LMFDB - Embedded newform 38.4.c.c.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,4,Mod(7,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("38.7");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	38.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.24207258022$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 64x^{4} + 33x^{3} + 3984x^{2} - 945x + 225 $ x^6 - x^5 + 64x^4 + 33x^3 + 3984x^2 - 945x + 225
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.3
Root			$4.16954 + 7.22186i$ of defining polynomial
Character	$\chi$	$=$	38.11
Dual form			38.4.c.c.7.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(3.16954 - 5.48981i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-2.96554 + 5.13646i) q^{5} +(-6.33908 - 10.9796i) q^{6} +0.660916 q^{7} -8.00000 q^{8} +(-6.59199 - 11.4177i) q^{9} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(3.16954 - 5.48981i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-2.96554 + 5.13646i) q^{5} +(-6.33908 - 10.9796i) q^{6} +0.660916 q^{7} -8.00000 q^{8} +(-6.59199 - 11.4177i) q^{9} +(5.93108 + 10.2729i) q^{10} +50.1496 q^{11} -25.3563 q^{12} +(-1.31325 - 2.27462i) q^{13} +(0.660916 - 1.14474i) q^{14} +(18.7988 + 32.5605i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-28.9052 + 50.0654i) q^{17} -26.3680 q^{18} +(-12.1437 + 81.9239i) q^{19} +23.7243 q^{20} +(2.09480 - 3.62830i) q^{21} +(50.1496 - 86.8616i) q^{22} +(-18.9828 - 32.8792i) q^{23} +(-25.3563 + 43.9185i) q^{24} +(44.9112 + 77.7884i) q^{25} -5.25300 q^{26} +87.5809 q^{27} +(-1.32183 - 2.28948i) q^{28} +(-154.914 - 268.319i) q^{29} +75.1952 q^{30} -282.420 q^{31} +(16.0000 + 27.7128i) q^{32} +(158.951 - 275.312i) q^{33} +(57.8105 + 100.131i) q^{34} +(-1.95997 + 3.39477i) q^{35} +(-26.3680 + 45.6707i) q^{36} -21.0744 q^{37} +(129.753 + 102.957i) q^{38} -16.6496 q^{39} +(23.7243 - 41.0917i) q^{40} +(172.046 - 297.992i) q^{41} +(-4.18960 - 7.25660i) q^{42} +(-132.675 + 229.800i) q^{43} +(-100.299 - 173.723i) q^{44} +78.1953 q^{45} -75.9312 q^{46} +(69.8967 + 121.065i) q^{47} +(50.7127 + 87.8369i) q^{48} -342.563 q^{49} +179.645 q^{50} +(183.233 + 317.368i) q^{51} +(-5.25300 + 9.09846i) q^{52} +(66.8936 + 115.863i) q^{53} +(87.5809 - 151.694i) q^{54} +(-148.721 + 257.592i) q^{55} -5.28733 q^{56} +(411.257 + 326.328i) q^{57} -619.656 q^{58} +(-227.911 + 394.754i) q^{59} +(75.1952 - 130.242i) q^{60} +(-54.2184 - 93.9090i) q^{61} +(-282.420 + 489.166i) q^{62} +(-4.35675 - 7.54612i) q^{63} +64.0000 q^{64} +15.5780 q^{65} +(-317.902 - 550.623i) q^{66} +(-13.1980 - 22.8596i) q^{67} +231.242 q^{68} -240.667 q^{69} +(3.91994 + 6.78954i) q^{70} +(559.526 - 969.128i) q^{71} +(52.7360 + 91.3414i) q^{72} +(235.224 - 407.421i) q^{73} +(-21.0744 + 36.5020i) q^{74} +569.391 q^{75} +(308.080 - 121.781i) q^{76} +33.1446 q^{77} +(-16.6496 + 28.8380i) q^{78} +(-190.946 + 330.729i) q^{79} +(-47.4486 - 82.1834i) q^{80} +(455.575 - 789.079i) q^{81} +(-344.092 - 595.985i) q^{82} +1322.28 q^{83} -16.7584 q^{84} +(-171.439 - 296.942i) q^{85} +(265.350 + 459.600i) q^{86} -1964.03 q^{87} -401.197 q^{88} +(-202.744 - 351.163i) q^{89} +(78.1953 - 135.438i) q^{90} +(-0.867948 - 1.50333i) q^{91} +(-75.9312 + 131.517i) q^{92} +(-895.142 + 1550.43i) q^{93} +279.587 q^{94} +(-384.787 - 305.324i) q^{95} +202.851 q^{96} +(-687.074 + 1190.05i) q^{97} +(-342.563 + 593.337i) q^{98} +(-330.586 - 572.591i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 5 q^{3} - 12 q^{4} - q^{5} + 10 q^{6} + 52 q^{7} - 48 q^{8} - 54 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 - 5 * q^3 - 12 * q^4 - q^5 + 10 * q^6 + 52 * q^7 - 48 * q^8 - 54 * q^9	\( 6 q + 6 q^{2} - 5 q^{3} - 12 q^{4} - q^{5} + 10 q^{6} + 52 q^{7} - 48 q^{8} - 54 q^{9} + 2 q^{10} + 8 q^{11} + 40 q^{12} + 129 q^{13} + 52 q^{14} - 77 q^{15} - 48 q^{16} - 51 q^{17} - 216 q^{18} + 40 q^{19} + 8 q^{20} - 170 q^{21} + 8 q^{22} + 47 q^{23} + 40 q^{24} - 338 q^{25} + 516 q^{26} + 718 q^{27} - 104 q^{28} - 125 q^{29} - 308 q^{30} - 100 q^{31} + 96 q^{32} + 274 q^{33} + 102 q^{34} - 84 q^{35} - 216 q^{36} - 376 q^{37} + 322 q^{38} - 1546 q^{39} + 8 q^{40} + 475 q^{41} + 340 q^{42} - 73 q^{43} - 16 q^{44} + 3188 q^{45} + 188 q^{46} - 241 q^{47} - 80 q^{48} - 1354 q^{49} - 1352 q^{50} + 69 q^{51} + 516 q^{52} + 29 q^{53} + 718 q^{54} - 1838 q^{55} - 416 q^{56} + 1755 q^{57} - 500 q^{58} - 1065 q^{59} - 308 q^{60} - 981 q^{61} - 100 q^{62} - 872 q^{63} + 384 q^{64} + 586 q^{65} - 548 q^{66} + 877 q^{67} + 408 q^{68} - 1526 q^{69} + 168 q^{70} + 2135 q^{71} + 432 q^{72} + 667 q^{73} - 376 q^{74} + 4584 q^{75} + 484 q^{76} - 492 q^{77} - 1546 q^{78} + 1671 q^{79} - 16 q^{80} - 1287 q^{81} - 950 q^{82} + 1176 q^{83} + 1360 q^{84} - 1929 q^{85} + 146 q^{86} - 6430 q^{87} - 64 q^{88} + 693 q^{89} + 3188 q^{90} + 1676 q^{91} + 188 q^{92} - 3138 q^{93} - 964 q^{94} + 4489 q^{95} - 320 q^{96} - 985 q^{97} - 1354 q^{98} - 3184 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 5 * q^3 - 12 * q^4 - q^5 + 10 * q^6 + 52 * q^7 - 48 * q^8 - 54 * q^9 + 2 * q^10 + 8 * q^11 + 40 * q^12 + 129 * q^13 + 52 * q^14 - 77 * q^15 - 48 * q^16 - 51 * q^17 - 216 * q^18 + 40 * q^19 + 8 * q^20 - 170 * q^21 + 8 * q^22 + 47 * q^23 + 40 * q^24 - 338 * q^25 + 516 * q^26 + 718 * q^27 - 104 * q^28 - 125 * q^29 - 308 * q^30 - 100 * q^31 + 96 * q^32 + 274 * q^33 + 102 * q^34 - 84 * q^35 - 216 * q^36 - 376 * q^37 + 322 * q^38 - 1546 * q^39 + 8 * q^40 + 475 * q^41 + 340 * q^42 - 73 * q^43 - 16 * q^44 + 3188 * q^45 + 188 * q^46 - 241 * q^47 - 80 * q^48 - 1354 * q^49 - 1352 * q^50 + 69 * q^51 + 516 * q^52 + 29 * q^53 + 718 * q^54 - 1838 * q^55 - 416 * q^56 + 1755 * q^57 - 500 * q^58 - 1065 * q^59 - 308 * q^60 - 981 * q^61 - 100 * q^62 - 872 * q^63 + 384 * q^64 + 586 * q^65 - 548 * q^66 + 877 * q^67 + 408 * q^68 - 1526 * q^69 + 168 * q^70 + 2135 * q^71 + 432 * q^72 + 667 * q^73 - 376 * q^74 + 4584 * q^75 + 484 * q^76 - 492 * q^77 - 1546 * q^78 + 1671 * q^79 - 16 * q^80 - 1287 * q^81 - 950 * q^82 + 1176 * q^83 + 1360 * q^84 - 1929 * q^85 + 146 * q^86 - 6430 * q^87 - 64 * q^88 + 693 * q^89 + 3188 * q^90 + 1676 * q^91 + 188 * q^92 - 3138 * q^93 - 964 * q^94 + 4489 * q^95 - 320 * q^96 - 985 * q^97 - 1354 * q^98 - 3184 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$3$	3.16954	−	5.48981i	0.609979	−	1.05651i	−0.381265	−	0.924466i	$-0.624511\pi$
$3$	3.16954	−	5.48981i	0.609979	−	1.05651i	0.991243	−	0.132048i	$-0.0421553\pi$
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	−2.96554	+	5.13646i	−0.265246	+	0.459419i	−0.967628	−	0.252381i	$-0.918786\pi$
$5$	−2.96554	+	5.13646i	−0.265246	+	0.459419i	0.702382	+	0.711800i	$0.252120\pi$
$6$	−6.33908	−	10.9796i	−0.431320	−	0.747068i
$7$	0.660916			0.0356861			0.0178430	−	0.999841i	$-0.494320\pi$
$7$	0.660916			0.0356861			0.0178430	+	0.999841i	$0.494320\pi$
$8$	−8.00000			−0.353553
$9$	−6.59199	−	11.4177i	−0.244148	−	0.422877i
$10$	5.93108	+	10.2729i	0.187557	+	0.324859i
$11$	50.1496			1.37461			0.687303	−	0.726371i	$-0.258794\pi$
$11$	50.1496			1.37461			0.687303	+	0.726371i	$0.258794\pi$
$12$	−25.3563			−0.609979
$13$	−1.31325	−	2.27462i	−0.0280177	−	0.0485281i	0.851677	−	0.524068i	$-0.175586\pi$
$13$	−1.31325	−	2.27462i	−0.0280177	−	0.0485281i	−0.879694	+	0.475540i	$0.842253\pi$
$14$	0.660916	−	1.14474i	0.0126169	−	0.0218532i
$15$	18.7988	+	32.5605i	0.323589	+	0.560472i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−28.9052	+	50.0654i	−0.412385	+	0.714272i	−0.995150	−	0.0983685i	$-0.968638\pi$
$17$	−28.9052	+	50.0654i	−0.412385	+	0.714272i	0.582765	+	0.812641i	$0.301971\pi$
$18$	−26.3680			−0.345277
$19$	−12.1437	+	81.9239i	−0.146629	+	0.989192i
$19$	−12.1437	+	81.9239i	−0.146629	+	0.989192i
$20$	23.7243			0.265246
$21$	2.09480	−	3.62830i	0.0217678	−	0.0377029i
$22$	50.1496	−	86.8616i	0.485997	−	0.841771i
$23$	−18.9828	−	32.8792i	−0.172095	−	0.298077i	0.767057	−	0.641579i	$-0.221720\pi$
$23$	−18.9828	−	32.8792i	−0.172095	−	0.298077i	−0.939152	+	0.343502i	$0.888387\pi$
$24$	−25.3563	+	43.9185i	−0.215660	+	0.373534i
$25$	44.9112	+	77.7884i	0.359289	+	0.622307i
$26$	−5.25300			−0.0396230
$27$	87.5809			0.624257
$28$	−1.32183	−	2.28948i	−0.00892152	−	0.0154525i
$29$	−154.914	−	268.319i	−0.991959	−	1.71812i	−0.605586	−	0.795780i	$-0.707061\pi$
$29$	−154.914	−	268.319i	−0.991959	−	1.71812i	−0.386373	−	0.922343i	$-0.626272\pi$
$30$	75.1952			0.457623
$31$	−282.420			−1.63626			−0.818131	−	0.575032i	$-0.804990\pi$
$31$	−282.420			−1.63626			−0.818131	+	0.575032i	$0.804990\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$	158.951	−	275.312i	0.838480	−	1.45229i
$34$	57.8105	+	100.131i	0.291600	+	0.505067i
$35$	−1.95997	+	3.39477i	−0.00946559	+	0.0163949i
$36$	−26.3680	+	45.6707i	−0.122074	+	0.211438i
$37$	−21.0744			−0.0936383			−0.0468192	−	0.998903i	$-0.514908\pi$
$37$	−21.0744			−0.0936383			−0.0468192	+	0.998903i	$0.514908\pi$
$38$	129.753	+	102.957i	0.553912	+	0.439524i
$39$	−16.6496			−0.0683608
$40$	23.7243	−	41.0917i	0.0937786	−	0.162429i
$41$	172.046	−	297.992i	0.655343	−	1.13509i	−0.326465	−	0.945209i	$-0.605857\pi$
$41$	172.046	−	297.992i	0.655343	−	1.13509i	0.981808	−	0.189878i	$-0.0608092\pi$
$42$	−4.18960	−	7.25660i	−0.0153921	−	0.0266600i
$43$	−132.675	+	229.800i	−0.470530	+	0.814981i	−0.999432	−	0.0337014i	$-0.989270\pi$
$43$	−132.675	+	229.800i	−0.470530	+	0.814981i	0.528902	+	0.848683i	$0.322604\pi$
$44$	−100.299	−	173.723i	−0.343651	−	0.595222i
$45$	78.1953			0.259037
$46$	−75.9312			−0.243379
$47$	69.8967	+	121.065i	0.216925	+	0.375725i	0.953866	−	0.300231i	$-0.0970639\pi$
$47$	69.8967	+	121.065i	0.216925	+	0.375725i	−0.736941	+	0.675957i	$0.763731\pi$
$48$	50.7127	+	87.8369i	0.152495	+	0.264129i
$49$	−342.563			−0.998727
$50$	179.645			0.508112
$51$	183.233	+	317.368i	0.503093	+	0.871382i
$52$	−5.25300	+	9.09846i	−0.0140088	+	0.0242640i
$53$	66.8936	+	115.863i	0.173369	+	0.300283i	0.939596	−	0.342287i	$-0.111201\pi$
$53$	66.8936	+	115.863i	0.173369	+	0.300283i	−0.766227	+	0.642570i	$0.777868\pi$
$54$	87.5809	−	151.694i	0.220708	−	0.382278i
$55$	−148.721	+	257.592i	−0.364609	+	0.631521i
$56$	−5.28733			−0.0126169
$57$	411.257	+	326.328i	0.955654	+	0.758302i
$58$	−619.656			−1.40284
$59$	−227.911	+	394.754i	−0.502907	+	0.871060i	0.497088	+	0.867700i	$0.334403\pi$
$59$	−227.911	+	394.754i	−0.502907	+	0.871060i	−0.999994	+	0.00335970i	$0.998931\pi$
$60$	75.1952	−	130.242i	0.161794	−	0.280236i
$61$	−54.2184	−	93.9090i	−0.113802	−	0.197112i	0.803498	−	0.595308i	$-0.202970\pi$
$61$	−54.2184	−	93.9090i	−0.113802	−	0.197112i	−0.917300	+	0.398196i	$0.869636\pi$
$62$	−282.420	+	489.166i	−0.578506	+	1.00200i
$63$	−4.35675	−	7.54612i	−0.00871269	−	0.0150908i
$64$	64.0000			0.125000
$65$	15.5780			0.0297263
$66$	−317.902	−	550.623i	−0.592895	−	1.02692i
$67$	−13.1980	−	22.8596i	−0.0240656	−	0.0416828i	0.853742	−	0.520697i	$-0.174328\pi$
$67$	−13.1980	−	22.8596i	−0.0240656	−	0.0416828i	−0.877807	+	0.479014i	$0.840994\pi$
$68$	231.242			0.412385
$69$	−240.667			−0.419897
$70$	3.91994	+	6.78954i	0.00669318	+	0.0115929i
$71$	559.526	−	969.128i	0.935261	−	1.61992i	0.161094	−	0.986939i	$-0.448498\pi$
$71$	559.526	−	969.128i	0.935261	−	1.61992i	0.774167	−	0.632981i	$-0.218169\pi$
$72$	52.7360	+	91.3414i	0.0863193	+	0.149509i
$73$	235.224	−	407.421i	0.377136	−	0.653219i	−0.613508	−	0.789688i	$-0.710242\pi$
$73$	235.224	−	407.421i	0.377136	−	0.653219i	0.990644	+	0.136470i	$0.0435756\pi$
$74$	−21.0744	+	36.5020i	−0.0331061	+	0.0573415i
$75$	569.391			0.876635
$76$	308.080	−	121.781i	0.464990	−	0.183806i
$77$	33.1446			0.0490543
$78$	−16.6496	+	28.8380i	−0.0241692	+	0.0418623i
$79$	−190.946	+	330.729i	−0.271938	+	0.471011i	−0.969358	−	0.245652i	$-0.920998\pi$
$79$	−190.946	+	330.729i	−0.271938	+	0.471011i	0.697420	+	0.716663i	$0.254331\pi$
$80$	−47.4486	−	82.1834i	−0.0663115	−	0.114855i
$81$	455.575	−	789.079i	0.624932	−	1.08241i
$82$	−344.092	−	595.985i	−0.463397	−	0.802628i
$83$	1322.28			1.74866			0.874330	−	0.485332i	$-0.161301\pi$
$83$	1322.28			1.74866			0.874330	+	0.485332i	$0.161301\pi$
$84$	−16.7584			−0.0217678
$85$	−171.439	−	296.942i	−0.218767	−	0.378916i
$86$	265.350	+	459.600i	0.332715	+	0.576279i
$87$	−1964.03			−2.42029
$88$	−401.197			−0.485997
$89$	−202.744	−	351.163i	−0.241470	−	0.418239i	0.719663	−	0.694323i	$-0.244296\pi$
$89$	−202.744	−	351.163i	−0.241470	−	0.418239i	−0.961133	+	0.276085i	$0.910963\pi$
$90$	78.1953	−	135.438i	0.0915834	−	0.158627i
$91$	−0.867948	−	1.50333i	−0.000999842	−	0.00173178i
$92$	−75.9312	+	131.517i	−0.0860475	+	0.149039i
$93$	−895.142	+	1550.43i	−0.998085	+	1.72873i
$94$	279.587			0.306779
$95$	−384.787	−	305.324i	−0.415561	−	0.329743i
$96$	202.851			0.215660
$97$	−687.074	+	1190.05i	−0.719194	+	1.24568i	0.242126	+	0.970245i	$0.422155\pi$
$97$	−687.074	+	1190.05i	−0.719194	+	1.24568i	−0.961320	+	0.275435i	$0.911178\pi$
$98$	−342.563	+	593.337i	−0.353103	+	0.611593i
$99$	−330.586	−	572.591i	−0.335607	−	0.581289i
$100$	179.645	−	311.154i	0.179645	−	0.311154i
$101$	−39.9417	−	69.1810i	−0.0393499	−	0.0681561i	0.845680	−	0.533691i	$-0.179195\pi$
$101$	−39.9417	−	69.1810i	−0.0393499	−	0.0681561i	−0.885030	+	0.465535i	$0.845862\pi$
$102$	732.931			0.711480
$103$	1799.73			1.72168			0.860838	−	0.508880i	$-0.169940\pi$
$103$	1799.73			1.72168			0.860838	+	0.508880i	$0.169940\pi$
$104$	10.5060	+	18.1969i	0.00990575	+	0.0171573i
$105$	12.4244	+	21.5197i	0.0115476	+	0.0200011i
$106$	267.574			0.245180
$107$	69.2556			0.0625718			0.0312859	−	0.999510i	$-0.490040\pi$
$107$	69.2556			0.0625718			0.0312859	+	0.999510i	$0.490040\pi$
$108$	−175.162	−	303.389i	−0.156064	−	0.270311i
$109$	−318.550	+	551.744i	−0.279922	+	0.484839i	−0.971365	−	0.237592i	$-0.923642\pi$
$109$	−318.550	+	551.744i	−0.279922	+	0.484839i	0.691443	+	0.722431i	$0.256975\pi$
$110$	297.441	+	515.183i	0.257817	+	0.446552i
$111$	−66.7963	+	115.695i	−0.0571174	+	0.0989302i
$112$	−5.28733	+	9.15792i	−0.00446076	+	0.00772627i
$113$	235.498			0.196051			0.0980256	−	0.995184i	$-0.468747\pi$
$113$	235.498			0.196051			0.0980256	+	0.995184i	$0.468747\pi$
$114$	976.473	−	385.989i	0.802238	−	0.317116i
$115$	225.177			0.182590
$116$	−619.656	+	1073.28i	−0.495979	+	0.859061i
$117$	−17.3139	+	29.9885i	−0.0136809	+	0.0236961i
$118$	455.822	+	789.507i	0.355609	+	0.615932i
$119$	−19.1039	+	33.0890i	−0.0147164	+	0.0254896i
$120$	−150.390	−	260.484i	−0.114406	−	0.198157i
$121$	1183.98			0.889541
$122$	−216.873			−0.160941
$123$	−1090.61	−	1889.00i	−0.799490	−	1.38476i
$124$	564.840	+	978.331i	0.409065	+	0.708522i
$125$	−1274.13			−0.911692
$126$	−17.4270			−0.0123216
$127$	−449.158	−	777.965i	−0.313830	−	0.543569i	0.665358	−	0.746524i	$-0.268279\pi$
$127$	−449.158	−	777.965i	−0.313830	−	0.543569i	−0.979188	+	0.202955i	$0.934945\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$	841.039	+	1456.72i	0.574026	+	0.994243i
$130$	15.5780	−	26.9818i	0.0105098	−	0.0182036i
$131$	−327.217	+	566.757i	−0.218237	+	0.377998i	−0.954269	−	0.298949i	$-0.903364\pi$
$131$	−327.217	+	566.757i	−0.218237	+	0.377998i	0.736032	+	0.676947i	$0.236697\pi$
$132$	−1271.61			−0.838480
$133$	−8.02597	+	54.1448i	−0.00523263	+	0.0353004i
$134$	−52.7921			−0.0340339
$135$	−259.724	+	449.856i	−0.165582	+	0.286796i
$136$	231.242	−	400.523i	0.145800	−	0.252533i
$137$	−1020.79	−	1768.07i	−0.636586	−	1.10260i	−0.986177	−	0.165697i	$-0.947013\pi$
$137$	−1020.79	−	1768.07i	−0.636586	−	1.10260i	0.349590	−	0.936903i	$-0.386321\pi$
$138$	−240.667	+	416.848i	−0.148456	+	0.257133i
$139$	−919.872	−	1593.27i	−0.561313	−	0.972223i	−0.997382	−	0.0723100i	$-0.976963\pi$
$139$	−919.872	−	1593.27i	−0.561313	−	0.972223i	0.436069	−	0.899913i	$-0.356370\pi$
$140$	15.6798			0.00946559
$141$	886.162			0.529279
$142$	−1119.05	−	1938.26i	−0.661330	−	1.14546i
$143$	−65.8589	−	114.071i	−0.0385133	−	0.0667070i
$144$	210.944			0.122074
$145$	1837.61			1.05245
$146$	−470.449	−	814.841i	−0.266675	−	0.461895i
$147$	−1085.77	+	1880.61i	−0.609202	+	1.05517i
$148$	42.1489	+	73.0040i	0.0234096	+	0.0405466i
$149$	166.629	−	288.610i	0.0916159	−	0.158683i	−0.816575	−	0.577239i	$-0.804130\pi$
$149$	166.629	−	288.610i	0.0916159	−	0.158683i	0.908191	+	0.418556i	$0.137463\pi$
$150$	569.391	−	986.214i	0.309937	−	0.536827i
$151$	3042.43			1.63966			0.819832	−	0.572604i	$-0.194067\pi$
$151$	3042.43			1.63966			0.819832	+	0.572604i	$0.194067\pi$
$152$	97.1497	−	655.391i	0.0518413	−	0.349732i
$153$	762.173			0.402732
$154$	33.1446	−	57.4082i	0.0173433	−	0.0300395i
$155$	837.527	−	1450.64i	0.434012	−	0.751730i
$156$	33.2992	+	57.6759i	0.0170902	+	0.0296011i
$157$	−984.390	+	1705.01i	−0.500400	+	0.866719i	0.499600	+	0.866256i	$0.333481\pi$
$157$	−984.390	+	1705.01i	−0.500400	+	0.866719i	−1.00000		0.000462343i	$0.999853\pi$
$158$	381.892	+	661.457i	0.192289	+	0.333055i
$159$	848.088			0.423005
$160$	−189.795			−0.0937786
$161$	−12.5460	−	21.7304i	−0.00614140	−	0.0106372i
$162$	−911.150	−	1578.16i	−0.441893	−	0.765382i
$163$	−1135.59			−0.545682			−0.272841	−	0.962059i	$-0.587963\pi$
$163$	−1135.59			−0.545682			−0.272841	+	0.962059i	$0.587963\pi$
$164$	−1376.37			−0.655343
$165$	942.752	+	1632.89i	0.444807	+	0.770428i
$166$	1322.28	−	2290.25i	0.618245	−	1.07083i
$167$	−395.161	−	684.440i	−0.183105	−	0.317147i	0.759831	−	0.650120i	$-0.225281\pi$
$167$	−395.161	−	684.440i	−0.183105	−	0.317147i	−0.942936	+	0.332973i	$0.891948\pi$
$168$	−16.7584	+	29.0264i	−0.00769606	+	0.0133300i
$169$	1095.05	−	1896.68i	0.498430	−	0.863306i
$170$	−685.757			−0.309383
$171$	1015.43	−	401.389i	0.454105	−	0.179503i
$172$	1061.40			0.470530
$173$	−1742.00	+	3017.24i	−0.765561	+	1.32599i	0.174388	+	0.984677i	$0.444205\pi$
$173$	−1742.00	+	3017.24i	−0.765561	+	1.32599i	−0.939949	+	0.341314i	$0.889128\pi$
$174$	−1964.03	+	3401.79i	−0.855703	+	1.48212i
$175$	29.6825	+	51.4116i	0.0128216	+	0.0222077i
$176$	−401.197	+	694.893i	−0.171826	+	0.297611i
$177$	1444.75	+	2502.38i	0.613525	+	1.06266i
$178$	−810.977			−0.341491
$179$	−2185.23			−0.912466			−0.456233	−	0.889860i	$-0.650802\pi$
$179$	−2185.23			−0.912466			−0.456233	+	0.889860i	$0.650802\pi$
$180$	−156.391	−	270.876i	−0.0647592	−	0.112166i
$181$	−527.946	−	914.429i	−0.216806	−	0.375519i	0.737024	−	0.675867i	$-0.236231\pi$
$181$	−527.946	−	914.429i	−0.216806	−	0.375519i	−0.953830	+	0.300348i	$0.902897\pi$
$182$	−3.47179			−0.00141399
$183$	−687.390			−0.277668
$184$	151.862	+	263.033i	0.0608448	+	0.105386i
$185$	62.4971	−	108.248i	0.0248372	−	0.0430193i
$186$	1790.28	+	3100.86i	0.705752	+	1.22240i
$187$	−1449.59	+	2510.76i	−0.566867	+	0.981843i
$188$	279.587	−	484.259i	0.108463	−	0.187863i
$189$	57.8836			0.0222773
$190$	−913.624	+	361.146i	−0.348849	+	0.137896i
$191$	2658.51			1.00714			0.503568	−	0.863955i	$-0.332020\pi$
$191$	2658.51			1.00714			0.503568	+	0.863955i	$0.332020\pi$
$192$	202.851	−	351.348i	0.0762473	−	0.132064i
$193$	2290.25	−	3966.82i	0.854173	−	1.47947i	−0.0232365	−	0.999730i	$-0.507397\pi$
$193$	2290.25	−	3966.82i	0.854173	−	1.47947i	0.877410	−	0.479742i	$-0.159270\pi$
$194$	1374.15	+	2380.09i	0.508547	+	0.880829i
$195$	49.3750	−	85.5201i	0.0181324	−	0.0314063i
$196$	685.126	+	1186.67i	0.249682	+	0.432461i
$197$	−4882.92			−1.76596			−0.882978	−	0.469414i	$-0.844465\pi$
$197$	−4882.92			−1.76596			−0.882978	+	0.469414i	$0.844465\pi$
$198$	−1322.34			−0.474620
$199$	1178.96	+	2042.02i	0.419972	+	0.727412i	0.995936	−	0.0900626i	$-0.0287067\pi$
$199$	1178.96	+	2042.02i	0.419972	+	0.727412i	−0.575965	+	0.817475i	$0.695373\pi$
$200$	−359.289	−	622.307i	−0.127028	−	0.220019i
$201$	−167.327			−0.0587180
$202$	−159.767			−0.0556492
$203$	−102.385	−	177.336i	−0.0353991	−	0.0613131i
$204$	732.931	−	1269.47i	0.251546	−	0.435691i
$205$	1020.42	+	1767.42i	0.347654	+	0.602154i
$206$	1799.73	−	3117.22i	0.608704	−	1.05431i
$207$	−250.269	+	433.478i	−0.0840333	+	0.145550i
$208$	42.0240			0.0140088
$209$	−609.002	+	4108.45i	−0.201558	+	1.35975i
$210$	49.6977			0.0163308
$211$	1607.63	−	2784.49i	0.524520	−	0.908495i	−0.475072	−	0.879947i	$-0.657578\pi$
$211$	1607.63	−	2784.49i	0.524520	−	0.908495i	0.999592	−	0.0285486i	$-0.00908855\pi$
$212$	267.574	−	463.452i	0.0866844	−	0.150142i
$213$	−3546.88	−	6143.38i	−1.14098	−	1.97623i
$214$	69.2556	−	119.954i	0.0221225	−	0.0383173i
$215$	−786.907	−	1362.96i	−0.249612	−	0.432341i
$216$	−700.647			−0.220708
$217$	−186.656			−0.0583918
$218$	637.099	+	1103.49i	0.197935	+	0.342833i
$219$	−1491.11	−	2582.67i	−0.460090	−	0.796899i
$220$	1189.76			0.364609
$221$	151.839			0.0462163
$222$	133.593	+	231.389i	0.0403881	+	0.0699542i
$223$	−1732.32	+	3000.47i	−0.520202	+	0.901016i	0.479522	+	0.877530i	$0.340810\pi$
$223$	−1732.32	+	3000.47i	−0.520202	+	0.901016i	−0.999724	+	0.0234864i	$0.992523\pi$
$224$	10.5747	+	18.3158i	0.00315424	+	0.00546330i
$225$	592.108	−	1025.56i	0.175439	−	0.303870i
$226$	235.498	−	407.894i	0.0693146	−	0.120056i
$227$	4831.61			1.41271			0.706354	−	0.707858i	$-0.250338\pi$
$227$	4831.61			1.41271			0.706354	+	0.707858i	$0.250338\pi$
$228$	307.920	−	2077.29i	0.0894408	−	0.603386i
$229$	−4645.49			−1.34054			−0.670268	−	0.742119i	$-0.733821\pi$
$229$	−4645.49			−1.34054			−0.670268	+	0.742119i	$0.733821\pi$
$230$	225.177	−	390.018i	0.0645553	−	0.111813i
$231$	105.053	−	181.958i	0.0299221	−	0.0518266i
$232$	1239.31	+	2146.55i	0.350710	+	0.607448i
$233$	414.255	−	717.511i	0.116475	−	0.201741i	−0.801893	−	0.597467i	$-0.796174\pi$
$233$	414.255	−	717.511i	0.116475	−	0.201741i	0.918369	+	0.395726i	$0.129507\pi$
$234$	34.6277	+	59.9770i	0.00967387	+	0.0167556i
$235$	−829.126			−0.230154
$236$	1823.29			0.502907
$237$	1210.42	+	2096.52i	0.331753	+	0.574613i
$238$	38.2079	+	66.1780i	0.0104061	+	0.0180239i
$239$	2735.22			0.740279			0.370139	−	0.928976i	$-0.379310\pi$
$239$	2735.22			0.740279			0.370139	+	0.928976i	$0.379310\pi$
$240$	−601.562			−0.161794
$241$	−2042.41	−	3537.56i	−0.545906	−	0.945537i	−0.998549	−	0.0538450i	$-0.982852\pi$
$241$	−2042.41	−	3537.56i	−0.545906	−	0.945537i	0.452644	−	0.891692i	$-0.350481\pi$
$242$	1183.98	−	2050.71i	0.314500	−	0.544731i
$243$	−1705.59	−	2954.16i	−0.450261	−	0.779875i
$244$	−216.873	+	375.636i	−0.0569012	+	0.0985558i
$245$	1015.88	−	1759.56i	0.264908	−	0.458834i
$246$	−4362.45			−1.13065
$247$	202.293	−	79.9643i	0.0521118	−	0.0205992i
$248$	2259.36			0.578506
$249$	4191.01	−	7259.05i	1.06665	−	1.84748i
$250$	−1274.13	+	2206.85i	−0.322332	+	0.558295i
$251$	1268.37	+	2196.89i	0.318960	+	0.552455i	0.980271	−	0.197657i	$-0.0633331\pi$
$251$	1268.37	+	2196.89i	0.318960	+	0.552455i	−0.661311	+	0.750112i	$0.730000\pi$
$252$	−17.4270	+	30.1845i	−0.00435634	+	0.00754541i
$253$	−951.979	−	1648.88i	−0.236563	−	0.409739i
$254$	−1796.63			−0.443822
$255$	−2173.54			−0.533773
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	3301.28	+	5717.98i	0.801276	+	1.38785i	0.918777	+	0.394778i	$0.129178\pi$
$257$	3301.28	+	5717.98i	0.801276	+	1.38785i	−0.117501	+	0.993073i	$0.537488\pi$
$258$	3364.16			0.811796
$259$	−13.9284			−0.00334159
$260$	−31.1560	−	53.9637i	−0.00743158	−	0.0128719i
$261$	−2042.38	+	3537.51i	−0.484369	+	0.838952i
$262$	654.434	+	1133.51i	0.154317	+	0.267285i
$263$	−1952.28	+	3381.44i	−0.457728	+	0.792808i	−0.998841	−	0.0481419i	$-0.984670\pi$
$263$	−1952.28	+	3381.44i	−0.457728	+	0.792808i	0.541112	+	0.840950i	$0.318003\pi$
$264$	−1271.61	+	2202.49i	−0.296448	+	0.513462i
$265$	−793.502			−0.183941
$266$	85.7556	+	68.0462i	0.0197670	+	0.0156849i
$267$	−2570.43			−0.589167
$268$	−52.7921	+	91.4386i	−0.0120328	+	0.0208414i
$269$	798.358	−	1382.80i	0.180955	−	0.313422i	−0.761251	−	0.648457i	$-0.775415\pi$
$269$	798.358	−	1382.80i	0.180955	−	0.313422i	0.942206	+	0.335035i	$0.108748\pi$
$270$	519.449	+	899.712i	0.117084	+	0.202795i
$271$	−2005.70	+	3473.97i	−0.449584	+	0.778703i	−0.998359	−	0.0572677i	$-0.981761\pi$
$271$	−2005.70	+	3473.97i	−0.449584	+	0.778703i	0.548775	+	0.835970i	$0.315094\pi$
$272$	−462.484	−	801.046i	−0.103096	−	0.178568i
$273$	−11.0040			−0.00243953
$274$	−4083.18			−0.900269
$275$	2252.28	+	3901.05i	0.493881	+	0.855427i
$276$	481.334	+	833.695i	0.104974	+	0.181821i
$277$	4850.78			1.05218			0.526092	−	0.850427i	$-0.323657\pi$
$277$	4850.78			1.05218			0.526092	+	0.850427i	$0.323657\pi$
$278$	−3679.49			−0.793817
$279$	1861.71	+	3224.58i	0.399490	+	0.691937i
$280$	15.6798	−	27.1582i	0.00334659	−	0.00579647i
$281$	−3149.49	−	5455.08i	−0.668623	−	1.15809i	−0.978289	−	0.207244i	$-0.933551\pi$
$281$	−3149.49	−	5455.08i	−0.668623	−	1.15809i	0.309666	−	0.950845i	$-0.399783\pi$
$282$	886.162	−	1534.88i	0.187128	−	0.324116i
$283$	−2878.50	+	4985.72i	−0.604627	+	1.04724i	0.387484	+	0.921877i	$0.373344\pi$
$283$	−2878.50	+	4985.72i	−0.604627	+	1.04724i	−0.992110	+	0.125368i	$0.959989\pi$
$284$	−4476.21			−0.935261
$285$	−2895.77	+	1144.67i	−0.601862	+	0.237910i
$286$	−263.436			−0.0544660
$287$	113.708	−	196.948i	0.0233866	−	0.0405068i
$288$	210.944	−	365.365i	0.0431597	−	0.0747547i
$289$	785.474	+	1360.48i	0.159877	+	0.276914i
$290$	1837.61	−	3182.84i	0.372098	−	0.644492i
$291$	4355.42	+	7543.81i	0.877386	+	1.51968i
$292$	−1881.80			−0.377136
$293$	5424.24			1.08153			0.540763	−	0.841175i	$-0.318135\pi$
$293$	5424.24			1.08153			0.540763	+	0.841175i	$0.318135\pi$
$294$	2171.54	+	3761.21i	0.430771	+	0.746117i
$295$	−1351.76	−	2341.31i	−0.266788	−	0.462090i
$296$	168.596			0.0331061
$297$	4392.14			0.858108
$298$	−333.258	−	577.219i	−0.0647822	−	0.112206i
$299$	−49.8583	+	86.3571i	−0.00964341	+	0.0167029i
$300$	−1138.78	−	1972.43i	−0.219159	−	0.379594i
$301$	−87.6871	+	151.879i	−0.0167914	+	0.0290835i
$302$	3042.43	−	5269.64i	0.579709	−	1.00409i
$303$	−506.387			−0.0960105
$304$	−1038.02	−	823.660i	−0.195838	−	0.155395i
$305$	643.147			0.120743
$306$	762.173	−	1320.12i	0.142387	−	0.246622i
$307$	−2814.93	+	4875.60i	−0.523311	+	0.906402i	0.476321	+	0.879272i	$0.341970\pi$
$307$	−2814.93	+	4875.60i	−0.523311	+	0.906402i	−0.999632	+	0.0271299i	$0.991363\pi$
$308$	−66.2893	−	114.816i	−0.0122636	−	0.0212411i
$309$	5704.32	−	9880.17i	1.05019	−	1.81897i
$310$	−1675.05	−	2901.28i	−0.306893	−	0.531554i
$311$	3054.01			0.556839			0.278420	−	0.960460i	$-0.410189\pi$
$311$	3054.01			0.556839			0.278420	+	0.960460i	$0.410189\pi$
$312$	133.197			0.0241692
$313$	1650.47	+	2858.70i	0.298051	+	0.516240i	0.975690	−	0.219155i	$-0.0703300\pi$
$313$	1650.47	+	2858.70i	0.298051	+	0.516240i	−0.677639	+	0.735395i	$0.736997\pi$
$314$	1968.78	+	3410.03i	0.353836	+	0.612863i
$315$	51.6805			0.00924402
$316$	1527.57			0.271938
$317$	1585.12	+	2745.51i	0.280850	+	0.486446i	0.971594	−	0.236653i	$-0.0760504\pi$
$317$	1585.12	+	2745.51i	0.280850	+	0.486446i	−0.690745	+	0.723099i	$0.742717\pi$
$318$	848.088	−	1468.93i	0.149555	−	0.259037i
$319$	−7768.87	−	13456.1i	−1.36355	−	2.36174i
$320$	−189.795	+	328.734i	−0.0331557	+	0.0574274i
$321$	219.508	−	380.200i	0.0381675	−	0.0661080i
$322$	−50.1841			−0.00868525
$323$	−3750.53	−	2976.01i	−0.646084	−	0.512661i
$324$	−3644.60			−0.624932
$325$	117.959	−	204.311i	0.0201329	−	0.0348712i
$326$	−1135.59	+	1966.90i	−0.192928	+	0.334160i
$327$	2019.31	+	3497.55i	0.341493	+	0.591483i
$328$	−1376.37	+	2383.94i	−0.231699	+	0.401314i
$329$	46.1958	+	80.0135i	0.00774121	+	0.0134082i
$330$	3771.01			0.629052
$331$	1414.75			0.234929			0.117465	−	0.993077i	$-0.462523\pi$
$331$	1414.75			0.234929			0.117465	+	0.993077i	$0.462523\pi$
$332$	−2644.55	−	4580.50i	−0.437165	−	0.757192i
$333$	138.923	+	240.621i	0.0228616	+	0.0395975i
$334$	−1580.65			−0.258949
$335$	156.557			0.0255332
$336$	33.5168	+	58.0528i	0.00544194	+	0.00942572i
$337$	1079.89	−	1870.42i	0.174555	−	0.302339i	−0.765452	−	0.643493i	$-0.777485\pi$
$337$	1079.89	−	1870.42i	0.174555	−	0.302339i	0.940007	+	0.341154i	$0.110818\pi$
$338$	−2190.10	−	3793.37i	−0.352443	−	0.610450i
$339$	746.421	−	1292.84i	0.119587	−	0.207131i
$340$	−685.757	+	1187.77i	−0.109384	+	0.189458i
$341$	−14163.2			−2.24922
$342$	320.205	−	2160.17i	0.0506278	−	0.341545i
$343$	−453.100			−0.0713267
$344$	1061.40	−	1838.40i	0.166357	−	0.288139i
$345$	713.708	−	1236.18i	0.111376	−	0.192909i
$346$	3484.01	+	6034.48i	0.541333	+	0.937617i
$347$	2734.38	−	4736.09i	0.423024	−	0.732699i	−0.573210	−	0.819409i	$-0.694302\pi$
$347$	2734.38	−	4736.09i	0.423024	−	0.732699i	0.996234	+	0.0867100i	$0.0276353\pi$
$348$	3928.05	+	6803.58i	0.605074	+	1.04802i
$349$	−3235.26			−0.496216			−0.248108	−	0.968732i	$-0.579809\pi$
$349$	−3235.26			−0.496216			−0.248108	+	0.968732i	$0.579809\pi$
$350$	118.730			0.0181325
$351$	−115.016	−	199.213i	−0.0174902	−	0.0302940i
$352$	802.393	+	1389.79i	0.121499	+	0.210443i
$353$	−6191.72			−0.933576			−0.466788	−	0.884369i	$-0.654589\pi$
$353$	−6191.72			−0.933576			−0.466788	+	0.884369i	$0.654589\pi$
$354$	5778.99			0.867655
$355$	3318.59	+	5747.97i	0.496148	+	0.859354i
$356$	−810.977	+	1404.65i	−0.120735	+	0.209119i
$357$	121.101	+	209.754i	0.0179534	+	0.0310962i
$358$	−2185.23	+	3784.92i	−0.322606	+	0.558769i
$359$	3203.54	−	5548.69i	0.470964	−	0.815734i	−0.528484	−	0.848943i	$-0.677239\pi$
$359$	3203.54	−	5548.69i	0.470964	−	0.815734i	0.999448	+	0.0332089i	$0.0105727\pi$
$360$	−625.562			−0.0915834
$361$	−6564.06	−	1989.72i	−0.957000	−	0.290089i
$362$	−2111.78			−0.306610
$363$	3752.67	−	6499.82i	0.542601	−	0.939813i
$364$	−3.47179	+	6.01332i	−0.000499921	+	0.000865889i
$365$	1395.13	+	2416.44i	0.200068	+	0.346527i
$366$	−687.390	+	1190.59i	−0.0981706	+	0.170036i
$367$	−4184.47	−	7247.72i	−0.595171	−	1.03087i	−0.993523	−	0.113633i	$-0.963751\pi$
$367$	−4184.47	−	7247.72i	−0.595171	−	1.03087i	0.398352	−	0.917233i	$-0.369582\pi$
$368$	607.449			0.0860475
$369$	−4536.50			−0.640003
$370$	−124.994	−	216.496i	−0.0175625	−	0.0304192i
$371$	44.2110	+	76.5758i	0.00618685	+	0.0107159i
$372$	7161.13			0.998085
$373$	10254.9			1.42354			0.711769	−	0.702414i	$-0.247894\pi$
$373$	10254.9			1.42354			0.711769	+	0.702414i	$0.247894\pi$
$374$	2899.17	+	5021.51i	0.400836	+	0.694268i
$375$	−4038.40	+	6994.72i	−0.556113	+	0.963215i
$376$	−559.174	−	968.517i	−0.0766946	−	0.132839i
$377$	−406.881	+	704.739i	−0.0555848	+	0.0962757i
$378$	57.8836	−	100.257i	0.00787622	−	0.0136420i
$379$	6607.19			0.895484			0.447742	−	0.894163i	$-0.352228\pi$
$379$	6607.19			0.895484			0.447742	+	0.894163i	$0.352228\pi$
$380$	−288.101	+	1943.59i	−0.0388928	+	0.262379i
$381$	−5694.50			−0.765717
$382$	2658.51	−	4604.68i	0.356077	−	0.616743i
$383$	4.97873	−	8.62342i	0.000664233	−	0.00115049i	−0.865693	−	0.500575i	$-0.833122\pi$
$383$	4.97873	−	8.62342i	0.000664233	−	0.00115049i	0.866357	+	0.499425i	$0.166455\pi$
$384$	−405.701	−	702.695i	−0.0539150	−	0.0933835i
$385$	−98.2917	+	170.246i	−0.0130115	+	0.0225365i
$386$	−4580.49	−	7933.64i	−0.603992	−	1.04614i
$387$	3498.38			0.459515
$388$	5496.59			0.719194
$389$	6190.75	+	10722.7i	0.806898	+	1.39759i	0.915002	+	0.403449i	$0.132189\pi$
$389$	6190.75	+	10722.7i	0.806898	+	1.39759i	−0.108104	+	0.994140i	$0.534478\pi$
$390$	−98.7501	−	171.040i	−0.0128216	−	0.0222076i
$391$	2194.81			0.283878
$392$	2740.51			0.353103
$393$	2074.26	+	3592.72i	0.266240	+	0.461142i
$394$	−4882.92	+	8457.46i	−0.624360	+	1.08142i
$395$	−1132.52	−	1961.58i	−0.144261	−	0.249867i
$396$	−1322.34	+	2290.36i	−0.167804	+	0.290644i
$397$	−301.966	+	523.020i	−0.0381744	+	0.0661199i	−0.884481	−	0.466576i	$-0.845488\pi$
$397$	−301.966	+	523.020i	−0.0381744	+	0.0661199i	0.846307	+	0.532696i	$0.178821\pi$
$398$	4715.84			0.593930
$399$	271.806	+	215.675i	0.0341036	+	0.0270608i
$400$	−1437.16			−0.179645
$401$	−5170.14	+	8954.94i	−0.643851	+	1.11518i	0.340715	+	0.940167i	$0.389331\pi$
$401$	−5170.14	+	8954.94i	−0.643851	+	1.11518i	−0.984566	+	0.175016i	$0.944002\pi$
$402$	−167.327	+	289.818i	−0.0207599	+	0.0359573i
$403$	370.888	+	642.397i	0.0458443	+	0.0794046i
$404$	−159.767	+	276.724i	−0.0196750	+	0.0340780i
$405$	2702.05	+	4680.09i	0.331521	+	0.574211i
$406$	−409.540			−0.0500619
$407$	−1056.87			−0.128716
$408$	−1465.86	−	2538.95i	−0.177870	−	0.308080i
$409$	80.7101	+	139.794i	0.00975760	+	0.0169007i	0.870863	−	0.491526i	$-0.163561\pi$
$409$	80.7101	+	139.794i	0.00975760	+	0.0169007i	−0.861105	+	0.508427i	$0.830227\pi$
$410$	4081.67			0.491657
$411$	−12941.8			−1.55322
$412$	−3599.46	−	6234.44i	−0.430419	−	0.745507i
$413$	−150.630	+	260.899i	−0.0179468	+	0.0310847i
$414$	500.538	+	866.957i	0.0594205	+	0.102919i
$415$	−3921.27	+	6791.83i	−0.463825	+	0.803368i
$416$	42.0240	−	72.7877i	0.00495287	−	0.00857863i
$417$	−11662.3			−1.36956
$418$	6507.04	+	5163.27i	0.761411	+	0.604172i
$419$	7483.41			0.872526			0.436263	−	0.899819i	$-0.356302\pi$
$419$	7483.41			0.872526			0.436263	+	0.899819i	$0.356302\pi$
$420$	49.6977	−	86.0789i	0.00577381	−	0.0100005i
$421$	−3024.77	+	5239.05i	−0.350162	+	0.606498i	−0.986278	−	0.165096i	$-0.947207\pi$
$421$	−3024.77	+	5239.05i	−0.350162	+	0.606498i	0.636116	+	0.771594i	$0.280540\pi$
$422$	−3215.26	−	5568.99i	−0.370892	−	0.642403i
$423$	921.517	−	1596.11i	0.105924	−	0.183465i
$424$	−535.149	−	926.905i	−0.0612951	−	0.106166i
$425$	−5192.67			−0.592663
$426$	−14187.5			−1.61359
$427$	−35.8338	−	62.0659i	−0.00406117	−	0.00703415i
$428$	−138.511	−	239.908i	−0.0156430	−	0.0270944i
$429$	−834.970			−0.0939691
$430$	−3147.63			−0.353005
$431$	−5454.85	−	9448.08i	−0.609631	−	1.05591i	−0.991301	−	0.131613i	$-0.957984\pi$
$431$	−5454.85	−	9448.08i	−0.609631	−	1.05591i	0.381670	−	0.924299i	$-0.375349\pi$
$432$	−700.647	+	1213.56i	−0.0780321	+	0.135156i
$433$	3824.48	+	6624.19i	0.424464	+	0.735193i	0.996370	−	0.0851261i	$-0.0271293\pi$
$433$	3824.48	+	6624.19i	0.424464	+	0.735193i	−0.571906	+	0.820319i	$0.693796\pi$
$434$	−186.656	+	323.297i	−0.0206446	+	0.0357575i
$435$	5824.39	−	10088.1i	0.641973	−	1.11193i
$436$	2548.40			0.279922
$437$	2924.11	−	1155.87i	0.320090	−	0.126528i
$438$	−5964.43			−0.650665
$439$	5707.94	−	9886.44i	0.620558	−	1.07484i	−0.368824	−	0.929499i	$-0.620239\pi$
$439$	5707.94	−	9886.44i	0.620558	−	1.07484i	0.989382	−	0.145339i	$-0.0464272\pi$
$440$	1189.76	−	2060.73i	0.128909	−	0.223276i
$441$	2258.17	+	3911.27i	0.243837	+	0.422338i
$442$	151.839	−	262.993i	0.0163399	−	0.0283016i
$443$	1576.33	+	2730.28i	0.169060	+	0.292820i	0.938090	−	0.346393i	$-0.112594\pi$
$443$	1576.33	+	2730.28i	0.169060	+	0.292820i	−0.769030	+	0.639213i	$0.779260\pi$
$444$	534.371			0.0571174
$445$	2404.98			0.256196
$446$	3464.65	+	6000.95i	0.367838	+	0.637115i
$447$	−1056.27	−	1829.52i	−0.111767	−	0.193587i
$448$	42.2986			0.00446076
$449$	5217.04			0.548346			0.274173	−	0.961680i	$-0.411596\pi$
$449$	5217.04			0.548346			0.274173	+	0.961680i	$0.411596\pi$
$450$	−1184.22	−	2051.12i	−0.124054	−	0.214869i
$451$	8628.03	−	14944.2i	0.900838	−	1.56030i
$452$	−470.996	−	815.789i	−0.0490128	−	0.0848927i
$453$	9643.10	−	16702.3i	1.00016	−	1.73233i
$454$	4831.61	−	8368.59i	0.499468	−	0.865104i
$455$	10.2957			0.00106082
$456$	−3290.05	−	2610.62i	−0.337875	−	0.268100i
$457$	15868.7			1.62430			0.812151	−	0.583447i	$-0.198297\pi$
$457$	15868.7			1.62430			0.812151	+	0.583447i	$0.198297\pi$
$458$	−4645.49	+	8046.23i	−0.473951	+	0.820907i
$459$	−2531.55	+	4384.77i	−0.257435	+	0.445890i
$460$	−450.354	−	780.036i	−0.0456475	−	0.0790638i
$461$	2170.58	−	3759.56i	0.219293	−	0.379827i	−0.735299	−	0.677743i	$-0.762958\pi$
$461$	2170.58	−	3759.56i	0.219293	−	0.379827i	0.954592	+	0.297916i	$0.0962915\pi$
$462$	−210.107	−	363.915i	−0.0211581	−	0.0366469i
$463$	−1394.23			−0.139946			−0.0699732	−	0.997549i	$-0.522291\pi$
$463$	−1394.23			−0.139946			−0.0699732	+	0.997549i	$0.522291\pi$
$464$	4957.25			0.495979
$465$	−5309.16	−	9195.73i	−0.529476	−	0.917079i
$466$	−828.510	−	1435.02i	−0.0823605	−	0.142653i
$467$	6138.35			0.608242			0.304121	−	0.952633i	$-0.401637\pi$
$467$	6138.35			0.608242			0.304121	+	0.952633i	$0.401637\pi$
$468$	138.511			0.0136809
$469$	−8.72278	−	15.1083i	−0.000858807	−	0.00148750i
$470$	−829.126	+	1436.09i	−0.0813717	+	0.140940i
$471$	6240.13	+	10808.2i	0.610467	+	1.05736i
$472$	1823.29	−	3158.03i	0.177804	−	0.307966i
$473$	−6653.60	+	11524.4i	−0.646793	+	1.12028i
$474$	4841.70			0.469170
$475$	−6918.12	+	2734.66i	−0.668263	+	0.264157i
$476$	152.831			0.0147164
$477$	881.925	−	1527.54i	0.0846552	−	0.146627i
$478$	2735.22	−	4737.54i	0.261728	−	0.453326i
$479$	−3566.47	−	6177.31i	−0.340201	−	0.589245i	0.644269	−	0.764799i	$-0.277162\pi$
$479$	−3566.47	−	6177.31i	−0.340201	−	0.589245i	−0.984470	+	0.175554i	$0.943828\pi$
$480$	−601.562	+	1041.94i	−0.0572029	+	0.0990784i
$481$	27.6760	+	47.9363i	0.00262353	+	0.00454409i
$482$	−8169.65			−0.772027
$483$	−159.061			−0.0149845
$484$	−2367.96	−	4101.43i	−0.222385	−	0.385183i
$485$	−4075.09	−	7058.26i	−0.381526	−	0.660823i
$486$	−6822.35			−0.636765
$487$	−14396.6			−1.33957			−0.669787	−	0.742553i	$-0.733615\pi$
$487$	−14396.6			−1.33957			−0.669787	+	0.742553i	$0.733615\pi$
$488$	433.747	+	751.272i	0.0402352	+	0.0696895i
$489$	−3599.29	+	6234.16i	−0.332854	+	0.576520i
$490$	−2031.77	−	3519.13i	−0.187318	−	0.324445i
$491$	−3827.91	+	6630.13i	−0.351835	+	0.609396i	−0.986571	−	0.163333i	$-0.947775\pi$
$491$	−3827.91	+	6630.13i	−0.351835	+	0.609396i	0.634736	+	0.772729i	$0.281109\pi$
$492$	−4362.45	+	7555.99i	−0.399745	+	0.692379i
$493$	17911.3			1.63628
$494$	63.7909	−	430.346i	0.00580989	−	0.0391947i
$495$	3921.46			0.356074
$496$	2259.36	−	3913.33i	0.204533	−	0.354261i
$497$	369.800	−	640.512i	0.0333758	−	0.0578086i
$498$	−8382.03	−	14518.1i	−0.754232	−	1.30637i
$499$	−9319.05	+	16141.1i	−0.836028	+	1.44804i	0.0571628	+	0.998365i	$0.481795\pi$
$499$	−9319.05	+	16141.1i	−0.836028	+	1.44804i	−0.893191	+	0.449678i	$0.851539\pi$
$500$	2548.26	+	4413.71i	0.227923	+	0.394774i
$501$	−5009.92			−0.446760
$502$	5073.49			0.451077
$503$	3739.79	+	6477.50i	0.331509	+	0.574190i	0.982808	−	0.184631i	$-0.0591091\pi$
$503$	3739.79	+	6477.50i	0.331509	+	0.574190i	−0.651299	+	0.758821i	$0.725776\pi$
$504$	34.8540	+	60.3689i	0.00308040	+	0.00533541i
$505$	473.794			0.0417496
$506$	−3807.92			−0.334550
$507$	−6941.62	−	12023.2i	−0.608063	−	1.05320i
$508$	−1796.63	+	3111.86i	−0.156915	+	0.271784i
$509$	9355.19	+	16203.7i	0.814659	+	1.41103i	0.909572	+	0.415546i	$0.136409\pi$
$509$	9355.19	+	16203.7i	0.814659	+	1.41103i	−0.0949131	+	0.995486i	$0.530257\pi$
$510$	−2173.54	+	3764.67i	−0.188717	+	0.326868i
$511$	155.464	−	269.271i	0.0134585	−	0.0233108i
$512$	−512.000			−0.0441942
$513$	−1063.56	+	7174.97i	−0.0915344	+	0.617510i
$514$	13205.1			1.13318
$515$	−5337.17	+	9244.24i	−0.456667	+	0.790971i
$516$	3364.16	−	5826.89i	0.287013	−	0.497121i
$517$	3505.29	+	6071.34i	0.298187	+	0.516474i
$518$	−13.9284	+	24.1248i	−0.00118143	+	0.00204630i
$519$	11042.7	+	19126.5i	0.933952	+	1.61765i
$520$	−124.624			−0.0105098
$521$	−13796.0			−1.16010			−0.580050	−	0.814581i	$-0.696967\pi$
$521$	−13796.0			−1.16010			−0.580050	+	0.814581i	$0.696967\pi$
$522$	4084.77	+	7075.03i	0.342501	+	0.593229i
$523$	−6222.14	−	10777.1i	−0.520221	−	0.901048i	−0.999724	−	0.0235083i	$-0.992516\pi$
$523$	−6222.14	−	10777.1i	−0.520221	−	0.901048i	0.479503	−	0.877540i	$-0.340817\pi$
$524$	2617.74			0.218237
$525$	376.320			0.0312837
$526$	3904.55	+	6762.88i	0.323663	+	0.560600i
$527$	8163.42	−	14139.5i	0.674770	−	1.16874i
$528$	2543.22	+	4404.98i	0.209620	+	0.363073i
$529$	5362.81	−	9288.65i	0.440767	−	0.763430i
$530$	−793.502	+	1374.39i	−0.0650331	+	0.112641i
$531$	6009.55			0.491135
$532$	203.615	−	80.4869i	0.0165937	−	0.00655930i
$533$	−903.757			−0.0734448
$534$	−2570.43	+	4452.11i	−0.208302	+	0.360790i
$535$	−205.380	+	355.729i	−0.0165969	+	0.0287467i
$536$	105.584	+	182.877i	0.00850847	+	0.0147371i
$537$	−6926.17	+	11996.5i	−0.556585	+	0.964034i
$538$	−1596.72	−	2765.59i	−0.127954	−	0.221623i
$539$	−17179.4			−1.37286
$540$	2077.80			0.165582
$541$	−8883.44	−	15386.6i	−0.705968	−	1.22277i	−0.966341	−	0.257265i	$-0.917179\pi$
$541$	−8883.44	−	15386.6i	−0.705968	−	1.22277i	0.260373	−	0.965508i	$-0.416155\pi$
$542$	4011.39	+	6947.93i	0.317904	+	0.550626i
$543$	−6693.39			−0.528988
$544$	−1849.94			−0.145800
$545$	−1889.34	−	3272.44i	−0.148496	−	0.257203i
$546$	−11.0040	+	19.0595i	−0.000862504	+	0.00149390i
$547$	3595.49	+	6227.58i	0.281046	+	0.486786i	0.971643	−	0.236454i	$-0.0759853\pi$
$547$	3595.49	+	6227.58i	0.281046	+	0.486786i	−0.690597	+	0.723240i	$0.742652\pi$
$548$	−4083.18	+	7072.27i	−0.318293	+	0.551300i
$549$	−714.814	+	1238.09i	−0.0555693	+	0.0962488i
$550$	9009.10			0.698453
$551$	23863.0	−	9432.77i	1.84500	−	0.729310i
$552$	1925.34			0.148456
$553$	−126.199	+	218.584i	−0.00970442	+	0.0168085i
$554$	4850.78	−	8401.80i	0.372003	−	0.644329i
$555$	−396.174	−	686.194i	−0.0303003	−	0.0524817i
$556$	−3679.49	+	6373.06i	−0.280657	+	0.486112i
$557$	−9244.53	−	16012.0i	−0.703238	−	1.21804i	−0.967324	−	0.253544i	$-0.918404\pi$
$557$	−9244.53	−	16012.0i	−0.703238	−	1.21804i	0.264086	−	0.964499i	$-0.414930\pi$
$558$	7446.84			0.564964
$559$	696.943			0.0527326
$560$	−31.3595	−	54.3163i	−0.00236640	−	0.00409872i
$561$	9189.05	+	15915.9i	0.691554	+	1.19781i
$562$	−12598.0			−0.945576
$563$	4932.37			0.369227			0.184613	−	0.982811i	$-0.440897\pi$
$563$	4932.37			0.369227			0.184613	+	0.982811i	$0.440897\pi$
$564$	−1772.32	−	3069.76i	−0.132320	−	0.229184i
$565$	−698.379	+	1209.63i	−0.0520018	+	0.0900697i
$566$	5757.01	+	9971.43i	0.427536	+	0.740513i
$567$	301.097	−	521.515i	0.0223014	−	0.0386271i
$568$	−4476.21	+	7753.02i	−0.330665	+	0.572728i
$569$	−15002.9			−1.10537			−0.552683	−	0.833392i	$-0.686396\pi$
$569$	−15002.9			−1.10537			−0.552683	+	0.833392i	$0.686396\pi$
$570$	−913.149	+	6160.29i	−0.0671010	+	0.452677i
$571$	−13385.3			−0.981013			−0.490507	−	0.871438i	$-0.663188\pi$
$571$	−13385.3			−0.981013			−0.490507	+	0.871438i	$0.663188\pi$
$572$	−263.436	+	456.284i	−0.0192566	+	0.0333535i
$573$	8426.26	−	14594.7i	0.614332	−	1.06405i
$574$	−227.416	−	393.896i	−0.0165368	−	0.0286427i
$575$	1705.08	−	2953.28i	0.123664	−	0.214192i
$576$	−421.888	−	730.731i	−0.0305185	−	0.0528596i
$577$	4891.89			0.352950			0.176475	−	0.984305i	$-0.443531\pi$
$577$	4891.89			0.352950			0.176475	+	0.984305i	$0.443531\pi$
$578$	3141.89			0.226100
$579$	−14518.1	−	25146.0i	−1.04206	−	1.80489i
$580$	−3675.23	−	6365.68i	−0.263113	−	0.455725i
$581$	873.914			0.0624029
$582$	17421.7			1.24081
$583$	3354.69	+	5810.49i	0.238314	+	0.412771i
$584$	−1881.80	+	3259.36i	−0.133338	+	0.230948i
$585$	−102.690	−	177.864i	−0.00725762	−	0.0125706i
$586$	5424.24	−	9395.05i	0.382377	−	0.662297i
$587$	6191.21	−	10723.5i	0.435330	−	0.754013i	−0.561993	−	0.827142i	$-0.689965\pi$
$587$	6191.21	−	10723.5i	0.435330	−	0.754013i	0.997322	+	0.0731291i	$0.0232985\pi$
$588$	8686.15			0.609202
$589$	3429.62	−	23136.9i	0.239924	−	1.61858i
$590$	−5407.03			−0.377295
$591$	−15476.6	+	26806.3i	−1.07720	+	1.86576i
$592$	168.596	−	292.016i	0.0117048	−	0.0202733i
$593$	−11263.1	−	19508.2i	−0.779964	−	1.35094i	−0.931962	−	0.362557i	$-0.881904\pi$
$593$	−11263.1	−	19508.2i	−0.779964	−	1.35094i	0.151998	−	0.988381i	$-0.451429\pi$
$594$	4392.14	−	7607.41i	0.303387	−	0.525481i
$595$	−113.307	−	196.253i	−0.00780694	−	0.0135220i
$596$	−1333.03			−0.0916159
$597$	14947.1			1.02469
$598$	99.7166	+	172.714i	0.00681892	+	0.0118107i
$599$	4370.13	+	7569.30i	0.298095	+	0.516316i	0.975700	−	0.219110i	$-0.0703155\pi$
$599$	4370.13	+	7569.30i	0.298095	+	0.516316i	−0.677605	+	0.735426i	$0.736982\pi$
$600$	−4555.13			−0.309937
$601$	−6198.75			−0.420719			−0.210360	−	0.977624i	$-0.567463\pi$
$601$	−6198.75			−0.420719			−0.210360	+	0.977624i	$0.567463\pi$
$602$	175.374	+	303.757i	0.0118733	+	0.0205651i
$603$	−174.003	+	301.381i	−0.0117511	+	0.0203536i
$604$	−6084.86	−	10539.3i	−0.409916	−	0.709995i
$605$	−3511.14	+	6081.47i	−0.235947	+	0.408673i
$606$	−506.387	+	877.088i	−0.0339448	+	0.0587942i
$607$	9848.40			0.658541			0.329271	−	0.944236i	$-0.393197\pi$
$607$	9848.40			0.658541			0.329271	+	0.944236i	$0.393197\pi$
$608$	−2464.64	+	974.247i	−0.164399	+	0.0649851i
$609$	−1298.06			−0.0863709
$610$	643.147	−	1113.96i	0.0426889	−	0.0739394i
$611$	183.584	−	317.976i	0.0121555	−	0.0210539i
$612$	−1524.35	−	2640.24i	−0.100683	−	0.174388i
$613$	−4831.89	+	8369.08i	−0.318366	+	0.551426i	−0.980147	−	0.198271i	$-0.936467\pi$
$613$	−4831.89	+	8369.08i	−0.318366	+	0.551426i	0.661782	+	0.749697i	$0.269801\pi$
$614$	5629.86	+	9751.20i	0.370037	+	0.640923i
$615$	12937.0			0.848246
$616$	−265.157			−0.0173433
$617$	−2596.83	−	4497.84i	−0.169440	−	0.293479i	0.768783	−	0.639510i	$-0.220863\pi$
$617$	−2596.83	−	4497.84i	−0.169440	−	0.293479i	−0.938223	+	0.346031i	$0.887529\pi$
$618$	−11408.6	−	19760.3i	−0.742593	−	1.28621i
$619$	5299.50			0.344112			0.172056	−	0.985087i	$-0.444959\pi$
$619$	5299.50			0.344112			0.172056	+	0.985087i	$0.444959\pi$
$620$	−6700.22			−0.434012
$621$	−1662.53	−	2879.59i	−0.107432	−	0.186077i
$622$	3054.01	−	5289.70i	0.196872	−	0.340993i
$623$	−133.997	−	232.089i	−0.00861713	−	0.0149253i
$624$	133.197	−	230.704i	0.00854510	−	0.0148005i
$625$	−1835.42	+	3179.04i	−0.117467	+	0.203458i
$626$	6601.88			0.421508
$627$	20624.3	+	16365.2i	1.31365	+	1.04237i
$628$	7875.12			0.500400
$629$	609.162	−	1055.10i	0.0386151	−	0.0668833i
$630$	51.6805	−	89.5132i	0.00326825	−	0.00566078i
$631$	7139.19	+	12365.4i	0.450407	+	0.780128i	0.998411	−	0.0563477i	$-0.0179455\pi$
$631$	7139.19	+	12365.4i	0.450407	+	0.780128i	−0.548004	+	0.836476i	$0.684612\pi$
$632$	1527.57	−	2645.83i	0.0961447	−	0.166528i
$633$	−10190.9	−	17651.1i	−0.639892	−	1.10833i
$634$	6340.49			0.397181
$635$	5327.99			0.332968
$636$	−1696.18	−	2937.86i	−0.105751	−	0.183167i
$637$	449.871	+	779.200i	0.0279820	+	0.0484663i
$638$	−31075.5			−1.92835
$639$	−14753.6			−0.913369
$640$	379.589	+	657.467i	0.0234446	+	0.0406073i
$641$	6435.92	−	11147.3i	0.396574	−	0.686886i	−0.596727	−	0.802444i	$-0.703532\pi$
$641$	6435.92	−	11147.3i	0.396574	−	0.686886i	0.993301	+	0.115559i	$0.0368658\pi$
$642$	−439.017	−	760.399i	−0.0269885	−	0.0467454i
$643$	−8535.69	+	14784.2i	−0.523506	+	0.906740i	0.476119	+	0.879381i	$0.342043\pi$
$643$	−8535.69	+	14784.2i	−0.523506	+	0.906740i	−0.999626	+	0.0273590i	$0.991290\pi$
$644$	−50.1841	+	86.9214i	−0.00307070	+	0.00531861i
$645$	−9976.54			−0.609032
$646$	−8905.13	+	3520.10i	−0.542365	+	0.214391i
$647$	−6628.94			−0.402798			−0.201399	−	0.979509i	$-0.564549\pi$
$647$	−6628.94			−0.402798			−0.201399	+	0.979509i	$0.564549\pi$
$648$	−3644.60	+	6312.63i	−0.220947	+	0.382691i
$649$	−11429.6	+	19796.7i	−0.691299	+	1.19736i
$650$	−235.918	−	408.622i	−0.0142361	−	0.0246577i
$651$	−591.613	+	1024.70i	−0.0356178	+	0.0616918i
$652$	2271.18	+	3933.79i	0.136420	+	0.236287i
$653$	30340.7			1.81826			0.909129	−	0.416515i	$-0.136749\pi$
$653$	30340.7			1.81826			0.909129	+	0.416515i	$0.136749\pi$
$654$	8077.25			0.482944
$655$	−1940.75	−	3361.48i	−0.115773	−	0.200525i
$656$	2752.74	+	4767.88i	0.163836	+	0.283772i
$657$	−6202.39			−0.368308
$658$	184.783			0.0109477
$659$	−1428.03	−	2473.43i	−0.0844132	−	0.146208i	0.820728	−	0.571319i	$-0.193568\pi$
$659$	−1428.03	−	2473.43i	−0.0844132	−	0.146208i	−0.905141	+	0.425111i	$0.860235\pi$
$660$	3771.01	−	6531.58i	0.222403	−	0.385214i
$661$	10640.5	+	18429.8i	0.626122	+	1.08447i	0.988323	+	0.152375i	$0.0486921\pi$
$661$	10640.5	+	18429.8i	0.626122	+	1.08447i	−0.362201	+	0.932100i	$0.617975\pi$
$662$	1414.75	−	2450.41i	0.0830600	−	0.143864i
$663$	481.261	−	833.568i	0.0281910	−	0.0488282i
$664$	−10578.2			−0.618245
$665$	−254.312	−	201.794i	−0.0148297	−	0.0117673i
$666$	555.690			0.0323312
$667$	−5881.40	+	10186.9i	−0.341422	+	0.591361i
$668$	−1580.65	+	2737.76i	−0.0915524	+	0.158573i
$669$	10981.3	+	19020.3i	0.634624	+	1.09920i
$670$	156.557	−	271.165i	0.00902735	−	0.0156358i
$671$	−2719.03	−	4709.49i	−0.156434	−	0.270951i
$672$	134.067			0.00769606
$673$	−14334.7			−0.821046			−0.410523	−	0.911850i	$-0.634654\pi$
$673$	−14334.7			−0.821046			−0.410523	+	0.911850i	$0.634654\pi$
$674$	−2159.77	−	3740.83i	−0.123429	−	0.213786i
$675$	3933.36	+	6812.77i	0.224289	+	0.388480i
$676$	−8760.41			−0.498430
$677$	3300.00			0.187340			0.0936700	−	0.995603i	$-0.470140\pi$
$677$	3300.00			0.187340			0.0936700	+	0.995603i	$0.470140\pi$
$678$	−1492.84	−	2585.68i	−0.0845608	−	0.146464i
$679$	−454.098	+	786.521i	−0.0256652	+	0.0444535i
$680$	1371.51	+	2375.53i	0.0773458	+	0.133967i
$681$	15314.0	−	26524.6i	0.861722	−	1.49255i
$682$	−14163.2	+	24531.4i	−0.795218	+	1.37736i
$683$	−1847.09			−0.103480			−0.0517400	−	0.998661i	$-0.516477\pi$
$683$	−1847.09			−0.103480			−0.0517400	+	0.998661i	$0.516477\pi$
$684$	−3421.32	−	2714.78i	−0.191253	−	0.151758i
$685$	12108.8			0.675408
$686$	−453.100	+	784.791i	−0.0252178	+	0.0436785i
$687$	−14724.1	+	25502.9i	−0.817698	+	1.41630i
$688$	−2122.80	−	3676.80i	−0.117632	−	0.203745i
$689$	175.696	−	304.314i	0.00971478	−	0.0168265i
$690$	−1427.42	−	2472.36i	−0.0787547	−	0.136407i
$691$	34144.6			1.87977			0.939886	−	0.341489i	$-0.110931\pi$
$691$	34144.6			1.87977			0.939886	+	0.341489i	$0.110931\pi$
$692$	13936.0			0.765561
$693$	−218.489	−	378.435i	−0.0119765	−	0.0207439i
$694$	−5468.76	−	9472.17i	−0.299123	−	0.518096i
$695$	10911.7			0.595544
$696$	15712.2			0.855703
$697$	9946.06	+	17227.1i	0.540508	+	0.936187i
$698$	−3235.26	+	5603.63i	−0.175439	+	0.303869i
$699$	−2626.00	−	4548.36i	−0.142095	−	0.246116i
$700$	118.730	−	205.646i	0.00641082	−	0.0111039i
$701$	−3366.06	+	5830.18i	−0.181361	+	0.314127i	−0.942344	−	0.334645i	$-0.891384\pi$
$701$	−3366.06	+	5830.18i	−0.181361	+	0.314127i	0.760983	+	0.648772i	$0.224717\pi$
$702$	−460.062			−0.0247349
$703$	255.922	−	1726.50i	0.0137301	−	0.0926262i
$704$	3209.57			0.171826
$705$	−2627.95	+	4551.74i	−0.140389	+	0.243161i
$706$	−6191.72	+	10724.4i	−0.330069	+	0.571696i
$707$	−26.3981	−	45.7228i	−0.00140425	−	0.00243223i
$708$	5778.99	−	10009.5i	0.306762	−	0.531328i
$709$	−15459.5	−	26776.7i	−0.818892	−	1.41836i	−0.906499	−	0.422208i	$-0.861255\pi$
$709$	−15459.5	−	26776.7i	−0.818892	−	1.41836i	0.0876068	−	0.996155i	$-0.472078\pi$
$710$	13274.4			0.701660
$711$	5034.87			0.265573
$712$	1621.95	+	2809.31i	0.0853726	+	0.147870i
$713$	5361.12	+	9285.73i	0.281593	+	0.487733i
$714$	484.406			0.0253900
$715$	781.229			0.0408620
$716$	4370.45	+	7569.85i	0.228117	+	0.395110i
$717$	8669.39	−	15015.8i	0.451554	−	0.782115i
$718$	−6407.07	−	11097.4i	−0.333022	−	0.576811i
$719$	3730.56	−	6461.52i	0.193500	−	0.335152i	−0.752908	−	0.658126i	$-0.771349\pi$
$719$	3730.56	−	6461.52i	0.193500	−	0.335152i	0.946408	+	0.322974i	$0.104683\pi$
$720$	−625.562	+	1083.51i	−0.0323796	+	0.0560831i
$721$	1189.47			0.0614399
$722$	−10010.4	+	9379.57i	−0.515993	+	0.483478i
$723$	−25894.0			−1.33196
$724$	−2111.78	+	3657.72i	−0.108403	+	0.187760i
$725$	13914.7	−	24101.0i	0.712800	−	1.23461i
$726$	−7505.35	−	12999.6i	−0.383677	−	0.664548i
$727$	5473.85	−	9480.99i	0.279249	−	0.483673i	−0.691949	−	0.721946i	$-0.743248\pi$
$727$	5473.85	−	9480.99i	0.279249	−	0.483673i	0.971198	+	0.238273i	$0.0765813\pi$
$728$	6.94358	+	12.0266i	0.000353498	+	0.000612276i
$729$	2977.33			0.151264
$730$	5580.54			0.282938
$731$	−7670.02	−	13284.9i	−0.388079	−	0.672173i
$732$	1374.78	+	2381.19i	0.0694171	+	0.120234i
$733$	−36104.8			−1.81932			−0.909661	−	0.415352i	$-0.863659\pi$
$733$	−36104.8			−1.81932			−0.909661	+	0.415352i	$0.863659\pi$
$734$	−16737.9			−0.841698
$735$	−6439.78	−	11154.0i	−0.323177	−	0.559758i
$736$	607.449	−	1052.13i	0.0304224	−	0.0526931i
$737$	−661.875	−	1146.40i	−0.0330807	−	0.0572975i
$738$	−4536.50	+	7857.45i	−0.226275	+	0.391920i
$739$	−11391.7	+	19731.0i	−0.567052	+	0.982162i	0.429804	+	0.902922i	$0.358583\pi$
$739$	−11391.7	+	19731.0i	−0.567052	+	0.982162i	−0.996856	+	0.0792399i	$0.974751\pi$
$740$	−499.977			−0.0248372
$741$	202.188	−	1364.00i	0.0100237	−	0.0676219i
$742$	176.844			0.00874953
$743$	−11318.0	+	19603.4i	−0.558839	+	0.967937i	0.438755	+	0.898607i	$0.355420\pi$
$743$	−11318.0	+	19603.4i	−0.558839	+	0.967937i	−0.997594	+	0.0693306i	$0.977914\pi$
$744$	7161.13	−	12403.4i	0.352876	−	0.611200i
$745$	988.289	+	1711.77i	0.0486015	+	0.0841802i
$746$	10254.9	−	17762.0i	0.503297	−	0.871735i
$747$	−8716.44	−	15097.3i	−0.426932	−	0.739467i
$748$	11596.7			0.566867
$749$	45.7721			0.00223294
$750$	8076.80	+	13989.4i	0.393231	+	0.681096i
$751$	1429.62	+	2476.17i	0.0694642	+	0.120315i	0.898666	−	0.438634i	$-0.144538\pi$
$751$	1429.62	+	2476.17i	0.0694642	+	0.120315i	−0.829201	+	0.558950i	$0.811204\pi$
$752$	−2236.69			−0.108463
$753$	16080.6			0.778235
$754$	813.763	+	1409.48i	0.0393044	+	0.0680772i
$755$	−9022.44	+	15627.3i	−0.434914	+	0.753294i
$756$	−115.767	−	200.515i	−0.00556933	−	0.00964636i
$757$	−10045.6	+	17399.4i	−0.482315	+	0.835394i	−0.999794	−	0.0203020i	$-0.993537\pi$
$757$	−10045.6	+	17399.4i	−0.482315	+	0.835394i	0.517479	+	0.855696i	$0.326871\pi$
$758$	6607.19	−	11444.0i	0.316601	−	0.548370i
$759$	−12069.3			−0.577193
$760$	3078.29	+	2442.59i	0.146923	+	0.116582i
$761$	−9968.77			−0.474859			−0.237430	−	0.971405i	$-0.576305\pi$
$761$	−9968.77			−0.474859			−0.237430	+	0.971405i	$0.576305\pi$
$762$	−5694.50	+	9863.17i	−0.270722	+	0.468904i
$763$	−210.534	+	364.656i	−0.00998933	+	0.0173020i
$764$	−5317.02	−	9209.35i	−0.251784	−	0.436103i
$765$	−2260.25	+	3914.87i	−0.106823	+	0.185023i
$766$	−9.95746	−	17.2468i	−0.000469684	−	0.000813516i
$767$	1197.22			0.0563611
$768$	−1622.81			−0.0762473
$769$	−10031.2	−	17374.5i	−0.470396	−	0.814749i	0.529031	−	0.848602i	$-0.322555\pi$
$769$	−10031.2	−	17374.5i	−0.470396	−	0.814749i	−0.999427	+	0.0338532i	$0.989222\pi$
$770$	196.583	+	340.493i	0.00920049	+	0.0159357i
$771$	41854.1			1.95504
$772$	−18322.0			−0.854173
$773$	−294.482	−	510.058i	−0.0137022	−	0.0237329i	0.859093	−	0.511820i	$-0.171028\pi$
$773$	−294.482	−	510.058i	−0.0137022	−	0.0237329i	−0.872795	+	0.488087i	$0.837695\pi$
$774$	3498.38	−	6059.37i	0.162463	−	0.281395i
$775$	−12683.8	−	21969.0i	−0.587891	−	1.01826i
$776$	5496.59	−	9520.38i	0.254273	−	0.440414i
$777$	−44.1468	+	76.4644i	−0.00203830	+	0.00353043i
$778$	24763.0			1.14113
$779$	22323.4	+	17713.4i	1.02673	+	0.814697i
$780$	−395.000			−0.0181324
$781$	28060.0	−	48601.4i	1.28562	−	2.22675i
$782$	2194.81	−	3801.52i	0.100366	−	0.173839i
$783$	−13567.5	−	23499.6i	−0.619237	−	1.07255i
$784$	2740.51	−	4746.69i	0.124841	−	0.216231i
$785$	−5838.49	−	10112.6i	−0.265458	−	0.459787i
$786$	8297.03			0.376521
$787$	−14959.0			−0.677550			−0.338775	−	0.940867i	$-0.610013\pi$
$787$	−14959.0			−0.677550			−0.338775	+	0.940867i	$0.610013\pi$
$788$	9765.83	+	16914.9i	0.441489	+	0.764682i
$789$	12375.6	+	21435.2i	0.558409	+	0.967192i
$790$	−4530.07			−0.204016
$791$	155.644			0.00699630
$792$	2644.69	+	4580.73i	0.118655	+	0.205517i
$793$	−142.405	+	246.652i	−0.00637696	+	0.0110452i
$794$	603.931	+	1046.04i	0.0269933	+	0.0467539i
$795$	−2515.04	+	4356.18i	−0.112200	+	0.194337i
$796$	4715.84	−	8168.08i	0.209986	−	0.363706i
$797$	−18464.2			−0.820622			−0.410311	−	0.911946i	$-0.634580\pi$
$797$	−18464.2			−0.820622			−0.410311	+	0.911946i	$0.634580\pi$
$798$	645.367	−	255.107i	0.0286287	−	0.0113166i
$799$	−8081.53			−0.357827
$800$	−1437.16	+	2489.23i	−0.0635140	+	0.110009i
$801$	−2672.98	+	4629.73i	−0.117909	+	0.204224i
$802$	10340.3	+	17909.9i	0.455271	+	0.788553i
$803$	11796.4	−	20432.0i	0.518413	−	0.897919i
$804$	334.653	+	579.637i	0.0146795	+	0.0254256i
$805$	148.823			0.00651592
$806$	1483.55			0.0648336
$807$	−5060.86	−	8765.67i	−0.220757	−	0.382362i
$808$	319.533	+	553.448i	0.0139123	+	0.0240968i
$809$	13632.5			0.592449			0.296225	−	0.955118i	$-0.404272\pi$
$809$	13632.5			0.592449			0.296225	+	0.955118i	$0.404272\pi$
$810$	10808.2			0.468842
$811$	−11453.1	−	19837.3i	−0.495896	−	0.858916i	0.504093	−	0.863649i	$-0.331827\pi$
$811$	−11453.1	−	19837.3i	−0.495896	−	0.858916i	−0.999989	+	0.00473284i	$0.998493\pi$
$812$	−409.540	+	709.345i	−0.0176996	+	0.0306565i
$813$	12714.3	+	22021.8i	0.548473	+	0.949984i
$814$	−1056.87	+	1830.56i	−0.0455079	+	0.0788220i
$815$	3367.63	−	5832.91i	0.144740	−	0.250697i
$816$	−5863.45			−0.251546
$817$	−17215.0	−	13659.9i	−0.737179	−	0.584944i
$818$	322.840			0.0137993
$819$	−11.4430	+	19.8199i	−0.000488219	+	0.000845620i
$820$	4081.67	−	7069.66i	0.173827	−	0.301077i
$821$	21072.8	+	36499.1i	0.895792	+	1.55156i	0.832822	+	0.553541i	$0.186724\pi$
$821$	21072.8	+	36499.1i	0.895792	+	1.55156i	0.0629700	+	0.998015i	$0.479943\pi$
$822$	−12941.8	+	22415.9i	−0.549145	+	0.951147i
$823$	14169.1	+	24541.6i	0.600126	+	1.03945i	0.992801	+	0.119772i	$0.0382162\pi$
$823$	14169.1	+	24541.6i	0.600126	+	1.03945i	−0.392676	+	0.919677i	$0.628450\pi$
$824$	−14397.8			−0.608704
$825$	28554.7			1.20503
$826$	301.260	+	521.798i	0.0126903	+	0.0219802i
$827$	−6794.88	−	11769.1i	−0.285709	−	0.494862i	0.687072	−	0.726589i	$-0.258896\pi$
$827$	−6794.88	−	11769.1i	−0.285709	−	0.494862i	−0.972781	+	0.231727i	$0.925562\pi$
$828$	2002.15			0.0840333
$829$	−25202.9			−1.05589			−0.527946	−	0.849278i	$-0.677038\pi$
$829$	−25202.9			−1.05589			−0.527946	+	0.849278i	$0.677038\pi$
$830$	7842.53	+	13583.7i	0.327974	+	0.568067i
$831$	15374.8	−	26629.9i	0.641810	−	1.11165i
$832$	−84.0480	−	145.575i	−0.00350221	−	0.00606601i
$833$	9901.87	−	17150.5i	0.411860	−	0.713363i
$834$	−11662.3	+	20199.7i	−0.484211	+	0.838679i
$835$	4687.47			0.194271
$836$	15450.1	−	6107.26i	0.639178	−	0.252660i
$837$	−24734.6			−1.02145
$838$	7483.41	−	12961.6i	0.308485	−	0.534311i
$839$	1877.33	−	3251.63i	0.0772497	−	0.133800i	−0.824813	−	0.565406i	$-0.808719\pi$
$839$	1877.33	−	3251.63i	0.0772497	−	0.133800i	0.902062	+	0.431606i	$0.142053\pi$
$840$	−99.3954	−	172.158i	−0.00408270	−	0.00707144i
$841$	−35802.2	+	62011.2i	−1.46796	+	2.54259i
$842$	6049.53	+	10478.1i	0.247602	+	0.428859i
$843$	−39929.8			−1.63138
$844$	−12861.0			−0.524520
$845$	6494.83	+	11249.4i	0.264413	+	0.457977i
$846$	−1843.03	−	3192.23i	−0.0748993	−	0.129729i
$847$	782.511			0.0317443
$848$	−2140.60			−0.0866844
$849$	18247.1	+	31604.9i	0.737619	+	1.27759i
$850$	−5192.67	+	8993.97i	−0.209538	+	0.362930i
$851$	400.052	+	692.910i	0.0161147	+	0.0279115i
$852$	−14187.5	+	24573.5i	−0.570489	+	0.988117i
$853$	−11744.1	+	20341.5i	−0.471409	+	0.816505i	−0.999465	−	0.0327050i	$-0.989588\pi$
$853$	−11744.1	+	20341.5i	−0.471409	+	0.816505i	0.528056	+	0.849210i	$0.322921\pi$
$854$	−143.335			−0.00574336
$855$	−949.581	+	6406.06i	−0.0379824	+	0.256237i
$856$	−554.044			−0.0221225
$857$	−1651.39	+	2860.29i	−0.0658231	+	0.114009i	−0.897059	−	0.441911i	$-0.854301\pi$
$857$	−1651.39	+	2860.29i	−0.0658231	+	0.114009i	0.831236	+	0.555920i	$0.187634\pi$
$858$	−834.970	+	1446.21i	−0.0332231	+	0.0575441i
$859$	4411.39	+	7640.75i	0.175221	+	0.303491i	0.940238	−	0.340519i	$-0.110603\pi$
$859$	4411.39	+	7640.75i	0.175221	+	0.303491i	−0.765017	+	0.644010i	$0.777269\pi$
$860$	−3147.63	+	5451.85i	−0.124806	+	0.216170i
$861$	−720.804	−	1248.47i	−0.0285307	−	0.0494166i
$862$	−21819.4			−0.862148
$863$	−20731.7			−0.817745			−0.408873	−	0.912591i	$-0.634078\pi$
$863$	−20731.7			−0.817745			−0.408873	+	0.912591i	$0.634078\pi$
$864$	1401.29	+	2427.11i	0.0551771	+	0.0955695i
$865$	−10332.0	−	17895.5i	−0.406124	−	0.703427i
$866$	15297.9			0.600282
$867$	9958.37			0.390085
$868$	373.312	+	646.595i	0.0145979	+	0.0252844i
$869$	−9575.87	+	16585.9i	−0.373808	+	0.647455i
$870$	−11648.8	−	20176.3i	−0.453944	−	0.786253i
$871$	−34.6646	+	60.0408i	−0.00134852	+	0.00233571i
$872$	2548.40	−	4413.95i	0.0989674	−	0.171417i
$873$	18116.8			0.702359
$874$	922.086	−	6220.58i	0.0356865	−	0.240749i
$875$	−842.091			−0.0325347
$876$	−5964.43	+	10330.7i	−0.230045	+	0.398450i
$877$	5516.25	−	9554.43i	0.212395	−	0.367879i	−0.740068	−	0.672532i	$-0.765207\pi$
$877$	5516.25	−	9554.43i	0.212395	−	0.367879i	0.952464	+	0.304652i	$0.0985402\pi$
$878$	−11415.9	−	19772.9i	−0.438801	−	0.760025i
$879$	17192.3	−	29778.0i	0.659708	−	1.14265i
$880$	−2379.53	−	4121.46i	−0.0911521	−	0.157880i
$881$	−23834.2			−0.911457			−0.455728	−	0.890119i	$-0.650621\pi$
$881$	−23834.2			−0.911457			−0.455728	+	0.890119i	$0.650621\pi$
$882$	9032.70			0.344838
$883$	22621.3	+	39181.3i	0.862138	+	1.49327i	0.869861	+	0.493296i	$0.164208\pi$
$883$	22621.3	+	39181.3i	0.862138	+	1.49327i	−0.00772377	+	0.999970i	$0.502459\pi$
$884$	−303.678	−	525.987i	−0.0115541	−	0.0200123i
$885$	−17137.8			−0.650940
$886$	6305.31			0.239087
$887$	1818.47	+	3149.68i	0.0688369	+	0.119229i	0.898390	−	0.439199i	$-0.144738\pi$
$887$	1818.47	+	3149.68i	0.0688369	+	0.119229i	−0.829553	+	0.558428i	$0.811405\pi$
$888$	534.371	−	925.557i	0.0201940	−	0.0349771i
$889$	−296.856	−	514.169i	−0.0111994	−	0.0193978i
$890$	2404.98	−	4165.56i	0.0905790	−	0.156887i
$891$	22846.9	−	39572.0i	0.859035	−	1.48789i
$892$	13858.6			0.520202
$893$	−10766.9	+	4256.04i	−0.403472	+	0.159488i
$894$	−4225.10			−0.158063
$895$	6480.38	−	11224.3i	0.242028	−	0.419205i
$896$	42.2986	−	73.2633i	0.00157712	−	0.00273165i
$897$	316.056	+	547.425i	0.0117645	+	0.0203768i
$898$	5217.04	−	9036.17i	0.193869	−	0.335792i
$899$	43750.8	+	75778.6i	1.62310	+	2.81130i
$900$	−4736.87			−0.175439
$901$	−7734.30			−0.285979
$902$	−17256.1	−	29888.4i	−0.636989	−	1.10330i
$903$	555.856	+	962.771i	0.0204848	+	0.0354806i
$904$	−1883.98			−0.0693146
$905$	6262.58			0.230028
$906$	−19286.2	−	33404.7i	−0.707220	−	1.22494i
$907$	22853.4	−	39583.2i	0.836641	−	1.44911i	−0.0560457	−	0.998428i	$-0.517849\pi$
$907$	22853.4	−	39583.2i	0.836641	−	1.44911i	0.892687	−	0.450677i	$-0.148817\pi$
$908$	−9663.21	−	16737.2i	−0.353177	−	0.611721i
$909$	−526.590	+	912.081i	−0.0192144	+	0.0332803i
$910$	10.2957	−	17.8327i	0.000375055	−	0.000649614i
$911$	−38271.0			−1.39185			−0.695924	−	0.718115i	$-0.745005\pi$
$911$	−38271.0			−1.39185			−0.695924	+	0.718115i	$0.745005\pi$
$912$	−7811.79	+	3087.92i	−0.283634	+	0.112117i
$913$	66311.6			2.40372
$914$	15868.7	−	27485.4i	0.574277	−	0.994678i
$915$	2038.48	−	3530.75i	0.0736504	−	0.127566i
$916$	9290.98	+	16092.5i	0.335134	+	0.580469i
$917$	−216.263	+	374.579i	−0.00778804	+	0.0134893i
$918$	5063.09	+	8769.53i	0.182034	+	0.315292i
$919$	15748.1			0.565267			0.282634	−	0.959228i	$-0.408792\pi$
$919$	15748.1			0.565267			0.282634	+	0.959228i	$0.408792\pi$
$920$	−1801.41			−0.0645553
$921$	17844.1	+	30906.8i	0.638417	+	1.10577i
$922$	−4341.17	−	7519.12i	−0.155064	−	0.268578i
$923$	−2939.19			−0.104815
$924$	−840.427			−0.0299221
$925$	−946.478	−	1639.35i	−0.0336432	−	0.0582718i
$926$	−1394.23	+	2414.87i	−0.0494785	+	0.0856993i
$927$	−11863.8	−	20548.7i	−0.420343	−	0.728056i
$928$	4957.25	−	8586.20i	0.175355	−	0.303724i
$929$	−7167.36	+	12414.2i	−0.253125	+	0.438426i	−0.964385	−	0.264504i	$-0.914792\pi$
$929$	−7167.36	+	12414.2i	−0.253125	+	0.438426i	0.711259	+	0.702930i	$0.248125\pi$
$930$	−21236.6			−0.748792
$931$	4159.99	−	28064.1i	0.146443	−	0.987932i
$932$	−3314.04			−0.116475
$933$	9679.81	−	16765.9i	0.339660	−	0.588308i
$934$	6138.35	−	10631.9i	0.215046	−	0.372471i
$935$	−8597.61	−	14891.5i	−0.300718	−	0.520860i
$936$	138.511	−	239.908i	0.00483694	−	0.00837782i
$937$	−9420.92	−	16317.5i	−0.328461	−	0.568911i	0.653746	−	0.756714i	$-0.273197\pi$
$937$	−9420.92	−	16317.5i	−0.328461	−	0.568911i	−0.982207	+	0.187803i	$0.939863\pi$
$938$	−34.8911			−0.00121454
$939$	20924.9			0.727220
$940$	1658.25	+	2872.18i	0.0575385	+	0.0996596i
$941$	−7510.34	−	13008.3i	−0.260181	−	0.450647i	0.706109	−	0.708103i	$-0.250449\pi$
$941$	−7510.34	−	13008.3i	−0.260181	−	0.450647i	−0.966290	+	0.257457i	$0.917116\pi$
$942$	24960.5			0.863331
$943$	−13063.6			−0.451125
$944$	−3646.58	−	6316.06i	−0.125727	−	0.217765i
$945$	−171.656	+	297.317i	−0.00590896	+	0.0102346i
$946$	13307.2	+	23048.8i	0.457352	+	0.792156i
$947$	11229.2	−	19449.5i	0.385321	−	0.667396i	−0.606492	−	0.795089i	$-0.707424\pi$
$947$	11229.2	−	19449.5i	0.385321	−	0.667396i	0.991814	+	0.127693i	$0.0407573\pi$
$948$	4841.70	−	8386.06i	0.165877	−	0.287307i
$949$	−1235.63			−0.0422659
$950$	−2181.55	+	14717.2i	−0.0745041	+	0.502620i
$951$	20096.5			0.685249
$952$	152.831	−	264.712i	0.00520304	−	0.00901193i
$953$	7481.14	−	12957.7i	0.254289	−	0.440442i	−0.710413	−	0.703785i	$-0.751492\pi$
$953$	7481.14	−	12957.7i	0.254289	−	0.440442i	0.964702	+	0.263343i	$0.0848251\pi$
$954$	−1763.85	−	3055.08i	−0.0598603	−	0.103681i
$955$	−7883.92	+	13655.3i	−0.267139	+	0.462698i
$956$	−5470.44	−	9475.08i	−0.185070	−	0.320550i
$957$	−98495.0			−3.32695
$958$	−14265.9			−0.481117
$959$	−674.659	−	1168.54i	−0.0227173	−	0.0393475i
$960$	1203.12	+	2083.87i	0.0404486	+	0.0700590i
$961$	49970.0			1.67735
$962$	110.704			0.00371023
$963$	−456.532	−	790.737i	−0.0152768	−	0.0264602i
$964$	−8169.65	+	14150.2i	−0.272953	+	0.472768i
$965$	13583.6	+	23527.5i	0.453132	+	0.784848i
$966$	−159.061	+	275.501i	−0.00529782	+	0.00917609i
$967$	20515.6	−	35534.1i	0.682253	−	1.18170i	−0.292039	−	0.956407i	$-0.594334\pi$
$967$	20515.6	−	35534.1i	0.682253	−	1.18170i	0.974292	−	0.225290i	$-0.0723331\pi$
$968$	−9471.84			−0.314500
$969$	−28225.2	+	11157.1i	−0.935732	+	0.369885i
$970$	−16300.4			−0.539560
$971$	−2012.11	+	3485.08i	−0.0665002	+	0.115182i	−0.897358	−	0.441302i	$-0.854517\pi$
$971$	−2012.11	+	3485.08i	−0.0665002	+	0.115182i	0.830858	+	0.556484i	$0.187850\pi$
$972$	−6822.35	+	11816.7i	−0.225131	+	0.389938i
$973$	−607.958	−	1053.01i	−0.0200311	−	0.0346949i
$974$	−14396.6	+	24935.6i	−0.473611	+	0.820318i
$975$	−747.753	−	1295.15i	−0.0245613	−	0.0425414i
$976$	1734.99			0.0569012
$977$	−42051.2			−1.37701			−0.688505	−	0.725232i	$-0.741733\pi$
$977$	−42051.2			−1.37701			−0.688505	+	0.725232i	$0.741733\pi$
$978$	7198.59	+	12468.3i	0.235363	+	0.407661i
$979$	−10167.5	−	17610.7i	−0.331926	−	0.574913i
$980$	−8127.08			−0.264908
$981$	8399.51			0.273370
$982$	7655.81	+	13260.3i	0.248785	+	0.430908i
$983$	−21502.2	+	37242.9i	−0.697674	+	1.20841i	0.271597	+	0.962411i	$0.412448\pi$
$983$	−21502.2	+	37242.9i	−0.697674	+	1.20841i	−0.969271	+	0.245996i	$0.920885\pi$
$984$	8724.91	+	15112.0i	0.282663	+	0.489586i
$985$	14480.5	−	25080.9i	0.468413	−	0.811315i
$986$	17911.3	−	31023.3i	0.578511	−	1.00201i
$987$	585.679			0.0188879
$988$	−681.591	−	540.835i	−0.0219477	−	0.0174152i
$989$	10074.2			0.323903
$990$	3921.46	−	6792.17i	0.125891	−	0.218050i
$991$	−3307.45	+	5728.68i	−0.106019	+	0.183630i	−0.914154	−	0.405367i	$-0.867144\pi$
$991$	−3307.45	+	5728.68i	−0.106019	+	0.183630i	0.808135	+	0.588997i	$0.200477\pi$
$992$	−4518.72	−	7826.65i	−0.144626	−	0.250500i
$993$	4484.10	−	7766.69i	0.143302	−	0.248206i
$994$	−739.600	−	1281.02i	−0.0236003	−	0.0408769i
$995$	−13985.0			−0.445583
$996$	−33528.1			−1.06665
$997$	23301.4	+	40359.2i	0.740184	+	1.28204i	0.952411	+	0.304815i	$0.0985948\pi$
$997$	23301.4	+	40359.2i	0.740184	+	1.28204i	−0.212228	+	0.977220i	$0.568072\pi$
$998$	18638.1	+	32282.1i	0.591161	+	1.02392i
$999$	−1845.72			−0.0584544

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.4.c.c.11.3	yes	6
3.2	odd	2		342.4.g.f.163.2		6
4.3	odd	2		304.4.i.e.49.1		6
19.7	even	3	inner	38.4.c.c.7.3	✓	6
19.8	odd	6		722.4.a.k.1.3		3
19.11	even	3		722.4.a.j.1.1		3
57.26	odd	6		342.4.g.f.235.2		6
76.7	odd	6		304.4.i.e.273.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.4.c.c.7.3	✓	6	19.7	even	3	inner
38.4.c.c.11.3	yes	6	1.1	even	1	trivial
304.4.i.e.49.1		6	4.3	odd	2
304.4.i.e.273.1		6	76.7	odd	6
342.4.g.f.163.2		6	3.2	odd	2
342.4.g.f.235.2		6	57.26	odd	6
722.4.a.j.1.1		3	19.11	even	3
722.4.a.k.1.3		3	19.8	odd	6

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	38.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(3.16954 - 5.48981i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-2.96554 + 5.13646i) q^{5} +(-6.33908 - 10.9796i) q^{6} +0.660916 q^{7} -8.00000 q^{8} +(-6.59199 - 11.4177i) q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(3.16954 - 5.48981i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-2.96554 + 5.13646i) q^{5} +(-6.33908 - 10.9796i) q^{6} +0.660916 q^{7} -8.00000 q^{8} +(-6.59199 - 11.4177i) q^{9} +(5.93108 + 10.2729i) q^{10} +50.1496 q^{11} -25.3563 q^{12} +(-1.31325 - 2.27462i) q^{13} +(0.660916 - 1.14474i) q^{14} +(18.7988 + 32.5605i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-28.9052 + 50.0654i) q^{17} -26.3680 q^{18} +(-12.1437 + 81.9239i) q^{19} +23.7243 q^{20} +(2.09480 - 3.62830i) q^{21} +(50.1496 - 86.8616i) q^{22} +(-18.9828 - 32.8792i) q^{23} +(-25.3563 + 43.9185i) q^{24} +(44.9112 + 77.7884i) q^{25} -5.25300 q^{26} +87.5809 q^{27} +(-1.32183 - 2.28948i) q^{28} +(-154.914 - 268.319i) q^{29} +75.1952 q^{30} -282.420 q^{31} +(16.0000 + 27.7128i) q^{32} +(158.951 - 275.312i) q^{33} +(57.8105 + 100.131i) q^{34} +(-1.95997 + 3.39477i) q^{35} +(-26.3680 + 45.6707i) q^{36} -21.0744 q^{37} +(129.753 + 102.957i) q^{38} -16.6496 q^{39} +(23.7243 - 41.0917i) q^{40} +(172.046 - 297.992i) q^{41} +(-4.18960 - 7.25660i) q^{42} +(-132.675 + 229.800i) q^{43} +(-100.299 - 173.723i) q^{44} +78.1953 q^{45} -75.9312 q^{46} +(69.8967 + 121.065i) q^{47} +(50.7127 + 87.8369i) q^{48} -342.563 q^{49} +179.645 q^{50} +(183.233 + 317.368i) q^{51} +(-5.25300 + 9.09846i) q^{52} +(66.8936 + 115.863i) q^{53} +(87.5809 - 151.694i) q^{54} +(-148.721 + 257.592i) q^{55} -5.28733 q^{56} +(411.257 + 326.328i) q^{57} -619.656 q^{58} +(-227.911 + 394.754i) q^{59} +(75.1952 - 130.242i) q^{60} +(-54.2184 - 93.9090i) q^{61} +(-282.420 + 489.166i) q^{62} +(-4.35675 - 7.54612i) q^{63} +64.0000 q^{64} +15.5780 q^{65} +(-317.902 - 550.623i) q^{66} +(-13.1980 - 22.8596i) q^{67} +231.242 q^{68} -240.667 q^{69} +(3.91994 + 6.78954i) q^{70} +(559.526 - 969.128i) q^{71} +(52.7360 + 91.3414i) q^{72} +(235.224 - 407.421i) q^{73} +(-21.0744 + 36.5020i) q^{74} +569.391 q^{75} +(308.080 - 121.781i) q^{76} +33.1446 q^{77} +(-16.6496 + 28.8380i) q^{78} +(-190.946 + 330.729i) q^{79} +(-47.4486 - 82.1834i) q^{80} +(455.575 - 789.079i) q^{81} +(-344.092 - 595.985i) q^{82} +1322.28 q^{83} -16.7584 q^{84} +(-171.439 - 296.942i) q^{85} +(265.350 + 459.600i) q^{86} -1964.03 q^{87} -401.197 q^{88} +(-202.744 - 351.163i) q^{89} +(78.1953 - 135.438i) q^{90} +(-0.867948 - 1.50333i) q^{91} +(-75.9312 + 131.517i) q^{92} +(-895.142 + 1550.43i) q^{93} +279.587 q^{94} +(-384.787 - 305.324i) q^{95} +202.851 q^{96} +(-687.074 + 1190.05i) q^{97} +(-342.563 + 593.337i) q^{98} +(-330.586 - 572.591i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 5 q^{3} - 12 q^{4} - q^{5} + 10 q^{6} + 52 q^{7} - 48 q^{8} - 54 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 - 5 * q^3 - 12 * q^4 - q^5 + 10 * q^6 + 52 * q^7 - 48 * q^8 - 54 * q^9	\( 6 q + 6 q^{2} - 5 q^{3} - 12 q^{4} - q^{5} + 10 q^{6} + 52 q^{7} - 48 q^{8} - 54 q^{9} + 2 q^{10} + 8 q^{11} + 40 q^{12} + 129 q^{13} + 52 q^{14} - 77 q^{15} - 48 q^{16} - 51 q^{17} - 216 q^{18} + 40 q^{19} + 8 q^{20} - 170 q^{21} + 8 q^{22} + 47 q^{23} + 40 q^{24} - 338 q^{25} + 516 q^{26} + 718 q^{27} - 104 q^{28} - 125 q^{29} - 308 q^{30} - 100 q^{31} + 96 q^{32} + 274 q^{33} + 102 q^{34} - 84 q^{35} - 216 q^{36} - 376 q^{37} + 322 q^{38} - 1546 q^{39} + 8 q^{40} + 475 q^{41} + 340 q^{42} - 73 q^{43} - 16 q^{44} + 3188 q^{45} + 188 q^{46} - 241 q^{47} - 80 q^{48} - 1354 q^{49} - 1352 q^{50} + 69 q^{51} + 516 q^{52} + 29 q^{53} + 718 q^{54} - 1838 q^{55} - 416 q^{56} + 1755 q^{57} - 500 q^{58} - 1065 q^{59} - 308 q^{60} - 981 q^{61} - 100 q^{62} - 872 q^{63} + 384 q^{64} + 586 q^{65} - 548 q^{66} + 877 q^{67} + 408 q^{68} - 1526 q^{69} + 168 q^{70} + 2135 q^{71} + 432 q^{72} + 667 q^{73} - 376 q^{74} + 4584 q^{75} + 484 q^{76} - 492 q^{77} - 1546 q^{78} + 1671 q^{79} - 16 q^{80} - 1287 q^{81} - 950 q^{82} + 1176 q^{83} + 1360 q^{84} - 1929 q^{85} + 146 q^{86} - 6430 q^{87} - 64 q^{88} + 693 q^{89} + 3188 q^{90} + 1676 q^{91} + 188 q^{92} - 3138 q^{93} - 964 q^{94} + 4489 q^{95} - 320 q^{96} - 985 q^{97} - 1354 q^{98} - 3184 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 5 * q^3 - 12 * q^4 - q^5 + 10 * q^6 + 52 * q^7 - 48 * q^8 - 54 * q^9 + 2 * q^10 + 8 * q^11 + 40 * q^12 + 129 * q^13 + 52 * q^14 - 77 * q^15 - 48 * q^16 - 51 * q^17 - 216 * q^18 + 40 * q^19 + 8 * q^20 - 170 * q^21 + 8 * q^22 + 47 * q^23 + 40 * q^24 - 338 * q^25 + 516 * q^26 + 718 * q^27 - 104 * q^28 - 125 * q^29 - 308 * q^30 - 100 * q^31 + 96 * q^32 + 274 * q^33 + 102 * q^34 - 84 * q^35 - 216 * q^36 - 376 * q^37 + 322 * q^38 - 1546 * q^39 + 8 * q^40 + 475 * q^41 + 340 * q^42 - 73 * q^43 - 16 * q^44 + 3188 * q^45 + 188 * q^46 - 241 * q^47 - 80 * q^48 - 1354 * q^49 - 1352 * q^50 + 69 * q^51 + 516 * q^52 + 29 * q^53 + 718 * q^54 - 1838 * q^55 - 416 * q^56 + 1755 * q^57 - 500 * q^58 - 1065 * q^59 - 308 * q^60 - 981 * q^61 - 100 * q^62 - 872 * q^63 + 384 * q^64 + 586 * q^65 - 548 * q^66 + 877 * q^67 + 408 * q^68 - 1526 * q^69 + 168 * q^70 + 2135 * q^71 + 432 * q^72 + 667 * q^73 - 376 * q^74 + 4584 * q^75 + 484 * q^76 - 492 * q^77 - 1546 * q^78 + 1671 * q^79 - 16 * q^80 - 1287 * q^81 - 950 * q^82 + 1176 * q^83 + 1360 * q^84 - 1929 * q^85 + 146 * q^86 - 6430 * q^87 - 64 * q^88 + 693 * q^89 + 3188 * q^90 + 1676 * q^91 + 188 * q^92 - 3138 * q^93 - 964 * q^94 + 4489 * q^95 - 320 * q^96 - 985 * q^97 - 1354 * q^98 - 3184 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more