LMFDB - Embedded newform 21.4.e.b.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,4,Mod(4,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("21.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	21.e (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:	$1.23904011012$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.9924270768.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 25x^{4} + 12x^{3} + 582x^{2} - 144x + 36 $ x^6 - x^5 + 25x^4 + 12x^3 + 582x^2 - 144x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			4.1
Root			$2.65415 + 4.59712i$ of defining polynomial
Character	$\chi$	$=$	21.4
Dual form			21.4.e.b.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.65415 - 4.59712i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-10.0890 + 17.4746i) q^{4} +(-2.78070 - 4.81631i) q^{5} -15.9249 q^{6} +(9.67799 - 15.7904i) q^{7} +64.6443 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(-2.65415 - 4.59712i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-10.0890 + 17.4746i) q^{4} +(-2.78070 - 4.81631i) q^{5} -15.9249 q^{6} +(9.67799 - 15.7904i) q^{7} +64.6443 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-14.7608 + 25.5664i) q^{10} +(6.95869 - 12.0528i) q^{11} +(30.2670 + 52.4239i) q^{12} +38.6718 q^{13} +(-98.2771 - 2.58082i) q^{14} -16.6842 q^{15} +(-90.8636 - 157.380i) q^{16} +(-21.7394 + 37.6537i) q^{17} +(-23.8873 + 41.3741i) q^{18} +(54.5139 + 94.4208i) q^{19} +112.218 q^{20} +(-26.5077 - 48.8297i) q^{21} -73.8775 q^{22} +(37.4389 + 64.8461i) q^{23} +(96.9665 - 167.951i) q^{24} +(47.0354 - 81.4677i) q^{25} +(-102.641 - 177.779i) q^{26} -27.0000 q^{27} +(178.290 + 328.429i) q^{28} -72.3589 q^{29} +(44.2823 + 76.6992i) q^{30} +(-32.0215 + 55.4629i) q^{31} +(-223.754 + 387.553i) q^{32} +(-20.8761 - 36.1584i) q^{33} +230.798 q^{34} +(-102.963 - 2.70387i) q^{35} +181.602 q^{36} +(-94.3636 - 163.443i) q^{37} +(289.376 - 501.213i) q^{38} +(58.0077 - 100.472i) q^{39} +(-179.756 - 311.347i) q^{40} -24.7923 q^{41} +(-154.121 + 251.460i) q^{42} -243.881 q^{43} +(140.412 + 243.201i) q^{44} +(-25.0263 + 43.3468i) q^{45} +(198.737 - 344.222i) q^{46} +(310.274 + 537.411i) q^{47} -545.182 q^{48} +(-155.673 - 305.638i) q^{49} -499.356 q^{50} +(65.2182 + 112.961i) q^{51} +(-390.159 + 675.776i) q^{52} +(143.919 - 249.276i) q^{53} +(71.6620 + 124.122i) q^{54} -77.4001 q^{55} +(625.627 - 1020.76i) q^{56} +327.083 q^{57} +(192.051 + 332.642i) q^{58} +(-262.526 + 454.708i) q^{59} +(168.327 - 291.551i) q^{60} +(191.718 + 332.065i) q^{61} +339.960 q^{62} +(-166.625 - 4.37567i) q^{63} +921.681 q^{64} +(-107.535 - 186.255i) q^{65} +(-110.816 + 191.939i) q^{66} +(-99.0583 + 171.574i) q^{67} +(-438.657 - 759.776i) q^{68} +224.634 q^{69} +(260.849 + 480.510i) q^{70} +785.432 q^{71} +(-290.900 - 503.853i) q^{72} +(165.570 - 286.776i) q^{73} +(-500.910 + 867.602i) q^{74} +(-141.106 - 244.403i) q^{75} -2199.96 q^{76} +(-122.972 - 226.527i) q^{77} -615.844 q^{78} +(-218.823 - 379.013i) q^{79} +(-505.329 + 875.255i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(65.8024 + 113.973i) q^{82} +241.241 q^{83} +(1120.72 + 29.4308i) q^{84} +241.803 q^{85} +(647.297 + 1121.15i) q^{86} +(-108.538 + 187.994i) q^{87} +(449.840 - 779.145i) q^{88} +(-792.772 - 1373.12i) q^{89} +265.694 q^{90} +(374.265 - 610.643i) q^{91} -1510.88 q^{92} +(96.0646 + 166.389i) q^{93} +(1647.03 - 2852.73i) q^{94} +(303.173 - 525.112i) q^{95} +(671.261 + 1162.66i) q^{96} +79.2754 q^{97} +(-991.877 + 1526.86i) q^{98} -125.256 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} + 9 q^{3} - 25 q^{4} - 11 q^{5} - 6 q^{6} - 13 q^{7} + 78 q^{8} - 27 q^{9}+O(q^{10}) $ 6 * q - q^2 + 9 * q^3 - 25 * q^4 - 11 * q^5 - 6 * q^6 - 13 * q^7 + 78 * q^8 - 27 * q^9	\( 6 q - q^{2} + 9 q^{3} - 25 q^{4} - 11 q^{5} - 6 q^{6} - 13 q^{7} + 78 q^{8} - 27 q^{9} + 55 q^{10} - 35 q^{11} + 75 q^{12} + 124 q^{13} - 326 q^{14} - 66 q^{15} - 241 q^{16} - 48 q^{17} - 9 q^{18} + 202 q^{19} + 878 q^{20} + 3 q^{21} - 14 q^{22} - 216 q^{23} + 117 q^{24} - 130 q^{25} - 274 q^{26} - 162 q^{27} - 201 q^{28} + 106 q^{29} - 165 q^{30} + 95 q^{31} - 683 q^{32} + 105 q^{33} - 48 q^{34} + 56 q^{35} + 450 q^{36} - 262 q^{37} + 398 q^{38} + 186 q^{39} - 21 q^{40} + 488 q^{41} - 219 q^{42} + 720 q^{43} + 905 q^{44} - 99 q^{45} + 1056 q^{46} + 210 q^{47} - 1446 q^{48} - 303 q^{49} - 2756 q^{50} + 144 q^{51} - 324 q^{52} - 393 q^{53} + 27 q^{54} - 2062 q^{55} + 1299 q^{56} + 1212 q^{57} + 1249 q^{58} - 1143 q^{59} + 1317 q^{60} + 70 q^{61} + 2118 q^{62} + 126 q^{63} - 798 q^{64} + 472 q^{65} - 21 q^{66} + 628 q^{67} - 1944 q^{68} - 1296 q^{69} + 3251 q^{70} + 636 q^{71} - 351 q^{72} - 988 q^{73} - 1002 q^{74} + 390 q^{75} - 4680 q^{76} + 1073 q^{77} - 1644 q^{78} - 861 q^{79} - 175 q^{80} - 243 q^{81} - 124 q^{82} + 1038 q^{83} + 1620 q^{84} + 3600 q^{85} + 3208 q^{86} + 159 q^{87} + 891 q^{88} - 1766 q^{89} - 990 q^{90} - 654 q^{91} - 1344 q^{92} - 285 q^{93} + 3294 q^{94} + 736 q^{95} + 2049 q^{96} + 38 q^{97} - 4267 q^{98} + 630 q^{99}+O(q^{100}) \) 6 * q - q^2 + 9 * q^3 - 25 * q^4 - 11 * q^5 - 6 * q^6 - 13 * q^7 + 78 * q^8 - 27 * q^9 + 55 * q^10 - 35 * q^11 + 75 * q^12 + 124 * q^13 - 326 * q^14 - 66 * q^15 - 241 * q^16 - 48 * q^17 - 9 * q^18 + 202 * q^19 + 878 * q^20 + 3 * q^21 - 14 * q^22 - 216 * q^23 + 117 * q^24 - 130 * q^25 - 274 * q^26 - 162 * q^27 - 201 * q^28 + 106 * q^29 - 165 * q^30 + 95 * q^31 - 683 * q^32 + 105 * q^33 - 48 * q^34 + 56 * q^35 + 450 * q^36 - 262 * q^37 + 398 * q^38 + 186 * q^39 - 21 * q^40 + 488 * q^41 - 219 * q^42 + 720 * q^43 + 905 * q^44 - 99 * q^45 + 1056 * q^46 + 210 * q^47 - 1446 * q^48 - 303 * q^49 - 2756 * q^50 + 144 * q^51 - 324 * q^52 - 393 * q^53 + 27 * q^54 - 2062 * q^55 + 1299 * q^56 + 1212 * q^57 + 1249 * q^58 - 1143 * q^59 + 1317 * q^60 + 70 * q^61 + 2118 * q^62 + 126 * q^63 - 798 * q^64 + 472 * q^65 - 21 * q^66 + 628 * q^67 - 1944 * q^68 - 1296 * q^69 + 3251 * q^70 + 636 * q^71 - 351 * q^72 - 988 * q^73 - 1002 * q^74 + 390 * q^75 - 4680 * q^76 + 1073 * q^77 - 1644 * q^78 - 861 * q^79 - 175 * q^80 - 243 * q^81 - 124 * q^82 + 1038 * q^83 + 1620 * q^84 + 3600 * q^85 + 3208 * q^86 + 159 * q^87 + 891 * q^88 - 1766 * q^89 - 990 * q^90 - 654 * q^91 - 1344 * q^92 - 285 * q^93 + 3294 * q^94 + 736 * q^95 + 2049 * q^96 + 38 * q^97 - 4267 * q^98 + 630 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.65415	−	4.59712i	−0.938383	−	1.62533i	−0.768488	−	0.639864i	$-0.778991\pi$
$2$	−2.65415	−	4.59712i	−0.938383	−	1.62533i	−0.169895	−	0.985462i	$-0.554343\pi$
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$4$	−10.0890	+	17.4746i	−1.26112	+	2.18433i
$5$	−2.78070	−	4.81631i	−0.248713	−	0.430784i	0.714456	−	0.699681i	$-0.246674\pi$
$5$	−2.78070	−	4.81631i	−0.248713	−	0.430784i	−0.963169	+	0.268897i	$0.913341\pi$
$6$	−15.9249			−1.08355
$7$	9.67799	−	15.7904i	0.522562	−	0.852601i
$7$	9.67799	−	15.7904i	0.522562	−	0.852601i
$8$	64.6443			2.85690
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$	−14.7608	+	25.5664i	−0.466777	+	0.808481i
$11$	6.95869	−	12.0528i	0.190738	−	0.330369i	−0.754757	−	0.656005i	$-0.772245\pi$
$11$	6.95869	−	12.0528i	0.190738	−	0.330369i	0.945495	+	0.325636i	$0.105578\pi$
$12$	30.2670	+	52.4239i	0.728110	+	1.26112i
$13$	38.6718			0.825048			0.412524	−	0.910947i	$-0.364647\pi$
$13$	38.6718			0.825048			0.412524	+	0.910947i	$0.364647\pi$
$14$	−98.2771	−	2.58082i	−1.87612	−	0.0492680i
$15$	−16.6842			−0.287189
$16$	−90.8636	−	157.380i	−1.41974	−	2.45907i
$17$	−21.7394	+	37.6537i	−0.310152	+	0.537198i	−0.978395	−	0.206744i	$-0.933713\pi$
$17$	−21.7394	+	37.6537i	−0.310152	+	0.537198i	0.668243	+	0.743943i	$0.267046\pi$
$18$	−23.8873	+	41.3741i	−0.312794	+	0.541776i
$19$	54.5139	+	94.4208i	0.658228	+	1.14009i	0.981074	+	0.193633i	$0.0620273\pi$
$19$	54.5139	+	94.4208i	0.658228	+	1.14009i	−0.322845	+	0.946452i	$0.604639\pi$
$20$	112.218			1.25463
$21$	−26.5077	−	48.8297i	−0.275450	−	0.507406i
$22$	−73.8775			−0.715943
$23$	37.4389	+	64.8461i	0.339415	+	0.587885i	0.984323	−	0.176376i	$-0.0564374\pi$
$23$	37.4389	+	64.8461i	0.339415	+	0.587885i	−0.644907	+	0.764261i	$0.723104\pi$
$24$	96.9665	−	167.951i	0.824717	−	1.42845i
$25$	47.0354	−	81.4677i	0.376283	−	0.651742i
$26$	−102.641	−	177.779i	−0.774211	−	1.34097i
$27$	−27.0000			−0.192450
$28$	178.290	+	328.429i	1.20335	+	2.21668i
$29$	−72.3589			−0.463335			−0.231667	−	0.972795i	$-0.574418\pi$
$29$	−72.3589			−0.463335			−0.231667	+	0.972795i	$0.574418\pi$
$30$	44.2823	+	76.6992i	0.269494	+	0.466777i
$31$	−32.0215	+	55.4629i	−0.185524	+	0.321337i	−0.943753	−	0.330652i	$-0.892732\pi$
$31$	−32.0215	+	55.4629i	−0.185524	+	0.321337i	0.758229	+	0.651988i	$0.226065\pi$
$32$	−223.754	+	387.553i	−1.23608	+	2.14095i
$33$	−20.8761	−	36.1584i	−0.110123	−	0.190738i
$34$	230.798			1.16416
$35$	−102.963	−	2.70387i	−0.497255	−	0.0130582i
$36$	181.602			0.840749
$37$	−94.3636	−	163.443i	−0.419278	−	0.726211i	0.576589	−	0.817034i	$-0.304383\pi$
$37$	−94.3636	−	163.443i	−0.419278	−	0.726211i	−0.995867	+	0.0908235i	$0.971050\pi$
$38$	289.376	−	501.213i	1.23534	−	2.13967i
$39$	58.0077	−	100.472i	0.238171	−	0.412524i
$40$	−179.756	−	311.347i	−0.710550	−	1.23071i
$41$	−24.7923			−0.0944367			−0.0472184	−	0.998885i	$-0.515036\pi$
$41$	−24.7923			−0.0944367			−0.0472184	+	0.998885i	$0.515036\pi$
$42$	−154.121	+	251.460i	−0.566223	+	0.923837i
$43$	−243.881			−0.864920			−0.432460	−	0.901653i	$-0.642354\pi$
$43$	−243.881			−0.864920			−0.432460	+	0.901653i	$0.642354\pi$
$44$	140.412	+	243.201i	0.481090	+	0.833272i
$45$	−25.0263	+	43.3468i	−0.0829044	+	0.143595i
$46$	198.737	−	344.222i	0.637003	−	1.10332i
$47$	310.274	+	537.411i	0.962940	+	1.66786i	0.715052	+	0.699071i	$0.246403\pi$
$47$	310.274	+	537.411i	0.962940	+	1.66786i	0.247888	+	0.968789i	$0.420264\pi$
$48$	−545.182			−1.63938
$49$	−155.673	−	305.638i	−0.453857	−	0.891074i
$50$	−499.356			−1.41239
$51$	65.2182	+	112.961i	0.179066	+	0.310152i
$52$	−390.159	+	675.776i	−1.04049	+	1.80218i
$53$	143.919	−	249.276i	0.372997	−	0.646050i	−0.617028	−	0.786941i	$-0.711663\pi$
$53$	143.919	−	249.276i	0.372997	−	0.646050i	0.990025	+	0.140891i	$0.0449967\pi$
$54$	71.6620	+	124.122i	0.180592	+	0.312794i
$55$	−77.4001			−0.189757
$56$	625.627	−	1020.76i	1.49291	−	2.43580i
$57$	327.083			0.760057
$58$	192.051	+	332.642i	0.434785	+	0.753070i
$59$	−262.526	+	454.708i	−0.579287	+	1.00335i	0.416275	+	0.909239i	$0.363336\pi$
$59$	−262.526	+	454.708i	−0.579287	+	1.00335i	−0.995561	+	0.0941152i	$0.969998\pi$
$60$	168.327	−	291.551i	0.362182	−	0.627317i
$61$	191.718	+	332.065i	0.402409	+	0.696993i	0.994016	−	0.109234i	$-0.0348397\pi$
$61$	191.718	+	332.065i	0.402409	+	0.696993i	−0.591607	+	0.806226i	$0.701506\pi$
$62$	339.960			0.696369
$63$	−166.625	−	4.37567i	−0.333218	−	0.00875052i
$64$	921.681			1.80016
$65$	−107.535	−	186.255i	−0.205200	−	0.355417i
$66$	−110.816	+	191.939i	−0.206675	+	0.357971i
$67$	−99.0583	+	171.574i	−0.180625	+	0.312852i	−0.942094	−	0.335350i	$-0.891145\pi$
$67$	−99.0583	+	171.574i	−0.180625	+	0.312852i	0.761468	+	0.648202i	$0.224479\pi$
$68$	−438.657	−	759.776i	−0.782279	−	1.35495i
$69$	224.634			0.391923
$70$	260.849	+	480.510i	0.445392	+	0.820456i
$71$	785.432			1.31287			0.656434	−	0.754384i	$-0.272064\pi$
$71$	785.432			1.31287			0.656434	+	0.754384i	$0.272064\pi$
$72$	−290.900	−	503.853i	−0.476151	−	0.824717i
$73$	165.570	−	286.776i	0.265459	−	0.459789i	−0.702224	−	0.711956i	$-0.747810\pi$
$73$	165.570	−	286.776i	0.265459	−	0.459789i	0.967684	+	0.252166i	$0.0811430\pi$
$74$	−500.910	+	867.602i	−0.786887	+	1.36293i
$75$	−141.106	−	244.403i	−0.217247	−	0.376283i
$76$	−2199.96			−3.32043
$77$	−122.972	−	226.527i	−0.182000	−	0.335262i
$78$	−615.844			−0.893981
$79$	−218.823	−	379.013i	−0.311640	−	0.539776i	0.667078	−	0.744988i	$-0.267545\pi$
$79$	−218.823	−	379.013i	−0.311640	−	0.539776i	−0.978718	+	0.205212i	$0.934212\pi$
$80$	−505.329	+	875.255i	−0.706219	+	1.22321i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	65.8024	+	113.973i	0.0886178	+	0.153491i
$83$	241.241			0.319032			0.159516	−	0.987195i	$-0.449007\pi$
$83$	241.241			0.319032			0.159516	+	0.987195i	$0.449007\pi$
$84$	1120.72	+	29.4308i	1.45572	+	0.0382281i
$85$	241.803			0.308555
$86$	647.297	+	1121.15i	0.811626	+	1.40578i
$87$	−108.538	+	187.994i	−0.133753	+	0.231667i
$88$	449.840	−	779.145i	0.544921	−	0.943831i
$89$	−792.772	−	1373.12i	−0.944198	−	1.63540i	−0.757349	−	0.653010i	$-0.773506\pi$
$89$	−792.772	−	1373.12i	−0.944198	−	1.63540i	−0.186849	−	0.982389i	$-0.559828\pi$
$90$	265.694			0.311184
$91$	374.265	−	610.643i	0.431139	−	0.703437i
$92$	−1510.88			−1.71218
$93$	96.0646	+	166.389i	0.107112	+	0.185524i
$94$	1647.03	−	2852.73i	1.80721	−	3.13018i
$95$	303.173	−	525.112i	0.327420	−	0.567109i
$96$	671.261	+	1162.66i	0.713649	+	1.23608i
$97$	79.2754			0.0829814			0.0414907	−	0.999139i	$-0.486789\pi$
$97$	79.2754			0.0829814			0.0414907	+	0.999139i	$0.486789\pi$
$98$	−991.877	+	1526.86i	−1.02239	+	1.57384i
$99$	−125.256			−0.127159
$100$	949.080	+	1643.85i	0.949080	+	1.64385i
$101$	−577.487	+	1000.24i	−0.568931	+	0.985418i	0.427741	+	0.903902i	$0.359310\pi$
$101$	−577.487	+	1000.24i	−0.568931	+	0.985418i	−0.996672	+	0.0815165i	$0.974024\pi$
$102$	346.197	−	599.631i	0.336065	−	0.582082i
$103$	722.430	+	1251.28i	0.691098	+	1.19702i	0.971478	+	0.237128i	$0.0762061\pi$
$103$	722.430	+	1251.28i	0.691098	+	1.19702i	−0.280380	+	0.959889i	$0.590461\pi$
$104$	2499.91			2.35708
$105$	−161.469	+	263.450i	−0.150074	+	0.244858i
$106$	−1527.93			−1.40006
$107$	−495.480	−	858.197i	−0.447662	−	0.775374i	0.550571	−	0.834788i	$-0.314410\pi$
$107$	−495.480	−	858.197i	−0.447662	−	0.775374i	−0.998233	+	0.0594143i	$0.981077\pi$
$108$	272.403	−	471.816i	0.242703	−	0.420375i
$109$	−976.585	+	1691.49i	−0.858164	+	1.48638i	0.0155145	+	0.999880i	$0.495061\pi$
$109$	−976.585	+	1691.49i	−0.858164	+	1.48638i	−0.873678	+	0.486504i	$0.838272\pi$
$110$	205.431	+	355.817i	0.178064	+	0.308417i
$111$	−566.182			−0.484141
$112$	−3364.48	−	88.3533i	−2.83851	−	0.0745410i
$113$	672.882			0.560172			0.280086	−	0.959975i	$-0.409637\pi$
$113$	672.882			0.560172			0.280086	+	0.959975i	$0.409637\pi$
$114$	−868.127	−	1503.64i	−0.713224	−	1.23534i
$115$	208.213	−	360.635i	0.168834	−	0.292430i
$116$	730.028	−	1264.45i	0.584323	−	1.01208i
$117$	−174.023	−	301.417i	−0.137508	−	0.238171i
$118$	2787.13			2.17437
$119$	384.174	+	707.686i	0.295942	+	0.545155i
$120$	−1078.54			−0.820472
$121$	568.653	+	984.936i	0.427238	+	0.739997i
$122$	1017.69	−	1762.70i	0.755227	−	1.30809i
$123$	−37.1884	+	64.4123i	−0.0272615	+	0.0472184i
$124$	−646.130	−	1119.13i	−0.467937	−	0.810491i
$125$	−1218.34			−0.871773
$126$	422.131	+	777.608i	0.298464	+	0.549800i
$127$	175.815			0.122843			0.0614216	−	0.998112i	$-0.480437\pi$
$127$	175.815			0.122843			0.0614216	+	0.998112i	$0.480437\pi$
$128$	−656.249	−	1136.66i	−0.453163	−	0.784900i
$129$	−365.822	+	633.622i	−0.249681	+	0.432460i
$130$	−570.825	+	988.698i	−0.385113	+	0.667035i
$131$	−562.965	−	975.085i	−0.375470	−	0.650332i	0.614928	−	0.788584i	$-0.289185\pi$
$131$	−562.965	−	975.085i	−0.375470	−	0.650332i	−0.990397	+	0.138251i	$0.955852\pi$
$132$	842.474			0.555515
$133$	2018.53	+	53.0078i	1.31600	+	0.0345591i
$134$	1051.66			0.677983
$135$	75.0789	+	130.040i	0.0478649	+	0.0829044i
$136$	−1405.33	+	2434.10i	−0.886073	+	1.53472i
$137$	−934.350	+	1618.34i	−0.582678	+	1.00923i	0.412483	+	0.910966i	$0.364662\pi$
$137$	−934.350	+	1618.34i	−0.582678	+	1.00923i	−0.995161	+	0.0982624i	$0.968672\pi$
$138$	−596.210	−	1032.67i	−0.367774	−	0.637003i
$139$	−2817.19			−1.71907			−0.859537	−	0.511074i	$-0.829248\pi$
$139$	−2817.19			−1.71907			−0.859537	+	0.511074i	$0.829248\pi$
$140$	1086.04	−	1771.96i	0.655624	−	1.06970i
$141$	1861.65			1.11191
$142$	−2084.65	−	3610.72i	−1.23197	−	2.13384i
$143$	269.105	−	466.103i	0.157368	−	0.272570i
$144$	−817.773	+	1416.42i	−0.473248	+	0.819690i
$145$	201.208	+	348.503i	0.115238	+	0.199597i
$146$	−1757.79			−0.996410
$147$	−1027.58	−	54.0071i	−0.576555	−	0.0303023i
$148$	3808.14			2.11505
$149$	−900.163	−	1559.13i	−0.494928	−	0.857240i	0.505055	−	0.863087i	$-0.331472\pi$
$149$	−900.163	−	1559.13i	−0.494928	−	0.857240i	−0.999983	+	0.00584714i	$0.998139\pi$
$150$	−749.034	+	1297.36i	−0.407722	+	0.706196i
$151$	226.492	−	392.296i	0.122064	−	0.211421i	−0.798517	−	0.601972i	$-0.794382\pi$
$151$	226.492	−	392.296i	0.122064	−	0.211421i	0.920581	+	0.390551i	$0.127715\pi$
$152$	3524.01	+	6103.77i	1.88050	+	3.25711i
$153$	391.309			0.206768
$154$	−714.986	+	1166.56i	−0.374125	+	0.610414i
$155$	356.169			0.184569
$156$	1170.48	+	2027.33i	0.600726	+	1.04049i
$157$	931.829	−	1613.98i	0.473682	−	0.820441i	−0.525864	−	0.850569i	$-0.676258\pi$
$157$	931.829	−	1613.98i	0.473682	−	0.820441i	0.999546	+	0.0301273i	$0.00959128\pi$
$158$	−1161.58	+	2011.91i	−0.584875	+	1.01303i
$159$	−431.758	−	747.827i	−0.215350	−	0.372997i
$160$	2488.77			1.22971
$161$	1386.28	+	36.4046i	0.678597	+	0.0178204i
$162$	429.972			0.208529
$163$	−1160.57	−	2010.16i	−0.557686	−	0.965940i	−0.997689	−	0.0679437i	$-0.978356\pi$
$163$	−1160.57	−	2010.16i	−0.557686	−	0.965940i	0.440004	−	0.897996i	$-0.354977\pi$
$164$	250.129	−	433.237i	0.119096	−	0.206281i
$165$	−116.100	+	201.091i	−0.0547781	+	0.0948784i
$166$	−640.290	−	1109.01i	−0.299374	−	0.518531i
$167$	3211.62			1.48816			0.744079	−	0.668092i	$-0.232889\pi$
$167$	3211.62			1.48816			0.744079	+	0.668092i	$0.232889\pi$
$168$	−1713.57	−	3156.57i	−0.786934	−	1.44961i
$169$	−701.494			−0.319296
$170$	−641.780	−	1111.60i	−0.289543	−	0.501503i
$171$	490.625	−	849.787i	0.219409	−	0.380028i
$172$	2460.52	−	4261.74i	1.09077	−	1.88927i
$173$	−107.139	−	185.569i	−0.0470844	−	0.0815525i	0.841523	−	0.540222i	$-0.181660\pi$
$173$	−107.139	−	185.569i	−0.0470844	−	0.0815525i	−0.888607	+	0.458669i	$0.848326\pi$
$174$	1152.31			0.502047
$175$	−831.199	−	1531.15i	−0.359044	−	0.661395i
$176$	−2529.17			−1.08320
$177$	787.577	+	1364.12i	0.334451	+	0.579287i
$178$	−4208.27	+	7288.93i	−1.77204	+	3.06926i
$179$	1218.61	−	2110.70i	0.508845	−	0.881345i	−0.491102	−	0.871102i	$-0.663406\pi$
$179$	1218.61	−	2110.70i	0.508845	−	0.881345i	0.999948	−	0.0102437i	$-0.00326072\pi$
$180$	−504.980	−	874.652i	−0.209106	−	0.362182i
$181$	−248.631			−0.102103			−0.0510514	−	0.998696i	$-0.516257\pi$
$181$	−248.631			−0.102103			−0.0510514	+	0.998696i	$0.516257\pi$
$182$	−3800.55	−	99.8048i	−1.54789	−	0.0406485i
$183$	1150.31			0.464662
$184$	2420.21	+	4191.93i	0.969677	+	1.67953i
$185$	−524.794	+	908.970i	−0.208560	+	0.361237i
$186$	509.939	−	883.241i	0.201025	−	0.348185i
$187$	302.555	+	524.041i	0.118316	+	0.204929i
$188$	−12521.4			−4.85755
$189$	−261.306	+	426.341i	−0.100567	+	0.164083i
$190$	−3218.67			−1.22898
$191$	2156.54	+	3735.24i	0.816972	+	1.41504i	0.907903	+	0.419180i	$0.137683\pi$
$191$	2156.54	+	3735.24i	0.816972	+	1.41504i	−0.0909306	+	0.995857i	$0.528984\pi$
$192$	1382.52	−	2394.60i	0.519661	−	0.900079i
$193$	−1030.43	+	1784.75i	−0.384309	+	0.665643i	−0.991673	−	0.128781i	$-0.958894\pi$
$193$	−1030.43	+	1784.75i	−0.384309	+	0.665643i	0.607364	+	0.794424i	$0.292227\pi$
$194$	−210.409	−	364.438i	−0.0778683	−	0.134872i
$195$	−645.208			−0.236945
$196$	6911.51	+	363.252i	2.51877	+	0.132380i
$197$	−1666.09			−0.602557			−0.301279	−	0.953536i	$-0.597413\pi$
$197$	−1666.09			−0.602557			−0.301279	+	0.953536i	$0.597413\pi$
$198$	332.449	+	575.818i	0.119324	+	0.206675i
$199$	543.767	−	941.832i	0.193702	−	0.335501i	−0.752773	−	0.658281i	$-0.771284\pi$
$199$	543.767	−	941.832i	0.193702	−	0.335501i	0.946474	+	0.322780i	$0.104617\pi$
$200$	3040.57	−	5266.43i	1.07501	−	1.86196i
$201$	297.175	+	514.722i	0.104284	+	0.180625i
$202$	6130.94			2.13550
$203$	−700.288	+	1142.58i	−0.242121	+	0.395040i
$204$	−2631.94			−0.903298
$205$	68.9399	+	119.407i	0.0234877	+	0.0406818i
$206$	3834.87	−	6642.19i	1.29703	−	2.24652i
$207$	336.950	−	583.615i	0.113138	−	0.195962i
$208$	−3513.86	−	6086.18i	−1.17136	−	2.02885i
$209$	1517.38			0.502198
$210$	1639.67	+	43.0589i	0.538801	+	0.0141493i
$211$	−4676.47			−1.52579			−0.762895	−	0.646522i	$-0.776223\pi$
$211$	−4676.47			−1.52579			−0.762895	+	0.646522i	$0.776223\pi$
$212$	2904.01	+	5029.88i	0.940792	+	1.62950i
$213$	1178.15	−	2040.61i	0.378992	−	0.656434i
$214$	−2630.15	+	4555.56i	−0.840157	+	1.45520i
$215$	678.161	+	1174.61i	0.215117	+	0.372594i
$216$	−1745.40			−0.549811
$217$	565.878	+	1042.40i	0.177024	+	0.326096i
$218$	10368.0			3.22114
$219$	−496.711	−	860.329i	−0.153263	−	0.265459i
$220$	780.889	−	1352.54i	0.239307	−	0.414492i
$221$	−840.701	+	1456.14i	−0.255890	+	0.443214i
$222$	1502.73	+	2602.80i	0.454309	+	0.786887i
$223$	3246.03			0.974754			0.487377	−	0.873192i	$-0.337954\pi$
$223$	3246.03			0.974754			0.487377	+	0.873192i	$0.337954\pi$
$224$	3954.12	+	7283.89i	1.17945	+	2.17266i
$225$	−846.638			−0.250856
$226$	−1785.93	−	3093.32i	−0.525656	−	0.910463i
$227$	−2569.08	+	4449.77i	−0.751171	+	1.30107i	0.196085	+	0.980587i	$0.437177\pi$
$227$	−2569.08	+	4449.77i	−0.751171	+	1.30107i	−0.947256	+	0.320479i	$0.896156\pi$
$228$	−3299.94	+	5715.67i	−0.958526	+	1.66022i
$229$	−307.403	−	532.438i	−0.0887064	−	0.153644i	0.818258	−	0.574851i	$-0.194940\pi$
$229$	−307.403	−	532.438i	−0.0887064	−	0.153644i	−0.906965	+	0.421207i	$0.861607\pi$
$230$	−2210.51			−0.633725
$231$	−772.994	−	20.2993i	−0.220170	−	0.00578180i
$232$	−4677.59			−1.32370
$233$	−1413.71	−	2448.61i	−0.397490	−	0.688472i	0.595926	−	0.803039i	$-0.296785\pi$
$233$	−1413.71	−	2448.61i	−0.397490	−	0.688472i	−0.993415	+	0.114567i	$0.963452\pi$
$234$	−923.765	+	1600.01i	−0.258070	+	0.446991i
$235$	1725.56	−	2988.76i	0.478992	−	0.829638i
$236$	−5297.24	−	9175.09i	−1.46111	−	2.53071i
$237$	−1312.94			−0.359851
$238$	2233.66	−	3644.39i	0.608348	−	0.992567i
$239$	−3432.45			−0.928983			−0.464491	−	0.885578i	$-0.653763\pi$
$239$	−3432.45			−0.928983			−0.464491	+	0.885578i	$0.653763\pi$
$240$	1515.99	+	2625.77i	0.407736	+	0.706219i
$241$	1318.06	−	2282.94i	0.352296	−	0.610195i	−0.634355	−	0.773042i	$-0.718734\pi$
$241$	1318.06	−	2282.94i	0.352296	−	0.610195i	0.986651	+	0.162847i	$0.0520675\pi$
$242$	3018.58	−	5228.33i	0.801825	−	1.38880i
$243$	121.500	+	210.444i	0.0320750	+	0.0555556i
$244$	−7736.96			−2.02995
$245$	−1039.17	+	1599.66i	−0.270980	+	0.417137i
$246$	394.814			0.102327
$247$	2108.15	+	3651.42i	0.543070	+	0.940625i
$248$	−2070.01	+	3585.37i	−0.530024	+	0.918028i
$249$	361.862	−	626.763i	0.0920967	−	0.159516i
$250$	3233.65	+	5600.85i	0.818057	+	1.41692i
$251$	2057.57			0.517422			0.258711	−	0.965955i	$-0.416702\pi$
$251$	2057.57			0.517422			0.258711	+	0.965955i	$0.416702\pi$
$252$	1757.54	−	2867.57i	0.439344	−	0.716824i
$253$	1042.10			0.258958
$254$	−466.639	−	808.243i	−0.115274	−	0.199660i
$255$	362.704	−	628.222i	0.0890722	−	0.154278i
$256$	203.161	−	351.885i	0.0495998	−	0.0859093i
$257$	−1075.10	−	1862.13i	−0.260946	−	0.451972i	0.705548	−	0.708663i	$-0.250701\pi$
$257$	−1075.10	−	1862.13i	−0.260946	−	0.451972i	−0.966494	+	0.256691i	$0.917368\pi$
$258$	3883.78			0.937185
$259$	−3494.07	−	91.7566i	−0.838267	−	0.0220134i
$260$	4339.66			1.03513
$261$	325.615	+	563.982i	0.0772225	+	0.133753i
$262$	−2988.39	+	5176.04i	−0.704668	+	1.22052i
$263$	2295.08	−	3975.19i	0.538100	−	0.932017i	−0.460906	−	0.887449i	$-0.652475\pi$
$263$	2295.08	−	3975.19i	0.538100	−	0.932017i	0.999006	−	0.0445683i	$-0.0141912\pi$
$264$	−1349.52	−	2337.44i	−0.314610	−	0.544921i
$265$	−1600.79			−0.371078
$266$	−5113.78	−	9420.09i	−1.17874	−	2.17136i
$267$	−4756.63			−1.09027
$268$	−1998.80	−	3462.02i	−0.455582	−	0.789091i
$269$	189.689	−	328.551i	0.0429945	−	0.0744687i	−0.843727	−	0.536772i	$-0.819644\pi$
$269$	189.689	−	328.551i	0.0429945	−	0.0744687i	0.886722	+	0.462303i	$0.152977\pi$
$270$	398.541	−	690.293i	0.0898312	−	0.155592i
$271$	2684.42	+	4649.55i	0.601723	+	1.04221i	0.992560	+	0.121755i	$0.0388521\pi$
$271$	2684.42	+	4649.55i	0.601723	+	1.04221i	−0.390837	+	0.920460i	$0.627815\pi$
$272$	7901.28			1.76134
$273$	−1025.10	−	1888.33i	−0.227259	−	0.418634i
$274$	9919.61			2.18710
$275$	−654.610	−	1133.82i	−0.143543	−	0.248624i
$276$	−2266.33	+	3925.39i	−0.494264	+	0.856090i
$277$	2390.80	−	4140.99i	0.518590	−	0.898224i	−0.481177	−	0.876624i	$-0.659791\pi$
$277$	2390.80	−	4140.99i	0.518590	−	0.898224i	0.999767	−	0.0216003i	$-0.00687613\pi$
$278$	7477.25	+	12951.0i	1.61315	+	2.79406i
$279$	576.388			0.123683
$280$	−6655.98	−	174.790i	−1.42061	−	0.0373061i
$281$	−2076.57			−0.440845			−0.220423	−	0.975404i	$-0.570744\pi$
$281$	−2076.57			−0.440845			−0.220423	+	0.975404i	$0.570744\pi$
$282$	−4941.08	−	8558.20i	−1.04339	−	1.80721i
$283$	−1278.81	+	2214.96i	−0.268612	+	0.465250i	−0.968504	−	0.248999i	$-0.919898\pi$
$283$	−1278.81	+	2214.96i	−0.268612	+	0.465250i	0.699892	+	0.714249i	$0.253232\pi$
$284$	−7924.21	+	13725.1i	−1.65569	+	2.86774i
$285$	−909.520	−	1575.34i	−0.189036	−	0.327420i
$286$	−2856.97			−0.590687
$287$	−239.940	+	391.480i	−0.0493491	+	0.0805169i
$288$	4027.56			0.824050
$289$	1511.30	+	2617.65i	0.307612	+	0.532800i
$290$	1068.07	−	1849.96i	0.216274	−	0.374597i
$291$	118.913	−	205.963i	0.0239547	−	0.0414907i
$292$	3340.88	+	5786.57i	0.669555	+	1.15970i
$293$	560.049			0.111667			0.0558335	−	0.998440i	$-0.482218\pi$
$293$	560.049			0.111667			0.0558335	+	0.998440i	$0.482218\pi$
$294$	2479.08	+	4867.26i	0.491778	+	0.965524i
$295$	2920.02			0.576305
$296$	−6100.08	−	10565.6i	−1.19784	−	2.07471i
$297$	−187.885	+	325.426i	−0.0367076	+	0.0635795i
$298$	−4778.33	+	8276.31i	−0.928863	+	1.60884i
$299$	1447.83	+	2507.71i	0.280034	+	0.485033i
$300$	5694.48			1.09590
$301$	−2360.28	+	3850.98i	−0.451975	+	0.737432i
$302$	−2404.57			−0.458171
$303$	1732.46	+	3000.71i	0.328473	+	0.568931i
$304$	9906.66	−	17158.8i	1.86903	−	3.23726i
$305$	1066.22	−	1846.75i	0.200169	−	0.346703i
$306$	−1038.59	−	1798.89i	−0.194027	−	0.336065i
$307$	3653.02			0.679117			0.339558	−	0.940585i	$-0.389722\pi$
$307$	3653.02			0.679117			0.339558	+	0.940585i	$0.389722\pi$
$308$	5199.15	+	136.533i	0.961848	+	0.0252587i
$309$	4334.58			0.798011
$310$	−945.325	−	1637.35i	−0.173196	−	0.299985i
$311$	−1746.13	+	3024.39i	−0.318374	+	0.551439i	−0.980149	−	0.198263i	$-0.936470\pi$
$311$	−1746.13	+	3024.39i	−0.318374	+	0.551439i	0.661775	+	0.749702i	$0.269803\pi$
$312$	3749.87	−	6494.96i	0.680431	−	1.17854i
$313$	−4356.05	−	7544.90i	−0.786640	−	1.36250i	−0.928014	−	0.372544i	$-0.878485\pi$
$313$	−4356.05	−	7544.90i	−0.786640	−	1.36250i	0.141374	−	0.989956i	$-0.454848\pi$
$314$	−9892.85			−1.77798
$315$	442.259	+	814.685i	0.0791063	+	0.145722i
$316$	8830.83			1.57207
$317$	−970.165	−	1680.37i	−0.171892	−	0.297726i	0.767189	−	0.641421i	$-0.221655\pi$
$317$	−970.165	−	1680.37i	−0.171892	−	0.297726i	−0.939081	+	0.343695i	$0.888321\pi$
$318$	−2291.90	+	3969.69i	−0.404162	+	0.700029i
$319$	−503.523	+	872.127i	−0.0883758	+	0.153071i
$320$	−2562.92	−	4439.11i	−0.447724	−	0.775480i
$321$	−2972.88			−0.516916
$322$	−3512.03	−	6469.51i	−0.607820	−	1.11966i
$323$	−4740.39			−0.816602
$324$	−817.208	−	1415.45i	−0.140125	−	0.242703i
$325$	1818.94	−	3150.50i	0.310452	−	0.537718i
$326$	−6160.64	+	10670.5i	−1.04665	+	1.81284i
$327$	2929.75	+	5074.48i	0.495461	+	0.858164i
$328$	−1602.68			−0.269797
$329$	11488.8	+	301.702i	1.92522	+	0.0505574i
$330$	1232.59			0.205611
$331$	2865.75	+	4963.63i	0.475879	+	0.824247i	0.999618	−	0.0276315i	$-0.00879650\pi$
$331$	2865.75	+	4963.63i	0.475879	+	0.824247i	−0.523739	+	0.851879i	$0.675463\pi$
$332$	−2433.88	+	4215.61i	−0.402339	+	0.696872i
$333$	−849.273	+	1470.98i	−0.139759	+	0.242070i
$334$	−8524.10	−	14764.2i	−1.39646	−	2.41874i
$335$	1101.81			0.179696
$336$	−5276.26	+	8608.64i	−0.856678	+	1.39774i
$337$	2403.74			0.388547			0.194273	−	0.980947i	$-0.437765\pi$
$337$	2403.74			0.388547			0.194273	+	0.980947i	$0.437765\pi$
$338$	1861.87	+	3224.85i	0.299622	+	0.518960i
$339$	1009.32	−	1748.20i	0.161708	−	0.280086i
$340$	−2439.55	+	4225.42i	−0.389127	+	0.673987i
$341$	445.656	+	771.898i	0.0707731	+	0.122583i
$342$	−5208.76			−0.823560
$343$	−6332.75	−	499.826i	−0.996900	−	0.0786824i
$344$	−15765.6			−2.47099
$345$	−624.638	−	1081.91i	−0.0974765	−	0.168834i
$346$	−568.723	+	985.057i	−0.0883663	+	0.153055i
$347$	1668.22	−	2889.45i	0.258083	−	0.447013i	−0.707645	−	0.706568i	$-0.750242\pi$
$347$	1668.22	−	2889.45i	0.258083	−	0.447013i	0.965728	+	0.259555i	$0.0835758\pi$
$348$	−2190.09	−	3793.34i	−0.337359	−	0.584323i
$349$	−2424.54			−0.371870			−0.185935	−	0.982562i	$-0.559531\pi$
$349$	−2424.54			−0.371870			−0.185935	+	0.982562i	$0.559531\pi$
$350$	−4832.76	+	7885.02i	−0.738062	+	1.20421i
$351$	−1044.14			−0.158781
$352$	3114.06	+	5393.71i	0.471534	+	0.816721i
$353$	6201.56	−	10741.4i	0.935059	−	1.61957i	0.160531	−	0.987031i	$-0.448679\pi$
$353$	6201.56	−	10741.4i	0.935059	−	1.61957i	0.774528	−	0.632540i	$-0.217987\pi$
$354$	4180.69	−	7241.17i	0.627687	−	1.08719i
$355$	−2184.05	−	3782.88i	−0.326528	−	0.565562i
$356$	31993.1			4.76300
$357$	2414.88	+	63.4163i	0.358009	+	0.00940153i
$358$	−12937.5			−1.90997
$359$	−676.921	−	1172.46i	−0.0995168	−	0.172368i	0.811968	−	0.583702i	$-0.198396\pi$
$359$	−676.921	−	1172.46i	−0.0995168	−	0.172368i	−0.911485	+	0.411334i	$0.865063\pi$
$360$	−1617.81	+	2802.13i	−0.236850	+	0.410236i
$361$	−2514.03	+	4354.42i	−0.366529	+	0.634848i
$362$	659.903	+	1142.99i	0.0958114	+	0.165950i
$363$	3411.92			0.493332
$364$	6894.81	+	12700.9i	0.992819	+	1.82887i
$365$	−1841.61			−0.264093
$366$	−3053.08	−	5288.10i	−0.436031	−	0.755227i
$367$	689.031	−	1193.44i	0.0980031	−	0.169746i	−0.812855	−	0.582466i	$-0.802088\pi$
$367$	689.031	−	1193.44i	0.0980031	−	0.169746i	0.910858	+	0.412720i	$0.135421\pi$
$368$	6803.67	−	11784.3i	0.963766	−	1.66929i
$369$	111.565	+	193.237i	0.0157395	+	0.0272615i
$370$	5571.52			0.782837
$371$	−2543.31	−	4685.03i	−0.355909	−	0.655619i
$372$	−3876.78			−0.540327
$373$	−2728.46	−	4725.83i	−0.378752	−	0.656017i	0.612129	−	0.790758i	$-0.290313\pi$
$373$	−2728.46	−	4725.83i	−0.378752	−	0.656017i	−0.990881	+	0.134741i	$0.956980\pi$
$374$	1606.05	−	2781.76i	0.222051	−	0.384603i
$375$	−1827.51	+	3165.34i	−0.251659	+	0.435887i
$376$	20057.5	+	34740.6i	2.75103	+	4.76492i
$377$	−2798.25			−0.382273
$378$	2653.48	+	69.6821i	0.361059	+	0.00948164i
$379$	554.675			0.0751761			0.0375881	−	0.999293i	$-0.488033\pi$
$379$	554.675			0.0751761			0.0375881	+	0.999293i	$0.488033\pi$
$380$	6117.43	+	10595.7i	0.825836	+	1.43039i
$381$	263.723	−	456.781i	0.0354618	−	0.0614216i
$382$	11447.5	−	19827.7i	1.53327	−	2.65569i
$383$	−2930.33	−	5075.48i	−0.390948	−	0.677141i	0.601627	−	0.798777i	$-0.294519\pi$
$383$	−2930.33	−	5075.48i	−0.390948	−	0.677141i	−0.992575	+	0.121636i	$0.961186\pi$
$384$	−3937.50			−0.523267
$385$	−749.077	+	1222.18i	−0.0991597	+	0.161787i
$386$	10939.6			1.44252
$387$	1097.47	+	1900.87i	0.144153	+	0.249681i
$388$	−799.809	+	1385.31i	−0.104650	+	0.181259i
$389$	−3889.43	+	6736.69i	−0.506946	+	0.878056i	0.493022	+	0.870017i	$0.335892\pi$
$389$	−3889.43	+	6736.69i	−0.506946	+	0.878056i	−0.999968	+	0.00803932i	$0.997441\pi$
$390$	1712.48	+	2966.10i	0.222345	+	0.385113i
$391$	−3255.60			−0.421081
$392$	−10063.4	−	19757.8i	−1.29663	−	2.54571i
$393$	−3377.79			−0.433555
$394$	4422.04	+	7659.20i	0.565429	+	0.979352i
$395$	−1216.96	+	2107.84i	−0.155018	+	0.268499i
$396$	1263.71	−	2188.81i	0.160363	−	0.277757i
$397$	−4013.94	−	6952.35i	−0.507440	−	0.878912i	−0.999963	−	0.00861270i	$-0.997258\pi$
$397$	−4013.94	−	6952.35i	−0.507440	−	0.878912i	0.492523	−	0.870300i	$-0.336075\pi$
$398$	−5772.95			−0.727065
$399$	3165.51	−	5164.77i	0.397177	−	0.648025i
$400$	−17095.2			−2.13690
$401$	−389.990	−	675.482i	−0.0485665	−	0.0841196i	0.840720	−	0.541470i	$-0.182132\pi$
$401$	−389.990	−	675.482i	−0.0485665	−	0.0841196i	−0.889287	+	0.457350i	$0.848799\pi$
$402$	1577.49	−	2732.30i	0.195717	−	0.338991i
$403$	−1238.33	+	2144.85i	−0.153066	+	0.265118i
$404$	−11652.5	−	20182.8i	−1.43499	−	2.48547i
$405$	450.473			0.0552696
$406$	7111.22	+	186.745i	0.869271	+	0.0228276i
$407$	−2626.59			−0.319890
$408$	4215.99	+	7302.30i	0.511574	+	0.886073i
$409$	−7346.25	+	12724.1i	−0.888139	+	1.53830i	−0.0460654	+	0.998938i	$0.514668\pi$
$409$	−7346.25	+	12724.1i	−0.888139	+	1.53830i	−0.842073	+	0.539363i	$0.818665\pi$
$410$	365.953	−	633.850i	0.0440809	−	0.0763503i
$411$	2803.05	+	4855.02i	0.336409	+	0.582678i
$412$	−29154.4			−3.48624
$413$	4639.29	+	8546.04i	0.552748	+	1.01822i
$414$	−3577.26			−0.424669
$415$	−670.820	−	1161.89i	−0.0793476	−	0.137434i
$416$	−8652.95	+	14987.3i	−1.01982	+	1.76638i
$417$	−4225.79	+	7319.28i	−0.496254	+	0.859537i
$418$	−4027.35	−	6975.57i	−0.471254	−	0.816236i
$419$	3370.31			0.392960			0.196480	−	0.980508i	$-0.437049\pi$
$419$	3370.31			0.392960			0.196480	+	0.980508i	$0.437049\pi$
$420$	−2974.63	−	5479.57i	−0.345589	−	0.636608i
$421$	15651.0			1.81184			0.905919	−	0.423450i	$-0.139181\pi$
$421$	15651.0			1.81184			0.905919	+	0.423450i	$0.139181\pi$
$422$	12412.0	+	21498.3i	1.43178	+	2.47991i
$423$	2792.47	−	4836.70i	0.320980	−	0.555953i
$424$	9303.58	−	16114.3i	1.06562	−	1.84570i
$425$	2045.04	+	3542.12i	0.233410	+	0.404277i
$426$	−12507.9			−1.42256
$427$	7098.88	+	186.421i	0.804541	+	0.0211277i
$428$	19995.6			2.25823
$429$	−807.314	−	1398.31i	−0.0908567	−	0.157368i
$430$	3599.88	−	6235.17i	0.403724	−	0.699271i
$431$	−2444.06	+	4233.24i	−0.273147	+	0.473104i	−0.969666	−	0.244434i	$-0.921398\pi$
$431$	−2444.06	+	4233.24i	−0.273147	+	0.473104i	0.696519	+	0.717538i	$0.254731\pi$
$432$	2453.32	+	4249.27i	0.273230	+	0.473248i
$433$	−5255.73			−0.583313			−0.291656	−	0.956523i	$-0.594206\pi$
$433$	−5255.73			−0.583313			−0.291656	+	0.956523i	$0.594206\pi$
$434$	3290.12	−	5368.10i	0.363896	−	0.593725i
$435$	1207.25			0.133065
$436$	−19705.5	−	34131.0i	−2.16450	−	3.74903i
$437$	−4081.88	+	7070.03i	−0.446826	+	0.773925i
$438$	−2636.69	+	4566.88i	−0.287639	+	0.498205i
$439$	412.488	+	714.451i	0.0448451	+	0.0776740i	0.887577	−	0.460660i	$-0.152387\pi$
$439$	412.488	+	714.451i	0.0448451	+	0.0776740i	−0.842732	+	0.538334i	$0.819054\pi$
$440$	−5003.48			−0.542117
$441$	−1681.69	+	2588.72i	−0.181588	+	0.279530i
$442$	8925.37			0.960490
$443$	−6513.64	−	11281.9i	−0.698583	−	1.20998i	−0.968958	−	0.247226i	$-0.920481\pi$
$443$	−6513.64	−	11281.9i	−0.698583	−	1.20998i	0.270375	−	0.962755i	$-0.412852\pi$
$444$	5712.21	−	9893.83i	0.610561	−	1.05752i
$445$	−4408.92	+	7636.47i	−0.469669	+	0.813491i
$446$	−8615.44	−	14922.4i	−0.914693	−	1.58429i
$447$	−5400.98			−0.571493
$448$	8920.02	−	14553.7i	0.940695	−	1.53482i
$449$	16526.1			1.73700			0.868500	−	0.495689i	$-0.165084\pi$
$449$	16526.1			1.73700			0.868500	+	0.495689i	$0.165084\pi$
$450$	2247.10	+	3892.09i	0.235399	+	0.407722i
$451$	−172.522	+	298.817i	−0.0180127	+	0.0311989i
$452$	−6788.71	+	11758.4i	−0.706447	+	1.22360i
$453$	−679.476	−	1176.89i	−0.0704737	−	0.122064i
$454$	27274.9			2.81954
$455$	−3981.76	−	104.564i	−0.410259	−	0.0107737i
$456$	21144.1			2.17141
$457$	1855.41	+	3213.67i	0.189918	+	0.328947i	0.945223	−	0.326426i	$-0.105844\pi$
$457$	1855.41	+	3213.67i	0.189918	+	0.328947i	−0.755305	+	0.655374i	$0.772511\pi$
$458$	−1631.79	+	2826.34i	−0.166481	+	0.288354i
$459$	586.963	−	1016.65i	0.0596887	−	0.103384i
$460$	4201.31	+	7276.89i	0.425842	+	0.737580i
$461$	−9714.00			−0.981401			−0.490701	−	0.871328i	$-0.663259\pi$
$461$	−9714.00			−0.981401			−0.490701	+	0.871328i	$0.663259\pi$
$462$	1958.32	+	3607.42i	0.197206	+	0.363274i
$463$	−43.2780			−0.00434406			−0.00217203	−	0.999998i	$-0.500691\pi$
$463$	−43.2780			−0.00434406			−0.00217203	+	0.999998i	$0.500691\pi$
$464$	6574.79	+	11387.9i	0.657817	+	1.13937i
$465$	534.254	−	925.355i	0.0532805	−	0.0922845i
$466$	−7504.38	+	12998.0i	−0.745995	+	1.29210i
$467$	766.618	+	1327.82i	0.0759633	+	0.131572i	0.901505	−	0.432769i	$-0.142463\pi$
$467$	766.618	+	1327.82i	0.0759633	+	0.131572i	−0.825541	+	0.564341i	$0.809130\pi$
$468$	7022.87			0.693659
$469$	1750.54	+	3224.66i	0.172350	+	0.317486i
$470$	−18319.6			−1.79791
$471$	−2795.49	−	4841.93i	−0.273480	−	0.473682i
$472$	−16970.8	+	29394.3i	−1.65497	+	2.86649i
$473$	−1697.09	+	2939.45i	−0.164974	+	0.285743i
$474$	3484.74	+	6035.74i	0.337678	+	0.584875i
$475$	10256.3			0.990722
$476$	−16242.5	−	426.538i	−1.56402	−	0.0410721i
$477$	−2590.55			−0.248665
$478$	9110.23	+	15779.4i	0.871741	+	1.50990i
$479$	3517.69	−	6092.81i	0.335547	−	0.581185i	−0.648042	−	0.761604i	$-0.724412\pi$
$479$	3517.69	−	6092.81i	0.335547	−	0.581185i	0.983590	+	0.180419i	$0.0577454\pi$
$480$	3733.15	−	6466.00i	0.354988	−	0.614857i
$481$	−3649.21	−	6320.62i	−0.345924	−	0.599159i
$482$	−13993.3			−1.32236
$483$	2174.00	−	3547.05i	0.204804	−	0.334154i
$484$	−22948.6			−2.15520
$485$	−220.441	−	381.815i	−0.0206386	−	0.0357471i
$486$	644.958	−	1117.10i	0.0601973	−	0.104265i
$487$	7685.64	−	13311.9i	0.715132	−	1.23865i	−0.247776	−	0.968817i	$-0.579700\pi$
$487$	7685.64	−	13311.9i	0.715132	−	1.23865i	0.962908	−	0.269828i	$-0.0869669\pi$
$488$	12393.5	+	21466.1i	1.14964	+	1.99124i
$489$	−6963.41			−0.643960
$490$	10111.9	+	531.458i	0.932266	+	0.0489976i
$491$	−2393.35			−0.219980			−0.109990	−	0.993933i	$-0.535082\pi$
$491$	−2393.35			−0.219980			−0.109990	+	0.993933i	$0.535082\pi$
$492$	−750.388	−	1299.71i	−0.0687604	−	0.119096i
$493$	1573.04	−	2724.58i	0.143704	−	0.248903i
$494$	11190.7	−	19382.8i	1.01921	−	1.76533i
$495$	348.300	+	603.274i	0.0316261	+	0.0547781i
$496$	11638.4			1.05359
$497$	7601.40	−	12402.3i	0.686055	−	1.11935i
$498$	−3841.74			−0.345688
$499$	−346.760	−	600.606i	−0.0311084	−	0.0538814i	0.850052	−	0.526699i	$-0.176570\pi$
$499$	−346.760	−	600.606i	−0.0311084	−	0.0538814i	−0.881160	+	0.472817i	$0.843237\pi$
$500$	12291.8	−	21290.1i	1.09941	−	1.90424i
$501$	4817.43	−	8344.03i	0.429594	−	0.744079i
$502$	−5461.10	−	9458.91i	−0.485540	−	0.840979i
$503$	−8646.95			−0.766498			−0.383249	−	0.923645i	$-0.625195\pi$
$503$	−8646.95			−0.766498			−0.383249	+	0.923645i	$0.625195\pi$
$504$	−10771.4	−	282.863i	−0.951973	−	0.0249994i
$505$	6423.27			0.566003
$506$	−2765.89	−	4790.67i	−0.243002	−	0.420892i
$507$	−1052.24	+	1822.53i	−0.0921729	+	0.159648i
$508$	−1773.80	+	3072.31i	−0.154920	+	0.268330i
$509$	7750.44	+	13424.1i	0.674916	+	1.16899i	0.976494	+	0.215546i	$0.0691533\pi$
$509$	7750.44	+	13424.1i	0.674916	+	1.16899i	−0.301578	+	0.953441i	$0.597513\pi$
$510$	−3850.68			−0.334335
$511$	−2925.92	−	5389.84i	−0.253298	−	0.466600i
$512$	−12656.9			−1.09250
$513$	−1471.87	−	2549.36i	−0.126676	−	0.219409i
$514$	−5706.96	+	9884.75i	−0.489734	+	0.848245i
$515$	4017.72	−	6958.89i	0.343771	−	0.595428i
$516$	−7381.55	−	12785.2i	−0.629757	−	1.09077i
$517$	8636.41			0.734678
$518$	8851.97	+	16306.2i	0.750836	+	1.38311i
$519$	−642.831			−0.0543683
$520$	−6951.50	−	12040.4i	−0.586238	−	1.01539i
$521$	−432.354	+	748.858i	−0.0363565	+	0.0629714i	−0.883631	−	0.468184i	$-0.844909\pi$
$521$	−432.354	+	748.858i	−0.0363565	+	0.0629714i	0.847275	+	0.531155i	$0.178242\pi$
$522$	1728.46	−	2993.78i	0.144928	−	0.251023i
$523$	3127.81	+	5417.52i	0.261509	+	0.452947i	0.966643	−	0.256127i	$-0.0824465\pi$
$523$	3127.81	+	5417.52i	0.261509	+	0.452947i	−0.705134	+	0.709074i	$0.749113\pi$
$524$	22719.0			1.89406
$525$	−5224.85	−	137.208i	−0.434345	−	0.0114062i
$526$	−24365.9			−2.01978
$527$	−1392.26	−	2411.46i	−0.115081	−	0.199326i
$528$	−3793.75	+	6570.97i	−0.312693	+	0.541600i
$529$	3280.15	−	5681.39i	0.269594	−	0.466951i
$530$	4248.72	+	7359.01i	0.348213	+	0.603122i
$531$	4725.46			0.386191
$532$	−21291.2	+	34738.2i	−1.73513	+	2.83100i
$533$	−958.762			−0.0779148
$534$	12624.8	+	21866.8i	1.02309	+	1.77204i
$535$	−2755.56	+	4772.78i	−0.222679	+	0.385692i
$536$	−6403.56	+	11091.3i	−0.516029	+	0.893789i
$537$	−3655.83	−	6332.09i	−0.293782	−	0.508845i
$538$	−2013.85			−0.161381
$539$	−4767.08	−	250.546i	−0.380951	−	0.0200218i
$540$	−3029.88			−0.241454
$541$	−71.9353	−	124.596i	−0.00571671	−	0.00990164i	0.863153	−	0.504943i	$-0.168486\pi$
$541$	−71.9353	−	124.596i	−0.00571671	−	0.00990164i	−0.868870	+	0.495041i	$0.835153\pi$
$542$	14249.7	−	24681.2i	1.12929	−	1.95599i
$543$	−372.946	+	645.962i	−0.0294745	+	0.0510514i
$544$	−9728.53	−	16850.3i	−0.766741	−	1.32804i
$545$	10862.4			0.853747
$546$	−5960.13	+	9724.41i	−0.467161	+	0.762210i
$547$	5455.65			0.426448			0.213224	−	0.977003i	$-0.431604\pi$
$547$	5455.65			0.426448			0.213224	+	0.977003i	$0.431604\pi$
$548$	−18853.3	−	32654.9i	−1.46966	−	2.54552i
$549$	1725.46	−	2988.58i	0.134136	−	0.232331i
$550$	−3474.86	+	6018.63i	−0.269397	+	0.466610i
$551$	−3944.56	−	6832.18i	−0.304980	−	0.528241i
$552$	14521.3			1.11969
$553$	−8102.54	−	212.778i	−0.623065	−	0.0163621i
$554$	−25382.2			−1.94654
$555$	1574.38	+	2726.91i	0.120412	+	0.208560i
$556$	28422.7	−	49229.5i	2.16797	−	3.75503i
$557$	−12404.9	+	21486.0i	−0.943652	+	1.63445i	−0.185223	+	0.982696i	$0.559301\pi$
$557$	−12404.9	+	21486.0i	−0.943652	+	1.63445i	−0.758428	+	0.651756i	$0.774032\pi$
$558$	−1529.82	−	2649.72i	−0.116062	−	0.201025i
$559$	−9431.33			−0.713600
$560$	8930.06	+	16450.1i	0.673864	+	1.24132i
$561$	1815.33			0.136619
$562$	5511.51	+	9546.22i	0.413682	+	0.716517i
$563$	−8184.91	+	14176.7i	−0.612705	+	1.06124i	0.378077	+	0.925774i	$0.376585\pi$
$563$	−8184.91	+	14176.7i	−0.612705	+	1.06124i	−0.990782	+	0.135462i	$0.956748\pi$
$564$	−18782.1	+	32531.6i	−1.40225	+	2.42877i
$565$	−1871.08	−	3240.81i	−0.139322	−	0.241313i
$566$	13576.6			1.00824
$567$	715.707	+	1318.40i	0.0530104	+	0.0976503i
$568$	50773.7			3.75074
$569$	9225.29	+	15978.7i	0.679691	+	1.17726i	0.975074	+	0.221881i	$0.0712195\pi$
$569$	9225.29	+	15978.7i	0.679691	+	1.17726i	−0.295383	+	0.955379i	$0.595447\pi$
$570$	−4828.00	+	8362.34i	−0.354777	+	0.614491i
$571$	3554.34	−	6156.30i	0.260499	−	0.451197i	−0.705876	−	0.708335i	$-0.749446\pi$
$571$	3554.34	−	6156.30i	0.260499	−	0.451197i	0.966374	+	0.257139i	$0.0827797\pi$
$572$	5429.99	+	9405.02i	0.396922	+	0.687489i
$573$	12939.2			0.943358
$574$	2436.52	+	63.9844i	0.177175	+	0.00465271i
$575$	7043.82			0.510865
$576$	−4147.57	−	7183.80i	−0.300026	−	0.519661i
$577$	−3797.09	+	6576.75i	−0.273960	+	0.474512i	−0.969872	−	0.243615i	$-0.921667\pi$
$577$	−3797.09	+	6576.75i	−0.273960	+	0.474512i	0.695912	+	0.718127i	$0.255000\pi$
$578$	8022.42	−	13895.2i	0.577316	−	0.999940i
$579$	3091.28	+	5354.25i	0.221881	+	0.384309i
$580$	−8119.96			−0.581315
$581$	2334.73	−	3809.30i	0.166714	−	0.272007i
$582$	−1262.45			−0.0899146
$583$	−2002.98	−	3469.26i	−0.142290	−	0.246453i
$584$	10703.2	−	18538.5i	0.758392	−	1.31357i
$585$	−967.811	+	1676.30i	−0.0684001	+	0.118472i
$586$	−1486.45	−	2574.61i	−0.104786	−	0.181495i
$587$	−1763.34			−0.123988			−0.0619939	−	0.998077i	$-0.519746\pi$
$587$	−1763.34			−0.123988			−0.0619939	+	0.998077i	$0.519746\pi$
$588$	11311.0	−	17411.8i	0.793297	−	1.22117i
$589$	−6982.47			−0.488468
$590$	−7750.16	−	13423.7i	−0.540795	−	0.936684i
$591$	−2499.13	+	4328.62i	−0.173943	+	0.301279i
$592$	−17148.4	+	29702.0i	−1.19054	+	2.06207i
$593$	6158.07	+	10666.1i	0.426445	+	0.738624i	0.996554	−	0.0829448i	$-0.0264325\pi$
$593$	6158.07	+	10666.1i	0.426445	+	0.738624i	−0.570109	+	0.821569i	$0.693099\pi$
$594$	1994.69			0.137783
$595$	2340.16	−	3818.16i	0.161239	−	0.263075i
$596$	36327.0			2.49666
$597$	−1631.30	−	2825.49i	−0.111834	−	0.193702i
$598$	7685.50	−	13311.7i	0.525558	−	0.910293i
$599$	4451.70	−	7710.57i	0.303659	−	0.525952i	−0.673303	−	0.739367i	$-0.735125\pi$
$599$	4451.70	−	7710.57i	0.303659	−	0.525952i	0.976962	+	0.213414i	$0.0684584\pi$
$600$	−9121.72	−	15799.3i	−0.620655	−	1.07501i
$601$	−19157.1			−1.30022			−0.650112	−	0.759838i	$-0.725278\pi$
$601$	−19157.1			−1.30022			−0.650112	+	0.759838i	$0.725278\pi$
$602$	23968.0	+	629.413i	1.62269	+	0.0426129i
$603$	1783.05			0.120417
$604$	4570.15	+	7915.74i	0.307876	+	0.533256i
$605$	3162.51	−	5477.62i	0.212519	−	0.368094i
$606$	9196.41	−	15928.6i	0.616466	−	1.06775i
$607$	3784.96	+	6555.75i	0.253092	+	0.438369i	0.964376	−	0.264537i	$-0.0852191\pi$
$607$	3784.96	+	6555.75i	0.253092	+	0.438369i	−0.711283	+	0.702905i	$0.751886\pi$
$608$	−48790.7			−3.25448
$609$	1918.07	+	3533.27i	0.127625	+	0.235099i
$610$	−11319.6			−0.751340
$611$	11998.9	+	20782.6i	0.794471	+	1.37606i
$612$	−3947.91	+	6837.99i	−0.260760	+	0.451649i
$613$	−1453.56	+	2517.65i	−0.0957730	+	0.165884i	−0.909931	−	0.414760i	$-0.863866\pi$
$613$	−1453.56	+	2517.65i	−0.0957730	+	0.165884i	0.814158	+	0.580643i	$0.197199\pi$
$614$	−9695.65	−	16793.4i	−0.637272	−	1.10379i
$615$	413.640			0.0271212
$616$	−7949.47	−	14643.7i	−0.519956	−	0.957811i
$617$	−12510.9			−0.816320			−0.408160	−	0.912910i	$-0.633829\pi$
$617$	−12510.9			−0.816320			−0.408160	+	0.912910i	$0.633829\pi$
$618$	−11504.6	−	19926.6i	−0.748840	−	1.29703i
$619$	−5032.78	+	8717.03i	−0.326792	+	0.566021i	−0.981873	−	0.189538i	$-0.939301\pi$
$619$	−5032.78	+	8717.03i	−0.326792	+	0.566021i	0.655081	+	0.755558i	$0.272634\pi$
$620$	−3593.39	+	6223.93i	−0.232764	+	0.403160i
$621$	−1010.85	−	1750.84i	−0.0653205	−	0.113138i
$622$	18538.0			1.19503
$623$	−29354.6	−	770.869i	−1.88775	−	0.0495734i
$624$	−21083.2			−1.35257
$625$	−2491.59	−	4315.56i	−0.159462	−	0.276196i
$626$	−23123.2	+	40050.5i	−1.47634	+	2.55709i
$627$	2276.07	−	3942.27i	0.144972	−	0.251099i
$628$	18802.4	+	32566.8i	1.19474	+	2.06936i
$629$	8205.63			0.520159
$630$	2571.38	−	4195.41i	0.162613	−	0.265316i
$631$	−25146.6			−1.58648			−0.793242	−	0.608907i	$-0.791608\pi$
$631$	−25146.6			−1.58648			−0.793242	+	0.608907i	$0.791608\pi$
$632$	−14145.7	−	24501.1i	−0.890325	−	1.54209i
$633$	−7014.71	+	12149.8i	−0.440458	+	0.762895i
$634$	−5149.92	+	8919.92i	−0.322602	+	0.558762i
$635$	−488.889	−	846.781i	−0.0305527	−	0.0529189i
$636$	17424.0			1.08633
$637$	−6020.16	−	11819.6i	−0.374454	−	0.735179i
$638$	5345.70			0.331721
$639$	−3534.44	−	6121.83i	−0.218811	−	0.378992i
$640$	−3649.66	+	6321.41i	−0.225415	+	0.390430i
$641$	14479.5	−	25079.1i	0.892206	−	1.54535i	0.0549809	−	0.998487i	$-0.482490\pi$
$641$	14479.5	−	25079.1i	0.892206	−	1.54535i	0.837225	−	0.546859i	$-0.184176\pi$
$642$	7890.46	+	13666.7i	0.485065	+	0.840157i
$643$	7341.90			0.450290			0.225145	−	0.974325i	$-0.427714\pi$
$643$	7341.90			0.450290			0.225145	+	0.974325i	$0.427714\pi$
$644$	−14622.3	+	23857.5i	−0.894721	+	1.45981i
$645$	4068.97			0.248396
$646$	12581.7	+	21792.1i	0.766285	+	1.32725i
$647$	−3035.99	+	5258.49i	−0.184478	+	0.319525i	−0.943400	−	0.331656i	$-0.892393\pi$
$647$	−3035.99	+	5258.49i	−0.184478	+	0.319525i	0.758923	+	0.651181i	$0.225726\pi$
$648$	−2618.10	+	4534.67i	−0.158717	+	0.274906i
$649$	3653.67	+	6328.34i	0.220985	+	0.382756i
$650$	−19311.0			−1.16529
$651$	3557.06	+	93.4105i	0.214151	+	0.00562373i
$652$	46835.9			2.81324
$653$	−13131.1	−	22743.7i	−0.786920	−	1.36298i	−0.927846	−	0.372965i	$-0.878341\pi$
$653$	−13131.1	−	22743.7i	−0.786920	−	1.36298i	0.140926	−	0.990020i	$-0.454992\pi$
$654$	15552.0	−	26936.9i	0.929864	−	1.61057i
$655$	−3130.88	+	5422.84i	−0.186769	+	0.323493i
$656$	2252.72	+	3901.82i	0.134076	+	0.232226i
$657$	−2980.27			−0.176973
$658$	−29105.9	−	53615.9i	−1.72442	−	3.17655i
$659$	26130.1			1.54459			0.772296	−	0.635263i	$-0.219108\pi$
$659$	26130.1			1.54459			0.772296	+	0.635263i	$0.219108\pi$
$660$	−2342.67	−	4057.62i	−0.138164	−	0.239307i
$661$	5962.75	−	10327.8i	0.350868	−	0.607722i	−0.635533	−	0.772073i	$-0.719220\pi$
$661$	5962.75	−	10327.8i	0.350868	−	0.607722i	0.986402	+	0.164351i	$0.0525531\pi$
$662$	15212.3	−	26348.4i	0.893114	−	1.54692i
$663$	2522.10	+	4368.41i	0.147738	+	0.255890i
$664$	15594.9			0.911444
$665$	−5357.61	−	9869.25i	−0.312420	−	0.575509i
$666$	9016.38			0.524591
$667$	−2709.04	−	4692.19i	−0.157263	−	0.272387i
$668$	−32402.0	+	56121.9i	−1.87675	+	3.25063i
$669$	4869.04	−	8433.43i	0.281387	−	0.487377i
$670$	−2924.35	−	5065.13i	−0.168623	−	0.292064i
$671$	5336.42			0.307019
$672$	24855.3	+	652.715i	1.42681	+	0.0374688i
$673$	−6359.85			−0.364271			−0.182135	−	0.983273i	$-0.558301\pi$
$673$	−6359.85			−0.364271			−0.182135	+	0.983273i	$0.558301\pi$
$674$	−6379.89	−	11050.3i	−0.364606	−	0.631516i
$675$	−1269.96	+	2199.63i	−0.0724158	+	0.125428i
$676$	7077.36	−	12258.4i	0.402672	−	0.697449i
$677$	−4280.81	−	7414.57i	−0.243020	−	0.420924i	0.718553	−	0.695472i	$-0.244805\pi$
$677$	−4280.81	−	7414.57i	−0.243020	−	0.420924i	−0.961573	+	0.274549i	$0.911472\pi$
$678$	−10715.6			−0.606975
$679$	767.226	−	1251.79i	0.0433629	−	0.0707500i
$680$	15631.2			0.881513
$681$	7707.24	+	13349.3i	0.433689	+	0.751171i
$682$	2365.67	−	4097.46i	0.132824	−	0.230059i
$683$	3352.94	−	5807.47i	0.187843	−	0.325354i	−0.756688	−	0.653776i	$-0.773184\pi$
$683$	3352.94	−	5807.47i	0.187843	−	0.325354i	0.944531	+	0.328423i	$0.106517\pi$
$684$	9899.82	+	17147.0i	0.553405	+	0.958526i
$685$	10392.6			0.579679
$686$	14510.3	+	30439.0i	0.807589	+	1.69412i
$687$	−1844.42			−0.102429
$688$	22160.0	+	38382.2i	1.22797	+	2.12690i
$689$	5565.62	−	9639.94i	0.307741	−	0.533022i
$690$	−3315.76	+	5743.07i	−0.182941	+	0.316862i
$691$	12665.3	+	21937.0i	0.697267	+	1.20770i	0.969410	+	0.245445i	$0.0789342\pi$
$691$	12665.3	+	21937.0i	0.697267	+	1.20770i	−0.272143	+	0.962257i	$0.587732\pi$
$692$	4323.68			0.237517
$693$	−1212.23	+	1977.85i	−0.0664485	+	0.108416i
$694$	−17710.8			−0.968723
$695$	7833.77	+	13568.5i	0.427557	+	0.740550i
$696$	−7016.39	+	12152.7i	−0.382120	+	0.661851i
$697$	538.969	−	933.522i	0.0292897	−	0.0507312i
$698$	6435.08	+	11145.9i	0.348956	+	0.604410i
$699$	−8482.25			−0.458981
$700$	35142.3	+	922.859i	1.89751	+	0.0498297i
$701$	−27184.1			−1.46467			−0.732333	−	0.680947i	$-0.761568\pi$
$701$	−27184.1			−1.46467			−0.732333	+	0.680947i	$0.761568\pi$
$702$	2771.30	+	4800.03i	0.148997	+	0.258070i
$703$	10288.3	−	17819.8i	0.551961	−	0.956025i
$704$	6413.69	−	11108.8i	0.343360	−	0.594716i
$705$	−5176.68	−	8966.27i	−0.276546	−	0.478992i
$706$	−65839.5			−3.50977
$707$	10205.2	+	18799.0i	0.542867	+	1.00001i
$708$	−31783.4			−1.68714
$709$	−8072.75	−	13982.4i	−0.427614	−	0.740649i	0.569047	−	0.822305i	$-0.307312\pi$
$709$	−8072.75	−	13982.4i	−0.427614	−	0.740649i	−0.996661	+	0.0816561i	$0.973979\pi$
$710$	−11593.6	+	20080.7i	−0.612816	+	1.06143i
$711$	−1969.41	+	3411.12i	−0.103880	+	0.179925i
$712$	−51248.2	−	88764.5i	−2.69748	−	4.67218i
$713$	−4795.41			−0.251879
$714$	−6117.92	−	11269.8i	−0.320669	−	0.590703i
$715$	−2993.20			−0.156558
$716$	24589.1	+	42589.6i	1.28343	+	2.22297i
$717$	−5148.68	+	8917.77i	−0.268174	+	0.464491i
$718$	−3593.30	+	6223.77i	−0.186770	+	0.323494i
$719$	−8648.74	−	14980.0i	−0.448600	−	0.776998i	0.549695	−	0.835365i	$-0.314744\pi$
$719$	−8648.74	−	14980.0i	−0.448600	−	0.776998i	−0.998295	+	0.0583673i	$0.981411\pi$
$720$	9095.92			0.470812
$721$	26749.9	+	702.470i	1.38172	+	0.0362848i
$722$	26690.4			1.37578
$723$	−3954.17	−	6848.82i	−0.203398	−	0.352296i
$724$	2508.44	−	4344.74i	0.128764	−	0.223026i
$725$	−3403.43	+	5894.91i	−0.174345	+	0.301975i
$726$	−9055.74	−	15685.0i	−0.462934	−	0.801825i
$727$	3514.71			0.179303			0.0896516	−	0.995973i	$-0.471425\pi$
$727$	3514.71			0.179303			0.0896516	+	0.995973i	$0.471425\pi$
$728$	24194.1	−	39474.6i	1.23172	−	2.00965i
$729$	729.000			0.0370370
$730$	4887.89	+	8466.08i	0.247821	+	0.429238i
$731$	5301.83	−	9183.04i	0.268256	−	0.464633i
$732$	−11605.4	+	20101.2i	−0.585996	+	1.01498i
$733$	13755.6	+	23825.4i	0.693144	+	1.20056i	0.970802	+	0.239881i	$0.0771083\pi$
$733$	13755.6	+	23825.4i	0.693144	+	1.20056i	−0.277658	+	0.960680i	$0.589558\pi$
$734$	−7315.16			−0.367858
$735$	2597.28	+	5099.33i	0.130343	+	0.255907i
$736$	−33508.4			−1.67817
$737$	1378.63	+	2387.86i	0.0689044	+	0.119346i
$738$	592.222	−	1025.76i	0.0295393	−	0.0511635i
$739$	−8050.80	+	13944.4i	−0.400749	+	0.694117i	−0.993816	−	0.111035i	$-0.964583\pi$
$739$	−8050.80	+	13944.4i	−0.400749	+	0.694117i	0.593068	+	0.805153i	$0.297917\pi$
$740$	−10589.3	−	18341.2i	−0.526040	−	0.911129i
$741$	12648.9			0.627083
$742$	−14787.3	+	24126.7i	−0.731617	+	1.19369i
$743$	14682.4			0.724961			0.362480	−	0.931991i	$-0.381930\pi$
$743$	14682.4			0.724961			0.362480	+	0.931991i	$0.381930\pi$
$744$	6210.03	+	10756.1i	0.306009	+	0.530024i
$745$	−5006.17	+	8670.93i	−0.246190	+	0.426414i
$746$	−14483.5	+	25086.1i	−0.710828	+	1.23119i
$747$	−1085.59	−	1880.29i	−0.0531720	−	0.0920967i
$748$	−12209.9			−0.596843
$749$	−18346.5	−	481.791i	−0.895016	−	0.0235037i
$750$	19401.9			0.944611
$751$	3636.53	+	6298.66i	0.176696	+	0.306047i	0.940747	−	0.339109i	$-0.110126\pi$
$751$	3636.53	+	6298.66i	0.176696	+	0.306047i	−0.764051	+	0.645156i	$0.776792\pi$
$752$	56385.3	−	97662.2i	2.73426	−	4.73587i
$753$	3086.36	−	5345.73i	0.149367	−	0.258711i
$754$	7426.96	+	12863.9i	0.358719	+	0.621319i
$755$	−2519.23			−0.121436
$756$	−4813.84	−	8867.57i	−0.231584	−	0.426601i
$757$	8505.93			0.408393			0.204196	−	0.978930i	$-0.434542\pi$
$757$	8505.93			0.408393			0.204196	+	0.978930i	$0.434542\pi$
$758$	−1472.19	−	2549.91i	−0.0705440	−	0.122186i
$759$	1563.15	−	2707.46i	0.0747548	−	0.129479i
$760$	19598.4	−	33945.5i	0.935408	−	1.62017i
$761$	−7108.86	−	12312.9i	−0.338628	−	0.586521i	0.645547	−	0.763721i	$-0.276630\pi$
$761$	−7108.86	−	12312.9i	−0.338628	−	0.586521i	−0.984175	+	0.177200i	$0.943296\pi$
$762$	−2799.84			−0.133107
$763$	17258.0	+	31790.9i	0.818848	+	1.50840i
$764$	−87029.3			−4.12121
$765$	−1088.11	−	1884.67i	−0.0514259	−	0.0890722i
$766$	−15555.1	+	26942.2i	−0.733717	+	1.27084i
$767$	−10152.3	+	17584.4i	−0.477939	+	0.827815i
$768$	−609.482	−	1055.65i	−0.0286364	−	0.0495998i
$769$	16379.1			0.768068			0.384034	−	0.923319i	$-0.374534\pi$
$769$	16379.1			0.768068			0.384034	+	0.923319i	$0.374534\pi$
$770$	7606.66	+	199.756i	0.356006	+	0.00934895i
$771$	−6450.62			−0.301314
$772$	−20791.9	−	36012.6i	−0.969323	−	1.67892i
$773$	19948.3	−	34551.6i	0.928192	−	1.60768i	0.141846	−	0.989889i	$-0.454696\pi$
$773$	19948.3	−	34551.6i	0.928192	−	1.60768i	0.786346	−	0.617787i	$-0.211970\pi$
$774$	5825.67	−	10090.4i	0.270542	−	0.468593i
$775$	3012.29	+	5217.45i	0.139619	+	0.241827i
$776$	5124.70			0.237070
$777$	−5479.50	+	8940.23i	−0.252994	+	0.412779i
$778$	41292.5			1.90284
$779$	−1351.52	−	2340.91i	−0.0621609	−	0.107666i
$780$	6509.50	−	11274.8i	0.298817	−	0.517566i
$781$	5465.57	−	9466.65i	0.250414	−	0.433730i
$782$	8640.83	+	14966.4i	0.395135	+	0.684394i
$783$	1953.69			0.0891688
$784$	−33956.5	+	52271.3i	−1.54685	+	2.38116i
$785$	−10364.5			−0.471244
$786$	8965.16	+	15528.1i	0.406840	+	0.704668i
$787$	16564.3	−	28690.2i	0.750257	−	1.29948i	−0.197440	−	0.980315i	$-0.563263\pi$
$787$	16564.3	−	28690.2i	0.750257	−	1.29948i	0.947698	−	0.319169i	$-0.103404\pi$
$788$	16809.1	−	29114.3i	0.759899	−	1.31618i
$789$	−6885.23	−	11925.6i	−0.310672	−	0.538100i
$790$	12920.0			0.581865
$791$	6512.15	−	10625.1i	0.292725	−	0.477603i
$792$	−8097.12			−0.363281
$793$	7414.07	+	12841.5i	0.332007	+	0.575052i
$794$	−21307.2	+	36905.1i	−0.952346	+	1.64951i
$795$	−2401.18	+	4158.97i	−0.107121	+	0.185539i
$796$	10972.1	+	19004.3i	0.488563	+	0.846216i
$797$	−17851.5			−0.793390			−0.396695	−	0.917951i	$-0.629843\pi$
$797$	−17851.5			−0.793390			−0.396695	+	0.917951i	$0.629843\pi$
$798$	−32144.8	−	844.142i	−1.42596	−	0.0374465i
$799$	−26980.7			−1.19463
$800$	21048.7	+	36457.4i	0.930229	+	1.61120i
$801$	−7134.94	+	12358.1i	−0.314733	+	0.545133i
$802$	−2070.18	+	3585.66i	−0.0911479	+	0.157873i
$803$	−2304.30	−	3991.17i	−0.101267	−	0.175399i
$804$	−11992.8			−0.526061
$805$	−3679.49	−	6777.98i	−0.161099	−	0.296761i
$806$	13146.8			0.574538
$807$	−569.066	−	985.652i	−0.0248229	−	0.0429945i
$808$	−37331.2	+	64659.6i	−1.62538	+	2.81524i
$809$	2528.52	−	4379.52i	0.109886	−	0.190328i	−0.805838	−	0.592136i	$-0.798285\pi$
$809$	2528.52	−	4379.52i	0.109886	−	0.190328i	0.915724	+	0.401808i	$0.131618\pi$
$810$	−1195.62	−	2070.88i	−0.0518641	−	0.0898312i
$811$	−17535.4			−0.759251			−0.379626	−	0.925140i	$-0.623947\pi$
$811$	−17535.4			−0.759251			−0.379626	+	0.925140i	$0.623947\pi$
$812$	−12900.9	−	23764.7i	−0.557553	−	1.02707i
$813$	16106.5			0.694810
$814$	6971.35	+	12074.7i	0.300179	+	0.519925i
$815$	−6454.39	+	11179.3i	−0.277408	+	0.480484i
$816$	11851.9	−	20528.1i	0.508456	−	0.880672i
$817$	−13294.9	−	23027.5i	−0.569315	−	0.986083i
$818$	77992.1			3.33366
$819$	−6443.68	−	169.215i	−0.274921	−	0.00721960i
$820$	−2782.14			−0.118484
$821$	9350.39	+	16195.3i	0.397480	+	0.688455i	0.993414	−	0.114578i	$-0.0365516\pi$
$821$	9350.39	+	16195.3i	0.397480	+	0.688455i	−0.595935	+	0.803033i	$0.703218\pi$
$822$	14879.4	−	25771.9i	0.631361	−	1.09355i
$823$	−11111.3	+	19245.4i	−0.470615	+	0.815129i	−0.999435	−	0.0336046i	$-0.989301\pi$
$823$	−11111.3	+	19245.4i	−0.470615	+	0.815129i	0.528820	+	0.848734i	$0.322635\pi$
$824$	46701.0	+	80888.5i	1.97440	+	3.41976i
$825$	−3927.66			−0.165750
$826$	26973.8	−	44009.8i	1.13624	−	1.85387i
$827$	25178.9			1.05872			0.529358	−	0.848399i	$-0.322433\pi$
$827$	25178.9			1.05872			0.529358	+	0.848399i	$0.322433\pi$
$828$	6798.98	+	11776.2i	0.285363	+	0.494264i
$829$	−6139.45	+	10633.8i	−0.257216	+	0.445511i	−0.965495	−	0.260421i	$-0.916139\pi$
$829$	−6139.45	+	10633.8i	−0.257216	+	0.445511i	0.708279	+	0.705933i	$0.249472\pi$
$830$	−3560.91	+	6167.67i	−0.148917	+	0.257931i
$831$	−7172.41	−	12423.0i	−0.299408	−	0.518590i
$832$	35643.1			1.48522
$833$	14892.7	+	782.721i	0.619448	+	0.0325566i
$834$	44863.5			1.86270
$835$	−8930.54	−	15468.2i	−0.370125	−	0.641075i
$836$	−15308.8	+	26515.7i	−0.633334	+	1.09697i
$837$	864.582	−	1497.50i	0.0357041	−	0.0618413i
$838$	−8945.30	−	15493.7i	−0.368747	−	0.638689i
$839$	−25765.0			−1.06020			−0.530098	−	0.847936i	$-0.677845\pi$
$839$	−25765.0			−1.06020			−0.530098	+	0.847936i	$0.677845\pi$
$840$	−10438.1	+	17030.6i	−0.428748	+	0.699536i
$841$	−19153.2			−0.785321
$842$	−41540.1	−	71949.6i	−1.70020	−	2.94483i
$843$	−3114.85	+	5395.08i	−0.127261	+	0.220423i
$844$	47180.9	−	81719.7i	1.92421	−	3.33283i
$845$	1950.64	+	3378.61i	0.0794132	+	0.137548i
$846$	−29646.5			−1.20481
$847$	21056.0	+	552.943i	0.854181	+	0.0224313i
$848$	−52308.2			−2.11824
$849$	3836.42	+	6644.88i	0.155083	+	0.268612i
$850$	10855.7	−	18802.6i	0.438055	−	0.758734i
$851$	7065.75	−	12238.2i	0.284619	−	0.492974i
$852$	23772.6	+	41175.4i	0.955912	+	1.65569i
$853$	37864.5			1.51988			0.759939	−	0.649995i	$-0.225229\pi$
$853$	37864.5			1.51988			0.759939	+	0.649995i	$0.225229\pi$
$854$	−17984.5	−	33129.2i	−0.720627	−	1.32747i
$855$	−5457.12			−0.218280
$856$	−32030.0	−	55477.6i	−1.27893	−	2.21517i
$857$	14604.4	−	25295.5i	0.582118	−	1.00826i	−0.413110	−	0.910681i	$-0.635557\pi$
$857$	14604.4	−	25295.5i	0.582118	−	1.00826i	0.995228	−	0.0975771i	$-0.0311093\pi$
$858$	−4285.46	+	7422.64i	−0.170517	+	0.295343i
$859$	−17451.5	−	30226.8i	−0.693173	−	1.20061i	−0.970793	−	0.239920i	$-0.922879\pi$
$859$	−17451.5	−	30226.8i	−0.693173	−	1.20061i	0.277619	−	0.960691i	$-0.410455\pi$
$860$	−27367.8			−1.08516
$861$	657.186	+	1210.60i	0.0260126	+	0.0479178i
$862$	25947.6			1.02527
$863$	6794.67	+	11768.7i	0.268011	+	0.464208i	0.968348	−	0.249604i	$-0.0803004\pi$
$863$	6794.67	+	11768.7i	0.268011	+	0.464208i	−0.700337	+	0.713812i	$0.746967\pi$
$864$	6041.35	−	10463.9i	0.237883	−	0.412025i
$865$	−595.840	+	1032.03i	−0.0234210	+	0.0405664i
$866$	13949.5	+	24161.2i	0.547371	+	0.948074i
$867$	9067.79			0.355200
$868$	−23924.8	−	628.279i	−0.935552	−	0.0245682i
$869$	−6090.89			−0.237767
$870$	−3204.22	−	5549.87i	−0.124866	−	0.216274i
$871$	−3830.76	+	6635.07i	−0.149025	+	0.258118i
$872$	−63130.7	+	109346.i	−2.45169	+	4.24645i
$873$	−356.739	−	617.890i	−0.0138302	−	0.0239547i
$874$	43335.7			1.67717
$875$	−11791.1	+	19238.1i	−0.455556	+	0.743275i
$876$	20045.3			0.773135
$877$	1189.87	+	2060.92i	0.0458144	+	0.0793528i	0.888023	−	0.459799i	$-0.152078\pi$
$877$	1189.87	+	2060.92i	0.0458144	+	0.0793528i	−0.842209	+	0.539151i	$0.818745\pi$
$878$	2189.61	−	3792.51i	0.0841637	−	0.145776i
$879$	840.074	−	1455.05i	0.0322355	−	0.0558335i
$880$	7032.85	+	12181.3i	0.269406	+	0.466625i
$881$	−24235.5			−0.926803			−0.463401	−	0.886148i	$-0.653371\pi$
$881$	−24235.5			−0.926803			−0.463401	+	0.886148i	$0.653371\pi$
$882$	16364.1	+	860.057i	0.624726	+	0.0328340i
$883$	−9844.13			−0.375177			−0.187589	−	0.982248i	$-0.560067\pi$
$883$	−9844.13			−0.375177			−0.187589	+	0.982248i	$0.560067\pi$
$884$	−16963.6	−	29381.9i	−0.645418	−	1.11790i
$885$	4380.03	−	7586.43i	0.166365	−	0.288153i
$886$	−34576.3	+	59887.9i	−1.31108	+	2.27085i
$887$	−14304.9	−	24776.9i	−0.541502	−	0.937910i	−0.998818	−	0.0486051i	$-0.984522\pi$
$887$	−14304.9	−	24776.9i	−0.541502	−	0.937910i	0.457316	−	0.889304i	$-0.348811\pi$
$888$	−36600.5			−1.38314
$889$	1701.54	−	2776.19i	0.0641932	−	0.104736i
$890$	46807.7			1.76292
$891$	563.654	+	976.277i	0.0211932	+	0.0367076i
$892$	−32749.2	+	56723.2i	−1.22929	+	2.12919i
$893$	−33828.5	+	58592.7i	−1.26767	+	2.19567i
$894$	14335.0	+	24828.9i	0.536279	+	0.928863i
$895$	−13554.4			−0.506226
$896$	−24299.4	−	638.118i	−0.906013	−	0.0237925i
$897$	8686.98			0.323355
$898$	−43862.6	−	75972.2i	−1.62997	−	2.82319i
$899$	2317.04	−	4013.24i	0.0859596	−	0.148886i
$900$	8541.72	−	14794.7i	0.316360	−	0.547952i
$901$	6257.44	+	10838.2i	0.231371	+	0.400747i
$902$	1831.59			0.0676113
$903$	6464.73	+	11908.7i	0.238242	+	0.438866i
$904$	43498.0			1.60036
$905$	691.368	+	1197.48i	0.0253943	+	0.0439842i
$906$	−3606.86	+	6247.26i	−0.132263	+	0.229086i
$907$	−22289.2	+	38606.0i	−0.815986	+	1.41333i	0.0926313	+	0.995700i	$0.470472\pi$
$907$	−22289.2	+	38606.0i	−0.815986	+	1.41333i	−0.908618	+	0.417629i	$0.862861\pi$
$908$	−51838.8	−	89787.5i	−1.89464	−	3.28161i
$909$	10394.8			0.379288
$910$	10087.5	+	18582.2i	0.367470	+	0.676915i
$911$	45870.6			1.66823			0.834116	−	0.551589i	$-0.185978\pi$
$911$	45870.6			1.66823			0.834116	+	0.551589i	$0.185978\pi$
$912$	−29720.0	−	51476.5i	−1.07909	−	1.86903i
$913$	1678.72	−	2907.63i	0.0608517	−	0.105398i
$914$	9849.07	−	17059.1i	0.356431	−	0.617357i
$915$	−3198.66	−	5540.24i	−0.115568	−	0.200169i
$916$	12405.6			0.447479
$917$	−20845.3	−	547.412i	−0.750680	−	0.0197133i
$918$	−6231.55			−0.224043
$919$	−15544.1	−	26923.3i	−0.557948	−	0.966394i	−0.997668	−	0.0682590i	$-0.978256\pi$
$919$	−15544.1	−	26923.3i	−0.557948	−	0.966394i	0.439720	−	0.898135i	$-0.355078\pi$
$920$	13459.8	−	23313.0i	0.482343	−	0.835443i
$921$	5479.53	−	9490.83i	0.196044	−	0.339558i
$922$	25782.4	+	44656.4i	0.920930	+	1.59510i
$923$	30374.0			1.08318
$924$	8153.45	−	13303.0i	0.290291	−	0.473632i
$925$	−17753.7			−0.631069
$926$	114.866	+	198.954i	0.00407639	+	0.00706052i
$927$	6501.87	−	11261.6i	0.230366	−	0.399006i
$928$	16190.6	−	28042.9i	0.572717	−	0.991975i
$929$	21047.3	+	36454.9i	0.743313	+	1.28746i	0.950979	+	0.309257i	$0.100080\pi$
$929$	21047.3	+	36454.9i	0.743313	+	1.28746i	−0.207665	+	0.978200i	$0.566586\pi$
$930$	−5671.95			−0.199990
$931$	20372.3	−	31360.3i	0.717159	−	1.10397i
$932$	57051.5			2.00513
$933$	5238.40	+	9073.18i	0.183813	+	0.318374i
$934$	4069.43	−	7048.47i	0.142565	−	0.246930i
$935$	1682.63	−	2914.40i	0.0588534	−	0.101937i
$936$	−11249.6	−	19484.9i	−0.392847	−	0.680431i
$937$	−44385.1			−1.54749			−0.773745	−	0.633497i	$-0.781619\pi$
$937$	−44385.1			−1.54749			−0.773745	+	0.633497i	$0.781619\pi$
$938$	10178.0	−	16606.1i	0.354288	−	0.578049i
$939$	−26136.3			−0.908334
$940$	34818.3	+	60307.1i	1.20814	+	2.09255i
$941$	−20495.8	+	35499.8i	−0.710036	+	1.22982i	0.254807	+	0.966992i	$0.417988\pi$
$941$	−20495.8	+	35499.8i	−0.710036	+	1.22982i	−0.964843	+	0.262827i	$0.915345\pi$
$942$	−14839.3	+	25702.4i	−0.513259	+	0.888990i
$943$	−928.197	−	1607.68i	−0.0320533	−	0.0555179i
$944$	95416.1			3.28976
$945$	2780.00	+	73.0046i	0.0956968	+	0.00251306i
$946$	18017.4			0.619233
$947$	26311.2	+	45572.4i	0.902851	+	1.56378i	0.823777	+	0.566914i	$0.191863\pi$
$947$	26311.2	+	45572.4i	0.902851	+	1.56378i	0.0790737	+	0.996869i	$0.474804\pi$
$948$	13246.2	−	22943.2i	0.453816	−	0.786033i
$949$	6402.90	−	11090.1i	0.219017	−	0.379348i
$950$	−27221.8	−	47149.6i	−0.929676	−	1.61025i
$951$	−5820.99			−0.198484
$952$	24834.7	+	45747.9i	0.845479	+	1.55746i
$953$	−10798.1			−0.367035			−0.183517	−	0.983016i	$-0.558748\pi$
$953$	−10798.1			−0.367035			−0.183517	+	0.983016i	$0.558748\pi$
$954$	6875.70	+	11909.1i	0.233343	+	0.404162i
$955$	11993.4	−	20773.1i	0.406384	−	0.703877i
$956$	34630.0	−	59980.9i	1.17156	−	2.02921i
$957$	1510.57	+	2616.38i	0.0510238	+	0.0883758i
$958$	−37345.8			−1.25949
$959$	16511.6	+	30416.0i	0.555983	+	1.02418i
$960$	−15377.5			−0.516987
$961$	12844.7	+	22247.7i	0.431162	+	0.746794i
$962$	−19371.1	+	33551.7i	−0.649219	+	1.12448i
$963$	−4459.32	+	7723.77i	−0.149221	+	0.258458i
$964$	26595.7	+	46065.1i	0.888579	+	1.53906i
$965$	11461.2			0.382331
$966$	−22076.3	−	579.738i	−0.735294	−	0.0193093i
$967$	15648.9			0.520408			0.260204	−	0.965554i	$-0.416210\pi$
$967$	15648.9			0.520408			0.260204	+	0.965554i	$0.416210\pi$
$968$	36760.2	+	63670.6i	1.22058	+	2.11410i
$969$	−7110.59	+	12315.9i	−0.235733	+	0.408301i
$970$	−1170.17	+	2026.79i	−0.0387338	+	0.0670889i
$971$	−23629.9	−	40928.2i	−0.780968	−	1.35268i	−0.931379	−	0.364052i	$-0.881393\pi$
$971$	−23629.9	−	40928.2i	−0.780968	−	1.35268i	0.150411	−	0.988624i	$-0.451940\pi$
$972$	−4903.25			−0.161802
$973$	−27264.8	+	44484.6i	−0.898323	+	1.46568i
$974$	−81595.2			−2.68427
$975$	−5456.83	−	9451.51i	−0.179239	−	0.310452i
$976$	34840.4	−	60345.3i	1.14264	−	1.97910i
$977$	24483.2	−	42406.2i	0.801728	−	1.38863i	−0.116749	−	0.993161i	$-0.537247\pi$
$977$	24483.2	−	42406.2i	0.801728	−	1.38863i	0.918478	−	0.395473i	$-0.129419\pi$
$978$	18481.9	+	32011.6i	0.604281	+	1.04665i
$979$	−22066.6			−0.720380
$980$	−17469.3	−	34298.1i	−0.569425	−	1.11797i
$981$	17578.5			0.572109
$982$	6352.29	+	11002.5i	0.206426	+	0.357540i
$983$	9555.64	−	16550.9i	0.310049	−	0.537020i	−0.668324	−	0.743870i	$-0.732988\pi$
$983$	9555.64	−	16550.9i	0.310049	−	0.537020i	0.978373	+	0.206850i	$0.0663214\pi$
$984$	−2404.02	+	4163.89i	−0.0778836	+	0.134898i
$985$	4632.89	+	8024.39i	0.149864	+	0.259572i
$986$	−16700.3			−0.539397
$987$	18017.0	−	29396.1i	0.581040	−	0.948013i
$988$	−85076.4			−2.73951
$989$	−9130.65	−	15814.8i	−0.293567	−	0.508473i
$990$	1848.88	−	3202.36i	0.0593548	−	0.102806i
$991$	27051.3	−	46854.1i	0.867115	−	1.50189i	0.00218424	−	0.999998i	$-0.499305\pi$
$991$	27051.3	−	46854.1i	0.867115	−	1.50189i	0.864931	−	0.501890i	$-0.167362\pi$
$992$	−14329.9	−	24820.1i	−0.458643	−	0.794393i
$993$	17194.5			0.549498
$994$	−77189.9	−	2027.06i	−2.46309	−	0.0646824i
$995$	−6048.21			−0.192705
$996$	7301.65	+	12646.8i	0.232291	+	0.402339i
$997$	−4596.40	+	7961.20i	−0.146008	+	0.252892i	−0.929748	−	0.368196i	$-0.879976\pi$
$997$	−4596.40	+	7961.20i	−0.146008	+	0.252892i	0.783741	+	0.621088i	$0.213309\pi$
$998$	−1840.70	+	3188.19i	−0.0583832	+	0.101123i
$999$	2547.82	+	4412.95i	0.0806901	+	0.139759i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.4.e.b.4.1	✓	6
3.2	odd	2		63.4.e.c.46.3		6
4.3	odd	2		336.4.q.k.193.2		6
7.2	even	3	inner	21.4.e.b.16.1	yes	6
7.3	odd	6		147.4.a.m.1.3		3
7.4	even	3		147.4.a.l.1.3		3
7.5	odd	6		147.4.e.n.79.1		6
7.6	odd	2		147.4.e.n.67.1		6
21.2	odd	6		63.4.e.c.37.3		6
21.5	even	6		441.4.e.w.226.3		6
21.11	odd	6		441.4.a.s.1.1		3
21.17	even	6		441.4.a.t.1.1		3
21.20	even	2		441.4.e.w.361.3		6
28.3	even	6		2352.4.a.cg.1.2		3
28.11	odd	6		2352.4.a.ci.1.2		3
28.23	odd	6		336.4.q.k.289.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.e.b.4.1	✓	6	1.1	even	1	trivial
21.4.e.b.16.1	yes	6	7.2	even	3	inner
63.4.e.c.37.3		6	21.2	odd	6
63.4.e.c.46.3		6	3.2	odd	2
147.4.a.l.1.3		3	7.4	even	3
147.4.a.m.1.3		3	7.3	odd	6
147.4.e.n.67.1		6	7.6	odd	2
147.4.e.n.79.1		6	7.5	odd	6
336.4.q.k.193.2		6	4.3	odd	2
336.4.q.k.289.2		6	28.23	odd	6
441.4.a.s.1.1		3	21.11	odd	6
441.4.a.t.1.1		3	21.17	even	6
441.4.e.w.226.3		6	21.5	even	6
441.4.e.w.361.3		6	21.20	even	2
2352.4.a.cg.1.2		3	28.3	even	6
2352.4.a.ci.1.2		3	28.11	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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	21.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.65415 - 4.59712i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-10.0890 + 17.4746i) q^{4} +(-2.78070 - 4.81631i) q^{5} -15.9249 q^{6} +(9.67799 - 15.7904i) q^{7} +64.6443 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(-2.65415 - 4.59712i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-10.0890 + 17.4746i) q^{4} +(-2.78070 - 4.81631i) q^{5} -15.9249 q^{6} +(9.67799 - 15.7904i) q^{7} +64.6443 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-14.7608 + 25.5664i) q^{10} +(6.95869 - 12.0528i) q^{11} +(30.2670 + 52.4239i) q^{12} +38.6718 q^{13} +(-98.2771 - 2.58082i) q^{14} -16.6842 q^{15} +(-90.8636 - 157.380i) q^{16} +(-21.7394 + 37.6537i) q^{17} +(-23.8873 + 41.3741i) q^{18} +(54.5139 + 94.4208i) q^{19} +112.218 q^{20} +(-26.5077 - 48.8297i) q^{21} -73.8775 q^{22} +(37.4389 + 64.8461i) q^{23} +(96.9665 - 167.951i) q^{24} +(47.0354 - 81.4677i) q^{25} +(-102.641 - 177.779i) q^{26} -27.0000 q^{27} +(178.290 + 328.429i) q^{28} -72.3589 q^{29} +(44.2823 + 76.6992i) q^{30} +(-32.0215 + 55.4629i) q^{31} +(-223.754 + 387.553i) q^{32} +(-20.8761 - 36.1584i) q^{33} +230.798 q^{34} +(-102.963 - 2.70387i) q^{35} +181.602 q^{36} +(-94.3636 - 163.443i) q^{37} +(289.376 - 501.213i) q^{38} +(58.0077 - 100.472i) q^{39} +(-179.756 - 311.347i) q^{40} -24.7923 q^{41} +(-154.121 + 251.460i) q^{42} -243.881 q^{43} +(140.412 + 243.201i) q^{44} +(-25.0263 + 43.3468i) q^{45} +(198.737 - 344.222i) q^{46} +(310.274 + 537.411i) q^{47} -545.182 q^{48} +(-155.673 - 305.638i) q^{49} -499.356 q^{50} +(65.2182 + 112.961i) q^{51} +(-390.159 + 675.776i) q^{52} +(143.919 - 249.276i) q^{53} +(71.6620 + 124.122i) q^{54} -77.4001 q^{55} +(625.627 - 1020.76i) q^{56} +327.083 q^{57} +(192.051 + 332.642i) q^{58} +(-262.526 + 454.708i) q^{59} +(168.327 - 291.551i) q^{60} +(191.718 + 332.065i) q^{61} +339.960 q^{62} +(-166.625 - 4.37567i) q^{63} +921.681 q^{64} +(-107.535 - 186.255i) q^{65} +(-110.816 + 191.939i) q^{66} +(-99.0583 + 171.574i) q^{67} +(-438.657 - 759.776i) q^{68} +224.634 q^{69} +(260.849 + 480.510i) q^{70} +785.432 q^{71} +(-290.900 - 503.853i) q^{72} +(165.570 - 286.776i) q^{73} +(-500.910 + 867.602i) q^{74} +(-141.106 - 244.403i) q^{75} -2199.96 q^{76} +(-122.972 - 226.527i) q^{77} -615.844 q^{78} +(-218.823 - 379.013i) q^{79} +(-505.329 + 875.255i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(65.8024 + 113.973i) q^{82} +241.241 q^{83} +(1120.72 + 29.4308i) q^{84} +241.803 q^{85} +(647.297 + 1121.15i) q^{86} +(-108.538 + 187.994i) q^{87} +(449.840 - 779.145i) q^{88} +(-792.772 - 1373.12i) q^{89} +265.694 q^{90} +(374.265 - 610.643i) q^{91} -1510.88 q^{92} +(96.0646 + 166.389i) q^{93} +(1647.03 - 2852.73i) q^{94} +(303.173 - 525.112i) q^{95} +(671.261 + 1162.66i) q^{96} +79.2754 q^{97} +(-991.877 + 1526.86i) q^{98} -125.256 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} + 9 q^{3} - 25 q^{4} - 11 q^{5} - 6 q^{6} - 13 q^{7} + 78 q^{8} - 27 q^{9}+O(q^{10}) \) 6 * q - q^2 + 9 * q^3 - 25 * q^4 - 11 * q^5 - 6 * q^6 - 13 * q^7 + 78 * q^8 - 27 * q^9	\( 6 q - q^{2} + 9 q^{3} - 25 q^{4} - 11 q^{5} - 6 q^{6} - 13 q^{7} + 78 q^{8} - 27 q^{9} + 55 q^{10} - 35 q^{11} + 75 q^{12} + 124 q^{13} - 326 q^{14} - 66 q^{15} - 241 q^{16} - 48 q^{17} - 9 q^{18} + 202 q^{19} + 878 q^{20} + 3 q^{21} - 14 q^{22} - 216 q^{23} + 117 q^{24} - 130 q^{25} - 274 q^{26} - 162 q^{27} - 201 q^{28} + 106 q^{29} - 165 q^{30} + 95 q^{31} - 683 q^{32} + 105 q^{33} - 48 q^{34} + 56 q^{35} + 450 q^{36} - 262 q^{37} + 398 q^{38} + 186 q^{39} - 21 q^{40} + 488 q^{41} - 219 q^{42} + 720 q^{43} + 905 q^{44} - 99 q^{45} + 1056 q^{46} + 210 q^{47} - 1446 q^{48} - 303 q^{49} - 2756 q^{50} + 144 q^{51} - 324 q^{52} - 393 q^{53} + 27 q^{54} - 2062 q^{55} + 1299 q^{56} + 1212 q^{57} + 1249 q^{58} - 1143 q^{59} + 1317 q^{60} + 70 q^{61} + 2118 q^{62} + 126 q^{63} - 798 q^{64} + 472 q^{65} - 21 q^{66} + 628 q^{67} - 1944 q^{68} - 1296 q^{69} + 3251 q^{70} + 636 q^{71} - 351 q^{72} - 988 q^{73} - 1002 q^{74} + 390 q^{75} - 4680 q^{76} + 1073 q^{77} - 1644 q^{78} - 861 q^{79} - 175 q^{80} - 243 q^{81} - 124 q^{82} + 1038 q^{83} + 1620 q^{84} + 3600 q^{85} + 3208 q^{86} + 159 q^{87} + 891 q^{88} - 1766 q^{89} - 990 q^{90} - 654 q^{91} - 1344 q^{92} - 285 q^{93} + 3294 q^{94} + 736 q^{95} + 2049 q^{96} + 38 q^{97} - 4267 q^{98} + 630 q^{99}+O(q^{100}) \) 6 * q - q^2 + 9 * q^3 - 25 * q^4 - 11 * q^5 - 6 * q^6 - 13 * q^7 + 78 * q^8 - 27 * q^9 + 55 * q^10 - 35 * q^11 + 75 * q^12 + 124 * q^13 - 326 * q^14 - 66 * q^15 - 241 * q^16 - 48 * q^17 - 9 * q^18 + 202 * q^19 + 878 * q^20 + 3 * q^21 - 14 * q^22 - 216 * q^23 + 117 * q^24 - 130 * q^25 - 274 * q^26 - 162 * q^27 - 201 * q^28 + 106 * q^29 - 165 * q^30 + 95 * q^31 - 683 * q^32 + 105 * q^33 - 48 * q^34 + 56 * q^35 + 450 * q^36 - 262 * q^37 + 398 * q^38 + 186 * q^39 - 21 * q^40 + 488 * q^41 - 219 * q^42 + 720 * q^43 + 905 * q^44 - 99 * q^45 + 1056 * q^46 + 210 * q^47 - 1446 * q^48 - 303 * q^49 - 2756 * q^50 + 144 * q^51 - 324 * q^52 - 393 * q^53 + 27 * q^54 - 2062 * q^55 + 1299 * q^56 + 1212 * q^57 + 1249 * q^58 - 1143 * q^59 + 1317 * q^60 + 70 * q^61 + 2118 * q^62 + 126 * q^63 - 798 * q^64 + 472 * q^65 - 21 * q^66 + 628 * q^67 - 1944 * q^68 - 1296 * q^69 + 3251 * q^70 + 636 * q^71 - 351 * q^72 - 988 * q^73 - 1002 * q^74 + 390 * q^75 - 4680 * q^76 + 1073 * q^77 - 1644 * q^78 - 861 * q^79 - 175 * q^80 - 243 * q^81 - 124 * q^82 + 1038 * q^83 + 1620 * q^84 + 3600 * q^85 + 3208 * q^86 + 159 * q^87 + 891 * q^88 - 1766 * q^89 - 990 * q^90 - 654 * q^91 - 1344 * q^92 - 285 * q^93 + 3294 * q^94 + 736 * q^95 + 2049 * q^96 + 38 * q^97 - 4267 * q^98 + 630 * q^99

Introduction

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