LMFDB - Embedded newform 177.2.d.a.176.4

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			176.4
Root			$-1.16170 - 1.28470i$ of defining polynomial
Character	$\chi$	$=$	177.176
Dual form			177.2.d.a.176.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.46260 q^{2} +(1.16170 + 1.28470i) q^{3} +0.139194 q^{4} -0.594299i q^{5} +(-1.69910 - 1.87900i) q^{6} +1.86081 q^{7} +2.72161 q^{8} +(-0.300896 + 2.98487i) q^{9} +O(q^{10})$	\(q-1.46260 q^{2} +(1.16170 + 1.28470i) q^{3} +0.139194 q^{4} -0.594299i q^{5} +(-1.69910 - 1.87900i) q^{6} +1.86081 q^{7} +2.72161 q^{8} +(-0.300896 + 2.98487i) q^{9} +0.869221i q^{10} +0.676596 q^{11} +(0.161702 + 0.178822i) q^{12} +5.37545i q^{13} -2.72161 q^{14} +(0.763495 - 0.690399i) q^{15} -4.25901 q^{16} +1.70017i q^{17} +(0.440090 - 4.36567i) q^{18} -2.25901 q^{19} -0.0827230i q^{20} +(2.16170 + 2.39057i) q^{21} -0.989588 q^{22} +4.86081 q^{23} +(3.16170 + 3.49645i) q^{24} +4.64681 q^{25} -7.86212i q^{26} +(-4.18421 + 3.08097i) q^{27} +0.259013 q^{28} -6.24467i q^{29} +(-1.11669 + 1.00978i) q^{30} +2.48667i q^{31} +0.786003 q^{32} +(0.786003 + 0.869221i) q^{33} -2.48667i q^{34} -1.10588i q^{35} +(-0.0418830 + 0.415477i) q^{36} -7.86212i q^{37} +3.30403 q^{38} +(-6.90582 + 6.24467i) q^{39} -1.61745i q^{40} -2.29447i q^{41} +(-3.16170 - 3.49645i) q^{42} -7.11389i q^{43} +0.0941782 q^{44} +(1.77391 + 0.178822i) q^{45} -7.10941 q^{46} -8.46260 q^{47} +(-4.94770 - 5.47154i) q^{48} -3.53740 q^{49} -6.79641 q^{50} +(-2.18421 + 1.97510i) q^{51} +0.748230i q^{52} -5.73309i q^{53} +(6.11982 - 4.50622i) q^{54} -0.402100i q^{55} +5.06439 q^{56} +(-2.62430 - 2.90215i) q^{57} +9.13344i q^{58} +(1.93561 + 7.43326i) q^{59} +(0.106274 - 0.0960994i) q^{60} -10.0027i q^{61} -3.63700i q^{62} +(-0.559910 + 5.55427i) q^{63} +7.36842 q^{64} +3.19462 q^{65} +(-1.14961 - 1.27132i) q^{66} -5.37545i q^{67} +0.236654i q^{68} +(5.64681 + 6.24467i) q^{69} +1.61745i q^{70} +5.92529i q^{71} +(-0.818923 + 8.12366i) q^{72} +8.26422i q^{73} +11.4991i q^{74} +(5.39821 + 5.96974i) q^{75} -0.314441 q^{76} +1.25901 q^{77} +(10.1004 - 9.13344i) q^{78} +8.29362 q^{79} +2.53113i q^{80} +(-8.81892 - 1.79627i) q^{81} +3.35589i q^{82} +0.0941782 q^{83} +(0.300896 + 0.332754i) q^{84} +1.01041 q^{85} +10.4048i q^{86} +(8.02251 - 7.25444i) q^{87} +1.84143 q^{88} -10.9806 q^{89} +(-2.59451 - 0.261545i) q^{90} +10.0027i q^{91} +0.676596 q^{92} +(-3.19462 + 2.88877i) q^{93} +12.3774 q^{94} +1.34253i q^{95} +(0.913101 + 1.00978i) q^{96} -17.8648i q^{97} +5.17380 q^{98} +(-0.203585 + 2.01955i) 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 $

$2$	−1.46260			−1.03421			−0.517107	−	0.855921i	$-0.672991\pi$
$2$	−1.46260			−1.03421			−0.517107	+	0.855921i	$0.672991\pi$
$3$	1.16170	+	1.28470i	0.670709	+	0.741721i
$3$	1.16170	+	1.28470i	0.670709	+	0.741721i
$4$	0.139194			0.0695971
$5$		−	0.594299i		−	0.265779i	−0.991131	−	0.132889i	$-0.957575\pi$
$5$		−	0.594299i		−	0.265779i	0.991131	−	0.132889i	$-0.0424255\pi$
$6$	−1.69910	−	1.87900i	−0.693656	−	0.767097i
$7$	1.86081			0.703319			0.351659	−	0.936128i	$-0.385618\pi$
$7$	1.86081			0.703319			0.351659	+	0.936128i	$0.385618\pi$
$8$	2.72161			0.962235
$9$	−0.300896	+	2.98487i	−0.100299	+	0.994957i
$10$			0.869221i			0.274872i
$11$	0.676596			0.204001			0.102001	−	0.994784i	$-0.467476\pi$
$11$	0.676596			0.204001			0.102001	+	0.994784i	$0.467476\pi$
$12$	0.161702	+	0.178822i	0.0466794	+	0.0516216i
$13$			5.37545i			1.49088i	0.666573	+	0.745440i	$0.267761\pi$
$13$			5.37545i			1.49088i	−0.666573	+	0.745440i	$0.732239\pi$
$14$	−2.72161			−0.727381
$15$	0.763495	−	0.690399i	0.197133	−	0.178260i
$16$	−4.25901			−1.06475
$17$			1.70017i			0.412353i	0.978515	+	0.206176i	$0.0661021\pi$
$17$			1.70017i			0.412353i	−0.978515	+	0.206176i	$0.933898\pi$
$18$	0.440090	−	4.36567i	0.103730	−	1.02900i
$19$	−2.25901			−0.518253			−0.259127	−	0.965843i	$-0.583435\pi$
$19$	−2.25901			−0.518253			−0.259127	+	0.965843i	$0.583435\pi$
$20$		−	0.0827230i		−	0.0184974i
$21$	2.16170	+	2.39057i	0.471722	+	0.521666i
$22$	−0.989588			−0.210981
$23$	4.86081			1.01355			0.506774	−	0.862079i	$-0.330838\pi$
$23$	4.86081			1.01355			0.506774	+	0.862079i	$0.330838\pi$
$24$	3.16170	+	3.49645i	0.645380	+	0.713710i
$25$	4.64681			0.929362
$26$		−	7.86212i		−	1.54189i
$27$	−4.18421	+	3.08097i	−0.805252	+	0.592933i
$28$	0.259013			0.0489489
$29$		−	6.24467i		−	1.15961i	−0.814757	−	0.579803i	$-0.803130\pi$
$29$		−	6.24467i		−	1.15961i	0.814757	−	0.579803i	$-0.196870\pi$
$30$	−1.11669	+	1.00978i	−0.203878	+	0.184359i
$31$			2.48667i			0.446620i	0.974748	+	0.223310i	$0.0716861\pi$
$31$			2.48667i			0.446620i	−0.974748	+	0.223310i	$0.928314\pi$
$32$	0.786003			0.138947
$33$	0.786003	+	0.869221i	0.136826	+	0.151312i
$34$		−	2.48667i		−	0.426461i
$35$		−	1.10588i		−	0.186927i
$36$	−0.0418830	+	0.415477i	−0.00698050	+	0.0692461i
$37$		−	7.86212i		−	1.29252i	−0.763116	−	0.646262i	$-0.776331\pi$
$37$		−	7.86212i		−	1.29252i	0.763116	−	0.646262i	$-0.223669\pi$
$38$	3.30403			0.535984
$39$	−6.90582	+	6.24467i	−1.10582	+	0.999947i
$40$		−	1.61745i		−	0.255742i
$41$		−	2.29447i		−	0.358337i	−0.983818	−	0.179168i	$-0.942659\pi$
$41$		−	2.29447i		−	0.358337i	0.983818	−	0.179168i	$-0.0573407\pi$
$42$	−3.16170	−	3.49645i	−0.487861	−	0.539514i
$43$		−	7.11389i		−	1.08486i	−0.840102	−	0.542429i	$-0.817505\pi$
$43$		−	7.11389i		−	1.08486i	0.840102	−	0.542429i	$-0.182495\pi$
$44$	0.0941782			0.0141979
$45$	1.77391	+	0.178822i	0.264438	+	0.0266573i
$46$	−7.10941			−1.04822
$47$	−8.46260			−1.23440			−0.617198	−	0.786808i	$-0.711732\pi$
$47$	−8.46260			−1.23440			−0.617198	+	0.786808i	$0.711732\pi$
$48$	−4.94770	−	5.47154i	−0.714140	−	0.789749i
$49$	−3.53740			−0.505343
$50$	−6.79641			−0.961158
$51$	−2.18421	+	1.97510i	−0.305851	+	0.276569i
$52$			0.748230i			0.103761i
$53$		−	5.73309i		−	0.787500i	−0.919217	−	0.393750i	$-0.871177\pi$
$53$		−	5.73309i		−	0.787500i	0.919217	−	0.393750i	$-0.128823\pi$
$54$	6.11982	−	4.50622i	0.832802	−	0.613219i
$55$		−	0.402100i		−	0.0542192i
$56$	5.06439			0.676758
$57$	−2.62430	−	2.90215i	−0.347597	−	0.384399i
$58$			9.13344i			1.19928i
$59$	1.93561	+	7.43326i	0.251995	+	0.967729i
$59$	1.93561	+	7.43326i	0.251995	+	0.967729i
$60$	0.106274	−	0.0960994i	0.0137199	−	0.0124064i
$61$		−	10.0027i		−	1.28071i	−0.768079	−	0.640355i	$-0.778787\pi$
$61$		−	10.0027i		−	1.28071i	0.768079	−	0.640355i	$-0.221213\pi$
$62$		−	3.63700i		−	0.461900i
$63$	−0.559910	+	5.55427i	−0.0705420	+	0.699772i
$64$	7.36842			0.921053
$65$	3.19462			0.396244
$66$	−1.14961	−	1.27132i	−0.141507	−	0.156489i
$67$		−	5.37545i		−	0.656715i	−0.944553	−	0.328358i	$-0.893505\pi$
$67$		−	5.37545i		−	0.656715i	0.944553	−	0.328358i	$-0.106495\pi$
$68$			0.236654i			0.0286986i
$69$	5.64681	+	6.24467i	0.679796	+	0.751769i
$70$			1.61745i			0.193322i
$71$			5.92529i			0.703202i	0.936150	+	0.351601i	$0.114363\pi$
$71$			5.92529i			0.703202i	−0.936150	+	0.351601i	$0.885637\pi$
$72$	−0.818923	+	8.12366i	−0.0965110	+	0.957383i
$73$			8.26422i			0.967254i	0.875274	+	0.483627i	$0.160681\pi$
$73$			8.26422i			0.967254i	−0.875274	+	0.483627i	$0.839319\pi$
$74$			11.4991i			1.33675i
$75$	5.39821	+	5.96974i	0.623331	+	0.689327i
$76$	−0.314441			−0.0360689
$77$	1.25901			0.143478
$78$	10.1004	−	9.13344i	1.14365	−	1.03416i
$79$	8.29362			0.933105			0.466552	−	0.884494i	$-0.345496\pi$
$79$	8.29362			0.933105			0.466552	+	0.884494i	$0.345496\pi$
$80$			2.53113i			0.282989i
$81$	−8.81892	−	1.79627i	−0.979880	−	0.199586i
$82$			3.35589i			0.370596i
$83$	0.0941782			0.0103374			0.00516870	−	0.999987i	$-0.498355\pi$
$83$	0.0941782			0.0103374			0.00516870	+	0.999987i	$0.498355\pi$
$84$	0.300896	+	0.332754i	0.0328305	+	0.0363064i
$85$	1.01041			0.109595
$86$			10.4048i			1.12197i
$87$	8.02251	−	7.25444i	0.860103	−	0.777758i
$88$	1.84143			0.196297
$89$	−10.9806			−1.16394			−0.581972	−	0.813209i	$-0.697719\pi$
$89$	−10.9806			−1.16394			−0.581972	+	0.813209i	$0.697719\pi$
$90$	−2.59451	−	0.261545i	−0.273486	−	0.0275693i
$91$			10.0027i			1.04856i
$92$	0.676596			0.0705400
$93$	−3.19462	+	2.88877i	−0.331267	+	0.299552i
$94$	12.3774			1.27663
$95$			1.34253i			0.137741i
$96$	0.913101	+	1.00978i	0.0931930	+	0.103060i
$97$		−	17.8648i		−	1.81389i	−0.421246	−	0.906947i	$-0.638407\pi$
$97$		−	17.8648i		−	1.81389i	0.421246	−	0.906947i	$-0.361593\pi$
$98$	5.17380			0.522633
$99$	−0.203585	+	2.01955i	−0.0204611	+	0.202973i
$100$	0.646809			0.0646809
$101$	8.36842			0.832689			0.416344	−	0.909207i	$-0.363311\pi$
$101$	8.36842			0.832689			0.416344	+	0.909207i	$0.363311\pi$
$102$	3.19462	−	2.88877i	0.316315	−	0.286031i
$103$			1.73844i			0.171294i	0.996326	+	0.0856469i	$0.0272957\pi$
$103$			1.73844i			0.171294i	−0.996326	+	0.0856469i	$0.972704\pi$
$104$			14.6299i			1.43458i
$105$	1.42072	−	1.28470i	0.138648	−	0.125374i
$106$			8.38521i			0.814443i
$107$		−	7.66992i		−	0.741479i	−0.928737	−	0.370740i	$-0.879104\pi$
$107$		−	7.66992i		−	0.741479i	0.928737	−	0.370740i	$-0.120896\pi$
$108$	−0.582418	+	0.428853i	−0.0560432	+	0.0412664i
$109$			15.3781i			1.47296i	0.676462	+	0.736478i	$0.263512\pi$
$109$			15.3781i			1.47296i	−0.676462	+	0.736478i	$0.736488\pi$
$110$			0.588111i			0.0560742i
$111$	10.1004	−	9.13344i	0.958692	−	0.866908i
$112$	−7.92520			−0.748861
$113$	−6.11982			−0.575704			−0.287852	−	0.957675i	$-0.592941\pi$
$113$	−6.11982			−0.575704			−0.287852	+	0.957675i	$0.592941\pi$
$114$	3.83830	+	4.24468i	0.359490	+	0.397551i
$115$		−	2.88877i		−	0.269379i
$116$		−	0.869221i		−	0.0807051i
$117$	−16.0450	−	1.61745i	−1.48336	−	0.149533i
$118$	−2.83102	−	10.8719i	−0.260616	−	1.00084i
$119$			3.16369i			0.290015i
$120$	2.07794	−	1.87900i	0.189689	−	0.171528i
$121$	−10.5422			−0.958383
$122$			14.6299i			1.32453i
$123$	2.94770	−	2.66549i	0.265786	−	0.240340i
$124$			0.346130i			0.0310834i
$125$		−	5.73309i		−	0.512783i
$126$	0.818923	−	8.12366i	0.0729554	−	0.723713i
$127$	6.20359			0.550479			0.275240	−	0.961376i	$-0.411243\pi$
$127$	6.20359			0.550479			0.275240	+	0.961376i	$0.411243\pi$
$128$	−12.3490			−1.09151
$129$	9.13919	−	8.26422i	0.804661	−	0.727624i
$130$	−4.67245			−0.409801
$131$	−16.5180			−1.44319			−0.721593	−	0.692317i	$-0.756590\pi$
$131$	−16.5180			−1.44319			−0.721593	+	0.692317i	$0.756590\pi$
$132$	0.109407	+	0.120990i	0.00952265	+	0.0105309i
$133$	−4.20359			−0.364497
$134$			7.86212i			0.679184i
$135$	1.83102	+	2.48667i	0.157589	+	0.214019i
$136$			4.62721i			0.396780i
$137$		−	17.5071i		−	1.49574i	−0.663848	−	0.747868i	$-0.731078\pi$
$137$		−	17.5071i		−	1.49574i	0.663848	−	0.747868i	$-0.268922\pi$
$138$	−8.25901	−	9.13344i	−0.703054	−	0.777490i
$139$	5.69182			0.482774			0.241387	−	0.970429i	$-0.422398\pi$
$139$	5.69182			0.482774			0.241387	+	0.970429i	$0.422398\pi$
$140$		−	0.153931i		−	0.0130096i
$141$	−9.83102	−	10.8719i	−0.827921	−	0.915578i
$142$		−	8.66632i		−	0.727261i
$143$			3.63700i			0.304141i
$144$	1.28152	−	12.7126i	0.106793	−	1.05938i
$145$	−3.71120			−0.308198
$146$		−	12.0872i		−	1.00035i
$147$	−4.10941	−	4.54449i	−0.338938	−	0.374823i
$148$		−	1.09436i		−	0.0899559i
$149$	21.5976			1.76935			0.884674	−	0.466210i	$-0.154381\pi$
$149$	21.5976			1.76935			0.884674	+	0.466210i	$0.154381\pi$
$150$	−7.89541	−	8.73134i	−0.644658	−	0.712911i
$151$			8.26422i			0.672533i	0.941767	+	0.336266i	$0.109164\pi$
$151$			8.26422i			0.672533i	−0.941767	+	0.336266i	$0.890836\pi$
$152$	−6.14816			−0.498681
$153$	−5.07480	−	0.511576i	−0.410274	−	0.0413585i
$154$	−1.84143			−0.148387
$155$	1.47783			0.118702
$156$	−0.961250	+	0.869221i	−0.0769616	+	0.0695934i
$157$			12.8914i			1.02885i	0.857536	+	0.514424i	$0.171994\pi$
$157$			12.8914i			1.02885i	−0.857536	+	0.514424i	$0.828006\pi$
$158$	−12.1302			−0.965029
$159$	7.36529	−	6.66014i	0.584105	−	0.528184i
$160$		−	0.467121i		−	0.0369291i
$161$	9.04502			0.712847
$162$	12.8985	+	2.62723i	1.01341	+	0.206414i
$163$	−15.7562			−1.23412			−0.617061	−	0.786915i	$-0.711677\pi$
$163$	−15.7562			−1.23412			−0.617061	+	0.786915i	$0.711677\pi$
$164$		−	0.319377i		−	0.0249392i
$165$	0.516577	−	0.467121i	0.0402155	−	0.0363653i
$166$	−0.137745			−0.0106911
$167$			13.0454i			1.00948i	0.863271	+	0.504740i	$0.168412\pi$
$167$			13.0454i			1.00948i	−0.863271	+	0.504740i	$0.831588\pi$
$168$	5.88331	+	6.50621i	0.453908	+	0.501965i
$169$	−15.8954			−1.22272
$170$	−1.47783			−0.113344
$171$	0.679729	−	6.74287i	0.0519802	−	0.515640i
$172$		−	0.990211i		−	0.0755029i
$173$	9.40862			0.715324			0.357662	−	0.933851i	$-0.383574\pi$
$173$	9.40862			0.715324			0.357662	+	0.933851i	$0.383574\pi$
$174$	−11.7337	+	10.6103i	−0.889530	+	0.804367i
$175$	8.64681			0.653637
$176$	−2.88163			−0.217211
$177$	−7.30090	+	11.1219i	−0.548769	+	0.835974i
$178$	16.0602			1.20377
$179$	23.0450			1.72247			0.861233	−	0.508211i	$-0.169693\pi$
$179$	23.0450			1.72247			0.861233	+	0.508211i	$0.169693\pi$
$180$	0.246917	+	0.0248910i	0.0184041	+	0.00185527i
$181$	−7.58242			−0.563597			−0.281798	−	0.959474i	$-0.590931\pi$
$181$	−7.58242			−0.563597			−0.281798	+	0.959474i	$0.590931\pi$
$182$		−	14.6299i		−	1.08444i
$183$	12.8504	−	11.6201i	0.949928	−	0.858983i
$184$	13.2292			0.975271
$185$	−4.67245			−0.343525
$186$	4.67245	−	4.22511i	0.342601	−	0.309800i
$187$			1.15033i			0.0841205i
$188$	−1.17794			−0.0859104
$189$	−7.78600	+	5.73309i	−0.566348	+	0.417021i
$190$		−	1.96358i		−	0.142453i
$191$	−6.11982			−0.442815			−0.221407	−	0.975181i	$-0.571065\pi$
$191$	−6.11982			−0.442815			−0.221407	+	0.975181i	$0.571065\pi$
$192$	8.55991	+	9.46619i	0.617758	+	0.683164i
$193$	−8.19462			−0.589862			−0.294931	−	0.955519i	$-0.595297\pi$
$193$	−8.19462			−0.589862			−0.294931	+	0.955519i	$0.595297\pi$
$194$			26.1290i			1.87595i
$195$	3.71120	+	4.10412i	0.265765	+	0.293902i
$196$	−0.492386			−0.0351704
$197$		−	24.4288i		−	1.74048i	−0.492627	−	0.870241i	$-0.663963\pi$
$197$		−	24.4288i		−	1.74048i	0.492627	−	0.870241i	$-0.336037\pi$
$198$	0.297763	−	2.95379i	0.0211611	−	0.209917i
$199$	11.8608			0.840790			0.420395	−	0.907341i	$-0.361891\pi$
$199$	11.8608			0.840790			0.420395	+	0.907341i	$0.361891\pi$
$200$	12.6468			0.894264
$201$	6.90582	−	6.24467i	0.487099	−	0.440465i
$202$	−12.2396			−0.861178
$203$		−	11.6201i		−	0.815572i
$204$	−0.304029	+	0.274922i	−0.0212863	+	0.0192484i
$205$	−1.36360			−0.0952382
$206$		−	2.54264i		−	0.177154i
$207$	−1.46260	+	14.5089i	−0.101658	+	1.00844i
$208$		−	22.8941i		−	1.58742i
$209$	−1.52844			−0.105724
$210$	−2.07794	+	1.87900i	−0.143391	+	0.129663i
$211$			17.1165i			1.17835i	0.808005	+	0.589176i	$0.200547\pi$
$211$			17.1165i			1.17835i	−0.808005	+	0.589176i	$0.799453\pi$
$212$		−	0.798013i		−	0.0548077i
$213$	−7.61220	+	6.88342i	−0.521580	+	0.471644i
$214$			11.2180i			0.766847i
$215$	−4.22778			−0.288332
$216$	−11.3878	+	8.38521i	−0.774841	+	0.570541i
$217$			4.62721i			0.314116i
$218$		−	22.4920i		−	1.52335i
$219$	−10.6170	+	9.60056i	−0.717432	+	0.648746i
$220$		−	0.0559700i		−	0.00377350i
$221$	−9.13919			−0.614769
$222$	−14.7729	+	13.3586i	−0.991492	+	0.896567i
$223$	−7.31444			−0.489811			−0.244906	−	0.969547i	$-0.578757\pi$
$223$	−7.31444			−0.489811			−0.244906	+	0.969547i	$0.578757\pi$
$224$	1.46260			0.0977240
$225$	−1.39821	+	13.8701i	−0.0932138	+	0.924675i
$226$	8.95084			0.595401
$227$	−15.7473			−1.04518			−0.522591	−	0.852584i	$-0.675034\pi$
$227$	−15.7473			−1.04518			−0.522591	+	0.852584i	$0.675034\pi$
$228$	−0.365287	−	0.403962i	−0.0241917	−	0.0267530i
$229$		−	26.5311i		−	1.75322i	−0.481198	−	0.876612i	$-0.659798\pi$
$229$		−	26.5311i		−	1.75322i	0.481198	−	0.876612i	$-0.340202\pi$
$230$			4.22511i			0.278596i
$231$	1.46260	+	1.61745i	0.0962319	+	0.106420i
$232$		−	16.9956i		−	1.11581i
$233$	15.1648			0.993481			0.496741	−	0.867899i	$-0.334530\pi$
$233$	15.1648			0.993481			0.496741	+	0.867899i	$0.334530\pi$
$234$	23.4674	+	2.36568i	1.53411	+	0.154649i
$235$			5.02931i			0.328076i
$236$	0.269425	+	1.03467i	0.0175381	+	0.0673511i
$237$	9.63471	+	10.6548i	0.625842	+	0.692103i
$238$		−	4.62721i		−	0.299938i
$239$			17.0338i			1.10183i	0.834563	+	0.550913i	$0.185720\pi$
$239$			17.0338i			1.10183i	−0.834563	+	0.550913i	$0.814280\pi$
$240$	−3.25173	+	2.94042i	−0.209899	+	0.189803i
$241$	−10.2847			−0.662493			−0.331246	−	0.943544i	$-0.607469\pi$
$241$	−10.2847			−0.662493			−0.331246	+	0.943544i	$0.607469\pi$
$242$	15.4190			0.991173
$243$	−7.93729	−	13.4164i	−0.509178	−	0.860661i
$244$		−	1.39231i		−	0.0891336i
$245$			2.10227i			0.134309i
$246$	−4.31131	+	3.89855i	−0.274879	+	0.248562i
$247$		−	12.1432i		−	0.772653i
$248$			6.76776i			0.429753i
$249$	0.109407	+	0.120990i	0.00693339	+	0.00766746i
$250$			8.38521i			0.530327i
$251$		−	15.1299i		−	0.954993i	−0.878634	−	0.477497i	$-0.841544\pi$
$251$		−	15.1299i		−	0.954993i	0.878634	−	0.477497i	$-0.158456\pi$
$252$	−0.0779361	+	0.773122i	−0.00490952	+	0.0487021i
$253$	3.28880			0.206765
$254$	−9.07335			−0.569313
$255$	1.17380	+	1.29807i	0.0735061	+	0.0812886i
$256$	3.32485			0.207803
$257$		−	6.13519i		−	0.382703i	−0.981522	−	0.191351i	$-0.938713\pi$
$257$		−	6.13519i		−	0.382703i	0.981522	−	0.191351i	$-0.0612870\pi$
$258$	−13.3670	+	12.0872i	−0.832191	+	0.752518i
$259$		−	14.6299i		−	0.909056i
$260$	0.444673			0.0275774
$261$	18.6395	+	1.87900i	1.15376	+	0.116307i
$262$	24.1592			1.49256
$263$			23.7073i			1.46186i	0.682454	+	0.730929i	$0.260913\pi$
$263$			23.7073i			1.46186i	−0.682454	+	0.730929i	$0.739087\pi$
$264$	2.13919	+	2.36568i	0.131658	+	0.145598i
$265$	−3.40717			−0.209301
$266$	6.14816			0.376968
$267$	−12.7562	−	14.1068i	−0.780668	−	0.863321i
$268$		−	0.748230i		−	0.0457055i
$269$	−26.1890			−1.59677			−0.798387	−	0.602145i	$-0.794313\pi$
$269$	−26.1890			−1.59677			−0.798387	+	0.602145i	$0.794313\pi$
$270$	−2.67805	−	3.63700i	−0.162981	−	0.221341i
$271$	22.3144			1.35551			0.677753	−	0.735290i	$-0.262954\pi$
$271$	22.3144			1.35551			0.677753	+	0.735290i	$0.262954\pi$
$272$		−	7.24107i		−	0.439054i
$273$	−12.8504	+	11.6201i	−0.777741	+	0.703281i
$274$			25.6059i			1.54691i
$275$	3.14401			0.189591
$276$	0.786003	+	0.869221i	0.0473118	+	0.0523210i
$277$	23.8269			1.43162			0.715809	−	0.698296i	$-0.246058\pi$
$277$	23.8269			1.43162			0.715809	+	0.698296i	$0.246058\pi$
$278$	−8.32485			−0.499292
$279$	−7.42240	−	0.748230i	−0.444367	−	0.0447954i
$280$		−	3.00976i		−	0.179868i
$281$		−	2.40395i		−	0.143408i	−0.997426	−	0.0717038i	$-0.977156\pi$
$281$		−	2.40395i		−	0.143408i	0.997426	−	0.0717038i	$-0.0228436\pi$
$282$	14.3788	+	15.9012i	0.856247	+	0.946902i
$283$			10.4048i			0.618499i	0.950981	+	0.309249i	$0.100078\pi$
$283$			10.4048i			0.618499i	−0.950981	+	0.309249i	$0.899922\pi$
$284$			0.824766i			0.0489408i
$285$	−1.72474	+	1.55962i	−0.102165	+	0.0923839i
$286$		−	5.31948i		−	0.314547i
$287$		−	4.26957i		−	0.252025i
$288$	−0.236505	+	2.34612i	−0.0139362	+	0.138246i
$289$	14.1094			0.829965
$290$	5.42799			0.318743
$291$	22.9508	−	20.7535i	1.34540	−	1.21659i
$292$			1.15033i			0.0673180i
$293$		−	26.3212i		−	1.53770i	−0.639429	−	0.768850i	$-0.720829\pi$
$293$		−	26.3212i		−	1.53770i	0.639429	−	0.768850i	$-0.279171\pi$
$294$	6.01041	+	6.64677i	0.350534	+	0.387647i
$295$	4.41758	−	1.15033i	0.257202	−	0.0669748i
$296$		−	21.3976i		−	1.24371i
$297$	−2.83102	+	2.08457i	−0.164272	+	0.120959i
$298$	−31.5887			−1.82988
$299$			26.1290i			1.51108i
$300$	0.751399	+	0.830953i	0.0433820	+	0.0479751i
$301$		−	13.2376i		−	0.763000i
$302$		−	12.0872i		−	0.695542i
$303$	9.72161	+	10.7509i	0.558492	+	0.617623i
$304$	9.62117			0.551812
$305$	−5.94457			−0.340385
$306$	7.42240	+	0.748230i	0.424310	+	0.0427735i
$307$	−7.89541			−0.450615			−0.225307	−	0.974288i	$-0.572339\pi$
$307$	−7.89541			−0.450615			−0.225307	+	0.974288i	$0.572339\pi$
$308$	0.175247			0.00998564
$309$	−2.23337	+	2.01955i	−0.127052	+	0.114888i
$310$	−2.16147			−0.122763
$311$			25.2980i			1.43452i	0.696805	+	0.717260i	$0.254604\pi$
$311$			25.2980i			1.43452i	−0.696805	+	0.717260i	$0.745396\pi$
$312$	−18.7950	+	16.9956i	−1.06406	+	0.962184i
$313$			2.08457i			0.117827i	0.998263	+	0.0589135i	$0.0187636\pi$
$313$			2.08457i			0.117827i	−0.998263	+	0.0589135i	$0.981236\pi$
$314$		−	18.8550i		−	1.06405i
$315$	3.30090	+	0.332754i	0.185984	+	0.0187486i
$316$	1.15442			0.0649414
$317$			18.8879i			1.06085i	0.847731	+	0.530426i	$0.177968\pi$
$317$			18.8879i			1.06085i	−0.847731	+	0.530426i	$0.822032\pi$
$318$	−10.7725	+	9.74111i	−0.604089	+	0.546255i
$319$		−	4.22511i		−	0.236561i
$320$		−	4.37905i		−	0.244796i
$321$	9.85353	−	8.91016i	0.549970	−	0.497317i
$322$	−13.2292			−0.737236
$323$		−	3.84072i		−	0.213703i
$324$	−1.22754	−	0.250031i	−0.0681968	−	0.0138906i
$325$			24.9787i			1.38557i
$326$	23.0450			1.27635
$327$	−19.7562	+	17.8648i	−1.09252	+	0.987924i
$328$		−	6.24467i		−	0.344804i
$329$	−15.7473			−0.868174
$330$	−0.755545	+	0.683210i	−0.0415914	+	0.0376095i
$331$	29.3595			1.61374			0.806871	−	0.590728i	$-0.201159\pi$
$331$	29.3595			1.61374			0.806871	+	0.590728i	$0.201159\pi$
$332$	0.0131090			0.000719453
$333$	23.4674	+	2.36568i	1.28601	+	0.129639i
$334$		−	19.0801i		−	1.04402i
$335$	−3.19462			−0.174541
$336$	−9.20672	−	10.1815i	−0.502268	−	0.555445i
$337$			12.8355i			0.699192i	0.936901	+	0.349596i	$0.113681\pi$
$337$			12.8355i			0.699192i	−0.936901	+	0.349596i	$0.886319\pi$
$338$	23.2486			1.26456
$339$	−7.10941	−	7.86212i	−0.386130	−	0.427012i
$340$	0.140643			0.00762746
$341$			1.68247i			0.0911110i
$342$	−0.994170	+	9.86210i	−0.0537586	+	0.533282i
$343$	−19.6081			−1.05874
$344$		−	19.3612i		−	1.04389i
$345$	3.71120	−	3.35589i	0.199804	−	0.180675i
$346$	−13.7610			−0.739798
$347$	27.7175			1.48795			0.743976	−	0.668207i	$-0.232938\pi$
$347$	27.7175			1.48795			0.743976	+	0.668207i	$0.232938\pi$
$348$	1.11669	−	1.00978i	0.0598607	−	0.0541297i
$349$			7.11389i			0.380798i	0.981707	+	0.190399i	$0.0609781\pi$
$349$			7.11389i			0.380798i	−0.981707	+	0.190399i	$0.939022\pi$
$350$	−12.6468			−0.676000
$351$	−16.5616	−	22.4920i	−0.883992	−	1.20053i
$352$	0.531806			0.0283454
$353$	8.00482			0.426053			0.213027	−	0.977046i	$-0.431668\pi$
$353$	8.00482			0.426053			0.213027	+	0.977046i	$0.431668\pi$
$354$	10.6783	−	16.2669i	0.567544	−	0.864575i
$355$	3.52139			0.186896
$356$	−1.52844			−0.0810071
$357$	−4.06439	+	3.67527i	−0.215110	+	0.194516i
$358$	−33.7056			−1.78140
$359$			3.75799i			0.198339i	0.995071	+	0.0991697i	$0.0316187\pi$
$359$			3.75799i			0.198339i	−0.995071	+	0.0991697i	$0.968381\pi$
$360$	4.82789	+	0.486685i	0.254452	+	0.0256506i
$361$	−13.8969			−0.731414
$362$	11.0900			0.582879
$363$	−12.2469	−	13.5436i	−0.642796	−	0.710853i
$364$			1.39231i			0.0729770i
$365$	4.91142			0.257075
$366$	−18.7950	+	16.9956i	−0.982429	+	0.888372i
$367$			11.1530i			0.582181i	0.956695	+	0.291091i	$0.0940181\pi$
$367$			11.1530i			0.582181i	−0.956695	+	0.291091i	$0.905982\pi$
$368$	−20.7022			−1.07918
$369$	6.84871	+	0.690399i	0.356530	+	0.0359407i
$370$	6.83392			0.355278
$371$		−	10.6682i		−	0.553864i
$372$	−0.444673	+	0.402100i	−0.0230552	+	0.0208479i
$373$	12.7320			0.659239			0.329620	−	0.944114i	$-0.393080\pi$
$373$	12.7320			0.659239			0.329620	+	0.944114i	$0.393080\pi$
$374$		−	1.68247i		−	0.0869986i
$375$	7.36529	−	6.66014i	0.380342	−	0.343928i
$376$	−23.0319			−1.18778
$377$	33.5679			1.72883
$378$	11.3878	−	8.38521i	0.585725	−	0.431289i
$379$	−21.8656			−1.12316			−0.561581	−	0.827422i	$-0.689807\pi$
$379$	−21.8656			−1.12316			−0.561581	+	0.827422i	$0.689807\pi$
$380$			0.186872i			0.00958634i
$381$	7.20672	+	7.96973i	0.369211	+	0.408302i
$382$	8.95084			0.457965
$383$			11.2295i			0.573802i	0.957960	+	0.286901i	$0.0926251\pi$
$383$			11.2295i			0.573802i	−0.957960	+	0.286901i	$0.907375\pi$
$384$	−14.3459	−	15.8648i	−0.732087	−	0.809597i
$385$		−	0.748230i		−	0.0381334i
$386$	11.9854			0.610043
$387$	21.2340	+	2.14054i	1.07939	+	0.108810i
$388$		−	2.48667i		−	0.126242i
$389$		−	27.3559i		−	1.38700i	−0.720458	−	0.693499i	$-0.756068\pi$
$389$		−	27.3559i		−	1.38700i	0.720458	−	0.693499i	$-0.243932\pi$
$390$	−5.42799	−	6.00269i	−0.274857	−	0.303958i
$391$			8.26422i			0.417939i
$392$	−9.62743			−0.486259
$393$	−19.1890	−	21.2207i	−0.967958	−	1.07044i
$394$			35.7296i			1.80003i
$395$		−	4.92889i		−	0.247999i
$396$	−0.0283379	+	0.281110i	−0.00142403	+	0.0141263i
$397$		−	10.3488i		−	0.519391i	−0.965691	−	0.259695i	$-0.916378\pi$
$397$		−	10.3488i		−	0.519391i	0.965691	−	0.259695i	$-0.0836222\pi$
$398$	−17.3476			−0.869556
$399$	−4.88331	−	5.40034i	−0.244471	−	0.270355i
$400$	−19.7908			−0.989541
$401$	−22.4120			−1.11920			−0.559601	−	0.828762i	$-0.689045\pi$
$401$	−22.4120			−1.11920			−0.559601	+	0.828762i	$0.689045\pi$
$402$	−10.1004	+	9.13344i	−0.503764	+	0.455535i
$403$	−13.3670			−0.665856
$404$	1.16484			0.0579527
$405$	−1.06752	+	5.24108i	−0.0530457	+	0.260431i
$406$			16.9956i			0.843475i
$407$		−	5.31948i		−	0.263677i
$408$	−5.94457	+	5.37545i	−0.294300	+	0.266124i
$409$		−	21.7438i		−	1.07516i	−0.843213	−	0.537580i	$-0.819339\pi$
$409$		−	21.7438i		−	1.07516i	0.843213	−	0.537580i	$-0.180661\pi$
$410$	1.99440			0.0984966
$411$	22.4914	−	20.3381i	1.10942	−	1.00320i
$412$			0.241981i			0.0119215i
$413$	3.60179	+	13.8319i	0.177233	+	0.680621i
$414$	2.13919	−	21.2207i	0.105136	−	1.04294i
$415$		−	0.0559700i		−	0.00274746i
$416$			4.22511i			0.207153i
$417$	6.61220	+	7.31227i	0.323801	+	0.358084i
$418$	2.23549			0.109341
$419$	−37.9404			−1.85351			−0.926756	−	0.375665i	$-0.877414\pi$
$419$	−37.9404			−1.85351			−0.926756	+	0.375665i	$0.877414\pi$
$420$	0.197755	−	0.178822i	0.00964947	−	0.00872564i
$421$			21.3417i			1.04013i	0.854127	+	0.520064i	$0.174092\pi$
$421$			21.3417i			1.04013i	−0.854127	+	0.520064i	$0.825908\pi$
$422$		−	25.0346i		−	1.21867i
$423$	2.54636	−	25.2598i	0.123808	−	1.22817i
$424$		−	15.6032i		−	0.757761i
$425$			7.90038i			0.383225i
$426$	11.1336	−	10.0677i	0.539425	−	0.487781i
$427$		−	18.6130i		−	0.900747i
$428$		−	1.06761i		−	0.0516048i
$429$	−4.67245	+	4.22511i	−0.225588	+	0.203990i
$430$	6.18354			0.298197
$431$	−19.5679			−0.942551			−0.471275	−	0.881986i	$-0.656206\pi$
$431$	−19.5679			−0.942551			−0.471275	+	0.881986i	$0.656206\pi$
$432$	17.8206	−	13.1219i	0.857394	−	0.631328i
$433$	15.0346			0.722517			0.361258	−	0.932466i	$-0.382347\pi$
$433$	15.0346			0.722517			0.361258	+	0.932466i	$0.382347\pi$
$434$		−	6.76776i		−	0.324863i
$435$	−4.31131	−	4.76777i	−0.206711	−	0.228597i
$436$			2.14054i			0.102513i
$437$	−10.9806			−0.525275
$438$	15.5284	−	14.0418i	0.741978	−	0.670941i
$439$	9.76518			0.466067			0.233033	−	0.972469i	$-0.425135\pi$
$439$	9.76518			0.466067			0.233033	+	0.972469i	$0.425135\pi$
$440$		−	1.09436i		−	0.0521716i
$441$	1.06439	−	10.5587i	0.0506853	−	0.502795i
$442$	13.3670			0.635802
$443$	0.0435667			0.00206991			0.00103496	−	0.999999i	$-0.499671\pi$
$443$	0.0435667			0.00206991			0.00103496	+	0.999999i	$0.499671\pi$
$444$	1.40592	−	1.27132i	0.0667221	−	0.0603342i
$445$			6.52578i			0.309351i
$446$	10.6981			0.506569
$447$	25.0900	+	27.7464i	1.18672	+	1.31236i
$448$	13.7112			0.647793
$449$			6.28293i			0.296510i	0.988949	+	0.148255i	$0.0473656\pi$
$449$			6.28293i			0.296510i	−0.988949	+	0.148255i	$0.952634\pi$
$450$	2.04502	−	20.2864i	0.0964030	−	0.956311i
$451$		−	1.55243i		−	0.0731011i
$452$	−0.851843			−0.0400673
$453$	−10.6170	+	9.60056i	−0.498831	+	0.451074i
$454$	23.0319			1.08094
$455$	5.94457			0.278686
$456$	−7.14233	−	7.89852i	−0.334470	−	0.369882i
$457$			1.55243i			0.0726197i	0.999341	+	0.0363098i	$0.0115603\pi$
$457$			1.55243i			0.0726197i	−0.999341	+	0.0363098i	$0.988440\pi$
$458$			38.8043i			1.81321i
$459$	−5.23819	−	7.11389i	−0.244498	−	0.332048i
$460$		−	0.402100i		−	0.0187480i
$461$			41.3799i			1.92726i	0.267249	+	0.963628i	$0.413885\pi$
$461$			41.3799i			1.92726i	−0.267249	+	0.963628i	$0.586115\pi$
$462$	−2.13919	−	2.36568i	−0.0995243	−	0.110061i
$463$		−	13.6397i		−	0.633889i	−0.948444	−	0.316944i	$-0.897343\pi$
$463$		−	13.6397i		−	0.633889i	0.948444	−	0.316944i	$-0.102657\pi$
$464$			26.5961i			1.23469i
$465$	1.71680	+	1.89856i	0.0796145	+	0.0880437i
$466$	−22.1801			−1.02747
$467$	7.01523			0.324626			0.162313	−	0.986739i	$-0.448105\pi$
$467$	7.01523			0.324626			0.162313	+	0.986739i	$0.448105\pi$
$468$	−2.23337	−	0.225140i	−0.103238	−	0.0104071i
$469$		−	10.0027i		−	0.461880i
$470$		−	7.35587i		−	0.339301i
$471$	−16.5616	+	14.9760i	−0.763118	+	0.690058i
$472$	5.26798	+	20.2305i	0.242478	+	0.931182i
$473$		−	4.81323i		−	0.221312i
$474$	−14.0917	−	15.5837i	−0.647254	−	0.715782i
$475$	−10.4972			−0.481645
$476$			0.440368i			0.0201842i
$477$	17.1125	+	1.72507i	0.783529	+	0.0789853i
$478$		−	24.9136i		−	1.13952i
$479$			9.76601i			0.446220i	0.974793	+	0.223110i	$0.0716209\pi$
$479$			9.76601i			0.446220i	−0.974793	+	0.223110i	$0.928379\pi$
$480$	0.600109	−	0.542655i	0.0273911	−	0.0247687i
$481$	42.2624			1.92700
$482$	15.0423			0.685159
$483$	10.5076	+	11.6201i	0.478113	+	0.528733i
$484$	−1.46742			−0.0667007
$485$	−10.6170			−0.482094
$486$	11.6091	+	19.6228i	0.526598	+	0.890108i
$487$	−11.2922			−0.511697			−0.255848	−	0.966717i	$-0.582355\pi$
$487$	−11.2922			−0.511697			−0.255848	+	0.966717i	$0.582355\pi$
$488$		−	27.2234i		−	1.23234i
$489$	−18.3040	−	20.2420i	−0.827737	−	0.915374i
$490$		−	3.07478i		−	0.138905i
$491$			19.8461i			0.895640i	0.894124	+	0.447820i	$0.147799\pi$
$491$			19.8461i			0.895640i	−0.894124	+	0.447820i	$0.852201\pi$
$492$	0.410303	−	0.371021i	0.0184979	−	0.0167269i
$493$	10.6170			0.478167
$494$			17.7606i			0.799088i
$495$	1.20022	+	0.120990i	0.0539458	+	0.00543812i
$496$		−	10.5908i		−	0.475540i
$497$			11.0258i			0.494575i
$498$	−0.160018	−	0.176960i	−0.00717060	−	0.00792979i
$499$	−35.8864			−1.60650			−0.803249	−	0.595643i	$-0.796897\pi$
$499$	−35.8864			−1.60650			−0.803249	+	0.595643i	$0.796897\pi$
$500$		−	0.798013i		−	0.0356882i
$501$	−16.7593	+	15.1548i	−0.748752	+	0.677068i
$502$			22.1290i			0.987667i
$503$	−4.72306			−0.210591			−0.105295	−	0.994441i	$-0.533579\pi$
$503$	−4.72306			−0.210591			−0.105295	+	0.994441i	$0.533579\pi$
$504$	−1.52386	+	15.1166i	−0.0678780	+	0.673345i
$505$		−	4.97334i		−	0.221311i
$506$	−4.81019			−0.213839
$507$	−18.4657	−	20.4208i	−0.820092	−	0.906919i
$508$	0.863503			0.0383117
$509$	0.501348			0.0222219			0.0111109	−	0.999938i	$-0.496463\pi$
$509$	0.501348			0.0222219			0.0111109	+	0.999938i	$0.496463\pi$
$510$	−1.71680	−	1.89856i	−0.0760210	−	0.0840697i
$511$			15.3781i			0.680287i
$512$	19.8352			0.876599
$513$	9.45219	−	6.95996i	0.417324	−	0.307290i
$514$			8.97332i			0.395796i
$515$	1.03315			0.0455262
$516$	1.27212	−	1.15033i	0.0560021	−	0.0506405i
$517$	−5.72576			−0.251819
$518$			21.3976i			0.940158i
$519$	10.9300	+	12.0872i	0.479774	+	0.530571i
$520$	8.69452			0.381280
$521$			34.5969i			1.51572i	0.652418	+	0.757859i	$0.273755\pi$
$521$			34.5969i			1.51572i	−0.652418	+	0.757859i	$0.726245\pi$
$522$	−27.2621	−	2.74822i	−1.19323	−	0.120286i
$523$	8.38365			0.366591			0.183296	−	0.983058i	$-0.441323\pi$
$523$	8.38365			0.366591			0.183296	+	0.983058i	$0.441323\pi$
$524$	−2.29921			−0.100442
$525$	10.0450	+	11.1085i	0.438400	+	0.484816i
$526$		−	34.6743i		−	1.51187i
$527$	−4.22778			−0.184165
$528$	−3.34760	−	3.70202i	−0.145685	−	0.161110i
$529$	0.627434			0.0272797
$530$	4.98332			0.216462
$531$	−22.7698	+	3.54090i	−0.988123	+	0.153662i
$532$	−0.585114			−0.0253679
$533$	12.3338			0.534237
$534$	18.6572	+	20.6326i	0.807377	+	0.892858i
$535$	−4.55823			−0.197069
$536$		−	14.6299i		−	0.631914i
$537$	26.7714	+	29.6059i	1.15527	+	1.27759i
$538$	38.3040			1.65140
$539$	−2.39339			−0.103091
$540$	0.254867	+	0.346130i	0.0109677	+	0.0148951i
$541$			10.3488i			0.444929i	0.974941	+	0.222465i	$0.0714102\pi$
$541$			10.3488i			0.444929i	−0.974941	+	0.222465i	$0.928590\pi$
$542$	−32.6371			−1.40188
$543$	−8.80851	−	9.74111i	−0.378009	−	0.418031i
$544$			1.33634i			0.0572952i
$545$	9.13919			0.391480
$546$	18.7950	−	16.9956i	0.804350	−	0.727343i
$547$	−35.9661			−1.53780			−0.768899	−	0.639370i	$-0.779195\pi$
$547$	−35.9661			−1.53780			−0.768899	+	0.639370i	$0.779195\pi$
$548$		−	2.43689i		−	0.104099i
$549$	29.8567	+	3.00976i	1.27425	+	0.128454i
$550$	−4.59843			−0.196078
$551$			14.1068i			0.600969i
$552$	15.3684	+	16.9956i	0.654123	+	0.723379i
$553$	15.4328			0.656270
$554$	−34.8491			−1.48060
$555$	−5.42799	−	6.00269i	−0.230406	−	0.254800i
$556$	0.792269			0.0335997
$557$		−	19.5588i		−	0.828731i	−0.910110	−	0.414366i	$-0.864003\pi$
$557$		−	19.5588i		−	0.828731i	0.910110	−	0.414366i	$-0.135997\pi$
$558$	10.8560	+	1.09436i	0.459571	+	0.0463280i
$559$	38.2403			1.61739
$560$			4.70994i			0.199031i
$561$	−1.47783	+	1.33634i	−0.0623939	+	0.0564204i
$562$			3.51601i			0.148314i
$563$	32.9854			1.39017			0.695085	−	0.718927i	$-0.255367\pi$
$563$	32.9854			1.39017			0.695085	+	0.718927i	$0.255367\pi$
$564$	−1.36842	−	1.51330i	−0.0576209	−	0.0637215i
$565$			3.63700i			0.153010i
$566$		−	15.2180i		−	0.639660i
$567$	−16.4103	−	3.34252i	−0.689168	−	0.140373i
$568$			16.1263i			0.676646i
$569$	−14.7202			−0.617101			−0.308551	−	0.951208i	$-0.599844\pi$
$569$	−14.7202			−0.617101			−0.308551	+	0.951208i	$0.599844\pi$
$570$	2.52261	−	2.28110i	0.105660	−	0.0955446i
$571$		−	32.0926i		−	1.34303i	−0.740990	−	0.671516i	$-0.765644\pi$
$571$		−	32.0926i		−	1.34303i	0.740990	−	0.671516i	$-0.234356\pi$
$572$			0.506250i			0.0211674i
$573$	−7.10941	−	7.86212i	−0.297000	−	0.328445i
$574$			6.24467i			0.260647i
$575$	22.5872			0.941953
$576$	−2.21713	+	21.9938i	−0.0923804	+	0.916408i
$577$	−7.00000			−0.291414			−0.145707	−	0.989328i	$-0.546546\pi$
$577$	−7.00000			−0.291414			−0.145707	+	0.989328i	$0.546546\pi$
$578$	−20.6364			−0.858361
$579$	−9.51971	−	10.5276i	−0.395626	−	0.437513i
$580$	−0.516577			−0.0214497
$581$	0.175247			0.00727048
$582$	−33.5679	+	30.3541i	−1.39143	+	1.25822i
$583$		−	3.87898i		−	0.160651i
$584$			22.4920i			0.930725i
$585$	−0.961250	+	9.53554i	−0.0397428	+	0.394246i
$586$			38.4973i			1.59031i
$587$	24.0782			0.993812			0.496906	−	0.867804i	$-0.334469\pi$
$587$	24.0782			0.993812			0.496906	+	0.867804i	$0.334469\pi$
$588$	−0.572005	−	0.632567i	−0.0235891	−	0.0260866i
$589$		−	5.61743i		−	0.231462i
$590$	−6.46115	+	1.68247i	−0.266001	+	0.0692663i
$591$	31.3836	−	28.3790i	1.29095	−	1.16736i
$592$			33.4849i			1.37622i
$593$			35.9012i			1.47429i	0.675737	+	0.737143i	$0.263825\pi$
$593$			35.9012i			1.47429i	−0.675737	+	0.737143i	$0.736175\pi$
$594$	4.14064	−	3.04889i	0.169893	−	0.125098i
$595$	1.88018			0.0770799
$596$	3.00627			0.123141
$597$	13.7787	+	15.2375i	0.563926	+	0.623631i
$598$		−	38.2162i		−	1.56278i
$599$		−	1.85411i		−	0.0757567i	−0.999282	−	0.0378784i	$-0.987940\pi$
$599$		−	1.85411i		−	0.0757567i	0.999282	−	0.0378784i	$-0.0120599\pi$
$600$	14.6918	+	16.2473i	0.599791	+	0.663294i
$601$			0.346130i			0.0141189i	0.999975	+	0.00705947i	$0.00224712\pi$
$601$			0.346130i			0.0141189i	−0.999975	+	0.00705947i	$0.997753\pi$
$602$			19.3612i			0.789105i
$603$	16.0450	+	1.61745i	0.653404	+	0.0658677i
$604$			1.15033i			0.0468063i
$605$			6.26523i			0.254718i
$606$	−14.2188	−	15.7242i	−0.577600	−	0.638753i
$607$	6.59283			0.267595			0.133797	−	0.991009i	$-0.457283\pi$
$607$	6.59283			0.267595			0.133797	+	0.991009i	$0.457283\pi$
$608$	−1.77559			−0.0720097
$609$	14.9283	−	13.4991i	0.604926	−	0.547011i
$610$	8.69452			0.352031
$611$		−	45.4902i		−	1.84034i
$612$	−0.706383	−	0.0712084i	−0.0285538	−	0.00287843i
$613$		−	18.2669i		−	0.737792i	−0.929471	−	0.368896i	$-0.879736\pi$
$613$		−	18.2669i		−	0.737792i	0.929471	−	0.368896i	$-0.120264\pi$
$614$	11.5478			0.466032
$615$	−1.58410	−	1.75182i	−0.0638771	−	0.0706401i
$616$	3.42655			0.138059
$617$		−	25.2215i		−	1.01538i	−0.861540	−	0.507690i	$-0.830500\pi$
$617$		−	25.2215i		−	1.01538i	0.861540	−	0.507690i	$-0.169500\pi$
$618$	3.26653	−	2.95379i	0.131399	−	0.118819i
$619$	−0.700787			−0.0281670			−0.0140835	−	0.999901i	$-0.504483\pi$
$619$	−0.700787			−0.0281670			−0.0140835	+	0.999901i	$0.504483\pi$
$620$	0.205705			0.00826131
$621$	−20.3386	+	14.9760i	−0.816161	+	0.600966i
$622$		−	37.0009i		−	1.48360i
$623$	−20.4328			−0.818623
$624$	29.4120	−	26.5961i	1.17742	−	1.06470i
$625$	19.8269			0.793075
$626$		−	3.04889i		−	0.121858i
$627$	−1.77559	−	1.96358i	−0.0709103	−	0.0784179i
$628$			1.79441i			0.0716048i
$629$	13.3670			0.532976
$630$	−4.82789	−	0.486685i	−0.192348	−	0.0193900i
$631$	−19.1559			−0.762583			−0.381292	−	0.924455i	$-0.624521\pi$
$631$	−19.1559			−0.762583			−0.381292	+	0.924455i	$0.624521\pi$
$632$	22.5720			0.897866
$633$	−21.9896	+	19.8843i	−0.874008	+	0.790331i
$634$		−	27.6255i		−	1.09715i
$635$		−	3.68679i		−	0.146306i
$636$	1.02520	−	0.927053i	0.0406520	−	0.0367600i
$637$		−	19.0151i		−	0.753406i
$638$			6.17965i			0.244655i
$639$	−17.6862	−	1.78290i	−0.699656	−	0.0705303i
$640$			7.33903i			0.290101i
$641$			28.5391i			1.12723i	0.826038	+	0.563614i	$0.190589\pi$
$641$			28.5391i			1.12723i	−0.826038	+	0.563614i	$0.809411\pi$
$642$	−14.4118	+	13.0320i	−0.568787	+	0.514332i
$643$	−46.4183			−1.83056			−0.915279	−	0.402821i	$-0.868030\pi$
$643$	−46.4183			−1.83056			−0.915279	+	0.402821i	$0.868030\pi$
$644$	1.25901			0.0496121
$645$	−4.91142	−	5.43142i	−0.193387	−	0.213862i
$646$			5.61743i			0.221015i
$647$		−	17.6014i		−	0.691981i	−0.938238	−	0.345991i	$-0.887543\pi$
$647$		−	17.6014i		−	0.691981i	0.938238	−	0.345991i	$-0.112457\pi$
$648$	−24.0017	−	4.88876i	−0.942875	−	0.192049i
$649$	1.30962	+	5.02931i	0.0514073	+	0.197418i
$650$		−	36.5338i		−	1.43297i
$651$	−5.94457	+	5.37545i	−0.232986	+	0.210680i
$652$	−2.19317			−0.0858913
$653$		−	32.0275i		−	1.25333i	−0.779287	−	0.626667i	$-0.784419\pi$
$653$		−	32.0275i		−	1.25333i	0.779287	−	0.626667i	$-0.215581\pi$
$654$	28.8954	−	26.1290i	1.12990	−	1.02172i
$655$			9.81665i			0.383568i
$656$			9.77219i			0.381540i
$657$	−24.6676	−	2.48667i	−0.962376	−	0.0970143i
$658$	23.0319			0.897877
$659$	−36.2236			−1.41107			−0.705536	−	0.708674i	$-0.749294\pi$
$659$	−36.2236			−1.41107			−0.705536	+	0.708674i	$0.749294\pi$
$660$	0.0719045	−	0.0650205i	0.00279888	−	0.00253092i
$661$	−10.8552			−0.422219			−0.211109	−	0.977462i	$-0.567708\pi$
$661$	−10.8552			−0.422219			−0.211109	+	0.977462i	$0.567708\pi$
$662$	−42.9411			−1.66895
$663$	−10.6170	−	11.7411i	−0.412331	−	0.455987i
$664$	0.256316			0.00994701
$665$			2.49819i			0.0968755i
$666$	−34.3234	−	3.46004i	−1.33000	−	0.134074i
$667$		−	30.3541i		−	1.17532i
$668$			1.81584i			0.0702569i
$669$	−8.49720	−	9.39685i	−0.328521	−	0.363303i
$670$	4.67245			0.180512
$671$		−	6.76776i		−	0.261266i
$672$	1.69910	+	1.87900i	0.0655443	+	0.0724839i
$673$			38.2722i			1.47528i	0.675192	+	0.737642i	$0.264061\pi$
$673$			38.2722i			1.47528i	−0.675192	+	0.737642i	$0.735939\pi$
$674$		−	18.7731i		−	0.723114i
$675$	−19.4432	+	14.3167i	−0.748370	+	0.551049i
$676$	−2.21255			−0.0850980
$677$		−	24.6478i		−	0.947291i	−0.880716	−	0.473645i	$-0.842938\pi$
$677$		−	24.6478i		−	0.947291i	0.880716	−	0.473645i	$-0.157062\pi$
$678$	10.3982	+	11.4991i	0.399341	+	0.441621i
$679$		−	33.2429i		−	1.27574i
$680$	2.74995			0.105456
$681$	−18.2936	−	20.2305i	−0.701013	−	0.775233i
$682$		−	2.46078i		−	0.0942282i
$683$	−41.1350			−1.57399			−0.786994	−	0.616960i	$-0.788364\pi$
$683$	−41.1350			−1.57399			−0.786994	+	0.616960i	$0.788364\pi$
$684$	0.0946143	−	0.938567i	0.00361767	−	0.0358870i
$685$	−10.4045			−0.397534
$686$	28.6787			1.09496
$687$	34.0844	−	30.8212i	1.30040	−	1.17590i
$688$			30.2981i			1.15511i
$689$	30.8179			1.17407
$690$	−5.42799	+	4.90832i	−0.206640	+	0.186857i
$691$		−	48.2189i		−	1.83433i	−0.398504	−	0.917166i	$-0.630471\pi$
$691$		−	48.2189i		−	1.83433i	0.398504	−	0.917166i	$-0.369529\pi$
$692$	1.30962			0.0497845
$693$	−0.378832	+	3.75799i	−0.0143907	+	0.142754i
$694$	−40.5395			−1.53886
$695$		−	3.38265i		−	0.128311i
$696$	21.8342	−	19.7438i	0.827621	−	0.748386i
$697$	3.90101			0.147761
$698$		−	10.4048i		−	0.393826i
$699$	17.6170	+	19.4822i	0.666337	+	0.736886i
$700$	1.20359			0.0454912
$701$	−17.0498			−0.643963			−0.321982	−	0.946746i	$-0.604349\pi$
$701$	−17.0498			−0.643963			−0.321982	+	0.946746i	$0.604349\pi$
$702$	24.2230	+	32.8968i	0.914237	+	1.24161i
$703$			17.7606i			0.669855i
$704$	4.98544			0.187896
$705$	−6.46115	+	5.84257i	−0.243341	+	0.220044i
$706$	−11.7078			−0.440630
$707$	15.5720			0.585646
$708$	−1.01624	+	1.54810i	−0.0381927	+	0.0581813i
$709$	−19.3178			−0.725496			−0.362748	−	0.931887i	$-0.618161\pi$
$709$	−19.3178			−0.725496			−0.362748	+	0.931887i	$0.618161\pi$
$710$	−5.15039			−0.193291
$711$	−2.49552	+	24.7554i	−0.0935893	+	0.928400i
$712$	−29.8850			−1.11999
$713$			12.0872i			0.452670i
$714$	5.94457	−	5.37545i	0.222470	−	0.201171i
$715$	2.16147			0.0808343
$716$	3.20773			0.119879
$717$	−21.8833	+	19.7882i	−0.817247	+	0.739005i
$718$		−	5.49644i		−	0.205125i
$719$	21.8165			0.813617			0.406808	−	0.913514i	$-0.366642\pi$
$719$	21.8165			0.813617			0.406808	+	0.913514i	$0.366642\pi$
$720$	−7.55509	−	0.761607i	−0.281562	−	0.0283834i
$721$			3.23490i			0.120474i
$722$	20.3255			0.756438
$723$	−11.9477	−	13.2127i	−0.444340	−	0.491385i
$724$	−1.05543			−0.0392247
$725$		−	29.0178i		−	1.07769i
$726$	17.9123	+	19.8088i	0.664789	+	0.735173i
$727$	−3.24523			−0.120359			−0.0601795	−	0.998188i	$-0.519167\pi$
$727$	−3.24523			−0.120359			−0.0601795	+	0.998188i	$0.519167\pi$
$728$			27.2234i			1.00896i
$729$	8.01523	−	25.7829i	0.296860	−	0.954921i
$730$	−7.18343			−0.265871
$731$	12.0948			0.447344
$732$	1.78870	−	1.61745i	0.0661122	−	0.0597827i
$733$	28.5754			1.05546			0.527728	−	0.849414i	$-0.323044\pi$
$733$	28.5754			1.05546			0.527728	+	0.849414i	$0.323044\pi$
$734$		−	16.3123i		−	0.602100i
$735$	−2.70079	+	2.44222i	−0.0996200	+	0.0900825i
$736$	3.82061			0.140829
$737$		−	3.63700i		−	0.133971i
$738$	−10.0169	−	1.00978i	−0.368728	−	0.0371704i
$739$			17.9207i			0.659225i	0.944116	+	0.329613i	$0.106918\pi$
$739$			17.9207i			0.659225i	−0.944116	+	0.329613i	$0.893082\pi$
$740$	−0.650378			−0.0239084
$741$	15.6003	−	14.1068i	0.573093	−	0.518226i
$742$			15.6032i			0.572813i
$743$		−	29.3639i		−	1.07726i	−0.842543	−	0.538628i	$-0.818943\pi$
$743$		−	29.3639i		−	1.07726i	0.842543	−	0.538628i	$-0.181057\pi$
$744$	−8.69452	+	7.86212i	−0.318757	+	0.288239i
$745$		−	12.8355i		−	0.470255i
$746$	−18.6218			−0.681794
$747$	−0.0283379	+	0.281110i	−0.00103683	+	0.0102853i
$748$			0.160119i			0.00585454i
$749$		−	14.2722i		−	0.521496i
$750$	−10.7725	+	9.74111i	−0.393355	+	0.355695i
$751$			29.2597i			1.06770i	0.845578	+	0.533852i	$0.179256\pi$
$751$			29.2597i			1.06770i	−0.845578	+	0.533852i	$0.820744\pi$
$752$	36.0423			1.31433
$753$	19.4374	−	17.5765i	0.708338	−	0.640522i
$754$	−49.0963			−1.78798
$755$	4.91142			0.178745
$756$	−1.08377	+	0.798013i	−0.0394162	+	0.0290234i
$757$	−13.6635			−0.496608			−0.248304	−	0.968682i	$-0.579873\pi$
$757$	−13.6635			−0.496608			−0.248304	+	0.968682i	$0.579873\pi$
$758$	31.9806			1.16159
$759$	3.82061	+	4.22511i	0.138679	+	0.153362i
$760$			3.65384i			0.132539i
$761$			9.99115i			0.362179i	0.983467	+	0.181089i	$0.0579623\pi$
$761$			9.99115i			0.362179i	−0.983467	+	0.181089i	$0.942038\pi$
$762$	−10.5405	−	11.6565i	−0.381843	−	0.422271i
$763$			28.6157i			1.03596i
$764$	−0.851843			−0.0308186
$765$	−0.304029	+	3.01595i	−0.0109922	+	0.109042i
$766$		−	16.4243i		−	0.593434i
$767$	−39.9571	+	10.4048i	−1.44277	+	0.375694i
$768$	3.86249	+	4.27143i	0.139376	+	0.154132i
$769$		−	11.3390i		−	0.408895i	−0.978878	−	0.204447i	$-0.934460\pi$
$769$		−	11.3390i		−	0.408895i	0.978878	−	0.204447i	$-0.0655397\pi$
$770$			1.09436i			0.0394380i
$771$	7.88186	−	7.12726i	0.283858	−	0.256682i
$772$	−1.14064			−0.0410527
$773$	−47.4737			−1.70751			−0.853755	−	0.520675i	$-0.825680\pi$
$773$	−47.4737			−1.70751			−0.853755	+	0.520675i	$0.825680\pi$
$774$	−31.0569	−	3.13075i	−1.11632	−	0.112533i
$775$			11.5551i			0.415071i
$776$		−	48.6210i		−	1.74539i
$777$	18.7950	−	16.9956i	0.674266	−	0.609712i
$778$			40.0106i			1.43445i
$779$			5.18325i			0.185709i
$780$	0.516577	+	0.571270i	0.0184964	+	0.0204547i
$781$			4.00903i			0.143454i
$782$		−	12.0872i		−	0.432239i
$783$	19.2396	+	26.1290i	0.687569	+	0.933774i
$784$	15.0658			0.538066
$785$	7.66137			0.273446
$786$	28.0658	+	31.0373i	1.00108	+	1.10706i
$787$	18.5693			0.661924			0.330962	−	0.943644i	$-0.392627\pi$
$787$	18.5693			0.661924			0.330962	+	0.943644i	$0.392627\pi$
$788$		−	3.40035i		−	0.121132i
$789$	−30.4568	+	27.5409i	−1.08429	+	0.980481i
$790$			7.20899i			0.256484i
$791$	−11.3878			−0.404903
$792$	−0.554080	+	5.49644i	−0.0196884	+	0.195307i
$793$	53.7687			1.90938
$794$			15.1361i			0.537161i
$795$	−3.95812	−	4.37718i	−0.140380	−	0.155243i
$796$	1.65095			0.0585165
$797$	36.7189			1.30065			0.650325	−	0.759656i	$-0.274633\pi$
$797$	36.7189			1.30065			0.650325	+	0.759656i	$0.274633\pi$
$798$	7.14233	+	7.89852i	0.252836	+	0.279605i
$799$		−	14.3879i		−	0.509007i
$800$	3.65240			0.129132
$801$	3.30403	−	32.7758i	0.116742	−	1.15807i
$802$	32.7797			1.15749
$803$			5.59153i			0.197321i
$804$	0.961250	−	0.869221i	0.0339007	−	0.0306551i
$805$		−	5.37545i		−	0.189460i
$806$	19.5505			0.688637
$807$	−30.4238	−	33.6450i	−1.07097	−	1.18436i
$808$	22.7756			0.801242
$809$	29.0200			1.02029			0.510145	−	0.860088i	$-0.329592\pi$
$809$	29.0200			1.02029			0.510145	+	0.860088i	$0.329592\pi$
$810$	1.56136	−	7.66559i	0.0548606	−	0.269341i
$811$			43.2455i			1.51856i	0.650766	+	0.759278i	$0.274448\pi$
$811$			43.2455i			1.51856i	−0.650766	+	0.759278i	$0.725552\pi$
$812$		−	1.61745i		−	0.0567614i
$813$	25.9227	+	28.6673i	0.909150	+	1.00541i
$814$			7.78026i			0.272698i
$815$			9.36391i			0.328003i
$816$	9.30258	−	8.41196i	0.325655	−	0.294478i
$817$			16.0704i			0.562231i
$818$			31.8024i			1.11194i
$819$	−29.8567	−	3.00976i	−1.04328	−	0.105170i
$820$	−0.189806			−0.00662830
$821$	−10.4418			−0.364420			−0.182210	−	0.983260i	$-0.558325\pi$
$821$	−10.4418			−0.364420			−0.182210	+	0.983260i	$0.558325\pi$
$822$	−32.8958	+	29.7464i	−1.14737	+	1.03753i
$823$			31.8506i			1.11024i	0.831770	+	0.555121i	$0.187328\pi$
$823$			31.8506i			1.11024i	−0.831770	+	0.555121i	$0.812672\pi$
$824$			4.73136i			0.164825i
$825$	3.65240	+	4.03910i	0.127160	+	0.140624i
$826$	−5.26798	−	20.2305i	−0.183296	−	0.703908i
$827$		−	30.6085i		−	1.06436i	−0.846631	−	0.532180i	$-0.821373\pi$
$827$		−	30.6085i		−	1.06436i	0.846631	−	0.532180i	$-0.178627\pi$
$828$	−0.203585	+	2.01955i	−0.00707507	+	0.0701843i
$829$	−44.7085			−1.55279			−0.776395	−	0.630246i	$-0.782954\pi$
$829$	−44.7085			−1.55279			−0.776395	+	0.630246i	$0.782954\pi$
$830$			0.0818616i			0.00284146i
$831$	27.6797	+	30.6103i	0.960199	+	1.06186i
$832$			39.6085i			1.37318i
$833$		−	6.01420i		−	0.208380i
$834$	−9.67100	−	10.6949i	−0.334879	−	0.370335i
$835$	7.75285			0.268298
$836$	−0.212750			−0.00735810
$837$	−7.66137	−	10.4048i	−0.264816	−	0.359641i
$838$	55.4916			1.91693
$839$	40.7279			1.40608			0.703041	−	0.711149i	$-0.251825\pi$
$839$	40.7279			1.40608			0.703041	+	0.711149i	$0.251825\pi$
$840$	3.86664	−	3.49645i	0.133412	−	0.120639i
$841$	−9.99585			−0.344685
$842$		−	31.2143i		−	1.07572i
$843$	3.08835	−	2.79267i	0.106368	−	0.0961848i
$844$			2.38252i			0.0820098i
$845$			9.44663i			0.324974i
$846$	−3.72431	+	36.9449i	−0.128044	+	1.27019i
$847$	−19.6170			−0.674049
$848$			24.4173i			0.838494i
$849$	−13.3670	+	12.0872i	−0.458753	+	0.414833i
$850$		−	11.5551i		−	0.396336i
$851$		−	38.2162i		−	1.31004i
$852$	−1.05957	+	0.958132i	−0.0363004	+	0.0328251i
$853$	−38.3795			−1.31409			−0.657045	−	0.753852i	$-0.728194\pi$
$853$	−38.3795			−1.31409			−0.657045	+	0.753852i	$0.728194\pi$
$854$			27.2234i			0.931564i
$855$	−4.00728	−	0.403962i	−0.137046	−	0.0138152i
$856$		−	20.8745i		−	0.713477i
$857$	−31.9523			−1.09147			−0.545735	−	0.837958i	$-0.683749\pi$
$857$	−31.9523			−1.09147			−0.545735	+	0.837958i	$0.683749\pi$
$858$	6.83392	−	6.17965i	0.233306	−	0.210970i
$859$			9.01245i			0.307501i	0.988110	+	0.153750i	$0.0491352\pi$
$859$			9.01245i			0.307501i	−0.988110	+	0.153750i	$0.950865\pi$
$860$	−0.588482			−0.0200671
$861$	5.48511	−	4.95997i	0.186932	−	0.169035i
$862$	28.6199			0.974798
$863$	13.6364			0.464188			0.232094	−	0.972693i	$-0.425442\pi$
$863$	13.6364			0.464188			0.232094	+	0.972693i	$0.425442\pi$
$864$	−3.28880	+	2.42165i	−0.111887	+	0.0823863i
$865$		−	5.59153i		−	0.190118i
$866$	−21.9896			−0.747237
$867$	16.3909	+	18.1263i	0.556665	+	0.615602i
$868$			0.644081i			0.0218615i
$869$	5.61143			0.190355
$870$	6.30571	+	6.97333i	0.213784	+	0.236418i
$871$	28.8954			0.979084
$872$			41.8532i			1.41733i
$873$	53.3241	+	5.37545i	1.80475	+	0.181931i
$874$	16.0602			0.543246
$875$		−	10.6682i		−	0.360650i
$876$	−1.47783	+	1.33634i	−0.0499312	+	0.0451508i
$877$	7.95498			0.268621			0.134310	−	0.990939i	$-0.457118\pi$
$877$	7.95498			0.268621			0.134310	+	0.990939i	$0.457118\pi$
$878$	−14.2825			−0.482012
$879$	33.8148	−	30.5774i	1.14054	−	1.03135i
$880$			1.71255i			0.0577301i
$881$	−20.8269			−0.701675			−0.350838	−	0.936436i	$-0.614103\pi$
$881$	−20.8269			−0.701675			−0.350838	+	0.936436i	$0.614103\pi$
$882$	−1.55678	+	15.4431i	−0.0524194	+	0.519997i
$883$	−1.67660			−0.0564219			−0.0282110	−	0.999602i	$-0.508981\pi$
$883$	−1.67660			−0.0564219			−0.0282110	+	0.999602i	$0.508981\pi$
$884$	−1.27212			−0.0427861
$885$	6.60974	+	4.33892i	0.222184	+	0.145851i
$886$	−0.0637205			−0.00214073
$887$	−1.08377			−0.0363893			−0.0181947	−	0.999834i	$-0.505792\pi$
$887$	−1.08377			−0.0363893			−0.0181947	+	0.999834i	$0.505792\pi$
$888$	27.4895	−	24.8577i	0.922487	−	0.834169i
$889$	11.5437			0.387162
$890$		−	9.54459i		−	0.319935i
$891$	−5.96685	−	1.21535i	−0.199897	−	0.0407158i
$892$	−1.01813			−0.0340894
$893$	19.1171			0.639730
$894$	−36.6966	−	40.5819i	−1.22732	−	1.35726i
$895$		−	13.6956i		−	0.457795i
$896$	−22.9792			−0.767680
$897$	−33.5679	+	30.3541i	−1.12080	+	1.01349i
$898$		−	9.18941i		−	0.306655i
$899$	15.5284			0.517902
$900$	−0.194622	+	1.93064i	−0.00648741	+	0.0643547i
$901$	9.74725			0.324728
$902$			2.27058i			0.0756021i
$903$	17.0063	−	15.3781i	0.565933	−	0.511751i
$904$	−16.6558			−0.553963
$905$			4.50622i			0.149792i
$906$	15.5284	−	14.0418i	0.515898	−	0.466506i
$907$	7.64681			0.253908			0.126954	−	0.991909i	$-0.459480\pi$
$907$	7.64681			0.253908			0.126954	+	0.991909i	$0.459480\pi$
$908$	−2.19193			−0.0727416
$909$	−2.51803	+	24.9787i	−0.0835177	+	0.828490i
$910$	−8.69452			−0.288221
$911$			34.4582i			1.14165i	0.821071	+	0.570826i	$0.193377\pi$
$911$			34.4582i			1.14165i	−0.821071	+	0.570826i	$0.806623\pi$
$912$	11.1769	+	12.3603i	0.370105	+	0.409290i
$913$	0.0637205			0.00210884
$914$		−	2.27058i		−	0.0751042i
$915$	−6.90582	−	7.63698i	−0.228299	−	0.252471i
$916$		−	3.69297i		−	0.122019i
$917$	−30.7368			−1.01502
$918$	7.66137	+	10.4048i	0.252863	+	0.343408i
$919$		−	52.0160i		−	1.71585i	−0.513775	−	0.857925i	$-0.671753\pi$
$919$		−	52.0160i		−	1.71585i	0.513775	−	0.857925i	$-0.328247\pi$
$920$		−	7.86212i		−	0.259206i
$921$	−9.17211	−	10.1432i	−0.302231	−	0.334230i
$922$		−	60.5222i		−	1.99319i
$923$	−31.8511			−1.04839
$924$	0.203585	+	0.225140i	0.00669746	+	0.00740655i
$925$		−	36.5338i		−	1.20122i
$926$			19.9493i			0.655576i
$927$	−5.18903	−	0.523091i	−0.170430	−	0.0171806i
$928$		−	4.90832i		−	0.161124i
$929$	−29.0271			−0.952348			−0.476174	−	0.879351i	$-0.657977\pi$
$929$	−29.0271			−0.952348			−0.476174	+	0.879351i	$0.657977\pi$
$930$	−2.51098	−	2.77683i	−0.0823383	−	0.0910559i
$931$	7.99104			0.261896
$932$	2.11086			0.0691434
$933$	−32.5003	+	29.3888i	−1.06401	+	0.962146i
$934$	−10.2605			−0.335733
$935$	0.683641			0.0223574
$936$	−43.6683	−	4.40207i	−1.42734	−	0.143886i
$937$			3.87898i			0.126721i	0.997991	+	0.0633604i	$0.0201818\pi$
$937$			3.87898i			0.126721i	−0.997991	+	0.0633604i	$0.979818\pi$
$938$			14.6299i			0.477682i
$939$	−2.67805	+	2.42165i	−0.0873947	+	0.0790276i
$940$			0.700051i			0.0228332i
$941$	17.7901			0.579942			0.289971	−	0.957035i	$-0.406354\pi$
$941$	17.7901			0.579942			0.289971	+	0.957035i	$0.406354\pi$
$942$	24.2230	−	21.9039i	0.789227	−	0.713667i
$943$		−	11.1530i		−	0.363191i
$944$	−8.24378	−	31.6584i	−0.268312	−	1.03039i
$945$	3.40717	+	4.62721i	0.110835	+	0.150523i
$946$			7.03982i			0.228884i
$947$			6.48665i			0.210788i	0.994431	+	0.105394i	$0.0336103\pi$
$947$			6.48665i			0.210788i	−0.994431	+	0.105394i	$0.966390\pi$
$948$	1.34110	+	1.48308i	0.0435568	+	0.0481683i
$949$	−44.4238			−1.44206
$950$	15.3532			0.498123
$951$	−24.2653	+	21.9421i	−0.786856	+	0.711523i
$952$			8.61035i			0.279063i
$953$			25.1211i			0.813752i	0.913483	+	0.406876i	$0.133382\pi$
$953$			25.1211i			0.813752i	−0.913483	+	0.406876i	$0.866618\pi$
$954$	−25.0288	−	2.52308i	−0.810336	−	0.0816877i
$955$			3.63700i			0.117691i
$956$			2.37101i			0.0766839i
$957$	5.42799	−	4.90832i	0.175462	−	0.158664i
$958$		−	14.2837i		−	0.461487i
$959$		−	32.5774i		−	1.05198i
$960$	5.62575	−	5.08715i	0.181570	−	0.164187i
$961$	24.8165			0.800531
$962$	−61.8129			−1.99293
$963$	22.8937	+	2.30785i	0.737740	+	0.0743694i
$964$	−1.43156			−0.0461076
$965$			4.87006i			0.156773i
$966$	−15.3684	−	16.9956i	−0.494471	−	0.546823i
$967$			45.3301i			1.45772i	0.684664	+	0.728859i	$0.259949\pi$
$967$			45.3301i			1.45772i	−0.684664	+	0.728859i	$0.740051\pi$
$968$	−28.6918			−0.922190
$969$	4.93416	−	4.46177i	0.158508	−	0.143333i
$970$	15.5284			0.498588
$971$			16.6700i			0.534965i	0.963563	+	0.267483i	$0.0861918\pi$
$971$			16.6700i			0.534965i	−0.963563	+	0.267483i	$0.913808\pi$
$972$	−1.10482	−	1.86748i	−0.0354373	−	0.0598995i
$973$	10.5914			0.339544
$974$	16.5159			0.529204
$975$	−32.0900	+	29.0178i	−1.02770	+	0.929312i
$976$			42.6015i			1.36364i
$977$	−7.91064			−0.253084			−0.126542	−	0.991961i	$-0.540388\pi$
$977$	−7.91064			−0.253084			−0.126542	+	0.991961i	$0.540388\pi$
$978$	26.7714	+	29.6059i	0.856056	+	0.946692i
$979$	−7.42944			−0.237446
$980$			0.292624i			0.00934754i
$981$	−45.9017	−	4.62721i	−1.46553	−	0.147736i
$982$		−	29.0268i		−	0.926283i
$983$	38.4287			1.22568			0.612842	−	0.790205i	$-0.290026\pi$
$983$	38.4287			1.22568			0.612842	+	0.790205i	$0.290026\pi$
$984$	8.02251	−	7.25444i	0.255748	−	0.231263i
$985$	−14.5180			−0.462583
$986$	−15.5284			−0.494526
$987$	−18.2936	−	20.2305i	−0.582292	−	0.643943i
$988$		−	1.69026i		−	0.0537744i
$989$		−	34.5792i		−	1.09956i
$990$	−1.75544	−	0.176960i	−0.0557914	−	0.00562417i
$991$		−	29.6059i		−	0.940462i	−0.882543	−	0.470231i	$-0.844171\pi$
$991$		−	29.6059i		−	0.940462i	0.882543	−	0.470231i	$-0.155829\pi$
$992$			1.95453i			0.0620564i
$993$	34.1069	+	37.7180i	1.08235	+	1.19695i
$994$		−	16.1263i		−	0.511496i
$995$		−	7.04887i		−	0.223464i
$996$	0.0152288	+	0.0168412i	0.000482543	+	0.000533633i
$997$	−9.75285			−0.308876			−0.154438	−	0.988002i	$-0.549357\pi$
$997$	−9.75285			−0.308876			−0.154438	+	0.988002i	$0.549357\pi$
$998$	52.4875			1.66146
$999$	24.2230	+	32.8968i	0.766381	+	1.04081i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.2.d.a.176.4	yes	6
3.2	odd	2		177.2.d.c.176.3	yes	6
59.58	odd	2		177.2.d.c.176.4	yes	6
177.176	even	2	inner	177.2.d.a.176.3	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.2.d.a.176.3	✓	6	177.176	even	2	inner
177.2.d.a.176.4	yes	6	1.1	even	1	trivial
177.2.d.c.176.3	yes	6	3.2	odd	2
177.2.d.c.176.4	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)

\(f(q)\)	\(=\)	\(q-1.46260 q^{2} +(1.16170 + 1.28470i) q^{3} +0.139194 q^{4} -0.594299i q^{5} +(-1.69910 - 1.87900i) q^{6} +1.86081 q^{7} +2.72161 q^{8} +(-0.300896 + 2.98487i) q^{9} +O(q^{10})\)	\(q-1.46260 q^{2} +(1.16170 + 1.28470i) q^{3} +0.139194 q^{4} -0.594299i q^{5} +(-1.69910 - 1.87900i) q^{6} +1.86081 q^{7} +2.72161 q^{8} +(-0.300896 + 2.98487i) q^{9} +0.869221i q^{10} +0.676596 q^{11} +(0.161702 + 0.178822i) q^{12} +5.37545i q^{13} -2.72161 q^{14} +(0.763495 - 0.690399i) q^{15} -4.25901 q^{16} +1.70017i q^{17} +(0.440090 - 4.36567i) q^{18} -2.25901 q^{19} -0.0827230i q^{20} +(2.16170 + 2.39057i) q^{21} -0.989588 q^{22} +4.86081 q^{23} +(3.16170 + 3.49645i) q^{24} +4.64681 q^{25} -7.86212i q^{26} +(-4.18421 + 3.08097i) q^{27} +0.259013 q^{28} -6.24467i q^{29} +(-1.11669 + 1.00978i) q^{30} +2.48667i q^{31} +0.786003 q^{32} +(0.786003 + 0.869221i) q^{33} -2.48667i q^{34} -1.10588i q^{35} +(-0.0418830 + 0.415477i) q^{36} -7.86212i q^{37} +3.30403 q^{38} +(-6.90582 + 6.24467i) q^{39} -1.61745i q^{40} -2.29447i q^{41} +(-3.16170 - 3.49645i) q^{42} -7.11389i q^{43} +0.0941782 q^{44} +(1.77391 + 0.178822i) q^{45} -7.10941 q^{46} -8.46260 q^{47} +(-4.94770 - 5.47154i) q^{48} -3.53740 q^{49} -6.79641 q^{50} +(-2.18421 + 1.97510i) q^{51} +0.748230i q^{52} -5.73309i q^{53} +(6.11982 - 4.50622i) q^{54} -0.402100i q^{55} +5.06439 q^{56} +(-2.62430 - 2.90215i) q^{57} +9.13344i q^{58} +(1.93561 + 7.43326i) q^{59} +(0.106274 - 0.0960994i) q^{60} -10.0027i q^{61} -3.63700i q^{62} +(-0.559910 + 5.55427i) q^{63} +7.36842 q^{64} +3.19462 q^{65} +(-1.14961 - 1.27132i) q^{66} -5.37545i q^{67} +0.236654i q^{68} +(5.64681 + 6.24467i) q^{69} +1.61745i q^{70} +5.92529i q^{71} +(-0.818923 + 8.12366i) q^{72} +8.26422i q^{73} +11.4991i q^{74} +(5.39821 + 5.96974i) q^{75} -0.314441 q^{76} +1.25901 q^{77} +(10.1004 - 9.13344i) q^{78} +8.29362 q^{79} +2.53113i q^{80} +(-8.81892 - 1.79627i) q^{81} +3.35589i q^{82} +0.0941782 q^{83} +(0.300896 + 0.332754i) q^{84} +1.01041 q^{85} +10.4048i q^{86} +(8.02251 - 7.25444i) q^{87} +1.84143 q^{88} -10.9806 q^{89} +(-2.59451 - 0.261545i) q^{90} +10.0027i q^{91} +0.676596 q^{92} +(-3.19462 + 2.88877i) q^{93} +12.3774 q^{94} +1.34253i q^{95} +(0.913101 + 1.00978i) q^{96} -17.8648i q^{97} +5.17380 q^{98} +(-0.203585 + 2.01955i) 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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