LMFDB - Embedded newform 48.4.k.a.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,4,Mod(11,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

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

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

chi := DirichletCharacter("48.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	48.k (of order $4$, 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:	$2.83209168028$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.3
Character	$\chi$	$=$	48.11
Dual form			48.4.k.a.35.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.56930 - 1.18266i) q^{2} +(-4.81196 - 1.96089i) q^{3} +(5.20263 + 6.07722i) q^{4} +(-6.30133 + 6.30133i) q^{5} +(10.0443 + 10.7290i) q^{6} +24.6728 q^{7} +(-6.17986 - 21.7672i) q^{8} +(19.3098 + 18.8714i) q^{9} +O(q^{10})$	\(q+(-2.56930 - 1.18266i) q^{2} +(-4.81196 - 1.96089i) q^{3} +(5.20263 + 6.07722i) q^{4} +(-6.30133 + 6.30133i) q^{5} +(10.0443 + 10.7290i) q^{6} +24.6728 q^{7} +(-6.17986 - 21.7672i) q^{8} +(19.3098 + 18.8714i) q^{9} +(23.6423 - 8.73769i) q^{10} +(40.4669 + 40.4669i) q^{11} +(-13.1181 - 39.4451i) q^{12} +(-47.3131 + 47.3131i) q^{13} +(-63.3920 - 29.1796i) q^{14} +(42.6779 - 17.9655i) q^{15} +(-9.86520 + 63.2351i) q^{16} -41.7727i q^{17} +(-27.2944 - 71.3233i) q^{18} +(10.6193 + 10.6193i) q^{19} +(-71.0780 - 5.51105i) q^{20} +(-118.725 - 48.3807i) q^{21} +(-56.1131 - 151.830i) q^{22} +53.4222i q^{23} +(-12.9457 + 116.861i) q^{24} +45.5866i q^{25} +(177.517 - 65.6064i) q^{26} +(-55.9134 - 128.673i) q^{27} +(128.364 + 149.942i) q^{28} +(105.268 + 105.268i) q^{29} +(-130.900 - 4.31457i) q^{30} -3.14755i q^{31} +(100.132 - 150.803i) q^{32} +(-115.374 - 274.076i) q^{33} +(-49.4029 + 107.327i) q^{34} +(-155.472 + 155.472i) q^{35} +(-14.2237 + 215.531i) q^{36} +(42.1756 + 42.1756i) q^{37} +(-14.7252 - 39.8434i) q^{38} +(320.444 - 134.893i) q^{39} +(176.103 + 98.2207i) q^{40} -152.486 q^{41} +(247.822 + 264.715i) q^{42} +(221.247 - 221.247i) q^{43} +(-35.3918 + 456.460i) q^{44} +(-240.593 + 2.76270i) q^{45} +(63.1802 - 137.258i) q^{46} +381.086 q^{47} +(171.468 - 284.940i) q^{48} +265.749 q^{49} +(53.9134 - 117.126i) q^{50} +(-81.9116 + 201.008i) q^{51} +(-533.685 - 41.3794i) q^{52} +(-294.048 + 294.048i) q^{53} +(-8.51768 + 396.726i) q^{54} -509.990 q^{55} +(-152.475 - 537.058i) q^{56} +(-30.2765 - 71.9231i) q^{57} +(-145.970 - 394.963i) q^{58} +(-445.445 - 445.445i) q^{59} +(331.218 + 165.895i) q^{60} +(21.8473 - 21.8473i) q^{61} +(-3.72249 + 8.08702i) q^{62} +(476.429 + 465.611i) q^{63} +(-435.619 + 269.036i) q^{64} -596.270i q^{65} +(-27.7080 + 840.632i) q^{66} +(-572.215 - 572.215i) q^{67} +(253.862 - 217.328i) q^{68} +(104.755 - 257.065i) q^{69} +(583.324 - 215.584i) q^{70} +612.406i q^{71} +(291.445 - 536.943i) q^{72} -331.477i q^{73} +(-58.4825 - 158.241i) q^{74} +(89.3901 - 219.361i) q^{75} +(-9.28753 + 119.785i) q^{76} +(998.433 + 998.433i) q^{77} +(-982.850 - 32.3957i) q^{78} +427.462i q^{79} +(-336.301 - 460.629i) q^{80} +(16.7398 + 728.808i) q^{81} +(391.782 + 180.339i) q^{82} +(245.236 - 245.236i) q^{83} +(-323.661 - 973.223i) q^{84} +(263.224 + 263.224i) q^{85} +(-830.109 + 306.790i) q^{86} +(-300.128 - 712.967i) q^{87} +(630.769 - 1130.93i) q^{88} +188.997 q^{89} +(621.422 + 277.441i) q^{90} +(-1167.35 + 1167.35i) q^{91} +(-324.658 + 277.936i) q^{92} +(-6.17200 + 15.1459i) q^{93} +(-979.125 - 450.695i) q^{94} -133.832 q^{95} +(-777.540 + 529.309i) q^{96} +1474.45 q^{97} +(-682.790 - 314.291i) q^{98} +(17.7419 + 1545.08i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{3} - 4 q^{4} + 28 q^{6} - 8 q^{7}+O(q^{10}) $ 44 * q - 2 * q^3 - 4 * q^4 + 28 * q^6 - 8 * q^7	$ 44 q - 2 q^{3} - 4 q^{4} + 28 q^{6} - 8 q^{7} + 56 q^{10} - 80 q^{12} - 4 q^{13} - 112 q^{16} + 52 q^{18} + 20 q^{19} - 56 q^{21} - 40 q^{22} - 120 q^{24} - 134 q^{27} - 296 q^{28} - 332 q^{30} - 4 q^{33} + 520 q^{34} - 604 q^{36} - 4 q^{37} + 596 q^{39} + 632 q^{40} + 696 q^{42} - 436 q^{43} - 252 q^{45} + 664 q^{46} + 1200 q^{48} + 972 q^{49} - 648 q^{51} + 320 q^{52} + 1592 q^{54} + 280 q^{55} - 424 q^{58} + 800 q^{60} - 916 q^{61} - 2056 q^{64} - 668 q^{66} - 1636 q^{67} + 52 q^{69} - 5192 q^{70} - 3704 q^{72} + 1454 q^{75} - 568 q^{76} - 4932 q^{78} - 4 q^{81} + 768 q^{82} - 2096 q^{84} + 736 q^{85} + 1284 q^{87} + 8864 q^{88} + 2672 q^{90} + 424 q^{91} - 2084 q^{93} + 5616 q^{94} + 8008 q^{96} - 8 q^{97} + 1196 q^{99}+O(q^{100}) $ 44 * q - 2 * q^3 - 4 * q^4 + 28 * q^6 - 8 * q^7 + 56 * q^10 - 80 * q^12 - 4 * q^13 - 112 * q^16 + 52 * q^18 + 20 * q^19 - 56 * q^21 - 40 * q^22 - 120 * q^24 - 134 * q^27 - 296 * q^28 - 332 * q^30 - 4 * q^33 + 520 * q^34 - 604 * q^36 - 4 * q^37 + 596 * q^39 + 632 * q^40 + 696 * q^42 - 436 * q^43 - 252 * q^45 + 664 * q^46 + 1200 * q^48 + 972 * q^49 - 648 * q^51 + 320 * q^52 + 1592 * q^54 + 280 * q^55 - 424 * q^58 + 800 * q^60 - 916 * q^61 - 2056 * q^64 - 668 * q^66 - 1636 * q^67 + 52 * q^69 - 5192 * q^70 - 3704 * q^72 + 1454 * q^75 - 568 * q^76 - 4932 * q^78 - 4 * q^81 + 768 * q^82 - 2096 * q^84 + 736 * q^85 + 1284 * q^87 + 8864 * q^88 + 2672 * q^90 + 424 * q^91 - 2084 * q^93 + 5616 * q^94 + 8008 * q^96 - 8 * q^97 + 1196 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.56930	−	1.18266i	−0.908386	−	0.418133i
$2$	−2.56930	−	1.18266i	−0.908386	−	0.418133i
$3$	−4.81196	−	1.96089i	−0.926061	−	0.377373i
$3$	−4.81196	−	1.96089i	−0.926061	−	0.377373i
$4$	5.20263	+	6.07722i	0.650329	+	0.759652i
$5$	−6.30133	+	6.30133i	−0.563608	+	0.563608i	−0.930330	−	0.366723i	$-0.880480\pi$
$5$	−6.30133	+	6.30133i	−0.563608	+	0.563608i	0.366723	+	0.930330i	$0.380480\pi$
$6$	10.0443	+	10.7290i	0.683429	+	0.730017i
$7$	24.6728			1.33221			0.666104	−	0.745859i	$-0.267961\pi$
$7$	24.6728			1.33221			0.666104	+	0.745859i	$0.267961\pi$
$8$	−6.17986	−	21.7672i	−0.273114	−	0.961982i
$9$	19.3098	+	18.8714i	0.715179	+	0.698941i
$10$	23.6423	−	8.73769i	0.747636	−	0.276310i
$11$	40.4669	+	40.4669i	1.10920	+	1.10920i	0.993255	+	0.115946i	$0.0369901\pi$
$11$	40.4669	+	40.4669i	1.10920	+	1.10920i	0.115946	+	0.993255i	$0.463010\pi$
$12$	−13.1181	−	39.4451i	−0.315572	−	0.948901i
$13$	−47.3131	+	47.3131i	−1.00941	+	1.00941i	−0.00945153	+	0.999955i	$0.503009\pi$
$13$	−47.3131	+	47.3131i	−1.00941	+	1.00941i	−0.999955	+	0.00945153i	$0.996991\pi$
$14$	−63.3920	−	29.1796i	−1.21016	−	0.557041i
$15$	42.6779	−	17.9655i	0.734626	−	0.309245i
$16$	−9.86520	+	63.2351i	−0.154144	+	0.988048i
$17$		−	41.7727i		−	0.595963i	−0.954572	−	0.297982i	$-0.903687\pi$
$17$		−	41.7727i		−	0.595963i	0.954572	−	0.297982i	$-0.0963134\pi$
$18$	−27.2944	−	71.3233i	−0.357408	−	0.933948i
$19$	10.6193	+	10.6193i	0.128223	+	0.128223i	0.768306	−	0.640083i	$-0.221100\pi$
$19$	10.6193	+	10.6193i	0.128223	+	0.128223i	−0.640083	+	0.768306i	$0.721100\pi$
$20$	−71.0780	−	5.51105i	−0.794677	−	0.0616154i
$21$	−118.725	−	48.3807i	−1.23371	−	0.502739i
$22$	−56.1131	−	151.830i	−0.543789	−	1.47138i
$23$			53.4222i			0.484317i	0.970237	+	0.242158i	$0.0778554\pi$
$23$			53.4222i			0.484317i	−0.970237	+	0.242158i	$0.922145\pi$
$24$	−12.9457	+	116.861i	−0.110106	+	0.993920i
$25$			45.5866i			0.364692i
$26$	177.517	−	65.6064i	1.33900	−	0.494864i
$27$	−55.9134	−	128.673i	−0.398538	−	0.917152i
$28$	128.364	+	149.942i	0.866374	+	1.01202i
$29$	105.268	+	105.268i	0.674064	+	0.674064i	0.958650	−	0.284586i	$-0.0918562\pi$
$29$	105.268	+	105.268i	0.674064	+	0.674064i	−0.284586	+	0.958650i	$0.591856\pi$
$30$	−130.900	−	4.31457i	−0.796629	−	0.0262576i
$31$		−	3.14755i		−	0.0182361i	−0.999958	−	0.00911803i	$-0.997098\pi$
$31$		−	3.14755i		−	0.0182361i	0.999958	−	0.00911803i	$-0.00290240\pi$
$32$	100.132	−	150.803i	0.553158	−	0.833076i
$33$	−115.374	−	274.076i	−0.608606	−	1.44577i
$34$	−49.4029	+	107.327i	−0.249192	+	0.541364i
$35$	−155.472	+	155.472i	−0.750843	+	0.750843i
$36$	−14.2237	+	215.531i	−0.0658503	+	0.997830i
$37$	42.1756	+	42.1756i	0.187395	+	0.187395i	0.794569	−	0.607174i	$-0.207697\pi$
$37$	42.1756	+	42.1756i	0.187395	+	0.187395i	−0.607174	+	0.794569i	$0.707697\pi$
$38$	−14.7252	−	39.8434i	−0.0628618	−	0.170091i
$39$	320.444	−	134.893i	1.31570	−	0.553850i
$40$	176.103	+	98.2207i	0.696109	+	0.388251i
$41$	−152.486			−0.580836			−0.290418	−	0.956900i	$-0.593794\pi$
$41$	−152.486			−0.580836			−0.290418	+	0.956900i	$0.593794\pi$
$42$	247.822	+	264.715i	0.910469	+	0.972535i
$43$	221.247	−	221.247i	0.784647	−	0.784647i	−0.195964	−	0.980611i	$-0.562784\pi$
$43$	221.247	−	221.247i	0.784647	−	0.784647i	0.980611	+	0.195964i	$0.0627836\pi$
$44$	−35.3918	+	456.460i	−0.121262	+	1.56395i
$45$	−240.593	+	2.76270i	−0.797009	+	0.00915197i
$46$	63.1802	−	137.258i	0.202509	−	0.439947i
$47$	381.086			1.18270			0.591352	−	0.806414i	$-0.298594\pi$
$47$	381.086			1.18270			0.591352	+	0.806414i	$0.298594\pi$
$48$	171.468	−	284.940i	0.515609	−	0.856824i
$49$	265.749			0.774779
$50$	53.9134	−	117.126i	0.152490	−	0.331281i
$51$	−81.9116	+	201.008i	−0.224900	+	0.551898i
$52$	−533.685	−	41.3794i	−1.42325	−	0.110352i
$53$	−294.048	+	294.048i	−0.762088	+	0.762088i	−0.976699	−	0.214612i	$-0.931151\pi$
$53$	−294.048	+	294.048i	−0.762088	+	0.762088i	0.214612	+	0.976699i	$0.431151\pi$
$54$	−8.51768	+	396.726i	−0.0214650	+	0.999770i
$55$	−509.990			−1.25031
$56$	−152.475	−	537.058i	−0.363845	−	1.28156i
$57$	−30.2765	−	71.9231i	−0.0703547	−	0.167131i
$58$	−145.970	−	394.963i	−0.330462	−	0.894159i
$59$	−445.445	−	445.445i	−0.982916	−	0.982916i	0.0169404	−	0.999857i	$-0.494607\pi$
$59$	−445.445	−	445.445i	−0.982916	−	0.982916i	−0.999857	+	0.0169404i	$0.994607\pi$
$60$	331.218	+	165.895i	0.712667	+	0.356949i
$61$	21.8473	−	21.8473i	0.0458568	−	0.0458568i	−0.683807	−	0.729663i	$-0.739677\pi$
$61$	21.8473	−	21.8473i	0.0458568	−	0.0458568i	0.729663	+	0.683807i	$0.239677\pi$
$62$	−3.72249	+	8.08702i	−0.00762510	+	0.0165654i
$63$	476.429	+	465.611i	0.952768	+	0.931135i
$64$	−435.619	+	269.036i	−0.850818	+	0.525461i
$65$		−	596.270i		−	1.13782i
$66$	−27.7080	+	840.632i	−0.0516761	+	1.56780i
$67$	−572.215	−	572.215i	−1.04339	−	1.04339i	−0.999015	−	0.0443759i	$-0.985870\pi$
$67$	−572.215	−	572.215i	−1.04339	−	1.04339i	−0.0443759	−	0.999015i	$-0.514130\pi$
$68$	253.862	−	217.328i	0.452725	−	0.387572i
$69$	104.755	−	257.065i	0.182768	−	0.448507i
$70$	583.324	−	215.584i	0.996007	−	0.368103i
$71$			612.406i			1.02365i	0.859089	+	0.511825i	$0.171031\pi$
$71$			612.406i			1.02365i	−0.859089	+	0.511825i	$0.828969\pi$
$72$	291.445	−	536.943i	0.477043	−	0.878880i
$73$		−	331.477i		−	0.531458i	−0.964048	−	0.265729i	$-0.914387\pi$
$73$		−	331.477i		−	0.531458i	0.964048	−	0.265729i	$-0.0856126\pi$
$74$	−58.4825	−	158.241i	−0.0918710	−	0.248583i
$75$	89.3901	−	219.361i	0.137625	−	0.337728i
$76$	−9.28753	+	119.785i	−0.0140178	+	0.180793i
$77$	998.433	+	998.433i	1.47769	+	1.47769i
$78$	−982.850	−	32.3957i	−1.42674	−	0.0470268i
$79$			427.462i			0.608775i	0.952548	+	0.304388i	$0.0984518\pi$
$79$			427.462i			0.608775i	−0.952548	+	0.304388i	$0.901548\pi$
$80$	−336.301	−	460.629i	−0.469995	−	0.643748i
$81$	16.7398	+	728.808i	0.0229628	+	0.999736i
$82$	391.782	+	180.339i	0.527623	+	0.242867i
$83$	245.236	−	245.236i	0.324314	−	0.324314i	−0.526105	−	0.850420i	$-0.676348\pi$
$83$	245.236	−	245.236i	0.324314	−	0.324314i	0.850420	+	0.526105i	$0.176348\pi$
$84$	−323.661	−	973.223i	−0.420408	−	1.26413i
$85$	263.224	+	263.224i	0.335889	+	0.335889i
$86$	−830.109	+	306.790i	−1.04085	+	0.384675i
$87$	−300.128	−	712.967i	−0.369851	−	0.878599i
$88$	630.769	−	1130.93i	0.764094	−	1.36997i
$89$	188.997			0.225097			0.112548	−	0.993646i	$-0.464099\pi$
$89$	188.997			0.225097			0.112548	+	0.993646i	$0.464099\pi$
$90$	621.422	+	277.441i	0.727819	+	0.324943i
$91$	−1167.35	+	1167.35i	−1.34474	+	1.34474i
$92$	−324.658	+	277.936i	−0.367913	+	0.314965i
$93$	−6.17200	+	15.1459i	−0.00688179	+	0.0168877i
$94$	−979.125	−	450.695i	−1.07435	−	0.494528i
$95$	−133.832			−0.144535
$96$	−777.540	+	529.309i	−0.826639	+	0.562733i
$97$	1474.45			1.54338			0.771689	−	0.636001i	$-0.219412\pi$
$97$	1474.45			1.54338			0.771689	+	0.636001i	$0.219412\pi$
$98$	−682.790	−	314.291i	−0.703798	−	0.323961i
$99$	17.7419	+	1545.08i	0.0180114	+	1.56854i
$100$	−277.040	+	237.170i	−0.277040	+	0.237170i
$101$	−223.136	+	223.136i	−0.219830	+	0.219830i	−0.808427	−	0.588597i	$-0.799681\pi$
$101$	−223.136	+	223.136i	−0.219830	+	0.219830i	0.588597	+	0.808427i	$0.299681\pi$
$102$	448.180	−	419.578i	0.435063	−	0.407298i
$103$	−217.914			−0.208463			−0.104232	−	0.994553i	$-0.533238\pi$
$103$	−217.914			−0.208463			−0.104232	+	0.994553i	$0.533238\pi$
$104$	1322.26	+	737.483i	1.24671	+	0.695348i
$105$	1052.99	−	443.260i	0.978675	−	0.411979i
$106$	1103.26	−	407.740i	1.01092	−	0.373615i
$107$	335.407	+	335.407i	0.303038	+	0.303038i	0.842201	−	0.539163i	$-0.181260\pi$
$107$	335.407	+	335.407i	0.303038	+	0.303038i	−0.539163	+	0.842201i	$0.681260\pi$
$108$	491.076	−	1009.24i	0.437535	−	0.899201i
$109$	1032.70	−	1032.70i	0.907477	−	0.907477i	−0.0885914	−	0.996068i	$-0.528237\pi$
$109$	1032.70	−	1032.70i	0.907477	−	0.907477i	0.996068	+	0.0885914i	$0.0282365\pi$
$110$	1310.32	+	603.144i	1.13576	+	0.522796i
$111$	−120.245	−	285.649i	−0.102822	−	0.244257i
$112$	−243.403	+	1560.19i	−0.205352	+	1.31629i
$113$		−	1010.24i		−	0.841020i	−0.907288	−	0.420510i	$-0.861851\pi$
$113$		−	1010.24i		−	0.841020i	0.907288	−	0.420510i	$-0.138149\pi$
$114$	−7.27115	+	220.599i	−0.00597374	+	0.181237i
$115$	−336.630	−	336.630i	−0.272965	−	0.272965i
$116$	−92.0663	+	1187.41i	−0.0736909	+	0.950418i
$117$	−1806.47	+	20.7435i	−1.42742	+	0.0163909i
$118$	617.674	+	1671.29i	0.481877	+	1.30386i
$119$		−	1030.65i		−	0.793947i
$120$	−654.802	−	817.952i	−0.498125	−	0.622237i
$121$			1944.14i			1.46066i
$122$	−81.9704	+	30.2945i	−0.0608299	+	0.0224814i
$123$	733.755	+	299.008i	0.537890	+	0.219192i
$124$	19.1284	−	16.3756i	0.0138531	−	0.0118594i
$125$	−1074.92	−	1074.92i	−0.769151	−	0.769151i
$126$	−673.430	−	1759.75i	−0.476142	−	1.24421i
$127$		−	1504.32i		−	1.05108i	−0.850769	−	0.525540i	$-0.823863\pi$
$127$		−	1504.32i		−	1.05108i	0.850769	−	0.525540i	$-0.176137\pi$
$128$	1437.41	−	176.047i	0.992583	−	0.121566i
$129$	−1498.47	+	630.790i	−1.02274	+	0.430527i
$130$	−705.185	+	1532.00i	−0.475760	+	1.03358i
$131$	1515.05	−	1515.05i	1.01046	−	1.01046i	0.0105196	−	0.999945i	$-0.496651\pi$
$131$	1515.05	−	1515.05i	1.01046	−	1.01046i	0.999945	−	0.0105196i	$-0.00334856\pi$
$132$	1065.37	−	2127.07i	0.702490	−	1.40256i
$133$	262.009	+	262.009i	0.170820	+	0.170820i
$134$	793.458	+	2146.93i	0.511525	+	1.38408i
$135$	1163.14	+	458.481i	0.741533	+	0.292294i
$136$	−909.273	+	258.150i	−0.573306	+	0.162766i
$137$	−2462.36			−1.53557			−0.767787	−	0.640706i	$-0.778642\pi$
$137$	−2462.36			−1.53557			−0.767787	+	0.640706i	$0.778642\pi$
$138$	−573.167	+	536.589i	−0.353560	+	0.330996i
$139$	782.125	−	782.125i	0.477259	−	0.477259i	−0.426995	−	0.904254i	$-0.640428\pi$
$139$	782.125	−	782.125i	0.477259	−	0.477259i	0.904254	+	0.426995i	$0.140428\pi$
$140$	−1753.70	−	135.973i	−1.05867	−	0.0820846i
$141$	−1833.77	−	747.266i	−1.09526	−	0.446320i
$142$	724.268	−	1573.46i	0.428022	−	0.929870i
$143$	−3829.23			−2.23927
$144$	−1383.83	+	1034.89i	−0.800828	+	0.598894i
$145$	−1326.66			−0.759816
$146$	−392.024	+	851.664i	−0.222220	+	0.482769i
$147$	−1278.77	−	521.104i	−0.717493	−	0.292381i
$148$	−36.8862	+	475.734i	−0.0204867	+	0.264224i
$149$	2532.54	−	2532.54i	1.39244	−	1.39244i	0.572616	−	0.819824i	$-0.305929\pi$
$149$	2532.54	−	2532.54i	1.39244	−	1.39244i	0.819824	−	0.572616i	$-0.194071\pi$
$150$	−489.099	+	457.886i	−0.266232	+	0.249241i
$151$	571.667			0.308090			0.154045	−	0.988064i	$-0.450770\pi$
$151$	571.667			0.308090			0.154045	+	0.988064i	$0.450770\pi$
$152$	165.527	−	296.779i	0.0883290	−	0.158368i
$153$	788.310	−	806.624i	0.416543	−	0.426220i
$154$	−1384.47	−	3746.08i	−0.724440	−	1.96018i
$155$	19.8338	+	19.8338i	0.0102780	+	0.0102780i
$156$	2486.93	+	1245.61i	1.27637	+	0.639287i
$157$	−1664.95	+	1664.95i	−0.846353	+	0.846353i	−0.989676	−	0.143323i	$-0.954221\pi$
$157$	−1664.95	+	1664.95i	−0.846353	+	0.846353i	0.143323	+	0.989676i	$0.454221\pi$
$158$	505.542	−	1098.28i	0.254549	−	0.553003i
$159$	1991.54	−	838.352i	0.993331	−	0.418149i
$160$	319.292	+	1581.22i	0.157764	+	0.781292i
$161$			1318.08i			0.645211i
$162$	818.922	−	1892.33i	0.397164	−	0.917748i
$163$	1893.19	+	1893.19i	0.909731	+	0.909731i	0.996250	−	0.0865194i	$-0.0275744\pi$
$163$	1893.19	+	1893.19i	0.909731	+	0.909731i	−0.0865194	+	0.996250i	$0.527574\pi$
$164$	−793.328	−	926.690i	−0.377735	−	0.441234i
$165$	2454.05	+	1000.03i	1.15786	+	0.471833i
$166$	−920.114	+	340.054i	−0.430209	+	0.158996i
$167$			2441.42i			1.13127i	0.824655	+	0.565636i	$0.191369\pi$
$167$			2441.42i			1.13127i	−0.824655	+	0.565636i	$0.808631\pi$
$168$	−319.408	+	2883.28i	−0.146684	+	1.32411i
$169$		−	2280.06i		−	1.03780i
$170$	−364.997	−	987.605i	−0.164671	−	0.445564i
$171$	4.65585	+	405.460i	0.00208212	+	0.181323i
$172$	2495.63	+	193.499i	1.10634	+	0.0857801i
$173$	856.168	+	856.168i	0.376262	+	0.376262i	0.869751	−	0.493490i	$-0.164279\pi$
$173$	856.168	+	856.168i	0.376262	+	0.376262i	−0.493490	+	0.869751i	$0.664279\pi$
$174$	−72.0782	+	2186.78i	−0.0314037	+	0.952754i
$175$			1124.75i			0.485846i
$176$	−2958.14	+	2159.71i	−1.26692	+	0.924969i
$177$	1270.00	+	3016.93i	0.539315	+	1.28117i
$178$	−485.590	−	223.519i	−0.204475	−	0.0941204i
$179$	2706.69	−	2706.69i	1.13021	−	1.13021i	0.140068	−	0.990142i	$-0.455268\pi$
$179$	2706.69	−	2706.69i	1.13021	−	1.13021i	0.990142	−	0.140068i	$-0.0447322\pi$
$180$	−1268.50	−	1447.76i	−0.525271	−	0.599498i
$181$	−155.849	−	155.849i	−0.0640008	−	0.0640008i	0.674382	−	0.738383i	$-0.264410\pi$
$181$	−155.849	−	155.849i	−0.0640008	−	0.0640008i	−0.738383	+	0.674382i	$0.764410\pi$
$182$	4379.85	−	1618.70i	1.78382	−	0.659262i
$183$	−147.969	+	62.2882i	−0.0597713	+	0.0251611i
$184$	1162.85	−	330.141i	0.465904	−	0.132274i
$185$	−531.524			−0.211235
$186$	33.7702	−	31.6150i	0.0133126	−	0.0124630i
$187$	1690.41	−	1690.41i	0.661043	−	0.661043i
$188$	1982.65	+	2315.94i	0.769147	+	0.898444i
$189$	−1379.54	−	3174.72i	−0.530936	−	1.22184i
$190$	343.855	+	158.278i	0.131294	+	0.0604350i
$191$	−1193.27			−0.452054			−0.226027	−	0.974121i	$-0.572574\pi$
$191$	−1193.27			−0.452054			−0.226027	+	0.974121i	$0.572574\pi$
$192$	2623.73	−	440.390i	0.986204	−	0.165534i
$193$	−5048.50			−1.88290			−0.941448	−	0.337158i	$-0.890534\pi$
$193$	−5048.50			−1.88290			−0.941448	+	0.337158i	$0.890534\pi$
$194$	−3788.31	−	1743.77i	−1.40198	−	0.645337i
$195$	−1169.22	+	2869.23i	−0.429382	+	1.05369i
$196$	1382.60	+	1615.02i	0.503861	+	0.588563i
$197$	−544.245	+	544.245i	−0.196832	+	0.196832i	−0.798640	−	0.601809i	$-0.794447\pi$
$197$	−544.245	+	544.245i	−0.196832	+	0.196832i	0.601809	+	0.798640i	$0.294447\pi$
$198$	1781.71	−	3990.75i	0.639499	−	1.43238i
$199$	609.004			0.216941			0.108470	−	0.994100i	$-0.465405\pi$
$199$	609.004			0.216941			0.108470	+	0.994100i	$0.465405\pi$
$200$	992.290	−	281.719i	0.350828	−	0.0996026i
$201$	1631.42	+	3875.52i	0.572496	+	1.35999i
$202$	837.196	−	309.409i	0.291608	−	0.107772i
$203$	2597.27	+	2597.27i	0.897994	+	0.897994i
$204$	−1647.73	+	547.979i	−0.565510	+	0.188070i
$205$	960.863	−	960.863i	0.327364	−	0.327364i
$206$	559.888	+	257.718i	0.189365	+	0.0871655i
$207$	−1008.15	+	1031.57i	−0.338509	+	0.346373i
$208$	−2525.09	−	3458.60i	−0.841749	−	1.15294i
$209$			859.463i			0.284451i
$210$	−3229.66	−	106.453i	−1.06128	−	0.0349807i
$211$	−407.803	−	407.803i	−0.133053	−	0.133053i	0.637444	−	0.770497i	$-0.279992\pi$
$211$	−407.803	−	407.803i	−0.133053	−	0.133053i	−0.770497	+	0.637444i	$0.779992\pi$
$212$	−3316.82	−	257.171i	−1.07453	−	0.0833139i
$213$	1200.86	−	2946.87i	0.386298	−	0.947964i
$214$	−465.090	−	1258.43i	−0.148565	−	0.401985i
$215$			2788.30i			0.884466i
$216$	−2455.30	+	2012.26i	−0.773437	+	0.633873i
$217$		−	77.6591i		−	0.0242942i
$218$	−3874.66	+	1431.99i	−1.20378	+	0.444893i
$219$	−649.989	+	1595.05i	−0.200558	+	0.492163i
$220$	−2653.29	−	3099.32i	−0.813113	−	0.949801i
$221$	1976.40	+	1976.40i	0.601569	+	0.601569i
$222$	−28.8780	+	876.127i	−0.00873046	+	0.264873i
$223$		−	2957.32i		−	0.888057i	−0.896013	−	0.444028i	$-0.853549\pi$
$223$		−	2957.32i		−	0.888057i	0.896013	−	0.444028i	$-0.146451\pi$
$224$	2470.55	−	3720.74i	0.736922	−	1.10983i
$225$	−860.283	+	880.269i	−0.254899	+	0.260821i
$226$	−1194.77	+	2595.61i	−0.351658	+	0.763971i
$227$	−254.883	+	254.883i	−0.0745250	+	0.0745250i	−0.743387	−	0.668862i	$-0.766782\pi$
$227$	−254.883	+	254.883i	−0.0745250	+	0.0745250i	0.668862	+	0.743387i	$0.266782\pi$
$228$	279.575	−	558.186i	0.0812076	−	0.162135i
$229$	349.739	+	349.739i	0.100923	+	0.100923i	0.755765	−	0.654842i	$-0.227265\pi$
$229$	349.739	+	349.739i	0.100923	+	0.100923i	−0.654842	+	0.755765i	$0.727265\pi$
$230$	466.786	+	1263.02i	0.133822	+	0.362093i
$231$	−2846.60	−	6762.23i	−0.810790	−	1.92607i
$232$	1640.85	−	2941.94i	0.464341	−	0.832534i
$233$	1869.42			0.525621			0.262810	−	0.964847i	$-0.415351\pi$
$233$	1869.42			0.525621			0.262810	+	0.964847i	$0.415351\pi$
$234$	4665.91	+	2083.15i	1.30350	+	0.581964i
$235$	−2401.35	+	2401.35i	−0.666581	+	0.666581i
$236$	389.580	−	5024.56i	0.107456	−	1.38589i
$237$	838.205	−	2056.93i	0.229735	−	0.563763i
$238$	−1218.91	+	2648.06i	−0.331976	+	0.721210i
$239$	2120.63			0.573943			0.286972	−	0.957939i	$-0.407351\pi$
$239$	2120.63			0.573943			0.286972	+	0.957939i	$0.407351\pi$
$240$	715.025	+	2875.97i	0.192311	+	0.773514i
$241$	3096.26			0.827584			0.413792	−	0.910372i	$-0.364204\pi$
$241$	3096.26			0.827584			0.413792	+	0.910372i	$0.364204\pi$
$242$	2299.25	−	4995.07i	0.610750	−	1.32684i
$243$	1348.56	−	3539.82i	0.356009	−	0.934483i
$244$	246.435	+	19.1074i	0.0646572	+	0.00501321i
$245$	−1674.57	+	1674.57i	−0.436671	+	0.436671i
$246$	−1531.61	−	1636.02i	−0.396960	−	0.424020i
$247$	−1004.87			−0.258859
$248$	−68.5133	+	19.4515i	−0.0175427	+	0.00498052i
$249$	−1660.94	+	699.183i	−0.422723	+	0.177948i
$250$	1490.53	+	4033.07i	0.377078	+	1.02029i
$251$	−2393.97	−	2393.97i	−0.602017	−	0.602017i	0.338830	−	0.940847i	$-0.389969\pi$
$251$	−2393.97	−	2393.97i	−0.602017	−	0.602017i	−0.940847	+	0.338830i	$0.889969\pi$
$252$	−350.938	+	5317.77i	−0.0877264	+	1.32932i
$253$	−2161.83	+	2161.83i	−0.537205	+	0.537205i
$254$	−1779.10	+	3865.06i	−0.439491	+	0.954786i
$255$	−750.468	−	1782.77i	−0.184299	−	0.437810i
$256$	−3901.36	−	1247.65i	−0.952479	−	0.304603i
$257$		−	3582.50i		−	0.869535i	−0.900543	−	0.434768i	$-0.856831\pi$
$257$		−	3582.50i		−	0.869535i	0.900543	−	0.434768i	$-0.143169\pi$
$258$	4596.03	+	151.490i	1.10906	+	0.0365555i
$259$	1040.59	+	1040.59i	0.249649	+	0.249649i
$260$	3623.67	−	3102.18i	0.864347	−	0.739957i
$261$	46.1530	+	4019.28i	0.0109456	+	0.953208i
$262$	−5684.42	+	2100.84i	−1.34040	+	0.495383i
$263$			2196.24i			0.514928i	0.966288	+	0.257464i	$0.0828869\pi$
$263$			2196.24i			0.514928i	−0.966288	+	0.257464i	$0.917113\pi$
$264$	−5252.86	+	4205.11i	−1.22459	+	0.980328i
$265$		−	3705.79i		−	0.859037i
$266$	−363.314	−	983.049i	−0.0837450	−	0.226596i
$267$	−909.443	−	370.601i	−0.208453	−	0.0849454i
$268$	500.451	−	6454.50i	0.114067	−	1.47116i
$269$	64.1764	+	64.1764i	0.0145461	+	0.0145461i	0.714342	−	0.699796i	$-0.246726\pi$
$269$	64.1764	+	64.1764i	0.0145461	+	0.0145461i	−0.699796	+	0.714342i	$0.746726\pi$
$270$	−2446.23	−	2553.57i	−0.551380	−	0.575576i
$271$			3627.40i			0.813095i	0.913630	+	0.406548i	$0.133268\pi$
$271$			3627.40i			0.813095i	−0.913630	+	0.406548i	$0.866732\pi$
$272$	2641.50	+	412.096i	0.588840	+	0.0918640i
$273$	7906.27	−	3328.19i	1.75278	−	0.737843i
$274$	6326.55	+	2912.13i	1.39489	+	0.642074i
$275$	−1844.75	+	1844.75i	−0.404518	+	0.404518i
$276$	2107.24	−	700.797i	0.459569	−	0.152837i
$277$	−3476.10	−	3476.10i	−0.754001	−	0.754001i	0.221222	−	0.975223i	$-0.428995\pi$
$277$	−3476.10	−	3476.10i	−0.754001	−	0.754001i	−0.975223	+	0.221222i	$0.928995\pi$
$278$	−2934.50	+	1084.53i	−0.633093	+	0.233977i
$279$	59.3988	−	60.7788i	0.0127459	−	0.0130420i
$280$	4344.97	+	2423.38i	0.927363	+	0.517232i
$281$	−5597.90			−1.18841			−0.594204	−	0.804314i	$-0.702533\pi$
$281$	−5597.90			−1.18841			−0.594204	+	0.804314i	$0.702533\pi$
$282$	3827.74	+	4088.68i	0.808294	+	0.863394i
$283$	236.800	−	236.800i	0.0497395	−	0.0497395i	−0.681800	−	0.731539i	$-0.738802\pi$
$283$	236.800	−	236.800i	0.0497395	−	0.0497395i	0.731539	+	0.681800i	$0.238802\pi$
$284$	−3721.73	+	3186.12i	−0.777619	+	0.665710i
$285$	643.993	+	262.429i	0.133849	+	0.0545437i
$286$	9838.44	+	4528.67i	2.03412	+	0.936314i
$287$	−3762.26			−0.773795
$288$	4779.40	−	1022.34i	0.977878	−	0.209174i
$289$	3168.04			0.644828
$290$	3408.60	+	1568.99i	0.690206	+	0.317704i
$291$	−7094.98	−	2891.23i	−1.42926	−	0.582429i
$292$	2014.46	−	1724.55i	0.403723	−	0.345623i
$293$	−3077.11	+	3077.11i	−0.613537	+	0.613537i	−0.943866	−	0.330329i	$-0.892840\pi$
$293$	−3077.11	+	3077.11i	−0.613537	+	0.613537i	0.330329	+	0.943866i	$0.392840\pi$
$294$	2669.27	+	2851.23i	0.529506	+	0.565602i
$295$	5613.79			1.10796
$296$	657.403	−	1178.68i	0.129091	−	0.231451i
$297$	2944.35	−	7469.63i	0.575247	−	1.45937i
$298$	−9501.98	+	3511.73i	−1.84710	+	0.682647i
$299$	−2527.57	−	2527.57i	−0.488873	−	0.488873i
$300$	1798.17	−	598.009i	0.346057	−	0.115087i
$301$	5458.79	−	5458.79i	1.04531	−	1.04531i
$302$	−1468.79	−	676.087i	−0.279865	−	0.128823i
$303$	1511.26	−	636.175i	0.286534	−	0.120618i
$304$	−776.277	+	566.753i	−0.146456	+	0.106926i
$305$			275.334i			0.0516905i
$306$	−2979.37	+	1140.16i	−0.556599	+	0.213002i
$307$	1749.92	+	1749.92i	0.325321	+	0.325321i	0.850804	−	0.525483i	$-0.176115\pi$
$307$	1749.92	+	1749.92i	0.325321	+	0.325321i	−0.525483	+	0.850804i	$0.676115\pi$
$308$	−873.215	+	11262.2i	−0.161546	+	2.08351i
$309$	1048.59	+	427.305i	0.193050	+	0.0786685i
$310$	−27.5024	−	74.4156i	−0.00503881	−	0.0136339i
$311$		−	7073.49i		−	1.28971i	−0.764304	−	0.644856i	$-0.776917\pi$
$311$		−	7073.49i		−	1.28971i	0.764304	−	0.644856i	$-0.223083\pi$
$312$	−4916.53	−	6141.54i	−0.892128	−	1.11441i
$313$			9046.73i			1.63371i	0.576843	+	0.816855i	$0.304284\pi$
$313$			9046.73i			1.63371i	−0.576843	+	0.816855i	$0.695716\pi$
$314$	6246.83	−	2308.69i	1.12270	−	0.414927i
$315$	−5936.10	+	68.1636i	−1.06178	+	0.0121923i
$316$	−2597.78	+	2223.93i	−0.462457	+	0.395904i
$317$	4477.40	+	4477.40i	0.793300	+	0.793300i	0.982029	−	0.188729i	$-0.0604369\pi$
$317$	4477.40	+	4477.40i	0.793300	+	0.793300i	−0.188729	+	0.982029i	$0.560437\pi$
$318$	−6108.36	−	201.337i	−1.07717	−	0.0355045i
$319$			8519.77i			1.49535i
$320$	1049.69	−	4440.26i	0.183374	−	0.775681i
$321$	−956.269	−	2271.66i	−0.166273	−	0.394990i
$322$	1558.84	−	3386.54i	0.269784	−	0.586100i
$323$	443.599	−	443.599i	0.0764164	−	0.0764164i
$324$	−4342.03	+	3893.45i	−0.744519	+	0.667601i
$325$	−2156.84	−	2156.84i	−0.368123	−	0.368123i
$326$	−2625.18	−	7103.18i	−0.445998	−	1.20678i
$327$	−6994.33	+	2944.31i	−1.18284	+	0.497922i
$328$	942.341	+	3319.18i	0.158634	+	0.558754i
$329$	9402.47			1.57561
$330$	−5122.50	−	5471.69i	−0.854498	−	0.912748i
$331$	1060.84	−	1060.84i	0.176160	−	0.176160i	−0.613519	−	0.789680i	$-0.710247\pi$
$331$	1060.84	−	1060.84i	0.176160	−	0.176160i	0.789680	+	0.613519i	$0.210247\pi$
$332$	2766.22	+	214.480i	0.457277	+	0.0354551i
$333$	18.4911	+	1610.32i	0.00304296	+	0.264999i
$334$	2887.36	−	6272.74i	0.473022	−	1.02763i
$335$	7211.43			1.17613
$336$	4230.60	−	7030.28i	0.686899	−	1.14147i
$337$	−127.151			−0.0205529			−0.0102765	−	0.999947i	$-0.503271\pi$
$337$	−127.151			−0.0205529			−0.0102765	+	0.999947i	$0.503271\pi$
$338$	−2696.53	+	5858.16i	−0.433941	+	0.942727i
$339$	−1980.96	+	4861.22i	−0.317378	+	0.778836i
$340$	−230.212	+	2969.12i	−0.0367205	+	0.473598i
$341$	127.372	−	127.372i	0.0202275	−	0.0202275i
$342$	467.558	−	1047.26i	0.0739259	−	0.165582i
$343$	−1906.00			−0.300041
$344$	−6183.19	−	3448.64i	−0.969114	−	0.540518i
$345$	959.756	+	2279.95i	0.149773	+	0.355792i
$346$	−1187.20	−	3212.31i	−0.184463	−	0.499118i
$347$	2671.89	+	2671.89i	0.413357	+	0.413357i	0.882906	−	0.469549i	$-0.155584\pi$
$347$	2671.89	+	2671.89i	0.413357	+	0.413357i	−0.469549	+	0.882906i	$0.655584\pi$
$348$	2771.40	−	5533.25i	0.426905	−	0.852337i
$349$	−7144.55	+	7144.55i	−1.09581	+	1.09581i	−0.100920	+	0.994895i	$0.532179\pi$
$349$	−7144.55	+	7144.55i	−1.09581	+	1.09581i	−0.994895	+	0.100920i	$0.967821\pi$
$350$	1330.20	−	2889.82i	0.203149	−	0.441336i
$351$	8733.34	+	3442.47i	1.32807	+	0.523492i
$352$	10154.6	−	2050.48i	1.53761	−	0.310486i
$353$		−	4391.32i		−	0.662114i	−0.943611	−	0.331057i	$-0.892595\pi$
$353$		−	4391.32i		−	0.662114i	0.943611	−	0.331057i	$-0.107405\pi$
$354$	305.000	−	9253.38i	0.0457926	−	1.38930i
$355$	−3858.97	−	3858.97i	−0.576938	−	0.576938i
$356$	983.280	+	1148.57i	0.146387	+	0.170995i
$357$	−2020.99	+	4959.45i	−0.299614	+	0.735244i
$358$	−10155.4	+	3753.22i	−1.49925	+	0.554088i
$359$			750.165i			0.110285i	0.998479	+	0.0551423i	$0.0175613\pi$
$359$			750.165i			0.110285i	−0.998479	+	0.0551423i	$0.982439\pi$
$360$	1546.96	+	5219.94i	0.226478	+	0.764209i
$361$		−	6633.46i		−	0.967118i
$362$	216.107	+	584.738i	0.0313765	+	0.0848983i
$363$	3812.23	−	9355.09i	0.551213	−	1.35266i
$364$	−13167.5	−	1020.95i	−1.89606	−	0.147011i
$365$	2088.74	+	2088.74i	0.299534	+	0.299534i
$366$	453.842	+	14.9591i	0.0648161	+	0.00213640i
$367$		−	8873.45i		−	1.26210i	−0.775743	−	0.631049i	$-0.782625\pi$
$367$		−	8873.45i		−	1.26210i	0.775743	−	0.631049i	$-0.217375\pi$
$368$	−3378.16	−	527.020i	−0.478529	−	0.0746544i
$369$	−2944.48	−	2877.62i	−0.415402	−	0.405970i
$370$	1365.65	+	628.612i	0.191883	+	0.0883243i
$371$	−7255.01	+	7255.01i	−1.01526	+	1.01526i
$372$	−124.156	+	41.2899i	−0.0173042	+	0.00575479i
$373$	257.833	+	257.833i	0.0357911	+	0.0357911i	0.724776	−	0.688985i	$-0.241943\pi$
$373$	257.833	+	257.833i	0.0357911	+	0.0357911i	−0.688985	+	0.724776i	$0.741943\pi$
$374$	−6342.36	+	2344.00i	−0.876887	+	0.324078i
$375$	3064.68	+	7280.28i	0.422024	+	1.00254i
$376$	−2355.06	−	8295.16i	−0.323013	−	1.13774i
$377$	−9961.15			−1.36081
$378$	−210.155	+	9788.36i	−0.0285958	+	1.33190i
$379$	3719.90	−	3719.90i	0.504164	−	0.504164i	−0.408565	−	0.912729i	$-0.633971\pi$
$379$	3719.90	−	3719.90i	0.504164	−	0.504164i	0.912729	+	0.408565i	$0.133971\pi$
$380$	−696.278	−	813.326i	−0.0939956	−	0.109797i
$381$	−2949.81	+	7238.74i	−0.396649	+	0.973364i
$382$	3065.88	+	1411.24i	0.410639	+	0.189019i
$383$	9336.03			1.24556			0.622779	−	0.782398i	$-0.286004\pi$
$383$	9336.03			1.24556			0.622779	+	0.782398i	$0.286004\pi$
$384$	−7261.98	−	1971.48i	−0.965069	−	0.261996i
$385$	−12582.9			−1.66567
$386$	12971.1	+	5970.66i	1.71040	+	0.787301i
$387$	8447.48	−	97.0015i	1.10959	−	0.0127412i
$388$	7671.02	+	8960.55i	1.00370	+	1.17243i
$389$	5797.69	−	5797.69i	0.755667	−	0.755667i	−0.219864	−	0.975531i	$-0.570561\pi$
$389$	5797.69	−	5797.69i	0.755667	−	0.755667i	0.975531	+	0.219864i	$0.0705613\pi$
$390$	6397.40	−	5989.13i	0.830628	−	0.777618i
$391$	2231.59			0.288635
$392$	−1642.29	−	5784.60i	−0.211603	−	0.745323i
$393$	−10261.2	+	4319.52i	−1.31707	+	0.554430i
$394$	2041.99	−	754.674i	0.261101	−	0.0964973i
$395$	−2693.58	−	2693.58i	−0.343110	−	0.343110i
$396$	−9297.46	+	8146.28i	−1.17984	+	1.03375i
$397$	−584.046	+	584.046i	−0.0738348	+	0.0738348i	−0.743060	−	0.669225i	$-0.766626\pi$
$397$	−584.046	+	584.046i	−0.0738348	+	0.0738348i	0.669225	+	0.743060i	$0.266626\pi$
$398$	−1564.72	−	720.245i	−0.197066	−	0.0907101i
$399$	−747.007	−	1774.55i	−0.0937271	−	0.222653i
$400$	−2882.67	−	449.721i	−0.360334	−	0.0562151i
$401$			1656.54i			0.206293i	0.994666	+	0.103147i	$0.0328911\pi$
$401$			1656.54i			0.206293i	−0.994666	+	0.103147i	$0.967109\pi$
$402$	391.800	−	11886.8i	0.0486100	−	1.47478i
$403$	148.921	+	148.921i	0.0184076	+	0.0184076i
$404$	−2516.94	−	195.151i	−0.309956	−	0.0240325i
$405$	−4697.94	−	4486.97i	−0.576401	−	0.550517i
$406$	−3601.49	−	9744.87i	−0.440244	−	1.19121i
$407$			3413.43i			0.415718i
$408$	4881.59	+	540.779i	0.592340	+	0.0656190i
$409$			2543.09i			0.307451i	0.988114	+	0.153726i	$0.0491272\pi$
$409$			2543.09i			0.307451i	−0.988114	+	0.153726i	$0.950873\pi$
$410$	−3605.12	+	1332.37i	−0.434254	+	0.160491i
$411$	11848.8	+	4828.41i	1.42204	+	0.579484i
$412$	−1133.73	−	1324.31i	−0.135570	−	0.158360i
$413$	−10990.4	−	10990.4i	−1.30945	−	1.30945i
$414$	3810.25	−	1458.12i	0.452327	−	0.173099i
$415$			3090.62i			0.365572i
$416$	2397.39	+	11872.5i	0.282552	+	1.39927i
$417$	−5297.21	+	2229.89i	−0.622076	+	0.261866i
$418$	1016.45	−	2208.22i	0.118938	−	0.258391i
$419$	3614.52	−	3614.52i	0.421434	−	0.421434i	−0.464263	−	0.885697i	$-0.653681\pi$
$419$	3614.52	−	3614.52i	0.421434	−	0.421434i	0.885697	+	0.464263i	$0.153681\pi$
$420$	8172.09	+	4093.10i	0.949421	+	0.475531i
$421$	10063.8	+	10063.8i	1.16504	+	1.16504i	0.983357	+	0.181683i	$0.0581545\pi$
$421$	10063.8	+	10063.8i	1.16504	+	1.16504i	0.181683	+	0.983357i	$0.441845\pi$
$422$	565.477	+	1530.06i	0.0652298	+	0.176498i
$423$	7358.71	+	7191.63i	0.845845	+	0.826640i
$424$	8217.78	+	4583.42i	0.941251	+	0.524978i
$425$	1904.27			0.217343
$426$	−6570.51	+	6151.20i	−0.747283	+	0.699592i
$427$	539.036	−	539.036i	0.0610908	−	0.0610908i
$428$	−293.342	+	3783.34i	−0.0331291	+	0.427278i
$429$	18426.1	+	7508.68i	2.07370	+	0.845041i
$430$	3297.60	−	7163.98i	0.369825	−	0.803436i
$431$	3495.35			0.390639			0.195319	−	0.980740i	$-0.437426\pi$
$431$	3495.35			0.390639			0.195319	+	0.980740i	$0.437426\pi$
$432$	8688.24	−	2266.31i	0.967622	−	0.252402i
$433$	16071.3			1.78369			0.891843	−	0.452345i	$-0.149413\pi$
$433$	16071.3			1.78369			0.891843	+	0.452345i	$0.149413\pi$
$434$	−91.8443	+	199.530i	−0.0101582	+	0.0220685i
$435$	6383.84	+	2601.44i	0.703636	+	0.286734i
$436$	11648.7	+	903.187i	1.27953	+	0.0992083i
$437$	−567.308	+	567.308i	−0.0621007	+	0.0621007i
$438$	3556.42	−	3329.46i	0.387973	−	0.363214i
$439$	−2550.46			−0.277282			−0.138641	−	0.990343i	$-0.544273\pi$
$439$	−2550.46			−0.277282			−0.138641	+	0.990343i	$0.544273\pi$
$440$	3151.67	+	11101.0i	0.341477	+	1.20278i
$441$	5131.57	+	5015.06i	0.554106	+	0.541525i
$442$	−2740.56	−	7415.36i	−0.294921	−	0.797993i
$443$	−6114.74	−	6114.74i	−0.655801	−	0.655801i	0.298582	−	0.954384i	$-0.403486\pi$
$443$	−6114.74	−	6114.74i	−0.655801	−	0.655801i	−0.954384	+	0.298582i	$0.903486\pi$
$444$	1110.36	−	2216.88i	0.118683	−	0.236956i
$445$	−1190.93	+	1190.93i	−0.126866	+	0.126866i
$446$	−3497.50	+	7598.24i	−0.371326	+	0.806698i
$447$	−17152.5	+	7220.44i	−1.81495	+	0.764016i
$448$	−10748.0	+	6637.88i	−1.13347	+	0.700024i
$449$		−	7434.00i		−	0.781364i	−0.920526	−	0.390682i	$-0.872239\pi$
$449$		−	7434.00i		−	0.781364i	0.920526	−	0.390682i	$-0.127761\pi$
$450$	3251.39	−	1244.26i	0.340604	−	0.130344i
$451$	−6170.62	−	6170.62i	−0.644265	−	0.644265i
$452$	6139.44	−	5255.90i	0.638883	−	0.546940i
$453$	−2750.84	−	1120.97i	−0.285310	−	0.116265i
$454$	956.311	−	353.432i	0.0988588	−	0.0365361i
$455$		−	14711.7i		−	1.51581i
$456$	−1378.46	+	1103.51i	−0.141562	+	0.113326i
$457$		−	1301.43i		−	0.133213i	−0.997779	−	0.0666063i	$-0.978783\pi$
$457$		−	1301.43i		−	0.133213i	0.997779	−	0.0666063i	$-0.0212172\pi$
$458$	−484.963	−	1312.21i	−0.0494778	−	0.133876i
$459$	−5375.01	+	2335.65i	−0.546589	+	0.237514i
$460$	294.412	−	3797.14i	0.0298414	−	0.384875i
$461$	−11243.0	−	11243.0i	−1.13587	−	1.13587i	−0.989183	−	0.146689i	$-0.953138\pi$
$461$	−11243.0	−	11243.0i	−1.13587	−	1.13587i	−0.146689	−	0.989183i	$-0.546862\pi$
$462$	−683.635	+	20740.8i	−0.0688433	+	2.08863i
$463$		−	7824.20i		−	0.785359i	−0.919675	−	0.392679i	$-0.871548\pi$
$463$		−	7824.20i		−	0.785359i	0.919675	−	0.392679i	$-0.128452\pi$
$464$	−7695.16	+	5618.17i	−0.769911	+	0.562105i
$465$	−56.5474	−	134.331i	−0.00563941	−	0.0133967i
$466$	−4803.10	−	2210.88i	−0.477466	−	0.219780i
$467$	−7493.61	+	7493.61i	−0.742533	+	0.742533i	−0.973065	−	0.230532i	$-0.925953\pi$
$467$	−7493.61	+	7493.61i	−0.742533	+	0.742533i	0.230532	+	0.973065i	$0.425953\pi$
$468$	−9524.48	−	10870.4i	−0.940746	−	1.07369i
$469$	−14118.2	−	14118.2i	−1.39001	−	1.39001i
$470$	9009.76	−	3329.81i	0.884232	−	0.326793i
$471$	11276.4	−	4746.88i	1.10317	−	0.464384i
$472$	−6943.29	+	12448.9i	−0.677099	+	1.21400i
$473$	17906.3			1.74066
$474$	−4586.25	+	4293.56i	−0.444416	+	0.416054i
$475$	−484.099	+	484.099i	−0.0467621	+	0.0467621i
$476$	6263.50	−	5362.10i	0.603124	−	0.516327i
$477$	−11227.1	+	128.920i	−1.07768	+	0.0123749i
$478$	−5448.55	−	2507.99i	−0.521362	−	0.239985i
$479$	−13051.7			−1.24499			−0.622493	−	0.782626i	$-0.713880\pi$
$479$	−13051.7			−1.24499			−0.622493	+	0.782626i	$0.713880\pi$
$480$	1564.18	−	8234.88i	0.148739	−	0.783061i
$481$	−3990.91			−0.378316
$482$	−7955.23	−	3661.82i	−0.751765	−	0.346040i
$483$	2584.60	−	6342.53i	0.243485	−	0.597505i
$484$	−11814.9	+	10114.6i	−1.10959	+	0.949908i
$485$	−9290.98	+	9290.98i	−0.869859	+	0.869859i
$486$	−7651.25	+	7499.97i	−0.714131	+	0.700012i
$487$	−7486.49			−0.696602			−0.348301	−	0.937383i	$-0.613241\pi$
$487$	−7486.49			−0.696602			−0.348301	+	0.937383i	$0.613241\pi$
$488$	−610.568	−	340.541i	−0.0566375	−	0.0315893i
$489$	−5397.62	−	12822.3i	−0.499159	−	1.18577i
$490$	6282.93	−	2322.03i	0.579253	−	0.214079i
$491$	6345.55	+	6345.55i	0.583239	+	0.583239i	0.935792	−	0.352553i	$-0.114686\pi$
$491$	6345.55	+	6345.55i	0.583239	+	0.583239i	−0.352553	+	0.935792i	$0.614686\pi$
$492$	2000.32	+	6014.82i	0.183296	+	0.551156i
$493$	4397.35	−	4397.35i	0.401717	−	0.401717i
$494$	2581.81	+	1188.42i	0.235144	+	0.108238i
$495$	−9847.82	−	9624.23i	−0.894196	−	0.873893i
$496$	199.036	+	31.0513i	0.0180181	+	0.00281097i
$497$			15109.8i			1.36372i
$498$	5094.36	+	167.915i	0.458401	+	0.0151093i
$499$	7412.65	+	7412.65i	0.665001	+	0.665001i	0.956555	−	0.291553i	$-0.0941721\pi$
$499$	7412.65	+	7412.65i	0.665001	+	0.665001i	−0.291553	+	0.956555i	$0.594172\pi$
$500$	940.112	−	12125.0i	0.0840861	−	1.08449i
$501$	4787.34	−	11748.0i	0.426911	−	1.04763i
$502$	3319.59	+	8982.10i	0.295140	+	0.798587i
$503$		−	3879.66i		−	0.343908i	−0.985105	−	0.171954i	$-0.944992\pi$
$503$		−	3879.66i		−	0.343908i	0.985105	−	0.171954i	$-0.0550080\pi$
$504$	7190.77	−	13247.9i	0.635521	−	1.17085i
$505$		−	2812.10i		−	0.247796i
$506$	8111.09	−	2997.68i	0.712613	−	0.263366i
$507$	−4470.93	+	10971.5i	−0.391639	+	0.961071i
$508$	9142.11	−	7826.45i	0.798455	−	0.683548i
$509$	−4843.90	−	4843.90i	−0.421811	−	0.421811i	0.464016	−	0.885827i	$-0.346408\pi$
$509$	−4843.90	−	4843.90i	−0.421811	−	0.421811i	−0.885827	+	0.464016i	$0.846408\pi$
$510$	−180.231	+	5468.03i	−0.0156486	+	0.474762i
$511$		−	8178.48i		−	0.708013i
$512$	8548.21	+	7819.58i	0.737854	+	0.674960i
$513$	772.657	−	1960.18i	0.0664983	−	0.168702i
$514$	−4236.88	+	9204.54i	−0.363582	+	0.789873i
$515$	1373.15	−	1373.15i	0.117492	−	0.117492i
$516$	−11629.4	−	5824.76i	−0.992165	−	0.496940i
$517$	15421.3	+	15421.3i	1.31186	+	1.31186i
$518$	−1442.93	−	3904.26i	−0.122391	−	0.331165i
$519$	−2440.99	−	5798.69i	−0.206450	−	0.490432i
$520$	−12979.1	+	3684.87i	−1.09456	+	0.310754i
$521$	1803.41			0.151649			0.0758244	−	0.997121i	$-0.475841\pi$
$521$	1803.41			0.151649			0.0758244	+	0.997121i	$0.475841\pi$
$522$	4634.86	−	10381.3i	0.388625	−	0.870457i
$523$	−15074.6	+	15074.6i	−1.26036	+	1.26036i	−0.309440	+	0.950919i	$0.600141\pi$
$523$	−15074.6	+	15074.6i	−1.26036	+	1.26036i	−0.950919	+	0.309440i	$0.899859\pi$
$524$	17089.6	+	1325.04i	1.42474	+	0.110467i
$525$	2205.51	−	5412.25i	0.183345	−	0.449924i
$526$	2597.40	−	5642.81i	0.215308	−	0.467753i
$527$	−131.482			−0.0108680
$528$	18469.4	−	4591.86i	1.52231	−	0.378476i
$529$	9313.07			0.765437
$530$	−4382.69	+	9521.30i	−0.359192	+	0.780337i
$531$	−195.297	−	17007.7i	−0.0159608	−	1.38996i
$532$	−229.150	+	2955.43i	−0.0186746	+	0.240853i
$533$	7214.57	−	7214.57i	0.586300	−	0.586300i
$534$	1898.34	+	2027.75i	0.153838	+	0.164324i
$535$	−4227.02			−0.341589
$536$	−8919.29	+	15991.7i	−0.718758	+	1.28869i
$537$	−18332.0	+	7716.96i	−1.47315	+	0.620133i
$538$	−88.9898	−	240.787i	−0.00713127	−	0.0192957i
$539$	10754.0	+	10754.0i	0.859386	+	0.859386i
$540$	3265.09	+	9453.95i	0.260198	+	0.753395i
$541$	13914.7	−	13914.7i	1.10580	−	1.10580i	0.112106	−	0.993696i	$-0.464240\pi$
$541$	13914.7	−	13914.7i	1.10580	−	1.10580i	0.993696	−	0.112106i	$-0.0357595\pi$
$542$	4289.98	−	9319.89i	0.339982	−	0.738604i
$543$	444.335	+	1055.54i	0.0351165	+	0.0834208i
$544$	−6299.45	−	4182.80i	−0.496483	−	0.329662i
$545$			13014.8i			1.02292i
$546$	−24249.7	−	799.293i	−1.90072	−	0.0626494i
$547$	−2457.00	−	2457.00i	−0.192054	−	0.192054i	0.604529	−	0.796583i	$-0.293361\pi$
$547$	−2457.00	−	2457.00i	−0.192054	−	0.192054i	−0.796583	+	0.604529i	$0.793361\pi$
$548$	−12810.8	−	14964.3i	−0.998628	−	1.16650i
$549$	834.158	−	9.57855i	0.0648470	−	0.000744631i
$550$	6921.42	−	2558.00i	0.536600	−	0.198316i
$551$			2235.76i			0.172862i
$552$	−6242.95	−	691.589i	−0.481372	−	0.0533261i
$553$			10546.7i			0.811015i
$554$	4820.11	+	13042.2i	0.369651	+	1.00020i
$555$	2557.67	+	1042.26i	0.195616	+	0.0797143i
$556$	8822.26	+	684.036i	0.672926	+	0.0521755i
$557$	13996.0	+	13996.0i	1.06468	+	1.06468i	0.997758	+	0.0669265i	$0.0213193\pi$
$557$	13996.0	+	13996.0i	1.06468	+	1.06468i	0.0669265	+	0.997758i	$0.478681\pi$
$558$	−224.494	+	85.9106i	−0.0170315	+	0.00651771i
$559$			20935.7i			1.58406i
$560$	−8297.51	−	11365.0i	−0.626131	−	0.857607i
$561$	−11448.9	+	4819.48i	−0.861627	+	0.362707i
$562$	14382.7	+	6620.41i	1.07953	+	0.496913i
$563$	10933.7	−	10933.7i	0.818474	−	0.818474i	−0.167413	−	0.985887i	$-0.553541\pi$
$563$	10933.7	−	10933.7i	0.818474	−	0.818474i	0.985887	+	0.167413i	$0.0535413\pi$
$564$	−4999.12	−	15032.0i	−0.373229	−	1.12227i
$565$	6365.84	+	6365.84i	0.474005	+	0.474005i
$566$	−888.464	+	328.357i	−0.0659805	+	0.0243849i
$567$	413.020	+	17981.8i	0.0305912	+	1.33186i
$568$	13330.3	−	3784.58i	0.984733	−	0.279573i
$569$	4515.04			0.332654			0.166327	−	0.986071i	$-0.446809\pi$
$569$	4515.04			0.332654			0.166327	+	0.986071i	$0.446809\pi$
$570$	−1344.25	−	1435.88i	−0.0987796	−	0.105513i
$571$	6425.75	−	6425.75i	0.470945	−	0.470945i	−0.431276	−	0.902220i	$-0.641936\pi$
$571$	6425.75	−	6425.75i	0.470945	−	0.470945i	0.902220	+	0.431276i	$0.141936\pi$
$572$	−19922.1	−	23271.0i	−1.45626	−	1.70107i
$573$	5741.98	+	2339.88i	0.418629	+	0.170593i
$574$	9666.38	+	4449.47i	0.702904	+	0.323549i
$575$	−2435.33			−0.176627
$576$	−13488.8	−	3025.69i	−0.975753	−	0.218873i
$577$	962.109			0.0694161			0.0347081	−	0.999397i	$-0.488950\pi$
$577$	962.109			0.0694161			0.0347081	+	0.999397i	$0.488950\pi$
$578$	−8139.65	−	3746.71i	−0.585753	−	0.269624i
$579$	24293.2	+	9899.54i	1.74368	+	0.710554i
$580$	−6902.14	−	8062.42i	−0.494130	−	0.577196i
$581$	6050.66	−	6050.66i	0.432054	−	0.432054i
$582$	14809.8	+	15819.4i	1.05479	+	1.12669i
$583$	−23798.4			−1.69062
$584$	−7215.31	+	2048.48i	−0.511253	+	0.145149i
$585$	11252.5	−	11513.9i	0.795269	−	0.813745i
$586$	11545.2	−	4266.85i	0.813869	−	0.300788i
$587$	−3139.23	−	3139.23i	−0.220732	−	0.220732i	0.588074	−	0.808807i	$-0.299886\pi$
$587$	−3139.23	−	3139.23i	−0.220732	−	0.220732i	−0.808807	+	0.588074i	$0.799886\pi$
$588$	−3486.12	−	10482.5i	−0.244499	−	0.735189i
$589$	33.4250	−	33.4250i	0.00233829	−	0.00233829i
$590$	−14423.5	−	6639.21i	−1.00645	−	0.463274i
$591$	3686.09	−	1551.68i	0.256557	−	0.107999i
$592$	−3083.05	+	2250.91i	−0.214041	+	0.156270i
$593$			28278.3i			1.95827i	0.203219	+	0.979133i	$0.434860\pi$
$593$			28278.3i			1.95827i	−0.203219	+	0.979133i	$0.565140\pi$
$594$	−16398.9	+	15709.6i	−1.13276	+	1.08514i
$595$	6494.47	+	6494.47i	0.447475	+	0.447475i
$596$	28566.6	+	2214.92i	1.96331	+	0.152226i
$597$	−2930.50	−	1194.19i	−0.200900	−	0.0818675i
$598$	3504.83	+	9483.34i	0.239671	+	0.648499i
$599$			10012.2i			0.682950i	0.939891	+	0.341475i	$0.110927\pi$
$599$			10012.2i			0.682950i	−0.939891	+	0.341475i	$0.889073\pi$
$600$	−5327.27	−	590.152i	−0.362475	−	0.0401547i
$601$			10154.9i			0.689229i	0.938744	+	0.344614i	$0.111990\pi$
$601$			10154.9i			0.689229i	−0.938744	+	0.344614i	$0.888010\pi$
$602$	−20481.2	+	7569.39i	−1.38663	+	0.512467i
$603$	−250.877	−	21847.9i	−0.0169428	−	1.47548i
$604$	2974.17	+	3474.15i	0.200360	+	0.234041i
$605$	−12250.6	−	12250.6i	−0.823238	−	0.823238i
$606$	−4635.27	−	152.783i	−0.310718	−	0.0102415i
$607$		−	25322.5i		−	1.69326i	−0.532183	−	0.846629i	$-0.678628\pi$
$607$		−	25322.5i		−	1.69326i	0.532183	−	0.846629i	$-0.321372\pi$
$608$	2664.77	−	538.089i	0.177748	−	0.0358921i
$609$	−7405.00	−	17590.9i	−0.492719	−	1.17048i
$610$	325.627	−	707.417i	0.0216135	−	0.0469549i
$611$	−18030.3	+	18030.3i	−1.19383	+	1.19383i
$612$	9003.32	+	594.162i	0.594670	+	0.0392444i
$613$	13323.5	+	13323.5i	0.877863	+	0.877863i	0.993313	−	0.115451i	$-0.0368312\pi$
$613$	13323.5	+	13323.5i	0.877863	+	0.877863i	−0.115451	+	0.993313i	$0.536831\pi$
$614$	−2426.52	−	6565.65i	−0.159489	−	0.431544i
$615$	−6507.77	+	2739.49i	−0.426697	+	0.179621i
$616$	15562.9	−	27903.2i	1.01793	−	1.82509i
$617$	−2727.73			−0.177981			−0.0889906	−	0.996032i	$-0.528364\pi$
$617$	−2727.73			−0.177981			−0.0889906	+	0.996032i	$0.528364\pi$
$618$	−2188.80	−	2338.01i	−0.142470	−	0.152182i
$619$	−9506.19	+	9506.19i	−0.617263	+	0.617263i	−0.944829	−	0.327565i	$-0.893772\pi$
$619$	−9506.19	+	9506.19i	−0.617263	+	0.617263i	0.327565	+	0.944829i	$0.393772\pi$
$620$	−17.3463	+	223.722i	−0.00112362	+	0.0144918i
$621$	6873.98	−	2987.01i	0.444192	−	0.193019i
$622$	−8365.53	+	18173.9i	−0.539272	+	1.17156i
$623$	4663.08			0.299876
$624$	5368.72	+	21594.1i	0.344424	+	1.38534i
$625$	7848.55			0.502307
$626$	10699.2	−	23243.8i	0.683108	−	1.48404i
$627$	1685.31	−	4135.70i	0.107344	−	0.263419i
$628$	−18780.4	−	1456.14i	−1.19334	−	0.0925261i
$629$	1761.79	−	1761.79i	0.111681	−	0.111681i
$630$	15332.3	+	6845.25i	0.969606	+	0.432891i
$631$	6939.01			0.437778			0.218889	−	0.975750i	$-0.429757\pi$
$631$	6939.01			0.437778			0.218889	+	0.975750i	$0.429757\pi$
$632$	9304.63	−	2641.66i	0.585630	−	0.166265i
$633$	1162.67	+	2761.98i	0.0730049	+	0.173426i
$634$	−6208.56	−	16799.0i	−0.388917	−	1.05233i
$635$	9479.23	+	9479.23i	0.592397	+	0.592397i
$636$	15456.1	+	7741.41i	0.963640	+	0.482652i
$637$	−12573.4	+	12573.4i	−0.782067	+	0.782067i
$638$	10076.0	−	21889.9i	0.625254	−	1.35835i
$639$	−11557.0	+	11825.5i	−0.715472	+	0.732094i
$640$	−7948.29	+	10166.9i	−0.490912	+	0.627943i
$641$			25374.4i			1.56354i	0.623567	+	0.781770i	$0.285683\pi$
$641$			25374.4i			1.56354i	−0.623567	+	0.781770i	$0.714317\pi$
$642$	−229.656	+	6967.52i	−0.0141181	+	0.428327i
$643$	−17483.4	−	17483.4i	−1.07228	−	1.07228i	−0.997175	−	0.0751092i	$-0.976069\pi$
$643$	−17483.4	−	17483.4i	−1.07228	−	1.07228i	−0.0751092	−	0.997175i	$-0.523931\pi$
$644$	−8010.24	+	6857.47i	−0.490136	+	0.419600i
$645$	5467.54	−	13417.2i	0.333774	−	0.819070i
$646$	−1664.37	+	615.113i	−0.101368	+	0.0374633i
$647$		−	23409.6i		−	1.42245i	−0.702964	−	0.711225i	$-0.748141\pi$
$647$		−	23409.6i		−	1.42245i	0.702964	−	0.711225i	$-0.251859\pi$
$648$	15760.6	−	4868.31i	0.955457	−	0.295132i
$649$		−	36051.6i		−	2.18050i
$650$	2990.77	+	8092.39i	0.180473	+	0.488322i
$651$	−152.281	+	373.692i	−0.00916798	+	0.0224979i
$652$	−1655.76	+	21354.9i	−0.0994547	+	1.28270i
$653$	−9012.83	−	9012.83i	−0.540122	−	0.540122i	0.383443	−	0.923565i	$-0.374738\pi$
$653$	−9012.83	−	9012.83i	−0.540122	−	0.540122i	−0.923565	+	0.383443i	$0.874738\pi$
$654$	21452.7	+	707.100i	1.28267	+	0.0422780i
$655$			19093.7i			1.13901i
$656$	1504.30	−	9642.46i	0.0895323	−	0.573894i
$657$	6255.44	−	6400.76i	0.371458	−	0.380088i
$658$	−24157.8	−	11119.9i	−1.43126	−	0.658814i
$659$	358.576	−	358.576i	0.0211960	−	0.0211960i	−0.696429	−	0.717625i	$-0.745229\pi$
$659$	358.576	−	358.576i	0.0211960	−	0.0211960i	0.717625	+	0.696429i	$0.245229\pi$
$660$	6690.10	+	20116.6i	0.394563	+	1.18642i
$661$	−14598.1	−	14598.1i	−0.859004	−	0.859004i	0.132217	−	0.991221i	$-0.457790\pi$
$661$	−14598.1	−	14598.1i	−0.859004	−	0.859004i	−0.991221	+	0.132217i	$0.957790\pi$
$662$	−3980.23	+	1471.01i	−0.233680	+	0.0863630i
$663$	−5634.84	−	13385.8i	−0.330074	−	0.784106i
$664$	−6853.60	−	3822.56i	−0.400559	−	0.223410i
$665$	−3302.01			−0.192551
$666$	1856.95	−	4159.26i	0.108041	−	0.241994i
$667$	−5623.67	+	5623.67i	−0.326461	+	0.326461i
$668$	−14837.0	+	12701.8i	−0.859374	+	0.735699i
$669$	−5798.97	+	14230.5i	−0.335129	+	0.822395i
$670$	−18528.3	−	8528.66i	−1.06838	−	0.491777i
$671$	1768.19			0.101729
$672$	−19184.1	+	13059.6i	−1.10125	+	0.749678i
$673$	−26625.5			−1.52502			−0.762509	−	0.646978i	$-0.776033\pi$
$673$	−26625.5			−1.52502			−0.762509	+	0.646978i	$0.776033\pi$
$674$	326.689	+	150.376i	0.0186700	+	0.00859386i
$675$	5865.75	−	2548.90i	0.334478	−	0.145344i
$676$	13856.4	−	11862.3i	0.788371	−	0.674915i
$677$	5301.22	−	5301.22i	0.300949	−	0.300949i	−0.540436	−	0.841385i	$-0.681741\pi$
$677$	5301.22	−	5301.22i	0.300949	−	0.300949i	0.841385	+	0.540436i	$0.181741\pi$
$678$	10838.9	−	10147.2i	0.613959	−	0.574777i
$679$	36378.8			2.05610
$680$	4102.94	−	7356.31i	0.231383	−	0.414856i
$681$	1726.28	−	726.688i	0.0971384	−	0.0408910i
$682$	−477.894	+	176.619i	−0.0268321	+	0.00991656i
$683$	−4314.17	−	4314.17i	−0.241694	−	0.241694i	0.575857	−	0.817551i	$-0.304669\pi$
$683$	−4314.17	−	4314.17i	−0.241694	−	0.241694i	−0.817551	+	0.575857i	$0.804669\pi$
$684$	−2439.85	+	2137.75i	−0.136389	+	0.119502i
$685$	15516.1	−	15516.1i	0.865461	−	0.865461i
$686$	4897.09	+	2254.15i	0.272553	+	0.125457i
$687$	−997.129	−	2368.73i	−0.0553753	−	0.131547i
$688$	11807.9	+	16173.2i	0.654321	+	0.896218i
$689$		−	27824.7i		−	1.53851i
$690$	230.494	−	6992.93i	0.0127170	−	0.385821i
$691$	−8509.21	−	8509.21i	−0.468460	−	0.468460i	0.432955	−	0.901415i	$-0.357471\pi$
$691$	−8509.21	−	8509.21i	−0.468460	−	0.468460i	−0.901415	+	0.432955i	$0.857471\pi$
$692$	−748.793	+	9657.45i	−0.0411341	+	0.530522i
$693$	437.744	+	38121.4i	0.0239950	+	2.08963i
$694$	−3704.96	−	10024.8i	−0.202649	−	0.548326i
$695$			9856.85i			0.537974i
$696$	−13664.5	+	10939.0i	−0.744184	+	0.595748i
$697$			6369.75i			0.346157i
$698$	26806.1	−	9906.95i	1.45362	−	0.537226i
$699$	−8995.56	−	3665.72i	−0.486757	−	0.198355i
$700$	−6835.35	+	5851.66i	−0.369074	+	0.315960i
$701$	−2086.28	−	2086.28i	−0.112408	−	0.112408i	0.648666	−	0.761073i	$-0.275327\pi$
$701$	−2086.28	−	2086.28i	−0.112408	−	0.112408i	−0.761073	+	0.648666i	$0.775327\pi$
$702$	−18367.3	−	19173.3i	−0.987507	−	1.03084i
$703$			895.754i			0.0480569i
$704$	−28515.2	−	6741.08i	−1.52657	−	0.360886i
$705$	16263.9	−	6846.40i	0.868845	−	0.365745i
$706$	−5193.43	+	11282.6i	−0.276852	+	0.601455i
$707$	−5505.39	+	5505.39i	−0.292859	+	0.292859i
$708$	−11727.2	+	23414.0i	−0.622509	+	1.24287i
$709$	−19902.7	−	19902.7i	−1.05425	−	1.05425i	−0.998442	−	0.0558039i	$-0.982228\pi$
$709$	−19902.7	−	19902.7i	−1.05425	−	1.05425i	−0.0558039	−	0.998442i	$-0.517772\pi$
$710$	5351.02	+	14478.7i	0.282845	+	0.765319i
$711$	−8066.81	+	8254.22i	−0.425498	+	0.435383i
$712$	−1167.97	−	4113.92i	−0.0614770	−	0.216539i
$713$	168.149			0.00883203
$714$	11057.9	−	10352.2i	0.579595	−	0.542606i
$715$	24129.2	−	24129.2i	1.26207	−	1.26207i
$716$	30531.1	+	2367.23i	1.59358	+	0.123558i
$717$	−10204.4	−	4158.33i	−0.531507	−	0.216591i
$718$	887.190	−	1927.40i	0.0461137	−	0.100181i
$719$	−6725.66			−0.348852			−0.174426	−	0.984670i	$-0.555807\pi$
$719$	−6725.66			−0.348852			−0.174426	+	0.984670i	$0.555807\pi$
$720$	2198.79	−	15241.1i	0.113811	−	0.788894i
$721$	−5376.57			−0.277717
$722$	−7845.12	+	17043.4i	−0.404384	+	0.878516i
$723$	−14899.1	−	6071.42i	−0.766393	−	0.312308i
$724$	136.303	−	1757.95i	0.00699677	−	0.0902399i
$725$	−4798.83	+	4798.83i	−0.245826	+	0.245826i
$726$	−20858.7	+	19527.5i	−1.06631	+	0.998256i
$727$	14601.8			0.744911			0.372456	−	0.928050i	$-0.378516\pi$
$727$	14601.8			0.744911			0.372456	+	0.928050i	$0.378516\pi$
$728$	32623.9	+	18195.8i	1.66088	+	0.926348i
$729$	−13430.4	+	14389.1i	−0.682334	+	0.731040i
$730$	−2896.34	−	7836.89i	−0.146847	−	0.397337i
$731$	−9242.08	−	9242.08i	−0.467621	−	0.467621i
$732$	−1148.37	−	575.175i	−0.0579847	−	0.0290424i
$733$	−16119.5	+	16119.5i	−0.812259	+	0.812259i	−0.984972	−	0.172713i	$-0.944747\pi$
$733$	−16119.5	+	16119.5i	−0.812259	+	0.812259i	0.172713	+	0.984972i	$0.444747\pi$
$734$	−10494.3	+	22798.6i	−0.527725	+	1.14647i
$735$	11341.6	−	4774.32i	0.569173	−	0.239597i
$736$	8056.22	+	5349.28i	0.403473	+	0.267904i
$737$		−	46311.5i		−	2.31466i
$738$	4162.01	+	10875.8i	0.207596	+	0.542471i
$739$	26403.6	+	26403.6i	1.31431	+	1.31431i	0.918208	+	0.396099i	$0.129636\pi$
$739$	26403.6	+	26403.6i	1.31431	+	1.31431i	0.396099	+	0.918208i	$0.370364\pi$
$740$	−2765.33	−	3230.19i	−0.137372	−	0.160465i
$741$	4835.38	+	1970.43i	0.239719	+	0.0976864i
$742$	27220.5	−	10060.1i	1.34676	−	0.497734i
$743$			24491.2i			1.20928i	0.796499	+	0.604640i	$0.206683\pi$
$743$			24491.2i			1.20928i	−0.796499	+	0.604640i	$0.793317\pi$
$744$	367.825	+	40.7474i	0.0181252	+	0.00200789i
$745$			31916.7i			1.56958i
$746$	−357.522	−	967.379i	−0.0175467	−	0.0474775i
$747$	9363.40	−	107.519i	0.458620	−	0.00526628i
$748$	19067.6	+	1478.41i	0.932059	+	0.0722674i
$749$	8275.45	+	8275.45i	0.403709	+	0.403709i
$750$	736.008	−	22329.7i	0.0358336	−	1.08715i
$751$		−	15477.7i		−	0.752050i	−0.926609	−	0.376025i	$-0.877291\pi$
$751$		−	15477.7i		−	0.752050i	0.926609	−	0.376025i	$-0.122709\pi$
$752$	−3759.49	+	24098.0i	−0.182306	+	1.16857i
$753$	6825.38	+	16214.0i	0.330320	+	0.784690i
$754$	25593.2	+	11780.7i	1.23614	+	0.569000i
$755$	−3602.26	+	3602.26i	−0.173642	+	0.173642i
$756$	12116.2	−	24900.7i	0.582888	−	1.19792i
$757$	−11191.6	−	11191.6i	−0.537340	−	0.537340i	0.385407	−	0.922747i	$-0.374061\pi$
$757$	−11191.6	−	11191.6i	−0.537340	−	0.537340i	−0.922747	+	0.385407i	$0.874061\pi$
$758$	−13956.9	+	5158.17i	−0.668783	+	0.247168i
$759$	14641.7	−	6163.52i	0.700212	−	0.294758i
$760$	827.062	+	2913.14i	0.0394746	+	0.139040i
$761$	−10016.9			−0.477153			−0.238576	−	0.971124i	$-0.576681\pi$
$761$	−10016.9			−0.477153			−0.238576	+	0.971124i	$0.576681\pi$
$762$	16139.9	−	15109.9i	0.767306	−	0.718338i
$763$	25479.7	−	25479.7i	1.20895	−	1.20895i
$764$	−6208.17	−	7251.79i	−0.293984	−	0.343404i
$765$	115.405	+	10050.2i	0.00545424	+	0.474988i
$766$	−23987.1	−	11041.3i	−1.13145	−	0.520809i
$767$	42150.8			1.98432
$768$	16326.6	+	13653.8i	0.767105	+	0.641521i
$769$	1463.91			0.0686475			0.0343238	−	0.999411i	$-0.489072\pi$
$769$	1463.91			0.0686475			0.0343238	+	0.999411i	$0.489072\pi$
$770$	32329.3	+	14881.3i	1.51307	+	0.696473i
$771$	−7024.89	+	17238.9i	−0.328139	+	0.805243i
$772$	−26265.5	−	30680.8i	−1.22450	−	1.43035i
$773$	−26695.6	+	26695.6i	−1.24214	+	1.24214i	−0.283030	+	0.959111i	$0.591340\pi$
$773$	−26695.6	+	26695.6i	−1.24214	+	1.24214i	−0.959111	+	0.283030i	$0.908660\pi$
$774$	−21818.8	−	9741.26i	−1.01326	−	0.452380i
$775$	143.486			0.00665055
$776$	−9111.89	−	32094.6i	−0.421518	−	1.48470i
$777$	−2966.80	−	7047.76i	−0.136980	−	0.325402i
$778$	−21752.7	+	8039.33i	−1.00241	+	0.370468i
$779$	−1619.30	−	1619.30i	−0.0744768	−	0.0744768i
$780$	−23519.9	+	7821.94i	−1.07968	+	0.359064i
$781$	−24782.2	+	24782.2i	−1.13544	+	1.13544i
$782$	−5733.63	−	2639.21i	−0.262192	−	0.120688i
$783$	7659.27	−	19431.1i	0.349579	−	0.886860i
$784$	−2621.67	+	16804.7i	−0.119427	+	0.765519i
$785$		−	20982.8i		−	0.954022i
$786$	31472.7	+	1037.37i	1.42824	+	0.0470760i
$787$	14529.3	+	14529.3i	0.658087	+	0.658087i	0.954927	−	0.296840i	$-0.0959328\pi$
$787$	14529.3	+	14529.3i	0.658087	+	0.658087i	−0.296840	+	0.954927i	$0.595933\pi$
$788$	−6139.01	−	475.989i	−0.277529	−	0.0215183i
$789$	4306.58	−	10568.2i	0.194320	−	0.476855i
$790$	3735.03	+	10106.2i	0.168211	+	0.455142i
$791$		−	24925.5i		−	1.12041i
$792$	33522.3	−	9934.54i	1.50399	−	0.445718i
$793$			2067.33i			0.0925763i
$794$	2191.32	−	809.864i	0.0979433	−	0.0361977i
$795$	−7266.64	+	17832.1i	−0.324177	+	0.795521i
$796$	3168.43	+	3701.05i	0.141083	+	0.164799i
$797$	18417.2	+	18417.2i	0.818532	+	0.818532i	0.985895	−	0.167363i	$-0.0535253\pi$
$797$	18417.2	+	18417.2i	0.818532	+	0.818532i	−0.167363	+	0.985895i	$0.553525\pi$
$798$	−179.400	+	5442.81i	−0.00795826	+	0.241445i
$799$		−	15919.0i		−	0.704848i
$800$	6874.59	+	4564.69i	0.303817	+	0.201733i
$801$	3649.49	+	3566.63i	0.160984	+	0.157329i
$802$	1959.12	−	4256.15i	0.0862581	−	0.187394i
$803$	13413.8	−	13413.8i	0.589494	−	0.589494i
$804$	−15064.7	+	30077.4i	−0.660810	+	1.31934i
$805$	−8305.63	−	8305.63i	−0.363646	−	0.363646i
$806$	−206.500	−	558.744i	−0.00902437	−	0.0244180i
$807$	−182.971	−	434.657i	−0.00798128	−	0.0189599i
$808$	6235.97	+	3478.08i	0.271511	+	0.151434i
$809$	14088.2			0.612253			0.306127	−	0.951991i	$-0.400967\pi$
$809$	14088.2			0.612253			0.306127	+	0.951991i	$0.400967\pi$
$810$	6763.87	+	17084.5i	0.293405	+	0.741094i
$811$	−16384.8	+	16384.8i	−0.709429	+	0.709429i	−0.966415	−	0.256986i	$-0.917271\pi$
$811$	−16384.8	+	16384.8i	−0.709429	+	0.709429i	0.256986	+	0.966415i	$0.417271\pi$
$812$	−2271.54	+	29296.9i	−0.0981716	+	1.26616i
$813$	7112.92	−	17454.9i	0.306840	−	0.752976i
$814$	4036.92	−	8770.13i	0.173826	−	0.377633i
$815$	−23859.2			−1.02546
$816$	−11902.7	−	7162.68i	−0.510635	−	0.307284i
$817$	4698.99			0.201220
$818$	3007.61	−	6533.96i	0.128556	−	0.279284i
$819$	−44570.8	+	511.802i	−1.90162	+	0.0218361i
$820$	10838.4	+	840.357i	0.461577	+	0.0357885i
$821$	−1002.06	+	1002.06i	−0.0425968	+	0.0425968i	−0.728084	−	0.685488i	$-0.759589\pi$
$821$	−1002.06	+	1002.06i	−0.0425968	+	0.0425968i	0.685488	+	0.728084i	$0.259589\pi$
$822$	−24732.7	−	26418.7i	−1.04945	−	1.12100i
$823$	−36539.2			−1.54760			−0.773802	−	0.633428i	$-0.781647\pi$
$823$	−36539.2			−1.54760			−0.773802	+	0.633428i	$0.781647\pi$
$824$	1346.68	+	4743.38i	0.0569343	+	0.200538i
$825$	12494.2	−	5259.50i	0.527262	−	0.221954i
$826$	15239.8	+	41235.6i	0.641961	+	1.73701i
$827$	1314.92	+	1314.92i	0.0552892	+	0.0552892i	0.734211	−	0.678922i	$-0.237552\pi$
$827$	1314.92	+	1314.92i	0.0552892	+	0.0552892i	−0.678922	+	0.734211i	$0.737552\pi$
$828$	−11514.1	−	759.859i	−0.483266	−	0.0318924i
$829$	18101.1	−	18101.1i	0.758357	−	0.758357i	−0.217667	−	0.976023i	$-0.569845\pi$
$829$	18101.1	−	18101.1i	0.758357	−	0.758357i	0.976023	+	0.217667i	$0.0698445\pi$
$830$	3655.15	−	7940.73i	0.152858	−	0.332081i
$831$	9910.59	+	23543.1i	0.413712	+	0.982791i
$832$	7881.54	−	33339.4i	0.328417	−	1.38923i
$833$		−	11101.1i		−	0.461740i
$834$	16247.3	+	535.528i	0.674580	+	0.0222348i
$835$	−15384.2	−	15384.2i	−0.637594	−	0.637594i
$836$	−5223.15	+	4471.47i	−0.216084	+	0.184987i
$837$	−405.005	+	175.990i	−0.0167252	+	0.00726777i
$838$	−13561.5	+	5012.05i	−0.559040	+	0.206609i
$839$			11658.5i			0.479734i	0.970806	+	0.239867i	$0.0771038\pi$
$839$			11658.5i			0.479734i	−0.970806	+	0.239867i	$0.922896\pi$
$840$	−16155.8	−	20181.2i	−0.663606	−	0.828950i
$841$		−	2226.09i		−	0.0912745i
$842$	−13955.0	−	37759.2i	−0.571164	−	1.54545i
$843$	26936.8	+	10976.8i	1.10054	+	0.448473i
$844$	356.658	−	4599.95i	0.0145458	−	0.187603i
$845$	14367.4	+	14367.4i	0.584915	+	0.584915i
$846$	−10401.5	−	27180.3i	−0.422708	−	1.10458i
$847$			47967.3i			1.94590i
$848$	−15693.3	−	21495.0i	−0.635509	−	0.870451i
$849$	−1603.81	+	675.133i	−0.0648322	+	0.0272915i
$850$	−4892.66	−	2252.11i	−0.197432	−	0.0908784i
$851$	−2253.11	+	2253.11i	−0.0907587	+	0.0907587i
$852$	24156.4	−	8033.60i	0.971344	−	0.323036i
$853$	8293.73	+	8293.73i	0.332910	+	0.332910i	0.853690	−	0.520781i	$-0.174359\pi$
$853$	8293.73	+	8293.73i	0.332910	+	0.332910i	−0.520781	+	0.853690i	$0.674359\pi$
$854$	−2022.44	+	747.450i	−0.0810381	+	0.0299499i
$855$	−2584.27	−	2525.60i	−0.103369	−	0.101022i
$856$	5228.09	−	9373.63i	0.208753	−	0.374280i
$857$	−5209.55			−0.207649			−0.103824	−	0.994596i	$-0.533108\pi$
$857$	−5209.55			−0.207649			−0.103824	+	0.994596i	$0.533108\pi$
$858$	−38461.9	−	41083.8i	−1.53038	−	1.63471i
$859$	−21529.9	+	21529.9i	−0.855168	+	0.855168i	−0.990764	−	0.135596i	$-0.956705\pi$
$859$	−21529.9	+	21529.9i	−0.855168	+	0.855168i	0.135596	+	0.990764i	$0.456705\pi$
$860$	−16945.1	+	14506.5i	−0.671887	+	0.575194i
$861$	18103.8	+	7377.37i	0.716581	+	0.292009i
$862$	−8980.62	−	4133.81i	−0.354850	−	0.163339i
$863$	31954.7			1.26043			0.630215	−	0.776420i	$-0.282967\pi$
$863$	31954.7			1.26043			0.630215	+	0.776420i	$0.282967\pi$
$864$	−25003.0	−	4452.40i	−0.984512	−	0.175317i
$865$	−10790.0			−0.424128
$866$	−41292.0	−	19006.8i	−1.62027	−	0.745818i
$867$	−15244.5	−	6212.17i	−0.597150	−	0.243341i
$868$	471.952	−	404.032i	0.0184552	−	0.0157992i
$869$	−17298.0	+	17298.0i	−0.675254	+	0.675254i
$870$	−13325.4	−	14233.8i	−0.519280	−	0.554679i
$871$	54146.5			2.10641
$872$	−28861.0	−	16097.0i	−1.12082	−	0.625131i
$873$	28471.4	+	27824.9i	1.10379	+	1.07873i
$874$	2128.52	−	786.654i	0.0823778	−	0.0304450i
$875$	−26521.4	−	26521.4i	−1.02467	−	1.02467i
$876$	−13075.1	+	4348.35i	−0.504301	+	0.167713i
$877$	−11937.5	+	11937.5i	−0.459636	+	0.459636i	−0.898536	−	0.438900i	$-0.855368\pi$
$877$	−11937.5	+	11937.5i	−0.459636	+	0.459636i	0.438900	+	0.898536i	$0.355368\pi$
$878$	6552.89	+	3016.32i	0.251879	+	0.115941i
$879$	20840.8	−	8773.04i	0.799706	−	0.336641i
$880$	5031.15	−	32249.3i	0.192727	−	1.23537i
$881$		−	30514.2i		−	1.16691i	−0.812144	−	0.583457i	$-0.801700\pi$
$881$		−	30514.2i		−	1.16691i	0.812144	−	0.583457i	$-0.198300\pi$
$882$	−7253.46	−	18954.1i	−0.276912	−	0.723603i
$883$	3179.05	+	3179.05i	0.121159	+	0.121159i	0.765087	−	0.643927i	$-0.222696\pi$
$883$	3179.05	+	3179.05i	0.121159	+	0.121159i	−0.643927	+	0.765087i	$0.722696\pi$
$884$	−1728.53	+	22293.5i	−0.0657655	+	0.848202i
$885$	−27013.3	−	11008.0i	−1.02604	−	0.418114i
$886$	8478.96	+	22942.3i	0.321508	+	0.869933i
$887$		−	24947.8i		−	0.944380i	−0.881497	−	0.472190i	$-0.843464\pi$
$887$		−	24947.8i		−	0.944380i	0.881497	−	0.472190i	$-0.156536\pi$
$888$	−5474.66	+	4382.67i	−0.206889	+	0.165623i
$889$		−	37115.9i		−	1.40026i
$890$	4468.32	−	1651.39i	0.168290	−	0.0621965i
$891$	−28815.2	+	30170.0i	−1.08344	+	1.13438i
$892$	17972.3	−	15385.8i	0.674614	−	0.577529i
$893$	4046.88	+	4046.88i	0.151650	+	0.151650i
$894$	52609.2	+	1734.05i	1.96814	+	0.0648717i
$895$			34111.5i			1.27399i
$896$	35465.1	−	4343.57i	1.32233	−	0.161951i
$897$	7206.27	+	17118.8i	0.268239	+	0.637214i
$898$	−8791.89	+	19100.2i	−0.326714	+	0.709780i
$899$	331.338	−	331.338i	0.0122923	−	0.0122923i
$900$	−9825.33	−	648.408i	−0.363901	−	0.0240151i
$901$	12283.2	+	12283.2i	0.454176	+	0.454176i
$902$	8556.46	+	23151.9i	0.315852	+	0.854629i
$903$	−36971.5	+	15563.4i	−1.36250	+	0.573551i
$904$	−21990.0	+	6243.13i	−0.809046	+	0.229694i
$905$	1964.11			0.0721427
$906$	5742.00	+	6133.43i	0.210558	+	0.224911i
$907$	19465.8	−	19465.8i	0.712626	−	0.712626i	−0.254458	−	0.967084i	$-0.581897\pi$
$907$	19465.8	−	19465.8i	0.712626	−	0.712626i	0.967084	+	0.254458i	$0.0818970\pi$
$908$	−2875.04	−	222.917i	−0.105079	−	0.00814731i
$909$	−8519.59	+	97.8296i	−0.310866	+	0.00356964i
$910$	−17398.9	+	37798.8i	−0.633811	+	1.37694i
$911$	−4256.52			−0.154802			−0.0774010	−	0.997000i	$-0.524662\pi$
$911$	−4256.52			−0.154802			−0.0774010	+	0.997000i	$0.524662\pi$
$912$	4846.75	−	1205.00i	0.175978	−	0.0437517i
$913$	19847.8			0.719460
$914$	−1539.14	+	3343.76i	−0.0557006	+	0.121008i
$915$	539.900	−	1324.90i	0.0195066	−	0.0478686i
$916$	−305.877	+	3945.00i	−0.0110332	+	0.142300i
$917$	37380.7	−	37380.7i	1.34615	−	1.34615i
$918$	16572.3	+	355.806i	0.595826	+	0.0127923i
$919$	−37455.2			−1.34443			−0.672216	−	0.740355i	$-0.734657\pi$
$919$	−37455.2			−1.34443			−0.672216	+	0.740355i	$0.734657\pi$
$920$	−5247.16	+	9407.82i	−0.188037	+	0.337138i
$921$	−4989.16	−	11852.0i	−0.178500	−	0.424034i
$922$	15590.0	+	42183.2i	0.556864	+	1.50676i
$923$	−28974.8	−	28974.8i	−1.03328	−	1.03328i
$924$	26285.7	−	52480.8i	0.935863	−	1.86850i
$925$	−1922.64	+	1922.64i	−0.0683416	+	0.0683416i
$926$	−9253.36	+	20102.7i	−0.328385	+	0.713409i
$927$	−4207.89	−	4112.35i	−0.149089	−	0.145704i
$928$	26415.6	−	5334.02i	0.934411	−	0.188683i
$929$			51223.8i			1.80904i	0.426429	+	0.904521i	$0.359771\pi$
$929$			51223.8i			1.80904i	−0.426429	+	0.904521i	$0.640229\pi$
$930$	−13.5804	+	412.013i	−0.000478836	+	0.0145274i
$931$	2822.08	+	2822.08i	0.0993448	+	0.0993448i
$932$	9725.90	+	11360.9i	0.341827	+	0.399289i
$933$	−13870.3	+	34037.3i	−0.486703	+	1.19435i
$934$	28115.7	−	10391.0i	0.984984	−	0.364029i
$935$			21303.7i			0.745138i
$936$	11615.3	+	39193.6i	0.405617	+	1.36868i
$937$		−	30708.1i		−	1.07064i	−0.844650	−	0.535320i	$-0.820191\pi$
$937$		−	30708.1i		−	1.07064i	0.844650	−	0.535320i	$-0.179809\pi$
$938$	19576.9	+	52970.8i	0.681458	+	1.84388i
$939$	17739.6	−	43532.4i	0.616518	−	1.51292i
$940$	−27086.8	−	2100.18i	−0.939867	−	0.0728728i
$941$	−817.247	−	817.247i	−0.0283119	−	0.0283119i	0.692809	−	0.721121i	$-0.256373\pi$
$941$	−817.247	−	817.247i	−0.0283119	−	0.0283119i	−0.721121	+	0.692809i	$0.756373\pi$
$942$	−34586.5	−	1140.00i	−1.19627	−	0.0394303i
$943$		−	8146.12i		−	0.281309i
$944$	32562.2	−	23773.4i	1.12268	−	0.819658i
$945$	28697.9	+	11312.0i	0.987877	+	0.389397i
$946$	−46006.8	−	21177.1i	−1.58119	−	0.727829i
$947$	18142.1	−	18142.1i	0.622535	−	0.622535i	−0.323644	−	0.946179i	$-0.604908\pi$
$947$	18142.1	−	18142.1i	0.622535	−	0.622535i	0.946179	+	0.323644i	$0.104908\pi$
$948$	16861.3	−	5607.49i	0.577668	−	0.192113i
$949$	15683.2	+	15683.2i	0.536457	+	0.536457i
$950$	1816.32	−	671.273i	0.0620308	−	0.0229252i
$951$	−12765.4	−	30324.8i	−0.435274	−	1.03401i
$952$	−22434.4	+	6369.28i	−0.763762	+	0.216838i
$953$	−8325.23			−0.282981			−0.141490	−	0.989940i	$-0.545189\pi$
$953$	−8325.23			−0.282981			−0.141490	+	0.989940i	$0.545189\pi$
$954$	28998.4	+	12946.6i	0.984127	+	0.439374i
$955$	7519.21	−	7519.21i	0.254781	−	0.254781i
$956$	11032.9	+	12887.6i	0.373252	+	0.435997i
$957$	16706.3	−	40996.8i	0.564304	−	1.38478i
$958$	33533.8	+	15435.7i	1.13093	+	0.520570i
$959$	−60753.4			−2.04570
$960$	−13757.9	+	19308.0i	−0.462536	+	0.649128i
$961$	29781.1			0.999667
$962$	10253.9	+	4719.89i	0.343657	+	0.158186i
$963$	147.053	+	12806.3i	0.00492078	+	0.428532i
$964$	16108.7	+	18816.7i	0.538202	+	0.628676i
$965$	31812.2	−	31812.2i	1.06122	−	1.06122i
$966$	−14141.7	+	13239.2i	−0.471015	+	0.440956i
$967$	8911.71			0.296361			0.148181	−	0.988960i	$-0.452658\pi$
$967$	8911.71			0.296361			0.148181	+	0.988960i	$0.452658\pi$
$968$	42318.3	−	12014.5i	1.40513	−	0.398926i
$969$	−3004.42	+	1264.73i	−0.0996037	+	0.0419288i
$970$	34859.4	−	12883.3i	1.15388	−	0.426451i
$971$	24556.5	+	24556.5i	0.811593	+	0.811593i	0.984873	−	0.173280i	$-0.0554365\pi$
$971$	24556.5	+	24556.5i	0.811593	+	0.811593i	−0.173280	+	0.984873i	$0.555437\pi$
$972$	28528.3	−	10220.9i	0.941405	−	0.337279i
$973$	19297.2	−	19297.2i	0.635808	−	0.635808i
$974$	19235.1	+	8853.96i	0.632783	+	0.291272i
$975$	6149.30	+	14607.9i	0.201985	+	0.479824i
$976$	1165.99	+	1597.05i	0.0382402	+	0.0523773i
$977$		−	501.936i		−	0.0164364i	−0.999966	−	0.00821819i	$-0.997384\pi$
$977$		−	501.936i		−	0.0164364i	0.999966	−	0.00821819i	$-0.00261596\pi$
$978$	−1296.28	+	39327.9i	−0.0423830	+	1.28586i
$979$	7648.10	+	7648.10i	0.249678	+	0.249678i
$980$	−18888.9	−	1464.56i	−0.615699	−	0.0477383i
$981$	39429.9	−	452.769i	1.28328	−	0.0147358i
$982$	−8799.01	−	23808.2i	−0.285935	−	0.773678i
$983$			52008.6i			1.68751i	0.536732	+	0.843753i	$0.319659\pi$
$983$			52008.6i			1.68751i	−0.536732	+	0.843753i	$0.680341\pi$
$984$	1974.04	−	17819.6i	0.0639534	−	0.577305i
$985$		−	6858.94i		−	0.221872i
$986$	−16498.7	+	6097.56i	−0.532886	+	0.196943i
$987$	−45244.3	−	18437.2i	−1.45911	−	0.594592i
$988$	−5227.96	−	6106.80i	−0.168344	−	0.196643i
$989$	11819.5	+	11819.5i	0.380018	+	0.380018i
$990$	13919.9	+	36374.2i	0.446871	+	1.16772i
$991$		−	27605.3i		−	0.884876i	−0.896799	−	0.442438i	$-0.854114\pi$
$991$		−	27605.3i		−	0.884876i	0.896799	−	0.442438i	$-0.145886\pi$
$992$	−474.661	−	315.172i	−0.0151920	−	0.0100874i
$993$	−7184.91	+	3024.53i	−0.229613	+	0.0966571i
$994$	17869.7	−	38821.6i	0.570215	−	1.23878i
$995$	−3837.54	+	3837.54i	−0.122269	+	0.122269i
$996$	−12890.4	−	6456.31i	−0.410087	−	0.205398i
$997$	−3224.20	−	3224.20i	−0.102419	−	0.102419i	0.654041	−	0.756459i	$-0.273073\pi$
$997$	−3224.20	−	3224.20i	−0.102419	−	0.102419i	−0.756459	+	0.654041i	$0.773073\pi$
$998$	−10278.7	−	27812.0i	−0.326019	−	0.882137i
$999$	3068.67	−	7785.03i	0.0971856	−	0.246554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.4.k.a.11.3	✓	44
3.2	odd	2	inner	48.4.k.a.11.20	yes	44
4.3	odd	2		192.4.k.a.143.20		44
8.3	odd	2		384.4.k.a.287.3		44
8.5	even	2		384.4.k.b.287.20		44
12.11	even	2		192.4.k.a.143.14		44
16.3	odd	4	inner	48.4.k.a.35.20	yes	44
16.5	even	4		384.4.k.a.95.9		44
16.11	odd	4		384.4.k.b.95.14		44
16.13	even	4		192.4.k.a.47.14		44
24.5	odd	2		384.4.k.b.287.14		44
24.11	even	2		384.4.k.a.287.9		44
48.5	odd	4		384.4.k.a.95.3		44
48.11	even	4		384.4.k.b.95.20		44
48.29	odd	4		192.4.k.a.47.20		44
48.35	even	4	inner	48.4.k.a.35.3	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.k.a.11.3	✓	44	1.1	even	1	trivial
48.4.k.a.11.20	yes	44	3.2	odd	2	inner
48.4.k.a.35.3	yes	44	48.35	even	4	inner
48.4.k.a.35.20	yes	44	16.3	odd	4	inner
192.4.k.a.47.14		44	16.13	even	4
192.4.k.a.47.20		44	48.29	odd	4
192.4.k.a.143.14		44	12.11	even	2
192.4.k.a.143.20		44	4.3	odd	2
384.4.k.a.95.3		44	48.5	odd	4
384.4.k.a.95.9		44	16.5	even	4
384.4.k.a.287.3		44	8.3	odd	2
384.4.k.a.287.9		44	24.11	even	2
384.4.k.b.95.14		44	16.11	odd	4
384.4.k.b.95.20		44	48.11	even	4
384.4.k.b.287.14		44	24.5	odd	2
384.4.k.b.287.20		44	8.5	even	2

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	48.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.56930 - 1.18266i) q^{2} +(-4.81196 - 1.96089i) q^{3} +(5.20263 + 6.07722i) q^{4} +(-6.30133 + 6.30133i) q^{5} +(10.0443 + 10.7290i) q^{6} +24.6728 q^{7} +(-6.17986 - 21.7672i) q^{8} +(19.3098 + 18.8714i) q^{9} +O(q^{10})\)	\(q+(-2.56930 - 1.18266i) q^{2} +(-4.81196 - 1.96089i) q^{3} +(5.20263 + 6.07722i) q^{4} +(-6.30133 + 6.30133i) q^{5} +(10.0443 + 10.7290i) q^{6} +24.6728 q^{7} +(-6.17986 - 21.7672i) q^{8} +(19.3098 + 18.8714i) q^{9} +(23.6423 - 8.73769i) q^{10} +(40.4669 + 40.4669i) q^{11} +(-13.1181 - 39.4451i) q^{12} +(-47.3131 + 47.3131i) q^{13} +(-63.3920 - 29.1796i) q^{14} +(42.6779 - 17.9655i) q^{15} +(-9.86520 + 63.2351i) q^{16} -41.7727i q^{17} +(-27.2944 - 71.3233i) q^{18} +(10.6193 + 10.6193i) q^{19} +(-71.0780 - 5.51105i) q^{20} +(-118.725 - 48.3807i) q^{21} +(-56.1131 - 151.830i) q^{22} +53.4222i q^{23} +(-12.9457 + 116.861i) q^{24} +45.5866i q^{25} +(177.517 - 65.6064i) q^{26} +(-55.9134 - 128.673i) q^{27} +(128.364 + 149.942i) q^{28} +(105.268 + 105.268i) q^{29} +(-130.900 - 4.31457i) q^{30} -3.14755i q^{31} +(100.132 - 150.803i) q^{32} +(-115.374 - 274.076i) q^{33} +(-49.4029 + 107.327i) q^{34} +(-155.472 + 155.472i) q^{35} +(-14.2237 + 215.531i) q^{36} +(42.1756 + 42.1756i) q^{37} +(-14.7252 - 39.8434i) q^{38} +(320.444 - 134.893i) q^{39} +(176.103 + 98.2207i) q^{40} -152.486 q^{41} +(247.822 + 264.715i) q^{42} +(221.247 - 221.247i) q^{43} +(-35.3918 + 456.460i) q^{44} +(-240.593 + 2.76270i) q^{45} +(63.1802 - 137.258i) q^{46} +381.086 q^{47} +(171.468 - 284.940i) q^{48} +265.749 q^{49} +(53.9134 - 117.126i) q^{50} +(-81.9116 + 201.008i) q^{51} +(-533.685 - 41.3794i) q^{52} +(-294.048 + 294.048i) q^{53} +(-8.51768 + 396.726i) q^{54} -509.990 q^{55} +(-152.475 - 537.058i) q^{56} +(-30.2765 - 71.9231i) q^{57} +(-145.970 - 394.963i) q^{58} +(-445.445 - 445.445i) q^{59} +(331.218 + 165.895i) q^{60} +(21.8473 - 21.8473i) q^{61} +(-3.72249 + 8.08702i) q^{62} +(476.429 + 465.611i) q^{63} +(-435.619 + 269.036i) q^{64} -596.270i q^{65} +(-27.7080 + 840.632i) q^{66} +(-572.215 - 572.215i) q^{67} +(253.862 - 217.328i) q^{68} +(104.755 - 257.065i) q^{69} +(583.324 - 215.584i) q^{70} +612.406i q^{71} +(291.445 - 536.943i) q^{72} -331.477i q^{73} +(-58.4825 - 158.241i) q^{74} +(89.3901 - 219.361i) q^{75} +(-9.28753 + 119.785i) q^{76} +(998.433 + 998.433i) q^{77} +(-982.850 - 32.3957i) q^{78} +427.462i q^{79} +(-336.301 - 460.629i) q^{80} +(16.7398 + 728.808i) q^{81} +(391.782 + 180.339i) q^{82} +(245.236 - 245.236i) q^{83} +(-323.661 - 973.223i) q^{84} +(263.224 + 263.224i) q^{85} +(-830.109 + 306.790i) q^{86} +(-300.128 - 712.967i) q^{87} +(630.769 - 1130.93i) q^{88} +188.997 q^{89} +(621.422 + 277.441i) q^{90} +(-1167.35 + 1167.35i) q^{91} +(-324.658 + 277.936i) q^{92} +(-6.17200 + 15.1459i) q^{93} +(-979.125 - 450.695i) q^{94} -133.832 q^{95} +(-777.540 + 529.309i) q^{96} +1474.45 q^{97} +(-682.790 - 314.291i) q^{98} +(17.7419 + 1545.08i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{3} - 4 q^{4} + 28 q^{6} - 8 q^{7}+O(q^{10}) \) 44 * q - 2 * q^3 - 4 * q^4 + 28 * q^6 - 8 * q^7	\( 44 q - 2 q^{3} - 4 q^{4} + 28 q^{6} - 8 q^{7} + 56 q^{10} - 80 q^{12} - 4 q^{13} - 112 q^{16} + 52 q^{18} + 20 q^{19} - 56 q^{21} - 40 q^{22} - 120 q^{24} - 134 q^{27} - 296 q^{28} - 332 q^{30} - 4 q^{33} + 520 q^{34} - 604 q^{36} - 4 q^{37} + 596 q^{39} + 632 q^{40} + 696 q^{42} - 436 q^{43} - 252 q^{45} + 664 q^{46} + 1200 q^{48} + 972 q^{49} - 648 q^{51} + 320 q^{52} + 1592 q^{54} + 280 q^{55} - 424 q^{58} + 800 q^{60} - 916 q^{61} - 2056 q^{64} - 668 q^{66} - 1636 q^{67} + 52 q^{69} - 5192 q^{70} - 3704 q^{72} + 1454 q^{75} - 568 q^{76} - 4932 q^{78} - 4 q^{81} + 768 q^{82} - 2096 q^{84} + 736 q^{85} + 1284 q^{87} + 8864 q^{88} + 2672 q^{90} + 424 q^{91} - 2084 q^{93} + 5616 q^{94} + 8008 q^{96} - 8 q^{97} + 1196 q^{99}+O(q^{100}) \) 44 * q - 2 * q^3 - 4 * q^4 + 28 * q^6 - 8 * q^7 + 56 * q^10 - 80 * q^12 - 4 * q^13 - 112 * q^16 + 52 * q^18 + 20 * q^19 - 56 * q^21 - 40 * q^22 - 120 * q^24 - 134 * q^27 - 296 * q^28 - 332 * q^30 - 4 * q^33 + 520 * q^34 - 604 * q^36 - 4 * q^37 + 596 * q^39 + 632 * q^40 + 696 * q^42 - 436 * q^43 - 252 * q^45 + 664 * q^46 + 1200 * q^48 + 972 * q^49 - 648 * q^51 + 320 * q^52 + 1592 * q^54 + 280 * q^55 - 424 * q^58 + 800 * q^60 - 916 * q^61 - 2056 * q^64 - 668 * q^66 - 1636 * q^67 + 52 * q^69 - 5192 * q^70 - 3704 * q^72 + 1454 * q^75 - 568 * q^76 - 4932 * q^78 - 4 * q^81 + 768 * q^82 - 2096 * q^84 + 736 * q^85 + 1284 * q^87 + 8864 * q^88 + 2672 * q^90 + 424 * q^91 - 2084 * q^93 + 5616 * q^94 + 8008 * q^96 - 8 * q^97 + 1196 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more