LMFDB - Embedded newform 273.2.bd.a.127.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(43,273)]

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, 0, 1]))

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

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

chi := DirichletCharacter("273.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bd (of order $6$, 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 22x^{14} + 187x^{12} + 774x^{10} + 1619x^{8} + 1618x^{6} + 690x^{4} + 96x^{2} + 1 $ x^16 + 22x^14 + 187x^12 + 774x^10 + 1619x^8 + 1618x^6 + 690x^4 + 96*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.5
Root			$-0.106359i$ of defining polynomial
Character	$\chi$	$=$	273.127
Dual form			273.2.bd.a.43.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0921099 - 0.0531797i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.994344 + 1.72225i) q^{4} +1.41292i q^{5} +(-0.0921099 - 0.0531797i) q^{6} +(-0.866025 - 0.500000i) q^{7} +0.424234i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.0921099 - 0.0531797i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.994344 + 1.72225i) q^{4} +1.41292i q^{5} +(-0.0921099 - 0.0531797i) q^{6} +(-0.866025 - 0.500000i) q^{7} +0.424234i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.0751388 + 0.130144i) q^{10} +(-2.59849 + 1.50024i) q^{11} +1.98869 q^{12} +(-2.15831 + 2.88820i) q^{13} -0.106359 q^{14} +(1.22363 - 0.706461i) q^{15} +(-1.96613 - 3.40543i) q^{16} +(-3.18356 + 5.51409i) q^{17} +0.106359i q^{18} +(4.59287 + 2.65169i) q^{19} +(-2.43341 - 1.40493i) q^{20} +1.00000i q^{21} +(-0.159564 + 0.276374i) q^{22} +(-0.335958 - 0.581896i) q^{23} +(0.367398 - 0.212117i) q^{24} +3.00365 q^{25} +(-0.0452086 + 0.380810i) q^{26} +1.00000 q^{27} +(1.72225 - 0.994344i) q^{28} +(-0.258294 - 0.447378i) q^{29} +(0.0751388 - 0.130144i) q^{30} +0.282012i q^{31} +(-1.09700 - 0.633350i) q^{32} +(2.59849 + 1.50024i) q^{33} +0.677203i q^{34} +(0.706461 - 1.22363i) q^{35} +(-0.994344 - 1.72225i) q^{36} +(5.58864 - 3.22660i) q^{37} +0.564065 q^{38} +(3.58041 + 0.425055i) q^{39} -0.599410 q^{40} +(-3.43979 + 1.98596i) q^{41} +(0.0531797 + 0.0921099i) q^{42} +(2.47219 - 4.28196i) q^{43} -5.96701i q^{44} +(-1.22363 - 0.706461i) q^{45} +(-0.0618900 - 0.0357322i) q^{46} -5.91777i q^{47} +(-1.96613 + 3.40543i) q^{48} +(0.500000 + 0.866025i) q^{49} +(0.276666 - 0.159733i) q^{50} +6.36712 q^{51} +(-2.82810 - 6.58902i) q^{52} -12.2506 q^{53} +(0.0921099 - 0.0531797i) q^{54} +(-2.11972 - 3.67146i) q^{55} +(0.212117 - 0.367398i) q^{56} -5.30339i q^{57} +(-0.0475828 - 0.0274720i) q^{58} +(-1.99362 - 1.15102i) q^{59} +2.80986i q^{60} +(-2.01942 + 3.49774i) q^{61} +(0.0149973 + 0.0259761i) q^{62} +(0.866025 - 0.500000i) q^{63} +7.72978 q^{64} +(-4.08080 - 3.04953i) q^{65} +0.319129 q^{66} +(1.83088 - 1.05706i) q^{67} +(-6.33111 - 10.9658i) q^{68} +(-0.335958 + 0.581896i) q^{69} -0.150278i q^{70} +(12.7089 + 7.33750i) q^{71} +(-0.367398 - 0.212117i) q^{72} +6.44186i q^{73} +(0.343180 - 0.594405i) q^{74} +(-1.50183 - 2.60124i) q^{75} +(-9.13378 + 5.27339i) q^{76} +3.00048 q^{77} +(0.352395 - 0.151253i) q^{78} +12.6905 q^{79} +(4.81161 - 2.77798i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.211226 + 0.365854i) q^{82} +8.49842i q^{83} +(-1.72225 - 0.994344i) q^{84} +(-7.79098 - 4.49812i) q^{85} -0.525881i q^{86} +(-0.258294 + 0.447378i) q^{87} +(-0.636453 - 1.10237i) q^{88} +(9.89266 - 5.71153i) q^{89} -0.150278 q^{90} +(3.31325 - 1.42210i) q^{91} +1.33623 q^{92} +(0.244229 - 0.141006i) q^{93} +(-0.314705 - 0.545085i) q^{94} +(-3.74664 + 6.48936i) q^{95} +1.26670i q^{96} +(0.317706 + 0.183428i) q^{97} +(0.0921099 + 0.0531797i) q^{98} -3.00048i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9	$ 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9} - 4 q^{10} - 12 q^{11} - 12 q^{12} + 4 q^{13} + 4 q^{14} - 10 q^{16} + 10 q^{17} + 6 q^{20} - 2 q^{22} - 2 q^{23} + 12 q^{25} + 20 q^{26} + 16 q^{27} + 12 q^{29} - 4 q^{30} + 30 q^{32} + 12 q^{33} - 2 q^{35} + 6 q^{36} + 18 q^{37} - 32 q^{38} - 8 q^{39} - 60 q^{40} + 18 q^{41} - 2 q^{42} - 10 q^{43} + 30 q^{46} - 10 q^{48} + 8 q^{49} - 24 q^{50} - 20 q^{51} - 26 q^{52} + 12 q^{53} + 10 q^{55} + 12 q^{56} - 54 q^{58} - 60 q^{59} - 6 q^{61} + 16 q^{62} + 16 q^{64} - 20 q^{65} + 4 q^{66} - 18 q^{67} - 20 q^{68} - 2 q^{69} + 6 q^{71} + 18 q^{74} - 6 q^{75} + 72 q^{76} - 16 q^{77} + 14 q^{78} - 4 q^{79} + 30 q^{80} - 8 q^{81} - 18 q^{82} - 24 q^{85} + 12 q^{87} - 2 q^{88} + 78 q^{89} + 8 q^{90} - 8 q^{91} - 20 q^{92} + 6 q^{93} + 16 q^{94} - 4 q^{95} - 54 q^{97}+O(q^{100}) $ 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9 - 4 * q^10 - 12 * q^11 - 12 * q^12 + 4 * q^13 + 4 * q^14 - 10 * q^16 + 10 * q^17 + 6 * q^20 - 2 * q^22 - 2 * q^23 + 12 * q^25 + 20 * q^26 + 16 * q^27 + 12 * q^29 - 4 * q^30 + 30 * q^32 + 12 * q^33 - 2 * q^35 + 6 * q^36 + 18 * q^37 - 32 * q^38 - 8 * q^39 - 60 * q^40 + 18 * q^41 - 2 * q^42 - 10 * q^43 + 30 * q^46 - 10 * q^48 + 8 * q^49 - 24 * q^50 - 20 * q^51 - 26 * q^52 + 12 * q^53 + 10 * q^55 + 12 * q^56 - 54 * q^58 - 60 * q^59 - 6 * q^61 + 16 * q^62 + 16 * q^64 - 20 * q^65 + 4 * q^66 - 18 * q^67 - 20 * q^68 - 2 * q^69 + 6 * q^71 + 18 * q^74 - 6 * q^75 + 72 * q^76 - 16 * q^77 + 14 * q^78 - 4 * q^79 + 30 * q^80 - 8 * q^81 - 18 * q^82 - 24 * q^85 + 12 * q^87 - 2 * q^88 + 78 * q^89 + 8 * q^90 - 8 * q^91 - 20 * q^92 + 6 * q^93 + 16 * q^94 - 4 * q^95 - 54 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	0.0921099	−	0.0531797i	0.0651315	−	0.0376037i	−0.467081	−	0.884215i	$-0.654694\pi$
$2$	0.0921099	−	0.0531797i	0.0651315	−	0.0376037i	0.532212	+	0.846611i	$0.321361\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.994344	+	1.72225i	−0.497172	+	0.861127i
$5$			1.41292i			0.631878i	0.948780	+	0.315939i	$0.102319\pi$
$5$			1.41292i			0.631878i	−0.948780	+	0.315939i	$0.897681\pi$
$6$	−0.0921099	−	0.0531797i	−0.0376037	−	0.0217105i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$			0.424234i			0.149989i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.0751388	+	0.130144i	0.0237610	+	0.0411552i
$11$	−2.59849	+	1.50024i	−0.783474	+	0.452339i	−0.837660	−	0.546192i	$-0.816077\pi$
$11$	−2.59849	+	1.50024i	−0.783474	+	0.452339i	0.0541862	+	0.998531i	$0.482744\pi$
$12$	1.98869			0.574085
$13$	−2.15831	+	2.88820i	−0.598608	+	0.801042i
$13$	−2.15831	+	2.88820i	−0.598608	+	0.801042i
$14$	−0.106359			−0.0284257
$15$	1.22363	−	0.706461i	0.315939	−	0.182407i
$16$	−1.96613	−	3.40543i	−0.491532	−	0.851358i
$17$	−3.18356	+	5.51409i	−0.772127	+	1.33736i	0.164268	+	0.986416i	$0.447474\pi$
$17$	−3.18356	+	5.51409i	−0.772127	+	1.33736i	−0.936395	+	0.350948i	$0.885859\pi$
$18$			0.106359i			0.0250691i
$19$	4.59287	+	2.65169i	1.05368	+	0.608340i	0.923676	−	0.383174i	$-0.125169\pi$
$19$	4.59287	+	2.65169i	1.05368	+	0.608340i	0.130000	+	0.991514i	$0.458502\pi$
$20$	−2.43341	−	1.40493i	−0.544127	−	0.314152i
$21$			1.00000i			0.218218i
$22$	−0.159564	+	0.276374i	−0.0340192	+	0.0589231i
$23$	−0.335958	−	0.581896i	−0.0700520	−	0.121334i	0.828872	−	0.559438i	$-0.188983\pi$
$23$	−0.335958	−	0.581896i	−0.0700520	−	0.121334i	−0.898924	+	0.438105i	$0.855650\pi$
$24$	0.367398	−	0.212117i	0.0749947	−	0.0432982i
$25$	3.00365			0.600730
$26$	−0.0452086	+	0.380810i	−0.00886614	+	0.0746830i
$27$	1.00000			0.192450
$28$	1.72225	−	0.994344i	0.325475	−	0.187913i
$29$	−0.258294	−	0.447378i	−0.0479639	−	0.0830760i	0.841047	−	0.540963i	$-0.181940\pi$
$29$	−0.258294	−	0.447378i	−0.0479639	−	0.0830760i	−0.889011	+	0.457887i	$0.848607\pi$
$30$	0.0751388	−	0.130144i	0.0137184	−	0.0237610i
$31$			0.282012i			0.0506508i	0.999679	+	0.0253254i	$0.00806218\pi$
$31$			0.282012i			0.0506508i	−0.999679	+	0.0253254i	$0.991938\pi$
$32$	−1.09700	−	0.633350i	−0.193923	−	0.111962i
$33$	2.59849	+	1.50024i	0.452339	+	0.261158i
$34$			0.677203i			0.116139i
$35$	0.706461	−	1.22363i	0.119414	−	0.206831i
$36$	−0.994344	−	1.72225i	−0.165724	−	0.287042i
$37$	5.58864	−	3.22660i	0.918767	−	0.530451i	0.0355257	−	0.999369i	$-0.488689\pi$
$37$	5.58864	−	3.22660i	0.918767	−	0.530451i	0.883242	+	0.468918i	$0.155356\pi$
$38$	0.564065			0.0915034
$39$	3.58041	+	0.425055i	0.573324	+	0.0680633i
$40$	−0.599410			−0.0947750
$41$	−3.43979	+	1.98596i	−0.537205	+	0.310155i	−0.743945	−	0.668240i	$-0.767048\pi$
$41$	−3.43979	+	1.98596i	−0.537205	+	0.310155i	0.206741	+	0.978396i	$0.433714\pi$
$42$	0.0531797	+	0.0921099i	0.00820580	+	0.0142129i
$43$	2.47219	−	4.28196i	0.377005	−	0.652993i	−0.613620	−	0.789602i	$-0.710287\pi$
$43$	2.47219	−	4.28196i	0.377005	−	0.652993i	0.990625	+	0.136609i	$0.0436205\pi$
$44$		−	5.96701i		−	0.899561i
$45$	−1.22363	−	0.706461i	−0.182407	−	0.105313i
$46$	−0.0618900	−	0.0357322i	−0.00912519	−	0.00526843i
$47$		−	5.91777i		−	0.863195i	−0.902066	−	0.431598i	$-0.857950\pi$
$47$		−	5.91777i		−	0.863195i	0.902066	−	0.431598i	$-0.142050\pi$
$48$	−1.96613	+	3.40543i	−0.283786	+	0.491532i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	0.276666	−	0.159733i	0.0391265	−	0.0225897i
$51$	6.36712			0.891576
$52$	−2.82810	−	6.58902i	−0.392187	−	0.913733i
$53$	−12.2506			−1.68275			−0.841375	−	0.540451i	$-0.818254\pi$
$53$	−12.2506			−1.68275			−0.841375	+	0.540451i	$0.818254\pi$
$54$	0.0921099	−	0.0531797i	0.0125346	−	0.00723684i
$55$	−2.11972	−	3.67146i	−0.285823	−	0.495060i
$56$	0.212117	−	0.367398i	0.0283453	−	0.0490956i
$57$		−	5.30339i		−	0.702451i
$58$	−0.0475828	−	0.0274720i	−0.00624793	−	0.00360724i
$59$	−1.99362	−	1.15102i	−0.259547	−	0.149850i	0.364581	−	0.931172i	$-0.381212\pi$
$59$	−1.99362	−	1.15102i	−0.259547	−	0.149850i	−0.624128	+	0.781322i	$0.714546\pi$
$60$			2.80986i			0.362751i
$61$	−2.01942	+	3.49774i	−0.258561	+	0.447840i	−0.965857	−	0.259077i	$-0.916582\pi$
$61$	−2.01942	+	3.49774i	−0.258561	+	0.447840i	0.707296	+	0.706918i	$0.249915\pi$
$62$	0.0149973	+	0.0259761i	0.00190466	+	0.00329896i
$63$	0.866025	−	0.500000i	0.109109	−	0.0629941i
$64$	7.72978			0.966223
$65$	−4.08080	−	3.04953i	−0.506161	−	0.378247i
$66$	0.319129			0.0392820
$67$	1.83088	−	1.05706i	0.223678	−	0.129140i	−0.383974	−	0.923344i	$-0.625445\pi$
$67$	1.83088	−	1.05706i	0.223678	−	0.129140i	0.607652	+	0.794203i	$0.292112\pi$
$68$	−6.33111	−	10.9658i	−0.767760	−	1.32980i
$69$	−0.335958	+	0.581896i	−0.0404445	+	0.0700520i
$70$		−	0.150278i		−	0.0179616i
$71$	12.7089	+	7.33750i	1.50827	+	0.870801i	0.999954	+	0.00963255i	$0.00306618\pi$
$71$	12.7089	+	7.33750i	1.50827	+	0.870801i	0.508319	+	0.861169i	$0.330267\pi$
$72$	−0.367398	−	0.212117i	−0.0432982	−	0.0249982i
$73$			6.44186i			0.753963i	0.926221	+	0.376981i	$0.123038\pi$
$73$			6.44186i			0.753963i	−0.926221	+	0.376981i	$0.876962\pi$
$74$	0.343180	−	0.594405i	0.0398938	−	0.0690981i
$75$	−1.50183	−	2.60124i	−0.173416	−	0.300365i
$76$	−9.13378	+	5.27339i	−1.04772	+	0.604899i
$77$	3.00048			0.341936
$78$	0.352395	−	0.151253i	0.0399009	−	0.0171261i
$79$	12.6905			1.42779			0.713894	−	0.700254i	$-0.246930\pi$
$79$	12.6905			1.42779			0.713894	+	0.700254i	$0.246930\pi$
$80$	4.81161	−	2.77798i	0.537954	−	0.310588i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−0.211226	+	0.365854i	−0.0233260	+	0.0404018i
$83$			8.49842i			0.932823i	0.884568	+	0.466412i	$0.154453\pi$
$83$			8.49842i			0.932823i	−0.884568	+	0.466412i	$0.845547\pi$
$84$	−1.72225	−	0.994344i	−0.187913	−	0.108492i
$85$	−7.79098	−	4.49812i	−0.845051	−	0.487890i
$86$		−	0.525881i		−	0.0567072i
$87$	−0.258294	+	0.447378i	−0.0276920	+	0.0479639i
$88$	−0.636453	−	1.10237i	−0.0678461	−	0.117513i
$89$	9.89266	−	5.71153i	1.04862	−	0.605421i	0.126357	−	0.991985i	$-0.459671\pi$
$89$	9.89266	−	5.71153i	1.04862	−	0.605421i	0.922263	+	0.386564i	$0.126338\pi$
$90$	−0.150278			−0.0158406
$91$	3.31325	−	1.42210i	0.347323	−	0.149076i
$92$	1.33623			0.139312
$93$	0.244229	−	0.141006i	0.0253254	−	0.0146216i
$94$	−0.314705	−	0.545085i	−0.0324593	−	0.0562212i
$95$	−3.74664	+	6.48936i	−0.384397	+	0.665795i
$96$			1.26670i			0.129282i
$97$	0.317706	+	0.183428i	0.0322582	+	0.0186243i	0.516042	−	0.856563i	$-0.327405\pi$
$97$	0.317706	+	0.183428i	0.0322582	+	0.0186243i	−0.483784	+	0.875187i	$0.660738\pi$
$98$	0.0921099	+	0.0531797i	0.00930451	+	0.00537196i
$99$		−	3.00048i		−	0.301559i
$100$	−2.98666	+	5.17305i	−0.298666	+	0.517305i
$101$	9.17591	+	15.8931i	0.913038	+	1.58143i	0.809749	+	0.586776i	$0.199603\pi$
$101$	9.17591	+	15.8931i	0.913038	+	1.58143i	0.103288	+	0.994651i	$0.467064\pi$
$102$	0.586475	−	0.338602i	0.0580697	−	0.0335266i
$103$	3.99871			0.394005			0.197003	−	0.980403i	$-0.436879\pi$
$103$	3.99871			0.394005			0.197003	+	0.980403i	$0.436879\pi$
$104$	−1.22527	−	0.915631i	−0.120148	−	0.0897850i
$105$	−1.41292			−0.137887
$106$	−1.12840	+	0.651484i	−0.109600	+	0.0632777i
$107$	0.0498285	+	0.0863055i	0.00481710	+	0.00834347i	0.868424	−	0.495822i	$-0.165133\pi$
$107$	0.0498285	+	0.0863055i	0.00481710	+	0.00834347i	−0.863607	+	0.504166i	$0.831800\pi$
$108$	−0.994344	+	1.72225i	−0.0956808	+	0.165724i
$109$		−	4.98762i		−	0.477727i	−0.971053	−	0.238864i	$-0.923225\pi$
$109$		−	4.98762i		−	0.477727i	0.971053	−	0.238864i	$-0.0767749\pi$
$110$	−0.390494	−	0.225452i	−0.0372322	−	0.0214960i
$111$	−5.58864	−	3.22660i	−0.530451	−	0.306256i
$112$			3.93225i			0.371563i
$113$	−2.01023	+	3.48182i	−0.189106	+	0.327542i	−0.944953	−	0.327207i	$-0.893892\pi$
$113$	−2.01023	+	3.48182i	−0.189106	+	0.327542i	0.755846	+	0.654749i	$0.227226\pi$
$114$	−0.282032	−	0.488495i	−0.0264148	−	0.0457517i
$115$	0.822173	−	0.474682i	0.0766680	−	0.0442643i
$116$	1.02733			0.0953853
$117$	−1.42210	−	3.31325i	−0.131473	−	0.306310i
$118$	−0.244843			−0.0225396
$119$	5.51409	−	3.18356i	0.505476	−	0.291837i
$120$	0.299705	+	0.519104i	0.0273592	+	0.0473875i
$121$	−0.998571	+	1.72957i	−0.0907791	+	0.157234i
$122$			0.429569i			0.0388914i
$123$	3.43979	+	1.98596i	0.310155	+	0.179068i
$124$	−0.485695	−	0.280416i	−0.0436167	−	0.0251821i
$125$			11.3085i			1.01147i
$126$	0.0531797	−	0.0921099i	0.00473762	−	0.00820580i
$127$	−8.29720	−	14.3712i	−0.736258	−	1.27524i	−0.954169	−	0.299267i	$-0.903258\pi$
$127$	−8.29720	−	14.3712i	−0.736258	−	1.27524i	0.217912	−	0.975968i	$-0.430075\pi$
$128$	2.90598	−	1.67777i	0.256855	−	0.148295i
$129$	−4.94438			−0.435328
$130$	−0.538055	−	0.0638763i	−0.0471905	−	0.00560232i
$131$	−18.6490			−1.62937			−0.814685	−	0.579903i	$-0.803090\pi$
$131$	−18.6490			−1.62937			−0.814685	+	0.579903i	$0.803090\pi$
$132$	−5.16758	+	2.98351i	−0.449780	+	0.259681i
$133$	−2.65169	−	4.59287i	−0.229931	−	0.398252i
$134$	0.112428	−	0.194731i	0.00971231	−	0.0168222i
$135$			1.41292i			0.121605i
$136$	−2.33927	−	1.35058i	−0.200590	−	0.115811i
$137$	−8.63202	−	4.98370i	−0.737483	−	0.425786i	0.0836703	−	0.996493i	$-0.473336\pi$
$137$	−8.63202	−	4.98370i	−0.737483	−	0.425786i	−0.821154	+	0.570707i	$0.806669\pi$
$138$			0.0714645i			0.00608346i
$139$	−10.7887	+	18.6865i	−0.915083	+	1.58497i	−0.108304	+	0.994118i	$0.534542\pi$
$139$	−10.7887	+	18.6865i	−0.915083	+	1.58497i	−0.806779	+	0.590853i	$0.798791\pi$
$140$	1.40493	+	2.43341i	0.118738	+	0.205661i
$141$	−5.12494	+	2.95888i	−0.431598	+	0.249183i
$142$	1.56082			0.130981
$143$	1.27537	−	10.7429i	0.106652	−	0.898369i
$144$	3.93225			0.327688
$145$	0.632110	−	0.364949i	0.0524939	−	0.0303074i
$146$	0.342576	+	0.593359i	0.0283518	+	0.0491068i
$147$	0.500000	−	0.866025i	0.0412393	−	0.0714286i
$148$			12.8334i			1.05490i
$149$	19.7528	+	11.4043i	1.61822	+	0.934278i	0.987381	+	0.158360i	$0.0506208\pi$
$149$	19.7528	+	11.4043i	1.61822	+	0.934278i	0.630835	+	0.775917i	$0.282713\pi$
$150$	−0.276666	−	0.159733i	−0.0225897	−	0.0130422i
$151$			16.9055i			1.37575i	0.725830	+	0.687874i	$0.241456\pi$
$151$			16.9055i			1.37575i	−0.725830	+	0.687874i	$0.758544\pi$
$152$	−1.12494	+	1.94845i	−0.0912446	+	0.158040i
$153$	−3.18356	−	5.51409i	−0.257376	−	0.445788i
$154$	0.276374	−	0.159564i	0.0222708	−	0.0128581i
$155$	−0.398460			−0.0320051
$156$	−4.29221	+	5.74372i	−0.343652	+	0.459866i
$157$	−11.9666			−0.955042			−0.477521	−	0.878620i	$-0.658464\pi$
$157$	−11.9666			−0.955042			−0.477521	+	0.878620i	$0.658464\pi$
$158$	1.16892	−	0.674875i	0.0929941	−	0.0536901i
$159$	6.12531	+	10.6093i	0.485768	+	0.841375i
$160$	0.894875	−	1.54997i	0.0707461	−	0.122536i
$161$			0.671915i			0.0529543i
$162$	−0.0921099	−	0.0531797i	−0.00723684	−	0.00417819i
$163$	0.243006	+	0.140300i	0.0190337	+	0.0109891i	0.509487	−	0.860479i	$-0.329835\pi$
$163$	0.243006	+	0.140300i	0.0190337	+	0.0109891i	−0.490453	+	0.871468i	$0.663169\pi$
$164$		−	7.89892i		−	0.616802i
$165$	−2.11972	+	3.67146i	−0.165020	+	0.285823i
$166$	0.451943	+	0.782789i	0.0350776	+	0.0607562i
$167$	18.0299	−	10.4096i	1.39519	−	0.805515i	0.401309	−	0.915943i	$-0.368555\pi$
$167$	18.0299	−	10.4096i	1.39519	−	0.805515i	0.993884	+	0.110427i	$0.0352219\pi$
$168$	−0.424234			−0.0327304
$169$	−3.68337	−	12.4673i	−0.283336	−	0.959021i
$170$	−0.956835			−0.0733859
$171$	−4.59287	+	2.65169i	−0.351225	+	0.202780i
$172$	4.91641	+	8.51548i	0.374873	+	0.649299i
$173$	−2.78360	+	4.82134i	−0.211633	+	0.366560i	−0.952226	−	0.305395i	$-0.901212\pi$
$173$	−2.78360	+	4.82134i	−0.211633	+	0.366560i	0.740593	+	0.671954i	$0.234545\pi$
$174$			0.0549439i			0.00416529i
$175$	−2.60124	−	1.50183i	−0.196635	−	0.113527i
$176$	10.2179	+	5.89932i	0.770205	+	0.444678i
$177$			2.30204i			0.173032i
$178$	0.607475	−	1.05218i	0.0455322	−	0.0788640i
$179$	−3.04664	−	5.27693i	−0.227716	−	0.394416i	0.729415	−	0.684072i	$-0.239793\pi$
$179$	−3.04664	−	5.27693i	−0.227716	−	0.394416i	−0.957131	+	0.289656i	$0.906459\pi$
$180$	2.43341	−	1.40493i	0.181376	−	0.104717i
$181$	−15.8856			−1.18077			−0.590383	−	0.807123i	$-0.701023\pi$
$181$	−15.8856			−1.18077			−0.590383	+	0.807123i	$0.701023\pi$
$182$	0.229557	−	0.307187i	0.0170159	−	0.0227702i
$183$	4.03885			0.298560
$184$	0.246860	−	0.142525i	0.0181988	−	0.0105071i
$185$	4.55894	+	7.89632i	0.335180	+	0.580549i
$186$	0.0149973	−	0.0259761i	0.00109965	−	0.00190466i
$187$		−	19.1044i		−	1.39705i
$188$	10.1919	+	5.88429i	0.743321	+	0.429156i
$189$	−0.866025	−	0.500000i	−0.0629941	−	0.0363696i
$190$			0.796980i			0.0578190i
$191$	−2.65336	+	4.59576i	−0.191990	+	0.332537i	−0.945910	−	0.324430i	$-0.894828\pi$
$191$	−2.65336	+	4.59576i	−0.191990	+	0.332537i	0.753919	+	0.656967i	$0.228161\pi$
$192$	−3.86489	−	6.69419i	−0.278925	−	0.483111i
$193$	1.80340	−	1.04120i	0.129812	−	0.0749469i	−0.433688	−	0.901063i	$-0.642788\pi$
$193$	1.80340	−	1.04120i	0.129812	−	0.0749469i	0.563500	+	0.826116i	$0.309455\pi$
$194$	0.0390185			0.00280137
$195$	−0.600570	+	5.05884i	−0.0430077	+	0.362271i
$196$	−1.98869			−0.142049
$197$	8.55171	−	4.93733i	0.609284	−	0.351770i	−0.163401	−	0.986560i	$-0.552246\pi$
$197$	8.55171	−	4.93733i	0.609284	−	0.351770i	0.772685	+	0.634789i	$0.218913\pi$
$198$	−0.159564	−	0.276374i	−0.0113397	−	0.0196410i
$199$	−1.65804	+	2.87181i	−0.117535	+	0.203577i	−0.918790	−	0.394746i	$-0.870833\pi$
$199$	−1.65804	+	2.87181i	−0.117535	+	0.203577i	0.801255	+	0.598323i	$0.204166\pi$
$200$			1.27425i			0.0901032i
$201$	−1.83088	−	1.05706i	−0.129140	−	0.0745592i
$202$	1.69039	+	0.975944i	0.118935	+	0.0686672i
$203$			0.516587i			0.0362573i
$204$	−6.33111	+	10.9658i	−0.443266	+	0.767760i
$205$	−2.80601	−	4.86015i	−0.195980	−	0.339448i
$206$	0.368321	−	0.212650i	0.0256622	−	0.0148161i
$207$	0.671915			0.0467013
$208$	14.0791	+	1.67143i	0.976208	+	0.115893i
$209$	−15.9127			−1.10070
$210$	−0.130144	+	0.0751388i	−0.00898080	+	0.00518507i
$211$	8.73070	+	15.1220i	0.601046	+	1.04104i	0.992663	+	0.120914i	$0.0385824\pi$
$211$	8.73070	+	15.1220i	0.601046	+	1.04104i	−0.391617	+	0.920128i	$0.628084\pi$
$212$	12.1813	−	21.0987i	0.836616	−	1.44906i
$213$		−	14.6750i		−	1.00551i
$214$	0.00917940	+	0.00529973i	0.000627491	+	0.000362282i
$215$	6.05007	+	3.49301i	0.412612	+	0.238221i
$216$			0.424234i			0.0288655i
$217$	0.141006	−	0.244229i	0.00957209	−	0.0165794i
$218$	−0.265240	−	0.459409i	−0.0179643	−	0.0311151i
$219$	5.57881	−	3.22093i	0.376981	−	0.217650i
$220$	8.43092			0.568413
$221$	−9.05466	−	21.0959i	−0.609082	−	1.41906i
$222$	−0.686359			−0.0460654
$223$	16.2437	−	9.37830i	1.08776	−	0.628018i	0.154780	−	0.987949i	$-0.450533\pi$
$223$	16.2437	−	9.37830i	1.08776	−	0.628018i	0.932979	+	0.359932i	$0.117200\pi$
$224$	0.633350	+	1.09700i	0.0423175	+	0.0732961i
$225$	−1.50183	+	2.60124i	−0.100122	+	0.173416i
$226$			0.427613i			0.0284444i
$227$	14.1388	+	8.16303i	0.938424	+	0.541800i	0.889466	−	0.457001i	$-0.151076\pi$
$227$	14.1388	+	8.16303i	0.938424	+	0.541800i	0.0489584	+	0.998801i	$0.484410\pi$
$228$	9.13378	+	5.27339i	0.604899	+	0.349239i
$229$			11.3658i			0.751071i	0.926808	+	0.375536i	$0.122541\pi$
$229$			11.3658i			0.751071i	−0.926808	+	0.375536i	$0.877459\pi$
$230$	0.0504869	−	0.0874458i	0.00332901	−	0.00576601i
$231$	−1.50024	−	2.59849i	−0.0987084	−	0.170968i
$232$	0.189793	−	0.109577i	0.0124605	−	0.00719409i
$233$	−30.2591			−1.98234			−0.991170	−	0.132600i	$-0.957668\pi$
$233$	−30.2591			−1.98234			−0.991170	+	0.132600i	$0.957668\pi$
$234$	−0.307187	−	0.229557i	−0.0200814	−	0.0150066i
$235$	8.36134			0.545434
$236$	3.96469	−	2.28901i	0.258079	−	0.149002i
$237$	−6.34523	−	10.9903i	−0.412167	−	0.713894i
$238$	0.338602	−	0.586475i	0.0219483	−	0.0380155i
$239$		−	17.1229i		−	1.10759i	−0.832653	−	0.553795i	$-0.813179\pi$
$239$		−	17.1229i		−	1.10759i	0.832653	−	0.553795i	$-0.186821\pi$
$240$	−4.81161	−	2.77798i	−0.310588	−	0.179318i
$241$	−15.0080	−	8.66488i	−0.966751	−	0.558154i	−0.0685070	−	0.997651i	$-0.521824\pi$
$241$	−15.0080	−	8.66488i	−0.966751	−	0.558154i	−0.898244	+	0.439497i	$0.855157\pi$
$242$			0.212415i			0.0136545i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−4.01600	−	6.95592i	−0.257098	−	0.445307i
$245$	−1.22363	+	0.706461i	−0.0781746	+	0.0451341i
$246$	0.422452			0.0269345
$247$	−17.5715	+	7.54192i	−1.11805	+	0.479881i
$248$	−0.119639			−0.00759708
$249$	7.35985	−	4.24921i	0.466412	−	0.269283i
$250$	0.601384	+	1.04163i	0.0380349	+	0.0658784i
$251$	5.68772	−	9.85141i	0.359005	−	0.621816i	−0.628790	−	0.777576i	$-0.716449\pi$
$251$	5.68772	−	9.85141i	0.359005	−	0.621816i	0.987795	+	0.155760i	$0.0497826\pi$
$252$			1.98869i			0.125276i
$253$	1.74596	+	1.00803i	0.109768	+	0.0633745i
$254$	−1.52851	−	0.882485i	−0.0959072	−	0.0553720i
$255$			8.99625i			0.563367i
$256$	−7.55134	+	13.0793i	−0.471959	+	0.817456i
$257$	8.96446	+	15.5269i	0.559187	+	0.968541i	0.997565	+	0.0697498i	$0.0222201\pi$
$257$	8.96446	+	15.5269i	0.559187	+	0.968541i	−0.438377	+	0.898791i	$0.644447\pi$
$258$	−0.455426	+	0.262941i	−0.0283536	+	0.0163700i
$259$	−6.45321			−0.400983
$260$	9.30978	−	3.99589i	0.577368	−	0.247815i
$261$	0.516587			0.0319760
$262$	−1.71776	+	0.991748i	−0.106123	+	0.0612704i
$263$	−10.3532	−	17.9322i	−0.638403	−	1.10575i	−0.985783	−	0.168022i	$-0.946262\pi$
$263$	−10.3532	−	17.9322i	−0.638403	−	1.10575i	0.347380	−	0.937724i	$-0.387071\pi$
$264$	−0.636453	+	1.10237i	−0.0391709	+	0.0678461i
$265$		−	17.3092i		−	1.06329i
$266$	−0.488495	−	0.282032i	−0.0299515	−	0.0172925i
$267$	−9.89266	−	5.71153i	−0.605421	−	0.349540i
$268$			4.20432i			0.256820i
$269$	3.78020	−	6.54749i	0.230483	−	0.399208i	−0.727468	−	0.686142i	$-0.759303\pi$
$269$	3.78020	−	6.54749i	0.230483	−	0.399208i	0.957950	+	0.286934i	$0.0926362\pi$
$270$	0.0751388	+	0.130144i	0.00457280	+	0.00792032i
$271$	16.1415	−	9.31929i	0.980525	−	0.566107i	0.0780967	−	0.996946i	$-0.475116\pi$
$271$	16.1415	−	9.31929i	0.980525	−	0.566107i	0.902429	+	0.430839i	$0.141782\pi$
$272$	25.0371			1.51810
$273$	−2.88820	−	2.15831i	−0.174802	−	0.130627i
$274$	−1.06013			−0.0640446
$275$	−7.80495	+	4.50619i	−0.470656	+	0.271734i
$276$	−0.668115	−	1.15721i	−0.0402158	−	0.0696558i
$277$	8.80206	−	15.2456i	0.528864	−	0.916020i	−0.470569	−	0.882363i	$-0.655951\pi$
$277$	8.80206	−	15.2456i	0.528864	−	0.916020i	0.999433	−	0.0336569i	$-0.0107154\pi$
$278$			2.29495i			0.137642i
$279$	−0.244229	−	0.141006i	−0.0146216	−	0.00844179i
$280$	0.519104	+	0.299705i	0.0310224	+	0.0179108i
$281$		−	17.5012i		−	1.04404i	−0.852934	−	0.522018i	$-0.825179\pi$
$281$		−	17.5012i		−	1.04404i	0.852934	−	0.522018i	$-0.174821\pi$
$282$	−0.314705	+	0.545085i	−0.0187404	+	0.0324593i
$283$	8.20550	+	14.2123i	0.487766	+	0.844836i	0.999901	−	0.0140690i	$-0.00447846\pi$
$283$	8.20550	+	14.2123i	0.487766	+	0.844836i	−0.512135	+	0.858905i	$0.671145\pi$
$284$	−25.2741	+	14.5920i	−1.49974	+	0.865876i
$285$	7.49327			0.443863
$286$	−0.453832	−	1.05735i	−0.0268356	−	0.0625227i
$287$	3.97193			0.234455
$288$	1.09700	−	0.633350i	0.0646411	−	0.0373205i
$289$	−11.7701	−	20.3865i	−0.692361	−	1.19920i
$290$	0.0388157	−	0.0672308i	0.00227934	−	0.00394793i
$291$		−	0.366855i		−	0.0215054i
$292$	−11.0945	−	6.40542i	−0.649258	−	0.374849i
$293$	24.2855	+	14.0212i	1.41877	+	0.819128i	0.996191	−	0.0871971i	$-0.0277910\pi$
$293$	24.2855	+	14.0212i	1.41877	+	0.819128i	0.422581	+	0.906325i	$0.361124\pi$
$294$		−	0.106359i		−	0.00620300i
$295$	1.62630	−	2.81683i	0.0946867	−	0.164002i
$296$	1.36884	+	2.37089i	0.0795620	+	0.137805i
$297$	−2.59849	+	1.50024i	−0.150780	+	0.0870527i
$298$	2.42591			0.140529
$299$	2.40573	+	0.285601i	0.139127	+	0.0165167i
$300$	5.97332			0.344870
$301$	−4.28196	+	2.47219i	−0.246808	+	0.142495i
$302$	0.899028	+	1.55716i	0.0517332	+	0.0896046i
$303$	9.17591	−	15.8931i	0.527142	−	0.913038i
$304$		−	20.8543i		−	1.19607i
$305$	−4.94204	−	2.85329i	−0.282980	−	0.163379i
$306$	−0.586475	−	0.338602i	−0.0335266	−	0.0193566i
$307$		−	23.6211i		−	1.34813i	−0.738674	−	0.674063i	$-0.764548\pi$
$307$		−	23.6211i		−	1.34813i	0.738674	−	0.674063i	$-0.235452\pi$
$308$	−2.98351	+	5.16758i	−0.170001	+	0.294450i
$309$	−1.99936	−	3.46299i	−0.113739	−	0.197003i
$310$	−0.0367021	+	0.0211900i	−0.00208454	+	0.00120351i
$311$	13.2516			0.751431			0.375716	−	0.926735i	$-0.377397\pi$
$311$	13.2516			0.751431			0.375716	+	0.926735i	$0.377397\pi$
$312$	−0.180323	+	1.51893i	−0.0102088	+	0.0859926i
$313$	−11.1849			−0.632210			−0.316105	−	0.948724i	$-0.602375\pi$
$313$	−11.1849			−0.632210			−0.316105	+	0.948724i	$0.602375\pi$
$314$	−1.10225	+	0.636382i	−0.0622033	+	0.0359131i
$315$	0.706461	+	1.22363i	0.0398046	+	0.0689435i
$316$	−12.6187	+	21.8562i	−0.709856	+	1.22951i
$317$			20.3673i			1.14394i	0.820274	+	0.571971i	$0.193821\pi$
$317$			20.3673i			1.14394i	−0.820274	+	0.571971i	$0.806179\pi$
$318$	1.12840	+	0.651484i	0.0632777	+	0.0365334i
$319$	1.34235	+	0.775004i	0.0751570	+	0.0433919i
$320$			10.9216i			0.610535i
$321$	0.0498285	−	0.0863055i	0.00278116	−	0.00481710i
$322$	0.0357322	+	0.0618900i	0.00199128	+	0.00344900i
$323$	−29.2434	+	16.8837i	−1.62714	+	0.939432i
$324$	1.98869			0.110483
$325$	−6.48282	+	8.67514i	−0.359602	+	0.481210i
$326$	0.0298443			0.00165293
$327$	−4.31940	+	2.49381i	−0.238864	+	0.137908i
$328$	−0.842514	−	1.45928i	−0.0465200	−	0.0805751i
$329$	−2.95888	+	5.12494i	−0.163129	+	0.282547i
$330$			0.450904i			0.0248215i
$331$	21.8214	+	12.5986i	1.19941	+	0.692481i	0.960424	−	0.278542i	$-0.0898511\pi$
$331$	21.8214	+	12.5986i	1.19941	+	0.692481i	0.238988	+	0.971023i	$0.423184\pi$
$332$	−14.6364	−	8.45035i	−0.803279	−	0.463773i
$333$			6.45321i			0.353634i
$334$	1.10715	−	1.91765i	0.0605807	−	0.104929i
$335$	1.49354	+	2.58689i	0.0816009	+	0.141337i
$336$	3.40543	−	1.96613i	0.185782	−	0.107261i
$337$	20.9316			1.14022			0.570108	−	0.821570i	$-0.306901\pi$
$337$	20.9316			1.14022			0.570108	+	0.821570i	$0.306901\pi$
$338$	−1.00228	−	0.952479i	−0.0545169	−	0.0518080i
$339$	4.02046			0.218361
$340$	15.4938	−	8.94537i	0.840271	−	0.485131i
$341$	−0.423084	−	0.732804i	−0.0229113	−	0.0396835i
$342$	−0.282032	+	0.488495i	−0.0152506	+	0.0264148i
$343$		−	1.00000i		−	0.0539949i
$344$	1.81655	+	1.04879i	0.0979420	+	0.0565469i
$345$	−0.822173	−	0.474682i	−0.0442643	−	0.0255560i
$346$			0.592124i			0.0318328i
$347$	11.8224	−	20.4769i	0.634658	−	1.09926i	−0.351930	−	0.936026i	$-0.614474\pi$
$347$	11.8224	−	20.4769i	0.634658	−	1.09926i	0.986588	−	0.163233i	$-0.0521922\pi$
$348$	−0.513666	−	0.889695i	−0.0275354	−	0.0476926i
$349$	20.6496	−	11.9221i	1.10535	−	0.638174i	0.167729	−	0.985833i	$-0.446357\pi$
$349$	20.6496	−	11.9221i	1.10535	−	0.638174i	0.937621	+	0.347659i	$0.113023\pi$
$350$	−0.319466			−0.0170762
$351$	−2.15831	+	2.88820i	−0.115202	+	0.154161i
$352$	3.80071			0.202578
$353$	7.42179	−	4.28497i	0.395022	−	0.228066i	−0.289312	−	0.957235i	$-0.593426\pi$
$353$	7.42179	−	4.28497i	0.395022	−	0.228066i	0.684334	+	0.729169i	$0.260093\pi$
$354$	0.122422	+	0.212040i	0.00650663	+	0.0112698i
$355$	−10.3673	+	17.9567i	−0.550240	+	0.953044i
$356$			22.7169i			1.20399i
$357$	−5.51409	−	3.18356i	−0.291837	−	0.168492i
$358$	−0.561251	−	0.324038i	−0.0296630	−	0.0171260i
$359$		−	7.78179i		−	0.410707i	−0.978688	−	0.205354i	$-0.934166\pi$
$359$		−	7.78179i		−	0.410707i	0.978688	−	0.205354i	$-0.0658345\pi$
$360$	0.299705	−	0.519104i	0.0157958	−	0.0273592i
$361$	4.56296	+	7.90328i	0.240156	+	0.415962i
$362$	−1.46322	+	0.844790i	−0.0769051	+	0.0444012i
$363$	1.99714			0.104823
$364$	−0.845302	+	7.12032i	−0.0443059	+	0.373206i
$365$	−9.10185			−0.476412
$366$	0.372018	−	0.214785i	0.0194457	−	0.0112270i
$367$	10.6801	+	18.4985i	0.557497	+	0.965613i	0.997705	+	0.0677170i	$0.0215715\pi$
$367$	10.6801	+	18.4985i	0.557497	+	0.965613i	−0.440208	+	0.897896i	$0.645095\pi$
$368$	−1.32107	+	2.28816i	−0.0688656	+	0.119279i
$369$		−	3.97193i		−	0.206770i
$370$	0.839847	+	0.484886i	0.0436616	+	0.0252080i
$371$	10.6093	+	6.12531i	0.550809	+	0.318010i
$372$			0.560833i			0.0290778i
$373$	−0.983516	+	1.70350i	−0.0509245	+	0.0882038i	−0.890364	−	0.455249i	$-0.849550\pi$
$373$	−0.983516	+	1.70350i	−0.0509245	+	0.0882038i	0.839439	+	0.543453i	$0.182883\pi$
$374$	−1.01597	−	1.75971i	−0.0525344	−	0.0909922i
$375$	9.79348	−	5.65427i	0.505733	−	0.291985i
$376$	2.51052			0.129470
$377$	1.84959	+	0.219578i	0.0952590	+	0.0113089i
$378$	−0.106359			−0.00547054
$379$	−27.9253	+	16.1227i	−1.43442	+	0.828166i	−0.997454	−	0.0713101i	$-0.977282\pi$
$379$	−27.9253	+	16.1227i	−1.43442	+	0.828166i	−0.436971	+	0.899476i	$0.643949\pi$
$380$	−7.45089	−	12.9053i	−0.382223	−	0.662029i
$381$	−8.29720	+	14.3712i	−0.425078	+	0.736258i
$382$			0.564420i			0.0288782i
$383$	−29.6304	−	17.1071i	−1.51404	−	0.874134i	−0.999865	−	0.0164510i	$-0.994763\pi$
$383$	−29.6304	−	17.1071i	−1.51404	−	0.874134i	−0.514179	−	0.857683i	$-0.671903\pi$
$384$	−2.90598	−	1.67777i	−0.148295	−	0.0856182i
$385$			4.23944i			0.216062i
$386$	0.110741	−	0.191809i	0.00563656	−	0.00976282i
$387$	2.47219	+	4.28196i	0.125668	+	0.217664i
$388$	−0.631818	+	0.364780i	−0.0320757	+	0.0185189i
$389$	0.953360			0.0483373			0.0241686	−	0.999708i	$-0.492306\pi$
$389$	0.953360			0.0483373			0.0241686	+	0.999708i	$0.492306\pi$
$390$	0.213709	+	0.497907i	0.0108216	+	0.0252125i
$391$	4.27817			0.216356
$392$	−0.367398	+	0.212117i	−0.0185564	+	0.0107135i
$393$	9.32450	+	16.1505i	0.470359	+	0.814685i
$394$	0.525132	−	0.909555i	0.0264558	−	0.0458227i
$395$			17.9306i			0.902188i
$396$	5.16758	+	2.98351i	0.259681	+	0.149927i
$397$	3.97200	+	2.29324i	0.199349	+	0.115094i	0.596352	−	0.802723i	$-0.296616\pi$
$397$	3.97200	+	2.29324i	0.199349	+	0.115094i	−0.397003	+	0.917817i	$0.629950\pi$
$398$			0.352696i			0.0176790i
$399$	−2.65169	+	4.59287i	−0.132751	+	0.229931i
$400$	−5.90556	−	10.2287i	−0.295278	−	0.511437i
$401$	−27.4317	+	15.8377i	−1.36987	+	0.790898i	−0.990912	−	0.134514i	$-0.957053\pi$
$401$	−27.4317	+	15.8377i	−1.36987	+	0.790898i	−0.378963	+	0.925412i	$0.623719\pi$
$402$	−0.224856			−0.0112148
$403$	−0.814505	−	0.608669i	−0.0405734	−	0.0303200i
$404$	−36.4961			−1.81575
$405$	1.22363	−	0.706461i	0.0608025	−	0.0351043i
$406$	0.0274720	+	0.0475828i	0.00136341	+	0.00236150i
$407$	−9.68135	+	16.7686i	−0.479887	+	0.831188i
$408$			2.70115i			0.133727i
$409$	9.42540	+	5.44175i	0.466056	+	0.269077i	0.714587	−	0.699546i	$-0.246615\pi$
$409$	9.42540	+	5.44175i	0.466056	+	0.269077i	−0.248531	+	0.968624i	$0.579948\pi$
$410$	−0.516923	−	0.298446i	−0.0255290	−	0.0147392i
$411$			9.96740i			0.491656i
$412$	−3.97610	+	6.88680i	−0.195888	+	0.339288i
$413$	1.15102	+	1.99362i	0.0566379	+	0.0980997i
$414$	0.0618900	−	0.0357322i	0.00304173	−	0.00175614i
$415$	−12.0076			−0.589430
$416$	4.19690	−	1.80137i	0.205770	−	0.0883194i
$417$	21.5773			1.05665
$418$	−1.46572	+	0.846232i	−0.0716905	+	0.0413906i
$419$	−8.41255	−	14.5710i	−0.410980	−	0.711838i	0.584017	−	0.811741i	$-0.301480\pi$
$419$	−8.41255	−	14.5710i	−0.410980	−	0.711838i	−0.994997	+	0.0999030i	$0.968147\pi$
$420$	1.40493	−	2.43341i	0.0685536	−	0.118738i
$421$			6.12271i			0.298403i	0.988807	+	0.149201i	$0.0476703\pi$
$421$			6.12271i			0.298403i	−0.988807	+	0.149201i	$0.952330\pi$
$422$	1.60837	+	0.928591i	0.0782941	+	0.0452031i
$423$	5.12494	+	2.95888i	0.249183	+	0.143866i
$424$		−	5.19713i		−	0.252395i
$425$	−9.56231	+	16.5624i	−0.463840	+	0.803395i
$426$	−0.780412	−	1.35171i	−0.0378111	−	0.0654907i
$427$	3.49774	−	2.01942i	0.169268	−	0.0977268i
$428$	−0.198187			−0.00957971
$429$	−9.94134	+	4.26696i	−0.479972	+	0.206011i
$430$	0.743029			0.0358320
$431$	−0.944545	+	0.545333i	−0.0454971	+	0.0262678i	−0.522576	−	0.852593i	$-0.675029\pi$
$431$	−0.944545	+	0.545333i	−0.0454971	+	0.0262678i	0.477079	+	0.878860i	$0.341696\pi$
$432$	−1.96613	−	3.40543i	−0.0945953	−	0.163844i
$433$	4.16989	−	7.22247i	0.200392	−	0.347090i	−0.748263	−	0.663403i	$-0.769112\pi$
$433$	4.16989	−	7.22247i	0.200392	−	0.347090i	0.948655	+	0.316313i	$0.102445\pi$
$434$		−	0.0299946i		−	0.00143979i
$435$	−0.632110	−	0.364949i	−0.0303074	−	0.0174980i
$436$	8.58994	+	4.95941i	0.411384	+	0.237512i
$437$		−	3.56343i		−	0.170462i
$438$	0.342576	−	0.593359i	0.0163689	−	0.0283518i
$439$	−2.87232	−	4.97500i	−0.137088	−	0.237444i	0.789305	−	0.614001i	$-0.210441\pi$
$439$	−2.87232	−	4.97500i	−0.137088	−	0.237444i	−0.926393	+	0.376557i	$0.877108\pi$
$440$	1.55756	−	0.899258i	0.0742538	−	0.0428704i
$441$	−1.00000			−0.0476190
$442$	−1.95590	−	1.46162i	−0.0930325	−	0.0695220i
$443$	−16.9750			−0.806505			−0.403252	−	0.915089i	$-0.632120\pi$
$443$	−16.9750			−0.806505			−0.403252	+	0.915089i	$0.632120\pi$
$444$	11.1141	−	6.41671i	0.527450	−	0.304524i
$445$	8.06995	+	13.9776i	0.382552	+	0.662600i
$446$	0.997470	−	1.72767i	0.0472316	−	0.0818075i
$447$		−	22.8086i		−	1.07881i
$448$	−6.69419	−	3.86489i	−0.316271	−	0.182599i
$449$	3.00681	+	1.73598i	0.141900	+	0.0819260i	0.569269	−	0.822151i	$-0.307226\pi$
$449$	3.00681	+	1.73598i	0.141900	+	0.0819260i	−0.427369	+	0.904077i	$0.640560\pi$
$450$			0.319466i			0.0150598i
$451$	5.95884	−	10.3210i	0.280591	−	0.485997i
$452$	−3.99772	−	6.92425i	−0.188037	−	0.325689i
$453$	14.6406	−	8.45274i	0.687874	−	0.397144i
$454$	1.73643			0.0814947
$455$	2.00931	+	4.68137i	0.0941979	+	0.219466i
$456$	2.24988			0.105360
$457$	−8.38992	+	4.84392i	−0.392464	+	0.226589i	−0.683227	−	0.730206i	$-0.739424\pi$
$457$	−8.38992	+	4.84392i	−0.392464	+	0.226589i	0.290763	+	0.956795i	$0.406091\pi$
$458$	0.604428	+	1.04690i	0.0282431	+	0.0489184i
$459$	−3.18356	+	5.51409i	−0.148596	+	0.257376i
$460$			1.88799i			0.0880279i
$461$	−9.60668	−	5.54642i	−0.447428	−	0.258322i	0.259316	−	0.965793i	$-0.416503\pi$
$461$	−9.60668	−	5.54642i	−0.447428	−	0.258322i	−0.706743	+	0.707470i	$0.749836\pi$
$462$	−0.276374	−	0.159564i	−0.0128581	−	0.00742361i
$463$		−	31.1633i		−	1.44828i	−0.689653	−	0.724140i	$-0.742237\pi$
$463$		−	31.1633i		−	1.44828i	0.689653	−	0.724140i	$-0.257763\pi$
$464$	−1.01568	+	1.75920i	−0.0471516	+	0.0816690i
$465$	0.199230	+	0.345077i	0.00923908	+	0.0160025i
$466$	−2.78716	+	1.60917i	−0.129113	+	0.0745433i
$467$	−27.7222			−1.28283			−0.641415	−	0.767194i	$-0.721652\pi$
$467$	−27.7222			−1.28283			−0.641415	+	0.767194i	$0.721652\pi$
$468$	7.12032	+	0.845302i	0.329137	+	0.0390741i
$469$	−2.11412			−0.0976209
$470$	0.770163	−	0.444654i	0.0355250	−	0.0205103i
$471$	5.98332	+	10.3634i	0.275697	+	0.477521i
$472$	0.488301	−	0.845763i	0.0224759	−	0.0389294i
$473$			14.8355i			0.682137i
$474$	−1.16892	−	0.674875i	−0.0536901	−	0.0309980i
$475$	13.7954	+	7.96476i	0.632975	+	0.365448i
$476$			12.6622i			0.580372i
$477$	6.12531	−	10.6093i	0.280458	−	0.485768i
$478$	−0.910591	−	1.57719i	−0.0416495	−	0.0721390i
$479$	4.95825	−	2.86265i	0.226548	−	0.130798i	−0.382430	−	0.923984i	$-0.624913\pi$
$479$	4.95825	−	2.86265i	0.226548	−	0.130798i	0.608979	+	0.793187i	$0.291579\pi$
$480$	−1.78975			−0.0816905
$481$	−2.74297	+	23.1051i	−0.125069	+	1.05350i
$482$	−1.84318			−0.0839547
$483$	0.581896	−	0.335958i	0.0264772	−	0.0152866i
$484$	−1.98585	−	3.43958i	−0.0902657	−	0.156345i
$485$	−0.259169	+	0.448894i	−0.0117683	+	0.0203832i
$486$			0.106359i			0.00482456i
$487$	−3.09809	−	1.78868i	−0.140388	−	0.0810530i	0.428161	−	0.903703i	$-0.359162\pi$
$487$	−3.09809	−	1.78868i	−0.140388	−	0.0810530i	−0.568549	+	0.822649i	$0.692495\pi$
$488$	−1.48386	−	0.856709i	−0.0671713	−	0.0387814i
$489$		−	0.280599i		−	0.0126891i
$490$	−0.0751388	+	0.130144i	−0.00339442	+	0.00587931i
$491$	1.73305	+	3.00172i	0.0782112	+	0.135466i	0.902478	−	0.430735i	$-0.141746\pi$
$491$	1.73305	+	3.00172i	0.0782112	+	0.135466i	−0.824267	+	0.566201i	$0.808412\pi$
$492$	−6.84067	+	3.94946i	−0.308401	+	0.178055i
$493$	3.28918			0.148137
$494$	−1.21743	+	1.62913i	−0.0547747	+	0.0732981i
$495$	4.23944			0.190549
$496$	0.960371	−	0.554470i	0.0431219	−	0.0248965i
$497$	−7.33750	−	12.7089i	−0.329132	−	0.570073i
$498$	0.451943	−	0.782789i	0.0202521	−	0.0350776i
$499$			34.0041i			1.52223i	0.648615	+	0.761117i	$0.275349\pi$
$499$			34.0041i			1.52223i	−0.648615	+	0.761117i	$0.724651\pi$
$500$	−19.4762	−	11.2446i	−0.871001	−	0.502873i
$501$	−18.0299	−	10.4096i	−0.805515	−	0.465064i
$502$		−	1.20988i		−	0.0539998i
$503$	15.9551	−	27.6351i	0.711405	−	1.23219i	−0.252925	−	0.967486i	$-0.581393\pi$
$503$	15.9551	−	27.6351i	0.711405	−	1.23219i	0.964330	−	0.264703i	$-0.0852741\pi$
$504$	0.212117	+	0.367398i	0.00944845	+	0.0163652i
$505$	−22.4558	+	12.9649i	−0.999269	+	0.576928i
$506$	0.214427			0.00953246
$507$	−8.95529	+	9.42352i	−0.397718	+	0.418513i
$508$	33.0011			1.46419
$509$	14.3010	−	8.25670i	0.633882	−	0.365972i	−0.148372	−	0.988932i	$-0.547403\pi$
$509$	14.3010	−	8.25670i	0.633882	−	0.365972i	0.782254	+	0.622960i	$0.214070\pi$
$510$	0.478418	+	0.828644i	0.0211847	+	0.0366930i
$511$	3.22093	−	5.57881i	0.142486	−	0.246792i
$512$			8.31738i			0.367580i
$513$	4.59287	+	2.65169i	0.202780	+	0.117075i
$514$	1.65143	+	0.953454i	0.0728415	+	0.0420550i
$515$			5.64987i			0.248963i
$516$	4.91641	−	8.51548i	0.216433	−	0.374873i
$517$	8.87806	+	15.3773i	0.390457	+	0.676291i
$518$	−0.594405	+	0.343180i	−0.0261166	+	0.0150784i
$519$	5.56720			0.244373
$520$	1.29371	−	1.73121i	0.0567331	−	0.0759188i
$521$	14.4961			0.635087			0.317544	−	0.948244i	$-0.397142\pi$
$521$	14.4961			0.635087			0.317544	+	0.948244i	$0.397142\pi$
$522$	0.0475828	−	0.0274720i	0.00208264	−	0.00120241i
$523$	−1.91544	−	3.31764i	−0.0837564	−	0.145070i	0.821104	−	0.570778i	$-0.193358\pi$
$523$	−1.91544	−	3.31764i	−0.0837564	−	0.145070i	−0.904861	+	0.425708i	$0.860025\pi$
$524$	18.5435	−	32.1183i	0.810077	−	1.40310i
$525$			3.00365i			0.131090i
$526$	−1.90726	−	1.10116i	−0.0831603	−	0.0480126i
$527$	−1.55504	−	0.897801i	−0.0677385	−	0.0391088i
$528$		−	11.7986i		−	0.513470i
$529$	11.2743	−	19.5276i	0.490185	−	0.849026i
$530$	−0.920496	−	1.59435i	−0.0399838	−	0.0692539i
$531$	1.99362	−	1.15102i	0.0865158	−	0.0499499i
$532$	10.5468			0.457261
$533$	1.68829	−	14.2211i	0.0731279	−	0.615985i
$534$	−1.21495			−0.0525760
$535$	−0.121943	+	0.0704038i	−0.00527205	+	0.00304382i
$536$	0.448441	+	0.776722i	0.0193697	+	0.0335493i
$537$	−3.04664	+	5.27693i	−0.131472	+	0.227716i
$538$		−	0.804119i		−	0.0346680i
$539$	−2.59849	−	1.50024i	−0.111925	−	0.0646198i
$540$	−2.43341	−	1.40493i	−0.104717	−	0.0604586i
$541$			0.948185i			0.0407656i	0.999792	+	0.0203828i	$0.00648850\pi$
$541$			0.948185i			0.0407656i	−0.999792	+	0.0203828i	$0.993511\pi$
$542$	0.991194	−	1.71680i	0.0425754	−	0.0737428i
$543$	7.94279	+	13.7573i	0.340858	+	0.590383i
$544$	6.98470	−	4.03262i	0.299467	−	0.172897i
$545$	7.04711			0.301865
$546$	−0.380810	−	0.0452086i	−0.0162972	−	0.00193475i
$547$	30.4804			1.30325			0.651624	−	0.758542i	$-0.274088\pi$
$547$	30.4804			1.30325			0.651624	+	0.758542i	$0.274088\pi$
$548$	17.1664	−	9.91102i	0.733312	−	0.423378i
$549$	−2.01942	−	3.49774i	−0.0861869	−	0.149280i
$550$	−0.479276	+	0.830130i	−0.0204364	+	0.0353969i
$551$		−	2.73966i		−	0.116714i
$552$	−0.246860	−	0.142525i	−0.0105071	−	0.00606626i
$553$	−10.9903	−	6.34523i	−0.467353	−	0.269827i
$554$		−	1.87236i		−	0.0795491i
$555$	4.55894	−	7.89632i	0.193516	−	0.335180i
$556$	−21.4553	−	37.1617i	−0.909907	−	1.57601i
$557$	10.9506	−	6.32232i	0.463991	−	0.267885i	−0.249730	−	0.968316i	$-0.580342\pi$
$557$	10.9506	−	6.32232i	0.463991	−	0.267885i	0.713721	+	0.700430i	$0.247009\pi$
$558$	−0.0299946			−0.00126977
$559$	7.03138	+	16.3820i	0.297396	+	0.692884i
$560$	−5.55597			−0.234783
$561$	−16.5449	+	9.55220i	−0.698526	+	0.403294i
$562$	−0.930711	−	1.61204i	−0.0392597	−	0.0679997i
$563$	−7.95571	+	13.7797i	−0.335293	+	0.580745i	−0.983541	−	0.180684i	$-0.942169\pi$
$563$	−7.95571	+	13.7797i	−0.335293	+	0.580745i	0.648248	+	0.761429i	$0.275502\pi$
$564$		−	11.7686i		−	0.495547i
$565$	−4.91954	−	2.84030i	−0.206967	−	0.119492i
$566$	1.51162	+	0.872732i	0.0635380	+	0.0366837i
$567$			1.00000i			0.0419961i
$568$	−3.11282	+	5.39156i	−0.130611	+	0.226225i
$569$	18.8112	+	32.5819i	0.788605	+	1.36590i	0.926821	+	0.375502i	$0.122530\pi$
$569$	18.8112	+	32.5819i	0.788605	+	1.36590i	−0.138216	+	0.990402i	$0.544137\pi$
$570$	0.690205	−	0.398490i	0.0289095	−	0.0166909i
$571$	4.29214			0.179620			0.0898102	−	0.995959i	$-0.471374\pi$
$571$	4.29214			0.179620			0.0898102	+	0.995959i	$0.471374\pi$
$572$	17.2339	+	12.8787i	0.720586	+	0.538485i
$573$	5.30672			0.221692
$574$	0.365854	−	0.211226i	0.0152704	−	0.00881640i
$575$	−1.00910	−	1.74781i	−0.0420824	−	0.0728888i
$576$	−3.86489	+	6.69419i	−0.161037	+	0.278925i
$577$		−	22.9788i		−	0.956621i	−0.878191	−	0.478310i	$-0.841249\pi$
$577$		−	22.9788i		−	0.956621i	0.878191	−	0.478310i	$-0.158751\pi$
$578$	−2.16829	−	1.25186i	−0.0901891	−	0.0520707i
$579$	−1.80340	−	1.04120i	−0.0749469	−	0.0432706i
$580$			1.45154i			0.0602719i
$581$	4.24921	−	7.35985i	0.176287	−	0.305338i
$582$	−0.0195093	−	0.0337910i	−0.000808685	−	0.00140068i
$583$	31.8331	−	18.3788i	1.31839	−	0.761174i
$584$	−2.73286			−0.113086
$585$	4.68137	−	2.00931i	0.193551	−	0.0830748i
$586$	2.98258			0.123209
$587$	−2.42168	+	1.39816i	−0.0999533	+	0.0577081i	−0.549143	−	0.835728i	$-0.685046\pi$
$587$	−2.42168	+	1.39816i	−0.0999533	+	0.0577081i	0.449190	+	0.893436i	$0.351713\pi$
$588$	0.994344	+	1.72225i	0.0410060	+	0.0710246i
$589$	−0.747808	+	1.29524i	−0.0308129	+	0.0533695i
$590$		−	0.345944i		−	0.0142423i
$591$	−8.55171	−	4.93733i	−0.351770	−	0.203095i
$592$	−21.9760	−	12.6878i	−0.903207	−	0.521467i
$593$		−	28.7209i		−	1.17943i	−0.807613	−	0.589713i	$-0.799241\pi$
$593$		−	28.7209i		−	1.17943i	0.807613	−	0.589713i	$-0.200759\pi$
$594$	−0.159564	+	0.276374i	−0.00654701	+	0.0113397i
$595$	4.49812	+	7.79098i	0.184405	+	0.319399i
$596$	−39.2822	+	22.6796i	−1.60906	+	0.928993i
$597$	3.31608			0.135718
$598$	0.236780	−	0.101629i	0.00968265	−	0.00415593i
$599$	−5.19953			−0.212447			−0.106223	−	0.994342i	$-0.533876\pi$
$599$	−5.19953			−0.212447			−0.106223	+	0.994342i	$0.533876\pi$
$600$	1.10353	−	0.637126i	0.0450516	−	0.0260106i
$601$	−4.20369	−	7.28101i	−0.171472	−	0.296998i	0.767463	−	0.641094i	$-0.221519\pi$
$601$	−4.20369	−	7.28101i	−0.171472	−	0.296998i	−0.938935	+	0.344095i	$0.888186\pi$
$602$	−0.262941	+	0.455426i	−0.0107167	+	0.0185618i
$603$			2.11412i			0.0860935i
$604$	−29.1155	−	16.8099i	−1.18469	−	0.683983i
$605$	−2.44375	−	1.41090i	−0.0993528	−	0.0573613i
$606$		−	1.95189i		−	0.0792901i
$607$	−3.93567	+	6.81677i	−0.159744	+	0.276684i	−0.934776	−	0.355237i	$-0.884400\pi$
$607$	−3.93567	+	6.81677i	−0.159744	+	0.276684i	0.775032	+	0.631921i	$0.217733\pi$
$608$	−3.35890	−	5.81779i	−0.136221	−	0.235943i
$609$	0.447378	−	0.258294i	0.0181287	−	0.0104666i
$610$	−0.606948			−0.0245746
$611$	17.0917	+	12.7724i	0.691455	+	0.516716i
$612$	12.6622			0.511840
$613$	−16.0814	+	9.28462i	−0.649523	+	0.375002i	−0.788274	−	0.615325i	$-0.789025\pi$
$613$	−16.0814	+	9.28462i	−0.649523	+	0.375002i	0.138750	+	0.990327i	$0.455691\pi$
$614$	−1.25616	−	2.17574i	−0.0506946	−	0.0878056i
$615$	−2.80601	+	4.86015i	−0.113149	+	0.195980i
$616$			1.27291i			0.0512868i
$617$	40.3953	+	23.3222i	1.62625	+	0.938918i	0.985197	+	0.171424i	$0.0548368\pi$
$617$	40.3953	+	23.3222i	1.62625	+	0.938918i	0.641056	+	0.767494i	$0.278497\pi$
$618$	−0.368321	−	0.212650i	−0.0148161	−	0.00855405i
$619$		−	9.30626i		−	0.374050i	−0.982355	−	0.187025i	$-0.940115\pi$
$619$		−	9.30626i		−	0.374050i	0.982355	−	0.187025i	$-0.0598846\pi$
$620$	0.396207	−	0.686250i	0.0159120	−	0.0275605i
$621$	−0.335958	−	0.581896i	−0.0134815	−	0.0233507i
$622$	1.22061	−	0.704718i	0.0489419	−	0.0282566i
$623$	−11.4231			−0.457655
$624$	−5.59204	−	13.0286i	−0.223861	−	0.521559i
$625$	−0.959821			−0.0383929
$626$	−1.03024	+	0.594811i	−0.0411768	+	0.0237734i
$627$	7.95634	+	13.7808i	0.317746	+	0.550352i
$628$	11.8990	−	20.6096i	0.474820	−	0.822412i
$629$			41.0884i			1.63830i
$630$	0.130144	+	0.0751388i	0.00518507	+	0.00299360i
$631$	−28.2791	−	16.3270i	−1.12577	−	0.649966i	−0.182906	−	0.983130i	$-0.558550\pi$
$631$	−28.2791	−	16.3270i	−1.12577	−	0.649966i	−0.942869	+	0.333164i	$0.891884\pi$
$632$			5.38373i			0.214153i
$633$	8.73070	−	15.1220i	0.347014	−	0.601046i
$634$	1.08313	+	1.87603i	0.0430164	+	0.0745067i
$635$	20.3053	−	11.7233i	0.805793	−	0.465225i
$636$	−24.3626			−0.966041
$637$	−3.58041	−	0.425055i	−0.141861	−	0.0168413i
$638$	0.164858			0.00652679
$639$	−12.7089	+	7.33750i	−0.502757	+	0.290267i
$640$	2.37056	+	4.10592i	0.0937044	+	0.162301i
$641$	9.25424	−	16.0288i	0.365520	−	0.633100i	−0.623339	−	0.781952i	$-0.714224\pi$
$641$	9.25424	−	16.0288i	0.365520	−	0.633100i	0.988860	+	0.148852i	$0.0475577\pi$
$642$		−	0.0105995i		−	0.000418327i
$643$	−21.7183	−	12.5391i	−0.856485	−	0.494492i	0.00634850	−	0.999980i	$-0.497979\pi$
$643$	−21.7183	−	12.5391i	−0.856485	−	0.494492i	−0.862834	+	0.505488i	$0.831313\pi$
$644$	−1.15721	−	0.668115i	−0.0456004	−	0.0263274i
$645$		−	6.98602i		−	0.275074i
$646$	−1.79574	+	3.11031i	−0.0706523	+	0.122373i
$647$	−3.29375	−	5.70494i	−0.129491	−	0.224284i	0.793989	−	0.607932i	$-0.208001\pi$
$647$	−3.29375	−	5.70494i	−0.129491	−	0.224284i	−0.923479	+	0.383648i	$0.874668\pi$
$648$	0.367398	−	0.212117i	0.0144327	−	0.00833275i
$649$	6.90720			0.271131
$650$	−0.135791	+	1.14382i	−0.00532616	+	0.0448643i
$651$	−0.282012			−0.0110529
$652$	−0.483263	+	0.279012i	−0.0189260	+	0.0109270i
$653$	−14.2853	−	24.7428i	−0.559027	−	0.968262i	−0.997578	−	0.0695564i	$-0.977842\pi$
$653$	−14.2853	−	24.7428i	−0.559027	−	0.968262i	0.438551	−	0.898706i	$-0.355492\pi$
$654$	−0.265240	+	0.459409i	−0.0103717	+	0.0179643i
$655$		−	26.3496i		−	1.02956i
$656$	13.5261	+	7.80931i	0.528107	+	0.304902i
$657$	−5.57881	−	3.22093i	−0.217650	−	0.125660i
$658$			0.629410i			0.0245370i
$659$	13.7786	−	23.8652i	0.536738	−	0.929658i	−0.462339	−	0.886703i	$-0.652990\pi$
$659$	13.7786	−	23.8652i	0.536738	−	0.929658i	0.999077	−	0.0429543i	$-0.0136770\pi$
$660$	−4.21546	−	7.30139i	−0.164087	−	0.284206i
$661$	−33.9620	+	19.6080i	−1.32097	+	0.762662i	−0.983883	−	0.178813i	$-0.942774\pi$
$661$	−33.9620	+	19.6080i	−1.32097	+	0.762662i	−0.337085	+	0.941474i	$0.609441\pi$
$662$	2.67995			0.104159
$663$	−13.7422	+	18.3895i	−0.533705	+	0.714189i
$664$	−3.60532			−0.139914
$665$	6.48936	−	3.74664i	0.251647	−	0.145288i
$666$	0.343180	+	0.594405i	0.0132979	+	0.0230327i
$667$	−0.173551	+	0.300600i	−0.00671994	+	0.0116393i
$668$			41.4027i			1.60192i
$669$	−16.2437	−	9.37830i	−0.628018	−	0.362586i
$670$	0.275140	+	0.158852i	0.0106296	+	0.00613699i
$671$		−	12.1185i		−	0.467828i
$672$	0.633350	−	1.09700i	0.0244320	−	0.0423175i
$673$	0.0372105	+	0.0644506i	0.00143436	+	0.00248439i	0.866742	−	0.498757i	$-0.166210\pi$
$673$	0.0372105	+	0.0644506i	0.00143436	+	0.00248439i	−0.865307	+	0.501242i	$0.832877\pi$
$674$	1.92801	−	1.11313i	0.0742640	−	0.0428764i
$675$	3.00365			0.115611
$676$	25.1343	+	6.05306i	0.966705	+	0.232810i
$677$	35.6966			1.37193			0.685966	−	0.727633i	$-0.259380\pi$
$677$	35.6966			1.37193			0.685966	+	0.727633i	$0.259380\pi$
$678$	0.370324	−	0.213807i	0.0142222	−	0.00821120i
$679$	−0.183428	−	0.317706i	−0.00703931	−	0.0121924i
$680$	1.90826	−	3.30520i	0.0731784	−	0.126749i
$681$		−	16.3261i		−	0.625616i
$682$	−0.0779405	−	0.0449990i	−0.00298450	−	0.00172310i
$683$	14.4371	+	8.33528i	0.552421	+	0.318941i	0.750098	−	0.661327i	$-0.230006\pi$
$683$	14.4371	+	8.33528i	0.552421	+	0.318941i	−0.197677	+	0.980267i	$0.563340\pi$
$684$		−	10.5468i		−	0.403266i
$685$	7.04158	−	12.1964i	0.269045	−	0.465999i
$686$	−0.0531797	−	0.0921099i	−0.00203041	−	0.00351677i
$687$	9.84304	−	5.68288i	0.375536	−	0.216816i
$688$	−19.4426			−0.741241
$689$	26.4407	−	35.3822i	1.00731	−	1.34795i
$690$	−0.100974			−0.00384400
$691$	−41.3851	+	23.8937i	−1.57436	+	0.908959i	−0.578739	+	0.815513i	$0.696455\pi$
$691$	−41.3851	+	23.8937i	−1.57436	+	0.908959i	−0.995624	+	0.0934463i	$0.970212\pi$
$692$	−5.53571	−	9.58814i	−0.210436	−	0.364486i
$693$	−1.50024	+	2.59849i	−0.0569893	+	0.0987084i
$694$		−	2.51484i		−	0.0954619i
$695$	−26.4026	−	15.2436i	−1.00151	−	0.578221i
$696$	−0.189793	−	0.109577i	−0.00719409	−	0.00415351i
$697$		−	25.2898i		−	0.957918i
$698$	1.26802	−	2.19628i	0.0479954	−	0.0831306i
$699$	15.1295	+	26.2051i	0.572252	+	0.991170i
$700$	5.17305	−	2.98666i	0.195523	−	0.112885i
$701$	30.5430			1.15359			0.576797	−	0.816887i	$-0.304302\pi$
$701$	30.5430			1.15359			0.576797	+	0.816887i	$0.304302\pi$
$702$	−0.0452086	+	0.380810i	−0.00170629	+	0.0143727i
$703$	34.2239			1.29078
$704$	−20.0858	+	11.5965i	−0.757010	+	0.437060i
$705$	−4.18067	−	7.24114i	−0.157453	−	0.272717i
$706$	0.455747	−	0.789377i	0.0171523	−	0.0297086i
$707$		−	18.3518i		−	0.690192i
$708$	−3.96469	−	2.28901i	−0.149002	−	0.0860264i
$709$	25.7978	+	14.8944i	0.968858	+	0.559370i	0.898888	−	0.438179i	$-0.144376\pi$
$709$	25.7978	+	14.8944i	0.968858	+	0.559370i	0.0699701	+	0.997549i	$0.477710\pi$
$710$			2.20532i			0.0827643i
$711$	−6.34523	+	10.9903i	−0.237965	+	0.412167i
$712$	2.42303	+	4.19681i	0.0908068	+	0.157282i
$713$	0.164101	−	0.0947439i	0.00614564	−	0.00354819i
$714$	−0.677203			−0.0253437
$715$	15.1789	+	1.80200i	0.567660	+	0.0673909i
$716$	12.1176			0.452857
$717$	−14.8289	+	8.56146i	−0.553795	+	0.319734i
$718$	−0.413833	−	0.716780i	−0.0154441	−	0.0267500i
$719$	7.52823	−	13.0393i	0.280756	−	0.486283i	−0.690815	−	0.723031i	$-0.742748\pi$
$719$	7.52823	−	13.0393i	0.280756	−	0.486283i	0.971571	+	0.236748i	$0.0760816\pi$
$720$			5.55597i			0.207059i
$721$	−3.46299	−	1.99936i	−0.128968	−	0.0744599i
$722$	0.840588	+	0.485314i	0.0312834	+	0.0180615i
$723$			17.3298i			0.644501i
$724$	15.7957	−	27.3590i	0.587044	−	1.01679i
$725$	−0.775824	−	1.34377i	−0.0288134	−	0.0499063i
$726$	0.183957	−	0.106207i	0.00682727	−	0.00394172i
$727$	−34.6564			−1.28533			−0.642667	−	0.766146i	$-0.722172\pi$
$727$	−34.6564			−1.28533			−0.642667	+	0.766146i	$0.722172\pi$
$728$	0.603302	+	1.40560i	0.0223599	+	0.0520948i
$729$	1.00000			0.0370370
$730$	−0.838370	+	0.484033i	−0.0310295	+	0.0179149i
$731$	15.7407	+	27.2638i	0.582192	+	1.00839i
$732$	−4.01600	+	6.95592i	−0.148436	+	0.257098i
$733$			34.3778i			1.26977i	0.772605	+	0.634886i	$0.218953\pi$
$733$			34.3778i			1.26977i	−0.772605	+	0.634886i	$0.781047\pi$
$734$	1.96749	+	1.13593i	0.0726213	+	0.0419279i
$735$	1.22363	+	0.706461i	0.0451341	+	0.0260582i
$736$			0.851115i			0.0313725i
$737$	−3.17168	+	5.49351i	−0.116830	+	0.202356i
$738$	−0.211226	−	0.365854i	−0.00777533	−	0.0134673i
$739$	−17.2427	+	9.95506i	−0.634282	+	0.366203i	−0.782408	−	0.622766i	$-0.786009\pi$
$739$	−17.2427	+	9.95506i	−0.634282	+	0.366203i	0.148127	+	0.988968i	$0.452676\pi$
$740$	−18.1326			−0.666568
$741$	15.3172	+	11.4464i	0.562693	+	0.420493i
$742$	1.30297			0.0478334
$743$	−22.4362	+	12.9536i	−0.823106	+	0.475220i	−0.851486	−	0.524377i	$-0.824298\pi$
$743$	−22.4362	+	12.9536i	−0.823106	+	0.475220i	0.0283806	+	0.999597i	$0.490965\pi$
$744$	0.0598195	+	0.103610i	0.00219309	+	0.00379854i
$745$	−16.1134	+	27.9092i	−0.590349	+	1.02252i
$746$			0.209212i			0.00765980i
$747$	−7.35985	−	4.24921i	−0.269283	−	0.155471i
$748$	32.9026	+	18.9963i	1.20304	+	0.694575i
$749$		−	0.0996570i		−	0.00364139i
$750$	0.601384	−	1.04163i	0.0219595	−	0.0380349i
$751$	−1.11113	−	1.92454i	−0.0405457	−	0.0702273i	0.845040	−	0.534702i	$-0.179576\pi$
$751$	−1.11113	−	1.92454i	−0.0405457	−	0.0702273i	−0.885586	+	0.464475i	$0.846243\pi$
$752$	−20.1526	+	11.6351i	−0.734888	+	0.424288i
$753$	−11.3754			−0.414544
$754$	0.182043	−	0.0781355i	0.00662962	−	0.00284553i
$755$	−23.8861			−0.869305
$756$	1.72225	−	0.994344i	0.0626378	−	0.0361639i
$757$	26.9891	+	46.7465i	0.980936	+	1.69903i	0.658763	+	0.752351i	$0.271080\pi$
$757$	26.9891	+	46.7465i	0.980936	+	1.69903i	0.322174	+	0.946681i	$0.395586\pi$
$758$	−1.71480	+	2.97011i	−0.0622842	+	0.107879i
$759$		−	2.01607i		−	0.0731785i
$760$	−2.75301	−	1.58945i	−0.0998622	−	0.0576555i
$761$	37.9015	+	21.8824i	1.37393	+	0.793237i	0.991420	−	0.130715i	$-0.0417273\pi$
$761$	37.9015	+	21.8824i	1.37393	+	0.793237i	0.382507	+	0.923952i	$0.375061\pi$
$762$			1.76497i			0.0639381i
$763$	−2.49381	+	4.31940i	−0.0902819	+	0.156373i
$764$	−5.27671	−	9.13953i	−0.190905	−	0.330656i
$765$	7.79098	−	4.49812i	0.281684	−	0.162630i
$766$	−3.63901			−0.131483
$767$	7.62723	−	3.27371i	0.275403	−	0.118207i
$768$	15.1027			0.544971
$769$	−13.2543	+	7.65237i	−0.477962	+	0.275951i	−0.719567	−	0.694423i	$-0.755660\pi$

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.bd (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0921099 - 0.0531797i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.994344 + 1.72225i) q^{4} +1.41292i q^{5} +(-0.0921099 - 0.0531797i) q^{6} +(-0.866025 - 0.500000i) q^{7} +0.424234i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.0921099 - 0.0531797i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.994344 + 1.72225i) q^{4} +1.41292i q^{5} +(-0.0921099 - 0.0531797i) q^{6} +(-0.866025 - 0.500000i) q^{7} +0.424234i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.0751388 + 0.130144i) q^{10} +(-2.59849 + 1.50024i) q^{11} +1.98869 q^{12} +(-2.15831 + 2.88820i) q^{13} -0.106359 q^{14} +(1.22363 - 0.706461i) q^{15} +(-1.96613 - 3.40543i) q^{16} +(-3.18356 + 5.51409i) q^{17} +0.106359i q^{18} +(4.59287 + 2.65169i) q^{19} +(-2.43341 - 1.40493i) q^{20} +1.00000i q^{21} +(-0.159564 + 0.276374i) q^{22} +(-0.335958 - 0.581896i) q^{23} +(0.367398 - 0.212117i) q^{24} +3.00365 q^{25} +(-0.0452086 + 0.380810i) q^{26} +1.00000 q^{27} +(1.72225 - 0.994344i) q^{28} +(-0.258294 - 0.447378i) q^{29} +(0.0751388 - 0.130144i) q^{30} +0.282012i q^{31} +(-1.09700 - 0.633350i) q^{32} +(2.59849 + 1.50024i) q^{33} +0.677203i q^{34} +(0.706461 - 1.22363i) q^{35} +(-0.994344 - 1.72225i) q^{36} +(5.58864 - 3.22660i) q^{37} +0.564065 q^{38} +(3.58041 + 0.425055i) q^{39} -0.599410 q^{40} +(-3.43979 + 1.98596i) q^{41} +(0.0531797 + 0.0921099i) q^{42} +(2.47219 - 4.28196i) q^{43} -5.96701i q^{44} +(-1.22363 - 0.706461i) q^{45} +(-0.0618900 - 0.0357322i) q^{46} -5.91777i q^{47} +(-1.96613 + 3.40543i) q^{48} +(0.500000 + 0.866025i) q^{49} +(0.276666 - 0.159733i) q^{50} +6.36712 q^{51} +(-2.82810 - 6.58902i) q^{52} -12.2506 q^{53} +(0.0921099 - 0.0531797i) q^{54} +(-2.11972 - 3.67146i) q^{55} +(0.212117 - 0.367398i) q^{56} -5.30339i q^{57} +(-0.0475828 - 0.0274720i) q^{58} +(-1.99362 - 1.15102i) q^{59} +2.80986i q^{60} +(-2.01942 + 3.49774i) q^{61} +(0.0149973 + 0.0259761i) q^{62} +(0.866025 - 0.500000i) q^{63} +7.72978 q^{64} +(-4.08080 - 3.04953i) q^{65} +0.319129 q^{66} +(1.83088 - 1.05706i) q^{67} +(-6.33111 - 10.9658i) q^{68} +(-0.335958 + 0.581896i) q^{69} -0.150278i q^{70} +(12.7089 + 7.33750i) q^{71} +(-0.367398 - 0.212117i) q^{72} +6.44186i q^{73} +(0.343180 - 0.594405i) q^{74} +(-1.50183 - 2.60124i) q^{75} +(-9.13378 + 5.27339i) q^{76} +3.00048 q^{77} +(0.352395 - 0.151253i) q^{78} +12.6905 q^{79} +(4.81161 - 2.77798i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.211226 + 0.365854i) q^{82} +8.49842i q^{83} +(-1.72225 - 0.994344i) q^{84} +(-7.79098 - 4.49812i) q^{85} -0.525881i q^{86} +(-0.258294 + 0.447378i) q^{87} +(-0.636453 - 1.10237i) q^{88} +(9.89266 - 5.71153i) q^{89} -0.150278 q^{90} +(3.31325 - 1.42210i) q^{91} +1.33623 q^{92} +(0.244229 - 0.141006i) q^{93} +(-0.314705 - 0.545085i) q^{94} +(-3.74664 + 6.48936i) q^{95} +1.26670i q^{96} +(0.317706 + 0.183428i) q^{97} +(0.0921099 + 0.0531797i) q^{98} -3.00048i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9	\( 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9} - 4 q^{10} - 12 q^{11} - 12 q^{12} + 4 q^{13} + 4 q^{14} - 10 q^{16} + 10 q^{17} + 6 q^{20} - 2 q^{22} - 2 q^{23} + 12 q^{25} + 20 q^{26} + 16 q^{27} + 12 q^{29} - 4 q^{30} + 30 q^{32} + 12 q^{33} - 2 q^{35} + 6 q^{36} + 18 q^{37} - 32 q^{38} - 8 q^{39} - 60 q^{40} + 18 q^{41} - 2 q^{42} - 10 q^{43} + 30 q^{46} - 10 q^{48} + 8 q^{49} - 24 q^{50} - 20 q^{51} - 26 q^{52} + 12 q^{53} + 10 q^{55} + 12 q^{56} - 54 q^{58} - 60 q^{59} - 6 q^{61} + 16 q^{62} + 16 q^{64} - 20 q^{65} + 4 q^{66} - 18 q^{67} - 20 q^{68} - 2 q^{69} + 6 q^{71} + 18 q^{74} - 6 q^{75} + 72 q^{76} - 16 q^{77} + 14 q^{78} - 4 q^{79} + 30 q^{80} - 8 q^{81} - 18 q^{82} - 24 q^{85} + 12 q^{87} - 2 q^{88} + 78 q^{89} + 8 q^{90} - 8 q^{91} - 20 q^{92} + 6 q^{93} + 16 q^{94} - 4 q^{95} - 54 q^{97}+O(q^{100}) \) 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9 - 4 * q^10 - 12 * q^11 - 12 * q^12 + 4 * q^13 + 4 * q^14 - 10 * q^16 + 10 * q^17 + 6 * q^20 - 2 * q^22 - 2 * q^23 + 12 * q^25 + 20 * q^26 + 16 * q^27 + 12 * q^29 - 4 * q^30 + 30 * q^32 + 12 * q^33 - 2 * q^35 + 6 * q^36 + 18 * q^37 - 32 * q^38 - 8 * q^39 - 60 * q^40 + 18 * q^41 - 2 * q^42 - 10 * q^43 + 30 * q^46 - 10 * q^48 + 8 * q^49 - 24 * q^50 - 20 * q^51 - 26 * q^52 + 12 * q^53 + 10 * q^55 + 12 * q^56 - 54 * q^58 - 60 * q^59 - 6 * q^61 + 16 * q^62 + 16 * q^64 - 20 * q^65 + 4 * q^66 - 18 * q^67 - 20 * q^68 - 2 * q^69 + 6 * q^71 + 18 * q^74 - 6 * q^75 + 72 * q^76 - 16 * q^77 + 14 * q^78 - 4 * q^79 + 30 * q^80 - 8 * q^81 - 18 * q^82 - 24 * q^85 + 12 * q^87 - 2 * q^88 + 78 * q^89 + 8 * q^90 - 8 * q^91 - 20 * q^92 + 6 * q^93 + 16 * q^94 - 4 * q^95 - 54 * q^97

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