LMFDB - Embedded newform 52.4.f.b.31.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [52,4,Mod(31,52)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(52, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("52.31");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 52 = 2^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	52.f (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:	$3.06809932030$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.6
Character	$\chi$	$=$	52.31
Dual form			52.4.f.b.47.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.70773 + 2.25470i) q^{2} +8.10067i q^{3} +(-2.16733 - 7.70082i) q^{4} +(-10.8445 + 10.8445i) q^{5} +(-18.2646 - 13.8337i) q^{6} +(18.4065 - 18.4065i) q^{7} +(21.0642 + 8.26423i) q^{8} -38.6209 q^{9} +(-5.93160 - 42.9704i) q^{10} +(-15.8378 + 15.8378i) q^{11} +(62.3818 - 17.5568i) q^{12} +(-45.8017 - 9.96005i) q^{13} +(10.0678 + 72.9343i) q^{14} +(-87.8474 - 87.8474i) q^{15} +(-54.6053 + 33.3805i) q^{16} +47.6833i q^{17} +(65.9540 - 87.0785i) q^{18} +(90.7289 + 90.7289i) q^{19} +(107.015 + 60.0077i) q^{20} +(149.105 + 149.105i) q^{21} +(-8.66280 - 62.7560i) q^{22} -40.1431 q^{23} +(-66.9458 + 170.635i) q^{24} -110.204i q^{25} +(100.674 - 86.2600i) q^{26} -94.1371i q^{27} +(-181.638 - 101.852i) q^{28} -77.7784 q^{29} +(348.089 - 48.0500i) q^{30} +(116.748 + 116.748i) q^{31} +(17.9881 - 180.123i) q^{32} +(-128.297 - 128.297i) q^{33} +(-107.512 - 81.4302i) q^{34} +399.217i q^{35} +(83.7043 + 297.413i) q^{36} +(81.5814 + 81.5814i) q^{37} +(-359.507 + 49.6261i) q^{38} +(80.6831 - 371.025i) q^{39} +(-318.051 + 138.809i) q^{40} +(-40.2235 + 40.2235i) q^{41} +(-590.817 + 81.5560i) q^{42} -219.561 q^{43} +(156.289 + 87.6381i) q^{44} +(418.823 - 418.823i) q^{45} +(68.5535 - 90.5107i) q^{46} +(266.450 - 266.450i) q^{47} +(-270.404 - 442.340i) q^{48} -334.597i q^{49} +(248.478 + 188.199i) q^{50} -386.267 q^{51} +(22.5669 + 374.298i) q^{52} +349.455 q^{53} +(212.251 + 160.761i) q^{54} -343.504i q^{55} +(539.834 - 235.603i) q^{56} +(-734.965 + 734.965i) q^{57} +(132.824 - 175.367i) q^{58} +(136.636 - 136.636i) q^{59} +(-486.103 + 866.892i) q^{60} -57.4537 q^{61} +(-462.606 + 63.8579i) q^{62} +(-710.875 + 710.875i) q^{63} +(375.405 + 348.159i) q^{64} +(604.706 - 388.683i) q^{65} +(508.366 - 70.1745i) q^{66} +(303.226 + 303.226i) q^{67} +(367.201 - 103.346i) q^{68} -325.186i q^{69} +(-900.113 - 681.753i) q^{70} +(755.177 + 755.177i) q^{71} +(-813.520 - 319.172i) q^{72} +(146.954 + 146.954i) q^{73} +(-323.260 + 44.6226i) q^{74} +892.730 q^{75} +(502.048 - 895.327i) q^{76} +583.035i q^{77} +(698.764 + 815.525i) q^{78} -555.507i q^{79} +(230.172 - 954.158i) q^{80} -280.190 q^{81} +(-22.0011 - 159.383i) q^{82} +(-431.879 - 431.879i) q^{83} +(825.071 - 1471.39i) q^{84} +(-517.100 - 517.100i) q^{85} +(374.950 - 495.044i) q^{86} -630.057i q^{87} +(-464.497 + 202.724i) q^{88} +(904.234 + 904.234i) q^{89} +(229.084 + 1659.55i) q^{90} +(-1026.38 + 659.719i) q^{91} +(87.0035 + 309.135i) q^{92} +(-945.740 + 945.740i) q^{93} +(145.740 + 1055.79i) q^{94} -1967.81 q^{95} +(1459.12 + 145.716i) q^{96} +(-14.4167 + 14.4167i) q^{97} +(754.416 + 571.401i) q^{98} +(611.669 - 611.669i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 2 q^{2} - 20 q^{5} - 16 q^{6} - 40 q^{8} - 332 q^{9} - 96 q^{13} + 204 q^{14} + 52 q^{16} + 330 q^{18} + 500 q^{20} + 224 q^{21} - 48 q^{22} - 496 q^{24} + 570 q^{26} - 356 q^{28} + 560 q^{29} + 292 q^{32}+ \cdots + 3226 q^{98}+O(q^{100}) $ 36 * q + 2 * q^2 - 20 * q^5 - 16 * q^6 - 40 * q^8 - 332 * q^9 - 96 * q^13 + 204 * q^14 + 52 * q^16 + 330 * q^18 + 500 * q^20 + 224 * q^21 - 48 * q^22 - 496 * q^24 + 570 * q^26 - 356 * q^28 + 560 * q^29 + 292 * q^32 + 104 * q^33 - 416 * q^34 - 788 * q^37 - 2788 * q^40 + 1124 * q^41 - 1172 * q^42 - 156 * q^44 - 972 * q^45 - 668 * q^46 + 1332 * q^48 + 1354 * q^50 - 164 * q^52 + 1208 * q^53 + 2272 * q^54 - 1248 * q^57 - 2972 * q^58 + 692 * q^60 + 2632 * q^61 + 596 * q^65 + 3312 * q^66 + 2948 * q^68 - 1008 * q^70 - 908 * q^72 - 196 * q^73 - 1504 * q^74 - 3472 * q^76 - 2688 * q^78 - 1096 * q^80 - 764 * q^81 + 3744 * q^84 + 600 * q^85 - 3952 * q^86 - 2748 * q^89 - 1224 * q^92 - 6128 * q^93 + 2884 * q^94 + 4792 * q^96 - 1820 * q^97 + 3226 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/52\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.70773	+	2.25470i	−0.603773	+	0.797156i
$2$	−1.70773	+	2.25470i	−0.603773	+	0.797156i
$3$			8.10067i			1.55898i	0.626418	+	0.779488i	$0.284520\pi$
$3$			8.10067i			1.55898i	−0.626418	+	0.779488i	$0.715480\pi$
$4$	−2.16733	−	7.70082i	−0.270917	−	0.962603i
$5$	−10.8445	+	10.8445i	−0.969958	+	0.969958i	−0.999562	−	0.0296042i	$-0.990575\pi$
$5$	−10.8445	+	10.8445i	−0.969958	+	0.969958i	0.0296042	+	0.999562i	$0.490575\pi$
$6$	−18.2646	−	13.8337i	−1.24275	−	0.941267i
$7$	18.4065	−	18.4065i	0.993857	−	0.993857i	−0.00612459	−	0.999981i	$-0.501950\pi$
$7$	18.4065	−	18.4065i	0.993857	−	0.993857i	0.999981	+	0.00612459i	$0.00194953\pi$
$8$	21.0642	+	8.26423i	0.930917	+	0.365231i
$9$	−38.6209			−1.43040
$10$	−5.93160	−	42.9704i	−0.187574	−	1.35884i
$11$	−15.8378	+	15.8378i	−0.434115	+	0.434115i	−0.890026	−	0.455911i	$-0.849314\pi$
$11$	−15.8378	+	15.8378i	−0.434115	+	0.434115i	0.455911	+	0.890026i	$0.349314\pi$
$12$	62.3818	−	17.5568i	1.50067	−	0.422352i
$13$	−45.8017	−	9.96005i	−0.977162	−	0.212494i
$13$	−45.8017	−	9.96005i	−0.977162	−	0.212494i
$14$	10.0678	+	72.9343i	0.192195	+	1.39232i
$15$	−87.8474	−	87.8474i	−1.51214	−	1.51214i
$16$	−54.6053	+	33.3805i	−0.853208	+	0.521570i
$17$			47.6833i			0.680289i	0.940373	+	0.340144i	$0.110476\pi$
$17$			47.6833i			0.680289i	−0.940373	+	0.340144i	$0.889524\pi$
$18$	65.9540	−	87.0785i	0.863639	−	1.14026i
$19$	90.7289	+	90.7289i	1.09551	+	1.09551i	0.994929	+	0.100578i	$0.0320693\pi$
$19$	90.7289	+	90.7289i	1.09551	+	1.09551i	0.100578	+	0.994929i	$0.467931\pi$
$20$	107.015	+	60.0077i	1.19646	+	0.670906i
$21$	149.105	+	149.105i	1.54940	+	1.54940i
$22$	−8.66280	−	62.7560i	−0.0839506	−	0.608164i
$23$	−40.1431			−0.363931			−0.181966	−	0.983305i	$-0.558246\pi$
$23$	−40.1431			−0.363931			−0.181966	+	0.983305i	$0.558246\pi$
$24$	−66.9458	+	170.635i	−0.569386	+	1.45128i
$25$		−	110.204i		−	0.881635i
$26$	100.674	−	86.2600i	0.759375	−	0.650653i
$27$		−	94.1371i		−	0.670989i
$28$	−181.638	−	101.852i	−1.22594	−	0.687437i
$29$	−77.7784			−0.498037			−0.249019	−	0.968499i	$-0.580108\pi$
$29$	−77.7784			−0.498037			−0.249019	+	0.968499i	$0.580108\pi$
$30$	348.089	−	48.0500i	2.11840	−	0.292423i
$31$	116.748	+	116.748i	0.676407	+	0.676407i	0.959185	−	0.282778i	$-0.0912561\pi$
$31$	116.748	+	116.748i	0.676407	+	0.676407i	−0.282778	+	0.959185i	$0.591256\pi$
$32$	17.9881	−	180.123i	0.0993713	−	0.995050i
$33$	−128.297	−	128.297i	−0.676775	−	0.676775i
$34$	−107.512	−	81.4302i	−0.542297	−	0.410740i
$35$			399.217i			1.92800i
$36$	83.7043	+	297.413i	0.387520	+	1.37691i
$37$	81.5814	+	81.5814i	0.362484	+	0.362484i	0.864727	−	0.502243i	$-0.167492\pi$
$37$	81.5814	+	81.5814i	0.362484	+	0.362484i	−0.502243	+	0.864727i	$0.667492\pi$
$38$	−359.507	+	49.6261i	−1.53473	+	0.211853i
$39$	80.6831	−	371.025i	0.331273	−	1.52337i
$40$	−318.051	+	138.809i	−1.25721	+	0.548692i
$41$	−40.2235	+	40.2235i	−0.153216	+	0.153216i	−0.779553	−	0.626337i	$-0.784554\pi$
$41$	−40.2235	+	40.2235i	−0.153216	+	0.153216i	0.626337	+	0.779553i	$0.284554\pi$
$42$	−590.817	+	81.5560i	−2.17060	+	0.299628i
$43$	−219.561			−0.778668			−0.389334	−	0.921097i	$-0.627295\pi$
$43$	−219.561			−0.778668			−0.389334	+	0.921097i	$0.627295\pi$
$44$	156.289	+	87.6381i	0.535489	+	0.300271i
$45$	418.823	−	418.823i	1.38743	−	1.38743i
$46$	68.5535	−	90.5107i	0.219732	−	0.290110i
$47$	266.450	−	266.450i	0.826930	−	0.826930i	−0.160161	−	0.987091i	$-0.551201\pi$
$47$	266.450	−	266.450i	0.826930	−	0.826930i	0.987091	+	0.160161i	$0.0512014\pi$
$48$	−270.404	−	442.340i	−0.813115	−	1.33013i
$49$		−	334.597i		−	0.975502i
$50$	248.478	+	188.199i	0.702801	+	0.532307i
$51$	−386.267			−1.06055
$52$	22.5669	+	374.298i	0.0601821	+	0.998187i
$53$	349.455			0.905686			0.452843	−	0.891590i	$-0.350410\pi$
$53$	349.455			0.905686			0.452843	+	0.891590i	$0.350410\pi$
$54$	212.251	+	160.761i	0.534883	+	0.405125i
$55$		−	343.504i		−	0.842146i
$56$	539.834	−	235.603i	1.28819	−	0.562211i
$57$	−734.965	+	734.965i	−1.70787	+	1.70787i
$58$	132.824	−	175.367i	0.300702	−	0.397014i
$59$	136.636	−	136.636i	0.301500	−	0.301500i	−0.540101	−	0.841600i	$-0.681614\pi$
$59$	136.636	−	136.636i	0.301500	−	0.301500i	0.841600	+	0.540101i	$0.181614\pi$
$60$	−486.103	+	866.892i	−1.04593	+	1.86525i
$61$	−57.4537			−0.120593			−0.0602966	−	0.998181i	$-0.519205\pi$
$61$	−57.4537			−0.120593			−0.0602966	+	0.998181i	$0.519205\pi$
$62$	−462.606	+	63.8579i	−0.947598	+	0.130806i
$63$	−710.875	+	710.875i	−1.42162	+	1.42162i
$64$	375.405	+	348.159i	0.733213	+	0.679999i
$65$	604.706	−	388.683i	1.15392	−	0.741696i
$66$	508.366	−	70.1745i	0.948113	−	0.130877i
$67$	303.226	+	303.226i	0.552910	+	0.552910i	0.927280	−	0.374370i	$-0.122141\pi$
$67$	303.226	+	303.226i	0.552910	+	0.552910i	−0.374370	+	0.927280i	$0.622141\pi$
$68$	367.201	−	103.346i	0.654848	−	0.184301i
$69$		−	325.186i		−	0.567360i
$70$	−900.113	−	681.753i	−1.53692	−	1.16407i
$71$	755.177	+	755.177i	1.26230	+	1.26230i	0.949977	+	0.312319i	$0.101106\pi$
$71$	755.177	+	755.177i	1.26230	+	1.26230i	0.312319	+	0.949977i	$0.398894\pi$
$72$	−813.520	−	319.172i	−1.33159	−	0.522427i
$73$	146.954	+	146.954i	0.235611	+	0.235611i	0.815030	−	0.579419i	$-0.196720\pi$
$73$	146.954	+	146.954i	0.235611	+	0.235611i	−0.579419	+	0.815030i	$0.696720\pi$
$74$	−323.260	+	44.6226i	−0.507814	+	0.0700983i
$75$	892.730			1.37445
$76$	502.048	−	895.327i	0.757748	−	1.35133i
$77$			583.035i			0.862896i
$78$	698.764	+	815.525i	1.01435	+	1.18385i
$79$		−	555.507i		−	0.791132i	−0.918438	−	0.395566i	$-0.870548\pi$
$79$		−	555.507i		−	0.791132i	0.918438	−	0.395566i	$-0.129452\pi$
$80$	230.172	−	954.158i	0.321675	−	1.33348i
$81$	−280.190			−0.384349
$82$	−22.0011	−	159.383i	−0.0296294	−	0.214645i
$83$	−431.879	−	431.879i	−0.571144	−	0.571144i	0.361304	−	0.932448i	$-0.382332\pi$
$83$	−431.879	−	431.879i	−0.571144	−	0.571144i	−0.932448	+	0.361304i	$0.882332\pi$
$84$	825.071	−	1471.39i	1.07170	−	1.91121i
$85$	−517.100	−	517.100i	−0.659851	−	0.659851i
$86$	374.950	−	495.044i	0.470139	−	0.620720i
$87$		−	630.057i		−	0.776428i
$88$	−464.497	+	202.724i	−0.562677	+	0.245573i
$89$	904.234	+	904.234i	1.07695	+	1.07695i	0.996781	+	0.0801690i	$0.0255460\pi$
$89$	904.234	+	904.234i	1.07695	+	1.07695i	0.0801690	+	0.996781i	$0.474454\pi$
$90$	229.084	+	1659.55i	0.268306	+	1.94369i
$91$	−1026.38	+	659.719i	−1.18235	+	0.759971i
$92$	87.0035	+	309.135i	0.0985950	+	0.350321i
$93$	−945.740	+	945.740i	−1.05450	+	1.05450i
$94$	145.740	+	1055.79i	0.159915	+	1.15847i
$95$	−1967.81			−2.12519
$96$	1459.12	+	145.716i	1.55126	+	0.154917i
$97$	−14.4167	+	14.4167i	−0.0150906	+	0.0150906i	−0.714612	−	0.699521i	$-0.753397\pi$
$97$	−14.4167	+	14.4167i	−0.0150906	+	0.0150906i	0.699521	+	0.714612i	$0.253397\pi$
$98$	754.416	+	571.401i	0.777628	+	0.588982i
$99$	611.669	−	611.669i	0.620960	−	0.620960i
$100$	−848.665	+	238.850i	−0.848665	+	0.238850i
$101$			240.367i			0.236806i	0.992966	+	0.118403i	$0.0377775\pi$
$101$			240.367i			0.236806i	−0.992966	+	0.118403i	$0.962223\pi$
$102$	659.639	−	870.916i	0.640333	−	0.845427i
$103$	1420.87			1.35924			0.679622	−	0.733562i	$-0.262144\pi$
$103$	1420.87			1.35924			0.679622	+	0.733562i	$0.262144\pi$
$104$	−882.467	−	588.317i	−0.832048	−	0.554704i
$105$	−3233.92			−3.00570
$106$	−596.775	+	787.916i	−0.546829	+	0.721974i
$107$		−	889.202i		−	0.803387i	−0.915774	−	0.401693i	$-0.868422\pi$
$107$		−	889.202i		−	0.803387i	0.915774	−	0.401693i	$-0.131578\pi$
$108$	−724.933	+	204.026i	−0.645896	+	0.181782i
$109$	1258.11	−	1258.11i	1.10555	−	1.10555i	0.111819	−	0.993729i	$-0.464332\pi$
$109$	1258.11	−	1258.11i	1.10555	−	1.10555i	0.993729	−	0.111819i	$-0.0356677\pi$
$110$	774.498	+	586.611i	0.671322	+	0.508465i
$111$	−660.864	+	660.864i	−0.565103	+	0.565103i
$112$	−390.675	+	1619.51i	−0.329601	+	1.36633i
$113$	−1563.96			−1.30199			−0.650997	−	0.759080i	$-0.725649\pi$
$113$	−1563.96			−1.30199			−0.650997	+	0.759080i	$0.725649\pi$
$114$	−402.005	−	2912.25i	−0.330274	−	2.39260i
$115$	435.330	−	435.330i	0.352998	−	0.352998i
$116$	168.572	+	598.958i	0.134927	+	0.479412i
$117$	1768.90	+	384.666i	1.39774	+	0.303952i
$118$	74.7359	+	541.410i	0.0583051	+	0.422380i
$119$	877.683	+	877.683i	0.676110	+	0.676110i
$120$	−1124.45	−	2576.43i	−0.855397	−	1.95996i
$121$			829.331i			0.623088i
$122$	98.1152	−	129.541i	0.0728109	−	0.0961317i
$123$	−325.837	−	325.837i	−0.238860	−	0.238860i
$124$	646.026	−	1152.09i	0.467861	−	0.834361i
$125$	−160.450	−	160.450i	−0.114809	−	0.114809i
$126$	−388.828	−	2816.79i	−0.274917	−	1.99158i
$127$	−661.895			−0.462470			−0.231235	−	0.972898i	$-0.574277\pi$
$127$	−661.895			−0.462470			−0.231235	+	0.972898i	$0.574277\pi$
$128$	−1426.08	+	251.864i	−0.984760	+	0.173920i
$129$		−	1778.59i		−	1.21392i
$130$	−156.309	+	2027.20i	−0.105456	+	1.36767i
$131$		−	144.173i		−	0.0961560i	−0.998844	−	0.0480780i	$-0.984690\pi$
$131$		−	144.173i		−	0.0961560i	0.998844	−	0.0480780i	$-0.0153096\pi$
$132$	−709.928	+	1266.05i	−0.468116	+	0.834814i
$133$	3340.00			2.17755
$134$	−1201.51	+	165.856i	−0.774588	+	0.106924i
$135$	1020.87	+	1020.87i	0.650831	+	0.650831i
$136$	−394.066	+	1004.41i	−0.248462	+	0.633292i
$137$	−1727.12	−	1727.12i	−1.07707	−	1.07707i	−0.996771	−	0.0802948i	$-0.974414\pi$
$137$	−1727.12	−	1727.12i	−1.07707	−	1.07707i	−0.0802948	−	0.996771i	$-0.525586\pi$
$138$	733.197	+	555.330i	0.452275	+	0.342557i
$139$			564.355i			0.344374i	0.985064	+	0.172187i	$0.0550833\pi$
$139$			564.355i			0.344374i	−0.985064	+	0.172187i	$0.944917\pi$
$140$	3074.30	−	865.235i	1.85590	−	0.522326i
$141$	2158.42	+	2158.42i	1.28916	+	1.28916i
$142$	−2992.33	+	413.060i	−1.76839	+	0.244107i
$143$	883.142	−	567.652i	0.516448	−	0.331954i
$144$	2108.91	−	1289.18i	1.22043	−	0.746056i
$145$	843.464	−	843.464i	0.483075	−	0.483075i
$146$	−582.293	+	80.3794i	−0.330075	+	0.0455633i
$147$	2710.46			1.52078
$148$	451.430	−	805.058i	0.250725	−	0.447131i
$149$	151.596	−	151.596i	0.0833504	−	0.0833504i	−0.664202	−	0.747553i	$-0.731229\pi$
$149$	151.596	−	151.596i	0.0833504	−	0.0833504i	0.747553	+	0.664202i	$0.231229\pi$
$150$	−1524.54	+	2012.84i	−0.829854	+	1.09565i
$151$	−2199.31	+	2199.31i	−1.18528	+	1.18528i	−0.206925	+	0.978357i	$0.566346\pi$
$151$	−2199.31	+	2199.31i	−1.18528	+	1.18528i	−0.978357	+	0.206925i	$0.933654\pi$
$152$	1161.33	+	2660.94i	0.619714	+	1.41994i
$153$		−	1841.57i		−	0.973088i
$154$	−1314.57	−	995.665i	−0.687863	−	0.520993i
$155$	−2532.14			−1.31217
$156$	−3032.06	+	182.807i	−1.55615	+	0.0938225i
$157$	−559.642			−0.284486			−0.142243	−	0.989832i	$-0.545431\pi$
$157$	−559.642			−0.284486			−0.142243	+	0.989832i	$0.545431\pi$
$158$	1252.50	+	948.655i	0.630656	+	0.477664i
$159$			2830.82i			1.41194i
$160$	1758.27	+	2148.41i	0.868771	+	1.06154i
$161$	−738.894	+	738.894i	−0.361696	+	0.361696i
$162$	478.489	−	631.745i	0.232059	−	0.306386i
$163$	1733.66	−	1733.66i	0.833071	−	0.833071i	−0.154864	−	0.987936i	$-0.549494\pi$
$163$	1733.66	−	1733.66i	0.833071	−	0.833071i	0.987936	+	0.154864i	$0.0494940\pi$
$164$	396.932	+	222.576i	0.188995	+	0.105977i
$165$	2782.61			1.31289
$166$	1711.29	−	236.226i	0.800132	−	0.110450i
$167$	1357.44	−	1357.44i	0.628995	−	0.628995i	−0.318820	−	0.947815i	$-0.603287\pi$
$167$	1357.44	−	1357.44i	0.628995	−	0.628995i	0.947815	+	0.318820i	$0.103287\pi$
$168$	1908.55	+	4373.02i	0.876473	+	2.00825i
$169$	1998.59	+	912.375i	0.909693	+	0.415282i
$170$	2048.97	−	282.839i	0.924405	−	0.127604i
$171$	−3504.03	−	3504.03i	−1.56702	−	1.56702i
$172$	475.861	+	1690.80i	0.210954	+	0.749548i
$173$			851.942i			0.374404i	0.982321	+	0.187202i	$0.0599419\pi$
$173$			851.942i			0.374404i	−0.982321	+	0.187202i	$0.940058\pi$
$174$	1420.59	+	1075.97i	0.618934	+	0.468786i
$175$	−2028.48	−	2028.48i	−0.876219	−	0.876219i
$176$	336.154	−	1393.50i	0.143969	−	0.596812i
$177$	1106.84	+	1106.84i	0.470031	+	0.470031i
$178$	−3582.96	+	494.590i	−1.50873	+	0.208264i
$179$	126.713			0.0529104			0.0264552	−	0.999650i	$-0.491578\pi$
$179$	126.713			0.0529104			0.0264552	+	0.999650i	$0.491578\pi$
$180$	−4133.01	−	2317.55i	−1.71142	−	0.959667i
$181$		−	3440.95i		−	1.41306i	−0.707684	−	0.706529i	$-0.750260\pi$
$181$		−	3440.95i		−	1.41306i	0.707684	−	0.706529i	$-0.249740\pi$
$182$	265.307	−	3440.79i	0.108054	−	1.40137i
$183$		−	465.413i		−	0.188002i
$184$	−845.585	−	331.752i	−0.338790	−	0.132919i
$185$	−1769.41			−0.703188
$186$	−517.292	−	3747.42i	−0.203923	−	1.47728i
$187$	−755.198	−	755.198i	−0.295324	−	0.295324i
$188$	−2629.37	−	1474.40i	−1.02003	−	0.571976i
$189$	−1732.73	−	1732.73i	−0.666867	−	0.666867i
$190$	3360.49	−	4436.82i	1.28313	−	1.69411i
$191$		−	185.003i		−	0.0700857i	−0.999386	−	0.0350429i	$-0.988843\pi$
$191$		−	185.003i		−	0.0700857i	0.999386	−	0.0350429i	$-0.0111568\pi$
$192$	−2820.33	+	3041.03i	−1.06010	+	1.14306i
$193$	−1510.74	−	1510.74i	−0.563447	−	0.563447i	0.366838	−	0.930285i	$-0.380440\pi$
$193$	−1510.74	−	1510.74i	−0.563447	−	0.563447i	−0.930285	+	0.366838i	$0.880440\pi$
$194$	−7.88549	−	57.1249i	−0.00291827	−	0.0211409i
$195$	3148.60	+	4898.53i	1.15629	+	1.79893i
$196$	−2576.67	+	725.183i	−0.939021	+	0.264280i
$197$	−2873.24	+	2873.24i	−1.03913	+	1.03913i	−0.0399323	+	0.999202i	$0.512714\pi$
$197$	−2873.24	+	2873.24i	−1.03913	+	1.03913i	−0.999202	+	0.0399323i	$0.987286\pi$
$198$	334.565	+	2423.69i	0.120083	+	0.869921i
$199$	3428.50			1.22131			0.610653	−	0.791899i	$-0.290907\pi$
$199$	3428.50			1.22131			0.610653	+	0.791899i	$0.290907\pi$
$200$	910.754	−	2321.37i	0.322000	−	0.820729i
$201$	−2456.34	+	2456.34i	−0.861973	+	0.861973i
$202$	−541.955	−	410.482i	−0.188772	−	0.142977i
$203$	−1431.63	+	1431.63i	−0.494978	+	0.494978i
$204$	837.169	+	2974.58i	0.287321	+	1.02089i
$205$		−	872.403i		−	0.297226i
$206$	−2426.45	+	3203.63i	−0.820675	+	1.08353i
$207$	1550.36			0.520569
$208$	2833.49	−	985.011i	0.944554	−	0.328357i
$209$	−2873.89			−0.951152
$210$	5522.66	−	7291.52i	1.81476	−	2.39601i
$211$			1491.53i			0.486639i	0.969946	+	0.243320i	$0.0782364\pi$
$211$			1491.53i			0.486639i	−0.969946	+	0.243320i	$0.921764\pi$
$212$	−757.386	−	2691.09i	−0.245365	−	0.871816i
$213$	−6117.44	+	6117.44i	−1.96789	+	1.96789i
$214$	2004.88	+	1518.51i	0.640425	+	0.485063i
$215$	2381.02	−	2381.02i	0.755275	−	0.755275i
$216$	777.971	−	1982.93i	0.245066	−	0.624635i
$217$	4297.85			1.34450
$218$	688.147	+	4985.15i	0.213795	+	1.54879i
$219$	−1190.42	+	1190.42i	−0.367312	+	0.367312i
$220$	−2645.26	+	744.487i	−0.810652	+	0.228151i
$221$	474.929	−	2183.98i	0.144557	−	0.664753i
$222$	−361.473	−	2618.63i	−0.109282	−	0.791670i
$223$	−391.815	−	391.815i	−0.117659	−	0.117659i	0.645826	−	0.763485i	$-0.276513\pi$
$223$	−391.815	−	391.815i	−0.117659	−	0.117659i	−0.763485	+	0.645826i	$0.776513\pi$
$224$	−2984.34	−	3646.54i	−0.890177	−	1.08770i
$225$			4256.19i			1.26109i
$226$	2670.82	−	3526.27i	0.786109	−	1.03789i
$227$	−154.544	−	154.544i	−0.0451869	−	0.0451869i	0.684152	−	0.729339i	$-0.260172\pi$
$227$	−154.544	−	154.544i	−0.0451869	−	0.0451869i	−0.729339	+	0.684152i	$0.760172\pi$
$228$	7252.75	+	4066.92i	2.10669	+	1.18131i
$229$	−4629.21	−	4629.21i	−1.33584	−	1.33584i	−0.900050	−	0.435787i	$-0.856470\pi$
$229$	−4629.21	−	4629.21i	−1.33584	−	1.33584i	−0.435787	−	0.900050i	$-0.643530\pi$
$230$	238.113	+	1724.96i	0.0682640	+	0.494525i
$231$	−4722.98			−1.34523
$232$	−1638.34	−	642.778i	−0.463632	−	0.181899i
$233$			996.172i			0.280092i	0.990145	+	0.140046i	$0.0447250\pi$
$233$			996.172i			0.280092i	−0.990145	+	0.140046i	$0.955275\pi$
$234$	−3888.11	+	3331.44i	−1.08621	+	0.930697i
$235$			5779.01i			1.60417i
$236$	−1348.35	−	756.074i	−0.371906	−	0.208543i
$237$	4499.98			1.23336
$238$	−3477.75	+	480.067i	−0.947182	+	0.130748i
$239$	−2894.45	−	2894.45i	−0.783375	−	0.783375i	0.197024	−	0.980399i	$-0.436872\pi$
$239$	−2894.45	−	2894.45i	−0.783375	−	0.783375i	−0.980399	+	0.197024i	$0.936872\pi$
$240$	7729.32	+	1864.55i	2.07886	+	0.501484i
$241$	3197.72	+	3197.72i	0.854704	+	0.854704i	0.990708	−	0.136005i	$-0.0434262\pi$
$241$	3197.72	+	3197.72i	0.854704	+	0.854704i	−0.136005	+	0.990708i	$0.543426\pi$
$242$	−1869.89	−	1416.27i	−0.496699	−	0.376204i
$243$		−	4811.43i		−	1.27018i
$244$	124.521	+	442.440i	0.0326707	+	0.116083i
$245$	3628.52	+	3628.52i	0.946196	+	0.946196i
$246$	1291.11	−	178.224i	0.334626	−	0.0461915i
$247$	−3251.88	−	5059.21i	−0.837700	−	1.30328i
$248$	1494.38	+	3424.05i	0.382634	+	0.876723i
$249$	3498.51	−	3498.51i	0.890399	−	0.890399i
$250$	635.772	−	87.7616i	0.160839	−	0.0222021i
$251$	2213.15			0.556544			0.278272	−	0.960502i	$-0.410238\pi$
$251$	2213.15			0.556544			0.278272	+	0.960502i	$0.410238\pi$
$252$	7015.02	+	3933.62i	1.75359	+	0.983313i
$253$	635.777	−	635.777i	0.157988	−	0.157988i
$254$	1130.34	−	1492.37i	0.279227	−	0.368661i
$255$	4188.86	−	4188.86i	1.02869	−	1.02869i
$256$	1867.49	−	3645.51i	0.455929	−	0.890016i
$257$		−	3065.39i		−	0.744024i	−0.928228	−	0.372012i	$-0.878668\pi$
$257$		−	3065.39i		−	0.744024i	0.928228	−	0.372012i	$-0.121332\pi$
$258$	4010.19	+	3037.35i	0.967687	+	0.732934i
$259$	3003.25			0.720514
$260$	−4303.78	−	3814.33i	−1.02657	−	0.909825i
$261$	3003.87			0.712395
$262$	325.066	+	246.208i	0.0766514	+	0.0580564i
$263$			5423.27i			1.27153i	0.771882	+	0.635766i	$0.219316\pi$
$263$			5423.27i			1.27153i	−0.771882	+	0.635766i	$0.780684\pi$
$264$	−1642.20	−	3762.74i	−0.382842	−	0.877200i
$265$	−3789.65	+	3789.65i	−0.878477	+	0.878477i
$266$	−5703.81	+	7530.69i	−1.31475	+	1.73585i
$267$	−7324.90	+	7324.90i	−1.67894	+	1.67894i
$268$	1677.90	−	2992.28i	0.382440	−	0.682025i
$269$	−856.554			−0.194145			−0.0970725	−	0.995277i	$-0.530948\pi$
$269$	−856.554			−0.194145			−0.0970725	+	0.995277i	$0.530948\pi$
$270$	−4045.11	+	558.384i	−0.911768	+	0.125860i
$271$	1751.45	−	1751.45i	0.392594	−	0.392594i	−0.483017	−	0.875611i	$-0.660459\pi$
$271$	1751.45	−	1751.45i	0.392594	−	0.392594i	0.875611	+	0.483017i	$0.160459\pi$
$272$	−1591.69	−	2603.77i	−0.354818	−	0.580428i
$273$	−5344.17	−	8314.35i	−1.18478	−	1.84325i
$274$	6843.60	−	944.686i	1.50889	−	0.208287i
$275$	1745.39	+	1745.39i	0.382731	+	0.382731i
$276$	−2504.20	+	704.787i	−0.546142	+	0.153707i
$277$			3055.06i			0.662675i	0.943512	+	0.331338i	$0.107500\pi$
$277$			3055.06i			0.662675i	−0.943512	+	0.331338i	$0.892500\pi$
$278$	−1272.45	−	963.765i	−0.274520	−	0.207924i
$279$	−4508.92	−	4508.92i	−0.967535	−	0.967535i
$280$	−3299.22	+	8409.20i	−0.704164	+	1.79481i
$281$	5940.13	+	5940.13i	1.26106	+	1.26106i	0.950579	+	0.310482i	$0.100491\pi$
$281$	5940.13	+	5940.13i	1.26106	+	1.26106i	0.310482	+	0.950579i	$0.399509\pi$
$282$	−8552.59	+	1180.59i	−1.80603	+	0.249303i
$283$	7602.82			1.59696			0.798482	−	0.602018i	$-0.205637\pi$
$283$	7602.82			1.59696			0.798482	+	0.602018i	$0.205637\pi$
$284$	4178.77	−	7452.21i	0.873113	−	1.55707i
$285$		−	15940.6i		−	3.31312i
$286$	−228.282	+	2960.61i	−0.0471978	+	0.612114i
$287$			1480.75i			0.304549i
$288$	−694.718	+	6956.53i	−0.142141	+	1.42332i
$289$	2639.30			0.537207
$290$	461.350	+	3342.17i	0.0934187	+	0.676754i
$291$	−116.785	−	116.785i	−0.0235259	−	0.0235259i
$292$	813.167	−	1450.16i	0.162969	−	0.290631i
$293$	−3553.37	−	3553.37i	−0.708499	−	0.708499i	0.257721	−	0.966219i	$-0.417029\pi$
$293$	−3553.37	−	3553.37i	−0.708499	−	0.708499i	−0.966219	+	0.257721i	$0.917029\pi$
$294$	−4628.73	+	6111.28i	−0.918208	+	1.21230i
$295$			2963.49i			0.584884i
$296$	1044.24	+	2392.66i	0.205052	+	0.469832i
$297$	1490.92	+	1490.92i	0.291286	+	0.291286i
$298$	82.9185	+	600.687i	0.0161186	+	0.116768i
$299$	1838.62	+	399.828i	0.355620	+	0.0773332i
$300$	−1934.84	−	6874.75i	−0.372360	−	1.32305i
$301$	−4041.34	+	4041.34i	−0.773884	+	0.773884i
$302$	−1202.96	−	8714.61i	−0.229214	−	1.66050i
$303$	−1947.14			−0.369175
$304$	−7982.86	−	1925.71i	−1.50608	−	0.363312i
$305$	623.054	−	623.054i	0.116970	−	0.116970i
$306$	4152.19	+	3144.91i	0.775703	+	0.587524i
$307$	−5150.34	+	5150.34i	−0.957478	+	0.957478i	−0.999132	−	0.0416544i	$-0.986737\pi$
$307$	−5150.34	+	5150.34i	−0.957478	+	0.957478i	0.0416544	+	0.999132i	$0.486737\pi$
$308$	4489.85	−	1263.63i	0.830626	−	0.233773i
$309$			11510.0i			2.11903i
$310$	4324.21	−	5709.22i	0.792254	−	1.04601i
$311$	4671.07			0.851678			0.425839	−	0.904799i	$-0.359979\pi$
$311$	4671.07			0.851678			0.425839	+	0.904799i	$0.359979\pi$
$312$	4765.76	−	7148.57i	0.864770	−	1.29714i
$313$	313.540			0.0566208			0.0283104	−	0.999599i	$-0.490987\pi$
$313$	313.540			0.0566208			0.0283104	+	0.999599i	$0.490987\pi$
$314$	955.716	−	1261.82i	0.171765	−	0.226780i
$315$		−	15418.1i		−	2.75781i
$316$	−4277.86	+	1203.97i	−0.761546	+	0.214331i
$317$	4783.31	−	4783.31i	0.847499	−	0.847499i	−0.142321	−	0.989821i	$-0.545457\pi$
$317$	4783.31	−	4783.31i	0.847499	−	0.847499i	0.989821	+	0.142321i	$0.0454565\pi$
$318$	−6382.65	−	4834.28i	−1.12554	−	0.852493i
$319$	1231.84	−	1231.84i	0.216206	−	0.216206i
$320$	−7846.66	+	295.464i	−1.37076	+	0.0516154i
$321$	7203.13			1.25246
$322$	−404.153	−	2927.81i	−0.0699459	−	0.506710i
$323$	−4326.26	+	4326.26i	−0.745262	+	0.745262i
$324$	607.266	+	2157.70i	0.104126	+	0.369975i
$325$	−1097.64	+	5047.55i	−0.187342	+	0.861501i
$326$	948.261	+	6869.50i	0.161102	+	1.16707i
$327$	10191.5	+	10191.5i	1.72352	+	1.72352i
$328$	−1179.69	+	514.861i	−0.198590	+	0.0866721i
$329$		−	9808.81i		−	1.64370i
$330$	−4751.94	+	6273.95i	−0.792684	+	1.04657i
$331$	8121.33	+	8121.33i	1.34861	+	1.34861i	0.887178	+	0.461428i	$0.152663\pi$
$331$	8121.33	+	8121.33i	1.34861	+	1.34861i	0.461428	+	0.887178i	$0.347337\pi$
$332$	−2389.80	+	4261.85i	−0.395052	+	0.704517i
$333$	−3150.75	−	3150.75i	−0.518498	−	0.518498i
$334$	742.483	+	5378.77i	0.121637	+	0.881178i
$335$	−6576.64			−1.07260
$336$	−13119.1	−	3164.73i	−2.13008	−	0.513840i
$337$		−	6458.66i		−	1.04399i	−0.852948	−	0.521996i	$-0.825188\pi$
$337$		−	6458.66i		−	1.04399i	0.852948	−	0.521996i	$-0.174812\pi$
$338$	−5470.19	+	2948.14i	−0.880293	+	0.474431i
$339$		−	12669.2i		−	2.02978i
$340$	−2861.37	+	5102.82i	−0.456410	+	0.813939i
$341$	−3698.06			−0.587277
$342$	13884.5	−	1916.60i	2.19528	−	0.303035i
$343$	154.666	+	154.666i	0.0243474	+	0.0243474i
$344$	−4624.88	−	1814.50i	−0.724875	−	0.284393i
$345$	3526.47	+	3526.47i	0.550315	+	0.550315i
$346$	−1920.87	−	1454.88i	−0.298459	−	0.226055i
$347$		−	3288.39i		−	0.508732i	−0.967108	−	0.254366i	$-0.918133\pi$
$347$		−	3288.39i		−	0.508732i	0.967108	−	0.254366i	$-0.0818668\pi$
$348$	−4851.96	+	1365.54i	−0.747392	+	0.210347i
$349$	−1898.84	−	1898.84i	−0.291240	−	0.291240i	0.546330	−	0.837570i	$-0.316024\pi$
$349$	−1898.84	−	1898.84i	−0.291240	−	0.291240i	−0.837570	+	0.546330i	$0.816024\pi$
$350$	8037.68	−	1109.52i	1.22752	−	0.169446i
$351$	−937.611	+	4311.64i	−0.142581	+	0.655665i
$352$	2567.86	+	3137.64i	0.388828	+	0.475105i
$353$	2676.26	−	2676.26i	0.403521	−	0.403521i	−0.475951	−	0.879472i	$-0.657896\pi$
$353$	2676.26	−	2676.26i	0.403521	−	0.403521i	0.879472	+	0.475951i	$0.157896\pi$
$354$	−4385.79	+	605.411i	−0.658480	+	0.0908962i
$355$	−16379.0			−2.44875
$356$	5003.57	−	8923.12i	0.744912	−	1.32844i
$357$	−7109.82	+	7109.82i	−1.05404	+	1.05404i
$358$	−216.391	+	285.700i	−0.0319459	+	0.0421779i
$359$	794.530	−	794.530i	0.116807	−	0.116807i	−0.646287	−	0.763094i	$-0.723679\pi$
$359$	794.530	−	794.530i	0.116807	−	0.116807i	0.763094	+	0.646287i	$0.223679\pi$
$360$	12283.4	−	5360.94i	1.79832	−	0.784851i
$361$			9604.47i			1.40027i
$362$	7758.30	+	5876.20i	1.12643	+	0.853166i
$363$	−6718.14			−0.971379
$364$	7304.88	+	6474.13i	1.05187	+	0.932243i
$365$	−3187.27			−0.457066
$366$	1049.37	+	794.799i	0.149867	+	0.113510i
$367$		−	3887.34i		−	0.552908i	−0.961027	−	0.276454i	$-0.910841\pi$
$367$		−	3887.34i		−	0.552908i	0.961027	−	0.276454i	$-0.0891594\pi$
$368$	2192.03	−	1340.00i	0.310509	−	0.189816i
$369$	1553.47	−	1553.47i	0.219161	−	0.219161i
$370$	3021.67	−	3989.49i	0.424566	−	0.560550i
$371$	6432.24	−	6432.24i	0.900122	−	0.900122i
$372$	9332.71	+	5233.24i	1.30075	+	0.729384i
$373$	−4155.95			−0.576909			−0.288454	−	0.957494i	$-0.593141\pi$
$373$	−4155.95			−0.576909			−0.288454	+	0.957494i	$0.593141\pi$
$374$	2992.41	−	413.071i	0.413727	−	0.0571107i
$375$	1299.75	−	1299.75i	0.178984	−	0.178984i
$376$	7814.57	−	3410.56i	1.07182	−	0.467783i
$377$	3562.38	+	774.677i	0.486663	+	0.105830i
$378$	6865.83	−	947.755i	0.934233	−	0.128961i
$379$	−7417.48	−	7417.48i	−1.00530	−	1.00530i	−0.999986	−	0.00531812i	$-0.998307\pi$
$379$	−7417.48	−	7417.48i	−1.00530	−	1.00530i	−0.00531812	−	0.999986i	$-0.501693\pi$
$380$	4264.90	+	15153.8i	0.575749	+	2.04572i
$381$		−	5361.79i		−	0.720979i
$382$	417.127	+	315.935i	0.0558693	+	0.0423159i
$383$	21.8159	+	21.8159i	0.00291054	+	0.00291054i	0.708561	−	0.705650i	$-0.249345\pi$
$383$	21.8159	+	21.8159i	0.00291054	+	0.00291054i	−0.705650	+	0.708561i	$0.749345\pi$
$384$	−2040.27	−	11552.2i	−0.271138	−	1.53522i
$385$	−6322.70	−	6322.70i	−0.836973	−	0.836973i
$386$	5986.19	−	826.330i	0.789350	−	0.108961i
$387$	8479.64			1.11381
$388$	142.266	+	79.7744i	0.0186146	+	0.0104380i
$389$			12539.7i			1.63442i	0.576340	+	0.817210i	$0.304480\pi$
$389$			12539.7i			1.63442i	−0.576340	+	0.817210i	$0.695520\pi$
$390$	−16421.6	−	1266.21i	−2.13216	−	0.164403i
$391$		−	1914.16i		−	0.247578i
$392$	2765.19	−	7048.04i	0.356283	−	0.908112i
$393$	1167.90			0.149905
$394$	−1571.58	−	11385.0i	−0.200951	−	1.45575i
$395$	6024.17	+	6024.17i	0.767365	+	0.767365i
$396$	−6036.04	−	3384.66i	−0.765966	−	0.429509i
$397$	5018.62	+	5018.62i	0.634451	+	0.634451i	0.949181	−	0.314730i	$-0.101914\pi$
$397$	5018.62	+	5018.62i	0.634451	+	0.634451i	−0.314730	+	0.949181i	$0.601914\pi$
$398$	−5854.94	+	7730.23i	−0.737391	+	0.973571i
$399$			27056.3i			3.39475i
$400$	3678.68	+	6017.75i	0.459834	+	0.752219i
$401$	6793.04	+	6793.04i	0.845956	+	0.845956i	0.989626	−	0.143670i	$-0.0458903\pi$
$401$	6793.04	+	6793.04i	0.845956	+	0.845956i	−0.143670	+	0.989626i	$0.545890\pi$
$402$	−1343.54	−	9733.05i	−0.166691	−	1.20756i
$403$	−4184.45	−	6510.09i	−0.517227	−	0.804692i
$404$	1851.02	−	520.955i	0.227950	−	0.0641547i
$405$	3038.51	−	3038.51i	0.372802	−	0.372802i
$406$	−783.058	−	5672.72i	−0.0957205	−	0.693429i
$407$	−2584.13			−0.314719
$408$	−8136.43	−	3192.20i	−0.987287	−	0.387347i
$409$	−6718.82	+	6718.82i	−0.812284	+	0.812284i	−0.984976	−	0.172692i	$-0.944754\pi$
$409$	−6718.82	+	6718.82i	−0.812284	+	0.812284i	0.172692	+	0.984976i	$0.444754\pi$
$410$	1967.01	+	1489.83i	0.236935	+	0.179457i
$411$	13990.9	−	13990.9i	1.67912	−	1.67912i
$412$	−3079.49	−	10941.8i	−0.368242	−	1.30841i
$413$		−	5029.98i		−	0.599295i
$414$	−2647.60	+	3495.60i	−0.314305	+	0.414975i
$415$	9366.99			1.10797
$416$	−2617.93	+	8070.80i	−0.308544	+	0.951210i
$417$	−4571.66			−0.536871
$418$	4907.82	−	6479.75i	0.574280	−	0.758217i
$419$			12413.1i			1.44730i	0.690169	+	0.723648i	$0.257536\pi$
$419$			12413.1i			1.44730i	−0.690169	+	0.723648i	$0.742464\pi$
$420$	7008.98	+	24903.9i	0.814294	+	2.89330i
$421$	−42.1133	+	42.1133i	−0.00487525	+	0.00487525i	−0.709540	−	0.704665i	$-0.751097\pi$
$421$	−42.1133	+	42.1133i	−0.00487525	+	0.00487525i	0.704665	+	0.709540i	$0.251097\pi$
$422$	−3362.94	−	2547.12i	−0.387928	−	0.293820i
$423$	−10290.5	+	10290.5i	−1.18284	+	1.18284i
$424$	7361.01	+	2887.98i	0.843119	+	0.330784i
$425$	5254.91			0.599767
$426$	−3346.06	−	24239.9i	−0.380557	−	2.75687i
$427$	−1057.52	+	1057.52i	−0.119852	+	0.119852i
$428$	−6847.59	+	1927.20i	−0.773343	+	0.217651i
$429$	4598.36	+	7154.04i	0.517508	+	0.805129i
$430$	1302.35	+	9434.61i	0.146058	+	1.05809i
$431$	−4890.36	−	4890.36i	−0.546544	−	0.546544i	0.378895	−	0.925440i	$-0.376304\pi$
$431$	−4890.36	−	4890.36i	−0.546544	−	0.546544i	−0.925440	+	0.378895i	$0.876304\pi$
$432$	3142.34	+	5140.39i	0.349968	+	0.572493i
$433$			6008.05i			0.666810i	0.942784	+	0.333405i	$0.108198\pi$
$433$			6008.05i			0.666810i	−0.942784	+	0.333405i	$0.891802\pi$
$434$	−7339.56	+	9690.36i	−0.811774	+	1.07178i
$435$	6832.63	+	6832.63i	0.753102	+	0.753102i
$436$	−12415.2	−	6961.72i	−1.36371	−	0.764692i
$437$	−3642.14	−	3642.14i	−0.398690	−	0.398690i
$438$	−651.127	−	4716.97i	−0.0710321	−	0.514579i
$439$	−15059.1			−1.63720			−0.818598	−	0.574366i	$-0.805248\pi$
$439$	−15059.1			−1.63720			−0.818598	+	0.574366i	$0.805248\pi$
$440$	2838.79	−	7235.65i	0.307578	−	0.783968i
$441$			12922.4i			1.39536i
$442$	4113.17	+	4800.46i	0.442632	+	0.516594i
$443$		−	400.033i		−	0.0429033i	−0.999770	−	0.0214516i	$-0.993171\pi$
$443$		−	400.033i		−	0.0429033i	0.999770	−	0.0214516i	$-0.00682879\pi$
$444$	6521.51	+	3656.89i	0.697066	+	0.390874i
$445$	−19611.8			−2.08919
$446$	1552.54	−	214.312i	0.164832	−	0.0227532i
$447$	1228.03	+	1228.03i	0.129941	+	0.129941i
$448$	13318.3	−	501.495i	1.40453	−	0.0528871i
$449$	−3959.43	−	3959.43i	−0.416163	−	0.416163i	0.467716	−	0.883879i	$-0.345077\pi$
$449$	−3959.43	−	3959.43i	−0.416163	−	0.416163i	−0.883879	+	0.467716i	$0.845077\pi$
$450$	−9596.43	−	7268.42i	−1.00529	−	0.761415i
$451$		−	1274.10i		−	0.133027i
$452$	3389.63	+	12043.8i	0.352732	+	1.25330i
$453$	−17815.9	−	17815.9i	−1.84782	−	1.84782i
$454$	612.369	−	84.5310i	0.0633037	−	0.00873840i
$455$	3976.22	−	18284.8i	0.409688	−	1.88397i
$456$	−21555.4	+	9407.57i	−2.21365	+	0.966118i
$457$	−2025.89	+	2025.89i	−0.207368	+	0.207368i	−0.803148	−	0.595780i	$-0.796843\pi$
$457$	−2025.89	+	2025.89i	−0.207368	+	0.207368i	0.595780	+	0.803148i	$0.296843\pi$
$458$	18342.9	−	2532.04i	1.87141	−	0.258329i
$459$	4488.77			0.456466
$460$	−4295.91	−	2408.90i	−0.435430	−	0.244164i
$461$	5425.59	−	5425.59i	0.548146	−	0.548146i	−0.377759	−	0.925904i	$-0.623305\pi$
$461$	5425.59	−	5425.59i	0.548146	−	0.548146i	0.925904	+	0.377759i	$0.123305\pi$
$462$	8065.56	−	10648.9i	0.812216	−	1.07236i
$463$	7789.98	−	7789.98i	0.781924	−	0.781924i	−0.198231	−	0.980155i	$-0.563520\pi$
$463$	7789.98	−	7789.98i	0.781924	−	0.781924i	0.980155	+	0.198231i	$0.0635197\pi$
$464$	4247.12	−	2596.28i	0.424930	−	0.259761i
$465$		−	20512.1i		−	2.04564i
$466$	−2246.07	−	1701.19i	−0.223277	−	0.169112i
$467$	−19551.1			−1.93729			−0.968646	−	0.248445i	$-0.920081\pi$
$467$	−19551.1			−1.93729			−0.968646	+	0.248445i	$0.920081\pi$
$468$	−871.556	−	14455.7i	−0.0860848	−	1.42781i
$469$	11162.7			1.09903
$470$	−13029.9	−	9868.97i	−1.27878	−	0.968557i
$471$		−	4533.47i		−	0.443506i
$472$	4007.33	−	1748.94i	0.390788	−	0.170554i
$473$	3477.35	−	3477.35i	0.338031	−	0.338031i
$474$	−7684.74	+	10146.1i	−0.744667	+	0.983177i
$475$	9998.73	−	9998.73i	0.965838	−	0.965838i
$476$	4856.65	−	8661.11i	0.467656	−	0.833994i
$477$	−13496.3			−1.29550
$478$	11469.1	−	1583.18i	1.09745	−	0.151492i
$479$	2029.01	−	2029.01i	0.193544	−	0.193544i	−0.603681	−	0.797226i	$-0.706300\pi$
$479$	2029.01	−	2029.01i	0.193544	−	0.193544i	0.797226	+	0.603681i	$0.206300\pi$
$480$	−17403.6	+	14243.2i	−1.65492	+	1.35439i
$481$	−2924.01	−	4549.12i	−0.277180	−	0.431231i
$482$	−12670.7	+	1749.06i	−1.19738	+	0.165286i
$483$	−5985.54	−	5985.54i	−0.563875	−	0.563875i
$484$	6386.53	−	1797.43i	0.599787	−	0.168805i
$485$		−	312.682i		−	0.0292745i
$486$	10848.3	+	8216.62i	1.01253	+	0.766900i
$487$	−5037.34	−	5037.34i	−0.468714	−	0.468714i	0.432784	−	0.901498i	$-0.357531\pi$
$487$	−5037.34	−	5037.34i	−0.468714	−	0.468714i	−0.901498	+	0.432784i	$0.857531\pi$
$488$	−1210.22	−	474.810i	−0.112262	−	0.0440444i
$489$	14043.8	+	14043.8i	1.29874	+	1.29874i
$490$	−14377.8	+	1984.70i	−1.32555	+	0.182979i
$491$	9131.48			0.839303			0.419652	−	0.907685i	$-0.362152\pi$
$491$	9131.48			0.839303			0.419652	+	0.907685i	$0.362152\pi$
$492$	−1803.02	+	3215.41i	−0.165216	+	0.294638i
$493$		−	3708.73i		−	0.338809i
$494$	16960.3	+	1307.75i	1.54470	+	0.119106i
$495$			13266.4i			1.20461i
$496$	−10272.2	−	2477.97i	−0.929910	−	0.224323i
$497$	27800.3			2.50908
$498$	1913.59	+	13862.6i	0.172188	+	1.24739i
$499$	5912.03	+	5912.03i	0.530378	+	0.530378i	0.920685	−	0.390307i	$-0.127631\pi$
$499$	5912.03	+	5912.03i	0.530378	+	0.530378i	−0.390307	+	0.920685i	$0.627631\pi$
$500$	−887.850	+	1583.35i	−0.0794117	+	0.141619i
$501$	10996.2	+	10996.2i	0.980588	+	0.980588i
$502$	−3779.45	+	4989.98i	−0.336026	+	0.443653i
$503$		−	15391.1i		−	1.36432i	−0.731202	−	0.682161i	$-0.761040\pi$
$503$		−	15391.1i		−	1.36432i	0.731202	−	0.682161i	$-0.238960\pi$
$504$	−20848.9	+	9099.21i	−1.84262	+	0.804189i
$505$	−2606.65	−	2606.65i	−0.229692	−	0.229692i
$506$	347.752	+	2519.22i	0.0305523	+	0.221330i
$507$	−7390.85	+	16190.0i	−0.647415	+	1.41819i
$508$	1434.55	+	5097.14i	0.125291	+	0.445175i
$509$	−354.812	+	354.812i	−0.0308974	+	0.0308974i	−0.722387	−	0.691489i	$-0.756955\pi$
$509$	−354.812	+	354.812i	−0.0308974	+	0.0308974i	0.691489	+	0.722387i	$0.256955\pi$
$510$	2291.18	+	16598.0i	0.198932	+	1.44112i
$511$	5409.80			0.468328
$512$	5030.36	+	10436.2i	0.434204	+	0.900815i
$513$	8540.96	−	8540.96i	0.735073	−	0.735073i
$514$	6911.54	+	5234.86i	0.593103	+	0.449221i
$515$	−15408.5	+	15408.5i	−1.31841	+	1.31841i
$516$	−13696.6	+	3854.80i	−1.16853	+	0.328872i
$517$			8439.94i			0.717965i
$518$	−5128.74	+	6771.43i	−0.435027	+	0.574362i
$519$	−6901.30			−0.583687
$520$	15949.8	−	3189.89i	1.34509	−	0.269012i
$521$	8770.30			0.737493			0.368746	−	0.929530i	$-0.379787\pi$
$521$	8770.30			0.737493			0.368746	+	0.929530i	$0.379787\pi$
$522$	−5129.79	+	6772.83i	−0.430125	+	0.567890i
$523$			12805.6i			1.07065i	0.844645	+	0.535327i	$0.179812\pi$
$523$			12805.6i			1.07065i	−0.844645	+	0.535327i	$0.820188\pi$
$524$	−1110.25	+	312.470i	−0.0925601	+	0.0260503i
$525$	16432.0	−	16432.0i	1.36600	−	1.36600i
$526$	−12227.8	−	9261.46i	−1.01361	−	0.767717i
$527$	−5566.95	+	5566.95i	−0.460152	+	0.460152i
$528$	11288.3	+	2723.08i	0.930415	+	0.224444i
$529$	−10555.5			−0.867554
$530$	−2072.83	−	15016.2i	−0.169883	−	1.23068i
$531$	−5277.01	+	5277.01i	−0.431267	+	0.431267i
$532$	−7238.89	−	25720.8i	−0.589936	−	2.09612i
$533$	2242.93	−	1441.68i	0.182274	−	0.117159i
$534$	−4006.51	−	29024.4i	−0.324679	−	2.35207i
$535$	9642.91	+	9642.91i	0.779251	+	0.779251i
$536$	3881.30	+	8893.16i	0.312774	+	0.716653i
$537$			1026.46i			0.0824861i
$538$	1462.76	−	1931.27i	0.117220	−	0.154764i
$539$	5299.27	+	5299.27i	0.423480	+	0.423480i
$540$	5648.95	−	10074.1i	0.450171	−	0.802812i
$541$	−1311.42	−	1311.42i	−0.104218	−	0.104218i	0.653075	−	0.757293i	$-0.273479\pi$
$541$	−1311.42	−	1311.42i	−0.104218	−	0.104218i	−0.757293	+	0.653075i	$0.773479\pi$
$542$	957.991	+	6939.98i	0.0759211	+	0.549996i
$543$	27874.0			2.20292
$544$	8588.89	+	857.734i	0.676922	+	0.0676012i
$545$			27286.9i			2.14467i
$546$	27872.7	+	2149.16i	2.18469	+	0.168454i
$547$		−	13430.9i		−	1.04984i	−0.851152	−	0.524920i	$-0.824095\pi$
$547$		−	13430.9i		−	1.04984i	0.851152	−	0.524920i	$-0.175905\pi$
$548$	−9557.02	+	17043.5i	−0.744992	+	1.32858i
$549$	2218.91			0.172497
$550$	−6915.98	+	954.678i	−0.536179	+	0.0740138i
$551$	−7056.75	−	7056.75i	−0.545604	−	0.545604i
$552$	2687.41	−	6849.81i	0.207217	−	0.528165i
$553$	−10224.9	−	10224.9i	−0.786272	−	0.786272i
$554$	−6888.25	−	5217.22i	−0.528256	−	0.400105i
$555$		−	14333.4i		−	1.09625i
$556$	4346.00	−	1223.15i	0.331495	−	0.0932966i
$557$	−5719.75	−	5719.75i	−0.435105	−	0.435105i	0.455255	−	0.890361i	$-0.349548\pi$
$557$	−5719.75	−	5719.75i	−0.435105	−	0.435105i	−0.890361	+	0.455255i	$0.849548\pi$
$558$	17866.3	−	2466.25i	1.35545	−	0.187105i
$559$	10056.3	+	2186.84i	0.760885	+	0.165462i
$560$	−13326.0	−	21799.4i	−1.00559	−	1.64498i
$561$	6117.61	−	6117.61i	0.460402	−	0.460402i
$562$	−23537.3	+	3249.08i	−1.76666	+	0.243868i
$563$	10864.9			0.813326			0.406663	−	0.913578i	$-0.366692\pi$
$563$	10864.9			0.813326			0.406663	+	0.913578i	$0.366692\pi$
$564$	11943.6	−	21299.7i	0.891697	−	1.59021i
$565$	16960.3	−	16960.3i	1.26288	−	1.26288i
$566$	−12983.6	+	17142.1i	−0.964204	+	1.27303i
$567$	−5157.32	+	5157.32i	−0.381988	+	0.381988i
$568$	9666.28	+	22148.2i	0.714064	+	1.63612i
$569$		−	12209.8i		−	0.899581i	−0.893134	−	0.449790i	$-0.851499\pi$
$569$		−	12209.8i		−	0.899581i	0.893134	−	0.449790i	$-0.148501\pi$
$570$	35941.2	+	27222.2i	2.64108	+	2.00037i
$571$	−2779.81			−0.203733			−0.101866	−	0.994798i	$-0.532481\pi$
$571$	−2779.81			−0.203733			−0.101866	+	0.994798i	$0.532481\pi$
$572$	−6285.45	−	5570.63i	−0.459454	−	0.407202i
$573$	1498.65			0.109262
$574$	−3338.64	−	2528.71i	−0.242773	−	0.183879i
$575$			4423.95i			0.320855i
$576$	−14498.5	−	13446.2i	−1.04879	−	0.972673i
$577$	−3806.59	+	3806.59i	−0.274645	+	0.274645i	−0.830967	−	0.556322i	$-0.812212\pi$
$577$	−3806.59	+	3806.59i	−0.274645	+	0.274645i	0.556322	+	0.830967i	$0.312212\pi$
$578$	−4507.20	+	5950.82i	−0.324351	+	0.428238i
$579$	12238.0	−	12238.0i	0.878400	−	0.878400i
$580$	−8323.44	−	4667.30i	−0.595883	−	0.334136i
$581$	−15898.8			−1.13527
$582$	462.750	−	63.8778i	0.0329581	−	0.00454952i
$583$	−5534.59	+	5534.59i	−0.393172	+	0.393172i
$584$	1881.01	+	4309.93i	0.133282	+	0.305387i
$585$	−23354.3	+	15011.3i	−1.65057	+	1.06092i
$586$	14080.0	−	1943.59i	0.992557	−	0.137012i
$587$	15963.5	+	15963.5i	1.12246	+	1.12246i	0.991370	+	0.131091i	$0.0418481\pi$
$587$	15963.5	+	15963.5i	1.12246	+	1.12246i	0.131091	+	0.991370i	$0.458152\pi$
$588$	−5874.47	−	20872.8i	−0.412005	−	1.46391i
$589$			21184.9i			1.48202i
$590$	−6681.77	−	5060.83i	−0.466244	−	0.353137i
$591$	−23275.1	−	23275.1i	−1.61999	−	1.61999i
$592$	−7178.01	−	1731.55i	−0.498335	−	0.120214i
$593$	3543.08	+	3543.08i	0.245357	+	0.245357i	0.819062	−	0.573705i	$-0.194494\pi$
$593$	3543.08	+	3543.08i	0.245357	+	0.245357i	−0.573705	+	0.819062i	$0.694494\pi$
$594$	−5907.67	+	815.491i	−0.408071	+	0.0563299i
$595$	−19036.0			−1.31160
$596$	−1495.97	−	838.854i	−0.102814	−	0.0576523i
$597$			27773.1i			1.90398i
$598$	−4041.36	+	3462.75i	−0.276360	+	0.236793i
$599$			4609.14i			0.314398i	0.987567	+	0.157199i	$0.0502464\pi$
$599$			4609.14i			0.314398i	−0.987567	+	0.157199i	$0.949754\pi$
$600$	18804.7	+	7377.72i	1.27950	+	0.501990i
$601$	−27066.1			−1.83702			−0.918511	−	0.395395i	$-0.870608\pi$
$601$	−27066.1			−1.83702			−0.918511	+	0.395395i	$0.870608\pi$
$602$	−2210.50	−	16013.5i	−0.149656	−	1.08416i
$603$	−11710.9	−	11710.9i	−0.790884	−	0.790884i
$604$	21703.2	+	12169.9i	1.46207	+	0.819843i
$605$	−8993.64	−	8993.64i	−0.604369	−	0.604369i
$606$	3325.18	−	4390.20i	0.222898	−	0.294290i
$607$		−	16149.3i		−	1.07987i	−0.841708	−	0.539934i	$-0.818449\pi$
$607$		−	16149.3i		−	1.07987i	0.841708	−	0.539934i	$-0.181551\pi$
$608$	17974.4	−	14710.4i	1.19895	−	0.981223i
$609$	−11597.1	−	11597.1i	−0.771658	−	0.771658i
$610$	340.792	+	2468.80i	0.0226201	+	0.163867i
$611$	−14857.7	+	9550.01i	−0.983762	+	0.632327i
$612$	−14181.6	+	3991.30i	−0.936697	+	0.263626i
$613$	8632.37	−	8632.37i	0.568773	−	0.568773i	−0.363011	−	0.931785i	$-0.618251\pi$
$613$	8632.37	−	8632.37i	0.568773	−	0.568773i	0.931785	+	0.363011i	$0.118251\pi$
$614$	−2817.09	−	20407.9i	−0.185160	−	1.34136i
$615$	7067.05			0.463368
$616$	−4818.33	+	12281.2i	−0.315156	+	0.803285i
$617$	2052.57	−	2052.57i	0.133928	−	0.133928i	−0.636965	−	0.770893i	$-0.719810\pi$
$617$	2052.57	−	2052.57i	0.133928	−	0.133928i	0.770893	+	0.636965i	$0.219810\pi$
$618$	−25951.5	−	19655.9i	−1.68920	−	1.27941i
$619$	−11337.6	+	11337.6i	−0.736180	+	0.736180i	−0.971836	−	0.235656i	$-0.924276\pi$
$619$	−11337.6	+	11337.6i	−0.736180	+	0.736180i	0.235656	+	0.971836i	$0.424276\pi$
$620$	5487.99	+	19499.6i	0.355489	+	1.26310i
$621$			3778.96i			0.244194i
$622$	−7976.91	+	10531.8i	−0.514220	+	0.678920i
$623$	33287.5			2.14067
$624$	7979.25	+	22953.2i	0.511900	+	1.47254i
$625$	17255.5			1.10435
$626$	−535.441	+	706.938i	−0.0341861	+	0.0451356i
$627$		−	23280.4i		−	1.48282i
$628$	1212.93	+	4309.70i	0.0770719	+	0.273847i
$629$	−3890.07	+	3890.07i	−0.246594	+	0.246594i
$630$	34763.2	+	26329.9i	2.19841	+	1.66509i
$631$	−13615.6	+	13615.6i	−0.859000	+	0.859000i	−0.991220	−	0.132221i	$-0.957789\pi$
$631$	−13615.6	+	13615.6i	−0.859000	+	0.859000i	0.132221	+	0.991220i	$0.457789\pi$
$632$	4590.84	−	11701.3i	0.288946	−	0.736478i
$633$	−12082.4			−0.758659
$634$	2616.33	+	18953.5i	0.163892	+	1.18729i
$635$	7177.89	−	7177.89i	0.448576	−	0.448576i
$636$	21799.7	−	6135.33i	1.35914	−	0.382519i
$637$	−3332.61	+	15325.1i	−0.207288	+	0.953224i
$638$	673.778	+	4881.06i	0.0418106	+	0.302889i
$639$	−29165.6	−	29165.6i	−1.80559	−	1.80559i
$640$	12733.8	−	18196.4i	0.786480	−	1.12387i
$641$		−	29898.7i		−	1.84232i	−0.389181	−	0.921161i	$-0.627242\pi$
$641$		−	29898.7i		−	1.84232i	0.389181	−	0.921161i	$-0.372758\pi$
$642$	−12301.0	+	16240.9i	−0.756202	+	0.998407i
$643$	7319.88	+	7319.88i	0.448939	+	0.448939i	0.895002	−	0.446063i	$-0.147174\pi$
$643$	7319.88	+	7319.88i	0.448939	+	0.448939i	−0.446063	+	0.895002i	$0.647174\pi$
$644$	7291.52	+	4088.66i	0.446159	+	0.250180i
$645$	19287.8	+	19287.8i	1.17745	+	1.17745i
$646$	−2366.34	−	17142.5i	−0.144121	−	1.04406i
$647$	−11635.5			−0.707016			−0.353508	−	0.935431i	$-0.615011\pi$
$647$	−11635.5			−0.707016			−0.353508	+	0.935431i	$0.615011\pi$
$648$	−5902.00	−	2315.56i	−0.357797	−	0.140376i
$649$			4328.02i			0.261771i
$650$	−9506.23	−	11094.7i	−0.573639	−	0.669492i
$651$			34815.5i			2.09605i
$652$	−17108.0	−	9593.19i	−1.02761	−	0.576224i
$653$	−13662.7			−0.818780			−0.409390	−	0.912359i	$-0.634259\pi$
$653$	−13662.7			−0.818780			−0.409390	+	0.912359i	$0.634259\pi$
$654$	−40383.1	+	5574.46i	−2.41453	+	0.333300i
$655$	1563.48	+	1563.48i	0.0932673	+	0.0932673i
$656$	853.738	−	3539.10i	0.0508123	−	0.210638i
$657$	−5675.48	−	5675.48i	−0.337019	−	0.337019i
$658$	22115.9	+	16750.8i	1.31029	+	0.992421i
$659$		−	1387.42i		−	0.0820123i	−0.999159	−	0.0410062i	$-0.986944\pi$
$659$		−	1387.42i		−	0.0820123i	0.999159	−	0.0410062i	$-0.0130563\pi$
$660$	−6030.84	−	21428.4i	−0.355682	−	1.26379i
$661$	14354.6	+	14354.6i	0.844671	+	0.844671i	0.989462	−	0.144791i	$-0.0462511\pi$
$661$	14354.6	+	14354.6i	0.844671	+	0.844671i	−0.144791	+	0.989462i	$0.546251\pi$
$662$	−32180.2	+	4442.13i	−1.88930	+	0.260798i
$663$	17691.7	+	3847.24i	1.03633	+	0.225361i
$664$	−5528.07	−	12666.4i	−0.323088	−	0.740287i
$665$	−36220.5	+	36220.5i	−2.11214	+	2.11214i
$666$	12484.6	−	1723.37i	0.726379	−	0.100269i
$667$	3122.27			0.181251
$668$	−13395.5	−	7511.41i	−0.775878	−	0.435067i
$669$	3173.97	−	3173.97i	0.183427	−	0.183427i
$670$	11231.1	−	14828.3i	0.647606	−	0.855029i
$671$	909.937	−	909.937i	0.0523513	−	0.0523513i
$672$	29539.4	−	24175.2i	1.69569	−	1.38776i
$673$		−	6237.71i		−	0.357275i	−0.983915	−	0.178638i	$-0.942831\pi$
$673$		−	6237.71i		−	0.357275i	0.983915	−	0.178638i	$-0.0571690\pi$
$674$	14562.3	+	11029.6i	0.832225	+	0.630334i
$675$	−10374.3			−0.591567
$676$	2694.42	−	17368.2i	0.153301	−	0.988180i
$677$	−12406.2			−0.704295			−0.352148	−	0.935944i	$-0.614548\pi$
$677$	−12406.2			−0.704295			−0.352148	+	0.935944i	$0.614548\pi$
$678$	28565.1	+	21635.5i	1.61805	+	1.22552i
$679$			530.720i			0.0299958i
$680$	−6618.89	−	15165.8i	−0.373269	−	0.855265i
$681$	1251.91	−	1251.91i	0.0704453	−	0.0704453i
$682$	6315.29	−	8338.02i	0.354582	−	0.468151i
$683$	10541.3	−	10541.3i	0.590558	−	0.590558i	−0.347224	−	0.937782i	$-0.612876\pi$
$683$	10541.3	−	10541.3i	0.590558	−	0.590558i	0.937782	+	0.347224i	$0.112876\pi$
$684$	−19389.5	+	34578.3i	−1.08388	+	1.93295i
$685$	37459.4			2.08942
$686$	−612.851	+	84.5975i	−0.0341090	+	0.00470838i
$687$	37499.7	−	37499.7i	2.08254	−	2.08254i
$688$	11989.2	−	7329.05i	0.664366	−	0.406130i
$689$	−16005.7	−	3480.59i	−0.885003	−	0.192453i
$690$	−13973.4	+	1928.88i	−0.770953	+	0.106422i
$691$	22789.6	+	22789.6i	1.25464	+	1.25464i	0.953617	+	0.301022i	$0.0973279\pi$
$691$	22789.6	+	22789.6i	1.25464	+	1.25464i	0.301022	+	0.953617i	$0.402672\pi$
$692$	6560.65	−	1846.44i	0.360403	−	0.101432i
$693$		−	22517.3i		−	1.23429i
$694$	7414.33	+	5615.68i	0.405539	+	0.307159i
$695$	−6120.13	−	6120.13i	−0.334028	−	0.334028i
$696$	5206.94	−	13271.7i	0.283575	−	0.722790i
$697$	−1917.99	−	1917.99i	−0.104231	−	0.104231i
$698$	7524.02	−	1038.61i	0.408006	−	0.0563209i
$699$	−8069.66			−0.436656
$700$	−11224.5	+	20017.3i	−0.606069	+	1.08083i
$701$			8422.36i			0.453792i	0.973919	+	0.226896i	$0.0728577\pi$
$701$			8422.36i			0.453792i	−0.973919	+	0.226896i	$0.927142\pi$
$702$	−8120.27	−	9477.14i	−0.436581	−	0.509532i
$703$			14803.6i			0.794207i
$704$	−11459.6	+	431.509i	−0.613497	+	0.0231010i
$705$	−46813.8			−2.50087
$706$	1463.84	+	10604.5i	0.0780343	+	0.565304i
$707$	4424.31	+	4424.31i	0.235351	+	0.235351i
$708$	6124.71	−	10922.5i	0.325114	−	0.579792i
$709$	17366.4	+	17366.4i	0.919898	+	0.919898i	0.997022	−	0.0771239i	$-0.0245737\pi$
$709$	17366.4	+	17366.4i	0.919898	+	0.919898i	−0.0771239	+	0.997022i	$0.524574\pi$
$710$	27970.8	−	36929.6i	1.47849	−	1.95203i
$711$			21454.2i			1.13164i
$712$	11574.2	+	26519.8i	0.609216	+	1.39589i
$713$	−4686.64	−	4686.64i	−0.246166	−	0.246166i
$714$	−3888.87	−	28172.1i	−0.203834	−	1.47663i
$715$	−3421.32	+	15733.1i	−0.178951	+	0.822914i
$716$	−274.629	−	975.794i	−0.0143343	−	0.0509317i
$717$	23447.0	−	23447.0i	1.22126	−	1.22126i
$718$	434.585	+	3148.27i	0.0225885	+	0.163638i
$719$	−2333.10			−0.121015			−0.0605076	−	0.998168i	$-0.519272\pi$
$719$	−2333.10			−0.121015			−0.0605076	+	0.998168i	$0.519272\pi$
$720$	−8889.45	+	36850.5i	−0.460125	+	1.90741i
$721$	26153.2	−	26153.2i	1.35089	−	1.35089i
$722$	−21655.2	−	16401.8i	−1.11624	−	0.845447i
$723$	−25903.7	+	25903.7i	−1.33246	+	1.33246i
$724$	−26498.1	+	7457.67i	−1.36021	+	0.382821i
$725$			8571.52i			0.439087i
$726$	11472.7	−	15147.4i	0.586492	−	0.774341i
$727$	753.769			0.0384536			0.0192268	−	0.999815i	$-0.493880\pi$
$727$	753.769			0.0384536			0.0192268	+	0.999815i	$0.493880\pi$
$728$	−27072.0	+	5414.26i	−1.37823	+	0.275640i
$729$	31410.7			1.59583
$730$	5442.98	−	7186.32i	0.275964	−	0.364353i
$731$		−	10469.4i		−	0.529719i
$732$	−3584.07	+	1008.71i	−0.180971	+	0.0509328i
$733$	22475.0	−	22475.0i	1.13251	−	1.13251i	0.142754	−	0.989758i	$-0.454404\pi$
$733$	22475.0	−	22475.0i	1.13251	−	1.13251i	0.989758	−	0.142754i	$-0.0455958\pi$
$734$	8764.77	+	6638.51i	0.440754	+	0.333831i
$735$	−29393.5	+	29393.5i	−1.47510	+	1.47510i
$736$	−722.100	+	7230.72i	−0.0361643	+	0.362130i
$737$	−9604.85			−0.480053
$738$	849.701	+	6155.50i	0.0423820	+	0.307029i
$739$	15838.8	−	15838.8i	0.788418	−	0.788418i	−0.192817	−	0.981235i	$-0.561762\pi$
$739$	15838.8	−	15838.8i	0.788418	−	0.788418i	0.981235	+	0.192817i	$0.0617622\pi$
$740$	3834.90	+	13625.9i	0.190505	+	0.676890i
$741$	40983.0	−	26342.4i	2.03178	−	1.30595i
$742$	3518.25	+	25487.3i	0.174069	+	1.26101i
$743$	−3536.41	−	3536.41i	−0.174614	−	0.174614i	0.614389	−	0.789003i	$-0.289403\pi$
$743$	−3536.41	−	3536.41i	−0.174614	−	0.174614i	−0.789003	+	0.614389i	$0.789403\pi$
$744$	−27737.1	+	12105.5i	−1.36679	+	0.596517i
$745$			3287.95i			0.161693i
$746$	7097.23	−	9370.42i	0.348322	−	0.459886i
$747$	16679.6	+	16679.6i	0.816966	+	0.816966i
$748$	−4178.88	+	7452.41i	−0.204271	+	0.364287i
$749$	−16367.1	−	16367.1i	−0.798451	−	0.798451i
$750$	710.928	+	5150.18i	0.0346126	+	0.250744i
$751$	−22865.8			−1.11103			−0.555517	−	0.831505i	$-0.687479\pi$
$751$	−22865.8			−1.11103			−0.555517	+	0.831505i	$0.687479\pi$
$752$	−5655.36	+	23443.8i	−0.274242	+	1.13685i
$753$			17928.0i			0.867638i
$754$	−7830.24	+	6709.17i	−0.378197	+	0.324050i
$755$		−	47700.7i		−	2.29935i
$756$	−9588.06	+	17098.9i	−0.461263	+	0.822593i
$757$	12368.1			0.593826			0.296913	−	0.954905i	$-0.404043\pi$
$757$	12368.1			0.593826			0.296913	+	0.954905i	$0.404043\pi$
$758$	29391.2	−	4057.14i	1.40836	−	0.194409i
$759$	5150.22	+	5150.22i	0.246299	+	0.246299i
$760$	−41450.5	−	16262.4i	−1.97838	−	0.776185i
$761$	25966.8	+	25966.8i	1.23692	+	1.23692i	0.961253	+	0.275667i	$0.0888988\pi$
$761$	25966.8	+	25966.8i	1.23692	+	1.23692i	0.275667	+	0.961253i	$0.411101\pi$
$762$	12089.2	+	9156.48i	0.574733	+	0.435308i
$763$		−	46314.6i		−	2.19751i
$764$	−1424.68	+	400.964i	−0.0674647	+	0.0189874i
$765$	19970.9	+	19970.9i	0.943854	+	0.943854i
$766$	−86.4437	+	11.9326i	−0.00407747	+	0.000562851i
$767$	−7619.07	+	4897.26i	−0.358681	+	0.230547i
$768$	29531.0	+	15127.9i	1.38751	+	0.710783i
$769$	17123.8	−	17123.8i	0.802989	−	0.802989i	−0.180572	−	0.983562i	$-0.557795\pi$
$769$	17123.8	−	17123.8i	0.802989	−	0.802989i	0.983562	+	0.180572i	$0.0577950\pi$
$770$	25053.2	−	3458.33i	1.17254	−	0.161857i
$771$	24831.8			1.15991
$772$	−8359.65	+	14908.2i	−0.389729	+	0.695023i
$773$	−22962.7	+	22962.7i	−1.06845	+	1.06845i	−0.0709681	+	0.997479i	$0.522609\pi$
$773$	−22962.7	+	22962.7i	−1.06845	+	1.06845i	−0.997479	+	0.0709681i	$0.977391\pi$
$774$	−14480.9	+	19119.0i	−0.672488	+	0.887880i
$775$	12866.2	−	12866.2i	0.596344	−	0.596344i
$776$	−422.819	+	184.533i	−0.0195597	+	0.00853655i
$777$			24328.4i			1.12326i
$778$	−28273.3	−	21414.4i	−1.30289	−	0.986819i
$779$	−7298.87			−0.335698
$780$	30898.6	−	34863.5i	1.41840	−	1.60040i
$781$	−23920.6			−1.09596
$782$	4315.85	+	3268.86i	0.197359	+	0.149481i
$783$			7321.83i			0.334178i
$784$	11169.0	+	18270.8i	0.508793	+	0.832307i
$785$	6069.01	−	6069.01i	0.275939	−	0.275939i
$786$	−1994.45	+	2633.26i	−0.0905085	+	0.119498i
$787$	15550.9	−	15550.9i	0.704358	−	0.704358i	−0.260985	−	0.965343i	$-0.584047\pi$
$787$	15550.9	−	15550.9i	0.704358	−	0.704358i	0.965343	+	0.260985i	$0.0840473\pi$
$788$	28353.5	+	15899.0i	1.28179	+	0.718755i
$789$	−43932.1			−1.98229
$790$	−23870.3	+	3295.05i	−1.07502	+	0.148396i
$791$	−28787.1	+	28787.1i	−1.29400	+	1.29400i
$792$	17939.3	−	7829.37i	0.804856	−	0.351268i
$793$	2631.48	+	572.241i	0.117839	+	0.0256253i
$794$	−19885.9	+	2745.04i	−0.888821	+	0.122692i
$795$	−30698.7	−	30698.7i	−1.36952	−	1.36952i
$796$	−7430.69	−	26402.3i	−0.330872	−	1.17563i
$797$		−	40327.3i		−	1.79230i	−0.443747	−	0.896152i	$-0.646351\pi$
$797$		−	40327.3i		−	1.79230i	0.443747	−	0.896152i	$-0.353649\pi$
$798$	−61003.7	−	46204.7i	−2.70615	−	2.04966i
$799$	12705.2	+	12705.2i	0.562551	+	0.562551i
$800$	−19850.4	−	1982.37i	−0.877271	−	0.0876093i
$801$	−34922.3	−	34922.3i	−1.54047	−	1.54047i
$802$	−26916.9	+	3715.60i	−1.18512	+	0.163594i
$803$	−4654.84			−0.204565
$804$	24239.5	+	13592.1i	1.06326	+	0.596215i
$805$		−	16025.8i		−	0.701659i
$806$	21824.2	+	1682.78i	0.953753	+	0.0735403i
$807$		−	6938.66i		−	0.302667i
$808$	−1986.45	+	5063.15i	−0.0864889	+	0.220447i
$809$	30906.2			1.34314			0.671572	−	0.740940i	$-0.265620\pi$
$809$	30906.2			1.34314			0.671572	+	0.740940i	$0.265620\pi$
$810$	1661.98	+	12039.9i	0.0720937	+	0.522269i
$811$	−12364.2	−	12364.2i	−0.535346	−	0.535346i	0.386812	−	0.922159i	$-0.373576\pi$
$811$	−12364.2	−	12364.2i	−0.535346	−	0.535346i	−0.922159	+	0.386812i	$0.873576\pi$
$812$	14127.5	+	7921.89i	0.610565	+	0.342369i
$813$	14187.9	+	14187.9i	0.612044	+	0.612044i
$814$	4413.00	−	5826.44i	0.190019	−	0.250880i
$815$			37601.2i			1.61609i
$816$	21092.3	−	12893.8i	0.904873	−	0.553153i
$817$	−19920.5	−	19920.5i	−0.853036	−	0.853036i
$818$	−3675.00	−	26622.8i	−0.157082	−	1.13795i
$819$	39639.6	−	25478.9i	1.69123	−	1.08707i
$820$	−6718.22	+	1890.79i	−0.286110	+	0.0805234i
$821$	−9112.59	+	9112.59i	−0.387371	+	0.387371i	−0.873749	−	0.486378i	$-0.838318\pi$
$821$	−9112.59	+	9112.59i	−0.387371	+	0.387371i	0.486378	+	0.873749i	$0.338318\pi$
$822$	7652.59	+	55437.7i	0.324714	+	2.35233i
$823$	−8163.93			−0.345780			−0.172890	−	0.984941i	$-0.555311\pi$
$823$	−8163.93			−0.345780			−0.172890	+	0.984941i	$0.555311\pi$
$824$	29929.5	+	11742.4i	1.26534	+	0.496438i
$825$	−14138.8	+	14138.8i	−0.596668	+	0.596668i
$826$	11341.1	+	8589.83i	0.477732	+	0.361838i
$827$	10027.9	−	10027.9i	0.421649	−	0.421649i	−0.464122	−	0.885771i	$-0.653630\pi$
$827$	10027.9	−	10027.9i	0.421649	−	0.421649i	0.885771	+	0.464122i	$0.153630\pi$
$828$	−3360.15	−	11939.1i	−0.141031	−	0.501101i
$829$		−	7755.84i		−	0.324935i	−0.986714	−	0.162468i	$-0.948055\pi$
$829$		−	7755.84i		−	0.324935i	0.986714	−	0.162468i	$-0.0519453\pi$
$830$	−15996.3	+	21119.8i	−0.668962	+	0.883226i
$831$	−24748.1			−1.03309
$832$	−13726.5	−	19685.4i	−0.571973	−	0.820273i
$833$	15954.7			0.663623
$834$	7807.15	−	10307.7i	0.324148	−	0.427970i
$835$			29441.5i			1.22020i
$836$	6228.67	+	22131.3i	0.257683	+	0.915582i
$837$	10990.3	−	10990.3i	0.453861	−	0.453861i
$838$	−27987.7	−	21198.1i	−1.15372	−	0.873839i
$839$	13617.2	−	13617.2i	0.560332	−	0.560332i	−0.369070	−	0.929402i	$-0.620324\pi$
$839$	13617.2	−	13617.2i	0.560332	−	0.560332i	0.929402	+	0.369070i	$0.120324\pi$
$840$	−68120.1	−	26725.9i	−2.79806	−	1.09777i
$841$	−18339.5			−0.751959
$842$	−23.0348	−	166.871i	−0.000942792	−	0.00682988i
$843$	−48119.0	+	48119.0i	−1.96596	+	1.96596i
$844$	11486.0	−	3232.63i	0.468440	−	0.131839i
$845$	−31567.9	+	11779.5i	−1.28517	+	0.479557i
$846$	−5628.62	−	40775.5i	−0.228742	−	1.65708i
$847$	15265.1	+	15265.1i	0.619260	+	0.619260i
$848$	−19082.1	+	11665.0i	−0.772739	+	0.472379i
$849$			61588.0i			2.48963i
$850$	−8973.96	+	11848.2i	−0.362123	+	0.478108i
$851$	−3274.93	−	3274.93i	−0.131919	−	0.131919i
$852$	60367.9	+	33850.8i	2.42743	+	1.36116i
$853$	−252.062	−	252.062i	−0.0101177	−	0.0101177i	0.702030	−	0.712148i	$-0.252277\pi$
$853$	−252.062	−	252.062i	−0.0101177	−	0.0101177i	−0.712148	+	0.702030i	$0.752277\pi$
$854$	−578.433	−	4190.34i	−0.0231775	−	0.167905i
$855$	75998.6			3.03988
$856$	7348.57	−	18730.4i	0.293422	−	0.747887i
$857$		−	42058.4i		−	1.67642i	−0.545350	−	0.838208i	$-0.683603\pi$
$857$		−	42058.4i		−	1.67642i	0.545350	−	0.838208i	$-0.316397\pi$
$858$	−23983.0	−	1849.24i	−0.954271	−	0.0735803i
$859$		−	1030.59i		−	0.0409351i	−0.999791	−	0.0204675i	$-0.993485\pi$
$859$		−	1030.59i		−	0.0409351i	0.999791	−	0.0204675i	$-0.00651547\pi$
$860$	−23496.3	−	13175.3i	−0.931646	−	0.522413i
$861$	−11995.0			−0.474785
$862$	19377.7	−	2674.89i	0.765670	−	0.105693i
$863$	25418.2	+	25418.2i	1.00260	+	1.00260i	0.999997	+	0.00260554i	$0.000829369\pi$
$863$	25418.2	+	25418.2i	1.00260	+	1.00260i	0.00260554	+	0.999997i	$0.499171\pi$
$864$	−16956.3	−	1693.35i	−0.667668	−	0.0666771i
$865$	−9238.84	−	9238.84i	−0.363156	−	0.363156i
$866$	−13546.3	−	10260.1i	−0.531551	−	0.402602i
$867$			21380.1i			0.837493i
$868$	−9314.87	−	33097.0i	−0.364248	−	1.29422i
$869$	8797.99	+	8797.99i	0.343442	+	0.343442i
$870$	−27073.8	+	3737.25i	−1.05504	+	0.145637i
$871$	−10868.1	−	16908.4i	−0.422793	−	0.657773i
$872$	36898.3	−	16103.8i	1.43295	−	0.625393i
$873$	556.784	−	556.784i	0.0215857	−	0.0215857i
$874$	14431.7	−	1992.15i	0.558536	−	0.0770999i
$875$	−5906.65			−0.228207
$876$	11747.3	+	6587.20i	0.453087	+	0.254065i
$877$	1248.93	−	1248.93i	0.0480881	−	0.0480881i	−0.682654	−	0.730742i	$-0.739174\pi$
$877$	1248.93	−	1248.93i	0.0480881	−	0.0480881i	0.730742	+	0.682654i	$0.239174\pi$
$878$	25716.8	−	33953.6i	0.988495	−	1.30510i
$879$	28784.7	−	28784.7i	1.10453	−	1.10453i
$880$	11466.3	+	18757.1i	0.439238	+	0.718526i
$881$			25746.3i			0.984578i	0.870432	+	0.492289i	$0.163840\pi$
$881$			25746.3i			0.984578i	−0.870432	+	0.492289i	$0.836160\pi$
$882$	−29136.2	−	22068.0i	−1.11232	−	0.842482i
$883$	−13787.7			−0.525473			−0.262737	−	0.964868i	$-0.584625\pi$
$883$	−13787.7			−0.525473			−0.262737	+	0.964868i	$0.584625\pi$
$884$	−17847.8	+	1076.07i	−0.679056	+	0.0409412i
$885$	−24006.2			−0.911820
$886$	901.954	+	683.147i	0.0342006	+	0.0259038i
$887$		−	2244.18i		−	0.0849519i	−0.999097	−	0.0424760i	$-0.986475\pi$
$887$		−	2244.18i		−	0.0849519i	0.999097	−	0.0424760i	$-0.0135246\pi$
$888$	−19382.1	+	8459.07i	−0.732457	+	0.319671i
$889$	−12183.2	+	12183.2i	−0.459629	+	0.459629i
$890$	33491.7	−	44218.8i	1.26140	−	1.66541i
$891$	4437.59	−	4437.59i	0.166852	−	0.166852i
$892$	−2168.11	+	3866.49i	−0.0813829	+	0.145134i
$893$	48349.4			1.81182
$894$	−4865.97	+	671.695i	−0.182038	+	0.0251285i
$895$	−1374.13	+	1374.13i	−0.0513209	+	0.0513209i
$896$	−21613.3	+	30885.1i	−0.805858	+	1.15156i
$897$	−3238.87	+	14894.1i	−0.120561	+	0.554403i
$898$	15689.0	−	2165.70i	0.583015	−	0.0804791i
$899$	−9080.49	−	9080.49i	−0.336876	−	0.336876i
$900$	32776.2	−	9224.58i	1.21393	−	0.341651i
$901$			16663.2i			0.616128i
$902$	2872.71	+	2175.82i	0.106043	+	0.0803179i
$903$	−32737.6	−	32737.6i	−1.20647	−	1.20647i
$904$	−32943.7	−	12924.9i	−1.21205	−	0.475528i
$905$	37315.2	+	37315.2i	1.37061	+	1.37061i
$906$	70594.2	−	9744.79i	2.58867	−	0.357339i
$907$	−12922.3			−0.473074			−0.236537	−	0.971622i	$-0.576012\pi$
$907$	−12922.3			−0.473074			−0.236537	+	0.971622i	$0.576012\pi$
$908$	−855.167	+	1525.06i	−0.0312552	+	0.0557390i
$909$		−	9283.20i		−	0.338728i
$910$	34436.4	+	40190.6i	1.25446	+	1.46407i
$911$			4647.63i			0.169026i	0.996422	+	0.0845131i	$0.0269335\pi$
$911$			4647.63i			0.169026i	−0.996422	+	0.0845131i	$0.973067\pi$
$912$	15599.5	−	64666.5i	0.566395	−	2.34794i
$913$	13680.0			0.495884
$914$	−1108.10	−	8027.42i	−0.0401014	−	0.290507i
$915$	5047.15	+	5047.15i	0.182354	+	0.182354i
$916$	−25615.7	+	45681.7i	−0.923980	+	1.64778i
$917$	−2653.71	−	2653.71i	−0.0955653	−	0.0955653i
$918$	−7665.60	+	10120.8i	−0.275602	+	0.363875i
$919$			35415.4i			1.27121i	0.772013	+	0.635607i	$0.219250\pi$
$919$			35415.4i			1.27121i	−0.772013	+	0.635607i	$0.780750\pi$
$920$	12767.6	−	5572.24i	0.457538	−	0.199686i
$921$	−41721.2	−	41721.2i	−1.49268	−	1.49268i
$922$	2967.64	+	21498.5i	0.106002	+	0.767913i
$923$	−27066.8	−	42110.0i	−0.965238	−	1.50170i
$924$	10236.3	+	36370.8i	0.364446	+	1.29493i
$925$	8990.63	−	8990.63i	0.319578	−	0.319578i
$926$	4260.89	+	30867.2i	0.151211	+	1.09542i
$927$	−54875.2			−1.94427
$928$	−1399.09	+	14009.7i	−0.0494906	+	0.495572i
$929$	−10704.0	+	10704.0i	−0.378026	+	0.378026i	−0.870390	−	0.492364i	$-0.836133\pi$
$929$	−10704.0	+	10704.0i	−0.378026	+	0.378026i	0.492364	+	0.870390i	$0.336133\pi$
$930$	46248.5	+	35029.0i	1.63070	+	1.23510i
$931$	30357.6	−	30357.6i	1.06867	−	1.06867i
$932$	7671.34	−	2159.03i	0.269617	−	0.0758815i
$933$			37838.8i			1.32774i
$934$	33387.9	−	44081.8i	1.16968	−	1.54432i
$935$	16379.4			0.572903
$936$	34081.7	+	22721.3i	1.19016	+	0.793451i
$937$	−18029.3			−0.628591			−0.314296	−	0.949325i	$-0.601768\pi$
$937$	−18029.3			−0.628591			−0.314296	+	0.949325i	$0.601768\pi$
$938$	−19062.8	+	25168.4i	−0.663562	+	0.876096i
$939$			2539.88i			0.0882705i
$940$	44503.1	−	12525.0i	1.54418	−	0.434597i
$941$	−9943.70	+	9943.70i	−0.344479	+	0.344479i	−0.858048	−	0.513569i	$-0.828323\pi$
$941$	−9943.70	+	9943.70i	−0.344479	+	0.344479i	0.513569	+	0.858048i	$0.328323\pi$
$942$	10221.6	+	7741.94i	0.353544	+	0.267777i
$943$	1614.70	−	1614.70i	0.0557601	−	0.0557601i
$944$	−2900.08	+	12022.0i	−0.0999890	+	0.414496i
$945$	37581.1			1.29366
$946$	1902.01	+	13778.8i	0.0653697	+	0.473558i
$947$	7541.89	−	7541.89i	0.258795	−	0.258795i	−0.565769	−	0.824564i	$-0.691421\pi$
$947$	7541.89	−	7541.89i	0.258795	−	0.258795i	0.824564	+	0.565769i	$0.191421\pi$
$948$	−9752.96	−	34653.6i	−0.334136	−	1.18723i
$949$	−5267.07	−	8194.40i	−0.180165	−	0.280297i
$950$	5469.01	+	39619.2i	0.186777	+	1.35307i
$951$	38748.0	+	38748.0i	1.32123	+	1.32123i
$952$	11234.4	+	25741.1i	0.382466	+	0.876338i
$953$			4078.95i			0.138646i	0.997594	+	0.0693232i	$0.0220840\pi$
$953$			4078.95i			0.138646i	−0.997594	+	0.0693232i	$0.977916\pi$
$954$	23048.0	−	30430.0i	0.782186	−	1.03271i
$955$	2006.26	+	2006.26i	0.0679802	+	0.0679802i
$956$	−16016.4	+	28562.9i	−0.541850	+	0.966308i
$957$	9978.70	+	9978.70i	0.337059	+	0.337059i
$958$	1109.81	+	8039.80i	0.0374283	+	0.271142i
$959$	−63580.5			−2.14090
$960$	−2393.45	−	63563.3i	−0.0804671	−	2.13697i
$961$		−	2530.67i		−	0.0849476i
$962$	15250.3	+	1175.89i	0.511112	+	0.0394099i
$963$			34341.8i			1.14917i
$964$	17694.6	−	31555.6i	0.591187	−	1.05429i
$965$	32766.3			1.09304
$966$	23717.3	−	3273.92i	0.789948	−	0.109044i
$967$	−24951.8	−	24951.8i	−0.829779	−	0.829779i	0.157707	−	0.987486i	$-0.449590\pi$
$967$	−24951.8	−	24951.8i	−0.829779	−	0.829779i	−0.987486	+	0.157707i	$0.949590\pi$
$968$	−6853.78	+	17469.2i	−0.227571	+	0.580044i
$969$	−35045.6	−	35045.6i	−1.16184	−	1.16184i
$970$	705.003	+	533.975i	0.0233364	+	0.0176752i
$971$		−	4023.87i		−	0.132989i	−0.997787	−	0.0664944i	$-0.978819\pi$
$971$		−	4023.87i		−	0.132989i	0.997787	−	0.0664944i	$-0.0211815\pi$
$972$	−37052.0	+	10428.0i	−1.22268	+	0.344113i
$973$	10387.8	+	10387.8i	0.342258	+	0.342258i
$974$	19960.1	−	2755.28i	0.656636	−	0.0906416i
$975$	−40888.6	−	8891.63i	−1.34306	−	0.292062i
$976$	3137.28	−	1917.83i	0.102891	−	0.0628978i
$977$	2392.80	−	2392.80i	0.0783545	−	0.0783545i	−0.666843	−	0.745198i	$-0.732355\pi$
$977$	2392.80	−	2392.80i	0.0783545	−	0.0783545i	0.745198	+	0.666843i	$0.232355\pi$
$978$	−55647.5	+	7681.55i	−1.81944	+	0.251154i
$979$	−28642.1			−0.935041
$980$	20078.4	−	35806.8i	0.654471	−	1.16715i
$981$	−48589.2	+	48589.2i	−1.58138	+	1.58138i
$982$	−15594.1	+	20588.7i	−0.506749	+	0.669056i
$983$	14185.7	−	14185.7i	0.460279	−	0.460279i	−0.438468	−	0.898747i	$-0.644479\pi$
$983$	14185.7	−	14185.7i	0.460279	−	0.460279i	0.898747	+	0.438468i	$0.144479\pi$
$984$	−4170.72	−	9556.31i	−0.135120	−	0.309598i
$985$		−	62317.3i		−	2.01583i
$986$	8362.08	+	6333.51i	0.270084	+	0.204564i
$987$	79457.9			2.56249
$988$	−31912.1	+	36007.1i	−1.02759	+	1.15945i
$989$	8813.86			0.283382
$990$	−29911.8	−	22655.4i	−0.960262	−	0.727310i
$991$		−	31069.6i		−	0.995922i	−0.867200	−	0.497961i	$-0.834082\pi$
$991$		−	31069.6i		−	0.995922i	0.867200	−	0.497961i	$-0.165918\pi$
$992$	23129.2	−	18929.0i	0.740274	−	0.605843i
$993$	−65788.2	+	65788.2i	−2.10244	+	2.10244i
$994$	−47475.4	+	62681.3i	−1.51492	+	2.00013i
$995$	−37180.2	+	37180.2i	−1.18461	+	1.18461i
$996$	−34523.9	−	19359.0i	−1.09832	−	0.615877i
$997$	12594.1			0.400059			0.200030	−	0.979790i	$-0.435896\pi$
$997$	12594.1			0.400059			0.200030	+	0.979790i	$0.435896\pi$
$998$	−23426.0	+	3233.71i	−0.743022	+	0.102566i
$999$	7679.84	−	7679.84i	0.243223	−	0.243223i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	52.4.f.b.31.6	yes	36
4.3	odd	2	inner	52.4.f.b.31.4	✓	36
13.8	odd	4	inner	52.4.f.b.47.4	yes	36
52.47	even	4	inner	52.4.f.b.47.6	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.4.f.b.31.4	✓	36	4.3	odd	2	inner
52.4.f.b.31.6	yes	36	1.1	even	1	trivial
52.4.f.b.47.4	yes	36	13.8	odd	4	inner
52.4.f.b.47.6	yes	36	52.47	even	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:	\( N \)	\(=\)	\( 52 = 2^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	52.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.70773 + 2.25470i) q^{2} +8.10067i q^{3} +(-2.16733 - 7.70082i) q^{4} +(-10.8445 + 10.8445i) q^{5} +(-18.2646 - 13.8337i) q^{6} +(18.4065 - 18.4065i) q^{7} +(21.0642 + 8.26423i) q^{8} -38.6209 q^{9} +(-5.93160 - 42.9704i) q^{10} +(-15.8378 + 15.8378i) q^{11} +(62.3818 - 17.5568i) q^{12} +(-45.8017 - 9.96005i) q^{13} +(10.0678 + 72.9343i) q^{14} +(-87.8474 - 87.8474i) q^{15} +(-54.6053 + 33.3805i) q^{16} +47.6833i q^{17} +(65.9540 - 87.0785i) q^{18} +(90.7289 + 90.7289i) q^{19} +(107.015 + 60.0077i) q^{20} +(149.105 + 149.105i) q^{21} +(-8.66280 - 62.7560i) q^{22} -40.1431 q^{23} +(-66.9458 + 170.635i) q^{24} -110.204i q^{25} +(100.674 - 86.2600i) q^{26} -94.1371i q^{27} +(-181.638 - 101.852i) q^{28} -77.7784 q^{29} +(348.089 - 48.0500i) q^{30} +(116.748 + 116.748i) q^{31} +(17.9881 - 180.123i) q^{32} +(-128.297 - 128.297i) q^{33} +(-107.512 - 81.4302i) q^{34} +399.217i q^{35} +(83.7043 + 297.413i) q^{36} +(81.5814 + 81.5814i) q^{37} +(-359.507 + 49.6261i) q^{38} +(80.6831 - 371.025i) q^{39} +(-318.051 + 138.809i) q^{40} +(-40.2235 + 40.2235i) q^{41} +(-590.817 + 81.5560i) q^{42} -219.561 q^{43} +(156.289 + 87.6381i) q^{44} +(418.823 - 418.823i) q^{45} +(68.5535 - 90.5107i) q^{46} +(266.450 - 266.450i) q^{47} +(-270.404 - 442.340i) q^{48} -334.597i q^{49} +(248.478 + 188.199i) q^{50} -386.267 q^{51} +(22.5669 + 374.298i) q^{52} +349.455 q^{53} +(212.251 + 160.761i) q^{54} -343.504i q^{55} +(539.834 - 235.603i) q^{56} +(-734.965 + 734.965i) q^{57} +(132.824 - 175.367i) q^{58} +(136.636 - 136.636i) q^{59} +(-486.103 + 866.892i) q^{60} -57.4537 q^{61} +(-462.606 + 63.8579i) q^{62} +(-710.875 + 710.875i) q^{63} +(375.405 + 348.159i) q^{64} +(604.706 - 388.683i) q^{65} +(508.366 - 70.1745i) q^{66} +(303.226 + 303.226i) q^{67} +(367.201 - 103.346i) q^{68} -325.186i q^{69} +(-900.113 - 681.753i) q^{70} +(755.177 + 755.177i) q^{71} +(-813.520 - 319.172i) q^{72} +(146.954 + 146.954i) q^{73} +(-323.260 + 44.6226i) q^{74} +892.730 q^{75} +(502.048 - 895.327i) q^{76} +583.035i q^{77} +(698.764 + 815.525i) q^{78} -555.507i q^{79} +(230.172 - 954.158i) q^{80} -280.190 q^{81} +(-22.0011 - 159.383i) q^{82} +(-431.879 - 431.879i) q^{83} +(825.071 - 1471.39i) q^{84} +(-517.100 - 517.100i) q^{85} +(374.950 - 495.044i) q^{86} -630.057i q^{87} +(-464.497 + 202.724i) q^{88} +(904.234 + 904.234i) q^{89} +(229.084 + 1659.55i) q^{90} +(-1026.38 + 659.719i) q^{91} +(87.0035 + 309.135i) q^{92} +(-945.740 + 945.740i) q^{93} +(145.740 + 1055.79i) q^{94} -1967.81 q^{95} +(1459.12 + 145.716i) q^{96} +(-14.4167 + 14.4167i) q^{97} +(754.416 + 571.401i) q^{98} +(611.669 - 611.669i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 2 q^{2} - 20 q^{5} - 16 q^{6} - 40 q^{8} - 332 q^{9} - 96 q^{13} + 204 q^{14} + 52 q^{16} + 330 q^{18} + 500 q^{20} + 224 q^{21} - 48 q^{22} - 496 q^{24} + 570 q^{26} - 356 q^{28} + 560 q^{29} + 292 q^{32}+ \cdots + 3226 q^{98}+O(q^{100}) \) 36 * q + 2 * q^2 - 20 * q^5 - 16 * q^6 - 40 * q^8 - 332 * q^9 - 96 * q^13 + 204 * q^14 + 52 * q^16 + 330 * q^18 + 500 * q^20 + 224 * q^21 - 48 * q^22 - 496 * q^24 + 570 * q^26 - 356 * q^28 + 560 * q^29 + 292 * q^32 + 104 * q^33 - 416 * q^34 - 788 * q^37 - 2788 * q^40 + 1124 * q^41 - 1172 * q^42 - 156 * q^44 - 972 * q^45 - 668 * q^46 + 1332 * q^48 + 1354 * q^50 - 164 * q^52 + 1208 * q^53 + 2272 * q^54 - 1248 * q^57 - 2972 * q^58 + 692 * q^60 + 2632 * q^61 + 596 * q^65 + 3312 * q^66 + 2948 * q^68 - 1008 * q^70 - 908 * q^72 - 196 * q^73 - 1504 * q^74 - 3472 * q^76 - 2688 * q^78 - 1096 * q^80 - 764 * q^81 + 3744 * q^84 + 600 * q^85 - 3952 * q^86 - 2748 * q^89 - 1224 * q^92 - 6128 * q^93 + 2884 * q^94 + 4792 * q^96 - 1820 * q^97 + 3226 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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