.77604i
$855$	−18.3622	−	46.9436i	−0.627973	−	1.60544i
$856$		−	26.0473i		−	0.890279i
$857$	−26.8036			−0.915595			−0.457797	−	0.889057i	$-0.651361\pi$
$857$	−26.8036			−0.915595			−0.457797	+	0.889057i	$0.651361\pi$
$858$	71.9310	−	13.5676i	2.45568	−	0.463189i
$859$		−	21.7829i		−	0.743222i	−0.928389	−	0.371611i	$-0.878805\pi$
$859$		−	21.7829i		−	0.743222i	0.928389	−	0.371611i	$-0.121195\pi$
$860$	79.4839			2.71038
$861$	1.03689	−	0.195577i	0.0353371	−	0.00666525i
$862$	−52.1003			−1.77454
$863$	−15.7221			−0.535186			−0.267593	−	0.963532i	$-0.586228\pi$
$863$	−15.7221			−0.535186			−0.267593	+	0.963532i	$0.586228\pi$
$864$	3.22357	+	5.14984i	0.109668	+	0.175201i
$865$			9.00947i			0.306331i
$866$	30.0062			1.01965
$867$	−2.94991	−	15.6395i	−0.100184	−	0.531145i
$868$			60.1462i			2.04150i
$869$	12.9960			0.440859
$870$	2.99800	+	15.8945i	0.101642	+	0.538872i
$871$	22.0194			0.746100
$872$			27.3608i			0.926553i
$873$	−1.83549	−	4.69249i	−0.0621218	−	0.158817i
$874$	−14.6700			−0.496220
$875$		−	19.7003i		−	0.665992i
$876$	−17.3253	+	3.26788i	−0.585367	+	0.110411i
$877$	18.8719			0.637258			0.318629	−	0.947879i	$-0.396778\pi$
$877$	18.8719			0.637258			0.318629	+	0.947879i	$0.396778\pi$
$878$	58.9604			1.98982
$879$	−18.3420	+	3.45965i	−0.618660	+	0.116691i
$880$		−	42.9353i		−	1.44735i
$881$	−28.7717			−0.969343			−0.484672	−	0.874696i	$-0.661061\pi$
$881$	−28.7717			−0.969343			−0.484672	+	0.874696i	$0.661061\pi$
$882$	17.4596	−	6.82941i	0.587896	−	0.229958i
$883$	−4.64207			−0.156218			−0.0781091	−	0.996945i	$-0.524888\pi$
$883$	−4.64207			−0.156218			−0.0781091	+	0.996945i	$0.524888\pi$
$884$	53.9666			1.81509
$885$	12.0780	−	31.0872i	0.405998	−	1.04499i
$886$	−54.5830			−1.83375
$887$	23.9930			0.805607			0.402804	−	0.915286i	$-0.368036\pi$
$887$	23.9930			0.805607			0.402804	+	0.915286i	$0.368036\pi$
$888$	103.289	−	19.4823i	3.46615	−	0.653782i
$889$	−34.2097			−1.14735
$890$		−	36.7750i		−	1.23270i
$891$	−24.0793	+	22.2402i	−0.806687	+	0.745076i
$892$	84.6880			2.83556
$893$	63.4931			2.12471
$894$	−8.05210	−	42.6897i	−0.269302	−	1.42776i
$895$		−	30.4030i		−	1.01626i
$896$	39.0125			1.30332
$897$	7.06905	−	1.33336i	0.236029	−	0.0445195i
$898$		−	41.2944i		−	1.37801i
$899$	10.4115			0.347244
$900$	14.7632	−	5.77470i	0.492107	−	0.192490i
$901$	−26.0342			−0.867324
$902$			2.59427i			0.0863798i
$903$	27.7368	−	5.23169i	0.923023	−	0.174100i
$904$	−35.6546			−1.18585
$905$			10.8914i			0.362044i
$906$	−10.4115	+	1.96381i	−0.345900	+	0.0652434i
$907$	1.71585			0.0569740			0.0284870	−	0.999594i	$-0.490931\pi$
$907$	1.71585			0.0569740			0.0284870	+	0.999594i	$0.490931\pi$
$908$	−82.4387			−2.73583
$909$	−15.4053	+	6.02585i	−0.510961	+	0.199865i
$910$	−61.5195			−2.03935
$911$			18.6881i			0.619165i	0.950873	+	0.309582i	$0.100189\pi$
$911$			18.6881i			0.619165i	−0.950873	+	0.309582i	$0.899811\pi$
$912$	−10.1191	−	53.6486i	−0.335078	−	1.77648i
$913$	54.5830			1.80643
$914$		−	2.59427i		−	0.0858109i
$915$	−7.98680	−	42.3435i	−0.264035	−	1.39983i
$916$		−	20.4788i		−	0.676639i
$917$	2.97208			0.0981466
$918$	−30.4402	+	19.0542i	−1.00468	+	0.628882i
$919$			59.3228i			1.95688i	0.206536	+	0.978439i	$0.433781\pi$
$919$			59.3228i			1.95688i	−0.206536	+	0.978439i	$0.566219\pi$
$920$		−	11.6037i		−	0.382564i
$921$	0.327280	+	1.73514i	0.0107842	+	0.0571747i
$922$			10.7803i			0.355030i
$923$	−12.6311			−0.415758
$924$	−10.1755	−	53.9473i	−0.334749	−	1.77474i
$925$		−	14.9009i		−	0.489939i
$926$			17.7208i			0.582343i
$927$	−13.5488	−	34.6381i	−0.445003	−	1.13767i
$928$			1.76141i			0.0578213i
$929$	−31.7493			−1.04166			−0.520830	−	0.853660i	$-0.674378\pi$
$929$	−31.7493			−1.04166			−0.520830	+	0.853660i	$0.674378\pi$
$930$	−13.7540	−	72.9196i	−0.451012	−	2.39113i
$931$	−16.9387			−0.555144
$932$	35.7563			1.17124
$933$	−8.23878	+	1.55399i	−0.269726	+	0.0508754i
$934$	31.6476			1.03554
$935$	25.5173			0.834503
$936$	26.8191	+	68.5640i	0.876609	+	2.24108i
$937$			33.9258i			1.10831i	0.832414	+	0.554154i	$0.186958\pi$
$937$			33.9258i			1.10831i	−0.832414	+	0.554154i	$0.813042\pi$
$938$		−	24.5408i		−	0.801287i
$939$	−27.3029	+	5.14984i	−0.890996	+	0.168059i
$940$			97.7154i			3.18713i
$941$	−52.5613			−1.71345			−0.856725	−	0.515773i	$-0.827505\pi$
$941$	−52.5613			−1.71345			−0.856725	+	0.515773i	$0.827505\pi$
$942$	51.1079	−	9.63993i	1.66519	−	0.314086i
$943$			0.254953i			0.00830242i
$944$	19.0955	−	30.6618i	0.621504	−	0.997955i
$945$	23.3510	−	14.6167i	0.759607	−	0.475480i
$946$			69.3968i			2.25628i
$947$		−	52.5227i		−	1.70676i	−0.521291	−	0.853379i	$-0.674550\pi$
$947$		−	52.5227i		−	1.70676i	0.521291	−	0.853379i	$-0.325450\pi$
$948$	4.71385	+	24.9914i	0.153099	+	0.811682i
$949$	−11.6079			−0.376809
$950$	−21.2841			−0.690549
$951$	29.4395	−	5.55284i	0.954640	−	0.180063i
$952$		−	30.9129i		−	1.00189i
$953$			58.2368i			1.88647i	0.332120	+	0.943237i	$0.392236\pi$
$953$			58.2368i			1.88647i	−0.332120	+	0.943237i	$0.607764\pi$
$954$	−25.1728	−	64.3551i	−0.814998	−	2.08357i
$955$		−	17.0904i		−	0.553032i
$956$		−	30.0975i		−	0.973422i
$957$	−9.33848	+	1.76141i	−0.301870	+	0.0569384i
$958$		−	52.9800i		−	1.71171i
$959$			33.1766i			1.07133i
$960$	−27.7932	+	5.24232i	−0.897020	+	0.169195i
$961$	−16.7655			−0.540821
$962$	134.647			4.34119
$963$	5.44290	+	13.9150i	0.175395	+	0.448404i
$964$	109.074			3.51303
$965$			16.9542i			0.545775i
$966$	−1.48604	−	7.87852i	−0.0478125	−	0.253487i
$967$		−	2.56498i		−	0.0824840i	−0.999149	−	0.0412420i	$-0.986869\pi$
$967$		−	2.56498i		−	0.0824840i	0.999149	−	0.0412420i	$-0.0131315\pi$
$968$	11.8440			0.380679
$969$	31.8844	−	6.01400i	1.02427	−	0.193197i
$970$	−10.4115			−0.334294
$971$		−	13.3770i		−	0.429289i	−0.976692	−	0.214644i	$-0.931141\pi$
$971$		−	13.3770i		−	0.429289i	0.976692	−	0.214644i	$-0.0688592\pi$
$972$	−51.5020	−	38.2378i	−1.65193	−	1.22648i
$973$	23.5940			0.756388
$974$	−80.0621			−2.56535
$975$	10.2562	−	1.93452i	0.328462	−	0.0619542i
$976$		−	46.6699i		−	1.49387i
$977$	−18.7787			−0.600783			−0.300391	−	0.953816i	$-0.597117\pi$
$977$	−18.7787			−0.600783			−0.300391	+	0.953816i	$0.597117\pi$
$978$	3.89357	+	20.6425i	0.124503	+	0.660075i
$979$	21.6065			0.690546
$980$		−	26.0686i		−	0.832730i
$981$	−5.71737	−	14.6167i	−0.182542	−	0.466674i
$982$			51.5648i			1.64550i
$983$	6.18396			0.197238			0.0986189	−	0.995125i	$-0.468558\pi$
$983$	6.18396			0.197238			0.0986189	+	0.995125i	$0.468558\pi$
$984$	−2.56406	+	0.483630i	−0.0817391	+	0.0154175i
$985$	3.40530			0.108502
$986$	−10.4115			−0.331571
$987$	6.43171	+	34.0989i	0.204723	+	1.08538i
$988$		−	129.422i		−	4.11748i
$989$			6.82000i			0.216863i
$990$	24.6730	+	63.0773i	0.784158	+	2.00473i
$991$		−	20.6425i		−	0.655731i	−0.944724	−	0.327866i	$-0.893671\pi$
$991$		−	20.6425i		−	0.655731i	0.944724	−	0.327866i	$-0.106329\pi$
$992$		−	8.08092i		−	0.256569i
$993$	3.03465	+	16.0888i	0.0963019	+	0.510563i
$994$			14.0775i			0.446510i
$995$			19.7665i			0.626640i
$996$	19.7981	+	104.963i	0.627327	+	3.32590i
$997$	22.2485			0.704618			0.352309	−	0.935884i	$-0.385397\pi$
$997$	22.2485			0.704618			0.352309	+	0.935884i	$0.385397\pi$
$998$	−10.0910			−0.319425
$999$	−51.1079	+	31.9913i	−1.61698	+	1.01216i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+2.47283 q^{2} +(-0.321037 - 1.70204i) q^{3} +4.11491 q^{4} +2.50682i q^{5} +(-0.793871 - 4.20886i) q^{6} -2.11491 q^{7} +5.22982 q^{8} +(-2.79387 + 1.09283i) q^{9} +O(q^{10})\)	\(q+2.47283 q^{2} +(-0.321037 - 1.70204i) q^{3} +4.11491 q^{4} +2.50682i q^{5} +(-0.793871 - 4.20886i) q^{6} -2.11491 q^{7} +5.22982 q^{8} +(-2.79387 + 1.09283i) q^{9} +6.19895i q^{10} -3.64207 q^{11} +(-1.32104 - 7.00373i) q^{12} -4.69249i q^{13} -5.22982 q^{14} +(4.26670 - 0.804782i) q^{15} +4.70265 q^{16} +2.79487i q^{17} +(-6.90878 + 2.70240i) q^{18} +6.70265 q^{19} +10.3153i q^{20} +(0.678963 + 3.59965i) q^{21} -9.00624 q^{22} -0.885092 q^{23} +(-1.67896 - 8.90135i) q^{24} -1.28415 q^{25} -11.6037i q^{26} +(2.75698 + 4.40444i) q^{27} -8.70265 q^{28} +1.50646i q^{29} +(10.5509 - 1.99009i) q^{30} -6.91126i q^{31} +1.16924 q^{32} +(1.16924 + 6.19895i) q^{33} +6.91126i q^{34} -5.30169i q^{35} +(-11.4965 + 4.49691i) q^{36} +11.6037i q^{37} +16.5745 q^{38} +(-7.98680 + 1.50646i) q^{39} +13.1102i q^{40} -0.288053i q^{41} +(1.67896 + 8.90135i) q^{42} -7.70541i q^{43} -14.9868 q^{44} +(-2.73954 - 7.00373i) q^{45} -2.18869 q^{46} +9.47283 q^{47} +(-1.50972 - 8.00409i) q^{48} -2.52717 q^{49} -3.17548 q^{50} +(4.75698 - 0.897257i) q^{51} -19.3092i q^{52} +9.31497i q^{53} +(6.81756 + 10.8914i) q^{54} -9.13002i q^{55} -11.0606 q^{56} +(-2.15180 - 11.4082i) q^{57} +3.72523i q^{58} +(4.06058 - 6.52010i) q^{59} +(17.5571 - 3.31160i) q^{60} -9.92418i q^{61} -17.0904i q^{62} +(5.90878 - 2.31124i) q^{63} -6.51396 q^{64} +11.7632 q^{65} +(2.89134 + 15.3290i) q^{66} +4.69249i q^{67} +11.5006i q^{68} +(0.284147 + 1.50646i) q^{69} -13.1102i q^{70} -2.69177i q^{71} +(-14.6114 + 5.71532i) q^{72} -2.47372i q^{73} +28.6941i q^{74} +(0.412259 + 2.18567i) q^{75} +27.5808 q^{76} +7.70265 q^{77} +(-19.7500 + 3.72523i) q^{78} -3.56829 q^{79} +11.7887i q^{80} +(6.61143 - 6.10647i) q^{81} -0.712306i q^{82} -14.9868 q^{83} +(2.79387 + 14.8122i) q^{84} -7.00624 q^{85} -19.0542i q^{86} +(2.56406 - 0.483630i) q^{87} -19.0474 q^{88} -5.93246 q^{89} +(-6.77442 - 17.3191i) q^{90} +9.92418i q^{91} -3.64207 q^{92} +(-11.7632 + 2.21877i) q^{93} +23.4247 q^{94} +16.8023i q^{95} +(-0.375369 - 1.99009i) q^{96} +1.67957i q^{97} -6.24926 q^{98} +(10.1755 - 3.98018i) 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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