LMFDB - Embedded newform 17.4.d.a.2.2

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			2.2
Root			$-0.705468i$ of defining polynomial
Character	$\chi$	$=$	17.2
Dual form			17.4.d.a.9.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20595 - 1.20595i) q^{2} +(4.10553 - 1.70057i) q^{3} -5.09138i q^{4} +(2.60601 + 6.29147i) q^{5} +(-7.00185 - 2.90026i) q^{6} +(-5.31013 + 12.8198i) q^{7} +(-15.7875 + 15.7875i) q^{8} +(-5.12843 + 5.12843i) q^{9} +O(q^{10})$	\(q+(-1.20595 - 1.20595i) q^{2} +(4.10553 - 1.70057i) q^{3} -5.09138i q^{4} +(2.60601 + 6.29147i) q^{5} +(-7.00185 - 2.90026i) q^{6} +(-5.31013 + 12.8198i) q^{7} +(-15.7875 + 15.7875i) q^{8} +(-5.12843 + 5.12843i) q^{9} +(4.44447 - 10.7299i) q^{10} +(28.4888 + 11.8005i) q^{11} +(-8.65823 - 20.9028i) q^{12} -66.0130i q^{13} +(21.8637 - 9.05625i) q^{14} +(21.3981 + 21.3981i) q^{15} -2.65318 q^{16} +(3.91802 + 69.9832i) q^{17} +12.3692 q^{18} +(-56.3670 - 56.3670i) q^{19} +(32.0322 - 13.2682i) q^{20} +61.6622i q^{21} +(-20.1253 - 48.5868i) q^{22} +(-26.6989 - 11.0590i) q^{23} +(-37.9684 + 91.6639i) q^{24} +(55.5971 - 55.5971i) q^{25} +(-79.6082 + 79.6082i) q^{26} +(-58.2490 + 140.625i) q^{27} +(65.2704 + 27.0359i) q^{28} +(-101.871 - 245.938i) q^{29} -51.6100i q^{30} +(-33.0662 + 13.6965i) q^{31} +(129.500 + 129.500i) q^{32} +137.029 q^{33} +(79.6712 - 89.1210i) q^{34} -94.4935 q^{35} +(26.1108 + 26.1108i) q^{36} +(330.633 - 136.953i) q^{37} +135.951i q^{38} +(-112.259 - 271.018i) q^{39} +(-140.469 - 58.1842i) q^{40} +(12.5311 - 30.2527i) q^{41} +(74.3614 - 74.3614i) q^{42} +(-364.978 + 364.978i) q^{43} +(60.0806 - 145.047i) q^{44} +(-45.6301 - 18.9006i) q^{45} +(18.8608 + 45.5340i) q^{46} +210.602i q^{47} +(-10.8927 + 4.51190i) q^{48} +(106.388 + 106.388i) q^{49} -134.094 q^{50} +(135.097 + 280.655i) q^{51} -336.097 q^{52} +(61.6826 + 61.6826i) q^{53} +(239.832 - 99.3418i) q^{54} +209.989i q^{55} +(-118.559 - 286.226i) q^{56} +(-327.272 - 135.561i) q^{57} +(-173.737 + 419.439i) q^{58} +(219.718 - 219.718i) q^{59} +(108.946 - 108.946i) q^{60} +(139.774 - 337.444i) q^{61} +(56.3933 + 23.3589i) q^{62} +(-38.5127 - 92.9779i) q^{63} -291.115i q^{64} +(415.318 - 172.030i) q^{65} +(-165.250 - 165.250i) q^{66} +660.131 q^{67} +(356.311 - 19.9481i) q^{68} -128.420 q^{69} +(113.954 + 113.954i) q^{70} +(-367.732 + 152.319i) q^{71} -161.930i q^{72} +(246.235 + 594.463i) q^{73} +(-563.884 - 233.568i) q^{74} +(133.709 - 322.802i) q^{75} +(-286.986 + 286.986i) q^{76} +(-302.558 + 302.558i) q^{77} +(-191.455 + 462.213i) q^{78} +(-355.241 - 147.146i) q^{79} +(-6.91421 - 16.6924i) q^{80} +480.576i q^{81} +(-51.5949 + 21.3713i) q^{82} +(108.533 + 108.533i) q^{83} +313.946 q^{84} +(-430.087 + 207.027i) q^{85} +880.289 q^{86} +(-836.467 - 836.467i) q^{87} +(-636.068 + 263.468i) q^{88} -599.053i q^{89} +(32.2344 + 77.8206i) q^{90} +(846.272 + 350.537i) q^{91} +(-56.3057 + 135.934i) q^{92} +(-112.462 + 112.462i) q^{93} +(253.975 - 253.975i) q^{94} +(207.738 - 501.524i) q^{95} +(751.888 + 311.442i) q^{96} +(-17.0560 - 41.1767i) q^{97} -256.598i q^{98} +(-206.621 + 85.5851i) 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 $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{8}\right)$

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 $

$2$	−1.20595	−	1.20595i	−0.426367	−	0.426367i	0.461022	−	0.887389i	$-0.347483\pi$
$2$	−1.20595	−	1.20595i	−0.426367	−	0.426367i	−0.887389	+	0.461022i	$0.847483\pi$
$3$	4.10553	−	1.70057i	0.790110	−	0.327274i	0.0491220	−	0.998793i	$-0.484358\pi$
$3$	4.10553	−	1.70057i	0.790110	−	0.327274i	0.740988	+	0.671519i	$0.234358\pi$
$4$		−	5.09138i		−	0.636422i
$5$	2.60601	+	6.29147i	0.233089	+	0.562726i	0.996538	−	0.0831423i	$-0.0264956\pi$
$5$	2.60601	+	6.29147i	0.233089	+	0.562726i	−0.763449	+	0.645868i	$0.776496\pi$
$6$	−7.00185	−	2.90026i	−0.476416	−	0.197338i
$7$	−5.31013	+	12.8198i	−0.286720	+	0.692203i	−0.999962	−	0.00871466i	$-0.997226\pi$
$7$	−5.31013	+	12.8198i	−0.286720	+	0.692203i	0.713242	+	0.700918i	$0.247226\pi$
$8$	−15.7875	+	15.7875i	−0.697716	+	0.697716i
$9$	−5.12843	+	5.12843i	−0.189942	+	0.189942i
$10$	4.44447	−	10.7299i	0.140546	−	0.339309i
$11$	28.4888	+	11.8005i	0.780882	+	0.323452i	0.737271	−	0.675597i	$-0.236114\pi$
$11$	28.4888	+	11.8005i	0.780882	+	0.323452i	0.0436106	+	0.999049i	$0.486114\pi$
$12$	−8.65823	−	20.9028i	−0.208285	−	0.502844i
$13$		−	66.0130i		−	1.40836i	−0.710021	−	0.704181i	$-0.751314\pi$
$13$		−	66.0130i		−	1.40836i	0.710021	−	0.704181i	$-0.248686\pi$
$14$	21.8637	−	9.05625i	0.417380	−	0.172885i
$15$	21.3981	+	21.3981i	0.368331	+	0.368331i
$16$	−2.65318			−0.0414559
$17$	3.91802	+	69.9832i	0.0558976	+	0.998437i
$17$	3.91802	+	69.9832i	0.0558976	+	0.998437i
$18$	12.3692			0.161970
$19$	−56.3670	−	56.3670i	−0.680604	−	0.680604i	0.279532	−	0.960136i	$-0.409821\pi$
$19$	−56.3670	−	56.3670i	−0.680604	−	0.680604i	−0.960136	+	0.279532i	$0.909821\pi$
$20$	32.0322	−	13.2682i	0.358131	−	0.148343i
$21$			61.6622i			0.640752i
$22$	−20.1253	−	48.5868i	−0.195033	−	0.470852i
$23$	−26.6989	−	11.0590i	−0.242048	−	0.100259i	0.258362	−	0.966048i	$-0.416817\pi$
$23$	−26.6989	−	11.0590i	−0.242048	−	0.100259i	−0.500410	+	0.865789i	$0.666817\pi$
$24$	−37.9684	+	91.6639i	−0.322928	+	0.779617i
$25$	55.5971	−	55.5971i	0.444777	−	0.444777i
$26$	−79.6082	+	79.6082i	−0.600479	+	0.600479i
$27$	−58.2490	+	140.625i	−0.415186	+	1.00235i
$28$	65.2704	+	27.0359i	0.440534	+	0.182475i
$29$	−101.871	−	245.938i	−0.652308	−	1.57481i	−0.809421	−	0.587229i	$-0.800219\pi$
$29$	−101.871	−	245.938i	−0.652308	−	1.57481i	0.157113	−	0.987581i	$-0.449781\pi$
$30$		−	51.6100i		−	0.314089i
$31$	−33.0662	+	13.6965i	−0.191576	+	0.0793534i	−0.476409	−	0.879224i	$-0.658062\pi$
$31$	−33.0662	+	13.6965i	−0.191576	+	0.0793534i	0.284833	+	0.958577i	$0.408062\pi$
$32$	129.500	+	129.500i	0.715392	+	0.715392i
$33$	137.029			0.722840
$34$	79.6712	−	89.1210i	0.401867	−	0.449533i
$35$	−94.4935			−0.456352
$36$	26.1108	+	26.1108i	0.120883	+	0.120883i
$37$	330.633	−	136.953i	1.46907	−	0.608510i	0.502426	−	0.864620i	$-0.332441\pi$
$37$	330.633	−	136.953i	1.46907	−	0.608510i	0.966648	+	0.256110i	$0.0824409\pi$
$38$			135.951i			0.580374i
$39$	−112.259	−	271.018i	−0.460920	−	1.11276i
$40$	−140.469	−	58.1842i	−0.555253	−	0.229993i
$41$	12.5311	−	30.2527i	0.0477323	−	0.115236i	−0.898215	−	0.439556i	$-0.855136\pi$
$41$	12.5311	−	30.2527i	0.0477323	−	0.115236i	0.945947	+	0.324321i	$0.105136\pi$
$42$	74.3614	−	74.3614i	0.273196	−	0.273196i
$43$	−364.978	+	364.978i	−1.29439	+	1.29439i	−0.362342	+	0.932045i	$0.618023\pi$
$43$	−364.978	+	364.978i	−1.29439	+	1.29439i	−0.932045	+	0.362342i	$0.881977\pi$
$44$	60.0806	−	145.047i	0.205852	−	0.496971i
$45$	−45.6301	−	18.9006i	−0.151158	−	0.0626119i
$46$	18.8608	+	45.5340i	0.0604538	+	0.145948i
$47$			210.602i			0.653606i	0.945093	+	0.326803i	$0.105971\pi$
$47$			210.602i			0.653606i	−0.945093	+	0.326803i	$0.894029\pi$
$48$	−10.8927	+	4.51190i	−0.0327547	+	0.0135674i
$49$	106.388	+	106.388i	0.310170	+	0.310170i
$50$	−134.094			−0.379276
$51$	135.097	+	280.655i	0.370928	+	0.770581i
$52$	−336.097			−0.896313
$53$	61.6826	+	61.6826i	0.159863	+	0.159863i	0.782506	−	0.622643i	$-0.213941\pi$
$53$	61.6826	+	61.6826i	0.159863	+	0.159863i	−0.622643	+	0.782506i	$0.713941\pi$
$54$	239.832	−	99.3418i	0.604390	−	0.250346i
$55$			209.989i			0.514815i
$56$	−118.559	−	286.226i	−0.282912	−	0.683011i
$57$	−327.272	−	135.561i	−0.760496	−	0.315008i
$58$	−173.737	+	419.439i	−0.393324	+	0.949569i
$59$	219.718	−	219.718i	0.484828	−	0.484828i	−0.421841	−	0.906670i	$-0.638616\pi$
$59$	219.718	−	219.718i	0.484828	−	0.484828i	0.906670	+	0.421841i	$0.138616\pi$
$60$	108.946	−	108.946i	0.234414	−	0.234414i
$61$	139.774	−	337.444i	0.293381	−	0.708284i	−0.706619	−	0.707594i	$-0.749780\pi$
$61$	139.774	−	337.444i	0.293381	−	0.708284i	1.00000		0.000689814i	$-0.000219575\pi$
$62$	56.3933	+	23.3589i	0.115515	+	0.0478481i
$63$	−38.5127	−	92.9779i	−0.0770182	−	0.185938i
$64$		−	291.115i		−	0.568583i
$65$	415.318	−	172.030i	0.792521	−	0.328273i
$66$	−165.250	−	165.250i	−0.308195	−	0.308195i
$67$	660.131			1.20370			0.601850	−	0.798609i	$-0.294431\pi$
$67$	660.131			1.20370			0.601850	+	0.798609i	$0.294431\pi$
$68$	356.311	−	19.9481i	0.635427	−	0.0355745i
$69$	−128.420			−0.224056
$70$	113.954	+	113.954i	0.194573	+	0.194573i
$71$	−367.732	+	152.319i	−0.614672	+	0.254605i	−0.668225	−	0.743960i	$-0.732946\pi$
$71$	−367.732	+	152.319i	−0.614672	+	0.254605i	0.0535526	+	0.998565i	$0.482946\pi$
$72$		−	161.930i		−	0.265051i
$73$	246.235	+	594.463i	0.394789	+	0.953105i	0.988881	+	0.148708i	$0.0475115\pi$
$73$	246.235	+	594.463i	0.394789	+	0.953105i	−0.594092	+	0.804397i	$0.702489\pi$
$74$	−563.884	−	233.568i	−0.885813	−	0.366916i
$75$	133.709	−	322.802i	0.205859	−	0.496986i
$76$	−286.986	+	286.986i	−0.433152	+	0.433152i
$77$	−302.558	+	302.558i	−0.447789	+	0.447789i
$78$	−191.455	+	462.213i	−0.277923	+	0.670965i
$79$	−355.241	−	147.146i	−0.505921	−	0.209559i	0.115099	−	0.993354i	$-0.463282\pi$
$79$	−355.241	−	147.146i	−0.505921	−	0.209559i	−0.621020	+	0.783795i	$0.713282\pi$
$80$	−6.91421	−	16.6924i	−0.00966290	−	0.0233283i
$81$			480.576i			0.659226i
$82$	−51.5949	+	21.3713i	−0.0694842	+	0.0287813i
$83$	108.533	+	108.533i	0.143530	+	0.143530i	0.775221	−	0.631690i	$-0.217639\pi$
$83$	108.533	+	108.533i	0.143530	+	0.143530i	−0.631690	+	0.775221i	$0.717639\pi$
$84$	313.946			0.407789
$85$	−430.087	+	207.027i	−0.548817	+	0.264179i
$86$	880.289			1.10377
$87$	−836.467	−	836.467i	−1.03079	−	1.03079i
$88$	−636.068	+	263.468i	−0.770512	+	0.319157i
$89$		−	599.053i		−	0.713477i	−0.934204	−	0.356738i	$-0.883889\pi$
$89$		−	599.053i		−	0.713477i	0.934204	−	0.356738i	$-0.116111\pi$
$90$	32.2344	+	77.8206i	0.0377533	+	0.0911446i
$91$	846.272	+	350.537i	0.974872	+	0.403805i
$92$	−56.3057	+	135.934i	−0.0638073	+	0.154045i
$93$	−112.462	+	112.462i	−0.125396	+	0.125396i
$94$	253.975	−	253.975i	0.278676	−	0.278676i
$95$	207.738	−	501.524i	0.224352	−	0.541635i
$96$	751.888	+	311.442i	0.799367	+	0.331109i
$97$	−17.0560	−	41.1767i	−0.0178533	−	0.0431017i	0.914701	−	0.404130i	$-0.132426\pi$
$97$	−17.0560	−	41.1767i	−0.0178533	−	0.0431017i	−0.932555	+	0.361028i	$0.882426\pi$
$98$		−	256.598i		−	0.264492i
$99$	−206.621	+	85.5851i	−0.209759	+	0.0868851i
$100$	−283.066	−	283.066i	−0.283066	−	0.283066i
$101$	−1478.33			−1.45643			−0.728215	−	0.685348i	$-0.759650\pi$
$101$	−1478.33			−1.45643			−0.728215	+	0.685348i	$0.759650\pi$
$102$	175.536	−	501.375i	0.170399	−	0.486701i
$103$	618.133			0.591325			0.295662	−	0.955293i	$-0.404460\pi$
$103$	618.133			0.591325			0.295662	+	0.955293i	$0.404460\pi$
$104$	1042.18	+	1042.18i	0.982637	+	0.982637i
$105$	−387.946	+	160.692i	−0.360568	+	0.149352i
$106$		−	148.772i		−	0.136321i
$107$	53.1850	+	128.400i	0.0480522	+	0.116008i	0.946083	−	0.323924i	$-0.105002\pi$
$107$	53.1850	+	128.400i	0.0480522	+	0.116008i	−0.898031	+	0.439933i	$0.855002\pi$
$108$	715.978	+	296.568i	0.637916	+	0.264234i
$109$	315.127	−	760.783i	0.276914	−	0.668531i	−0.722833	−	0.691023i	$-0.757160\pi$
$109$	315.127	−	760.783i	0.276914	−	0.668531i	0.999747	+	0.0224926i	$0.00716024\pi$
$110$	253.235	−	253.235i	0.219500	−	0.219500i
$111$	1124.53	−	1124.53i	0.961580	−	0.961580i
$112$	14.0887	−	34.0132i	0.0118862	−	0.0286959i
$113$	−556.614	−	230.557i	−0.463379	−	0.191938i	0.138765	−	0.990325i	$-0.455687\pi$
$113$	−556.614	−	230.557i	−0.463379	−	0.191938i	−0.602144	+	0.798387i	$0.705687\pi$
$114$	231.194	+	558.152i	0.189941	+	0.458559i
$115$		−	196.795i		−	0.159576i
$116$	−1252.16	+	518.663i	−1.00224	+	0.415143i
$117$	338.543	+	338.543i	0.267507	+	0.267507i
$118$	−529.937			−0.413430
$119$	−917.975	−	321.392i	−0.707148	−	0.247579i
$120$	−675.646			−0.513982
$121$	−268.797	−	268.797i	−0.201951	−	0.201951i
$122$	−575.501	+	238.380i	−0.427077	+	0.176901i
$123$		−	145.513i		−	0.106671i
$124$	69.7339	+	168.352i	0.0505023	+	0.121923i
$125$	1281.11	+	530.652i	0.916686	+	0.379704i
$126$	−65.6822	+	158.571i	−0.0464400	+	0.112116i
$127$	−1065.60	+	1065.60i	−0.744538	+	0.744538i	−0.973448	−	0.228909i	$-0.926484\pi$
$127$	−1065.60	+	1065.60i	−0.744538	+	0.744538i	0.228909	+	0.973448i	$0.426484\pi$
$128$	684.929	−	684.929i	0.472967	−	0.472967i
$129$	−877.759	+	2119.10i	−0.599088	+	1.44633i
$130$	−708.312	−	293.392i	−0.477870	−	0.197940i
$131$	1065.23	+	2571.69i	0.710455	+	1.71519i	0.698861	+	0.715257i	$0.253691\pi$
$131$	1065.23	+	2571.69i	0.710455	+	1.71519i	0.0115939	+	0.999933i	$0.496309\pi$
$132$		−	697.667i		−	0.460032i
$133$	1021.93	−	423.297i	0.666259	−	0.275974i
$134$	−796.084	−	796.084i	−0.513218	−	0.513218i
$135$	−1036.54			−0.660822
$136$	−1166.72	−	1043.01i	−0.735626	−	0.657625i
$137$	−629.783			−0.392744			−0.196372	−	0.980529i	$-0.562916\pi$
$137$	−629.783			−0.392744			−0.196372	+	0.980529i	$0.562916\pi$
$138$	154.867	+	154.867i	0.0955303	+	0.0955303i
$139$	2452.07	−	1015.68i	1.49627	−	0.619775i	0.523599	−	0.851965i	$-0.324589\pi$
$139$	2452.07	−	1015.68i	1.49627	−	0.619775i	0.972671	+	0.232190i	$0.0745890\pi$
$140$			481.102i			0.290432i
$141$	358.143	+	864.633i	0.213908	+	0.516420i
$142$	627.154	+	259.776i	0.370631	+	0.153520i
$143$	778.983	−	1880.63i	0.455537	−	1.09976i
$144$	13.6066	−	13.6066i	0.00787421	−	0.00787421i
$145$	1281.83	−	1281.83i	0.734141	−	0.734141i
$146$	419.946	−	1013.84i	0.238048	−	0.574698i
$147$	617.701	+	255.860i	0.346579	+	0.143558i
$148$	−697.278	−	1683.38i	−0.387270	−	0.934951i
$149$			2216.30i			1.21857i	0.792953	+	0.609283i	$0.208543\pi$
$149$			2216.30i			1.21857i	−0.792953	+	0.609283i	$0.791457\pi$
$150$	−550.529	+	228.036i	−0.299670	+	0.124127i
$151$	−1508.37	−	1508.37i	−0.812908	−	0.812908i	0.172161	−	0.985069i	$-0.444925\pi$
$151$	−1508.37	−	1508.37i	−0.812908	−	0.812908i	−0.985069	+	0.172161i	$0.944925\pi$
$152$	1779.79			0.949737
$153$	−378.997	−	338.811i	−0.200262	−	0.179028i
$154$	729.740			0.381845
$155$	−172.342	−	172.342i	−0.0893085	−	0.0893085i
$156$	−1379.86	+	571.555i	−0.708186	+	0.293340i
$157$		−	345.107i		−	0.175430i	−0.996146	−	0.0877152i	$-0.972043\pi$
$157$		−	345.107i		−	0.175430i	0.996146	−	0.0877152i	$-0.0279565\pi$
$158$	250.952	+	605.853i	0.126359	+	0.305057i
$159$	358.135	+	148.344i	0.178629	+	0.0739904i
$160$	−477.266	+	1152.22i	−0.235820	+	0.569319i
$161$	283.549	−	283.549i	0.138800	−	0.138800i
$162$	579.549	−	579.549i	0.281072	−	0.281072i
$163$	259.661	−	626.876i	0.124774	−	0.301231i	−0.849133	−	0.528180i	$-0.822875\pi$
$163$	259.661	−	626.876i	0.124774	−	0.301231i	0.973907	+	0.226948i	$0.0728748\pi$
$164$	−154.028	−	63.8004i	−0.0733387	−	0.0303779i
$165$	357.099	+	862.114i	0.168486	+	0.406761i
$166$		−	261.770i		−	0.122393i
$167$	−738.909	+	306.066i	−0.342386	+	0.141821i	−0.547249	−	0.836970i	$-0.684325\pi$
$167$	−738.909	+	306.066i	−0.342386	+	0.141821i	0.204863	+	0.978791i	$0.434325\pi$
$168$	−973.494	−	973.494i	−0.447063	−	0.447063i
$169$	−2160.71			−0.983483
$170$	768.326	+	268.998i	0.346635	+	0.121360i
$171$	578.148			0.258550
$172$	1858.24	+	1858.24i	0.823777	+	0.823777i
$173$	−1741.96	+	721.542i	−0.765540	+	0.317097i	−0.731064	−	0.682308i	$-0.760976\pi$
$173$	−1741.96	+	721.542i	−0.765540	+	0.317097i	−0.0344756	+	0.999406i	$0.510976\pi$
$174$			2017.47i			0.878989i
$175$	417.515	+	1007.97i	0.180350	+	0.435402i
$176$	−75.5859	−	31.3087i	−0.0323722	−	0.0134090i
$177$	528.414	−	1275.70i	0.224396	−	0.541739i
$178$	−722.426	+	722.426i	−0.304203	+	0.304203i
$179$	−2537.71	+	2537.71i	−1.05965	+	1.05965i	−0.0615460	+	0.998104i	$0.519603\pi$
$179$	−2537.71	+	2537.71i	−1.05965	+	1.05965i	−0.998104	+	0.0615460i	$0.980397\pi$
$180$	−96.2301	+	232.320i	−0.0398476	+	0.0962006i
$181$	−426.229	−	176.550i	−0.175035	−	0.0725020i	0.293445	−	0.955976i	$-0.405198\pi$
$181$	−426.229	−	176.550i	−0.175035	−	0.0725020i	−0.468480	+	0.883474i	$0.655198\pi$
$182$	−597.830	−	1443.29i	−0.243484	−	0.587823i
$183$		−	1623.08i		−	0.655638i
$184$	596.103	−	246.914i	0.238833	−	0.0989280i
$185$	1723.27	+	1723.27i	0.684849	+	0.684849i
$186$	271.248			0.106929
$187$	−714.214	+	2039.97i	−0.279297	+	0.797741i
$188$	1072.26			0.415969
$189$	−1493.48	−	1493.48i	−0.574786	−	0.574786i
$190$	−855.333	+	354.291i	−0.326592	+	0.135279i
$191$		−	4519.91i		−	1.71230i	−0.516728	−	0.856149i	$-0.672850\pi$
$191$		−	4519.91i		−	1.71230i	0.516728	−	0.856149i	$-0.327150\pi$
$192$	−495.060	−	1195.18i	−0.186083	−	0.449243i
$193$	−2705.97	−	1120.85i	−1.00922	−	0.418034i	−0.184052	−	0.982916i	$-0.558922\pi$
$193$	−2705.97	−	1120.85i	−1.00922	−	0.418034i	−0.825171	+	0.564882i	$0.808922\pi$
$194$	−29.0884	+	70.2256i	−0.0107651	+	0.0259892i
$195$	1412.55	−	1412.55i	0.518744	−	0.518744i
$196$	541.663	−	541.663i	0.197399	−	0.197399i
$197$	737.100	−	1779.52i	0.266580	−	0.643580i	−0.732738	−	0.680511i	$-0.761758\pi$
$197$	737.100	−	1779.52i	0.266580	−	0.643580i	0.999318	+	0.0369306i	$0.0117581\pi$
$198$	352.385	+	145.963i	0.126479	+	0.0523895i
$199$	1181.20	+	2851.66i	0.420767	+	1.01582i	0.982122	+	0.188247i	$0.0602805\pi$
$199$	1181.20	+	2851.66i	0.420767	+	1.01582i	−0.561354	+	0.827576i	$0.689720\pi$
$200$			1755.48i			0.620656i
$201$	2710.19	−	1122.60i	0.951055	−	0.393940i
$202$	1782.79	+	1782.79i	0.620974	+	0.620974i
$203$	3693.81			1.27712
$204$	1428.92	−	687.828i	0.490415	−	0.236067i
$205$	222.990			0.0759721
$206$	−745.436	−	745.436i	−0.252121	−	0.252121i
$207$	193.639	−	80.2077i	0.0650184	−	0.0269315i
$208$			175.144i			0.0583849i
$209$	−940.673	−	2270.99i	−0.311329	−	0.751614i
$210$	661.629	+	274.056i	0.217413	+	0.0900554i
$211$	−1378.58	+	3328.18i	−0.449787	+	1.08588i	0.522614	+	0.852569i	$0.324957\pi$
$211$	−1378.58	+	3328.18i	−0.449787	+	1.08588i	−0.972402	+	0.233314i	$0.925043\pi$
$212$	314.050	−	314.050i	0.101741	−	0.101741i
$213$	−1250.70	+	1250.70i	−0.402333	+	0.402333i
$214$	90.7053	−	218.982i	0.0289742	−	0.0699500i
$215$	−3247.38	−	1345.11i	−1.03009	−	0.426678i
$216$	−1300.52	−	3139.73i	−0.409672	−	0.989037i
$217$		−	496.631i		−	0.155362i
$218$	−1297.49	+	537.439i	−0.403106	+	0.166972i
$219$	2021.85	+	2021.85i	0.623853	+	0.623853i
$220$	1069.13			0.327640
$221$	4619.80	−	258.640i	1.40616	−	0.0787241i
$222$	−2712.24			−0.819972
$223$	−1115.41	−	1115.41i	−0.334948	−	0.334948i	0.519514	−	0.854462i	$-0.326113\pi$
$223$	−1115.41	−	1115.41i	−0.334948	−	0.334948i	−0.854462	+	0.519514i	$0.826113\pi$
$224$	−2347.82	+	972.498i	−0.700314	+	0.290079i
$225$			570.252i			0.168963i
$226$	393.208	+	949.287i	0.115734	+	0.279405i
$227$	−3966.12	−	1642.82i	−1.15965	−	0.480343i	−0.281892	−	0.959446i	$-0.590962\pi$
$227$	−3966.12	−	1642.82i	−1.15965	−	0.480343i	−0.877759	+	0.479103i	$0.840962\pi$
$228$	−690.191	+	1666.27i	−0.200478	+	0.483997i
$229$	−410.753	+	410.753i	−0.118530	+	0.118530i	−0.763884	−	0.645354i	$-0.776710\pi$
$229$	−410.753	+	410.753i	−0.118530	+	0.118530i	0.645354	+	0.763884i	$0.276710\pi$
$230$	−237.324	+	237.324i	−0.0680378	+	0.0680378i
$231$	−727.642	+	1756.68i	−0.207253	+	0.500352i
$232$	5491.03	+	2274.46i	1.55390	+	0.643645i
$233$	−257.078	−	620.642i	−0.0722823	−	0.174505i	0.883609	−	0.468225i	$-0.155106\pi$
$233$	−257.078	−	620.642i	−0.0722823	−	0.174505i	−0.955891	+	0.293721i	$0.905106\pi$
$234$		−	816.530i		−	0.228112i
$235$	−1325.00	+	548.831i	−0.367801	+	0.152348i
$236$	−1118.67	−	1118.67i	−0.308556	−	0.308556i
$237$	−1708.69			−0.468317
$238$	719.448	+	1494.61i	0.195945	+	0.407064i
$239$	−273.635			−0.0740584			−0.0370292	−	0.999314i	$-0.511789\pi$
$239$	−273.635			−0.0740584			−0.0370292	+	0.999314i	$0.511789\pi$
$240$	−56.7730	−	56.7730i	−0.0152695	−	0.0152695i
$241$	5992.80	−	2482.30i	1.60178	−	0.663481i	0.610117	−	0.792311i	$-0.291122\pi$
$241$	5992.80	−	2482.30i	1.60178	−	0.663481i	0.991667	+	0.128831i	$0.0411223\pi$
$242$			648.310i			0.172211i
$243$	−755.472	−	1823.87i	−0.199438	−	0.481487i
$244$	−1718.06	−	711.643i	−0.450768	−	0.186714i
$245$	−392.089	+	946.587i	−0.102244	+	0.246838i
$246$	−175.481	+	175.481i	−0.0454808	+	0.0454808i
$247$	−3720.95	+	3720.95i	−0.958537	+	0.958537i
$248$	305.800	−	738.266i	0.0782996	−	0.189032i
$249$	630.152	+	261.017i	0.160378	+	0.0664309i
$250$	−905.010	−	2184.89i	−0.228951	−	0.552738i
$251$			2527.58i			0.635615i	0.948155	+	0.317808i	$0.102947\pi$
$251$			2527.58i			0.635615i	−0.948155	+	0.317808i	$0.897053\pi$
$252$	−473.386	+	196.083i	−0.118335	+	0.0490161i
$253$	−630.117	−	630.117i	−0.156582	−	0.156582i
$254$	2570.11			0.634893
$255$	−1413.67	+	1581.35i	−0.347166	+	0.388344i
$256$	−3980.89			−0.971898
$257$	1203.81	+	1203.81i	0.292184	+	0.292184i	0.837943	−	0.545758i	$-0.183758\pi$
$257$	1203.81	+	1203.81i	0.292184	+	0.292184i	−0.545758	+	0.837943i	$0.683758\pi$
$258$	3614.05	−	1496.99i	0.872098	−	0.361235i
$259$			4965.88i			1.19137i
$260$	−875.872	−	2114.54i	−0.208920	−	0.504378i
$261$	1783.71	+	738.837i	0.423023	+	0.175222i
$262$	1816.72	−	4385.94i	0.428386	−	1.03421i
$263$	3022.46	−	3022.46i	0.708641	−	0.708641i	−0.257608	−	0.966249i	$-0.582934\pi$
$263$	3022.46	−	3022.46i	0.708641	−	0.708641i	0.966249	+	0.257608i	$0.0829344\pi$
$264$	−2163.35	+	2163.35i	−0.504337	+	0.504337i
$265$	−227.328	+	548.819i	−0.0526969	+	0.127222i
$266$	−1742.87	−	721.919i	−0.401737	−	0.166405i
$267$	−1018.73	−	2459.43i	−0.233503	−	0.563725i
$268$		−	3360.98i		−	0.766061i
$269$	7387.65	−	3060.07i	1.67447	−	0.693589i	0.675434	−	0.737420i	$-0.263956\pi$
$269$	7387.65	−	3060.07i	1.67447	−	0.693589i	0.999039	+	0.0438311i	$0.0139563\pi$
$270$	1250.01	+	1250.01i	0.281753	+	0.281753i
$271$	−474.268			−0.106309			−0.0531545	−	0.998586i	$-0.516928\pi$
$271$	−474.268			−0.106309			−0.0531545	+	0.998586i	$0.516928\pi$
$272$	−10.3952	−	185.678i	−0.00231729	−	0.0413911i
$273$	4070.51			0.902411
$274$	759.485	+	759.485i	0.167453	+	0.167453i
$275$	2239.97	−	927.825i	0.491182	−	0.203454i
$276$			653.833i			0.142595i
$277$	−1081.56	−	2611.11i	−0.234601	−	0.566378i	0.762107	−	0.647451i	$-0.224165\pi$
$277$	−1081.56	−	2611.11i	−0.234601	−	0.566378i	−0.996708	+	0.0810736i	$0.974165\pi$
$278$	−4181.92	−	1732.21i	−0.902212	−	0.373708i
$279$	99.3362	−	239.819i	0.0213158	−	0.0514609i
$280$	1491.82	−	1491.82i	0.318404	−	0.318404i
$281$	−1766.46	+	1766.46i	−0.375011	+	0.375011i	−0.869299	−	0.494287i	$-0.835429\pi$
$281$	−1766.46	+	1766.46i	−0.375011	+	0.375011i	0.494287	+	0.869299i	$0.335429\pi$
$282$	610.801	−	1474.60i	0.128981	−	0.311388i
$283$	2233.09	+	924.974i	0.469057	+	0.194290i	0.604676	−	0.796471i	$-0.293302\pi$
$283$	2233.09	+	924.974i	0.469057	+	0.194290i	−0.135619	+	0.990761i	$0.543302\pi$
$284$	775.516	+	1872.26i	0.162037	+	0.391191i
$285$		−	2412.29i		−	0.501375i
$286$	−3207.36	+	1328.53i	−0.663129	+	0.274677i
$287$	321.291	+	321.291i	0.0660808	+	0.0660808i
$288$	−1328.26			−0.271766
$289$	−4882.30	+	548.391i	−0.993751	+	0.111620i
$290$	−3091.65			−0.626027
$291$	−140.047	−	140.047i	−0.0282121	−	0.0282121i
$292$	3026.64	−	1253.67i	0.606577	−	0.251253i
$293$			6652.17i			1.32636i	0.748459	+	0.663181i	$0.230794\pi$
$293$			6652.17i			1.32636i	−0.748459	+	0.663181i	$0.769206\pi$
$294$	−436.361	−	1053.47i	−0.0865616	−	0.208978i
$295$	1954.94	+	809.761i	0.385833	+	0.159817i
$296$	−3057.73	+	7382.02i	−0.600429	+	1.44956i
$297$	−3318.89	+	3318.89i	−0.648423	+	0.648423i
$298$	2672.74	−	2672.74i	0.519557	−	0.519557i
$299$	−730.039	+	1762.47i	−0.141202	+	0.340891i
$300$	−1643.51	−	680.763i	−0.316293	−	0.131013i
$301$	−2740.86	−	6617.02i	−0.524852	−	1.26711i
$302$			3638.02i			0.693194i
$303$	−6069.34	+	2514.00i	−1.15074	+	0.476652i
$304$	149.552	+	149.552i	0.0282151	+	0.0282151i
$305$	2487.27			0.466954
$306$	48.4629	+	865.639i	0.00905373	+	0.161717i
$307$	−2511.18			−0.466842			−0.233421	−	0.972376i	$-0.574992\pi$
$307$	−2511.18			−0.466842			−0.233421	+	0.972376i	$0.574992\pi$
$308$	1540.44	+	1540.44i	0.284983	+	0.284983i
$309$	2537.76	−	1051.18i	0.467211	−	0.193525i
$310$			415.670i			0.0761563i
$311$	1371.96	+	3312.20i	0.250150	+	0.603916i	0.998216	−	0.0597089i	$-0.0190172\pi$
$311$	1371.96	+	3312.20i	0.250150	+	0.603916i	−0.748066	+	0.663625i	$0.769017\pi$
$312$	6051.00	+	2506.41i	1.09798	+	0.454799i
$313$	−999.691	+	2413.47i	−0.180530	+	0.435838i	−0.988076	−	0.153967i	$-0.950795\pi$
$313$	−999.691	+	2413.47i	−0.180530	+	0.435838i	0.807546	+	0.589804i	$0.200795\pi$
$314$	−416.182	+	416.182i	−0.0747977	+	0.0747977i
$315$	484.603	−	484.603i	0.0866803	−	0.0866803i
$316$	−749.175	+	1808.67i	−0.133368	+	0.321980i
$317$	−3606.64	−	1493.92i	−0.639019	−	0.264690i	0.0395609	−	0.999217i	$-0.487404\pi$
$317$	−3606.64	−	1493.92i	−0.639019	−	0.264690i	−0.678579	+	0.734527i	$0.737404\pi$
$318$	−252.997	−	610.788i	−0.0446143	−	0.107708i
$319$		−	8208.60i		−	1.44073i
$320$	1831.54	−	758.647i	0.319956	−	0.132530i
$321$	436.705	+	436.705i	0.0759331	+	0.0759331i
$322$	−683.890			−0.118359
$323$	3723.90	−	4165.59i	0.641496	−	0.717584i
$324$	2446.79			0.419546
$325$	−3670.13	−	3670.13i	−0.626407	−	0.626407i
$326$	−1069.12	+	442.843i	−0.181635	+	0.0752355i
$327$		−	3659.31i		−	0.618839i
$328$	279.780	+	675.449i	0.0470984	+	0.113706i
$329$	−2699.87	−	1118.32i	−0.452428	−	0.187402i
$330$	609.022	−	1470.31i	0.101593	−	0.245266i
$331$	4409.54	−	4409.54i	0.732236	−	0.732236i	−0.238826	−	0.971062i	$-0.576763\pi$
$331$	4409.54	−	4409.54i	0.732236	−	0.732236i	0.971062	+	0.238826i	$0.0767626\pi$
$332$	552.581	−	552.581i	0.0913459	−	0.0913459i
$333$	−993.276	+	2397.98i	−0.163457	+	0.394620i
$334$	1260.19	+	521.986i	0.206450	+	0.0855144i
$335$	1720.31	+	4153.19i	0.280569	+	0.677353i
$336$		−	163.601i		−	0.0265630i
$337$	3549.62	−	1470.30i	0.573769	−	0.237663i	−0.0768818	−	0.997040i	$-0.524496\pi$
$337$	3549.62	−	1470.30i	0.573769	−	0.237663i	0.650650	+	0.759378i	$0.274496\pi$
$338$	2605.71	+	2605.71i	0.419325	+	0.419325i
$339$	−2677.27			−0.428936
$340$	1054.05	+	2189.73i	0.168130	+	0.349279i
$341$	−1103.64			−0.175265
$342$	−697.217	−	697.217i	−0.110237	−	0.110237i
$343$	−6325.99	+	2620.31i	−0.995836	+	0.412489i
$344$		−	11524.2i		−	1.80623i
$345$	−334.663	−	807.947i	−0.0522250	−	0.126082i
$346$	2970.85	+	1230.57i	0.461601	+	0.191201i
$347$	3176.99	−	7669.92i	0.491497	−	1.18658i	−0.462461	−	0.886640i	$-0.653034\pi$
$347$	3176.99	−	7669.92i	0.491497	−	1.18658i	0.953958	−	0.299940i	$-0.0969665\pi$
$348$	−4258.77	+	4258.77i	−0.656017	+	0.656017i
$349$	3485.45	−	3485.45i	0.534590	−	0.534590i	−0.387345	−	0.921935i	$-0.626608\pi$
$349$	3485.45	−	3485.45i	0.534590	−	0.534590i	0.921935	+	0.387345i	$0.126608\pi$
$350$	712.058	−	1719.06i	0.108746	−	0.262536i
$351$	9283.10	+	3845.19i	1.41167	+	0.584732i
$352$	2161.14	+	5217.45i	0.327242	+	0.790032i
$353$			9607.54i			1.44861i	0.689482	+	0.724303i	$0.257838\pi$
$353$			9607.54i			1.44861i	−0.689482	+	0.724303i	$0.742162\pi$
$354$	−2175.67	+	901.194i	−0.326655	+	0.135305i
$355$	−1916.62	−	1916.62i	−0.286546	−	0.286546i
$356$	−3050.00			−0.454073
$357$	−4315.32	+	241.594i	−0.639751	+	0.0358165i
$358$	6120.69			0.903600
$359$	−1387.88	−	1387.88i	−0.204038	−	0.204038i	0.597690	−	0.801728i	$-0.296085\pi$
$359$	−1387.88	−	1387.88i	−0.204038	−	0.204038i	−0.801728	+	0.597690i	$0.796085\pi$
$360$	1018.78	−	421.992i	0.149151	−	0.0617804i
$361$		−	504.522i		−	0.0735561i
$362$	301.100	+	726.921i	0.0437168	+	0.105542i
$363$	−1560.66	−	646.447i	−0.225657	−	0.0934702i
$364$	1784.72	−	4308.69i	0.256991	−	0.620431i
$365$	−3098.36	+	3098.36i	−0.444316	+	0.444316i
$366$	−1957.35	+	1957.35i	−0.279542	+	0.279542i
$367$	−1323.43	+	3195.04i	−0.188235	+	0.454441i	−0.989620	−	0.143709i	$-0.954097\pi$
$367$	−1323.43	+	3195.04i	−0.188235	+	0.454441i	0.801385	+	0.598149i	$0.204097\pi$
$368$	70.8368	+	29.3416i	0.0100343	+	0.00415634i
$369$	90.8840	+	219.413i	0.0128218	+	0.0309545i
$370$		−	4156.34i		−	0.583994i
$371$	−1118.30	+	463.215i	−0.156494	+	0.0648219i
$372$	572.589	+	572.589i	0.0798047	+	0.0798047i
$373$	−2661.22			−0.369418			−0.184709	−	0.982793i	$-0.559134\pi$
$373$	−2661.22			−0.369418			−0.184709	+	0.982793i	$0.559134\pi$
$374$	3321.41	−	1598.80i	0.459213	−	0.221048i
$375$	6162.03			0.848549
$376$	−3324.88	−	3324.88i	−0.456031	−	0.456031i
$377$	−16235.1	+	6724.79i	−2.21790	+	0.918685i
$378$			3602.11i			0.490140i
$379$	2136.53	+	5158.04i	0.289568	+	0.699079i	0.999989	−	0.00469813i	$-0.00149547\pi$
$379$	2136.53	+	5158.04i	0.289568	+	0.699079i	−0.710421	+	0.703777i	$0.751495\pi$
$380$	−2553.45	−	1057.67i	−0.344708	−	0.142783i
$381$	−2562.72	+	6186.95i	−0.344599	+	0.831935i
$382$	−5450.77	+	5450.77i	−0.730068	+	0.730068i
$383$	5538.16	−	5538.16i	0.738868	−	0.738868i	−0.233491	−	0.972359i	$-0.575015\pi$
$383$	5538.16	−	5538.16i	0.738868	−	0.738868i	0.972359	+	0.233491i	$0.0750149\pi$
$384$	1647.23	−	3976.77i	0.218906	−	0.528486i
$385$	−2692.01	−	1115.07i	−0.356357	−	0.147608i
$386$	1911.57	+	4614.95i	0.252064	+	0.608535i
$387$		−	3743.53i		−	0.491717i
$388$	−209.646	+	86.8383i	−0.0274309	+	0.0113622i
$389$	−5255.89	−	5255.89i	−0.685050	−	0.685050i	0.276084	−	0.961134i	$-0.410963\pi$
$389$	−5255.89	−	5255.89i	−0.685050	−	0.685050i	−0.961134	+	0.276084i	$0.910963\pi$
$390$	−3406.93			−0.442350
$391$	669.339	−	1911.80i	0.0865728	−	0.247273i
$392$	−3359.22			−0.432821
$393$	8746.67	+	8746.67i	1.12267	+	1.12267i
$394$	−3034.91	+	1257.10i	−0.388062	+	0.160741i
$395$		−	2618.45i		−	0.333541i
$396$	435.746	+	1051.98i	0.0552956	+	0.133495i
$397$	8814.05	+	3650.90i	1.11427	+	0.461545i	0.862406	−	0.506218i	$-0.168957\pi$
$397$	8814.05	+	3650.90i	1.11427	+	0.461545i	0.251863	+	0.967763i	$0.418957\pi$
$398$	2014.49	−	4863.41i	0.253712	−	0.612514i
$399$	3475.71	−	3475.71i	0.436099	−	0.436099i
$400$	−147.509	+	147.509i	−0.0184386	+	0.0184386i
$401$	3315.30	−	8003.85i	0.412863	−	0.996741i	−0.571502	−	0.820601i	$-0.693639\pi$
$401$	3315.30	−	8003.85i	0.412863	−	0.996741i	0.984365	−	0.176140i	$-0.0563611\pi$
$402$	−4622.14	−	1914.55i	−0.573461	−	0.237535i
$403$	904.144	+	2182.80i	0.111758	+	0.269808i
$404$			7526.75i			0.926905i
$405$	−3023.53	+	1252.39i	−0.370963	+	0.153658i
$406$	−4454.55	−	4454.55i	−0.544521	−	0.544521i
$407$	11035.4			1.34400
$408$	−6563.69	−	2298.01i	−0.796449	−	0.278844i
$409$	5279.17			0.638235			0.319117	−	0.947715i	$-0.396614\pi$
$409$	5279.17			0.638235			0.319117	+	0.947715i	$0.396614\pi$
$410$	−268.914	−	268.914i	−0.0323920	−	0.0323920i
$411$	−2585.59	+	1070.99i	−0.310311	+	0.128535i
$412$		−	3147.15i		−	0.376332i
$413$	1650.01	+	3983.47i	0.196590	+	0.474610i
$414$	−330.244	−	136.792i	−0.0392044	−	0.0162390i
$415$	−399.993	+	965.668i	−0.0473129	+	0.114224i
$416$	8548.66	−	8548.66i	1.00753	−	1.00753i
$417$	8339.80	−	8339.80i	0.979381	−	0.979381i
$418$	−1604.29	+	3873.09i	−0.187723	+	0.453204i
$419$	−8692.08	−	3600.38i	−1.01345	−	0.419785i	−0.186738	−	0.982410i	$-0.559792\pi$
$419$	−8692.08	−	3600.38i	−1.01345	−	0.419785i	−0.826713	+	0.562624i	$0.809792\pi$
$420$	818.146	+	1975.18i	0.0950510	+	0.229473i
$421$			8191.97i			0.948343i	0.880433	+	0.474171i	$0.157252\pi$
$421$			8191.97i			0.948343i	−0.880433	+	0.474171i	$0.842748\pi$
$422$	5676.10	−	2351.12i	0.654759	−	0.271210i
$423$	−1080.06	−	1080.06i	−0.124147	−	0.124147i
$424$	−1947.63			−0.223079
$425$	4108.69	+	3673.03i	0.468943	+	0.419219i
$426$	3016.57			0.343083
$427$	3583.75	+	3583.75i	0.406158	+	0.406158i
$428$	653.733	−	270.785i	0.0738303	−	0.0305815i
$429$		−	9045.70i		−	1.01802i
$430$	2294.04	+	5538.31i	0.257276	+	0.621119i
$431$	1801.84	+	746.345i	0.201372	+	0.0834111i	0.481090	−	0.876671i	$-0.340241\pi$
$431$	1801.84	+	746.345i	0.201372	+	0.0834111i	−0.279718	+	0.960082i	$0.590241\pi$
$432$	154.545	−	373.104i	0.0172119	−	0.0415532i
$433$	−7885.88	+	7885.88i	−0.875223	+	0.875223i	−0.993036	−	0.117813i	$-0.962412\pi$
$433$	−7885.88	+	7885.88i	−0.875223	+	0.875223i	0.117813	+	0.993036i	$0.462412\pi$
$434$	−598.911	+	598.911i	−0.0662411	+	0.0662411i
$435$	3082.76	−	7442.44i	0.339786	−	0.820317i
$436$	−3873.44	−	1604.43i	−0.425468	−	0.176235i
$437$	881.570	+	2128.30i	0.0965016	+	0.232976i
$438$		−	4876.49i		−	0.531981i
$439$	−434.369	+	179.922i	−0.0472240	+	0.0195608i	−0.406170	−	0.913797i	$-0.633136\pi$
$439$	−434.369	+	179.922i	−0.0472240	+	0.0195608i	0.358946	+	0.933358i	$0.383136\pi$
$440$	−3315.20	−	3315.20i	−0.359195	−	0.359195i
$441$	−1091.21			−0.117829
$442$	−5883.14	−	5259.33i	−0.633105	−	0.565975i
$443$	−13132.9			−1.40849			−0.704246	−	0.709956i	$-0.748715\pi$
$443$	−13132.9			−1.40849			−0.704246	+	0.709956i	$0.748715\pi$
$444$	−5725.39	−	5725.39i	−0.611971	−	0.611971i
$445$	3768.92	−	1561.14i	0.401492	−	0.166303i
$446$			2690.25i			0.285621i
$447$	3768.97	+	9099.09i	0.398805	+	0.962801i
$448$	3732.02	+	1545.86i	0.393575	+	0.163024i
$449$	3992.55	−	9638.87i	0.419644	−	1.01311i	−0.562807	−	0.826588i	$-0.690279\pi$
$449$	3992.55	−	9638.87i	0.419644	−	1.01311i	0.982451	−	0.186522i	$-0.0597214\pi$
$450$	687.694	−	687.694i	0.0720404	−	0.0720404i
$451$	713.990	−	713.990i	0.0745465	−	0.0745465i
$452$	−1173.85	+	2833.93i	−0.122154	+	0.294905i
$453$	−8757.72	−	3627.57i	−0.908330	−	0.376243i
$454$	2801.78	+	6764.09i	0.289634	+	0.699239i
$455$			6237.79i			0.642708i
$456$	7306.98	−	3026.65i	0.750397	−	0.310824i
$457$	179.170	+	179.170i	0.0183397	+	0.0183397i	0.716217	−	0.697877i	$-0.245872\pi$
$457$	179.170	+	179.170i	0.0183397	+	0.0183397i	−0.697877	+	0.716217i	$0.745872\pi$
$458$	990.694			0.101074
$459$	−10069.6	−	3525.48i	−1.02399	−	0.358508i
$460$	−1001.96			−0.101558
$461$	11002.7	+	11002.7i	1.11160	+	1.11160i	0.992934	+	0.118665i	$0.0378613\pi$
$461$	11002.7	+	11002.7i	1.11160	+	1.11160i	0.118665	+	0.992934i	$0.462139\pi$
$462$	2995.97	−	1240.97i	0.301699	−	0.124968i
$463$			10727.9i			1.07682i	0.842684	+	0.538409i	$0.180974\pi$
$463$			10727.9i			1.07682i	−0.842684	+	0.538409i	$0.819026\pi$
$464$	270.281	+	652.516i	0.0270420	+	0.0652852i
$465$	−1000.63	−	414.475i	−0.0997918	−	0.0413351i
$466$	−438.439	+	1058.49i	−0.0435843	+	0.105222i
$467$	1386.27	−	1386.27i	0.137364	−	0.137364i	−0.635081	−	0.772445i	$-0.719033\pi$
$467$	1386.27	−	1386.27i	0.137364	−	0.137364i	0.772445	+	0.635081i	$0.219033\pi$
$468$	1723.65	−	1723.65i	0.170247	−	0.170247i
$469$	−3505.38	+	8462.74i	−0.345125	+	0.833205i
$470$	2259.74	+	936.014i	0.221774	+	0.0918619i
$471$	−586.878	−	1416.85i	−0.0574138	−	0.138609i
$472$			6937.61i			0.676545i
$473$	−14704.7	+	6090.89i	−1.42944	+	0.592092i
$474$	2060.59	+	2060.59i	0.199675	+	0.199675i
$475$	−6267.68			−0.605434
$476$	−1636.33	+	4673.76i	−0.157565	+	0.450045i
$477$	−632.670			−0.0607295
$478$	329.989	+	329.989i	0.0315761	+	0.0315761i
$479$	−3967.31	+	1643.31i	−0.378436	+	0.156754i	−0.563790	−	0.825918i	$-0.690657\pi$
$479$	−3967.31	+	1643.31i	−0.378436	+	0.156754i	0.185353	+	0.982672i	$0.440657\pi$
$480$			5542.10i			0.527002i
$481$	−9040.65	−	21826.1i	−0.857002	−	2.06899i
$482$	−10220.5	−	4233.48i	−0.965834	−	0.400062i
$483$	681.924	−	1646.31i	0.0642415	−	0.155093i
$484$	−1368.55	+	1368.55i	−0.128526	+	0.128526i
$485$	214.614	−	214.614i	0.0200930	−	0.0200930i
$486$	−1288.43	+	3110.55i	−0.120256	+	0.290324i
$487$	16642.3	+	6893.47i	1.54853	+	0.641423i	0.983050	−	0.183337i	$-0.0586899\pi$
$487$	16642.3	+	6893.47i	1.54853	+	0.641423i	0.565483	+	0.824760i	$0.308690\pi$
$488$	3120.73	+	7534.10i	0.289485	+	0.698878i
$489$		−	3015.23i		−	0.278841i
$490$	1614.37	−	668.696i	0.148837	−	0.0616502i
$491$	−9710.80	−	9710.80i	−0.892551	−	0.892551i	0.102212	−	0.994763i	$-0.467408\pi$
$491$	−9710.80	−	9710.80i	−0.892551	−	0.892551i	−0.994763	+	0.102212i	$0.967408\pi$
$492$	−740.862			−0.0678875
$493$	16812.4	−	8092.83i	1.53589	−	0.739316i
$494$	8974.55			0.817377
$495$	−1076.91	−	1076.91i	−0.0977850	−	0.0977850i
$496$	87.7304	−	36.3391i	0.00794196	−	0.00328967i
$497$		−	5523.07i		−	0.498478i
$498$	−445.157	−	1074.70i	−0.0400561	−	0.0967040i
$499$	7157.95	+	2964.92i	0.642152	+	0.265988i	0.679906	−	0.733299i	$-0.262020\pi$
$499$	7157.95	+	2964.92i	0.642152	+	0.265988i	−0.0377542	+	0.999287i	$0.512020\pi$
$500$	2701.75	−	6522.60i	0.241652	−	0.583399i
$501$	−2513.13	+	2513.13i	−0.224108	+	0.224108i
$502$	3048.13	−	3048.13i	0.271005	−	0.271005i
$503$	7348.93	−	17741.9i	0.651436	−	1.57271i	−0.159258	−	0.987237i	$-0.550910\pi$
$503$	7348.93	−	17741.9i	0.651436	−	1.57271i	0.810694	−	0.585470i	$-0.199090\pi$
$504$	2075.91	+	859.871i	0.183469	+	0.0759954i
$505$	−3852.55	−	9300.87i	−0.339478	−	0.819571i
$506$			1519.78i			0.133522i
$507$	−8870.87	+	3674.43i	−0.777059	+	0.321868i
$508$	5425.35	+	5425.35i	0.473841	+	0.473841i
$509$	−151.325			−0.0131775			−0.00658876	−	0.999978i	$-0.502097\pi$
$509$	−151.325			−0.0131775			−0.00658876	+	0.999978i	$0.502097\pi$
$510$	3611.83	−	202.209i	0.313597	−	0.0175568i
$511$	−8928.43			−0.772936
$512$	−678.683	−	678.683i	−0.0585817	−	0.0585817i
$513$	11210.0	−	4643.32i	0.964779	−	0.399625i
$514$		−	2903.45i		−	0.249155i
$515$	1610.86	+	3888.96i	0.137831	+	0.332754i
$516$	10789.1	+	4469.01i	0.920475	+	0.381273i
$517$	−2485.20	+	5999.80i	−0.211410	+	0.510389i
$518$	5988.59	−	5988.59i	0.507961	−	0.507961i
$519$	−5924.62	+	5924.62i	−0.501083	+	0.501083i
$520$	−3840.91	+	9272.78i	−0.323914	+	0.781997i
$521$	7897.89	+	3271.41i	0.664133	+	0.275093i	0.689176	−	0.724594i	$-0.257973\pi$
$521$	7897.89	+	3271.41i	0.664133	+	0.275093i	−0.0250438	+	0.999686i	$0.507973\pi$
$522$	−1260.06	−	3042.06i	−0.105654	−	0.255072i
$523$		−	17874.0i		−	1.49441i	−0.664593	−	0.747205i	$-0.731395\pi$
$523$		−	17874.0i		−	1.49441i	0.664593	−	0.747205i	$-0.268605\pi$
$524$	13093.5	−	5423.49i	1.09159	−	0.452150i
$525$	3428.24	+	3428.24i	0.284992	+	0.284992i
$526$	−7289.85			−0.604283
$527$	−1088.08	−	2260.41i	−0.0899380	−	0.186841i
$528$	−363.563			−0.0299660
$529$	−8012.84	−	8012.84i	−0.658572	−	0.658572i
$530$	935.994	−	387.701i	0.0767113	−	0.0317749i
$531$			2253.62i			0.184178i
$532$	−2155.16	−	5203.03i	−0.175636	−	0.424022i
$533$	−1997.07	−	827.212i	−0.162294	−	0.0672243i
$534$	−1737.41	+	4194.48i	−0.140796	+	0.339911i
$535$	−669.223	+	669.223i	−0.0540805	+	0.0540805i
$536$	−10421.8	+	10421.8i	−0.839841	+	0.839841i
$537$	−6103.10	+	14734.2i	−0.490444	+	1.18404i
$538$	−12599.4	−	5218.85i	−1.00966	−	0.418216i
$539$	1775.45	+	4286.31i	0.141881	+	0.342531i
$540$			5277.41i			0.420562i
$541$	−1960.69	+	812.146i	−0.155817	+	0.0645414i	−0.459229	−	0.888318i	$-0.651874\pi$
$541$	−1960.69	+	812.146i	−0.155817	+	0.0645414i	0.303412	+	0.952859i	$0.401874\pi$
$542$	571.942	+	571.942i	0.0453266	+	0.0453266i
$543$	−2050.13			−0.162025
$544$	−8555.43	+	9570.19i	−0.674285	+	0.754262i
$545$	5607.67			0.440745
$546$	−4908.82	−	4908.82i	−0.384758	−	0.384758i
$547$	262.443	−	108.707i	0.0205141	−	0.00849724i	−0.372403	−	0.928071i	$-0.621466\pi$
$547$	262.443	−	108.707i	0.0205141	−	0.00849724i	0.392917	+	0.919574i	$0.371466\pi$
$548$			3206.46i			0.249951i
$549$	1013.74	+	2447.38i	0.0788075	+	0.190258i
$550$	−3820.19	−	1582.38i	−0.296170	−	0.122678i
$551$	−8120.62	+	19604.9i	−0.627859	+	1.51579i
$552$	2027.43	−	2027.43i	0.156328	−	0.156328i
$553$	3772.75	−	3772.75i	0.290115	−	0.290115i
$554$	−1844.56	+	4453.17i	−0.141459	+	0.341511i
$555$	10005.4	+	4144.39i	0.765239	+	0.316972i
$556$	−5171.21	−	12484.4i	−0.394439	−	0.952260i
$557$		−	9915.36i		−	0.754268i	−0.926159	−	0.377134i	$-0.876910\pi$
$557$		−	9915.36i		−	0.754268i	0.926159	−	0.377134i	$-0.123090\pi$
$558$	−409.003	+	169.415i	−0.0310296	+	0.0128529i
$559$	24093.3	+	24093.3i	1.82297	+	1.82297i
$560$	250.708			0.0189185
$561$	536.883	+	9589.74i	0.0404050	+	0.721710i
$562$	4260.52			0.319785
$563$	−3569.84	−	3569.84i	−0.267231	−	0.267231i	0.560753	−	0.827983i	$-0.310512\pi$
$563$	−3569.84	−	3569.84i	−0.267231	−	0.267231i	−0.827983	+	0.560753i	$0.810512\pi$
$564$	4402.18	−	1823.44i	0.328661	−	0.136136i
$565$		−	4102.75i		−	0.305494i
$566$	−1577.51	−	3808.46i	−0.117152	−	0.282829i
$567$	−6160.87	−	2551.92i	−0.456318	−	0.189013i
$568$	3400.82	−	8210.32i	0.251224	−	0.606509i
$569$	−7753.04	+	7753.04i	−0.571220	+	0.571220i	−0.932469	−	0.361249i	$-0.882350\pi$
$569$	−7753.04	+	7753.04i	−0.571220	+	0.571220i	0.361249	+	0.932469i	$0.382350\pi$
$570$	−2909.10	+	2909.10i	−0.213770	+	0.213770i
$571$	2586.01	−	6243.18i	0.189529	−	0.457564i	−0.800340	−	0.599546i	$-0.795348\pi$
$571$	2586.01	−	6243.18i	0.189529	−	0.457564i	0.989869	+	0.141983i	$0.0453477\pi$
$572$	−9575.01	−	3966.10i	−0.699915	−	0.289914i
$573$	−7686.40	−	18556.6i	−0.560391	−	1.35290i
$574$		−	774.920i		−	0.0563494i
$575$	−2099.23	+	869.529i	−0.152250	+	0.0630641i
$576$	1492.96	+	1492.96i	0.107998	+	0.107998i
$577$	18050.9			1.30237			0.651187	−	0.758917i	$-0.274271\pi$
$577$	18050.9			1.30237			0.651187	+	0.758917i	$0.274271\pi$
$578$	6549.13	+	5226.47i	0.471294	+	0.376111i
$579$	−13015.5			−0.934209
$580$	−6526.29	−	6526.29i	−0.467224	−	0.467224i
$581$	−1967.69	+	815.043i	−0.140505	+	0.0581991i
$582$			337.780i			0.0240574i
$583$	1029.38	+	2485.15i	0.0731263	+	0.176543i
$584$	−13272.5	−	5497.67i	−0.940448	−	0.389546i
$585$	−1247.68	+	3012.18i	−0.0881802	+	0.212886i
$586$	8022.17	−	8022.17i	0.565517	−	0.565517i
$587$	−5265.87	+	5265.87i	−0.370265	+	0.370265i	−0.867574	−	0.497309i	$-0.834322\pi$
$587$	−5265.87	+	5265.87i	−0.370265	+	0.370265i	0.497309	+	0.867574i	$0.334322\pi$
$588$	1302.68	−	3144.95i	0.0913633	−	0.220571i
$589$	2635.87	+	1091.81i	0.184396	+	0.0763792i
$590$	−1381.02	−	3334.08i	−0.0963657	−	0.232647i
$591$		−	8559.34i		−	0.595743i
$592$	−877.228	+	363.360i	−0.0609018	+	0.0252263i
$593$	869.258	+	869.258i	0.0601958	+	0.0601958i	0.736564	−	0.676368i	$-0.236447\pi$
$593$	869.258	+	869.258i	0.0601958	+	0.0601958i	−0.676368	+	0.736564i	$0.736447\pi$
$594$	8004.82			0.552932
$595$	−370.227	−	6612.95i	−0.0255090	−	0.455638i
$596$	11284.0			0.775523
$597$	9698.87	+	9698.87i	0.664905	+	0.664905i
$598$	3005.84	−	1245.06i	0.205548	−	0.0851408i
$599$			10655.6i			0.726840i	0.931625	+	0.363420i	$0.118391\pi$
$599$			10655.6i			0.726840i	−0.931625	+	0.363420i	$0.881609\pi$
$600$	2985.31	+	7207.18i	0.203125	+	0.490386i
$601$	1972.01	+	816.833i	0.133843	+	0.0554398i	0.448600	−	0.893733i	$-0.351923\pi$
$601$	1972.01	+	816.833i	0.133843	+	0.0554398i	−0.314756	+	0.949172i	$0.601923\pi$
$602$	−4674.45	+	11285.1i	−0.316472	+	0.764032i
$603$	−3385.44	+	3385.44i	−0.228633	+	0.228633i
$604$	−7679.66	+	7679.66i	−0.517353	+	0.517353i
$605$	990.639	−	2391.62i	0.0665706	−	0.160716i
$606$	10351.1	+	4287.55i	0.693866	+	0.287409i
$607$	−4731.84	−	11423.7i	−0.316407	−	0.763875i	−0.999439	−	0.0334863i	$-0.989339\pi$
$607$	−4731.84	−	11423.7i	−0.316407	−	0.763875i	0.683032	−	0.730389i	$-0.260661\pi$
$608$		−	14599.0i		−	0.973797i
$609$	15165.1	−	6281.58i	1.00906	−	0.417968i
$610$	−2999.52	−	2999.52i	−0.199094	−	0.199094i
$611$	13902.5			0.920513
$612$	−1725.01	+	1929.62i	−0.113937	+	0.127451i
$613$	4888.87			0.322120			0.161060	−	0.986945i	$-0.448509\pi$
$613$	4888.87			0.322120			0.161060	+	0.986945i	$0.448509\pi$
$614$	3028.35	+	3028.35i	0.199046	+	0.199046i
$615$	915.491	−	379.209i	0.0600263	−	0.0248637i
$616$		−	9553.30i		−	0.624859i
$617$	−9471.41	−	22866.0i	−0.617998	−	1.49198i	−0.854025	−	0.520232i	$-0.825845\pi$
$617$	−9471.41	−	22866.0i	−0.617998	−	1.49198i	0.236027	−	0.971747i	$-0.424155\pi$
$618$	−4328.07	−	1792.75i	−0.281716	−	0.116691i
$619$	−4131.00	+	9973.11i	−0.268237	+	0.647582i	−0.999401	−	0.0346207i	$-0.988978\pi$
$619$	−4131.00	+	9973.11i	−0.268237	+	0.647582i	0.731163	+	0.682202i	$0.238978\pi$
$620$	−877.456	+	877.456i	−0.0568379	+	0.0568379i
$621$	3110.36	−	3110.36i	0.200990	−	0.200990i
$622$	2339.83	−	5648.86i	0.150834	−	0.364145i
$623$	7679.72	+	3181.05i	0.493871	+	0.204568i
$624$	297.844	+	719.059i	0.0191079	+	0.0461305i
$625$		−	385.346i		−	0.0246621i
$626$	4116.09	−	1704.94i	0.262799	−	0.108855i
$627$	−7723.92	−	7723.92i	−0.491968	−	0.491968i
$628$	−1757.07			−0.111648
$629$	10879.8	+	22602.2i	0.689677	+	1.43276i
$630$	−1168.81			−0.0739152
$631$	−5359.80	−	5359.80i	−0.338146	−	0.338146i	0.517523	−	0.855669i	$-0.326854\pi$
$631$	−5359.80	−	5359.80i	−0.338146	−	0.338146i	−0.855669	+	0.517523i	$0.826854\pi$
$632$	7931.45	−	3285.31i	0.499203	−	0.206777i
$633$			16008.3i			1.00517i
$634$	2547.83	+	6151.00i	0.159601	+	0.385312i
$635$	−9481.12	−	3927.21i	−0.592514	−	0.245427i
$636$	755.278	−	1823.40i	0.0470892	−	0.113683i
$637$	7023.01	−	7023.01i	0.436832	−	0.436832i
$638$	−9899.14	+	9899.14i	−0.614280	+	0.614280i
$639$	1104.73	−	2667.05i	0.0683917	−	0.165112i
$640$	6094.14	+	2524.28i	0.376394	+	0.155907i
$641$	−1217.52	−	2939.35i	−0.0750219	−	0.181119i	0.881920	−	0.471400i	$-0.156251\pi$
$641$	−1217.52	−	2939.35i	−0.0750219	−	0.181119i	−0.956941	+	0.290281i	$0.906251\pi$
$642$		−	1053.29i		−	0.0647507i
$643$	−9749.51	+	4038.38i	−0.597952	+	0.247680i	−0.661068	−	0.750326i	$-0.729896\pi$
$643$	−9749.51	+	4038.38i	−0.597952	+	0.247680i	0.0631154	+	0.998006i	$0.479896\pi$
$644$	−1443.65	−	1443.65i	−0.0883353	−	0.0883353i
$645$	−15619.7			−0.953526
$646$	−9514.31	+	532.660i	−0.579467	+	0.0324415i
$647$	−10952.0			−0.665483			−0.332742	−	0.943018i	$-0.607974\pi$
$647$	−10952.0			−0.665483			−0.332742	+	0.943018i	$0.607974\pi$
$648$	−7587.10	−	7587.10i	−0.459953	−	0.459953i
$649$	8852.29	−	3666.74i	0.535412	−	0.221775i
$650$			8851.97i			0.534158i
$651$	−844.554	−	2038.93i	−0.0508459	−	0.122753i
$652$	−3191.66	−	1322.03i	−0.191710	−	0.0794090i
$653$	2497.68	−	6029.94i	0.149681	−	0.361362i	−0.831199	−	0.555975i	$-0.812345\pi$
$653$	2497.68	−	6029.94i	0.149681	−	0.361362i	0.980880	+	0.194613i	$0.0623450\pi$
$654$	−4412.94	+	4412.94i	−0.263853	+	0.263853i
$655$	−13403.7	+	13403.7i	−0.799583	+	0.799583i
$656$	−33.2471	+	80.2657i	−0.00197878	+	0.00477721i
$657$	−4311.46	−	1785.87i	−0.256022	−	0.106048i
$658$	1907.27	+	4604.55i	0.112998	+	0.272802i
$659$			25717.9i			1.52022i	0.649793	+	0.760111i	$0.274855\pi$
$659$			25717.9i			1.52022i	−0.649793	+	0.760111i	$0.725145\pi$
$660$	4389.35	−	1818.13i	0.258872	−	0.107228i
$661$	−8350.18	−	8350.18i	−0.491353	−	0.491353i	0.417379	−	0.908732i	$-0.362949\pi$
$661$	−8350.18	−	8350.18i	−0.491353	−	0.491353i	−0.908732	+	0.417379i	$0.862949\pi$
$662$	−10635.3			−0.624403
$663$	18526.9	−	8918.13i	1.08526	−	0.522400i
$664$	−3426.93			−0.200287
$665$	5326.31	+	5326.31i	0.310595	+	0.310595i
$666$	4089.68	−	1694.00i	0.237946	−	0.0985603i
$667$			7692.85i			0.446579i
$668$	1558.30	+	3762.07i	0.0902581	+	0.217902i
$669$	−6476.17	−	2682.52i	−0.374265	−	0.155026i
$670$	2933.93	−	7083.14i	0.169176	−	0.408426i
$671$	7964.00	−	7964.00i	0.458192	−	0.458192i
$672$	−7985.24	+	7985.24i	−0.458389	+	0.458389i
$673$	−2404.34	+	5804.60i	−0.137713	+	0.332468i	−0.977658	−	0.210204i	$-0.932587\pi$
$673$	−2404.34	+	5804.60i	−0.137713	+	0.332468i	0.839945	+	0.542672i	$0.182587\pi$
$674$	−6053.76	−	2507.55i	−0.345967	−	0.143304i
$675$	4579.89	+	11056.8i	0.261156	+	0.630486i
$676$			11001.0i			0.625910i
$677$	17094.4	−	7080.72i	0.970443	−	0.401970i	0.159566	−	0.987187i	$-0.448991\pi$
$677$	17094.4	−	7080.72i	0.970443	−	0.401970i	0.810877	+	0.585217i	$0.198991\pi$
$678$	3228.65	+	3228.65i	0.182884	+	0.182884i
$679$	618.446			0.0349540
$680$	3521.56	−	10058.4i	0.198596	−	0.567241i
$681$	−19076.8			−1.07346
$682$	1330.93	+	1330.93i	0.0747274	+	0.0747274i
$683$	127.050	−	52.6260i	0.00711779	−	0.00294828i	−0.379122	−	0.925347i	$-0.623774\pi$
$683$	127.050	−	52.6260i	0.00711779	−	0.00294828i	0.386239	+	0.922399i	$0.373774\pi$
$684$		−	2943.57i		−	0.164547i
$685$	−1641.22	−	3962.26i	−0.0915442	−	0.221007i
$686$	10788.8	+	4468.86i	0.600463	+	0.248720i
$687$	−987.847	+	2384.87i	−0.0548598	+	0.132443i
$688$	968.352	−	968.352i	0.0536600	−	0.0536600i
$689$	4071.85	−	4071.85i	0.225145	−	0.225145i
$690$	−570.756	+	1377.93i	−0.0314903	+	0.0760244i
$691$	−280.152	−	116.043i	−0.0154233	−	0.00638854i	0.374958	−	0.927042i	$-0.377657\pi$
$691$	−280.152	−	116.043i	−0.0154233	−	0.00638854i	−0.390382	+	0.920653i	$0.627657\pi$
$692$	3673.64	+	8868.96i	0.201808	+	0.487207i
$693$		−	3103.30i		−	0.170108i
$694$	−13080.8	+	5418.25i	−0.715476	+	0.296360i
$695$	12780.2	+	12780.2i	0.697527	+	0.697527i
$696$	26411.5			1.43840
$697$	2166.27	+	758.433i	0.117724	+	0.0412162i
$698$	−8406.54			−0.455863
$699$	−2110.89	−	2110.89i	−0.114222	−	0.114222i
$700$	5131.96	−	2125.73i	0.277100	−	0.114778i
$701$		−	23434.3i		−	1.26263i	−0.775528	−	0.631313i	$-0.782516\pi$
$701$		−	23434.3i		−	1.26263i	0.775528	−	0.631313i	$-0.217484\pi$
$702$	−6557.84	−	15832.0i	−0.352578	−	0.851199i
$703$	−26356.4	−	10917.2i	−1.41401	−	0.585703i
$704$	3435.28	−	8293.51i	0.183909	−	0.443996i
$705$	−4506.49	+	4506.49i	−0.240743	+	0.240743i
$706$	11586.2	−	11586.2i	0.617638	−	0.617638i
$707$	7850.13	−	18951.9i	0.417588	−	1.00815i
$708$	−6495.10	−	2690.36i	−0.344775	−	0.142810i
$709$	19.9707	+	48.2136i	0.00105785	+	0.00255388i	0.924408	−	0.381406i	$-0.124560\pi$
$709$	19.9707	+	48.2136i	0.00105785	+	0.00255388i	−0.923350	+	0.383960i	$0.874560\pi$
$710$			4622.70i			0.244348i
$711$	2576.46	−	1067.20i	0.135900	−	0.0562915i
$712$	9457.56	+	9457.56i	0.497805	+	0.497805i
$713$	1034.30			0.0543265
$714$	5495.40	+	4912.70i	0.288039	+	0.257498i
$715$	13862.0			0.725046
$716$	12920.4	+	12920.4i	0.674385	+	0.674385i
$717$	−1123.42	+	465.334i	−0.0585143	+	0.0242374i
$718$			3347.43i			0.173990i
$719$	−859.046	−	2073.92i	−0.0445577	−	0.107572i	0.900034	−	0.435820i	$-0.143542\pi$
$719$	−859.046	−	2073.92i	−0.0445577	−	0.107572i	−0.944591	+	0.328248i	$0.893542\pi$
$720$	121.065	+	50.1466i	0.00626641	+	0.00259563i
$721$	−3282.36	+	7924.33i	−0.169545	+	0.409317i
$722$	−608.427	+	608.427i	−0.0313619	+	0.0313619i
$723$	20382.3	−	20382.3i	1.04844	−	1.04844i
$724$	−898.883	+	2170.10i	−0.0461419	+	0.111396i
$725$	−19337.1	−	8009.71i	−0.990570	−	0.410308i
$726$	1102.49	+	2661.66i	0.0563601	+	0.136065i
$727$			2971.90i			0.151612i	0.997123	+	0.0758059i	$0.0241529\pi$
$727$			2971.90i			0.151612i	−0.997123	+	0.0758059i	$0.975847\pi$
$728$	−18894.6	+	7826.42i	−0.961926	+	0.398443i
$729$	−15378.3	−	15378.3i	−0.781299	−	0.781299i
$730$	7472.91			0.378883
$731$	−26972.3	−	24112.4i	−1.36472	−	1.22001i
$732$	−8263.73			−0.417263
$733$	22418.7	+	22418.7i	1.12968	+	1.12968i	0.990230	+	0.139447i	$0.0445324\pi$
$733$	22418.7	+	22418.7i	1.12968	+	1.12968i	0.139447	+	0.990230i	$0.455468\pi$
$734$	5449.04	−	2257.07i	0.274016	−	0.113501i
$735$			4553.02i			0.228491i
$736$	−2025.35	−	4889.64i	−0.101434	−	0.244884i
$737$	18806.4	+	7789.85i	0.939947	+	0.389339i
$738$	155.000	−	374.202i	0.00773119	−	0.0186647i
$739$	26152.8	−	26152.8i	1.30182	−	1.30182i	0.374657	−	0.927163i	$-0.377760\pi$
$739$	26152.8	−	26152.8i	1.30182	−	1.30182i	0.927163	−	0.374657i	$-0.122240\pi$
$740$	8773.80	−	8773.80i	0.435853	−	0.435853i
$741$	−8948.76	+	21604.2i	−0.443645	+	1.07105i
$742$	1907.22	+	789.998i	0.0943617	+	0.0390859i
$743$	−4057.18	−	9794.89i	−0.200328	−	0.483633i	0.791508	−	0.611159i	$-0.209296\pi$
$743$	−4057.18	−	9794.89i	−0.200328	−	0.483633i	−0.991835	+	0.127526i	$0.959296\pi$
$744$		−	3551.01i		−	0.174981i
$745$	−13943.8	+	5775.70i	−0.685719	+	0.284034i
$746$	3209.30	+	3209.30i	0.157508	+	0.157508i
$747$	−1113.21			−0.0545248
$748$	10386.3	+	3636.33i	0.507700	+	0.177751i
$749$	−1928.48			−0.0940789
$750$	−7431.09	−	7431.09i	−0.361793	−	0.361793i
$751$	−26941.7	+	11159.6i	−1.30908	+	0.542238i	−0.924615	−	0.380903i	$-0.875613\pi$
$751$	−26941.7	+	11159.6i	−1.30908	+	0.542238i	−0.384463	+	0.923141i	$0.625613\pi$
$752$		−	558.765i		−	0.0270958i
$753$	4298.32	+	10377.1i	0.208020	+	0.502206i
$754$	27688.4	+	11468.9i	1.33734	+	0.553943i
$755$	5559.01	−	13420.6i	0.267965	−	0.646924i
$756$	−7603.86	+	7603.86i	−0.365807	+	0.365807i
$757$	−24358.4	+	24358.4i	−1.16951	+	1.16951i	−0.187186	+	0.982325i	$0.559937\pi$
$757$	−24358.4	+	24358.4i	−1.16951	+	1.16951i	−0.982325	+	0.187186i	$0.940063\pi$
$758$	3643.79	−	8796.88i	0.174602	−	0.421526i
$759$	−3658.52	−	1515.41i	−0.174962	−	0.0724715i
$760$	4638.15	+	11197.5i	0.221373	+	0.534442i
$761$			14414.5i			0.686632i	0.939220	+	0.343316i	$0.111550\pi$
$761$			14414.5i			0.686632i	−0.939220	+	0.343316i	$0.888450\pi$
$762$	10551.7	−	4370.64i	0.501635	−	0.207784i
$763$	8079.71	+	8079.71i	0.383362	+	0.383362i
$764$	−23012.6			−1.08975
$765$	1143.94	−	3267.39i	0.0540646	−	0.154422i
$766$	−13357.5			−0.630058
$767$	−14504.2	−	14504.2i	−0.682814	−	0.682814i
$768$	−16343.7	+	6769.77i	−0.767906	+	0.318077i
$769$		−	7049.33i		−	0.330566i	−0.986246	−	0.165283i	$-0.947146\pi$
$769$		−	7049.33i		−	0.330566i	0.986246	−	0.165283i	$-0.0528537\pi$
$770$	1901.71	+	4591.13i	0.0890037	+	0.214874i
$771$	6989.41	+	2895.11i	0.326482	+	0.135233i
$772$	−5706.67	+	13777.1i	−0.266046	+	0.642292i
$773$	−18928.0	+	18928.0i	−0.880716	+	0.880716i	−0.993607	−	0.112891i	$-0.963989\pi$
$773$	−18928.0	+	18928.0i	−0.880716	+	0.880716i	0.112891	+	0.993607i	$0.463989\pi$
$774$	−4514.50	+	4514.50i	−0.209652	+	0.209652i
$775$	−1076.90	+	2599.87i	−0.0499141	+	0.120503i
$776$	919.349	+	380.807i	0.0425293	+	0.0176162i
$777$	8444.80	+	20387.6i	0.389904	+	0.941312i
$778$			12676.7i			0.584165i
$779$	−2411.59	+	998.913i	−0.110917	+	0.0459432i
$780$	−7191.84	−	7191.84i	−0.330140	−	0.330140i
$781$	−12273.7			−0.562339
$782$	−3112.72	+	1498.34i	−0.142341	+	0.0685175i
$783$	40519.0			1.84934
$784$	−282.267	−	282.267i	−0.0128584	−	0.0128584i
$785$	2171.23	−	899.353i	0.0987192	−	0.0408908i
$786$		−	21096.1i		−	0.957343i
$787$	9982.50	+	24099.9i	0.452144	+	1.09157i	0.971505	+	0.237018i	$0.0761700\pi$
$787$	9982.50	+	24099.9i	0.452144	+	1.09157i	−0.519361	+	0.854555i	$0.673830\pi$
$788$	−9060.19	−	3752.85i	−0.409589	−	0.169657i
$789$	7268.90	−	17548.7i	0.327984	−	0.791824i
$790$	−3157.72	+	3157.72i	−0.142211	+	0.142211i
$791$	5911.38	−	5911.38i	0.265720	−	0.265720i
$792$	1910.85	−	4613.21i	0.0857313	−	0.206974i
$793$	−22275.7	−	9226.90i	−0.997520	−	0.413186i
$794$	−6226.49	−	15032.1i	−0.278300	−	0.671875i
$795$			2639.78i			0.117765i
$796$	14518.9	−	6013.91i	0.646492	−	0.267786i
$797$	−12804.7	−	12804.7i	−0.569092	−	0.569092i	0.362782	−	0.931874i	$-0.381827\pi$
$797$	−12804.7	−	12804.7i	−0.569092	−	0.569092i	−0.931874	+	0.362782i	$0.881827\pi$
$798$	−8383.06			−0.371876
$799$	−14738.6	+	825.143i	−0.652584	+	0.0365350i
$800$	14399.6			0.636379
$801$	3072.20	+	3072.20i	0.135519	+	0.135519i
$802$	−13650.3	+	5654.14i	−0.601009	+	0.248946i
$803$			19841.2i			0.871958i
$804$	−5715.57	−	13798.6i	−0.250712	−	0.605273i
$805$	2522.87	+	1045.01i	0.110459	+	0.0457536i
$806$	1541.99	−	3722.69i	0.0673874	−	0.162687i
$807$	25126.4	−	25126.4i	1.09602	−	1.09602i
$808$	23339.2	−	23339.2i	1.01618	−	1.01618i
$809$	2795.36	−	6748.59i	0.121483	−	0.293285i	−0.851426	−	0.524475i	$-0.824262\pi$
$809$	2795.36	−	6748.59i	0.121483	−	0.293285i	0.972909	+	0.231189i	$0.0742617\pi$
$810$	5156.53	+	2135.90i	0.223681	+	0.0926518i
$811$	7466.79	+	18026.4i	0.323298	+	0.780510i	0.999058	+	0.0433884i	$0.0138153\pi$
$811$	7466.79	+	18026.4i	0.323298	+	0.780510i	−0.675761	+	0.737121i	$0.736185\pi$
$812$		−	18806.6i		−	0.812786i
$813$	−1947.12	+	806.524i	−0.0839957	+	0.0347922i
$814$	−13308.2	−	13308.2i	−0.573036	−	0.573036i
$815$	4620.65			0.198594
$816$	−358.435	−	744.628i	−0.0153771	−	0.0319451i
$817$	41145.5			1.76193
$818$	−6366.40	−	6366.40i	−0.272122	−	0.272122i
$819$	−6137.75	+	2542.34i	−0.261869	+	0.108470i
$820$		−	1135.32i		−	0.0483503i
$821$	11237.2	+	27129.1i	0.477689	+	1.15324i	0.960690	+	0.277623i	$0.0895467\pi$
$821$	11237.2	+	27129.1i	0.477689	+	1.15324i	−0.483001	+	0.875620i	$0.660453\pi$
$822$	4409.64	+	1826.53i	0.187109	+	0.0775033i
$823$	10758.2	−	25972.5i	0.455657	−	1.10005i	−0.514481	−	0.857502i	$-0.672015\pi$
$823$	10758.2	−	25972.5i	0.455657	−	1.10005i	0.970138	−	0.242552i	$-0.0779846\pi$
$824$	−9758.78	+	9758.78i	−0.412577	+	0.412577i
$825$	7618.42	−	7618.42i	0.321502	−	0.321502i
$826$	2814.03	−	6793.68i	0.118538	−	0.286177i
$827$	36364.4	+	15062.6i	1.52904	+	0.633348i	0.979377	−	0.202041i	$-0.0647575\pi$
$827$	36364.4	+	15062.6i	1.52904	+	0.633348i	0.549659	+	0.835389i	$0.314757\pi$
$828$	−408.368	−	985.888i	−0.0171398	−	0.0413792i
$829$		−	15525.3i		−	0.650443i	−0.945638	−	0.325221i	$-0.894561\pi$
$829$		−	15525.3i		−	0.650443i	0.945638	−	0.325221i	$-0.105439\pi$
$830$	1646.92	−	682.175i	0.0688738	−	0.0285285i
$831$	−8880.75	−	8880.75i	−0.370722	−	0.370722i
$832$	−19217.3			−0.800771
$833$	−7028.56	+	7862.23i	−0.292347	+	0.327023i
$834$	−20114.7			−0.835151
$835$	−3851.21	−	3851.21i	−0.159613	−	0.159613i
$836$	−11562.4	+	4789.32i	−0.478344	+	0.198137i
$837$		−	5447.75i		−	0.224972i
$838$	6140.33	+	14824.1i	0.253120	+	0.611085i
$839$	27723.7	+	11483.5i	1.14079	+	0.472533i	0.871437	−	0.490508i	$-0.163189\pi$
$839$	27723.7	+	11483.5i	1.14079	+	0.472533i	0.269358	+	0.963040i	$0.413189\pi$
$840$	3587.77	−	8661.64i	0.147369	−	0.355780i
$841$	−32862.1	+	32862.1i	−1.34741	+	1.34741i
$842$	9879.09	−	9879.09i	0.404342	−	0.404342i
$843$	−4248.27	+	10256.2i	−0.173568	+	0.419031i
$844$	16945.0	+	7018.86i	0.691080	+	0.286255i
$845$	−5630.84	−	13594.0i	−0.229239	−	0.553431i
$846$			2604.99i			0.105864i
$847$	4873.27	−	2018.57i	0.197695	−	0.0818878i
$848$	−163.655	−	163.655i	−0.00662728	−	0.00662728i
$849$	10741.0			0.434193
$850$	−525.385	−	9384.36i	−0.0212006	−	0.378683i
$851$	−10342.1			−0.416595
$852$	6367.81	+	6367.81i	0.256053	+	0.256053i
$853$	−4020.20	+	1665.22i	−0.161371	+	0.0668419i	−0.461907	−	0.886929i	$-0.652834\pi$
$853$	−4020.20	+	1665.22i	−0.161371	+	0.0668419i	0.300536	+	0.953770i	$0.402834\pi$
$854$		−	8643.62i		−	0.346345i
$855$	1506.66	+	3637.40i	0.0602652	+	0.145493i
$856$	−2866.78	−	1187.46i	−0.114468	−	0.0474141i
$857$	−9896.77	+	23892.9i	−0.394478	+	0.952353i	0.594474	+	0.804115i	$0.297360\pi$
$857$	−9896.77	+	23892.9i	−0.394478	+	0.952353i	−0.988952	+	0.148238i	$0.952640\pi$
$858$	−10908.6	+	10908.6i	−0.434050	+	0.434050i
$859$	13494.4	−	13494.4i	0.535999	−	0.535999i	−0.386352	−	0.922351i	$-0.626265\pi$
$859$	13494.4	−	13494.4i	0.535999	−	0.535999i	0.922351	+	0.386352i	$0.126265\pi$
$860$	−6848.47	+	16533.7i	−0.271548	+	0.655574i
$861$	1865.45	+	772.693i	0.0738377	+	0.0305846i
$862$	−1272.87	−	3072.97i	−0.0502947	−	0.121422i
$863$		−	24790.2i		−	0.977831i	−0.872331	−	0.488916i	$-0.837393\pi$
$863$		−	24790.2i		−	0.977831i	0.872331	−	0.488916i	$-0.162607\pi$
$864$	−25754.2	+	10667.7i	−1.01409	+	0.420051i
$865$	−9079.11	−	9079.11i	−0.356877	−	0.356877i
$866$	19019.9			0.746332
$867$	−19111.8	+	10554.1i	−0.748642	+	0.413421i
$868$	−2528.54			−0.0988757
$869$	−8384.02	−	8384.02i	−0.327282	−	0.327282i
$870$	−12692.8	+	5257.55i	−0.494630	+	0.204882i
$871$		−	43577.2i		−	1.69524i
$872$	7035.81	+	16986.0i	0.273237	+	0.659653i
$873$	298.642	+	123.702i	0.0115779	+	0.00479572i
$874$	1503.49	−	3629.74i	0.0581880	−	0.140478i
$875$	−13605.7	+	13605.7i	−0.525664	+	0.525664i
$876$	10294.0	−	10294.0i	0.397034	−	0.397034i
$877$	−5508.33	+	13298.3i	−0.212090	+	0.512031i	−0.993744	−	0.111681i	$-0.964376\pi$
$877$	−5508.33	+	13298.3i	−0.212090	+	0.512031i	0.781654	+	0.623713i	$0.214376\pi$
$878$	740.803	+	306.851i	0.0284748	+	0.0117947i
$879$	11312.5	+	27310.7i	0.434084	+	1.04797i
$880$		−	557.137i		−	0.0213421i
$881$	14161.8	−	5866.00i	0.541569	−	0.224325i	−0.0950925	−	0.995468i	$-0.530315\pi$
$881$	14161.8	−	5866.00i	0.541569	−	0.224325i	0.636662	+	0.771143i	$0.280315\pi$
$882$	1315.94	+	1315.94i	0.0502382	+	0.0502382i
$883$	−8385.90			−0.319602			−0.159801	−	0.987149i	$-0.551085\pi$
$883$	−8385.90			−0.319602			−0.159801	+	0.987149i	$0.551085\pi$
$884$	−1316.84	−	23521.1i	−0.0501018	−	0.894912i
$885$	9403.11			0.357155
$886$	15837.6	+	15837.6i	0.600534	+	0.600534i
$887$	8514.38	−	3526.77i	0.322305	−	0.133503i	−0.215664	−	0.976468i	$-0.569192\pi$
$887$	8514.38	−	3526.77i	0.322305	−	0.133503i	0.537969	+	0.842964i	$0.319192\pi$
$888$			35507.0i			1.34182i
$889$	−8002.26	−	19319.2i	−0.301898	−	0.728846i
$890$	−6427.77	−	2662.47i	−0.242089	−	0.100277i
$891$	−5671.01	+	13691.0i	−0.213228	+	0.514778i
$892$	−5678.97	+	5678.97i	−0.213168	+	0.213168i
$893$	11871.0	−	11871.0i	0.444847	−	0.444847i
$894$	6427.85	−	15518.2i	0.240469	−	0.580544i
$895$	−22579.2	−	9352.62i	−0.843285	−	0.349300i
$896$	5143.58	+	12417.7i	0.191780	+	0.462998i
$897$			8477.36i			0.315553i
$898$	−16438.8	+	6809.17i	−0.610879	+	0.253034i
$899$	6736.95	+	6736.95i	0.249933	+	0.249933i
$900$	2903.37			0.107532
$901$	−4075.07	+	4558.42i	−0.150677	+	0.168549i
$902$	−1722.07			−0.0635684
$903$	−22505.4	−	22505.4i	−0.829382	−	0.829382i
$904$	12427.5	−	5147.63i	0.457225	−	0.189389i
$905$		−	3141.70i		−	0.115396i
$906$	6186.70	+	14936.0i	0.226864	+	0.547699i
$907$	−6900.44	−	2858.25i	−0.252619	−	0.104638i	0.252781	−	0.967524i	$-0.418655\pi$
$907$	−6900.44	−	2858.25i	−0.252619	−	0.104638i	−0.505400	+	0.862885i	$0.668655\pi$
$908$	−8364.23	+	20193.0i	−0.305701	+	0.738028i
$909$	7581.52	−	7581.52i	0.276637	−	0.276637i
$910$	7522.45	−	7522.45i	0.274030	−	0.274030i
$911$	−11747.7	+	28361.5i	−0.427244	+	1.03146i	0.552913	+	0.833239i	$0.313516\pi$
$911$	−11747.7	+	28361.5i	−0.427244	+	1.03146i	−0.980157	+	0.198220i	$0.936484\pi$
$912$	868.311	+	359.666i	0.0315270	+	0.0130589i
$913$	1811.23	+	4372.71i	0.0656551	+	0.158505i
$914$		−	432.140i		−	0.0156389i
$915$	10211.6	−	4229.77i	0.368945	−	0.152822i
$916$	2091.30	+	2091.30i	0.0754351	+	0.0754351i
$917$	−38625.1			−1.39096
$918$	7891.92	+	16395.0i	0.283739	+	0.589451i
$919$	−24550.8			−0.881237			−0.440619	−	0.897694i	$-0.645241\pi$
$919$	−24550.8			−0.881237			−0.440619	+	0.897694i	$0.645241\pi$
$920$	3106.90	+	3106.90i	0.111339	+	0.111339i
$921$	−10309.7	+	4270.42i	−0.368856	+	0.152785i
$922$		−	26537.4i		−	0.947898i
$923$	10055.1	+	24275.1i	0.358577	+	0.865681i
$924$	8943.94	+	3704.70i	0.318435	+	0.131900i
$925$	10768.1	−	25996.4i	0.382759	−	0.924061i
$926$	12937.3	−	12937.3i	0.459119	−	0.459119i
$927$	−3170.05	+	3170.05i	−0.112317	+	0.112317i
$928$	18656.6	−	45041.1i	0.659951	−	1.59326i
$929$	−38484.2	−	15940.7i	−1.35912	−	0.562967i	−0.420306	−	0.907383i	$-0.638077\pi$
$929$	−38484.2	−	15940.7i	−1.35912	−	0.562967i	−0.938817	+	0.344415i	$0.888077\pi$
$930$	706.874	+	1706.55i	0.0249240	+	0.0601719i
$931$		−	11993.6i		−	0.422206i
$932$	−3159.93	+	1308.88i	−0.111059	+	0.0460021i
$933$	11265.2	+	11265.2i	0.395292	+	0.395292i
$934$	−3343.54			−0.117135
$935$	−14695.7	+	822.739i	−0.514011	+	0.0287770i
$936$	−10689.5			−0.373288
$937$	59.2109	+	59.2109i	0.00206439	+	0.00206439i	0.708138	−	0.706074i	$-0.249535\pi$
$937$	59.2109	+	59.2109i	0.00206439	+	0.00206439i	−0.706074	+	0.708138i	$0.749535\pi$
$938$	14432.9	−	5978.31i	0.502401	−	0.208101i
$939$			11608.6i			0.403442i
$940$	2794.31	+	6746.06i	0.0969577	+	0.234077i
$941$	45541.8	+	18864.0i	1.57770	+	0.653507i	0.988048	−	0.154147i	$-0.0492630\pi$
$941$	45541.8	+	18864.0i	1.57770	+	0.653507i	0.589657	+	0.807654i	$0.299263\pi$
$942$	−1000.90	+	2416.39i	−0.0346190	+	0.0835778i
$943$	−669.130	+	669.130i	−0.0231070	+	0.0231070i
$944$	−582.951	+	582.951i	−0.0200990	+	0.0200990i
$945$	5504.15	−	13288.2i	0.189471	−	0.457423i
$946$	25078.4	+	10387.8i	0.861913	+	0.357016i
$947$	3614.55	+	8726.29i	0.124031	+	0.299436i	0.973683	−	0.227907i	$-0.0731882\pi$
$947$	3614.55	+	8726.29i	0.124031	+	0.299436i	−0.849652	+	0.527343i	$0.823188\pi$
$948$			8699.57i			0.298047i
$949$	39242.3	−	16254.7i	1.34232	−	0.556006i
$950$	7558.50	+	7558.50i	0.258137	+	0.258137i
$951$	−17347.7			−0.591521
$952$	19566.5	−	9418.57i	0.666129	−	0.320649i
$953$	41693.4			1.41719			0.708595	−	0.705616i	$-0.249329\pi$
$953$	41693.4			1.41719			0.708595	+	0.705616i	$0.249329\pi$
$954$	762.967	+	762.967i	0.0258930	+	0.0258930i
$955$	28436.8	−	11778.9i	0.963555	−	0.399117i
$956$			1393.18i			0.0471324i
$957$	−13959.3	−	33700.6i	−0.471514	−	1.13834i
$958$	6766.12	+	2802.62i	0.228187	+	0.0945183i
$959$	3344.23	−	8073.68i	0.112608	−	0.271859i
$960$	6229.30	−	6229.30i	0.209427	−	0.209427i
$961$	−20159.6	+	20159.6i	−0.676702	+	0.676702i
$962$	−15418.5	+	37223.6i	−0.516750	+	1.24755i
$963$	−931.246	−	385.735i	−0.0311620	−	0.0129077i
$964$	−12638.3	−	30511.6i	−0.422254	−	1.01941i
$965$		−	19945.5i		−	0.665355i
$966$	−2807.73	+	1163.00i	−0.0935168	+	0.0387359i
$967$	−22896.1	−	22896.1i	−0.761416	−	0.761416i	0.215162	−	0.976578i	$-0.430972\pi$
$967$	−22896.1	−	22896.1i	−0.761416	−	0.761416i	−0.976578	+	0.215162i	$0.930972\pi$
$968$	8487.28			0.281809
$969$	8204.71	−	23434.7i	0.272005	−	0.776915i
$970$	−517.626			−0.0171340
$971$	3819.26	+	3819.26i	0.126226	+	0.126226i	0.767398	−	0.641171i	$-0.221551\pi$
$971$	3819.26	+	3819.26i	0.126226	+	0.126226i	−0.641171	+	0.767398i	$0.721551\pi$
$972$	−9286.01	+	3846.39i	−0.306429	+	0.126927i
$973$			36828.3i			1.21342i
$974$	−11756.6	−	28382.9i	−0.386762	−	0.933725i
$975$	−21309.1	−	8826.53i	−0.699937	−	0.289923i
$976$	−370.845	+	895.300i	−0.0121624	+	0.0293626i
$977$	17738.6	−	17738.6i	0.580869	−	0.580869i	−0.354273	−	0.935142i	$-0.615272\pi$
$977$	17738.6	−	17738.6i	0.580869	−	0.580869i	0.935142	+	0.354273i	$0.115272\pi$
$978$	−3636.21	+	3636.21i	−0.118889	+	0.118889i
$979$	7069.09	−	17066.3i	0.230775	−	0.557141i
$980$	4819.44	+	1996.28i	0.157093	+	0.0650701i
$981$	2285.52	+	5517.73i	0.0743843	+	0.179580i
$982$			23421.4i			0.761108i
$983$	−55092.4	+	22820.0i	−1.78756	+	0.740433i	−0.796900	+	0.604112i	$0.793528\pi$
$983$	−55092.4	+	22820.0i	−1.78756	+	0.740433i	−0.990665	+	0.136322i	$0.956472\pi$
$984$	2297.29	+	2297.29i	0.0744258	+	0.0744258i
$985$	13116.7			0.424296
$986$	−30034.4	−	10515.3i	−0.970071	−	0.339631i
$987$	−12986.2			−0.418799
$988$	18944.8	+	18944.8i	0.610034	+	0.610034i
$989$	13780.8	−	5708.20i	0.443078	−	0.183529i
$990$			2597.40i			0.0833846i
$991$	−15331.8	−	37014.1i	−0.491452	−	1.18647i	−0.953981	−	0.299867i	$-0.903058\pi$
$991$	−15331.8	−	37014.1i	−0.491452	−	1.18647i	0.462529	−	0.886604i	$-0.346942\pi$
$992$	−6055.75	−	2508.37i	−0.193821	−	0.0802832i
$993$	10604.8	−	25602.2i	0.338905	−	0.818189i
$994$	−6660.54	+	6660.54i	−0.212535	+	0.212535i
$995$	−14862.9	+	14862.9i	−0.473553	+	0.473553i
$996$	1328.94	−	3208.34i	0.0422781	−	0.102068i
$997$	−9994.87	−	4140.01i	−0.317493	−	0.131510i	0.218245	−	0.975894i	$-0.429967\pi$
$997$	−9994.87	−	4140.01i	−0.317493	−	0.131510i	−0.535738	+	0.844384i	$0.679967\pi$
$998$	−5056.58	−	12207.7i	−0.160384	−	0.387201i
$999$			54472.8i			1.72517i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.4.d.a.2.2	✓	12
3.2	odd	2		153.4.l.a.19.2		12
17.3	odd	16		289.4.a.g.1.6		12
17.5	odd	16		289.4.b.e.288.8		12
17.9	even	8	inner	17.4.d.a.9.2	yes	12
17.12	odd	16		289.4.b.e.288.7		12
17.14	odd	16		289.4.a.g.1.5		12
51.26	odd	8		153.4.l.a.145.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.d.a.2.2	✓	12	1.1	even	1	trivial
17.4.d.a.9.2	yes	12	17.9	even	8	inner
153.4.l.a.19.2		12	3.2	odd	2
153.4.l.a.145.2		12	51.26	odd	8
289.4.a.g.1.5		12	17.14	odd	16
289.4.a.g.1.6		12	17.3	odd	16
289.4.b.e.288.7		12	17.12	odd	16
289.4.b.e.288.8		12	17.5	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)

\(f(q)\)	\(=\)	\(q+(-1.20595 - 1.20595i) q^{2} +(4.10553 - 1.70057i) q^{3} -5.09138i q^{4} +(2.60601 + 6.29147i) q^{5} +(-7.00185 - 2.90026i) q^{6} +(-5.31013 + 12.8198i) q^{7} +(-15.7875 + 15.7875i) q^{8} +(-5.12843 + 5.12843i) q^{9} +O(q^{10})\)	\(q+(-1.20595 - 1.20595i) q^{2} +(4.10553 - 1.70057i) q^{3} -5.09138i q^{4} +(2.60601 + 6.29147i) q^{5} +(-7.00185 - 2.90026i) q^{6} +(-5.31013 + 12.8198i) q^{7} +(-15.7875 + 15.7875i) q^{8} +(-5.12843 + 5.12843i) q^{9} +(4.44447 - 10.7299i) q^{10} +(28.4888 + 11.8005i) q^{11} +(-8.65823 - 20.9028i) q^{12} -66.0130i q^{13} +(21.8637 - 9.05625i) q^{14} +(21.3981 + 21.3981i) q^{15} -2.65318 q^{16} +(3.91802 + 69.9832i) q^{17} +12.3692 q^{18} +(-56.3670 - 56.3670i) q^{19} +(32.0322 - 13.2682i) q^{20} +61.6622i q^{21} +(-20.1253 - 48.5868i) q^{22} +(-26.6989 - 11.0590i) q^{23} +(-37.9684 + 91.6639i) q^{24} +(55.5971 - 55.5971i) q^{25} +(-79.6082 + 79.6082i) q^{26} +(-58.2490 + 140.625i) q^{27} +(65.2704 + 27.0359i) q^{28} +(-101.871 - 245.938i) q^{29} -51.6100i q^{30} +(-33.0662 + 13.6965i) q^{31} +(129.500 + 129.500i) q^{32} +137.029 q^{33} +(79.6712 - 89.1210i) q^{34} -94.4935 q^{35} +(26.1108 + 26.1108i) q^{36} +(330.633 - 136.953i) q^{37} +135.951i q^{38} +(-112.259 - 271.018i) q^{39} +(-140.469 - 58.1842i) q^{40} +(12.5311 - 30.2527i) q^{41} +(74.3614 - 74.3614i) q^{42} +(-364.978 + 364.978i) q^{43} +(60.0806 - 145.047i) q^{44} +(-45.6301 - 18.9006i) q^{45} +(18.8608 + 45.5340i) q^{46} +210.602i q^{47} +(-10.8927 + 4.51190i) q^{48} +(106.388 + 106.388i) q^{49} -134.094 q^{50} +(135.097 + 280.655i) q^{51} -336.097 q^{52} +(61.6826 + 61.6826i) q^{53} +(239.832 - 99.3418i) q^{54} +209.989i q^{55} +(-118.559 - 286.226i) q^{56} +(-327.272 - 135.561i) q^{57} +(-173.737 + 419.439i) q^{58} +(219.718 - 219.718i) q^{59} +(108.946 - 108.946i) q^{60} +(139.774 - 337.444i) q^{61} +(56.3933 + 23.3589i) q^{62} +(-38.5127 - 92.9779i) q^{63} -291.115i q^{64} +(415.318 - 172.030i) q^{65} +(-165.250 - 165.250i) q^{66} +660.131 q^{67} +(356.311 - 19.9481i) q^{68} -128.420 q^{69} +(113.954 + 113.954i) q^{70} +(-367.732 + 152.319i) q^{71} -161.930i q^{72} +(246.235 + 594.463i) q^{73} +(-563.884 - 233.568i) q^{74} +(133.709 - 322.802i) q^{75} +(-286.986 + 286.986i) q^{76} +(-302.558 + 302.558i) q^{77} +(-191.455 + 462.213i) q^{78} +(-355.241 - 147.146i) q^{79} +(-6.91421 - 16.6924i) q^{80} +480.576i q^{81} +(-51.5949 + 21.3713i) q^{82} +(108.533 + 108.533i) q^{83} +313.946 q^{84} +(-430.087 + 207.027i) q^{85} +880.289 q^{86} +(-836.467 - 836.467i) q^{87} +(-636.068 + 263.468i) q^{88} -599.053i q^{89} +(32.2344 + 77.8206i) q^{90} +(846.272 + 350.537i) q^{91} +(-56.3057 + 135.934i) q^{92} +(-112.462 + 112.462i) q^{93} +(253.975 - 253.975i) q^{94} +(207.738 - 501.524i) q^{95} +(751.888 + 311.442i) q^{96} +(-17.0560 - 41.1767i) q^{97} -256.598i q^{98} +(-206.621 + 85.5851i) 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

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