LMFDB - Embedded newform 182.2.m.b.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [182,2,Mod(43,182)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(182, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("182.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 182 = 2 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	182.m (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:	$1.45327731679$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 460 x^{8} - 1066 x^{7} + 2127 x^{6} - 3172 x^{5} + \cdots + 169 $ x^12 - 6x^11 + 39x^10 - 140x^9 + 460x^8 - 1066x^7 + 2127x^6 - 3172x^5 + 3842x^4 - 3394x^3 + 2141x^2 - 832*x + 169
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.1
Root			$0.500000 + 2.47866i$ of defining polynomial
Character	$\chi$	$=$	182.43
Dual form			182.2.m.b.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-1.67234 + 2.89658i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.56356i q^{5} +(2.89658 - 1.67234i) q^{6} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-4.09347 - 7.09010i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.67234 + 2.89658i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.56356i q^{5} +(2.89658 - 1.67234i) q^{6} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-4.09347 - 7.09010i) q^{9} +(0.781779 - 1.35408i) q^{10} +(-2.48215 - 1.43307i) q^{11} -3.34469 q^{12} +(2.99598 + 2.00602i) q^{13} +1.00000 q^{14} +(-4.52898 - 2.61481i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.11481 - 1.93090i) q^{17} +8.18694i q^{18} +(-6.26657 + 3.61801i) q^{19} +(-1.35408 + 0.781779i) q^{20} -3.34469i q^{21} +(1.43307 + 2.48215i) q^{22} +(-0.833676 + 1.44397i) q^{23} +(2.89658 + 1.67234i) q^{24} +2.55529 q^{25} +(-1.59158 - 3.23525i) q^{26} +17.3487 q^{27} +(-0.866025 - 0.500000i) q^{28} +(-2.41379 + 4.18080i) q^{29} +(2.61481 + 4.52898i) q^{30} -0.597963i q^{31} +(0.866025 - 0.500000i) q^{32} +(8.30201 - 4.79317i) q^{33} +2.22961i q^{34} +(-0.781779 - 1.35408i) q^{35} +(4.09347 - 7.09010i) q^{36} +(0.0333971 + 0.0192818i) q^{37} +7.23602 q^{38} +(-10.8209 + 5.32335i) q^{39} +1.56356 q^{40} +(-6.88896 - 3.97734i) q^{41} +(-1.67234 + 2.89658i) q^{42} +(5.04571 + 8.73942i) q^{43} -2.86614i q^{44} +(11.0858 - 6.40037i) q^{45} +(1.44397 - 0.833676i) q^{46} +7.02636i q^{47} +(-1.67234 - 2.89658i) q^{48} +(0.500000 - 0.866025i) q^{49} +(-2.21294 - 1.27764i) q^{50} +7.45736 q^{51} +(-0.239275 + 3.59760i) q^{52} -5.98404 q^{53} +(-15.0244 - 8.67434i) q^{54} +(2.24069 - 3.88098i) q^{55} +(0.500000 + 0.866025i) q^{56} -24.2022i q^{57} +(4.18080 - 2.41379i) q^{58} +(0.776138 - 0.448103i) q^{59} -5.22961i q^{60} +(7.12846 + 12.3469i) q^{61} +(-0.298982 + 0.517851i) q^{62} +(7.09010 + 4.09347i) q^{63} -1.00000 q^{64} +(-3.13653 + 4.68438i) q^{65} -9.58634 q^{66} +(-1.42103 - 0.820432i) q^{67} +(1.11481 - 1.93090i) q^{68} +(-2.78838 - 4.82962i) q^{69} +1.56356i q^{70} +(-1.98724 + 1.14733i) q^{71} +(-7.09010 + 4.09347i) q^{72} +11.2277i q^{73} +(-0.0192818 - 0.0333971i) q^{74} +(-4.27332 + 7.40161i) q^{75} +(-6.26657 - 3.61801i) q^{76} +2.86614 q^{77} +(12.0329 + 0.800299i) q^{78} +4.26098 q^{79} +(-1.35408 - 0.781779i) q^{80} +(-16.7326 + 28.9816i) q^{81} +(3.97734 + 6.88896i) q^{82} -4.94829i q^{83} +(2.89658 - 1.67234i) q^{84} +(3.01907 - 1.74306i) q^{85} -10.0914i q^{86} +(-8.07337 - 13.9835i) q^{87} +(-1.43307 + 2.48215i) q^{88} +(2.09682 + 1.21060i) q^{89} -12.8007 q^{90} +(-3.59760 - 0.239275i) q^{91} -1.66735 q^{92} +(1.73205 + 1.00000i) q^{93} +(3.51318 - 6.08501i) q^{94} +(-5.65696 - 9.79815i) q^{95} +3.34469i q^{96} +(-4.23338 + 2.44414i) q^{97} +(-0.866025 + 0.500000i) q^{98} +23.4649i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3} + 6 q^{4} + 6 q^{6} - 6 q^{9}+O(q^{10}) $ 12 * q - 2 * q^3 + 6 * q^4 + 6 * q^6 - 6 * q^9	$ 12 q - 2 q^{3} + 6 q^{4} + 6 q^{6} - 6 q^{9} - 2 q^{10} - 18 q^{11} - 4 q^{12} - 8 q^{13} + 12 q^{14} - 6 q^{15} - 6 q^{16} + 4 q^{17} + 12 q^{19} - 2 q^{22} - 6 q^{23} + 6 q^{24} - 24 q^{25} - 14 q^{26} + 40 q^{27} - 10 q^{29} + 14 q^{30} + 12 q^{33} + 2 q^{35} + 6 q^{36} - 6 q^{37} + 8 q^{38} - 54 q^{39} - 4 q^{40} - 24 q^{41} - 2 q^{42} + 26 q^{43} + 72 q^{45} - 6 q^{46} - 2 q^{48} + 6 q^{49} - 12 q^{50} - 36 q^{51} - 4 q^{52} + 36 q^{53} - 36 q^{54} - 6 q^{55} + 6 q^{56} + 24 q^{58} + 6 q^{59} - 28 q^{61} - 2 q^{62} - 12 q^{64} - 34 q^{65} - 42 q^{67} - 4 q^{68} + 32 q^{69} + 48 q^{71} - 48 q^{75} + 12 q^{76} - 4 q^{77} - 8 q^{78} + 44 q^{79} - 34 q^{81} + 6 q^{82} + 6 q^{84} + 54 q^{85} + 2 q^{87} + 2 q^{88} + 12 q^{89} + 12 q^{90} - 16 q^{91} - 12 q^{92} + 8 q^{94} + 32 q^{95} + 60 q^{97}+O(q^{100}) $ 12 * q - 2 * q^3 + 6 * q^4 + 6 * q^6 - 6 * q^9 - 2 * q^10 - 18 * q^11 - 4 * q^12 - 8 * q^13 + 12 * q^14 - 6 * q^15 - 6 * q^16 + 4 * q^17 + 12 * q^19 - 2 * q^22 - 6 * q^23 + 6 * q^24 - 24 * q^25 - 14 * q^26 + 40 * q^27 - 10 * q^29 + 14 * q^30 + 12 * q^33 + 2 * q^35 + 6 * q^36 - 6 * q^37 + 8 * q^38 - 54 * q^39 - 4 * q^40 - 24 * q^41 - 2 * q^42 + 26 * q^43 + 72 * q^45 - 6 * q^46 - 2 * q^48 + 6 * q^49 - 12 * q^50 - 36 * q^51 - 4 * q^52 + 36 * q^53 - 36 * q^54 - 6 * q^55 + 6 * q^56 + 24 * q^58 + 6 * q^59 - 28 * q^61 - 2 * q^62 - 12 * q^64 - 34 * q^65 - 42 * q^67 - 4 * q^68 + 32 * q^69 + 48 * q^71 - 48 * q^75 + 12 * q^76 - 4 * q^77 - 8 * q^78 + 44 * q^79 - 34 * q^81 + 6 * q^82 + 6 * q^84 + 54 * q^85 + 2 * q^87 + 2 * q^88 + 12 * q^89 + 12 * q^90 - 16 * q^91 - 12 * q^92 + 8 * q^94 + 32 * q^95 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/182\mathbb{Z}\right)^\times$.

$n$	$15$	$157$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−1.67234	+	2.89658i	−0.965528	+	1.67234i	−0.257339	+	0.966321i	$0.582846\pi$
$3$	−1.67234	+	2.89658i	−0.965528	+	1.67234i	−0.708189	+	0.706023i	$0.750488\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$			1.56356i			0.699244i	0.936891	+	0.349622i	$0.113690\pi$
$5$			1.56356i			0.699244i	−0.936891	+	0.349622i	$0.886310\pi$
$6$	2.89658	−	1.67234i	1.18253	−	0.682732i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$8$		−	1.00000i		−	0.353553i
$9$	−4.09347	−	7.09010i	−1.36449	−	2.36337i
$10$	0.781779	−	1.35408i	0.247220	−	0.428198i
$11$	−2.48215	−	1.43307i	−0.748396	−	0.432087i	0.0767180	−	0.997053i	$-0.475556\pi$
$11$	−2.48215	−	1.43307i	−0.748396	−	0.432087i	−0.825114	+	0.564966i	$0.808889\pi$
$12$	−3.34469			−0.965528
$13$	2.99598	+	2.00602i	0.830935	+	0.556370i
$13$	2.99598	+	2.00602i	0.830935	+	0.556370i
$14$	1.00000			0.267261
$15$	−4.52898	−	2.61481i	−1.16938	−	0.675140i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.11481	−	1.93090i	−0.270380	−	0.468312i	0.698579	−	0.715533i	$-0.253816\pi$
$17$	−1.11481	−	1.93090i	−0.270380	−	0.468312i	−0.968959	+	0.247221i	$0.920483\pi$
$18$			8.18694i			1.92968i
$19$	−6.26657	+	3.61801i	−1.43765	+	0.830028i	−0.997686	−	0.0679872i	$-0.978342\pi$
$19$	−6.26657	+	3.61801i	−1.43765	+	0.830028i	−0.439964	+	0.898015i	$0.645009\pi$
$20$	−1.35408	+	0.781779i	−0.302782	+	0.174811i
$21$		−	3.34469i		−	0.729871i
$22$	1.43307	+	2.48215i	0.305531	+	0.529196i
$23$	−0.833676	+	1.44397i	−0.173833	+	0.301088i	−0.939757	−	0.341843i	$-0.888949\pi$
$23$	−0.833676	+	1.44397i	−0.173833	+	0.301088i	0.765924	+	0.642932i	$0.222282\pi$
$24$	2.89658	+	1.67234i	0.591263	+	0.341366i
$25$	2.55529			0.511058
$26$	−1.59158	−	3.23525i	−0.312135	−	0.634485i
$27$	17.3487			3.33876
$28$	−0.866025	−	0.500000i	−0.163663	−	0.0944911i
$29$	−2.41379	+	4.18080i	−0.448229	+	0.776356i	−0.998271	−	0.0587816i	$-0.981278\pi$
$29$	−2.41379	+	4.18080i	−0.448229	+	0.776356i	0.550042	+	0.835137i	$0.314612\pi$
$30$	2.61481	+	4.52898i	0.477396	+	0.826874i
$31$		−	0.597963i		−	0.107397i	−0.998557	−	0.0536987i	$-0.982899\pi$
$31$		−	0.597963i		−	0.107397i	0.998557	−	0.0536987i	$-0.0171010\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	8.30201	−	4.79317i	1.44519	−	0.834384i
$34$			2.22961i			0.382375i
$35$	−0.781779	−	1.35408i	−0.132145	−	0.228881i
$36$	4.09347	−	7.09010i	0.682245	−	1.18168i
$37$	0.0333971	+	0.0192818i	0.00549045	+	0.00316991i	0.502743	−	0.864436i	$-0.332324\pi$
$37$	0.0333971	+	0.0192818i	0.00549045	+	0.00316991i	−0.497252	+	0.867606i	$0.665658\pi$
$38$	7.23602			1.17384
$39$	−10.8209	+	5.32335i	−1.73273	+	0.852418i
$40$	1.56356			0.247220
$41$	−6.88896	−	3.97734i	−1.07588	−	0.621157i	−0.146095	−	0.989271i	$-0.546670\pi$
$41$	−6.88896	−	3.97734i	−1.07588	−	0.621157i	−0.929781	+	0.368114i	$0.880004\pi$
$42$	−1.67234	+	2.89658i	−0.258048	+	0.446953i
$43$	5.04571	+	8.73942i	0.769463	+	1.33275i	0.937854	+	0.347029i	$0.112809\pi$
$43$	5.04571	+	8.73942i	0.769463	+	1.33275i	−0.168391	+	0.985720i	$0.553857\pi$
$44$		−	2.86614i		−	0.432087i
$45$	11.0858	−	6.40037i	1.65257	−	0.954111i
$46$	1.44397	−	0.833676i	0.212902	−	0.122919i
$47$			7.02636i			1.02490i	0.858717	+	0.512450i	$0.171262\pi$
$47$			7.02636i			1.02490i	−0.858717	+	0.512450i	$0.828738\pi$
$48$	−1.67234	−	2.89658i	−0.241382	−	0.418086i
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	−2.21294	−	1.27764i	−0.312958	−	0.180686i
$51$	7.45736			1.04424
$52$	−0.239275	+	3.59760i	−0.0331814	+	0.498898i
$53$	−5.98404			−0.821971			−0.410985	−	0.911642i	$-0.634815\pi$
$53$	−5.98404			−0.821971			−0.410985	+	0.911642i	$0.634815\pi$
$54$	−15.0244	−	8.67434i	−2.04456	−	1.18043i
$55$	2.24069	−	3.88098i	0.302134	−	0.523312i
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$		−	24.2022i		−	3.20566i
$58$	4.18080	−	2.41379i	0.548966	−	0.316946i
$59$	0.776138	−	0.448103i	0.101044	−	0.0583381i	−0.448626	−	0.893719i	$-0.648087\pi$
$59$	0.776138	−	0.448103i	0.101044	−	0.0583381i	0.549671	+	0.835381i	$0.314753\pi$
$60$		−	5.22961i		−	0.675140i
$61$	7.12846	+	12.3469i	0.912706	+	1.58085i	0.810225	+	0.586119i	$0.199345\pi$
$61$	7.12846	+	12.3469i	0.912706	+	1.58085i	0.102481	+	0.994735i	$0.467322\pi$
$62$	−0.298982	+	0.517851i	−0.0379707	+	0.0657672i
$63$	7.09010	+	4.09347i	0.893268	+	0.515729i
$64$	−1.00000			−0.125000
$65$	−3.13653	+	4.68438i	−0.389038	+	0.581026i
$66$	−9.58634			−1.18000
$67$	−1.42103	−	0.820432i	−0.173606	−	0.100232i	0.410679	−	0.911780i	$-0.365292\pi$
$67$	−1.42103	−	0.820432i	−0.173606	−	0.100232i	−0.584285	+	0.811548i	$0.698625\pi$
$68$	1.11481	−	1.93090i	0.135190	−	0.234156i
$69$	−2.78838	−	4.82962i	−0.335682	−	0.581418i
$70$			1.56356i			0.186881i
$71$	−1.98724	+	1.14733i	−0.235841	+	0.136163i	−0.613264	−	0.789878i	$-0.710144\pi$
$71$	−1.98724	+	1.14733i	−0.235841	+	0.136163i	0.377422	+	0.926041i	$0.376810\pi$
$72$	−7.09010	+	4.09347i	−0.835576	+	0.482420i
$73$			11.2277i			1.31411i	0.753844	+	0.657054i	$0.228198\pi$
$73$			11.2277i			1.31411i	−0.753844	+	0.657054i	$0.771802\pi$
$74$	−0.0192818	−	0.0333971i	−0.00224147	−	0.00388233i
$75$	−4.27332	+	7.40161i	−0.493441	+	0.854664i
$76$	−6.26657	−	3.61801i	−0.718825	−	0.415014i
$77$	2.86614			0.326627
$78$	12.0329	+	0.800299i	1.36245	+	0.0906160i
$79$	4.26098			0.479397			0.239699	−	0.970847i	$-0.422951\pi$
$79$	4.26098			0.479397			0.239699	+	0.970847i	$0.422951\pi$
$80$	−1.35408	−	0.781779i	−0.151391	−	0.0874055i
$81$	−16.7326	+	28.9816i	−1.85917	+	3.22018i
$82$	3.97734	+	6.88896i	0.439224	+	0.760759i
$83$		−	4.94829i		−	0.543145i	−0.962418	−	0.271572i	$-0.912456\pi$
$83$		−	4.94829i		−	0.543145i	0.962418	−	0.271572i	$-0.0875437\pi$
$84$	2.89658	−	1.67234i	0.316043	−	0.182468i
$85$	3.01907	−	1.74306i	0.327465	−	0.189062i
$86$		−	10.0914i		−	1.08818i
$87$	−8.07337	−	13.9835i	−0.865556	−	1.49919i
$88$	−1.43307	+	2.48215i	−0.152766	+	0.264598i
$89$	2.09682	+	1.21060i	0.222263	+	0.128323i	0.606997	−	0.794704i	$-0.292374\pi$
$89$	2.09682	+	1.21060i	0.222263	+	0.128323i	−0.384735	+	0.923027i	$0.625707\pi$
$90$	−12.8007			−1.34932
$91$	−3.59760	−	0.239275i	−0.377131	−	0.0250828i
$92$	−1.66735			−0.173833
$93$	1.73205	+	1.00000i	0.179605	+	0.103695i
$94$	3.51318	−	6.08501i	0.362357	−	0.627621i
$95$	−5.65696	−	9.79815i	−0.580392	−	1.00527i
$96$			3.34469i			0.341366i
$97$	−4.23338	+	2.44414i	−0.429835	+	0.248165i	−0.699276	−	0.714852i	$-0.746494\pi$
$97$	−4.23338	+	2.44414i	−0.429835	+	0.248165i	0.269442	+	0.963017i	$0.413161\pi$
$98$	−0.866025	+	0.500000i	−0.0874818	+	0.0505076i
$99$			23.4649i			2.35831i
$100$	1.27764	+	2.21294i	0.127764	+	0.221294i
$101$	3.68373	−	6.38042i	0.366545	−	0.634875i	−0.622478	−	0.782638i	$-0.713874\pi$
$101$	3.68373	−	6.38042i	0.366545	−	0.634875i	0.989023	+	0.147763i	$0.0472072\pi$
$102$	−6.45826	−	3.72868i	−0.639463	−	0.369194i
$103$	−5.78525			−0.570038			−0.285019	−	0.958522i	$-0.592000\pi$
$103$	−5.78525			−0.570038			−0.285019	+	0.958522i	$0.592000\pi$
$104$	2.00602	−	2.99598i	0.196706	−	0.293780i
$105$	5.22961			0.510358
$106$	5.18233	+	2.99202i	0.503352	+	0.290611i
$107$	0.514478	−	0.891102i	0.0497365	−	0.0861461i	−0.840085	−	0.542454i	$-0.817495\pi$
$107$	0.514478	−	0.891102i	0.0497365	−	0.0861461i	0.889822	+	0.456308i	$0.150829\pi$
$108$	8.67434	+	15.0244i	0.834689	+	1.44572i
$109$		−	14.1535i		−	1.35566i	−0.735220	−	0.677829i	$-0.762921\pi$
$109$		−	14.1535i		−	1.35566i	0.735220	−	0.677829i	$-0.237079\pi$
$110$	−3.88098	+	2.24069i	−0.370037	+	0.213641i
$111$	−0.111703	+	0.0644917i	−0.0106024	+	0.00612128i
$112$		−	1.00000i		−	0.0944911i
$113$	6.77051	+	11.7269i	0.636916	+	1.10317i	0.986106	+	0.166119i	$0.0531237\pi$
$113$	6.77051	+	11.7269i	0.636916	+	1.10317i	−0.349189	+	0.937052i	$0.613543\pi$
$114$	−12.1011	+	20.9597i	−1.13337	+	1.96306i
$115$	−2.25773	−	1.30350i	−0.210534	−	0.121552i
$116$	−4.82757			−0.448229
$117$	1.95893	−	29.4533i	0.181103	−	2.72296i
$118$	−0.896206			−0.0825025
$119$	1.93090	+	1.11481i	0.177005	+	0.102194i
$120$	−2.61481	+	4.52898i	−0.238698	+	0.413437i
$121$	−1.39263	−	2.41210i	−0.126602	−	0.219282i
$122$		−	14.2569i		−	1.29076i
$123$	23.0414	−	13.3030i	2.07758	−	1.19949i
$124$	0.517851	−	0.298982i	0.0465044	−	0.0268493i
$125$			11.8131i			1.05660i
$126$	−4.09347	−	7.09010i	−0.364675	−	0.631636i
$127$	4.92583	−	8.53178i	0.437096	−	0.757073i	−0.560368	−	0.828244i	$-0.689340\pi$
$127$	4.92583	−	8.53178i	0.437096	−	0.757073i	0.997464	+	0.0711707i	$0.0226735\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−33.7526			−2.97175
$130$	5.05850	−	2.48853i	0.443660	−	0.218259i
$131$	14.7923			1.29241			0.646204	−	0.763165i	$-0.276355\pi$
$131$	14.7923			1.29241			0.646204	+	0.763165i	$0.276355\pi$
$132$	8.30201	+	4.79317i	0.722597	+	0.417192i
$133$	3.61801	−	6.26657i	0.313721	−	0.543381i
$134$	0.820432	+	1.42103i	0.0708746	+	0.122758i
$135$			27.1257i			2.33461i
$136$	−1.93090	+	1.11481i	−0.165573	+	0.0955938i
$137$	0.397503	−	0.229499i	0.0339610	−	0.0196074i	−0.482923	−	0.875663i	$-0.660425\pi$
$137$	0.397503	−	0.229499i	0.0339610	−	0.0196074i	0.516884	+	0.856055i	$0.327092\pi$
$138$			5.57677i			0.474726i
$139$	−7.65731	−	13.2628i	−0.649485	−	1.12494i	−0.983246	−	0.182283i	$-0.941651\pi$
$139$	−7.65731	−	13.2628i	−0.649485	−	1.12494i	0.333762	−	0.942658i	$-0.391682\pi$
$140$	0.781779	−	1.35408i	0.0660724	−	0.114441i
$141$	−20.3525	−	11.7505i	−1.71399	−	0.989570i
$142$	2.29466			0.192564
$143$	−4.56170	−	9.27268i	−0.381468	−	0.775421i
$144$	8.18694			0.682245
$145$	−6.53693	−	3.77410i	−0.542862	−	0.313422i
$146$	5.61387	−	9.72351i	0.464607	−	0.804723i
$147$	1.67234	+	2.89658i	0.137933	+	0.238906i
$148$			0.0385636i			0.00316991i
$149$	8.86563	−	5.11858i	0.726301	−	0.419330i	−0.0907665	−	0.995872i	$-0.528932\pi$
$149$	8.86563	−	5.11858i	0.726301	−	0.419330i	0.817067	+	0.576542i	$0.195598\pi$
$150$	7.40161	−	4.27332i	0.604339	−	0.348915i
$151$		−	15.2110i		−	1.23785i	−0.785448	−	0.618927i	$-0.787568\pi$
$151$		−	15.2110i		−	1.23785i	0.785448	−	0.618927i	$-0.212432\pi$
$152$	3.61801	+	6.26657i	0.293459	+	0.508286i
$153$	−9.12684	+	15.8082i	−0.737862	+	1.27801i
$154$	−2.48215	−	1.43307i	−0.200017	−	0.115480i
$155$	0.934950			0.0750970
$156$	−10.0206	−	6.70951i	−0.802291	−	0.537191i
$157$	−2.27419			−0.181500			−0.0907500	−	0.995874i	$-0.528926\pi$
$157$	−2.27419			−0.181500			−0.0907500	+	0.995874i	$0.528926\pi$
$158$	−3.69011	−	2.13049i	−0.293570	−	0.169493i
$159$	10.0074	−	17.3333i	0.793636	−	1.37462i
$160$	0.781779	+	1.35408i	0.0618050	+	0.107049i
$161$		−	1.66735i		−	0.131406i
$162$	28.9816	−	16.7326i	2.27701	−	1.31463i
$163$	0.00848066	−	0.00489631i	0.000664256	−	0.000383509i	−0.499668	−	0.866217i	$-0.666545\pi$
$163$	0.00848066	−	0.00489631i	0.000664256	−	0.000383509i	0.500332	+	0.865834i	$0.333211\pi$
$164$		−	7.95469i		−	0.621157i
$165$	7.49440	+	12.9807i	0.583438	+	1.01054i
$166$	−2.47414	+	4.28534i	−0.192031	+	0.332607i
$167$	21.6080	+	12.4754i	1.67208	+	0.965376i	0.966472	+	0.256773i	$0.0826593\pi$
$167$	21.6080	+	12.4754i	1.67208	+	0.965376i	0.705608	+	0.708603i	$0.250674\pi$
$168$	−3.34469			−0.258048
$169$	4.95177	+	12.0200i	0.380906	+	0.924614i
$170$	−3.48613			−0.267374
$171$	51.3040	+	29.6204i	3.92332	+	2.26513i
$172$	−5.04571	+	8.73942i	−0.384731	+	0.666374i
$173$	−1.60275	−	2.77604i	−0.121855	−	0.211058i	0.798644	−	0.601803i	$-0.205551\pi$
$173$	−1.60275	−	2.77604i	−0.121855	−	0.211058i	−0.920499	+	0.390745i	$0.872218\pi$
$174$			16.1467i			1.22408i
$175$	−2.21294	+	1.27764i	−0.167283	+	0.0965808i
$176$	2.48215	−	1.43307i	0.187099	−	0.108022i
$177$			2.99753i			0.225308i
$178$	−1.21060	−	2.09682i	−0.0907383	−	0.157163i
$179$	−7.89998	+	13.6832i	−0.590472	+	1.02273i	0.403697	+	0.914893i	$0.367725\pi$
$179$	−7.89998	+	13.6832i	−0.590472	+	1.02273i	−0.994169	+	0.107835i	$0.965608\pi$
$180$	11.0858	+	6.40037i	0.826285	+	0.477056i
$181$	9.11907			0.677815			0.338908	−	0.940820i	$-0.389943\pi$
$181$	9.11907			0.677815			0.338908	+	0.940820i	$0.389943\pi$
$182$	2.99598	+	2.00602i	0.222077	+	0.148696i
$183$	−47.6850			−3.52497
$184$	1.44397	+	0.833676i	0.106451	+	0.0614594i
$185$	−0.0301482	+	0.0522183i	−0.00221654	+	0.00383916i
$186$	−1.00000	−	1.73205i	−0.0733236	−	0.127000i
$187$			6.39038i			0.467311i
$188$	−6.08501	+	3.51318i	−0.443795	+	0.256225i
$189$	−15.0244	+	8.67434i	−1.09286	+	0.630966i
$190$			11.3139i			0.820799i
$191$	1.63068	+	2.82443i	0.117992	+	0.204368i	0.918972	−	0.394323i	$-0.129021\pi$
$191$	1.63068	+	2.82443i	0.117992	+	0.204368i	−0.800980	+	0.598691i	$0.795688\pi$
$192$	1.67234	−	2.89658i	0.120691	−	0.209043i
$193$	19.1158	+	11.0365i	1.37599	+	0.794426i	0.991674	−	0.128777i	$-0.0411051\pi$
$193$	19.1158	+	11.0365i	1.37599	+	0.794426i	0.384313	+	0.923203i	$0.374438\pi$
$194$	4.88829			0.350959
$195$	−8.32336	−	16.9191i	−0.596048	−	1.21160i
$196$	1.00000			0.0714286
$197$	−4.56660	−	2.63653i	−0.325357	−	0.187845i	0.328421	−	0.944531i	$-0.393484\pi$
$197$	−4.56660	−	2.63653i	−0.325357	−	0.187845i	−0.653778	+	0.756687i	$0.726817\pi$
$198$	11.7324	−	20.3212i	0.833789	−	1.44416i
$199$	4.43381	+	7.67958i	0.314304	+	0.544391i	0.979289	−	0.202466i	$-0.0648954\pi$
$199$	4.43381	+	7.67958i	0.314304	+	0.544391i	−0.664985	+	0.746857i	$0.731562\pi$
$200$		−	2.55529i		−	0.180686i
$201$	4.75290	−	2.74409i	0.335244	−	0.193553i
$202$	−6.38042	+	3.68373i	−0.448924	+	0.259187i
$203$		−	4.82757i		−	0.338829i
$204$	3.72868	+	6.45826i	0.261060	+	0.452169i
$205$	6.21881	−	10.7713i	0.434340	−	0.752300i
$206$	5.01017	+	2.89263i	0.349075	+	0.201539i
$207$	13.6505			0.948775
$208$	−3.23525	+	1.59158i	−0.224324	+	0.110356i
$209$	20.7394			1.43458
$210$	−4.52898	−	2.61481i	−0.312529	−	0.180439i
$211$	−3.28453	+	5.68898i	−0.226117	+	0.391646i	−0.956654	−	0.291227i	$-0.905936\pi$
$211$	−3.28453	+	5.68898i	−0.226117	+	0.391646i	0.730537	+	0.682873i	$0.239270\pi$
$212$	−2.99202	−	5.18233i	−0.205493	−	0.355924i
$213$		−	7.67493i		−	0.525877i
$214$	−0.891102	+	0.514478i	−0.0609145	+	0.0351690i
$215$	−13.6646	+	7.88925i	−0.931917	+	0.538043i
$216$		−	17.3487i		−	1.18043i
$217$	0.298982	+	0.517851i	0.0202962	+	0.0351540i
$218$	−7.07674	+	12.2573i	−0.479297	+	0.830167i
$219$	−32.5221	−	18.7766i	−2.19764	−	1.26881i
$220$	4.48137			0.302134
$221$	0.533490	−	8.02126i	0.0358864	−	0.539568i
$222$	0.128983			0.00865679
$223$	−14.6463	−	8.45606i	−0.980790	−	0.566260i	−0.0782817	−	0.996931i	$-0.524943\pi$
$223$	−14.6463	−	8.45606i	−0.980790	−	0.566260i	−0.902509	+	0.430672i	$0.858277\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$	−10.4600	−	18.1172i	−0.697333	−	1.20782i
$226$		−	13.5410i		−	0.900736i
$227$	−13.9709	+	8.06611i	−0.927282	+	0.535367i	−0.885951	−	0.463779i	$-0.846493\pi$
$227$	−13.9709	+	8.06611i	−0.927282	+	0.535367i	−0.0413312	+	0.999146i	$0.513160\pi$
$228$	20.9597	−	12.1011i	1.38809	−	0.801415i
$229$		−	6.91184i		−	0.456747i	−0.973574	−	0.228374i	$-0.926659\pi$
$229$		−	6.91184i		−	0.456747i	0.973574	−	0.228374i	$-0.0733408\pi$
$230$	1.30350	+	2.25773i	0.0859502	+	0.148870i
$231$	−4.79317	+	8.30201i	−0.315367	+	0.546232i
$232$	4.18080	+	2.41379i	0.274483	+	0.158473i
$233$	7.47405			0.489641			0.244821	−	0.969568i	$-0.421271\pi$
$233$	7.47405			0.489641			0.244821	+	0.969568i	$0.421271\pi$
$234$	−16.4232	+	24.5279i	−1.07362	+	1.60344i
$235$	−10.9861			−0.716656
$236$	0.776138	+	0.448103i	0.0505222	+	0.0291690i
$237$	−7.12582	+	12.3423i	−0.462872	+	0.801717i
$238$	−1.11481	−	1.93090i	−0.0722621	−	0.125162i
$239$		−	19.8696i		−	1.28526i	−0.766179	−	0.642628i	$-0.777844\pi$
$239$		−	19.8696i		−	1.28526i	0.766179	−	0.642628i	$-0.222156\pi$
$240$	4.52898	−	2.61481i	0.292344	−	0.168785i
$241$	−9.21842	+	5.32226i	−0.593811	+	0.342837i	−0.766603	−	0.642121i	$-0.778054\pi$
$241$	−9.21842	+	5.32226i	−0.593811	+	0.342837i	0.172792	+	0.984958i	$0.444721\pi$
$242$			2.78525i			0.179043i
$243$	−29.9422	−	51.8613i	−1.92079	−	3.32691i
$244$	−7.12846	+	12.3469i	−0.456353	+	0.790427i
$245$	1.35408	+	0.781779i	0.0865090	+	0.0499460i
$246$	−26.6060			−1.69633
$247$	−26.0323	−	1.73140i	−1.65640	−	0.110166i
$248$	−0.597963			−0.0379707
$249$	14.3331	+	8.27524i	0.908325	+	0.524422i
$250$	5.90656	−	10.2305i	0.373564	−	0.647032i
$251$	7.95696	+	13.7819i	0.502239	+	0.869904i	0.999997	+	0.00258749i	$0.000823625\pi$
$251$	7.95696	+	13.7819i	0.502239	+	0.869904i	−0.497757	+	0.867316i	$0.665843\pi$
$252$			8.18694i			0.515729i
$253$	4.13861	−	2.38943i	0.260192	−	0.150222i
$254$	−8.53178	+	4.92583i	−0.535332	+	0.309074i
$255$			11.6600i			0.730178i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−15.5509	+	26.9350i	−0.970039	+	1.68016i	−0.274619	+	0.961553i	$0.588552\pi$
$257$	−15.5509	+	26.9350i	−0.970039	+	1.68016i	−0.695420	+	0.718603i	$0.744782\pi$
$258$	29.2306	+	16.8763i	1.81982	+	1.05067i
$259$	−0.0385636			−0.00239623
$260$	−5.62506	−	0.374120i	−0.348851	−	0.0232019i
$261$	39.5230			2.44642
$262$	−12.8105	−	7.39614i	−0.791435	−	0.456935i
$263$	14.1873	−	24.5732i	0.874829	−	1.51525i	0.0178837	−	0.999840i	$-0.494307\pi$
$263$	14.1873	−	24.5732i	0.874829	−	1.51525i	0.856945	−	0.515408i	$-0.172360\pi$
$264$	−4.79317	−	8.30201i	−0.294999	−	0.510954i
$265$		−	9.35639i		−	0.574758i
$266$	−6.26657	+	3.61801i	−0.384228	+	0.221834i
$267$	−7.01321	+	4.04908i	−0.429202	+	0.247800i
$268$		−	1.64086i		−	0.100232i
$269$	10.7008	+	18.5344i	0.652441	+	1.13006i	0.982529	+	0.186111i	$0.0595883\pi$
$269$	10.7008	+	18.5344i	0.652441	+	1.13006i	−0.330088	+	0.943950i	$0.607078\pi$
$270$	13.5628	−	23.4915i	0.825408	−	1.42965i
$271$	4.97667	+	2.87328i	0.302311	+	0.174539i	0.643481	−	0.765462i	$-0.277490\pi$
$271$	4.97667	+	2.87328i	0.302311	+	0.174539i	−0.341170	+	0.940002i	$0.610823\pi$
$272$	2.22961			0.135190
$273$	6.70951	−	10.0206i	0.406078	−	0.606475i
$274$	−0.458997			−0.0277290
$275$	−6.34260	−	3.66190i	−0.382473	−	0.220821i
$276$	2.78838	−	4.82962i	0.167841	−	0.290709i
$277$	13.3010	+	23.0380i	0.799180	+	1.38422i	0.920151	+	0.391564i	$0.128066\pi$
$277$	13.3010	+	23.0380i	0.799180	+	1.38422i	−0.120971	+	0.992656i	$0.538601\pi$
$278$			15.3146i			0.918510i
$279$	−4.23962	+	2.44774i	−0.253819	+	0.146543i
$280$	−1.35408	+	0.781779i	−0.0809218	+	0.0467202i
$281$		−	6.69143i		−	0.399177i	−0.979880	−	0.199589i	$-0.936039\pi$
$281$		−	6.69143i		−	0.399177i	0.979880	−	0.199589i	$-0.0639606\pi$
$282$	11.7505	+	20.3525i	0.699732	+	1.21197i
$283$	9.96692	−	17.2632i	0.592472	−	1.02619i	−0.401426	−	0.915891i	$-0.631485\pi$
$283$	9.96692	−	17.2632i	0.592472	−	1.02619i	0.993898	−	0.110300i	$-0.0351812\pi$
$284$	−1.98724	−	1.14733i	−0.117921	−	0.0680816i
$285$	37.8416			2.24154
$286$	−0.685794	+	10.3112i	−0.0405519	+	0.609716i
$287$	7.95469			0.469550
$288$	−7.09010	−	4.09347i	−0.417788	−	0.241210i
$289$	6.01442	−	10.4173i	0.353789	−	0.612781i
$290$	3.77410	+	6.53693i	0.221623	+	0.383861i
$291$		−	16.3498i		−	0.958442i
$292$	−9.72351	+	5.61387i	−0.569025	+	0.328527i
$293$	−7.67375	+	4.43044i	−0.448305	+	0.258829i	−0.707114	−	0.707099i	$-0.750003\pi$
$293$	−7.67375	+	4.43044i	−0.448305	+	0.258829i	0.258809	+	0.965929i	$0.416670\pi$
$294$		−	3.34469i		−	0.195066i
$295$	0.700635	+	1.21354i	0.0407926	+	0.0706548i
$296$	0.0192818	−	0.0333971i	0.00112073	−	0.00194117i
$297$	−43.0620	−	24.8619i	−2.49871	−	1.44263i
$298$	−10.2372			−0.593022
$299$	−5.39430	+	2.65373i	−0.311961	+	0.153469i
$300$	−8.54664			−0.493441
$301$	−8.73942	−	5.04571i	−0.503732	−	0.290830i
$302$	−7.60551	+	13.1731i	−0.437648	+	0.758028i
$303$	12.3209	+	21.3405i	0.707820	+	1.22598i
$304$		−	7.23602i		−	0.415014i
$305$	−19.3050	+	11.1458i	−1.10540	+	0.638205i
$306$	15.8082	−	9.12684i	0.903692	−	0.521747i
$307$			8.34636i			0.476352i	0.971222	+	0.238176i	$0.0765495\pi$
$307$			8.34636i			0.476352i	−0.971222	+	0.238176i	$0.923450\pi$
$308$	1.43307	+	2.48215i	0.0816567	+	0.141434i
$309$	9.67493	−	16.7575i	0.550387	−	0.953299i
$310$	−0.809690	−	0.467475i	−0.0459873	−	0.0265508i
$311$	−6.68896			−0.379296			−0.189648	−	0.981852i	$-0.560735\pi$
$311$	−6.68896			−0.379296			−0.189648	+	0.981852i	$0.560735\pi$
$312$	5.32335	+	10.8209i	0.301375	+	0.612613i
$313$	−21.3788			−1.20840			−0.604199	−	0.796833i	$-0.706507\pi$
$313$	−21.3788			−1.20840			−0.604199	+	0.796833i	$0.706507\pi$
$314$	1.96950	+	1.13709i	0.111146	+	0.0641699i
$315$	−6.40037	+	11.0858i	−0.360620	+	0.624612i
$316$	2.13049	+	3.69011i	0.119849	+	0.207585i
$317$			31.6776i			1.77919i	0.456748	+	0.889596i	$0.349014\pi$
$317$			31.6776i			1.77919i	−0.456748	+	0.889596i	$0.650986\pi$
$318$	−17.3333	+	10.0074i	−0.972002	+	0.561185i
$319$	11.9828	−	6.91825i	0.670906	−	0.387348i
$320$		−	1.56356i		−	0.0874055i
$321$	1.72077	+	2.98046i	0.0960439	+	0.166353i
$322$	−0.833676	+	1.44397i	−0.0464589	+	0.0804692i
$323$	13.9720	+	8.06675i	0.777424	+	0.448846i
$324$	−33.4651			−1.85917
$325$	7.65559	+	5.12596i	0.424656	+	0.284337i
$326$	−0.00979262			−0.000542363
$327$	40.9967	+	23.6695i	2.26713	+	1.30893i
$328$	−3.97734	+	6.88896i	−0.219612	+	0.380379i
$329$	−3.51318	−	6.08501i	−0.193688	−	0.335477i
$330$		−	14.9888i		−	0.825106i
$331$	−21.3644	+	12.3347i	−1.17429	+	0.677979i	−0.954688	−	0.297609i	$-0.903811\pi$
$331$	−21.3644	+	12.3347i	−1.17429	+	0.677979i	−0.219606	+	0.975589i	$0.570477\pi$
$332$	4.28534	−	2.47414i	0.235189	−	0.135786i
$333$		−	0.315718i		−	0.0173012i
$334$	−12.4754	−	21.6080i	−0.682624	−	1.18234i
$335$	1.28279	−	2.22186i	0.0700865	−	0.121393i
$336$	2.89658	+	1.67234i	0.158022	+	0.0912338i
$337$	28.0871			1.53000			0.765002	−	0.644028i	$-0.222738\pi$
$337$	28.0871			1.53000			0.765002	+	0.644028i	$0.222738\pi$
$338$	1.72163	−	12.8855i	0.0936444	−	0.700879i
$339$	−45.2905			−2.45984
$340$	3.01907	+	1.74306i	0.163732	+	0.0945309i
$341$	−0.856923	+	1.48423i	−0.0464050	+	0.0803757i
$342$	−29.6204	−	51.3040i	−1.60169	−	2.77420i
$343$			1.00000i			0.0539949i
$344$	8.73942	−	5.04571i	0.471198	−	0.272046i
$345$	7.55139	−	4.35980i	0.406553	−	0.234724i
$346$			3.20550i			0.172329i
$347$	5.05398	+	8.75374i	0.271312	+	0.469926i	0.969198	−	0.246283i	$-0.0792093\pi$
$347$	5.05398	+	8.75374i	0.271312	+	0.469926i	−0.697886	+	0.716209i	$0.745876\pi$
$348$	8.07337	−	13.9835i	0.432778	−	0.749593i
$349$	−15.0596	−	8.69465i	−0.806121	−	0.465414i	0.0394863	−	0.999220i	$-0.487428\pi$
$349$	−15.0596	−	8.69465i	−0.806121	−	0.465414i	−0.845607	+	0.533806i	$0.820761\pi$
$350$	2.55529			0.136586
$351$	51.9763	+	34.8018i	2.77429	+	1.85758i
$352$	−2.86614			−0.152766
$353$	2.88091	+	1.66329i	0.153335	+	0.0885282i	0.574704	−	0.818361i	$-0.305117\pi$
$353$	2.88091	+	1.66329i	0.153335	+	0.0885282i	−0.421369	+	0.906889i	$0.638450\pi$
$354$	1.49877	−	2.59594i	0.0796585	−	0.137973i
$355$	−1.79392	−	3.10716i	−0.0952113	−	0.164911i
$356$			2.42120i			0.128323i
$357$	−6.45826	+	3.72868i	−0.341807	+	0.197343i
$358$	13.6832	−	7.89998i	0.723177	−	0.417527i
$359$		−	8.02414i		−	0.423498i	−0.977324	−	0.211749i	$-0.932084\pi$
$359$		−	8.02414i		−	0.423498i	0.977324	−	0.211749i	$-0.0679159\pi$
$360$	−6.40037	−	11.0858i	−0.337329	−	0.584271i
$361$	16.6800	−	28.8905i	0.877893	−	1.52055i
$362$	−7.89735	−	4.55954i	−0.415075	−	0.239644i
$363$	9.31579			0.488952
$364$	−1.59158	−	3.23525i	−0.0834216	−	0.169573i
$365$	−17.5552			−0.918882
$366$	41.2964	+	23.8425i	2.15860	+	1.24627i
$367$	−0.519540	+	0.899869i	−0.0271198	+	0.0469728i	−0.879267	−	0.476330i	$-0.841967\pi$
$367$	−0.519540	+	0.899869i	−0.0271198	+	0.0469728i	0.852147	+	0.523302i	$0.175300\pi$
$368$	−0.833676	−	1.44397i	−0.0434583	−	0.0752721i
$369$			65.1245i			3.39025i
$370$	0.0522183	−	0.0301482i	0.00271470	−	0.00156733i
$371$	5.18233	−	2.99202i	0.269053	−	0.155338i
$372$			2.00000i			0.103695i
$373$	−13.6562	−	23.6532i	−0.707092	−	1.22472i	−0.965931	−	0.258798i	$-0.916673\pi$
$373$	−13.6562	−	23.6532i	−0.707092	−	1.22472i	0.258840	−	0.965920i	$-0.416660\pi$
$374$	3.19519	−	5.53423i	0.165219	−	0.286168i
$375$	−34.2177	−	19.7556i	−1.76700	−	1.02018i
$376$	7.02636			0.362357
$377$	−15.6184	+	7.68349i	−0.804390	+	0.395720i
$378$	17.3487			0.892320
$379$	−1.91535	−	1.10583i	−0.0983850	−	0.0568026i	0.450000	−	0.893028i	$-0.351424\pi$
$379$	−1.91535	−	1.10583i	−0.0983850	−	0.0568026i	−0.548385	+	0.836226i	$0.684757\pi$
$380$	5.65696	−	9.79815i	0.290196	−	0.502634i
$381$	16.4754	+	28.5361i	0.844058	+	1.46195i
$382$		−	3.26137i		−	0.166866i
$383$	19.3458	−	11.1693i	0.988522	−	0.570724i	0.0836900	−	0.996492i	$-0.473329\pi$
$383$	19.3458	−	11.1693i	0.988522	−	0.570724i	0.904832	+	0.425768i	$0.139996\pi$
$384$	−2.89658	+	1.67234i	−0.147816	+	0.0853414i
$385$			4.48137i			0.228392i
$386$	−11.0365	−	19.1158i	−0.561744	−	0.972969i
$387$	41.3089	−	71.5491i	2.09985	−	3.63704i
$388$	−4.23338	−	2.44414i	−0.214917	−	0.124083i
$389$	−12.2604			−0.621629			−0.310814	−	0.950471i	$-0.600602\pi$
$389$	−12.2604			−0.621629			−0.310814	+	0.950471i	$0.600602\pi$
$390$	−1.25131	+	18.8141i	−0.0633627	+	0.952687i
$391$	3.71755			0.188004
$392$	−0.866025	−	0.500000i	−0.0437409	−	0.0252538i
$393$	−24.7378	+	42.8471i	−1.24786	+	2.16135i
$394$	2.63653	+	4.56660i	0.132826	+	0.230062i
$395$			6.66228i			0.335216i
$396$	−20.3212	+	11.7324i	−1.02118	+	0.589578i
$397$	2.54193	−	1.46759i	0.127576	−	0.0736561i	−0.434854	−	0.900501i	$-0.643200\pi$
$397$	2.54193	−	1.46759i	0.127576	−	0.0736561i	0.562430	+	0.826845i	$0.309867\pi$
$398$		−	8.86762i		−	0.444493i
$399$	12.1011	+	20.9597i	0.605813	+	1.04930i
$400$	−1.27764	+	2.21294i	−0.0638822	+	0.110647i
$401$	18.9229	+	10.9251i	0.944963	+	0.545575i	0.891513	−	0.452996i	$-0.149645\pi$
$401$	18.9229	+	10.9251i	0.944963	+	0.545575i	0.0534502	+	0.998571i	$0.482978\pi$
$402$	−5.48818			−0.273726
$403$	1.19953	−	1.79148i	0.0597526	−	0.0892402i
$404$	7.36747			0.366545
$405$	−45.3145	−	26.1623i	−2.25169	−	1.30002i
$406$	−2.41379	+	4.18080i	−0.119794	+	0.207490i
$407$	−0.0552644	−	0.0957207i	−0.00273935	−	0.00474470i
$408$		−	7.45736i		−	0.369194i
$409$	−6.39292	+	3.69095i	−0.316109	+	0.182506i	−0.649657	−	0.760227i	$-0.725088\pi$
$409$	−6.39292	+	3.69095i	−0.316109	+	0.182506i	0.333548	+	0.942733i	$0.391754\pi$
$410$	−10.7713	+	6.21881i	−0.531956	+	0.307125i
$411$			1.53520i			0.0757260i
$412$	−2.89263	−	5.01017i	−0.142509	−	0.246834i
$413$	−0.448103	+	0.776138i	−0.0220497	+	0.0381912i
$414$	−11.8217	−	6.82525i	−0.581004	−	0.335443i
$415$	7.73693			0.379791
$416$	3.59760	+	0.239275i	0.176387	+	0.0117314i
$417$	51.2226			2.50838
$418$	−17.9609	−	10.3697i	−0.878495	−	0.507199i
$419$	4.29137	−	7.43287i	0.209647	−	0.363119i	−0.741956	−	0.670448i	$-0.766102\pi$
$419$	4.29137	−	7.43287i	0.209647	−	0.363119i	0.951603	+	0.307329i	$0.0994352\pi$
$420$	2.61481	+	4.52898i	0.127589	+	0.220991i
$421$			7.49525i			0.365296i	0.983178	+	0.182648i	$0.0584669\pi$
$421$			7.49525i			0.365296i	−0.983178	+	0.182648i	$0.941533\pi$
$422$	5.68898	−	3.28453i	0.276935	−	0.159889i
$423$	49.8176	−	28.7622i	2.42221	−	1.39847i
$424$			5.98404i			0.290611i
$425$	−2.84865	−	4.93401i	−0.138180	−	0.239334i
$426$	−3.83746	+	6.64668i	−0.185926	+	0.322033i
$427$	−12.3469	−	7.12846i	−0.597507	−	0.344971i
$428$	1.02896			0.0497365
$429$	34.4878	+	2.29377i	1.66509	+	0.110744i
$430$	15.7785			0.760907
$431$	−14.2713	−	8.23956i	−0.687426	−	0.396886i	0.115221	−	0.993340i	$-0.463242\pi$
$431$	−14.2713	−	8.23956i	−0.687426	−	0.396886i	−0.802647	+	0.596454i	$0.796576\pi$
$432$	−8.67434	+	15.0244i	−0.417344	+	0.722862i
$433$	−12.7805	−	22.1365i	−0.614192	−	1.06381i	−0.990526	−	0.137328i	$-0.956149\pi$
$433$	−12.7805	−	22.1365i	−0.614192	−	1.06381i	0.376333	−	0.926484i	$-0.377185\pi$
$434$		−	0.597963i		−	0.0287031i
$435$	21.8640	−	12.6232i	1.04830	−	0.605235i
$436$	12.2573	−	7.07674i	0.587017	−	0.338914i
$437$		−	12.0650i		−	0.577146i
$438$	18.7766	+	32.5221i	0.897183	+	1.55397i
$439$	4.60420	−	7.97470i	0.219746	−	0.380612i	−0.734984	−	0.678084i	$-0.762810\pi$
$439$	4.60420	−	7.97470i	0.219746	−	0.380612i	0.954730	+	0.297473i	$0.0961437\pi$
$440$	−3.88098	−	2.24069i	−0.185019	−	0.106821i
$441$	−8.18694			−0.389854
$442$	−4.47264	+	6.67987i	−0.212742	+	0.317729i
$443$	−6.20759			−0.294931			−0.147466	−	0.989067i	$-0.547112\pi$
$443$	−6.20759			−0.294931			−0.147466	+	0.989067i	$0.547112\pi$
$444$	−0.111703	−	0.0644917i	−0.00530118	−	0.00306064i
$445$	−1.89284	+	3.27850i	−0.0897294	+	0.155416i
$446$	8.45606	+	14.6463i	0.400406	+	0.693523i
$447$			34.2401i			1.61950i
$448$	0.866025	−	0.500000i	0.0409159	−	0.0236228i
$449$	4.51968	−	2.60944i	0.213297	−	0.123147i	−0.389546	−	0.921007i	$-0.627368\pi$
$449$	4.51968	−	2.60944i	0.213297	−	0.123147i	0.602843	+	0.797860i	$0.294035\pi$
$450$			20.9200i			0.986177i
$451$	11.3996	+	19.7447i	0.536787	+	0.929743i
$452$	−6.77051	+	11.7269i	−0.318458	+	0.551586i
$453$	44.0600	+	25.4380i	2.07012	+	1.19518i
$454$	16.1322			0.757123
$455$	0.374120	−	5.62506i	0.0175390	−	0.263707i
$456$	−24.2022			−1.13337
$457$	−29.3870	−	16.9666i	−1.37467	−	0.793664i	−0.383155	−	0.923684i	$-0.625162\pi$
$457$	−29.3870	−	16.9666i	−1.37467	−	0.793664i	−0.991511	+	0.130021i	$0.958496\pi$
$458$	−3.45592	+	5.98583i	−0.161484	+	0.279699i
$459$	−19.3404	−	33.4986i	−0.902733	−	1.56358i
$460$		−	2.60700i		−	0.121552i
$461$	0.731583	−	0.422380i	0.0340732	−	0.0196722i	−0.482867	−	0.875694i	$-0.660404\pi$
$461$	0.731583	−	0.422380i	0.0340732	−	0.0196722i	0.516940	+	0.856022i	$0.327071\pi$
$462$	8.30201	−	4.79317i	0.386245	−	0.222998i
$463$		−	6.50221i		−	0.302183i	−0.988520	−	0.151092i	$-0.951721\pi$
$463$		−	6.50221i		−	0.302183i	0.988520	−	0.151092i	$-0.0482789\pi$
$464$	−2.41379	−	4.18080i	−0.112057	−	0.194089i
$465$	−1.56356	+	2.70816i	−0.0725082	+	0.125588i
$466$	−6.47272	−	3.73702i	−0.299843	−	0.173114i
$467$	9.52759			0.440884			0.220442	−	0.975400i	$-0.429250\pi$
$467$	9.52759			0.440884			0.220442	+	0.975400i	$0.429250\pi$
$468$	26.4868	−	13.0302i	1.22435	−	0.602321i
$469$	1.64086			0.0757681
$470$	9.51426	+	5.49306i	0.438860	+	0.253376i
$471$	3.80322	−	6.58738i	0.175243	−	0.303530i
$472$	−0.448103	−	0.776138i	−0.0206256	−	0.0357246i
$473$		−	28.9234i		−	1.32990i
$474$	12.3423	−	7.12582i	0.566900	−	0.327300i
$475$	−16.0129	+	9.24505i	−0.734722	+	0.424192i
$476$			2.22961i			0.102194i
$477$	24.4955	+	42.4274i	1.12157	+	1.94262i
$478$	−9.93478	+	17.2075i	−0.454406	+	0.787055i
$479$	−2.46123	−	1.42099i	−0.112457	−	0.0649268i	0.442717	−	0.896662i	$-0.354015\pi$
$479$	−2.46123	−	1.42099i	−0.112457	−	0.0649268i	−0.555173	+	0.831735i	$0.687348\pi$
$480$	−5.22961			−0.238698
$481$	0.0613773	+	0.124763i	0.00279856	+	0.00568871i
$482$	10.6445			0.484844
$483$	4.82962	+	2.78838i	0.219755	+	0.126876i
$484$	1.39263	−	2.41210i	0.0633011	−	0.109641i
$485$	−3.82156	−	6.61913i	−0.173528	−	0.300559i
$486$			59.8843i			2.71641i
$487$	−4.55853	+	2.63187i	−0.206567	+	0.119261i	−0.599715	−	0.800214i	$-0.704719\pi$
$487$	−4.55853	+	2.63187i	−0.206567	+	0.119261i	0.393148	+	0.919475i	$0.371386\pi$
$488$	12.3469	−	7.12846i	0.558916	−	0.322690i
$489$			0.0327533i			0.00148115i
$490$	−0.781779	−	1.35408i	−0.0353172	−	0.0611711i
$491$	11.4457	−	19.8245i	0.516536	−	0.894666i	−0.483280	−	0.875466i	$-0.660555\pi$
$491$	11.4457	−	19.8245i	0.516536	−	0.894666i	0.999816	−	0.0192004i	$-0.00611205\pi$
$492$	23.0414	+	13.3030i	1.03879	+	0.599745i
$493$	10.7636			0.484769
$494$	21.6789	+	14.5156i	0.975382	+	0.653087i
$495$	−36.6887			−1.64903
$496$	0.517851	+	0.298982i	0.0232522	+	0.0134247i
$497$	1.14733	−	1.98724i	0.0514648	−	0.0891397i
$498$	−8.27524	−	14.3331i	−0.370822	−	0.642283i
$499$			6.79877i			0.304355i	0.988353	+	0.152177i	$0.0486285\pi$
$499$			6.79877i			0.304355i	−0.988353	+	0.152177i	$0.951372\pi$
$500$	−10.2305	+	5.90656i	−0.457520	+	0.264150i
$501$	−72.2721	+	41.7263i	−3.22888	+	1.86419i
$502$		−	15.9139i		−	0.710273i
$503$	−5.40300	−	9.35827i	−0.240908	−	0.417265i	0.720065	−	0.693906i	$-0.244112\pi$
$503$	−5.40300	−	9.35827i	−0.240908	−	0.417265i	−0.960973	+	0.276642i	$0.910779\pi$
$504$	4.09347	−	7.09010i	0.182338	−	0.315818i
$505$	9.97615	+	5.75973i	0.443933	+	0.256305i
$506$	−4.77886			−0.212446
$507$	−43.0980	−	5.75832i	−1.91405	−	0.255736i
$508$	9.85165			0.437096
$509$	−23.6593	−	13.6597i	−1.04868	−	0.605455i	−0.126400	−	0.991979i	$-0.540342\pi$
$509$	−23.6593	−	13.6597i	−1.04868	−	0.605455i	−0.922279	+	0.386524i	$0.873676\pi$
$510$	5.83000	−	10.0979i	0.258157	−	0.447141i
$511$	−5.61387	−	9.72351i	−0.248343	−	0.430143i
$512$			1.00000i			0.0441942i
$513$	−108.717	+	62.7677i	−4.79996	+	2.77126i
$514$	26.9350	−	15.5509i	1.18805	−	0.685921i
$515$		−	9.04557i		−	0.398595i
$516$	−16.8763	−	29.2306i	−0.742938	−	1.28681i
$517$	10.0693	−	17.4405i	0.442846	−	0.767031i
$518$	0.0333971	+	0.0192818i	0.00146738	+	0.000847194i
$519$	10.7214			0.470616
$520$	4.68438	+	3.13653i	0.205424	+	0.137546i
$521$	−3.63580			−0.159287			−0.0796437	−	0.996823i	$-0.525378\pi$
$521$	−3.63580			−0.159287			−0.0796437	+	0.996823i	$0.525378\pi$
$522$	−34.2280	−	19.7615i	−1.49812	−	0.864938i
$523$	3.59223	−	6.22193i	0.157077	−	0.272066i	−0.776736	−	0.629826i	$-0.783126\pi$
$523$	3.59223	−	6.22193i	0.157077	−	0.272066i	0.933813	+	0.357760i	$0.116459\pi$
$524$	7.39614	+	12.8105i	0.323102	+	0.559629i
$525$		−	8.54664i		−	0.373006i
$526$	−24.5732	+	14.1873i	−1.07144	+	0.618597i
$527$	−1.15461	+	0.666613i	−0.0502955	+	0.0290381i
$528$			9.58634i			0.417192i
$529$	10.1100	+	17.5110i	0.439564	+	0.761347i
$530$	−4.67819	+	8.10287i	−0.203208	+	0.351966i
$531$	−6.35419	−	3.66859i	−0.275748	−	0.159203i
$532$	7.23602			0.313721
$533$	−12.6606	−	25.7354i	−0.548389	−	1.11473i
$534$	8.09816			0.350442
$535$	1.39329	+	0.804416i	0.0602371	+	0.0347779i
$536$	−0.820432	+	1.42103i	−0.0354373	+	0.0613792i
$537$	−26.4230	−	45.7659i	−1.14023	−	1.97494i
$538$		−	21.4017i		−	0.922691i
$539$	−2.48215	+	1.43307i	−0.106914	+	0.0617267i
$540$	−23.4915	+	13.5628i	−1.01091	+	0.583651i
$541$			0.445063i			0.0191347i	0.999954	+	0.00956737i	$0.00304543\pi$
$541$			0.445063i			0.0191347i	−0.999954	+	0.00956737i	$0.996955\pi$
$542$	−2.87328	−	4.97667i	−0.123418	−	0.213766i
$543$	−15.2502	+	26.4142i	−0.654450	+	1.13354i
$544$	−1.93090	−	1.11481i	−0.0827867	−	0.0477969i
$545$	22.1298			0.947935
$546$	−10.8209	+	5.32335i	−0.463092	+	0.227818i
$547$	−5.67129			−0.242487			−0.121243	−	0.992623i	$-0.538688\pi$
$547$	−5.67129			−0.242487			−0.121243	+	0.992623i	$0.538688\pi$
$548$	0.397503	+	0.229499i	0.0169805	+	0.00980370i
$549$	58.3603	−	101.083i	2.49076	−	4.31412i
$550$	3.66190	+	6.34260i	0.156144	+	0.270450i
$551$		−	34.9324i		−	1.48817i
$552$	−4.82962	+	2.78838i	−0.205562	+	0.118682i
$553$	−3.69011	+	2.13049i	−0.156920	+	0.0905976i
$554$		−	26.6020i		−	1.13021i
$555$	−0.100836	−	0.174654i	−0.00428027	−	0.00741364i
$556$	7.65731	−	13.2628i	0.324742	−	0.562470i
$557$	22.9561	+	13.2537i	0.972683	+	0.561579i	0.900053	−	0.435780i	$-0.143528\pi$
$557$	22.9561	+	13.2537i	0.972683	+	0.561579i	0.0726298	+	0.997359i	$0.476861\pi$
$558$	4.89549			0.207242
$559$	−2.41462	+	36.3049i	−0.102128	+	1.53553i
$560$	1.56356			0.0660724
$561$	−18.5103	−	10.6869i	−0.781504	−	0.451202i
$562$	−3.34571	+	5.79495i	−0.141130	+	0.244445i
$563$	−5.76880	−	9.99186i	−0.243126	−	0.421107i	0.718477	−	0.695551i	$-0.244840\pi$
$563$	−5.76880	−	9.99186i	−0.243126	−	0.421107i	−0.961603	+	0.274444i	$0.911506\pi$
$564$		−	23.5010i		−	0.989570i
$565$	−18.3356	+	10.5861i	−0.771386	+	0.445360i
$566$	−17.2632	+	9.96692i	−0.725627	+	0.418941i
$567$		−	33.4651i		−	1.40540i
$568$	1.14733	+	1.98724i	0.0481409	+	0.0833826i
$569$	−16.0791	+	27.8497i	−0.674069	+	1.16752i	0.302671	+	0.953095i	$0.402122\pi$
$569$	−16.0791	+	27.8497i	−0.674069	+	1.16752i	−0.976740	+	0.214427i	$0.931212\pi$
$570$	−32.7717	−	18.9208i	−1.37266	−	0.792504i
$571$	−11.5540			−0.483521			−0.241761	−	0.970336i	$-0.577725\pi$
$571$	−11.5540			−0.483521			−0.241761	+	0.970336i	$0.577725\pi$
$572$	5.74953	−	8.58689i	0.240400	−	0.359036i
$573$	−10.9083			−0.455699
$574$	−6.88896	−	3.97734i	−0.287540	−	0.166011i
$575$	−2.13028	+	3.68976i	−0.0888389	+	0.153873i
$576$	4.09347	+	7.09010i	0.170561	+	0.295421i
$577$		−	9.14050i		−	0.380524i	−0.981733	−	0.190262i	$-0.939066\pi$
$577$		−	9.14050i		−	0.380524i	0.981733	−	0.190262i	$-0.0609337\pi$
$578$	−10.4173	+	6.01442i	−0.433301	+	0.250167i
$579$	−63.9364	+	36.9137i	−2.65711	+	1.53408i
$580$		−	7.54819i		−	0.313422i
$581$	2.47414	+	4.28534i	0.102645	+	0.177786i
$582$	−8.17490	+	14.1593i	−0.338860	+	0.586923i
$583$	14.8533	+	8.57554i	0.615160	+	0.355163i
$584$	11.2277			0.464607
$585$	46.0520	+	3.06289i	1.90402	+	0.126635i
$586$	8.86088			0.366040
$587$	37.0629	+	21.3983i	1.52975	+	0.883201i	0.999372	+	0.0354398i	$0.0112832\pi$
$587$	37.0629	+	21.3983i	1.52975	+	0.883201i	0.530378	+	0.847761i	$0.322050\pi$
$588$	−1.67234	+	2.89658i	−0.0689663	+	0.119453i
$589$	2.16344	+	3.74718i	0.0891428	+	0.154400i
$590$		−	1.40127i		−	0.0576894i
$591$	15.2738	−	8.81836i	0.628282	−	0.362739i
$592$	−0.0333971	+	0.0192818i	−0.00137261	+	0.000792478i
$593$			14.2439i			0.584927i	0.956277	+	0.292463i	$0.0944750\pi$
$593$			14.2439i			0.584927i	−0.956277	+	0.292463i	$0.905525\pi$
$594$	24.8619	+	43.0620i	1.02009	+	1.76686i
$595$	−1.74306	+	3.01907i	−0.0714586	+	0.123770i
$596$	8.86563	+	5.11858i	0.363150	+	0.209665i
$597$	−29.6594			−1.21388
$598$	5.99847	+	0.398955i	0.245296	+	0.0163145i
$599$	3.74735			0.153113			0.0765563	−	0.997065i	$-0.475608\pi$
$599$	3.74735			0.153113			0.0765563	+	0.997065i	$0.475608\pi$
$600$	7.40161	+	4.27332i	0.302169	+	0.174458i
$601$	−5.33462	+	9.23984i	−0.217604	+	0.376901i	−0.954075	−	0.299568i	$-0.903157\pi$
$601$	−5.33462	+	9.23984i	−0.217604	+	0.376901i	0.736471	+	0.676469i	$0.236491\pi$
$602$	5.04571	+	8.73942i	0.205648	+	0.356192i
$603$			13.4337i			0.547061i
$604$	13.1731	−	7.60551i	0.536007	−	0.309464i
$605$	3.77145	−	2.17745i	0.153331	−	0.0885259i
$606$		−	24.6419i		−	1.00101i
$607$	−4.82628	−	8.35936i	−0.195893	−	0.339296i	0.751300	−	0.659961i	$-0.229427\pi$
$607$	−4.82628	−	8.35936i	−0.195893	−	0.339296i	−0.947193	+	0.320665i	$0.896094\pi$
$608$	−3.61801	+	6.26657i	−0.146730	+	0.254143i
$609$	13.9835	+	8.07337i	0.566639	+	0.327149i
$610$	22.2915			0.902558
$611$	−14.0950	+	21.0508i	−0.570223	+	0.851625i
$612$	−18.2537			−0.737862
$613$	−3.45968	−	1.99745i	−0.139735	−	0.0806761i	0.428503	−	0.903541i	$-0.359041\pi$
$613$	−3.45968	−	1.99745i	−0.139735	−	0.0806761i	−0.568238	+	0.822864i	$0.692375\pi$
$614$	4.17318	−	7.22816i	0.168416	−	0.291705i
$615$	20.8000	+	36.0266i	0.838736	+	1.45273i
$616$		−	2.86614i		−	0.115480i
$617$	2.80199	−	1.61773i	0.112804	−	0.0651273i	−0.442537	−	0.896750i	$-0.645921\pi$
$617$	2.80199	−	1.61773i	0.112804	−	0.0651273i	0.555340	+	0.831623i	$0.312588\pi$
$618$	−16.7575	+	9.67493i	−0.674084	+	0.389183i
$619$			39.2679i			1.57831i	0.614193	+	0.789156i	$0.289482\pi$
$619$			39.2679i			1.57831i	−0.614193	+	0.789156i	$0.710518\pi$
$620$	0.467475	+	0.809690i	0.0187742	+	0.0325179i
$621$	−14.4632	+	25.0510i	−0.580387	+	1.00526i
$622$	5.79281	+	3.34448i	0.232270	+	0.134101i
$623$	−2.42120			−0.0970033
$624$	0.800299	−	12.0329i	0.0320376	−	0.481700i
$625$	−5.69406			−0.227763
$626$	18.5145	+	10.6894i	0.739990	+	0.427233i
$627$	−34.6834	+	60.0735i	−1.38512	+	2.39910i
$628$	−1.13709	−	1.96950i	−0.0453750	−	0.0785918i
$629$		−	0.0859819i		−	0.00342832i
$630$	11.0858	−	6.40037i	0.441668	−	0.254997i
$631$	25.4983	−	14.7215i	1.01507	−	0.586052i	0.102400	−	0.994743i	$-0.467348\pi$
$631$	25.4983	−	14.7215i	1.01507	−	0.586052i	0.912673	+	0.408691i	$0.134015\pi$
$632$		−	4.26098i		−	0.169493i
$633$	−10.9857	−	19.0279i	−0.436644	−	0.756290i
$634$	15.8388	−	27.4336i	0.629040	−	1.08953i
$635$	13.3399	+	7.70181i	0.529379	+	0.305637i
$636$	20.0147			0.793636
$637$	3.23525	−	1.59158i	0.128185	−	0.0630608i
$638$	−13.8365			−0.547792
$639$	16.2694	+	9.39313i	0.643606	+	0.371586i
$640$	−0.781779	+	1.35408i	−0.0309025	+	0.0535247i
$641$	2.04559	+	3.54307i	0.0807961	+	0.139943i	0.903592	−	0.428394i	$-0.140920\pi$
$641$	2.04559	+	3.54307i	0.0807961	+	0.139943i	−0.822796	+	0.568337i	$0.807587\pi$
$642$		−	3.44154i		−	0.135827i
$643$	19.2672	−	11.1239i	0.759825	−	0.438685i	−0.0694080	−	0.997588i	$-0.522111\pi$
$643$	19.2672	−	11.1239i	0.759825	−	0.438685i	0.829233	+	0.558903i	$0.188778\pi$
$644$	1.44397	−	0.833676i	0.0569003	−	0.0328514i
$645$		−	52.7742i		−	2.07798i
$646$	−8.06675	−	13.9720i	−0.317382	−	0.549722i
$647$	−24.9292	+	43.1786i	−0.980066	+	1.69752i	−0.317980	+	0.948097i	$0.603004\pi$
$647$	−24.9292	+	43.1786i	−0.980066	+	1.69752i	−0.662086	+	0.749427i	$0.730329\pi$
$648$	28.9816	+	16.7326i	1.13851	+	0.657317i
$649$	−2.56865			−0.100828
$650$	−4.06695	−	8.26700i	−0.159519	−	0.324259i
$651$	−2.00000			−0.0783862
$652$	0.00848066	+	0.00489631i	0.000332128	+	0.000191754i
$653$	−3.70177	+	6.41165i	−0.144861	+	0.250907i	−0.929321	−	0.369272i	$-0.879607\pi$
$653$	−3.70177	+	6.41165i	−0.144861	+	0.250907i	0.784460	+	0.620180i	$0.212940\pi$
$654$	−23.6695	−	40.9967i	−0.925550	−	1.60310i
$655$			23.1286i			0.903709i
$656$	6.88896	−	3.97734i	0.268969	−	0.155289i
$657$	79.6058	−	45.9604i	3.10572	−	1.79309i
$658$			7.02636i			0.273916i
$659$	−15.0410	−	26.0518i	−0.585914	−	1.01483i	−0.994761	−	0.102230i	$-0.967402\pi$
$659$	−15.0410	−	26.0518i	−0.585914	−	1.01483i	0.408847	−	0.912603i	$-0.365931\pi$
$660$	−7.49440	+	12.9807i	−0.291719	+	0.505272i
$661$	23.0639	+	13.3160i	0.897082	+	0.517931i	0.876252	−	0.481852i	$-0.160036\pi$
$661$	23.0639	+	13.3160i	0.897082	+	0.517931i	0.0208300	+	0.999783i	$0.493369\pi$
$662$	24.6695			0.958807
$663$	22.3421	+	14.9596i	0.867694	+	0.580983i
$664$	−4.94829			−0.192031
$665$	9.79815	+	5.65696i	0.379956	+	0.219368i
$666$	−0.157859	+	0.273420i	−0.00611691	+	0.0105948i
$667$	−4.02463	−	6.97087i	−0.155834	−	0.269913i
$668$			24.9508i			0.965376i
$669$	48.9874	−	28.2829i	1.89396	−	1.09348i
$670$	−2.22186	+	1.28279i	−0.0858380	+	0.0495586i
$671$		−	40.8623i		−	1.57747i
$672$	−1.67234	−	2.89658i	−0.0645121	−	0.111738i
$673$	−1.84652	+	3.19827i	−0.0711783	+	0.123284i	−0.899418	−	0.437090i	$-0.856009\pi$
$673$	−1.84652	+	3.19827i	−0.0711783	+	0.123284i	0.828240	+	0.560374i	$0.189343\pi$
$674$	−24.3242	−	14.0436i	−0.936932	−	0.540938i
$675$	44.3309			1.70630
$676$	−7.93372	+	10.2984i	−0.305143	+	0.396090i
$677$	−35.6533			−1.37027			−0.685134	−	0.728417i	$-0.740256\pi$
$677$	−35.6533			−1.37027			−0.685134	+	0.728417i	$0.740256\pi$
$678$	39.2227	+	22.6453i	1.50634	+	0.869686i
$679$	2.44414	−	4.23338i	0.0937976	−	0.162462i
$680$	−1.74306	−	3.01907i	−0.0668434	−	0.115776i
$681$		−	53.9572i		−	2.06765i
$682$	1.48423	−	0.856923i	0.0568342	−	0.0328133i
$683$	−26.2105	+	15.1326i	−1.00292	+	0.579034i	−0.909110	−	0.416557i	$-0.863237\pi$
$683$	−26.2105	+	15.1326i	−1.00292	+	0.579034i	−0.0938062	+	0.995590i	$0.529903\pi$
$684$			59.2408i			2.26513i
$685$	0.358834	+	0.621519i	0.0137104	+	0.0237470i
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$	20.0207	+	11.5590i	0.763838	+	0.441002i
$688$	−10.0914			−0.384731
$689$	−17.9280	−	12.0041i	−0.683004	−	0.457320i
$690$	−8.71960			−0.331949
$691$	3.03377	+	1.75155i	0.115410	+	0.0666320i	0.556594	−	0.830785i	$-0.312108\pi$
$691$	3.03377	+	1.75155i	0.115410	+	0.0666320i	−0.441184	+	0.897417i	$0.645441\pi$
$692$	1.60275	−	2.77604i	0.0609273	−	0.105529i
$693$	−11.7324	−	20.3212i	−0.445679	−	0.771938i
$694$		−	10.1080i		−	0.383693i
$695$	20.7372	−	11.9726i	0.786608	−	0.454148i
$696$	−13.9835	+	8.07337i	−0.530042	+	0.306020i
$697$			17.7359i			0.671794i
$698$	8.69465	+	15.0596i	0.329097	+	0.570013i
$699$	−12.4992	+	21.6492i	−0.472762	+	0.818849i
$700$	−2.21294	−	1.27764i	−0.0836414	−	0.0482904i
$701$	−45.2243			−1.70810			−0.854048	−	0.520194i	$-0.825860\pi$
$701$	−45.2243			−1.70810			−0.854048	+	0.520194i	$0.825860\pi$
$702$	−27.6119	−	56.1274i	−1.04214	−	2.11839i
$703$	−0.279047			−0.0105245
$704$	2.48215	+	1.43307i	0.0935495	+	0.0540108i
$705$	18.3726	−	31.8222i	0.691951	−	1.19849i
$706$	−1.66329	−	2.88091i	−0.0625989	−	0.108424i
$707$			7.36747i			0.277082i
$708$	−2.59594	+	1.49877i	−0.0975613	+	0.0563270i
$709$	2.59657	−	1.49913i	0.0975161	−	0.0563009i	−0.450449	−	0.892802i	$-0.648736\pi$
$709$	2.59657	−	1.49913i	0.0975161	−	0.0563009i	0.547965	+	0.836501i	$0.315403\pi$
$710$			3.58784i			0.134649i
$711$	−17.4422	−	30.2107i	−0.654133	−	1.13299i
$712$	1.21060	−	2.09682i	0.0453692	−	0.0785817i
$713$	0.863440	+	0.498507i	0.0323361	+	0.0186692i
$714$	7.45736			0.279085
$715$	14.4984	−	7.13248i	0.542208	−	0.266740i
$716$	−15.8000			−0.590472
$717$	57.5539	+	33.2287i	2.14939	+	1.24095i
$718$	−4.01207	+	6.94911i	−0.149729	+	0.259339i
$719$	−10.0397	−	17.3892i	−0.374417	−	0.648509i	0.615823	−	0.787885i	$-0.288824\pi$
$719$	−10.0397	−	17.3892i	−0.374417	−	0.648509i	−0.990240	+	0.139376i	$0.955490\pi$
$720$			12.8007i			0.477056i
$721$	5.01017	−	2.89263i	0.186589	−	0.107727i
$722$	−28.8905	+	16.6800i	−1.07519	+	0.620764i
$723$		−	35.6026i		−	1.32407i
$724$	4.55954	+	7.89735i	0.169454	+	0.293503i
$725$	−6.16792	+	10.6832i	−0.229071	+	0.396762i
$726$	−8.06771	−	4.65790i	−0.299421	−	0.172871i
$727$	−32.5895			−1.20868			−0.604338	−	0.796728i	$-0.706562\pi$
$727$	−32.5895			−1.20868			−0.604338	+	0.796728i	$0.706562\pi$
$728$	−0.239275	+	3.59760i	−0.00886811	+	0.133336i
$729$	99.8990			3.69996
$730$	15.2033	+	8.77761i	0.562698	+	0.324874i
$731$	11.2500	−	19.4855i	0.416095	−	0.720698i
$732$	−23.8425	−	41.2964i	−0.881244	−	1.52636i
$733$		−	18.5190i		−	0.684017i	−0.939697	−	0.342008i	$-0.888893\pi$
$733$		−	18.5190i		−	0.684017i	0.939697	−	0.342008i	$-0.111107\pi$
$734$	0.899869	−	0.519540i	0.0332148	−	0.0191766i
$735$	−4.52898	+	2.61481i	−0.167054	+	0.0964486i
$736$			1.66735i			0.0614594i
$737$	2.35147	+	4.07287i	0.0866176	+	0.150026i
$738$	32.5623	−	56.3995i	1.19863	−	2.07609i
$739$	13.7968	+	7.96559i	0.507524	+	0.293019i	0.731815	−	0.681503i	$-0.238673\pi$
$739$	13.7968	+	7.96559i	0.507524	+	0.293019i	−0.224291	+	0.974522i	$0.572007\pi$
$740$	−0.0602965			−0.00221654
$741$	48.5501	−	72.5093i	1.78353	−	2.66370i
$742$	−5.98404			−0.219681
$743$	10.5962	+	6.11773i	0.388738	+	0.224438i	0.681613	−	0.731713i	$-0.261279\pi$
$743$	10.5962	+	6.11773i	0.388738	+	0.224438i	−0.292875	+	0.956151i	$0.594612\pi$
$744$	1.00000	−	1.73205i	0.0366618	−	0.0635001i
$745$	8.00319	+	13.8619i	0.293214	+	0.507862i
$746$			27.3124i			0.999979i
$747$	−35.0838	+	20.2556i	−1.28365	+	0.741115i
$748$	−5.53423	+	3.19519i	−0.202351	+	0.116828i
$749$			1.02896i			0.0375972i
$750$	19.7556	+	34.2177i	0.721373	+	1.24945i
$751$	−10.4107	+	18.0318i	−0.379891	+	0.657990i	−0.991046	−	0.133521i	$-0.957372\pi$
$751$	−10.4107	+	18.0318i	−0.379891	+	0.657990i	0.611155	+	0.791511i	$0.290705\pi$
$752$	−6.08501	−	3.51318i	−0.221897	−	0.128113i
$753$	−53.2271			−1.93970
$754$	17.3677	+	1.15512i	0.632494	+	0.0420669i
$755$	23.7833			0.865563
$756$	−15.0244	−	8.67434i	−0.546432	−	0.315483i
$757$	−13.5575	+	23.4823i	−0.492757	+	0.853480i	−0.999965	−	0.00834344i	$-0.997344\pi$
$757$	−13.5575	+	23.4823i	−0.492757	+	0.853480i	0.507208	+	0.861824i	$0.330678\pi$
$758$	1.10583	+	1.91535i	0.0401655	+	0.0695687i
$759$			15.9838i			0.580175i
$760$	−9.79815	+	5.65696i	−0.355416	+	0.205200i
$761$	41.8920	−	24.1864i	1.51858	−	0.876755i	0.518824	−	0.854881i	$-0.326370\pi$
$761$	41.8920	−	24.1864i	1.51858	−	0.876755i	0.999761	−	0.0218739i	$-0.00696324\pi$
$762$		−	32.9507i		−	1.19368i
$763$	7.07674	+	12.2573i	0.256195	+	0.443743i
$764$	−1.63068	+	2.82443i	−0.0589961	+	0.102184i
$765$	−24.7170	−	14.2703i	−0.893644	−	0.515945i
$766$	−22.3386			−0.807125
$767$	3.22419	+	0.214439i	0.116419	+	0.00774296i
$768$	3.34469			0.120691
$769$	−15.0214	−	8.67264i	−0.541687	−	0.312743i

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:	\( N \)	\(=\)	\( 182 = 2 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	182.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.67234 + 2.89658i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.56356i q^{5} +(2.89658 - 1.67234i) q^{6} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-4.09347 - 7.09010i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.67234 + 2.89658i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.56356i q^{5} +(2.89658 - 1.67234i) q^{6} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-4.09347 - 7.09010i) q^{9} +(0.781779 - 1.35408i) q^{10} +(-2.48215 - 1.43307i) q^{11} -3.34469 q^{12} +(2.99598 + 2.00602i) q^{13} +1.00000 q^{14} +(-4.52898 - 2.61481i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.11481 - 1.93090i) q^{17} +8.18694i q^{18} +(-6.26657 + 3.61801i) q^{19} +(-1.35408 + 0.781779i) q^{20} -3.34469i q^{21} +(1.43307 + 2.48215i) q^{22} +(-0.833676 + 1.44397i) q^{23} +(2.89658 + 1.67234i) q^{24} +2.55529 q^{25} +(-1.59158 - 3.23525i) q^{26} +17.3487 q^{27} +(-0.866025 - 0.500000i) q^{28} +(-2.41379 + 4.18080i) q^{29} +(2.61481 + 4.52898i) q^{30} -0.597963i q^{31} +(0.866025 - 0.500000i) q^{32} +(8.30201 - 4.79317i) q^{33} +2.22961i q^{34} +(-0.781779 - 1.35408i) q^{35} +(4.09347 - 7.09010i) q^{36} +(0.0333971 + 0.0192818i) q^{37} +7.23602 q^{38} +(-10.8209 + 5.32335i) q^{39} +1.56356 q^{40} +(-6.88896 - 3.97734i) q^{41} +(-1.67234 + 2.89658i) q^{42} +(5.04571 + 8.73942i) q^{43} -2.86614i q^{44} +(11.0858 - 6.40037i) q^{45} +(1.44397 - 0.833676i) q^{46} +7.02636i q^{47} +(-1.67234 - 2.89658i) q^{48} +(0.500000 - 0.866025i) q^{49} +(-2.21294 - 1.27764i) q^{50} +7.45736 q^{51} +(-0.239275 + 3.59760i) q^{52} -5.98404 q^{53} +(-15.0244 - 8.67434i) q^{54} +(2.24069 - 3.88098i) q^{55} +(0.500000 + 0.866025i) q^{56} -24.2022i q^{57} +(4.18080 - 2.41379i) q^{58} +(0.776138 - 0.448103i) q^{59} -5.22961i q^{60} +(7.12846 + 12.3469i) q^{61} +(-0.298982 + 0.517851i) q^{62} +(7.09010 + 4.09347i) q^{63} -1.00000 q^{64} +(-3.13653 + 4.68438i) q^{65} -9.58634 q^{66} +(-1.42103 - 0.820432i) q^{67} +(1.11481 - 1.93090i) q^{68} +(-2.78838 - 4.82962i) q^{69} +1.56356i q^{70} +(-1.98724 + 1.14733i) q^{71} +(-7.09010 + 4.09347i) q^{72} +11.2277i q^{73} +(-0.0192818 - 0.0333971i) q^{74} +(-4.27332 + 7.40161i) q^{75} +(-6.26657 - 3.61801i) q^{76} +2.86614 q^{77} +(12.0329 + 0.800299i) q^{78} +4.26098 q^{79} +(-1.35408 - 0.781779i) q^{80} +(-16.7326 + 28.9816i) q^{81} +(3.97734 + 6.88896i) q^{82} -4.94829i q^{83} +(2.89658 - 1.67234i) q^{84} +(3.01907 - 1.74306i) q^{85} -10.0914i q^{86} +(-8.07337 - 13.9835i) q^{87} +(-1.43307 + 2.48215i) q^{88} +(2.09682 + 1.21060i) q^{89} -12.8007 q^{90} +(-3.59760 - 0.239275i) q^{91} -1.66735 q^{92} +(1.73205 + 1.00000i) q^{93} +(3.51318 - 6.08501i) q^{94} +(-5.65696 - 9.79815i) q^{95} +3.34469i q^{96} +(-4.23338 + 2.44414i) q^{97} +(-0.866025 + 0.500000i) q^{98} +23.4649i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} + 6 q^{4} + 6 q^{6} - 6 q^{9}+O(q^{10}) \) 12 * q - 2 * q^3 + 6 * q^4 + 6 * q^6 - 6 * q^9	\( 12 q - 2 q^{3} + 6 q^{4} + 6 q^{6} - 6 q^{9} - 2 q^{10} - 18 q^{11} - 4 q^{12} - 8 q^{13} + 12 q^{14} - 6 q^{15} - 6 q^{16} + 4 q^{17} + 12 q^{19} - 2 q^{22} - 6 q^{23} + 6 q^{24} - 24 q^{25} - 14 q^{26} + 40 q^{27} - 10 q^{29} + 14 q^{30} + 12 q^{33} + 2 q^{35} + 6 q^{36} - 6 q^{37} + 8 q^{38} - 54 q^{39} - 4 q^{40} - 24 q^{41} - 2 q^{42} + 26 q^{43} + 72 q^{45} - 6 q^{46} - 2 q^{48} + 6 q^{49} - 12 q^{50} - 36 q^{51} - 4 q^{52} + 36 q^{53} - 36 q^{54} - 6 q^{55} + 6 q^{56} + 24 q^{58} + 6 q^{59} - 28 q^{61} - 2 q^{62} - 12 q^{64} - 34 q^{65} - 42 q^{67} - 4 q^{68} + 32 q^{69} + 48 q^{71} - 48 q^{75} + 12 q^{76} - 4 q^{77} - 8 q^{78} + 44 q^{79} - 34 q^{81} + 6 q^{82} + 6 q^{84} + 54 q^{85} + 2 q^{87} + 2 q^{88} + 12 q^{89} + 12 q^{90} - 16 q^{91} - 12 q^{92} + 8 q^{94} + 32 q^{95} + 60 q^{97}+O(q^{100}) \) 12 * q - 2 * q^3 + 6 * q^4 + 6 * q^6 - 6 * q^9 - 2 * q^10 - 18 * q^11 - 4 * q^12 - 8 * q^13 + 12 * q^14 - 6 * q^15 - 6 * q^16 + 4 * q^17 + 12 * q^19 - 2 * q^22 - 6 * q^23 + 6 * q^24 - 24 * q^25 - 14 * q^26 + 40 * q^27 - 10 * q^29 + 14 * q^30 + 12 * q^33 + 2 * q^35 + 6 * q^36 - 6 * q^37 + 8 * q^38 - 54 * q^39 - 4 * q^40 - 24 * q^41 - 2 * q^42 + 26 * q^43 + 72 * q^45 - 6 * q^46 - 2 * q^48 + 6 * q^49 - 12 * q^50 - 36 * q^51 - 4 * q^52 + 36 * q^53 - 36 * q^54 - 6 * q^55 + 6 * q^56 + 24 * q^58 + 6 * q^59 - 28 * q^61 - 2 * q^62 - 12 * q^64 - 34 * q^65 - 42 * q^67 - 4 * q^68 + 32 * q^69 + 48 * q^71 - 48 * q^75 + 12 * q^76 - 4 * q^77 - 8 * q^78 + 44 * q^79 - 34 * q^81 + 6 * q^82 + 6 * q^84 + 54 * q^85 + 2 * q^87 + 2 * q^88 + 12 * q^89 + 12 * q^90 - 16 * q^91 - 12 * q^92 + 8 * q^94 + 32 * q^95 + 60 * q^97

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