LMFDB - Embedded newform 45.4.e.c.31.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,4,Mod(16,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("45.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	45.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:	$2.65508595026$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + 48 x^{12} - 60 x^{11} + 1605 x^{10} - 1800 x^{9} + 23232 x^{8} - 2346 x^{7} + \cdots + 82944 $ x^14 - 2x^13 + 48x^12 - 60x^11 + 1605x^10 - 1800x^9 + 23232x^8 - 2346x^7 + 209529x^6 - 55412x^5 + 765088x^4 + 276096x^3 + 1572480x^2 - 345600*x + 82944
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			31.7
Root			$2.65775 - 4.60336i$ of defining polynomial
Character	$\chi$	$=$	45.31
Dual form			45.4.e.c.16.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.65775 + 4.60336i) q^{2} +(-5.19389 - 0.153351i) q^{3} +(-10.1273 + 17.5410i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-13.0981 - 24.3169i) q^{6} +(6.71686 + 11.6339i) q^{7} -65.1396 q^{8} +(26.9530 + 1.59298i) q^{9} +O(q^{10})$	\(q+(2.65775 + 4.60336i) q^{2} +(-5.19389 - 0.153351i) q^{3} +(-10.1273 + 17.5410i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-13.0981 - 24.3169i) q^{6} +(6.71686 + 11.6339i) q^{7} -65.1396 q^{8} +(26.9530 + 1.59298i) q^{9} +26.5775 q^{10} +(23.4628 + 40.6388i) q^{11} +(55.2901 - 89.5531i) q^{12} +(18.0673 - 31.2935i) q^{13} +(-35.7035 + 61.8403i) q^{14} +(-13.6488 + 22.1068i) q^{15} +(-92.1064 - 159.533i) q^{16} -54.6071 q^{17} +(64.3013 + 128.308i) q^{18} +111.339 q^{19} +(50.6366 + 87.7051i) q^{20} +(-33.1026 - 61.4555i) q^{21} +(-124.717 + 216.016i) q^{22} +(17.9870 - 31.1544i) q^{23} +(338.328 + 9.98925i) q^{24} +(-12.5000 - 21.6506i) q^{25} +192.074 q^{26} +(-139.746 - 12.4070i) q^{27} -272.095 q^{28} +(-29.0588 - 50.3312i) q^{29} +(-138.041 - 4.07570i) q^{30} +(147.833 - 256.055i) q^{31} +(229.034 - 396.699i) q^{32} +(-115.631 - 214.671i) q^{33} +(-145.132 - 251.377i) q^{34} +67.1686 q^{35} +(-300.904 + 456.650i) q^{36} -53.0417 q^{37} +(295.911 + 512.533i) q^{38} +(-98.6386 + 159.765i) q^{39} +(-162.849 + 282.063i) q^{40} +(-64.1795 + 111.162i) q^{41} +(194.924 - 315.717i) q^{42} +(82.0858 + 142.177i) q^{43} -950.461 q^{44} +(74.2802 - 112.727i) q^{45} +191.220 q^{46} +(-43.9159 - 76.0646i) q^{47} +(453.926 + 842.721i) q^{48} +(81.2675 - 140.759i) q^{49} +(66.4439 - 115.084i) q^{50} +(283.623 + 8.37409i) q^{51} +(365.947 + 633.839i) q^{52} -479.247 q^{53} +(-314.297 - 676.279i) q^{54} +234.628 q^{55} +(-437.533 - 757.830i) q^{56} +(-578.281 - 17.0739i) q^{57} +(154.462 - 267.536i) q^{58} +(-317.807 + 550.458i) q^{59} +(-249.551 - 463.296i) q^{60} +(-24.0128 - 41.5915i) q^{61} +1571.62 q^{62} +(162.507 + 324.269i) q^{63} +961.163 q^{64} +(-90.3367 - 156.468i) q^{65} +(680.892 - 1102.84i) q^{66} +(14.4592 - 25.0440i) q^{67} +(553.024 - 957.865i) q^{68} +(-98.2001 + 159.054i) q^{69} +(178.518 + 309.202i) q^{70} +576.183 q^{71} +(-1755.70 - 103.766i) q^{72} +835.057 q^{73} +(-140.972 - 244.170i) q^{74} +(61.6035 + 114.368i) q^{75} +(-1127.56 + 1952.99i) q^{76} +(-315.193 + 545.930i) q^{77} +(-997.612 - 29.4548i) q^{78} +(101.869 + 176.442i) q^{79} -921.064 q^{80} +(723.925 + 85.8711i) q^{81} -682.294 q^{82} +(-232.239 - 402.249i) q^{83} +(1413.23 + 41.7262i) q^{84} +(-136.518 + 236.456i) q^{85} +(-436.328 + 755.742i) q^{86} +(143.210 + 265.871i) q^{87} +(-1528.36 - 2647.19i) q^{88} +993.782 q^{89} +(716.344 + 42.3375i) q^{90} +485.423 q^{91} +(364.320 + 631.021i) q^{92} +(-807.097 + 1307.25i) q^{93} +(233.435 - 404.322i) q^{94} +(278.347 - 482.111i) q^{95} +(-1250.41 + 2025.29i) q^{96} +(-440.708 - 763.328i) q^{97} +863.956 q^{98} +(567.656 + 1132.71i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{2} - 5 q^{3} - 36 q^{4} + 35 q^{5} - 31 q^{6} - 22 q^{7} - 36 q^{8} + 17 q^{9}+O(q^{10}) $ 14 * q + 2 * q^2 - 5 * q^3 - 36 * q^4 + 35 * q^5 - 31 * q^6 - 22 * q^7 - 36 * q^8 + 17 * q^9	\( 14 q + 2 q^{2} - 5 q^{3} - 36 q^{4} + 35 q^{5} - 31 q^{6} - 22 q^{7} - 36 q^{8} + 17 q^{9} + 20 q^{10} + 23 q^{11} + 287 q^{12} - 96 q^{13} - 21 q^{14} - 20 q^{15} - 324 q^{16} - 322 q^{17} - 89 q^{18} + 558 q^{19} + 180 q^{20} + 180 q^{21} - 311 q^{22} + 96 q^{23} + 48 q^{24} - 175 q^{25} + 716 q^{26} - 470 q^{27} + 674 q^{28} - 296 q^{29} + 80 q^{30} - 244 q^{31} - 314 q^{32} - 211 q^{33} - 125 q^{34} - 220 q^{35} - 2399 q^{36} + 808 q^{37} + 305 q^{38} + 634 q^{39} - 90 q^{40} - 47 q^{41} + 1941 q^{42} - 525 q^{43} - 110 q^{44} + 185 q^{45} + 1434 q^{46} + 164 q^{47} + 2051 q^{48} - 1225 q^{49} + 50 q^{50} + 1517 q^{51} - 1682 q^{52} - 1012 q^{53} - 4066 q^{54} + 230 q^{55} - 981 q^{56} + 337 q^{57} - 1183 q^{58} - 85 q^{59} + 65 q^{60} - 828 q^{61} + 1572 q^{62} - 828 q^{63} + 4472 q^{64} + 480 q^{65} + 4930 q^{66} - 1093 q^{67} + 2473 q^{68} - 822 q^{69} + 105 q^{70} - 656 q^{71} - 4626 q^{72} + 4170 q^{73} - 1316 q^{74} + 25 q^{75} - 2789 q^{76} + 24 q^{77} - 5314 q^{78} - 2110 q^{79} - 3240 q^{80} - 2167 q^{81} - 124 q^{82} + 1290 q^{83} + 5775 q^{84} - 805 q^{85} - 2569 q^{86} + 3604 q^{87} - 2271 q^{88} + 6096 q^{89} + 730 q^{90} + 6676 q^{91} + 2763 q^{92} - 696 q^{93} + 517 q^{94} + 1395 q^{95} - 593 q^{96} - 1787 q^{97} - 2558 q^{98} + 2320 q^{99}+O(q^{100}) \) 14 * q + 2 * q^2 - 5 * q^3 - 36 * q^4 + 35 * q^5 - 31 * q^6 - 22 * q^7 - 36 * q^8 + 17 * q^9 + 20 * q^10 + 23 * q^11 + 287 * q^12 - 96 * q^13 - 21 * q^14 - 20 * q^15 - 324 * q^16 - 322 * q^17 - 89 * q^18 + 558 * q^19 + 180 * q^20 + 180 * q^21 - 311 * q^22 + 96 * q^23 + 48 * q^24 - 175 * q^25 + 716 * q^26 - 470 * q^27 + 674 * q^28 - 296 * q^29 + 80 * q^30 - 244 * q^31 - 314 * q^32 - 211 * q^33 - 125 * q^34 - 220 * q^35 - 2399 * q^36 + 808 * q^37 + 305 * q^38 + 634 * q^39 - 90 * q^40 - 47 * q^41 + 1941 * q^42 - 525 * q^43 - 110 * q^44 + 185 * q^45 + 1434 * q^46 + 164 * q^47 + 2051 * q^48 - 1225 * q^49 + 50 * q^50 + 1517 * q^51 - 1682 * q^52 - 1012 * q^53 - 4066 * q^54 + 230 * q^55 - 981 * q^56 + 337 * q^57 - 1183 * q^58 - 85 * q^59 + 65 * q^60 - 828 * q^61 + 1572 * q^62 - 828 * q^63 + 4472 * q^64 + 480 * q^65 + 4930 * q^66 - 1093 * q^67 + 2473 * q^68 - 822 * q^69 + 105 * q^70 - 656 * q^71 - 4626 * q^72 + 4170 * q^73 - 1316 * q^74 + 25 * q^75 - 2789 * q^76 + 24 * q^77 - 5314 * q^78 - 2110 * q^79 - 3240 * q^80 - 2167 * q^81 - 124 * q^82 + 1290 * q^83 + 5775 * q^84 - 805 * q^85 - 2569 * q^86 + 3604 * q^87 - 2271 * q^88 + 6096 * q^89 + 730 * q^90 + 6676 * q^91 + 2763 * q^92 - 696 * q^93 + 517 * q^94 + 1395 * q^95 - 593 * q^96 - 1787 * q^97 - 2558 * q^98 + 2320 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	2.65775	+	4.60336i	0.939658	+	1.62754i	0.766110	+	0.642710i	$0.222190\pi$
$2$	2.65775	+	4.60336i	0.939658	+	1.62754i	0.173548	+	0.984825i	$0.444477\pi$
$3$	−5.19389	−	0.153351i	−0.999564	−	0.0295125i
$3$	−5.19389	−	0.153351i	−0.999564	−	0.0295125i
$4$	−10.1273	+	17.5410i	−1.26591	+	2.19263i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$6$	−13.0981	−	24.3169i	−0.891216	−	1.65456i
$7$	6.71686	+	11.6339i	0.362676	+	0.628174i	0.988400	−	0.151871i	$-0.0485297\pi$
$7$	6.71686	+	11.6339i	0.362676	+	0.628174i	−0.625724	+	0.780045i	$0.715196\pi$
$8$	−65.1396			−2.87879
$9$	26.9530	+	1.59298i	0.998258	+	0.0589993i
$10$	26.5775			0.840456
$11$	23.4628	+	40.6388i	0.643119	+	1.11391i	0.984733	+	0.174074i	$0.0556932\pi$
$11$	23.4628	+	40.6388i	0.643119	+	1.11391i	−0.341614	+	0.939840i	$0.610974\pi$
$12$	55.2901	−	89.5531i	1.33007	−	2.15431i
$13$	18.0673	−	31.2935i	0.385460	−	0.667636i	−0.606373	−	0.795180i	$-0.707376\pi$
$13$	18.0673	−	31.2935i	0.385460	−	0.667636i	0.991833	+	0.127544i	$0.0407095\pi$
$14$	−35.7035	+	61.8403i	−0.681584	+	1.18054i
$15$	−13.6488	+	22.1068i	−0.234940	+	0.380530i
$16$	−92.1064	−	159.533i	−1.43916	−	2.49270i
$17$	−54.6071			−0.779069			−0.389535	−	0.921012i	$-0.627364\pi$
$17$	−54.6071			−0.779069			−0.389535	+	0.921012i	$0.627364\pi$
$18$	64.3013	+	128.308i	0.841998	+	1.68014i
$19$	111.339			1.34436			0.672180	−	0.740388i	$-0.265358\pi$
$19$	111.339			1.34436			0.672180	+	0.740388i	$0.265358\pi$
$20$	50.6366	+	87.7051i	0.566134	+	0.980573i
$21$	−33.1026	−	61.4555i	−0.343980	−	0.638604i
$22$	−124.717	+	216.016i	−1.20862	+	2.09340i
$23$	17.9870	−	31.1544i	0.163067	−	0.282441i	−0.772900	−	0.634528i	$-0.781195\pi$
$23$	17.9870	−	31.1544i	0.163067	−	0.282441i	0.935967	+	0.352087i	$0.114528\pi$
$24$	338.328	+	9.98925i	2.87754	+	0.0849603i
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	192.074			1.44880
$27$	−139.746	−	12.4070i	−0.996082	−	0.0884347i
$28$	−272.095			−1.83647
$29$	−29.0588	−	50.3312i	−0.186072	−	0.322285i	0.757866	−	0.652411i	$-0.226242\pi$
$29$	−29.0588	−	50.3312i	−0.186072	−	0.322285i	−0.943937	+	0.330125i	$0.892909\pi$
$30$	−138.041	−	4.07570i	−0.840090	−	0.0248039i
$31$	147.833	−	256.055i	0.856506	−	1.48351i	−0.0187353	−	0.999824i	$-0.505964\pi$
$31$	147.833	−	256.055i	0.856506	−	1.48351i	0.875241	−	0.483687i	$-0.160703\pi$
$32$	229.034	−	396.699i	1.26525	−	2.19147i
$33$	−115.631	−	214.671i	−0.609964	−	1.13241i
$34$	−145.132	−	251.377i	−0.732059	−	1.26796i
$35$	67.1686			0.324388
$36$	−300.904	+	456.650i	−1.39307	+	2.11412i
$37$	−53.0417			−0.235676			−0.117838	−	0.993033i	$-0.537596\pi$
$37$	−53.0417			−0.235676			−0.117838	+	0.993033i	$0.537596\pi$
$38$	295.911	+	512.533i	1.26324	+	2.18799i
$39$	−98.6386	+	159.765i	−0.404995	+	0.655969i
$40$	−162.849	+	282.063i	−0.643717	+	1.11495i
$41$	−64.1795	+	111.162i	−0.244467	+	0.423430i	−0.961982	−	0.273114i	$-0.911946\pi$
$41$	−64.1795	+	111.162i	−0.244467	+	0.423430i	0.717514	+	0.696544i	$0.245280\pi$
$42$	194.924	−	315.717i	0.716127	−	1.15991i
$43$	82.0858	+	142.177i	0.291116	+	0.504227i	0.974074	−	0.226230i	$-0.0726402\pi$
$43$	82.0858	+	142.177i	0.291116	+	0.504227i	−0.682958	+	0.730457i	$0.739307\pi$
$44$	−950.461			−3.25653
$45$	74.2802	−	112.727i	0.246068	−	0.373431i
$46$	191.220			0.612910
$47$	−43.9159	−	76.0646i	−0.136294	−	0.236067i	0.789797	−	0.613368i	$-0.210186\pi$
$47$	−43.9159	−	76.0646i	−0.136294	−	0.236067i	−0.926091	+	0.377301i	$0.876852\pi$
$48$	453.926	+	842.721i	1.36497	+	2.53409i
$49$	81.2675	−	140.759i	0.236932	−	0.410378i
$50$	66.4439	−	115.084i	0.187932	−	0.325507i
$51$	283.623	+	8.37409i	0.778730	+	0.0229923i
$52$	365.947	+	633.839i	0.975918	+	1.69034i
$53$	−479.247			−1.24207			−0.621035	−	0.783783i	$-0.713287\pi$
$53$	−479.247			−1.24207			−0.621035	+	0.783783i	$0.713287\pi$
$54$	−314.297	−	676.279i	−0.792046	−	1.70426i
$55$	234.628			0.575223
$56$	−437.533	−	757.830i	−1.04407	−	1.80838i
$57$	−578.281	−	17.0739i	−1.34377	−	0.0396754i
$58$	154.462	−	267.536i	0.349687	−	0.605676i
$59$	−317.807	+	550.458i	−0.701271	+	1.21464i	0.266750	+	0.963766i	$0.414050\pi$
$59$	−317.807	+	550.458i	−0.701271	+	1.21464i	−0.968021	+	0.250871i	$0.919283\pi$
$60$	−249.551	−	463.296i	−0.536948	−	0.996854i
$61$	−24.0128	−	41.5915i	−0.0504021	−	0.0872990i	0.839724	−	0.543014i	$-0.182717\pi$
$61$	−24.0128	−	41.5915i	−0.0504021	−	0.0872990i	−0.890126	+	0.455715i	$0.849384\pi$
$62$	1571.62			3.21929
$63$	162.507	+	324.269i	0.324983	+	0.648477i
$64$	961.163			1.87727
$65$	−90.3367	−	156.468i	−0.172383	−	0.298576i
$66$	680.892	−	1102.84i	1.26988	−	2.05682i
$67$	14.4592	−	25.0440i	0.0263652	−	0.0456658i	−0.852542	−	0.522659i	$-0.824940\pi$
$67$	14.4592	−	25.0440i	0.0263652	−	0.0456658i	0.878907	+	0.476993i	$0.158273\pi$
$68$	553.024	−	957.865i	0.986235	−	1.70821i
$69$	−98.2001	+	159.054i	−0.171332	+	0.277505i
$70$	178.518	+	309.202i	0.304813	+	0.527952i
$71$	576.183			0.963103			0.481552	−	0.876418i	$-0.340073\pi$
$71$	576.183			0.963103			0.481552	+	0.876418i	$0.340073\pi$
$72$	−1755.70	−	103.766i	−2.87377	−	0.169847i
$73$	835.057			1.33885			0.669425	−	0.742880i	$-0.266541\pi$
$73$	835.057			1.33885			0.669425	+	0.742880i	$0.266541\pi$
$74$	−140.972	−	244.170i	−0.221455	−	0.383571i
$75$	61.6035	+	114.368i	0.0948447	+	0.176081i
$76$	−1127.56	+	1952.99i	−1.70184	+	2.94768i
$77$	−315.193	+	545.930i	−0.466488	+	0.807981i
$78$	−997.612	−	29.4548i	−1.44817	−	0.0427577i
$79$	101.869	+	176.442i	0.145078	+	0.251282i	0.929402	−	0.369069i	$-0.120324\pi$
$79$	101.869	+	176.442i	0.145078	+	0.251282i	−0.784324	+	0.620351i	$0.786990\pi$
$80$	−921.064			−1.28723
$81$	723.925	+	85.8711i	0.993038	+	0.117793i
$82$	−682.294			−0.918863
$83$	−232.239	−	402.249i	−0.307127	−	0.531959i	0.670606	−	0.741814i	$-0.266034\pi$
$83$	−232.239	−	402.249i	−0.307127	−	0.531959i	−0.977733	+	0.209855i	$0.932701\pi$
$84$	1413.23	+	41.7262i	1.83567	+	0.0541988i
$85$	−136.518	+	236.456i	−0.174205	+	0.301732i
$86$	−436.328	+	755.742i	−0.547098	+	0.947602i
$87$	143.210	+	265.871i	0.176479	+	0.327636i
$88$	−1528.36	−	2647.19i	−1.85140	−	3.20672i
$89$	993.782			1.18360			0.591801	−	0.806084i	$-0.298417\pi$
$89$	993.782			1.18360			0.591801	+	0.806084i	$0.298417\pi$
$90$	716.344	+	42.3375i	0.838992	+	0.0495863i
$91$	485.423			0.559189
$92$	364.320	+	631.021i	0.412859	+	0.715092i
$93$	−807.097	+	1307.25i	−0.899915	+	1.45759i
$94$	233.435	−	404.322i	0.256139	−	0.443645i
$95$	278.347	−	482.111i	0.300608	−	0.520668i
$96$	−1250.41	+	2025.29i	−1.32937	+	2.15318i
$97$	−440.708	−	763.328i	−0.461310	−	0.799012i	0.537717	−	0.843126i	$-0.319287\pi$
$97$	−440.708	−	763.328i	−0.461310	−	0.799012i	−0.999027	+	0.0441134i	$0.985954\pi$
$98$	863.956			0.890538
$99$	567.656	+	1132.71i	0.576278	+	1.14992i
$100$	506.366			0.506366
$101$	−604.869	−	1047.66i	−0.595909	−	1.03214i	−0.993418	−	0.114546i	$-0.963459\pi$
$101$	−604.869	−	1047.66i	−0.595909	−	1.03214i	0.397509	−	0.917598i	$-0.369875\pi$
$102$	715.252	+	1327.88i	0.694319	+	1.28902i
$103$	−372.421	+	645.053i	−0.356270	+	0.617077i	−0.987334	−	0.158653i	$-0.949285\pi$
$103$	−372.421	+	645.053i	−0.356270	+	0.617077i	0.631065	+	0.775730i	$0.282618\pi$
$104$	−1176.90	+	2038.45i	−1.10966	+	1.92198i
$105$	−348.866	−	10.3004i	−0.324246	−	0.00957349i
$106$	−1273.72	−	2206.15i	−1.16712	−	2.02151i
$107$	−1000.14			−0.903622			−0.451811	−	0.892114i	$-0.649222\pi$
$107$	−1000.14			−0.903622			−0.451811	+	0.892114i	$0.649222\pi$
$108$	1632.89	−	2325.65i	1.45486	−	2.07209i
$109$	−915.517			−0.804502			−0.402251	−	0.915530i	$-0.631772\pi$
$109$	−915.517			−0.804502			−0.402251	+	0.915530i	$0.631772\pi$
$110$	623.584	+	1080.08i	0.540513	+	0.936196i
$111$	275.493	+	8.13403i	0.235573	+	0.00695538i
$112$	1237.33	−	2143.12i	1.04390	−	1.80809i
$113$	662.451	−	1147.40i	0.551488	−	0.955206i	−0.446679	−	0.894694i	$-0.647394\pi$
$113$	662.451	−	1147.40i	0.551488	−	0.955206i	0.998168	−	0.0605114i	$-0.0192732\pi$
$114$	−1458.33	−	2707.42i	−1.19812	−	2.22432i
$115$	−89.9350	−	155.772i	−0.0729260	−	0.126311i
$116$	1177.15			0.942202
$117$	536.818	−	814.673i	0.424178	−	0.643731i
$118$	−3378.61			−2.63582
$119$	−366.789	−	635.297i	−0.282550	−	0.489391i
$120$	889.074	−	1440.03i	0.676341	−	1.09547i
$121$	−435.508	+	754.321i	−0.327203	+	0.566733i
$122$	127.640	−	221.080i	0.0947215	−	0.164062i
$123$	350.388	−	567.522i	0.256857	−	0.416030i
$124$	2994.31	+	5186.30i	2.16853	+	3.75600i
$125$	−125.000			−0.0894427
$126$	−1060.83	+	1609.91i	−0.750047	+	1.13827i
$127$	−993.635			−0.694259			−0.347129	−	0.937817i	$-0.612843\pi$
$127$	−993.635			−0.694259			−0.347129	+	0.937817i	$0.612843\pi$
$128$	722.262	+	1251.00i	0.498747	+	0.863855i
$129$	−404.542	−	751.039i	−0.276108	−	0.512599i
$130$	480.185	−	831.705i	0.323962	−	0.561118i
$131$	−691.995	+	1198.57i	−0.461526	+	0.799386i	−0.999037	−	0.0438704i	$-0.986031\pi$
$131$	−691.995	+	1198.57i	−0.461526	+	0.799386i	0.537512	+	0.843256i	$0.319364\pi$
$132$	4936.59	+	145.755i	3.25511	+	0.0961084i
$133$	747.847	+	1295.31i	0.487568	+	0.844492i
$134$	153.715			0.0990970
$135$	−403.090	+	574.102i	−0.256981	+	0.366006i
$136$	3557.09			2.24278
$137$	−773.568	−	1339.86i	−0.482411	−	0.835561i	0.517385	−	0.855753i	$-0.326906\pi$
$137$	−773.568	−	1339.86i	−0.482411	−	0.835561i	−0.999796	+	0.0201918i	$0.993572\pi$
$138$	−993.176	−	29.3239i	−0.612643	−	0.0180885i
$139$	269.752	−	467.225i	0.164605	−	0.285104i	−0.771910	−	0.635732i	$-0.780698\pi$
$139$	269.752	−	467.225i	0.164605	−	0.285104i	0.936515	+	0.350628i	$0.114032\pi$
$140$	−680.238	+	1178.21i	−0.410647	+	0.711261i
$141$	216.430	+	401.806i	0.129267	+	0.239987i
$142$	1531.35	+	2652.38i	0.904988	+	1.56748i
$143$	1695.64			0.991586
$144$	−2228.41	−	4446.61i	−1.28959	−	2.57327i
$145$	−290.588			−0.166427
$146$	2219.38	+	3844.07i	1.25806	+	2.17902i
$147$	−443.680	+	718.627i	−0.248940	+	0.403206i
$148$	537.170	−	930.406i	0.298345	−	0.516749i
$149$	602.335	−	1043.27i	0.331176	−	0.573613i	−0.651567	−	0.758591i	$-0.725888\pi$
$149$	602.335	−	1043.27i	0.331176	−	0.573613i	0.982743	+	0.184978i	$0.0592214\pi$
$150$	−362.750	+	587.545i	−0.197456	+	0.319819i
$151$	−1486.46	−	2574.62i	−0.801100	−	1.38755i	−0.918893	−	0.394508i	$-0.870915\pi$
$151$	−1486.46	−	2574.62i	−0.801100	−	1.38755i	0.117793	−	0.993038i	$-0.462418\pi$
$152$	−7252.55			−3.87013
$153$	−1471.82	−	86.9881i	−0.777712	−	0.0459645i
$154$	−3350.82			−1.75336
$155$	−739.167	−	1280.28i	−0.383041	−	0.663446i
$156$	−1803.49	−	3348.21i	−0.925607	−	1.71840i
$157$	197.880	−	342.739i	0.100590	−	0.174226i	−0.811338	−	0.584577i	$-0.801260\pi$
$157$	197.880	−	342.739i	0.100590	−	0.174226i	0.911928	+	0.410351i	$0.134594\pi$
$158$	−541.484	+	937.877i	−0.272646	+	0.472238i
$159$	2489.16	+	73.4932i	1.24153	+	0.0366566i
$160$	−1145.17	−	1983.49i	−0.565836	−	0.980056i
$161$	483.265			0.236563
$162$	1528.72	+	3560.71i	0.741404	+	1.72689i
$163$	3861.43			1.85553			0.927764	−	0.373169i	$-0.121729\pi$
$163$	3861.43			1.85553			0.927764	+	0.373169i	$0.121729\pi$
$164$	−1299.93	−	2251.55i	−0.618949	−	1.07205i
$165$	−1218.63	−	35.9806i	−0.574972	−	0.0169763i
$166$	1234.47	−	2138.16i	0.577188	−	0.999719i
$167$	−1017.49	+	1762.34i	−0.471470	+	0.816609i	−0.999467	−	0.0326366i	$-0.989610\pi$
$167$	−1017.49	+	1762.34i	−0.471470	+	0.816609i	0.527998	+	0.849246i	$0.322943\pi$
$168$	2156.29	+	4003.18i	0.990244	+	1.83841i
$169$	445.643	+	771.876i	0.202842	+	0.351332i
$170$	−1451.32			−0.654773
$171$	3000.91	+	177.360i	1.34202	+	0.0793163i
$172$	−3325.24			−1.47411
$173$	−773.458	−	1339.67i	−0.339913	−	0.588746i	0.644503	−	0.764602i	$-0.277064\pi$
$173$	−773.458	−	1339.67i	−0.339913	−	0.588746i	−0.984416	+	0.175855i	$0.943731\pi$
$174$	−843.286	+	1365.87i	−0.367410	+	0.595092i
$175$	167.922	−	290.849i	0.0725353	−	0.125635i
$176$	4322.15	−	7486.19i	1.85111	−	3.20621i
$177$	1735.07	−	2810.28i	0.736812	−	1.19341i
$178$	2641.23	+	4574.74i	1.11218	+	1.92636i
$179$	−823.973			−0.344059			−0.172030	−	0.985092i	$-0.555033\pi$
$179$	−823.973			−0.344059			−0.172030	+	0.985092i	$0.555033\pi$
$180$	1225.09	+	2444.58i	0.507295	+	1.01227i
$181$	−4403.55			−1.80836			−0.904180	−	0.427152i	$-0.859517\pi$
$181$	−4403.55			−1.80836			−0.904180	+	0.427152i	$0.859517\pi$
$182$	1290.14	+	2234.58i	0.525446	+	0.910099i
$183$	118.342	+	219.704i	0.0478037	+	0.0887485i
$184$	−1171.67	+	2029.38i	−0.469437	+	0.813088i
$185$	−132.604	+	229.677i	−0.0526987	+	0.0912769i
$186$	−8162.82	−	241.010i	−3.21789	−	0.0950093i
$187$	−1281.24	−	2219.17i	−0.501034	−	0.867816i
$188$	1779.00			0.690144
$189$	−794.315	−	1709.14i	−0.305703	−	0.657786i
$190$	2959.11			1.12988
$191$	1523.46	+	2638.72i	0.577141	+	0.999637i	0.995805	+	0.0914964i	$0.0291650\pi$
$191$	1523.46	+	2638.72i	0.577141	+	0.999637i	−0.418664	+	0.908141i	$0.637502\pi$
$192$	−4992.18	−	147.396i	−1.87645	−	0.0554030i
$193$	−945.452	+	1637.57i	−0.352617	+	0.610751i	−0.986707	−	0.162508i	$-0.948042\pi$
$193$	−945.452	+	1637.57i	−0.352617	+	0.610751i	0.634090	+	0.773259i	$0.281375\pi$
$194$	2342.58	−	4057.48i	0.866947	−	1.50160i
$195$	445.204	+	826.529i	0.163496	+	0.303533i
$196$	1646.04	+	2851.03i	0.599870	+	1.03901i
$197$	3652.00			1.32078			0.660392	−	0.750921i	$-0.270390\pi$
$197$	3652.00			1.32078			0.660392	+	0.750921i	$0.270390\pi$
$198$	−3705.60	+	5623.60i	−1.33003	+	2.01844i
$199$	3217.26			1.14606			0.573029	−	0.819535i	$-0.305768\pi$
$199$	3217.26			1.14606			0.573029	+	0.819535i	$0.305768\pi$
$200$	814.245	+	1410.31i	0.287879	+	0.498621i
$201$	−78.9398	+	127.858i	−0.0277014	+	0.0448678i
$202$	3215.19	−	5568.87i	1.11990	−	1.93972i
$203$	390.367	−	676.136i	0.134968	−	0.233771i
$204$	−3019.23	+	4890.24i	−1.03622	+	1.67836i
$205$	320.898	+	555.811i	0.109329	+	0.189364i
$206$	−3959.22			−1.33909
$207$	534.432	−	811.051i	0.179447	−	0.272328i
$208$	−6656.47			−2.21896
$209$	2612.32	+	4524.67i	0.864583	+	1.49750i
$210$	−879.784	−	1633.34i	−0.289100	−	0.536718i
$211$	−2473.90	+	4284.92i	−0.807159	+	1.39804i	0.107666	+	0.994187i	$0.465662\pi$
$211$	−2473.90	+	4284.92i	−0.807159	+	1.39804i	−0.914824	+	0.403853i	$0.867671\pi$
$212$	4853.49	−	8406.48i	1.57235	−	2.72339i
$213$	−2992.63	−	88.3585i	−0.962684	−	0.0284236i
$214$	−2658.14	−	4604.03i	−0.849096	−	1.47068i
$215$	820.858			0.260382
$216$	9103.02	+	808.189i	2.86751	+	0.254585i
$217$	3971.91			1.24254
$218$	−2433.22	−	4214.46i	−0.755956	−	1.30935i
$219$	−4337.19	−	128.057i	−1.33827	−	0.0395128i
$220$	−2376.15	+	4115.62i	−0.728183	+	1.26125i
$221$	−986.606	+	1708.85i	−0.300300	+	0.520135i
$222$	694.748	+	1289.81i	0.210038	+	0.389939i
$223$	−552.056	−	956.189i	−0.165778	−	0.287135i	0.771154	−	0.636649i	$-0.219680\pi$
$223$	−552.056	−	956.189i	−0.165778	−	0.287135i	−0.936931	+	0.349514i	$0.886347\pi$
$224$	6153.56			1.83550
$225$	−302.423	−	603.461i	−0.0896068	−	0.178803i
$226$	7042.53			2.07284
$227$	1910.12	+	3308.43i	0.558498	+	0.967348i	0.997622	+	0.0689210i	$0.0219556\pi$
$227$	1910.12	+	3308.43i	0.558498	+	0.967348i	−0.439124	+	0.898427i	$0.644711\pi$
$228$	6155.92	−	9970.72i	1.78810	−	2.89617i
$229$	−72.3848	+	125.374i	−0.0208879	+	0.0361788i	−0.876280	−	0.481801i	$-0.839983\pi$
$229$	−72.3848	+	125.374i	−0.0208879	+	0.0361788i	0.855393	+	0.517980i	$0.173316\pi$
$230$	478.050	−	828.008i	0.137051	−	0.237379i
$231$	1720.80	−	2787.17i	0.490130	−	0.793862i
$232$	1892.87	+	3278.55i	0.535661	+	0.927792i
$233$	1286.31			0.361670			0.180835	−	0.983513i	$-0.442120\pi$
$233$	1286.31			0.361670			0.180835	+	0.983513i	$0.442120\pi$
$234$	5176.97	+	305.970i	1.44628	+	0.0854782i
$235$	−439.159			−0.121905
$236$	−6437.07	−	11149.3i	−1.77550	−	3.07525i
$237$	−502.037	−	932.041i	−0.137598	−	0.255454i
$238$	1949.67	−	3376.92i	0.531001	−	0.919721i
$239$	−2109.73	+	3654.15i	−0.570991	+	0.988986i	0.425473	+	0.904971i	$0.360108\pi$
$239$	−2109.73	+	3654.15i	−0.570991	+	0.988986i	−0.996465	+	0.0840147i	$0.973226\pi$
$240$	4783.91	+	141.247i	1.28667	+	0.0379893i
$241$	−1141.57	−	1977.25i	−0.305124	−	0.528490i	0.672165	−	0.740401i	$-0.265364\pi$
$241$	−1141.57	−	1977.25i	−0.305124	−	0.528490i	−0.977289	+	0.211912i	$0.932031\pi$
$242$	−4629.89			−1.22984
$243$	−3746.82	−	557.020i	−0.989129	−	0.147049i
$244$	972.742			0.255219
$245$	−406.338	−	703.797i	−0.105959	−	0.183526i
$246$	3543.76	+	104.631i	0.918462	+	0.0271179i
$247$	2011.59	−	3484.18i	0.518197	−	0.897543i
$248$	−9629.81	+	16679.3i	−2.46570	+	4.27072i
$249$	1144.54	+	2124.85i	0.291293	+	0.540791i
$250$	−332.219	−	575.421i	−0.0840456	−	0.145571i
$251$	−7922.23			−1.99222			−0.996109	−	0.0881290i	$-0.971911\pi$
$251$	−7922.23			−1.99222			−0.996109	+	0.0881290i	$0.971911\pi$
$252$	−7333.77	−	433.442i	−1.83327	−	0.108350i
$253$	1688.10			0.419487
$254$	−2640.84	−	4574.06i	−0.652366	−	1.12993i
$255$	745.320	−	1207.19i	0.183034	−	0.296460i
$256$	5.46197	−	9.46041i	0.00133349	−	0.00230967i
$257$	−1131.09	+	1959.10i	−0.274535	+	0.475508i	−0.970018	−	0.243035i	$-0.921857\pi$
$257$	−1131.09	+	1959.10i	−0.274535	+	0.475508i	0.695483	+	0.718542i	$0.255190\pi$
$258$	2382.13	−	3858.33i	0.574826	−	0.931043i
$259$	−356.274	−	617.085i	−0.0854741	−	0.148045i
$260$	3659.47			0.872888
$261$	−703.043	−	1402.87i	−0.166733	−	0.332702i
$262$	−7356.61			−1.73471
$263$	−81.7349	−	141.569i	−0.0191635	−	0.0331921i	0.856285	−	0.516504i	$-0.172767\pi$
$263$	−81.7349	−	141.569i	−0.0191635	−	0.0331921i	−0.875448	+	0.483312i	$0.839434\pi$
$264$	7532.17	+	13983.6i	1.75596	+	3.25997i
$265$	−1198.12	+	2075.20i	−0.277735	+	0.481051i
$266$	−3975.18	+	6885.22i	−0.916294	+	1.58707i
$267$	−5161.59	−	152.398i	−1.18309	−	0.0349311i
$268$	292.865	+	507.257i	0.0667521	+	0.115618i
$269$	3304.13			0.748908			0.374454	−	0.927246i	$-0.377830\pi$
$269$	3304.13			0.748908			0.374454	+	0.927246i	$0.377830\pi$
$270$	−3714.12	−	329.749i	−0.837163	−	0.0743254i
$271$	−1954.96			−0.438212			−0.219106	−	0.975701i	$-0.570314\pi$
$271$	−1954.96			−0.438212			−0.219106	+	0.975701i	$0.570314\pi$
$272$	5029.67	+	8711.64i	1.12121	+	1.94199i
$273$	−2521.23	−	74.4403i	−0.558945	−	0.0165031i
$274$	4111.91	−	7122.03i	0.906603	−	1.57028i
$275$	586.570	−	1015.97i	0.128624	−	0.222783i
$276$	−1795.47	−	3333.32i	−0.391575	−	0.726965i
$277$	2121.67	+	3674.85i	0.460213	+	0.797112i	0.998971	−	0.0453482i	$-0.0144397\pi$
$277$	2121.67	+	3674.85i	0.460213	+	0.797112i	−0.538758	+	0.842460i	$0.681106\pi$
$278$	2867.74			0.618689
$279$	4392.44	−	6665.95i	0.942540	−	1.43039i
$280$	−4375.33			−0.933844
$281$	1311.15	+	2270.97i	0.278350	+	0.482117i	0.970975	−	0.239181i	$-0.0768791\pi$
$281$	1311.15	+	2270.97i	0.278350	+	0.482117i	−0.692625	+	0.721298i	$0.743546\pi$
$282$	−1274.44	+	2064.21i	−0.269120	+	0.435893i
$283$	3.53735	−	6.12688i	0.000743017	−	0.00128694i	−0.865654	−	0.500643i	$-0.833097\pi$
$283$	3.53735	−	6.12688i	0.000743017	−	0.00128694i	0.866397	+	0.499356i	$0.166430\pi$
$284$	−5835.18	+	10106.8i	−1.21921	+	2.11173i
$285$	−1519.63	+	2461.34i	−0.315843	+	0.511570i
$286$	4506.60	+	7805.66i	0.931751	+	1.61384i
$287$	−1724.34			−0.354650
$288$	6805.08	−	10327.4i	1.39234	−	2.11301i
$289$	−1931.06			−0.393051
$290$	−772.310	−	1337.68i	−0.156385	−	0.270867i
$291$	2171.93	+	4032.22i	0.437528	+	0.812279i
$292$	−8456.88	+	14647.7i	−1.69487	+	2.93560i
$293$	2238.75	−	3877.62i	0.446378	−	0.773150i	−0.551769	−	0.833997i	$-0.686047\pi$
$293$	2238.75	−	3877.62i	0.446378	−	0.773150i	0.998147	+	0.0608470i	$0.0193802\pi$
$294$	−4487.29	−	132.489i	−0.890151	−	0.0262820i
$295$	1589.04	+	2752.29i	0.313618	+	0.543202i
$296$	3455.12			0.678461
$297$	−2774.64	−	5970.23i	−0.542090	−	1.16642i
$298$	6403.43			1.24477
$299$	−649.955	−	1125.75i	−0.125712	−	0.217739i
$300$	−2630.01	−	77.6519i	−0.506145	−	0.0149441i
$301$	−1102.72	+	1909.96i	−0.211162	+	0.365743i
$302$	7901.27	−	13685.4i	1.50552	−	2.60764i
$303$	2980.96	+	5534.21i	0.565188	+	1.04928i
$304$	−10255.0	−	17762.2i	−1.93475	−	3.35109i
$305$	−240.128			−0.0450810
$306$	−3511.31	−	7006.54i	−0.655975	−	1.30895i
$307$	−3889.78			−0.723132			−0.361566	−	0.932347i	$-0.617758\pi$
$307$	−3889.78			−0.723132			−0.361566	+	0.932347i	$0.617758\pi$
$308$	−6384.12	−	11057.6i	−1.18107	−	2.04567i
$309$	2033.24	−	3293.22i	0.374326	−	0.606294i
$310$	3929.05	−	6805.31i	0.719855	−	1.24683i
$311$	3647.83	−	6318.23i	0.665111	−	1.15201i	−0.314145	−	0.949375i	$-0.601718\pi$
$311$	3647.83	−	6318.23i	0.665111	−	1.15201i	0.979255	−	0.202630i	$-0.0649490\pi$
$312$	6425.28	−	10407.0i	1.16590	−	1.88840i
$313$	318.036	+	550.854i	0.0574328	+	0.0994765i	0.893312	−	0.449436i	$-0.148375\pi$
$313$	318.036	+	550.854i	0.0574328	+	0.0994765i	−0.835880	+	0.548913i	$0.815042\pi$
$314$	2103.67			0.378080
$315$	1810.39	+	106.998i	0.323823	+	0.0191386i
$316$	−4126.62			−0.734623
$317$	3073.18	+	5322.90i	0.544501	+	0.943104i	0.998638	+	0.0521721i	$0.0166144\pi$
$317$	3073.18	+	5322.90i	0.544501	+	0.943104i	−0.454137	+	0.890932i	$0.650052\pi$
$318$	6277.25	+	11653.8i	1.10695	+	2.05508i
$319$	1363.60	−	2361.83i	0.239332	−	0.414536i
$320$	2402.91	−	4161.96i	0.419771	−	0.727064i
$321$	5194.64	+	153.374i	0.903229	+	0.0266682i
$322$	1284.40	+	2224.65i	0.222288	+	0.385014i
$323$	−6079.89			−1.04735
$324$	−8837.68	+	11828.7i	−1.51538	+	2.02825i
$325$	−903.367			−0.154184
$326$	10262.7	+	17775.6i	1.74356	+	3.01994i
$327$	4755.10	+	140.396i	0.804151	+	0.0237429i
$328$	4180.63	−	7241.06i	0.703770	−	1.21897i
$329$	589.954	−	1021.83i	0.0988609	−	0.171232i
$330$	−3073.19	−	5705.44i	−0.512648	−	0.951740i
$331$	−5867.20	−	10162.3i	−0.974291	−	1.68752i	−0.682255	−	0.731114i	$-0.739001\pi$
$331$	−5867.20	−	10162.3i	−0.974291	−	1.68752i	−0.292036	−	0.956407i	$-0.594333\pi$
$332$	9407.82			1.55518
$333$	−1429.63	−	84.4945i	−0.235265	−	0.0139047i
$334$	−10816.9			−1.77208
$335$	−72.2958	−	125.220i	−0.0117909	−	0.0204224i
$336$	−6755.22	+	10941.4i	−1.09681	+	1.77649i
$337$	−3141.65	+	5441.49i	−0.507823	+	0.879575i	0.492136	+	0.870518i	$0.336216\pi$
$337$	−3141.65	+	5441.49i	−0.507823	+	0.879575i	−0.999959	+	0.00905696i	$0.997117\pi$
$338$	−2368.82	+	4102.91i	−0.381203	+	0.660264i
$339$	−3616.65	+	5857.88i	−0.579438	+	0.938514i
$340$	−2765.12	−	4789.33i	−0.441058	−	0.763934i
$341$	13874.4			2.20334
$342$	7159.22	+	14285.7i	1.13195	+	2.25871i
$343$	6791.22			1.06907
$344$	−5347.04	−	9261.34i	−0.838061	−	1.45156i
$345$	443.225	+	822.854i	0.0691664	+	0.128409i
$346$	4111.32	−	7121.02i	0.638803	−	1.10644i
$347$	−2400.41	+	4157.63i	−0.371357	+	0.643209i	−0.989775	−	0.142641i	$-0.954441\pi$
$347$	−2400.41	+	4157.63i	−0.371357	+	0.643209i	0.618418	+	0.785849i	$0.287774\pi$
$348$	−6113.98	−	180.517i	−0.941792	−	0.0278068i
$349$	1946.23	+	3370.97i	0.298508	+	0.517031i	0.975795	−	0.218688i	$-0.0701778\pi$
$349$	1946.23	+	3370.97i	0.298508	+	0.517031i	−0.677287	+	0.735719i	$0.736844\pi$
$350$	1785.18			0.272633
$351$	−2913.11	+	4149.00i	−0.442992	+	0.630932i
$352$	21495.2			3.25482
$353$	1483.14	+	2568.87i	0.223624	+	0.387329i	0.955906	−	0.293673i	$-0.0948778\pi$
$353$	1483.14	+	2568.87i	0.223624	+	0.387329i	−0.732281	+	0.681002i	$0.761544\pi$
$354$	17548.1	+	518.115i	2.63467	+	0.0777896i
$355$	1440.46	−	2494.94i	0.215356	−	0.373008i
$356$	−10064.3	+	17431.9i	−1.49834	+	2.59520i
$357$	1807.64	+	3355.91i	0.267984	+	0.497517i
$358$	−2189.92	−	3793.05i	−0.323298	−	0.559969i
$359$	−9584.91			−1.40911			−0.704557	−	0.709647i	$-0.748854\pi$
$359$	−9584.91			−1.40911			−0.704557	+	0.709647i	$0.748854\pi$
$360$	−4838.58	+	7343.01i	−0.708377	+	1.07503i
$361$	5537.30			0.807304
$362$	−11703.5	−	20271.1i	−1.69924	−	2.94317i
$363$	2377.65	−	3851.08i	0.343787	−	0.556829i
$364$	−4916.03	+	8514.82i	−0.707885	+	1.22609i
$365$	2087.64	−	3615.90i	0.299376	−	0.518534i
$366$	−696.853	+	1128.69i	−0.0995221	+	0.161195i
$367$	−2268.59	−	3929.31i	−0.322669	−	0.558879i	0.658369	−	0.752695i	$-0.271247\pi$
$367$	−2268.59	−	3929.31i	−0.322669	−	0.558879i	−0.981038	+	0.193817i	$0.937913\pi$
$368$	−6626.88			−0.938722
$369$	−1906.91	+	2893.91i	−0.269023	+	0.408269i
$370$	−1409.72			−0.198075
$371$	−3219.04	−	5575.54i	−0.450469	−	0.780236i
$372$	−14756.8	−	27396.3i	−2.05673	−	3.81836i
$373$	−6565.65	+	11372.0i	−0.911411	+	1.57861i	−0.0993385	+	0.995054i	$0.531673\pi$
$373$	−6565.65	+	11372.0i	−0.911411	+	1.57861i	−0.812073	+	0.583557i	$0.801661\pi$
$374$	6810.43	−	11796.0i	0.941601	−	1.63090i
$375$	649.236	+	19.1689i	0.0894038	+	0.00263968i
$376$	2860.66	+	4954.82i	0.392360	+	0.679588i
$377$	−2100.06			−0.286892
$378$	5756.70	−	8198.99i	0.783314	−	1.11564i
$379$	−9451.10			−1.28092			−0.640462	−	0.767990i	$-0.721257\pi$
$379$	−9451.10			−1.28092			−0.640462	+	0.767990i	$0.721257\pi$
$380$	5637.81	+	9764.97i	0.761088	+	1.31824i
$381$	5160.83	+	152.375i	0.693956	+	0.0204893i
$382$	−8097.98	+	14026.1i	−1.08463	+	1.87863i
$383$	4298.52	−	7445.25i	0.573483	−	0.993301i	−0.422722	−	0.906260i	$-0.638925\pi$
$383$	4298.52	−	7445.25i	0.573483	−	0.993301i	0.996205	−	0.0870420i	$-0.0277414\pi$
$384$	−3559.51	−	6608.29i	−0.473035	−	0.878198i
$385$	1575.97	+	2729.65i	0.208620	+	0.361340i
$386$	−10051.1			−1.32536
$387$	1985.97	+	3962.85i	0.260860	+	0.520524i
$388$	17852.7			2.33592
$389$	−2221.04	−	3846.95i	−0.289489	−	0.501410i	0.684199	−	0.729295i	$-0.260152\pi$
$389$	−2221.04	−	3846.95i	−0.289489	−	0.501410i	−0.973688	+	0.227886i	$0.926819\pi$
$390$	−2621.57	+	4246.15i	−0.340381	+	0.551313i
$391$	−982.219	+	1701.25i	−0.127041	+	0.220041i
$392$	−5293.73	+	9169.01i	−0.682076	+	1.18139i
$393$	3777.95	−	6119.12i	0.484917	−	0.785417i
$394$	9706.13	+	16811.5i	1.24109	+	2.14962i
$395$	1018.69			0.129761
$396$	−25617.7	−	1514.07i	−3.25086	−	0.192133i
$397$	10445.6			1.32053			0.660265	−	0.751033i	$-0.270444\pi$
$397$	10445.6			1.32053			0.660265	+	0.751033i	$0.270444\pi$
$398$	8550.68	+	14810.2i	1.07690	+	1.86525i
$399$	−3685.59	−	6842.37i	−0.462432	−	0.858514i
$400$	−2302.66	+	3988.33i	−0.287833	+	0.498541i
$401$	6341.72	−	10984.2i	0.789751	−	1.36789i	−0.136368	−	0.990658i	$-0.543543\pi$
$401$	6341.72	−	10984.2i	0.789751	−	1.36789i	0.926119	−	0.377231i	$-0.123124\pi$
$402$	−798.381	−	23.5725i	−0.0990538	−	0.00292460i
$403$	−5341.91	−	9252.47i	−0.660297	−	1.14367i
$404$	24502.8			3.01748
$405$	2181.64	−	2920.01i	0.267671	−	0.358263i
$406$	4150.00			0.507293
$407$	−1244.51	−	2155.55i	−0.151568	−	0.262523i
$408$	−18475.1	−	545.484i	−2.24180	−	0.0661899i
$409$	5556.30	−	9623.79i	0.671739	−	1.16349i	−0.305671	−	0.952137i	$-0.598881\pi$
$409$	5556.30	−	9623.79i	0.671739	−	1.16349i	0.977411	−	0.211349i	$-0.0677858\pi$
$410$	−1705.73	+	2954.42i	−0.205464	+	0.355874i
$411$	3812.36	+	7077.71i	0.457542	+	0.849434i
$412$	−7543.26	−	13065.3i	−0.902014	−	1.56233i
$413$	−8538.67			−1.01734
$414$	5153.95	+	304.610i	0.611843	+	0.0361613i
$415$	−2322.39			−0.274702
$416$	−8276.08	−	14334.6i	−0.975404	−	1.68945i
$417$	−1472.71	+	2385.35i	−0.172947	+	0.280122i
$418$	−13885.8	+	24050.9i	−1.62482	+	2.81428i
$419$	−1009.26	+	1748.09i	−0.117675	+	0.203818i	−0.918846	−	0.394617i	$-0.870877\pi$
$419$	−1009.26	+	1748.09i	−0.117675	+	0.203818i	0.801171	+	0.598435i	$0.204211\pi$
$420$	3713.76	−	6015.16i	0.431459	−	0.698832i
$421$	5478.85	+	9489.65i	0.634259	+	1.09857i	0.986672	+	0.162724i	$0.0520280\pi$
$421$	5478.85	+	9489.65i	0.634259	+	1.09857i	−0.352413	+	0.935845i	$0.614639\pi$
$422$	−26300.1			−3.03381
$423$	−1062.49	−	2120.12i	−0.122128	−	0.243697i
$424$	31218.0			3.57565
$425$	682.589	+	1182.28i	0.0779069	+	0.134939i
$426$	−7546.93	−	14011.0i	−0.858333	−	1.59351i
$427$	322.582	−	558.728i	0.0365593	−	0.0633226i
$428$	10128.8	−	17543.5i	1.14391	−	1.98131i
$429$	−8806.98	−	260.029i	−0.991154	−	0.0292642i
$430$	2181.64	+	3778.71i	0.244670	+	0.423781i
$431$	−2124.75			−0.237460			−0.118730	−	0.992927i	$-0.537882\pi$
$431$	−2124.75			−0.237460			−0.118730	+	0.992927i	$0.537882\pi$
$432$	10892.2	+	23436.9i	1.21308	+	2.61021i
$433$	−16169.2			−1.79456			−0.897279	−	0.441463i	$-0.854460\pi$
$433$	−16169.2			−1.79456			−0.897279	+	0.441463i	$0.854460\pi$
$434$	10556.4	+	18284.1i	1.16756	+	2.02227i
$435$	1509.28	+	44.5620i	0.166355	+	0.00491169i
$436$	9271.73	−	16059.1i	1.01843	−	1.76397i
$437$	2002.65	−	3468.69i	0.219221	−	0.379702i
$438$	−10937.7	−	20306.0i	−1.19320	−	2.21520i
$439$	−346.098	−	599.460i	−0.0376273	−	0.0651724i	0.846598	−	0.532232i	$-0.178647\pi$
$439$	−346.098	−	599.460i	−0.0376273	−	0.0651724i	−0.884226	+	0.467060i	$0.845313\pi$
$440$	−15283.6			−1.65595
$441$	2414.63	−	3664.43i	0.260731	−	0.395684i
$442$	−10488.6			−1.12872
$443$	3335.26	+	5776.83i	0.357704	+	0.619561i	0.987577	−	0.157137i	$-0.0502264\pi$
$443$	3335.26	+	5776.83i	0.357704	+	0.619561i	−0.629873	+	0.776698i	$0.716893\pi$
$444$	−2932.68	+	4750.05i	−0.313466	+	0.507719i
$445$	2484.45	−	4303.20i	0.264662	−	0.458407i
$446$	2934.46	−	5082.63i	0.311549	−	0.539618i
$447$	−3288.45	+	5326.28i	−0.347960	+	0.563589i
$448$	6456.00	+	11182.1i	0.680843	+	1.17925i
$449$	−9743.18			−1.02407			−0.512037	−	0.858964i	$-0.671109\pi$
$449$	−9743.18			−1.02407			−0.512037	+	0.858964i	$0.671109\pi$
$450$	1974.19	−	2996.01i	0.206809	−	0.313852i
$451$	−6023.33			−0.628886
$452$	13417.7	+	23240.1i	1.39627	+	2.41842i
$453$	7325.67	+	13600.2i	0.759801	+	1.41058i
$454$	−10153.3	+	17586.0i	−1.04959	+	1.81795i
$455$	1213.56	−	2101.94i	0.125038	−	0.216573i
$456$	37669.0	+	1112.19i	3.86844	+	0.114217i
$457$	−2221.36	−	3847.51i	−0.227376	−	0.393827i	0.729654	−	0.683817i	$-0.239681\pi$
$457$	−2221.36	−	3847.51i	−0.227376	−	0.393827i	−0.957030	+	0.289990i	$0.906348\pi$
$458$	−769.524			−0.0785098
$459$	7631.15	+	677.513i	0.776017	+	0.0688967i
$460$	3643.20			0.369272
$461$	−9469.70	−	16402.0i	−0.956720	−	1.65709i	−0.730383	−	0.683038i	$-0.760658\pi$
$461$	−9469.70	−	16402.0i	−0.956720	−	1.65709i	−0.226337	−	0.974049i	$-0.572675\pi$
$462$	17403.8	+	513.853i	1.75259	+	0.0517459i
$463$	8396.10	−	14542.5i	0.842764	−	1.45971i	−0.0447846	−	0.998997i	$-0.514260\pi$
$463$	8396.10	−	14542.5i	0.842764	−	1.45971i	0.887549	−	0.460714i	$-0.152407\pi$
$464$	−5353.00	+	9271.66i	−0.535575	+	0.927642i
$465$	3642.82	+	6762.96i	0.363294	+	0.674462i
$466$	3418.70	+	5921.36i	0.339846	+	0.588630i
$467$	1367.93			0.135547			0.0677735	−	0.997701i	$-0.478410\pi$
$467$	1367.93			0.135547			0.0677735	+	0.997701i	$0.478410\pi$
$468$	8853.67	+	17666.8i	0.874489	+	1.74497i
$469$	388.480			0.0382481
$470$	−1167.18	−	2021.61i	−0.114549	−	0.198404i
$471$	−1080.33	+	1749.80i	−0.105688	+	0.171182i
$472$	20701.8	−	35856.6i	2.01881	−	3.49668i
$473$	−3851.93	+	6671.74i	−0.374444	+	0.648556i
$474$	2956.23	−	4788.19i	0.286465	−	0.463985i
$475$	−1391.73	−	2410.55i	−0.134436	−	0.232850i
$476$	14858.3			1.43074
$477$	−12917.1	−	763.432i	−1.23991	−	0.0732812i
$478$	−22428.5			−2.14615
$479$	−101.371	−	175.579i	−0.00966960	−	0.0167482i	0.861150	−	0.508351i	$-0.169745\pi$
$479$	−101.371	−	175.579i	−0.00966960	−	0.0167482i	−0.870820	+	0.491603i	$0.836411\pi$
$480$	5643.72	+	10477.7i	0.536665	+	0.996329i
$481$	−958.323	+	1659.86i	−0.0908436	+	0.157346i
$482$	6068.01	−	10510.1i	0.573424	−	0.993199i
$483$	−2510.02	−	74.1094i	−0.236460	−	0.00698156i
$484$	−8821.04	−	15278.5i	−0.828423	−	1.43487i
$485$	−4407.08			−0.412608
$486$	−7393.95	−	18728.4i	−0.690116	−	1.74802i
$487$	18961.3			1.76431			0.882153	−	0.470964i	$-0.156094\pi$
$487$	18961.3			1.76431			0.882153	+	0.470964i	$0.156094\pi$
$488$	1564.19	+	2709.25i	0.145097	+	0.251315i
$489$	−20055.9	−	592.157i	−1.85472	−	0.0547612i
$490$	2159.89	−	3741.04i	0.199130	−	0.344904i
$491$	−5856.15	+	10143.1i	−0.538257	+	0.932289i	0.460741	+	0.887535i	$0.347584\pi$
$491$	−5856.15	+	10143.1i	−0.538257	+	0.932289i	−0.998998	+	0.0447541i	$0.985750\pi$
$492$	6406.43	+	11893.6i	0.587041	+	1.08985i
$493$	1586.82	+	2748.45i	0.144963	+	0.251083i
$494$	21385.3			1.94771
$495$	6323.93	+	373.758i	0.574221	+	0.0339377i
$496$	−54465.7			−4.93061
$497$	3870.14	+	6703.28i	0.349295	+	0.604996i
$498$	−6739.57	+	10916.1i	−0.606441	+	0.982249i
$499$	−4312.44	+	7469.36i	−0.386876	+	0.670089i	−0.992028	−	0.126021i	$-0.959779\pi$
$499$	−4312.44	+	7469.36i	−0.386876	+	0.670089i	0.605151	+	0.796110i	$0.293113\pi$
$500$	1265.91	−	2192.63i	0.113227	−	0.196115i
$501$	5554.97	−	8997.35i	0.495364	−	0.802339i
$502$	−21055.3	−	36468.9i	−1.87200	−	3.24241i
$503$	4856.12			0.430465			0.215232	−	0.976563i	$-0.430949\pi$
$503$	4856.12			0.430465			0.215232	+	0.976563i	$0.430949\pi$
$504$	−10585.6	−	21122.8i	−0.935557	−	1.86683i
$505$	−6048.69			−0.532997
$506$	4486.56	+	7770.96i	0.394174	+	0.682730i
$507$	−2196.25	−	4077.38i	−0.192384	−	0.357165i
$508$	10062.9	−	17429.4i	0.878872	−	1.52225i
$509$	5425.17	−	9396.67i	0.472429	−	0.818271i	−0.527073	−	0.849820i	$-0.676711\pi$
$509$	5425.17	−	9396.67i	0.472429	−	0.818271i	0.999502	+	0.0315486i	$0.0100439\pi$
$510$	7538.01	+	222.563i	0.654488	+	0.0193240i
$511$	5608.96	+	9715.01i	0.485569	+	0.841030i
$512$	11614.3			1.00251
$513$	−15559.2	−	1381.38i	−1.33909	−	0.118888i
$514$	−12024.6			−1.03187
$515$	1862.11	+	3225.26i	0.159329	+	0.275965i
$516$	17270.9	+	509.930i	1.47347	+	0.0435047i
$517$	2060.78	−	3569.38i	0.175306	−	0.303639i
$518$	1893.78	−	3280.12i	0.160633	−	0.278224i
$519$	3811.81	+	7076.70i	0.322389	+	0.598521i
$520$	5884.49	+	10192.2i	0.496254	+	0.859537i
$521$	3559.30			0.299301			0.149651	−	0.988739i	$-0.452185\pi$
$521$	3559.30			0.299301			0.149651	+	0.988739i	$0.452185\pi$
$522$	4589.39	−	6964.84i	0.384813	−	0.583990i
$523$	22191.7			1.85540			0.927702	−	0.373321i	$-0.121781\pi$
$523$	22191.7			1.85540			0.927702	+	0.373321i	$0.121781\pi$
$524$	−14016.1	−	24276.6i	−1.16850	−	2.02391i
$525$	−916.768	+	1484.88i	−0.0762115	+	0.123439i
$526$	434.463	−	752.511i	0.0360142	−	0.0623784i
$527$	−8072.77	+	13982.4i	−0.667277	+	1.15576i
$528$	−23596.8	+	38219.6i	−1.94492	+	3.15018i
$529$	5436.44	+	9416.18i	0.446818	+	0.773912i
$530$	−12737.2			−1.04390
$531$	−9442.72	+	14330.2i	−0.771712	+	1.17115i
$532$	−30294.7			−2.46888
$533$	2319.11	+	4016.81i	0.188465	+	0.326430i
$534$	−13016.7	−	24165.7i	−1.05485	−	1.95834i
$535$	−2500.36	+	4330.75i	−0.202056	+	0.349971i
$536$	−941.863	+	1631.35i	−0.0758998	+	0.131462i
$537$	4279.63	+	126.357i	0.343910	+	0.0101541i
$538$	8781.56	+	15210.1i	0.703717	+	1.21887i
$539$	7627.06			0.609500
$540$	−5988.12	−	12884.7i	−0.477199	−	1.02680i
$541$	4257.08			0.338311			0.169155	−	0.985589i	$-0.445896\pi$
$541$	4257.08			0.338311			0.169155	+	0.985589i	$0.445896\pi$
$542$	−5195.81	−	8999.40i	−0.411770	−	0.713206i
$543$	22871.5	+	675.290i	1.80757	+	0.0533692i
$544$	−12506.9	+	21662.6i	−0.985715	+	1.70731i
$545$	−2288.79	+	3964.31i	−0.179892	+	0.311582i
$546$	−6358.14	−	11804.0i	−0.498358	−	0.925210i
$547$	10609.1	+	18375.5i	0.829272	+	1.43634i	0.898610	+	0.438748i	$0.144578\pi$
$547$	10609.1	+	18375.5i	0.829272	+	1.43634i	−0.0693385	+	0.997593i	$0.522089\pi$
$548$	31336.7			2.44277
$549$	−580.963	−	1159.27i	−0.0451637	−	0.0901206i
$550$	6235.84			0.483449
$551$	−3235.36	−	5603.81i	−0.250147	−	0.433268i
$552$	6396.71	−	10360.7i	0.493228	−	0.798880i
$553$	−1368.48	+	2370.27i	−0.105232	+	0.182268i
$554$	−11277.8	+	19533.7i	−0.864885	+	1.49803i
$555$	723.954	−	1172.58i	0.0553696	−	0.0896818i
$556$	5463.73	+	9463.46i	0.416752	+	0.721835i
$557$	2506.42			0.190665			0.0953324	−	0.995445i	$-0.469609\pi$
$557$	2506.42			0.190665			0.0953324	+	0.995445i	$0.469609\pi$
$558$	42359.8	+	2503.56i	3.21368	+	0.189936i
$559$	5932.29			0.448854
$560$	−6186.66	−	10715.6i	−0.466847	−	0.808602i
$561$	6314.29	+	11722.6i	0.475204	+	0.882225i
$562$	−6969.41	+	12071.4i	−0.523108	+	0.906050i
$563$	−8639.80	+	14964.6i	−0.646757	+	1.12022i	0.337136	+	0.941456i	$0.390542\pi$
$563$	−8639.80	+	14964.6i	−0.646757	+	1.12022i	−0.983893	+	0.178759i	$0.942792\pi$
$564$	−9239.93	−	272.812i	−0.689843	−	0.0203679i
$565$	−3312.26	−	5737.00i	−0.246633	−	0.427181i
$566$	37.6057			0.00279273
$567$	3863.48	+	8998.89i	0.286157	+	0.666522i
$568$	−37532.3			−2.77257
$569$	10254.1	+	17760.5i	0.755487	+	1.30854i	0.945132	+	0.326689i	$0.105933\pi$
$569$	10254.1	+	17760.5i	0.755487	+	1.30854i	−0.189645	+	0.981853i	$0.560734\pi$
$570$	−15369.3	−	453.783i	−1.12938	−	0.0333454i
$571$	−3412.53	+	5910.68i	−0.250105	+	0.433195i	−0.963555	−	0.267512i	$-0.913799\pi$
$571$	−3412.53	+	5910.68i	−0.250105	+	0.433195i	0.713449	+	0.700707i	$0.247132\pi$
$572$	−17172.3	+	29743.3i	−1.25526	+	2.17418i
$573$	−7508.05	−	13938.8i	−0.547388	−	1.01623i
$574$	−4582.87	−	7937.77i	−0.333250	−	0.577206i
$575$	−899.350			−0.0652270
$576$	25906.2	+	1531.11i	1.87400	+	0.110758i
$577$	4249.00			0.306565			0.153283	−	0.988182i	$-0.451016\pi$
$577$	4249.00			0.306565			0.153283	+	0.988182i	$0.451016\pi$
$578$	−5132.28	−	8889.37i	−0.369333	−	0.639704i
$579$	5161.70	−	8360.38i	0.370489	−	0.600079i
$580$	2942.87	−	5097.20i	0.210683	−	0.364913i
$581$	3119.83	−	5403.71i	0.222775	−	0.385858i
$582$	−12789.3	+	20714.8i	−0.910885	+	1.47536i
$583$	−11244.5	−	19476.0i	−0.798798	−	1.38356i
$584$	−54395.2			−3.85426
$585$	−2185.59	−	4361.17i	−0.154467	−	0.308226i
$586$	23800.1			1.67777
$587$	−9344.04	−	16184.3i	−0.657018	−	1.13799i	−0.981384	−	0.192057i	$-0.938484\pi$
$587$	−9344.04	−	16184.3i	−0.657018	−	1.13799i	0.324365	−	0.945932i	$-0.394849\pi$
$588$	−8112.16	−	15060.4i	−0.568945	−	1.05626i
$589$	16459.6	−	28508.8i	1.15145	−	1.99437i
$590$	−8446.53	+	14629.8i	−0.589387	+	1.02085i
$591$	−18968.1	−	560.040i	−1.32021	−	0.0389797i
$592$	4885.48	+	8461.91i	0.339176	+	0.587470i
$593$	−12434.5			−0.861084			−0.430542	−	0.902570i	$-0.641678\pi$
$593$	−12434.5			−0.861084			−0.430542	+	0.902570i	$0.641678\pi$
$594$	20108.8	−	28640.1i	1.38902	−	1.97831i
$595$	−3667.89			−0.252721
$596$	12200.1	+	21131.1i	0.838480	+	1.45229i
$597$	−16710.1	−	493.371i	−1.14556	−	0.0338230i
$598$	3454.84	−	5983.96i	0.236252	−	0.409201i
$599$	3021.52	−	5233.42i	0.206103	−	0.356981i	−0.744380	−	0.667756i	$-0.767255\pi$
$599$	3021.52	−	5233.42i	0.206103	−	0.356981i	0.950484	+	0.310774i	$0.100588\pi$
$600$	−4012.82	−	7449.87i	−0.273038	−	0.506900i
$601$	315.654	+	546.729i	0.0214239	+	0.0371074i	0.876539	−	0.481332i	$-0.159847\pi$
$601$	315.654	+	546.729i	0.0214239	+	0.0371074i	−0.855115	+	0.518439i	$0.826513\pi$
$602$	−11723.0			−0.793679
$603$	429.612	−	651.977i	0.0290135	−	0.0440307i
$604$	60215.2			4.05649
$605$	2177.54	+	3771.61i	0.146330	+	0.253451i
$606$	−17553.3	+	28431.0i	−1.17666	+	1.90583i
$607$	4727.43	−	8188.16i	0.316113	−	0.547524i	−0.663560	−	0.748123i	$-0.730955\pi$
$607$	4727.43	−	8188.16i	0.316113	−	0.547524i	0.979673	+	0.200599i	$0.0642888\pi$
$608$	25500.4	−	44167.9i	1.70095	−	2.94613i
$609$	−2131.21	+	3451.91i	−0.141808	+	0.229686i
$610$	−638.202	−	1105.40i	−0.0423607	−	0.0733709i
$611$	−3173.77			−0.210143
$612$	16431.5	−	24936.3i	1.08530	−	1.64705i
$613$	−2682.66			−0.176757			−0.0883783	−	0.996087i	$-0.528168\pi$
$613$	−2682.66			−0.176757			−0.0883783	+	0.996087i	$0.528168\pi$
$614$	−10338.1	−	17906.1i	−0.679497	−	1.17692i
$615$	−1581.47	−	2936.03i	−0.103693	−	0.192508i
$616$	20531.5	−	35561.7i	1.34292	−	2.32601i
$617$	1169.26	−	2025.22i	0.0762930	−	0.132143i	−0.825355	−	0.564614i	$-0.809025\pi$
$617$	1169.26	−	2025.22i	0.0762930	−	0.132143i	0.901648	+	0.432471i	$0.142358\pi$
$618$	20563.7	+	607.152i	1.33850	+	0.0395198i
$619$	5965.11	+	10331.9i	0.387331	+	0.670878i	0.992090	−	0.125531i	$-0.0400636\pi$
$619$	5965.11	+	10331.9i	0.387331	+	0.670878i	−0.604758	+	0.796409i	$0.706730\pi$
$620$	29943.1			1.93959
$621$	−2900.15	+	4130.55i	−0.187406	+	0.266914i
$622$	38780.1			2.49991
$623$	6675.09	+	11561.6i	0.429265	+	0.743509i
$624$	34573.0	+	1020.78i	2.21799	+	0.0654870i
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	−1690.52	+	2928.07i	−0.107934	+	0.186948i
$627$	−12874.2	−	23901.2i	−0.820012	−	1.52237i
$628$	4008.00	+	6942.05i	0.254676	+	0.441111i
$629$	2896.46			0.183608
$630$	4319.03	+	8618.28i	0.273134	+	0.545017i
$631$	4106.81			0.259096			0.129548	−	0.991573i	$-0.458647\pi$
$631$	4106.81			0.259096			0.129548	+	0.991573i	$0.458647\pi$
$632$	−6635.68	−	11493.3i	−0.417648	−	0.723387i
$633$	13506.3	−	21876.0i	0.848067	−	1.37361i
$634$	−16335.5	+	28293.9i	−1.02329	+	1.77239i
$635$	−2484.09	+	4302.57i	−0.155241	+	0.268885i
$636$	−26497.6	+	42918.1i	−1.65204	+	2.67580i
$637$	−2936.58	−	5086.30i	−0.182655	−	0.316368i
$638$	14496.5			0.899562
$639$	15529.8	+	917.848i	0.961425	+	0.0568224i
$640$	7222.62			0.446093
$641$	−7462.65	−	12925.7i	−0.459839	−	0.796465i	0.539113	−	0.842234i	$-0.318760\pi$
$641$	−7462.65	−	12925.7i	−0.459839	−	0.796465i	−0.998952	+	0.0457684i	$0.985426\pi$
$642$	13100.0	+	24320.4i	0.805323	+	1.49510i
$643$	−9502.84	+	16459.4i	−0.582823	+	1.00948i	0.412319	+	0.911039i	$0.364719\pi$
$643$	−9502.84	+	16459.4i	−0.582823	+	1.00948i	−0.995143	+	0.0984406i	$0.968615\pi$
$644$	−4894.18	+	8476.96i	−0.299468	+	0.518694i
$645$	−4263.45	−	125.880i	−0.260268	−	0.00768452i
$646$	−16158.8	−	27987.9i	−0.984151	−	1.70460i
$647$	9252.81			0.562234			0.281117	−	0.959673i	$-0.409295\pi$
$647$	9252.81			0.562234			0.281117	+	0.959673i	$0.409295\pi$
$648$	−47156.1	−	5593.61i	−2.85875	−	0.339101i
$649$	−29826.6			−1.80400
$650$	−2400.93	−	4158.53i	−0.144880	−	0.250940i
$651$	−20629.7	−	609.098i	−1.24200	−	0.0366704i
$652$	−39106.0	+	67733.5i	−2.34894	+	4.06848i
$653$	−11475.3	+	19875.9i	−0.687695	+	1.19112i	0.284887	+	0.958561i	$0.408044\pi$
$653$	−11475.3	+	19875.9i	−0.687695	+	1.19112i	−0.972582	+	0.232561i	$0.925289\pi$
$654$	11991.6	+	22262.6i	0.716985	+	1.33109i
$655$	3459.97	+	5992.85i	0.206401	+	0.357496i
$656$	23645.4			1.40731
$657$	22507.3	+	1330.23i	1.33652	+	0.0789912i
$658$	6271.81			0.371582
$659$	−3258.54	−	5643.96i	−0.192617	−	0.333623i	0.753500	−	0.657448i	$-0.228364\pi$
$659$	−3258.54	−	5643.96i	−0.192617	−	0.333623i	−0.946117	+	0.323826i	$0.895031\pi$
$660$	12972.6	−	21011.7i	0.765088	−	1.23921i
$661$	2598.16	−	4500.15i	0.152885	−	0.264804i	−0.779402	−	0.626524i	$-0.784477\pi$
$661$	2598.16	−	4500.15i	0.152885	−	0.264804i	0.932287	+	0.361720i	$0.117810\pi$
$662$	31187.1	−	54017.7i	1.83100	−	3.17139i
$663$	5386.37	−	8724.29i	0.315520	−	0.511045i
$664$	15127.9	+	26202.3i	0.884153	+	1.53140i
$665$	7478.47			0.436094
$666$	−3410.65	−	6805.68i	−0.198439	−	0.395968i
$667$	−2090.72			−0.121369
$668$	−20608.8	−	35695.5i	−1.19368	−	2.06751i
$669$	2720.69	+	5051.00i	0.157231	+	0.291903i
$670$	384.289	−	665.607i	0.0221588	−	0.0383801i
$671$	1126.82	−	1951.71i	0.0648291	−	0.112287i
$672$	−31960.9	−	943.658i	−1.83470	−	0.0541702i
$673$	−14095.0	−	24413.2i	−0.807313	−	1.39831i	−0.914718	−	0.404093i	$-0.867587\pi$
$673$	−14095.0	−	24413.2i	−0.807313	−	1.39831i	0.107405	−	0.994215i	$-0.465746\pi$
$674$	−33398.9			−1.90872
$675$	1478.21	+	3180.69i	0.0842909	+	0.181370i
$676$	−18052.7			−1.02712
$677$	−4338.44	−	7514.40i	−0.246292	−	0.426590i	0.716202	−	0.697893i	$-0.245879\pi$
$677$	−4338.44	−	7514.40i	−0.246292	−	0.426590i	−0.962494	+	0.271303i	$0.912546\pi$
$678$	−36578.1	−	1079.98i	−2.07194	−	0.0611747i
$679$	5920.34	−	10254.3i	0.334613	−	0.579566i
$680$	8892.71	−	15402.6i	0.501500	−	0.868624i
$681$	−9413.60	−	17476.5i	−0.529706	−	0.983409i
$682$	36874.6	+	63868.7i	2.07039	+	3.58601i
$683$	20624.1			1.15543			0.577714	−	0.816239i	$-0.303945\pi$
$683$	20624.1			1.15543			0.577714	+	0.816239i	$0.303945\pi$
$684$	−33502.2	+	50842.8i	−1.87279	+	2.84214i
$685$	−7735.68			−0.431482
$686$	18049.4	+	31262.5i	1.00456	+	1.73995i
$687$	395.185	−	640.079i	0.0219465	−	0.0355466i
$688$	15121.3	−	26190.8i	0.837926	−	1.45133i
$689$	−8658.72	+	14997.3i	−0.478768	+	0.829250i
$690$	−2609.92	+	4227.27i	−0.143997	+	0.233231i
$691$	−3493.03	−	6050.10i	−0.192303	−	0.333078i	0.753710	−	0.657207i	$-0.228262\pi$
$691$	−3493.03	−	6050.10i	−0.192303	−	0.333078i	−0.946013	+	0.324129i	$0.894929\pi$
$692$	31332.2			1.72120
$693$	−9365.04	+	14212.3i	−0.513346	+	0.779051i
$694$	−25518.8			−1.39579
$695$	−1348.76	−	2336.12i	−0.0736136	−	0.127502i
$696$	−9328.61	−	17318.7i	−0.508046	−	0.943196i
$697$	3504.66	−	6070.25i	0.190457	−	0.329881i
$698$	−10345.2	+	17918.4i	−0.560991	+	0.971664i
$699$	−6680.96	−	197.258i	−0.361512	−	0.0106738i
$700$	3401.19	+	5891.03i	0.183647	+	0.318086i
$701$	7848.55			0.422875			0.211438	−	0.977391i	$-0.432185\pi$
$701$	7848.55			0.422875			0.211438	+	0.977391i	$0.432185\pi$
$702$	−26841.7	−	2383.07i	−1.44312	−	0.128124i
$703$	−5905.60			−0.316833
$704$	22551.6	+	39060.5i	1.20731	+	2.09112i
$705$	2280.94	+	67.3457i	0.121852	+	0.00359771i
$706$	−7883.63	+	13654.8i	−0.420261	+	0.727913i
$707$	8125.65	−	14074.0i	0.432244	−	0.748669i
$708$	31723.6	+	58895.5i	1.68397	+	3.12631i
$709$	12712.3	+	22018.3i	0.673371	+	1.16631i	0.976942	+	0.213504i	$0.0684876\pi$
$709$	12712.3	+	22018.3i	0.673371	+	1.16631i	−0.303571	+	0.952809i	$0.598179\pi$
$710$	15313.5			0.809445
$711$	2464.60	+	4917.90i	0.129999	+	0.259403i
$712$	−64734.5			−3.40734
$713$	−5318.16	−	9211.33i	−0.279336	−	0.483825i
$714$	−10644.2	+	17240.4i	−0.557913	+	0.903649i
$715$	4239.11	−	7342.35i	0.221725	−	0.384039i
$716$	8344.63	−	14453.3i	0.435550	−	0.754394i
$717$	11518.1	−	18655.7i	0.599930	−	0.971703i
$718$	−25474.3	−	44122.8i	−1.32409	−	2.29338i
$719$	16707.2			0.866584			0.433292	−	0.901254i	$-0.357352\pi$
$719$	16707.2			0.866584			0.433292	+	0.901254i	$0.357352\pi$
$720$	−24825.4	−	1467.24i	−1.28498	−	0.0759454i
$721$	−10006.0			−0.516843
$722$	14716.8	+	25490.2i	0.758590	+	1.31392i
$723$	5625.96	+	10444.7i	0.289394	+	0.537264i
$724$	44596.1	−	77242.7i	2.28923	−	3.96506i
$725$	−726.469	+	1258.28i	−0.0372143	+	0.0644571i
$726$	24047.1	+	710.000i	1.22930	+	0.0362956i
$727$	−718.240	−	1244.03i	−0.0366410	−	0.0634642i	0.847123	−	0.531396i	$-0.178332\pi$
$727$	−718.240	−	1244.03i	−0.0366410	−	0.0634642i	−0.883764	+	0.467932i	$0.844999\pi$
$728$	−31620.3			−1.60979
$729$	19375.1	+	3467.68i	0.984359	+	0.176176i
$730$	22193.8			1.12524
$731$	−4482.47	−	7763.87i	−0.226799	−	0.392828i
$732$	−5052.31	−	149.171i	−0.255108	−	0.00753215i
$733$	−5770.44	+	9994.70i	−0.290772	+	0.503633i	−0.973993	−	0.226580i	$-0.927246\pi$
$733$	−5770.44	+	9994.70i	−0.290772	+	0.503633i	0.683220	+	0.730212i	$0.260579\pi$
$734$	12058.7	−	20886.3i	0.606397	−	1.05031i
$735$	2002.54	+	3717.76i	0.100497	+	0.186574i
$736$	−8239.28	−	14270.9i	−0.412641	−	0.714715i
$737$	1357.01			0.0678237
$738$	−18389.8	−	1086.88i	−0.917262	−	0.0542122i
$739$	4127.87			0.205475			0.102737	−	0.994709i	$-0.467240\pi$
$739$	4127.87			0.205475			0.102737	+	0.994709i	$0.467240\pi$
$740$	−2685.85	−	4652.03i	−0.133424	−	0.231097i
$741$	−10982.3	+	17788.0i	−0.544460	+	0.881859i
$742$	17110.8	−	29636.8i	0.846574	−	1.46631i
$743$	13748.5	−	23813.1i	0.678846	−	1.17580i	−0.296482	−	0.955038i	$-0.595814\pi$
$743$	13748.5	−	23813.1i	0.678846	−	1.17580i	0.975329	−	0.220758i	$-0.0708530\pi$
$744$	52574.0	−	85153.8i	2.59066	−	4.19609i
$745$	−3011.67	−	5216.37i	−0.148106	−	0.256528i
$746$	−69799.5			−3.42566
$747$	−5618.75	−	11211.8i	−0.275207	−	0.549153i
$748$	51902.0			2.53706
$749$	−6717.83	−	11635.6i	−0.327723	−	0.567632i
$750$	1637.27	+	3039.62i	0.0797128	+	0.147988i
$751$	−17197.1	+	29786.2i	−0.835592	+	1.44729i	0.0579559	+	0.998319i	$0.481542\pi$
$751$	−17197.1	+	29786.2i	−0.835592	+	1.44729i	−0.893548	+	0.448968i	$0.851792\pi$
$752$	−8089.88	+	14012.1i	−0.392297	+	0.679479i
$753$	41147.2	+	1214.89i	1.99135	+	0.0587953i
$754$	−5581.44	−	9667.33i	−0.269581	−	0.466928i
$755$	−14864.6			−0.716526
$756$	38024.3	+	3375.89i	1.82927	+	0.162408i
$757$	−30459.8			−1.46246			−0.731229	−	0.682132i	$-0.761053\pi$
$757$	−30459.8			−1.46246			−0.731229	+	0.682132i	$0.761053\pi$
$758$	−25118.7	−	43506.8i	−1.20363	−	2.08475i
$759$	−8767.82	−	258.873i	−0.419304	−	0.0123801i
$760$	−18131.4	+	31404.5i	−0.865387	+	1.49889i
$761$	−223.584	+	387.259i	−0.0106504	+	0.0184469i	−0.871301	−	0.490748i	$-0.836724\pi$
$761$	−223.584	+	387.259i	−0.0106504	+	0.0184469i	0.860651	+	0.509195i	$0.170057\pi$
$762$	13014.8	+	24162.2i	0.618734	+	1.14869i
$763$	−6149.40	−	10651.1i	−0.291774	−	0.505367i
$764$	−61714.3			−2.92244
$765$	−4056.23	+	6155.72i	−0.191704	+	0.290929i
$766$	45697.6			2.15551
$767$	11483.9	+	19890.6i	0.540623	+	0.936387i
$768$	−29.8196	+	48.2987i	−0.00140107	+	0.00226931i
$769$	4028.59	−	6977.71i	0.188914	−	0.327208i	−0.755975	−	0.654601i	$-0.772837\pi$
$769$	4028.59	−	6977.71i	0.188914	−	0.327208i	0.944888	+	0.327393i	$0.106170\pi$
$770$	−8377.06	+	14509.5i	−0.392062	+	0.679072i
$771$	6175.18	−	10001.9i	0.288448	−	0.467198i
$772$	−19149.8	−	33168.4i	−0.892767	−	1.54632i
$773$	−19600.4			−0.912001			−0.456000	−	0.889980i	$-0.650718\pi$
$773$	−19600.4			−0.912001			−0.456000	+	0.889980i	$0.650718\pi$
$774$	−12964.2	+	19674.4i	−0.602053	+	0.913673i
$775$	−7391.67			−0.342602
$776$	28707.5	+	49722.8i	1.32801	+	2.30019i
$777$	1755.82	+	3259.70i	0.0810677	+	0.150504i
$778$	11806.0	−	20448.5i	0.544041	−	0.942307i
$779$	−7145.66	+	12376.7i	−0.328652	+	0.569242i
$780$	−19006.9	−	561.185i	−0.872507	−	0.0257611i
$781$	13518.9	+	23415.4i	0.619390	+	1.07281i
$782$	−10442.0			−0.477500
$783$	3436.40	+	7394.14i	0.156841	+	0.337478i
$784$	−29941.0			−1.36393
$785$	−989.402	−	1713.70i	−0.0449851	−	0.0779164i
$786$	38209.4	+	1128.15i	1.73395	+	0.0511955i
$787$	−8968.18	+	15533.3i	−0.406202	+	0.703563i	−0.994461	−	0.105110i	$-0.966480\pi$
$787$	−8968.18	+	15533.3i	−0.406202	+	0.703563i	0.588258	+	0.808673i	$0.299814\pi$
$788$	−36985.0	+	64059.9i	−1.67200	+	2.89599i
$789$	402.812	+	747.828i	0.0181755	+	0.0337432i
$790$	2707.42	+	4689.39i	0.121931	+	0.211191i
$791$	17798.4			0.800047
$792$	−36976.8	−	73784.4i	−1.65898	−	3.31037i
$793$	−1735.39			−0.0777119
$794$	27761.9	+	48085.0i	1.24085	+	2.14921i
$795$	6541.13	−	10594.6i	0.291811	−	0.472645i
$796$	−32582.2	+	56434.0i	−1.45081	+	2.51288i
$797$	8971.31	−	15538.8i	0.398720	−	0.690604i	−0.594848	−	0.803838i	$-0.702788\pi$
$797$	8971.31	−	15538.8i	0.398720	−	0.690604i	0.993568	+	0.113235i	$0.0361211\pi$
$798$	21702.5	−	35151.5i	0.962733	−	1.55933i
$799$	2398.12	+	4153.67i	0.106182	+	0.183913i
$800$	−11451.7			−0.506099
$801$	26785.4	+	1583.08i	1.18154	+	0.0698317i
$802$	67418.9			2.96838
$803$	19592.8	+	33935.7i	0.861039	+	1.49136i
$804$	−1443.32	−	2679.55i	−0.0633108	−	0.117538i
$805$	1208.16	−	2092.60i	0.0528971	−	0.0916204i
$806$	28395.0	−	49181.6i	1.24091	−	2.14931i
$807$	−17161.3	−	506.693i	−0.748582	−	0.0221021i
$808$	39400.9	+	68244.4i	1.71549	+	2.97132i
$809$	29094.2			1.26440			0.632200	−	0.774806i	$-0.282152\pi$
$809$	29094.2			1.26440			0.632200	+	0.774806i	$0.282152\pi$
$810$	19240.1	+	2282.24i	0.834605	+	0.0989998i
$811$	1438.31			0.0622760			0.0311380	−	0.999515i	$-0.490087\pi$
$811$	1438.31			0.0622760			0.0311380	+	0.999515i	$0.490087\pi$
$812$	7906.74	+	13694.9i	0.341715	+	0.591867i
$813$	10153.9	+	299.796i	0.438021	+	0.0129327i
$814$	6615.19	−	11457.9i	0.284843	−	0.493363i
$815$	9653.59	−	16720.5i	0.414908	−	0.718643i
$816$	−24787.6	−	46018.6i	−1.06341	−	1.97423i
$817$	9139.33	+	15829.8i	0.391364	+	0.677863i
$818$	59069.1			2.52482
$819$	13083.6	+	773.270i	0.558215	+	0.0329917i
$820$	−12999.3			−0.553605
$821$	121.415	+	210.297i	0.00516128	+	0.00893959i	0.868595	−	0.495524i	$-0.165024\pi$
$821$	121.415	+	210.297i	0.00516128	+	0.00893959i	−0.863433	+	0.504463i	$0.831690\pi$
$822$	−22449.0	+	36360.5i	−0.952552	+	1.54284i
$823$	−9085.50	+	15736.5i	−0.384812	+	0.666515i	−0.991743	−	0.128240i	$-0.959067\pi$
$823$	−9085.50	+	15736.5i	−0.384812	+	0.666515i	0.606931	+	0.794755i	$0.292401\pi$
$824$	24259.4	−	42018.5i	1.02563	−	1.77644i
$825$	−3202.38	+	5186.88i	−0.135143	+	0.218890i
$826$	−22693.7	−	39306.6i	−0.955949	−	1.65575i
$827$	12181.7			0.512213			0.256107	−	0.966649i	$-0.417560\pi$
$827$	12181.7			0.512213			0.256107	+	0.966649i	$0.417560\pi$
$828$	8814.30	+	17588.2i	0.369950	+	0.738205i
$829$	−17370.0			−0.727724			−0.363862	−	0.931453i	$-0.618542\pi$
$829$	−17370.0			−0.727724			−0.363862	+	0.931453i	$0.618542\pi$
$830$	−6172.34	−	10690.8i	−0.258126	−	0.447088i
$831$	−10456.2	−	19412.1i	−0.436488	−	0.810347i
$832$	17365.7	−	30078.2i	0.723613	−	1.25333i
$833$	−4437.79	+	7686.47i	−0.184586	+	0.319713i
$834$	−14894.7	−	439.772i	−0.618420	−	0.0182591i
$835$	5087.43	+	8811.69i	0.210848	+	0.365199i
$836$	−105823.			−4.37795
$837$	−23836.1	+	33948.6i	−0.984344	+	1.40195i
$838$	−10729.5			−0.442296
$839$	−15681.5	−	27161.2i	−0.645275	−	1.11765i	−0.984238	−	0.176849i	$-0.943409\pi$
$839$	−15681.5	−	27161.2i	−0.645275	−	1.11765i	0.338963	−	0.940800i	$-0.389924\pi$
$840$	22725.0	+	670.964i	0.933437	+	0.0275601i
$841$	10505.7	−	18196.4i	0.430755	−	0.746089i
$842$	−29122.9	+	50442.3i	−1.19197	+	2.06456i
$843$	−6461.69	−	11996.2i	−0.264001	−	0.490122i
$844$	−50108.0	−	86789.5i	−2.04359	−	3.53960i
$845$	4456.43			0.181427
$846$	6935.85	−	10525.8i	0.281867	−	0.427760i
$847$	−11701.0			−0.474676
$848$	44141.7	+	76455.7i	1.78754	+	3.09611i
$849$	−19.3122	+	31.2799i	−0.000780674	+	0.00126445i
$850$	−3628.31	+	6284.42i	−0.146412	+	0.253593i
$851$	−954.062	+	1652.48i	−0.0384311	+	0.0665645i
$852$	31857.2	−	51598.9i	1.28100	−	2.07482i
$853$	19838.8	+	34361.8i	0.796326	+	1.37928i	0.921993	+	0.387205i	$0.126560\pi$
$853$	19838.8	+	34361.8i	0.796326	+	1.37928i	−0.125667	+	0.992072i	$0.540107\pi$
$854$	3429.37			0.137413
$855$	8270.26	−	12550.9i	0.330803	−	0.502026i
$856$	65149.0			2.60134
$857$	−16604.7	−	28760.1i	−0.661849	−	1.14636i	−0.980129	−	0.198360i	$-0.936439\pi$
$857$	−16604.7	−	28760.1i	−0.661849	−	1.14636i	0.318280	−	0.947997i	$-0.396895\pi$
$858$	−22209.8	−	41232.8i	−0.883717	−	1.64064i
$859$	−17202.4	+	29795.5i	−0.683282	+	1.18348i	0.290691	+	0.956817i	$0.406115\pi$
$859$	−17202.4	+	29795.5i	−0.683282	+	1.18348i	−0.973973	+	0.226663i	$0.927219\pi$
$860$	−8313.09	+	14398.7i	−0.329621	+	0.570920i
$861$	8956.03	+	264.430i	0.354496	+	0.0104666i
$862$	−5647.05	−	9780.98i	−0.223131	−	0.386475i
$863$	12999.7			0.512765			0.256382	−	0.966575i	$-0.417469\pi$
$863$	12999.7			0.512765			0.256382	+	0.966575i	$0.417469\pi$
$864$	−36928.6	+	52595.6i	−1.45409	+	2.07099i
$865$	−7734.58			−0.304027
$866$	−42973.9	−	74432.9i	−1.68627	−	2.92071i
$867$	10029.7	+	296.131i	0.392880	+	0.0115999i
$868$	−40224.8	+	69671.3i	−1.57295	+	2.72442i
$869$	−4780.25	+	8279.64i	−0.186604	+	0.323208i
$870$	3806.16	+	7066.20i	0.148323	+	0.275364i
$871$	−522.477	−	904.956i	−0.0203254	−	0.0352047i
$872$	59636.4			2.31599
$873$	−10662.4	−	21276.0i	−0.413365	−	0.824837i
$874$	21290.2			0.823972
$875$	−839.608	−	1454.24i	−0.0324388	−	0.0561856i
$876$	46170.4	−	74781.9i	1.78077	−	2.88430i
$877$	11415.7	−	19772.6i	0.439546	−	0.761317i	−0.558108	−	0.829768i	$-0.688473\pi$
$877$	11415.7	−	19772.6i	0.439546	−	0.761317i	0.997654	+	0.0684517i	$0.0218059\pi$
$878$	1839.69	−	3186.43i	0.0707135	−	0.122479i
$879$	−12222.4	+	19796.6i	−0.469002	+	0.759640i
$880$	−21610.8	−	37430.9i	−0.827839	−	1.43386i
$881$	−1889.31			−0.0722502			−0.0361251	−	0.999347i	$-0.511501\pi$
$881$	−1889.31			−0.0722502			−0.0361251	+	0.999347i	$0.511501\pi$
$882$	23286.2	+	1376.27i	0.888987	+	0.0525411i
$883$	−1778.37			−0.0677768			−0.0338884	−	0.999426i	$-0.510789\pi$
$883$	−1778.37			−0.0677768			−0.0338884	+	0.999426i	$0.510789\pi$
$884$	−19983.3	−	34612.1i	−0.760308	−	1.31689i
$885$	−7831.21	−	14538.8i	−0.297450	−	0.552221i
$886$	−17728.6	+	30706.8i	−0.672239	+	1.16435i
$887$	−11492.1	+	19904.8i	−0.435023	+	0.753482i	−0.997298	−	0.0734685i	$-0.976593\pi$
$887$	−11492.1	+	19904.8i	−0.435023	+	0.753482i	0.562274	+	0.826951i	$0.309927\pi$
$888$	−17945.5	−	529.847i	−0.678166	−	0.0200231i
$889$	−6674.11	−	11559.9i	−0.251791	−	0.436115i
$890$	26412.3			0.994766
$891$	13495.6	+	31434.2i	0.507430	+	1.18191i
$892$	22363.4			0.839441
$893$	−4889.54	−	8468.93i	−0.183228	−	0.317359i
$894$	−33258.7	−	981.975i	−1.24423	−	0.0367362i
$895$	−2059.93	+	3567.91i	−0.0769340	+	0.133254i
$896$	−9702.67	+	16805.5i	−0.361767	+	0.626600i
$897$	3203.16	+	5946.71i	0.119231	+	0.221355i
$898$	−25895.0	−	44851.4i	−0.962279	−	1.66672i
$899$	−17183.4			−0.637485
$900$	13648.1	+	806.631i	0.505484	+	0.0298752i
$901$	26170.3			0.967658
$902$	−16008.5	−	27727.6i	−0.590938	−	1.02353i
$903$	6020.29	−	9751.04i	0.221864	−	0.359351i
$904$	−43151.8	+	74741.1i	−1.58762	+	2.74984i
$905$	−11008.9	+	19067.9i	−0.404362	+	0.700375i
$906$	−43137.0	+	69868.8i	−1.58182	+	2.56207i
$907$	−22705.0	−	39326.3i	−0.831211	−	1.43970i	−0.897078	−	0.441872i	$-0.854315\pi$
$907$	−22705.0	−	39326.3i	−0.831211	−	1.43970i	0.0658671	−	0.997828i	$-0.479019\pi$
$908$	−77377.5			−2.82804
$909$	−14634.1	−	29201.2i	−0.533975	−	1.06550i
$910$	12901.4			0.469973
$911$	15390.9	+	26657.8i	0.559740	+	0.969497i	0.997518	+	0.0704143i	$0.0224321\pi$
$911$	15390.9	+	26657.8i	0.559740	+	0.969497i	−0.437778	+	0.899083i	$0.644235\pi$
$912$	50539.5	+	93827.5i	1.83501	+	3.40673i
$913$	10898.0	−	18875.8i	0.395038	−	0.684226i
$914$	11807.7	−	20451.5i	0.427311	−	0.740125i
$915$	1247.20	+	36.8240i	0.0450614	+	0.00133045i
$916$	−1466.13	−	2539.41i	−0.0528845	−	0.0915986i
$917$	−18592.1			−0.669538
$918$	17162.9	+	36929.7i	0.617059	+	1.32773i
$919$	−22457.3			−0.806093			−0.403046	−	0.915180i	$-0.632049\pi$
$919$	−22457.3			−0.806093			−0.403046	+	0.915180i	$0.632049\pi$
$920$	5858.33	+	10146.9i	0.209938	+	0.363624i
$921$	20203.1	+	596.503i	0.722817	+	0.0213414i
$922$	50336.3	−	87185.0i	1.79798	−	3.11419i
$923$	10410.1	−	18030.8i	0.371238	−	0.643002i
$924$	31462.7	+	58411.0i	1.12018	+	2.07963i
$925$	663.022	+	1148.39i	0.0235676	+	0.0408203i
$926$	89259.1			3.16764
$927$	−11065.4	+	16792.8i	−0.392056	+	0.594983i
$928$	−26621.8			−0.941706
$929$	21827.1	+	37805.7i	0.770855	+	1.33516i	0.937095	+	0.349075i	$0.113504\pi$
$929$	21827.1	+	37805.7i	0.770855	+	1.33516i	−0.166240	+	0.986085i	$0.553163\pi$
$930$	−21450.7	+	34743.5i	−0.756338	+	1.22504i
$931$	9048.22	−	15672.0i	0.318521	−	0.551695i
$932$	−13026.9	+	22563.2i	−0.457843	+	0.793007i
$933$	−19915.3	+	32256.8i	−0.698819	+	1.13187i
$934$	3635.63	+	6297.10i	0.127368	+	0.220607i
$935$	−12812.4			−0.448138
$936$	−34968.1	+	53067.4i	−1.22112	+	1.85317i
$937$	−41123.3			−1.43377			−0.716884	−	0.697193i	$-0.754432\pi$
$937$	−41123.3			−1.43377			−0.716884	+	0.697193i	$0.754432\pi$
$938$	1032.49	+	1788.32i	0.0359401	+	0.0622501i
$939$	−1567.37	−	2909.85i	−0.0544720	−	0.101128i
$940$	4447.50	−	7703.30i	0.154321	−	0.267291i
$941$	−11038.9	+	19119.9i	−0.382419	+	0.662370i	−0.991408	−	0.130810i	$-0.958242\pi$
$941$	−11038.9	+	19119.9i	−0.382419	+	0.662370i	0.608988	+	0.793179i	$0.291576\pi$
$942$	−10926.2	−	322.601i	−0.377915	−	0.0111581i
$943$	2308.80	+	3998.95i	0.0797293	+	0.138095i
$944$	117088.			4.03697
$945$	−9386.58	−	833.364i	−0.323117	−	0.0286871i
$946$	−40949.9			−1.40740
$947$	−4308.20	−	7462.03i	−0.147833	−	0.256054i	0.782593	−	0.622533i	$-0.213896\pi$
$947$	−4308.20	−	7462.03i	−0.147833	−	0.256054i	−0.930426	+	0.366479i	$0.880563\pi$
$948$	21433.2	+	632.824i	0.734303	+	0.0216805i
$949$	15087.3	−	26131.9i	0.516073	−	0.893864i
$950$	7397.77	−	12813.3i	0.252648	−	0.437599i
$951$	−15145.5	−	28117.8i	−0.516431	−	0.958763i
$952$	23892.5	+	41382.9i	0.813402	+	1.40885i
$953$	−29558.0			−1.00470			−0.502350	−	0.864664i	$-0.667531\pi$
$953$	−29558.0			−1.00470			−0.502350	+	0.864664i	$0.667531\pi$
$954$	−30816.2	−	61491.3i	−1.04582	−	2.08685i
$955$	15234.6			0.516211
$956$	−42731.7	−	74013.5i	−1.44565	−	2.50394i
$957$	−7444.58	+	12057.9i	−0.251462	+	0.407292i
$958$	538.836	−	933.291i	0.0181722	−	0.0314752i
$959$	10391.9	−	17999.3i	0.349919	−	0.606077i
$960$	−13118.7	+	21248.3i	−0.441046	+	0.714359i
$961$	−28814.0	−	49907.3i	−0.967204	−	1.67525i
$962$	−10187.9			−0.341448
$963$	−26956.9	−	1593.21i	−0.902048	−	0.0533131i
$964$	46244.0			1.54504
$965$	4727.26	+	8187.86i	0.157695	+	0.273136i
$966$	−6329.88	−	11751.5i	−0.210829	−	0.391407i
$967$	−22288.0	+	38603.9i	−0.741192	+	1.28378i	0.210761	+	0.977538i	$0.432406\pi$
$967$	−22288.0	+	38603.9i	−0.741192	+	1.28378i	−0.951953	+	0.306244i	$0.900928\pi$
$968$	28368.8	−	49136.2i	0.941949	−	1.63150i
$969$	31578.3	+	932.360i	1.04689	+	0.0309099i
$970$	−11712.9	−	20287.4i	−0.387711	−	0.671534i
$971$	43702.8			1.44438			0.722188	−	0.691696i	$-0.243136\pi$
$971$	43702.8			1.44438			0.722188	+	0.691696i	$0.243136\pi$
$972$	47715.9	−	60081.9i	1.57458	−	1.98264i
$973$	7247.56			0.238793
$974$	50394.4	+	87285.6i	1.65784	+	2.87147i
$975$	4691.99	+	138.533i	0.154117	+	0.00455035i
$976$	−4423.47	+	7661.68i	−0.145074	+	0.251275i
$977$	−22670.9	+	39267.1i	−0.742381	+	1.28584i	0.209027	+	0.977910i	$0.432970\pi$
$977$	−22670.9	+	39267.1i	−0.742381	+	1.28584i	−0.951408	+	0.307932i	$0.900363\pi$
$978$	−50577.6	−	93898.3i	−1.65368	−	3.07008i
$979$	23316.9	+	40386.1i	0.761197	+	1.31843i
$980$	16460.4			0.536540
$981$	−24675.9	−	1458.40i	−0.803100	−	0.0474650i
$982$	−62256.8			−2.02311
$983$	−3680.26	−	6374.40i	−0.119412	−	0.206828i	0.800123	−	0.599836i	$-0.204768\pi$
$983$	−3680.26	−	6374.40i	−0.119412	−	0.206828i	−0.919535	+	0.393009i	$0.871434\pi$
$984$	−22824.1	+	36968.1i	−0.739438	+	1.19766i
$985$	9130.01	−	15813.6i	0.295336	−	0.511538i
$986$	−8434.73	+	14609.4i	−0.272431	+	0.471864i
$987$	−3220.86	+	5216.81i	−0.103871	+	0.168240i
$988$	40744.1	+	70570.8i	1.31199	+	2.27242i
$989$	5905.91			0.189886
$990$	15086.9	+	30104.7i	0.484336	+	0.966455i
$991$	33328.4			1.06833			0.534164	−	0.845381i	$-0.320627\pi$
$991$	33328.4			1.06833			0.534164	+	0.845381i	$0.320627\pi$
$992$	−67717.8	−	117291.i	−2.16738	−	3.75402i
$993$	28915.2	+	53681.5i	0.924064	+	1.71554i
$994$	−20571.8	+	35631.3i	−0.656435	+	1.13698i
$995$	8043.15	−	13931.1i	0.256266	−	0.443866i
$996$	−48863.2	−	1442.70i	−1.55451	−	0.0458974i
$997$	17665.8	+	30598.1i	0.561166	+	0.971968i	0.997395	+	0.0721326i	$0.0229805\pi$
$997$	17665.8	+	30598.1i	0.561166	+	0.971968i	−0.436229	+	0.899836i	$0.643686\pi$
$998$	−45845.6			−1.45412
$999$	7412.39	+	658.091i	0.234752	+	0.0208419i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.4.e.c.31.7	yes	14
3.2	odd	2		135.4.e.c.91.1		14
5.2	odd	4		225.4.k.d.49.2		28
5.3	odd	4		225.4.k.d.49.13		28
5.4	even	2		225.4.e.d.76.1		14
9.2	odd	6		135.4.e.c.46.1		14
9.4	even	3		405.4.a.m.1.1		7
9.5	odd	6		405.4.a.n.1.7		7
9.7	even	3	inner	45.4.e.c.16.7	✓	14
45.4	even	6		2025.4.a.bb.1.7		7
45.7	odd	12		225.4.k.d.124.13		28
45.14	odd	6		2025.4.a.ba.1.1		7
45.34	even	6		225.4.e.d.151.1		14
45.43	odd	12		225.4.k.d.124.2		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.c.16.7	✓	14	9.7	even	3	inner
45.4.e.c.31.7	yes	14	1.1	even	1	trivial
135.4.e.c.46.1		14	9.2	odd	6
135.4.e.c.91.1		14	3.2	odd	2
225.4.e.d.76.1		14	5.4	even	2
225.4.e.d.151.1		14	45.34	even	6
225.4.k.d.49.2		28	5.2	odd	4
225.4.k.d.49.13		28	5.3	odd	4
225.4.k.d.124.2		28	45.43	odd	12
225.4.k.d.124.13		28	45.7	odd	12
405.4.a.m.1.1		7	9.4	even	3
405.4.a.n.1.7		7	9.5	odd	6
2025.4.a.ba.1.1		7	45.14	odd	6
2025.4.a.bb.1.7		7	45.4	even	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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	45.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.65775 + 4.60336i) q^{2} +(-5.19389 - 0.153351i) q^{3} +(-10.1273 + 17.5410i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-13.0981 - 24.3169i) q^{6} +(6.71686 + 11.6339i) q^{7} -65.1396 q^{8} +(26.9530 + 1.59298i) q^{9} +O(q^{10})\)	\(q+(2.65775 + 4.60336i) q^{2} +(-5.19389 - 0.153351i) q^{3} +(-10.1273 + 17.5410i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-13.0981 - 24.3169i) q^{6} +(6.71686 + 11.6339i) q^{7} -65.1396 q^{8} +(26.9530 + 1.59298i) q^{9} +26.5775 q^{10} +(23.4628 + 40.6388i) q^{11} +(55.2901 - 89.5531i) q^{12} +(18.0673 - 31.2935i) q^{13} +(-35.7035 + 61.8403i) q^{14} +(-13.6488 + 22.1068i) q^{15} +(-92.1064 - 159.533i) q^{16} -54.6071 q^{17} +(64.3013 + 128.308i) q^{18} +111.339 q^{19} +(50.6366 + 87.7051i) q^{20} +(-33.1026 - 61.4555i) q^{21} +(-124.717 + 216.016i) q^{22} +(17.9870 - 31.1544i) q^{23} +(338.328 + 9.98925i) q^{24} +(-12.5000 - 21.6506i) q^{25} +192.074 q^{26} +(-139.746 - 12.4070i) q^{27} -272.095 q^{28} +(-29.0588 - 50.3312i) q^{29} +(-138.041 - 4.07570i) q^{30} +(147.833 - 256.055i) q^{31} +(229.034 - 396.699i) q^{32} +(-115.631 - 214.671i) q^{33} +(-145.132 - 251.377i) q^{34} +67.1686 q^{35} +(-300.904 + 456.650i) q^{36} -53.0417 q^{37} +(295.911 + 512.533i) q^{38} +(-98.6386 + 159.765i) q^{39} +(-162.849 + 282.063i) q^{40} +(-64.1795 + 111.162i) q^{41} +(194.924 - 315.717i) q^{42} +(82.0858 + 142.177i) q^{43} -950.461 q^{44} +(74.2802 - 112.727i) q^{45} +191.220 q^{46} +(-43.9159 - 76.0646i) q^{47} +(453.926 + 842.721i) q^{48} +(81.2675 - 140.759i) q^{49} +(66.4439 - 115.084i) q^{50} +(283.623 + 8.37409i) q^{51} +(365.947 + 633.839i) q^{52} -479.247 q^{53} +(-314.297 - 676.279i) q^{54} +234.628 q^{55} +(-437.533 - 757.830i) q^{56} +(-578.281 - 17.0739i) q^{57} +(154.462 - 267.536i) q^{58} +(-317.807 + 550.458i) q^{59} +(-249.551 - 463.296i) q^{60} +(-24.0128 - 41.5915i) q^{61} +1571.62 q^{62} +(162.507 + 324.269i) q^{63} +961.163 q^{64} +(-90.3367 - 156.468i) q^{65} +(680.892 - 1102.84i) q^{66} +(14.4592 - 25.0440i) q^{67} +(553.024 - 957.865i) q^{68} +(-98.2001 + 159.054i) q^{69} +(178.518 + 309.202i) q^{70} +576.183 q^{71} +(-1755.70 - 103.766i) q^{72} +835.057 q^{73} +(-140.972 - 244.170i) q^{74} +(61.6035 + 114.368i) q^{75} +(-1127.56 + 1952.99i) q^{76} +(-315.193 + 545.930i) q^{77} +(-997.612 - 29.4548i) q^{78} +(101.869 + 176.442i) q^{79} -921.064 q^{80} +(723.925 + 85.8711i) q^{81} -682.294 q^{82} +(-232.239 - 402.249i) q^{83} +(1413.23 + 41.7262i) q^{84} +(-136.518 + 236.456i) q^{85} +(-436.328 + 755.742i) q^{86} +(143.210 + 265.871i) q^{87} +(-1528.36 - 2647.19i) q^{88} +993.782 q^{89} +(716.344 + 42.3375i) q^{90} +485.423 q^{91} +(364.320 + 631.021i) q^{92} +(-807.097 + 1307.25i) q^{93} +(233.435 - 404.322i) q^{94} +(278.347 - 482.111i) q^{95} +(-1250.41 + 2025.29i) q^{96} +(-440.708 - 763.328i) q^{97} +863.956 q^{98} +(567.656 + 1132.71i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{2} - 5 q^{3} - 36 q^{4} + 35 q^{5} - 31 q^{6} - 22 q^{7} - 36 q^{8} + 17 q^{9}+O(q^{10}) \) 14 * q + 2 * q^2 - 5 * q^3 - 36 * q^4 + 35 * q^5 - 31 * q^6 - 22 * q^7 - 36 * q^8 + 17 * q^9	\( 14 q + 2 q^{2} - 5 q^{3} - 36 q^{4} + 35 q^{5} - 31 q^{6} - 22 q^{7} - 36 q^{8} + 17 q^{9} + 20 q^{10} + 23 q^{11} + 287 q^{12} - 96 q^{13} - 21 q^{14} - 20 q^{15} - 324 q^{16} - 322 q^{17} - 89 q^{18} + 558 q^{19} + 180 q^{20} + 180 q^{21} - 311 q^{22} + 96 q^{23} + 48 q^{24} - 175 q^{25} + 716 q^{26} - 470 q^{27} + 674 q^{28} - 296 q^{29} + 80 q^{30} - 244 q^{31} - 314 q^{32} - 211 q^{33} - 125 q^{34} - 220 q^{35} - 2399 q^{36} + 808 q^{37} + 305 q^{38} + 634 q^{39} - 90 q^{40} - 47 q^{41} + 1941 q^{42} - 525 q^{43} - 110 q^{44} + 185 q^{45} + 1434 q^{46} + 164 q^{47} + 2051 q^{48} - 1225 q^{49} + 50 q^{50} + 1517 q^{51} - 1682 q^{52} - 1012 q^{53} - 4066 q^{54} + 230 q^{55} - 981 q^{56} + 337 q^{57} - 1183 q^{58} - 85 q^{59} + 65 q^{60} - 828 q^{61} + 1572 q^{62} - 828 q^{63} + 4472 q^{64} + 480 q^{65} + 4930 q^{66} - 1093 q^{67} + 2473 q^{68} - 822 q^{69} + 105 q^{70} - 656 q^{71} - 4626 q^{72} + 4170 q^{73} - 1316 q^{74} + 25 q^{75} - 2789 q^{76} + 24 q^{77} - 5314 q^{78} - 2110 q^{79} - 3240 q^{80} - 2167 q^{81} - 124 q^{82} + 1290 q^{83} + 5775 q^{84} - 805 q^{85} - 2569 q^{86} + 3604 q^{87} - 2271 q^{88} + 6096 q^{89} + 730 q^{90} + 6676 q^{91} + 2763 q^{92} - 696 q^{93} + 517 q^{94} + 1395 q^{95} - 593 q^{96} - 1787 q^{97} - 2558 q^{98} + 2320 q^{99}+O(q^{100}) \) 14 * q + 2 * q^2 - 5 * q^3 - 36 * q^4 + 35 * q^5 - 31 * q^6 - 22 * q^7 - 36 * q^8 + 17 * q^9 + 20 * q^10 + 23 * q^11 + 287 * q^12 - 96 * q^13 - 21 * q^14 - 20 * q^15 - 324 * q^16 - 322 * q^17 - 89 * q^18 + 558 * q^19 + 180 * q^20 + 180 * q^21 - 311 * q^22 + 96 * q^23 + 48 * q^24 - 175 * q^25 + 716 * q^26 - 470 * q^27 + 674 * q^28 - 296 * q^29 + 80 * q^30 - 244 * q^31 - 314 * q^32 - 211 * q^33 - 125 * q^34 - 220 * q^35 - 2399 * q^36 + 808 * q^37 + 305 * q^38 + 634 * q^39 - 90 * q^40 - 47 * q^41 + 1941 * q^42 - 525 * q^43 - 110 * q^44 + 185 * q^45 + 1434 * q^46 + 164 * q^47 + 2051 * q^48 - 1225 * q^49 + 50 * q^50 + 1517 * q^51 - 1682 * q^52 - 1012 * q^53 - 4066 * q^54 + 230 * q^55 - 981 * q^56 + 337 * q^57 - 1183 * q^58 - 85 * q^59 + 65 * q^60 - 828 * q^61 + 1572 * q^62 - 828 * q^63 + 4472 * q^64 + 480 * q^65 + 4930 * q^66 - 1093 * q^67 + 2473 * q^68 - 822 * q^69 + 105 * q^70 - 656 * q^71 - 4626 * q^72 + 4170 * q^73 - 1316 * q^74 + 25 * q^75 - 2789 * q^76 + 24 * q^77 - 5314 * q^78 - 2110 * q^79 - 3240 * q^80 - 2167 * q^81 - 124 * q^82 + 1290 * q^83 + 5775 * q^84 - 805 * q^85 - 2569 * q^86 + 3604 * q^87 - 2271 * q^88 + 6096 * q^89 + 730 * q^90 + 6676 * q^91 + 2763 * q^92 - 696 * q^93 + 517 * q^94 + 1395 * q^95 - 593 * q^96 - 1787 * q^97 - 2558 * q^98 + 2320 * q^99

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