LMFDB - Embedded newform 693.2.m.a.379.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(64,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("693.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (of order $5$, degree $4$, 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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			379.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	693.379
Dual form			693.2.m.a.64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.690983 - 2.12663i) q^{2} +(-2.42705 + 1.76336i) q^{4} +(0.190983 - 0.587785i) q^{5} +(-0.809017 + 0.587785i) q^{7} +(1.80902 + 1.31433i) q^{8} +O(q^{10})$	\(q+(-0.690983 - 2.12663i) q^{2} +(-2.42705 + 1.76336i) q^{4} +(0.190983 - 0.587785i) q^{5} +(-0.809017 + 0.587785i) q^{7} +(1.80902 + 1.31433i) q^{8} -1.38197 q^{10} +(0.309017 + 3.30220i) q^{11} +(1.00000 + 3.07768i) q^{13} +(1.80902 + 1.31433i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-1.50000 + 4.61653i) q^{17} +(-2.30902 - 1.67760i) q^{19} +(0.572949 + 1.76336i) q^{20} +(6.80902 - 2.93893i) q^{22} -4.38197 q^{23} +(3.73607 + 2.71441i) q^{25} +(5.85410 - 4.25325i) q^{26} +(0.927051 - 2.85317i) q^{28} +(-4.85410 + 3.52671i) q^{29} +(-0.954915 - 2.93893i) q^{31} +6.70820 q^{32} +10.8541 q^{34} +(0.190983 + 0.587785i) q^{35} +(-3.73607 + 2.71441i) q^{37} +(-1.97214 + 6.06961i) q^{38} +(1.11803 - 0.812299i) q^{40} +(5.97214 + 4.33901i) q^{41} +9.70820 q^{43} +(-6.57295 - 7.46969i) q^{44} +(3.02786 + 9.31881i) q^{46} +(3.61803 + 2.62866i) q^{47} +(0.309017 - 0.951057i) q^{49} +(3.19098 - 9.82084i) q^{50} +(-7.85410 - 5.70634i) q^{52} +(-2.09017 - 6.43288i) q^{53} +(2.00000 + 0.449028i) q^{55} -2.23607 q^{56} +(10.8541 + 7.88597i) q^{58} +(2.61803 - 1.90211i) q^{59} +(-5.59017 + 4.06150i) q^{62} +(-4.01722 - 12.3637i) q^{64} +2.00000 q^{65} +(-4.50000 - 13.8496i) q^{68} +(1.11803 - 0.812299i) q^{70} +(1.52786 - 4.70228i) q^{71} +(-11.0902 + 8.05748i) q^{73} +(8.35410 + 6.06961i) q^{74} +8.56231 q^{76} +(-2.19098 - 2.48990i) q^{77} +(-3.09017 - 9.51057i) q^{79} +(0.500000 + 0.363271i) q^{80} +(5.10081 - 15.6987i) q^{82} +(-5.09017 + 15.6659i) q^{83} +(2.42705 + 1.76336i) q^{85} +(-6.70820 - 20.6457i) q^{86} +(-3.78115 + 6.37988i) q^{88} -5.61803 q^{89} +(-2.61803 - 1.90211i) q^{91} +(10.6353 - 7.72696i) q^{92} +(3.09017 - 9.51057i) q^{94} +(-1.42705 + 1.03681i) q^{95} +(-1.85410 - 5.70634i) q^{97} -2.23607 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 5 q^{2} - 3 q^{4} + 3 q^{5} - q^{7} + 5 q^{8}+O(q^{10}) $ 4 * q - 5 * q^2 - 3 * q^4 + 3 * q^5 - q^7 + 5 * q^8	$ 4 q - 5 q^{2} - 3 q^{4} + 3 q^{5} - q^{7} + 5 q^{8} - 10 q^{10} - q^{11} + 4 q^{13} + 5 q^{14} + q^{16} - 6 q^{17} - 7 q^{19} + 9 q^{20} + 25 q^{22} - 22 q^{23} + 6 q^{25} + 10 q^{26} - 3 q^{28} - 6 q^{29} - 15 q^{31} + 30 q^{34} + 3 q^{35} - 6 q^{37} + 10 q^{38} + 6 q^{41} + 12 q^{43} - 33 q^{44} + 30 q^{46} + 10 q^{47} - q^{49} + 15 q^{50} - 18 q^{52} + 14 q^{53} + 8 q^{55} + 30 q^{58} + 6 q^{59} + 13 q^{64} + 8 q^{65} - 18 q^{68} + 24 q^{71} - 22 q^{73} + 20 q^{74} - 6 q^{76} - 11 q^{77} + 10 q^{79} + 2 q^{80} + 45 q^{82} + 2 q^{83} + 3 q^{85} + 5 q^{88} - 18 q^{89} - 6 q^{91} + 9 q^{92} - 10 q^{94} + q^{95} + 6 q^{97}+O(q^{100}) $ 4 * q - 5 * q^2 - 3 * q^4 + 3 * q^5 - q^7 + 5 * q^8 - 10 * q^10 - q^11 + 4 * q^13 + 5 * q^14 + q^16 - 6 * q^17 - 7 * q^19 + 9 * q^20 + 25 * q^22 - 22 * q^23 + 6 * q^25 + 10 * q^26 - 3 * q^28 - 6 * q^29 - 15 * q^31 + 30 * q^34 + 3 * q^35 - 6 * q^37 + 10 * q^38 + 6 * q^41 + 12 * q^43 - 33 * q^44 + 30 * q^46 + 10 * q^47 - q^49 + 15 * q^50 - 18 * q^52 + 14 * q^53 + 8 * q^55 + 30 * q^58 + 6 * q^59 + 13 * q^64 + 8 * q^65 - 18 * q^68 + 24 * q^71 - 22 * q^73 + 20 * q^74 - 6 * q^76 - 11 * q^77 + 10 * q^79 + 2 * q^80 + 45 * q^82 + 2 * q^83 + 3 * q^85 + 5 * q^88 - 18 * q^89 - 6 * q^91 + 9 * q^92 - 10 * q^94 + q^95 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.690983	−	2.12663i	−0.488599	−	1.50375i	−0.826700	−	0.562643i	$-0.809785\pi$
$2$	−0.690983	−	2.12663i	−0.488599	−	1.50375i	0.338101	−	0.941110i	$-0.390215\pi$
$3$		0			0
$3$		0			0
$4$	−2.42705	+	1.76336i	−1.21353	+	0.881678i
$5$	0.190983	−	0.587785i	0.0854102	−	0.262866i	−0.899226	−	0.437485i	$-0.855869\pi$
$5$	0.190983	−	0.587785i	0.0854102	−	0.262866i	0.984636	+	0.174619i	$0.0558694\pi$
$6$		0			0
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$8$	1.80902	+	1.31433i	0.639584	+	0.464685i
$9$		0			0
$10$	−1.38197			−0.437016
$11$	0.309017	+	3.30220i	0.0931721	+	0.995650i
$11$	0.309017	+	3.30220i	0.0931721	+	0.995650i
$12$		0			0
$13$	1.00000	+	3.07768i	0.277350	+	0.853596i	0.988588	+	0.150644i	$0.0481349\pi$
$13$	1.00000	+	3.07768i	0.277350	+	0.853596i	−0.711238	+	0.702951i	$0.751865\pi$
$14$	1.80902	+	1.31433i	0.483480	+	0.351269i
$15$		0			0
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	−1.50000	+	4.61653i	−0.363803	+	1.11967i	0.586924	+	0.809642i	$0.300339\pi$
$17$	−1.50000	+	4.61653i	−0.363803	+	1.11967i	−0.950727	+	0.310029i	$0.899661\pi$
$18$		0			0
$19$	−2.30902	−	1.67760i	−0.529725	−	0.384868i	0.290530	−	0.956866i	$-0.406168\pi$
$19$	−2.30902	−	1.67760i	−0.529725	−	0.384868i	−0.820255	+	0.571998i	$0.806168\pi$
$20$	0.572949	+	1.76336i	0.128115	+	0.394298i
$21$		0			0
$22$	6.80902	−	2.93893i	1.45169	−	0.626581i
$23$	−4.38197			−0.913703			−0.456852	−	0.889543i	$-0.651023\pi$
$23$	−4.38197			−0.913703			−0.456852	+	0.889543i	$0.651023\pi$
$24$		0			0
$25$	3.73607	+	2.71441i	0.747214	+	0.542882i
$26$	5.85410	−	4.25325i	1.14808	−	0.834132i
$27$		0			0
$28$	0.927051	−	2.85317i	0.175196	−	0.539198i
$29$	−4.85410	+	3.52671i	−0.901384	+	0.654894i	−0.938821	−	0.344405i	$-0.888081\pi$
$29$	−4.85410	+	3.52671i	−0.901384	+	0.654894i	0.0374370	+	0.999299i	$0.488081\pi$
$30$		0			0
$31$	−0.954915	−	2.93893i	−0.171508	−	0.527847i	0.827949	−	0.560803i	$-0.189508\pi$
$31$	−0.954915	−	2.93893i	−0.171508	−	0.527847i	−0.999457	+	0.0329567i	$0.989508\pi$
$32$	6.70820			1.18585
$33$		0			0
$34$	10.8541			1.86146
$35$	0.190983	+	0.587785i	0.0322820	+	0.0993538i
$36$		0			0
$37$	−3.73607	+	2.71441i	−0.614206	+	0.446247i	−0.850893	−	0.525339i	$-0.823938\pi$
$37$	−3.73607	+	2.71441i	−0.614206	+	0.446247i	0.236687	+	0.971586i	$0.423938\pi$
$38$	−1.97214	+	6.06961i	−0.319923	+	0.984621i
$39$		0			0
$40$	1.11803	−	0.812299i	0.176777	−	0.128436i
$41$	5.97214	+	4.33901i	0.932691	+	0.677640i	0.946650	−	0.322263i	$-0.104444\pi$
$41$	5.97214	+	4.33901i	0.932691	+	0.677640i	−0.0139593	+	0.999903i	$0.504444\pi$
$42$		0			0
$43$	9.70820			1.48049			0.740244	−	0.672339i	$-0.234710\pi$
$43$	9.70820			1.48049			0.740244	+	0.672339i	$0.234710\pi$
$44$	−6.57295	−	7.46969i	−0.990909	−	1.12610i
$45$		0			0
$46$	3.02786	+	9.31881i	0.446434	+	1.37398i
$47$	3.61803	+	2.62866i	0.527744	+	0.383429i	0.819513	−	0.573060i	$-0.194244\pi$
$47$	3.61803	+	2.62866i	0.527744	+	0.383429i	−0.291769	+	0.956489i	$0.594244\pi$
$48$		0			0
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	3.19098	−	9.82084i	0.451273	−	1.38888i
$51$		0			0
$52$	−7.85410	−	5.70634i	−1.08917	−	0.791327i
$53$	−2.09017	−	6.43288i	−0.287107	−	0.883624i	−0.985759	−	0.168163i	$-0.946217\pi$
$53$	−2.09017	−	6.43288i	−0.287107	−	0.883624i	0.698652	−	0.715461i	$-0.253783\pi$
$54$		0			0
$55$	2.00000	+	0.449028i	0.269680	+	0.0605469i
$56$	−2.23607			−0.298807
$57$		0			0
$58$	10.8541	+	7.88597i	1.42521	+	1.03548i
$59$	2.61803	−	1.90211i	0.340839	−	0.247634i	−0.404177	−	0.914681i	$-0.632442\pi$
$59$	2.61803	−	1.90211i	0.340839	−	0.247634i	0.745016	+	0.667047i	$0.232442\pi$
$60$		0			0
$61$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$61$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$62$	−5.59017	+	4.06150i	−0.709952	+	0.515811i
$63$		0			0
$64$	−4.01722	−	12.3637i	−0.502153	−	1.54547i
$65$	2.00000			0.248069
$66$		0			0
$67$		0			0			−	1.00000i	$-0.5\pi$
$67$		0			0				1.00000i	$0.5\pi$
$68$	−4.50000	−	13.8496i	−0.545705	−	1.67951i
$69$		0			0
$70$	1.11803	−	0.812299i	0.133631	−	0.0970883i
$71$	1.52786	−	4.70228i	0.181324	−	0.558058i	−0.818542	−	0.574447i	$-0.805217\pi$
$71$	1.52786	−	4.70228i	0.181324	−	0.558058i	0.999866	+	0.0163891i	$0.00521704\pi$
$72$		0			0
$73$	−11.0902	+	8.05748i	−1.29801	+	0.943057i	−0.999934	−	0.0114866i	$-0.996344\pi$
$73$	−11.0902	+	8.05748i	−1.29801	+	0.943057i	−0.298072	+	0.954543i	$0.596344\pi$
$74$	8.35410	+	6.06961i	0.971145	+	0.705578i
$75$		0			0
$76$	8.56231			0.982164
$77$	−2.19098	−	2.48990i	−0.249686	−	0.283750i
$78$		0			0
$79$	−3.09017	−	9.51057i	−0.347671	−	1.07002i	−0.960138	−	0.279526i	$-0.909823\pi$
$79$	−3.09017	−	9.51057i	−0.347671	−	1.07002i	0.612467	−	0.790496i	$-0.290177\pi$
$80$	0.500000	+	0.363271i	0.0559017	+	0.0406150i
$81$		0			0
$82$	5.10081	−	15.6987i	0.563291	−	1.73363i
$83$	−5.09017	+	15.6659i	−0.558719	+	1.71956i	0.127196	+	0.991878i	$0.459402\pi$
$83$	−5.09017	+	15.6659i	−0.558719	+	1.71956i	−0.685915	+	0.727682i	$0.740598\pi$
$84$		0			0
$85$	2.42705	+	1.76336i	0.263251	+	0.191263i
$86$	−6.70820	−	20.6457i	−0.723364	−	2.22629i
$87$		0			0
$88$	−3.78115	+	6.37988i	−0.403072	+	0.680098i
$89$	−5.61803			−0.595510			−0.297755	−	0.954642i	$-0.596238\pi$
$89$	−5.61803			−0.595510			−0.297755	+	0.954642i	$0.596238\pi$
$90$		0			0
$91$	−2.61803	−	1.90211i	−0.274445	−	0.199396i
$92$	10.6353	−	7.72696i	1.10880	−	0.805592i
$93$		0			0
$94$	3.09017	−	9.51057i	0.318727	−	0.980940i
$95$	−1.42705	+	1.03681i	−0.146412	+	0.106375i
$96$		0			0
$97$	−1.85410	−	5.70634i	−0.188256	−	0.579391i	0.811734	−	0.584028i	$-0.198524\pi$
$97$	−1.85410	−	5.70634i	−0.188256	−	0.579391i	−0.999989	+	0.00463676i	$0.998524\pi$
$98$	−2.23607			−0.225877
$99$		0			0
$100$	−13.8541			−1.38541
$101$	2.10081	+	6.46564i	0.209039	+	0.643355i	0.999523	+	0.0308731i	$0.00982877\pi$
$101$	2.10081	+	6.46564i	0.209039	+	0.643355i	−0.790485	+	0.612482i	$0.790171\pi$
$102$		0			0
$103$	−1.07295	+	0.779543i	−0.105721	+	0.0768107i	−0.639390	−	0.768883i	$-0.720813\pi$
$103$	−1.07295	+	0.779543i	−0.105721	+	0.0768107i	0.533669	+	0.845694i	$0.320813\pi$
$104$	−2.23607	+	6.88191i	−0.219265	+	0.674827i
$105$		0			0
$106$	−12.2361	+	8.89002i	−1.18847	+	0.863475i
$107$	12.7812	+	9.28605i	1.23560	+	0.897716i	0.997297	−	0.0734743i	$-0.0234087\pi$
$107$	12.7812	+	9.28605i	1.23560	+	0.897716i	0.238304	+	0.971191i	$0.423409\pi$
$108$		0			0
$109$	−17.5623			−1.68216			−0.841082	−	0.540908i	$-0.818081\pi$
$109$	−17.5623			−1.68216			−0.841082	+	0.540908i	$0.818081\pi$
$110$	−0.427051	−	4.56352i	−0.0407177	−	0.435115i
$111$		0			0
$112$	−0.309017	−	0.951057i	−0.0291994	−	0.0898664i
$113$	−4.23607	−	3.07768i	−0.398496	−	0.289524i	0.370432	−	0.928859i	$-0.379210\pi$
$113$	−4.23607	−	3.07768i	−0.398496	−	0.289524i	−0.768928	+	0.639335i	$0.779210\pi$
$114$		0			0
$115$	−0.836881	+	2.57565i	−0.0780396	+	0.240181i
$116$	5.56231	−	17.1190i	0.516447	−	1.58946i
$117$		0			0
$118$	−5.85410	−	4.25325i	−0.538914	−	0.391544i
$119$	−1.50000	−	4.61653i	−0.137505	−	0.423196i
$120$		0			0
$121$	−10.8090	+	2.04087i	−0.982638	+	0.185534i
$122$		0			0
$123$		0			0
$124$	7.50000	+	5.44907i	0.673520	+	0.489341i
$125$	4.80902	−	3.49396i	0.430132	−	0.312509i
$126$		0			0
$127$	0.0901699	−	0.277515i	0.00800129	−	0.0246254i	−0.946976	−	0.321304i	$-0.895879\pi$
$127$	0.0901699	−	0.277515i	0.00800129	−	0.0246254i	0.954977	+	0.296678i	$0.0958789\pi$
$128$	−12.6631	+	9.20029i	−1.11927	+	0.813199i
$129$		0			0
$130$	−1.38197	−	4.25325i	−0.121206	−	0.373035i
$131$	16.6525			1.45493			0.727467	−	0.686143i	$-0.240698\pi$
$131$	16.6525			1.45493			0.727467	+	0.686143i	$0.240698\pi$
$132$		0			0
$133$	2.85410			0.247482
$134$		0			0
$135$		0			0
$136$	−8.78115	+	6.37988i	−0.752978	+	0.547070i
$137$	−2.52786	+	7.77997i	−0.215970	+	0.664687i	0.783113	+	0.621879i	$0.213630\pi$
$137$	−2.52786	+	7.77997i	−0.215970	+	0.664687i	−0.999083	+	0.0428083i	$0.986370\pi$
$138$		0			0
$139$	−10.6353	+	7.72696i	−0.902071	+	0.655393i	−0.938997	−	0.343925i	$-0.888243\pi$
$139$	−10.6353	+	7.72696i	−0.902071	+	0.655393i	0.0369264	+	0.999318i	$0.488243\pi$
$140$	−1.50000	−	1.08981i	−0.126773	−	0.0921061i
$141$		0			0
$142$	−11.0557			−0.927776
$143$	−9.85410	+	4.25325i	−0.824041	+	0.355675i
$144$		0			0
$145$	1.14590	+	3.52671i	0.0951617	+	0.292877i
$146$	24.7984	+	18.0171i	2.05233	+	1.49110i
$147$		0			0
$148$	4.28115	−	13.1760i	0.351909	−	1.08306i
$149$	1.52786	−	4.70228i	0.125167	−	0.385226i	−0.868764	−	0.495226i	$-0.835085\pi$
$149$	1.52786	−	4.70228i	0.125167	−	0.385226i	0.993932	+	0.110000i	$0.0350852\pi$
$150$		0			0
$151$	12.5623	+	9.12705i	1.02231	+	0.742749i	0.966754	−	0.255707i	$-0.0823083\pi$
$151$	12.5623	+	9.12705i	1.02231	+	0.742749i	0.0555516	+	0.998456i	$0.482308\pi$
$152$	−1.97214	−	6.06961i	−0.159961	−	0.492310i
$153$		0			0
$154$	−3.78115	+	6.37988i	−0.304694	+	0.514105i
$155$	−1.90983			−0.153401
$156$		0			0
$157$	18.7082	+	13.5923i	1.49308	+	1.08478i	0.973039	+	0.230641i	$0.0740824\pi$
$157$	18.7082	+	13.5923i	1.49308	+	1.08478i	0.520038	+	0.854143i	$0.325918\pi$
$158$	−18.0902	+	13.1433i	−1.43918	+	1.04562i
$159$		0			0
$160$	1.28115	−	3.94298i	0.101284	−	0.311720i
$161$	3.54508	−	2.57565i	0.279392	−	0.202990i
$162$		0			0
$163$	−3.09017	−	9.51057i	−0.242041	−	0.744925i	−0.996109	−	0.0881289i	$-0.971911\pi$
$163$	−3.09017	−	9.51057i	−0.242041	−	0.744925i	0.754068	−	0.656796i	$-0.228089\pi$
$164$	−22.1459			−1.72930
$165$		0			0
$166$	36.8328			2.85878
$167$	6.56231	+	20.1967i	0.507806	+	1.56287i	0.796001	+	0.605296i	$0.206945\pi$
$167$	6.56231	+	20.1967i	0.507806	+	1.56287i	−0.288194	+	0.957572i	$0.593055\pi$
$168$		0			0
$169$	2.04508	−	1.48584i	0.157314	−	0.114295i
$170$	2.07295	−	6.37988i	0.158988	−	0.489315i
$171$		0			0
$172$	−23.5623	+	17.1190i	−1.79661	+	1.30531i
$173$	−11.0172	−	8.00448i	−0.837624	−	0.608569i	0.0840821	−	0.996459i	$-0.473204\pi$
$173$	−11.0172	−	8.00448i	−0.837624	−	0.608569i	−0.921706	+	0.387890i	$0.873204\pi$
$174$		0			0
$175$	−4.61803			−0.349091
$176$	−3.23607	−	0.726543i	−0.243928	−	0.0547652i
$177$		0			0
$178$	3.88197	+	11.9475i	0.290966	+	0.895500i
$179$	−11.9721	−	8.69827i	−0.894839	−	0.650139i	0.0422959	−	0.999105i	$-0.486533\pi$
$179$	−11.9721	−	8.69827i	−0.894839	−	0.650139i	−0.937135	+	0.348966i	$0.886533\pi$
$180$		0			0
$181$	−6.14590	+	18.9151i	−0.456821	+	1.40595i	0.412163	+	0.911110i	$0.364773\pi$
$181$	−6.14590	+	18.9151i	−0.456821	+	1.40595i	−0.868984	+	0.494840i	$0.835227\pi$
$182$	−2.23607	+	6.88191i	−0.165748	+	0.510121i
$183$		0			0
$184$	−7.92705	−	5.75934i	−0.584390	−	0.424584i
$185$	0.881966	+	2.71441i	0.0648434	+	0.199568i
$186$		0			0
$187$	−15.7082	−	3.52671i	−1.14870	−	0.257899i
$188$	−13.4164			−0.978492
$189$		0			0
$190$	3.19098	+	2.31838i	0.231498	+	0.168193i
$191$	3.97214	−	2.88593i	0.287414	−	0.208818i	−0.434731	−	0.900560i	$-0.643157\pi$
$191$	3.97214	−	2.88593i	0.287414	−	0.208818i	0.722145	+	0.691742i	$0.243157\pi$
$192$		0			0
$193$	−6.75329	+	20.7845i	−0.486112	+	1.49610i	0.344251	+	0.938878i	$0.388133\pi$
$193$	−6.75329	+	20.7845i	−0.486112	+	1.49610i	−0.830363	+	0.557222i	$0.811867\pi$
$194$	−10.8541	+	7.88597i	−0.779279	+	0.566179i
$195$		0			0
$196$	0.927051	+	2.85317i	0.0662179	+	0.203798i
$197$	−22.4721			−1.60107			−0.800537	−	0.599284i	$-0.795452\pi$
$197$	−22.4721			−1.60107			−0.800537	+	0.599284i	$0.795452\pi$
$198$		0			0
$199$	13.1459			0.931888			0.465944	−	0.884814i	$-0.345715\pi$
$199$	13.1459			0.931888			0.465944	+	0.884814i	$0.345715\pi$
$200$	3.19098	+	9.82084i	0.225637	+	0.694438i
$201$		0			0
$202$	12.2984	−	8.93529i	0.865311	−	0.628685i
$203$	1.85410	−	5.70634i	0.130132	−	0.400506i
$204$		0			0
$205$	3.69098	−	2.68166i	0.257789	−	0.187295i
$206$	2.39919	+	1.74311i	0.167159	+	0.121448i
$207$		0			0
$208$	−3.23607			−0.224381
$209$	4.82624	−	8.14324i	0.333838	−	0.563279i
$210$		0			0
$211$	−5.67376	−	17.4620i	−0.390598	−	1.20214i	−0.932337	−	0.361590i	$-0.882234\pi$
$211$	−5.67376	−	17.4620i	−0.390598	−	1.20214i	0.541739	−	0.840547i	$-0.317766\pi$
$212$	16.4164	+	11.9272i	1.12748	+	0.819165i
$213$		0			0
$214$	10.9164	−	33.5972i	0.746230	−	2.29666i
$215$	1.85410	−	5.70634i	0.126449	−	0.389169i
$216$		0			0
$217$	2.50000	+	1.81636i	0.169711	+	0.123302i
$218$	12.1353	+	37.3485i	0.821903	+	2.52956i
$219$		0			0
$220$	−5.64590	+	2.43690i	−0.380646	+	0.164296i
$221$	−15.7082			−1.05665
$222$		0			0
$223$	−15.8713	−	11.5312i	−1.06282	−	0.772186i	−0.0882139	−	0.996102i	$-0.528116\pi$
$223$	−15.8713	−	11.5312i	−1.06282	−	0.772186i	−0.974608	+	0.223916i	$0.928116\pi$
$224$	−5.42705	+	3.94298i	−0.362610	+	0.263452i
$225$		0			0
$226$	−3.61803	+	11.1352i	−0.240668	+	0.740700i
$227$	10.0902	−	7.33094i	0.669708	−	0.486571i	−0.200219	−	0.979751i	$-0.564165\pi$
$227$	10.0902	−	7.33094i	0.669708	−	0.486571i	0.869927	+	0.493180i	$0.164165\pi$
$228$		0			0
$229$	5.00000	+	15.3884i	0.330409	+	1.01690i	0.968939	+	0.247298i	$0.0795428\pi$
$229$	5.00000	+	15.3884i	0.330409	+	1.01690i	−0.638530	+	0.769597i	$0.720457\pi$
$230$	6.05573			0.399303
$231$		0			0
$232$	−13.4164			−0.880830
$233$	4.85410	+	14.9394i	0.318003	+	0.978712i	0.974501	+	0.224384i	$0.0720370\pi$
$233$	4.85410	+	14.9394i	0.318003	+	0.978712i	−0.656498	+	0.754328i	$0.727963\pi$
$234$		0			0
$235$	2.23607	−	1.62460i	0.145865	−	0.105977i
$236$	−3.00000	+	9.23305i	−0.195283	+	0.601020i
$237$		0			0
$238$	−8.78115	+	6.37988i	−0.569198	+	0.413546i
$239$	−15.3992	−	11.1882i	−0.996091	−	0.723702i	−0.0348442	−	0.999393i	$-0.511093\pi$
$239$	−15.3992	−	11.1882i	−0.996091	−	0.723702i	−0.961246	+	0.275691i	$0.911093\pi$
$240$		0			0
$241$	12.0000			0.772988			0.386494	−	0.922292i	$-0.373686\pi$
$241$	12.0000			0.772988			0.386494	+	0.922292i	$0.373686\pi$
$242$	11.8090	+	21.5765i	0.759112	+	1.38699i
$243$		0			0
$244$		0			0
$245$	−0.500000	−	0.363271i	−0.0319438	−	0.0232085i
$246$		0			0
$247$	2.85410	−	8.78402i	0.181602	−	0.558914i
$248$	2.13525	−	6.57164i	0.135589	−	0.417299i
$249$		0			0
$250$	−10.7533	−	7.81272i	−0.680098	−	0.494120i
$251$	−8.56231	−	26.3521i	−0.540448	−	1.66333i	−0.731574	−	0.681762i	$-0.761214\pi$
$251$	−8.56231	−	26.3521i	−0.540448	−	1.66333i	0.191126	−	0.981566i	$-0.438786\pi$
$252$		0			0
$253$	−1.35410	−	14.4701i	−0.0851317	−	0.909728i
$254$	−0.652476			−0.0409400
$255$		0			0
$256$	7.28115	+	5.29007i	0.455072	+	0.330629i
$257$	19.7812	−	14.3718i	1.23391	−	0.896491i	0.236737	−	0.971574i	$-0.423922\pi$
$257$	19.7812	−	14.3718i	1.23391	−	0.896491i	0.997177	+	0.0750824i	$0.0239220\pi$
$258$		0			0
$259$	1.42705	−	4.39201i	0.0886726	−	0.272906i
$260$	−4.85410	+	3.52671i	−0.301039	+	0.218717i
$261$		0			0
$262$	−11.5066	−	35.4136i	−0.710879	−	2.18786i
$263$	−10.8541			−0.669293			−0.334646	−	0.942344i	$-0.608617\pi$
$263$	−10.8541			−0.669293			−0.334646	+	0.942344i	$0.608617\pi$
$264$		0			0
$265$	−4.18034			−0.256796
$266$	−1.97214	−	6.06961i	−0.120919	−	0.372152i
$267$		0			0
$268$		0			0
$269$	4.14590	−	12.7598i	0.252780	−	0.777976i	−0.741479	−	0.670976i	$-0.765875\pi$
$269$	4.14590	−	12.7598i	0.252780	−	0.777976i	0.994259	−	0.107000i	$-0.0341246\pi$
$270$		0			0
$271$	18.2082	−	13.2290i	1.10607	−	0.803607i	0.124029	−	0.992279i	$-0.460418\pi$
$271$	18.2082	−	13.2290i	1.10607	−	0.803607i	0.982040	+	0.188672i	$0.0604183\pi$
$272$	−3.92705	−	2.85317i	−0.238112	−	0.172999i
$273$		0			0
$274$	18.2918			1.10505
$275$	−7.80902	+	13.1760i	−0.470901	+	0.794545i
$276$		0			0
$277$	−0.0278640	−	0.0857567i	−0.00167419	−	0.00515262i	0.950216	−	0.311592i	$-0.100862\pi$
$277$	−0.0278640	−	0.0857567i	−0.00167419	−	0.00515262i	−0.951890	+	0.306440i	$0.900862\pi$
$278$	23.7812	+	17.2780i	1.42630	+	1.03627i
$279$		0			0
$280$	−0.427051	+	1.31433i	−0.0255212	+	0.0785461i
$281$	8.32624	−	25.6255i	0.496702	−	1.52869i	−0.317586	−	0.948229i	$-0.602872\pi$
$281$	8.32624	−	25.6255i	0.496702	−	1.52869i	0.814288	−	0.580461i	$-0.197128\pi$
$282$		0			0
$283$	13.9721	+	10.1514i	0.830557	+	0.603435i	0.919717	−	0.392582i	$-0.128418\pi$
$283$	13.9721	+	10.1514i	0.830557	+	0.603435i	−0.0891597	+	0.996017i	$0.528418\pi$
$284$	4.58359	+	14.1068i	0.271986	+	0.837087i
$285$		0			0
$286$	15.8541	+	18.0171i	0.937473	+	1.06537i
$287$	−7.38197			−0.435744
$288$		0			0
$289$	−5.30902	−	3.85723i	−0.312295	−	0.226896i
$290$	6.70820	−	4.87380i	0.393919	−	0.286199i
$291$		0			0
$292$	12.7082	−	39.1118i	0.743691	−	2.28885i
$293$	−14.7361	+	10.7064i	−0.860890	+	0.625473i	−0.928127	−	0.372264i	$-0.878582\pi$
$293$	−14.7361	+	10.7064i	−0.860890	+	0.625473i	0.0672367	+	0.997737i	$0.478582\pi$
$294$		0			0
$295$	−0.618034	−	1.90211i	−0.0359833	−	0.110745i
$296$	−10.3262			−0.600200
$297$		0			0
$298$	−11.0557			−0.640441
$299$	−4.38197	−	13.4863i	−0.253416	−	0.779933i
$300$		0			0
$301$	−7.85410	+	5.70634i	−0.452703	+	0.328908i
$302$	10.7295	−	33.0220i	0.617413	−	1.90020i
$303$		0			0
$304$	2.30902	−	1.67760i	0.132431	−	0.0962169i
$305$		0			0
$306$		0			0
$307$	−17.5623			−1.00233			−0.501167	−	0.865351i	$-0.667096\pi$
$307$	−17.5623			−1.00233			−0.501167	+	0.865351i	$0.667096\pi$
$308$	9.70820	+	2.17963i	0.553176	+	0.124196i
$309$		0			0
$310$	1.31966	+	4.06150i	0.0749517	+	0.230677i
$311$	16.7082	+	12.1392i	0.947435	+	0.688352i	0.950199	−	0.311644i	$-0.100880\pi$
$311$	16.7082	+	12.1392i	0.947435	+	0.688352i	−0.00276357	+	0.999996i	$0.500880\pi$
$312$		0			0
$313$	−2.41641	+	7.43694i	−0.136583	+	0.420361i	−0.995833	−	0.0911961i	$-0.970931\pi$
$313$	−2.41641	+	7.43694i	−0.136583	+	0.420361i	0.859250	+	0.511557i	$0.170931\pi$
$314$	15.9787	−	49.1774i	0.901731	−	2.77524i
$315$		0			0
$316$	24.2705	+	17.6336i	1.36532	+	0.991965i
$317$	−2.09017	−	6.43288i	−0.117396	−	0.361307i	0.875044	−	0.484044i	$-0.160833\pi$
$317$	−2.09017	−	6.43288i	−0.117396	−	0.361307i	−0.992439	+	0.122738i	$0.960833\pi$
$318$		0			0
$319$	−13.1459	−	14.9394i	−0.736029	−	0.836445i
$320$	−8.03444			−0.449139
$321$		0			0
$322$	−7.92705	−	5.75934i	−0.441757	−	0.320955i
$323$	11.2082	−	8.14324i	0.623641	−	0.453102i
$324$		0			0
$325$	−4.61803	+	14.2128i	−0.256162	+	0.788387i
$326$	−18.0902	+	13.1433i	−1.00192	+	0.727939i
$327$		0			0
$328$	5.10081	+	15.6987i	0.281645	+	0.866815i
$329$	−4.47214			−0.246557
$330$		0			0
$331$	17.4164			0.957292			0.478646	−	0.878008i	$-0.341128\pi$
$331$	17.4164			0.957292			0.478646	+	0.878008i	$0.341128\pi$
$332$	−15.2705	−	46.9978i	−0.838078	−	2.57934i
$333$		0			0
$334$	38.4164	−	27.9112i	2.10205	−	1.52723i
$335$		0			0
$336$		0			0
$337$	−21.9164	+	15.9232i	−1.19386	+	0.867392i	−0.993667	−	0.112364i	$-0.964158\pi$
$337$	−21.9164	+	15.9232i	−1.19386	+	0.867392i	−0.200196	+	0.979756i	$0.564158\pi$
$338$	−4.57295	−	3.32244i	−0.248736	−	0.180717i
$339$		0			0
$340$	−9.00000			−0.488094
$341$	9.40983	−	4.06150i	0.509571	−	0.219942i
$342$		0			0
$343$	0.309017	+	0.951057i	0.0166853	+	0.0513522i
$344$	17.5623	+	12.7598i	0.946896	+	0.687960i
$345$		0			0
$346$	−9.40983	+	28.9605i	−0.505876	+	1.55692i
$347$	4.48278	−	13.7966i	0.240648	−	0.740639i	−0.755674	−	0.654948i	$-0.772690\pi$
$347$	4.48278	−	13.7966i	0.240648	−	0.740639i	0.996322	−	0.0856906i	$-0.0273096\pi$
$348$		0			0
$349$	17.5623	+	12.7598i	0.940089	+	0.683014i	0.948442	−	0.316951i	$-0.102659\pi$
$349$	17.5623	+	12.7598i	0.940089	+	0.683014i	−0.00835333	+	0.999965i	$0.502659\pi$
$350$	3.19098	+	9.82084i	0.170565	+	0.524946i
$351$		0			0
$352$	2.07295	+	22.1518i	0.110489	+	1.18070i
$353$	18.0000			0.958043			0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000			0.958043			0.479022	+	0.877803i	$0.340992\pi$
$354$		0			0
$355$	−2.47214	−	1.79611i	−0.131207	−	0.0953277i
$356$	13.6353	−	9.90659i	0.722667	−	0.525048i
$357$		0			0
$358$	−10.2254	+	31.4706i	−0.540430	+	1.66327i
$359$	5.20820	−	3.78398i	0.274878	−	0.199711i	−0.441802	−	0.897113i	$-0.645661\pi$
$359$	5.20820	−	3.78398i	0.274878	−	0.199711i	0.716680	+	0.697402i	$0.245661\pi$
$360$		0			0
$361$	−3.35410	−	10.3229i	−0.176532	−	0.543309i
$362$	44.4721			2.33740
$363$		0			0
$364$	9.70820			0.508848
$365$	2.61803	+	8.05748i	0.137034	+	0.421748i
$366$		0			0
$367$	−2.20820	+	1.60435i	−0.115267	+	0.0837466i	−0.643926	−	0.765088i	$-0.722695\pi$
$367$	−2.20820	+	1.60435i	−0.115267	+	0.0837466i	0.528658	+	0.848835i	$0.322695\pi$
$368$	1.35410	−	4.16750i	0.0705874	−	0.217246i
$369$		0			0
$370$	5.16312	−	3.75123i	0.268418	−	0.195017i
$371$	5.47214	+	3.97574i	0.284099	+	0.206410i
$372$		0			0
$373$	16.3262			0.845341			0.422670	−	0.906284i	$-0.361093\pi$
$373$	16.3262			0.845341			0.422670	+	0.906284i	$0.361093\pi$
$374$	3.35410	+	35.8424i	0.173436	+	1.85337i
$375$		0			0
$376$	3.09017	+	9.51057i	0.159363	+	0.490470i
$377$	−15.7082	−	11.4127i	−0.809014	−	0.587783i
$378$		0			0
$379$	6.65248	−	20.4742i	0.341715	−	1.05169i	−0.621604	−	0.783331i	$-0.713519\pi$
$379$	6.65248	−	20.4742i	0.341715	−	1.05169i	0.963319	−	0.268358i	$-0.0864812\pi$
$380$	1.63525	−	5.03280i	0.0838868	−	0.258177i
$381$		0			0
$382$	−8.88197	−	6.45313i	−0.454441	−	0.330171i
$383$	6.43769	+	19.8132i	0.328951	+	1.01241i	0.969626	+	0.244594i	$0.0786547\pi$
$383$	6.43769	+	19.8132i	0.328951	+	1.01241i	−0.640675	+	0.767812i	$0.721345\pi$
$384$		0			0
$385$	−1.88197	+	0.812299i	−0.0959139	+	0.0413986i
$386$	48.8673			2.48728
$387$		0			0
$388$	14.5623	+	10.5801i	0.739289	+	0.537125i
$389$	12.3262	−	8.95554i	0.624965	−	0.454064i	−0.229687	−	0.973264i	$-0.573770\pi$
$389$	12.3262	−	8.95554i	0.624965	−	0.454064i	0.854652	+	0.519201i	$0.173770\pi$
$390$		0			0
$391$	6.57295	−	20.2295i	0.332408	−	1.02305i
$392$	1.80902	−	1.31433i	0.0913692	−	0.0663836i
$393$		0			0
$394$	15.5279	+	47.7899i	0.782282	+	2.40762i
$395$	−6.18034			−0.310967
$396$		0			0
$397$	30.5410			1.53281			0.766405	−	0.642358i	$-0.222044\pi$
$397$	30.5410			1.53281			0.766405	+	0.642358i	$0.222044\pi$
$398$	−9.08359	−	27.9564i	−0.455319	−	1.40133i
$399$		0			0
$400$	−3.73607	+	2.71441i	−0.186803	+	0.135721i
$401$	−2.29180	+	7.05342i	−0.114447	+	0.352231i	−0.991831	−	0.127557i	$-0.959286\pi$
$401$	−2.29180	+	7.05342i	−0.114447	+	0.352231i	0.877384	+	0.479788i	$0.159286\pi$
$402$		0			0
$403$	8.09017	−	5.87785i	0.403000	−	0.292797i
$404$	−16.5000	−	11.9880i	−0.820906	−	0.596423i
$405$		0			0
$406$	−13.4164			−0.665845
$407$	−10.1180	−	11.4984i	−0.501532	−	0.569956i
$408$		0			0
$409$	−6.85410	−	21.0948i	−0.338914	−	1.04307i	−0.964762	−	0.263124i	$-0.915247\pi$
$409$	−6.85410	−	21.0948i	−0.338914	−	1.04307i	0.625849	−	0.779945i	$-0.284753\pi$
$410$	−8.25329	−	5.99637i	−0.407601	−	0.296139i
$411$		0			0
$412$	1.22949	−	3.78398i	0.0605726	−	0.186423i
$413$	−1.00000	+	3.07768i	−0.0492068	+	0.151443i
$414$		0			0
$415$	8.23607	+	5.98385i	0.404293	+	0.293736i
$416$	6.70820	+	20.6457i	0.328897	+	1.01224i
$417$		0			0
$418$	−20.6525	−	4.63677i	−1.01015	−	0.226792i
$419$	3.23607			0.158092			0.0790461	−	0.996871i	$-0.474813\pi$
$419$	3.23607			0.158092			0.0790461	+	0.996871i	$0.474813\pi$
$420$		0			0
$421$	−7.92705	−	5.75934i	−0.386341	−	0.280693i	0.377614	−	0.925963i	$-0.376745\pi$
$421$	−7.92705	−	5.75934i	−0.386341	−	0.280693i	−0.763954	+	0.645270i	$0.776745\pi$
$422$	−33.2148	+	24.1320i	−1.61687	+	1.17473i
$423$		0			0
$424$	4.67376	−	14.3844i	0.226978	−	0.698566i
$425$	−18.1353	+	13.1760i	−0.879689	+	0.639132i
$426$		0			0
$427$		0			0
$428$	−47.3951			−2.29093
$429$		0			0
$430$	−13.4164			−0.646997
$431$	−4.66312	−	14.3516i	−0.224615	−	0.691292i	−0.998331	−	0.0577598i	$-0.981604\pi$
$431$	−4.66312	−	14.3516i	−0.224615	−	0.691292i	0.773716	−	0.633533i	$-0.218396\pi$
$432$		0			0
$433$	25.2705	−	18.3601i	1.21442	−	0.882330i	0.218798	−	0.975770i	$-0.429786\pi$
$433$	25.2705	−	18.3601i	1.21442	−	0.882330i	0.995625	+	0.0934400i	$0.0297863\pi$
$434$	2.13525	−	6.57164i	0.102496	−	0.315449i
$435$		0			0
$436$	42.6246	−	30.9686i	2.04135	−	1.48313i
$437$	10.1180	+	7.35118i	0.484011	+	0.351655i
$438$		0			0
$439$	1.85410			0.0884915			0.0442457	−	0.999021i	$-0.485912\pi$
$439$	1.85410			0.0884915			0.0442457	+	0.999021i	$0.485912\pi$
$440$	3.02786	+	3.44095i	0.144348	+	0.164041i
$441$		0			0
$442$	10.8541	+	33.4055i	0.516277	+	1.58894i
$443$	16.4894	+	11.9802i	0.783433	+	0.569197i	0.906007	−	0.423262i	$-0.139115\pi$
$443$	16.4894	+	11.9802i	0.783433	+	0.569197i	−0.122574	+	0.992459i	$0.539115\pi$
$444$		0			0
$445$	−1.07295	+	3.30220i	−0.0508627	+	0.156539i
$446$	−13.5557	+	41.7202i	−0.641882	+	1.97551i
$447$		0			0
$448$	10.5172	+	7.64121i	0.496892	+	0.361013i
$449$	12.9443	+	39.8384i	0.610878	+	1.88009i	0.449747	+	0.893156i	$0.351514\pi$
$449$	12.9443	+	39.8384i	0.610878	+	1.88009i	0.161131	+	0.986933i	$0.448486\pi$
$450$		0			0
$451$	−12.4828	+	21.0620i	−0.587791	+	0.991771i
$452$	15.7082			0.738852
$453$		0			0
$454$	−22.5623	−	16.3925i	−1.05890	−	0.769337i
$455$	−1.61803	+	1.17557i	−0.0758546	+	0.0551116i
$456$		0			0
$457$	6.61803	−	20.3682i	0.309579	−	0.952785i	−0.668350	−	0.743847i	$-0.732999\pi$
$457$	6.61803	−	20.3682i	0.309579	−	0.952785i	0.977929	−	0.208938i	$-0.0670007\pi$
$458$	29.2705	−	21.2663i	1.36772	−	0.993708i
$459$		0			0
$460$	−2.51064	−	7.72696i	−0.117059	−	0.360272i
$461$	6.00000			0.279448			0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000			0.279448			0.139724	+	0.990190i	$0.455378\pi$
$462$		0			0
$463$	−23.4164			−1.08825			−0.544126	−	0.839003i	$-0.683139\pi$
$463$	−23.4164			−1.08825			−0.544126	+	0.839003i	$0.683139\pi$
$464$	−1.85410	−	5.70634i	−0.0860745	−	0.264910i
$465$		0			0
$466$	28.4164	−	20.6457i	1.31636	−	0.956395i
$467$	−8.09017	+	24.8990i	−0.374368	+	1.15219i	0.569535	+	0.821967i	$0.307123\pi$
$467$	−8.09017	+	24.8990i	−0.374368	+	1.15219i	−0.943904	+	0.330221i	$0.892877\pi$
$468$		0			0
$469$		0			0
$470$	−5.00000	−	3.63271i	−0.230633	−	0.167565i
$471$		0			0
$472$	7.23607			0.333067
$473$	3.00000	+	32.0584i	0.137940	+	1.47405i
$474$		0			0
$475$	−4.07295	−	12.5352i	−0.186880	−	0.575157i
$476$	11.7812	+	8.55951i	0.539988	+	0.392324i
$477$		0			0
$478$	−13.1525	+	40.4792i	−0.601580	+	1.85147i
$479$	0.291796	−	0.898056i	0.0133325	−	0.0410332i	−0.944169	−	0.329462i	$-0.893133\pi$
$479$	0.291796	−	0.898056i	0.0133325	−	0.0410332i	0.957501	+	0.288428i	$0.0931327\pi$
$480$		0			0
$481$	−12.0902	−	8.78402i	−0.551264	−	0.400517i
$482$	−8.29180	−	25.5195i	−0.377681	−	1.16238i
$483$		0			0
$484$	22.6353	−	24.0134i	1.02888	−	1.09152i
$485$	−3.70820			−0.168381
$486$		0			0
$487$	−22.4164	−	16.2865i	−1.01578	−	0.738011i	−0.0503700	−	0.998731i	$-0.516040\pi$
$487$	−22.4164	−	16.2865i	−1.01578	−	0.738011i	−0.965414	+	0.260720i	$0.916040\pi$
$488$		0			0
$489$		0			0
$490$	−0.427051	+	1.31433i	−0.0192922	+	0.0593753i
$491$	1.21885	−	0.885544i	0.0550058	−	0.0399641i	−0.559943	−	0.828531i	$-0.689177\pi$
$491$	1.21885	−	0.885544i	0.0550058	−	0.0399641i	0.614948	+	0.788567i	$0.289177\pi$
$492$		0			0
$493$	−9.00000	−	27.6992i	−0.405340	−	1.24751i
$494$	−20.6525			−0.929199
$495$		0			0
$496$	3.09017			0.138753
$497$	1.52786	+	4.70228i	0.0685341	+	0.210926i
$498$		0			0
$499$	−17.0902	+	12.4167i	−0.765061	+	0.555849i	−0.900458	−	0.434942i	$-0.856769\pi$
$499$	−17.0902	+	12.4167i	−0.765061	+	0.555849i	0.135397	+	0.990791i	$0.456769\pi$
$500$	−5.51064	+	16.9600i	−0.246443	+	0.758475i
$501$		0			0
$502$	−50.1246	+	36.4177i	−2.23717	+	1.62540i
$503$	−11.7082	−	8.50651i	−0.522043	−	0.379286i	0.295330	−	0.955395i	$-0.404570\pi$
$503$	−11.7082	−	8.50651i	−0.522043	−	0.379286i	−0.817373	+	0.576109i	$0.804570\pi$
$504$		0			0
$505$	4.20163			0.186970
$506$	−29.8369	+	12.8783i	−1.32641	+	0.572509i
$507$		0			0
$508$	0.270510	+	0.832544i	0.0120019	+	0.0369382i
$509$	−21.9164	−	15.9232i	−0.971428	−	0.705784i	−0.0156512	−	0.999878i	$-0.504982\pi$
$509$	−21.9164	−	15.9232i	−0.971428	−	0.705784i	−0.955777	+	0.294094i	$0.904982\pi$
$510$		0			0
$511$	4.23607	−	13.0373i	0.187393	−	0.576735i
$512$	−3.45492	+	10.6331i	−0.152687	+	0.469923i
$513$		0			0
$514$	−44.2320	−	32.1364i	−1.95099	−	1.41748i
$515$	0.253289	+	0.779543i	0.0111612	+	0.0343508i
$516$		0			0
$517$	−7.56231	+	12.7598i	−0.332590	+	0.561174i
$518$	−10.3262			−0.453709
$519$		0			0
$520$	3.61803	+	2.62866i	0.158661	+	0.115274i
$521$	−9.97214	+	7.24518i	−0.436887	+	0.317417i	−0.784397	−	0.620259i	$-0.787027\pi$
$521$	−9.97214	+	7.24518i	−0.436887	+	0.317417i	0.347510	+	0.937676i	$0.387027\pi$
$522$		0			0
$523$	4.06231	−	12.5025i	0.177632	−	0.546696i	−0.822112	−	0.569326i	$-0.807204\pi$
$523$	4.06231	−	12.5025i	0.177632	−	0.546696i	0.999744	+	0.0226305i	$0.00720412\pi$
$524$	−40.4164	+	29.3642i	−1.76560	+	1.28278i
$525$		0			0
$526$	7.50000	+	23.0826i	0.327016	+	1.00645i
$527$	15.0000			0.653410
$528$		0			0
$529$	−3.79837			−0.165147
$530$	2.88854	+	8.89002i	0.125470	+	0.386158i
$531$		0			0
$532$	−6.92705	+	5.03280i	−0.300326	+	0.218199i
$533$	−7.38197	+	22.7194i	−0.319748	+	0.984085i
$534$		0			0
$535$	7.89919	−	5.73910i	0.341512	−	0.248123i
$536$		0			0
$537$		0			0
$538$	−30.0000			−1.29339
$539$	3.23607	+	0.726543i	0.139387	+	0.0312944i
$540$		0			0
$541$	−5.04508	−	15.5272i	−0.216905	−	0.667565i	−0.999013	−	0.0444221i	$-0.985855\pi$
$541$	−5.04508	−	15.5272i	−0.216905	−	0.667565i	0.782108	−	0.623143i	$-0.214145\pi$
$542$	−40.7148	−	29.5810i	−1.74885	−	1.27061i
$543$		0			0
$544$	−10.0623	+	30.9686i	−0.431418	+	1.32777i
$545$	−3.35410	+	10.3229i	−0.143674	+	0.442183i
$546$		0			0
$547$	29.5066	+	21.4378i	1.26161	+	0.916613i	0.998836	−	0.0482438i	$-0.0153624\pi$
$547$	29.5066	+	21.4378i	1.26161	+	0.916613i	0.262775	+	0.964857i	$0.415362\pi$
$548$	−7.58359	−	23.3399i	−0.323955	−	0.997031i
$549$		0			0
$550$	33.4164	+	7.50245i	1.42488	+	0.319906i
$551$	17.1246			0.729533
$552$		0			0
$553$	8.09017	+	5.87785i	0.344029	+	0.249952i
$554$	−0.163119	+	0.118513i	−0.00693026	+	0.00503513i
$555$		0			0
$556$	12.1869	−	37.5075i	0.516840	−	1.59067i
$557$	18.0902	−	13.1433i	0.766505	−	0.556899i	−0.134394	−	0.990928i	$-0.542909\pi$
$557$	18.0902	−	13.1433i	0.766505	−	0.556899i	0.900899	+	0.434029i	$0.142909\pi$
$558$		0			0
$559$	9.70820	+	29.8788i	0.410613	+	1.26374i
$560$	−0.618034			−0.0261167
$561$		0			0
$562$	−60.2492			−2.54146
$563$	2.94427	+	9.06154i	0.124086	+	0.381898i	0.993733	−	0.111775i	$-0.0356537\pi$
$563$	2.94427	+	9.06154i	0.124086	+	0.381898i	−0.869647	+	0.493674i	$0.835654\pi$
$564$		0			0
$565$	−2.61803	+	1.90211i	−0.110142	+	0.0800225i
$566$	11.9336	−	36.7279i	0.501608	−	1.54379i
$567$		0			0
$568$	8.94427	−	6.49839i	0.375293	−	0.272667i
$569$	9.38197	+	6.81640i	0.393312	+	0.285758i	0.766812	−	0.641872i	$-0.221842\pi$
$569$	9.38197	+	6.81640i	0.393312	+	0.285758i	−0.373499	+	0.927631i	$0.621842\pi$
$570$		0			0
$571$	15.3475			0.642274			0.321137	−	0.947033i	$-0.395935\pi$
$571$	15.3475			0.642274			0.321137	+	0.947033i	$0.395935\pi$
$572$	16.4164	−	27.6992i	0.686404	−	1.15816i
$573$		0			0
$574$	5.10081	+	15.6987i	0.212904	+	0.655251i
$575$	−16.3713	−	11.8945i	−0.682731	−	0.496033i
$576$		0			0
$577$	−11.0344	+	33.9605i	−0.459370	+	1.41379i	0.406558	+	0.913625i	$0.366729\pi$
$577$	−11.0344	+	33.9605i	−0.459370	+	1.41379i	−0.865927	+	0.500170i	$0.833271\pi$
$578$	−4.53444	+	13.9556i	−0.188608	+	0.580475i
$579$		0			0
$580$	−9.00000	−	6.53888i	−0.373705	−	0.271512i
$581$	−5.09017	−	15.6659i	−0.211176	−	0.649932i
$582$		0			0
$583$	20.5967	−	8.89002i	0.853030	−	0.368187i
$584$	−30.6525			−1.26841
$585$		0			0
$586$	32.9508	+	23.9402i	1.36119	+	0.988960i
$587$	−1.14590	+	0.832544i	−0.0472963	+	0.0343628i	−0.611182	−	0.791490i	$-0.709306\pi$
$587$	−1.14590	+	0.832544i	−0.0472963	+	0.0343628i	0.563886	+	0.825853i	$0.309306\pi$
$588$		0			0
$589$	−2.72542	+	8.38800i	−0.112299	+	0.345621i
$590$	−3.61803	+	2.62866i	−0.148952	+	0.108220i
$591$		0			0
$592$	−1.42705	−	4.39201i	−0.0586514	−	0.180511i
$593$	−22.5066			−0.924234			−0.462117	−	0.886819i	$-0.652910\pi$
$593$	−22.5066			−0.924234			−0.462117	+	0.886819i	$0.652910\pi$
$594$		0			0
$595$	−3.00000			−0.122988
$596$	4.58359	+	14.1068i	0.187751	+	0.577839i
$597$		0			0
$598$	−25.6525	+	18.6376i	−1.04901	+	0.762149i
$599$	7.29837	−	22.4621i	0.298203	−	0.917776i	−0.683923	−	0.729554i	$-0.739728\pi$
$599$	7.29837	−	22.4621i	0.298203	−	0.917776i	0.982127	−	0.188222i	$-0.0602724\pi$
$600$		0			0
$601$	−2.85410	+	2.07363i	−0.116421	+	0.0845850i	−0.644472	−	0.764628i	$-0.722923\pi$
$601$	−2.85410	+	2.07363i	−0.116421	+	0.0845850i	0.528051	+	0.849213i	$0.322923\pi$
$602$	17.5623	+	12.7598i	0.715786	+	0.520049i
$603$		0			0
$604$	−46.5836			−1.89546
$605$	−0.864745	+	6.74315i	−0.0351569	+	0.274148i
$606$		0			0
$607$	−3.70163	−	11.3924i	−0.150244	−	0.462405i	0.847404	−	0.530949i	$-0.178164\pi$
$607$	−3.70163	−	11.3924i	−0.150244	−	0.462405i	−0.997648	+	0.0685445i	$0.978164\pi$
$608$	−15.4894	−	11.2537i	−0.628176	−	0.456397i
$609$		0			0
$610$		0			0
$611$	−4.47214	+	13.7638i	−0.180923	+	0.556825i
$612$		0			0
$613$	17.7812	+	12.9188i	0.718174	+	0.521784i	0.885800	−	0.464067i	$-0.153610\pi$
$613$	17.7812	+	12.9188i	0.718174	+	0.521784i	−0.167626	+	0.985851i	$0.553610\pi$
$614$	12.1353	+	37.3485i	0.489739	+	1.50726i
$615$		0			0
$616$	−0.690983	−	7.38394i	−0.0278405	−	0.297507i
$617$	14.0689			0.566392			0.283196	−	0.959062i	$-0.408605\pi$
$617$	14.0689			0.566392			0.283196	+	0.959062i	$0.408605\pi$
$618$		0			0
$619$	29.6803	+	21.5640i	1.19295	+	0.866732i	0.993573	−	0.113191i	$-0.0361071\pi$
$619$	29.6803	+	21.5640i	1.19295	+	0.866732i	0.199380	+	0.979922i	$0.436107\pi$
$620$	4.63525	−	3.36771i	0.186156	−	0.135250i
$621$		0			0
$622$	14.2705	−	43.9201i	0.572195	−	1.76104i
$623$	4.54508	−	3.30220i	0.182095	−	0.132300i
$624$		0			0
$625$	6.00000	+	18.4661i	0.240000	+	0.738644i
$626$	17.4853			0.698853
$627$		0			0
$628$	−69.3738			−2.76832
$629$	−6.92705	−	21.3193i	−0.276200	−	0.850055i
$630$		0			0
$631$	36.6525	−	26.6296i	1.45911	−	1.06011i	0.475519	−	0.879705i	$-0.342260\pi$
$631$	36.6525	−	26.6296i	1.45911	−	1.06011i	0.983593	−	0.180401i	$-0.0577397\pi$
$632$	6.90983	−	21.2663i	0.274858	−	0.845927i
$633$		0			0
$634$	−12.2361	+	8.89002i	−0.485956	+	0.353068i
$635$	−0.145898	−	0.106001i	−0.00578979	−	0.00420653i
$636$		0			0
$637$	3.23607			0.128218
$638$	−22.6869	+	38.2793i	−0.898184	+	1.51549i
$639$		0			0
$640$	2.98936	+	9.20029i	0.118165	+	0.363674i
$641$	10.3262	+	7.50245i	0.407862	+	0.296329i	0.772736	−	0.634728i	$-0.218888\pi$
$641$	10.3262	+	7.50245i	0.407862	+	0.296329i	−0.364874	+	0.931057i	$0.618888\pi$
$642$		0			0
$643$	3.17376	−	9.76784i	0.125161	−	0.385206i	−0.868769	−	0.495217i	$-0.835089\pi$
$643$	3.17376	−	9.76784i	0.125161	−	0.385206i	0.993930	+	0.110011i	$0.0350886\pi$
$644$	−4.06231	+	12.5025i	−0.160077	+	0.492667i
$645$		0			0
$646$	−25.0623	−	18.2088i	−0.986063	−	0.716417i
$647$	−11.2705	−	34.6871i	−0.443089	−	1.36369i	−0.884565	−	0.466416i	$-0.845545\pi$
$647$	−11.2705	−	34.6871i	−0.443089	−	1.36369i	0.441476	−	0.897273i	$-0.354455\pi$
$648$		0			0
$649$	7.09017	+	8.05748i	0.278314	+	0.316284i
$650$	33.4164			1.31070
$651$		0			0
$652$	24.2705	+	17.6336i	0.950507	+	0.690583i
$653$	13.2361	−	9.61657i	0.517967	−	0.376325i	−0.297870	−	0.954606i	$-0.596276\pi$
$653$	13.2361	−	9.61657i	0.517967	−	0.376325i	0.815838	+	0.578281i	$0.196276\pi$
$654$		0			0
$655$	3.18034	−	9.78808i	0.124266	−	0.382452i
$656$	−5.97214	+	4.33901i	−0.233173	+	0.169410i
$657$		0			0
$658$	3.09017	+	9.51057i	0.120467	+	0.370760i
$659$	25.8541			1.00713			0.503566	−	0.863957i	$-0.332021\pi$
$659$	25.8541			1.00713			0.503566	+	0.863957i	$0.332021\pi$
$660$		0			0
$661$	−32.5410			−1.26570			−0.632849	−	0.774275i	$-0.718115\pi$
$661$	−32.5410			−1.26570			−0.632849	+	0.774275i	$0.718115\pi$
$662$	−12.0344	−	37.0382i	−0.467732	−	1.43953i
$663$		0			0
$664$	−29.7984	+	21.6498i	−1.15640	+	0.840175i
$665$	0.545085	−	1.67760i	0.0211375	−	0.0650545i
$666$		0			0
$667$	21.2705	−	15.4539i	0.823597	−	0.598379i
$668$	−51.5410	−	37.4467i	−1.99418	−	1.44886i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−13.8541	−	42.6385i	−0.534036	−	1.64359i	−0.745722	−	0.666257i	$-0.767895\pi$
$673$	−13.8541	−	42.6385i	−0.534036	−	1.64359i	0.211686	−	0.977338i	$-0.432105\pi$
$674$	49.0066	+	35.6054i	1.88766	+	1.37147i
$675$		0			0
$676$	−2.34346	+	7.21242i	−0.0901330	+	0.277401i
$677$	−10.6180	+	32.6789i	−0.408084	+	1.25595i	0.510208	+	0.860051i	$0.329568\pi$
$677$	−10.6180	+	32.6789i	−0.408084	+	1.25595i	−0.918292	+	0.395903i	$0.870432\pi$
$678$		0			0
$679$	4.85410	+	3.52671i	0.186283	+	0.135343i
$680$	2.07295	+	6.37988i	0.0794940	+	0.244657i
$681$		0			0
$682$	−15.1393	−	17.2048i	−0.579715	−	0.658805i
$683$	−26.7984			−1.02541			−0.512706	−	0.858564i	$-0.671357\pi$
$683$	−26.7984			−1.02541			−0.512706	+	0.858564i	$0.671357\pi$
$684$		0			0
$685$	4.09017	+	2.97168i	0.156277	+	0.113542i
$686$	1.80902	−	1.31433i	0.0690686	−	0.0501813i
$687$		0			0
$688$	−3.00000	+	9.23305i	−0.114374	+	0.352007i
$689$	17.7082	−	12.8658i	0.674629	−	0.490147i
$690$		0			0
$691$	15.0623	+	46.3570i	0.572997	+	1.76350i	0.642900	+	0.765950i	$0.277731\pi$
$691$	15.0623	+	46.3570i	0.572997	+	1.76350i	−0.0699030	+	0.997554i	$0.522269\pi$
$692$	40.8541			1.55304
$693$		0			0
$694$	−32.4377			−1.23132
$695$	2.51064	+	7.72696i	0.0952341	+	0.293100i
$696$		0			0
$697$	−28.9894	+	21.0620i	−1.09805	+	0.797780i
$698$	15.0000	−	46.1653i	0.567758	−	1.74738i
$699$		0			0
$700$	11.2082	−	8.14324i	0.423630	−	0.307785i
$701$	32.0344	+	23.2744i	1.20992	+	0.879061i	0.995224	−	0.0976186i	$-0.0311225\pi$
$701$	32.0344	+	23.2744i	1.20992	+	0.879061i	0.214700	+	0.976680i	$0.431123\pi$
$702$		0			0
$703$	13.1803			0.497106
$704$	39.5861	−	17.0863i	1.49196	−	0.643963i
$705$		0			0
$706$	−12.4377	−	38.2793i	−0.468099	−	1.44066i
$707$	−5.50000	−	3.99598i	−0.206849	−	0.150284i
$708$		0			0
$709$	−2.48278	+	7.64121i	−0.0932427	+	0.286972i	−0.986792	−	0.161994i	$-0.948207\pi$
$709$	−2.48278	+	7.64121i	−0.0932427	+	0.286972i	0.893549	+	0.448966i	$0.148207\pi$
$710$	−2.11146	+	6.49839i	−0.0792415	+	0.243880i
$711$		0			0
$712$	−10.1631	−	7.38394i	−0.380879	−	0.276725i
$713$	4.18441	+	12.8783i	0.156707	+	0.482295i
$714$		0			0
$715$	0.618034	+	6.60440i	0.0231132	+	0.246990i
$716$	44.3951			1.65912
$717$		0			0
$718$	−11.6459	−	8.46124i	−0.434621	−	0.315771i
$719$	31.5623	−	22.9314i	1.17708	−	0.855195i	0.185237	−	0.982694i	$-0.440695\pi$
$719$	31.5623	−	22.9314i	1.17708	−	0.855195i	0.991839	+	0.127499i	$0.0406948\pi$
$720$		0			0
$721$	0.409830	−	1.26133i	0.0152629	−	0.0469743i
$722$	−19.6353	+	14.2658i	−0.730749	+	0.530920i
$723$		0			0
$724$	−18.4377	−	56.7454i	−0.685232	−	2.10893i
$725$	−27.7082			−1.02906
$726$		0			0
$727$	−18.8541			−0.699260			−0.349630	−	0.936888i	$-0.613693\pi$
$727$	−18.8541			−0.699260			−0.349630	+	0.936888i	$0.613693\pi$
$728$	−2.23607	−	6.88191i	−0.0828742	−	0.255061i
$729$		0			0
$730$	15.3262	−	11.1352i	0.567250	−	0.412131i
$731$	−14.5623	+	44.8182i	−0.538606	+	1.65766i
$732$		0			0
$733$	14.6180	−	10.6206i	0.539929	−	0.392282i	−0.284129	−	0.958786i	$-0.591705\pi$
$733$	14.6180	−	10.6206i	0.539929	−	0.392282i	0.824059	+	0.566504i	$0.191705\pi$
$734$	4.93769	+	3.58744i	0.182254	+	0.132415i
$735$		0			0
$736$	−29.3951			−1.08352
$737$		0			0
$738$		0			0
$739$	12.7082	+	39.1118i	0.467479	+	1.43875i	0.855838	+	0.517244i	$0.173042\pi$
$739$	12.7082	+	39.1118i	0.467479	+	1.43875i	−0.388359	+	0.921508i	$0.626958\pi$
$740$	−6.92705	−	5.03280i	−0.254643	−	0.185009i
$741$		0			0
$742$	4.67376	−	14.3844i	0.171579	−	0.528066i
$743$	5.04508	−	15.5272i	0.185086	−	0.569637i	−0.814864	−	0.579653i	$-0.803188\pi$
$743$	5.04508	−	15.5272i	0.185086	−	0.569637i	0.999950	+	0.0100159i	$0.00318822\pi$
$744$		0			0
$745$	−2.47214	−	1.79611i	−0.0905721	−	0.0658044i
$746$	−11.2812	−	34.7198i	−0.413032	−	1.27118i
$747$		0			0
$748$	44.3435	−	19.1396i	1.62136	−	0.699815i
$749$	−15.7984			−0.577260
$750$		0			0
$751$	−19.4164	−	14.1068i	−0.708515	−	0.514766i	0.174179	−	0.984714i	$-0.444273\pi$
$751$	−19.4164	−	14.1068i	−0.708515	−	0.514766i	−0.882694	+	0.469948i	$0.844273\pi$
$752$	−3.61803	+	2.62866i	−0.131936	+	0.0958572i
$753$		0			0
$754$	−13.4164	+	41.2915i	−0.488597	+	1.50375i
$755$	7.76393	−	5.64083i	0.282558	−	0.205291i
$756$		0			0
$757$	3.26393	+	10.0453i	0.118630	+	0.365104i	0.992687	−	0.120719i	$-0.0385199\pi$
$757$	3.26393	+	10.0453i	0.118630	+	0.365104i	−0.874057	+	0.485823i	$0.838520\pi$
$758$	−48.1378			−1.74844
$759$		0			0
$760$	−3.94427			−0.143074
$761$	−0.437694	−	1.34708i	−0.0158664	−	0.0488318i	0.942810	−	0.333331i	$-0.108173\pi$
$761$	−0.437694	−	1.34708i	−0.0158664	−	0.0488318i	−0.958676	+	0.284499i	$0.908173\pi$
$762$		0			0
$763$	14.2082	−	10.3229i	0.514372	−	0.373713i
$764$	−4.55166	+	14.0086i	−0.164673	+	0.506813i
$765$		0			0
$766$	37.6869	−	27.3811i	1.36168	−	0.989321i
$767$	8.47214	+	6.15537i	0.305911	+	0.222257i
$768$		0			0
$769$	1.05573			0.0380705			0.0190353	−	0.999819i	$-0.493941\pi$
$769$	1.05573			0.0380705			0.0190353	+	0.999819i	$0.493941\pi$
$770$	3.02786	+	3.44095i	0.109117	+	0.124003i
$771$		0			0
$772$	−20.2599	−	62.3535i	−0.729169	−	2.24415i
$773$	6.85410	+	4.97980i	0.246525	+	0.179111i	0.704185	−	0.710016i	$-0.251312\pi$
$773$	6.85410	+	4.97980i	0.246525	+	0.179111i	−0.457660	+	0.889127i	$0.651312\pi$
$774$		0			0
$775$	4.40983	−	13.5721i	0.158406	−	0.487523i
$776$	4.14590	−	12.7598i	0.148829	−	0.458049i
$777$		0			0
$778$	−27.5623	−	20.0252i	−0.988157	−	0.717938i
$779$	−6.51064	−	20.0377i	−0.233268	−	0.717925i
$780$		0			0
$781$	16.0000	+	3.59222i	0.572525	+	0.128540i
$782$	−47.5623			−1.70082
$783$		0			0
$784$	0.809017	+	0.587785i	0.0288935	+	0.0209923i
$785$	11.5623	−	8.40051i	0.412676	−	0.299827i
$786$		0			0
$787$	−7.98936	+	24.5887i	−0.284790	+	0.876493i	0.701672	+	0.712500i	$0.252437\pi$
$787$	−7.98936	+	24.5887i	−0.284790	+	0.876493i	−0.986462	+	0.163993i	$0.947563\pi$
$788$	54.5410	−	39.6264i	1.94294	−	1.41163i
$789$		0			0
$790$	4.27051	+	13.1433i	0.151938	+	0.467617i
$791$	5.23607			0.186173
$792$		0			0
$793$		0			0
$794$	−21.1033	−	64.9494i	−0.748929	−	2.30497i
$795$		0			0
$796$	−31.9058	+	23.1809i	−1.13087	+	0.821625i
$797$	−12.8435	+	39.5281i	−0.454939	+	1.40016i	0.416269	+	0.909242i	$0.363338\pi$
$797$	−12.8435	+	39.5281i	−0.454939	+	1.40016i	−0.871207	+	0.490915i	$0.836662\pi$
$798$		0			0
$799$	−17.5623	+	12.7598i	−0.621310	+	0.451408i
$800$	25.0623	+	18.2088i	0.886086	+	0.643779i
$801$		0			0
$802$	16.5836			0.585587
$803$	−30.0344	−	34.1320i	−1.05989	−	1.20449i
$804$		0			0
$805$	−0.836881	−	2.57565i	−0.0294962	−	0.0907799i
$806$	−18.0902	−	13.1433i	−0.637199	−	0.462952i
$807$		0			0
$808$	−4.69756	+	14.4576i	−0.165260	+	0.508617i
$809$	−2.23607	+	6.88191i	−0.0786160	+	0.241955i	−0.982639	−	0.185529i	$-0.940600\pi$
$809$	−2.23607	+	6.88191i	−0.0786160	+	0.241955i	0.904023	+	0.427484i	$0.140600\pi$
$810$		0			0
$811$	−6.94427	−	5.04531i	−0.243846	−	0.177165i	0.459149	−	0.888359i	$-0.348154\pi$
$811$	−6.94427	−	5.04531i	−0.243846	−	0.177165i	−0.702995	+	0.711195i	$0.748154\pi$
$812$	5.56231	+	17.1190i	0.195199	+	0.600760i
$813$		0			0
$814$	−17.4615	+	29.4625i	−0.612025	+	1.03266i
$815$	−6.18034			−0.216488
$816$		0			0
$817$	−22.4164	−	16.2865i	−0.784251	−	0.569792i
$818$	−40.1246	+	29.1522i	−1.40292	+	1.01928i
$819$		0			0
$820$	−4.22949	+	13.0170i	−0.147700	+	0.454574i
$821$	−8.85410	+	6.43288i	−0.309010	+	0.224509i	−0.731472	−	0.681872i	$-0.761166\pi$
$821$	−8.85410	+	6.43288i	−0.309010	+	0.224509i	0.422461	+	0.906381i	$0.361166\pi$
$822$		0			0
$823$	1.49342	+	4.59628i	0.0520574	+	0.160216i	0.973705	−	0.227811i	$-0.0731567\pi$
$823$	1.49342	+	4.59628i	0.0520574	+	0.160216i	−0.921648	+	0.388027i	$0.873157\pi$
$824$	−2.96556			−0.103310
$825$		0			0
$826$	7.23607			0.251775
$827$	−9.22949	−	28.4054i	−0.320941	−	0.987754i	−0.973240	−	0.229792i	$-0.926195\pi$
$827$	−9.22949	−	28.4054i	−0.320941	−	0.987754i	0.652299	−	0.757962i	$-0.273805\pi$
$828$		0			0
$829$	24.4721	−	17.7800i	0.849952	−	0.617527i	−0.0751805	−	0.997170i	$-0.523953\pi$
$829$	24.4721	−	17.7800i	0.849952	−	0.617527i	0.925133	+	0.379643i	$0.123953\pi$
$830$	7.03444	−	21.6498i	0.244169	−	0.751475i
$831$		0			0
$832$	34.0344	−	24.7275i	1.17993	−	0.857271i
$833$	3.92705	+	2.85317i	0.136064	+	0.0988565i
$834$		0			0
$835$	13.1246			0.454196
$836$	2.64590	+	28.2744i	0.0915103	+	0.977891i
$837$		0			0
$838$	−2.23607	−	6.88191i	−0.0772437	−	0.237732i
$839$	−32.5623	−	23.6579i	−1.12418	−	0.816761i	−0.139339	−	0.990245i	$-0.544498\pi$
$839$	−32.5623	−	23.6579i	−1.12418	−	0.816761i	−0.984837	+	0.173483i	$0.944498\pi$
$840$		0			0
$841$	2.16312	−	6.65740i	0.0745903	−	0.229565i
$842$	−6.77051	+	20.8375i	−0.233327	+	0.718107i
$843$		0			0
$844$	44.5623	+	32.3764i	1.53390	+	1.11444i
$845$	−0.482779	−	1.48584i	−0.0166081	−	0.0511145i
$846$		0			0
$847$	7.54508	−	8.00448i	0.259252	−	0.275037i
$848$	6.76393			0.232274
$849$		0			0
$850$	40.5517	+	29.4625i	1.39091	+	1.01056i
$851$	16.3713	−	11.8945i	0.561202	−	0.407737i
$852$		0			0
$853$	−12.8885	+	39.6669i	−0.441295	+	1.35817i	0.445201	+	0.895431i	$0.353132\pi$
$853$	−12.8885	+	39.6669i	−0.441295	+	1.35817i	−0.886496	+	0.462736i	$0.846868\pi$
$854$		0			0
$855$		0			0
$856$	10.9164	+	33.5972i	0.373115	+	1.14833i
$857$	34.3607			1.17374			0.586869	−	0.809682i	$-0.300360\pi$
$857$	34.3607			1.17374			0.586869	+	0.809682i	$0.300360\pi$
$858$		0			0
$859$	12.0000			0.409435			0.204717	−	0.978821i	$-0.434372\pi$
$859$	12.0000			0.409435			0.204717	+	0.978821i	$0.434372\pi$
$860$	5.56231	+	17.1190i	0.189673	+	0.583754i
$861$		0			0
$862$	−27.2984	+	19.8334i	−0.929786	+	0.675529i
$863$	3.80902	−	11.7229i	0.129660	−	0.399054i	−0.865061	−	0.501667i	$-0.832720\pi$
$863$	3.80902	−	11.7229i	0.129660	−	0.399054i	0.994721	+	0.102613i	$0.0327203\pi$
$864$		0			0
$865$	−6.80902	+	4.94704i	−0.231514	+	0.168204i
$866$	−56.5066	−	41.0544i	−1.92017	−	1.39509i
$867$		0			0
$868$	−9.27051			−0.314662
$869$	30.4508	−	13.1433i	1.03297	−	0.445855i
$870$		0			0
$871$		0			0
$872$	−31.7705	−	23.0826i	−1.07589	−	0.781676i
$873$		0			0
$874$	8.64183	−	26.5968i	0.292314	−	0.899651i
$875$	−1.83688	+	5.65334i	−0.0620979	+	0.191118i
$876$		0			0
$877$	−10.0902	−	7.33094i	−0.340721	−	0.247548i	0.404245	−	0.914651i	$-0.367534\pi$
$877$	−10.0902	−	7.33094i	−0.340721	−	0.247548i	−0.744966	+	0.667103i	$0.767534\pi$
$878$	−1.28115	−	3.94298i	−0.0432368	−	0.133069i
$879$		0			0
$880$	−1.04508	+	1.76336i	−0.0352298	+	0.0594427i
$881$	−11.3262			−0.381591			−0.190795	−	0.981630i	$-0.561107\pi$
$881$	−11.3262			−0.381591			−0.190795	+	0.981630i	$0.561107\pi$
$882$		0			0
$883$	−15.8541	−	11.5187i	−0.533533	−	0.387634i	0.288145	−	0.957587i	$-0.406962\pi$
$883$	−15.8541	−	11.5187i	−0.533533	−	0.387634i	−0.821678	+	0.569952i	$0.806962\pi$
$884$	38.1246	−	27.6992i	1.28227	−	0.931623i
$885$		0			0
$886$	14.0836	−	43.3448i	0.473148	−	1.45620i
$887$	22.3262	−	16.2210i	0.749642	−	0.544647i	−0.146074	−	0.989274i	$-0.546664\pi$
$887$	22.3262	−	16.2210i	0.749642	−	0.544647i	0.895716	+	0.444627i	$0.146664\pi$
$888$		0			0
$889$	0.0901699	+	0.277515i	0.00302420	+	0.00930754i
$890$	7.76393			0.260248
$891$		0			0
$892$	58.8541			1.97058
$893$	−3.94427	−	12.1392i	−0.131990	−	0.406224i
$894$		0			0
$895$	−7.39919	+	5.37582i	−0.247328	+	0.179694i
$896$	4.83688	−	14.8864i	0.161589	−	0.497319i
$897$		0			0
$898$	75.7771	−	55.0553i	2.52871	−	1.83722i
$899$	15.0000	+	10.8981i	0.500278	+	0.363473i
$900$		0			0
$901$	32.8328			1.09382
$902$	53.4164	+	11.9927i	1.77857	+	0.399314i
$903$		0			0
$904$	−3.61803	−	11.1352i	−0.120334	−	0.370350i
$905$	9.94427	+	7.22494i	0.330559	+	0.240165i
$906$		0			0
$907$	5.03444	−	15.4944i	0.167166	−	0.514484i	−0.832023	−	0.554740i	$-0.812818\pi$
$907$	5.03444	−	15.4944i	0.167166	−	0.514484i	0.999189	+	0.0402567i	$0.0128176\pi$
$908$	−11.5623	+	35.5851i	−0.383709	+	1.18093i
$909$		0			0
$910$	3.61803	+	2.62866i	0.119937	+	0.0871391i
$911$	0.291796	+	0.898056i	0.00966764	+	0.0297539i	0.955774	−	0.294102i	$-0.0950206\pi$
$911$	0.291796	+	0.898056i	0.00966764	+	0.0297539i	−0.946106	+	0.323856i	$0.895021\pi$
$912$		0			0
$913$	−53.3050	−	11.9677i	−1.76414	−	0.396073i
$914$	−47.8885			−1.58401
$915$		0			0
$916$	−39.2705	−	28.5317i	−1.29753	−	0.942714i
$917$	−13.4721	+	9.78808i	−0.444889	+	0.323231i
$918$		0			0
$919$	−9.41641	+	28.9807i	−0.310619	+	0.955986i	0.666902	+	0.745146i	$0.267620\pi$
$919$	−9.41641	+	28.9807i	−0.310619	+	0.955986i	−0.977521	+	0.210840i	$0.932380\pi$
$920$	−4.89919	+	3.55947i	−0.161521	+	0.117352i
$921$		0			0
$922$	−4.14590	−	12.7598i	−0.136538	−	0.420220i
$923$	16.0000			0.526646
$924$		0			0
$925$	−21.3262			−0.701202
$926$	16.1803	+	49.7980i	0.531719	+	1.63646i
$927$		0			0
$928$	−32.5623	+	23.6579i	−1.06891	+	0.776609i
$929$	−7.33282	+	22.5681i	−0.240582	+	0.740435i	0.755750	+	0.654860i	$0.227273\pi$
$929$	−7.33282	+	22.5681i	−0.240582	+	0.740435i	−0.996332	+	0.0855745i	$0.972727\pi$
$930$		0			0
$931$	−2.30902	+	1.67760i	−0.0756750	+	0.0549811i
$932$	−38.1246	−	27.6992i	−1.24881	−	0.907316i
$933$		0			0
$934$	58.5410			1.91552
$935$	−5.07295	+	8.55951i	−0.165903	+	0.279926i
$936$		0			0
$937$	10.5279	+	32.4014i	0.343930	+	1.05851i	0.962154	+	0.272506i	$0.0878526\pi$
$937$	10.5279	+	32.4014i	0.343930	+	1.05851i	−0.618224	+	0.786002i	$0.712147\pi$
$938$		0			0
$939$		0			0
$940$	−2.56231	+	7.88597i	−0.0835732	+	0.257212i
$941$	0.152476	−	0.469272i	0.00497057	−	0.0152978i	−0.948540	−	0.316656i	$-0.897440\pi$
$941$	0.152476	−	0.469272i	0.00497057	−	0.0152978i	0.953511	+	0.301358i	$0.0974399\pi$
$942$		0			0
$943$	−26.1697	−	19.0134i	−0.852203	−	0.619161i
$944$	1.00000	+	3.07768i	0.0325472	+	0.100170i
$945$		0			0
$946$	66.1033	−	28.5317i	2.14920	−	0.927645i
$947$	−13.8541			−0.450198			−0.225099	−	0.974336i	$-0.572271\pi$
$947$	−13.8541			−0.450198			−0.225099	+	0.974336i	$0.572271\pi$
$948$		0			0
$949$	−35.8885	−	26.0746i	−1.16499	−	0.846416i
$950$	−23.8435	+	17.3233i	−0.773584	+	0.562042i
$951$		0			0
$952$	3.35410	−	10.3229i	0.108707	−	0.334566i
$953$	9.61803	−	6.98791i	0.311559	−	0.226361i	−0.421006	−	0.907058i	$-0.638323\pi$
$953$	9.61803	−	6.98791i	0.311559	−	0.226361i	0.732565	+	0.680697i	$0.238323\pi$
$954$		0			0
$955$	−0.937694	−	2.88593i	−0.0303431	−	0.0933864i
$956$	57.1033			1.84685
$957$		0			0
$958$	−2.11146			−0.0682181
$959$	−2.52786	−	7.77997i	−0.0816290	−	0.251228i
$960$		0			0
$961$	17.3541	−	12.6085i	0.559810	−	0.406726i
$962$	−10.3262	+	31.7809i	−0.332931	+	1.02466i
$963$		0			0
$964$	−29.1246	+	21.1603i	−0.938041	+	0.681526i
$965$	10.9271	+	7.93897i	0.351754	+	0.255564i
$966$		0			0
$967$	−3.63932			−0.117033			−0.0585163	−	0.998286i	$-0.518637\pi$
$967$	−3.63932			−0.117033			−0.0585163	+	0.998286i	$0.518637\pi$
$968$	−22.2361	−	10.5146i	−0.714694	−	0.337953i
$969$		0			0
$970$	2.56231	+	7.88597i	0.0822707	+	0.253203i
$971$	44.1246	+	32.0584i	1.41603	+	1.02880i	0.992412	+	0.122961i	$0.0392389\pi$
$971$	44.1246	+	32.0584i	1.41603	+	1.02880i	0.423615	+	0.905842i	$0.360761\pi$
$972$		0			0
$973$	4.06231	−	12.5025i	0.130232	−	0.400811i
$974$	−19.1459	+	58.9250i	−0.613474	+	1.88808i
$975$		0			0
$976$		0			0
$977$	4.21478	+	12.9718i	0.134843	+	0.415004i	0.995566	−	0.0940706i	$-0.0299879\pi$
$977$	4.21478	+	12.9718i	0.134843	+	0.415004i	−0.860723	+	0.509074i	$0.829988\pi$
$978$		0			0
$979$	−1.73607	−	18.5519i	−0.0554850	−	0.592920i
$980$	1.85410			0.0592271
$981$		0			0
$982$	−2.72542	−	1.98014i	−0.0869718	−	0.0631887i
$983$	−8.85410	+	6.43288i	−0.282402	+	0.205177i	−0.719964	−	0.694011i	$-0.755842\pi$
$983$	−8.85410	+	6.43288i	−0.282402	+	0.205177i	0.437562	+	0.899188i	$0.355842\pi$
$984$		0			0
$985$	−4.29180	+	13.2088i	−0.136748	+	0.420867i
$986$	−52.6869	+	38.2793i	−1.67789	+	1.21906i
$987$		0			0
$988$	8.56231	+	26.3521i	0.272403	+	0.838371i
$989$	−42.5410			−1.35273
$990$		0			0
$991$	−33.2361			−1.05578			−0.527889	−	0.849313i	$-0.677016\pi$
$991$	−33.2361			−1.05578			−0.527889	+	0.849313i	$0.677016\pi$
$992$	−6.40576	−	19.7149i	−0.203383	−	0.625949i
$993$		0			0
$994$	8.94427	−	6.49839i	0.283695	−	0.206117i
$995$	2.51064	−	7.72696i	0.0795927	−	0.244961i
$996$		0			0
$997$	35.9443	−	26.1150i	1.13837	−	0.827072i	0.151476	−	0.988461i	$-0.451597\pi$
$997$	35.9443	−	26.1150i	1.13837	−	0.827072i	0.986891	+	0.161389i	$0.0515975\pi$
$998$	38.2148	+	27.7647i	1.20967	+	0.878875i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.a.379.1		4
3.2	odd	2		231.2.j.e.148.1	yes	4
11.3	even	5		7623.2.a.bk.1.1		2
11.8	odd	10		7623.2.a.bj.1.2		2
11.9	even	5	inner	693.2.m.a.64.1		4
33.8	even	10		2541.2.a.v.1.1		2
33.14	odd	10		2541.2.a.w.1.2		2
33.20	odd	10		231.2.j.e.64.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.e.64.1	✓	4	33.20	odd	10
231.2.j.e.148.1	yes	4	3.2	odd	2
693.2.m.a.64.1		4	11.9	even	5	inner
693.2.m.a.379.1		4	1.1	even	1	trivial
2541.2.a.v.1.1		2	33.8	even	10
2541.2.a.w.1.2		2	33.14	odd	10
7623.2.a.bj.1.2		2	11.8	odd	10
7623.2.a.bk.1.1		2	11.3	even	5

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.690983 - 2.12663i) q^{2} +(-2.42705 + 1.76336i) q^{4} +(0.190983 - 0.587785i) q^{5} +(-0.809017 + 0.587785i) q^{7} +(1.80902 + 1.31433i) q^{8} +O(q^{10})\)	\(q+(-0.690983 - 2.12663i) q^{2} +(-2.42705 + 1.76336i) q^{4} +(0.190983 - 0.587785i) q^{5} +(-0.809017 + 0.587785i) q^{7} +(1.80902 + 1.31433i) q^{8} -1.38197 q^{10} +(0.309017 + 3.30220i) q^{11} +(1.00000 + 3.07768i) q^{13} +(1.80902 + 1.31433i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-1.50000 + 4.61653i) q^{17} +(-2.30902 - 1.67760i) q^{19} +(0.572949 + 1.76336i) q^{20} +(6.80902 - 2.93893i) q^{22} -4.38197 q^{23} +(3.73607 + 2.71441i) q^{25} +(5.85410 - 4.25325i) q^{26} +(0.927051 - 2.85317i) q^{28} +(-4.85410 + 3.52671i) q^{29} +(-0.954915 - 2.93893i) q^{31} +6.70820 q^{32} +10.8541 q^{34} +(0.190983 + 0.587785i) q^{35} +(-3.73607 + 2.71441i) q^{37} +(-1.97214 + 6.06961i) q^{38} +(1.11803 - 0.812299i) q^{40} +(5.97214 + 4.33901i) q^{41} +9.70820 q^{43} +(-6.57295 - 7.46969i) q^{44} +(3.02786 + 9.31881i) q^{46} +(3.61803 + 2.62866i) q^{47} +(0.309017 - 0.951057i) q^{49} +(3.19098 - 9.82084i) q^{50} +(-7.85410 - 5.70634i) q^{52} +(-2.09017 - 6.43288i) q^{53} +(2.00000 + 0.449028i) q^{55} -2.23607 q^{56} +(10.8541 + 7.88597i) q^{58} +(2.61803 - 1.90211i) q^{59} +(-5.59017 + 4.06150i) q^{62} +(-4.01722 - 12.3637i) q^{64} +2.00000 q^{65} +(-4.50000 - 13.8496i) q^{68} +(1.11803 - 0.812299i) q^{70} +(1.52786 - 4.70228i) q^{71} +(-11.0902 + 8.05748i) q^{73} +(8.35410 + 6.06961i) q^{74} +8.56231 q^{76} +(-2.19098 - 2.48990i) q^{77} +(-3.09017 - 9.51057i) q^{79} +(0.500000 + 0.363271i) q^{80} +(5.10081 - 15.6987i) q^{82} +(-5.09017 + 15.6659i) q^{83} +(2.42705 + 1.76336i) q^{85} +(-6.70820 - 20.6457i) q^{86} +(-3.78115 + 6.37988i) q^{88} -5.61803 q^{89} +(-2.61803 - 1.90211i) q^{91} +(10.6353 - 7.72696i) q^{92} +(3.09017 - 9.51057i) q^{94} +(-1.42705 + 1.03681i) q^{95} +(-1.85410 - 5.70634i) q^{97} -2.23607 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 5 q^{2} - 3 q^{4} + 3 q^{5} - q^{7} + 5 q^{8}+O(q^{10}) \) 4 * q - 5 * q^2 - 3 * q^4 + 3 * q^5 - q^7 + 5 * q^8	\( 4 q - 5 q^{2} - 3 q^{4} + 3 q^{5} - q^{7} + 5 q^{8} - 10 q^{10} - q^{11} + 4 q^{13} + 5 q^{14} + q^{16} - 6 q^{17} - 7 q^{19} + 9 q^{20} + 25 q^{22} - 22 q^{23} + 6 q^{25} + 10 q^{26} - 3 q^{28} - 6 q^{29} - 15 q^{31} + 30 q^{34} + 3 q^{35} - 6 q^{37} + 10 q^{38} + 6 q^{41} + 12 q^{43} - 33 q^{44} + 30 q^{46} + 10 q^{47} - q^{49} + 15 q^{50} - 18 q^{52} + 14 q^{53} + 8 q^{55} + 30 q^{58} + 6 q^{59} + 13 q^{64} + 8 q^{65} - 18 q^{68} + 24 q^{71} - 22 q^{73} + 20 q^{74} - 6 q^{76} - 11 q^{77} + 10 q^{79} + 2 q^{80} + 45 q^{82} + 2 q^{83} + 3 q^{85} + 5 q^{88} - 18 q^{89} - 6 q^{91} + 9 q^{92} - 10 q^{94} + q^{95} + 6 q^{97}+O(q^{100}) \) 4 * q - 5 * q^2 - 3 * q^4 + 3 * q^5 - q^7 + 5 * q^8 - 10 * q^10 - q^11 + 4 * q^13 + 5 * q^14 + q^16 - 6 * q^17 - 7 * q^19 + 9 * q^20 + 25 * q^22 - 22 * q^23 + 6 * q^25 + 10 * q^26 - 3 * q^28 - 6 * q^29 - 15 * q^31 + 30 * q^34 + 3 * q^35 - 6 * q^37 + 10 * q^38 + 6 * q^41 + 12 * q^43 - 33 * q^44 + 30 * q^46 + 10 * q^47 - q^49 + 15 * q^50 - 18 * q^52 + 14 * q^53 + 8 * q^55 + 30 * q^58 + 6 * q^59 + 13 * q^64 + 8 * q^65 - 18 * q^68 + 24 * q^71 - 22 * q^73 + 20 * q^74 - 6 * q^76 - 11 * q^77 + 10 * q^79 + 2 * q^80 + 45 * q^82 + 2 * q^83 + 3 * q^85 + 5 * q^88 - 18 * q^89 - 6 * q^91 + 9 * q^92 - 10 * q^94 + q^95 + 6 * q^97

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