LMFDB - Embedded newform 357.2.k.b.64.4

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			64.4
Root			$-1.51109i$ of defining polynomial
Character	$\chi$	$=$	357.64
Dual form			357.2.k.b.106.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.51109i q^{2} +(-0.707107 - 0.707107i) q^{3} -0.283389 q^{4} +(-1.65084 - 1.65084i) q^{5} +(-1.06850 + 1.06850i) q^{6} +(-0.707107 + 0.707107i) q^{7} -2.59395i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q-1.51109i q^{2} +(-0.707107 - 0.707107i) q^{3} -0.283389 q^{4} +(-1.65084 - 1.65084i) q^{5} +(-1.06850 + 1.06850i) q^{6} +(-0.707107 + 0.707107i) q^{7} -2.59395i q^{8} +1.00000i q^{9} +(-2.49457 + 2.49457i) q^{10} +(2.73442 - 2.73442i) q^{11} +(0.200386 + 0.200386i) q^{12} -7.04427 q^{13} +(1.06850 + 1.06850i) q^{14} +2.33464i q^{15} -4.48647 q^{16} +(0.965114 + 4.00856i) q^{17} +1.51109 q^{18} -0.992753i q^{19} +(0.467830 + 0.467830i) q^{20} +1.00000 q^{21} +(-4.13195 - 4.13195i) q^{22} +(-0.461170 + 0.461170i) q^{23} +(-1.83420 + 1.83420i) q^{24} +0.450549i q^{25} +10.6445i q^{26} +(0.707107 - 0.707107i) q^{27} +(0.200386 - 0.200386i) q^{28} +(-3.56926 - 3.56926i) q^{29} +3.52785 q^{30} +(1.46992 + 1.46992i) q^{31} +1.59155i q^{32} -3.86705 q^{33} +(6.05729 - 1.45837i) q^{34} +2.33464 q^{35} -0.283389i q^{36} +(4.07799 + 4.07799i) q^{37} -1.50014 q^{38} +(4.98105 + 4.98105i) q^{39} +(-4.28220 + 4.28220i) q^{40} +(8.45995 - 8.45995i) q^{41} -1.51109i q^{42} -2.40741i q^{43} +(-0.774904 + 0.774904i) q^{44} +(1.65084 - 1.65084i) q^{45} +(0.696868 + 0.696868i) q^{46} -6.81302 q^{47} +(3.17241 + 3.17241i) q^{48} -1.00000i q^{49} +0.680819 q^{50} +(2.15204 - 3.51692i) q^{51} +1.99627 q^{52} -5.04239i q^{53} +(-1.06850 - 1.06850i) q^{54} -9.02818 q^{55} +(1.83420 + 1.83420i) q^{56} +(-0.701983 + 0.701983i) q^{57} +(-5.39348 + 5.39348i) q^{58} -1.56548i q^{59} -0.661611i q^{60} +(8.83396 - 8.83396i) q^{61} +(2.22118 - 2.22118i) q^{62} +(-0.707107 - 0.707107i) q^{63} -6.56797 q^{64} +(11.6290 + 11.6290i) q^{65} +5.84346i q^{66} +4.95686 q^{67} +(-0.273503 - 1.13598i) q^{68} +0.652192 q^{69} -3.52785i q^{70} +(-5.53082 - 5.53082i) q^{71} +2.59395 q^{72} +(3.24064 + 3.24064i) q^{73} +(6.16220 - 6.16220i) q^{74} +(0.318586 - 0.318586i) q^{75} +0.281335i q^{76} +3.86705i q^{77} +(7.52681 - 7.52681i) q^{78} +(0.679318 - 0.679318i) q^{79} +(7.40644 + 7.40644i) q^{80} -1.00000 q^{81} +(-12.7837 - 12.7837i) q^{82} -12.8881i q^{83} -0.283389 q^{84} +(5.02425 - 8.21074i) q^{85} -3.63780 q^{86} +5.04770i q^{87} +(-7.09295 - 7.09295i) q^{88} +3.82872 q^{89} +(-2.49457 - 2.49457i) q^{90} +(4.98105 - 4.98105i) q^{91} +(0.130690 - 0.130690i) q^{92} -2.07878i q^{93} +10.2951i q^{94} +(-1.63888 + 1.63888i) q^{95} +(1.12539 - 1.12539i) q^{96} +(2.10281 + 2.10281i) q^{97} -1.51109 q^{98} +(2.73442 + 2.73442i) 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 $

$2$		−	1.51109i		−	1.06850i	−0.845326	−	0.534251i	$-0.820594\pi$
$2$		−	1.51109i		−	1.06850i	0.845326	−	0.534251i	$-0.179406\pi$
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	−0.283389			−0.141694
$5$	−1.65084	−	1.65084i	−0.738278	−	0.738278i	0.233966	−	0.972245i	$-0.424829\pi$
$5$	−1.65084	−	1.65084i	−0.738278	−	0.738278i	−0.972245	+	0.233966i	$0.924829\pi$
$6$	−1.06850	+	1.06850i	−0.436214	+	0.436214i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$		−	2.59395i		−	0.917100i
$9$			1.00000i			0.333333i
$10$	−2.49457	+	2.49457i	−0.788851	+	0.788851i
$11$	2.73442	−	2.73442i	0.824459	−	0.824459i	−0.162285	−	0.986744i	$-0.551886\pi$
$11$	2.73442	−	2.73442i	0.824459	−	0.824459i	0.986744	+	0.162285i	$0.0518864\pi$
$12$	0.200386	+	0.200386i	0.0578465	+	0.0578465i
$13$	−7.04427			−1.95373			−0.976864	−	0.213859i	$-0.931397\pi$
$13$	−7.04427			−1.95373			−0.976864	+	0.213859i	$0.931397\pi$
$14$	1.06850	+	1.06850i	0.285569	+	0.285569i
$15$			2.33464i			0.602802i
$16$	−4.48647			−1.12162
$17$	0.965114	+	4.00856i	0.234074	+	0.972219i
$17$	0.965114	+	4.00856i	0.234074	+	0.972219i
$18$	1.51109			0.356167
$19$		−	0.992753i		−	0.227753i	−0.993495	−	0.113877i	$-0.963673\pi$
$19$		−	0.992753i		−	0.227753i	0.993495	−	0.113877i	$-0.0363269\pi$
$20$	0.467830	+	0.467830i	0.104610	+	0.104610i
$21$	1.00000			0.218218
$22$	−4.13195	−	4.13195i	−0.880935	−	0.880935i
$23$	−0.461170	+	0.461170i	−0.0961605	+	0.0961605i	−0.753551	−	0.657390i	$-0.771660\pi$
$23$	−0.461170	+	0.461170i	−0.0961605	+	0.0961605i	0.657390	+	0.753551i	$0.271660\pi$
$24$	−1.83420	+	1.83420i	−0.374405	+	0.374405i
$25$			0.450549i			0.0901097i
$26$			10.6445i			2.08756i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	0.200386	−	0.200386i	0.0378694	−	0.0378694i
$29$	−3.56926	−	3.56926i	−0.662796	−	0.662796i	0.293242	−	0.956038i	$-0.405266\pi$
$29$	−3.56926	−	3.56926i	−0.662796	−	0.662796i	−0.956038	+	0.293242i	$0.905266\pi$
$30$	3.52785			0.644094
$31$	1.46992	+	1.46992i	0.264006	+	0.264006i	0.826679	−	0.562673i	$-0.190227\pi$
$31$	1.46992	+	1.46992i	0.264006	+	0.264006i	−0.562673	+	0.826679i	$0.690227\pi$
$32$			1.59155i			0.281349i
$33$	−3.86705			−0.673168
$34$	6.05729	−	1.45837i	1.03882	−	0.250109i
$35$	2.33464			0.394626
$36$		−	0.283389i		−	0.0472315i
$37$	4.07799	+	4.07799i	0.670417	+	0.670417i	0.957812	−	0.287395i	$-0.0927892\pi$
$37$	4.07799	+	4.07799i	0.670417	+	0.670417i	−0.287395	+	0.957812i	$0.592789\pi$
$38$	−1.50014			−0.243355
$39$	4.98105	+	4.98105i	0.797607	+	0.797607i
$40$	−4.28220	+	4.28220i	−0.677075	+	0.677075i
$41$	8.45995	−	8.45995i	1.32122	−	1.32122i	0.408433	−	0.912788i	$-0.366075\pi$
$41$	8.45995	−	8.45995i	1.32122	−	1.32122i	0.912788	−	0.408433i	$-0.133925\pi$
$42$		−	1.51109i		−	0.233166i
$43$		−	2.40741i		−	0.367126i	−0.983008	−	0.183563i	$-0.941237\pi$
$43$		−	2.40741i		−	0.367126i	0.983008	−	0.183563i	$-0.0587631\pi$
$44$	−0.774904	+	0.774904i	−0.116821	+	0.116821i
$45$	1.65084	−	1.65084i	0.246093	−	0.246093i
$46$	0.696868	+	0.696868i	0.102748	+	0.102748i
$47$	−6.81302			−0.993781			−0.496890	−	0.867813i	$-0.665525\pi$
$47$	−6.81302			−0.993781			−0.496890	+	0.867813i	$0.665525\pi$
$48$	3.17241	+	3.17241i	0.457898	+	0.457898i
$49$		−	1.00000i		−	0.142857i
$50$	0.680819			0.0962823
$51$	2.15204	−	3.51692i	0.301346	−	0.492467i
$52$	1.99627			0.276833
$53$		−	5.04239i		−	0.692626i	−0.938119	−	0.346313i	$-0.887434\pi$
$53$		−	5.04239i		−	0.692626i	0.938119	−	0.346313i	$-0.112566\pi$
$54$	−1.06850	−	1.06850i	−0.145405	−	0.145405i
$55$	−9.02818			−1.21736
$56$	1.83420	+	1.83420i	0.245105	+	0.245105i
$57$	−0.701983	+	0.701983i	−0.0929799	+	0.0929799i
$58$	−5.39348	+	5.39348i	−0.708198	+	0.708198i
$59$		−	1.56548i		−	0.203808i	−0.994794	−	0.101904i	$-0.967507\pi$
$59$		−	1.56548i		−	0.203808i	0.994794	−	0.101904i	$-0.0324934\pi$
$60$		−	0.661611i		−	0.0854137i
$61$	8.83396	−	8.83396i	1.13107	−	1.13107i	0.141074	−	0.989999i	$-0.454944\pi$
$61$	8.83396	−	8.83396i	1.13107	−	1.13107i	0.989999	−	0.141074i	$-0.0450555\pi$
$62$	2.22118	−	2.22118i	0.282090	−	0.282090i
$63$	−0.707107	−	0.707107i	−0.0890871	−	0.0890871i
$64$	−6.56797			−0.820996
$65$	11.6290	+	11.6290i	1.44240	+	1.44240i
$66$			5.84346i			0.719280i
$67$	4.95686			0.605577			0.302788	−	0.953058i	$-0.402082\pi$
$67$	4.95686			0.605577			0.302788	+	0.953058i	$0.402082\pi$
$68$	−0.273503	−	1.13598i	−0.0331671	−	0.137758i
$69$	0.652192			0.0785147
$70$		−	3.52785i		−	0.421659i
$71$	−5.53082	−	5.53082i	−0.656387	−	0.656387i	0.298136	−	0.954523i	$-0.403635\pi$
$71$	−5.53082	−	5.53082i	−0.656387	−	0.656387i	−0.954523	+	0.298136i	$0.903635\pi$
$72$	2.59395			0.305700
$73$	3.24064	+	3.24064i	0.379289	+	0.379289i	0.870846	−	0.491557i	$-0.163572\pi$
$73$	3.24064	+	3.24064i	0.379289	+	0.379289i	−0.491557	+	0.870846i	$0.663572\pi$
$74$	6.16220	−	6.16220i	0.716341	−	0.716341i
$75$	0.318586	−	0.318586i	0.0367871	−	0.0367871i
$76$			0.281335i			0.0322714i
$77$			3.86705i			0.440692i
$78$	7.52681	−	7.52681i	0.852243	−	0.852243i
$79$	0.679318	−	0.679318i	0.0764293	−	0.0764293i	−0.667859	−	0.744288i	$-0.732789\pi$
$79$	0.679318	−	0.679318i	0.0764293	−	0.0764293i	0.744288	+	0.667859i	$0.232789\pi$
$80$	7.40644	+	7.40644i	0.828066	+	0.828066i
$81$	−1.00000			−0.111111
$82$	−12.7837	−	12.7837i	−1.41173	−	1.41173i
$83$		−	12.8881i		−	1.41465i	−0.706889	−	0.707324i	$-0.749902\pi$
$83$		−	12.8881i		−	1.41465i	0.706889	−	0.707324i	$-0.250098\pi$
$84$	−0.283389			−0.0309203
$85$	5.02425	−	8.21074i	0.544956	−	0.890580i
$86$	−3.63780			−0.392275
$87$			5.04770i			0.541170i
$88$	−7.09295	−	7.09295i	−0.756111	−	0.756111i
$89$	3.82872			0.405843			0.202922	−	0.979195i	$-0.434956\pi$
$89$	3.82872			0.405843			0.202922	+	0.979195i	$0.434956\pi$
$90$	−2.49457	−	2.49457i	−0.262950	−	0.262950i
$91$	4.98105	−	4.98105i	0.522156	−	0.522156i
$92$	0.130690	−	0.130690i	0.0136254	−	0.0136254i
$93$		−	2.07878i		−	0.215560i
$94$			10.2951i			1.06186i
$95$	−1.63888	+	1.63888i	−0.168145	+	0.168145i
$96$	1.12539	−	1.12539i	0.114860	−	0.114860i
$97$	2.10281	+	2.10281i	0.213508	+	0.213508i	0.805756	−	0.592248i	$-0.201759\pi$
$97$	2.10281	+	2.10281i	0.213508	+	0.213508i	−0.592248	+	0.805756i	$0.701759\pi$
$98$	−1.51109			−0.152643
$99$	2.73442	+	2.73442i	0.274820	+	0.274820i
$100$		−	0.127680i		−	0.0127680i
$101$	−1.00557			−0.100058			−0.0500290	−	0.998748i	$-0.515931\pi$
$101$	−1.00557			−0.100058			−0.0500290	+	0.998748i	$0.515931\pi$
$102$	−5.31438	−	3.25193i	−0.526202	−	0.321989i
$103$	−1.58496			−0.156170			−0.0780852	−	0.996947i	$-0.524881\pi$
$103$	−1.58496			−0.156170			−0.0780852	+	0.996947i	$0.524881\pi$
$104$			18.2725i			1.79177i
$105$	−1.65084	−	1.65084i	−0.161106	−	0.161106i
$106$	−7.61950			−0.740071
$107$	4.33329	+	4.33329i	0.418915	+	0.418915i	0.884829	−	0.465915i	$-0.154275\pi$
$107$	4.33329	+	4.33329i	0.418915	+	0.418915i	−0.465915	+	0.884829i	$0.654275\pi$
$108$	−0.200386	+	0.200386i	−0.0192822	+	0.0192822i
$109$	9.35507	−	9.35507i	0.896053	−	0.896053i	−0.0990316	−	0.995084i	$-0.531574\pi$
$109$	9.35507	−	9.35507i	0.896053	−	0.896053i	0.995084	+	0.0990316i	$0.0315745\pi$
$110$			13.6424i			1.30075i
$111$		−	5.76715i		−	0.547393i
$112$	3.17241	−	3.17241i	0.299765	−	0.299765i
$113$	13.3488	−	13.3488i	1.25575	−	1.25575i	0.302642	−	0.953104i	$-0.402131\pi$
$113$	13.3488	−	13.3488i	1.25575	−	1.25575i	0.953104	−	0.302642i	$-0.0978687\pi$
$114$	1.06076	+	1.06076i	0.0993491	+	0.0993491i
$115$	1.52264			0.141986
$116$	1.01149	+	1.01149i	0.0939145	+	0.0939145i
$117$		−	7.04427i		−	0.651243i
$118$	−2.36558			−0.217769
$119$	−3.51692	−	2.15204i	−0.322395	−	0.197277i
$120$	6.05595			0.552830
$121$		−	3.95411i		−	0.359464i
$122$	−13.3489	−	13.3489i	−1.20855	−	1.20855i
$123$	−11.9642			−1.07877
$124$	−0.416560	−	0.416560i	−0.0374082	−	0.0374082i
$125$	−7.51042	+	7.51042i	−0.671752	+	0.671752i
$126$	−1.06850	+	1.06850i	−0.0951896	+	0.0951896i
$127$			22.2222i			1.97190i	0.167035	+	0.985951i	$0.446581\pi$
$127$			22.2222i			1.97190i	−0.167035	+	0.985951i	$0.553419\pi$
$128$			13.1079i			1.15858i
$129$	−1.70229	+	1.70229i	−0.149879	+	0.149879i
$130$	17.5724	−	17.5724i	1.54120	−	1.54120i
$131$	−5.73121	−	5.73121i	−0.500738	−	0.500738i	0.410929	−	0.911667i	$-0.365204\pi$
$131$	−5.73121	−	5.73121i	−0.500738	−	0.500738i	−0.911667	+	0.410929i	$0.865204\pi$
$132$	1.09588			0.0953841
$133$	0.701983	+	0.701983i	0.0608696	+	0.0608696i
$134$		−	7.49025i		−	0.647059i
$135$	−2.33464			−0.200934
$136$	10.3980	−	2.50346i	0.891622	−	0.214670i
$137$	−7.66715			−0.655049			−0.327524	−	0.944843i	$-0.606214\pi$
$137$	−7.66715			−0.655049			−0.327524	+	0.944843i	$0.606214\pi$
$138$		−	0.985521i		−	0.0838931i
$139$	−3.45909	−	3.45909i	−0.293396	−	0.293396i	0.545024	−	0.838420i	$-0.316520\pi$
$139$	−3.45909	−	3.45909i	−0.293396	−	0.293396i	−0.838420	+	0.545024i	$0.816520\pi$
$140$	−0.661611			−0.0559164
$141$	4.81753	+	4.81753i	0.405709	+	0.405709i
$142$	−8.35755	+	8.35755i	−0.701350	+	0.701350i
$143$	−19.2620	+	19.2620i	−1.61077	+	1.61077i
$144$		−	4.48647i		−	0.373872i
$145$			11.7846i			0.978655i
$146$	4.89690	−	4.89690i	0.405270	−	0.405270i
$147$	−0.707107	+	0.707107i	−0.0583212	+	0.0583212i
$148$	−1.15566	−	1.15566i	−0.0949944	−	0.0949944i
$149$	13.7753			1.12852			0.564258	−	0.825599i	$-0.309162\pi$
$149$	13.7753			1.12852			0.564258	+	0.825599i	$0.309162\pi$
$150$	−0.481412	−	0.481412i	−0.0393071	−	0.0393071i
$151$			20.5923i			1.67578i	0.545841	+	0.837889i	$0.316210\pi$
$151$			20.5923i			1.67578i	−0.545841	+	0.837889i	$0.683790\pi$
$152$	−2.57515			−0.208873
$153$	−4.00856	+	0.965114i	−0.324073	+	0.0780248i
$154$	5.84346			0.470880
$155$		−	4.85321i		−	0.389819i
$156$	−1.41157	−	1.41157i	−0.113016	−	0.113016i
$157$	−23.0384			−1.83866			−0.919331	−	0.393484i	$-0.871270\pi$
$157$	−23.0384			−1.83866			−0.919331	+	0.393484i	$0.871270\pi$
$158$	−1.02651	−	1.02651i	−0.0816648	−	0.0816648i
$159$	−3.56551	+	3.56551i	−0.282763	+	0.282763i
$160$	2.62739	−	2.62739i	0.207714	−	0.207714i
$161$		−	0.652192i		−	0.0514000i
$162$			1.51109i			0.118722i
$163$	−3.40803	+	3.40803i	−0.266937	+	0.266937i	−0.827865	−	0.560927i	$-0.810445\pi$
$163$	−3.40803	+	3.40803i	−0.266937	+	0.266937i	0.560927	+	0.827865i	$0.310445\pi$
$164$	−2.39745	+	2.39745i	−0.187210	+	0.187210i
$165$	6.38389	+	6.38389i	0.496985	+	0.496985i
$166$	−19.4750			−1.51155
$167$	10.0111	+	10.0111i	0.774680	+	0.774680i	0.978921	−	0.204241i	$-0.0654725\pi$
$167$	10.0111	+	10.0111i	0.774680	+	0.774680i	−0.204241	+	0.978921i	$0.565473\pi$
$168$		−	2.59395i		−	0.200128i
$169$	36.6217			2.81706
$170$	−12.4072	−	7.59208i	−0.951586	−	0.582286i
$171$	0.992753			0.0759178
$172$			0.682232i			0.0520197i
$173$	14.3926	+	14.3926i	1.09425	+	1.09425i	0.995069	+	0.0991809i	$0.0316223\pi$
$173$	14.3926	+	14.3926i	1.09425	+	1.09425i	0.0991809	+	0.995069i	$0.468378\pi$
$174$	7.62753			0.578241
$175$	−0.318586	−	0.318586i	−0.0240828	−	0.0240828i
$176$	−12.2679	+	12.2679i	−0.924727	+	0.924727i
$177$	−1.10696	+	1.10696i	−0.0832042	+	0.0832042i
$178$		−	5.78553i		−	0.433644i
$179$			15.0614i			1.12574i	0.826544	+	0.562872i	$0.190304\pi$
$179$			15.0614i			1.12574i	−0.826544	+	0.562872i	$0.809696\pi$
$180$	−0.467830	+	0.467830i	−0.0348700	+	0.0348700i
$181$	−3.31493	+	3.31493i	−0.246397	+	0.246397i	−0.819490	−	0.573093i	$-0.805743\pi$
$181$	−3.31493	+	3.31493i	−0.246397	+	0.246397i	0.573093	+	0.819490i	$0.305743\pi$
$182$	−7.52681	−	7.52681i	−0.557924	−	0.557924i
$183$	−12.4931			−0.923517
$184$	1.19625	+	1.19625i	0.0881889	+	0.0881889i
$185$		−	13.4642i		−	0.989909i
$186$	−3.14123			−0.230326
$187$	13.6001	+	8.32206i	0.994539	+	0.608569i
$188$	1.93073			0.140813
$189$			1.00000i			0.0727393i
$190$	2.47649	+	2.47649i	0.179663	+	0.179663i
$191$	−17.6598			−1.27782			−0.638908	−	0.769283i	$-0.720614\pi$
$191$	−17.6598			−1.27782			−0.638908	+	0.769283i	$0.720614\pi$
$192$	4.64425	+	4.64425i	0.335170	+	0.335170i
$193$	−10.4528	+	10.4528i	−0.752408	+	0.752408i	−0.974928	−	0.222520i	$-0.928572\pi$
$193$	−10.4528	+	10.4528i	−0.752408	+	0.752408i	0.222520	+	0.974928i	$0.428572\pi$
$194$	3.17753	−	3.17753i	0.228133	−	0.228133i
$195$		−	16.4458i		−	1.17771i
$196$			0.283389i			0.0202421i
$197$	3.21831	−	3.21831i	0.229295	−	0.229295i	−0.583103	−	0.812398i	$-0.698162\pi$
$197$	3.21831	−	3.21831i	0.229295	−	0.229295i	0.812398	+	0.583103i	$0.198162\pi$
$198$	4.13195	−	4.13195i	0.293645	−	0.293645i
$199$	14.3092	+	14.3092i	1.01435	+	1.01435i	0.999895	+	0.0144592i	$0.00460267\pi$
$199$	14.3092	+	14.3092i	1.01435	+	1.01435i	0.0144592	+	0.999895i	$0.495397\pi$
$200$	1.16870			0.0826396
$201$	−3.50503	−	3.50503i	−0.247226	−	0.247226i
$202$			1.51951i			0.106912i
$203$	5.04770			0.354279
$204$	−0.609865	+	0.996656i	−0.0426991	+	0.0697799i
$205$	−27.9320			−1.95086
$206$			2.39501i			0.166868i
$207$	−0.461170	−	0.461170i	−0.0320535	−	0.0320535i
$208$	31.6039			2.19134
$209$	−2.71461	−	2.71461i	−0.187773	−	0.187773i
$210$	−2.49457	+	2.49457i	−0.172141	+	0.172141i
$211$	1.06695	−	1.06695i	0.0734519	−	0.0734519i	−0.669426	−	0.742878i	$-0.733460\pi$
$211$	1.06695	−	1.06695i	0.0734519	−	0.0734519i	0.742878	+	0.669426i	$0.233460\pi$
$212$			1.42896i			0.0981412i
$213$			7.82176i			0.535938i
$214$	6.54798	−	6.54798i	0.447611	−	0.447611i
$215$	−3.97424	+	3.97424i	−0.271041	+	0.271041i
$216$	−1.83420	−	1.83420i	−0.124802	−	0.124802i
$217$	−2.07878			−0.141117
$218$	−14.1363	−	14.1363i	−0.957433	−	0.957433i
$219$		−	4.58296i		−	0.309688i
$220$	2.55849			0.172493
$221$	−6.79852	−	28.2374i	−0.457318	−	1.89945i
$222$	−8.71467			−0.584890
$223$		−	29.2730i		−	1.96027i	−0.198337	−	0.980134i	$-0.563554\pi$
$223$		−	29.2730i		−	1.96027i	0.198337	−	0.980134i	$-0.436446\pi$
$224$	−1.12539	−	1.12539i	−0.0751936	−	0.0751936i
$225$	−0.450549			−0.0300366
$226$	−20.1712	−	20.1712i	−1.34177	−	1.34177i
$227$	−16.0152	+	16.0152i	−1.06296	+	1.06296i	−0.0650831	+	0.997880i	$0.520731\pi$
$227$	−16.0152	+	16.0152i	−1.06296	+	1.06296i	−0.997880	+	0.0650831i	$0.979269\pi$
$228$	0.198934	−	0.198934i	0.0131747	−	0.0131747i
$229$		−	20.5349i		−	1.35699i	−0.734607	−	0.678493i	$-0.762633\pi$
$229$		−	20.5349i		−	1.35699i	0.734607	−	0.678493i	$-0.237367\pi$
$230$		−	2.30084i		−	0.151713i
$231$	2.73442	−	2.73442i	0.179912	−	0.179912i
$232$	−9.25850	+	9.25850i	−0.607850	+	0.607850i
$233$	2.75026	+	2.75026i	0.180176	+	0.180176i	0.791432	−	0.611257i	$-0.209336\pi$
$233$	2.75026	+	2.75026i	0.180176	+	0.180176i	−0.611257	+	0.791432i	$0.709336\pi$
$234$	−10.6445			−0.695854
$235$	11.2472	+	11.2472i	0.733687	+	0.733687i
$236$			0.443639i			0.0288785i
$237$	−0.960701			−0.0624042
$238$	−3.25193	+	5.31438i	−0.210791	+	0.344480i
$239$	−7.00766			−0.453288			−0.226644	−	0.973978i	$-0.572775\pi$
$239$	−7.00766			−0.453288			−0.226644	+	0.973978i	$0.572775\pi$
$240$		−	10.4743i		−	0.676113i
$241$	11.6350	+	11.6350i	0.749476	+	0.749476i	0.974381	−	0.224905i	$-0.0722070\pi$
$241$	11.6350	+	11.6350i	0.749476	+	0.749476i	−0.224905	+	0.974381i	$0.572207\pi$
$242$	−5.97501			−0.384088
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−2.50345	+	2.50345i	−0.160267	+	0.160267i
$245$	−1.65084	+	1.65084i	−0.105468	+	0.105468i
$246$			18.0789i			1.15267i
$247$			6.99322i			0.444968i
$248$	3.81291	−	3.81291i	0.242120	−	0.242120i
$249$	−9.11323	+	9.11323i	−0.577528	+	0.577528i
$250$	11.3489	+	11.3489i	0.717768	+	0.717768i
$251$	−12.6735			−0.799941			−0.399971	−	0.916528i	$-0.630980\pi$
$251$	−12.6735			−0.799941			−0.399971	+	0.916528i	$0.630980\pi$
$252$	0.200386	+	0.200386i	0.0126231	+	0.0126231i
$253$			2.52206i			0.158561i
$254$	33.5797			2.10698
$255$	−9.35855	+	2.25319i	−0.586055	+	0.141100i
$256$	6.67123			0.416952
$257$		−	14.4557i		−	0.901719i	−0.892595	−	0.450859i	$-0.851118\pi$
$257$		−	14.4557i		−	0.901719i	0.892595	−	0.450859i	$-0.148882\pi$
$258$	2.57232	+	2.57232i	0.160145	+	0.160145i
$259$	−5.76715			−0.358353
$260$	−3.29552	−	3.29552i	−0.204379	−	0.204379i
$261$	3.56926	−	3.56926i	0.220932	−	0.220932i
$262$	−8.66036	+	8.66036i	−0.535039	+	0.535039i
$263$		−	17.9342i		−	1.10587i	−0.833225	−	0.552935i	$-0.813508\pi$
$263$		−	17.9342i		−	1.10587i	0.833225	−	0.552935i	$-0.186492\pi$
$264$			10.0310i			0.617362i
$265$	−8.32418	+	8.32418i	−0.511351	+	0.511351i
$266$	1.06076	−	1.06076i	0.0650393	−	0.0650393i
$267$	−2.70731	−	2.70731i	−0.165685	−	0.165685i
$268$	−1.40472			−0.0858069
$269$	3.04172	+	3.04172i	0.185457	+	0.185457i	0.793729	−	0.608272i	$-0.208137\pi$
$269$	3.04172	+	3.04172i	0.185457	+	0.185457i	−0.608272	+	0.793729i	$0.708137\pi$
$270$			3.52785i			0.214698i
$271$	26.7775			1.62662			0.813310	−	0.581831i	$-0.197664\pi$
$271$	26.7775			1.62662			0.813310	+	0.581831i	$0.197664\pi$
$272$	−4.32995	−	17.9843i	−0.262542	−	1.09046i
$273$	−7.04427			−0.426339
$274$			11.5857i			0.699920i
$275$	1.23199	+	1.23199i	0.0742917	+	0.0742917i
$276$	−0.184824			−0.0111251
$277$	−6.21835	−	6.21835i	−0.373625	−	0.373625i	0.495171	−	0.868796i	$-0.335105\pi$
$277$	−6.21835	−	6.21835i	−0.373625	−	0.373625i	−0.868796	+	0.495171i	$0.835105\pi$
$278$	−5.22699	+	5.22699i	−0.313494	+	0.313494i
$279$	−1.46992	+	1.46992i	−0.0880019	+	0.0880019i
$280$		−	6.05595i		−	0.361912i
$281$		−	13.5121i		−	0.806065i	−0.915186	−	0.403033i	$-0.867956\pi$
$281$		−	13.5121i		−	0.806065i	0.915186	−	0.403033i	$-0.132044\pi$
$282$	7.27972	−	7.27972i	0.433501	−	0.433501i
$283$	18.1685	−	18.1685i	1.08000	−	1.08000i	0.0834957	−	0.996508i	$-0.473392\pi$
$283$	18.1685	−	18.1685i	1.08000	−	1.08000i	0.996508	−	0.0834957i	$-0.0266085\pi$
$284$	1.56737	+	1.56737i	0.0930064	+	0.0930064i
$285$	2.31772			0.137290
$286$	29.1066	+	29.1066i	1.72111	+	1.72111i
$287$			11.9642i			0.706223i
$288$	−1.59155			−0.0937829
$289$	−15.1371	+	7.73743i	−0.890418	+	0.455143i
$290$	17.8075			1.04569
$291$		−	2.97382i		−	0.174328i
$292$	−0.918363	−	0.918363i	−0.0537431	−	0.0537431i
$293$	19.3056			1.12784			0.563922	−	0.825828i	$-0.309292\pi$
$293$	19.3056			1.12784			0.563922	+	0.825828i	$0.309292\pi$
$294$	1.06850	+	1.06850i	0.0623162	+	0.0623162i
$295$	−2.58436	+	2.58436i	−0.150467	+	0.150467i
$296$	10.5781	−	10.5781i	0.614840	−	0.614840i
$297$		−	3.86705i		−	0.224389i
$298$		−	20.8157i		−	1.20582i
$299$	3.24860	−	3.24860i	0.187872	−	0.187872i
$300$	−0.0902837	+	0.0902837i	−0.00521253	+	0.00521253i
$301$	1.70229	+	1.70229i	0.0981186	+	0.0981186i
$302$	31.1168			1.79057
$303$	0.711046	+	0.711046i	0.0408485	+	0.0408485i
$304$			4.45396i			0.255452i
$305$	−29.1669			−1.67009
$306$	1.45837	+	6.05729i	0.0833696	+	0.346272i
$307$	−0.224246			−0.0127984			−0.00639920	−	0.999980i	$-0.502037\pi$
$307$	−0.224246			−0.0127984			−0.00639920	+	0.999980i	$0.502037\pi$
$308$		−	1.09588i		−	0.0624436i
$309$	1.12073	+	1.12073i	0.0637563	+	0.0637563i
$310$	−7.33364			−0.416523
$311$	−22.8463	−	22.8463i	−1.29549	−	1.29549i	−0.931339	−	0.364153i	$-0.881358\pi$
$311$	−22.8463	−	22.8463i	−1.29549	−	1.29549i	−0.364153	−	0.931339i	$-0.618642\pi$
$312$	12.9206	−	12.9206i	0.731485	−	0.731485i
$313$	6.97873	−	6.97873i	0.394461	−	0.394461i	−0.481813	−	0.876274i	$-0.660022\pi$
$313$	6.97873	−	6.97873i	0.394461	−	0.394461i	0.876274	+	0.481813i	$0.160022\pi$
$314$			34.8130i			1.96461i
$315$			2.33464i			0.131542i
$316$	−0.192511	+	0.192511i	−0.0108296	+	0.0108296i
$317$	2.70321	−	2.70321i	0.151827	−	0.151827i	−0.627106	−	0.778934i	$-0.715761\pi$
$317$	2.70321	−	2.70321i	0.151827	−	0.151827i	0.778934	+	0.627106i	$0.215761\pi$
$318$	5.38780	+	5.38780i	0.302133	+	0.302133i
$319$	−19.5197			−1.09290
$320$	10.8427	+	10.8427i	0.606123	+	0.606123i
$321$		−	6.12819i		−	0.342042i
$322$	−0.985521			−0.0549209
$323$	3.97951	−	0.958120i	0.221426	−	0.0533112i
$324$	0.283389			0.0157438
$325$		−	3.17379i		−	0.176050i
$326$	5.14983	+	5.14983i	0.285223	+	0.285223i
$327$	−13.2301			−0.731624
$328$	−21.9447	−	21.9447i	−1.21169	−	1.21169i
$329$	4.81753	−	4.81753i	0.265599	−	0.265599i
$330$	9.64662	−	9.64662i	0.531029	−	0.531029i
$331$			20.4933i			1.12641i	0.826317	+	0.563206i	$0.190432\pi$
$331$			20.4933i			1.12641i	−0.826317	+	0.563206i	$0.809568\pi$
$332$			3.65233i			0.200448i
$333$	−4.07799	+	4.07799i	−0.223472	+	0.223472i
$334$	15.1276	−	15.1276i	0.827746	−	0.827746i
$335$	−8.18298	−	8.18298i	−0.447084	−	0.447084i
$336$	−4.48647			−0.244757
$337$	−16.3891	−	16.3891i	−0.892772	−	0.892772i	0.102011	−	0.994783i	$-0.467472\pi$
$337$	−16.3891	−	16.3891i	−0.892772	−	0.892772i	−0.994783	+	0.102011i	$0.967472\pi$
$338$		−	55.3387i		−	3.01003i
$339$	−18.8780			−1.02531
$340$	−1.42382	+	2.32683i	−0.0772172	+	0.126190i
$341$	8.03877			0.435324
$342$		−	1.50014i		−	0.0811182i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	−6.24470			−0.336691
$345$	−1.07667	−	1.07667i	−0.0579657	−	0.0579657i
$346$	21.7485	−	21.7485i	1.16921	−	1.16921i
$347$	0.767240	−	0.767240i	0.0411876	−	0.0411876i	−0.686213	−	0.727401i	$-0.740728\pi$
$347$	0.767240	−	0.767240i	0.0411876	−	0.0411876i	0.727401	+	0.686213i	$0.240728\pi$
$348$		−	1.43046i		−	0.0766809i
$349$			12.8669i			0.688749i	0.938832	+	0.344374i	$0.111909\pi$
$349$			12.8669i			0.688749i	−0.938832	+	0.344374i	$0.888091\pi$
$350$	−0.481412	+	0.481412i	−0.0257325	+	0.0257325i
$351$	−4.98105	+	4.98105i	−0.265869	+	0.265869i
$352$	4.35196	+	4.35196i	0.231960	+	0.231960i
$353$	6.81692			0.362828			0.181414	−	0.983407i	$-0.441933\pi$
$353$	6.81692			0.362828			0.181414	+	0.983407i	$0.441933\pi$
$354$	1.67272	+	1.67272i	0.0889038	+	0.0889038i
$355$			18.2610i			0.969193i
$356$	−1.08502			−0.0575058
$357$	0.965114	+	4.00856i	0.0510792	+	0.212156i
$358$	22.7592			1.20286
$359$		−	6.71484i		−	0.354396i	−0.984175	−	0.177198i	$-0.943297\pi$
$359$		−	6.71484i		−	0.354396i	0.984175	−	0.177198i	$-0.0567033\pi$
$360$	−4.28220	−	4.28220i	−0.225692	−	0.225692i
$361$	18.0144			0.948128
$362$	5.00916	+	5.00916i	0.263275	+	0.263275i
$363$	−2.79598	+	2.79598i	−0.146751	+	0.146751i
$364$	−1.41157	+	1.41157i	−0.0739866	+	0.0739866i
$365$		−	10.6996i		−	0.560041i
$366$			18.8782i			0.986779i
$367$	13.7945	−	13.7945i	0.720070	−	0.720070i	−0.248550	−	0.968619i	$-0.579954\pi$
$367$	13.7945	−	13.7945i	0.720070	−	0.720070i	0.968619	+	0.248550i	$0.0799539\pi$
$368$	2.06902	−	2.06902i	0.107855	−	0.107855i
$369$	8.45995	+	8.45995i	0.440407	+	0.440407i
$370$	−20.3456			−1.05772
$371$	3.56551	+	3.56551i	0.185112	+	0.185112i
$372$			0.589104i			0.0305436i
$373$	11.5715			0.599152			0.299576	−	0.954072i	$-0.403155\pi$
$373$	11.5715			0.599152			0.299576	+	0.954072i	$0.403155\pi$
$374$	12.5754	−	20.5510i	0.650257	−	1.06267i
$375$	10.6213			0.548483
$376$			17.6726i			0.911397i
$377$	25.1429	+	25.1429i	1.29492	+	1.29492i
$378$	1.51109			0.0777220
$379$	10.0319	+	10.0319i	0.515306	+	0.515306i	0.916147	−	0.400842i	$-0.131282\pi$
$379$	10.0319	+	10.0319i	0.515306	+	0.515306i	−0.400842	+	0.916147i	$0.631282\pi$
$380$	0.464440	−	0.464440i	0.0238253	−	0.0238253i
$381$	15.7135	−	15.7135i	0.805026	−	0.805026i
$382$			26.6855i			1.36535i
$383$			10.0566i			0.513871i	0.966429	+	0.256935i	$0.0827128\pi$
$383$			10.0566i			0.513871i	−0.966429	+	0.256935i	$0.917287\pi$
$384$	9.26867	−	9.26867i	0.472990	−	0.472990i
$385$	6.38389	−	6.38389i	0.325353	−	0.325353i
$386$	15.7951	+	15.7951i	0.803949	+	0.803949i
$387$	2.40741			0.122375
$388$	−0.595912	−	0.595912i	−0.0302528	−	0.0302528i
$389$			15.1409i			0.767672i	0.923401	+	0.383836i	$0.125397\pi$
$389$			15.1409i			0.767672i	−0.923401	+	0.383836i	$0.874603\pi$
$390$	−24.8511			−1.25839
$391$	−2.29371	−	1.40355i	−0.115998	−	0.0709803i
$392$	−2.59395			−0.131014
$393$			8.10515i			0.408851i
$394$	−4.86315	−	4.86315i	−0.245002	−	0.245002i
$395$	−2.24289			−0.112852
$396$	−0.774904	−	0.774904i	−0.0389404	−	0.0389404i
$397$	20.2301	−	20.2301i	1.01532	−	1.01532i	0.0154374	−	0.999881i	$-0.495086\pi$
$397$	20.2301	−	20.2301i	1.01532	−	1.01532i	0.999881	−	0.0154374i	$-0.00491407\pi$
$398$	21.6225	−	21.6225i	1.08384	−	1.08384i
$399$		−	0.992753i		−	0.0496998i
$400$		−	2.02137i		−	0.101069i
$401$	−4.45942	+	4.45942i	−0.222693	+	0.222693i	−0.809631	−	0.586939i	$-0.800333\pi$
$401$	−4.45942	+	4.45942i	−0.222693	+	0.222693i	0.586939	+	0.809631i	$0.300333\pi$
$402$	−5.29641	+	5.29641i	−0.264161	+	0.264161i
$403$	−10.3545	−	10.3545i	−0.515796	−	0.515796i
$404$	0.284968			0.0141777
$405$	1.65084	+	1.65084i	0.0820309	+	0.0820309i
$406$		−	7.62753i		−	0.378548i
$407$	22.3019			1.10546
$408$	−9.12272	−	5.58229i	−0.451642	−	0.276365i
$409$	−0.539984			−0.0267005			−0.0133503	−	0.999911i	$-0.504250\pi$
$409$	−0.539984			−0.0267005			−0.0133503	+	0.999911i	$0.504250\pi$
$410$			42.2078i			2.08449i
$411$	5.42149	+	5.42149i	0.267422	+	0.267422i
$412$	0.449159			0.0221285
$413$	1.10696	+	1.10696i	0.0544700	+	0.0544700i
$414$	−0.696868	+	0.696868i	−0.0342492	+	0.0342492i
$415$	−21.2761	+	21.2761i	−1.04440	+	1.04440i
$416$		−	11.2113i		−	0.549679i
$417$			4.89189i			0.239557i
$418$	−4.10201	+	4.10201i	−0.200636	+	0.200636i
$419$	−22.3051	+	22.3051i	−1.08967	+	1.08967i	−0.0941132	+	0.995562i	$0.530002\pi$
$419$	−22.3051	+	22.3051i	−1.08967	+	1.08967i	−0.995562	+	0.0941132i	$0.969998\pi$
$420$	0.467830	+	0.467830i	0.0228278	+	0.0228278i
$421$	1.65742			0.0807778			0.0403889	−	0.999184i	$-0.487140\pi$
$421$	1.65742			0.0807778			0.0403889	+	0.999184i	$0.487140\pi$
$422$	−1.61226	−	1.61226i	−0.0784834	−	0.0784834i
$423$		−	6.81302i		−	0.331260i
$424$	−13.0797			−0.635207
$425$	−1.80605	+	0.434830i	−0.0876063	+	0.0210924i
$426$	11.8194			0.572650
$427$			12.4931i			0.604584i
$428$	−1.22801	−	1.22801i	−0.0593579	−	0.0593579i
$429$	27.2406			1.31519
$430$	6.00543	+	6.00543i	0.289608	+	0.289608i
$431$	−19.6916	+	19.6916i	−0.948510	+	0.948510i	−0.998738	−	0.0502281i	$-0.984005\pi$
$431$	−19.6916	+	19.6916i	−0.948510	+	0.948510i	0.0502281	+	0.998738i	$0.484005\pi$
$432$	−3.17241	+	3.17241i	−0.152633	+	0.152633i
$433$		−	27.9567i		−	1.34352i	−0.740771	−	0.671758i	$-0.765540\pi$
$433$		−	27.9567i		−	1.34352i	0.740771	−	0.671758i	$-0.234460\pi$
$434$			3.14123i			0.150784i
$435$	8.33295	−	8.33295i	0.399534	−	0.399534i
$436$	−2.65112	+	2.65112i	−0.126966	+	0.126966i
$437$	0.457828	+	0.457828i	0.0219009	+	0.0219009i
$438$	−6.92526			−0.330902
$439$	−1.51580	−	1.51580i	−0.0723453	−	0.0723453i	0.670008	−	0.742354i	$-0.266291\pi$
$439$	−1.51580	−	1.51580i	−0.0723453	−	0.0723453i	−0.742354	+	0.670008i	$0.766291\pi$
$440$			23.4187i			1.11644i
$441$	1.00000			0.0476190
$442$	−42.6692	+	10.2732i	−2.02957	+	0.488645i
$443$	−26.1035			−1.24022			−0.620108	−	0.784516i	$-0.712911\pi$
$443$	−26.1035			−1.24022			−0.620108	+	0.784516i	$0.712911\pi$
$444$			1.63435i			0.0775626i
$445$	−6.32060	−	6.32060i	−0.299625	−	0.299625i
$446$	−44.2342			−2.09455
$447$	−9.74060	−	9.74060i	−0.460714	−	0.460714i
$448$	4.64425	−	4.64425i	0.219420	−	0.219420i
$449$	−16.3399	+	16.3399i	−0.771126	+	0.771126i	−0.978303	−	0.207177i	$-0.933572\pi$
$449$	−16.3399	+	16.3399i	−0.771126	+	0.771126i	0.207177	+	0.978303i	$0.433572\pi$
$450$			0.680819i			0.0320941i
$451$		−	46.2661i		−	2.17859i
$452$	−3.78289	+	3.78289i	−0.177932	+	0.177932i
$453$	14.5610	−	14.5610i	0.684133	−	0.684133i
$454$	24.2003	+	24.2003i	1.13578	+	1.13578i
$455$	−16.4458			−0.770993
$456$	1.82091	+	1.82091i	0.0852719	+	0.0852719i
$457$			28.4649i			1.33153i	0.746160	+	0.665766i	$0.231895\pi$
$457$			28.4649i			1.33153i	−0.746160	+	0.665766i	$0.768105\pi$
$458$	−31.0301			−1.44994
$459$	3.51692	+	2.15204i	0.164156	+	0.100449i
$460$	−0.431498			−0.0201187
$461$			23.9790i			1.11681i	0.829567	+	0.558407i	$0.188587\pi$
$461$			23.9790i			1.11681i	−0.829567	+	0.558407i	$0.811413\pi$
$462$	−4.13195	−	4.13195i	−0.192236	−	0.192236i
$463$	−20.5076			−0.953068			−0.476534	−	0.879156i	$-0.658107\pi$
$463$	−20.5076			−0.953068			−0.476534	+	0.879156i	$0.658107\pi$
$464$	16.0134	+	16.0134i	0.743403	+	0.743403i
$465$	−3.43174	+	3.43174i	−0.159143	+	0.159143i
$466$	4.15589	−	4.15589i	0.192518	−	0.192518i
$467$		−	17.9740i		−	0.831739i	−0.909424	−	0.415869i	$-0.863477\pi$
$467$		−	17.9740i		−	0.831739i	0.909424	−	0.415869i	$-0.136523\pi$
$468$			1.99627i			0.0922775i
$469$	−3.50503	+	3.50503i	−0.161847	+	0.161847i
$470$	16.9955	−	16.9955i	0.783945	−	0.783945i
$471$	16.2906	+	16.2906i	0.750631	+	0.750631i
$472$	−4.06078			−0.186912
$473$	−6.58286	−	6.58286i	−0.302680	−	0.302680i
$474$			1.45170i			0.0666790i
$475$	0.447284			0.0205228
$476$	0.996656	+	0.609865i	0.0456816	+	0.0279531i
$477$	5.04239			0.230875
$478$			10.5892i			0.484339i
$479$	16.6378	+	16.6378i	0.760202	+	0.760202i	0.976359	−	0.216157i	$-0.0693523\pi$
$479$	16.6378	+	16.6378i	0.760202	+	0.760202i	−0.216157	+	0.976359i	$0.569352\pi$
$480$	−3.71570			−0.169597
$481$	−28.7265	−	28.7265i	−1.30981	−	1.30981i
$482$	17.5815	−	17.5815i	0.800816	−	0.800816i
$483$	−0.461170	+	0.461170i	−0.0209839	+	0.0209839i
$484$			1.12055i			0.0509341i
$485$		−	6.94279i		−	0.315256i
$486$	1.06850	−	1.06850i	0.0484682	−	0.0484682i
$487$	0.249268	−	0.249268i	0.0112954	−	0.0112954i	−0.701437	−	0.712732i	$-0.747458\pi$
$487$	0.249268	−	0.249268i	0.0112954	−	0.0112954i	0.712732	+	0.701437i	$0.247458\pi$
$488$	−22.9149	−	22.9149i	−1.03731	−	1.03731i
$489$	4.81968			0.217953
$490$	2.49457	+	2.49457i	0.112693	+	0.112693i
$491$		−	9.73907i		−	0.439518i	−0.975554	−	0.219759i	$-0.929473\pi$
$491$		−	9.73907i		−	0.439518i	0.975554	−	0.219759i	$-0.0705271\pi$
$492$	3.39051			0.152856
$493$	10.8629	−	17.7524i	0.489239	−	0.799526i
$494$	10.5674			0.475449
$495$		−	9.02818i		−	0.405787i
$496$	−6.59476	−	6.59476i	−0.296113	−	0.296113i
$497$	7.82176			0.350854
$498$	13.7709	+	13.7709i	0.617089	+	0.617089i
$499$	18.5957	−	18.5957i	0.832459	−	0.832459i	−0.155393	−	0.987853i	$-0.549664\pi$
$499$	18.5957	−	18.5957i	0.832459	−	0.832459i	0.987853	+	0.155393i	$0.0496645\pi$
$500$	2.12837	−	2.12837i	0.0951836	−	0.0951836i
$501$		−	14.1578i		−	0.632524i
$502$			19.1507i			0.854738i
$503$	2.35428	−	2.35428i	0.104972	−	0.104972i	−0.652670	−	0.757642i	$-0.726351\pi$
$503$	2.35428	−	2.35428i	0.104972	−	0.104972i	0.757642	+	0.652670i	$0.226351\pi$
$504$	−1.83420	+	1.83420i	−0.0817018	+	0.0817018i
$505$	1.66004	+	1.66004i	0.0738706	+	0.0738706i
$506$	3.81106			0.169422
$507$	−25.8955	−	25.8955i	−1.15006	−	1.15006i
$508$		−	6.29753i		−	0.279408i
$509$	13.6249			0.603914			0.301957	−	0.953321i	$-0.402360\pi$
$509$	13.6249			0.603914			0.301957	+	0.953321i	$0.402360\pi$
$510$	3.40478	+	14.1416i	0.150766	+	0.626200i
$511$	−4.58296			−0.202738
$512$			16.1349i			0.713070i
$513$	−0.701983	−	0.701983i	−0.0309933	−	0.0309933i
$514$	−21.8438			−0.963488
$515$	2.61651	+	2.61651i	0.115297	+	0.115297i
$516$	0.482411	−	0.482411i	0.0212370	−	0.0212370i
$517$	−18.6297	+	18.6297i	−0.819331	+	0.819331i
$518$			8.71467i			0.382901i
$519$		−	20.3542i		−	0.893452i
$520$	30.1650	−	30.1650i	1.32282	−	1.32282i
$521$	−1.76032	+	1.76032i	−0.0771212	+	0.0771212i	−0.744615	−	0.667494i	$-0.767367\pi$
$521$	−1.76032	+	1.76032i	−0.0771212	+	0.0771212i	0.667494	+	0.744615i	$0.267367\pi$
$522$	−5.39348	−	5.39348i	−0.236066	−	0.236066i
$523$	−5.84412			−0.255546			−0.127773	−	0.991803i	$-0.540783\pi$
$523$	−5.84412			−0.255546			−0.127773	+	0.991803i	$0.540783\pi$
$524$	1.62416	+	1.62416i	0.0709518	+	0.0709518i
$525$			0.450549i			0.0196635i
$526$	−27.1001			−1.18162
$527$	−4.47363	+	7.31091i	−0.194874	+	0.318468i
$528$	17.3494			0.755036
$529$			22.5746i			0.981506i
$530$	12.5786	+	12.5786i	0.546379	+	0.546379i
$531$	1.56548			0.0679360
$532$	−0.198934	−	0.198934i	−0.00862489	−	0.00862489i
$533$	−59.5941	+	59.5941i	−2.58131	+	2.58131i
$534$	−4.09099	+	4.09099i	−0.177034	+	0.177034i
$535$		−	14.3071i		−	0.618551i
$536$		−	12.8578i		−	0.555374i
$537$	10.6500	−	10.6500i	0.459583	−	0.459583i
$538$	4.59631	−	4.59631i	0.198161	−	0.198161i
$539$	−2.73442	−	2.73442i	−0.117780	−	0.117780i
$540$	0.661611			0.0284712
$541$	−17.7427	−	17.7427i	−0.762819	−	0.762819i	0.214012	−	0.976831i	$-0.431347\pi$
$541$	−17.7427	−	17.7427i	−0.762819	−	0.762819i	−0.976831	+	0.214012i	$0.931347\pi$
$542$		−	40.4632i		−	1.73804i
$543$	4.68802			0.201182
$544$	−6.37982	+	1.53603i	−0.273532	+	0.0658565i
$545$	−30.8874			−1.32307
$546$			10.6445i			0.455543i
$547$	−31.4484	−	31.4484i	−1.34463	−	1.34463i	−0.891382	−	0.453253i	$-0.850264\pi$
$547$	−31.4484	−	31.4484i	−1.34463	−	1.34463i	−0.453253	−	0.891382i	$-0.649736\pi$
$548$	2.17278			0.0928168
$549$	8.83396	+	8.83396i	0.377024	+	0.377024i
$550$	1.86164	−	1.86164i	0.0793808	−	0.0793808i
$551$	−3.54340	+	3.54340i	−0.150954	+	0.150954i
$552$		−	1.69176i		−	0.0720059i
$553$			0.960701i			0.0408532i
$554$	−9.39649	+	9.39649i	−0.399218	+	0.399218i
$555$	−9.52064	+	9.52064i	−0.404129	+	0.404129i
$556$	0.980268	+	0.980268i	0.0415726	+	0.0415726i
$557$	23.7598			1.00674			0.503368	−	0.864072i	$-0.332094\pi$
$557$	23.7598			1.00674			0.503368	+	0.864072i	$0.332094\pi$
$558$	2.22118	+	2.22118i	0.0940301	+	0.0940301i
$559$			16.9584i			0.717265i
$560$	−10.4743			−0.442620
$561$	−3.73215	−	15.5013i	−0.157571	−	0.654466i
$562$	−20.4180			−0.861282
$563$			41.4704i			1.74777i	0.486134	+	0.873884i	$0.338407\pi$
$563$			41.4704i			1.74777i	−0.486134	+	0.873884i	$0.661593\pi$
$564$	−1.36523	−	1.36523i	−0.0574868	−	0.0574868i
$565$	−44.0734			−1.85418
$566$	−27.4542	−	27.4542i	−1.15399	−	1.15399i
$567$	0.707107	−	0.707107i	0.0296957	−	0.0296957i
$568$	−14.3467	+	14.3467i	−0.601973	+	0.601973i
$569$			2.56184i			0.107398i	0.998557	+	0.0536990i	$0.0171011\pi$
$569$			2.56184i			0.107398i	−0.998557	+	0.0536990i	$0.982899\pi$
$570$		−	3.50228i		−	0.146695i
$571$	16.2523	−	16.2523i	0.680137	−	0.680137i	−0.279894	−	0.960031i	$-0.590299\pi$
$571$	16.2523	−	16.2523i	0.680137	−	0.680137i	0.960031	+	0.279894i	$0.0902992\pi$
$572$	5.45864	−	5.45864i	0.228237	−	0.228237i
$573$	12.4874	+	12.4874i	0.521667	+	0.521667i
$574$	18.0789			0.754600
$575$	−0.207779	−	0.207779i	−0.00866500	−	0.00866500i
$576$		−	6.56797i		−	0.273665i
$577$	−6.98932			−0.290969			−0.145485	−	0.989361i	$-0.546474\pi$
$577$	−6.98932			−0.290969			−0.145485	+	0.989361i	$0.546474\pi$
$578$	11.6919	+	22.8735i	0.486321	+	0.951413i
$579$	14.7825			0.614339
$580$		−	3.33962i		−	0.138670i
$581$	9.11323	+	9.11323i	0.378081	+	0.378081i
$582$	−4.49370			−0.186270
$583$	−13.7880	−	13.7880i	−0.571041	−	0.571041i
$584$	8.40607	−	8.40607i	0.347846	−	0.347846i
$585$	−11.6290	+	11.6290i	−0.480799	+	0.480799i
$586$		−	29.1724i		−	1.20510i
$587$		−	22.3808i		−	0.923753i	−0.886944	−	0.461877i	$-0.847176\pi$
$587$		−	22.3808i		−	0.923753i	0.886944	−	0.461877i	$-0.152824\pi$
$588$	0.200386	−	0.200386i	0.00826379	−	0.00826379i
$589$	1.45927	−	1.45927i	0.0601282	−	0.0601282i
$590$	3.90519	+	3.90519i	0.160774	+	0.160774i
$591$	−4.55138			−0.187219
$592$	−18.2958	−	18.2958i	−0.751951	−	0.751951i
$593$		−	14.3719i		−	0.590183i	−0.955469	−	0.295092i	$-0.904650\pi$
$593$		−	14.3719i		−	0.590183i	0.955469	−	0.295092i	$-0.0953502\pi$
$594$	−5.84346			−0.239760
$595$	2.25319	+	9.35855i	0.0923719	+	0.383663i
$596$	−3.90376			−0.159904
$597$		−	20.2363i		−	0.828217i
$598$	−4.90893	−	4.90893i	−0.200741	−	0.200741i
$599$	13.0016			0.531231			0.265616	−	0.964079i	$-0.414425\pi$
$599$	13.0016			0.531231			0.265616	+	0.964079i	$0.414425\pi$
$600$	−0.826396	−	0.826396i	−0.0337375	−	0.0337375i
$601$	−9.67071	+	9.67071i	−0.394477	+	0.394477i	−0.876280	−	0.481803i	$-0.839982\pi$
$601$	−9.67071	+	9.67071i	−0.394477	+	0.394477i	0.481803	+	0.876280i	$0.339982\pi$
$602$	2.57232	−	2.57232i	0.104840	−	0.104840i
$603$			4.95686i			0.201859i
$604$		−	5.83563i		−	0.237448i
$605$	−6.52760	+	6.52760i	−0.265385	+	0.265385i
$606$	1.07445	−	1.07445i	0.0436467	−	0.0436467i
$607$	−9.95811	−	9.95811i	−0.404187	−	0.404187i	0.475519	−	0.879706i	$-0.342260\pi$
$607$	−9.95811	−	9.95811i	−0.404187	−	0.404187i	−0.879706	+	0.475519i	$0.842260\pi$
$608$	1.58002			0.0640781
$609$	−3.56926	−	3.56926i	−0.144634	−	0.144634i
$610$			44.0738i			1.78450i
$611$	47.9927			1.94158
$612$	1.13598	−	0.273503i	0.0459193	−	0.0110557i
$613$	31.7030			1.28047			0.640236	−	0.768178i	$-0.278836\pi$
$613$	31.7030			1.28047			0.640236	+	0.768178i	$0.278836\pi$
$614$			0.338856i			0.0136751i
$615$	19.7509	+	19.7509i	0.796435	+	0.796435i
$616$	10.0310			0.404159
$617$	10.5201	+	10.5201i	0.423524	+	0.423524i	0.886415	−	0.462891i	$-0.153188\pi$
$617$	10.5201	+	10.5201i	0.423524	+	0.423524i	−0.462891	+	0.886415i	$0.653188\pi$
$618$	1.69353	−	1.69353i	0.0681236	−	0.0681236i
$619$	15.2920	−	15.2920i	0.614638	−	0.614638i	−0.329513	−	0.944151i	$-0.606885\pi$
$619$	15.2920	−	15.2920i	0.614638	−	0.614638i	0.944151	+	0.329513i	$0.106885\pi$
$620$			1.37535i			0.0552353i
$621$			0.652192i			0.0261716i
$622$	−34.5227	+	34.5227i	−1.38423	+	1.38423i
$623$	−2.70731	+	2.70731i	−0.108466	+	0.108466i
$624$	−22.3473	−	22.3473i	−0.894609	−	0.894609i
$625$	27.0497			1.08199
$626$	−10.5455	−	10.5455i	−0.421482	−	0.421482i
$627$			3.83903i			0.153316i
$628$	6.52882			0.260528
$629$	−12.4111	+	20.2826i	−0.494865	+	0.808720i
$630$	3.52785			0.140553
$631$		−	17.3657i		−	0.691319i	−0.938360	−	0.345659i	$-0.887655\pi$
$631$		−	17.3657i		−	0.691319i	0.938360	−	0.345659i	$-0.112345\pi$
$632$	−1.76212	−	1.76212i	−0.0700933	−	0.0700933i
$633$	−1.50890			−0.0599732
$634$	−4.08478	−	4.08478i	−0.162227	−	0.162227i
$635$	36.6853	−	36.6853i	1.45581	−	1.45581i
$636$	1.01043	−	1.01043i	0.0400660	−	0.0400660i
$637$			7.04427i			0.279104i
$638$			29.4961i			1.16776i
$639$	5.53082	−	5.53082i	0.218796	−	0.218796i
$640$	21.6390	−	21.6390i	0.855357	−	0.855357i
$641$	−3.19471	−	3.19471i	−0.126183	−	0.126183i	0.641195	−	0.767378i	$-0.278439\pi$
$641$	−3.19471	−	3.19471i	−0.126183	−	0.126183i	−0.767378	+	0.641195i	$0.778439\pi$
$642$	−9.26024			−0.365473
$643$	4.29555	+	4.29555i	0.169400	+	0.169400i	0.786716	−	0.617316i	$-0.211780\pi$
$643$	4.29555	+	4.29555i	0.169400	+	0.169400i	−0.617316	+	0.786716i	$0.711780\pi$
$644$			0.184824i			0.00728309i
$645$	5.62043			0.221304
$646$	−1.44780	−	6.01340i	−0.0569631	−	0.236594i
$647$	44.3110			1.74204			0.871022	−	0.491245i	$-0.163458\pi$
$647$	44.3110			1.74204			0.871022	+	0.491245i	$0.163458\pi$
$648$			2.59395i			0.101900i
$649$	−4.28068	−	4.28068i	−0.168031	−	0.168031i
$650$	−4.79587			−0.188110
$651$	1.46992	+	1.46992i	0.0576108	+	0.0576108i
$652$	0.965798	−	0.965798i	0.0378236	−	0.0378236i
$653$	35.1940	−	35.1940i	1.37725	−	1.37725i	0.528012	−	0.849237i	$-0.322937\pi$
$653$	35.1940	−	35.1940i	1.37725	−	1.37725i	0.849237	−	0.528012i	$-0.177063\pi$
$654$			19.9918i			0.781741i
$655$			18.9226i			0.739368i
$656$	−37.9553	+	37.9553i	−1.48190	+	1.48190i
$657$	−3.24064	+	3.24064i	−0.126430	+	0.126430i
$658$	−7.27972	−	7.27972i	−0.283793	−	0.283793i
$659$	32.2608			1.25670			0.628351	−	0.777930i	$-0.283730\pi$
$659$	32.2608			1.25670			0.628351	+	0.777930i	$0.283730\pi$
$660$	−1.80912	−	1.80912i	−0.0704200	−	0.0704200i
$661$			43.8186i			1.70435i	0.523260	+	0.852173i	$0.324716\pi$
$661$			43.8186i			1.70435i	−0.523260	+	0.852173i	$0.675284\pi$
$662$	30.9671			1.20357
$663$	−15.1596	+	24.7741i	−0.588749	+	0.962147i
$664$	−33.4310			−1.29737
$665$		−	2.31772i		−	0.0898774i
$666$	6.16220	+	6.16220i	0.238780	+	0.238780i
$667$	3.29207			0.127470
$668$	−2.83703	−	2.83703i	−0.109768	−	0.109768i
$669$	−20.6992	+	20.6992i	−0.800276	+	0.800276i
$670$	−12.3652	+	12.3652i	−0.477710	+	0.477710i
$671$		−	48.3115i		−	1.86505i
$672$			1.59155i			0.0613953i
$673$	−1.49798	+	1.49798i	−0.0577430	+	0.0577430i	−0.735389	−	0.677646i	$-0.763000\pi$
$673$	−1.49798	+	1.49798i	−0.0577430	+	0.0577430i	0.677646	+	0.735389i	$0.263000\pi$
$674$	−24.7654	+	24.7654i	−0.953928	+	0.953928i
$675$	0.318586	+	0.318586i	0.0122624	+	0.0122624i
$676$	−10.3782			−0.399161
$677$	7.71518	+	7.71518i	0.296519	+	0.296519i	0.839649	−	0.543130i	$-0.182761\pi$
$677$	7.71518	+	7.71518i	0.296519	+	0.296519i	−0.543130	+	0.839649i	$0.682761\pi$
$678$			28.5263i			1.09555i
$679$	−2.97382			−0.114125
$680$	−21.2983	−	13.0326i	−0.816751	−	0.499779i
$681$	22.6488			0.867906
$682$		−	12.1473i		−	0.465144i
$683$	−3.26234	−	3.26234i	−0.124830	−	0.124830i	0.641932	−	0.766762i	$-0.278133\pi$
$683$	−3.26234	−	3.26234i	−0.124830	−	0.124830i	−0.766762	+	0.641932i	$0.778133\pi$
$684$	−0.281335			−0.0107571
$685$	12.6572	+	12.6572i	0.483608	+	0.483608i
$686$	1.06850	−	1.06850i	0.0407956	−	0.0407956i
$687$	−14.5204	+	14.5204i	−0.553987	+	0.553987i
$688$			10.8008i			0.411775i
$689$			35.5200i			1.35320i
$690$	−1.62694	+	1.62694i	−0.0619364	+	0.0619364i
$691$	−25.3809	+	25.3809i	−0.965534	+	0.965534i	−0.999426	−	0.0338916i	$-0.989210\pi$
$691$	−25.3809	+	25.3809i	−0.965534	+	0.965534i	0.0338916	+	0.999426i	$0.489210\pi$
$692$	−4.07871	−	4.07871i	−0.155049	−	0.155049i
$693$	−3.86705			−0.146897
$694$	−1.15937	−	1.15937i	−0.0440090	−	0.0440090i
$695$			11.4208i			0.433216i
$696$	13.0935			0.496308
$697$	42.0770	+	25.7474i	1.59378	+	0.975252i
$698$	19.4430			0.735929
$699$		−	3.88946i		−	0.147113i
$700$	0.0902837	+	0.0902837i	0.00341240	+	0.00341240i
$701$	10.4646			0.395244			0.197622	−	0.980278i	$-0.436678\pi$
$701$	10.4646			0.395244			0.197622	+	0.980278i	$0.436678\pi$
$702$	7.52681	+	7.52681i	0.284081	+	0.284081i
$703$	4.04844	−	4.04844i	0.152690	−	0.152690i
$704$	−17.9596	+	17.9596i	−0.676877	+	0.676877i
$705$		−	15.9059i		−	0.599053i
$706$		−	10.3010i		−	0.387682i
$707$	0.711046	−	0.711046i	0.0267416	−	0.0267416i
$708$	0.313700	−	0.313700i	0.0117896	−	0.0117896i
$709$	−15.6687	−	15.6687i	−0.588451	−	0.588451i	0.348760	−	0.937212i	$-0.386603\pi$
$709$	−15.6687	−	15.6687i	−0.588451	−	0.588451i	−0.937212	+	0.348760i	$0.886603\pi$
$710$	27.5940			1.03558
$711$	0.679318	+	0.679318i	0.0254764	+	0.0254764i
$712$		−	9.93151i		−	0.372199i
$713$	−1.35577			−0.0507739
$714$	6.05729	−	1.45837i	0.226688	−	0.0545782i
$715$	63.5970			2.37839
$716$		−	4.26825i		−	0.159512i
$717$	4.95517	+	4.95517i	0.185054	+	0.185054i
$718$	−10.1467			−0.378672
$719$	−22.3270	−	22.3270i	−0.832657	−	0.832657i	0.155223	−	0.987880i	$-0.450391\pi$
$719$	−22.3270	−	22.3270i	−0.832657	−	0.832657i	−0.987880	+	0.155223i	$0.950391\pi$
$720$	−7.40644	+	7.40644i	−0.276022	+	0.276022i
$721$	1.12073	−	1.12073i	0.0417383	−	0.0417383i
$722$		−	27.2214i		−	1.01308i
$723$		−	16.4544i		−	0.611945i
$724$	0.939415	−	0.939415i	0.0349131	−	0.0349131i
$725$	1.60813	−	1.60813i	0.0597243	−	0.0597243i
$726$	4.22497	+	4.22497i	0.156803	+	0.156803i
$727$	−8.26117			−0.306390			−0.153195	−	0.988196i	$-0.548956\pi$
$727$	−8.26117			−0.306390			−0.153195	+	0.988196i	$0.548956\pi$
$728$	−12.9206	−	12.9206i	−0.478869	−	0.478869i
$729$		−	1.00000i		−	0.0370370i
$730$	−16.1680			−0.598405
$731$	9.65023	−	2.32342i	0.356927	−	0.0859348i
$732$	3.54041			0.130857
$733$			2.49710i			0.0922326i	0.998936	+	0.0461163i	$0.0146845\pi$
$733$			2.49710i			0.0922326i	−0.998936	+	0.0461163i	$0.985316\pi$
$734$	−20.8448	−	20.8448i	−0.769395	−	0.769395i
$735$	2.33464			0.0861145
$736$	−0.733974	−	0.733974i	−0.0270546	−	0.0270546i
$737$	13.5541	−	13.5541i	0.499273	−	0.499273i
$738$	12.7837	−	12.7837i	0.470576	−	0.470576i
$739$			42.6527i			1.56900i	0.620127	+	0.784502i	$0.287081\pi$
$739$			42.6527i			1.56900i	−0.620127	+	0.784502i	$0.712919\pi$
$740$			3.81561i			0.140265i
$741$	4.94496	−	4.94496i	0.181657	−	0.181657i
$742$	5.38780	−	5.38780i	0.197792	−	0.197792i
$743$	1.94900	+	1.94900i	0.0715017	+	0.0715017i	0.741953	−	0.670452i	$-0.233900\pi$
$743$	1.94900	+	1.94900i	0.0715017	+	0.0715017i	−0.670452	+	0.741953i	$0.733900\pi$
$744$	−5.39226			−0.197690
$745$	−22.7408	−	22.7408i	−0.833158	−	0.833158i
$746$		−	17.4856i		−	0.640195i
$747$	12.8881			0.471549
$748$	−3.85412	−	2.35838i	−0.140921	−	0.0862309i
$749$	−6.12819			−0.223919
$750$		−	16.0498i		−	0.586055i
$751$	37.4310	+	37.4310i	1.36588	+	1.36588i	0.866230	+	0.499645i	$0.166536\pi$
$751$	37.4310	+	37.4310i	1.36588	+	1.36588i	0.499645	+	0.866230i	$0.333464\pi$
$752$	30.5664			1.11464
$753$	8.96149	+	8.96149i	0.326575	+	0.326575i
$754$	37.9931	−	37.9931i	1.38363	−	1.38363i
$755$	33.9946	−	33.9946i	1.23719	−	1.23719i
$756$		−	0.283389i		−	0.0103068i
$757$		−	40.7526i		−	1.48118i	−0.671957	−	0.740590i	$-0.734546\pi$
$757$		−	40.7526i		−	1.48118i	0.671957	−	0.740590i	$-0.265454\pi$
$758$	15.1591	−	15.1591i	0.550604	−	0.550604i
$759$	1.78337	−	1.78337i	0.0647322	−	0.0647322i
$760$	4.25117	+	4.25117i	0.154206	+	0.154206i
$761$	−15.2173			−0.551628			−0.275814	−	0.961211i	$-0.588947\pi$
$761$	−15.2173			−0.551628			−0.275814	+	0.961211i	$0.588947\pi$
$762$	−23.7445	−	23.7445i	−0.860171	−	0.860171i
$763$			13.2301i			0.478960i
$764$	5.00459			0.181060
$765$	8.21074	+	5.02425i	0.296860	+	0.181652i
$766$	15.1965			0.549071
$767$			11.0277i			0.398185i
$768$	−4.71727	−	4.71727i	−0.170220	−	0.170220i
$769$	5.04641			0.181978			0.0909891	−	0.995852i	$-0.470997\pi$
$769$	5.04641			0.181978			0.0909891	+	0.995852i	$0.470997\pi$
$770$	−9.64662	−	9.64662i	−0.347640	−	0.347640i
$771$	−10.2217	+	10.2217i	−0.368125	+	0.368125i
$772$	2.96221	−	2.96221i	0.106612	−	0.106612i
$773$			23.6553i			0.850823i	0.905000	+	0.425411i	$0.139871\pi$
$773$			23.6553i			0.850823i	−0.905000	+	0.425411i	$0.860129\pi$
$774$		−	3.63780i		−	0.130758i
$775$	−0.662271	+	0.662271i	−0.0237895	+	0.0237895i
$776$	5.45458	−	5.45458i	0.195808	−	0.195808i
$777$	4.07799	+	4.07799i	0.146297	+	0.146297i
$778$	22.8792			0.820258
$779$	−8.39864	−	8.39864i	−0.300913	−	0.300913i
$780$			4.66057i			0.166875i
$781$	−30.2472			−1.08233
$782$	−2.12088	+	3.46600i	−0.0758426	+	0.123944i
$783$	−5.04770			−0.180390
$784$			4.48647i			0.160231i
$785$	38.0327	+	38.0327i	1.35744	+	1.35744i
$786$	12.2476			0.436857
$787$	26.5970	+	26.5970i	0.948081	+	0.948081i	0.998717	−	0.0506365i	$-0.0161250\pi$
$787$	26.5970	+	26.5970i	0.948081	+	0.948081i	−0.0506365	+	0.998717i	$0.516125\pi$
$788$	−0.912034	+	0.912034i	−0.0324899	+	0.0324899i
$789$	−12.6814	+	12.6814i	−0.451469	+	0.451469i
$790$			3.38921i			0.120583i
$791$			18.8780i			0.671225i
$792$	7.09295	−	7.09295i	0.252037	−	0.252037i
$793$	−62.2288	+	62.2288i	−2.20981	+	2.20981i
$794$	−30.5694	−	30.5694i	−1.08487	−	1.08487i
$795$	11.7722			0.417516
$796$	−4.05508	−	4.05508i	−0.143728	−	0.143728i
$797$		−	39.1927i		−	1.38828i	−0.719841	−	0.694139i	$-0.755785\pi$
$797$		−	39.1927i		−	1.38828i	0.719841	−	0.694139i	$-0.244215\pi$
$798$	−1.50014			−0.0531043
$799$	−6.57533	−	27.3104i	−0.232619	−	0.966172i
$800$	−0.717070			−0.0253523
$801$			3.82872i			0.135281i
$802$	6.73857	+	6.73857i	0.237947	+	0.237947i
$803$	17.7226			0.625416
$804$	0.993286	+	0.993286i	0.0350305	+	0.0350305i
$805$	−1.07667	+	1.07667i	−0.0379475	+	0.0379475i
$806$	−15.6466	+	15.6466i	−0.551128	+	0.551128i
$807$		−	4.30164i		−	0.151425i
$808$			2.60840i			0.0917632i
$809$	1.40949	−	1.40949i	0.0495551	−	0.0495551i	−0.681895	−	0.731450i	$-0.738844\pi$
$809$	1.40949	−	1.40949i	0.0495551	−	0.0495551i	0.731450	+	0.681895i	$0.238844\pi$
$810$	2.49457	−	2.49457i	0.0876501	−	0.0876501i
$811$	9.31564	+	9.31564i	0.327116	+	0.327116i	0.851489	−	0.524373i	$-0.175700\pi$
$811$	9.31564	+	9.31564i	0.327116	+	0.327116i	−0.524373	+	0.851489i	$0.675700\pi$
$812$	−1.43046			−0.0501994
$813$	−18.9346	−	18.9346i	−0.664064	−	0.664064i
$814$		−	33.7001i		−	1.18119i
$815$	11.2522			0.394148
$816$	−9.65507	+	15.7785i	−0.337995	+	0.552360i
$817$	−2.38996			−0.0836142
$818$			0.815964i			0.0285295i
$819$	4.98105	+	4.98105i	0.174052	+	0.174052i
$820$	7.91563			0.276426
$821$	−30.5863	−	30.5863i	−1.06747	−	1.06747i	−0.997553	−	0.0699175i	$-0.977726\pi$
$821$	−30.5863	−	30.5863i	−1.06747	−	1.06747i	−0.0699175	−	0.997553i	$-0.522274\pi$
$822$	8.19235	−	8.19235i	0.285741	−	0.285741i
$823$	3.51823	−	3.51823i	0.122638	−	0.122638i	−0.643124	−	0.765762i	$-0.722362\pi$
$823$	3.51823	−	3.51823i	0.122638	−	0.122638i	0.765762	+	0.643124i	$0.222362\pi$
$824$			4.11130i			0.143224i
$825$		−	1.74230i		−	0.0606589i
$826$	1.67272	−	1.67272i	0.0582012	−	0.0582012i
$827$	−18.1677	+	18.1677i	−0.631753	+	0.631753i	−0.948507	−	0.316755i	$-0.897407\pi$
$827$	−18.1677	+	18.1677i	−0.631753	+	0.631753i	0.316755	+	0.948507i	$0.397407\pi$
$828$	0.130690	+	0.130690i	0.00454180	+	0.00454180i
$829$	19.6638			0.682952			0.341476	−	0.939891i	$-0.389073\pi$
$829$	19.6638			0.682952			0.341476	+	0.939891i	$0.389073\pi$
$830$	32.1501	+	32.1501i	1.11595	+	1.11595i
$831$			8.79408i			0.305063i
$832$	46.2665			1.60400
$833$	4.00856	−	0.965114i	0.138888	−	0.0334392i
$834$	7.39208			0.255967
$835$		−	33.0534i		−	1.14386i
$836$	0.769289	+	0.769289i	0.0266064	+	0.0266064i
$837$	2.07878			0.0718533
$838$	33.7050	+	33.7050i	1.16432	+	1.16432i
$839$	20.2884	−	20.2884i	0.700435	−	0.700435i	−0.264069	−	0.964504i	$-0.585065\pi$
$839$	20.2884	−	20.2884i	0.700435	−	0.700435i	0.964504	+	0.264069i	$0.0850647\pi$
$840$	−4.28220	+	4.28220i	−0.147750	+	0.147750i
$841$		−	3.52070i		−	0.121404i
$842$		−	2.50451i		−	0.0863111i
$843$	−9.55451	+	9.55451i	−0.329075	+	0.329075i
$844$	−0.302362	+	0.302362i	−0.0104077	+	0.0104077i
$845$	−60.4567	−	60.4567i	−2.07977	−	2.07977i
$846$	−10.2951			−0.353952
$847$	2.79598	+	2.79598i	0.0960709	+	0.0960709i
$848$			22.6225i			0.776861i
$849$	−25.6941			−0.881819
$850$	0.657067	+	2.72910i	0.0225372	+	0.0936075i
$851$	−3.76129			−0.128935
$852$		−	2.21660i		−	0.0759394i
$853$	−8.46564	−	8.46564i	−0.289858	−	0.289858i	0.547166	−	0.837024i	$-0.315707\pi$
$853$	−8.46564	−	8.46564i	−0.289858	−	0.289858i	−0.837024	+	0.547166i	$0.815707\pi$
$854$	18.8782			0.645999
$855$	−1.63888	−	1.63888i	−0.0560484	−	0.0560484i
$856$	11.2403	−	11.2403i	0.384187	−	0.384187i
$857$	14.8086	−	14.8086i	0.505852	−	0.505852i	−0.407399	−	0.913250i	$-0.633564\pi$
$857$	14.8086	−	14.8086i	0.505852	−	0.505852i	0.913250	+	0.407399i	$0.133564\pi$
$858$		−	41.1629i		−	1.40528i
$859$			17.7440i			0.605416i	0.953083	+	0.302708i	$0.0978908\pi$
$859$			17.7440i			0.605416i	−0.953083	+	0.302708i	$0.902109\pi$
$860$	1.12626	−	1.12626i	0.0384050	−	0.0384050i
$861$	8.45995	−	8.45995i	0.288314	−	0.288314i
$862$	29.7557	+	29.7557i	1.01348	+	1.01348i
$863$	−51.0360			−1.73729			−0.868643	−	0.495438i	$-0.835008\pi$
$863$	−51.0360			−1.73729			−0.868643	+	0.495438i	$0.835008\pi$
$864$	1.12539	+	1.12539i	0.0382867	+	0.0382867i
$865$		−	47.5198i		−	1.61572i
$866$	−42.2451			−1.43555
$867$	16.1747	+	5.23236i	0.549323	+	0.177700i
$868$	0.589104			0.0199955
$869$		−	3.71508i		−	0.126026i
$870$	−12.5918	−	12.5918i	−0.426903	−	0.426903i
$871$	−34.9174			−1.18313
$872$	−24.2666	−	24.2666i	−0.821770	−	0.821770i
$873$	−2.10281	+	2.10281i	−0.0711692	+	0.0711692i
$874$	0.691818	−	0.691818i	0.0234011	−	0.0234011i
$875$		−	10.6213i		−	0.359067i
$876$			1.29876i			0.0438811i
$877$	35.0271	−	35.0271i	1.18278	−	1.18278i	0.203762	−	0.979020i	$-0.434683\pi$
$877$	35.0271	−	35.0271i	1.18278	−	1.18278i	0.979020	−	0.203762i	$-0.0653168\pi$
$878$	−2.29051	+	2.29051i	−0.0773010	+	0.0773010i
$879$	−13.6511	−	13.6511i	−0.460440	−	0.460440i
$880$	40.5047			1.36541
$881$	30.7682	+	30.7682i	1.03661	+	1.03661i	0.999304	+	0.0373037i	$0.0118769\pi$
$881$	30.7682	+	30.7682i	1.03661	+	1.03661i	0.0373037	+	0.999304i	$0.488123\pi$
$882$		−	1.51109i		−	0.0508810i
$883$	4.04610			0.136162			0.0680810	−	0.997680i	$-0.478312\pi$
$883$	4.04610			0.136162			0.0680810	+	0.997680i	$0.478312\pi$
$884$	1.92663	+	8.00216i	0.0647994	+	0.269142i
$885$	3.65483			0.122856
$886$			39.4447i			1.32517i
$887$	−5.63293	−	5.63293i	−0.189135	−	0.189135i	0.606187	−	0.795322i	$-0.292698\pi$
$887$	−5.63293	−	5.63293i	−0.189135	−	0.189135i	−0.795322	+	0.606187i	$0.792698\pi$
$888$	−14.9597			−0.502015
$889$	−15.7135	−	15.7135i	−0.527013	−	0.527013i
$890$	−9.55099	+	9.55099i	−0.320150	+	0.320150i
$891$	−2.73442	+	2.73442i	−0.0916065	+	0.0916065i
$892$			8.29566i			0.277759i
$893$			6.76365i			0.226337i
$894$	−14.7189	+	14.7189i	−0.492274	+	0.492274i
$895$	24.8640	−	24.8640i	0.831113	−	0.831113i
$896$	−9.26867	−	9.26867i	−0.309644	−	0.309644i
$897$	−4.59422			−0.153397
$898$	24.6910	+	24.6910i	0.823949	+	0.823949i
$899$		−	10.4931i		−	0.349964i
$900$	0.127680			0.00425602
$901$	20.2127	−	4.86648i	0.673384	−	0.162126i
$902$	−69.9122			−2.32782
$903$		−	2.40741i		−	0.0801135i
$904$	−34.6261	−	34.6261i	−1.15165	−	1.15165i
$905$	10.9448			0.363819
$906$	−22.0029	−	22.0029i	−0.730997	−	0.730997i
$907$	9.69792	−	9.69792i	0.322014	−	0.322014i	−0.527525	−	0.849539i	$-0.676880\pi$
$907$	9.69792	−	9.69792i	0.322014	−	0.322014i	0.849539	+	0.527525i	$0.176880\pi$
$908$	4.53852	−	4.53852i	0.150616	−	0.150616i
$909$		−	1.00557i		−	0.0333527i
$910$			24.8511i			0.823807i
$911$	−23.3268	+	23.3268i	−0.772851	+	0.772851i	−0.978604	−	0.205753i	$-0.934036\pi$
$911$	−23.3268	+	23.3268i	−0.772851	+	0.772851i	0.205753	+	0.978604i	$0.434036\pi$
$912$	3.14942	−	3.14942i	0.104288	−	0.104288i
$913$	−35.2414	−	35.2414i	−1.16632	−	1.16632i
$914$	43.0130			1.42274
$915$	20.6241	+	20.6241i	0.681813	+	0.681813i
$916$			5.81937i			0.192277i
$917$	8.10515			0.267656
$918$	3.25193	−	5.31438i	0.107330	−	0.175401i
$919$	−42.3458			−1.39686			−0.698430	−	0.715678i	$-0.746118\pi$
$919$	−42.3458			−1.39686			−0.698430	+	0.715678i	$0.746118\pi$
$920$		−	3.94964i		−	0.130216i
$921$	0.158566	+	0.158566i	0.00522493	+	0.00522493i
$922$	36.2344			1.19332
$923$	38.9606	+	38.9606i	1.28240	+	1.28240i
$924$	−0.774904	+	0.774904i	−0.0254925	+	0.0254925i
$925$	−1.83733	+	1.83733i	−0.0604111	+	0.0604111i
$926$			30.9888i			1.01835i
$927$		−	1.58496i		−	0.0520568i
$928$	5.68066	−	5.68066i	0.186477	−	0.186477i
$929$	5.25405	−	5.25405i	0.172380	−	0.172380i	−0.615644	−	0.788024i	$-0.711104\pi$
$929$	5.25405	−	5.25405i	0.172380	−	0.172380i	0.788024	+	0.615644i	$0.211104\pi$
$930$	5.18566	+	5.18566i	0.170045	+	0.170045i
$931$	−0.992753			−0.0325362
$932$	−0.779393	−	0.779393i	−0.0255299	−	0.0255299i
$933$			32.3095i			1.05777i
$934$	−27.1604			−0.888714
$935$	−8.71322	−	36.1900i	−0.284953	−	1.18354i
$936$	−18.2725			−0.597255
$937$		−	2.79023i		−	0.0911529i	−0.998961	−	0.0455765i	$-0.985488\pi$
$937$		−	2.79023i		−	0.0911529i	0.998961	−	0.0455765i	$-0.0145125\pi$
$938$	5.29641	+	5.29641i	0.172934	+	0.172934i
$939$	−9.86941			−0.322076
$940$	−3.18733	−	3.18733i	−0.103959	−	0.103959i
$941$	18.1581	−	18.1581i	0.591937	−	0.591937i	−0.346217	−	0.938154i	$-0.612534\pi$
$941$	18.1581	−	18.1581i	0.591937	−	0.591937i	0.938154	+	0.346217i	$0.112534\pi$
$942$	24.6165	−	24.6165i	0.802050	−	0.802050i
$943$			7.80294i			0.254099i
$944$			7.02347i			0.228594i
$945$	1.65084	−	1.65084i	0.0537018	−	0.0537018i
$946$	−9.94729	+	9.94729i	−0.323414	+	0.323414i
$947$	16.9612	+	16.9612i	0.551165	+	0.551165i	0.926777	−	0.375612i	$-0.122567\pi$
$947$	16.9612	+	16.9612i	0.551165	+	0.551165i	−0.375612	+	0.926777i	$0.622567\pi$
$948$	0.272252			0.00884234
$949$	−22.8280	−	22.8280i	−0.741027	−	0.741027i
$950$		−	0.675885i		−	0.0219286i
$951$	−3.82291			−0.123966
$952$	−5.58229	+	9.12272i	−0.180923	+	0.295669i
$953$	−5.89788			−0.191051			−0.0955255	−	0.995427i	$-0.530453\pi$
$953$	−5.89788			−0.191051			−0.0955255	+	0.995427i	$0.530453\pi$
$954$		−	7.61950i		−	0.246690i
$955$	29.1535	+	29.1535i	0.943385	+	0.943385i
$956$	1.98589			0.0642284
$957$	13.8025	+	13.8025i	0.446173	+	0.446173i
$958$	25.1412	−	25.1412i	0.812276	−	0.812276i
$959$	5.42149	−	5.42149i	0.175069	−	0.175069i
$960$		−	15.3338i		−	0.494898i
$961$		−	26.6787i		−	0.860602i
$962$	−43.4082	+	43.4082i	−1.39954	+	1.39954i
$963$	−4.33329	+	4.33329i	−0.139638	+	0.139638i
$964$	−3.29723	−	3.29723i	−0.106197	−	0.106197i
$965$	34.5118			1.11097
$966$	0.696868	+	0.696868i	0.0224214	+	0.0224214i
$967$			41.8868i			1.34699i	0.739192	+	0.673495i	$0.235208\pi$
$967$			41.8868i			1.34699i	−0.739192	+	0.673495i	$0.764792\pi$
$968$	−10.2568			−0.329665
$969$	−3.49143	−	2.13645i	−0.112161	−	0.0686326i
$970$	−10.4912			−0.336851
$971$		−	43.4097i		−	1.39308i	−0.717517	−	0.696541i	$-0.754721\pi$
$971$		−	43.4097i		−	1.39308i	0.717517	−	0.696541i	$-0.245279\pi$
$972$	−0.200386	−	0.200386i	−0.00642739	−	0.00642739i
$973$	4.89189			0.156827
$974$	−0.376666	−	0.376666i	−0.0120691	−	0.0120691i
$975$	−2.24421	+	2.24421i	−0.0718721	+	0.0718721i
$976$	−39.6333	+	39.6333i	−1.26863	+	1.26863i
$977$		−	33.0140i		−	1.05621i	−0.849179	−	0.528105i	$-0.822903\pi$
$977$		−	33.0140i		−	1.05621i	0.849179	−	0.528105i	$-0.177097\pi$
$978$		−	7.28296i		−	0.232884i
$979$	10.4693	−	10.4693i	0.334601	−	0.334601i
$980$	0.467830	−	0.467830i	0.0149443	−	0.0149443i
$981$	9.35507	+	9.35507i	0.298684	+	0.298684i
$982$	−14.7166			−0.469625
$983$	−31.2458	−	31.2458i	−0.996586	−	0.996586i	0.00340834	−	0.999994i	$-0.498915\pi$
$983$	−31.2458	−	31.2458i	−0.996586	−	0.996586i	−0.999994	+	0.00340834i	$0.998915\pi$
$984$			31.0345i			0.989343i
$985$	−10.6258			−0.338567
$986$	−26.8254	−	16.4148i	−0.854294	−	0.522752i
$987$	−6.81302			−0.216861
$988$		−	1.98180i		−	0.0630495i
$989$	1.11022	+	1.11022i	0.0353030	+	0.0353030i
$990$	−13.6424			−0.433583
$991$	−6.79452	−	6.79452i	−0.215835	−	0.215835i	0.590906	−	0.806741i	$-0.298771\pi$
$991$	−6.79452	−	6.79452i	−0.215835	−	0.215835i	−0.806741	+	0.590906i	$0.798771\pi$
$992$	−2.33945	+	2.33945i	−0.0742777	+	0.0742777i
$993$	14.4909	−	14.4909i	0.459856	−	0.459856i
$994$		−	11.8194i		−	0.374888i
$995$		−	47.2445i		−	1.49775i
$996$	2.58259	−	2.58259i	0.0818325	−	0.0818325i
$997$	−34.4116	+	34.4116i	−1.08983	+	1.08983i	−0.0942822	+	0.995546i	$0.530056\pi$
$997$	−34.4116	+	34.4116i	−1.08983	+	1.08983i	−0.995546	+	0.0942822i	$0.969944\pi$
$998$	−28.0998	−	28.0998i	−0.889484	−	0.889484i
$999$	5.76715			0.182464

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.k.b.64.4	✓	20
3.2	odd	2		1071.2.n.b.64.7		20
17.2	even	8		6069.2.a.bd.1.7		10
17.4	even	4	inner	357.2.k.b.106.7	yes	20
17.15	even	8		6069.2.a.be.1.7		10
51.38	odd	4		1071.2.n.b.820.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.k.b.64.4	✓	20	1.1	even	1	trivial
357.2.k.b.106.7	yes	20	17.4	even	4	inner
1071.2.n.b.64.7		20	3.2	odd	2
1071.2.n.b.820.4		20	51.38	odd	4
6069.2.a.bd.1.7		10	17.2	even	8
6069.2.a.be.1.7		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)

\(f(q)\)	\(=\)	\(q-1.51109i q^{2} +(-0.707107 - 0.707107i) q^{3} -0.283389 q^{4} +(-1.65084 - 1.65084i) q^{5} +(-1.06850 + 1.06850i) q^{6} +(-0.707107 + 0.707107i) q^{7} -2.59395i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q-1.51109i q^{2} +(-0.707107 - 0.707107i) q^{3} -0.283389 q^{4} +(-1.65084 - 1.65084i) q^{5} +(-1.06850 + 1.06850i) q^{6} +(-0.707107 + 0.707107i) q^{7} -2.59395i q^{8} +1.00000i q^{9} +(-2.49457 + 2.49457i) q^{10} +(2.73442 - 2.73442i) q^{11} +(0.200386 + 0.200386i) q^{12} -7.04427 q^{13} +(1.06850 + 1.06850i) q^{14} +2.33464i q^{15} -4.48647 q^{16} +(0.965114 + 4.00856i) q^{17} +1.51109 q^{18} -0.992753i q^{19} +(0.467830 + 0.467830i) q^{20} +1.00000 q^{21} +(-4.13195 - 4.13195i) q^{22} +(-0.461170 + 0.461170i) q^{23} +(-1.83420 + 1.83420i) q^{24} +0.450549i q^{25} +10.6445i q^{26} +(0.707107 - 0.707107i) q^{27} +(0.200386 - 0.200386i) q^{28} +(-3.56926 - 3.56926i) q^{29} +3.52785 q^{30} +(1.46992 + 1.46992i) q^{31} +1.59155i q^{32} -3.86705 q^{33} +(6.05729 - 1.45837i) q^{34} +2.33464 q^{35} -0.283389i q^{36} +(4.07799 + 4.07799i) q^{37} -1.50014 q^{38} +(4.98105 + 4.98105i) q^{39} +(-4.28220 + 4.28220i) q^{40} +(8.45995 - 8.45995i) q^{41} -1.51109i q^{42} -2.40741i q^{43} +(-0.774904 + 0.774904i) q^{44} +(1.65084 - 1.65084i) q^{45} +(0.696868 + 0.696868i) q^{46} -6.81302 q^{47} +(3.17241 + 3.17241i) q^{48} -1.00000i q^{49} +0.680819 q^{50} +(2.15204 - 3.51692i) q^{51} +1.99627 q^{52} -5.04239i q^{53} +(-1.06850 - 1.06850i) q^{54} -9.02818 q^{55} +(1.83420 + 1.83420i) q^{56} +(-0.701983 + 0.701983i) q^{57} +(-5.39348 + 5.39348i) q^{58} -1.56548i q^{59} -0.661611i q^{60} +(8.83396 - 8.83396i) q^{61} +(2.22118 - 2.22118i) q^{62} +(-0.707107 - 0.707107i) q^{63} -6.56797 q^{64} +(11.6290 + 11.6290i) q^{65} +5.84346i q^{66} +4.95686 q^{67} +(-0.273503 - 1.13598i) q^{68} +0.652192 q^{69} -3.52785i q^{70} +(-5.53082 - 5.53082i) q^{71} +2.59395 q^{72} +(3.24064 + 3.24064i) q^{73} +(6.16220 - 6.16220i) q^{74} +(0.318586 - 0.318586i) q^{75} +0.281335i q^{76} +3.86705i q^{77} +(7.52681 - 7.52681i) q^{78} +(0.679318 - 0.679318i) q^{79} +(7.40644 + 7.40644i) q^{80} -1.00000 q^{81} +(-12.7837 - 12.7837i) q^{82} -12.8881i q^{83} -0.283389 q^{84} +(5.02425 - 8.21074i) q^{85} -3.63780 q^{86} +5.04770i q^{87} +(-7.09295 - 7.09295i) q^{88} +3.82872 q^{89} +(-2.49457 - 2.49457i) q^{90} +(4.98105 - 4.98105i) q^{91} +(0.130690 - 0.130690i) q^{92} -2.07878i q^{93} +10.2951i q^{94} +(-1.63888 + 1.63888i) q^{95} +(1.12539 - 1.12539i) q^{96} +(2.10281 + 2.10281i) q^{97} -1.51109 q^{98} +(2.73442 + 2.73442i) 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

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