LMFDB - Embedded newform 550.2.h.g.201.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [550,2,Mod(201,550)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(550, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("550.201"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	550.h (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,1,2,-1,0,3,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.39177211117$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			201.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	550.201
Dual form			550.2.h.g.301.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.809017 - 0.587785i) q^{2} +(0.500000 + 1.53884i) q^{3} +(0.309017 - 0.951057i) q^{4} +(1.30902 + 0.951057i) q^{6} +(0.690983 - 2.12663i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.309017 - 0.224514i) q^{9} +(3.23607 + 0.726543i) q^{11} +1.61803 q^{12} +(0.190983 - 0.138757i) q^{13} +(-0.690983 - 2.12663i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-0.309017 - 0.224514i) q^{17} +(0.118034 - 0.363271i) q^{18} +(0.809017 + 2.48990i) q^{19} +3.61803 q^{21} +(3.04508 - 1.31433i) q^{22} -3.85410 q^{23} +(1.30902 - 0.951057i) q^{24} +(0.0729490 - 0.224514i) q^{26} +(4.42705 + 3.21644i) q^{27} +(-1.80902 - 1.31433i) q^{28} +(-0.163119 + 0.502029i) q^{29} +(8.28115 - 6.01661i) q^{31} -1.00000 q^{32} +(0.500000 + 5.34307i) q^{33} -0.381966 q^{34} +(-0.118034 - 0.363271i) q^{36} +(-2.73607 + 8.42075i) q^{37} +(2.11803 + 1.53884i) q^{38} +(0.309017 + 0.224514i) q^{39} +(-1.14590 - 3.52671i) q^{41} +(2.92705 - 2.12663i) q^{42} -9.47214 q^{43} +(1.69098 - 2.85317i) q^{44} +(-3.11803 + 2.26538i) q^{46} +(0.0729490 + 0.224514i) q^{47} +(0.500000 - 1.53884i) q^{48} +(1.61803 + 1.17557i) q^{49} +(0.190983 - 0.587785i) q^{51} +(-0.0729490 - 0.224514i) q^{52} +(-1.11803 + 0.812299i) q^{53} +5.47214 q^{54} -2.23607 q^{56} +(-3.42705 + 2.48990i) q^{57} +(0.163119 + 0.502029i) q^{58} +(-3.54508 + 10.9106i) q^{59} +(-1.80902 - 1.31433i) q^{61} +(3.16312 - 9.73508i) q^{62} +(-0.263932 - 0.812299i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(3.54508 + 4.02874i) q^{66} -9.32624 q^{67} +(-0.309017 + 0.224514i) q^{68} +(-1.92705 - 5.93085i) q^{69} +(-7.92705 - 5.75934i) q^{71} +(-0.309017 - 0.224514i) q^{72} +(2.51722 - 7.74721i) q^{73} +(2.73607 + 8.42075i) q^{74} +2.61803 q^{76} +(3.78115 - 6.37988i) q^{77} +0.381966 q^{78} +(9.66312 - 7.02067i) q^{79} +(-2.38197 + 7.33094i) q^{81} +(-3.00000 - 2.17963i) q^{82} +(-7.28115 - 5.29007i) q^{83} +(1.11803 - 3.44095i) q^{84} +(-7.66312 + 5.56758i) q^{86} -0.854102 q^{87} +(-0.309017 - 3.30220i) q^{88} -13.1803 q^{89} +(-0.163119 - 0.502029i) q^{91} +(-1.19098 + 3.66547i) q^{92} +(13.3992 + 9.73508i) q^{93} +(0.190983 + 0.138757i) q^{94} +(-0.500000 - 1.53884i) q^{96} +(-9.70820 + 7.05342i) q^{97} +2.00000 q^{98} +(1.16312 - 0.502029i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + 2 q^{3} - q^{4} + 3 q^{6} + 5 q^{7} + q^{8} - q^{9} + 4 q^{11} + 2 q^{12} + 3 q^{13} - 5 q^{14} - q^{16} + q^{17} - 4 q^{18} + q^{19} + 10 q^{21} + q^{22} - 2 q^{23} + 3 q^{24} + 7 q^{26}+ \cdots - 11 q^{99}+O(q^{100}) $ 4 * q + q^2 + 2 * q^3 - q^4 + 3 * q^6 + 5 * q^7 + q^8 - q^9 + 4 * q^11 + 2 * q^12 + 3 * q^13 - 5 * q^14 - q^16 + q^17 - 4 * q^18 + q^19 + 10 * q^21 + q^22 - 2 * q^23 + 3 * q^24 + 7 * q^26 + 11 * q^27 - 5 * q^28 + 15 * q^29 + 13 * q^31 - 4 * q^32 + 2 * q^33 - 6 * q^34 + 4 * q^36 - 2 * q^37 + 4 * q^38 - q^39 - 18 * q^41 + 5 * q^42 - 20 * q^43 + 9 * q^44 - 8 * q^46 + 7 * q^47 + 2 * q^48 + 2 * q^49 + 3 * q^51 - 7 * q^52 + 4 * q^54 - 7 * q^57 - 15 * q^58 - 3 * q^59 - 5 * q^61 - 3 * q^62 - 10 * q^63 - q^64 + 3 * q^66 - 6 * q^67 + q^68 - q^69 - 25 * q^71 + q^72 - 19 * q^73 + 2 * q^74 + 6 * q^76 - 5 * q^77 + 6 * q^78 + 23 * q^79 - 14 * q^81 - 12 * q^82 - 9 * q^83 - 15 * q^86 + 10 * q^87 + q^88 - 8 * q^89 + 15 * q^91 - 7 * q^92 + 29 * q^93 + 3 * q^94 - 2 * q^96 - 12 * q^97 + 8 * q^98 - 11 * 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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	0.500000	+	1.53884i	0.288675	+	0.888451i	0.985273	+	0.170989i	$0.0546962\pi$
$3$	0.500000	+	1.53884i	0.288675	+	0.888451i	−0.696598	+	0.717462i	$0.745304\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$		0			0
$5$		0			0
$6$	1.30902	+	0.951057i	0.534404	+	0.388267i
$7$	0.690983	−	2.12663i	0.261167	−	0.803789i	−0.731385	−	0.681965i	$-0.761126\pi$
$7$	0.690983	−	2.12663i	0.261167	−	0.803789i	0.992552	−	0.121824i	$-0.0388744\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	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
$12$	1.61803			0.467086
$13$	0.190983	−	0.138757i	0.0529692	−	0.0384843i	−0.560986	−	0.827826i	$-0.689578\pi$
$13$	0.190983	−	0.138757i	0.0529692	−	0.0384843i	0.613955	+	0.789341i	$0.289578\pi$
$14$	−0.690983	−	2.12663i	−0.184673	−	0.568365i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−0.309017	−	0.224514i	−0.0749476	−	0.0544526i	0.549681	−	0.835375i	$-0.314749\pi$
$17$	−0.309017	−	0.224514i	−0.0749476	−	0.0544526i	−0.624628	+	0.780922i	$0.714749\pi$
$18$	0.118034	−	0.363271i	0.0278209	−	0.0856239i
$19$	0.809017	+	2.48990i	0.185601	+	0.571222i	0.999958	−	0.00914245i	$-0.00291017\pi$
$19$	0.809017	+	2.48990i	0.185601	+	0.571222i	−0.814357	+	0.580364i	$0.802910\pi$
$20$		0			0
$21$	3.61803			0.789520
$22$	3.04508	−	1.31433i	0.649214	−	0.280216i
$23$	−3.85410			−0.803636			−0.401818	−	0.915720i	$-0.631622\pi$
$23$	−3.85410			−0.803636			−0.401818	+	0.915720i	$0.631622\pi$
$24$	1.30902	−	0.951057i	0.267202	−	0.194134i
$25$		0			0
$26$	0.0729490	−	0.224514i	0.0143065	−	0.0440308i
$27$	4.42705	+	3.21644i	0.851986	+	0.619004i
$28$	−1.80902	−	1.31433i	−0.341872	−	0.248385i
$29$	−0.163119	+	0.502029i	−0.0302904	+	0.0932244i	−0.965059	−	0.262033i	$-0.915607\pi$
$29$	−0.163119	+	0.502029i	−0.0302904	+	0.0932244i	0.934768	+	0.355258i	$0.115607\pi$
$30$		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	$-0.0711844\pi$
$32$	−1.00000			−0.176777
$33$	0.500000	+	5.34307i	0.0870388	+	0.930109i
$34$	−0.381966			−0.0655066
$35$		0			0
$36$	−0.118034	−	0.363271i	−0.0196723	−	0.0605452i
$37$	−2.73607	+	8.42075i	−0.449807	+	1.38436i	0.427318	+	0.904101i	$0.359458\pi$
$37$	−2.73607	+	8.42075i	−0.449807	+	1.38436i	−0.877125	+	0.480262i	$0.840542\pi$
$38$	2.11803	+	1.53884i	0.343590	+	0.249633i
$39$	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	$0.993510\pi$
$42$	2.92705	−	2.12663i	0.451654	−	0.328146i
$43$	−9.47214			−1.44449			−0.722244	−	0.691639i	$-0.756889\pi$
$43$	−9.47214			−1.44449			−0.722244	+	0.691639i	$0.756889\pi$
$44$	1.69098	−	2.85317i	0.254925	−	0.430131i
$45$		0			0
$46$	−3.11803	+	2.26538i	−0.459729	+	0.334013i
$47$	0.0729490	+	0.224514i	0.0106407	+	0.0327487i	0.956236	−	0.292597i	$-0.0945194\pi$
$47$	0.0729490	+	0.224514i	0.0106407	+	0.0327487i	−0.945595	+	0.325346i	$0.894519\pi$
$48$	0.500000	−	1.53884i	0.0721688	−	0.222113i
$49$	1.61803	+	1.17557i	0.231148	+	0.167939i
$50$		0			0
$51$	0.190983	−	0.587785i	0.0267430	−	0.0823064i
$52$	−0.0729490	−	0.224514i	−0.0101162	−	0.0311345i
$53$	−1.11803	+	0.812299i	−0.153574	+	0.111578i	−0.661919	−	0.749576i	$-0.730258\pi$
$53$	−1.11803	+	0.812299i	−0.153574	+	0.111578i	0.508345	+	0.861154i	$0.330258\pi$
$54$	5.47214			0.744663
$55$		0			0
$56$	−2.23607			−0.298807
$57$	−3.42705	+	2.48990i	−0.453924	+	0.329795i
$58$	0.163119	+	0.502029i	0.0214186	+	0.0659196i
$59$	−3.54508	+	10.9106i	−0.461531	+	1.42045i	0.401763	+	0.915744i	$0.368398\pi$
$59$	−3.54508	+	10.9106i	−0.461531	+	1.42045i	−0.863294	+	0.504702i	$0.831602\pi$
$60$		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	$0.745723\pi$
$62$	3.16312	−	9.73508i	0.401717	−	1.23636i
$63$	−0.263932	−	0.812299i	−0.0332523	−	0.102340i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$		0			0
$66$	3.54508	+	4.02874i	0.436370	+	0.495904i
$67$	−9.32624			−1.13938			−0.569691	−	0.821859i	$-0.692937\pi$
$67$	−9.32624			−1.13938			−0.569691	+	0.821859i	$0.692937\pi$
$68$	−0.309017	+	0.224514i	−0.0374738	+	0.0272263i
$69$	−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	$0.897505\pi$
$72$	−0.309017	−	0.224514i	−0.0364180	−	0.0264592i
$73$	2.51722	−	7.74721i	0.294618	−	0.906742i	−0.688731	−	0.725017i	$-0.741832\pi$
$73$	2.51722	−	7.74721i	0.294618	−	0.906742i	0.983349	−	0.181725i	$-0.0581681\pi$
$74$	2.73607	+	8.42075i	0.318061	+	0.978892i
$75$		0			0
$76$	2.61803			0.300309
$77$	3.78115	−	6.37988i	0.430902	−	0.727055i
$78$	0.381966			0.0432491
$79$	9.66312	−	7.02067i	1.08719	−	0.789887i	0.108264	−	0.994122i	$-0.465471\pi$
$79$	9.66312	−	7.02067i	1.08719	−	0.789887i	0.978922	+	0.204235i	$0.0654708\pi$
$80$		0			0
$81$	−2.38197	+	7.33094i	−0.264663	+	0.814549i
$82$	−3.00000	−	2.17963i	−0.331295	−	0.240700i
$83$	−7.28115	−	5.29007i	−0.799210	−	0.580660i	0.111472	−	0.993768i	$-0.464443\pi$
$83$	−7.28115	−	5.29007i	−0.799210	−	0.580660i	−0.910682	+	0.413107i	$0.864443\pi$
$84$	1.11803	−	3.44095i	0.121988	−	0.375439i
$85$		0			0
$86$	−7.66312	+	5.56758i	−0.826335	+	0.600368i
$87$	−0.854102			−0.0915693
$88$	−0.309017	−	3.30220i	−0.0329413	−	0.352015i
$89$	−13.1803			−1.39711			−0.698557	−	0.715555i	$-0.746174\pi$
$89$	−13.1803			−1.39711			−0.698557	+	0.715555i	$0.746174\pi$
$90$		0			0
$91$	−0.163119	−	0.502029i	−0.0170995	−	0.0526269i
$92$	−1.19098	+	3.66547i	−0.124169	+	0.382152i
$93$	13.3992	+	9.73508i	1.38943	+	1.00948i
$94$	0.190983	+	0.138757i	0.0196984	+	0.0143117i
$95$		0			0
$96$	−0.500000	−	1.53884i	−0.0510310	−	0.157057i
$97$	−9.70820	+	7.05342i	−0.985719	+	0.716167i	−0.958979	−	0.283476i	$-0.908512\pi$
$97$	−9.70820	+	7.05342i	−0.985719	+	0.716167i	−0.0267394	+	0.999642i	$0.508512\pi$
$98$	2.00000			0.202031
$99$	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	$0.919140\pi$
$102$	−0.190983	−	0.587785i	−0.0189101	−	0.0581994i
$103$	5.21885	−	16.0620i	0.514228	−	1.58263i	−0.270453	−	0.962733i	$-0.587174\pi$
$103$	5.21885	−	16.0620i	0.514228	−	1.58263i	0.784682	−	0.619899i	$-0.212826\pi$
$104$	−0.190983	−	0.138757i	−0.0187274	−	0.0136063i
$105$		0			0
$106$	−0.427051	+	1.31433i	−0.0414789	+	0.127659i
$107$	−2.52786	−	7.77997i	−0.244378	−	0.752118i	−0.995738	−	0.0922255i	$-0.970602\pi$
$107$	−2.52786	−	7.77997i	−0.244378	−	0.752118i	0.751360	−	0.659892i	$-0.229398\pi$
$108$	4.42705	−	3.21644i	0.425993	−	0.309502i
$109$	−11.6180			−1.11281			−0.556403	−	0.830913i	$-0.687819\pi$
$109$	−11.6180			−1.11281			−0.556403	+	0.830913i	$0.687819\pi$
$110$		0			0
$111$	−14.3262			−1.35979
$112$	−1.80902	+	1.31433i	−0.170936	+	0.124192i
$113$	4.54508	+	13.9883i	0.427566	+	1.31591i	0.900516	+	0.434823i	$0.143189\pi$
$113$	4.54508	+	13.9883i	0.427566	+	1.31591i	−0.472950	+	0.881089i	$0.656811\pi$
$114$	−1.30902	+	4.02874i	−0.122601	+	0.377326i
$115$		0			0
$116$	0.427051	+	0.310271i	0.0396507	+	0.0288079i
$117$	0.0278640	−	0.0857567i	0.00257603	−	0.00792821i
$118$	3.54508	+	10.9106i	0.326352	+	1.00441i
$119$	−0.690983	+	0.502029i	−0.0633423	+	0.0460209i
$120$		0			0
$121$	9.94427	+	4.70228i	0.904025	+	0.427480i
$122$	−2.23607			−0.202444
$123$	4.85410	−	3.52671i	0.437680	−	0.317993i
$124$	−3.16312	−	9.73508i	−0.284056	−	0.874236i
$125$		0			0
$126$	−0.690983	−	0.502029i	−0.0615577	−	0.0447243i
$127$	2.35410	+	1.71036i	0.208893	+	0.151769i	0.687313	−	0.726362i	$-0.258790\pi$
$127$	2.35410	+	1.71036i	0.208893	+	0.151769i	−0.478420	+	0.878131i	$0.658790\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	−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	$0.338124\pi$
$132$	5.23607	+	1.17557i	0.455741	+	0.102320i
$133$	5.85410			0.507615
$134$	−7.54508	+	5.48183i	−0.651796	+	0.473558i
$135$		0			0
$136$	−0.118034	+	0.363271i	−0.0101213	+	0.0311503i
$137$	12.7533	+	9.26581i	1.08959	+	0.791631i	0.979329	−	0.202272i	$-0.0648324\pi$
$137$	12.7533	+	9.26581i	1.08959	+	0.791631i	0.110258	+	0.993903i	$0.464832\pi$
$138$	−5.04508	−	3.66547i	−0.429466	−	0.312025i
$139$	−0.881966	+	2.71441i	−0.0748074	+	0.230233i	−0.981468	−	0.191628i	$-0.938623\pi$
$139$	−0.881966	+	2.71441i	−0.0748074	+	0.230233i	0.906660	+	0.421862i	$0.138623\pi$
$140$		0			0
$141$	−0.309017	+	0.224514i	−0.0260239	+	0.0189075i
$142$	−9.79837			−0.822261
$143$	0.718847	−	0.310271i	0.0601130	−	0.0259461i
$144$	−0.381966			−0.0318305
$145$		0			0
$146$	−2.51722	−	7.74721i	−0.208327	−	0.641164i
$147$	−1.00000	+	3.07768i	−0.0824786	+	0.253843i
$148$	7.16312	+	5.20431i	0.588805	+	0.427792i
$149$	8.66312	+	6.29412i	0.709710	+	0.515635i	0.883080	−	0.469222i	$-0.155466\pi$
$149$	8.66312	+	6.29412i	0.709710	+	0.515635i	−0.173370	+	0.984857i	$0.555466\pi$
$150$		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	$-0.381999\pi$
$152$	2.11803	−	1.53884i	0.171795	−	0.124817i
$153$	−0.145898			−0.0117952
$154$	−0.690983	−	7.38394i	−0.0556810	−	0.595015i
$155$		0			0
$156$	0.309017	−	0.224514i	0.0247412	−	0.0179755i
$157$	−2.09017	−	6.43288i	−0.166814	−	0.513400i	0.832352	−	0.554248i	$-0.186994\pi$
$157$	−2.09017	−	6.43288i	−0.166814	−	0.513400i	−0.999165	+	0.0408481i	$0.986994\pi$
$158$	3.69098	−	11.3597i	0.293639	−	0.903727i
$159$	−1.80902	−	1.31433i	−0.143464	−	0.104233i
$160$		0			0
$161$	−2.66312	+	8.19624i	−0.209883	+	0.645954i
$162$	2.38197	+	7.33094i	0.187145	+	0.575973i
$163$	0.145898	−	0.106001i	0.0114276	−	0.00830265i	−0.582057	−	0.813148i	$-0.697752\pi$
$163$	0.145898	−	0.106001i	0.0114276	−	0.00830265i	0.593484	+	0.804845i	$0.297752\pi$
$164$	−3.70820			−0.289562
$165$		0			0
$166$	−9.00000			−0.698535
$167$	−1.80902	+	1.31433i	−0.139986	+	0.101706i	−0.655574	−	0.755131i	$-0.727573\pi$
$167$	−1.80902	+	1.31433i	−0.139986	+	0.101706i	0.515588	+	0.856836i	$0.327573\pi$
$168$	−1.11803	−	3.44095i	−0.0862582	−	0.265475i
$169$	−4.00000	+	12.3107i	−0.307692	+	0.946980i
$170$		0			0
$171$	0.809017	+	0.587785i	0.0618671	+	0.0449491i
$172$	−2.92705	+	9.00854i	−0.223186	+	0.686894i
$173$	4.11803	+	12.6740i	0.313088	+	0.963587i	0.976534	+	0.215362i	$0.0690933\pi$
$173$	4.11803	+	12.6740i	0.313088	+	0.963587i	−0.663446	+	0.748224i	$0.730907\pi$
$174$	−0.690983	+	0.502029i	−0.0523833	+	0.0380587i
$175$		0			0
$176$	−2.19098	−	2.48990i	−0.165152	−	0.187683i
$177$	−18.5623			−1.39523
$178$	−10.6631	+	7.74721i	−0.799235	+	0.580678i
$179$	4.52786	+	13.9353i	0.338428	+	1.04158i	0.965009	+	0.262219i	$0.0844541\pi$
$179$	4.52786	+	13.9353i	0.338428	+	1.04158i	−0.626580	+	0.779357i	$0.715546\pi$
$180$		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	$0.615544\pi$
$182$	−0.427051	−	0.310271i	−0.0316551	−	0.0229988i
$183$	1.11803	−	3.44095i	0.0826475	−	0.254363i
$184$	1.19098	+	3.66547i	0.0878004	+	0.270222i
$185$		0			0
$186$	16.5623			1.21441
$187$	−0.836881	−	0.951057i	−0.0611988	−	0.0695481i
$188$	0.236068			0.0172170
$189$	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	$0.844922\pi$
$192$	−1.30902	−	0.951057i	−0.0944702	−	0.0686366i
$193$	1.97214	+	1.43284i	0.141957	+	0.103138i	0.656497	−	0.754328i	$-0.272037\pi$
$193$	1.97214	+	1.43284i	0.141957	+	0.103138i	−0.514540	+	0.857466i	$0.672037\pi$
$194$	−3.70820	+	11.4127i	−0.266234	+	0.819383i
$195$		0			0
$196$	1.61803	−	1.17557i	0.115574	−	0.0839693i
$197$	27.5967			1.96619			0.983093	−	0.183105i	$-0.0586147\pi$
$197$	27.5967			1.96619			0.983093	+	0.183105i	$0.0586147\pi$
$198$	0.645898	−	1.08981i	0.0459020	−	0.0774497i
$199$	−1.29180			−0.0915730			−0.0457865	−	0.998951i	$-0.514579\pi$
$199$	−1.29180			−0.0915730			−0.0457865	+	0.998951i	$0.514579\pi$
$200$		0			0
$201$	−4.66312	−	14.3516i	−0.328911	−	1.01228i
$202$	−5.78115	+	17.7926i	−0.406761	+	1.25188i
$203$	0.954915	+	0.693786i	0.0670219	+	0.0486943i
$204$	−0.500000	−	0.363271i	−0.0350070	−	0.0254341i
$205$		0			0
$206$	−5.21885	−	16.0620i	−0.363614	−	1.11909i
$207$	−1.19098	+	0.865300i	−0.0827790	+	0.0601425i
$208$	−0.236068			−0.0163684
$209$	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	$0.466423\pi$
$212$	0.427051	+	1.31433i	0.0293300	+	0.0902684i
$213$	4.89919	−	15.0781i	0.335687	−	1.03314i
$214$	−6.61803	−	4.80828i	−0.452399	−	0.328687i
$215$		0			0
$216$	1.69098	−	5.20431i	0.115057	−	0.354108i
$217$	−7.07295	−	21.7683i	−0.480143	−	1.47773i
$218$	−9.39919	+	6.82891i	−0.636593	+	0.462512i
$219$	13.1803			0.890645
$220$		0			0
$221$	−0.0901699			−0.00606549
$222$	−11.5902	+	8.42075i	−0.777881	+	0.565164i
$223$	0.635255	+	1.95511i	0.0425398	+	0.130924i	0.970071	−	0.242822i	$-0.0780731\pi$
$223$	0.635255	+	1.95511i	0.0425398	+	0.130924i	−0.927531	+	0.373746i	$0.878073\pi$
$224$	−0.690983	+	2.12663i	−0.0461682	+	0.142091i
$225$		0			0
$226$	11.8992	+	8.64527i	0.791522	+	0.575074i
$227$	6.10081	−	18.7764i	0.404925	−	1.24623i	−0.516033	−	0.856569i	$-0.672592\pi$
$227$	6.10081	−	18.7764i	0.404925	−	1.24623i	0.920958	−	0.389663i	$-0.127408\pi$
$228$	1.30902	+	4.02874i	0.0866918	+	0.266810i
$229$	12.5172	−	9.09429i	0.827161	−	0.600968i	−0.0915935	−	0.995796i	$-0.529196\pi$
$229$	12.5172	−	9.09429i	0.827161	−	0.600968i	0.918755	+	0.394829i	$0.129196\pi$
$230$		0			0
$231$	11.7082	+	2.62866i	0.770343	+	0.172953i
$232$	0.527864			0.0346560
$233$	−16.4443	+	11.9475i	−1.07730	+	0.782704i	−0.977210	−	0.212274i	$-0.931913\pi$
$233$	−16.4443	+	11.9475i	−1.07730	+	0.782704i	−0.100090	+	0.994978i	$0.531913\pi$
$234$	−0.0278640	−	0.0857567i	−0.00182153	−	0.00560609i
$235$		0			0
$236$	9.28115	+	6.74315i	0.604152	+	0.438942i
$237$	15.6353	+	11.3597i	1.01562	+	0.737890i
$238$	−0.263932	+	0.812299i	−0.0171082	+	0.0526535i
$239$	−5.39919	−	16.6170i	−0.349244	−	1.07486i	−0.959272	−	0.282484i	$-0.908842\pi$
$239$	−5.39919	−	16.6170i	−0.349244	−	1.07486i	0.610028	−	0.792380i	$-0.291158\pi$
$240$		0			0
$241$	18.0000			1.15948			0.579741	−	0.814801i	$-0.303154\pi$
$241$	18.0000			1.15948			0.579741	+	0.814801i	$0.303154\pi$
$242$	10.8090	−	2.04087i	0.694830	−	0.131192i
$243$	3.94427			0.253025
$244$	−1.80902	+	1.31433i	−0.115810	+	0.0841412i
$245$		0			0
$246$	1.85410	−	5.70634i	0.118213	−	0.363823i
$247$	0.500000	+	0.363271i	0.0318142	+	0.0231144i
$248$	−8.28115	−	6.01661i	−0.525854	−	0.382055i
$249$	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	$0.348390\pi$
$252$	−0.854102			−0.0538034
$253$	−12.4721	−	2.80017i	−0.784116	−	0.176045i
$254$	2.90983			0.182579
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	4.28115	−	13.1760i	0.267051	−	0.821898i	−0.724163	−	0.689629i	$-0.757774\pi$
$257$	4.28115	−	13.1760i	0.267051	−	0.821898i	0.991214	−	0.132269i	$-0.0422264\pi$
$258$	−12.3992	−	9.00854i	−0.771940	−	0.560847i
$259$	16.0172	+	11.6372i	0.995262	+	0.723100i
$260$		0			0
$261$	0.0623059	+	0.191758i	0.00385664	+	0.0118695i
$262$	9.01722	−	6.55139i	0.557086	−	0.404747i
$263$	−16.0902			−0.992162			−0.496081	−	0.868276i	$-0.665228\pi$
$263$	−16.0902			−0.992162			−0.496081	+	0.868276i	$0.665228\pi$
$264$	4.92705	−	2.12663i	0.303239	−	0.130885i
$265$		0			0
$266$	4.73607	−	3.44095i	0.290387	−	0.210978i
$267$	−6.59017	−	20.2825i	−0.403312	−	1.24127i
$268$	−2.88197	+	8.86978i	−0.176044	+	0.541808i
$269$	−8.01722	−	5.82485i	−0.488819	−	0.355147i	0.315911	−	0.948789i	$-0.397690\pi$
$269$	−8.01722	−	5.82485i	−0.488819	−	0.355147i	−0.804730	+	0.593641i	$0.797690\pi$
$270$		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	$-0.223273\pi$
$272$	0.118034	+	0.363271i	0.00715686	+	0.0220266i
$273$	0.690983	−	0.502029i	0.0418202	−	0.0303841i
$274$	15.7639			0.952334
$275$		0			0
$276$	−6.23607			−0.375367
$277$	15.5623	−	11.3067i	0.935048	−	0.679352i	−0.0121753	−	0.999926i	$-0.503876\pi$
$277$	15.5623	−	11.3067i	0.935048	−	0.679352i	0.947224	+	0.320573i	$0.103876\pi$
$278$	0.881966	+	2.71441i	0.0528968	+	0.162800i
$279$	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	$0.457721\pi$
$282$	−0.118034	+	0.363271i	−0.00702882	+	0.0216325i
$283$	−6.79837	−	20.9232i	−0.404121	−	1.24376i	−0.921627	−	0.388078i	$-0.873139\pi$
$283$	−6.79837	−	20.9232i	−0.404121	−	1.24376i	0.517505	−	0.855680i	$-0.326861\pi$
$284$	−7.92705	+	5.75934i	−0.470384	+	0.341754i
$285$		0			0
$286$	0.399187	−	0.673542i	0.0236044	−	0.0398274i
$287$	−8.29180			−0.489449
$288$	−0.309017	+	0.224514i	−0.0182090	+	0.0132296i
$289$	−5.20820	−	16.0292i	−0.306365	−	0.942894i
$290$		0			0
$291$	−15.7082	−	11.4127i	−0.920831	−	0.669023i
$292$	−6.59017	−	4.78804i	−0.385661	−	0.280199i
$293$	−3.24671	+	9.99235i	−0.189675	+	0.583759i	−0.999998	−	0.00222470i	$-0.999292\pi$
$293$	−3.24671	+	9.99235i	−0.189675	+	0.583759i	0.810323	+	0.585984i	$0.199292\pi$
$294$	1.00000	+	3.07768i	0.0583212	+	0.179494i
$295$		0			0
$296$	8.85410			0.514634
$297$	11.9894	+	13.6251i	0.695693	+	0.790606i
$298$	10.7082			0.620310
$299$	−0.736068	+	0.534785i	−0.0425679	+	0.0309274i
$300$		0			0
$301$	−6.54508	+	20.1437i	−0.377252	+	1.16106i
$302$	−15.3992	−	11.1882i	−0.886124	−	0.643807i
$303$	−24.4894	−	17.7926i	−1.40688	−	1.02216i
$304$	0.809017	−	2.48990i	0.0464003	−	0.142805i
$305$		0			0
$306$	−0.118034	+	0.0857567i	−0.00674755	+	0.00490238i
$307$	28.7984			1.64361			0.821805	−	0.569769i	$-0.192967\pi$
$307$	28.7984			1.64361			0.821805	+	0.569769i	$0.192967\pi$
$308$	−4.89919	−	5.56758i	−0.279157	−	0.317242i
$309$	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	$0.861678\pi$
$312$	0.118034	−	0.363271i	0.00668236	−	0.0205662i
$313$	−0.809017	−	0.587785i	−0.0457283	−	0.0332236i	0.564686	−	0.825306i	$-0.308997\pi$
$313$	−0.809017	−	0.587785i	−0.0457283	−	0.0332236i	−0.610415	+	0.792082i	$0.708997\pi$
$314$	−5.47214	−	3.97574i	−0.308810	−	0.224364i
$315$		0			0
$316$	−3.69098	−	11.3597i	−0.207634	−	0.639032i
$317$	−2.26393	+	1.64484i	−0.127155	+	0.0923836i	−0.649545	−	0.760323i	$-0.725041\pi$
$317$	−2.26393	+	1.64484i	−0.127155	+	0.0923836i	0.522390	+	0.852707i	$0.325041\pi$
$318$	−2.23607			−0.125392
$319$	−0.892609	+	1.50609i	−0.0499765	+	0.0843246i
$320$		0			0
$321$	10.7082	−	7.77997i	0.597674	−	0.434235i
$322$	2.66312	+	8.19624i	0.148410	+	0.456758i
$323$	0.309017	−	0.951057i	0.0171942	−	0.0529182i
$324$	6.23607	+	4.53077i	0.346448	+	0.251709i
$325$		0			0
$326$	0.0557281	−	0.171513i	0.00308649	−	0.00949925i
$327$	−5.80902	−	17.8783i	−0.321239	−	0.988673i
$328$	−3.00000	+	2.17963i	−0.165647	+	0.120350i
$329$	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	$0.654187\pi$
$332$	−7.28115	+	5.29007i	−0.399605	+	0.290330i
$333$	1.04508	+	3.21644i	0.0572703	+	0.176260i
$334$	−0.690983	+	2.12663i	−0.0378089	+	0.116364i
$335$		0			0
$336$	−2.92705	−	2.12663i	−0.159684	−	0.116017i
$337$	−9.30902	+	28.6502i	−0.507094	+	1.56068i	0.290126	+	0.956988i	$0.406303\pi$
$337$	−9.30902	+	28.6502i	−0.507094	+	1.56068i	−0.797221	+	0.603688i	$0.793697\pi$
$338$	4.00000	+	12.3107i	0.217571	+	0.669616i
$339$	−19.2533	+	13.9883i	−1.04570	+	0.759742i
$340$		0			0
$341$	31.1697	−	13.4535i	1.68793	−	0.728550i
$342$	1.00000			0.0540738
$343$	16.2812	−	11.8290i	0.879100	−	0.638703i
$344$	2.92705	+	9.00854i	0.157816	+	0.485708i
$345$		0			0
$346$	10.7812	+	7.83297i	0.579598	+	0.421103i
$347$	15.2533	+	11.0822i	0.818839	+	0.594922i	0.916380	−	0.400310i	$-0.131098\pi$
$347$	15.2533	+	11.0822i	0.818839	+	0.594922i	−0.0975404	+	0.995232i	$0.531098\pi$
$348$	−0.263932	+	0.812299i	−0.0141482	+	0.0435438i
$349$	−7.29180	−	22.4418i	−0.390321	−	1.20128i	−0.932546	−	0.361051i	$-0.882418\pi$
$349$	−7.29180	−	22.4418i	−0.390321	−	1.20128i	0.542225	−	0.840233i	$-0.317582\pi$
$350$		0			0
$351$	1.29180			0.0689510
$352$	−3.23607	−	0.726543i	−0.172483	−	0.0387248i
$353$	4.43769			0.236195			0.118097	−	0.993002i	$-0.462321\pi$
$353$	4.43769			0.236195			0.118097	+	0.993002i	$0.462321\pi$
$354$	−15.0172	+	10.9106i	−0.798156	+	0.579894i
$355$		0			0
$356$	−4.07295	+	12.5352i	−0.215866	+	0.664367i
$357$	−1.11803	−	0.812299i	−0.0591726	−	0.0429914i
$358$	11.8541	+	8.61251i	0.626509	+	0.455185i
$359$	0.291796	−	0.898056i	0.0154004	−	0.0473976i	−0.943061	−	0.332620i	$-0.892067\pi$
$359$	0.291796	−	0.898056i	0.0154004	−	0.0473976i	0.958461	+	0.285222i	$0.0920674\pi$
$360$		0			0
$361$	9.82624	−	7.13918i	0.517170	−	0.375746i
$362$	7.05573			0.370841
$363$	−2.26393	+	17.6538i	−0.118826	+	0.926584i
$364$	−0.527864			−0.0276676
$365$		0			0
$366$	−1.11803	−	3.44095i	−0.0584406	−	0.179862i
$367$	−1.65248	+	5.08580i	−0.0862585	+	0.265476i	−0.984877	−	0.173254i	$-0.944572\pi$
$367$	−1.65248	+	5.08580i	−0.0862585	+	0.265476i	0.898619	+	0.438731i	$0.144572\pi$
$368$	3.11803	+	2.26538i	0.162539	+	0.118091i
$369$	−1.14590	−	0.832544i	−0.0596531	−	0.0433405i
$370$		0			0
$371$	0.954915	+	2.93893i	0.0495767	+	0.152581i
$372$	13.3992	−	9.73508i	0.694715	−	0.504740i
$373$	−2.38197			−0.123334			−0.0616668	−	0.998097i	$-0.519642\pi$
$373$	−2.38197			−0.123334			−0.0616668	+	0.998097i	$0.519642\pi$
$374$	−1.23607	−	0.277515i	−0.0639156	−	0.0143499i
$375$		0			0
$376$	0.190983	−	0.138757i	0.00984920	−	0.00715586i
$377$	0.0385072	+	0.118513i	0.00198322	+	0.00610372i
$378$	3.78115	−	11.6372i	0.194482	−	0.598553i
$379$	4.78115	+	3.47371i	0.245591	+	0.178433i	0.703771	−	0.710427i	$-0.251498\pi$
$379$	4.78115	+	3.47371i	0.245591	+	0.178433i	−0.458179	+	0.888860i	$0.651498\pi$
$380$		0			0
$381$	−1.45492	+	4.47777i	−0.0745376	+	0.229403i
$382$	6.13525	+	18.8824i	0.313907	+	0.966106i
$383$	−1.61803	+	1.17557i	−0.0826777	+	0.0600688i	−0.628356	−	0.777926i	$-0.716272\pi$
$383$	−1.61803	+	1.17557i	−0.0826777	+	0.0600688i	0.545679	+	0.837995i	$0.316272\pi$
$384$	−1.61803			−0.0825700
$385$		0			0
$386$	2.43769			0.124075
$387$	−2.92705	+	2.12663i	−0.148790	+	0.108103i
$388$	3.70820	+	11.4127i	0.188256	+	0.579391i
$389$	0.545085	−	1.67760i	0.0276369	−	0.0850576i	−0.936287	−	0.351237i	$-0.885761\pi$
$389$	0.545085	−	1.67760i	0.0276369	−	0.0850576i	0.963924	+	0.266179i	$0.0857612\pi$
$390$		0			0
$391$	1.19098	+	0.865300i	0.0602306	+	0.0437601i
$392$	0.618034	−	1.90211i	0.0312154	−	0.0960712i
$393$	5.57295	+	17.1518i	0.281118	+	0.865193i
$394$	22.3262	−	16.2210i	1.12478	−	0.817200i
$395$		0			0
$396$	−0.118034	−	1.26133i	−0.00593143	−	0.0633841i
$397$	17.4721			0.876901			0.438451	−	0.898755i	$-0.355527\pi$
$397$	17.4721			0.876901			0.438451	+	0.898755i	$0.355527\pi$
$398$	−1.04508	+	0.759299i	−0.0523854	+	0.0380602i
$399$	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	$0.684815\pi$
$402$	−12.2082	−	8.86978i	−0.608890	−	0.442384i
$403$	0.746711	−	2.29814i	0.0371963	−	0.114479i
$404$	5.78115	+	17.7926i	0.287623	+	0.885213i
$405$		0			0
$406$	1.18034			0.0585793
$407$	−14.9721	+	25.2623i	−0.742141	+	1.25220i
$408$	−0.618034			−0.0305972
$409$	−14.9721	+	10.8779i	−0.740324	+	0.537877i	−0.892813	−	0.450428i	$-0.851271\pi$
$409$	−14.9721	+	10.8779i	−0.740324	+	0.537877i	0.152488	+	0.988305i	$0.451271\pi$
$410$		0			0
$411$	−7.88197	+	24.2582i	−0.388789	+	1.19657i
$412$	−13.6631	−	9.92684i	−0.673134	−	0.489060i
$413$	20.7533	+	15.0781i	1.02120	+	0.741947i
$414$	−0.454915	+	1.40008i	−0.0223579	+	0.0688104i
$415$		0			0
$416$	−0.190983	+	0.138757i	−0.00936371	+	0.00680314i
$417$	−4.61803			−0.226146
$418$	5.73607	+	6.51864i	0.280560	+	0.318837i
$419$	−31.1803			−1.52326			−0.761630	−	0.648013i	$-0.775600\pi$
$419$	−31.1803			−1.52326			−0.761630	+	0.648013i	$0.775600\pi$
$420$		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	$-0.241727\pi$
$422$	−4.48278	+	13.7966i	−0.218218	+	0.671607i
$423$	0.0729490	+	0.0530006i	0.00354690	+	0.00257698i
$424$	1.11803	+	0.812299i	0.0542965	+	0.0394487i
$425$		0			0
$426$	−4.89919	−	15.0781i	−0.237366	−	0.730539i
$427$	−4.04508	+	2.93893i	−0.195755	+	0.142225i
$428$	−8.18034			−0.395412
$429$	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	$0.345727\pi$
$432$	−1.69098	−	5.20431i	−0.0813575	−	0.250393i
$433$	2.61803	−	8.05748i	0.125815	−	0.387218i	−0.868234	−	0.496155i	$-0.834745\pi$
$433$	2.61803	−	8.05748i	0.125815	−	0.387218i	0.994049	+	0.108937i	$0.0347448\pi$
$434$	−18.5172	−	13.4535i	−0.888855	−	0.645791i
$435$		0			0
$436$	−3.59017	+	11.0494i	−0.171938	+	0.529171i
$437$	−3.11803	−	9.59632i	−0.149156	−	0.459054i
$438$	10.6631	−	7.74721i	0.509504	−	0.370176i
$439$	22.7082			1.08380			0.541902	−	0.840442i	$-0.317704\pi$
$439$	22.7082			1.08380			0.541902	+	0.840442i	$0.317704\pi$
$440$		0			0
$441$	0.763932			0.0363777
$442$	−0.0729490	+	0.0530006i	−0.00346983	+	0.00252098i
$443$	9.42705	+	29.0135i	0.447893	+	1.37847i	0.879280	+	0.476305i	$0.158024\pi$
$443$	9.42705	+	29.0135i	0.447893	+	1.37847i	−0.431387	+	0.902167i	$0.641976\pi$
$444$	−4.42705	+	13.6251i	−0.210099	+	0.646617i
$445$		0			0
$446$	1.66312	+	1.20833i	0.0787510	+	0.0572159i
$447$	−5.35410	+	16.4782i	−0.253240	+	0.779394i
$448$	0.690983	+	2.12663i	0.0326459	+	0.100474i
$449$	−13.1803	+	9.57608i	−0.622019	+	0.451923i	−0.853626	−	0.520886i	$-0.825602\pi$
$449$	−13.1803	+	9.57608i	−0.622019	+	0.451923i	0.231607	+	0.972809i	$0.425602\pi$
$450$		0			0
$451$	−1.14590	−	12.2452i	−0.0539582	−	0.576605i
$452$	14.7082			0.691816
$453$	24.9164	−	18.1028i	1.17067	−	0.850545i
$454$	−6.10081	−	18.7764i	−0.286325	−	0.881219i
$455$		0			0
$456$	3.42705	+	2.48990i	0.160486	+	0.116600i
$457$	−9.80902	−	7.12667i	−0.458846	−	0.333371i	0.334232	−	0.942491i	$-0.391523\pi$
$457$	−9.80902	−	7.12667i	−0.458846	−	0.333371i	−0.793079	+	0.609119i	$0.791523\pi$
$458$	4.78115	−	14.7149i	0.223409	−	0.687581i
$459$	−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	$0.822218\pi$
$462$	11.0172	−	4.75528i	0.512568	−	0.221236i
$463$	38.5967			1.79374			0.896871	−	0.442291i	$-0.145834\pi$
$463$	38.5967			1.79374			0.896871	+	0.442291i	$0.145834\pi$
$464$	0.427051	−	0.310271i	0.0198253	−	0.0144040i
$465$		0			0
$466$	−6.28115	+	19.3314i	−0.290969	+	0.895510i
$467$	−26.0344	−	18.9151i	−1.20473	−	0.875288i	−0.209989	−	0.977704i	$-0.567343\pi$
$467$	−26.0344	−	18.9151i	−1.20473	−	0.875288i	−0.994742	+	0.102416i	$0.967343\pi$
$468$	−0.0729490	−	0.0530006i	−0.00337207	−	0.00244995i
$469$	−6.44427	+	19.8334i	−0.297569	+	0.915823i
$470$		0			0
$471$	8.85410	−	6.43288i	0.407975	−	0.296412i
$472$	11.4721			0.528048
$473$	−30.6525	−	6.88191i	−1.40940	−	0.316431i
$474$	19.3262			0.887684
$475$		0			0
$476$	0.263932	+	0.812299i	0.0120973	+	0.0372317i
$477$	−0.163119	+	0.502029i	−0.00746870	+	0.0229863i
$478$	−14.1353	−	10.2699i	−0.646532	−	0.469733i
$479$	−8.04508	−	5.84510i	−0.367589	−	0.267069i	0.388621	−	0.921398i	$-0.372951\pi$
$479$	−8.04508	−	5.84510i	−0.367589	−	0.267069i	−0.756211	+	0.654328i	$0.772951\pi$
$480$		0			0
$481$	0.645898	+	1.98787i	0.0294504	+	0.0906391i
$482$	14.5623	−	10.5801i	0.663295	−	0.481912i
$483$	−13.9443			−0.634486
$484$	7.54508	−	8.00448i	0.342958	−	0.363840i
$485$		0			0
$486$	3.19098	−	2.31838i	0.144746	−	0.105164i
$487$	3.36475	+	10.3556i	0.152471	+	0.469258i	0.997896	−	0.0648366i	$-0.0206526\pi$
$487$	3.36475	+	10.3556i	0.152471	+	0.469258i	−0.845425	+	0.534095i	$0.820653\pi$
$488$	−0.690983	+	2.12663i	−0.0312793	+	0.0962679i
$489$	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	$0.0113733\pi$
$492$	−1.85410	−	5.70634i	−0.0835894	−	0.257262i
$493$	0.163119	−	0.118513i	0.00734651	−	0.00533755i
$494$	0.618034			0.0278067
$495$		0			0
$496$	−10.2361			−0.459613
$497$	−17.7254	+	12.8783i	−0.795094	+	0.577670i
$498$	−4.50000	−	13.8496i	−0.201650	−	0.620614i
$499$	4.77458	−	14.6946i	0.213739	−	0.657822i	−0.785501	−	0.618860i	$-0.787595\pi$
$499$	4.77458	−	14.6946i	0.213739	−	0.657822i	0.999241	−	0.0389621i	$-0.0124052\pi$
$500$		0			0
$501$	−2.92705	−	2.12663i	−0.130771	−	0.0950107i
$502$	−1.48278	+	4.56352i	−0.0661797	+	0.203680i
$503$	−9.73607	−	29.9645i	−0.434110	−	1.33605i	−0.893996	−	0.448075i	$-0.852110\pi$
$503$	−9.73607	−	29.9645i	−0.434110	−	1.33605i	0.459886	−	0.887978i	$-0.347890\pi$
$504$	−0.690983	+	0.502029i	−0.0307788	+	0.0223621i
$505$		0			0
$506$	−11.7361	+	5.06555i	−0.521732	+	0.225191i
$507$	−20.9443			−0.930168
$508$	2.35410	−	1.71036i	0.104446	−	0.0758847i
$509$	3.17376	+	9.76784i	0.140675	+	0.432952i	0.996429	−	0.0844297i	$-0.0269069\pi$
$509$	3.17376	+	9.76784i	0.140675	+	0.432952i	−0.855755	+	0.517381i	$0.826907\pi$
$510$		0			0
$511$	−14.7361	−	10.7064i	−0.651885	−	0.473622i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−4.42705	+	13.6251i	−0.195459	+	0.601561i
$514$	−4.28115	−	13.1760i	−0.188834	−	0.581170i
$515$		0			0
$516$	−15.3262			−0.674700
$517$	0.0729490	+	0.779543i	0.00320829	+	0.0342843i
$518$	19.7984			0.869891
$519$	−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	$0.170543\pi$
$522$	0.163119	+	0.118513i	0.00713952	+	0.00518717i
$523$	22.2533	+	16.1680i	0.973068	+	0.706976i	0.956149	−	0.292881i	$-0.0946141\pi$
$523$	22.2533	+	16.1680i	0.973068	+	0.706976i	0.0169196	+	0.999857i	$0.494614\pi$
$524$	3.44427	−	10.6004i	0.150464	−	0.463080i
$525$		0			0
$526$	−13.0172	+	9.45756i	−0.567578	+	0.412369i
$527$	−3.90983			−0.170315
$528$	2.73607	−	4.61653i	0.119072	−	0.200908i
$529$	−8.14590			−0.354169
$530$		0			0
$531$	1.35410	+	4.16750i	0.0587630	+	0.180854i
$532$	1.80902	−	5.56758i	0.0784308	−	0.241385i
$533$	−0.708204	−	0.514540i	−0.0306757	−	0.0222872i
$534$	−17.2533	−	12.5352i	−0.746623	−	0.542453i
$535$		0			0
$536$	2.88197	+	8.86978i	0.124482	+	0.383116i
$537$	−19.1803	+	13.9353i	−0.827693	+	0.601354i
$538$	−9.90983			−0.427243
$539$	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	$0.542843\pi$
$542$	−8.64590	−	26.6093i	−0.371373	−	1.14297i
$543$	−3.52786	+	10.8576i	−0.151395	+	0.465946i
$544$	0.309017	+	0.224514i	0.0132490	+	0.00962596i
$545$		0			0
$546$	0.263932	−	0.812299i	0.0112952	−	0.0347632i
$547$	−5.54508	−	17.0660i	−0.237091	−	0.729690i	−0.996837	−	0.0794708i	$-0.974677\pi$
$547$	−5.54508	−	17.0660i	−0.237091	−	0.729690i	0.759746	−	0.650219i	$-0.225323\pi$
$548$	12.7533	−	9.26581i	0.544794	−	0.395816i
$549$	−0.854102			−0.0364522
$550$		0			0
$551$	−1.38197			−0.0588737
$552$	−5.04508	+	3.66547i	−0.214733	+	0.156013i
$553$	−8.25329	−	25.4010i	−0.350966	−	1.08016i
$554$	5.94427	−	18.2946i	0.252548	−	0.777263i
$555$		0			0
$556$	2.30902	+	1.67760i	0.0979241	+	0.0711460i
$557$	1.81966	−	5.60034i	0.0771015	−	0.237294i	−0.905076	−	0.425250i	$-0.860186\pi$
$557$	1.81966	−	5.60034i	0.0771015	−	0.237294i	0.982177	+	0.187956i	$0.0601862\pi$
$558$	−1.20820	−	3.71847i	−0.0511474	−	0.157415i
$559$	−1.80902	+	1.31433i	−0.0765133	+	0.0555901i
$560$		0			0
$561$	1.04508	−	1.76336i	0.0441235	−	0.0744489i
$562$	23.1246			0.975453
$563$	14.2533	−	10.3556i	0.600705	−	0.436437i	−0.245424	−	0.969416i	$-0.578927\pi$
$563$	14.2533	−	10.3556i	0.600705	−	0.436437i	0.846129	+	0.532978i	$0.178927\pi$
$564$	0.118034	+	0.363271i	0.00497013	+	0.0152965i
$565$		0			0
$566$	−17.7984	−	12.9313i	−0.748121	−	0.543542i
$567$	13.9443	+	10.1311i	0.585604	+	0.425466i
$568$	−3.02786	+	9.31881i	−0.127046	+	0.391008i
$569$	−0.645898	−	1.98787i	−0.0270775	−	0.0833358i	0.936605	−	0.350388i	$-0.113950\pi$
$569$	−0.645898	−	1.98787i	−0.0270775	−	0.0833358i	−0.963682	+	0.267052i	$0.913950\pi$
$570$		0			0
$571$	−8.52786			−0.356880			−0.178440	−	0.983951i	$-0.557105\pi$
$571$	−8.52786			−0.356880			−0.178440	+	0.983951i	$0.557105\pi$
$572$	−0.0729490	−	0.779543i	−0.00305015	−	0.0325943i
$573$	−32.1246			−1.34202
$574$	−6.70820	+	4.87380i	−0.279995	+	0.203428i
$575$		0			0
$576$	−0.118034	+	0.363271i	−0.00491808	+	0.0151363i
$577$	−17.6074	−	12.7925i	−0.733005	−	0.532560i	0.157507	−	0.987518i	$-0.449654\pi$
$577$	−17.6074	−	12.7925i	−0.733005	−	0.532560i	−0.890513	+	0.454958i	$0.849654\pi$
$578$	−13.6353	−	9.90659i	−0.567152	−	0.412060i
$579$	−1.21885	+	3.75123i	−0.0506536	+	0.155896i
$580$		0			0
$581$	−16.2812	+	11.8290i	−0.675456	+	0.490748i
$582$	−19.4164			−0.804836
$583$	−4.20820	+	1.81636i	−0.174286	+	0.0752258i
$584$	−8.14590			−0.337080
$585$		0			0
$586$	3.24671	+	9.99235i	0.134120	+	0.412780i
$587$	−5.01064	+	15.4212i	−0.206811	+	0.636500i	0.792823	+	0.609452i	$0.208611\pi$
$587$	−5.01064	+	15.4212i	−0.206811	+	0.636500i	−0.999634	+	0.0270477i	$0.991389\pi$
$588$	2.61803	+	1.90211i	0.107966	+	0.0784418i
$589$	21.6803	+	15.7517i	0.893323	+	0.649037i
$590$		0			0
$591$	13.7984	+	42.4670i	0.567589	+	1.74686i
$592$	7.16312	−	5.20431i	0.294402	−	0.213896i
$593$	42.3951			1.74096			0.870479	−	0.492205i	$-0.163809\pi$
$593$	42.3951			1.74096			0.870479	+	0.492205i	$0.163809\pi$
$594$	17.7082	+	3.97574i	0.726576	+	0.163127i
$595$		0			0
$596$	8.66312	−	6.29412i	0.354855	−	0.257817i
$597$	−0.645898	−	1.98787i	−0.0264348	−	0.0813581i
$598$	−0.281153	+	0.865300i	−0.0114972	+	0.0353847i
$599$	−2.47214	−	1.79611i	−0.101009	−	0.0733871i	0.536134	−	0.844133i	$-0.319884\pi$
$599$	−2.47214	−	1.79611i	−0.101009	−	0.0733871i	−0.637143	+	0.770745i	$0.719884\pi$
$600$		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	$0.142731\pi$
$602$	6.54508	+	20.1437i	0.266758	+	0.820996i
$603$	−2.88197	+	2.09387i	−0.117363	+	0.0852690i
$604$	−19.0344			−0.774500
$605$		0			0
$606$	−30.2705			−1.22966
$607$	10.8262	−	7.86572i	0.439423	−	0.319260i	−0.345982	−	0.938241i	$-0.612454\pi$
$607$	10.8262	−	7.86572i	0.439423	−	0.319260i	0.785406	+	0.618981i	$0.212454\pi$
$608$	−0.809017	−	2.48990i	−0.0328100	−	0.100979i
$609$	−0.590170	+	1.81636i	−0.0239149	+	0.0736025i
$610$		0			0
$611$	0.0450850	+	0.0327561i	0.00182394	+	0.00132517i
$612$	−0.0450850	+	0.138757i	−0.00182245	+	0.00560893i
$613$	2.21885	+	6.82891i	0.0896184	+	0.275817i	0.985814	−	0.167842i	$-0.0536800\pi$
$613$	2.21885	+	6.82891i	0.0896184	+	0.275817i	−0.896195	+	0.443659i	$0.853680\pi$
$614$	23.2984	−	16.9273i	0.940246	−	0.683129i
$615$		0			0
$616$	−7.23607	−	1.62460i	−0.291549	−	0.0654569i
$617$	−25.7984			−1.03860			−0.519302	−	0.854591i	$-0.673808\pi$
$617$	−25.7984			−1.03860			−0.519302	+	0.854591i	$0.673808\pi$
$618$	22.1074	−	16.0620i	0.889290	−	0.646107i
$619$	−8.10739	−	24.9520i	−0.325864	−	1.00290i	−0.971049	−	0.238879i	$-0.923220\pi$
$619$	−8.10739	−	24.9520i	−0.325864	−	1.00290i	0.645186	−	0.764026i	$-0.276780\pi$
$620$		0			0
$621$	−17.0623	−	12.3965i	−0.684687	−	0.497454i
$622$	3.42705	+	2.48990i	0.137412	+	0.0998358i
$623$	−9.10739	+	28.0297i	−0.364880	+	1.12298i
$624$	−0.118034	−	0.363271i	−0.00472514	−	0.0145425i
$625$		0			0
$626$	−1.00000			−0.0399680
$627$	−12.8992	+	5.56758i	−0.515144	+	0.222348i
$628$	−6.76393			−0.269910
$629$	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	$0.142630\pi$
$632$	−9.66312	−	7.02067i	−0.384378	−	0.279267i
$633$	−18.9894	−	13.7966i	−0.754759	−	0.548365i
$634$	−0.864745	+	2.66141i	−0.0343434	+	0.105698i
$635$		0			0
$636$	−1.80902	+	1.31433i	−0.0717322	+	0.0521165i
$637$	0.472136			0.0187067
$638$	0.163119	+	1.74311i	0.00645794	+	0.0690104i
$639$	−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	$-0.412123\pi$
$642$	4.09017	−	12.5882i	0.161426	−	0.496819i
$643$	−11.4271	−	8.30224i	−0.450639	−	0.327408i	0.339209	−	0.940711i	$-0.389841\pi$
$643$	−11.4271	−	8.30224i	−0.450639	−	0.327408i	−0.789848	+	0.613303i	$0.789841\pi$
$644$	6.97214	+	5.06555i	0.274741	+	0.199611i
$645$		0			0
$646$	−0.309017	−	0.951057i	−0.0121581	−	0.0374188i
$647$	−0.854102	+	0.620541i	−0.0335782	+	0.0243960i	−0.604448	−	0.796645i	$-0.706606\pi$
$647$	−0.854102	+	0.620541i	−0.0335782	+	0.0243960i	0.570870	+	0.821041i	$0.306606\pi$
$648$	7.70820			0.302807
$649$	−19.3992	+	32.7319i	−0.761485	+	1.28484i
$650$		0			0
$651$	29.9615	−	21.7683i	1.17428	−	0.853167i
$652$	−0.0557281	−	0.171513i	−0.00218248	−	0.00671698i
$653$	3.23607	−	9.95959i	0.126637	−	0.389749i	−0.867559	−	0.497335i	$-0.834312\pi$
$653$	3.23607	−	9.95959i	0.126637	−	0.389749i	0.994196	+	0.107586i	$0.0343121\pi$
$654$	−15.2082	−	11.0494i	−0.594688	−	0.432066i
$655$		0			0
$656$	−1.14590	+	3.52671i	−0.0447398	+	0.137695i
$657$	−0.961493	−	2.95917i	−0.0375114	−	0.115448i
$658$	0.427051	−	0.310271i	0.0166482	−	0.0120956i
$659$	43.4508			1.69260			0.846302	−	0.532703i	$-0.178824\pi$
$659$	43.4508			1.69260			0.846302	+	0.532703i	$0.178824\pi$
$660$		0			0
$661$	27.5967			1.07339			0.536695	−	0.843777i	$-0.319673\pi$
$661$	27.5967			1.07339			0.536695	+	0.843777i	$0.319673\pi$
$662$	−13.7082	+	9.95959i	−0.532784	+	0.387091i
$663$	−0.0450850	−	0.138757i	−0.00175096	−	0.00538889i
$664$	−2.78115	+	8.55951i	−0.107930	+	0.332173i
$665$		0			0
$666$	2.73607	+	1.98787i	0.106020	+	0.0770284i
$667$	0.628677	−	1.93487i	0.0243425	−	0.0749184i
$668$	0.690983	+	2.12663i	0.0267349	+	0.0822817i
$669$	−2.69098	+	1.95511i	−0.104039	+	0.0755891i
$670$		0			0
$671$	−4.89919	−	5.56758i	−0.189131	−	0.214934i
$672$	−3.61803			−0.139569
$673$	−9.37132	+	6.80866i	−0.361238	+	0.262455i	−0.753568	−	0.657370i	$-0.771669\pi$
$673$	−9.37132	+	6.80866i	−0.361238	+	0.262455i	0.392330	+	0.919824i	$0.371669\pi$
$674$	9.30902	+	28.6502i	0.358570	+	1.10356i
$675$		0			0
$676$	10.4721	+	7.60845i	0.402774	+	0.292633i
$677$	8.76393	+	6.36737i	0.336825	+	0.244718i	0.743321	−	0.668935i	$-0.233249\pi$
$677$	8.76393	+	6.36737i	0.336825	+	0.244718i	−0.406496	+	0.913653i	$0.633249\pi$
$678$	−7.35410	+	22.6336i	−0.282433	+	0.869238i
$679$	8.29180	+	25.5195i	0.318210	+	0.979349i
$680$		0			0
$681$	31.9443			1.22411
$682$	17.3090	−	29.2052i	0.662797	−	1.11833i
$683$	−6.11146			−0.233848			−0.116924	−	0.993141i	$-0.537303\pi$
$683$	−6.11146			−0.233848			−0.116924	+	0.993141i	$0.537303\pi$
$684$	0.809017	−	0.587785i	0.0309335	−	0.0224745i
$685$		0			0
$686$	6.21885	−	19.1396i	0.237437	−	0.730755i
$687$	20.2533	+	14.7149i	0.772711	+	0.561408i
$688$	7.66312	+	5.56758i	0.292154	+	0.212262i
$689$	−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	$0.0255068\pi$
$692$	13.3262			0.506588
$693$	−0.263932	−	2.82041i	−0.0100259	−	0.107139i
$694$	18.8541			0.715692
$695$		0			0
$696$	0.263932	+	0.812299i	0.0100043	+	0.0307901i
$697$	−0.437694	+	1.34708i	−0.0165788	+	0.0510244i
$698$	−19.0902	−	13.8698i	−0.722574	−	0.524980i
$699$	−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	$0.976586\pi$
$702$	1.04508	−	0.759299i	0.0394442	−	0.0286579i
$703$	−23.1803			−0.874263
$704$	−3.04508	+	1.31433i	−0.114766	+	0.0495356i
$705$		0			0
$706$	3.59017	−	2.60841i	0.135118	−	0.0981688i
$707$	12.9271	+	39.7854i	0.486172	+	1.49628i
$708$	−5.73607	+	17.6538i	−0.215575	+	0.663471i
$709$	37.3156	+	27.1114i	1.40142	+	1.01819i	0.994501	+	0.104723i	$0.0333955\pi$
$709$	37.3156	+	27.1114i	1.40142	+	1.01819i	0.406915	+	0.913466i	$0.366604\pi$
$710$		0			0
$711$	1.40983	−	4.33901i	0.0528728	−	0.162726i
$712$	4.07295	+	12.5352i	0.152640	+	0.469778i
$713$	−31.9164	+	23.1886i	−1.19528	+	0.868421i
$714$	−1.38197			−0.0517188
$715$		0			0
$716$	14.6525			0.547589
$717$	22.8713	−	16.6170i	0.854145	−	0.620573i
$718$	−0.291796	−	0.898056i	−0.0108897	−	0.0335152i
$719$	6.16312	−	18.9681i	0.229846	−	0.707392i	−0.767918	−	0.640548i	$-0.778707\pi$
$719$	6.16312	−	18.9681i	0.229846	−	0.707392i	0.997763	−	0.0668436i	$-0.0212929\pi$
$720$		0			0
$721$	−30.5517	−	22.1971i	−1.13780	−	0.826663i
$722$	3.75329	−	11.5514i	0.139683	−	0.429900i
$723$	9.00000	+	27.6992i	0.334714	+	1.03014i
$724$	5.70820	−	4.14725i	0.212144	−	0.154131i
$725$		0			0
$726$	8.54508	+	15.6129i	0.317138	+	0.579450i
$727$	13.8197			0.512543			0.256271	−	0.966605i	$-0.417506\pi$
$727$	13.8197			0.512543			0.256271	+	0.966605i	$0.417506\pi$
$728$	−0.427051	+	0.310271i	−0.0158276	+	0.0114994i
$729$	9.11803	+	28.0624i	0.337705	+	1.03935i
$730$		0			0
$731$	2.92705	+	2.12663i	0.108261	+	0.0786561i
$732$	−2.92705	−	2.12663i	−0.108187	−	0.0786024i
$733$	6.74671	−	20.7642i	0.249195	−	0.766945i	−0.745723	−	0.666257i	$-0.767896\pi$
$733$	6.74671	−	20.7642i	0.249195	−	0.766945i	0.994918	−	0.100688i	$-0.0321044\pi$
$734$	1.65248	+	5.08580i	0.0609940	+	0.187720i
$735$		0			0
$736$	3.85410			0.142064
$737$	−30.1803	−	6.77591i	−1.11171	−	0.249594i
$738$	−1.41641			−0.0521387
$739$	−7.85410	+	5.70634i	−0.288918	+	0.209911i	−0.722798	−	0.691060i	$-0.757144\pi$
$739$	−7.85410	+	5.70634i	−0.288918	+	0.209911i	0.433880	+	0.900971i	$0.357144\pi$
$740$		0			0
$741$	−0.309017	+	0.951057i	−0.0113520	+	0.0349379i
$742$	2.50000	+	1.81636i	0.0917779	+	0.0666805i
$743$	34.4058	+	24.9973i	1.26223	+	0.917060i	0.998865	−	0.0476373i	$-0.0151692\pi$
$743$	34.4058	+	24.9973i	1.26223	+	0.917060i	0.263360	+	0.964698i	$0.415169\pi$
$744$	5.11803	−	15.7517i	0.187636	−	0.577485i
$745$		0			0
$746$	−1.92705	+	1.40008i	−0.0705543	+	0.0512607i
$747$	−3.43769			−0.125779
$748$	−1.16312	+	0.502029i	−0.0425278	+	0.0183560i
$749$	−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	$0.736640\pi$
$752$	0.0729490	−	0.224514i	0.00266018	−	0.00818718i
$753$	−6.28115	−	4.56352i	−0.228898	−	0.166304i
$754$	0.100813	+	0.0732450i	0.00367140	+	0.00266742i
$755$		0			0
$756$	−3.78115	−	11.6372i	−0.137519	−	0.423241i
$757$	−12.3090	+	8.94302i	−0.447379	+	0.325040i	−0.788560	−	0.614958i	$-0.789173\pi$
$757$	−12.3090	+	8.94302i	−0.447379	+	0.325040i	0.341181	+	0.939998i	$0.389173\pi$
$758$	5.90983			0.214655
$759$	−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	$0.173886\pi$
$762$	1.45492	+	4.47777i	0.0527060	+	0.162212i
$763$	−8.02786	+	24.7072i	−0.290628	+	0.894462i
$764$	16.0623	+	11.6699i	0.581114	+	0.422204i
$765$		0			0
$766$	−0.618034	+	1.90211i	−0.0223305	+	0.0687261i
$767$	0.836881	+	2.57565i	0.0302180	+	0.0930015i
$768$	−1.30902	+	0.951057i	−0.0472351	+	0.0343183i
$769$	−42.2361			−1.52307			−0.761536	−	0.648123i	$-0.775554\pi$
$769$	−42.2361			−1.52307			−0.761536	+	0.648123i	$0.775554\pi$
$770$		0			0
$771$	22.4164			0.807307
$772$	1.97214	−	1.43284i	0.0709787	−	0.0515691i
$773$	−12.7984	−	39.3893i	−0.460326	−	1.41674i	−0.864767	−	0.502173i	$-0.832534\pi$
$773$	−12.7984	−	39.3893i	−0.460326	−	1.41674i	0.404442	−	0.914564i	$-0.367466\pi$
$774$	−1.11803	+	3.44095i	−0.0401869	+	0.123683i
$775$		0			0
$776$	9.70820	+	7.05342i	0.348504	+	0.253203i
$777$	−9.89919	+	30.4666i	−0.355131	+	1.09298i
$778$	−0.545085	−	1.67760i	−0.0195422	−	0.0601448i
$779$	7.85410	−	5.70634i	0.281402	−	0.204451i
$780$		0			0
$781$	−21.4681	−	24.3970i	−0.768188	−	0.872992i
$782$	1.47214			0.0526435
$783$	−2.33688	+	1.69784i	−0.0835133	+	0.0606760i
$784$	−0.618034	−	1.90211i	−0.0220726	−	0.0679326i
$785$		0			0
$786$	14.5902	+	10.6004i	0.520414	+	0.378103i
$787$	14.5623	+	10.5801i	0.519090	+	0.377141i	0.816261	−	0.577683i	$-0.196043\pi$
$787$	14.5623	+	10.5801i	0.519090	+	0.377141i	−0.297171	+	0.954824i	$0.596043\pi$
$788$	8.52786	−	26.2461i	0.303793	−	0.934977i
$789$	−8.04508	−	24.7602i	−0.286413	−	0.881487i
$790$		0			0
$791$	32.8885			1.16938
$792$	−0.836881	−	0.951057i	−0.0297373	−	0.0337943i
$793$	−0.527864			−0.0187450
$794$	14.1353	−	10.2699i	0.501641	−	0.364464i
$795$		0			0
$796$	−0.399187	+	1.22857i	−0.0141488	+	0.0435455i
$797$	40.4615	+	29.3970i	1.43322	+	1.04129i	0.989406	+	0.145176i	$0.0463748\pi$
$797$	40.4615	+	29.3970i	1.43322	+	1.04129i	0.443814	+	0.896119i	$0.353625\pi$
$798$	7.66312	+	5.56758i	0.271271	+	0.197090i
$799$	0.0278640	−	0.0857567i	0.000985759	−	0.00303385i
$800$		0			0
$801$	−4.07295	+	2.95917i	−0.143911	+	0.104557i
$802$	1.90983			0.0674384
$803$	13.7746	−	23.2416i	0.486094	−	0.820179i
$804$	−15.0902			−0.532189
$805$		0			0
$806$	−0.746711	−	2.29814i	−0.0263018	−	0.0809485i
$807$	4.95492	−	15.2497i	0.174421	−	0.536813i
$808$	15.1353	+	10.9964i	0.532456	+	0.386852i
$809$	−26.7533	−	19.4374i	−0.940596	−	0.683383i	0.00796840	−	0.999968i	$-0.497464\pi$
$809$	−26.7533	−	19.4374i	−0.940596	−	0.683383i	−0.948564	+	0.316586i	$0.897464\pi$
$810$		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	$0.822950\pi$
$812$	0.954915	−	0.693786i	0.0335109	−	0.0243471i
$813$	45.2705			1.58771
$814$	2.73607	+	29.2380i	0.0958991	+	1.02479i
$815$		0			0
$816$	−0.500000	+	0.363271i	−0.0175035	+	0.0127170i
$817$	−7.66312	−	23.5847i	−0.268099	−	0.825123i
$818$	−5.71885	+	17.6008i	−0.199955	+	0.615398i
$819$	−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	$0.858994\pi$
$822$	7.88197	+	24.2582i	0.274915	+	0.846102i
$823$	1.79180	−	1.30182i	0.0624581	−	0.0453785i	−0.556118	−	0.831103i	$-0.687710\pi$
$823$	1.79180	−	1.30182i	0.0624581	−	0.0453785i	0.618576	+	0.785725i	$0.287710\pi$
$824$	−16.8885			−0.588340
$825$		0			0
$826$	25.6525			0.892564
$827$	18.3713	−	13.3475i	0.638833	−	0.464140i	−0.220616	−	0.975361i	$-0.570807\pi$
$827$	18.3713	−	13.3475i	0.638833	−	0.464140i	0.859449	+	0.511221i	$0.170807\pi$
$828$	0.454915	+	1.40008i	0.0158094	+	0.0486563i
$829$	11.4377	−	35.2016i	0.397248	−	1.22260i	−0.529950	−	0.848029i	$-0.677789\pi$
$829$	11.4377	−	35.2016i	0.397248	−	1.22260i	0.927197	−	0.374573i	$-0.122211\pi$
$830$		0			0
$831$	25.1803	+	18.2946i	0.873496	+	0.634632i
$832$	−0.0729490	+	0.224514i	−0.00252905	+	0.00778362i
$833$	−0.236068	−	0.726543i	−0.00817927	−	0.0251732i
$834$	−3.73607	+	2.71441i	−0.129369	+	0.0939924i
$835$		0			0
$836$	8.47214	+	1.90211i	0.293015	+	0.0657860i
$837$	56.0132			1.93610
$838$	−25.2254	+	18.3273i	−0.871398	+	0.633108i
$839$	−9.03851	−	27.8177i	−0.312044	−	0.960372i	−0.976954	−	0.213449i	$-0.931530\pi$
$839$	−9.03851	−	27.8177i	−0.312044	−	0.960372i	0.664910	−	0.746923i	$-0.268470\pi$
$840$		0			0
$841$	23.2361	+	16.8820i	0.801244	+	0.582138i
$842$	−14.2984	−	10.3884i	−0.492755	−	0.358007i
$843$	−11.5623	+	35.5851i	−0.398227	+	1.22562i
$844$	4.48278	+	13.7966i	0.154304	+	0.474898i
$845$		0			0
$846$	0.0901699			0.00310011
$847$	16.8713	−	17.8986i	0.579706	−	0.615002i
$848$	1.38197			0.0474569
$849$	28.7984	−	20.9232i	0.988358	−	0.718084i
$850$		0			0
$851$	10.5451	−	32.4544i	0.361481	−	1.11252i
$852$	−12.8262	−	9.31881i	−0.439420	−	0.319257i
$853$	−2.70820	−	1.96763i	−0.0927271	−	0.0673702i	0.540456	−	0.841372i	$-0.318252\pi$
$853$	−2.70820	−	1.96763i	−0.0927271	−	0.0673702i	−0.633183	+	0.774002i	$0.718252\pi$
$854$	−1.54508	+	4.75528i	−0.0528717	+	0.162722i
$855$		0			0
$856$	−6.61803	+	4.80828i	−0.226200	+	0.164344i
$857$	−25.2705			−0.863224			−0.431612	−	0.902059i	$-0.642055\pi$
$857$	−25.2705			−0.863224			−0.431612	+	0.902059i	$0.642055\pi$
$858$	1.23607	+	0.277515i	0.0421987	+	0.00947419i
$859$	−1.18034			−0.0402727			−0.0201363	−	0.999797i	$-0.506410\pi$
$859$	−1.18034			−0.0402727			−0.0201363	+	0.999797i	$0.506410\pi$
$860$		0			0
$861$	−4.14590	−	12.7598i	−0.141292	−	0.434852i
$862$	−1.83688	+	5.65334i	−0.0625644	+	0.192553i
$863$	0.899187	+	0.653298i	0.0306087	+	0.0222385i	0.602984	−	0.797753i	$-0.293978\pi$
$863$	0.899187	+	0.653298i	0.0306087	+	0.0222385i	−0.572376	+	0.819991i	$0.693978\pi$
$864$	−4.42705	−	3.21644i	−0.150611	−	0.109426i
$865$		0			0
$866$	−2.61803	−	8.05748i	−0.0889644	−	0.273804i
$867$	22.0623	−	16.0292i	0.749275	−	0.544380i
$868$	−22.8885			−0.776888
$869$	36.3713	−	15.6987i	1.23381	−	0.532542i
$870$		0			0
$871$	−1.78115	+	1.29408i	−0.0603521	+	0.0438483i
$872$	3.59017	+	11.0494i	0.121578	+	0.374180i
$873$	−1.41641	+	4.35926i	−0.0479381	+	0.147538i
$874$	−8.16312	−	5.93085i	−0.276122	−	0.200614i
$875$		0			0
$876$	4.07295	−	12.5352i	0.137612	−	0.423527i
$877$	−11.6738	−	35.9281i	−0.394195	−	1.21321i	−0.929587	−	0.368603i	$-0.879836\pi$
$877$	−11.6738	−	35.9281i	−0.394195	−	1.21321i	0.535392	−	0.844604i	$-0.320164\pi$
$878$	18.3713	−	13.3475i	0.620002	−	0.450458i
$879$	−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	$0.458737\pi$
$882$	0.618034	−	0.449028i	0.0208103	−	0.0151196i
$883$	−12.0344	−	37.0382i	−0.404991	−	1.24643i	−0.920903	−	0.389793i	$-0.872547\pi$
$883$	−12.0344	−	37.0382i	−0.404991	−	1.24643i	0.515911	−	0.856642i	$-0.327453\pi$
$884$	−0.0278640	+	0.0857567i	−0.000937169	+	0.00288431i
$885$		0			0
$886$	24.6803	+	17.9313i	0.829152	+	0.602414i
$887$	12.4443	−	38.2995i	0.417838	−	1.28597i	−0.491850	−	0.870680i	$-0.663679\pi$
$887$	12.4443	−	38.2995i	0.417838	−	1.28597i	0.909688	−	0.415293i	$-0.136321\pi$
$888$	4.42705	+	13.6251i	0.148562	+	0.457227i
$889$	5.26393	−	3.82447i	0.176547	−	0.128269i
$890$		0			0
$891$	−13.0344	+	21.9928i	−0.436670	+	0.736787i
$892$	2.05573			0.0688309
$893$	−0.500000	+	0.363271i	−0.0167319	+	0.0121564i
$894$	5.35410	+	16.4782i	0.179068	+	0.551115i
$895$		0			0
$896$	1.80902	+	1.31433i	0.0604350	+	0.0439086i
$897$	−1.19098	−	0.865300i	−0.0397658	−	0.0288915i
$898$	−5.03444	+	15.4944i	−0.168002	+	0.517055i
$899$	1.66970	+	5.13880i	0.0556875	+	0.171389i
$900$		0			0
$901$	0.527864			0.0175857
$902$	−8.12461	−	9.23305i	−0.270520	−	0.307427i
$903$	−34.2705			−1.14045
$904$	11.8992	−	8.64527i	0.395761	−	0.287537i
$905$		0			0
$906$	9.51722	−	29.2910i	0.316188	−	0.973128i
$907$	32.0344	+	23.2744i	1.06369	+	0.772813i	0.974767	−	0.223226i	$-0.0716587\pi$
$907$	32.0344	+	23.2744i	1.06369	+	0.772813i	0.0889194	+	0.996039i	$0.471659\pi$
$908$	−15.9721	−	11.6044i	−0.530054	−	0.385107i
$909$	−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	$0.232785\pi$
$912$	4.23607			0.140270
$913$	−19.7188	−	22.4091i	−0.652599	−	0.741632i
$914$	−12.1246			−0.401047
$915$		0			0
$916$	−4.78115	−	14.7149i	−0.157974	−	0.486193i
$917$	7.70163	−	23.7032i	0.254330	−	0.782748i
$918$	−1.69098	−	1.22857i	−0.0558108	−	0.0405489i
$919$	17.2082	+	12.5025i	0.567646	+	0.412419i	0.834249	−	0.551387i	$-0.185901\pi$
$919$	17.2082	+	12.5025i	0.567646	+	0.412419i	−0.266603	+	0.963806i	$0.585901\pi$
$920$		0			0
$921$	14.3992	+	44.3161i	0.474469	+	1.46027i
$922$	−29.4615	+	21.4050i	−0.970263	+	0.704937i
$923$	−2.31308			−0.0761360
$924$	6.11803	−	10.3229i	0.201269	−	0.339597i
$925$		0			0
$926$	31.2254	−	22.6866i	1.02613	−	0.745528i
$927$	−1.99342	−	6.13512i	−0.0654726	−	0.201504i
$928$	0.163119	−	0.502029i	0.00535464	−	0.0164799i
$929$	18.9443	+	13.7638i	0.621541	+	0.451576i	0.853460	−	0.521159i	$-0.174500\pi$
$929$	18.9443	+	13.7638i	0.621541	+	0.451576i	−0.231918	+	0.972735i	$0.574500\pi$
$930$		0			0
$931$	−1.61803	+	4.97980i	−0.0530289	+	0.163206i
$932$	6.28115	+	19.3314i	0.205746	+	0.633221i
$933$	−5.54508	+	4.02874i	−0.181538	+	0.131895i
$934$	−32.1803			−1.05297
$935$		0			0
$936$	−0.0901699			−0.00294730
$937$	19.1353	−	13.9026i	0.625122	−	0.454177i	−0.229585	−	0.973289i	$-0.573737\pi$
$937$	19.1353	−	13.9026i	0.625122	−	0.454177i	0.854707	+	0.519111i	$0.173737\pi$
$938$	6.44427	+	19.8334i	0.210413	+	0.647584i
$939$	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	$0.835647\pi$
$942$	3.38197	−	10.4086i	0.110190	−	0.339131i
$943$	4.41641	+	13.5923i	0.143818	+	0.442626i
$944$	9.28115	−	6.74315i	0.302076	−	0.219471i
$945$		0			0
$946$	−28.8435	+	12.4495i	−0.937782	+	0.404768i
$947$	−18.0000			−0.584921			−0.292461	−	0.956278i	$-0.594474\pi$
$947$	−18.0000			−0.584921			−0.292461	+	0.956278i	$0.594474\pi$
$948$	15.6353	−	11.3597i	0.507809	−	0.368945i
$949$	−0.594235	−	1.82887i	−0.0192897	−	0.0593676i
$950$		0			0
$951$	−3.66312	−	2.66141i	−0.118785	−	0.0863022i
$952$	0.690983	+	0.502029i	0.0223949	+	0.0162708i
$953$	12.7082	−	39.1118i	0.411659	−	1.26696i	−0.503546	−	0.863968i	$-0.667972\pi$
$953$	12.7082	−	39.1118i	0.411659	−	1.26696i	0.915205	−	0.402988i	$-0.132028\pi$
$954$	0.163119	+	0.502029i	0.00528117	+	0.0162538i
$955$		0			0
$956$	−17.4721			−0.565089
$957$	−2.76393	−	0.620541i	−0.0893452	−	0.0200593i
$958$	−9.94427			−0.321285
$959$	28.5172	−	20.7190i	0.920869	−	0.669051i
$960$		0			0
$961$	22.7984	−	70.1662i	0.735431	−	2.26343i
$962$	1.69098	+	1.22857i	0.0545195	+	0.0396107i
$963$	−2.52786	−	1.83660i	−0.0814593	−	0.0591836i
$964$	5.56231	−	17.1190i	0.179150	−	0.551366i
$965$		0			0
$966$	−11.2812	+	8.19624i	−0.362965	+	0.263710i
$967$	−20.0557			−0.644949			−0.322474	−	0.946578i	$-0.604515\pi$
$967$	−20.0557			−0.644949			−0.322474	+	0.946578i	$0.604515\pi$
$968$	1.39919	−	10.9106i	0.0449716	−	0.350682i
$969$	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	$0.599055\pi$
$972$	1.21885	−	3.75123i	0.0390945	−	0.120321i
$973$	5.16312	+	3.75123i	0.165522	+	0.120259i
$974$	8.80902	+	6.40013i	0.282259	+	0.205073i
$975$		0			0
$976$	0.690983	+	2.12663i	0.0221178	+	0.0680717i
$977$	−6.87132	+	4.99231i	−0.219833	+	0.159718i	−0.692252	−	0.721656i	$-0.743381\pi$
$977$	−6.87132	+	4.99231i	−0.219833	+	0.159718i	0.472418	+	0.881374i	$0.343381\pi$
$978$	0.291796			0.00933061
$979$	−42.6525	−	9.57608i	−1.36318	−	0.306053i
$980$		0			0
$981$	−3.59017	+	2.60841i	−0.114625	+	0.0832802i
$982$	−3.76393	−	11.5842i	−0.120112	−	0.369666i
$983$	−8.52786	+	26.2461i	−0.271997	+	0.837120i	0.718002	+	0.696041i	$0.245057\pi$
$983$	−8.52786	+	26.2461i	−0.271997	+	0.837120i	−0.989998	+	0.141078i	$0.954943\pi$
$984$	−4.85410	−	3.52671i	−0.154743	−	0.112427i
$985$		0			0
$986$	0.0623059	−	0.191758i	0.00198422	−	0.00610681i
$987$	0.263932	+	0.812299i	0.00840105	+	0.0258558i
$988$	0.500000	−	0.363271i	0.0159071	−	0.0115572i
$989$	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	$0.510677\pi$
$992$	−8.28115	+	6.01661i	−0.262927	+	0.191028i
$993$	−8.47214	−	26.0746i	−0.268855	−	0.827451i
$994$	−6.77051	+	20.8375i	−0.214748	+	0.660925i
$995$		0			0
$996$	−11.7812	−	8.55951i	−0.373300	−	0.271218i
$997$	8.93363	−	27.4949i	0.282931	−	0.870772i	−0.704080	−	0.710120i	$-0.748641\pi$
$997$	8.93363	−	27.4949i	0.282931	−	0.870772i	0.987011	−	0.160651i	$-0.0513595\pi$
$998$	−4.77458	−	14.6946i	−0.151137	−	0.465150i
$999$	−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.h.g.201.1	yes	4
5.2	odd	4		550.2.ba.e.399.2		8
5.3	odd	4		550.2.ba.e.399.1		8
5.4	even	2		550.2.h.c.201.1	✓	4
11.2	odd	10		6050.2.a.cr.1.2		2
11.4	even	5	inner	550.2.h.g.301.1	yes	4
11.9	even	5		6050.2.a.ca.1.2		2
55.4	even	10		550.2.h.c.301.1	yes	4
55.9	even	10		6050.2.a.co.1.1		2
55.24	odd	10		6050.2.a.bx.1.1		2
55.37	odd	20		550.2.ba.e.499.1		8
55.48	odd	20		550.2.ba.e.499.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
550.2.h.c.201.1	✓	4	5.4	even	2
550.2.h.c.301.1	yes	4	55.4	even	10
550.2.h.g.201.1	yes	4	1.1	even	1	trivial
550.2.h.g.301.1	yes	4	11.4	even	5	inner
550.2.ba.e.399.1		8	5.3	odd	4
550.2.ba.e.399.2		8	5.2	odd	4
550.2.ba.e.499.1		8	55.37	odd	20
550.2.ba.e.499.2		8	55.48	odd	20
6050.2.a.bx.1.1		2	55.24	odd	10
6050.2.a.ca.1.2		2	11.9	even	5
6050.2.a.co.1.1		2	55.9	even	10
6050.2.a.cr.1.2		2	11.2	odd	10

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.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.500000 + 1.53884i) q^{3} +(0.309017 - 0.951057i) q^{4} +(1.30902 + 0.951057i) q^{6} +(0.690983 - 2.12663i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.309017 - 0.224514i) q^{9} +(3.23607 + 0.726543i) q^{11} +1.61803 q^{12} +(0.190983 - 0.138757i) q^{13} +(-0.690983 - 2.12663i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-0.309017 - 0.224514i) q^{17} +(0.118034 - 0.363271i) q^{18} +(0.809017 + 2.48990i) q^{19} +3.61803 q^{21} +(3.04508 - 1.31433i) q^{22} -3.85410 q^{23} +(1.30902 - 0.951057i) q^{24} +(0.0729490 - 0.224514i) q^{26} +(4.42705 + 3.21644i) q^{27} +(-1.80902 - 1.31433i) q^{28} +(-0.163119 + 0.502029i) q^{29} +(8.28115 - 6.01661i) q^{31} -1.00000 q^{32} +(0.500000 + 5.34307i) q^{33} -0.381966 q^{34} +(-0.118034 - 0.363271i) q^{36} +(-2.73607 + 8.42075i) q^{37} +(2.11803 + 1.53884i) q^{38} +(0.309017 + 0.224514i) q^{39} +(-1.14590 - 3.52671i) q^{41} +(2.92705 - 2.12663i) q^{42} -9.47214 q^{43} +(1.69098 - 2.85317i) q^{44} +(-3.11803 + 2.26538i) q^{46} +(0.0729490 + 0.224514i) q^{47} +(0.500000 - 1.53884i) q^{48} +(1.61803 + 1.17557i) q^{49} +(0.190983 - 0.587785i) q^{51} +(-0.0729490 - 0.224514i) q^{52} +(-1.11803 + 0.812299i) q^{53} +5.47214 q^{54} -2.23607 q^{56} +(-3.42705 + 2.48990i) q^{57} +(0.163119 + 0.502029i) q^{58} +(-3.54508 + 10.9106i) q^{59} +(-1.80902 - 1.31433i) q^{61} +(3.16312 - 9.73508i) q^{62} +(-0.263932 - 0.812299i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(3.54508 + 4.02874i) q^{66} -9.32624 q^{67} +(-0.309017 + 0.224514i) q^{68} +(-1.92705 - 5.93085i) q^{69} +(-7.92705 - 5.75934i) q^{71} +(-0.309017 - 0.224514i) q^{72} +(2.51722 - 7.74721i) q^{73} +(2.73607 + 8.42075i) q^{74} +2.61803 q^{76} +(3.78115 - 6.37988i) q^{77} +0.381966 q^{78} +(9.66312 - 7.02067i) q^{79} +(-2.38197 + 7.33094i) q^{81} +(-3.00000 - 2.17963i) q^{82} +(-7.28115 - 5.29007i) q^{83} +(1.11803 - 3.44095i) q^{84} +(-7.66312 + 5.56758i) q^{86} -0.854102 q^{87} +(-0.309017 - 3.30220i) q^{88} -13.1803 q^{89} +(-0.163119 - 0.502029i) q^{91} +(-1.19098 + 3.66547i) q^{92} +(13.3992 + 9.73508i) q^{93} +(0.190983 + 0.138757i) q^{94} +(-0.500000 - 1.53884i) q^{96} +(-9.70820 + 7.05342i) q^{97} +2.00000 q^{98} +(1.16312 - 0.502029i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + 2 q^{3} - q^{4} + 3 q^{6} + 5 q^{7} + q^{8} - q^{9} + 4 q^{11} + 2 q^{12} + 3 q^{13} - 5 q^{14} - q^{16} + q^{17} - 4 q^{18} + q^{19} + 10 q^{21} + q^{22} - 2 q^{23} + 3 q^{24} + 7 q^{26}+ \cdots - 11 q^{99}+O(q^{100}) \) 4 * q + q^2 + 2 * q^3 - q^4 + 3 * q^6 + 5 * q^7 + q^8 - q^9 + 4 * q^11 + 2 * q^12 + 3 * q^13 - 5 * q^14 - q^16 + q^17 - 4 * q^18 + q^19 + 10 * q^21 + q^22 - 2 * q^23 + 3 * q^24 + 7 * q^26 + 11 * q^27 - 5 * q^28 + 15 * q^29 + 13 * q^31 - 4 * q^32 + 2 * q^33 - 6 * q^34 + 4 * q^36 - 2 * q^37 + 4 * q^38 - q^39 - 18 * q^41 + 5 * q^42 - 20 * q^43 + 9 * q^44 - 8 * q^46 + 7 * q^47 + 2 * q^48 + 2 * q^49 + 3 * q^51 - 7 * q^52 + 4 * q^54 - 7 * q^57 - 15 * q^58 - 3 * q^59 - 5 * q^61 - 3 * q^62 - 10 * q^63 - q^64 + 3 * q^66 - 6 * q^67 + q^68 - q^69 - 25 * q^71 + q^72 - 19 * q^73 + 2 * q^74 + 6 * q^76 - 5 * q^77 + 6 * q^78 + 23 * q^79 - 14 * q^81 - 12 * q^82 - 9 * q^83 - 15 * q^86 + 10 * q^87 + q^88 - 8 * q^89 + 15 * q^91 - 7 * q^92 + 29 * q^93 + 3 * q^94 - 2 * q^96 - 12 * q^97 + 8 * q^98 - 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more