LMFDB - Embedded newform 105.4.m.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(13,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("105.13");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.1
Character	$\chi$	$=$	105.13
Dual form			105.4.m.a.97.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.58711 + 3.58711i) q^{2} +(-2.12132 + 2.12132i) q^{3} -17.7347i q^{4} +(10.0305 - 4.93863i) q^{5} -15.2188i q^{6} +(2.02215 + 18.4095i) q^{7} +(34.9193 + 34.9193i) q^{8} -9.00000i q^{9} +O(q^{10})$	\(q+(-3.58711 + 3.58711i) q^{2} +(-2.12132 + 2.12132i) q^{3} -17.7347i q^{4} +(10.0305 - 4.93863i) q^{5} -15.2188i q^{6} +(2.02215 + 18.4095i) q^{7} +(34.9193 + 34.9193i) q^{8} -9.00000i q^{9} +(-18.2649 + 53.6957i) q^{10} +70.3785 q^{11} +(37.6209 + 37.6209i) q^{12} +(-20.4623 + 20.4623i) q^{13} +(-73.2906 - 58.7833i) q^{14} +(-10.8014 + 31.7542i) q^{15} -108.641 q^{16} +(0.412364 + 0.412364i) q^{17} +(32.2840 + 32.2840i) q^{18} -88.5161 q^{19} +(-87.5850 - 177.887i) q^{20} +(-43.3422 - 34.7629i) q^{21} +(-252.455 + 252.455i) q^{22} +(37.1006 + 37.1006i) q^{23} -148.150 q^{24} +(76.2199 - 99.0734i) q^{25} -146.801i q^{26} +(19.0919 + 19.0919i) q^{27} +(326.487 - 35.8622i) q^{28} +116.827i q^{29} +(-75.1600 - 152.651i) q^{30} +227.473i q^{31} +(110.353 - 110.353i) q^{32} +(-149.295 + 149.295i) q^{33} -2.95839 q^{34} +(111.201 + 174.669i) q^{35} -159.612 q^{36} +(83.7560 - 83.7560i) q^{37} +(317.517 - 317.517i) q^{38} -86.8142i q^{39} +(522.710 + 177.803i) q^{40} +438.988i q^{41} +(280.171 - 30.7748i) q^{42} +(199.545 + 199.545i) q^{43} -1248.14i q^{44} +(-44.4477 - 90.2741i) q^{45} -266.167 q^{46} +(-72.8580 - 72.8580i) q^{47} +(230.463 - 230.463i) q^{48} +(-334.822 + 74.4538i) q^{49} +(81.9779 + 628.796i) q^{50} -1.74951 q^{51} +(362.892 + 362.892i) q^{52} +(-141.512 - 141.512i) q^{53} -136.969 q^{54} +(705.928 - 347.573i) q^{55} +(-572.236 + 713.460i) q^{56} +(187.771 - 187.771i) q^{57} +(-419.070 - 419.070i) q^{58} +380.867 q^{59} +(563.151 + 191.559i) q^{60} -349.378i q^{61} +(-815.970 - 815.970i) q^{62} +(165.686 - 18.1994i) q^{63} -77.4326i q^{64} +(-104.190 + 306.302i) q^{65} -1071.08i q^{66} +(8.87381 - 8.87381i) q^{67} +(7.31313 - 7.31313i) q^{68} -157.404 q^{69} +(-1025.45 - 227.667i) q^{70} +860.765 q^{71} +(314.274 - 314.274i) q^{72} +(-817.495 + 817.495i) q^{73} +600.883i q^{74} +(48.4795 + 371.853i) q^{75} +1569.80i q^{76} +(142.316 + 1295.63i) q^{77} +(311.412 + 311.412i) q^{78} -698.586i q^{79} +(-1089.72 + 536.539i) q^{80} -81.0000 q^{81} +(-1574.70 - 1574.70i) q^{82} +(191.562 - 191.562i) q^{83} +(-616.508 + 768.659i) q^{84} +(6.17271 + 2.09968i) q^{85} -1431.58 q^{86} +(-247.827 - 247.827i) q^{87} +(2457.57 + 2457.57i) q^{88} +412.560 q^{89} +(483.261 + 164.384i) q^{90} +(-418.079 - 335.323i) q^{91} +(657.967 - 657.967i) q^{92} +(-482.543 - 482.543i) q^{93} +522.699 q^{94} +(-887.857 + 437.148i) q^{95} +468.189i q^{96} +(267.427 + 267.427i) q^{97} +(933.968 - 1468.12i) q^{98} -633.406i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{7} - 168 q^{8}+O(q^{10}) $ 48 * q + 4 * q^7 - 168 * q^8	$ 48 q + 4 q^{7} - 168 q^{8} + 112 q^{11} + 168 q^{15} - 544 q^{16} - 96 q^{21} - 192 q^{22} + 400 q^{23} + 520 q^{25} + 1052 q^{28} - 48 q^{30} - 1344 q^{32} + 392 q^{35} - 1728 q^{36} - 456 q^{37} + 1068 q^{42} + 192 q^{43} - 208 q^{46} + 3528 q^{50} + 672 q^{51} - 1728 q^{53} - 48 q^{56} + 696 q^{57} + 3016 q^{58} + 840 q^{60} - 36 q^{63} - 4720 q^{65} - 4784 q^{67} + 2220 q^{70} - 3088 q^{71} - 1512 q^{72} + 2352 q^{77} + 1416 q^{78} - 3888 q^{81} - 472 q^{85} + 10832 q^{86} + 2128 q^{88} - 5664 q^{91} + 10600 q^{92} - 1368 q^{93} - 6912 q^{95} - 3888 q^{98}+O(q^{100}) $ 48 * q + 4 * q^7 - 168 * q^8 + 112 * q^11 + 168 * q^15 - 544 * q^16 - 96 * q^21 - 192 * q^22 + 400 * q^23 + 520 * q^25 + 1052 * q^28 - 48 * q^30 - 1344 * q^32 + 392 * q^35 - 1728 * q^36 - 456 * q^37 + 1068 * q^42 + 192 * q^43 - 208 * q^46 + 3528 * q^50 + 672 * q^51 - 1728 * q^53 - 48 * q^56 + 696 * q^57 + 3016 * q^58 + 840 * q^60 - 36 * q^63 - 4720 * q^65 - 4784 * q^67 + 2220 * q^70 - 3088 * q^71 - 1512 * q^72 + 2352 * q^77 + 1416 * q^78 - 3888 * q^81 - 472 * q^85 + 10832 * q^86 + 2128 * q^88 - 5664 * q^91 + 10600 * q^92 - 1368 * q^93 - 6912 * q^95 - 3888 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−3.58711	+	3.58711i	−1.26823	+	1.26823i	−0.321234	+	0.947000i	$0.604098\pi$
$2$	−3.58711	+	3.58711i	−1.26823	+	1.26823i	−0.947000	+	0.321234i	$0.895902\pi$
$3$	−2.12132	+	2.12132i	−0.408248	+	0.408248i
$3$	−2.12132	+	2.12132i	−0.408248	+	0.408248i
$4$		−	17.7347i		−	2.21683i
$5$	10.0305	−	4.93863i	0.897151	−	0.441724i
$5$	10.0305	−	4.93863i	0.897151	−	0.441724i
$6$		−	15.2188i		−	1.03551i
$7$	2.02215	+	18.4095i	0.109186	+	0.994021i
$7$	2.02215	+	18.4095i	0.109186	+	0.994021i
$8$	34.9193	+	34.9193i	1.54323	+	1.54323i
$9$		−	9.00000i		−	0.333333i
$10$	−18.2649	+	53.6957i	−0.577587	+	1.69801i
$11$	70.3785			1.92908			0.964541	−	0.263932i	$-0.0850194\pi$
$11$	70.3785			1.92908			0.964541	+	0.263932i	$0.0850194\pi$
$12$	37.6209	+	37.6209i	0.905019	+	0.905019i
$13$	−20.4623	+	20.4623i	−0.436555	+	0.436555i	−0.890851	−	0.454296i	$-0.849891\pi$
$13$	−20.4623	+	20.4623i	−0.436555	+	0.436555i	0.454296	+	0.890851i	$0.349891\pi$
$14$	−73.2906	−	58.7833i	−1.39912	−	1.12218i
$15$	−10.8014	+	31.7542i	−0.185927	+	0.546594i
$16$	−108.641			−1.69752
$17$	0.412364	+	0.412364i	0.00588311	+	0.00588311i	0.710042	−	0.704159i	$-0.248676\pi$
$17$	0.412364	+	0.412364i	0.00588311	+	0.00588311i	−0.704159	+	0.710042i	$0.748676\pi$
$18$	32.2840	+	32.2840i	0.422745	+	0.422745i
$19$	−88.5161			−1.06879			−0.534395	−	0.845235i	$-0.679460\pi$
$19$	−88.5161			−1.06879			−0.534395	+	0.845235i	$0.679460\pi$
$20$	−87.5850	−	177.887i	−0.979230	−	1.98883i
$21$	−43.3422	−	34.7629i	−0.450383	−	0.361232i
$22$	−252.455	+	252.455i	−2.44653	+	2.44653i
$23$	37.1006	+	37.1006i	0.336348	+	0.336348i	0.854991	−	0.518643i	$-0.173563\pi$
$23$	37.1006	+	37.1006i	0.336348	+	0.336348i	−0.518643	+	0.854991i	$0.673563\pi$
$24$	−148.150			−1.26004
$25$	76.2199	−	99.0734i	0.609759	−	0.792587i
$26$		−	146.801i		−	1.10731i
$27$	19.0919	+	19.0919i	0.136083	+	0.136083i
$28$	326.487	−	35.8622i	2.20358	−	0.242047i
$29$			116.827i			0.748074i	0.927414	+	0.374037i	$0.122027\pi$
$29$			116.827i			0.748074i	−0.927414	+	0.374037i	$0.877973\pi$
$30$	−75.1600	−	152.651i	−0.457409	−	0.929007i
$31$			227.473i			1.31791i	0.752181	+	0.658957i	$0.229002\pi$
$31$			227.473i			1.31791i	−0.752181	+	0.658957i	$0.770998\pi$
$32$	110.353	−	110.353i	0.609621	−	0.609621i
$33$	−149.295	+	149.295i	−0.787545	+	0.787545i
$34$	−2.95839			−0.0149223
$35$	111.201	+	174.669i	0.537040	+	0.843557i
$36$	−159.612			−0.738945
$37$	83.7560	−	83.7560i	0.372146	−	0.372146i	−0.496112	−	0.868258i	$-0.665240\pi$
$37$	83.7560	−	83.7560i	0.372146	−	0.372146i	0.868258	+	0.496112i	$0.165240\pi$
$38$	317.517	−	317.517i	1.35547	−	1.35547i
$39$		−	86.8142i		−	0.356446i
$40$	522.710	+	177.803i	2.06619	+	0.702828i
$41$			438.988i			1.67215i	0.548612	+	0.836077i	$0.315157\pi$
$41$			438.988i			1.67215i	−0.548612	+	0.836077i	$0.684843\pi$
$42$	280.171	−	30.7748i	1.02932	−	0.113063i
$43$	199.545	+	199.545i	0.707683	+	0.707683i	0.966047	−	0.258365i	$-0.0831836\pi$
$43$	199.545	+	199.545i	0.707683	+	0.707683i	−0.258365	+	0.966047i	$0.583184\pi$
$44$		−	1248.14i		−	4.27646i
$45$	−44.4477	−	90.2741i	−0.147241	−	0.299050i
$46$	−266.167			−0.853136
$47$	−72.8580	−	72.8580i	−0.226116	−	0.226116i	0.584952	−	0.811068i	$-0.301113\pi$
$47$	−72.8580	−	72.8580i	−0.226116	−	0.226116i	−0.811068	+	0.584952i	$0.801113\pi$
$48$	230.463	−	230.463i	0.693009	−	0.693009i
$49$	−334.822	+	74.4538i	−0.976157	+	0.217067i
$50$	81.9779	+	628.796i	0.231868	+	1.77850i
$51$	−1.74951			−0.00480354
$52$	362.892	+	362.892i	0.967771	+	0.967771i
$53$	−141.512	−	141.512i	−0.366757	−	0.366757i	0.499536	−	0.866293i	$-0.333504\pi$
$53$	−141.512	−	141.512i	−0.366757	−	0.366757i	−0.866293	+	0.499536i	$0.833504\pi$
$54$	−136.969			−0.345170
$55$	705.928	−	347.573i	1.73068	−	0.852123i
$56$	−572.236	+	713.460i	−1.36550	+	1.70250i
$57$	187.771	−	187.771i	0.436331	−	0.436331i
$58$	−419.070	−	419.070i	−0.948733	−	0.948733i
$59$	380.867			0.840417			0.420208	−	0.907428i	$-0.361957\pi$
$59$	380.867			0.840417			0.420208	+	0.907428i	$0.361957\pi$
$60$	563.151	+	191.559i	1.21171	+	0.412169i
$61$		−	349.378i		−	0.733332i	−0.930353	−	0.366666i	$-0.880499\pi$
$61$		−	349.378i		−	0.733332i	0.930353	−	0.366666i	$-0.119501\pi$
$62$	−815.970	−	815.970i	−1.67142	−	1.67142i
$63$	165.686	−	18.1994i	0.331340	−	0.0363954i
$64$		−	77.4326i		−	0.151236i
$65$	−104.190	+	306.302i	−0.198819	+	0.584493i
$66$		−	1071.08i		−	1.99758i
$67$	8.87381	−	8.87381i	0.0161807	−	0.0161807i	−0.698970	−	0.715151i	$-0.746358\pi$
$67$	8.87381	−	8.87381i	0.0161807	−	0.0161807i	0.715151	+	0.698970i	$0.246358\pi$
$68$	7.31313	−	7.31313i	0.0130419	−	0.0130419i
$69$	−157.404			−0.274627
$70$	−1025.45	−	227.667i	−1.75092	−	0.388735i
$71$	860.765			1.43879			0.719395	−	0.694602i	$-0.244419\pi$
$71$	860.765			1.43879			0.719395	+	0.694602i	$0.244419\pi$
$72$	314.274	−	314.274i	0.514410	−	0.514410i
$73$	−817.495	+	817.495i	−1.31069	+	1.31069i	−0.389789	+	0.920904i	$0.627452\pi$
$73$	−817.495	+	817.495i	−1.31069	+	1.31069i	−0.920904	+	0.389789i	$0.872548\pi$
$74$			600.883i			0.943936i
$75$	48.4795	+	371.853i	0.0746391	+	0.572505i
$76$			1569.80i			2.36933i
$77$	142.316	+	1295.63i	0.210629	+	1.91755i
$78$	311.412	+	311.412i	0.452057	+	0.452057i
$79$		−	698.586i		−	0.994899i	−0.867493	−	0.497449i	$-0.834270\pi$
$79$		−	698.586i		−	0.994899i	0.867493	−	0.497449i	$-0.165730\pi$
$80$	−1089.72	+	536.539i	−1.52293	+	0.749836i
$81$	−81.0000			−0.111111
$82$	−1574.70	−	1574.70i	−2.12068	−	2.12068i
$83$	191.562	−	191.562i	0.253333	−	0.253333i	−0.569003	−	0.822336i	$-0.692671\pi$
$83$	191.562	−	191.562i	0.253333	−	0.253333i	0.822336	+	0.569003i	$0.192671\pi$
$84$	−616.508	+	768.659i	−0.800792	+	0.998423i
$85$	6.17271	+	2.09968i	0.00787675	+	0.00267932i
$86$	−1431.58			−1.79501
$87$	−247.827	−	247.827i	−0.305400	−	0.305400i
$88$	2457.57	+	2457.57i	2.97702	+	2.97702i
$89$	412.560			0.491363			0.245682	−	0.969351i	$-0.420988\pi$
$89$	412.560			0.491363			0.245682	+	0.969351i	$0.420988\pi$
$90$	483.261	+	164.384i	0.566002	+	0.192529i
$91$	−418.079	−	335.323i	−0.481611	−	0.386280i
$92$	657.967	−	657.967i	0.745628	−	0.745628i
$93$	−482.543	−	482.543i	−0.538036	−	0.538036i
$94$	522.699			0.573535
$95$	−887.857	+	437.148i	−0.958865	+	0.472110i
$96$			468.189i			0.497753i
$97$	267.427	+	267.427i	0.279929	+	0.279929i	0.833081	−	0.553152i	$-0.186575\pi$
$97$	267.427	+	267.427i	0.279929	+	0.279929i	−0.553152	+	0.833081i	$0.686575\pi$
$98$	933.968	−	1468.12i	0.962704	−	1.51329i
$99$		−	633.406i		−	0.643028i
$100$	−1757.03	−	1351.73i	−1.75703	−	1.35173i
$101$		−	1085.86i		−	1.06977i	−0.844925	−	0.534885i	$-0.820355\pi$
$101$		−	1085.86i		−	1.06977i	0.844925	−	0.534885i	$-0.179645\pi$
$102$	6.27568	−	6.27568i	0.00609201	−	0.00609201i
$103$	631.714	−	631.714i	0.604317	−	0.604317i	−0.337138	−	0.941455i	$-0.609459\pi$
$103$	631.714	−	631.714i	0.604317	−	0.604317i	0.941455	+	0.337138i	$0.109459\pi$
$104$	−1429.06			−1.34741
$105$	−606.422	−	134.636i	−0.563626	−	0.125135i
$106$	1015.23			0.930267
$107$	508.687	−	508.687i	0.459595	−	0.459595i	−0.438928	−	0.898522i	$-0.644642\pi$
$107$	508.687	−	508.687i	0.459595	−	0.459595i	0.898522	+	0.438928i	$0.144642\pi$
$108$	338.588	−	338.588i	0.301673	−	0.301673i
$109$			662.443i			0.582115i	0.956706	+	0.291058i	$0.0940071\pi$
$109$			662.443i			0.582115i	−0.956706	+	0.291058i	$0.905993\pi$
$110$	−1285.46	+	3779.02i	−1.11421	+	3.27560i
$111$			355.347i			0.303856i
$112$	−219.689	−	2000.03i	−0.185345	−	1.68737i
$113$	−598.581	−	598.581i	−0.498316	−	0.498316i	0.412597	−	0.910914i	$-0.364622\pi$
$113$	−598.581	−	598.581i	−0.498316	−	0.498316i	−0.910914	+	0.412597i	$0.864622\pi$
$114$			1347.11i			1.10674i
$115$	555.362	+	188.910i	0.450328	+	0.153182i
$116$	2071.88			1.65836
$117$	184.161	+	184.161i	0.145518	+	0.145518i
$118$	−1366.21	+	1366.21i	−1.06585	+	1.06585i
$119$	−6.75756	+	8.42529i	−0.00520558	+	0.00649029i
$120$	−1486.01	+	731.658i	−1.13045	+	0.556591i
$121$	3622.13			2.72136
$122$	1253.26	+	1253.26i	0.930037	+	0.930037i
$123$	−931.233	−	931.233i	−0.682654	−	0.682654i
$124$	4034.16			2.92160
$125$	275.233	−	1370.17i	0.196941	−	0.980415i
$126$	−529.049	+	659.616i	−0.374059	+	0.466375i
$127$	−96.9750	+	96.9750i	−0.0677570	+	0.0677570i	−0.740173	−	0.672416i	$-0.765257\pi$
$127$	−96.9750	+	96.9750i	−0.0677570	+	0.0677570i	0.672416	+	0.740173i	$0.265257\pi$
$128$	1160.58	+	1160.58i	0.801423	+	0.801423i
$129$	−846.599			−0.577821
$130$	−724.995	−	1472.48i	−0.489125	−	0.993423i
$131$		−	1504.75i		−	1.00359i	−0.864986	−	0.501796i	$-0.832673\pi$
$131$		−	1504.75i		−	1.00359i	0.864986	−	0.501796i	$-0.167327\pi$
$132$	2647.70	+	2647.70i	1.74586	+	1.74586i
$133$	−178.993	−	1629.54i	−0.116697	−	1.06240i
$134$			63.6626i			0.0410419i
$135$	285.788	+	97.2125i	0.182198	+	0.0619757i
$136$			28.7989i			0.0181580i
$137$	−255.434	+	255.434i	−0.159294	+	0.159294i	−0.782254	−	0.622960i	$-0.785930\pi$
$137$	−255.434	+	255.434i	−0.159294	+	0.159294i	0.622960	+	0.782254i	$0.285930\pi$
$138$	564.626	−	564.626i	0.348291	−	0.348291i
$139$	−1477.98			−0.901878			−0.450939	−	0.892555i	$-0.648911\pi$
$139$	−1477.98			−0.901878			−0.450939	+	0.892555i	$0.648911\pi$
$140$	3097.70	−	1972.11i	1.87003	−	1.19053i
$141$	309.110			0.184623
$142$	−3087.66	+	3087.66i	−1.82472	+	1.82472i
$143$	−1440.11	+	1440.11i	−0.842152	+	0.842152i
$144$			977.771i			0.565840i
$145$	576.963	+	1171.82i	0.330443	+	0.671135i
$146$		−	5864.89i		−	3.32453i
$147$	552.324	−	868.205i	0.309897	−	0.487131i
$148$	−1485.38	−	1485.38i	−0.824986	−	0.824986i
$149$			1450.33i			0.797420i	0.917077	+	0.398710i	$0.130542\pi$
$149$			1450.33i			0.797420i	−0.917077	+	0.398710i	$0.869458\pi$
$150$	−1507.78	−	1159.98i	−0.820730	−	0.631411i
$151$	−1079.66			−0.581863			−0.290932	−	0.956744i	$-0.593965\pi$
$151$	−1079.66			−0.581863			−0.290932	+	0.956744i	$0.593965\pi$
$152$	−3090.92	−	3090.92i	−1.64939	−	1.64939i
$153$	3.71127	−	3.71127i	0.00196104	−	0.00196104i
$154$	−5158.08	−	4137.08i	−2.69903	−	2.16477i
$155$	1123.40	+	2281.66i	0.582155	+	1.18237i
$156$	−1539.62			−0.790182
$157$	−2496.53	−	2496.53i	−1.26908	−	1.26908i	−0.946567	−	0.322509i	$-0.895474\pi$
$157$	−2496.53	−	2496.53i	−1.26908	−	1.26908i	−0.322509	−	0.946567i	$-0.604526\pi$
$158$	2505.90	+	2505.90i	1.26176	+	1.26176i
$159$	600.383			0.299456
$160$	561.898	−	1651.88i	0.277637	−	0.816206i
$161$	−607.981	+	758.027i	−0.297613	+	0.371062i
$162$	290.556	−	290.556i	0.140915	−	0.140915i
$163$	−1372.53	−	1372.53i	−0.659538	−	0.659538i	0.295732	−	0.955271i	$-0.404436\pi$
$163$	−1372.53	−	1372.53i	−0.659538	−	0.659538i	−0.955271	+	0.295732i	$0.904436\pi$
$164$	7785.30			3.70689
$165$	−760.185	+	2234.81i	−0.358669	+	1.05442i
$166$			1374.31i			0.642571i
$167$	1083.57	+	1083.57i	0.502090	+	0.502090i	0.912087	−	0.409997i	$-0.134470\pi$
$167$	1083.57	+	1083.57i	0.502090	+	0.502090i	−0.409997	+	0.912087i	$0.634470\pi$
$168$	−299.582	−	2727.37i	−0.137579	−	1.25251i
$169$			1359.59i			0.618839i
$170$	−29.6739	+	14.6104i	−0.0133876	+	0.00659155i
$171$			796.645i			0.356263i
$172$	3538.87	−	3538.87i	1.56882	−	1.56882i
$173$	−1548.22	+	1548.22i	−0.680401	+	0.680401i	−0.960090	−	0.279690i	$-0.909768\pi$
$173$	−1548.22	+	1548.22i	−0.680401	+	0.680401i	0.279690	+	0.960090i	$0.409768\pi$
$174$	1777.96			0.774637
$175$	1978.02	+	1202.83i	0.854425	+	0.519574i
$176$	−7646.00			−3.27465
$177$	−807.940	+	807.940i	−0.343099	+	0.343099i
$178$	−1479.90	+	1479.90i	−0.623163	+	0.623163i
$179$		−	1834.01i		−	0.765812i	−0.923787	−	0.382906i	$-0.874923\pi$
$179$		−	1834.01i		−	0.765812i	0.923787	−	0.382906i	$-0.125077\pi$
$180$	−1600.98	+	788.265i	−0.662945	+	0.326410i
$181$			400.922i			0.164643i	0.996606	+	0.0823213i	$0.0262334\pi$
$181$			400.922i			0.164643i	−0.996606	+	0.0823213i	$0.973767\pi$
$182$	2702.54	−	296.854i	1.10069	−	0.120903i
$183$	741.143	+	741.143i	0.299382	+	0.299382i
$184$			2591.05i			1.03812i
$185$	426.470	−	1253.75i	0.169485	−	0.498257i
$186$	3461.87			1.36471
$187$	29.0215	+	29.0215i	0.0113490	+	0.0113490i
$188$	−1292.11	+	1292.11i	−0.501261	+	0.501261i
$189$	−312.866	+	390.079i	−0.120411	+	0.150128i
$190$	1616.74	−	4752.94i	0.617319	−	1.81481i
$191$	−3561.35			−1.34916			−0.674582	−	0.738200i	$-0.735676\pi$
$191$	−3561.35			−1.34916			−0.674582	+	0.738200i	$0.735676\pi$
$192$	164.259	+	164.259i	0.0617417	+	0.0617417i
$193$	−173.296	−	173.296i	−0.0646328	−	0.0646328i	0.674052	−	0.738684i	$-0.264553\pi$
$193$	−173.296	−	173.296i	−0.0646328	−	0.0646328i	−0.738684	+	0.674052i	$0.764553\pi$
$194$	−1918.58			−0.710030
$195$	−428.743	−	870.785i	−0.157451	−	0.319786i
$196$	1320.41	+	5937.95i	0.481201	+	2.16398i
$197$	2984.41	−	2984.41i	1.07934	−	1.07934i	0.0827723	−	0.996568i	$-0.473623\pi$
$197$	2984.41	−	2984.41i	1.07934	−	1.07934i	0.996568	−	0.0827723i	$-0.0263774\pi$
$198$	2272.10	+	2272.10i	0.815509	+	0.815509i
$199$	3126.20			1.11362			0.556810	−	0.830640i	$-0.312025\pi$
$199$	3126.20			1.11362			0.556810	+	0.830640i	$0.312025\pi$
$200$	6121.12	−	798.028i	2.16414	−	0.282145i
$201$			37.6484i			0.0132115i
$202$	3895.09	+	3895.09i	1.35672	+	1.35672i
$203$	−2150.72	+	236.241i	−0.743602	+	0.0816793i
$204$			31.0270i			0.0106487i
$205$	2168.00	+	4403.24i	0.738632	+	1.50017i
$206$			4532.05i			1.53283i
$207$	333.905	−	333.905i	0.112116	−	0.112116i
$208$	2223.05	−	2223.05i	0.741061	−	0.741061i
$209$	−6229.63			−2.06178
$210$	2658.26	−	1692.35i	0.873510	−	0.556109i
$211$	2785.72			0.908895			0.454448	−	0.890774i	$-0.349837\pi$
$211$	2785.72			0.908895			0.454448	+	0.890774i	$0.349837\pi$
$212$	−2509.66	+	2509.66i	−0.813039	+	0.813039i
$213$	−1825.96	+	1825.96i	−0.587383	+	0.587383i
$214$			3649.43i			1.16575i
$215$	2987.01	+	1016.05i	0.947499	+	0.322297i
$216$			1333.35i			0.420014i
$217$	−4187.67	+	459.985i	−1.31003	+	0.143898i
$218$	−2376.25	−	2376.25i	−0.738258	−	0.738258i
$219$		−	3468.34i		−	1.07018i
$220$	−6164.10	−	12519.4i	−1.88902	−	3.83663i
$221$	−16.8758			−0.00513661
$222$	−1274.67	−	1274.67i	−0.385360	−	0.385360i
$223$	2366.26	−	2366.26i	0.710567	−	0.710567i	−0.256087	−	0.966654i	$-0.582433\pi$
$223$	2366.26	−	2366.26i	0.710567	−	0.710567i	0.966654	+	0.256087i	$0.0824333\pi$
$224$	2254.70	+	1808.40i	0.672538	+	0.539414i
$225$	−891.660	−	685.979i	−0.264196	−	0.203253i
$226$	4294.35			1.26396
$227$	2870.03	+	2870.03i	0.839166	+	0.839166i	0.988749	−	0.149583i	$-0.0477931\pi$
$227$	2870.03	+	2870.03i	0.839166	+	0.839166i	−0.149583	+	0.988749i	$0.547793\pi$
$228$	−3330.06	−	3330.06i	−0.967274	−	0.967274i
$229$	−711.326			−0.205265			−0.102633	−	0.994719i	$-0.532727\pi$
$229$	−711.326			−0.205265			−0.102633	+	0.994719i	$0.532727\pi$
$230$	−2669.78	+	1314.50i	−0.765392	+	0.376851i
$231$	−3050.35	−	2446.56i	−0.868825	−	0.696847i
$232$	−4079.50	+	4079.50i	−1.15445	+	1.15445i
$233$	1361.77	+	1361.77i	0.382887	+	0.382887i	0.872141	−	0.489254i	$-0.162731\pi$
$233$	1361.77	+	1361.77i	0.382887	+	0.382887i	−0.489254	+	0.872141i	$0.662731\pi$
$234$	−1321.21			−0.369103
$235$	−1090.62	−	370.980i	−0.302741	−	0.102979i
$236$		−	6754.54i		−	1.86306i
$237$	1481.92	+	1481.92i	0.406166	+	0.406166i
$238$	−5.98231	−	54.4625i	−0.00162931	−	0.0148331i
$239$		−	2221.92i		−	0.601357i	−0.953726	−	0.300679i	$-0.902787\pi$
$239$		−	2221.92i		−	0.601357i	0.953726	−	0.300679i	$-0.0972131\pi$
$240$	1173.48	−	3449.82i	0.315615	−	0.927853i
$241$		−	3247.19i		−	0.867924i	−0.900931	−	0.433962i	$-0.857115\pi$
$241$		−	3247.19i		−	0.867924i	0.900931	−	0.433962i	$-0.142885\pi$
$242$	−12993.0	+	12993.0i	−3.45132	+	3.45132i
$243$	171.827	−	171.827i	0.0453609	−	0.0453609i
$244$	−6196.10			−1.62568
$245$	−2990.71	+	2400.37i	−0.779876	+	0.625934i
$246$	6680.87			1.73153
$247$	1811.24	−	1811.24i	0.466586	−	0.466586i
$248$	−7943.20	+	7943.20i	−2.03384	+	2.03384i
$249$			812.728i			0.206846i
$250$	3927.66	+	5902.24i	0.993629	+	1.49316i
$251$		−	1556.68i		−	0.391462i	−0.980658	−	0.195731i	$-0.937292\pi$
$251$		−	1556.68i		−	0.391462i	0.980658	−	0.195731i	$-0.0627079\pi$
$252$	−322.760	−	2938.38i	−0.0806825	−	0.734527i
$253$	2611.08	+	2611.08i	0.648843	+	0.648843i
$254$		−	695.719i		−	0.171863i
$255$	−17.5484	+	8.64019i	−0.00430950	+	0.00212184i
$256$	−7706.82			−1.88155
$257$	−4439.57	−	4439.57i	−1.07756	−	1.07756i	−0.996728	−	0.0808318i	$-0.974242\pi$
$257$	−4439.57	−	4439.57i	−1.07756	−	1.07756i	−0.0808318	−	0.996728i	$-0.525758\pi$
$258$	3036.84	−	3036.84i	0.732811	−	0.732811i
$259$	1711.28	+	1372.54i	0.410554	+	0.329288i
$260$	5432.16	+	1847.78i	1.29572	+	0.440748i
$261$	1051.44			0.249358
$262$	5397.69	+	5397.69i	1.27279	+	1.27279i
$263$	−4148.29	−	4148.29i	−0.972602	−	0.972602i	0.0270324	−	0.999635i	$-0.491394\pi$
$263$	−4148.29	−	4148.29i	−0.972602	−	0.972602i	−0.999635	+	0.0270324i	$0.991394\pi$
$264$	−10426.6			−2.43072
$265$	−2118.30	−	720.552i	−0.491042	−	0.167031i
$266$	6487.41	+	5203.27i	1.49537	+	1.19937i
$267$	−875.173	+	875.173i	−0.200598	+	0.200598i
$268$	−157.374	−	157.374i	−0.0358700	−	0.0358700i
$269$	3776.72			0.856024			0.428012	−	0.903773i	$-0.359214\pi$
$269$	3776.72			0.856024			0.428012	+	0.903773i	$0.359214\pi$
$270$	−1373.86	+	676.440i	−0.309669	+	0.152470i
$271$			2476.78i			0.555179i	0.960700	+	0.277589i	$0.0895354\pi$
$271$			2476.78i			0.555179i	−0.960700	+	0.277589i	$0.910465\pi$
$272$	−44.7997	−	44.7997i	−0.00998669	−	0.00998669i
$273$	1598.21	−	175.552i	0.354315	−	0.0389189i
$274$		−	1832.54i		−	0.404043i
$275$	5364.24	−	6972.63i	1.17628	−	1.52897i
$276$			2791.52i			0.608803i
$277$	−619.102	+	619.102i	−0.134290	+	0.134290i	−0.771056	−	0.636767i	$-0.780271\pi$
$277$	−619.102	+	619.102i	−0.134290	+	0.134290i	0.636767	+	0.771056i	$0.280271\pi$
$278$	5301.69	−	5301.69i	1.14379	−	1.14379i
$279$	2047.26			0.439305
$280$	−2216.27	+	9982.39i	−0.473026	+	2.13058i
$281$	−906.674			−0.192483			−0.0962413	−	0.995358i	$-0.530682\pi$
$281$	−906.674			−0.192483			−0.0962413	+	0.995358i	$0.530682\pi$
$282$	−1108.81	+	1108.81i	−0.234145	+	0.234145i
$283$	−309.470	+	309.470i	−0.0650038	+	0.0650038i	−0.738861	−	0.673858i	$-0.764636\pi$
$283$	−309.470	+	309.470i	−0.0650038	+	0.0650038i	0.673858	+	0.738861i	$0.264636\pi$
$284$		−	15265.4i		−	3.18956i
$285$	956.097	−	2810.76i	0.198717	−	0.584193i
$286$		−	10331.6i		−	2.13609i
$287$	−8081.56	+	887.701i	−1.66216	+	0.182576i
$288$	−993.178	−	993.178i	−0.203207	−	0.203207i
$289$		−	4912.66i		−	0.999931i
$290$	−6273.09	−	2133.83i	−1.27024	−	0.432078i
$291$	−1134.60			−0.228561
$292$	14498.0	+	14498.0i	2.90559	+	2.90559i
$293$	−1817.77	+	1817.77i	−0.362442	+	0.362442i	−0.864711	−	0.502269i	$-0.832499\pi$
$293$	−1817.77	+	1817.77i	−0.362442	+	0.362442i	0.502269	+	0.864711i	$0.332499\pi$
$294$	1133.10	+	5095.59i	0.224774	+	1.01082i
$295$	3820.26	−	1880.96i	0.753981	−	0.371233i
$296$	5849.40			1.14861
$297$	1343.66	+	1343.66i	0.262515	+	0.262515i
$298$	−5202.48	−	5202.48i	−1.01131	−	1.01131i
$299$	−1518.33			−0.293669
$300$	6594.69	−	859.769i	1.26915	−	0.165463i
$301$	−3270.02	+	4077.04i	−0.626183	+	0.780721i
$302$	3872.85	−	3872.85i	0.737939	−	0.737939i
$303$	2303.45	+	2303.45i	0.436732	+	0.436732i
$304$	9616.50			1.81429
$305$	−1725.45	−	3504.42i	−0.323931	−	0.657910i
$306$			26.6255i			0.00497411i
$307$	154.832	+	154.832i	0.0287841	+	0.0287841i	0.721352	−	0.692568i	$-0.243521\pi$
$307$	154.832	+	154.832i	0.0287841	+	0.0287841i	−0.692568	+	0.721352i	$0.743521\pi$
$308$	22977.7	−	2523.93i	4.25089	−	0.466929i
$309$			2680.14i			0.493423i
$310$	−12214.3	−	4154.77i	−2.23783	−	0.761210i
$311$		−	5675.63i		−	1.03484i	−0.855731	−	0.517420i	$-0.826892\pi$
$311$		−	5675.63i		−	1.03484i	0.855731	−	0.517420i	$-0.173108\pi$
$312$	3031.49	−	3031.49i	0.550078	−	0.550078i
$313$	3392.35	−	3392.35i	0.612610	−	0.612610i	−0.331015	−	0.943625i	$-0.607391\pi$
$313$	3392.35	−	3392.35i	0.612610	−	0.612610i	0.943625	+	0.331015i	$0.107391\pi$
$314$	17910.6			3.21897
$315$	1572.02	−	1000.81i	0.281186	−	0.179013i
$316$	−12389.2			−2.20553
$317$	5052.71	−	5052.71i	0.895231	−	0.895231i	−0.0997785	−	0.995010i	$-0.531813\pi$
$317$	5052.71	−	5052.71i	0.895231	−	0.895231i	0.995010	+	0.0997785i	$0.0318134\pi$
$318$	−2153.64	+	2153.64i	−0.379780	+	0.379780i
$319$			8222.08i			1.44310i
$320$	−382.411	−	776.684i	−0.0668044	−	0.135681i
$321$			2158.18i			0.375258i
$322$	−538.232	−	4900.02i	−0.0931506	−	0.848035i
$323$	−36.5008	−	36.5008i	−0.00628781	−	0.00628781i
$324$			1436.51i			0.246315i
$325$	467.635	+	3586.90i	0.0798145	+	0.612202i
$326$	9846.81			1.67290
$327$	−1405.25	−	1405.25i	−0.237648	−	0.237648i
$328$	−15329.1	+	15329.1i	−2.58052	+	2.58052i
$329$	1193.95	−	1488.61i	0.200075	−	0.249452i
$330$	−5289.65	−	10743.4i	−0.882381	−	1.79213i
$331$	714.851			0.118706			0.0593531	−	0.998237i	$-0.481096\pi$
$331$	714.851			0.118706			0.0593531	+	0.998237i	$0.481096\pi$
$332$	−3397.29	−	3397.29i	−0.561597	−	0.561597i
$333$	−753.804	−	753.804i	−0.124049	−	0.124049i
$334$	−7773.75			−1.27354
$335$	45.1839	−	132.833i	0.00736913	−	0.0216640i
$336$	4708.74	+	3776.68i	0.764533	+	0.613199i
$337$	−168.763	+	168.763i	−0.0272792	+	0.0272792i	−0.720615	−	0.693336i	$-0.756140\pi$
$337$	−168.763	+	168.763i	−0.0272792	+	0.0272792i	0.693336	+	0.720615i	$0.256140\pi$
$338$	−4876.99	−	4876.99i	−0.784832	−	0.784832i
$339$	2539.56			0.406874
$340$	37.2372	−	109.471i	0.00593962	−	0.0174614i
$341$			16009.2i			2.54237i
$342$	−2857.65	−	2857.65i	−0.451825	−	0.451825i
$343$	−2047.72	−	6013.36i	−0.322352	−	0.946620i
$344$			13936.0i			2.18423i
$345$	−1578.84	+	777.362i	−0.246382	+	0.121309i
$346$		−	11107.3i		−	1.72581i
$347$	5073.83	−	5073.83i	0.784949	−	0.784949i	−0.195712	−	0.980661i	$-0.562702\pi$
$347$	5073.83	−	5073.83i	0.784949	−	0.784949i	0.980661	+	0.195712i	$0.0627019\pi$
$348$	−4395.12	+	4395.12i	−0.677021	+	0.677021i
$349$	4580.50			0.702546			0.351273	−	0.936273i	$-0.385749\pi$
$349$	4580.50			0.702546			0.351273	+	0.936273i	$0.385749\pi$
$350$	−11410.1	+	2780.70i	−1.74255	+	0.424670i
$351$	−781.328			−0.118815
$352$	7766.49	−	7766.49i	1.17601	−	1.17601i
$353$	2591.29	−	2591.29i	0.390710	−	0.390710i	−0.484231	−	0.874940i	$-0.660900\pi$
$353$	2591.29	−	2591.29i	0.390710	−	0.390710i	0.874940	+	0.484231i	$0.160900\pi$
$354$		−	5796.33i		−	0.870259i
$355$	8633.86	−	4251.00i	1.29081	−	0.635548i
$356$		−	7316.62i		−	1.08927i
$357$	−3.53778	−	32.2077i	−0.000524480	−	0.00477482i
$358$	6578.79	+	6578.79i	0.971229	+	0.971229i
$359$		−	3881.10i		−	0.570575i	−0.958442	−	0.285288i	$-0.907911\pi$
$359$		−	3881.10i		−	0.570575i	0.958442	−	0.285288i	$-0.0920891\pi$
$360$	1600.23	−	4704.39i	0.234276	−	0.688731i
$361$	976.107			0.142310
$362$	−1438.15	−	1438.15i	−0.208805	−	0.208805i
$363$	−7683.70	+	7683.70i	−1.11099	+	1.11099i
$364$	−5946.85	+	7414.50i	−0.856318	+	1.06765i
$365$	−4162.54	+	12237.2i	−0.596924	+	1.75485i
$366$	−5317.12			−0.759372
$367$	3936.91	+	3936.91i	0.559959	+	0.559959i	0.929296	−	0.369337i	$-0.120415\pi$
$367$	3936.91	+	3936.91i	0.559959	+	0.559959i	−0.369337	+	0.929296i	$0.620415\pi$
$368$	−4030.65	−	4030.65i	−0.570957	−	0.570957i
$369$	3950.89			0.557385
$370$	2967.54	+	6027.13i	0.416960	+	0.846853i
$371$	2319.00	−	2891.32i	0.324519	−	0.404609i
$372$	−8557.74	+	8557.74i	−1.19274	+	1.19274i
$373$	−4646.88	−	4646.88i	−0.645057	−	0.645057i	0.306738	−	0.951794i	$-0.400763\pi$
$373$	−4646.88	−	4646.88i	−0.645057	−	0.645057i	−0.951794	+	0.306738i	$0.900763\pi$
$374$	−208.207			−0.0287864
$375$	2322.72	+	3490.43i	0.319852	+	0.480654i
$376$		−	5088.30i		−	0.697897i
$377$	−2390.54	−	2390.54i	−0.326576	−	0.326576i
$378$	−276.973	−	2521.54i	−0.0376877	−	0.343106i
$379$			7104.55i			0.962893i	0.876476	+	0.481446i	$0.159888\pi$
$379$			7104.55i			0.962893i	−0.876476	+	0.481446i	$0.840112\pi$
$380$	7752.68	+	15745.8i	1.04659	+	2.12564i
$381$		−	411.430i		−	0.0553234i
$382$	12774.9	−	12774.9i	1.71106	−	1.71106i
$383$	−9137.69	+	9137.69i	−1.21910	+	1.21910i	−0.251148	+	0.967949i	$0.580808\pi$
$383$	−9137.69	+	9137.69i	−1.21910	+	1.21910i	−0.967949	+	0.251148i	$0.919192\pi$
$384$	−4923.94			−0.654359
$385$	7826.16	+	12293.0i	1.03599	+	1.62729i
$386$	1243.26			0.163939
$387$	1795.91	−	1795.91i	0.235894	−	0.235894i
$388$	4742.73	−	4742.73i	0.620556	−	0.620556i
$389$			3792.18i			0.494271i	0.968981	+	0.247135i	$0.0794892\pi$
$389$			3792.18i			0.494271i	−0.968981	+	0.247135i	$0.920511\pi$
$390$	4661.55	+	1585.65i	0.605248	+	0.205879i
$391$			30.5979i			0.00395755i
$392$	−14291.6	−	9091.87i	−1.84142	−	1.17145i
$393$	3192.05	+	3192.05i	0.409714	+	0.409714i
$394$			21410.8i			2.73771i
$395$	−3450.05	−	7007.13i	−0.439471	−	0.892574i
$396$	−11233.3			−1.42549
$397$	−10234.5	−	10234.5i	−1.29384	−	1.29384i	−0.932391	−	0.361451i	$-0.882282\pi$
$397$	−10234.5	−	10234.5i	−1.29384	−	1.29384i	−0.361451	−	0.932391i	$-0.617718\pi$
$398$	−11214.0	+	11214.0i	−1.41233	+	1.41233i
$399$	3836.48	+	3077.08i	0.481364	+	0.386081i
$400$	−8280.62	+	10763.4i	−1.03508	+	1.34543i
$401$	−7796.35			−0.970901			−0.485451	−	0.874264i	$-0.661344\pi$
$401$	−7796.35			−0.970901			−0.485451	+	0.874264i	$0.661344\pi$
$402$	−135.049	−	135.049i	−0.0167553	−	0.0167553i
$403$	−4654.62	−	4654.62i	−0.575343	−	0.575343i
$404$	−19257.3			−2.37150
$405$	−812.467	+	400.029i	−0.0996834	+	0.0490805i
$406$	6867.45	−	8562.30i	0.839473	−	1.04665i
$407$	5894.62	−	5894.62i	0.717900	−	0.717900i
$408$	−61.0917	−	61.0917i	−0.00741297	−	0.00741297i
$409$	−14014.4			−1.69429			−0.847146	−	0.531360i	$-0.821681\pi$
$409$	−14014.4			−1.69429			−0.847146	+	0.531360i	$0.821681\pi$
$410$	−23571.7	−	8018.07i	−2.83933	−	0.965815i
$411$		−	1083.72i		−	0.130063i
$412$	−11203.2	−	11203.2i	−1.33967	−	1.33967i
$413$	770.171	+	7011.57i	0.0917618	+	0.835392i
$414$			2395.51i			0.284379i
$415$	975.399	−	2867.50i	0.115375	−	0.339181i
$416$			4516.16i			0.532266i
$417$	3135.28	−	3135.28i	0.368190	−	0.368190i
$418$	22346.4	−	22346.4i	2.61482	−	2.61482i
$419$	16684.6			1.94533			0.972667	−	0.232203i	$-0.0745933\pi$
$419$	16684.6			1.94533			0.972667	+	0.232203i	$0.0745933\pi$
$420$	−2387.73	+	10754.7i	−0.277404	+	1.24947i
$421$	−2591.53			−0.300008			−0.150004	−	0.988685i	$-0.547929\pi$
$421$	−2591.53			−0.300008			−0.150004	+	0.988685i	$0.547929\pi$
$422$	−9992.67	+	9992.67i	−1.15269	+	1.15269i
$423$	−655.722	+	655.722i	−0.0753719	+	0.0753719i
$424$		−	9882.97i		−	1.13198i
$425$	72.2846	−	9.42394i	0.00825016	−	0.00107560i
$426$		−	13099.8i		−	1.48988i
$427$	6431.89	−	706.496i	0.728948	−	0.0800697i
$428$	−9021.40	−	9021.40i	−1.01885	−	1.01885i
$429$		−	6109.85i		−	0.687614i
$430$	−14359.4	+	7070.04i	−1.61040	+	0.792902i
$431$	−872.272			−0.0974846			−0.0487423	−	0.998811i	$-0.515521\pi$
$431$	−872.272			−0.0974846			−0.0487423	+	0.998811i	$0.515521\pi$
$432$	−2074.17	−	2074.17i	−0.231003	−	0.231003i
$433$	2237.45	−	2237.45i	0.248326	−	0.248326i	−0.571957	−	0.820283i	$-0.693816\pi$
$433$	2237.45	−	2237.45i	0.248326	−	0.248326i	0.820283	+	0.571957i	$0.193816\pi$
$434$	13371.6	−	16671.6i	1.47893	−	1.84393i
$435$	−3709.74	−	1261.89i	−0.408893	−	0.139087i
$436$	11748.2			1.29045
$437$	−3284.00	−	3284.00i	−0.359485	−	0.359485i
$438$	12441.3	+	12441.3i	1.35723	+	1.35723i
$439$	−5294.47			−0.575606			−0.287803	−	0.957690i	$-0.592925\pi$
$439$	−5294.47			−0.575606			−0.287803	+	0.957690i	$0.592925\pi$
$440$	36787.5	+	12513.5i	3.98586	+	1.35581i
$441$	670.085	+	3013.40i	0.0723555	+	0.325386i
$442$	60.5354	−	60.5354i	0.00651442	−	0.00651442i
$443$	10465.8	+	10465.8i	1.12245	+	1.12245i	0.991373	+	0.131074i	$0.0418426\pi$
$443$	10465.8	+	10465.8i	1.12245	+	1.12245i	0.131074	+	0.991373i	$0.458157\pi$
$444$	6301.95			0.673598
$445$	4138.17	−	2037.48i	0.440827	−	0.217047i
$446$			16976.0i			1.80233i
$447$	−3076.61	−	3076.61i	−0.325545	−	0.325545i
$448$	1425.50	−	156.581i	0.150331	−	0.0165128i
$449$			8796.04i			0.924522i	0.886744	+	0.462261i	$0.152962\pi$
$449$			8796.04i			0.924522i	−0.886744	+	0.462261i	$0.847038\pi$
$450$	5659.16	−	737.801i	0.592834	−	0.0772895i
$451$			30895.3i			3.22572i
$452$	−10615.6	+	10615.6i	−1.10468	+	1.10468i
$453$	2290.30	−	2290.30i	0.237545	−	0.237545i
$454$	−20590.2			−2.12852
$455$	−5849.56	−	1298.71i	−0.602707	−	0.133812i
$456$	13113.7			1.34672
$457$	10447.6	−	10447.6i	1.06940	−	1.06940i	0.0719962	−	0.997405i	$-0.477063\pi$
$457$	10447.6	−	10447.6i	1.06940	−	1.06940i	0.997405	−	0.0719962i	$-0.0229370\pi$
$458$	2551.60	−	2551.60i	0.260324	−	0.260324i
$459$			15.7456i			0.00160118i
$460$	3350.25	−	9849.15i	0.339579	−	0.998303i
$461$			4878.44i			0.492867i	0.969160	+	0.246434i	$0.0792587\pi$
$461$			4878.44i			0.492867i	−0.969160	+	0.246434i	$0.920741\pi$
$462$	19718.0	−	2165.88i	1.98564	−	0.218108i
$463$	−1284.21	−	1284.21i	−0.128904	−	0.128904i	0.639711	−	0.768615i	$-0.279054\pi$
$463$	−1284.21	−	1284.21i	−0.128904	−	0.128904i	−0.768615	+	0.639711i	$0.779054\pi$
$464$		−	12692.2i		−	1.26987i
$465$	−7223.22	−	2457.02i	−0.720363	−	0.245036i
$466$	−9769.65			−0.971181
$467$	5744.79	+	5744.79i	0.569245	+	0.569245i	0.931917	−	0.362672i	$-0.118135\pi$
$467$	5744.79	+	5744.79i	0.569245	+	0.569245i	−0.362672	+	0.931917i	$0.618135\pi$
$468$	3266.03	−	3266.03i	0.322590	−	0.322590i
$469$	181.307	+	145.419i	0.0178507	+	0.0143173i
$470$	5242.91	−	2581.42i	0.514547	−	0.253344i
$471$	10591.9			1.03620
$472$	13299.6	+	13299.6i	1.29696	+	1.29696i
$473$	14043.7	+	14043.7i	1.36518	+	1.36518i
$474$	−10631.6			−1.03023
$475$	−6746.69	+	8769.59i	−0.651704	+	0.847108i
$476$	149.420	+	119.843i	0.0143879	+	0.0115399i
$477$	−1273.60	+	1273.60i	−0.122252	+	0.122252i
$478$	7970.28	+	7970.28i	0.762662	+	0.762662i
$479$	7944.76			0.757840			0.378920	−	0.925429i	$-0.376296\pi$
$479$	7944.76			0.757840			0.378920	+	0.925429i	$0.376296\pi$
$480$	2312.21	+	4696.14i	0.219870	+	0.446560i
$481$			3427.68i			0.324925i
$482$	11648.0	+	11648.0i	1.10073	+	1.10073i
$483$	−318.296	−	2897.74i	−0.0299855	−	0.272985i
$484$		−	64237.3i		−	6.03280i
$485$	4003.14	+	1361.69i	0.374790	+	0.127487i
$486$			1232.72i			0.115057i
$487$	−4301.40	+	4301.40i	−0.400236	+	0.400236i	−0.878316	−	0.478080i	$-0.841333\pi$
$487$	−4301.40	+	4301.40i	−0.400236	+	0.400236i	0.478080	+	0.878316i	$0.341333\pi$
$488$	12200.0	−	12200.0i	1.13170	−	1.13170i
$489$	5823.15			0.538511
$490$	2117.64	−	19338.4i	0.195235	−	1.78290i
$491$	−15023.7			−1.38087			−0.690436	−	0.723394i	$-0.742581\pi$
$491$	−15023.7			−1.38087			−0.690436	+	0.723394i	$0.742581\pi$
$492$	−16515.1	+	16515.1i	−1.51333	+	1.51333i
$493$	−48.1751	+	48.1751i	−0.00440100	+	0.00440100i
$494$			12994.3i			1.18348i
$495$	−3128.16	−	6353.35i	−0.284041	−	0.576893i
$496$		−	24712.9i		−	2.23718i
$497$	1740.60	+	15846.3i	0.157096	+	1.43019i
$498$	−2915.34	−	2915.34i	−0.262329	−	0.262329i
$499$			18993.6i			1.70395i	0.523581	+	0.851976i	$0.324596\pi$
$499$			18993.6i			1.70395i	−0.523581	+	0.851976i	$0.675404\pi$
$500$	−24299.6	−	4881.17i	−2.17342	−	0.436585i
$501$	−4597.19			−0.409955
$502$	5583.98	+	5583.98i	0.496465	+	0.496465i
$503$	10550.5	−	10550.5i	0.935238	−	0.935238i	−0.0627886	−	0.998027i	$-0.519999\pi$
$503$	10550.5	−	10550.5i	0.935238	−	0.935238i	0.998027	+	0.0627886i	$0.0199994\pi$
$504$	6421.14	+	5150.12i	0.567501	+	0.455168i
$505$	−5362.65	−	10891.6i	−0.472544	−	0.959746i
$506$	−18732.5			−1.64577
$507$	−2884.12	−	2884.12i	−0.252640	−	0.252640i
$508$	1719.82	+	1719.82i	0.150206	+	0.150206i
$509$	−1431.04			−0.124617			−0.0623084	−	0.998057i	$-0.519846\pi$
$509$	−1431.04			−0.124617			−0.0623084	+	0.998057i	$0.519846\pi$
$510$	31.9547	−	93.9412i	0.00277446	−	0.00815644i
$511$	−16702.8	−	13396.6i	−1.44597	−	1.15975i
$512$	18360.5	−	18360.5i	1.58482	−	1.58482i
$513$	−1689.94	−	1689.94i	−0.145444	−	0.145444i
$514$	31850.4			2.73319
$515$	3216.58	−	9456.18i	0.275222	−	0.809105i
$516$			15014.1i			1.28093i
$517$	−5127.64	−	5127.64i	−0.436196	−	0.436196i
$518$	−11062.0	+	1215.08i	−0.938292	+	0.103065i
$519$		−	6568.56i		−	0.555545i
$520$	−14334.1	+	7057.59i	−1.20883	+	0.595184i
$521$		−	14201.5i		−	1.19421i	−0.802165	−	0.597103i	$-0.796319\pi$
$521$		−	14201.5i		−	1.19421i	0.802165	−	0.597103i	$-0.203681\pi$
$522$	−3771.63	+	3771.63i	−0.316244	+	0.316244i
$523$	−1308.59	+	1308.59i	−0.109408	+	0.109408i	−0.759692	−	0.650283i	$-0.774650\pi$
$523$	−1308.59	+	1308.59i	−0.109408	+	0.109408i	0.650283	+	0.759692i	$0.274650\pi$
$524$	−26686.2			−2.22480
$525$	−6747.61	+	1644.43i	−0.560933	+	0.136703i
$526$	29760.7			2.46697
$527$	−93.8016	+	93.8016i	−0.00775344	+	0.00775344i
$528$	16219.6	−	16219.6i	1.33687	−	1.33687i
$529$		−	9414.09i		−	0.773740i
$530$	10183.3	−	5013.87i	0.834590	−	0.410922i
$531$		−	3427.80i		−	0.280139i
$532$	−28899.4	+	3174.39i	−2.35516	+	0.258698i
$533$	−8982.69	−	8982.69i	−0.729988	−	0.729988i
$534$		−	6278.68i		−	0.508811i
$535$	2590.14	−	7614.58i	0.209312	−	0.615340i
$536$	619.735			0.0499412
$537$	3890.52	+	3890.52i	0.312642	+	0.312642i
$538$	−13547.5	+	13547.5i	−1.08564	+	1.08564i
$539$	−23564.2	+	5239.95i	−1.88309	+	0.418739i
$540$	1724.03	−	5068.35i	0.137390	−	0.403902i
$541$	−10792.1			−0.857651			−0.428825	−	0.903387i	$-0.641072\pi$
$541$	−10792.1			−0.857651			−0.428825	+	0.903387i	$0.641072\pi$
$542$	−8884.46	−	8884.46i	−0.704096	−	0.704096i
$543$	−850.485	−	850.485i	−0.0672151	−	0.0672151i
$544$	91.0113			0.00717293
$545$	3271.56	+	6644.60i	0.257135	+	0.522245i
$546$	−5103.22	+	6362.67i	−0.399996	+	0.498713i
$547$	−15500.5	+	15500.5i	−1.21162	+	1.21162i	−0.241123	+	0.970495i	$0.577516\pi$
$547$	−15500.5	+	15500.5i	−1.21162	+	1.21162i	−0.970495	+	0.241123i	$0.922484\pi$
$548$	4530.05	+	4530.05i	0.353128	+	0.353128i
$549$	−3144.40			−0.244444
$550$	5769.48	+	44253.7i	0.447293	+	3.43088i
$551$		−	10341.0i		−	0.799534i
$552$	−5496.45	−	5496.45i	−0.423813	−	0.423813i
$553$	12860.6	−	1412.65i	0.988951	−	0.108629i
$554$		−	4441.57i		−	0.340621i
$555$	1754.92	+	3564.29i	0.134221	+	0.272605i
$556$			26211.6i			1.99931i
$557$	4681.20	−	4681.20i	0.356102	−	0.356102i	−0.506272	−	0.862374i	$-0.668977\pi$
$557$	4681.20	−	4681.20i	0.356102	−	0.356102i	0.862374	+	0.506272i	$0.168977\pi$
$558$	−7343.73	+	7343.73i	−0.557141	+	0.557141i
$559$	−8166.31			−0.617885
$560$	−12081.0	−	18976.3i	−0.911635	−	1.43195i
$561$	−123.128			−0.00926643
$562$	3252.33	−	3252.33i	0.244113	−	0.244113i
$563$	7069.31	−	7069.31i	0.529193	−	0.529193i	−0.391139	−	0.920332i	$-0.627919\pi$
$563$	7069.31	−	7069.31i	0.529193	−	0.529193i	0.920332	+	0.391139i	$0.127919\pi$
$564$		−	5481.97i		−	0.409278i
$565$	−8960.21	−	3047.87i	−0.667184	−	0.226946i
$566$		−	2220.20i		−	0.164880i
$567$	−163.795	−	1491.17i	−0.0121318	−	0.110447i
$568$	30057.3	+	30057.3i	2.22038	+	2.22038i
$569$		−	6591.68i		−	0.485655i	−0.970069	−	0.242828i	$-0.921925\pi$
$569$		−	6591.68i		−	0.485655i	0.970069	−	0.242828i	$-0.0780749\pi$
$570$	6652.88	+	13512.1i	0.488874	+	0.992913i
$571$	24540.1			1.79855			0.899273	−	0.437388i	$-0.144096\pi$
$571$	24540.1			1.79855			0.899273	+	0.437388i	$0.144096\pi$
$572$	25539.8	+	25539.8i	1.86691	+	1.86691i
$573$	7554.77	−	7554.77i	0.550794	−	0.550794i
$574$	25805.1	−	32173.7i	1.87645	−	2.33955i
$575$	6503.48	−	847.877i	0.471676	−	0.0614938i
$576$	−696.893			−0.0504118
$577$	−414.647	−	414.647i	−0.0299168	−	0.0299168i	0.691990	−	0.721907i	$-0.256734\pi$
$577$	−414.647	−	414.647i	−0.0299168	−	0.0299168i	−0.721907	+	0.691990i	$0.756734\pi$
$578$	17622.2	+	17622.2i	1.26815	+	1.26815i
$579$	735.233			0.0527725
$580$	20781.9	−	10232.3i	1.48780	−	0.732537i
$581$	3913.93	+	3139.20i	0.279479	+	0.224158i
$582$	4069.92	−	4069.92i	0.289869	−	0.289869i
$583$	−9959.37	−	9959.37i	−0.707504	−	0.707504i
$584$	−57092.7			−4.04540
$585$	2756.72	+	937.713i	0.194831	+	0.0662729i
$586$		−	13041.1i		−	0.919322i
$587$	11523.4	+	11523.4i	0.810257	+	0.810257i	0.984672	−	0.174415i	$-0.0558034\pi$
$587$	11523.4	+	11523.4i	0.810257	+	0.810257i	−0.174415	+	0.984672i	$0.555803\pi$
$588$	−15397.3	−	9795.28i	−1.07989	−	0.686991i
$589$		−	20135.0i		−	1.40857i
$590$	−6956.49	+	20450.9i	−0.485414	+	1.42703i
$591$			12661.8i			0.881278i
$592$	−9099.35	+	9099.35i	−0.631725	+	0.631725i
$593$	4075.41	−	4075.41i	0.282221	−	0.282221i	−0.551773	−	0.833994i	$-0.686049\pi$
$593$	4075.41	−	4075.41i	0.282221	−	0.282221i	0.833994	+	0.551773i	$0.186049\pi$
$594$	−9639.69			−0.665861
$595$	−26.1720	+	117.882i	−0.00180327	+	0.00812220i
$596$	25721.1			1.76775
$597$	−6631.67	+	6631.67i	−0.454633	+	0.454633i
$598$	5446.40	−	5446.40i	0.372441	−	0.372441i
$599$			15118.2i			1.03124i	0.856817	+	0.515621i	$0.172439\pi$
$599$			15118.2i			1.03124i	−0.856817	+	0.515621i	$0.827561\pi$
$600$	−11292.0	+	14677.7i	−0.768322	+	0.998693i
$601$		−	12299.7i		−	0.834802i	−0.908722	−	0.417401i	$-0.862941\pi$
$601$		−	12299.7i		−	0.834802i	0.908722	−	0.417401i	$-0.137059\pi$
$602$	−2894.88	−	26354.7i	−0.195991	−	1.78428i
$603$	−79.8643	−	79.8643i	−0.00539358	−	0.00539358i
$604$			19147.4i			1.28989i
$605$	36331.6	−	17888.4i	2.44147	−	1.20209i
$606$	−16525.5			−1.10776
$607$	−10607.5	−	10607.5i	−0.709303	−	0.709303i	0.257086	−	0.966389i	$-0.417238\pi$
$607$	−10607.5	−	10607.5i	−0.709303	−	0.709303i	−0.966389	+	0.257086i	$0.917238\pi$
$608$	−9768.03	+	9768.03i	−0.651556	+	0.651556i
$609$	4061.23	−	5063.52i	0.270229	−	0.336920i
$610$	18760.1	+	6381.36i	1.24520	+	0.423563i
$611$	2981.68			0.197424
$612$	−65.8182	−	65.8182i	−0.00434729	−	0.00434729i
$613$	−13156.9	−	13156.9i	−0.866890	−	0.866890i	0.125237	−	0.992127i	$-0.460031\pi$
$613$	−13156.9	−	13156.9i	−0.866890	−	0.866890i	−0.992127	+	0.125237i	$0.960031\pi$
$614$	−1110.80			−0.0730099
$615$	−13939.7	−	4741.67i	−0.913989	−	0.310899i
$616$	−40273.1	+	50212.3i	−2.63417	+	3.28427i
$617$	−3239.35	+	3239.35i	−0.211363	+	0.211363i	−0.804846	−	0.593483i	$-0.797752\pi$
$617$	−3239.35	+	3239.35i	−0.211363	+	0.211363i	0.593483	+	0.804846i	$0.297752\pi$
$618$	−9613.93	−	9613.93i	−0.625775	−	0.625775i
$619$	−3023.96			−0.196354			−0.0981772	−	0.995169i	$-0.531301\pi$
$619$	−3023.96			−0.196354			−0.0981772	+	0.995169i	$0.531301\pi$
$620$	40464.4	−	19923.2i	2.62111	−	1.29054i
$621$			1416.64i			0.0915423i
$622$	20359.1	+	20359.1i	1.31242	+	1.31242i
$623$	834.261	+	7595.04i	0.0536500	+	0.488425i
$624$			9431.60i			0.605074i
$625$	−4006.06	−	15102.7i	−0.256388	−	0.966574i
$626$			24337.5i			1.55387i
$627$	13215.0	−	13215.0i	0.841719	−	0.841719i
$628$	−44275.1	+	44275.1i	−2.81333	+	2.81333i
$629$	69.0758			0.00437875
$630$	−2049.01	+	9229.02i	−0.129578	+	0.583640i
$631$	−28289.4			−1.78476			−0.892381	−	0.451283i	$-0.850966\pi$
$631$	−28289.4			−1.78476			−0.892381	+	0.451283i	$0.850966\pi$
$632$	24394.1	−	24394.1i	1.53536	−	1.53536i
$633$	−5909.40	+	5909.40i	−0.371055	+	0.371055i
$634$			36249.2i			2.27072i
$635$	−493.779	+	1451.63i	−0.0308583	+	0.0907182i
$636$		−	10647.6i		−	0.663844i
$637$	5327.73	−	8374.72i	0.331385	−	0.520908i
$638$	−29493.5	−	29493.5i	−1.83018	−	1.83018i
$639$		−	7746.89i		−	0.479596i
$640$	17372.9	+	5909.49i	1.07301	+	0.364989i
$641$	−12161.4			−0.749368			−0.374684	−	0.927153i	$-0.622249\pi$
$641$	−12161.4			−0.749368			−0.374684	+	0.927153i	$0.622249\pi$
$642$	−7741.61	−	7741.61i	−0.475914	−	0.475914i
$643$	6799.55	−	6799.55i	0.417026	−	0.417026i	−0.467151	−	0.884178i	$-0.654720\pi$
$643$	6799.55	−	6799.55i	0.417026	−	0.417026i	0.884178	+	0.467151i	$0.154720\pi$
$644$	13443.4	+	10782.3i	0.822582	+	0.659758i
$645$	−8491.76	+	4181.04i	−0.518392	+	0.255237i
$646$	261.865			0.0159488
$647$	−11124.5	−	11124.5i	−0.675967	−	0.675967i	0.283118	−	0.959085i	$-0.408631\pi$
$647$	−11124.5	−	11124.5i	−0.675967	−	0.675967i	−0.959085	+	0.283118i	$0.908631\pi$
$648$	−2828.46	−	2828.46i	−0.171470	−	0.171470i
$649$	26804.8			1.62123
$650$	−14544.1	−	11189.1i	−0.877638	−	0.675192i
$651$	7907.61	−	9859.17i	0.476073	−	0.593566i
$652$	−24341.3	+	24341.3i	−1.46209	+	1.46209i
$653$	1452.05	+	1452.05i	0.0870187	+	0.0870187i	0.749276	−	0.662258i	$-0.230402\pi$
$653$	1452.05	+	1452.05i	0.0870187	+	0.0870187i	−0.662258	+	0.749276i	$0.730402\pi$
$654$	10081.6			0.602785
$655$	−7431.39	−	15093.3i	−0.443311	−	0.900373i
$656$		−	47692.1i		−	2.83851i
$657$	7357.46	+	7357.46i	0.436898	+	0.436898i
$658$	1056.98	+	9622.64i	0.0626220	+	0.570106i
$659$			31260.9i			1.84788i	0.382539	+	0.923940i	$0.375050\pi$
$659$			31260.9i			1.84788i	−0.382539	+	0.923940i	$0.624950\pi$
$660$	39633.7	+	13481.6i	2.33748	+	0.795109i
$661$			14666.7i			0.863040i	0.902103	+	0.431520i	$0.142023\pi$
$661$			14666.7i			0.863040i	−0.902103	+	0.431520i	$0.857977\pi$
$662$	−2564.25	+	2564.25i	−0.150547	+	0.150547i
$663$	35.7990	−	35.7990i	0.00209701	−	0.00209701i
$664$	13378.4			0.781902
$665$	−9843.08	−	15461.0i	−0.573982	−	0.901584i
$666$	5407.95			0.314645
$667$	−4334.33	+	4334.33i	−0.251613	+	0.251613i
$668$	19216.7	−	19216.7i	1.11305	−	1.11305i
$669$			10039.2i			0.580176i
$670$	314.406	+	638.565i	0.0181292	+	0.0368208i
$671$		−	24588.7i		−	1.41466i
$672$	−8619.14	+	946.750i	−0.494777	+	0.0543477i
$673$	−1968.65	−	1968.65i	−0.112758	−	0.112758i	0.648477	−	0.761234i	$-0.275406\pi$
$673$	−1968.65	−	1968.65i	−0.112758	−	0.112758i	−0.761234	+	0.648477i	$0.775406\pi$
$674$		−	1210.74i		−	0.0691927i
$675$	3346.68	−	436.316i	0.190835	−	0.0248797i
$676$	24111.9			1.37186
$677$	−8293.59	−	8293.59i	−0.470825	−	0.470825i	0.431357	−	0.902182i	$-0.358035\pi$
$677$	−8293.59	−	8293.59i	−0.470825	−	0.470825i	−0.902182	+	0.431357i	$0.858035\pi$
$678$	−9109.69	+	9109.69i	−0.516011	+	0.516011i
$679$	−4382.43	+	5463.98i	−0.247691	+	0.308819i
$680$	142.227	+	288.866i	0.00802083	+	0.0162905i
$681$	−12176.5			−0.685176
$682$	−57426.7	−	57426.7i	−3.22431	−	3.22431i
$683$	182.678	+	182.678i	0.0102342	+	0.0102342i	0.712205	−	0.701971i	$-0.247696\pi$
$683$	182.678	+	182.678i	0.0102342	+	0.0102342i	−0.701971	+	0.712205i	$0.747696\pi$
$684$	14128.2			0.789776
$685$	−1300.63	+	3823.62i	−0.0725466	+	0.213274i
$686$	28915.9	+	14225.2i	1.60935	+	0.791718i
$687$	1508.95	−	1508.95i	0.0837992	−	0.0837992i
$688$	−21678.8	−	21678.8i	−1.20130	−	1.20130i
$689$	5791.31			0.320219
$690$	2874.98	−	8451.94i	0.158621	−	0.466319i
$691$			17894.1i			0.985127i	0.870276	+	0.492564i	$0.163940\pi$
$691$			17894.1i			0.985127i	−0.870276	+	0.492564i	$0.836060\pi$
$692$	27457.2	+	27457.2i	1.50834	+	1.50834i
$693$	11660.7	−	1280.85i	0.639183	−	0.0702097i
$694$			36400.7i			1.99100i
$695$	−14824.9	+	7299.22i	−0.809120	+	0.398381i
$696$		−	17307.9i		−	0.942605i
$697$	−181.023	+	181.023i	−0.00983747	+	0.00983747i
$698$	−16430.7	+	16430.7i	−0.890993	+	0.890993i
$699$	−5777.52			−0.312626
$700$	21331.8	−	35079.6i	1.15181	−	1.89412i
$701$	−26293.5			−1.41668			−0.708341	−	0.705871i	$-0.750556\pi$
$701$	−26293.5			−1.41668			−0.708341	+	0.705871i	$0.750556\pi$
$702$	2802.71	−	2802.71i	0.150686	−	0.150686i
$703$	−7413.76	+	7413.76i	−0.397746	+	0.397746i
$704$		−	5449.59i		−	0.291746i
$705$	3100.52	−	1526.58i	0.165634	−	0.0815523i
$706$			18590.5i			0.991022i
$707$	19990.1	−	2195.77i	1.06338	−	0.116804i
$708$	14328.5	+	14328.5i	0.760593	+	0.760593i
$709$		−	5154.38i		−	0.273028i	−0.990638	−	0.136514i	$-0.956410\pi$
$709$		−	5154.38i		−	0.273028i	0.990638	−	0.136514i	$-0.0435899\pi$
$710$	−15721.8	+	46219.4i	−0.831026	+	2.44307i
$711$	−6287.27			−0.331633
$712$	14406.3	+	14406.3i	0.758286	+	0.758286i
$713$	−8439.38	+	8439.38i	−0.443278	+	0.443278i
$714$	128.223	+	102.842i	0.00672075	+	0.00539043i
$715$	−7332.76	+	21557.1i	−0.383538	+	1.12754i
$716$	−32525.6			−1.69768
$717$	4713.41	+	4713.41i	0.245503	+	0.245503i
$718$	13921.9	+	13921.9i	0.723623	+	0.723623i
$719$	13517.4			0.701134			0.350567	−	0.936538i	$-0.385989\pi$
$719$	13517.4			0.701134			0.350567	+	0.936538i	$0.385989\pi$
$720$	4828.85	+	9807.48i	0.249945	+	0.507643i
$721$	12907.0	+	10352.1i	0.666687	+	0.534721i
$722$	−3501.40	+	3501.40i	−0.180483	+	0.180483i
$723$	6888.33	+	6888.33i	0.354329	+	0.354329i
$724$	7110.23			0.364985
$725$	11574.4	+	8904.51i	0.592914	+	0.456145i
$726$		−	55124.5i		−	2.81799i
$727$	−10375.5	−	10375.5i	−0.529308	−	0.529308i	0.391058	−	0.920366i	$-0.372109\pi$
$727$	−10375.5	−	10375.5i	−0.529308	−	0.529308i	−0.920366	+	0.391058i	$0.872109\pi$
$728$	−2889.78	−	26308.3i	−0.147119	−	1.33936i
$729$			729.000i			0.0370370i
$730$	−28964.5	−	58827.5i	−1.46853	−	2.98261i
$731$			164.570i			0.00832675i
$732$	13143.9	−	13143.9i	0.663679	−	0.663679i
$733$	5292.93	−	5292.93i	0.266710	−	0.266710i	−0.561063	−	0.827773i	$-0.689607\pi$
$733$	5292.93	−	5292.93i	0.266710	−	0.266710i	0.827773	+	0.561063i	$0.189607\pi$
$734$	−28244.2			−1.42032
$735$	1252.32	−	11436.2i	0.0628467	−	0.573920i
$736$	8188.33			0.410089
$737$	624.525	−	624.525i	0.0312140	−	0.0312140i
$738$	−14172.3	+	14172.3i	−0.706894	+	0.706894i
$739$		−	4867.18i		−	0.242276i	−0.992636	−	0.121138i	$-0.961346\pi$
$739$		−	4867.18i		−	0.242276i	0.992636	−	0.121138i	$-0.0386544\pi$
$740$	−22234.8	−	7563.31i	−1.10455	−	0.375720i
$741$			7684.46i			0.380966i
$742$	2052.96	+	18690.0i	0.101572	+	0.924705i
$743$	19383.9	+	19383.9i	0.957101	+	0.957101i	0.999117	−	0.0420163i	$-0.0133781\pi$
$743$	19383.9	+	19383.9i	0.957101	+	0.957101i	−0.0420163	+	0.999117i	$0.513378\pi$
$744$		−	33700.1i		−	1.66063i
$745$	7162.63	+	14547.4i	0.352240	+	0.715406i
$746$	33337.7			1.63617
$747$	−1724.06	−	1724.06i	−0.0844444	−	0.0844444i
$748$	514.687	−	514.687i	0.0251589	−	0.0251589i
$749$	10393.3	+	8336.05i	0.507028	+	0.406666i
$750$	−20852.4	−	4188.72i	−1.01523	−	0.203934i
$751$	22983.4			1.11675			0.558374	−	0.829589i	$-0.311425\pi$
$751$	22983.4			1.11675			0.558374	+	0.829589i	$0.311425\pi$
$752$	7915.38	+	7915.38i	0.383835	+	0.383835i
$753$	3302.22	+	3302.22i	0.159814	+	0.159814i
$754$	17150.3			0.828349
$755$	−10829.5	+	5332.03i	−0.522019	+	0.257023i
$756$	6917.93	+	5548.57i	0.332808	+	0.266931i
$757$	−16083.9	+	16083.9i	−0.772231	+	0.772231i	−0.978496	−	0.206265i	$-0.933869\pi$
$757$	−16083.9	+	16083.9i	−0.772231	+	0.772231i	0.206265	+	0.978496i	$0.433869\pi$
$758$	−25484.8	−	25484.8i	−1.22117	−	1.22117i
$759$	−11077.9			−0.529778
$760$	−46268.3	−	15738.4i	−2.20832	−	0.751175i
$761$		−	5157.25i		−	0.245664i	−0.992427	−	0.122832i	$-0.960802\pi$
$761$		−	5157.25i		−	0.245664i	0.992427	−	0.122832i	$-0.0391976\pi$
$762$	1475.84	+	1475.84i	0.0701629	+	0.0701629i
$763$	−12195.3	+	1339.56i	−0.578635	+	0.0635589i
$764$			63159.4i			2.99087i
$765$	18.8971	−	55.5543i	0.000893108	−	0.00262558i
$766$		−	65555.7i		−	3.09220i
$767$	−7793.40	+	7793.40i	−0.366889	+	0.366889i
$768$	16348.6	−	16348.6i	0.768138	−	0.768138i
$769$	−26292.1			−1.23292			−0.616461	−	0.787385i	$-0.711434\pi$
$769$	−26292.1			−1.23292			−0.616461	+	0.787385i	$0.711434\pi$
$770$	−72169.4	−	16022.9i	−3.37767	−	0.749902i
$771$	18835.5			0.879824
$772$	−3073.35	+	3073.35i	−0.143280	+	0.143280i
$773$	4102.80	−	4102.80i	0.190902	−	0.190902i	−0.605184	−	0.796086i	$-0.706900\pi$
$773$	4102.80	−	4102.80i	0.190902	−	0.190902i	0.796086	+	0.605184i	$0.206900\pi$
$774$			12884.2i			0.598338i
$775$	22536.5	+	17338.0i	1.04456	+	0.803610i
$776$			18676.7i			0.863989i
$777$	−6541.76	+	718.566i	−0.302039	+	0.0331768i
$778$	−13603.0	−	13603.0i	−0.626851	−	0.626851i
$779$		−	38857.5i		−	1.78718i
$780$	−15443.1	+	7603.62i	−0.708912	+	0.349043i
$781$	60579.3			2.77554
$782$	−109.758	−	109.758i	−0.00501909	−	0.00501909i
$783$	−2230.44	+	2230.44i	−0.101800	+	0.101800i
$784$	36375.4	−	8088.76i	1.65704	−	0.368475i
$785$	−37370.8	−	12711.9i	−1.69913	−	0.577970i
$786$	−22900.5			−1.03923
$787$	−2076.69	−	2076.69i	−0.0940609	−	0.0940609i	0.658511	−	0.752571i	$-0.271187\pi$
$787$	−2076.69	−	2076.69i	−0.0940609	−	0.0940609i	−0.752571	+	0.658511i	$0.771187\pi$
$788$	−52927.5	−	52927.5i	−2.39272	−	2.39272i
$789$	17599.7			0.794126
$790$	37511.0	+	12759.6i	1.68935	+	0.574641i
$791$	9809.17	−	12230.0i	0.440928	−	0.549746i
$792$	22118.1	−	22118.1i	0.992339	−	0.992339i
$793$	7149.08	+	7149.08i	0.320140	+	0.320140i
$794$	73424.5			3.28179
$795$	6022.11	−	2965.07i	0.268657	−	0.132277i
$796$		−	55442.1i		−	2.46871i
$797$	25440.5	+	25440.5i	1.13068	+	1.13068i	0.990065	+	0.140611i	$0.0449066\pi$
$797$	25440.5	+	25440.5i	1.13068	+	1.13068i	0.140611	+	0.990065i	$0.455093\pi$
$798$	−24799.7	+	2724.06i	−1.10012	+	0.120841i
$799$		−	60.0880i		−	0.00266053i
$800$	−2521.95	−	19344.2i	−0.111456	−	0.854899i
$801$		−	3713.04i		−	0.163788i
$802$	27966.4	−	27966.4i	1.23133	−	1.23133i
$803$	−57534.1	+	57534.1i	−2.52844	+	2.52844i
$804$	667.682			0.0292877
$805$	−2354.71	+	10606.0i	−0.103096	+	0.464361i
$806$	33393.2			1.45934
$807$	−8011.62	+	8011.62i	−0.349470	+	0.349470i
$808$	37917.4	−	37917.4i	1.65090	−	1.65090i
$809$		−	10215.4i		−	0.443947i	−0.975053	−	0.221973i	$-0.928750\pi$
$809$		−	10215.4i		−	0.443947i	0.975053	−	0.221973i	$-0.0712498\pi$
$810$	1479.46	−	4349.35i	0.0641763	−	0.188667i
$811$		−	2191.10i		−	0.0948703i	−0.998874	−	0.0474351i	$-0.984895\pi$
$811$		−	2191.10i		−	0.0948703i	0.998874	−	0.0474351i	$-0.0151047\pi$
$812$	4189.67	+	38142.4i	0.181069	+	1.64844i
$813$	−5254.03	−	5254.03i	−0.226651	−	0.226651i
$814$			42289.2i			1.82093i
$815$	−20545.5	−	6988.67i	−0.883040	−	0.300371i
$816$	190.069			0.00815410
$817$	−17663.0	−	17663.0i	−0.756364	−	0.756364i
$818$	50271.0	−	50271.0i	2.14876	−	2.14876i
$819$	−3017.91	+	3762.71i	−0.128760	+	0.160537i
$820$	78090.1	−	38448.7i	3.32564	−	1.63742i
$821$	33470.6			1.42282			0.711408	−	0.702780i	$-0.248058\pi$
$821$	33470.6			1.42282			0.711408	+	0.702780i	$0.248058\pi$
$822$	3887.41	+	3887.41i	0.164950	+	0.164950i
$823$	235.103	+	235.103i	0.00995769	+	0.00995769i	0.712068	−	0.702110i	$-0.247759\pi$
$823$	235.103	+	235.103i	0.00995769	+	0.00995769i	−0.702110	+	0.712068i	$0.747759\pi$
$824$	44118.0			1.86520
$825$	3411.92	+	26170.5i	0.143985	+	1.10441i
$826$	−27914.0	−	22388.6i	−1.17585	−	0.943097i
$827$	5925.19	−	5925.19i	0.249140	−	0.249140i	−0.571477	−	0.820618i	$-0.693630\pi$
$827$	5925.19	−	5925.19i	0.249140	−	0.249140i	0.820618	+	0.571477i	$0.193630\pi$
$828$	−5921.70	−	5921.70i	−0.248543	−	0.248543i
$829$	−36374.7			−1.52394			−0.761970	−	0.647612i	$-0.775768\pi$
$829$	−36374.7			−1.52394			−0.761970	+	0.647612i	$0.775768\pi$
$830$	6787.19	+	13784.9i	0.283839	+	0.576483i
$831$		−	2626.63i		−	0.109647i
$832$	1584.45	+	1584.45i	0.0660227	+	0.0660227i
$833$	−168.770	−	107.366i	−0.00701987	−	0.00446581i
$834$			22493.2i			0.933902i
$835$	16220.0	+	5517.34i	0.672236	+	0.228665i
$836$			110480.i			4.57063i
$837$	−4342.89	+	4342.89i	−0.179345	+	0.179345i
$838$	−59849.4	+	59849.4i	−2.46714	+	2.46714i
$839$	−45914.6			−1.88933			−0.944665	−	0.328036i	$-0.893613\pi$
$839$	−45914.6			−1.88933			−0.944665	+	0.328036i	$0.893613\pi$
$840$	−16474.4	−	25877.3i	−0.676693	−	1.06292i
$841$	10740.5			0.440385
$842$	9296.09	−	9296.09i	0.380480	−	0.380480i
$843$	1923.35	−	1923.35i	0.0785807	−	0.0785807i
$844$		−	49403.8i		−	2.01487i
$845$	6714.50	+	13637.3i	0.273356	+	0.555192i
$846$		−	4704.29i		−	0.191178i
$847$	7324.51	+	66681.7i	0.297135	+	2.70509i
$848$	15374.0	+	15374.0i	0.622577	+	0.622577i
$849$		−	1312.97i		−	0.0530754i
$850$	−225.488	+	293.097i	−0.00909902	+	0.0118272i
$851$	6214.79			0.250341
$852$	32382.8	+	32382.8i	1.30213	+	1.30213i
$853$	24888.0	−	24888.0i	0.999002	−	0.999002i	−0.000997402	−	1.00000i	$-0.500317\pi$
$853$	24888.0	−	24888.0i	0.999002	−	0.999002i	1.00000		0.000997402i	$0.000317483\pi$
$854$	−20537.6	+	25606.1i	−0.822929	+	1.02602i
$855$	3934.34	+	7990.71i	0.157370	+	0.319622i
$856$	35526.0			1.41852
$857$	12943.8	+	12943.8i	0.515928	+	0.515928i	0.916337	−	0.400409i	$-0.131132\pi$
$857$	12943.8	+	12943.8i	0.515928	+	0.515928i	−0.400409	+	0.916337i	$0.631132\pi$
$858$	21916.7	+	21916.7i	0.872055	+	0.872055i
$859$	36773.4			1.46064			0.730321	−	0.683104i	$-0.239371\pi$
$859$	36773.4			1.46064			0.730321	+	0.683104i	$0.239371\pi$
$860$	18019.3	−	52973.6i	0.714480	−	2.10045i
$861$	15260.5	−	19026.7i	0.604037	−	0.753109i
$862$	3128.93	−	3128.93i	0.123633	−	0.123633i
$863$	−27948.7	−	27948.7i	−1.10242	−	1.10242i	−0.994118	−	0.108298i	$-0.965460\pi$
$863$	−27948.7	−	27948.7i	−1.10242	−	1.10242i	−0.108298	−	0.994118i	$-0.534540\pi$
$864$	4213.70			0.165918
$865$	−7883.28	+	23175.5i	−0.309872	+	0.910971i
$866$			16052.0i			0.629870i
$867$	10421.3	+	10421.3i	0.408220	+	0.408220i
$868$	8157.69	+	74267.0i	0.318998	+	2.90413i
$869$		−	49165.4i		−	1.91924i
$870$	17833.8	−	8780.69i	0.694967	−	0.342176i
$871$			363.157i			0.0141276i
$872$	−23132.1	+	23132.1i	−0.898338	+	0.898338i
$873$	2406.84	−	2406.84i	0.0933096	−	0.0933096i
$874$	23560.1			0.911823
$875$	25780.8	+	2296.21i	0.996057	+	0.0887156i
$876$	−61509.9			−2.37240
$877$	28411.2	−	28411.2i	1.09393	−	1.09393i	0.0988285	−	0.995104i	$-0.468490\pi$
$877$	28411.2	−	28411.2i	1.09393	−	1.09393i	0.995104	−	0.0988285i	$-0.0315095\pi$
$878$	18991.8	−	18991.8i	0.730003	−	0.730003i
$879$		−	7712.16i		−	0.295932i
$880$	−76692.8	+	37760.8i	−2.93786	+	1.44649i
$881$		−	3261.29i		−	0.124717i	−0.998054	−	0.0623585i	$-0.980138\pi$
$881$		−	3261.29i		−	0.124717i	0.998054	−	0.0623585i	$-0.0198622\pi$
$882$	−13213.0	−	8405.71i	−0.504429	−	0.320901i
$883$	11275.9	+	11275.9i	0.429745	+	0.429745i	0.888541	−	0.458796i	$-0.151719\pi$
$883$	11275.9	+	11275.9i	0.429745	+	0.429745i	−0.458796	+	0.888541i	$0.651719\pi$
$884$			299.287i			0.0113870i
$885$	−4113.89	+	12094.1i	−0.156256	+	0.459366i
$886$	−75083.7			−2.84705
$887$	−20296.9	−	20296.9i	−0.768325	−	0.768325i	0.209487	−	0.977811i	$-0.432821\pi$
$887$	−20296.9	−	20296.9i	−0.768325	−	0.768325i	−0.977811	+	0.209487i	$0.932821\pi$
$888$	−12408.5	+	12408.5i	−0.468919	+	0.468919i
$889$	−1981.36	−	1589.17i	−0.0747500	−	0.0599538i
$890$	−7535.38	+	22152.7i	−0.283805	+	0.834338i
$891$	−5700.66			−0.214343
$892$	−41964.8	−	41964.8i	−1.57521	−	1.57521i
$893$	6449.11	+	6449.11i	0.241670	+	0.241670i
$894$	22072.3			0.825735
$895$	−9057.50	−	18396.0i	−0.338278	−	0.687049i
$896$	−19018.9	+	23712.7i	−0.709127	+	0.884136i
$897$	3220.86	−	3220.86i	0.119890	−	0.119890i
$898$	−31552.3	−	31552.3i	−1.17251	−	1.17251i
$899$	−26574.9			−0.985898
$900$	−12165.6	+	15813.3i	−0.450578	+	0.585678i
$901$		−	116.708i		−	0.00431534i
$902$	−110825.	−	110825.i	−4.09097	−	4.09097i
$903$	−1711.95	−	15585.5i	−0.0630900	−	0.574366i
$904$		−	41804.1i		−	1.53803i
$905$	1980.01	+	4021.43i	0.0727267	+	0.147709i
$906$			16431.1i			0.602524i
$907$	−29546.4	+	29546.4i	−1.08167	+	1.08167i	−0.0853129	+	0.996354i	$0.527189\pi$
$907$	−29546.4	+	29546.4i	−1.08167	+	1.08167i	−0.996354	+	0.0853129i	$0.972811\pi$
$908$	50899.1	−	50899.1i	1.86029	−	1.86029i
$909$	−9772.72			−0.356590
$910$	25641.6	−	16324.4i	0.934078	−	0.594669i
$911$	30695.3			1.11633			0.558167	−	0.829729i	$-0.311505\pi$
$911$	30695.3			1.11633			0.558167	+	0.829729i	$0.311505\pi$
$912$	−20399.7	+	20399.7i	−0.740681	+	0.740681i
$913$	13481.8	−	13481.8i	0.488700	−	0.488700i
$914$			74953.0i			2.71250i
$915$	11094.2	+	3773.77i	0.400835	+	0.136346i
$916$			12615.1i			0.455039i
$917$	27701.7	−	3042.83i	0.997591	−	0.109578i
$918$	−56.4811	−	56.4811i	−0.00203067	−	0.00203067i
$919$			30970.6i			1.11167i	0.831292	+	0.555835i	$0.187602\pi$
$919$			30970.6i			1.11167i	−0.831292	+	0.555835i	$0.812398\pi$
$920$	12796.2	+	25989.4i	0.458565	+	0.931354i
$921$	−656.896			−0.0235021
$922$	−17499.5	−	17499.5i	−0.625071	−	0.625071i
$923$	−17613.2	+	17613.2i	−0.628111	+	0.628111i
$924$	−43388.9	+	54097.0i	−1.54479	+	1.92604i
$925$	−1914.12	−	14681.9i	−0.0680386	−	0.521877i
$926$	9213.22			0.326960
$927$	−5685.43	−	5685.43i	−0.201439	−	0.201439i
$928$	12892.2	+	12892.2i	0.456042	+	0.456042i
$929$	15787.5			0.557558			0.278779	−	0.960355i	$-0.410070\pi$
$929$	15787.5			0.557558			0.278779	+	0.960355i	$0.410070\pi$
$930$	34724.1	−	17096.9i	1.22435	−	0.602826i
$931$	29637.1	−	6590.37i	1.04331	−	0.231998i
$932$	24150.6	−	24150.6i	0.848798	−	0.848798i
$933$	12039.8	+	12039.8i	0.422472	+	0.422472i
$934$	−41214.4			−1.44387
$935$	434.426	+	147.772i	0.0151949	+	0.00516864i
$936$			12861.5i			0.449137i
$937$	14283.9	+	14283.9i	0.498008	+	0.498008i	0.910817	−	0.412809i	$-0.135452\pi$
$937$	14283.9	+	14283.9i	0.498008	+	0.498008i	−0.412809	+	0.910817i	$0.635452\pi$
$938$	−1172.00	+	128.736i	−0.0407965	+	0.00448120i
$939$			14392.5i			0.500194i
$940$	−6579.21	+	19341.7i	−0.228287	+	0.671126i
$941$		−	31384.6i		−	1.08726i	−0.839326	−	0.543629i	$-0.817050\pi$
$941$		−	31384.6i		−	1.08726i	0.839326	−	0.543629i	$-0.182950\pi$
$942$	−37994.2	+	37994.2i	−1.31414	+	1.31414i
$943$	−16286.7	+	16286.7i	−0.562426	+	0.562426i
$944$	−41377.8			−1.42662
$945$	−1211.73	+	5457.80i	−0.0417117	+	0.187875i
$946$	−100752.			−3.46273
$947$	−37084.6	+	37084.6i	−1.27253	+	1.27253i	−0.327774	+	0.944756i	$0.606298\pi$
$947$	−37084.6	+	37084.6i	−1.27253	+	1.27253i	−0.944756	+	0.327774i	$0.893702\pi$
$948$	26281.4	−	26281.4i	0.900402	−	0.900402i
$949$		−	33455.7i		−	1.14438i
$950$	−7256.36	−	55658.6i	−0.247818	−	1.90084i
$951$			21436.8i			0.730953i
$952$	−530.174	+	58.2358i	−0.0180494	+	0.00198260i
$953$	922.939	+	922.939i	0.0313714	+	0.0313714i	0.722618	−	0.691247i	$-0.242938\pi$
$953$	922.939	+	922.939i	0.0313714	+	0.0313714i	−0.691247	+	0.722618i	$0.742938\pi$
$954$		−	9137.11i		−	0.310089i
$955$	−35721.9	+	17588.2i	−1.21040	+	0.595959i
$956$	−39405.1			−1.33311
$957$	−17441.7	−	17441.7i	−0.589142	−	0.589142i
$958$	−28498.7	+	28498.7i	−0.961118	+	0.961118i
$959$	−5218.96	−	4185.90i	−0.175734	−	0.140949i
$960$	2458.81	+	836.379i	0.0826644	+	0.0281188i
$961$	−21952.9			−0.736898
$962$	−12295.5	−	12295.5i	−0.412080	−	0.412080i
$963$	−4578.19	−	4578.19i	−0.153198	−	0.153198i
$964$	−57587.8			−1.92404
$965$	−2594.08	−	882.393i	−0.0865353	−	0.0294355i
$966$	11536.3	+	9252.75i	0.384238	+	0.308180i
$967$	8098.90	−	8098.90i	0.269331	−	0.269331i	−0.559500	−	0.828831i	$-0.689007\pi$
$967$	8098.90	−	8098.90i	0.269331	−	0.269331i	0.828831	+	0.559500i	$0.189007\pi$
$968$	126482.	+	126482.i	4.19968	+	4.19968i
$969$	154.860			0.00513397
$970$	−19244.2	+	9475.15i	−0.637004	+	0.313638i
$971$			9500.63i			0.313996i	0.987599	+	0.156998i	$0.0501816\pi$
$971$			9500.63i			0.313996i	−0.987599	+	0.156998i	$0.949818\pi$
$972$	−3047.29	−	3047.29i	−0.100558	−	0.100558i
$973$	−2988.71	−	27209.0i	−0.0984725	−	0.896486i
$974$		−	30859.2i		−	1.01519i
$975$	−8600.97	−	6616.97i	−0.282514	−	0.217346i
$976$			37956.8i			1.24485i
$977$	−1509.71	+	1509.71i	−0.0494370	+	0.0494370i	−0.731393	−	0.681956i	$-0.761129\pi$
$977$	−1509.71	+	1509.71i	−0.0494370	+	0.0494370i	0.681956	+	0.731393i	$0.261129\pi$
$978$	−20888.2	+	20888.2i	−0.682958	+	0.682958i
$979$	29035.4			0.947880
$980$	42569.7	+	53039.3i	1.38759	+	1.72886i
$981$	5961.99			0.194038
$982$	53891.5	−	53891.5i	1.75127	−	1.75127i
$983$	37722.4	−	37722.4i	1.22397	−	1.22397i	0.257756	−	0.966210i	$-0.417017\pi$
$983$	37722.4	−	37722.4i	1.22397	−	1.22397i	0.966210	−	0.257756i	$-0.0829829\pi$
$984$		−	65036.0i		−	2.10698i
$985$	15196.1	−	44673.8i	0.491560	−	1.44510i
$986$		−	345.618i		−	0.0111630i
$987$	625.069	+	5690.58i	0.0201582	+	0.183519i
$988$	−32121.8	−	32121.8i	−1.03434	−	1.03434i
$989$			14806.5i			0.476055i
$990$	34011.2	+	11569.1i	1.09187	+	0.371404i
$991$	−46087.9			−1.47733			−0.738664	−	0.674074i	$-0.764543\pi$
$991$	−46087.9			−1.47733			−0.738664	+	0.674074i	$0.764543\pi$
$992$	25102.3	+	25102.3i	0.803428	+	0.803428i
$993$	−1516.43	+	1516.43i	−0.0484616	+	0.0484616i
$994$	−63086.0	−	50598.6i	−2.01305	−	1.61458i
$995$	31357.2	−	15439.1i	0.999084	−	0.491913i
$996$	14413.5			0.458542
$997$	29408.5	+	29408.5i	0.934180	+	0.934180i	0.997964	−	0.0637838i	$-0.0203168\pi$
$997$	29408.5	+	29408.5i	0.934180	+	0.934180i	−0.0637838	+	0.997964i	$0.520317\pi$
$998$	−68132.2	−	68132.2i	−2.16101	−	2.16101i
$999$	3198.12			0.101285

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.m.a.13.1	✓	48
5.2	odd	4	inner	105.4.m.a.97.2	yes	48
7.6	odd	2	inner	105.4.m.a.13.2	yes	48
35.27	even	4	inner	105.4.m.a.97.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.m.a.13.1	✓	48	1.1	even	1	trivial
105.4.m.a.13.2	yes	48	7.6	odd	2	inner
105.4.m.a.97.1	yes	48	35.27	even	4	inner
105.4.m.a.97.2	yes	48	5.2	odd	4	inner

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.58711 + 3.58711i) q^{2} +(-2.12132 + 2.12132i) q^{3} -17.7347i q^{4} +(10.0305 - 4.93863i) q^{5} -15.2188i q^{6} +(2.02215 + 18.4095i) q^{7} +(34.9193 + 34.9193i) q^{8} -9.00000i q^{9} +O(q^{10})\)	\(q+(-3.58711 + 3.58711i) q^{2} +(-2.12132 + 2.12132i) q^{3} -17.7347i q^{4} +(10.0305 - 4.93863i) q^{5} -15.2188i q^{6} +(2.02215 + 18.4095i) q^{7} +(34.9193 + 34.9193i) q^{8} -9.00000i q^{9} +(-18.2649 + 53.6957i) q^{10} +70.3785 q^{11} +(37.6209 + 37.6209i) q^{12} +(-20.4623 + 20.4623i) q^{13} +(-73.2906 - 58.7833i) q^{14} +(-10.8014 + 31.7542i) q^{15} -108.641 q^{16} +(0.412364 + 0.412364i) q^{17} +(32.2840 + 32.2840i) q^{18} -88.5161 q^{19} +(-87.5850 - 177.887i) q^{20} +(-43.3422 - 34.7629i) q^{21} +(-252.455 + 252.455i) q^{22} +(37.1006 + 37.1006i) q^{23} -148.150 q^{24} +(76.2199 - 99.0734i) q^{25} -146.801i q^{26} +(19.0919 + 19.0919i) q^{27} +(326.487 - 35.8622i) q^{28} +116.827i q^{29} +(-75.1600 - 152.651i) q^{30} +227.473i q^{31} +(110.353 - 110.353i) q^{32} +(-149.295 + 149.295i) q^{33} -2.95839 q^{34} +(111.201 + 174.669i) q^{35} -159.612 q^{36} +(83.7560 - 83.7560i) q^{37} +(317.517 - 317.517i) q^{38} -86.8142i q^{39} +(522.710 + 177.803i) q^{40} +438.988i q^{41} +(280.171 - 30.7748i) q^{42} +(199.545 + 199.545i) q^{43} -1248.14i q^{44} +(-44.4477 - 90.2741i) q^{45} -266.167 q^{46} +(-72.8580 - 72.8580i) q^{47} +(230.463 - 230.463i) q^{48} +(-334.822 + 74.4538i) q^{49} +(81.9779 + 628.796i) q^{50} -1.74951 q^{51} +(362.892 + 362.892i) q^{52} +(-141.512 - 141.512i) q^{53} -136.969 q^{54} +(705.928 - 347.573i) q^{55} +(-572.236 + 713.460i) q^{56} +(187.771 - 187.771i) q^{57} +(-419.070 - 419.070i) q^{58} +380.867 q^{59} +(563.151 + 191.559i) q^{60} -349.378i q^{61} +(-815.970 - 815.970i) q^{62} +(165.686 - 18.1994i) q^{63} -77.4326i q^{64} +(-104.190 + 306.302i) q^{65} -1071.08i q^{66} +(8.87381 - 8.87381i) q^{67} +(7.31313 - 7.31313i) q^{68} -157.404 q^{69} +(-1025.45 - 227.667i) q^{70} +860.765 q^{71} +(314.274 - 314.274i) q^{72} +(-817.495 + 817.495i) q^{73} +600.883i q^{74} +(48.4795 + 371.853i) q^{75} +1569.80i q^{76} +(142.316 + 1295.63i) q^{77} +(311.412 + 311.412i) q^{78} -698.586i q^{79} +(-1089.72 + 536.539i) q^{80} -81.0000 q^{81} +(-1574.70 - 1574.70i) q^{82} +(191.562 - 191.562i) q^{83} +(-616.508 + 768.659i) q^{84} +(6.17271 + 2.09968i) q^{85} -1431.58 q^{86} +(-247.827 - 247.827i) q^{87} +(2457.57 + 2457.57i) q^{88} +412.560 q^{89} +(483.261 + 164.384i) q^{90} +(-418.079 - 335.323i) q^{91} +(657.967 - 657.967i) q^{92} +(-482.543 - 482.543i) q^{93} +522.699 q^{94} +(-887.857 + 437.148i) q^{95} +468.189i q^{96} +(267.427 + 267.427i) q^{97} +(933.968 - 1468.12i) q^{98} -633.406i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{7} - 168 q^{8}+O(q^{10}) \) 48 * q + 4 * q^7 - 168 * q^8	\( 48 q + 4 q^{7} - 168 q^{8} + 112 q^{11} + 168 q^{15} - 544 q^{16} - 96 q^{21} - 192 q^{22} + 400 q^{23} + 520 q^{25} + 1052 q^{28} - 48 q^{30} - 1344 q^{32} + 392 q^{35} - 1728 q^{36} - 456 q^{37} + 1068 q^{42} + 192 q^{43} - 208 q^{46} + 3528 q^{50} + 672 q^{51} - 1728 q^{53} - 48 q^{56} + 696 q^{57} + 3016 q^{58} + 840 q^{60} - 36 q^{63} - 4720 q^{65} - 4784 q^{67} + 2220 q^{70} - 3088 q^{71} - 1512 q^{72} + 2352 q^{77} + 1416 q^{78} - 3888 q^{81} - 472 q^{85} + 10832 q^{86} + 2128 q^{88} - 5664 q^{91} + 10600 q^{92} - 1368 q^{93} - 6912 q^{95} - 3888 q^{98}+O(q^{100}) \) 48 * q + 4 * q^7 - 168 * q^8 + 112 * q^11 + 168 * q^15 - 544 * q^16 - 96 * q^21 - 192 * q^22 + 400 * q^23 + 520 * q^25 + 1052 * q^28 - 48 * q^30 - 1344 * q^32 + 392 * q^35 - 1728 * q^36 - 456 * q^37 + 1068 * q^42 + 192 * q^43 - 208 * q^46 + 3528 * q^50 + 672 * q^51 - 1728 * q^53 - 48 * q^56 + 696 * q^57 + 3016 * q^58 + 840 * q^60 - 36 * q^63 - 4720 * q^65 - 4784 * q^67 + 2220 * q^70 - 3088 * q^71 - 1512 * q^72 + 2352 * q^77 + 1416 * q^78 - 3888 * q^81 - 472 * q^85 + 10832 * q^86 + 2128 * q^88 - 5664 * q^91 + 10600 * q^92 - 1368 * q^93 - 6912 * q^95 - 3888 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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