LMFDB - Embedded newform 680.2.t.a.523.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(523,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.523"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.t (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$208$
Relative dimension:	$104$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			523.17
Character	$\chi$	$=$	680.523
Dual form			680.2.t.a.667.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.23139 - 0.695478i) q^{2} -2.83257i q^{3} +(1.03262 + 1.71280i) q^{4} +(1.41742 - 1.72943i) q^{5} +(-1.96999 + 3.48799i) q^{6} -3.96131 q^{7} +(-0.0803370 - 2.82729i) q^{8} -5.02347 q^{9} +(-2.94817 + 1.14381i) q^{10} +(4.48255 - 4.48255i) q^{11} +(4.85164 - 2.92497i) q^{12} +(-2.99784 + 2.99784i) q^{13} +(4.87790 + 2.75500i) q^{14} +(-4.89873 - 4.01494i) q^{15} +(-1.86739 + 3.53735i) q^{16} +(-2.84925 + 2.98023i) q^{17} +(6.18583 + 3.49371i) q^{18} -0.774926 q^{19} +(4.42583 + 0.641918i) q^{20} +11.2207i q^{21} +(-8.63727 + 2.40223i) q^{22} -3.16329i q^{23} +(-8.00849 + 0.227560i) q^{24} +(-0.981842 - 4.90265i) q^{25} +(5.77642 - 1.60656i) q^{26} +5.73162i q^{27} +(-4.09053 - 6.78494i) q^{28} +(-0.715095 - 0.715095i) q^{29} +(3.23992 + 8.35090i) q^{30} +(-3.89586 + 3.89586i) q^{31} +(4.75963 - 3.05712i) q^{32} +(-12.6972 - 12.6972i) q^{33} +(5.58121 - 1.68822i) q^{34} +(-5.61483 + 6.85079i) q^{35} +(-5.18734 - 8.60421i) q^{36} -2.82223i q^{37} +(0.954233 + 0.538944i) q^{38} +(8.49159 + 8.49159i) q^{39} +(-5.00346 - 3.86851i) q^{40} +(-0.420361 + 0.420361i) q^{41} +(7.80374 - 13.8170i) q^{42} +(4.23204 - 4.23204i) q^{43} +(12.3065 + 3.04895i) q^{44} +(-7.12036 + 8.68773i) q^{45} +(-2.20000 + 3.89523i) q^{46} +(5.32420 + 5.32420i) q^{47} +(10.0198 + 5.28952i) q^{48} +8.69195 q^{49} +(-2.20066 + 6.71990i) q^{50} +(8.44172 + 8.07071i) q^{51} +(-8.23033 - 2.03908i) q^{52} +(-5.72750 - 5.72750i) q^{53} +(3.98622 - 7.05783i) q^{54} +(-1.39859 - 14.1059i) q^{55} +(0.318239 + 11.1997i) q^{56} +2.19503i q^{57} +(0.383225 + 1.37789i) q^{58} -10.4162 q^{59} +(1.81828 - 12.5365i) q^{60} +(7.58216 + 7.58216i) q^{61} +(7.50680 - 2.08782i) q^{62} +19.8995 q^{63} +(-7.98709 + 0.454271i) q^{64} +(0.935349 + 9.43373i) q^{65} +(6.80450 + 24.4657i) q^{66} +(2.87710 - 2.87710i) q^{67} +(-8.04674 - 1.80276i) q^{68} -8.96024 q^{69} +(11.6786 - 4.53098i) q^{70} +(5.10666 - 5.10666i) q^{71} +(0.403570 + 14.2028i) q^{72} +10.9501i q^{73} +(-1.96280 + 3.47526i) q^{74} +(-13.8871 + 2.78114i) q^{75} +(-0.800205 - 1.32730i) q^{76} +(-17.7568 + 17.7568i) q^{77} +(-4.55071 - 16.3621i) q^{78} +(-1.01300 + 1.01300i) q^{79} +(3.47072 + 8.24343i) q^{80} +1.16483 q^{81} +(0.809978 - 0.225275i) q^{82} +(2.19557 - 2.19557i) q^{83} +(-19.2188 + 11.5867i) q^{84} +(1.11551 + 9.15181i) q^{85} +(-8.15456 + 2.26798i) q^{86} +(-2.02556 + 2.02556i) q^{87} +(-13.0336 - 12.3133i) q^{88} -6.44059i q^{89} +(14.8100 - 5.74588i) q^{90} +(11.8753 - 11.8753i) q^{91} +(5.41809 - 3.26648i) q^{92} +(11.0353 + 11.0353i) q^{93} +(-2.85328 - 10.2590i) q^{94} +(-1.09840 + 1.34018i) q^{95} +(-8.65950 - 13.4820i) q^{96} -4.39822 q^{97} +(-10.7031 - 6.04506i) q^{98} +(-22.5180 + 22.5180i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 208 q - 8 q^{6} - 192 q^{9} + 2 q^{10} - 8 q^{11} + 8 q^{12} - 16 q^{14} - 16 q^{16} - 12 q^{18} - 10 q^{20} + 4 q^{22} + 16 q^{24} + 12 q^{28} - 24 q^{30} + 20 q^{32} - 8 q^{33} - 4 q^{34} - 8 q^{35} - 12 q^{38}+ \cdots + 24 q^{99}+O(q^{100}) $ 208 * q - 8 * q^6 - 192 * q^9 + 2 * q^10 - 8 * q^11 + 8 * q^12 - 16 * q^14 - 16 * q^16 - 12 * q^18 - 10 * q^20 + 4 * q^22 + 16 * q^24 + 12 * q^28 - 24 * q^30 + 20 * q^32 - 8 * q^33 - 4 * q^34 - 8 * q^35 - 12 * q^38 - 42 * q^40 - 8 * q^41 - 32 * q^42 + 8 * q^44 - 16 * q^46 + 160 * q^49 + 16 * q^50 - 8 * q^51 - 20 * q^52 + 36 * q^54 + 4 * q^56 - 56 * q^58 - 64 * q^59 + 32 * q^60 - 48 * q^65 - 8 * q^67 - 56 * q^68 - 28 * q^70 - 56 * q^72 + 8 * q^74 + 8 * q^75 - 12 * q^78 + 6 * q^80 + 128 * q^81 + 44 * q^82 + 8 * q^86 - 82 * q^90 + 24 * q^91 + 64 * q^94 - 48 * q^96 - 16 * q^97 - 40 * q^98 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$

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 $

$2$	−1.23139	−	0.695478i	−0.870721	−	0.491777i
$2$	−1.23139	−	0.695478i	−0.870721	−	0.491777i
$3$		−	2.83257i		−	1.63539i	−0.575654	−	0.817693i	$-0.695253\pi$
$3$		−	2.83257i		−	1.63539i	0.575654	−	0.817693i	$-0.304747\pi$
$4$	1.03262	+	1.71280i	0.516310	+	0.856402i
$5$	1.41742	−	1.72943i	0.633889	−	0.773424i
$5$	1.41742	−	1.72943i	0.633889	−	0.773424i
$6$	−1.96999	+	3.48799i	−0.804246	+	1.42397i
$7$	−3.96131			−1.49723			−0.748617	−	0.663003i	$-0.769282\pi$
$7$	−3.96131			−1.49723			−0.748617	+	0.663003i	$0.769282\pi$
$8$	−0.0803370	−	2.82729i	−0.0284034	−	0.999597i
$9$	−5.02347			−1.67449
$10$	−2.94817	+	1.14381i	−0.932293	+	0.361704i
$11$	4.48255	−	4.48255i	1.35154	−	1.35154i	0.467601	−	0.883940i	$-0.345119\pi$
$11$	4.48255	−	4.48255i	1.35154	−	1.35154i	0.883940	−	0.467601i	$-0.154881\pi$
$12$	4.85164	−	2.92497i	1.40055	−	0.844367i
$13$	−2.99784	+	2.99784i	−0.831450	+	0.831450i	−0.987715	−	0.156265i	$-0.950055\pi$
$13$	−2.99784	+	2.99784i	−0.831450	+	0.831450i	0.156265	+	0.987715i	$0.450055\pi$
$14$	4.87790	+	2.75500i	1.30367	+	0.736305i
$15$	−4.89873	−	4.01494i	−1.26485	−	1.03665i
$16$	−1.86739	+	3.53735i	−0.466847	+	0.884338i
$17$	−2.84925	+	2.98023i	−0.691045	+	0.722812i
$17$	−2.84925	+	2.98023i	−0.691045	+	0.722812i
$18$	6.18583	+	3.49371i	1.45801	+	0.823476i
$19$	−0.774926			−0.177780			−0.0888901	−	0.996041i	$-0.528332\pi$
$19$	−0.774926			−0.177780			−0.0888901	+	0.996041i	$0.528332\pi$
$20$	4.42583	+	0.641918i	0.989645	+	0.143537i
$21$			11.2207i			2.44856i
$22$	−8.63727	+	2.40223i	−1.84147	+	0.512158i
$23$		−	3.16329i		−	0.659591i	−0.944052	−	0.329796i	$-0.893020\pi$
$23$		−	3.16329i		−	0.659591i	0.944052	−	0.329796i	$-0.106980\pi$
$24$	−8.00849	+	0.227560i	−1.63473	+	0.0464506i
$25$	−0.981842	−	4.90265i	−0.196368	−	0.980530i
$26$	5.77642	−	1.60656i	1.13285	−	0.315073i
$27$			5.73162i			1.10305i
$28$	−4.09053	−	6.78494i	−0.773037	−	1.28223i
$29$	−0.715095	−	0.715095i	−0.132790	−	0.132790i	0.637588	−	0.770378i	$-0.279932\pi$
$29$	−0.715095	−	0.715095i	−0.132790	−	0.132790i	−0.770378	+	0.637588i	$0.779932\pi$
$30$	3.23992	+	8.35090i	0.591526	+	1.52466i
$31$	−3.89586	+	3.89586i	−0.699718	+	0.699718i	−0.964350	−	0.264632i	$-0.914750\pi$
$31$	−3.89586	+	3.89586i	−0.699718	+	0.699718i	0.264632	+	0.964350i	$0.414750\pi$
$32$	4.75963	−	3.05712i	0.841391	−	0.540427i
$33$	−12.6972	−	12.6972i	−2.21029	−	2.21029i
$34$	5.58121	−	1.68822i	0.957170	−	0.289528i
$35$	−5.61483	+	6.85079i	−0.949080	+	1.15800i
$36$	−5.18734	−	8.60421i	−0.864556	−	1.43404i
$37$		−	2.82223i		−	0.463972i	−0.972719	−	0.231986i	$-0.925478\pi$
$37$		−	2.82223i		−	0.463972i	0.972719	−	0.231986i	$-0.0745224\pi$
$38$	0.954233	+	0.538944i	0.154797	+	0.0874283i
$39$	8.49159	+	8.49159i	1.35974	+	1.35974i
$40$	−5.00346	−	3.86851i	−0.791116	−	0.611666i
$41$	−0.420361	+	0.420361i	−0.0656493	+	0.0656493i	−0.739169	−	0.673520i	$-0.764782\pi$
$41$	−0.420361	+	0.420361i	−0.0656493	+	0.0656493i	0.673520	+	0.739169i	$0.264782\pi$
$42$	7.80374	−	13.8170i	1.20414	−	2.13201i
$43$	4.23204	−	4.23204i	0.645380	−	0.645380i	−0.306493	−	0.951873i	$-0.599156\pi$
$43$	4.23204	−	4.23204i	0.645380	−	0.645380i	0.951873	+	0.306493i	$0.0991557\pi$
$44$	12.3065	+	3.04895i	1.85528	+	0.459647i
$45$	−7.12036	+	8.68773i	−1.06144	+	1.29509i
$46$	−2.20000	+	3.89523i	−0.324372	+	0.574320i
$47$	5.32420	+	5.32420i	0.776614	+	0.776614i	0.979253	−	0.202640i	$-0.0649520\pi$
$47$	5.32420	+	5.32420i	0.776614	+	0.776614i	−0.202640	+	0.979253i	$0.564952\pi$
$48$	10.0198	+	5.28952i	1.44623	+	0.763476i
$49$	8.69195			1.24171
$50$	−2.20066	+	6.71990i	−0.311220	+	0.950338i
$51$	8.44172	+	8.07071i	1.18208	+	1.13013i
$52$	−8.23033	−	2.03908i	−1.14134	−	0.282769i
$53$	−5.72750	−	5.72750i	−0.786732	−	0.786732i	0.194225	−	0.980957i	$-0.437781\pi$
$53$	−5.72750	−	5.72750i	−0.786732	−	0.786732i	−0.980957	+	0.194225i	$0.937781\pi$
$54$	3.98622	−	7.05783i	0.542455	−	0.960450i
$55$	−1.39859	−	14.1059i	−0.188586	−	1.90204i
$56$	0.318239	+	11.1997i	0.0425265	+	1.49663i
$57$			2.19503i			0.290739i
$58$	0.383225	+	1.37789i	0.0503199	+	0.180926i
$59$	−10.4162			−1.35608			−0.678040	−	0.735025i	$-0.737170\pi$
$59$	−10.4162			−1.35608			−0.678040	+	0.735025i	$0.737170\pi$
$60$	1.81828	−	12.5365i	0.234739	−	1.61845i
$61$	7.58216	+	7.58216i	0.970796	+	0.970796i	0.999586	−	0.0287893i	$-0.00916519\pi$
$61$	7.58216	+	7.58216i	0.970796	+	0.970796i	−0.0287893	+	0.999586i	$0.509165\pi$
$62$	7.50680	−	2.08782i	0.953364	−	0.265154i
$63$	19.8995			2.50710
$64$	−7.98709	+	0.454271i	−0.998386	+	0.0567839i
$65$	0.935349	+	9.43373i	0.116016	+	1.17011i
$66$	6.80450	+	24.4657i	0.837576	+	3.01152i
$67$	2.87710	−	2.87710i	0.351493	−	0.351493i	−0.509172	−	0.860665i	$-0.670048\pi$
$67$	2.87710	−	2.87710i	0.351493	−	0.351493i	0.860665	+	0.509172i	$0.170048\pi$
$68$	−8.04674	−	1.80276i	−0.975811	−	0.218616i
$69$	−8.96024			−1.07869
$70$	11.6786	−	4.53098i	1.39586	−	0.541555i
$71$	5.10666	−	5.10666i	0.606049	−	0.606049i	−0.335862	−	0.941911i	$-0.609028\pi$
$71$	5.10666	−	5.10666i	0.606049	−	0.606049i	0.941911	+	0.335862i	$0.109028\pi$
$72$	0.403570	+	14.2028i	0.0475612	+	1.67381i
$73$			10.9501i			1.28162i	0.767702	+	0.640808i	$0.221400\pi$
$73$			10.9501i			1.28162i	−0.767702	+	0.640808i	$0.778600\pi$
$74$	−1.96280	+	3.47526i	−0.228171	+	0.403990i
$75$	−13.8871	+	2.78114i	−1.60355	+	0.321138i
$76$	−0.800205	−	1.32730i	−0.0917898	−	0.152251i
$77$	−17.7568	+	17.7568i	−2.02357	+	2.02357i
$78$	−4.55071	−	16.3621i	−0.515266	−	1.85265i
$79$	−1.01300	+	1.01300i	−0.113971	+	0.113971i	−0.761792	−	0.647821i	$-0.775680\pi$
$79$	−1.01300	+	1.01300i	−0.113971	+	0.113971i	0.647821	+	0.761792i	$0.275680\pi$
$80$	3.47072	+	8.24343i	0.388038	+	0.921643i
$81$	1.16483			0.129425
$82$	0.809978	−	0.225275i	0.0894471	−	0.0248774i
$83$	2.19557	−	2.19557i	0.240995	−	0.240995i	−0.576267	−	0.817262i	$-0.695491\pi$
$83$	2.19557	−	2.19557i	0.240995	−	0.240995i	0.817262	+	0.576267i	$0.195491\pi$
$84$	−19.2188	+	11.5867i	−2.09695	+	1.26421i
$85$	1.11551	+	9.15181i	0.120994	+	0.992653i
$86$	−8.15456	+	2.26798i	−0.879329	+	0.244563i
$87$	−2.02556	+	2.02556i	−0.217163	+	0.217163i
$88$	−13.0336	−	12.3133i	−1.38938	−	1.31261i
$89$		−	6.44059i		−	0.682701i	−0.939936	−	0.341351i	$-0.889116\pi$
$89$		−	6.44059i		−	0.682701i	0.939936	−	0.341351i	$-0.110884\pi$
$90$	14.8100	−	5.74588i	1.56111	−	0.605669i
$91$	11.8753	−	11.8753i	1.24487	−	1.24487i
$92$	5.41809	−	3.26648i	0.564875	−	0.340554i
$93$	11.0353	+	11.0353i	1.14431	+	1.14431i
$94$	−2.85328	−	10.2590i	−0.294293	−	1.05814i
$95$	−1.09840	+	1.34018i	−0.112693	+	0.137499i
$96$	−8.65950	−	13.4820i	−0.883807	−	1.37600i
$97$	−4.39822			−0.446571			−0.223286	−	0.974753i	$-0.571678\pi$
$97$	−4.39822			−0.446571			−0.223286	+	0.974753i	$0.571678\pi$
$98$	−10.7031	−	6.04506i	−1.08118	−	0.610643i
$99$	−22.5180	+	22.5180i	−2.26314	+	2.26314i
$100$	7.38341	−	6.74428i	0.738341	−	0.674428i
$101$		−	2.49860i		−	0.248620i	−0.992243	−	0.124310i	$-0.960328\pi$
$101$		−	2.49860i		−	0.248620i	0.992243	−	0.124310i	$-0.0396717\pi$
$102$	−4.78201	−	15.8092i	−0.473490	−	1.56534i
$103$	2.50948	−	2.50948i	0.247266	−	0.247266i	−0.572582	−	0.819848i	$-0.694058\pi$
$103$	2.50948	−	2.50948i	0.247266	−	0.247266i	0.819848	+	0.572582i	$0.194058\pi$
$104$	8.71658	+	8.23490i	0.854731	+	0.807499i
$105$	19.4054	+	15.9044i	1.89377	+	1.55211i
$106$	3.06941	+	11.0361i	0.298127	+	1.07192i
$107$	2.41439			0.233408			0.116704	−	0.993167i	$-0.462767\pi$
$107$	2.41439			0.233408			0.116704	+	0.993167i	$0.462767\pi$
$108$	−9.81714	+	5.91859i	−0.944655	+	0.569517i
$109$	−0.464364	+	0.464364i	−0.0444780	+	0.0444780i	−0.728996	−	0.684518i	$-0.760013\pi$
$109$	−0.464364	+	0.464364i	−0.0444780	+	0.0444780i	0.684518	+	0.728996i	$0.260013\pi$
$110$	−8.08814	+	18.3425i	−0.771174	+	1.74889i
$111$	−7.99418			−0.758774
$112$	7.39730	−	14.0125i	0.698979	−	1.32406i
$113$	0.658607			0.0619566			0.0309783	−	0.999520i	$-0.490138\pi$
$113$	0.658607			0.0619566			0.0309783	+	0.999520i	$0.490138\pi$
$114$	1.52660	−	2.70293i	0.142979	−	0.253153i
$115$	−5.47068	−	4.48371i	−0.510143	−	0.418108i
$116$	0.486395	−	1.96324i	0.0451607	−	0.182282i
$117$	15.0595	−	15.0595i	1.39225	−	1.39225i
$118$	12.8264	+	7.24427i	1.18077	+	0.666889i
$119$	11.2868	−	11.8056i	1.03466	−	1.08222i
$120$	−10.9578	+	14.1727i	−1.00031	+	1.29378i
$121$		−	29.1866i		−	2.65332i
$122$	−4.06334	−	14.6098i	−0.367877	−	1.32271i
$123$	1.19070	+	1.19070i	0.107362	+	0.107362i
$124$	−10.6958	−	2.64990i	−0.960511	−	0.237968i
$125$	−9.87046	−	5.25109i	−0.882841	−	0.469672i
$126$	−24.5040	−	13.8397i	−2.18299	−	1.23294i
$127$	5.02540	−	5.02540i	0.445933	−	0.445933i	−0.448067	−	0.894000i	$-0.647888\pi$
$127$	5.02540	−	5.02540i	0.445933	−	0.445933i	0.894000	+	0.448067i	$0.147888\pi$
$128$	10.1511	+	4.99546i	0.897241	+	0.441541i
$129$	−11.9876	−	11.9876i	−1.05545	−	1.05545i
$130$	5.40918	−	12.2671i	0.474416	−	1.07589i
$131$	−5.09343	−	5.09343i	−0.445015	−	0.445015i	0.448678	−	0.893693i	$-0.351895\pi$
$131$	−5.09343	−	5.09343i	−0.445015	−	0.445015i	−0.893693	+	0.448678i	$0.851895\pi$
$132$	8.63638	−	34.8591i	0.751701	−	3.03409i
$133$	3.06972			0.266179
$134$	−5.54377	+	1.54186i	−0.478909	+	0.133196i
$135$	9.91243	+	8.12411i	0.853126	+	0.699212i
$136$	8.65486	+	7.81622i	0.742148	+	0.670236i
$137$	−2.25763	+	2.25763i	−0.192883	+	0.192883i	−0.796940	−	0.604058i	$-0.793550\pi$
$137$	−2.25763	+	2.25763i	−0.192883	+	0.192883i	0.604058	+	0.796940i	$0.293550\pi$
$138$	11.0335	+	6.23165i	0.939235	+	0.530473i
$139$	13.5356	−	13.5356i	1.14807	−	1.14807i	0.161144	−	0.986931i	$-0.448482\pi$
$139$	13.5356	−	13.5356i	1.14807	−	1.14807i	0.986931	−	0.161144i	$-0.0515183\pi$
$140$	−17.5321	−	2.54284i	−1.48173	−	0.214909i
$141$	15.0812	−	15.0812i	1.27006	−	1.27006i
$142$	−9.83984	+	2.73670i	−0.825741	+	0.229659i
$143$			26.8759i			2.24748i
$144$	9.38077	−	17.7698i	0.781731	−	1.48081i
$145$	−2.25030	+	0.223115i	−0.186877	+	0.0185287i
$146$	7.61557	−	13.4838i	0.630269	−	1.11593i
$147$		−	24.6206i		−	2.03067i
$148$	4.83393	−	2.91430i	0.397347	−	0.239554i
$149$	−7.14570			−0.585399			−0.292699	−	0.956204i	$-0.594554\pi$
$149$	−7.14570			−0.585399			−0.292699	+	0.956204i	$0.594554\pi$
$150$	19.0346	+	6.23353i	1.55417	+	0.508966i
$151$	−16.1485			−1.31415			−0.657074	−	0.753826i	$-0.728206\pi$
$151$	−16.1485			−1.31415			−0.657074	+	0.753826i	$0.728206\pi$
$152$	0.0622552	+	2.19094i	0.00504957	+	0.177709i
$153$	14.3131	−	14.9711i	1.15715	−	1.21034i
$154$	34.2149	−	9.51598i	2.75711	−	0.766820i
$155$	1.21554	+	12.2597i	0.0976346	+	0.984722i
$156$	−5.77583	+	23.3130i	−0.462437	+	1.86653i
$157$	−7.15502	−	7.15502i	−0.571033	−	0.571033i	0.361384	−	0.932417i	$-0.382304\pi$
$157$	−7.15502	−	7.15502i	−0.571033	−	0.571033i	−0.932417	+	0.361384i	$0.882304\pi$
$158$	1.95191	−	0.542873i	0.155285	−	0.0431886i
$159$	−16.2236	+	16.2236i	−1.28661	+	1.28661i
$160$	1.45933	−	12.5646i	0.115370	−	0.993323i
$161$			12.5308i			0.987562i
$162$	−1.43435	−	0.810112i	−0.112693	−	0.0636484i
$163$	−16.1590			−1.26567			−0.632836	−	0.774286i	$-0.718109\pi$
$163$	−16.1590			−1.26567			−0.632836	+	0.774286i	$0.718109\pi$
$164$	−1.15407	−	0.285922i	−0.0901176	−	0.0223268i
$165$	−39.9560	+	3.96162i	−3.11057	+	0.308411i
$166$	−4.23056	+	1.17662i	−0.328355	+	0.0913234i
$167$		−	18.0902i		−	1.39986i	−0.714209	−	0.699932i	$-0.753214\pi$
$167$		−	18.0902i		−	1.39986i	0.714209	−	0.699932i	$-0.246786\pi$
$168$	31.7241	−	0.901437i	2.44757	−	0.0695473i
$169$		−	4.97404i		−	0.382619i
$170$	4.99126	−	12.0452i	0.382812	−	0.923826i
$171$	3.89282			0.297691
$172$	11.6187	+	2.87856i	0.885920	+	0.219488i
$173$	10.4310			0.793058			0.396529	−	0.918022i	$-0.370215\pi$
$173$	10.4310			0.793058			0.396529	+	0.918022i	$0.370215\pi$
$174$	3.90298	−	1.08551i	0.295884	−	0.0822925i
$175$	3.88938	+	19.4209i	0.294009	+	1.46808i
$176$	7.48569	+	24.2270i	0.564255	+	1.82618i
$177$			29.5048i			2.21771i
$178$	−4.47929	+	7.93085i	−0.335737	+	0.594442i
$179$	−5.75799			−0.430372			−0.215186	−	0.976573i	$-0.569036\pi$
$179$	−5.75799			−0.430372			−0.215186	+	0.976573i	$0.569036\pi$
$180$	−22.2330	−	3.22466i	−1.65715	−	0.240352i
$181$	0.0861720	+	0.0861720i	0.00640511	+	0.00640511i	0.710302	−	0.703897i	$-0.248558\pi$
$181$	0.0861720	+	0.0861720i	0.00640511	+	0.00640511i	−0.703897	+	0.710302i	$0.748558\pi$
$182$	−22.8822	+	6.36409i	−1.69614	+	0.471738i
$183$	21.4770	−	21.4770i	1.58763	−	1.58763i
$184$	−8.94352	+	0.254129i	−0.659325	+	0.0187346i
$185$	−4.88085	−	4.00029i	−0.358847	−	0.294107i
$186$	−5.91391	−	21.2635i	−0.433629	−	1.55912i
$187$	0.587125	+	26.1310i	0.0429348	+	1.91088i
$188$	−3.62143	+	14.6172i	−0.264120	+	1.06607i
$189$		−	22.7047i		−	1.65152i
$190$	2.28461	−	0.886367i	0.165743	−	0.0643038i
$191$		−	14.3693i		−	1.03973i	−0.854249	−	0.519864i	$-0.825983\pi$
$191$		−	14.3693i		−	1.03973i	0.854249	−	0.519864i	$-0.174017\pi$
$192$	1.28676	+	22.6240i	0.0928637	+	1.63275i
$193$	20.2298			1.45617			0.728087	−	0.685485i	$-0.240410\pi$
$193$	20.2298			1.45617			0.728087	+	0.685485i	$0.240410\pi$
$194$	5.41590	+	3.05886i	0.388839	+	0.219614i
$195$	26.7217	−	2.64944i	1.91358	−	0.189731i
$196$	8.97549	+	14.8876i	0.641106	+	1.06340i
$197$	−23.0535			−1.64249			−0.821245	−	0.570575i	$-0.806720\pi$
$197$	−23.0535			−1.64249			−0.821245	+	0.570575i	$0.806720\pi$
$198$	43.3890	−	12.0675i	3.08352	−	0.857603i
$199$	−19.0179	−	19.0179i	−1.34814	−	1.34814i	−0.887677	−	0.460467i	$-0.847682\pi$
$199$	−19.0179	−	19.0179i	−1.34814	−	1.34814i	−0.460467	−	0.887677i	$-0.652318\pi$
$200$	−13.7823	+	3.16981i	−0.974557	+	0.224140i
$201$	−8.14959	−	8.14959i	−0.574828	−	0.574828i
$202$	−1.73772	+	3.07674i	−0.122266	+	0.216479i
$203$	2.83271	+	2.83271i	0.198817	+	0.198817i
$204$	−5.10644	+	22.7930i	−0.357522	+	1.59583i
$205$	0.131156	+	1.32281i	0.00916033	+	0.0923892i
$206$	−4.83542	+	1.34485i	−0.336899	+	0.0936999i
$207$			15.8907i			1.10448i
$208$	−5.00627	−	16.2025i	−0.347123	−	1.12344i
$209$	−3.47365	+	3.47365i	−0.240277	+	0.240277i
$210$	−12.8343	−	33.0805i	−0.885652	−	2.28277i
$211$	−0.514628	+	0.514628i	−0.0354285	+	0.0354285i	−0.724599	−	0.689171i	$-0.757975\pi$
$211$	−0.514628	+	0.514628i	−0.0354285	+	0.0354285i	0.689171	+	0.724599i	$0.257975\pi$
$212$	3.89574	−	15.7244i	0.267561	−	1.07996i
$213$	−14.4650	−	14.4650i	−0.991125	−	0.991125i
$214$	−2.97304	−	1.67915i	−0.203233	−	0.114785i
$215$	−1.32043	−	13.3176i	−0.0900526	−	0.908251i
$216$	16.2049	−	0.460461i	1.10261	−	0.0313304i
$217$	15.4327	−	15.4327i	1.04764	−	1.04764i
$218$	0.894766	−	0.248856i	0.0606012	−	0.0168547i
$219$	31.0170			2.09594
$220$	22.7164	−	16.9616i	1.53154	−	1.14355i
$221$	−0.392657	−	17.4758i	−0.0264130	−	1.17555i
$222$	9.84392	+	5.55978i	0.660680	+	0.373148i
$223$	−20.2840	−	20.2840i	−1.35831	−	1.35831i	−0.875996	−	0.482317i	$-0.839795\pi$
$223$	−20.2840	−	20.2840i	−1.35831	−	1.35831i	−0.482317	−	0.875996i	$-0.660205\pi$
$224$	−18.8543	+	12.1102i	−1.25976	+	0.809145i
$225$	4.93225	+	24.6283i	0.328817	+	1.64189i
$226$	−0.810999	−	0.458047i	−0.0539469	−	0.0304688i
$227$		−	4.26142i		−	0.282840i	−0.989950	−	0.141420i	$-0.954833\pi$
$227$		−	4.26142i		−	0.282840i	0.989950	−	0.141420i	$-0.0451668\pi$
$228$	−3.75966	+	2.26664i	−0.248990	+	0.150112i
$229$		−	25.2809i		−	1.67061i	−0.549786	−	0.835306i	$-0.685291\pi$
$229$		−	25.2809i		−	1.67061i	0.549786	−	0.835306i	$-0.314709\pi$
$230$	3.61819	+	9.32591i	0.238577	+	0.614932i
$231$	50.2973	+	50.2973i	3.30932	+	3.30932i
$232$	−1.96433	+	2.07923i	−0.128965	+	0.136508i
$233$			4.93751i			0.323467i	0.986834	+	0.161734i	$0.0517085\pi$
$233$			4.93751i			0.323467i	−0.986834	+	0.161734i	$0.948291\pi$
$234$	−29.0177	+	8.07052i	−1.89694	+	0.527586i
$235$	16.7544	−	1.66119i	1.09294	−	0.108364i
$236$	−10.7560	−	17.8410i	−0.700158	−	1.16135i
$237$	2.86939	+	2.86939i	0.186387	+	0.186387i
$238$	−22.1089	+	6.68756i	−1.43311	+	0.433490i
$239$	2.45773			0.158977			0.0794887	−	0.996836i	$-0.474671\pi$
$239$	2.45773			0.158977			0.0794887	+	0.996836i	$0.474671\pi$
$240$	23.3501	−	9.83107i	1.50724	−	0.634593i
$241$	−8.81988	−	8.81988i	−0.568139	−	0.568139i	0.363468	−	0.931607i	$-0.381593\pi$
$241$	−8.81988	−	8.81988i	−0.568139	−	0.568139i	−0.931607	+	0.363468i	$0.881593\pi$
$242$	−20.2986	+	35.9399i	−1.30484	+	2.31030i
$243$			13.8954i			0.891390i
$244$	−5.15725	+	20.8162i	−0.330159	+	1.33262i
$245$	12.3201	−	15.0321i	0.787105	−	0.960366i
$246$	−0.638106	−	2.29432i	−0.0406842	−	0.146281i
$247$	2.32310	−	2.32310i	0.147815	−	0.147815i
$248$	11.3277	+	10.7017i	0.719310	+	0.679561i
$249$	−6.21910	−	6.21910i	−0.394119	−	0.394119i
$250$	8.50233	+	13.3308i	0.537734	+	0.843114i
$251$	23.2059			1.46474			0.732370	−	0.680907i	$-0.238414\pi$
$251$	23.2059			1.46474			0.732370	+	0.680907i	$0.238414\pi$
$252$	20.5486	+	34.0839i	1.29444	+	2.14709i
$253$	−14.1796	−	14.1796i	−0.891464	−	0.891464i
$254$	−9.68327	+	2.69315i	−0.607582	+	0.168983i
$255$	25.9232	−	3.15976i	1.62337	−	0.197872i
$256$	−9.02571	−	13.2112i	−0.564107	−	0.825702i
$257$	3.02777	+	3.02777i	0.188867	+	0.188867i	0.795206	−	0.606339i	$-0.207363\pi$
$257$	3.02777	+	3.02777i	0.188867	+	0.188867i	−0.606339	+	0.795206i	$0.707363\pi$
$258$	6.42422	+	23.0984i	0.399954	+	1.43804i
$259$			11.1797i			0.694675i
$260$	−15.1923	+	11.3435i	−0.942184	+	0.703496i
$261$	3.59226	+	3.59226i	0.222355	+	0.222355i
$262$	2.72961	+	9.81435i	0.168636	+	0.606332i
$263$	5.37115	+	5.37115i	0.331199	+	0.331199i	0.853042	−	0.521843i	$-0.174755\pi$
$263$	5.37115	+	5.37115i	0.331199	+	0.331199i	−0.521843	+	0.853042i	$0.674755\pi$
$264$	−34.8784	+	36.9185i	−2.14662	+	2.27218i
$265$	−18.0236	+	1.78703i	−1.10718	+	0.109776i
$266$	−3.78001	−	2.13492i	−0.231767	−	0.130901i
$267$	−18.2434			−1.11648
$268$	7.89885	+	1.95695i	0.482499	+	0.119540i
$269$	19.0129	+	19.0129i	1.15924	+	1.15924i	0.984640	+	0.174596i	$0.0558621\pi$
$269$	19.0129	+	19.0129i	1.15924	+	1.15924i	0.174596	+	0.984640i	$0.444138\pi$
$270$	−6.55587	−	16.8978i	−0.398978	−	1.02837i
$271$			12.9640i			0.787509i	0.919216	+	0.393755i	$0.128824\pi$
$271$			12.9640i			0.787509i	−0.919216	+	0.393755i	$0.871176\pi$
$272$	−5.22146	−	15.6441i	−0.316598	−	0.948560i
$273$	−33.6378	−	33.6378i	−2.03585	−	2.03585i
$274$	4.35015	−	1.20988i	0.262802	−	0.0730916i
$275$	−26.3775	−	17.5752i	−1.59063	−	1.05983i
$276$	−9.25253	−	15.3471i	−0.556937	−	0.923789i
$277$			0.418408i			0.0251397i	0.999921	+	0.0125699i	$0.00400121\pi$
$277$			0.418408i			0.0251397i	−0.999921	+	0.0125699i	$0.995999\pi$
$278$	−26.0813	+	7.25383i	−1.56425	+	0.435056i
$279$	19.5707	−	19.5707i	1.17167	−	1.17167i
$280$	19.8202	+	15.3244i	1.18449	+	0.915806i
$281$			1.16539i			0.0695215i	0.999396	+	0.0347608i	$0.0110669\pi$
$281$			1.16539i			0.0695215i	−0.999396	+	0.0347608i	$0.988933\pi$
$282$	−29.0594	+	8.08211i	−1.73046	+	0.481283i
$283$	−8.58446			−0.510293			−0.255147	−	0.966902i	$-0.582124\pi$
$283$	−8.58446			−0.510293			−0.255147	+	0.966902i	$0.582124\pi$
$284$	14.0200	+	3.47346i	0.831931	+	0.206112i
$285$	3.79615	+	3.11129i	0.224865	+	0.184297i
$286$	18.6916	−	33.0946i	1.10526	−	1.95693i
$287$	1.66518	−	1.66518i	0.0982924	−	0.0982924i
$288$	−23.9098	+	15.3573i	−1.40890	+	0.904939i
$289$	−0.763546	−	16.9828i	−0.0449145	−	0.998991i
$290$	2.92615	+	1.29029i	0.171830	+	0.0757684i
$291$			12.4583i			0.730317i
$292$	−18.7554	+	11.3073i	−1.09758	+	0.661711i
$293$	−0.0155663	+	0.0155663i	−0.000909391	+	0.000909391i	−0.707561	−	0.706652i	$-0.750205\pi$
$293$	−0.0155663	+	0.0155663i	−0.000909391	+	0.000909391i	0.706652	+	0.707561i	$0.250205\pi$
$294$	−17.1231	+	30.3174i	−0.998638	+	1.76815i
$295$	−14.7642	+	18.0141i	−0.859604	+	1.04882i
$296$	−7.97926	+	0.226730i	−0.463785	+	0.0131784i
$297$	25.6923	+	25.6923i	1.49082	+	1.49082i
$298$	8.79912	+	4.96968i	0.509719	+	0.287886i
$299$	9.48302	+	9.48302i	0.548417	+	0.548417i
$300$	−19.1037	−	20.9140i	−1.10295	−	1.20747i
$301$	−16.7644	+	16.7644i	−0.966284	+	0.966284i
$302$	19.8851	+	11.2309i	1.14426	+	0.646268i
$303$	−7.07747			−0.406590
$304$	1.44709	−	2.74119i	0.0829962	−	0.157218i
$305$	23.8599	−	2.36570i	1.36621	−	0.135459i
$306$	−28.0370	+	8.48073i	−1.60277	+	0.484811i
$307$	−1.54294	+	1.54294i	−0.0880605	+	0.0880605i	−0.749765	−	0.661704i	$-0.769833\pi$
$307$	−1.54294	+	1.54294i	−0.0880605	+	0.0880605i	0.661704	+	0.749765i	$0.269833\pi$
$308$	−48.7498	−	12.0778i	−2.77778	−	0.688199i
$309$	−7.10827	−	7.10827i	−0.404375	−	0.404375i
$310$	7.02954	−	15.9418i	0.399251	−	0.905433i
$311$	6.32646	−	6.32646i	0.358741	−	0.358741i	−0.504608	−	0.863349i	$-0.668363\pi$
$311$	6.32646	−	6.32646i	0.358741	−	0.358741i	0.863349	+	0.504608i	$0.168363\pi$
$312$	23.3260	−	24.6903i	1.32057	−	1.39782i
$313$	27.7463			1.56831			0.784155	−	0.620564i	$-0.213096\pi$
$313$	27.7463			1.56831			0.784155	+	0.620564i	$0.213096\pi$
$314$	3.83443	+	13.7868i	0.216389	+	0.778031i
$315$	28.2059	−	34.4147i	1.58922	−	1.93905i
$316$	−2.78111	−	0.689023i	−0.156449	−	0.0387606i
$317$	23.9145			1.34317			0.671586	−	0.740927i	$-0.265613\pi$
$317$	23.9145			1.34317			0.671586	+	0.740927i	$0.265613\pi$
$318$	31.2606	−	8.69432i	1.75301	−	0.487553i
$319$	−6.41090			−0.358942
$320$	−10.5354	+	14.4570i	−0.588949	+	0.808170i
$321$		−	6.83893i		−	0.381712i
$322$	8.71486	−	15.4302i	0.485660	−	0.859891i
$323$	2.20796	−	2.30946i	0.122854	−	0.128502i
$324$	1.20283	+	1.99512i	0.0668236	+	0.110840i
$325$	17.6407	+	11.7539i	0.978532	+	0.651991i
$326$	19.8980	+	11.2382i	1.10205	+	0.622428i
$327$	1.31534	+	1.31534i	0.0727387	+	0.0727387i
$328$	1.22225	+	1.15471i	0.0674875	+	0.0637582i
$329$	−21.0908	−	21.0908i	−1.16277	−	1.16277i
$330$	51.9565	+	22.9103i	2.86011	+	1.26117i
$331$			20.8684i			1.14703i	0.819195	+	0.573515i	$0.194421\pi$
$331$			20.8684i			1.14703i	−0.819195	+	0.573515i	$0.805579\pi$
$332$	6.02776	+	1.49339i	0.330816	+	0.0819602i
$333$			14.1774i			0.776917i
$334$	−12.5814	+	22.2761i	−0.688421	+	1.21889i
$335$	−0.897678	−	9.05379i	−0.0490454	−	0.494661i
$336$	−39.6915	−	20.9534i	−2.16535	−	1.14310i
$337$	9.53032			0.519149			0.259575	−	0.965723i	$-0.416418\pi$
$337$	9.53032			0.519149			0.259575	+	0.965723i	$0.416418\pi$
$338$	−3.45934	+	6.12496i	−0.188163	+	0.333154i
$339$		−	1.86555i		−	0.101323i
$340$	−14.5234	+	11.3610i	−0.787639	+	0.616137i
$341$			34.9268i			1.89139i
$342$	−4.79356	−	2.70737i	−0.259206	−	0.146398i
$343$	−6.70234			−0.361892
$344$	−12.3052	−	11.6252i	−0.663450	−	0.626788i
$345$	−12.7004	+	15.4961i	−0.683768	+	0.834282i
$346$	−12.8446	−	7.25456i	−0.690532	−	0.390008i
$347$		−	7.63781i		−	0.410019i	−0.978760	−	0.205009i	$-0.934277\pi$
$347$		−	7.63781i		−	0.410019i	0.978760	−	0.205009i	$-0.0657225\pi$
$348$	−5.56102	−	1.37775i	−0.298102	−	0.0738552i
$349$			30.9360i			1.65596i	0.560755	+	0.827982i	$0.310511\pi$
$349$			30.9360i			1.65596i	−0.560755	+	0.827982i	$0.689489\pi$
$350$	8.71749	−	26.6196i	0.465969	−	1.42288i
$351$	−17.1825	−	17.1825i	−0.917132	−	0.917132i
$352$	7.63160	−	35.0390i	0.406766	−	1.86758i
$353$	17.4423	+	17.4423i	0.928360	+	0.928360i	0.997600	−	0.0692400i	$-0.0220574\pi$
$353$	17.4423	+	17.4423i	0.928360	+	0.928360i	−0.0692400	+	0.997600i	$0.522057\pi$
$354$	20.5199	−	36.3317i	1.09062	−	1.93101i
$355$	−1.59332	−	16.0699i	−0.0845646	−	0.852901i
$356$	11.0315	−	6.65068i	0.584666	−	0.352486i
$357$	−33.4402	−	31.9706i	−1.76985	−	1.69206i
$358$	7.09030	+	4.00455i	0.374734	+	0.211647i
$359$		−	5.38926i		−	0.284434i	−0.989835	−	0.142217i	$-0.954577\pi$
$359$		−	5.38926i		−	0.284434i	0.989835	−	0.142217i	$-0.0454231\pi$
$360$	25.1347	+	19.4334i	1.32472	+	1.02423i
$361$	−18.3995			−0.968394
$362$	−0.0461802	−	0.166042i	−0.00242718	−	0.00872696i
$363$	−82.6730			−4.33921
$364$	32.6029	+	8.07741i	1.70885	+	0.423371i
$365$	18.9375	+	15.5209i	0.991231	+	0.812402i
$366$	−41.3833	+	11.5097i	−2.16314	+	0.601621i
$367$	−6.40541			−0.334360			−0.167180	−	0.985926i	$-0.553466\pi$
$367$	−6.40541			−0.334360			−0.167180	+	0.985926i	$0.553466\pi$
$368$	11.1897	+	5.90709i	0.583301	+	0.307928i
$369$	2.11167	−	2.11167i	0.109929	−	0.109929i
$370$	3.22809	+	8.32042i	0.167821	+	0.432558i
$371$	22.6884	+	22.6884i	1.17792	+	1.17792i
$372$	−7.50603	+	30.2966i	−0.389170	+	1.57081i
$373$	0.520047	−	0.520047i	0.0269270	−	0.0269270i	−0.693515	−	0.720442i	$-0.743939\pi$
$373$	0.520047	−	0.520047i	0.0269270	−	0.0269270i	0.720442	+	0.693515i	$0.243939\pi$
$374$	17.4505	−	32.5856i	0.902345	−	1.68496i
$375$	−14.8741	+	27.9588i	−0.768095	+	1.44379i
$376$	14.6253	−	15.4808i	0.754242	−	0.798359i
$377$	4.28748			0.220816
$378$	−15.7906	+	27.9582i	−0.812182	+	1.43802i
$379$	−19.9985	+	19.9985i	−1.02725	+	1.02725i	−0.0276362	+	0.999618i	$0.508798\pi$
$379$	−19.9985	+	19.9985i	−1.02725	+	1.02725i	−0.999618	+	0.0276362i	$0.991202\pi$
$380$	−3.42969	−	0.497439i	−0.175939	−	0.0255181i
$381$	−14.2348	−	14.2348i	−0.729272	−	0.729272i
$382$	−9.99355	+	17.6942i	−0.511314	+	0.905313i
$383$	−8.15727	−	8.15727i	−0.416817	−	0.416817i	0.467288	−	0.884105i	$-0.345231\pi$
$383$	−8.15727	−	8.15727i	−0.416817	−	0.416817i	−0.884105	+	0.467288i	$0.845231\pi$
$384$	14.1500	−	28.7538i	0.722090	−	1.46734i
$385$	5.54026	+	55.8778i	0.282358	+	2.84780i
$386$	−24.9107	−	14.0694i	−1.26792	−	0.716113i
$387$	−21.2595	+	21.2595i	−1.08068	+	1.08068i
$388$	−4.54169	−	7.53328i	−0.230569	−	0.382444i
$389$		−	6.98167i		−	0.353985i	−0.984212	−	0.176992i	$-0.943363\pi$
$389$		−	6.98167i		−	0.353985i	0.984212	−	0.176992i	$-0.0566368\pi$
$390$	−34.7474	−	15.3219i	−1.75950	−	0.775854i
$391$	9.42733	+	9.01300i	0.476760	+	0.455807i
$392$	−0.698285	−	24.5746i	−0.0352687	−	1.24121i
$393$	−14.4275	+	14.4275i	−0.727772	+	0.727772i
$394$	28.3877	+	16.0332i	1.43015	+	0.807740i
$395$	0.316063	+	3.18775i	0.0159029	+	0.160393i
$396$	−61.8213	−	15.3163i	−3.10664	−	0.769674i
$397$	37.1717			1.86559			0.932796	−	0.360404i	$-0.117361\pi$
$397$	37.1717			1.86559			0.932796	+	0.360404i	$0.117361\pi$
$398$	10.1918	+	36.6449i	0.510871	+	1.83684i
$399$		−	8.69521i		−	0.435305i
$400$	19.1759	+	5.68204i	0.958794	+	0.284102i
$401$	9.84964	−	9.84964i	0.491867	−	0.491867i	−0.417027	−	0.908894i	$-0.636928\pi$
$401$	9.84964	−	9.84964i	0.491867	−	0.491867i	0.908894	+	0.417027i	$0.136928\pi$
$402$	4.36743	+	15.7031i	0.217827	+	0.783202i
$403$		−	23.3583i		−	1.16356i
$404$	4.27961	−	2.58011i	0.212919	−	0.128365i
$405$	1.65105	−	2.01449i	0.0820413	−	0.100101i
$406$	−1.51807	−	5.45825i	−0.0753406	−	0.270888i
$407$	−12.6508	−	12.6508i	−0.627077	−	0.627077i
$408$	22.1400	−	24.5155i	1.09609	−	1.21370i
$409$			3.23767i			0.160093i	0.996791	+	0.0800463i	$0.0255068\pi$
$409$			3.23767i			0.160093i	−0.996791	+	0.0800463i	$0.974493\pi$
$410$	0.758483	−	1.72011i	0.0374588	−	0.0849500i
$411$	6.39491	+	6.39491i	0.315438	+	0.315438i
$412$	6.88957	+	1.70690i	0.339425	+	0.0840930i
$413$	41.2619			2.03037
$414$	11.0516	−	19.5675i	0.543157	−	0.961693i
$415$	−0.685034	−	6.90911i	−0.0336270	−	0.339155i
$416$	−5.10385	+	23.4333i	−0.250237	+	1.14891i
$417$	−38.3406	−	38.3406i	−1.87755	−	1.87755i
$418$	6.69324	−	1.86155i	0.327377	−	0.0910516i
$419$	4.05212	+	4.05212i	0.197959	+	0.197959i	0.799125	−	0.601165i	$-0.205297\pi$
$419$	4.05212	+	4.05212i	0.197959	+	0.197959i	−0.601165	+	0.799125i	$0.705297\pi$
$420$	−7.20277	+	49.6608i	−0.351459	+	2.42320i
$421$		−	27.0692i		−	1.31927i	−0.751585	−	0.659636i	$-0.770710\pi$
$421$		−	27.0692i		−	1.31927i	0.751585	−	0.659636i	$-0.229290\pi$
$422$	0.991619	−	0.275793i	0.0482712	−	0.0134254i
$423$	−26.7459	−	26.7459i	−1.30043	−	1.30043i
$424$	−15.7331	+	16.6534i	−0.764069	+	0.808761i
$425$	17.4085	+	11.0428i	0.844438	+	0.535653i
$426$	7.75190	+	27.8721i	0.375581	+	1.35041i
$427$	−30.0353	−	30.0353i	−1.45351	−	1.45351i
$428$	2.49315	+	4.13537i	0.120511	+	0.199891i
$429$	76.1280			3.67549
$430$	−7.63612	+	17.3174i	−0.368247	+	0.835119i
$431$	−28.3313	−	28.3313i	−1.36467	−	1.36467i	−0.867856	−	0.496815i	$-0.834503\pi$
$431$	−28.3313	−	28.3313i	−1.36467	−	1.36467i	−0.496815	−	0.867856i	$-0.665497\pi$
$432$	−20.2748	−	10.7032i	−0.975470	−	0.514956i
$433$	−22.5355	+	22.5355i	−1.08299	+	1.08299i	−0.0867573	+	0.996229i	$0.527650\pi$
$433$	−22.5355	+	22.5355i	−1.08299	+	1.08299i	−0.996229	+	0.0867573i	$0.972350\pi$
$434$	−29.7367	+	8.27050i	−1.42741	+	0.396997i
$435$	0.631991	+	6.37413i	0.0303016	+	0.305616i
$436$	−1.27488	−	0.315852i	−0.0610555	−	0.0151266i
$437$			2.45131i			0.117262i
$438$	−38.1939	−	21.5717i	−1.82498	−	1.03073i
$439$	−3.55648	−	3.55648i	−0.169742	−	0.169742i	0.617124	−	0.786866i	$-0.288298\pi$
$439$	−3.55648	−	3.55648i	−0.169742	−	0.169742i	−0.786866	+	0.617124i	$0.788298\pi$
$440$	−39.7691	+	5.08745i	−1.89592	+	0.242535i
$441$	−43.6637			−2.07923
$442$	−11.6705	+	21.7926i	−0.555111	+	1.03657i
$443$	16.0726	+	16.0726i	0.763632	+	0.763632i	0.976977	−	0.213345i	$-0.0684359\pi$
$443$	16.0726	+	16.0726i	0.763632	+	0.763632i	−0.213345	+	0.976977i	$0.568436\pi$
$444$	−8.25495	−	13.6925i	−0.391763	−	0.649815i
$445$	−11.1385	−	9.12902i	−0.528017	−	0.432757i
$446$	10.8703	+	39.0844i	0.514725	+	1.85070i
$447$			20.2407i			0.957354i
$448$	31.6393	−	1.79951i	1.49482	−	0.0850188i
$449$	−5.69502	−	5.69502i	−0.268765	−	0.268765i	0.559838	−	0.828602i	$-0.310863\pi$
$449$	−5.69502	−	5.69502i	−0.268765	−	0.268765i	−0.828602	+	0.559838i	$0.810863\pi$
$450$	11.0549	−	33.7572i	0.521135	−	1.59133i
$451$			3.76858i			0.177455i
$452$	0.680091	+	1.12806i	0.0319888	+	0.0530597i
$453$			45.7419i			2.14914i
$454$	−2.96372	+	5.24745i	−0.139094	+	0.246275i
$455$	−3.70521	−	37.3699i	−0.173703	−	1.75193i
$456$	6.20599	−	0.176342i	0.290622	−	0.00825799i
$457$	16.0390	+	16.0390i	0.750275	+	0.750275i	0.974530	−	0.224255i	$-0.0719950\pi$
$457$	16.0390	+	16.0390i	0.750275	+	0.750275i	−0.224255	+	0.974530i	$0.571995\pi$
$458$	−17.5823	+	31.1306i	−0.821569	+	1.45464i
$459$	−17.0815	−	16.3308i	−0.797298	−	0.762257i
$460$	2.03057	−	14.0002i	0.0946759	−	0.652761i
$461$	25.0074			1.16471			0.582355	−	0.812935i	$-0.302131\pi$
$461$	25.0074			1.16471			0.582355	+	0.812935i	$0.302131\pi$
$462$	−26.9547	−	96.9161i	−1.25405	−	4.50894i
$463$	17.8690	−	17.8690i	0.830442	−	0.830442i	−0.157136	−	0.987577i	$-0.550226\pi$
$463$	17.8690	−	17.8690i	0.830442	−	0.830442i	0.987577	+	0.157136i	$0.0502259\pi$
$464$	3.86490	−	1.19418i	0.179424	−	0.0554385i
$465$	34.7265	−	3.44311i	1.61040	−	0.159670i
$466$	3.43393	−	6.07998i	0.159074	−	0.281650i
$467$	−2.52384	−	2.52384i	−0.116789	−	0.116789i	0.646297	−	0.763086i	$-0.276317\pi$
$467$	−2.52384	−	2.52384i	−0.116789	−	0.116789i	−0.763086	+	0.646297i	$0.776317\pi$
$468$	41.3448	+	10.2432i	1.91116	+	0.473494i
$469$	−11.3971	+	11.3971i	−0.526268	+	0.526268i
$470$	−21.7865	−	9.60677i	−1.00494	−	0.443127i
$471$	−20.2671	+	20.2671i	−0.933860	+	0.933860i
$472$	0.836810	+	29.4497i	0.0385173	+	1.35553i
$473$		−	37.9407i		−	1.74451i
$474$	−1.53773	−	5.52892i	−0.0706301	−	0.253952i
$475$	0.760855	+	3.79919i	0.0349104	+	0.174319i
$476$	31.8756	+	7.14128i	1.46102	+	0.327320i
$477$	28.7719	+	28.7719i	1.31738	+	1.31738i
$478$	−3.02641	−	1.70930i	−0.138425	−	0.0781814i
$479$	23.6684	+	23.6684i	1.08144	+	1.08144i	0.996376	+	0.0850595i	$0.0271080\pi$
$479$	23.6684	+	23.6684i	1.08144	+	1.08144i	0.0850595	+	0.996376i	$0.472892\pi$
$480$	−35.5903	−	4.13366i	−1.62447	−	0.188675i
$481$	8.46059	+	8.46059i	0.385770	+	0.385770i
$482$	4.72664	+	16.9947i	0.215293	+	0.774088i
$483$	35.4943			1.61505
$484$	49.9908	−	30.1386i	2.27231	−	1.36994i
$485$	−6.23412	+	7.60640i	−0.283077	+	0.345389i
$486$	9.66395	−	17.1106i	0.438366	−	0.776152i
$487$	16.4195			0.744040			0.372020	−	0.928225i	$-0.378665\pi$
$487$	16.4195			0.744040			0.372020	+	0.928225i	$0.378665\pi$
$488$	20.8278	−	22.0461i	0.942831	−	0.997978i
$489$			45.7716i			2.06986i
$490$	−25.6253	+	9.94193i	−1.15764	+	0.449130i
$491$			0.375173i			0.0169313i	0.999964	+	0.00846565i	$0.00269473\pi$
$491$			0.375173i			0.0169313i	−0.999964	+	0.00846565i	$0.997305\pi$
$492$	−0.809895	+	3.26898i	−0.0365129	+	0.147377i
$493$	4.16863	−	0.0936632i	0.187746	−	0.00421838i
$494$	−4.47630	+	1.24497i	−0.201398	+	0.0560137i
$495$	7.02579	+	70.8606i	0.315786	+	3.18495i
$496$	−6.50594	−	21.0561i	−0.292126	−	0.945448i
$497$	−20.2291	+	20.2291i	−0.907397	+	0.907397i
$498$	3.33286	+	11.9834i	0.149349	+	0.536987i
$499$	24.1090	+	24.1090i	1.07927	+	1.07927i	0.996575	+	0.0826912i	$0.0263515\pi$
$499$	24.1090	+	24.1090i	1.07927	+	1.07927i	0.0826912	+	0.996575i	$0.473648\pi$
$500$	−1.19836	−	22.3285i	−0.0535923	−	0.998563i
$501$	−51.2419			−2.28932
$502$	−28.5753	−	16.1392i	−1.27538	−	0.720326i
$503$			24.5093i			1.09282i	0.837519	+	0.546408i	$0.184005\pi$
$503$			24.5093i			1.09282i	−0.837519	+	0.546408i	$0.815995\pi$
$504$	−1.59867	−	56.2616i	−0.0712102	−	2.50609i
$505$	−4.32115	−	3.54157i	−0.192289	−	0.157598i
$506$	7.59896	+	27.3222i	0.337815	+	1.21462i
$507$	−14.0893			−0.625729
$508$	13.7969	+	3.41819i	0.612137	+	0.151658i
$509$	12.9200			0.572671			0.286336	−	0.958129i	$-0.407563\pi$
$509$	12.9200			0.572671			0.286336	+	0.958129i	$0.407563\pi$
$510$	−34.1190	−	14.1381i	−1.51081	−	0.626046i
$511$		−	43.3768i		−	1.91888i
$512$	1.92601	+	22.5453i	0.0851186	+	0.996371i
$513$		−	4.44158i		−	0.196101i
$514$	−1.62260	−	5.83409i	−0.0715699	−	0.257331i
$515$	−0.782977	−	7.89694i	−0.0345021	−	0.347981i
$516$	8.15372	−	32.9109i	0.358948	−	1.44882i
$517$	47.7320			2.09925
$518$	7.77526	−	13.7666i	0.341625	−	0.604868i
$519$		−	29.5467i		−	1.29696i
$520$	26.5967	−	3.40238i	1.16634	−	0.149204i
$521$	20.2898	−	20.2898i	0.888914	−	0.888914i	−0.105505	−	0.994419i	$-0.533646\pi$
$521$	20.2898	−	20.2898i	0.888914	−	0.888914i	0.994419	+	0.105505i	$0.0336458\pi$
$522$	−1.92512	−	6.92179i	−0.0842601	−	0.302959i
$523$	11.4938	+	11.4938i	0.502591	+	0.502591i	0.912242	−	0.409651i	$-0.134350\pi$
$523$	11.4938	+	11.4938i	0.502591	+	0.502591i	−0.409651	+	0.912242i	$0.634350\pi$
$524$	3.46446	−	13.9836i	0.151346	−	0.610878i
$525$	55.0111	−	11.0169i	2.40088	−	0.480819i
$526$	−2.87844	−	10.3495i	−0.125506	−	0.451259i
$527$	−0.510280	−	22.7109i	−0.0222282	−	0.989301i
$528$	68.6248	−	21.2038i	2.98651	−	0.922776i
$529$	12.9936			0.564940
$530$	23.4368	+	10.3345i	1.01803	+	0.448901i
$531$	52.3257			2.27074
$532$	3.16986	+	5.25783i	0.137431	+	0.227956i
$533$		−	2.52035i		−	0.109168i
$534$	22.4647	+	12.6879i	0.972143	+	0.549060i
$535$	3.42220	−	4.17551i	0.147955	−	0.180523i
$536$	−8.36552	−	7.90324i	−0.361335	−	0.341368i
$537$			16.3099i			0.703825i
$538$	−10.1892	−	36.6352i	−0.439285	−	1.57946i
$539$	38.9621	−	38.9621i	1.67822	−	1.67822i
$540$	−3.67923	+	25.3672i	−0.158329	+	1.09163i
$541$	9.83879	−	9.83879i	0.423003	−	0.423003i	−0.463234	−	0.886236i	$-0.653311\pi$
$541$	9.83879	−	9.83879i	0.423003	−	0.423003i	0.886236	+	0.463234i	$0.153311\pi$
$542$	9.01621	−	15.9637i	0.387279	−	0.685701i
$543$	0.244088	−	0.244088i	0.0104748	−	0.0104748i
$544$	−4.45046	+	22.8953i	−0.190812	+	0.981627i
$545$	0.144885	+	1.46128i	0.00620621	+	0.0625945i
$546$	18.0267	+	64.8154i	0.771473	+	2.77384i
$547$	13.3818			0.572166			0.286083	−	0.958205i	$-0.407647\pi$
$547$	13.3818			0.572166			0.286083	+	0.958205i	$0.407647\pi$
$548$	−6.19816	−	1.53560i	−0.264772	−	0.0655977i
$549$	−38.0887	−	38.0887i	−1.62559	−	1.62559i
$550$	20.2577	+	39.9869i	0.863793	+	1.70505i
$551$	0.554146	+	0.554146i	0.0236074	+	0.0236074i
$552$	0.719839	+	25.3332i	0.0306384	+	1.07825i
$553$	4.01279	−	4.01279i	0.170641	−	0.170641i
$554$	0.290994	−	0.515222i	0.0123631	−	0.0218897i
$555$	−11.3311	+	13.8254i	−0.480979	+	0.586854i
$556$	37.1610	+	9.20668i	1.57598	+	0.390450i
$557$	−11.3921	−	11.3921i	−0.482697	−	0.482697i	0.423295	−	0.905992i	$-0.360873\pi$
$557$	−11.3921	−	11.3921i	−0.482697	−	0.482697i	−0.905992	+	0.423295i	$0.860873\pi$
$558$	−37.7102	+	10.4881i	−1.59640	+	0.443997i
$559$			25.3739i			1.07320i
$560$	−13.7486	−	32.6547i	−0.580984	−	1.37991i
$561$	74.0178	−	1.66307i	3.12503	−	0.0702151i
$562$	0.810505	−	1.43505i	0.0341891	−	0.0605339i
$563$	−3.73416	+	3.73416i	−0.157376	+	0.157376i	−0.781403	−	0.624027i	$-0.785496\pi$
$563$	−3.73416	+	3.73416i	−0.157376	+	0.157376i	0.624027	+	0.781403i	$0.285496\pi$
$564$	41.4042	+	10.2580i	1.74343	+	0.431938i
$565$	0.933523	−	1.13901i	0.0392736	−	0.0479187i
$566$	10.5708	+	5.97030i	0.444323	+	0.250951i
$567$	−4.61424			−0.193780
$568$	−14.8482	−	14.0277i	−0.623019	−	0.588591i
$569$	−11.8528			−0.496895			−0.248447	−	0.968645i	$-0.579920\pi$
$569$	−11.8528			−0.496895			−0.248447	+	0.968645i	$0.579920\pi$
$570$	−2.51070	−	6.47133i	−0.105162	−	0.271054i
$571$	14.1611	−	14.1611i	0.592623	−	0.592623i	−0.345716	−	0.938339i	$-0.612364\pi$
$571$	14.1611	−	14.1611i	0.592623	−	0.592623i	0.938339	+	0.345716i	$0.112364\pi$
$572$	−46.0332	+	27.7526i	−1.92474	+	1.16040i
$573$	−40.7021			−1.70036
$574$	−3.20857	+	0.892381i	−0.133923	+	0.0372473i
$575$	−15.5085	+	3.10585i	−0.646749	+	0.129523i
$576$	40.1229	−	2.28202i	1.67179	−	0.0950841i
$577$	20.6428	−	20.6428i	0.859369	−	0.859369i	−0.131894	−	0.991264i	$-0.542106\pi$
$577$	20.6428	−	20.6428i	0.859369	−	0.859369i	0.991264	+	0.131894i	$0.0421060\pi$
$578$	−10.8710	+	21.4435i	−0.452173	+	0.891930i
$579$		−	57.3024i		−	2.38141i
$580$	−2.70585	−	3.62392i	−0.112354	−	0.150475i
$581$	−8.69731	+	8.69731i	−0.360825	+	0.360825i
$582$	8.66445	−	15.3409i	0.359153	−	0.635902i
$583$	−51.3476			−2.12660
$584$	30.9591	−	0.879700i	1.28110	−	0.0364022i
$585$	−4.69870	−	47.3901i	−0.194267	−	1.95934i
$586$	0.0299941	−	0.00834208i	0.00123904	−	0.000344608i
$587$	−9.85829	−	9.85829i	−0.406895	−	0.406895i	0.473759	−	0.880654i	$-0.342897\pi$
$587$	−9.85829	−	9.85829i	−0.406895	−	0.406895i	−0.880654	+	0.473759i	$0.842897\pi$
$588$	42.1702	−	25.4237i	1.73907	−	1.04846i
$589$	3.01901	−	3.01901i	0.124396	−	0.124396i
$590$	30.7088	−	11.9142i	1.26426	−	0.490499i
$591$			65.3006i			2.68611i
$592$	9.98323	+	5.27021i	0.410308	+	0.216604i
$593$	−32.7390	+	32.7390i	−1.34443	+	1.34443i	−0.452839	+	0.891592i	$0.649589\pi$
$593$	−32.7390	+	32.7390i	−1.34443	+	1.34443i	−0.891592	+	0.452839i	$0.850411\pi$
$594$	−13.7687	−	49.5055i	−0.564936	−	2.03124i
$595$	−4.41888	−	36.2531i	−0.181156	−	1.48623i
$596$	−7.37880	−	12.2392i	−0.302247	−	0.501337i
$597$	−53.8696	+	53.8696i	−2.20474	+	2.20474i
$598$	−5.08202	−	18.2725i	−0.207819	−	0.747217i
$599$	21.7862			0.890159			0.445079	−	0.895491i	$-0.353175\pi$
$599$	21.7862			0.890159			0.445079	+	0.895491i	$0.353175\pi$
$600$	8.97872	+	39.0394i	0.366555	+	1.59378i
$601$	−16.8759	+	16.8759i	−0.688382	+	0.688382i	−0.961874	−	0.273492i	$-0.911821\pi$
$601$	−16.8759	+	16.8759i	−0.688382	+	0.688382i	0.273492	+	0.961874i	$0.411821\pi$
$602$	32.3027	−	8.98416i	1.31656	−	0.366167i
$603$	−14.4530	+	14.4530i	−0.588572	+	0.588572i
$604$	−16.6753	−	27.6592i	−0.678508	−	1.12544i
$605$	−50.4760	−	41.3696i	−2.05214	−	1.68191i
$606$	8.71509	+	4.92222i	0.354026	+	0.199952i
$607$		−	35.3030i		−	1.43290i	−0.697636	−	0.716452i	$-0.745765\pi$
$607$		−	35.3030i		−	1.43290i	0.697636	−	0.716452i	$-0.254235\pi$
$608$	−3.68836	+	2.36904i	−0.149583	+	0.0960772i
$609$	8.02386	−	8.02386i	0.325143	−	0.325143i
$610$	−31.0260	−	13.6810i	−1.25621	−	0.553926i
$611$	−31.9221			−1.29143
$612$	40.4226	+	9.05610i	1.63398	+	0.366071i
$613$	3.32327	−	3.32327i	0.134226	−	0.134226i	−0.636802	−	0.771027i	$-0.719743\pi$
$613$	3.32327	−	3.32327i	0.134226	−	0.134226i	0.771027	+	0.636802i	$0.219743\pi$
$614$	2.97304	−	0.826875i	0.119982	−	0.0333700i
$615$	3.74696	−	0.371509i	0.151092	−	0.0149807i
$616$	51.6300	+	48.7769i	2.08023	+	1.96528i
$617$	18.8391			0.758434			0.379217	−	0.925308i	$-0.376193\pi$
$617$	18.8391			0.758434			0.379217	+	0.925308i	$0.376193\pi$
$618$	3.80938	+	13.6967i	0.153236	+	0.550961i
$619$	−20.5571	−	20.5571i	−0.826261	−	0.826261i	0.160737	−	0.986997i	$-0.448613\pi$
$619$	−20.5571	−	20.5571i	−0.826261	−	0.826261i	−0.986997	+	0.160737i	$0.948613\pi$
$620$	−19.7432	+	14.7416i	−0.792908	+	0.592036i
$621$	18.1308			0.727563
$622$	−12.1902	+	3.39040i	−0.488783	+	0.135943i
$623$			25.5132i			1.02216i
$624$	−45.8948	+	14.1806i	−1.83726	+	0.567680i
$625$	−23.0720	+	9.62726i	−0.922879	+	0.385090i
$626$	−34.1663	−	19.2969i	−1.36556	−	0.771260i
$627$	9.83936	+	9.83936i	0.392946	+	0.392946i
$628$	4.86672	−	19.6436i	0.194203	−	0.783864i
$629$	8.41090	+	8.04125i	0.335365	+	0.320626i
$630$	−58.6671	+	22.7612i	−2.33735	+	0.906828i
$631$	−13.9283			−0.554476			−0.277238	−	0.960801i	$-0.589419\pi$
$631$	−13.9283			−0.554476			−0.277238	+	0.960801i	$0.589419\pi$
$632$	2.94541	+	2.78265i	0.117162	+	0.110688i
$633$	1.45772	+	1.45772i	0.0579393	+	0.0579393i
$634$	−29.4480	−	16.6320i	−1.16953	−	0.660542i
$635$	−1.56797	−	15.8142i	−0.0622229	−	0.627567i
$636$	−44.5405	−	11.0350i	−1.76615	−	0.437565i
$637$	−26.0570	+	26.0570i	−1.03242	+	1.03242i
$638$	7.89429	+	4.45864i	0.312538	+	0.176519i
$639$	−25.6532	+	25.6532i	−1.01482	+	1.01482i
$640$	23.0277	−	10.4750i	0.910250	−	0.414060i
$641$	−10.2407	−	10.2407i	−0.404483	−	0.404483i	0.475326	−	0.879810i	$-0.342330\pi$
$641$	−10.2407	−	10.2407i	−0.404483	−	0.404483i	−0.879810	+	0.475326i	$0.842330\pi$
$642$	−4.75632	+	8.42135i	−0.187717	+	0.332364i
$643$		−	7.15313i		−	0.282092i	−0.990003	−	0.141046i	$-0.954953\pi$
$643$		−	7.15313i		−	0.282092i	0.990003	−	0.141046i	$-0.0450466\pi$
$644$	−21.4627	+	12.9395i	−0.845749	+	0.509888i
$645$	−37.7230	+	3.74021i	−1.48534	+	0.147271i
$646$	−4.32503	+	1.30825i	−0.170166	+	0.0514723i
$647$	−26.1057	−	26.1057i	−1.02632	−	1.02632i	−0.999644	−	0.0266760i	$-0.991508\pi$
$647$	−26.1057	−	26.1057i	−1.02632	−	1.02632i	−0.0266760	−	0.999644i	$-0.508492\pi$
$648$	−0.0935788	−	3.29330i	−0.00367612	−	0.129373i
$649$	−46.6914	+	46.6914i	−1.83280	+	1.83280i
$650$	−13.5479	−	26.7424i	−0.531394	−	1.04892i
$651$	−43.7143	−	43.7143i	−1.71330	−	1.71330i
$652$	−16.6861	−	27.6772i	−0.653479	−	1.08392i
$653$		−	5.26762i		−	0.206138i	−0.994674	−	0.103069i	$-0.967134\pi$
$653$		−	5.26762i		−	0.206138i	0.994674	−	0.103069i	$-0.0328662\pi$
$654$	−0.704903	−	2.53449i	−0.0275639	−	0.0991064i
$655$	−16.0283	+	1.58919i	−0.626276	+	0.0620949i
$656$	−0.701987	−	2.27194i	−0.0274080	−	0.0887044i
$657$		−	55.0076i		−	2.14605i
$658$	11.3027	+	40.6390i	0.440625	+	1.58427i
$659$		−	49.4899i		−	1.92785i	−0.266168	−	0.963927i	$-0.585757\pi$
$659$		−	49.4899i		−	1.92785i	0.266168	−	0.963927i	$-0.414243\pi$
$660$	−48.0449	−	64.3459i	−1.87014	−	2.50466i
$661$	34.1170			1.32700			0.663499	−	0.748177i	$-0.269071\pi$
$661$	34.1170			1.32700			0.663499	+	0.748177i	$0.269071\pi$
$662$	14.5135	−	25.6970i	0.564084	−	0.998744i
$663$	−49.5016	+	1.11223i	−1.92248	+	0.0431954i
$664$	−6.38388	−	6.03111i	−0.247742	−	0.234052i
$665$	4.35108	−	5.30886i	0.168728	−	0.205869i
$666$	9.86007	−	17.4578i	0.382070	−	0.676478i
$667$	−2.26205	+	2.26205i	−0.0875870	+	0.0875870i
$668$	30.9850	−	18.6803i	1.19885	−	0.722764i
$669$	−57.4558	+	57.4558i	−2.22137	+	2.22137i
$670$	−5.19132	+	11.7730i	−0.200558	+	0.454831i
$671$	67.9749			2.62414
$672$	34.3029	+	53.4063i	1.32326	+	2.06019i
$673$	−27.6753			−1.06681			−0.533403	−	0.845861i	$-0.679087\pi$
$673$	−27.6753			−1.06681			−0.533403	+	0.845861i	$0.679087\pi$
$674$	−11.7355	−	6.62813i	−0.452034	−	0.255306i
$675$	28.1001	−	5.62755i	1.08157	−	0.216604i
$676$	8.51955	−	5.13630i	0.327675	−	0.197550i
$677$			4.53230i			0.174191i	0.996200	+	0.0870953i	$0.0277585\pi$
$677$			4.53230i			0.174191i	−0.996200	+	0.0870953i	$0.972242\pi$
$678$	−1.29745	+	2.29722i	−0.0498283	+	0.0882240i
$679$	17.4227			0.668621
$680$	25.7852	−	3.88909i	0.988816	−	0.149140i
$681$	−12.0708			−0.462553
$682$	24.2908	−	43.0084i	0.930144	−	1.64688i
$683$			7.32301i			0.280207i	0.990137	+	0.140104i	$0.0447436\pi$
$683$			7.32301i			0.280207i	−0.990137	+	0.140104i	$0.955256\pi$
$684$	4.01980	+	6.66763i	0.153701	+	0.254943i
$685$	0.704400	+	7.10443i	0.0269137	+	0.271446i
$686$	8.25317	+	4.66133i	0.315107	+	0.177970i
$687$	−71.6101			−2.73210
$688$	7.06734	+	22.8731i	0.269440	+	0.872027i
$689$	34.3402			1.30826
$690$	26.4163	−	10.2488i	1.00565	−	0.390165i
$691$	−25.0249	+	25.0249i	−0.951994	+	0.951994i	−0.998899	−	0.0469056i	$-0.985064\pi$
$691$	−25.0249	+	25.0249i	−0.951994	+	0.951994i	0.0469056	+	0.998899i	$0.485064\pi$
$692$	10.7713	+	17.8663i	0.409464	+	0.679176i
$693$	89.2005	−	89.2005i	3.38845	−	3.38845i
$694$	−5.31193	+	9.40508i	−0.201638	+	0.357012i
$695$	−4.22322	−	42.5945i	−0.160196	−	1.61570i
$696$	5.88956	+	5.56411i	0.223243	+	0.210907i
$697$	−0.0550589	−	2.45049i	−0.00208550	−	0.0928187i
$698$	21.5153	−	38.0941i	0.814365	−	1.44188i
$699$	13.9859			0.528994
$700$	−29.2479	+	26.7162i	−1.10547	+	1.00978i
$701$			23.5447i			0.889273i	0.895711	+	0.444636i	$0.146667\pi$
$701$			23.5447i			0.889273i	−0.895711	+	0.444636i	$0.853333\pi$
$702$	9.20821	+	33.1083i	0.347541	+	1.24959i
$703$			2.18702i			0.0824851i
$704$	−33.7663	+	37.8389i	−1.27261	+	1.42611i
$705$	−4.70545	−	47.4582i	−0.177217	−	1.78738i
$706$	−9.34746	−	33.6089i	−0.351796	−	1.26489i
$707$			9.89772i			0.372242i
$708$	−50.5359	+	30.4672i	−1.89925	+	1.14503i
$709$	34.3112	+	34.3112i	1.28858	+	1.28858i	0.935647	+	0.352937i	$0.114817\pi$
$709$	34.3112	+	34.3112i	1.28858	+	1.28858i	0.352937	+	0.935647i	$0.385183\pi$
$710$	−9.21426	+	20.8963i	−0.345805	+	0.784226i
$711$	5.08876	−	5.08876i	0.190843	−	0.190843i
$712$	−18.2094	+	0.517418i	−0.682426	+	0.0193910i
$713$	12.3237	+	12.3237i	0.461528	+	0.461528i
$714$	18.9430	+	62.6250i	0.708924	+	2.34368i
$715$	46.4800	+	38.0945i	1.73825	+	1.42465i
$716$	−5.94582	−	9.86230i	−0.222206	−	0.368571i
$717$		−	6.96170i		−	0.259989i
$718$	−3.74811	+	6.63625i	−0.139878	+	0.247663i
$719$	13.6465	+	13.6465i	0.508929	+	0.508929i	0.914198	−	0.405269i	$-0.132822\pi$
$719$	13.6465	+	13.6465i	0.508929	+	0.508929i	−0.405269	+	0.914198i	$0.632822\pi$
$720$	−17.4351	−	41.4106i	−0.649766	−	1.54328i
$721$	−9.94080	+	9.94080i	−0.370215	+	0.370215i
$722$	22.6569	+	12.7964i	0.843201	+	0.476234i
$723$	−24.9830	+	24.9830i	−0.929126	+	0.929126i
$724$	−0.0586127	+	0.236579i	−0.00217832	+	0.00879238i
$725$	−2.80375	+	4.20797i	−0.104129	+	0.156280i
$726$	101.802	+	57.4973i	3.77824	+	2.13392i
$727$	19.5298	+	19.5298i	0.724319	+	0.724319i	0.969482	−	0.245163i	$-0.0788415\pi$
$727$	19.5298	+	19.5298i	0.724319	+	0.724319i	−0.245163	+	0.969482i	$0.578841\pi$
$728$	−34.5290	−	32.6210i	−1.27973	−	1.20901i
$729$	42.8542			1.58719
$730$	−12.5248	−	32.2828i	−0.463565	−	1.19484i
$731$	0.554312	+	24.6706i	0.0205020	+	0.912474i
$732$	58.9635	+	14.6083i	2.17935	+	0.539938i
$733$	−16.9836	−	16.9836i	−0.627302	−	0.627302i	0.320086	−	0.947388i	$-0.396288\pi$
$733$	−16.9836	−	16.9836i	−0.627302	−	0.627302i	−0.947388	+	0.320086i	$0.896288\pi$
$734$	7.88753	+	4.45482i	0.291134	+	0.164430i
$735$	−42.5795	−	34.8977i	−1.57057	−	1.28722i
$736$	−9.67054	−	15.0561i	−0.356461	−	0.554974i
$737$		−	25.7935i		−	0.950115i
$738$	−4.06890	+	1.13166i	−0.149778	+	0.0416570i
$739$	10.6397			0.391386			0.195693	−	0.980665i	$-0.437304\pi$
$739$	10.6397			0.391386			0.195693	+	0.980665i	$0.437304\pi$
$740$	1.81164	−	12.4907i	0.0665973	−	0.459168i
$741$	−6.58035	−	6.58035i	−0.241735	−	0.241735i
$742$	−12.1589	−	43.7174i	−0.446366	−	1.60492i
$743$	−10.2782			−0.377071			−0.188535	−	0.982066i	$-0.560374\pi$
$743$	−10.2782			−0.377071			−0.188535	+	0.982066i	$0.560374\pi$
$744$	30.3134	−	32.0865i	1.11134	−	1.17635i
$745$	−10.1285	+	12.3580i	−0.371078	+	0.452761i
$746$	−1.00206	+	0.278697i	−0.0366880	+	0.0102038i
$747$	−11.0294	+	11.0294i	−0.403543	+	0.403543i
$748$	−44.1509	+	27.9890i	−1.61432	+	1.02338i
$749$	−9.56413			−0.349466
$750$	37.7605	−	24.0835i	1.37882	−	0.879404i
$751$	−21.3098	+	21.3098i	−0.777607	+	0.777607i	−0.979423	−	0.201817i	$-0.935316\pi$
$751$	−21.3098	+	21.3098i	−0.777607	+	0.777607i	0.201817	+	0.979423i	$0.435316\pi$
$752$	−28.7759	+	8.89121i	−1.04935	+	0.324229i
$753$		−	65.7323i		−	2.39542i
$754$	−5.27954	−	2.98185i	−0.192269	−	0.108592i
$755$	−22.8892	+	27.9277i	−0.833024	+	1.01639i
$756$	38.8887	−	23.4453i	1.41437	−	0.852699i
$757$	19.3377	−	19.3377i	0.702840	−	0.702840i	−0.262179	−	0.965019i	$-0.584441\pi$
$757$	19.3377	−	19.3377i	0.702840	−	0.702840i	0.965019	+	0.262179i	$0.0844412\pi$
$758$	38.5344	−	10.7173i	1.39963	−	0.389272i
$759$	−40.1648	+	40.1648i	−1.45789	+	1.45789i
$760$	3.87731	+	2.99781i	0.140645	+	0.108742i
$761$	18.6969			0.677761			0.338881	−	0.940829i	$-0.389952\pi$
$761$	18.6969			0.677761			0.338881	+	0.940829i	$0.389952\pi$
$762$	7.62855	+	27.4286i	0.276353	+	0.993632i
$763$	1.83949	−	1.83949i	0.0665940	−	0.0665940i
$764$	24.6118	−	14.8381i	0.890424	−	0.536822i
$765$	−5.60373	−	45.9738i	−0.202603	−	1.66219i
$766$	4.37154	+	15.7179i	0.157950	+	0.567912i
$767$	31.2262	−	31.2262i	1.12751	−	1.12751i
$768$	−37.4218	+	25.5660i	−1.35034	+	0.922533i
$769$		−	32.5459i		−	1.17363i	−0.809719	−	0.586817i	$-0.800381\pi$
$769$		−	32.5459i		−	1.17363i	0.809719	−	0.586817i	$-0.199619\pi$
$770$	32.0396	−	72.6603i	1.15463	−	2.61850i
$771$	8.57637	−	8.57637i	0.308870	−	0.308870i
$772$	20.8897	+	34.6497i	0.751837	+	1.24707i
$773$	−18.1546	−	18.1546i	−0.652974	−	0.652974i	0.300734	−	0.953708i	$-0.402768\pi$
$773$	−18.1546	−	18.1546i	−0.652974	−	0.652974i	−0.953708	+	0.300734i	$0.902768\pi$
$774$	40.9642	−	11.3931i	1.47243	−	0.409517i
$775$	22.9252	+	15.2749i	0.823497	+	0.548692i
$776$	0.353340	+	12.4350i	0.0126842	+	0.446391i
$777$	31.6674			1.13606
$778$	−4.85560	+	8.59713i	−0.174082	+	0.308222i
$779$	0.325749	−	0.325749i	0.0116712	−	0.0116712i
$780$	32.1314	+	43.0332i	1.15049	+	1.54084i
$781$		−	45.7818i		−	1.63820i
$782$	−5.34033	−	17.6550i	−0.190970	−	0.631341i
$783$	4.09865	−	4.09865i	0.146474	−	0.146474i
$784$	−16.2313	+	30.7465i	−0.579688	+	1.09809i
$785$	−22.5158	+	2.23243i	−0.803622	+	0.0796787i
$786$	27.7998	−	7.73181i	0.991588	−	0.275785i
$787$	4.63427			0.165194			0.0825970	−	0.996583i	$-0.473679\pi$
$787$	4.63427			0.165194			0.0825970	+	0.996583i	$0.473679\pi$
$788$	−23.8055	−	39.4860i	−0.848035	−	1.40663i
$789$	15.2142	−	15.2142i	0.541639	−	0.541639i
$790$	1.82781	−	4.14516i	0.0650307	−	0.147478i
$791$	−2.60895			−0.0927634
$792$	65.4737	+	61.8557i	2.32651	+	2.19795i
$793$	−45.4601			−1.61434
$794$	−45.7727	−	25.8521i	−1.62441	−	0.917456i
$795$	5.06188	+	51.0531i	0.179526	+	1.81067i
$796$	12.9357	−	52.2122i	0.458492	−	1.85061i
$797$	−8.82381	+	8.82381i	−0.312555	+	0.312555i	−0.845899	−	0.533343i	$-0.820935\pi$
$797$	−8.82381	+	8.82381i	−0.312555	+	0.312555i	0.533343	+	0.845899i	$0.320935\pi$
$798$	−6.04732	+	10.7072i	−0.214073	+	0.379029i
$799$	−31.0373	+	0.697364i	−1.09802	+	0.0246710i
$800$	−19.6612	−	20.3332i	−0.695127	−	0.718887i
$801$			32.3541i			1.14318i
$802$	−18.9789	+	5.27849i	−0.670169	+	0.186390i
$803$	49.0845	+	49.0845i	1.73215	+	1.73215i
$804$	5.54321	−	22.3741i	0.195494	−	0.789073i
$805$	21.6710	+	17.7613i	0.763804	+	0.626005i
$806$	−16.2452	+	28.7631i	−0.572213	+	1.01314i
$807$	53.8554	−	53.8554i	1.89580	−	1.89580i
$808$	−7.06426	+	0.200730i	−0.248520	+	0.00706166i
$809$	37.5030	+	37.5030i	1.31853	+	1.31853i	0.914936	+	0.403598i	$0.132241\pi$
$809$	37.5030	+	37.5030i	1.31853	+	1.31853i	0.403598	+	0.914936i	$0.367759\pi$
$810$	−3.43411	+	1.33234i	−0.120662	+	0.0468136i
$811$	−25.5651	−	25.5651i	−0.897711	−	0.897711i	0.0975225	−	0.995233i	$-0.468908\pi$
$811$	−25.5651	−	25.5651i	−0.897711	−	0.897711i	−0.995233	+	0.0975225i	$0.968908\pi$
$812$	−1.92676	+	7.77699i	−0.0676161	+	0.272919i
$813$	36.7216			1.28788
$814$	6.77966	+	24.3764i	0.237627	+	0.854392i
$815$	−22.9041	+	27.9458i	−0.802296	+	0.978900i
$816$	−44.3129	+	14.7902i	−1.55126	+	0.517760i
$817$	−3.27952	+	3.27952i	−0.114736	+	0.114736i
$818$	2.25173	−	3.98682i	0.0787299	−	0.139396i
$819$	−59.6554	+	59.6554i	−2.08453	+	2.08453i
$820$	−2.13028	+	1.59061i	−0.0743927	+	0.0555464i
$821$	1.79772	−	1.79772i	0.0627408	−	0.0627408i	−0.675040	−	0.737781i	$-0.735874\pi$
$821$	1.79772	−	1.79772i	0.0627408	−	0.0627408i	0.737781	+	0.675040i	$0.235874\pi$
$822$	−3.42708	−	12.3221i	−0.119533	−	0.429783i
$823$			15.8441i			0.552291i	0.961116	+	0.276146i	$0.0890572\pi$
$823$			15.8441i			0.552291i	−0.961116	+	0.276146i	$0.910943\pi$
$824$	−7.29661	−	6.89340i	−0.254189	−	0.240143i
$825$	−49.7831	+	74.7163i	−1.73323	+	2.60129i
$826$	−50.8093	−	28.6968i	−1.76788	−	0.998488i
$827$		−	40.3102i		−	1.40172i	−0.713297	−	0.700862i	$-0.752799\pi$
$827$		−	40.3102i		−	1.40172i	0.713297	−	0.700862i	$-0.247201\pi$
$828$	−27.2176	+	16.4090i	−0.945877	+	0.570254i
$829$	37.6890			1.30899			0.654497	−	0.756065i	$-0.272880\pi$
$829$	37.6890			1.30899			0.654497	+	0.756065i	$0.272880\pi$
$830$	−3.96159	+	8.98420i	−0.137509	+	0.311846i
$831$	1.18517			0.0411131
$832$	22.5822	−	25.3058i	0.782896	−	0.877322i
$833$	−24.7655	+	25.9040i	−0.858075	+	0.897521i
$834$	20.5470	+	73.8771i	0.711484	+	2.55815i
$835$	−31.2858	−	25.6415i	−1.08269	−	0.887359i
$836$	−9.53663	−	2.36271i	−0.329831	−	0.0817162i
$837$	−22.3296	−	22.3296i	−0.771824	−	0.771824i
$838$	−2.17156	−	7.80788i	−0.0750154	−	0.269719i
$839$	5.04653	−	5.04653i	0.174226	−	0.174226i	−0.614608	−	0.788833i	$-0.710686\pi$
$839$	5.04653	−	5.04653i	0.174226	−	0.174226i	0.788833	+	0.614608i	$0.210686\pi$
$840$	43.4074	−	56.1423i	1.49770	−	1.93709i
$841$		−	27.9773i		−	0.964734i
$842$	−18.8260	+	33.3326i	−0.648788	+	1.14872i
$843$	3.30106			0.113695
$844$	−1.41287	−	0.350041i	−0.0486331	−	0.0120489i
$845$	−8.60225	−	7.05031i	−0.295926	−	0.242538i
$846$	14.3333	+	51.5358i	0.492791	+	1.77184i
$847$			115.617i			3.97264i
$848$	30.9556	−	9.56470i	1.06302	−	0.328453i
$849$			24.3161i			0.834527i
$850$	−13.7566	−	25.7052i	−0.471848	−	0.881680i
$851$	−8.92753			−0.306032
$852$	9.83884	−	39.7125i	0.337073	−	1.36053i
$853$	−9.87416			−0.338085			−0.169042	−	0.985609i	$-0.554067\pi$
$853$	−9.87416			−0.338085			−0.169042	+	0.985609i	$0.554067\pi$
$854$	16.0961	+	57.8739i	0.550798	+	1.98040i
$855$	5.51776	−	6.73235i	0.188703	−	0.230241i
$856$	−0.193965	−	6.82616i	−0.00662957	−	0.233313i
$857$			29.5861i			1.01064i	0.862931	+	0.505321i	$0.168626\pi$
$857$			29.5861i			1.01064i	−0.862931	+	0.505321i	$0.831374\pi$
$858$	−93.7429	−	52.9453i	−3.20033	−	1.80752i
$859$	24.3041			0.829246			0.414623	−	0.909993i	$-0.363913\pi$
$859$	24.3041			0.829246			0.414623	+	0.909993i	$0.363913\pi$
$860$	21.4469	−	16.0136i	0.731333	−	0.546061i
$861$	−4.71674	−	4.71674i	−0.160746	−	0.160746i
$862$	15.1830	+	54.5906i	0.517134	+	1.85936i
$863$	−18.7016	+	18.7016i	−0.636611	+	0.636611i	−0.949718	−	0.313107i	$-0.898630\pi$
$863$	−18.7016	+	18.7016i	−0.636611	+	0.636611i	0.313107	+	0.949718i	$0.398630\pi$
$864$	17.5222	+	27.2804i	0.596118	+	0.928097i
$865$	14.7852	−	18.0397i	0.502711	−	0.613370i
$866$	43.4228	−	12.0769i	1.47557	−	0.410391i
$867$	−48.1051	+	2.16280i	−1.63374	+	0.0734525i
$868$	42.3693	+	10.4971i	1.43811	+	0.356293i
$869$			9.08163i			0.308073i
$870$	3.65484	−	8.28854i	0.123911	−	0.281008i
$871$			17.2501i			0.584499i
$872$	1.35020	+	1.27558i	0.0457234	+	0.0431967i
$873$	22.0943			0.747779
$874$	1.70484	−	3.01851i	0.0576669	−	0.102103i
$875$	39.0999	+	20.8012i	1.32182	+	0.703208i
$876$	32.0288	+	53.1261i	1.08215	+	1.79496i
$877$	−7.75049			−0.261716			−0.130858	−	0.991401i	$-0.541773\pi$
$877$	−7.75049			−0.261716			−0.130858	+	0.991401i	$0.541773\pi$
$878$	1.90595	+	6.85286i	0.0643226	+	0.231273i
$879$	0.0440926	+	0.0440926i	0.00148721	+	0.00148721i
$880$	52.5093	+	21.3939i	1.77009	+	0.721189i
$881$	0.400246	+	0.400246i	0.0134846	+	0.0134846i	0.713817	−	0.700332i	$-0.246965\pi$
$881$	0.400246	+	0.400246i	0.0134846	+	0.0134846i	−0.700332	+	0.713817i	$0.746965\pi$
$882$	53.7669	+	30.3672i	1.81043	+	1.02252i
$883$	18.8749	+	18.8749i	0.635192	+	0.635192i	0.949366	−	0.314174i	$-0.101727\pi$
$883$	18.8749	+	18.8749i	0.635192	+	0.635192i	−0.314174	+	0.949366i	$0.601727\pi$
$884$	29.5272	−	18.7184i	0.993107	−	0.629569i
$885$	51.0264	+	41.8206i	1.71523	+	1.40579i
$886$	−8.61342	−	30.9697i	−0.289373	−	1.04045i
$887$			39.8172i			1.33693i	0.743743	+	0.668466i	$0.233049\pi$
$887$			39.8172i			1.33693i	−0.743743	+	0.668466i	$0.766951\pi$
$888$	0.642228	+	22.6018i	0.0215518	+	0.758468i
$889$	−19.9072	+	19.9072i	−0.667665	+	0.667665i
$890$	7.36680	+	18.9879i	0.246936	+	0.636477i
$891$	5.22140	−	5.22140i	0.174924	−	0.174924i
$892$	13.7968	−	55.6880i	0.461951	−	1.86457i
$893$	−4.12586	−	4.12586i	−0.138067	−	0.138067i
$894$	14.0770	−	24.9241i	0.470805	−	0.833588i
$895$	−8.16148	+	9.95802i	−0.272808	+	0.332860i
$896$	−40.2117	−	19.7886i	−1.34338	−	0.661090i
$897$	26.8613	−	26.8613i	0.896874	−	0.896874i
$898$	3.05200	+	10.9735i	0.101847	+	0.366191i
$899$	5.57183			0.185831
$900$	−37.0903	+	33.8797i	−1.23634	+	1.12932i
$901$	33.3883	−	0.750188i	1.11233	−	0.0249924i
$902$	2.62096	−	4.64057i	0.0872686	−	0.154514i
$903$	47.4864	+	47.4864i	1.58025	+	1.58025i
$904$	−0.0529105	−	1.86207i	−0.00175978	−	0.0619316i
$905$	0.271170	−	0.0268864i	0.00901400	−	0.000893733i
$906$	31.8125	−	56.3259i	1.05690	−	1.87130i
$907$		−	19.4920i		−	0.647223i	−0.946190	−	0.323611i	$-0.895103\pi$
$907$		−	19.4920i		−	0.647223i	0.946190	−	0.323611i	$-0.104897\pi$
$908$	7.29897	−	4.40043i	0.242225	−	0.146033i
$909$			12.5516i			0.416312i
$910$	−21.4274	+	48.5937i	−0.710312	+	1.61086i
$911$	−1.01477	−	1.01477i	−0.0336208	−	0.0336208i	0.690097	−	0.723717i	$-0.257568\pi$
$911$	−1.01477	−	1.01477i	−0.0336208	−	0.0336208i	−0.723717	+	0.690097i	$0.757568\pi$
$912$	−7.76461	−	4.09898i	−0.257112	−	0.135731i
$913$		−	19.6835i		−	0.651428i
$914$	−8.59544	−	30.9051i	−0.284312	−	1.02225i
$915$	−6.70101	−	67.5849i	−0.221528	−	2.23429i
$916$	43.3013	−	26.1056i	1.43071	−	0.862554i
$917$	20.1766	+	20.1766i	0.666291	+	0.666291i
$918$	9.67625	+	31.9894i	0.319364	+	1.05581i
$919$	−38.2443			−1.26156			−0.630782	−	0.775960i	$-0.717266\pi$
$919$	−38.2443			−1.26156			−0.630782	+	0.775960i	$0.717266\pi$
$920$	−12.2372	+	15.8274i	−0.403449	+	0.521813i
$921$	4.37050	+	4.37050i	0.144013	+	0.144013i
$922$	−30.7937	−	17.3921i	−1.01414	−	0.572778i
$923$			30.6179i			1.00780i
$924$	−34.2114	+	138.087i	−1.12547	+	4.54274i
$925$	−13.8364	+	2.77099i	−0.454939	+	0.0911095i
$926$	−34.4311	+	9.57612i	−1.13148	+	0.314691i
$927$	−12.6063	+	12.6063i	−0.414044	+	0.414044i
$928$	−5.58971	−	1.21746i	−0.183491	−	0.0399650i
$929$	−14.6967	−	14.6967i	−0.482182	−	0.482182i	0.423646	−	0.905828i	$-0.360750\pi$
$929$	−14.6967	−	14.6967i	−0.482182	−	0.482182i	−0.905828	+	0.423646i	$0.860750\pi$
$930$	−45.1563	−	19.9117i	−1.48073	−	0.652930i
$931$	−6.73562			−0.220751
$932$	−8.45699	+	5.09858i	−0.277018	+	0.167009i
$933$	−17.9202	−	17.9202i	−0.586679	−	0.586679i
$934$	1.35255	+	4.86310i	0.0442566	+	0.159125i
$935$	46.0238	+	36.0231i	1.50514	+	1.17808i
$936$	−43.7874	−	41.3678i	−1.43124	−	1.35215i
$937$	32.0418	+	32.0418i	1.04676	+	1.04676i	0.998852	+	0.0479099i	$0.0152560\pi$
$937$	32.0418	+	32.0418i	1.04676	+	1.04676i	0.0479099	+	0.998852i	$0.484744\pi$
$938$	21.9606	−	6.10777i	0.717039	−	0.199426i
$939$		−	78.5933i		−	2.56479i
$940$	20.1463	+	26.9817i	0.657099	+	0.880045i
$941$	−11.5769	−	11.5769i	−0.377397	−	0.377397i	0.492765	−	0.870162i	$-0.335986\pi$
$941$	−11.5769	−	11.5769i	−0.377397	−	0.377397i	−0.870162	+	0.492765i	$0.835986\pi$
$942$	39.0520	−	10.8613i	1.27238	−	0.353880i
$943$	1.32972	+	1.32972i	0.0433017	+	0.0433017i
$944$	19.4512	−	36.8459i	0.633082	−	1.19923i
$945$	−39.2662	−	32.1821i	−1.27733	−	1.04688i
$946$	−26.3869	+	46.7196i	−0.857912	+	1.51898i
$947$	21.3606			0.694128			0.347064	−	0.937841i	$-0.387179\pi$
$947$	21.3606			0.694128			0.347064	+	0.937841i	$0.387179\pi$
$948$	−1.95171	+	7.87769i	−0.0633885	+	0.255855i
$949$	−32.8267	−	32.8267i	−1.06560	−	1.06560i
$950$	1.70535	−	5.20743i	0.0553288	−	0.168951i
$951$		−	67.7396i		−	2.19661i
$952$	−34.2846	−	30.9625i	−1.11117	−	1.00350i
$953$	9.06278	+	9.06278i	0.293572	+	0.293572i	0.838490	−	0.544917i	$-0.183439\pi$
$953$	9.06278	+	9.06278i	0.293572	+	0.293572i	−0.544917	+	0.838490i	$0.683439\pi$
$954$	−15.4191	−	55.4395i	−0.499211	−	1.79492i
$955$	−24.8507	−	20.3674i	−0.804150	−	0.659072i
$956$	2.53790	+	4.20961i	0.0820816	+	0.136148i
$957$			18.1593i			0.587008i
$958$	−12.6841	−	45.6057i	−0.409803	−	1.47345i
$959$	8.94317	−	8.94317i	0.288790	−	0.288790i
$960$	40.9505	+	29.8424i	1.32167	+	0.963159i
$961$			0.644501i			0.0207903i
$962$	−4.53409	−	16.3024i	−0.146185	−	0.525611i
$963$	−12.1286			−0.390839
$964$	5.99913	−	24.2143i	0.193219	−	0.779891i
$965$	28.6741	−	34.9860i	0.923053	−	1.12624i
$966$	−43.7071	−	24.6855i	−1.40625	−	0.794243i
$967$	−30.0406	+	30.0406i	−0.966041	+	0.966041i	−0.999442	−	0.0334011i	$-0.989366\pi$
$967$	−30.0406	+	30.0406i	−0.966041	+	0.966041i	0.0334011	+	0.999442i	$0.489366\pi$
$968$	−82.5187	+	2.34476i	−2.65225	+	0.0753634i
$969$	−6.54171	−	6.25420i	−0.210150	−	0.200914i
$970$	12.9667	−	5.03072i	0.416335	−	0.161527i
$971$			50.4418i			1.61875i	0.587289	+	0.809377i	$0.300195\pi$
$971$			50.4418i			1.61875i	−0.587289	+	0.809377i	$0.699805\pi$
$972$	−23.8001	+	14.3487i	−0.763388	+	0.460234i
$973$	−53.6187	+	53.6187i	−1.71894	+	1.71894i
$974$	−20.2188	−	11.4194i	−0.647851	−	0.365902i
$975$	33.2939	−	49.9687i	1.06626	−	1.60028i
$976$	−40.9796	+	12.6619i	−1.31173	+	0.405298i
$977$	−10.5898	−	10.5898i	−0.338799	−	0.338799i	0.517116	−	0.855915i	$-0.327005\pi$
$977$	−10.5898	−	10.5898i	−0.338799	−	0.338799i	−0.855915	+	0.517116i	$0.827005\pi$
$978$	31.8331	−	56.3624i	1.01791	−	1.80227i
$979$	−28.8703	−	28.8703i	−0.922698	−	0.922698i
$980$	38.4691	+	5.57952i	1.22885	+	0.178231i
$981$	2.33272	−	2.33272i	0.0744780	−	0.0744780i
$982$	0.260924	−	0.461982i	0.00832643	−	0.0147424i
$983$	38.2469			1.21989			0.609944	−	0.792445i	$-0.291192\pi$
$983$	38.2469			1.21989			0.609944	+	0.792445i	$0.291192\pi$
$984$	3.27080	−	3.46211i	0.104269	−	0.110368i
$985$	−32.6764	+	39.8693i	−1.04116	+	1.27034i
$986$	−5.19834	−	2.78386i	−0.165549	−	0.0886561i
$987$	−59.7412	+	59.7412i	−1.90158	+	1.90158i
$988$	6.37790	+	1.58013i	0.202908	+	0.0502707i
$989$	−13.3872	−	13.3872i	−0.425687	−	0.425687i
$990$	40.6305	−	92.1430i	1.29132	−	2.92850i
$991$	13.7638	−	13.7638i	0.437222	−	0.437222i	−0.453854	−	0.891076i	$-0.649951\pi$
$991$	13.7638	−	13.7638i	0.437222	−	0.437222i	0.891076	+	0.453854i	$0.149951\pi$
$992$	−6.63275	+	30.4530i	−0.210590	+	0.966882i
$993$	59.1112			1.87584
$994$	38.9786	−	10.8409i	1.23633	−	0.343853i
$995$	−59.8465	+	5.93374i	−1.89726	+	0.188112i
$996$	4.23012	−	17.0741i	0.134037	−	0.541012i
$997$	33.7510			1.06890			0.534452	−	0.845199i	$-0.320518\pi$
$997$	33.7510			1.06890			0.534452	+	0.845199i	$0.320518\pi$
$998$	−12.9202	−	46.4547i	−0.408981	−	1.47050i
$999$	16.1760			0.511785

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.t.a.523.17	✓	208
5.2	odd	4		680.2.bl.a.387.70	yes	208
8.3	odd	2	inner	680.2.t.a.523.35	yes	208
17.4	even	4		680.2.bl.a.123.88	yes	208
40.27	even	4		680.2.bl.a.387.88	yes	208
85.72	odd	4	inner	680.2.t.a.667.35	yes	208
136.123	odd	4		680.2.bl.a.123.70	yes	208
680.667	even	4	inner	680.2.t.a.667.17	yes	208

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.t.a.523.17	✓	208	1.1	even	1	trivial
680.2.t.a.523.35	yes	208	8.3	odd	2	inner
680.2.t.a.667.17	yes	208	680.667	even	4	inner
680.2.t.a.667.35	yes	208	85.72	odd	4	inner
680.2.bl.a.123.70	yes	208	136.123	odd	4
680.2.bl.a.123.88	yes	208	17.4	even	4
680.2.bl.a.387.70	yes	208	5.2	odd	4
680.2.bl.a.387.88	yes	208	40.27	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23139 - 0.695478i) q^{2} -2.83257i q^{3} +(1.03262 + 1.71280i) q^{4} +(1.41742 - 1.72943i) q^{5} +(-1.96999 + 3.48799i) q^{6} -3.96131 q^{7} +(-0.0803370 - 2.82729i) q^{8} -5.02347 q^{9} +(-2.94817 + 1.14381i) q^{10} +(4.48255 - 4.48255i) q^{11} +(4.85164 - 2.92497i) q^{12} +(-2.99784 + 2.99784i) q^{13} +(4.87790 + 2.75500i) q^{14} +(-4.89873 - 4.01494i) q^{15} +(-1.86739 + 3.53735i) q^{16} +(-2.84925 + 2.98023i) q^{17} +(6.18583 + 3.49371i) q^{18} -0.774926 q^{19} +(4.42583 + 0.641918i) q^{20} +11.2207i q^{21} +(-8.63727 + 2.40223i) q^{22} -3.16329i q^{23} +(-8.00849 + 0.227560i) q^{24} +(-0.981842 - 4.90265i) q^{25} +(5.77642 - 1.60656i) q^{26} +5.73162i q^{27} +(-4.09053 - 6.78494i) q^{28} +(-0.715095 - 0.715095i) q^{29} +(3.23992 + 8.35090i) q^{30} +(-3.89586 + 3.89586i) q^{31} +(4.75963 - 3.05712i) q^{32} +(-12.6972 - 12.6972i) q^{33} +(5.58121 - 1.68822i) q^{34} +(-5.61483 + 6.85079i) q^{35} +(-5.18734 - 8.60421i) q^{36} -2.82223i q^{37} +(0.954233 + 0.538944i) q^{38} +(8.49159 + 8.49159i) q^{39} +(-5.00346 - 3.86851i) q^{40} +(-0.420361 + 0.420361i) q^{41} +(7.80374 - 13.8170i) q^{42} +(4.23204 - 4.23204i) q^{43} +(12.3065 + 3.04895i) q^{44} +(-7.12036 + 8.68773i) q^{45} +(-2.20000 + 3.89523i) q^{46} +(5.32420 + 5.32420i) q^{47} +(10.0198 + 5.28952i) q^{48} +8.69195 q^{49} +(-2.20066 + 6.71990i) q^{50} +(8.44172 + 8.07071i) q^{51} +(-8.23033 - 2.03908i) q^{52} +(-5.72750 - 5.72750i) q^{53} +(3.98622 - 7.05783i) q^{54} +(-1.39859 - 14.1059i) q^{55} +(0.318239 + 11.1997i) q^{56} +2.19503i q^{57} +(0.383225 + 1.37789i) q^{58} -10.4162 q^{59} +(1.81828 - 12.5365i) q^{60} +(7.58216 + 7.58216i) q^{61} +(7.50680 - 2.08782i) q^{62} +19.8995 q^{63} +(-7.98709 + 0.454271i) q^{64} +(0.935349 + 9.43373i) q^{65} +(6.80450 + 24.4657i) q^{66} +(2.87710 - 2.87710i) q^{67} +(-8.04674 - 1.80276i) q^{68} -8.96024 q^{69} +(11.6786 - 4.53098i) q^{70} +(5.10666 - 5.10666i) q^{71} +(0.403570 + 14.2028i) q^{72} +10.9501i q^{73} +(-1.96280 + 3.47526i) q^{74} +(-13.8871 + 2.78114i) q^{75} +(-0.800205 - 1.32730i) q^{76} +(-17.7568 + 17.7568i) q^{77} +(-4.55071 - 16.3621i) q^{78} +(-1.01300 + 1.01300i) q^{79} +(3.47072 + 8.24343i) q^{80} +1.16483 q^{81} +(0.809978 - 0.225275i) q^{82} +(2.19557 - 2.19557i) q^{83} +(-19.2188 + 11.5867i) q^{84} +(1.11551 + 9.15181i) q^{85} +(-8.15456 + 2.26798i) q^{86} +(-2.02556 + 2.02556i) q^{87} +(-13.0336 - 12.3133i) q^{88} -6.44059i q^{89} +(14.8100 - 5.74588i) q^{90} +(11.8753 - 11.8753i) q^{91} +(5.41809 - 3.26648i) q^{92} +(11.0353 + 11.0353i) q^{93} +(-2.85328 - 10.2590i) q^{94} +(-1.09840 + 1.34018i) q^{95} +(-8.65950 - 13.4820i) q^{96} -4.39822 q^{97} +(-10.7031 - 6.04506i) q^{98} +(-22.5180 + 22.5180i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 208 q - 8 q^{6} - 192 q^{9} + 2 q^{10} - 8 q^{11} + 8 q^{12} - 16 q^{14} - 16 q^{16} - 12 q^{18} - 10 q^{20} + 4 q^{22} + 16 q^{24} + 12 q^{28} - 24 q^{30} + 20 q^{32} - 8 q^{33} - 4 q^{34} - 8 q^{35} - 12 q^{38}+ \cdots + 24 q^{99}+O(q^{100}) \) 208 * q - 8 * q^6 - 192 * q^9 + 2 * q^10 - 8 * q^11 + 8 * q^12 - 16 * q^14 - 16 * q^16 - 12 * q^18 - 10 * q^20 + 4 * q^22 + 16 * q^24 + 12 * q^28 - 24 * q^30 + 20 * q^32 - 8 * q^33 - 4 * q^34 - 8 * q^35 - 12 * q^38 - 42 * q^40 - 8 * q^41 - 32 * q^42 + 8 * q^44 - 16 * q^46 + 160 * q^49 + 16 * q^50 - 8 * q^51 - 20 * q^52 + 36 * q^54 + 4 * q^56 - 56 * q^58 - 64 * q^59 + 32 * q^60 - 48 * q^65 - 8 * q^67 - 56 * q^68 - 28 * q^70 - 56 * q^72 + 8 * q^74 + 8 * q^75 - 12 * q^78 + 6 * q^80 + 128 * q^81 + 44 * q^82 + 8 * q^86 - 82 * q^90 + 24 * q^91 + 64 * q^94 - 48 * q^96 - 16 * q^97 - 40 * q^98 + 24 * q^99

Introduction

L-functions

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