LMFDB - Embedded newform 930.2.be.b.37.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(37,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("930.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.be (of order $12$, degree $4$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.14
Character	$\chi$	$=$	930.37
Dual form			930.2.be.b.553.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(1.24237 + 1.85917i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.725743 + 2.70851i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(1.24237 + 1.85917i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.725743 + 2.70851i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.436149 + 2.19312i) q^{10} +(3.03355 + 1.75142i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(3.02236 - 0.809838i) q^{13} +(-2.42838 + 1.40203i) q^{14} +(-2.11737 + 0.718844i) q^{15} -1.00000 q^{16} +(2.60924 + 0.699144i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(3.48540 - 2.01230i) q^{19} +(-1.85917 + 1.24237i) q^{20} +(-2.42838 - 1.40203i) q^{21} +(0.906601 + 3.38348i) q^{22} +(-4.26333 - 4.26333i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-1.91305 + 4.61955i) q^{25} +(2.70977 + 1.56449i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-2.70851 - 0.725743i) q^{28} -10.2006 q^{29} +(-2.00551 - 0.988908i) q^{30} +(-5.51894 + 0.735742i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-2.47688 + 2.47688i) q^{33} +(1.35064 + 2.33938i) q^{34} +(-5.93723 + 2.01568i) q^{35} +(0.500000 - 0.866025i) q^{36} +(0.0201573 + 0.00540114i) q^{37} +(3.88746 + 1.04164i) q^{38} +3.12897i q^{39} +(-2.19312 - 0.436149i) q^{40} +(5.33146 - 9.23436i) q^{41} +(-0.725743 - 2.70851i) q^{42} +(0.367072 - 1.36993i) q^{43} +(-1.75142 + 3.03355i) q^{44} +(-0.146334 - 2.23127i) q^{45} -6.02926i q^{46} +(6.73089 + 6.73089i) q^{47} +(0.258819 - 0.965926i) q^{48} +(-0.747153 - 0.431369i) q^{49} +(-4.61925 + 1.91378i) q^{50} +(-1.35064 + 2.33938i) q^{51} +(0.809838 + 3.02236i) q^{52} +(6.26990 - 1.68002i) q^{53} +1.00000 q^{54} +(0.512585 + 7.81580i) q^{55} +(-1.40203 - 2.42838i) q^{56} +(1.04164 + 3.88746i) q^{57} +(-7.21289 - 7.21289i) q^{58} +(-5.98077 + 3.45300i) q^{59} +(-0.718844 - 2.11737i) q^{60} -8.20722i q^{61} +(-4.42273 - 3.38223i) q^{62} +(1.98277 - 1.98277i) q^{63} -1.00000i q^{64} +(5.26050 + 4.61297i) q^{65} -3.50284 q^{66} +(-1.64395 + 0.440496i) q^{67} +(-0.699144 + 2.60924i) q^{68} +(5.22149 - 3.01463i) q^{69} +(-5.62356 - 2.77296i) q^{70} +(-5.02604 + 8.70536i) q^{71} +(0.965926 - 0.258819i) q^{72} +(11.1207 - 2.97979i) q^{73} +(0.0104342 + 0.0180726i) q^{74} +(-3.96701 - 3.04349i) q^{75} +(2.01230 + 3.48540i) q^{76} +(-6.94532 + 6.94532i) q^{77} +(-2.21252 + 2.21252i) q^{78} +(-5.93604 - 10.2815i) q^{79} +(-1.24237 - 1.85917i) q^{80} +(0.500000 + 0.866025i) q^{81} +(10.2996 - 2.75977i) q^{82} +(-2.79615 + 0.749226i) q^{83} +(1.40203 - 2.42838i) q^{84} +(1.94180 + 5.71962i) q^{85} +(1.22825 - 0.709129i) q^{86} +(2.64010 - 9.85299i) q^{87} +(-3.38348 + 0.906601i) q^{88} +14.2622 q^{89} +(1.47428 - 1.68122i) q^{90} +8.77382i q^{91} +(4.26333 - 4.26333i) q^{92} +(0.717734 - 5.52131i) q^{93} +9.51892i q^{94} +(8.07136 + 3.97996i) q^{95} +(0.866025 - 0.500000i) q^{96} +(5.44993 + 5.44993i) q^{97} +(-0.223293 - 0.833341i) q^{98} +(-1.75142 - 3.03355i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{7}+O(q^{10}) $ 64 * q + 4 * q^7	$ 64 q + 4 q^{7} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 64 q^{16} - 4 q^{17} + 12 q^{20} - 24 q^{21} - 4 q^{22} - 32 q^{24} + 28 q^{25} + 8 q^{28} - 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 16 q^{37} - 28 q^{38} - 8 q^{41} + 4 q^{42} - 40 q^{43} + 4 q^{44} - 12 q^{45} + 8 q^{47} + 60 q^{49} - 8 q^{50} - 24 q^{53} + 64 q^{54} + 44 q^{55} + 4 q^{57} - 52 q^{58} - 24 q^{59} + 20 q^{62} - 4 q^{63} + 44 q^{65} + 8 q^{66} - 44 q^{67} - 4 q^{68} + 12 q^{69} - 44 q^{70} + 8 q^{71} + 4 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{76} + 104 q^{77} - 56 q^{79} + 32 q^{81} - 16 q^{82} - 48 q^{83} - 32 q^{85} - 24 q^{86} - 32 q^{87} + 8 q^{88} + 176 q^{89} + 16 q^{93} + 64 q^{95} - 68 q^{97} + 32 q^{98} + 4 q^{99}+O(q^{100}) $ 64 * q + 4 * q^7 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 64 * q^16 - 4 * q^17 + 12 * q^20 - 24 * q^21 - 4 * q^22 - 32 * q^24 + 28 * q^25 + 8 * q^28 - 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 16 * q^37 - 28 * q^38 - 8 * q^41 + 4 * q^42 - 40 * q^43 + 4 * q^44 - 12 * q^45 + 8 * q^47 + 60 * q^49 - 8 * q^50 - 24 * q^53 + 64 * q^54 + 44 * q^55 + 4 * q^57 - 52 * q^58 - 24 * q^59 + 20 * q^62 - 4 * q^63 + 44 * q^65 + 8 * q^66 - 44 * q^67 - 4 * q^68 + 12 * q^69 - 44 * q^70 + 8 * q^71 + 4 * q^73 - 12 * q^74 + 8 * q^75 - 8 * q^76 + 104 * q^77 - 56 * q^79 + 32 * q^81 - 16 * q^82 - 48 * q^83 - 32 * q^85 - 24 * q^86 - 32 * q^87 + 8 * q^88 + 176 * q^89 + 16 * q^93 + 64 * q^95 - 68 * q^97 + 32 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$4$			1.00000i			0.500000i
$5$	1.24237	+	1.85917i	0.555603	+	0.831448i
$5$	1.24237	+	1.85917i	0.555603	+	0.831448i
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	−0.725743	+	2.70851i	−0.274305	+	1.02372i	0.682000	+	0.731352i	$0.261110\pi$
$7$	−0.725743	+	2.70851i	−0.274305	+	1.02372i	−0.956306	+	0.292369i	$0.905556\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	−0.436149	+	2.19312i	−0.137922	+	0.693525i
$11$	3.03355	+	1.75142i	0.914649	+	0.528073i	0.881924	−	0.471392i	$-0.156248\pi$
$11$	3.03355	+	1.75142i	0.914649	+	0.528073i	0.0327250	+	0.999464i	$0.489581\pi$
$12$	−0.965926	−	0.258819i	−0.278839	−	0.0747146i
$13$	3.02236	−	0.809838i	0.838251	−	0.224609i	0.185941	−	0.982561i	$-0.440467\pi$
$13$	3.02236	−	0.809838i	0.838251	−	0.224609i	0.652310	+	0.757952i	$0.273800\pi$
$14$	−2.42838	+	1.40203i	−0.649013	+	0.374708i
$15$	−2.11737	+	0.718844i	−0.546703	+	0.185605i
$16$	−1.00000			−0.250000
$17$	2.60924	+	0.699144i	0.632834	+	0.169567i	0.560955	−	0.827846i	$-0.310434\pi$
$17$	2.60924	+	0.699144i	0.632834	+	0.169567i	0.0718784	+	0.997413i	$0.477101\pi$
$18$	−0.258819	−	0.965926i	−0.0610042	−	0.227671i
$19$	3.48540	−	2.01230i	0.799606	−	0.461653i	−0.0437272	−	0.999044i	$-0.513923\pi$
$19$	3.48540	−	2.01230i	0.799606	−	0.461653i	0.843333	+	0.537391i	$0.180590\pi$
$20$	−1.85917	+	1.24237i	−0.415724	+	0.277802i
$21$	−2.42838	−	1.40203i	−0.529917	−	0.305948i
$22$	0.906601	+	3.38348i	0.193288	+	0.721361i
$23$	−4.26333	−	4.26333i	−0.888966	−	0.888966i	0.105458	−	0.994424i	$-0.466369\pi$
$23$	−4.26333	−	4.26333i	−0.888966	−	0.888966i	−0.994424	+	0.105458i	$0.966369\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−1.91305	+	4.61955i	−0.382610	+	0.923910i
$26$	2.70977	+	1.56449i	0.531430	+	0.306821i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−2.70851	−	0.725743i	−0.511861	−	0.137153i
$29$	−10.2006			−1.89420			−0.947099	−	0.320941i	$-0.896001\pi$
$29$	−10.2006			−1.89420			−0.947099	+	0.320941i	$0.896001\pi$
$30$	−2.00551	−	0.988908i	−0.366154	−	0.180549i
$31$	−5.51894	+	0.735742i	−0.991231	+	0.132143i
$31$	−5.51894	+	0.735742i	−0.991231	+	0.132143i
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−2.47688	+	2.47688i	−0.431170	+	0.431170i
$34$	1.35064	+	2.33938i	0.231633	+	0.401200i
$35$	−5.93723	+	2.01568i	−1.00358	+	0.340712i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	0.0201573	+	0.00540114i	0.00331385	+	0.000887942i	0.260476	−	0.965480i	$-0.416121\pi$
$37$	0.0201573	+	0.00540114i	0.00331385	+	0.000887942i	−0.257162	+	0.966368i	$0.582787\pi$
$38$	3.88746	+	1.04164i	0.630630	+	0.168977i
$39$			3.12897i			0.501037i
$40$	−2.19312	−	0.436149i	−0.346763	−	0.0689611i
$41$	5.33146	−	9.23436i	0.832634	−	1.44216i	−0.0633080	−	0.997994i	$-0.520165\pi$
$41$	5.33146	−	9.23436i	0.832634	−	1.44216i	0.895942	−	0.444171i	$-0.146502\pi$
$42$	−0.725743	−	2.70851i	−0.111985	−	0.417932i
$43$	0.367072	−	1.36993i	0.0559780	−	0.208913i	−0.932272	−	0.361758i	$-0.882177\pi$
$43$	0.367072	−	1.36993i	0.0559780	−	0.208913i	0.988250	+	0.152845i	$0.0488435\pi$
$44$	−1.75142	+	3.03355i	−0.264036	+	0.457324i
$45$	−0.146334	−	2.23127i	−0.0218142	−	0.332619i
$46$		−	6.02926i		−	0.888966i
$47$	6.73089	+	6.73089i	0.981802	+	0.981802i	0.999837	−	0.0180358i	$-0.00574130\pi$
$47$	6.73089	+	6.73089i	0.981802	+	0.981802i	−0.0180358	+	0.999837i	$0.505741\pi$
$48$	0.258819	−	0.965926i	0.0373573	−	0.139419i
$49$	−0.747153	−	0.431369i	−0.106736	−	0.0616242i
$50$	−4.61925	+	1.91378i	−0.653260	+	0.270650i
$51$	−1.35064	+	2.33938i	−0.189128	+	0.327579i
$52$	0.809838	+	3.02236i	0.112304	+	0.419125i
$53$	6.26990	−	1.68002i	0.861238	−	0.230768i	0.198943	−	0.980011i	$-0.436249\pi$
$53$	6.26990	−	1.68002i	0.861238	−	0.230768i	0.662295	+	0.749243i	$0.269583\pi$
$54$	1.00000			0.136083
$55$	0.512585	+	7.81580i	0.0691169	+	1.05388i
$56$	−1.40203	−	2.42838i	−0.187354	−	0.324507i
$57$	1.04164	+	3.88746i	0.137969	+	0.514907i
$58$	−7.21289	−	7.21289i	−0.947099	−	0.947099i
$59$	−5.98077	+	3.45300i	−0.778630	+	0.449542i	−0.835944	−	0.548814i	$-0.815080\pi$
$59$	−5.98077	+	3.45300i	−0.778630	+	0.449542i	0.0573146	+	0.998356i	$0.481746\pi$
$60$	−0.718844	−	2.11737i	−0.0928024	−	0.273352i
$61$		−	8.20722i		−	1.05083i	−0.850847	−	0.525414i	$-0.823911\pi$
$61$		−	8.20722i		−	1.05083i	0.850847	−	0.525414i	$-0.176089\pi$
$62$	−4.42273	−	3.38223i	−0.561687	−	0.429544i
$63$	1.98277	−	1.98277i	0.249805	−	0.249805i
$64$		−	1.00000i		−	0.125000i
$65$	5.26050	+	4.61297i	0.652485	+	0.572168i
$66$	−3.50284			−0.431170
$67$	−1.64395	+	0.440496i	−0.200841	+	0.0538151i	−0.357837	−	0.933784i	$-0.616486\pi$
$67$	−1.64395	+	0.440496i	−0.200841	+	0.0538151i	0.156996	+	0.987599i	$0.449819\pi$
$68$	−0.699144	+	2.60924i	−0.0847836	+	0.316417i
$69$	5.22149	−	3.01463i	0.628594	−	0.362919i
$70$	−5.62356	−	2.77296i	−0.672144	−	0.331432i
$71$	−5.02604	+	8.70536i	−0.596481	+	1.03314i	0.396855	+	0.917882i	$0.370102\pi$
$71$	−5.02604	+	8.70536i	−0.596481	+	1.03314i	−0.993336	+	0.115255i	$0.963232\pi$
$72$	0.965926	−	0.258819i	0.113835	−	0.0305021i
$73$	11.1207	−	2.97979i	1.30158	−	0.348758i	0.459534	−	0.888160i	$-0.348017\pi$
$73$	11.1207	−	2.97979i	1.30158	−	0.348758i	0.842048	+	0.539403i	$0.181350\pi$
$74$	0.0104342	+	0.0180726i	0.00121295	+	0.00210089i
$75$	−3.96701	−	3.04349i	−0.458071	−	0.351432i
$76$	2.01230	+	3.48540i	0.230826	+	0.399803i
$77$	−6.94532	+	6.94532i	−0.791492	+	0.791492i
$78$	−2.21252	+	2.21252i	−0.250518	+	0.250518i
$79$	−5.93604	−	10.2815i	−0.667856	−	1.15676i	−0.978502	−	0.206235i	$-0.933879\pi$
$79$	−5.93604	−	10.2815i	−0.667856	−	1.15676i	0.310646	−	0.950526i	$-0.399455\pi$
$80$	−1.24237	−	1.85917i	−0.138901	−	0.207862i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	10.2996	−	2.75977i	1.13740	−	0.304765i
$83$	−2.79615	+	0.749226i	−0.306917	+	0.0822382i	−0.408990	−	0.912539i	$-0.634119\pi$
$83$	−2.79615	+	0.749226i	−0.306917	+	0.0822382i	0.102073	+	0.994777i	$0.467452\pi$
$84$	1.40203	−	2.42838i	0.152974	−	0.264959i
$85$	1.94180	+	5.71962i	0.210618	+	0.620380i
$86$	1.22825	−	0.709129i	0.132445	−	0.0764673i
$87$	2.64010	−	9.85299i	0.283049	−	1.05635i
$88$	−3.38348	+	0.906601i	−0.360680	+	0.0966440i
$89$	14.2622			1.51178			0.755892	−	0.654696i	$-0.227203\pi$
$89$	14.2622			1.51178			0.755892	+	0.654696i	$0.227203\pi$
$90$	1.47428	−	1.68122i	0.155402	−	0.177216i
$91$			8.77382i			0.919746i
$92$	4.26333	−	4.26333i	0.444483	−	0.444483i
$93$	0.717734	−	5.52131i	0.0744256	−	0.572533i
$94$			9.51892i			0.981802i
$95$	8.07136	+	3.97996i	0.828104	+	0.408335i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	5.44993	+	5.44993i	0.553356	+	0.553356i	0.927408	−	0.374052i	$-0.122032\pi$
$97$	5.44993	+	5.44993i	0.553356	+	0.553356i	−0.374052	+	0.927408i	$0.622032\pi$
$98$	−0.223293	−	0.833341i	−0.0225560	−	0.0841802i
$99$	−1.75142	−	3.03355i	−0.176024	−	0.304883i
$100$	−4.61955	−	1.91305i	−0.461955	−	0.191305i
$101$	−16.4136			−1.63322			−0.816609	−	0.577192i	$-0.804148\pi$
$101$	−16.4136			−1.63322			−0.816609	+	0.577192i	$0.804148\pi$
$102$	−2.60924	+	0.699144i	−0.258353	+	0.0692255i
$103$	−2.16197	−	8.06859i	−0.213025	−	0.795022i	−0.986852	−	0.161625i	$-0.948327\pi$
$103$	−2.16197	−	8.06859i	−0.213025	−	0.795022i	0.773827	−	0.633397i	$-0.218340\pi$
$104$	−1.56449	+	2.70977i	−0.153411	+	0.265715i
$105$	−0.410329	−	6.25662i	−0.0400440	−	0.610584i
$106$	5.62144	+	3.24554i	0.546003	+	0.315235i
$107$	−3.65509	+	13.6410i	−0.353350	+	1.31872i	0.529197	+	0.848499i	$0.322493\pi$
$107$	−3.65509	+	13.6410i	−0.353350	+	1.31872i	−0.882548	+	0.470223i	$0.844174\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$		−	15.0255i		−	1.43918i	−0.694398	−	0.719591i	$-0.744329\pi$
$109$		−	15.0255i		−	1.43918i	0.694398	−	0.719591i	$-0.255671\pi$
$110$	−5.16415	+	5.88905i	−0.492382	+	0.561499i
$111$	−0.0104342	+	0.0180726i	−0.000990371	+	0.00171537i
$112$	0.725743	−	2.70851i	0.0685763	−	0.255930i
$113$	2.10319	+	7.84920i	0.197851	+	0.738391i	0.991510	+	0.130028i	$0.0415067\pi$
$113$	2.10319	+	7.84920i	0.197851	+	0.738391i	−0.793659	+	0.608363i	$0.791827\pi$
$114$	−2.01230	+	3.48540i	−0.188469	+	0.326438i
$115$	2.62965	−	13.2229i	0.245216	−	1.23304i
$116$		−	10.2006i		−	0.947099i
$117$	−3.02236	−	0.809838i	−0.279417	−	0.0748695i
$118$	−6.67068	−	1.78740i	−0.614086	−	0.164544i
$119$	−3.78728	+	6.55976i	−0.347179	+	0.601332i
$120$	0.988908	−	2.00551i	0.0902746	−	0.183077i
$121$	0.634940	+	1.09975i	0.0577219	+	0.0999772i
$122$	5.80338	−	5.80338i	0.525414	−	0.525414i
$123$	7.53982	+	7.53982i	0.679843	+	0.679843i
$124$	−0.735742	−	5.51894i	−0.0660716	−	0.495615i
$125$	−10.9653	+	2.18248i	−0.980762	+	0.195207i
$126$	2.80406			0.249805
$127$	10.8370	+	2.90375i	0.961624	+	0.257666i	0.705288	−	0.708921i	$-0.250818\pi$
$127$	10.8370	+	2.90375i	0.961624	+	0.257666i	0.256337	+	0.966588i	$0.417484\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	1.22825	+	0.709129i	0.108141	+	0.0624353i
$130$	0.457875	+	6.98160i	0.0401583	+	0.612327i
$131$	9.14499	+	15.8396i	0.799001	+	1.38391i	0.920267	+	0.391291i	$0.127971\pi$
$131$	9.14499	+	15.8396i	0.799001	+	1.38391i	−0.121266	+	0.992620i	$0.538695\pi$
$132$	−2.47688	−	2.47688i	−0.215585	−	0.215585i
$133$	2.92082	+	10.9007i	0.253268	+	0.945208i
$134$	−1.47393	−	0.850973i	−0.127328	−	0.0735129i
$135$	2.19312	+	0.436149i	0.188754	+	0.0375377i
$136$	−2.33938	+	1.35064i	−0.200600	+	0.115817i
$137$	−3.06534	−	11.4400i	−0.261890	−	0.977386i	−0.964127	−	0.265442i	$-0.914482\pi$
$137$	−3.06534	−	11.4400i	−0.261890	−	0.977386i	0.702237	−	0.711943i	$-0.252185\pi$
$138$	5.82382	+	1.56049i	0.495756	+	0.132837i
$139$	4.81775			0.408636			0.204318	−	0.978905i	$-0.434502\pi$
$139$	4.81775			0.408636			0.204318	+	0.978905i	$0.434502\pi$
$140$	−2.01568	−	5.93723i	−0.170356	−	0.501788i
$141$	−8.24363	+	4.75946i	−0.694239	+	0.400819i
$142$	−9.70957	+	2.60167i	−0.814809	+	0.218327i
$143$	10.5868	+	2.83673i	0.885315	+	0.237219i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$	−12.6728	−	18.9646i	−1.05242	−	1.57493i
$146$	9.97056	+	5.75651i	0.825170	+	0.476412i
$147$	0.610048	−	0.610048i	0.0503159	−	0.0503159i
$148$	−0.00540114	+	0.0201573i	−0.000443971	+	0.00165692i
$149$	19.2453	−	11.1113i	1.57663	−	0.910269i	0.581308	−	0.813683i	$-0.302541\pi$
$149$	19.2453	−	11.1113i	1.57663	−	0.910269i	0.995325	−	0.0965859i	$-0.0307922\pi$
$150$	−0.653023	−	4.95717i	−0.0533191	−	0.404751i
$151$		−	3.98238i		−	0.324081i	−0.986784	−	0.162041i	$-0.948192\pi$
$151$		−	3.98238i		−	0.324081i	0.986784	−	0.162041i	$-0.0518075\pi$
$152$	−1.04164	+	3.88746i	−0.0844883	+	0.315315i
$153$	−1.91010	−	1.91010i	−0.154422	−	0.154422i
$154$	−9.82216			−0.791492
$155$	−8.22442	−	9.34660i	−0.660601	−	0.750737i
$156$	−3.12897			−0.250518
$157$	7.29579	+	7.29579i	0.582267	+	0.582267i	0.935526	−	0.353258i	$-0.114926\pi$
$157$	7.29579	+	7.29579i	0.582267	+	0.582267i	−0.353258	+	0.935526i	$0.614926\pi$
$158$	3.07272	−	11.4675i	0.244452	−	0.912309i
$159$			6.49108i			0.514776i
$160$	0.436149	−	2.19312i	0.0344806	−	0.173381i
$161$	14.6414	−	8.45320i	1.15390	−	0.666205i
$162$	−0.258819	+	0.965926i	−0.0203347	+	0.0758903i
$163$	15.9085	−	15.9085i	1.24605	−	1.24605i	0.288601	−	0.957449i	$-0.406810\pi$
$163$	15.9085	−	15.9085i	1.24605	−	1.24605i	0.957449	−	0.288601i	$-0.0931902\pi$
$164$	9.23436	+	5.33146i	0.721082	+	0.416317i
$165$	−7.68215	−	1.52776i	−0.598054	−	0.118936i
$166$	−2.50696	−	1.44739i	−0.194578	−	0.112340i
$167$	12.2943	+	3.29425i	0.951362	+	0.254917i	0.700940	−	0.713220i	$-0.252764\pi$
$167$	12.2943	+	3.29425i	0.951362	+	0.254917i	0.250422	+	0.968137i	$0.419431\pi$
$168$	2.70851	−	0.725743i	0.208966	−	0.0559923i
$169$	−2.77953	+	1.60477i	−0.213810	+	0.123443i
$170$	−2.67132	+	5.41744i	−0.204881	+	0.415499i
$171$	−4.02460			−0.307769
$172$	1.36993	+	0.367072i	0.104456	+	0.0279890i
$173$	−3.89751	−	14.5457i	−0.296322	−	1.10589i	−0.940162	−	0.340728i	$-0.889326\pi$
$173$	−3.89751	−	14.5457i	−0.296322	−	1.10589i	0.643840	−	0.765160i	$-0.277340\pi$
$174$	8.83395	−	5.10029i	0.669700	−	0.386652i
$175$	−11.1237	−	8.53413i	−0.840874	−	0.645120i
$176$	−3.03355	−	1.75142i	−0.228662	−	0.132018i
$177$	−1.78740	−	6.67068i	−0.134349	−	0.501399i
$178$	10.0849	+	10.0849i	0.755892	+	0.755892i
$179$	12.1068	+	20.9696i	0.904904	+	1.56734i	0.821046	+	0.570862i	$0.193391\pi$
$179$	12.1068	+	20.9696i	0.904904	+	1.56734i	0.0838586	+	0.996478i	$0.473276\pi$
$180$	2.23127	−	0.146334i	0.166309	−	0.0109071i
$181$	−9.64816	−	5.57037i	−0.717142	−	0.414042i	0.0965577	−	0.995327i	$-0.469217\pi$
$181$	−9.64816	−	5.57037i	−0.717142	−	0.414042i	−0.813700	+	0.581285i	$0.802550\pi$
$182$	−6.20403	+	6.20403i	−0.459873	+	0.459873i
$183$	7.92757	+	2.12419i	0.586023	+	0.157024i
$184$	6.02926			0.444483
$185$	0.0150011	+	0.0441862i	0.00110291	+	0.00324863i
$186$	4.41167	−	3.39664i	0.323479	−	0.249054i
$187$	6.69076	+	6.69076i	0.489277	+	0.489277i
$188$	−6.73089	+	6.73089i	−0.490901	+	0.490901i
$189$	1.40203	+	2.42838i	0.101983	+	0.176639i
$190$	2.89306	+	8.52157i	0.209884	+	0.618219i
$191$	−0.278233	+	0.481913i	−0.0201322	+	0.0348700i	−0.875916	−	0.482464i	$-0.839742\pi$
$191$	−0.278233	+	0.481913i	−0.0201322	+	0.0348700i	0.855784	+	0.517334i	$0.173075\pi$
$192$	0.965926	+	0.258819i	0.0697097	+	0.0186787i
$193$	12.6950	+	3.40161i	0.913804	+	0.244853i	0.684935	−	0.728604i	$-0.259831\pi$
$193$	12.6950	+	3.40161i	0.913804	+	0.244853i	0.228869	+	0.973457i	$0.426497\pi$
$194$			7.70736i			0.553356i
$195$	−5.81730	+	3.88733i	−0.416586	+	0.278378i
$196$	0.431369	−	0.747153i	0.0308121	−	0.0533681i
$197$	4.10394	+	15.3161i	0.292394	+	1.09123i	0.943265	+	0.332040i	$0.107737\pi$
$197$	4.10394	+	15.3161i	0.292394	+	1.09123i	−0.650872	+	0.759188i	$0.725596\pi$
$198$	0.906601	−	3.38348i	0.0644294	−	0.240454i
$199$	5.55244	−	9.61712i	0.393602	−	0.681739i	−0.599319	−	0.800510i	$-0.704562\pi$
$199$	5.55244	−	9.61712i	0.393602	−	0.681739i	0.992922	+	0.118771i	$0.0378954\pi$
$200$	−1.91378	−	4.61925i	−0.135325	−	0.326630i
$201$		−	1.70195i		−	0.120046i
$202$	−11.6062	−	11.6062i	−0.816609	−	0.816609i
$203$	7.40300	−	27.6284i	0.519589	−	1.93913i
$204$	−2.33938	−	1.35064i	−0.163789	−	0.0945638i
$205$	23.7919	−	1.56035i	1.66170	−	0.108979i
$206$	4.17661	−	7.23410i	0.290998	−	0.504024i
$207$	1.56049	+	5.82382i	0.108461	+	0.404783i
$208$	−3.02236	+	0.809838i	−0.209563	+	0.0561521i
$209$	14.0975			0.975145
$210$	4.13395	−	4.71425i	0.285270	−	0.325314i
$211$	−3.84401	−	6.65802i	−0.264633	−	0.458357i	0.702835	−	0.711353i	$-0.251917\pi$
$211$	−3.84401	−	6.65802i	−0.264633	−	0.458357i	−0.967467	+	0.252996i	$0.918584\pi$
$212$	1.68002	+	6.26990i	0.115384	+	0.430619i
$213$	−7.10790	−	7.10790i	−0.487025	−	0.487025i
$214$	−12.2302	+	7.06108i	−0.836036	+	0.482686i
$215$	3.00298	−	1.01951i	0.204801	−	0.0695298i
$216$			1.00000i			0.0680414i
$217$	2.01257	−	15.4821i	0.136622	−	1.05099i
$218$	10.6246	−	10.6246i	0.719591	−	0.719591i
$219$			11.5130i			0.777977i
$220$	−7.81580	+	0.512585i	−0.526941	+	0.0345585i
$221$	8.45224			0.568559
$222$	−0.0201573	+	0.00540114i	−0.00135287	+	0.000362501i
$223$	−1.76868	+	6.60080i	−0.118440	+	0.442023i	−0.999521	−	0.0309417i	$-0.990149\pi$
$223$	−1.76868	+	6.60080i	−0.118440	+	0.442023i	0.881082	+	0.472964i	$0.156816\pi$
$224$	2.42838	−	1.40203i	0.162253	−	0.0936770i
$225$	3.96653	−	3.04412i	0.264435	−	0.202941i
$226$	−4.06304	+	7.03740i	−0.270270	+	0.468121i
$227$	−12.2309	+	3.27727i	−0.811795	+	0.217520i	−0.640756	−	0.767744i	$-0.721379\pi$
$227$	−12.2309	+	3.27727i	−0.811795	+	0.217520i	−0.171039	+	0.985264i	$0.554712\pi$
$228$	−3.88746	+	1.04164i	−0.257453	+	0.0689844i
$229$	−0.547120	−	0.947640i	−0.0361547	−	0.0626218i	0.847382	−	0.530984i	$-0.178178\pi$
$229$	−0.547120	−	0.947640i	−0.0361547	−	0.0626218i	−0.883537	+	0.468362i	$0.844844\pi$
$230$	11.2094	−	7.49055i	0.739129	−	0.493912i
$231$	−4.91108	−	8.50624i	−0.323125	−	0.559670i
$232$	7.21289	−	7.21289i	0.473550	−	0.473550i
$233$	−13.7039	+	13.7039i	−0.897771	+	0.897771i	−0.995239	−	0.0974679i	$-0.968926\pi$
$233$	−13.7039	+	13.7039i	−0.897771	+	0.897771i	0.0974679	+	0.995239i	$0.468926\pi$
$234$	−1.56449	−	2.70977i	−0.102274	−	0.177143i
$235$	−4.15166	+	20.8761i	−0.270825	+	1.36181i
$236$	−3.45300	−	5.98077i	−0.224771	−	0.389315i
$237$	11.4675	−	3.07272i	0.744897	−	0.199595i
$238$	−7.31646	+	1.96044i	−0.474256	+	0.127076i
$239$	−7.74599	+	13.4164i	−0.501046	+	0.867838i	0.498953	+	0.866629i	$0.333718\pi$
$239$	−7.74599	+	13.4164i	−0.501046	+	0.867838i	−0.999999	+	0.00120852i	$0.999615\pi$
$240$	2.11737	−	0.718844i	0.136676	−	0.0464012i
$241$	−21.0303	+	12.1419i	−1.35468	+	0.782125i	−0.988901	−	0.148576i	$-0.952531\pi$
$241$	−21.0303	+	12.1419i	−1.35468	+	0.782125i	−0.365780	+	0.930701i	$0.619198\pi$
$242$	−0.328669	+	1.22661i	−0.0211277	+	0.0788495i
$243$	−0.965926	+	0.258819i	−0.0619642	+	0.0166032i
$244$	8.20722			0.525414
$245$	−0.126248	−	1.92501i	−0.00806569	−	0.122984i
$246$			10.6629i			0.679843i
$247$	8.90449	−	8.90449i	0.566579	−	0.566579i
$248$	3.38223	−	4.42273i	0.214772	−	0.280843i
$249$		−	2.89479i		−	0.183450i
$250$	−9.29685	−	6.21036i	−0.587984	−	0.392778i
$251$	−13.5820	+	7.84156i	−0.857287	+	0.494955i	−0.863103	−	0.505028i	$-0.831482\pi$
$251$	−13.5820	+	7.84156i	−0.857287	+	0.494955i	0.00581607	+	0.999983i	$0.498149\pi$
$252$	1.98277	+	1.98277i	0.124903	+	0.124903i
$253$	−5.46614	−	20.3999i	−0.343653	−	1.28253i
$254$	5.60962	+	9.71615i	0.351979	+	0.609645i
$255$	−6.02731	+	0.395290i	−0.377445	+	0.0247540i
$256$	1.00000			0.0625000
$257$	−8.97146	+	2.40390i	−0.559624	+	0.149951i	−0.527534	−	0.849534i	$-0.676883\pi$
$257$	−8.97146	+	2.40390i	−0.559624	+	0.149951i	−0.0320907	+	0.999485i	$0.510217\pi$
$258$	0.367072	+	1.36993i	0.0228529	+	0.0852882i
$259$	−0.0292581	+	0.0506765i	−0.00181801	+	0.00314889i
$260$	−4.61297	+	5.26050i	−0.286084	+	0.326242i
$261$	8.83395	+	5.10029i	0.546808	+	0.315700i
$262$	−4.73379	+	17.6668i	−0.292455	+	1.09146i
$263$	−0.144789	−	0.144789i	−0.00892808	−	0.00892808i	0.702629	−	0.711557i	$-0.252010\pi$
$263$	−0.144789	−	0.144789i	−0.00892808	−	0.00892808i	−0.711557	+	0.702629i	$0.752010\pi$
$264$		−	3.50284i		−	0.215585i
$265$	10.9130	+	9.56964i	0.670378	+	0.587859i
$266$	−5.64260	+	9.77327i	−0.345970	+	0.599238i
$267$	−3.69132	+	13.7762i	−0.225905	+	0.843088i
$268$	−0.440496	−	1.64395i	−0.0269076	−	0.100420i
$269$	−1.89999	+	3.29088i	−0.115845	+	0.200649i	−0.918117	−	0.396309i	$-0.870291\pi$
$269$	−1.89999	+	3.29088i	−0.115845	+	0.200649i	0.802272	+	0.596958i	$0.203624\pi$
$270$	1.24237	+	1.85917i	0.0756080	+	0.113146i
$271$		−	8.60473i		−	0.522700i	−0.965244	−	0.261350i	$-0.915832\pi$
$271$		−	8.60473i		−	0.522700i	0.965244	−	0.261350i	$-0.0841677\pi$
$272$	−2.60924	−	0.699144i	−0.158208	−	0.0423918i
$273$	−8.47486	−	2.27083i	−0.512922	−	0.137437i
$274$	5.92178	−	10.2568i	0.357748	−	0.619638i
$275$	−13.8941	+	10.6631i	−0.837846	+	0.643007i
$276$	3.01463	+	5.22149i	0.181459	+	0.314297i
$277$	16.4760	−	16.4760i	0.989945	−	0.989945i	−0.0100046	−	0.999950i	$-0.503185\pi$
$277$	16.4760	−	16.4760i	0.989945	−	0.989945i	0.999950	+	0.0100046i	$0.00318461\pi$
$278$	3.40666	+	3.40666i	0.204318	+	0.204318i
$279$	5.14741	+	2.12230i	0.308167	+	0.127059i
$280$	2.77296	−	5.62356i	0.165716	−	0.336072i
$281$	−9.79099			−0.584081			−0.292041	−	0.956406i	$-0.594334\pi$
$281$	−9.79099			−0.584081			−0.292041	+	0.956406i	$0.594334\pi$
$282$	−9.19457	−	2.46368i	−0.547529	−	0.146710i
$283$	−1.79917	+	1.79917i	−0.106949	+	0.106949i	−0.758557	−	0.651607i	$-0.774095\pi$
$283$	−1.79917	+	1.79917i	−0.106949	+	0.106949i	0.651607	+	0.758557i	$0.274095\pi$
$284$	−8.70536	−	5.02604i	−0.516568	−	0.298241i
$285$	−5.93336	+	6.76624i	−0.351462	+	0.400798i
$286$	5.48014	+	9.49189i	0.324048	+	0.561267i
$287$	21.1421	+	21.1421i	1.24798	+	1.24798i
$288$	0.258819	+	0.965926i	0.0152511	+	0.0569177i
$289$	−8.40310	−	4.85153i	−0.494300	−	0.285384i
$290$	4.44896	−	22.3711i	0.261252	−	1.31367i
$291$	−6.67477	+	3.85368i	−0.391282	+	0.225907i
$292$	2.97979	+	11.1207i	0.174379	+	0.650791i
$293$	8.49579	+	2.27644i	0.496330	+	0.132991i	0.498296	−	0.867007i	$-0.333959\pi$
$293$	8.49579	+	2.27644i	0.496330	+	0.132991i	−0.00196645	+	0.999998i	$0.500626\pi$
$294$	0.862738			0.0503159
$295$	−13.8500	−	6.82940i	−0.806380	−	0.397623i
$296$	−0.0180726	+	0.0104342i	−0.00105045	+	0.000606476i
$297$	3.38348	−	0.906601i	0.196330	−	0.0526064i
$298$	21.4653	+	5.75161i	1.24345	+	0.333182i
$299$	−16.3379	−	9.43269i	−0.944846	−	0.545507i
$300$	3.04349	−	3.96701i	0.175716	−	0.229035i
$301$	3.44408	+	1.98844i	0.198513	+	0.114612i
$302$	2.81596	−	2.81596i	0.162041	−	0.162041i
$303$	4.24816	−	15.8543i	0.244050	−	0.910808i
$304$	−3.48540	+	2.01230i	−0.199902	+	0.115413i
$305$	15.2586	−	10.1964i	0.873708	−	0.583843i
$306$		−	2.70128i		−	0.154422i
$307$	−2.22684	+	8.31067i	−0.127092	+	0.474315i	−0.999906	−	0.0137392i	$-0.995627\pi$
$307$	−2.22684	+	8.31067i	−0.127092	+	0.474315i	0.872813	+	0.488054i	$0.162293\pi$
$308$	−6.94532	−	6.94532i	−0.395746	−	0.395746i
$309$	8.35322			0.475198
$310$	0.793507	−	12.4246i	0.0450682	−	0.705669i
$311$	1.79302			0.101673			0.0508365	−	0.998707i	$-0.483811\pi$
$311$	1.79302			0.101673			0.0508365	+	0.998707i	$0.483811\pi$
$312$	−2.21252	−	2.21252i	−0.125259	−	0.125259i
$313$	−2.89848	+	10.8173i	−0.163832	+	0.611428i	0.834355	+	0.551228i	$0.185841\pi$
$313$	−2.89848	+	10.8173i	−0.163832	+	0.611428i	−0.998186	+	0.0602001i	$0.980826\pi$
$314$			10.3178i			0.582267i
$315$	6.14963	+	1.22299i	0.346493	+	0.0689074i
$316$	10.2815	−	5.93604i	0.578381	−	0.333928i
$317$	7.14094	−	26.6504i	0.401075	−	1.49683i	−0.410106	−	0.912038i	$-0.634508\pi$
$317$	7.14094	−	26.6504i	0.401075	−	1.49683i	0.811181	−	0.584795i	$-0.198825\pi$
$318$	−4.58989	+	4.58989i	−0.257388	+	0.257388i
$319$	−30.9439	−	17.8655i	−1.73253	−	1.00027i
$320$	1.85917	−	1.24237i	0.103931	−	0.0694504i
$321$	−12.2302	−	7.06108i	−0.682621	−	0.394111i
$322$	16.3303	+	4.37570i	0.910053	+	0.243848i
$323$	10.5011	−	2.81377i	0.584299	−	0.156562i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	−2.04084	+	15.5112i	−0.113205	+	0.860406i
$326$	22.4980			1.24605
$327$	14.5135	+	3.88888i	0.802599	+	0.215056i
$328$	2.75977	+	10.2996i	0.152383	+	0.568700i
$329$	−23.1156	+	13.3458i	−1.27440	+	0.735778i
$330$	−4.35181	−	6.51239i	−0.239559	−	0.358495i
$331$	−1.96569	−	1.13489i	−0.108044	−	0.0623794i	0.445004	−	0.895529i	$-0.353202\pi$
$331$	−1.96569	−	1.13489i	−0.108044	−	0.0623794i	−0.553048	+	0.833149i	$0.686536\pi$
$332$	−0.749226	−	2.79615i	−0.0411191	−	0.153459i
$333$	−0.0147562	−	0.0147562i	−0.000808635	−	0.000808635i
$334$	6.36400	+	11.0228i	0.348223	+	0.603139i
$335$	−2.86135	−	2.50914i	−0.156332	−	0.137089i
$336$	2.42838	+	1.40203i	0.132479	+	0.0764869i
$337$	13.4113	−	13.4113i	0.730563	−	0.730563i	−0.240169	−	0.970731i	$-0.577203\pi$
$337$	13.4113	−	13.4113i	0.730563	−	0.730563i	0.970731	+	0.240169i	$0.0772027\pi$
$338$	−3.10017	−	0.830688i	−0.168627	−	0.0451834i
$339$	−8.12609			−0.441349
$340$	−5.71962	+	1.94180i	−0.310190	+	0.105309i
$341$	−18.0306	−	7.43407i	−0.976409	−	0.402577i
$342$	−2.84582	−	2.84582i	−0.153884	−	0.153884i
$343$	−12.1688	+	12.1688i	−0.657052	+	0.657052i
$344$	0.709129	+	1.22825i	0.0382337	+	0.0662227i
$345$	12.0917	+	5.96238i	0.650997	+	0.321004i
$346$	7.52941	−	13.0413i	0.404783	−	0.701105i
$347$	−15.1859	−	4.06905i	−0.815222	−	0.218438i	−0.172966	−	0.984928i	$-0.555335\pi$
$347$	−15.1859	−	4.06905i	−0.815222	−	0.218438i	−0.642257	+	0.766490i	$0.722002\pi$
$348$	9.85299	+	2.64010i	0.528176	+	0.141524i
$349$		−	13.7983i		−	0.738605i	−0.929309	−	0.369303i	$-0.879597\pi$
$349$		−	13.7983i		−	0.738605i	0.929309	−	0.369303i	$-0.120403\pi$
$350$	−1.83111	−	13.9002i	−0.0978772	−	0.742997i
$351$	1.56449	−	2.70977i	0.0835061	−	0.144637i
$352$	−0.906601	−	3.38348i	−0.0483220	−	0.180340i
$353$	6.97505	−	26.0312i	0.371244	−	1.38550i	−0.487511	−	0.873117i	$-0.662095\pi$
$353$	6.97505	−	26.0312i	0.371244	−	1.38550i	0.858755	−	0.512386i	$-0.171238\pi$
$354$	3.45300	−	5.98077i	0.183525	−	0.317874i
$355$	−22.4290	+	1.47096i	−1.19041	+	0.0780706i
$356$			14.2622i			0.755892i
$357$	−5.35602	−	5.35602i	−0.283471	−	0.283471i
$358$	−6.26694	+	23.3885i	−0.331218	+	1.23612i
$359$	6.23727	+	3.60109i	0.329191	+	0.190058i	0.655482	−	0.755211i	$-0.272466\pi$
$359$	6.23727	+	3.60109i	0.329191	+	0.190058i	−0.326291	+	0.945269i	$0.605799\pi$
$360$	1.68122	+	1.47428i	0.0886082	+	0.0777011i
$361$	−1.40131	+	2.42714i	−0.0737533	+	0.127744i
$362$	−2.88344	−	10.7611i	−0.151550	−	0.565592i
$363$	−1.22661	+	0.328669i	−0.0643804	+	0.0172507i
$364$	−8.77382			−0.459873
$365$	19.3559	+	16.9734i	1.01314	+	0.888426i
$366$	4.10361	+	7.10766i	0.214499	+	0.371523i
$367$	1.36448	+	5.09232i	0.0712254	+	0.265817i	0.992351	−	0.123449i	$-0.0393955\pi$
$367$	1.36448	+	5.09232i	0.0712254	+	0.265817i	−0.921126	+	0.389266i	$0.872729\pi$
$368$	4.26333	+	4.26333i	0.222241	+	0.222241i
$369$	−9.23436	+	5.33146i	−0.480722	+	0.277545i
$370$	−0.0206369	+	0.0418518i	−0.00107286	+	0.00217577i
$371$			18.2014i			0.944968i
$372$	5.52131	+	0.717734i	0.286267	+	0.0372128i
$373$	11.1863	−	11.1863i	0.579202	−	0.579202i	−0.355481	−	0.934683i	$-0.615683\pi$
$373$	11.1863	−	11.1863i	0.579202	−	0.579202i	0.934683	+	0.355481i	$0.115683\pi$
$374$			9.46216i			0.489277i
$375$	0.729906	−	11.1565i	0.0376922	−	0.576119i
$376$	−9.51892			−0.490901
$377$	−30.8297	+	8.26081i	−1.58781	+	0.425453i
$378$	−0.725743	+	2.70851i	−0.0373282	+	0.139311i
$379$	−7.23270	+	4.17580i	−0.371519	+	0.214497i	−0.674122	−	0.738620i	$-0.735478\pi$
$379$	−7.23270	+	4.17580i	−0.371519	+	0.214497i	0.302603	+	0.953117i	$0.402144\pi$
$380$	−3.97996	+	8.07136i	−0.204167	+	0.414052i
$381$	−5.60962	+	9.71615i	−0.287390	+	0.497773i
$382$	−0.537504	+	0.144024i	−0.0275011	+	0.00736890i
$383$	−6.94133	+	1.85992i	−0.354686	+	0.0950377i	−0.431762	−	0.901987i	$-0.642108\pi$
$383$	−6.94133	+	1.85992i	−0.354686	+	0.0950377i	0.0770767	+	0.997025i	$0.475441\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	−21.5412	−	4.28392i	−1.09784	−	0.218329i
$386$	6.57140	+	11.3820i	0.334476	+	0.579329i
$387$	−1.00286	+	1.00286i	−0.0509782	+	0.0509782i
$388$	−5.44993	+	5.44993i	−0.276678	+	0.276678i
$389$	14.5568	+	25.2132i	0.738060	+	1.27836i	0.953368	+	0.301812i	$0.0975914\pi$
$389$	14.5568	+	25.2132i	0.738060	+	1.27836i	−0.215307	+	0.976546i	$0.569075\pi$
$390$	−6.86221	−	1.36470i	−0.347482	−	0.0691041i
$391$	−8.14337	−	14.1047i	−0.411828	−	0.713307i
$392$	0.833341	−	0.223293i	0.0420901	−	0.0112780i
$393$	−17.6668	+	4.73379i	−0.891170	+	0.238788i
$394$	−7.92820	+	13.7320i	−0.399417	+	0.691811i
$395$	11.7404	−	23.8095i	0.590723	−	1.19799i
$396$	3.03355	−	1.75142i	0.152441	−	0.0880121i
$397$	−0.406942	+	1.51873i	−0.0204238	+	0.0762228i	−0.975386	−	0.220506i	$-0.929229\pi$
$397$	−0.406942	+	1.51873i	−0.0204238	+	0.0762228i	0.954962	+	0.296729i	$0.0958958\pi$
$398$	10.7265	−	2.87416i	0.537671	−	0.144068i
$399$	−11.2852			−0.564967
$400$	1.91305	−	4.61955i	0.0956526	−	0.230977i
$401$		−	5.37209i		−	0.268270i	−0.990963	−	0.134135i	$-0.957174\pi$
$401$		−	5.37209i		−	0.268270i	0.990963	−	0.134135i	$-0.0428255\pi$
$402$	1.20346	−	1.20346i	0.0600230	−	0.0600230i
$403$	−16.0844	+	6.69312i	−0.801219	+	0.333408i
$404$		−	16.4136i		−	0.816609i
$405$	−0.988908	+	2.00551i	−0.0491392	+	0.0996545i
$406$	24.7709	−	14.3015i	1.22936	−	0.709771i
$407$	0.0516886	+	0.0516886i	0.00256211	+	0.00256211i
$408$	−0.699144	−	2.60924i	−0.0346128	−	0.129177i
$409$	−0.764214	−	1.32366i	−0.0377879	−	0.0654506i	0.846513	−	0.532368i	$-0.178698\pi$
$409$	−0.764214	−	1.32366i	−0.0377879	−	0.0654506i	−0.884301	+	0.466918i	$0.845364\pi$
$410$	17.9267	+	15.7201i	0.885339	+	0.776360i
$411$	11.8436			0.584200
$412$	8.06859	−	2.16197i	0.397511	−	0.106513i
$413$	−5.01198	−	18.7050i	−0.246624	−	0.920412i
$414$	−3.01463	+	5.22149i	−0.148161	+	0.256622i
$415$	−4.86678	−	4.26771i	−0.238901	−	0.209494i
$416$	−2.70977	−	1.56449i	−0.132857	−	0.0767053i
$417$	−1.24692	+	4.65359i	−0.0610622	+	0.227887i
$418$	9.96845	+	9.96845i	0.487573	+	0.487573i
$419$		−	19.8786i		−	0.971133i	−0.874200	−	0.485567i	$-0.838613\pi$
$419$		−	19.8786i		−	0.971133i	0.874200	−	0.485567i	$-0.161387\pi$
$420$	6.25662	−	0.410329i	0.305292	−	0.0200220i
$421$	−11.1404	+	19.2958i	−0.542951	+	0.940420i	0.455781	+	0.890092i	$0.349360\pi$
$421$	−11.1404	+	19.2958i	−0.542951	+	0.940420i	−0.998733	+	0.0503277i	$0.983973\pi$
$422$	1.98981	−	7.42606i	0.0968622	−	0.361495i
$423$	−2.46368	−	9.19457i	−0.119788	−	0.447055i
$424$	−3.24554	+	5.62144i	−0.157617	+	0.273001i
$425$	−8.22134	+	10.7160i	−0.398794	+	0.519803i
$426$		−	10.0521i		−	0.487025i
$427$	22.2294	+	5.95634i	1.07575	+	0.288247i
$428$	−13.6410	−	3.65509i	−0.659361	−	0.176675i
$429$	−5.48014	+	9.49189i	−0.264584	+	0.458273i
$430$	2.84433	+	1.40253i	0.137166	+	0.0676359i
$431$	−16.2769	−	28.1924i	−0.784031	−	1.35798i	−0.929577	−	0.368629i	$-0.879827\pi$
$431$	−16.2769	−	28.1924i	−0.784031	−	1.35798i	0.145546	−	0.989351i	$-0.453506\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	−7.36963	−	7.36963i	−0.354162	−	0.354162i	0.507494	−	0.861655i	$-0.330572\pi$
$433$	−7.36963	−	7.36963i	−0.354162	−	0.354162i	−0.861655	+	0.507494i	$0.830572\pi$
$434$	12.3706	−	9.52437i	0.593807	−	0.457185i
$435$	21.5984	−	7.33262i	1.03556	−	0.351572i
$436$	15.0255			0.719591
$437$	−23.4385	−	6.28033i	−1.12122	−	0.300429i
$438$	−8.14093	+	8.14093i	−0.388989	+	0.388989i
$439$	−5.70968	−	3.29648i	−0.272508	−	0.157333i	0.357519	−	0.933906i	$-0.383623\pi$
$439$	−5.70968	−	3.29648i	−0.272508	−	0.157333i	−0.630027	+	0.776573i	$0.716956\pi$
$440$	−5.88905	−	5.16415i	−0.280750	−	0.246191i
$441$	0.431369	+	0.747153i	0.0205414	+	0.0355787i
$442$	5.97664	+	5.97664i	0.284280	+	0.284280i
$443$	6.11958	+	22.8386i	0.290750	+	1.08509i	0.944534	+	0.328413i	$0.106514\pi$
$443$	6.11958	+	22.8386i	0.290750	+	1.08509i	−0.653785	+	0.756681i	$0.726820\pi$
$444$	−0.0180726	−	0.0104342i	−0.000857686	−	0.000495185i
$445$	17.7188	+	26.5158i	0.839952	+	1.25697i
$446$	−5.91812	+	3.41683i	−0.280231	+	0.161791i
$447$	5.75161	+	21.4653i	0.272042	+	1.01527i
$448$	2.70851	+	0.725743i	0.127965	+	0.0342882i
$449$	35.7446			1.68689			0.843446	−	0.537215i	$-0.180523\pi$
$449$	35.7446			1.68689			0.843446	+	0.537215i	$0.180523\pi$
$450$	4.95728	+	0.652239i	0.233688	+	0.0307468i
$451$	32.3465	−	18.6752i	1.52314	−	0.879383i
$452$	−7.84920	+	2.10319i	−0.369195	+	0.0989256i
$453$	3.84668	+	1.03071i	0.180733	+	0.0484272i
$454$	−10.9660	−	6.33120i	−0.514658	−	0.297138i
$455$	−16.3121	+	10.9003i	−0.764721	+	0.511014i
$456$	−3.48540	−	2.01230i	−0.163219	−	0.0942345i
$457$	3.67223	−	3.67223i	0.171780	−	0.171780i	−0.615981	−	0.787761i	$-0.711240\pi$
$457$	3.67223	−	3.67223i	0.171780	−	0.171780i	0.787761	+	0.615981i	$0.211240\pi$
$458$	0.283210	−	1.05695i	0.0132335	−	0.0493882i
$459$	2.33938	−	1.35064i	0.109193	−	0.0630426i
$460$	13.2229	+	2.62965i	0.616520	+	0.122608i
$461$		−	15.6696i		−	0.729807i	−0.931045	−	0.364903i	$-0.881102\pi$
$461$		−	15.6696i		−	0.729807i	0.931045	−	0.364903i	$-0.118898\pi$
$462$	2.54216	−	9.48748i	0.118272	−	0.441398i
$463$	−7.04131	−	7.04131i	−0.327237	−	0.327237i	0.524298	−	0.851535i	$-0.324328\pi$
$463$	−7.04131	−	7.04131i	−0.327237	−	0.327237i	−0.851535	+	0.524298i	$0.824328\pi$
$464$	10.2006			0.473550
$465$	11.1568	−	5.52510i	0.517382	−	0.256220i
$466$	−19.3802			−0.897771
$467$	−2.83811	−	2.83811i	−0.131332	−	0.131332i	0.638385	−	0.769717i	$-0.279603\pi$
$467$	−2.83811	−	2.83811i	−0.131332	−	0.131332i	−0.769717	+	0.638385i	$0.779603\pi$
$468$	0.809838	−	3.02236i	0.0374348	−	0.139708i
$469$		−	4.77235i		−	0.220367i
$470$	−17.6973	+	11.8260i	−0.816317	+	0.545492i
$471$	−8.93548	+	5.15890i	−0.411725	+	0.237710i
$472$	1.78740	−	6.67068i	0.0822719	−	0.307043i
$473$	3.51286	−	3.51286i	0.161521	−	0.161521i
$474$	10.2815	+	5.93604i	0.472246	+	0.272651i
$475$	2.62815	+	19.9506i	0.120588	+	0.915397i
$476$	−6.55976	−	3.78728i	−0.300666	−	0.173590i
$477$	−6.26990	−	1.68002i	−0.287079	−	0.0769226i
$478$	−14.9641	+	4.00962i	−0.684442	+	0.183396i
$479$	−1.02663	+	0.592725i	−0.0469079	+	0.0270823i	−0.523271	−	0.852167i	$-0.675288\pi$
$479$	−1.02663	+	0.592725i	−0.0469079	+	0.0270823i	0.476363	+	0.879249i	$0.341955\pi$
$480$	2.00551	+	0.988908i	0.0915385	+	0.0451373i
$481$	0.0652967			0.00297727
$482$	−23.4563	−	6.28508i	−1.06840	−	0.286278i
$483$	4.37570	+	16.3303i	0.199101	+	0.743055i
$484$	−1.09975	+	0.634940i	−0.0499886	+	0.0288609i
$485$	−3.36155	+	16.9032i	−0.152640	+	0.767533i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$	−8.38690	−	31.3004i	−0.380047	−	1.41835i	−0.845829	−	0.533455i	$-0.820893\pi$
$487$	−8.38690	−	31.3004i	−0.380047	−	1.41835i	0.465782	−	0.884900i	$-0.345773\pi$
$488$	5.80338	+	5.80338i	0.262707	+	0.262707i
$489$	11.2490	+	19.4839i	0.508698	+	0.881091i
$490$	1.27191	−	1.45046i	0.0574592	−	0.0655249i
$491$	16.9541	+	9.78846i	0.765128	+	0.441747i	0.831134	−	0.556072i	$-0.187692\pi$
$491$	16.9541	+	9.78846i	0.765128	+	0.441747i	−0.0660058	+	0.997819i	$0.521026\pi$
$492$	−7.53982	+	7.53982i	−0.339921	+	0.339921i
$493$	−26.6157	−	7.13166i	−1.19871	−	0.321194i
$494$	12.5929			0.566579
$495$	3.46399	−	7.02497i	0.155695	−	0.315749i
$496$	5.51894	−	0.735742i	0.247808	−	0.0330358i
$497$	−19.9310	−	19.9310i	−0.894025	−	0.894025i
$498$	2.04692	−	2.04692i	0.0917248	−	0.0917248i
$499$	15.3798	+	26.6385i	0.688493	+	1.19250i	0.972325	+	0.233631i	$0.0750607\pi$
$499$	15.3798	+	26.6385i	0.688493	+	1.19250i	−0.283833	+	0.958874i	$0.591606\pi$
$500$	−2.18248	−	10.9653i	−0.0976033	−	0.490381i
$501$	−6.36400	+	11.0228i	−0.284323	+	0.492461i
$502$	−15.1487	−	4.05909i	−0.676121	−	0.181166i
$503$	−29.9623	−	8.02838i	−1.33595	−	0.357968i	−0.481022	−	0.876708i	$-0.659734\pi$
$503$	−29.9623	−	8.02838i	−1.33595	−	0.357968i	−0.854932	+	0.518741i	$0.826401\pi$
$504$			2.80406i			0.124903i
$505$	−20.3917	−	30.5158i	−0.907421	−	1.35793i
$506$	10.5598	−	18.2900i	0.469439	−	0.813092i
$507$	−0.830688	−	3.10017i	−0.0368921	−	0.137683i
$508$	−2.90375	+	10.8370i	−0.128833	+	0.480812i
$509$	0.796759	−	1.38003i	0.0353157	−	0.0611687i	−0.847827	−	0.530272i	$-0.822090\pi$
$509$	0.796759	−	1.38003i	0.0353157	−	0.0611687i	0.883143	+	0.469104i	$0.155423\pi$
$510$	−4.54146	−	3.98244i	−0.201099	−	0.176345i
$511$			32.2832i			1.42812i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	1.04164	−	3.88746i	0.0459896	−	0.171636i
$514$	−8.04359	−	4.64397i	−0.354788	−	0.204837i
$515$	12.3149	−	14.0436i	0.542661	−	0.618836i
$516$	−0.709129	+	1.22825i	−0.0312177	+	0.0540706i
$517$	8.62987	+	32.2071i	0.379541	+	1.41647i
$518$	−0.0565223	+	0.0151451i	−0.00248345	+	0.000665438i
$519$	15.0588			0.661009
$520$	−6.98160	+	0.457875i	−0.306163	+	0.0200792i
$521$	−14.5988	−	25.2858i	−0.639584	−	1.10779i	−0.985524	−	0.169535i	$-0.945773\pi$
$521$	−14.5988	−	25.2858i	−0.639584	−	1.10779i	0.345941	−	0.938256i	$-0.387560\pi$
$522$	2.64010	+	9.85299i	0.115554	+	0.431254i
$523$	2.45889	+	2.45889i	0.107520	+	0.107520i	0.758820	−	0.651300i	$-0.225776\pi$
$523$	2.45889	+	2.45889i	0.107520	+	0.107520i	−0.651300	+	0.758820i	$0.725776\pi$
$524$	−15.8396	+	9.14499i	−0.691955	+	0.399501i
$525$	11.1224	−	8.53589i	0.485420	−	0.372537i
$526$		−	0.204763i		−	0.00892808i
$527$	−14.9146	−	1.93880i	−0.649691	−	0.0844556i
$528$	2.47688	−	2.47688i	0.107792	−	0.107792i
$529$			13.3520i			0.580521i
$530$	0.949867	+	14.4834i	0.0412596	+	0.629118i
$531$	6.90600			0.299695
$532$	−10.9007	+	2.92082i	−0.472604	+	0.126634i
$533$	8.63524	−	32.2271i	0.374034	−	1.39591i
$534$	−12.3514	+	7.13108i	−0.534497	+	0.308592i
$535$	−29.9019	+	10.1516i	−1.29277	+	0.438894i
$536$	0.850973	−	1.47393i	0.0367564	−	0.0636640i
$537$	−23.3885	+	6.26694i	−1.00929	+	0.270438i
$538$	−3.67050	+	0.983508i	−0.158247	+	0.0424020i
$539$	−1.51102	−	2.61716i	−0.0650841	−	0.112729i
$540$	−0.436149	+	2.19312i	−0.0187688	+	0.0943768i
$541$	4.94499	+	8.56497i	0.212602	+	0.368237i	0.952528	−	0.304451i	$-0.0984730\pi$
$541$	4.94499	+	8.56497i	0.212602	+	0.368237i	−0.739926	+	0.672688i	$0.765140\pi$
$542$	6.08447	−	6.08447i	0.261350	−	0.261350i
$543$	7.87769	−	7.87769i	0.338064	−	0.338064i
$544$	−1.35064	−	2.33938i	−0.0579083	−	0.100300i
$545$	27.9350	−	18.6672i	1.19660	−	0.799614i
$546$	−4.38691	−	7.59835i	−0.187742	−	0.325179i
$547$	−20.1542	+	5.40031i	−0.861733	+	0.230901i	−0.662510	−	0.749053i	$-0.730509\pi$
$547$	−20.1542	+	5.40031i	−0.861733	+	0.230901i	−0.199224	+	0.979954i	$0.563842\pi$
$548$	11.4400	−	3.06534i	0.488693	−	0.130945i
$549$	−4.10361	+	7.10766i	−0.175138	+	0.303348i
$550$	−17.3645	−	2.28469i	−0.740426	−	0.0974194i
$551$	−35.5531	+	20.5266i	−1.51461	+	0.874462i
$552$	−1.56049	+	5.82382i	−0.0664187	+	0.247878i
$553$	32.1556	−	8.61608i	1.36740	−	0.366393i
$554$	23.3005			0.989945
$555$	−0.0465632	+	0.00305376i	−0.00197650	+	0.000129625i
$556$			4.81775i			0.204318i
$557$	2.72253	−	2.72253i	0.115357	−	0.115357i	−0.647072	−	0.762429i	$-0.724007\pi$
$557$	2.72253	−	2.72253i	0.115357	−	0.115357i	0.762429	+	0.647072i	$0.224007\pi$
$558$	2.13908	+	5.14046i	0.0905544	+	0.217613i
$559$		−	4.43769i		−	0.187694i
$560$	5.93723	−	2.01568i	0.250894	−	0.0851780i
$561$	−8.19447	+	4.73108i	−0.345971	+	0.199746i
$562$	−6.92327	−	6.92327i	−0.292041	−	0.292041i
$563$	−3.17452	−	11.8475i	−0.133790	−	0.499312i	0.866210	−	0.499681i	$-0.166549\pi$
$563$	−3.17452	−	11.8475i	−0.133790	−	0.499312i	−1.00000		0.000368843i	$0.999883\pi$
$564$	−4.75946	−	8.24363i	−0.200409	−	0.347119i
$565$	−11.9801	+	13.6618i	−0.504006	+	0.574755i
$566$	−2.54440			−0.106949
$567$	−2.70851	+	0.725743i	−0.113747	+	0.0304784i
$568$	−2.60167	−	9.70957i	−0.109164	−	0.407404i
$569$	−18.4030	+	31.8749i	−0.771494	+	1.33627i	0.165250	+	0.986252i	$0.447157\pi$
$569$	−18.4030	+	31.8749i	−0.771494	+	1.33627i	−0.936744	+	0.350015i	$0.886176\pi$
$570$	−8.97998	+	0.588936i	−0.376130	+	0.0246678i
$571$	−20.7389	−	11.9736i	−0.867898	−	0.501081i	−0.00124885	−	0.999999i	$-0.500398\pi$
$571$	−20.7389	−	11.9736i	−0.867898	−	0.501081i	−0.866649	+	0.498918i	$0.833731\pi$
$572$	−2.83673	+	10.5868i	−0.118610	+	0.442657i
$573$	−0.393480	−	0.393480i	−0.0164379	−	0.0164379i
$574$			29.8994i			1.24798i
$575$	27.8506	−	11.5387i	1.16145	−	0.481197i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	2.58084	−	9.63184i	0.107442	−	0.400979i	−0.891169	−	0.453672i	$-0.850114\pi$
$577$	2.58084	−	9.63184i	0.107442	−	0.400979i	0.998611	+	0.0526930i	$0.0167805\pi$
$578$	−2.51134	−	9.37244i	−0.104458	−	0.389842i
$579$	−6.57140	+	11.3820i	−0.273098	+	0.473020i
$580$	18.9646	−	12.6728i	0.787463	−	0.526211i
$581$		−	8.11715i		−	0.336756i
$582$	−7.44474	−	1.99481i	−0.308594	−	0.0826876i
$583$	21.9625	+	5.88482i	0.909592	+	0.243725i
$584$	−5.75651	+	9.97056i	−0.238206	+	0.412585i
$585$	−2.24924	−	6.62520i	−0.0929948	−	0.273918i
$586$	4.39775	+	7.61712i	0.181669	+	0.314660i
$587$	−5.53505	+	5.53505i	−0.228456	+	0.228456i	−0.812047	−	0.583592i	$-0.801647\pi$
$587$	−5.53505	+	5.53505i	−0.228456	+	0.228456i	0.583592	+	0.812047i	$0.301647\pi$
$588$	0.610048	+	0.610048i	0.0251580	+	0.0251580i
$589$	−17.7552	+	13.6701i	−0.731590	+	0.563267i
$590$	−4.96434	−	14.6226i	−0.204379	−	0.602001i
$591$	−15.8564			−0.652245
$592$	−0.0201573	−	0.00540114i	−0.000828461	−	0.000221986i
$593$	−12.1105	+	12.1105i	−0.497318	+	0.497318i	−0.910602	−	0.413284i	$-0.864382\pi$
$593$	−12.1105	+	12.1105i	−0.497318	+	0.497318i	0.413284	+	0.910602i	$0.364382\pi$
$594$	3.03355	+	1.75142i	0.124468	+	0.0718616i
$595$	−16.9009	+	1.10842i	−0.692870	+	0.0454406i
$596$	11.1113	+	19.2453i	0.455135	+	0.788316i
$597$	7.85234	+	7.85234i	0.321375	+	0.321375i
$598$	−4.88272	−	18.2226i	−0.199669	−	0.745176i
$599$	−31.1481	−	17.9834i	−1.27268	−	0.734780i	−0.297186	−	0.954820i	$-0.596048\pi$
$599$	−31.1481	−	17.9834i	−1.27268	−	0.734780i	−0.975491	+	0.220039i	$0.929381\pi$
$600$	4.95717	−	0.653023i	0.202376	−	0.0266596i
$601$	12.9704	−	7.48849i	0.529075	−	0.305462i	−0.211564	−	0.977364i	$-0.567856\pi$
$601$	12.9704	−	7.48849i	0.529075	−	0.305462i	0.740640	+	0.671902i	$0.234522\pi$
$602$	1.02929	+	3.84137i	0.0419508	+	0.156562i
$603$	1.64395	+	0.440496i	0.0669470	+	0.0179384i
$604$	3.98238			0.162041
$605$	−1.25580	+	2.54676i	−0.0510554	+	0.103540i
$606$	14.2146	−	8.20681i	0.577429	−	0.333379i
$607$	9.41047	−	2.52153i	0.381959	−	0.102346i	−0.0627301	−	0.998031i	$-0.519981\pi$
$607$	9.41047	−	2.52153i	0.381959	−	0.102346i	0.444689	+	0.895685i	$0.353314\pi$
$608$	−3.88746	−	1.04164i	−0.157657	−	0.0422442i
$609$	24.7709	+	14.3015i	1.00377	+	0.579526i
$610$	17.9994	+	3.57957i	0.728775	+	0.144932i
$611$	25.7941	+	14.8922i	1.04352	+	0.602475i
$612$	1.91010	−	1.91010i	0.0772111	−	0.0772111i
$613$	5.34598	−	19.9515i	0.215922	−	0.805832i	−0.769918	−	0.638143i	$-0.779703\pi$
$613$	5.34598	−	19.9515i	0.215922	−	0.805832i	0.985840	−	0.167689i	$-0.0536305\pi$
$614$	−7.45114	+	4.30192i	−0.300704	+	0.173611i
$615$	−4.65062	+	23.3851i	−0.187531	+	0.942977i
$616$		−	9.82216i		−	0.395746i
$617$	4.49149	−	16.7625i	0.180821	−	0.674832i	−0.814666	−	0.579931i	$-0.803080\pi$
$617$	4.49149	−	16.7625i	0.180821	−	0.674832i	0.995487	−	0.0949017i	$-0.0302537\pi$
$618$	5.90662	+	5.90662i	0.237599	+	0.237599i
$619$	−11.7401			−0.471873			−0.235936	−	0.971769i	$-0.575816\pi$
$619$	−11.7401			−0.471873			−0.235936	+	0.971769i	$0.575816\pi$
$620$	9.34660	−	8.22442i	0.375369	−	0.330300i
$621$	−6.02926			−0.241946
$622$	1.26786	+	1.26786i	0.0508365	+	0.0508365i
$623$	−10.3507	+	38.6292i	−0.414691	+	1.54765i
$624$		−	3.12897i		−	0.125259i
$625$	−17.6805	−	17.6749i	−0.707219	−	0.706995i
$626$	−9.69850	+	5.59943i	−0.387630	+	0.223798i
$627$	−3.64870	+	13.6172i	−0.145715	+	0.543817i
$628$	−7.29579	+	7.29579i	−0.291134	+	0.291134i
$629$	0.0488192	+	0.0281858i	0.00194655	+	0.00112384i
$630$	3.48367	+	5.21323i	0.138793	+	0.207700i
$631$	19.6781	+	11.3611i	0.783372	+	0.452280i	0.837624	−	0.546247i	$-0.183944\pi$
$631$	19.6781	+	11.3611i	0.783372	+	0.452280i	−0.0542521	+	0.998527i	$0.517277\pi$
$632$	11.4675	+	3.07272i	0.456154	+	0.122226i
$633$	7.42606	−	1.98981i	0.295159	−	0.0790877i
$634$	23.8941	−	13.7952i	0.948954	−	0.547879i
$635$	8.06489	+	23.7553i	0.320045	+	0.942701i
$636$	−6.49108			−0.257388
$637$	−2.60750	−	0.698678i	−0.103313	−	0.0276826i
$638$	−9.24785	−	34.5135i	−0.366126	−	1.36640i
$639$	8.70536	−	5.02604i	0.344379	−	0.198827i
$640$	2.19312	+	0.436149i	0.0866907	+	0.0172403i
$641$	−2.43513	−	1.40592i	−0.0961817	−	0.0555306i	0.451138	−	0.892454i	$-0.351018\pi$
$641$	−2.43513	−	1.40592i	−0.0961817	−	0.0555306i	−0.547319	+	0.836924i	$0.684352\pi$
$642$	−3.65509	−	13.6410i	−0.144255	−	0.538366i
$643$	20.3298	+	20.3298i	0.801730	+	0.801730i	0.983366	−	0.181636i	$-0.0581393\pi$
$643$	20.3298	+	20.3298i	0.801730	+	0.801730i	−0.181636	+	0.983366i	$0.558139\pi$
$644$	8.45320	+	14.6414i	0.333103	+	0.576951i
$645$	0.207539	+	3.16452i	0.00817186	+	0.124603i
$646$	9.41506	+	5.43579i	0.370431	+	0.213868i
$647$	−7.02449	+	7.02449i	−0.276161	+	0.276161i	−0.831574	−	0.555413i	$-0.812560\pi$
$647$	−7.02449	+	7.02449i	−0.276161	+	0.276161i	0.555413	+	0.831574i	$0.312560\pi$
$648$	−0.965926	−	0.258819i	−0.0379452	−	0.0101674i
$649$	−24.1906			−0.949564
$650$	−12.4112	+	9.52497i	−0.486805	+	0.373600i
$651$	14.4336	+	5.95105i	0.565699	+	0.233240i
$652$	15.9085	+	15.9085i	0.623025	+	0.623025i
$653$	−35.1358	+	35.1358i	−1.37497	+	1.37497i	−0.522066	+	0.852905i	$0.674838\pi$
$653$	−35.1358	+	35.1358i	−1.37497	+	1.37497i	−0.852905	+	0.522066i	$0.825162\pi$
$654$	7.51275	+	13.0125i	0.293772	+	0.508828i
$655$	−18.0871	+	36.6807i	−0.706722	+	1.43323i
$656$	−5.33146	+	9.23436i	−0.208159	+	0.360541i
$657$	−11.1207	−	2.97979i	−0.433861	−	0.116253i
$658$	−25.7821	−	6.90829i	−1.00509	−	0.269313i
$659$			1.30311i			0.0507619i	0.999678	+	0.0253809i	$0.00807987\pi$
$659$			1.30311i			0.0507619i	−0.999678	+	0.0253809i	$0.991920\pi$
$660$	1.52776	−	7.68215i	0.0594679	−	0.299027i
$661$	−12.1803	+	21.0969i	−0.473759	+	0.820575i	−0.999549	−	0.0300397i	$-0.990437\pi$
$661$	−12.1803	+	21.0969i	−0.473759	+	0.820575i	0.525790	+	0.850615i	$0.323770\pi$
$662$	−0.587464	−	2.19245i	−0.0228324	−	0.0852118i
$663$	−2.18760	+	8.16424i	−0.0849594	+	0.317073i
$664$	1.44739	−	2.50696i	0.0561698	−	0.0972889i
$665$	−16.6375	+	18.9729i	−0.645174	+	0.735739i
$666$		−	0.0208684i		−	0.000808635i
$667$	43.4884	+	43.4884i	1.68388	+	1.68388i
$668$	−3.29425	+	12.2943i	−0.127458	+	0.475681i
$669$	−5.91812	−	3.41683i	−0.228808	−	0.132102i
$670$	−0.249053	−	3.79751i	−0.00962174	−	0.146711i
$671$	14.3743	−	24.8970i	0.554913	−	0.961138i
$672$	0.725743	+	2.70851i	0.0279962	+	0.104483i
$673$	13.5331	−	3.62618i	0.521662	−	0.139779i	0.0116265	−	0.999932i	$-0.496299\pi$
$673$	13.5331	−	3.62618i	0.521662	−	0.139779i	0.510035	+	0.860154i	$0.329632\pi$
$674$	18.9665			0.730563
$675$	1.91378	+	4.61925i	0.0736615	+	0.177795i
$676$	−1.60477	−	2.77953i	−0.0617217	−	0.106905i
$677$	−8.11914	−	30.3010i	−0.312044	−	1.16456i	−0.926710	−	0.375777i	$-0.877376\pi$
$677$	−8.11914	−	30.3010i	−0.312044	−	1.16456i	0.614666	−	0.788787i	$-0.289291\pi$
$678$	−5.74601	−	5.74601i	−0.220674	−	0.220674i
$679$	−18.7164	+	10.8059i	−0.718271	+	0.414694i
$680$	−5.41744	−	2.67132i	−0.207750	−	0.102441i
$681$		−	12.6624i		−	0.485224i
$682$	−7.49285	−	18.0062i	−0.286916	−	0.689493i
$683$	10.9160	−	10.9160i	0.417690	−	0.417690i	−0.466717	−	0.884407i	$-0.654563\pi$
$683$	10.9160	−	10.9160i	0.417690	−	0.417690i	0.884407	+	0.466717i	$0.154563\pi$
$684$		−	4.02460i		−	0.153884i
$685$	17.4607	−	19.9117i	0.667138	−	0.760786i
$686$	−17.2092			−0.657052
$687$	1.05695	−	0.283210i	0.0403253	−	0.0108051i
$688$	−0.367072	+	1.36993i	−0.0139945	+	0.0522282i
$689$	17.5893	−	10.1552i	0.670100	−	0.386883i
$690$	4.33410	+	12.7662i	0.164996	+	0.486000i
$691$	7.11720	−	12.3274i	0.270751	−	0.468955i	−0.698303	−	0.715802i	$-0.746061\pi$
$691$	7.11720	−	12.3274i	0.270751	−	0.468955i	0.969054	+	0.246847i	$0.0793946\pi$
$692$	14.5457	−	3.89751i	0.552944	−	0.148161i
$693$	9.48748	−	2.54216i	0.360400	−	0.0965688i
$694$	−7.86081	−	13.6153i	−0.298392	−	0.516830i
$695$	5.98541	+	8.95703i	0.227039	+	0.339759i
$696$	5.10029	+	8.83395i	0.193326	+	0.334850i
$697$	20.3672	−	20.3672i	0.771463	−	0.771463i
$698$	9.75686	−	9.75686i	0.369303	−	0.369303i
$699$	−9.69010	−	16.7838i	−0.366513	−	0.634820i
$700$	8.53413	−	11.1237i	0.322560	−	0.420437i
$701$	−2.47442	−	4.28583i	−0.0934577	−	0.161874i	0.815506	−	0.578748i	$-0.196459\pi$
$701$	−2.47442	−	4.28583i	−0.0934577	−	0.161874i	−0.908964	+	0.416875i	$0.863125\pi$
$702$	3.02236	−	0.809838i	0.114071	−	0.0305654i
$703$	0.0811251	−	0.0217374i	0.00305969	−	0.000819842i
$704$	1.75142	−	3.03355i	0.0660091	−	0.114331i
$705$	−19.0903	−	9.41334i	−0.718981	−	0.354527i
$706$	23.3390	−	13.4748i	0.878373	−	0.507129i
$707$	11.9121	−	44.4565i	0.448000	−	1.67196i
$708$	6.67068	−	1.78740i	0.250700	−	0.0671747i
$709$	11.0868			0.416374			0.208187	−	0.978089i	$-0.433244\pi$
$709$	11.0868			0.416374			0.208187	+	0.978089i	$0.433244\pi$
$710$	−16.8998	−	14.8195i	−0.634238	−	0.556167i
$711$			11.8721i			0.445238i
$712$	−10.0849	+	10.0849i	−0.377946	+	0.377946i
$713$	26.6658	+	20.3923i	0.998641	+	0.763699i
$714$		−	7.57455i		−	0.283471i
$715$	7.87874	+	23.2070i	0.294648	+	0.867893i
$716$	−20.9696	+	12.1068i	−0.783670	+	0.452452i
$717$	−10.9545	−	10.9545i	−0.409103	−	0.409103i
$718$	1.86406	+	6.95677i	0.0695662	+	0.259625i
$719$	−4.18116	−	7.24199i	−0.155931	−	0.270081i	0.777467	−	0.628924i	$-0.216504\pi$
$719$	−4.18116	−	7.24199i	−0.155931	−	0.270081i	−0.933398	+	0.358844i	$0.883171\pi$
$720$	0.146334	+	2.23127i	0.00545355	+	0.0831547i
$721$	23.4229			0.872315
$722$	−2.70713	+	0.725373i	−0.100749	+	0.0269956i
$723$	−6.28508	−	23.4563i	−0.233745	−	0.872348i
$724$	5.57037	−	9.64816i	0.207021	−	0.358571i
$725$	19.5142	−	47.1220i	0.724740	−	1.75007i
$726$	−1.09975	−	0.634940i	−0.0408155	−	0.0235648i
$727$	−5.41789	+	20.2199i	−0.200939	+	0.749913i	0.789711	+	0.613479i	$0.210231\pi$
$727$	−5.41789	+	20.2199i	−0.200939	+	0.749913i	−0.990649	+	0.136433i	$0.956436\pi$
$728$	−6.20403	−	6.20403i	−0.229937	−	0.229937i
$729$		−	1.00000i		−	0.0370370i
$730$	1.68475	+	25.6887i	0.0623553	+	0.950781i
$731$	1.91556	−	3.31784i	0.0708495	−	0.122715i
$732$	−2.12419	+	7.92757i	−0.0785121	+	0.293011i
$733$	−1.06659	−	3.98056i	−0.0393953	−	0.147025i	0.943427	−	0.331581i	$-0.107582\pi$
$733$	−1.06659	−	3.98056i	−0.0393953	−	0.147025i	−0.982822	+	0.184556i	$0.940915\pi$
$734$	−2.63598	+	4.56565i	−0.0972957	+	0.168521i
$735$	1.89209	+	0.376282i	0.0697907	+	0.0138794i
$736$			6.02926i			0.222241i
$737$	−5.75850	−	1.54299i	−0.212117	−	0.0568366i
$738$	−10.2996	−	2.75977i	−0.379133	−	0.101588i
$739$	14.7135	−	25.4845i	0.541244	−	0.937463i	−0.457589	−	0.889164i	$-0.651287\pi$
$739$	14.7135	−	25.4845i	0.541244	−	0.937463i	0.998833	−	0.0482986i	$-0.0153799\pi$
$740$	−0.0441862	+	0.0150011i	−0.00162432	+	0.000551453i
$741$	6.29643	+	10.9057i	0.231305	+	0.400632i
$742$	−12.8703	+	12.8703i	−0.472484	+	0.472484i
$743$	−23.3000	−	23.3000i	−0.854793	−	0.854793i	0.135926	−	0.990719i	$-0.456599\pi$
$743$	−23.3000	−	23.3000i	−0.854793	−	0.854793i	−0.990719	+	0.135926i	$0.956599\pi$
$744$	3.39664	+	4.41167i	0.124527	+	0.161740i
$745$	44.5674	+	21.9760i	1.63282	+	0.805139i
$746$	15.8198			0.579202
$747$	2.79615	+	0.749226i	0.102306	+	0.0274127i
$748$	−6.69076	+	6.69076i	−0.244638	+	0.244638i
$749$	−34.2941	−	19.7997i	−1.25308	−	0.723465i
$750$	8.40495	−	7.37271i	0.306905	−	0.269213i
$751$	−4.56446	−	7.90587i	−0.166559	−	0.288489i	0.770649	−	0.637260i	$-0.219932\pi$
$751$	−4.56446	−	7.90587i	−0.166559	−	0.288489i	−0.937208	+	0.348771i	$0.886599\pi$
$752$	−6.73089	−	6.73089i	−0.245450	−	0.245450i
$753$	−4.05909	−	15.1487i	−0.147921	−	0.552050i
$754$	−27.6412	−	15.9587i	−1.00663	−	0.581180i
$755$	7.40393	−	4.94757i	0.269456	−	0.180060i
$756$	−2.42838	+	1.40203i	−0.0883195	+	0.0509913i
$757$	10.1413	+	37.8480i	0.368593	+	1.37561i	0.862484	+	0.506084i	$0.168907\pi$
$757$	10.1413	+	37.8480i	0.368593	+	1.37561i	−0.493891	+	0.869524i	$0.664426\pi$
$758$	−8.06703	−	2.16155i	−0.293008	−	0.0785112i
$759$	21.1195			0.766590
$760$	−8.52157	+	2.89306i	−0.309110	+	0.104942i
$761$	−44.8385	+	25.8875i	−1.62540	+	0.938423i	−0.639953	+	0.768414i	$0.721046\pi$
$761$	−44.8385	+	25.8875i	−1.62540	+	0.938423i	−0.985443	+	0.170008i	$0.945621\pi$
$762$	−10.8370	+	2.90375i	−0.392581	+	0.105192i
$763$	40.6967	+	10.9047i	1.47332	+	0.394775i
$764$	−0.481913	−	0.278233i	−0.0174350	−	0.0100661i
$765$	1.17816	−	5.92424i	0.0425965	−	0.214191i
$766$	−6.22343	−	3.59310i	−0.224862	−	0.129824i
$767$	−15.2796	+	15.2796i	−0.551716	+	0.551716i
$768$	−0.258819	+	0.965926i	−0.00933933	+	0.0348548i
$769$	29.6216	−	17.1020i	1.06818	−	0.616715i	0.140498	−	0.990081i	$-0.455130\pi$
$769$	29.6216	−	17.1020i	1.06818	−	0.616715i	0.927684	+	0.373366i	$0.121796\pi$
$770$	−12.2027	−	18.2611i	−0.439756	−	0.658084i
$771$		−	9.28794i		−	0.334497i
$772$	−3.40161	+	12.6950i	−0.122427	+	0.456902i
$773$	29.4644	+	29.4644i	1.05976	+	1.05976i	0.998097	+	0.0616624i	$0.0196402\pi$
$773$	29.4644	+	29.4644i	1.05976	+	1.05976i	0.0616624	+	0.998097i	$0.480360\pi$
$774$	−1.41826			−0.0509782
$775$	7.15922	−	26.9025i	0.257167	−	0.966367i
$776$	−7.70736			−0.276678
$777$	−0.0413772	−	0.0413772i	−0.00148440	−	0.00148440i
$778$	−7.53517	+	28.1216i	−0.270149	+	1.00821i
$779$		−	42.9140i		−	1.53755i
$780$	−3.88733	−	5.81730i	−0.139189	−	0.208293i
$781$	−30.4935	+	17.6054i	−1.09114	+	0.629971i
$782$	4.21532	−	15.7318i	0.150739	−	0.562567i
$783$	−7.21289	+	7.21289i	−0.257768	+	0.257768i
$784$	0.747153	+	0.431369i	0.0266840	+	0.0154060i
$785$	−4.50009	+	22.6282i	−0.160615	+	0.807634i
$786$	−15.8396	−	9.14499i	−0.564979	−	0.326191i
$787$	−23.8090	−	6.37961i	−0.848700	−	0.227409i	−0.191845	−	0.981425i	$-0.561447\pi$
$787$	−23.8090	−	6.37961i	−0.848700	−	0.227409i	−0.656855	+	0.754017i	$0.728114\pi$
$788$	−15.3161	+	4.10394i	−0.545614	+	0.146197i
$789$	0.177330	−	0.102381i	0.00631310	−	0.00364487i
$790$	25.1376	−	8.53417i	0.894355	−	0.303632i
$791$	−22.7860			−0.810178
$792$	3.38348	+	0.906601i	0.120227	+	0.0322147i
$793$	−6.64652	−	24.8051i	−0.236025	−	0.880856i
$794$	−1.36165	+	0.786151i	−0.0483233	+	0.0278995i
$795$	−12.0680	+	8.06430i	−0.428010	+	0.286011i
$796$	9.61712	+	5.55244i	0.340870	+	0.196801i
$797$	−3.52464	−	13.1541i	−0.124849	−	0.465943i	0.874985	−	0.484150i	$-0.160871\pi$
$797$	−3.52464	−	13.1541i	−0.124849	−	0.465943i	−0.999834	+	0.0182067i	$0.994204\pi$
$798$	−7.97984	−	7.97984i	−0.282483	−	0.282483i
$799$	12.8567	+	22.2684i	0.454836	+	0.787798i
$800$	4.61925	−	1.91378i	0.163315	−	0.0676624i
$801$	−12.3514	−	7.13108i	−0.436415	−	0.251964i
$802$	3.79864	−	3.79864i	0.134135	−	0.134135i
$803$	38.9541	+	10.4377i	1.37466	+	0.368339i
$804$	1.70195			0.0600230
$805$	33.9059	+	16.7189i	1.19503	+	0.589263i
$806$	−16.1061	−	6.64061i	−0.567314	−	0.233906i
$807$	−2.68699	−	2.68699i	−0.0945867	−	0.0945867i
$808$	11.6062	−	11.6062i	0.408304	−	0.408304i
$809$	−20.4852	−	35.4815i	−0.720222	−	1.24746i	−0.960911	−	0.276859i	$-0.910706\pi$
$809$	−20.4852	−	35.4815i	−0.720222	−	1.24746i	0.240688	−	0.970602i	$-0.422627\pi$
$810$	−2.11737	+	0.718844i	−0.0743969	+	0.0252576i
$811$	9.41331	−	16.3043i	0.330546	−	0.572523i	−0.652073	−	0.758156i	$-0.726100\pi$
$811$	9.41331	−	16.3043i	0.330546	−	0.572523i	0.982619	+	0.185634i	$0.0594338\pi$
$812$	27.6284	+	7.40300i	0.969565	+	0.259794i
$813$	8.31154	+	2.22707i	0.291498	+	0.0781067i
$814$			0.0730987i			0.00256211i
$815$	49.3409	+	9.81248i	1.72834	+	0.343716i
$816$	1.35064	−	2.33938i	0.0472819	−	0.0818947i
$817$	−1.47732	−	5.51342i	−0.0516848	−	0.192890i
$818$	0.395586	−	1.47635i	0.0138313	−	0.0516193i
$819$	4.38691	−	7.59835i	0.153291	−	0.265508i
$820$	1.56035	+	23.7919i	0.0544897	+	0.830849i
$821$		−	49.2431i		−	1.71860i	−0.511474	−	0.859299i	$-0.670900\pi$
$821$		−	49.2431i		−	1.71860i	0.511474	−	0.859299i	$-0.329100\pi$
$822$	8.37467	+	8.37467i	0.292100	+	0.292100i
$823$	−9.31883	+	34.7783i	−0.324834	+	1.21230i	0.589645	+	0.807663i	$0.299268\pi$
$823$	−9.31883	+	34.7783i	−0.324834	+	1.21230i	−0.914479	+	0.404634i	$0.867399\pi$
$824$	7.23410	+	4.17661i	0.252012	+	0.145499i
$825$	−6.70367	−	16.1805i	−0.233392	−	0.563332i
$826$	9.68241	−	16.7704i	0.336894	−	0.583518i
$827$	0.274212	+	1.02337i	0.00953527	+	0.0355861i	0.970530	−	0.240982i	$-0.0774695\pi$
$827$	0.274212	+	1.02337i	0.00953527	+	0.0355861i	−0.960994	+	0.276568i	$0.910803\pi$
$828$	−5.82382	+	1.56049i	−0.202392	+	0.0542307i
$829$	35.6148			1.23695			0.618477	−	0.785803i	$-0.287750\pi$
$829$	35.6148			1.23695			0.618477	+	0.785803i	$0.287750\pi$
$830$	−0.423606	−	6.45906i	−0.0147036	−	0.224197i
$831$	11.6503	+	20.1789i	0.404144	+	0.699997i
$832$	−0.809838	−	3.02236i	−0.0280761	−	0.104781i
$833$	−1.64791	−	1.64791i	−0.0570968	−	0.0570968i
$834$	−4.17229	+	2.40887i	−0.144475	+	0.0834125i
$835$	9.14945	+	26.9499i	0.316630	+	0.932640i
$836$			14.0975i			0.487573i
$837$	−3.38223	+	4.42273i	−0.116907	+	0.152872i
$838$	14.0563	−	14.0563i	0.485567	−	0.485567i
$839$		−	23.1695i		−	0.799899i	−0.916537	−	0.399949i	$-0.869028\pi$
$839$		−	23.1695i		−	0.799899i	0.916537	−	0.399949i	$-0.130972\pi$
$840$	4.71425	+	4.13395i	0.162657	+	0.142635i
$841$	75.0516			2.58799
$842$	−21.5217	+	5.76671i	−0.741685	+	0.198734i
$843$	2.53409	−	9.45737i	0.0872788	−	0.325729i
$844$	6.65802	−	3.84401i	0.229178	−	0.132316i
$845$	−6.43674	−	3.17393i	−0.221430	−	0.109187i
$846$	4.75946	−	8.24363i	0.163634	−	0.283422i
$847$	−3.43949	+	0.921608i	−0.118182	+	0.0316668i
$848$	−6.26990	+	1.68002i	−0.215309	+	0.0576920i
$849$	−1.27220	−	2.20352i	−0.0436619	−	0.0756245i
$850$	−13.3907	+	1.76400i	−0.459298	+	0.0605047i
$851$	−0.0629105	−	0.108964i	−0.00215655	−	0.00373525i
$852$	7.10790	−	7.10790i	0.243513	−	0.243513i
$853$	−29.8009	+	29.8009i	−1.02036	+	1.02036i	−0.0205744	+	0.999788i	$0.506549\pi$
$853$	−29.8009	+	29.8009i	−1.02036	+	1.02036i	−0.999788	+	0.0205744i	$0.993451\pi$
$854$	11.5068	+	19.9303i	0.393753	+	0.682001i
$855$	−5.00002	−	7.48242i	−0.170997	−	0.255893i
$856$	−7.06108	−	12.2302i	−0.241343	−	0.418018i
$857$	−52.9942	+	14.1997i	−1.81025	+	0.485054i	−0.995500	−	0.0947636i	$-0.969790\pi$
$857$	−52.9942	+	14.1997i	−1.81025	+	0.485054i	−0.814746	+	0.579818i	$0.803124\pi$
$858$	−10.5868	+	2.83673i	−0.361428	+	0.0968444i
$859$	24.2286	−	41.9653i	0.826671	−	1.43184i	−0.0739648	−	0.997261i	$-0.523565\pi$
$859$	24.2286	−	41.9653i	0.826671	−	1.43184i	0.900636	−	0.434575i	$-0.143101\pi$
$860$	1.01951	+	3.00298i	0.0347649	+	0.102401i
$861$	−25.8937	+	14.9497i	−0.882454	+	0.509485i
$862$	8.42554	−	31.4445i	0.286975	−	1.07101i
$863$	10.0915	−	2.70401i	0.343519	−	0.0920457i	−0.0829347	−	0.996555i	$-0.526429\pi$
$863$	10.0915	−	2.70401i	0.343519	−	0.0920457i	0.426454	+	0.904509i	$0.359763\pi$
$864$	−1.00000			−0.0340207
$865$	22.2008	−	25.3172i	0.754851	−	0.860812i
$866$		−	10.4222i		−	0.354162i
$867$	6.86110	−	6.86110i	0.233015	−	0.233015i
$868$	15.4821	+	2.01257i	0.525496	+	0.0683110i
$869$		−	41.5860i		−	1.41071i
$870$	20.4573	+	10.0874i	0.693568	+	0.341996i
$871$	−4.61188	+	2.66267i	−0.156268	+	0.0902212i
$872$	10.6246	+	10.6246i	0.359795	+	0.359795i
$873$	−1.99481	−	7.44474i	−0.0675142	−	0.251966i
$874$	−12.1327	−	21.0144i	−0.410394	−	0.710823i
$875$	2.04670	−	31.2834i	0.0691910	−	1.05757i
$876$	−11.5130			−0.388989
$877$	−3.53326	+	0.946735i	−0.119310	+	0.0319690i	−0.317980	−	0.948097i	$-0.603004\pi$
$877$	−3.53326	+	0.946735i	−0.119310	+	0.0319690i	0.198670	+	0.980066i	$0.436338\pi$
$878$	−1.70639	−	6.36832i	−0.0575877	−	0.214920i
$879$	−4.39775	+	7.61712i	−0.148332	+	0.256919i
$880$	−0.512585	−	7.81580i	−0.0172792	−	0.263470i
$881$	3.86823	+	2.23332i	0.130324	+	0.0752426i	0.563745	−	0.825949i	$-0.309360\pi$
$881$	3.86823	+	2.23332i	0.130324	+	0.0752426i	−0.433421	+	0.901192i	$0.642694\pi$
$882$	−0.223293	+	0.833341i	−0.00751867	+	0.0280601i
$883$	3.49883	+	3.49883i	0.117745	+	0.117745i	0.763524	−	0.645779i	$-0.223467\pi$
$883$	3.49883	+	3.49883i	0.117745	+	0.117745i	−0.645779	+	0.763524i	$0.723467\pi$
$884$			8.45224i			0.284280i
$885$	10.1813	−	11.6105i	0.342242	−	0.390283i
$886$	−11.8221	+	20.4765i	−0.397172	+	0.687922i
$887$	10.0645	−	37.5614i	0.337934	−	1.26119i	−0.562719	−	0.826648i	$-0.690245\pi$
$887$	10.0645	−	37.5614i	0.337934	−	1.26119i	0.900653	−	0.434539i	$-0.143089\pi$
$888$	−0.00540114	−	0.0201573i	−0.000181250	−	0.000676436i
$889$	−15.7297	+	27.2446i	−0.527557	+	0.913756i
$890$	−6.22042	+	31.2786i	−0.208509	+	1.04846i
$891$			3.50284i			0.117350i
$892$	−6.60080	−	1.76868i	−0.221011	−	0.0592198i
$893$	37.0044	+	9.91531i	1.23831	+	0.331803i
$894$	−11.1113	+	19.2453i	−0.371616	+	0.643658i
$895$	−23.9450	+	48.5605i	−0.800394	+	1.62320i
$896$	1.40203	+	2.42838i	0.0468385	+	0.0811266i
$897$	13.3398	−	13.3398i	0.445404	−	0.445404i
$898$	25.2752	+	25.2752i	0.843446	+	0.843446i
$899$	56.2963	−	7.50499i	1.87759	−	0.250305i
$900$	3.04412	+	3.96653i	0.101471	+	0.132218i
$901$	17.5343			0.584151
$902$	36.0778	+	9.66702i	1.20126	+	0.321877i
$903$	−2.81208	+	2.81208i	−0.0935801	+	0.0935801i
$904$	−7.03740	−	4.06304i	−0.234060	−	0.135135i
$905$	−1.63027	−	24.8580i	−0.0541920	−	0.826309i
$906$	1.99119	+	3.44884i	0.0661528	+	0.114580i
$907$	−16.9582	−	16.9582i	−0.563089	−	0.563089i	0.367094	−	0.930184i	$-0.380353\pi$
$907$	−16.9582	−	16.9582i	−0.563089	−	0.563089i	−0.930184	+	0.367094i	$0.880353\pi$
$908$	−3.27727	−	12.2309i	−0.108760	−	0.405898i
$909$	14.2146	+	8.20681i	0.471469	+	0.272203i
$910$	−19.2420	−	3.82669i	−0.637867	−	0.126853i
$911$	22.3757	−	12.9186i	0.741341	−	0.428013i	−0.0812158	−	0.996697i	$-0.525880\pi$
$911$	22.3757	−	12.9186i	0.741341	−	0.428013i	0.822557	+	0.568683i	$0.192547\pi$
$912$	−1.04164	−	3.88746i	−0.0344922	−	0.128727i
$913$	−9.79446	−	2.62442i	−0.324149	−	0.0868556i
$914$	5.19332			0.171780
$915$	5.89971	+	17.3777i	0.195039	+	0.574490i
$916$	0.947640	−	0.547120i	0.0313109	−	0.0180774i
$917$	−49.5386	+	13.2738i	−1.63591	+	0.438341i
$918$	2.60924	+	0.699144i	0.0861177	+	0.0230752i
$919$	−46.6431	−	26.9294i	−1.53861	−	0.888319i	−0.998920	−	0.0464584i	$-0.985207\pi$
$919$	−46.6431	−	26.9294i	−1.53861	−	0.888319i	−0.539694	−	0.841861i	$-0.681460\pi$
$920$	7.49055	+	11.2094i	0.246956	+	0.369564i
$921$	−7.45114	−	4.30192i	−0.245524	−	0.141753i
$922$	11.0801	−	11.0801i	0.364903	−	0.364903i
$923$	−8.14056	+	30.3810i	−0.267950	+	1.00000i
$924$	8.50624	−	4.91108i	0.279835	−	0.161563i
$925$	−0.0635129	+	0.0827851i	−0.00208829	+	0.00272196i
$926$		−	9.95791i		−	0.327237i
$927$	−2.16197	+	8.06859i	−0.0710085	+	0.265007i
$928$	7.21289	+	7.21289i	0.236775	+	0.236775i
$929$	−13.7790			−0.452073			−0.226036	−	0.974119i	$-0.572577\pi$
$929$	−13.7790			−0.452073			−0.226036	+	0.974119i	$0.572577\pi$
$930$	11.7959	+	3.98219i	0.386801	+	0.130581i
$931$	−3.47217			−0.113796
$932$	−13.7039	−	13.7039i	−0.448885	−	0.448885i
$933$	−0.464069	+	1.73193i	−0.0151929	+	0.0567008i
$934$		−	4.01369i		−	0.131332i
$935$	−4.12691	+	20.7517i	−0.134964	+	0.678652i
$936$	2.70977	−	1.56449i	0.0885716	−	0.0511368i
$937$	−3.01619	+	11.2566i	−0.0985346	+	0.367736i	−0.997532	−	0.0702187i	$-0.977630\pi$
$937$	−3.01619	+	11.2566i	−0.0985346	+	0.367736i	0.898997	+	0.437955i	$0.144297\pi$
$938$	3.37456	−	3.37456i	0.110183	−	0.110183i
$939$	−9.69850	−	5.59943i	−0.316498	−	0.182730i
$940$	−20.8761	−	4.15166i	−0.680904	−	0.135412i
$941$	16.0355	+	9.25812i	0.522744	+	0.301806i	0.738056	−	0.674739i	$-0.235744\pi$
$941$	16.0355	+	9.25812i	0.522744	+	0.301806i	−0.215313	+	0.976545i	$0.569077\pi$
$942$	−9.96623	−	2.67044i	−0.324717	−	0.0870078i
$943$	−62.0989	+	16.6394i	−2.02222	+	0.541852i
$944$	5.98077	−	3.45300i	0.194657	−	0.112386i
$945$	−2.77296	+	5.62356i	−0.0902043	+	0.182934i
$946$	4.96793			0.161521
$947$	46.5226	+	12.4657i	1.51178	+	0.405080i	0.917026	−	0.398827i	$-0.130583\pi$
$947$	46.5226	+	12.4657i	1.51178	+	0.405080i	0.594755	+	0.803907i	$0.297249\pi$
$948$	3.07272	+	11.4675i	0.0997973	+	0.372448i
$949$	31.1976	−	18.0120i	1.01272	−	0.584693i
$950$	−12.2488	+	15.9656i	−0.397405	+	0.517993i
$951$	23.8941	+	13.7952i	0.774818	+	0.447341i
$952$	−1.96044	−	7.31646i	−0.0635382	−	0.237128i
$953$	34.5002	+	34.5002i	1.11757	+	1.11757i	0.992097	+	0.125474i	$0.0400451\pi$
$953$	34.5002	+	34.5002i	1.11757	+	1.11757i	0.125474	+	0.992097i	$0.459955\pi$
$954$	−3.24554	−	5.62144i	−0.105078	−	0.182001i
$955$	−1.24163	+	0.0814298i	−0.0401781	+	0.00263501i
$956$	−13.4164	−	7.74599i	−0.433919	−	0.250523i
$957$	25.2656	−	25.2656i	0.816721	−	0.816721i
$958$	−1.14506	−	0.306817i	−0.0369951	−	0.00991281i
$959$	33.2100			1.07241
$960$	0.718844	+	2.11737i	0.0232006	+	0.0683379i
$961$	29.9174	−	8.12103i	0.965076	−	0.261969i
$962$	0.0461717	+	0.0461717i	0.00148864	+	0.00148864i
$963$	9.98588	−	9.98588i	0.321790	−	0.321790i
$964$	−12.1419	−	21.0303i	−0.391063	−	0.677340i
$965$	9.44763	+	27.8282i	0.304130	+	0.895821i
$966$	−8.45320	+	14.6414i	−0.271977	+	0.471078i
$967$	22.6157	+	6.05985i	0.727271	+	0.194872i	0.603414	−	0.797428i	$-0.293807\pi$
$967$	22.6157	+	6.05985i	0.727271	+	0.194872i	0.123857	+	0.992300i	$0.460473\pi$
$968$	−1.22661	−	0.328669i	−0.0394248	−	0.0105638i
$969$			10.8716i			0.349245i
$970$	−14.3293	+	9.57537i	−0.460087	+	0.307447i
$971$	−18.8334	+	32.6204i	−0.604392	+	1.04684i	0.387755	+	0.921763i	$0.373251\pi$
$971$	−18.8334	+	32.6204i	−0.604392	+	1.04684i	−0.992147	+	0.125076i	$0.960083\pi$
$972$	−0.258819	−	0.965926i	−0.00830162	−	0.0309821i
$973$	−3.49645	+	13.0489i	−0.112091	+	0.418329i
$974$	16.2023	−	28.0631i	0.519154	−	0.899201i
$975$	−14.4544	−	5.98589i	−0.462913	−	0.191702i
$976$			8.20722i			0.262707i
$977$	−5.02777	−	5.02777i	−0.160853	−	0.160853i	0.622092	−	0.782944i	$-0.286283\pi$
$977$	−5.02777	−	5.02777i	−0.160853	−	0.160853i	−0.782944	+	0.622092i	$0.786283\pi$
$978$	−5.82292	+	21.7314i	−0.186196	+	0.694894i
$979$	43.2649	+	24.9790i	1.38275	+	0.798333i
$980$	1.92501	−	0.126248i	0.0614921	−	0.00403284i
$981$	−7.51275	+	13.0125i	−0.239864	+	0.415456i
$982$	5.06688	+	18.9098i	0.161691	+	0.603438i
$983$	6.12473	−	1.64112i	0.195348	−	0.0523434i	−0.159818	−	0.987146i	$-0.551091\pi$
$983$	6.12473	−	1.64112i	0.195348	−	0.0523434i	0.355167	+	0.934803i	$0.384424\pi$
$984$	−10.6629			−0.339921
$985$	−23.3767	+	26.6582i	−0.744844	+	0.849399i
$986$	−13.7773	−	23.8630i	−0.438759	−	0.759953i
$987$	−6.90829	−	25.7821i	−0.219893	−	0.820653i
$988$	8.90449	+	8.90449i	0.283290	+	0.283290i
$989$	−7.40542	+	4.27552i	−0.235479	+	0.135954i
$990$	7.41681	−	2.51800i	0.235722	−	0.0800272i
$991$		−	42.7761i		−	1.35883i	−0.733755	−	0.679414i	$-0.762234\pi$
$991$		−	42.7761i		−	1.35883i	0.733755	−	0.679414i	$-0.237766\pi$
$992$	4.42273	+	3.38223i	0.140422	+	0.107386i
$993$	1.60498	−	1.60498i	0.0509326	−	0.0509326i
$994$		−	28.1866i		−	0.894025i
$995$	24.7781	−	1.62502i	0.785517	−	0.0515167i
$996$	2.89479			0.0917248
$997$	6.93843	−	1.85915i	0.219742	−	0.0588797i	−0.147268	−	0.989097i	$-0.547048\pi$
$997$	6.93843	−	1.85915i	0.219742	−	0.0588797i	0.367010	+	0.930217i	$0.380381\pi$
$998$	−7.96115	+	29.7114i	−0.252006	+	0.940499i
$999$	0.0180726	−	0.0104342i	0.000571791	−	0.000330124i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.be.b.37.14	yes	64
5.3	odd	4		930.2.be.a.223.9	✓	64
31.26	odd	6		930.2.be.a.367.9	yes	64
155.88	even	12	inner	930.2.be.b.553.14	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.be.a.223.9	✓	64	5.3	odd	4
930.2.be.a.367.9	yes	64	31.26	odd	6
930.2.be.b.37.14	yes	64	1.1	even	1	trivial
930.2.be.b.553.14	yes	64	155.88	even	12	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(1.24237 + 1.85917i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.725743 + 2.70851i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(1.24237 + 1.85917i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.725743 + 2.70851i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.436149 + 2.19312i) q^{10} +(3.03355 + 1.75142i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(3.02236 - 0.809838i) q^{13} +(-2.42838 + 1.40203i) q^{14} +(-2.11737 + 0.718844i) q^{15} -1.00000 q^{16} +(2.60924 + 0.699144i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(3.48540 - 2.01230i) q^{19} +(-1.85917 + 1.24237i) q^{20} +(-2.42838 - 1.40203i) q^{21} +(0.906601 + 3.38348i) q^{22} +(-4.26333 - 4.26333i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-1.91305 + 4.61955i) q^{25} +(2.70977 + 1.56449i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-2.70851 - 0.725743i) q^{28} -10.2006 q^{29} +(-2.00551 - 0.988908i) q^{30} +(-5.51894 + 0.735742i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-2.47688 + 2.47688i) q^{33} +(1.35064 + 2.33938i) q^{34} +(-5.93723 + 2.01568i) q^{35} +(0.500000 - 0.866025i) q^{36} +(0.0201573 + 0.00540114i) q^{37} +(3.88746 + 1.04164i) q^{38} +3.12897i q^{39} +(-2.19312 - 0.436149i) q^{40} +(5.33146 - 9.23436i) q^{41} +(-0.725743 - 2.70851i) q^{42} +(0.367072 - 1.36993i) q^{43} +(-1.75142 + 3.03355i) q^{44} +(-0.146334 - 2.23127i) q^{45} -6.02926i q^{46} +(6.73089 + 6.73089i) q^{47} +(0.258819 - 0.965926i) q^{48} +(-0.747153 - 0.431369i) q^{49} +(-4.61925 + 1.91378i) q^{50} +(-1.35064 + 2.33938i) q^{51} +(0.809838 + 3.02236i) q^{52} +(6.26990 - 1.68002i) q^{53} +1.00000 q^{54} +(0.512585 + 7.81580i) q^{55} +(-1.40203 - 2.42838i) q^{56} +(1.04164 + 3.88746i) q^{57} +(-7.21289 - 7.21289i) q^{58} +(-5.98077 + 3.45300i) q^{59} +(-0.718844 - 2.11737i) q^{60} -8.20722i q^{61} +(-4.42273 - 3.38223i) q^{62} +(1.98277 - 1.98277i) q^{63} -1.00000i q^{64} +(5.26050 + 4.61297i) q^{65} -3.50284 q^{66} +(-1.64395 + 0.440496i) q^{67} +(-0.699144 + 2.60924i) q^{68} +(5.22149 - 3.01463i) q^{69} +(-5.62356 - 2.77296i) q^{70} +(-5.02604 + 8.70536i) q^{71} +(0.965926 - 0.258819i) q^{72} +(11.1207 - 2.97979i) q^{73} +(0.0104342 + 0.0180726i) q^{74} +(-3.96701 - 3.04349i) q^{75} +(2.01230 + 3.48540i) q^{76} +(-6.94532 + 6.94532i) q^{77} +(-2.21252 + 2.21252i) q^{78} +(-5.93604 - 10.2815i) q^{79} +(-1.24237 - 1.85917i) q^{80} +(0.500000 + 0.866025i) q^{81} +(10.2996 - 2.75977i) q^{82} +(-2.79615 + 0.749226i) q^{83} +(1.40203 - 2.42838i) q^{84} +(1.94180 + 5.71962i) q^{85} +(1.22825 - 0.709129i) q^{86} +(2.64010 - 9.85299i) q^{87} +(-3.38348 + 0.906601i) q^{88} +14.2622 q^{89} +(1.47428 - 1.68122i) q^{90} +8.77382i q^{91} +(4.26333 - 4.26333i) q^{92} +(0.717734 - 5.52131i) q^{93} +9.51892i q^{94} +(8.07136 + 3.97996i) q^{95} +(0.866025 - 0.500000i) q^{96} +(5.44993 + 5.44993i) q^{97} +(-0.223293 - 0.833341i) q^{98} +(-1.75142 - 3.03355i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{7}+O(q^{10}) \) 64 * q + 4 * q^7	\( 64 q + 4 q^{7} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 64 q^{16} - 4 q^{17} + 12 q^{20} - 24 q^{21} - 4 q^{22} - 32 q^{24} + 28 q^{25} + 8 q^{28} - 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 16 q^{37} - 28 q^{38} - 8 q^{41} + 4 q^{42} - 40 q^{43} + 4 q^{44} - 12 q^{45} + 8 q^{47} + 60 q^{49} - 8 q^{50} - 24 q^{53} + 64 q^{54} + 44 q^{55} + 4 q^{57} - 52 q^{58} - 24 q^{59} + 20 q^{62} - 4 q^{63} + 44 q^{65} + 8 q^{66} - 44 q^{67} - 4 q^{68} + 12 q^{69} - 44 q^{70} + 8 q^{71} + 4 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{76} + 104 q^{77} - 56 q^{79} + 32 q^{81} - 16 q^{82} - 48 q^{83} - 32 q^{85} - 24 q^{86} - 32 q^{87} + 8 q^{88} + 176 q^{89} + 16 q^{93} + 64 q^{95} - 68 q^{97} + 32 q^{98} + 4 q^{99}+O(q^{100}) \) 64 * q + 4 * q^7 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 64 * q^16 - 4 * q^17 + 12 * q^20 - 24 * q^21 - 4 * q^22 - 32 * q^24 + 28 * q^25 + 8 * q^28 - 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 16 * q^37 - 28 * q^38 - 8 * q^41 + 4 * q^42 - 40 * q^43 + 4 * q^44 - 12 * q^45 + 8 * q^47 + 60 * q^49 - 8 * q^50 - 24 * q^53 + 64 * q^54 + 44 * q^55 + 4 * q^57 - 52 * q^58 - 24 * q^59 + 20 * q^62 - 4 * q^63 + 44 * q^65 + 8 * q^66 - 44 * q^67 - 4 * q^68 + 12 * q^69 - 44 * q^70 + 8 * q^71 + 4 * q^73 - 12 * q^74 + 8 * q^75 - 8 * q^76 + 104 * q^77 - 56 * q^79 + 32 * q^81 - 16 * q^82 - 48 * q^83 - 32 * q^85 - 24 * q^86 - 32 * q^87 + 8 * q^88 + 176 * q^89 + 16 * q^93 + 64 * q^95 - 68 * q^97 + 32 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

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