LMFDB - Embedded newform 357.2.k.b.64.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [357,2,Mod(64,357)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(357, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("357.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.k (of order $4$, 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:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 32 x^{18} + 426 x^{16} + 3072 x^{14} + 13121 x^{12} + 34148 x^{10} + 53608 x^{8} + 48276 x^{6} + \cdots + 4 $ x^20 + 32x^18 + 426x^16 + 3072x^14 + 13121x^12 + 34148x^10 + 53608x^8 + 48276x^6 + 22224x^4 + 3920*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			64.7
Root			$0.661473i$ of defining polynomial
Character	$\chi$	$=$	357.64
Dual form			357.2.k.b.106.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.661473i q^{2} +(-0.707107 - 0.707107i) q^{3} +1.56245 q^{4} +(-1.66372 - 1.66372i) q^{5} +(0.467732 - 0.467732i) q^{6} +(-0.707107 + 0.707107i) q^{7} +2.35647i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+0.661473i q^{2} +(-0.707107 - 0.707107i) q^{3} +1.56245 q^{4} +(-1.66372 - 1.66372i) q^{5} +(0.467732 - 0.467732i) q^{6} +(-0.707107 + 0.707107i) q^{7} +2.35647i q^{8} +1.00000i q^{9} +(1.10050 - 1.10050i) q^{10} +(3.71291 - 3.71291i) q^{11} +(-1.10482 - 1.10482i) q^{12} +4.49854 q^{13} +(-0.467732 - 0.467732i) q^{14} +2.35286i q^{15} +1.56617 q^{16} +(-0.686963 - 4.06547i) q^{17} -0.661473 q^{18} -3.58834i q^{19} +(-2.59949 - 2.59949i) q^{20} +1.00000 q^{21} +(2.45599 + 2.45599i) q^{22} +(0.426792 - 0.426792i) q^{23} +(1.66627 - 1.66627i) q^{24} +0.535927i q^{25} +2.97566i q^{26} +(0.707107 - 0.707107i) q^{27} +(-1.10482 + 1.10482i) q^{28} +(-4.07014 - 4.07014i) q^{29} -1.55635 q^{30} +(-0.141237 - 0.141237i) q^{31} +5.74891i q^{32} -5.25085 q^{33} +(2.68920 - 0.454407i) q^{34} +2.35286 q^{35} +1.56245i q^{36} +(5.41429 + 5.41429i) q^{37} +2.37359 q^{38} +(-3.18095 - 3.18095i) q^{39} +(3.92050 - 3.92050i) q^{40} +(-4.30993 + 4.30993i) q^{41} +0.661473i q^{42} +9.93667i q^{43} +(5.80125 - 5.80125i) q^{44} +(1.66372 - 1.66372i) q^{45} +(0.282311 + 0.282311i) q^{46} +6.16149 q^{47} +(-1.10745 - 1.10745i) q^{48} -1.00000i q^{49} -0.354501 q^{50} +(-2.38897 + 3.36048i) q^{51} +7.02876 q^{52} +9.47974i q^{53} +(0.467732 + 0.467732i) q^{54} -12.3545 q^{55} +(-1.66627 - 1.66627i) q^{56} +(-2.53734 + 2.53734i) q^{57} +(2.69228 - 2.69228i) q^{58} -1.92313i q^{59} +3.67623i q^{60} +(-7.45587 + 7.45587i) q^{61} +(0.0934241 - 0.0934241i) q^{62} +(-0.707107 - 0.707107i) q^{63} -0.670404 q^{64} +(-7.48431 - 7.48431i) q^{65} -3.47329i q^{66} -7.47259 q^{67} +(-1.07335 - 6.35212i) q^{68} -0.603575 q^{69} +1.55635i q^{70} +(-1.09194 - 1.09194i) q^{71} -2.35647 q^{72} +(-6.99329 - 6.99329i) q^{73} +(-3.58140 + 3.58140i) q^{74} +(0.378957 - 0.378957i) q^{75} -5.60662i q^{76} +5.25085i q^{77} +(2.10411 - 2.10411i) q^{78} +(7.40415 - 7.40415i) q^{79} +(-2.60567 - 2.60567i) q^{80} -1.00000 q^{81} +(-2.85090 - 2.85090i) q^{82} +8.09294i q^{83} +1.56245 q^{84} +(-5.62090 + 7.90672i) q^{85} -6.57283 q^{86} +5.75604i q^{87} +(8.74934 + 8.74934i) q^{88} -12.3039 q^{89} +(1.10050 + 1.10050i) q^{90} +(-3.18095 + 3.18095i) q^{91} +(0.666843 - 0.666843i) q^{92} +0.199739i q^{93} +4.07566i q^{94} +(-5.97000 + 5.97000i) q^{95} +(4.06509 - 4.06509i) q^{96} +(5.83964 + 5.83964i) q^{97} +0.661473 q^{98} +(3.71291 + 3.71291i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 24 q^{4} + 8 q^{5} - 4 q^{6}+O(q^{10}) $ 20 * q - 24 * q^4 + 8 * q^5 - 4 * q^6	$ 20 q - 24 q^{4} + 8 q^{5} - 4 q^{6} + 16 q^{10} + 4 q^{11} - 12 q^{13} + 4 q^{14} + 40 q^{16} + 4 q^{17} + 8 q^{18} - 52 q^{20} + 20 q^{21} - 24 q^{22} - 4 q^{23} + 4 q^{24} - 8 q^{29} + 8 q^{31} - 4 q^{33} - 44 q^{34} + 12 q^{35} + 24 q^{37} - 64 q^{38} - 12 q^{39} - 52 q^{40} - 20 q^{41} + 72 q^{44} - 8 q^{45} + 28 q^{46} - 32 q^{47} + 32 q^{48} + 104 q^{50} + 8 q^{51} + 48 q^{52} - 4 q^{54} - 36 q^{55} - 4 q^{56} - 16 q^{57} - 60 q^{58} + 28 q^{61} + 36 q^{62} - 112 q^{64} - 4 q^{65} + 40 q^{67} - 52 q^{68} + 36 q^{69} + 16 q^{71} - 24 q^{72} - 72 q^{73} - 24 q^{74} - 8 q^{75} + 40 q^{78} - 8 q^{79} + 120 q^{80} - 20 q^{81} + 108 q^{82} - 24 q^{84} + 40 q^{85} - 28 q^{88} - 64 q^{89} + 16 q^{90} - 12 q^{91} - 56 q^{92} + 60 q^{95} + 16 q^{96} + 60 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) $ 20 * q - 24 * q^4 + 8 * q^5 - 4 * q^6 + 16 * q^10 + 4 * q^11 - 12 * q^13 + 4 * q^14 + 40 * q^16 + 4 * q^17 + 8 * q^18 - 52 * q^20 + 20 * q^21 - 24 * q^22 - 4 * q^23 + 4 * q^24 - 8 * q^29 + 8 * q^31 - 4 * q^33 - 44 * q^34 + 12 * q^35 + 24 * q^37 - 64 * q^38 - 12 * q^39 - 52 * q^40 - 20 * q^41 + 72 * q^44 - 8 * q^45 + 28 * q^46 - 32 * q^47 + 32 * q^48 + 104 * q^50 + 8 * q^51 + 48 * q^52 - 4 * q^54 - 36 * q^55 - 4 * q^56 - 16 * q^57 - 60 * q^58 + 28 * q^61 + 36 * q^62 - 112 * q^64 - 4 * q^65 + 40 * q^67 - 52 * q^68 + 36 * q^69 + 16 * q^71 - 24 * q^72 - 72 * q^73 - 24 * q^74 - 8 * q^75 + 40 * q^78 - 8 * q^79 + 120 * q^80 - 20 * q^81 + 108 * q^82 - 24 * q^84 + 40 * q^85 - 28 * q^88 - 64 * q^89 + 16 * q^90 - 12 * q^91 - 56 * q^92 + 60 * q^95 + 16 * q^96 + 60 * q^97 - 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$			0.661473i			0.467732i	0.972269	+	0.233866i	$0.0751377\pi$
$2$			0.661473i			0.467732i	−0.972269	+	0.233866i	$0.924862\pi$
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	1.56245			0.781227
$5$	−1.66372	−	1.66372i	−0.744038	−	0.744038i	0.229314	−	0.973352i	$-0.426352\pi$
$5$	−1.66372	−	1.66372i	−0.744038	−	0.744038i	−0.973352	+	0.229314i	$0.926352\pi$
$6$	0.467732	−	0.467732i	0.190951	−	0.190951i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$			2.35647i			0.833136i
$9$			1.00000i			0.333333i
$10$	1.10050	−	1.10050i	0.348010	−	0.348010i
$11$	3.71291	−	3.71291i	1.11948	−	1.11948i	0.127668	−	0.991817i	$-0.459251\pi$
$11$	3.71291	−	3.71291i	1.11948	−	1.11948i	0.991817	−	0.127668i	$-0.0407490\pi$
$12$	−1.10482	−	1.10482i	−0.318935	−	0.318935i
$13$	4.49854			1.24767			0.623835	−	0.781556i	$-0.285574\pi$
$13$	4.49854			1.24767			0.623835	+	0.781556i	$0.285574\pi$
$14$	−0.467732	−	0.467732i	−0.125007	−	0.125007i
$15$			2.35286i			0.607505i
$16$	1.56617			0.391543
$17$	−0.686963	−	4.06547i	−0.166613	−	0.986022i
$17$	−0.686963	−	4.06547i	−0.166613	−	0.986022i
$18$	−0.661473			−0.155911
$19$		−	3.58834i		−	0.823222i	−0.911360	−	0.411611i	$-0.864966\pi$
$19$		−	3.58834i		−	0.823222i	0.911360	−	0.411611i	$-0.135034\pi$
$20$	−2.59949	−	2.59949i	−0.581263	−	0.581263i
$21$	1.00000			0.218218
$22$	2.45599	+	2.45599i	0.523618	+	0.523618i
$23$	0.426792	−	0.426792i	0.0889923	−	0.0889923i	−0.661209	−	0.750202i	$-0.729956\pi$
$23$	0.426792	−	0.426792i	0.0889923	−	0.0889923i	0.750202	+	0.661209i	$0.229956\pi$
$24$	1.66627	−	1.66627i	0.340127	−	0.340127i
$25$			0.535927i			0.107185i
$26$			2.97566i			0.583575i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−1.10482	+	1.10482i	−0.208792	+	0.208792i
$29$	−4.07014	−	4.07014i	−0.755805	−	0.755805i	0.219751	−	0.975556i	$-0.429476\pi$
$29$	−4.07014	−	4.07014i	−0.755805	−	0.755805i	−0.975556	+	0.219751i	$0.929476\pi$
$30$	−1.55635			−0.284149
$31$	−0.141237	−	0.141237i	−0.0253668	−	0.0253668i	0.694310	−	0.719676i	$-0.255710\pi$
$31$	−0.141237	−	0.141237i	−0.0253668	−	0.0253668i	−0.719676	+	0.694310i	$0.755710\pi$
$32$			5.74891i			1.01627i
$33$	−5.25085			−0.914055
$34$	2.68920	−	0.454407i	0.461194	−	0.0779302i
$35$	2.35286			0.397705
$36$			1.56245i			0.260409i
$37$	5.41429	+	5.41429i	0.890104	+	0.890104i	0.994532	−	0.104429i	$-0.0333014\pi$
$37$	5.41429	+	5.41429i	0.890104	+	0.890104i	−0.104429	+	0.994532i	$0.533301\pi$
$38$	2.37359			0.385047
$39$	−3.18095	−	3.18095i	−0.509359	−	0.509359i
$40$	3.92050	−	3.92050i	0.619885	−	0.619885i
$41$	−4.30993	+	4.30993i	−0.673098	+	0.673098i	−0.958429	−	0.285331i	$-0.907897\pi$
$41$	−4.30993	+	4.30993i	−0.673098	+	0.673098i	0.285331	+	0.958429i	$0.407897\pi$
$42$			0.661473i			0.102067i
$43$			9.93667i			1.51533i	0.652645	+	0.757664i	$0.273659\pi$
$43$			9.93667i			1.51533i	−0.652645	+	0.757664i	$0.726341\pi$
$44$	5.80125	−	5.80125i	0.874572	−	0.874572i
$45$	1.66372	−	1.66372i	0.248013	−	0.248013i
$46$	0.282311	+	0.282311i	0.0416245	+	0.0416245i
$47$	6.16149			0.898745			0.449373	−	0.893344i	$-0.351648\pi$
$47$	6.16149			0.898745			0.449373	+	0.893344i	$0.351648\pi$
$48$	−1.10745	−	1.10745i	−0.159847	−	0.159847i
$49$		−	1.00000i		−	0.142857i
$50$	−0.354501			−0.0501340
$51$	−2.38897	+	3.36048i	−0.334522	+	0.470561i
$52$	7.02876			0.974714
$53$			9.47974i			1.30214i	0.759017	+	0.651071i	$0.225680\pi$
$53$			9.47974i			1.30214i	−0.759017	+	0.651071i	$0.774320\pi$
$54$	0.467732	+	0.467732i	0.0636502	+	0.0636502i
$55$	−12.3545			−1.66588
$56$	−1.66627	−	1.66627i	−0.222665	−	0.222665i
$57$	−2.53734	+	2.53734i	−0.336079	+	0.336079i
$58$	2.69228	−	2.69228i	0.353514	−	0.353514i
$59$		−	1.92313i		−	0.250370i	−0.992133	−	0.125185i	$-0.960048\pi$
$59$		−	1.92313i		−	0.250370i	0.992133	−	0.125185i	$-0.0399525\pi$
$60$			3.67623i			0.474599i
$61$	−7.45587	+	7.45587i	−0.954626	+	0.954626i	−0.999014	−	0.0443882i	$-0.985866\pi$
$61$	−7.45587	+	7.45587i	−0.954626	+	0.954626i	0.0443882	+	0.999014i	$0.485866\pi$
$62$	0.0934241	−	0.0934241i	0.0118649	−	0.0118649i
$63$	−0.707107	−	0.707107i	−0.0890871	−	0.0890871i
$64$	−0.670404			−0.0838006
$65$	−7.48431	−	7.48431i	−0.928314	−	0.928314i
$66$		−	3.47329i		−	0.427533i
$67$	−7.47259			−0.912922			−0.456461	−	0.889743i	$-0.650883\pi$
$67$	−7.47259			−0.912922			−0.456461	+	0.889743i	$0.650883\pi$
$68$	−1.07335	−	6.35212i	−0.130163	−	0.770307i
$69$	−0.603575			−0.0726619
$70$			1.55635i			0.186019i
$71$	−1.09194	−	1.09194i	−0.129590	−	0.129590i	0.639337	−	0.768927i	$-0.279209\pi$
$71$	−1.09194	−	1.09194i	−0.129590	−	0.129590i	−0.768927	+	0.639337i	$0.779209\pi$
$72$	−2.35647			−0.277712
$73$	−6.99329	−	6.99329i	−0.818503	−	0.818503i	0.167388	−	0.985891i	$-0.446467\pi$
$73$	−6.99329	−	6.99329i	−0.818503	−	0.818503i	−0.985891	+	0.167388i	$0.946467\pi$
$74$	−3.58140	+	3.58140i	−0.416330	+	0.416330i
$75$	0.378957	−	0.378957i	0.0437582	−	0.0437582i
$76$		−	5.60662i		−	0.643123i
$77$			5.25085i			0.598390i
$78$	2.10411	−	2.10411i	0.238243	−	0.238243i
$79$	7.40415	−	7.40415i	0.833032	−	0.833032i	−0.154898	−	0.987930i	$-0.549505\pi$
$79$	7.40415	−	7.40415i	0.833032	−	0.833032i	0.987930	+	0.154898i	$0.0495049\pi$
$80$	−2.60567	−	2.60567i	−0.291323	−	0.291323i
$81$	−1.00000			−0.111111
$82$	−2.85090	−	2.85090i	−0.314829	−	0.314829i
$83$			8.09294i			0.888316i	0.895949	+	0.444158i	$0.146497\pi$
$83$			8.09294i			0.888316i	−0.895949	+	0.444158i	$0.853503\pi$
$84$	1.56245			0.170478
$85$	−5.62090	+	7.90672i	−0.609672	+	0.857605i
$86$	−6.57283			−0.708767
$87$			5.75604i			0.617113i
$88$	8.74934	+	8.74934i	0.932683	+	0.932683i
$89$	−12.3039			−1.30421			−0.652105	−	0.758129i	$-0.726114\pi$
$89$	−12.3039			−1.30421			−0.652105	+	0.758129i	$0.726114\pi$
$90$	1.10050	+	1.10050i	0.116003	+	0.116003i
$91$	−3.18095	+	3.18095i	−0.333454	+	0.333454i
$92$	0.666843	−	0.666843i	0.0695232	−	0.0695232i
$93$			0.199739i			0.0207119i
$94$			4.07566i			0.420372i
$95$	−5.97000	+	5.97000i	−0.612509	+	0.612509i
$96$	4.06509	−	4.06509i	0.414892	−	0.414892i
$97$	5.83964	+	5.83964i	0.592925	+	0.592925i	0.938421	−	0.345495i	$-0.112289\pi$
$97$	5.83964	+	5.83964i	0.592925	+	0.592925i	−0.345495	+	0.938421i	$0.612289\pi$
$98$	0.661473			0.0668188
$99$	3.71291	+	3.71291i	0.373162	+	0.373162i
$100$			0.837361i			0.0837361i
$101$	12.3613			1.22999			0.614995	−	0.788531i	$-0.289158\pi$
$101$	12.3613			1.22999			0.614995	+	0.788531i	$0.289158\pi$
$102$	−2.22287	−	1.58024i	−0.220097	−	0.156467i
$103$	3.48146			0.343039			0.171519	−	0.985181i	$-0.445132\pi$
$103$	3.48146			0.343039			0.171519	+	0.985181i	$0.445132\pi$
$104$			10.6007i			1.03948i
$105$	−1.66372	−	1.66372i	−0.162362	−	0.162362i
$106$	−6.27059			−0.609053
$107$	−3.28575	−	3.28575i	−0.317645	−	0.317645i	0.530217	−	0.847862i	$-0.322111\pi$
$107$	−3.28575	−	3.28575i	−0.317645	−	0.317645i	−0.847862	+	0.530217i	$0.822111\pi$
$108$	1.10482	−	1.10482i	0.106312	−	0.106312i
$109$	9.85208	−	9.85208i	0.943659	−	0.943659i	−0.0548368	−	0.998495i	$-0.517464\pi$
$109$	9.85208	−	9.85208i	0.943659	−	0.943659i	0.998495	+	0.0548368i	$0.0174638\pi$
$110$		−	8.17215i		−	0.779184i
$111$		−	7.65696i		−	0.726767i
$112$	−1.10745	+	1.10745i	−0.104644	+	0.104644i
$113$	−6.98837	+	6.98837i	−0.657411	+	0.657411i	−0.954767	−	0.297356i	$-0.903895\pi$
$113$	−6.98837	+	6.98837i	−0.657411	+	0.657411i	0.297356	+	0.954767i	$0.403895\pi$
$114$	−1.67838	−	1.67838i	−0.157195	−	0.157195i
$115$	−1.42012			−0.132427
$116$	−6.35940	−	6.35940i	−0.590456	−	0.590456i
$117$			4.49854i			0.415890i
$118$	1.27210			0.117106
$119$	3.36048	+	2.38897i	0.308055	+	0.218996i
$120$	−5.54442			−0.506134
$121$		−	16.5714i		−	1.50649i
$122$	−4.93185	−	4.93185i	−0.446509	−	0.446509i
$123$	6.09517			0.549583
$124$	−0.220676	−	0.220676i	−0.0198173	−	0.0198173i
$125$	−7.42697	+	7.42697i	−0.664288	+	0.664288i
$126$	0.467732	−	0.467732i	0.0416689	−	0.0416689i
$127$		−	14.8193i		−	1.31500i	−0.753456	−	0.657499i	$-0.771614\pi$
$127$		−	14.8193i		−	1.31500i	0.753456	−	0.657499i	$-0.228386\pi$
$128$			11.0544i			0.977077i
$129$	7.02628	−	7.02628i	0.618630	−	0.618630i
$130$	4.95066	−	4.95066i	0.434202	−	0.434202i
$131$	6.46192	+	6.46192i	0.564580	+	0.564580i	0.930605	−	0.366025i	$-0.119281\pi$
$131$	6.46192	+	6.46192i	0.564580	+	0.564580i	−0.366025	+	0.930605i	$0.619281\pi$
$132$	−8.20421			−0.714085
$133$	2.53734	+	2.53734i	0.220015	+	0.220015i
$134$		−	4.94291i		−	0.427003i
$135$	−2.35286			−0.202502
$136$	9.58015	−	1.61881i	0.821491	−	0.138811i
$137$	−7.53516			−0.643772			−0.321886	−	0.946778i	$-0.604317\pi$
$137$	−7.53516			−0.643772			−0.321886	+	0.946778i	$0.604317\pi$
$138$		−	0.399248i		−	0.0339863i
$139$	−0.364800	−	0.364800i	−0.0309419	−	0.0309419i	0.691467	−	0.722408i	$-0.256965\pi$
$139$	−0.364800	−	0.364800i	−0.0309419	−	0.0309419i	−0.722408	+	0.691467i	$0.756965\pi$
$140$	3.67623			0.310698
$141$	−4.35683	−	4.35683i	−0.366911	−	0.366911i
$142$	0.722289	−	0.722289i	0.0606132	−	0.0606132i
$143$	16.7027	−	16.7027i	1.39675	−	1.39675i
$144$			1.56617i			0.130514i
$145$			13.5431i			1.12470i
$146$	4.62587	−	4.62587i	0.382840	−	0.382840i
$147$	−0.707107	+	0.707107i	−0.0583212	+	0.0583212i
$148$	8.45958	+	8.45958i	0.695373	+	0.695373i
$149$	2.24948			0.184284			0.0921422	−	0.995746i	$-0.470629\pi$
$149$	2.24948			0.184284			0.0921422	+	0.995746i	$0.470629\pi$
$150$	0.250670	+	0.250670i	0.0204671	+	0.0204671i
$151$			10.1044i			0.822286i	0.911571	+	0.411143i	$0.134870\pi$
$151$			10.1044i			0.822286i	−0.911571	+	0.411143i	$0.865130\pi$
$152$	8.45580			0.685856
$153$	4.06547	−	0.686963i	0.328674	−	0.0555377i
$154$	−3.47329			−0.279886
$155$			0.469956i			0.0377478i
$156$	−4.97008	−	4.97008i	−0.397925	−	0.397925i
$157$	−23.6643			−1.88862			−0.944310	−	0.329058i	$-0.893269\pi$
$157$	−23.6643			−1.88862			−0.944310	+	0.329058i	$0.893269\pi$
$158$	4.89764	+	4.89764i	0.389636	+	0.389636i
$159$	6.70319	−	6.70319i	0.531597	−	0.531597i
$160$	9.56458	−	9.56458i	0.756146	−	0.756146i
$161$			0.603575i			0.0475684i
$162$		−	0.661473i		−	0.0519702i
$163$	16.9353	−	16.9353i	1.32648	−	1.32648i	0.418054	−	0.908422i	$-0.362712\pi$
$163$	16.9353	−	16.9353i	1.32648	−	1.32648i	0.908422	−	0.418054i	$-0.137288\pi$
$164$	−6.73407	+	6.73407i	−0.525843	+	0.525843i
$165$	8.73594	+	8.73594i	0.680092	+	0.680092i
$166$	−5.35326			−0.415493
$167$	17.8008	+	17.8008i	1.37747	+	1.37747i	0.848875	+	0.528593i	$0.177280\pi$
$167$	17.8008	+	17.8008i	1.37747	+	1.37747i	0.528593	+	0.848875i	$0.322720\pi$
$168$			2.35647i			0.181805i
$169$	7.23686			0.556681
$170$	−5.23008	−	3.71807i	−0.401129	−	0.285163i
$171$	3.58834			0.274407
$172$			15.5256i			1.18381i
$173$	7.89482	+	7.89482i	0.600232	+	0.600232i	0.940374	−	0.340142i	$-0.110475\pi$
$173$	7.89482	+	7.89482i	0.600232	+	0.600232i	−0.340142	+	0.940374i	$0.610475\pi$
$174$	−3.80746			−0.288643
$175$	−0.378957	−	0.378957i	−0.0286465	−	0.0286465i
$176$	5.81505	−	5.81505i	0.438326	−	0.438326i
$177$	−1.35986	+	1.35986i	−0.102213	+	0.102213i
$178$		−	8.13869i		−	0.610020i
$179$		−	2.39571i		−	0.179064i	−0.995984	−	0.0895320i	$-0.971463\pi$
$179$		−	2.39571i		−	0.179064i	0.995984	−	0.0895320i	$-0.0285371\pi$
$180$	2.59949	−	2.59949i	0.193754	−	0.193754i
$181$	−13.8862	+	13.8862i	−1.03216	+	1.03216i	−0.0326907	+	0.999466i	$0.510408\pi$
$181$	−13.8862	+	13.8862i	−1.03216	+	1.03216i	−0.999466	+	0.0326907i	$0.989592\pi$
$182$	−2.10411	−	2.10411i	−0.155967	−	0.155967i
$183$	10.5442			0.779449
$184$	1.00572	+	1.00572i	0.0741427	+	0.0741427i
$185$		−	18.0157i		−	1.32454i
$186$	−0.132122			−0.00968763
$187$	−17.6454	−	12.5441i	−1.29036	−	0.917316i
$188$	9.62704			0.702124
$189$			1.00000i			0.0727393i
$190$	−3.94899	−	3.94899i	−0.286490	−	0.286490i
$191$	5.22705			0.378216			0.189108	−	0.981956i	$-0.439440\pi$
$191$	5.22705			0.378216			0.189108	+	0.981956i	$0.439440\pi$
$192$	0.474048	+	0.474048i	0.0342114	+	0.0342114i
$193$	−15.3421	+	15.3421i	−1.10435	+	1.10435i	−0.110467	+	0.993880i	$0.535235\pi$
$193$	−15.3421	+	15.3421i	−1.10435	+	1.10435i	−0.993880	+	0.110467i	$0.964765\pi$
$194$	−3.86276	+	3.86276i	−0.277330	+	0.277330i
$195$			10.5844i			0.757965i
$196$		−	1.56245i		−	0.111604i
$197$	4.73493	−	4.73493i	0.337350	−	0.337350i	−0.518019	−	0.855369i	$-0.673330\pi$
$197$	4.73493	−	4.73493i	0.337350	−	0.337350i	0.855369	+	0.518019i	$0.173330\pi$
$198$	−2.45599	+	2.45599i	−0.174539	+	0.174539i
$199$	−4.74936	−	4.74936i	−0.336673	−	0.336673i	0.518441	−	0.855114i	$-0.326513\pi$
$199$	−4.74936	−	4.74936i	−0.336673	−	0.336673i	−0.855114	+	0.518441i	$0.826513\pi$
$200$	−1.26289			−0.0893000
$201$	5.28392	+	5.28392i	0.372699	+	0.372699i
$202$			8.17663i			0.575306i
$203$	5.75604			0.403995
$204$	−3.73265	+	5.25060i	−0.261338	+	0.367615i
$205$	14.3410			1.00162
$206$			2.30289i			0.160450i
$207$	0.426792	+	0.426792i	0.0296641	+	0.0296641i
$208$	7.04548			0.488516
$209$	−13.3232	−	13.3232i	−0.921584	−	0.921584i
$210$	1.10050	−	1.10050i	0.0759421	−	0.0759421i
$211$	−9.31494	+	9.31494i	−0.641267	+	0.641267i	−0.950867	−	0.309600i	$-0.899805\pi$
$211$	−9.31494	+	9.31494i	−0.641267	+	0.641267i	0.309600	+	0.950867i	$0.399805\pi$
$212$			14.8117i			1.01727i
$213$			1.54424i			0.105809i
$214$	2.17343	−	2.17343i	0.148573	−	0.148573i
$215$	16.5318	−	16.5318i	1.12746	−	1.12746i
$216$	1.66627	+	1.66627i	0.113376	+	0.113376i
$217$	0.199739			0.0135591
$218$	6.51688	+	6.51688i	0.441379	+	0.441379i
$219$			9.89000i			0.668305i
$220$	−19.3033			−1.30143
$221$	−3.09033	−	18.2887i	−0.207878	−	1.23023i
$222$	5.06487			0.339932
$223$		−	12.0749i		−	0.808596i	−0.914627	−	0.404298i	$-0.867516\pi$
$223$		−	12.0749i		−	0.808596i	0.914627	−	0.404298i	$-0.132484\pi$
$224$	−4.06509	−	4.06509i	−0.271610	−	0.271610i
$225$	−0.535927			−0.0357285
$226$	−4.62262	−	4.62262i	−0.307492	−	0.307492i
$227$	7.04430	−	7.04430i	0.467547	−	0.467547i	−0.433572	−	0.901119i	$-0.642747\pi$
$227$	7.04430	−	7.04430i	0.467547	−	0.467547i	0.901119	+	0.433572i	$0.142747\pi$
$228$	−3.96448	+	3.96448i	−0.262554	+	0.262554i
$229$			0.341524i			0.0225685i	0.999936	+	0.0112843i	$0.00359197\pi$
$229$			0.341524i			0.0225685i	−0.999936	+	0.0112843i	$0.996408\pi$
$230$		−	0.939374i		−	0.0619405i
$231$	3.71291	−	3.71291i	0.244292	−	0.244292i
$232$	9.59114	−	9.59114i	0.629689	−	0.629689i
$233$	11.2402	+	11.2402i	0.736371	+	0.736371i	0.971874	−	0.235502i	$-0.0756736\pi$
$233$	11.2402	+	11.2402i	0.736371	+	0.736371i	−0.235502	+	0.971874i	$0.575674\pi$
$234$	−2.97566			−0.194525
$235$	−10.2510	−	10.2510i	−0.668701	−	0.668701i
$236$		−	3.00480i		−	0.195596i
$237$	−10.4711			−0.680168
$238$	−1.58024	+	2.22287i	−0.102432	+	0.144087i
$239$	−1.16131			−0.0751187			−0.0375594	−	0.999294i	$-0.511958\pi$
$239$	−1.16131			−0.0751187			−0.0375594	+	0.999294i	$0.511958\pi$
$240$			3.68497i			0.237864i
$241$	6.45266	+	6.45266i	0.415652	+	0.415652i	0.883702	−	0.468050i	$-0.155043\pi$
$241$	6.45266	+	6.45266i	0.415652	+	0.415652i	−0.468050	+	0.883702i	$0.655043\pi$
$242$	10.9615			0.704634
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−11.6495	+	11.6495i	−0.745780	+	0.745780i
$245$	−1.66372	+	1.66372i	−0.106291	+	0.106291i
$246$			4.03178i			0.257057i
$247$		−	16.1423i		−	1.02711i
$248$	0.332819	−	0.332819i	0.0211340	−	0.0211340i
$249$	5.72257	−	5.72257i	0.362653	−	0.362653i
$250$	−4.91273	−	4.91273i	−0.310709	−	0.310709i
$251$	−2.02464			−0.127794			−0.0638970	−	0.997956i	$-0.520353\pi$
$251$	−2.02464			−0.127794			−0.0638970	+	0.997956i	$0.520353\pi$
$252$	−1.10482	−	1.10482i	−0.0695972	−	0.0695972i
$253$		−	3.16928i		−	0.199251i
$254$	9.80254			0.615066
$255$	9.56547	−	1.61632i	0.599013	−	0.101218i
$256$	−8.65297			−0.540811
$257$			19.5756i			1.22109i	0.791982	+	0.610545i	$0.209049\pi$
$257$			19.5756i			1.22109i	−0.791982	+	0.610545i	$0.790951\pi$
$258$	4.64769	+	4.64769i	0.289353	+	0.289353i
$259$	−7.65696			−0.475780
$260$	−11.6939	−	11.6939i	−0.725224	−	0.725224i
$261$	4.07014	−	4.07014i	0.251935	−	0.251935i
$262$	−4.27438	+	4.27438i	−0.264072	+	0.264072i
$263$		−	23.4356i		−	1.44510i	−0.691319	−	0.722550i	$-0.742970\pi$
$263$		−	23.4356i		−	1.44510i	0.691319	−	0.722550i	$-0.257030\pi$
$264$		−	12.3734i		−	0.761533i
$265$	15.7716	−	15.7716i	0.968843	−	0.968843i
$266$	−1.67838	+	1.67838i	−0.102908	+	0.102908i
$267$	8.70017	+	8.70017i	0.532441	+	0.532441i
$268$	−11.6756			−0.713200
$269$	5.65950	+	5.65950i	0.345066	+	0.345066i	0.858268	−	0.513202i	$-0.171541\pi$
$269$	5.65950	+	5.65950i	0.345066	+	0.345066i	−0.513202	+	0.858268i	$0.671541\pi$
$270$		−	1.55635i		−	0.0947164i
$271$	24.5987			1.49427			0.747133	−	0.664675i	$-0.231430\pi$
$271$	24.5987			1.49427			0.747133	+	0.664675i	$0.231430\pi$
$272$	−1.07590	−	6.36723i	−0.0652361	−	0.386070i
$273$	4.49854			0.272264
$274$		−	4.98430i		−	0.301112i
$275$	1.98985	+	1.98985i	0.119992	+	0.119992i
$276$	−0.943058			−0.0567654
$277$	−18.9255	−	18.9255i	−1.13712	−	1.13712i	−0.988963	−	0.148162i	$-0.952664\pi$
$277$	−18.9255	−	18.9255i	−1.13712	−	1.13712i	−0.148162	−	0.988963i	$-0.547336\pi$
$278$	0.241305	−	0.241305i	0.0144725	−	0.0144725i
$279$	0.141237	−	0.141237i	0.00845562	−	0.00845562i
$280$			5.54442i			0.331343i
$281$			24.2978i			1.44948i	0.689020	+	0.724742i	$0.258041\pi$
$281$			24.2978i			1.44948i	−0.689020	+	0.724742i	$0.741959\pi$
$282$	2.88192	−	2.88192i	0.171616	−	0.171616i
$283$	−6.48189	+	6.48189i	−0.385308	+	0.385308i	−0.873010	−	0.487702i	$-0.837835\pi$
$283$	−6.48189	+	6.48189i	−0.385308	+	0.385308i	0.487702	+	0.873010i	$0.337835\pi$
$284$	−1.70611	−	1.70611i	−0.101239	−	0.101239i
$285$	8.44285			0.500111
$286$	11.0484	+	11.0484i	0.653303	+	0.653303i
$287$		−	6.09517i		−	0.359786i
$288$	−5.74891			−0.338758
$289$	−16.0562	+	5.58566i	−0.944480	+	0.328568i
$290$	−8.95841			−0.526056
$291$		−	8.25850i		−	0.484122i
$292$	−10.9267	−	10.9267i	−0.639436	−	0.639436i
$293$	2.19698			0.128349			0.0641746	−	0.997939i	$-0.479559\pi$
$293$	2.19698			0.128349			0.0641746	+	0.997939i	$0.479559\pi$
$294$	−0.467732	−	0.467732i	−0.0272787	−	0.0272787i
$295$	−3.19955	+	3.19955i	−0.186285	+	0.186285i
$296$	−12.7586	+	12.7586i	−0.741578	+	0.741578i
$297$		−	5.25085i		−	0.304685i
$298$			1.48797i			0.0861956i
$299$	1.91994	−	1.91994i	0.111033	−	0.111033i
$300$	0.592104	−	0.592104i	0.0341851	−	0.0341851i
$301$	−7.02628	−	7.02628i	−0.404988	−	0.404988i
$302$	−6.68379			−0.384609
$303$	−8.74073	−	8.74073i	−0.502142	−	0.502142i
$304$		−	5.61996i		−	0.322327i
$305$	24.8090			1.42056
$306$	0.454407	+	2.68920i	0.0259767	+	0.153731i
$307$	21.0887			1.20360			0.601798	−	0.798648i	$-0.294451\pi$
$307$	21.0887			1.20360			0.601798	+	0.798648i	$0.294451\pi$
$308$			8.20421i			0.467478i
$309$	−2.46176	−	2.46176i	−0.140045	−	0.140045i
$310$	−0.310863			−0.0176558
$311$	−7.97525	−	7.97525i	−0.452235	−	0.452235i	0.443861	−	0.896096i	$-0.353608\pi$
$311$	−7.97525	−	7.97525i	−0.452235	−	0.452235i	−0.896096	+	0.443861i	$0.853608\pi$
$312$	7.49579	−	7.49579i	0.424366	−	0.424366i
$313$	−14.0917	+	14.0917i	−0.796511	+	0.796511i	−0.982544	−	0.186033i	$-0.940437\pi$
$313$	−14.0917	+	14.0917i	−0.796511	+	0.796511i	0.186033	+	0.982544i	$0.440437\pi$
$314$		−	15.6533i		−	0.883367i
$315$			2.35286i			0.132568i
$316$	11.5686	−	11.5686i	0.650787	−	0.650787i
$317$	−21.5746	+	21.5746i	−1.21175	+	1.21175i	−0.241299	+	0.970451i	$0.577574\pi$
$317$	−21.5746	+	21.5746i	−1.21175	+	1.21175i	−0.970451	+	0.241299i	$0.922426\pi$
$318$	4.43397	+	4.43397i	0.248645	+	0.248645i
$319$	−30.2241			−1.69222
$320$	1.11537	+	1.11537i	0.0623508	+	0.0623508i
$321$			4.64675i			0.259356i
$322$	−0.399248			−0.0222492
$323$	−14.5883	+	2.46506i	−0.811715	+	0.137160i
$324$	−1.56245			−0.0868030
$325$			2.41089i			0.133732i
$326$	11.2022	+	11.2022i	0.620435	+	0.620435i
$327$	−13.9330			−0.770494
$328$	−10.1562	−	10.1562i	−0.560783	−	0.560783i
$329$	−4.35683	+	4.35683i	−0.240200	+	0.240200i
$330$	−5.77858	+	5.77858i	−0.318101	+	0.318101i
$331$			24.7998i			1.36312i	0.731763	+	0.681560i	$0.238698\pi$
$331$			24.7998i			1.36312i	−0.731763	+	0.681560i	$0.761302\pi$
$332$			12.6448i			0.693976i
$333$	−5.41429	+	5.41429i	−0.296701	+	0.296701i
$334$	−11.7748	+	11.7748i	−0.644286	+	0.644286i
$335$	12.4323	+	12.4323i	0.679249	+	0.679249i
$336$	1.56617			0.0854416
$337$	6.17698	+	6.17698i	0.336482	+	0.336482i	0.855041	−	0.518560i	$-0.173532\pi$
$337$	6.17698	+	6.17698i	0.336482	+	0.336482i	−0.518560	+	0.855041i	$0.673532\pi$
$338$			4.78698i			0.260378i
$339$	9.88305			0.536774
$340$	−8.78239	+	12.3539i	−0.476292	+	0.669984i
$341$	−1.04880			−0.0567956
$342$			2.37359i			0.128349i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	−23.4154			−1.26247
$345$	1.00418	+	1.00418i	0.0540632	+	0.0540632i
$346$	−5.22221	+	5.22221i	−0.280748	+	0.280748i
$347$	−5.65098	+	5.65098i	−0.303360	+	0.303360i	−0.842327	−	0.538967i	$-0.818815\pi$
$347$	−5.65098	+	5.65098i	−0.303360	+	0.303360i	0.538967	+	0.842327i	$0.318815\pi$
$348$			8.99355i			0.482105i
$349$		−	20.2193i		−	1.08232i	−0.840921	−	0.541158i	$-0.817986\pi$
$349$		−	20.2193i		−	1.08232i	0.840921	−	0.541158i	$-0.182014\pi$
$350$	0.250670	−	0.250670i	0.0133989	−	0.0133989i
$351$	3.18095	−	3.18095i	0.169786	−	0.169786i
$352$	21.3452	+	21.3452i	1.13770	+	1.13770i
$353$	0.363744			0.0193601			0.00968007	−	0.999953i	$-0.496919\pi$
$353$	0.363744			0.0193601			0.00968007	+	0.999953i	$0.496919\pi$
$354$	−0.899509	−	0.899509i	−0.0478084	−	0.0478084i
$355$			3.63337i			0.192839i
$356$	−19.2243			−1.01888
$357$	−0.686963	−	4.06547i	−0.0363579	−	0.215168i
$358$	1.58470			0.0837539
$359$		−	26.3254i		−	1.38940i	−0.719299	−	0.694701i	$-0.755537\pi$
$359$		−	26.3254i		−	1.38940i	0.719299	−	0.694701i	$-0.244463\pi$
$360$	3.92050	+	3.92050i	0.206628	+	0.206628i
$361$	6.12380			0.322305
$362$	−9.18537	−	9.18537i	−0.482772	−	0.482772i
$363$	−11.7178	+	11.7178i	−0.615022	+	0.615022i
$364$	−4.97008	+	4.97008i	−0.260503	+	0.260503i
$365$			23.2697i			1.21799i
$366$			6.97469i			0.364573i
$367$	−6.99722	+	6.99722i	−0.365252	+	0.365252i	−0.865742	−	0.500490i	$-0.833153\pi$
$367$	−6.99722	+	6.99722i	−0.365252	+	0.365252i	0.500490	+	0.865742i	$0.333153\pi$
$368$	0.668429	−	0.668429i	0.0348443	−	0.0348443i
$369$	−4.30993	−	4.30993i	−0.224366	−	0.224366i
$370$	11.9169			0.619530
$371$	−6.70319	−	6.70319i	−0.348012	−	0.348012i
$372$			0.312083i			0.0161807i
$373$	12.9157			0.668751			0.334376	−	0.942440i	$-0.391475\pi$
$373$	12.9157			0.668751			0.334376	+	0.942440i	$0.391475\pi$
$374$	8.29758	−	11.6719i	0.429058	−	0.603541i
$375$	10.5033			0.542389
$376$			14.5193i			0.748778i
$377$	−18.3097	−	18.3097i	−0.942996	−	0.942996i
$378$	−0.661473			−0.0340225
$379$	11.2530	+	11.2530i	0.578026	+	0.578026i	0.934359	−	0.356333i	$-0.115973\pi$
$379$	11.2530	+	11.2530i	0.578026	+	0.578026i	−0.356333	+	0.934359i	$0.615973\pi$
$380$	−9.32784	+	9.32784i	−0.478508	+	0.478508i
$381$	−10.4788	+	10.4788i	−0.536846	+	0.536846i
$382$			3.45755i			0.176904i
$383$			19.1824i			0.980176i	0.871673	+	0.490088i	$0.163035\pi$
$383$			19.1824i			0.980176i	−0.871673	+	0.490088i	$0.836965\pi$
$384$	7.81662	−	7.81662i	0.398890	−	0.398890i
$385$	8.73594	−	8.73594i	0.445225	−	0.445225i
$386$	−10.1484	−	10.1484i	−0.516538	−	0.516538i
$387$	−9.93667			−0.505109
$388$	9.12417	+	9.12417i	0.463209	+	0.463209i
$389$		−	24.5986i		−	1.24720i	−0.781745	−	0.623598i	$-0.785670\pi$
$389$		−	24.5986i		−	1.24720i	0.781745	−	0.623598i	$-0.214330\pi$
$390$	−7.00130			−0.354524
$391$	−2.02830	−	1.44192i	−0.102576	−	0.0729211i
$392$	2.35647			0.119019
$393$		−	9.13853i		−	0.460978i
$394$	3.13203	+	3.13203i	0.157789	+	0.157789i
$395$	−24.6369			−1.23962
$396$	5.80125	+	5.80125i	0.291524	+	0.291524i
$397$	−15.7916	+	15.7916i	−0.792560	+	0.792560i	−0.981910	−	0.189350i	$-0.939362\pi$
$397$	−15.7916	+	15.7916i	−0.792560	+	0.792560i	0.189350	+	0.981910i	$0.439362\pi$
$398$	3.14157	−	3.14157i	0.157473	−	0.157473i
$399$		−	3.58834i		−	0.179642i
$400$			0.839353i			0.0419676i
$401$	−18.2732	+	18.2732i	−0.912518	+	0.912518i	−0.996470	−	0.0839522i	$-0.973246\pi$
$401$	−18.2732	+	18.2732i	−0.912518	+	0.912518i	0.0839522	+	0.996470i	$0.473246\pi$
$402$	−3.49517	+	3.49517i	−0.174323	+	0.174323i
$403$	−0.635358	−	0.635358i	−0.0316495	−	0.0316495i
$404$	19.3139			0.960902
$405$	1.66372	+	1.66372i	0.0826709	+	0.0826709i
$406$			3.80746i			0.188961i
$407$	40.2055			1.99291
$408$	−7.91886	−	5.62952i	−0.392042	−	0.278703i
$409$	15.7611			0.779339			0.389669	−	0.920955i	$-0.372589\pi$
$409$	15.7611			0.779339			0.389669	+	0.920955i	$0.372589\pi$
$410$			9.48620i			0.468490i
$411$	5.32816	+	5.32816i	0.262819	+	0.262819i
$412$	5.43962			0.267991
$413$	1.35986	+	1.35986i	0.0669143	+	0.0669143i
$414$	−0.282311	+	0.282311i	−0.0138748	+	0.0138748i
$415$	13.4644	−	13.4644i	0.660941	−	0.660941i
$416$			25.8617i			1.26797i
$417$			0.515904i			0.0252640i
$418$	8.81293	−	8.81293i	0.431054	−	0.431054i
$419$	9.48958	−	9.48958i	0.463597	−	0.463597i	−0.436236	−	0.899832i	$-0.643689\pi$
$419$	9.48958	−	9.48958i	0.463597	−	0.463597i	0.899832	+	0.436236i	$0.143689\pi$
$420$	−2.59949	−	2.59949i	−0.126842	−	0.126842i
$421$	−10.2759			−0.500818			−0.250409	−	0.968140i	$-0.580565\pi$
$421$	−10.2759			−0.500818			−0.250409	+	0.968140i	$0.580565\pi$
$422$	−6.16158	−	6.16158i	−0.299941	−	0.299941i
$423$			6.16149i			0.299582i
$424$	−22.3387			−1.08486
$425$	2.17880	−	0.368162i	0.105687	−	0.0178585i
$426$	−1.02147			−0.0494904
$427$		−	10.5442i		−	0.510269i
$428$	−5.13383	−	5.13383i	−0.248153	−	0.248153i
$429$	−23.6211			−1.14044
$430$	10.9353	+	10.9353i	0.527349	+	0.527349i
$431$	20.3715	−	20.3715i	0.981261	−	0.981261i	−0.0185668	−	0.999828i	$-0.505910\pi$
$431$	20.3715	−	20.3715i	0.981261	−	0.981261i	0.999828	+	0.0185668i	$0.00591032\pi$
$432$	1.10745	−	1.10745i	0.0532822	−	0.0532822i
$433$		−	25.4783i		−	1.22441i	−0.790699	−	0.612205i	$-0.790283\pi$
$433$		−	25.4783i		−	1.22441i	0.790699	−	0.612205i	$-0.209717\pi$
$434$			0.132122i			0.00634204i
$435$	9.57644	−	9.57644i	0.459155	−	0.459155i
$436$	15.3934	−	15.3934i	0.737212	−	0.737212i
$437$	−1.53148	−	1.53148i	−0.0732604	−	0.0732604i
$438$	−6.54197			−0.312587
$439$	−23.9545	−	23.9545i	−1.14329	−	1.14329i	−0.987845	−	0.155441i	$-0.950320\pi$
$439$	−23.9545	−	23.9545i	−1.14329	−	1.14329i	−0.155441	−	0.987845i	$-0.549680\pi$
$440$		−	29.1129i		−	1.38790i
$441$	1.00000			0.0476190
$442$	12.0975	−	2.04417i	0.575418	−	0.0972312i
$443$	−10.6561			−0.506289			−0.253144	−	0.967429i	$-0.581465\pi$
$443$	−10.6561			−0.506289			−0.253144	+	0.967429i	$0.581465\pi$
$444$		−	11.9637i		−	0.567770i
$445$	20.4702	+	20.4702i	0.970382	+	0.970382i
$446$	7.98722			0.378206
$447$	−1.59062	−	1.59062i	−0.0752338	−	0.0752338i
$448$	0.474048	−	0.474048i	0.0223966	−	0.0223966i
$449$	29.1315	−	29.1315i	1.37480	−	1.37480i	0.521622	−	0.853176i	$-0.325327\pi$
$449$	29.1315	−	29.1315i	1.37480	−	1.37480i	0.853176	−	0.521622i	$-0.174673\pi$
$450$		−	0.354501i		−	0.0167113i
$451$			32.0048i			1.50705i
$452$	−10.9190	+	10.9190i	−0.513587	+	0.513587i
$453$	7.14490	−	7.14490i	0.335697	−	0.335697i
$454$	4.65961	+	4.65961i	0.218686	+	0.218686i
$455$	10.5844			0.496205
$456$	−5.97916	−	5.97916i	−0.280000	−	0.280000i
$457$		−	42.1677i		−	1.97252i	−0.165202	−	0.986260i	$-0.552828\pi$
$457$		−	42.1677i		−	1.97252i	0.165202	−	0.986260i	$-0.447172\pi$
$458$	−0.225909			−0.0105560
$459$	−3.36048	−	2.38897i	−0.156854	−	0.111507i
$460$	−2.21888			−0.103456
$461$		−	8.08845i		−	0.376717i	−0.982100	−	0.188358i	$-0.939683\pi$
$461$		−	8.08845i		−	0.376717i	0.982100	−	0.188358i	$-0.0603167\pi$
$462$	2.45599	+	2.45599i	0.114263	+	0.114263i
$463$	31.1333			1.44688			0.723442	−	0.690385i	$-0.242559\pi$
$463$	31.1333			1.44688			0.723442	+	0.690385i	$0.242559\pi$
$464$	−6.37453	−	6.37453i	−0.295930	−	0.295930i
$465$	0.332309	−	0.332309i	0.0154105	−	0.0154105i
$466$	−7.43510	+	7.43510i	−0.344424	+	0.344424i
$467$			7.39951i			0.342408i	0.985236	+	0.171204i	$0.0547658\pi$
$467$			7.39951i			0.342408i	−0.985236	+	0.171204i	$0.945234\pi$
$468$			7.02876i			0.324905i
$469$	5.28392	−	5.28392i	0.243989	−	0.243989i
$470$	6.78075	−	6.78075i	0.312773	−	0.312773i
$471$	16.7332	+	16.7332i	0.771026	+	0.771026i
$472$	4.53179			0.208593
$473$	36.8939	+	36.8939i	1.69639	+	1.69639i
$474$		−	6.92631i		−	0.318136i
$475$	1.92309			0.0882374
$476$	5.25060	+	3.73265i	0.240661	+	0.171086i
$477$	−9.47974			−0.434047
$478$		−	0.768173i		−	0.0351354i
$479$	19.1726	+	19.1726i	0.876019	+	0.876019i	0.993120	−	0.117101i	$-0.0373601\pi$
$479$	19.1726	+	19.1726i	0.876019	+	0.876019i	−0.117101	+	0.993120i	$0.537360\pi$
$480$	−13.5264			−0.617391
$481$	24.3564	+	24.3564i	1.11056	+	1.11056i
$482$	−4.26825	+	4.26825i	−0.194414	+	0.194414i
$483$	0.426792	−	0.426792i	0.0194197	−	0.0194197i
$484$		−	25.8921i		−	1.17691i
$485$		−	19.4310i		−	0.882318i
$486$	−0.467732	+	0.467732i	−0.0212167	+	0.0212167i
$487$	22.2738	−	22.2738i	1.00932	−	1.00932i	0.00936691	−	0.999956i	$-0.497018\pi$
$487$	22.2738	−	22.2738i	1.00932	−	1.00932i	0.999956	−	0.00936691i	$-0.00298162\pi$
$488$	−17.5695	−	17.5695i	−0.795334	−	0.795334i
$489$	−23.9501			−1.08306
$490$	−1.10050	−	1.10050i	−0.0497157	−	0.0497157i
$491$			3.17369i			0.143227i	0.997432	+	0.0716133i	$0.0228148\pi$
$491$			3.17369i			0.143227i	−0.997432	+	0.0716133i	$0.977185\pi$
$492$	9.52342			0.429349
$493$	−13.7510	+	19.3431i	−0.619314	+	0.871168i
$494$	10.6777			0.480412
$495$		−	12.3545i		−	0.555293i
$496$	−0.221201	−	0.221201i	−0.00993220	−	0.00993220i
$497$	1.54424			0.0692686
$498$	3.78532	+	3.78532i	0.169624	+	0.169624i
$499$	−7.08666	+	7.08666i	−0.317242	+	0.317242i	−0.847707	−	0.530465i	$-0.822017\pi$
$499$	−7.08666	+	7.08666i	−0.317242	+	0.317242i	0.530465	+	0.847707i	$0.322017\pi$
$500$	−11.6043	+	11.6043i	−0.518960	+	0.518960i
$501$		−	25.1742i		−	1.12470i
$502$		−	1.33924i		−	0.0597734i
$503$	−23.0866	+	23.0866i	−1.02938	+	1.02938i	−0.0298242	+	0.999555i	$0.509495\pi$
$503$	−23.0866	+	23.0866i	−1.02938	+	1.02938i	−0.999555	+	0.0298242i	$0.990505\pi$
$504$	1.66627	−	1.66627i	0.0742217	−	0.0742217i
$505$	−20.5657	−	20.5657i	−0.915160	−	0.915160i
$506$	2.09639			0.0931960
$507$	−5.11723	−	5.11723i	−0.227264	−	0.227264i
$508$		−	23.1544i		−	1.02731i
$509$	−6.78115			−0.300569			−0.150285	−	0.988643i	$-0.548019\pi$
$509$	−6.78115			−0.300569			−0.150285	+	0.988643i	$0.548019\pi$
$510$	1.06915	+	6.32730i	0.0473430	+	0.280177i
$511$	9.89000			0.437508
$512$			16.3850i			0.724123i
$513$	−2.53734	−	2.53734i	−0.112026	−	0.112026i
$514$	−12.9487			−0.571142
$515$	−5.79217	−	5.79217i	−0.255234	−	0.255234i
$516$	10.9782	−	10.9782i	0.483290	−	0.483290i
$517$	22.8771	−	22.8771i	1.00613	−	1.00613i
$518$		−	5.06487i		−	0.222538i
$519$		−	11.1650i		−	0.490088i
$520$	17.6365	−	17.6365i	0.773412	−	0.773412i
$521$	9.60414	−	9.60414i	0.420765	−	0.420765i	−0.464702	−	0.885467i	$-0.653839\pi$
$521$	9.60414	−	9.60414i	0.420765	−	0.420765i	0.885467	+	0.464702i	$0.153839\pi$
$522$	2.69228	+	2.69228i	0.117838	+	0.117838i
$523$	−43.7951			−1.91502			−0.957512	−	0.288392i	$-0.906879\pi$
$523$	−43.7951			−1.91502			−0.957512	+	0.288392i	$0.906879\pi$
$524$	10.0965	+	10.0965i	0.441065	+	0.441065i
$525$			0.535927i			0.0233898i
$526$	15.5020			0.675919
$527$	−0.477169	+	0.671218i	−0.0207858	+	0.0292387i
$528$	−8.22373			−0.357892
$529$			22.6357i			0.984161i
$530$	10.4325	+	10.4325i	0.453159	+	0.453159i
$531$	1.92313			0.0834568
$532$	3.96448	+	3.96448i	0.171882	+	0.171882i
$533$	−19.3884	+	19.3884i	−0.839805	+	0.839805i
$534$	−5.75492	+	5.75492i	−0.249040	+	0.249040i
$535$			10.9331i			0.472681i
$536$		−	17.6089i		−	0.760589i
$537$	−1.69403	+	1.69403i	−0.0731026	+	0.0731026i
$538$	−3.74360	+	3.74360i	−0.161398	+	0.161398i
$539$	−3.71291	−	3.71291i	−0.159926	−	0.159926i
$540$	−3.67623			−0.158200
$541$	−1.33085	−	1.33085i	−0.0572177	−	0.0572177i	0.677919	−	0.735137i	$-0.262882\pi$
$541$	−1.33085	−	1.33085i	−0.0572177	−	0.0572177i	−0.735137	+	0.677919i	$0.762882\pi$
$542$			16.2714i			0.698915i
$543$	19.6381			0.842752
$544$	23.3720	−	3.94929i	1.00207	−	0.169324i
$545$	−32.7822			−1.40424
$546$			2.97566i			0.127347i
$547$	−12.7406	−	12.7406i	−0.544751	−	0.544751i	0.380167	−	0.924918i	$-0.375866\pi$
$547$	−12.7406	−	12.7406i	−0.544751	−	0.544751i	−0.924918	+	0.380167i	$0.875866\pi$
$548$	−11.7733			−0.502932
$549$	−7.45587	−	7.45587i	−0.318209	−	0.318209i
$550$	−1.31623	+	1.31623i	−0.0561242	+	0.0561242i
$551$	−14.6050	+	14.6050i	−0.622196	+	0.622196i
$552$		−	1.42230i		−	0.0605373i
$553$			10.4711i			0.445275i
$554$	12.5187	−	12.5187i	0.531869	−	0.531869i
$555$	−12.7390	+	12.7390i	−0.540742	+	0.540742i
$556$	−0.569983	−	0.569983i	−0.0241726	−	0.0241726i
$557$	−19.5144			−0.826851			−0.413426	−	0.910538i	$-0.635668\pi$
$557$	−19.5144			−0.826851			−0.413426	+	0.910538i	$0.635668\pi$
$558$	0.0934241	+	0.0934241i	0.00395496	+	0.00395496i
$559$			44.7005i			1.89063i
$560$	3.68497			0.155719
$561$	3.60714	+	21.3472i	0.152294	+	0.901279i
$562$	−16.0723			−0.677970
$563$			32.4814i			1.36893i	0.729046	+	0.684465i	$0.239964\pi$
$563$			32.4814i			1.36893i	−0.729046	+	0.684465i	$0.760036\pi$
$564$	−6.80735	−	6.80735i	−0.286641	−	0.286641i
$565$	23.2534			0.978278
$566$	−4.28759	−	4.28759i	−0.180221	−	0.180221i
$567$	0.707107	−	0.707107i	0.0296957	−	0.0296957i
$568$	2.57312	−	2.57312i	0.107966	−	0.107966i
$569$		−	32.6889i		−	1.37039i	−0.728361	−	0.685194i	$-0.759717\pi$
$569$		−	32.6889i		−	1.37039i	0.728361	−	0.685194i	$-0.240283\pi$
$570$			5.58471i			0.233918i
$571$	13.8918	−	13.8918i	0.581353	−	0.581353i	−0.353922	−	0.935275i	$-0.615152\pi$
$571$	13.8918	−	13.8918i	0.581353	−	0.581353i	0.935275	+	0.353922i	$0.115152\pi$
$572$	26.0972	−	26.0972i	1.09118	−	1.09118i
$573$	−3.69608	−	3.69608i	−0.154406	−	0.154406i
$574$	4.03178			0.168283
$575$	0.228729	+	0.228729i	0.00953867	+	0.00953867i
$576$		−	0.670404i		−	0.0279335i
$577$	−22.6080			−0.941182			−0.470591	−	0.882351i	$-0.655959\pi$
$577$	−22.6080			−0.941182			−0.470591	+	0.882351i	$0.655959\pi$
$578$	−3.69476	−	10.6207i	−0.153682	−	0.441763i
$579$	21.6970			0.901696
$580$			21.1605i			0.878643i
$581$	−5.72257	−	5.72257i	−0.237412	−	0.237412i
$582$	5.46277			0.226439
$583$	35.1974	+	35.1974i	1.45773	+	1.45773i
$584$	16.4794	−	16.4794i	0.681924	−	0.681924i
$585$	7.48431	−	7.48431i	0.309438	−	0.309438i
$586$			1.45324i			0.0600330i
$587$			1.89079i			0.0780414i	0.999238	+	0.0390207i	$0.0124238\pi$
$587$			1.89079i			0.0780414i	−0.999238	+	0.0390207i	$0.987576\pi$
$588$	−1.10482	+	1.10482i	−0.0455621	+	0.0455621i
$589$	−0.506805	+	0.506805i	−0.0208825	+	0.0208825i
$590$	−2.11642	−	2.11642i	−0.0871314	−	0.0871314i
$591$	−6.69620			−0.275445
$592$	8.47970	+	8.47970i	0.348514	+	0.348514i
$593$		−	33.0067i		−	1.35542i	−0.735329	−	0.677711i	$-0.762972\pi$
$593$		−	33.0067i		−	1.35542i	0.735329	−	0.677711i	$-0.237028\pi$
$594$	3.47329			0.142511
$595$	−1.61632	−	9.56547i	−0.0662629	−	0.392146i
$596$	3.51470			0.143968
$597$			6.71661i			0.274892i
$598$	1.26999	+	1.26999i	0.0519337	+	0.0519337i
$599$	−12.9658			−0.529767			−0.264884	−	0.964280i	$-0.585334\pi$
$599$	−12.9658			−0.529767			−0.264884	+	0.964280i	$0.585334\pi$
$600$	0.893000	+	0.893000i	0.0364566	+	0.0364566i
$601$	24.5515	−	24.5515i	1.00148	−	1.00148i	0.00147859	−	0.999999i	$-0.499529\pi$
$601$	24.5515	−	24.5515i	1.00148	−	1.00148i	0.999999	−	0.00147859i	$-0.000470649\pi$
$602$	4.64769	−	4.64769i	0.189426	−	0.189426i
$603$		−	7.47259i		−	0.304307i
$604$			15.7877i			0.642392i
$605$	−27.5702	+	27.5702i	−1.12089	+	1.12089i
$606$	5.78175	−	5.78175i	0.234868	−	0.234868i
$607$	14.3918	+	14.3918i	0.584143	+	0.584143i	0.936039	−	0.351896i	$-0.114463\pi$
$607$	14.3918	+	14.3918i	0.584143	+	0.584143i	−0.351896	+	0.936039i	$0.614463\pi$
$608$	20.6291			0.836619
$609$	−4.07014	−	4.07014i	−0.164930	−	0.164930i
$610$			16.4104i			0.664439i
$611$	27.7177			1.12134
$612$	6.35212	−	1.07335i	0.256769	−	0.0433875i
$613$	34.0233			1.37419			0.687095	−	0.726568i	$-0.258886\pi$
$613$	34.0233			1.37419			0.687095	+	0.726568i	$0.258886\pi$
$614$			13.9496i			0.562960i
$615$	−10.1406	−	10.1406i	−0.408910	−	0.408910i
$616$	−12.3734			−0.498540
$617$	−20.8759	−	20.8759i	−0.840433	−	0.840433i	0.148482	−	0.988915i	$-0.452561\pi$
$617$	−20.8759	−	20.8759i	−0.840433	−	0.840433i	−0.988915	+	0.148482i	$0.952561\pi$
$618$	1.62839	−	1.62839i	0.0655034	−	0.0655034i
$619$	4.38648	−	4.38648i	0.176308	−	0.176308i	−0.613436	−	0.789744i	$-0.710213\pi$
$619$	4.38648	−	4.38648i	0.176308	−	0.176308i	0.789744	+	0.613436i	$0.210213\pi$
$620$			0.734285i			0.0294896i
$621$		−	0.603575i		−	0.0242206i
$622$	5.27541	−	5.27541i	0.211525	−	0.211525i
$623$	8.70017	−	8.70017i	0.348565	−	0.348565i
$624$	−4.98191	−	4.98191i	−0.199436	−	0.199436i
$625$	27.3924			1.09570
$626$	−9.32128	−	9.32128i	−0.372553	−	0.372553i
$627$			18.8418i			0.752471i
$628$	−36.9744			−1.47544
$629$	18.2922	−	25.7311i	0.729359	−	1.02597i
$630$	−1.55635			−0.0620064
$631$		−	5.22637i		−	0.208059i	−0.994574	−	0.104029i	$-0.966826\pi$
$631$		−	5.22637i		−	0.208059i	0.994574	−	0.104029i	$-0.0331736\pi$
$632$	17.4476	+	17.4476i	0.694030	+	0.694030i
$633$	13.1733			0.523592
$634$	−14.2710	−	14.2710i	−0.566774	−	0.566774i
$635$	−24.6551	+	24.6551i	−0.978408	+	0.978408i
$636$	10.4734	−	10.4734i	0.415298	−	0.415298i
$637$		−	4.49854i		−	0.178239i
$638$		−	19.9924i		−	0.791507i
$639$	1.09194	−	1.09194i	0.0431965	−	0.0431965i
$640$	18.3914	−	18.3914i	0.726983	−	0.726983i
$641$	−16.2540	−	16.2540i	−0.641994	−	0.641994i	0.309051	−	0.951045i	$-0.399989\pi$
$641$	−16.2540	−	16.2540i	−0.641994	−	0.641994i	−0.951045	+	0.309051i	$0.899989\pi$
$642$	−3.07370			−0.121309
$643$	−2.55336	−	2.55336i	−0.100695	−	0.100695i	0.654965	−	0.755659i	$-0.272683\pi$
$643$	−2.55336	−	2.55336i	−0.100695	−	0.100695i	−0.755659	+	0.654965i	$0.772683\pi$
$644$			0.943058i			0.0371617i
$645$	−23.3795			−0.920568
$646$	−1.63057	−	9.64977i	−0.0641539	−	0.379665i
$647$	7.56712			0.297494			0.148747	−	0.988875i	$-0.452476\pi$
$647$	7.56712			0.297494			0.148747	+	0.988875i	$0.452476\pi$
$648$		−	2.35647i		−	0.0925707i
$649$	−7.14041	−	7.14041i	−0.280286	−	0.280286i
$650$	−1.59474			−0.0625507
$651$	−0.141237	−	0.141237i	−0.00553550	−	0.00553550i
$652$	26.4606	−	26.4606i	1.03628	−	1.03628i
$653$	−11.7538	+	11.7538i	−0.459964	+	0.459964i	−0.898643	−	0.438680i	$-0.855446\pi$
$653$	−11.7538	+	11.7538i	−0.459964	+	0.459964i	0.438680	+	0.898643i	$0.355446\pi$
$654$		−	9.21627i		−	0.360384i
$655$		−	21.5016i		−	0.840139i
$656$	−6.75009	+	6.75009i	−0.263547	+	0.263547i
$657$	6.99329	−	6.99329i	0.272834	−	0.272834i
$658$	−2.88192	−	2.88192i	−0.112349	−	0.112349i
$659$	−20.8412			−0.811859			−0.405929	−	0.913904i	$-0.633052\pi$
$659$	−20.8412			−0.811859			−0.405929	+	0.913904i	$0.633052\pi$
$660$	13.6495	+	13.6495i	0.531306	+	0.531306i
$661$			8.01914i			0.311908i	0.987764	+	0.155954i	$0.0498452\pi$
$661$			8.01914i			0.311908i	−0.987764	+	0.155954i	$0.950155\pi$
$662$	−16.4044			−0.637574
$663$	−10.7469	+	15.1173i	−0.417374	+	0.587106i
$664$	−19.0707			−0.740088
$665$		−	8.44285i		−	0.327400i
$666$	−3.58140	−	3.58140i	−0.138777	−	0.138777i
$667$	−3.47420			−0.134522
$668$	27.8130	+	27.8130i	1.07612	+	1.07612i
$669$	−8.53825	+	8.53825i	−0.330108	+	0.330108i
$670$	−8.22362	+	8.22362i	−0.317706	+	0.317706i
$671$			55.3659i			2.13738i
$672$			5.74891i			0.221769i
$673$	−2.05382	+	2.05382i	−0.0791688	+	0.0791688i	−0.745582	−	0.666414i	$-0.767829\pi$
$673$	−2.05382	+	2.05382i	−0.0791688	+	0.0791688i	0.666414	+	0.745582i	$0.267829\pi$
$674$	−4.08590	+	4.08590i	−0.157383	+	0.157383i
$675$	0.378957	+	0.378957i	0.0145861	+	0.0145861i
$676$	11.3073			0.434894
$677$	−10.6917	−	10.6917i	−0.410917	−	0.410917i	0.471141	−	0.882058i	$-0.343842\pi$
$677$	−10.6917	−	10.6917i	−0.410917	−	0.410917i	−0.882058	+	0.471141i	$0.843842\pi$
$678$			6.53737i			0.251066i
$679$	−8.25850			−0.316932
$680$	−18.6319	−	13.2454i	−0.714502	−	0.507940i
$681$	−9.96214			−0.381750
$682$		−	0.693751i		−	0.0265651i
$683$	−14.5366	−	14.5366i	−0.556228	−	0.556228i	0.372003	−	0.928231i	$-0.378671\pi$
$683$	−14.5366	−	14.5366i	−0.556228	−	0.556228i	−0.928231	+	0.372003i	$0.878671\pi$
$684$	5.60662			0.214374
$685$	12.5364	+	12.5364i	0.478991	+	0.478991i
$686$	−0.467732	+	0.467732i	−0.0178581	+	0.0178581i
$687$	0.241494	−	0.241494i	0.00921357	−	0.00921357i
$688$			15.5625i			0.593315i
$689$			42.6450i			1.62464i
$690$	−0.664237	+	0.664237i	−0.0252871	+	0.0252871i
$691$	−10.5531	+	10.5531i	−0.401458	+	0.401458i	−0.878747	−	0.477288i	$-0.841620\pi$
$691$	−10.5531	+	10.5531i	−0.401458	+	0.401458i	0.477288	+	0.878747i	$0.341620\pi$
$692$	12.3353	+	12.3353i	0.468918	+	0.468918i
$693$	−5.25085			−0.199463
$694$	−3.73797	−	3.73797i	−0.141891	−	0.141891i
$695$			1.21385i			0.0460439i
$696$	−13.5639			−0.514139
$697$	20.4827	+	14.5612i	0.775837	+	0.551543i
$698$	13.3745			0.506234
$699$		−	15.8961i		−	0.601245i
$700$	−0.592104	−	0.592104i	−0.0223794	−	0.0223794i
$701$	42.2529			1.59587			0.797936	−	0.602743i	$-0.205925\pi$
$701$	42.2529			1.59587			0.797936	+	0.602743i	$0.205925\pi$
$702$	2.10411	+	2.10411i	0.0794145	+	0.0794145i
$703$	19.4283	−	19.4283i	0.732753	−	0.732753i
$704$	−2.48915	+	2.48915i	−0.0938134	+	0.0938134i
$705$			14.4971i			0.545992i
$706$			0.240607i			0.00905535i
$707$	−8.74073	+	8.74073i	−0.328729	+	0.328729i
$708$	−2.12472	+	2.12472i	−0.0798518	+	0.0798518i
$709$	29.5551	+	29.5551i	1.10997	+	1.10997i	0.993154	+	0.116813i	$0.0372678\pi$
$709$	29.5551	+	29.5551i	1.10997	+	1.10997i	0.116813	+	0.993154i	$0.462732\pi$
$710$	−2.40337			−0.0901970
$711$	7.40415	+	7.40415i	0.277677	+	0.277677i
$712$		−	28.9937i		−	1.08658i
$713$	−0.120557			−0.00451491
$714$	2.68920	−	0.454407i	0.100641	−	0.0170058i
$715$	−55.5771			−2.07847
$716$		−	3.74319i		−	0.139890i
$717$	0.821168	+	0.821168i	0.0306671	+	0.0306671i
$718$	17.4135			0.649867
$719$	−18.4733	−	18.4733i	−0.688936	−	0.688936i	0.273060	−	0.961997i	$-0.411964\pi$
$719$	−18.4733	−	18.4733i	−0.688936	−	0.688936i	−0.961997	+	0.273060i	$0.911964\pi$
$720$	2.60567	−	2.60567i	0.0971076	−	0.0971076i
$721$	−2.46176	+	2.46176i	−0.0916809	+	0.0916809i
$722$			4.05073i			0.150752i
$723$		−	9.12543i		−	0.339379i
$724$	−21.6966	+	21.6966i	−0.806348	+	0.806348i
$725$	2.18130	−	2.18130i	0.0810113	−	0.0810113i
$726$	−7.75097	−	7.75097i	−0.287666	−	0.287666i
$727$	−18.5323			−0.687325			−0.343663	−	0.939093i	$-0.611668\pi$
$727$	−18.5323			−0.687325			−0.343663	+	0.939093i	$0.611668\pi$
$728$	−7.49579	−	7.49579i	−0.277813	−	0.277813i
$729$		−	1.00000i		−	0.0370370i
$730$	−15.3923			−0.569695
$731$	40.3973	−	6.82612i	1.49415	−	0.252473i
$732$	16.4748			0.608927
$733$			42.9060i			1.58477i	0.610021	+	0.792385i	$0.291161\pi$
$733$			42.9060i			1.58477i	−0.610021	+	0.792385i	$0.708839\pi$
$734$	−4.62847	−	4.62847i	−0.170840	−	0.170840i
$735$	2.35286			0.0867864
$736$	2.45359	+	2.45359i	0.0904405	+	0.0904405i
$737$	−27.7451	+	27.7451i	−1.02200	+	1.02200i
$738$	2.85090	−	2.85090i	0.104943	−	0.104943i
$739$			19.1622i			0.704893i	0.935832	+	0.352446i	$0.114650\pi$
$739$			19.1622i			0.704893i	−0.935832	+	0.352446i	$0.885350\pi$
$740$		−	28.1487i		−	1.03477i
$741$	−11.4143	+	11.4143i	−0.419316	+	0.419316i
$742$	4.43397	−	4.43397i	0.162776	−	0.162776i
$743$	−20.2472	−	20.2472i	−0.742797	−	0.742797i	0.230319	−	0.973115i	$-0.426023\pi$
$743$	−20.2472	−	20.2472i	−0.742797	−	0.742797i	−0.973115	+	0.230319i	$0.926023\pi$
$744$	−0.470677			−0.0172559
$745$	−3.74250	−	3.74250i	−0.137115	−	0.137115i
$746$			8.54340i			0.312796i
$747$	−8.09294			−0.296105
$748$	−27.5701	−	19.5996i	−1.00806	−	0.716632i
$749$	4.64675			0.169789
$750$			6.94766i			0.253693i
$751$	−6.54293	−	6.54293i	−0.238755	−	0.238755i	0.577580	−	0.816334i	$-0.303997\pi$
$751$	−6.54293	−	6.54293i	−0.238755	−	0.238755i	−0.816334	+	0.577580i	$0.803997\pi$
$752$	9.64994			0.351897
$753$	1.43164	+	1.43164i	0.0521717	+	0.0521717i
$754$	12.1113	−	12.1113i	0.441069	−	0.441069i
$755$	16.8109	−	16.8109i	0.611812	−	0.611812i
$756$			1.56245i			0.0568259i
$757$			30.7343i			1.11706i	0.829485	+	0.558529i	$0.188634\pi$
$757$			30.7343i			1.11706i	−0.829485	+	0.558529i	$0.811366\pi$
$758$	−7.44352	+	7.44352i	−0.270361	+	0.270361i
$759$	−2.24102	+	2.24102i	−0.0813439	+	0.0813439i
$760$	−14.0681	−	14.0681i	−0.510303	−	0.510303i
$761$	2.54666			0.0923164			0.0461582	−	0.998934i	$-0.485302\pi$
$761$	2.54666			0.0923164			0.0461582	+	0.998934i	$0.485302\pi$
$762$	−6.93144	−	6.93144i	−0.251100	−	0.251100i
$763$			13.9330i			0.504407i
$764$	8.16703			0.295473
$765$	−7.90672	−	5.62090i	−0.285868	−	0.203224i
$766$	−12.6886			−0.458459
$767$		−	8.65128i		−	0.312380i
$768$	6.11857	+	6.11857i	0.220785	+	0.220785i
$769$	8.31448			0.299828			0.149914	−	0.988699i	$-0.452100\pi$
$769$	8.31448			0.299828			0.149914	+	0.988699i	$0.452100\pi$
$770$	5.77858	+	5.77858i	0.208246	+	0.208246i
$771$	13.8420	−	13.8420i	0.498508	−	0.498508i
$772$	−23.9713	+	23.9713i	−0.862746	+	0.862746i
$773$		−	37.8279i		−	1.36058i	−0.732945	−	0.680288i	$-0.761855\pi$
$773$		−	37.8279i		−	1.36058i	0.732945	−	0.680288i	$-0.238145\pi$
$774$		−	6.57283i		−	0.236256i
$775$	0.0756925	−	0.0756925i	0.00271895	−	0.00271895i
$776$	−13.7609	+	13.7609i	−0.493988	+	0.493988i
$777$	5.41429	+	5.41429i	0.194237	+	0.194237i
$778$	16.2713			0.583353
$779$	15.4655	+	15.4655i	0.554110	+	0.554110i
$780$			16.5377i			0.592143i
$781$	−8.10856			−0.290147
$782$	0.953792	−	1.34167i	0.0341075	−	0.0479779i
$783$	−5.75604			−0.205704
$784$		−	1.56617i		−	0.0559347i
$785$	39.3708	+	39.3708i	1.40520	+	1.40520i
$786$	6.04489			0.215614
$787$	−31.9408	−	31.9408i	−1.13857	−	1.13857i	−0.988707	−	0.149859i	$-0.952118\pi$
$787$	−31.9408	−	31.9408i	−1.13857	−	1.13857i	−0.149859	−	0.988707i	$-0.547882\pi$
$788$	7.39811	−	7.39811i	0.263547	−	0.263547i
$789$	−16.5715	+	16.5715i	−0.589959	+	0.589959i
$790$		−	16.2966i		−	0.579808i
$791$		−	9.88305i		−	0.351401i
$792$	−8.74934	+	8.74934i	−0.310894	+	0.310894i
$793$	−33.5405	+	33.5405i	−1.19106	+	1.19106i
$794$	−10.4457	−	10.4457i	−0.370705	−	0.370705i
$795$	−22.3044			−0.791057
$796$	−7.42066	−	7.42066i	−0.263018	−	0.263018i
$797$			6.59399i			0.233571i	0.993157	+	0.116786i	$0.0372590\pi$
$797$			6.59399i			0.233571i	−0.993157	+	0.116786i	$0.962741\pi$
$798$	2.37359			0.0840242
$799$	−4.23272	−	25.0494i	−0.149743	−	0.886183i
$800$	−3.08099			−0.108930
$801$		−	12.3039i		−	0.434737i
$802$	−12.0872	−	12.0872i	−0.426813	−	0.426813i
$803$	−51.9309			−1.83260
$804$	8.25588	+	8.25588i	0.291163	+	0.291163i
$805$	1.00418	−	1.00418i	0.0353927	−	0.0353927i
$806$	0.420272	−	0.420272i	0.0148035	−	0.0148035i
$807$		−	8.00374i		−	0.281745i
$808$			29.1289i			1.02475i
$809$	−28.8037	+	28.8037i	−1.01268	+	1.01268i	−0.0127642	+	0.999919i	$0.504063\pi$
$809$	−28.8037	+	28.8037i	−1.01268	+	1.01268i	−0.999919	+	0.0127642i	$0.995937\pi$
$810$	−1.10050	+	1.10050i	−0.0386678	+	0.0386678i
$811$	12.4244	+	12.4244i	0.436279	+	0.436279i	0.890758	−	0.454479i	$-0.150175\pi$
$811$	12.4244	+	12.4244i	0.436279	+	0.436279i	−0.454479	+	0.890758i	$0.650175\pi$
$812$	8.99355			0.315612
$813$	−17.3939	−	17.3939i	−0.610031	−	0.610031i
$814$			26.5949i			0.932149i
$815$	−56.3512			−1.97390
$816$	−3.74153	+	5.26309i	−0.130980	+	0.184245i
$817$	35.6562			1.24745
$818$			10.4256i			0.364521i
$819$	−3.18095	−	3.18095i	−0.111151	−	0.111151i
$820$	22.4072			0.782494
$821$	−2.39839	−	2.39839i	−0.0837045	−	0.0837045i	0.664015	−	0.747719i	$-0.268851\pi$
$821$	−2.39839	−	2.39839i	−0.0837045	−	0.0837045i	−0.747719	+	0.664015i	$0.768851\pi$
$822$	−3.52443	+	3.52443i	−0.122929	+	0.122929i
$823$	−17.9237	+	17.9237i	−0.624781	+	0.624781i	−0.946750	−	0.321969i	$-0.895655\pi$
$823$	−17.9237	+	17.9237i	−0.624781	+	0.624781i	0.321969	+	0.946750i	$0.395655\pi$
$824$			8.20394i			0.285798i
$825$		−	2.81407i		−	0.0979733i
$826$	−0.899509	+	0.899509i	−0.0312979	+	0.0312979i
$827$	5.93889	−	5.93889i	0.206516	−	0.206516i	−0.596269	−	0.802785i	$-0.703351\pi$
$827$	5.93889	−	5.93889i	0.206516	−	0.206516i	0.802785	+	0.596269i	$0.203351\pi$
$828$	0.666843	+	0.666843i	0.0231744	+	0.0231744i
$829$	0.720245			0.0250151			0.0125076	−	0.999922i	$-0.496019\pi$
$829$	0.720245			0.0250151			0.0125076	+	0.999922i	$0.496019\pi$
$830$	8.90632	+	8.90632i	0.309143	+	0.309143i
$831$			26.7647i			0.928458i
$832$	−3.01584			−0.104555
$833$	−4.06547	+	0.686963i	−0.140860	+	0.0238019i
$834$	−0.341257			−0.0118168
$835$		−	59.2311i		−	2.04978i
$836$	−20.8169	−	20.8169i	−0.719967	−	0.719967i
$837$	−0.199739			−0.00690398
$838$	6.27710	+	6.27710i	0.216839	+	0.216839i
$839$	−31.6356	+	31.6356i	−1.09218	+	1.09218i	−0.0968861	+	0.995295i	$0.530888\pi$
$839$	−31.6356	+	31.6356i	−1.09218	+	1.09218i	−0.995295	+	0.0968861i	$0.969112\pi$
$840$	3.92050	−	3.92050i	0.135270	−	0.135270i
$841$			4.13202i			0.142484i
$842$		−	6.79724i		−	0.234248i
$843$	17.1811	−	17.1811i	0.591749	−	0.591749i
$844$	−14.5542	+	14.5542i	−0.500975	+	0.500975i
$845$	−12.0401	−	12.0401i	−0.414192	−	0.414192i
$846$	−4.07566			−0.140124
$847$	11.7178	+	11.7178i	0.402627	+	0.402627i
$848$			14.8469i			0.509844i
$849$	9.16677			0.314603
$850$	0.243529	+	1.44121i	0.00835298	+	0.0494332i
$851$	4.62155			0.158425
$852$			2.41280i			0.0826612i
$853$	4.85222	+	4.85222i	0.166137	+	0.166137i	0.785279	−	0.619142i	$-0.212519\pi$
$853$	4.85222	+	4.85222i	0.166137	+	0.166137i	−0.619142	+	0.785279i	$0.712519\pi$
$854$	6.97469			0.238669
$855$	−5.97000	−	5.97000i	−0.204170	−	0.204170i
$856$	7.74276	−	7.74276i	0.264642	−	0.264642i
$857$	14.6055	−	14.6055i	0.498916	−	0.498916i	−0.412185	−	0.911100i	$-0.635234\pi$
$857$	14.6055	−	14.6055i	0.498916	−	0.498916i	0.911100	+	0.412185i	$0.135234\pi$
$858$		−	15.6247i		−	0.533420i
$859$			5.76996i			0.196868i	0.995144	+	0.0984342i	$0.0313834\pi$
$859$			5.76996i			0.196868i	−0.995144	+	0.0984342i	$0.968617\pi$
$860$	25.8302	−	25.8302i	0.880803	−	0.880803i
$861$	−4.30993	+	4.30993i	−0.146882	+	0.146882i
$862$	13.4752	+	13.4752i	0.458967	+	0.458967i
$863$	45.6981			1.55558			0.777790	−	0.628524i	$-0.216341\pi$
$863$	45.6981			1.55558			0.777790	+	0.628524i	$0.216341\pi$
$864$	4.06509	+	4.06509i	0.138297	+	0.138297i
$865$		−	26.2696i		−	0.893191i
$866$	16.8532			0.572696
$867$	15.3031	+	7.40376i	0.519720	+	0.251445i
$868$	0.312083			0.0105928
$869$		−	54.9819i		−	1.86513i
$870$	6.33455	+	6.33455i	0.214761	+	0.214761i
$871$	−33.6158			−1.13903
$872$	23.2161	+	23.2161i	0.786196	+	0.786196i
$873$	−5.83964	+	5.83964i	−0.197642	+	0.197642i
$874$	1.01303	−	1.01303i	0.0342662	−	0.0342662i
$875$		−	10.5033i		−	0.355077i
$876$			15.4527i			0.522098i
$877$	4.16940	−	4.16940i	0.140791	−	0.140791i	−0.633199	−	0.773989i	$-0.718258\pi$
$877$	4.16940	−	4.16940i	0.140791	−	0.140791i	0.773989	+	0.633199i	$0.218258\pi$
$878$	15.8452	−	15.8452i	0.534751	−	0.534751i
$879$	−1.55350	−	1.55350i	−0.0523983	−	0.0523983i
$880$	−19.3492			−0.652263
$881$	−20.0194	−	20.0194i	−0.674471	−	0.674471i	0.284273	−	0.958744i	$-0.408248\pi$
$881$	−20.0194	−	20.0194i	−0.674471	−	0.674471i	−0.958744	+	0.284273i	$0.908248\pi$
$882$			0.661473i			0.0222729i
$883$	−39.7453			−1.33754			−0.668768	−	0.743471i	$-0.733178\pi$
$883$	−39.7453			−1.33754			−0.668768	+	0.743471i	$0.733178\pi$
$884$	−4.82850	−	28.5752i	−0.162400	−	0.961090i
$885$	4.52485			0.152101
$886$		−	7.04875i		−	0.236807i
$887$	9.02914	+	9.02914i	0.303169	+	0.303169i	0.842252	−	0.539083i	$-0.181229\pi$
$887$	9.02914	+	9.02914i	0.303169	+	0.303169i	−0.539083	+	0.842252i	$0.681229\pi$
$888$	18.0434			0.605496
$889$	10.4788	+	10.4788i	0.351448	+	0.351448i
$890$	−13.5405	+	13.5405i	−0.453878	+	0.453878i
$891$	−3.71291	+	3.71291i	−0.124387	+	0.124387i
$892$		−	18.8665i		−	0.631697i
$893$		−	22.1095i		−	0.739867i
$894$	1.05215	−	1.05215i	0.0351892	−	0.0351892i
$895$	−3.98580	+	3.98580i	−0.133230	+	0.133230i
$896$	−7.81662	−	7.81662i	−0.261135	−	0.261135i
$897$	−2.71521			−0.0906581
$898$	19.2697	+	19.2697i	0.643037	+	0.643037i
$899$			1.14970i			0.0383448i
$900$	−0.837361			−0.0279120
$901$	38.5396	−	6.51223i	1.28394	−	0.216954i
$902$	−21.1703			−0.704893
$903$			9.93667i			0.330672i
$904$	−16.4679	−	16.4679i	−0.547713	−	0.547713i
$905$	46.2056			1.53593
$906$	4.72616	+	4.72616i	0.157016	+	0.157016i
$907$	8.76923	−	8.76923i	0.291177	−	0.291177i	−0.546368	−	0.837545i	$-0.683990\pi$
$907$	8.76923	−	8.76923i	0.291177	−	0.291177i	0.837545	+	0.546368i	$0.183990\pi$
$908$	11.0064	−	11.0064i	0.365260	−	0.365260i
$909$			12.3613i			0.409997i
$910$			7.00130i			0.232091i
$911$	−4.06611	+	4.06611i	−0.134716	+	0.134716i	−0.771249	−	0.636533i	$-0.780368\pi$
$911$	−4.06611	+	4.06611i	−0.134716	+	0.134716i	0.636533	+	0.771249i	$0.280368\pi$
$912$	−3.97391	+	3.97391i	−0.131589	+	0.131589i
$913$	30.0484	+	30.0484i	0.994455	+	0.994455i
$914$	27.8927			0.922610
$915$	−17.5426	−	17.5426i	−0.579940	−	0.579940i
$916$			0.533616i			0.0176312i
$917$	−9.13853			−0.301781
$918$	1.58024	−	2.22287i	0.0521556	−	0.0733655i
$919$	−42.2895			−1.39500			−0.697500	−	0.716585i	$-0.745704\pi$
$919$	−42.2895			−1.39500			−0.697500	+	0.716585i	$0.745704\pi$
$920$		−	3.34648i		−	0.110330i
$921$	−14.9120	−	14.9120i	−0.491366	−	0.491366i
$922$	5.35029			0.176202
$923$	−4.91214	−	4.91214i	−0.161685	−	0.161685i
$924$	5.80125	−	5.80125i	0.190847	−	0.190847i
$925$	−2.90166	+	2.90166i	−0.0954061	+	0.0954061i
$926$			20.5938i			0.676754i
$927$			3.48146i			0.114346i
$928$	23.3988	−	23.3988i	0.768105	−	0.768105i
$929$	8.33116	−	8.33116i	0.273337	−	0.273337i	−0.557105	−	0.830442i	$-0.688088\pi$
$929$	8.33116	−	8.33116i	0.273337	−	0.273337i	0.830442	+	0.557105i	$0.188088\pi$
$930$	0.219813	+	0.219813i	0.00720797	+	0.00720797i
$931$	−3.58834			−0.117603
$932$	17.5623	+	17.5623i	0.575273	+	0.575273i
$933$			11.2787i			0.369248i
$934$	−4.89457			−0.160155
$935$	8.48708	+	50.2268i	0.277557	+	1.64259i
$936$	−10.6007			−0.346493
$937$		−	39.3993i		−	1.28712i	−0.765396	−	0.643560i	$-0.777457\pi$
$937$		−	39.3993i		−	1.28712i	0.765396	−	0.643560i	$-0.222543\pi$
$938$	3.49517	+	3.49517i	0.114121	+	0.114121i
$939$	19.9287			0.650348
$940$	−16.0167	−	16.0167i	−0.522407	−	0.522407i
$941$	−1.20597	+	1.20597i	−0.0393135	+	0.0393135i	−0.726490	−	0.687177i	$-0.758850\pi$
$941$	−1.20597	+	1.20597i	−0.0393135	+	0.0393135i	0.687177	+	0.726490i	$0.258850\pi$
$942$	−11.0686	+	11.0686i	−0.360633	+	0.360633i
$943$			3.67889i			0.119801i
$944$		−	3.01195i		−	0.0980307i
$945$	1.66372	−	1.66372i	0.0541208	−	0.0541208i
$946$	−24.4043	+	24.4043i	−0.793453	+	0.793453i
$947$	−27.1014	−	27.1014i	−0.880678	−	0.880678i	0.112926	−	0.993603i	$-0.463978\pi$
$947$	−27.1014	−	27.1014i	−0.880678	−	0.880678i	−0.993603	+	0.112926i	$0.963978\pi$
$948$	−16.3605			−0.531366
$949$	−31.4596	−	31.4596i	−1.02122	−	1.02122i
$950$			1.27207i			0.0412714i
$951$	30.5111			0.989390
$952$	−5.62952	+	7.91886i	−0.182454	+	0.256652i
$953$	−43.5262			−1.40995			−0.704975	−	0.709232i	$-0.749042\pi$
$953$	−43.5262			−1.40995			−0.704975	+	0.709232i	$0.749042\pi$
$954$		−	6.27059i		−	0.203018i
$955$	−8.69635	−	8.69635i	−0.281407	−	0.281407i
$956$	−1.81449			−0.0586848
$957$	21.3717	+	21.3717i	0.690848	+	0.690848i
$958$	−12.6822	+	12.6822i	−0.409742	+	0.409742i
$959$	5.32816	−	5.32816i	0.172055	−	0.172055i
$960$		−	1.57736i		−	0.0509092i
$961$		−	30.9601i		−	0.998713i
$962$	−16.1111	+	16.1111i	−0.519442	+	0.519442i
$963$	3.28575	−	3.28575i	0.105882	−	0.105882i
$964$	10.0820	+	10.0820i	0.324719	+	0.324719i
$965$	51.0498			1.64335
$966$	0.282311	+	0.282311i	0.00908322	+	0.00908322i
$967$		−	9.46568i		−	0.304396i	−0.988350	−	0.152198i	$-0.951365\pi$
$967$		−	9.46568i		−	0.304396i	0.988350	−	0.152198i	$-0.0486351\pi$
$968$	39.0499			1.25511
$969$	12.0586	+	8.57243i	0.387377	+	0.275386i
$970$	12.8531			0.412688
$971$			1.89708i			0.0608801i	0.999537	+	0.0304400i	$0.00969086\pi$
$971$			1.89708i			0.0608801i	−0.999537	+	0.0304400i	$0.990309\pi$
$972$	1.10482	+	1.10482i	0.0354372	+	0.0354372i
$973$	0.515904			0.0165391
$974$	14.7335	+	14.7335i	0.472092	+	0.472092i
$975$	1.70476	−	1.70476i	0.0545959	−	0.0545959i
$976$	−11.6772	+	11.6772i	−0.373777	+	0.373777i
$977$			13.9325i			0.445739i	0.974848	+	0.222869i	$0.0715423\pi$
$977$			13.9325i			0.445739i	−0.974848	+	0.222869i	$0.928458\pi$
$978$		−	15.8424i		−	0.506583i
$979$	−45.6832	+	45.6832i	−1.46004	+	1.46004i
$980$	−2.59949	+	2.59949i	−0.0830375	+	0.0830375i
$981$	9.85208	+	9.85208i	0.314553	+	0.314553i
$982$	−2.09931			−0.0669917
$983$	−18.0017	−	18.0017i	−0.574164	−	0.574164i	0.359125	−	0.933289i	$-0.383075\pi$
$983$	−18.0017	−	18.0017i	−0.574164	−	0.574164i	−0.933289	+	0.359125i	$0.883075\pi$
$984$			14.3630i			0.457877i
$985$	−15.7552			−0.502002
$986$	−12.7949	−	9.09591i	−0.407473	−	0.289673i
$987$	6.16149			0.196122
$988$		−	25.2216i		−	0.802406i
$989$	4.24089	+	4.24089i	0.134852	+	0.134852i
$990$	8.17215			0.259728
$991$	21.4207	+	21.4207i	0.680452	+	0.680452i	0.960102	−	0.279650i	$-0.0902184\pi$
$991$	21.4207	+	21.4207i	0.680452	+	0.680452i	−0.279650	+	0.960102i	$0.590218\pi$
$992$	0.811957	−	0.811957i	0.0257796	−	0.0257796i
$993$	17.5361	−	17.5361i	0.556491	−	0.556491i
$994$			1.02147i			0.0323991i
$995$			15.8032i			0.500995i
$996$	8.94126	−	8.94126i	0.283315	−	0.283315i
$997$	21.0161	−	21.0161i	0.665587	−	0.665587i	−0.291104	−	0.956691i	$-0.594023\pi$
$997$	21.0161	−	21.0161i	0.665587	−	0.665587i	0.956691	+	0.291104i	$0.0940227\pi$
$998$	−4.68763	−	4.68763i	−0.148384	−	0.148384i
$999$	7.65696			0.242256

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.k.b.64.7	✓	20
3.2	odd	2		1071.2.n.b.64.4		20
17.2	even	8		6069.2.a.bd.1.4		10
17.4	even	4	inner	357.2.k.b.106.4	yes	20
17.15	even	8		6069.2.a.be.1.4		10
51.38	odd	4		1071.2.n.b.820.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.k.b.64.7	✓	20	1.1	even	1	trivial
357.2.k.b.106.4	yes	20	17.4	even	4	inner
1071.2.n.b.64.4		20	3.2	odd	2
1071.2.n.b.820.7		20	51.38	odd	4
6069.2.a.bd.1.4		10	17.2	even	8
6069.2.a.be.1.4		10	17.15	even	8

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:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.661473i q^{2} +(-0.707107 - 0.707107i) q^{3} +1.56245 q^{4} +(-1.66372 - 1.66372i) q^{5} +(0.467732 - 0.467732i) q^{6} +(-0.707107 + 0.707107i) q^{7} +2.35647i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+0.661473i q^{2} +(-0.707107 - 0.707107i) q^{3} +1.56245 q^{4} +(-1.66372 - 1.66372i) q^{5} +(0.467732 - 0.467732i) q^{6} +(-0.707107 + 0.707107i) q^{7} +2.35647i q^{8} +1.00000i q^{9} +(1.10050 - 1.10050i) q^{10} +(3.71291 - 3.71291i) q^{11} +(-1.10482 - 1.10482i) q^{12} +4.49854 q^{13} +(-0.467732 - 0.467732i) q^{14} +2.35286i q^{15} +1.56617 q^{16} +(-0.686963 - 4.06547i) q^{17} -0.661473 q^{18} -3.58834i q^{19} +(-2.59949 - 2.59949i) q^{20} +1.00000 q^{21} +(2.45599 + 2.45599i) q^{22} +(0.426792 - 0.426792i) q^{23} +(1.66627 - 1.66627i) q^{24} +0.535927i q^{25} +2.97566i q^{26} +(0.707107 - 0.707107i) q^{27} +(-1.10482 + 1.10482i) q^{28} +(-4.07014 - 4.07014i) q^{29} -1.55635 q^{30} +(-0.141237 - 0.141237i) q^{31} +5.74891i q^{32} -5.25085 q^{33} +(2.68920 - 0.454407i) q^{34} +2.35286 q^{35} +1.56245i q^{36} +(5.41429 + 5.41429i) q^{37} +2.37359 q^{38} +(-3.18095 - 3.18095i) q^{39} +(3.92050 - 3.92050i) q^{40} +(-4.30993 + 4.30993i) q^{41} +0.661473i q^{42} +9.93667i q^{43} +(5.80125 - 5.80125i) q^{44} +(1.66372 - 1.66372i) q^{45} +(0.282311 + 0.282311i) q^{46} +6.16149 q^{47} +(-1.10745 - 1.10745i) q^{48} -1.00000i q^{49} -0.354501 q^{50} +(-2.38897 + 3.36048i) q^{51} +7.02876 q^{52} +9.47974i q^{53} +(0.467732 + 0.467732i) q^{54} -12.3545 q^{55} +(-1.66627 - 1.66627i) q^{56} +(-2.53734 + 2.53734i) q^{57} +(2.69228 - 2.69228i) q^{58} -1.92313i q^{59} +3.67623i q^{60} +(-7.45587 + 7.45587i) q^{61} +(0.0934241 - 0.0934241i) q^{62} +(-0.707107 - 0.707107i) q^{63} -0.670404 q^{64} +(-7.48431 - 7.48431i) q^{65} -3.47329i q^{66} -7.47259 q^{67} +(-1.07335 - 6.35212i) q^{68} -0.603575 q^{69} +1.55635i q^{70} +(-1.09194 - 1.09194i) q^{71} -2.35647 q^{72} +(-6.99329 - 6.99329i) q^{73} +(-3.58140 + 3.58140i) q^{74} +(0.378957 - 0.378957i) q^{75} -5.60662i q^{76} +5.25085i q^{77} +(2.10411 - 2.10411i) q^{78} +(7.40415 - 7.40415i) q^{79} +(-2.60567 - 2.60567i) q^{80} -1.00000 q^{81} +(-2.85090 - 2.85090i) q^{82} +8.09294i q^{83} +1.56245 q^{84} +(-5.62090 + 7.90672i) q^{85} -6.57283 q^{86} +5.75604i q^{87} +(8.74934 + 8.74934i) q^{88} -12.3039 q^{89} +(1.10050 + 1.10050i) q^{90} +(-3.18095 + 3.18095i) q^{91} +(0.666843 - 0.666843i) q^{92} +0.199739i q^{93} +4.07566i q^{94} +(-5.97000 + 5.97000i) q^{95} +(4.06509 - 4.06509i) q^{96} +(5.83964 + 5.83964i) q^{97} +0.661473 q^{98} +(3.71291 + 3.71291i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 24 q^{4} + 8 q^{5} - 4 q^{6}+O(q^{10}) \) 20 * q - 24 * q^4 + 8 * q^5 - 4 * q^6	\( 20 q - 24 q^{4} + 8 q^{5} - 4 q^{6} + 16 q^{10} + 4 q^{11} - 12 q^{13} + 4 q^{14} + 40 q^{16} + 4 q^{17} + 8 q^{18} - 52 q^{20} + 20 q^{21} - 24 q^{22} - 4 q^{23} + 4 q^{24} - 8 q^{29} + 8 q^{31} - 4 q^{33} - 44 q^{34} + 12 q^{35} + 24 q^{37} - 64 q^{38} - 12 q^{39} - 52 q^{40} - 20 q^{41} + 72 q^{44} - 8 q^{45} + 28 q^{46} - 32 q^{47} + 32 q^{48} + 104 q^{50} + 8 q^{51} + 48 q^{52} - 4 q^{54} - 36 q^{55} - 4 q^{56} - 16 q^{57} - 60 q^{58} + 28 q^{61} + 36 q^{62} - 112 q^{64} - 4 q^{65} + 40 q^{67} - 52 q^{68} + 36 q^{69} + 16 q^{71} - 24 q^{72} - 72 q^{73} - 24 q^{74} - 8 q^{75} + 40 q^{78} - 8 q^{79} + 120 q^{80} - 20 q^{81} + 108 q^{82} - 24 q^{84} + 40 q^{85} - 28 q^{88} - 64 q^{89} + 16 q^{90} - 12 q^{91} - 56 q^{92} + 60 q^{95} + 16 q^{96} + 60 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) 20 * q - 24 * q^4 + 8 * q^5 - 4 * q^6 + 16 * q^10 + 4 * q^11 - 12 * q^13 + 4 * q^14 + 40 * q^16 + 4 * q^17 + 8 * q^18 - 52 * q^20 + 20 * q^21 - 24 * q^22 - 4 * q^23 + 4 * q^24 - 8 * q^29 + 8 * q^31 - 4 * q^33 - 44 * q^34 + 12 * q^35 + 24 * q^37 - 64 * q^38 - 12 * q^39 - 52 * q^40 - 20 * q^41 + 72 * q^44 - 8 * q^45 + 28 * q^46 - 32 * q^47 + 32 * q^48 + 104 * q^50 + 8 * q^51 + 48 * q^52 - 4 * q^54 - 36 * q^55 - 4 * q^56 - 16 * q^57 - 60 * q^58 + 28 * q^61 + 36 * q^62 - 112 * q^64 - 4 * q^65 + 40 * q^67 - 52 * q^68 + 36 * q^69 + 16 * q^71 - 24 * q^72 - 72 * q^73 - 24 * q^74 - 8 * q^75 + 40 * q^78 - 8 * q^79 + 120 * q^80 - 20 * q^81 + 108 * q^82 - 24 * q^84 + 40 * q^85 - 28 * q^88 - 64 * q^89 + 16 * q^90 - 12 * q^91 - 56 * q^92 + 60 * q^95 + 16 * q^96 + 60 * q^97 - 8 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

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