LMFDB - Embedded newform 342.2.j.d.65.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(65,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("342.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.j (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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.764411904.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 6x^{6} + 21x^{4} - 54x^{2} + 81 $ x^8 - 6x^6 + 21x^4 - 54*x^2 + 81
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			65.3
Root			$-1.27970 + 1.16721i$ of defining polynomial
Character	$\chi$	$=$	342.65
Dual form			342.2.j.d.221.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(1.27970 + 1.16721i) q^{3} +(-0.500000 + 0.866025i) q^{4} -0.317837i q^{5} +(-0.370982 + 1.69185i) q^{6} +(-1.37098 + 2.37461i) q^{7} -1.00000 q^{8} +(0.275255 + 2.98735i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(1.27970 + 1.16721i) q^{3} +(-0.500000 + 0.866025i) q^{4} -0.317837i q^{5} +(-0.370982 + 1.69185i) q^{6} +(-1.37098 + 2.37461i) q^{7} -1.00000 q^{8} +(0.275255 + 2.98735i) q^{9} +(0.275255 - 0.158919i) q^{10} +(0.427828 + 0.247006i) q^{11} +(-1.65068 + 0.524648i) q^{12} +(-3.13461 - 1.80977i) q^{13} -2.74196 q^{14} +(0.370982 - 0.406736i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(4.85821 + 2.80489i) q^{17} +(-2.44949 + 1.73205i) q^{18} +(2.54077 - 3.54182i) q^{19} +(0.275255 + 0.158919i) q^{20} +(-4.52611 + 1.43856i) q^{21} +0.494013i q^{22} +(3.72730 + 2.15196i) q^{23} +(-1.27970 - 1.16721i) q^{24} +4.89898 q^{25} -3.61953i q^{26} +(-3.13461 + 4.14418i) q^{27} +(-1.37098 - 2.37461i) q^{28} -9.71641 q^{29} +(0.537734 + 0.117912i) q^{30} +(7.64794 - 4.41554i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.259183 + 0.815457i) q^{33} +5.60977i q^{34} +(0.754740 + 0.435749i) q^{35} +(-2.72474 - 1.25529i) q^{36} -10.1162i q^{37} +(4.33769 + 0.429466i) q^{38} +(-1.89898 - 5.97469i) q^{39} +0.317837i q^{40} -3.85187 q^{41} +(-3.50889 - 3.20044i) q^{42} +(-2.65068 - 4.59111i) q^{43} +(-0.427828 + 0.247006i) q^{44} +(0.949490 - 0.0874863i) q^{45} +4.30391i q^{46} +3.90406i q^{47} +(0.370982 - 1.69185i) q^{48} +(-0.259183 - 0.448918i) q^{49} +(2.44949 + 4.24264i) q^{50} +(2.94315 + 9.25994i) q^{51} +(3.13461 - 1.80977i) q^{52} +(2.35187 + 4.07356i) q^{53} +(-5.15627 - 0.642559i) q^{54} +(0.0785079 - 0.135980i) q^{55} +(1.37098 - 2.37461i) q^{56} +(7.38546 - 1.56685i) q^{57} +(-4.85821 - 8.41466i) q^{58} +4.89519 q^{59} +(0.166753 + 0.524648i) q^{60} -2.70374 q^{61} +(7.64794 + 4.41554i) q^{62} +(-7.47115 - 3.44197i) q^{63} +1.00000 q^{64} +(-0.575211 + 0.996295i) q^{65} +(-0.576615 + 0.632187i) q^{66} +(2.86076 + 1.65166i) q^{67} +(-4.85821 + 2.80489i) q^{68} +(2.25804 + 7.10438i) q^{69} +0.871498i q^{70} +(6.72919 - 11.6553i) q^{71} +(-0.275255 - 2.98735i) q^{72} +(3.11624 - 5.39749i) q^{73} +(8.76088 - 5.05810i) q^{74} +(6.26922 + 5.71812i) q^{75} +(1.79692 + 3.97128i) q^{76} +(-1.17309 + 0.677283i) q^{77} +(4.22474 - 4.63191i) q^{78} +(0.273851 - 0.158108i) q^{79} +(-0.275255 + 0.158919i) q^{80} +(-8.84847 + 1.64456i) q^{81} +(-1.92594 - 3.33582i) q^{82} +(-1.66346 - 0.960397i) q^{83} +(1.01722 - 4.63900i) q^{84} +(0.891497 - 1.54412i) q^{85} +(2.65068 - 4.59111i) q^{86} +(-12.4341 - 11.3411i) q^{87} +(-0.427828 - 0.247006i) q^{88} +(1.39009 + 2.40771i) q^{89} +(0.550510 + 0.778539i) q^{90} +(8.59498 - 4.96231i) q^{91} +(-3.72730 + 2.15196i) q^{92} +(14.9409 + 3.27617i) q^{93} +(-3.38101 + 1.95203i) q^{94} +(-1.12572 - 0.807552i) q^{95} +(1.65068 - 0.524648i) q^{96} +(-4.17793 + 2.41213i) q^{97} +(0.259183 - 0.448918i) q^{98} +(-0.620132 + 1.34606i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{4} - 8 q^{7} - 8 q^{8} + 12 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^7 - 8 * q^8 + 12 * q^9	$ 8 q + 4 q^{2} - 4 q^{4} - 8 q^{7} - 8 q^{8} + 12 q^{9} + 12 q^{10} - 16 q^{14} - 4 q^{16} + 12 q^{17} + 8 q^{19} + 12 q^{20} - 8 q^{28} - 24 q^{29} - 24 q^{31} + 4 q^{32} + 24 q^{35} - 12 q^{36} + 16 q^{38} + 24 q^{39} - 24 q^{41} + 12 q^{42} - 8 q^{43} - 12 q^{45} + 24 q^{51} + 12 q^{53} - 16 q^{55} + 8 q^{56} - 12 q^{57} - 12 q^{58} - 8 q^{61} - 24 q^{62} - 24 q^{63} + 8 q^{64} + 12 q^{66} - 24 q^{67} - 12 q^{68} + 24 q^{69} + 24 q^{71} - 12 q^{72} + 4 q^{73} - 24 q^{74} + 8 q^{76} + 12 q^{77} + 24 q^{78} + 24 q^{79} - 12 q^{80} - 12 q^{81} - 12 q^{82} - 24 q^{83} + 12 q^{84} - 4 q^{85} + 8 q^{86} - 48 q^{87} + 12 q^{89} + 24 q^{90} + 48 q^{91} + 60 q^{93} + 24 q^{94} - 24 q^{95} + 24 q^{97} - 48 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^7 - 8 * q^8 + 12 * q^9 + 12 * q^10 - 16 * q^14 - 4 * q^16 + 12 * q^17 + 8 * q^19 + 12 * q^20 - 8 * q^28 - 24 * q^29 - 24 * q^31 + 4 * q^32 + 24 * q^35 - 12 * q^36 + 16 * q^38 + 24 * q^39 - 24 * q^41 + 12 * q^42 - 8 * q^43 - 12 * q^45 + 24 * q^51 + 12 * q^53 - 16 * q^55 + 8 * q^56 - 12 * q^57 - 12 * q^58 - 8 * q^61 - 24 * q^62 - 24 * q^63 + 8 * q^64 + 12 * q^66 - 24 * q^67 - 12 * q^68 + 24 * q^69 + 24 * q^71 - 12 * q^72 + 4 * q^73 - 24 * q^74 + 8 * q^76 + 12 * q^77 + 24 * q^78 + 24 * q^79 - 12 * q^80 - 12 * q^81 - 12 * q^82 - 24 * q^83 + 12 * q^84 - 4 * q^85 + 8 * q^86 - 48 * q^87 + 12 * q^89 + 24 * q^90 + 48 * q^91 + 60 * q^93 + 24 * q^94 - 24 * q^95 + 24 * q^97 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	1.27970	+	1.16721i	0.738834	+	0.673887i
$3$	1.27970	+	1.16721i	0.738834	+	0.673887i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		−	0.317837i		−	0.142141i	−0.997471	−	0.0710706i	$-0.977358\pi$
$5$		−	0.317837i		−	0.142141i	0.997471	−	0.0710706i	$-0.0226416\pi$
$6$	−0.370982	+	1.69185i	−0.151453	+	0.690697i
$7$	−1.37098	+	2.37461i	−0.518182	+	0.897518i	0.481594	+	0.876394i	$0.340058\pi$
$7$	−1.37098	+	2.37461i	−0.518182	+	0.897518i	−0.999777	+	0.0211241i	$0.993275\pi$
$8$	−1.00000			−0.353553
$9$	0.275255	+	2.98735i	0.0917517	+	0.995782i
$10$	0.275255	−	0.158919i	0.0870433	−	0.0502545i
$11$	0.427828	+	0.247006i	0.128995	+	0.0744752i	0.563109	−	0.826383i	$-0.309605\pi$
$11$	0.427828	+	0.247006i	0.128995	+	0.0744752i	−0.434114	+	0.900858i	$0.642938\pi$
$12$	−1.65068	+	0.524648i	−0.476510	+	0.151453i
$13$	−3.13461	−	1.80977i	−0.869384	−	0.501939i	−0.00224035	−	0.999997i	$-0.500713\pi$
$13$	−3.13461	−	1.80977i	−0.869384	−	0.501939i	−0.867143	+	0.498059i	$0.834046\pi$
$14$	−2.74196			−0.732821
$15$	0.370982	−	0.406736i	0.0957871	−	0.105019i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	4.85821	+	2.80489i	1.17829	+	0.680285i	0.955618	−	0.294609i	$-0.0951894\pi$
$17$	4.85821	+	2.80489i	1.17829	+	0.680285i	0.222670	+	0.974894i	$0.428523\pi$
$18$	−2.44949	+	1.73205i	−0.577350	+	0.408248i
$19$	2.54077	−	3.54182i	0.582893	−	0.812549i
$19$	2.54077	−	3.54182i	0.582893	−	0.812549i
$20$	0.275255	+	0.158919i	0.0615489	+	0.0355353i
$21$	−4.52611	+	1.43856i	−0.987677	+	0.313921i
$22$			0.494013i			0.105324i
$23$	3.72730	+	2.15196i	0.777195	+	0.448714i	0.835435	−	0.549589i	$-0.185216\pi$
$23$	3.72730	+	2.15196i	0.777195	+	0.448714i	−0.0582404	+	0.998303i	$0.518549\pi$
$24$	−1.27970	−	1.16721i	−0.261217	−	0.238255i
$25$	4.89898			0.979796
$26$		−	3.61953i		−	0.709849i
$27$	−3.13461	+	4.14418i	−0.603256	+	0.797548i
$28$	−1.37098	−	2.37461i	−0.259091	−	0.448759i
$29$	−9.71641			−1.80429			−0.902146	−	0.431430i	$-0.858009\pi$
$29$	−9.71641			−1.80429			−0.902146	+	0.431430i	$0.858009\pi$
$30$	0.537734	+	0.117912i	0.0981764	+	0.0215277i
$31$	7.64794	−	4.41554i	1.37361	−	0.793054i	0.382229	−	0.924067i	$-0.375156\pi$
$31$	7.64794	−	4.41554i	1.37361	−	0.793054i	0.991381	+	0.131013i	$0.0418231\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	0.259183	+	0.815457i	0.0451179	+	0.141953i
$34$			5.60977i			0.962068i
$35$	0.754740	+	0.435749i	0.127574	+	0.0736550i
$36$	−2.72474	−	1.25529i	−0.454124	−	0.209216i
$37$		−	10.1162i		−	1.66309i	−0.555456	−	0.831546i	$-0.687456\pi$
$37$		−	10.1162i		−	1.66309i	0.555456	−	0.831546i	$-0.312544\pi$
$38$	4.33769	+	0.429466i	0.703666	+	0.0696685i
$39$	−1.89898	−	5.97469i	−0.304080	−	0.956716i
$40$			0.317837i			0.0502545i
$41$	−3.85187			−0.601561			−0.300781	−	0.953693i	$-0.597247\pi$
$41$	−3.85187			−0.601561			−0.300781	+	0.953693i	$0.597247\pi$
$42$	−3.50889	−	3.20044i	−0.541433	−	0.493839i
$43$	−2.65068	−	4.59111i	−0.404225	−	0.700138i	0.590006	−	0.807399i	$-0.299125\pi$
$43$	−2.65068	−	4.59111i	−0.404225	−	0.700138i	−0.994231	+	0.107261i	$0.965792\pi$
$44$	−0.427828	+	0.247006i	−0.0644975	+	0.0372376i
$45$	0.949490	−	0.0874863i	0.141542	−	0.0130417i
$46$			4.30391i			0.634577i
$47$			3.90406i			0.569466i	0.958607	+	0.284733i	$0.0919049\pi$
$47$			3.90406i			0.569466i	−0.958607	+	0.284733i	$0.908095\pi$
$48$	0.370982	−	1.69185i	0.0535466	−	0.244198i
$49$	−0.259183	−	0.448918i	−0.0370261	−	0.0641311i
$50$	2.44949	+	4.24264i	0.346410	+	0.600000i
$51$	2.94315	+	9.25994i	0.412124	+	1.29665i
$52$	3.13461	−	1.80977i	0.434692	−	0.250969i
$53$	2.35187	+	4.07356i	0.323054	+	0.559546i	0.981117	−	0.193417i	$-0.0619570\pi$
$53$	2.35187	+	4.07356i	0.323054	+	0.559546i	−0.658062	+	0.752963i	$0.728624\pi$
$54$	−5.15627	−	0.642559i	−0.701679	−	0.0874413i
$55$	0.0785079	−	0.135980i	0.0105860	−	0.0183355i
$56$	1.37098	−	2.37461i	0.183205	−	0.317321i
$57$	7.38546	−	1.56685i	0.978228	−	0.207534i
$58$	−4.85821	−	8.41466i	−0.637914	−	1.10490i
$59$	4.89519			0.637300			0.318650	−	0.947872i	$-0.396771\pi$
$59$	4.89519			0.637300			0.318650	+	0.947872i	$0.396771\pi$
$60$	0.166753	+	0.524648i	0.0215277	+	0.0677317i
$61$	−2.70374			−0.346179			−0.173089	−	0.984906i	$-0.555375\pi$
$61$	−2.70374			−0.346179			−0.173089	+	0.984906i	$0.555375\pi$
$62$	7.64794	+	4.41554i	0.971289	+	0.560774i
$63$	−7.47115	−	3.44197i	−0.941277	−	0.433648i
$64$	1.00000			0.125000
$65$	−0.575211	+	0.996295i	−0.0713462	+	0.123575i
$66$	−0.576615	+	0.632187i	−0.0709764	+	0.0778169i
$67$	2.86076	+	1.65166i	0.349497	+	0.201782i	0.664464	−	0.747321i	$-0.268660\pi$
$67$	2.86076	+	1.65166i	0.349497	+	0.201782i	−0.314967	+	0.949103i	$0.601993\pi$
$68$	−4.85821	+	2.80489i	−0.589144	+	0.340142i
$69$	2.25804	+	7.10438i	0.271836	+	0.855267i
$70$			0.871498i			0.104164i
$71$	6.72919	−	11.6553i	0.798608	−	1.38323i	−0.121915	−	0.992541i	$-0.538904\pi$
$71$	6.72919	−	11.6553i	0.798608	−	1.38323i	0.920523	−	0.390689i	$-0.127763\pi$
$72$	−0.275255	−	2.98735i	−0.0324391	−	0.352062i
$73$	3.11624	−	5.39749i	0.364729	−	0.631728i	−0.624004	−	0.781421i	$-0.714495\pi$
$73$	3.11624	−	5.39749i	0.364729	−	0.631728i	0.988733	+	0.149693i	$0.0478284\pi$
$74$	8.76088	−	5.05810i	1.01843	−	0.587992i
$75$	6.26922	+	5.71812i	0.723907	+	0.660272i
$76$	1.79692	+	3.97128i	0.206121	+	0.455537i
$77$	−1.17309	+	0.677283i	−0.133686	+	0.0771835i
$78$	4.22474	−	4.63191i	0.478358	−	0.524461i
$79$	0.273851	−	0.158108i	0.0308106	−	0.0177885i	−0.484516	−	0.874783i	$-0.661004\pi$
$79$	0.273851	−	0.158108i	0.0308106	−	0.0177885i	0.515326	+	0.856994i	$0.327671\pi$
$80$	−0.275255	+	0.158919i	−0.0307745	+	0.0177676i
$81$	−8.84847	+	1.64456i	−0.983163	+	0.182729i
$82$	−1.92594	−	3.33582i	−0.212684	−	0.368379i
$83$	−1.66346	−	0.960397i	−0.182588	−	0.105417i	0.405920	−	0.913909i	$-0.366951\pi$
$83$	−1.66346	−	0.960397i	−0.182588	−	0.105417i	−0.588508	+	0.808491i	$0.700284\pi$
$84$	1.01722	−	4.63900i	0.110988	−	0.506157i
$85$	0.891497	−	1.54412i	0.0966965	−	0.167483i
$86$	2.65068	−	4.59111i	0.285830	−	0.495072i
$87$	−12.4341	−	11.3411i	−1.33307	−	1.21589i
$88$	−0.427828	−	0.247006i	−0.0456066	−	0.0263310i
$89$	1.39009	+	2.40771i	0.147350	+	0.255217i	0.930247	−	0.366934i	$-0.119592\pi$
$89$	1.39009	+	2.40771i	0.147350	+	0.255217i	−0.782897	+	0.622151i	$0.786259\pi$
$90$	0.550510	+	0.778539i	0.0580289	+	0.0820652i
$91$	8.59498	−	4.96231i	0.900999	−	0.520192i
$92$	−3.72730	+	2.15196i	−0.388597	+	0.224357i
$93$	14.9409	+	3.27617i	1.54930	+	0.339723i
$94$	−3.38101	+	1.95203i	−0.348725	+	0.201336i
$95$	−1.12572	−	0.807552i	−0.115497	−	0.0828531i
$96$	1.65068	−	0.524648i	0.168472	−	0.0535466i
$97$	−4.17793	+	2.41213i	−0.424205	+	0.244915i	−0.696875	−	0.717193i	$-0.745427\pi$
$97$	−4.17793	+	2.41213i	−0.424205	+	0.244915i	0.272670	+	0.962108i	$0.412093\pi$
$98$	0.259183	−	0.448918i	0.0261814	−	0.0453475i
$99$	−0.620132	+	1.34606i	−0.0623256	+	0.135284i
$100$	−2.44949	+	4.24264i	−0.244949	+	0.424264i
$101$			9.64293i			0.959507i	0.877403	+	0.479754i	$0.159274\pi$
$101$			9.64293i			0.959507i	−0.877403	+	0.479754i	$0.840726\pi$
$102$	−6.54777	+	7.17882i	−0.648326	+	0.710809i
$103$	−9.19615	+	5.30940i	−0.906124	+	0.523151i	−0.879182	−	0.476486i	$-0.841910\pi$
$103$	−9.19615	+	5.30940i	−0.906124	+	0.523151i	−0.0269420	+	0.999637i	$0.508577\pi$
$104$	3.13461	+	1.80977i	0.307374	+	0.177462i
$105$	0.457229	+	1.43856i	0.0446210	+	0.140390i
$106$	−2.35187	+	4.07356i	−0.228434	+	0.395659i
$107$	2.11598			0.204560			0.102280	−	0.994756i	$-0.467386\pi$
$107$	2.11598			0.204560			0.102280	+	0.994756i	$0.467386\pi$
$108$	−2.02166	−	4.78674i	−0.194535	−	0.460604i
$109$	−12.6573	−	7.30770i	−1.21235	−	0.699951i	−0.249080	−	0.968483i	$-0.580128\pi$
$109$	−12.6573	−	7.30770i	−1.21235	−	0.699951i	−0.963271	+	0.268532i	$0.913461\pi$
$110$	0.157016			0.0149709
$111$	11.8077	−	12.9457i	1.12074	−	1.22875i
$112$	2.74196			0.259091
$113$	2.22730	+	3.85779i	0.209526	+	0.362910i	0.951565	−	0.307446i	$-0.0994745\pi$
$113$	2.22730	+	3.85779i	0.209526	+	0.362910i	−0.742039	+	0.670357i	$0.766141\pi$
$114$	5.04966	+	5.61257i	0.472944	+	0.525665i
$115$	0.683971	−	1.18467i	0.0637807	−	0.110471i
$116$	4.85821	−	8.41466i	0.451073	−	0.781282i
$117$	4.54358	−	9.86230i	0.420054	−	0.911770i
$118$	2.44760	+	4.23936i	0.225320	+	0.390265i
$119$	−13.3210	+	7.69090i	−1.22114	+	0.705023i
$120$	−0.370982	+	0.406736i	−0.0338659	+	0.0371297i
$121$	−5.37798	−	9.31493i	−0.488907	−	0.846812i
$122$	−1.35187	−	2.34151i	−0.122393	−	0.211990i
$123$	−4.92923	−	4.49593i	−0.444454	−	0.405384i
$124$			8.83108i			0.793054i
$125$		−	3.14626i		−	0.281410i
$126$	−0.754740	−	8.19119i	−0.0672375	−	0.729730i
$127$	8.32681	−	4.80748i	0.738885	−	0.426595i	−0.0827790	−	0.996568i	$-0.526380\pi$
$127$	8.32681	−	4.80748i	0.738885	−	0.426595i	0.821664	+	0.569973i	$0.193046\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	1.96671	−	8.96913i	0.173159	−	0.789688i
$130$	−1.15042			−0.100899
$131$		−	20.8417i		−	1.82095i	−0.413564	−	0.910475i	$-0.635716\pi$
$131$		−	20.8417i		−	1.82095i	0.413564	−	0.910475i	$-0.364284\pi$
$132$	−0.835798	−	0.183270i	−0.0727469	−	0.0159516i
$133$	4.92708	+	10.8891i	0.427232	+	0.944206i
$134$			3.30332i			0.285363i
$135$	1.31718	+	0.996295i	0.113364	+	0.0857474i
$136$	−4.85821	−	2.80489i	−0.416588	−	0.240517i
$137$		−	1.17021i		−	0.0999780i	−0.998750	−	0.0499890i	$-0.984081\pi$
$137$		−	1.17021i		−	0.0999780i	0.998750	−	0.0499890i	$-0.0159186\pi$
$138$	−5.02355	+	5.50771i	−0.427633	+	0.468847i
$139$	−7.80884	+	13.5253i	−0.662337	+	1.14720i	0.317663	+	0.948204i	$0.397102\pi$
$139$	−7.80884	+	13.5253i	−0.662337	+	1.14720i	−0.980000	+	0.198998i	$0.936231\pi$
$140$	−0.754740	+	0.435749i	−0.0637871	+	0.0368275i
$141$	−4.55685	+	4.99602i	−0.383756	+	0.420741i
$142$	13.4584			1.12940
$143$	−0.894048	−	1.54854i	−0.0747641	−	0.129495i
$144$	2.44949	−	1.73205i	0.204124	−	0.144338i
$145$			3.08824i			0.256464i
$146$	6.23248			0.515804
$147$	0.192304	−	0.876999i	0.0158610	−	0.0723337i
$148$	8.76088	+	5.05810i	0.720140	+	0.415773i
$149$			19.0959i			1.56440i	0.623029	+	0.782199i	$0.285902\pi$
$149$			19.0959i			1.56440i	−0.623029	+	0.782199i	$0.714098\pi$
$150$	−1.81743	+	8.28836i	−0.148393	+	0.676742i
$151$	−5.12154	−	2.95692i	−0.416785	−	0.240631i	0.276916	−	0.960894i	$-0.410688\pi$
$151$	−5.12154	−	2.95692i	−0.416785	−	0.240631i	−0.693701	+	0.720263i	$0.744021\pi$
$152$	−2.54077	+	3.54182i	−0.206084	+	0.287279i
$153$	−7.04192	+	15.2852i	−0.569305	+	1.23574i
$154$	−1.17309	−	0.677283i	−0.0945301	−	0.0545770i
$155$	−1.40342	−	2.43080i	−0.112726	−	0.195246i
$156$	6.12372	+	1.34278i	0.490290	+	0.107509i
$157$	−19.4323			−1.55087			−0.775434	−	0.631429i	$-0.782469\pi$
$157$	−19.4323			−1.55087			−0.775434	+	0.631429i	$0.782469\pi$
$158$	0.273851	+	0.158108i	0.0217864	+	0.0125784i
$159$	−1.74500	+	7.95805i	−0.138388	+	0.631114i
$160$	−0.275255	−	0.158919i	−0.0217608	−	0.0125636i
$161$	−10.2201	+	5.90058i	−0.805457	+	0.465031i
$162$	−5.84847	−	6.84072i	−0.459499	−	0.537457i
$163$	13.0895			1.02525			0.512623	−	0.858614i	$-0.328674\pi$
$163$	13.0895			1.02525			0.512623	+	0.858614i	$0.328674\pi$
$164$	1.92594	−	3.33582i	0.150390	−	0.260484i
$165$	0.259183	−	0.0823779i	0.0201773	−	0.00641311i
$166$		−	1.92079i		−	0.149082i
$167$	0.383758	−	0.664688i	0.0296961	−	0.0514351i	−0.850795	−	0.525497i	$-0.823879\pi$
$167$	0.383758	−	0.664688i	0.0296961	−	0.0514351i	0.880491	+	0.474062i	$0.157213\pi$
$168$	4.52611	−	1.43856i	0.349197	−	0.110988i
$169$	0.0505103	+	0.0874863i	0.00388540	+	0.00672972i
$170$	1.78299			0.136749
$171$	11.2800	+	6.61527i	0.862603	+	0.505882i
$172$	5.30136			0.404225
$173$	0.702595	+	1.21693i	0.0534173	+	0.0925214i	0.891498	−	0.453025i	$-0.149655\pi$
$173$	0.702595	+	1.21693i	0.0534173	+	0.0925214i	−0.838080	+	0.545547i	$0.816322\pi$
$174$	3.60461	−	16.4388i	0.273265	−	1.24622i
$175$	−6.71641	+	11.6332i	−0.507713	+	0.879385i
$176$		−	0.494013i		−	0.0372376i
$177$	6.26437	+	5.71371i	0.470859	+	0.429468i
$178$	−1.39009	+	2.40771i	−0.104192	+	0.180466i
$179$	−24.0695			−1.79904			−0.899518	−	0.436883i	$-0.856082\pi$
$179$	−24.0695			−1.79904			−0.899518	+	0.436883i	$0.856082\pi$
$180$	−0.398979	+	0.866025i	−0.0297382	+	0.0645497i
$181$	−7.90038	+	4.56129i	−0.587231	+	0.339038i	−0.764002	−	0.645214i	$-0.776768\pi$
$181$	−7.90038	+	4.56129i	−0.587231	+	0.339038i	0.176771	+	0.984252i	$0.443435\pi$
$182$	8.59498	+	4.96231i	0.637102	+	0.367831i
$183$	−3.45997	−	3.15583i	−0.255769	−	0.233285i
$184$	−3.72730	−	2.15196i	−0.274780	−	0.158644i
$185$	−3.21530			−0.236394
$186$	4.63320	+	14.5773i	0.339723	+	1.06886i
$187$	1.38565	+	2.40002i	0.101329	+	0.175507i
$188$	−3.38101	−	1.95203i	−0.246586	−	0.142366i
$189$	−5.54332	−	13.1251i	−0.403217	−	0.954708i
$190$	0.136500	−	1.37868i	0.00990276	−	0.100020i
$191$	−10.7981	−	6.23426i	−0.781320	−	0.451096i	0.0555776	−	0.998454i	$-0.482300\pi$
$191$	−10.7981	−	6.23426i	−0.781320	−	0.451096i	−0.836898	+	0.547359i	$0.815633\pi$
$192$	1.27970	+	1.16721i	0.0923543	+	0.0842359i
$193$			21.7729i			1.56725i	0.621237	+	0.783623i	$0.286631\pi$
$193$			21.7729i			1.56725i	−0.621237	+	0.783623i	$0.713369\pi$
$194$	−4.17793	−	2.41213i	−0.299958	−	0.173181i
$195$	−1.89898	+	0.603566i	−0.135989	+	0.0432223i
$196$	0.518365			0.0370261
$197$			26.2753i			1.87204i	0.351947	+	0.936020i	$0.385520\pi$
$197$			26.2753i			1.87204i	−0.351947	+	0.936020i	$0.614480\pi$
$198$	−1.47579	+	0.135980i	−0.104880	+	0.00966365i
$199$	−0.352359	−	0.610303i	−0.0249781	−	0.0432633i	0.853266	−	0.521476i	$-0.174618\pi$
$199$	−0.352359	−	0.610303i	−0.0249781	−	0.0432633i	−0.878244	+	0.478212i	$0.841285\pi$
$200$	−4.89898			−0.346410
$201$	1.73308	+	5.45272i	0.122242	+	0.384605i
$202$	−8.35102	+	4.82146i	−0.587576	+	0.339237i
$203$	13.3210	−	23.0727i	0.934953	−	1.61939i
$204$	−9.49092	−	2.08112i	−0.664497	−	0.145708i
$205$			1.22427i			0.0855066i
$206$	−9.19615	−	5.30940i	−0.640726	−	0.369924i
$207$	−5.40268	+	11.7271i	−0.375512	+	0.815087i
$208$			3.61953i			0.250969i
$209$	1.96187	−	0.887700i	0.135705	−	0.0614035i
$210$	−1.01722	+	1.11525i	−0.0701948	+	0.0769599i
$211$		−	20.2727i		−	1.39563i	−0.716279	−	0.697814i	$-0.754156\pi$
$211$		−	20.2727i		−	1.39563i	0.716279	−	0.697814i	$-0.245844\pi$
$212$	−4.70374			−0.323054
$213$	22.2155	−	7.06090i	1.52218	−	0.483805i
$214$	1.05799	+	1.83250i	0.0723229	+	0.125267i
$215$	−1.45923	+	0.842485i	−0.0995184	+	0.0574570i
$216$	3.13461	−	4.14418i	0.213283	−	0.281976i
$217$			24.2145i			1.64379i
$218$		−	14.6154i		−	0.989880i
$219$	10.2878	−	3.26986i	0.695188	−	0.220957i
$220$	0.0785079	+	0.135980i	0.00529300	+	0.00916774i
$221$	−10.1524	−	17.5844i	−0.682923	−	1.18286i
$222$	17.1151	+	3.75293i	1.14869	+	0.251880i
$223$	9.53963	−	5.50771i	0.638821	−	0.368823i	−0.145339	−	0.989382i	$-0.546427\pi$
$223$	9.53963	−	5.50771i	0.638821	−	0.368823i	0.784160	+	0.620559i	$0.213094\pi$
$224$	1.37098	+	2.37461i	0.0916026	+	0.158660i
$225$	1.34847	+	14.6349i	0.0898979	+	0.975663i
$226$	−2.22730	+	3.85779i	−0.148157	+	0.256616i
$227$	0.189561	−	0.328329i	0.0125816	−	0.0217920i	−0.859666	−	0.510856i	$-0.829328\pi$
$227$	0.189561	−	0.328329i	0.0125816	−	0.0217920i	0.872248	+	0.489064i	$0.162662\pi$
$228$	−2.33580	+	7.17942i	−0.154692	+	0.475469i
$229$	−6.17045	−	10.6875i	−0.407755	−	0.706252i	0.586883	−	0.809672i	$-0.300355\pi$
$229$	−6.17045	−	10.6875i	−0.407755	−	0.706252i	−0.994638	+	0.103420i	$0.967022\pi$
$230$	1.36794			0.0901995
$231$	−2.29173	−	0.502519i	−0.150785	−	0.0330633i
$232$	9.71641			0.637914
$233$	−10.4076	−	6.00881i	−0.681823	−	0.393650i	0.118719	−	0.992928i	$-0.462121\pi$
$233$	−10.4076	−	6.00881i	−0.681823	−	0.393650i	−0.800541	+	0.599277i	$0.795455\pi$
$234$	10.8128	−	0.996295i	0.706855	−	0.0651298i
$235$	1.24086			0.0809445
$236$	−2.44760	+	4.23936i	−0.159325	+	0.275959i
$237$	0.534991	+	0.117310i	0.0347514	+	0.00762013i
$238$	−13.3210	−	7.69090i	−0.863474	−	0.498527i
$239$	−4.53510	+	2.61834i	−0.293351	+	0.169366i	−0.639452	−	0.768831i	$-0.720839\pi$
$239$	−4.53510	+	2.61834i	−0.293351	+	0.169366i	0.346101	+	0.938197i	$0.387505\pi$
$240$	−0.537734	−	0.117912i	−0.0347106	−	0.00761118i
$241$			16.7932i			1.08174i	0.841105	+	0.540872i	$0.181906\pi$
$241$			16.7932i			1.08174i	−0.841105	+	0.540872i	$0.818094\pi$
$242$	5.37798	−	9.31493i	0.345709	−	0.598786i
$243$	−13.2429	−	8.22345i	−0.849534	−	0.527535i
$244$	1.35187	−	2.34151i	0.0865446	−	0.149900i
$245$	−0.142683	+	0.0823779i	−0.00911567	+	0.00526293i
$246$	1.42897	−	6.51681i	0.0911081	−	0.415496i
$247$	−14.3742	+	6.50400i	−0.914608	+	0.413840i
$248$	−7.64794	+	4.41554i	−0.485644	+	0.280387i
$249$	−1.00774	−	3.17062i	−0.0638629	−	0.200930i
$250$	2.72474	−	1.57313i	0.172328	−	0.0994936i
$251$	−13.6697	+	7.89221i	−0.862824	+	0.498152i	−0.864957	−	0.501846i	$-0.832654\pi$
$251$	−13.6697	+	7.89221i	−0.862824	+	0.498152i	0.00213293	+	0.999998i	$0.499321\pi$
$252$	6.71641	−	4.74922i	0.423094	−	0.299173i
$253$	1.06309	+	1.84133i	0.0668361	+	0.115764i
$254$	8.32681	+	4.80748i	0.522470	+	0.301648i
$255$	2.94315	−	0.935444i	0.184307	−	0.0585798i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.62742	+	6.28288i	−0.226272	+	0.391915i	−0.956700	−	0.291074i	$-0.905987\pi$
$257$	−3.62742	+	6.28288i	−0.226272	+	0.391915i	0.730428	+	0.682990i	$0.239321\pi$
$258$	8.75085	−	2.78135i	0.544804	−	0.173159i
$259$	24.0220	+	13.8691i	1.49266	+	0.861785i
$260$	−0.575211	−	0.996295i	−0.0356731	−	0.0617876i
$261$	−2.67449	−	29.0263i	−0.165547	−	1.79668i
$262$	18.0495	−	10.4209i	1.11510	−	0.643803i
$263$	20.4733	−	11.8203i	1.26244	−	0.728870i	0.288894	−	0.957361i	$-0.406712\pi$
$263$	20.4733	−	11.8203i	1.26244	−	0.728870i	0.973546	+	0.228491i	$0.0733791\pi$
$264$	−0.259183	−	0.815457i	−0.0159516	−	0.0501879i
$265$	1.29473	−	0.747512i	0.0795346	−	0.0459193i
$266$	−6.96671	+	9.71154i	−0.427156	+	0.595452i
$267$	−1.03140	+	4.70367i	−0.0631206	+	0.287860i
$268$	−2.86076	+	1.65166i	−0.174749	+	0.100891i
$269$	4.14179	−	7.17380i	0.252530	−	0.437394i	−0.711692	−	0.702492i	$-0.752071\pi$
$269$	4.14179	−	7.17380i	0.252530	−	0.437394i	0.964222	+	0.265098i	$0.0854041\pi$
$270$	−0.204229	+	1.63885i	−0.0124290	+	0.0997375i
$271$	9.25036	−	16.0221i	0.561919	−	0.973273i	−0.435410	−	0.900232i	$-0.643396\pi$
$271$	9.25036	−	16.0221i	0.561919	−	0.973273i	0.997329	−	0.0730405i	$-0.0232702\pi$
$272$		−	5.60977i		−	0.340142i
$273$	16.7910	+	3.68186i	1.01624	+	0.222836i
$274$	1.01343	−	0.585106i	0.0612238	−	0.0353476i
$275$	2.09592	+	1.21008i	0.126389	+	0.0729705i
$276$	−7.28159	−	1.59667i	−0.438300	−	0.0961084i
$277$	6.87912	−	11.9150i	0.413326	−	0.715902i	−0.581925	−	0.813243i	$-0.697700\pi$
$277$	6.87912	−	11.9150i	0.413326	−	0.715902i	0.995251	+	0.0973403i	$0.0310335\pi$
$278$	−15.6177			−0.936686
$279$	15.2959	+	21.6316i	0.915740	+	1.29505i
$280$	−0.754740	−	0.435749i	−0.0451043	−	0.0260410i
$281$	12.2371			0.730002			0.365001	−	0.931007i	$-0.381069\pi$
$281$	12.2371			0.730002			0.365001	+	0.931007i	$0.381069\pi$
$282$	−6.60510	−	1.44834i	−0.393328	−	0.0862471i
$283$	21.6432			1.28656			0.643278	−	0.765632i	$-0.277574\pi$
$283$	21.6432			1.28656			0.643278	+	0.765632i	$0.277574\pi$
$284$	6.72919	+	11.6553i	0.399304	+	0.691615i
$285$	−0.498003	−	2.34737i	−0.0294991	−	0.139046i
$286$	0.894048	−	1.54854i	0.0528662	−	0.0915669i
$287$	5.28084	−	9.14669i	0.311718	−	0.539912i
$288$	2.72474	+	1.25529i	0.160557	+	0.0739690i
$289$	7.23478	+	12.5310i	0.425575	+	0.737118i
$290$	−2.67449	+	1.54412i	−0.157052	+	0.0906738i
$291$	−8.16195	−	1.78971i	−0.478462	−	0.104915i
$292$	3.11624	+	5.39749i	0.182364	+	0.315864i
$293$	−12.0645	−	20.8963i	−0.704815	−	1.22078i	−0.966758	−	0.255693i	$-0.917696\pi$
$293$	−12.0645	−	20.8963i	−0.704815	−	1.22078i	0.261943	−	0.965083i	$-0.415637\pi$
$294$	0.855655	−	0.271959i	0.0499028	−	0.0158610i
$295$		−	1.55588i		−	0.0905866i
$296$			10.1162i			0.587992i
$297$	−2.36471	+	0.998727i	−0.137214	+	0.0579520i
$298$	−16.5375	+	9.54795i	−0.957994	+	0.553098i
$299$	−7.78907	−	13.4911i	−0.450454	−	0.780209i
$300$	−8.08665	+	2.57024i	−0.466883	+	0.148393i
$301$	14.5361			0.837849
$302$		−	5.91384i		−	0.340303i
$303$	−11.2553	+	12.3400i	−0.646600	+	0.708917i
$304$	−4.33769	−	0.429466i	−0.248784	−	0.0246315i
$305$			0.859350i			0.0492062i
$306$	−16.7583	+	1.54412i	−0.958010	+	0.0882714i
$307$	1.24755	+	0.720275i	0.0712016	+	0.0411083i	0.535178	−	0.844739i	$-0.320244\pi$
$307$	1.24755	+	0.720275i	0.0712016	+	0.0411083i	−0.463977	+	0.885847i	$0.653578\pi$
$308$		−	1.35457i		−	0.0771835i
$309$	−17.9655	−	3.93938i	−1.02202	−	0.224104i
$310$	1.40342	−	2.43080i	0.0797090	−	0.138060i
$311$	6.78947	−	3.91990i	0.384996	−	0.222277i	−0.294994	−	0.955499i	$-0.595318\pi$
$311$	6.78947	−	3.91990i	0.384996	−	0.222277i	0.679990	+	0.733222i	$0.261984\pi$
$312$	1.89898	+	5.97469i	0.107509	+	0.338250i
$313$	11.5384			0.652191			0.326095	−	0.945337i	$-0.394267\pi$
$313$	11.5384			0.652191			0.326095	+	0.945337i	$0.394267\pi$
$314$	−9.71615	−	16.8289i	−0.548314	−	0.949708i
$315$	−1.09399	+	2.37461i	−0.0616392	+	0.133794i
$316$			0.316216i			0.0177885i
$317$	−1.24686			−0.0700305			−0.0350152	−	0.999387i	$-0.511148\pi$
$317$	−1.24686			−0.0700305			−0.0350152	+	0.999387i	$0.511148\pi$
$318$	−7.76437	+	2.46781i	−0.435404	+	0.138388i
$319$	−4.15695	−	2.40002i	−0.232745	−	0.134375i
$320$		−	0.317837i		−	0.0177676i
$321$	2.70782	+	2.46979i	0.151136	+	0.137850i
$322$	−10.2201	−	5.90058i	−0.569544	−	0.328827i
$323$	22.2780	−	10.0803i	1.23958	−	0.560883i
$324$	3.00000	−	8.48528i	0.166667	−	0.471405i
$325$	−15.3564	−	8.86601i	−0.851819	−	0.491798i
$326$	6.54473	+	11.3358i	0.362479	+	0.627832i
$327$	−7.66794	−	24.1254i	−0.424038	−	1.33414i
$328$	3.85187			0.212684
$329$	−9.27062	−	5.35239i	−0.511106	−	0.295087i
$330$	0.200933	+	0.183270i	0.0110610	+	0.0100887i
$331$	11.2469	+	6.49338i	0.618184	+	0.356909i	0.776162	−	0.630534i	$-0.217164\pi$
$331$	11.2469	+	6.49338i	0.618184	+	0.356909i	−0.157978	+	0.987443i	$0.550497\pi$
$332$	1.66346	−	0.960397i	0.0912940	−	0.0527086i
$333$	30.2206	−	2.78453i	1.65608	−	0.152592i
$334$	0.767515			0.0419966
$335$	0.524959	−	0.909255i	0.0286816	−	0.0496779i
$336$	3.50889	+	3.20044i	0.191425	+	0.174598i
$337$		−	24.7330i		−	1.34729i	−0.739054	−	0.673646i	$-0.764727\pi$
$337$		−	24.7330i		−	1.34729i	0.739054	−	0.673646i	$-0.235273\pi$
$338$	−0.0505103	+	0.0874863i	−0.00274740	+	0.00475863i
$339$	−1.65257	+	7.53652i	−0.0897554	+	0.409328i
$340$	0.891497	+	1.54412i	0.0483482	+	0.0837416i
$341$	4.36267			0.236252
$342$	−0.0889907	+	13.0764i	−0.00481207	+	0.707090i
$343$	−17.7724			−0.959620
$344$	2.65068	+	4.59111i	0.142915	+	0.247536i
$345$	2.25804	−	0.717688i	0.121569	−	0.0386390i
$346$	−0.702595	+	1.21693i	−0.0377717	+	0.0654225i
$347$			35.6479i			1.91368i	0.290615	+	0.956840i	$0.406140\pi$
$347$			35.6479i			1.91368i	−0.290615	+	0.956840i	$0.593860\pi$
$348$	16.0387	−	5.09769i	0.859764	−	0.273265i
$349$	−3.98014	+	6.89381i	−0.213052	+	0.369017i	−0.952668	−	0.304012i	$-0.901674\pi$
$349$	−3.98014	+	6.89381i	−0.213052	+	0.369017i	0.739616	+	0.673029i	$0.235007\pi$
$350$	−13.4328			−0.718015
$351$	17.3258	−	7.31747i	0.924781	−	0.390578i
$352$	0.427828	−	0.247006i	0.0228033	−	0.0131655i
$353$	−10.0732	−	5.81577i	−0.536143	−	0.309542i	0.207371	−	0.978262i	$-0.433509\pi$
$353$	−10.0732	−	5.81577i	−0.536143	−	0.309542i	−0.743514	+	0.668720i	$0.766843\pi$
$354$	−1.81603	+	8.28196i	−0.0965208	+	0.440181i
$355$	−3.70449	−	2.13879i	−0.196614	−	0.113515i
$356$	−2.78019			−0.147350
$357$	−26.0238	−	5.70637i	−1.37732	−	0.302013i
$358$	−12.0347	−	20.8448i	−0.636055	−	1.10168i
$359$	9.33259	+	5.38817i	0.492555	+	0.284377i	0.725634	−	0.688081i	$-0.241547\pi$
$359$	9.33259	+	5.38817i	0.492555	+	0.284377i	−0.233079	+	0.972458i	$0.574880\pi$
$360$	−0.949490	+	0.0874863i	−0.0500425	+	0.00461093i
$361$	−6.08894	−	17.9979i	−0.320471	−	0.947258i
$362$	−7.90038	−	4.56129i	−0.415235	−	0.239736i
$363$	3.99026	−	18.1975i	0.209435	−	0.955121i
$364$			9.92463i			0.520192i
$365$	−1.71552	−	0.990458i	−0.0897946	−	0.0518429i
$366$	1.00304	−	4.57434i	0.0524297	−	0.239104i
$367$	−7.29587			−0.380842			−0.190421	−	0.981703i	$-0.560985\pi$
$367$	−7.29587			−0.380842			−0.190421	+	0.981703i	$0.560985\pi$
$368$		−	4.30391i		−	0.224357i
$369$	−1.06025	−	11.5069i	−0.0551943	−	0.599024i
$370$	−1.60765	−	2.78453i	−0.0835778	−	0.144761i
$371$	−12.8975			−0.669604
$372$	−10.3077	+	11.3011i	−0.534429	+	0.585935i
$373$	27.4833	−	15.8675i	1.42303	−	0.821589i	0.426476	−	0.904499i	$-0.359755\pi$
$373$	27.4833	−	15.8675i	1.42303	−	0.821589i	0.996557	+	0.0829103i	$0.0264215\pi$
$374$	−1.38565	+	2.40002i	−0.0716503	+	0.124102i
$375$	3.67234	−	4.02627i	0.189639	−	0.207916i
$376$		−	3.90406i		−	0.201336i
$377$	30.4571	+	17.5844i	1.56862	+	0.905645i
$378$	8.59498	−	11.3632i	0.442078	−	0.584460i
$379$			36.3198i			1.86562i	0.360365	+	0.932811i	$0.382652\pi$
$379$			36.3198i			1.86562i	−0.360365	+	0.932811i	$0.617348\pi$
$380$	1.26222	−	0.571127i	0.0647506	−	0.0292982i
$381$	16.2671	+	3.56698i	0.833390	+	0.182742i
$382$		−	12.4685i		−	0.637945i
$383$	7.22929			0.369400			0.184700	−	0.982795i	$-0.440869\pi$
$383$	7.22929			0.369400			0.184700	+	0.982795i	$0.440869\pi$
$384$	−0.370982	+	1.69185i	−0.0189316	+	0.0863371i
$385$	0.215266	+	0.372851i	0.0109710	+	0.0190023i
$386$	−18.8559	+	10.8864i	−0.959738	+	0.554105i
$387$	12.9856	−	9.18223i	0.660097	−	0.466759i
$388$		−	4.82426i		−	0.244915i
$389$		−	22.4934i		−	1.14046i	−0.821485	−	0.570230i	$-0.806854\pi$
$389$		−	22.4934i		−	1.14046i	0.821485	−	0.570230i	$-0.193146\pi$
$390$	−1.47219	−	1.34278i	−0.0745474	−	0.0679944i
$391$	12.0720	+	20.9093i	0.610506	+	1.05743i
$392$	0.259183	+	0.448918i	0.0130907	+	0.0226738i
$393$	24.3266	−	26.6711i	1.22712	−	1.34538i
$394$	−22.7551	+	13.1377i	−1.14639	+	0.661866i
$395$	−0.0502526	−	0.0870400i	−0.00252848	−	0.00437946i
$396$	−0.855655	−	1.21008i	−0.0429983	−	0.0608088i
$397$	−5.86909	+	10.1656i	−0.294561	+	0.510195i	−0.974883	−	0.222719i	$-0.928507\pi$
$397$	−5.86909	+	10.1656i	−0.294561	+	0.510195i	0.680322	+	0.732914i	$0.261840\pi$
$398$	0.352359	−	0.610303i	0.0176622	−	0.0305917i
$399$	−6.40467	+	19.6857i	−0.320635	+	0.985518i
$400$	−2.44949	−	4.24264i	−0.122474	−	0.212132i
$401$	32.1645			1.60622			0.803110	−	0.595830i	$-0.203177\pi$
$401$	32.1645			1.60622			0.803110	+	0.595830i	$0.203177\pi$
$402$	−3.85566	+	4.22725i	−0.192303	+	0.210836i
$403$	−31.9644			−1.59226
$404$	−8.35102	−	4.82146i	−0.415479	−	0.239877i
$405$	0.522704	+	2.81237i	0.0259734	+	0.139748i
$406$	26.6421			1.32222
$407$	2.49877	−	4.32799i	0.123859	−	0.214530i
$408$	−2.94315	−	9.25994i	−0.145708	−	0.458435i
$409$	−19.6689	−	11.3559i	−0.972565	−	0.561511i	−0.0725480	−	0.997365i	$-0.523113\pi$
$409$	−19.6689	−	11.3559i	−0.972565	−	0.561511i	−0.900017	+	0.435854i	$0.856446\pi$
$410$	−1.06025	+	0.612134i	−0.0523619	+	0.0302311i
$411$	1.36588	−	1.49752i	0.0673739	−	0.0738672i
$412$		−	10.6188i		−	0.523151i
$413$	−6.71122	+	11.6242i	−0.330238	+	0.571988i
$414$	−12.8573	+	1.18467i	−0.631900	+	0.0582235i
$415$	−0.305250	+	0.528708i	−0.0149841	+	0.0259533i
$416$	−3.13461	+	1.80977i	−0.153687	+	0.0887311i
$417$	−25.7798	+	8.19378i	−1.26244	+	0.401251i
$418$	1.74970	+	1.25517i	0.0855808	+	0.0613926i
$419$	5.78208	−	3.33828i	0.282473	−	0.163086i	−0.352069	−	0.935974i	$-0.614522\pi$
$419$	5.78208	−	3.33828i	0.282473	−	0.163086i	0.634542	+	0.772888i	$0.281189\pi$
$420$	−1.47445	−	0.323310i	−0.0719457	−	0.0157759i
$421$	2.73422	−	1.57860i	0.133258	−	0.0769365i	−0.431889	−	0.901927i	$-0.642153\pi$
$421$	2.73422	−	1.57860i	0.133258	−	0.0769365i	0.565147	+	0.824990i	$0.308819\pi$
$422$	17.5567	−	10.1363i	0.854645	−	0.493429i
$423$	−11.6628	+	1.07461i	−0.567064	+	0.0522494i
$424$	−2.35187	−	4.07356i	−0.114217	−	0.197830i
$425$	23.8003	+	13.7411i	1.15448	+	0.666540i
$426$	17.2227	+	15.7087i	0.834441	+	0.761090i
$427$	3.70678	−	6.42033i	0.179384	−	0.310702i
$428$	−1.05799	+	1.83250i	−0.0511400	+	0.0885771i
$429$	0.663351	−	3.02520i	0.0320269	−	0.146058i
$430$	−1.45923	−	0.842485i	−0.0703702	−	0.0406282i
$431$	−6.09250	−	10.5525i	−0.293465	−	0.508297i	0.681162	−	0.732133i	$-0.261475\pi$
$431$	−6.09250	−	10.5525i	−0.293465	−	0.508297i	−0.974627	+	0.223837i	$0.928142\pi$
$432$	5.15627	+	0.642559i	0.248081	+	0.0309152i
$433$	0.218755	−	0.126298i	0.0105127	−	0.00606950i	−0.494734	−	0.869044i	$-0.664735\pi$
$433$	0.218755	−	0.126298i	0.0105127	−	0.00606950i	0.505247	+	0.862975i	$0.331401\pi$
$434$	−20.9704	+	12.1072i	−1.00661	+	0.581166i
$435$	−3.60461	+	3.95201i	−0.172828	+	0.189484i
$436$	12.6573	−	7.30770i	0.606175	−	0.349975i
$437$	17.0920	−	7.73377i	0.817623	−	0.369956i
$438$	7.97570	+	7.27460i	0.381094	+	0.347594i
$439$	−28.4179	+	16.4071i	−1.35631	+	0.783068i	−0.989125	−	0.147078i	$-0.953013\pi$
$439$	−28.4179	+	16.4071i	−1.35631	+	0.783068i	−0.367189	+	0.930146i	$0.619680\pi$
$440$	−0.0785079	+	0.135980i	−0.00374271	+	0.00648257i
$441$	1.26973	−	0.897835i	0.0604634	−	0.0427541i
$442$	10.1524	−	17.5844i	0.482899	−	0.836406i
$443$		−	36.5998i		−	1.73891i	−0.494013	−	0.869455i	$-0.664470\pi$
$443$		−	36.5998i		−	1.73891i	0.494013	−	0.869455i	$-0.335530\pi$
$444$	5.30744	+	16.6986i	0.251880	+	0.792481i
$445$	0.765261	−	0.441823i	0.0362768	−	0.0209444i
$446$	9.53963	+	5.50771i	0.451714	+	0.260797i
$447$	−22.2889	+	24.4370i	−1.05423	+	1.15583i
$448$	−1.37098	+	2.37461i	−0.0647728	+	0.112190i
$449$	13.3834			0.631603			0.315801	−	0.948825i	$-0.397727\pi$
$449$	13.3834			0.631603			0.315801	+	0.948825i	$0.397727\pi$
$450$	−12.0000	+	8.48528i	−0.565685	+	0.400000i
$451$	−1.64794	−	0.951437i	−0.0775983	−	0.0448014i
$452$	−4.45459			−0.209526
$453$	−3.10268	−	9.76186i	−0.145777	−	0.458652i
$454$	0.379122			0.0177931
$455$	−1.57721	−	2.73181i	−0.0739407	−	0.128069i
$456$	−7.38546	+	1.56685i	−0.345856	+	0.0733744i
$457$	13.9859	−	24.2243i	0.654232	−	1.13316i	−0.327854	−	0.944729i	$-0.606325\pi$
$457$	13.9859	−	24.2243i	0.654232	−	1.13316i	0.982086	−	0.188435i	$-0.0603414\pi$
$458$	6.17045	−	10.6875i	0.288326	−	0.499396i
$459$	−26.8525	+	11.3411i	−1.25337	+	0.529356i
$460$	0.683971	+	1.18467i	0.0318903	+	0.0552357i
$461$	−2.48078	+	1.43228i	−0.115542	+	0.0667080i	−0.556657	−	0.830742i	$-0.687916\pi$
$461$	−2.48078	+	1.43228i	−0.115542	+	0.0667080i	0.441115	+	0.897450i	$0.354583\pi$
$462$	−0.710670	−	2.23595i	−0.0330633	−	0.104026i
$463$	15.1652	+	26.2668i	0.704785	+	1.22072i	0.966769	+	0.255651i	$0.0822897\pi$
$463$	15.1652	+	26.2668i	0.704785	+	1.22072i	−0.261985	+	0.965072i	$0.584377\pi$
$464$	4.85821	+	8.41466i	0.225537	+	0.390641i
$465$	1.04129	−	4.74877i	0.0482886	−	0.220219i
$466$		−	12.0176i		−	0.556706i
$467$			20.9149i			0.967826i	0.875116	+	0.483913i	$0.160785\pi$
$467$			20.9149i			0.967826i	−0.875116	+	0.483913i	$0.839215\pi$
$468$	6.26922	+	8.86601i	0.289795	+	0.409831i
$469$	−7.84409	+	4.52879i	−0.362206	+	0.209120i
$470$	0.620428	+	1.07461i	0.0286182	+	0.0495682i
$471$	−24.8675	−	22.6815i	−1.14583	−	1.04511i
$472$	−4.89519			−0.225320
$473$		−	2.61894i		−	0.120419i
$474$	0.165902	+	0.521971i	0.00762013	+	0.0239749i
$475$	12.4472	−	17.3513i	0.571117	−	0.796132i
$476$		−	15.3818i		−	0.705023i
$477$	−11.5218	+	8.14712i	−0.527545	+	0.373031i
$478$	−4.53510	−	2.61834i	−0.207430	−	0.119760i
$479$			11.7970i			0.539019i	0.962998	+	0.269510i	$0.0868616\pi$
$479$			11.7970i			0.539019i	−0.962998	+	0.269510i	$0.913138\pi$
$480$	−0.166753	−	0.524648i	−0.00761118	−	0.0239468i
$481$	−18.3080	+	31.7103i	−0.834771	+	1.44587i
$482$	−14.5433	+	8.39659i	−0.662430	+	0.382454i
$483$	−19.9659	−	4.37802i	−0.908478	−	0.199207i
$484$	10.7560			0.488907
$485$	0.766665	+	1.32790i	0.0348125	+	0.0602969i
$486$	0.500258	−	15.5804i	0.0226921	−	0.706743i
$487$			11.7862i			0.534083i	0.963685	+	0.267042i	$0.0860461\pi$
$487$			11.7862i			0.534083i	−0.963685	+	0.267042i	$0.913954\pi$
$488$	2.70374			0.122393
$489$	16.7506	+	15.2781i	0.757486	+	0.690900i
$490$	−0.142683	−	0.0823779i	−0.00644575	−	0.00372145i
$491$			18.2927i			0.825536i	0.910836	+	0.412768i	$0.135438\pi$
$491$			18.2927i			0.825536i	−0.910836	+	0.412768i	$0.864562\pi$
$492$	6.35821	−	2.02087i	0.286650	−	0.0911081i
$493$	−47.2043	−	27.2534i	−2.12598	−	1.22743i
$494$	−12.8197	−	9.19641i	−0.576787	−	0.413766i
$495$	0.427828	+	0.197101i	0.0192294	+	0.00885903i
$496$	−7.64794	−	4.41554i	−0.343403	−	0.198264i
$497$	18.4512	+	31.9584i	0.827649	+	1.43353i
$498$	2.24196	−	2.45804i	0.100465	−	0.110147i
$499$	21.6195			0.967822			0.483911	−	0.875117i	$-0.339216\pi$
$499$	21.6195			0.967822			0.483911	+	0.875117i	$0.339216\pi$
$500$	2.72474	+	1.57313i	0.121854	+	0.0703526i
$501$	1.26692	−	0.402675i	0.0566019	−	0.0179902i
$502$	−13.6697	−	7.89221i	−0.610109	−	0.352246i
$503$	−3.33259	+	1.92407i	−0.148593	+	0.0857901i	−0.572453	−	0.819938i	$-0.694008\pi$
$503$	−3.33259	+	1.92407i	−0.148593	+	0.0857901i	0.423860	+	0.905728i	$0.360675\pi$
$504$	7.47115	+	3.44197i	0.332792	+	0.153318i
$505$	3.06488			0.136385
$506$	−1.06309	+	1.84133i	−0.0472603	+	0.0818572i
$507$	−0.0374768	+	0.170912i	−0.00166440	+	0.00759047i
$508$			9.61497i			0.426595i
$509$	−22.5206	+	39.0069i	−0.998209	+	1.72895i	−0.447294	+	0.894387i	$0.647612\pi$
$509$	−22.5206	+	39.0069i	−0.998209	+	1.72895i	−0.550914	+	0.834562i	$0.685721\pi$
$510$	2.28170	+	2.08112i	0.101035	+	0.0921537i
$511$	8.54462	+	14.7997i	0.377992	+	0.654701i
$512$	−1.00000			−0.0441942
$513$	6.71360	+	21.6316i	0.296413	+	0.955060i
$514$	−7.25484			−0.319997
$515$	1.68753	+	2.92288i	0.0743613	+	0.128797i
$516$	6.78414	+	6.18779i	0.298655	+	0.272402i
$517$	−0.964328	+	1.67026i	−0.0424111	+	0.0734582i
$518$			27.7382i			1.21875i
$519$	−0.521300	+	2.37738i	−0.0228825	+	0.104355i
$520$	0.575211	−	0.996295i	0.0252247	−	0.0436904i
$521$	12.1832			0.533754			0.266877	−	0.963731i	$-0.414008\pi$
$521$	12.1832			0.533754			0.266877	+	0.963731i	$0.414008\pi$
$522$	23.8003	−	16.8293i	1.04171	−	0.736599i
$523$	7.37872	−	4.26011i	0.322649	−	0.186281i	−0.329924	−	0.944008i	$-0.607023\pi$
$523$	7.37872	−	4.26011i	0.322649	−	0.186281i	0.652573	+	0.757726i	$0.273690\pi$
$524$	18.0495	+	10.4209i	0.788495	+	0.455238i
$525$	−22.1733	+	7.04750i	−0.967722	+	0.307578i
$526$	20.4733	+	11.8203i	0.892680	+	0.515389i
$527$	49.5403			2.15801
$528$	0.576615	−	0.632187i	0.0250940	−	0.0275124i
$529$	−2.23818	−	3.87664i	−0.0973121	−	0.168550i
$530$	1.29473	+	0.747512i	0.0562394	+	0.0324698i
$531$	1.34743	+	14.6236i	0.0584734	+	0.634612i
$532$	−11.8938	−	1.17758i	−0.515661	−	0.0510545i
$533$	12.0741	+	6.97099i	0.522987	+	0.301947i
$534$	−4.58920	+	1.45862i	−0.198594	+	0.0631206i
$535$		−	0.672539i		−	0.0290764i
$536$	−2.86076	−	1.65166i	−0.123566	−	0.0713408i
$537$	−30.8017	−	28.0941i	−1.32919	−	1.21235i
$538$	8.28359			0.357131
$539$		−	0.256079i		−	0.0110301i
$540$	−1.52140	+	0.642559i	−0.0654708	+	0.0276514i
$541$	−10.8633	−	18.8158i	−0.467050	−	0.808954i	0.532241	−	0.846593i	$-0.321350\pi$
$541$	−10.8633	−	18.8158i	−0.467050	−	0.808954i	−0.999291	+	0.0376382i	$0.988017\pi$
$542$	18.5007			0.794674
$543$	−15.4341	−	3.38431i	−0.662340	−	0.145235i
$544$	4.85821	−	2.80489i	0.208294	−	0.120259i
$545$	−2.32266	+	4.02297i	−0.0994918	+	0.172325i
$546$	5.20693	+	16.3824i	0.222836	+	0.701101i
$547$			10.1926i			0.435805i	0.975971	+	0.217902i	$0.0699215\pi$
$547$			10.1926i			0.435805i	−0.975971	+	0.217902i	$0.930079\pi$
$548$	1.01343	+	0.585106i	0.0432918	+	0.0249945i
$549$	−0.744219	−	8.07701i	−0.0317625	−	0.344718i
$550$			2.42016i			0.103196i
$551$	−24.6872	+	34.4138i	−1.05171	+	1.46608i
$552$	−2.25804	−	7.10438i	−0.0961084	−	0.302382i
$553$			0.867052i			0.0368708i
$554$	13.7582			0.584532
$555$	−4.11462	−	3.75293i	−0.174656	−	0.159303i
$556$	−7.80884	−	13.5253i	−0.331169	−	0.573601i
$557$	−2.73682	+	1.58011i	−0.115963	+	0.0669513i	−0.556860	−	0.830607i	$-0.687994\pi$
$557$	−2.73682	+	1.58011i	−0.115963	+	0.0669513i	0.440897	+	0.897558i	$0.354661\pi$
$558$	−11.0856	+	24.0624i	−0.469291	+	1.01864i
$559$			19.1884i			0.811585i
$560$		−	0.871498i		−	0.0368275i
$561$	−1.02810	+	4.68864i	−0.0434065	+	0.197954i
$562$	6.11854	+	10.5976i	0.258095	+	0.447033i
$563$	−3.78225	−	6.55105i	−0.159403	−	0.276094i	0.775251	−	0.631654i	$-0.217624\pi$
$563$	−3.78225	−	6.55105i	−0.159403	−	0.276094i	−0.934653	+	0.355560i	$0.884290\pi$
$564$	−2.04826	−	6.44435i	−0.0862471	−	0.271356i
$565$	1.22615	−	0.707917i	0.0515845	−	0.0297823i
$566$	10.8216	+	18.7436i	0.454867	+	0.787852i
$567$	8.22589	−	23.2663i	0.345455	−	0.977094i
$568$	−6.72919	+	11.6553i	−0.282350	+	0.489045i
$569$	−20.6624	+	35.7883i	−0.866213	+	1.50033i	−0.000376125		1.00000i	$0.500120\pi$
$569$	−20.6624	+	35.7883i	−0.866213	+	1.50033i	−0.865837	+	0.500326i	$0.833214\pi$
$570$	1.78388	−	1.60497i	0.0747187	−	0.0672248i
$571$	5.60925	+	9.71550i	0.234740	+	0.406581i	0.959197	−	0.282739i	$-0.0912429\pi$
$571$	5.60925	+	9.71550i	0.234740	+	0.406581i	−0.724457	+	0.689320i	$0.757910\pi$
$572$	1.78810			0.0747641
$573$	−6.54158	−	20.5816i	−0.273279	−	0.859807i
$574$	10.5617			0.440836
$575$	18.2599	+	10.5424i	0.761492	+	0.439648i
$576$	0.275255	+	2.98735i	0.0114690	+	0.124473i
$577$	7.34788			0.305896			0.152948	−	0.988234i	$-0.451123\pi$
$577$	7.34788			0.305896			0.152948	+	0.988234i	$0.451123\pi$
$578$	−7.23478	+	12.5310i	−0.300927	+	0.521221i
$579$	−25.4135	+	27.8627i	−1.05615	+	1.15793i
$580$	−2.67449	−	1.54412i	−0.111052	−	0.0641160i
$581$	4.56114	−	2.63337i	0.189228	−	0.109251i
$582$	−2.53104	−	7.96331i	−0.104915	−	0.330090i
$583$			2.32371i			0.0962382i
$584$	−3.11624	+	5.39749i	−0.128951	+	0.223350i
$585$	−3.13461	−	1.44412i	−0.129600	−	0.0597070i
$586$	12.0645	−	20.8963i	0.498380	−	0.863219i
$587$	21.7778	−	12.5734i	0.898866	−	0.518961i	0.0220340	−	0.999757i	$-0.492986\pi$
$587$	21.7778	−	12.5734i	0.898866	−	0.518961i	0.876832	+	0.480797i	$0.159652\pi$
$588$	0.663351	+	0.605040i	0.0273561	+	0.0249514i
$589$	3.79264	−	38.3065i	0.156273	−	1.57839i
$590$	1.34743	−	0.777938i	0.0554727	−	0.0320272i
$591$	−30.6687	+	33.6245i	−1.26154	+	1.38313i
$592$	−8.76088	+	5.05810i	−0.360070	+	0.207887i
$593$	−37.4358	+	21.6136i	−1.53731	+	0.887564i	−0.538311	+	0.842747i	$0.680937\pi$
$593$	−37.4358	+	21.6136i	−1.53731	+	0.887564i	−0.998995	+	0.0448173i	$0.985729\pi$
$594$	−2.04728	−	1.54854i	−0.0840009	−	0.0635372i
$595$	2.44445	+	4.23392i	0.100213	+	0.173574i
$596$	−16.5375	−	9.54795i	−0.677404	−	0.391099i
$597$	0.261437	−	1.19228i	0.0106999	−	0.0487968i
$598$	7.78907	−	13.4911i	0.318519	−	0.551691i
$599$	7.97211	−	13.8081i	0.325731	−	0.564183i	−0.655929	−	0.754823i	$-0.727723\pi$
$599$	7.97211	−	13.8081i	0.325731	−	0.564183i	0.981660	+	0.190639i	$0.0610561\pi$
$600$	−6.26922	−	5.71812i	−0.255940	−	0.233441i
$601$	−29.0452	−	16.7692i	−1.18478	−	0.684031i	−0.227662	−	0.973740i	$-0.573108\pi$
$601$	−29.0452	−	16.7692i	−1.18478	−	0.684031i	−0.957115	+	0.289709i	$0.906441\pi$
$602$	7.26807	+	12.5887i	0.296224	+	0.513076i
$603$	−4.14664	+	9.00070i	−0.168864	+	0.366537i
$604$	5.12154	−	2.95692i	0.208392	−	0.120315i
$605$	−2.96063	+	1.70932i	−0.120367	+	0.0694938i
$606$	−16.3144	−	3.57735i	−0.662728	−	0.145320i
$607$	23.5567	−	13.6004i	0.956135	−	0.552025i	0.0611537	−	0.998128i	$-0.480522\pi$
$607$	23.5567	−	13.6004i	0.956135	−	0.552025i	0.894981	+	0.446104i	$0.147189\pi$
$608$	−1.79692	−	3.97128i	−0.0728746	−	0.161057i
$609$	43.9775	−	13.9777i	1.78206	−	0.566405i
$610$	−0.744219	+	0.429675i	−0.0301325	+	0.0173970i
$611$	7.06544	−	12.2377i	0.285837	−	0.495084i
$612$	−9.71641	−	13.7411i	−0.392763	−	0.555450i
$613$	4.81339	−	8.33704i	0.194411	−	0.336730i	−0.752296	−	0.658825i	$-0.771054\pi$
$613$	4.81339	−	8.33704i	0.194411	−	0.336730i	0.946707	+	0.322095i	$0.104387\pi$
$614$			1.44055i			0.0581359i
$615$	−1.42897	+	1.56669i	−0.0576218	+	0.0631752i
$616$	1.17309	−	0.677283i	0.0472651	−	0.0272885i
$617$	−22.0588	−	12.7357i	−0.888056	−	0.512719i	−0.0147496	−	0.999891i	$-0.504695\pi$
$617$	−22.0588	−	12.7357i	−0.888056	−	0.512719i	−0.873306	+	0.487172i	$0.838028\pi$
$618$	−5.57113	−	17.5282i	−0.224104	−	0.705090i
$619$	−3.25614	+	5.63981i	−0.130875	+	0.226683i	−0.924014	−	0.382358i	$-0.875112\pi$
$619$	−3.25614	+	5.63981i	−0.130875	+	0.226683i	0.793139	+	0.609041i	$0.208445\pi$
$620$	2.80685			0.112726
$621$	−20.6017	+	8.70105i	−0.826718	+	0.349161i
$622$	6.78947	+	3.91990i	0.272233	+	0.157174i
$623$	−7.62317			−0.305416
$624$	−4.22474	+	4.63191i	−0.169125	+	0.185425i
$625$	23.4949			0.939796
$626$	5.76922	+	9.99257i	0.230584	+	0.399384i
$627$	3.54673	+	1.15391i	0.141643	+	0.0460829i
$628$	9.71615	−	16.8289i	0.387717	−	0.671545i
$629$	28.3748	−	49.1466i	1.13138	−	1.95960i
$630$	−2.60347	+	0.239884i	−0.103725	+	0.00955722i
$631$	14.0897	+	24.4041i	0.560902	+	0.971510i	0.997418	+	0.0718138i	$0.0228787\pi$
$631$	14.0897	+	24.4041i	0.560902	+	0.971510i	−0.436516	+	0.899696i	$0.643788\pi$
$632$	−0.273851	+	0.158108i	−0.0108932	+	0.00628920i
$633$	23.6624	−	25.9429i	0.940496	−	1.03114i
$634$	−0.623429	−	1.07981i	−0.0247595	−	0.0428847i
$635$	−1.52800	−	2.64657i	−0.0606367	−	0.105026i
$636$	−6.01937	−	5.49024i	−0.238684	−	0.217702i
$637$			1.87624i			0.0743394i
$638$		−	4.80003i		−	0.190035i
$639$	36.6706	+	16.8942i	1.45067	+	0.668325i
$640$	0.275255	−	0.158919i	0.0108804	−	0.00628181i
$641$	−17.0290	−	29.4950i	−0.672603	−	1.16498i	−0.977163	−	0.212490i	$-0.931843\pi$
$641$	−17.0290	−	29.4950i	−0.672603	−	1.16498i	0.304560	−	0.952493i	$-0.401491\pi$
$642$	−0.784992	+	3.57994i	−0.0309812	+	0.141289i
$643$	−0.665518			−0.0262455			−0.0131227	−	0.999914i	$-0.504177\pi$
$643$	−0.665518			−0.0262455			−0.0131227	+	0.999914i	$0.504177\pi$
$644$		−	11.8012i		−	0.465031i
$645$	−2.85072	−	0.625093i	−0.112247	−	0.0246130i
$646$	19.8688	+	14.2532i	0.781727	+	0.560783i
$647$			30.6089i			1.20336i	0.798737	+	0.601680i	$0.205502\pi$
$647$			30.6089i			1.20336i	−0.798737	+	0.601680i	$0.794498\pi$
$648$	8.84847	−	1.64456i	0.347601	−	0.0646046i
$649$	2.09430	+	1.20914i	0.0822085	+	0.0474631i
$650$		−	17.7320i		−	0.695507i
$651$	−28.2633	+	30.9872i	−1.10773	+	1.21449i
$652$	−6.54473	+	11.3358i	−0.256311	+	0.443944i
$653$	6.97798	−	4.02874i	0.273069	−	0.157657i	−0.357212	−	0.934023i	$-0.616273\pi$
$653$	6.97798	−	4.02874i	0.273069	−	0.157657i	0.630282	+	0.776367i	$0.282939\pi$
$654$	17.0592	−	18.7033i	0.667068	−	0.731357i
$655$	−6.62428			−0.258832
$656$	1.92594	+	3.33582i	0.0751951	+	0.130242i
$657$	16.9819	+	7.82361i	0.662528	+	0.305228i
$658$		−	10.7048i		−	0.417316i
$659$	−42.3332			−1.64907			−0.824534	−	0.565813i	$-0.808562\pi$
$659$	−42.3332			−1.64907			−0.824534	+	0.565813i	$0.808562\pi$
$660$	−0.0582500	+	0.265648i	−0.00226738	+	0.0103403i
$661$	−17.9708	−	10.3754i	−0.698983	−	0.403558i	0.107986	−	0.994152i	$-0.465560\pi$
$661$	−17.9708	−	10.3754i	−0.698983	−	0.403558i	−0.806968	+	0.590595i	$0.798893\pi$
$662$			12.9868i			0.504745i
$663$	7.53270	−	34.3527i	0.292546	−	1.33415i
$664$	1.66346	+	0.960397i	0.0645546	+	0.0372706i
$665$	3.46097	−	1.56601i	0.134211	−	0.0607273i
$666$	17.5218	+	24.7795i	0.678955	+	0.960187i
$667$	−36.2159	−	20.9093i	−1.40229	−	0.809611i
$668$	0.383758	+	0.664688i	0.0148480	+	0.0257175i
$669$	18.6365	+	4.08652i	0.720528	+	0.157994i
$670$	1.04992			0.0405618
$671$	−1.15674	−	0.667841i	−0.0446553	−	0.0257817i
$672$	−1.01722	+	4.63900i	−0.0392401	+	0.178953i
$673$	15.3082	+	8.83817i	0.590086	+	0.340686i	0.765132	−	0.643874i	$-0.222674\pi$
$673$	15.3082	+	8.83817i	0.590086	+	0.340686i	−0.175045	+	0.984560i	$0.556007\pi$
$674$	21.4194	−	12.3665i	0.825044	−	0.476339i
$675$	−15.3564	+	20.3023i	−0.591067	+	0.781434i
$676$	−0.101021			−0.00388540
$677$	20.6377	−	35.7456i	0.793172	−	1.37381i	−0.130822	−	0.991406i	$-0.541762\pi$
$677$	20.6377	−	35.7456i	0.793172	−	1.37381i	0.923994	−	0.382408i	$-0.124905\pi$
$678$	−7.35310	+	2.33709i	−0.282394	+	0.0897554i
$679$		−	13.2279i		−	0.507642i
$680$	−0.891497	+	1.54412i	−0.0341874	+	0.0592143i
$681$	0.625809	−	0.198906i	0.0239811	−	0.00762208i
$682$	2.18133	+	3.77818i	0.0835276	+	0.144674i
$683$	24.0477			0.920160			0.460080	−	0.887878i	$-0.347821\pi$
$683$	24.0477			0.920160			0.460080	+	0.887878i	$0.347821\pi$
$684$	−11.3690	+	6.46113i	−0.434704	+	0.247047i
$685$	−0.371937			−0.0142110
$686$	−8.88620	−	15.3914i	−0.339277	−	0.587645i
$687$	4.57825	−	20.8790i	0.174671	−	0.796584i
$688$	−2.65068	+	4.59111i	−0.101056	+	0.175035i
$689$		−	17.0253i		−	0.648614i
$690$	1.75055	+	1.59667i	0.0666425	+	0.0607843i
$691$	1.07816	−	1.86743i	0.0410152	−	0.0710405i	−0.844789	−	0.535099i	$-0.820274\pi$
$691$	1.07816	−	1.86743i	0.0410152	−	0.0710405i	0.885804	+	0.464059i	$0.153607\pi$
$692$	−1.40519			−0.0534173
$693$	−2.34618	−	3.31799i	−0.0891239	−	0.126040i
$694$	−30.8720	+	17.8240i	−1.17189	+	0.676588i
$695$	4.29885	+	2.48194i	0.163065	+	0.0941454i
$696$	12.4341	+	11.3411i	0.471312	+	0.429882i
$697$	−18.7132	−	10.8041i	−0.708812	−	0.409233i
$698$	−7.96029			−0.301301
$699$	−6.30502	−	19.8373i	−0.238478	−	0.750314i
$700$	−6.71641	−	11.6332i	−0.253857	−	0.439692i
$701$	−12.5290	−	7.23359i	−0.473212	−	0.273209i	0.244371	−	0.969682i	$-0.421418\pi$
$701$	−12.5290	−	7.23359i	−0.473212	−	0.273209i	−0.717583	+	0.696473i	$0.754752\pi$
$702$	15.0000	+	11.3458i	0.566139	+	0.428220i
$703$	−35.8297	−	25.7030i	−1.35134	−	0.969406i
$704$	0.427828	+	0.247006i	0.0161244	+	0.00930941i
$705$	1.58792	+	1.44834i	0.0598045	+	0.0545475i
$706$		−	11.6315i		−	0.437759i
$707$	−22.8982	−	13.2203i	−0.861175	−	0.497200i
$708$	−8.08040	+	2.56825i	−0.303680	+	0.0965208i
$709$	47.8827			1.79827			0.899137	−	0.437668i	$-0.144195\pi$
$709$	47.8827			1.79827			0.899137	+	0.437668i	$0.144195\pi$
$710$		−	4.27757i		−	0.160534i
$711$	0.547702	+	0.774568i	0.0205404	+	0.0290486i
$712$	−1.39009	−	2.40771i	−0.0520959	−	0.0902328i
$713$	38.0082			1.42342
$714$	−8.07002	−	25.3904i	−0.302013	−	0.950213i
$715$	−0.492183	+	0.284162i	−0.0184066	+	0.0106270i
$716$	12.0347	−	20.8448i	0.449759	−	0.779006i
$717$	−8.85970	−	1.94271i	−0.330871	−	0.0725519i
$718$			10.7763i			0.402170i
$719$	8.56691	+	4.94611i	0.319492	+	0.184459i	0.651166	−	0.758935i	$-0.274280\pi$
$719$	8.56691	+	4.94611i	0.319492	+	0.184459i	−0.331674	+	0.943394i	$0.607614\pi$
$720$	−0.550510	−	0.778539i	−0.0205163	−	0.0290144i
$721$		−	29.1164i		−	1.08435i
$722$	12.5422	−	14.2721i	0.466772	−	0.531154i
$723$	−19.6011	+	21.4902i	−0.728974	+	0.799229i
$724$		−	9.12258i		−	0.339038i
$725$	−47.6005			−1.76784
$726$	17.7546	−	5.64308i	0.658936	−	0.209435i
$727$	−21.9798	−	38.0702i	−0.815187	−	1.41195i	−0.909193	−	0.416374i	$-0.863301\pi$
$727$	−21.9798	−	38.0702i	−0.815187	−	1.41195i	0.0940060	−	0.995572i	$-0.470033\pi$
$728$	−8.59498	+	4.96231i	−0.318551	+	0.183916i
$729$	−7.34847	−	25.9808i	−0.272166	−	0.962250i
$730$		−	1.98092i		−	0.0733170i
$731$		−	29.7394i		−	1.09995i
$732$	4.46301	−	1.41851i	0.164958	−	0.0524297i
$733$	6.59524	+	11.4233i	0.243601	+	0.421929i	0.961737	−	0.273973i	$-0.0883380\pi$
$733$	6.59524	+	11.4233i	0.243601	+	0.421929i	−0.718137	+	0.695902i	$0.755005\pi$
$734$	−3.64794	−	6.31841i	−0.134648	−	0.233217i
$735$	−0.278743	−	0.0611214i	−0.0102816	−	0.00225450i
$736$	3.72730	−	2.15196i	0.137390	−	0.0793221i
$737$	0.815941	+	1.41325i	0.0300556	+	0.0520578i
$738$	9.43512	−	6.67164i	0.347311	−	0.245586i
$739$	3.33374	−	5.77420i	0.122633	−	0.212407i	−0.798172	−	0.602430i	$-0.794199\pi$
$739$	3.33374	−	5.77420i	0.122633	−	0.212407i	0.920805	+	0.390022i	$0.127533\pi$
$740$	1.60765	−	2.78453i	0.0590985	−	0.102362i
$741$	−25.9861	−	8.45450i	−0.954625	−	0.310584i
$742$	−6.44874	−	11.1696i	−0.236741	−	0.410047i
$743$	39.5358			1.45043			0.725213	−	0.688525i	$-0.241741\pi$
$743$	39.5358			1.45043			0.725213	+	0.688525i	$0.241741\pi$
$744$	−14.9409	−	3.27617i	−0.547760	−	0.120110i
$745$	6.06939			0.222365
$746$	27.4833	+	15.8675i	1.00624	+	0.580951i
$747$	2.41116	−	5.23367i	0.0882198	−	0.191490i
$748$	−2.77130			−0.101329
$749$	−2.90098	+	5.02464i	−0.105999	+	0.183596i
$750$	5.32302	+	1.16721i	0.194369	+	0.0426204i
$751$	11.1840	+	6.45707i	0.408109	+	0.235622i	0.689977	−	0.723831i	$-0.257621\pi$
$751$	11.1840	+	6.45707i	0.408109	+	0.235622i	−0.281868	+	0.959453i	$0.590954\pi$
$752$	3.38101	−	1.95203i	0.123293	−	0.0711832i
$753$	−26.7049	−	5.85573i	−0.973182	−	0.213395i
$754$			35.1689i			1.28077i
$755$	−0.939819	+	1.62781i	−0.0342035	+	0.0592423i
$756$	14.1383	+	1.76187i	0.514205	+	0.0640788i
$757$	−9.40872	+	16.2964i	−0.341966	+	0.592302i	−0.984798	−	0.173705i	$-0.944426\pi$
$757$	−9.40872	+	16.2964i	−0.341966	+	0.592302i	0.642832	+	0.766007i	$0.277759\pi$
$758$	−31.4539	+	18.1599i	−1.14246	+	0.659597i
$759$	−0.788777	+	3.59720i	−0.0286308	+	0.130570i
$760$	1.12572	+	0.807552i	0.0408342	+	0.0292930i
$761$	−30.1496	+	17.4069i	−1.09292	+	0.630999i	−0.934353	−	0.356349i	$-0.884022\pi$
$761$	−30.1496	+	17.4069i	−1.09292	+	0.630999i	−0.158569	+	0.987348i	$0.550688\pi$
$762$	5.04447	+	15.8712i	0.182742	+	0.574954i
$763$	34.7059	−	20.0375i	1.25644	−	0.725405i
$764$	10.7981	−	6.23426i	0.390660	−	0.225548i
$765$	4.85821	+	2.23818i	0.175649	+	0.0809217i
$766$	3.61465	+	6.26075i	0.130602	+	0.226210i
$767$	−15.3445	−	8.85916i	−0.554058	−	0.319886i
$768$	−1.65068	+	0.524648i	−0.0595638	+	0.0189316i
$769$	−13.8364	+	23.9653i	−0.498952	+	0.864210i	−0.999999	−	0.00121017i	$-0.999615\pi$
$769$	−13.8364	+	23.9653i	−0.498952	+	0.864210i	0.501048	+	0.865420i	$0.332948\pi$
$770$	−0.215266	+	0.372851i	−0.00775764	+	0.0134366i
$771$	−11.9754	+	3.80624i	−0.431284	+	0.137078i
$772$	−18.8559	−	10.8864i	−0.678637	−	0.391811i
$773$	−17.3327	−	30.0211i	−0.623414	−	1.07978i	−0.988845	−	0.148946i	$-0.952412\pi$
$773$	−17.3327	−	30.0211i	−0.623414	−	1.07978i	0.365432	−	0.930838i	$-0.380921\pi$
$774$	14.4449	+	6.65477i	0.519210	+	0.239201i
$775$	37.4671	−	21.6316i	1.34586	−	0.777031i
$776$	4.17793	−	2.41213i	0.149979	−	0.0865904i
$777$	14.5528	+	45.7870i	0.522079	+	1.64260i
$778$	19.4798	−	11.2467i	0.698386	−	0.403214i
$779$	−9.78673	+	13.6426i	−0.350646	+	0.488798i
$780$	0.426786	−	1.94635i	0.0152814	−	0.0696904i
$781$	5.75787	−	3.32431i	0.206033	−	0.118953i
$782$	−12.0720	+	20.9093i	−0.431693	+	0.747714i
$783$	30.4571	−	40.2666i	1.08845	−	1.43901i
$784$	−0.259183	+	0.448918i	−0.00925652	+	0.0160328i
$785$			6.17631i			0.220442i
$786$	35.2612	+	7.73190i	1.25772	+	0.275788i
$787$	−3.53395	+	2.04033i	−0.125972	+	0.0727298i	−0.561662	−	0.827367i	$-0.689838\pi$
$787$	−3.53395	+	2.04033i	−0.125972	+	0.0727298i	0.435690	+	0.900097i	$0.356504\pi$
$788$	−22.7551	−	13.1377i	−0.810617	−	0.468010i
$789$	39.9964	+	8.77023i	1.42391	+	0.312228i
$790$	0.0502526	−	0.0870400i	0.00178791	−	0.00309675i
$791$	−12.2143			−0.434291
$792$	0.620132	−	1.34606i	0.0220354	−	0.0478301i
$793$	8.47517	+	4.89314i	0.300962	+	0.173761i
$794$	−11.7382			−0.416572
$795$	2.52936	+	0.554627i	0.0897073	+	0.0196706i
$796$	0.704718			0.0249781
$797$	−2.24196	−	3.88320i	−0.0794144	−	0.137550i	0.823583	−	0.567196i	$-0.191972\pi$
$797$	−2.24196	−	3.88320i	−0.0794144	−	0.137550i	−0.902997	+	0.429646i	$0.858638\pi$
$798$	−20.2507	+	4.29624i	−0.716866	+	0.152085i
$799$	−10.9504	+	18.9667i	−0.387399	+	0.670994i
$800$	2.44949	−	4.24264i	0.0866025	−	0.150000i
$801$	−6.81004	+	4.81542i	−0.240621	+	0.170145i
$802$	16.0823	+	27.8553i	0.567885	+	0.983605i
$803$	2.66643	−	1.53946i	0.0940963	−	0.0543265i
$804$	−5.58873	−	1.22547i	−0.197099	−	0.0432190i
$805$	1.87542	+	3.24833i	0.0661000	+	0.114489i
$806$	−15.9822	−	27.6820i	−0.562949	−	0.975056i
$807$	13.6736	−	4.34596i	0.481332	−	0.152985i
$808$		−	9.64293i		−	0.339237i
$809$		−	4.38153i		−	0.154047i	−0.997029	−	0.0770233i	$-0.975458\pi$
$809$		−	4.38153i		−	0.154047i	0.997029	−	0.0770233i	$-0.0245416\pi$
$810$	−2.17423	+	1.85886i	−0.0763948	+	0.0653137i
$811$	−43.1755	+	24.9274i	−1.51610	+	0.875320i	−0.516277	+	0.856422i	$0.672682\pi$
$811$	−43.1755	+	24.9274i	−1.51610	+	0.875320i	−0.999821	+	0.0188977i	$0.993984\pi$
$812$	13.3210	+	23.0727i	0.467476	+	0.809693i
$813$	30.5388	−	9.70636i	1.07104	−	0.340417i
$814$	4.99753			0.175163
$815$		−	4.16032i		−	0.145730i
$816$	6.54777	−	7.17882i	0.229218	−	0.251309i
$817$	−22.9957	−	2.27675i	−0.804516	−	0.0796535i
$818$		−	22.7117i		−	0.794096i
$819$	17.1900	+	24.3103i	0.600666	+	0.849470i
$820$	−1.06025	−	0.612134i	−0.0370254	−	0.0213766i
$821$			19.4498i			0.678804i	0.940641	+	0.339402i	$0.110225\pi$
$821$			19.4498i			0.678804i	−0.940641	+	0.339402i	$0.889775\pi$
$822$	1.97983	+	0.434128i	0.0690545	+	0.0151419i
$823$	−4.27202	+	7.39936i	−0.148913	+	0.257926i	−0.930826	−	0.365462i	$-0.880911\pi$
$823$	−4.27202	+	7.39936i	−0.148913	+	0.257926i	0.781913	+	0.623388i	$0.214244\pi$
$824$	9.19615	−	5.30940i	0.320363	−	0.184962i
$825$	1.26973	+	3.99491i	0.0442063	+	0.139085i
$826$	−13.4224			−0.467027
$827$	−21.7071	−	37.5978i	−0.754829	−	1.30740i	−0.945459	−	0.325740i	$-0.894387\pi$
$827$	−21.7071	−	37.5978i	−0.754829	−	1.30740i	0.190630	−	0.981662i	$-0.438947\pi$
$828$	−7.45459	−	10.5424i	−0.259065	−	0.366373i
$829$			55.5704i			1.93004i	0.262180	+	0.965019i	$0.415559\pi$
$829$			55.5704i			1.93004i	−0.262180	+	0.965019i	$0.584441\pi$
$830$	−0.610500			−0.0211908
$831$	22.7105	−	7.21823i	0.787817	−	0.250398i
$832$	−3.13461	−	1.80977i	−0.108673	−	0.0627424i
$833$		−	2.90791i		−	0.100753i
$834$	−19.9859	−	18.2291i	−0.692056	−	0.631221i
$835$	−0.211263	−	0.121972i	−0.00731104	−	0.00422103i
$836$	−0.212162	+	2.14288i	−0.00733776	+	0.0741129i
$837$	−5.67449	+	45.5354i	−0.196139	+	1.57393i
$838$	5.78208	+	3.33828i	0.199739	+	0.115319i
$839$	−11.1133	−	19.2488i	−0.383674	−	0.664543i	0.607910	−	0.794006i	$-0.292008\pi$
$839$	−11.1133	−	19.2488i	−0.383674	−	0.664543i	−0.991584	+	0.129463i	$0.958675\pi$
$840$	−0.457229	−	1.43856i	−0.0157759	−	0.0496352i
$841$	65.4087			2.25547
$842$	2.73422	+	1.57860i	0.0942276	+	0.0544023i
$843$	15.6598	+	14.2832i	0.539351	+	0.491939i
$844$	17.5567	+	10.1363i	0.604325	+	0.348907i
$845$	0.0278064	−	0.0160540i	0.000956570	−	0.000552276i
$846$	−6.76203	−	9.56295i	−0.232483	−	0.328781i
$847$	29.4924			1.01337
$848$	2.35187	−	4.07356i	0.0807636	−	0.139887i
$849$	27.6968	+	25.2621i	0.950552	+	0.866994i
$850$			27.4822i			0.942630i
$851$	21.7696	−	37.7061i	0.746252	−	1.29255i
$852$	−4.99281	+	22.7696i	−0.171051	+	0.780074i
$853$	9.44715	+	16.3629i	0.323464	+	0.560256i	0.981200	−	0.192992i	$-0.0618192\pi$
$853$	9.44715	+	16.3629i	0.323464	+	0.560256i	−0.657736	+	0.753248i	$0.728486\pi$
$854$	7.41356			0.253687
$855$	2.10258	−	3.58520i	0.0719066	−	0.122611i
$856$	−2.11598			−0.0723229
$857$	22.3869	+	38.7752i	0.764721	+	1.32453i	0.940394	+	0.340087i	$0.110456\pi$
$857$	22.3869	+	38.7752i	0.764721	+	1.32453i	−0.175674	+	0.984448i	$0.556210\pi$
$858$	2.95157	−	0.938120i	0.100765	−	0.0320269i
$859$	−0.605013	+	1.04791i	−0.0206428	+	0.0357544i	−0.876162	−	0.482016i	$-0.839905\pi$
$859$	−0.605013	+	1.04791i	−0.0206428	+	0.0357544i	0.855519	+	0.517771i	$0.173238\pi$
$860$		−	1.68497i		−	0.0574570i
$861$	17.4340	−	5.54117i	0.594148	−	0.188842i
$862$	6.09250	−	10.5525i	0.207511	−	0.359420i
$863$	−5.34378			−0.181905			−0.0909523	−	0.995855i	$-0.528991\pi$
$863$	−5.34378			−0.181905			−0.0909523	+	0.995855i	$0.528991\pi$
$864$	2.02166	+	4.78674i	0.0687783	+	0.162848i
$865$	0.386785	−	0.223311i	0.0131511	−	0.00759279i
$866$	0.218755	+	0.126298i	0.00743359	+	0.00429179i
$867$	−5.36794	+	24.4804i	−0.182305	+	0.831397i
$868$	−20.9704	−	12.1072i	−0.711781	−	0.410947i
$869$	0.156215			0.00529922
$870$	−5.22485	−	1.14568i	−0.177139	−	0.0388422i
$871$	−5.97823	−	10.3546i	−0.202565	−	0.350852i
$872$	12.6573	+	7.30770i	0.428631	+	0.247470i
$873$	−8.35586	−	11.8170i	−0.282803	−	0.399944i
$874$	15.2437	+	10.9353i	0.515625	+	0.369891i
$875$	7.47115	+	4.31347i	0.252571	+	0.145822i
$876$	−2.31214	+	10.5445i	−0.0781199	+	0.356264i
$877$		−	12.4847i		−	0.421577i	−0.977532	−	0.210788i	$-0.932397\pi$
$877$		−	12.4847i		−	0.421577i	0.977532	−	0.210788i	$-0.0676031\pi$
$878$	−28.4179	−	16.4071i	−0.959059	−	0.553713i
$879$	8.95142	−	40.8228i	0.301924	−	1.37692i
$880$	−0.157016			−0.00529300
$881$		−	18.5298i		−	0.624283i	−0.950036	−	0.312142i	$-0.898954\pi$
$881$		−	18.5298i		−	0.624283i	0.950036	−	0.312142i	$-0.101046\pi$
$882$	1.41241	+	0.650701i	0.0475584	+	0.0219103i
$883$	15.6893	+	27.1746i	0.527986	+	0.914498i	0.999468	+	0.0326225i	$0.0103859\pi$
$883$	15.6893	+	27.1746i	0.527986	+	0.914498i	−0.471482	+	0.881876i	$0.656281\pi$
$884$	20.3048			0.682923
$885$	1.81603	−	1.99105i	0.0610451	−	0.0669284i
$886$	31.6964	−	18.2999i	1.06486	−	0.614797i
$887$	−1.25323	+	2.17066i	−0.0420794	+	0.0728836i	−0.886298	−	0.463115i	$-0.846732\pi$
$887$	−1.25323	+	2.17066i	−0.0420794	+	0.0728836i	0.844219	+	0.535999i	$0.180065\pi$
$888$	−11.8077	+	12.9457i	−0.396240	+	0.434429i
$889$			26.3639i			0.884217i
$890$	0.765261	+	0.441823i	0.0256516	+	0.0148100i
$891$	−4.19184	−	1.48204i	−0.140432	−	0.0496502i
$892$			11.0154i			0.368823i
$893$	13.8275	+	9.91933i	0.462718	+	0.331938i
$894$	−32.3075	−	7.08424i	−1.08052	−	0.236932i
$895$			7.65017i			0.255717i
$896$	−2.74196			−0.0916026
$897$	5.77921	−	26.3560i	0.192962	−	0.880000i
$898$	6.69171	+	11.5904i	0.223305	+	0.386776i
$899$	−74.3105	+	42.9032i	−2.47839	+	1.43090i
$900$	−13.3485	−	6.14966i	−0.444949	−	0.204989i
$901$			26.3869i			0.879076i
$902$		−	1.90287i		−	0.0633588i
$903$	18.6019	+	16.9667i	0.619031	+	0.564616i
$904$	−2.22730	−	3.85779i	−0.0740787	−	0.128308i
$905$	1.44975	+	2.51104i	0.0481912	+	0.0834697i
$906$	6.90268	−	7.56793i	0.229326	−	0.251428i
$907$	5.49047	−	3.16992i	0.182308	−	0.105256i	−0.406069	−	0.913843i	$-0.633101\pi$
$907$	5.49047	−	3.16992i	0.182308	−	0.105256i	0.588377	+	0.808587i	$0.299767\pi$
$908$	0.189561	+	0.328329i	0.00629080	+	0.0108960i
$909$	−28.8068	+	2.65427i	−0.955460	+	0.0880364i
$910$	1.57721	−	2.73181i	0.0522839	−	0.0905585i
$911$	−13.1513	+	22.7788i	−0.435723	+	0.754695i	−0.997354	−	0.0726929i	$-0.976841\pi$
$911$	−13.1513	+	22.7788i	−0.435723	+	0.754695i	0.561631	+	0.827388i	$0.310174\pi$
$912$	−5.04966	−	5.61257i	−0.167211	−	0.185851i
$913$	−0.474448	−	0.821769i	−0.0157019	−	0.0271966i
$914$	27.9718			0.925224
$915$	−1.00304	+	1.09971i	−0.0331594	+	0.0363552i
$916$	12.3409			0.407755
$917$	49.4910	+	28.5736i	1.63434	+	0.943585i
$918$	−23.2479	−	17.5844i	−0.767296	−	0.580373i
$919$	−39.5968			−1.30618			−0.653090	−	0.757281i	$-0.726528\pi$
$919$	−39.5968			−1.30618			−0.653090	+	0.757281i	$0.726528\pi$
$920$	−0.683971	+	1.18467i	−0.0225499	+	0.0390575i
$921$	0.755781	+	2.37789i	0.0249038	+	0.0783541i
$922$	−2.48078	−	1.43228i	−0.0817003	−	0.0471697i
$923$	−42.1867	+	24.3565i	−1.38859	+	0.801705i
$924$	1.58106	−	1.73344i	0.0520130	−	0.0570258i
$925$		−	49.5590i		−	1.62949i
$926$	−15.1652	+	26.2668i	−0.498358	+	0.863181i
$927$	−18.3923	−	26.0107i	−0.604083	−	0.854302i
$928$	−4.85821	+	8.41466i	−0.159478	+	0.276225i
$929$	−25.4841	+	14.7132i	−0.836105	+	0.482725i	−0.855938	−	0.517078i	$-0.827020\pi$
$929$	−25.4841	+	14.7132i	−0.836105	+	0.482725i	0.0198335	+	0.999803i	$0.493686\pi$
$930$	4.63320	−	1.47260i	0.151929	−	0.0482886i
$931$	−2.24851	−	0.222620i	−0.0736919	−	0.00729608i
$932$	10.4076	−	6.00881i	0.340911	−	0.196825i
$933$	13.2638	+	2.90843i	0.434238	+	0.0952176i
$934$	−18.1128	+	10.4575i	−0.592670	+	0.342178i
$935$	0.762815	−	0.440411i	0.0249467	−	0.0144030i
$936$	−4.54358	+	9.86230i	−0.148512	+	0.322360i
$937$	15.6328	+	27.0768i	0.510701	+	0.884560i	0.999923	+	0.0124005i	$0.00394729\pi$
$937$	15.6328	+	27.0768i	0.510701	+	0.884560i	−0.489222	+	0.872159i	$0.662719\pi$
$938$	−7.84409	−	4.52879i	−0.256119	−	0.147870i
$939$	14.7657	+	13.4677i	0.481861	+	0.439503i
$940$	−0.620428	+	1.07461i	−0.0202361	+	0.0350500i
$941$	−24.0916	+	41.7278i	−0.785363	+	1.36029i	0.143419	+	0.989662i	$0.454190\pi$
$941$	−24.0916	+	41.7278i	−0.785363	+	1.36029i	−0.928782	+	0.370627i	$0.879143\pi$
$942$	7.20903	−	32.8766i	0.234883	−	1.07118i
$943$	−14.3571	−	8.28905i	−0.467530	−	0.269929i
$944$	−2.44760	−	4.23936i	−0.0796625	−	0.137980i
$945$	−4.17164	+	1.76187i	−0.135703	+	0.0573138i
$946$	2.26807	−	1.30947i	0.0737413	−	0.0425745i
$947$	−0.364925	+	0.210690i	−0.0118585	+	0.00684650i	−0.505918	−	0.862582i	$-0.668846\pi$
$947$	−0.364925	+	0.210690i	−0.0118585	+	0.00684650i	0.494059	+	0.869428i	$0.335513\pi$
$948$	−0.369089	+	0.404661i	−0.0119875	+	0.0131428i
$949$	−19.5364	+	11.2793i	−0.634178	+	0.366143i
$950$	21.2503	+	2.10394i	0.689449	+	0.0682609i
$951$	−1.59560	−	1.45534i	−0.0517409	−	0.0471926i
$952$	13.3210	−	7.69090i	0.431737	−	0.249263i
$953$	23.9224	−	41.4349i	0.774924	−	1.34221i	−0.159913	−	0.987131i	$-0.551121\pi$
$953$	23.9224	−	41.4349i	0.774924	−	1.34221i	0.934837	−	0.355077i	$-0.115545\pi$
$954$	−12.8165	−	5.90458i	−0.414949	−	0.191168i
$955$	−1.98148	+	3.43203i	−0.0641192	+	0.111058i
$956$		−	5.23668i		−	0.169366i
$957$	−2.51833	−	7.92332i	−0.0814059	−	0.256125i
$958$	−10.2165	+	5.89851i	−0.330081	+	0.190572i
$959$	2.77880	+	1.60434i	0.0897321	+	0.0518069i
$960$	0.370982	−	0.406736i	0.0119734	−	0.0131273i
$961$	23.4940	−	40.6927i	0.757870	−	1.31267i
$962$	−36.6159			−1.18054
$963$	0.582436	+	6.32118i	0.0187687	+	0.203697i
$964$	−14.5433	−	8.39659i	−0.468409	−	0.270436i
$965$	6.92023			0.222770
$966$	−6.19145	−	19.4799i	−0.199207	−	0.626757i
$967$	−51.5021			−1.65620			−0.828098	−	0.560584i	$-0.810577\pi$
$967$	−51.5021			−1.65620			−0.828098	+	0.560584i	$0.810577\pi$
$968$	5.37798	+	9.31493i	0.172855	+	0.299393i
$969$	40.2749	+	13.1033i	1.29382	+	0.420939i
$970$	−0.766665	+	1.32790i	−0.0246161	+	0.0426364i
$971$	−24.2447	+	41.9931i	−0.778050	+	1.34762i	0.155015	+	0.987912i	$0.450457\pi$
$971$	−24.2447	+	41.9931i	−0.778050	+	1.34762i	−0.933064	+	0.359709i	$0.882876\pi$
$972$	13.7432	−	7.35698i	0.440813	−	0.235975i
$973$	−21.4116	−	37.0859i	−0.686423	−	1.18892i
$974$	−10.2071	+	5.89310i	−0.327058	+	0.188827i
$975$	−9.30306	−	29.2699i	−0.297936	−	0.937387i
$976$	1.35187	+	2.34151i	0.0432723	+	0.0749499i
$977$	−26.0687	−	45.1524i	−0.834013	−	1.44455i	−0.894831	−	0.446404i	$-0.852704\pi$
$977$	−26.0687	−	45.1524i	−0.834013	−	1.44455i	0.0608182	−	0.998149i	$-0.480629\pi$
$978$	−4.85595	+	22.1455i	−0.155276	+	0.708134i
$979$			1.37345i			0.0438956i
$980$		−	0.164756i		−	0.00526293i
$981$	18.3466	−	39.8232i	0.585763	−	1.27146i
$982$	−15.8419	+	9.14633i	−0.505535	+	0.291871i
$983$	9.37483	+	16.2377i	0.299011	+	0.517902i	0.975910	−	0.218174i	$-0.0700100\pi$
$983$	9.37483	+	16.2377i	0.299011	+	0.517902i	−0.676899	+	0.736076i	$0.736677\pi$
$984$	4.92923	+	4.49593i	0.157138	+	0.143325i
$985$	8.35128			0.266094
$986$		−	54.5069i		−	1.73585i
$987$	−5.61624	−	17.6702i	−0.178767	−	0.562448i
$988$	1.55447	−	15.7004i	0.0494541	−	0.499497i
$989$		−	22.8166i		−	0.725525i
$990$	0.0432194	+	0.469060i	0.00137360	+	0.0149077i
$991$	26.0009	+	15.0116i	0.825945	+	0.476860i	0.852462	−	0.522789i	$-0.175108\pi$
$991$	26.0009	+	15.0116i	0.825945	+	0.476860i	−0.0265172	+	0.999648i	$0.508442\pi$
$992$		−	8.83108i		−	0.280387i
$993$	6.81348	+	21.4370i	0.216219	+	0.680283i
$994$	−18.4512	+	31.9584i	−0.585236	+	1.01366i
$995$	−0.193977	+	0.111993i	−0.00614949	+	0.00355041i
$996$	3.24970	+	0.712580i	0.102971	+	0.0225789i
$997$	−53.7594			−1.70258			−0.851289	−	0.524697i	$-0.824179\pi$
$997$	−53.7594			−1.70258			−0.851289	+	0.524697i	$0.824179\pi$
$998$	10.8098	+	18.7231i	0.342177	+	0.592668i
$999$	41.9233	+	31.7103i	1.32640	+	1.00327i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.j.d.65.3	✓	8
3.2	odd	2		1026.2.j.d.521.1		8
9.4	even	3		1026.2.n.d.179.3		8
9.5	odd	6		342.2.n.d.293.4	yes	8
19.12	odd	6		342.2.n.d.335.4	yes	8
57.50	even	6		1026.2.n.d.791.3		8
171.31	odd	6		1026.2.j.d.449.3		8
171.50	even	6	inner	342.2.j.d.221.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.j.d.65.3	✓	8	1.1	even	1	trivial
342.2.j.d.221.3	yes	8	171.50	even	6	inner
342.2.n.d.293.4	yes	8	9.5	odd	6
342.2.n.d.335.4	yes	8	19.12	odd	6
1026.2.j.d.449.3		8	171.31	odd	6
1026.2.j.d.521.1		8	3.2	odd	2
1026.2.n.d.179.3		8	9.4	even	3
1026.2.n.d.791.3		8	57.50	even	6

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.27970 + 1.16721i) q^{3} +(-0.500000 + 0.866025i) q^{4} -0.317837i q^{5} +(-0.370982 + 1.69185i) q^{6} +(-1.37098 + 2.37461i) q^{7} -1.00000 q^{8} +(0.275255 + 2.98735i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.27970 + 1.16721i) q^{3} +(-0.500000 + 0.866025i) q^{4} -0.317837i q^{5} +(-0.370982 + 1.69185i) q^{6} +(-1.37098 + 2.37461i) q^{7} -1.00000 q^{8} +(0.275255 + 2.98735i) q^{9} +(0.275255 - 0.158919i) q^{10} +(0.427828 + 0.247006i) q^{11} +(-1.65068 + 0.524648i) q^{12} +(-3.13461 - 1.80977i) q^{13} -2.74196 q^{14} +(0.370982 - 0.406736i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(4.85821 + 2.80489i) q^{17} +(-2.44949 + 1.73205i) q^{18} +(2.54077 - 3.54182i) q^{19} +(0.275255 + 0.158919i) q^{20} +(-4.52611 + 1.43856i) q^{21} +0.494013i q^{22} +(3.72730 + 2.15196i) q^{23} +(-1.27970 - 1.16721i) q^{24} +4.89898 q^{25} -3.61953i q^{26} +(-3.13461 + 4.14418i) q^{27} +(-1.37098 - 2.37461i) q^{28} -9.71641 q^{29} +(0.537734 + 0.117912i) q^{30} +(7.64794 - 4.41554i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.259183 + 0.815457i) q^{33} +5.60977i q^{34} +(0.754740 + 0.435749i) q^{35} +(-2.72474 - 1.25529i) q^{36} -10.1162i q^{37} +(4.33769 + 0.429466i) q^{38} +(-1.89898 - 5.97469i) q^{39} +0.317837i q^{40} -3.85187 q^{41} +(-3.50889 - 3.20044i) q^{42} +(-2.65068 - 4.59111i) q^{43} +(-0.427828 + 0.247006i) q^{44} +(0.949490 - 0.0874863i) q^{45} +4.30391i q^{46} +3.90406i q^{47} +(0.370982 - 1.69185i) q^{48} +(-0.259183 - 0.448918i) q^{49} +(2.44949 + 4.24264i) q^{50} +(2.94315 + 9.25994i) q^{51} +(3.13461 - 1.80977i) q^{52} +(2.35187 + 4.07356i) q^{53} +(-5.15627 - 0.642559i) q^{54} +(0.0785079 - 0.135980i) q^{55} +(1.37098 - 2.37461i) q^{56} +(7.38546 - 1.56685i) q^{57} +(-4.85821 - 8.41466i) q^{58} +4.89519 q^{59} +(0.166753 + 0.524648i) q^{60} -2.70374 q^{61} +(7.64794 + 4.41554i) q^{62} +(-7.47115 - 3.44197i) q^{63} +1.00000 q^{64} +(-0.575211 + 0.996295i) q^{65} +(-0.576615 + 0.632187i) q^{66} +(2.86076 + 1.65166i) q^{67} +(-4.85821 + 2.80489i) q^{68} +(2.25804 + 7.10438i) q^{69} +0.871498i q^{70} +(6.72919 - 11.6553i) q^{71} +(-0.275255 - 2.98735i) q^{72} +(3.11624 - 5.39749i) q^{73} +(8.76088 - 5.05810i) q^{74} +(6.26922 + 5.71812i) q^{75} +(1.79692 + 3.97128i) q^{76} +(-1.17309 + 0.677283i) q^{77} +(4.22474 - 4.63191i) q^{78} +(0.273851 - 0.158108i) q^{79} +(-0.275255 + 0.158919i) q^{80} +(-8.84847 + 1.64456i) q^{81} +(-1.92594 - 3.33582i) q^{82} +(-1.66346 - 0.960397i) q^{83} +(1.01722 - 4.63900i) q^{84} +(0.891497 - 1.54412i) q^{85} +(2.65068 - 4.59111i) q^{86} +(-12.4341 - 11.3411i) q^{87} +(-0.427828 - 0.247006i) q^{88} +(1.39009 + 2.40771i) q^{89} +(0.550510 + 0.778539i) q^{90} +(8.59498 - 4.96231i) q^{91} +(-3.72730 + 2.15196i) q^{92} +(14.9409 + 3.27617i) q^{93} +(-3.38101 + 1.95203i) q^{94} +(-1.12572 - 0.807552i) q^{95} +(1.65068 - 0.524648i) q^{96} +(-4.17793 + 2.41213i) q^{97} +(0.259183 - 0.448918i) q^{98} +(-0.620132 + 1.34606i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{7} - 8 q^{8} + 12 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^7 - 8 * q^8 + 12 * q^9	\( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{7} - 8 q^{8} + 12 q^{9} + 12 q^{10} - 16 q^{14} - 4 q^{16} + 12 q^{17} + 8 q^{19} + 12 q^{20} - 8 q^{28} - 24 q^{29} - 24 q^{31} + 4 q^{32} + 24 q^{35} - 12 q^{36} + 16 q^{38} + 24 q^{39} - 24 q^{41} + 12 q^{42} - 8 q^{43} - 12 q^{45} + 24 q^{51} + 12 q^{53} - 16 q^{55} + 8 q^{56} - 12 q^{57} - 12 q^{58} - 8 q^{61} - 24 q^{62} - 24 q^{63} + 8 q^{64} + 12 q^{66} - 24 q^{67} - 12 q^{68} + 24 q^{69} + 24 q^{71} - 12 q^{72} + 4 q^{73} - 24 q^{74} + 8 q^{76} + 12 q^{77} + 24 q^{78} + 24 q^{79} - 12 q^{80} - 12 q^{81} - 12 q^{82} - 24 q^{83} + 12 q^{84} - 4 q^{85} + 8 q^{86} - 48 q^{87} + 12 q^{89} + 24 q^{90} + 48 q^{91} + 60 q^{93} + 24 q^{94} - 24 q^{95} + 24 q^{97} - 48 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^7 - 8 * q^8 + 12 * q^9 + 12 * q^10 - 16 * q^14 - 4 * q^16 + 12 * q^17 + 8 * q^19 + 12 * q^20 - 8 * q^28 - 24 * q^29 - 24 * q^31 + 4 * q^32 + 24 * q^35 - 12 * q^36 + 16 * q^38 + 24 * q^39 - 24 * q^41 + 12 * q^42 - 8 * q^43 - 12 * q^45 + 24 * q^51 + 12 * q^53 - 16 * q^55 + 8 * q^56 - 12 * q^57 - 12 * q^58 - 8 * q^61 - 24 * q^62 - 24 * q^63 + 8 * q^64 + 12 * q^66 - 24 * q^67 - 12 * q^68 + 24 * q^69 + 24 * q^71 - 12 * q^72 + 4 * q^73 - 24 * q^74 + 8 * q^76 + 12 * q^77 + 24 * q^78 + 24 * q^79 - 12 * q^80 - 12 * q^81 - 12 * q^82 - 24 * q^83 + 12 * q^84 - 4 * q^85 + 8 * q^86 - 48 * q^87 + 12 * q^89 + 24 * q^90 + 48 * q^91 + 60 * q^93 + 24 * q^94 - 24 * q^95 + 24 * q^97 - 48 * q^99

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