LMFDB - Embedded newform 273.2.bd.a.43.5

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			43.5
Root			$0.106359i$ of defining polynomial
Character	$\chi$	$=$	273.43
Dual form			273.2.bd.a.127.5

$q$-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 $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

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

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	0.532212	−	0.846611i	$-0.321361\pi$
$2$	0.0921099	+	0.0531797i	0.0651315	+	0.0376037i	−0.467081	+	0.884215i	$0.654694\pi$
$3$	−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	$-0.897681\pi$
$5$		−	1.41292i		−	0.631878i	0.948780	−	0.315939i	$-0.102319\pi$
$6$	−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	0.0541862	−	0.998531i	$-0.482744\pi$
$11$	−2.59849	−	1.50024i	−0.783474	−	0.452339i	−0.837660	+	0.546192i	$0.816077\pi$
$12$	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	−0.936395	−	0.350948i	$-0.885859\pi$
$17$	−3.18356	−	5.51409i	−0.772127	−	1.33736i	0.164268	−	0.986416i	$-0.447474\pi$
$18$		−	0.106359i		−	0.0250691i
$19$	4.59287	−	2.65169i	1.05368	−	0.608340i	0.130000	−	0.991514i	$-0.458502\pi$
$19$	4.59287	−	2.65169i	1.05368	−	0.608340i	0.923676	+	0.383174i	$0.125169\pi$
$20$	−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	−0.898924	−	0.438105i	$-0.855650\pi$
$23$	−0.335958	+	0.581896i	−0.0700520	+	0.121334i	0.828872	+	0.559438i	$0.188983\pi$
$24$	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	−0.889011	−	0.457887i	$-0.848607\pi$
$29$	−0.258294	+	0.447378i	−0.0479639	+	0.0830760i	0.841047	+	0.540963i	$0.181940\pi$
$30$	0.0751388	+	0.130144i	0.0137184	+	0.0237610i
$31$		−	0.282012i		−	0.0506508i	−0.999679	−	0.0253254i	$-0.991938\pi$
$31$		−	0.282012i		−	0.0506508i	0.999679	−	0.0253254i	$-0.00806218\pi$
$32$	−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	0.883242	−	0.468918i	$-0.155356\pi$
$37$	5.58864	+	3.22660i	0.918767	+	0.530451i	0.0355257	+	0.999369i	$0.488689\pi$
$38$	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	0.206741	−	0.978396i	$-0.433714\pi$
$41$	−3.43979	−	1.98596i	−0.537205	−	0.310155i	−0.743945	+	0.668240i	$0.767048\pi$
$42$	0.0531797	−	0.0921099i	0.00820580	−	0.0142129i
$43$	2.47219	+	4.28196i	0.377005	+	0.652993i	0.990625	−	0.136609i	$-0.0436205\pi$
$43$	2.47219	+	4.28196i	0.377005	+	0.652993i	−0.613620	+	0.789602i	$0.710287\pi$
$44$			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	$0.142050\pi$
$47$			5.91777i			0.863195i	−0.902066	+	0.431598i	$0.857950\pi$
$48$	−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	−0.624128	−	0.781322i	$-0.714546\pi$
$59$	−1.99362	+	1.15102i	−0.259547	+	0.149850i	0.364581	+	0.931172i	$0.381212\pi$
$60$		−	2.80986i		−	0.362751i
$61$	−2.01942	−	3.49774i	−0.258561	−	0.447840i	0.707296	−	0.706918i	$-0.249915\pi$
$61$	−2.01942	−	3.49774i	−0.258561	−	0.447840i	−0.965857	+	0.259077i	$0.916582\pi$
$62$	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	0.607652	−	0.794203i	$-0.292112\pi$
$67$	1.83088	+	1.05706i	0.223678	+	0.129140i	−0.383974	+	0.923344i	$0.625445\pi$
$68$	−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	0.508319	−	0.861169i	$-0.330267\pi$
$71$	12.7089	−	7.33750i	1.50827	−	0.870801i	0.999954	−	0.00963255i	$-0.00306618\pi$
$72$	−0.367398	+	0.212117i	−0.0432982	+	0.0249982i
$73$		−	6.44186i		−	0.753963i	−0.926221	−	0.376981i	$-0.876962\pi$
$73$		−	6.44186i		−	0.753963i	0.926221	−	0.376981i	$-0.123038\pi$
$74$	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	$-0.845547\pi$
$83$		−	8.49842i		−	0.932823i	0.884568	−	0.466412i	$-0.154453\pi$
$84$	−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	0.922263	−	0.386564i	$-0.126338\pi$
$89$	9.89266	+	5.71153i	1.04862	+	0.605421i	0.126357	+	0.991985i	$0.459671\pi$
$90$	−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	−0.483784	−	0.875187i	$-0.660738\pi$
$97$	0.317706	−	0.183428i	0.0322582	−	0.0186243i	0.516042	+	0.856563i	$0.327405\pi$
$98$	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	0.103288	−	0.994651i	$-0.467064\pi$
$101$	9.17591	−	15.8931i	0.913038	−	1.58143i	0.809749	−	0.586776i	$-0.199603\pi$
$102$	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	−0.863607	−	0.504166i	$-0.831800\pi$
$107$	0.0498285	−	0.0863055i	0.00481710	−	0.00834347i	0.868424	+	0.495822i	$0.165133\pi$
$108$	−0.994344	−	1.72225i	−0.0956808	−	0.165724i
$109$			4.98762i			0.477727i	0.971053	+	0.238864i	$0.0767749\pi$
$109$			4.98762i			0.477727i	−0.971053	+	0.238864i	$0.923225\pi$
$110$	−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	0.755846	−	0.654749i	$-0.227226\pi$
$113$	−2.01023	−	3.48182i	−0.189106	−	0.327542i	−0.944953	+	0.327207i	$0.893892\pi$
$114$	−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	0.217912	+	0.975968i	$0.430075\pi$
$127$	−8.29720	+	14.3712i	−0.736258	+	1.27524i	−0.954169	+	0.299267i	$0.903258\pi$
$128$	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	−0.821154	−	0.570707i	$-0.806669\pi$
$137$	−8.63202	+	4.98370i	−0.737483	+	0.425786i	0.0836703	+	0.996493i	$0.473336\pi$
$138$		−	0.0714645i		−	0.00608346i
$139$	−10.7887	−	18.6865i	−0.915083	−	1.58497i	−0.806779	−	0.590853i	$-0.798791\pi$
$139$	−10.7887	−	18.6865i	−0.915083	−	1.58497i	−0.108304	−	0.994118i	$-0.534542\pi$
$140$	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	0.630835	−	0.775917i	$-0.282713\pi$
$149$	19.7528	−	11.4043i	1.61822	−	0.934278i	0.987381	−	0.158360i	$-0.0506208\pi$
$150$	−0.276666	+	0.159733i	−0.0225897	+	0.0130422i
$151$		−	16.9055i		−	1.37575i	−0.725830	−	0.687874i	$-0.758544\pi$
$151$		−	16.9055i		−	1.37575i	0.725830	−	0.687874i	$-0.241456\pi$
$152$	−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	−0.490453	−	0.871468i	$-0.663169\pi$
$163$	0.243006	−	0.140300i	0.0190337	−	0.0109891i	0.509487	+	0.860479i	$0.329835\pi$
$164$			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	0.993884	−	0.110427i	$-0.0352219\pi$
$167$	18.0299	+	10.4096i	1.39519	+	0.805515i	0.401309	+	0.915943i	$0.368555\pi$
$168$	−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	0.740593	−	0.671954i	$-0.234545\pi$
$173$	−2.78360	−	4.82134i	−0.211633	−	0.366560i	−0.952226	+	0.305395i	$0.901212\pi$
$174$		−	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	−0.957131	−	0.289656i	$-0.906459\pi$
$179$	−3.04664	+	5.27693i	−0.227716	+	0.394416i	0.729415	+	0.684072i	$0.239793\pi$
$180$	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	0.753919	−	0.656967i	$-0.228161\pi$
$191$	−2.65336	−	4.59576i	−0.191990	−	0.332537i	−0.945910	+	0.324430i	$0.894828\pi$
$192$	−3.86489	+	6.69419i	−0.278925	+	0.483111i
$193$	1.80340	+	1.04120i	0.129812	+	0.0749469i	0.563500	−	0.826116i	$-0.309455\pi$
$193$	1.80340	+	1.04120i	0.129812	+	0.0749469i	−0.433688	+	0.901063i	$0.642788\pi$
$194$	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	0.772685	−	0.634789i	$-0.218913\pi$
$197$	8.55171	+	4.93733i	0.609284	+	0.351770i	−0.163401	+	0.986560i	$0.552246\pi$
$198$	−0.159564	+	0.276374i	−0.0113397	+	0.0196410i
$199$	−1.65804	−	2.87181i	−0.117535	−	0.203577i	0.801255	−	0.598323i	$-0.204166\pi$
$199$	−1.65804	−	2.87181i	−0.117535	−	0.203577i	−0.918790	+	0.394746i	$0.870833\pi$
$200$		−	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	−0.391617	−	0.920128i	$-0.628084\pi$
$211$	8.73070	−	15.1220i	0.601046	−	1.04104i	0.992663	−	0.120914i	$-0.0385824\pi$
$212$	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	0.932979	−	0.359932i	$-0.117200\pi$
$223$	16.2437	+	9.37830i	1.08776	+	0.628018i	0.154780	+	0.987949i	$0.450533\pi$
$224$	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	0.0489584	−	0.998801i	$-0.484410\pi$
$227$	14.1388	−	8.16303i	0.938424	−	0.541800i	0.889466	+	0.457001i	$0.151076\pi$
$228$	9.13378	−	5.27339i	0.604899	−	0.349239i
$229$		−	11.3658i		−	0.751071i	−0.926808	−	0.375536i	$-0.877459\pi$
$229$		−	11.3658i		−	0.751071i	0.926808	−	0.375536i	$-0.122541\pi$
$230$	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	$0.186821\pi$
$239$			17.1229i			1.10759i	−0.832653	+	0.553795i	$0.813179\pi$
$240$	−4.81161	+	2.77798i	−0.310588	+	0.179318i
$241$	−15.0080	+	8.66488i	−0.966751	+	0.558154i	−0.898244	−	0.439497i	$-0.855157\pi$
$241$	−15.0080	+	8.66488i	−0.966751	+	0.558154i	−0.0685070	+	0.997651i	$0.521824\pi$
$242$		−	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	0.987795	−	0.155760i	$-0.0497826\pi$
$251$	5.68772	+	9.85141i	0.359005	+	0.621816i	−0.628790	+	0.777576i	$0.716449\pi$
$252$		−	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	−0.438377	−	0.898791i	$-0.644447\pi$
$257$	8.96446	−	15.5269i	0.559187	−	0.968541i	0.997565	−	0.0697498i	$-0.0222201\pi$
$258$	−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	0.347380	+	0.937724i	$0.387071\pi$
$263$	−10.3532	+	17.9322i	−0.638403	+	1.10575i	−0.985783	+	0.168022i	$0.946262\pi$
$264$	−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	0.957950	−	0.286934i	$-0.0926362\pi$
$269$	3.78020	+	6.54749i	0.230483	+	0.399208i	−0.727468	+	0.686142i	$0.759303\pi$
$270$	0.0751388	−	0.130144i	0.00457280	−	0.00792032i
$271$	16.1415	+	9.31929i	0.980525	+	0.566107i	0.902429	−	0.430839i	$-0.141782\pi$
$271$	16.1415	+	9.31929i	0.980525	+	0.566107i	0.0780967	+	0.996946i	$0.475116\pi$
$272$	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	0.999433	+	0.0336569i	$0.0107154\pi$
$277$	8.80206	+	15.2456i	0.528864	+	0.916020i	−0.470569	+	0.882363i	$0.655951\pi$
$278$		−	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	$0.174821\pi$
$281$			17.5012i			1.04404i	−0.852934	+	0.522018i	$0.825179\pi$
$282$	−0.314705	−	0.545085i	−0.0187404	−	0.0324593i
$283$	8.20550	−	14.2123i	0.487766	−	0.844836i	−0.512135	−	0.858905i	$-0.671145\pi$
$283$	8.20550	−	14.2123i	0.487766	−	0.844836i	0.999901	+	0.0140690i	$0.00447846\pi$
$284$	−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	0.422581	−	0.906325i	$-0.361124\pi$
$293$	24.2855	−	14.0212i	1.41877	−	0.819128i	0.996191	+	0.0871971i	$0.0277910\pi$
$294$			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	$0.235452\pi$
$307$			23.6211i			1.34813i	−0.738674	+	0.674063i	$0.764548\pi$
$308$	−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	$-0.806179\pi$
$317$		−	20.3673i		−	1.14394i	0.820274	−	0.571971i	$-0.193821\pi$
$318$	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	0.238988	−	0.971023i	$-0.423184\pi$
$331$	21.8214	−	12.5986i	1.19941	−	0.692481i	0.960424	+	0.278542i	$0.0898511\pi$
$332$	−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	0.986588	+	0.163233i	$0.0521922\pi$
$347$	11.8224	+	20.4769i	0.634658	+	1.09926i	−0.351930	+	0.936026i	$0.614474\pi$
$348$	−0.513666	+	0.889695i	−0.0275354	+	0.0476926i
$349$	20.6496	+	11.9221i	1.10535	+	0.638174i	0.937621	−	0.347659i	$-0.113023\pi$
$349$	20.6496	+	11.9221i	1.10535	+	0.638174i	0.167729	+	0.985833i	$0.446357\pi$
$350$	−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	0.684334	−	0.729169i	$-0.260093\pi$
$353$	7.42179	+	4.28497i	0.395022	+	0.228066i	−0.289312	+	0.957235i	$0.593426\pi$
$354$	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	$0.0658345\pi$
$359$			7.78179i			0.410707i	−0.978688	+	0.205354i	$0.934166\pi$
$360$	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	−0.440208	−	0.897896i	$-0.645095\pi$
$367$	10.6801	−	18.4985i	0.557497	−	0.965613i	0.997705	−	0.0677170i	$-0.0215715\pi$
$368$	−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	0.839439	−	0.543453i	$-0.182883\pi$
$373$	−0.983516	−	1.70350i	−0.0509245	−	0.0882038i	−0.890364	+	0.455249i	$0.849550\pi$
$374$	−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	−0.436971	−	0.899476i	$-0.643949\pi$
$379$	−27.9253	−	16.1227i	−1.43442	−	0.828166i	−0.997454	+	0.0713101i	$0.977282\pi$
$380$	−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	−0.514179	+	0.857683i	$0.671903\pi$
$383$	−29.6304	+	17.1071i	−1.51404	+	0.874134i	−0.999865	+	0.0164510i	$0.994763\pi$
$384$	−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	−0.397003	−	0.917817i	$-0.629950\pi$
$397$	3.97200	−	2.29324i	0.199349	−	0.115094i	0.596352	+	0.802723i	$0.296616\pi$
$398$		−	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	−0.378963	−	0.925412i	$-0.623719\pi$
$401$	−27.4317	−	15.8377i	−1.36987	−	0.790898i	−0.990912	+	0.134514i	$0.957053\pi$
$402$	−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	−0.248531	−	0.968624i	$-0.579948\pi$
$409$	9.42540	−	5.44175i	0.466056	−	0.269077i	0.714587	+	0.699546i	$0.246615\pi$
$410$	−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	−0.994997	−	0.0999030i	$-0.968147\pi$
$419$	−8.41255	+	14.5710i	−0.410980	+	0.711838i	0.584017	+	0.811741i	$0.301480\pi$
$420$	1.40493	+	2.43341i	0.0685536	+	0.118738i
$421$		−	6.12271i		−	0.298403i	−0.988807	−	0.149201i	$-0.952330\pi$
$421$		−	6.12271i		−	0.298403i	0.988807	−	0.149201i	$-0.0476703\pi$
$422$	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	0.477079	−	0.878860i	$-0.341696\pi$
$431$	−0.944545	−	0.545333i	−0.0454971	−	0.0262678i	−0.522576	+	0.852593i	$0.675029\pi$
$432$	−1.96613	+	3.40543i	−0.0945953	+	0.163844i
$433$	4.16989	+	7.22247i	0.200392	+	0.347090i	0.948655	−	0.316313i	$-0.102445\pi$
$433$	4.16989	+	7.22247i	0.200392	+	0.347090i	−0.748263	+	0.663403i	$0.769112\pi$
$434$			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	−0.926393	−	0.376557i	$-0.877108\pi$
$439$	−2.87232	+	4.97500i	−0.137088	+	0.237444i	0.789305	+	0.614001i	$0.210441\pi$
$440$	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	−0.427369	−	0.904077i	$-0.640560\pi$
$449$	3.00681	−	1.73598i	0.141900	−	0.0819260i	0.569269	+	0.822151i	$0.307226\pi$
$450$		−	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	0.290763	−	0.956795i	$-0.406091\pi$
$457$	−8.38992	−	4.84392i	−0.392464	−	0.226589i	−0.683227	+	0.730206i	$0.739424\pi$
$458$	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	−0.706743	−	0.707470i	$-0.749836\pi$
$461$	−9.60668	+	5.54642i	−0.447428	+	0.258322i	0.259316	+	0.965793i	$0.416503\pi$
$462$	−0.276374	+	0.159564i	−0.0128581	+	0.00742361i
$463$			31.1633i			1.44828i	0.689653	+	0.724140i	$0.257763\pi$
$463$			31.1633i			1.44828i	−0.689653	+	0.724140i	$0.742237\pi$
$464$	−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	0.608979	−	0.793187i	$-0.291579\pi$
$479$	4.95825	+	2.86265i	0.226548	+	0.130798i	−0.382430	+	0.923984i	$0.624913\pi$
$480$	−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	−0.568549	−	0.822649i	$-0.692495\pi$
$487$	−3.09809	+	1.78868i	−0.140388	+	0.0810530i	0.428161	+	0.903703i	$0.359162\pi$
$488$	−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	−0.824267	−	0.566201i	$-0.808412\pi$
$491$	1.73305	−	3.00172i	0.0782112	−	0.135466i	0.902478	+	0.430735i	$0.141746\pi$
$492$	−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	$-0.724651\pi$
$499$		−	34.0041i		−	1.52223i	0.648615	−	0.761117i	$-0.275349\pi$
$500$	−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	0.964330	+	0.264703i	$0.0852741\pi$
$503$	15.9551	+	27.6351i	0.711405	+	1.23219i	−0.252925	+	0.967486i	$0.581393\pi$
$504$	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	0.782254	−	0.622960i	$-0.214070\pi$
$509$	14.3010	+	8.25670i	0.633882	+	0.365972i	−0.148372	+	0.988932i	$0.547403\pi$
$510$	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	−0.904861	−	0.425708i	$-0.860025\pi$
$523$	−1.91544	+	3.31764i	−0.0837564	+	0.145070i	0.821104	+	0.570778i	$0.193358\pi$
$524$	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	$-0.993511\pi$
$541$		−	0.948185i		−	0.0407656i	0.999792	−	0.0203828i	$-0.00648850\pi$
$542$	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	0.713721	−	0.700430i	$-0.247009\pi$
$557$	10.9506	+	6.32232i	0.463991	+	0.267885i	−0.249730	+	0.968316i	$0.580342\pi$
$558$	−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	0.648248	−	0.761429i	$-0.275502\pi$
$563$	−7.95571	−	13.7797i	−0.335293	−	0.580745i	−0.983541	+	0.180684i	$0.942169\pi$
$564$			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	−0.138216	−	0.990402i	$-0.544137\pi$
$569$	18.8112	−	32.5819i	0.788605	−	1.36590i	0.926821	−	0.375502i	$-0.122530\pi$
$570$	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	$0.158751\pi$
$577$			22.9788i			0.956621i	−0.878191	+	0.478310i	$0.841249\pi$
$578$	−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	0.449190	−	0.893436i	$-0.351713\pi$
$587$	−2.42168	−	1.39816i	−0.0999533	−	0.0577081i	−0.549143	+	0.835728i	$0.685046\pi$
$588$	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	$0.200759\pi$
$593$			28.7209i			1.17943i	−0.807613	+	0.589713i	$0.799241\pi$
$594$	−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	−0.938935	−	0.344095i	$-0.888186\pi$
$601$	−4.20369	+	7.28101i	−0.171472	+	0.296998i	0.767463	+	0.641094i	$0.221519\pi$
$602$	−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	0.775032	−	0.631921i	$-0.217733\pi$
$607$	−3.93567	−	6.81677i	−0.159744	−	0.276684i	−0.934776	+	0.355237i	$0.884400\pi$
$608$	−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	0.138750	−	0.990327i	$-0.455691\pi$
$613$	−16.0814	−	9.28462i	−0.649523	−	0.375002i	−0.788274	+	0.615325i	$0.789025\pi$
$614$	−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	0.641056	−	0.767494i	$-0.278497\pi$
$617$	40.3953	−	23.3222i	1.62625	−	0.938918i	0.985197	−	0.171424i	$-0.0548368\pi$
$618$	−0.368321	+	0.212650i	−0.0148161	+	0.00855405i
$619$			9.30626i			0.374050i	0.982355	+	0.187025i	$0.0598846\pi$
$619$			9.30626i			0.374050i	−0.982355	+	0.187025i	$0.940115\pi$
$620$	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	−0.942869	−	0.333164i	$-0.891884\pi$
$631$	−28.2791	+	16.3270i	−1.12577	+	0.649966i	−0.182906	+	0.983130i	$0.558550\pi$
$632$		−	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	0.988860	−	0.148852i	$-0.0475577\pi$
$641$	9.25424	+	16.0288i	0.365520	+	0.633100i	−0.623339	+	0.781952i	$0.714224\pi$
$642$			0.0105995i			0.000418327i
$643$	−21.7183	+	12.5391i	−0.856485	+	0.494492i	−0.862834	−	0.505488i	$-0.831313\pi$
$643$	−21.7183	+	12.5391i	−0.856485	+	0.494492i	0.00634850	+	0.999980i	$0.497979\pi$
$644$	−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	−0.923479	−	0.383648i	$-0.874668\pi$
$647$	−3.29375	+	5.70494i	−0.129491	+	0.224284i	0.793989	+	0.607932i	$0.208001\pi$
$648$	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	0.438551	+	0.898706i	$0.355492\pi$
$653$	−14.2853	+	24.7428i	−0.559027	+	0.968262i	−0.997578	+	0.0695564i	$0.977842\pi$
$654$	−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	0.999077	+	0.0429543i	$0.0136770\pi$
$659$	13.7786	+	23.8652i	0.536738	+	0.929658i	−0.462339	+	0.886703i	$0.652990\pi$
$660$	−4.21546	+	7.30139i	−0.164087	+	0.284206i
$661$	−33.9620	−	19.6080i	−1.32097	−	0.762662i	−0.337085	−	0.941474i	$-0.609441\pi$
$661$	−33.9620	−	19.6080i	−1.32097	−	0.762662i	−0.983883	+	0.178813i	$0.942774\pi$
$662$	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	−0.865307	−	0.501242i	$-0.832877\pi$
$673$	0.0372105	−	0.0644506i	0.00143436	−	0.00248439i	0.866742	+	0.498757i	$0.166210\pi$
$674$	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	−0.197677	−	0.980267i	$-0.563340\pi$
$683$	14.4371	−	8.33528i	0.552421	−	0.318941i	0.750098	+	0.661327i	$0.230006\pi$
$684$			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	−0.995624	−	0.0934463i	$-0.970212\pi$
$691$	−41.3851	−	23.8937i	−1.57436	−	0.908959i	−0.578739	−	0.815513i	$-0.696455\pi$
$692$	−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	0.0699701	−	0.997549i	$-0.477710\pi$
$709$	25.7978	−	14.8944i	0.968858	−	0.559370i	0.898888	+	0.438179i	$0.144376\pi$
$710$		−	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	0.971571	−	0.236748i	$-0.0760816\pi$
$719$	7.52823	+	13.0393i	0.280756	+	0.486283i	−0.690815	+	0.723031i	$0.742748\pi$
$720$		−	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	$-0.781047\pi$
$733$		−	34.3778i		−	1.26977i	0.772605	−	0.634886i	$-0.218953\pi$
$734$	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	0.148127	−	0.988968i	$-0.452676\pi$
$739$	−17.2427	−	9.95506i	−0.634282	−	0.366203i	−0.782408	+	0.622766i	$0.786009\pi$
$740$	−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	0.0283806	−	0.999597i	$-0.490965\pi$
$743$	−22.4362	−	12.9536i	−0.823106	−	0.475220i	−0.851486	+	0.524377i	$0.824298\pi$
$744$	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	−0.885586	−	0.464475i	$-0.846243\pi$
$751$	−1.11113	+	1.92454i	−0.0405457	+	0.0702273i	0.845040	+	0.534702i	$0.179576\pi$
$752$	−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	0.322174	−	0.946681i	$-0.395586\pi$
$757$	26.9891	−	46.7465i	0.980936	−	1.69903i	0.658763	−	0.752351i	$-0.271080\pi$
$758$	−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	0.382507	−	0.923952i	$-0.375061\pi$
$761$	37.9015	−	21.8824i	1.37393	−	0.793237i	0.991420	+	0.130715i	$0.0417273\pi$
$762$		−	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	0.241605	−	0.970375i	$-0.422326\pi$
$769$	−13.2543	−	7.65237i	−0.477962	−	0.275951i	−0.719567	+	0.694423i	$0.755660\pi$
$770$	0.225452	−	0.390494i	0.00812473	−	0.0140724i
$771$	8.96446	+	15.5269i	0.322847	+	0.559187i
$772$		−	4.14123i		−	0.149046i
$773$	−1.46429	+	0.845408i	−0.0526669	+	0.0304072i	−0.526102	−	0.850421i	$-0.676347\pi$
$773$	−1.46429	+	0.845408i	−0.0526669	+	0.0304072i	0.473435	+	0.880829i	$0.343014\pi$
$774$	0.455426	−	0.262941i	0.0163700	−	0.00945121i
$775$		−	0.847064i		−	0.0304274i
$776$	−0.0778163	−	0.134782i	−0.00279344	−	0.00483839i
$777$	3.22660	−	5.58864i	0.115754	−	0.200491i
$778$	0.0878139	+	0.0506994i	0.00314828	+	0.00181766i
$779$	−21.0647			−0.754720
$780$	−8.11543	+	6.06456i	−0.290579	+	0.217146i
$781$	−44.0320			−1.57559
$782$	0.394062	+	0.227512i	0.0140916	+	0.00813580i
$783$	−0.258294	+	0.447378i	−0.00923066	+	0.0159880i
$784$	1.96613	+	3.40543i	0.0702188	+	0.121623i
$785$			16.9079i			0.603470i
$786$	1.71776	−	0.991748i	0.0612704	−	0.0353745i
$787$	−3.88456	+	2.24275i	−0.138470	+	0.0799455i	−0.567634	−	0.823281i	$-0.692141\pi$
$787$	−3.88456	+	2.24275i	−0.138470	+	0.0799455i	0.429165	+	0.903226i	$0.358808\pi$
$788$		−	19.6376i		−	0.699562i
$789$	−10.3532	−	17.9322i	−0.368582	−	0.638403i
$790$	0.953545	−	1.65159i	0.0339256	−	0.0587609i
$791$	3.48182	+	2.01023i	0.123799	+	0.0714755i
$792$	1.27291			0.0452307
$793$	−5.74363	+	13.3817i	−0.203962	+	0.475199i
$794$	0.487814			0.0173119
$795$	−14.9902	−	8.65458i	−0.531647	−	0.306946i
$796$	−3.29732	+	5.71113i	−0.116870	+	0.202426i
$797$	−2.54226	−	4.40333i	−0.0900516	−	0.155974i	0.817481	−	0.575956i	$-0.195370\pi$
$797$	−2.54226	−	4.40333i	−0.0900516	−	0.155974i	−0.907533	+	0.419982i	$0.862037\pi$
$798$		−	0.564065i		−	0.0199677i
$799$	32.6311	−	18.8396i	1.15441	−	0.666496i
$800$	−3.29499	+	1.90236i	−0.116496	+	0.0672587i
$801$		−	11.4231i		−	0.403614i
$802$	−1.68449	−	2.91762i	−0.0594814	−	0.103025i
$803$	−9.66432	+	16.7391i	−0.341047	+	0.590710i
$804$	3.64105	+	2.10216i	0.128410	+	0.0741375i
$805$	−0.949364			−0.0334607
$806$	−0.107393	+	0.0127494i	−0.00378275	+	0.000449077i
$807$	−7.56039			−0.266138
$808$	−6.74242	−	3.89274i	−0.237197	−	0.136946i
$809$	21.4135	−	37.0893i	0.752860	−	1.30399i	−0.193571	−	0.981086i	$-0.562007\pi$
$809$	21.4135	−	37.0893i	0.752860	−	1.30399i	0.946431	−	0.322905i	$-0.104660\pi$
$810$	0.0751388	+	0.130144i	0.00264011	+	0.00457280i
$811$			7.34880i			0.258051i	0.991641	+	0.129026i	$0.0411849\pi$
$811$			7.34880i			0.258051i	−0.991641	+	0.129026i	$0.958815\pi$
$812$	−0.889695	+	0.513666i	−0.0312222	+	0.0180261i
$813$	−16.1415	+	9.31929i	−0.566107	+	0.326842i
$814$		−	2.05941i		−	0.0721821i
$815$	−0.198232	−	0.343349i	−0.00694378	−	0.0120270i
$816$	−12.5186	+	21.6828i	−0.438238	+	0.759050i
$817$	22.7089	+	13.1110i	0.794483	+	0.458695i
$818$	1.15756			0.0404733
$819$	−0.425055	−	3.58041i	−0.0148526	−	0.125110i
$820$	11.1606			0.389744
$821$	41.0920	+	23.7245i	1.43412	+	0.827989i	0.997432	−	0.0716241i	$-0.0228182\pi$
$821$	41.0920	+	23.7245i	1.43412	+	0.827989i	0.436688	+	0.899613i	$0.356152\pi$
$822$	0.530063	−	0.918096i	0.0184881	−	0.0320223i
$823$	−17.4411	−	30.2089i	−0.607960	−	1.05302i	−0.991576	−	0.129525i	$-0.958655\pi$
$823$	−17.4411	−	30.2089i	−0.607960	−	1.05302i	0.383617	−	0.923492i	$-0.374678\pi$
$824$		−	1.69639i		−	0.0590966i
$825$	7.80495	−	4.50619i	0.271734	−	0.156885i
$826$	0.212040	−	0.122422i	0.00737783	−	0.00425959i
$827$			10.6148i			0.369111i	0.982822	+	0.184556i	$0.0590846\pi$
$827$			10.6148i			0.369111i	−0.982822	+	0.184556i	$0.940915\pi$
$828$	−0.668115	−	1.15721i	−0.0232186	−	0.0402158i
$829$	11.0646	−	19.1644i	0.384288	−	0.665606i	−0.607382	−	0.794410i	$-0.707780\pi$
$829$	11.0646	−	19.1644i	0.384288	−	0.665606i	0.991670	+	0.128803i	$0.0411136\pi$
$830$	−1.10602	−	0.638561i	−0.0383905	−	0.0221648i
$831$	−17.6041			−0.610680
$832$	−16.6833	−	22.3251i	−0.578389	−	0.773985i
$833$	−6.36712			−0.220608
$834$	1.98749	+	1.14748i	0.0688211	+	0.0397339i
$835$	14.7079	−	25.4748i	0.508987	−	0.881592i
$836$	15.8227	+	27.4057i	0.547239	+	0.947846i
$837$		−	0.282012i		−	0.00974774i
$838$	−1.54976	+	0.894754i	−0.0535355	+	0.0309088i
$839$	−5.84009	+	3.37178i	−0.201622	+	0.116407i	−0.597412	−	0.801934i	$-0.703804\pi$
$839$	−5.84009	+	3.37178i	−0.201622	+	0.116407i	0.395790	+	0.918341i	$0.370471\pi$
$840$			0.599410i			0.0206816i
$841$	14.3666	+	24.8836i	0.495399	+	0.858056i
$842$	0.325604	−	0.563963i	0.0112211	−	0.0194354i
$843$	−15.1565	−	8.75062i	−0.522018	−	0.301387i
$844$	−34.7253			−1.19529
$845$	17.6153	+	5.20431i	0.605984	+	0.179034i
$846$	0.629410			0.0216396
$847$	1.72957	+	0.998571i	0.0594289	+	0.0343113i
$848$	24.0863	−	41.7186i	0.827125	−	1.43262i
$849$	8.20550	+	14.2123i	0.281612	+	0.487766i
$850$		−	2.03408i		−	0.0697685i
$851$	−3.75509	+	2.16800i	−0.128723	+	0.0743182i
$852$	25.2741	−	14.5920i	0.865876	−	0.499914i
$853$		−	44.1129i		−	1.51040i	−0.655496	−	0.755199i	$-0.727540\pi$
$853$		−	44.1129i		−	1.51040i	0.655496	−	0.755199i	$-0.272460\pi$
$854$	0.214785	+	0.372018i	0.00734978	+	0.0127302i
$855$	−3.74664	+	6.48936i	−0.128132	+	0.221932i
$856$	−0.0366138	−	0.0211390i	−0.00125143	−	0.000722515i
$857$	−57.0811			−1.94985			−0.974927	−	0.222526i	$-0.928570\pi$
$857$	−57.0811			−1.94985			−0.974927	+	0.222526i	$0.928570\pi$
$858$	−0.688780	−	0.921707i	−0.0235146	−	0.0314666i
$859$	−24.1100			−0.822624			−0.411312	−	0.911495i	$-0.634929\pi$
$859$	−24.1100			−0.822624			−0.411312	+	0.911495i	$0.634929\pi$
$860$	−12.0317	−	6.94651i	−0.410278	−	0.236874i
$861$	−1.98596	+	3.43979i	−0.0676815	+	0.117228i
$862$	−0.0580013	−	0.100461i	−0.00197553	−	0.00342172i
$863$			4.28266i			0.145783i	0.997340	+	0.0728917i	$0.0232228\pi$
$863$			4.28266i			0.145783i	−0.997340	+	0.0728917i	$0.976777\pi$
$864$	−1.09700	+	0.633350i	−0.0373205	+	0.0215470i
$865$	−6.81218	+	3.93301i	−0.231621	+	0.133726i
$866$			0.887014i			0.0301420i
$867$	−11.7701	−	20.3865i	−0.399735	−	0.692361i
$868$	0.280416	−	0.485695i	0.00951795	−	0.0164856i
$869$	−32.9760	−	19.0387i	−1.11863	−	0.645844i
$870$	−0.0776315			−0.00263195
$871$	−0.898617	−	7.56941i	−0.0304485	−	0.256480i
$872$	2.11592			0.0716540
$873$	−0.317706	−	0.183428i	−0.0107527	−	0.00620809i
$874$	−0.189502	+	0.328227i	−0.00641000	+	0.0111024i
$875$	5.65427	+	9.79348i	0.191149	+	0.331080i
$876$		−	12.8108i		−	0.432838i
$877$	−37.5471	+	21.6779i	−1.26788	+	0.732009i	−0.974586	−	0.224014i	$-0.928084\pi$
$877$	−37.5471	+	21.6779i	−1.26788	+	0.732009i	−0.293291	+	0.956023i	$0.594751\pi$
$878$	−0.529138	+	0.305498i	−0.0178575	+	0.0103101i
$879$			28.0424i			0.945848i
$880$	−8.33528	−	14.4371i	−0.280982	−	0.486675i
$881$	4.49959	−	7.79353i	0.151595	−	0.262571i	−0.780219	−	0.625507i	$-0.784892\pi$
$881$	4.49959	−	7.79353i	0.151595	−	0.262571i	0.931814	+	0.362936i	$0.118226\pi$
$882$	−0.0921099	−	0.0531797i	−0.00310150	−	0.00179065i
$883$	−57.3615			−1.93037			−0.965183	−	0.261574i	$-0.915758\pi$
$883$	−57.3615			−1.93037			−0.965183	+	0.261574i	$0.915758\pi$
$884$	45.3359	−	5.38215i	1.52481	−	0.181021i
$885$	−3.25260			−0.109335
$886$	−1.56356	−	0.902723i	−0.0525289	−	0.0303276i
$887$	−11.8661	+	20.5526i	−0.398423	+	0.690090i	−0.993532	−	0.113556i	$-0.963776\pi$
$887$	−11.8661	+	20.5526i	−0.398423	+	0.690090i	0.595108	+	0.803646i	$0.297109\pi$
$888$	1.36884	+	2.37089i	0.0459351	+	0.0795620i
$889$		−	16.5944i		−	0.556558i
$890$	1.48664	−	0.858315i	0.0498324	−	0.0287708i
$891$	2.59849	−	1.50024i	0.0870527	−	0.0502599i
$892$		−	37.3010i		−	1.24893i
$893$	15.6921	+	27.1795i	0.525116	+	0.909528i
$894$	−1.21296	+	2.10090i	−0.0405673	+	0.0702646i
$895$	7.45589	+	4.30466i	0.249223	+	0.143889i
$896$	−3.35554			−0.112101
$897$	−0.955528	+	2.22622i	−0.0319041	+	0.0743315i
$898$	0.369275			0.0123229
$899$	0.126166	+	0.0728418i	0.00420786	+	0.00242941i
$900$	−2.98666	+	5.17305i	−0.0995554	+	0.172435i
$901$	39.0006	+	67.5510i	1.29930	+	2.25045i
$902$			1.26756i			0.0422050i
$903$	4.28196	−	2.47219i	0.142495	−	0.0822693i
$904$	−1.47711	+	0.852808i	−0.0491279	+	0.0283640i
$905$			22.4451i			0.746100i
$906$	0.899028	+	1.55716i	0.0298682	+	0.0517332i
$907$	7.06921	−	12.2442i	0.234729	−	0.406563i	−0.724465	−	0.689312i	$-0.757913\pi$
$907$	7.06921	−	12.2442i	0.234729	−	0.406563i	0.959194	+	0.282749i	$0.0912463\pi$
$908$	−28.1176	−	16.2337i	−0.933117	−	0.538735i
$909$	−18.3518			−0.608692
$910$	0.434031	−	0.324346i	0.0143880	−	0.0107520i
$911$	26.2323			0.869113			0.434557	−	0.900644i	$-0.356905\pi$
$911$	26.2323			0.869113			0.434557	+	0.900644i	$0.356905\pi$
$912$	−18.0603	−	10.4271i	−0.598037	−	0.345277i
$913$	−12.7497	+	22.0831i	−0.421952	+	0.730843i
$914$	−0.515197	−	0.892347i	−0.0170412	−	0.0295162i
$915$		−	5.70658i		−	0.188654i
$916$	−19.5747	+	11.3015i	−0.646768	+	0.373411i
$917$	16.1505	−	9.32450i	0.533337	−	0.307922i
$918$		−	0.677203i		−	0.0223510i
$919$	27.5462	+	47.7114i	0.908665	+	1.57385i	0.815921	+	0.578164i	$0.196231\pi$
$919$	27.5462	+	47.7114i	0.908665	+	1.57385i	0.0927442	+	0.995690i	$0.470436\pi$
$920$	0.201376	−	0.348794i	0.00663918	−	0.0114994i
$921$	−20.4565	−	11.8105i	−0.674063	−	0.389171i
$922$	−1.17983			−0.0388555
$923$	−48.6220	−	20.8693i	−1.60041	−	0.686920i
$924$	5.96701			0.196300
$925$	16.7863	+	9.69160i	0.551931	+	0.318658i
$926$	−1.65725	+	2.87045i	−0.0544607	+	0.0943288i
$927$	−1.99936	−	3.46299i	−0.0656675	−	0.113739i
$928$		−	0.654362i		−	0.0214805i
$929$	30.4003	−	17.5516i	0.997403	−	0.575851i	0.0899240	−	0.995949i	$-0.471338\pi$
$929$	30.4003	−	17.5516i	0.997403	−	0.575851i	0.907479	+	0.420098i	$0.138004\pi$
$930$	0.0367021	−	0.0211900i	0.00120351	−	0.000694847i
$931$		−	5.30339i		−	0.173812i
$932$	30.0879	+	52.1139i	0.985563	+	1.70705i
$933$	−6.62582	+	11.4763i	−0.216919	+	0.375716i
$934$	−2.55349	−	1.47426i	−0.0835527	−	0.0482392i
$935$	26.9930			0.882767
$936$	1.40560	+	0.603302i	0.0459433	+	0.0197195i
$937$	22.6413			0.739658			0.369829	−	0.929100i	$-0.379416\pi$
$937$	22.6413			0.739658			0.369829	+	0.929100i	$0.379416\pi$
$938$	−0.194731	−	0.112428i	−0.00635820	−	0.00367091i
$939$	5.59247	−	9.68644i	0.182503	−	0.316105i
$940$	−8.31405	−	14.4004i	−0.271174	−	0.469688i
$941$		−	13.4907i		−	0.439785i	−0.975524	−	0.219892i	$-0.929429\pi$
$941$		−	13.4907i		−	0.439785i	0.975524	−	0.219892i	$-0.0705706\pi$
$942$	1.10225	−	0.636382i	0.0359131	−	0.0207344i
$943$	2.31125	−	1.33440i	0.0752645	−	0.0434540i
$944$		−	9.05219i		−	0.294624i
$945$	0.706461	+	1.22363i	0.0229812	+	0.0398046i
$946$	0.788947	−	1.36650i	0.0256509	−	0.0444286i
$947$	23.5864	+	13.6176i	0.766455	+	0.442513i	0.831609	−	0.555362i	$-0.187420\pi$
$947$	23.5864	+	13.6176i	0.766455	+	0.442513i	−0.0651533	+	0.997875i	$0.520754\pi$
$948$	25.2374			0.819671
$949$	−18.6054	+	13.9036i	−0.603956	+	0.451328i
$950$	1.69425			0.0549689
$951$	17.6386	+	10.1836i	0.571971	+	0.330227i
$952$	1.35058	−	2.33927i	0.0437724	−	0.0758161i
$953$	−28.9727	−	50.1823i	−0.938519	−	1.62556i	−0.768235	−	0.640168i	$-0.778865\pi$
$953$	−28.9727	−	50.1823i	−0.938519	−	1.62556i	−0.170284	−	0.985395i	$-0.554469\pi$
$954$			1.30297i			0.0421851i
$955$	−6.49345	+	3.74899i	−0.210123	+	0.121315i
$956$	29.4900	−	17.0261i	0.953775	−	0.550662i
$957$			1.55001i			0.0501047i
$958$	0.304470	+	0.527357i	0.00983697	+	0.0170381i
$959$	4.98370	−	8.63202i	0.160932	−	0.278742i
$960$	9.45837	+	5.46079i	0.305267	+	0.176246i
$961$	30.9205			0.997435
$962$	0.976069	−	2.27408i	0.0314697	−	0.0733193i
$963$	−0.0996570			−0.00321140
$964$	29.8463	+	17.2317i	0.961283	+	0.554997i
$965$	1.47113	−	2.54807i	0.0473573	−	0.0820252i
$966$	0.0357322	+	0.0618900i	0.00114967	+	0.00199128i
$967$			61.3188i			1.97188i	0.167101	+	0.985940i	$0.446559\pi$
$967$			61.3188i			1.97188i	−0.167101	+	0.985940i	$0.553441\pi$
$968$	−0.733745	+	0.423628i	−0.0235835	+	0.0136159i
$969$	29.2434	−	16.8837i	0.939432	−	0.542381i
$970$		−	0.0551301i		−	0.00177012i
$971$	9.17522	+	15.8919i	0.294447	+	0.509997i	0.974856	−	0.222836i	$-0.0715313\pi$
$971$	9.17522	+	15.8919i	0.294447	+	0.509997i	−0.680409	+	0.732832i	$0.738198\pi$
$972$	−0.994344	+	1.72225i	−0.0318936	+	0.0552413i
$973$	18.6865	+	10.7887i	0.599063	+	0.345869i
$974$	−0.380487			−0.0121916
$975$	10.7543	−	1.27672i	0.344413	−	0.0408877i
$976$	15.8818			0.508363
$977$	4.17067	+	2.40794i	0.133432	+	0.0770368i	0.565230	−	0.824933i	$-0.308787\pi$
$977$	4.17067	+	2.40794i	0.133432	+	0.0770368i	−0.431798	+	0.901970i	$0.642121\pi$
$978$	−0.0149222	+	0.0258460i	−0.000477159	+	0.000826463i
$979$	−17.1373	−	29.6827i	−0.547711	−	0.948663i
$980$			2.80986i			0.0897577i
$981$	4.31940	−	2.49381i	0.137908	−	0.0796212i
$982$	0.319261	−	0.184326i	0.0101880	−	0.00588207i
$983$			46.0686i			1.46936i	0.678414	+	0.734679i	$0.262667\pi$
$983$			46.0686i			1.46936i	−0.678414	+	0.734679i	$0.737333\pi$
$984$	−0.842514	−	1.45928i	−0.0268584	−	0.0465200i
$985$	6.97607	−	12.0829i	0.222276	−	0.384993i
$986$	0.302966	+	0.174917i	0.00964840	+	0.00557050i
$987$	5.91777			0.188365
$988$	4.48297	+	37.7618i	0.142622	+	1.20136i
$989$	−3.32220			−0.105640
$990$	0.390494	+	0.225452i	0.0124107	+	0.00716534i
$991$	6.41212	−	11.1061i	0.203688	−	0.352798i	−0.746026	−	0.665917i	$-0.768041\pi$
$991$	6.41212	−	11.1061i	0.203688	−	0.352798i	0.949714	+	0.313119i	$0.101374\pi$
$992$	0.178612	+	0.309365i	0.00567094	+	0.00982236i
$993$			25.1972i			0.799608i
$994$	−1.35171	+	0.780412i	−0.0428738	+	0.0247532i
$995$	−4.05764	+	2.34268i	−0.128636	+	0.0742679i
$996$		−	16.9007i		−	0.535519i
$997$	−15.0553	−	26.0766i	−0.476807	−	0.825854i	0.522840	−	0.852431i	$-0.324873\pi$
$997$	−15.0553	−	26.0766i	−0.476807	−	0.825854i	−0.999647	+	0.0265769i	$0.991539\pi$
$998$	1.80833	−	3.13212i	0.0572416	−	0.0991454i
$999$	5.58864	+	3.22660i	0.176817	+	0.102085i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bd.a.43.5	✓	16
3.2	odd	2		819.2.ct.b.316.4		16
13.6	odd	12		3549.2.a.bd.1.4		8
13.7	odd	12		3549.2.a.bb.1.5		8
13.10	even	6	inner	273.2.bd.a.127.5	yes	16
39.23	odd	6		819.2.ct.b.127.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bd.a.43.5	✓	16	1.1	even	1	trivial
273.2.bd.a.127.5	yes	16	13.10	even	6	inner
819.2.ct.b.127.4		16	39.23	odd	6
819.2.ct.b.316.4		16	3.2	odd	2
3549.2.a.bb.1.5		8	13.7	odd	12
3549.2.a.bd.1.4		8	13.6	odd	12

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

Introduction

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