LMFDB - Embedded newform 45.5.i.a.41.2

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			41.2
Character	$\chi$	$=$	45.41
Dual form			45.5.i.a.11.2

$q$-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 $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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	−0.997889	−	0.0649425i	$-0.979314\pi$
$2$	−5.76237	+	3.32690i	−1.44059	+	0.831726i	−0.442703	+	0.896668i	$0.645980\pi$
$3$	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	−0.845211	−	0.534433i	$-0.820525\pi$
$7$	−43.3865	−	75.1475i	−0.885438	−	1.53362i	−0.0402267	−	0.999191i	$-0.512808\pi$
$8$			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	−0.416476	−	0.909147i	$-0.636735\pi$
$11$	19.6784	−	11.3613i	0.162631	−	0.0938951i	0.579107	+	0.815252i	$0.303402\pi$
$12$	159.284	−	198.438i	1.10614	−	1.37804i
$13$	134.910	−	233.671i	0.798283	−	1.38267i	−0.122450	−	0.992475i	$-0.539075\pi$
$13$	134.910	−	233.671i	0.798283	−	1.38267i	0.920733	−	0.390192i	$-0.127592\pi$
$14$	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	$0.0452761\pi$
$17$			81.9372i			0.283520i	−0.989901	+	0.141760i	$0.954724\pi$
$18$	−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	−0.236174	−	0.971711i	$-0.575893\pi$
$23$	−632.571	−	365.215i	−1.19579	−	0.690388i	−0.959613	+	0.281323i	$0.909227\pi$
$24$	−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	0.165697	−	0.986177i	$-0.447013\pi$
$29$	927.286	−	535.369i	1.10260	−	0.636586i	0.936903	+	0.349590i	$0.113679\pi$
$30$	661.728	+	101.891i	0.735253	+	0.113212i
$31$	97.2845	−	168.502i	0.101233	−	0.175340i	−0.810960	−	0.585101i	$-0.801055\pi$
$31$	97.2845	−	168.502i	0.101233	−	0.175340i	0.912193	+	0.409761i	$0.134388\pi$
$32$	−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	−0.229543	−	0.973299i	$-0.573723\pi$
$41$	−1995.71	−	1152.22i	−1.18722	−	0.685439i	−0.957673	+	0.287860i	$0.907056\pi$
$42$	4052.34	+	3252.75i	2.29724	+	1.84397i
$43$	636.534	+	1102.51i	0.344258	+	0.596273i	0.985219	−	0.171301i	$-0.0547970\pi$
$43$	636.534	+	1102.51i	0.344258	+	0.596273i	−0.640960	+	0.767574i	$0.721464\pi$
$44$		−	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	−0.559473	−	0.828849i	$-0.688996\pi$
$47$	−268.185	+	154.836i	−0.121405	+	0.0700934i	0.438068	+	0.898942i	$0.355663\pi$
$48$	−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	$-0.929970\pi$
$53$		−	1226.04i		−	0.436468i	0.975896	−	0.218234i	$-0.0700297\pi$
$54$	−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	0.637575	−	0.770388i	$-0.279937\pi$
$59$	1006.66	+	581.197i	0.289188	+	0.166963i	−0.348388	+	0.937350i	$0.613271\pi$
$60$	−2651.56	+	1030.95i	−0.736545	+	0.286375i
$61$	1842.41	+	3191.15i	0.495138	+	0.857604i	0.999984	−	0.00560491i	$-0.00178411\pi$
$61$	1842.41	+	3191.15i	0.495138	+	0.857604i	−0.504846	+	0.863209i	$0.668451\pi$
$62$			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	−0.376521	−	0.926408i	$-0.622880\pi$
$67$	2756.39	−	4774.21i	0.614032	−	1.06354i	0.990553	−	0.137127i	$-0.0437870\pi$
$68$	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	$0.193337\pi$
$71$			5754.02i			1.14144i	−0.821143	+	0.570722i	$0.806663\pi$
$72$	−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	0.854558	−	0.519357i	$-0.173828\pi$
$79$	−140.406	−	243.190i	−0.0224973	−	0.0389665i	−0.877055	+	0.480390i	$0.840495\pi$
$80$			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	−0.660246	−	0.751049i	$-0.729548\pi$
$83$	−2341.86	+	1352.07i	−0.339942	+	0.196265i	0.320305	+	0.947315i	$0.396215\pi$
$84$	−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	$-0.994197\pi$
$89$		−	288.786i		−	0.0364583i	0.999834	−	0.0182291i	$-0.00580284\pi$
$90$	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	0.927637	−	0.373483i	$-0.121837\pi$
$97$	1320.77	+	2287.63i	0.140373	+	0.243132i	−0.787264	+	0.616616i	$0.788503\pi$
$98$		−	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	0.345819	−	0.938301i	$-0.387601\pi$
$101$	13580.8	−	7840.88i	1.33132	−	0.768638i	0.985502	+	0.169663i	$0.0542679\pi$
$102$	−1778.11	−	4573.24i	−0.170907	−	0.439565i
$103$	−5510.77	+	9544.94i	−0.519443	+	0.899702i	0.480301	+	0.877103i	$0.340527\pi$
$103$	−5510.77	+	9544.94i	−0.519443	+	0.899702i	−0.999745	+	0.0225985i	$0.992806\pi$
$104$	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	$0.159187\pi$
$107$			10979.9i			0.959028i	−0.877534	+	0.479514i	$0.840813\pi$
$108$	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	0.902016	−	0.431702i	$-0.142087\pi$
$113$	12502.9	+	7218.55i	0.979160	+	0.565318i	0.0771434	+	0.997020i	$0.475420\pi$
$114$	−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	0.206792	−	0.978385i	$-0.433698\pi$
$131$	−9217.50	−	5321.73i	−0.537119	−	0.310106i	−0.743911	+	0.668279i	$0.767031\pi$
$132$	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	−0.275966	−	0.961167i	$-0.588998\pi$
$137$	7853.83	−	4534.41i	0.418447	−	0.241590i	0.694413	+	0.719577i	$0.255664\pi$
$138$	43231.8	+	6656.72i	2.27010	+	0.349544i
$139$	9210.88	−	15953.7i	0.476729	−	0.825719i	−0.522915	−	0.852385i	$-0.675156\pi$
$139$	9210.88	−	15953.7i	0.476729	−	0.825719i	0.999644	+	0.0266658i	$0.00848898\pi$
$140$	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	0.818987	−	0.573813i	$-0.194536\pi$
$149$	16241.0	+	9376.75i	0.731544	+	0.422357i	−0.0874430	+	0.996170i	$0.527870\pi$
$150$	−5837.56	−	4685.73i	−0.259447	−	0.208255i
$151$	−15365.0	−	26613.0i	−0.673875	−	1.16719i	−0.976796	−	0.214171i	$-0.931295\pi$
$151$	−15365.0	−	26613.0i	−0.673875	−	1.16719i	0.302921	−	0.953016i	$-0.402038\pi$
$152$			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	0.0833500	+	0.996520i	$0.473438\pi$
$157$	−20245.1	+	35065.6i	−0.821337	+	1.42260i	−0.904687	+	0.426077i	$0.859895\pi$
$158$	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	0.812649	−	0.582753i	$-0.198024\pi$
$167$	19921.0	+	11501.4i	0.714295	+	0.412399i	−0.0983540	+	0.995151i	$0.531358\pi$
$168$	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	0.396903	−	0.917861i	$-0.370085\pi$
$173$	41608.6	−	24022.8i	1.39024	−	0.802658i	0.993342	+	0.115203i	$0.0367518\pi$
$174$	−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	$-0.883258\pi$
$179$		−	22979.1i		−	0.717179i	0.933495	−	0.358590i	$-0.116742\pi$
$180$	−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	−0.460123	−	0.887855i	$-0.652195\pi$
$191$	2871.83	−	1658.05i	0.0787213	−	0.0454498i	0.538844	+	0.842406i	$0.318861\pi$
$192$	54447.9	+	8383.74i	1.47699	+	0.227423i
$193$	16547.5	−	28661.1i	0.444240	−	0.769447i	−0.553759	−	0.832677i	$-0.686807\pi$
$193$	16547.5	−	28661.1i	0.444240	−	0.769447i	0.997999	+	0.0632303i	$0.0201403\pi$
$194$	−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	$0.0603982\pi$
$197$			14639.5i			0.377220i	−0.982052	+	0.188610i	$0.939602\pi$
$198$	−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	0.0785636	−	0.996909i	$-0.474967\pi$
$211$	40186.0	−	69604.2i	0.902630	−	1.56340i	0.824067	−	0.566493i	$-0.191700\pi$
$212$	−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	0.999830	+	0.0184586i	$0.00587589\pi$
$223$	25655.2	+	44436.1i	0.515900	+	0.893566i	−0.483929	+	0.875107i	$0.660791\pi$
$224$			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	−0.733121	−	0.680099i	$-0.761937\pi$
$227$	−26315.8	+	15193.4i	−0.510698	+	0.294852i	0.222422	+	0.974950i	$0.428604\pi$
$228$	4998.00	−	6226.59i	0.0961449	−	0.119779i
$229$	6835.33	−	11839.1i	0.130343	−	0.225761i	−0.793466	−	0.608615i	$-0.791725\pi$
$229$	6835.33	−	11839.1i	0.130343	−	0.225761i	0.923809	+	0.382854i	$0.125059\pi$
$230$	−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	$-0.863948\pi$
$233$		−	45008.2i		−	0.829049i	0.910038	−	0.414524i	$-0.136052\pi$
$234$	−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	0.224944	−	0.974372i	$-0.427780\pi$
$239$	−28926.9	−	16700.9i	−0.506414	−	0.292378i	−0.731358	+	0.681993i	$0.761113\pi$
$240$	−1393.52	+	9050.15i	−0.0241930	+	0.157121i
$241$	20244.2	+	35063.9i	0.348551	+	0.603708i	0.985992	−	0.166791i	$-0.0533406\pi$
$241$	20244.2	+	35063.9i	0.348551	+	0.603708i	−0.637441	+	0.770499i	$0.720007\pi$
$242$		−	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	$-0.966188\pi$
$251$		−	13359.3i		−	0.212049i	0.994364	−	0.106025i	$-0.0338122\pi$
$252$	−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	−0.124328	−	0.992241i	$-0.539678\pi$
$257$	−69074.0	−	39879.9i	−1.04580	−	0.603792i	−0.921470	+	0.388449i	$0.873011\pi$
$258$	−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	0.0147741	−	0.999891i	$-0.495297\pi$
$263$	61428.4	−	35465.7i	0.888092	−	0.512740i	0.873318	+	0.487151i	$0.161964\pi$
$264$	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	$0.0432681\pi$
$269$			19611.7i			0.271025i	−0.990776	+	0.135513i	$0.956732\pi$
$270$	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	0.999766	−	0.0216263i	$-0.00688440\pi$
$277$	36918.5	+	63944.7i	0.481154	+	0.833383i	−0.518612	+	0.855010i	$0.673551\pi$
$278$			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	−0.391371	−	0.920233i	$-0.627999\pi$
$281$	16573.0	−	9568.40i	0.209888	−	0.121179i	0.601259	+	0.799054i	$0.294666\pi$
$282$	11608.3	−	14461.9i	0.145973	−	0.181856i
$283$	−9547.88	+	16537.4i	−0.119216	+	0.206488i	−0.919457	−	0.393190i	$-0.871371\pi$
$283$	−9547.88	+	16537.4i	−0.119216	+	0.206488i	0.800241	+	0.599678i	$0.204705\pi$
$284$	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	−0.0771355	−	0.997021i	$-0.524577\pi$
$293$	−84058.9	−	48531.4i	−0.979148	−	0.565312i	−0.902013	+	0.431709i	$0.857911\pi$
$294$	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	0.712879	−	0.701288i	$-0.247391\pi$
$311$	44683.7	+	25798.1i	0.461985	+	0.266727i	−0.250894	+	0.968015i	$0.580724\pi$
$312$	154651.	+	124136.i	1.58870	+	1.27523i
$313$	58825.2	+	101888.i	0.600447	+	1.04001i	0.992753	+	0.120171i	$0.0383442\pi$
$313$	58825.2	+	101888.i	0.600447	+	1.04001i	−0.392306	+	0.919835i	$0.628322\pi$
$314$		−	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	−0.999194	−	0.0401296i	$-0.987223\pi$
$317$	−147120.	+	84939.6i	−1.46404	+	0.845263i	−0.464844	+	0.885393i	$0.653890\pi$
$318$	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	−1.00000		0.000309522i	$-0.999901\pi$
$331$	−54809.9	−	94933.5i	−0.500268	−	0.866490i	0.499732	−	0.866180i	$-0.333432\pi$
$332$			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	0.0675912	+	0.997713i	$0.478469\pi$
$337$	−94290.6	+	163316.i	−0.830249	+	1.43803i	−0.897840	+	0.440321i	$0.854865\pi$
$338$	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	0.212200	−	0.977226i	$-0.431937\pi$
$347$	−63576.4	−	36705.8i	−0.528003	−	0.304843i	−0.740203	+	0.672383i	$0.765271\pi$
$348$	41463.8	−	269285.i	0.342382	−	2.22358i
$349$	68646.1	+	118898.i	0.563592	+	0.976170i	0.997179	+	0.0750582i	$0.0239142\pi$
$349$	68646.1	+	118898.i	0.563592	+	0.976170i	−0.433587	+	0.901112i	$0.642752\pi$
$350$			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	−0.208942	−	0.977928i	$-0.567002\pi$
$353$	66478.7	−	38381.5i	0.533498	−	0.308015i	0.742440	+	0.669913i	$0.233669\pi$
$354$	−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	$-0.769071\pi$
$359$		−	171025.i		−	1.32700i	0.748178	−	0.663498i	$-0.230929\pi$
$360$	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	−0.977111	−	0.212732i	$-0.931764\pi$
$367$	−90616.9	−	156953.i	−0.672786	−	1.16530i	0.304324	−	0.952569i	$-0.401569\pi$
$368$			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	−0.814449	−	0.580236i	$-0.802960\pi$
$373$	13255.4	−	22959.1i	0.0952744	−	0.165020i	0.909723	+	0.415215i	$0.136294\pi$
$374$	−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	0.553813	−	0.832641i	$-0.313172\pi$
$383$	16081.6	+	9284.73i	0.109631	+	0.0632953i	−0.444182	+	0.895937i	$0.646506\pi$
$384$	−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	0.0892579	−	0.996009i	$-0.471550\pi$
$389$	150785.	−	87055.6i	0.996456	−	0.575304i	0.907198	+	0.420705i	$0.138217\pi$
$390$	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	0.979602	+	0.200950i	$0.0644027\pi$
$401$	264265.	+	152574.i	1.64343	+	0.948835i	0.663828	+	0.747885i	$0.268931\pi$
$402$	−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	−0.569075	−	0.822286i	$-0.692698\pi$
$409$	71526.5	−	123888.i	0.427583	−	0.740596i	0.996658	+	0.0816901i	$0.0260318\pi$
$410$	−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	0.587750	−	0.809042i	$-0.300014\pi$
$419$	31772.1	+	18343.6i	0.180975	+	0.104486i	−0.406776	+	0.913528i	$0.633347\pi$
$420$	192515.	+	154529.i	1.09136	+	0.876016i
$421$	−34142.4	−	59136.4i	−0.192633	−	0.333650i	0.753489	−	0.657460i	$-0.228369\pi$
$421$	−34142.4	−	59136.4i	−0.192633	−	0.333650i	−0.946122	+	0.323811i	$0.895036\pi$
$422$			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	$0.0182737\pi$
$431$			21316.8i			0.114754i	−0.998353	+	0.0573770i	$0.981726\pi$
$432$	−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	0.991134	−	0.132868i	$-0.0424187\pi$
$439$	73330.3	+	127012.i	0.380500	+	0.659045i	−0.610634	+	0.791913i	$0.709085\pi$
$440$		−	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	−0.699857	−	0.714283i	$-0.746753\pi$
$443$	−84622.1	+	48856.6i	−0.431198	+	0.248952i	0.268659	+	0.963235i	$0.413419\pi$
$444$	−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	$0.104512\pi$
$449$			130019.i			0.644934i	−0.946581	+	0.322467i	$0.895488\pi$
$450$	−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	0.761066	−	0.648675i	$-0.224676\pi$
$457$	−37850.9	−	65559.7i	−0.181236	−	0.313910i	−0.942302	+	0.334765i	$0.891343\pi$
$458$			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	−0.133354	−	0.991068i	$-0.542575\pi$
$461$	139894.	−	80767.8i	0.658260	−	0.380046i	0.791614	+	0.611022i	$0.209241\pi$
$462$	116699.	+	17969.0i	0.546743	+	0.0841860i
$463$	−21982.2	+	38074.3i	−0.102544	+	0.177611i	−0.912732	−	0.408559i	$-0.866031\pi$
$463$	−21982.2	+	38074.3i	−0.102544	+	0.177611i	0.810188	+	0.586170i	$0.199365\pi$
$464$	−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	$0.0600730\pi$
$467$			81829.8i			0.375213i	−0.982244	+	0.187606i	$0.939927\pi$
$468$	−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	−0.560868	−	0.827905i	$-0.689533\pi$
$479$	−28523.0	+	16467.8i	−0.124315	+	0.0717734i	0.436553	+	0.899679i	$0.356199\pi$
$480$	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	0.169170	−	0.985587i	$-0.445891\pi$
$491$	−144597.	−	83483.4i	−0.599788	−	0.346288i	−0.768958	+	0.639299i	$0.779225\pi$
$492$	−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	−0.866413	−	0.499329i	$-0.833580\pi$
$499$	−192.909	+	334.129i	−0.000774733	+	0.00134188i	0.865638	+	0.500671i	$0.166913\pi$
$500$	−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	$-0.975667\pi$
$503$		−	38644.0i		−	0.152738i	0.997080	−	0.0763688i	$-0.0243326\pi$
$504$	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	0.550285	−	0.834977i	$-0.314519\pi$
$509$	26508.4	+	15304.6i	0.102317	+	0.0590727i	−0.447968	+	0.894049i	$0.647852\pi$
$510$	−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	$0.0857138\pi$
$521$			144426.i			0.532071i	−0.963963	+	0.266035i	$0.914286\pi$
$522$	−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	0.903789	+	0.427979i	$0.140774\pi$
$547$	246110.	+	426275.i	0.822535	+	1.42467i	−0.0812533	+	0.996693i	$0.525892\pi$
$548$		−	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	$0.0554816\pi$
$557$			107606.i			0.346839i	−0.984848	+	0.173419i	$0.944518\pi$
$558$	−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	0.999906	−	0.0136800i	$-0.00435461\pi$
$563$	471654.	+	272309.i	1.48801	+	0.859104i	0.488106	+	0.872784i	$0.337688\pi$
$564$	−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	−0.835589	−	0.549355i	$-0.814874\pi$
$569$	−251766.	+	145357.i	−0.777629	+	0.448964i	0.0579603	+	0.998319i	$0.481540\pi$
$570$	20763.7	+	3197.14i	0.0639079	+	0.00984037i
$571$	−180733.	+	313038.i	−0.554325	+	0.960120i	0.443630	+	0.896210i	$0.353690\pi$
$571$	−180733.	+	313038.i	−0.554325	+	0.960120i	−0.997956	+	0.0639099i	$0.979643\pi$
$572$	−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	−0.767906	−	0.640562i	$-0.778701\pi$
$587$	−205748.	+	118789.i	−0.597116	+	0.344745i	0.170790	+	0.985307i	$0.445368\pi$
$588$	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	$-0.761970\pi$
$593$		−	478258.i		−	1.36004i	0.733192	−	0.680022i	$-0.238030\pi$
$594$	−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	0.272140	−	0.962258i	$-0.412269\pi$
$599$	−152537.	−	88067.3i	−0.425130	−	0.245449i	−0.697270	+	0.716809i	$0.745602\pi$
$600$	−85626.7	+	33292.4i	−0.237852	+	0.0924788i
$601$	55921.1	+	96858.2i	0.154820	+	0.268156i	0.932993	−	0.359893i	$-0.117187\pi$
$601$	55921.1	+	96858.2i	0.154820	+	0.268156i	−0.778174	+	0.628049i	$0.783854\pi$
$602$			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	−0.763575	−	0.645719i	$-0.776558\pi$
$607$	65371.0	−	113226.i	0.177422	−	0.307304i	0.940997	+	0.338415i	$0.109891\pi$
$608$	−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	0.791166	−	0.611601i	$-0.209474\pi$
$617$	250146.	+	144422.i	0.657087	+	0.379369i	−0.134079	+	0.990971i	$0.542808\pi$
$618$	100444.	−	652329.i	0.262995	−	1.70801i
$619$	−89030.6	−	154205.i	−0.232358	−	0.402456i	0.726143	−	0.687543i	$-0.241311\pi$
$619$	−89030.6	−	154205.i	−0.232358	−	0.402456i	−0.958502	+	0.285087i	$0.907977\pi$
$620$			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	0.392504	−	0.919750i	$-0.371609\pi$
$641$	569187.	−	328620.i	1.38528	−	0.799794i	0.992779	+	0.119957i	$0.0382755\pi$
$642$	−238274.	−	612832.i	−0.578105	−	1.48686i
$643$	−279552.	+	484197.i	−0.676145	+	1.17112i	0.299988	+	0.953943i	$0.403017\pi$
$643$	−279552.	+	484197.i	−0.676145	+	1.17112i	−0.976133	+	0.217175i	$0.930316\pi$
$644$	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	$-0.774783\pi$
$647$		−	544163.i		−	1.29993i	0.759963	−	0.649966i	$-0.225217\pi$
$648$	−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	0.999763	+	0.0217795i	$0.00693318\pi$
$653$	647505.	+	373837.i	1.51851	+	0.876710i	0.518743	+	0.854930i	$0.326400\pi$
$654$	−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	−0.899480	−	0.436962i	$-0.856054\pi$
$659$	−421600.	+	243411.i	−0.970800	+	0.560492i	−0.0713200	+	0.997453i	$0.522721\pi$
$660$	−40465.5	+	50412.6i	−0.0928959	+	0.115731i
$661$	49031.1	−	84924.3i	0.112220	−	0.194370i	−0.804445	−	0.594027i	$-0.797537\pi$
$661$	49031.1	−	84924.3i	0.112220	−	0.194370i	0.916665	+	0.399657i	$0.130871\pi$
$662$	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	−0.994423	−	0.105462i	$-0.966368\pi$
$673$	−266569.	−	461711.i	−0.588544	−	1.01939i	0.405879	−	0.913927i	$-0.366965\pi$
$674$		−	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	−0.996601	−	0.0823757i	$-0.973749\pi$
$677$	−652460.	+	376698.i	−1.42356	+	0.821894i	−0.426961	+	0.904270i	$0.640416\pi$
$678$	−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	$0.273088\pi$
$683$			705789.i			1.51298i	−0.654004	+	0.756491i	$0.726912\pi$
$684$	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	0.849049	−	0.528315i	$-0.177176\pi$
$691$	−15761.6	−	27299.8i	−0.0330098	−	0.0571747i	−0.882058	+	0.471140i	$0.843843\pi$
$692$		−	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	$0.0695697\pi$
$701$			213095.i			0.433647i	−0.976211	+	0.216824i	$0.930430\pi$
$702$	−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	0.927042	+	0.374958i	$0.122343\pi$
$709$	396235.	+	686299.i	0.788244	+	1.36528i	−0.138798	+	0.990321i	$0.544324\pi$
$710$			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	$0.226511\pi$
$719$			675203.i			1.30610i	−0.757314	+	0.653050i	$0.773489\pi$
$720$	−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	−0.912483	−	0.409116i	$-0.865837\pi$
$727$	−428397.	−	742005.i	−0.810546	−	1.40391i	0.101937	−	0.994791i	$-0.467496\pi$
$728$		−	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	0.397092	+	0.917779i	$0.370019\pi$
$733$	−320371.	+	554899.i	−0.596274	+	1.03278i	−0.993366	+	0.114998i	$0.963314\pi$
$734$	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	−0.479669	−	0.877450i	$-0.659243\pi$
$743$	−816699.	−	471522.i	−1.47940	−	0.854130i	−0.999728	+	0.0233197i	$0.992576\pi$
$744$	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	−0.686713	−	0.726929i	$-0.740947\pi$
$751$	161407.	−	279566.i	0.286183	−	0.495683i	0.972895	+	0.231246i	$0.0742803\pi$
$752$	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	0.101721	−	0.994813i	$-0.467565\pi$
$761$	−410568.	−	237042.i	−0.708951	−	0.409313i	−0.810673	+	0.585500i	$0.800898\pi$
$762$	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	−0.994574	−	0.104032i	$-0.966826\pi$
$769$	−240798.	+	417074.i	−0.407193	+	0.705279i	0.587381	+	0.809310i	$0.300159\pi$
$770$	−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	$-0.825958\pi$
$773$		−	621347.i		−	1.03986i	0.854209	−	0.519930i	$-0.174042\pi$
$774$	−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	−0.247552	+	0.968875i	$0.579626\pi$
$787$	−596357.	+	1.03292e6i	−0.962846	+	1.66770i	−0.715294	+	0.698824i	$0.753707\pi$
$788$	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	0.948627	−	0.316396i	$-0.102473\pi$
$797$	729813.	+	421358.i	1.14893	+	0.663337i	0.200307	+	0.979733i	$0.435806\pi$
$798$	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	$-0.973891\pi$
$809$		−	107245.i		−	0.163863i	0.996638	−	0.0819314i	$-0.0261088\pi$
$810$	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	0.0885938	−	0.996068i	$-0.471763\pi$
$821$	671015.	−	387411.i	0.995511	−	0.574758i	0.906917	+	0.421309i	$0.138429\pi$
$822$	−339952.	+	423519.i	−0.503123	+	0.626800i
$823$	127840.	−	221426.i	0.188742	−	0.326910i	−0.756089	−	0.654468i	$-0.772892\pi$
$823$	127840.	−	221426.i	0.188742	−	0.326910i	0.944831	+	0.327558i	$0.106226\pi$
$824$	−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	$0.118099\pi$
$827$			495939.i			0.725133i	−0.931958	+	0.362566i	$0.881901\pi$
$828$	−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	−0.300748	−	0.953704i	$-0.597236\pi$
$839$	263836.	−	152326.i	0.374810	−	0.216396i	0.675558	+	0.737307i	$0.263903\pi$
$840$	−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	−0.941047	−	0.338275i	$-0.890157\pi$
$853$	−555514.	−	962178.i	−0.763478	−	1.32238i	0.177569	−	0.984108i	$-0.443177\pi$
$854$			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	−0.772060	−	0.635550i	$-0.780773\pi$
$857$	−446315.	+	257680.i	−0.607687	+	0.350848i	0.164372	+	0.986398i	$0.447440\pi$
$858$	133049.	+	342196.i	0.180732	+	0.464836i
$859$	46714.0	−	80911.0i	0.0633083	−	0.109653i	−0.832634	−	0.553824i	$-0.813168\pi$
$859$	46714.0	−	80911.0i	0.0633083	−	0.109653i	0.895942	+	0.444170i	$0.146502\pi$
$860$	−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	$0.257031\pi$
$863$			1.07627e6i			1.44510i	−0.691317	+	0.722552i	$0.742969\pi$
$864$	−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	−0.371793	−	0.928316i	$-0.621257\pi$
$877$	475359.	−	823346.i	0.618049	−	1.07049i	0.989841	−	0.142176i	$-0.0454098\pi$
$878$	−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	$0.0120198\pi$
$881$			58603.7i			0.0755046i	−0.999287	+	0.0377523i	$0.987980\pi$
$882$	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	−0.999489	−	0.0319776i	$-0.989819\pi$
$887$	−1.20134e6	−	693593.i	−1.52693	−	0.881571i	−0.527438	−	0.849594i	$-0.676847\pi$
$888$	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	0.766951	−	0.641706i	$-0.221773\pi$
$907$	−141708.	−	245446.i	−0.172258	−	0.298360i	−0.939209	+	0.343346i	$0.888440\pi$
$908$			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	0.558995	−	0.829171i	$-0.311187\pi$
$911$	1.29183e6	−	745841.i	1.55658	−	0.898689i	0.997581	−	0.0695178i	$-0.0221461\pi$
$912$	−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	−0.260811	−	0.965390i	$-0.583990\pi$
$929$	383911.	−	221651.i	0.444835	−	0.256826i	0.705647	+	0.708564i	$0.250657\pi$
$930$	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	−0.325043	−	0.945699i	$-0.605379\pi$
$941$	−1.15694e6	−	667958.i	−1.30656	−	0.754345i	−0.981521	+	0.191355i	$0.938712\pi$
$942$	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	−0.417069	−	0.908875i	$-0.636943\pi$
$947$	144839.	−	83623.1i	0.161505	−	0.0932452i	0.578574	+	0.815630i	$0.303609\pi$
$948$	−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	$0.285585\pi$
$953$			1.41967e6i			1.56316i	−0.623807	+	0.781579i	$0.714415\pi$
$954$	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	0.305428	+	0.952215i	$0.401200\pi$
$967$	−628313.	+	1.08827e6i	−0.671928	+	1.16381i	−0.977357	+	0.211599i	$0.932133\pi$
$968$	−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	$-0.748285\pi$
$971$		−	1.34054e6i		−	1.42181i	0.703286	−	0.710907i	$-0.251715\pi$
$972$	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	0.616610	−	0.787269i	$-0.288506\pi$
$977$	232065.	+	133983.i	0.243120	+	0.140365i	−0.373490	+	0.927634i	$0.621839\pi$
$978$	−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	−0.858425	−	0.512940i	$-0.828557\pi$
$983$	−814986.	+	470532.i	−0.843418	+	0.486948i	0.0150063	+	0.999887i	$0.495223\pi$
$984$	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	−0.889446	−	0.457040i	$-0.848909\pi$
$997$	−835496.	−	1.44712e6i	−0.840532	−	1.45584i	0.0489144	−	0.998803i	$-0.484424\pi$
$998$		−	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.41.2	yes	32
3.2	odd	2		135.5.i.a.71.15		32
9.2	odd	6	inner	45.5.i.a.11.2	✓	32
9.4	even	3		405.5.c.b.161.4		32
9.5	odd	6		405.5.c.b.161.29		32
9.7	even	3		135.5.i.a.116.15		32

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

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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