LMFDB - Embedded newform 550.2.ba.e.499.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [550,2,Mod(49,550)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			499.1
Root			$-0.587785 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	550.499
Dual form			550.2.ba.e.399.1

$q$-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 $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$.

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

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	−0.170989	−	0.985273i	$-0.554696\pi$
$3$	−1.53884	−	0.500000i	−0.888451	−	0.288675i	−0.717462	+	0.696598i	$0.754696\pi$
$4$	−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	−0.681965	−	0.731385i	$-0.738874\pi$
$7$	−2.12663	+	0.690983i	−0.803789	+	0.261167i	−0.121824	+	0.992552i	$0.538874\pi$
$8$	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	−0.789341	−	0.613955i	$-0.789578\pi$
$13$	0.138757	−	0.190983i	0.0384843	−	0.0529692i	0.827826	+	0.560986i	$0.189578\pi$
$14$	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	0.780922	−	0.624628i	$-0.214749\pi$
$17$	−0.224514	−	0.309017i	−0.0544526	−	0.0749476i	−0.835375	+	0.549681i	$0.814749\pi$
$18$	0.363271	−	0.118034i	0.0856239	−	0.0278209i
$19$	−0.809017	+	2.48990i	−0.185601	+	0.571222i	−0.999958	−	0.00914245i	$-0.997090\pi$
$19$	−0.809017	+	2.48990i	−0.185601	+	0.571222i	0.814357	+	0.580364i	$0.197090\pi$
$20$		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	$0.131622\pi$
$23$			3.85410i			0.803636i	−0.915720	+	0.401818i	$0.868378\pi$
$24$	−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	0.965059	−	0.262033i	$-0.0843931\pi$
$29$	0.163119	+	0.502029i	0.0302904	+	0.0932244i	−0.934768	+	0.355258i	$0.884393\pi$
$30$		0			0
$31$	8.28115	+	6.01661i	1.48734	+	1.08062i	0.975098	+	0.221773i	$0.0711844\pi$
$31$	8.28115	+	6.01661i	1.48734	+	1.08062i	0.512241	+	0.858842i	$0.328816\pi$
$32$		−	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	0.480262	−	0.877125i	$-0.340542\pi$
$37$	8.42075	−	2.73607i	1.38436	−	0.449807i	0.904101	+	0.427318i	$0.140542\pi$
$38$	−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	−0.999792	−	0.0203886i	$-0.993510\pi$
$41$	−1.14590	+	3.52671i	−0.178959	+	0.550780i	0.820833	+	0.571168i	$0.193510\pi$
$42$	−2.12663	+	2.92705i	−0.328146	+	0.451654i
$43$			9.47214i			1.44449i	0.691639	+	0.722244i	$0.256889\pi$
$43$			9.47214i			1.44449i	−0.691639	+	0.722244i	$0.743111\pi$
$44$	−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	0.325346	−	0.945595i	$-0.394519\pi$
$47$	0.224514	+	0.0729490i	0.0327487	+	0.0106407i	−0.292597	+	0.956236i	$0.594519\pi$
$48$	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	−0.861154	−	0.508345i	$-0.830258\pi$
$53$	−0.812299	+	1.11803i	−0.111578	+	0.153574i	0.749576	+	0.661919i	$0.230258\pi$
$54$	−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	0.863294	+	0.504702i	$0.168398\pi$
$59$	3.54508	+	10.9106i	0.461531	+	1.42045i	−0.401763	+	0.915744i	$0.631602\pi$
$60$		0			0
$61$	−1.80902	+	1.31433i	−0.231621	+	0.168282i	−0.697542	−	0.716544i	$-0.745723\pi$
$61$	−1.80902	+	1.31433i	−0.231621	+	0.168282i	0.465921	+	0.884826i	$0.345723\pi$
$62$	−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	$-0.807063\pi$
$67$		−	9.32624i		−	1.13938i	0.821859	−	0.569691i	$-0.192937\pi$
$68$	−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	−0.948605	−	0.316461i	$-0.897505\pi$
$71$	−7.92705	+	5.75934i	−0.940768	+	0.683508i	0.00783751	+	0.999969i	$0.497505\pi$
$72$	−0.224514	−	0.309017i	−0.0264592	−	0.0364180i
$73$	7.74721	−	2.51722i	0.906742	−	0.294618i	0.181725	−	0.983349i	$-0.441832\pi$
$73$	7.74721	−	2.51722i	0.906742	−	0.294618i	0.725017	+	0.688731i	$0.241832\pi$
$74$	−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	−0.108264	−	0.994122i	$-0.534529\pi$
$79$	−9.66312	−	7.02067i	−1.08719	−	0.789887i	−0.978922	+	0.204235i	$0.934529\pi$
$80$		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	0.993768	−	0.111472i	$-0.0355565\pi$
$83$	5.29007	+	7.28115i	0.580660	+	0.799210i	−0.413107	+	0.910682i	$0.635557\pi$
$84$	−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	−0.283476	−	0.958979i	$-0.591488\pi$
$97$	7.05342	−	9.70820i	0.716167	−	0.985719i	0.999642	−	0.0267394i	$-0.00851242\pi$
$98$		−	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	−0.967908	−	0.251307i	$-0.919140\pi$
$101$	−15.1353	−	10.9964i	−1.50601	−	1.09418i	−0.538107	−	0.842877i	$-0.680860\pi$
$102$	−0.587785	−	0.190983i	−0.0581994	−	0.0189101i
$103$	16.0620	−	5.21885i	1.58263	−	0.514228i	0.619899	−	0.784682i	$-0.287174\pi$
$103$	16.0620	−	5.21885i	1.58263	−	0.514228i	0.962733	+	0.270453i	$0.0871736\pi$
$104$	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	−0.0922255	−	0.995738i	$-0.529398\pi$
$107$	−7.77997	−	2.52786i	−0.752118	−	0.244378i	−0.659892	+	0.751360i	$0.729398\pi$
$108$	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	−0.434823	−	0.900516i	$-0.643189\pi$
$113$	−13.9883	−	4.54508i	−1.31591	−	0.427566i	−0.881089	+	0.472950i	$0.843189\pi$
$114$	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	0.878131	−	0.478420i	$-0.158790\pi$
$127$	1.71036	+	2.35410i	0.151769	+	0.208893i	−0.726362	+	0.687313i	$0.758790\pi$
$128$	−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	0.993903	+	0.110258i	$0.0351676\pi$
$137$	9.26581	+	12.7533i	0.791631	+	1.08959i	−0.202272	+	0.979329i	$0.564832\pi$
$138$	3.66547	+	5.04508i	0.312025	+	0.429466i
$139$	0.881966	+	2.71441i	0.0748074	+	0.230233i	0.981468	−	0.191628i	$-0.0613768\pi$
$139$	0.881966	+	2.71441i	0.0748074	+	0.230233i	−0.906660	+	0.421862i	$0.861377\pi$
$140$		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	−0.883080	−	0.469222i	$-0.844534\pi$
$149$	−8.66312	+	6.29412i	−0.709710	+	0.515635i	0.173370	+	0.984857i	$0.444534\pi$
$150$		0			0
$151$	−5.88197	+	18.1028i	−0.478668	+	1.47319i	0.362279	+	0.932070i	$0.381999\pi$
$151$	−5.88197	+	18.1028i	−0.478668	+	1.47319i	−0.840947	+	0.541118i	$0.818001\pi$
$152$	−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	0.0408481	−	0.999165i	$-0.486994\pi$
$157$	−6.43288	−	2.09017i	−0.513400	−	0.166814i	−0.554248	+	0.832352i	$0.686994\pi$
$158$	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	−0.804845	−	0.593484i	$-0.797752\pi$
$163$	0.106001	−	0.145898i	0.00830265	−	0.0114276i	0.813148	+	0.582057i	$0.197752\pi$
$164$	3.70820			0.289562
$165$		0			0
$166$	−9.00000			−0.698535
$167$	1.31433	−	1.80902i	0.101706	−	0.139986i	−0.755131	−	0.655574i	$-0.772427\pi$
$167$	1.31433	−	1.80902i	0.101706	−	0.139986i	0.856836	+	0.515588i	$0.172427\pi$
$168$	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	−0.215362	−	0.976534i	$-0.569093\pi$
$173$	−12.6740	−	4.11803i	−0.963587	−	0.313088i	−0.748224	+	0.663446i	$0.769093\pi$
$174$	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	0.626580	+	0.779357i	$0.284454\pi$
$179$	−4.52786	+	13.9353i	−0.338428	+	1.04158i	−0.965009	+	0.262219i	$0.915546\pi$
$180$		0			0
$181$	5.70820	−	4.14725i	0.424287	−	0.308263i	−0.355073	−	0.934839i	$-0.615544\pi$
$181$	5.70820	−	4.14725i	0.424287	−	0.308263i	0.779361	+	0.626576i	$0.215544\pi$
$182$	−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	−0.883651	−	0.468146i	$-0.844922\pi$
$191$	−6.13525	−	18.8824i	−0.443931	−	1.36628i	0.439720	−	0.898135i	$-0.355078\pi$
$192$	−0.951057	−	1.30902i	−0.0686366	−	0.0944702i
$193$	−1.43284	−	1.97214i	−0.103138	−	0.141957i	0.754328	−	0.656497i	$-0.227963\pi$
$193$	−1.43284	−	1.97214i	−0.103138	−	0.141957i	−0.857466	+	0.514540i	$0.827963\pi$
$194$	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	$0.441385\pi$
$197$			27.5967i			1.96619i	−0.183105	+	0.983093i	$0.558615\pi$
$198$	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	0.105290	−	0.994442i	$-0.466423\pi$
$211$	−11.7361	−	8.52675i	−0.807944	−	0.587006i	−0.913234	+	0.407436i	$0.866423\pi$
$212$	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	0.242822	−	0.970071i	$-0.421927\pi$
$223$	−1.95511	−	0.635255i	−0.130924	−	0.0425398i	−0.373746	+	0.927531i	$0.621927\pi$
$224$	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	−0.856569	−	0.516033i	$-0.827408\pi$
$227$	−18.7764	+	6.10081i	−1.24623	+	0.404925i	−0.389663	+	0.920958i	$0.627408\pi$
$228$	−4.02874	−	1.30902i	−0.266810	−	0.0866918i
$229$	−12.5172	−	9.09429i	−0.827161	−	0.600968i	0.0915935	−	0.995796i	$-0.470804\pi$
$229$	−12.5172	−	9.09429i	−0.827161	−	0.600968i	−0.918755	+	0.394829i	$0.870804\pi$
$230$		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	0.212274	+	0.977210i	$0.431913\pi$
$233$	−11.9475	+	16.4443i	−0.782704	+	1.07730i	−0.994978	+	0.100090i	$0.968087\pi$
$234$	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	−0.610028	−	0.792380i	$-0.708842\pi$
$239$	5.39919	−	16.6170i	0.349244	−	1.07486i	0.959272	−	0.282484i	$-0.0911583\pi$
$240$		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	0.458493	−	0.888698i	$-0.348390\pi$
$251$	−3.88197	−	2.82041i	−0.245028	−	0.178023i	−0.703520	+	0.710675i	$0.748390\pi$
$252$		−	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	−0.689629	−	0.724163i	$-0.742226\pi$
$257$	−13.1760	+	4.28115i	−0.821898	+	0.267051i	−0.132269	+	0.991214i	$0.542226\pi$
$258$	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	$0.165228\pi$
$263$			16.0902i			0.992162i	−0.868276	+	0.496081i	$0.834772\pi$
$264$	−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	−0.315911	−	0.948789i	$-0.602310\pi$
$269$	8.01722	−	5.82485i	0.488819	−	0.355147i	0.804730	+	0.593641i	$0.202310\pi$
$270$		0			0
$271$	8.64590	+	26.6093i	0.525201	+	1.61640i	0.763918	+	0.645313i	$0.223273\pi$
$271$	8.64590	+	26.6093i	0.525201	+	1.61640i	−0.238717	+	0.971089i	$0.576727\pi$
$272$	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	−0.999926	−	0.0121753i	$-0.996124\pi$
$277$	−11.3067	+	15.5623i	−0.679352	+	0.935048i	0.320573	+	0.947224i	$0.396124\pi$
$278$	−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	0.132434	−	0.991192i	$-0.457721\pi$
$281$	18.7082	−	13.5923i	1.11604	−	0.810849i	0.983604	+	0.180343i	$0.0577207\pi$
$282$	0.363271	−	0.118034i	0.0216325	−	0.00702882i
$283$	20.9232	+	6.79837i	1.24376	+	0.404121i	0.855680	−	0.517505i	$-0.173139\pi$
$283$	20.9232	+	6.79837i	1.24376	+	0.404121i	0.388078	+	0.921627i	$0.373139\pi$
$284$	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	−0.585984	−	0.810323i	$-0.699292\pi$
$293$	−9.99235	+	3.24671i	−0.583759	+	0.189675i	0.00222470	+	0.999998i	$0.499292\pi$
$294$	−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	$0.307033\pi$
$307$			28.7984i			1.64361i	−0.569769	+	0.821805i	$0.692967\pi$
$308$	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	−0.907058	−	0.421005i	$-0.861678\pi$
$311$	1.30902	−	4.02874i	0.0742275	−	0.228449i	0.981286	+	0.192556i	$0.0616776\pi$
$312$	−0.363271	+	0.118034i	−0.0205662	+	0.00668236i
$313$	0.587785	+	0.809017i	0.0332236	+	0.0457283i	0.825306	−	0.564686i	$-0.191003\pi$
$313$	0.587785	+	0.809017i	0.0332236	+	0.0457283i	−0.792082	+	0.610415i	$0.791003\pi$
$314$	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	−0.760323	−	0.649545i	$-0.774959\pi$
$317$	1.64484	−	2.26393i	0.0923836	−	0.127155i	0.852707	+	0.522390i	$0.174959\pi$
$318$			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	0.603688	−	0.797221i	$-0.293697\pi$
$337$	28.6502	−	9.30902i	1.56068	−	0.507094i	0.956988	+	0.290126i	$0.0936973\pi$
$338$	−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	0.995232	−	0.0975404i	$-0.0310975\pi$
$347$	11.0822	+	15.2533i	0.594922	+	0.818839i	−0.400310	+	0.916380i	$0.631098\pi$
$348$	−0.812299	+	0.263932i	−0.0435438	+	0.0141482i
$349$	7.29180	−	22.4418i	0.390321	−	1.20128i	−0.542225	−	0.840233i	$-0.682418\pi$
$349$	7.29180	−	22.4418i	0.390321	−	1.20128i	0.932546	−	0.361051i	$-0.117582\pi$
$350$		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	$-0.962321\pi$
$353$		−	4.43769i		−	0.236195i	0.993002	−	0.118097i	$-0.0376795\pi$
$354$	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	0.943061	−	0.332620i	$-0.107933\pi$
$359$	−0.291796	−	0.898056i	−0.0154004	−	0.0473976i	−0.958461	+	0.285222i	$0.907933\pi$
$360$		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	−0.173254	−	0.984877i	$-0.555428\pi$
$367$	5.08580	−	1.65248i	0.265476	−	0.0862585i	0.438731	+	0.898619i	$0.355428\pi$
$368$	−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	$0.0196416\pi$
$373$			2.38197i			0.123334i	−0.998097	+	0.0616668i	$0.980358\pi$
$374$	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	−0.703771	−	0.710427i	$-0.748502\pi$
$379$	−4.78115	+	3.47371i	−0.245591	+	0.178433i	0.458179	+	0.888860i	$0.348502\pi$
$380$		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	−0.837995	−	0.545679i	$-0.816272\pi$
$383$	−1.17557	+	1.61803i	−0.0600688	+	0.0826777i	0.777926	+	0.628356i	$0.216272\pi$
$384$	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	0.936287	−	0.351237i	$-0.114239\pi$
$389$	−0.545085	−	1.67760i	−0.0276369	−	0.0850576i	−0.963924	+	0.266179i	$0.914239\pi$
$390$		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	$0.144473\pi$
$397$			17.4721i			0.876901i	−0.898755	+	0.438451i	$0.855527\pi$
$398$	−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	−0.548538	−	0.836126i	$-0.684815\pi$
$401$	1.54508	−	1.12257i	0.0771579	−	0.0560585i	0.625695	+	0.780067i	$0.284815\pi$
$402$	−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	0.892813	−	0.450428i	$-0.148729\pi$
$409$	14.9721	+	10.8779i	0.740324	+	0.537877i	−0.152488	+	0.988305i	$0.548729\pi$
$410$		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	0.725243	+	0.688493i	$0.241727\pi$
$421$	−5.46149	+	16.8087i	−0.266177	+	0.819208i	−0.991420	+	0.130715i	$0.958273\pi$
$422$	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	0.465909	−	0.884832i	$-0.345727\pi$
$431$	−4.80902	−	3.49396i	−0.231642	−	0.168298i	−0.697552	+	0.716534i	$0.745727\pi$
$432$	−5.20431	−	1.69098i	−0.250393	−	0.0813575i
$433$	8.05748	−	2.61803i	0.387218	−	0.125815i	−0.108937	−	0.994049i	$-0.534745\pi$
$433$	8.05748	−	2.61803i	0.387218	−	0.125815i	0.496155	+	0.868234i	$0.334745\pi$
$434$	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	−0.476305	−	0.879280i	$-0.658024\pi$
$443$	−29.0135	−	9.42705i	−1.37847	−	0.447893i	−0.902167	+	0.431387i	$0.858024\pi$
$444$	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	0.853626	−	0.520886i	$-0.174398\pi$
$449$	13.1803	+	9.57608i	0.622019	+	0.451923i	−0.231607	+	0.972809i	$0.574398\pi$
$450$		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	0.609119	−	0.793079i	$-0.291523\pi$
$457$	−7.12667	−	9.80902i	−0.333371	−	0.458846i	−0.942491	+	0.334232i	$0.891523\pi$
$458$	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	$-0.645834\pi$
$463$		−	38.5967i		−	1.79374i	0.442291	−	0.896871i	$-0.354166\pi$
$464$	−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	−0.977704	−	0.209989i	$-0.932657\pi$
$467$	−18.9151	−	26.0344i	−0.875288	−	1.20473i	0.102416	−	0.994742i	$-0.467343\pi$
$468$	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	−0.388621	−	0.921398i	$-0.627049\pi$
$479$	8.04508	−	5.84510i	0.367589	−	0.267069i	0.756211	+	0.654328i	$0.227049\pi$
$480$		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	0.534095	−	0.845425i	$-0.320653\pi$
$487$	10.3556	+	3.36475i	0.469258	+	0.152471i	−0.0648366	+	0.997896i	$0.520653\pi$
$488$	−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	0.999362	−	0.0357226i	$-0.0113733\pi$
$491$	3.76393	+	11.5842i	0.169864	+	0.522787i	−0.829498	+	0.558510i	$0.811373\pi$
$492$	−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	−0.999241	−	0.0389621i	$-0.987595\pi$
$499$	−4.77458	−	14.6946i	−0.213739	−	0.657822i	0.785501	−	0.618860i	$-0.212405\pi$
$500$		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	0.887978	−	0.459886i	$-0.152110\pi$
$503$	29.9645	+	9.73607i	1.33605	+	0.434110i	0.448075	+	0.893996i	$0.352110\pi$
$504$	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	−0.996429	−	0.0844297i	$-0.973093\pi$
$509$	−3.17376	+	9.76784i	−0.140675	+	0.432952i	0.855755	+	0.517381i	$0.173093\pi$
$510$		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	0.859872	−	0.510510i	$-0.170543\pi$
$521$	−3.10081	−	9.54332i	−0.135849	−	0.418100i	−0.995721	+	0.0924091i	$0.970543\pi$
$522$	0.118513	+	0.163119i	0.00518717	+	0.00713952i
$523$	−16.1680	−	22.2533i	−0.706976	−	0.973068i	−0.999857	−	0.0169196i	$-0.994614\pi$
$523$	−16.1680	−	22.2533i	−0.706976	−	0.973068i	0.292881	−	0.956149i	$-0.405386\pi$
$524$	−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	−0.134189	−	0.990956i	$-0.542843\pi$
$541$	−26.0066	−	18.8949i	−1.11811	−	0.812355i	−0.983922	+	0.178601i	$0.942843\pi$
$542$	−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	−0.0794708	−	0.996837i	$-0.525323\pi$
$547$	−17.0660	−	5.54508i	−0.729690	−	0.237091i	−0.650219	+	0.759746i	$0.725323\pi$
$548$	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	−0.425250	−	0.905076i	$-0.639814\pi$
$557$	−5.60034	+	1.81966i	−0.237294	+	0.0771015i	0.187956	+	0.982177i	$0.439814\pi$
$558$	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	−0.532978	−	0.846129i	$-0.678927\pi$
$563$	10.3556	−	14.2533i	0.436437	−	0.600705i	0.969416	+	0.245424i	$0.0789273\pi$
$564$	−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	−0.936605	−	0.350388i	$-0.886050\pi$
$569$	0.645898	−	1.98787i	0.0270775	−	0.0833358i	0.963682	+	0.267052i	$0.0860497\pi$
$570$		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	0.454958	−	0.890513i	$-0.349654\pi$
$577$	−12.7925	−	17.6074i	−0.532560	−	0.733005i	−0.987518	+	0.157507i	$0.949654\pi$
$578$	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	0.0270477	−	0.999634i	$-0.491389\pi$
$587$	15.4212	−	5.01064i	0.636500	−	0.206811i	0.609452	+	0.792823i	$0.291389\pi$
$588$	−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	$-0.663809\pi$
$593$		−	42.3951i		−	1.74096i	0.492205	−	0.870479i	$-0.336191\pi$
$594$	−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	−0.536134	−	0.844133i	$-0.680116\pi$
$599$	2.47214	−	1.79611i	0.101009	−	0.0733871i	0.637143	+	0.770745i	$0.280116\pi$
$600$		0			0
$601$	−2.02786	−	6.24112i	−0.0827183	−	0.254581i	0.901141	−	0.433527i	$-0.142731\pi$
$601$	−2.02786	−	6.24112i	−0.0827183	−	0.254581i	−0.983859	+	0.178946i	$0.942731\pi$
$602$	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	−0.938241	−	0.345982i	$-0.887546\pi$
$607$	−7.86572	+	10.8262i	−0.319260	+	0.439423i	0.618981	+	0.785406i	$0.287546\pi$
$608$	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	0.167842	−	0.985814i	$-0.446320\pi$
$613$	−6.82891	−	2.21885i	−0.275817	−	0.0896184i	−0.443659	+	0.896195i	$0.646320\pi$
$614$	−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	$-0.826192\pi$
$617$		−	25.7984i		−	1.03860i	0.854591	−	0.519302i	$-0.173808\pi$
$618$	16.0620	−	22.1074i	0.646107	−	0.889290i
$619$	8.10739	−	24.9520i	0.325864	−	1.00290i	−0.645186	−	0.764026i	$-0.723220\pi$
$619$	8.10739	−	24.9520i	0.325864	−	1.00290i	0.971049	−	0.238879i	$-0.0767800\pi$
$620$		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	0.901279	−	0.433239i	$-0.142630\pi$
$631$	−2.07295	−	6.37988i	−0.0825228	−	0.253979i	−0.983802	+	0.179260i	$0.942630\pi$
$632$	−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	0.272581	+	0.962133i	$0.412123\pi$
$641$	−13.0000	+	40.0099i	−0.513469	+	1.58030i	−0.786050	+	0.618163i	$0.787877\pi$
$642$	−12.5882	+	4.09017i	−0.496819	+	0.161426i
$643$	8.30224	+	11.4271i	0.327408	+	0.450639i	0.940711	−	0.339209i	$-0.110159\pi$
$643$	8.30224	+	11.4271i	0.327408	+	0.450639i	−0.613303	+	0.789848i	$0.710159\pi$
$644$	−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	−0.796645	−	0.604448i	$-0.793394\pi$
$647$	0.620541	−	0.854102i	0.0243960	−	0.0335782i	0.821041	+	0.570870i	$0.193394\pi$
$648$		−	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	−0.107586	−	0.994196i	$-0.534312\pi$
$653$	9.95959	−	3.23607i	0.389749	−	0.126637i	0.497335	+	0.867559i	$0.334312\pi$
$654$	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	−0.919824	−	0.392330i	$-0.871669\pi$
$673$	−6.80866	+	9.37132i	−0.262455	+	0.361238i	0.657370	+	0.753568i	$0.271669\pi$
$674$	−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	0.913653	−	0.406496i	$-0.133249\pi$
$677$	6.36737	+	8.76393i	0.244718	+	0.336825i	−0.668935	+	0.743321i	$0.733249\pi$
$678$	−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	$0.0373035\pi$
$683$			6.11146i			0.233848i	−0.993141	+	0.116924i	$0.962697\pi$
$684$	−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	0.996791	−	0.0800463i	$-0.0255068\pi$
$691$	32.2984	+	23.4661i	1.22869	+	0.892694i	0.231897	+	0.972740i	$0.425507\pi$
$692$			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	−0.997296	−	0.0734900i	$-0.976586\pi$
$701$	−3.89919	+	12.0005i	−0.147270	+	0.453251i	0.850026	+	0.526741i	$0.176586\pi$
$702$	−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	−0.406915	+	0.913466i	$0.633396\pi$
$709$	−37.3156	+	27.1114i	−1.40142	+	1.01819i	−0.994501	+	0.104723i	$0.966604\pi$
$710$		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	−0.997763	−	0.0668436i	$-0.978707\pi$
$719$	−6.16312	−	18.9681i	−0.229846	−	0.707392i	0.767918	−	0.640548i	$-0.221293\pi$
$720$		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	$0.0824941\pi$
$727$			13.8197i			0.512543i	−0.966605	+	0.256271i	$0.917506\pi$
$728$	−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	0.100688	−	0.994918i	$-0.467896\pi$
$733$	20.7642	−	6.74671i	0.766945	−	0.249195i	0.666257	+	0.745723i	$0.267896\pi$
$734$	−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	0.722798	−	0.691060i	$-0.242856\pi$
$739$	7.85410	+	5.70634i	0.288918	+	0.209911i	−0.433880	+	0.900971i	$0.642856\pi$
$740$		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	−0.964698	−	0.263360i	$-0.915169\pi$
$743$	−24.9973	−	34.4058i	−0.917060	−	1.26223i	0.0476373	−	0.998865i	$-0.484831\pi$
$744$	−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	−0.676814	−	0.736154i	$-0.736640\pi$
$751$	8.31559	−	25.5928i	0.303440	−	0.933893i	0.980255	−	0.197740i	$-0.0633600\pi$
$752$	−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	−0.614958	−	0.788560i	$-0.710827\pi$
$757$	8.94302	−	12.3090i	0.325040	−	0.447379i	0.939998	+	0.341181i	$0.110827\pi$
$758$		−	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	0.854463	−	0.519512i	$-0.173886\pi$
$761$	17.2254	+	12.5150i	0.624421	+	0.453669i	−0.230042	+	0.973181i	$0.573886\pi$
$762$	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	0.914564	−	0.404442i	$-0.132534\pi$
$773$	39.3893	+	12.7984i	1.41674	+	0.460326i	0.502173	+	0.864767i	$0.332534\pi$
$774$	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	0.954824	−	0.297171i	$-0.0960431\pi$
$787$	10.5801	+	14.5623i	0.377141	+	0.519090i	−0.577683	+	0.816261i	$0.696043\pi$
$788$	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	0.896119	+	0.443814i	$0.146375\pi$
$797$	29.3970	+	40.4615i	1.04129	+	1.43322i	0.145176	+	0.989406i	$0.453625\pi$
$798$	−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	−0.00796840	−	0.999968i	$-0.502536\pi$
$809$	26.7533	−	19.4374i	0.940596	−	0.683383i	0.948564	+	0.316586i	$0.102536\pi$
$810$		0			0
$811$	4.21885	−	12.9843i	0.148144	−	0.455940i	−0.849258	−	0.527978i	$-0.822950\pi$
$811$	4.21885	−	12.9843i	0.148144	−	0.455940i	0.997402	+	0.0720383i	$0.0229504\pi$
$812$	−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	−0.903476	−	0.428638i	$-0.858994\pi$
$821$	−12.1631	−	37.4342i	−0.424496	−	1.30646i	0.478980	−	0.877826i	$-0.341006\pi$
$822$	24.2582	+	7.88197i	0.846102	+	0.274915i
$823$	1.30182	−	1.79180i	0.0453785	−	0.0624581i	−0.785725	−	0.618576i	$-0.787710\pi$
$823$	1.30182	−	1.79180i	0.0453785	−	0.0624581i	0.831103	+	0.556118i	$0.187710\pi$
$824$	16.8885			0.588340
$825$		0			0
$826$	25.6525			0.892564
$827$	−13.3475	+	18.3713i	−0.464140	+	0.638833i	−0.975361	−	0.220616i	$-0.929193\pi$
$827$	−13.3475	+	18.3713i	−0.464140	+	0.638833i	0.511221	+	0.859449i	$0.329193\pi$
$828$	−1.40008	−	0.454915i	−0.0486563	−	0.0158094i
$829$	−11.4377	−	35.2016i	−0.397248	−	1.22260i	−0.927197	−	0.374573i	$-0.877789\pi$
$829$	−11.4377	−	35.2016i	−0.397248	−	1.22260i	0.529950	−	0.848029i	$-0.322211\pi$
$830$		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	−0.664910	−	0.746923i	$-0.731530\pi$
$839$	9.03851	−	27.8177i	0.312044	−	0.960372i	0.976954	−	0.213449i	$-0.0684698\pi$
$840$		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	0.841372	−	0.540456i	$-0.181748\pi$
$853$	1.96763	+	2.70820i	0.0673702	+	0.0927271i	−0.774002	+	0.633183i	$0.781748\pi$
$854$	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	$-0.857945\pi$
$857$		−	25.2705i		−	0.863224i	0.902059	−	0.431612i	$-0.142055\pi$
$858$	−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	0.797753	−	0.602984i	$-0.206022\pi$
$863$	−0.653298	−	0.899187i	−0.0222385	−	0.0306087i	−0.819991	+	0.572376i	$0.806022\pi$
$864$	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	−0.368603	−	0.929587i	$-0.620164\pi$
$877$	−35.9281	−	11.6738i	−1.21321	−	0.394195i	−0.844604	+	0.535392i	$0.820164\pi$
$878$	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	0.856642	−	0.515911i	$-0.172547\pi$
$883$	37.0382	+	12.0344i	1.24643	+	0.404991i	0.389793	+	0.920903i	$0.372547\pi$
$884$	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	−0.870680	−	0.491850i	$-0.836321\pi$
$887$	−38.2995	+	12.4443i	−1.28597	+	0.417838i	−0.415293	+	0.909688i	$0.636321\pi$
$888$	−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	0.996039	+	0.0889194i	$0.0283413\pi$
$907$	23.2744	+	32.0344i	0.772813	+	1.06369i	−0.223226	+	0.974767i	$0.571659\pi$
$908$	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	0.744297	−	0.667849i	$-0.232785\pi$
$911$	10.2361	+	7.43694i	0.339136	+	0.246397i	−0.405161	+	0.914245i	$0.632785\pi$
$912$			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	−0.834249	−	0.551387i	$-0.814099\pi$
$919$	−17.2082	+	12.5025i	−0.567646	+	0.412419i	0.266603	+	0.963806i	$0.414099\pi$
$920$		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	−0.853460	−	0.521159i	$-0.825500\pi$
$929$	−18.9443	+	13.7638i	−0.621541	+	0.451576i	0.231918	+	0.972735i	$0.425500\pi$
$930$		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	−0.973289	−	0.229585i	$-0.926263\pi$
$937$	−13.9026	+	19.1353i	−0.454177	+	0.625122i	0.519111	+	0.854707i	$0.326263\pi$
$938$	−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	−0.869637	−	0.493691i	$-0.835647\pi$
$941$	−20.5172	+	14.9066i	−0.668842	+	0.485942i	0.200795	+	0.979633i	$0.435647\pi$
$942$	−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	$-0.905526\pi$
$947$		−	18.0000i		−	0.584921i	0.956278	−	0.292461i	$-0.0944741\pi$
$948$	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	0.402988	−	0.915205i	$-0.367972\pi$
$953$	39.1118	−	12.7082i	1.26696	−	0.411659i	0.863968	+	0.503546i	$0.167972\pi$
$954$	−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	$-0.895485\pi$
$967$		−	20.0557i		−	0.644949i	0.946578	−	0.322474i	$-0.104515\pi$
$968$	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	−0.306193	−	0.951970i	$-0.599055\pi$
$971$	15.6140	−	48.0549i	0.501076	−	1.54215i	0.807269	−	0.590184i	$-0.200945\pi$
$972$	−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	−0.721656	−	0.692252i	$-0.756619\pi$
$977$	4.99231	−	6.87132i	0.159718	−	0.219833i	0.881374	+	0.472418i	$0.156619\pi$
$978$		−	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	−0.696041	−	0.718002i	$-0.745057\pi$
$983$	−26.2461	+	8.52786i	−0.837120	+	0.271997i	−0.141078	+	0.989998i	$0.545057\pi$
$984$	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	−0.710120	−	0.704080i	$-0.751359\pi$
$997$	−27.4949	+	8.93363i	−0.870772	+	0.282931i	−0.160651	+	0.987011i	$0.551359\pi$
$998$	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.499.1		8
5.2	odd	4		550.2.h.c.301.1	yes	4
5.3	odd	4		550.2.h.g.301.1	yes	4
5.4	even	2	inner	550.2.ba.e.499.2		8
11.3	even	5	inner	550.2.ba.e.399.2		8
55.3	odd	20		550.2.h.g.201.1	yes	4
55.14	even	10	inner	550.2.ba.e.399.1		8
55.17	even	20		6050.2.a.bx.1.1		2
55.27	odd	20		6050.2.a.co.1.1		2
55.28	even	20		6050.2.a.cr.1.2		2
55.38	odd	20		6050.2.a.ca.1.2		2
55.47	odd	20		550.2.h.c.201.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
550.2.h.c.201.1	✓	4	55.47	odd	20
550.2.h.c.301.1	yes	4	5.2	odd	4
550.2.h.g.201.1	yes	4	55.3	odd	20
550.2.h.g.301.1	yes	4	5.3	odd	4
550.2.ba.e.399.1		8	55.14	even	10	inner
550.2.ba.e.399.2		8	11.3	even	5	inner
550.2.ba.e.499.1		8	1.1	even	1	trivial
550.2.ba.e.499.2		8	5.4	even	2	inner
6050.2.a.bx.1.1		2	55.17	even	20
6050.2.a.ca.1.2		2	55.38	odd	20
6050.2.a.co.1.1		2	55.27	odd	20
6050.2.a.cr.1.2		2	55.28	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 $\F_{q}$

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

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Representations

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Database

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