LMFDB - Embedded newform 670.2.h.c.439.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [670,2,Mod(29,670)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(670, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("670.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 670 = 2 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	670.h (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.34997693543$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			439.23
Character	$\chi$	$=$	670.439
Dual form			670.2.h.c.29.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +1.76407i q^{3} +(0.500000 - 0.866025i) q^{4} +(0.428350 + 2.19466i) q^{5} +(0.882037 + 1.52773i) q^{6} +(2.08791 + 1.20545i) q^{7} -1.00000i q^{8} -0.111955 q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +1.76407i q^{3} +(0.500000 - 0.866025i) q^{4} +(0.428350 + 2.19466i) q^{5} +(0.882037 + 1.52773i) q^{6} +(2.08791 + 1.20545i) q^{7} -1.00000i q^{8} -0.111955 q^{9} +(1.46829 + 1.68645i) q^{10} +(1.36074 - 2.35686i) q^{11} +(1.52773 + 0.882037i) q^{12} +(-2.79091 + 1.61133i) q^{13} +2.41091 q^{14} +(-3.87154 + 0.755641i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.94722 - 1.12423i) q^{17} +(-0.0969562 + 0.0559777i) q^{18} +(0.0706641 + 0.122394i) q^{19} +(2.11480 + 0.726366i) q^{20} +(-2.12651 + 3.68322i) q^{21} -2.72147i q^{22} +(-3.60460 + 2.08111i) q^{23} +1.76407 q^{24} +(-4.63303 + 1.88016i) q^{25} +(-1.61133 + 2.79091i) q^{26} +5.09472i q^{27} +(2.08791 - 1.20545i) q^{28} +(-0.582043 + 1.00813i) q^{29} +(-2.97503 + 2.59017i) q^{30} +(0.242953 - 0.420807i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(4.15768 + 2.40044i) q^{33} +(1.12423 - 1.94722i) q^{34} +(-1.75120 + 5.09859i) q^{35} +(-0.0559777 + 0.0969562i) q^{36} +(8.73193 - 5.04138i) q^{37} +(0.122394 + 0.0706641i) q^{38} +(-2.84251 - 4.92337i) q^{39} +(2.19466 - 0.428350i) q^{40} +(-3.77105 + 6.53165i) q^{41} +4.25301i q^{42} -3.17137i q^{43} +(-1.36074 - 2.35686i) q^{44} +(-0.0479561 - 0.245704i) q^{45} +(-2.08111 + 3.60460i) q^{46} +(0.647473 + 0.373819i) q^{47} +(1.52773 - 0.882037i) q^{48} +(-0.593767 - 1.02843i) q^{49} +(-3.07224 + 3.94478i) q^{50} +(1.98322 + 3.43504i) q^{51} +3.22266i q^{52} -9.72672i q^{53} +(2.54736 + 4.41216i) q^{54} +(5.75537 + 1.97678i) q^{55} +(1.20545 - 2.08791i) q^{56} +(-0.215912 + 0.124657i) q^{57} +1.16409i q^{58} +0.299657 q^{59} +(-1.28136 + 3.73067i) q^{60} +(-0.853586 - 1.47845i) q^{61} -0.485906i q^{62} +(-0.233752 - 0.134957i) q^{63} -1.00000 q^{64} +(-4.73181 - 5.43487i) q^{65} +4.80087 q^{66} +(5.79258 + 5.78325i) q^{67} -2.24845i q^{68} +(-3.67124 - 6.35877i) q^{69} +(1.03271 + 5.29111i) q^{70} +(5.98485 - 10.3661i) q^{71} +0.111955i q^{72} +(-9.03136 + 5.21426i) q^{73} +(5.04138 - 8.73193i) q^{74} +(-3.31674 - 8.17301i) q^{75} +0.141328 q^{76} +(5.68217 - 3.28060i) q^{77} +(-4.92337 - 2.84251i) q^{78} +(6.45842 - 11.1863i) q^{79} +(1.68645 - 1.46829i) q^{80} -9.32333 q^{81} +7.54210i q^{82} +(2.26112 - 1.30546i) q^{83} +(2.12651 + 3.68322i) q^{84} +(3.30138 + 3.79191i) q^{85} +(-1.58568 - 2.74648i) q^{86} +(-1.77841 - 1.02677i) q^{87} +(-2.35686 - 1.36074i) q^{88} +3.08258 q^{89} +(-0.164383 - 0.188808i) q^{90} -7.76954 q^{91} +4.16223i q^{92} +(0.742335 + 0.428587i) q^{93} +0.747637 q^{94} +(-0.238343 + 0.207511i) q^{95} +(0.882037 - 1.52773i) q^{96} +(-7.86369 + 4.54011i) q^{97} +(-1.02843 - 0.593767i) q^{98} +(-0.152342 + 0.263863i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 26 q^{4} - 16 q^{5} - 6 q^{6} - 48 q^{9}+O(q^{10}) $ 52 * q + 26 * q^4 - 16 * q^5 - 6 * q^6 - 48 * q^9	$ 52 q + 26 q^{4} - 16 q^{5} - 6 q^{6} - 48 q^{9} - 10 q^{10} + 24 q^{11} + 24 q^{14} + 28 q^{15} - 26 q^{16} - 24 q^{19} - 8 q^{20} + 4 q^{21} - 12 q^{24} - 28 q^{25} + 4 q^{26} - 20 q^{29} - 10 q^{30} - 30 q^{31} - 16 q^{34} - 14 q^{35} - 24 q^{36} - 8 q^{39} - 20 q^{40} - 10 q^{41} - 24 q^{44} - 16 q^{45} - 8 q^{46} + 14 q^{49} - 8 q^{50} - 44 q^{51} + 42 q^{54} + 16 q^{55} + 12 q^{56} + 80 q^{59} + 14 q^{60} - 20 q^{61} - 52 q^{64} + 10 q^{65} - 40 q^{66} - 4 q^{69} + 48 q^{70} - 74 q^{71} + 34 q^{74} - 16 q^{75} - 48 q^{76} + 32 q^{79} + 8 q^{80} + 4 q^{81} - 4 q^{84} + 20 q^{85} + 12 q^{86} + 84 q^{89} - 30 q^{90} - 16 q^{91} + 136 q^{94} + 2 q^{95} - 6 q^{96} - 96 q^{99}+O(q^{100}) $ 52 * q + 26 * q^4 - 16 * q^5 - 6 * q^6 - 48 * q^9 - 10 * q^10 + 24 * q^11 + 24 * q^14 + 28 * q^15 - 26 * q^16 - 24 * q^19 - 8 * q^20 + 4 * q^21 - 12 * q^24 - 28 * q^25 + 4 * q^26 - 20 * q^29 - 10 * q^30 - 30 * q^31 - 16 * q^34 - 14 * q^35 - 24 * q^36 - 8 * q^39 - 20 * q^40 - 10 * q^41 - 24 * q^44 - 16 * q^45 - 8 * q^46 + 14 * q^49 - 8 * q^50 - 44 * q^51 + 42 * q^54 + 16 * q^55 + 12 * q^56 + 80 * q^59 + 14 * q^60 - 20 * q^61 - 52 * q^64 + 10 * q^65 - 40 * q^66 - 4 * q^69 + 48 * q^70 - 74 * q^71 + 34 * q^74 - 16 * q^75 - 48 * q^76 + 32 * q^79 + 8 * q^80 + 4 * q^81 - 4 * q^84 + 20 * q^85 + 12 * q^86 + 84 * q^89 - 30 * q^90 - 16 * q^91 + 136 * q^94 + 2 * q^95 - 6 * q^96 - 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/670\mathbb{Z}\right)^\times$.

$n$	$471$	$537$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$			1.76407i			1.01849i	0.860622	+	0.509244i	$0.170075\pi$
$3$			1.76407i			1.01849i	−0.860622	+	0.509244i	$0.829925\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.428350	+	2.19466i	0.191564	+	0.981480i
$5$	0.428350	+	2.19466i	0.191564	+	0.981480i
$6$	0.882037	+	1.52773i	0.360090	+	0.623694i
$7$	2.08791	+	1.20545i	0.789154	+	0.455618i	0.839665	−	0.543105i	$-0.182752\pi$
$7$	2.08791	+	1.20545i	0.789154	+	0.455618i	−0.0505106	+	0.998724i	$0.516085\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.111955			−0.0373185
$10$	1.46829	+	1.68645i	0.464314	+	0.533303i
$11$	1.36074	−	2.35686i	0.410277	−	0.710621i	−0.584643	−	0.811291i	$-0.698765\pi$
$11$	1.36074	−	2.35686i	0.410277	−	0.710621i	0.994920	+	0.100670i	$0.0320986\pi$
$12$	1.52773	+	0.882037i	0.441018	+	0.254622i
$13$	−2.79091	+	1.61133i	−0.774059	+	0.446903i	−0.834321	−	0.551279i	$-0.814140\pi$
$13$	−2.79091	+	1.61133i	−0.774059	+	0.446903i	0.0602617	+	0.998183i	$0.480806\pi$
$14$	2.41091			0.644342
$15$	−3.87154	+	0.755641i	−0.999626	+	0.195106i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.94722	−	1.12423i	0.472270	−	0.272665i	−0.244920	−	0.969543i	$-0.578762\pi$
$17$	1.94722	−	1.12423i	0.472270	−	0.272665i	0.717189	+	0.696878i	$0.245428\pi$
$18$	−0.0969562	+	0.0559777i	−0.0228528	+	0.0131941i
$19$	0.0706641	+	0.122394i	0.0162115	+	0.0280791i	0.874017	−	0.485895i	$-0.161506\pi$
$19$	0.0706641	+	0.122394i	0.0162115	+	0.0280791i	−0.857806	+	0.513974i	$0.828173\pi$
$20$	2.11480	+	0.726366i	0.472884	+	0.162420i
$21$	−2.12651	+	3.68322i	−0.464042	+	0.803744i
$22$		−	2.72147i		−	0.580219i
$23$	−3.60460	+	2.08111i	−0.751610	+	0.433942i	−0.826275	−	0.563266i	$-0.809545\pi$
$23$	−3.60460	+	2.08111i	−0.751610	+	0.433942i	0.0746651	+	0.997209i	$0.476211\pi$
$24$	1.76407			0.360090
$25$	−4.63303	+	1.88016i	−0.926607	+	0.376032i
$26$	−1.61133	+	2.79091i	−0.316008	+	0.547342i
$27$			5.09472i			0.980480i
$28$	2.08791	−	1.20545i	0.394577	−	0.227809i
$29$	−0.582043	+	1.00813i	−0.108083	+	0.187205i	−0.914994	−	0.403469i	$-0.867804\pi$
$29$	−0.582043	+	1.00813i	−0.108083	+	0.187205i	0.806911	+	0.590673i	$0.201138\pi$
$30$	−2.97503	+	2.59017i	−0.543163	+	0.472898i
$31$	0.242953	−	0.420807i	0.0436357	−	0.0755792i	−0.843383	−	0.537313i	$-0.819439\pi$
$31$	0.242953	−	0.420807i	0.0436357	−	0.0755792i	0.887018	+	0.461734i	$0.152773\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	4.15768	+	2.40044i	0.723759	+	0.417862i
$34$	1.12423	−	1.94722i	0.192803	−	0.333945i
$35$	−1.75120	+	5.09859i	−0.296007	+	0.861819i
$36$	−0.0559777	+	0.0969562i	−0.00932961	+	0.0161594i
$37$	8.73193	−	5.04138i	1.43552	−	0.828798i	0.437986	−	0.898982i	$-0.355692\pi$
$37$	8.73193	−	5.04138i	1.43552	−	0.828798i	0.997534	+	0.0701836i	$0.0223585\pi$
$38$	0.122394	+	0.0706641i	0.0198549	+	0.0114632i
$39$	−2.84251	−	4.92337i	−0.455166	−	0.788370i
$40$	2.19466	−	0.428350i	0.347006	−	0.0677281i
$41$	−3.77105	+	6.53165i	−0.588939	+	1.02007i	0.405432	+	0.914125i	$0.367121\pi$
$41$	−3.77105	+	6.53165i	−0.588939	+	1.02007i	−0.994372	+	0.105948i	$0.966212\pi$
$42$			4.25301i			0.656254i
$43$		−	3.17137i		−	0.483629i	−0.970322	−	0.241815i	$-0.922257\pi$
$43$		−	3.17137i		−	0.483629i	0.970322	−	0.241815i	$-0.0777425\pi$
$44$	−1.36074	−	2.35686i	−0.205139	−	0.355310i
$45$	−0.0479561	−	0.245704i	−0.00714887	−	0.0366273i
$46$	−2.08111	+	3.60460i	−0.306844	+	0.531469i
$47$	0.647473	+	0.373819i	0.0944436	+	0.0545270i	0.546478	−	0.837473i	$-0.315968\pi$
$47$	0.647473	+	0.373819i	0.0944436	+	0.0545270i	−0.452034	+	0.892001i	$0.649302\pi$
$48$	1.52773	−	0.882037i	0.220509	−	0.127311i
$49$	−0.593767	−	1.02843i	−0.0848239	−	0.146919i
$50$	−3.07224	+	3.94478i	−0.434481	+	0.557877i
$51$	1.98322	+	3.43504i	0.277706	+	0.481001i
$52$			3.22266i			0.446903i
$53$		−	9.72672i		−	1.33607i	−0.744131	−	0.668034i	$-0.767136\pi$
$53$		−	9.72672i		−	1.33607i	0.744131	−	0.668034i	$-0.232864\pi$
$54$	2.54736	+	4.41216i	0.346652	+	0.600419i
$55$	5.75537	+	1.97678i	0.776054	+	0.266550i
$56$	1.20545	−	2.08791i	0.161085	−	0.279008i
$57$	−0.215912	+	0.124657i	−0.0285982	+	0.0165112i
$58$			1.16409i			0.152852i
$59$	0.299657			0.0390120			0.0195060	−	0.999810i	$-0.493791\pi$
$59$	0.299657			0.0390120			0.0195060	+	0.999810i	$0.493791\pi$
$60$	−1.28136	+	3.73067i	−0.165423	+	0.481627i
$61$	−0.853586	−	1.47845i	−0.109290	−	0.189297i	0.806193	−	0.591653i	$-0.201525\pi$
$61$	−0.853586	−	1.47845i	−0.109290	−	0.189297i	−0.915483	+	0.402357i	$0.868191\pi$
$62$		−	0.485906i		−	0.0617101i
$63$	−0.233752	−	0.134957i	−0.0294500	−	0.0170030i
$64$	−1.00000			−0.125000
$65$	−4.73181	−	5.43487i	−0.586908	−	0.674113i
$66$	4.80087			0.590947
$67$	5.79258	+	5.78325i	0.707676	+	0.706537i
$67$	5.79258	+	5.78325i	0.707676	+	0.706537i
$68$		−	2.24845i		−	0.272665i
$69$	−3.67124	−	6.35877i	−0.441965	−	0.765506i
$70$	1.03271	+	5.29111i	0.123433	+	0.632409i
$71$	5.98485	−	10.3661i	0.710271	−	1.23023i	−0.254484	−	0.967077i	$-0.581906\pi$
$71$	5.98485	−	10.3661i	0.710271	−	1.23023i	0.964755	−	0.263149i	$-0.0847611\pi$
$72$			0.111955i			0.0131941i
$73$	−9.03136	+	5.21426i	−1.05704	+	0.610283i	−0.924612	−	0.380910i	$-0.875611\pi$
$73$	−9.03136	+	5.21426i	−1.05704	+	0.610283i	−0.132428	+	0.991193i	$0.542277\pi$
$74$	5.04138	−	8.73193i	0.586049	−	1.01507i
$75$	−3.31674	−	8.17301i	−0.382984	−	0.943738i
$76$	0.141328			0.0162115
$77$	5.68217	−	3.28060i	0.647544	−	0.373860i
$78$	−4.92337	−	2.84251i	−0.557462	−	0.321851i
$79$	6.45842	−	11.1863i	0.726629	−	1.25856i	−0.231671	−	0.972794i	$-0.574419\pi$
$79$	6.45842	−	11.1863i	0.726629	−	1.25856i	0.958300	−	0.285764i	$-0.0922473\pi$
$80$	1.68645	−	1.46829i	0.188551	−	0.164160i
$81$	−9.32333			−1.03593
$82$			7.54210i			0.832886i
$83$	2.26112	−	1.30546i	0.248190	−	0.143293i	−0.370745	−	0.928735i	$-0.620898\pi$
$83$	2.26112	−	1.30546i	0.248190	−	0.143293i	0.618935	+	0.785442i	$0.287564\pi$
$84$	2.12651	+	3.68322i	0.232021	+	0.401872i
$85$	3.30138	+	3.79191i	0.358085	+	0.411291i
$86$	−1.58568	−	2.74648i	−0.170989	−	0.296161i
$87$	−1.77841	−	1.02677i	−0.190666	−	0.110081i
$88$	−2.35686	−	1.36074i	−0.251242	−	0.145055i
$89$	3.08258			0.326753			0.163377	−	0.986564i	$-0.447761\pi$
$89$	3.08258			0.326753			0.163377	+	0.986564i	$0.447761\pi$
$90$	−0.164383	−	0.188808i	−0.0173275	−	0.0199021i
$91$	−7.76954			−0.814469
$92$			4.16223i			0.433942i
$93$	0.742335	+	0.428587i	0.0769765	+	0.0444424i
$94$	0.747637			0.0771129
$95$	−0.238343	+	0.207511i	−0.0244535	+	0.0212902i
$96$	0.882037	−	1.52773i	0.0900225	−	0.155924i
$97$	−7.86369	+	4.54011i	−0.798437	+	0.460978i	−0.842924	−	0.538032i	$-0.819168\pi$
$97$	−7.86369	+	4.54011i	−0.798437	+	0.460978i	0.0444872	+	0.999010i	$0.485835\pi$
$98$	−1.02843	−	0.593767i	−0.103888	−	0.0599795i
$99$	−0.152342	+	0.263863i	−0.0153109	+	0.0265193i
$100$	−0.688249	+	4.95240i	−0.0688249	+	0.495240i
$101$	4.10259	−	7.10589i	0.408223	−	0.707063i	−0.586468	−	0.809973i	$-0.699482\pi$
$101$	4.10259	−	7.10589i	0.408223	−	0.707063i	0.994691	+	0.102910i	$0.0328153\pi$
$102$	3.43504	+	1.98322i	0.340119	+	0.196368i
$103$	3.54364	+	2.04592i	0.349165	+	0.201591i	0.664318	−	0.747450i	$-0.268722\pi$
$103$	3.54364	+	2.04592i	0.349165	+	0.201591i	−0.315152	+	0.949041i	$0.602056\pi$
$104$	1.61133	+	2.79091i	0.158004	+	0.273671i
$105$	−8.99429	−	3.08925i	−0.877753	−	0.301480i
$106$	−4.86336	−	8.42359i	−0.472372	−	0.818171i
$107$		−	11.2907i		−	1.09152i	−0.837943	−	0.545758i	$-0.816242\pi$
$107$		−	11.2907i		−	1.09152i	0.837943	−	0.545758i	$-0.183758\pi$
$108$	4.41216	+	2.54736i	0.424560	+	0.245120i
$109$	−4.46899			−0.428052			−0.214026	−	0.976828i	$-0.568658\pi$
$109$	−4.46899			−0.428052			−0.214026	+	0.976828i	$0.568658\pi$
$110$	5.97269	−	1.16574i	0.569474	−	0.111149i
$111$	8.89337	+	15.4038i	0.844121	+	1.46206i
$112$		−	2.41091i		−	0.227809i
$113$	−17.1481	−	9.90046i	−1.61316	−	0.931357i	−0.988633	−	0.150352i	$-0.951959\pi$
$113$	−17.1481	−	9.90046i	−1.61316	−	0.931357i	−0.624525	−	0.781005i	$-0.714707\pi$
$114$	−0.124657	+	0.215912i	−0.0116752	+	0.0202220i
$115$	−6.11136	−	7.01941i	−0.569887	−	0.654563i
$116$	0.582043	+	1.00813i	0.0540414	+	0.0936024i
$117$	0.312457	−	0.180397i	0.0288867	−	0.0166777i
$118$	0.259511	−	0.149828i	0.0238899	−	0.0137928i
$119$	5.42081			0.496925
$120$	0.755641	+	3.87154i	0.0689802	+	0.353421i
$121$	1.79680	+	3.11215i	0.163345	+	0.282923i
$122$	−1.47845	−	0.853586i	−0.133853	−	0.0772800i
$123$	−11.5223	−	6.65241i	−1.03893	−	0.599828i
$124$	−0.242953	−	0.420807i	−0.0218178	−	0.0377896i
$125$	−6.11087	−	9.36255i	−0.546573	−	0.837412i
$126$	−0.269914			−0.0240458
$127$	1.19932	+	0.692427i	0.106422	+	0.0614429i	0.552266	−	0.833668i	$-0.313763\pi$
$127$	1.19932	+	0.692427i	0.106422	+	0.0614429i	−0.445844	+	0.895111i	$0.647096\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	5.59453			0.492571
$130$	−6.81530	−	2.34083i	−0.597741	−	0.205305i
$131$	1.79905			0.157183			0.0785917	−	0.996907i	$-0.474958\pi$
$131$	1.79905			0.157183			0.0785917	+	0.996907i	$0.474958\pi$
$132$	4.15768	−	2.40044i	0.361879	−	0.208931i
$133$			0.340729i			0.0295449i
$134$	7.90815	+	2.11215i	0.683160	+	0.182462i
$135$	−11.1812	+	2.18232i	−0.962322	+	0.187825i
$136$	−1.12423	−	1.94722i	−0.0964017	−	0.166973i
$137$		−	7.75077i		−	0.662193i	−0.943597	−	0.331097i	$-0.892581\pi$
$137$		−	7.75077i		−	0.662193i	0.943597	−	0.331097i	$-0.107419\pi$
$138$	−6.35877	−	3.67124i	−0.541295	−	0.312517i
$139$	16.4464			1.39497			0.697484	−	0.716600i	$-0.254303\pi$
$139$	16.4464			1.39497			0.697484	+	0.716600i	$0.254303\pi$
$140$	3.53991	+	4.06588i	0.299177	+	0.343630i
$141$	−0.659444	+	1.14219i	−0.0555352	+	0.0961897i
$142$		−	11.9697i		−	1.00448i
$143$			8.77039i			0.733417i
$144$	0.0559777	+	0.0969562i	0.00466481	+	0.00807968i
$145$	−2.46181	−	0.845553i	−0.204443	−	0.0702194i
$146$	−5.21426	+	9.03136i	−0.431535	+	0.747440i
$147$	1.81423	−	1.04745i	0.149636	−	0.0863921i
$148$		−	10.0828i		−	0.828798i
$149$	4.29361			0.351747			0.175873	−	0.984413i	$-0.443725\pi$
$149$	4.29361			0.351747			0.175873	+	0.984413i	$0.443725\pi$
$150$	−6.95889	−	5.41966i	−0.568191	−	0.442514i
$151$	−1.40234	−	2.42892i	−0.114121	−	0.197663i	0.803307	−	0.595565i	$-0.203072\pi$
$151$	−1.40234	−	2.42892i	−0.114121	−	0.197663i	−0.917428	+	0.397902i	$0.869738\pi$
$152$	0.122394	−	0.0706641i	0.00992745	−	0.00573162i
$153$	−0.218002	+	0.125863i	−0.0176244	+	0.0101754i
$154$	3.28060	−	5.68217i	0.264359	−	0.457883i
$155$	1.02760	+	0.352946i	0.0825385	+	0.0283493i
$156$	−5.68502			−0.455166
$157$	0.551675	−	0.318510i	0.0440285	−	0.0254198i	−0.477824	−	0.878455i	$-0.658574\pi$
$157$	0.551675	−	0.318510i	0.0440285	−	0.0254198i	0.521853	+	0.853036i	$0.325241\pi$
$158$		−	12.9168i		−	1.02761i
$159$	17.1587			1.36077
$160$	0.726366	−	2.11480i	0.0574243	−	0.167190i
$161$	−10.0347			−0.790849
$162$	−8.07424	+	4.66167i	−0.634372	+	0.366255i
$163$	18.9023	+	10.9133i	1.48055	+	0.854793i	0.999757	−	0.0220437i	$-0.00701728\pi$
$163$	18.9023	+	10.9133i	1.48055	+	0.854793i	0.480788	+	0.876837i	$0.340351\pi$
$164$	3.77105	+	6.53165i	0.294470	+	0.510036i
$165$	−3.48719	+	10.1529i	−0.271478	+	0.790402i
$166$	1.30546	−	2.26112i	0.101323	−	0.175497i
$167$	−4.41022	−	2.54624i	−0.341273	−	0.197034i	0.319562	−	0.947565i	$-0.396464\pi$
$167$	−4.41022	−	2.54624i	−0.341273	−	0.197034i	−0.660835	+	0.750531i	$0.729798\pi$
$168$	3.68322	+	2.12651i	0.284166	+	0.164064i
$169$	−1.30722	+	2.26417i	−0.100555	+	0.174167i
$170$	4.75504	+	1.63320i	0.364695	+	0.125261i
$171$	−0.00791123	−	0.0137026i	−0.000604987	−	0.00104787i
$172$	−2.74648	−	1.58568i	−0.209418	−	0.120907i
$173$	0.356605	−	0.205886i	0.0271122	−	0.0156532i	−0.486383	−	0.873746i	$-0.661684\pi$
$173$	0.356605	−	0.205886i	0.0271122	−	0.0156532i	0.513495	+	0.858093i	$0.328351\pi$
$174$	−2.05353			−0.155678
$175$	−11.9398	−	1.65930i	−0.902563	−	0.125432i
$176$	−2.72147			−0.205139
$177$			0.528617i			0.0397333i
$178$	2.66959	−	1.54129i	0.200095	−	0.115525i
$179$	17.5052			1.30840			0.654200	−	0.756322i	$-0.273005\pi$
$179$	17.5052			1.30840			0.654200	+	0.756322i	$0.273005\pi$
$180$	−0.236764	−	0.0813206i	−0.0176473	−	0.00606128i
$181$	1.70698	−	2.95658i	0.126879	−	0.219761i	−0.795587	−	0.605840i	$-0.792837\pi$
$181$	1.70698	−	2.95658i	0.126879	−	0.219761i	0.922466	+	0.386079i	$0.126171\pi$
$182$	−6.72862	+	3.88477i	−0.498758	+	0.287958i
$183$	2.60810	−	1.50579i	0.192796	−	0.111311i
$184$	2.08111	+	3.60460i	0.153422	+	0.265734i
$185$	14.8044	+	17.0041i	1.08844	+	1.25017i
$186$	0.857174			0.0628511
$187$		−	6.11910i		−	0.447473i
$188$	0.647473	−	0.373819i	0.0472218	−	0.0272635i
$189$	−6.14145	+	10.6373i	−0.446725	+	0.773750i
$190$	−0.102656	+	0.298881i	−0.00744745	+	0.0216831i
$191$	−5.10200	−	8.83692i	−0.369168	−	0.639417i	0.620268	−	0.784390i	$-0.287024\pi$
$191$	−5.10200	−	8.83692i	−0.369168	−	0.639417i	−0.989436	+	0.144973i	$0.953691\pi$
$192$		−	1.76407i		−	0.127311i
$193$			19.3631i			1.39378i	0.717176	+	0.696892i	$0.245434\pi$
$193$			19.3631i			1.39378i	−0.717176	+	0.696892i	$0.754566\pi$
$194$	−4.54011	+	7.86369i	−0.325961	+	0.564580i
$195$	9.58752	−	8.34725i	0.686576	−	0.597759i
$196$	−1.18753			−0.0848239
$197$	−20.1064	−	11.6085i	−1.43252	−	0.827068i	−0.435211	−	0.900329i	$-0.643326\pi$
$197$	−20.1064	−	11.6085i	−1.43252	−	0.827068i	−0.997313	+	0.0732607i	$0.976659\pi$
$198$			0.304683i			0.0216529i
$199$	−9.82088	−	17.0103i	−0.696184	−	1.20583i	−0.969780	−	0.243981i	$-0.921546\pi$
$199$	−9.82088	−	17.0103i	−0.696184	−	1.20583i	0.273596	−	0.961845i	$-0.411787\pi$
$200$	1.88016	+	4.63303i	0.132947	+	0.327605i
$201$	−10.2021	+	10.2185i	−0.719599	+	0.720760i
$202$		−	8.20518i		−	0.577314i
$203$	−2.43050	+	1.40325i	−0.170588	+	0.0984889i
$204$	3.96644			0.277706
$205$	−15.9501	−	5.47833i	−1.11400	−	0.382623i
$206$	4.09184			0.285092
$207$	0.403554	−	0.232992i	0.0280489	−	0.0161941i
$208$	2.79091	+	1.61133i	0.193515	+	0.111726i
$209$	0.384621			0.0266048
$210$	−9.33391	+	1.82178i	−0.644101	+	0.125715i
$211$	7.04574	+	12.2036i	0.485048	+	0.840129i	0.999852	−	0.0171793i	$-0.00546861\pi$
$211$	7.04574	+	12.2036i	0.485048	+	0.840129i	−0.514804	+	0.857308i	$0.672135\pi$
$212$	−8.42359	−	4.86336i	−0.578535	−	0.334017i
$213$	18.2865	+	10.5577i	1.25297	+	0.723403i
$214$	−5.64537	−	9.77806i	−0.385909	−	0.668414i
$215$	6.96006	−	1.35845i	0.474672	−	0.0926458i
$216$	5.09472			0.346652
$217$	1.01453	−	0.585737i	0.0688705	−	0.0397624i
$218$	−3.87026	+	2.23450i	−0.262127	+	0.151339i
$219$	−9.19833	−	15.9320i	−0.621566	−	1.07658i
$220$	4.58963	−	3.99591i	0.309433	−	0.269404i
$221$	−3.62301	+	6.27523i	−0.243710	+	0.422118i
$222$	15.4038	+	8.89337i	1.03383	+	0.596884i
$223$			9.58093i			0.641587i	0.947149	+	0.320793i	$0.103950\pi$
$223$			9.58093i			0.641587i	−0.947149	+	0.320793i	$0.896050\pi$
$224$	−1.20545	−	2.08791i	−0.0805427	−	0.139504i
$225$	0.518693	−	0.210494i	0.0345795	−	0.0140329i
$226$	−19.8009			−1.31714
$227$	−18.3048	−	10.5683i	−1.21493	−	0.701442i	−0.251103	−	0.967960i	$-0.580793\pi$
$227$	−18.3048	−	10.5683i	−1.21493	−	0.701442i	−0.963830	+	0.266519i	$0.914127\pi$
$228$			0.249313i			0.0165112i
$229$	−9.05835	−	15.6895i	−0.598593	−	1.03679i	−0.993029	−	0.117870i	$-0.962393\pi$
$229$	−9.05835	−	15.6895i	−0.598593	−	1.03679i	0.394436	−	0.918923i	$-0.370940\pi$
$230$	−8.80230	−	3.02330i	−0.580406	−	0.199351i
$231$	5.78723	+	10.0238i	0.380772	+	0.659516i
$232$	1.00813	+	0.582043i	0.0661869	+	0.0382130i
$233$	−16.5814	−	9.57325i	−1.08628	−	0.627164i	−0.153697	−	0.988118i	$-0.549118\pi$
$233$	−16.5814	−	9.57325i	−1.08628	−	0.627164i	−0.932584	+	0.360954i	$0.882451\pi$
$234$	0.180397	−	0.312457i	0.0117929	−	0.0204260i
$235$	−0.543059	+	1.58111i	−0.0354252	+	0.103140i
$236$	0.149828	−	0.259511i	0.00975300	−	0.0168927i
$237$	19.7335	+	11.3931i	1.28183	+	0.740063i
$238$	4.69456	−	2.71041i	0.304303	−	0.175690i
$239$	−1.89450	+	3.28138i	−0.122545	+	0.212255i	−0.920771	−	0.390104i	$-0.872439\pi$
$239$	−1.89450	+	3.28138i	−0.122545	+	0.212255i	0.798225	+	0.602359i	$0.205772\pi$
$240$	2.59017	+	2.97503i	0.167195	+	0.192037i
$241$	−1.00300			−0.0646086			−0.0323043	−	0.999478i	$-0.510285\pi$
$241$	−1.00300			−0.0646086			−0.0323043	+	0.999478i	$0.510285\pi$
$242$	3.11215	+	1.79680i	0.200056	+	0.115503i
$243$		−	1.16287i		−	0.0745984i
$244$	−1.70717			−0.109290
$245$	2.00272	−	1.74364i	0.127949	−	0.111397i
$246$	−13.3048			−0.848285
$247$	−0.394434	−	0.227727i	−0.0250972	−	0.0144899i
$248$	−0.420807	−	0.242953i	−0.0267213	−	0.0154275i
$249$	2.30292	+	3.98878i	0.145942	+	0.252779i
$250$	−9.97344	−	5.05277i	−0.630776	−	0.319565i
$251$	0.998430	+	1.72933i	0.0630204	+	0.109154i	0.895814	−	0.444429i	$-0.146593\pi$
$251$	0.998430	+	1.72933i	0.0630204	+	0.109154i	−0.832794	+	0.553583i	$0.813260\pi$
$252$	−0.233752	+	0.134957i	−0.0147250	+	0.00850149i
$253$			11.3274i			0.712147i
$254$	1.38485			0.0868934
$255$	−6.68921	+	5.82388i	−0.418895	+	0.364706i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.98459	−	4.60991i	−0.498065	−	0.287558i	0.229849	−	0.973226i	$-0.426177\pi$
$257$	−7.98459	−	4.60991i	−0.498065	−	0.287558i	−0.727914	+	0.685668i	$0.759510\pi$
$258$	4.84500	−	2.79726i	0.301637	−	0.174150i
$259$	24.3086			1.51046
$260$	−7.07264	+	1.38043i	−0.438627	+	0.0856105i
$261$	0.0651629	−	0.112865i	0.00403348	−	0.00698619i
$262$	1.55802	−	0.899523i	0.0962548	−	0.0555727i
$263$			30.6810i			1.89187i	0.324353	+	0.945936i	$0.394854\pi$
$263$			30.6810i			1.89187i	−0.324353	+	0.945936i	$0.605146\pi$
$264$	2.40044	−	4.15768i	0.147737	−	0.255887i
$265$	21.3468	−	4.16644i	1.31132	−	0.255942i
$266$	0.170364	+	0.295080i	0.0104457	+	0.0180925i
$267$			5.43790i			0.332794i
$268$	7.90473	−	2.12490i	0.482858	−	0.129799i
$269$	−10.5906			−0.645719			−0.322859	−	0.946447i	$-0.604644\pi$
$269$	−10.5906			−0.645719			−0.322859	+	0.946447i	$0.604644\pi$
$270$	−8.59201	+	7.48053i	−0.522893	+	0.455251i
$271$	19.9547			1.21216			0.606080	−	0.795403i	$-0.292741\pi$
$271$	19.9547			1.21216			0.606080	+	0.795403i	$0.292741\pi$
$272$	−1.94722	−	1.12423i	−0.118067	−	0.0681663i
$273$		−	13.7060i		−	0.829527i
$274$	−3.87539	−	6.71237i	−0.234121	−	0.405509i
$275$	−1.87305	+	13.4778i	−0.112949	+	0.812743i
$276$	−7.34248			−0.441965
$277$			7.04992i			0.423589i	0.977314	+	0.211794i	$0.0679307\pi$
$277$			7.04992i			0.423589i	−0.977314	+	0.211794i	$0.932069\pi$
$278$	14.2430	−	8.22322i	0.854240	−	0.493196i
$279$	−0.0271999	+	0.0471116i	−0.00162842	+	0.00282050i
$280$	5.09859	+	1.75120i	0.304699	+	0.104654i
$281$	1.40168	+	2.42778i	0.0836173	+	0.144829i	0.904801	−	0.425834i	$-0.140019\pi$
$281$	1.40168	+	2.42778i	0.0836173	+	0.144829i	−0.821184	+	0.570664i	$0.806686\pi$
$282$			1.31889i			0.0785386i
$283$			9.09679i			0.540748i	0.962755	+	0.270374i	$0.0871473\pi$
$283$			9.09679i			0.540748i	−0.962755	+	0.270374i	$0.912853\pi$
$284$	−5.98485	−	10.3661i	−0.355136	−	0.615113i
$285$	−0.366064	−	0.420455i	−0.0216838	−	0.0249056i
$286$	4.38519	+	7.59538i	0.259302	+	0.449124i
$287$	−15.7472	+	9.09165i	−0.929528	+	0.536663i
$288$	0.0969562	+	0.0559777i	0.00571320	+	0.00329852i
$289$	−5.97223	+	10.3442i	−0.351307	+	0.608482i
$290$	−2.55477	+	0.498636i	−0.150021	+	0.0292809i
$291$	−8.00908	−	13.8721i	−0.469501	−	0.813199i
$292$			10.4285i			0.610283i
$293$			8.08904i			0.472567i	0.971684	+	0.236283i	$0.0759294\pi$
$293$			8.08904i			0.472567i	−0.971684	+	0.236283i	$0.924071\pi$
$294$	1.04745	−	1.81423i	0.0610885	−	0.105808i
$295$	0.128358	+	0.657644i	0.00747329	+	0.0382895i
$296$	−5.04138	−	8.73193i	−0.293024	−	0.507533i
$297$	12.0076	+	6.93257i	0.696749	+	0.402268i
$298$	3.71838	−	2.14681i	0.215400	−	0.124361i
$299$	6.70674	−	11.6164i	0.387861	−	0.671794i
$300$	−8.73641	−	1.21412i	−0.504397	−	0.0700974i
$301$	3.82293	−	6.62152i	0.220350	−	0.381658i
$302$	−2.42892	−	1.40234i	−0.139769	−	0.0806955i
$303$	12.5353	+	7.23727i	0.720135	+	0.415770i
$304$	0.0706641	−	0.122394i	0.00405286	−	0.00701977i
$305$	2.87907	−	2.50662i	0.164855	−	0.143529i
$306$	−0.125863	+	0.218002i	−0.00719513	+	0.0124623i
$307$	21.1622	−	12.2180i	1.20779	−	0.697320i	0.245516	−	0.969392i	$-0.421043\pi$
$307$	21.1622	−	12.2180i	1.20779	−	0.697320i	0.962277	+	0.272073i	$0.0877092\pi$
$308$		−	6.56121i		−	0.373860i
$309$	−3.60916	+	6.25124i	−0.205318	+	0.355621i
$310$	1.06640	−	0.208138i	0.0605673	−	0.0118214i
$311$	−3.37146			−0.191178			−0.0955891	−	0.995421i	$-0.530473\pi$
$311$	−3.37146			−0.191178			−0.0955891	+	0.995421i	$0.530473\pi$
$312$	−4.92337	+	2.84251i	−0.278731	+	0.160925i
$313$			30.6300i			1.73131i	0.500642	+	0.865655i	$0.333097\pi$
$313$			30.6300i			1.73131i	−0.500642	+	0.865655i	$0.666903\pi$
$314$	0.318510	−	0.551675i	0.0179745	−	0.0311328i
$315$	0.196056	−	0.570815i	0.0110465	−	0.0321618i
$316$	−6.45842	−	11.1863i	−0.363314	−	0.629279i
$317$	−4.91108	+	2.83541i	−0.275834	+	0.159253i	−0.631536	−	0.775347i	$-0.717575\pi$
$317$	−4.91108	+	2.83541i	−0.275834	+	0.159253i	0.355702	+	0.934599i	$0.384242\pi$
$318$	14.8598	−	8.57933i	0.833298	−	0.481105i
$319$	1.58401	+	2.74359i	0.0886877	+	0.153612i
$320$	−0.428350	−	2.19466i	−0.0239455	−	0.122685i
$321$	19.9177			1.11170
$322$	−8.69034	+	5.01737i	−0.484294	+	0.279607i
$323$	0.275197	+	0.158885i	0.0153124	+	0.00884060i
$324$	−4.66167	+	8.07424i	−0.258981	+	0.448569i
$325$	9.90081	−	12.7127i	0.549198	−	0.705175i
$326$	21.8265			1.20886
$327$		−	7.88363i		−	0.435966i
$328$	6.53165	+	3.77105i	0.360650	+	0.208222i
$329$	0.901241	+	1.56100i	0.0496870	+	0.0860605i
$330$	2.05645	+	10.5363i	0.113204	+	0.580002i
$331$	−14.8797	+	25.7724i	−0.817863	+	1.41658i	0.0893903	+	0.995997i	$0.471508\pi$
$331$	−14.8797	+	25.7724i	−0.817863	+	1.41658i	−0.907254	+	0.420584i	$0.861825\pi$
$332$		−	2.61092i		−	0.143293i
$333$	−0.977586	+	0.564410i	−0.0535714	+	0.0309295i
$334$	−5.09248			−0.278648
$335$	−10.2110	+	15.1900i	−0.557887	+	0.829917i
$336$	4.25301			0.232021
$337$	4.49033	−	2.59249i	0.244604	−	0.141222i	−0.372687	−	0.927957i	$-0.621563\pi$
$337$	4.49033	−	2.59249i	0.244604	−	0.141222i	0.617291	+	0.786735i	$0.288230\pi$
$338$			2.61443i			0.142206i
$339$	17.4651	−	30.2505i	0.948576	−	1.64298i
$340$	4.93459	−	0.963125i	0.267615	−	0.0522328i
$341$	−0.661190	−	1.14521i	−0.0358054	−	0.0620168i
$342$	−0.0137026	−	0.00791123i	−0.000740954	−	0.000427790i
$343$		−	19.7394i		−	1.06583i
$344$	−3.17137			−0.170989
$345$	12.3827	−	10.7809i	0.666665	−	0.580424i
$346$	0.205886	−	0.356605i	0.0110685	−	0.0191712i
$347$	15.4021	+	8.89240i	0.826827	+	0.477369i	0.852765	−	0.522295i	$-0.174924\pi$
$347$	15.4021	+	8.89240i	0.826827	+	0.477369i	−0.0259379	+	0.999664i	$0.508257\pi$
$348$	−1.77841	+	1.02677i	−0.0953329	+	0.0550405i
$349$	34.4540			1.84428			0.922139	−	0.386858i	$-0.126440\pi$
$349$	34.4540			1.84428			0.922139	+	0.386858i	$0.126440\pi$
$350$	−11.1698	+	4.53289i	−0.597051	+	0.242293i
$351$	−8.20929	−	14.2189i	−0.438180	−	0.758949i
$352$	−2.35686	+	1.36074i	−0.125621	+	0.0725274i
$353$	23.4414	−	13.5339i	1.24766	−	0.720337i	0.277018	−	0.960865i	$-0.410654\pi$
$353$	23.4414	−	13.5339i	1.24766	−	0.720337i	0.970642	+	0.240528i	$0.0773205\pi$
$354$	0.264308	+	0.457796i	0.0140478	+	0.0243316i
$355$	25.3136	+	8.69439i	1.34350	+	0.461450i
$356$	1.54129	−	2.66959i	0.0816883	−	0.141488i
$357$			9.56271i			0.506112i
$358$	15.1599	−	8.75260i	0.801228	−	0.462589i
$359$	−15.0656			−0.795132			−0.397566	−	0.917574i	$-0.630145\pi$
$359$	−15.0656			−0.795132			−0.397566	+	0.917574i	$0.630145\pi$
$360$	−0.245704	+	0.0479561i	−0.0129497	+	0.00252751i
$361$	9.49001	−	16.4372i	0.499474	−	0.865115i
$362$		−	3.41397i		−	0.179434i
$363$	−5.49006	+	3.16969i	−0.288153	+	0.166365i
$364$	−3.88477	+	6.72862i	−0.203617	+	0.352675i
$365$	−15.3121	−	17.5872i	−0.801471	−	0.920556i
$366$	1.50579	−	2.60810i	0.0787088	−	0.136328i
$367$	−23.3843	−	13.5009i	−1.22065	−	0.704743i	−0.255593	−	0.966784i	$-0.582271\pi$
$367$	−23.3843	−	13.5009i	−1.22065	−	0.704743i	−0.965057	+	0.262042i	$0.915604\pi$
$368$	3.60460	+	2.08111i	0.187903	+	0.108486i
$369$	0.422190	−	0.731254i	0.0219783	−	0.0380676i
$370$	21.3231	+	7.32378i	1.10853	+	0.380745i
$371$	11.7251	−	20.3085i	0.608737	−	1.05436i
$372$	0.742335	−	0.428587i	0.0384883	−	0.0222212i
$373$	19.7225	+	11.3868i	1.02119	+	0.589587i	0.914450	−	0.404699i	$-0.132624\pi$
$373$	19.7225	+	11.3868i	1.02119	+	0.589587i	0.106745	+	0.994286i	$0.465957\pi$
$374$	−3.05955	−	5.29930i	−0.158206	−	0.274020i
$375$	16.5162	−	10.7800i	0.852894	−	0.556678i
$376$	0.373819	−	0.647473i	0.0192782	−	0.0333909i
$377$		−	3.75146i		−	0.193210i
$378$			12.2829i			0.631764i
$379$	−8.07052	−	13.9785i	−0.414555	−	0.718030i	0.580827	−	0.814027i	$-0.302729\pi$
$379$	−8.07052	−	13.9785i	−0.414555	−	0.718030i	−0.995382	+	0.0959973i	$0.969396\pi$
$380$	0.0605379	+	0.310167i	0.00310553	+	0.0159112i
$381$	−1.22149	+	2.11568i	−0.0625789	+	0.108390i
$382$	−8.83692	−	5.10200i	−0.452136	−	0.261041i
$383$	−27.5748	+	15.9203i	−1.40901	+	0.813490i	−0.995292	−	0.0969174i	$-0.969102\pi$
$383$	−27.5748	+	15.9203i	−1.40901	+	0.813490i	−0.413713	+	0.910407i	$0.635768\pi$
$384$	−0.882037	−	1.52773i	−0.0450112	−	0.0779618i
$385$	9.63376	+	11.0652i	0.490982	+	0.563933i
$386$	9.68154	+	16.7689i	0.492777	+	0.853515i
$387$			0.355052i			0.0180483i
$388$			9.08021i			0.460978i
$389$	1.14101	+	1.97629i	0.0578516	+	0.100202i	0.893501	−	0.449062i	$-0.148242\pi$
$389$	1.14101	+	1.97629i	0.0578516	+	0.100202i	−0.835649	+	0.549264i	$0.814908\pi$
$390$	4.12941	−	12.0227i	0.209101	−	0.608793i
$391$	−4.67929	+	8.10477i	−0.236642	+	0.409876i
$392$	−1.02843	+	0.593767i	−0.0519438	+	0.0299898i
$393$			3.17365i			0.160089i
$394$	−23.2169			−1.16965
$395$	27.3166	+	9.38236i	1.37445	+	0.472078i
$396$	0.152342	+	0.263863i	0.00765545	+	0.0132596i
$397$			28.3878i			1.42474i	0.701804	+	0.712371i	$0.252378\pi$
$397$			28.3878i			1.42474i	−0.701804	+	0.712371i	$0.747622\pi$
$398$	−17.0103	−	9.82088i	−0.852648	−	0.492276i
$399$	−0.601071			−0.0300912
$400$	3.94478	+	3.07224i	0.197239	+	0.153612i
$401$	−34.5001			−1.72285			−0.861427	−	0.507881i	$-0.830429\pi$
$401$	−34.5001			−1.72285			−0.861427	+	0.507881i	$0.830429\pi$
$402$	−3.72599	+	13.9506i	−0.185836	+	0.695790i
$403$			1.56591i			0.0780036i
$404$	−4.10259	−	7.10589i	−0.204111	−	0.353531i
$405$	−3.99365	−	20.4615i	−0.198446	−	1.01674i
$406$	−1.40325	+	2.43050i	−0.0696422	+	0.120624i
$407$		−	27.4399i		−	1.36015i
$408$	3.43504	−	1.98322i	0.170060	−	0.0981840i
$409$	−9.94465	+	17.2246i	−0.491731	+	0.851703i	−0.999955	−	0.00952182i	$-0.996969\pi$
$409$	−9.94465	+	17.2246i	−0.491731	+	0.851703i	0.508223	+	0.861225i	$0.330302\pi$
$410$	−16.5523	+	3.23066i	−0.817461	+	0.159551i
$411$	13.6729			0.674436
$412$	3.54364	−	2.04592i	0.174583	−	0.100795i
$413$	0.625655	+	0.361222i	0.0307865	+	0.0177746i
$414$	0.232992	−	0.403554i	0.0114509	−	0.0198336i
$415$	3.83358	+	4.40319i	0.188183	+	0.216144i
$416$	3.22266			0.158004
$417$			29.0127i			1.42076i
$418$	0.333091	−	0.192310i	0.0162920	−	0.00940620i
$419$	7.58951	+	13.1454i	0.370772	+	0.642195i	0.989684	−	0.143264i	$-0.0457599\pi$
$419$	7.58951	+	13.1454i	0.370772	+	0.642195i	−0.618913	+	0.785460i	$0.712427\pi$
$420$	−7.17251	+	6.24466i	−0.349983	+	0.304708i
$421$	3.94814	+	6.83839i	0.192421	+	0.333283i	0.946052	−	0.324015i	$-0.105033\pi$
$421$	3.94814	+	6.83839i	0.192421	+	0.333283i	−0.753631	+	0.657298i	$0.771699\pi$
$422$	12.2036	+	7.04574i	0.594061	+	0.342981i
$423$	−0.0724881	−	0.0418510i	−0.00352449	−	0.00203487i
$424$	−9.72672			−0.472372
$425$	−6.90780	+	8.86967i	−0.335078	+	0.430242i
$426$	21.1154			1.02305
$427$		−	4.11583i		−	0.199179i
$428$	−9.77806	−	5.64537i	−0.472640	−	0.272879i
$429$	−15.4716			−0.746976
$430$	5.34836	−	4.65649i	0.257921	−	0.224556i
$431$	12.0111	−	20.8039i	0.578556	−	1.00209i	−0.417089	−	0.908866i	$-0.636950\pi$
$431$	12.0111	−	20.8039i	0.578556	−	1.00209i	0.995645	−	0.0932235i	$-0.0297171\pi$
$432$	4.41216	−	2.54736i	0.212280	−	0.122560i
$433$	−33.2659	−	19.2061i	−1.59866	−	0.922984i	−0.991747	−	0.128213i	$-0.959076\pi$
$433$	−33.2659	−	19.2061i	−1.59866	−	0.922984i	−0.606909	−	0.794771i	$-0.707591\pi$
$434$	0.585737	−	1.01453i	0.0281163	−	0.0486988i
$435$	1.49162	−	4.34282i	0.0715176	−	0.208222i
$436$	−2.23450	+	3.87026i	−0.107013	+	0.185352i
$437$	−0.509431	−	0.294120i	−0.0243694	−	0.0140697i
$438$	−15.9320	−	9.19833i	−0.761259	−	0.439513i
$439$	14.1308	+	24.4752i	0.674426	+	1.16814i	0.976636	+	0.214898i	$0.0689420\pi$
$439$	14.1308	+	24.4752i	0.674426	+	1.16814i	−0.302211	+	0.953241i	$0.597725\pi$
$440$	1.97678	−	5.75537i	0.0942395	−	0.274377i
$441$	0.0664754	+	0.115139i	0.00316550	+	0.00548280i
$442$			7.24601i			0.344658i
$443$	13.6660	+	7.89006i	0.649290	+	0.374868i	0.788184	−	0.615439i	$-0.211021\pi$
$443$	13.6660	+	7.89006i	0.649290	+	0.374868i	−0.138894	+	0.990307i	$0.544355\pi$
$444$	17.7867			0.844121
$445$	1.32042	+	6.76521i	0.0625941	+	0.320702i
$446$	4.79047	+	8.29733i	0.226835	+	0.392890i
$447$			7.57425i			0.358250i
$448$	−2.08791	−	1.20545i	−0.0986443	−	0.0569523i
$449$	−6.91529	+	11.9776i	−0.326353	+	0.565260i	−0.981785	−	0.189994i	$-0.939153\pi$
$449$	−6.91529	+	11.9776i	−0.326353	+	0.565260i	0.655432	+	0.755254i	$0.272486\pi$
$450$	0.343954	−	0.441640i	0.0162142	−	0.0208191i
$451$	10.2628	+	17.7757i	0.483257	+	0.837025i
$452$	−17.1481	+	9.90046i	−0.806579	+	0.465678i
$453$	4.28480	−	2.47383i	0.201317	−	0.116231i
$454$	−21.1366			−0.991988
$455$	−3.32808	−	17.0515i	−0.156023	−	0.799385i
$456$	0.124657	+	0.215912i	0.00583758	+	0.0101110i
$457$	1.50701	+	0.870071i	0.0704948	+	0.0407002i	0.534833	−	0.844958i	$-0.320374\pi$
$457$	1.50701	+	0.870071i	0.0704948	+	0.0407002i	−0.464338	+	0.885658i	$0.653708\pi$
$458$	−15.6895	−	9.05835i	−0.733124	−	0.423269i
$459$	5.72763	+	9.92054i	0.267343	+	0.463051i
$460$	−9.13466	+	1.78289i	−0.425906	+	0.0831277i
$461$	9.14095			0.425736			0.212868	−	0.977081i	$-0.431719\pi$
$461$	9.14095			0.425736			0.212868	+	0.977081i	$0.431719\pi$
$462$	10.0238	+	5.78723i	0.466348	+	0.269246i
$463$	−7.30219	+	4.21592i	−0.339362	+	0.195931i	−0.659990	−	0.751275i	$-0.729439\pi$
$463$	−7.30219	+	4.21592i	−0.339362	+	0.195931i	0.320628	+	0.947205i	$0.396106\pi$
$464$	1.16409			0.0540414
$465$	−0.622622	+	1.81275i	−0.0288734	+	0.0840645i
$466$	−19.1465			−0.886944
$467$	−6.57962	+	3.79875i	−0.304469	+	0.175785i	−0.644449	−	0.764648i	$-0.722913\pi$
$467$	−6.57962	+	3.79875i	−0.304469	+	0.175785i	0.339980	+	0.940433i	$0.389580\pi$
$468$		−	0.360795i		−	0.0166777i
$469$	5.12292	+	19.0576i	0.236555	+	0.879997i
$470$	0.320250	+	1.64081i	0.0147720	+	0.0756848i
$471$	0.561874	+	0.973195i	0.0258898	+	0.0448425i
$472$		−	0.299657i		−	0.0137928i
$473$	−7.47448	−	4.31539i	−0.343677	−	0.198422i
$474$	22.7863			1.04661
$475$	−0.557509	−	0.434195i	−0.0255803	−	0.0199222i
$476$	2.71041	−	4.69456i	0.124231	−	0.215175i
$477$			1.08896i			0.0498600i
$478$			3.78901i			0.173305i
$479$	1.46338	+	2.53465i	0.0668635	+	0.115811i	0.897519	−	0.440976i	$-0.145367\pi$
$479$	1.46338	+	2.53465i	0.0668635	+	0.115811i	−0.830656	+	0.556787i	$0.812034\pi$
$480$	3.73067	+	1.28136i	0.170281	+	0.0584860i
$481$	−16.2467	+	28.1401i	−0.740785	+	1.28308i
$482$	−0.868620	+	0.501498i	−0.0395645	+	0.0228426i
$483$		−	17.7020i		−	0.805470i
$484$	3.59360			0.163345
$485$	−13.3324	−	15.3134i	−0.605392	−	0.695344i
$486$	−0.581437	−	1.00708i	−0.0263745	−	0.0456820i
$487$	−20.6759	+	11.9373i	−0.936916	+	0.540929i	−0.888992	−	0.457922i	$-0.848594\pi$
$487$	−20.6759	+	11.9373i	−0.936916	+	0.540929i	−0.0479239	+	0.998851i	$0.515261\pi$
$488$	−1.47845	+	0.853586i	−0.0669265	+	0.0386400i
$489$	−19.2518	+	33.3451i	−0.870597	+	1.50792i
$490$	0.862585	−	2.51140i	0.0389676	−	0.113454i
$491$	−5.24509			−0.236708			−0.118354	−	0.992971i	$-0.537762\pi$
$491$	−5.24509			−0.236708			−0.118354	+	0.992971i	$0.537762\pi$
$492$	−11.5223	+	6.65241i	−0.519466	+	0.299914i
$493$			2.61740i			0.117882i
$494$	−0.455453			−0.0204918
$495$	−0.644345	−	0.221312i	−0.0289612	−	0.00994722i
$496$	−0.485906			−0.0218178
$497$	24.9916	−	14.4289i	1.12103	−	0.647225i
$498$	3.98878	+	2.30292i	0.178742	+	0.103196i
$499$	−0.820225	−	1.42067i	−0.0367183	−	0.0635980i	0.847082	−	0.531462i	$-0.178357\pi$
$499$	−0.820225	−	1.42067i	−0.0367183	−	0.0635980i	−0.883801	+	0.467864i	$0.845024\pi$
$500$	−11.1636	+	0.610891i	−0.499253	+	0.0273199i
$501$	4.49175	−	7.77995i	0.200677	−	0.347582i
$502$	1.72933	+	0.998430i	0.0771839	+	0.0445621i
$503$	−3.31208	−	1.91223i	−0.147678	−	0.0852622i	0.424340	−	0.905503i	$-0.360506\pi$
$503$	−3.31208	−	1.91223i	−0.147678	−	0.0852622i	−0.572018	+	0.820241i	$0.693839\pi$
$504$	−0.134957	+	0.233752i	−0.00601146	+	0.0104122i
$505$	17.3523	+	5.95997i	0.772169	+	0.265215i
$506$	5.66369	+	9.80980i	0.251782	+	0.436099i
$507$	−3.99416	−	2.30603i	−0.177387	−	0.102414i
$508$	1.19932	−	0.692427i	0.0532111	−	0.0307215i
$509$	−25.9318			−1.14941			−0.574704	−	0.818362i	$-0.694883\pi$
$509$	−25.9318			−1.14941			−0.574704	+	0.818362i	$0.694883\pi$
$510$	−2.88109	+	8.38824i	−0.127577	+	0.371437i
$511$	−25.1422			−1.11222
$512$			1.00000i			0.0441942i
$513$	−0.623563	+	0.360014i	−0.0275310	+	0.0158950i
$514$	−9.21981			−0.406668
$515$	−2.97218	+	8.65344i	−0.130970	+	0.381316i
$516$	2.79726	−	4.84500i	0.123143	−	0.213289i
$517$	1.76208	−	1.01734i	0.0774961	−	0.0447424i
$518$	21.0519	−	12.1543i	0.924965	−	0.534029i
$519$	0.363198	+	0.629077i	0.0159426	+	0.0276134i
$520$	−5.43487	+	4.73181i	−0.238335	+	0.207503i
$521$	−7.53921			−0.330299			−0.165149	−	0.986269i	$-0.552811\pi$
$521$	−7.53921			−0.330299			−0.165149	+	0.986269i	$0.552811\pi$
$522$		−	0.130326i		−	0.00570420i
$523$	10.1444	−	5.85688i	0.443584	−	0.256104i	−0.261533	−	0.965195i	$-0.584228\pi$
$523$	10.1444	−	5.85688i	0.443584	−	0.256104i	0.705117	+	0.709091i	$0.250895\pi$
$524$	0.899523	−	1.55802i	0.0392958	−	0.0680624i
$525$	2.92713	−	21.0627i	0.127751	−	0.919249i
$526$	15.3405	+	26.5705i	0.668878	+	1.15853i
$527$		−	1.09254i		−	0.0475917i
$528$		−	4.80087i		−	0.208931i
$529$	−2.83792	+	4.91542i	−0.123388	+	0.213714i
$530$	16.4037	−	14.2817i	0.712530	−	0.620355i
$531$	−0.0335482			−0.00145587
$532$	0.295080	+	0.170364i	0.0127933	+	0.00738624i
$533$		−	24.3057i		−	1.05280i
$534$	2.71895	+	4.70936i	0.117660	+	0.203794i
$535$	24.7793	−	4.83638i	1.07130	−	0.209095i
$536$	5.78325	−	5.79258i	0.249798	−	0.250201i
$537$			30.8805i			1.33259i
$538$	−9.17171	+	5.29529i	−0.395420	+	0.228296i
$539$	−3.23184			−0.139205
$540$	−3.70064	+	10.7743i	−0.159250	+	0.463654i
$541$	−42.7047			−1.83602			−0.918010	−	0.396557i	$-0.870205\pi$
$541$	−42.7047			−1.83602			−0.918010	+	0.396557i	$0.870205\pi$
$542$	17.2813	−	9.97734i	0.742294	−	0.428563i
$543$	5.21563	+	3.01125i	0.223824	+	0.129225i
$544$	−2.24845			−0.0964017
$545$	−1.91429	−	9.80790i	−0.0819993	−	0.420124i
$546$	−6.85302	−	11.8698i	−0.293282	−	0.507980i
$547$	−25.3992	−	14.6642i	−1.08599	−	0.626997i	−0.153484	−	0.988151i	$-0.549050\pi$
$547$	−25.3992	−	14.6642i	−1.08599	−	0.626997i	−0.932506	+	0.361154i	$0.882383\pi$
$548$	−6.71237	−	3.87539i	−0.286738	−	0.165548i
$549$	0.0955635	+	0.165521i	0.00407855	+	0.00706426i
$550$	5.11680	+	12.6087i	0.218181	+	0.537635i
$551$	−0.164518			−0.00700871
$552$	−6.35877	+	3.67124i	−0.270647	+	0.156258i
$553$	26.9691	−	15.5706i	1.14684	−	0.662131i
$554$	3.52496	+	6.10541i	0.149761	+	0.259394i
$555$	−29.9965	+	26.1161i	−1.27328	+	1.10857i
$556$	8.22322	−	14.2430i	0.348742	−	0.604039i
$557$	−10.8734	−	6.27775i	−0.460720	−	0.265997i	0.251627	−	0.967824i	$-0.419034\pi$
$557$	−10.8734	−	6.27775i	−0.460720	−	0.265997i	−0.712347	+	0.701827i	$0.752368\pi$
$558$			0.0543998i			0.00230293i
$559$	5.11013	+	8.85100i	0.216135	+	0.374357i
$560$	5.29111	−	1.03271i	0.223590	−	0.0436400i
$561$	10.7945			0.455746
$562$	2.42778	+	1.40168i	0.102410	+	0.0591263i
$563$		−	30.2040i		−	1.27295i	−0.771298	−	0.636474i	$-0.780392\pi$
$563$		−	30.2040i		−	1.27295i	0.771298	−	0.636474i	$-0.219608\pi$
$564$	0.659444	+	1.14219i	0.0277676	+	0.0480949i
$565$	14.3827	−	41.8750i	0.605086	−	1.76170i
$566$	4.54839	+	7.87805i	0.191183	+	0.331139i
$567$	−19.4662	−	11.2388i	−0.817505	−	0.471987i
$568$	−10.3661	−	5.98485i	−0.434951	−	0.251119i
$569$	−15.6122	+	27.0412i	−0.654499	+	1.13363i	0.327520	+	0.944844i	$0.393787\pi$
$569$	−15.6122	+	27.0412i	−0.654499	+	1.13363i	−0.982019	+	0.188782i	$0.939546\pi$
$570$	−0.527249	−	0.181093i	−0.0220840	−	0.00758514i
$571$	−2.59371	+	4.49244i	−0.108543	+	0.188003i	−0.915180	−	0.403044i	$-0.867952\pi$
$571$	−2.59371	+	4.49244i	−0.108543	+	0.188003i	0.806637	+	0.591047i	$0.201285\pi$
$572$	7.59538	+	4.38519i	0.317579	+	0.183354i
$573$	15.5890	−	9.00030i	0.651239	−	0.375993i
$574$	−9.09165	+	15.7472i	−0.379478	+	0.657275i
$575$	12.7874	−	16.4191i	0.533271	−	0.684724i
$576$	0.111955			0.00466481
$577$	−12.1241	−	6.99986i	−0.504734	−	0.291408i	0.225933	−	0.974143i	$-0.427457\pi$
$577$	−12.1241	−	6.99986i	−0.504734	−	0.291408i	−0.730666	+	0.682735i	$0.760790\pi$
$578$			11.9445i			0.496824i
$579$	−34.1579			−1.41955
$580$	−1.96318	+	1.70922i	−0.0815165	+	0.0709714i
$581$	6.29467			0.261147
$582$	−13.8721	−	8.00908i	−0.575019	−	0.331987i
$583$	−22.9246	−	13.2355i	−0.949438	−	0.548158i
$584$	5.21426	+	9.03136i	0.215767	+	0.373720i
$585$	0.529751	+	0.608463i	0.0219025	+	0.0251569i
$586$	4.04452	+	7.00531i	0.167078	+	0.289387i
$587$	10.7543	−	6.20899i	0.443877	−	0.256272i	−0.261364	−	0.965240i	$-0.584172\pi$
$587$	10.7543	−	6.20899i	0.443877	−	0.256272i	0.705241	+	0.708968i	$0.250839\pi$
$588$		−	2.09490i		−	0.0863921i
$589$	0.0686722			0.00282959
$590$	0.439983	+	0.505357i	0.0181138	+	0.0208052i
$591$	20.4782	−	35.4692i	0.842359	−	1.45901i
$592$	−8.73193	−	5.04138i	−0.358880	−	0.207200i
$593$	−31.4238	+	18.1425i	−1.29042	+	0.745025i	−0.978729	−	0.205159i	$-0.934229\pi$
$593$	−31.4238	+	18.1425i	−1.29042	+	0.745025i	−0.311692	+	0.950183i	$0.600896\pi$
$594$	13.8651			0.568894
$595$	2.32200	+	11.8968i	0.0951929	+	0.487722i
$596$	2.14681	−	3.71838i	0.0879366	−	0.152311i
$597$	30.0074	−	17.3248i	1.22812	−	0.709055i
$598$		−	13.4135i		−	0.548518i
$599$	−2.83480	+	4.91002i	−0.115827	+	0.200618i	−0.918110	−	0.396326i	$-0.870285\pi$
$599$	−2.83480	+	4.91002i	−0.115827	+	0.200618i	0.802283	+	0.596944i	$0.203618\pi$
$600$	−8.17301	+	3.31674i	−0.333662	+	0.135405i
$601$	3.00118	+	5.19820i	0.122421	+	0.212039i	0.920722	−	0.390220i	$-0.127601\pi$
$601$	3.00118	+	5.19820i	0.122421	+	0.212039i	−0.798301	+	0.602259i	$0.794268\pi$
$602$		−	7.64587i		−	0.311622i
$603$	−0.648511	−	0.647466i	−0.0264094	−	0.0263669i
$604$	−2.80468			−0.114121
$605$	−6.06044	+	5.27644i	−0.246392	+	0.214518i
$606$	14.4745			0.587988
$607$	−38.0620	−	21.9751i	−1.54489	−	0.891943i	−0.998519	−	0.0544004i	$-0.982675\pi$
$607$	−38.0620	−	21.9751i	−1.54489	−	0.891943i	−0.546372	−	0.837543i	$-0.683991\pi$
$608$		−	0.141328i		−	0.00573162i
$609$	−2.47544	−	4.28759i	−0.100310	−	0.173742i
$610$	1.24003	−	3.61033i	0.0502074	−	0.146178i
$611$	−2.40938			−0.0974732
$612$			0.251727i			0.0101754i
$613$	17.3719	−	10.0297i	0.701645	−	0.405095i	−0.106315	−	0.994333i	$-0.533905\pi$
$613$	17.3719	−	10.0297i	0.701645	−	0.405095i	0.807960	+	0.589237i	$0.200572\pi$
$614$	12.2180	−	21.1622i	0.493079	−	0.854039i
$615$	9.66418	−	28.1371i	0.389697	−	1.13460i
$616$	−3.28060	−	5.68217i	−0.132179	−	0.228941i
$617$			9.06969i			0.365132i	0.983194	+	0.182566i	$0.0584403\pi$
$617$			9.06969i			0.365132i	−0.983194	+	0.182566i	$0.941560\pi$
$618$			7.21831i			0.290363i
$619$	−10.0964	−	17.4875i	−0.405809	−	0.702883i	0.588606	−	0.808420i	$-0.299677\pi$
$619$	−10.0964	−	17.4875i	−0.405809	−	0.702883i	−0.994415	+	0.105538i	$0.966344\pi$
$620$	0.819458	−	0.713451i	0.0329102	−	0.0286529i
$621$	−10.6027	−	18.3644i	−0.425472	−	0.736939i
$622$	−2.91977	+	1.68573i	−0.117072	+	0.0675917i
$623$	6.43614	+	3.71591i	0.257858	+	0.148875i
$624$	−2.84251	+	4.92337i	−0.113791	+	0.197092i
$625$	17.9300	−	17.4217i	0.717199	−	0.696868i
$626$	15.3150	+	26.5263i	0.612110	+	1.06021i
$627$			0.678499i			0.0270966i
$628$		−	0.637019i		−	0.0254198i
$629$	11.3353	−	19.6333i	0.451969	−	0.782833i
$630$	−0.115618	−	0.592368i	−0.00460631	−	0.0236005i
$631$	−9.26479	−	16.0471i	−0.368826	−	0.638825i	0.620557	−	0.784162i	$-0.286907\pi$
$631$	−9.26479	−	16.0471i	−0.368826	−	0.638825i	−0.989382	+	0.145337i	$0.953573\pi$
$632$	−11.1863	−	6.45842i	−0.444968	−	0.256902i
$633$	−21.5280	+	12.4292i	−0.855661	+	0.494016i
$634$	−2.83541	+	4.91108i	−0.112609	+	0.195044i
$635$	−1.00591	+	2.92869i	−0.0399183	+	0.116222i
$636$	8.57933	−	14.8598i	0.340193	−	0.589231i
$637$	3.31430	+	1.91351i	0.131317	+	0.0758161i
$638$	2.74359	+	1.58401i	0.108620	+	0.0627117i
$639$	−0.670036	+	1.16054i	−0.0265062	+	0.0459101i
$640$	−1.46829	−	1.68645i	−0.0580393	−	0.0666629i
$641$	10.4367	−	18.0769i	0.412226	−	0.713996i	−0.582907	−	0.812539i	$-0.698085\pi$
$641$	10.4367	−	18.0769i	0.412226	−	0.713996i	0.995133	+	0.0985428i	$0.0314181\pi$
$642$	17.2492	−	9.95884i	0.680772	−	0.393044i
$643$			7.05734i			0.278314i	0.990270	+	0.139157i	$0.0444393\pi$
$643$			7.05734i			0.278314i	−0.990270	+	0.139157i	$0.955561\pi$
$644$	−5.01737	+	8.69034i	−0.197712	+	0.342447i
$645$	2.39641	+	12.2781i	0.0943587	+	0.483448i
$646$	0.317770			0.0125025
$647$	20.5407	−	11.8592i	0.807539	−	0.466233i	−0.0385618	−	0.999256i	$-0.512278\pi$
$647$	20.5407	−	11.8592i	0.807539	−	0.466233i	0.846100	+	0.533024i	$0.178944\pi$
$648$			9.32333i			0.366255i
$649$	0.407754	−	0.706250i	0.0160057	−	0.0277227i
$650$	2.21800	−	15.9599i	0.0869969	−	0.626000i
$651$	1.03328	+	1.78970i	0.0404975	+	0.0701438i
$652$	18.9023	−	10.9133i	0.740273	−	0.427397i
$653$	−39.3237	+	22.7035i	−1.53885	+	0.888458i	−0.539948	+	0.841699i	$0.681556\pi$
$653$	−39.3237	+	22.7035i	−1.53885	+	0.888458i	−0.998906	+	0.0467592i	$0.985111\pi$
$654$	−3.94182	−	6.82743i	−0.154137	−	0.266973i
$655$	0.770621	+	3.94829i	0.0301107	+	0.154272i
$656$	7.54210			0.294470
$657$	1.01111	−	0.583764i	0.0394471	−	0.0227748i
$658$	1.56100	+	0.901241i	0.0608540	+	0.0351340i
$659$	4.50497	−	7.80284i	0.175489	−	0.303956i	−0.764842	−	0.644218i	$-0.777183\pi$
$659$	4.50497	−	7.80284i	0.175489	−	0.303956i	0.940330	+	0.340263i	$0.110516\pi$
$660$	7.04908	+	8.09645i	0.274385	+	0.315154i
$661$	19.9612			0.776402			0.388201	−	0.921575i	$-0.373097\pi$
$661$	19.9612			0.776402			0.388201	+	0.921575i	$0.373097\pi$
$662$			29.7594i			1.15663i
$663$	−11.0700	−	6.39125i	−0.429922	−	0.248216i
$664$	−1.30546	−	2.26112i	−0.0506616	−	0.0877484i
$665$	−0.747783	+	0.145951i	−0.0289978	+	0.00565974i
$666$	−0.564410	+	0.977586i	−0.0218704	+	0.0378807i
$667$		−	4.84520i		−	0.187607i
$668$	−4.41022	+	2.54624i	−0.170636	+	0.0985170i
$669$	−16.9015			−0.653449
$670$	−1.24800	+	18.2604i	−0.0482143	+	0.705461i
$671$	−4.64602			−0.179358
$672$	3.68322	−	2.12651i	0.142083	−	0.0820318i
$673$		−	17.3542i		−	0.668954i	−0.942404	−	0.334477i	$-0.891440\pi$
$673$		−	17.3542i		−	0.668954i	0.942404	−	0.334477i	$-0.108560\pi$
$674$	2.59249	−	4.49033i	0.0998591	−	0.172961i
$675$	−9.57890	−	23.6040i	−0.368692	−	0.908519i
$676$	1.30722	+	2.26417i	0.0502776	+	0.0870833i
$677$	13.4017	+	7.73749i	0.515070	+	0.297376i	0.734915	−	0.678159i	$-0.237222\pi$
$677$	13.4017	+	7.73749i	0.515070	+	0.297376i	−0.219845	+	0.975535i	$0.570555\pi$
$678$		−	34.9303i		−	1.34149i
$679$	−21.8915			−0.840120
$680$	3.79191	−	3.30138i	0.145413	−	0.126602i
$681$	18.6432	−	32.2910i	0.714410	−	1.23739i
$682$	−1.14521	−	0.661190i	−0.0438525	−	0.0253183i
$683$	−18.5295	+	10.6980i	−0.709010	+	0.409347i	−0.810694	−	0.585470i	$-0.800910\pi$
$683$	−18.5295	+	10.6980i	−0.709010	+	0.409347i	0.101684	+	0.994817i	$0.467577\pi$
$684$	−0.0158225			−0.000604987
$685$	17.0103	−	3.32004i	0.649929	−	0.126852i
$686$	−9.86969	−	17.0948i	−0.376826	−	0.652682i
$687$	27.6775	−	15.9796i	1.05596	−	0.609660i
$688$	−2.74648	+	1.58568i	−0.104709	+	0.0604536i
$689$	15.6730	+	27.1464i	0.597093	+	1.03420i
$690$	5.33333	−	15.5279i	0.203036	−	0.591137i
$691$	−16.9040	+	29.2787i	−0.643060	+	1.11381i	0.341686	+	0.939814i	$0.389002\pi$
$691$	−16.9040	+	29.2787i	−0.643060	+	1.11381i	−0.984746	+	0.173998i	$0.944331\pi$
$692$		−	0.411772i		−	0.0156532i
$693$	−0.636150	+	0.367281i	−0.0241653	+	0.0139519i
$694$	17.7848			0.675102
$695$	7.04483	+	36.0943i	0.267225	+	1.36913i
$696$	−1.02677	+	1.77841i	−0.0389195	+	0.0674106i
$697$			16.9581i			0.642333i
$698$	29.8380	−	17.2270i	1.12939	−	0.652051i
$699$	16.8879	−	29.2507i	0.638760	−	1.10636i
$700$	−7.40689	+	9.51050i	−0.279954	+	0.359463i
$701$	17.1905	−	29.7749i	0.649277	−	1.12458i	−0.334018	−	0.942567i	$-0.608405\pi$
$701$	17.1905	−	29.7749i	0.649277	−	1.12458i	0.983296	−	0.182015i	$-0.0582619\pi$
$702$	−14.2189	−	8.20929i	−0.536658	−	0.309840i
$703$	1.23407	+	0.712489i	0.0465437	+	0.0268720i
$704$	−1.36074	+	2.35686i	−0.0512846	+	0.0888276i
$705$	−2.78919	−	0.957995i	−0.105047	−	0.0360802i
$706$	13.5339	−	23.4414i	0.509355	−	0.882229i
$707$	17.1316	−	9.89095i	0.644301	−	0.371988i
$708$	0.457796	+	0.264308i	0.0172050	+	0.00993332i
$709$	2.52612	+	4.37537i	0.0948704	+	0.164320i	0.909555	−	0.415585i	$-0.136423\pi$
$709$	2.52612	+	4.37537i	0.0948704	+	0.164320i	−0.814684	+	0.579905i	$0.803090\pi$
$710$	26.2694	−	5.12722i	0.985873	−	0.192421i
$711$	−0.723055	+	1.25237i	−0.0271167	+	0.0469675i
$712$		−	3.08258i		−	0.115525i
$713$			2.02245i			0.0757415i
$714$	4.78136	+	8.28155i	0.178938	+	0.309929i
$715$	−19.2480	+	3.75679i	−0.719834	+	0.140496i
$716$	8.75260	−	15.1599i	0.327100	−	0.566554i
$717$	−5.78859	−	3.34204i	−0.216179	−	0.124811i
$718$	−13.0472	+	7.53280i	−0.486917	+	0.281121i
$719$	−9.13252	−	15.8180i	−0.340586	−	0.589912i	0.643956	−	0.765063i	$-0.277292\pi$
$719$	−9.13252	−	15.8180i	−0.340586	−	0.589912i	−0.984542	+	0.175151i	$0.943959\pi$
$720$	−0.188808	+	0.164383i	−0.00703644	+	0.00612619i
$721$	4.93252	+	8.54338i	0.183697	+	0.318172i
$722$		−	18.9800i		−	0.706363i
$723$		−	1.76936i		−	0.0658031i
$724$	−1.70698	−	2.95658i	−0.0634396	−	0.109881i
$725$	0.801181	−	5.76503i	0.0297551	−	0.214108i
$726$	−3.16969	+	5.49006i	−0.117638	+	0.203755i
$727$	12.2490	−	7.07196i	0.454290	−	0.262284i	−0.255350	−	0.966849i	$-0.582191\pi$
$727$	12.2490	−	7.07196i	0.454290	−	0.262284i	0.709640	+	0.704564i	$0.248857\pi$
$728$			7.76954i			0.287958i
$729$	−25.9186			−0.959948
$730$	−22.0542	−	7.57492i	−0.816264	−	0.280360i
$731$	−3.56534	−	6.17535i	−0.131869	−	0.228403i
$732$		−	3.01158i		−	0.111311i
$733$	−22.4876	−	12.9832i	−0.830598	−	0.479546i	0.0234597	−	0.999725i	$-0.492532\pi$
$733$	−22.4876	−	12.9832i	−0.830598	−	0.479546i	−0.854057	+	0.520179i	$0.825865\pi$
$734$	−27.0019			−0.996656
$735$	3.07592	+	3.53295i	0.113457	+	0.130315i
$736$	4.16223			0.153422
$737$	21.5125	−	5.78284i	0.792423	−	0.213014i
$738$		−	0.844379i		−	0.0310820i
$739$	15.9707	+	27.6621i	0.587492	+	1.01757i	0.994560	+	0.104168i	$0.0332179\pi$
$739$	15.9707	+	27.6621i	0.587492	+	1.01757i	−0.407068	+	0.913398i	$0.633449\pi$
$740$	22.1282	−	4.31895i	0.813449	−	0.158768i
$741$	0.401727	−	0.695811i	0.0147578	−	0.0255613i
$742$		−	23.4502i		−	0.860884i
$743$	16.7375	−	9.66341i	0.614040	−	0.354516i	−0.160505	−	0.987035i	$-0.551312\pi$
$743$	16.7375	−	9.66341i	0.614040	−	0.354516i	0.774545	+	0.632519i	$0.217979\pi$
$744$	0.428587	−	0.742335i	0.0157128	−	0.0272153i
$745$	1.83917	+	9.42301i	0.0673819	+	0.345232i
$746$	22.7736			0.833802
$747$	−0.253144	+	0.146153i	−0.00926207	+	0.00534746i
$748$	−5.29930	−	3.05955i	−0.193762	−	0.111868i
$749$	13.6104	−	23.5740i	0.497315	−	0.861375i
$750$	8.91346	−	17.5939i	0.325474	−	0.642438i
$751$	−17.3260			−0.632235			−0.316118	−	0.948720i	$-0.602379\pi$
$751$	−17.3260			−0.632235			−0.316118	+	0.948720i	$0.602379\pi$
$752$		−	0.747637i		−	0.0272635i
$753$	−3.05067	+	1.76130i	−0.111173	+	0.0641855i
$754$	−1.87573	−	3.24886i	−0.0683101	−	0.118316i
$755$	4.72996	−	4.11808i	0.172141	−	0.149872i
$756$	6.14145	+	10.6373i	0.223362	+	0.386875i
$757$	16.6687	+	9.62367i	0.605833	+	0.349778i	0.771333	−	0.636432i	$-0.219590\pi$
$757$	16.6687	+	9.62367i	0.605833	+	0.349778i	−0.165500	+	0.986210i	$0.552924\pi$
$758$	−13.9785	−	8.07052i	−0.507724	−	0.293134i
$759$	−19.9823			−0.725313
$760$	0.207511	+	0.238343i	0.00752721	+	0.00864562i
$761$	41.0468			1.48795			0.743973	−	0.668210i	$-0.232939\pi$
$761$	41.0468			1.48795			0.743973	+	0.668210i	$0.232939\pi$
$762$			2.44298i			0.0884999i
$763$	−9.33083	−	5.38716i	−0.337799	−	0.195028i
$764$	−10.2040			−0.369168
$765$	−0.369608	−	0.424525i	−0.0133632	−	0.0153487i
$766$	−15.9203	+	27.5748i	−0.575224	+	0.996317i
$767$	−0.836315	+	0.482847i	−0.0301976	+	0.0174346i
$768$	−1.52773	−	0.882037i	−0.0551273	−	0.0318278i
$769$	4.10817	−	7.11556i	0.148144	−	0.256594i	−0.782397	−	0.622780i	$-0.786003\pi$
$769$	4.10817	−	7.11556i	0.148144	−	0.256594i	0.930542	+	0.366186i	$0.119337\pi$
$770$	13.8757	+	4.76584i	0.500044	+	0.171749i
$771$	8.13221	−	14.0854i	0.292874	−	0.507273i
$772$	16.7689	+	9.68154i	0.603526	+	0.348446i
$773$	−34.8767	−	20.1361i	−1.25443	−	0.724244i	−0.282441	−	0.959285i	$-0.591144\pi$
$773$	−34.8767	−	20.1361i	−1.25443	−	0.724244i	−0.971986	+	0.235041i	$0.924478\pi$
$774$	0.177526	+	0.307484i	0.00638103	+	0.0110523i
$775$	−0.334424	+	2.40640i	−0.0120129	+	0.0864406i
$776$	4.54011	+	7.86369i	0.162980	+	0.282290i
$777$			42.8821i			1.53839i
$778$	1.97629	+	1.14101i	0.0708535	+	0.0409073i
$779$	−1.06591			−0.0381903
$780$	−2.43518	−	12.4767i	−0.0871933	−	0.446736i
$781$	−16.2876	−	28.2109i	−0.582816	−	1.00947i
$782$			9.35859i			0.334662i
$783$	−5.13614	−	2.96535i	−0.183551	−	0.105973i
$784$	−0.593767	+	1.02843i	−0.0212060	+	0.0367298i
$785$	0.935329	+	1.07430i	0.0333833	+	0.0383435i
$786$	1.58682	+	2.74846i	0.0566002	+	0.0980344i
$787$	−25.1164	+	14.5009i	−0.895302	+	0.516903i	−0.875673	−	0.482905i	$-0.839582\pi$
$787$	−25.1164	+	14.5009i	−0.895302	+	0.516903i	−0.0196287	+	0.999807i	$0.506248\pi$
$788$	−20.1064	+	11.6085i	−0.716262	+	0.413534i
$789$	−54.1236			−1.92685
$790$	28.3480	−	5.53293i	1.00858	−	0.196853i
$791$	−23.8691	−	41.3424i	−0.848686	−	1.46997i
$792$	0.263863	+	0.152342i	0.00937598	+	0.00541322i
$793$	4.76456	+	2.75082i	0.169195	+	0.0976845i
$794$	14.1939	+	24.5845i	0.503722	+	0.872472i
$795$	7.34991	+	37.6574i	0.260674	+	1.33557i
$796$	−19.6418			−0.696184
$797$	−16.6361	−	9.60483i	−0.589279	−	0.340221i	0.175533	−	0.984474i	$-0.443835\pi$
$797$	−16.6361	−	9.60483i	−0.589279	−	0.340221i	−0.764813	+	0.644253i	$0.777168\pi$
$798$	−0.520543	+	0.300535i	−0.0184270	+	0.0106388i
$799$	1.68103			0.0594705
$800$	4.95240	+	0.688249i	0.175094	+	0.0243333i
$801$	−0.345112			−0.0121939
$802$	−29.8780	+	17.2501i	−1.05503	+	0.609121i
$803$			28.3809i			1.00154i
$804$	3.74847	+	13.9445i	0.132198	+	0.491786i
$805$	−4.29838	−	22.0228i	−0.151498	−	0.776202i
$806$	0.782956	+	1.35612i	0.0275785	+	0.0477673i
$807$		−	18.6826i		−	0.657657i
$808$	−7.10589	−	4.10259i	−0.249984	−	0.144329i
$809$	−37.2453			−1.30948			−0.654738	−	0.755856i	$-0.727221\pi$
$809$	−37.2453			−1.30948			−0.654738	+	0.755856i	$0.727221\pi$
$810$	−13.6894	−	15.7234i	−0.480995	−	0.552463i
$811$	−27.1889	+	47.0925i	−0.954730	+	1.65364i	−0.219745	+	0.975557i	$0.570522\pi$
$811$	−27.1889	+	47.0925i	−0.954730	+	1.65364i	−0.734985	+	0.678083i	$0.762811\pi$
$812$			2.80650i			0.0984889i
$813$			35.2015i			1.23457i
$814$	−13.7200	−	23.7637i	−0.480885	−	0.832917i
$815$	−15.8541	+	46.1588i	−0.555344	+	1.61687i
$816$	1.98322	−	3.43504i	0.0694266	−	0.120250i
$817$	0.388156	−	0.224102i	0.0135799	−	0.00784033i
$818$			19.8893i			0.695413i
$819$	0.869842			0.0303947
$820$	−12.7194	+	11.0740i	−0.444181	+	0.386721i
$821$	2.73355	+	4.73464i	0.0954014	+	0.165240i	0.909776	−	0.415099i	$-0.136253\pi$
$821$	2.73355	+	4.73464i	0.0954014	+	0.165240i	−0.814375	+	0.580339i	$0.802920\pi$
$822$	11.8411	−	6.83647i	0.413006	−	0.238449i
$823$	37.4174	−	21.6030i	1.30429	−	0.753032i	0.323153	−	0.946347i	$-0.395257\pi$
$823$	37.4174	−	21.6030i	1.30429	−	0.753032i	0.981137	+	0.193315i	$0.0619239\pi$
$824$	2.04592	−	3.54364i	0.0712731	−	0.123449i
$825$	−23.7759	−	3.30420i	−0.827770	−	0.115037i
$826$	0.722445			0.0251371
$827$	46.2906	−	26.7259i	1.60968	−	0.929351i	0.620242	−	0.784410i	$-0.287034\pi$
$827$	46.2906	−	26.7259i	1.60968	−	0.929351i	0.989440	−	0.144941i	$-0.0462991\pi$
$828$		−	0.465984i		−	0.0161941i
$829$	3.20355			0.111264			0.0556319	−	0.998451i	$-0.482283\pi$
$829$	3.20355			0.111264			0.0556319	+	0.998451i	$0.482283\pi$
$830$	5.52157	+	1.89648i	0.191657	+	0.0658278i
$831$	−12.4366			−0.431420
$832$	2.79091	−	1.61133i	0.0967574	−	0.0558629i
$833$	−2.31239	−	1.33506i	−0.0801195	−	0.0462570i
$834$	14.5064	+	25.1257i	0.502314	+	0.870033i
$835$	3.69901	−	10.7696i	0.128009	−	0.372697i
$836$	0.192310	−	0.333091i	0.00665119	−	0.0115202i
$837$	2.14390	+	1.23778i	0.0741039	+	0.0427839i
$838$	13.1454	+	7.58951i	0.454101	+	0.262175i
$839$	−18.3076	+	31.7096i	−0.632047	+	1.09474i	0.355086	+	0.934834i	$0.384452\pi$
$839$	−18.3076	+	31.7096i	−0.632047	+	1.09474i	−0.987133	+	0.159904i	$0.948882\pi$
$840$	−3.08925	+	8.99429i	−0.106589	+	0.310332i
$841$	13.8225	+	23.9412i	0.476636	+	0.825558i
$842$	6.83839	+	3.94814i	0.235666	+	0.136062i
$843$	−4.28279	+	2.47267i	−0.147507	+	0.0851632i
$844$	14.0915			0.485048
$845$	−5.52901	−	1.89904i	−0.190204	−	0.0653289i
$846$	−0.0837020			−0.00287773
$847$			8.66383i			0.297693i
$848$	−8.42359	+	4.86336i	−0.289267	+	0.167009i
$849$	−16.0474			−0.550745
$850$	−1.54750	+	11.1353i	−0.0530787	+	0.381936i
$851$	−20.9834	+	36.3443i	−0.719301	+	1.24587i
$852$	18.2865	−	10.5577i	0.626485	−	0.361702i
$853$	38.5128	−	22.2354i	1.31865	−	0.761325i	0.335142	−	0.942168i	$-0.391216\pi$
$853$	38.5128	−	22.2354i	1.31865	−	0.761325i	0.983512	+	0.180842i	$0.0578823\pi$
$854$	−2.05791	−	3.56441i	−0.0704204	−	0.121972i
$855$	0.0266838	−	0.0232319i	0.000912568	−	0.000794516i
$856$	−11.2907			−0.385909
$857$		−	19.3738i		−	0.661795i	−0.943667	−	0.330898i	$-0.892649\pi$
$857$		−	19.3738i		−	0.661795i	0.943667	−	0.330898i	$-0.107351\pi$
$858$	−13.3988	+	7.73580i	−0.457428	+	0.264096i
$859$	−10.2580	+	17.7675i	−0.350000	+	0.606218i	−0.986249	−	0.165266i	$-0.947152\pi$
$859$	−10.2580	+	17.7675i	−0.350000	+	0.606218i	0.636249	+	0.771484i	$0.280485\pi$
$860$	2.30357	−	6.70682i	0.0785512	−	0.228701i
$861$	−16.0383	−	27.7792i	−0.546585	−	0.946713i
$862$		−	24.0223i		−	0.818202i
$863$			24.2047i			0.823937i	0.911198	+	0.411969i	$0.135159\pi$
$863$			24.2047i			0.823937i	−0.911198	+	0.411969i	$0.864841\pi$
$864$	2.54736	−	4.41216i	0.0866630	−	0.150105i
$865$	0.604600	+	0.694434i	0.0205570	+	0.0236115i
$866$	−38.4121			−1.30530
$867$	−18.2479	−	10.5354i	−0.619732	−	0.357802i
$868$		−	1.17147i		−	0.0397624i
$869$	−17.5764	−	30.4432i	−0.596238	−	1.03272i
$870$	−0.879631	−	4.50680i	−0.0298223	−	0.152795i
$871$	−25.4853	−	6.80676i	−0.863537	−	0.230638i
$872$			4.46899i			0.151339i
$873$	0.880383	−	0.508289i	0.0297964	−	0.0172030i
$874$	−0.588240			−0.0198975
$875$	−1.47280	−	26.9145i	−0.0497898	−	0.909875i
$876$	−18.3967			−0.621566
$877$	−12.8436	+	7.41524i	−0.433696	+	0.250395i	−0.700920	−	0.713240i	$-0.747227\pi$
$877$	−12.8436	+	7.41524i	−0.433696	+	0.250395i	0.267224	+	0.963635i	$0.413894\pi$
$878$	24.4752	+	14.1308i	0.825999	+	0.476891i
$879$	−14.2697			−0.481304
$880$	−1.16574	−	5.97269i	−0.0392971	−	0.201339i
$881$	9.22804	+	15.9834i	0.310901	+	0.538496i	0.978558	−	0.205973i	$-0.0660360\pi$
$881$	9.22804	+	15.9834i	0.310901	+	0.538496i	−0.667657	+	0.744469i	$0.732703\pi$
$882$	0.115139	+	0.0664754i	0.00387693	+	0.00223834i
$883$	24.5602	+	14.1798i	0.826516	+	0.477190i	0.852658	−	0.522469i	$-0.174989\pi$
$883$	24.5602	+	14.1798i	0.826516	+	0.477190i	−0.0261420	+	0.999658i	$0.508322\pi$
$884$	3.62301	+	6.27523i	0.121855	+	0.211059i
$885$	−1.16013	+	0.226433i	−0.0389974	+	0.00761146i
$886$	15.7801			0.530143
$887$	−24.8258	+	14.3332i	−0.833569	+	0.481261i	−0.855073	−	0.518508i	$-0.826488\pi$
$887$	−24.8258	+	14.3332i	−0.833569	+	0.481261i	0.0215043	+	0.999769i	$0.493154\pi$
$888$	15.4038	−	8.89337i	0.516917	−	0.298442i
$889$	1.66937	+	2.89144i	0.0559890	+	0.0969759i
$890$	4.52612	+	5.19863i	0.151716	+	0.174258i
$891$	−12.6866	+	21.9738i	−0.425017	+	0.736150i
$892$	8.29733	+	4.79047i	0.277815	+	0.160397i
$893$			0.105662i			0.00353585i
$894$	3.78712	+	6.55949i	0.126660	+	0.219382i
$895$	7.49835	+	38.4179i	0.250642	+	1.28417i
$896$	−2.41091			−0.0805427
$897$	20.4922	+	11.8312i	0.684214	+	0.395031i
$898$			13.8306i			0.461533i
$899$	0.282818	+	0.489856i	0.00943252	+	0.0163376i
$900$	0.0770532	−	0.554448i	0.00256844	−	0.0184816i
$901$	−10.9350	−	18.9401i	−0.364299	−	0.630985i
$902$	17.7757	+	10.2628i	0.591866	+	0.341714i
$903$	11.6808	+	6.74394i	0.388714	+	0.224424i
$904$	−9.90046	+	17.1481i	−0.329284	+	0.570337i
$905$	7.21987	+	2.47979i	0.239997	+	0.0824311i
$906$	2.47383	−	4.28480i	0.0821875	−	0.142353i
$907$	10.9683	+	6.33253i	0.364195	+	0.210268i	0.670920	−	0.741530i	$-0.265900\pi$
$907$	10.9683	+	6.33253i	0.364195	+	0.210268i	−0.306724	+	0.951798i	$0.599233\pi$
$908$	−18.3048	+	10.5683i	−0.607466	+	0.350721i
$909$	−0.459307	+	0.795543i	−0.0152342	+	0.0263865i
$910$	−11.4079	−	13.1030i	−0.378169	−	0.434359i
$911$	−6.34678			−0.210278			−0.105139	−	0.994458i	$-0.533529\pi$
$911$	−6.34678			−0.210278			−0.105139	+	0.994458i	$0.533529\pi$
$912$	0.215912	+	0.124657i	0.00714955	+	0.00412779i
$913$		−	7.10553i		−	0.235159i
$914$	1.74014			0.0575588
$915$	4.42187	+	5.07888i	0.146182	+	0.167903i
$916$	−18.1167			−0.598593
$917$	3.75624	+	2.16866i	0.124042	+	0.0716156i
$918$	9.92054	+	5.72763i	0.327427	+	0.189040i
$919$	18.4277	+	31.9178i	0.607875	+	1.05287i	0.991590	+	0.129419i	$0.0413112\pi$
$919$	18.4277	+	31.9178i	0.607875	+	1.05287i	−0.383715	+	0.923452i	$0.625355\pi$
$920$	−7.01941	+	6.11136i	−0.231423	+	0.201486i
$921$	21.5535	+	37.3317i	0.710212	+	1.23012i
$922$	7.91629	−	4.57047i	0.260709	−	0.150521i
$923$			38.5743i			1.26969i
$924$	11.5745			0.380772
$925$	−30.9767	+	39.7743i	−1.01851	+	1.30777i
$926$	−4.21592	+	7.30219i	−0.138544	+	0.239965i
$927$	−0.396730	−	0.229052i	−0.0130303	−	0.00752305i
$928$	1.00813	−	0.582043i	0.0330934	−	0.0191065i
$929$	47.7857			1.56780			0.783899	−	0.620888i	$-0.213228\pi$
$929$	47.7857			1.56780			0.783899	+	0.620888i	$0.213228\pi$
$930$	0.367170	+	1.88120i	0.0120400	+	0.0616871i
$931$	0.0839160	−	0.145347i	0.00275024	−	0.00476355i
$932$	−16.5814	+	9.57325i	−0.543140	+	0.313582i
$933$		−	5.94751i		−	0.194713i
$934$	−3.79875	+	6.57962i	−0.124299	+	0.215292i
$935$	13.4293	−	2.62112i	0.439186	−	0.0857197i
$936$	−0.180397	−	0.312457i	−0.00589647	−	0.0102130i
$937$		−	38.3610i		−	1.25320i	−0.779341	−	0.626599i	$-0.784446\pi$
$937$		−	38.3610i		−	1.25320i	0.779341	−	0.626599i	$-0.215554\pi$
$938$	13.9654	+	13.9429i	0.455985	+	0.455251i
$939$	−54.0335			−1.76332
$940$	1.09775	+	1.26086i	0.0358046	+	0.0411246i
$941$	54.7699			1.78545			0.892724	−	0.450604i	$-0.148791\pi$
$941$	54.7699			1.78545			0.892724	+	0.450604i	$0.148791\pi$
$942$	0.973195	+	0.561874i	0.0317084	+	0.0183069i
$943$		−	31.3920i		−	1.02226i
$944$	−0.149828	−	0.259511i	−0.00487650	−	0.00844635i
$945$	−25.9759	−	8.92188i	−0.844996	−	0.290229i
$946$	−8.63078			−0.280611
$947$		−	1.39955i		−	0.0454792i	−0.999741	−	0.0227396i	$-0.992761\pi$
$947$		−	1.39955i		−	0.0454792i	0.999741	−	0.0227396i	$-0.00723887\pi$
$948$	19.7335	−	11.3931i	0.640913	−	0.370032i
$949$	16.8038	−	29.1050i	0.545474	−	0.944789i
$950$	−0.699914	−	0.0972690i	−0.0227082	−	0.00315582i
$951$	−5.00188	−	8.66351i	−0.162197	−	0.280933i
$952$		−	5.42081i		−	0.175690i
$953$			24.2122i			0.784310i	0.919899	+	0.392155i	$0.128270\pi$
$953$			24.2122i			0.784310i	−0.919899	+	0.392155i	$0.871730\pi$
$954$	0.544480	+	0.943066i	0.0176282	+	0.0305329i
$955$	17.2086	−	14.9824i	0.556856	−	0.484820i
$956$	1.89450	+	3.28138i	0.0612726	+	0.106127i
$957$	−4.83990	+	2.79432i	−0.156452	+	0.0903274i
$958$	2.53465	+	1.46338i	0.0818907	+	0.0472796i
$959$	9.34319	−	16.1829i	0.301707	−	0.522572i
$960$	3.87154	−	0.755641i	0.124953	−	0.0243882i
$961$	15.3819	+	26.6423i	0.496192	+	0.859430i
$962$			32.4934i			1.04763i
$963$			1.26406i			0.0407337i
$964$	−0.501498	+	0.868620i	−0.0161522	+	0.0279764i
$965$	−42.4953	+	8.29417i	−1.36797	+	0.266999i
$966$	−8.85101	−	15.3304i	−0.284777	−	0.493248i
$967$	35.0274	+	20.2231i	1.12641	+	0.650331i	0.943029	−	0.332712i	$-0.107964\pi$
$967$	35.0274	+	20.2231i	1.12641	+	0.650331i	0.183377	+	0.983043i	$0.441297\pi$
$968$	3.11215	−	1.79680i	0.100028	−	0.0577513i
$969$	−0.280285	+	0.485468i	−0.00900405	+	0.0155955i
$970$	−19.2029	−	6.59556i	−0.616567	−	0.211771i
$971$	24.3181	−	42.1202i	0.780405	−	1.35170i	−0.151302	−	0.988488i	$-0.548346\pi$
$971$	24.3181	−	42.1202i	0.780405	−	1.35170i	0.931706	−	0.363213i	$-0.118320\pi$
$972$	−1.00708	−	0.581437i	−0.0323021	−	0.0186496i
$973$	34.3386	+	19.8254i	1.10084	+	0.635573i
$974$	−11.9373	+	20.6759i	−0.382494	+	0.662500i
$975$	22.4262	+	17.4658i	0.718212	+	0.559352i
$976$	−0.853586	+	1.47845i	−0.0273226	+	0.0473242i
$977$	38.9436	−	22.4841i	1.24591	−	0.719329i	0.275623	−	0.961266i	$-0.411116\pi$
$977$	38.9436	−	22.4841i	1.24591	−	0.719329i	0.970292	+	0.241937i	$0.0777827\pi$
$978$			38.5036i			1.23121i
$979$	4.19458	−	7.26522i	0.134059	−	0.232197i
$980$	−0.508680	−	2.60623i	−0.0162492	−	0.0832529i
$981$	0.500328			0.0159742
$982$	−4.54238	+	2.62255i	−0.144953	+	0.0836888i
$983$		−	7.42753i		−	0.236901i	−0.992960	−	0.118451i	$-0.962207\pi$
$983$		−	7.42753i		−	0.236901i	0.992960	−	0.118451i	$-0.0377928\pi$
$984$	−6.65241	+	11.5223i	−0.212071	+	0.367318i
$985$	16.8640	−	49.0992i	0.537331	−	1.56443i
$986$	1.30870	+	2.26673i	0.0416774	+	0.0721874i
$987$	−2.75371	+	1.58986i	−0.0876516	+	0.0506057i
$988$	−0.394434	+	0.227727i	−0.0125486	+	0.00724495i
$989$	6.59998	+	11.4315i	0.209867	+	0.363501i
$990$	−0.668675	+	0.130511i	−0.0212519	+	0.00414791i
$991$	59.1008			1.87740			0.938700	−	0.344736i	$-0.112032\pi$
$991$	59.1008			1.87740			0.938700	+	0.344736i	$0.112032\pi$
$992$	−0.420807	+	0.242953i	−0.0133606	+	0.00771377i
$993$	−45.4645	−	26.2489i	−1.44277	−	0.832984i
$994$	14.4289	−	24.9916i	0.457657	−	0.792686i
$995$	33.1249	−	28.8398i	1.05013	−	0.914283i
$996$	4.60585			0.145942
$997$			16.4653i			0.521462i	0.965412	+	0.260731i	$0.0839635\pi$
$997$			16.4653i			0.521462i	−0.965412	+	0.260731i	$0.916036\pi$
$998$	−1.42067	−	0.820225i	−0.0449706	−	0.0259638i
$999$	25.6844	+	44.4868i	0.812620	+	1.40750i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.h.c.439.23	yes	52
5.4	even	2	inner	670.2.h.c.439.4	yes	52
67.29	even	3	inner	670.2.h.c.29.10	✓	52
335.29	even	6	inner	670.2.h.c.29.17	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.h.c.29.10	✓	52	67.29	even	3	inner
670.2.h.c.29.17	yes	52	335.29	even	6	inner
670.2.h.c.439.4	yes	52	5.4	even	2	inner
670.2.h.c.439.23	yes	52	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 670 = 2 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	670.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +1.76407i q^{3} +(0.500000 - 0.866025i) q^{4} +(0.428350 + 2.19466i) q^{5} +(0.882037 + 1.52773i) q^{6} +(2.08791 + 1.20545i) q^{7} -1.00000i q^{8} -0.111955 q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +1.76407i q^{3} +(0.500000 - 0.866025i) q^{4} +(0.428350 + 2.19466i) q^{5} +(0.882037 + 1.52773i) q^{6} +(2.08791 + 1.20545i) q^{7} -1.00000i q^{8} -0.111955 q^{9} +(1.46829 + 1.68645i) q^{10} +(1.36074 - 2.35686i) q^{11} +(1.52773 + 0.882037i) q^{12} +(-2.79091 + 1.61133i) q^{13} +2.41091 q^{14} +(-3.87154 + 0.755641i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.94722 - 1.12423i) q^{17} +(-0.0969562 + 0.0559777i) q^{18} +(0.0706641 + 0.122394i) q^{19} +(2.11480 + 0.726366i) q^{20} +(-2.12651 + 3.68322i) q^{21} -2.72147i q^{22} +(-3.60460 + 2.08111i) q^{23} +1.76407 q^{24} +(-4.63303 + 1.88016i) q^{25} +(-1.61133 + 2.79091i) q^{26} +5.09472i q^{27} +(2.08791 - 1.20545i) q^{28} +(-0.582043 + 1.00813i) q^{29} +(-2.97503 + 2.59017i) q^{30} +(0.242953 - 0.420807i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(4.15768 + 2.40044i) q^{33} +(1.12423 - 1.94722i) q^{34} +(-1.75120 + 5.09859i) q^{35} +(-0.0559777 + 0.0969562i) q^{36} +(8.73193 - 5.04138i) q^{37} +(0.122394 + 0.0706641i) q^{38} +(-2.84251 - 4.92337i) q^{39} +(2.19466 - 0.428350i) q^{40} +(-3.77105 + 6.53165i) q^{41} +4.25301i q^{42} -3.17137i q^{43} +(-1.36074 - 2.35686i) q^{44} +(-0.0479561 - 0.245704i) q^{45} +(-2.08111 + 3.60460i) q^{46} +(0.647473 + 0.373819i) q^{47} +(1.52773 - 0.882037i) q^{48} +(-0.593767 - 1.02843i) q^{49} +(-3.07224 + 3.94478i) q^{50} +(1.98322 + 3.43504i) q^{51} +3.22266i q^{52} -9.72672i q^{53} +(2.54736 + 4.41216i) q^{54} +(5.75537 + 1.97678i) q^{55} +(1.20545 - 2.08791i) q^{56} +(-0.215912 + 0.124657i) q^{57} +1.16409i q^{58} +0.299657 q^{59} +(-1.28136 + 3.73067i) q^{60} +(-0.853586 - 1.47845i) q^{61} -0.485906i q^{62} +(-0.233752 - 0.134957i) q^{63} -1.00000 q^{64} +(-4.73181 - 5.43487i) q^{65} +4.80087 q^{66} +(5.79258 + 5.78325i) q^{67} -2.24845i q^{68} +(-3.67124 - 6.35877i) q^{69} +(1.03271 + 5.29111i) q^{70} +(5.98485 - 10.3661i) q^{71} +0.111955i q^{72} +(-9.03136 + 5.21426i) q^{73} +(5.04138 - 8.73193i) q^{74} +(-3.31674 - 8.17301i) q^{75} +0.141328 q^{76} +(5.68217 - 3.28060i) q^{77} +(-4.92337 - 2.84251i) q^{78} +(6.45842 - 11.1863i) q^{79} +(1.68645 - 1.46829i) q^{80} -9.32333 q^{81} +7.54210i q^{82} +(2.26112 - 1.30546i) q^{83} +(2.12651 + 3.68322i) q^{84} +(3.30138 + 3.79191i) q^{85} +(-1.58568 - 2.74648i) q^{86} +(-1.77841 - 1.02677i) q^{87} +(-2.35686 - 1.36074i) q^{88} +3.08258 q^{89} +(-0.164383 - 0.188808i) q^{90} -7.76954 q^{91} +4.16223i q^{92} +(0.742335 + 0.428587i) q^{93} +0.747637 q^{94} +(-0.238343 + 0.207511i) q^{95} +(0.882037 - 1.52773i) q^{96} +(-7.86369 + 4.54011i) q^{97} +(-1.02843 - 0.593767i) q^{98} +(-0.152342 + 0.263863i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 26 q^{4} - 16 q^{5} - 6 q^{6} - 48 q^{9}+O(q^{10}) \) 52 * q + 26 * q^4 - 16 * q^5 - 6 * q^6 - 48 * q^9	\( 52 q + 26 q^{4} - 16 q^{5} - 6 q^{6} - 48 q^{9} - 10 q^{10} + 24 q^{11} + 24 q^{14} + 28 q^{15} - 26 q^{16} - 24 q^{19} - 8 q^{20} + 4 q^{21} - 12 q^{24} - 28 q^{25} + 4 q^{26} - 20 q^{29} - 10 q^{30} - 30 q^{31} - 16 q^{34} - 14 q^{35} - 24 q^{36} - 8 q^{39} - 20 q^{40} - 10 q^{41} - 24 q^{44} - 16 q^{45} - 8 q^{46} + 14 q^{49} - 8 q^{50} - 44 q^{51} + 42 q^{54} + 16 q^{55} + 12 q^{56} + 80 q^{59} + 14 q^{60} - 20 q^{61} - 52 q^{64} + 10 q^{65} - 40 q^{66} - 4 q^{69} + 48 q^{70} - 74 q^{71} + 34 q^{74} - 16 q^{75} - 48 q^{76} + 32 q^{79} + 8 q^{80} + 4 q^{81} - 4 q^{84} + 20 q^{85} + 12 q^{86} + 84 q^{89} - 30 q^{90} - 16 q^{91} + 136 q^{94} + 2 q^{95} - 6 q^{96} - 96 q^{99}+O(q^{100}) \) 52 * q + 26 * q^4 - 16 * q^5 - 6 * q^6 - 48 * q^9 - 10 * q^10 + 24 * q^11 + 24 * q^14 + 28 * q^15 - 26 * q^16 - 24 * q^19 - 8 * q^20 + 4 * q^21 - 12 * q^24 - 28 * q^25 + 4 * q^26 - 20 * q^29 - 10 * q^30 - 30 * q^31 - 16 * q^34 - 14 * q^35 - 24 * q^36 - 8 * q^39 - 20 * q^40 - 10 * q^41 - 24 * q^44 - 16 * q^45 - 8 * q^46 + 14 * q^49 - 8 * q^50 - 44 * q^51 + 42 * q^54 + 16 * q^55 + 12 * q^56 + 80 * q^59 + 14 * q^60 - 20 * q^61 - 52 * q^64 + 10 * q^65 - 40 * q^66 - 4 * q^69 + 48 * q^70 - 74 * q^71 + 34 * q^74 - 16 * q^75 - 48 * q^76 + 32 * q^79 + 8 * q^80 + 4 * q^81 - 4 * q^84 + 20 * q^85 + 12 * q^86 + 84 * q^89 - 30 * q^90 - 16 * q^91 + 136 * q^94 + 2 * q^95 - 6 * q^96 - 96 * q^99

Introduction

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