LMFDB - Embedded newform 38.4.c.c.7.1

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			7.1
Root			$-3.78825 + 6.56144i$ of defining polynomial
Character	$\chi$	$=$	38.7
Dual form			38.4.c.c.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(-4.78825 - 8.29349i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-7.88908 - 13.6643i) q^{5} +(9.57650 - 16.5870i) q^{6} +16.5765 q^{7} -8.00000 q^{8} +(-32.3546 + 56.0399i) q^{9} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(-4.78825 - 8.29349i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-7.88908 - 13.6643i) q^{5} +(9.57650 - 16.5870i) q^{6} +16.5765 q^{7} -8.00000 q^{8} +(-32.3546 + 56.0399i) q^{9} +(15.7782 - 27.3286i) q^{10} +16.0285 q^{11} +38.3060 q^{12} +(33.5522 - 58.1141i) q^{13} +(16.5765 + 28.7113i) q^{14} +(-75.5497 + 130.856i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-19.8025 - 34.2989i) q^{17} -129.419 q^{18} +(14.7639 + 81.4925i) q^{19} +63.1126 q^{20} +(-79.3724 - 137.477i) q^{21} +(16.0285 + 27.7621i) q^{22} +(23.8404 - 41.2928i) q^{23} +(38.3060 + 66.3479i) q^{24} +(-61.9750 + 107.344i) q^{25} +134.209 q^{26} +361.123 q^{27} +(-33.1530 + 57.4227i) q^{28} +(59.2021 - 102.541i) q^{29} -302.199 q^{30} +120.050 q^{31} +(16.0000 - 27.7128i) q^{32} +(-76.7483 - 132.932i) q^{33} +(39.6050 - 68.5978i) q^{34} +(-130.773 - 226.506i) q^{35} +(-129.419 - 224.160i) q^{36} +22.0924 q^{37} +(-126.385 + 107.064i) q^{38} -642.624 q^{39} +(63.1126 + 109.314i) q^{40} +(-54.5508 - 94.4847i) q^{41} +(158.745 - 274.954i) q^{42} +(180.312 + 312.310i) q^{43} +(-32.0569 + 55.5242i) q^{44} +1020.99 q^{45} +95.3617 q^{46} +(-96.4726 + 167.095i) q^{47} +(-76.6120 + 132.696i) q^{48} -68.2197 q^{49} -247.900 q^{50} +(-189.638 + 328.463i) q^{51} +(134.209 + 232.456i) q^{52} +(-108.922 + 188.659i) q^{53} +(361.123 + 625.483i) q^{54} +(-126.450 - 219.017i) q^{55} -132.612 q^{56} +(605.164 - 512.651i) q^{57} +236.808 q^{58} +(-211.595 - 366.493i) q^{59} +(-302.199 - 523.424i) q^{60} +(-281.960 + 488.369i) q^{61} +(120.050 + 207.932i) q^{62} +(-536.327 + 928.945i) q^{63} +64.0000 q^{64} -1058.78 q^{65} +(153.497 - 265.864i) q^{66} +(471.426 - 816.534i) q^{67} +158.420 q^{68} -456.615 q^{69} +(261.546 - 453.012i) q^{70} +(332.873 + 576.552i) q^{71} +(258.837 - 448.319i) q^{72} +(93.4728 + 161.900i) q^{73} +(22.0924 + 38.2652i) q^{74} +1187.01 q^{75} +(-311.826 - 111.841i) q^{76} +265.696 q^{77} +(-642.624 - 1113.06i) q^{78} +(438.177 + 758.945i) q^{79} +(-126.225 + 218.628i) q^{80} +(-855.571 - 1481.89i) q^{81} +(109.102 - 188.969i) q^{82} -476.297 q^{83} +634.979 q^{84} +(-312.447 + 541.173i) q^{85} +(-360.624 + 624.620i) q^{86} -1133.90 q^{87} -128.228 q^{88} +(482.370 - 835.489i) q^{89} +(1020.99 + 1768.41i) q^{90} +(556.177 - 963.328i) q^{91} +(95.3617 + 165.171i) q^{92} +(-574.827 - 995.629i) q^{93} -385.890 q^{94} +(997.063 - 844.639i) q^{95} -306.448 q^{96} +(792.961 + 1373.45i) q^{97} +(-68.2197 - 118.160i) q^{98} +(-518.595 + 898.234i) 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 $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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
$3$	−4.78825	−	8.29349i	−0.921499	−	1.59608i	−0.797097	−	0.603851i	$-0.793632\pi$
$3$	−4.78825	−	8.29349i	−0.921499	−	1.59608i	−0.124402	−	0.992232i	$-0.539701\pi$
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	−7.88908	−	13.6643i	−0.705620	−	1.22217i	−0.966467	−	0.256790i	$-0.917335\pi$
$5$	−7.88908	−	13.6643i	−0.705620	−	1.22217i	0.260847	−	0.965380i	$-0.415998\pi$
$6$	9.57650	−	16.5870i	0.651598	−	1.12860i
$7$	16.5765			0.895047			0.447523	−	0.894272i	$-0.352306\pi$
$7$	16.5765			0.895047			0.447523	+	0.894272i	$0.352306\pi$
$8$	−8.00000			−0.353553
$9$	−32.3546	+	56.0399i	−1.19832	+	2.07555i
$10$	15.7782	−	27.3286i	0.498949	−	0.864205i
$11$	16.0285			0.439342			0.219671	−	0.975574i	$-0.429502\pi$
$11$	16.0285			0.439342			0.219671	+	0.975574i	$0.429502\pi$
$12$	38.3060			0.921499
$13$	33.5522	−	58.1141i	0.715823	−	1.23984i	−0.246818	−	0.969062i	$-0.579385\pi$
$13$	33.5522	−	58.1141i	0.715823	−	1.23984i	0.962641	−	0.270780i	$-0.0872815\pi$
$14$	16.5765	+	28.7113i	0.316447	+	0.548102i
$15$	−75.5497	+	130.856i	−1.30046	+	2.25246i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−19.8025	−	34.2989i	−0.282518	−	0.489336i	0.689486	−	0.724299i	$-0.257836\pi$
$17$	−19.8025	−	34.2989i	−0.282518	−	0.489336i	−0.972004	+	0.234963i	$0.924503\pi$
$18$	−129.419			−1.69468
$19$	14.7639	+	81.4925i	0.178267	+	0.983982i
$19$	14.7639	+	81.4925i	0.178267	+	0.983982i
$20$	63.1126			0.705620
$21$	−79.3724	−	137.477i	−0.824785	−	1.42857i
$22$	16.0285	+	27.7621i	0.155331	+	0.269041i
$23$	23.8404	−	41.2928i	0.216133	−	0.374354i	−0.737489	−	0.675359i	$-0.763989\pi$
$23$	23.8404	−	41.2928i	0.216133	−	0.374354i	0.953623	+	0.301005i	$0.0973220\pi$
$24$	38.3060	+	66.3479i	0.325799	+	0.564301i
$25$	−61.9750	+	107.344i	−0.495800	+	0.858751i
$26$	134.209			1.01233
$27$	361.123			2.57401
$28$	−33.1530	+	57.4227i	−0.223762	+	0.387567i
$29$	59.2021	−	102.541i	0.379088	−	0.656600i	−0.611842	−	0.790980i	$-0.709571\pi$
$29$	59.2021	−	102.541i	0.379088	−	0.656600i	0.990930	+	0.134381i	$0.0429045\pi$
$30$	−302.199			−1.83912
$31$	120.050			0.695533			0.347767	−	0.937581i	$-0.386940\pi$
$31$	120.050			0.695533			0.347767	+	0.937581i	$0.386940\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$	−76.7483	−	132.932i	−0.404853	−	0.701227i
$34$	39.6050	−	68.5978i	0.199770	−	0.346013i
$35$	−130.773	−	226.506i	−0.631563	−	1.09390i
$36$	−129.419	−	224.160i	−0.599160	−	1.03778i
$37$	22.0924			0.0981614			0.0490807	−	0.998795i	$-0.484371\pi$
$37$	22.0924			0.0981614			0.0490807	+	0.998795i	$0.484371\pi$
$38$	−126.385	+	107.064i	−0.539537	+	0.457056i
$39$	−642.624			−2.63852
$40$	63.1126	+	109.314i	0.249474	+	0.432102i
$41$	−54.5508	−	94.4847i	−0.207790	−	0.359903i	0.743228	−	0.669038i	$-0.233294\pi$
$41$	−54.5508	−	94.4847i	−0.207790	−	0.359903i	−0.951018	+	0.309135i	$0.899960\pi$
$42$	158.745	−	274.954i	0.583211	−	1.01015i
$43$	180.312	+	312.310i	0.639473	+	1.10760i	0.985548	+	0.169394i	$0.0541809\pi$
$43$	180.312	+	312.310i	0.639473	+	1.10760i	−0.346075	+	0.938207i	$0.612486\pi$
$44$	−32.0569	+	55.5242i	−0.109836	+	0.190241i
$45$	1020.99			3.38224
$46$	95.3617			0.305659
$47$	−96.4726	+	167.095i	−0.299404	+	0.518582i	−0.976000	−	0.217772i	$-0.930121\pi$
$47$	−96.4726	+	167.095i	−0.299404	+	0.518582i	0.676596	+	0.736354i	$0.263454\pi$
$48$	−76.6120	+	132.696i	−0.230375	+	0.399021i
$49$	−68.2197			−0.198891
$50$	−247.900			−0.701168
$51$	−189.638	+	328.463i	−0.520680	+	0.901845i
$52$	134.209	+	232.456i	0.357911	+	0.619921i
$53$	−108.922	+	188.659i	−0.282294	+	0.488948i	−0.971949	−	0.235190i	$-0.924429\pi$
$53$	−108.922	+	188.659i	−0.282294	+	0.488948i	0.689655	+	0.724138i	$0.257762\pi$
$54$	361.123	+	625.483i	0.910048	+	1.57625i
$55$	−126.450	−	219.017i	−0.310009	−	0.536951i
$56$	−132.612			−0.316447
$57$	605.164	−	512.651i	1.40624	−	1.19127i
$58$	236.808			0.536111
$59$	−211.595	−	366.493i	−0.466903	−	0.808701i	0.532382	−	0.846504i	$-0.321297\pi$
$59$	−211.595	−	366.493i	−0.466903	−	0.808701i	−0.999285	+	0.0378039i	$0.987964\pi$
$60$	−302.199	−	523.424i	−0.650228	−	1.12623i
$61$	−281.960	+	488.369i	−0.591824	+	1.02507i	0.402162	+	0.915568i	$0.368259\pi$
$61$	−281.960	+	488.369i	−0.591824	+	1.02507i	−0.993987	+	0.109501i	$0.965075\pi$
$62$	120.050	+	207.932i	0.245908	+	0.425925i
$63$	−536.327	+	928.945i	−1.07255	+	1.85772i
$64$	64.0000			0.125000
$65$	−1058.78			−2.02040
$66$	153.497	−	265.864i	0.286275	−	0.495842i
$67$	471.426	−	816.534i	0.859610	−	1.48889i	−0.0126922	−	0.999919i	$-0.504040\pi$
$67$	471.426	−	816.534i	0.859610	−	1.48889i	0.872302	−	0.488968i	$-0.162627\pi$
$68$	158.420			0.282518
$69$	−456.615			−0.796667
$70$	261.546	−	453.012i	0.446583	−	0.773504i
$71$	332.873	+	576.552i	0.556404	+	0.963721i	0.997793	+	0.0664045i	$0.0211528\pi$
$71$	332.873	+	576.552i	0.556404	+	0.963721i	−0.441388	+	0.897316i	$0.645514\pi$
$72$	258.837	−	448.319i	0.423670	−	0.733818i
$73$	93.4728	+	161.900i	0.149865	+	0.259574i	0.931178	−	0.364566i	$-0.118783\pi$
$73$	93.4728	+	161.900i	0.149865	+	0.259574i	−0.781312	+	0.624140i	$0.785449\pi$
$74$	22.0924	+	38.2652i	0.0347053	+	0.0601113i
$75$	1187.01			1.82752
$76$	−311.826	−	111.841i	−0.470644	−	0.168804i
$77$	265.696			0.393232
$78$	−642.624	−	1113.06i	−0.932858	−	1.61576i
$79$	438.177	+	758.945i	0.624035	+	1.08086i	0.988727	+	0.149732i	$0.0478410\pi$
$79$	438.177	+	758.945i	0.624035	+	1.08086i	−0.364692	+	0.931128i	$0.618826\pi$
$80$	−126.225	+	218.628i	−0.176405	+	0.305543i
$81$	−855.571	−	1481.89i	−1.17362	−	2.03277i
$82$	109.102	−	188.969i	0.146930	−	0.254490i
$83$	−476.297			−0.629885			−0.314942	−	0.949111i	$-0.601985\pi$
$83$	−476.297			−0.629885			−0.314942	+	0.949111i	$0.601985\pi$
$84$	634.979			0.824785
$85$	−312.447	+	541.173i	−0.398701	+	0.690570i
$86$	−360.624	+	624.620i	−0.452176	+	0.783192i
$87$	−1133.90			−1.39732
$88$	−128.228			−0.155331
$89$	482.370	−	835.489i	0.574507	−	0.995075i	−0.421588	−	0.906787i	$-0.638527\pi$
$89$	482.370	−	835.489i	0.574507	−	0.995075i	0.996095	−	0.0882878i	$-0.0281395\pi$
$90$	1020.99	+	1768.41i	1.19580	+	2.07119i
$91$	556.177	−	963.328i	0.640695	−	1.10972i
$92$	95.3617	+	165.171i	0.108067	+	0.187177i
$93$	−574.827	−	995.629i	−0.640933	−	1.11013i
$94$	−385.890			−0.423421
$95$	997.063	−	844.639i	1.07680	−	0.912191i
$96$	−306.448			−0.325799
$97$	792.961	+	1373.45i	0.830031	+	1.43766i	0.898013	+	0.439969i	$0.145011\pi$
$97$	792.961	+	1373.45i	0.830031	+	1.43766i	−0.0679822	+	0.997687i	$0.521656\pi$
$98$	−68.2197	−	118.160i	−0.0703187	−	0.121796i
$99$	−518.595	+	898.234i	−0.526473	+	0.911878i
$100$	−247.900	−	429.376i	−0.247900	−	0.429376i
$101$	521.913	−	903.980i	0.514181	−	0.890588i	−0.485683	−	0.874135i	$-0.661429\pi$
$101$	521.913	−	903.980i	0.514181	−	0.890588i	0.999865	−	0.0164532i	$-0.00523746\pi$
$102$	−758.554			−0.736353
$103$	1427.83			1.36591			0.682954	−	0.730461i	$-0.260695\pi$
$103$	1427.83			1.36591			0.682954	+	0.730461i	$0.260695\pi$
$104$	−268.417	+	464.912i	−0.253082	+	0.438350i
$105$	−1252.35	+	2169.13i	−1.16397	+	2.01605i
$106$	−435.688			−0.399225
$107$	500.924			0.452581			0.226290	−	0.974060i	$-0.427340\pi$
$107$	500.924			0.452581			0.226290	+	0.974060i	$0.427340\pi$
$108$	−722.246	+	1250.97i	−0.643501	+	1.11458i
$109$	−606.462	−	1050.42i	−0.532922	−	0.923048i	−0.999261	−	0.0384417i	$-0.987761\pi$
$109$	−606.462	−	1050.42i	−0.532922	−	0.923048i	0.466339	−	0.884606i	$-0.345573\pi$
$110$	252.900	−	438.035i	0.219209	−	0.379682i
$111$	−105.784	−	183.223i	−0.0904556	−	0.156674i
$112$	−132.612	−	229.691i	−0.111881	−	0.193783i
$113$	738.956			0.615178			0.307589	−	0.951519i	$-0.400478\pi$
$113$	738.956			0.615178			0.307589	+	0.951519i	$0.400478\pi$
$114$	1493.10	+	535.524i	1.22668	+	0.439968i
$115$	−752.315			−0.610033
$116$	236.808	+	410.164i	0.189544	+	0.328300i
$117$	2171.14	+	3760.52i	1.71557	+	2.97145i
$118$	423.190	−	732.986i	0.330151	−	0.571838i
$119$	−328.256	−	568.556i	−0.252867	−	0.437978i
$120$	604.398	−	1046.85i	0.459781	−	0.796364i
$121$	−1074.09			−0.806978
$122$	−1127.84			−0.836966
$123$	−522.405	+	904.832i	−0.382957	+	0.663301i
$124$	−240.099	+	415.864i	−0.173883	+	0.301175i
$125$	−16.5658			−0.0118535
$126$	−2145.31			−1.51682
$127$	−119.454	+	206.900i	−0.0834632	+	0.144563i	−0.904735	−	0.425974i	$-0.859931\pi$
$127$	−119.454	+	206.900i	−0.0834632	+	0.144563i	0.821272	+	0.570537i	$0.193265\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$	1726.76	−	2990.84i	1.17855	−	2.04131i
$130$	−1058.78	−	1833.86i	−0.714318	−	1.23724i
$131$	−132.624	−	229.712i	−0.0884537	−	0.153206i	0.818404	−	0.574643i	$-0.194859\pi$
$131$	−132.624	−	229.712i	−0.0884537	−	0.153206i	−0.906858	+	0.421437i	$0.861526\pi$
$132$	613.986			0.404853
$133$	244.734	+	1350.86i	0.159557	+	0.880710i
$134$	1885.70			1.21567
$135$	−2848.93	−	4934.49i	−1.81627	−	3.14587i
$136$	158.420	+	274.391i	0.0998852	+	0.173006i
$137$	−1219.22	+	2111.76i	−0.760331	+	1.31693i	0.182349	+	0.983234i	$0.441630\pi$
$137$	−1219.22	+	2111.76i	−0.760331	+	1.31693i	−0.942680	+	0.333698i	$0.891703\pi$
$138$	−456.615	−	790.881i	−0.281664	−	0.487857i
$139$	183.397	−	317.653i	0.111910	−	0.193835i	−0.804630	−	0.593776i	$-0.797636\pi$
$139$	183.397	−	317.653i	0.111910	−	0.193835i	0.916541	+	0.399942i	$0.130970\pi$
$140$	1046.19			0.631563
$141$	1847.74			1.10360
$142$	−665.745	+	1153.10i	−0.393437	+	0.681453i
$143$	537.790	−	931.479i	0.314491	−	0.544715i
$144$	1035.35			0.599160
$145$	−1868.20			−1.06997
$146$	−186.946	+	323.799i	−0.105971	+	0.183547i
$147$	326.653	+	565.780i	0.183278	+	0.317447i
$148$	−44.1848	+	76.5304i	−0.0245403	+	0.0425051i
$149$	1120.88	+	1941.42i	0.616281	+	1.06743i	0.990158	+	0.139952i	$0.0446949\pi$
$149$	1120.88	+	1941.42i	0.616281	+	1.06743i	−0.373877	+	0.927478i	$0.621972\pi$
$150$	1187.01	+	2055.96i	0.646125	+	1.11912i
$151$	−638.195			−0.343944			−0.171972	−	0.985102i	$-0.555014\pi$
$151$	−638.195			−0.343944			−0.171972	+	0.985102i	$0.555014\pi$
$152$	−118.111	−	651.940i	−0.0630269	−	0.347890i
$153$	2562.81			1.35419
$154$	265.696	+	460.199i	0.139028	+	0.240804i
$155$	−947.080	−	1640.39i	−0.490782	−	0.850060i
$156$	1285.25	−	2226.12i	0.659630	−	1.14251i
$157$	−1063.00	−	1841.16i	−0.540358	−	0.935928i	−0.998883	−	0.0472466i	$-0.984955\pi$
$157$	−1063.00	−	1841.16i	−0.540358	−	0.935928i	0.458525	−	0.888682i	$-0.348378\pi$
$158$	−876.354	+	1517.89i	−0.441259	+	0.764283i
$159$	2086.18			1.04054
$160$	−504.901			−0.249474
$161$	395.191	−	684.490i	0.193450	−	0.335064i
$162$	1711.14	−	2963.79i	0.829877	−	1.43739i
$163$	−160.043			−0.0769053			−0.0384526	−	0.999260i	$-0.512243\pi$
$163$	−160.043			−0.0769053			−0.0384526	+	0.999260i	$0.512243\pi$
$164$	436.406			0.207790
$165$	−1210.95	+	2097.42i	−0.571346	+	0.989600i
$166$	−476.297	−	824.971i	−0.222698	−	0.385724i
$167$	−1051.08	+	1820.52i	−0.487036	+	0.843571i	−0.999889	−	0.0149055i	$-0.995255\pi$
$167$	−1051.08	+	1820.52i	−0.487036	+	0.843571i	0.512853	+	0.858476i	$0.328589\pi$
$168$	634.979	+	1099.82i	0.291605	+	0.505075i
$169$	−1153.00	−	1997.05i	−0.524805	−	0.908988i
$170$	−1249.79			−0.563848
$171$	−5044.51	−	1809.29i	−2.25593	−	0.809123i
$172$	−1442.50			−0.639473
$173$	202.732	+	351.142i	0.0890949	+	0.154317i	0.907129	−	0.420853i	$-0.138269\pi$
$173$	202.732	+	351.142i	0.0890949	+	0.154317i	−0.818034	+	0.575170i	$0.804936\pi$
$174$	−1133.90	−	1963.97i	−0.494026	−	0.855678i
$175$	−1027.33	+	1779.39i	−0.443764	+	0.768623i
$176$	−128.228	−	222.097i	−0.0549178	−	0.0951204i
$177$	−2026.34	+	3509.72i	−0.860502	+	1.49043i
$178$	1929.48			0.812476
$179$	−1628.76			−0.680107			−0.340053	−	0.940406i	$-0.610445\pi$
$179$	−1628.76			−0.680107			−0.340053	+	0.940406i	$0.610445\pi$
$180$	−2041.99	+	3536.82i	−0.845559	+	1.46455i
$181$	−1418.42	+	2456.77i	−0.582487	+	1.00890i	0.412696	+	0.910869i	$0.364587\pi$
$181$	−1418.42	+	2456.77i	−0.582487	+	1.00890i	−0.995184	+	0.0980291i	$0.968746\pi$
$182$	2224.71			0.906079
$183$	5400.38			2.18146
$184$	−190.723	+	330.342i	−0.0764147	+	0.132354i
$185$	−174.289	−	301.877i	−0.0692647	−	0.119970i
$186$	1149.65	−	1991.26i	0.453208	−	0.784979i
$187$	−317.403	−	549.759i	−0.124122	−	0.214986i
$188$	−385.890	−	668.382i	−0.149702	−	0.259291i
$189$	5986.15			2.30386
$190$	2460.02	+	882.324i	0.939308	+	0.336898i
$191$	3521.85			1.33420			0.667099	−	0.744969i	$-0.267536\pi$
$191$	3521.85			1.33420			0.667099	+	0.744969i	$0.267536\pi$
$192$	−306.448	−	530.783i	−0.115187	−	0.199510i
$193$	−2367.70	−	4100.97i	−0.883060	−	1.52950i	−0.847922	−	0.530121i	$-0.822146\pi$
$193$	−2367.70	−	4100.97i	−0.883060	−	1.52950i	−0.0351378	−	0.999382i	$-0.511187\pi$
$194$	−1585.92	+	2746.90i	−0.586920	+	1.01658i
$195$	5069.71	+	8781.00i	1.86179	+	3.22472i
$196$	136.439	−	236.320i	0.0497228	−	0.0861225i
$197$	2357.30			0.852541			0.426270	−	0.904596i	$-0.359827\pi$
$197$	2357.30			0.852541			0.426270	+	0.904596i	$0.359827\pi$
$198$	−2074.38			−0.744545
$199$	−342.578	+	593.362i	−0.122034	+	0.211369i	−0.920570	−	0.390579i	$-0.872275\pi$
$199$	−342.578	+	593.362i	−0.122034	+	0.211369i	0.798536	+	0.601947i	$0.205608\pi$
$200$	495.800	−	858.751i	0.175292	−	0.303614i
$201$	−9029.22			−3.16852
$202$	2087.65			0.727162
$203$	981.363	−	1699.77i	0.339301	−	0.587687i
$204$	−758.554	−	1313.85i	−0.260340	−	0.450922i
$205$	−860.710	+	1490.79i	−0.293242	+	0.507910i
$206$	1427.83	+	2473.08i	0.482922	+	0.836445i
$207$	1542.70	+	2672.03i	0.517994	+	0.897192i
$208$	−1073.67			−0.357911
$209$	236.643	+	1306.20i	0.0783203	+	0.432305i
$210$	−5009.40			−1.64610
$211$	265.510	+	459.876i	0.0866277	+	0.150044i	0.906084	−	0.423099i	$-0.139058\pi$
$211$	265.510	+	459.876i	0.0866277	+	0.150044i	−0.819456	+	0.573142i	$0.805724\pi$
$212$	−435.688	−	754.634i	−0.141147	−	0.244474i
$213$	3187.75	−	5521.35i	1.02545	−	1.77613i
$214$	500.924	+	867.626i	0.160012	+	0.277148i
$215$	2844.99	−	4927.67i	0.902451	−	1.56309i
$216$	−2888.98			−0.910048
$217$	1990.00			0.622535
$218$	1212.92	−	2100.84i	0.376833	−	0.652693i
$219$	895.142	−	1550.43i	0.276201	−	0.478395i
$220$	1011.60			0.310009
$221$	−2657.66			−0.808932
$222$	211.568	−	366.446i	0.0639618	−	0.110785i
$223$	−2425.86	−	4201.71i	−0.728463	−	1.26174i	−0.957533	−	0.288325i	$-0.906902\pi$
$223$	−2425.86	−	4201.71i	−0.728463	−	1.26174i	0.229069	−	0.973410i	$-0.426432\pi$
$224$	265.224	−	459.381i	0.0791117	−	0.137025i
$225$	−4010.36	−	6946.15i	−1.18826	−	2.05812i
$226$	738.956	+	1279.91i	0.217498	+	0.376718i
$227$	−3971.88			−1.16134			−0.580668	−	0.814141i	$-0.697208\pi$
$227$	−3971.88			−1.16134			−0.580668	+	0.814141i	$0.697208\pi$
$228$	565.546	+	3121.65i	0.164273	+	0.906738i
$229$	−78.9844			−0.0227923			−0.0113961	−	0.999935i	$-0.503628\pi$
$229$	−78.9844			−0.0227923			−0.0113961	+	0.999935i	$0.503628\pi$
$230$	−752.315	−	1303.05i	−0.215679	−	0.373567i
$231$	−1272.22	−	2203.55i	−0.362363	−	0.627631i
$232$	−473.617	+	820.328i	−0.134028	+	0.232143i
$233$	821.646	+	1423.13i	0.231021	+	0.400140i	0.958109	−	0.286405i	$-0.0924601\pi$
$233$	821.646	+	1423.13i	0.231021	+	0.400140i	−0.727088	+	0.686544i	$0.759127\pi$
$234$	−4342.27	+	7521.04i	−1.21309	+	2.10114i
$235$	3044.32			0.845061
$236$	1692.76			0.466903
$237$	4196.20	−	7268.03i	1.15009	−	1.99202i
$238$	656.512	−	1137.11i	0.178804	−	0.309697i
$239$	−6316.74			−1.70961			−0.854803	−	0.518952i	$-0.826322\pi$
$239$	−6316.74			−1.70961			−0.854803	+	0.518952i	$0.826322\pi$
$240$	2417.59			0.650228
$241$	1747.33	−	3026.46i	0.467034	−	0.808927i	−0.532257	−	0.846583i	$-0.678656\pi$
$241$	1747.33	−	3026.46i	0.467034	−	0.808927i	0.999291	+	0.0376561i	$0.0119891\pi$
$242$	−1074.09	−	1860.38i	−0.285310	−	0.494171i
$243$	−3318.21	+	5747.32i	−0.875982	+	1.51724i
$244$	−1127.84	−	1953.48i	−0.295912	−	0.512535i
$245$	538.191	+	932.174i	0.140342	+	0.243079i
$246$	−2089.62			−0.541583
$247$	5231.22	+	1876.26i	1.34759	+	0.483334i
$248$	−960.396			−0.245908
$249$	2280.63	+	3950.17i	0.580438	+	1.00535i
$250$	−16.5658	−	28.6928i	−0.00419086	−	0.00725878i
$251$	−1815.19	+	3143.99i	−0.456468	+	0.790626i	−0.998771	−	0.0495570i	$-0.984219\pi$
$251$	−1815.19	+	3143.99i	−0.456468	+	0.790626i	0.542303	+	0.840183i	$0.317552\pi$
$252$	−2145.31	−	3715.78i	−0.536276	−	0.928858i
$253$	382.125	−	661.860i	0.0949566	−	0.164470i
$254$	−477.816			−0.118035
$255$	5984.29			1.46961
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	774.708	−	1341.83i	0.188035	−	0.325686i	−0.756560	−	0.653924i	$-0.773122\pi$
$257$	774.708	−	1341.83i	0.188035	−	0.325686i	0.944595	+	0.328238i	$0.106455\pi$
$258$	6907.04			1.66672
$259$	366.215			0.0878590
$260$	2117.56	−	3667.73i	0.505099	−	0.874857i
$261$	3830.92	+	6635.36i	0.908538	+	1.57363i
$262$	265.249	−	459.424i	0.0625462	−	0.108333i
$263$	1904.91	+	3299.39i	0.446622	+	0.773571i	0.998164	−	0.0605757i	$-0.0192937\pi$
$263$	1904.91	+	3299.39i	0.446622	+	0.773571i	−0.551542	+	0.834147i	$0.685960\pi$
$264$	613.986	+	1063.46i	0.143137	+	0.247921i
$265$	3437.18			0.796771
$266$	−2095.02	+	1774.75i	−0.482910	+	0.409087i
$267$	−9238.83			−2.11763
$268$	1885.70	+	3266.13i	0.429805	+	0.744444i
$269$	1688.20	+	2924.05i	0.382644	+	0.662759i	0.991439	−	0.130568i	$-0.0416801\pi$
$269$	1688.20	+	2924.05i	0.382644	+	0.662759i	−0.608795	+	0.793328i	$0.708347\pi$
$270$	5697.85	−	9868.97i	1.28430	−	2.22447i
$271$	1762.75	+	3053.17i	0.395127	+	0.684380i	0.993117	−	0.117123i	$-0.0373673\pi$
$271$	1762.75	+	3053.17i	0.395127	+	0.684380i	−0.597991	+	0.801503i	$0.704034\pi$
$272$	−316.840	+	548.782i	−0.0706295	+	0.122334i
$273$	−10652.5			−2.36160
$274$	−4876.90			−1.07527
$275$	−993.365	+	1720.56i	−0.217826	+	0.377286i
$276$	913.231	−	1581.76i	0.199167	−	0.344967i
$277$	6557.88			1.42247			0.711236	−	0.702953i	$-0.248136\pi$
$277$	6557.88			1.42247			0.711236	+	0.702953i	$0.248136\pi$
$278$	733.589			0.158265
$279$	−3884.16	+	6727.56i	−0.833472	+	1.44362i
$280$	1046.19	+	1812.05i	0.223291	+	0.386752i
$281$	−3943.90	+	6831.04i	−0.837272	+	1.45020i	0.0548952	+	0.998492i	$0.482518\pi$
$281$	−3943.90	+	6831.04i	−0.837272	+	1.45020i	−0.892167	+	0.451705i	$0.850816\pi$
$282$	1847.74	+	3200.38i	0.390182	+	0.675815i
$283$	−1036.37	−	1795.04i	−0.217687	−	0.377046i	0.736413	−	0.676532i	$-0.236518\pi$
$283$	−1036.37	−	1795.04i	−0.217687	−	0.377046i	−0.954101	+	0.299486i	$0.903185\pi$
$284$	−2662.98			−0.556404
$285$	−11779.2	−	4224.79i	−2.44821	−	0.878087i
$286$	2151.16			0.444758
$287$	−904.261	−	1566.23i	−0.185982	−	0.322130i
$288$	1035.35	+	1793.28i	0.211835	+	0.366909i
$289$	1672.22	−	2896.38i	0.340367	−	0.589533i
$290$	−1868.20	−	3235.82i	−0.378291	−	0.655219i
$291$	7593.79	−	13152.8i	1.52974	−	2.64960i
$292$	−747.782			−0.149865
$293$	−7820.84			−1.55938			−0.779690	−	0.626165i	$-0.784624\pi$
$293$	−7820.84			−1.55938			−0.779690	+	0.626165i	$0.784624\pi$
$294$	−653.306	+	1131.56i	−0.129597	+	0.224469i
$295$	−3338.58	+	5782.58i	−0.658913	+	1.14127i
$296$	−176.739			−0.0347053
$297$	5788.25			1.13087
$298$	−2241.76	+	3882.84i	−0.435777	+	0.754787i
$299$	−1599.80	−	2770.93i	−0.309427	−	0.535943i
$300$	−2374.02	+	4111.91i	−0.456879	+	0.791338i
$301$	2988.95	+	5177.00i	0.572359	+	0.991354i
$302$	−638.195	−	1105.39i	−0.121603	−	0.210622i
$303$	−9996.20			−1.89527
$304$	1011.08	−	856.515i	0.190755	−	0.161594i
$305$	8897.62			1.67041
$306$	2562.81	+	4438.92i	0.478778	+	0.829268i
$307$	2968.90	+	5142.28i	0.551934	+	0.955978i	0.998135	+	0.0610453i	$0.0194434\pi$
$307$	2968.90	+	5142.28i	0.551934	+	0.955978i	−0.446201	+	0.894933i	$0.647223\pi$
$308$	−531.392	+	920.397i	−0.0983080	+	0.170274i
$309$	−6836.82	−	11841.7i	−1.25868	−	2.18010i
$310$	1894.16	−	3280.78i	0.347036	−	0.601083i
$311$	1832.63			0.334145			0.167073	−	0.985945i	$-0.446569\pi$
$311$	1832.63			0.334145			0.167073	+	0.985945i	$0.446569\pi$
$312$	5141.00			0.932858
$313$	469.166	−	812.619i	0.0847247	−	0.146747i	−0.820549	−	0.571576i	$-0.806332\pi$
$313$	469.166	−	812.619i	0.0847247	−	0.146747i	0.905274	+	0.424828i	$0.139666\pi$
$314$	2125.99	−	3682.32i	0.382091	−	0.661801i
$315$	16924.5			3.02726
$316$	−3505.42			−0.624035
$317$	3705.73	−	6418.51i	0.656576	−	1.13722i	−0.324920	−	0.945741i	$-0.605337\pi$
$317$	3705.73	−	6418.51i	0.656576	−	1.13722i	0.981496	−	0.191481i	$-0.0613292\pi$
$318$	2086.18	+	3613.38i	0.367885	+	0.637195i
$319$	948.919	−	1643.58i	0.166549	−	0.288472i
$320$	−504.901	−	874.514i	−0.0882026	−	0.152771i
$321$	−2398.55	−	4154.41i	−0.417053	−	0.722357i
$322$	1580.76			0.273579
$323$	2502.74	−	2120.14i	0.431134	−	0.365225i
$324$	6844.57			1.17362
$325$	4158.79	+	7203.24i	0.709810	+	1.22943i
$326$	−160.043	−	277.203i	−0.0271901	−	0.0470947i
$327$	−5807.78	+	10059.4i	−0.982174	+	1.70117i
$328$	436.406	+	755.878i	0.0734649	+	0.127245i
$329$	−1599.18	+	2769.86i	−0.267980	+	0.464155i
$330$	−4843.78			−0.808005
$331$	−5412.69			−0.898817			−0.449408	−	0.893326i	$-0.648365\pi$
$331$	−5412.69			−0.898817			−0.449408	+	0.893326i	$0.648365\pi$
$332$	952.595	−	1649.94i	0.157471	−	0.272748i
$333$	−714.792	+	1238.06i	−0.117629	+	0.203739i
$334$	−4204.32			−0.688773
$335$	−14876.5			−2.42623
$336$	−1269.96	+	2199.63i	−0.206196	+	0.357142i
$337$	−4636.79	−	8031.15i	−0.749501	−	1.29817i	−0.948062	−	0.318085i	$-0.896960\pi$
$337$	−4636.79	−	8031.15i	−0.749501	−	1.29817i	0.198561	−	0.980088i	$-0.436373\pi$
$338$	2305.99	−	3994.09i	0.371093	−	0.642752i
$339$	−3538.31	−	6128.52i	−0.566886	−	0.981875i
$340$	−1249.79	−	2164.69i	−0.199351	−	0.345285i
$341$	1924.21			0.305577
$342$	−1910.73	−	10546.6i	−0.302106	−	1.66754i
$343$	−6816.58			−1.07306
$344$	−1442.50	−	2498.48i	−0.226088	−	0.391596i
$345$	3602.27	+	6239.32i	0.562145	+	0.973663i
$346$	−405.464	+	702.284i	−0.0629996	+	0.109119i
$347$	4837.24	+	8378.35i	0.748348	+	1.29618i	0.948614	+	0.316435i	$0.102486\pi$
$347$	4837.24	+	8378.35i	0.748348	+	1.29618i	−0.200266	+	0.979741i	$0.564181\pi$
$348$	2267.79	−	3927.93i	0.349329	−	0.605056i
$349$	1300.56			0.199477			0.0997387	−	0.995014i	$-0.468199\pi$
$349$	1300.56			0.199477			0.0997387	+	0.995014i	$0.468199\pi$
$350$	−4109.32			−0.627578
$351$	12116.5	−	20986.3i	1.84253	−	3.19136i
$352$	256.455	−	444.194i	0.0388327	−	0.0672603i
$353$	11985.4			1.80713			0.903564	−	0.428454i	$-0.140942\pi$
$353$	11985.4			1.80713			0.903564	+	0.428454i	$0.140942\pi$
$354$	−8105.35			−1.21693
$355$	5252.11	−	9096.93i	0.785221	−	1.36004i
$356$	1929.48	+	3341.96i	0.287253	+	0.497538i
$357$	−3143.54	+	5444.77i	−0.466033	+	0.807193i
$358$	−1628.76	−	2821.09i	−0.240454	−	0.416478i
$359$	2203.95	+	3817.35i	0.324011	+	0.561204i	0.981312	−	0.192425i	$-0.0616352\pi$
$359$	2203.95	+	3817.35i	0.324011	+	0.561204i	−0.657301	+	0.753628i	$0.728302\pi$
$360$	−8167.95			−1.19580
$361$	−6423.05	+	2406.30i	−0.936442	+	0.350823i
$362$	−5673.68			−0.823762
$363$	5143.00	+	8907.94i	0.743630	+	1.28800i
$364$	2224.71	+	3853.31i	0.320347	+	0.554858i
$365$	1474.83	−	2554.48i	0.211496	−	0.366322i
$366$	5400.38	+	9353.73i	0.771263	+	1.33587i
$367$	−3130.04	+	5421.39i	−0.445196	+	0.771102i	−0.998066	−	0.0621658i	$-0.980199\pi$
$367$	−3130.04	+	5421.39i	−0.445196	+	0.771102i	0.552870	+	0.833267i	$0.313533\pi$
$368$	−762.893			−0.108067
$369$	7059.88			0.995997
$370$	348.577	−	603.754i	0.0489775	−	0.0848315i
$371$	−1805.55	+	3127.30i	−0.252667	+	0.437631i
$372$	4598.62			0.640933
$373$	−2745.24			−0.381081			−0.190541	−	0.981679i	$-0.561024\pi$
$373$	−2745.24			−0.381081			−0.190541	+	0.981679i	$0.561024\pi$
$374$	634.807	−	1099.52i	0.0877676	−	0.152018i
$375$	79.3212	+	137.388i	0.0109230	+	0.0189192i
$376$	771.781	−	1336.76i	0.105855	−	0.183347i
$377$	−3972.72	−	6880.95i	−0.542720	−	0.940018i
$378$	5986.15	+	10368.3i	0.814536	+	1.41082i
$379$	10772.3			1.45998			0.729992	−	0.683455i	$-0.239524\pi$
$379$	10772.3			1.45998			0.729992	+	0.683455i	$0.239524\pi$
$380$	931.789	+	5143.20i	0.125789	+	0.694318i
$381$	2287.90			0.307645
$382$	3521.85	+	6100.02i	0.471711	+	0.817027i
$383$	1689.97	+	2927.12i	0.225466	+	0.390519i	0.956459	−	0.291866i	$-0.0942761\pi$
$383$	1689.97	+	2927.12i	0.225466	+	0.390519i	−0.730993	+	0.682385i	$0.760943\pi$
$384$	612.896	−	1061.57i	0.0814498	−	0.141075i
$385$	−2096.09	−	3630.54i	−0.277472	−	0.480596i
$386$	4735.39	−	8201.94i	0.624417	−	1.08152i
$387$	−23335.8			−3.06518
$388$	−6343.69			−0.830031
$389$	−2351.28	+	4072.54i	−0.306464	+	0.530812i	−0.977586	−	0.210535i	$-0.932479\pi$
$389$	−2351.28	+	4072.54i	−0.306464	+	0.530812i	0.671122	+	0.741347i	$0.265813\pi$
$390$	−10139.4	+	17562.0i	−1.31649	+	2.28022i
$391$	−1888.40			−0.244246
$392$	545.758			0.0703187
$393$	−1270.08	+	2199.84i	−0.163020	+	0.282359i
$394$	2357.30	+	4082.96i	0.301419	+	0.522073i
$395$	6913.62	−	11974.7i	0.880663	−	1.52535i
$396$	−2074.38	−	3592.93i	−0.263236	−	0.455939i
$397$	−125.749	−	217.804i	−0.0158972	−	0.0275347i	0.857967	−	0.513704i	$-0.171727\pi$
$397$	−125.749	−	217.804i	−0.0158972	−	0.0275347i	−0.873865	+	0.486169i	$0.838394\pi$
$398$	−1370.31			−0.172582
$399$	10031.5	−	8497.95i	1.25865	−	1.06624i
$400$	1983.20			0.247900
$401$	3225.16	+	5586.15i	0.401638	+	0.695658i	0.993924	−	0.110070i	$-0.0351075\pi$
$401$	3225.16	+	5586.15i	0.401638	+	0.695658i	−0.592285	+	0.805728i	$0.701774\pi$
$402$	−9029.22	−	15639.1i	−1.12024	−	1.94031i
$403$	4027.92	−	6976.56i	0.497879	−	0.862351i
$404$	2087.65	+	3615.92i	0.257091	+	0.445294i
$405$	−13499.3	+	23381.5i	−1.65626	+	2.86873i
$406$	3925.45			0.479845
$407$	354.108			0.0431264
$408$	1517.11	−	2627.71i	0.184088	−	0.318850i
$409$	−1007.96	+	1745.84i	−0.121859	+	0.211066i	−0.920501	−	0.390741i	$-0.872219\pi$
$409$	−1007.96	+	1745.84i	−0.121859	+	0.211066i	0.798642	+	0.601807i	$0.205552\pi$
$410$	−3442.84			−0.414707
$411$	23351.8			2.80258
$412$	−2855.67	+	4946.16i	−0.341477	+	0.591456i
$413$	−3507.50	−	6075.17i	−0.417900	−	0.723825i
$414$	−3085.39	+	5344.06i	−0.366277	+	0.634411i
$415$	3757.55	+	6508.26i	0.444460	+	0.769827i
$416$	−1073.67	−	1859.65i	−0.126541	−	0.219175i
$417$	−3512.61			−0.412501
$418$	−2025.76	+	1716.08i	−0.237041	+	0.200804i
$419$	−10124.5			−1.18046			−0.590232	−	0.807234i	$-0.700964\pi$
$419$	−10124.5			−1.18046			−0.590232	+	0.807234i	$0.700964\pi$
$420$	−5009.40	−	8676.53i	−0.581985	−	1.00803i
$421$	−1573.13	−	2724.75i	−0.182114	−	0.315430i	0.760487	−	0.649354i	$-0.224961\pi$
$421$	−1573.13	−	2724.75i	−0.182114	−	0.315430i	−0.942600	+	0.333924i	$0.891627\pi$
$422$	−531.020	+	919.753i	−0.0612550	+	0.106097i
$423$	−6242.67	−	10812.6i	−0.717563	−	1.24286i
$424$	871.377	−	1509.27i	0.0998061	−	0.172869i
$425$	4909.04			0.560290
$426$	12751.0			1.45021
$427$	−4673.91	+	8095.45i	−0.529710	+	0.917485i
$428$	−1001.85	+	1735.25i	−0.113145	+	0.195973i
$429$	−10300.3			−1.15921
$430$	11380.0			1.27626
$431$	−5831.16	+	10099.9i	−0.651687	+	1.12875i	0.331027	+	0.943621i	$0.392605\pi$
$431$	−5831.16	+	10099.9i	−0.651687	+	1.12875i	−0.982713	+	0.185133i	$0.940728\pi$
$432$	−2888.98	−	5003.87i	−0.321751	−	0.557289i
$433$	4484.52	−	7767.42i	0.497719	−	0.862074i	−0.502278	−	0.864706i	$-0.667504\pi$
$433$	4484.52	−	7767.42i	0.497719	−	0.862074i	0.999997	+	0.00263209i	$0.000837820\pi$
$434$	1990.00	+	3446.78i	0.220099	+	0.381223i
$435$	8945.40	+	15493.9i	0.985975	+	1.70776i
$436$	4851.69			0.532922
$437$	3717.03	+	1333.17i	0.406887	+	0.145936i
$438$	3580.57			0.390608
$439$	−49.1536	−	85.1366i	−0.00534391	−	0.00925592i	0.863341	−	0.504621i	$-0.168368\pi$
$439$	−49.1536	−	85.1366i	−0.00534391	−	0.00925592i	−0.868685	+	0.495365i	$0.835034\pi$
$440$	1011.60	+	1752.14i	0.109605	+	0.189841i
$441$	2207.23	−	3823.03i	0.238336	−	0.412809i
$442$	−2657.66	−	4603.21i	−0.286000	−	0.495367i
$443$	4660.23	−	8071.75i	0.499806	−	0.865690i	−0.500194	−	0.865914i	$-0.666738\pi$
$443$	4660.23	−	8071.75i	0.499806	−	0.865690i	1.00000		0.000223670i	$7.11963e-5\pi$
$444$	846.272			0.0904556
$445$	−15221.8			−1.62154
$446$	4851.71	−	8403.41i	0.515101	−	0.892182i
$447$	10734.1	−	18592.0i	1.13580	−	1.96727i
$448$	1060.90			0.111881
$449$	9992.53			1.05028			0.525141	−	0.851015i	$-0.324013\pi$
$449$	9992.53			1.05028			0.525141	+	0.851015i	$0.324013\pi$
$450$	8020.72	−	13892.3i	0.840223	−	1.45531i
$451$	−874.365	−	1514.44i	−0.0912910	−	0.158121i
$452$	−1477.91	+	2559.82i	−0.153795	+	0.266380i
$453$	3055.84	+	5292.86i	0.316944	+	0.548963i
$454$	−3971.88	−	6879.50i	−0.410594	−	0.711170i
$455$	−17550.9			−1.80835
$456$	−4841.31	+	4101.21i	−0.497182	+	0.421177i
$457$	−1536.89			−0.157314			−0.0786572	−	0.996902i	$-0.525063\pi$
$457$	−1536.89			−0.157314			−0.0786572	+	0.996902i	$0.525063\pi$
$458$	−78.9844	−	136.805i	−0.00805829	−	0.0139574i
$459$	−7151.13	−	12386.1i	−0.727203	−	1.25955i
$460$	1504.63	−	2606.10i	0.152508	−	0.264152i
$461$	8312.46	+	14397.6i	0.839804	+	1.45458i	0.890058	+	0.455847i	$0.150664\pi$
$461$	8312.46	+	14397.6i	0.839804	+	1.45458i	−0.0502537	+	0.998736i	$0.516003\pi$
$462$	2544.44	−	4407.09i	0.256229	−	0.443802i
$463$	7191.48			0.721850			0.360925	−	0.932595i	$-0.382461\pi$
$463$	7191.48			0.721850			0.360925	+	0.932595i	$0.382461\pi$
$464$	−1894.47			−0.189544
$465$	−9069.71	+	15709.2i	−0.904511	+	1.56666i
$466$	−1643.29	+	2846.27i	−0.163356	+	0.282942i
$467$	−7001.51			−0.693772			−0.346886	−	0.937907i	$-0.612761\pi$
$467$	−7001.51			−0.693772			−0.346886	+	0.937907i	$0.612761\pi$
$468$	−17369.1			−1.71557
$469$	7814.59	−	13535.3i	0.769391	−	1.33262i
$470$	3044.32	+	5272.91i	0.298774	+	0.517492i
$471$	−10179.8	+	17631.9i	−0.995879	+	1.72491i
$472$	1692.76	+	2931.94i	0.165075	+	0.285919i
$473$	2890.13	+	5005.85i	0.280948	+	0.486616i
$474$	16784.8			1.62648
$475$	−9662.72	−	3465.68i	−0.933381	−	0.334772i
$476$	2626.05			0.252867
$477$	−7048.27	−	12208.0i	−0.676558	−	1.17183i
$478$	−6316.74	−	10940.9i	−0.604437	−	1.04692i
$479$	−955.918	+	1655.70i	−0.0911837	+	0.157935i	−0.908009	−	0.418950i	$-0.862398\pi$
$479$	−955.918	+	1655.70i	−0.0911837	+	0.157935i	0.816826	+	0.576884i	$0.195732\pi$
$480$	2417.59	+	4187.39i	0.229890	+	0.398182i
$481$	741.248	−	1283.88i	0.0702661	−	0.121705i
$482$	6989.31			0.660486
$483$	−7569.08			−0.713054
$484$	2148.18	−	3720.75i	0.201745	−	0.349432i
$485$	12511.5	−	21670.5i	1.17137	−	2.02888i
$486$	−13272.9			−1.23883
$487$	−6061.32			−0.563993			−0.281997	−	0.959415i	$-0.590997\pi$
$487$	−6061.32			−0.563993			−0.281997	+	0.959415i	$0.590997\pi$
$488$	2255.68	−	3906.95i	0.209241	−	0.362417i
$489$	766.327	+	1327.32i	0.0708681	+	0.122747i
$490$	−1076.38	+	1864.35i	−0.0992366	+	0.171883i
$491$	−3219.51	−	5576.36i	−0.295916	−	0.512541i	0.679282	−	0.733877i	$-0.262291\pi$
$491$	−3219.51	−	5576.36i	−0.295916	−	0.512541i	−0.975197	+	0.221337i	$0.928958\pi$
$492$	−2089.62	−	3619.33i	−0.191478	−	0.331650i
$493$	−4689.39			−0.428397
$494$	1981.45	+	10937.0i	0.180464	+	0.996111i
$495$	16365.0			1.48596
$496$	−960.396	−	1663.45i	−0.0869416	−	0.150587i
$497$	5517.86	+	9557.22i	0.498008	+	0.862575i
$498$	−4561.26	+	7900.34i	−0.410432	+	0.710889i
$499$	−8229.07	−	14253.2i	−0.738244	−	1.27868i	−0.953285	−	0.302071i	$-0.902322\pi$
$499$	−8229.07	−	14253.2i	−0.738244	−	1.27868i	0.215041	−	0.976605i	$-0.431011\pi$
$500$	33.1316	−	57.3857i	0.00296338	−	0.00513273i
$501$	20131.3			1.79521
$502$	−7260.74			−0.645543
$503$	1362.42	−	2359.78i	0.120770	−	0.209179i	−0.799302	−	0.600930i	$-0.794797\pi$
$503$	1362.42	−	2359.78i	0.120770	−	0.209179i	0.920071	+	0.391751i	$0.128130\pi$
$504$	4290.61	−	7431.56i	0.379205	−	0.656802i
$505$	−16469.7			−1.45127
$506$	1528.50			0.134289
$507$	−11041.7	+	19124.7i	−0.967214	+	1.67526i
$508$	−477.816	−	827.602i	−0.0417316	−	0.0722813i
$509$	−2730.41	+	4729.20i	−0.237767	+	0.411824i	−0.960073	−	0.279749i	$-0.909749\pi$
$509$	−2730.41	+	4729.20i	−0.237767	+	0.411824i	0.722307	+	0.691573i	$0.243082\pi$
$510$	5984.29	+	10365.1i	0.519586	+	0.899949i
$511$	1549.45	+	2683.73i	0.134136	+	0.232331i
$512$	−512.000			−0.0441942
$513$	5331.59	+	29428.8i	0.458861	+	2.53278i
$514$	3098.83			0.265921
$515$	−11264.3	−	19510.3i	−0.963813	−	1.66937i
$516$	6907.04	+	11963.3i	0.589274	+	1.02065i
$517$	−1546.31	+	2678.28i	−0.131541	+	0.227835i
$518$	366.215	+	634.303i	0.0310629	+	0.0538024i
$519$	1941.46	−	3362.71i	0.164202	−	0.284406i
$520$	8470.26			0.714318
$521$	7411.04			0.623193			0.311596	−	0.950215i	$-0.399136\pi$
$521$	7411.04			0.623193			0.311596	+	0.950215i	$0.399136\pi$
$522$	−7661.85	+	13270.7i	−0.642433	+	1.11273i
$523$	399.710	−	692.318i	0.0334189	−	0.0578833i	−0.848832	−	0.528662i	$-0.822694\pi$
$523$	399.710	−	692.318i	0.0334189	−	0.0578833i	0.882251	+	0.470779i	$0.156027\pi$
$524$	1060.99			0.0884537
$525$	19676.4			1.63571
$526$	−3809.81	+	6598.79i	−0.315809	+	0.546998i
$527$	−2377.28	−	4117.57i	−0.196501	−	0.340349i
$528$	−1227.97	+	2126.91i	−0.101213	+	0.175307i
$529$	4946.77	+	8568.06i	0.406573	+	0.704204i
$530$	3437.18	+	5953.37i	0.281701	+	0.487920i
$531$	27384.3			2.23800
$532$	−5168.98	−	1853.94i	−0.421248	−	0.151087i
$533$	−7321.19			−0.594964
$534$	−9238.83	−	16002.1i	−0.748695	−	1.29678i
$535$	−3951.83	−	6844.77i	−0.319350	−	0.553131i
$536$	−3771.41	+	6532.27i	−0.303918	+	0.526401i
$537$	7798.90	+	13508.1i	0.626717	+	1.08551i
$538$	−3376.40	+	5848.09i	−0.270570	+	0.468642i
$539$	−1093.46			−0.0873814
$540$	22791.4			1.81627
$541$	−2947.56	+	5105.33i	−0.234243	+	0.405721i	−0.959052	−	0.283228i	$-0.908595\pi$
$541$	−2947.56	+	5105.33i	−0.234243	+	0.405721i	0.724809	+	0.688950i	$0.241928\pi$
$542$	−3525.50	+	6106.34i	−0.279397	+	0.483930i
$543$	27167.0			2.14705
$544$	−1267.36			−0.0998852
$545$	−9568.84	+	16573.7i	−0.752081	+	1.30264i
$546$	−10652.5	−	18450.6i	−0.834951	−	1.44618i
$547$	−5745.64	+	9951.74i	−0.449115	+	0.777890i	−0.998329	−	0.0577920i	$-0.981594\pi$
$547$	−5745.64	+	9951.74i	−0.449115	+	0.777890i	0.549214	+	0.835682i	$0.314927\pi$
$548$	−4876.90	−	8447.03i	−0.380166	−	0.658466i
$549$	−18245.4	−	31602.0i	−1.41839	−	2.45672i
$550$	−3973.46			−0.308053
$551$	9230.38	+	3310.62i	0.713661	+	0.255966i
$552$	3652.92			0.281664
$553$	7263.44	+	12580.6i	0.558540	+	0.967420i
$554$	6557.88	+	11358.6i	0.502920	+	0.871083i
$555$	−1669.08	+	2890.92i	−0.127655	+	0.221104i
$556$	733.589	+	1270.61i	0.0559552	+	0.0969173i
$557$	1122.30	−	1943.88i	0.0853740	−	0.147872i	−0.820176	−	0.572111i	$-0.806125\pi$
$557$	1122.30	−	1943.88i	0.0853740	−	0.147872i	0.905551	+	0.424238i	$0.139458\pi$
$558$	−15536.6			−1.17871
$559$	24199.5			1.83100
$560$	−2092.37	+	3624.09i	−0.157891	+	0.273475i
$561$	−3039.61	+	5264.76i	−0.228757	+	0.396218i
$562$	−15775.6			−1.18408
$563$	−19529.8			−1.46196			−0.730978	−	0.682401i	$-0.760936\pi$
$563$	−19529.8			−1.46196			−0.730978	+	0.682401i	$0.760936\pi$
$564$	−3695.48	+	6400.76i	−0.275900	+	0.477873i
$565$	−5829.68	−	10097.3i	−0.434082	−	0.751853i
$566$	2072.73	−	3590.08i	0.153928	−	0.266612i
$567$	−14182.4	−	24564.6i	−1.05045	−	1.81943i
$568$	−2662.98	−	4612.42i	−0.196719	−	0.340727i
$569$	−3300.68			−0.243184			−0.121592	−	0.992580i	$-0.538800\pi$
$569$	−3300.68			−0.243184			−0.121592	+	0.992580i	$0.538800\pi$
$570$	−4461.64	−	24626.9i	−0.327855	−	1.80966i
$571$	3080.76			0.225789			0.112895	−	0.993607i	$-0.463988\pi$
$571$	3080.76			0.225789			0.112895	+	0.993607i	$0.463988\pi$
$572$	2151.16	+	3725.92i	0.157246	+	0.272357i
$573$	−16863.5	−	29208.4i	−1.22946	−	2.12949i
$574$	1808.52	−	3132.45i	0.131509	−	0.227780i
$575$	2955.02	+	5118.25i	0.214318	+	0.371210i
$576$	−2070.70	+	3586.55i	−0.149790	+	0.259444i
$577$	4946.52			0.356892			0.178446	−	0.983950i	$-0.442893\pi$
$577$	4946.52			0.356892			0.178446	+	0.983950i	$0.442893\pi$
$578$	6688.89			0.481352
$579$	−22674.2	+	39272.9i	−1.62748	+	2.81887i
$580$	3736.40	−	6471.63i	0.267492	−	0.463310i
$581$	−7895.34			−0.563776
$582$	30375.2			2.16339
$583$	−1745.85	+	3023.91i	−0.124024	+	0.214816i
$584$	−747.782	−	1295.20i	−0.0529854	−	0.0917733i
$585$	34256.5	−	59334.1i	2.42108	−	4.19344i
$586$	−7820.84	−	13546.1i	−0.551324	−	0.954922i
$587$	−7278.01	−	12605.9i	−0.511748	−	0.886373i	−0.999907	−	0.0136184i	$-0.995665\pi$
$587$	−7278.01	−	12605.9i	−0.511748	−	0.886373i	0.488160	−	0.872754i	$-0.337668\pi$
$588$	−2613.22			−0.183278
$589$	1772.40	+	9783.13i	0.123991	+	0.684392i
$590$	−13354.3			−0.931844
$591$	−11287.3	−	19550.2i	−0.785615	−	1.36073i
$592$	−176.739	−	306.121i	−0.0122702	−	0.0212526i
$593$	10308.6	−	17855.1i	0.713869	−	1.23646i	−0.249525	−	0.968368i	$-0.580275\pi$
$593$	10308.6	−	17855.1i	0.713869	−	1.23646i	0.963394	−	0.268089i	$-0.0863921\pi$
$594$	5788.25	+	10025.5i	0.399823	+	0.692513i
$595$	−5179.27	+	8970.76i	−0.356856	+	0.618093i
$596$	−8967.02			−0.616281
$597$	6561.39			0.449816
$598$	3199.59	−	5541.85i	0.218798	−	0.378969i
$599$	−10652.2	+	18450.2i	−0.726608	+	1.25852i	0.231700	+	0.972787i	$0.425571\pi$
$599$	−10652.2	+	18450.2i	−0.726608	+	1.25852i	−0.958309	+	0.285735i	$0.907762\pi$
$600$	−9496.06			−0.646125
$601$	−26351.4			−1.78852			−0.894258	−	0.447553i	$-0.852296\pi$
$601$	−26351.4			−1.78852			−0.894258	+	0.447553i	$0.852296\pi$
$602$	−5977.89	+	10354.0i	−0.404719	+	0.700993i
$603$	30505.6	+	52837.3i	2.06018	+	3.56833i
$604$	1276.39	−	2210.77i	0.0859860	−	0.148932i
$605$	8473.56	+	14676.6i	0.569420	+	0.986265i
$606$	−9996.20	−	17313.9i	−0.670079	−	1.16061i
$607$	24027.8			1.60669			0.803344	−	0.595516i	$-0.203052\pi$
$607$	24027.8			1.60669			0.803344	+	0.595516i	$0.203052\pi$
$608$	2494.61	+	894.730i	0.166398	+	0.0596811i
$609$	−18796.0			−1.25066
$610$	8897.62	+	15411.1i	0.590580	+	1.02292i
$611$	6473.73	+	11212.8i	0.428640	+	0.742426i
$612$	−5125.62	+	8877.83i	−0.338547	+	0.586381i
$613$	−7619.00	−	13196.5i	−0.502004	−	0.869497i	−0.999997	−	0.00231571i	$-0.999263\pi$
$613$	−7619.00	−	13196.5i	−0.502004	−	0.869497i	0.497993	−	0.867181i	$-0.334070\pi$
$614$	−5937.79	+	10284.6i	−0.390276	+	0.675979i
$615$	16485.2			1.08089
$616$	−2125.57			−0.139028
$617$	14065.4	−	24362.0i	0.917751	−	1.58959i	0.114929	−	0.993374i	$-0.463336\pi$
$617$	14065.4	−	24362.0i	0.917751	−	1.58959i	0.802822	−	0.596218i	$-0.203331\pi$
$618$	13673.6	−	23683.4i	0.890023	−	1.54157i
$619$	9482.23			0.615708			0.307854	−	0.951434i	$-0.400389\pi$
$619$	9482.23			0.615708			0.307854	+	0.951434i	$0.400389\pi$
$620$	7576.64			0.490782
$621$	8609.32	−	14911.8i	0.556329	−	0.963590i
$622$	1832.63	+	3174.21i	0.118138	+	0.204621i
$623$	7996.01	−	13849.5i	0.514211	−	0.890639i
$624$	5141.00	+	8904.47i	0.329815	+	0.571256i
$625$	7877.57	+	13644.3i	0.504164	+	0.873238i
$626$	1876.66			0.119819
$627$	9699.85	−	8217.01i	0.617822	−	0.523374i
$628$	8503.96			0.540358
$629$	−437.485	−	757.746i	−0.0277324	−	0.0480339i
$630$	16924.5	+	29314.1i	1.07030	+	1.85381i
$631$	850.702	−	1473.46i	0.0536702	−	0.0929595i	−0.837942	−	0.545759i	$-0.816241\pi$
$631$	850.702	−	1473.46i	0.0536702	−	0.0929595i	0.891612	+	0.452800i	$0.149575\pi$
$632$	−3505.42	−	6071.56i	−0.220630	−	0.382142i
$633$	2542.65	−	4404.01i	0.159655	−	0.276530i
$634$	14822.9			0.928539
$635$	3769.53			0.235573
$636$	−4172.37	+	7226.75i	−0.260134	+	0.450565i
$637$	−2288.92	+	3964.53i	−0.142371	+	0.246594i
$638$	3795.67			0.235536
$639$	−43079.9			−2.66700
$640$	1009.80	−	1749.03i	0.0623686	−	0.108026i
$641$	−10815.8	−	18733.5i	−0.666454	−	1.15433i	−0.978889	−	0.204393i	$-0.934478\pi$
$641$	−10815.8	−	18733.5i	−0.666454	−	1.15433i	0.312435	−	0.949939i	$-0.398855\pi$
$642$	4797.10	−	8308.82i	0.294901	−	0.510783i
$643$	2722.31	+	4715.17i	0.166963	+	0.289189i	0.937351	−	0.348387i	$-0.113271\pi$
$643$	2722.31	+	4715.17i	0.166963	+	0.289189i	−0.770388	+	0.637576i	$0.779937\pi$
$644$	1580.76	+	2737.96i	0.0967248	+	0.167532i
$645$	−54490.2			−3.32643
$646$	6174.93	+	2214.73i	0.376083	+	0.134888i
$647$	27393.8			1.66454			0.832272	−	0.554367i	$-0.187040\pi$
$647$	27393.8			1.66454			0.832272	+	0.554367i	$0.187040\pi$
$648$	6844.57	+	11855.1i	0.414938	+	0.718694i
$649$	−3391.54	−	5874.32i	−0.205130	−	0.355296i
$650$	−8317.59	+	14406.5i	−0.501912	+	0.869337i
$651$	−9528.62	−	16504.0i	−0.573665	−	0.993617i
$652$	320.087	−	554.406i	0.0192263	−	0.0333010i
$653$	−23390.6			−1.40175			−0.700875	−	0.713284i	$-0.747207\pi$
$653$	−23390.6			−1.40175			−0.700875	+	0.713284i	$0.747207\pi$
$654$	−23231.1			−1.38900
$655$	−2092.57	+	3624.43i	−0.124830	+	0.216211i
$656$	−872.812	+	1511.76i	−0.0519476	+	0.0899758i
$657$	−12097.1			−0.718346
$658$	−6396.71			−0.378981
$659$	10029.5	−	17371.6i	0.592860	−	1.02686i	−0.400985	−	0.916084i	$-0.631332\pi$
$659$	10029.5	−	17371.6i	0.592860	−	1.02686i	0.993845	−	0.110779i	$-0.0353345\pi$
$660$	−4843.78	−	8389.68i	−0.285673	−	0.494800i
$661$	−11618.9	+	20124.5i	−0.683696	+	1.18420i	0.290149	+	0.956981i	$0.406295\pi$
$661$	−11618.9	+	20124.5i	−0.683696	+	1.18420i	−0.973845	+	0.227214i	$0.927038\pi$
$662$	−5412.69	−	9375.05i	−0.317780	−	0.550410i
$663$	12725.6	+	22041.3i	0.745430	+	1.29112i
$664$	3810.38			0.222698
$665$	16527.8	−	14001.2i	0.963791	−	0.816453i
$666$	−2859.17			−0.166352
$667$	−2822.80	−	4889.24i	−0.163867	−	0.283826i
$668$	−4204.32	−	7282.09i	−0.243518	−	0.421785i
$669$	−23231.2	+	40237.6i	−1.34256	+	2.32538i
$670$	−14876.5	−	25766.8i	−0.857803	−	1.48576i
$671$	−4519.39	+	7827.81i	−0.260013	+	0.450356i
$672$	−5079.83			−0.291605
$673$	−10185.3			−0.583378			−0.291689	−	0.956513i	$-0.594217\pi$
$673$	−10185.3			−0.583378			−0.291689	+	0.956513i	$0.594217\pi$
$674$	9273.57	−	16062.3i	0.529977	−	0.917947i
$675$	−22380.6	+	38764.4i	−1.27619	+	2.21043i
$676$	9223.97			0.524805
$677$	3202.89			0.181827			0.0909136	−	0.995859i	$-0.471021\pi$
$677$	3202.89			0.181827			0.0909136	+	0.995859i	$0.471021\pi$
$678$	7076.61	−	12257.0i	0.400849	−	0.694291i
$679$	13144.5	+	22767.0i	0.742916	+	1.28677i
$680$	2499.57	−	4329.39i	0.140962	−	0.244154i
$681$	19018.4	+	32940.8i	1.07017	+	1.85359i
$682$	1924.21	+	3332.83i	0.108038	+	0.187127i
$683$	1625.51			0.0910662			0.0455331	−	0.998963i	$-0.485501\pi$
$683$	1625.51			0.0910662			0.0455331	+	0.998963i	$0.485501\pi$
$684$	16356.6	−	13856.1i	0.914342	−	0.774564i
$685$	38474.2			2.14602
$686$	−6816.58	−	11806.7i	−0.379385	−	0.657115i
$687$	378.197	+	655.056i	0.0210031	+	0.0363784i
$688$	2885.00	−	4996.96i	0.159868	−	0.276900i
$689$	7309.15	+	12659.8i	0.404146	+	0.700001i
$690$	−7204.55	+	12478.6i	−0.397496	+	0.688484i
$691$	839.130			0.0461968			0.0230984	−	0.999733i	$-0.492647\pi$
$691$	839.130			0.0461968			0.0230984	+	0.999733i	$0.492647\pi$
$692$	−1621.85			−0.0890949
$693$	−8596.50	+	14889.6i	−0.471218	+	0.816173i
$694$	−9674.48	+	16756.7i	−0.529162	+	0.916535i
$695$	−5787.34			−0.315865
$696$	9071.18			0.494026
$697$	−2160.48	+	3742.06i	−0.117409	+	0.203358i
$698$	1300.56	+	2252.64i	0.0705259	+	0.122154i
$699$	7868.49	−	13628.6i	0.425771	−	0.737457i
$700$	−4109.32	−	7117.54i	−0.221882	−	0.384311i
$701$	729.064	+	1262.78i	0.0392816	+	0.0680377i	0.884998	−	0.465595i	$-0.154160\pi$
$701$	729.064	+	1262.78i	0.0392816	+	0.0680377i	−0.845716	+	0.533633i	$0.820826\pi$
$702$	48465.8			2.60573
$703$	326.171	+	1800.37i	0.0174989	+	0.0965890i
$704$	1025.82			0.0549178
$705$	−14577.0	−	25248.0i	−0.778723	−	1.34879i
$706$	11985.4	+	20759.2i	0.638916	+	1.10663i
$707$	8651.49	−	14984.8i	0.460216	−	0.797118i
$708$	−8105.35	−	14038.9i	−0.430251	−	0.745217i
$709$	16159.9	−	27989.8i	0.855993	−	1.48262i	−0.0197278	−	0.999805i	$-0.506280\pi$
$709$	16159.9	−	27989.8i	0.855993	−	1.48262i	0.875721	−	0.482818i	$-0.160387\pi$
$710$	21008.5			1.11047
$711$	−56708.2			−2.99117
$712$	−3858.96	+	6683.91i	−0.203119	+	0.351812i
$713$	2862.03	−	4957.18i	0.150328	−	0.260376i
$714$	−12574.2			−0.659070
$715$	−16970.7			−0.887646
$716$	3257.52	−	5642.18i	0.170027	−	0.294495i
$717$	30246.1	+	52387.8i	1.57540	+	2.72867i
$718$	−4407.90	+	7634.70i	−0.229110	+	0.396831i
$719$	2885.84	+	4998.42i	0.149685	+	0.259262i	0.931111	−	0.364736i	$-0.118841\pi$
$719$	2885.84	+	4998.42i	0.149685	+	0.259262i	−0.781426	+	0.623998i	$0.785507\pi$
$720$	−8167.95	−	14147.3i	−0.422780	−	0.732276i
$721$	23668.5			1.22255
$722$	−10590.9	−	8718.76i	−0.545917	−	0.449416i
$723$	−33466.6			−1.72149
$724$	−5673.68	−	9827.09i	−0.291244	−	0.504449i
$725$	7338.10	+	12710.0i	0.375904	+	0.651085i
$726$	−10286.0	+	17815.9i	−0.525826	+	0.910757i
$727$	−2726.16	−	4721.84i	−0.139075	−	0.240885i	0.788072	−	0.615583i	$-0.211080\pi$
$727$	−2726.16	−	4721.84i	−0.139075	−	0.240885i	−0.927147	+	0.374698i	$0.877746\pi$
$728$	−4449.42	+	7706.62i	−0.226520	+	0.392344i
$729$	17352.9			0.881618
$730$	5899.31			0.299100
$731$	7141.26	−	12369.0i	0.361326	−	0.625834i
$732$	−10800.8	+	18707.5i	−0.545365	+	0.944601i
$733$	9558.30			0.481643			0.240821	−	0.970569i	$-0.422583\pi$
$733$	9558.30			0.481643			0.240821	+	0.970569i	$0.422583\pi$
$734$	−12520.2			−0.629602
$735$	5153.98	−	8926.96i	0.258650	−	0.447994i
$736$	−762.893	−	1321.37i	−0.0382074	−	0.0661771i
$737$	7556.23	−	13087.8i	0.377663	−	0.654131i
$738$	7059.88	+	12228.1i	0.352138	+	0.609921i
$739$	−6476.74	−	11218.0i	−0.322396	−	0.558406i	0.658586	−	0.752506i	$-0.271155\pi$
$739$	−6476.74	−	11218.0i	−0.322396	−	0.558406i	−0.980982	+	0.194099i	$0.937822\pi$
$740$	1394.31			0.0692647
$741$	−9487.66	−	52369.1i	−0.470361	−	2.59626i
$742$	−7222.19			−0.357325
$743$	91.9794	+	159.313i	0.00454158	+	0.00786625i	0.868287	−	0.496062i	$-0.165221\pi$
$743$	91.9794	+	159.313i	0.00454158	+	0.00786625i	−0.863746	+	0.503928i	$0.831888\pi$
$744$	4598.62	+	7965.03i	0.226604	+	0.392490i
$745$	17685.4	−	30632.0i	0.869721	−	1.50640i
$746$	−2745.24	−	4754.90i	−0.134733	−	0.233364i
$747$	15410.4	−	26691.7i	0.754804	−	1.30736i
$748$	2539.23			0.124122
$749$	8303.57			0.405081
$750$	−158.642	+	274.777i	−0.00772374	+	0.0133779i
$751$	−5247.19	+	9088.39i	−0.254957	+	0.441598i	−0.964884	−	0.262677i	$-0.915395\pi$
$751$	−5247.19	+	9088.39i	−0.254957	+	0.441598i	0.709927	+	0.704275i	$0.248728\pi$
$752$	3087.12			0.149702
$753$	34766.2			1.68254
$754$	7945.43	−	13761.9i	0.383761	−	0.664693i
$755$	5034.77	+	8720.47i	0.242694	+	0.420358i
$756$	−11972.3	+	20736.6i	−0.575964	+	0.997599i
$757$	4731.24	+	8194.75i	0.227160	+	0.393452i	0.956965	−	0.290203i	$-0.0937227\pi$
$757$	4731.24	+	8194.75i	0.227160	+	0.393452i	−0.729805	+	0.683655i	$0.760389\pi$
$758$	10772.3	+	18658.1i	0.516183	+	0.894054i
$759$	−7318.84			−0.350009
$760$	−7976.50	+	6757.11i	−0.380708	+	0.322508i
$761$	−38400.1			−1.82918			−0.914588	−	0.404388i	$-0.867485\pi$
$761$	−38400.1			−1.82918			−0.914588	+	0.404388i	$0.867485\pi$
$762$	2287.90	+	3962.76i	0.108769	+	0.188393i
$763$	−10053.0	−	17412.3i	−0.476990	−	0.826171i
$764$	−7043.70	+	12200.0i	−0.333550	+	0.577725i
$765$	−20218.2	−	35018.9i	−0.955543	−	1.65505i
$766$	−3379.95	+	5854.24i	−0.159429	+	0.276139i
$767$	−28397.9			−1.33688
$768$	2451.58			0.115187
$769$	1535.93	−	2660.31i	0.0720249	−	0.124751i	−0.827764	−	0.561077i	$-0.810387\pi$
$769$	1535.93	−	2660.31i	0.0720249	−	0.124751i	0.899789	+	0.436326i	$0.143721\pi$
$770$	4192.19	−	7261.08i	0.196203	−	0.339833i
$771$	−14838.0			−0.693095
$772$	18941.6			0.883060
$773$	−3588.67	+	6215.75i	−0.166980	+	0.289218i	−0.937357	−	0.348371i	$-0.886735\pi$
$773$	−3588.67	+	6215.75i	−0.166980	+	0.289218i	0.770377	+	0.637589i	$0.220068\pi$
$774$	−23335.8	−	40418.7i	−1.08370	−	1.87703i
$775$	−7440.07	+	12886.6i	−0.344846	+	0.597290i
$776$	−6343.69	−	10987.6i	−0.293460	−	0.508288i
$777$	−1753.53	−	3037.20i	−0.0809620	−	0.140230i
$778$	−9405.12			−0.433406
$779$	6894.41	−	5840.44i	0.317096	−	0.268621i
$780$	−40557.7			−1.86179
$781$	5335.44	+	9241.25i	0.244452	+	0.423403i
$782$	−1888.40	−	3270.80i	−0.0863542	−	0.149570i
$783$	21379.2	−	37029.9i	0.975774	−	1.69009i
$784$	545.758	+	945.280i	0.0248614	+	0.0430612i
$785$	−16772.1	+	29050.1i	−0.762576	+	1.32082i
$786$	−5080.31			−0.230545
$787$	40299.0			1.82529			0.912645	−	0.408754i	$-0.134037\pi$
$787$	40299.0			1.82529			0.912645	+	0.408754i	$0.134037\pi$
$788$	−4714.60	+	8165.92i	−0.213135	+	0.369161i
$789$	18242.3	−	31596.6i	0.823123	−	1.42569i
$790$	27654.5			1.24545
$791$	12249.3			0.550613
$792$	4148.76	−	7185.87i	0.186136	−	0.322397i
$793$	18920.7	+	32771.7i	0.847283	+	1.46754i
$794$	251.499	−	435.608i	0.0112410	−	0.0194700i
$795$	−16458.1	−	28506.2i	−0.734223	−	1.27171i
$796$	−1370.31	−	2373.45i	−0.0610168	−	0.105684i
$797$	−33505.8			−1.48913			−0.744565	−	0.667550i	$-0.767343\pi$
$797$	−33505.8			−1.48913			−0.744565	+	0.667550i	$0.767343\pi$
$798$	24750.4	+	8877.11i	1.09794	+	0.393792i
$799$	7641.59			0.338348
$800$	1983.20	+	3435.01i	0.0876459	+	0.151807i
$801$	31213.8	+	54063.9i	1.37689	+	2.38484i
$802$	−6450.33	+	11172.3i	−0.284001	+	0.491905i
$803$	1498.23	+	2595.00i	0.0658421	+	0.114042i
$804$	18058.4	−	31278.1i	0.792129	−	1.37201i
$805$	−12470.8			−0.546008
$806$	16111.7			0.704107
$807$	16167.0	−	28002.1i	0.705213	−	1.22146i
$808$	−4175.31	+	7231.84i	−0.181791	+	0.314870i
$809$	−20863.7			−0.906710			−0.453355	−	0.891330i	$-0.649773\pi$
$809$	−20863.7			−0.906710			−0.453355	+	0.891330i	$0.649773\pi$
$810$	−53997.3			−2.34231
$811$	−8728.82	+	15118.8i	−0.377941	+	0.654613i	−0.990763	−	0.135608i	$-0.956701\pi$
$811$	−8728.82	+	15118.8i	−0.377941	+	0.654613i	0.612821	+	0.790221i	$0.290034\pi$
$812$	3925.45	+	6799.08i	0.169651	+	0.293844i
$813$	16881.0	−	29238.7i	0.728218	−	1.26131i
$814$	354.108	+	613.332i	0.0152475	+	0.0264094i
$815$	1262.59	+	2186.88i	0.0542659	+	0.0939914i
$816$	6068.43			0.260340
$817$	−22788.8	+	19305.0i	−0.975862	+	0.826679i
$818$	−4031.84			−0.172335
$819$	35989.8	+	62336.2i	1.53552	+	2.65959i
$820$	−3442.84	−	5963.18i	−0.146621	−	0.253955i
$821$	−14635.8	+	25349.9i	−0.622158	+	1.07761i	0.366925	+	0.930251i	$0.380411\pi$
$821$	−14635.8	+	25349.9i	−0.622158	+	1.07761i	−0.989083	+	0.147359i	$0.952923\pi$
$822$	23351.8	+	40446.5i	0.990861	+	1.71622i
$823$	−19338.7	+	33495.5i	−0.819080	+	1.41869i	0.0872806	+	0.996184i	$0.472182\pi$
$823$	−19338.7	+	33495.5i	−0.819080	+	1.41869i	−0.906361	+	0.422505i	$0.861151\pi$
$824$	−11422.7			−0.482922
$825$	19025.9			0.802906
$826$	7015.00	−	12150.3i	0.295500	−	0.511821i
$827$	−2321.06	+	4020.19i	−0.0975951	+	0.169040i	−0.910689	−	0.413093i	$-0.864448\pi$
$827$	−2321.06	+	4020.19i	−0.0975951	+	0.169040i	0.813094	+	0.582133i	$0.197782\pi$
$828$	−12341.6			−0.517994
$829$	−7918.14			−0.331735			−0.165868	−	0.986148i	$-0.553042\pi$
$829$	−7918.14			−0.331735			−0.165868	+	0.986148i	$0.553042\pi$
$830$	−7515.09	+	13016.5i	−0.314280	+	0.544350i
$831$	−31400.7	−	54387.7i	−1.31081	−	2.27038i
$832$	2147.34	−	3719.30i	0.0894779	−	0.154980i
$833$	1350.92	+	2339.86i	0.0561904	+	0.0973246i
$834$	−3512.61	−	6084.01i	−0.145841	−	0.252605i
$835$	33168.2			1.37465
$836$	−4998.09	−	1792.64i	−0.206774	−	0.0741626i
$837$	43352.6			1.79031
$838$	−10124.5	−	17536.1i	−0.417357	−	0.722883i
$839$	−4061.92	−	7035.45i	−0.167143	−	0.289500i	0.770271	−	0.637716i	$-0.220121\pi$
$839$	−4061.92	−	7035.45i	−0.167143	−	0.289500i	−0.937414	+	0.348216i	$0.886788\pi$
$840$	10018.8	−	17353.1i	0.411525	−	0.712783i
$841$	5184.73	+	8980.21i	0.212585	+	0.368207i
$842$	3146.27	−	5449.49i	0.128774	−	0.223043i
$843$	75537.5			3.08618
$844$	−2124.08			−0.0866277
$845$	−18192.1	+	31509.7i	−0.740626	+	1.28280i
$846$	12485.3	−	21625.3i	0.507394	−	0.878832i
$847$	−17804.6			−0.722283
$848$	3485.51			0.141147
$849$	−9924.75	+	17190.2i	−0.401198	+	0.694895i
$850$	4909.04	+	8502.70i	0.198093	+	0.343106i
$851$	526.692	−	912.258i	0.0212160	−	0.0367471i
$852$	12751.0	+	22085.4i	0.512726	+	0.888067i
$853$	−22594.4	−	39134.7i	−0.906938	−	1.57086i	−0.818295	−	0.574799i	$-0.805080\pi$
$853$	−22594.4	−	39134.7i	−0.906938	−	1.57086i	−0.0886427	−	0.996063i	$-0.528253\pi$
$854$	−18695.6			−0.749124
$855$	15073.9	+	83203.3i	0.602942	+	3.32806i
$856$	−4007.39			−0.160012
$857$	−15246.2	−	26407.1i	−0.607700	−	1.05257i	−0.991618	−	0.129201i	$-0.958759\pi$
$857$	−15246.2	−	26407.1i	−0.607700	−	1.05257i	0.383918	−	0.923367i	$-0.374574\pi$
$858$	−10300.3	−	17840.6i	−0.409844	−	0.709870i
$859$	19527.3	−	33822.2i	0.775625	−	1.34342i	−0.158818	−	0.987308i	$-0.550768\pi$
$859$	19527.3	−	33822.2i	0.775625	−	1.34342i	0.934443	−	0.356113i	$-0.115898\pi$
$860$	11380.0	+	19710.7i	0.451226	+	0.781545i
$861$	−8659.65	+	14999.0i	−0.342764	+	0.593685i
$862$	−23324.6			−0.921624
$863$	−21510.4			−0.848461			−0.424230	−	0.905554i	$-0.639455\pi$
$863$	−21510.4			−0.848461			−0.424230	+	0.905554i	$0.639455\pi$
$864$	5777.97	−	10007.7i	0.227512	−	0.394063i
$865$	3198.73	−	5540.37i	0.125734	−	0.217778i
$866$	17938.1			0.703881
$867$	−32028.1			−1.25459
$868$	−3980.00	+	6893.56i	−0.155634	+	0.269565i
$869$	7023.30	+	12164.7i	0.274165	+	0.474867i
$870$	−17890.8	+	30987.8i	−0.697190	+	1.20757i
$871$	−31634.7	−	54792.9i	−1.23066	−	2.13156i
$872$	4851.69	+	8403.38i	0.188416	+	0.326347i
$873$	−102624.			−3.97857
$874$	1407.91	+	7771.26i	0.0544889	+	0.300763i
$875$	−274.603			−0.0106095
$876$	3580.57	+	6201.73i	0.138101	+	0.239197i
$877$	−4199.45	−	7273.66i	−0.161694	−	0.280062i	0.773783	−	0.633451i	$-0.218362\pi$
$877$	−4199.45	−	7273.66i	−0.161694	−	0.280062i	−0.935476	+	0.353390i	$0.885029\pi$
$878$	98.3073	−	170.273i	0.00377871	−	0.00654492i
$879$	37448.1	+	64862.1i	1.43697	+	2.48890i
$880$	−2023.20	+	3504.28i	−0.0775022	+	0.134238i
$881$	−46320.2			−1.77136			−0.885679	−	0.464298i	$-0.846307\pi$
$881$	−46320.2			−1.77136			−0.885679	+	0.464298i	$0.846307\pi$
$882$	8828.90			0.337057
$883$	−16002.0	+	27716.2i	−0.609863	+	1.05631i	0.381399	+	0.924411i	$0.375442\pi$
$883$	−16002.0	+	27716.2i	−0.609863	+	1.05631i	−0.991262	+	0.131904i	$0.957891\pi$
$884$	5315.33	−	9206.42i	0.202233	−	0.350278i
$885$	63943.7			2.42875
$886$	18640.9			0.706833
$887$	16782.7	−	29068.6i	0.635298	−	1.10037i	−0.351154	−	0.936318i	$-0.614211\pi$
$887$	16782.7	−	29068.6i	0.635298	−	1.10037i	0.986452	−	0.164051i	$-0.0524561\pi$
$888$	846.272	+	1465.79i	0.0319809	+	0.0553925i
$889$	−1980.13	+	3429.68i	−0.0747035	+	0.129390i
$890$	−15221.8	−	26365.0i	−0.573299	−	0.992984i
$891$	−13713.5	−	23752.5i	−0.515622	−	0.893084i
$892$	19406.8			0.728463
$893$	−15041.3	−	5394.81i	−0.563650	−	0.202162i
$894$	42936.3			1.60627
$895$	12849.4	+	22255.8i	0.479897	+	0.831206i
$896$	1060.90	+	1837.53i	0.0395559	+	0.0685127i
$897$	−15320.4	+	26535.8i	−0.570272	+	0.987741i
$898$	9992.53	+	17307.6i	0.371331	+	0.643164i
$899$	7107.18	−	12310.0i	0.263668	−	0.456687i
$900$	32082.9			1.18826
$901$	8627.71			0.319013
$902$	1748.73	−	3028.89i	0.0645525	−	0.111808i
$903$	28623.6	−	49577.6i	1.05486	−	1.82706i
$904$	−5911.65			−0.217498
$905$	44760.1			1.64406
$906$	−6111.67	+	10585.7i	−0.224113	+	0.388176i
$907$	−19984.2	−	34613.7i	−0.731604	−	1.26718i	−0.956197	−	0.292723i	$-0.905439\pi$
$907$	−19984.2	−	34613.7i	−0.731604	−	1.26718i	0.224593	−	0.974453i	$-0.427895\pi$
$908$	7943.77	−	13759.0i	0.290334	−	0.502873i
$909$	33772.6	+	58495.9i	1.23231	+	2.13442i
$910$	−17550.9	−	30399.1i	−0.639348	−	1.10738i
$911$	38734.2			1.40869			0.704347	−	0.709855i	$-0.251240\pi$
$911$	38734.2			1.40869			0.704347	+	0.709855i	$0.251240\pi$
$912$	−11944.8	−	4284.19i	−0.433697	−	0.155552i
$913$	−7634.32			−0.276735
$914$	−1536.89	−	2661.97i	−0.0556190	−	0.0963350i
$915$	−42604.0	−	73792.3i	−1.53928	−	2.66612i
$916$	157.969	−	273.610i	0.00569807	−	0.00986935i
$917$	−2198.45	−	3807.82i	−0.0791702	−	0.137127i
$918$	14302.3	−	24772.2i	0.514210	−	0.890638i
$919$	7565.87			0.271572			0.135786	−	0.990738i	$-0.456644\pi$
$919$	7565.87			0.271572			0.135786	+	0.990738i	$0.456644\pi$
$920$	6018.52			0.215679
$921$	28431.6	−	49245.0i	1.01721	−	1.76187i
$922$	−16624.9	+	28795.2i	−0.593831	+	1.02855i
$923$	44674.4			1.59315
$924$	10177.7			0.362363
$925$	−1369.18	+	2371.49i	−0.0486684	+	0.0842962i
$926$	7191.48	+	12456.0i	0.255212	+	0.442041i
$927$	−46197.0	+	80015.6i	−1.63680	+	2.83501i
$928$	−1894.47	−	3281.31i	−0.0670139	−	0.116071i
$929$	11858.4	+	20539.3i	0.418796	+	0.725376i	0.995819	−	0.0913524i	$-0.0291190\pi$
$929$	11858.4	+	20539.3i	0.418796	+	0.725376i	−0.577023	+	0.816728i	$0.695786\pi$
$930$	−36278.8			−1.27917
$931$	−1007.19	−	5559.40i	−0.0354558	−	0.195706i
$932$	−6573.17			−0.231021
$933$	−8775.11	−	15198.9i	−0.307914	−	0.533323i
$934$	−7001.51	−	12127.0i	−0.245285	−	0.424847i
$935$	−5008.04	+	8674.18i	−0.175166	+	0.303397i
$936$	−17369.1	−	30084.2i	−0.606546	−	1.05057i
$937$	−22291.9	+	38610.8i	−0.777210	+	1.34617i	0.156334	+	0.987704i	$0.450032\pi$
$937$	−22291.9	+	38610.8i	−0.777210	+	1.34617i	−0.933544	+	0.358463i	$0.883301\pi$
$938$	31258.4			1.08808
$939$	−8985.93			−0.312295
$940$	−6088.64	+	10545.8i	−0.211265	+	0.365922i
$941$	20086.2	−	34790.3i	0.695846	−	1.20524i	−0.274049	−	0.961716i	$-0.588363\pi$
$941$	20086.2	−	34790.3i	0.695846	−	1.20524i	0.969895	−	0.243525i	$-0.0783037\pi$
$942$	−40719.1			−1.40839
$943$	−5202.05			−0.179642
$944$	−3385.52	+	5863.89i	−0.116726	+	0.202175i
$945$	−47225.2	−	81796.5i	−1.62565	−	2.81570i
$946$	−5780.26	+	10011.7i	−0.198660	+	0.344089i
$947$	21487.4	+	37217.2i	0.737324	+	1.27708i	0.953696	+	0.300772i	$0.0972442\pi$
$947$	21487.4	+	37217.2i	0.737324	+	1.27708i	−0.216372	+	0.976311i	$0.569423\pi$
$948$	16784.8	+	29072.1i	0.575047	+	0.996011i
$949$	12544.9			0.429108
$950$	−3659.98	−	20202.0i	−0.124995	−	0.689936i
$951$	−70975.8			−2.42014
$952$	2626.05	+	4548.45i	0.0894019	+	0.154849i
$953$	−16391.0	−	28390.0i	−0.557141	−	0.964997i	−0.997733	−	0.0672898i	$-0.978565\pi$
$953$	−16391.0	−	28390.0i	−0.557141	−	0.964997i	0.440592	−	0.897707i	$-0.354769\pi$
$954$	14096.5	−	24415.9i	0.478399	−	0.828611i
$955$	−27784.1	−	48123.5i	−0.941438	−	1.63062i
$956$	12633.5	−	21881.8i	0.427402	−	0.740281i
$957$	−18174.6			−0.613900
$958$	−3823.67			−0.128953
$959$	−20210.5	+	35005.6i	−0.680532	+	1.17872i
$960$	−4835.18	+	8374.78i	−0.162557	+	0.281557i
$961$	−15379.1			−0.516234
$962$	2964.99			0.0993713
$963$	−16207.2	+	28071.7i	−0.542337	+	0.939355i
$964$	6989.31	+	12105.8i	0.233517	+	0.404464i
$965$	−37357.9	+	64705.7i	−1.24621	+	2.15850i
$966$	−7569.08	−	13110.0i	−0.252103	−	0.436655i
$967$	−9881.92	−	17116.0i	−0.328626	−	0.569196i	0.653614	−	0.756828i	$-0.273252\pi$
$967$	−9881.92	−	17116.0i	−0.328626	−	0.569196i	−0.982239	+	0.187632i	$0.939919\pi$
$968$	8592.71			0.285310
$969$	−29567.1	−	10604.7i	−0.980219	−	0.351571i
$970$	50045.8			1.65657
$971$	−6926.88	−	11997.7i	−0.228933	−	0.396524i	0.728559	−	0.684983i	$-0.240190\pi$
$971$	−6926.88	−	11997.7i	−0.228933	−	0.396524i	−0.957492	+	0.288459i	$0.906857\pi$
$972$	−13272.9	−	22989.3i	−0.437991	−	0.758622i
$973$	3040.08	−	5265.58i	0.100165	−	0.173491i
$974$	−6061.32	−	10498.5i	−0.199402	−	0.345374i
$975$	39826.7	−	68981.8i	1.30818	−	2.26583i
$976$	9022.72			0.295912
$977$	53113.0			1.73924			0.869620	−	0.493722i	$-0.164364\pi$
$977$	53113.0			1.73924			0.869620	+	0.493722i	$0.164364\pi$
$978$	−1532.65	+	2654.64i	−0.0501113	+	0.0867954i
$979$	7731.65	−	13391.6i	0.252405	−	0.437179i
$980$	−4305.53			−0.140342
$981$	78487.4			2.55444
$982$	6439.02	−	11152.7i	0.209244	−	0.362421i
$983$	8672.89	+	15021.9i	0.281406	+	0.487410i	0.971731	−	0.236090i	$-0.0758659\pi$
$983$	8672.89	+	15021.9i	0.281406	+	0.487410i	−0.690325	+	0.723499i	$0.742533\pi$
$984$	4179.24	−	7238.66i	0.135396	−	0.234512i
$985$	−18596.9	−	32210.8i	−0.601570	−	1.04195i
$986$	−4689.39	−	8122.27i	−0.151461	−	0.262338i
$987$	30629.0			0.987774
$988$	−16962.0	+	14369.0i	−0.546187	+	0.462690i
$989$	17194.9			0.552847
$990$	16365.0	+	28344.9i	0.525366	+	0.909961i
$991$	3316.70	+	5744.69i	0.106315	+	0.184143i	0.914275	−	0.405095i	$-0.132761\pi$
$991$	3316.70	+	5744.69i	0.106315	+	0.184143i	−0.807960	+	0.589238i	$0.799428\pi$
$992$	1920.79	−	3326.91i	0.0614770	−	0.106481i
$993$	25917.3	+	44890.1i	0.828258	+	1.43459i
$994$	−11035.7	+	19114.4i	−0.352145	+	0.609933i
$995$	10810.5			0.344438
$996$	−18245.0			−0.580438
$997$	10306.3	−	17851.0i	0.327386	−	0.567049i	−0.654606	−	0.755970i	$-0.727166\pi$
$997$	10306.3	−	17851.0i	0.327386	−	0.567049i	0.981992	+	0.188921i	$0.0604989\pi$
$998$	16458.1	−	28506.3i	0.522017	−	0.904161i
$999$	7978.08			0.252668

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.4.c.c.7.1	✓	6
3.2	odd	2		342.4.g.f.235.3		6
4.3	odd	2		304.4.i.e.273.3		6
19.7	even	3		722.4.a.j.1.3		3
19.11	even	3	inner	38.4.c.c.11.1	yes	6
19.12	odd	6		722.4.a.k.1.1		3
57.11	odd	6		342.4.g.f.163.3		6
76.11	odd	6		304.4.i.e.49.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.4.c.c.7.1	✓	6	1.1	even	1	trivial
38.4.c.c.11.1	yes	6	19.11	even	3	inner
304.4.i.e.49.3		6	76.11	odd	6
304.4.i.e.273.3		6	4.3	odd	2
342.4.g.f.163.3		6	57.11	odd	6
342.4.g.f.235.3		6	3.2	odd	2
722.4.a.j.1.3		3	19.7	even	3
722.4.a.k.1.1		3	19.12	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)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(-4.78825 - 8.29349i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-7.88908 - 13.6643i) q^{5} +(9.57650 - 16.5870i) q^{6} +16.5765 q^{7} -8.00000 q^{8} +(-32.3546 + 56.0399i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(-4.78825 - 8.29349i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-7.88908 - 13.6643i) q^{5} +(9.57650 - 16.5870i) q^{6} +16.5765 q^{7} -8.00000 q^{8} +(-32.3546 + 56.0399i) q^{9} +(15.7782 - 27.3286i) q^{10} +16.0285 q^{11} +38.3060 q^{12} +(33.5522 - 58.1141i) q^{13} +(16.5765 + 28.7113i) q^{14} +(-75.5497 + 130.856i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-19.8025 - 34.2989i) q^{17} -129.419 q^{18} +(14.7639 + 81.4925i) q^{19} +63.1126 q^{20} +(-79.3724 - 137.477i) q^{21} +(16.0285 + 27.7621i) q^{22} +(23.8404 - 41.2928i) q^{23} +(38.3060 + 66.3479i) q^{24} +(-61.9750 + 107.344i) q^{25} +134.209 q^{26} +361.123 q^{27} +(-33.1530 + 57.4227i) q^{28} +(59.2021 - 102.541i) q^{29} -302.199 q^{30} +120.050 q^{31} +(16.0000 - 27.7128i) q^{32} +(-76.7483 - 132.932i) q^{33} +(39.6050 - 68.5978i) q^{34} +(-130.773 - 226.506i) q^{35} +(-129.419 - 224.160i) q^{36} +22.0924 q^{37} +(-126.385 + 107.064i) q^{38} -642.624 q^{39} +(63.1126 + 109.314i) q^{40} +(-54.5508 - 94.4847i) q^{41} +(158.745 - 274.954i) q^{42} +(180.312 + 312.310i) q^{43} +(-32.0569 + 55.5242i) q^{44} +1020.99 q^{45} +95.3617 q^{46} +(-96.4726 + 167.095i) q^{47} +(-76.6120 + 132.696i) q^{48} -68.2197 q^{49} -247.900 q^{50} +(-189.638 + 328.463i) q^{51} +(134.209 + 232.456i) q^{52} +(-108.922 + 188.659i) q^{53} +(361.123 + 625.483i) q^{54} +(-126.450 - 219.017i) q^{55} -132.612 q^{56} +(605.164 - 512.651i) q^{57} +236.808 q^{58} +(-211.595 - 366.493i) q^{59} +(-302.199 - 523.424i) q^{60} +(-281.960 + 488.369i) q^{61} +(120.050 + 207.932i) q^{62} +(-536.327 + 928.945i) q^{63} +64.0000 q^{64} -1058.78 q^{65} +(153.497 - 265.864i) q^{66} +(471.426 - 816.534i) q^{67} +158.420 q^{68} -456.615 q^{69} +(261.546 - 453.012i) q^{70} +(332.873 + 576.552i) q^{71} +(258.837 - 448.319i) q^{72} +(93.4728 + 161.900i) q^{73} +(22.0924 + 38.2652i) q^{74} +1187.01 q^{75} +(-311.826 - 111.841i) q^{76} +265.696 q^{77} +(-642.624 - 1113.06i) q^{78} +(438.177 + 758.945i) q^{79} +(-126.225 + 218.628i) q^{80} +(-855.571 - 1481.89i) q^{81} +(109.102 - 188.969i) q^{82} -476.297 q^{83} +634.979 q^{84} +(-312.447 + 541.173i) q^{85} +(-360.624 + 624.620i) q^{86} -1133.90 q^{87} -128.228 q^{88} +(482.370 - 835.489i) q^{89} +(1020.99 + 1768.41i) q^{90} +(556.177 - 963.328i) q^{91} +(95.3617 + 165.171i) q^{92} +(-574.827 - 995.629i) q^{93} -385.890 q^{94} +(997.063 - 844.639i) q^{95} -306.448 q^{96} +(792.961 + 1373.45i) q^{97} +(-68.2197 - 118.160i) q^{98} +(-518.595 + 898.234i) 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

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