LMFDB - Embedded newform 48.4.k.a.11.20

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			11.20
Character	$\chi$	$=$	48.11
Dual form			48.4.k.a.35.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.56930 + 1.18266i) q^{2} +(-1.96089 - 4.81196i) q^{3} +(5.20263 + 6.07722i) q^{4} +(6.30133 - 6.30133i) q^{5} +(0.652791 - 14.6824i) q^{6} +24.6728 q^{7} +(6.17986 + 21.7672i) q^{8} +(-19.3098 + 18.8714i) q^{9} +O(q^{10})$	\(q+(2.56930 + 1.18266i) q^{2} +(-1.96089 - 4.81196i) q^{3} +(5.20263 + 6.07722i) q^{4} +(6.30133 - 6.30133i) q^{5} +(0.652791 - 14.6824i) 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} +(19.0415 - 36.9516i) 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} +(-71.9313 + 25.6494i) q^{18} +(10.6193 + 10.6193i) q^{19} +(71.0780 + 5.51105i) q^{20} +(-48.3807 - 118.725i) q^{21} +(-56.1131 - 151.830i) q^{22} -53.4222i q^{23} +(92.6246 - 72.4202i) q^{24} +45.5866i q^{25} +(-177.517 + 65.6064i) q^{26} +(128.673 + 55.9134i) q^{27} +(128.364 + 149.942i) q^{28} +(-105.268 - 105.268i) q^{29} +(-88.4054 - 96.6323i) 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} +(-215.148 - 19.1691i) 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} +(16.1062 - 362.257i) q^{42} +(221.247 - 221.247i) q^{43} +(35.3918 - 456.460i) q^{44} +(-2.76270 + 240.593i) q^{45} +(63.1802 - 137.258i) q^{46} -381.086 q^{47} +(323.629 - 76.5260i) q^{48} +265.749 q^{49} +(-53.9134 + 117.126i) q^{50} +(201.008 - 81.9116i) q^{51} +(-533.685 - 41.3794i) q^{52} +(294.048 - 294.048i) q^{53} +(264.473 + 295.835i) 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} +(-112.857 - 352.831i) 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} +(-620.569 + 567.736i) q^{66} +(-572.215 - 572.215i) q^{67} +(-253.862 + 217.328i) q^{68} +(-257.065 + 104.755i) q^{69} +(583.324 - 215.584i) q^{70} -612.406i q^{71} +(-530.109 - 303.698i) q^{72} -331.477i q^{73} +(58.4825 + 158.241i) q^{74} +(219.361 - 89.3901i) q^{75} +(-9.28753 + 119.785i) q^{76} +(-998.433 - 998.433i) q^{77} +(663.786 + 725.557i) 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} +(469.809 - 911.701i) 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} +(-291.637 + 614.888i) q^{90} +(-1167.35 + 1167.35i) q^{91} +(324.658 - 277.936i) q^{92} +(-15.1459 + 6.17200i) q^{93} +(-979.125 - 450.695i) q^{94} +133.832 q^{95} +(922.005 + 186.124i) q^{96} +1474.45 q^{97} +(682.790 + 314.291i) q^{98} +(1545.08 + 17.7419i) 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
$3$	−1.96089	−	4.81196i	−0.377373	−	0.926061i
$3$	−1.96089	−	4.81196i	−0.377373	−	0.926061i
$4$	5.20263	+	6.07722i	0.650329	+	0.759652i
$5$	6.30133	−	6.30133i	0.563608	−	0.563608i	−0.366723	−	0.930330i	$-0.619520\pi$
$5$	6.30133	−	6.30133i	0.563608	−	0.563608i	0.930330	+	0.366723i	$0.119520\pi$
$6$	0.652791	−	14.6824i	0.0444168	−	0.999013i
$7$	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	$-0.963010\pi$
$11$	−40.4669	−	40.4669i	−1.10920	−	1.10920i	−0.115946	−	0.993255i	$-0.536990\pi$
$12$	19.0415	−	36.9516i	0.458068	−	0.888917i
$13$	−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	$0.0963134\pi$
$17$			41.7727i			0.595963i	−0.954572	+	0.297982i	$0.903687\pi$
$18$	−71.9313	+	25.6494i	−0.941909	+	0.335868i
$19$	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
$21$	−48.3807	−	118.725i	−0.502739	−	1.23371i
$22$	−56.1131	−	151.830i	−0.543789	−	1.47138i
$23$		−	53.4222i		−	0.484317i	−0.970237	−	0.242158i	$-0.922145\pi$
$23$		−	53.4222i		−	0.484317i	0.970237	−	0.242158i	$-0.0778554\pi$
$24$	92.6246	−	72.4202i	0.787788	−	0.615946i
$25$			45.5866i			0.364692i
$26$	−177.517	+	65.6064i	−1.33900	+	0.494864i
$27$	128.673	+	55.9134i	0.917152	+	0.398538i
$28$	128.364	+	149.942i	0.866374	+	1.01202i
$29$	−105.268	−	105.268i	−0.674064	−	0.674064i	0.284586	−	0.958650i	$-0.408144\pi$
$29$	−105.268	−	105.268i	−0.674064	−	0.674064i	−0.958650	+	0.284586i	$0.908144\pi$
$30$	−88.4054	−	96.6323i	−0.538018	−	0.588085i
$31$		−	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
$36$	−215.148	−	19.1691i	−0.996054	−	0.0887459i
$37$	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	$-0.406206\pi$
$41$	152.486			0.580836			0.290418	+	0.956900i	$0.406206\pi$
$42$	16.1062	−	362.257i	0.0591724	−	1.33089i
$43$	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
$45$	−2.76270	+	240.593i	−0.00915197	+	0.797009i
$46$	63.1802	−	137.258i	0.202509	−	0.439947i
$47$	−381.086			−1.18270			−0.591352	−	0.806414i	$-0.701406\pi$
$47$	−381.086			−1.18270			−0.591352	+	0.806414i	$0.701406\pi$
$48$	323.629	−	76.5260i	0.973163	−	0.230116i
$49$	265.749			0.774779
$50$	−53.9134	+	117.126i	−0.152490	+	0.331281i
$51$	201.008	−	81.9116i	0.551898	−	0.224900i
$52$	−533.685	−	41.3794i	−1.42325	−	0.110352i
$53$	294.048	−	294.048i	0.762088	−	0.762088i	−0.214612	−	0.976699i	$-0.568849\pi$
$53$	294.048	−	294.048i	0.762088	−	0.762088i	0.976699	+	0.214612i	$0.0688486\pi$
$54$	264.473	+	295.835i	0.666485	+	0.745518i
$55$	−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	0.999857	−	0.0169404i	$-0.00539256\pi$
$59$	445.445	+	445.445i	0.982916	+	0.982916i	−0.0169404	+	0.999857i	$0.505393\pi$
$60$	−112.857	−	352.831i	−0.242830	−	0.759171i
$61$	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
$66$	−620.569	+	567.736i	−1.15737	+	1.05884i
$67$	−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
$69$	−257.065	+	104.755i	−0.448507	+	0.182768i
$70$	583.324	−	215.584i	0.996007	−	0.368103i
$71$		−	612.406i		−	1.02365i	−0.859089	−	0.511825i	$-0.828969\pi$
$71$		−	612.406i		−	1.02365i	0.859089	−	0.511825i	$-0.171031\pi$
$72$	−530.109	−	303.698i	−0.867694	−	0.497099i
$73$		−	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
$75$	219.361	−	89.3901i	0.337728	−	0.137625i
$76$	−9.28753	+	119.785i	−0.0140178	+	0.180793i
$77$	−998.433	−	998.433i	−1.47769	−	1.47769i
$78$	663.786	+	725.557i	0.963576	+	1.05325i
$79$			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	−0.850420	−	0.526105i	$-0.823652\pi$
$83$	−245.236	+	245.236i	−0.324314	+	0.324314i	0.526105	+	0.850420i	$0.323652\pi$
$84$	469.809	−	911.701i	0.610242	−	1.18422i
$85$	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	$-0.535901\pi$
$89$	−188.997			−0.225097			−0.112548	+	0.993646i	$0.535901\pi$
$90$	−291.637	+	614.888i	−0.341570	+	0.720165i
$91$	−1167.35	+	1167.35i	−1.34474	+	1.34474i
$92$	324.658	−	277.936i	0.367913	−	0.314965i
$93$	−15.1459	+	6.17200i	−0.0168877	+	0.00688179i
$94$	−979.125	−	450.695i	−1.07435	−	0.494528i
$95$	133.832			0.144535
$96$	922.005	+	186.124i	0.980227	+	0.197878i
$97$	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
$99$	1545.08	+	17.7419i	1.56854	+	0.0180114i
$100$	−277.040	+	237.170i	−0.277040	+	0.237170i
$101$	223.136	−	223.136i	0.219830	−	0.219830i	−0.588597	−	0.808427i	$-0.700319\pi$
$101$	223.136	−	223.136i	0.219830	−	0.219830i	0.808427	+	0.588597i	$0.200319\pi$
$102$	613.325	+	27.2688i	0.595375	+	0.0264708i
$103$	−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	0.539163	−	0.842201i	$-0.318740\pi$
$107$	−335.407	−	335.407i	−0.303038	−	0.303038i	−0.842201	+	0.539163i	$0.818740\pi$
$108$	329.640	+	1072.87i	0.293700	+	0.955898i
$109$	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	$0.138149\pi$
$113$			1010.24i			0.841020i	−0.907288	+	0.420510i	$0.861851\pi$
$114$	162.850	−	148.986i	0.133792	−	0.122402i
$115$	−336.630	−	336.630i	−0.272965	−	0.272965i
$116$	92.0663	−	1187.41i	0.0736909	−	0.950418i
$117$	20.7435	−	1806.47i	0.0163909	−	1.42742i
$118$	617.674	+	1671.29i	0.481877	+	1.30386i
$119$			1030.65i			0.793947i
$120$	127.315	−	1040.00i	0.0968516	−	0.791156i
$121$			1944.14i			1.46066i
$122$	81.9704	−	30.2945i	0.0608299	−	0.0224814i
$123$	−299.008	−	733.755i	−0.219192	−	0.537890i
$124$	19.1284	−	16.3756i	0.0138531	−	0.0118594i
$125$	1074.92	+	1074.92i	0.769151	+	0.769151i
$126$	−1774.75	+	632.844i	−1.25482	+	0.447446i
$127$		−	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	$0.503349\pi$
$131$	−1515.05	+	1515.05i	−1.01046	+	1.01046i	−0.999945	+	0.0105196i	$0.996651\pi$
$132$	−2265.87	+	724.764i	−1.49408	+	0.477898i
$133$	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	$-0.221358\pi$
$137$	2462.36			1.53557			0.767787	+	0.640706i	$0.221358\pi$
$138$	−784.367	−	34.8735i	−0.483839	−	0.0215118i
$139$	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
$141$	747.266	+	1833.77i	0.446320	+	1.09526i
$142$	724.268	−	1573.46i	0.428022	−	0.929870i
$143$	3829.23			2.23927
$144$	−1002.84	−	1407.23i	−0.580347	−	0.814369i
$145$	−1326.66			−0.759816
$146$	392.024	−	851.664i	0.222220	−	0.482769i
$147$	−521.104	−	1278.77i	−0.292381	−	0.717493i
$148$	−36.8862	+	475.734i	−0.0204867	+	0.264224i
$149$	−2532.54	+	2532.54i	−1.39244	+	1.39244i	−0.572616	+	0.819824i	$0.694071\pi$
$149$	−2532.54	+	2532.54i	−1.39244	+	1.39244i	−0.819824	+	0.572616i	$0.805929\pi$
$150$	669.322	+	29.7585i	0.364333	+	0.0161985i
$151$	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
$156$	847.380	+	2649.21i	0.434902	+	1.35966i
$157$	−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
$162$	904.941	−	1852.73i	0.438882	−	0.898545i
$163$	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
$165$	1000.03	+	2454.05i	0.471833	+	1.15786i
$166$	−920.114	+	340.054i	−0.430209	+	0.158996i
$167$		−	2441.42i		−	1.13127i	−0.824655	−	0.565636i	$-0.808631\pi$
$167$		−	2441.42i		−	1.13127i	0.824655	−	0.565636i	$-0.191369\pi$
$168$	2285.31	−	1786.81i	1.04950	−	0.820568i
$169$		−	2280.06i		−	1.03780i
$170$	364.997	+	987.605i	0.164671	+	0.445564i
$171$	−405.460	−	4.65585i	−0.181323	−	0.00208212i
$172$	2495.63	+	193.499i	1.10634	+	0.0857801i
$173$	−856.168	−	856.168i	−0.376262	−	0.376262i	0.493490	−	0.869751i	$-0.335721\pi$
$173$	−856.168	−	856.168i	−0.376262	−	0.376262i	−0.869751	+	0.493490i	$0.835721\pi$
$174$	−1614.32	+	1476.88i	−0.703339	+	0.643459i
$175$			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	$0.544732\pi$
$179$	−2706.69	+	2706.69i	−1.13021	+	1.13021i	−0.990142	+	0.140068i	$0.955268\pi$
$180$	−1476.51	+	1234.93i	−0.611402	+	0.511366i
$181$	−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
$186$	−46.2138	−	2.05469i	−0.0182181	−	0.000809987i
$187$	1690.41	−	1690.41i	0.661043	−	0.661043i
$188$	−1982.65	−	2315.94i	−0.769147	−	0.898444i
$189$	3174.72	+	1379.54i	1.22184	+	0.530936i
$190$	343.855	+	158.278i	0.131294	+	0.0604350i
$191$	1193.27			0.452054			0.226027	−	0.974121i	$-0.427426\pi$
$191$	1193.27			0.452054			0.226027	+	0.974121i	$0.427426\pi$
$192$	2148.79	+	1568.63i	0.807685	+	0.589615i
$193$	−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
$195$	2869.23	−	1169.22i	1.05369	−	0.429382i
$196$	1382.60	+	1615.02i	0.503861	+	0.588563i
$197$	544.245	−	544.245i	0.196832	−	0.196832i	−0.601809	−	0.798640i	$-0.705553\pi$
$197$	544.245	−	544.245i	0.196832	−	0.196832i	0.798640	+	0.601809i	$0.205553\pi$
$198$	3948.78	+	1872.88i	1.41731	+	0.672222i
$199$	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
$204$	1543.57	+	795.417i	0.529762	+	0.272992i
$205$	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
$210$	−2181.21	−	2384.19i	−0.716752	−	0.783452i
$211$	−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
$213$	−2946.87	+	1200.86i	−0.947964	+	0.386298i
$214$	−465.090	−	1258.43i	−0.148565	−	0.401985i
$215$		−	2788.30i		−	0.884466i
$216$	−421.896	+	3146.38i	−0.132900	+	0.991129i
$217$		−	77.6591i		−	0.0242942i
$218$	3874.66	−	1431.99i	1.20378	−	0.444893i
$219$	−1595.05	+	649.989i	−0.492163	+	0.200558i
$220$	−2653.29	−	3099.32i	−0.813113	−	0.949801i
$221$	−1976.40	−	1976.40i	−0.601569	−	0.601569i
$222$	646.772	−	591.708i	0.195534	−	0.178887i
$223$		−	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	−0.668862	−	0.743387i	$-0.733218\pi$
$227$	254.883	−	254.883i	0.0745250	−	0.0745250i	0.743387	+	0.668862i	$0.233218\pi$
$228$	594.610	−	190.193i	0.172715	−	0.0552449i
$229$	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	$-0.584649\pi$
$233$	−1869.42			−0.525621			−0.262810	+	0.964847i	$0.584649\pi$
$234$	2189.74	−	4616.84i	0.611742	−	1.28980i
$235$	−2401.35	+	2401.35i	−0.666581	+	0.666581i
$236$	−389.580	+	5024.56i	−0.107456	+	1.38589i
$237$	2056.93	−	838.205i	0.563763	−	0.229735i
$238$	−1218.91	+	2648.06i	−0.331976	+	0.721210i
$239$	−2120.63			−0.573943			−0.286972	−	0.957939i	$-0.592649\pi$
$239$	−2120.63			−0.573943			−0.286972	+	0.957939i	$0.592649\pi$
$240$	1557.08	−	2521.51i	0.418787	−	0.678178i
$241$	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
$243$	−3539.82	+	1348.56i	−0.934483	+	0.356009i
$244$	246.435	+	19.1074i	0.0646572	+	0.00501321i
$245$	1674.57	−	1674.57i	0.436671	−	0.436671i
$246$	99.5413	−	2238.86i	0.0257989	−	0.580263i
$247$	−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	0.940847	−	0.338830i	$-0.110031\pi$
$251$	2393.97	+	2393.97i	0.602017	+	0.602017i	−0.338830	+	0.940847i	$0.610031\pi$
$252$	−5308.31	−	472.957i	−1.32695	−	0.118228i
$253$	−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	$0.143169\pi$
$257$			3582.50i			0.869535i	−0.900543	+	0.434768i	$0.856831\pi$
$258$	−3104.01	−	3392.87i	−0.749021	−	0.818724i
$259$	1040.59	+	1040.59i	0.249649	+	0.249649i
$260$	−3623.67	+	3102.18i	−0.864347	+	0.739957i
$261$	4019.28	+	46.1530i	0.953208	+	0.0109456i
$262$	−5684.42	+	2100.84i	−1.34040	+	0.495383i
$263$		−	2196.24i		−	0.514928i	−0.966288	−	0.257464i	$-0.917113\pi$
$263$		−	2196.24i		−	0.514928i	0.966288	−	0.257464i	$-0.0828869\pi$
$264$	−6678.85	−	817.610i	−1.55702	−	0.190608i
$265$		−	3705.79i		−	0.859037i
$266$	363.314	+	983.049i	0.0837450	+	0.226596i
$267$	370.601	+	909.443i	0.0849454	+	0.208453i
$268$	500.451	−	6454.50i	0.114067	−	1.47116i
$269$	−64.1764	−	64.1764i	−0.0145461	−	0.0145461i	0.699796	−	0.714342i	$-0.253274\pi$
$269$	−64.1764	−	64.1764i	−0.0145461	−	0.0145461i	−0.714342	+	0.699796i	$0.753274\pi$
$270$	3530.68	+	197.620i	0.795816	+	0.0445435i
$271$			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
$276$	−1974.03	−	1017.24i	−0.430518	−	0.221850i
$277$	−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	$-0.297467\pi$
$281$	5597.90			1.18841			0.594204	+	0.804314i	$0.297467\pi$
$282$	−248.769	+	5595.27i	−0.0525319	+	1.18154i
$283$	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
$285$	−262.429	−	643.993i	−0.0545437	−	0.133849i
$286$	9838.44	+	4528.67i	2.03412	+	0.936314i
$287$	3762.26			0.773795
$288$	−912.326	−	4801.62i	−0.186664	−	0.982424i
$289$	3168.04			0.644828
$290$	−3408.60	−	1568.99i	−0.690206	−	0.317704i
$291$	−2891.23	−	7094.98i	−0.582429	−	1.42926i
$292$	2014.46	−	1724.55i	0.403723	−	0.345623i
$293$	3077.11	−	3077.11i	0.613537	−	0.613537i	−0.330329	−	0.943866i	$-0.607160\pi$
$293$	3077.11	−	3077.11i	0.613537	−	0.613537i	0.943866	+	0.330329i	$0.107160\pi$
$294$	173.479	−	3901.84i	0.0344132	−	0.774014i
$295$	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
$300$	1684.50	+	868.038i	0.324181	+	0.167054i
$301$	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
$306$	−1071.45	−	3004.76i	−0.200165	−	0.561343i
$307$	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
$309$	427.305	+	1048.59i	0.0786685	+	0.193050i
$310$	−27.5024	−	74.4156i	−0.00503881	−	0.0136339i
$311$			7073.49i			1.28971i	0.764304	+	0.644856i	$0.223083\pi$
$311$			7073.49i			1.28971i	−0.764304	+	0.644856i	$0.776917\pi$
$312$	−955.934	+	7808.78i	−0.173459	+	1.41694i
$313$			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
$315$	−68.1636	+	5936.10i	−0.0121923	+	1.06178i
$316$	−2597.78	+	2223.93i	−0.462457	+	0.395904i
$317$	−4477.40	−	4477.40i	−0.793300	−	0.793300i	0.188729	−	0.982029i	$-0.439563\pi$
$317$	−4477.40	−	4477.40i	−0.793300	−	0.793300i	−0.982029	+	0.188729i	$0.939563\pi$
$318$	−4125.39	−	4509.30i	−0.727486	−	0.795185i
$319$			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
$324$	4516.22	−	3689.99i	0.774386	−	0.632714i
$325$	−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
$330$	−332.917	+	7487.89i	−0.0555347	+	1.24908i
$331$	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
$333$	−1610.32	−	18.4911i	−0.264999	−	0.00304296i
$334$	2887.36	−	6272.74i	0.473022	−	1.02763i
$335$	−7211.43			−1.17613
$336$	7984.85	−	1888.11i	1.29646	−	0.306563i
$337$	−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
$339$	4861.22	−	1980.96i	0.778836	−	0.317378i
$340$	−230.212	+	2969.12i	−0.0367205	+	0.473598i
$341$	−127.372	+	127.372i	−0.0202275	+	0.0202275i
$342$	−1036.24	−	491.483i	−0.163841	−	0.0777086i
$343$	−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	0.469549	−	0.882906i	$-0.344416\pi$
$347$	−2671.89	−	2671.89i	−0.413357	−	0.413357i	−0.882906	+	0.469549i	$0.844416\pi$
$348$	−5894.31	+	1885.36i	−0.907955	+	0.290420i
$349$	−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	$0.107405\pi$
$353$			4391.32i			0.662114i	−0.943611	+	0.331057i	$0.892595\pi$
$354$	6831.00	−	6249.44i	1.02560	−	0.938288i
$355$	−3858.97	−	3858.97i	−0.576938	−	0.576938i
$356$	−983.280	−	1148.57i	−0.146387	−	0.170995i
$357$	4959.45	−	2020.99i	0.735244	−	0.299614i
$358$	−10155.4	+	3753.22i	−1.49925	+	0.554088i
$359$		−	750.165i		−	0.110285i	−0.998479	−	0.0551423i	$-0.982439\pi$
$359$		−	750.165i		−	0.110285i	0.998479	−	0.0551423i	$-0.0175613\pi$
$360$	−5254.09	+	1426.69i	−0.769208	+	0.208870i
$361$		−	6633.46i		−	0.967118i
$362$	−216.107	−	584.738i	−0.0313765	−	0.0848983i
$363$	9355.09	−	3812.23i	1.35266	−	0.551213i
$364$	−13167.5	−	1020.95i	−1.89606	−	0.147011i
$365$	−2088.74	−	2088.74i	−0.299534	−	0.299534i
$366$	−306.510	−	335.034i	−0.0437747	−	0.0478483i
$367$		−	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
$372$	−116.307	−	59.9343i	−0.0162103	−	0.00835335i
$373$	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
$378$	6525.30	+	7299.08i	0.887897	+	0.993185i
$379$	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
$381$	−7238.74	+	2949.81i	−0.973364	+	0.396649i
$382$	3065.88	+	1411.24i	0.410639	+	0.189019i
$383$	−9336.03			−1.24556			−0.622779	−	0.782398i	$-0.713996\pi$
$383$	−9336.03			−1.24556			−0.622779	+	0.782398i	$0.713996\pi$
$384$	3665.74	+	6571.57i	0.487152	+	0.873317i
$385$	−12582.9			−1.66567
$386$	−12971.1	−	5970.66i	−1.71040	−	0.787301i
$387$	−97.0015	+	8447.48i	−0.0127412	+	1.10959i
$388$	7671.02	+	8960.55i	1.00370	+	1.17243i
$389$	−5797.69	+	5797.69i	−0.755667	+	0.755667i	−0.975531	−	0.219864i	$-0.929439\pi$
$389$	−5797.69	+	5797.69i	−0.755667	+	0.755667i	0.219864	+	0.975531i	$0.429439\pi$
$390$	8754.70	+	389.240i	1.13670	+	0.0505383i
$391$	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
$396$	7930.64	+	9482.07i	1.00639	+	1.20326i
$397$	−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	$-0.967109\pi$
$401$		−	1656.54i		−	0.206293i	0.994666	−	0.103147i	$-0.0328911\pi$
$402$	−8775.04	+	8027.97i	−1.08871	+	0.996017i
$403$	148.921	+	148.921i	0.0184076	+	0.0184076i
$404$	2516.94	+	195.151i	0.309956	+	0.0240325i
$405$	−4486.97	−	4697.94i	−0.550517	−	0.576401i
$406$	−3601.49	−	9744.87i	−0.440244	−	1.19121i
$407$		−	3413.43i		−	0.415718i
$408$	3025.19	+	3869.18i	0.367081	+	0.469493i
$409$			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
$411$	−4828.41	−	11848.8i	−0.579484	−	1.42204i
$412$	−1133.73	−	1324.31i	−0.135570	−	0.158360i
$413$	10990.4	+	10990.4i	1.30945	+	1.30945i
$414$	1370.25	+	3842.72i	0.162666	+	0.456183i
$415$			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	−0.885697	−	0.464263i	$-0.846319\pi$
$419$	−3614.52	+	3614.52i	−0.421434	+	0.421434i	0.464263	+	0.885697i	$0.346319\pi$
$420$	−2784.51	−	8705.34i	−0.323500	−	1.01137i
$421$	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
$426$	−8991.61	−	399.773i	−1.02264	−	0.0454673i
$427$	539.036	−	539.036i	0.0610908	−	0.0610908i
$428$	293.342	−	3783.34i	0.0331291	−	0.427278i
$429$	−7508.68	−	18426.1i	−0.845041	−	2.07370i
$430$	3297.60	−	7163.98i	0.369825	−	0.803436i
$431$	−3495.35			−0.390639			−0.195319	−	0.980740i	$-0.562574\pi$
$431$	−3495.35			−0.390639			−0.195319	+	0.980740i	$0.562574\pi$
$432$	−4805.07	+	7585.04i	−0.535148	+	0.844758i
$433$	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
$435$	2601.44	+	6383.84i	0.286734	+	0.703636i
$436$	11648.7	+	903.187i	1.27953	+	0.0992083i
$437$	567.308	−	567.308i	0.0621007	−	0.0621007i
$438$	−4866.89	−	216.385i	−0.530933	−	0.0236057i
$439$	−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	0.954384	−	0.298582i	$-0.0965138\pi$
$443$	6114.74	+	6114.74i	0.655801	+	0.655801i	−0.298582	+	0.954384i	$0.596514\pi$
$444$	2361.54	−	755.367i	0.252419	−	0.0807390i
$445$	−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	$0.127761\pi$
$449$			7434.00i			0.781364i	−0.920526	+	0.390682i	$0.872239\pi$
$450$	−1169.27	−	3279.10i	−0.122488	−	0.343507i
$451$	−6170.62	−	6170.62i	−0.644265	−	0.644265i
$452$	−6139.44	+	5255.90i	−0.638883	+	0.546940i
$453$	−1120.97	−	2750.84i	−0.116265	−	0.285310i
$454$	956.311	−	353.432i	0.0988588	−	0.0365361i
$455$			14711.7i			1.51581i
$456$	1752.67	+	214.558i	0.179992	+	0.0220342i
$457$		−	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
$459$	−2335.65	+	5375.01i	−0.237514	+	0.546589i
$460$	294.412	−	3797.14i	0.0298414	−	0.384875i
$461$	11243.0	+	11243.0i	1.13587	+	1.13587i	0.989183	+	0.146689i	$0.0468616\pi$
$461$	11243.0	+	11243.0i	1.13587	+	1.13587i	0.146689	+	0.989183i	$0.453138\pi$
$462$	−15311.2	+	14007.7i	−1.54186	+	1.41060i
$463$		−	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	−0.230532	−	0.973065i	$-0.574047\pi$
$467$	7493.61	−	7493.61i	0.742533	−	0.742533i	0.973065	+	0.230532i	$0.0740465\pi$
$468$	11086.3	−	9272.35i	1.09500	−	0.915843i
$469$	−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
$474$	6276.18	+	279.043i	0.608174	+	0.0270398i
$475$	−484.099	+	484.099i	−0.0467621	+	0.0467621i
$476$	−6263.50	+	5362.10i	−0.603124	+	0.516327i
$477$	−128.920	+	11227.1i	−0.0123749	+	1.07768i
$478$	−5448.55	−	2507.99i	−0.521362	−	0.239985i
$479$	13051.7			1.24499			0.622493	−	0.782626i	$-0.286120\pi$
$479$	13051.7			1.24499			0.622493	+	0.782626i	$0.286120\pi$
$480$	6982.69	−	4637.03i	0.663989	−	0.440938i
$481$	−3990.91			−0.378316
$482$	7955.23	+	3661.82i	0.751765	+	0.346040i
$483$	−6342.53	+	2584.60i	−0.597505	+	0.243485i
$484$	−11814.9	+	10114.6i	−1.10959	+	0.949908i
$485$	9290.98	−	9290.98i	0.869859	−	0.869859i
$486$	−10689.7	−	721.541i	−0.997730	−	0.0673452i
$487$	−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	0.352553	−	0.935792i	$-0.385314\pi$
$491$	−6345.55	−	6345.55i	−0.583239	−	0.583239i	−0.935792	+	0.352553i	$0.885314\pi$
$492$	2903.56	−	5634.59i	0.266063	−	0.516315i
$493$	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
$498$	3440.57	+	3760.74i	0.309589	+	0.338399i
$499$	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
$501$	−11748.0	+	4787.34i	−1.04763	+	0.426911i
$502$	3319.59	+	8982.10i	0.295140	+	0.798587i
$503$			3879.66i			0.343908i	0.985105	+	0.171954i	$0.0550080\pi$
$503$			3879.66i			0.343908i	−0.985105	+	0.171954i	$0.944992\pi$
$504$	−13079.3	−	7493.09i	−1.15595	−	0.662239i
$505$		−	2812.10i		−	0.247796i
$506$	−8111.09	+	2997.68i	−0.712613	+	0.263366i
$507$	−10971.5	+	4470.93i	−0.961071	+	0.391639i
$508$	9142.11	−	7826.45i	0.798455	−	0.683548i
$509$	4843.90	+	4843.90i	0.421811	+	0.421811i	0.885827	−	0.464016i	$-0.153592\pi$
$509$	4843.90	+	4843.90i	0.421811	+	0.421811i	−0.464016	+	0.885827i	$0.653592\pi$
$510$	4036.59	−	3692.93i	0.350477	−	0.320639i
$511$		−	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
$516$	−3962.54	−	12388.3i	−0.338064	−	1.05691i
$517$	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	$-0.524159\pi$
$521$	−1803.41			−0.151649			−0.0758244	+	0.997121i	$0.524159\pi$
$522$	10272.2	+	4872.02i	0.861304	+	0.408511i
$523$	−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
$525$	5412.25	−	2205.51i	0.449924	−	0.183345i
$526$	2597.40	−	5642.81i	0.215308	−	0.467753i
$527$	131.482			0.0108680
$528$	−16193.0	−	9999.49i	−1.33468	−	0.824189i
$529$	9313.07			0.765437
$530$	4382.69	−	9521.30i	0.359192	−	0.780337i
$531$	−17007.7	−	195.297i	−1.38996	−	0.0159608i
$532$	−229.150	+	2955.43i	−0.0186746	+	0.240853i
$533$	−7214.57	+	7214.57i	−0.586300	+	0.586300i
$534$	−123.375	+	2774.93i	−0.00999807	+	0.224874i
$535$	−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
$540$	8837.67	+	4683.34i	0.704283	+	0.373220i
$541$	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
$546$	16377.5	+	17901.5i	1.28368	+	1.40314i
$547$	−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
$549$	−9.57855	+	834.158i	−0.000744631	+	0.0648470i
$550$	6921.42	−	2558.00i	0.536600	−	0.198316i
$551$		−	2235.76i		−	0.172862i
$552$	−3868.84	−	4948.21i	−0.298313	−	0.381539i
$553$			10546.7i			0.811015i
$554$	−4820.11	−	13042.2i	−0.369651	−	1.00020i
$555$	−1042.26	−	2557.67i	−0.0797143	−	0.195616i
$556$	8822.26	+	684.036i	0.672926	+	0.0521755i
$557$	−13996.0	−	13996.0i	−1.06468	−	1.06468i	−0.997758	−	0.0669265i	$-0.978681\pi$
$557$	−13996.0	−	13996.0i	−1.06468	−	1.06468i	−0.0669265	−	0.997758i	$-0.521319\pi$
$558$	80.7329	+	226.408i	0.00612490	+	0.0171767i
$559$			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	−0.985887	−	0.167413i	$-0.946459\pi$
$563$	−10933.7	+	10933.7i	−0.818474	+	0.818474i	0.167413	+	0.985887i	$0.446459\pi$
$564$	−7256.46	+	14081.7i	−0.541759	+	1.05133i
$565$	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	$-0.553191\pi$
$569$	−4515.04			−0.332654			−0.166327	+	0.986071i	$0.553191\pi$
$570$	87.3642	−	1964.98i	0.00641980	−	0.144393i
$571$	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
$573$	−2339.88	−	5741.98i	−0.170593	−	0.418629i
$574$	9666.38	+	4449.47i	0.702904	+	0.323549i
$575$	2435.33			0.176627
$576$	3334.64	−	13415.8i	0.241221	−	0.970470i
$577$	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
$579$	9899.54	+	24293.2i	0.710554	+	1.74368i
$580$	−6902.14	−	8062.42i	−0.494130	−	0.577196i
$581$	−6050.66	+	6050.66i	−0.432054	+	0.432054i
$582$	962.506	−	21648.5i	0.0685518	−	1.54185i
$583$	−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	0.808807	−	0.588074i	$-0.200114\pi$
$587$	3139.23	+	3139.23i	0.220732	+	0.220732i	−0.588074	+	0.808807i	$0.700114\pi$
$588$	5060.27	−	9819.85i	0.354902	−	0.688714i
$589$	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	$-0.565140\pi$
$593$		−	28278.3i		−	1.95827i	0.203219	−	0.979133i	$-0.434860\pi$
$594$	1269.11	−	22673.9i	0.0876634	−	1.56620i
$595$	6494.47	+	6494.47i	0.447475	+	0.447475i
$596$	−28566.6	−	2214.92i	−1.96331	−	0.152226i
$597$	−1194.19	−	2930.50i	−0.0818675	−	0.200900i
$598$	3504.83	+	9483.34i	0.239671	+	0.648499i
$599$		−	10012.2i		−	0.682950i	−0.939891	−	0.341475i	$-0.889073\pi$
$599$		−	10012.2i		−	0.682950i	0.939891	−	0.341475i	$-0.110927\pi$
$600$	3301.39	+	4222.44i	0.224631	+	0.287300i
$601$			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
$603$	21847.9	+	250.877i	1.47548	+	0.0169428i
$604$	2974.17	+	3474.15i	0.200360	+	0.234041i
$605$	12250.6	+	12250.6i	0.823238	+	0.823238i
$606$	−3130.51	−	3421.83i	−0.209849	−	0.229377i
$607$		−	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
$612$	800.746	−	8987.31i	0.0528893	−	0.593612i
$613$	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	$-0.471636\pi$
$617$	2727.73			0.177981			0.0889906	+	0.996032i	$0.471636\pi$
$618$	−142.252	+	3199.51i	−0.00925928	+	0.208258i
$619$	−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
$621$	2987.01	−	6873.98i	0.193019	−	0.444192i
$622$	−8365.53	+	18173.9i	−0.539272	+	1.17156i
$623$	−4663.08			−0.299876
$624$	−11691.2	+	18932.6i	−0.750037	+	1.21460i
$625$	7848.55			0.502307
$626$	−10699.2	+	23243.8i	−0.683108	+	1.48404i
$627$	−4135.70	+	1685.31i	−0.263419	+	0.107344i
$628$	−18780.4	−	1456.14i	−1.19334	−	0.0925261i
$629$	−1761.79	+	1761.79i	−0.111681	+	0.111681i
$630$	−7195.52	+	15171.0i	−0.455042	+	0.959410i
$631$	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
$636$	−5266.42	−	16464.7i	−0.328345	−	1.02652i
$637$	−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	$-0.714317\pi$
$641$		−	25374.4i		−	1.56354i	0.623567	−	0.781770i	$-0.285683\pi$
$642$	−5143.54	+	4705.64i	−0.316199	+	0.289279i
$643$	−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
$645$	−13417.2	+	5467.54i	−0.819070	+	0.333774i
$646$	−1664.37	+	615.113i	−0.101368	+	0.0374633i
$647$			23409.6i			1.42245i	0.702964	+	0.711225i	$0.251859\pi$
$647$			23409.6i			1.42245i	−0.702964	+	0.711225i	$0.748141\pi$
$648$	15967.5	−	4139.55i	0.968000	−	0.250952i
$649$		−	36051.6i		−	2.18050i
$650$	−2990.77	−	8092.39i	−0.180473	−	0.488322i
$651$	−373.692	+	152.281i	−0.0224979	+	0.00916798i
$652$	−1655.76	+	21354.9i	−0.0994547	+	1.28270i
$653$	9012.83	+	9012.83i	0.540122	+	0.540122i	0.923565	−	0.383443i	$-0.125262\pi$
$653$	9012.83	+	9012.83i	0.540122	+	0.540122i	−0.383443	+	0.923565i	$0.625262\pi$
$654$	−14488.4	−	15836.7i	−0.866274	−	0.946888i
$655$			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	−0.717625	−	0.696429i	$-0.754771\pi$
$659$	−358.576	+	358.576i	−0.0211960	+	0.0211960i	0.696429	+	0.717625i	$0.254771\pi$
$660$	−9710.99	+	18844.9i	−0.572727	+	1.11142i
$661$	−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
$666$	−4115.52	−	1951.96i	−0.239449	−	0.113569i
$667$	−5623.67	+	5623.67i	−0.326461	+	0.326461i
$668$	14837.0	−	12701.8i	0.859374	−	0.735699i
$669$	−14230.5	+	5798.97i	−0.822395	+	0.335129i
$670$	−18528.3	−	8528.66i	−1.06838	−	0.491777i
$671$	−1768.19			−0.101729
$672$	22748.5	+	4592.22i	1.30587	+	0.263614i
$673$	−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
$675$	−2548.90	+	5865.75i	−0.145344	+	0.334478i
$676$	13856.4	−	11862.3i	0.788371	−	0.674915i
$677$	−5301.22	+	5301.22i	−0.300949	+	0.300949i	−0.841385	−	0.540436i	$-0.818259\pi$
$677$	−5301.22	+	5301.22i	−0.300949	+	0.300949i	0.540436	+	0.841385i	$0.318259\pi$
$678$	14832.8	+	659.474i	0.840190	+	0.0373554i
$679$	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	0.817551	−	0.575857i	$-0.195331\pi$
$683$	4314.17	+	4314.17i	0.241694	+	0.241694i	−0.575857	+	0.817551i	$0.695331\pi$
$684$	−2081.16	−	2488.29i	−0.116338	−	0.139097i
$685$	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
$690$	−5162.30	+	4722.80i	−0.284820	+	0.260571i
$691$	−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
$693$	38121.4	+	437.744i	2.08963	+	0.0239950i
$694$	−3704.96	−	10024.8i	−0.202649	−	0.548326i
$695$		−	9856.85i		−	0.537974i
$696$	−17374.0	−	2126.89i	−0.946207	−	0.115833i
$697$			6369.75i			0.346157i
$698$	−26806.1	+	9906.95i	−1.45362	+	0.537226i
$699$	3665.72	+	8995.56i	0.198355	+	0.486757i
$700$	−6835.35	+	5851.66i	−0.369074	+	0.315960i
$701$	2086.28	+	2086.28i	0.112408	+	0.112408i	0.761073	−	0.648666i	$-0.224673\pi$
$701$	2086.28	+	2086.28i	0.112408	+	0.112408i	−0.648666	+	0.761073i	$0.724673\pi$
$702$	−26509.9	−	1483.81i	−1.42529	−	0.0797763i
$703$			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
$708$	24941.9	−	7977.95i	1.32397	−	0.423488i
$709$	−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
$714$	15132.5	+	672.800i	0.793163	+	0.0352646i
$715$	24129.2	−	24129.2i	1.26207	−	1.26207i
$716$	−30531.1	−	2367.23i	−1.59358	−	0.123558i
$717$	4158.33	+	10204.4i	0.216591	+	0.531507i
$718$	887.190	−	1927.40i	0.0461137	−	0.100181i
$719$	6725.66			0.348852			0.174426	−	0.984670i	$-0.444193\pi$
$719$	6725.66			0.348852			0.174426	+	0.984670i	$0.444193\pi$
$720$	−15186.6	−	2548.19i	−0.786073	−	0.131897i
$721$	−5376.57			−0.277717
$722$	7845.12	−	17043.4i	0.404384	−	0.878516i
$723$	−6071.42	−	14899.1i	−0.312308	−	0.766393i
$724$	136.303	−	1757.95i	0.00699677	−	0.0902399i
$725$	4798.83	−	4798.83i	0.245826	−	0.245826i
$726$	28544.6	+	1269.11i	1.45922	+	0.0648777i
$727$	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
$732$	−391.287	−	1223.30i	−0.0197573	−	0.0617684i
$733$	−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
$738$	−10968.5	+	3911.17i	−0.547095	+	0.195084i
$739$	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
$741$	1970.43	+	4835.38i	0.0976864	+	0.239719i
$742$	27220.5	−	10060.1i	1.34676	−	0.497734i
$743$		−	24491.2i		−	1.20928i	−0.796499	−	0.604640i	$-0.793317\pi$
$743$		−	24491.2i		−	1.20928i	0.796499	−	0.604640i	$-0.206683\pi$
$744$	−227.946	−	291.541i	−0.0112324	−	0.0143661i
$745$			31916.7i			1.56958i
$746$	357.522	+	967.379i	0.0175467	+	0.0474775i
$747$	107.519	−	9363.40i	0.00526628	−	0.458620i
$748$	19067.6	+	1478.41i	0.932059	+	0.0722674i
$749$	−8275.45	−	8275.45i	−0.403709	−	0.403709i
$750$	16484.2	−	15080.8i	0.802555	−	0.734229i
$751$		−	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
$756$	8133.15	+	26470.7i	0.391269	+	1.27345i
$757$	−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	$-0.423319\pi$
$761$	10016.9			0.477153			0.238576	+	0.971124i	$0.423319\pi$
$762$	−22087.1	−	982.009i	−1.05004	−	0.0466856i
$763$	25479.7	−	25479.7i	1.20895	−	1.20895i
$764$	6208.17	+	7251.79i	0.293984	+	0.343404i
$765$	−10050.2	−	115.405i	−0.474988	−	0.00545424i
$766$	−23987.1	−	11041.3i	−1.13145	−	0.520809i
$767$	−42150.8			−1.98432
$768$	1646.46	+	21219.7i	0.0773589	+	0.997003i
$769$	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
$771$	17238.9	−	7024.89i	0.805243	−	0.328139i
$772$	−26265.5	−	30680.8i	−1.22450	−	1.43035i
$773$	26695.6	−	26695.6i	1.24214	−	1.24214i	0.283030	−	0.959111i	$-0.408660\pi$
$773$	26695.6	−	26695.6i	1.24214	−	1.24214i	0.959111	−	0.283030i	$-0.0913397\pi$
$774$	−10239.7	+	21589.4i	−0.475528	+	1.00260i
$775$	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
$780$	22033.1	+	11353.9i	1.01143	+	0.521199i
$781$	−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
$786$	21255.7	+	23233.7i	0.964585	+	1.05435i
$787$	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
$789$	−10568.2	+	4306.58i	−0.476855	+	0.194320i
$790$	3735.03	+	10106.2i	0.168211	+	0.455142i
$791$			24925.5i			1.12041i
$792$	9162.16	+	33741.6i	0.411065	+	1.51383i
$793$			2067.33i			0.0925763i
$794$	−2191.32	+	809.864i	−0.0979433	+	0.0361977i
$795$	−17832.1	+	7266.64i	−0.795521	+	0.324177i
$796$	3168.43	+	3701.05i	0.141083	+	0.164799i
$797$	−18417.2	−	18417.2i	−0.818532	−	0.818532i	0.167363	−	0.985895i	$-0.446475\pi$
$797$	−18417.2	−	18417.2i	−0.818532	−	0.818532i	−0.985895	+	0.167363i	$0.946475\pi$
$798$	4017.97	−	3675.90i	0.178239	−	0.163064i
$799$		−	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
$804$	−32040.1	+	10248.4i	−1.40543	+	0.449544i
$805$	−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	$-0.599033\pi$
$809$	−14088.2			−0.612253			−0.306127	+	0.951991i	$0.599033\pi$
$810$	−5972.33	−	17377.0i	−0.259069	−	0.753784i
$811$	−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
$813$	17454.9	−	7112.92i	0.752976	−	0.306840i
$814$	4036.92	−	8770.13i	0.173826	−	0.377633i
$815$	23859.2			1.02546
$816$	3196.70	+	13518.9i	0.137141	+	0.579969i
$817$	4698.99			0.201220
$818$	−3007.61	+	6533.96i	−0.128556	+	0.279284i
$819$	511.802	−	44570.8i	0.0218361	−	1.90162i
$820$	10838.4	+	840.357i	0.461577	+	0.0357885i
$821$	1002.06	−	1002.06i	0.0425968	−	0.0425968i	−0.685488	−	0.728084i	$-0.740411\pi$
$821$	1002.06	−	1002.06i	0.0425968	−	0.0425968i	0.728084	+	0.685488i	$0.240411\pi$
$822$	1607.41	−	36153.4i	0.0682052	−	1.53406i
$823$	−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	0.678922	−	0.734211i	$-0.262448\pi$
$827$	−1314.92	−	1314.92i	−0.0552892	−	0.0552892i	−0.734211	+	0.678922i	$0.762448\pi$
$828$	−1024.06	+	11493.7i	−0.0429811	+	0.482406i
$829$	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
$834$	−10972.9	−	11994.1i	−0.455590	−	0.497986i
$835$	−15384.2	−	15384.2i	−0.637594	−	0.637594i
$836$	5223.15	−	4471.47i	0.216084	−	0.184987i
$837$	175.990	−	405.005i	0.00726777	−	0.0167252i
$838$	−13561.5	+	5012.05i	−0.559040	+	0.206609i
$839$		−	11658.5i		−	0.479734i	−0.970806	−	0.239867i	$-0.922896\pi$
$839$		−	11658.5i		−	0.479734i	0.970806	−	0.239867i	$-0.0771038\pi$
$840$	3141.22	−	25659.8i	0.129027	−	1.05398i
$841$		−	2226.09i		−	0.0912745i
$842$	13955.0	+	37759.2i	0.571164	+	1.54545i
$843$	−10976.8	−	26936.8i	−0.448473	−	1.10054i
$844$	356.658	−	4599.95i	0.0145458	−	0.187603i
$845$	−14367.4	−	14367.4i	−0.584915	−	0.584915i
$846$	27412.0	−	9774.62i	1.11400	−	0.397232i
$847$			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
$852$	−22629.4	−	11661.1i	−0.909941	−	0.468902i
$853$	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	$-0.466892\pi$
$857$	5209.55			0.207649			0.103824	+	0.994596i	$0.466892\pi$
$858$	2499.68	−	56222.3i	0.0994613	−	2.23706i
$859$	−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
$861$	−7377.37	−	18103.8i	−0.292009	−	0.716581i
$862$	−8980.62	−	4133.81i	−0.354850	−	0.163339i
$863$	−31954.7			−1.26043			−0.630215	−	0.776420i	$-0.717033\pi$
$863$	−31954.7			−1.26043			−0.630215	+	0.776420i	$0.717033\pi$
$864$	−21316.2	+	13805.5i	−0.839343	+	0.543603i
$865$	−10790.0			−0.424128
$866$	41292.0	+	19006.8i	1.62027	+	0.745818i
$867$	−6212.17	−	15244.5i	−0.243341	−	0.597150i
$868$	471.952	−	404.032i	0.0184552	−	0.0157992i
$869$	17298.0	−	17298.0i	0.675254	−	0.675254i
$870$	−866.033	+	19478.6i	−0.0337486	+	0.759066i
$871$	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
$876$	−12248.6	−	6311.83i	−0.472422	−	0.243444i
$877$	−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	$0.198300\pi$
$881$			30514.2i			1.16691i	−0.812144	+	0.583457i	$0.801700\pi$
$882$	−19115.7	+	6816.31i	−0.729771	+	0.260223i
$883$	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
$885$	−11008.0	−	27013.3i	−0.418114	−	1.02604i
$886$	8478.96	+	22942.3i	0.321508	+	0.869933i
$887$			24947.8i			0.944380i	0.881497	+	0.472190i	$0.156536\pi$
$887$			24947.8i			0.944380i	−0.881497	+	0.472190i	$0.843464\pi$
$888$	6960.86	+	852.134i	0.263053	+	0.0322024i
$889$		−	37115.9i		−	1.40026i
$890$	−4468.32	+	1651.39i	−0.168290	+	0.0621965i
$891$	−30170.0	+	28815.2i	−1.13438	+	1.08344i
$892$	17972.3	−	15385.8i	0.674614	−	0.577529i
$893$	−4046.88	−	4046.88i	−0.151650	−	0.151650i
$894$	35530.6	+	38837.0i	1.32922	+	1.45291i
$895$			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
$900$	873.854	−	9807.85i	0.0323650	−	0.363254i
$901$	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
$906$	373.179	−	8393.46i	0.0136844	−	0.307786i
$907$	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
$909$	−97.8296	+	8519.59i	−0.00356964	+	0.310866i
$910$	−17398.9	+	37798.8i	−0.633811	+	1.37694i
$911$	4256.52			0.154802			0.0774010	−	0.997000i	$-0.475338\pi$
$911$	4256.52			0.154802			0.0774010	+	0.997000i	$0.475338\pi$
$912$	4249.38	+	2624.07i	0.154289	+	0.0952760i
$913$	19847.8			0.719460
$914$	1539.14	−	3343.76i	0.0557006	−	0.121008i
$915$	−1324.90	+	539.900i	−0.0478686	+	0.0195066i
$916$	−305.877	+	3945.00i	−0.0110332	+	0.142300i
$917$	−37380.7	+	37380.7i	−1.34615	+	1.34615i
$918$	−12357.8	+	11047.8i	−0.444301	+	0.397201i
$919$	−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
$924$	−55905.4	+	17882.0i	−1.99042	+	0.636660i
$925$	−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	$-0.640229\pi$
$929$		−	51223.8i		−	1.80904i	0.426429	−	0.904521i	$-0.359771\pi$
$930$	−304.155	+	278.261i	−0.0107244	+	0.00981132i
$931$	2822.08	+	2822.08i	0.0993448	+	0.0993448i
$932$	−9725.90	−	11360.9i	−0.341827	−	0.399289i
$933$	34037.3	−	13870.3i	1.19435	−	0.486703i
$934$	28115.7	−	10391.0i	0.984984	−	0.364029i
$935$		−	21303.7i		−	0.745138i
$936$	39450.0	−	10712.2i	1.37763	−	0.374081i
$937$		−	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
$939$	43532.4	−	17739.6i	1.51292	−	0.616518i
$940$	−27086.8	−	2100.18i	−0.939867	−	0.0728728i
$941$	817.247	+	817.247i	0.0283119	+	0.0283119i	0.721121	−	0.692809i	$-0.243627\pi$
$941$	817.247	+	817.247i	0.0283119	+	0.0283119i	−0.692809	+	0.721121i	$0.743627\pi$
$942$	23358.6	+	25532.4i	0.807925	+	0.883110i
$943$		−	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	−0.946179	−	0.323644i	$-0.895092\pi$
$947$	−18142.1	+	18142.1i	−0.622535	+	0.622535i	0.323644	+	0.946179i	$0.395092\pi$
$948$	15795.4	+	8139.53i	0.541151	+	0.278860i
$949$	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	$-0.454811\pi$
$953$	8325.23			0.282981			0.141490	+	0.989940i	$0.454811\pi$
$954$	−13609.1	+	28693.4i	−0.461857	+	0.973778i
$955$	7519.21	−	7519.21i	0.254781	−	0.254781i
$956$	−11032.9	−	12887.6i	−0.373252	−	0.435997i
$957$	40996.8	−	16706.3i	1.38478	−	0.564304i
$958$	33533.8	+	15435.7i	1.13093	+	0.520570i
$959$	60753.4			2.04570
$960$	23424.7	−	3655.78i	0.787529	−	0.122906i
$961$	29781.1			0.999667
$962$	−10253.9	−	4719.89i	−0.343657	−	0.158186i
$963$	12806.3	+	147.053i	0.428532	+	0.00492078i
$964$	16108.7	+	18816.7i	0.538202	+	0.628676i
$965$	−31812.2	+	31812.2i	−1.06122	+	1.06122i
$966$	−19352.6	−	860.428i	−0.644574	−	0.0286582i
$967$	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	0.173280	−	0.984873i	$-0.444563\pi$
$971$	−24556.5	−	24556.5i	−0.811593	−	0.811593i	−0.984873	+	0.173280i	$0.944563\pi$
$972$	−26611.9	−	14496.2i	−0.878164	−	0.478359i
$973$	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	$0.00261596\pi$
$977$			501.936i			0.0164364i	−0.999966	+	0.00821819i	$0.997384\pi$
$978$	29032.5	−	26560.8i	0.949240	−	0.868426i
$979$	7648.10	+	7648.10i	0.249678	+	0.249678i
$980$	18888.9	+	1464.56i	0.615699	+	0.0477383i
$981$	−452.769	+	39429.9i	−0.0147358	+	1.28328i
$982$	−8799.01	−	23808.2i	−0.285935	−	0.773678i
$983$		−	52008.6i		−	1.68751i	−0.536732	−	0.843753i	$-0.680341\pi$
$983$		−	52008.6i		−	1.68751i	0.536732	−	0.843753i	$-0.319659\pi$
$984$	14123.9	−	11043.0i	0.457576	−	0.357764i
$985$		−	6858.94i		−	0.221872i
$986$	16498.7	−	6097.56i	0.532886	−	0.196943i
$987$	18437.2	+	45244.3i	0.594592	+	1.45911i
$988$	−5227.96	−	6106.80i	−0.168344	−	0.196643i
$989$	−11819.5	−	11819.5i	−0.380018	−	0.380018i
$990$	36684.2	−	13080.9i	1.17768	−	0.419939i
$991$		−	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
$996$	4392.18	+	13731.5i	0.139731	+	0.436847i
$997$	−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.11.20	yes	44
3.2	odd	2	inner	48.4.k.a.11.3	✓	44
4.3	odd	2		192.4.k.a.143.14		44
8.3	odd	2		384.4.k.a.287.9		44
8.5	even	2		384.4.k.b.287.14		44
12.11	even	2		192.4.k.a.143.20		44
16.3	odd	4	inner	48.4.k.a.35.3	yes	44
16.5	even	4		384.4.k.a.95.3		44
16.11	odd	4		384.4.k.b.95.20		44
16.13	even	4		192.4.k.a.47.20		44
24.5	odd	2		384.4.k.b.287.20		44
24.11	even	2		384.4.k.a.287.3		44
48.5	odd	4		384.4.k.a.95.9		44
48.11	even	4		384.4.k.b.95.14		44
48.29	odd	4		192.4.k.a.47.14		44
48.35	even	4	inner	48.4.k.a.35.20	yes	44

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

\(f(q)\)	\(=\)	\(q+(2.56930 + 1.18266i) q^{2} +(-1.96089 - 4.81196i) q^{3} +(5.20263 + 6.07722i) q^{4} +(6.30133 - 6.30133i) q^{5} +(0.652791 - 14.6824i) q^{6} +24.6728 q^{7} +(6.17986 + 21.7672i) q^{8} +(-19.3098 + 18.8714i) q^{9} +O(q^{10})\)	\(q+(2.56930 + 1.18266i) q^{2} +(-1.96089 - 4.81196i) q^{3} +(5.20263 + 6.07722i) q^{4} +(6.30133 - 6.30133i) q^{5} +(0.652791 - 14.6824i) 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} +(19.0415 - 36.9516i) 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} +(-71.9313 + 25.6494i) q^{18} +(10.6193 + 10.6193i) q^{19} +(71.0780 + 5.51105i) q^{20} +(-48.3807 - 118.725i) q^{21} +(-56.1131 - 151.830i) q^{22} -53.4222i q^{23} +(92.6246 - 72.4202i) q^{24} +45.5866i q^{25} +(-177.517 + 65.6064i) q^{26} +(128.673 + 55.9134i) q^{27} +(128.364 + 149.942i) q^{28} +(-105.268 - 105.268i) q^{29} +(-88.4054 - 96.6323i) 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} +(-215.148 - 19.1691i) 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} +(16.1062 - 362.257i) q^{42} +(221.247 - 221.247i) q^{43} +(35.3918 - 456.460i) q^{44} +(-2.76270 + 240.593i) q^{45} +(63.1802 - 137.258i) q^{46} -381.086 q^{47} +(323.629 - 76.5260i) q^{48} +265.749 q^{49} +(-53.9134 + 117.126i) q^{50} +(201.008 - 81.9116i) q^{51} +(-533.685 - 41.3794i) q^{52} +(294.048 - 294.048i) q^{53} +(264.473 + 295.835i) 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} +(-112.857 - 352.831i) 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} +(-620.569 + 567.736i) q^{66} +(-572.215 - 572.215i) q^{67} +(-253.862 + 217.328i) q^{68} +(-257.065 + 104.755i) q^{69} +(583.324 - 215.584i) q^{70} -612.406i q^{71} +(-530.109 - 303.698i) q^{72} -331.477i q^{73} +(58.4825 + 158.241i) q^{74} +(219.361 - 89.3901i) q^{75} +(-9.28753 + 119.785i) q^{76} +(-998.433 - 998.433i) q^{77} +(663.786 + 725.557i) 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} +(469.809 - 911.701i) 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} +(-291.637 + 614.888i) q^{90} +(-1167.35 + 1167.35i) q^{91} +(324.658 - 277.936i) q^{92} +(-15.1459 + 6.17200i) q^{93} +(-979.125 - 450.695i) q^{94} +133.832 q^{95} +(922.005 + 186.124i) q^{96} +1474.45 q^{97} +(682.790 + 314.291i) q^{98} +(1545.08 + 17.7419i) 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

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