LMFDB - Embedded newform 738.2.v.a.137.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [738,2,Mod(137,738)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("738.137"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(738, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([4, 15])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 738 = 2 \cdot 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	738.v (of order $24$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [168,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.89295966917$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$21$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			137.11
Character	$\chi$	$=$	738.137
Dual form			738.2.v.a.167.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.258819 + 0.965926i) q^{2} +(-0.442169 + 1.67466i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.752912 - 2.80991i) q^{5} +(-1.73204 + 0.00633171i) q^{6} +(-1.62918 - 0.214486i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.60897 - 1.48096i) q^{9} +2.90903 q^{10} +(-2.48572 - 0.327251i) q^{11} +(-0.454401 - 1.67138i) q^{12} +(2.91283 - 3.79607i) q^{13} +(-0.214486 - 1.62918i) q^{14} +(4.37272 + 2.50332i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.95350 + 1.22338i) q^{17} +(0.755250 - 2.90338i) q^{18} +(1.33777 - 3.22967i) q^{19} +(0.752912 + 2.80991i) q^{20} +(1.07956 - 2.63349i) q^{21} +(-0.327251 - 2.48572i) q^{22} +(-0.00218589 - 0.00378607i) q^{23} +(1.49682 - 0.871503i) q^{24} +(-2.99857 - 1.73122i) q^{25} +(4.42062 + 1.83108i) q^{26} +(3.63372 - 3.71431i) q^{27} +(1.51815 - 0.628840i) q^{28} +(0.742436 - 5.63936i) q^{29} +(-1.28628 + 4.87163i) q^{30} +(3.30388 - 1.90750i) q^{31} +(0.965926 + 0.258819i) q^{32} +(1.64714 - 4.01803i) q^{33} +(-0.417272 + 3.16950i) q^{34} +(-1.82931 + 4.41636i) q^{35} +(2.99992 - 0.0219335i) q^{36} -1.01659 q^{37} +(3.46586 + 0.456290i) q^{38} +(5.06917 + 6.55650i) q^{39} +(-2.51929 + 1.45451i) q^{40} +(-3.54889 - 5.32967i) q^{41} +(2.82316 + 0.361182i) q^{42} +(-1.38876 + 0.372118i) q^{43} +(2.31632 - 0.959451i) q^{44} +(-6.12570 + 6.21593i) q^{45} +(0.00309132 - 0.00309132i) q^{46} +(-3.27913 + 2.51616i) q^{47} +(1.22921 + 1.22026i) q^{48} +(-4.15325 - 1.11286i) q^{49} +(0.896147 - 3.34447i) q^{50} +(-3.35469 + 4.40517i) q^{51} +(-0.624547 + 4.74391i) q^{52} +(-2.48026 - 5.98787i) q^{53} +(4.52822 + 2.54857i) q^{54} +(-2.79107 + 6.73824i) q^{55} +(1.00034 + 1.30367i) q^{56} +(4.81708 + 3.66838i) q^{57} +(5.63936 - 0.742436i) q^{58} +(1.59222 - 0.919266i) q^{59} +(-5.03855 + 0.0184191i) q^{60} +(8.92490 - 2.39142i) q^{61} +(2.69761 + 2.69761i) q^{62} +(3.93284 + 2.97235i) q^{63} +1.00000i q^{64} +(-8.47350 - 11.0429i) q^{65} +(4.30743 + 0.551073i) q^{66} +(3.34027 - 0.439755i) q^{67} +(-3.16950 + 0.417272i) q^{68} +(0.00730692 - 0.00198654i) q^{69} +(-4.73933 - 0.623945i) q^{70} +(-2.85971 + 1.18453i) q^{71} +(0.797623 + 2.89202i) q^{72} +(6.45897 + 6.45897i) q^{73} +(-0.263113 - 0.981950i) q^{74} +(4.22508 - 4.25609i) q^{75} +(0.456290 + 3.46586i) q^{76} +(3.97949 + 1.06630i) q^{77} +(-5.02109 + 6.59338i) q^{78} +(-1.50718 + 11.4482i) q^{79} +(-2.05699 - 2.05699i) q^{80} +(4.61349 + 7.72760i) q^{81} +(4.22955 - 4.80738i) q^{82} +(-3.08241 - 1.77963i) q^{83} +(0.381813 + 2.82045i) q^{84} +(5.66131 - 7.37796i) q^{85} +(-0.718877 - 1.24513i) q^{86} +(9.11573 + 3.73688i) q^{87} +(1.52627 + 1.98907i) q^{88} +(-10.4788 + 4.34044i) q^{89} +(-7.58958 - 4.30817i) q^{90} +(-5.55972 + 5.55972i) q^{91} +(0.00378607 + 0.00218589i) q^{92} +(1.73354 + 6.37631i) q^{93} +(-3.27913 - 2.51616i) q^{94} +(-8.06784 - 6.19068i) q^{95} +(-0.860536 + 1.50316i) q^{96} +(10.2395 - 7.85706i) q^{97} -4.29977i q^{98} +(6.00052 + 4.53505i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 4 q^{3} - 12 q^{7} - 4 q^{9} + 8 q^{15} + 84 q^{16} - 12 q^{17} - 8 q^{21} - 12 q^{22} + 48 q^{25} - 40 q^{27} + 16 q^{30} - 64 q^{33} - 36 q^{34} + 24 q^{35} - 4 q^{36} + 32 q^{39} - 32 q^{42}+ \cdots + 68 q^{99}+O(q^{100}) $ 168 * q - 4 * q^3 - 12 * q^7 - 4 * q^9 + 8 * q^15 + 84 * q^16 - 12 * q^17 - 8 * q^21 - 12 * q^22 + 48 * q^25 - 40 * q^27 + 16 * q^30 - 64 * q^33 - 36 * q^34 + 24 * q^35 - 4 * q^36 + 32 * q^39 - 32 * q^42 + 12 * q^44 + 72 * q^45 - 12 * q^47 - 8 * q^48 + 12 * q^49 - 44 * q^51 + 12 * q^56 - 64 * q^57 - 24 * q^58 - 108 * q^61 + 48 * q^63 - 84 * q^65 - 4 * q^66 - 60 * q^67 + 40 * q^69 + 12 * q^70 + 20 * q^75 - 60 * q^79 + 68 * q^81 + 12 * q^82 - 120 * q^83 + 8 * q^84 + 24 * q^85 + 72 * q^89 + 40 * q^90 - 16 * q^93 - 12 * q^94 - 120 * q^95 + 96 * q^97 + 68 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/738\mathbb{Z}\right)^\times$.

$n$	$83$	$703$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{8}\right)$

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 $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	−0.442169	+	1.67466i	−0.255286	+	0.966866i
$3$	−0.442169	+	1.67466i	−0.255286	+	0.966866i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	0.752912	−	2.80991i	0.336712	−	1.25663i	−0.565288	−	0.824893i	$-0.691235\pi$
$5$	0.752912	−	2.80991i	0.336712	−	1.25663i	0.902001	−	0.431735i	$-0.142098\pi$
$6$	−1.73204	+	0.00633171i	−0.707102	+	0.00258491i
$7$	−1.62918	−	0.214486i	−0.615772	−	0.0810680i	−0.183813	−	0.982961i	$-0.558844\pi$
$7$	−1.62918	−	0.214486i	−0.615772	−	0.0810680i	−0.431959	+	0.901893i	$0.642178\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.60897	−	1.48096i	−0.869658	−	0.493655i
$10$	2.90903			0.919916
$11$	−2.48572	−	0.327251i	−0.749472	−	0.0986699i	−0.253892	−	0.967232i	$-0.581711\pi$
$11$	−2.48572	−	0.327251i	−0.749472	−	0.0986699i	−0.495579	+	0.868563i	$0.665044\pi$
$12$	−0.454401	−	1.67138i	−0.131174	−	0.482487i
$13$	2.91283	−	3.79607i	0.807873	−	1.05284i	−0.189605	−	0.981860i	$-0.560721\pi$
$13$	2.91283	−	3.79607i	0.807873	−	1.05284i	0.997478	−	0.0709797i	$-0.0226126\pi$
$14$	−0.214486	−	1.62918i	−0.0573237	−	0.435417i
$15$	4.37272	+	2.50332i	1.12903	+	0.646356i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	2.95350	+	1.22338i	0.716329	+	0.296713i	0.710921	−	0.703272i	$-0.248278\pi$
$17$	2.95350	+	1.22338i	0.716329	+	0.296713i	0.00540859	+	0.999985i	$0.498278\pi$
$18$	0.755250	−	2.90338i	0.178014	−	0.684332i
$19$	1.33777	−	3.22967i	0.306906	−	0.740937i	−0.692896	−	0.721038i	$-0.743665\pi$
$19$	1.33777	−	3.22967i	0.306906	−	0.740937i	0.999802	−	0.0198995i	$-0.00633461\pi$
$20$	0.752912	+	2.80991i	0.168356	+	0.628314i
$21$	1.07956	−	2.63349i	0.235580	−	0.574674i
$22$	−0.327251	−	2.48572i	−0.0697701	−	0.529957i
$23$	−0.00218589	−	0.00378607i	−0.000455790	−	0.000789451i	0.865797	−	0.500395i	$-0.166812\pi$
$23$	−0.00218589	−	0.00378607i	−0.000455790	−	0.000789451i	−0.866253	+	0.499605i	$0.833478\pi$
$24$	1.49682	−	0.871503i	0.305538	−	0.177895i
$25$	−2.99857	−	1.73122i	−0.599713	−	0.346245i
$26$	4.42062	+	1.83108i	0.866954	+	0.359104i
$27$	3.63372	−	3.71431i	0.699310	−	0.714819i
$28$	1.51815	−	0.628840i	0.286904	−	0.118840i
$29$	0.742436	−	5.63936i	0.137867	−	1.04720i	−0.772972	−	0.634441i	$-0.781231\pi$
$29$	0.742436	−	5.63936i	0.137867	−	1.04720i	0.910839	−	0.412763i	$-0.135436\pi$
$30$	−1.28628	+	4.87163i	−0.234842	+	0.889435i
$31$	3.30388	−	1.90750i	0.593394	−	0.342596i	−0.173044	−	0.984914i	$-0.555360\pi$
$31$	3.30388	−	1.90750i	0.593394	−	0.342596i	0.766439	+	0.642318i	$0.222027\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	1.64714	−	4.01803i	0.286730	−	0.699450i
$34$	−0.417272	+	3.16950i	−0.0715616	+	0.543564i
$35$	−1.82931	+	4.41636i	−0.309211	+	0.746500i
$36$	2.99992	−	0.0219335i	0.499987	−	0.00365559i
$37$	−1.01659			−0.167126			−0.0835632	−	0.996502i	$-0.526630\pi$
$37$	−1.01659			−0.167126			−0.0835632	+	0.996502i	$0.526630\pi$
$38$	3.46586	+	0.456290i	0.562237	+	0.0740199i
$39$	5.06917	+	6.55650i	0.811716	+	1.04988i
$40$	−2.51929	+	1.45451i	−0.398335	+	0.229979i
$41$	−3.54889	−	5.32967i	−0.554243	−	0.832355i
$41$	−3.54889	−	5.32967i	−0.554243	−	0.832355i
$42$	2.82316	+	0.361182i	0.435624	+	0.0557316i
$43$	−1.38876	+	0.372118i	−0.211784	+	0.0567475i	−0.363151	−	0.931730i	$-0.618299\pi$
$43$	−1.38876	+	0.372118i	−0.211784	+	0.0567475i	0.151367	+	0.988478i	$0.451633\pi$
$44$	2.31632	−	0.959451i	0.349198	−	0.144643i
$45$	−6.12570	+	6.21593i	−0.913165	+	0.926617i
$46$	0.00309132	−	0.00309132i	0.000455790	−	0.000455790i
$47$	−3.27913	+	2.51616i	−0.478310	+	0.367020i	−0.819598	−	0.572938i	$-0.805803\pi$
$47$	−3.27913	+	2.51616i	−0.478310	+	0.367020i	0.341288	+	0.939959i	$0.389137\pi$
$48$	1.22921	+	1.22026i	0.177422	+	0.176129i
$49$	−4.15325	−	1.11286i	−0.593322	−	0.158980i
$50$	0.896147	−	3.34447i	0.126734	−	0.472979i
$51$	−3.35469	+	4.40517i	−0.469751	+	0.616847i
$52$	−0.624547	+	4.74391i	−0.0866091	+	0.657861i
$53$	−2.48026	−	5.98787i	−0.340690	−	0.822498i	−0.997646	−	0.0685694i	$-0.978157\pi$
$53$	−2.48026	−	5.98787i	−0.340690	−	0.822498i	0.656957	−	0.753928i	$-0.271843\pi$
$54$	4.52822	+	2.54857i	0.616213	+	0.346816i
$55$	−2.79107	+	6.73824i	−0.376348	+	0.908584i
$56$	1.00034	+	1.30367i	0.133676	+	0.174210i
$57$	4.81708	+	3.66838i	0.638038	+	0.485888i
$58$	5.63936	−	0.742436i	0.740484	−	0.0974866i
$59$	1.59222	−	0.919266i	0.207289	−	0.119678i	−0.392762	−	0.919640i	$-0.628480\pi$
$59$	1.59222	−	0.919266i	0.207289	−	0.119678i	0.600051	+	0.799962i	$0.295147\pi$
$60$	−5.03855	+	0.0184191i	−0.650474	+	0.00237790i
$61$	8.92490	−	2.39142i	1.14272	−	0.306190i	0.362674	−	0.931916i	$-0.381864\pi$
$61$	8.92490	−	2.39142i	1.14272	−	0.306190i	0.780043	+	0.625726i	$0.215197\pi$
$62$	2.69761	+	2.69761i	0.342596	+	0.342596i
$63$	3.93284	+	2.97235i	0.495492	+	0.374481i
$64$			1.00000i			0.125000i
$65$	−8.47350	−	11.0429i	−1.05101	−	1.36970i
$66$	4.30743	+	0.551073i	0.530208	+	0.0678323i
$67$	3.34027	−	0.439755i	0.408079	−	0.0537246i	0.0763073	−	0.997084i	$-0.475687\pi$
$67$	3.34027	−	0.439755i	0.408079	−	0.0537246i	0.331772	+	0.943360i	$0.392354\pi$
$68$	−3.16950	+	0.417272i	−0.384358	+	0.0506017i
$69$	0.00730692	−	0.00198654i	0.000879650	−	0.000239151i
$70$	−4.73933	−	0.623945i	−0.566459	−	0.0745757i
$71$	−2.85971	+	1.18453i	−0.339385	+	0.140578i	−0.545865	−	0.837873i	$-0.683799\pi$
$71$	−2.85971	+	1.18453i	−0.339385	+	0.140578i	0.206480	+	0.978451i	$0.433799\pi$
$72$	0.797623	+	2.89202i	0.0940007	+	0.340828i
$73$	6.45897	+	6.45897i	0.755966	+	0.755966i	0.975586	−	0.219620i	$-0.0704817\pi$
$73$	6.45897	+	6.45897i	0.755966	+	0.755966i	−0.219620	+	0.975586i	$0.570482\pi$
$74$	−0.263113	−	0.981950i	−0.0305862	−	0.114149i
$75$	4.22508	−	4.25609i	0.487871	−	0.491451i
$76$	0.456290	+	3.46586i	0.0523400	+	0.397562i
$77$	3.97949	+	1.06630i	0.453505	+	0.121516i
$78$	−5.02109	+	6.59338i	−0.568527	+	0.746554i
$79$	−1.50718	+	11.4482i	−0.169571	+	1.28802i	0.669014	+	0.743249i	$0.266716\pi$
$79$	−1.50718	+	11.4482i	−0.169571	+	1.28802i	−0.838585	+	0.544770i	$0.816617\pi$
$80$	−2.05699	−	2.05699i	−0.229979	−	0.229979i
$81$	4.61349	+	7.72760i	0.512610	+	0.858622i
$82$	4.22955	−	4.80738i	0.467075	−	0.530887i
$83$	−3.08241	−	1.77963i	−0.338338	−	0.195340i	0.321199	−	0.947012i	$-0.395914\pi$
$83$	−3.08241	−	1.77963i	−0.338338	−	0.195340i	−0.659537	+	0.751672i	$0.729248\pi$
$84$	0.381813	+	2.82045i	0.0416592	+	0.307736i
$85$	5.66131	−	7.37796i	0.614055	−	0.800253i
$86$	−0.718877	−	1.24513i	−0.0775185	−	0.134266i
$87$	9.11573	+	3.73688i	0.977309	+	0.400635i
$88$	1.52627	+	1.98907i	0.162701	+	0.212035i
$89$	−10.4788	+	4.34044i	−1.11075	+	0.460086i	−0.861194	−	0.508276i	$-0.830283\pi$
$89$	−10.4788	+	4.34044i	−1.11075	+	0.460086i	−0.249551	+	0.968362i	$0.580283\pi$
$90$	−7.58958	−	4.30817i	−0.800012	−	0.454121i
$91$	−5.55972	+	5.55972i	−0.582817	+	0.582817i
$92$	0.00378607	+	0.00218589i	0.000394725	+	0.000227895i
$93$	1.73354	+	6.37631i	0.179759	+	0.661193i
$94$	−3.27913	−	2.51616i	−0.338216	−	0.259523i
$95$	−8.06784	−	6.19068i	−0.827743	−	0.635150i
$96$	−0.860536	+	1.50316i	−0.0878281	+	0.153415i
$97$	10.2395	−	7.85706i	1.03967	−	0.797764i	0.0599593	−	0.998201i	$-0.480903\pi$
$97$	10.2395	−	7.85706i	1.03967	−	0.797764i	0.979707	+	0.200437i	$0.0642362\pi$
$98$		−	4.29977i		−	0.434342i
$99$	6.00052	+	4.53505i	0.603075	+	0.455790i
$100$	3.46245			0.346245
$101$	−1.14926	+	0.881855i	−0.114355	+	0.0877479i	−0.664356	−	0.747416i	$-0.731294\pi$
$101$	−1.14926	+	0.881855i	−0.114355	+	0.0877479i	0.550001	+	0.835164i	$0.314627\pi$
$102$	−5.12333	−	2.10024i	−0.507285	−	0.207955i
$103$	16.3241	+	4.37403i	1.60846	+	0.430986i	0.947583	−	0.319508i	$-0.103518\pi$
$103$	16.3241	+	4.37403i	1.60846	+	0.430986i	0.660877	+	0.750494i	$0.270184\pi$
$104$	−4.74391	+	0.624547i	−0.465178	+	0.0612419i
$105$	−6.58703	−	5.01625i	−0.642828	−	0.489536i
$106$	5.14190	−	3.94552i	0.499426	−	0.383223i
$107$	−19.9001			−1.92382			−0.961910	−	0.273367i	$-0.911863\pi$
$107$	−19.9001			−1.92382			−0.961910	+	0.273367i	$0.911863\pi$
$108$	−1.28974	+	5.03354i	−0.124105	+	0.484353i
$109$	−10.8300	−	4.48592i	−1.03732	−	0.429674i	−0.201973	−	0.979391i	$-0.564735\pi$
$109$	−10.8300	−	4.48592i	−1.03732	−	0.429674i	−0.835351	+	0.549717i	$0.814735\pi$
$110$	−7.23102	−	0.951982i	−0.689451	−	0.0907679i
$111$	0.449504	−	1.70244i	0.0426651	−	0.161589i
$112$	−1.00034	+	1.30367i	−0.0945233	+	0.123185i
$113$	−5.35238	−	9.27059i	−0.503509	−	0.872104i	−0.999992	−	0.00405717i	$-0.998709\pi$
$113$	−5.35238	−	9.27059i	−0.503509	−	0.872104i	0.496482	−	0.868047i	$-0.334625\pi$
$114$	−2.29663	+	5.60239i	−0.215099	+	0.524712i
$115$	−0.0122843	+	0.00329157i	−0.00114552	+	0.000306940i
$116$	2.17671	+	5.25505i	0.202103	+	0.487919i
$117$	−13.2213	+	5.59005i	−1.22231	+	0.516800i
$118$	1.30004	+	1.30004i	0.119678	+	0.119678i
$119$	−4.54939	−	2.62659i	−0.417042	−	0.240779i
$120$	−1.32186	−	4.86210i	−0.120669	−	0.443847i
$121$	−4.55349	−	1.22010i	−0.413953	−	0.110918i
$122$	4.61987	+	8.00185i	0.418263	+	0.724453i
$123$	10.4946	−	3.58657i	0.946266	−	0.323390i
$124$	−1.90750	+	3.30388i	−0.171298	+	0.296697i
$125$	3.16274	−	3.16274i	0.282884	−	0.282884i
$126$	−1.85317	+	4.56814i	−0.165094	+	0.406962i
$127$		−	5.72884i		−	0.508352i	−0.967158	−	0.254176i	$-0.918196\pi$
$127$		−	5.72884i		−	0.508352i	0.967158	−	0.254176i	$-0.0818043\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	−0.00910344	−	2.49025i	−0.000801513	−	0.219254i
$130$	8.47350	−	11.0429i	0.743175	−	0.968524i
$131$	4.92993	−	18.3987i	0.430730	−	1.60751i	−0.320354	−	0.947298i	$-0.603802\pi$
$131$	4.92993	−	18.3987i	0.430730	−	1.60751i	0.751083	−	0.660207i	$-0.229532\pi$
$132$	0.582550	+	4.30329i	0.0507045	+	0.374553i
$133$	−2.87219	+	4.97478i	−0.249051	+	0.431368i
$134$	1.28930	+	3.11264i	0.111378	+	0.268891i
$135$	−7.70098	−	13.0070i	−0.662795	−	1.11946i
$136$	−1.22338	−	2.95350i	−0.104904	−	0.253261i
$137$	2.05853	−	1.57956i	0.175872	−	0.134951i	−0.517075	−	0.855940i	$-0.672979\pi$
$137$	2.05853	−	1.57956i	0.175872	−	0.134951i	0.692946	+	0.720989i	$0.256312\pi$
$138$	0.00381002	+	0.00654379i	0.000324331	+	0.000557044i
$139$	−4.71663	−	8.16944i	−0.400059	−	0.692923i	0.593673	−	0.804706i	$-0.297677\pi$
$139$	−4.71663	−	8.16944i	−0.400059	−	0.692923i	−0.993733	+	0.111783i	$0.964344\pi$
$140$	−0.623945	−	4.73933i	−0.0527330	−	0.400547i
$141$	−2.76379	−	6.60400i	−0.232753	−	0.556157i
$142$	−1.88431	−	2.45569i	−0.158128	−	0.206077i
$143$	−8.48273	+	8.48273i	−0.709362	+	0.709362i
$144$	−2.58704	+	1.51895i	−0.215587	+	0.126580i
$145$	−15.2871	−	6.33212i	−1.26952	−	0.525854i
$146$	−4.56718	+	7.91060i	−0.377983	+	0.654686i
$147$	3.70010	−	6.46322i	0.305179	−	0.533077i
$148$	0.880392	−	0.508295i	0.0723678	−	0.0417816i
$149$	0.327772	+	2.48967i	0.0268521	+	0.203962i	0.999612	−	0.0278529i	$-0.00886699\pi$
$149$	0.327772	+	2.48967i	0.0268521	+	0.203962i	−0.972760	+	0.231815i	$0.925534\pi$
$150$	5.20460	+	2.97956i	0.424954	+	0.243280i
$151$	−2.44054	+	18.5377i	−0.198608	+	1.50858i	0.544133	+	0.838999i	$0.316859\pi$
$151$	−2.44054	+	18.5377i	−0.198608	+	1.50858i	−0.742741	+	0.669579i	$0.766474\pi$
$152$	−3.22967	+	1.33777i	−0.261961	+	0.108508i
$153$	−5.89383	−	7.56580i	−0.476488	−	0.611659i
$154$			4.11987i			0.331989i
$155$	−2.87235	−	10.7198i	−0.230713	−	0.861033i
$156$	−7.66827	−	3.14351i	−0.613953	−	0.251682i
$157$	3.20044	+	2.45578i	0.255423	+	0.195993i	0.728533	−	0.685010i	$-0.240202\pi$
$157$	3.20044	+	2.45578i	0.255423	+	0.195993i	−0.473111	+	0.881003i	$0.656869\pi$
$158$	−11.4482	+	1.50718i	−0.910767	+	0.119905i
$159$	11.1243	−	1.50594i	0.882218	−	0.119429i
$160$	1.45451	−	2.51929i	0.114989	−	0.199168i
$161$	0.00274915	+	0.00663704i	0.000216664	+	0.000523072i
$162$	−6.27023	+	6.45633i	−0.492636	+	0.507258i
$163$		−	0.994696i		−	0.0779106i	−0.999241	−	0.0389553i	$-0.987597\pi$
$163$		−	0.994696i		−	0.0779106i	0.999241	−	0.0389553i	$-0.0124030\pi$
$164$	5.73826	+	2.84119i	0.448083	+	0.221859i
$165$	−10.0501	−	7.65353i	−0.782402	−	0.595827i
$166$	0.921203	−	3.43798i	0.0714992	−	0.266839i
$167$	−2.61884	−	2.00951i	−0.202652	−	0.155500i	0.502450	−	0.864606i	$-0.332432\pi$
$167$	−2.61884	−	2.00951i	−0.202652	−	0.155500i	−0.705102	+	0.709106i	$0.749099\pi$
$168$	−2.62552	+	1.09879i	−0.202563	+	0.0847734i
$169$	−2.56094	−	9.55755i	−0.196995	−	0.735196i
$170$	8.59182	+	3.55885i	0.658963	+	0.272951i
$171$	−8.27324	+	6.44493i	−0.632671	+	0.492856i
$172$	1.01665	−	1.01665i	0.0775185	−	0.0775185i
$173$	12.4806	−	3.34416i	0.948880	−	0.254252i	0.248993	−	0.968505i	$-0.419900\pi$
$173$	12.4806	−	3.34416i	0.948880	−	0.254252i	0.699887	+	0.714254i	$0.253234\pi$
$174$	−1.25022	+	9.77230i	−0.0947791	+	0.740836i
$175$	4.51389	+	3.46363i	0.341218	+	0.261826i
$176$	−1.52627	+	1.98907i	−0.115047	+	0.149932i
$177$	0.835431	+	3.07289i	0.0627948	+	0.230973i
$178$	−6.90465	−	8.99831i	−0.517525	−	0.674452i
$179$	−2.61333	+	6.30914i	−0.195330	+	0.471567i	−0.990951	−	0.134227i	$-0.957145\pi$
$179$	−2.61333	+	6.30914i	−0.195330	+	0.471567i	0.795621	+	0.605795i	$0.207145\pi$
$180$	2.19704	−	8.44601i	0.163758	−	0.629528i
$181$	−9.24738	+	22.3252i	−0.687352	+	1.65942i	0.0626959	+	0.998033i	$0.480030\pi$
$181$	−9.24738	+	22.3252i	−0.687352	+	1.65942i	−0.750048	+	0.661383i	$0.769970\pi$
$182$	−6.80924	−	3.93132i	−0.504735	−	0.291409i
$183$	0.0585034	+	16.0036i	0.00432469	+	1.18302i
$184$	−0.00113150	+	0.00422282i	−8.34153e−5	+	0.000311310i
$185$	−0.765403	+	2.85652i	−0.0562735	+	0.210016i
$186$	−5.71037	+	3.32478i	−0.418705	+	0.243785i
$187$	−6.94122	−	4.00751i	−0.507592	−	0.293058i
$188$	1.58173	−	3.81863i	0.115359	−	0.278502i
$189$	−6.71665	+	5.27190i	−0.488565	+	0.383474i
$190$	3.89162	−	9.39520i	0.282328	−	0.681600i
$191$	0.523431	+	0.682148i	0.0378741	+	0.0493585i	0.811906	−	0.583788i	$-0.198430\pi$
$191$	0.523431	+	0.682148i	0.0378741	+	0.0493585i	−0.774032	+	0.633146i	$0.781763\pi$
$192$	−1.67466	−	0.442169i	−0.120858	−	0.0319108i
$193$	3.84030	−	5.00478i	0.276431	−	0.360252i	−0.634419	−	0.772989i	$-0.718761\pi$
$193$	3.84030	−	5.00478i	0.276431	−	0.360252i	0.910850	+	0.412737i	$0.135427\pi$
$194$	10.2395	+	7.85706i	0.735155	+	0.564104i
$195$	22.2398	−	9.30741i	1.59262	−	0.666518i
$196$	4.15325	−	1.11286i	0.296661	−	0.0794901i
$197$	7.94828	−	7.94828i	0.566292	−	0.566292i	−0.364796	−	0.931087i	$-0.618861\pi$
$197$	7.94828	−	7.94828i	0.566292	−	0.566292i	0.931087	+	0.364796i	$0.118861\pi$
$198$	−2.82747	+	6.96982i	−0.200940	+	0.495323i
$199$	10.8804	+	4.50682i	0.771293	+	0.319480i	0.733396	−	0.679801i	$-0.237934\pi$
$199$	10.8804	+	4.50682i	0.771293	+	0.319480i	0.0378972	+	0.999282i	$0.487934\pi$
$200$	0.896147	+	3.34447i	0.0633672	+	0.236490i
$201$	−0.740523	+	5.78826i	−0.0522325	+	0.408273i
$202$	−1.14926	−	0.881855i	−0.0808614	−	0.0620471i
$203$	−2.41913	+	9.02830i	−0.169789	+	0.633662i
$204$	0.702664	−	5.49234i	0.0491963	−	0.384541i
$205$	−17.6479	+	5.95927i	−1.23258	+	0.416213i
$206$			16.8999i			1.17747i
$207$	9.58887e−5		0.0131150i	6.66472e−6		0.000911555i
$208$	−1.83108	−	4.42062i	−0.126962	−	0.306515i
$209$	−4.38224	+	7.59026i	−0.303126	+	0.525029i
$210$	3.14048	−	7.66088i	0.216714	−	0.528651i
$211$	13.5835	−	1.78830i	0.935124	−	0.123111i	0.352462	−	0.935826i	$-0.385345\pi$
$211$	13.5835	−	1.78830i	0.935124	−	0.123111i	0.582662	+	0.812715i	$0.302011\pi$
$212$	5.14190	+	3.94552i	0.353147	+	0.270980i
$213$	−0.719211	−	5.31280i	−0.0492795	−	0.364027i
$214$	−5.15054	−	19.2221i	−0.352083	−	1.31399i
$215$			4.18247i			0.285242i
$216$	−5.19584	+	0.0569844i	−0.353532	+	0.00387730i
$217$	−5.79175	+	2.39902i	−0.393170	+	0.162856i
$218$	1.53007	−	11.6220i	0.103629	−	0.787141i
$219$	−13.6725	+	7.96063i	−0.923905	+	0.537930i
$220$	−0.951982	−	7.23102i	−0.0641826	−	0.487515i
$221$	13.2471	−	7.64820i	0.891095	−	0.514474i
$222$	1.76077	−	0.00643675i	0.118175	−	0.000432006i
$223$	9.46640	−	16.3963i	0.633917	−	1.09798i	−0.352826	−	0.935689i	$-0.614779\pi$
$223$	9.46640	−	16.3963i	0.633917	−	1.09798i	0.986743	−	0.162288i	$-0.0518873\pi$
$224$	−1.51815	−	0.628840i	−0.101436	−	0.0420162i
$225$	5.25930	+	8.95749i	0.350620	+	0.597166i
$226$	7.56941	−	7.56941i	0.503509	−	0.503509i
$227$	7.18798	+	9.36756i	0.477083	+	0.621747i	0.968451	−	0.249206i	$-0.0801695\pi$
$227$	7.18798	+	9.36756i	0.477083	+	0.621747i	−0.491368	+	0.870952i	$0.663503\pi$
$228$	−6.00590	−	0.768367i	−0.397750	−	0.0508863i
$229$	2.04908	+	15.5643i	0.135407	+	1.02852i	0.915348	+	0.402664i	$0.131916\pi$
$229$	2.04908	+	15.5643i	0.135407	+	1.02852i	−0.779941	+	0.625853i	$0.784751\pi$
$230$	−0.00635882	−	0.0110138i	−0.000419288	−	0.000726228i
$231$	−3.54530	+	6.19281i	−0.233264	+	0.407457i
$232$	−4.51261	+	3.46265i	−0.296268	+	0.227334i
$233$	7.57938	+	18.2982i	0.496541	+	1.19876i	0.951335	+	0.308160i	$0.0997132\pi$
$233$	7.57938	+	18.2982i	0.496541	+	1.19876i	−0.454793	+	0.890597i	$0.650287\pi$
$234$	−8.82151	−	11.3240i	−0.576680	−	0.740274i
$235$	4.60129	+	11.1085i	0.300155	+	0.724638i
$236$	−0.919266	+	1.59222i	−0.0598391	+	0.103644i
$237$	−18.5054	−	7.58604i	−1.20205	−	0.492766i
$238$	1.35962	−	5.07419i	0.0881313	−	0.328911i
$239$	13.2335	−	17.2463i	0.856005	−	1.11557i	−0.136166	−	0.990686i	$-0.543478\pi$
$239$	13.2335	−	17.2463i	0.856005	−	1.11557i	0.992172	−	0.124882i	$-0.0398552\pi$
$240$	4.35430	−	2.53523i	0.281069	−	0.163648i
$241$	24.2739	−	6.50416i	1.56362	−	0.418970i	0.629810	−	0.776749i	$-0.283133\pi$
$241$	24.2739	−	6.50416i	1.56362	−	0.418970i	0.933806	+	0.357779i	$0.116466\pi$
$242$		−	4.71412i		−	0.303035i
$243$	−14.9810	+	4.30912i	−0.961034	+	0.276430i
$244$	−6.53348	+	6.53348i	−0.418263	+	0.418263i
$245$	−6.25407	+	10.8324i	−0.399558	+	0.692055i
$246$	6.18056	+	9.20873i	0.394058	+	0.587127i
$247$	−8.36335	−	14.4858i	−0.532147	−	0.921706i
$248$	−3.68500	−	0.987393i	−0.233998	−	0.0626995i
$249$	4.34322	−	4.37509i	0.275240	−	0.277260i
$250$	3.87355	+	2.23639i	0.244985	+	0.141442i
$251$	19.8040	+	19.8040i	1.25002	+	1.25002i	0.955711	+	0.294305i	$0.0950883\pi$
$251$	19.8040	+	19.8040i	1.25002	+	1.25002i	0.294305	+	0.955711i	$0.404912\pi$
$252$	−4.89212	−	0.607706i	−0.308174	−	0.0382819i
$253$	0.00419451	+	0.0101264i	0.000263707	+	0.000636644i
$254$	5.53363	−	1.48273i	0.347211	−	0.0930349i
$255$	9.85233	+	12.7431i	0.616977	+	0.798003i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.86215	−	5.03325i	0.240914	−	0.313966i	−0.657210	−	0.753708i	$-0.728263\pi$
$257$	3.86215	−	5.03325i	0.240914	−	0.313966i	0.898124	+	0.439742i	$0.144930\pi$
$258$	2.40304	−	0.653316i	0.149607	−	0.0406737i
$259$	1.65621	+	0.218044i	0.102912	+	0.0135486i
$260$	12.8597	+	5.32666i	0.797525	+	0.330346i
$261$	−10.2887	+	13.6134i	−0.636854	+	0.842650i
$262$	19.0478			1.17678
$263$	−23.6847	+	18.1739i	−1.46046	+	1.12065i	−0.492266	+	0.870445i	$0.663831\pi$
$263$	−23.6847	+	18.1739i	−1.46046	+	1.12065i	−0.968193	+	0.250205i	$0.919502\pi$
$264$	−4.00588	+	1.67647i	−0.246545	+	0.103180i
$265$	−18.6928	+	2.46095i	−1.14829	+	0.151175i
$266$	−5.54865	−	1.48676i	−0.340210	−	0.0911589i
$267$	−2.63539	−	19.4676i	−0.161283	−	1.19140i
$268$	−2.67288	+	2.05097i	−0.163272	+	0.125283i
$269$	−4.05761			−0.247397			−0.123698	−	0.992320i	$-0.539476\pi$
$269$	−4.05761			−0.247397			−0.123698	+	0.992320i	$0.539476\pi$
$270$	10.5706	−	10.8050i	0.643306	−	0.657573i
$271$			0.598838i			0.0363768i	0.999835	+	0.0181884i	$0.00578987\pi$
$271$			0.598838i			0.0363768i	−0.999835	+	0.0181884i	$0.994210\pi$
$272$	2.53623	−	1.94612i	0.153782	−	0.118001i
$273$	−6.85231	−	11.7690i	−0.414721	−	0.712291i
$274$	2.05853	+	1.57956i	0.124360	+	0.0954248i
$275$	6.88705	+	5.28462i	0.415304	+	0.318674i
$276$	−0.00533471	+	0.00537385i	−0.000321112	+	0.000323468i
$277$	16.7807	+	9.68835i	1.00826	+	0.582117i	0.910680	−	0.413112i	$-0.135558\pi$
$277$	16.7807	+	9.68835i	1.00826	+	0.582117i	0.0975751	+	0.995228i	$0.468891\pi$
$278$	6.67032	−	6.67032i	0.400059	−	0.400059i
$279$	−11.4447	+	0.0836763i	−0.685175	+	0.00500957i
$280$	4.41636	−	1.82931i	0.263928	−	0.109322i
$281$	−1.29489	−	1.68753i	−0.0772467	−	0.100670i	0.753132	−	0.657870i	$-0.228542\pi$
$281$	−1.29489	−	1.68753i	−0.0772467	−	0.100670i	−0.830378	+	0.557200i	$0.811876\pi$
$282$	5.66365	−	4.37886i	0.337265	−	0.260757i
$283$	12.4096	+	21.4941i	0.737677	+	1.27769i	0.953539	+	0.301270i	$0.0974106\pi$
$283$	12.4096	+	21.4941i	0.737677	+	1.27769i	−0.215862	+	0.976424i	$0.569256\pi$
$284$	1.88431	−	2.45569i	0.111814	−	0.145718i
$285$	13.9346	−	10.7736i	0.825416	−	0.638172i
$286$	−10.3892	−	5.99820i	−0.614325	−	0.354681i
$287$	4.63864	+	9.44418i	0.273810	+	0.557473i
$288$	−2.13677	−	2.10575i	−0.125911	−	0.124083i
$289$	−4.79430	−	4.79430i	−0.282018	−	0.282018i
$290$	2.15977	−	16.4051i	0.126826	−	0.963339i
$291$	8.63031	+	20.6219i	0.505918	+	1.20888i
$292$	−8.82312	−	2.36415i	−0.516334	−	0.138351i
$293$	2.15497	+	16.3686i	0.125895	+	0.956265i	0.931482	+	0.363788i	$0.118517\pi$
$293$	2.15497	+	16.3686i	0.125895	+	0.956265i	−0.805587	+	0.592477i	$0.798150\pi$
$294$	7.20065	+	1.90122i	0.419950	+	0.110882i
$295$	−1.38425	−	5.16610i	−0.0805944	−	0.300782i
$296$	0.718837	+	0.718837i	0.0417816	+	0.0417816i
$297$	−10.2479	+	8.04358i	−0.594644	+	0.466736i
$298$	−2.32001	+	0.960978i	−0.134394	+	0.0556680i
$299$	−0.0207393	−	0.00273038i	−0.00119939	−	0.000157902i
$300$	−1.53099	+	5.79842i	−0.0883915	+	0.334772i
$301$	2.34236	−	0.308378i	0.135011	−	0.0177746i
$302$	−18.5377	+	2.44054i	−1.06673	+	0.140437i
$303$	−0.968643	−	2.31454i	−0.0556471	−	0.132967i
$304$	−2.12809	−	2.77338i	−0.122054	−	0.159064i
$305$		−	26.8787i		−	1.53907i
$306$	5.78257	−	7.65117i	0.330567	−	0.437388i
$307$	−18.8557	−	18.8557i	−1.07615	−	1.07615i	−0.996851	−	0.0793004i	$-0.974731\pi$
$307$	−18.8557	−	18.8557i	−1.07615	−	1.07615i	−0.0793004	−	0.996851i	$-0.525269\pi$
$308$	−3.97949	+	1.06630i	−0.226753	+	0.0607582i
$309$	−14.5430	+	25.4032i	−0.827323	+	1.44514i
$310$	9.61108	−	5.54896i	0.545873	−	0.315160i
$311$	−29.1712	+	3.84047i	−1.65415	+	0.217773i	−0.899053	−	0.437841i	$-0.855743\pi$
$311$	−29.1712	+	3.84047i	−1.65415	+	0.217773i	−0.755097	+	0.655613i	$0.772410\pi$
$312$	1.05170	−	8.22058i	0.0595410	−	0.465399i
$313$	5.49758	+	7.16458i	0.310741	+	0.404966i	0.922450	−	0.386117i	$-0.126184\pi$
$313$	5.49758	+	7.16458i	0.310741	+	0.404966i	−0.611708	+	0.791083i	$0.709517\pi$
$314$	−1.54377	+	3.72699i	−0.0871199	+	0.210326i
$315$	11.3131	−	8.81300i	0.637421	−	0.496557i
$316$	−4.41883	−	10.6680i	−0.248578	−	0.600122i
$317$	−4.21481	+	32.0146i	−0.236727	+	1.79812i	0.299552	+	0.954080i	$0.403163\pi$
$317$	−4.21481	+	32.0146i	−0.236727	+	1.79812i	−0.536279	+	0.844041i	$0.680170\pi$
$318$	4.33382	+	10.3555i	0.243029	+	0.580709i
$319$	−3.69097	+	13.7749i	−0.206655	+	0.771246i
$320$	2.80991	+	0.752912i	0.157079	+	0.0420891i
$321$	8.79922	−	33.3260i	0.491125	−	1.86007i
$322$	−0.00569936	+	0.00437327i	−0.000317613	+	0.000243713i
$323$	7.90223	−	7.90223i	0.439692	−	0.439692i
$324$	−7.85919	−	4.38555i	−0.436622	−	0.243642i
$325$	−15.3061	+	6.34001i	−0.849032	+	0.351681i
$326$	0.960802	−	0.257446i	0.0532139	−	0.0142586i
$327$	12.3011	−	16.1530i	0.680251	−	0.893263i
$328$	−1.25920	+	6.27809i	−0.0695279	+	0.346649i
$329$	5.88198	−	3.39596i	0.324284	−	0.187225i
$330$	4.79158	−	11.6886i	0.263768	−	0.643435i
$331$	25.9895	+	3.42158i	1.42851	+	0.188067i	0.804781	−	0.593572i	$-0.202283\pi$
$331$	25.9895	+	3.42158i	1.42851	+	0.188067i	0.623731	+	0.781639i	$0.285616\pi$
$332$	3.55926			0.195340
$333$	2.65226	+	1.50553i	0.145343	+	0.0825027i
$334$	1.26323	−	3.04970i	0.0691208	−	0.166872i
$335$	1.27926	−	9.71694i	0.0698934	−	0.530893i
$336$	−1.74088	−	2.25167i	−0.0949730	−	0.122839i
$337$	−35.2467	−	9.44433i	−1.92001	−	0.514466i	−0.988617	−	0.150456i	$-0.951926\pi$
$337$	−35.2467	−	9.44433i	−1.92001	−	0.514466i	−0.931395	−	0.364010i	$-0.881407\pi$
$338$	8.56906	−	4.94735i	0.466095	−	0.269100i
$339$	17.8917	−	4.86425i	0.971746	−	0.264190i
$340$	−1.21386	+	9.22016i	−0.0658306	+	0.500033i
$341$	−8.83674	+	3.66030i	−0.478536	+	0.198216i
$342$	−8.36660	−	6.32327i	−0.452414	−	0.341923i
$343$	17.1548	+	7.10575i	0.926272	+	0.383674i
$344$	1.24513	+	0.718877i	0.0671330	+	0.0387592i
$345$	−8.05244e−5	−	0.0220274i	−4.33529e−6	−	0.00118592i
$346$	6.46042	+	11.1898i	0.347314	+	0.601566i
$347$	−3.27549	−	24.8798i	−0.175838	−	1.33562i	−0.820717	−	0.571335i	$-0.806426\pi$
$347$	−3.27549	−	24.8798i	−0.175838	−	1.33562i	0.644879	−	0.764284i	$-0.276908\pi$
$348$	−9.76289	+	1.32164i	−0.523346	+	0.0708471i
$349$	−2.00439	−	7.48049i	−0.107293	−	0.400422i	0.891303	−	0.453409i	$-0.149792\pi$
$349$	−2.00439	−	7.48049i	−0.107293	−	0.400422i	−0.998595	+	0.0529874i	$0.983126\pi$
$350$	−2.17733	+	5.25653i	−0.116383	+	0.280973i
$351$	−3.51537	−	24.6130i	−0.187637	−	1.31374i
$352$	−2.31632	−	0.959451i	−0.123460	−	0.0511389i
$353$	−6.44458	+	11.1623i	−0.343011	+	0.594112i	−0.984990	−	0.172610i	$-0.944780\pi$
$353$	−6.44458	+	11.1623i	−0.343011	+	0.594112i	0.641980	+	0.766722i	$0.278113\pi$
$354$	−2.75196	+	1.60229i	−0.146265	+	0.0851606i
$355$	1.17531	+	8.92736i	0.0623789	+	0.473815i
$356$	6.90465	−	8.99831i	0.365945	−	0.476909i
$357$	6.41025	−	6.45729i	0.339266	−	0.341756i
$358$	−6.77054	−	0.891359i	−0.357834	−	0.0471098i
$359$	8.09384			0.427177			0.213588	−	0.976924i	$-0.431485\pi$
$359$	8.09384			0.427177			0.213588	+	0.976924i	$0.431485\pi$
$360$	8.72685	−	0.0638053i	0.459946	−	0.00336283i
$361$	4.79389	+	4.79389i	0.252310	+	0.252310i
$362$	−23.9578	−	3.15411i	−1.25920	−	0.165776i
$363$	4.05667	−	7.08605i	0.212920	−	0.371921i
$364$	2.03500	−	7.59472i	0.106663	−	0.398072i
$365$	23.0121	−	13.2861i	1.20451	−	0.695425i
$366$	−15.4431	+	4.19854i	−0.807226	+	0.219461i
$367$	−4.00547	−	14.9486i	−0.209084	−	0.780311i	−0.988166	−	0.153389i	$-0.950981\pi$
$367$	−4.00547	−	14.9486i	−0.209084	−	0.780311i	0.779082	−	0.626922i	$-0.215686\pi$
$368$	−0.00437178			−0.000227895
$369$	1.36590	+	19.1607i	0.0711059	+	0.997469i
$370$	−2.95729			−0.153742
$371$	2.75648	+	10.2873i	0.143109	+	0.534091i
$372$	−4.68944	−	4.65528i	−0.243136	−	0.241365i
$373$	15.5874	−	8.99939i	0.807085	−	0.465971i	−0.0388573	−	0.999245i	$-0.512372\pi$
$373$	15.5874	−	8.99939i	0.807085	−	0.465971i	0.845943	+	0.533274i	$0.179038\pi$
$374$	2.07444	−	7.74192i	0.107267	−	0.400325i
$375$	3.89805	+	6.69497i	0.201294	+	0.345727i
$376$	4.09789	+	0.539498i	0.211333	+	0.0278225i
$377$	−19.2448	−	19.2448i	−0.991159	−	0.991159i
$378$	−6.83066	−	5.12332i	−0.351331	−	0.263515i
$379$	9.41306			0.483516			0.241758	−	0.970337i	$-0.422276\pi$
$379$	9.41306			0.483516			0.241758	+	0.970337i	$0.422276\pi$
$380$	10.0823	+	1.32736i	0.517211	+	0.0680921i
$381$	9.59386	+	2.53311i	0.491508	+	0.129775i
$382$	−0.523431	+	0.682148i	−0.0267810	+	0.0349017i
$383$	−3.17173	−	24.0917i	−0.162068	−	1.23103i	−0.858276	−	0.513188i	$-0.828464\pi$
$383$	−3.17173	−	24.0917i	−0.162068	−	1.23103i	0.696208	−	0.717840i	$-0.254869\pi$
$384$	−0.00633171	−	1.73204i	−0.000323114	−	0.0883878i
$385$	5.99241	−	10.3792i	0.305402	−	0.528971i
$386$	5.82819	+	2.41411i	0.296647	+	0.122875i
$387$	4.17434	+	1.08586i	0.212194	+	0.0551976i
$388$	−4.93916	+	11.9242i	−0.250748	+	0.605358i
$389$	7.27010	+	27.1324i	0.368609	+	1.37567i	0.862462	+	0.506121i	$0.168921\pi$
$389$	7.27010	+	27.1324i	0.368609	+	1.37567i	−0.493854	+	0.869545i	$0.664412\pi$
$390$	14.7463	+	19.0730i	0.746710	+	0.965801i
$391$	−0.00182422	−	0.0138564i	−9.22550e−5	−	0.000700746i
$392$	2.14988	+	3.72371i	0.108585	+	0.188076i
$393$	28.6318	+	16.3913i	1.44428	+	0.826832i
$394$	9.73462	+	5.62028i	0.490423	+	0.283146i
$395$	31.0335	+	12.8545i	1.56146	+	0.646780i
$396$	−7.46413	−	0.927206i	−0.375087	−	0.0465938i
$397$	−7.48028	+	3.09843i	−0.375425	+	0.155506i	−0.562414	−	0.826856i	$-0.690127\pi$
$397$	−7.48028	+	3.09843i	−0.375425	+	0.155506i	0.186989	+	0.982362i	$0.440127\pi$
$398$	−1.53719	+	11.6761i	−0.0770525	+	0.585272i
$399$	−7.06108	−	7.00964i	−0.353496	−	0.350921i
$400$	−2.99857	+	1.73122i	−0.149928	+	0.0865612i
$401$	33.2820	+	8.91787i	1.66202	+	0.445337i	0.962942	−	0.269707i	$-0.0869269\pi$
$401$	33.2820	+	8.91787i	1.66202	+	0.445337i	0.699079	+	0.715044i	$0.253594\pi$
$402$	−5.78269	+	0.782822i	−0.288415	+	0.0390436i
$403$	2.38264	−	18.0980i	0.118688	−	0.901524i
$404$	0.554357	−	1.33834i	0.0275803	−	0.0665848i
$405$	25.1874	−	7.14526i	1.25157	−	0.355051i
$406$	−9.34678			−0.463873
$407$	2.52695	+	0.332680i	0.125256	+	0.0164903i
$408$	5.48705	−	0.742800i	0.271650	−	0.0367741i
$409$	−31.6045	+	18.2469i	−1.56274	+	0.902249i	−0.565764	+	0.824568i	$0.691419\pi$
$409$	−31.6045	+	18.2469i	−1.56274	+	0.902249i	−0.996978	+	0.0776818i	$0.975248\pi$
$410$	−10.3238	−	15.5042i	−0.509857	−	0.765696i
$411$	1.73501	+	4.14576i	0.0855819	+	0.204495i
$412$	−16.3241	+	4.37403i	−0.804230	+	0.215493i
$413$	−2.79118	+	1.15614i	−0.137345	+	0.0568901i
$414$	−0.0126433	+	0.00348703i	−0.000621384	+	0.000171378i
$415$	−7.32137	+	7.32137i	−0.359392	+	0.359392i
$416$	3.79607	−	2.91283i	0.186118	−	0.142813i
$417$	15.7666	−	4.28648i	0.772093	−	0.209910i
$418$	−8.46584	−	2.26841i	−0.414078	−	0.110952i
$419$	−5.22041	+	19.4828i	−0.255033	+	0.951798i	0.713038	+	0.701125i	$0.247319\pi$
$419$	−5.22041	+	19.4828i	−0.255033	+	0.951798i	−0.968072	+	0.250673i	$0.919348\pi$
$420$	8.21266	+	1.05069i	0.400737	+	0.0512684i
$421$	−3.23092	+	24.5413i	−0.157466	+	1.19607i	0.712037	+	0.702141i	$0.247773\pi$
$421$	−3.23092	+	24.5413i	−0.157466	+	1.19607i	−0.869503	+	0.493928i	$0.835561\pi$
$422$	5.24302	+	12.6578i	0.255226	+	0.616171i
$423$	12.2815	−	1.70833i	0.597148	−	0.0830619i
$424$	−2.48026	+	5.98787i	−0.120452	+	0.290797i
$425$	−6.73833	−	8.78156i	−0.326857	−	0.425968i
$426$	4.94563	−	2.06976i	0.239616	−	0.100280i
$427$	−15.0532	+	1.98179i	−0.728476	+	0.0959057i
$428$	17.2340	−	9.95007i	0.833038	−	0.480955i
$429$	−10.4549	−	17.9565i	−0.504767	−	0.866947i
$430$	−4.03995	+	1.08250i	−0.194824	+	0.0522029i
$431$	21.9808	+	21.9808i	1.05878	+	1.05878i	0.998161	+	0.0606169i	$0.0193068\pi$
$431$	21.9808	+	21.9808i	1.05878	+	1.05878i	0.0606169	+	0.998161i	$0.480693\pi$
$432$	−1.39983	−	5.00405i	−0.0673491	−	0.240757i
$433$		−	4.55403i		−	0.218853i	−0.993995	−	0.109426i	$-0.965099\pi$
$433$		−	4.55403i		−	0.218853i	0.993995	−	0.109426i	$-0.0349014\pi$
$434$	−3.81629	−	4.97349i	−0.183188	−	0.238735i
$435$	17.3636	−	22.8008i	0.832522	−	1.09322i
$436$	11.6220	−	1.53007i	0.556593	−	0.0732768i
$437$	−0.0151520	+	0.00199480i	−0.000724818	+	9.54241e-5i
$438$	−11.2281	−	11.1463i	−0.536499	−	0.532591i
$439$	−2.63877	−	0.347400i	−0.125942	−	0.0165805i	0.0672919	−	0.997733i	$-0.478564\pi$
$439$	−2.63877	−	0.347400i	−0.125942	−	0.0165805i	−0.193233	+	0.981153i	$0.561897\pi$
$440$	6.73824	−	2.79107i	0.321233	−	0.133059i
$441$	9.18762	+	9.05425i	0.437506	+	0.431155i
$442$	10.8162	+	10.8162i	0.514474	+	0.514474i
$443$	−3.62959	−	13.5458i	−0.172447	−	0.643581i	−0.996972	−	0.0777561i	$-0.975224\pi$
$443$	−3.62959	−	13.5458i	−0.172447	−	0.643581i	0.824525	−	0.565825i	$-0.191442\pi$
$444$	0.461939	+	1.69911i	0.0219227	+	0.0806362i
$445$	4.30665	+	32.7123i	0.204155	+	1.55071i
$446$	18.2877	+	4.90017i	0.865947	+	0.232030i
$447$	−4.31429	−	0.551950i	−0.204059	−	0.0261063i
$448$	0.214486	−	1.62918i	0.0101335	−	0.0769716i
$449$	15.8837	+	15.8837i	0.749596	+	0.749596i	0.974403	−	0.224807i	$-0.0721753\pi$
$449$	15.8837	+	15.8837i	0.749596	+	0.749596i	−0.224807	+	0.974403i	$0.572175\pi$
$450$	−7.29106	+	7.39846i	−0.343704	+	0.348767i
$451$	7.07739	+	14.4094i	0.333261	+	0.678514i
$452$	9.27059	+	5.35238i	0.436052	+	0.251755i
$453$	−29.9653	−	12.2839i	−1.40789	−	0.577147i
$454$	−7.18798	+	9.36756i	−0.337349	+	0.439641i
$455$	11.4363	+	19.8083i	0.536143	+	0.928627i
$456$	−0.812256	−	6.00012i	−0.0380374	−	0.280981i
$457$	−15.0553	−	19.6204i	−0.704255	−	0.917803i	0.295035	−	0.955487i	$-0.404669\pi$
$457$	−15.0553	−	19.6204i	−0.704255	−	0.917803i	−0.999290	+	0.0376833i	$0.988002\pi$
$458$	−14.5036	+	6.00759i	−0.677709	+	0.280716i
$459$	15.2762	−	6.52479i	0.713032	−	0.304551i
$460$	0.00899273	−	0.00899273i	0.000419288	−	0.000419288i
$461$	−0.325257	−	0.187787i	−0.0151487	−	0.00874613i	0.492407	−	0.870365i	$-0.336117\pi$
$461$	−0.325257	−	0.187787i	−0.0151487	−	0.00874613i	−0.507555	+	0.861619i	$0.669451\pi$
$462$	−6.89939	−	1.82168i	−0.320989	−	0.0847522i
$463$	25.3762	+	19.4719i	1.17933	+	0.904935i	0.996931	−	0.0782892i	$-0.0249457\pi$
$463$	25.3762	+	19.4719i	1.17933	+	0.904935i	0.182403	+	0.983224i	$0.441612\pi$
$464$	−4.51261	−	3.46265i	−0.209493	−	0.160749i
$465$	19.2220	−	0.0702688i	0.891401	−	0.00325864i
$466$	−15.7130	+	12.0570i	−0.727893	+	0.558532i
$467$		−	35.4327i		−	1.63963i	−0.572630	−	0.819814i	$-0.694077\pi$
$467$		−	35.4327i		−	1.63963i	0.572630	−	0.819814i	$-0.305923\pi$
$468$	8.65498	−	11.4518i	0.400077	−	0.529359i
$469$	−5.53623			−0.255639
$470$	−9.53908	+	7.31959i	−0.440005	+	0.337628i
$471$	−5.52773	+	4.27378i	−0.254705	+	0.196925i
$472$	−1.77589	−	0.475847i	−0.0817418	−	0.0219026i
$473$	3.57385	−	0.470506i	0.164326	−	0.0216339i
$474$	2.53801	−	19.8382i	0.116575	−	0.911200i
$475$	−9.60269	+	7.36840i	−0.440601	+	0.338085i
$476$	5.25318			0.240779
$477$	−2.39690	+	19.2954i	−0.109747	+	0.883475i
$478$	20.0837	+	8.31894i	0.918607	+	0.380499i
$479$	−31.1045	−	4.09498i	−1.42120	−	0.187104i	−0.619577	−	0.784936i	$-0.712696\pi$
$479$	−31.1045	−	4.09498i	−1.42120	−	0.187104i	−0.801622	+	0.597831i	$0.796029\pi$
$480$	3.57582	+	3.54977i	0.163213	+	0.162024i
$481$	−2.96115	+	3.85904i	−0.135017	+	0.175957i
$482$	12.5651	+	21.7633i	0.572323	+	0.991293i
$483$	−0.0123304	+	0.00166920i	−0.000561052	+	7.59514e-5i
$484$	4.55349	−	1.22010i	0.206977	−	0.0554592i
$485$	−14.3681	−	34.6878i	−0.652424	−	1.57509i
$486$	−8.03967	−	13.3553i	−0.364687	−	0.605808i
$487$	2.71873	+	2.71873i	0.123197	+	0.123197i	0.766017	−	0.642820i	$-0.222236\pi$
$487$	2.71873	+	2.71873i	0.123197	+	0.123197i	−0.642820	+	0.766017i	$0.722236\pi$
$488$	−8.00185	−	4.61987i	−0.362227	−	0.209132i
$489$	1.66578	+	0.439823i	0.0753291	+	0.0198895i
$490$	−12.0819	−	3.23735i	−0.545806	−	0.146248i
$491$	5.00225	+	8.66415i	0.225748	+	0.391007i	0.956544	−	0.291589i	$-0.0941840\pi$
$491$	5.00225	+	8.66415i	0.225748	+	0.391007i	−0.730795	+	0.682597i	$0.760851\pi$
$492$	−7.29530	+	8.35336i	−0.328898	+	0.376598i
$493$	9.09187	−	15.7476i	0.409477	−	0.709236i
$494$	11.8276	−	11.8276i	0.532147	−	0.532147i
$495$	17.2609	−	13.4464i	0.775821	−	0.604371i
$496$		−	3.81499i		−	0.171298i
$497$	4.91305	−	1.31645i	0.220380	−	0.0590507i
$498$	5.35012	+	3.06287i	0.239744	+	0.137250i
$499$	−2.81749	+	3.67182i	−0.126128	+	0.164373i	−0.852149	−	0.523299i	$-0.824701\pi$
$499$	−2.81749	+	3.67182i	−0.126128	+	0.164373i	0.726021	+	0.687673i	$0.241368\pi$
$500$	−1.15764	+	4.32038i	−0.0517713	+	0.193213i
$501$	4.52321	−	3.49713i	0.202082	−	0.156240i
$502$	−14.0035	+	24.2548i	−0.625008	+	1.08255i
$503$	−7.64101	−	18.4470i	−0.340696	−	0.822512i	−0.997646	−	0.0685782i	$-0.978154\pi$
$503$	−7.64101	−	18.4470i	−0.340696	−	0.822512i	0.656950	−	0.753934i	$-0.271846\pi$
$504$	−0.679174	−	4.88271i	−0.0302528	−	0.217493i
$505$	1.61264	+	3.89326i	0.0717616	+	0.173248i
$506$	−0.00869577	+	0.00667250i	−0.000386574	+	0.000296629i
$507$	17.1380	−	0.0626504i	0.761126	−	0.00278240i
$508$	2.86442	+	4.96132i	0.127088	+	0.220123i
$509$	−1.73774	−	13.1995i	−0.0770242	−	0.585057i	−0.985819	−	0.167813i	$-0.946330\pi$
$509$	−1.73774	−	13.1995i	−0.0770242	−	0.585057i	0.908795	−	0.417244i	$-0.137004\pi$
$510$	−9.75890	+	12.8148i	−0.432131	+	0.567448i
$511$	−9.13748	−	11.9082i	−0.404218	−	0.526788i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−7.13490	−	16.7046i	−0.315013	−	0.737527i
$514$	5.86135	+	2.42785i	0.258533	+	0.107088i
$515$	24.5812	−	42.5759i	1.08318	−	1.87612i
$516$	1.25301	+	2.15206i	0.0551605	+	0.0947393i
$517$	8.97441	−	5.18138i	0.394694	−	0.227877i
$518$	0.218044	+	1.65621i	0.00958030	+	0.0727696i
$519$	0.0818110	+	22.3794i	0.00359110	+	0.982346i
$520$	−1.81683	+	13.8002i	−0.0796731	+	0.605177i
$521$	21.2863	−	8.81709i	0.932571	−	0.386284i	0.135918	−	0.990720i	$-0.456602\pi$
$521$	21.2863	−	8.81709i	0.932571	−	0.386284i	0.796653	+	0.604437i	$0.206602\pi$
$522$	−15.8125	−	6.41470i	−0.692093	−	0.280764i
$523$		−	8.69043i		−	0.380006i	−0.981784	−	0.190003i	$-0.939150\pi$
$523$		−	8.69043i		−	0.380006i	0.981784	−	0.190003i	$-0.0608497\pi$
$524$	4.92993	+	18.3987i	0.215365	+	0.803753i
$525$	−7.79630	+	6.02772i	−0.340258	+	0.263071i
$526$	−23.6847	−	18.1739i	−1.03270	−	0.792419i
$527$	12.0916	−	1.59189i	0.526719	−	0.0693439i
$528$	−2.65615	−	3.43548i	−0.115594	−	0.149510i
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$	−7.21514	−	17.4189i	−0.313406	−	0.756629i
$531$	−5.51545	+	0.0403255i	−0.239350	+	0.00174998i
$532$		−	5.74439i		−	0.249051i
$533$	−30.5691	−	2.05258i	−1.32409	−	0.0889071i
$534$	18.1221	−	7.58416i	0.784221	−	0.328199i
$535$	−14.9831	+	55.9175i	−0.647774	+	2.41753i
$536$	−2.67288	−	2.05097i	−0.115451	−	0.0885886i
$537$	−9.41013	−	7.16615i	−0.406077	−	0.309242i
$538$	−1.05019	−	3.91935i	−0.0452768	−	0.168975i
$539$	9.95963	+	4.12541i	0.428992	+	0.177694i
$540$	13.1727	+	7.41386i	0.566864	+	0.319042i
$541$	30.6667	−	30.6667i	1.31847	−	1.31847i	0.403476	−	0.914990i	$-0.367802\pi$
$541$	30.6667	−	30.6667i	1.31847	−	1.31847i	0.914990	−	0.403476i	$-0.132198\pi$
$542$	−0.578433	+	0.154991i	−0.0248458	+	0.00665742i
$543$	−33.2981	−	25.3577i	−1.42896	−	1.08820i
$544$	2.53623	+	1.94612i	0.108740	+	0.0834391i
$545$	−20.7590	+	27.0537i	−0.889220	+	1.15885i
$546$	9.59446	−	9.66486i	0.410605	−	0.413618i
$547$	−9.66892	−	12.6008i	−0.413413	−	0.538771i	0.539511	−	0.841978i	$-0.318609\pi$
$547$	−9.66892	−	12.6008i	−0.413413	−	0.538771i	−0.952924	+	0.303208i	$0.901942\pi$
$548$	−0.992954	+	2.39720i	−0.0424169	+	0.102403i
$549$	−26.8264	−	6.97832i	−1.14492	−	0.297827i
$550$	−3.32205	+	8.02013i	−0.141653	+	0.341980i
$551$	−17.2201	−	9.94201i	−0.733600	−	0.423544i
$552$	−0.00657147	−	0.00376208i	−0.000279700	−	0.000160125i
$553$	4.91094	−	18.3279i	0.208834	−	0.779380i
$554$	−5.01506	+	18.7165i	−0.213069	+	0.795186i
$555$	−4.44527	−	2.54485i	−0.188691	−	0.108023i
$556$	8.16944	+	4.71663i	0.346461	+	0.200030i
$557$	−1.65712	+	4.00064i	−0.0702143	+	0.169512i	−0.955091	−	0.296313i	$-0.904243\pi$
$557$	−1.65712	+	4.00064i	−0.0702143	+	0.169512i	0.884876	+	0.465826i	$0.154243\pi$
$558$	−3.04292	−	11.0330i	−0.128817	−	0.467066i
$559$	−2.63264	+	6.35576i	−0.111349	+	0.268820i
$560$	2.91002	+	3.79241i	0.122971	+	0.160259i
$561$	9.78042	−	9.85218i	0.412929	−	0.415960i
$562$	1.29489	−	1.68753i	0.0546217	−	0.0711843i
$563$	18.8912	+	14.4957i	0.796168	+	0.610922i	0.924662	−	0.380789i	$-0.124348\pi$
$563$	18.8912	+	14.4957i	0.796168	+	0.610922i	−0.128494	+	0.991710i	$0.541014\pi$
$564$	5.69551	+	4.33733i	0.239824	+	0.182635i
$565$	−30.0794	+	8.05974i	−1.26545	+	0.339076i
$566$	−17.5499	+	17.5499i	−0.737677	+	0.737677i
$567$	−5.85874	−	13.5792i	−0.246044	−	0.570272i
$568$	2.85971	+	1.18453i	0.119991	+	0.0497018i
$569$	−2.33924	−	8.73017i	−0.0980661	−	0.365988i	0.899400	−	0.437126i	$-0.144004\pi$
$569$	−2.33924	−	8.73017i	−0.0980661	−	0.365988i	−0.997466	+	0.0711381i	$0.977337\pi$
$570$	14.0130	+	10.6714i	0.586941	+	0.446976i
$571$	8.69282	+	6.67023i	0.363783	+	0.279141i	0.774437	−	0.632651i	$-0.218033\pi$
$571$	8.69282	+	6.67023i	0.363783	+	0.279141i	−0.410654	+	0.911791i	$0.634700\pi$
$572$	3.10489	−	11.5876i	0.129822	−	0.484503i
$573$	−1.37381	+	0.574944i	−0.0573918	+	0.0240186i
$574$	−7.92181	+	6.92492i	−0.330650	+	0.289041i
$575$			0.0151371i			0.000631259i
$576$	1.48096	−	2.60897i	0.0617069	−	0.108707i
$577$	−5.46599	−	13.1961i	−0.227552	−	0.549359i	0.768326	−	0.640058i	$-0.221090\pi$
$577$	−5.46599	−	13.1961i	−0.227552	−	0.549359i	−0.995878	+	0.0906992i	$0.971090\pi$
$578$	3.39008	−	5.87180i	0.141009	−	0.244234i
$579$	6.68324	+	8.64416i	0.277746	+	0.359239i
$580$	16.4051	−	2.15977i	0.681183	−	0.0896795i
$581$	4.64009	+	3.56047i	0.192503	+	0.147713i
$582$	−17.6855	+	13.6736i	−0.733088	+	0.566788i
$583$	4.20568	+	15.6958i	0.174182	+	0.650055i
$584$		−	9.13437i		−	0.377983i
$585$	5.75302	+	41.3595i	0.237858	+	1.71001i
$586$	−15.2531	+	6.31805i	−0.630101	+	0.260996i
$587$	−1.60076	+	12.1590i	−0.0660703	+	0.501854i	0.926130	+	0.377203i	$0.123114\pi$
$587$	−1.60076	+	12.1590i	−0.0660703	+	0.501854i	−0.992201	+	0.124650i	$0.960219\pi$
$588$	0.0272249	+	7.44736i	0.00112273	+	0.307124i
$589$	−1.74074	−	13.2222i	−0.0717260	−	0.544813i
$590$	4.63180	−	2.67417i	0.190688	−	0.110094i
$591$	9.79619	+	16.8252i	0.402961	+	0.692094i
$592$	−0.508295	+	0.880392i	−0.0208908	+	0.0361839i
$593$	18.2917	+	7.57667i	0.751150	+	0.311137i	0.725211	−	0.688527i	$-0.241742\pi$
$593$	18.2917	+	7.57667i	0.751150	+	0.311137i	0.0259394	+	0.999664i	$0.491742\pi$
$594$	−10.4219	−	7.81689i	−0.427614	−	0.320731i
$595$	−10.8058	+	10.8058i	−0.442993	+	0.442993i
$596$	−1.52870	−	1.99223i	−0.0626178	−	0.0816051i
$597$	−12.3584	+	16.2283i	−0.505795	+	0.664178i
$598$	−0.00273038	−	0.0207393i	−0.000111654	−	0.000848094i
$599$	−19.2256	−	33.2997i	−0.785538	−	1.36059i	−0.928677	−	0.370888i	$-0.879053\pi$
$599$	−19.2256	−	33.2997i	−0.785538	−	1.36059i	0.143140	−	0.989702i	$-0.454280\pi$
$600$	−5.99709	+	0.0219232i	−0.244830	+	0.000895011i
$601$	−20.1557	+	15.4660i	−0.822170	+	0.630873i	−0.931748	−	0.363105i	$-0.881717\pi$
$601$	−20.1557	+	15.4660i	−0.822170	+	0.630873i	0.109579	+	0.993978i	$0.465050\pi$
$602$	0.904117	+	2.18273i	0.0368491	+	0.0889615i
$603$	−9.36594	−	3.79951i	−0.381411	−	0.154728i
$604$	−7.15529	−	17.2744i	−0.291145	−	0.702886i
$605$	−6.85675	+	11.8762i	−0.278767	+	0.482838i
$606$	1.98497	−	1.53468i	0.0806340	−	0.0623423i
$607$	−6.86472	+	25.6195i	−0.278631	+	1.03986i	0.674739	+	0.738057i	$0.264256\pi$
$607$	−6.86472	+	25.6195i	−0.278631	+	1.03986i	−0.953369	+	0.301807i	$0.902410\pi$
$608$	2.12809	−	2.77338i	0.0863055	−	0.112475i
$609$	−14.0497	−	8.04324i	−0.569321	−	0.325929i
$610$	25.9628	−	6.95671i	1.05120	−	0.281669i
$611$			19.7770i			0.800090i
$612$	8.88710	+	3.60526i	0.359240	+	0.145734i
$613$	22.6028	−	22.6028i	0.912920	−	0.912920i	−0.0835813	−	0.996501i	$-0.526636\pi$
$613$	22.6028	−	22.6028i	0.912920	−	0.912920i	0.996501	+	0.0835813i	$0.0266358\pi$
$614$	13.3330	−	23.0934i	0.538076	−	0.931974i
$615$	−2.17641	−	32.1892i	−0.0877613	−	1.29799i
$616$	−2.05994	−	3.56792i	−0.0829972	−	0.143755i
$617$	−8.71656	−	2.33559i	−0.350915	−	0.0940275i	0.0790556	−	0.996870i	$-0.474810\pi$
$617$	−8.71656	−	2.33559i	−0.350915	−	0.0940275i	−0.429971	+	0.902843i	$0.641476\pi$
$618$	−28.3017	−	7.47263i	−1.13846	−	0.300593i
$619$	24.3345	+	14.0495i	0.978087	+	0.564699i	0.901692	−	0.432379i	$-0.142326\pi$
$619$	24.3345	+	14.0495i	0.978087	+	0.564699i	0.0763947	+	0.997078i	$0.475659\pi$
$620$	7.84742	+	7.84742i	0.315160	+	0.315160i
$621$	−0.0220056	−	0.00563846i	−0.000883053	−	0.000226264i
$622$	−11.2597	−	27.1833i	−0.451472	−	1.08995i
$623$	18.0027	−	4.82382i	0.721265	−	0.193262i
$624$	8.21268	−	1.11178i	0.328770	−	0.0445067i
$625$	−15.1618	−	26.2611i	−0.606474	−	1.05044i
$626$	−5.49758	+	7.16458i	−0.219727	+	0.286354i
$627$	−10.7734	−	10.6949i	−0.430249	−	0.427115i
$628$	−3.99955	−	0.526551i	−0.159599	−	0.0210117i
$629$	−3.00250	−	1.24368i	−0.119717	−	0.0495886i
$630$	11.4408	+	8.64664i	0.455811	+	0.344490i
$631$	−27.8643			−1.10926			−0.554629	−	0.832098i	$-0.687140\pi$
$631$	−27.8643			−1.10926			−0.554629	+	0.832098i	$0.687140\pi$
$632$	9.16081	−	7.02934i	0.364398	−	0.279612i
$633$	−3.01139	+	23.5384i	−0.119692	+	0.935568i
$634$	−32.0146	+	4.21481i	−1.27146	+	0.167391i
$635$	−16.0975	−	4.31331i	−0.638810	−	0.171169i
$636$	−8.88100	+	6.86636i	−0.352154	+	0.272269i
$637$	−16.3222	+	12.5245i	−0.646709	+	0.496238i
$638$	−14.2608			−0.564591
$639$	9.21515	+	1.14472i	0.364546	+	0.0452844i
$640$			2.90903i			0.114989i
$641$	4.68288	−	3.59330i	0.184963	−	0.141927i	−0.512130	−	0.858908i	$-0.671143\pi$
$641$	4.68288	−	3.59330i	0.184963	−	0.141927i	0.697093	+	0.716981i	$0.254477\pi$
$642$	34.4678	−	0.126002i	1.36034	−	0.00497290i
$643$	−9.12154	−	6.99920i	−0.359718	−	0.276022i	0.413052	−	0.910707i	$-0.364463\pi$
$643$	−9.12154	−	6.99920i	−0.359718	−	0.276022i	−0.772770	+	0.634686i	$0.781129\pi$
$644$	−0.00569936	−	0.00437327i	−0.000224586	−	0.000172331i
$645$	−7.00421	−	1.84936i	−0.275790	−	0.0728183i
$646$	9.67822	+	5.58772i	0.380784	+	0.219846i
$647$	−18.7041	+	18.7041i	−0.735335	+	0.735335i	−0.971671	−	0.236336i	$-0.924053\pi$
$647$	−18.7041	+	18.7041i	−0.735335	+	0.735335i	0.236336	+	0.971671i	$0.424053\pi$
$648$	2.20201	−	8.72646i	0.0865031	−	0.342808i
$649$	−4.25863	+	1.76398i	−0.167166	+	0.0692424i
$650$	−10.0855	−	13.1437i	−0.395586	−	0.515538i
$651$	−1.45661	−	10.7600i	−0.0570892	−	0.421717i
$652$	0.497348	+	0.861432i	0.0194776	+	0.0337363i
$653$	0.534028	−	0.695958i	0.0208981	−	0.0272350i	−0.782787	−	0.622289i	$-0.786203\pi$
$653$	0.534028	−	0.695958i	0.0208981	−	0.0272350i	0.803686	+	0.595054i	$0.202869\pi$
$654$	18.7864	+	7.70122i	0.734604	+	0.301142i
$655$	−47.9869	−	27.7053i	−1.87500	−	1.08253i
$656$	−6.39007	+	0.408592i	−0.249490	+	0.0159528i
$657$	−7.28578	−	26.4168i	−0.284245	−	1.03062i
$658$	4.80261	+	4.80261i	0.187225	+	0.187225i
$659$	−1.12800	+	8.56798i	−0.0439405	+	0.333761i	0.955329	+	0.295544i	$0.0955010\pi$
$659$	−1.12800	+	8.56798i	−0.0439405	+	0.333761i	−0.999269	+	0.0382166i	$0.987832\pi$
$660$	12.5304	+	1.60309i	0.487747	+	0.0624000i
$661$	−8.40511	−	2.25214i	−0.326921	−	0.0875982i	0.0916258	−	0.995794i	$-0.470794\pi$
$661$	−8.40511	−	2.25214i	−0.326921	−	0.0875982i	−0.418547	+	0.908195i	$0.637460\pi$
$662$	3.42158	+	25.9895i	0.132984	+	1.01011i
$663$	6.95070	+	25.5661i	0.269943	+	0.992907i
$664$	0.921203	+	3.43798i	0.0357496	+	0.133419i
$665$	11.8162	+	11.8162i	0.458211	+	0.458211i
$666$	−0.767780	+	2.95154i	−0.0297509	+	0.114370i
$667$	−0.0229739	+	0.00951611i	−0.000889554	+	0.000368465i
$668$	3.27274	+	0.430864i	0.126626	+	0.0166706i
$669$	23.2725	+	23.1029i	0.899766	+	0.893211i
$670$	9.71694	−	1.27926i	0.375398	−	0.0494221i
$671$	−22.9674	+	3.02371i	−0.886646	+	0.116729i
$672$	1.72437	−	2.26434i	0.0665192	−	0.0873488i
$673$	11.3851	+	14.8373i	0.438863	+	0.571937i	0.959453	−	0.281870i	$-0.0909547\pi$
$673$	11.3851	+	14.8373i	0.438863	+	0.571937i	−0.520590	+	0.853807i	$0.674288\pi$
$674$		−	36.4901i		−	1.40555i
$675$	−17.3262	+	4.84682i	−0.666888	+	0.186554i
$676$	6.99661	+	6.99661i	0.269100	+	0.269100i
$677$	11.2161	−	3.00534i	0.431068	−	0.115504i	−0.0367592	−	0.999324i	$-0.511703\pi$
$677$	11.2161	−	3.00534i	0.431068	−	0.115504i	0.467828	+	0.883820i	$0.345037\pi$
$678$	9.32923	+	16.0231i	0.358287	+	0.615365i
$679$	−18.3673	+	10.6043i	−0.704871	+	0.406957i
$680$	−9.22016	+	1.21386i	−0.353577	+	0.0465493i
$681$	−18.8658	+	7.89538i	−0.722938	+	0.302552i
$682$	−5.82269	−	7.58828i	−0.222962	−	0.290570i
$683$	18.5461	−	44.7743i	0.709648	−	1.71324i	0.00877020	−	0.999962i	$-0.497208\pi$
$683$	18.5461	−	44.7743i	0.709648	−	1.71324i	0.700878	−	0.713281i	$-0.252792\pi$
$684$	3.94237	−	9.71810i	0.150740	−	0.371581i
$685$	−2.88853	−	6.97353i	−0.110365	−	0.266445i
$686$	−2.42364	+	18.4094i	−0.0925349	+	0.702873i
$687$	−26.9709	−	3.45054i	−1.02901	−	0.131646i
$688$	−0.372118	+	1.38876i	−0.0141869	+	0.0529461i
$689$	−29.9549	−	8.02640i	−1.14119	−	0.305782i
$690$	0.0212560	−	0.00577890i	0.000809204	−	0.000219999i
$691$	−11.3068	+	8.67598i	−0.430129	+	0.330050i	−0.801032	−	0.598622i	$-0.795715\pi$
$691$	−11.3068	+	8.67598i	−0.430129	+	0.330050i	0.370902	+	0.928672i	$0.379048\pi$
$692$	−9.13641	+	9.13641i	−0.347314	+	0.347314i
$693$	−8.80323	−	8.67544i	−0.334407	−	0.329553i
$694$	23.1843	−	9.60326i	0.880064	−	0.364535i
$695$	−26.5066	+	7.10241i	−1.00545	+	0.269410i
$696$	−3.80342	−	9.08817i	−0.144168	−	0.344486i
$697$	−3.96143	−	20.0828i	−0.150050	−	0.760692i
$698$	6.70683	−	3.87219i	0.253857	−	0.146565i
$699$	−33.9947	+	4.60197i	−1.28580	+	0.174063i
$700$	−5.64095	−	0.742645i	−0.213208	−	0.0280694i
$701$	34.2968			1.29537			0.647686	−	0.761908i	$-0.275737\pi$
$701$	34.2968			1.29537			0.647686	+	0.761908i	$0.275737\pi$
$702$	22.8645	−	9.76590i	0.862964	−	0.368590i
$703$	−1.35997	+	3.28325i	−0.0512921	+	0.123830i
$704$	0.327251	−	2.48572i	0.0123337	−	0.0936840i
$705$	−20.6375	+	2.79377i	−0.777253	+	0.105219i
$706$	−12.4500	−	3.33596i	−0.468561	−	0.125551i
$707$	2.06149	−	1.19020i	0.0775304	−	0.0447622i
$708$	−2.25995	−	2.24349i	−0.0849341	−	0.0843154i
$709$	−2.60653	+	19.7986i	−0.0978903	+	0.743550i	0.870156	+	0.492777i	$0.164018\pi$
$709$	−2.60653	+	19.7986i	−0.0978903	+	0.743550i	−0.968046	+	0.250773i	$0.919315\pi$
$710$	−8.31897	+	3.44583i	−0.312205	+	0.129320i
$711$	20.8865	−	27.6359i	0.783306	−	1.03643i
$712$	10.4788	+	4.34044i	0.392708	+	0.162665i
$713$	−0.0144438	−	0.00833916i	−0.000540926	−	0.000312304i
$714$	7.89635	+	4.52056i	0.295514	+	0.169178i
$715$	17.4489	+	30.2224i	0.652553	+	1.13025i
$716$	−0.891359	−	6.77054i	−0.0333116	−	0.253027i
$717$	23.0302	+	29.7874i	0.860078	+	1.11243i
$718$	2.09484	+	7.81805i	0.0781788	+	0.291767i
$719$	−18.6668	+	45.0657i	−0.696155	+	1.68067i	0.0358406	+	0.999358i	$0.488589\pi$
$719$	−18.6668	+	45.0657i	−0.696155	+	1.68067i	−0.731996	+	0.681309i	$0.761411\pi$
$720$	2.32031	+	8.41298i	0.0864727	+	0.313533i
$721$	−25.6567	−	10.6274i	−0.955507	−	0.395784i
$722$	−3.38979	+	5.87130i	−0.126155	+	0.218507i
$723$	0.159117	+	43.5264i	0.00591762	+	1.61876i
$724$	−3.15411	−	23.9578i	−0.117222	−	0.890386i
$725$	−11.9892	+	15.6247i	−0.445269	+	0.580286i
$726$	7.89454	+	2.08444i	0.292994	+	0.0773606i
$727$	−7.98708	−	1.05152i	−0.296224	−	0.0389987i	−0.0190508	−	0.999819i	$-0.506064\pi$
$727$	−7.98708	−	1.05152i	−0.296224	−	0.0389987i	−0.277174	+	0.960820i	$0.589398\pi$
$728$	7.86264			0.291409
$729$	−0.592163	−	26.9935i	−0.0219320	−	0.999759i
$730$	18.7893	+	18.7893i	0.695425	+	0.695425i
$731$	−4.55696	−	0.599935i	−0.168545	−	0.0221894i
$732$	−8.05246	−	13.8303i	−0.297628	−	0.511181i
$733$	13.4387	−	50.1541i	0.496372	−	1.85248i	−0.0258373	−	0.999666i	$-0.508225\pi$
$733$	13.4387	−	50.1541i	0.496372	−	1.85248i	0.522209	−	0.852818i	$-0.325108\pi$
$734$	13.4026	−	7.73797i	0.494697	−	0.285614i
$735$	−15.3752	−	15.2632i	−0.567122	−	0.562991i
$736$	−0.00113150	−	0.00422282i	−4.17077e−5	−	0.000155655i
$737$	−8.44688			−0.311145
$738$	−18.1543	+	6.27852i	−0.668271	+	0.231116i
$739$	22.9465			0.844101			0.422051	−	0.906572i	$-0.361310\pi$
$739$	22.9465			0.844101			0.422051	+	0.906572i	$0.361310\pi$
$740$	−0.765403	−	2.85652i	−0.0281368	−	0.105008i
$741$	27.9567	−	7.60063i	1.02702	−	0.279216i
$742$	−9.22335	+	5.32510i	−0.338600	+	0.195491i
$743$	−11.0333	+	41.1770i	−0.404774	+	1.51064i	0.399698	+	0.916647i	$0.369115\pi$
$743$	−11.0333	+	41.1770i	−0.404774	+	1.51064i	−0.804472	+	0.593990i	$0.797552\pi$
$744$	3.28294	−	5.73453i	0.120358	−	0.210238i
$745$	7.24253	+	0.953497i	0.265346	+	0.0349334i
$746$	12.7271	+	12.7271i	0.465971	+	0.465971i
$747$	5.40635	+	9.20794i	0.197808	+	0.336901i
$748$	8.01503			0.293058
$749$	32.4209	+	4.26830i	1.18463	+	0.155960i
$750$	−5.45796	+	5.49801i	−0.199296	+	0.200759i
$751$	22.9931	−	29.9652i	0.839030	−	1.09344i	−0.155380	−	0.987855i	$-0.549660\pi$
$751$	22.9931	−	29.9652i	0.839030	−	1.09344i	0.994410	−	0.105590i	$-0.0336731\pi$
$752$	0.539498	+	4.09789i	0.0196735	+	0.149435i
$753$	−41.9217	+	24.4082i	−1.52771	+	0.889486i
$754$	13.6081	−	23.5700i	0.495579	−	0.858369i
$755$	50.2517	+	20.8150i	1.82885	+	0.757534i
$756$	3.18084	−	7.92392i	0.115686	−	0.288190i
$757$	9.44004	−	22.7903i	0.343104	−	0.828326i	−0.654294	−	0.756240i	$-0.727034\pi$
$757$	9.44004	−	22.7903i	0.343104	−	0.828326i	0.997398	−	0.0720863i	$-0.0229657\pi$
$758$	2.43628	+	9.09232i	0.0884896	+	0.330248i
$759$	−0.0188130	+	0.00254678i	−0.000682870	+	9.24423e-5i
$760$	1.32736	+	10.0823i	0.0481484	+	0.365723i
$761$	19.3964	+	33.5956i	0.703120	+	1.21784i	0.967366	+	0.253384i	$0.0815436\pi$
$761$	19.3964	+	33.5956i	0.703120	+	1.21784i	−0.264246	+	0.964455i	$0.585123\pi$
$762$	0.0362733	+	9.92257i	0.00131404	+	0.359457i
$763$	16.6818	+	9.63126i	0.603923	+	0.348675i
$764$	−0.794378	−	0.329042i	−0.0287396	−	0.0119043i
$765$	−25.6967	+	10.8647i	−0.929067	+	0.392814i
$766$	22.4499	−	9.29905i	0.811148	−	0.335988i
$767$	1.14825	−	8.72183i	0.0414609	−	0.314927i
$768$	1.67138	−	0.454401i	0.0603108	−	0.0163968i
$769$	−1.33303	+	0.769624i	−0.0480702	+	0.0277533i	−0.523843	−	0.851815i	$-0.675502\pi$
$769$	−1.33303	+	0.769624i	−0.0480702	+	0.0277533i	0.475772	+	0.879568i	$0.342169\pi$
$770$	11.5765	+	3.10190i	0.417187	+	0.111785i
$771$	6.72126	+	8.69334i	0.242060	+	0.313083i
$772$	−0.823410	+	6.25442i	−0.0296352	+	0.225101i
$773$	12.3869	−	29.9047i	0.445527	−	1.07560i	−0.528453	−	0.848963i	$-0.677228\pi$
$773$	12.3869	−	29.9047i	0.445527	−	1.07560i	0.973980	−	0.226634i	$-0.0727723\pi$
$774$	0.0315350	+	4.31315i	0.00113350	+	0.155033i
$775$	−13.2092			−0.474489
$776$	−12.7962	−	1.68465i	−0.459357	−	0.0604755i
$777$	−1.09747	+	2.67717i	−0.0393716	+	0.0960431i
$778$	−24.3262	+	14.0448i	−0.872138	+	0.503529i
$779$	−21.9607	+	4.33185i	−0.786823	+	0.155205i
$780$	−14.6065	+	19.1803i	−0.522997	+	0.686766i
$781$	7.49606	−	2.00856i	0.268230	−	0.0718721i
$782$	0.0129121	−	0.00534835i	0.000461735	−	0.000191257i
$783$	−18.2485	−	23.2495i	−0.652149	−	0.830869i
$784$	−3.04039	+	3.04039i	−0.108585	+	0.108585i
$785$	9.31016	−	7.14394i	0.332294	−	0.254978i
$786$	−8.42233	+	31.8986i	−0.300415	+	1.13778i
$787$	−3.70458	−	0.992640i	−0.132054	−	0.0353838i	0.192187	−	0.981358i	$-0.438442\pi$
$787$	−3.70458	−	0.992640i	−0.132054	−	0.0353838i	−0.324241	+	0.945975i	$0.605109\pi$
$788$	−2.90927	+	10.8576i	−0.103639	+	0.386784i
$789$	−19.9625	−	47.6997i	−0.710682	−	1.69815i
$790$	−4.38443	+	33.3030i	−0.155991	+	1.18487i
$791$	6.73158	+	16.2515i	0.239348	+	0.577836i
$792$	−1.03625	−	7.44977i	−0.0368214	−	0.264716i
$793$	16.9187	−	40.8453i	0.600801	−	1.45046i
$794$	−4.92890	−	6.42346i	−0.174920	−	0.227960i
$795$	4.14411	−	32.3922i	0.146976	−	1.14883i
$796$	−11.6761	+	1.53719i	−0.413850	+	0.0544844i
$797$	−9.76227	+	5.63625i	−0.345797	+	0.199646i	−0.662833	−	0.748767i	$-0.730646\pi$
$797$	−9.76227	+	5.63625i	−0.345797	+	0.199646i	0.317035	+	0.948414i	$0.397313\pi$
$798$	4.94325	−	8.63471i	0.174989	−	0.305665i
$799$	−12.7631	+	3.41987i	−0.451527	+	0.120986i
$800$	−2.44832	−	2.44832i	−0.0865612	−	0.0865612i
$801$	33.7668	+	4.19457i	1.19309	+	0.148208i
$802$			34.4560i			1.21668i
$803$	−13.9415	−	18.1689i	−0.491984	−	0.641166i
$804$	−2.25282	−	5.38305i	−0.0794508	−	0.189845i
$805$	0.0207193	−	0.00272775i	0.000730260	−	9.61406e-5i
$806$	18.0980	−	2.38264i	0.637474	−	0.0839250i
$807$	1.79415	−	6.79512i	0.0631570	−	0.239200i
$808$	1.43621	+	0.189081i	0.0505258	+	0.00665185i
$809$	−19.4067	+	8.03852i	−0.682303	+	0.282619i	−0.696789	−	0.717276i	$-0.745389\pi$
$809$	−19.4067	+	8.03852i	−0.682303	+	0.282619i	0.0144861	+	0.999895i	$0.495389\pi$
$810$	13.4208	+	22.4798i	0.471558	+	0.789860i
$811$	9.91335	+	9.91335i	0.348105	+	0.348105i	0.859403	−	0.511298i	$-0.170835\pi$
$811$	9.91335	+	9.91335i	0.348105	+	0.348105i	−0.511298	+	0.859403i	$0.670835\pi$
$812$	−2.41913	−	9.02830i	−0.0848946	−	0.316831i
$813$	−1.00285	−	0.264788i	−0.0351715	−	0.00928651i
$814$	0.332680	+	2.52695i	0.0116604	+	0.0885697i
$815$	−2.79500	−	0.748918i	−0.0979046	−	0.0262335i
$816$	2.13764	+	5.10784i	0.0748325	+	0.178810i
$817$	−0.656032	+	4.98306i	−0.0229517	+	0.174335i
$818$	−25.8050	−	25.8050i	−0.902249	−	0.902249i
$819$	22.7389	−	6.27142i	0.794562	−	0.219141i
$820$	12.3039	−	13.9848i	0.429670	−	0.488371i
$821$	11.1170	+	6.41841i	0.387986	+	0.224004i	0.681287	−	0.732016i	$-0.261420\pi$
$821$	11.1170	+	6.41841i	0.387986	+	0.224004i	−0.293301	+	0.956020i	$0.594754\pi$
$822$	−3.55544	+	2.74890i	−0.124010	+	0.0958788i
$823$	−0.0418849	+	0.0545854i	−0.00146001	+	0.00190273i	−0.794083	−	0.607810i	$-0.792048\pi$
$823$	−0.0418849	+	0.0545854i	−0.00146001	+	0.00190273i	0.792623	+	0.609712i	$0.208715\pi$
$824$	−8.44997	−	14.6358i	−0.294369	−	0.509862i
$825$	−11.8952	+	9.19677i	−0.414137	+	0.320190i
$826$	−1.83916	−	2.39684i	−0.0639925	−	0.0833967i
$827$	−1.74099	+	0.721141i	−0.0605401	+	0.0250765i	−0.412748	−	0.910845i	$-0.635431\pi$
$827$	−1.74099	+	0.721141i	−0.0605401	+	0.0250765i	0.352208	+	0.935922i	$0.385431\pi$
$828$	−0.00664054	−	0.0113100i	−0.000230775	−	0.000393049i
$829$	−30.7631	+	30.7631i	−1.06845	+	1.06845i	−0.0709692	+	0.997479i	$0.522609\pi$
$829$	−30.7631	+	30.7631i	−1.06845	+	1.06845i	−0.997479	+	0.0709692i	$0.977391\pi$
$830$	−8.96681	−	5.17699i	−0.311242	−	0.179696i
$831$	−23.6446	+	23.8181i	−0.820222	+	0.826241i
$832$	3.79607	+	2.91283i	0.131605	+	0.100984i
$833$	−10.9052	−	8.36785i	−0.377843	−	0.289929i
$834$	8.22111	+	14.1199i	0.284674	+	0.488933i
$835$	−7.61828	+	5.84571i	−0.263641	+	0.202299i
$836$		−	8.76448i		−	0.303126i
$837$	4.92035	−	19.2029i	0.170072	−	0.663751i
$838$	−20.1701			−0.696764
$839$	16.5311	−	12.6848i	0.570718	−	0.437927i	−0.282660	−	0.959220i	$-0.591217\pi$
$839$	16.5311	−	12.6848i	0.570718	−	0.437927i	0.853378	+	0.521293i	$0.174550\pi$
$840$	1.11071	+	8.20476i	0.0383230	+	0.283091i
$841$	−3.23934	−	0.867979i	−0.111701	−	0.0299303i
$842$	−24.5413	+	3.23092i	−0.845749	+	0.111345i
$843$	3.39861	−	1.42233i	0.117054	−	0.0489875i
$844$	−10.8695	+	8.34044i	−0.374143	+	0.287090i
$845$	−28.7840			−0.990198
$846$	4.82881	+	11.4209i	0.166018	+	0.392658i
$847$	7.15676	+	2.96443i	0.245909	+	0.101859i
$848$	−6.42578	−	0.845970i	−0.220662	−	0.0290507i
$849$	−41.4825	+	11.2779i	−1.42368	+	0.387057i
$850$	6.73833	−	8.78156i	0.231123	−	0.301205i
$851$	0.00222215	+	0.00384888i	7.61745e−5	+	0.000131938i
$852$	3.27926	+	4.24141i	0.112345	+	0.145308i
$853$	24.3319	−	6.51971i	0.833109	−	0.223231i	0.183039	−	0.983106i	$-0.441406\pi$
$853$	24.3319	−	6.51971i	0.833109	−	0.223231i	0.650069	+	0.759875i	$0.274740\pi$
$854$	−5.81032	−	14.0274i	−0.198825	−	0.480006i
$855$	11.8806	+	28.0995i	0.406309	+	0.960983i
$856$	14.0715	+	14.0715i	0.480955	+	0.480955i
$857$	24.8214	+	14.3306i	0.847883	+	0.489525i	0.859936	−	0.510402i	$-0.170503\pi$
$857$	24.8214	+	14.3306i	0.847883	+	0.489525i	−0.0120530	+	0.999927i	$0.503837\pi$
$858$	14.6387	−	14.7461i	0.499757	−	0.503425i
$859$	−27.8963	−	7.47480i	−0.951810	−	0.255037i	−0.250680	−	0.968070i	$-0.580654\pi$
$859$	−27.8963	−	7.47480i	−0.951810	−	0.255037i	−0.701130	+	0.713033i	$0.747321\pi$
$860$	−2.09123	−	3.62212i	−0.0713105	−	0.123513i
$861$	−17.8669	+	3.59223i	−0.608901	+	0.122423i
$862$	−15.5428	+	26.9209i	−0.529389	+	0.916929i
$863$	7.70238	−	7.70238i	0.262192	−	0.262192i	−0.563752	−	0.825944i	$-0.690643\pi$
$863$	7.70238	−	7.70238i	0.262192	−	0.262192i	0.825944	+	0.563752i	$0.190643\pi$
$864$	4.47124	−	2.64727i	0.152115	−	0.0900620i
$865$		−	37.5871i		−	1.27800i
$866$	4.39886	−	1.17867i	0.149479	−	0.0400528i
$867$	10.1487	−	5.90893i	0.344668	−	0.200678i
$868$	3.81629	−	4.97349i	0.129533	−	0.168811i
$869$	7.49285	−	27.9637i	0.254177	−	0.948603i
$870$	26.5179	+	10.8707i	0.899042	+	0.368551i
$871$	8.06029	−	13.9608i	0.273112	−	0.473045i
$872$	4.48592	+	10.8300i	0.151913	+	0.366749i
$873$	−38.3507	+	5.33449i	−1.29797	+	0.180545i
$874$	−0.00584845	−	0.0141194i	−0.000197827	−	0.000477596i
$875$	−5.83103	+	4.47431i	−0.197125	+	0.151259i
$876$	7.86046	−	13.7304i	0.265580	−	0.463907i
$877$	15.0088	+	25.9960i	0.506811	+	0.877822i	0.999969	+	0.00788226i	$0.00250903\pi$
$877$	15.0088	+	25.9960i	0.506811	+	0.877822i	−0.493158	+	0.869940i	$0.664158\pi$
$878$	−0.347400	−	2.63877i	−0.0117242	−	0.0890541i
$879$	−28.3647	−	3.62885i	−0.956719	−	0.122398i
$880$	4.43995	+	5.78626i	0.149671	+	0.195055i
$881$	0.667807	−	0.667807i	0.0224990	−	0.0224990i	−0.695768	−	0.718267i	$-0.744936\pi$
$881$	0.667807	−	0.667807i	0.0224990	−	0.0224990i	0.718267	+	0.695768i	$0.244936\pi$
$882$	−6.36780	+	11.2180i	−0.214415	+	0.377729i
$883$	−31.1493	−	12.9025i	−1.04826	−	0.434202i	−0.208988	−	0.977918i	$-0.567017\pi$
$883$	−31.1493	−	12.9025i	−1.04826	−	0.434202i	−0.839269	+	0.543716i	$0.817017\pi$
$884$	−7.64820	+	13.2471i	−0.257237	+	0.445547i
$885$	9.26354	−	0.0338642i	0.311391	−	0.00113833i
$886$	12.1448	−	7.01183i	0.408014	−	0.235567i
$887$	−6.07123	−	46.1156i	−0.203852	−	1.54841i	−0.721256	−	0.692669i	$-0.756435\pi$
$887$	−6.07123	−	46.1156i	−0.203852	−	1.54841i	0.517404	−	0.855741i	$-0.326898\pi$
$888$	−1.52166	+	0.885961i	−0.0510634	+	0.0297309i
$889$	−1.22875	+	9.33331i	−0.0412111	+	0.313029i
$890$	−30.4830	+	12.6265i	−1.02179	+	0.423240i
$891$	−8.93896	−	20.7184i	−0.299466	−	0.694092i
$892$			18.9328i			0.633917i
$893$	3.73965	+	13.9566i	0.125143	+	0.467039i
$894$	−0.583477	−	4.31014i	−0.0195144	−	0.144153i
$895$	15.7605	+	12.0934i	0.526815	+	0.404239i
$896$	1.62918	−	0.214486i	0.0544271	−	0.00716546i
$897$	0.0137427	−	0.0335240i	0.000458857	−	0.00111933i
$898$	−11.2314	+	19.4534i	−0.374798	+	0.649169i
$899$	−8.30414	−	20.0480i	−0.276959	−	0.668637i
$900$	−9.03343	−	5.12776i	−0.301114	−	0.170925i
$901$		−	20.7195i		−	0.690267i
$902$	−12.0867	+	10.5657i	−0.402442	+	0.351798i
$903$	−0.519291	+	4.05901i	−0.0172809	+	0.135075i
$904$	−2.77060	+	10.3400i	−0.0921486	+	0.343903i
$905$	55.7691	+	42.7931i	1.85383	+	1.42249i
$906$	4.10973	−	32.1235i	0.136537	−	1.06723i
$907$	−0.268593	−	1.00240i	−0.00891850	−	0.0332843i	0.961323	−	0.275423i	$-0.0888178\pi$
$907$	−0.268593	−	1.00240i	−0.00891850	−	0.0332843i	−0.970242	+	0.242138i	$0.922151\pi$
$908$	−10.9088	−	4.51855i	−0.362020	−	0.149953i
$909$	4.30438	−	0.598729i	0.142767	−	0.0198586i
$910$	−16.1734	+	16.1734i	−0.536143	+	0.536143i
$911$	25.4530	−	6.82012i	0.843297	−	0.225961i	0.188791	−	0.982017i	$-0.439543\pi$
$911$	25.4530	−	6.82012i	0.843297	−	0.225961i	0.654506	+	0.756057i	$0.272877\pi$
$912$	5.58545	−	2.33753i	0.184953	−	0.0774032i
$913$	7.07960	+	5.43237i	0.234301	+	0.179785i
$914$	15.0553	−	19.6204i	0.497984	−	0.648985i
$915$	45.0126	+	11.8849i	1.48807	+	0.392903i
$916$	−9.55670	−	12.4545i	−0.315762	−	0.411509i
$917$	−11.9780	+	28.9175i	−0.395549	+	0.954939i
$918$	10.2562	+	13.0669i	0.338506	+	0.431273i
$919$	−14.0775	+	33.9862i	−0.464375	+	1.12110i	0.502208	+	0.864747i	$0.332521\pi$
$919$	−14.0775	+	33.9862i	−0.464375	+	1.12110i	−0.966583	+	0.256354i	$0.917479\pi$
$920$	0.0110138	+	0.00635882i	0.000363114	+	0.000209644i
$921$	39.9143	−	23.2395i	1.31522	−	0.765767i
$922$	0.0972059	−	0.362778i	0.00320131	−	0.0119474i
$923$	−3.83328	+	14.3060i	−0.126174	+	0.470887i
$924$	−0.0260858	−	7.13578i	−0.000858161	−	0.234750i
$925$	3.04831	+	1.75994i	0.100228	+	0.0578666i
$926$	−12.2405	+	29.5513i	−0.402249	+	0.971115i
$927$	−36.1113	−	35.5871i	−1.18605	−	1.16883i
$928$	2.17671	−	5.25505i	0.0714541	−	0.172505i
$929$	−1.41661	−	1.84616i	−0.0464775	−	0.0605707i	0.769536	−	0.638603i	$-0.220487\pi$
$929$	−1.41661	−	1.84616i	−0.0464775	−	0.0605707i	−0.816014	+	0.578032i	$0.803821\pi$
$930$	5.04290	+	18.5489i	0.165363	+	0.608242i
$931$	−9.15029	+	11.9249i	−0.299889	+	0.390822i
$932$	−15.7130	−	12.0570i	−0.514698	−	0.394942i
$933$	6.46714	−	50.5501i	0.211725	−	1.65493i
$934$	34.2253	−	9.17065i	1.11989	−	0.300073i
$935$	−16.4869	+	16.4869i	−0.539178	+	0.539178i
$936$	13.3017	+	5.39613i	0.434778	+	0.176378i
$937$	−40.7963	−	16.8984i	−1.33276	−	0.552046i	−0.401316	−	0.915940i	$-0.631447\pi$
$937$	−40.7963	−	16.8984i	−1.33276	−	0.552046i	−0.931440	+	0.363894i	$0.881447\pi$
$938$	−1.43288	−	5.34758i	−0.0467852	−	0.174605i
$939$	−14.4291	+	6.03862i	−0.470876	+	0.197063i
$940$	−9.53908	−	7.31959i	−0.311131	−	0.238739i
$941$	5.36088	−	20.0071i	0.174760	−	0.652212i	−0.821833	−	0.569729i	$-0.807048\pi$
$941$	5.36088	−	20.0071i	0.174760	−	0.652212i	0.996592	−	0.0824835i	$-0.0262852\pi$
$942$	−5.55883	−	4.23325i	−0.181117	−	0.137927i
$943$	−0.0124210	+	0.0250864i	−0.000404485	+	0.000816927i
$944$		−	1.83853i		−	0.0598391i
$945$	9.75649	+	22.8424i	0.317379	+	0.743064i
$946$	1.37945	+	3.33030i	0.0448499	+	0.108277i
$947$	−14.0509	+	24.3368i	−0.456592	+	0.790840i	−0.998778	−	0.0494184i	$-0.984263\pi$
$947$	−14.0509	+	24.3368i	−0.456592	+	0.790840i	0.542187	+	0.840258i	$0.317597\pi$
$948$	19.8191	−	2.68298i	0.643695	−	0.0871392i
$949$	43.3326	−	5.70484i	1.40664	−	0.185187i
$950$	−9.60269	−	7.36840i	−0.311552	−	0.239062i
$951$	−51.7500	−	21.2142i	−1.67811	−	0.687919i
$952$	1.35962	+	5.07419i	0.0440657	+	0.164455i
$953$			40.0017i			1.29578i	0.761732	+	0.647892i	$0.224349\pi$
$953$			40.0017i			1.29578i	−0.761732	+	0.647892i	$0.775651\pi$
$954$	−19.2583	+	2.67878i	−0.623510	+	0.0867288i
$955$	2.31087	−	0.957193i	0.0747780	−	0.0309740i
$956$	−2.83744	+	21.5525i	−0.0917692	+	0.697056i
$957$	−21.4362	−	12.2720i	−0.692935	−	0.396696i
$958$	−4.09498	−	31.1045i	−0.132303	−	1.00494i
$959$	−3.69250	+	2.13187i	−0.119237	+	0.0688416i
$960$	−2.50332	+	4.37272i	−0.0807944	+	0.141129i
$961$	−8.22292	+	14.2425i	−0.265255	+	0.459436i
$962$	−4.49395	−	1.86146i	−0.144891	−	0.0600158i
$963$	51.9189	+	29.4714i	1.67306	+	0.949703i
$964$	−17.7697	+	17.7697i	−0.572323	+	0.572323i
$965$	−11.1715	−	14.5590i	−0.359625	−	0.468672i
$966$	−0.00480366	−	0.0114782i	−0.000154555	−	0.000369305i
$967$	−4.86655	−	36.9651i	−0.156498	−	1.18872i	−0.871785	−	0.489888i	$-0.837038\pi$
$967$	−4.86655	−	36.9651i	−0.156498	−	1.18872i	0.715288	−	0.698830i	$-0.246296\pi$
$968$	2.35706	+	4.08254i	0.0757587	+	0.131218i
$969$	9.73943	+	16.7277i	0.312876	+	0.537370i
$970$	29.7871	−	22.8564i	0.956405	−	0.733875i
$971$	−16.4381	−	39.6851i	−0.527524	−	1.27355i	−0.933141	−	0.359511i	$-0.882943\pi$
$971$	−16.4381	−	39.6851i	−0.527524	−	1.27355i	0.405617	−	0.914043i	$-0.367057\pi$
$972$	10.8194	−	11.2223i	0.347032	−	0.359956i
$973$	5.93201	+	14.3211i	0.190172	+	0.459115i
$974$	−1.92243	+	3.32975i	−0.0615986	+	0.106692i
$975$	−3.84947	−	28.4360i	−0.123282	−	0.910679i
$976$	2.39142	−	8.92490i	0.0765475	−	0.285679i
$977$	2.02789	−	2.64279i	0.0648778	−	0.0845505i	−0.759787	−	0.650172i	$-0.774697\pi$
$977$	2.02789	−	2.64279i	0.0648778	−	0.0845505i	0.824665	+	0.565621i	$0.191364\pi$
$978$	0.00629813	+	1.72285i	0.000201392	+	0.0550907i
$979$	27.4676	−	7.35993i	0.877869	−	0.235224i
$980$		−	12.5081i		−	0.399558i
$981$	21.6116	+	27.7425i	0.690006	+	0.885749i
$982$	−7.07425	+	7.07425i	−0.225748	+	0.225748i
$983$	21.1756	−	36.6773i	0.675398	−	1.16982i	−0.300954	−	0.953639i	$-0.597305\pi$
$983$	21.1756	−	36.6773i	0.675398	−	1.16982i	0.976352	−	0.216185i	$-0.0693615\pi$
$984$	−9.95689	−	4.88471i	−0.317414	−	0.155719i
$985$	−16.3496	−	28.3183i	−0.520940	−	0.902295i
$986$	17.5641	+	4.70630i	0.559356	+	0.149879i
$987$	3.08625	+	11.3519i	0.0982365	+	0.361335i
$988$	14.4858	+	8.36335i	0.460853	+	0.266074i
$989$	0.00444455	+	0.00444455i	0.000141329	+	0.000141329i
$990$	17.4557	+	13.1926i	0.554778	+	0.419288i
$991$	−9.71902	−	23.4638i	−0.308735	−	0.745352i	−0.999747	−	0.0225084i	$-0.992835\pi$
$991$	−9.71902	−	23.4638i	−0.308735	−	0.745352i	0.691012	−	0.722843i	$-0.257165\pi$
$992$	3.68500	−	0.987393i	0.116999	−	0.0313498i
$993$	−17.2217	+	42.0107i	−0.546515	+	1.33317i
$994$	2.54318	+	4.40492i	0.0806648	+	0.139715i
$995$	20.8558	−	27.1798i	0.661172	−	0.861656i
$996$	−1.57379	+	5.96054i	−0.0498675	+	0.188867i
$997$	49.1875	+	6.47566i	1.55778	+	0.205086i	0.859651	−	0.510881i	$-0.170681\pi$
$997$	49.1875	+	6.47566i	1.55778	+	0.205086i	0.698134	+	0.715968i	$0.254014\pi$
$998$	−4.27593	−	1.77115i	−0.135352	−	0.0560647i
$999$	−3.69400	+	3.77593i	−0.116873	+	0.119465i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	738.2.v.a.137.11	✓	168
9.5	odd	6		738.2.v.b.383.18	yes	168
41.3	odd	8		738.2.v.b.659.18	yes	168
369.167	even	24	inner	738.2.v.a.167.11	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
738.2.v.a.137.11	✓	168	1.1	even	1	trivial
738.2.v.a.167.11	yes	168	369.167	even	24	inner
738.2.v.b.383.18	yes	168	9.5	odd	6
738.2.v.b.659.18	yes	168	41.3	odd	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 738 = 2 \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	738.v (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.442169 + 1.67466i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.752912 - 2.80991i) q^{5} +(-1.73204 + 0.00633171i) q^{6} +(-1.62918 - 0.214486i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.60897 - 1.48096i) q^{9} +2.90903 q^{10} +(-2.48572 - 0.327251i) q^{11} +(-0.454401 - 1.67138i) q^{12} +(2.91283 - 3.79607i) q^{13} +(-0.214486 - 1.62918i) q^{14} +(4.37272 + 2.50332i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.95350 + 1.22338i) q^{17} +(0.755250 - 2.90338i) q^{18} +(1.33777 - 3.22967i) q^{19} +(0.752912 + 2.80991i) q^{20} +(1.07956 - 2.63349i) q^{21} +(-0.327251 - 2.48572i) q^{22} +(-0.00218589 - 0.00378607i) q^{23} +(1.49682 - 0.871503i) q^{24} +(-2.99857 - 1.73122i) q^{25} +(4.42062 + 1.83108i) q^{26} +(3.63372 - 3.71431i) q^{27} +(1.51815 - 0.628840i) q^{28} +(0.742436 - 5.63936i) q^{29} +(-1.28628 + 4.87163i) q^{30} +(3.30388 - 1.90750i) q^{31} +(0.965926 + 0.258819i) q^{32} +(1.64714 - 4.01803i) q^{33} +(-0.417272 + 3.16950i) q^{34} +(-1.82931 + 4.41636i) q^{35} +(2.99992 - 0.0219335i) q^{36} -1.01659 q^{37} +(3.46586 + 0.456290i) q^{38} +(5.06917 + 6.55650i) q^{39} +(-2.51929 + 1.45451i) q^{40} +(-3.54889 - 5.32967i) q^{41} +(2.82316 + 0.361182i) q^{42} +(-1.38876 + 0.372118i) q^{43} +(2.31632 - 0.959451i) q^{44} +(-6.12570 + 6.21593i) q^{45} +(0.00309132 - 0.00309132i) q^{46} +(-3.27913 + 2.51616i) q^{47} +(1.22921 + 1.22026i) q^{48} +(-4.15325 - 1.11286i) q^{49} +(0.896147 - 3.34447i) q^{50} +(-3.35469 + 4.40517i) q^{51} +(-0.624547 + 4.74391i) q^{52} +(-2.48026 - 5.98787i) q^{53} +(4.52822 + 2.54857i) q^{54} +(-2.79107 + 6.73824i) q^{55} +(1.00034 + 1.30367i) q^{56} +(4.81708 + 3.66838i) q^{57} +(5.63936 - 0.742436i) q^{58} +(1.59222 - 0.919266i) q^{59} +(-5.03855 + 0.0184191i) q^{60} +(8.92490 - 2.39142i) q^{61} +(2.69761 + 2.69761i) q^{62} +(3.93284 + 2.97235i) q^{63} +1.00000i q^{64} +(-8.47350 - 11.0429i) q^{65} +(4.30743 + 0.551073i) q^{66} +(3.34027 - 0.439755i) q^{67} +(-3.16950 + 0.417272i) q^{68} +(0.00730692 - 0.00198654i) q^{69} +(-4.73933 - 0.623945i) q^{70} +(-2.85971 + 1.18453i) q^{71} +(0.797623 + 2.89202i) q^{72} +(6.45897 + 6.45897i) q^{73} +(-0.263113 - 0.981950i) q^{74} +(4.22508 - 4.25609i) q^{75} +(0.456290 + 3.46586i) q^{76} +(3.97949 + 1.06630i) q^{77} +(-5.02109 + 6.59338i) q^{78} +(-1.50718 + 11.4482i) q^{79} +(-2.05699 - 2.05699i) q^{80} +(4.61349 + 7.72760i) q^{81} +(4.22955 - 4.80738i) q^{82} +(-3.08241 - 1.77963i) q^{83} +(0.381813 + 2.82045i) q^{84} +(5.66131 - 7.37796i) q^{85} +(-0.718877 - 1.24513i) q^{86} +(9.11573 + 3.73688i) q^{87} +(1.52627 + 1.98907i) q^{88} +(-10.4788 + 4.34044i) q^{89} +(-7.58958 - 4.30817i) q^{90} +(-5.55972 + 5.55972i) q^{91} +(0.00378607 + 0.00218589i) q^{92} +(1.73354 + 6.37631i) q^{93} +(-3.27913 - 2.51616i) q^{94} +(-8.06784 - 6.19068i) q^{95} +(-0.860536 + 1.50316i) q^{96} +(10.2395 - 7.85706i) q^{97} -4.29977i q^{98} +(6.00052 + 4.53505i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 4 q^{3} - 12 q^{7} - 4 q^{9} + 8 q^{15} + 84 q^{16} - 12 q^{17} - 8 q^{21} - 12 q^{22} + 48 q^{25} - 40 q^{27} + 16 q^{30} - 64 q^{33} - 36 q^{34} + 24 q^{35} - 4 q^{36} + 32 q^{39} - 32 q^{42}+ \cdots + 68 q^{99}+O(q^{100}) \) 168 * q - 4 * q^3 - 12 * q^7 - 4 * q^9 + 8 * q^15 + 84 * q^16 - 12 * q^17 - 8 * q^21 - 12 * q^22 + 48 * q^25 - 40 * q^27 + 16 * q^30 - 64 * q^33 - 36 * q^34 + 24 * q^35 - 4 * q^36 + 32 * q^39 - 32 * q^42 + 12 * q^44 + 72 * q^45 - 12 * q^47 - 8 * q^48 + 12 * q^49 - 44 * q^51 + 12 * q^56 - 64 * q^57 - 24 * q^58 - 108 * q^61 + 48 * q^63 - 84 * q^65 - 4 * q^66 - 60 * q^67 + 40 * q^69 + 12 * q^70 + 20 * q^75 - 60 * q^79 + 68 * q^81 + 12 * q^82 - 120 * q^83 + 8 * q^84 + 24 * q^85 + 72 * q^89 + 40 * q^90 - 16 * q^93 - 12 * q^94 - 120 * q^95 + 96 * q^97 + 68 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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