LMFDB - Embedded newform 17.4.d.a.8.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,4,Mod(2,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7]))

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

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

chi := DirichletCharacter("17.2");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	17.d (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.00303247010$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 54x^{10} + 1085x^{8} + 9836x^{6} + 38276x^{4} + 49664x^{2} + 16384 $ x^12 + 54x^10 + 1085x^8 + 9836x^6 + 38276x^4 + 49664*x^2 + 16384
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			8.1
Root			$-3.68604i$ of defining polynomial
Character	$\chi$	$=$	17.8
Dual form			17.4.d.a.15.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.89932 + 1.89932i) q^{2} +(-1.65755 + 4.00167i) q^{3} +0.785167i q^{4} +(1.92782 + 0.798529i) q^{5} +(-4.45224 - 10.7487i) q^{6} +(23.0956 - 9.56650i) q^{7} +(-16.6858 - 16.6858i) q^{8} +(5.82599 + 5.82599i) q^{9} +O(q^{10})$	\(q+(-1.89932 + 1.89932i) q^{2} +(-1.65755 + 4.00167i) q^{3} +0.785167i q^{4} +(1.92782 + 0.798529i) q^{5} +(-4.45224 - 10.7487i) q^{6} +(23.0956 - 9.56650i) q^{7} +(-16.6858 - 16.6858i) q^{8} +(5.82599 + 5.82599i) q^{9} +(-5.17821 + 2.14488i) q^{10} +(1.46245 + 3.53068i) q^{11} +(-3.14198 - 1.30145i) q^{12} +17.6726i q^{13} +(-25.6960 + 62.0357i) q^{14} +(-6.39089 + 6.39089i) q^{15} +57.1022 q^{16} +(-69.7847 + 6.56433i) q^{17} -22.1309 q^{18} +(113.784 - 113.784i) q^{19} +(-0.626979 + 1.51366i) q^{20} +108.278i q^{21} +(-9.48355 - 3.92822i) q^{22} +(-38.2560 - 92.3581i) q^{23} +(94.4287 - 39.1137i) q^{24} +(-85.3095 - 85.3095i) q^{25} +(-33.5659 - 33.5659i) q^{26} +(-141.016 + 58.4106i) q^{27} +(7.51131 + 18.1339i) q^{28} +(185.315 + 76.7600i) q^{29} -24.2767i q^{30} +(-29.2899 + 70.7121i) q^{31} +(25.0315 - 25.0315i) q^{32} -16.5527 q^{33} +(120.076 - 145.011i) q^{34} +52.1632 q^{35} +(-4.57438 + 4.57438i) q^{36} +(-93.6650 + 226.127i) q^{37} +432.224i q^{38} +(-70.7198 - 29.2931i) q^{39} +(-18.8432 - 45.4914i) q^{40} +(-49.9941 + 20.7082i) q^{41} +(-205.654 - 205.654i) q^{42} +(-100.471 - 100.471i) q^{43} +(-2.77217 + 1.14827i) q^{44} +(6.57924 + 15.8837i) q^{45} +(248.078 + 102.757i) q^{46} -468.451i q^{47} +(-94.6494 + 228.504i) q^{48} +(199.350 - 199.350i) q^{49} +324.060 q^{50} +(89.4031 - 290.136i) q^{51} -13.8759 q^{52} +(68.2834 - 68.2834i) q^{53} +(156.893 - 378.774i) q^{54} +7.97432i q^{55} +(-544.994 - 225.744i) q^{56} +(266.723 + 643.927i) q^{57} +(-497.764 + 206.181i) q^{58} +(257.729 + 257.729i) q^{59} +(-5.01792 - 5.01792i) q^{60} +(-653.988 + 270.891i) q^{61} +(-78.6740 - 189.936i) q^{62} +(190.289 + 78.8203i) q^{63} +551.903i q^{64} +(-14.1121 + 34.0695i) q^{65} +(31.4388 - 31.4388i) q^{66} +304.454 q^{67} +(-5.15410 - 54.7927i) q^{68} +432.997 q^{69} +(-99.0747 + 99.0747i) q^{70} +(-179.862 + 434.226i) q^{71} -194.423i q^{72} +(-131.243 - 54.3626i) q^{73} +(-251.588 - 607.388i) q^{74} +(482.785 - 199.976i) q^{75} +(89.3393 + 89.3393i) q^{76} +(67.5525 + 67.5525i) q^{77} +(189.956 - 78.6825i) q^{78} +(-274.715 - 663.221i) q^{79} +(110.083 + 45.5977i) q^{80} -438.657i q^{81} +(55.6232 - 134.286i) q^{82} +(-259.960 + 259.960i) q^{83} -85.0162 q^{84} +(-139.774 - 43.0703i) q^{85} +381.653 q^{86} +(-614.336 + 614.336i) q^{87} +(34.5100 - 83.3146i) q^{88} -1042.28i q^{89} +(-42.6643 - 17.6721i) q^{90} +(169.065 + 408.158i) q^{91} +(72.5165 - 30.0373i) q^{92} +(-234.417 - 234.417i) q^{93} +(889.738 + 889.738i) q^{94} +(310.214 - 128.495i) q^{95} +(58.6768 + 141.658i) q^{96} +(-834.757 - 345.768i) q^{97} +757.260i q^{98} +(-12.0495 + 29.0899i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - 4 q^{3} - 20 q^{5} + 20 q^{6} - 4 q^{7} + 28 q^{8} - 64 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 - 4 * q^3 - 20 * q^5 + 20 * q^6 - 4 * q^7 + 28 * q^8 - 64 * q^9	\( 12 q - 4 q^{2} - 4 q^{3} - 20 q^{5} + 20 q^{6} - 4 q^{7} + 28 q^{8} - 64 q^{9} - 116 q^{10} + 40 q^{11} + 56 q^{12} - 132 q^{14} + 244 q^{15} + 184 q^{16} + 52 q^{17} - 12 q^{19} + 572 q^{20} - 620 q^{22} - 276 q^{23} - 184 q^{24} - 464 q^{25} - 708 q^{26} - 664 q^{27} + 452 q^{28} + 632 q^{29} + 188 q^{31} + 700 q^{32} + 1400 q^{33} + 764 q^{34} - 632 q^{35} + 524 q^{36} + 940 q^{37} - 1112 q^{39} - 1864 q^{40} + 176 q^{41} + 48 q^{42} - 1360 q^{43} - 1364 q^{44} - 32 q^{45} + 452 q^{46} - 540 q^{48} + 1044 q^{49} + 2856 q^{50} + 340 q^{51} + 792 q^{52} - 360 q^{53} - 244 q^{54} - 1788 q^{56} - 148 q^{57} - 360 q^{58} - 584 q^{59} - 1792 q^{60} - 1052 q^{61} - 380 q^{62} + 1752 q^{63} + 404 q^{65} + 1372 q^{66} + 1080 q^{67} + 2532 q^{68} - 344 q^{69} + 2072 q^{70} + 28 q^{71} + 824 q^{73} - 2292 q^{74} + 400 q^{75} + 1328 q^{76} - 1252 q^{77} + 1128 q^{78} - 196 q^{79} - 904 q^{80} - 1528 q^{82} - 1008 q^{83} - 4768 q^{84} - 2824 q^{85} - 1200 q^{86} - 2516 q^{87} - 56 q^{88} - 860 q^{90} + 2456 q^{91} + 396 q^{92} - 836 q^{93} + 6360 q^{94} + 2172 q^{95} + 1668 q^{96} - 904 q^{97} + 3280 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - 4 * q^3 - 20 * q^5 + 20 * q^6 - 4 * q^7 + 28 * q^8 - 64 * q^9 - 116 * q^10 + 40 * q^11 + 56 * q^12 - 132 * q^14 + 244 * q^15 + 184 * q^16 + 52 * q^17 - 12 * q^19 + 572 * q^20 - 620 * q^22 - 276 * q^23 - 184 * q^24 - 464 * q^25 - 708 * q^26 - 664 * q^27 + 452 * q^28 + 632 * q^29 + 188 * q^31 + 700 * q^32 + 1400 * q^33 + 764 * q^34 - 632 * q^35 + 524 * q^36 + 940 * q^37 - 1112 * q^39 - 1864 * q^40 + 176 * q^41 + 48 * q^42 - 1360 * q^43 - 1364 * q^44 - 32 * q^45 + 452 * q^46 - 540 * q^48 + 1044 * q^49 + 2856 * q^50 + 340 * q^51 + 792 * q^52 - 360 * q^53 - 244 * q^54 - 1788 * q^56 - 148 * q^57 - 360 * q^58 - 584 * q^59 - 1792 * q^60 - 1052 * q^61 - 380 * q^62 + 1752 * q^63 + 404 * q^65 + 1372 * q^66 + 1080 * q^67 + 2532 * q^68 - 344 * q^69 + 2072 * q^70 + 28 * q^71 + 824 * q^73 - 2292 * q^74 + 400 * q^75 + 1328 * q^76 - 1252 * q^77 + 1128 * q^78 - 196 * q^79 - 904 * q^80 - 1528 * q^82 - 1008 * q^83 - 4768 * q^84 - 2824 * q^85 - 1200 * q^86 - 2516 * q^87 - 56 * q^88 - 860 * q^90 + 2456 * q^91 + 396 * q^92 - 836 * q^93 + 6360 * q^94 + 2172 * q^95 + 1668 * q^96 - 904 * q^97 + 3280 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{8}\right)$

Coefficient data

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

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

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

$2$	−1.89932	+	1.89932i	−0.671511	+	0.671511i	−0.958064	−	0.286553i	$-0.907490\pi$
$2$	−1.89932	+	1.89932i	−0.671511	+	0.671511i	0.286553	+	0.958064i	$0.407490\pi$
$3$	−1.65755	+	4.00167i	−0.318995	+	0.770121i	0.680313	+	0.732922i	$0.261844\pi$
$3$	−1.65755	+	4.00167i	−0.318995	+	0.770121i	−0.999308	+	0.0371998i	$0.988156\pi$
$4$			0.785167i			0.0981459i
$5$	1.92782	+	0.798529i	0.172429	+	0.0714226i	0.467228	−	0.884137i	$-0.345253\pi$
$5$	1.92782	+	0.798529i	0.172429	+	0.0714226i	−0.294799	+	0.955559i	$0.595253\pi$
$6$	−4.45224	−	10.7487i	−0.302936	−	0.731353i
$7$	23.0956	−	9.56650i	1.24704	−	0.516543i	0.341135	−	0.940014i	$-0.389189\pi$
$7$	23.0956	−	9.56650i	1.24704	−	0.516543i	0.905909	+	0.423472i	$0.139189\pi$
$8$	−16.6858	−	16.6858i	−0.737417	−	0.737417i
$9$	5.82599	+	5.82599i	0.215778	+	0.215778i
$10$	−5.17821	+	2.14488i	−0.163749	+	0.0678272i
$11$	1.46245	+	3.53068i	0.0400860	+	0.0967763i	0.942655	−	0.333770i	$-0.108321\pi$
$11$	1.46245	+	3.53068i	0.0400860	+	0.0967763i	−0.902568	+	0.430546i	$0.858321\pi$
$12$	−3.14198	−	1.30145i	−0.0755843	−	0.0313080i
$13$			17.6726i			0.377038i	0.982070	+	0.188519i	$0.0603687\pi$
$13$			17.6726i			0.377038i	−0.982070	+	0.188519i	$0.939631\pi$
$14$	−25.6960	+	62.0357i	−0.490540	+	1.18427i
$15$	−6.39089	+	6.39089i	−0.110008	+	0.110008i
$16$	57.1022			0.892221
$17$	−69.7847	+	6.56433i	−0.995605	+	0.0936520i
$17$	−69.7847	+	6.56433i	−0.995605	+	0.0936520i
$18$	−22.1309			−0.289794
$19$	113.784	−	113.784i	1.37388	−	1.37388i	0.519279	−	0.854605i	$-0.326201\pi$
$19$	113.784	−	113.784i	1.37388	−	1.37388i	0.854605	−	0.519279i	$-0.173799\pi$
$20$	−0.626979	+	1.51366i	−0.00700984	+	0.0169232i
$21$			108.278i			1.12515i
$22$	−9.48355	−	3.92822i	−0.0919046	−	0.0380681i
$23$	−38.2560	−	92.3581i	−0.346823	−	0.837304i	−0.996991	−	0.0775138i	$-0.975302\pi$
$23$	−38.2560	−	92.3581i	−0.346823	−	0.837304i	0.650169	−	0.759790i	$-0.274698\pi$
$24$	94.4287	−	39.1137i	0.803133	−	0.332668i
$25$	−85.3095	−	85.3095i	−0.682476	−	0.682476i
$26$	−33.5659	−	33.5659i	−0.253185	−	0.253185i
$27$	−141.016	+	58.4106i	−1.00513	+	0.416338i
$28$	7.51131	+	18.1339i	0.0506966	+	0.122392i
$29$	185.315	+	76.7600i	1.18662	+	0.491516i	0.886655	−	0.462432i	$-0.153023\pi$
$29$	185.315	+	76.7600i	1.18662	+	0.491516i	0.299970	+	0.953949i	$0.403023\pi$
$30$		−	24.2767i		−	0.147743i
$31$	−29.2899	+	70.7121i	−0.169697	+	0.409686i	−0.985733	−	0.168316i	$-0.946167\pi$
$31$	−29.2899	+	70.7121i	−0.169697	+	0.409686i	0.816036	+	0.578001i	$0.196167\pi$
$32$	25.0315	−	25.0315i	0.138281	−	0.138281i
$33$	−16.5527			−0.0873167
$34$	120.076	−	145.011i	0.605671	−	0.731448i
$35$	52.1632			0.251920
$36$	−4.57438	+	4.57438i	−0.0211777	+	0.0211777i
$37$	−93.6650	+	226.127i	−0.416174	+	1.00473i	0.567272	+	0.823531i	$0.307999\pi$
$37$	−93.6650	+	226.127i	−0.416174	+	1.00473i	−0.983446	+	0.181202i	$0.942001\pi$
$38$			432.224i			1.84516i
$39$	−70.7198	−	29.2931i	−0.290365	−	0.120273i
$40$	−18.8432	−	45.4914i	−0.0744841	−	0.179821i
$41$	−49.9941	+	20.7082i	−0.190433	+	0.0788800i	−0.475862	−	0.879520i	$-0.657864\pi$
$41$	−49.9941	+	20.7082i	−0.190433	+	0.0788800i	0.285429	+	0.958400i	$0.407864\pi$
$42$	−205.654	−	205.654i	−0.755550	−	0.755550i
$43$	−100.471	−	100.471i	−0.356318	−	0.356318i	0.506136	−	0.862454i	$-0.331073\pi$
$43$	−100.471	−	100.471i	−0.356318	−	0.356318i	−0.862454	+	0.506136i	$0.831073\pi$
$44$	−2.77217	+	1.14827i	−0.00949820	+	0.00393428i
$45$	6.57924	+	15.8837i	0.0217950	+	0.0526178i
$46$	248.078	+	102.757i	0.795154	+	0.329363i
$47$		−	468.451i		−	1.45384i	−0.686721	−	0.726921i	$-0.740951\pi$
$47$		−	468.451i		−	1.45384i	0.686721	−	0.726921i	$-0.259049\pi$
$48$	−94.6494	+	228.504i	−0.284614	+	0.687119i
$49$	199.350	−	199.350i	0.581196	−	0.581196i
$50$	324.060			0.916580
$51$	89.4031	−	290.136i	0.245469	−	0.796611i
$52$	−13.8759			−0.0370047
$53$	68.2834	−	68.2834i	0.176971	−	0.176971i	−0.613063	−	0.790034i	$-0.710063\pi$
$53$	68.2834	−	68.2834i	0.176971	−	0.176971i	0.790034	+	0.613063i	$0.210063\pi$
$54$	156.893	−	378.774i	0.395379	−	0.954530i
$55$			7.97432i			0.0195501i
$56$	−544.994	−	225.744i	−1.30050	−	0.538684i
$57$	266.723	+	643.927i	0.619796	+	1.49632i
$58$	−497.764	+	206.181i	−1.12689	+	0.466773i
$59$	257.729	+	257.729i	0.568703	+	0.568703i	0.931765	−	0.363062i	$-0.118269\pi$
$59$	257.729	+	257.729i	0.568703	+	0.568703i	−0.363062	+	0.931765i	$0.618269\pi$
$60$	−5.01792	−	5.01792i	−0.0107968	−	0.0107968i
$61$	−653.988	+	270.891i	−1.37270	+	0.568590i	−0.942519	−	0.334153i	$-0.891550\pi$
$61$	−653.988	+	270.891i	−1.37270	+	0.568590i	−0.430179	+	0.902743i	$0.641550\pi$
$62$	−78.6740	−	189.936i	−0.161155	−	0.389062i
$63$	190.289	+	78.8203i	0.380542	+	0.157626i
$64$			551.903i			1.07794i
$65$	−14.1121	+	34.0695i	−0.0269290	+	0.0650124i
$66$	31.4388	−	31.4388i	0.0586341	−	0.0586341i
$67$	304.454			0.555150			0.277575	−	0.960704i	$-0.410469\pi$
$67$	304.454			0.555150			0.277575	+	0.960704i	$0.410469\pi$
$68$	−5.15410	−	54.7927i	−0.00919156	−	0.0977146i
$69$	432.997			0.755460
$70$	−99.0747	+	99.0747i	−0.169167	+	0.169167i
$71$	−179.862	+	434.226i	−0.300644	+	0.725819i	0.699296	+	0.714833i	$0.253497\pi$
$71$	−179.862	+	434.226i	−0.300644	+	0.725819i	−0.999940	+	0.0109864i	$0.996503\pi$
$72$		−	194.423i		−	0.318236i
$73$	−131.243	−	54.3626i	−0.210422	−	0.0871597i	0.274983	−	0.961449i	$-0.411328\pi$
$73$	−131.243	−	54.3626i	−0.210422	−	0.0871597i	−0.485405	+	0.874289i	$0.661328\pi$
$74$	−251.588	−	607.388i	−0.395224	−	0.954155i
$75$	482.785	−	199.976i	0.743296	−	0.307883i
$76$	89.3393	+	89.3393i	0.134841	+	0.134841i
$77$	67.5525	+	67.5525i	0.0999781	+	0.0999781i
$78$	189.956	−	78.6825i	0.275748	−	0.114219i
$79$	−274.715	−	663.221i	−0.391239	−	0.944534i	−0.989671	−	0.143360i	$-0.954209\pi$
$79$	−274.715	−	663.221i	−0.391239	−	0.944534i	0.598432	−	0.801174i	$-0.295791\pi$
$80$	110.083	+	45.5977i	0.153845	+	0.0637248i
$81$		−	438.657i		−	0.601725i
$82$	55.6232	−	134.286i	0.0749092	−	0.180847i
$83$	−259.960	+	259.960i	−0.343787	+	0.343787i	−0.857789	−	0.514002i	$-0.828162\pi$
$83$	−259.960	+	259.960i	−0.343787	+	0.343787i	0.514002	+	0.857789i	$0.328162\pi$
$84$	−85.0162			−0.110429
$85$	−139.774	−	43.0703i	−0.178360	−	0.0549603i
$86$	381.653			0.478542
$87$	−614.336	+	614.336i	−0.757054	+	0.757054i
$88$	34.5100	−	83.3146i	0.0418043	−	0.100925i
$89$		−	1042.28i		−	1.24137i	−0.784061	−	0.620684i	$-0.786855\pi$
$89$		−	1042.28i		−	1.24137i	0.784061	−	0.620684i	$-0.213145\pi$
$90$	−42.6643	−	17.6721i	−0.0499690	−	0.0206978i
$91$	169.065	+	408.158i	0.194756	+	0.470183i
$92$	72.5165	−	30.0373i	0.0821780	−	0.0340392i
$93$	−234.417	−	234.417i	−0.261375	−	0.261375i
$94$	889.738	+	889.738i	0.976271	+	0.976271i
$95$	310.214	−	128.495i	0.335024	−	0.138772i
$96$	58.6768	+	141.658i	0.0623820	+	0.150604i
$97$	−834.757	−	345.768i	−0.873781	−	0.361932i	−0.0996991	−	0.995018i	$-0.531788\pi$
$97$	−834.757	−	345.768i	−0.873781	−	0.361932i	−0.774082	+	0.633086i	$0.781788\pi$
$98$			757.260i			0.780559i
$99$	−12.0495	+	29.0899i	−0.0122325	+	0.0295318i
$100$	66.9823	−	66.9823i	0.0669823	−	0.0669823i
$101$	−443.233			−0.436667			−0.218333	−	0.975874i	$-0.570062\pi$
$101$	−443.233			−0.436667			−0.218333	+	0.975874i	$0.570062\pi$
$102$	381.256	+	720.866i	0.370098	+	0.699768i
$103$	−1396.36			−1.33580			−0.667901	−	0.744250i	$-0.732807\pi$
$103$	−1396.36			−1.33580			−0.667901	+	0.744250i	$0.732807\pi$
$104$	294.882	−	294.882i	0.278034	−	0.278034i
$105$	−86.4629	+	208.740i	−0.0803611	+	0.194009i
$106$			259.384i			0.237676i
$107$	1703.54	+	705.628i	1.53913	+	0.637529i	0.981310	−	0.192432i	$-0.0616374\pi$
$107$	1703.54	+	705.628i	1.53913	+	0.637529i	0.557821	+	0.829961i	$0.311637\pi$
$108$	−45.8621	−	110.721i	−0.0408619	−	0.0986492i
$109$	344.570	−	142.726i	0.302788	−	0.125419i	−0.226117	−	0.974100i	$-0.572603\pi$
$109$	344.570	−	142.726i	0.302788	−	0.125419i	0.528904	+	0.848681i	$0.322603\pi$
$110$	−15.1458	−	15.1458i	−0.0131281	−	0.0131281i
$111$	−749.633	−	749.633i	−0.641009	−	0.641009i
$112$	1318.81	−	546.268i	1.11264	−	0.460870i
$113$	680.844	+	1643.70i	0.566800	+	1.36838i	0.904238	+	0.427029i	$0.140440\pi$
$113$	680.844	+	1643.70i	0.566800	+	1.36838i	−0.337438	+	0.941348i	$0.609560\pi$
$114$	−1729.62	−	716.430i	−1.42099	−	0.588595i
$115$		−	208.598i		−	0.169147i
$116$	−60.2694	+	145.503i	−0.0482403	+	0.116462i
$117$	−102.960	+	102.960i	−0.0813563	+	0.0813563i
$118$	−979.020			−0.763781
$119$	−1548.92	+	819.203i	−1.19319	+	0.631061i
$120$	213.275			0.162244
$121$	930.832	−	930.832i	0.699348	−	0.699348i
$122$	727.624	−	1756.64i	0.539967	−	1.30360i
$123$		−	234.384i		−	0.171819i
$124$	−55.5208	−	22.9975i	−0.0402090	−	0.0166551i
$125$	−196.155	−	473.561i	−0.140357	−	0.338852i
$126$	−511.125	+	211.715i	−0.361386	+	0.149691i
$127$	1226.83	+	1226.83i	0.857192	+	0.857192i	0.991006	−	0.133814i	$-0.0427225\pi$
$127$	1226.83	+	1226.83i	0.857192	+	0.857192i	−0.133814	+	0.991006i	$0.542723\pi$
$128$	−847.988	−	847.988i	−0.585565	−	0.585565i
$129$	568.586	−	235.516i	0.388071	−	0.160744i
$130$	−37.9056	−	91.5123i	−0.0255734	−	0.0617397i
$131$	522.374	+	216.374i	0.348397	+	0.144311i	0.550018	−	0.835153i	$-0.314621\pi$
$131$	522.374	+	216.374i	0.348397	+	0.144311i	−0.201621	+	0.979464i	$0.564621\pi$
$132$		−	12.9966i		−	0.00856978i
$133$	1539.39	−	3716.42i	1.00362	−	2.42296i
$134$	−578.256	+	578.256i	−0.372789	+	0.372789i
$135$	−318.495			−0.203050
$136$	1273.95	+	1054.89i	0.803237	+	0.665116i
$137$	−1150.24			−0.717314			−0.358657	−	0.933469i	$-0.616765\pi$
$137$	−1150.24			−0.717314			−0.358657	+	0.933469i	$0.616765\pi$
$138$	−822.400	+	822.400i	−0.507300	+	0.507300i
$139$	−376.814	+	909.710i	−0.229935	+	0.555112i	−0.996169	−	0.0874493i	$-0.972128\pi$
$139$	−376.814	+	909.710i	−0.229935	+	0.555112i	0.766234	+	0.642562i	$0.222128\pi$
$140$			40.9569i			0.0247249i
$141$	1874.59	+	776.479i	1.11964	+	0.463768i
$142$	−483.118	−	1166.35i	−0.285510	−	0.689281i
$143$	−62.3962	+	25.8453i	−0.0364883	+	0.0151140i
$144$	332.677	+	332.677i	0.192521	+	0.192521i
$145$	295.959	+	295.959i	0.169504	+	0.169504i
$146$	352.524	−	146.020i	0.199830	−	0.0827721i
$147$	467.301	+	1128.17i	0.262193	+	0.632990i
$148$	−177.548	−	73.5428i	−0.0986105	−	0.0408458i
$149$			1772.18i			0.974382i	0.873295	+	0.487191i	$0.161979\pi$
$149$			1772.18i			0.974382i	−0.873295	+	0.487191i	$0.838021\pi$
$150$	−537.144	+	1296.78i	−0.292384	+	0.705878i
$151$	−1337.91	+	1337.91i	−0.721044	+	0.721044i	−0.968818	−	0.247774i	$-0.920301\pi$
$151$	−1337.91	+	1337.91i	−0.721044	+	0.721044i	0.247774	+	0.968818i	$0.420301\pi$
$152$	−3797.16			−2.02625
$153$	−444.809	−	368.322i	−0.235037	−	0.194621i
$154$	−256.607			−0.134273
$155$	−112.931	+	112.931i	−0.0585216	+	0.0585216i
$156$	23.0000	−	55.5269i	0.0118043	−	0.0284981i
$157$		−	289.955i		−	0.147395i	−0.997281	−	0.0736973i	$-0.976520\pi$
$157$		−	289.955i		−	0.147395i	0.997281	−	0.0736973i	$-0.0234799\pi$
$158$	1781.44	+	737.897i	0.896986	+	0.371544i
$159$	160.065	+	386.430i	0.0798362	+	0.192742i
$160$	68.2445	−	28.2678i	0.0337200	−	0.0139673i
$161$	−1767.09	−	1767.09i	−0.865006	−	0.865006i
$162$	833.150	+	833.150i	0.404065	+	0.404065i
$163$	1563.14	−	647.475i	0.751134	−	0.311130i	0.0259298	−	0.999664i	$-0.491745\pi$
$163$	1563.14	−	647.475i	0.751134	−	0.311130i	0.725204	+	0.688534i	$0.241745\pi$
$164$	−16.2594	−	39.2537i	−0.00774175	−	0.0186902i
$165$	−31.9106	−	13.2178i	−0.0150560	−	0.00623638i
$166$		−	987.495i		−	0.461714i
$167$	480.582	−	1160.23i	0.222686	−	0.537612i	−0.772567	−	0.634933i	$-0.781028\pi$
$167$	480.582	−	1160.23i	0.222686	−	0.537612i	0.995253	+	0.0973216i	$0.0310275\pi$
$168$	1806.71	−	1806.71i	0.829705	−	0.829705i
$169$	1884.68			0.857842
$170$	347.280	−	183.672i	0.156677	−	0.0828645i
$171$	1325.81			0.592907
$172$	78.8864	−	78.8864i	0.0349711	−	0.0349711i
$173$	153.530	−	370.654i	0.0674720	−	0.162892i	−0.886547	−	0.462639i	$-0.846902\pi$
$173$	153.530	−	370.654i	0.0674720	−	0.162892i	0.954019	+	0.299748i	$0.0969025\pi$
$174$		−	2333.64i		−	1.01674i
$175$	−2786.39	−	1154.16i	−1.20361	−	0.498550i
$176$	83.5093	+	201.609i	0.0357656	+	0.0863459i
$177$	−1458.54	+	604.149i	−0.619384	+	0.256557i
$178$	1979.63	+	1979.63i	0.833593	+	0.833593i
$179$	543.928	+	543.928i	0.227123	+	0.227123i	0.811490	−	0.584366i	$-0.198657\pi$
$179$	543.928	+	543.928i	0.227123	+	0.227123i	−0.584366	+	0.811490i	$0.698657\pi$
$180$	−12.4714	+	5.16580i	−0.00516422	+	0.00213909i
$181$	−1005.65	−	2427.86i	−0.412980	−	0.997022i	−0.984333	−	0.176318i	$-0.943581\pi$
$181$	−1005.65	−	2427.86i	−0.412980	−	0.997022i	0.571353	−	0.820704i	$-0.306419\pi$
$182$	−1096.33	−	454.115i	−0.446514	−	0.184952i
$183$		−	3066.06i		−	1.23852i
$184$	−902.739	+	2179.40i	−0.361689	+	0.873195i
$185$	−361.139	+	361.139i	−0.143521	+	0.143521i
$186$	890.465			0.351033
$187$	−125.233	−	236.787i	−0.0489732	−	0.0925968i
$188$	367.812			0.142689
$189$	−2698.05	+	2698.05i	−1.03838	+	1.03838i
$190$	−345.143	+	833.249i	−0.131786	+	0.318159i
$191$		−	207.856i		−	0.0787430i	−0.999225	−	0.0393715i	$-0.987464\pi$
$191$		−	207.856i		−	0.0787430i	0.999225	−	0.0393715i	$-0.0125356\pi$
$192$	−2208.53	−	914.804i	−0.830141	−	0.343856i
$193$	1751.78	+	4229.18i	0.653348	+	1.57732i	0.807889	+	0.589335i	$0.200610\pi$
$193$	1751.78	+	4229.18i	0.653348	+	1.57732i	−0.154541	+	0.987986i	$0.549390\pi$
$194$	2242.19	−	928.747i	0.829795	−	0.343712i
$195$	−112.944	−	112.944i	−0.0414772	−	0.0414772i
$196$	156.523	+	156.523i	0.0570420	+	0.0570420i
$197$	−2439.95	+	1010.66i	−0.882434	+	0.365516i	−0.777440	−	0.628957i	$-0.783482\pi$
$197$	−2439.95	+	1010.66i	−0.882434	+	0.365516i	−0.104994	+	0.994473i	$0.533482\pi$
$198$	−32.3654	−	78.1369i	−0.0116167	−	0.0280452i
$199$	−1525.28	−	631.793i	−0.543339	−	0.225059i	0.0940949	−	0.995563i	$-0.470004\pi$
$199$	−1525.28	−	631.793i	−0.543339	−	0.225059i	−0.637434	+	0.770505i	$0.720004\pi$
$200$			2846.92i			1.00654i
$201$	−504.647	+	1218.33i	−0.177090	+	0.427533i
$202$	841.842	−	841.842i	0.293227	−	0.293227i
$203$	5014.28			1.73366
$204$	227.805	+	70.1964i	0.0781841	+	0.0240918i
$205$	−112.916			−0.0384701
$206$	2652.14	−	2652.14i	0.897006	−	0.897006i
$207$	315.198	−	760.956i	0.105835	−	0.255508i
$208$			1009.14i			0.336401i
$209$	568.137	+	235.330i	0.188033	+	0.0778858i
$210$	−232.243	−	560.685i	−0.0763157	−	0.184242i
$211$	−1020.47	+	422.694i	−0.332949	+	0.137912i	−0.542894	−	0.839801i	$-0.682672\pi$
$211$	−1020.47	+	422.694i	−0.332949	+	0.137912i	0.209945	+	0.977713i	$0.432672\pi$
$212$	53.6139	+	53.6139i	0.0173690	+	0.0173690i
$213$	−1439.50	−	1439.50i	−0.463065	−	0.463065i
$214$	−4575.77	+	1895.35i	−1.46165	+	0.605436i
$215$	−113.461	−	273.918i	−0.0359905	−	0.0868888i
$216$	3327.59	+	1378.33i	1.04821	+	0.434184i
$217$			1913.34i			0.598552i
$218$	−383.367	+	925.531i	−0.119105	+	0.287545i
$219$	435.082	−	435.082i	0.134247	−	0.134247i
$220$	−6.26117			−0.00191876
$221$	−116.009	−	1233.28i	−0.0353103	−	0.375381i
$222$	2847.59			0.860889
$223$	−1530.74	+	1530.74i	−0.459667	+	0.459667i	−0.898546	−	0.438879i	$-0.855376\pi$
$223$	−1530.74	+	1530.74i	−0.459667	+	0.459667i	0.438879	+	0.898546i	$0.355376\pi$
$224$	338.653	−	817.580i	0.101014	−	0.243870i
$225$		−	994.025i		−	0.294526i
$226$	−4415.06	−	1828.78i	−1.29949	−	0.538267i
$227$	−997.159	−	2407.36i	−0.291559	−	0.703885i	0.708440	−	0.705771i	$-0.249399\pi$
$227$	−997.159	−	2407.36i	−0.291559	−	0.703885i	−0.999998	+	0.00188682i	$0.999399\pi$
$228$	−505.590	+	209.422i	−0.146858	+	0.0608304i
$229$	−798.278	−	798.278i	−0.230357	−	0.230357i	0.582485	−	0.812842i	$-0.302081\pi$
$229$	−798.278	−	798.278i	−0.230357	−	0.230357i	−0.812842	+	0.582485i	$0.802081\pi$
$230$	396.194	+	396.194i	0.113584	+	0.113584i
$231$	−382.294	+	158.351i	−0.108888	+	0.0451028i
$232$	−1811.33	−	4372.94i	−0.512585	−	1.23749i
$233$	3987.43	+	1651.65i	1.12114	+	0.464391i	0.864760	−	0.502185i	$-0.167470\pi$
$233$	3987.43	+	1651.65i	1.12114	+	0.464391i	0.256379	+	0.966576i	$0.417470\pi$
$234$		−	391.109i		−	0.109263i
$235$	374.072	−	903.089i	0.103837	−	0.250685i
$236$	−202.361	+	202.361i	−0.0558159	+	0.0558159i
$237$	3109.34			0.852209
$238$	1385.97	−	4497.83i	0.377475	−	1.22500i
$239$	788.197			0.213323			0.106662	−	0.994295i	$-0.465984\pi$
$239$	788.197			0.213323			0.106662	+	0.994295i	$0.465984\pi$
$240$	−364.934	+	364.934i	−0.0981516	+	0.0981516i
$241$	−1386.41	+	3347.08i	−0.370566	+	0.894625i	0.623089	+	0.782151i	$0.285877\pi$
$241$	−1386.41	+	3347.08i	−0.370566	+	0.894625i	−0.993655	+	0.112474i	$0.964123\pi$
$242$			3535.90i			0.939240i
$243$	−2052.06	−	849.991i	−0.541727	−	0.224391i
$244$	−212.695	−	513.490i	−0.0558048	−	0.134725i
$245$	543.498	−	225.124i	0.141726	−	0.0587047i
$246$	445.171	+	445.171i	0.115378	+	0.115378i
$247$	2010.85	+	2010.85i	0.518006	+	0.518006i
$248$	1668.62	−	691.164i	0.427247	−	0.176972i
$249$	−609.378	−	1471.17i	−0.155092	−	0.374424i
$250$	1272.01	+	526.882i	0.321795	+	0.133292i
$251$		−	5974.99i		−	1.50254i	−0.659994	−	0.751271i	$-0.729441\pi$
$251$		−	5974.99i		−	1.50254i	0.659994	−	0.751271i	$-0.270559\pi$
$252$	−61.8872	+	149.409i	−0.0154703	+	0.0373487i
$253$	270.139	−	270.139i	0.0671284	−	0.0671284i
$254$	−4660.28			−1.15123
$255$	404.035	−	487.939i	0.0992221	−	0.119827i
$256$	−1194.02			−0.291509
$257$	2652.30	−	2652.30i	0.643758	−	0.643758i	−0.307719	−	0.951477i	$-0.599566\pi$
$257$	2652.30	−	2652.30i	0.643758	−	0.643758i	0.951477	+	0.307719i	$0.0995658\pi$
$258$	−632.606	+	1527.25i	−0.152653	+	0.368536i
$259$			6118.59i			1.46792i
$260$	−26.7503	−	11.0803i	−0.00638070	−	0.00264297i
$261$	632.441	+	1526.85i	0.149989	+	0.362105i
$262$	−1403.12	+	581.191i	−0.330859	+	0.137046i
$263$	−5350.27	−	5350.27i	−1.25442	−	1.25442i	−0.953719	−	0.300699i	$-0.902780\pi$
$263$	−5350.27	−	5350.27i	−1.25442	−	1.25442i	−0.300699	−	0.953719i	$-0.597220\pi$
$264$	276.195	+	276.195i	0.0643888	+	0.0643888i
$265$	186.164	−	77.1118i	0.0431547	−	0.0178752i
$266$	4134.87	+	9982.46i	0.953102	+	2.30099i
$267$	4170.87	+	1727.63i	0.956004	+	0.395990i
$268$			239.048i			0.0544857i
$269$	−2675.20	+	6458.50i	−0.606356	+	1.46387i	0.260579	+	0.965453i	$0.416087\pi$
$269$	−2675.20	+	6458.50i	−0.606356	+	1.46387i	−0.866935	+	0.498421i	$0.833913\pi$
$270$	604.924	−	604.924i	0.136350	−	0.136350i
$271$	1356.64			0.304097			0.152049	−	0.988373i	$-0.451413\pi$
$271$	1356.64			0.304097			0.152049	+	0.988373i	$0.451413\pi$
$272$	−3984.86	+	374.837i	−0.888300	+	0.0835583i
$273$	−1913.55			−0.424224
$274$	2184.68	−	2184.68i	0.481684	−	0.481684i
$275$	176.439	−	425.962i	0.0386897	−	0.0934053i
$276$			339.975i			0.0741453i
$277$	6628.70	+	2745.70i	1.43783	+	0.595570i	0.959272	−	0.282484i	$-0.0911583\pi$
$277$	6628.70	+	2745.70i	1.43783	+	0.595570i	0.478562	+	0.878054i	$0.341158\pi$
$278$	−1012.14	−	2443.52i	−0.218360	−	0.527168i
$279$	−582.611	+	241.325i	−0.125018	+	0.0517841i
$280$	−870.387	−	870.387i	−0.185770	−	0.185770i
$281$	−4674.98	−	4674.98i	−0.992476	−	0.992476i	0.00749542	−	0.999972i	$-0.497614\pi$
$281$	−4674.98	−	4674.98i	−0.992476	−	0.992476i	−0.999972	+	0.00749542i	$0.997614\pi$
$282$	−5035.22	+	2085.66i	−1.06327	+	0.440422i
$283$	−884.335	−	2134.97i	−0.185754	−	0.448449i	0.803380	−	0.595466i	$-0.203033\pi$
$283$	−884.335	−	2134.97i	−0.185754	−	0.448449i	−0.989134	+	0.147017i	$0.953033\pi$
$284$	−340.940	−	141.222i	−0.0712362	−	0.0295070i
$285$			1454.36i			0.302277i
$286$	69.4217	−	167.599i	0.0143531	−	0.0346515i
$287$	−956.537	+	956.537i	−0.196734	+	0.196734i
$288$	291.666			0.0596757
$289$	4826.82	−	916.180i	0.982459	−	0.186481i
$290$	−1124.24			−0.227647
$291$	2767.29	−	2767.29i	0.557463	−	0.557463i
$292$	42.6837	−	103.048i	0.00855437	−	0.0206521i
$293$			6445.85i			1.28522i	0.766192	+	0.642612i	$0.222149\pi$
$293$			6445.85i			1.28522i	−0.766192	+	0.642612i	$0.777851\pi$
$294$	−3030.30	−	1255.19i	−0.601125	−	0.248994i
$295$	291.051	+	702.659i	0.0574429	+	0.138679i
$296$	5336.01	−	2210.25i	1.04780	−	0.434013i
$297$	−412.458	−	412.458i	−0.0805832	−	0.0805832i
$298$	−3365.94	−	3365.94i	−0.654309	−	0.654309i
$299$	1632.20	−	676.081i	0.315695	−	0.130765i
$300$	157.015	+	379.067i	0.0302175	+	0.0729514i
$301$	−3281.59	−	1359.28i	−0.628397	−	0.260291i
$302$		−	5082.24i		−	0.968378i
$303$	734.679	−	1773.67i	0.139294	−	0.336286i
$304$	6497.30	−	6497.30i	1.22581	−	1.22581i
$305$	−1477.08			−0.277304
$306$	1544.40	−	145.274i	0.288520	−	0.0271398i
$307$	221.421			0.0411634			0.0205817	−	0.999788i	$-0.493448\pi$
$307$	221.421			0.0411634			0.0205817	+	0.999788i	$0.493448\pi$
$308$	−53.0400	+	53.0400i	−0.00981245	+	0.00981245i
$309$	2314.53	−	5587.78i	0.426114	−	1.02873i
$310$		−	428.985i		−	0.0785959i
$311$	1195.38	+	495.142i	0.217954	+	0.0902795i	0.488989	−	0.872290i	$-0.337366\pi$
$311$	1195.38	+	495.142i	0.217954	+	0.0902795i	−0.271035	+	0.962570i	$0.587366\pi$
$312$	691.239	+	1668.80i	0.125429	+	0.302811i
$313$	−356.107	+	147.504i	−0.0643079	+	0.0266372i	−0.414606	−	0.910001i	$-0.636080\pi$
$313$	−356.107	+	147.504i	−0.0643079	+	0.0266372i	0.350298	+	0.936638i	$0.386080\pi$
$314$	550.718	+	550.718i	0.0989772	+	0.0989772i
$315$	303.903	+	303.903i	0.0543586	+	0.0543586i
$316$	520.739	−	215.697i	0.0927021	−	0.0383985i
$317$	248.380	+	599.641i	0.0440075	+	0.106244i	0.944355	−	0.328929i	$-0.106688\pi$
$317$	248.380	+	599.641i	0.0440075	+	0.106244i	−0.900347	+	0.435172i	$0.856688\pi$
$318$	−1037.97	−	429.941i	−0.183039	−	0.0758172i
$319$			766.545i			0.134540i
$320$	−440.710	+	1063.97i	−0.0769889	+	0.185868i
$321$	−5647.38	+	5647.38i	−0.981950	+	0.981950i
$322$	6712.53			1.16172
$323$	−7193.46	+	8687.29i	−1.23918	+	1.49651i
$324$	344.419			0.0590568
$325$	1507.64	−	1507.64i	0.257319	−	0.257319i
$326$	−1739.15	+	4198.67i	−0.295468	+	0.713322i
$327$			1615.43i			0.273191i
$328$	1179.73	+	488.659i	0.198596	+	0.0822612i
$329$	−4481.44	−	10819.1i	−0.750972	−	1.81301i
$330$	85.7132	−	35.5036i	0.0142980	−	0.00592244i
$331$	1010.96	+	1010.96i	0.167877	+	0.167877i	0.786046	−	0.618168i	$-0.212125\pi$
$331$	1010.96	+	1010.96i	0.167877	+	0.167877i	−0.618168	+	0.786046i	$0.712125\pi$
$332$	−204.112	−	204.112i	−0.0337413	−	0.0337413i
$333$	−1863.11	+	771.725i	−0.306600	+	0.126998i
$334$	1290.87	+	3116.42i	0.211476	+	0.510548i
$335$	586.933	+	243.116i	0.0957241	+	0.0396502i
$336$			6182.89i			1.00388i
$337$	216.355	−	522.328i	0.0349722	−	0.0844303i	−0.905428	−	0.424499i	$-0.860450\pi$
$337$	216.355	−	522.328i	0.0349722	−	0.0844303i	0.940401	+	0.340069i	$0.110450\pi$
$338$	−3579.61	+	3579.61i	−0.576051	+	0.576051i
$339$	−7706.08			−1.23462
$340$	33.8174	−	109.746i	0.00539413	−	0.0175053i
$341$	−292.497			−0.0464504
$342$	−2518.13	+	2518.13i	−0.398143	+	0.398143i
$343$	−584.286	+	1410.59i	−0.0919780	+	0.222055i
$344$			3352.88i			0.525509i
$345$	834.740	+	345.761i	0.130263	+	0.0539569i
$346$	412.388	+	995.592i	0.0640754	+	0.154692i
$347$	3500.32	−	1449.88i	0.541518	−	0.224304i	−0.0951212	−	0.995466i	$-0.530324\pi$
$347$	3500.32	−	1449.88i	0.541518	−	0.224304i	0.636640	+	0.771161i	$0.280324\pi$
$348$	−482.356	−	482.356i	−0.0743018	−	0.0743018i
$349$	4516.50	+	4516.50i	0.692730	+	0.692730i	0.962832	−	0.270102i	$-0.0870573\pi$
$349$	4516.50	+	4516.50i	0.692730	+	0.692730i	−0.270102	+	0.962832i	$0.587057\pi$
$350$	7484.36	−	3100.12i	1.14302	−	0.473453i
$351$	−1032.27	−	2492.11i	−0.156975	−	0.378971i
$352$	124.985	+	51.7706i	0.0189254	+	0.00783916i
$353$			6291.34i			0.948595i	0.880365	+	0.474298i	$0.157298\pi$
$353$			6291.34i			0.948595i	−0.880365	+	0.474298i	$0.842702\pi$
$354$	1622.77	−	3917.71i	0.243642	−	0.588204i
$355$	−693.484	+	693.484i	−0.103680	+	0.103680i
$356$	818.367			0.121835
$357$	−710.771	−	7556.13i	−0.105372	−	1.12020i
$358$	−2066.19			−0.305032
$359$	2382.60	−	2382.60i	0.350275	−	0.350275i	−0.509937	−	0.860212i	$-0.670331\pi$
$359$	2382.60	−	2382.60i	0.350275	−	0.350275i	0.860212	+	0.509937i	$0.170331\pi$
$360$	155.253	−	374.813i	0.0227292	−	0.0548733i
$361$		−	19034.5i		−	2.77511i
$362$	6521.33	+	2701.22i	0.946832	+	0.392191i
$363$	2181.98	+	5267.78i	0.315495	+	0.761671i
$364$	−320.473	+	132.744i	−0.0461465	+	0.0191145i
$365$	−209.602	−	209.602i	−0.0300578	−	0.0300578i
$366$	5823.42	+	5823.42i	0.831681	+	0.831681i
$367$	−921.585	+	381.733i	−0.131080	+	0.0542951i	−0.447259	−	0.894404i	$-0.647600\pi$
$367$	−921.585	+	381.733i	−0.131080	+	0.0542951i	0.316179	+	0.948699i	$0.397600\pi$
$368$	−2184.50	−	5273.85i	−0.309443	−	0.747060i
$369$	−411.911	−	170.619i	−0.0581117	−	0.0240707i
$370$		−	1371.84i		−	0.192752i
$371$	923.812	−	2230.28i	0.129277	−	0.312103i
$372$	184.057	−	184.057i	0.0256529	−	0.0256529i
$373$	−3180.59			−0.441514			−0.220757	−	0.975329i	$-0.570853\pi$
$373$	−3180.59			−0.441514			−0.220757	+	0.975329i	$0.570853\pi$
$374$	687.593	+	211.876i	0.0950658	+	0.0292938i
$375$	2220.17			0.305731
$376$	−7816.50	+	7816.50i	−1.07209	+	1.07209i
$377$	−1356.55	+	3274.99i	−0.185320	+	0.447402i
$378$		−	10248.9i		−	1.39457i
$379$	−10009.2	−	4145.96i	−1.35657	−	0.561910i	−0.418456	−	0.908237i	$-0.637429\pi$
$379$	−10009.2	−	4145.96i	−1.35657	−	0.561910i	−0.938114	+	0.346327i	$0.887429\pi$
$380$	100.890	+	243.570i	0.0136199	+	0.0328813i
$381$	−6942.88	+	2875.84i	−0.933582	+	0.386702i
$382$	394.785	+	394.785i	0.0528768	+	0.0528768i
$383$	5351.33	+	5351.33i	0.713944	+	0.713944i	0.967358	−	0.253414i	$-0.0815536\pi$
$383$	5351.33	+	5351.33i	0.713944	+	0.713944i	−0.253414	+	0.967358i	$0.581554\pi$
$384$	4798.95	−	1987.79i	0.637748	−	0.264164i
$385$	76.2863	+	184.171i	0.0100985	+	0.0243799i
$386$	−11359.8	−	4705.37i	−1.49792	−	0.620458i
$387$		−	1170.69i		−	0.153771i
$388$	271.486	−	655.424i	0.0355221	−	0.0857580i
$389$	6787.77	−	6787.77i	0.884714	−	0.884714i	−0.109295	−	0.994009i	$-0.534859\pi$
$389$	6787.77	−	6787.77i	0.884714	−	0.884714i	0.994009	+	0.109295i	$0.0348594\pi$
$390$	429.032			0.0557048
$391$	3275.95	+	6194.06i	0.423713	+	0.801143i
$392$	−6652.65			−0.857168
$393$	−1731.72	+	1731.72i	−0.222274	+	0.222274i
$394$	2714.68	−	6553.82i	0.347116	−	0.838013i
$395$		−	1497.94i		−	0.190809i
$396$	−22.8405	−	9.46084i	−0.00289843	−	0.00120057i
$397$	2017.52	+	4870.72i	0.255054	+	0.615754i	0.998598	−	0.0529327i	$-0.0168569\pi$
$397$	2017.52	+	4870.72i	0.255054	+	0.615754i	−0.743545	+	0.668686i	$0.766857\pi$
$398$	4096.98	−	1697.03i	0.515988	−	0.213729i
$399$	12320.3	+	12320.3i	1.54582	+	1.54582i
$400$	−4871.36	−	4871.36i	−0.608920	−	0.608920i
$401$	3326.28	−	1377.79i	0.414231	−	0.171580i	−0.165828	−	0.986155i	$-0.553030\pi$
$401$	3326.28	−	1377.79i	0.414231	−	0.171580i	0.580059	+	0.814575i	$0.303030\pi$
$402$	−1355.50	−	3272.48i	−0.168175	−	0.406011i
$403$	−1249.66	−	517.628i	−0.154467	−	0.0639824i
$404$		−	348.012i		−	0.0428571i
$405$	350.280	−	845.652i	0.0429767	−	0.103755i
$406$	−9523.72	+	9523.72i	−1.16417	+	1.16417i
$407$	−935.364			−0.113917
$408$	−6332.93	+	3349.40i	−0.768448	+	0.406421i
$409$	9516.13			1.15047			0.575235	−	0.817988i	$-0.304911\pi$
$409$	9516.13			1.15047			0.575235	+	0.817988i	$0.304911\pi$
$410$	214.463	−	214.463i	0.0258331	−	0.0258331i
$411$	1906.58	−	4602.89i	0.228819	−	0.552418i
$412$		−	1096.38i		−	0.131104i
$413$	8417.97	+	3486.84i	1.00296	+	0.415439i
$414$	846.637	+	2043.96i	0.100507	+	0.242646i
$415$	−708.742	+	293.570i	−0.0838332	+	0.0347248i
$416$	442.370	+	442.370i	0.0521370	+	0.0521370i
$417$	−3015.77	−	3015.77i	−0.354156	−	0.354156i
$418$	−1526.04	+	632.107i	−0.178567	+	0.0739650i
$419$	2414.93	+	5830.16i	0.281568	+	0.679766i	0.999873	−	0.0159630i	$-0.00508140\pi$
$419$	2414.93	+	5830.16i	0.281568	+	0.679766i	−0.718304	+	0.695729i	$0.755081\pi$
$420$	−163.896	−	67.8879i	−0.0190412	−	0.00788711i
$421$		−	1544.81i		−	0.178835i	−0.995994	−	0.0894177i	$-0.971499\pi$
$421$		−	1544.81i		−	0.178835i	0.995994	−	0.0894177i	$-0.0285006\pi$
$422$	1135.37	−	2741.04i	0.130970	−	0.316188i
$423$	2729.19	−	2729.19i	0.313707	−	0.313707i
$424$	−2278.73			−0.261002
$425$	6513.30	+	5393.30i	0.743392	+	0.615561i
$426$	5468.14			0.621906
$427$	−12512.8	+	12512.8i	−1.41811	+	1.41811i
$428$	−554.036	+	1337.56i	−0.0625709	+	0.151060i
$429$		−	292.528i		−	0.0329217i
$430$	735.757	+	304.761i	0.0825148	+	0.0341787i
$431$	343.395	+	829.029i	0.0383776	+	0.0926518i	0.941906	−	0.335876i	$-0.109032\pi$
$431$	343.395	+	829.029i	0.0383776	+	0.0926518i	−0.903529	+	0.428528i	$0.859032\pi$
$432$	−8052.30	+	3335.37i	−0.896797	+	0.371465i
$433$	3462.33	+	3462.33i	0.384270	+	0.384270i	0.872638	−	0.488368i	$-0.162408\pi$
$433$	3462.33	+	3462.33i	0.384270	+	0.384270i	−0.488368	+	0.872638i	$0.662408\pi$
$434$	−3634.04	−	3634.04i	−0.401934	−	0.401934i
$435$	−1674.89	+	693.763i	−0.184609	+	0.0764676i
$436$	112.064	+	270.545i	0.0123093	+	0.0297174i
$437$	−14861.8	−	6155.94i	−1.62685	−	0.673864i
$438$			1652.72i			0.180297i
$439$	537.292	−	1297.14i	0.0584136	−	0.141023i	−0.891978	−	0.452079i	$-0.850683\pi$
$439$	537.292	−	1297.14i	0.0584136	−	0.141023i	0.950392	+	0.311056i	$0.100683\pi$
$440$	133.058	−	133.058i	0.0144166	−	0.0144166i
$441$	2322.83			0.250818
$442$	2562.72	+	2122.05i	0.275784	+	0.228361i
$443$	−6453.57			−0.692141			−0.346070	−	0.938209i	$-0.612484\pi$
$443$	−6453.57			−0.692141			−0.346070	+	0.938209i	$0.612484\pi$
$444$	588.587	−	588.587i	0.0629124	−	0.0629124i
$445$	832.293	−	2009.33i	0.0886617	−	0.214048i
$446$		−	5814.71i		−	0.617342i
$447$	−7091.69	−	2937.48i	−0.750393	−	0.310823i
$448$	5279.78	+	12746.5i	0.556799	+	1.34423i
$449$	−4073.49	+	1687.29i	−0.428151	+	0.177346i	−0.586344	−	0.810062i	$-0.699433\pi$
$449$	−4073.49	+	1687.29i	−0.428151	+	0.177346i	0.158193	+	0.987408i	$0.449433\pi$
$450$	1887.97	+	1887.97i	0.197777	+	0.197777i
$451$	−146.228	−	146.228i	−0.0152674	−	0.0152674i
$452$	−1290.58	+	534.577i	−0.134301	+	0.0556291i
$453$	−3136.23	−	7571.52i	−0.325282	−	0.785300i
$454$	6466.26	+	2678.41i	0.668451	+	0.276881i
$455$			921.859i			0.0949833i
$456$	6293.96	−	15195.0i	0.646363	−	1.56046i
$457$	8889.44	−	8889.44i	0.909913	−	0.909913i	−0.0863515	−	0.996265i	$-0.527521\pi$
$457$	8889.44	−	8889.44i	0.909913	−	0.909913i	0.996265	+	0.0863515i	$0.0275208\pi$
$458$	3032.37			0.309374
$459$	9457.31	−	5001.84i	0.961720	−	0.508640i
$460$	163.784			0.0166011
$461$	3616.85	−	3616.85i	0.365409	−	0.365409i	−0.500391	−	0.865800i	$-0.666810\pi$
$461$	3616.85	−	3616.85i	0.365409	−	0.365409i	0.865800	+	0.500391i	$0.166810\pi$
$462$	425.338	−	1026.86i	0.0428323	−	0.103406i
$463$		−	5280.96i		−	0.530080i	−0.964237	−	0.265040i	$-0.914615\pi$
$463$		−	5280.96i		−	0.530080i	0.964237	−	0.265040i	$-0.0853852\pi$
$464$	10581.9	+	4383.16i	1.05873	+	0.438541i
$465$	−264.725	−	639.102i	−0.0264007	−	0.0637369i
$466$	−10710.4	+	4436.40i	−1.06470	+	0.441014i
$467$	−3132.80	−	3132.80i	−0.310425	−	0.310425i	0.534649	−	0.845074i	$-0.320444\pi$
$467$	−3132.80	−	3132.80i	−0.310425	−	0.310425i	−0.845074	+	0.534649i	$0.820444\pi$
$468$	−80.8411	−	80.8411i	−0.00798479	−	0.00798479i
$469$	7031.55	−	2912.56i	0.692296	−	0.286758i
$470$	1004.77	+	2425.74i	0.0986100	+	0.238066i
$471$	1160.31	+	480.614i	0.113512	+	0.0470181i
$472$		−	8600.86i		−	0.838743i
$473$	207.796	−	501.664i	0.0201997	−	0.0487665i
$474$	−5905.63	+	5905.63i	−0.572267	+	0.572267i
$475$	−19413.7			−1.87529
$476$	−643.211	−	1216.16i	−0.0619360	−	0.117107i
$477$	795.637			0.0763726
$478$	−1497.04	+	1497.04i	−0.143249	+	0.143249i
$479$	3328.23	−	8035.07i	0.317476	−	0.766454i	−0.681911	−	0.731435i	$-0.738851\pi$
$479$	3328.23	−	8035.07i	0.317476	−	0.766454i	0.999387	−	0.0350190i	$-0.0111492\pi$
$480$			319.947i			0.0304240i
$481$	−3996.25	−	1655.30i	−0.378822	−	0.156913i
$482$	−3723.95	−	8990.41i	−0.351911	−	0.849589i
$483$	10000.3	−	4142.27i	0.942092	−	0.390227i
$484$	730.859	+	730.859i	0.0686382	+	0.0686382i
$485$	−1333.15	−	1333.15i	−0.124815	−	0.124815i
$486$	5511.92	−	2283.11i	0.514457	−	0.213095i
$487$	4986.78	+	12039.2i	0.464010	+	1.12022i	0.966737	+	0.255773i	$0.0823301\pi$
$487$	4986.78	+	12039.2i	0.464010	+	1.12022i	−0.502727	+	0.864445i	$0.667670\pi$
$488$	15432.4	+	6392.30i	1.43154	+	0.592963i
$489$			7328.40i			0.677713i
$490$	−604.694	+	1459.86i	−0.0557495	+	0.134591i
$491$	−8315.81	+	8315.81i	−0.764332	+	0.764332i	−0.977102	−	0.212770i	$-0.931751\pi$
$491$	−8315.81	+	8315.81i	−0.764332	+	0.764332i	0.212770	+	0.977102i	$0.431751\pi$
$492$	184.031			0.0168633
$493$	−13436.0	−	4140.21i	−1.22744	−	0.378226i
$494$	−7638.51			−0.695694
$495$	−46.4583	+	46.4583i	−0.00421848	+	0.00421848i
$496$	−1672.52	+	4037.81i	−0.151408	+	0.365531i
$497$			11749.4i			1.06042i
$498$	3951.63	+	1636.82i	0.355576	+	0.147284i
$499$	−4104.11	−	9908.19i	−0.368187	−	0.888881i	−0.994048	−	0.108946i	$-0.965252\pi$
$499$	−4104.11	−	9908.19i	−0.368187	−	0.888881i	0.625861	−	0.779935i	$-0.284748\pi$
$500$	371.825	−	154.015i	0.0332570	−	0.0137755i
$501$	3846.26	+	3846.26i	0.342991	+	0.342991i
$502$	11348.4	+	11348.4i	1.00897	+	1.00897i
$503$	3607.71	−	1494.36i	0.319801	−	0.132466i	−0.217008	−	0.976170i	$-0.569630\pi$
$503$	3607.71	−	1494.36i	0.319801	−	0.132466i	0.536809	+	0.843704i	$0.319630\pi$
$504$	−1859.95	−	4490.32i	−0.164383	−	0.396854i
$505$	−854.473	−	353.934i	−0.0752942	−	0.0311879i
$506$			1026.16i			0.0901549i
$507$	−3123.94	+	7541.86i	−0.273647	+	0.660643i
$508$	−963.266	+	963.266i	−0.0841299	+	0.0841299i
$509$	−15132.3			−1.31774			−0.658870	−	0.752257i	$-0.728965\pi$
$509$	−15132.3			−1.31774			−0.658870	+	0.752257i	$0.728965\pi$
$510$	159.360	+	1694.14i	0.0138364	+	0.147094i
$511$	−3551.19			−0.307427
$512$	9051.73	−	9051.73i	0.781316	−	0.781316i
$513$	−9399.11	+	22691.5i	−0.808930	+	1.95293i
$514$			10075.1i			0.864581i
$515$	−2691.93	−	1115.04i	−0.230332	−	0.0954065i
$516$	184.919	+	446.435i	0.0157764	+	0.0380876i
$517$	1653.95	−	685.088i	0.140697	−	0.0582788i
$518$	−11621.2	−	11621.2i	−0.985723	−	0.985723i
$519$	1228.75	+	1228.75i	0.103923	+	0.103923i
$520$	803.951	−	333.007i	0.0677992	−	0.0280833i
$521$	6327.62	+	15276.2i	0.532088	+	1.28457i	0.930138	+	0.367210i	$0.119687\pi$
$521$	6327.62	+	15276.2i	0.532088	+	1.28457i	−0.398050	+	0.917364i	$0.630313\pi$
$522$	−4101.18	−	1698.76i	−0.343877	−	0.142438i
$523$		−	8724.36i		−	0.729426i	−0.931120	−	0.364713i	$-0.881167\pi$
$523$		−	8724.36i		−	0.729426i	0.931120	−	0.364713i	$-0.118833\pi$
$524$	−169.890	+	410.151i	−0.0141635	+	0.0341938i
$525$	9237.12	−	9237.12i	0.767888	−	0.767888i
$526$	20323.8			1.68471
$527$	1579.81	−	5126.89i	0.130584	−	0.423778i
$528$	−945.194			−0.0779058
$529$	1536.88	−	1536.88i	0.126315	−	0.126315i
$530$	−207.126	+	500.046i	−0.0169754	+	0.0409822i
$531$			3003.06i			0.245427i
$532$	2918.01	+	1208.68i	0.237804	+	0.0985016i
$533$	−365.968	−	883.524i	−0.0297407	−	0.0718005i
$534$	−11203.1	+	4640.49i	−0.907879	+	0.376056i
$535$	2720.65	+	2720.65i	0.219858	+	0.219858i
$536$	−5080.08	−	5080.08i	−0.409377	−	0.409377i
$537$	−3078.21	+	1275.03i	−0.247364	+	0.102461i
$538$	−7185.70	−	17347.8i	−0.575832	−	1.39018i
$539$	995.382	+	412.301i	0.0795438	+	0.0329481i
$540$		−	250.072i		−	0.0199285i
$541$	−3155.65	+	7618.42i	−0.250780	+	0.605437i	−0.998267	−	0.0588391i	$-0.981260\pi$
$541$	−3155.65	+	7618.42i	−0.250780	+	0.605437i	0.747487	+	0.664276i	$0.231260\pi$
$542$	−2576.70	+	2576.70i	−0.204205	+	0.204205i
$543$	11382.4			0.899567
$544$	−1582.50	+	1911.13i	−0.124723	+	0.150623i
$545$	778.240			0.0611672
$546$	3634.44	−	3634.44i	0.284871	−	0.284871i
$547$	9124.03	−	22027.4i	0.713191	−	1.72179i	0.0213210	−	0.999773i	$-0.493213\pi$
$547$	9124.03	−	22027.4i	0.713191	−	1.72179i	0.691870	−	0.722022i	$-0.256787\pi$
$548$		−	903.134i		−	0.0704014i
$549$	−5388.34	−	2231.92i	−0.418886	−	0.173508i
$550$	473.923	+	1144.15i	0.0367421	+	0.0887032i
$551$	29819.9	−	12351.8i	2.30557	−	0.954999i
$552$	−7224.92	−	7224.92i	−0.557089	−	0.557089i
$553$	−12689.4	−	12689.4i	−0.975784	−	0.975784i
$554$	−17805.0	+	7375.06i	−1.36545	+	0.565589i
$555$	−846.553	−	2043.76i	−0.0647463	−	0.156311i
$556$	−714.275	−	295.862i	−0.0544820	−	0.0225672i
$557$			19341.5i			1.47132i	0.677350	+	0.735661i	$0.263128\pi$
$557$			19341.5i			1.47132i	−0.677350	+	0.735661i	$0.736872\pi$
$558$	648.210	−	1564.92i	0.0491773	−	0.118725i
$559$	1775.58	−	1775.58i	0.134345	−	0.134345i
$560$	2978.63			0.224768
$561$	1155.12	−	108.657i	0.0869329	−	0.00817738i
$562$	17758.6			1.33292
$563$	10048.2	−	10048.2i	0.752189	−	0.752189i	−0.222698	−	0.974887i	$-0.571487\pi$
$563$	10048.2	−	10048.2i	0.752189	−	0.752189i	0.974887	+	0.222698i	$0.0714865\pi$
$564$	−609.666	+	1471.86i	−0.0455169	+	0.109888i
$565$			3712.44i			0.276431i
$566$	5734.63	+	2375.36i	0.425874	+	0.176403i
$567$	−4196.42	−	10131.0i	−0.310816	−	0.750377i
$568$	10246.6	−	4244.27i	0.756932	−	0.313531i
$569$	−6771.36	−	6771.36i	−0.498893	−	0.498893i	0.412200	−	0.911093i	$-0.364761\pi$
$569$	−6771.36	−	6771.36i	−0.498893	−	0.498893i	−0.911093	+	0.412200i	$0.864761\pi$
$570$	−2762.30	−	2762.30i	−0.202982	−	0.202982i
$571$	−13659.5	+	5657.96i	−1.00111	+	0.414673i	−0.822203	−	0.569194i	$-0.807255\pi$
$571$	−13659.5	+	5657.96i	−1.00111	+	0.414673i	−0.178905	+	0.983866i	$0.557255\pi$
$572$	−20.2929	−	48.9914i	−0.00148337	−	0.00358118i
$573$	831.770	+	344.530i	0.0606417	+	0.0251186i
$574$		−	3633.54i		−	0.264218i
$575$	−4615.42	+	11142.6i	−0.334742	+	0.808138i
$576$	−3215.38	+	3215.38i	−0.232594	+	0.232594i
$577$	11438.5			0.825284			0.412642	−	0.910893i	$-0.364606\pi$
$577$	11438.5			0.825284			0.412642	+	0.910893i	$0.364606\pi$
$578$	−7427.56	+	10907.8i	−0.534508	+	0.784956i
$579$	−19827.4			−1.42314
$580$	−232.377	+	232.377i	−0.0166361	+	0.0166361i
$581$	−3517.02	+	8490.84i	−0.251137	+	0.606298i
$582$			10512.0i			0.748685i
$583$	340.948	+	141.225i	0.0242206	+	0.0100325i
$584$	1282.81	+	3096.98i	0.0908958	+	0.219442i
$585$	−280.706	+	116.272i	−0.0198389	+	0.00821754i
$586$	−12242.7	−	12242.7i	−0.863042	−	0.863042i
$587$	5580.55	+	5580.55i	0.392392	+	0.392392i	0.875539	−	0.483147i	$-0.160507\pi$
$587$	5580.55	+	5580.55i	0.392392	+	0.392392i	−0.483147	+	0.875539i	$0.660507\pi$
$588$	−885.799	+	366.910i	−0.0621254	+	0.0257332i
$589$	4713.17	+	11378.6i	0.329716	+	0.796005i
$590$	−1887.37	−	781.776i	−0.131698	−	0.0545512i
$591$		−	11439.1i		−	0.796179i
$592$	−5348.48	+	12912.4i	−0.371319	+	0.896444i
$593$	5536.25	−	5536.25i	0.383384	−	0.383384i	−0.488936	−	0.872320i	$-0.662615\pi$
$593$	5536.25	−	5536.25i	0.383384	−	0.383384i	0.872320	+	0.488936i	$0.162615\pi$
$594$	1566.78			0.108225
$595$	−3640.20	+	342.416i	−0.250813	+	0.0235928i
$596$	−1391.46			−0.0956317
$597$	5056.46	−	5056.46i	0.346645	−	0.346645i
$598$	−1815.98	+	4384.17i	−0.124182	+	0.299803i
$599$			18939.7i			1.29191i	0.763375	+	0.645956i	$0.223541\pi$
$599$			18939.7i			1.29191i	−0.763375	+	0.645956i	$0.776459\pi$
$600$	−11392.4	−	4718.90i	−0.775157	−	0.321081i
$601$	−6803.11	−	16424.1i	−0.461738	−	1.11473i	−0.967683	−	0.252168i	$-0.918856\pi$
$601$	−6803.11	−	16424.1i	−0.461738	−	1.11473i	0.505945	−	0.862565i	$-0.331144\pi$
$602$	8814.49	−	3651.08i	0.596764	−	0.247188i
$603$	1773.75	+	1773.75i	0.119789	+	0.119789i
$604$	−1050.48	−	1050.48i	−0.0707675	−	0.0707675i
$605$	2537.77	−	1051.18i	0.170537	−	0.0706389i
$606$	1973.38	+	4764.16i	0.132282	+	0.319358i
$607$	16364.9	+	6778.57i	1.09429	+	0.453268i	0.855499	−	0.517804i	$-0.173250\pi$
$607$	16364.9	+	6778.57i	1.09429	+	0.453268i	0.238787	+	0.971072i	$0.423250\pi$
$608$		−	5696.35i		−	0.379963i
$609$	−8311.40	+	20065.5i	−0.553029	+	1.33513i
$610$	2805.46	−	2805.46i	0.186212	−	0.186212i
$611$	8278.74			0.548154
$612$	289.194	−	349.250i	0.0191013	−	0.0230679i
$613$	25427.3			1.67537			0.837683	−	0.546156i	$-0.183910\pi$
$613$	25427.3			1.67537			0.837683	+	0.546156i	$0.183910\pi$
$614$	−420.549	+	420.549i	−0.0276417	+	0.0276417i
$615$	187.163	−	451.851i	0.0122718	−	0.0296266i
$616$		−	2254.34i		−	0.147451i
$617$	−9265.07	−	3837.72i	−0.604534	−	0.250406i	0.0593552	−	0.998237i	$-0.481096\pi$
$617$	−9265.07	−	3837.72i	−0.604534	−	0.250406i	−0.663890	+	0.747831i	$0.731096\pi$
$618$	6216.94	+	15009.0i	0.404663	+	0.976944i
$619$	−4121.37	+	1707.13i	−0.267612	+	0.110849i	−0.512455	−	0.858714i	$-0.671264\pi$
$619$	−4121.37	+	1707.13i	−0.267612	+	0.110849i	0.244842	+	0.969563i	$0.421264\pi$
$620$	−88.6699	−	88.6699i	−0.00574366	−	0.00574366i
$621$	10789.4	+	10789.4i	0.697202	+	0.697202i
$622$	−3210.84	+	1329.97i	−0.206982	+	0.0857348i
$623$	−9971.00	−	24072.1i	−0.641220	−	1.54804i
$624$	−4038.25	−	1672.70i	−0.259070	−	0.107310i
$625$			14011.2i			0.896714i
$626$	396.203	−	956.520i	0.0252963	−	0.0610706i
$627$	−1883.43	+	1883.43i	−0.119963	+	0.119963i
$628$	227.664			0.0144662
$629$	5052.02	−	16395.1i	0.320250	−	1.03929i
$630$	−1154.42			−0.0730049
$631$	776.752	−	776.752i	0.0490048	−	0.0490048i	−0.682180	−	0.731185i	$-0.738968\pi$
$631$	776.752	−	776.752i	0.0490048	−	0.0490048i	0.731185	+	0.682180i	$0.238968\pi$
$632$	−6482.55	+	15650.3i	−0.408009	+	0.985021i
$633$		−	4784.23i		−	0.300404i
$634$	−1610.66	−	667.158i	−0.100895	−	0.0417922i
$635$	1385.45	+	3344.76i	0.0865822	+	0.209028i
$636$	−303.413	+	125.678i	−0.0189168	+	0.00783560i
$637$	3523.03	+	3523.03i	0.219133	+	0.219133i
$638$	−1455.91	−	1455.91i	−0.0903451	−	0.0903451i
$639$	−3577.68	+	1481.92i	−0.221488	+	0.0917432i
$640$	−957.625	−	2311.91i	−0.0591460	−	0.142791i
$641$	982.245	+	406.859i	0.0605247	+	0.0250702i	0.412740	−	0.910849i	$-0.364572\pi$
$641$	982.245	+	406.859i	0.0605247	+	0.0250702i	−0.352216	+	0.935919i	$0.614572\pi$
$642$		−	21452.4i		−	1.31878i
$643$	2514.71	−	6071.06i	0.154231	−	0.372347i	−0.827811	−	0.561006i	$-0.810414\pi$
$643$	2514.71	−	6071.06i	0.154231	−	0.372347i	0.982043	+	0.188660i	$0.0604143\pi$
$644$	1387.46	−	1387.46i	0.0848968	−	0.0848968i
$645$	1284.20			0.0783957
$646$	−2837.26	−	30162.6i	−0.172802	−	1.83705i
$647$	−14783.1			−0.898273			−0.449137	−	0.893463i	$-0.648268\pi$
$647$	−14783.1			−0.898273			−0.449137	+	0.893463i	$0.648268\pi$
$648$	−7319.37	+	7319.37i	−0.443722	+	0.443722i
$649$	−533.041	+	1286.88i	−0.0322399	+	0.0778340i
$650$			5726.98i			0.345585i
$651$	−7656.54	−	3171.44i	−0.460958	−	0.190935i
$652$	508.377	+	1227.33i	0.0305361	+	0.0737208i
$653$	−23939.5	+	9916.08i	−1.43465	+	0.594251i	−0.958495	−	0.285110i	$-0.907970\pi$
$653$	−23939.5	+	9916.08i	−1.43465	+	0.594251i	−0.476155	+	0.879362i	$0.657970\pi$
$654$	−3068.22	−	3068.22i	−0.183451	−	0.183451i
$655$	834.261	+	834.261i	0.0497668	+	0.0497668i
$656$	−2854.77	+	1182.48i	−0.169909	+	0.0703784i
$657$	−447.904	−	1081.34i	−0.0265973	−	0.0642115i
$658$	29060.7	+	12037.3i	1.72174	+	0.713168i
$659$			4302.30i			0.254315i	0.991883	+	0.127158i	$0.0405854\pi$
$659$			4302.30i			0.254315i	−0.991883	+	0.127158i	$0.959415\pi$
$660$	10.3782	−	25.0551i	0.000612076	−	0.00147768i
$661$	−5280.43	+	5280.43i	−0.310719	+	0.310719i	−0.845188	−	0.534469i	$-0.820512\pi$
$661$	−5280.43	+	5280.43i	−0.310719	+	0.310719i	0.534469	+	0.845188i	$0.320512\pi$
$662$	−3840.28			−0.225463
$663$	5127.45	+	1579.98i	0.300353	+	0.0925512i
$664$	8675.31			0.507029
$665$	5935.33	−	5935.33i	0.346109	−	0.346109i
$666$	2072.89	−	5004.39i	0.120605	−	0.291166i
$667$		−	20051.9i		−	1.16403i
$668$	910.974	+	377.338i	0.0527644	+	0.0218557i
$669$	−3588.23	−	8662.76i	−0.207368	−	0.500630i
$670$	−1576.53	+	653.019i	−0.0909054	+	0.0376542i
$671$	−1912.85	−	1912.85i	−0.110052	−	0.110052i
$672$	2710.35	+	2710.35i	0.155586	+	0.155586i
$673$	3914.28	−	1621.35i	0.224197	−	0.0928654i	−0.267758	−	0.963486i	$-0.586283\pi$
$673$	3914.28	−	1621.35i	0.224197	−	0.0928654i	0.491955	+	0.870621i	$0.336283\pi$
$674$	581.140	+	1403.00i	0.0332117	+	0.0801801i
$675$	17012.9	+	7046.99i	0.970116	+	0.401835i
$676$			1479.79i			0.0841938i
$677$	8851.64	−	21369.8i	0.502506	−	1.21316i	−0.445609	−	0.895228i	$-0.647013\pi$
$677$	8851.64	−	21369.8i	0.502506	−	1.21316i	0.948115	−	0.317928i	$-0.102987\pi$
$678$	14636.3	−	14636.3i	0.829062	−	0.829062i
$679$	−22587.0			−1.27660
$680$	1613.59	+	3050.91i	0.0909973	+	0.172055i
$681$	11286.3			0.635082
$682$	555.545	−	555.545i	0.0311919	−	0.0311919i
$683$	4391.09	−	10601.0i	0.246004	−	0.593905i	−0.751854	−	0.659330i	$-0.770840\pi$
$683$	4391.09	−	10601.0i	0.246004	−	0.593905i	0.997858	+	0.0654244i	$0.0208401\pi$
$684$			1040.98i			0.0581914i
$685$	−2217.46	−	918.503i	−0.123686	−	0.0512324i
$686$	−1569.42	−	3788.91i	−0.0873478	−	0.210876i
$687$	4517.63	−	1871.26i	0.250885	−	0.103920i
$688$	−5737.10	−	5737.10i	−0.317914	−	0.317914i
$689$	1206.74	+	1206.74i	0.0667246	+	0.0667246i
$690$	−2242.15	+	928.728i	−0.123706	+	0.0512407i
$691$	5825.05	+	14062.9i	0.320688	+	0.774209i	0.999214	+	0.0396328i	$0.0126188\pi$
$691$	5825.05	+	14062.9i	0.320688	+	0.774209i	−0.678527	+	0.734576i	$0.737381\pi$
$692$	291.025	+	120.547i	0.0159872	+	0.00662210i
$693$			787.120i			0.0431461i
$694$	−3894.44	+	9402.01i	−0.213013	+	0.514258i
$695$	−1452.86	+	1452.86i	−0.0792951	+	0.0792951i
$696$	20501.4			1.11653
$697$	3352.89	−	1773.29i	0.182209	−	0.0963678i
$698$	−17156.6			−0.930352
$699$	−13218.7	+	13218.7i	−0.715275	+	0.715275i
$700$	906.208	−	2187.78i	0.0489306	−	0.118129i
$701$			23996.1i			1.29289i	0.762959	+	0.646447i	$0.223746\pi$
$701$			23996.1i			1.29289i	−0.762959	+	0.646447i	$0.776254\pi$
$702$	6693.91	+	2772.71i	0.359894	+	0.149073i
$703$	15072.1	+	36387.2i	0.808612	+	1.95216i
$704$	−1948.59	+	807.133i	−0.104319	+	0.0432102i
$705$	2993.82	+	2993.82i	0.159934	+	0.159934i
$706$	−11949.3	−	11949.3i	−0.636992	−	0.636992i
$707$	−10236.7	+	4240.19i	−0.544543	+	0.225557i
$708$	−474.358	−	1145.20i	−0.0251800	−	0.0607900i
$709$	−20645.7	−	8551.75i	−1.09361	−	0.452987i	−0.238344	−	0.971181i	$-0.576605\pi$
$709$	−20645.7	−	8551.75i	−1.09361	−	0.452987i	−0.855263	+	0.518194i	$0.826605\pi$
$710$		−	2634.30i		−	0.139244i
$711$	2263.43	−	5464.41i	0.119389	−	0.288230i
$712$	−17391.4	+	17391.4i	−0.915406	+	0.915406i
$713$	7651.34			0.401886
$714$	15701.5	+	13001.5i	0.822988	+	0.681471i
$715$	−140.927			−0.00737113
$716$	−427.075	+	427.075i	−0.0222912	+	0.0222912i
$717$	−1306.47	+	3154.10i	−0.0680489	+	0.164285i
$718$			9050.64i			0.470427i
$719$	−29996.7	−	12425.0i	−1.55590	−	0.644473i	−0.571525	−	0.820584i	$-0.693648\pi$
$719$	−29996.7	−	12425.0i	−1.55590	−	0.644473i	−0.984370	+	0.176111i	$0.943648\pi$
$720$	375.689	+	906.993i	0.0194460	+	0.0469467i
$721$	−32249.8	+	13358.3i	−1.66581	+	0.689999i
$722$	36152.6	+	36152.6i	1.86352	+	1.86352i
$723$	−11095.9	−	11095.9i	−0.570761	−	0.570761i
$724$	1906.27	−	789.604i	0.0978537	−	0.0405323i
$725$	−9260.77	−	22357.5i	−0.474395	−	1.14529i
$726$	−14149.5	−	5860.91i	−0.723329	−	0.299613i
$727$		−	2899.33i		−	0.147909i	−0.997262	−	0.0739547i	$-0.976438\pi$
$727$		−	2899.33i		−	0.147909i	0.997262	−	0.0739547i	$-0.0235620\pi$
$728$	3989.48	−	9631.46i	0.203104	−	0.490337i
$729$	15177.6	−	15177.6i	0.771100	−	0.771100i
$730$	796.204			0.0403683
$731$	7670.86	+	6351.81i	0.388122	+	0.321382i
$732$	2407.37			0.121556
$733$	−11596.5	+	11596.5i	−0.584346	+	0.584346i	−0.936095	−	0.351749i	$-0.885587\pi$
$733$	−11596.5	+	11596.5i	−0.584346	+	0.584346i	0.351749	+	0.936095i	$0.385587\pi$
$734$	1025.35	−	2475.42i	0.0515619	−	0.124481i
$735$			2548.05i			0.127873i
$736$	−3269.46	−	1354.25i	−0.163742	−	0.0678240i
$737$	445.251	+	1074.93i	0.0222538	+	0.0537253i
$738$	1106.41	−	458.291i	0.0551864	−	0.0228590i
$739$	4575.44	+	4575.44i	0.227754	+	0.227754i	0.811754	−	0.584000i	$-0.198513\pi$
$739$	4575.44	+	4575.44i	0.227754	+	0.227754i	−0.584000	+	0.811754i	$0.698513\pi$
$740$	−283.554	−	283.554i	−0.0140860	−	0.0140860i
$741$	−11379.8	+	4713.69i	−0.564169	+	0.233686i
$742$	2481.40	+	5990.63i	0.122770	+	0.296392i
$743$	6947.76	+	2877.86i	0.343053	+	0.142097i	0.547557	−	0.836769i	$-0.315558\pi$
$743$	6947.76	+	2877.86i	0.343053	+	0.142097i	−0.204504	+	0.978866i	$0.565558\pi$
$744$			7822.89i			0.385485i
$745$	−1415.14	+	3416.45i	−0.0695929	+	0.168012i
$746$	6040.96	−	6040.96i	0.296481	−	0.296481i
$747$	−3029.05			−0.148363
$748$	185.918	−	98.3293i	0.00908800	−	0.00480652i
$749$	46094.6			2.24868
$750$	−4216.81	+	4216.81i	−0.205302	+	0.205302i
$751$	4179.61	−	10090.5i	0.203084	−	0.490289i	−0.789220	−	0.614110i	$-0.789515\pi$
$751$	4179.61	−	10090.5i	0.203084	−	0.490289i	0.992305	+	0.123821i	$0.0395150\pi$
$752$		−	26749.6i		−	1.29715i
$753$	23909.9	+	9903.81i	1.15714	+	0.479303i
$754$	−3643.74	−	8796.78i	−0.175991	−	0.424880i
$755$	−3647.61	+	1510.89i	−0.175828	+	0.0728303i
$756$	−2118.42	−	2118.42i	−0.101913	−	0.101913i
$757$	−12100.6	−	12100.6i	−0.580984	−	0.580984i	0.354189	−	0.935174i	$-0.384757\pi$
$757$	−12100.6	−	12100.6i	−0.580984	−	0.580984i	−0.935174	+	0.354189i	$0.884757\pi$
$758$	26885.3	−	11136.2i	1.28828	−	0.533623i
$759$	633.239	+	1528.77i	0.0302834	+	0.0731106i
$760$	−7320.23	−	3032.14i	−0.349385	−	0.144720i
$761$		−	35934.3i		−	1.71172i	−0.517207	−	0.855860i	$-0.673028\pi$
$761$		−	35934.3i		−	1.71172i	0.517207	−	0.855860i	$-0.326972\pi$
$762$	7724.62	−	18648.9i	0.367236	−	0.886585i
$763$	6592.67	−	6592.67i	0.312805	−	0.312805i
$764$	163.202			0.00772831
$765$	−563.396	−	1065.25i	−0.0266270	−	0.0503454i
$766$	−20327.8			−0.958842
$767$	−4554.74	+	4554.74i	−0.214423	+	0.214423i
$768$	1979.14	−	4778.07i	0.0929898	−	0.224497i
$769$		−	29085.3i		−	1.36390i	−0.731397	−	0.681952i	$-0.761131\pi$
$769$		−	29085.3i		−	1.36390i	0.731397	−	0.681952i	$-0.238869\pi$
$770$	−494.693	−	204.908i	−0.0231526	−	0.00959011i
$771$	6217.31	+	15009.9i	0.290416	+	0.701127i
$772$	−3320.61	+	1375.44i	−0.154808	+	0.0641234i
$773$	−11669.3	−	11669.3i	−0.542968	−	0.542968i	0.381430	−	0.924398i	$-0.375432\pi$
$773$	−11669.3	−	11669.3i	−0.542968	−	0.542968i	−0.924398	+	0.381430i	$0.875432\pi$
$774$	2223.51	+	2223.51i	0.103259	+	0.103259i
$775$	8531.12	−	3533.71i	0.395415	−	0.163786i
$776$	8159.20	+	19698.0i	0.377446	+	0.911236i
$777$	−24484.6	−	10141.8i	−1.13047	−	0.468258i
$778$			25784.3i			1.18819i
$779$	−3332.25	+	8044.77i	−0.153261	+	0.370005i
$780$	88.6796	−	88.6796i	0.00407082	−	0.00407082i
$781$	−1796.15			−0.0822937
$782$	−17986.6	−	5542.42i	−0.822505	−	0.253448i
$783$	−30615.9			−1.39735
$784$	11383.3	−	11383.3i	0.518556	−	0.518556i
$785$	231.538	−	558.982i	0.0105273	−	0.0254152i
$786$		−	6578.17i		−	0.298518i
$787$	25290.4	+	10475.6i	1.14550	+	0.474480i	0.873021	−	0.487683i	$-0.162158\pi$
$787$	25290.4	+	10475.6i	1.14550	+	0.474480i	0.272474	+	0.962163i	$0.412158\pi$
$788$	−793.539	−	1915.77i	−0.0358739	−	0.0866073i
$789$	30278.3	−	12541.7i	1.36621	−	0.565901i
$790$	2845.06	+	2845.06i	0.128130	+	0.128130i
$791$	31449.0	+	31449.0i	1.41365	+	1.41365i
$792$	686.446	−	284.335i	0.0307977	−	0.0127568i
$793$	−4787.34	−	11557.7i	−0.214380	−	0.517559i
$794$	−13083.0	−	5419.14i	−0.584757	−	0.242214i
$795$			872.784i			0.0389364i
$796$	496.064	−	1197.60i	0.0220886	−	0.0533266i
$797$	−22469.1	+	22469.1i	−0.998615	+	0.998615i	−0.999999	−	0.00138359i	$-0.999560\pi$
$797$	−22469.1	+	22469.1i	−0.998615	+	0.998615i	0.00138359	+	0.999999i	$0.499560\pi$
$798$	−46800.2			−2.07608
$799$	3075.07	+	32690.7i	0.136155	+	1.44745i
$800$	−4270.84			−0.188746
$801$	6072.33	−	6072.33i	0.267859	−	0.267859i
$802$	−3700.81	+	8934.54i	−0.162943	+	0.393379i
$803$		−	542.879i		−	0.0238578i
$804$	−956.590	−	396.232i	−0.0419606	−	0.0173806i
$805$	−1995.55	−	4817.69i	−0.0873715	−	0.210933i
$806$	3356.65	−	1390.37i	0.146691	−	0.0607615i
$807$	−21410.5	−	21410.5i	−0.933936	−	0.933936i
$808$	7395.72	+	7395.72i	0.322006	+	0.322006i
$809$	31751.1	−	13151.8i	1.37986	−	0.571559i	0.435420	−	0.900228i	$-0.356600\pi$
$809$	31751.1	−	13151.8i	1.37986	−	0.571559i	0.944445	+	0.328669i	$0.106600\pi$
$810$	940.869	+	2271.46i	0.0408133	+	0.0985320i
$811$	1216.74	+	503.991i	0.0526826	+	0.0218218i	0.408869	−	0.912593i	$-0.365923\pi$
$811$	1216.74	+	503.991i	0.0526826	+	0.0218218i	−0.356187	+	0.934415i	$0.615923\pi$
$812$			3937.05i			0.170152i
$813$	−2248.70	+	5428.84i	−0.0970054	+	0.234192i
$814$	1776.55	−	1776.55i	0.0764966	−	0.0764966i
$815$	3530.49			0.151739
$816$	5105.11	−	16567.4i	0.219013	−	0.710754i
$817$	−22863.9			−0.979078
$818$	−18074.2	+	18074.2i	−0.772553	+	0.772553i
$819$	−1392.96	+	3362.90i	−0.0594309	+	0.143479i
$820$		−	88.6577i		−	0.00377568i
$821$	30932.5	+	12812.7i	1.31492	+	0.544659i	0.926317	−	0.376744i	$-0.122956\pi$
$821$	30932.5	+	12812.7i	1.31492	+	0.544659i	0.388607	+	0.921404i	$0.372956\pi$
$822$	5121.16	+	12363.6i	0.217300	+	0.524610i
$823$	10852.6	−	4495.29i	0.459657	−	0.190396i	−0.140825	−	0.990035i	$-0.544975\pi$
$823$	10852.6	−	4495.29i	0.459657	−	0.190396i	0.600482	+	0.799638i	$0.294975\pi$
$824$	23299.5	+	23299.5i	0.985044	+	0.985044i
$825$	1412.10	+	1412.10i	0.0595916	+	0.0595916i
$826$	−22611.0	+	9365.80i	−0.952468	+	0.394525i
$827$	1671.50	+	4035.36i	0.0702827	+	0.169678i	0.955117	−	0.296228i	$-0.0957287\pi$
$827$	1671.50	+	4035.36i	0.0702827	+	0.169678i	−0.884835	+	0.465905i	$0.845729\pi$
$828$	597.478	+	247.484i	0.0250771	+	0.0103873i
$829$			19994.7i			0.837689i	0.908058	+	0.418844i	$0.137565\pi$
$829$			19994.7i			0.837689i	−0.908058	+	0.418844i	$0.862435\pi$
$830$	788.543	−	1903.71i	0.0329768	−	0.0796130i
$831$	−21974.7	+	21974.7i	−0.917323	+	0.917323i
$832$	−9753.55			−0.406422
$833$	−12603.0	+	15220.2i	−0.524211	+	0.633072i
$834$	11455.8			0.475639
$835$	1852.95	−	1852.95i	0.0767952	−	0.0767952i
$836$	−184.774	+	446.083i	−0.00764417	+	0.0184547i
$837$		−	11682.3i		−	0.482438i
$838$	−15660.1	−	6486.61i	−0.645547	−	0.267394i
$839$	−9824.30	−	23718.0i	−0.404258	−	0.975965i	−0.986620	−	0.163036i	$-0.947871\pi$
$839$	−9824.30	−	23718.0i	−0.404258	−	0.975965i	0.582362	−	0.812929i	$-0.302129\pi$
$840$	4925.71	−	2040.29i	0.202325	−	0.0838058i
$841$	11203.9	+	11203.9i	0.459384	+	0.459384i
$842$	2934.10	+	2934.10i	0.120090	+	0.120090i
$843$	26456.7	−	10958.7i	1.08092	−	0.447733i
$844$	−331.885	−	801.242i	−0.0135355	−	0.0326776i
$845$	3633.32	+	1504.97i	0.147917	+	0.0612693i
$846$			10367.2i			0.421315i
$847$	12593.3	−	30402.9i	0.510875	−	1.23336i
$848$	3899.13	−	3899.13i	0.157897	−	0.157897i
$849$	10009.3			0.404614
$850$	−22614.4	+	2127.24i	−0.912552	+	0.0858395i
$851$	24467.9			0.985605
$852$	1130.25	−	1130.25i	0.0454479	−	0.0454479i
$853$	−5933.37	+	14324.4i	−0.238165	+	0.574981i	−0.997093	−	0.0761933i	$-0.975723\pi$
$853$	−5933.37	+	14324.4i	−0.238165	+	0.574981i	0.758928	+	0.651174i	$0.225723\pi$
$854$		−	47531.5i		−	1.90456i
$855$	2555.92	+	1058.70i	0.102235	+	0.0423469i
$856$	−16650.9	−	40198.9i	−0.664857	−	1.60511i
$857$	−33181.2	+	13744.1i	−1.32258	+	0.547830i	−0.928529	−	0.371260i	$-0.878926\pi$
$857$	−33181.2	+	13744.1i	−1.32258	+	0.547830i	−0.394049	+	0.919089i	$0.628926\pi$
$858$	555.605	+	555.605i	0.0221073	+	0.0221073i
$859$	25862.4	+	25862.4i	1.02726	+	1.02726i	0.999618	+	0.0276409i	$0.00879949\pi$
$859$	25862.4	+	25862.4i	1.02726	+	1.02726i	0.0276409	+	0.999618i	$0.491201\pi$
$860$	215.072	−	89.0857i	0.00852778	−	0.00353232i
$861$	−2242.24	−	5413.24i	−0.0887518	−	0.214266i
$862$	−2226.81	−	922.374i	−0.0879877	−	0.0364457i
$863$			11402.6i			0.449768i	0.974386	+	0.224884i	$0.0722003\pi$
$863$			11402.6i			0.449768i	−0.974386	+	0.224884i	$0.927800\pi$
$864$	−2067.72	+	4991.93i	−0.0814183	+	0.196561i
$865$	591.955	−	591.955i	0.0232683	−	0.0232683i
$866$	−13152.1			−0.516083
$867$	−4334.42	+	20833.9i	−0.169786	+	0.816099i
$868$	−1502.29			−0.0587455
$869$	1939.86	−	1939.86i	0.0757252	−	0.0757252i
$870$	1863.48	−	4498.84i	0.0726182	−	0.175316i
$871$			5380.50i			0.209312i
$872$	−8130.94	−	3367.95i	−0.315767	−	0.130795i
$873$	−2848.85	−	6877.73i	−0.110446	−	0.266639i
$874$	39919.3	−	16535.1i	1.54496	−	0.639942i
$875$	−9060.64	−	9060.64i	−0.350063	−	0.350063i
$876$	341.612	+	341.612i	0.0131758	+	0.0131758i
$877$	21641.6	−	8964.22i	0.833276	−	0.345154i	0.0750774	−	0.997178i	$-0.476080\pi$
$877$	21641.6	−	8964.22i	0.833276	−	0.345154i	0.758199	+	0.652023i	$0.226080\pi$
$878$	1443.19	+	3484.17i	0.0554731	+	0.133924i
$879$	−25794.1	−	10684.3i	−0.989778	−	0.409980i
$880$			455.351i			0.0174430i
$881$	−938.538	+	2265.83i	−0.0358912	+	0.0866490i	−0.940809	−	0.338938i	$-0.889932\pi$
$881$	−938.538	+	2265.83i	−0.0358912	+	0.0866490i	0.904918	+	0.425587i	$0.139932\pi$
$882$	−4411.79	+	4411.79i	−0.168427	+	0.168427i
$883$	−3832.99			−0.146082			−0.0730409	−	0.997329i	$-0.523270\pi$
$883$	−3832.99			−0.146082			−0.0730409	+	0.997329i	$0.523270\pi$
$884$	968.328	−	91.0862i	0.0368421	−	0.00346557i
$885$	−3294.24			−0.125124
$886$	12257.4	−	12257.4i	0.464780	−	0.464780i
$887$	5102.84	−	12319.3i	0.193164	−	0.466340i	−0.797390	−	0.603465i	$-0.793786\pi$
$887$	5102.84	−	12319.3i	0.193164	−	0.466340i	0.990554	+	0.137125i	$0.0437863\pi$
$888$			25016.5i			0.945382i
$889$	40070.8	+	16597.9i	1.51173	+	0.626180i
$890$	2235.58	+	5397.16i	0.0841985	+	0.203273i
$891$	1548.76	−	641.516i	0.0582327	−	0.0241208i
$892$	−1201.88	−	1201.88i	−0.0451144	−	0.0451144i
$893$	−53302.1	−	53302.1i	−1.99741	−	1.99741i
$894$	19048.6	−	7890.19i	0.712618	−	0.295176i
$895$	614.253	+	1482.94i	0.0229410	+	0.0553845i
$896$	−27697.1	−	11472.5i	−1.03269	−	0.427756i
$897$			7652.18i			0.284837i
$898$	4532.15	−	10941.6i	0.168418	−	0.406598i
$899$	−10855.7	+	10855.7i	−0.402734	+	0.402734i
$900$	780.476			0.0289065
$901$	−4316.90	+	5213.37i	−0.159619	+	0.192767i
$902$	555.468			0.0205045
$903$	10878.8	−	10878.8i	0.400911	−	0.400911i
$904$	16066.1	−	38787.0i	0.591096	−	1.42703i
$905$		−	5483.51i		−	0.201412i
$906$	20337.4	+	8424.04i	0.745768	+	0.308907i
$907$	−5523.15	−	13334.1i	−0.202198	−	0.488148i	0.789957	−	0.613162i	$-0.210103\pi$
$907$	−5523.15	−	13334.1i	−0.202198	−	0.488148i	−0.992155	+	0.125013i	$0.960103\pi$
$908$	1890.18	−	782.937i	0.0690834	−	0.0286153i
$909$	−2582.27	−	2582.27i	−0.0942229	−	0.0942229i
$910$	−1750.90	−	1750.90i	−0.0637823	−	0.0637823i
$911$	−46624.0	+	19312.3i	−1.69563	+	0.702354i	−0.999873	−	0.0159195i	$-0.994932\pi$
$911$	−46624.0	+	19312.3i	−1.69563	+	0.702354i	−0.695760	+	0.718274i	$0.744932\pi$
$912$	15230.5	+	36769.6i	0.552995	+	1.33505i
$913$	−1298.01	−	537.655i	−0.0470515	−	0.0194894i
$914$			33767.8i			1.22203i
$915$	2448.33	−	5910.80i	0.0884584	−	0.213557i
$916$	626.782	−	626.782i	0.0226086	−	0.0226086i
$917$	14134.5			0.509009
$918$	−8462.36	+	27462.5i	−0.304248	+	0.987363i
$919$	−33955.2			−1.21880			−0.609401	−	0.792862i	$-0.708590\pi$
$919$	−33955.2			−1.21880			−0.609401	+	0.792862i	$0.708590\pi$
$920$	−3480.63	+	3480.63i	−0.124732	+	0.124732i
$921$	−367.015	+	886.053i	−0.0131309	+	0.0317008i
$922$			13739.1i			0.490753i
$923$	−7673.90	−	3178.63i	−0.273661	−	0.113354i
$924$	−124.332	−	300.165i	−0.00442666	−	0.0106869i
$925$	27281.3	−	11300.3i	0.969735	−	0.401677i
$926$	10030.2	+	10030.2i	0.355955	+	0.355955i
$927$	−8135.20	−	8135.20i	−0.288236	−	0.288236i
$928$	6560.12	−	2717.29i	0.232054	−	0.0961200i
$929$	−5666.65	−	13680.5i	−0.200126	−	0.483146i	0.791675	−	0.610943i	$-0.209210\pi$
$929$	−5666.65	−	13680.5i	−0.200126	−	0.483146i	−0.991800	+	0.127797i	$0.959210\pi$
$930$	1716.66	+	711.062i	0.0605283	+	0.0250717i
$931$		−	45365.6i		−	1.59699i
$932$	−1296.82	+	3130.80i	−0.0455781	+	0.110035i
$933$	−3962.79	+	3962.79i	−0.139052	+	0.139052i
$934$	11900.4			0.416908
$935$	−52.3460	−	556.486i	−0.00183091	−	0.0194642i
$936$	3435.96			0.119987
$937$	3635.47	−	3635.47i	0.126751	−	0.126751i	−0.640885	−	0.767637i	$-0.721433\pi$
$937$	3635.47	−	3635.47i	0.126751	−	0.126751i	0.767637	+	0.640885i	$0.221433\pi$
$938$	−7823.28	+	18887.1i	−0.272323	+	0.657446i
$939$		−	1669.52i		−	0.0580220i
$940$	709.076	+	293.709i	0.0246037	+	0.0101912i
$941$	14908.7	+	35992.9i	0.516484	+	1.24690i	0.940050	+	0.341037i	$0.110778\pi$
$941$	14908.7	+	35992.9i	0.516484	+	1.24690i	−0.423566	+	0.905865i	$0.639222\pi$
$942$	−3116.63	+	1290.95i	−0.107798	+	0.0446512i
$943$	3825.14	+	3825.14i	0.132093	+	0.132093i
$944$	14716.9	+	14716.9i	0.507409	+	0.507409i
$945$	−7355.83	+	3046.88i	−0.253212	+	0.104884i
$946$	558.149	+	1347.49i	0.0191829	+	0.0463116i
$947$	13111.3	+	5430.89i	0.449906	+	0.186357i	0.596119	−	0.802896i	$-0.296709\pi$
$947$	13111.3	+	5430.89i	0.449906	+	0.186357i	−0.146213	+	0.989253i	$0.546709\pi$
$948$			2441.35i			0.0836408i
$949$	960.727	−	2319.40i	0.0328625	−	0.0793371i
$950$	36872.8	−	36872.8i	1.25927	−	1.25927i
$951$	−2811.27			−0.0958586
$952$	39514.2	+	12176.0i	1.34523	+	0.414523i
$953$	−32646.8			−1.10969			−0.554844	−	0.831955i	$-0.687222\pi$
$953$	−32646.8			−1.10969			−0.554844	+	0.831955i	$0.687222\pi$
$954$	−1511.17	+	1511.17i	−0.0512850	+	0.0512850i
$955$	165.979	−	400.708i	0.00562403	−	0.0135776i
$956$			618.867i			0.0209368i
$957$	−3067.46	−	1270.58i	−0.103612	−	0.0429176i
$958$	8939.78	+	21582.5i	0.301494	+	0.727871i
$959$	−26565.5	+	11003.8i	−0.894522	+	0.370523i
$960$	−3527.15	−	3527.15i	−0.118582	−	0.118582i
$961$	16923.1	+	16923.1i	0.568061	+	0.568061i
$962$	10734.1	−	4446.22i	0.359752	−	0.149014i
$963$	5813.81	+	14035.8i	0.194546	+	0.469675i
$964$	−2628.02	−	1088.56i	−0.0878038	−	0.0363695i
$965$			9551.94i			0.318640i
$966$	−11126.3	+	26861.3i	−0.370583	+	0.894667i
$967$	−11443.7	+	11443.7i	−0.380562	+	0.380562i	−0.871305	−	0.490743i	$-0.836726\pi$
$967$	−11443.7	+	11443.7i	−0.380562	+	0.380562i	0.490743	+	0.871305i	$0.336726\pi$
$968$	−31063.4			−1.03142
$969$	−22840.2	−	43185.4i	−0.757205	−	1.43170i
$970$	5064.18			0.167630
$971$	−20370.1	+	20370.1i	−0.673233	+	0.673233i	−0.958460	−	0.285227i	$-0.907931\pi$
$971$	−20370.1	+	20370.1i	−0.673233	+	0.673233i	0.285227	+	0.958460i	$0.407931\pi$
$972$	667.385	−	1611.21i	0.0220230	−	0.0531683i
$973$			24615.1i			0.811021i
$974$	−32337.7	−	13394.7i	−1.06383	−	0.440651i
$975$	3534.09	+	8532.05i	0.116084	+	0.280251i
$976$	−37344.1	+	15468.4i	−1.22475	+	0.507308i
$977$	2231.39	+	2231.39i	0.0730689	+	0.0730689i	0.742697	−	0.669628i	$-0.233546\pi$
$977$	2231.39	+	2231.39i	0.0730689	+	0.0730689i	−0.669628	+	0.742697i	$0.733546\pi$
$978$	−13919.0	−	13919.0i	−0.455092	−	0.455092i
$979$	3679.96	−	1524.29i	0.120135	−	0.0497615i
$980$	176.760	+	426.737i	0.00576163	+	0.0139098i
$981$	2838.98	+	1175.95i	0.0923973	+	0.0382722i
$982$		−	31588.8i		−	1.02651i
$983$	5670.86	−	13690.7i	0.184000	−	0.444216i	−0.804784	−	0.593568i	$-0.797719\pi$
$983$	5670.86	−	13690.7i	0.184000	−	0.444216i	0.988784	+	0.149352i	$0.0477187\pi$
$984$	−3910.90	+	3910.90i	−0.126702	+	0.126702i
$985$	−5510.83			−0.178264
$986$	33382.9	−	17655.7i	1.07822	−	0.570257i
$987$	50722.8			1.63579
$988$	−1578.86	+	1578.86i	−0.0508402	+	0.0508402i
$989$	−5435.68	+	13122.9i	−0.174767	+	0.421925i
$990$		−	176.478i		−	0.00566551i
$991$	820.788	+	339.981i	0.0263100	+	0.0108979i	0.395800	−	0.918337i	$-0.370467\pi$
$991$	820.788	+	339.981i	0.0263100	+	0.0108979i	−0.369490	+	0.929235i	$0.620467\pi$
$992$	1036.86	+	2503.19i	0.0331857	+	0.0801175i
$993$	−5721.24	+	2369.82i	−0.182838	+	0.0757340i
$994$	−22315.8	−	22315.8i	−0.712086	−	0.712086i
$995$	−2435.97	−	2435.97i	−0.0776134	−	0.0776134i
$996$	1155.11	−	478.464i	0.0367482	−	0.0152216i
$997$	1958.18	+	4727.46i	0.0622027	+	0.150171i	0.951925	−	0.306332i	$-0.0991018\pi$
$997$	1958.18	+	4727.46i	0.0622027	+	0.150171i	−0.889722	+	0.456503i	$0.849102\pi$
$998$	26613.8	+	11023.8i	0.844135	+	0.349652i
$999$		−	37358.5i		−	1.18315i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.4.d.a.8.1	✓	12
3.2	odd	2		153.4.l.a.127.3		12
17.6	odd	16		289.4.b.e.288.4		12
17.7	odd	16		289.4.a.g.1.10		12
17.10	odd	16		289.4.a.g.1.9		12
17.11	odd	16		289.4.b.e.288.3		12
17.15	even	8	inner	17.4.d.a.15.1	yes	12
51.32	odd	8		153.4.l.a.100.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.d.a.8.1	✓	12	1.1	even	1	trivial
17.4.d.a.15.1	yes	12	17.15	even	8	inner
153.4.l.a.100.3		12	51.32	odd	8
153.4.l.a.127.3		12	3.2	odd	2
289.4.a.g.1.9		12	17.10	odd	16
289.4.a.g.1.10		12	17.7	odd	16
289.4.b.e.288.3		12	17.11	odd	16
289.4.b.e.288.4		12	17.6	odd	16

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:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	17.d (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.89932 + 1.89932i) q^{2} +(-1.65755 + 4.00167i) q^{3} +0.785167i q^{4} +(1.92782 + 0.798529i) q^{5} +(-4.45224 - 10.7487i) q^{6} +(23.0956 - 9.56650i) q^{7} +(-16.6858 - 16.6858i) q^{8} +(5.82599 + 5.82599i) q^{9} +O(q^{10})\)	\(q+(-1.89932 + 1.89932i) q^{2} +(-1.65755 + 4.00167i) q^{3} +0.785167i q^{4} +(1.92782 + 0.798529i) q^{5} +(-4.45224 - 10.7487i) q^{6} +(23.0956 - 9.56650i) q^{7} +(-16.6858 - 16.6858i) q^{8} +(5.82599 + 5.82599i) q^{9} +(-5.17821 + 2.14488i) q^{10} +(1.46245 + 3.53068i) q^{11} +(-3.14198 - 1.30145i) q^{12} +17.6726i q^{13} +(-25.6960 + 62.0357i) q^{14} +(-6.39089 + 6.39089i) q^{15} +57.1022 q^{16} +(-69.7847 + 6.56433i) q^{17} -22.1309 q^{18} +(113.784 - 113.784i) q^{19} +(-0.626979 + 1.51366i) q^{20} +108.278i q^{21} +(-9.48355 - 3.92822i) q^{22} +(-38.2560 - 92.3581i) q^{23} +(94.4287 - 39.1137i) q^{24} +(-85.3095 - 85.3095i) q^{25} +(-33.5659 - 33.5659i) q^{26} +(-141.016 + 58.4106i) q^{27} +(7.51131 + 18.1339i) q^{28} +(185.315 + 76.7600i) q^{29} -24.2767i q^{30} +(-29.2899 + 70.7121i) q^{31} +(25.0315 - 25.0315i) q^{32} -16.5527 q^{33} +(120.076 - 145.011i) q^{34} +52.1632 q^{35} +(-4.57438 + 4.57438i) q^{36} +(-93.6650 + 226.127i) q^{37} +432.224i q^{38} +(-70.7198 - 29.2931i) q^{39} +(-18.8432 - 45.4914i) q^{40} +(-49.9941 + 20.7082i) q^{41} +(-205.654 - 205.654i) q^{42} +(-100.471 - 100.471i) q^{43} +(-2.77217 + 1.14827i) q^{44} +(6.57924 + 15.8837i) q^{45} +(248.078 + 102.757i) q^{46} -468.451i q^{47} +(-94.6494 + 228.504i) q^{48} +(199.350 - 199.350i) q^{49} +324.060 q^{50} +(89.4031 - 290.136i) q^{51} -13.8759 q^{52} +(68.2834 - 68.2834i) q^{53} +(156.893 - 378.774i) q^{54} +7.97432i q^{55} +(-544.994 - 225.744i) q^{56} +(266.723 + 643.927i) q^{57} +(-497.764 + 206.181i) q^{58} +(257.729 + 257.729i) q^{59} +(-5.01792 - 5.01792i) q^{60} +(-653.988 + 270.891i) q^{61} +(-78.6740 - 189.936i) q^{62} +(190.289 + 78.8203i) q^{63} +551.903i q^{64} +(-14.1121 + 34.0695i) q^{65} +(31.4388 - 31.4388i) q^{66} +304.454 q^{67} +(-5.15410 - 54.7927i) q^{68} +432.997 q^{69} +(-99.0747 + 99.0747i) q^{70} +(-179.862 + 434.226i) q^{71} -194.423i q^{72} +(-131.243 - 54.3626i) q^{73} +(-251.588 - 607.388i) q^{74} +(482.785 - 199.976i) q^{75} +(89.3393 + 89.3393i) q^{76} +(67.5525 + 67.5525i) q^{77} +(189.956 - 78.6825i) q^{78} +(-274.715 - 663.221i) q^{79} +(110.083 + 45.5977i) q^{80} -438.657i q^{81} +(55.6232 - 134.286i) q^{82} +(-259.960 + 259.960i) q^{83} -85.0162 q^{84} +(-139.774 - 43.0703i) q^{85} +381.653 q^{86} +(-614.336 + 614.336i) q^{87} +(34.5100 - 83.3146i) q^{88} -1042.28i q^{89} +(-42.6643 - 17.6721i) q^{90} +(169.065 + 408.158i) q^{91} +(72.5165 - 30.0373i) q^{92} +(-234.417 - 234.417i) q^{93} +(889.738 + 889.738i) q^{94} +(310.214 - 128.495i) q^{95} +(58.6768 + 141.658i) q^{96} +(-834.757 - 345.768i) q^{97} +757.260i q^{98} +(-12.0495 + 29.0899i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - 4 q^{3} - 20 q^{5} + 20 q^{6} - 4 q^{7} + 28 q^{8} - 64 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 - 4 * q^3 - 20 * q^5 + 20 * q^6 - 4 * q^7 + 28 * q^8 - 64 * q^9	\( 12 q - 4 q^{2} - 4 q^{3} - 20 q^{5} + 20 q^{6} - 4 q^{7} + 28 q^{8} - 64 q^{9} - 116 q^{10} + 40 q^{11} + 56 q^{12} - 132 q^{14} + 244 q^{15} + 184 q^{16} + 52 q^{17} - 12 q^{19} + 572 q^{20} - 620 q^{22} - 276 q^{23} - 184 q^{24} - 464 q^{25} - 708 q^{26} - 664 q^{27} + 452 q^{28} + 632 q^{29} + 188 q^{31} + 700 q^{32} + 1400 q^{33} + 764 q^{34} - 632 q^{35} + 524 q^{36} + 940 q^{37} - 1112 q^{39} - 1864 q^{40} + 176 q^{41} + 48 q^{42} - 1360 q^{43} - 1364 q^{44} - 32 q^{45} + 452 q^{46} - 540 q^{48} + 1044 q^{49} + 2856 q^{50} + 340 q^{51} + 792 q^{52} - 360 q^{53} - 244 q^{54} - 1788 q^{56} - 148 q^{57} - 360 q^{58} - 584 q^{59} - 1792 q^{60} - 1052 q^{61} - 380 q^{62} + 1752 q^{63} + 404 q^{65} + 1372 q^{66} + 1080 q^{67} + 2532 q^{68} - 344 q^{69} + 2072 q^{70} + 28 q^{71} + 824 q^{73} - 2292 q^{74} + 400 q^{75} + 1328 q^{76} - 1252 q^{77} + 1128 q^{78} - 196 q^{79} - 904 q^{80} - 1528 q^{82} - 1008 q^{83} - 4768 q^{84} - 2824 q^{85} - 1200 q^{86} - 2516 q^{87} - 56 q^{88} - 860 q^{90} + 2456 q^{91} + 396 q^{92} - 836 q^{93} + 6360 q^{94} + 2172 q^{95} + 1668 q^{96} - 904 q^{97} + 3280 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - 4 * q^3 - 20 * q^5 + 20 * q^6 - 4 * q^7 + 28 * q^8 - 64 * q^9 - 116 * q^10 + 40 * q^11 + 56 * q^12 - 132 * q^14 + 244 * q^15 + 184 * q^16 + 52 * q^17 - 12 * q^19 + 572 * q^20 - 620 * q^22 - 276 * q^23 - 184 * q^24 - 464 * q^25 - 708 * q^26 - 664 * q^27 + 452 * q^28 + 632 * q^29 + 188 * q^31 + 700 * q^32 + 1400 * q^33 + 764 * q^34 - 632 * q^35 + 524 * q^36 + 940 * q^37 - 1112 * q^39 - 1864 * q^40 + 176 * q^41 + 48 * q^42 - 1360 * q^43 - 1364 * q^44 - 32 * q^45 + 452 * q^46 - 540 * q^48 + 1044 * q^49 + 2856 * q^50 + 340 * q^51 + 792 * q^52 - 360 * q^53 - 244 * q^54 - 1788 * q^56 - 148 * q^57 - 360 * q^58 - 584 * q^59 - 1792 * q^60 - 1052 * q^61 - 380 * q^62 + 1752 * q^63 + 404 * q^65 + 1372 * q^66 + 1080 * q^67 + 2532 * q^68 - 344 * q^69 + 2072 * q^70 + 28 * q^71 + 824 * q^73 - 2292 * q^74 + 400 * q^75 + 1328 * q^76 - 1252 * q^77 + 1128 * q^78 - 196 * q^79 - 904 * q^80 - 1528 * q^82 - 1008 * q^83 - 4768 * q^84 - 2824 * q^85 - 1200 * q^86 - 2516 * q^87 - 56 * q^88 - 860 * q^90 + 2456 * q^91 + 396 * q^92 - 836 * q^93 + 6360 * q^94 + 2172 * q^95 + 1668 * q^96 - 904 * q^97 + 3280 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more