LMFDB - Embedded newform 273.2.i.b.235.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(79,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("273.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.i (of order $3$, degree $2$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			235.3
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	273.235
Dual form			273.2.i.b.79.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 1.32683i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.173648 + 0.300767i) q^{4} +(0.266044 + 0.460802i) q^{5} +1.53209 q^{6} +(-0.418748 + 2.61240i) q^{7} +2.53209 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.766044 + 1.32683i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.173648 + 0.300767i) q^{4} +(0.266044 + 0.460802i) q^{5} +1.53209 q^{6} +(-0.418748 + 2.61240i) q^{7} +2.53209 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.407604 + 0.705990i) q^{10} +(1.43969 - 2.49362i) q^{11} +(0.173648 + 0.300767i) q^{12} +1.00000 q^{13} +(-3.78699 + 1.44561i) q^{14} +0.532089 q^{15} +(2.28699 + 3.96118i) q^{16} +(-1.67365 + 2.89884i) q^{17} +(0.766044 - 1.32683i) q^{18} +(1.03209 + 1.78763i) q^{19} -0.184793 q^{20} +(2.05303 + 1.66885i) q^{21} +4.41147 q^{22} +(-3.93242 - 6.81115i) q^{23} +(1.26604 - 2.19285i) q^{24} +(2.35844 - 4.08494i) q^{25} +(0.766044 + 1.32683i) q^{26} -1.00000 q^{27} +(-0.713011 - 0.579585i) q^{28} -7.04963 q^{29} +(0.407604 + 0.705990i) q^{30} +(-3.11334 + 5.39246i) q^{31} +(-0.971782 + 1.68317i) q^{32} +(-1.43969 - 2.49362i) q^{33} -5.12836 q^{34} +(-1.31521 + 0.502055i) q^{35} +0.347296 q^{36} +(0.326352 + 0.565258i) q^{37} +(-1.58125 + 2.73881i) q^{38} +(0.500000 - 0.866025i) q^{39} +(0.673648 + 1.16679i) q^{40} -4.59627 q^{41} +(-0.641559 + 4.00243i) q^{42} -6.10607 q^{43} +(0.500000 + 0.866025i) q^{44} +(0.266044 - 0.460802i) q^{45} +(6.02481 - 10.4353i) q^{46} +(-4.75877 - 8.24243i) q^{47} +4.57398 q^{48} +(-6.64930 - 2.18788i) q^{49} +7.22668 q^{50} +(1.67365 + 2.89884i) q^{51} +(-0.173648 + 0.300767i) q^{52} +(-0.439693 + 0.761570i) q^{53} +(-0.766044 - 1.32683i) q^{54} +1.53209 q^{55} +(-1.06031 + 6.61484i) q^{56} +2.06418 q^{57} +(-5.40033 - 9.35365i) q^{58} +(1.12314 - 1.94534i) q^{59} +(-0.0923963 + 0.160035i) q^{60} +(4.14930 + 7.18680i) q^{61} -9.53983 q^{62} +(2.47178 - 0.943555i) q^{63} +6.17024 q^{64} +(0.266044 + 0.460802i) q^{65} +(2.20574 - 3.82045i) q^{66} +(6.19846 - 10.7361i) q^{67} +(-0.581252 - 1.00676i) q^{68} -7.86484 q^{69} +(-1.67365 - 1.36046i) q^{70} +10.6159 q^{71} +(-1.26604 - 2.19285i) q^{72} +(0.275845 - 0.477777i) q^{73} +(-0.500000 + 0.866025i) q^{74} +(-2.35844 - 4.08494i) q^{75} -0.716881 q^{76} +(5.91147 + 4.80526i) q^{77} +1.53209 q^{78} +(5.80793 + 10.0596i) q^{79} +(-1.21688 + 2.10770i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.52094 - 6.09845i) q^{82} -5.87939 q^{83} +(-0.858441 + 0.327693i) q^{84} -1.78106 q^{85} +(-4.67752 - 8.10170i) q^{86} +(-3.52481 + 6.10516i) q^{87} +(3.64543 - 6.31407i) q^{88} +(-2.74510 - 4.75465i) q^{89} +0.815207 q^{90} +(-0.418748 + 2.61240i) q^{91} +2.73143 q^{92} +(3.11334 + 5.39246i) q^{93} +(7.29086 - 12.6281i) q^{94} +(-0.549163 + 0.951178i) q^{95} +(0.971782 + 1.68317i) q^{96} +12.7811 q^{97} +(-2.19072 - 10.4985i) q^{98} -2.87939 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} - 3 q^{5} + 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 - 3 * q^5 + 6 * q^8 - 3 * q^9	$ 6 q + 3 q^{3} - 3 q^{5} + 6 q^{8} - 3 q^{9} - 6 q^{10} + 3 q^{11} + 6 q^{13} - 15 q^{14} - 6 q^{15} + 6 q^{16} - 9 q^{17} - 3 q^{19} + 6 q^{20} + 6 q^{22} + 3 q^{24} + 6 q^{25} - 6 q^{27} - 12 q^{28} + 12 q^{29} + 6 q^{30} - 12 q^{31} + 9 q^{32} - 3 q^{33} + 6 q^{34} - 15 q^{35} + 3 q^{37} - 12 q^{38} + 3 q^{39} + 3 q^{40} - 12 q^{42} - 12 q^{43} + 3 q^{44} - 3 q^{45} + 9 q^{46} - 6 q^{47} + 12 q^{48} + 30 q^{50} + 9 q^{51} + 3 q^{53} - 12 q^{56} - 6 q^{57} - 18 q^{58} + 3 q^{59} + 3 q^{60} - 15 q^{61} - 6 q^{64} - 3 q^{65} + 3 q^{66} + 9 q^{67} - 6 q^{68} - 9 q^{70} + 42 q^{71} - 3 q^{72} - 3 q^{74} - 6 q^{75} + 12 q^{76} + 15 q^{77} + 24 q^{79} + 9 q^{80} - 3 q^{81} - 18 q^{82} - 24 q^{83} + 3 q^{84} + 24 q^{85} - 3 q^{86} + 6 q^{87} + 6 q^{88} - 15 q^{89} + 12 q^{90} + 36 q^{92} + 12 q^{93} + 12 q^{94} - 15 q^{95} - 9 q^{96} + 42 q^{97} - 33 q^{98} - 6 q^{99}+O(q^{100}) $ 6 * q + 3 * q^3 - 3 * q^5 + 6 * q^8 - 3 * q^9 - 6 * q^10 + 3 * q^11 + 6 * q^13 - 15 * q^14 - 6 * q^15 + 6 * q^16 - 9 * q^17 - 3 * q^19 + 6 * q^20 + 6 * q^22 + 3 * q^24 + 6 * q^25 - 6 * q^27 - 12 * q^28 + 12 * q^29 + 6 * q^30 - 12 * q^31 + 9 * q^32 - 3 * q^33 + 6 * q^34 - 15 * q^35 + 3 * q^37 - 12 * q^38 + 3 * q^39 + 3 * q^40 - 12 * q^42 - 12 * q^43 + 3 * q^44 - 3 * q^45 + 9 * q^46 - 6 * q^47 + 12 * q^48 + 30 * q^50 + 9 * q^51 + 3 * q^53 - 12 * q^56 - 6 * q^57 - 18 * q^58 + 3 * q^59 + 3 * q^60 - 15 * q^61 - 6 * q^64 - 3 * q^65 + 3 * q^66 + 9 * q^67 - 6 * q^68 - 9 * q^70 + 42 * q^71 - 3 * q^72 - 3 * q^74 - 6 * q^75 + 12 * q^76 + 15 * q^77 + 24 * q^79 + 9 * q^80 - 3 * q^81 - 18 * q^82 - 24 * q^83 + 3 * q^84 + 24 * q^85 - 3 * q^86 + 6 * q^87 + 6 * q^88 - 15 * q^89 + 12 * q^90 + 36 * q^92 + 12 * q^93 + 12 * q^94 - 15 * q^95 - 9 * q^96 + 42 * q^97 - 33 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.766044	+	1.32683i	0.541675	+	0.938209i	0.998808	+	0.0488106i	$0.0155431\pi$
$2$	0.766044	+	1.32683i	0.541675	+	0.938209i	−0.457133	+	0.889398i	$0.651124\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−0.173648	+	0.300767i	−0.0868241	+	0.150384i
$5$	0.266044	+	0.460802i	0.118979	+	0.206077i	0.919363	−	0.393410i	$-0.128705\pi$
$5$	0.266044	+	0.460802i	0.118979	+	0.206077i	−0.800385	+	0.599487i	$0.795371\pi$
$6$	1.53209			0.625473
$7$	−0.418748	+	2.61240i	−0.158272	+	0.987396i
$7$	−0.418748	+	2.61240i	−0.158272	+	0.987396i
$8$	2.53209			0.895229
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.407604	+	0.705990i	−0.128896	+	0.223254i
$11$	1.43969	−	2.49362i	0.434084	−	0.751855i	−0.563137	−	0.826364i	$-0.690406\pi$
$11$	1.43969	−	2.49362i	0.434084	−	0.751855i	0.997220	+	0.0745088i	$0.0237389\pi$
$12$	0.173648	+	0.300767i	0.0501279	+	0.0868241i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	−3.78699	+	1.44561i	−1.01212	+	0.386356i
$15$	0.532089			0.137385
$16$	2.28699	+	3.96118i	0.571747	+	0.990295i
$17$	−1.67365	+	2.89884i	−0.405919	+	0.703073i	−0.994428	−	0.105418i	$-0.966382\pi$
$17$	−1.67365	+	2.89884i	−0.405919	+	0.703073i	0.588509	+	0.808491i	$0.299715\pi$
$18$	0.766044	−	1.32683i	0.180558	−	0.312736i
$19$	1.03209	+	1.78763i	0.236777	+	0.410111i	0.959788	−	0.280727i	$-0.0905754\pi$
$19$	1.03209	+	1.78763i	0.236777	+	0.410111i	−0.723010	+	0.690837i	$0.757242\pi$
$20$	−0.184793			−0.0413209
$21$	2.05303	+	1.66885i	0.448009	+	0.364172i
$22$	4.41147			0.940529
$23$	−3.93242	−	6.81115i	−0.819966	−	1.42022i	−0.905707	−	0.423905i	$-0.860659\pi$
$23$	−3.93242	−	6.81115i	−0.819966	−	1.42022i	0.0857406	−	0.996317i	$-0.472674\pi$
$24$	1.26604	−	2.19285i	0.258430	−	0.447614i
$25$	2.35844	−	4.08494i	0.471688	−	0.816988i
$26$	0.766044	+	1.32683i	0.150234	+	0.260212i
$27$	−1.00000			−0.192450
$28$	−0.713011	−	0.579585i	−0.134746	−	0.109531i
$29$	−7.04963			−1.30908			−0.654542	−	0.756026i	$-0.727138\pi$
$29$	−7.04963			−1.30908			−0.654542	+	0.756026i	$0.727138\pi$
$30$	0.407604	+	0.705990i	0.0744179	+	0.128896i
$31$	−3.11334	+	5.39246i	−0.559173	+	0.968515i	0.438393	+	0.898783i	$0.355548\pi$
$31$	−3.11334	+	5.39246i	−0.559173	+	0.968515i	−0.997566	+	0.0697319i	$0.977786\pi$
$32$	−0.971782	+	1.68317i	−0.171788	+	0.297546i
$33$	−1.43969	−	2.49362i	−0.250618	−	0.434084i
$34$	−5.12836			−0.879506
$35$	−1.31521	+	0.502055i	−0.222311	+	0.0848628i
$36$	0.347296			0.0578827
$37$	0.326352	+	0.565258i	0.0536519	+	0.0929278i	0.891604	−	0.452816i	$-0.149581\pi$
$37$	0.326352	+	0.565258i	0.0536519	+	0.0929278i	−0.837952	+	0.545744i	$0.816247\pi$
$38$	−1.58125	+	2.73881i	−0.256513	+	0.444293i
$39$	0.500000	−	0.866025i	0.0800641	−	0.138675i
$40$	0.673648	+	1.16679i	0.106513	+	0.184486i
$41$	−4.59627			−0.717816			−0.358908	−	0.933373i	$-0.616851\pi$
$41$	−4.59627			−0.717816			−0.358908	+	0.933373i	$0.616851\pi$
$42$	−0.641559	+	4.00243i	−0.0989947	+	0.617589i
$43$	−6.10607			−0.931166			−0.465583	−	0.885004i	$-0.654155\pi$
$43$	−6.10607			−0.931166			−0.465583	+	0.885004i	$0.654155\pi$
$44$	0.500000	+	0.866025i	0.0753778	+	0.130558i
$45$	0.266044	−	0.460802i	0.0396596	−	0.0686924i
$46$	6.02481	−	10.4353i	0.888310	−	1.53860i
$47$	−4.75877	−	8.24243i	−0.694138	−	1.20228i	−0.970470	−	0.241220i	$-0.922452\pi$
$47$	−4.75877	−	8.24243i	−0.694138	−	1.20228i	0.276332	−	0.961062i	$-0.410881\pi$
$48$	4.57398			0.660197
$49$	−6.64930	−	2.18788i	−0.949900	−	0.312554i
$50$	7.22668			1.02201
$51$	1.67365	+	2.89884i	0.234358	+	0.405919i
$52$	−0.173648	+	0.300767i	−0.0240807	+	0.0417089i
$53$	−0.439693	+	0.761570i	−0.0603964	+	0.104610i	−0.894643	−	0.446782i	$-0.852570\pi$
$53$	−0.439693	+	0.761570i	−0.0603964	+	0.104610i	0.834246	+	0.551392i	$0.185903\pi$
$54$	−0.766044	−	1.32683i	−0.104245	−	0.180558i
$55$	1.53209			0.206587
$56$	−1.06031	+	6.61484i	−0.141690	+	0.883945i
$57$	2.06418			0.273407
$58$	−5.40033	−	9.35365i	−0.709098	−	1.22819i
$59$	1.12314	−	1.94534i	0.146221	−	0.253261i	−0.783607	−	0.621257i	$-0.786622\pi$
$59$	1.12314	−	1.94534i	0.146221	−	0.253261i	0.929828	+	0.367995i	$0.119956\pi$
$60$	−0.0923963	+	0.160035i	−0.0119283	+	0.0206604i
$61$	4.14930	+	7.18680i	0.531263	+	0.920175i	0.999334	+	0.0364843i	$0.0116159\pi$
$61$	4.14930	+	7.18680i	0.531263	+	0.920175i	−0.468071	+	0.883691i	$0.655051\pi$
$62$	−9.53983			−1.21156
$63$	2.47178	−	0.943555i	0.311415	−	0.118877i
$64$	6.17024			0.771281
$65$	0.266044	+	0.460802i	0.0329988	+	0.0571555i
$66$	2.20574	−	3.82045i	0.271507	−	0.470265i
$67$	6.19846	−	10.7361i	0.757263	−	1.31162i	−0.186979	−	0.982364i	$-0.559870\pi$
$67$	6.19846	−	10.7361i	0.757263	−	1.31162i	0.944242	−	0.329254i	$-0.106797\pi$
$68$	−0.581252	−	1.00676i	−0.0704871	−	0.122087i
$69$	−7.86484			−0.946815
$70$	−1.67365	−	1.36046i	−0.200039	−	0.162606i
$71$	10.6159			1.25987			0.629936	−	0.776647i	$-0.283081\pi$
$71$	10.6159			1.25987			0.629936	+	0.776647i	$0.283081\pi$
$72$	−1.26604	−	2.19285i	−0.149205	−	0.258430i
$73$	0.275845	−	0.477777i	0.0322852	−	0.0559196i	−0.849431	−	0.527699i	$-0.823055\pi$
$73$	0.275845	−	0.477777i	0.0322852	−	0.0559196i	0.881717	+	0.471780i	$0.156388\pi$
$74$	−0.500000	+	0.866025i	−0.0581238	+	0.100673i
$75$	−2.35844	−	4.08494i	−0.272329	−	0.471688i
$76$	−0.716881			−0.0822319
$77$	5.91147	+	4.80526i	0.673675	+	0.547610i
$78$	1.53209			0.173475
$79$	5.80793	+	10.0596i	0.653444	+	1.13180i	0.982282	+	0.187411i	$0.0600097\pi$
$79$	5.80793	+	10.0596i	0.653444	+	1.13180i	−0.328838	+	0.944386i	$0.606657\pi$
$80$	−1.21688	+	2.10770i	−0.136051	+	0.235648i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.52094	−	6.09845i	−0.388823	−	0.673462i
$83$	−5.87939			−0.645346			−0.322673	−	0.946510i	$-0.604581\pi$
$83$	−5.87939			−0.645346			−0.322673	+	0.946510i	$0.604581\pi$
$84$	−0.858441	+	0.327693i	−0.0936636	+	0.0357543i
$85$	−1.78106			−0.193183
$86$	−4.67752	−	8.10170i	−0.504390	−	0.873629i
$87$	−3.52481	+	6.10516i	−0.377900	+	0.654542i
$88$	3.64543	−	6.31407i	0.388604	−	0.673082i
$89$	−2.74510	−	4.75465i	−0.290980	−	0.503992i	0.683062	−	0.730361i	$-0.260648\pi$
$89$	−2.74510	−	4.75465i	−0.290980	−	0.503992i	−0.974042	+	0.226368i	$0.927315\pi$
$90$	0.815207			0.0859304
$91$	−0.418748	+	2.61240i	−0.0438967	+	0.273854i
$92$	2.73143			0.284771
$93$	3.11334	+	5.39246i	0.322838	+	0.559173i
$94$	7.29086	−	12.6281i	0.751995	−	1.30249i
$95$	−0.549163	+	0.951178i	−0.0563429	+	0.0975888i
$96$	0.971782	+	1.68317i	0.0991820	+	0.171788i
$97$	12.7811			1.29772			0.648860	−	0.760908i	$-0.275246\pi$
$97$	12.7811			1.29772			0.648860	+	0.760908i	$0.275246\pi$
$98$	−2.19072	−	10.4985i	−0.221296	−	1.06051i
$99$	−2.87939			−0.289389
$100$	0.819078	+	1.41868i	0.0819078	+	0.141868i
$101$	−7.26604	+	12.5852i	−0.722998	+	1.25227i	0.236794	+	0.971560i	$0.423903\pi$
$101$	−7.26604	+	12.5852i	−0.722998	+	1.25227i	−0.959793	+	0.280710i	$0.909430\pi$
$102$	−2.56418	+	4.44129i	−0.253891	+	0.439753i
$103$	−5.84730	−	10.1278i	−0.576151	−	0.997923i	−0.995916	−	0.0902900i	$-0.971221\pi$
$103$	−5.84730	−	10.1278i	−0.576151	−	0.997923i	0.419764	−	0.907633i	$-0.362113\pi$
$104$	2.53209			0.248292
$105$	−0.222811	+	1.39003i	−0.0217441	+	0.135653i
$106$	−1.34730			−0.130861
$107$	1.29426	+	2.24173i	0.125121	+	0.216716i	0.921780	−	0.387713i	$-0.126735\pi$
$107$	1.29426	+	2.24173i	0.125121	+	0.216716i	−0.796659	+	0.604429i	$0.793401\pi$
$108$	0.173648	−	0.300767i	0.0167093	−	0.0289414i
$109$	−7.77244	+	13.4623i	−0.744465	+	1.28945i	0.205980	+	0.978556i	$0.433962\pi$
$109$	−7.77244	+	13.4623i	−0.744465	+	1.28945i	−0.950444	+	0.310895i	$0.899371\pi$
$110$	1.17365	+	2.03282i	0.111903	+	0.193822i
$111$	0.652704			0.0619519
$112$	−11.3059	+	4.31580i	−1.06830	+	0.407805i
$113$	20.9736			1.97303			0.986515	−	0.163672i	$-0.0523339\pi$
$113$	20.9736			1.97303			0.986515	+	0.163672i	$0.0523339\pi$
$114$	1.58125	+	2.73881i	0.148098	+	0.256513i
$115$	2.09240	−	3.62414i	0.195117	−	0.337952i
$116$	1.22416	−	2.12030i	0.113660	−	0.196865i
$117$	−0.500000	−	0.866025i	−0.0462250	−	0.0800641i
$118$	3.44150			0.316816
$119$	−6.87211	−	5.58613i	−0.629965	−	0.512080i
$120$	1.34730			0.122991
$121$	1.35457	+	2.34618i	0.123143	+	0.213290i
$122$	−6.35710	+	11.0108i	−0.575544	+	0.996872i
$123$	−2.29813	+	3.98048i	−0.207216	+	0.358908i
$124$	−1.08125	−	1.87278i	−0.0970993	−	0.168181i
$125$	5.17024			0.462441
$126$	3.14543	+	2.55682i	0.280217	+	0.227780i
$127$	−14.0719			−1.24868			−0.624340	−	0.781152i	$-0.714632\pi$
$127$	−14.0719			−1.24868			−0.624340	+	0.781152i	$0.714632\pi$
$128$	6.67024	+	11.5532i	0.589572	+	1.02117i
$129$	−3.05303	+	5.28801i	−0.268805	+	0.465583i
$130$	−0.407604	+	0.705990i	−0.0357492	+	0.0619195i
$131$	−2.34864	−	4.06796i	−0.205202	−	0.355420i	0.744995	−	0.667070i	$-0.232452\pi$
$131$	−2.34864	−	4.06796i	−0.205202	−	0.355420i	−0.950197	+	0.311650i	$0.899118\pi$
$132$	1.00000			0.0870388
$133$	−5.10220	+	1.94767i	−0.442417	+	0.168884i
$134$	18.9932			1.64076
$135$	−0.266044	−	0.460802i	−0.0228975	−	0.0396596i
$136$	−4.23783	+	7.34013i	−0.363391	+	0.629411i
$137$	−5.17365	+	8.96102i	−0.442015	+	0.765592i	−0.997839	−	0.0657081i	$-0.979069\pi$
$137$	−5.17365	+	8.96102i	−0.442015	+	0.765592i	0.555824	+	0.831300i	$0.312403\pi$
$138$	−6.02481	−	10.4353i	−0.512866	−	0.888310i
$139$	5.64496			0.478800			0.239400	−	0.970921i	$-0.423049\pi$
$139$	5.64496			0.478800			0.239400	+	0.970921i	$0.423049\pi$
$140$	0.0773815	−	0.482753i	0.00653993	−	0.0408000i
$141$	−9.51754			−0.801522
$142$	8.13223	+	14.0854i	0.682441	+	1.18202i
$143$	1.43969	−	2.49362i	0.120393	−	0.208527i
$144$	2.28699	−	3.96118i	0.190582	−	0.330098i
$145$	−1.87551	−	3.24849i	−0.155753	−	0.269772i
$146$	0.845237			0.0699523
$147$	−5.21941	+	4.66452i	−0.430489	+	0.384723i
$148$	−0.226682			−0.0186331
$149$	−2.89393	−	5.01244i	−0.237080	−	0.410635i	0.722795	−	0.691063i	$-0.242857\pi$
$149$	−2.89393	−	5.01244i	−0.237080	−	0.410635i	−0.959875	+	0.280428i	$0.909524\pi$
$150$	3.61334	−	6.25849i	0.295028	−	0.511004i
$151$	0.369585	−	0.640140i	0.0300764	−	0.0520939i	−0.850595	−	0.525821i	$-0.823758\pi$
$151$	0.369585	−	0.640140i	0.0300764	−	0.0520939i	0.880672	+	0.473727i	$0.157092\pi$
$152$	2.61334	+	4.52644i	0.211970	+	0.367143i
$153$	3.34730			0.270613
$154$	−1.84730	+	11.5245i	−0.148859	+	0.928675i
$155$	−3.31315			−0.266118
$156$	0.173648	+	0.300767i	0.0139030	+	0.0240807i
$157$	−10.7836	+	18.6777i	−0.860624	+	1.49064i	0.0107040	+	0.999943i	$0.496593\pi$
$157$	−10.7836	+	18.6777i	−0.860624	+	1.49064i	−0.871328	+	0.490701i	$0.836741\pi$
$158$	−8.89827	+	15.4123i	−0.707908	+	1.22613i
$159$	0.439693	+	0.761570i	0.0348699	+	0.0603964i
$160$	−1.03415			−0.0817566
$161$	19.4402	−	7.42091i	1.53210	−	0.584849i
$162$	−1.53209			−0.120372
$163$	0.790393	+	1.36900i	0.0619083	+	0.107228i	0.895318	−	0.445427i	$-0.146948\pi$
$163$	0.790393	+	1.36900i	0.0619083	+	0.107228i	−0.833410	+	0.552655i	$0.813615\pi$
$164$	0.798133	−	1.38241i	0.0623237	−	0.107948i
$165$	0.766044	−	1.32683i	0.0596365	−	0.103293i
$166$	−4.50387	−	7.80093i	−0.349568	−	0.605470i
$167$	11.3405			0.877553			0.438777	−	0.898596i	$-0.355412\pi$
$167$	11.3405			0.877553			0.438777	+	0.898596i	$0.355412\pi$
$168$	5.19846	+	4.22567i	0.401070	+	0.326018i
$169$	1.00000			0.0769231
$170$	−1.36437	−	2.36316i	−0.104642	−	0.181246i
$171$	1.03209	−	1.78763i	0.0789258	−	0.136704i
$172$	1.06031	−	1.83651i	0.0808477	−	0.140032i
$173$	−1.17499	−	2.03515i	−0.0893330	−	0.154729i	0.817896	−	0.575366i	$-0.195140\pi$
$173$	−1.17499	−	2.03515i	−0.0893330	−	0.154729i	−0.907229	+	0.420636i	$0.861807\pi$
$174$	−10.8007			−0.818796
$175$	9.68392	+	7.87176i	0.732035	+	0.595049i
$176$	13.1702			0.992745
$177$	−1.12314	−	1.94534i	−0.0844204	−	0.146221i
$178$	4.20574	−	7.28455i	0.315233	−	0.546000i
$179$	5.90286	−	10.2240i	0.441200	−	0.764181i	−0.556579	−	0.830795i	$-0.687886\pi$
$179$	5.90286	−	10.2240i	0.441200	−	0.764181i	0.997779	+	0.0666138i	$0.0212195\pi$
$180$	0.0923963	+	0.160035i	0.00688681	+	0.0119283i
$181$	19.8111			1.47255			0.736273	−	0.676684i	$-0.236584\pi$
$181$	19.8111			1.47255			0.736273	+	0.676684i	$0.236584\pi$
$182$	−3.78699	+	1.44561i	−0.280710	+	0.107156i
$183$	8.29860			0.613450
$184$	−9.95723	−	17.2464i	−0.734057	−	1.27142i
$185$	−0.173648	+	0.300767i	−0.0127669	+	0.0221129i
$186$	−4.76991	+	8.26173i	−0.349747	+	0.605780i
$187$	4.81908	+	8.34689i	0.352406	+	0.610385i
$188$	3.30541			0.241072
$189$	0.418748	−	2.61240i	0.0304594	−	0.190024i
$190$	−1.68273			−0.122078
$191$	−5.82042	−	10.0813i	−0.421151	−	0.729455i	0.574901	−	0.818223i	$-0.305040\pi$
$191$	−5.82042	−	10.0813i	−0.421151	−	0.729455i	−0.996052	+	0.0887679i	$0.971707\pi$
$192$	3.08512	−	5.34359i	0.222650	−	0.385640i
$193$	0.296789	−	0.514054i	0.0213634	−	0.0370024i	−0.855146	−	0.518387i	$-0.826533\pi$
$193$	0.296789	−	0.514054i	0.0213634	−	0.0370024i	0.876509	+	0.481385i	$0.159866\pi$
$194$	9.79086	+	16.9583i	0.702943	+	1.21753i
$195$	0.532089			0.0381037
$196$	1.81268	−	1.61997i	0.129477	−	0.115712i
$197$	7.07873			0.504338			0.252169	−	0.967683i	$-0.418856\pi$
$197$	7.07873			0.504338			0.252169	+	0.967683i	$0.418856\pi$
$198$	−2.20574	−	3.82045i	−0.156755	−	0.271507i
$199$	1.87551	−	3.24849i	0.132952	−	0.230279i	−0.791861	−	0.610701i	$-0.790888\pi$
$199$	1.87551	−	3.24849i	0.132952	−	0.230279i	0.924813	+	0.380422i	$0.124221\pi$
$200$	5.97178	−	10.3434i	0.422269	−	0.731391i
$201$	−6.19846	−	10.7361i	−0.437206	−	0.757263i
$202$	−22.2645			−1.56652
$203$	2.95202	−	18.4165i	0.207191	−	1.29258i
$204$	−1.16250			−0.0813915
$205$	−1.22281	−	2.11797i	−0.0854048	−	0.147926i
$206$	8.95858	−	15.5167i	0.624174	−	1.08110i
$207$	−3.93242	+	6.81115i	−0.273322	+	0.473408i
$208$	2.28699	+	3.96118i	0.158574	+	0.274658i
$209$	5.94356			0.411125
$210$	−2.01501	+	0.769193i	−0.139049	+	0.0530794i
$211$	−10.3500			−0.712522			−0.356261	−	0.934386i	$-0.615949\pi$
$211$	−10.3500			−0.712522			−0.356261	+	0.934386i	$0.615949\pi$
$212$	−0.152704	−	0.264490i	−0.0104877	−	0.0181653i
$213$	5.30793	−	9.19361i	0.363694	−	0.629936i
$214$	−1.98293	+	3.43453i	−0.135550	+	0.234780i
$215$	−1.62449	−	2.81369i	−0.110789	−	0.191892i
$216$	−2.53209			−0.172287
$217$	−12.7836	−	10.3914i	−0.867806	−	0.705413i
$218$	−23.8161			−1.61303
$219$	−0.275845	−	0.477777i	−0.0186399	−	0.0322852i
$220$	−0.266044	+	0.460802i	−0.0179367	+	0.0310673i
$221$	−1.67365	+	2.89884i	−0.112582	+	0.194997i
$222$	0.500000	+	0.866025i	0.0335578	+	0.0581238i
$223$	20.6955			1.38587			0.692937	−	0.720998i	$-0.256316\pi$
$223$	20.6955			1.38587			0.692937	+	0.720998i	$0.256316\pi$
$224$	−3.99020	−	3.24351i	−0.266606	−	0.216716i
$225$	−4.71688			−0.314459
$226$	16.0667	+	27.8283i	1.06874	+	1.85111i
$227$	8.70233	−	15.0729i	0.577594	−	1.00042i	−0.418160	−	0.908373i	$-0.637325\pi$
$227$	8.70233	−	15.0729i	0.577594	−	1.00042i	0.995754	−	0.0920492i	$-0.0293417\pi$
$228$	−0.358441	+	0.620838i	−0.0237383	+	0.0411160i
$229$	−0.953363	−	1.65127i	−0.0630000	−	0.109119i	0.832805	−	0.553566i	$-0.186733\pi$
$229$	−0.953363	−	1.65127i	−0.0630000	−	0.109119i	−0.895805	+	0.444447i	$0.853400\pi$
$230$	6.41147			0.422760
$231$	7.11721	−	2.71686i	0.468278	−	0.178756i
$232$	−17.8503			−1.17193
$233$	5.49660	+	9.52038i	0.360094	+	0.623701i	0.987976	−	0.154607i	$-0.0494113\pi$
$233$	5.49660	+	9.52038i	0.360094	+	0.623701i	−0.627882	+	0.778309i	$0.716078\pi$
$234$	0.766044	−	1.32683i	0.0500779	−	0.0867375i
$235$	2.53209	−	4.38571i	0.165175	−	0.286092i
$236$	0.390063	+	0.675609i	0.0253909	+	0.0439784i
$237$	11.6159			0.754532
$238$	2.14749	−	13.3973i	0.139201	−	0.868420i
$239$	11.9736			0.774507			0.387254	−	0.921973i	$-0.373424\pi$
$239$	11.9736			0.774507			0.387254	+	0.921973i	$0.373424\pi$
$240$	1.21688	+	2.10770i	0.0785494	+	0.136051i
$241$	−12.0103	+	20.8024i	−0.773649	+	1.34000i	0.161901	+	0.986807i	$0.448237\pi$
$241$	−12.0103	+	20.8024i	−0.773649	+	1.34000i	−0.935551	+	0.353193i	$0.885096\pi$
$242$	−2.07532	+	3.59456i	−0.133407	+	0.231067i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−2.88207			−0.184506
$245$	−0.760830	−	3.64609i	−0.0486076	−	0.232940i
$246$	−7.04189			−0.448974
$247$	1.03209	+	1.78763i	0.0656702	+	0.113744i
$248$	−7.88326	+	13.6542i	−0.500587	+	0.867043i
$249$	−2.93969	+	5.09170i	−0.186295	+	0.322673i
$250$	3.96064	+	6.86002i	0.250493	+	0.433866i
$251$	10.8280			0.683457			0.341729	−	0.939799i	$-0.388988\pi$
$251$	10.8280			0.683457			0.341729	+	0.939799i	$0.388988\pi$
$252$	−0.145430	+	0.907278i	−0.00916121	+	0.0571531i
$253$	−22.6459			−1.42374
$254$	−10.7797	−	18.6710i	−0.676379	−	1.17152i
$255$	−0.890530	+	1.54244i	−0.0557671	+	0.0965915i
$256$	−4.04916	+	7.01336i	−0.253073	+	0.438335i
$257$	−13.6616	−	23.6626i	−0.852189	−	1.47603i	−0.879229	−	0.476400i	$-0.841941\pi$
$257$	−13.6616	−	23.6626i	−0.852189	−	1.47603i	0.0270398	−	0.999634i	$-0.491392\pi$
$258$	−9.35504			−0.582419
$259$	−1.61334	+	0.615862i	−0.100248	+	0.0382678i
$260$	−0.184793			−0.0114603
$261$	3.52481	+	6.10516i	0.218181	+	0.377900i
$262$	3.59833	−	6.23248i	0.222305	−	0.385044i
$263$	−7.08512	+	12.2718i	−0.436887	+	0.756711i	−0.997448	−	0.0714026i	$-0.977253\pi$
$263$	−7.08512	+	12.2718i	−0.436887	+	0.756711i	0.560560	+	0.828114i	$0.310586\pi$
$264$	−3.64543	−	6.31407i	−0.224361	−	0.388604i
$265$	−0.467911			−0.0287436
$266$	−6.49273	−	5.27774i	−0.398095	−	0.323599i
$267$	−5.49020			−0.335995
$268$	2.15270	+	3.72859i	0.131497	+	0.227760i
$269$	−14.7947	+	25.6252i	−0.902051	+	1.56240i	−0.0772225	+	0.997014i	$0.524605\pi$
$269$	−14.7947	+	25.6252i	−0.902051	+	1.56240i	−0.824828	+	0.565384i	$0.808728\pi$
$270$	0.407604	−	0.705990i	0.0248060	−	0.0429652i
$271$	−2.65657	−	4.60132i	−0.161375	−	0.279510i	0.773987	−	0.633202i	$-0.218260\pi$
$271$	−2.65657	−	4.60132i	−0.161375	−	0.279510i	−0.935362	+	0.353691i	$0.884926\pi$
$272$	−15.3105			−0.928333
$273$	2.05303	+	1.66885i	0.124255	+	0.101003i
$274$	−15.8530			−0.957713
$275$	−6.79086	−	11.7621i	−0.409504	−	0.709282i
$276$	1.36571	−	2.36549i	0.0822064	−	0.142386i
$277$	2.68345	−	4.64787i	0.161233	−	0.279263i	−0.774078	−	0.633090i	$-0.781786\pi$
$277$	2.68345	−	4.64787i	0.161233	−	0.279263i	0.935311	+	0.353827i	$0.115120\pi$
$278$	4.32429	+	7.48989i	0.259354	+	0.449214i
$279$	6.22668			0.372782
$280$	−3.33022	+	1.27125i	−0.199019	+	0.0759716i
$281$	14.6432			0.873541			0.436770	−	0.899573i	$-0.356122\pi$
$281$	14.6432			0.873541			0.436770	+	0.899573i	$0.356122\pi$
$282$	−7.29086	−	12.6281i	−0.434164	−	0.751995i
$283$	15.1275	−	26.2016i	0.899235	−	1.55752i	0.0707615	−	0.997493i	$-0.477457\pi$
$283$	15.1275	−	26.2016i	0.899235	−	1.55752i	0.828474	−	0.560028i	$-0.189210\pi$
$284$	−1.84343	+	3.19291i	−0.109387	+	0.189464i
$285$	0.549163	+	0.951178i	0.0325296	+	0.0563429i
$286$	4.41147			0.260856
$287$	1.92468	−	12.0073i	0.113610	−	0.708769i
$288$	1.94356			0.114526
$289$	2.89780	+	5.01914i	0.170459	+	0.295244i
$290$	2.87346	−	4.97697i	0.168735	−	0.292258i
$291$	6.39053	−	11.0687i	0.374619	−	0.648860i
$292$	0.0957998	+	0.165930i	0.00560626	+	0.00971033i
$293$	−8.32594			−0.486407			−0.243203	−	0.969975i	$-0.578198\pi$
$293$	−8.32594			−0.486407			−0.243203	+	0.969975i	$0.578198\pi$
$294$	−10.1873	−	3.35202i	−0.594136	−	0.195494i
$295$	1.19522			0.0695885
$296$	0.826352	+	1.43128i	0.0480307	+	0.0831917i
$297$	−1.43969	+	2.49362i	−0.0835394	+	0.144695i
$298$	4.43376	−	7.67950i	0.256841	−	0.444862i
$299$	−3.93242	−	6.81115i	−0.227418	−	0.393899i
$300$	1.63816			0.0945790
$301$	2.55690	−	15.9515i	0.147377	−	0.919430i
$302$	1.13247			0.0651666
$303$	7.26604	+	12.5852i	0.417423	+	0.722998i
$304$	−4.72075	+	8.17658i	−0.270754	+	0.468959i
$305$	−2.20780	+	3.82402i	−0.126418	+	0.218962i
$306$	2.56418	+	4.44129i	0.146584	+	0.253891i
$307$	−22.9486			−1.30975			−0.654873	−	0.755739i	$-0.727278\pi$
$307$	−22.9486			−1.30975			−0.654873	+	0.755739i	$0.727278\pi$
$308$	−2.47178	+	0.943555i	−0.140843	+	0.0537640i
$309$	−11.6946			−0.665282
$310$	−2.53802	−	4.39598i	−0.144150	−	0.249675i
$311$	−0.592396	+	1.02606i	−0.0335917	+	0.0581825i	−0.882333	−	0.470627i	$-0.844028\pi$
$311$	−0.592396	+	1.02606i	−0.0335917	+	0.0581825i	0.848741	+	0.528809i	$0.177361\pi$
$312$	1.26604	−	2.19285i	0.0716757	−	0.124146i
$313$	2.19325	+	3.79882i	0.123970	+	0.214722i	0.921330	−	0.388782i	$-0.127104\pi$
$313$	2.19325	+	3.79882i	0.123970	+	0.214722i	−0.797360	+	0.603504i	$0.793771\pi$
$314$	−33.0428			−1.86471
$315$	1.09240	+	0.887975i	0.0615496	+	0.0500318i
$316$	−4.03415			−0.226939
$317$	−0.900330	−	1.55942i	−0.0505676	−	0.0875856i	0.839634	−	0.543153i	$-0.182770\pi$
$317$	−0.900330	−	1.55942i	−0.0505676	−	0.0875856i	−0.890201	+	0.455568i	$0.849436\pi$
$318$	−0.673648	+	1.16679i	−0.0377763	+	0.0654305i
$319$	−10.1493	+	17.5791i	−0.568252	+	0.984241i
$320$	1.64156	+	2.84326i	0.0917660	+	0.158943i
$321$	2.58853			0.144477
$322$	24.7383	+	20.1090i	1.37861	+	1.12063i
$323$	−6.90941			−0.384450
$324$	−0.173648	−	0.300767i	−0.00964712	−	0.0167093i
$325$	2.35844	−	4.08494i	0.130823	−	0.226592i
$326$	−1.21095	+	2.09743i	−0.0670684	+	0.116166i
$327$	7.77244	+	13.4623i	0.429817	+	0.744465i
$328$	−11.6382			−0.642610
$329$	23.5253	−	8.98032i	1.29699	−	0.495101i
$330$	2.34730			0.129214
$331$	−12.5903	−	21.8071i	−0.692028	−	1.19863i	−0.971172	−	0.238378i	$-0.923384\pi$
$331$	−12.5903	−	21.8071i	−0.692028	−	1.19863i	0.279145	−	0.960249i	$-0.409949\pi$
$332$	1.02094	−	1.76833i	0.0560316	−	0.0970496i
$333$	0.326352	−	0.565258i	0.0178840	−	0.0309759i
$334$	8.68732	+	15.0469i	0.475349	+	0.823329i
$335$	6.59627			0.360393
$336$	−1.91534	+	11.9491i	−0.104491	+	0.651875i
$337$	−19.5963			−1.06748			−0.533738	−	0.845650i	$-0.679213\pi$
$337$	−19.5963			−1.06748			−0.533738	+	0.845650i	$0.679213\pi$
$338$	0.766044	+	1.32683i	0.0416673	+	0.0721699i
$339$	10.4868	−	18.1637i	0.569565	−	0.986515i
$340$	0.309278	−	0.535685i	0.0167729	−	0.0290516i
$341$	8.96451	+	15.5270i	0.485455	+	0.840833i
$342$	3.16250			0.171009
$343$	8.50000	−	16.4545i	0.458957	−	0.888459i
$344$	−15.4611			−0.833607
$345$	−2.09240	−	3.62414i	−0.112651	−	0.195117i
$346$	1.80019	−	3.11803i	0.0967790	−	0.167626i
$347$	−5.64677	+	9.78050i	−0.303135	+	0.525045i	−0.976844	−	0.213952i	$-0.931367\pi$
$347$	−5.64677	+	9.78050i	−0.303135	+	0.525045i	0.673710	+	0.738996i	$0.264700\pi$
$348$	−1.22416	−	2.12030i	−0.0656216	−	0.113660i
$349$	14.1848			0.759295			0.379647	−	0.925131i	$-0.376045\pi$
$349$	14.1848			0.759295			0.379647	+	0.925131i	$0.376045\pi$
$350$	−3.02616	+	18.8790i	−0.161755	+	1.00913i
$351$	−1.00000			−0.0533761
$352$	2.79813	+	4.84651i	0.149141	+	0.258320i
$353$	−11.2836	+	19.5437i	−0.600565	+	1.04021i	0.392171	+	0.919892i	$0.371724\pi$
$353$	−11.2836	+	19.5437i	−0.600565	+	1.04021i	−0.992736	+	0.120316i	$0.961609\pi$
$354$	1.72075	−	2.98043i	0.0914569	−	0.158408i
$355$	2.82429	+	4.89182i	0.149898	+	0.259631i
$356$	1.90673			0.101056
$357$	−8.27379	+	3.15836i	−0.437895	+	0.167158i
$358$	18.0874			0.955949
$359$	11.0556	+	19.1488i	0.583490	+	1.01063i	0.995062	+	0.0992571i	$0.0316466\pi$
$359$	11.0556	+	19.1488i	0.583490	+	1.01063i	−0.411572	+	0.911377i	$0.635020\pi$
$360$	0.673648	−	1.16679i	0.0355044	−	0.0614954i
$361$	7.36959	−	12.7645i	0.387873	−	0.671816i
$362$	15.1762	+	26.2859i	0.797642	+	1.38156i
$363$	2.70914			0.142193
$364$	−0.713011	−	0.579585i	−0.0373719	−	0.0303785i
$365$	0.293548			0.0153650
$366$	6.35710	+	11.0108i	0.332291	+	0.575544i
$367$	15.4809	−	26.8136i	0.808095	−	1.39966i	−0.106087	−	0.994357i	$-0.533832\pi$
$367$	15.4809	−	26.8136i	0.808095	−	1.39966i	0.914182	−	0.405304i	$-0.132834\pi$
$368$	17.9868	−	31.1540i	0.937627	−	1.62402i
$369$	2.29813	+	3.98048i	0.119636	+	0.207216i
$370$	−0.532089			−0.0276620
$371$	−1.80541	−	1.46756i	−0.0937321	−	0.0761919i
$372$	−2.16250			−0.112121
$373$	−14.6702	−	25.4096i	−0.759596	−	1.31566i	−0.943057	−	0.332633i	$-0.892063\pi$
$373$	−14.6702	−	25.4096i	−0.759596	−	1.31566i	0.183460	−	0.983027i	$-0.441270\pi$
$374$	−7.38326	+	12.7882i	−0.381779	+	0.661261i
$375$	2.58512	−	4.47756i	0.133495	−	0.231220i
$376$	−12.0496	−	20.8706i	−0.621412	−	1.07632i
$377$	−7.04963			−0.363074
$378$	3.78699	−	1.44561i	0.194782	−	0.0743542i
$379$	37.2208			1.91190			0.955952	−	0.293522i	$-0.0948275\pi$
$379$	37.2208			1.91190			0.955952	+	0.293522i	$0.0948275\pi$
$380$	−0.190722	−	0.330341i	−0.00978385	−	0.0169461i
$381$	−7.03596	+	12.1866i	−0.360463	+	0.624340i
$382$	8.91740	−	15.4454i	0.456254	−	0.790255i
$383$	7.42262	+	12.8564i	0.379278	+	0.656929i	0.990957	−	0.134177i	$-0.0428390\pi$
$383$	7.42262	+	12.8564i	0.379278	+	0.656929i	−0.611679	+	0.791106i	$0.709506\pi$
$384$	13.3405			0.680779
$385$	−0.641559	+	4.00243i	−0.0326969	+	0.203983i
$386$	0.909415			0.0462880
$387$	3.05303	+	5.28801i	0.155194	+	0.268805i
$388$	−2.21941	+	3.84413i	−0.112673	+	0.195156i
$389$	−4.35117	+	7.53644i	−0.220613	+	0.382113i	−0.954994	−	0.296624i	$-0.904139\pi$
$389$	−4.35117	+	7.53644i	−0.220613	+	0.382113i	0.734381	+	0.678737i	$0.237472\pi$
$390$	0.407604	+	0.705990i	0.0206398	+	0.0357492i
$391$	26.3259			1.33136
$392$	−16.8366	−	5.53990i	−0.850378	−	0.279807i
$393$	−4.69728			−0.236946
$394$	5.42262	+	9.39225i	0.273188	+	0.473175i
$395$	−3.09034	+	5.35262i	−0.155492	+	0.269320i
$396$	0.500000	−	0.866025i	0.0251259	−	0.0435194i
$397$	4.18227	+	7.24390i	0.209902	+	0.363561i	0.951683	−	0.307081i	$-0.0993522\pi$
$397$	4.18227	+	7.24390i	0.209902	+	0.363561i	−0.741782	+	0.670642i	$0.766019\pi$
$398$	5.74691			0.288067
$399$	−0.864370	+	5.39246i	−0.0432726	+	0.269961i
$400$	21.5749			1.07875
$401$	−1.88413	−	3.26341i	−0.0940891	−	0.162967i	0.815139	−	0.579265i	$-0.196661\pi$
$401$	−1.88413	−	3.26341i	−0.0940891	−	0.162967i	−0.909228	+	0.416298i	$0.863327\pi$
$402$	9.49660	−	16.4486i	0.473647	−	0.820381i
$403$	−3.11334	+	5.39246i	−0.155087	+	0.268618i
$404$	−2.52347	−	4.37078i	−0.125547	−	0.217454i
$405$	−0.532089			−0.0264397
$406$	26.6969	−	10.1910i	1.32494	−	0.505772i
$407$	1.87939			0.0931577
$408$	4.23783	+	7.34013i	0.209804	+	0.363391i
$409$	1.52094	−	2.63435i	0.0752059	−	0.130260i	−0.825970	−	0.563714i	$-0.809372\pi$
$409$	1.52094	−	2.63435i	0.0752059	−	0.130260i	0.901176	+	0.433454i	$0.142705\pi$
$410$	1.87346	−	3.24492i	0.0925234	−	0.160255i
$411$	5.17365	+	8.96102i	0.255197	+	0.442015i
$412$	4.06149			0.200095
$413$	4.61169	+	3.74870i	0.226927	+	0.184462i
$414$	−12.0496			−0.592207
$415$	−1.56418	−	2.70924i	−0.0767825	−	0.132991i
$416$	−0.971782	+	1.68317i	−0.0476455	+	0.0825244i
$417$	2.82248	−	4.88868i	0.138218	−	0.239400i
$418$	4.55303	+	7.88609i	0.222696	+	0.385721i
$419$	−26.6168			−1.30032			−0.650158	−	0.759799i	$-0.725297\pi$
$419$	−26.6168			−1.30032			−0.650158	+	0.759799i	$0.725297\pi$
$420$	−0.379385	−	0.308391i	−0.0185121	−	0.0150479i
$421$	22.0506			1.07468			0.537339	−	0.843366i	$-0.319429\pi$
$421$	22.0506			1.07468			0.537339	+	0.843366i	$0.319429\pi$
$422$	−7.92855	−	13.7326i	−0.385956	−	0.668495i
$423$	−4.75877	+	8.24243i	−0.231379	+	0.400761i
$424$	−1.11334	+	1.92836i	−0.0540686	+	0.0936496i
$425$	7.89440	+	13.6735i	0.382935	+	0.663262i
$426$	16.2645			0.788015
$427$	−20.5123	+	7.83019i	−0.992661	+	0.378929i
$428$	−0.898986			−0.0434541
$429$	−1.43969	−	2.49362i	−0.0695090	−	0.120393i
$430$	2.48886	−	4.31082i	0.120023	−	0.207886i
$431$	−5.76604	+	9.98708i	−0.277741	+	0.481061i	−0.970823	−	0.239798i	$-0.922919\pi$
$431$	−5.76604	+	9.98708i	−0.277741	+	0.481061i	0.693082	+	0.720858i	$0.256252\pi$
$432$	−2.28699	−	3.96118i	−0.110033	−	0.190582i
$433$	−26.4911			−1.27308			−0.636541	−	0.771243i	$-0.719636\pi$
$433$	−26.4911			−1.27308			−0.636541	+	0.771243i	$0.719636\pi$
$434$	3.99479	−	24.9219i	0.191756	−	1.19629i
$435$	−3.75103			−0.179848
$436$	−2.69934	−	4.67539i	−0.129275	−	0.223911i
$437$	8.11721	−	14.0594i	0.388299	−	0.672553i
$438$	0.422618	−	0.731997i	0.0201935	−	0.0349762i
$439$	15.7900	+	27.3491i	0.753615	+	1.30530i	0.946060	+	0.323991i	$0.105025\pi$
$439$	15.7900	+	27.3491i	0.753615	+	1.30530i	−0.192445	+	0.981308i	$0.561642\pi$
$440$	3.87939			0.184942
$441$	1.42989	+	6.85240i	0.0680901	+	0.326305i
$442$	−5.12836			−0.243931
$443$	7.96198	+	13.7906i	0.378285	+	0.655209i	0.990813	−	0.135240i	$-0.0431805\pi$
$443$	7.96198	+	13.7906i	0.378285	+	0.655209i	−0.612528	+	0.790449i	$0.709847\pi$
$444$	−0.113341	+	0.196312i	−0.00537892	+	0.00931656i
$445$	1.46064	−	2.52990i	0.0692408	−	0.119929i
$446$	15.8537	+	27.4594i	0.750694	+	1.30024i
$447$	−5.78787			−0.273757
$448$	−2.58378	+	16.1192i	−0.122072	+	0.761559i
$449$	−34.1462			−1.61146			−0.805729	−	0.592284i	$-0.798226\pi$
$449$	−34.1462			−1.61146			−0.805729	+	0.592284i	$0.798226\pi$
$450$	−3.61334	−	6.25849i	−0.170335	−	0.295028i
$451$	−6.61721	+	11.4613i	−0.311592	+	0.539694i
$452$	−3.64203	+	6.30817i	−0.171306	+	0.296712i
$453$	−0.369585	−	0.640140i	−0.0173646	−	0.0300764i
$454$	26.6655			1.25147
$455$	−1.31521	+	0.502055i	−0.0616579	+	0.0235367i
$456$	5.22668			0.244762
$457$	−1.83497	−	3.17826i	−0.0858363	−	0.148673i	0.819911	−	0.572491i	$-0.194023\pi$
$457$	−1.83497	−	3.17826i	−0.0858363	−	0.148673i	−0.905747	+	0.423818i	$0.860690\pi$
$458$	1.46064	−	2.52990i	0.0682511	−	0.118214i
$459$	1.67365	−	2.89884i	0.0781192	−	0.135306i
$460$	0.726682	+	1.25865i	0.0338817	+	0.0586848i
$461$	18.0077			0.838704			0.419352	−	0.907824i	$-0.362257\pi$
$461$	18.0077			0.838704			0.419352	+	0.907824i	$0.362257\pi$
$462$	9.05690	+	7.36208i	0.421365	+	0.342515i
$463$	−8.73648			−0.406019			−0.203009	−	0.979177i	$-0.565072\pi$
$463$	−8.73648			−0.406019			−0.203009	+	0.979177i	$0.565072\pi$
$464$	−16.1224	−	27.9249i	−0.748465	−	1.29638i
$465$	−1.65657	+	2.86927i	−0.0768218	+	0.133059i
$466$	−8.42127	+	14.5861i	−0.390108	+	0.675687i
$467$	−5.19506	−	8.99811i	−0.240399	−	0.416383i	0.720429	−	0.693528i	$-0.243945\pi$
$467$	−5.19506	−	8.99811i	−0.240399	−	0.416383i	−0.960828	+	0.277146i	$0.910612\pi$
$468$	0.347296			0.0160538
$469$	25.4513	+	20.6886i	1.17523	+	0.955310i
$470$	7.75877			0.357885
$471$	10.7836	+	18.6777i	0.496881	+	0.860624i
$472$	2.84389	−	4.92577i	0.130901	−	0.226727i
$473$	−8.79086	+	15.2262i	−0.404204	+	0.700102i
$474$	8.89827	+	15.4123i	0.408711	+	0.707908i
$475$	9.73648			0.446740
$476$	2.87346	−	1.09689i	0.131705	−	0.0502757i
$477$	0.879385			0.0402643
$478$	9.17230	+	15.8869i	0.419531	+	0.726650i
$479$	8.30675	−	14.3877i	0.379545	−	0.657392i	−0.611451	−	0.791282i	$-0.709414\pi$
$479$	8.30675	−	14.3877i	0.379545	−	0.657392i	0.990996	+	0.133891i	$0.0427472\pi$
$480$	−0.517074	+	0.895599i	−0.0236011	+	0.0408783i
$481$	0.326352	+	0.565258i	0.0148804	+	0.0257735i
$482$	−36.8016			−1.67627
$483$	3.29339	−	20.5461i	0.149854	−	0.934881i
$484$	−0.940875			−0.0427670
$485$	3.40033	+	5.88954i	0.154401	+	0.267430i
$486$	−0.766044	+	1.32683i	−0.0347485	+	0.0601861i
$487$	−9.52734	+	16.5018i	−0.431725	+	0.747770i	−0.997022	−	0.0771178i	$-0.975428\pi$
$487$	−9.52734	+	16.5018i	−0.431725	+	0.747770i	0.565297	+	0.824887i	$0.308762\pi$
$488$	10.5064	+	18.1976i	0.475602	+	0.823767i
$489$	1.58079			0.0714856
$490$	4.25490	−	3.80255i	0.192217	−	0.171782i
$491$	−21.0036			−0.947880			−0.473940	−	0.880557i	$-0.657169\pi$
$491$	−21.0036			−0.947880			−0.473940	+	0.880557i	$0.657169\pi$
$492$	−0.798133	−	1.38241i	−0.0359826	−	0.0623237i
$493$	11.7986	−	20.4358i	0.531382	−	0.920381i
$494$	−1.58125	+	2.73881i	−0.0711439	+	0.123225i
$495$	−0.766044	−	1.32683i	−0.0344311	−	0.0596365i
$496$	−28.4807			−1.27882
$497$	−4.44537	+	27.7329i	−0.199402	+	1.24399i
$498$	−9.00774			−0.403647
$499$	−7.34049	−	12.7141i	−0.328605	−	0.569161i	0.653630	−	0.756814i	$-0.273245\pi$
$499$	−7.34049	−	12.7141i	−0.328605	−	0.569161i	−0.982235	+	0.187653i	$0.939912\pi$
$500$	−0.897804	+	1.55504i	−0.0401510	+	0.0695436i
$501$	5.67024	−	9.82115i	0.253328	−	0.438777i
$502$	8.29473	+	14.3669i	0.370212	+	0.641226i
$503$	−34.1566			−1.52297			−0.761484	−	0.648183i	$-0.775529\pi$
$503$	−34.1566			−1.52297			−0.761484	+	0.648183i	$0.775529\pi$
$504$	6.25877	−	2.38917i	0.278788	−	0.106422i
$505$	−7.73236			−0.344086
$506$	−17.3478	−	30.0472i	−0.771202	−	1.33576i
$507$	0.500000	−	0.866025i	0.0222058	−	0.0384615i
$508$	2.44356	−	4.23238i	0.108416	−	0.187781i
$509$	10.7935	+	18.6950i	0.478416	+	0.828640i	0.999694	−	0.0247467i	$-0.00787793\pi$
$509$	10.7935	+	18.6950i	0.478416	+	0.828640i	−0.521278	+	0.853387i	$0.674545\pi$
$510$	−2.72874			−0.120831
$511$	1.13264	+	0.920686i	0.0501049	+	0.0407287i
$512$	14.2736			0.630811
$513$	−1.03209	−	1.78763i	−0.0455678	−	0.0789258i
$514$	20.9308	−	36.2533i	0.923219	−	1.59906i
$515$	3.11128	−	5.38890i	0.137099	−	0.237463i
$516$	−1.06031	−	1.83651i	−0.0466774	−	0.0808477i
$517$	−27.4047			−1.20526
$518$	−2.05303	−	1.66885i	−0.0902051	−	0.0733250i
$519$	−2.34998			−0.103153
$520$	0.673648	+	1.16679i	0.0295414	+	0.0511673i
$521$	13.0783	−	22.6523i	0.572971	−	0.992416i	−0.423287	−	0.905995i	$-0.639124\pi$
$521$	13.0783	−	22.6523i	0.572971	−	0.992416i	0.996259	−	0.0864201i	$-0.0275427\pi$
$522$	−5.40033	+	9.35365i	−0.236366	+	0.409398i
$523$	−17.3405	−	30.0346i	−0.758247	−	1.31332i	−0.943744	−	0.330677i	$-0.892723\pi$
$523$	−17.3405	−	30.0346i	−0.758247	−	1.31332i	0.185497	−	0.982645i	$-0.440610\pi$
$524$	1.63135			0.0712658
$525$	11.6591	−	4.45064i	0.508845	−	0.194242i
$526$	−21.7101			−0.946604
$527$	−10.4213	−	18.0502i	−0.453958	−	0.786278i
$528$	6.58512	−	11.4058i	0.286581	−	0.496372i
$529$	−19.4278	+	33.6500i	−0.844688	+	1.46304i
$530$	−0.358441	−	0.620838i	−0.0155697	−	0.0269675i
$531$	−2.24628			−0.0974803
$532$	0.300193	−	1.87278i	0.0130150	−	0.0811955i
$533$	−4.59627			−0.199086
$534$	−4.20574	−	7.28455i	−0.182000	−	0.315233i
$535$	−0.688663	+	1.19280i	−0.0297735	+	0.0515692i
$536$	15.6951	−	27.1846i	0.677923	−	1.17420i
$537$	−5.90286	−	10.2240i	−0.254727	−	0.441200i
$538$	−45.3337			−1.95447
$539$	−15.0287	+	13.4310i	−0.647331	+	0.578512i
$540$	0.184793			0.00795220
$541$	−18.7763	−	32.5215i	−0.807257	−	1.39821i	−0.914757	−	0.404005i	$-0.867618\pi$
$541$	−18.7763	−	32.5215i	−0.807257	−	1.39821i	0.107500	−	0.994205i	$-0.465715\pi$
$542$	4.07011	−	7.04963i	0.174826	−	0.302808i
$543$	9.90554	−	17.1569i	0.425088	−	0.736273i
$544$	−3.25284	−	5.63409i	−0.139464	−	0.241559i
$545$	−8.27126			−0.354302
$546$	−0.641559	+	4.00243i	−0.0274562	+	0.171288i
$547$	−7.61856			−0.325746			−0.162873	−	0.986647i	$-0.552076\pi$
$547$	−7.61856			−0.325746			−0.162873	+	0.986647i	$0.552076\pi$
$548$	−1.79679	−	3.11213i	−0.0767550	−	0.132944i
$549$	4.14930	−	7.18680i	0.177088	−	0.306725i
$550$	10.4042	−	18.0206i	0.443637	−	0.768401i
$551$	−7.27584	−	12.6021i	−0.309961	−	0.536869i
$552$	−19.9145			−0.847616
$553$	−28.7119	+	10.9602i	−1.22095	+	0.466076i
$554$	8.22256			0.349343
$555$	0.173648	+	0.300767i	0.00737095	+	0.0127669i
$556$	−0.980238	+	1.69782i	−0.0415713	+	0.0720037i
$557$	9.25196	−	16.0249i	0.392018	−	0.678996i	−0.600697	−	0.799476i	$-0.705110\pi$
$557$	9.25196	−	16.0249i	0.392018	−	0.678996i	0.992716	+	0.120481i	$0.0384437\pi$
$558$	4.76991	+	8.26173i	0.201927	+	0.349747i
$559$	−6.10607			−0.258259
$560$	−4.99660	−	4.06158i	−0.211145	−	0.171633i
$561$	9.63816			0.406923
$562$	11.2173	+	19.4290i	0.473175	+	0.819564i
$563$	−9.06805	+	15.7063i	−0.382173	+	0.661942i	−0.991373	−	0.131074i	$-0.958157\pi$
$563$	−9.06805	+	15.7063i	−0.382173	+	0.661942i	0.609200	+	0.793017i	$0.291491\pi$
$564$	1.65270	−	2.86257i	0.0695914	−	0.120536i
$565$	5.57991	+	9.66468i	0.234748	+	0.406596i
$566$	46.3533			1.94837
$567$	−2.05303	−	1.66885i	−0.0862193	−	0.0700850i
$568$	26.8803			1.12787
$569$	12.9488	+	22.4279i	0.542841	+	0.940228i	0.998739	+	0.0501963i	$0.0159847\pi$
$569$	12.9488	+	22.4279i	0.542841	+	0.940228i	−0.455898	+	0.890032i	$0.650682\pi$
$570$	−0.841367	+	1.45729i	−0.0352410	+	0.0610391i
$571$	−13.0052	+	22.5257i	−0.544251	+	0.942671i	0.454402	+	0.890797i	$0.349853\pi$
$571$	−13.0052	+	22.5257i	−0.544251	+	0.942671i	−0.998654	+	0.0518743i	$0.983480\pi$
$572$	0.500000	+	0.866025i	0.0209061	+	0.0362103i
$573$	−11.6408			−0.486303
$574$	17.4060	−	6.64441i	0.726513	−	0.277332i
$575$	−37.0975			−1.54707
$576$	−3.08512	−	5.34359i	−0.128547	−	0.222650i
$577$	−0.606944	+	1.05126i	−0.0252674	+	0.0437645i	−0.878383	−	0.477958i	$-0.841377\pi$
$577$	−0.606944	+	1.05126i	−0.0252674	+	0.0437645i	0.853115	+	0.521723i	$0.174710\pi$
$578$	−4.43969	+	7.68977i	−0.184667	+	0.319852i
$579$	−0.296789	−	0.514054i	−0.0123341	−	0.0213634i
$580$	1.30272			0.0540925
$581$	2.46198	−	15.3593i	0.102140	−	0.637212i
$582$	19.5817			0.811688
$583$	1.26604	+	2.19285i	0.0524342	+	0.0908187i
$584$	0.698463	−	1.20977i	0.0289026	−	0.0500608i
$585$	0.266044	−	0.460802i	0.0109996	−	0.0190518i
$586$	−6.37804	−	11.0471i	−0.263474	−	0.456351i
$587$	−27.9881			−1.15519			−0.577597	−	0.816322i	$-0.696010\pi$
$587$	−27.9881			−1.15519			−0.577597	+	0.816322i	$0.696010\pi$
$588$	−0.496596	−	2.37981i	−0.0204793	−	0.0981419i
$589$	−12.8530			−0.529598
$590$	0.915593	+	1.58585i	0.0376944	+	0.0652886i
$591$	3.53936	−	6.13036i	0.145590	−	0.252169i
$592$	−1.49273	+	2.58548i	−0.0613507	+	0.106262i
$593$	9.93154	+	17.2019i	0.407840	+	0.706399i	0.994647	−	0.103327i	$-0.0329490\pi$
$593$	9.93154	+	17.2019i	0.407840	+	0.706399i	−0.586808	+	0.809726i	$0.699616\pi$
$594$	−4.41147			−0.181005
$595$	0.745815	−	4.65284i	0.0305754	−	0.190748i
$596$	2.01010			0.0823371
$597$	−1.87551	−	3.24849i	−0.0767597	−	0.132952i
$598$	6.02481	−	10.4353i	0.246373	−	0.426731i
$599$	−4.59580	+	7.96016i	−0.187779	+	0.325243i	−0.944510	−	0.328484i	$-0.893462\pi$
$599$	−4.59580	+	7.96016i	−0.187779	+	0.325243i	0.756730	+	0.653727i	$0.226796\pi$
$600$	−5.97178	−	10.3434i	−0.243797	−	0.422269i
$601$	19.2317			0.784479			0.392239	−	0.919863i	$-0.371700\pi$
$601$	19.2317			0.784479			0.392239	+	0.919863i	$0.371700\pi$
$602$	23.1236	−	8.82699i	0.942448	−	0.359761i
$603$	−12.3969			−0.504842
$604$	0.128356	+	0.222318i	0.00522271	+	0.00904600i
$605$	−0.720752	+	1.24838i	−0.0293027	+	0.0507538i
$606$	−11.1322	+	19.2816i	−0.452216	+	0.783261i
$607$	−9.32934	−	16.1589i	−0.378666	−	0.655869i	0.612202	−	0.790701i	$-0.290284\pi$
$607$	−9.32934	−	16.1589i	−0.378666	−	0.655869i	−0.990868	+	0.134832i	$0.956951\pi$
$608$	−4.01186			−0.162702
$609$	−14.4731	−	11.7648i	−0.586481	−	0.476732i
$610$	−6.76508			−0.273910
$611$	−4.75877	−	8.24243i	−0.192519	−	0.333453i
$612$	−0.581252	+	1.00676i	−0.0234957	+	0.0406958i
$613$	−7.99660	+	13.8505i	−0.322979	+	0.559417i	−0.981101	−	0.193495i	$-0.938018\pi$
$613$	−7.99660	+	13.8505i	−0.322979	+	0.559417i	0.658122	+	0.752911i	$0.271351\pi$
$614$	−17.5797	−	30.4489i	−0.709457	−	1.22882i
$615$	−2.44562			−0.0986170
$616$	14.9684	+	12.1673i	0.603093	+	0.490236i
$617$	39.4056			1.58641			0.793205	−	0.608955i	$-0.208411\pi$
$617$	39.4056			1.58641			0.793205	+	0.608955i	$0.208411\pi$
$618$	−8.95858	−	15.5167i	−0.360367	−	0.624174i
$619$	−15.3528	+	26.5919i	−0.617082	+	1.06882i	0.372934	+	0.927858i	$0.378352\pi$
$619$	−15.3528	+	26.5919i	−0.617082	+	1.06882i	−0.990015	+	0.140959i	$0.954981\pi$
$620$	0.575322	−	0.996487i	0.0231055	−	0.0400199i
$621$	3.93242	+	6.81115i	0.157803	+	0.273322i
$622$	−1.81521			−0.0727832
$623$	13.5706	−	5.18031i	0.543694	−	0.207545i
$624$	4.57398			0.183106
$625$	−10.4167	−	18.0422i	−0.416668	−	0.721689i
$626$	−3.36025	+	5.82013i	−0.134303	+	0.232619i
$627$	2.97178	−	5.14728i	0.118682	−	0.205562i
$628$	−3.74510	−	6.48670i	−0.149446	−	0.258848i
$629$	−2.18479			−0.0871134
$630$	−0.341367	+	2.12965i	−0.0136004	+	0.0848473i
$631$	21.4270			0.852994			0.426497	−	0.904489i	$-0.359748\pi$
$631$	21.4270			0.852994			0.426497	+	0.904489i	$0.359748\pi$
$632$	14.7062	+	25.4719i	0.584981	+	1.01322i
$633$	−5.17499	+	8.96335i	−0.205687	+	0.356261i
$634$	1.37939	−	2.38917i	0.0547824	−	0.0948859i
$635$	−3.74376	−	6.48438i	−0.148566	−	0.257325i
$636$	−0.305407			−0.0121102
$637$	−6.64930	−	2.18788i	−0.263455	−	0.0866869i
$638$	−31.0993			−1.23123
$639$	−5.30793	−	9.19361i	−0.209979	−	0.363694i
$640$	−3.54916	+	6.14733i	−0.140293	+	0.242995i
$641$	18.6395	−	32.2846i	0.736216	−	1.27516i	−0.217972	−	0.975955i	$-0.569944\pi$
$641$	18.6395	−	32.2846i	0.736216	−	1.27516i	0.954188	−	0.299208i	$-0.0967226\pi$
$642$	1.98293	+	3.43453i	0.0782598	+	0.135550i
$643$	23.7169			0.935303			0.467651	−	0.883913i	$-0.345100\pi$
$643$	23.7169			0.935303			0.467651	+	0.883913i	$0.345100\pi$
$644$	−1.14378	+	7.13559i	−0.0450713	+	0.281182i
$645$	−3.24897			−0.127928
$646$	−5.29292	−	9.16760i	−0.208247	−	0.360695i
$647$	−5.03462	+	8.72021i	−0.197931	+	0.342827i	−0.947857	−	0.318695i	$-0.896756\pi$
$647$	−5.03462	+	8.72021i	−0.197931	+	0.342827i	0.749926	+	0.661521i	$0.230089\pi$
$648$	−1.26604	+	2.19285i	−0.0497349	+	0.0861434i
$649$	−3.23396	−	5.60138i	−0.126944	−	0.219873i
$650$	7.22668			0.283454
$651$	−15.3910	+	5.87522i	−0.603221	+	0.230268i
$652$	−0.549001			−0.0215005
$653$	9.87480	+	17.1037i	0.386431	+	0.669318i	0.991967	−	0.126500i	$-0.0403745\pi$
$653$	9.87480	+	17.1037i	0.386431	+	0.669318i	−0.605536	+	0.795818i	$0.707041\pi$
$654$	−11.9081	+	20.6254i	−0.465642	+	0.806516i
$655$	1.24969	−	2.16452i	0.0488293	−	0.0845747i
$656$	−10.5116	−	18.2066i	−0.410409	−	0.710850i
$657$	−0.551689			−0.0215234
$658$	29.9368	+	24.3347i	1.16706	+	0.948664i
$659$	12.8075			0.498908			0.249454	−	0.968387i	$-0.419749\pi$
$659$	12.8075			0.498908			0.249454	+	0.968387i	$0.419749\pi$
$660$	0.266044	+	0.460802i	0.0103558	+	0.0179367i
$661$	17.3824	−	30.1072i	0.676096	−	1.17103i	−0.300051	−	0.953923i	$-0.597004\pi$
$661$	17.3824	−	30.1072i	0.676096	−	1.17103i	0.976147	−	0.217110i	$-0.0696630\pi$
$662$	19.2895	−	33.4104i	0.749708	−	1.29853i
$663$	1.67365	+	2.89884i	0.0649991	+	0.112582i
$664$	−14.8871			−0.577733
$665$	−2.25490	−	1.83294i	−0.0874413	−	0.0710783i
$666$	1.00000			0.0387492
$667$	27.7221	+	48.0161i	1.07340	+	1.85919i
$668$	−1.96926	+	3.41085i	−0.0761928	+	0.131970i
$669$	10.3478	−	17.9229i	0.400068	−	0.692937i
$670$	5.05303	+	8.75211i	0.195216	+	0.338124i
$671$	23.8949			0.922451
$672$	−4.80406	+	1.83386i	−0.185321	+	0.0707426i
$673$	12.8479			0.495251			0.247626	−	0.968856i	$-0.420350\pi$
$673$	12.8479			0.495251			0.247626	+	0.968856i	$0.420350\pi$
$674$	−15.0116	−	26.0009i	−0.578226	−	1.00152i
$675$	−2.35844	+	4.08494i	−0.0907764	+	0.157229i
$676$	−0.173648	+	0.300767i	−0.00667878	+	0.0115680i
$677$	−4.86571	−	8.42767i	−0.187005	−	0.323901i	0.757246	−	0.653130i	$-0.226545\pi$
$677$	−4.86571	−	8.42767i	−0.187005	−	0.323901i	−0.944250	+	0.329229i	$0.893211\pi$
$678$	32.1334			1.23408
$679$	−5.35204	+	33.3893i	−0.205393	+	1.28136i
$680$	−4.50980			−0.172943
$681$	−8.70233	−	15.0729i	−0.333474	−	0.577594i
$682$	−13.7344	+	23.7887i	−0.525918	+	0.910917i
$683$	−21.1125	+	36.5679i	−0.807846	+	1.39923i	0.106507	+	0.994312i	$0.466033\pi$
$683$	−21.1125	+	36.5679i	−0.807846	+	1.39923i	−0.914353	+	0.404918i	$0.867300\pi$
$684$	0.358441	+	0.620838i	0.0137053	+	0.0237383i
$685$	−5.50568			−0.210361
$686$	28.3436	−	1.32683i	1.08217	−	0.0506585i
$687$	−1.90673			−0.0727461
$688$	−13.9645	−	24.1872i	−0.532392	−	0.922130i
$689$	−0.439693	+	0.761570i	−0.0167510	+	0.0290135i
$690$	3.20574	−	5.55250i	0.122040	−	0.211380i
$691$	−3.51114	−	6.08148i	−0.133570	−	0.231350i	0.791480	−	0.611195i	$-0.209311\pi$
$691$	−3.51114	−	6.08148i	−0.133570	−	0.231350i	−0.925050	+	0.379844i	$0.875978\pi$
$692$	0.816141			0.0310250
$693$	1.20574	−	7.52211i	0.0458022	−	0.285742i
$694$	−17.3027			−0.656802
$695$	1.50181	+	2.60121i	0.0569669	+	0.0986696i
$696$	−8.92514	+	15.4588i	−0.338307	+	0.585964i
$697$	7.69253	−	13.3239i	0.291375	−	0.504677i
$698$	10.8662	+	18.8208i	0.411291	+	0.712377i
$699$	10.9932			0.415801
$700$	−4.04916	+	1.54569i	−0.153044	+	0.0584216i
$701$	−7.47834			−0.282453			−0.141227	−	0.989977i	$-0.545105\pi$
$701$	−7.47834			−0.282453			−0.141227	+	0.989977i	$0.545105\pi$
$702$	−0.766044	−	1.32683i	−0.0289125	−	0.0500779i
$703$	−0.673648	+	1.16679i	−0.0254071	+	0.0440064i
$704$	8.88326	−	15.3863i	0.334800	−	0.579891i
$705$	−2.53209	−	4.38571i	−0.0953640	−	0.165175i
$706$	−34.5749			−1.30124
$707$	−29.8349	−	24.2518i	−1.12206	−	0.912085i
$708$	0.780126			0.0293189
$709$	8.05010	+	13.9432i	0.302328	+	0.523647i	0.976663	−	0.214779i	$-0.0689030\pi$
$709$	8.05010	+	13.9432i	0.302328	+	0.523647i	−0.674335	+	0.738426i	$0.735570\pi$
$710$	−4.32707	+	7.49470i	−0.162392	+	0.281271i
$711$	5.80793	−	10.0596i	0.217815	−	0.377266i
$712$	−6.95084	−	12.0392i	−0.260494	−	0.451188i
$713$	48.9718			1.83401
$714$	−10.5287	−	8.55845i	−0.394026	−	0.320292i
$715$	1.53209			0.0572969
$716$	2.05004	+	3.55077i	0.0766136	+	0.132699i
$717$	5.98680	−	10.3694i	0.223581	−	0.387254i
$718$	−16.9381	+	29.3376i	−0.632124	+	1.09487i
$719$	−13.8584	−	24.0035i	−0.516833	−	0.895180i	−0.999809	−	0.0195470i	$-0.993778\pi$
$719$	−13.8584	−	24.0035i	−0.516833	−	0.895180i	0.482976	−	0.875633i	$-0.339556\pi$
$720$	2.43376			0.0907010
$721$	28.9065	−	11.0345i	1.07653	−	0.410946i
$722$	22.5817			0.840405
$723$	12.0103	+	20.8024i	0.446667	+	0.773649i
$724$	−3.44016	+	5.95853i	−0.127853	+	0.221447i
$725$	−16.6261	+	28.7973i	−0.617479	+	1.06951i
$726$	2.07532	+	3.59456i	0.0770224	+	0.133407i
$727$	−19.4543			−0.721520			−0.360760	−	0.932659i	$-0.617483\pi$
$727$	−19.4543			−0.721520			−0.360760	+	0.932659i	$0.617483\pi$
$728$	−1.06031	+	6.61484i	−0.0392976	+	0.245162i
$729$	1.00000			0.0370370
$730$	0.224871	+	0.389487i	0.00832283	+	0.0144156i
$731$	10.2194	−	17.7005i	0.377978	−	0.654678i
$732$	−1.44104	+	2.49595i	−0.0532623	+	0.0922529i
$733$	−20.8705	−	36.1488i	−0.770870	−	1.33519i	−0.937087	−	0.349097i	$-0.886488\pi$
$733$	−20.8705	−	36.1488i	−0.770870	−	1.33519i	0.166216	−	0.986089i	$-0.446845\pi$
$734$	47.4361			1.75090
$735$	−3.53802	−	1.16415i	−0.130502	−	0.0429401i
$736$	15.2858			0.563442
$737$	−17.8478	−	30.9132i	−0.657431	−	1.13870i
$738$	−3.52094	+	6.09845i	−0.129608	+	0.224487i
$739$	−10.2173	+	17.6970i	−0.375851	+	0.650993i	−0.990454	−	0.137843i	$-0.955983\pi$
$739$	−10.2173	+	17.6970i	−0.375851	+	0.650993i	0.614603	+	0.788837i	$0.289316\pi$
$740$	−0.0603074	−	0.104455i	−0.00221694	−	0.00383986i
$741$	2.06418			0.0758295
$742$	0.564178	−	3.51968i	0.0207116	−	0.129212i
$743$	42.7965			1.57005			0.785026	−	0.619462i	$-0.212649\pi$
$743$	42.7965			1.57005			0.785026	+	0.619462i	$0.212649\pi$
$744$	7.88326	+	13.6542i	0.289014	+	0.500587i
$745$	1.53983	−	2.66706i	0.0564150	−	0.0977136i
$746$	22.4761	−	38.9298i	0.822909	−	1.42532i
$747$	2.93969	+	5.09170i	0.107558	+	0.186295i
$748$	−3.34730			−0.122389
$749$	−6.39827	+	2.44242i	−0.233788	+	0.0892440i
$750$	7.92127			0.289244
$751$	22.0476	+	38.1875i	0.804527	+	1.39348i	0.916610	+	0.399783i	$0.130915\pi$
$751$	22.0476	+	38.1875i	0.804527	+	1.39348i	−0.112082	+	0.993699i	$0.535752\pi$
$752$	21.7665	−	37.7007i	0.793743	−	1.37480i
$753$	5.41400	−	9.37732i	0.197297	−	0.341729i
$754$	−5.40033	−	9.35365i	−0.196668	−	0.340640i
$755$	0.393304			0.0143138
$756$	0.713011	+	0.579585i	0.0259320	+	0.0210793i
$757$	−3.65951			−0.133007			−0.0665036	−	0.997786i	$-0.521184\pi$
$757$	−3.65951			−0.133007			−0.0665036	+	0.997786i	$0.521184\pi$
$758$	28.5128	+	49.3856i	1.03563	+	1.79377i
$759$	−11.3229	+	19.6119i	−0.410997	+	0.711868i
$760$	−1.39053	+	2.40847i	−0.0504398	+	0.0873643i
$761$	4.33915	+	7.51562i	0.157294	+	0.272441i	0.933892	−	0.357555i	$-0.116390\pi$
$761$	4.33915	+	7.51562i	0.157294	+	0.272441i	−0.776598	+	0.629996i	$0.783056\pi$
$762$	−21.5594			−0.781016
$763$	−31.9142	−	25.9420i	−1.15537	−	0.939165i
$764$	4.04282			0.146264
$765$	0.890530	+	1.54244i	0.0321972	+	0.0557671i
$766$	−11.3721	+	19.6971i	−0.410891	+	0.711684i
$767$	1.12314	−	1.94534i	0.0405543	−	0.0702421i
$768$	4.04916	+	7.01336i	0.146112	+	0.253073i
$769$	35.8939			1.29437			0.647184	−	0.762334i	$-0.275946\pi$
$769$	35.8939			1.29437			0.647184	+	0.762334i	$0.275946\pi$
$770$	−5.80200	+	2.21480i	−0.209090	+	0.0798160i
$771$

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 1.32683i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.173648 + 0.300767i) q^{4} +(0.266044 + 0.460802i) q^{5} +1.53209 q^{6} +(-0.418748 + 2.61240i) q^{7} +2.53209 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 1.32683i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.173648 + 0.300767i) q^{4} +(0.266044 + 0.460802i) q^{5} +1.53209 q^{6} +(-0.418748 + 2.61240i) q^{7} +2.53209 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.407604 + 0.705990i) q^{10} +(1.43969 - 2.49362i) q^{11} +(0.173648 + 0.300767i) q^{12} +1.00000 q^{13} +(-3.78699 + 1.44561i) q^{14} +0.532089 q^{15} +(2.28699 + 3.96118i) q^{16} +(-1.67365 + 2.89884i) q^{17} +(0.766044 - 1.32683i) q^{18} +(1.03209 + 1.78763i) q^{19} -0.184793 q^{20} +(2.05303 + 1.66885i) q^{21} +4.41147 q^{22} +(-3.93242 - 6.81115i) q^{23} +(1.26604 - 2.19285i) q^{24} +(2.35844 - 4.08494i) q^{25} +(0.766044 + 1.32683i) q^{26} -1.00000 q^{27} +(-0.713011 - 0.579585i) q^{28} -7.04963 q^{29} +(0.407604 + 0.705990i) q^{30} +(-3.11334 + 5.39246i) q^{31} +(-0.971782 + 1.68317i) q^{32} +(-1.43969 - 2.49362i) q^{33} -5.12836 q^{34} +(-1.31521 + 0.502055i) q^{35} +0.347296 q^{36} +(0.326352 + 0.565258i) q^{37} +(-1.58125 + 2.73881i) q^{38} +(0.500000 - 0.866025i) q^{39} +(0.673648 + 1.16679i) q^{40} -4.59627 q^{41} +(-0.641559 + 4.00243i) q^{42} -6.10607 q^{43} +(0.500000 + 0.866025i) q^{44} +(0.266044 - 0.460802i) q^{45} +(6.02481 - 10.4353i) q^{46} +(-4.75877 - 8.24243i) q^{47} +4.57398 q^{48} +(-6.64930 - 2.18788i) q^{49} +7.22668 q^{50} +(1.67365 + 2.89884i) q^{51} +(-0.173648 + 0.300767i) q^{52} +(-0.439693 + 0.761570i) q^{53} +(-0.766044 - 1.32683i) q^{54} +1.53209 q^{55} +(-1.06031 + 6.61484i) q^{56} +2.06418 q^{57} +(-5.40033 - 9.35365i) q^{58} +(1.12314 - 1.94534i) q^{59} +(-0.0923963 + 0.160035i) q^{60} +(4.14930 + 7.18680i) q^{61} -9.53983 q^{62} +(2.47178 - 0.943555i) q^{63} +6.17024 q^{64} +(0.266044 + 0.460802i) q^{65} +(2.20574 - 3.82045i) q^{66} +(6.19846 - 10.7361i) q^{67} +(-0.581252 - 1.00676i) q^{68} -7.86484 q^{69} +(-1.67365 - 1.36046i) q^{70} +10.6159 q^{71} +(-1.26604 - 2.19285i) q^{72} +(0.275845 - 0.477777i) q^{73} +(-0.500000 + 0.866025i) q^{74} +(-2.35844 - 4.08494i) q^{75} -0.716881 q^{76} +(5.91147 + 4.80526i) q^{77} +1.53209 q^{78} +(5.80793 + 10.0596i) q^{79} +(-1.21688 + 2.10770i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.52094 - 6.09845i) q^{82} -5.87939 q^{83} +(-0.858441 + 0.327693i) q^{84} -1.78106 q^{85} +(-4.67752 - 8.10170i) q^{86} +(-3.52481 + 6.10516i) q^{87} +(3.64543 - 6.31407i) q^{88} +(-2.74510 - 4.75465i) q^{89} +0.815207 q^{90} +(-0.418748 + 2.61240i) q^{91} +2.73143 q^{92} +(3.11334 + 5.39246i) q^{93} +(7.29086 - 12.6281i) q^{94} +(-0.549163 + 0.951178i) q^{95} +(0.971782 + 1.68317i) q^{96} +12.7811 q^{97} +(-2.19072 - 10.4985i) q^{98} -2.87939 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} - 3 q^{5} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 - 3 * q^5 + 6 * q^8 - 3 * q^9	\( 6 q + 3 q^{3} - 3 q^{5} + 6 q^{8} - 3 q^{9} - 6 q^{10} + 3 q^{11} + 6 q^{13} - 15 q^{14} - 6 q^{15} + 6 q^{16} - 9 q^{17} - 3 q^{19} + 6 q^{20} + 6 q^{22} + 3 q^{24} + 6 q^{25} - 6 q^{27} - 12 q^{28} + 12 q^{29} + 6 q^{30} - 12 q^{31} + 9 q^{32} - 3 q^{33} + 6 q^{34} - 15 q^{35} + 3 q^{37} - 12 q^{38} + 3 q^{39} + 3 q^{40} - 12 q^{42} - 12 q^{43} + 3 q^{44} - 3 q^{45} + 9 q^{46} - 6 q^{47} + 12 q^{48} + 30 q^{50} + 9 q^{51} + 3 q^{53} - 12 q^{56} - 6 q^{57} - 18 q^{58} + 3 q^{59} + 3 q^{60} - 15 q^{61} - 6 q^{64} - 3 q^{65} + 3 q^{66} + 9 q^{67} - 6 q^{68} - 9 q^{70} + 42 q^{71} - 3 q^{72} - 3 q^{74} - 6 q^{75} + 12 q^{76} + 15 q^{77} + 24 q^{79} + 9 q^{80} - 3 q^{81} - 18 q^{82} - 24 q^{83} + 3 q^{84} + 24 q^{85} - 3 q^{86} + 6 q^{87} + 6 q^{88} - 15 q^{89} + 12 q^{90} + 36 q^{92} + 12 q^{93} + 12 q^{94} - 15 q^{95} - 9 q^{96} + 42 q^{97} - 33 q^{98} - 6 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 - 3 * q^5 + 6 * q^8 - 3 * q^9 - 6 * q^10 + 3 * q^11 + 6 * q^13 - 15 * q^14 - 6 * q^15 + 6 * q^16 - 9 * q^17 - 3 * q^19 + 6 * q^20 + 6 * q^22 + 3 * q^24 + 6 * q^25 - 6 * q^27 - 12 * q^28 + 12 * q^29 + 6 * q^30 - 12 * q^31 + 9 * q^32 - 3 * q^33 + 6 * q^34 - 15 * q^35 + 3 * q^37 - 12 * q^38 + 3 * q^39 + 3 * q^40 - 12 * q^42 - 12 * q^43 + 3 * q^44 - 3 * q^45 + 9 * q^46 - 6 * q^47 + 12 * q^48 + 30 * q^50 + 9 * q^51 + 3 * q^53 - 12 * q^56 - 6 * q^57 - 18 * q^58 + 3 * q^59 + 3 * q^60 - 15 * q^61 - 6 * q^64 - 3 * q^65 + 3 * q^66 + 9 * q^67 - 6 * q^68 - 9 * q^70 + 42 * q^71 - 3 * q^72 - 3 * q^74 - 6 * q^75 + 12 * q^76 + 15 * q^77 + 24 * q^79 + 9 * q^80 - 3 * q^81 - 18 * q^82 - 24 * q^83 + 3 * q^84 + 24 * q^85 - 3 * q^86 + 6 * q^87 + 6 * q^88 - 15 * q^89 + 12 * q^90 + 36 * q^92 + 12 * q^93 + 12 * q^94 - 15 * q^95 - 9 * q^96 + 42 * q^97 - 33 * q^98 - 6 * q^99

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