LMFDB - Embedded newform 550.2.ba.e.399.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [550,2,Mod(49,550)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("550.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(550, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	550.ba (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,2,0,6,0,0,2,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.39177211117$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			399.1
Root			$-0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	550.399
Dual form			550.2.ba.e.499.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.587785 - 0.809017i) q^{2} +(-1.53884 + 0.500000i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(1.30902 + 0.951057i) q^{6} +(-2.12663 - 0.690983i) q^{7} +(0.951057 - 0.309017i) q^{8} +(-0.309017 + 0.224514i) q^{9} +(3.23607 + 0.726543i) q^{11} -1.61803i q^{12} +(0.138757 + 0.190983i) q^{13} +(0.690983 + 2.12663i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-0.224514 + 0.309017i) q^{17} +(0.363271 + 0.118034i) q^{18} +(-0.809017 - 2.48990i) q^{19} +3.61803 q^{21} +(-1.31433 - 3.04508i) q^{22} -3.85410i q^{23} +(-1.30902 + 0.951057i) q^{24} +(0.0729490 - 0.224514i) q^{26} +(3.21644 - 4.42705i) q^{27} +(1.31433 - 1.80902i) q^{28} +(0.163119 - 0.502029i) q^{29} +(8.28115 - 6.01661i) q^{31} +1.00000i q^{32} +(-5.34307 + 0.500000i) q^{33} +0.381966 q^{34} +(-0.118034 - 0.363271i) q^{36} +(8.42075 + 2.73607i) q^{37} +(-1.53884 + 2.11803i) q^{38} +(-0.309017 - 0.224514i) q^{39} +(-1.14590 - 3.52671i) q^{41} +(-2.12663 - 2.92705i) q^{42} -9.47214i q^{43} +(-1.69098 + 2.85317i) q^{44} +(-3.11803 + 2.26538i) q^{46} +(0.224514 - 0.0729490i) q^{47} +(1.53884 + 0.500000i) q^{48} +(-1.61803 - 1.17557i) q^{49} +(0.190983 - 0.587785i) q^{51} +(-0.224514 + 0.0729490i) q^{52} +(-0.812299 - 1.11803i) q^{53} -5.47214 q^{54} -2.23607 q^{56} +(2.48990 + 3.42705i) q^{57} +(-0.502029 + 0.163119i) q^{58} +(3.54508 - 10.9106i) q^{59} +(-1.80902 - 1.31433i) q^{61} +(-9.73508 - 3.16312i) q^{62} +(0.812299 - 0.263932i) q^{63} +(0.809017 - 0.587785i) q^{64} +(3.54508 + 4.02874i) q^{66} +9.32624i q^{67} +(-0.224514 - 0.309017i) q^{68} +(1.92705 + 5.93085i) q^{69} +(-7.92705 - 5.75934i) q^{71} +(-0.224514 + 0.309017i) q^{72} +(7.74721 + 2.51722i) q^{73} +(-2.73607 - 8.42075i) q^{74} +2.61803 q^{76} +(-6.37988 - 3.78115i) q^{77} +0.381966i q^{78} +(-9.66312 + 7.02067i) q^{79} +(-2.38197 + 7.33094i) q^{81} +(-2.17963 + 3.00000i) q^{82} +(5.29007 - 7.28115i) q^{83} +(-1.11803 + 3.44095i) q^{84} +(-7.66312 + 5.56758i) q^{86} +0.854102i q^{87} +(3.30220 - 0.309017i) q^{88} +13.1803 q^{89} +(-0.163119 - 0.502029i) q^{91} +(3.66547 + 1.19098i) q^{92} +(-9.73508 + 13.3992i) q^{93} +(-0.190983 - 0.138757i) q^{94} +(-0.500000 - 1.53884i) q^{96} +(7.05342 + 9.70820i) q^{97} +2.00000i q^{98} +(-1.16312 + 0.502029i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} + 6 q^{6} + 2 q^{9} + 8 q^{11} + 10 q^{14} - 2 q^{16} - 2 q^{19} + 20 q^{21} - 6 q^{24} + 14 q^{26} - 30 q^{29} + 26 q^{31} + 12 q^{34} + 8 q^{36} + 2 q^{39} - 36 q^{41} - 18 q^{44} - 16 q^{46}+ \cdots + 22 q^{99}+O(q^{100}) $ 8 * q + 2 * q^4 + 6 * q^6 + 2 * q^9 + 8 * q^11 + 10 * q^14 - 2 * q^16 - 2 * q^19 + 20 * q^21 - 6 * q^24 + 14 * q^26 - 30 * q^29 + 26 * q^31 + 12 * q^34 + 8 * q^36 + 2 * q^39 - 36 * q^41 - 18 * q^44 - 16 * q^46 - 4 * q^49 + 6 * q^51 - 8 * q^54 + 6 * q^59 - 10 * q^61 + 2 * q^64 + 6 * q^66 + 2 * q^69 - 50 * q^71 - 4 * q^74 + 12 * q^76 - 46 * q^79 - 28 * q^81 - 30 * q^86 + 16 * q^89 + 30 * q^91 - 6 * q^94 - 4 * q^96 + 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$3$	−1.53884	+	0.500000i	−0.888451	+	0.288675i	−0.717462	−	0.696598i	$-0.754696\pi$
$3$	−1.53884	+	0.500000i	−0.888451	+	0.288675i	−0.170989	+	0.985273i	$0.554696\pi$
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$		0			0
$5$		0			0
$6$	1.30902	+	0.951057i	0.534404	+	0.388267i
$7$	−2.12663	−	0.690983i	−0.803789	−	0.261167i	−0.121824	−	0.992552i	$-0.538874\pi$
$7$	−2.12663	−	0.690983i	−0.803789	−	0.261167i	−0.681965	+	0.731385i	$0.738874\pi$
$8$	0.951057	−	0.309017i	0.336249	−	0.109254i
$9$	−0.309017	+	0.224514i	−0.103006	+	0.0748380i
$10$		0			0
$11$	3.23607	+	0.726543i	0.975711	+	0.219061i
$11$	3.23607	+	0.726543i	0.975711	+	0.219061i
$12$		−	1.61803i		−	0.467086i
$13$	0.138757	+	0.190983i	0.0384843	+	0.0529692i	0.827826	−	0.560986i	$-0.189578\pi$
$13$	0.138757	+	0.190983i	0.0384843	+	0.0529692i	−0.789341	+	0.613955i	$0.789578\pi$
$14$	0.690983	+	2.12663i	0.184673	+	0.568365i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−0.224514	+	0.309017i	−0.0544526	+	0.0749476i	−0.835375	−	0.549681i	$-0.814749\pi$
$17$	−0.224514	+	0.309017i	−0.0544526	+	0.0749476i	0.780922	+	0.624628i	$0.214749\pi$
$18$	0.363271	+	0.118034i	0.0856239	+	0.0278209i
$19$	−0.809017	−	2.48990i	−0.185601	−	0.571222i	0.814357	−	0.580364i	$-0.197090\pi$
$19$	−0.809017	−	2.48990i	−0.185601	−	0.571222i	−0.999958	+	0.00914245i	$0.997090\pi$
$20$		0			0
$21$	3.61803			0.789520
$22$	−1.31433	−	3.04508i	−0.280216	−	0.649214i
$23$		−	3.85410i		−	0.803636i	−0.915720	−	0.401818i	$-0.868378\pi$
$23$		−	3.85410i		−	0.803636i	0.915720	−	0.401818i	$-0.131622\pi$
$24$	−1.30902	+	0.951057i	−0.267202	+	0.194134i
$25$		0			0
$26$	0.0729490	−	0.224514i	0.0143065	−	0.0440308i
$27$	3.21644	−	4.42705i	0.619004	−	0.851986i
$28$	1.31433	−	1.80902i	0.248385	−	0.341872i
$29$	0.163119	−	0.502029i	0.0302904	−	0.0932244i	−0.934768	−	0.355258i	$-0.884393\pi$
$29$	0.163119	−	0.502029i	0.0302904	−	0.0932244i	0.965059	+	0.262033i	$0.0843931\pi$
$30$		0			0
$31$	8.28115	−	6.01661i	1.48734	−	1.08062i	0.512241	−	0.858842i	$-0.328816\pi$
$31$	8.28115	−	6.01661i	1.48734	−	1.08062i	0.975098	−	0.221773i	$-0.0711844\pi$
$32$			1.00000i			0.176777i
$33$	−5.34307	+	0.500000i	−0.930109	+	0.0870388i
$34$	0.381966			0.0655066
$35$		0			0
$36$	−0.118034	−	0.363271i	−0.0196723	−	0.0605452i
$37$	8.42075	+	2.73607i	1.38436	+	0.449807i	0.904101	−	0.427318i	$-0.140542\pi$
$37$	8.42075	+	2.73607i	1.38436	+	0.449807i	0.480262	+	0.877125i	$0.340542\pi$
$38$	−1.53884	+	2.11803i	−0.249633	+	0.343590i
$39$	−0.309017	−	0.224514i	−0.0494823	−	0.0359510i
$40$		0			0
$41$	−1.14590	−	3.52671i	−0.178959	−	0.550780i	0.820833	−	0.571168i	$-0.193510\pi$
$41$	−1.14590	−	3.52671i	−0.178959	−	0.550780i	−0.999792	+	0.0203886i	$0.993510\pi$
$42$	−2.12663	−	2.92705i	−0.328146	−	0.451654i
$43$		−	9.47214i		−	1.44449i	−0.691639	−	0.722244i	$-0.743111\pi$
$43$		−	9.47214i		−	1.44449i	0.691639	−	0.722244i	$-0.256889\pi$
$44$	−1.69098	+	2.85317i	−0.254925	+	0.430131i
$45$		0			0
$46$	−3.11803	+	2.26538i	−0.459729	+	0.334013i
$47$	0.224514	−	0.0729490i	0.0327487	−	0.0106407i	−0.292597	−	0.956236i	$-0.594519\pi$
$47$	0.224514	−	0.0729490i	0.0327487	−	0.0106407i	0.325346	+	0.945595i	$0.394519\pi$
$48$	1.53884	+	0.500000i	0.222113	+	0.0721688i
$49$	−1.61803	−	1.17557i	−0.231148	−	0.167939i
$50$		0			0
$51$	0.190983	−	0.587785i	0.0267430	−	0.0823064i
$52$	−0.224514	+	0.0729490i	−0.0311345	+	0.0101162i
$53$	−0.812299	−	1.11803i	−0.111578	−	0.153574i	0.749576	−	0.661919i	$-0.230258\pi$
$53$	−0.812299	−	1.11803i	−0.111578	−	0.153574i	−0.861154	+	0.508345i	$0.830258\pi$
$54$	−5.47214			−0.744663
$55$		0			0
$56$	−2.23607			−0.298807
$57$	2.48990	+	3.42705i	0.329795	+	0.453924i
$58$	−0.502029	+	0.163119i	−0.0659196	+	0.0214186i
$59$	3.54508	−	10.9106i	0.461531	−	1.42045i	−0.401763	−	0.915744i	$-0.631602\pi$
$59$	3.54508	−	10.9106i	0.461531	−	1.42045i	0.863294	−	0.504702i	$-0.168398\pi$
$60$		0			0
$61$	−1.80902	−	1.31433i	−0.231621	−	0.168282i	0.465921	−	0.884826i	$-0.345723\pi$
$61$	−1.80902	−	1.31433i	−0.231621	−	0.168282i	−0.697542	+	0.716544i	$0.745723\pi$
$62$	−9.73508	−	3.16312i	−1.23636	−	0.401717i
$63$	0.812299	−	0.263932i	0.102340	−	0.0332523i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$		0			0
$66$	3.54508	+	4.02874i	0.436370	+	0.495904i
$67$			9.32624i			1.13938i	0.821859	+	0.569691i	$0.192937\pi$
$67$			9.32624i			1.13938i	−0.821859	+	0.569691i	$0.807063\pi$
$68$	−0.224514	−	0.309017i	−0.0272263	−	0.0374738i
$69$	1.92705	+	5.93085i	0.231990	+	0.713991i
$70$		0			0
$71$	−7.92705	−	5.75934i	−0.940768	−	0.683508i	0.00783751	−	0.999969i	$-0.497505\pi$
$71$	−7.92705	−	5.75934i	−0.940768	−	0.683508i	−0.948605	+	0.316461i	$0.897505\pi$
$72$	−0.224514	+	0.309017i	−0.0264592	+	0.0364180i
$73$	7.74721	+	2.51722i	0.906742	+	0.294618i	0.725017	−	0.688731i	$-0.241832\pi$
$73$	7.74721	+	2.51722i	0.906742	+	0.294618i	0.181725	+	0.983349i	$0.441832\pi$
$74$	−2.73607	−	8.42075i	−0.318061	−	0.978892i
$75$		0			0
$76$	2.61803			0.300309
$77$	−6.37988	−	3.78115i	−0.727055	−	0.430902i
$78$			0.381966i			0.0432491i
$79$	−9.66312	+	7.02067i	−1.08719	+	0.789887i	−0.978922	−	0.204235i	$-0.934529\pi$
$79$	−9.66312	+	7.02067i	−1.08719	+	0.789887i	−0.108264	+	0.994122i	$0.534529\pi$
$80$		0			0
$81$	−2.38197	+	7.33094i	−0.264663	+	0.814549i
$82$	−2.17963	+	3.00000i	−0.240700	+	0.331295i
$83$	5.29007	−	7.28115i	0.580660	−	0.799210i	−0.413107	−	0.910682i	$-0.635557\pi$
$83$	5.29007	−	7.28115i	0.580660	−	0.799210i	0.993768	+	0.111472i	$0.0355565\pi$
$84$	−1.11803	+	3.44095i	−0.121988	+	0.375439i
$85$		0			0
$86$	−7.66312	+	5.56758i	−0.826335	+	0.600368i
$87$			0.854102i			0.0915693i
$88$	3.30220	−	0.309017i	0.352015	−	0.0329413i
$89$	13.1803			1.39711			0.698557	−	0.715555i	$-0.253826\pi$
$89$	13.1803			1.39711			0.698557	+	0.715555i	$0.253826\pi$
$90$		0			0
$91$	−0.163119	−	0.502029i	−0.0170995	−	0.0526269i
$92$	3.66547	+	1.19098i	0.382152	+	0.124169i
$93$	−9.73508	+	13.3992i	−1.00948	+	1.38943i
$94$	−0.190983	−	0.138757i	−0.0196984	−	0.0143117i
$95$		0			0
$96$	−0.500000	−	1.53884i	−0.0510310	−	0.157057i
$97$	7.05342	+	9.70820i	0.716167	+	0.985719i	0.999642	+	0.0267394i	$0.00851242\pi$
$97$	7.05342	+	9.70820i	0.716167	+	0.985719i	−0.283476	+	0.958979i	$0.591488\pi$
$98$			2.00000i			0.202031i
$99$	−1.16312	+	0.502029i	−0.116898	+	0.0504558i
$100$		0			0
$101$	−15.1353	+	10.9964i	−1.50601	+	1.09418i	−0.538107	+	0.842877i	$0.680860\pi$
$101$	−15.1353	+	10.9964i	−1.50601	+	1.09418i	−0.967908	+	0.251307i	$0.919140\pi$
$102$	−0.587785	+	0.190983i	−0.0581994	+	0.0189101i
$103$	16.0620	+	5.21885i	1.58263	+	0.514228i	0.962733	−	0.270453i	$-0.0871736\pi$
$103$	16.0620	+	5.21885i	1.58263	+	0.514228i	0.619899	+	0.784682i	$0.287174\pi$
$104$	0.190983	+	0.138757i	0.0187274	+	0.0136063i
$105$		0			0
$106$	−0.427051	+	1.31433i	−0.0414789	+	0.127659i
$107$	−7.77997	+	2.52786i	−0.752118	+	0.244378i	−0.659892	−	0.751360i	$-0.729398\pi$
$107$	−7.77997	+	2.52786i	−0.752118	+	0.244378i	−0.0922255	+	0.995738i	$0.529398\pi$
$108$	3.21644	+	4.42705i	0.309502	+	0.425993i
$109$	11.6180			1.11281			0.556403	−	0.830913i	$-0.312181\pi$
$109$	11.6180			1.11281			0.556403	+	0.830913i	$0.312181\pi$
$110$		0			0
$111$	−14.3262			−1.35979
$112$	1.31433	+	1.80902i	0.124192	+	0.170936i
$113$	−13.9883	+	4.54508i	−1.31591	+	0.427566i	−0.881089	−	0.472950i	$-0.843189\pi$
$113$	−13.9883	+	4.54508i	−1.31591	+	0.427566i	−0.434823	+	0.900516i	$0.643189\pi$
$114$	1.30902	−	4.02874i	0.122601	−	0.377326i
$115$		0			0
$116$	0.427051	+	0.310271i	0.0396507	+	0.0288079i
$117$	−0.0857567	−	0.0278640i	−0.00792821	−	0.00257603i
$118$	−10.9106	+	3.54508i	−1.00441	+	0.326352i
$119$	0.690983	−	0.502029i	0.0633423	−	0.0460209i
$120$		0			0
$121$	9.94427	+	4.70228i	0.904025	+	0.427480i
$122$			2.23607i			0.202444i
$123$	3.52671	+	4.85410i	0.317993	+	0.437680i
$124$	3.16312	+	9.73508i	0.284056	+	0.874236i
$125$		0			0
$126$	−0.690983	−	0.502029i	−0.0615577	−	0.0447243i
$127$	1.71036	−	2.35410i	0.151769	−	0.208893i	−0.726362	−	0.687313i	$-0.758790\pi$
$127$	1.71036	−	2.35410i	0.151769	−	0.208893i	0.878131	+	0.478420i	$0.158790\pi$
$128$	−0.951057	−	0.309017i	−0.0840623	−	0.0273135i
$129$	4.73607	+	14.5761i	0.416988	+	1.28336i
$130$		0			0
$131$	11.1459			0.973822			0.486911	−	0.873452i	$-0.338124\pi$
$131$	11.1459			0.973822			0.486911	+	0.873452i	$0.338124\pi$
$132$	1.17557	−	5.23607i	0.102320	−	0.455741i
$133$			5.85410i			0.507615i
$134$	7.54508	−	5.48183i	0.651796	−	0.473558i
$135$		0			0
$136$	−0.118034	+	0.363271i	−0.0101213	+	0.0311503i
$137$	9.26581	−	12.7533i	0.791631	−	1.08959i	−0.202272	−	0.979329i	$-0.564832\pi$
$137$	9.26581	−	12.7533i	0.791631	−	1.08959i	0.993903	−	0.110258i	$-0.0351676\pi$
$138$	3.66547	−	5.04508i	0.312025	−	0.429466i
$139$	0.881966	−	2.71441i	0.0748074	−	0.230233i	−0.906660	−	0.421862i	$-0.861377\pi$
$139$	0.881966	−	2.71441i	0.0748074	−	0.230233i	0.981468	+	0.191628i	$0.0613768\pi$
$140$		0			0
$141$	−0.309017	+	0.224514i	−0.0260239	+	0.0189075i
$142$			9.79837i			0.822261i
$143$	0.310271	+	0.718847i	0.0259461	+	0.0601130i
$144$	0.381966			0.0318305
$145$		0			0
$146$	−2.51722	−	7.74721i	−0.208327	−	0.641164i
$147$	3.07768	+	1.00000i	0.253843	+	0.0824786i
$148$	−5.20431	+	7.16312i	−0.427792	+	0.588805i
$149$	−8.66312	−	6.29412i	−0.709710	−	0.515635i	0.173370	−	0.984857i	$-0.444534\pi$
$149$	−8.66312	−	6.29412i	−0.709710	−	0.515635i	−0.883080	+	0.469222i	$0.844534\pi$
$150$		0			0
$151$	−5.88197	−	18.1028i	−0.478668	−	1.47319i	−0.840947	−	0.541118i	$-0.818001\pi$
$151$	−5.88197	−	18.1028i	−0.478668	−	1.47319i	0.362279	−	0.932070i	$-0.381999\pi$
$152$	−1.53884	−	2.11803i	−0.124817	−	0.171795i
$153$		−	0.145898i		−	0.0117952i
$154$	0.690983	+	7.38394i	0.0556810	+	0.595015i
$155$		0			0
$156$	0.309017	−	0.224514i	0.0247412	−	0.0179755i
$157$	−6.43288	+	2.09017i	−0.513400	+	0.166814i	−0.554248	−	0.832352i	$-0.686994\pi$
$157$	−6.43288	+	2.09017i	−0.513400	+	0.166814i	0.0408481	+	0.999165i	$0.486994\pi$
$158$	11.3597	+	3.69098i	0.903727	+	0.293639i
$159$	1.80902	+	1.31433i	0.143464	+	0.104233i
$160$		0			0
$161$	−2.66312	+	8.19624i	−0.209883	+	0.645954i
$162$	7.33094	−	2.38197i	0.575973	−	0.187145i
$163$	0.106001	+	0.145898i	0.00830265	+	0.0114276i	0.813148	−	0.582057i	$-0.197752\pi$
$163$	0.106001	+	0.145898i	0.00830265	+	0.0114276i	−0.804845	+	0.593484i	$0.797752\pi$
$164$	3.70820			0.289562
$165$		0			0
$166$	−9.00000			−0.698535
$167$	1.31433	+	1.80902i	0.101706	+	0.139986i	0.856836	−	0.515588i	$-0.172427\pi$
$167$	1.31433	+	1.80902i	0.101706	+	0.139986i	−0.755131	+	0.655574i	$0.772427\pi$
$168$	3.44095	−	1.11803i	0.265475	−	0.0862582i
$169$	4.00000	−	12.3107i	0.307692	−	0.946980i
$170$		0			0
$171$	0.809017	+	0.587785i	0.0618671	+	0.0449491i
$172$	9.00854	+	2.92705i	0.686894	+	0.223186i
$173$	−12.6740	+	4.11803i	−0.963587	+	0.313088i	−0.748224	−	0.663446i	$-0.769093\pi$
$173$	−12.6740	+	4.11803i	−0.963587	+	0.313088i	−0.215362	+	0.976534i	$0.569093\pi$
$174$	0.690983	−	0.502029i	0.0523833	−	0.0380587i
$175$		0			0
$176$	−2.19098	−	2.48990i	−0.165152	−	0.187683i
$177$			18.5623i			1.39523i
$178$	−7.74721	−	10.6631i	−0.580678	−	0.799235i
$179$	−4.52786	−	13.9353i	−0.338428	−	1.04158i	−0.965009	−	0.262219i	$-0.915546\pi$
$179$	−4.52786	−	13.9353i	−0.338428	−	1.04158i	0.626580	−	0.779357i	$-0.284454\pi$
$180$		0			0
$181$	5.70820	+	4.14725i	0.424287	+	0.308263i	0.779361	−	0.626576i	$-0.215544\pi$
$181$	5.70820	+	4.14725i	0.424287	+	0.308263i	−0.355073	+	0.934839i	$0.615544\pi$
$182$	−0.310271	+	0.427051i	−0.0229988	+	0.0316551i
$183$	3.44095	+	1.11803i	0.254363	+	0.0826475i
$184$	−1.19098	−	3.66547i	−0.0878004	−	0.270222i
$185$		0			0
$186$	16.5623			1.21441
$187$	−0.951057	+	0.836881i	−0.0695481	+	0.0611988i
$188$			0.236068i			0.0172170i
$189$	−9.89919	+	7.19218i	−0.720060	+	0.523154i
$190$		0			0
$191$	−6.13525	+	18.8824i	−0.443931	+	1.36628i	0.439720	+	0.898135i	$0.355078\pi$
$191$	−6.13525	+	18.8824i	−0.443931	+	1.36628i	−0.883651	+	0.468146i	$0.844922\pi$
$192$	−0.951057	+	1.30902i	−0.0686366	+	0.0944702i
$193$	−1.43284	+	1.97214i	−0.103138	+	0.141957i	−0.857466	−	0.514540i	$-0.827963\pi$
$193$	−1.43284	+	1.97214i	−0.103138	+	0.141957i	0.754328	+	0.656497i	$0.227963\pi$
$194$	3.70820	−	11.4127i	0.266234	−	0.819383i
$195$		0			0
$196$	1.61803	−	1.17557i	0.115574	−	0.0839693i
$197$		−	27.5967i		−	1.96619i	−0.183105	−	0.983093i	$-0.558615\pi$
$197$		−	27.5967i		−	1.96619i	0.183105	−	0.983093i	$-0.441385\pi$
$198$	1.08981	+	0.645898i	0.0774497	+	0.0459020i
$199$	1.29180			0.0915730			0.0457865	−	0.998951i	$-0.485421\pi$
$199$	1.29180			0.0915730			0.0457865	+	0.998951i	$0.485421\pi$
$200$		0			0
$201$	−4.66312	−	14.3516i	−0.328911	−	1.01228i
$202$	17.7926	+	5.78115i	1.25188	+	0.406761i
$203$	−0.693786	+	0.954915i	−0.0486943	+	0.0670219i
$204$	0.500000	+	0.363271i	0.0350070	+	0.0254341i
$205$		0			0
$206$	−5.21885	−	16.0620i	−0.363614	−	1.11909i
$207$	0.865300	+	1.19098i	0.0601425	+	0.0827790i
$208$		−	0.236068i		−	0.0163684i
$209$	−0.809017	−	8.64527i	−0.0559609	−	0.598006i
$210$		0			0
$211$	−11.7361	+	8.52675i	−0.807944	+	0.587006i	−0.913234	−	0.407436i	$-0.866423\pi$
$211$	−11.7361	+	8.52675i	−0.807944	+	0.587006i	0.105290	+	0.994442i	$0.466423\pi$
$212$	1.31433	−	0.427051i	0.0902684	−	0.0293300i
$213$	15.0781	+	4.89919i	1.03314	+	0.335687i
$214$	6.61803	+	4.80828i	0.452399	+	0.328687i
$215$		0			0
$216$	1.69098	−	5.20431i	0.115057	−	0.354108i
$217$	−21.7683	+	7.07295i	−1.47773	+	0.480143i
$218$	−6.82891	−	9.39919i	−0.462512	−	0.636593i
$219$	−13.1803			−0.890645
$220$		0			0
$221$	−0.0901699			−0.00606549
$222$	8.42075	+	11.5902i	0.565164	+	0.777881i
$223$	−1.95511	+	0.635255i	−0.130924	+	0.0425398i	−0.373746	−	0.927531i	$-0.621927\pi$
$223$	−1.95511	+	0.635255i	−0.130924	+	0.0425398i	0.242822	+	0.970071i	$0.421927\pi$
$224$	0.690983	−	2.12663i	0.0461682	−	0.142091i
$225$		0			0
$226$	11.8992	+	8.64527i	0.791522	+	0.575074i
$227$	−18.7764	−	6.10081i	−1.24623	−	0.404925i	−0.389663	−	0.920958i	$-0.627408\pi$
$227$	−18.7764	−	6.10081i	−1.24623	−	0.404925i	−0.856569	+	0.516033i	$0.827408\pi$
$228$	−4.02874	+	1.30902i	−0.266810	+	0.0866918i
$229$	−12.5172	+	9.09429i	−0.827161	+	0.600968i	−0.918755	−	0.394829i	$-0.870804\pi$
$229$	−12.5172	+	9.09429i	−0.827161	+	0.600968i	0.0915935	+	0.995796i	$0.470804\pi$
$230$		0			0
$231$	11.7082	+	2.62866i	0.770343	+	0.172953i
$232$		−	0.527864i		−	0.0346560i
$233$	−11.9475	−	16.4443i	−0.782704	−	1.07730i	−0.994978	−	0.100090i	$-0.968087\pi$
$233$	−11.9475	−	16.4443i	−0.782704	−	1.07730i	0.212274	−	0.977210i	$-0.431913\pi$
$234$	0.0278640	+	0.0857567i	0.00182153	+	0.00560609i
$235$		0			0
$236$	9.28115	+	6.74315i	0.604152	+	0.438942i
$237$	11.3597	−	15.6353i	0.737890	−	1.01562i
$238$	−0.812299	−	0.263932i	−0.0526535	−	0.0171082i
$239$	5.39919	+	16.6170i	0.349244	+	1.07486i	0.959272	+	0.282484i	$0.0911583\pi$
$239$	5.39919	+	16.6170i	0.349244	+	1.07486i	−0.610028	+	0.792380i	$0.708842\pi$
$240$		0			0
$241$	18.0000			1.15948			0.579741	−	0.814801i	$-0.303154\pi$
$241$	18.0000			1.15948			0.579741	+	0.814801i	$0.303154\pi$
$242$	−2.04087	−	10.8090i	−0.131192	−	0.694830i
$243$			3.94427i			0.253025i
$244$	1.80902	−	1.31433i	0.115810	−	0.0841412i
$245$		0			0
$246$	1.85410	−	5.70634i	0.118213	−	0.363823i
$247$	0.363271	−	0.500000i	0.0231144	−	0.0318142i
$248$	6.01661	−	8.28115i	0.382055	−	0.525854i
$249$	−4.50000	+	13.8496i	−0.285176	+	0.877681i
$250$		0			0
$251$	−3.88197	+	2.82041i	−0.245028	+	0.178023i	−0.703520	−	0.710675i	$-0.748390\pi$
$251$	−3.88197	+	2.82041i	−0.245028	+	0.178023i	0.458493	+	0.888698i	$0.348390\pi$
$252$			0.854102i			0.0538034i
$253$	2.80017	−	12.4721i	0.176045	−	0.784116i
$254$	−2.90983			−0.182579
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−13.1760	−	4.28115i	−0.821898	−	0.267051i	−0.132269	−	0.991214i	$-0.542226\pi$
$257$	−13.1760	−	4.28115i	−0.821898	−	0.267051i	−0.689629	+	0.724163i	$0.742226\pi$
$258$	9.00854	−	12.3992i	0.560847	−	0.771940i
$259$	−16.0172	−	11.6372i	−0.995262	−	0.723100i
$260$		0			0
$261$	0.0623059	+	0.191758i	0.00385664	+	0.0118695i
$262$	−6.55139	−	9.01722i	−0.404747	−	0.557086i
$263$		−	16.0902i		−	0.992162i	−0.868276	−	0.496081i	$-0.834772\pi$
$263$		−	16.0902i		−	0.992162i	0.868276	−	0.496081i	$-0.165228\pi$
$264$	−4.92705	+	2.12663i	−0.303239	+	0.130885i
$265$		0			0
$266$	4.73607	−	3.44095i	0.290387	−	0.210978i
$267$	−20.2825	+	6.59017i	−1.24127	+	0.403312i
$268$	−8.86978	−	2.88197i	−0.541808	−	0.176044i
$269$	8.01722	+	5.82485i	0.488819	+	0.355147i	0.804730	−	0.593641i	$-0.202310\pi$
$269$	8.01722	+	5.82485i	0.488819	+	0.355147i	−0.315911	+	0.948789i	$0.602310\pi$
$270$		0			0
$271$	8.64590	−	26.6093i	0.525201	−	1.61640i	−0.238717	−	0.971089i	$-0.576727\pi$
$271$	8.64590	−	26.6093i	0.525201	−	1.61640i	0.763918	−	0.645313i	$-0.223273\pi$
$272$	0.363271	−	0.118034i	0.0220266	−	0.00715686i
$273$	0.502029	+	0.690983i	0.0303841	+	0.0418202i
$274$	−15.7639			−0.952334
$275$		0			0
$276$	−6.23607			−0.375367
$277$	−11.3067	−	15.5623i	−0.679352	−	0.935048i	0.320573	−	0.947224i	$-0.396124\pi$
$277$	−11.3067	−	15.5623i	−0.679352	−	0.935048i	−0.999926	+	0.0121753i	$0.996124\pi$
$278$	−2.71441	+	0.881966i	−0.162800	+	0.0528968i
$279$	−1.20820	+	3.71847i	−0.0723333	+	0.222619i
$280$		0			0
$281$	18.7082	+	13.5923i	1.11604	+	0.810849i	0.983604	−	0.180343i	$-0.0577207\pi$
$281$	18.7082	+	13.5923i	1.11604	+	0.810849i	0.132434	+	0.991192i	$0.457721\pi$
$282$	0.363271	+	0.118034i	0.0216325	+	0.00702882i
$283$	20.9232	−	6.79837i	1.24376	−	0.404121i	0.388078	−	0.921627i	$-0.373139\pi$
$283$	20.9232	−	6.79837i	1.24376	−	0.404121i	0.855680	+	0.517505i	$0.173139\pi$
$284$	7.92705	−	5.75934i	0.470384	−	0.341754i
$285$		0			0
$286$	0.399187	−	0.673542i	0.0236044	−	0.0398274i
$287$			8.29180i			0.489449i
$288$	−0.224514	−	0.309017i	−0.0132296	−	0.0182090i
$289$	5.20820	+	16.0292i	0.306365	+	0.942894i
$290$		0			0
$291$	−15.7082	−	11.4127i	−0.920831	−	0.669023i
$292$	−4.78804	+	6.59017i	−0.280199	+	0.385661i
$293$	−9.99235	−	3.24671i	−0.583759	−	0.189675i	0.00222470	−	0.999998i	$-0.499292\pi$
$293$	−9.99235	−	3.24671i	−0.583759	−	0.189675i	−0.585984	+	0.810323i	$0.699292\pi$
$294$	−1.00000	−	3.07768i	−0.0583212	−	0.179494i
$295$		0			0
$296$	8.85410			0.514634
$297$	13.6251	−	11.9894i	0.790606	−	0.695693i
$298$			10.7082i			0.620310i
$299$	0.736068	−	0.534785i	0.0425679	−	0.0309274i
$300$		0			0
$301$	−6.54508	+	20.1437i	−0.377252	+	1.16106i
$302$	−11.1882	+	15.3992i	−0.643807	+	0.886124i
$303$	17.7926	−	24.4894i	1.02216	−	1.40688i
$304$	−0.809017	+	2.48990i	−0.0464003	+	0.142805i
$305$		0			0
$306$	−0.118034	+	0.0857567i	−0.00674755	+	0.00490238i
$307$		−	28.7984i		−	1.64361i	−0.569769	−	0.821805i	$-0.692967\pi$
$307$		−	28.7984i		−	1.64361i	0.569769	−	0.821805i	$-0.307033\pi$
$308$	5.56758	−	4.89919i	0.317242	−	0.279157i
$309$	−27.3262			−1.55454
$310$		0			0
$311$	1.30902	+	4.02874i	0.0742275	+	0.228449i	0.981286	−	0.192556i	$-0.0616776\pi$
$311$	1.30902	+	4.02874i	0.0742275	+	0.228449i	−0.907058	+	0.421005i	$0.861678\pi$
$312$	−0.363271	−	0.118034i	−0.0205662	−	0.00668236i
$313$	0.587785	−	0.809017i	0.0332236	−	0.0457283i	−0.792082	−	0.610415i	$-0.791003\pi$
$313$	0.587785	−	0.809017i	0.0332236	−	0.0457283i	0.825306	+	0.564686i	$0.191003\pi$
$314$	5.47214	+	3.97574i	0.308810	+	0.224364i
$315$		0			0
$316$	−3.69098	−	11.3597i	−0.207634	−	0.639032i
$317$	1.64484	+	2.26393i	0.0923836	+	0.127155i	0.852707	−	0.522390i	$-0.174959\pi$
$317$	1.64484	+	2.26393i	0.0923836	+	0.127155i	−0.760323	+	0.649545i	$0.774959\pi$
$318$		−	2.23607i		−	0.125392i
$319$	0.892609	−	1.50609i	0.0499765	−	0.0843246i
$320$		0			0
$321$	10.7082	−	7.77997i	0.597674	−	0.434235i
$322$	8.19624	−	2.66312i	0.456758	−	0.148410i
$323$	0.951057	+	0.309017i	0.0529182	+	0.0171942i
$324$	−6.23607	−	4.53077i	−0.346448	−	0.251709i
$325$		0			0
$326$	0.0557281	−	0.171513i	0.00308649	−	0.00949925i
$327$	−17.8783	+	5.80902i	−0.988673	+	0.321239i
$328$	−2.17963	−	3.00000i	−0.120350	−	0.165647i
$329$	−0.527864			−0.0291021
$330$		0			0
$331$	−16.9443			−0.931341			−0.465671	−	0.884958i	$-0.654187\pi$
$331$	−16.9443			−0.931341			−0.465671	+	0.884958i	$0.654187\pi$
$332$	5.29007	+	7.28115i	0.290330	+	0.399605i
$333$	−3.21644	+	1.04508i	−0.176260	+	0.0572703i
$334$	0.690983	−	2.12663i	0.0378089	−	0.116364i
$335$		0			0
$336$	−2.92705	−	2.12663i	−0.159684	−	0.116017i
$337$	28.6502	+	9.30902i	1.56068	+	0.507094i	0.956988	−	0.290126i	$-0.0936973\pi$
$337$	28.6502	+	9.30902i	1.56068	+	0.507094i	0.603688	+	0.797221i	$0.293697\pi$
$338$	−12.3107	+	4.00000i	−0.669616	+	0.217571i
$339$	19.2533	−	13.9883i	1.04570	−	0.759742i
$340$		0			0
$341$	31.1697	−	13.4535i	1.68793	−	0.728550i
$342$		−	1.00000i		−	0.0540738i
$343$	11.8290	+	16.2812i	0.638703	+	0.879100i
$344$	−2.92705	−	9.00854i	−0.157816	−	0.485708i
$345$		0			0
$346$	10.7812	+	7.83297i	0.579598	+	0.421103i
$347$	11.0822	−	15.2533i	0.594922	−	0.818839i	−0.400310	−	0.916380i	$-0.631098\pi$
$347$	11.0822	−	15.2533i	0.594922	−	0.818839i	0.995232	+	0.0975404i	$0.0310975\pi$
$348$	−0.812299	−	0.263932i	−0.0435438	−	0.0141482i
$349$	7.29180	+	22.4418i	0.390321	+	1.20128i	0.932546	+	0.361051i	$0.117582\pi$
$349$	7.29180	+	22.4418i	0.390321	+	1.20128i	−0.542225	+	0.840233i	$0.682418\pi$
$350$		0			0
$351$	1.29180			0.0689510
$352$	−0.726543	+	3.23607i	−0.0387248	+	0.172483i
$353$			4.43769i			0.236195i	0.993002	+	0.118097i	$0.0376795\pi$
$353$			4.43769i			0.236195i	−0.993002	+	0.118097i	$0.962321\pi$
$354$	15.0172	−	10.9106i	0.798156	−	0.579894i
$355$		0			0
$356$	−4.07295	+	12.5352i	−0.215866	+	0.664367i
$357$	−0.812299	+	1.11803i	−0.0429914	+	0.0591726i
$358$	−8.61251	+	11.8541i	−0.455185	+	0.626509i
$359$	−0.291796	+	0.898056i	−0.0154004	+	0.0473976i	−0.958461	−	0.285222i	$-0.907933\pi$
$359$	−0.291796	+	0.898056i	−0.0154004	+	0.0473976i	0.943061	+	0.332620i	$0.107933\pi$
$360$		0			0
$361$	9.82624	−	7.13918i	0.517170	−	0.375746i
$362$		−	7.05573i		−	0.370841i
$363$	−17.6538	−	2.26393i	−0.926584	−	0.118826i
$364$	0.527864			0.0276676
$365$		0			0
$366$	−1.11803	−	3.44095i	−0.0584406	−	0.179862i
$367$	5.08580	+	1.65248i	0.265476	+	0.0862585i	0.438731	−	0.898619i	$-0.355428\pi$
$367$	5.08580	+	1.65248i	0.265476	+	0.0862585i	−0.173254	+	0.984877i	$0.555428\pi$
$368$	−2.26538	+	3.11803i	−0.118091	+	0.162539i
$369$	1.14590	+	0.832544i	0.0596531	+	0.0433405i
$370$		0			0
$371$	0.954915	+	2.93893i	0.0495767	+	0.152581i
$372$	−9.73508	−	13.3992i	−0.504740	−	0.694715i
$373$		−	2.38197i		−	0.123334i	−0.998097	−	0.0616668i	$-0.980358\pi$
$373$		−	2.38197i		−	0.123334i	0.998097	−	0.0616668i	$-0.0196416\pi$
$374$	1.23607	+	0.277515i	0.0639156	+	0.0143499i
$375$		0			0
$376$	0.190983	−	0.138757i	0.00984920	−	0.00715586i
$377$	0.118513	−	0.0385072i	0.00610372	−	0.00198322i
$378$	11.6372	+	3.78115i	0.598553	+	0.194482i
$379$	−4.78115	−	3.47371i	−0.245591	−	0.178433i	0.458179	−	0.888860i	$-0.348502\pi$
$379$	−4.78115	−	3.47371i	−0.245591	−	0.178433i	−0.703771	+	0.710427i	$0.748502\pi$
$380$		0			0
$381$	−1.45492	+	4.47777i	−0.0745376	+	0.229403i
$382$	18.8824	−	6.13525i	0.966106	−	0.313907i
$383$	−1.17557	−	1.61803i	−0.0600688	−	0.0826777i	0.777926	−	0.628356i	$-0.216272\pi$
$383$	−1.17557	−	1.61803i	−0.0600688	−	0.0826777i	−0.837995	+	0.545679i	$0.816272\pi$
$384$	1.61803			0.0825700
$385$		0			0
$386$	2.43769			0.124075
$387$	2.12663	+	2.92705i	0.108103	+	0.148790i
$388$	−11.4127	+	3.70820i	−0.579391	+	0.188256i
$389$	−0.545085	+	1.67760i	−0.0276369	+	0.0850576i	−0.963924	−	0.266179i	$-0.914239\pi$
$389$	−0.545085	+	1.67760i	−0.0276369	+	0.0850576i	0.936287	+	0.351237i	$0.114239\pi$
$390$		0			0
$391$	1.19098	+	0.865300i	0.0602306	+	0.0437601i
$392$	−1.90211	−	0.618034i	−0.0960712	−	0.0312154i
$393$	−17.1518	+	5.57295i	−0.865193	+	0.281118i
$394$	−22.3262	+	16.2210i	−1.12478	+	0.817200i
$395$		0			0
$396$	−0.118034	−	1.26133i	−0.00593143	−	0.0633841i
$397$		−	17.4721i		−	0.876901i	−0.898755	−	0.438451i	$-0.855527\pi$
$397$		−	17.4721i		−	0.876901i	0.898755	−	0.438451i	$-0.144473\pi$
$398$	−0.759299	−	1.04508i	−0.0380602	−	0.0523854i
$399$	−2.92705	−	9.00854i	−0.146536	−	0.450991i
$400$		0			0
$401$	1.54508	+	1.12257i	0.0771579	+	0.0560585i	0.625695	−	0.780067i	$-0.284815\pi$
$401$	1.54508	+	1.12257i	0.0771579	+	0.0560585i	−0.548538	+	0.836126i	$0.684815\pi$
$402$	−8.86978	+	12.2082i	−0.442384	+	0.608890i
$403$	2.29814	+	0.746711i	0.114479	+	0.0371963i
$404$	−5.78115	−	17.7926i	−0.287623	−	0.885213i
$405$		0			0
$406$	1.18034			0.0585793
$407$	25.2623	+	14.9721i	1.25220	+	0.742141i
$408$		−	0.618034i		−	0.0305972i
$409$	14.9721	−	10.8779i	0.740324	−	0.537877i	−0.152488	−	0.988305i	$-0.548729\pi$
$409$	14.9721	−	10.8779i	0.740324	−	0.537877i	0.892813	+	0.450428i	$0.148729\pi$
$410$		0			0
$411$	−7.88197	+	24.2582i	−0.388789	+	1.19657i
$412$	−9.92684	+	13.6631i	−0.489060	+	0.673134i
$413$	−15.0781	+	20.7533i	−0.741947	+	1.02120i
$414$	0.454915	−	1.40008i	0.0223579	−	0.0688104i
$415$		0			0
$416$	−0.190983	+	0.138757i	−0.00936371	+	0.00680314i
$417$			4.61803i			0.226146i
$418$	−6.51864	+	5.73607i	−0.318837	+	0.280560i
$419$	31.1803			1.52326			0.761630	−	0.648013i	$-0.224400\pi$
$419$	31.1803			1.52326			0.761630	+	0.648013i	$0.224400\pi$
$420$		0			0
$421$	−5.46149	−	16.8087i	−0.266177	−	0.819208i	−0.991420	−	0.130715i	$-0.958273\pi$
$421$	−5.46149	−	16.8087i	−0.266177	−	0.819208i	0.725243	−	0.688493i	$-0.241727\pi$
$422$	13.7966	+	4.48278i	0.671607	+	0.218218i
$423$	−0.0530006	+	0.0729490i	−0.00257698	+	0.00354690i
$424$	−1.11803	−	0.812299i	−0.0542965	−	0.0394487i
$425$		0			0
$426$	−4.89919	−	15.0781i	−0.237366	−	0.730539i
$427$	2.93893	+	4.04508i	0.142225	+	0.195755i
$428$		−	8.18034i		−	0.395412i
$429$	−0.836881	−	0.951057i	−0.0404050	−	0.0459174i
$430$		0			0
$431$	−4.80902	+	3.49396i	−0.231642	+	0.168298i	−0.697552	−	0.716534i	$-0.745727\pi$
$431$	−4.80902	+	3.49396i	−0.231642	+	0.168298i	0.465909	+	0.884832i	$0.345727\pi$
$432$	−5.20431	+	1.69098i	−0.250393	+	0.0813575i
$433$	8.05748	+	2.61803i	0.387218	+	0.125815i	0.496155	−	0.868234i	$-0.334745\pi$
$433$	8.05748	+	2.61803i	0.387218	+	0.125815i	−0.108937	+	0.994049i	$0.534745\pi$
$434$	18.5172	+	13.4535i	0.888855	+	0.645791i
$435$		0			0
$436$	−3.59017	+	11.0494i	−0.171938	+	0.529171i
$437$	−9.59632	+	3.11803i	−0.459054	+	0.149156i
$438$	7.74721	+	10.6631i	0.370176	+	0.509504i
$439$	−22.7082			−1.08380			−0.541902	−	0.840442i	$-0.682296\pi$
$439$	−22.7082			−1.08380			−0.541902	+	0.840442i	$0.682296\pi$
$440$		0			0
$441$	0.763932			0.0363777
$442$	0.0530006	+	0.0729490i	0.00252098	+	0.00346983i
$443$	−29.0135	+	9.42705i	−1.37847	+	0.447893i	−0.902167	−	0.431387i	$-0.858024\pi$
$443$	−29.0135	+	9.42705i	−1.37847	+	0.447893i	−0.476305	+	0.879280i	$0.658024\pi$
$444$	4.42705	−	13.6251i	0.210099	−	0.646617i
$445$		0			0
$446$	1.66312	+	1.20833i	0.0787510	+	0.0572159i
$447$	16.4782	+	5.35410i	0.779394	+	0.253240i
$448$	−2.12663	+	0.690983i	−0.100474	+	0.0326459i
$449$	13.1803	−	9.57608i	0.622019	−	0.451923i	−0.231607	−	0.972809i	$-0.574398\pi$
$449$	13.1803	−	9.57608i	0.622019	−	0.451923i	0.853626	+	0.520886i	$0.174398\pi$
$450$		0			0
$451$	−1.14590	−	12.2452i	−0.0539582	−	0.576605i
$452$		−	14.7082i		−	0.691816i
$453$	18.1028	+	24.9164i	0.850545	+	1.17067i
$454$	6.10081	+	18.7764i	0.286325	+	0.881219i
$455$		0			0
$456$	3.42705	+	2.48990i	0.160486	+	0.116600i
$457$	−7.12667	+	9.80902i	−0.333371	+	0.458846i	−0.942491	−	0.334232i	$-0.891523\pi$
$457$	−7.12667	+	9.80902i	−0.333371	+	0.458846i	0.609119	+	0.793079i	$0.291523\pi$
$458$	14.7149	+	4.78115i	0.687581	+	0.223409i
$459$	0.645898	+	1.98787i	0.0301479	+	0.0927858i
$460$		0			0
$461$	−36.4164			−1.69608			−0.848041	−	0.529931i	$-0.822218\pi$
$461$	−36.4164			−1.69608			−0.848041	+	0.529931i	$0.822218\pi$
$462$	−4.75528	−	11.0172i	−0.221236	−	0.512568i
$463$			38.5967i			1.79374i	0.442291	+	0.896871i	$0.354166\pi$
$463$			38.5967i			1.79374i	−0.442291	+	0.896871i	$0.645834\pi$
$464$	−0.427051	+	0.310271i	−0.0198253	+	0.0144040i
$465$		0			0
$466$	−6.28115	+	19.3314i	−0.290969	+	0.895510i
$467$	−18.9151	+	26.0344i	−0.875288	+	1.20473i	0.102416	+	0.994742i	$0.467343\pi$
$467$	−18.9151	+	26.0344i	−0.875288	+	1.20473i	−0.977704	+	0.209989i	$0.932657\pi$
$468$	0.0530006	−	0.0729490i	0.00244995	−	0.00337207i
$469$	6.44427	−	19.8334i	0.297569	−	0.915823i
$470$		0			0
$471$	8.85410	−	6.43288i	0.407975	−	0.296412i
$472$		−	11.4721i		−	0.528048i
$473$	6.88191	−	30.6525i	0.316431	−	1.40940i
$474$	−19.3262			−0.887684
$475$		0			0
$476$	0.263932	+	0.812299i	0.0120973	+	0.0372317i
$477$	0.502029	+	0.163119i	0.0229863	+	0.00746870i
$478$	10.2699	−	14.1353i	0.469733	−	0.646532i
$479$	8.04508	+	5.84510i	0.367589	+	0.267069i	0.756211	−	0.654328i	$-0.227049\pi$
$479$	8.04508	+	5.84510i	0.367589	+	0.267069i	−0.388621	+	0.921398i	$0.627049\pi$
$480$		0			0
$481$	0.645898	+	1.98787i	0.0294504	+	0.0906391i
$482$	−10.5801	−	14.5623i	−0.481912	−	0.663295i
$483$		−	13.9443i		−	0.634486i
$484$	−7.54508	+	8.00448i	−0.342958	+	0.363840i
$485$		0			0
$486$	3.19098	−	2.31838i	0.144746	−	0.105164i
$487$	10.3556	−	3.36475i	0.469258	−	0.152471i	−0.0648366	−	0.997896i	$-0.520653\pi$
$487$	10.3556	−	3.36475i	0.469258	−	0.152471i	0.534095	+	0.845425i	$0.320653\pi$
$488$	−2.12663	−	0.690983i	−0.0962679	−	0.0312793i
$489$	−0.236068	−	0.171513i	−0.0106754	−	0.00775611i
$490$		0			0
$491$	3.76393	−	11.5842i	0.169864	−	0.522787i	−0.829498	−	0.558510i	$-0.811373\pi$
$491$	3.76393	−	11.5842i	0.169864	−	0.522787i	0.999362	+	0.0357226i	$0.0113733\pi$
$492$	−5.70634	+	1.85410i	−0.257262	+	0.0835894i
$493$	0.118513	+	0.163119i	0.00533755	+	0.00734651i
$494$	−0.618034			−0.0278067
$495$		0			0
$496$	−10.2361			−0.459613
$497$	12.8783	+	17.7254i	0.577670	+	0.795094i
$498$	13.8496	−	4.50000i	0.620614	−	0.201650i
$499$	−4.77458	+	14.6946i	−0.213739	+	0.657822i	0.785501	+	0.618860i	$0.212405\pi$
$499$	−4.77458	+	14.6946i	−0.213739	+	0.657822i	−0.999241	+	0.0389621i	$0.987595\pi$
$500$		0			0
$501$	−2.92705	−	2.12663i	−0.130771	−	0.0950107i
$502$	4.56352	+	1.48278i	0.203680	+	0.0661797i
$503$	29.9645	−	9.73607i	1.33605	−	0.434110i	0.448075	−	0.893996i	$-0.352110\pi$
$503$	29.9645	−	9.73607i	1.33605	−	0.434110i	0.887978	+	0.459886i	$0.152110\pi$
$504$	0.690983	−	0.502029i	0.0307788	−	0.0223621i
$505$		0			0
$506$	−11.7361	+	5.06555i	−0.521732	+	0.225191i
$507$			20.9443i			0.930168i
$508$	1.71036	+	2.35410i	0.0758847	+	0.104446i
$509$	−3.17376	−	9.76784i	−0.140675	−	0.432952i	0.855755	−	0.517381i	$-0.173093\pi$
$509$	−3.17376	−	9.76784i	−0.140675	−	0.432952i	−0.996429	+	0.0844297i	$0.973093\pi$
$510$		0			0
$511$	−14.7361	−	10.7064i	−0.651885	−	0.473622i
$512$	0.587785	−	0.809017i	0.0259767	−	0.0357538i
$513$	−13.6251	−	4.42705i	−0.601561	−	0.195459i
$514$	4.28115	+	13.1760i	0.188834	+	0.581170i
$515$		0			0
$516$	−15.3262			−0.674700
$517$	0.779543	−	0.0729490i	0.0342843	−	0.00320829i
$518$			19.7984i			0.869891i
$519$	17.4443	−	12.6740i	0.765719	−	0.556327i
$520$		0			0
$521$	−3.10081	+	9.54332i	−0.135849	+	0.418100i	−0.995721	−	0.0924091i	$-0.970543\pi$
$521$	−3.10081	+	9.54332i	−0.135849	+	0.418100i	0.859872	+	0.510510i	$0.170543\pi$
$522$	0.118513	−	0.163119i	0.00518717	−	0.00713952i
$523$	−16.1680	+	22.2533i	−0.706976	+	0.973068i	0.292881	+	0.956149i	$0.405386\pi$
$523$	−16.1680	+	22.2533i	−0.706976	+	0.973068i	−0.999857	+	0.0169196i	$0.994614\pi$
$524$	−3.44427	+	10.6004i	−0.150464	+	0.463080i
$525$		0			0
$526$	−13.0172	+	9.45756i	−0.567578	+	0.412369i
$527$			3.90983i			0.170315i
$528$	4.61653	+	2.73607i	0.200908	+	0.119072i
$529$	8.14590			0.354169
$530$		0			0
$531$	1.35410	+	4.16750i	0.0587630	+	0.180854i
$532$	−5.56758	−	1.80902i	−0.241385	−	0.0784308i
$533$	0.514540	−	0.708204i	0.0222872	−	0.0306757i
$534$	17.2533	+	12.5352i	0.746623	+	0.542453i
$535$		0			0
$536$	2.88197	+	8.86978i	0.124482	+	0.383116i
$537$	13.9353	+	19.1803i	0.601354	+	0.827693i
$538$		−	9.90983i		−	0.427243i
$539$	−4.38197	−	4.97980i	−0.188745	−	0.214495i
$540$		0			0
$541$	−26.0066	+	18.8949i	−1.11811	+	0.812355i	−0.983922	−	0.178601i	$-0.942843\pi$
$541$	−26.0066	+	18.8949i	−1.11811	+	0.812355i	−0.134189	+	0.990956i	$0.542843\pi$
$542$	−26.6093	+	8.64590i	−1.14297	+	0.371373i
$543$	−10.8576	−	3.52786i	−0.465946	−	0.151395i
$544$	−0.309017	−	0.224514i	−0.0132490	−	0.00962596i
$545$		0			0
$546$	0.263932	−	0.812299i	0.0112952	−	0.0347632i
$547$	−17.0660	+	5.54508i	−0.729690	+	0.237091i	−0.650219	−	0.759746i	$-0.725323\pi$
$547$	−17.0660	+	5.54508i	−0.729690	+	0.237091i	−0.0794708	+	0.996837i	$0.525323\pi$
$548$	9.26581	+	12.7533i	0.395816	+	0.544794i
$549$	0.854102			0.0364522
$550$		0			0
$551$	−1.38197			−0.0588737
$552$	3.66547	+	5.04508i	0.156013	+	0.214733i
$553$	25.4010	−	8.25329i	1.08016	−	0.350966i
$554$	−5.94427	+	18.2946i	−0.252548	+	0.777263i
$555$		0			0
$556$	2.30902	+	1.67760i	0.0979241	+	0.0711460i
$557$	−5.60034	−	1.81966i	−0.237294	−	0.0771015i	0.187956	−	0.982177i	$-0.439814\pi$
$557$	−5.60034	−	1.81966i	−0.237294	−	0.0771015i	−0.425250	+	0.905076i	$0.639814\pi$
$558$	3.71847	−	1.20820i	0.157415	−	0.0511474i
$559$	1.80902	−	1.31433i	0.0765133	−	0.0555901i
$560$		0			0
$561$	1.04508	−	1.76336i	0.0441235	−	0.0744489i
$562$		−	23.1246i		−	0.975453i
$563$	10.3556	+	14.2533i	0.436437	+	0.600705i	0.969416	−	0.245424i	$-0.0789273\pi$
$563$	10.3556	+	14.2533i	0.436437	+	0.600705i	−0.532978	+	0.846129i	$0.678927\pi$
$564$	−0.118034	−	0.363271i	−0.00497013	−	0.0152965i
$565$		0			0
$566$	−17.7984	−	12.9313i	−0.748121	−	0.543542i
$567$	10.1311	−	13.9443i	0.425466	−	0.585604i
$568$	−9.31881	−	3.02786i	−0.391008	−	0.127046i
$569$	0.645898	+	1.98787i	0.0270775	+	0.0833358i	0.963682	−	0.267052i	$-0.0860497\pi$
$569$	0.645898	+	1.98787i	0.0270775	+	0.0833358i	−0.936605	+	0.350388i	$0.886050\pi$
$570$		0			0
$571$	−8.52786			−0.356880			−0.178440	−	0.983951i	$-0.557105\pi$
$571$	−8.52786			−0.356880			−0.178440	+	0.983951i	$0.557105\pi$
$572$	−0.779543	+	0.0729490i	−0.0325943	+	0.00305015i
$573$		−	32.1246i		−	1.34202i
$574$	6.70820	−	4.87380i	0.279995	−	0.203428i
$575$		0			0
$576$	−0.118034	+	0.363271i	−0.00491808	+	0.0151363i
$577$	−12.7925	+	17.6074i	−0.532560	+	0.733005i	−0.987518	−	0.157507i	$-0.949654\pi$
$577$	−12.7925	+	17.6074i	−0.532560	+	0.733005i	0.454958	+	0.890513i	$0.349654\pi$
$578$	9.90659	−	13.6353i	0.412060	−	0.567152i
$579$	1.21885	−	3.75123i	0.0506536	−	0.155896i
$580$		0			0
$581$	−16.2812	+	11.8290i	−0.675456	+	0.490748i
$582$			19.4164i			0.804836i
$583$	−1.81636	−	4.20820i	−0.0752258	−	0.174286i
$584$	8.14590			0.337080
$585$		0			0
$586$	3.24671	+	9.99235i	0.134120	+	0.412780i
$587$	15.4212	+	5.01064i	0.636500	+	0.206811i	0.609452	−	0.792823i	$-0.291389\pi$
$587$	15.4212	+	5.01064i	0.636500	+	0.206811i	0.0270477	+	0.999634i	$0.491389\pi$
$588$	−1.90211	+	2.61803i	−0.0784418	+	0.107966i
$589$	−21.6803	−	15.7517i	−0.893323	−	0.649037i
$590$		0			0
$591$	13.7984	+	42.4670i	0.567589	+	1.74686i
$592$	−5.20431	−	7.16312i	−0.213896	−	0.294402i
$593$			42.3951i			1.74096i	0.492205	+	0.870479i	$0.336191\pi$
$593$			42.3951i			1.74096i	−0.492205	+	0.870479i	$0.663809\pi$
$594$	−17.7082	−	3.97574i	−0.726576	−	0.163127i
$595$		0			0
$596$	8.66312	−	6.29412i	0.354855	−	0.257817i
$597$	−1.98787	+	0.645898i	−0.0813581	+	0.0264348i
$598$	−0.865300	−	0.281153i	−0.0353847	−	0.0114972i
$599$	2.47214	+	1.79611i	0.101009	+	0.0733871i	0.637143	−	0.770745i	$-0.280116\pi$
$599$	2.47214	+	1.79611i	0.101009	+	0.0733871i	−0.536134	+	0.844133i	$0.680116\pi$
$600$		0			0
$601$	−2.02786	+	6.24112i	−0.0827183	+	0.254581i	−0.983859	−	0.178946i	$-0.942731\pi$
$601$	−2.02786	+	6.24112i	−0.0827183	+	0.254581i	0.901141	+	0.433527i	$0.142731\pi$
$602$	20.1437	−	6.54508i	0.820996	−	0.266758i
$603$	−2.09387	−	2.88197i	−0.0852690	−	0.117363i
$604$	19.0344			0.774500
$605$		0			0
$606$	−30.2705			−1.22966
$607$	−7.86572	−	10.8262i	−0.319260	−	0.439423i	0.618981	−	0.785406i	$-0.287546\pi$
$607$	−7.86572	−	10.8262i	−0.319260	−	0.439423i	−0.938241	+	0.345982i	$0.887546\pi$
$608$	2.48990	−	0.809017i	0.100979	−	0.0328100i
$609$	0.590170	−	1.81636i	0.0239149	−	0.0736025i
$610$		0			0
$611$	0.0450850	+	0.0327561i	0.00182394	+	0.00132517i
$612$	0.138757	+	0.0450850i	0.00560893	+	0.00182245i
$613$	−6.82891	+	2.21885i	−0.275817	+	0.0896184i	−0.443659	−	0.896195i	$-0.646320\pi$
$613$	−6.82891	+	2.21885i	−0.275817	+	0.0896184i	0.167842	+	0.985814i	$0.446320\pi$
$614$	−23.2984	+	16.9273i	−0.940246	+	0.683129i
$615$		0			0
$616$	−7.23607	−	1.62460i	−0.291549	−	0.0654569i
$617$			25.7984i			1.03860i	0.854591	+	0.519302i	$0.173808\pi$
$617$			25.7984i			1.03860i	−0.854591	+	0.519302i	$0.826192\pi$
$618$	16.0620	+	22.1074i	0.646107	+	0.889290i
$619$	8.10739	+	24.9520i	0.325864	+	1.00290i	0.971049	+	0.238879i	$0.0767800\pi$
$619$	8.10739	+	24.9520i	0.325864	+	1.00290i	−0.645186	+	0.764026i	$0.723220\pi$
$620$		0			0
$621$	−17.0623	−	12.3965i	−0.684687	−	0.497454i
$622$	2.48990	−	3.42705i	0.0998358	−	0.137412i
$623$	−28.0297	−	9.10739i	−1.12298	−	0.364880i
$624$	0.118034	+	0.363271i	0.00472514	+	0.0145425i
$625$		0			0
$626$	−1.00000			−0.0399680
$627$	5.56758	+	12.8992i	0.222348	+	0.515144i
$628$		−	6.76393i		−	0.269910i
$629$	−2.73607	+	1.98787i	−0.109094	+	0.0792616i
$630$		0			0
$631$	−2.07295	+	6.37988i	−0.0825228	+	0.253979i	−0.983802	−	0.179260i	$-0.942630\pi$
$631$	−2.07295	+	6.37988i	−0.0825228	+	0.253979i	0.901279	+	0.433239i	$0.142630\pi$
$632$	−7.02067	+	9.66312i	−0.279267	+	0.384378i
$633$	13.7966	−	18.9894i	0.548365	−	0.754759i
$634$	0.864745	−	2.66141i	0.0343434	−	0.105698i
$635$		0			0
$636$	−1.80902	+	1.31433i	−0.0717322	+	0.0521165i
$637$		−	0.472136i		−	0.0187067i
$638$	−1.74311	+	0.163119i	−0.0690104	+	0.00645794i
$639$	3.74265			0.148057
$640$		0			0
$641$	−13.0000	−	40.0099i	−0.513469	−	1.58030i	−0.786050	−	0.618163i	$-0.787877\pi$
$641$	−13.0000	−	40.0099i	−0.513469	−	1.58030i	0.272581	−	0.962133i	$-0.412123\pi$
$642$	−12.5882	−	4.09017i	−0.496819	−	0.161426i
$643$	8.30224	−	11.4271i	0.327408	−	0.450639i	−0.613303	−	0.789848i	$-0.710159\pi$
$643$	8.30224	−	11.4271i	0.327408	−	0.450639i	0.940711	+	0.339209i	$0.110159\pi$
$644$	−6.97214	−	5.06555i	−0.274741	−	0.199611i
$645$		0			0
$646$	−0.309017	−	0.951057i	−0.0121581	−	0.0374188i
$647$	0.620541	+	0.854102i	0.0243960	+	0.0335782i	0.821041	−	0.570870i	$-0.193394\pi$
$647$	0.620541	+	0.854102i	0.0243960	+	0.0335782i	−0.796645	+	0.604448i	$0.793394\pi$
$648$			7.70820i			0.302807i
$649$	19.3992	−	32.7319i	0.761485	−	1.28484i
$650$		0			0
$651$	29.9615	−	21.7683i	1.17428	−	0.853167i
$652$	−0.171513	+	0.0557281i	−0.00671698	+	0.00218248i
$653$	9.95959	+	3.23607i	0.389749	+	0.126637i	0.497335	−	0.867559i	$-0.334312\pi$
$653$	9.95959	+	3.23607i	0.389749	+	0.126637i	−0.107586	+	0.994196i	$0.534312\pi$
$654$	15.2082	+	11.0494i	0.594688	+	0.432066i
$655$		0			0
$656$	−1.14590	+	3.52671i	−0.0447398	+	0.137695i
$657$	−2.95917	+	0.961493i	−0.115448	+	0.0375114i
$658$	0.310271	+	0.427051i	0.0120956	+	0.0166482i
$659$	−43.4508			−1.69260			−0.846302	−	0.532703i	$-0.821176\pi$
$659$	−43.4508			−1.69260			−0.846302	+	0.532703i	$0.821176\pi$
$660$		0			0
$661$	27.5967			1.07339			0.536695	−	0.843777i	$-0.319673\pi$
$661$	27.5967			1.07339			0.536695	+	0.843777i	$0.319673\pi$
$662$	9.95959	+	13.7082i	0.387091	+	0.532784i
$663$	0.138757	−	0.0450850i	0.00538889	−	0.00175096i
$664$	2.78115	−	8.55951i	0.107930	−	0.332173i
$665$		0			0
$666$	2.73607	+	1.98787i	0.106020	+	0.0770284i
$667$	−1.93487	−	0.628677i	−0.0749184	−	0.0243425i
$668$	−2.12663	+	0.690983i	−0.0822817	+	0.0267349i
$669$	2.69098	−	1.95511i	0.104039	−	0.0755891i
$670$		0			0
$671$	−4.89919	−	5.56758i	−0.189131	−	0.214934i
$672$			3.61803i			0.139569i
$673$	−6.80866	−	9.37132i	−0.262455	−	0.361238i	0.657370	−	0.753568i	$-0.271669\pi$
$673$	−6.80866	−	9.37132i	−0.262455	−	0.361238i	−0.919824	+	0.392330i	$0.871669\pi$
$674$	−9.30902	−	28.6502i	−0.358570	−	1.10356i
$675$		0			0
$676$	10.4721	+	7.60845i	0.402774	+	0.292633i
$677$	6.36737	−	8.76393i	0.244718	−	0.336825i	−0.668935	−	0.743321i	$-0.733249\pi$
$677$	6.36737	−	8.76393i	0.244718	−	0.336825i	0.913653	+	0.406496i	$0.133249\pi$
$678$	−22.6336	−	7.35410i	−0.869238	−	0.282433i
$679$	−8.29180	−	25.5195i	−0.318210	−	0.979349i
$680$		0			0
$681$	31.9443			1.22411
$682$	−29.2052	−	17.3090i	−1.11833	−	0.662797i
$683$		−	6.11146i		−	0.233848i	−0.993141	−	0.116924i	$-0.962697\pi$
$683$		−	6.11146i		−	0.233848i	0.993141	−	0.116924i	$-0.0373035\pi$
$684$	−0.809017	+	0.587785i	−0.0309335	+	0.0224745i
$685$		0			0
$686$	6.21885	−	19.1396i	0.237437	−	0.730755i
$687$	14.7149	−	20.2533i	0.561408	−	0.772711i
$688$	−5.56758	+	7.66312i	−0.212262	+	0.292154i
$689$	0.100813	−	0.310271i	0.00384067	−	0.0118204i
$690$		0			0
$691$	32.2984	−	23.4661i	1.22869	−	0.892694i	0.231897	−	0.972740i	$-0.425507\pi$
$691$	32.2984	−	23.4661i	1.22869	−	0.892694i	0.996791	+	0.0800463i	$0.0255068\pi$
$692$		−	13.3262i		−	0.506588i
$693$	2.82041	−	0.263932i	0.107139	−	0.0100259i
$694$	−18.8541			−0.715692
$695$		0			0
$696$	0.263932	+	0.812299i	0.0100043	+	0.0307901i
$697$	1.34708	+	0.437694i	0.0510244	+	0.0165788i
$698$	13.8698	−	19.0902i	0.524980	−	0.722574i
$699$	26.6074	+	19.3314i	1.00638	+	0.731181i
$700$		0			0
$701$	−3.89919	−	12.0005i	−0.147270	−	0.453251i	0.850026	−	0.526741i	$-0.176586\pi$
$701$	−3.89919	−	12.0005i	−0.147270	−	0.453251i	−0.997296	+	0.0734900i	$0.976586\pi$
$702$	−0.759299	−	1.04508i	−0.0286579	−	0.0394442i
$703$		−	23.1803i		−	0.874263i
$704$	3.04508	−	1.31433i	0.114766	−	0.0495356i
$705$		0			0
$706$	3.59017	−	2.60841i	0.135118	−	0.0981688i
$707$	39.7854	−	12.9271i	1.49628	−	0.486172i
$708$	−17.6538	−	5.73607i	−0.663471	−	0.215575i
$709$	−37.3156	−	27.1114i	−1.40142	−	1.01819i	−0.994501	−	0.104723i	$-0.966604\pi$
$709$	−37.3156	−	27.1114i	−1.40142	−	1.01819i	−0.406915	−	0.913466i	$-0.633396\pi$
$710$		0			0
$711$	1.40983	−	4.33901i	0.0528728	−	0.162726i
$712$	12.5352	−	4.07295i	0.469778	−	0.152640i
$713$	−23.1886	−	31.9164i	−0.868421	−	1.19528i
$714$	1.38197			0.0517188
$715$		0			0
$716$	14.6525			0.547589
$717$	−16.6170	−	22.8713i	−0.620573	−	0.854145i
$718$	0.898056	−	0.291796i	0.0335152	−	0.0108897i
$719$	−6.16312	+	18.9681i	−0.229846	+	0.707392i	0.767918	+	0.640548i	$0.221293\pi$
$719$	−6.16312	+	18.9681i	−0.229846	+	0.707392i	−0.997763	+	0.0668436i	$0.978707\pi$
$720$		0			0
$721$	−30.5517	−	22.1971i	−1.13780	−	0.826663i
$722$	−11.5514	−	3.75329i	−0.429900	−	0.139683i
$723$	−27.6992	+	9.00000i	−1.03014	+	0.334714i
$724$	−5.70820	+	4.14725i	−0.212144	+	0.154131i
$725$		0			0
$726$	8.54508	+	15.6129i	0.317138	+	0.579450i
$727$		−	13.8197i		−	0.512543i	−0.966605	−	0.256271i	$-0.917506\pi$
$727$		−	13.8197i		−	0.512543i	0.966605	−	0.256271i	$-0.0824941\pi$
$728$	−0.310271	−	0.427051i	−0.0114994	−	0.0158276i
$729$	−9.11803	−	28.0624i	−0.337705	−	1.03935i
$730$		0			0
$731$	2.92705	+	2.12663i	0.108261	+	0.0786561i
$732$	−2.12663	+	2.92705i	−0.0786024	+	0.108187i
$733$	20.7642	+	6.74671i	0.766945	+	0.249195i	0.666257	−	0.745723i	$-0.267896\pi$
$733$	20.7642	+	6.74671i	0.766945	+	0.249195i	0.100688	+	0.994918i	$0.467896\pi$
$734$	−1.65248	−	5.08580i	−0.0609940	−	0.187720i
$735$		0			0
$736$	3.85410			0.142064
$737$	−6.77591	+	30.1803i	−0.249594	+	1.11171i
$738$		−	1.41641i		−	0.0521387i
$739$	7.85410	−	5.70634i	0.288918	−	0.209911i	−0.433880	−	0.900971i	$-0.642856\pi$
$739$	7.85410	−	5.70634i	0.288918	−	0.209911i	0.722798	+	0.691060i	$0.242856\pi$
$740$		0			0
$741$	−0.309017	+	0.951057i	−0.0113520	+	0.0349379i
$742$	1.81636	−	2.50000i	0.0666805	−	0.0917779i
$743$	−24.9973	+	34.4058i	−0.917060	+	1.26223i	0.0476373	+	0.998865i	$0.484831\pi$
$743$	−24.9973	+	34.4058i	−0.917060	+	1.26223i	−0.964698	+	0.263360i	$0.915169\pi$
$744$	−5.11803	+	15.7517i	−0.187636	+	0.577485i
$745$		0			0
$746$	−1.92705	+	1.40008i	−0.0705543	+	0.0512607i
$747$			3.43769i			0.125779i
$748$	−0.502029	−	1.16312i	−0.0183560	−	0.0425278i
$749$	18.2918			0.668368
$750$		0			0
$751$	8.31559	+	25.5928i	0.303440	+	0.933893i	0.980255	+	0.197740i	$0.0633600\pi$
$751$	8.31559	+	25.5928i	0.303440	+	0.933893i	−0.676814	+	0.736154i	$0.736640\pi$
$752$	−0.224514	−	0.0729490i	−0.00818718	−	0.00266018i
$753$	4.56352	−	6.28115i	0.166304	−	0.228898i
$754$	−0.100813	−	0.0732450i	−0.00367140	−	0.00266742i
$755$		0			0
$756$	−3.78115	−	11.6372i	−0.137519	−	0.423241i
$757$	8.94302	+	12.3090i	0.325040	+	0.447379i	0.939998	−	0.341181i	$-0.110827\pi$
$757$	8.94302	+	12.3090i	0.325040	+	0.447379i	−0.614958	+	0.788560i	$0.710827\pi$
$758$			5.90983i			0.214655i
$759$	1.92705	+	20.5927i	0.0699475	+	0.747469i
$760$		0			0
$761$	17.2254	−	12.5150i	0.624421	−	0.453669i	−0.230042	−	0.973181i	$-0.573886\pi$
$761$	17.2254	−	12.5150i	0.624421	−	0.453669i	0.854463	+	0.519512i	$0.173886\pi$
$762$	4.47777	−	1.45492i	0.162212	−	0.0527060i
$763$	−24.7072	−	8.02786i	−0.894462	−	0.290628i
$764$	−16.0623	−	11.6699i	−0.581114	−	0.422204i
$765$		0			0
$766$	−0.618034	+	1.90211i	−0.0223305	+	0.0687261i
$767$	2.57565	−	0.836881i	0.0930015	−	0.0302180i
$768$	−0.951057	−	1.30902i	−0.0343183	−	0.0472351i
$769$	42.2361			1.52307			0.761536	−	0.648123i	$-0.224446\pi$
$769$	42.2361			1.52307			0.761536	+	0.648123i	$0.224446\pi$
$770$		0			0
$771$	22.4164			0.807307
$772$	−1.43284	−	1.97214i	−0.0515691	−	0.0709787i
$773$	39.3893	−	12.7984i	1.41674	−	0.460326i	0.502173	−	0.864767i	$-0.332534\pi$
$773$	39.3893	−	12.7984i	1.41674	−	0.460326i	0.914564	+	0.404442i	$0.132534\pi$
$774$	1.11803	−	3.44095i	0.0401869	−	0.123683i
$775$		0			0
$776$	9.70820	+	7.05342i	0.348504	+	0.253203i
$777$	30.4666	+	9.89919i	1.09298	+	0.355131i
$778$	1.67760	−	0.545085i	0.0601448	−	0.0195422i
$779$	−7.85410	+	5.70634i	−0.281402	+	0.204451i
$780$		0			0
$781$	−21.4681	−	24.3970i	−0.768188	−	0.872992i
$782$		−	1.47214i		−	0.0526435i
$783$	−1.69784	−	2.33688i	−0.0606760	−	0.0835133i
$784$	0.618034	+	1.90211i	0.0220726	+	0.0679326i
$785$		0			0
$786$	14.5902	+	10.6004i	0.520414	+	0.378103i
$787$	10.5801	−	14.5623i	0.377141	−	0.519090i	−0.577683	−	0.816261i	$-0.696043\pi$
$787$	10.5801	−	14.5623i	0.377141	−	0.519090i	0.954824	+	0.297171i	$0.0960431\pi$
$788$	26.2461	+	8.52786i	0.934977	+	0.303793i
$789$	8.04508	+	24.7602i	0.286413	+	0.881487i
$790$		0			0
$791$	32.8885			1.16938
$792$	−0.951057	+	0.836881i	−0.0337943	+	0.0297373i
$793$		−	0.527864i		−	0.0187450i
$794$	−14.1353	+	10.2699i	−0.501641	+	0.364464i
$795$		0			0
$796$	−0.399187	+	1.22857i	−0.0141488	+	0.0435455i
$797$	29.3970	−	40.4615i	1.04129	−	1.43322i	0.145176	−	0.989406i	$-0.453625\pi$
$797$	29.3970	−	40.4615i	1.04129	−	1.43322i	0.896119	−	0.443814i	$-0.146375\pi$
$798$	−5.56758	+	7.66312i	−0.197090	+	0.271271i
$799$	−0.0278640	+	0.0857567i	−0.000985759	+	0.00303385i
$800$		0			0
$801$	−4.07295	+	2.95917i	−0.143911	+	0.104557i
$802$		−	1.90983i		−	0.0674384i
$803$	23.2416	+	13.7746i	0.820179	+	0.486094i
$804$	15.0902			0.532189
$805$		0			0
$806$	−0.746711	−	2.29814i	−0.0263018	−	0.0809485i
$807$	−15.2497	−	4.95492i	−0.536813	−	0.174421i
$808$	−10.9964	+	15.1353i	−0.386852	+	0.532456i
$809$	26.7533	+	19.4374i	0.940596	+	0.683383i	0.948564	−	0.316586i	$-0.102536\pi$
$809$	26.7533	+	19.4374i	0.940596	+	0.683383i	−0.00796840	+	0.999968i	$0.502536\pi$
$810$		0			0
$811$	4.21885	+	12.9843i	0.148144	+	0.455940i	0.997402	−	0.0720383i	$-0.0229504\pi$
$811$	4.21885	+	12.9843i	0.148144	+	0.455940i	−0.849258	+	0.527978i	$0.822950\pi$
$812$	−0.693786	−	0.954915i	−0.0243471	−	0.0335109i
$813$			45.2705i			1.58771i
$814$	−2.73607	−	29.2380i	−0.0958991	−	1.02479i
$815$		0			0
$816$	−0.500000	+	0.363271i	−0.0175035	+	0.0127170i
$817$	−23.5847	+	7.66312i	−0.825123	+	0.268099i
$818$	−17.6008	−	5.71885i	−0.615398	−	0.199955i
$819$	0.163119	+	0.118513i	0.00569984	+	0.00414117i
$820$		0			0
$821$	−12.1631	+	37.4342i	−0.424496	+	1.30646i	0.478980	+	0.877826i	$0.341006\pi$
$821$	−12.1631	+	37.4342i	−0.424496	+	1.30646i	−0.903476	+	0.428638i	$0.858994\pi$
$822$	24.2582	−	7.88197i	0.846102	−	0.274915i
$823$	1.30182	+	1.79180i	0.0453785	+	0.0624581i	0.831103	−	0.556118i	$-0.187710\pi$
$823$	1.30182	+	1.79180i	0.0453785	+	0.0624581i	−0.785725	+	0.618576i	$0.787710\pi$
$824$	16.8885			0.588340
$825$		0			0
$826$	25.6525			0.892564
$827$	−13.3475	−	18.3713i	−0.464140	−	0.638833i	0.511221	−	0.859449i	$-0.329193\pi$
$827$	−13.3475	−	18.3713i	−0.464140	−	0.638833i	−0.975361	+	0.220616i	$0.929193\pi$
$828$	−1.40008	+	0.454915i	−0.0486563	+	0.0158094i
$829$	−11.4377	+	35.2016i	−0.397248	+	1.22260i	0.529950	+	0.848029i	$0.322211\pi$
$829$	−11.4377	+	35.2016i	−0.397248	+	1.22260i	−0.927197	+	0.374573i	$0.877789\pi$
$830$		0			0
$831$	25.1803	+	18.2946i	0.873496	+	0.634632i
$832$	0.224514	+	0.0729490i	0.00778362	+	0.00252905i
$833$	0.726543	−	0.236068i	0.0251732	−	0.00817927i
$834$	3.73607	−	2.71441i	0.129369	−	0.0939924i
$835$		0			0
$836$	8.47214	+	1.90211i	0.293015	+	0.0657860i
$837$		−	56.0132i		−	1.93610i
$838$	−18.3273	−	25.2254i	−0.633108	−	0.871398i
$839$	9.03851	+	27.8177i	0.312044	+	0.960372i	0.976954	+	0.213449i	$0.0684698\pi$
$839$	9.03851	+	27.8177i	0.312044	+	0.960372i	−0.664910	+	0.746923i	$0.731530\pi$
$840$		0			0
$841$	23.2361	+	16.8820i	0.801244	+	0.582138i
$842$	−10.3884	+	14.2984i	−0.358007	+	0.492755i
$843$	−35.5851	−	11.5623i	−1.22562	−	0.398227i
$844$	−4.48278	−	13.7966i	−0.154304	−	0.474898i
$845$		0			0
$846$	0.0901699			0.00310011
$847$	−17.8986	−	16.8713i	−0.615002	−	0.579706i
$848$			1.38197i			0.0474569i
$849$	−28.7984	+	20.9232i	−0.988358	+	0.718084i
$850$		0			0
$851$	10.5451	−	32.4544i	0.361481	−	1.11252i
$852$	−9.31881	+	12.8262i	−0.319257	+	0.439420i
$853$	1.96763	−	2.70820i	0.0673702	−	0.0927271i	−0.774002	−	0.633183i	$-0.781748\pi$
$853$	1.96763	−	2.70820i	0.0673702	−	0.0927271i	0.841372	+	0.540456i	$0.181748\pi$
$854$	1.54508	−	4.75528i	0.0528717	−	0.162722i
$855$		0			0
$856$	−6.61803	+	4.80828i	−0.226200	+	0.164344i
$857$			25.2705i			0.863224i	0.902059	+	0.431612i	$0.142055\pi$
$857$			25.2705i			0.863224i	−0.902059	+	0.431612i	$0.857945\pi$
$858$	−0.277515	+	1.23607i	−0.00947419	+	0.0421987i
$859$	1.18034			0.0402727			0.0201363	−	0.999797i	$-0.493590\pi$
$859$	1.18034			0.0402727			0.0201363	+	0.999797i	$0.493590\pi$
$860$		0			0
$861$	−4.14590	−	12.7598i	−0.141292	−	0.434852i
$862$	5.65334	+	1.83688i	0.192553	+	0.0625644i
$863$	−0.653298	+	0.899187i	−0.0222385	+	0.0306087i	−0.819991	−	0.572376i	$-0.806022\pi$
$863$	−0.653298	+	0.899187i	−0.0222385	+	0.0306087i	0.797753	+	0.602984i	$0.206022\pi$
$864$	4.42705	+	3.21644i	0.150611	+	0.109426i
$865$		0			0
$866$	−2.61803	−	8.05748i	−0.0889644	−	0.273804i
$867$	−16.0292	−	22.0623i	−0.544380	−	0.749275i
$868$		−	22.8885i		−	0.776888i
$869$	−36.3713	+	15.6987i	−1.23381	+	0.532542i
$870$		0			0
$871$	−1.78115	+	1.29408i	−0.0603521	+	0.0438483i
$872$	11.0494	−	3.59017i	0.374180	−	0.121578i
$873$	−4.35926	−	1.41641i	−0.147538	−	0.0479381i
$874$	8.16312	+	5.93085i	0.276122	+	0.200614i
$875$		0			0
$876$	4.07295	−	12.5352i	0.137612	−	0.423527i
$877$	−35.9281	+	11.6738i	−1.21321	+	0.394195i	−0.844604	−	0.535392i	$-0.820164\pi$
$877$	−35.9281	+	11.6738i	−1.21321	+	0.394195i	−0.368603	+	0.929587i	$0.620164\pi$
$878$	13.3475	+	18.3713i	0.450458	+	0.620002i
$879$	17.0000			0.573396
$880$		0			0
$881$	7.67376			0.258536			0.129268	−	0.991610i	$-0.458737\pi$
$881$	7.67376			0.258536			0.129268	+	0.991610i	$0.458737\pi$
$882$	−0.449028	−	0.618034i	−0.0151196	−	0.0208103i
$883$	37.0382	−	12.0344i	1.24643	−	0.404991i	0.389793	−	0.920903i	$-0.372547\pi$
$883$	37.0382	−	12.0344i	1.24643	−	0.404991i	0.856642	+	0.515911i	$0.172547\pi$
$884$	0.0278640	−	0.0857567i	0.000937169	−	0.00288431i
$885$		0			0
$886$	24.6803	+	17.9313i	0.829152	+	0.602414i
$887$	−38.2995	−	12.4443i	−1.28597	−	0.417838i	−0.415293	−	0.909688i	$-0.636321\pi$
$887$	−38.2995	−	12.4443i	−1.28597	−	0.417838i	−0.870680	+	0.491850i	$0.836321\pi$
$888$	−13.6251	+	4.42705i	−0.457227	+	0.148562i
$889$	−5.26393	+	3.82447i	−0.176547	+	0.128269i
$890$		0			0
$891$	−13.0344	+	21.9928i	−0.436670	+	0.736787i
$892$		−	2.05573i		−	0.0688309i
$893$	−0.363271	−	0.500000i	−0.0121564	−	0.0167319i
$894$	−5.35410	−	16.4782i	−0.179068	−	0.551115i
$895$		0			0
$896$	1.80902	+	1.31433i	0.0604350	+	0.0439086i
$897$	−0.865300	+	1.19098i	−0.0288915	+	0.0397658i
$898$	−15.4944	−	5.03444i	−0.517055	−	0.168002i
$899$	−1.66970	−	5.13880i	−0.0556875	−	0.171389i
$900$		0			0
$901$	0.527864			0.0175857
$902$	−9.23305	+	8.12461i	−0.307427	+	0.270520i
$903$		−	34.2705i		−	1.14045i
$904$	−11.8992	+	8.64527i	−0.395761	+	0.287537i
$905$		0			0
$906$	9.51722	−	29.2910i	0.316188	−	0.973128i
$907$	23.2744	−	32.0344i	0.772813	−	1.06369i	−0.223226	−	0.974767i	$-0.571659\pi$
$907$	23.2744	−	32.0344i	0.772813	−	1.06369i	0.996039	−	0.0889194i	$-0.0283413\pi$
$908$	11.6044	−	15.9721i	0.385107	−	0.530054i
$909$	2.20820	−	6.79615i	0.0732415	−	0.225414i
$910$		0			0
$911$	10.2361	−	7.43694i	0.339136	−	0.246397i	−0.405161	−	0.914245i	$-0.632785\pi$
$911$	10.2361	−	7.43694i	0.339136	−	0.246397i	0.744297	+	0.667849i	$0.232785\pi$
$912$		−	4.23607i		−	0.140270i
$913$	22.4091	−	19.7188i	0.741632	−	0.652599i
$914$	12.1246			0.401047
$915$		0			0
$916$	−4.78115	−	14.7149i	−0.157974	−	0.486193i
$917$	−23.7032	−	7.70163i	−0.782748	−	0.254330i
$918$	1.22857	−	1.69098i	0.0405489	−	0.0558108i
$919$	−17.2082	−	12.5025i	−0.567646	−	0.412419i	0.266603	−	0.963806i	$-0.414099\pi$
$919$	−17.2082	−	12.5025i	−0.567646	−	0.412419i	−0.834249	+	0.551387i	$0.814099\pi$
$920$		0			0
$921$	14.3992	+	44.3161i	0.474469	+	1.46027i
$922$	21.4050	+	29.4615i	0.704937	+	0.970263i
$923$		−	2.31308i		−	0.0761360i
$924$	−6.11803	+	10.3229i	−0.201269	+	0.339597i
$925$		0			0
$926$	31.2254	−	22.6866i	1.02613	−	0.745528i
$927$	−6.13512	+	1.99342i	−0.201504	+	0.0654726i
$928$	0.502029	+	0.163119i	0.0164799	+	0.00535464i
$929$	−18.9443	−	13.7638i	−0.621541	−	0.451576i	0.231918	−	0.972735i	$-0.425500\pi$
$929$	−18.9443	−	13.7638i	−0.621541	−	0.451576i	−0.853460	+	0.521159i	$0.825500\pi$
$930$		0			0
$931$	−1.61803	+	4.97980i	−0.0530289	+	0.163206i
$932$	19.3314	−	6.28115i	0.633221	−	0.205746i
$933$	−4.02874	−	5.54508i	−0.131895	−	0.181538i
$934$	32.1803			1.05297
$935$		0			0
$936$	−0.0901699			−0.00294730
$937$	−13.9026	−	19.1353i	−0.454177	−	0.625122i	0.519111	−	0.854707i	$-0.326263\pi$
$937$	−13.9026	−	19.1353i	−0.454177	−	0.625122i	−0.973289	+	0.229585i	$0.926263\pi$
$938$	−19.8334	+	6.44427i	−0.647584	+	0.210413i
$939$	−0.500000	+	1.53884i	−0.0163169	+	0.0502182i
$940$		0			0
$941$	−20.5172	−	14.9066i	−0.668842	−	0.485942i	0.200795	−	0.979633i	$-0.435647\pi$
$941$	−20.5172	−	14.9066i	−0.668842	−	0.485942i	−0.869637	+	0.493691i	$0.835647\pi$
$942$	−10.4086	−	3.38197i	−0.339131	−	0.110190i
$943$	−13.5923	+	4.41641i	−0.442626	+	0.143818i
$944$	−9.28115	+	6.74315i	−0.302076	+	0.219471i
$945$		0			0
$946$	−28.8435	+	12.4495i	−0.937782	+	0.404768i
$947$			18.0000i			0.584921i	0.956278	+	0.292461i	$0.0944741\pi$
$947$			18.0000i			0.584921i	−0.956278	+	0.292461i	$0.905526\pi$
$948$	11.3597	+	15.6353i	0.368945	+	0.507809i
$949$	0.594235	+	1.82887i	0.0192897	+	0.0593676i
$950$		0			0
$951$	−3.66312	−	2.66141i	−0.118785	−	0.0863022i
$952$	0.502029	−	0.690983i	0.0162708	−	0.0223949i
$953$	39.1118	+	12.7082i	1.26696	+	0.411659i	0.863968	−	0.503546i	$-0.167972\pi$
$953$	39.1118	+	12.7082i	1.26696	+	0.411659i	0.402988	+	0.915205i	$0.367972\pi$
$954$	−0.163119	−	0.502029i	−0.00528117	−	0.0162538i
$955$		0			0
$956$	−17.4721			−0.565089
$957$	−0.620541	+	2.76393i	−0.0200593	+	0.0893452i
$958$		−	9.94427i		−	0.321285i
$959$	−28.5172	+	20.7190i	−0.920869	+	0.669051i
$960$		0			0
$961$	22.7984	−	70.1662i	0.735431	−	2.26343i
$962$	1.22857	−	1.69098i	0.0396107	−	0.0545195i
$963$	1.83660	−	2.52786i	0.0591836	−	0.0814593i
$964$	−5.56231	+	17.1190i	−0.179150	+	0.551366i
$965$		0			0
$966$	−11.2812	+	8.19624i	−0.362965	+	0.263710i
$967$			20.0557i			0.644949i	0.946578	+	0.322474i	$0.104515\pi$
$967$			20.0557i			0.644949i	−0.946578	+	0.322474i	$0.895485\pi$
$968$	10.9106	+	1.39919i	0.350682	+	0.0449716i
$969$	−1.61803			−0.0519787
$970$		0			0
$971$	15.6140	+	48.0549i	0.501076	+	1.54215i	0.807269	+	0.590184i	$0.200945\pi$
$971$	15.6140	+	48.0549i	0.501076	+	1.54215i	−0.306193	+	0.951970i	$0.599055\pi$
$972$	−3.75123	−	1.21885i	−0.120321	−	0.0390945i
$973$	−3.75123	+	5.16312i	−0.120259	+	0.165522i
$974$	−8.80902	−	6.40013i	−0.282259	−	0.205073i
$975$		0			0
$976$	0.690983	+	2.12663i	0.0221178	+	0.0680717i
$977$	4.99231	+	6.87132i	0.159718	+	0.219833i	0.881374	−	0.472418i	$-0.156619\pi$
$977$	4.99231	+	6.87132i	0.159718	+	0.219833i	−0.721656	+	0.692252i	$0.756619\pi$
$978$			0.291796i			0.00933061i
$979$	42.6525	+	9.57608i	1.36318	+	0.306053i
$980$		0			0
$981$	−3.59017	+	2.60841i	−0.114625	+	0.0832802i
$982$	−11.5842	+	3.76393i	−0.369666	+	0.120112i
$983$	−26.2461	−	8.52786i	−0.837120	−	0.271997i	−0.141078	−	0.989998i	$-0.545057\pi$
$983$	−26.2461	−	8.52786i	−0.837120	−	0.271997i	−0.696041	+	0.718002i	$0.745057\pi$
$984$	4.85410	+	3.52671i	0.154743	+	0.112427i
$985$		0			0
$986$	0.0623059	−	0.191758i	0.00198422	−	0.00610681i
$987$	0.812299	−	0.263932i	0.0258558	−	0.00840105i
$988$	0.363271	+	0.500000i	0.0115572	+	0.0159071i
$989$	−36.5066			−1.16084
$990$		0			0
$991$	−2.11146			−0.0670726			−0.0335363	−	0.999437i	$-0.510677\pi$
$991$	−2.11146			−0.0670726			−0.0335363	+	0.999437i	$0.510677\pi$
$992$	6.01661	+	8.28115i	0.191028	+	0.262927i
$993$	26.0746	−	8.47214i	0.827451	−	0.268855i
$994$	6.77051	−	20.8375i	0.214748	−	0.660925i
$995$		0			0
$996$	−11.7812	−	8.55951i	−0.373300	−	0.271218i
$997$	−27.4949	−	8.93363i	−0.870772	−	0.282931i	−0.160651	−	0.987011i	$-0.551359\pi$
$997$	−27.4949	−	8.93363i	−0.870772	−	0.282931i	−0.710120	+	0.704080i	$0.751359\pi$
$998$	14.6946	−	4.77458i	0.465150	−	0.151137i
$999$	39.1976	−	28.4787i	1.24016	−	0.901026i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	550.2.ba.e.399.1		8
5.2	odd	4		550.2.h.g.201.1	yes	4
5.3	odd	4		550.2.h.c.201.1	✓	4
5.4	even	2	inner	550.2.ba.e.399.2		8
11.4	even	5	inner	550.2.ba.e.499.2		8
55.2	even	20		6050.2.a.cr.1.2		2
55.4	even	10	inner	550.2.ba.e.499.1		8
55.13	even	20		6050.2.a.bx.1.1		2
55.37	odd	20		550.2.h.g.301.1	yes	4
55.42	odd	20		6050.2.a.ca.1.2		2
55.48	odd	20		550.2.h.c.301.1	yes	4
55.53	odd	20		6050.2.a.co.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
550.2.h.c.201.1	✓	4	5.3	odd	4
550.2.h.c.301.1	yes	4	55.48	odd	20
550.2.h.g.201.1	yes	4	5.2	odd	4
550.2.h.g.301.1	yes	4	55.37	odd	20
550.2.ba.e.399.1		8	1.1	even	1	trivial
550.2.ba.e.399.2		8	5.4	even	2	inner
550.2.ba.e.499.1		8	55.4	even	10	inner
550.2.ba.e.499.2		8	11.4	even	5	inner
6050.2.a.bx.1.1		2	55.13	even	20
6050.2.a.ca.1.2		2	55.42	odd	20
6050.2.a.co.1.1		2	55.53	odd	20
6050.2.a.cr.1.2		2	55.2	even	20

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.ba (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 0.809017i) q^{2} +(-1.53884 + 0.500000i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(1.30902 + 0.951057i) q^{6} +(-2.12663 - 0.690983i) q^{7} +(0.951057 - 0.309017i) q^{8} +(-0.309017 + 0.224514i) q^{9} +(3.23607 + 0.726543i) q^{11} -1.61803i q^{12} +(0.138757 + 0.190983i) q^{13} +(0.690983 + 2.12663i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-0.224514 + 0.309017i) q^{17} +(0.363271 + 0.118034i) q^{18} +(-0.809017 - 2.48990i) q^{19} +3.61803 q^{21} +(-1.31433 - 3.04508i) q^{22} -3.85410i q^{23} +(-1.30902 + 0.951057i) q^{24} +(0.0729490 - 0.224514i) q^{26} +(3.21644 - 4.42705i) q^{27} +(1.31433 - 1.80902i) q^{28} +(0.163119 - 0.502029i) q^{29} +(8.28115 - 6.01661i) q^{31} +1.00000i q^{32} +(-5.34307 + 0.500000i) q^{33} +0.381966 q^{34} +(-0.118034 - 0.363271i) q^{36} +(8.42075 + 2.73607i) q^{37} +(-1.53884 + 2.11803i) q^{38} +(-0.309017 - 0.224514i) q^{39} +(-1.14590 - 3.52671i) q^{41} +(-2.12663 - 2.92705i) q^{42} -9.47214i q^{43} +(-1.69098 + 2.85317i) q^{44} +(-3.11803 + 2.26538i) q^{46} +(0.224514 - 0.0729490i) q^{47} +(1.53884 + 0.500000i) q^{48} +(-1.61803 - 1.17557i) q^{49} +(0.190983 - 0.587785i) q^{51} +(-0.224514 + 0.0729490i) q^{52} +(-0.812299 - 1.11803i) q^{53} -5.47214 q^{54} -2.23607 q^{56} +(2.48990 + 3.42705i) q^{57} +(-0.502029 + 0.163119i) q^{58} +(3.54508 - 10.9106i) q^{59} +(-1.80902 - 1.31433i) q^{61} +(-9.73508 - 3.16312i) q^{62} +(0.812299 - 0.263932i) q^{63} +(0.809017 - 0.587785i) q^{64} +(3.54508 + 4.02874i) q^{66} +9.32624i q^{67} +(-0.224514 - 0.309017i) q^{68} +(1.92705 + 5.93085i) q^{69} +(-7.92705 - 5.75934i) q^{71} +(-0.224514 + 0.309017i) q^{72} +(7.74721 + 2.51722i) q^{73} +(-2.73607 - 8.42075i) q^{74} +2.61803 q^{76} +(-6.37988 - 3.78115i) q^{77} +0.381966i q^{78} +(-9.66312 + 7.02067i) q^{79} +(-2.38197 + 7.33094i) q^{81} +(-2.17963 + 3.00000i) q^{82} +(5.29007 - 7.28115i) q^{83} +(-1.11803 + 3.44095i) q^{84} +(-7.66312 + 5.56758i) q^{86} +0.854102i q^{87} +(3.30220 - 0.309017i) q^{88} +13.1803 q^{89} +(-0.163119 - 0.502029i) q^{91} +(3.66547 + 1.19098i) q^{92} +(-9.73508 + 13.3992i) q^{93} +(-0.190983 - 0.138757i) q^{94} +(-0.500000 - 1.53884i) q^{96} +(7.05342 + 9.70820i) q^{97} +2.00000i q^{98} +(-1.16312 + 0.502029i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} + 6 q^{6} + 2 q^{9} + 8 q^{11} + 10 q^{14} - 2 q^{16} - 2 q^{19} + 20 q^{21} - 6 q^{24} + 14 q^{26} - 30 q^{29} + 26 q^{31} + 12 q^{34} + 8 q^{36} + 2 q^{39} - 36 q^{41} - 18 q^{44} - 16 q^{46}+ \cdots + 22 q^{99}+O(q^{100}) \) 8 * q + 2 * q^4 + 6 * q^6 + 2 * q^9 + 8 * q^11 + 10 * q^14 - 2 * q^16 - 2 * q^19 + 20 * q^21 - 6 * q^24 + 14 * q^26 - 30 * q^29 + 26 * q^31 + 12 * q^34 + 8 * q^36 + 2 * q^39 - 36 * q^41 - 18 * q^44 - 16 * q^46 - 4 * q^49 + 6 * q^51 - 8 * q^54 + 6 * q^59 - 10 * q^61 + 2 * q^64 + 6 * q^66 + 2 * q^69 - 50 * q^71 - 4 * q^74 + 12 * q^76 - 46 * q^79 - 28 * q^81 - 30 * q^86 + 16 * q^89 + 30 * q^91 - 6 * q^94 - 4 * q^96 + 22 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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