LMFDB - Embedded newform 670.2.h.c.439.19

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			439.19
Character	$\chi$	$=$	670.439
Dual form			670.2.h.c.29.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} -1.04987i q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.0350949 - 2.23579i) q^{5} +(-0.524935 - 0.909214i) q^{6} +(0.779249 + 0.449900i) q^{7} -1.00000i q^{8} +1.89777 q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} -1.04987i q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.0350949 - 2.23579i) q^{5} +(-0.524935 - 0.909214i) q^{6} +(0.779249 + 0.449900i) q^{7} -1.00000i q^{8} +1.89777 q^{9} +(-1.14829 - 1.91871i) q^{10} +(3.00535 - 5.20541i) q^{11} +(-0.909214 - 0.524935i) q^{12} +(-5.41531 + 3.12653i) q^{13} +0.899799 q^{14} +(-2.34729 + 0.0368451i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.60685 + 0.927714i) q^{17} +(1.64352 - 0.948887i) q^{18} +(2.52338 + 4.37063i) q^{19} +(-1.95380 - 1.08750i) q^{20} +(0.472336 - 0.818110i) q^{21} -6.01069i q^{22} +(0.762026 - 0.439956i) q^{23} -1.04987 q^{24} +(-4.99754 + 0.156930i) q^{25} +(-3.12653 + 5.41531i) q^{26} -5.14202i q^{27} +(0.779249 - 0.449900i) q^{28} +(3.25459 - 5.63712i) q^{29} +(-2.01439 + 1.20555i) q^{30} +(-4.73376 + 8.19912i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-5.46500 - 3.15522i) q^{33} +(-0.927714 + 1.60685i) q^{34} +(0.978535 - 1.75803i) q^{35} +(0.948887 - 1.64352i) q^{36} +(4.82799 - 2.78744i) q^{37} +(4.37063 + 2.52338i) q^{38} +(3.28245 + 5.68537i) q^{39} +(-2.23579 + 0.0350949i) q^{40} +(1.76857 - 3.06326i) q^{41} -0.944672i q^{42} -0.284949i q^{43} +(-3.00535 - 5.20541i) q^{44} +(-0.0666022 - 4.24303i) q^{45} +(0.439956 - 0.762026i) q^{46} +(-4.96644 - 2.86738i) q^{47} +(-0.909214 + 0.524935i) q^{48} +(-3.09518 - 5.36101i) q^{49} +(-4.24953 + 2.63467i) q^{50} +(0.973979 + 1.68698i) q^{51} +6.25306i q^{52} +7.19683i q^{53} +(-2.57101 - 4.45312i) q^{54} +(-11.7437 - 6.53665i) q^{55} +(0.449900 - 0.779249i) q^{56} +(4.58859 - 2.64922i) q^{57} -6.50919i q^{58} -1.23160 q^{59} +(-1.14174 + 2.05124i) q^{60} +(6.28859 + 10.8922i) q^{61} +9.46753i q^{62} +(1.47884 + 0.853808i) q^{63} -1.00000 q^{64} +(7.18032 + 11.9978i) q^{65} -6.31044 q^{66} +(6.69356 + 4.71129i) q^{67} +1.85543i q^{68} +(-0.461897 - 0.800028i) q^{69} +(-0.0315784 - 2.01176i) q^{70} +(-2.52497 + 4.37338i) q^{71} -1.89777i q^{72} +(1.36943 - 0.790643i) q^{73} +(2.78744 - 4.82799i) q^{74} +(0.164756 + 5.24676i) q^{75} +5.04677 q^{76} +(4.68383 - 2.70421i) q^{77} +(5.68537 + 3.28245i) q^{78} +(-2.05844 + 3.56532i) q^{79} +(-1.91871 + 1.14829i) q^{80} +0.294869 q^{81} -3.53715i q^{82} +(4.76407 - 2.75054i) q^{83} +(-0.472336 - 0.818110i) q^{84} +(2.13057 + 3.56002i) q^{85} +(-0.142474 - 0.246773i) q^{86} +(-5.91824 - 3.41690i) q^{87} +(-5.20541 - 3.00535i) q^{88} +18.2765 q^{89} +(-2.17919 - 3.64127i) q^{90} -5.62650 q^{91} -0.879912i q^{92} +(8.60801 + 4.96984i) q^{93} -5.73475 q^{94} +(9.68326 - 5.79515i) q^{95} +(-0.524935 + 0.909214i) q^{96} +(5.97904 - 3.45200i) q^{97} +(-5.36101 - 3.09518i) q^{98} +(5.70347 - 9.87870i) 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
$3$		−	1.04987i		−	0.606142i	−0.952968	−	0.303071i	$-0.901988\pi$
$3$		−	1.04987i		−	0.606142i	0.952968	−	0.303071i	$-0.0980120\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.0350949	−	2.23579i	−0.0156949	−	0.999877i
$5$	−0.0350949	−	2.23579i	−0.0156949	−	0.999877i
$6$	−0.524935	−	0.909214i	−0.214304	−	0.371185i
$7$	0.779249	+	0.449900i	0.294528	+	0.170046i	0.639982	−	0.768390i	$-0.278942\pi$
$7$	0.779249	+	0.449900i	0.294528	+	0.170046i	−0.345454	+	0.938436i	$0.612275\pi$
$8$		−	1.00000i		−	0.353553i
$9$	1.89777			0.632591
$10$	−1.14829	−	1.91871i	−0.363121	−	0.606748i
$11$	3.00535	−	5.20541i	0.906146	−	1.56949i	0.0867746	−	0.996228i	$-0.472344\pi$
$11$	3.00535	−	5.20541i	0.906146	−	1.56949i	0.819371	−	0.573263i	$-0.194323\pi$
$12$	−0.909214	−	0.524935i	−0.262467	−	0.151536i
$13$	−5.41531	+	3.12653i	−1.50194	+	0.867144i	−0.501939	+	0.864903i	$0.667380\pi$
$13$	−5.41531	+	3.12653i	−1.50194	+	0.867144i	−0.999997	+	0.00224065i	$0.999287\pi$
$14$	0.899799			0.240481
$15$	−2.34729	+	0.0368451i	−0.606068	+	0.00951335i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.60685	+	0.927714i	−0.389718	+	0.225004i	−0.682038	−	0.731317i	$-0.738906\pi$
$17$	−1.60685	+	0.927714i	−0.389718	+	0.225004i	0.292320	+	0.956321i	$0.405573\pi$
$18$	1.64352	−	0.948887i	0.387382	−	0.223655i
$19$	2.52338	+	4.37063i	0.578904	+	1.00269i	0.995605	+	0.0936477i	$0.0298527\pi$
$19$	2.52338	+	4.37063i	0.578904	+	1.00269i	−0.416701	+	0.909043i	$0.636814\pi$
$20$	−1.95380	−	1.08750i	−0.436883	−	0.243173i
$21$	0.472336	−	0.818110i	0.103072	−	0.178526i
$22$		−	6.01069i		−	1.28148i
$23$	0.762026	−	0.439956i	0.158894	−	0.0917372i	−0.418445	−	0.908242i	$-0.637425\pi$
$23$	0.762026	−	0.439956i	0.158894	−	0.0917372i	0.577338	+	0.816505i	$0.304091\pi$
$24$	−1.04987			−0.214304
$25$	−4.99754	+	0.156930i	−0.999507	+	0.0313860i
$26$	−3.12653	+	5.41531i	−0.613163	+	1.06203i
$27$		−	5.14202i		−	0.989583i
$28$	0.779249	−	0.449900i	0.147264	−	0.0850230i
$29$	3.25459	−	5.63712i	0.604363	−	1.04679i	−0.387789	−	0.921748i	$-0.626761\pi$
$29$	3.25459	−	5.63712i	0.604363	−	1.04679i	0.992152	−	0.125039i	$-0.0399057\pi$
$30$	−2.01439	+	1.20555i	−0.367776	+	0.220103i
$31$	−4.73376	+	8.19912i	−0.850209	+	1.47261i	0.0308101	+	0.999525i	$0.490191\pi$
$31$	−4.73376	+	8.19912i	−0.850209	+	1.47261i	−0.881019	+	0.473080i	$0.843142\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−5.46500	−	3.15522i	−0.951335	−	0.549254i
$34$	−0.927714	+	1.60685i	−0.159102	+	0.275572i
$35$	0.978535	−	1.75803i	0.165403	−	0.297161i
$36$	0.948887	−	1.64352i	0.158148	−	0.273920i
$37$	4.82799	−	2.78744i	0.793717	−	0.458253i	−0.0475523	−	0.998869i	$-0.515142\pi$
$37$	4.82799	−	2.78744i	0.793717	−	0.458253i	0.841270	+	0.540616i	$0.181809\pi$
$38$	4.37063	+	2.52338i	0.709010	+	0.409347i
$39$	3.28245	+	5.68537i	0.525612	+	0.910388i
$40$	−2.23579	+	0.0350949i	−0.353510	+	0.00554899i
$41$	1.76857	−	3.06326i	0.276205	−	0.478401i	−0.694233	−	0.719750i	$-0.744256\pi$
$41$	1.76857	−	3.06326i	0.276205	−	0.478401i	0.970438	+	0.241349i	$0.0775898\pi$
$42$		−	0.944672i		−	0.145766i
$43$		−	0.284949i		−	0.0434542i	−0.999764	−	0.0217271i	$-0.993083\pi$
$43$		−	0.284949i		−	0.0434542i	0.999764	−	0.0217271i	$-0.00691650\pi$
$44$	−3.00535	−	5.20541i	−0.453073	−	0.784745i
$45$	−0.0666022	−	4.24303i	−0.00992847	−	0.632513i
$46$	0.439956	−	0.762026i	0.0648680	−	0.112355i
$47$	−4.96644	−	2.86738i	−0.724430	−	0.418250i	0.0919509	−	0.995764i	$-0.470690\pi$
$47$	−4.96644	−	2.86738i	−0.724430	−	0.418250i	−0.816381	+	0.577514i	$0.804023\pi$
$48$	−0.909214	+	0.524935i	−0.131234	+	0.0757678i
$49$	−3.09518	−	5.36101i	−0.442169	−	0.765859i
$50$	−4.24953	+	2.63467i	−0.600974	+	0.372599i
$51$	0.973979	+	1.68698i	0.136384	+	0.236225i
$52$			6.25306i			0.867144i
$53$			7.19683i			0.988561i	0.869303	+	0.494280i	$0.164568\pi$
$53$			7.19683i			0.988561i	−0.869303	+	0.494280i	$0.835432\pi$
$54$	−2.57101	−	4.45312i	−0.349870	−	0.605993i
$55$	−11.7437	−	6.53665i	−1.58352	−	0.881401i
$56$	0.449900	−	0.779249i	0.0601204	−	0.104132i
$57$	4.58859	−	2.64922i	0.607774	−	0.350898i
$58$		−	6.50919i		−	0.854698i
$59$	−1.23160			−0.160341			−0.0801707	−	0.996781i	$-0.525547\pi$
$59$	−1.23160			−0.160341			−0.0801707	+	0.996781i	$0.525547\pi$
$60$	−1.14174	+	2.05124i	−0.147398	+	0.264813i
$61$	6.28859	+	10.8922i	0.805172	+	1.39460i	0.916175	+	0.400778i	$0.131260\pi$
$61$	6.28859	+	10.8922i	0.805172	+	1.39460i	−0.111004	+	0.993820i	$0.535407\pi$
$62$			9.46753i			1.20238i
$63$	1.47884	+	0.853808i	0.186316	+	0.107570i
$64$	−1.00000			−0.125000
$65$	7.18032	+	11.9978i	0.890610	+	1.48814i
$66$	−6.31044			−0.776762
$67$	6.69356	+	4.71129i	0.817749	+	0.575575i
$67$	6.69356	+	4.71129i	0.817749	+	0.575575i
$68$			1.85543i			0.225004i
$69$	−0.461897	−	0.800028i	−0.0556058	−	0.0963121i
$70$	−0.0315784	−	2.01176i	−0.00377434	−	0.240452i
$71$	−2.52497	+	4.37338i	−0.299659	+	0.519025i	−0.976058	−	0.217511i	$-0.930206\pi$
$71$	−2.52497	+	4.37338i	−0.299659	+	0.519025i	0.676399	+	0.736536i	$0.263540\pi$
$72$		−	1.89777i		−	0.223655i
$73$	1.36943	−	0.790643i	0.160280	−	0.0925378i	−0.417715	−	0.908578i	$-0.637169\pi$
$73$	1.36943	−	0.790643i	0.160280	−	0.0925378i	0.577995	+	0.816041i	$0.303835\pi$
$74$	2.78744	−	4.82799i	0.324034	−	0.561243i
$75$	0.164756	+	5.24676i	0.0190244	+	0.605844i
$76$	5.04677			0.578904
$77$	4.68383	−	2.70421i	0.533772	−	0.308173i
$78$	5.68537	+	3.28245i	0.643741	+	0.371664i
$79$	−2.05844	+	3.56532i	−0.231593	+	0.401130i	−0.958277	−	0.285841i	$-0.907727\pi$
$79$	−2.05844	+	3.56532i	−0.231593	+	0.401130i	0.726684	+	0.686971i	$0.241060\pi$
$80$	−1.91871	+	1.14829i	−0.214518	+	0.128383i
$81$	0.294869			0.0327632
$82$		−	3.53715i		−	0.390613i
$83$	4.76407	−	2.75054i	0.522925	−	0.301911i	−0.215206	−	0.976569i	$-0.569042\pi$
$83$	4.76407	−	2.75054i	0.522925	−	0.301911i	0.738130	+	0.674658i	$0.235709\pi$
$84$	−0.472336	−	0.818110i	−0.0515361	−	0.0892631i
$85$	2.13057	+	3.56002i	0.231093	+	0.386138i
$86$	−0.142474	−	0.246773i	−0.0153634	−	0.0266102i
$87$	−5.91824	−	3.41690i	−0.634502	−	0.366330i
$88$	−5.20541	−	3.00535i	−0.554899	−	0.320371i
$89$	18.2765			1.93731			0.968654	−	0.248414i	$-0.0799093\pi$
$89$	18.2765			1.93731			0.968654	+	0.248414i	$0.0799093\pi$
$90$	−2.17919	−	3.64127i	−0.229707	−	0.383824i
$91$	−5.62650			−0.589817
$92$		−	0.879912i		−	0.0917372i
$93$	8.60801	+	4.96984i	0.892609	+	0.515348i
$94$	−5.73475			−0.591495
$95$	9.68326	−	5.79515i	0.993482	−	0.594570i
$96$	−0.524935	+	0.909214i	−0.0535759	+	0.0927962i
$97$	5.97904	−	3.45200i	0.607079	−	0.350497i	−0.164742	−	0.986337i	$-0.552679\pi$
$97$	5.97904	−	3.45200i	0.607079	−	0.350497i	0.771822	+	0.635839i	$0.219346\pi$
$98$	−5.36101	−	3.09518i	−0.541544	−	0.312660i
$99$	5.70347	−	9.87870i	0.573220	−	0.992846i
$100$	−2.36286	+	4.40646i	−0.236286	+	0.440646i
$101$	−2.41669	+	4.18582i	−0.240469	+	0.416505i	−0.960848	−	0.277076i	$-0.910635\pi$
$101$	−2.41669	+	4.18582i	−0.240469	+	0.416505i	0.720379	+	0.693581i	$0.243968\pi$
$102$	1.68698	+	0.973979i	0.167036	+	0.0964383i
$103$	−4.08432	−	2.35809i	−0.402440	−	0.232349i	0.285096	−	0.958499i	$-0.407975\pi$
$103$	−4.08432	−	2.35809i	−0.402440	−	0.232349i	−0.687536	+	0.726150i	$0.741308\pi$
$104$	3.12653	+	5.41531i	0.306582	+	0.531015i
$105$	−1.84570	−	1.02733i	−0.180122	−	0.100258i
$106$	3.59842	+	6.23264i	0.349509	+	0.605367i
$107$			13.3224i			1.28793i	0.765056	+	0.643964i	$0.222711\pi$
$107$			13.3224i			1.28793i	−0.765056	+	0.643964i	$0.777289\pi$
$108$	−4.45312	−	2.57101i	−0.428502	−	0.247396i
$109$	17.1530			1.64296			0.821479	−	0.570239i	$-0.193149\pi$
$109$	17.1530			1.64296			0.821479	+	0.570239i	$0.193149\pi$
$110$	−13.4387	+	0.210945i	−1.28133	+	0.0201128i
$111$	−2.92645	−	5.06876i	−0.277766	−	0.481106i
$112$		−	0.899799i		−	0.0850230i
$113$	0.859123	+	0.496015i	0.0808195	+	0.0466612i	0.539865	−	0.841752i	$-0.318475\pi$
$113$	0.859123	+	0.496015i	0.0808195	+	0.0466612i	−0.459046	+	0.888413i	$0.651809\pi$
$114$	2.64922	−	4.58859i	0.248123	−	0.429761i
$115$	−1.01039	−	1.68829i	−0.0942197	−	0.157434i
$116$	−3.25459	−	5.63712i	−0.302182	−	0.523394i
$117$	−10.2770	+	5.93345i	−0.950112	+	0.548548i
$118$	−1.06660	+	0.615802i	−0.0981886	+	0.0566892i
$119$	−1.66951			−0.153044
$120$	0.0368451	+	2.34729i	0.00336348	+	0.214277i
$121$	−12.5642	−	21.7619i	−1.14220	−	1.97835i
$122$	10.8922	+	6.28859i	0.986130	+	0.569342i
$123$	−3.21602	−	1.85677i	−0.289979	−	0.167420i
$124$	4.73376	+	8.19912i	0.425105	+	0.736303i
$125$	0.526250	+	11.1679i	0.0470693	+	0.998892i
$126$	1.70762			0.152127
$127$	8.95679	+	5.17121i	0.794787	+	0.458870i	0.841645	−	0.540031i	$-0.181588\pi$
$127$	8.95679	+	5.17121i	0.794787	+	0.458870i	−0.0468584	+	0.998902i	$0.514921\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−0.299159			−0.0263395
$130$	12.2172	+	6.80022i	1.07152	+	0.596419i
$131$	−10.4556			−0.913506			−0.456753	−	0.889594i	$-0.650988\pi$
$131$	−10.4556			−0.913506			−0.456753	+	0.889594i	$0.650988\pi$
$132$	−5.46500	+	3.15522i	−0.475668	+	0.274627i
$133$			4.54108i			0.393761i
$134$	8.15244	+	0.733312i	0.704263	+	0.0633485i
$135$	−11.4965	+	0.180459i	−0.989461	+	0.0155314i
$136$	0.927714	+	1.60685i	0.0795508	+	0.137786i
$137$		−	5.65700i		−	0.483310i	−0.970362	−	0.241655i	$-0.922310\pi$
$137$		−	5.65700i		−	0.483310i	0.970362	−	0.241655i	$-0.0776902\pi$
$138$	−0.800028	−	0.461897i	−0.0681029	−	0.0393192i
$139$	1.37294			0.116451			0.0582257	−	0.998303i	$-0.481456\pi$
$139$	1.37294			0.116451			0.0582257	+	0.998303i	$0.481456\pi$
$140$	−1.03323	−	1.72645i	−0.0873239	−	0.145912i
$141$	−3.01037	+	5.21412i	−0.253519	+	0.439108i
$142$			5.04995i			0.423782i
$143$			37.5852i			3.14303i
$144$	−0.948887	−	1.64352i	−0.0790739	−	0.136960i
$145$	−12.7177	−	7.07876i	−1.05614	−	0.587859i
$146$	0.790643	−	1.36943i	0.0654341	−	0.113335i
$147$	−5.62836	+	3.24954i	−0.464219	+	0.268017i
$148$		−	5.57489i		−	0.458253i
$149$	0.478368			0.0391895			0.0195947	−	0.999808i	$-0.493762\pi$
$149$	0.478368			0.0391895			0.0195947	+	0.999808i	$0.493762\pi$
$150$	2.76606	+	4.46145i	0.225848	+	0.364276i
$151$	2.99474	+	5.18704i	0.243709	+	0.422116i	0.961768	−	0.273866i	$-0.0883026\pi$
$151$	2.99474	+	5.18704i	0.243709	+	0.422116i	−0.718059	+	0.695982i	$0.754969\pi$
$152$	4.37063	−	2.52338i	0.354505	−	0.204673i
$153$	−3.04943	+	1.76059i	−0.246532	+	0.142335i
$154$	2.70421	−	4.68383i	0.217911	−	0.377434i
$155$	18.4977	+	10.2960i	1.48577	+	0.826992i
$156$	6.56490			0.525612
$157$	17.6066	−	10.1652i	1.40516	−	0.811271i	0.410246	−	0.911975i	$-0.365443\pi$
$157$	17.6066	−	10.1652i	1.40516	−	0.811271i	0.994916	+	0.100704i	$0.0321095\pi$
$158$			4.11688i			0.327521i
$159$	7.55573			0.599209
$160$	−1.08750	+	1.95380i	−0.0859747	+	0.154461i
$161$	0.791745			0.0623982
$162$	0.255364	−	0.147434i	0.0200633	−	0.0115835i
$163$	−17.1947	−	9.92734i	−1.34679	−	0.777569i	−0.358996	−	0.933339i	$-0.616881\pi$
$163$	−17.1947	−	9.92734i	−1.34679	−	0.777569i	−0.987793	+	0.155770i	$0.950214\pi$
$164$	−1.76857	−	3.06326i	−0.138102	−	0.239201i
$165$	−6.86263	+	12.3293i	−0.534255	+	0.959838i
$166$	2.75054	−	4.76407i	0.213483	−	0.369764i
$167$	1.93052	+	1.11458i	0.149388	+	0.0862492i	0.572831	−	0.819674i	$-0.305845\pi$
$167$	1.93052	+	1.11458i	0.149388	+	0.0862492i	−0.423443	+	0.905923i	$0.639179\pi$
$168$	−0.818110	−	0.472336i	−0.0631185	−	0.0364415i
$169$	13.0504	−	22.6039i	1.00388	−	1.73876i
$170$	3.62514	+	2.01778i	0.278035	+	0.154757i
$171$	4.78881	+	8.29447i	0.366210	+	0.634294i
$172$	−0.246773	−	0.142474i	−0.0188162	−	0.0108636i
$173$	−2.99209	+	1.72749i	−0.227485	+	0.131338i	−0.609411	−	0.792854i	$-0.708594\pi$
$173$	−2.99209	+	1.72749i	−0.227485	+	0.131338i	0.381926	+	0.924193i	$0.375261\pi$
$174$	−6.83380			−0.518069
$175$	−3.96493	−	2.12610i	−0.299720	−	0.160718i
$176$	−6.01069			−0.453073
$177$			1.29302i			0.0971897i
$178$	15.8279	−	9.13826i	1.18635	−	0.684942i
$179$	−16.3222			−1.21998			−0.609990	−	0.792409i	$-0.708827\pi$
$179$	−16.3222			−1.21998			−0.609990	+	0.792409i	$0.708827\pi$
$180$	−3.70787	−	2.06384i	−0.276368	−	0.153829i
$181$	−8.40572	+	14.5591i	−0.624792	+	1.08217i	0.363789	+	0.931481i	$0.381483\pi$
$181$	−8.40572	+	14.5591i	−0.624792	+	1.08217i	−0.988581	+	0.150690i	$0.951850\pi$
$182$	−4.87269	+	2.81325i	−0.361188	+	0.208532i
$183$	11.4353	−	6.60220i	0.845325	−	0.488049i
$184$	−0.439956	−	0.762026i	−0.0324340	−	0.0561773i
$185$	−6.40158	−	10.6966i	−0.470654	−	0.786427i
$186$	9.93967			0.728812
$187$			11.1524i			0.815545i
$188$	−4.96644	+	2.86738i	−0.362215	+	0.209125i
$189$	2.31339	−	4.00692i	0.168275	−	0.291460i
$190$	5.48838	−	9.86038i	0.398169	−	0.715347i
$191$	−9.37152	−	16.2319i	−0.678099	−	1.17450i	−0.975553	−	0.219766i	$-0.929471\pi$
$191$	−9.37152	−	16.2319i	−0.678099	−	1.17450i	0.297454	−	0.954736i	$-0.403863\pi$
$192$			1.04987i			0.0757678i
$193$			12.6015i			0.907074i	0.891237	+	0.453537i	$0.149838\pi$
$193$			12.6015i			0.907074i	−0.891237	+	0.453537i	$0.850162\pi$
$194$	3.45200	−	5.97904i	0.247839	−	0.429270i
$195$	12.5961	−	7.53840i	0.902026	−	0.539836i
$196$	−6.19036			−0.442169
$197$	3.93943	+	2.27443i	0.280673	+	0.162047i	0.633728	−	0.773556i	$-0.281524\pi$
$197$	3.93943	+	2.27443i	0.280673	+	0.162047i	−0.353055	+	0.935603i	$0.614857\pi$
$198$		−	11.4069i		−	0.810656i
$199$	−1.21127	−	2.09798i	−0.0858647	−	0.148722i	0.819895	−	0.572514i	$-0.194032\pi$
$199$	−1.21127	−	2.09798i	−0.0858647	−	0.148722i	−0.905759	+	0.423792i	$0.860699\pi$
$200$	0.156930	+	4.99754i	0.0110966	+	0.353379i
$201$	4.94624	−	7.02737i	0.348881	−	0.495672i
$202$			4.83337i			0.340075i
$203$	5.07228	−	2.92848i	0.356004	−	0.205539i
$204$	1.94796			0.136384
$205$	−6.91088	−	3.84666i	−0.482677	−	0.268662i
$206$	−4.71617			−0.328591
$207$	1.44615	−	0.834937i	0.100515	−	0.0580322i
$208$	5.41531	+	3.12653i	0.375484	+	0.216786i
$209$	30.3346			2.09829
$210$	−2.11209	+	0.0331532i	−0.145748	+	0.00228779i
$211$	7.21988	+	12.5052i	0.497037	+	0.860893i	0.999994	−	0.00341831i	$-0.00108809\pi$
$211$	7.21988	+	12.5052i	0.497037	+	0.860893i	−0.502957	+	0.864311i	$0.667755\pi$
$212$	6.23264	+	3.59842i	0.428059	+	0.247140i
$213$	4.59148	+	2.65089i	0.314603	+	0.181636i
$214$	6.66122	+	11.5376i	0.455351	+	0.788692i
$215$	−0.637086	+	0.0100002i	−0.0434489	+	0.000682011i
$216$	−5.14202			−0.349870
$217$	−7.37756	+	4.25944i	−0.500822	+	0.289150i
$218$	14.8549	−	8.57649i	1.00610	−	0.580873i
$219$	−0.830072	−	1.43773i	−0.0560911	−	0.0971526i
$220$	−11.5328	+	6.90201i	−0.777538	+	0.465334i
$221$	5.80105	−	10.0477i	0.390221	−	0.675883i
$222$	−5.06876	−	2.92645i	−0.340193	−	0.196411i
$223$			11.1028i			0.743498i	0.928333	+	0.371749i	$0.121242\pi$
$223$			11.1028i			0.743498i	−0.928333	+	0.371749i	$0.878758\pi$
$224$	−0.449900	−	0.779249i	−0.0300602	−	0.0520658i
$225$	−9.48420	+	0.297817i	−0.632280	+	0.0198545i
$226$	0.992030			0.0659888
$227$	13.3033	+	7.68064i	0.882969	+	0.509782i	0.871636	−	0.490154i	$-0.163059\pi$
$227$	13.3033	+	7.68064i	0.882969	+	0.509782i	0.0113326	+	0.999936i	$0.496393\pi$
$228$		−	5.29845i		−	0.350898i
$229$	−6.57157	−	11.3823i	−0.434261	−	0.752163i	0.562974	−	0.826475i	$-0.309657\pi$
$229$	−6.57157	−	11.3823i	−0.434261	−	0.752163i	−0.997235	+	0.0743121i	$0.976324\pi$
$230$	−1.71917	−	0.956908i	−0.113359	−	0.0630966i
$231$	−2.83907	−	4.91741i	−0.186797	−	0.323542i
$232$	−5.63712	−	3.25459i	−0.370095	−	0.213675i
$233$	−21.9553	−	12.6759i	−1.43834	−	0.830424i	−0.440603	−	0.897702i	$-0.645235\pi$
$233$	−21.9553	−	12.6759i	−1.43834	−	0.830424i	−0.997734	+	0.0672779i	$0.978569\pi$
$234$	−5.93345	+	10.2770i	−0.387882	+	0.671831i
$235$	−6.23656	+	11.2046i	−0.406829	+	0.730905i
$236$	−0.615802	+	1.06660i	−0.0400853	+	0.0694298i
$237$	3.74312	+	2.16109i	0.243142	+	0.140378i
$238$	−1.44584	+	0.834757i	−0.0937199	+	0.0541092i
$239$	−8.97082	+	15.5379i	−0.580274	+	1.00506i	0.415172	+	0.909743i	$0.363721\pi$
$239$	−8.97082	+	15.5379i	−0.580274	+	1.00506i	−0.995447	+	0.0953214i	$0.969612\pi$
$240$	1.20555	+	2.01439i	0.0778182	+	0.130028i
$241$	−15.1726			−0.977354			−0.488677	−	0.872465i	$-0.662520\pi$
$241$	−15.1726			−0.977354			−0.488677	+	0.872465i	$0.662520\pi$
$242$	−21.7619	−	12.5642i	−1.39891	−	0.807658i
$243$		−	15.7356i		−	1.00944i
$244$	12.5772			0.805172
$245$	−11.8775	+	7.10833i	−0.758824	+	0.454134i
$246$	−3.71355			−0.236767
$247$	−27.3298	−	15.7789i	−1.73895	−	1.00399i
$248$	8.19912	+	4.73376i	0.520645	+	0.300594i
$249$	−2.88771	−	5.00165i	−0.183001	−	0.316967i
$250$	6.03972	+	9.40860i	0.381985	+	0.595052i
$251$	−0.214168	−	0.370949i	−0.0135181	−	0.0234141i	0.859187	−	0.511661i	$-0.170970\pi$
$251$	−0.214168	−	0.370949i	−0.0135181	−	0.0234141i	−0.872705	+	0.488247i	$0.837636\pi$
$252$	1.47884	−	0.853808i	0.0931581	−	0.0537848i
$253$		−	5.28888i		−	0.332509i
$254$	10.3424			0.648941
$255$	3.73756	−	2.23682i	0.234055	−	0.140075i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	14.0653	+	8.12058i	0.877367	+	0.506548i	0.869789	−	0.493423i	$-0.164255\pi$
$257$	14.0653	+	8.12058i	0.877367	+	0.506548i	0.00757741	+	0.999971i	$0.497588\pi$
$258$	−0.259079	+	0.149579i	−0.0161296	+	0.00931241i
$259$	5.01628			0.311696
$260$	13.9805	−	0.219451i	0.867037	−	0.0136097i
$261$	6.17649	−	10.6980i	0.382315	−	0.662189i
$262$	−9.05477	+	5.22778i	−0.559406	+	0.322973i
$263$			3.37672i			0.208217i	0.994566	+	0.104109i	$0.0331990\pi$
$263$			3.37672i			0.208217i	−0.994566	+	0.104109i	$0.966801\pi$
$264$	−3.15522	+	5.46500i	−0.194190	+	0.336348i
$265$	16.0906	−	0.252572i	0.988439	−	0.0155154i
$266$	2.27054	+	3.93269i	0.139216	+	0.241129i
$267$		−	19.1880i		−	1.17428i
$268$	7.42687	−	3.44115i	0.453669	−	0.210202i
$269$	−6.52333			−0.397735			−0.198867	−	0.980026i	$-0.563726\pi$
$269$	−6.52333			−0.397735			−0.198867	+	0.980026i	$0.563726\pi$
$270$	−9.86603	+	5.90453i	−0.600427	+	0.359338i
$271$	−11.7274			−0.712391			−0.356196	−	0.934411i	$-0.615926\pi$
$271$	−11.7274			−0.712391			−0.356196	+	0.934411i	$0.615926\pi$
$272$	1.60685	+	0.927714i	0.0974295	+	0.0562509i
$273$			5.90709i			0.357513i
$274$	−2.82850	−	4.89910i	−0.170876	−	0.295966i
$275$	−14.2024	+	26.4859i	−0.856440	+	1.59716i
$276$	−0.923793			−0.0556058
$277$		−	16.2680i		−	0.977450i	−0.872438	−	0.488725i	$-0.837462\pi$
$277$		−	16.2680i		−	0.977450i	0.872438	−	0.488725i	$-0.162538\pi$
$278$	1.18900	−	0.686470i	0.0713116	−	0.0411718i
$279$	−8.98362	+	15.5601i	−0.537835	+	0.931558i
$280$	−1.75803	−	0.978535i	−0.105062	−	0.0584786i
$281$	−12.6097	−	21.8406i	−0.752232	−	1.30290i	−0.946739	−	0.322002i	$-0.895644\pi$
$281$	−12.6097	−	21.8406i	−0.752232	−	1.30290i	0.194507	−	0.980901i	$-0.437689\pi$
$282$			6.02074i			0.358530i
$283$			26.0317i			1.54742i	0.633538	+	0.773712i	$0.281602\pi$
$283$			26.0317i			1.54742i	−0.633538	+	0.773712i	$0.718398\pi$
$284$	2.52497	+	4.37338i	0.149830	+	0.259513i
$285$	−6.08415	−	10.1662i	−0.360394	−	0.602191i
$286$	18.7926	+	32.5498i	1.11123	+	1.92471i
$287$	2.75632	−	1.59136i	0.162700	−	0.0939351i
$288$	−1.64352	−	0.948887i	−0.0968454	−	0.0559137i
$289$	−6.77869	+	11.7410i	−0.398747	+	0.690649i
$290$	−14.5532	+	0.228439i	−0.854593	+	0.0134144i
$291$	−3.62415	−	6.27721i	−0.212451	−	0.367977i
$292$		−	1.58129i		−	0.0925378i
$293$		−	34.0458i		−	1.98898i	−0.104849	−	0.994488i	$-0.533436\pi$
$293$		−	34.0458i		−	1.98898i	0.104849	−	0.994488i	$-0.466564\pi$
$294$	−3.24954	+	5.62836i	−0.189517	+	0.328253i
$295$	0.0432230	+	2.75361i	0.00251654	+	0.160322i
$296$	−2.78744	−	4.82799i	−0.162017	−	0.280621i
$297$	−26.7664	−	15.4536i	−1.55314	−	0.896707i
$298$	0.414279	−	0.239184i	0.0239986	−	0.0138556i
$299$	−2.75107	+	4.76500i	−0.159099	+	0.275567i
$300$	4.62621	+	2.48070i	0.267094	+	0.143223i
$301$	0.128198	−	0.222046i	0.00738922	−	0.0127985i
$302$	5.18704	+	2.99474i	0.298481	+	0.172328i
$303$	4.39457	+	2.53720i	0.252461	+	0.145759i
$304$	2.52338	−	4.37063i	0.144726	−	0.250673i
$305$	24.1319	−	14.4422i	1.38179	−	0.826960i
$306$	−1.76059	+	3.04943i	−0.100646	+	0.174325i
$307$	4.74725	−	2.74083i	0.270940	−	0.156427i	−0.358375	−	0.933578i	$-0.616669\pi$
$307$	4.74725	−	2.74083i	0.270940	−	0.156427i	0.629315	+	0.777151i	$0.283336\pi$
$308$		−	5.40842i		−	0.308173i
$309$	−2.47568	+	4.28801i	−0.140837	+	0.243936i
$310$	21.1674	−	0.332262i	1.20223	−	0.0188712i
$311$	3.76476			0.213480			0.106740	−	0.994287i	$-0.465959\pi$
$311$	3.76476			0.213480			0.106740	+	0.994287i	$0.465959\pi$
$312$	5.68537	−	3.28245i	0.321871	−	0.185832i
$313$			5.31316i			0.300317i	0.988662	+	0.150159i	$0.0479784\pi$
$313$			5.31316i			0.300317i	−0.988662	+	0.150159i	$0.952022\pi$
$314$	10.1652	−	17.6066i	0.573655	−	0.993600i
$315$	1.85704	−	3.33634i	0.104632	−	0.187982i
$316$	2.05844	+	3.56532i	0.115796	+	0.200565i
$317$	−4.23203	+	2.44336i	−0.237694	+	0.137233i	−0.614117	−	0.789215i	$-0.710488\pi$
$317$	−4.23203	+	2.44336i	−0.237694	+	0.137233i	0.376422	+	0.926448i	$0.377154\pi$
$318$	6.54346	−	3.77787i	0.366939	−	0.211852i
$319$	−19.5624	−	33.8830i	−1.09528	−	1.89708i
$320$	0.0350949	+	2.23579i	0.00196186	+	0.124985i
$321$	13.9868			0.780668
$322$	0.685671	−	0.395872i	0.0382109	−	0.0220611i
$323$	−8.10939	−	4.68196i	−0.451218	−	0.260511i
$324$	0.147434	−	0.255364i	0.00819080	−	0.0141869i
$325$	26.5726	−	16.4748i	1.47398	−	0.913856i
$326$	−19.8547			−1.09965
$327$		−	18.0084i		−	0.995866i
$328$	−3.06326	−	1.76857i	−0.169140	−	0.0976532i
$329$	−2.58006	−	4.46880i	−0.142244	−	0.246373i
$330$	0.221464	+	14.1088i	0.0121912	+	0.776666i
$331$	3.24082	−	5.61326i	0.178131	−	0.308533i	−0.763109	−	0.646270i	$-0.776328\pi$
$331$	3.24082	−	5.61326i	0.178131	−	0.308533i	0.941241	+	0.337737i	$0.109661\pi$
$332$		−	5.50107i		−	0.301911i
$333$	9.16244	−	5.28994i	0.502099	−	0.289887i
$334$	2.22917			0.121975
$335$	10.2985	−	15.1308i	0.562670	−	0.826682i
$336$	−0.944672			−0.0515361
$337$	−14.1174	+	8.15069i	−0.769025	+	0.443997i	−0.832527	−	0.553985i	$-0.813106\pi$
$337$	−14.1174	+	8.15069i	−0.769025	+	0.443997i	0.0635020	+	0.997982i	$0.479773\pi$
$338$		−	26.1008i		−	1.41969i
$339$	0.520751	−	0.901967i	0.0282833	−	0.0489881i
$340$	4.14835	−	0.0651161i	0.224976	−	0.00353141i
$341$	28.4532	+	49.2824i	1.54083	+	2.66879i
$342$	8.29447	+	4.78881i	0.448513	+	0.258949i
$343$		−	11.8687i		−	0.640848i
$344$	−0.284949			−0.0153634
$345$	−1.77249	+	1.06078i	−0.0954275	+	0.0571106i
$346$	−1.72749	+	2.99209i	−0.0928703	+	0.160856i
$347$	−10.8651	−	6.27299i	−0.583271	−	0.336752i	0.179161	−	0.983820i	$-0.442662\pi$
$347$	−10.8651	−	6.27299i	−0.583271	−	0.336752i	−0.762432	+	0.647068i	$0.775995\pi$
$348$	−5.91824	+	3.41690i	−0.317251	+	0.183165i
$349$	−14.6610			−0.784787			−0.392393	−	0.919797i	$-0.628353\pi$
$349$	−14.6610			−0.784787			−0.392393	+	0.919797i	$0.628353\pi$
$350$	−4.49678	+	0.141205i	−0.240363	+	0.00754774i
$351$	16.0767	+	27.8456i	0.858110	+	1.48629i
$352$	−5.20541	+	3.00535i	−0.277449	+	0.160186i
$353$	−17.9050	+	10.3375i	−0.952988	+	0.550208i	−0.894008	−	0.448051i	$-0.852118\pi$
$353$	−17.9050	+	10.3375i	−0.952988	+	0.550208i	−0.0589803	+	0.998259i	$0.518785\pi$
$354$	0.646512	+	1.11979i	0.0343617	+	0.0595163i
$355$	9.86659	+	5.49183i	0.523664	+	0.291476i
$356$	9.13826	−	15.8279i	0.484327	−	0.838879i
$357$			1.75277i			0.0927665i
$358$	−14.1355	+	8.16111i	−0.747083	+	0.431328i
$359$	−13.5195			−0.713532			−0.356766	−	0.934194i	$-0.616121\pi$
$359$	−13.5195			−0.713532			−0.356766	+	0.934194i	$0.616121\pi$
$360$	−4.24303	+	0.0666022i	−0.223627	+	0.00351024i
$361$	−3.23493	+	5.60307i	−0.170260	+	0.294898i
$362$			16.8114i			0.883589i
$363$	−22.8471	+	13.1908i	−1.19916	+	0.692337i
$364$	−2.81325	+	4.87269i	−0.147454	+	0.255398i
$365$	−1.81577	−	3.03402i	−0.0950419	−	0.158808i
$366$	6.60220	−	11.4353i	0.345102	−	0.597735i
$367$	−25.5432	−	14.7474i	−1.33335	−	0.769807i	−0.347535	−	0.937667i	$-0.612981\pi$
$367$	−25.5432	−	14.7474i	−1.33335	−	0.769807i	−0.985811	+	0.167860i	$0.946314\pi$
$368$	−0.762026	−	0.439956i	−0.0397234	−	0.0229343i
$369$	3.35636	−	5.81338i	0.174725	−	0.302632i
$370$	−10.8922	−	6.06271i	−0.566259	−	0.315185i
$371$	−3.23785	+	5.60812i	−0.168101	+	0.291159i
$372$	8.60801	−	4.96984i	0.446304	−	0.257674i
$373$	10.3718	+	5.98816i	0.537032	+	0.310055i	0.743875	−	0.668319i	$-0.232986\pi$
$373$	10.3718	+	5.98816i	0.537032	+	0.310055i	−0.206843	+	0.978374i	$0.566319\pi$
$374$	5.57620	+	9.65827i	0.288339	+	0.499417i
$375$	11.7249	−	0.552494i	0.605471	−	0.0285307i
$376$	−2.86738	+	4.96644i	−0.147874	+	0.256125i
$377$			40.7024i			2.09628i
$378$		−	4.62679i		−	0.237976i
$379$	7.44445	+	12.8942i	0.382396	+	0.662329i	0.991404	−	0.130835i	$-0.0417657\pi$
$379$	7.44445	+	12.8942i	0.382396	+	0.662329i	−0.609008	+	0.793164i	$0.708432\pi$
$380$	−0.177116	−	11.2835i	−0.00908585	−	0.578833i
$381$	5.42909	−	9.40346i	0.278141	−	0.481754i
$382$	−16.2319	−	9.37152i	−0.830498	−	0.479488i
$383$	−33.0360	+	19.0734i	−1.68806	+	0.974603i	−0.732062	+	0.681238i	$0.761442\pi$
$383$	−33.0360	+	19.0734i	−1.68806	+	0.974603i	−0.956001	+	0.293365i	$0.905225\pi$
$384$	0.524935	+	0.909214i	0.0267880	+	0.0463981i
$385$	−6.21043	−	10.3772i	−0.316513	−	0.528869i
$386$	6.30074	+	10.9132i	0.320699	+	0.555467i
$387$		−	0.540768i		−	0.0274888i
$388$		−	6.90400i		−	0.350497i
$389$	7.43359	+	12.8754i	0.376898	+	0.652807i	0.990609	−	0.136724i	$-0.0436573\pi$
$389$	7.43359	+	12.8754i	0.376898	+	0.652807i	−0.613711	+	0.789531i	$0.710324\pi$
$390$	7.13935	−	12.8265i	0.361515	−	0.649495i
$391$	−0.816307	+	1.41389i	−0.0412824	+	0.0715033i
$392$	−5.36101	+	3.09518i	−0.270772	+	0.156330i
$393$			10.9770i			0.553715i
$394$	4.54887			0.229169
$395$	8.04356	+	4.47712i	0.404715	+	0.225268i
$396$	−5.70347	−	9.87870i	−0.286610	−	0.496423i
$397$			12.8534i			0.645092i	0.946554	+	0.322546i	$0.104539\pi$
$397$			12.8534i			0.645092i	−0.946554	+	0.322546i	$0.895461\pi$
$398$	−2.09798	−	1.21127i	−0.105162	−	0.0607155i
$399$	4.76754			0.238676
$400$	2.63467	+	4.24953i	0.131734	+	0.212476i
$401$	−10.6995			−0.534305			−0.267153	−	0.963654i	$-0.586083\pi$
$401$	−10.6995			−0.534305			−0.267153	+	0.963654i	$0.586083\pi$
$402$	0.769882	−	8.55900i	0.0383982	−	0.426884i
$403$		−	59.2010i		−	2.94901i
$404$	2.41669	+	4.18582i	0.120235	+	0.208252i
$405$	−0.0103484	−	0.659266i	−0.000514216	−	0.0327592i
$406$	2.92848	−	5.07228i	0.145338	−	0.251733i
$407$		−	33.5089i		−	1.66098i
$408$	1.68698	−	0.973979i	0.0835180	−	0.0482191i
$409$	4.51712	−	7.82387i	0.223357	−	0.386866i	−0.732468	−	0.680801i	$-0.761632\pi$
$409$	4.51712	−	7.82387i	0.223357	−	0.386866i	0.955825	+	0.293936i	$0.0949651\pi$
$410$	−7.90833	+	0.124136i	−0.390565	+	0.00613063i
$411$	−5.93911			−0.292955
$412$	−4.08432	+	2.35809i	−0.201220	+	0.116175i
$413$	−0.959727	−	0.554099i	−0.0472251	−	0.0272654i
$414$	0.834937	−	1.44615i	0.0410349	−	0.0710746i
$415$	−6.31683	−	10.5549i	−0.310081	−	0.518122i
$416$	6.25306			0.306582
$417$		−	1.44141i		−	0.0705861i
$418$	26.2705	−	15.1673i	1.28493	−	0.741856i
$419$	−3.65327	−	6.32766i	−0.178474	−	0.309126i	0.762884	−	0.646535i	$-0.223783\pi$
$419$	−3.65327	−	6.32766i	−0.178474	−	0.309126i	−0.941358	+	0.337409i	$0.890449\pi$
$420$	−1.81255	+	1.08476i	−0.0884433	+	0.0529307i
$421$	−9.29217	−	16.0945i	−0.452873	−	0.784399i	0.545690	−	0.837987i	$-0.316267\pi$
$421$	−9.29217	−	16.0945i	−0.452873	−	0.784399i	−0.998563	+	0.0535883i	$0.982934\pi$
$422$	12.5052	+	7.21988i	0.608743	+	0.351458i
$423$	−9.42519	−	5.44163i	−0.458268	−	0.264581i
$424$	7.19683			0.349509
$425$	7.88470	−	4.88845i	0.382464	−	0.237125i
$426$	5.30179			0.256872
$427$			11.3169i			0.547665i
$428$	11.5376	+	6.66122i	0.557689	+	0.321982i
$429$	39.4596			1.90513
$430$	−0.546732	+	0.327203i	−0.0263658	+	0.0157791i
$431$	−0.969542	+	1.67930i	−0.0467012	+	0.0808889i	−0.888431	−	0.459010i	$-0.848204\pi$
$431$	−0.969542	+	1.67930i	−0.0467012	+	0.0808889i	0.841730	+	0.539899i	$0.181538\pi$
$432$	−4.45312	+	2.57101i	−0.214251	+	0.123698i
$433$	−4.38622	−	2.53238i	−0.210788	−	0.121699i	0.390889	−	0.920438i	$-0.372167\pi$
$433$	−4.38622	−	2.53238i	−0.210788	−	0.121699i	−0.601678	+	0.798739i	$0.705501\pi$
$434$	−4.25944	+	7.37756i	−0.204460	+	0.354134i
$435$	−7.43178	+	13.3519i	−0.356327	+	0.640174i
$436$	8.57649	−	14.8549i	0.410739	−	0.711422i
$437$	3.84577	+	2.22036i	0.183968	+	0.106214i
$438$	−1.43773	−	0.830072i	−0.0686972	−	0.0396624i
$439$	−13.5911	−	23.5404i	−0.648667	−	1.12352i	−0.983442	−	0.181226i	$-0.941994\pi$
$439$	−13.5911	−	23.5404i	−0.648667	−	1.12352i	0.334775	−	0.942298i	$-0.391340\pi$
$440$	−6.53665	+	11.7437i	−0.311622	+	0.559859i
$441$	−5.87395	−	10.1740i	−0.279712	−	0.484476i
$442$		−	11.6021i		−	0.551856i
$443$	23.2288	+	13.4111i	1.10363	+	0.637183i	0.937173	−	0.348866i	$-0.113433\pi$
$443$	23.2288	+	13.4111i	1.10363	+	0.637183i	0.166460	+	0.986048i	$0.446766\pi$
$444$	−5.85290			−0.277766
$445$	−0.641413	−	40.8625i	−0.0304059	−	1.93707i
$446$	5.55140	+	9.61530i	0.262866	+	0.455298i
$447$		−	0.502224i		−	0.0237544i
$448$	−0.779249	−	0.449900i	−0.0368161	−	0.0212558i
$449$	1.49906	−	2.59645i	0.0707451	−	0.122534i	−0.828483	−	0.560014i	$-0.810796\pi$
$449$	1.49906	−	2.59645i	0.0707451	−	0.122534i	0.899228	+	0.437480i	$0.144129\pi$
$450$	−8.06465	+	5.00002i	−0.380171	+	0.235703i
$451$	−10.6304	−	18.4123i	−0.500564	−	0.867002i
$452$	0.859123	−	0.496015i	0.0404098	−	0.0233306i
$453$	5.44572	−	3.14409i	0.255862	−	0.147722i
$454$	15.3613			0.720941
$455$	0.197461	+	12.5797i	0.00925713	+	0.589745i
$456$	−2.64922	−	4.58859i	−0.124061	−	0.214880i
$457$	22.7499	+	13.1346i	1.06419	+	0.614412i	0.926589	−	0.376075i	$-0.122727\pi$
$457$	22.7499	+	13.1346i	1.06419	+	0.614412i	0.137604	+	0.990487i	$0.456060\pi$
$458$	−11.3823	−	6.57157i	−0.531859	−	0.307069i
$459$	4.77033	+	8.26245i	0.222660	+	0.385658i
$460$	−1.96730	+	0.0308804i	−0.0917259	+	0.00143981i
$461$	33.9966			1.58338			0.791689	−	0.610924i	$-0.209202\pi$
$461$	33.9966			1.58338			0.791689	+	0.610924i	$0.209202\pi$
$462$	−4.91741	−	2.83907i	−0.228778	−	0.132085i
$463$	−26.7719	+	15.4568i	−1.24420	+	0.718337i	−0.969946	−	0.243321i	$-0.921763\pi$
$463$	−26.7719	+	15.4568i	−1.24420	+	0.718337i	−0.274250	+	0.961658i	$0.588430\pi$
$464$	−6.50919			−0.302182
$465$	10.8094	−	19.4201i	0.501275	−	0.900587i
$466$	−25.3518			−1.17440
$467$	16.1717	−	9.33673i	0.748337	−	0.432052i	−0.0767558	−	0.997050i	$-0.524456\pi$
$467$	16.1717	−	9.33673i	0.748337	−	0.432052i	0.825093	+	0.564997i	$0.191123\pi$
$468$			11.8669i			0.548548i
$469$	3.09635	+	6.68270i	0.142976	+	0.308578i
$470$	0.201261	+	12.8217i	0.00928346	+	0.591422i
$471$	−10.6721	−	18.4847i	−0.491746	−	0.851729i
$472$			1.23160i			0.0566892i
$473$	−1.48327	−	0.856369i	−0.0682010	−	0.0393759i
$474$	4.32219			0.198525
$475$	−13.2966	−	21.4464i	−0.610089	−	0.984028i
$476$	−0.834757	+	1.44584i	−0.0382610	+	0.0662700i
$477$			13.6580i			0.625355i
$478$			17.9416i			0.820631i
$479$	15.4292	+	26.7242i	0.704979	+	1.22106i	0.966699	+	0.255916i	$0.0823770\pi$
$479$	15.4292	+	26.7242i	0.704979	+	1.22106i	−0.261720	+	0.965144i	$0.584290\pi$
$480$	2.05124	+	1.14174i	0.0936257	+	0.0521129i
$481$	−17.4301	+	30.1897i	−0.794742	+	1.37653i
$482$	−13.1399	+	7.58630i	−0.598504	+	0.345547i
$483$		−	0.831228i		−	0.0378222i
$484$	−25.1284			−1.14220
$485$	−7.92779	−	13.2467i	−0.359982	−	0.601504i
$486$	−7.86782	−	13.6275i	−0.356892	−	0.618154i
$487$	23.0695	−	13.3192i	1.04538	−	0.603551i	0.124028	−	0.992279i	$-0.460419\pi$
$487$	23.0695	−	13.3192i	1.04538	−	0.603551i	0.921353	+	0.388728i	$0.127085\pi$
$488$	10.8922	−	6.28859i	0.493065	−	0.284671i
$489$	−10.4224	+	18.0521i	−0.471318	+	0.816346i
$490$	−6.73204	+	12.0947i	−0.304122	+	0.546384i
$491$	−32.5453			−1.46875			−0.734374	−	0.678745i	$-0.762524\pi$
$491$	−32.5453			−1.46875			−0.734374	+	0.678745i	$0.762524\pi$
$492$	−3.21602	+	1.85677i	−0.144990	+	0.0837098i
$493$			12.0773i			0.543936i
$494$	−31.5577			−1.41985
$495$	−22.2869	−	12.4051i	−1.00172	−	0.557567i
$496$	9.46753			0.425105
$497$	−3.93517	+	2.27197i	−0.176516	+	0.101912i
$498$	−5.00165	−	2.88771i	−0.224129	−	0.129401i
$499$	−14.6774	−	25.4219i	−0.657049	−	1.13804i	−0.981376	−	0.192097i	$-0.938471\pi$
$499$	−14.6774	−	25.4219i	−0.657049	−	1.13804i	0.324327	−	0.945945i	$-0.394862\pi$
$500$	9.93485	+	5.12823i	0.444300	+	0.229341i
$501$	1.17017	−	2.02679i	0.0522793	−	0.0905504i
$502$	−0.370949	−	0.214168i	−0.0165563	−	0.00955877i
$503$	18.0021	+	10.3935i	0.802672	+	0.463423i	0.844405	−	0.535706i	$-0.179954\pi$
$503$	18.0021	+	10.3935i	0.802672	+	0.463423i	−0.0417324	+	0.999129i	$0.513288\pi$
$504$	0.853808	−	1.47884i	0.0380316	−	0.0658727i
$505$	9.44344	+	5.25631i	0.420228	+	0.233903i
$506$	−2.64444	−	4.58031i	−0.117560	−	0.203619i
$507$	−23.7312	−	13.7012i	−1.05394	−	0.608492i
$508$	8.95679	−	5.17121i	0.397393	−	0.229435i
$509$	−26.9362			−1.19393			−0.596963	−	0.802269i	$-0.703626\pi$
$509$	−26.9362			−1.19393			−0.596963	+	0.802269i	$0.703626\pi$
$510$	2.11841	−	3.80592i	0.0938048	−	0.168529i
$511$	1.42284			0.0629427
$512$			1.00000i			0.0441942i
$513$	22.4739	−	12.9753i	0.992246	−	0.572873i
$514$	16.2412			0.716367
$515$	−5.12885	+	9.21446i	−0.226004	+	0.406038i
$516$	−0.149579	+	0.259079i	−0.00658487	+	0.0114053i
$517$	−29.8518	+	17.2349i	−1.31288	+	0.757991i
$518$	4.34423	−	2.50814i	0.190874	−	0.110201i
$519$	1.81364	+	3.14131i	0.0796098	+	0.137888i
$520$	11.9978	−	7.18032i	0.526138	−	0.314878i
$521$	32.4275			1.42067			0.710336	−	0.703863i	$-0.248543\pi$
$521$	32.4275			1.42067			0.710336	+	0.703863i	$0.248543\pi$
$522$		−	12.3530i		−	0.540675i
$523$	35.9386	−	20.7492i	1.57148	−	0.907297i	0.575497	−	0.817804i	$-0.304808\pi$
$523$	35.9386	−	20.7492i	1.57148	−	0.907297i	0.995987	−	0.0894937i	$-0.0285249\pi$
$524$	−5.22778	+	9.05477i	−0.228376	+	0.395560i
$525$	−2.23213	+	4.16266i	−0.0974182	+	0.181673i
$526$	1.68836	+	2.92432i	0.0736159	+	0.127507i
$527$		−	17.5663i		−	0.765201i
$528$			6.31044i			0.274627i
$529$	−11.1129	+	19.2481i	−0.483169	+	0.836873i
$530$	13.8086	−	8.26405i	0.599807	−	0.358967i
$531$	−2.33731			−0.101431
$532$	3.93269	+	2.27054i	0.170504	+	0.0984404i
$533$			22.1180i			0.958037i
$534$	−9.59398	−	16.6173i	−0.415172	−	0.719099i
$535$	29.7862	−	0.467549i	1.28777	−	0.0202139i
$536$	4.71129	−	6.69356i	0.203497	−	0.289118i
$537$			17.1362i			0.739482i
$538$	−5.64937	+	3.26167i	−0.243562	+	0.140620i
$539$	−37.2084			−1.60268
$540$	−5.59197	+	10.0465i	−0.240640	+	0.432332i
$541$	13.7790			0.592405			0.296203	−	0.955125i	$-0.404280\pi$
$541$	13.7790			0.592405			0.296203	+	0.955125i	$0.404280\pi$
$542$	−10.1563	+	5.86372i	−0.436249	+	0.251868i
$543$	15.2852	+	8.82491i	0.655950	+	0.378713i
$544$	1.85543			0.0795508
$545$	−0.601982	−	38.3505i	−0.0257861	−	1.64276i
$546$	2.95355	+	5.11569i	0.126400	+	0.218931i
$547$	−24.3427	−	14.0542i	−1.04082	−	0.600916i	−0.120752	−	0.992683i	$-0.538531\pi$
$547$	−24.3427	−	14.0542i	−1.04082	−	0.600916i	−0.920065	+	0.391767i	$0.871864\pi$
$548$	−4.89910	−	2.82850i	−0.209279	−	0.120828i
$549$	11.9343	+	20.6709i	0.509345	+	0.882211i
$550$	0.943257	+	30.0387i	0.0402206	+	1.28085i
$551$	32.8504			1.39947
$552$	−0.800028	+	0.461897i	−0.0340515	+	0.0196596i
$553$	−3.20807	+	1.85218i	−0.136421	+	0.0787628i
$554$	−8.13400	−	14.0885i	−0.345581	−	0.598563i
$555$	−11.2300	+	6.72083i	−0.476687	+	0.285283i
$556$	0.686470	−	1.18900i	0.0291128	−	0.0504249i
$557$	31.3630	+	18.1074i	1.32889	+	0.767237i	0.985128	−	0.171819i	$-0.0549646\pi$
$557$	31.3630	+	18.1074i	1.32889	+	0.767237i	0.343764	+	0.939056i	$0.388298\pi$
$558$			17.9672i			0.760614i
$559$	0.890900	+	1.54308i	0.0376811	+	0.0652655i
$560$	−2.01176	+	0.0315784i	−0.0850126	+	0.00133443i
$561$	11.7086			0.494336
$562$	−21.8406	−	12.6097i	−0.921292	−	0.531908i
$563$			40.8558i			1.72187i	0.508717	+	0.860934i	$0.330120\pi$
$563$			40.8558i			1.72187i	−0.508717	+	0.860934i	$0.669880\pi$
$564$	3.01037	+	5.21412i	0.126760	+	0.219554i
$565$	1.07884	−	1.93823i	0.0453870	−	0.0815419i
$566$	13.0158	+	22.5441i	0.547097	+	0.947600i
$567$	0.229776	+	0.132661i	0.00964970	+	0.00557126i
$568$	4.37338	+	2.52497i	0.183503	+	0.105946i
$569$	9.36907	−	16.2277i	0.392772	−	0.680301i	−0.600042	−	0.799968i	$-0.704850\pi$
$569$	9.36907	−	16.2277i	0.392772	−	0.680301i	0.992814	+	0.119668i	$0.0381829\pi$
$570$	−10.3521	−	5.76208i	−0.433602	−	0.241347i
$571$	−13.6593	+	23.6586i	−0.571625	+	0.990083i	0.424775	+	0.905299i	$0.360353\pi$
$571$	−13.6593	+	23.6586i	−0.571625	+	0.990083i	−0.996399	+	0.0847838i	$0.972980\pi$
$572$	32.5498	+	18.7926i	1.36097	+	0.785759i
$573$	−17.0414	+	9.83887i	−0.711916	+	0.411025i
$574$	1.59136	−	2.75632i	0.0664222	−	0.115047i
$575$	−3.73921	+	2.31828i	−0.155936	+	0.0966790i
$576$	−1.89777			−0.0790739
$577$	−22.8127	−	13.1709i	−0.949703	−	0.548311i	−0.0567146	−	0.998390i	$-0.518063\pi$
$577$	−22.8127	−	13.1709i	−0.949703	−	0.548311i	−0.892989	+	0.450079i	$0.851396\pi$
$578$			13.5574i			0.563913i
$579$	13.2299			0.549816
$580$	−12.4892	+	7.47443i	−0.518587	+	0.310359i
$581$	4.94986			0.205355
$582$	−6.27721	−	3.62415i	−0.260199	−	0.150226i
$583$	37.4625	+	21.6290i	1.55154	+	0.895781i
$584$	−0.790643	−	1.36943i	−0.0327170	−	0.0566676i
$585$	13.6266	+	22.7691i	0.563392	+	0.941386i
$586$	−17.0229	−	29.4845i	−0.703209	−	1.21799i
$587$	3.70986	−	2.14189i	0.153122	−	0.0884053i	−0.421481	−	0.906837i	$-0.638490\pi$
$587$	3.70986	−	2.14189i	0.153122	−	0.0884053i	0.574604	+	0.818432i	$0.305156\pi$
$588$			6.49907i			0.268017i
$589$	−47.7804			−1.96876
$590$	1.41424	+	2.36309i	0.0582233	+	0.0972868i
$591$	2.38786	−	4.13589i	0.0982234	−	0.170128i
$592$	−4.82799	−	2.78744i	−0.198429	−	0.114563i
$593$	19.4222	−	11.2134i	0.797573	−	0.460479i	−0.0450485	−	0.998985i	$-0.514344\pi$
$593$	19.4222	−	11.2134i	0.797573	−	0.460479i	0.842622	+	0.538506i	$0.181011\pi$
$594$	−30.9071			−1.26813
$595$	0.0585914	+	3.73268i	0.00240201	+	0.153025i
$596$	0.239184	−	0.414279i	0.00979737	−	0.0169695i
$597$	−2.20261	+	1.27168i	−0.0901467	+	0.0520462i
$598$			5.50215i			0.224999i
$599$	11.2291	−	19.4493i	0.458808	−	0.794678i	−0.540091	−	0.841607i	$-0.681610\pi$
$599$	11.2291	−	19.4493i	0.458808	−	0.794678i	0.998898	+	0.0469287i	$0.0149434\pi$
$600$	5.24676	−	0.164756i	0.214198	−	0.00672613i
$601$	−16.5311	−	28.6326i	−0.674316	−	1.16795i	−0.976668	−	0.214753i	$-0.931105\pi$
$601$	−16.5311	−	28.6326i	−0.674316	−	1.16795i	0.302352	−	0.953196i	$-0.402228\pi$
$602$		−	0.256397i		−	0.0104499i
$603$	12.7029	+	8.94096i	0.517301	+	0.364104i
$604$	5.98948			0.243709
$605$	−48.2141	+	28.8547i	−1.96018	+	1.17311i
$606$	5.07441			0.206134
$607$	28.6282	+	16.5285i	1.16198	+	0.670871i	0.951778	−	0.306786i	$-0.0992537\pi$
$607$	28.6282	+	16.5285i	1.16198	+	0.670871i	0.210204	+	0.977657i	$0.432587\pi$
$608$		−	5.04677i		−	0.204673i
$609$	−3.07452	−	5.32523i	−0.124586	−	0.215789i
$610$	13.6777	−	24.5733i	0.553795	−	0.994944i
$611$	35.8598			1.45073
$612$			3.52118i			0.142335i
$613$	20.6649	−	11.9309i	0.834645	−	0.481883i	−0.0207951	−	0.999784i	$-0.506620\pi$
$613$	20.6649	−	11.9309i	0.834645	−	0.481883i	0.855441	+	0.517901i	$0.173286\pi$
$614$	2.74083	−	4.74725i	0.110611	−	0.191583i
$615$	−4.03849	+	7.25553i	−0.162848	+	0.292571i
$616$	−2.70421	−	4.68383i	−0.108956	−	0.188717i
$617$			23.7631i			0.956667i	0.878178	+	0.478334i	$0.158759\pi$
$617$			23.7631i			0.956667i	−0.878178	+	0.478334i	$0.841241\pi$
$618$			4.95136i			0.199173i
$619$	3.97468	+	6.88434i	0.159756	+	0.276705i	0.934781	−	0.355226i	$-0.115596\pi$
$619$	3.97468	+	6.88434i	0.159756	+	0.276705i	−0.775025	+	0.631931i	$0.782263\pi$
$620$	18.1654	−	10.8715i	0.729540	−	0.436608i
$621$	−2.26227	−	3.91836i	−0.0907816	−	0.157238i
$622$	3.26038	−	1.88238i	0.130729	−	0.0754766i
$623$	14.2420	+	8.22260i	0.570592	+	0.329432i
$624$	3.28245	−	5.68537i	0.131403	−	0.227597i
$625$	24.9507	−	1.56852i	0.998030	−	0.0627410i
$626$	2.65658	+	4.60133i	0.106178	+	0.183906i
$627$		−	31.8473i		−	1.27186i
$628$		−	20.3304i		−	0.811271i
$629$	−5.17190	+	8.95800i	−0.206217	+	0.357179i
$630$	−0.0599286	−	3.81787i	−0.00238761	−	0.152108i
$631$	21.5840	+	37.3845i	0.859244	+	1.48825i	0.872651	+	0.488344i	$0.162399\pi$
$631$	21.5840	+	37.3845i	0.859244	+	1.48825i	−0.0134072	+	0.999910i	$0.504268\pi$
$632$	3.56532	+	2.05844i	0.141821	+	0.0818803i
$633$	13.1288	−	7.57993i	0.521824	−	0.301275i
$634$	−2.44336	+	4.23203i	−0.0970383	+	0.168075i
$635$	11.2474	−	20.2070i	0.446340	−	0.801891i
$636$	3.77787	−	6.54346i	0.149802	−	0.259465i
$637$	33.5227	+	19.3544i	1.32822	+	0.766847i
$638$	−33.8830	−	19.5624i	−1.34144	−	0.774482i
$639$	−4.79183	+	8.29969i	−0.189562	+	0.328331i
$640$	1.14829	+	1.91871i	0.0453901	+	0.0758435i
$641$	12.0846	−	20.9311i	0.477312	−	0.826729i	−0.522350	−	0.852731i	$-0.674944\pi$
$641$	12.0846	−	20.9311i	0.477312	−	0.826729i	0.999662	+	0.0260022i	$0.00827769\pi$
$642$	12.1129	−	6.99341i	0.478060	−	0.276008i
$643$		−	2.55230i		−	0.100653i	−0.998733	−	0.0503264i	$-0.983974\pi$
$643$		−	2.55230i		−	0.100653i	0.998733	−	0.0503264i	$-0.0160262\pi$
$644$	0.395872	−	0.685671i	0.0155996	−	0.0270192i
$645$	0.0104989	+	0.668857i	0.000413396	+	0.0263362i
$646$	−9.36392			−0.368418
$647$	3.37045	−	1.94593i	0.132506	−	0.0765024i	−0.432282	−	0.901739i	$-0.642291\pi$
$647$	3.37045	−	1.94593i	0.132506	−	0.0765024i	0.564788	+	0.825236i	$0.308958\pi$
$648$		−	0.294869i		−	0.0115835i
$649$	−3.70140	+	6.41101i	−0.145293	+	0.251654i
$650$	14.7751	−	27.5539i	0.579528	−	1.08075i
$651$	4.47185	+	7.74548i	0.175266	+	0.303569i
$652$	−17.1947	+	9.92734i	−0.673394	+	0.388784i
$653$	−10.3289	+	5.96340i	−0.404201	+	0.233366i	−0.688295	−	0.725431i	$-0.741641\pi$
$653$	−10.3289	+	5.96340i	−0.404201	+	0.233366i	0.284094	+	0.958796i	$0.408307\pi$
$654$	−9.00420	−	15.5957i	−0.352092	−	0.609841i
$655$	0.366937	+	23.3764i	0.0143374	+	0.913393i
$656$	−3.53715			−0.138102
$657$	2.59888	−	1.50046i	0.101392	−	0.0585386i
$658$	−4.46880	−	2.58006i	−0.174212	−	0.100581i
$659$	−12.5211	+	21.6872i	−0.487753	+	0.844813i	−0.999901	−	0.0140841i	$-0.995517\pi$
$659$	−12.5211	+	21.6872i	−0.487753	+	0.844813i	0.512148	+	0.858897i	$0.328850\pi$
$660$	7.24621	+	12.1079i	0.282059	+	0.471299i
$661$	−25.2416			−0.981783			−0.490892	−	0.871221i	$-0.663329\pi$
$661$	−25.2416			−0.981783			−0.490892	+	0.871221i	$0.663329\pi$
$662$		−	6.48163i		−	0.251916i
$663$	−10.5488	−	6.09035i	−0.409681	−	0.236530i
$664$	−2.75054	−	4.76407i	−0.106742	−	0.184882i
$665$	10.1529	−	0.159369i	0.393713	−	0.00618005i
$666$	5.28994	−	9.16244i	0.204981	−	0.355037i
$667$		−	5.72752i		−	0.221770i
$668$	1.93052	−	1.11458i	0.0746940	−	0.0431246i
$669$	11.6565			0.450666
$670$	1.35343	−	18.2529i	0.0522874	−	0.705171i
$671$	75.5976			2.91841
$672$	−0.818110	+	0.472336i	−0.0315593	+	0.0182208i
$673$			42.7574i			1.64818i	0.566461	+	0.824089i	$0.308312\pi$
$673$			42.7574i			1.64818i	−0.566461	+	0.824089i	$0.691688\pi$
$674$	−8.15069	+	14.1174i	−0.313953	+	0.543782i
$675$	0.806937	+	25.6975i	0.0310590	+	0.989095i
$676$	−13.0504	−	22.6039i	−0.501938	−	0.869382i
$677$	−25.9925	−	15.0068i	−0.998972	−	0.576756i	−0.0910277	−	0.995848i	$-0.529015\pi$
$677$	−25.9925	−	15.0068i	−0.998972	−	0.576756i	−0.907944	+	0.419092i	$0.862349\pi$
$678$		−	1.04150i		−	0.0399986i
$679$	6.21221			0.238403
$680$	3.56002	−	2.13057i	0.136521	−	0.0817036i
$681$	8.06367	−	13.9667i	0.309001	−	0.535205i
$682$	49.2824	+	28.4532i	1.88712	+	1.08953i
$683$	−34.1246	+	19.7018i	−1.30574	+	0.753870i	−0.981382	−	0.192064i	$-0.938482\pi$
$683$	−34.1246	+	19.7018i	−1.30574	+	0.753870i	−0.324359	+	0.945934i	$0.605148\pi$
$684$	9.57763			0.366210
$685$	−12.6479	+	0.198532i	−0.483250	+	0.00758551i
$686$	−5.93434	−	10.2786i	−0.226574	−	0.392438i
$687$	−11.9499	+	6.89929i	−0.455918	+	0.263224i
$688$	−0.246773	+	0.142474i	−0.00940812	+	0.00543178i
$689$	−22.5011	−	38.9731i	−0.857224	−	1.48476i
$690$	−1.00463	+	1.80491i	−0.0382455	+	0.0687117i
$691$	4.66884	−	8.08666i	0.177611	−	0.307631i	−0.763451	−	0.645866i	$-0.776496\pi$
$691$	4.66884	−	8.08666i	0.177611	−	0.307631i	0.941062	+	0.338235i	$0.109830\pi$
$692$			3.45497i			0.131338i
$693$	8.88885	−	5.13198i	0.337659	−	0.194948i
$694$	−12.5460			−0.476239
$695$	−0.0481832	−	3.06961i	−0.00182769	−	0.116437i
$696$	−3.41690	+	5.91824i	−0.129517	+	0.224330i
$697$			6.56293i			0.248589i
$698$	−12.6968	+	7.33051i	−0.480582	+	0.277464i
$699$	−13.3080	+	23.0502i	−0.503355	+	0.871837i
$700$	−3.82372	+	2.37068i	−0.144523	+	0.0896032i
$701$	−5.52858	+	9.57578i	−0.208812	+	0.361672i	−0.951340	−	0.308142i	$-0.900293\pi$
$701$	−5.52858	+	9.57578i	−0.208812	+	0.361672i	0.742529	+	0.669814i	$0.233626\pi$
$702$	27.8456	+	16.0767i	1.05097	+	0.606776i
$703$	24.3658	+	14.0676i	0.918972	+	0.530569i
$704$	−3.00535	+	5.20541i	−0.113268	+	0.196186i
$705$	11.7633	+	6.54758i	0.443033	+	0.246596i
$706$	−10.3375	+	17.9050i	−0.389056	+	0.673864i
$707$	−3.76640	+	2.17453i	−0.141650	+	0.0817817i
$708$	1.11979	+	0.646512i	0.0420844	+	0.0242974i
$709$	21.9596	+	38.0351i	0.824708	+	1.42844i	0.902142	+	0.431439i	$0.141994\pi$
$709$	21.9596	+	38.0351i	0.824708	+	1.42844i	−0.0774338	+	0.996997i	$0.524673\pi$
$710$	11.2906	−	0.177227i	0.423730	−	0.00665123i
$711$	−3.90645	+	6.76618i	−0.146503	+	0.253751i
$712$		−	18.2765i		−	0.684942i
$713$			8.33060i			0.311983i
$714$	0.876385	+	1.51794i	0.0327979	+	0.0568076i
$715$	84.0328	−	1.31905i	3.14265	−	0.0493297i
$716$	−8.16111	+	14.1355i	−0.304995	+	0.528267i
$717$	16.3128	+	9.41819i	0.609212	+	0.351729i
$718$	−11.7082	+	6.75975i	−0.436947	+	0.252272i
$719$	−1.57257	−	2.72376i	−0.0586468	−	0.101579i	0.835211	−	0.549929i	$-0.185345\pi$
$719$	−1.57257	−	2.72376i	−0.0586468	−	0.101579i	−0.893858	+	0.448350i	$0.852012\pi$
$720$	−3.64127	+	2.17919i	−0.135702	+	0.0812138i
$721$	−2.12180	−	3.67507i	−0.0790201	−	0.136867i
$722$			6.46986i			0.240783i
$723$			15.9293i			0.592415i
$724$	8.40572	+	14.5591i	0.312396	+	0.541086i
$725$	−15.3803	+	28.6825i	−0.571211	+	1.06524i
$726$	−13.1908	+	22.8471i	−0.489556	+	0.847936i
$727$	−29.1344	+	16.8207i	−1.08053	+	0.623846i	−0.931040	−	0.364917i	$-0.881097\pi$
$727$	−29.1344	+	16.8207i	−1.08053	+	0.623846i	−0.149493	+	0.988763i	$0.547764\pi$
$728$			5.62650i			0.208532i
$729$	−15.6358			−0.579102
$730$	−3.08952	−	1.71965i	−0.114348	−	0.0636472i
$731$	0.264351	+	0.457869i	0.00977737	+	0.0169349i
$732$		−	13.2044i		−	0.488049i
$733$	−32.2868	−	18.6408i	−1.19254	−	0.688514i	−0.233659	−	0.972319i	$-0.575070\pi$
$733$	−32.2868	−	18.6408i	−1.19254	−	0.688514i	−0.958882	+	0.283805i	$0.908403\pi$
$734$	−29.4948			−1.08867
$735$	7.46281	+	12.4698i	0.275270	+	0.459956i
$736$	−0.879912			−0.0324340
$737$	44.6407	−	20.6837i	1.64436	−	0.761894i
$738$		−	6.71271i		−	0.247098i
$739$	−6.38472	−	11.0587i	−0.234866	−	0.406799i	0.724368	−	0.689414i	$-0.242132\pi$
$739$	−6.38472	−	11.0587i	−0.234866	−	0.406799i	−0.959234	+	0.282614i	$0.908798\pi$
$740$	−12.4643	+	0.195650i	−0.458196	+	0.00719224i
$741$	−16.5658	+	28.6927i	−0.608558	+	1.05405i
$742$			6.47570i			0.237731i
$743$	−33.1203	+	19.1220i	−1.21507	+	0.701519i	−0.963859	−	0.266415i	$-0.914161\pi$
$743$	−33.1203	+	19.1220i	−1.21507	+	0.701519i	−0.251208	+	0.967933i	$0.580828\pi$
$744$	4.96984	−	8.60801i	0.182203	−	0.315585i
$745$	−0.0167883	−	1.06953i	−0.000615075	−	0.0391846i
$746$	11.9763			0.438485
$747$	9.04113	−	5.21990i	0.330798	−	0.190986i
$748$	9.65827	+	5.57620i	0.353141	+	0.203886i
$749$	−5.99376	+	10.3815i	−0.219007	+	0.379332i
$750$	9.87780	−	6.34092i	0.360686	−	0.231538i
$751$	−25.6146			−0.934689			−0.467344	−	0.884075i	$-0.654789\pi$
$751$	−25.6146			−0.934689			−0.467344	+	0.884075i	$0.654789\pi$
$752$			5.73475i			0.209125i
$753$	−0.389448	+	0.224848i	−0.0141923	+	0.00819392i
$754$	20.3512	+	35.2493i	0.741146	+	1.28370i
$755$	11.4921	−	6.87766i	0.418239	−	0.250304i
$756$	−2.31339	−	4.00692i	−0.0841374	−	0.145730i
$757$	−4.93771	−	2.85079i	−0.179464	−	0.103614i	0.407577	−	0.913171i	$-0.366374\pi$
$757$	−4.93771	−	2.85079i	−0.179464	−	0.103614i	−0.587041	+	0.809557i	$0.699707\pi$
$758$	12.8942	+	7.44445i	0.468337	+	0.270395i
$759$	−5.55264			−0.201548
$760$	−5.79515	−	9.68326i	−0.210212	−	0.351249i
$761$	−44.6287			−1.61779			−0.808895	−	0.587953i	$-0.799934\pi$
$761$	−44.6287			−1.61779			−0.808895	+	0.587953i	$0.799934\pi$
$762$		−	10.8582i		−	0.393350i
$763$	13.3664	+	7.71712i	0.483898	+	0.279379i
$764$	−18.7430			−0.678099
$765$	4.04334	+	6.75612i	0.146187	+	0.244268i
$766$	−19.0734	+	33.0360i	−0.689148	+	1.19364i
$767$	6.66952	−	3.85065i	0.240822	−	0.139039i
$768$	0.909214	+	0.524935i	0.0328084	+	0.0189420i
$769$	−3.14753	+	5.45168i	−0.113503	+	0.196593i	−0.917180	−	0.398472i	$-0.869540\pi$
$769$	−3.14753	+	5.45168i	−0.113503	+	0.196593i	0.803677	+	0.595065i	$0.202874\pi$
$770$	−10.5670	−	5.88167i	−0.380807	−	0.211961i
$771$	8.52555	−	14.7667i	0.307040	−	0.531809i
$772$	10.9132	+	6.30074i	0.392775	+	0.226768i
$773$	−30.6655	−	17.7047i	−1.10296	−	0.636795i	−0.165963	−	0.986132i	$-0.553073\pi$
$773$	−30.6655	−	17.7047i	−1.10296	−	0.636795i	−0.936997	+	0.349337i	$0.886407\pi$
$774$	−0.270384	−	0.468319i	−0.00971875	−	0.0168334i
$775$	22.3705	−	41.7183i	0.803571	−	1.49856i
$776$	−3.45200	−	5.97904i	−0.123920	−	0.214635i
$777$		−	5.26644i		−	0.188932i
$778$	12.8754	+	7.43359i	0.461604	+	0.266507i
$779$	17.8512			0.639585
$780$	−0.230394	−	14.6777i	−0.00824944	−	0.525548i
$781$	15.1768	+	26.2871i	0.543070	+	0.940625i
$782$			1.63261i			0.0583822i
$783$	−28.9862	−	16.7352i	−1.03588	−	0.598067i
$784$	−3.09518	+	5.36101i	−0.110542	+	0.191465i
$785$	−23.3452	−	39.0080i	−0.833225	−	1.39226i
$786$	5.48848	+	9.50633i	0.195768	+	0.339080i
$787$	1.10091	−	0.635613i	0.0392433	−	0.0226571i	−0.480250	−	0.877132i	$-0.659454\pi$
$787$	1.10091	−	0.635613i	0.0392433	−	0.0226571i	0.519493	+	0.854475i	$0.326121\pi$
$788$	3.93943	−	2.27443i	0.140337	−	0.0810233i
$789$	3.54511			0.126209
$790$	9.20449	−	0.144481i	0.327481	−	0.00514042i
$791$	0.446314	+	0.773038i	0.0158691	+	0.0274861i
$792$	−9.87870	−	5.70347i	−0.351024	−	0.202664i
$793$	−68.1093	−	39.3229i	−2.41863	−	1.39640i
$794$	6.42668	+	11.1313i	0.228074	+	0.395036i
$795$	−0.265168	−	16.8931i	−0.00940453	−	0.599135i
$796$	−2.42254			−0.0858647
$797$	25.5129	+	14.7299i	0.903713	+	0.521759i	0.878403	−	0.477921i	$-0.158609\pi$
$797$	25.5129	+	14.7299i	0.903713	+	0.521759i	0.0253098	+	0.999680i	$0.491943\pi$
$798$	4.12881	−	2.38377i	0.146158	−	0.0843845i
$799$	10.6404			0.376431
$800$	4.40646	+	2.36286i	0.155792	+	0.0835398i
$801$	34.6847			1.22552
$802$	−9.26600	+	5.34973i	−0.327194	+	0.188905i
$803$		−	9.50462i		−	0.335411i
$804$	−3.61276	−	7.79725i	−0.127412	−	0.274988i
$805$	−0.0277862	−	1.77018i	−0.000979335	−	0.0623905i
$806$	−29.6005	−	51.2696i	−1.04263	−	1.80589i
$807$			6.84865i			0.241084i
$808$	4.18582	+	2.41669i	0.147257	+	0.0850187i
$809$	14.7664			0.519158			0.259579	−	0.965722i	$-0.416416\pi$
$809$	14.7664			0.519158			0.259579	+	0.965722i	$0.416416\pi$
$810$	−0.338595	−	0.565767i	−0.0118970	−	0.0198790i
$811$	25.7227	−	44.5530i	0.903245	−	1.56447i	0.0799899	−	0.996796i	$-0.474511\pi$
$811$	25.7227	−	44.5530i	0.903245	−	1.56447i	0.823255	−	0.567671i	$-0.192155\pi$
$812$		−	5.85696i		−	0.205539i
$813$			12.3123i			0.431811i
$814$	−16.7545	−	29.0196i	−0.587244	−	1.01714i
$815$	−21.5920	+	38.7921i	−0.756335	+	1.35883i
$816$	0.973979	−	1.68698i	0.0340961	−	0.0590561i
$817$	1.24540	−	0.719035i	0.0435712	−	0.0251558i
$818$		−	9.03423i		−	0.315874i
$819$	−10.6778			−0.373113
$820$	−6.78675	+	4.06167i	−0.237004	+	0.141840i
$821$	14.6693	+	25.4079i	0.511961	+	0.886743i	0.999904	+	0.0138674i	$0.00441426\pi$
$821$	14.6693	+	25.4079i	0.511961	+	0.886743i	−0.487942	+	0.872876i	$0.662252\pi$
$822$	−5.14342	+	2.96956i	−0.179397	+	0.103575i
$823$	37.0682	−	21.4014i	1.29212	−	0.746004i	0.313088	−	0.949724i	$-0.398636\pi$
$823$	37.0682	−	21.4014i	1.29212	−	0.746004i	0.979029	+	0.203720i	$0.0653031\pi$
$824$	−2.35809	+	4.08432i	−0.0821478	+	0.142284i
$825$	27.8067	+	14.9107i	0.968105	+	0.519124i
$826$	−1.10820			−0.0385591
$827$	−8.10752	+	4.68088i	−0.281926	+	0.162770i	−0.634295	−	0.773091i	$-0.718710\pi$
$827$	−8.10752	+	4.68088i	−0.281926	+	0.162770i	0.352369	+	0.935861i	$0.385376\pi$
$828$		−	1.66987i		−	0.0580322i
$829$	−49.2374			−1.71009			−0.855043	−	0.518557i	$-0.826469\pi$
$829$	−49.2374			−1.71009			−0.855043	+	0.518557i	$0.826469\pi$
$830$	−10.7480	−	5.98244i	−0.373069	−	0.207653i
$831$	−17.0793			−0.592474
$832$	5.41531	−	3.12653i	0.187742	−	0.108393i
$833$	9.94697	+	5.74289i	0.344642	+	0.198979i
$834$	−0.720704	−	1.24830i	−0.0249560	−	0.0432250i
$835$	2.42423	−	4.35535i	0.0838939	−	0.150723i
$836$	15.1673	−	26.2705i	0.524572	−	0.908585i
$837$	42.1601	+	24.3411i	1.45727	+	0.841353i
$838$	−6.32766	−	3.65327i	−0.218585	−	0.126200i
$839$	−14.1933	+	24.5835i	−0.490008	+	0.848718i	−0.999934	−	0.0114999i	$-0.996339\pi$
$839$	−14.1933	+	24.5835i	−0.490008	+	0.848718i	0.509926	+	0.860218i	$0.329673\pi$
$840$	−1.02733	+	1.84570i	−0.0354464	+	0.0636827i
$841$	−6.68477	−	11.5784i	−0.230509	−	0.399254i
$842$	−16.0945	−	9.29217i	−0.554654	−	0.320229i
$843$	−22.9298	+	13.2385i	−0.789745	+	0.455960i
$844$	14.4398			0.497037
$845$	−50.9957	−	28.3847i	−1.75431	−	0.976462i
$846$	−10.8833			−0.374174
$847$		−	22.6105i		−	0.776907i
$848$	6.23264	−	3.59842i	0.214030	−	0.123570i
$849$	27.3299			0.937959
$850$	4.38412	−	8.17587i	0.150374	−	0.280430i
$851$	2.45271	−	4.24821i	0.0840777	−	0.145627i
$852$	4.59148	−	2.65089i	0.157302	−	0.0908181i
$853$	−4.02393	+	2.32322i	−0.137777	+	0.0795455i	−0.567304	−	0.823508i	$-0.692014\pi$
$853$	−4.02393	+	2.32322i	−0.137777	+	0.0795455i	0.429527	+	0.903054i	$0.358680\pi$
$854$	5.65847	+	9.80076i	0.193629	+	0.335375i
$855$	18.3766	−	10.9979i	0.628468	−	0.376120i
$856$	13.3224			0.455351
$857$		−	38.9897i		−	1.33186i	−0.746012	−	0.665932i	$-0.768034\pi$
$857$		−	38.9897i		−	1.33186i	0.746012	−	0.665932i	$-0.231966\pi$
$858$	34.1730	−	19.7298i	1.16665	−	0.673564i
$859$	−21.2084	+	36.7340i	−0.723620	+	1.25335i	0.235919	+	0.971773i	$0.424190\pi$
$859$	−21.2084	+	36.7340i	−0.723620	+	1.25335i	−0.959539	+	0.281575i	$0.909143\pi$
$860$	−0.309882	+	0.556733i	−0.0105669	+	0.0189844i
$861$	−1.67072	−	2.89378i	−0.0569381	−	0.0986196i
$862$			1.93908i			0.0660455i
$863$		−	8.67149i		−	0.295181i	−0.989049	−	0.147590i	$-0.952848\pi$
$863$		−	8.67149i		−	0.295181i	0.989049	−	0.147590i	$-0.0471518\pi$
$864$	−2.57101	+	4.45312i	−0.0874676	+	0.151498i
$865$	3.96731	+	6.62908i	0.134893	+	0.225395i
$866$	−5.06477			−0.172108
$867$	12.3266	+	7.11674i	0.418632	+	0.241697i
$868$			8.51888i			0.289150i
$869$	12.3726	+	21.4301i	0.419713	+	0.726965i
$870$	0.239831	+	15.2790i	0.00813105	+	0.518005i
$871$	−50.9777	−	4.58545i	−1.72731	−	0.155372i
$872$		−	17.1530i		−	0.580873i
$873$	11.3469	−	6.55112i	0.384033	−	0.221722i
$874$	4.44071			0.150209
$875$	−4.61438	+	8.93937i	−0.155994	+	0.302206i
$876$	−1.66014			−0.0560911
$877$	3.49768	−	2.01938i	0.118108	−	0.0681897i	−0.439782	−	0.898104i	$-0.644944\pi$
$877$	3.49768	−	2.01938i	0.118108	−	0.0681897i	0.557890	+	0.829915i	$0.311611\pi$
$878$	−23.5404	−	13.5911i	−0.794451	−	0.458677i
$879$	−35.7436			−1.20560
$880$	0.210945	+	13.4387i	0.00711094	+	0.453017i
$881$	10.3905	+	17.9969i	0.350065	+	0.606331i	0.986261	−	0.165197i	$-0.0528261\pi$
$881$	10.3905	+	17.9969i	0.350065	+	0.606331i	−0.636195	+	0.771528i	$0.719493\pi$
$882$	−10.1740	−	5.87395i	−0.342576	−	0.197786i
$883$	−12.9694	−	7.48790i	−0.436456	−	0.251988i	0.265637	−	0.964073i	$-0.414418\pi$
$883$	−12.9694	−	7.48790i	−0.436456	−	0.251988i	−0.702093	+	0.712085i	$0.747751\pi$
$884$	−5.80105	−	10.0477i	−0.195111	−	0.337941i
$885$	2.89093	−	0.0453786i	0.0971777	−	0.00152538i
$886$	26.8223			0.901112
$887$	19.2780	−	11.1302i	0.647292	−	0.373714i	−0.140126	−	0.990134i	$-0.544751\pi$
$887$	19.2780	−	11.1302i	0.647292	−	0.373714i	0.787418	+	0.616420i	$0.211417\pi$
$888$	−5.06876	+	2.92645i	−0.170097	+	0.0982053i
$889$	4.65305	+	8.05931i	0.156058	+	0.270301i
$890$	−20.9867	−	35.0673i	−0.703477	−	1.17546i
$891$	0.886183	−	1.53491i	0.0296883	−	0.0514216i
$892$	9.61530	+	5.55140i	0.321944	+	0.185874i
$893$		−	28.9420i		−	0.968506i
$894$	−0.251112	−	0.434939i	−0.00839845	−	0.0145465i
$895$	0.572827	+	36.4931i	0.0191475	+	1.21983i
$896$	−0.899799			−0.0300602
$897$	5.00263	+	2.88827i	0.167033	+	0.0964364i
$898$		−	2.99812i		−	0.100049i
$899$	30.8130	+	53.3696i	1.02767	+	1.77998i
$900$	−4.48418	+	8.36246i	−0.149473	+	0.278749i
$901$	−6.67660	−	11.5642i	−0.222430	−	0.385260i
$902$	−18.4123	−	10.6304i	−0.613063	−	0.353952i
$903$	−0.233119	−	0.134591i	−0.00775772	−	0.00447892i
$904$	0.496015	−	0.859123i	0.0164972	−	0.0285740i
$905$	32.8462	+	18.2825i	1.09184	+	0.607730i
$906$	3.14409	−	5.44572i	0.104455	−	0.180922i
$907$	15.1705	+	8.75869i	0.503728	+	0.290828i	0.730252	−	0.683178i	$-0.239403\pi$
$907$	15.1705	+	8.75869i	0.503728	+	0.290828i	−0.226524	+	0.974006i	$0.572736\pi$
$908$	13.3033	−	7.68064i	0.441484	−	0.254891i
$909$	−4.58632	+	7.94375i	−0.152119	+	0.263477i
$910$	6.46085	+	10.7956i	0.214175	+	0.357871i
$911$	−12.8999			−0.427392			−0.213696	−	0.976900i	$-0.568550\pi$
$911$	−12.8999			−0.427392			−0.213696	+	0.976900i	$0.568550\pi$
$912$	−4.58859	−	2.64922i	−0.151943	−	0.0877246i
$913$		−	33.0653i		−	1.09430i
$914$	26.2693			0.868910
$915$	−15.1625	−	25.3354i	−0.501256	−	0.837561i
$916$	−13.1431			−0.434261
$917$	−8.14748	−	4.70395i	−0.269054	−	0.155338i
$918$	8.26245	+	4.77033i	0.272701	+	0.157444i
$919$	5.48785	+	9.50523i	0.181027	+	0.313549i	0.942231	−	0.334965i	$-0.108724\pi$
$919$	5.48785	+	9.50523i	0.181027	+	0.313549i	−0.761203	+	0.648513i	$0.775391\pi$
$920$	−1.68829	+	1.01039i	−0.0556614	+	0.0333117i
$921$	−2.87751	−	4.98399i	−0.0948171	−	0.164228i
$922$	29.4419	−	16.9983i	0.969618	−	0.559809i
$923$		−	31.5776i		−	1.03939i
$924$	−5.67813			−0.186797
$925$	−23.6906	+	14.6880i	−0.778943	+	0.482939i
$926$	−15.4568	+	26.7719i	−0.507941	+	0.879779i
$927$	−7.75112	−	4.47511i	−0.254580	−	0.146982i
$928$	−5.63712	+	3.25459i	−0.185048	+	0.106837i
$929$	−21.0722			−0.691357			−0.345678	−	0.938353i	$-0.612351\pi$
$929$	−21.0722			−0.691357			−0.345678	+	0.938353i	$0.612351\pi$
$930$	−0.348832	−	22.2230i	−0.0114386	−	0.728722i
$931$	15.6207	−	27.0558i	0.511946	−	0.886717i
$932$	−21.9553	+	12.6759i	−0.719169	+	0.415212i
$933$		−	3.95251i		−	0.129399i
$934$	9.33673	−	16.1717i	0.305507	−	0.529154i
$935$	24.9345	−	0.391393i	0.815444	−	0.0127999i
$936$	5.93345	+	10.2770i	0.193941	+	0.335915i
$937$			17.3731i			0.567555i	0.958890	+	0.283778i	$0.0915877\pi$
$937$			17.3731i			0.567555i	−0.958890	+	0.283778i	$0.908412\pi$
$938$	6.02286	+	4.23921i	0.196653	+	0.138415i
$939$	5.57812			0.182035
$940$	6.58516	+	11.0033i	0.214784	+	0.358888i
$941$	−12.3506			−0.402618			−0.201309	−	0.979528i	$-0.564520\pi$
$941$	−12.3506			−0.402618			−0.201309	+	0.979528i	$0.564520\pi$
$942$	−18.4847	−	10.6721i	−0.602263	−	0.347717i
$943$		−	3.11238i		−	0.101353i
$944$	0.615802	+	1.06660i	0.0200427	+	0.0347149i
$945$	−9.03982	−	5.03165i	−0.294065	−	0.163680i
$946$	−1.71274			−0.0556859
$947$			19.3836i			0.629883i	0.949111	+	0.314942i	$0.101985\pi$
$947$			19.3836i			0.629883i	−0.949111	+	0.314942i	$0.898015\pi$
$948$	3.74312	−	2.16109i	0.121571	−	0.0701890i
$949$	−4.94394	+	8.56315i	−0.160487	+	0.277972i
$950$	−22.2384	−	11.9248i	−0.721508	−	0.386892i
$951$	2.56521	+	4.44307i	0.0831826	+	0.144077i
$952$			1.66951i			0.0541092i
$953$		−	59.3110i		−	1.92127i	−0.277813	−	0.960635i	$-0.589609\pi$
$953$		−	59.3110i		−	1.92127i	0.277813	−	0.960635i	$-0.410391\pi$
$954$	6.82898	+	11.8281i	0.221096	+	0.382950i
$955$	−35.9624	+	21.5224i	−1.16371	+	0.696449i
$956$	8.97082	+	15.5379i	0.290137	+	0.502532i
$957$	−35.5727	+	20.5379i	−1.14990	+	0.663897i
$958$	26.7242	+	15.4292i	0.863419	+	0.498495i
$959$	2.54508	−	4.40821i	0.0821850	−	0.142349i
$960$	2.34729	−	0.0368451i	0.0757585	−	0.00118917i
$961$	−29.3171	−	50.7786i	−0.945712	−	1.63802i
$962$			34.8601i			1.12393i
$963$			25.2830i			0.814732i
$964$	−7.58630	+	13.1399i	−0.244338	+	0.423207i
$965$	28.1743	−	0.442247i	0.906962	−	0.0142364i
$966$	−0.415614	−	0.719865i	−0.0133722	−	0.0231613i
$967$	−16.4372	−	9.49005i	−0.528586	−	0.305179i	0.211854	−	0.977301i	$-0.432050\pi$
$967$	−16.4372	−	9.49005i	−0.528586	−	0.305179i	−0.740441	+	0.672122i	$0.765383\pi$
$968$	−21.7619	+	12.5642i	−0.699453	+	0.403829i
$969$	−4.91544	+	8.51380i	−0.157907	+	0.273503i
$970$	−13.4890	−	7.50812i	−0.433107	−	0.241071i
$971$	27.3193	−	47.3184i	0.876717	−	1.51852i	0.0217953	−	0.999762i	$-0.493062\pi$
$971$	27.3193	−	47.3184i	0.876717	−	1.51852i	0.854922	−	0.518756i	$-0.173605\pi$
$972$	−13.6275	−	7.86782i	−0.437101	−	0.252361i
$973$	1.06986	+	0.617686i	0.0342982	+	0.0198021i
$974$	13.3192	−	23.0695i	0.426775	−	0.739196i
$975$	−17.2964	−	27.8977i	−0.553927	−	0.893442i
$976$	6.28859	−	10.8922i	0.201293	−	0.348650i
$977$	26.6024	−	15.3589i	0.851085	−	0.491374i	−0.00993178	−	0.999951i	$-0.503161\pi$
$977$	26.6024	−	15.3589i	0.851085	−	0.491374i	0.861017	+	0.508577i	$0.169828\pi$
$978$			20.8448i			0.666544i
$979$	54.9273	−	95.1369i	1.75548	−	3.04059i
$980$	0.217250	+	13.8404i	0.00693980	+	0.442114i
$981$	32.5525			1.03932
$982$	−28.1850	+	16.2726i	−0.899421	+	0.519281i
$983$			38.6107i			1.23149i	0.787945	+	0.615745i	$0.211145\pi$
$983$			38.6107i			1.23149i	−0.787945	+	0.615745i	$0.788855\pi$
$984$	−1.85677	+	3.21602i	−0.0591917	+	0.102523i
$985$	4.94691	−	8.88758i	0.157622	−	0.283182i
$986$	6.03867	+	10.4593i	0.192310	+	0.333091i
$987$	−4.69166	+	2.70873i	−0.149337	+	0.0862198i
$988$	−27.3298	+	15.7789i	−0.869477	+	0.501993i
$989$	−0.125365	−	0.217138i	−0.00398637	−	0.00690460i
$990$	−25.5035	+	0.400325i	−0.810556	+	0.0127232i
$991$	−55.6761			−1.76861			−0.884304	−	0.466911i	$-0.845367\pi$
$991$	−55.6761			−1.76861			−0.884304	+	0.466911i	$0.845367\pi$
$992$	8.19912	−	4.73376i	0.260322	−	0.150297i
$993$	−5.89319	−	3.40243i	−0.187015	−	0.107973i
$994$	−2.27197	+	3.93517i	−0.0720625	+	0.124816i
$995$	−4.64814	+	2.78178i	−0.147356	+	0.0881883i
$996$	−5.77541			−0.183001
$997$		−	21.5824i		−	0.683520i	−0.939787	−	0.341760i	$-0.888977\pi$
$997$		−	21.5824i		−	0.683520i	0.939787	−	0.341760i	$-0.111023\pi$
$998$	−25.4219	−	14.6774i	−0.804717	−	0.464604i
$999$	−14.3331	−	24.8257i	−0.453479	−	0.785449i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.h.c.439.19	yes	52
5.4	even	2	inner	670.2.h.c.439.8	yes	52
67.29	even	3	inner	670.2.h.c.29.6	✓	52
335.29	even	6	inner	670.2.h.c.29.21	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.h.c.29.6	✓	52	67.29	even	3	inner
670.2.h.c.29.21	yes	52	335.29	even	6	inner
670.2.h.c.439.8	yes	52	5.4	even	2	inner
670.2.h.c.439.19	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)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} -1.04987i q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.0350949 - 2.23579i) q^{5} +(-0.524935 - 0.909214i) q^{6} +(0.779249 + 0.449900i) q^{7} -1.00000i q^{8} +1.89777 q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} -1.04987i q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.0350949 - 2.23579i) q^{5} +(-0.524935 - 0.909214i) q^{6} +(0.779249 + 0.449900i) q^{7} -1.00000i q^{8} +1.89777 q^{9} +(-1.14829 - 1.91871i) q^{10} +(3.00535 - 5.20541i) q^{11} +(-0.909214 - 0.524935i) q^{12} +(-5.41531 + 3.12653i) q^{13} +0.899799 q^{14} +(-2.34729 + 0.0368451i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.60685 + 0.927714i) q^{17} +(1.64352 - 0.948887i) q^{18} +(2.52338 + 4.37063i) q^{19} +(-1.95380 - 1.08750i) q^{20} +(0.472336 - 0.818110i) q^{21} -6.01069i q^{22} +(0.762026 - 0.439956i) q^{23} -1.04987 q^{24} +(-4.99754 + 0.156930i) q^{25} +(-3.12653 + 5.41531i) q^{26} -5.14202i q^{27} +(0.779249 - 0.449900i) q^{28} +(3.25459 - 5.63712i) q^{29} +(-2.01439 + 1.20555i) q^{30} +(-4.73376 + 8.19912i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-5.46500 - 3.15522i) q^{33} +(-0.927714 + 1.60685i) q^{34} +(0.978535 - 1.75803i) q^{35} +(0.948887 - 1.64352i) q^{36} +(4.82799 - 2.78744i) q^{37} +(4.37063 + 2.52338i) q^{38} +(3.28245 + 5.68537i) q^{39} +(-2.23579 + 0.0350949i) q^{40} +(1.76857 - 3.06326i) q^{41} -0.944672i q^{42} -0.284949i q^{43} +(-3.00535 - 5.20541i) q^{44} +(-0.0666022 - 4.24303i) q^{45} +(0.439956 - 0.762026i) q^{46} +(-4.96644 - 2.86738i) q^{47} +(-0.909214 + 0.524935i) q^{48} +(-3.09518 - 5.36101i) q^{49} +(-4.24953 + 2.63467i) q^{50} +(0.973979 + 1.68698i) q^{51} +6.25306i q^{52} +7.19683i q^{53} +(-2.57101 - 4.45312i) q^{54} +(-11.7437 - 6.53665i) q^{55} +(0.449900 - 0.779249i) q^{56} +(4.58859 - 2.64922i) q^{57} -6.50919i q^{58} -1.23160 q^{59} +(-1.14174 + 2.05124i) q^{60} +(6.28859 + 10.8922i) q^{61} +9.46753i q^{62} +(1.47884 + 0.853808i) q^{63} -1.00000 q^{64} +(7.18032 + 11.9978i) q^{65} -6.31044 q^{66} +(6.69356 + 4.71129i) q^{67} +1.85543i q^{68} +(-0.461897 - 0.800028i) q^{69} +(-0.0315784 - 2.01176i) q^{70} +(-2.52497 + 4.37338i) q^{71} -1.89777i q^{72} +(1.36943 - 0.790643i) q^{73} +(2.78744 - 4.82799i) q^{74} +(0.164756 + 5.24676i) q^{75} +5.04677 q^{76} +(4.68383 - 2.70421i) q^{77} +(5.68537 + 3.28245i) q^{78} +(-2.05844 + 3.56532i) q^{79} +(-1.91871 + 1.14829i) q^{80} +0.294869 q^{81} -3.53715i q^{82} +(4.76407 - 2.75054i) q^{83} +(-0.472336 - 0.818110i) q^{84} +(2.13057 + 3.56002i) q^{85} +(-0.142474 - 0.246773i) q^{86} +(-5.91824 - 3.41690i) q^{87} +(-5.20541 - 3.00535i) q^{88} +18.2765 q^{89} +(-2.17919 - 3.64127i) q^{90} -5.62650 q^{91} -0.879912i q^{92} +(8.60801 + 4.96984i) q^{93} -5.73475 q^{94} +(9.68326 - 5.79515i) q^{95} +(-0.524935 + 0.909214i) q^{96} +(5.97904 - 3.45200i) q^{97} +(-5.36101 - 3.09518i) q^{98} +(5.70347 - 9.87870i) 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

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