LMFDB - Embedded newform 45.5.i.a.11.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,5,Mod(11,45)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("45.11"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	45.i (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.65164833877$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.2
Character	$\chi$	$=$	45.11
Dual form			45.5.i.a.41.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.76237 - 3.32690i) q^{2} +(8.89517 - 1.36966i) q^{3} +(14.1366 + 24.4853i) q^{4} +(-9.68246 + 5.59017i) q^{5} +(-55.8139 - 21.7009i) q^{6} +(-43.3865 + 75.1475i) q^{7} -81.6633i q^{8} +(77.2481 - 24.3666i) q^{9} +74.3918 q^{10} +(19.6784 + 11.3613i) q^{11} +(159.284 + 198.438i) q^{12} +(134.910 + 233.671i) q^{13} +(500.017 - 288.685i) q^{14} +(-78.4705 + 62.9871i) q^{15} +(-45.5005 + 78.8092i) q^{16} -81.9372i q^{17} +(-526.197 - 116.588i) q^{18} +31.3780 q^{19} +(-273.754 - 158.052i) q^{20} +(-283.004 + 727.875i) q^{21} +(-75.5959 - 130.936i) q^{22} +(-632.571 + 365.215i) q^{23} +(-111.851 - 726.409i) q^{24} +(62.5000 - 108.253i) q^{25} -1795.33i q^{26} +(653.761 - 322.549i) q^{27} -2453.34 q^{28} +(927.286 + 535.369i) q^{29} +(661.728 - 101.891i) q^{30} +(97.2845 + 168.502i) q^{31} +(-607.178 + 350.554i) q^{32} +(190.603 + 74.1082i) q^{33} +(-272.597 + 472.152i) q^{34} -970.151i q^{35} +(1688.65 + 1546.98i) q^{36} -818.423 q^{37} +(-180.811 - 104.391i) q^{38} +(1520.09 + 1893.76i) q^{39} +(456.512 + 790.701i) q^{40} +(-1995.71 + 1152.22i) q^{41} +(4052.34 - 3252.75i) q^{42} +(636.534 - 1102.51i) q^{43} +642.440i q^{44} +(-611.738 + 667.759i) q^{45} +4860.14 q^{46} +(-268.185 - 154.836i) q^{47} +(-296.794 + 763.342i) q^{48} +(-2564.27 - 4441.44i) q^{49} +(-720.296 + 415.863i) q^{50} +(-112.226 - 728.845i) q^{51} +(-3814.33 + 6606.61i) q^{52} +1226.04i q^{53} +(-4840.30 - 316.357i) q^{54} -254.047 q^{55} +(6136.79 + 3543.08i) q^{56} +(279.112 - 42.9770i) q^{57} +(-3562.24 - 6169.99i) q^{58} +(1006.66 - 581.197i) q^{59} +(-2651.56 - 1030.95i) q^{60} +(1842.41 - 3191.15i) q^{61} -1294.63i q^{62} +(-1520.43 + 6862.19i) q^{63} +6121.06 q^{64} +(-2612.52 - 1508.34i) q^{65} +(-851.776 - 1061.16i) q^{66} +(2756.39 + 4774.21i) q^{67} +(2006.25 - 1158.31i) q^{68} +(-5126.61 + 4115.05i) q^{69} +(-3227.60 + 5590.36i) q^{70} -5754.02i q^{71} +(-1989.86 - 6308.33i) q^{72} +7237.24 q^{73} +(4716.05 + 2722.81i) q^{74} +(407.679 - 1048.53i) q^{75} +(443.577 + 768.298i) q^{76} +(-1707.55 + 985.853i) q^{77} +(-2458.98 - 15969.8i) q^{78} +(-140.406 + 243.190i) q^{79} -1017.42i q^{80} +(5373.53 - 3764.55i) q^{81} +15333.3 q^{82} +(-2341.86 - 1352.07i) q^{83} +(-21822.9 + 3360.24i) q^{84} +(458.043 + 793.353i) q^{85} +(-7335.88 + 4235.37i) q^{86} +(8981.64 + 3492.14i) q^{87} +(927.801 - 1607.00i) q^{88} +288.786i q^{89} +(5746.63 - 1812.68i) q^{90} -23413.0 q^{91} +(-17884.8 - 10325.8i) q^{92} +(1096.15 + 1365.61i) q^{93} +(1030.25 + 1784.45i) q^{94} +(-303.816 + 175.408i) q^{95} +(-4920.81 + 3949.86i) q^{96} +(1320.77 - 2287.63i) q^{97} +34124.3i q^{98} +(1796.95 + 398.144i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{3} + 128 q^{4} + 98 q^{6} - 26 q^{7} - 220 q^{9} - 738 q^{11} - 214 q^{12} + 10 q^{13} + 1998 q^{14} - 50 q^{15} - 1024 q^{16} - 2504 q^{18} + 508 q^{19} - 1620 q^{21} + 672 q^{22} + 1998 q^{23}+ \cdots + 53512 q^{99}+O(q^{100}) $ 32 * q - 8 * q^3 + 128 * q^4 + 98 * q^6 - 26 * q^7 - 220 * q^9 - 738 * q^11 - 214 * q^12 + 10 * q^13 + 1998 * q^14 - 50 * q^15 - 1024 * q^16 - 2504 * q^18 + 508 * q^19 - 1620 * q^21 + 672 * q^22 + 1998 * q^23 + 4164 * q^24 + 2000 * q^25 + 2158 * q^27 - 1664 * q^28 - 270 * q^29 + 2000 * q^30 - 1472 * q^31 - 6048 * q^32 - 1354 * q^33 - 594 * q^34 + 4498 * q^36 + 2068 * q^37 - 7164 * q^38 - 4616 * q^39 + 1650 * q^40 - 13428 * q^41 - 10230 * q^42 + 568 * q^43 - 100 * q^45 + 5724 * q^46 + 12528 * q^47 + 25844 * q^48 - 1674 * q^49 + 1454 * q^51 + 1534 * q^52 + 8456 * q^54 + 21294 * q^56 - 12512 * q^57 - 8190 * q^58 - 4374 * q^59 - 5050 * q^60 - 4478 * q^61 + 5604 * q^63 - 37216 * q^64 - 8550 * q^65 - 19472 * q^66 + 12838 * q^67 + 65736 * q^68 + 8706 * q^69 + 2400 * q^70 - 36372 * q^72 + 29236 * q^73 - 20628 * q^74 + 1000 * q^75 + 6190 * q^76 - 31806 * q^77 - 42430 * q^78 - 3512 * q^79 - 3088 * q^81 + 34692 * q^82 - 43074 * q^83 - 19350 * q^84 - 4350 * q^85 - 10746 * q^86 + 69622 * q^87 - 16128 * q^88 - 26750 * q^90 - 48904 * q^91 + 27036 * q^92 + 27030 * q^93 + 5118 * q^94 + 6300 * q^95 + 53566 * q^96 + 23266 * q^97 + 53512 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−5.76237	−	3.32690i	−1.44059	−	0.831726i	−0.442703	−	0.896668i	$-0.645980\pi$
$2$	−5.76237	−	3.32690i	−1.44059	−	0.831726i	−0.997889	+	0.0649425i	$0.979314\pi$
$3$	8.89517	−	1.36966i	0.988352	−	0.152184i
$3$	8.89517	−	1.36966i	0.988352	−	0.152184i
$4$	14.1366	+	24.4853i	0.883536	+	1.53033i
$5$	−9.68246	+	5.59017i	−0.387298	+	0.223607i
$5$	−9.68246	+	5.59017i	−0.387298	+	0.223607i
$6$	−55.8139	−	21.7009i	−1.55039	−	0.602803i
$7$	−43.3865	+	75.1475i	−0.885438	+	1.53362i	−0.0402267	+	0.999191i	$0.512808\pi$
$7$	−43.3865	+	75.1475i	−0.885438	+	1.53362i	−0.845211	+	0.534433i	$0.820525\pi$
$8$		−	81.6633i		−	1.27599i
$9$	77.2481	−	24.3666i	0.953680	−	0.300823i
$10$	74.3918			0.743918
$11$	19.6784	+	11.3613i	0.162631	+	0.0938951i	0.579107	−	0.815252i	$-0.303402\pi$
$11$	19.6784	+	11.3613i	0.162631	+	0.0938951i	−0.416476	+	0.909147i	$0.636735\pi$
$12$	159.284	+	198.438i	1.10614	+	1.37804i
$13$	134.910	+	233.671i	0.798283	+	1.38267i	0.920733	+	0.390192i	$0.127592\pi$
$13$	134.910	+	233.671i	0.798283	+	1.38267i	−0.122450	+	0.992475i	$0.539075\pi$
$14$	500.017	−	288.685i	2.55111	−	1.47288i
$15$	−78.4705	+	62.9871i	−0.348758	+	0.279943i
$16$	−45.5005	+	78.8092i	−0.177736	+	0.307849i
$17$		−	81.9372i		−	0.283520i	−0.989901	−	0.141760i	$-0.954724\pi$
$17$		−	81.9372i		−	0.283520i	0.989901	−	0.141760i	$-0.0452761\pi$
$18$	−526.197	−	116.588i	−1.62407	−	0.359838i
$19$	31.3780			0.0869196			0.0434598	−	0.999055i	$-0.486162\pi$
$19$	31.3780			0.0869196			0.0434598	+	0.999055i	$0.486162\pi$
$20$	−273.754	−	158.052i	−0.684384	−	0.395129i
$21$	−283.004	+	727.875i	−0.641732	+	1.65051i
$22$	−75.5959	−	130.936i	−0.156190	−	0.270529i
$23$	−632.571	+	365.215i	−1.19579	+	0.690388i	−0.959613	−	0.281323i	$-0.909227\pi$
$23$	−632.571	+	365.215i	−1.19579	+	0.690388i	−0.236174	+	0.971711i	$0.575893\pi$
$24$	−111.851	−	726.409i	−0.194185	−	1.26113i
$25$	62.5000	−	108.253i	0.100000	−	0.173205i
$26$		−	1795.33i		−	2.65581i
$27$	653.761	−	322.549i	0.896791	−	0.442453i
$28$	−2453.34			−3.12927
$29$	927.286	+	535.369i	1.10260	+	0.636586i	0.936903	−	0.349590i	$-0.113679\pi$
$29$	927.286	+	535.369i	1.10260	+	0.636586i	0.165697	+	0.986177i	$0.447013\pi$
$30$	661.728	−	101.891i	0.735253	−	0.113212i
$31$	97.2845	+	168.502i	0.101233	+	0.175340i	0.912193	−	0.409761i	$-0.134388\pi$
$31$	97.2845	+	168.502i	0.101233	+	0.175340i	−0.810960	+	0.585101i	$0.801055\pi$
$32$	−607.178	+	350.554i	−0.592947	+	0.342338i
$33$	190.603	+	74.1082i	0.175026	+	0.0680516i
$34$	−272.597	+	472.152i	−0.235811	+	0.408436i
$35$		−	970.151i		−	0.791960i
$36$	1688.65	+	1546.98i	1.30297	+	1.19366i
$37$	−818.423			−0.597825			−0.298913	−	0.954280i	$-0.596624\pi$
$37$	−818.423			−0.597825			−0.298913	+	0.954280i	$0.596624\pi$
$38$	−180.811	−	104.391i	−0.125216	−	0.0722933i
$39$	1520.09	+	1893.76i	0.999405	+	1.24508i
$40$	456.512	+	790.701i	0.285320	+	0.494188i
$41$	−1995.71	+	1152.22i	−1.18722	+	0.685439i	−0.957673	−	0.287860i	$-0.907056\pi$
$41$	−1995.71	+	1152.22i	−1.18722	+	0.685439i	−0.229543	+	0.973299i	$0.573723\pi$
$42$	4052.34	−	3252.75i	2.29724	−	1.84397i
$43$	636.534	−	1102.51i	0.344258	−	0.596273i	−0.640960	−	0.767574i	$-0.721464\pi$
$43$	636.534	−	1102.51i	0.344258	−	0.596273i	0.985219	+	0.171301i	$0.0547970\pi$
$44$			642.440i			0.331839i
$45$	−611.738	+	667.759i	−0.302093	+	0.329757i
$46$	4860.14			2.29685
$47$	−268.185	−	154.836i	−0.121405	−	0.0700934i	0.438068	−	0.898942i	$-0.355663\pi$
$47$	−268.185	−	154.836i	−0.121405	−	0.0700934i	−0.559473	+	0.828849i	$0.688996\pi$
$48$	−296.794	+	763.342i	−0.128817	+	0.331311i
$49$	−2564.27	−	4441.44i	−1.06800	−	1.84983i
$50$	−720.296	+	415.863i	−0.288118	+	0.166345i
$51$	−112.226	−	728.845i	−0.0431471	−	0.280217i
$52$	−3814.33	+	6606.61i	−1.41062	+	2.44327i
$53$			1226.04i			0.436468i	0.975896	+	0.218234i	$0.0700297\pi$
$53$			1226.04i			0.436468i	−0.975896	+	0.218234i	$0.929970\pi$
$54$	−4840.30	−	316.357i	−1.65991	−	0.108490i
$55$	−254.047			−0.0839823
$56$	6136.79	+	3543.08i	1.95689	+	1.12981i
$57$	279.112	−	42.9770i	0.0859071	−	0.0132278i
$58$	−3562.24	−	6169.99i	−1.05893	−	1.83412i
$59$	1006.66	−	581.197i	0.289188	−	0.166963i	−0.348388	−	0.937350i	$-0.613271\pi$
$59$	1006.66	−	581.197i	0.289188	−	0.166963i	0.637575	+	0.770388i	$0.279937\pi$
$60$	−2651.56	−	1030.95i	−0.736545	−	0.286375i
$61$	1842.41	−	3191.15i	0.495138	−	0.857604i	−0.504846	−	0.863209i	$-0.668451\pi$
$61$	1842.41	−	3191.15i	0.495138	−	0.857604i	0.999984	+	0.00560491i	$0.00178411\pi$
$62$		−	1294.63i		−	0.336791i
$63$	−1520.43	+	6862.19i	−0.383076	+	1.72895i
$64$	6121.06			1.49440
$65$	−2612.52	−	1508.34i	−0.618348	−	0.357003i
$66$	−851.776	−	1061.16i	−0.195541	−	0.243608i
$67$	2756.39	+	4774.21i	0.614032	+	1.06354i	0.990553	+	0.137127i	$0.0437870\pi$
$67$	2756.39	+	4774.21i	0.614032	+	1.06354i	−0.376521	+	0.926408i	$0.622880\pi$
$68$	2006.25	−	1158.31i	0.433878	−	0.250500i
$69$	−5126.61	+	4115.05i	−1.07679	+	0.864326i
$70$	−3227.60	+	5590.36i	−0.658693	+	1.14089i
$71$		−	5754.02i		−	1.14144i	−0.821143	−	0.570722i	$-0.806663\pi$
$71$		−	5754.02i		−	1.14144i	0.821143	−	0.570722i	$-0.193337\pi$
$72$	−1989.86	−	6308.33i	−0.383846	−	1.21688i
$73$	7237.24			1.35809			0.679043	−	0.734099i	$-0.262395\pi$
$73$	7237.24			1.35809			0.679043	+	0.734099i	$0.262395\pi$
$74$	4716.05	+	2722.81i	0.861222	+	0.497227i
$75$	407.679	−	1048.53i	0.0724762	−	0.186406i
$76$	443.577	+	768.298i	0.0767966	+	0.133016i
$77$	−1707.55	+	985.853i	−0.287999	+	0.166277i
$78$	−2458.98	−	15969.8i	−0.404172	−	2.62488i
$79$	−140.406	+	243.190i	−0.0224973	+	0.0389665i	−0.877055	−	0.480390i	$-0.840495\pi$
$79$	−140.406	+	243.190i	−0.0224973	+	0.0389665i	0.854558	+	0.519357i	$0.173828\pi$
$80$		−	1017.42i		−	0.158972i
$81$	5373.53	−	3764.55i	0.819012	−	0.573777i
$82$	15333.3			2.28039
$83$	−2341.86	−	1352.07i	−0.339942	−	0.196265i	0.320305	−	0.947315i	$-0.396215\pi$
$83$	−2341.86	−	1352.07i	−0.339942	−	0.196265i	−0.660246	+	0.751049i	$0.729548\pi$
$84$	−21822.9	+	3360.24i	−3.09282	+	0.476224i
$85$	458.043	+	793.353i	0.0633969	+	0.109807i
$86$	−7335.88	+	4235.37i	−0.991872	+	0.572657i
$87$	8981.64	+	3492.14i	1.18664	+	0.461373i
$88$	927.801	−	1607.00i	0.119809	−	0.207515i
$89$			288.786i			0.0364583i	0.999834	+	0.0182291i	$0.00580284\pi$
$89$			288.786i			0.0364583i	−0.999834	+	0.0182291i	$0.994197\pi$
$90$	5746.63	−	1812.68i	0.709460	−	0.223787i
$91$	−23413.0			−2.82732
$92$	−17884.8	−	10325.8i	−2.11304	−	1.21997i
$93$	1096.15	+	1365.61i	0.126737	+	0.157892i
$94$	1030.25	+	1784.45i	0.116597	+	0.201952i
$95$	−303.816	+	175.408i	−0.0336638	+	0.0194358i
$96$	−4920.81	+	3949.86i	−0.533942	+	0.428588i
$97$	1320.77	−	2287.63i	0.140373	−	0.243132i	−0.787264	−	0.616616i	$-0.788503\pi$
$97$	1320.77	−	2287.63i	0.140373	−	0.243132i	0.927637	+	0.373483i	$0.121837\pi$
$98$			34124.3i			3.55313i
$99$	1796.95	+	398.144i	0.183344	+	0.0406228i
$100$	3534.15			0.353415
$101$	13580.8	+	7840.88i	1.33132	+	0.768638i	0.985502	−	0.169663i	$-0.0542679\pi$
$101$	13580.8	+	7840.88i	1.33132	+	0.768638i	0.345819	+	0.938301i	$0.387601\pi$
$102$	−1778.11	+	4573.24i	−0.170907	+	0.439565i
$103$	−5510.77	−	9544.94i	−0.519443	−	0.899702i	−0.999745	−	0.0225985i	$-0.992806\pi$
$103$	−5510.77	−	9544.94i	−0.519443	−	0.899702i	0.480301	−	0.877103i	$-0.340527\pi$
$104$	19082.3	−	11017.2i	1.76427	−	1.01860i
$105$	−1328.77	−	8629.65i	−0.120524	−	0.782735i
$106$	4078.92	−	7064.89i	0.363022	−	0.628773i
$107$		−	10979.9i		−	0.959028i	−0.877534	−	0.479514i	$-0.840813\pi$
$107$		−	10979.9i		−	0.959028i	0.877534	−	0.479514i	$-0.159187\pi$
$108$	17139.6	+	11447.8i	1.46945	+	0.981463i
$109$	13014.0			1.09537			0.547683	−	0.836686i	$-0.315510\pi$
$109$	13014.0			1.09537			0.547683	+	0.836686i	$0.315510\pi$
$110$	1463.91	+	845.188i	0.120984	+	0.0698503i
$111$	−7280.01	+	1120.96i	−0.590862	+	0.0909794i
$112$	−3948.21	−	6838.51i	−0.314749	−	0.545162i
$113$	12502.9	−	7218.55i	0.979160	−	0.565318i	0.0771434	−	0.997020i	$-0.475420\pi$
$113$	12502.9	−	7218.55i	0.979160	−	0.565318i	0.902016	+	0.431702i	$0.142087\pi$
$114$	−1751.33	−	680.931i	−0.134759	−	0.0523954i
$115$	4083.23	−	7072.36i	0.308751	−	0.534772i
$116$			30273.2i			2.24979i
$117$	16115.3	+	14763.3i	1.17724	+	1.07848i
$118$	−7734.34			−0.555468
$119$	6157.38	+	3554.96i	0.434812	+	0.251039i
$120$	5143.74	+	6408.16i	0.357204	+	0.445011i
$121$	−7062.34	−	12232.3i	−0.482367	−	0.835485i
$122$	−21233.3	+	12259.0i	−1.42658	+	0.823639i
$123$	−16174.0	+	12982.7i	−1.06907	+	0.858130i
$124$	−2750.54	+	4764.08i	−0.178885	+	0.309839i
$125$			1397.54i			0.0894427i
$126$	31591.1	−	34484.1i	1.98986	−	2.17209i
$127$	−11099.1			−0.688143			−0.344072	−	0.938943i	$-0.611806\pi$
$127$	−11099.1			−0.688143			−0.344072	+	0.938943i	$0.611806\pi$
$128$	−25556.9	−	14755.3i	−1.55987	−	0.900592i
$129$	4152.02	−	10678.8i	0.249505	−	0.641718i
$130$	10036.2	+	17383.2i	0.593858	+	1.02859i
$131$	−9217.50	+	5321.73i	−0.537119	+	0.310106i	−0.743911	−	0.668279i	$-0.767031\pi$
$131$	−9217.50	+	5321.73i	−0.537119	+	0.310106i	0.206792	+	0.978385i	$0.433698\pi$
$132$	879.921	+	5714.61i	0.0505005	+	0.327974i
$133$	−1361.38	+	2357.98i	−0.0769619	+	0.133302i
$134$		−	36681.0i		−	2.04283i
$135$	−4526.91	+	6777.70i	−0.248390	+	0.371890i
$136$	−6691.26			−0.361768
$137$	7853.83	+	4534.41i	0.418447	+	0.241590i	0.694413	−	0.719577i	$-0.255664\pi$
$137$	7853.83	+	4534.41i	0.418447	+	0.241590i	−0.275966	+	0.961167i	$0.588998\pi$
$138$	43231.8	−	6656.72i	2.27010	−	0.349544i
$139$	9210.88	+	15953.7i	0.476729	+	0.825719i	0.999644	−	0.0266658i	$-0.00848898\pi$
$139$	9210.88	+	15953.7i	0.476729	+	0.825719i	−0.522915	+	0.852385i	$0.675156\pi$
$140$	23754.4	−	13714.6i	1.21196	−	0.699725i
$141$	−2597.62	−	1009.98i	−0.130658	−	0.0508011i
$142$	−19143.1	+	33156.8i	−0.949369	+	1.64436i
$143$			6131.01i			0.299819i
$144$	−1594.51	+	7196.56i	−0.0768959	+	0.347056i
$145$	−11971.2			−0.569380
$146$	−41703.6	−	24077.6i	−1.95645	−	1.12955i
$147$	−28892.8	−	35995.2i	−1.33707	−	1.66575i
$148$	−11569.7	−	20039.3i	−0.528200	−	0.914870i
$149$	16241.0	−	9376.75i	0.731544	−	0.422357i	−0.0874430	−	0.996170i	$-0.527870\pi$
$149$	16241.0	−	9376.75i	0.731544	−	0.422357i	0.818987	+	0.573813i	$0.194536\pi$
$150$	−5837.56	+	4685.73i	−0.259447	+	0.208255i
$151$	−15365.0	+	26613.0i	−0.673875	+	1.16719i	0.302921	+	0.953016i	$0.402038\pi$
$151$	−15365.0	+	26613.0i	−0.673875	+	1.16719i	−0.976796	+	0.214171i	$0.931295\pi$
$152$		−	2562.43i		−	0.110908i
$153$	−1996.53	−	6329.49i	−0.0852891	−	0.270387i
$154$	13119.4			0.553186
$155$	−1883.91	−	1087.67i	−0.0784144	−	0.0452726i
$156$	−24880.3	+	63991.2i	−1.02237	+	2.62949i
$157$	−20245.1	−	35065.6i	−0.821337	−	1.42260i	−0.904687	−	0.426077i	$-0.859895\pi$
$157$	−20245.1	−	35065.6i	−0.821337	−	1.42260i	0.0833500	−	0.996520i	$-0.473438\pi$
$158$	1618.14	−	934.234i	0.0648189	−	0.0374232i
$159$	1679.25	+	10905.8i	0.0664235	+	0.431384i
$160$	3919.32	−	6788.45i	0.153098	−	0.265174i
$161$		−	63381.5i		−	2.44518i
$162$	−43488.6	+	3815.49i	−1.65709	+	0.145385i
$163$	7005.43			0.263669			0.131835	−	0.991272i	$-0.457913\pi$
$163$	7005.43			0.263669			0.131835	+	0.991272i	$0.457913\pi$
$164$	−56425.0	−	32577.0i	−2.09790	−	1.21122i
$165$	−2259.79	+	347.956i	−0.0830041	+	0.0127808i
$166$	8996.43	+	15582.3i	0.326478	+	0.565477i
$167$	19921.0	−	11501.4i	0.714295	−	0.412399i	−0.0983540	−	0.995151i	$-0.531358\pi$
$167$	19921.0	−	11501.4i	0.714295	−	0.412399i	0.812649	+	0.582753i	$0.198024\pi$
$168$	59440.6	+	23111.0i	2.10603	+	0.818842i
$169$	−22120.8	+	38314.4i	−0.774512	+	1.34149i
$170$		−	6095.46i		−	0.210915i
$171$	2423.89	−	764.575i	0.0828935	−	0.0261474i
$172$	35993.6			1.21666
$173$	41608.6	+	24022.8i	1.39024	+	0.802658i	0.993342	−	0.115203i	$-0.0367518\pi$
$173$	41608.6	+	24022.8i	1.39024	+	0.802658i	0.396903	+	0.917861i	$0.370085\pi$
$174$	−40137.5	−	50004.0i	−1.32572	−	1.65161i
$175$	5423.31	+	9393.44i	0.177088	+	0.306725i
$176$	−1790.75	+	1033.89i	−0.0578109	+	0.0333772i
$177$	8158.39	−	6548.62i	0.260410	−	0.209027i
$178$	960.764	−	1664.09i	0.0303233	−	0.0525215i
$179$			22979.1i			0.717179i	0.933495	+	0.358590i	$0.116742\pi$
$179$			22979.1i			0.717179i	−0.933495	+	0.358590i	$0.883258\pi$
$180$	−24998.1	−	5538.74i	−0.771548	−	0.170949i
$181$	10675.2			0.325850			0.162925	−	0.986638i	$-0.447907\pi$
$181$	10675.2			0.325850			0.162925	+	0.986638i	$0.447907\pi$
$182$	134915.	+	77892.9i	4.07301	+	2.35156i
$183$	12017.8	−	30909.3i	0.358857	−	0.922967i
$184$	29824.7	+	51657.8i	0.880927	+	1.52581i
$185$	7924.35	−	4575.12i	0.231537	−	0.133678i
$186$	−1773.19	−	11515.9i	−0.0512542	−	0.332868i
$187$	930.913	−	1612.39i	0.0266211	−	0.0461091i
$188$		−	8755.43i		−	0.247720i
$189$	−4125.64	+	63122.8i	−0.115496	+	1.76711i
$190$	2334.26			0.0646611
$191$	2871.83	+	1658.05i	0.0787213	+	0.0454498i	0.538844	−	0.842406i	$-0.318861\pi$
$191$	2871.83	+	1658.05i	0.0787213	+	0.0454498i	−0.460123	+	0.887855i	$0.652195\pi$
$192$	54447.9	−	8383.74i	1.47699	−	0.227423i
$193$	16547.5	+	28661.1i	0.444240	+	0.769447i	0.997999	−	0.0632303i	$-0.0201403\pi$
$193$	16547.5	+	28661.1i	0.444240	+	0.769447i	−0.553759	+	0.832677i	$0.686807\pi$
$194$	−15221.5	+	8788.12i	−0.404439	+	0.233503i
$195$	−25304.7	−	9838.67i	−0.665475	−	0.258742i
$196$	72500.0	−	125574.i	1.88723	−	3.26878i
$197$		−	14639.5i		−	0.377220i	−0.982052	−	0.188610i	$-0.939602\pi$
$197$		−	14639.5i		−	0.377220i	0.982052	−	0.188610i	$-0.0603982\pi$
$198$	−9030.11	−	8272.54i	−0.230336	−	0.211013i
$199$	−43010.4			−1.08609			−0.543047	−	0.839702i	$-0.682729\pi$
$199$	−43010.4			−1.08609			−0.543047	+	0.839702i	$0.682729\pi$
$200$	−8840.31	−	5103.95i	−0.221008	−	0.127599i
$201$	31057.6	+	38692.1i	0.768733	+	0.957702i
$202$	−52171.7	−	90364.1i	−1.27859	−	2.21459i
$203$	−80463.3	+	46455.5i	−1.95257	+	1.12732i
$204$	16259.5	−	13051.3i	0.390703	−	0.313611i
$205$	12882.2	−	22312.7i	0.306538	−	0.530939i
$206$			73335.2i			1.72814i
$207$	−39965.8	+	43625.8i	−0.932714	+	1.01813i
$208$	−24553.9			−0.567536
$209$	617.467	+	356.495i	0.0141358	+	0.00816132i
$210$	−21053.2	+	54147.9i	−0.477396	+	1.22784i
$211$	40186.0	+	69604.2i	0.902630	+	1.56340i	0.824067	+	0.566493i	$0.191700\pi$
$211$	40186.0	+	69604.2i	0.902630	+	1.56340i	0.0785636	+	0.996909i	$0.474967\pi$
$212$	−30019.9	+	17332.0i	−0.667940	+	0.385636i
$213$	−7881.02	−	51183.0i	−0.173709	−	1.12815i
$214$	−36529.1	+	63270.3i	−0.797648	+	1.38157i
$215$			14233.3i			0.307914i
$216$	−26340.4	−	53388.3i	−0.564565	−	1.14430i
$217$	−16883.3			−0.358541
$218$	−74991.7	−	43296.5i	−1.57798	−	0.911045i
$219$	64376.4	−	9912.52i	1.34227	−	0.206679i
$220$	−3591.35	−	6220.40i	−0.0742014	−	0.128521i
$221$	19146.3	−	11054.1i	0.392013	−	0.226329i
$222$	45679.4	+	17760.5i	0.926861	+	0.360371i
$223$	25655.2	−	44436.1i	0.515900	−	0.893566i	−0.483929	−	0.875107i	$-0.660791\pi$
$223$	25655.2	−	44436.1i	0.515900	−	0.893566i	0.999830	−	0.0184586i	$-0.00587589\pi$
$224$		−	60837.2i		−	1.21248i
$225$	2190.24	−	9885.27i	0.0432640	−	0.195265i
$226$	−96061.7			−1.88076
$227$	−26315.8	−	15193.4i	−0.510698	−	0.294852i	0.222422	−	0.974950i	$-0.428604\pi$
$227$	−26315.8	−	15193.4i	−0.510698	−	0.294852i	−0.733121	+	0.680099i	$0.761937\pi$
$228$	4998.00	+	6226.59i	0.0961449	+	0.119779i
$229$	6835.33	+	11839.1i	0.130343	+	0.225761i	0.923809	−	0.382854i	$-0.125059\pi$
$229$	6835.33	+	11839.1i	0.130343	+	0.225761i	−0.793466	+	0.608615i	$0.791725\pi$
$230$	−47058.1	+	27169.0i	−0.889568	+	0.513592i
$231$	−13838.7	+	11108.1i	−0.259340	+	0.208169i
$232$	43720.0	−	75725.2i	0.812277	−	1.40690i
$233$			45008.2i			0.829049i	0.910038	+	0.414524i	$0.136052\pi$
$233$			45008.2i			0.829049i	−0.910038	+	0.414524i	$0.863948\pi$
$234$	−43746.1	−	138686.i	−0.798928	−	2.53279i
$235$	3462.25			0.0626935
$236$	28461.5	+	16432.3i	0.511015	+	0.295035i
$237$	−915.847	+	2355.52i	−0.0163052	+	0.0419364i
$238$	−23654.0	−	40970.0i	−0.417591	−	0.723289i
$239$	−28926.9	+	16700.9i	−0.506414	+	0.292378i	−0.731358	−	0.681993i	$-0.761113\pi$
$239$	−28926.9	+	16700.9i	−0.506414	+	0.292378i	0.224944	+	0.974372i	$0.427780\pi$
$240$	−1393.52	−	9050.15i	−0.0241930	−	0.157121i
$241$	20244.2	−	35063.9i	0.348551	−	0.603708i	−0.637441	−	0.770499i	$-0.720007\pi$
$241$	20244.2	−	35063.9i	0.348551	−	0.603708i	0.985992	+	0.166791i	$0.0533406\pi$
$242$			93982.9i			1.60479i
$243$	42642.4	−	40846.2i	0.722152	−	0.691734i
$244$	104181.			1.74989
$245$	49656.8	+	28669.4i	0.827269	+	0.477624i
$246$	136393.	−	21001.4i	2.25383	−	0.347039i
$247$	4233.20	+	7332.11i	0.0693864	+	0.120181i
$248$	13760.4	−	7944.57i	0.223732	−	0.129172i
$249$	−22683.1	−	8819.38i	−0.365851	−	0.142246i
$250$	4649.49	−	8053.15i	0.0743918	−	0.128850i
$251$			13359.3i			0.212049i	0.994364	+	0.106025i	$0.0338122\pi$
$251$			13359.3i			0.212049i	−0.994364	+	0.106025i	$0.966188\pi$
$252$	−189516.	+	59779.7i	−2.98432	+	0.941354i
$253$	−16597.3			−0.259296
$254$	63956.9	+	36925.5i	0.991334	+	0.572347i
$255$	5160.99	+	6429.65i	0.0793693	+	0.0988797i
$256$	49210.5	+	85235.1i	0.750893	+	1.30058i
$257$	−69074.0	+	39879.9i	−1.04580	+	0.603792i	−0.921470	−	0.388449i	$-0.873011\pi$
$257$	−69074.0	+	39879.9i	−1.04580	+	0.603792i	−0.124328	+	0.992241i	$0.539678\pi$
$258$	−59452.9	+	47722.0i	−0.893169	+	0.716934i
$259$	35508.5	−	61502.5i	0.529337	−	0.916839i
$260$		−	85291.0i		−	1.26170i
$261$	84676.2	+	18761.4i	1.24303	+	0.275413i
$262$	70819.5			1.03169
$263$	61428.4	+	35465.7i	0.888092	+	0.512740i	0.873318	−	0.487151i	$-0.161964\pi$
$263$	61428.4	+	35465.7i	0.888092	+	0.512740i	0.0147741	+	0.999891i	$0.495297\pi$
$264$	6051.92	−	15565.3i	0.0868330	−	0.223331i
$265$	−6853.77	−	11871.1i	−0.0975973	−	0.169043i
$266$	15689.5	−	9058.35i	0.221741	−	0.128022i
$267$	395.537	+	2568.80i	0.00554836	+	0.0360336i
$268$	−77931.9	+	134982.i	−1.08504	+	1.87934i
$269$		−	19611.7i		−	0.271025i	−0.990776	−	0.135513i	$-0.956732\pi$
$269$		−	19611.7i		−	0.271025i	0.990776	−	0.135513i	$-0.0432681\pi$
$270$	48634.5	−	23995.0i	0.667140	−	0.329149i
$271$	−108480.			−1.47710			−0.738552	−	0.674196i	$-0.764490\pi$
$271$	−108480.			−1.47710			−0.738552	+	0.674196i	$0.764490\pi$
$272$	6457.41	+	3728.18i	0.0872811	+	0.0503918i
$273$	−208263.	+	32067.8i	−2.79439	+	0.430273i
$274$	−30171.1	−	52257.9i	−0.401874	−	0.696066i
$275$	2459.79	−	1420.16i	0.0325262	−	0.0187790i
$276$	−173231.	−	67353.6i	−2.27409	−	0.884184i
$277$	36918.5	−	63944.7i	0.481154	−	0.833383i	−0.518612	−	0.855010i	$-0.673551\pi$
$277$	36918.5	−	63944.7i	0.481154	−	0.833383i	0.999766	+	0.0216263i	$0.00688440\pi$
$278$		−	122575.i		−	1.58603i
$279$	11620.9	+	10645.9i	0.149290	+	0.136765i
$280$	−79225.7			−1.01053
$281$	16573.0	+	9568.40i	0.209888	+	0.121179i	0.601259	−	0.799054i	$-0.294666\pi$
$281$	16573.0	+	9568.40i	0.209888	+	0.121179i	−0.391371	+	0.920233i	$0.627999\pi$
$282$	11608.3	+	14461.9i	0.145973	+	0.181856i
$283$	−9547.88	−	16537.4i	−0.119216	−	0.206488i	0.800241	−	0.599678i	$-0.204705\pi$
$283$	−9547.88	−	16537.4i	−0.119216	−	0.206488i	−0.919457	+	0.393190i	$0.871371\pi$
$284$	140889.	−	81342.2i	1.74679	−	1.00851i
$285$	−2462.24	+	1976.41i	−0.0303139	+	0.0243325i
$286$	20397.3	−	35329.1i	0.249368	−	0.431917i
$287$		−	199963.i		−	2.42765i
$288$	−38361.5	+	41874.5i	−0.462499	+	0.504853i
$289$	76807.3			0.919617
$290$	68982.5	+	39827.1i	0.820244	+	0.473568i
$291$	8615.17	−	22157.9i	0.101737	−	0.261663i
$292$	102310.	+	177206.i	1.19992	+	2.07832i
$293$	−84058.9	+	48531.4i	−0.979148	+	0.565312i	−0.902013	−	0.431709i	$-0.857911\pi$
$293$	−84058.9	+	48531.4i	−0.979148	+	0.565312i	−0.0771355	+	0.997021i	$0.524577\pi$
$294$	46738.5	+	303541.i	0.540730	+	3.51175i
$295$	−6497.98	+	11254.8i	−0.0746679	+	0.129329i
$296$			66835.1i			0.762818i
$297$	16529.5	+	1080.35i	0.187390	+	0.0122476i
$298$	−124782.			−1.40514
$299$	−170680.	−	98542.2i	−1.90915	−	1.10225i
$300$	31436.8	−	4840.56i	0.349298	−	0.0537840i
$301$	55233.9	+	95667.9i	0.609639	+	1.05593i
$302$	177078.	−	102236.i	1.94156	−	1.12096i
$303$	131543.	+	51144.9i	1.43279	+	0.557080i
$304$	−1427.71	+	2472.87i	−0.0154488	+	0.0267581i
$305$			41197.5i			0.442865i
$306$	−9552.85	+	43115.1i	−0.102021	+	0.460454i
$307$	78376.4			0.831588			0.415794	−	0.909459i	$-0.363504\pi$
$307$	78376.4			0.831588			0.415794	+	0.909459i	$0.363504\pi$
$308$	−48277.8	−	27873.2i	−0.508916	−	0.293823i
$309$	−62092.5	−	77356.0i	−0.650313	−	0.810172i
$310$	7237.18	+	12535.2i	0.0753088	+	0.130439i
$311$	44683.7	−	25798.1i	0.461985	−	0.266727i	−0.250894	−	0.968015i	$-0.580724\pi$
$311$	44683.7	−	25798.1i	0.461985	−	0.266727i	0.712879	+	0.701288i	$0.247391\pi$
$312$	154651.	−	124136.i	1.58870	−	1.27523i
$313$	58825.2	−	101888.i	0.600447	−	1.04001i	−0.392306	−	0.919835i	$-0.628322\pi$
$313$	58825.2	−	101888.i	0.600447	−	1.04001i	0.992753	−	0.120171i	$-0.0383442\pi$
$314$			269414.i			2.73251i
$315$	−23639.3	−	74942.3i	−0.238239	−	0.755276i
$316$	−7939.43			−0.0795088
$317$	−147120.	−	84939.6i	−1.46404	−	0.845263i	−0.464844	−	0.885393i	$-0.653890\pi$
$317$	−147120.	−	84939.6i	−1.46404	−	0.845263i	−0.999194	+	0.0401296i	$0.987223\pi$
$318$	26606.2	−	68430.1i	0.263105	−	0.676695i
$319$	12165.0	+	21070.4i	0.119545	+	0.207057i
$320$	−59266.9	+	34217.8i	−0.578778	+	0.334158i
$321$	−15038.7	−	97668.2i	−0.145949	−	0.947857i
$322$	−210864.	+	365228.i	−2.03372	+	3.52251i
$323$		−	2571.02i		−	0.0246434i
$324$	168139.	+	78354.6i	1.60169	+	0.746405i
$325$	33727.5			0.319313
$326$	−40367.9	−	23306.4i	−0.379840	−	0.219301i
$327$	115762.	−	17824.8i	1.08261	−	0.166697i
$328$	94094.3	+	162976.i	0.874612	+	1.51487i
$329$	23271.2	−	13435.6i	0.214994	−	0.124127i
$330$	14179.3	+	5513.04i	0.130205	+	0.0506248i
$331$	−54809.9	+	94933.5i	−0.500268	+	0.866490i	0.499732	+	0.866180i	$0.333432\pi$
$331$	−54809.9	+	94933.5i	−0.500268	+	0.866490i	−1.00000		0.000309522i	$0.999901\pi$
$332$		−	76454.8i		−	0.693631i
$333$	−63221.6	+	19942.2i	−0.570134	+	0.179839i
$334$	−153056.			−1.37201
$335$	−53377.3	−	30817.4i	−0.475628	−	0.274604i
$336$	−44486.4	−	55422.0i	−0.394048	−	0.490912i
$337$	−94290.6	−	163316.i	−0.830249	−	1.43803i	−0.897840	−	0.440321i	$-0.854865\pi$
$337$	−94290.6	−	163316.i	−0.830249	−	1.43803i	0.0675912	−	0.997713i	$-0.478469\pi$
$338$	254937.	−	147188.i	2.23151	−	1.28836i
$339$	101328.	−	81334.8i	0.881722	−	0.707746i
$340$	−12950.3	+	22430.6i	−0.112027	+	0.194036i
$341$			4421.12i			0.0380210i
$342$	−16511.0	−	3658.28i	−0.141163	−	0.0312770i
$343$	236676.			2.01171
$344$	−90034.5	−	51981.4i	−0.760838	−	0.439270i
$345$	26634.3	−	68502.5i	0.223771	−	0.575530i
$346$	−159843.	−	276856.i	−1.33518	−	2.31261i
$347$	−63576.4	+	36705.8i	−0.528003	+	0.304843i	−0.740203	−	0.672383i	$-0.765271\pi$
$347$	−63576.4	+	36705.8i	−0.528003	+	0.304843i	0.212200	+	0.977226i	$0.431937\pi$
$348$	41463.8	+	269285.i	0.342382	+	2.22358i
$349$	68646.1	−	118898.i	0.563592	−	0.976170i	−0.433587	−	0.901112i	$-0.642752\pi$
$349$	68646.1	−	118898.i	0.563592	−	0.976170i	0.997179	−	0.0750582i	$-0.0239142\pi$
$350$		−	72171.3i		−	0.589153i
$351$	163569.	+	109250.i	1.32766	+	0.886761i
$352$	−15931.0			−0.128575
$353$	66478.7	+	38381.5i	0.533498	+	0.308015i	0.742440	−	0.669913i	$-0.233669\pi$
$353$	66478.7	+	38381.5i	0.533498	+	0.308015i	−0.208942	+	0.977928i	$0.567002\pi$
$354$	−68798.3	+	10593.4i	−0.548998	+	0.0845333i
$355$	32166.0	+	55713.1i	0.255235	+	0.442079i
$356$	−7071.01	+	4082.45i	−0.0557932	+	0.0322122i
$357$	59640.0	+	23188.5i	0.467952	+	0.181943i
$358$	76449.4	−	132414.i	0.596497	−	1.03316i
$359$			171025.i			1.32700i	0.748178	+	0.663498i	$0.230929\pi$
$359$			171025.i			1.32700i	−0.748178	+	0.663498i	$0.769071\pi$
$360$	54531.4	+	49956.5i	0.420767	+	0.385467i
$361$	−129336.			−0.992445
$362$	−61514.2	−	35515.2i	−0.469416	−	0.271018i
$363$	−79574.8	−	99135.7i	−0.603896	−	0.752345i
$364$	−330980.	−	573275.i	−2.49804	−	4.32673i
$365$	−70074.2	+	40457.4i	−0.525984	+	0.303677i
$366$	−172083.	+	138128.i	−1.28462	+	1.03115i
$367$	−90616.9	+	156953.i	−0.672786	+	1.16530i	0.304324	+	0.952569i	$0.401569\pi$
$367$	−90616.9	+	156953.i	−0.672786	+	1.16530i	−0.977111	+	0.212732i	$0.931764\pi$
$368$		−	66469.9i		−	0.490828i
$369$	−126089.	+	137636.i	−0.926028	+	1.01083i
$370$	−60884.0			−0.444733
$371$	−92133.8	−	53193.5i	−0.669378	−	0.386466i
$372$	−17941.4	+	46144.6i	−0.129649	+	0.333453i
$373$	13255.4	+	22959.1i	0.0952744	+	0.165020i	0.909723	−	0.415215i	$-0.136294\pi$
$373$	13255.4	+	22959.1i	0.0952744	+	0.165020i	−0.814449	+	0.580236i	$0.802960\pi$
$374$	−10728.5	+	6194.12i	−0.0767003	+	0.0442829i
$375$	1914.15	+	12431.4i	0.0136117	+	0.0884009i
$376$	−12644.4	+	21900.8i	−0.0894384	+	0.154912i
$377$			288906.i			2.03270i
$378$	233777.	−	350011.i	1.63613	−	2.44962i
$379$	−142615.			−0.992855			−0.496427	−	0.868078i	$-0.665355\pi$
$379$	−142615.			−0.992855			−0.496427	+	0.868078i	$0.665355\pi$
$380$	−8589.83	−	4959.34i	−0.0594864	−	0.0343445i
$381$	−98728.1	+	15201.9i	−0.680128	+	0.104724i
$382$	−11032.4	−	19108.6i	−0.0756035	−	0.130949i
$383$	16081.6	−	9284.73i	0.109631	−	0.0632953i	−0.444182	−	0.895937i	$-0.646506\pi$
$383$	16081.6	−	9284.73i	0.109631	−	0.0632953i	0.553813	+	0.832641i	$0.313172\pi$
$384$	−247543.	−	96246.8i	−1.67876	−	0.652715i
$385$	11022.2	−	19091.0i	0.0743611	−	0.128797i
$386$		−	220208.i		−	1.47795i
$387$	22306.6	−	100677.i	0.148940	−	0.672214i
$388$	74684.4			0.496097
$389$	150785.	+	87055.6i	0.996456	+	0.575304i	0.907198	−	0.420705i	$-0.138217\pi$
$389$	150785.	+	87055.6i	0.996456	+	0.575304i	0.0892579	+	0.996009i	$0.471550\pi$
$390$	113083.	+	140880.i	0.743475	+	0.926235i
$391$	29924.7	+	51831.1i	0.195738	+	0.339029i
$392$	−362703.	+	209407.i	−2.36036	+	1.36276i
$393$	−74702.3	+	59962.4i	−0.483670	+	0.388235i
$394$	−48704.3	+	84358.4i	−0.313744	+	0.543420i
$395$		−	3139.57i		−	0.0201222i
$396$	15654.1	+	49627.3i	0.0998246	+	0.316468i
$397$	−66990.2			−0.425040			−0.212520	−	0.977157i	$-0.568167\pi$
$397$	−66990.2			−0.425040			−0.212520	+	0.977157i	$0.568167\pi$
$398$	247842.	+	143091.i	1.56462	+	0.903333i
$399$	−8880.08	+	22839.2i	−0.0557790	+	0.143462i
$400$	5687.57	+	9851.16i	0.0355473	+	0.0615697i
$401$	264265.	−	152574.i	1.64343	−	0.948835i	0.663828	−	0.747885i	$-0.268931\pi$
$401$	264265.	−	152574.i	1.64343	−	0.948835i	0.979602	−	0.200950i	$-0.0644027\pi$
$402$	−50240.3	−	326284.i	−0.310885	−	2.01903i
$403$	−26249.3	+	45465.1i	−0.161625	+	0.279942i
$404$			443373.i			2.71648i
$405$	−30984.5	+	66489.1i	−0.188901	+	0.405359i
$406$	618212.			3.75047
$407$	−16105.2	−	9298.35i	−0.0972250	−	0.0561329i
$408$	−59519.9	+	9164.71i	−0.357554	+	0.0550552i
$409$	71526.5	+	123888.i	0.427583	+	0.740596i	0.996658	−	0.0816901i	$-0.0260318\pi$
$409$	71526.5	+	123888.i	0.427583	+	0.740596i	−0.569075	+	0.822286i	$0.692698\pi$
$410$	−148464.	+	85716.0i	−0.883191	+	0.509911i
$411$	76071.7	+	29577.3i	0.450339	+	0.175096i
$412$	155807.	−	269866.i	0.917894	−	1.58984i
$413$			100864.i			0.591340i
$414$	375437.	−	118425.i	2.19046	−	0.690945i
$415$	30233.3			0.175545
$416$	−163829.	−	94586.4i	−0.946679	−	0.546566i
$417$	103783.	+	129295.i	0.596837	+	0.743551i
$418$	−2372.05	−	4108.51i	−0.0135760	−	0.0235143i
$419$	31772.1	−	18343.6i	0.180975	−	0.104486i	−0.406776	−	0.913528i	$-0.633347\pi$
$419$	31772.1	−	18343.6i	0.180975	−	0.104486i	0.587750	+	0.809042i	$0.300014\pi$
$420$	192515.	−	154529.i	1.09136	−	0.876016i
$421$	−34142.4	+	59136.4i	−0.192633	+	0.333650i	−0.946122	−	0.323811i	$-0.895036\pi$
$421$	−34142.4	+	59136.4i	−0.192633	+	0.333650i	0.753489	+	0.657460i	$0.228369\pi$
$422$		−	534780.i		−	3.00296i
$423$	−24489.6	−	5426.06i	−0.136868	−	0.0303252i
$424$	100122.			0.556929
$425$	−8869.96	−	5121.07i	−0.0491070	−	0.0283520i
$426$	−124868.	+	321155.i	−0.688066	+	1.76968i
$427$	159871.	+	276905.i	0.876828	+	1.51871i
$428$	268846.	−	155218.i	1.46763	−	0.847336i
$429$	8397.37	+	54536.4i	0.0456277	+	0.296327i
$430$	47352.9	−	82017.7i	0.256100	−	0.443578i
$431$		−	21316.8i		−	0.114754i	−0.998353	−	0.0573770i	$-0.981726\pi$
$431$		−	21316.8i		−	0.114754i	0.998353	−	0.0573770i	$-0.0182737\pi$
$432$	−4326.67	+	66198.5i	−0.0231839	+	0.354716i
$433$	123133.			0.656747			0.328374	−	0.944548i	$-0.393500\pi$
$433$	123133.			0.656747			0.328374	+	0.944548i	$0.393500\pi$
$434$	97287.9	+	56169.2i	0.516511	+	0.298208i
$435$	−106486.	+	16396.4i	−0.562748	+	0.0866505i
$436$	183974.	+	318653.i	0.967796	+	1.67627i
$437$	−19848.8	+	11459.7i	−0.103937	+	0.0600082i
$438$	−403939.	−	157055.i	−2.10556	−	0.818658i
$439$	73330.3	−	127012.i	0.380500	−	0.659045i	−0.610634	−	0.791913i	$-0.709085\pi$
$439$	73330.3	−	127012.i	0.380500	−	0.659045i	0.991134	+	0.132868i	$0.0424187\pi$
$440$			20746.3i			0.107160i
$441$	−306308.	−	280610.i	−1.57500	−	1.44287i
$442$	−147104.			−0.752975
$443$	−84622.1	−	48856.6i	−0.431198	−	0.248952i	0.268659	−	0.963235i	$-0.413419\pi$
$443$	−84622.1	−	48856.6i	−0.431198	−	0.248952i	−0.699857	+	0.714283i	$0.746753\pi$
$444$	−130361.	−	162407.i	−0.661277	−	0.823830i
$445$	−1614.36	−	2796.16i	−0.00815232	−	0.0141202i
$446$	−295669.	+	170705.i	−1.48640	+	0.858176i
$447$	131624.	−	105652.i	0.658747	−	0.528767i
$448$	−265571.	+	459982.i	−1.32320	+	2.29185i
$449$		−	130019.i		−	0.644934i	−0.946581	−	0.322467i	$-0.895488\pi$
$449$		−	130019.i		−	0.644934i	0.946581	−	0.322467i	$-0.104512\pi$
$450$	−45508.3	+	49675.8i	−0.224732	+	0.245313i
$451$	−52363.0			−0.257437
$452$	353496.	+	204091.i	1.73025	+	0.998958i
$453$	−100224.	+	257772.i	−0.488399	+	1.25614i
$454$	101094.	+	175100.i	0.490472	+	0.849522i
$455$	226696.	−	130883.i	1.09502	−	0.632208i
$456$	−3509.64	−	22793.2i	−0.0168785	−	0.109617i
$457$	−37850.9	+	65559.7i	−0.181236	+	0.313910i	−0.942302	−	0.334765i	$-0.891343\pi$
$457$	−37850.9	+	65559.7i	−0.181236	+	0.313910i	0.761066	+	0.648675i	$0.224676\pi$
$458$		−	90962.0i		−	0.433640i
$459$	−26428.7	−	53567.3i	−0.125444	−	0.254258i
$460$	230892.			1.09117
$461$	139894.	+	80767.8i	0.658260	+	0.380046i	0.791614	−	0.611022i	$-0.209241\pi$
$461$	139894.	+	80767.8i	0.658260	+	0.380046i	−0.133354	+	0.991068i	$0.542575\pi$
$462$	116699.	−	17969.0i	0.546743	−	0.0841860i
$463$	−21982.2	−	38074.3i	−0.102544	−	0.177611i	0.810188	−	0.586170i	$-0.199365\pi$
$463$	−21982.2	−	38074.3i	−0.102544	−	0.177611i	−0.912732	+	0.408559i	$0.866031\pi$
$464$	−84384.1	+	48719.2i	−0.391944	+	0.226289i
$465$	−18247.4	−	7094.74i	−0.0843909	−	0.0328119i
$466$	149738.	−	259354.i	0.689541	−	1.19432i
$467$		−	81829.8i		−	0.375213i	−0.982244	−	0.187606i	$-0.939927\pi$
$467$		−	81829.8i		−	0.375213i	0.982244	−	0.187606i	$-0.0600730\pi$
$468$	−133669.	+	603290.i	−0.610293	+	2.75445i
$469$	−478360.			−2.17475
$470$	−19950.7	−	11518.6i	−0.0903157	−	0.0521438i
$471$	−228112.	−	284186.i	−1.02827	−	1.28103i
$472$	−47462.4	−	82207.3i	−0.213042	−	0.369000i
$473$	25051.9	−	14463.7i	0.111974	−	0.0646483i
$474$	13114.1	−	10526.5i	0.0583687	−	0.0468517i
$475$	1961.12	−	3396.76i	0.00869196	−	0.0150549i
$476$			201020.i			0.887208i
$477$	29874.5	+	94709.2i	0.131300	+	0.416251i
$478$	222250.			0.972715
$479$	−28523.0	−	16467.8i	−0.124315	−	0.0717734i	0.436553	−	0.899679i	$-0.356199\pi$
$479$	−28523.0	−	16467.8i	−0.124315	−	0.0717734i	−0.560868	+	0.827905i	$0.689533\pi$
$480$	25565.1	−	65752.6i	0.110960	−	0.285384i
$481$	−110413.	−	191242.i	−0.477234	−	0.826594i
$482$	−233309.	+	134701.i	−1.00424	+	0.579797i
$483$	−86810.9	−	563790.i	−0.372117	−	2.41670i
$484$	199675.	−	345847.i	0.852378	−	1.47636i
$485$			29533.2i			0.125553i
$486$	−381612.	+	93503.8i	−1.61566	+	0.395874i
$487$	165832.			0.699216			0.349608	−	0.936896i	$-0.386315\pi$
$487$	165832.			0.699216			0.349608	+	0.936896i	$0.386315\pi$
$488$	−260599.	−	150457.i	−1.09429	−	0.631791i
$489$	62314.5	−	9595.03i	0.260598	−	0.0401263i
$490$	−190761.	−	330407.i	−0.794505	−	1.37612i
$491$	−144597.	+	83483.4i	−0.599788	+	0.346288i	−0.768958	−	0.639299i	$-0.779225\pi$
$491$	−144597.	+	83483.4i	−0.599788	+	0.346288i	0.169170	+	0.985587i	$0.445891\pi$
$492$	−546529.	−	212495.i	−2.25779	−	0.877847i
$493$	43866.6	−	75979.2i	0.180485	−	0.312609i
$494$		−	56333.8i		−	0.230842i
$495$	−19624.6	+	6190.26i	−0.0800923	+	0.0252638i
$496$	−17706.0			−0.0719709
$497$	432400.	+	249647.i	1.75055	+	1.01068i
$498$	101367.	+	126285.i	0.408732	+	0.509206i
$499$	−192.909	−	334.129i	−0.000774733	−	0.00134188i	0.865638	−	0.500671i	$-0.166913\pi$
$499$	−192.909	−	334.129i	−0.000774733	−	0.00134188i	−0.866413	+	0.499329i	$0.833580\pi$
$500$	−34219.2	+	19756.5i	−0.136877	+	0.0790259i
$501$	161448.	−	129592.i	0.643215	−	0.516299i
$502$	44445.1	−	76981.2i	0.176367	−	0.305476i
$503$			38644.0i			0.152738i	0.997080	+	0.0763688i	$0.0243326\pi$
$503$			38644.0i			0.152738i	−0.997080	+	0.0763688i	$0.975667\pi$
$504$	560388.	+	124163.i	2.20611	+	0.488800i
$505$	−175327.			−0.687491
$506$	95639.6	+	55217.6i	0.373540	+	0.215663i
$507$	−144291.	+	371111.i	−0.561337	+	1.44374i
$508$	−156903.	−	271764.i	−0.608000	−	1.05309i
$509$	26508.4	−	15304.6i	0.102317	−	0.0590727i	−0.447968	−	0.894049i	$-0.647852\pi$
$509$	26508.4	−	15304.6i	0.102317	−	0.0590727i	0.550285	+	0.834977i	$0.314519\pi$
$510$	−8348.67	−	54220.1i	−0.0320979	−	0.208459i
$511$	−313998.	+	543860.i	−1.20250	+	2.08279i
$512$		−	182705.i		−	0.696963i
$513$	20513.7	−	10120.9i	0.0779487	−	0.0384579i
$514$	530706.			2.00876
$515$	106716.	+	61612.3i	0.402359	+	0.232302i
$516$	320170.	−	49298.9i	1.20249	−	0.185156i
$517$	−3518.29	−	6093.85i	−0.0131629	−	0.0227987i
$518$	−409226.	+	236267.i	−1.52512	+	0.880527i
$519$	403019.	+	156697.i	1.49620	+	0.581736i
$520$	−123176.	+	213347.i	−0.455532	+	0.789004i
$521$		−	144426.i		−	0.532071i	−0.963963	−	0.266035i	$-0.914286\pi$
$521$		−	144426.i		−	0.532071i	0.963963	−	0.266035i	$-0.0857138\pi$
$522$	−425518.	−	389820.i	−1.56163	−	1.43062i
$523$	−103801.			−0.379488			−0.189744	−	0.981834i	$-0.560766\pi$
$523$	−103801.			−0.379488			−0.189744	+	0.981834i	$0.560766\pi$
$524$	−260608.	−	150462.i	−0.949128	−	0.547979i
$525$	61107.0	+	76128.2i	0.221703	+	0.276202i
$526$	−235982.	−	408733.i	−0.852919	−	1.47730i
$527$	13806.6	−	7971.22i	0.0497123	−	0.0287014i
$528$	−14513.0	+	11649.3i	−0.0520581	+	0.0417863i
$529$	126844.	−	219700.i	0.453270	−	0.785087i
$530$			91207.3i			0.324697i
$531$	63600.9	−	69425.3i	0.225566	−	0.246223i
$532$	−76981.0			−0.271994
$533$	−538482.	−	310892.i	−1.89547	−	1.09435i
$534$	6266.92	−	16118.3i	0.0219772	−	0.0565245i
$535$	61379.6	+	106313.i	0.214445	+	0.371430i
$536$	389878.	−	225096.i	1.35706	−	0.783498i
$537$	31473.5	+	204403.i	0.109143	+	0.708826i
$538$	−65246.1	+	113010.i	−0.225419	+	0.390437i
$539$		−	116534.i		−	0.401120i
$540$	−229949.	−	15029.2i	−0.788576	−	0.0515405i
$541$	−226296.			−0.773183			−0.386592	−	0.922251i	$-0.626348\pi$
$541$	−226296.			−0.773183			−0.386592	+	0.922251i	$0.626348\pi$
$542$	625102.	+	360903.i	2.12790	+	1.22855i
$543$	94957.4	−	14621.3i	0.322054	−	0.0495891i
$544$	28723.4	+	49750.4i	0.0970596	+	0.168112i
$545$	−126008.	+	72750.7i	−0.424234	+	0.244931i
$546$	1.30677e6	+	508085.i	4.38344	+	1.70432i
$547$	246110.	−	426275.i	0.822535	−	1.42467i	−0.0812533	−	0.996693i	$-0.525892\pi$
$547$	246110.	−	426275.i	0.822535	−	1.42467i	0.903789	−	0.427979i	$-0.140774\pi$
$548$			256404.i			0.853816i
$549$	64565.1	−	291403.i	0.214217	−	0.966829i
$550$	−18899.0			−0.0624760
$551$	29096.4	+	16798.8i	0.0958375	+	0.0553318i
$552$	336049.	+	418656.i	1.10287	+	1.37397i
$553$	−12183.4	−	21102.3i	−0.0398400	−	0.0690049i
$554$	−425476.	+	245648.i	−1.38629	+	0.800377i
$555$	64222.1	−	51550.1i	0.208496	−	0.167357i
$556$	−260421.	+	451062.i	−0.842415	+	1.45911i
$557$		−	107606.i		−	0.346839i	−0.984848	−	0.173419i	$-0.944518\pi$
$557$		−	107606.i		−	0.346839i	0.984848	−	0.173419i	$-0.0554816\pi$
$558$	−31545.7	−	100007.i	−0.101314	−	0.321191i
$559$	343499.			1.09926
$560$	76456.8	+	44142.4i	0.243804	+	0.140760i
$561$	6072.21	−	15617.5i	0.0192940	−	0.0496233i
$562$	−63666.3	−	110273.i	−0.201575	−	0.349138i
$563$	471654.	−	272309.i	1.48801	−	0.859104i	0.488106	−	0.872784i	$-0.337688\pi$
$563$	471654.	−	272309.i	1.48801	−	0.859104i	0.999906	+	0.0136800i	$0.00435461\pi$
$564$	−11991.9	−	77881.0i	−0.0376991	−	0.244835i
$565$	−80705.8	+	139787.i	−0.252818	+	0.437894i
$566$			127060.i			0.396620i
$567$	49758.2	+	567138.i	0.154774	+	1.76410i
$568$	−469892.			−1.45647
$569$	−251766.	−	145357.i	−0.777629	−	0.448964i	0.0579603	−	0.998319i	$-0.481540\pi$
$569$	−251766.	−	145357.i	−0.777629	−	0.448964i	−0.835589	+	0.549355i	$0.814874\pi$
$570$	20763.7	−	3197.14i	0.0639079	−	0.00984037i
$571$	−180733.	−	313038.i	−0.554325	−	0.960120i	−0.997956	−	0.0639099i	$-0.979643\pi$
$571$	−180733.	−	313038.i	−0.554325	−	0.960120i	0.443630	−	0.896210i	$-0.353690\pi$
$572$	−150119.	+	86671.5i	−0.458823	+	0.264901i
$573$	27816.4	+	10815.2i	0.0847211	+	0.0329403i
$574$	−665259.	+	1.15226e6i	−2.01914	+	3.49726i
$575$			91303.8i			0.276155i
$576$	472840.	−	149150.i	1.42518	−	0.449549i
$577$	17214.4			0.0517060			0.0258530	−	0.999666i	$-0.491770\pi$
$577$	17214.4			0.0517060			0.0258530	+	0.999666i	$0.491770\pi$
$578$	−442592.	−	255531.i	−1.32479	−	0.764869i
$579$	186449.	+	232281.i	0.556163	+	0.692878i
$580$	−169232.	−	293119.i	−0.503068	−	0.871339i
$581$	203210.	−	117323.i	0.601995	−	0.347562i
$582$	−123361.	+	99020.0i	−0.364193	+	0.292332i
$583$	−13929.4	+	24126.4i	−0.0409822	+	0.0709833i
$584$		−	591016.i		−	1.73290i
$585$	−238565.	−	52858.0i	−0.697100	−	0.154454i
$586$	645838.			1.88074
$587$	−205748.	−	118789.i	−0.597116	−	0.344745i	0.170790	−	0.985307i	$-0.445368\pi$
$587$	−205748.	−	118789.i	−0.597116	−	0.344745i	−0.767906	+	0.640562i	$0.778701\pi$
$588$	472907.	−	1.21630e6i	1.36780	−	3.51792i
$589$	3052.59	+	5287.24i	0.00879910	+	0.0152405i
$590$	74887.4	−	43236.3i	0.215132	−	0.124206i
$591$	−20051.1	−	130221.i	−0.0574068	−	0.372826i
$592$	37238.7	−	64499.3i	0.106255	−	0.184040i
$593$			478258.i			1.36004i	0.733192	+	0.680022i	$0.238030\pi$
$593$			478258.i			1.36004i	−0.733192	+	0.680022i	$0.761970\pi$
$594$	−91654.9	−	61217.5i	−0.259766	−	0.173501i
$595$	−79491.4			−0.224536
$596$	459184.	+	265110.i	1.29269	+	0.746335i
$597$	−382585.	+	58909.4i	−1.07344	+	0.165286i
$598$	655681.	+	1.13567e6i	1.83354	+	3.17578i
$599$	−152537.	+	88067.3i	−0.425130	+	0.245449i	−0.697270	−	0.716809i	$-0.745602\pi$
$599$	−152537.	+	88067.3i	−0.425130	+	0.245449i	0.272140	+	0.962258i	$0.412269\pi$
$600$	−85626.7	−	33292.4i	−0.237852	−	0.0924788i
$601$	55921.1	−	96858.2i	0.154820	−	0.268156i	−0.778174	−	0.628049i	$-0.783854\pi$
$601$	55921.1	−	96858.2i	0.154820	−	0.268156i	0.932993	+	0.359893i	$0.117187\pi$
$602$		−	735031.i		−	2.02821i
$603$	329257.	+	301635.i	0.905526	+	0.829558i
$604$	−868836.			−2.38157
$605$	136762.	+	78959.4i	0.373640	+	0.215721i
$606$	−587844.	−	732346.i	−1.60073	−	1.99421i
$607$	65371.0	+	113226.i	0.177422	+	0.307304i	0.940997	−	0.338415i	$-0.109891\pi$
$607$	65371.0	+	113226.i	0.177422	+	0.307304i	−0.763575	+	0.645719i	$0.776558\pi$
$608$	−19052.0	+	10999.7i	−0.0515387	+	0.0297559i
$609$	−652107.	+	523437.i	−1.75826	+	1.41133i
$610$	137060.	−	237395.i	0.368342	−	0.637988i
$611$		−	83555.8i		−	0.223818i
$612$	126755.	−	138363.i	0.338425	−	0.369417i
$613$	−470908.			−1.25318			−0.626592	−	0.779348i	$-0.715551\pi$
$613$	−470908.			−1.25318			−0.626592	+	0.779348i	$0.715551\pi$
$614$	−451633.	−	260751.i	−1.19798	−	0.691654i
$615$	84029.0	−	216120.i	0.222167	−	0.571405i
$616$	80508.0	+	139444.i	0.212167	+	0.367484i
$617$	250146.	−	144422.i	0.657087	−	0.379369i	−0.134079	−	0.990971i	$-0.542808\pi$
$617$	250146.	−	144422.i	0.657087	−	0.379369i	0.791166	+	0.611601i	$0.209474\pi$
$618$	100444.	+	652329.i	0.262995	+	1.70801i
$619$	−89030.6	+	154205.i	−0.232358	+	0.402456i	−0.958502	−	0.285087i	$-0.907977\pi$
$619$	−89030.6	+	154205.i	−0.232358	+	0.402456i	0.726143	+	0.687543i	$0.241311\pi$
$620$		−	61504.0i		−	0.160000i
$621$	−295751.	+	442798.i	−0.766907	+	1.14821i
$622$	−343311.			−0.887376
$623$	−21701.6	−	12529.4i	−0.0559133	−	0.0322815i
$624$	−218411.	+	33630.4i	−0.560926	+	0.0863699i
$625$	−7812.50	−	13531.6i	−0.0200000	−	0.0346410i
$626$	−677945.	+	391412.i	−1.73000	+	0.998816i
$627$	5980.75	+	2325.36i	0.0152132	+	0.00591501i
$628$	572394.	−	991415.i	1.45136	−	2.51383i
$629$			67059.3i			0.169495i
$630$	−113107.	+	510491.i	−0.284977	+	1.28619i
$631$	647567.			1.62639			0.813197	−	0.581988i	$-0.197725\pi$
$631$	647567.			1.62639			0.813197	+	0.581988i	$0.197725\pi$
$632$	19859.7	+	11466.0i	0.0497208	+	0.0287063i
$633$	452795.	+	564100.i	1.13004	+	1.40783i
$634$	565172.	+	978907.i	1.40605	+	2.43536i
$635$	107466.	−	62045.7i	0.266517	−	0.153874i
$636$	−243293.	+	195288.i	−0.601473	+	0.482794i
$637$	691890.	−	1.19839e6i	1.70513	−	2.95338i
$638$		−	161887.i		−	0.397714i
$639$	−140206.	−	444487.i	−0.343372	−	1.08857i
$640$	329939.			0.805514
$641$	569187.	+	328620.i	1.38528	+	0.799794i	0.992779	−	0.119957i	$-0.0382755\pi$
$641$	569187.	+	328620.i	1.38528	+	0.799794i	0.392504	+	0.919750i	$0.371609\pi$
$642$	−238274.	+	612832.i	−0.578105	+	1.48686i
$643$	−279552.	−	484197.i	−0.676145	−	1.17112i	−0.976133	−	0.217175i	$-0.930316\pi$
$643$	−279552.	−	484197.i	−0.676145	−	1.17112i	0.299988	−	0.953943i	$-0.403017\pi$
$644$	1.55191e6	−	895998.i	3.74193	−	2.16041i
$645$	19494.8	+	126608.i	0.0468596	+	0.304328i
$646$	−8553.54	+	14815.2i	−0.0204966	+	0.0355011i
$647$			544163.i			1.29993i	0.759963	+	0.649966i	$0.225217\pi$
$647$			544163.i			1.29993i	−0.759963	+	0.649966i	$0.774783\pi$
$648$	−307426.	−	438820.i	−0.732133	−	1.04505i
$649$	26412.6			0.0627078
$650$	−194350.	−	112208.i	−0.460000	−	0.265581i
$651$	−150180.	+	23124.3i	−0.354365	+	0.0545641i
$652$	99032.9	+	171530.i	0.232962	+	0.403501i
$653$	647505.	−	373837.i	1.51851	−	0.876710i	0.518743	−	0.854930i	$-0.326400\pi$
$653$	647505.	−	373837.i	1.51851	−	0.876710i	0.999763	−	0.0217795i	$-0.00693318\pi$
$654$	−726365.	−	282417.i	−1.69824	−	0.660290i
$655$	59498.7	−	103055.i	0.138684	−	0.240207i
$656$		−	209707.i		−	0.487310i
$657$	559063.	−	176347.i	1.29518	−	0.408543i
$658$	−178796.			−0.412958
$659$	−421600.	−	243411.i	−0.970800	−	0.560492i	−0.0713200	−	0.997453i	$-0.522721\pi$
$659$	−421600.	−	243411.i	−0.970800	−	0.560492i	−0.899480	+	0.436962i	$0.856054\pi$
$660$	−40465.5	−	50412.6i	−0.0928959	−	0.115731i
$661$	49031.1	+	84924.3i	0.112220	+	0.194370i	0.916665	−	0.399657i	$-0.130871\pi$
$661$	49031.1	+	84924.3i	0.112220	+	0.194370i	−0.804445	+	0.594027i	$0.797537\pi$
$662$	631669.	−	364694.i	1.44136	−	0.832172i
$663$	155169.	−	124552.i	0.353003	−	0.283351i
$664$	−110415.	+	191244.i	−0.250432	+	0.433762i
$665$		−	30441.3i		−	0.0688368i
$666$	430652.	+	95417.9i	0.970908	+	0.215120i
$667$	−782099.			−1.75797
$668$	563229.	+	325181.i	1.26221	+	0.728738i
$669$	167345.	−	430406.i	0.373905	−	0.961669i
$670$	205053.	+	355162.i	0.456790	+	0.791184i
$671$	72511.2	−	41864.3i	0.161050	−	0.0929821i
$672$	−83326.0	−	541157.i	−0.184519	−	1.19835i
$673$	−266569.	+	461711.i	−0.588544	+	1.01939i	0.405879	+	0.913927i	$0.366965\pi$
$673$	−266569.	+	461711.i	−0.588544	+	1.01939i	−0.994423	+	0.105462i	$0.966368\pi$
$674$			1.25478e6i			2.76216i
$675$	5943.16	−	90931.0i	0.0130440	−	0.199574i
$676$	−1.25085e6			−2.73724
$677$	−652460.	−	376698.i	−1.42356	−	0.821894i	−0.426961	−	0.904270i	$-0.640416\pi$
$677$	−652460.	−	376698.i	−1.42356	−	0.821894i	−0.996601	+	0.0823757i	$0.973749\pi$
$678$	−854485.	+	131571.i	−1.85885	+	0.286221i
$679$	114607.	+	198505.i	0.248582	+	0.430557i
$680$	64787.8	−	37405.3i	0.140112	−	0.0808937i
$681$	−254893.	−	99104.5i	−0.549621	−	0.213697i
$682$	14708.6	−	25476.1i	0.0316230	−	0.0547727i
$683$		−	705789.i		−	1.51298i	−0.654004	−	0.756491i	$-0.726912\pi$
$683$		−	705789.i		−	1.51298i	0.654004	−	0.756491i	$-0.273088\pi$
$684$	52986.3	+	48541.1i	0.113253	+	0.103752i
$685$	−101392.			−0.216085
$686$	−1.36382e6	−	787399.i	−2.89806	−	1.67320i
$687$	77017.0	+	95949.1i	0.163182	+	0.203295i
$688$	57925.3	+	100329.i	0.122375	+	0.211959i
$689$	−286490.	+	165405.i	−0.603490	+	0.348425i
$690$	−381378.	+	306126.i	−0.801046	+	0.642988i
$691$	−15761.6	+	27299.8i	−0.0330098	+	0.0571747i	−0.882058	−	0.471140i	$-0.843843\pi$
$691$	−15761.6	+	27299.8i	−0.0330098	+	0.0571747i	0.849049	+	0.528315i	$0.177176\pi$
$692$			1.35840e6i			2.83671i
$693$	−107883.	+	117762.i	−0.224640	+	0.245211i
$694$	488467.			1.01418
$695$	−178368.	−	102981.i	−0.369273	−	0.213200i
$696$	285179.	−	733470.i	0.588707	−	1.51413i
$697$	94409.9	+	163523.i	0.194335	+	0.336599i
$698$	−791127.	+	456758.i	−1.62381	+	0.937508i
$699$	61645.7	+	400356.i	0.126168	+	0.819392i
$700$	−153334.	+	265582.i	−0.312927	+	0.542005i
$701$		−	213095.i		−	0.433647i	−0.976211	−	0.216824i	$-0.930430\pi$
$701$		−	213095.i		−	0.433647i	0.976211	−	0.216824i	$-0.0695697\pi$
$702$	−579081.	−	1.17372e6i	−1.17507	−	2.38171i
$703$	−25680.4			−0.0519627
$704$	120452.	+	69543.2i	0.243036	+	0.140317i
$705$	30797.3	−	4742.09i	0.0619632	−	0.00954094i
$706$	−255383.	−	442336.i	−0.512369	−	0.887449i
$707$	−1.17845e6	+	680376.i	−2.35760	+	1.36116i
$708$	275677.	+	107185.i	0.549963	+	0.213830i
$709$	396235.	−	686299.i	0.788244	−	1.36528i	−0.138798	−	0.990321i	$-0.544324\pi$
$709$	396235.	−	686299.i	0.788244	−	1.36528i	0.927042	−	0.374958i	$-0.122343\pi$
$710$		−	428052.i		−	0.849141i
$711$	−4920.36	+	22207.2i	−0.00973325	+	0.0439293i
$712$	23583.2			0.0465203
$713$	−123079.	−	71059.6i	−0.242105	−	0.139780i
$714$	−266521.	−	332037.i	−0.522800	−	0.651314i
$715$	−34273.4	−	59363.2i	−0.0670417	−	0.116120i
$716$	−562651.	+	324847.i	−1.09752	+	0.633654i
$717$	−234435.	+	188178.i	−0.456020	+	0.366041i
$718$	568982.	−	985506.i	1.10370	−	1.91166i
$719$		−	675203.i		−	1.30610i	−0.757314	−	0.653050i	$-0.773489\pi$
$719$		−	675203.i		−	1.30610i	0.757314	−	0.653050i	$-0.226511\pi$
$720$	−24791.2	−	78594.0i	−0.0478225	−	0.151609i
$721$	956371.			1.83974
$722$	745284.	+	430290.i	1.42971	+	0.825442i
$723$	132050.	−	339627.i	0.252616	−	0.649720i
$724$	150910.	+	261384.i	0.287900	+	0.498658i
$725$	115911.	−	66921.1i	0.220520	−	0.127317i
$726$	128724.	+	835994.i	0.244223	+	1.58610i
$727$	−428397.	+	742005.i	−0.810546	+	1.40391i	0.101937	+	0.994791i	$0.467496\pi$
$727$	−428397.	+	742005.i	−0.810546	+	1.40391i	−0.912483	+	0.409116i	$0.865837\pi$
$728$			1.91199e6i			3.60763i
$729$	323366.	−	421739.i	0.608470	−	0.793577i
$730$	538391.			1.01030
$731$	−90336.4	−	52155.8i	−0.169055	−	0.0976040i
$732$	926712.	−	142693.i	1.72951	−	0.266305i
$733$	−320371.	−	554899.i	−0.596274	−	1.03278i	−0.993366	−	0.114998i	$-0.963314\pi$
$733$	−320371.	−	554899.i	−0.596274	−	1.03278i	0.397092	−	0.917779i	$-0.370019\pi$
$734$	1.04434e6	−	602948.i	1.93842	−	1.11915i
$735$	480973.	+	187006.i	0.890320	+	0.346164i
$736$	256055.	−	443501.i	0.472692	−	0.818727i
$737$			125265.i			0.230619i
$738$	1.18447e6	−	373622.i	2.17476	−	0.685993i
$739$	−256752.			−0.470138			−0.235069	−	0.971979i	$-0.575532\pi$
$739$	−256752.			−0.470138			−0.235069	+	0.971979i	$0.575532\pi$
$740$	224046.	+	129353.i	0.409142	+	0.236218i
$741$	47697.5	+	59422.4i	0.0868678	+	0.108221i
$742$	353939.	+	613041.i	0.642867	+	1.11348i
$743$	−816699.	+	471522.i	−1.47940	+	0.854130i	−0.999728	−	0.0233197i	$-0.992576\pi$
$743$	−816699.	+	471522.i	−1.47940	+	0.854130i	−0.479669	+	0.877450i	$0.659243\pi$
$744$	111520.	−	89515.3i	0.201468	−	0.161715i
$745$	−104835.	+	181580.i	−0.188884	+	0.327156i
$746$		−	176398.i		−	0.316969i
$747$	−213850.	−	47381.8i	−0.383237	−	0.0849123i
$748$	52639.7			0.0940828
$749$	825113.	+	476379.i	1.47079	+	0.849160i
$750$	30328.0	−	78002.4i	0.0539164	−	0.138671i
$751$	161407.	+	279566.i	0.286183	+	0.495683i	0.972895	−	0.231246i	$-0.0742803\pi$
$751$	161407.	+	279566.i	0.286183	+	0.495683i	−0.686713	+	0.726929i	$0.740947\pi$
$752$	24405.1	−	14090.3i	0.0431563	−	0.0249163i
$753$	18297.6	+	118833.i	0.0322705	+	0.209579i
$754$	961163.	−	1.66478e6i	1.69065	−	2.92830i
$755$		−	343573.i		−	0.602733i
$756$	−1.60390e6	+	791323.i	−2.80630	+	1.38455i
$757$	327291.			0.571139			0.285569	−	0.958358i	$-0.407817\pi$
$757$	327291.			0.571139			0.285569	+	0.958358i	$0.407817\pi$
$758$	821798.	+	474465.i	1.43030	+	0.825783i
$759$	−147636.	+	22732.6i	−0.256276	+	0.0394607i
$760$	14324.4	+	24810.6i	0.0247999	+	0.0429546i
$761$	−410568.	+	237042.i	−0.708951	+	0.409313i	−0.810673	−	0.585500i	$-0.800898\pi$
$761$	−410568.	+	237042.i	−0.708951	+	0.409313i	0.101721	+	0.994813i	$0.467565\pi$
$762$	619483.	+	240860.i	1.06689	+	0.414815i
$763$	−564633.	+	977974.i	−0.969879	+	1.67988i
$764$			93756.8i			0.160626i
$765$	54714.3	+	50124.1i	0.0934927	+	0.0856492i
$766$	−123558.			−0.210578
$767$	271617.	+	156818.i	0.461707	+	0.266567i
$768$	554479.	+	690779.i	0.940075	+	1.17116i
$769$	−240798.	−	417074.i	−0.407193	−	0.705279i	0.587381	−	0.809310i	$-0.300159\pi$
$769$	−240798.	−	417074.i	−0.407193	−	0.705279i	−0.994574	+	0.104032i	$0.966826\pi$
$770$	−127028.	+	73339.4i	−0.214248	+	0.123696i
$771$	−559803.	+	449346.i	−0.941730	+	0.755913i
$772$	−467850.	+	810341.i	−0.785005	+	1.35967i
$773$			621347.i			1.03986i	0.854209	+	0.519930i	$0.174042\pi$
$773$			621347.i			1.03986i	−0.854209	+	0.519930i	$0.825958\pi$
$774$	−463481.	+	505925.i	−0.773660	+	0.844509i
$775$	24321.1			0.0404930
$776$	−186816.	−	107858.i	−0.310234	−	0.179114i
$777$	231617.	−	595709.i	0.383643	−	0.986716i
$778$	−579251.	−	1.00329e6i	−0.956990	−	1.65756i
$779$	−62621.3	+	36154.4i	−0.103192	+	0.0595781i
$780$	−116819.	−	758678.i	−0.192011	−	1.24700i
$781$	65373.2	−	113230.i	0.107176	−	0.185634i
$782$		−	398226.i		−	0.651203i
$783$	778906.	+	50908.5i	1.27046	+	0.0830361i
$784$	466702.			0.759290
$785$	392045.	+	226347.i	0.636205	+	0.367313i
$786$	629951.	−	96998.3i	1.01968	−	0.157007i
$787$	−596357.	−	1.03292e6i	−0.962846	−	1.66770i	−0.715294	−	0.698824i	$-0.753707\pi$
$787$	−596357.	−	1.03292e6i	−0.962846	−	1.66770i	−0.247552	−	0.968875i	$-0.579626\pi$
$788$	358453.	−	206953.i	0.577271	−	0.333288i
$789$	594992.	+	231338.i	0.955779	+	0.371615i
$790$	−10445.0	+	18091.4i	−0.0167362	+	0.0289879i
$791$			1.25275e6i			2.00222i
$792$	32513.7	−	146745.i	0.0518342	−	0.233945i
$793$	994237.			1.58104
$794$	386022.	+	222870.i	0.612310	+	0.353517i
$795$	−77224.7	−	96207.9i	−0.122186	−	0.152222i
$796$	−608020.	−	1.05312e6i	−0.959603	−	1.66208i
$797$	729813.	−	421358.i	1.14893	−	0.663337i	0.200307	−	0.979733i	$-0.435806\pi$
$797$	729813.	−	421358.i	1.14893	−	0.663337i	0.948627	+	0.316396i	$0.102473\pi$
$798$	127154.	−	102065.i	0.199676	−	0.160277i
$799$	−12686.9	+	21974.3i	−0.0198729	+	0.0344208i
$800$			87638.6i			0.136935i
$801$	7036.74	+	22308.2i	0.0109675	+	0.0347695i
$802$	−2.03039e6			−3.15668
$803$	142417.	+	82224.4i	0.220867	+	0.127518i
$804$	−508339.	+	1.30743e6i	−0.786396	+	2.02258i
$805$	354314.	+	613689.i	0.546759	+	0.947015i
$806$	302516.	−	174658.i	0.465670	−	0.268855i
$807$	−26861.2	−	174449.i	−0.0412457	−	0.267868i
$808$	640312.	−	1.10905e6i	0.980774	−	1.69875i
$809$			107245.i			0.163863i	0.996638	+	0.0819314i	$0.0261088\pi$
$809$			107245.i			0.163863i	−0.996638	+	0.0819314i	$0.973891\pi$
$810$	399747.	−	280052.i	0.609278	−	0.426843i
$811$	−192720.			−0.293011			−0.146506	−	0.989210i	$-0.546803\pi$
$811$	−192720.			−0.293011			−0.146506	+	0.989210i	$0.546803\pi$
$812$	−2.27495e6	−	1.31344e6i	−3.45033	−	1.99205i
$813$	−964948.	+	148580.i	−1.45990	+	0.224792i
$814$	61869.5	+	107161.i	0.0933743	+	0.161729i
$815$	−67829.8	+	39161.6i	−0.102119	+	0.0589583i
$816$	62546.0	+	24318.4i	0.0939333	+	0.0365220i
$817$	19973.1	−	34594.5i	0.0299228	−	0.0518278i
$818$		−	951848.i		−	1.42253i
$819$	−1.80861e6	+	570497.i	−2.69636	+	0.850522i
$820$	728444.			1.08335
$821$	671015.	+	387411.i	0.995511	+	0.574758i	0.906917	−	0.421309i	$-0.138429\pi$
$821$	671015.	+	387411.i	0.995511	+	0.574758i	0.0885938	+	0.996068i	$0.471763\pi$
$822$	−339952.	−	423519.i	−0.503123	−	0.626800i
$823$	127840.	+	221426.i	0.188742	+	0.326910i	0.944831	−	0.327558i	$-0.106226\pi$
$823$	127840.	+	221426.i	0.188742	+	0.326910i	−0.756089	+	0.654468i	$0.772892\pi$
$824$	−779471.	+	450028.i	−1.14801	+	0.662804i
$825$	19935.2	−	16001.7i	0.0292895	−	0.0235102i
$826$	335566.	−	581217.i	0.491833	−	0.851879i
$827$		−	495939.i		−	0.725133i	−0.931958	−	0.362566i	$-0.881901\pi$
$827$		−	495939.i		−	0.725133i	0.931958	−	0.362566i	$-0.118099\pi$
$828$	−1.63317e6	−	361855.i	−2.38216	−	0.527806i
$829$	−523080.			−0.761130			−0.380565	−	0.924754i	$-0.624270\pi$
$829$	−523080.			−0.761130			−0.380565	+	0.924754i	$0.624270\pi$
$830$	−174215.	−	100583.i	−0.252889	−	0.146005i
$831$	240814.	−	619364.i	0.348722	−	0.896900i
$832$	825791.	+	1.43031e6i	1.19295	+	2.06626i
$833$	−363919.	+	210109.i	−0.524463	+	0.302799i
$834$	−167885.	−	1.09032e6i	−0.241368	−	1.56756i
$835$	−128589.	+	222723.i	−0.184430	+	0.319443i
$836$			20158.5i			0.0288433i
$837$	117951.	+	78780.9i	0.168364	+	0.112453i
$838$	−244110.			−0.347614
$839$	263836.	+	152326.i	0.374810	+	0.216396i	0.675558	−	0.737307i	$-0.263903\pi$
$839$	263836.	+	152326.i	0.374810	+	0.216396i	−0.300748	+	0.953704i	$0.597236\pi$
$840$	−704726.	+	108512.i	−0.998761	+	0.153787i
$841$	219600.	+	380357.i	0.310484	+	0.537774i
$842$	393482.	−	227177.i	0.555010	−	0.320435i
$843$	160525.	+	62413.3i	0.225885	+	0.0878258i
$844$	−1.13619e6	+	1.96793e6i	−1.59501	+	2.76264i
$845$		−	494637.i		−	0.692745i
$846$	123066.	+	112741.i	0.171948	+	0.157523i
$847$	1.22564e6			1.70843
$848$	−96623.2	−	55785.5i	−0.134366	−	0.0775763i
$849$	−107581.	−	134026.i	−0.149251	−	0.185940i
$850$	34074.6	+	59019.0i	0.0471621	+	0.0816872i
$851$	517711.	−	298900.i	0.714872	−	0.412731i
$852$	1.14182e6	−	916521.i	1.57296	−	1.26259i
$853$	−555514.	+	962178.i	−0.763478	+	1.32238i	0.177569	+	0.984108i	$0.443177\pi$
$853$	−555514.	+	962178.i	−0.763478	+	1.32238i	−0.941047	+	0.338275i	$0.890157\pi$
$854$		−	2.12750e6i		−	2.91712i
$855$	−19195.1	+	20952.9i	−0.0262578	+	0.0286624i
$856$	−896655.			−1.22371
$857$	−446315.	−	257680.i	−0.607687	−	0.350848i	0.164372	−	0.986398i	$-0.447440\pi$
$857$	−446315.	−	257680.i	−0.607687	−	0.350848i	−0.772060	+	0.635550i	$0.780773\pi$
$858$	133049.	−	342196.i	0.180732	−	0.464836i
$859$	46714.0	+	80911.0i	0.0633083	+	0.109653i	0.895942	−	0.444170i	$-0.146502\pi$
$859$	46714.0	+	80911.0i	0.0633083	+	0.109653i	−0.832634	+	0.553824i	$0.813168\pi$
$860$	−348507.	+	201211.i	−0.471210	+	0.272053i
$861$	−273881.	−	1.77871e6i	−0.369450	−	2.39938i
$862$	−70919.0	+	122835.i	−0.0954439	+	0.165314i
$863$		−	1.07627e6i		−	1.44510i	−0.691317	−	0.722552i	$-0.742969\pi$
$863$		−	1.07627e6i		−	1.44510i	0.691317	−	0.722552i	$-0.257031\pi$
$864$	−283878.	+	425023.i	−0.380281	+	0.569357i
$865$	−537165.			−0.717919
$866$	−709537.	−	409651.i	−0.946104	−	0.546234i
$867$	683214.	−	105200.i	0.908905	−	0.139951i
$868$	−238672.	−	413393.i	−0.316784	−	0.548686i
$869$	−5525.91	+	3190.39i	−0.00731753	+	0.00422478i
$870$	668161.	+	259786.i	0.882760	+	0.343224i
$871$	−743729.	+	1.28818e6i	−0.980344	+	1.69800i
$872$		−	1.06277e6i		−	1.39767i
$873$	46284.7	−	208898.i	0.0607308	−	0.274098i
$874$	152501.			0.199642
$875$	−105022.	−	60634.4i	−0.137171	−	0.0791960i
$876$	1.15277e6	+	1.43615e6i	1.50223	+	1.87150i
$877$	475359.	+	823346.i	0.618049	+	1.07049i	0.989841	+	0.142176i	$0.0454098\pi$
$877$	475359.	+	823346.i	0.618049	+	1.07049i	−0.371793	+	0.928316i	$0.621257\pi$
$878$	−845112.	+	487926.i	−1.09629	+	0.632943i
$879$	−681247.	+	546827.i	−0.881712	+	0.707738i
$880$	11559.3	−	20021.2i	0.0149267	−	0.0258538i
$881$		−	58603.7i		−	0.0755046i	−0.999287	−	0.0377523i	$-0.987980\pi$
$881$		−	58603.7i		−	0.0755046i	0.999287	−	0.0377523i	$-0.0120198\pi$
$882$	831494.	+	2.63604e6i	1.06886	+	3.38855i
$883$	681006.			0.873433			0.436716	−	0.899599i	$-0.356141\pi$
$883$	681006.			0.873433			0.436716	+	0.899599i	$0.356141\pi$
$884$	541327.	+	312535.i	0.692716	+	0.399940i
$885$	−42385.4	+	109014.i	−0.0541165	+	0.139185i
$886$	325082.	+	563059.i	0.414120	+	0.717277i
$887$	−1.20134e6	+	693593.i	−1.52693	+	0.881571i	−0.527438	+	0.849594i	$0.676847\pi$
$887$	−1.20134e6	+	693593.i	−1.52693	+	0.881571i	−0.999489	+	0.0319776i	$0.989819\pi$
$888$	91541.0	+	594509.i	0.116089	+	0.753933i
$889$	481549.	−	834067.i	0.609308	−	1.05535i
$890$			21483.3i			0.0271220i
$891$	148513.	−	13029.8i	0.187072	−	0.0164128i
$892$	1.45071e6			1.82327
$893$	−8415.09	−	4858.45i	−0.0105525	−	0.00609249i
$894$	−1.10996e6	+	170908.i	−1.38877	+	0.213840i
$895$	−128457.	−	222495.i	−0.160366	−	0.277762i
$896$	2.21765e6	−	1.28036e6i	2.76234	−	1.59484i
$897$	−1.65320e6	−	642777.i	−2.05466	−	0.798869i
$898$	−432562.	+	749219.i	−0.536408	+	0.929087i
$899$			208333.i			0.257773i
$900$	273006.	−	86115.2i	0.337044	−	0.106315i
$901$	100458.			0.123747
$902$	301735.	+	174207.i	0.370862	+	0.214117i
$903$	622347.	+	775331.i	0.763233	+	0.950849i
$904$	−589490.	−	1.02103e6i	−0.721339	−	1.24940i
$905$	−103362.	+	59676.0i	−0.126201	+	0.0728622i
$906$	1.43511e6	−	1.15194e6i	1.74835	−	1.40338i
$907$	−141708.	+	245446.i	−0.172258	+	0.298360i	−0.939209	−	0.343346i	$-0.888440\pi$
$907$	−141708.	+	245446.i	−0.172258	+	0.298360i	0.766951	+	0.641706i	$0.221773\pi$
$908$		−	859132.i		−	1.04205i
$909$	1.24015e6	+	274775.i	1.50088	+	0.332544i
$910$	−1.74174e6			−2.10330
$911$	1.29183e6	+	745841.i	1.55658	+	0.898689i	0.997581	+	0.0695178i	$0.0221461\pi$
$911$	1.29183e6	+	745841.i	1.55658	+	0.898689i	0.558995	+	0.829171i	$0.311187\pi$
$912$	−9312.78	+	23952.1i	−0.0111967	+	0.0287975i
$913$	−30722.6	−	53213.1i	−0.0368567	−	0.0638377i
$914$	436222.	−	251853.i	0.522174	−	0.301477i
$915$	56426.4	+	366459.i	0.0673969	+	0.437707i
$916$	−193256.	+	334730.i	−0.230326	+	0.398936i
$917$		−	923563.i		−	1.09832i
$918$	−25921.4	+	396600.i	−0.0307590	+	0.470617i
$919$	−230950.			−0.273456			−0.136728	−	0.990609i	$-0.543659\pi$
$919$	−230950.			−0.273456			−0.136728	+	0.990609i	$0.543659\pi$
$920$	−577552.	−	333450.i	−0.682363	−	0.393962i
$921$	697171.	−	107349.i	0.821902	−	0.126554i
$922$	−537414.	−	930828.i	−0.632189	−	1.09498i
$923$	1.34455e6	−	776274.i	1.57824	−	0.911196i
$924$	−467616.	−	181813.i	−0.547703	−	0.212951i
$925$	−51151.4	+	88596.9i	−0.0597825	+	0.103546i
$926$			292531.i			0.341153i
$927$	−658275.	−	603049.i	−0.766033	−	0.701768i
$928$	−750704.			−0.871711
$929$	383911.	+	221651.i	0.444835	+	0.256826i	0.705647	−	0.708564i	$-0.250657\pi$
$929$	383911.	+	221651.i	0.444835	+	0.256826i	−0.260811	+	0.965390i	$0.583990\pi$
$930$	81544.8	+	101590.i	0.0942823	+	0.117459i
$931$	−80461.5	−	139363.i	−0.0928301	−	0.160786i
$932$	−1.10204e6	+	636262.i	−1.26872	+	0.732494i
$933$	362134.	−	290680.i	0.416012	−	0.333927i
$934$	−272240.	+	471533.i	−0.312074	+	0.540529i
$935$			20815.8i			0.0238106i
$936$	1.20562e6	−	1.31603e6i	1.37613	−	1.50215i
$937$	1.14657e6			1.30594			0.652969	−	0.757385i	$-0.273523\pi$
$937$	1.14657e6			1.30594			0.652969	+	0.757385i	$0.273523\pi$
$938$	2.75649e6	+	1.59146e6i	3.13293	+	1.80880i
$939$	383709.	−	986884.i	0.435181	−	1.11927i
$940$	48944.3	+	84774.1i	0.0553920	+	0.0959417i
$941$	−1.15694e6	+	667958.i	−1.30656	+	0.754345i	−0.981521	−	0.191355i	$-0.938712\pi$
$941$	−1.15694e6	+	667958.i	−1.30656	+	0.754345i	−0.325043	+	0.945699i	$0.605379\pi$
$942$	369005.	+	2.39649e6i	0.415844	+	2.70068i
$943$	841618.	−	1.45773e6i	0.946437	−	1.63928i
$944$			105779.i			0.118701i
$945$	−312921.	−	634247.i	−0.350405	−	0.710223i
$946$	−192477.			−0.215079
$947$	144839.	+	83623.1i	0.161505	+	0.0932452i	0.578574	−	0.815630i	$-0.303609\pi$
$947$	144839.	+	83623.1i	0.161505	+	0.0932452i	−0.417069	+	0.908875i	$0.636943\pi$
$948$	−70622.6	+	10874.3i	−0.0785827	+	0.0121000i
$949$	976374.	+	1.69113e6i	1.08414	+	1.87778i
$950$	−22601.4	+	13048.9i	−0.0250431	+	0.0144587i
$951$	−1.42499e6	−	554049.i	−1.57562	−	0.612614i
$952$	290310.	−	502831.i	0.320323	−	0.554815i
$953$		−	1.41967e6i		−	1.56316i	−0.623807	−	0.781579i	$-0.714415\pi$
$953$		−	1.41967e6i		−	1.56316i	0.623807	−	0.781579i	$-0.285585\pi$
$954$	142941.	−	645139.i	0.157058	−	0.708853i
$955$	−37075.2			−0.0406515
$956$	−817855.	−	472189.i	−0.894871	−	0.516654i
$957$	137069.	+	170763.i	0.149663	+	0.186453i
$958$	109573.	+	189787.i	0.119392	+	0.206792i
$959$	−681499.	+	393464.i	−0.741017	+	0.427827i
$960$	−480323.	+	385548.i	−0.521183	+	0.418346i
$961$	442832.	−	767007.i	0.479504	−	0.830525i
$962$			1.46934e6i			1.58771i
$963$	−267543.	−	848177.i	−0.288497	−	0.914606i
$964$	1.14473e6			1.23183
$965$	−320441.	−	185007.i	−0.344107	−	0.198670i
$966$	−1.37544e6	+	3.53757e6i	−1.47396	+	3.79098i
$967$	−628313.	−	1.08827e6i	−0.671928	−	1.16381i	−0.977357	−	0.211599i	$-0.932133\pi$
$967$	−628313.	−	1.08827e6i	−0.671928	−	1.16381i	0.305428	−	0.952215i	$-0.401200\pi$
$968$	−998932.	+	576734.i	−1.06607	+	0.615495i
$969$	−3521.41	−	22869.7i	−0.00375033	−	0.0243564i
$970$	98254.2	−	170181.i	0.104426	−	0.180871i
$971$			1.34054e6i			1.42181i	0.703286	+	0.710907i	$0.251715\pi$
$971$			1.34054e6i			1.42181i	−0.703286	+	0.710907i	$0.748285\pi$
$972$	1.60295e6	+	466684.i	1.69663	+	0.493959i
$973$	−1.59851e6			−1.68846
$974$	−955587.	−	551709.i	−1.00729	−	0.581556i
$975$	300012.	−	46195.0i	0.315594	−	0.0485943i
$976$	167661.	+	290398.i	0.176008	+	0.304855i
$977$	232065.	−	133983.i	0.243120	−	0.140365i	−0.373490	−	0.927634i	$-0.621839\pi$
$977$	232065.	−	133983.i	0.243120	−	0.140365i	0.616610	+	0.787269i	$0.288506\pi$
$978$	−391001.	−	152024.i	−0.408790	−	0.158941i
$979$	−3280.99	+	5682.84i	−0.00342325	+	0.00592925i
$980$			1.62115e6i			1.68799i
$981$	1.00531e6	−	317108.i	1.04463	−	0.329511i
$982$	1.11096e6			1.15207
$983$	−814986.	−	470532.i	−0.843418	−	0.486948i	0.0150063	−	0.999887i	$-0.495223\pi$
$983$	−814986.	−	470532.i	−0.843418	−	0.486948i	−0.858425	+	0.512940i	$0.828557\pi$
$984$	1.06021e6	+	1.32082e6i	1.09496	+	1.36413i
$985$	81837.5	+	141747.i	0.0843490	+	0.146097i
$986$	−505551.	+	291880.i	−0.520009	+	0.300228i
$987$	188599.	−	151385.i	0.193600	−	0.155400i
$988$	−119686.	+	207302.i	−0.122611	+	0.212368i
$989$			929887.i			0.950687i
$990$	133679.	+	29618.7i	0.136393	+	0.0302200i
$991$	−527900.			−0.537532			−0.268766	−	0.963205i	$-0.586616\pi$
$991$	−527900.			−0.537532			−0.268766	+	0.963205i	$0.586616\pi$
$992$	−118138.	−	68207.0i	−0.120051	−	0.0693116i
$993$	−357517.	+	919520.i	−0.362575	+	0.932530i
$994$	−1.66110e6	−	2.87711e6i	−1.68121	−	2.91195i
$995$	416446.	−	240435.i	0.420642	−	0.242858i
$996$	−104717.	−	680078.i	−0.105559	−	0.685551i
$997$	−835496.	+	1.44712e6i	−0.840532	+	1.45584i	0.0489144	+	0.998803i	$0.484424\pi$
$997$	−835496.	+	1.44712e6i	−0.840532	+	1.45584i	−0.889446	+	0.457040i	$0.848909\pi$
$998$			2567.16i			0.00257746i
$999$	−535053.	+	263981.i	−0.536125	+	0.264510i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.i.a.11.2	✓	32
3.2	odd	2		135.5.i.a.116.15		32
9.2	odd	6		405.5.c.b.161.4		32
9.4	even	3		135.5.i.a.71.15		32
9.5	odd	6	inner	45.5.i.a.41.2	yes	32
9.7	even	3		405.5.c.b.161.29		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.i.a.11.2	✓	32	1.1	even	1	trivial
45.5.i.a.41.2	yes	32	9.5	odd	6	inner
135.5.i.a.71.15		32	9.4	even	3
135.5.i.a.116.15		32	3.2	odd	2
405.5.c.b.161.4		32	9.2	odd	6
405.5.c.b.161.29		32	9.7	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	45.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.76237 - 3.32690i) q^{2} +(8.89517 - 1.36966i) q^{3} +(14.1366 + 24.4853i) q^{4} +(-9.68246 + 5.59017i) q^{5} +(-55.8139 - 21.7009i) q^{6} +(-43.3865 + 75.1475i) q^{7} -81.6633i q^{8} +(77.2481 - 24.3666i) q^{9} +74.3918 q^{10} +(19.6784 + 11.3613i) q^{11} +(159.284 + 198.438i) q^{12} +(134.910 + 233.671i) q^{13} +(500.017 - 288.685i) q^{14} +(-78.4705 + 62.9871i) q^{15} +(-45.5005 + 78.8092i) q^{16} -81.9372i q^{17} +(-526.197 - 116.588i) q^{18} +31.3780 q^{19} +(-273.754 - 158.052i) q^{20} +(-283.004 + 727.875i) q^{21} +(-75.5959 - 130.936i) q^{22} +(-632.571 + 365.215i) q^{23} +(-111.851 - 726.409i) q^{24} +(62.5000 - 108.253i) q^{25} -1795.33i q^{26} +(653.761 - 322.549i) q^{27} -2453.34 q^{28} +(927.286 + 535.369i) q^{29} +(661.728 - 101.891i) q^{30} +(97.2845 + 168.502i) q^{31} +(-607.178 + 350.554i) q^{32} +(190.603 + 74.1082i) q^{33} +(-272.597 + 472.152i) q^{34} -970.151i q^{35} +(1688.65 + 1546.98i) q^{36} -818.423 q^{37} +(-180.811 - 104.391i) q^{38} +(1520.09 + 1893.76i) q^{39} +(456.512 + 790.701i) q^{40} +(-1995.71 + 1152.22i) q^{41} +(4052.34 - 3252.75i) q^{42} +(636.534 - 1102.51i) q^{43} +642.440i q^{44} +(-611.738 + 667.759i) q^{45} +4860.14 q^{46} +(-268.185 - 154.836i) q^{47} +(-296.794 + 763.342i) q^{48} +(-2564.27 - 4441.44i) q^{49} +(-720.296 + 415.863i) q^{50} +(-112.226 - 728.845i) q^{51} +(-3814.33 + 6606.61i) q^{52} +1226.04i q^{53} +(-4840.30 - 316.357i) q^{54} -254.047 q^{55} +(6136.79 + 3543.08i) q^{56} +(279.112 - 42.9770i) q^{57} +(-3562.24 - 6169.99i) q^{58} +(1006.66 - 581.197i) q^{59} +(-2651.56 - 1030.95i) q^{60} +(1842.41 - 3191.15i) q^{61} -1294.63i q^{62} +(-1520.43 + 6862.19i) q^{63} +6121.06 q^{64} +(-2612.52 - 1508.34i) q^{65} +(-851.776 - 1061.16i) q^{66} +(2756.39 + 4774.21i) q^{67} +(2006.25 - 1158.31i) q^{68} +(-5126.61 + 4115.05i) q^{69} +(-3227.60 + 5590.36i) q^{70} -5754.02i q^{71} +(-1989.86 - 6308.33i) q^{72} +7237.24 q^{73} +(4716.05 + 2722.81i) q^{74} +(407.679 - 1048.53i) q^{75} +(443.577 + 768.298i) q^{76} +(-1707.55 + 985.853i) q^{77} +(-2458.98 - 15969.8i) q^{78} +(-140.406 + 243.190i) q^{79} -1017.42i q^{80} +(5373.53 - 3764.55i) q^{81} +15333.3 q^{82} +(-2341.86 - 1352.07i) q^{83} +(-21822.9 + 3360.24i) q^{84} +(458.043 + 793.353i) q^{85} +(-7335.88 + 4235.37i) q^{86} +(8981.64 + 3492.14i) q^{87} +(927.801 - 1607.00i) q^{88} +288.786i q^{89} +(5746.63 - 1812.68i) q^{90} -23413.0 q^{91} +(-17884.8 - 10325.8i) q^{92} +(1096.15 + 1365.61i) q^{93} +(1030.25 + 1784.45i) q^{94} +(-303.816 + 175.408i) q^{95} +(-4920.81 + 3949.86i) q^{96} +(1320.77 - 2287.63i) q^{97} +34124.3i q^{98} +(1796.95 + 398.144i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{3} + 128 q^{4} + 98 q^{6} - 26 q^{7} - 220 q^{9} - 738 q^{11} - 214 q^{12} + 10 q^{13} + 1998 q^{14} - 50 q^{15} - 1024 q^{16} - 2504 q^{18} + 508 q^{19} - 1620 q^{21} + 672 q^{22} + 1998 q^{23}+ \cdots + 53512 q^{99}+O(q^{100}) \) 32 * q - 8 * q^3 + 128 * q^4 + 98 * q^6 - 26 * q^7 - 220 * q^9 - 738 * q^11 - 214 * q^12 + 10 * q^13 + 1998 * q^14 - 50 * q^15 - 1024 * q^16 - 2504 * q^18 + 508 * q^19 - 1620 * q^21 + 672 * q^22 + 1998 * q^23 + 4164 * q^24 + 2000 * q^25 + 2158 * q^27 - 1664 * q^28 - 270 * q^29 + 2000 * q^30 - 1472 * q^31 - 6048 * q^32 - 1354 * q^33 - 594 * q^34 + 4498 * q^36 + 2068 * q^37 - 7164 * q^38 - 4616 * q^39 + 1650 * q^40 - 13428 * q^41 - 10230 * q^42 + 568 * q^43 - 100 * q^45 + 5724 * q^46 + 12528 * q^47 + 25844 * q^48 - 1674 * q^49 + 1454 * q^51 + 1534 * q^52 + 8456 * q^54 + 21294 * q^56 - 12512 * q^57 - 8190 * q^58 - 4374 * q^59 - 5050 * q^60 - 4478 * q^61 + 5604 * q^63 - 37216 * q^64 - 8550 * q^65 - 19472 * q^66 + 12838 * q^67 + 65736 * q^68 + 8706 * q^69 + 2400 * q^70 - 36372 * q^72 + 29236 * q^73 - 20628 * q^74 + 1000 * q^75 + 6190 * q^76 - 31806 * q^77 - 42430 * q^78 - 3512 * q^79 - 3088 * q^81 + 34692 * q^82 - 43074 * q^83 - 19350 * q^84 - 4350 * q^85 - 10746 * q^86 + 69622 * q^87 - 16128 * q^88 - 26750 * q^90 - 48904 * q^91 + 27036 * q^92 + 27030 * q^93 + 5118 * q^94 + 6300 * q^95 + 53566 * q^96 + 23266 * q^97 + 53512 * q^99

Introduction

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