LMFDB - Embedded newform 120.4.b.a.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,4,Mod(11,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("120.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	120.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.08022920069$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.3
Character	$\chi$	$=$	120.11
Dual form			120.4.b.a.11.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.65744 - 0.968509i) q^{2} +(-4.88069 + 1.78294i) q^{3} +(6.12398 + 5.14751i) q^{4} +5.00000 q^{5} +(14.6969 - 0.0110603i) q^{6} +12.1872i q^{7} +(-11.2887 - 19.6103i) q^{8} +(20.6423 - 17.4039i) q^{9} +O(q^{10})$	\(q+(-2.65744 - 0.968509i) q^{2} +(-4.88069 + 1.78294i) q^{3} +(6.12398 + 5.14751i) q^{4} +5.00000 q^{5} +(14.6969 - 0.0110603i) q^{6} +12.1872i q^{7} +(-11.2887 - 19.6103i) q^{8} +(20.6423 - 17.4039i) q^{9} +(-13.2872 - 4.84254i) q^{10} -47.5839i q^{11} +(-39.0669 - 14.2047i) q^{12} +55.3088i q^{13} +(11.8034 - 32.3866i) q^{14} +(-24.4034 + 8.91469i) q^{15} +(11.0063 + 63.0465i) q^{16} +90.1721i q^{17} +(-71.7115 + 26.2577i) q^{18} -123.391 q^{19} +(30.6199 + 25.7375i) q^{20} +(-21.7289 - 59.4817i) q^{21} +(-46.0854 + 126.451i) q^{22} -136.806 q^{23} +(90.0607 + 75.5849i) q^{24} +25.0000 q^{25} +(53.5671 - 146.980i) q^{26} +(-69.7184 + 121.747i) q^{27} +(-62.7335 + 74.6339i) q^{28} -122.976 q^{29} +(73.4847 - 0.0553013i) q^{30} +217.380i q^{31} +(31.8125 - 178.202i) q^{32} +(84.8391 + 232.242i) q^{33} +(87.3325 - 239.627i) q^{34} +60.9358i q^{35} +(216.000 - 0.325104i) q^{36} -359.253i q^{37} +(327.905 + 119.506i) q^{38} +(-98.6121 - 269.945i) q^{39} +(-56.4435 - 98.0517i) q^{40} +158.349i q^{41} +(0.134793 + 179.114i) q^{42} -334.514 q^{43} +(244.938 - 291.403i) q^{44} +(103.211 - 87.0197i) q^{45} +(363.553 + 132.498i) q^{46} -55.8595 q^{47} +(-166.126 - 288.087i) q^{48} +194.473 q^{49} +(-66.4360 - 24.2127i) q^{50} +(-160.771 - 440.102i) q^{51} +(-284.703 + 338.710i) q^{52} -494.078 q^{53} +(303.186 - 256.013i) q^{54} -237.919i q^{55} +(238.994 - 137.577i) q^{56} +(602.235 - 219.999i) q^{57} +(326.801 + 119.103i) q^{58} +151.479i q^{59} +(-195.335 - 71.0236i) q^{60} +316.631i q^{61} +(210.535 - 577.675i) q^{62} +(212.104 + 251.570i) q^{63} +(-257.130 + 442.751i) q^{64} +276.544i q^{65} +(-0.526290 - 699.337i) q^{66} +460.078 q^{67} +(-464.162 + 552.212i) q^{68} +(667.706 - 243.916i) q^{69} +(59.0168 - 161.933i) q^{70} +55.3268 q^{71} +(-574.321 - 208.334i) q^{72} -284.535 q^{73} +(-347.940 + 954.694i) q^{74} +(-122.017 + 44.5734i) q^{75} +(-755.647 - 635.158i) q^{76} +579.912 q^{77} +(0.611730 + 812.870i) q^{78} +374.804i q^{79} +(55.0315 + 315.233i) q^{80} +(123.206 - 718.513i) q^{81} +(153.363 - 420.803i) q^{82} +561.093i q^{83} +(173.115 - 476.115i) q^{84} +450.860i q^{85} +(888.951 + 323.980i) q^{86} +(600.207 - 219.258i) q^{87} +(-933.135 + 537.160i) q^{88} +3.39319i q^{89} +(-358.557 + 131.289i) q^{90} -674.057 q^{91} +(-837.796 - 704.209i) q^{92} +(-387.576 - 1060.97i) q^{93} +(148.443 + 54.1005i) q^{94} -616.957 q^{95} +(162.456 + 926.469i) q^{96} +1046.62 q^{97} +(-516.801 - 188.349i) q^{98} +(-828.146 - 982.239i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{2} - 3 q^{4} + 120 q^{5} + 19 q^{6} + 21 q^{8}+O(q^{10}) $ 24 * q - 3 * q^2 - 3 * q^4 + 120 * q^5 + 19 * q^6 + 21 * q^8	$ 24 q - 3 q^{2} - 3 q^{4} + 120 q^{5} + 19 q^{6} + 21 q^{8} - 15 q^{10} + 65 q^{12} - 54 q^{14} + 153 q^{16} - 175 q^{18} + 12 q^{19} - 15 q^{20} - 4 q^{21} - 102 q^{22} + 228 q^{23} - 407 q^{24} + 600 q^{25} + 336 q^{26} + 132 q^{27} - 186 q^{28} + 95 q^{30} + 177 q^{32} + 116 q^{33} + 408 q^{34} + 673 q^{36} + 312 q^{38} - 656 q^{39} + 105 q^{40} - 990 q^{42} - 450 q^{44} - 1104 q^{46} - 924 q^{47} - 535 q^{48} - 816 q^{49} - 75 q^{50} - 700 q^{51} - 1548 q^{52} + 528 q^{53} + 1331 q^{54} - 390 q^{56} - 172 q^{57} + 1410 q^{58} + 325 q^{60} - 978 q^{62} + 476 q^{63} + 1137 q^{64} - 2794 q^{66} + 1632 q^{67} - 1608 q^{68} + 980 q^{69} - 270 q^{70} + 216 q^{71} - 3699 q^{72} - 216 q^{73} + 768 q^{74} - 1812 q^{76} + 4140 q^{78} + 765 q^{80} + 152 q^{81} + 2244 q^{82} + 5086 q^{84} - 2808 q^{86} + 252 q^{87} + 2622 q^{88} - 875 q^{90} - 1800 q^{91} - 1836 q^{92} - 1968 q^{94} + 60 q^{95} - 5455 q^{96} + 792 q^{97} + 4851 q^{98} - 1328 q^{99}+O(q^{100}) $ 24 * q - 3 * q^2 - 3 * q^4 + 120 * q^5 + 19 * q^6 + 21 * q^8 - 15 * q^10 + 65 * q^12 - 54 * q^14 + 153 * q^16 - 175 * q^18 + 12 * q^19 - 15 * q^20 - 4 * q^21 - 102 * q^22 + 228 * q^23 - 407 * q^24 + 600 * q^25 + 336 * q^26 + 132 * q^27 - 186 * q^28 + 95 * q^30 + 177 * q^32 + 116 * q^33 + 408 * q^34 + 673 * q^36 + 312 * q^38 - 656 * q^39 + 105 * q^40 - 990 * q^42 - 450 * q^44 - 1104 * q^46 - 924 * q^47 - 535 * q^48 - 816 * q^49 - 75 * q^50 - 700 * q^51 - 1548 * q^52 + 528 * q^53 + 1331 * q^54 - 390 * q^56 - 172 * q^57 + 1410 * q^58 + 325 * q^60 - 978 * q^62 + 476 * q^63 + 1137 * q^64 - 2794 * q^66 + 1632 * q^67 - 1608 * q^68 + 980 * q^69 - 270 * q^70 + 216 * q^71 - 3699 * q^72 - 216 * q^73 + 768 * q^74 - 1812 * q^76 + 4140 * q^78 + 765 * q^80 + 152 * q^81 + 2244 * q^82 + 5086 * q^84 - 2808 * q^86 + 252 * q^87 + 2622 * q^88 - 875 * q^90 - 1800 * q^91 - 1836 * q^92 - 1968 * q^94 + 60 * q^95 - 5455 * q^96 + 792 * q^97 + 4851 * q^98 - 1328 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−2.65744	−	0.968509i	−0.939547	−	0.342420i
$2$	−2.65744	−	0.968509i	−0.939547	−	0.342420i
$3$	−4.88069	+	1.78294i	−0.939289	+	0.343127i
$3$	−4.88069	+	1.78294i	−0.939289	+	0.343127i
$4$	6.12398	+	5.14751i	0.765498	+	0.643439i
$5$	5.00000			0.447214
$5$	5.00000			0.447214
$6$	14.6969	−	0.0110603i	1.00000	−	0.000752556i
$7$			12.1872i			0.658044i	0.944322	+	0.329022i	$0.106719\pi$
$7$			12.1872i			0.658044i	−0.944322	+	0.329022i	$0.893281\pi$
$8$	−11.2887	−	19.6103i	−0.498895	−	0.866662i
$9$	20.6423	−	17.4039i	0.764528	−	0.644590i
$10$	−13.2872	−	4.84254i	−0.420178	−	0.153135i
$11$		−	47.5839i		−	1.30428i	−0.758099	−	0.652140i	$-0.773872\pi$
$11$		−	47.5839i		−	1.30428i	0.758099	−	0.652140i	$-0.226128\pi$
$12$	−39.0669	−	14.2047i	−0.939805	−	0.341712i
$13$			55.3088i			1.17999i	0.807406	+	0.589996i	$0.200871\pi$
$13$			55.3088i			1.17999i	−0.807406	+	0.589996i	$0.799129\pi$
$14$	11.8034	−	32.3866i	0.225327	−	0.618264i
$15$	−24.4034	+	8.91469i	−0.420063	+	0.153451i
$16$	11.0063	+	63.0465i	0.171973	+	0.985102i
$17$			90.1721i			1.28647i	0.765670	+	0.643234i	$0.222408\pi$
$17$			90.1721i			1.28647i	−0.765670	+	0.643234i	$0.777592\pi$
$18$	−71.7115	+	26.2577i	−0.939031	+	0.343833i
$19$	−123.391			−1.48989			−0.744946	−	0.667125i	$-0.767525\pi$
$19$	−123.391			−1.48989			−0.744946	+	0.667125i	$0.767525\pi$
$20$	30.6199	+	25.7375i	0.342341	+	0.287755i
$21$	−21.7289	−	59.4817i	−0.225792	−	0.618094i
$22$	−46.0854	+	126.451i	−0.446611	+	1.22543i
$23$	−136.806			−1.24026			−0.620130	−	0.784499i	$-0.712920\pi$
$23$	−136.806			−1.24026			−0.620130	+	0.784499i	$0.712920\pi$
$24$	90.0607	+	75.5849i	0.765982	+	0.642862i
$25$	25.0000			0.200000
$26$	53.5671	−	146.980i	0.404052	−	1.10866i
$27$	−69.7184	+	121.747i	−0.496937	+	0.867786i
$28$	−62.7335	+	74.6339i	−0.423411	+	0.503731i
$29$	−122.976			−0.787450			−0.393725	−	0.919228i	$-0.628814\pi$
$29$	−122.976			−0.787450			−0.393725	+	0.919228i	$0.628814\pi$
$30$	73.4847	−	0.0553013i	0.447213	−	0.000336553i
$31$			217.380i			1.25944i	0.776822	+	0.629720i	$0.216830\pi$
$31$			217.380i			1.25944i	−0.776822	+	0.629720i	$0.783170\pi$
$32$	31.8125	−	178.202i	0.175741	−	0.984436i
$33$	84.8391	+	232.242i	0.447533	+	1.22510i
$34$	87.3325	−	239.627i	0.440512	−	1.20870i
$35$			60.9358i			0.294286i
$36$	216.000	−	0.325104i	0.999999	−	0.00150511i
$37$		−	359.253i		−	1.59624i	−0.602499	−	0.798120i	$-0.705828\pi$
$37$		−	359.253i		−	1.59624i	0.602499	−	0.798120i	$-0.294172\pi$
$38$	327.905	+	119.506i	1.39982	+	0.510168i
$39$	−98.6121	−	269.945i	−0.404887	−	1.10835i
$40$	−56.4435	−	98.0517i	−0.223113	−	0.387583i
$41$			158.349i			0.603170i	0.953439	+	0.301585i	$0.0975157\pi$
$41$			158.349i			0.603170i	−0.953439	+	0.301585i	$0.902484\pi$
$42$	0.134793	+	179.114i	0.000495215	+	0.658044i
$43$	−334.514			−1.18635			−0.593173	−	0.805075i	$-0.702125\pi$
$43$	−334.514			−1.18635			−0.593173	+	0.805075i	$0.702125\pi$
$44$	244.938	−	291.403i	0.839224	−	0.998423i
$45$	103.211	−	87.0197i	0.341907	−	0.288269i
$46$	363.553	+	132.498i	1.16528	+	0.424689i
$47$	−55.8595			−0.173361			−0.0866803	−	0.996236i	$-0.527626\pi$
$47$	−55.8595			−0.173361			−0.0866803	+	0.996236i	$0.527626\pi$
$48$	−166.126	−	288.087i	−0.499547	−	0.866287i
$49$	194.473			0.566978
$50$	−66.4360	−	24.2127i	−0.187909	−	0.0684839i
$51$	−160.771	−	440.102i	−0.441421	−	1.20836i
$52$	−284.703	+	338.710i	−0.759253	+	0.903281i
$53$	−494.078			−1.28051			−0.640254	−	0.768164i	$-0.721171\pi$
$53$	−494.078			−1.28051			−0.640254	+	0.768164i	$0.721171\pi$
$54$	303.186	−	256.013i	0.764043	−	0.645165i
$55$		−	237.919i		−	0.583291i
$56$	238.994	−	137.577i	0.570302	−	0.328295i
$57$	602.235	−	219.999i	1.39944	−	0.511221i
$58$	326.801	+	119.103i	0.739846	+	0.269638i
$59$			151.479i			0.334253i	0.985935	+	0.167127i	$0.0534489\pi$
$59$			151.479i			0.334253i	−0.985935	+	0.167127i	$0.946551\pi$
$60$	−195.335	−	71.0236i	−0.420293	−	0.152818i
$61$			316.631i			0.664598i	0.943174	+	0.332299i	$0.107824\pi$
$61$			316.631i			0.664598i	−0.943174	+	0.332299i	$0.892176\pi$
$62$	210.535	−	577.675i	0.431257	−	1.18330i
$63$	212.104	+	251.570i	0.424169	+	0.503094i
$64$	−257.130	+	442.751i	−0.502207	+	0.864747i
$65$			276.544i			0.527709i
$66$	−0.526290	−	699.337i	−0.000981543	−	1.30428i
$67$	460.078			0.838918			0.419459	−	0.907774i	$-0.362220\pi$
$67$	460.078			0.838918			0.419459	+	0.907774i	$0.362220\pi$
$68$	−464.162	+	552.212i	−0.827763	+	0.984788i
$69$	667.706	−	243.916i	1.16496	−	0.425566i
$70$	59.0168	−	161.933i	0.100769	−	0.276496i
$71$	55.3268			0.0924801			0.0462401	−	0.998930i	$-0.485276\pi$
$71$	55.3268			0.0924801			0.0462401	+	0.998930i	$0.485276\pi$
$72$	−574.321	−	208.334i	−0.940061	−	0.341005i
$73$	−284.535			−0.456196			−0.228098	−	0.973638i	$-0.573251\pi$
$73$	−284.535			−0.456196			−0.228098	+	0.973638i	$0.573251\pi$
$74$	−347.940	+	954.694i	−0.546584	+	1.49974i
$75$	−122.017	+	44.5734i	−0.187858	+	0.0686253i
$76$	−755.647	−	635.158i	−1.14051	−	0.958654i
$77$	579.912			0.858274
$78$	0.611730	+	812.870i	0.000888010	+	1.17999i
$79$			374.804i			0.533782i	0.963727	+	0.266891i	$0.0859963\pi$
$79$			374.804i			0.533782i	−0.963727	+	0.266891i	$0.914004\pi$
$80$	55.0315	+	315.233i	0.0769088	+	0.440551i
$81$	123.206	−	718.513i	0.169007	−	0.985615i
$82$	153.363	−	420.803i	0.206537	−	0.566707i
$83$			561.093i			0.742024i	0.928628	+	0.371012i	$0.120989\pi$
$83$			561.093i			0.742024i	−0.928628	+	0.371012i	$0.879011\pi$
$84$	173.115	−	476.115i	0.224862	−	0.618433i
$85$			450.860i			0.575326i
$86$	888.951	+	323.980i	1.11463	+	0.406228i
$87$	600.207	−	219.258i	0.739643	−	0.270195i
$88$	−933.135	+	537.160i	−1.13037	+	0.650699i
$89$			3.39319i			0.00404132i	0.999998	+	0.00202066i	$0.000643197\pi$
$89$			3.39319i			0.00404132i	−0.999998	+	0.00202066i	$0.999357\pi$
$90$	−358.557	+	131.289i	−0.419947	+	0.153767i
$91$	−674.057			−0.776487
$92$	−837.796	−	704.209i	−0.949416	−	0.798031i
$93$	−387.576	−	1060.97i	−0.432147	−	1.18298i
$94$	148.443	+	54.1005i	0.162881	+	0.0593621i
$95$	−616.957			−0.666300
$96$	162.456	+	926.469i	0.172715	+	0.984972i
$97$	1046.62			1.09554			0.547772	−	0.836627i	$-0.315476\pi$
$97$	1046.62			1.09554			0.547772	+	0.836627i	$0.315476\pi$
$98$	−516.801	−	188.349i	−0.532702	−	0.194144i
$99$	−828.146	−	982.239i	−0.840726	−	0.997158i
$100$	153.100	+	128.688i	0.153100	+	0.128688i
$101$	−223.022			−0.219718			−0.109859	−	0.993947i	$-0.535040\pi$
$101$	−223.022			−0.219718			−0.109859	+	0.993947i	$0.535040\pi$
$102$	0.997327	+	1325.25i	0.000968138	+	1.28647i
$103$			801.665i			0.766897i	0.923562	+	0.383449i	$0.125264\pi$
$103$			801.665i			0.766897i	−0.923562	+	0.383449i	$0.874736\pi$
$104$	1084.62	−	624.365i	1.02265	−	0.588692i
$105$	−108.645	−	297.409i	−0.100977	−	0.276420i
$106$	1312.98	+	478.519i	1.20310	+	0.438471i
$107$		−	445.481i		−	0.402489i	−0.979541	−	0.201244i	$-0.935501\pi$
$107$		−	445.481i		−	0.402489i	0.979541	−	0.201244i	$-0.0644985\pi$
$108$	−1053.65	+	386.701i	−0.938772	+	0.344540i
$109$			1071.43i			0.941511i	0.882264	+	0.470756i	$0.156019\pi$
$109$			1071.43i			0.941511i	−0.882264	+	0.470756i	$0.843981\pi$
$110$	−230.427	+	632.256i	−0.199730	+	0.548030i
$111$	640.526	+	1753.40i	0.547712	+	1.49933i
$112$	−768.357	+	134.135i	−0.648241	+	0.113166i
$113$			778.048i			0.647722i	0.946105	+	0.323861i	$0.104981\pi$
$113$			778.048i			0.647722i	−0.946105	+	0.323861i	$0.895019\pi$
$114$	−1813.48	+	1.36474i	−1.48989	+	0.00112123i
$115$	−684.029			−0.554661
$116$	−753.102	−	633.019i	−0.602791	−	0.506676i
$117$	962.591	+	1141.70i	0.760611	+	0.902138i
$118$	146.709	−	402.547i	0.114455	−	0.314047i
$119$	−1098.94			−0.846552
$120$	450.303	+	377.924i	0.342557	+	0.287497i
$121$	−933.223			−0.701144
$122$	306.660	−	841.429i	0.227571	−	0.624421i
$123$	−282.327	−	772.853i	−0.206964	−	0.566551i
$124$	−1118.97	+	1331.23i	−0.810373	+	0.964099i
$125$	125.000			0.0894427
$126$	−320.007	−	873.958i	−0.226258	−	0.617924i
$127$		−	1820.12i		−	1.27173i	−0.771800	−	0.635865i	$-0.780643\pi$
$127$		−	1820.12i		−	1.27173i	0.771800	−	0.635865i	$-0.219357\pi$
$128$	1112.12	−	927.551i	0.767954	−	0.640505i
$129$	1632.66	−	596.418i	1.11432	−	0.407067i
$130$	267.835	−	734.899i	0.180698	−	0.495807i
$131$		−	2056.54i		−	1.37161i	−0.727785	−	0.685805i	$-0.759450\pi$
$131$		−	2056.54i		−	1.37161i	0.727785	−	0.685805i	$-0.240550\pi$
$132$	−675.915	+	1858.96i	−0.445688	+	1.22577i
$133$		−	1503.79i		−	0.980414i
$134$	−1222.63	−	445.590i	−0.788203	−	0.287262i
$135$	−348.592	+	608.735i	−0.222237	+	0.388086i
$136$	1768.30	−	1017.93i	1.11493	−	0.641812i
$137$			489.409i			0.305205i	0.988288	+	0.152602i	$0.0487654\pi$
$137$			489.409i			0.305205i	−0.988288	+	0.152602i	$0.951235\pi$
$138$	−2010.62	+	1.51311i	−1.24026	+	0.000933364i
$139$	1891.05			1.15393			0.576966	−	0.816768i	$-0.304236\pi$
$139$	1891.05			1.15393			0.576966	+	0.816768i	$0.304236\pi$
$140$	−313.667	+	373.169i	−0.189355	+	0.225276i
$141$	272.633	−	99.5941i	0.162836	−	0.0594846i
$142$	−147.028	−	53.5845i	−0.0868894	−	0.0316670i
$143$	2631.81			1.53904
$144$	1324.45	+	1109.87i	0.766465	+	0.642286i
$145$	−614.879			−0.352158
$146$	756.135	+	275.575i	0.428618	+	0.156210i
$147$	−949.164	+	346.734i	−0.532556	+	0.194545i
$148$	1849.26	−	2200.06i	1.02708	−	1.22192i
$149$	126.333			0.0694602			0.0347301	−	0.999397i	$-0.488943\pi$
$149$	126.333			0.0694602			0.0347301	+	0.999397i	$0.488943\pi$
$150$	367.423	−	0.276507i	0.200000	−	0.000150511i
$151$		−	458.807i		−	0.247266i	−0.992328	−	0.123633i	$-0.960545\pi$
$151$		−	458.807i		−	0.247266i	0.992328	−	0.123633i	$-0.0394545\pi$
$152$	1392.93	+	2419.75i	0.743299	+	1.29123i
$153$	1569.35	+	1861.36i	0.829244	+	0.983541i
$154$	−1541.08	−	561.650i	−0.806388	−	0.293890i
$155$			1086.90i			0.563239i
$156$	785.646	−	2160.75i	0.403218	−	1.10896i
$157$		−	2094.65i		−	1.06478i	−0.846498	−	0.532392i	$-0.821293\pi$
$157$		−	2094.65i		−	1.06478i	0.846498	−	0.532392i	$-0.178707\pi$
$158$	363.001	−	996.019i	0.182777	−	0.501513i
$159$	2411.44	−	880.911i	1.20277	−	0.439376i
$160$	159.063	−	891.010i	0.0785938	−	0.440253i
$161$		−	1667.27i		−	0.816146i
$162$	−1023.30	+	1790.08i	−0.496284	+	0.868160i
$163$	2760.88			1.32668			0.663341	−	0.748317i	$-0.269138\pi$
$163$	2760.88			1.32668			0.663341	+	0.748317i	$0.269138\pi$
$164$	−815.104	+	969.727i	−0.388103	+	0.461725i
$165$	424.195	+	1161.21i	0.200143	+	0.547879i
$166$	543.424	−	1491.07i	0.254083	−	0.697166i
$167$	−3296.23			−1.52736			−0.763682	−	0.645593i	$-0.776610\pi$
$167$	−3296.23			−1.52736			−0.763682	+	0.645593i	$0.776610\pi$
$168$	−921.164	+	1097.58i	−0.423032	+	0.504050i
$169$	−862.063			−0.392382
$170$	436.662	−	1198.13i	0.197003	−	0.540546i
$171$	−2547.08	+	2147.50i	−1.13906	+	0.960369i
$172$	−2048.56	−	1721.91i	−0.908146	−	0.763341i
$173$	−2267.55			−0.996525			−0.498263	−	0.867026i	$-0.666028\pi$
$173$	−2267.55			−0.996525			−0.498263	+	0.867026i	$0.666028\pi$
$174$	−1807.37	+	1.36015i	−0.787450	+	0.000592600i
$175$			304.679i			0.131609i
$176$	3000.00	−	523.722i	1.28485	−	0.224301i
$177$	−270.078	−	739.324i	−0.114691	−	0.313960i
$178$	3.28634	−	9.01721i	0.00138383	−	0.00379701i
$179$			3380.44i			1.41154i	0.708440	+	0.705771i	$0.249399\pi$
$179$			3380.44i			1.41154i	−0.708440	+	0.705771i	$0.750601\pi$
$180$	1080.00	−	1.62552i	0.447213	−	0.000673106i
$181$			2425.54i			0.996070i	0.867157	+	0.498035i	$0.165945\pi$
$181$			2425.54i			0.996070i	−0.867157	+	0.498035i	$0.834055\pi$
$182$	1791.27	+	652.830i	0.729546	+	0.265884i
$183$	−564.534	−	1545.38i	−0.228041	−	0.624250i
$184$	1544.36	+	2682.81i	0.618759	+	1.07489i
$185$		−	1796.27i		−	0.713860i
$186$	2.40428	+	3194.82i	0.000947799	+	1.25944i
$187$	4290.74			1.67791
$188$	−342.083	−	287.537i	−0.132707	−	0.111547i
$189$	−1483.75	−	849.668i	−0.571042	−	0.327007i
$190$	1639.53	+	597.528i	0.626020	+	0.228154i
$191$	544.275			0.206190			0.103095	−	0.994671i	$-0.467125\pi$
$191$	544.275			0.206190			0.103095	+	0.994671i	$0.467125\pi$
$192$	465.576	−	2619.38i	0.175000	−	0.984568i
$193$	−3964.43			−1.47858			−0.739290	−	0.673388i	$-0.764839\pi$
$193$	−3964.43			−1.47858			−0.739290	+	0.673388i	$0.764839\pi$
$194$	−2781.32	−	1013.66i	−1.02932	−	0.375136i
$195$	−493.061	−	1349.73i	−0.181071	−	0.495671i
$196$	1190.95	+	1001.05i	0.434020	+	0.364815i
$197$	3182.98			1.15116			0.575579	−	0.817746i	$-0.304777\pi$
$197$	3182.98			1.15116			0.575579	+	0.817746i	$0.304777\pi$
$198$	1249.44	+	3412.31i	0.448455	+	1.22476i
$199$		−	3438.47i		−	1.22486i	−0.790525	−	0.612429i	$-0.790192\pi$
$199$		−	3438.47i		−	1.22486i	0.790525	−	0.612429i	$-0.209808\pi$
$200$	−282.218	−	490.258i	−0.0997790	−	0.173332i
$201$	−2245.50	+	820.291i	−0.787986	+	0.287855i
$202$	592.668	+	215.999i	0.206436	+	0.0752358i
$203$		−	1498.73i		−	0.518177i
$204$	1280.87	−	3522.75i	0.439602	−	1.20903i
$205$			791.746i			0.269746i
$206$	776.420	−	2130.38i	0.262601	−	0.720536i
$207$	−2823.98	+	2380.96i	−0.948213	+	0.799459i
$208$	−3487.03	+	608.745i	−1.16241	+	0.202927i
$209$			5871.44i			1.94323i
$210$	0.673966	+	895.569i	0.000221467	+	0.294286i
$211$	2919.28			0.952472			0.476236	−	0.879318i	$-0.342001\pi$
$211$	2919.28			0.952472			0.476236	+	0.879318i	$0.342001\pi$
$212$	−3025.73	−	2543.27i	−0.980225	−	0.823928i
$213$	−270.033	+	98.6443i	−0.0868656	+	0.0317324i
$214$	−431.452	+	1183.84i	−0.137820	+	0.378157i
$215$	−1672.57			−0.530550
$216$	3174.53	−	7.16705i	0.999997	−	0.00225767i
$217$	−2649.25			−0.828768
$218$	1037.69	−	2847.27i	0.322392	−	0.884594i
$219$	1388.73	−	507.308i	0.428500	−	0.156533i
$220$	1224.69	−	1457.01i	0.375312	−	0.446508i
$221$	−4987.31			−1.51802
$222$	−3.97344	−	5279.92i	−0.00120126	−	1.59624i
$223$			108.869i			0.0326924i	0.999866	+	0.0163462i	$0.00520339\pi$
$223$			108.869i			0.0326924i	−0.999866	+	0.0163462i	$0.994797\pi$
$224$	2171.78	+	387.704i	0.647803	+	0.115645i
$225$	516.057	−	435.098i	0.152906	−	0.128918i
$226$	753.546	−	2067.62i	0.221793	−	0.608565i
$227$			5686.70i			1.66273i	0.555726	+	0.831365i	$0.312440\pi$
$227$			5686.70i			1.66273i	−0.555726	+	0.831365i	$0.687560\pi$
$228$	4820.52	+	1752.74i	1.40021	+	0.509114i
$229$		−	2969.65i		−	0.856943i	−0.903555	−	0.428472i	$-0.859052\pi$
$229$		−	2969.65i		−	0.856943i	0.903555	−	0.428472i	$-0.140948\pi$
$230$	1817.77	+	662.488i	0.521130	+	0.189927i
$231$	−2830.37	+	1033.95i	−0.806167	+	0.294496i
$232$	1388.24	+	2411.60i	0.392855	+	0.682453i
$233$		−	4901.20i		−	1.37806i	−0.724732	−	0.689031i	$-0.758036\pi$
$233$		−	4901.20i		−	1.37806i	0.724732	−	0.689031i	$-0.241964\pi$
$234$	−1452.28	−	3966.27i	−0.405721	−	1.10805i
$235$	−279.298			−0.0775292
$236$	−779.742	+	927.657i	−0.215071	+	0.255870i
$237$	−668.252	−	1829.30i	−0.183155	−	0.501375i
$238$	2920.37	+	1064.33i	0.795376	+	0.289876i
$239$	3875.41			1.04887			0.524434	−	0.851451i	$-0.324277\pi$
$239$	3875.41			1.04887			0.524434	+	0.851451i	$0.324277\pi$
$240$	−830.631	−	1440.43i	−0.223404	−	0.387415i
$241$	−6369.26			−1.70241			−0.851203	−	0.524837i	$-0.824126\pi$
$241$	−6369.26			−1.70241			−0.851203	+	0.524837i	$0.824126\pi$
$242$	2479.99	+	903.835i	0.658758	+	0.240086i
$243$	679.733	+	3726.51i	0.179444	+	0.983768i
$244$	−1629.86	+	1939.04i	−0.427628	+	0.508748i
$245$	972.367			0.253560
$246$	1.75138	+	2327.25i	0.000453919	+	0.603170i
$247$		−	6824.63i		−	1.75806i
$248$	4262.90	−	2453.94i	1.09151	−	0.628329i
$249$	−1000.39	−	2738.52i	−0.254608	−	0.696975i
$250$	−332.180	−	121.064i	−0.0840357	−	0.0306269i
$251$			928.355i			0.233455i	0.993164	+	0.116728i	$0.0372405\pi$
$251$			928.355i			0.233455i	−0.993164	+	0.116728i	$0.962760\pi$
$252$	3.96209	+	2632.42i	0.000990430	+	0.658044i
$253$			6509.74i			1.61764i
$254$	−1762.80	+	4836.87i	−0.435465	+	1.19485i
$255$	−803.856	−	2200.51i	−0.197410	−	0.540397i
$256$	−3853.72	+	1387.82i	−0.940850	+	0.338822i
$257$		−	3950.69i		−	0.958900i	−0.877569	−	0.479450i	$-0.840836\pi$
$257$		−	3950.69i		−	0.958900i	0.877569	−	0.479450i	$-0.159164\pi$
$258$	−4916.33	+	3.69981i	−1.18635	+	0.000892792i
$259$	4378.27			1.05040
$260$	−1423.51	+	1693.55i	−0.339548	+	0.403960i
$261$	−2538.50	+	2140.26i	−0.602028	+	0.507582i
$262$	−1991.78	+	5465.14i	−0.469666	+	1.28869i
$263$	1966.12			0.460975			0.230487	−	0.973075i	$-0.425968\pi$
$263$	1966.12			0.460975			0.230487	+	0.973075i	$0.425968\pi$
$264$	3596.62	−	4285.43i	0.838472	−	0.999054i
$265$	−2470.39			−0.572660
$266$	−1456.43	+	3996.23i	−0.335713	+	0.921145i
$267$	−6.04985	−	16.5611i	−0.00138669	−	0.00379597i
$268$	2817.51	+	2368.26i	0.642189	+	0.539792i
$269$	−8154.84			−1.84836			−0.924181	−	0.381955i	$-0.875251\pi$
$269$	−8154.84			−1.84836			−0.924181	+	0.381955i	$0.875251\pi$
$270$	1515.93	−	1280.06i	0.341690	−	0.288527i
$271$			4348.89i			0.974821i	0.873173	+	0.487411i	$0.162059\pi$
$271$			4348.89i			0.974821i	−0.873173	+	0.487411i	$0.837941\pi$
$272$	−5685.03	+	992.460i	−1.26730	+	0.221238i
$273$	3289.86	−	1201.80i	0.729346	−	0.266433i
$274$	473.997	−	1300.58i	0.104508	−	0.286754i
$275$		−	1189.60i		−	0.260856i
$276$	5344.58	+	1943.29i	1.16560	+	0.423812i
$277$			8081.26i			1.75291i	0.481485	+	0.876454i	$0.340097\pi$
$277$			8081.26i			1.75291i	−0.481485	+	0.876454i	$0.659903\pi$
$278$	−5025.35	−	1831.50i	−1.08417	−	0.395129i
$279$	3783.27	+	4487.22i	0.811823	+	0.962878i
$280$	1194.97	−	687.886i	0.255047	−	0.146818i
$281$			4060.17i			0.861956i	0.902362	+	0.430978i	$0.141831\pi$
$281$			4060.17i			0.861956i	−0.902362	+	0.430978i	$0.858169\pi$
$282$	−820.964	+	0.617821i	−0.173361	+	0.000130464i
$283$	−759.102			−0.159449			−0.0797243	−	0.996817i	$-0.525404\pi$
$283$	−759.102			−0.159449			−0.0797243	+	0.996817i	$0.525404\pi$
$284$	338.821	+	284.795i	0.0707933	+	0.0595053i
$285$	3011.18	−	1100.00i	0.625848	−	0.228625i
$286$	−6993.87	−	2548.93i	−1.44600	−	0.526997i
$287$	−1929.82			−0.396913
$288$	−2444.73	−	4232.16i	−0.500199	−	0.865910i
$289$	−3218.01			−0.654998
$290$	1634.01	+	595.516i	0.330869	+	0.120586i
$291$	−5108.21	+	1866.05i	−1.02903	+	0.375910i
$292$	−1742.49	−	1464.65i	−0.349217	−	0.293534i
$293$	7603.78			1.51610			0.758050	−	0.652196i	$-0.226152\pi$
$293$	7603.78			1.51610			0.758050	+	0.652196i	$0.226152\pi$
$294$	2858.16	−	2.15093i	0.566978	−	0.000426682i
$295$			757.397i			0.149483i
$296$	−7045.08	+	4055.51i	−1.38340	+	0.796356i
$297$	5793.20	+	3317.47i	1.13184	+	0.648145i
$298$	−335.721	−	122.354i	−0.0652611	−	0.0237845i
$299$		−	7566.56i		−	1.46350i
$300$	−976.674	−	355.118i	−0.187961	−	0.0683425i
$301$		−	4076.77i		−	0.780669i
$302$	−444.358	+	1219.25i	−0.0846687	+	0.232318i
$303$	1088.50	−	397.635i	0.206379	−	0.0753911i
$304$	−1358.08	−	7779.40i	−0.256221	−	1.46769i
$305$			1583.16i			0.297217i
$306$	−2367.71	−	6466.37i	−0.442330	−	1.20803i
$307$	−940.547			−0.174853			−0.0874264	−	0.996171i	$-0.527864\pi$
$307$	−940.547			−0.174853			−0.0874264	+	0.996171i	$0.527864\pi$
$308$	3551.37	+	2985.10i	0.657006	+	0.552246i
$309$	−1429.32	−	3912.68i	−0.263143	−	0.720338i
$310$	1052.67	−	2888.38i	0.192864	−	0.529189i
$311$	1883.73			0.343462			0.171731	−	0.985144i	$-0.445064\pi$
$311$	1883.73			0.343462			0.171731	+	0.985144i	$0.445064\pi$
$312$	−4180.51	+	4981.15i	−0.758573	+	0.903852i
$313$	937.647			0.169326			0.0846629	−	0.996410i	$-0.473019\pi$
$313$	937.647			0.169326			0.0846629	+	0.996410i	$0.473019\pi$
$314$	−2028.69	+	5566.41i	−0.364603	+	1.00042i
$315$	1060.52	+	1257.85i	0.189694	+	0.224990i
$316$	−1929.31	+	2295.29i	−0.343456	+	0.408609i
$317$	10736.4			1.90227			0.951133	−	0.308780i	$-0.0999208\pi$
$317$	10736.4			1.90227			0.951133	+	0.308780i	$0.0999208\pi$
$318$	−7261.44	+	5.46464i	−1.28051	+	0.000963653i
$319$			5851.67i			1.02705i
$320$	−1285.65	+	2213.75i	−0.224594	+	0.386727i
$321$	794.265	+	2174.26i	0.138105	+	0.378053i
$322$	−1614.77	+	4430.68i	−0.279464	+	0.766807i
$323$		−	11126.5i		−	1.91670i
$324$	4453.07	−	3765.96i	0.763557	−	0.645740i
$325$			1382.72i			0.235998i
$326$	−7336.89	−	2673.94i	−1.24648	−	0.454282i
$327$	−1910.30	−	5229.34i	−0.323058	−	0.884351i
$328$	3105.28	−	1787.56i	0.522745	−	0.300919i
$329$		−	680.769i		−	0.114079i
$330$	−2.63145	−	3496.68i	−0.000438959	−	0.583291i
$331$	116.777			0.0193916			0.00969582	−	0.999953i	$-0.496914\pi$
$331$	116.777			0.0193916			0.00969582	+	0.999953i	$0.496914\pi$
$332$	−2888.23	+	3436.12i	−0.477447	+	0.568018i
$333$	−6252.42	−	7415.80i	−1.02892	−	1.22037i
$334$	8759.53	+	3192.43i	1.43503	+	0.522999i
$335$	2300.39			0.375175
$336$	3510.96	−	2024.61i	0.570055	−	0.328724i
$337$	8347.59			1.34932			0.674662	−	0.738127i	$-0.264289\pi$
$337$	8347.59			1.34932			0.674662	+	0.738127i	$0.264289\pi$
$338$	2290.88	+	834.915i	0.368661	+	0.134359i
$339$	−1387.21	−	3797.41i	−0.222251	−	0.608398i
$340$	−2320.81	+	2761.06i	−0.370187	+	0.440410i
$341$	10343.8			1.64266
$342$	8848.58	−	3239.97i	1.39905	−	0.512274i
$343$			6550.27i			1.03114i
$344$	3776.23	+	6559.93i	0.591863	+	1.02816i
$345$	3338.53	−	1219.58i	0.520987	−	0.190319i
$346$	6025.89	+	2196.15i	0.936282	+	0.341230i
$347$			3345.39i			0.517550i	0.965938	+	0.258775i	$0.0833188\pi$
$347$			3345.39i			0.517550i	−0.965938	+	0.258775i	$0.916681\pi$
$348$	4804.29	+	1746.84i	0.740049	+	0.269081i
$349$		−	6358.88i		−	0.975310i	−0.873036	−	0.487655i	$-0.837852\pi$
$349$		−	6358.88i		−	0.975310i	0.873036	−	0.487655i	$-0.162148\pi$
$350$	295.084	−	809.666i	0.0450655	−	0.123653i
$351$	−6733.68	−	3856.04i	−1.02398	−	0.586382i
$352$	−8479.54	−	1513.76i	−1.28398	−	0.229215i
$353$		−	5333.32i		−	0.804147i	−0.915607	−	0.402074i	$-0.868290\pi$
$353$		−	5333.32i		−	0.804147i	0.915607	−	0.402074i	$-0.131710\pi$
$354$	1.67540	+	2226.28i	0.000251544	+	0.334253i
$355$	276.634			0.0413584
$356$	−17.4665	+	20.7798i	−0.00260034	+	0.00309362i
$357$	5363.59	−	1959.34i	0.795158	−	0.290475i
$358$	3273.99	−	8983.32i	0.483340	−	1.32621i
$359$	12278.3			1.80508			0.902538	−	0.430611i	$-0.141702\pi$
$359$	12278.3			1.80508			0.902538	+	0.430611i	$0.141702\pi$
$360$	−2871.61	−	1041.67i	−0.420408	−	0.152502i
$361$	8366.44			1.21978
$362$	2349.15	−	6445.72i	0.341074	−	0.935855i
$363$	4554.77	−	1663.88i	0.658577	−	0.240581i
$364$	−4127.91	−	3469.71i	−0.594399	−	0.499622i
$365$	−1422.68			−0.204017
$366$	3.50203	+	4653.51i	0.000500147	+	0.664598i
$367$		−	798.997i		−	0.113644i	−0.998384	−	0.0568219i	$-0.981903\pi$
$367$		−	798.997i		−	0.113644i	0.998384	−	0.0568219i	$-0.0180967\pi$
$368$	−1505.72	−	8625.12i	−0.213292	−	1.22178i
$369$	2755.90	+	3268.68i	0.388798	+	0.461141i
$370$	−1739.70	+	4773.47i	−0.244440	+	0.670705i
$371$		−	6021.41i		−	0.842630i
$372$	3087.83	−	8492.38i	0.430366	−	1.18363i
$373$			3471.74i			0.481930i	0.970534	+	0.240965i	$0.0774640\pi$
$373$			3471.74i			0.481930i	−0.970534	+	0.240965i	$0.922536\pi$
$374$	−11402.4	−	4155.62i	−1.57648	−	0.574550i
$375$	−610.086	+	222.867i	−0.0840126	+	0.0306902i
$376$	630.582	+	1095.42i	0.0864888	+	0.150245i
$377$		−	6801.65i		−	0.929185i
$378$	3120.07	+	3694.97i	0.424547	+	0.502774i
$379$	−6739.53			−0.913421			−0.456710	−	0.889615i	$-0.650972\pi$
$379$	−6739.53			−0.913421			−0.456710	+	0.889615i	$0.650972\pi$
$380$	−3778.23	−	3175.79i	−0.510051	−	0.428723i
$381$	3245.17	+	8883.45i	0.436364	+	1.19452i
$382$	−1446.38	−	527.135i	−0.193725	−	0.0706036i
$383$	979.094			0.130625			0.0653125	−	0.997865i	$-0.479196\pi$
$383$	979.094			0.130625			0.0653125	+	0.997865i	$0.479196\pi$
$384$	−3774.13	+	6509.92i	−0.501556	+	0.865125i
$385$	2899.56			0.383832
$386$	10535.2	+	3839.58i	1.38919	+	0.506294i
$387$	−6905.13	+	5821.86i	−0.906996	+	0.764707i
$388$	6409.46	+	5387.47i	0.838637	+	0.704916i
$389$	−9010.62			−1.17444			−0.587219	−	0.809428i	$-0.699777\pi$
$389$	−9010.62			−1.17444			−0.587219	+	0.809428i	$0.699777\pi$
$390$	3.05865	+	4064.35i	0.000397130	+	0.527708i
$391$		−	12336.1i		−	1.59555i
$392$	−2195.35	−	3813.69i	−0.282862	−	0.491378i
$393$	3666.69	+	10037.3i	0.470636	+	1.28834i
$394$	−8458.59	−	3082.75i	−1.08157	−	0.394179i
$395$			1874.02i			0.238714i
$396$	−15.4697	−	10278.1i	−0.00196309	−	1.30428i
$397$		−	698.162i		−	0.0882614i	−0.999026	−	0.0441307i	$-0.985948\pi$
$397$		−	698.162i		−	0.0882614i	0.999026	−	0.0441307i	$-0.0140518\pi$
$398$	−3330.19	+	9137.54i	−0.419416	+	1.15081i
$399$	2681.16	+	7339.53i	0.336406	+	0.920893i
$400$	275.157	+	1576.16i	0.0343947	+	0.197020i
$401$		−	4497.43i		−	0.560078i	−0.959989	−	0.280039i	$-0.909653\pi$
$401$		−	4497.43i		−	0.560078i	0.959989	−	0.280039i	$-0.0903474\pi$
$402$	6761.74	−	5.08859i	0.838917	−	0.000631332i
$403$	−12023.0			−1.48613
$404$	−1365.78	−	1148.01i	−0.168194	−	0.141375i
$405$	616.031	−	3592.57i	0.0755823	−	0.440780i
$406$	−1451.53	+	3982.77i	−0.177434	+	0.486852i
$407$	−17094.7			−2.08194
$408$	−6815.65	+	8120.96i	−0.827021	+	0.985410i
$409$	722.578			0.0873574			0.0436787	−	0.999046i	$-0.486092\pi$
$409$	722.578			0.0873574			0.0436787	+	0.999046i	$0.486092\pi$
$410$	766.813	−	2104.02i	0.0923663	−	0.253439i
$411$	−872.586	−	2388.66i	−0.104724	−	0.286676i
$412$	−4126.58	+	4909.38i	−0.493451	+	0.587058i
$413$	−1846.10			−0.219953
$414$	9810.54	−	3592.20i	1.16464	−	0.426443i
$415$			2805.47i			0.331843i
$416$	9856.14	+	1759.51i	1.16163	+	0.207373i
$417$	−9229.62	+	3371.62i	−1.08388	+	0.395945i
$418$	5686.54	−	15603.0i	0.665401	−	1.82576i
$419$			5358.98i			0.624829i	0.949946	+	0.312414i	$0.101138\pi$
$419$			5358.98i			0.624829i	−0.949946	+	0.312414i	$0.898862\pi$
$420$	865.575	−	2380.57i	0.100561	−	0.276572i
$421$		−	8487.11i		−	0.982509i	−0.871016	−	0.491255i	$-0.836538\pi$
$421$		−	8487.11i		−	0.982509i	0.871016	−	0.491255i	$-0.163462\pi$
$422$	−7757.81	−	2827.35i	−0.894892	−	0.326145i
$423$	−1153.07	+	972.176i	−0.132539	+	0.111747i
$424$	5577.51	+	9689.04i	0.638839	+	1.10977i
$425$			2254.30i			0.257293i
$426$	813.135	−	0.611929i	0.0924801	−	6.95964e-5i
$427$	−3858.83			−0.437335
$428$	2293.12	−	2728.12i	0.258977	−	0.308104i
$429$	−12845.0	+	4692.35i	−1.44560	+	0.528085i
$430$	4444.76	+	1619.90i	0.498477	+	0.181671i
$431$	8048.68			0.899516			0.449758	−	0.893151i	$-0.351510\pi$
$431$	8048.68			0.899516			0.449758	+	0.893151i	$0.351510\pi$
$432$	−8443.07	−	3055.51i	−0.940318	−	0.340298i
$433$	−6551.12			−0.727082			−0.363541	−	0.931578i	$-0.618432\pi$
$433$	−6551.12			−0.727082			−0.363541	+	0.931578i	$0.618432\pi$
$434$	7040.22	+	2565.82i	0.778666	+	0.283786i
$435$	3001.04	−	1096.29i	0.330778	−	0.120835i
$436$	−5515.22	+	6561.44i	−0.605805	+	0.720725i
$437$	16880.7			1.84785
$438$	−4181.79	+	3.14703i	−0.456196	+	0.000343313i
$439$			11769.4i			1.27956i	0.768560	+	0.639778i	$0.220974\pi$
$439$			11769.4i			1.27956i	−0.768560	+	0.639778i	$0.779026\pi$
$440$	−4665.68	+	2685.80i	−0.505517	+	0.291001i
$441$	4014.37	−	3384.60i	0.433471	−	0.365468i
$442$	13253.5	+	4830.25i	1.42625	+	0.519800i
$443$			7230.86i			0.775505i	0.921764	+	0.387752i	$0.126748\pi$
$443$			7230.86i			0.775505i	−0.921764	+	0.387752i	$0.873252\pi$
$444$	−5103.09	+	14034.9i	−0.545455	+	1.50015i
$445$			16.9660i			0.00180733i
$446$	105.441	−	289.313i	0.0111945	−	0.0307160i
$447$	−616.590	+	225.243i	−0.0652432	+	0.0238336i
$448$	−5395.87	−	3133.68i	−0.569042	−	0.330475i
$449$			5070.18i			0.532910i	0.963847	+	0.266455i	$0.0858524\pi$
$449$			5070.18i			0.532910i	−0.963847	+	0.266455i	$0.914148\pi$
$450$	−1792.79	+	656.443i	−0.187806	+	0.0687667i
$451$	7534.86			0.786702
$452$	−4005.01	+	4764.75i	−0.416769	+	0.495830i
$453$	818.024	+	2239.29i	0.0848435	+	0.232254i
$454$	5507.62	−	15112.1i	0.569352	−	1.56221i
$455$	−3370.28			−0.347256
$456$	−11112.7	−	9326.52i	−1.14123	−	0.957795i
$457$	−1309.30			−0.134019			−0.0670094	−	0.997752i	$-0.521346\pi$
$457$	−1309.30			−0.134019			−0.0670094	+	0.997752i	$0.521346\pi$
$458$	−2876.13	+	7891.67i	−0.293434	+	0.805139i
$459$	−10978.2	−	6286.65i	−1.11638	−	0.639293i
$460$	−4188.98	−	3521.04i	−0.424592	−	0.356890i
$461$	−17618.9			−1.78003			−0.890014	−	0.455933i	$-0.849305\pi$
$461$	−17618.9			−1.78003			−0.890014	+	0.455933i	$0.849305\pi$
$462$	8522.92	−	6.41398i	0.858273	−	0.000645899i
$463$		−	13086.4i		−	1.31356i	−0.754083	−	0.656779i	$-0.771919\pi$
$463$		−	13086.4i		−	1.31356i	0.754083	−	0.656779i	$-0.228081\pi$
$464$	−1353.51	−	7753.20i	−0.135420	−	0.775718i
$465$	−1937.88	−	5304.83i	−0.193262	−	0.529044i
$466$	−4746.86	+	13024.6i	−0.471875	+	1.29475i
$467$		−	14480.0i		−	1.43481i	−0.696658	−	0.717403i	$-0.745330\pi$
$467$		−	14480.0i		−	1.43481i	0.696658	−	0.717403i	$-0.254670\pi$
$468$	17.9811	+	11946.7i	0.00177602	+	1.17999i
$469$			5607.04i			0.552045i
$470$	742.217	+	270.502i	0.0728424	+	0.0265475i
$471$	3734.63	+	10223.3i	0.365356	+	1.00014i
$472$	2970.56	−	1710.01i	0.289685	−	0.166757i
$473$			15917.5i			1.54733i
$474$	4.14543	+	5508.47i	0.000401700	+	0.533781i
$475$	−3084.79			−0.297978
$476$	−6729.89	−	5656.81i	−0.648034	−	0.544705i
$477$	−10198.9	+	8598.91i	−0.978984	+	0.825402i
$478$	−10298.7	−	3753.37i	−0.985461	−	0.359153i
$479$	−4000.34			−0.381587			−0.190794	−	0.981630i	$-0.561106\pi$
$479$	−4000.34			−0.381587			−0.190794	+	0.981630i	$0.561106\pi$
$480$	812.280	+	4632.34i	0.0772403	+	0.440493i
$481$	19869.9			1.88355
$482$	16925.9	+	6168.68i	1.59949	+	0.582937i
$483$	2972.64	+	8137.44i	0.280041	+	0.766597i
$484$	−5715.04	−	4803.78i	−0.536724	−	0.451143i
$485$	5233.08			0.489942
$486$	1802.81	−	10561.3i	0.168265	−	0.985742i
$487$			17027.8i			1.58440i	0.610259	+	0.792202i	$0.291065\pi$
$487$			17027.8i			1.58440i	−0.610259	+	0.792202i	$0.708935\pi$
$488$	6209.24	−	3574.36i	0.575982	−	0.331565i
$489$	−13475.0	+	4922.49i	−1.24614	+	0.455220i
$490$	−2584.01	−	941.746i	−0.238232	−	0.0868240i
$491$			9980.30i			0.917321i	0.888612	+	0.458661i	$0.151671\pi$
$491$			9980.30i			0.917321i	−0.888612	+	0.458661i	$0.848329\pi$
$492$	2249.30	−	6186.22i	0.206111	−	0.566862i
$493$		−	11089.0i		−	1.01303i
$494$	−6609.71	+	18136.0i	−0.601994	+	1.65178i
$495$	−4140.73	−	4911.19i	−0.375984	−	0.445943i
$496$	−13705.1	+	2392.55i	−1.24068	+	0.216590i
$497$			674.277i			0.0608560i
$498$	6.20584	+	8246.35i	0.000558414	+	0.742024i
$499$	9115.55			0.817772			0.408886	−	0.912586i	$-0.365917\pi$
$499$	9115.55			0.817772			0.408886	+	0.912586i	$0.365917\pi$
$500$	765.498	+	643.439i	0.0684682	+	0.0575509i
$501$	16087.9	−	5876.97i	1.43464	−	0.524079i
$502$	899.120	−	2467.05i	0.0799397	−	0.219342i
$503$	−2795.36			−0.247791			−0.123895	−	0.992295i	$-0.539539\pi$
$503$	−2795.36			−0.247791			−0.123895	+	0.992295i	$0.539539\pi$
$504$	2538.99	−	6999.34i	0.224396	−	0.618602i
$505$	−1115.11			−0.0982610
$506$	6304.74	−	17299.3i	0.553913	−	1.51985i
$507$	4207.46	−	1537.00i	0.368560	−	0.134637i
$508$	9369.10	−	11146.4i	0.818281	−	0.973507i
$509$	−7072.90			−0.615915			−0.307957	−	0.951400i	$-0.599645\pi$
$509$	−7072.90			−0.615915			−0.307957	+	0.951400i	$0.599645\pi$
$510$	4.98664	+	6626.27i	0.000432965	+	0.575325i
$511$		−	3467.67i		−	0.300197i
$512$	11585.2	+	44.3250i	0.999993	+	0.00382599i
$513$	8602.65	−	15022.5i	0.740382	−	1.29291i
$514$	−3826.28	+	10498.7i	−0.328346	+	0.900932i
$515$			4008.33i			0.342967i
$516$	13068.4	+	4751.68i	1.11493	+	0.405389i
$517$			2658.01i			0.226111i
$518$	−11635.0	−	4240.40i	−0.986897	−	0.359676i
$519$	11067.2	−	4042.91i	0.936025	−	0.341934i
$520$	5423.12	−	3121.82i	0.457345	−	0.263271i
$521$			106.720i			0.00897409i	0.999990	+	0.00448704i	$0.00142827\pi$
$521$			106.720i			0.00897409i	−0.999990	+	0.00448704i	$0.998572\pi$
$522$	8818.78	−	3229.06i	0.739440	−	0.270752i
$523$	−12142.2			−1.01518			−0.507592	−	0.861598i	$-0.669464\pi$
$523$	−12142.2			−1.01518			−0.507592	+	0.861598i	$0.669464\pi$
$524$	10586.1	−	12594.2i	0.882547	−	1.04996i
$525$	−543.223	−	1487.04i	−0.0451585	−	0.123619i
$526$	−5224.86	−	1904.21i	−0.433108	−	0.157847i
$527$	−19601.6			−1.62023
$528$	−13708.3	+	7904.93i	−1.12988	+	0.651549i
$529$	6548.81			0.538243
$530$	6564.92	+	2392.60i	0.538041	+	0.196090i
$531$	2636.34	+	3126.88i	0.215456	+	0.255546i
$532$	7740.77	−	9209.18i	0.630836	−	0.750505i
$533$	−8758.10			−0.711736
$534$	0.0375296	+	49.8695i	3.04132e−6	+	0.00404132i
$535$		−	2227.41i		−	0.179998i
$536$	−5193.69	−	9022.28i	−0.418532	−	0.727058i
$537$	−6027.12	−	16498.9i	−0.484338	−	1.32585i
$538$	21671.0	+	7898.04i	1.73662	+	0.632915i
$539$		−	9253.79i		−	0.739497i
$540$	−5268.24	+	1933.50i	−0.419831	+	0.154083i
$541$		−	12696.8i		−	1.00902i	−0.863407	−	0.504508i	$-0.831674\pi$
$541$		−	12696.8i		−	1.00902i	0.863407	−	0.504508i	$-0.168326\pi$
$542$	4211.94	−	11556.9i	0.333798	−	0.915890i
$543$	−4324.58	−	11838.3i	−0.341778	−	0.935598i
$544$	16068.8	+	2868.60i	1.26645	+	0.226085i
$545$			5357.17i			0.421057i
$546$	−9906.57	+	7.45525i	−0.776487	+	0.000584350i
$547$	−18897.4			−1.47714			−0.738568	−	0.674179i	$-0.764497\pi$
$547$	−18897.4			−1.47714			−0.738568	+	0.674179i	$0.764497\pi$
$548$	−2519.24	+	2997.13i	−0.196381	+	0.233634i
$549$	5510.63	+	6535.99i	0.428393	+	0.508104i
$550$	−1152.13	+	3161.28i	−0.0893222	+	0.245086i
$551$	15174.2			1.17321
$552$	−12320.8	−	10340.4i	−0.950016	−	0.797316i
$553$	−4567.79			−0.351252
$554$	7826.77	−	21475.5i	0.600230	−	1.64694i
$555$	3202.63	+	8767.02i	0.244944	+	0.670521i
$556$	11580.7	+	9734.19i	0.883333	+	0.742485i
$557$	−7151.12			−0.543990			−0.271995	−	0.962299i	$-0.587683\pi$
$557$	−7151.12			−0.543990			−0.271995	+	0.962299i	$0.587683\pi$
$558$	−5707.91	−	15588.7i	−0.433038	−	1.18265i
$559$		−	18501.6i		−	1.39988i
$560$	−3841.79	+	670.677i	−0.289902	+	0.0506094i
$561$	−20941.7	+	7650.11i	−1.57605	+	0.575736i
$562$	3932.31	−	10789.7i	0.295151	−	0.809848i
$563$			11568.0i			0.865957i	0.901404	+	0.432978i	$0.142537\pi$
$563$			11568.0i			0.865957i	−0.901404	+	0.432978i	$0.857463\pi$
$564$	2182.26	+	793.469i	0.162925	+	0.0592395i
$565$			3890.24i			0.289670i
$566$	2017.27	+	735.197i	0.149809	+	0.0545983i
$567$	8756.63	+	1501.53i	0.648578	+	0.111214i
$568$	−624.569	−	1084.98i	−0.0461379	−	0.0801490i
$569$		−	3063.69i		−	0.225723i	−0.993611	−	0.112862i	$-0.963998\pi$
$569$		−	3063.69i		−	0.225723i	0.993611	−	0.112862i	$-0.0360017\pi$
$570$	−9067.38	+	6.82371i	−0.666299	+	0.000501428i
$571$	12960.1			0.949846			0.474923	−	0.880027i	$-0.342476\pi$
$571$	12960.1			0.949846			0.474923	+	0.880027i	$0.342476\pi$
$572$	16117.1	+	13547.2i	1.17813	+	0.990278i
$573$	−2656.44	+	970.408i	−0.193672	+	0.0707494i
$574$	5128.39	+	1869.05i	0.372918	+	0.135911i
$575$	−3420.14			−0.248052
$576$	2397.85	+	13614.5i	0.173456	+	0.984842i
$577$	−3781.06			−0.272803			−0.136402	−	0.990654i	$-0.543554\pi$
$577$	−3781.06			−0.272803			−0.136402	+	0.990654i	$0.543554\pi$
$578$	8551.66	+	3116.67i	0.615402	+	0.224284i
$579$	19349.1	−	7068.33i	1.38881	−	0.507340i
$580$	−3765.51	−	3165.10i	−0.269576	−	0.226592i
$581$	−6838.13			−0.488285
$582$	15382.1	−	11.5759i	1.09554	−	0.000824458i
$583$			23510.1i			1.67014i
$584$	3212.03	+	5579.83i	0.227594	+	0.395368i
$585$	4812.95	+	5708.49i	0.340156	+	0.403448i
$586$	−20206.6	−	7364.32i	−1.42445	−	0.519142i
$587$			18930.0i			1.33105i	0.746377	+	0.665524i	$0.231792\pi$
$587$			18930.0i			1.33105i	−0.746377	+	0.665524i	$0.768208\pi$
$588$	−7597.48	−	2762.44i	−0.532848	−	0.193743i
$589$		−	26822.9i		−	1.87643i
$590$	733.546	−	2012.74i	0.0511858	−	0.140446i
$591$	−15535.2	+	5675.06i	−1.08127	+	0.394993i
$592$	22649.7	−	3954.05i	1.57246	−	0.274511i
$593$			18469.4i			1.27900i	0.768792	+	0.639499i	$0.220858\pi$
$593$			18469.4i			1.27900i	−0.768792	+	0.639499i	$0.779142\pi$
$594$	−12182.1	−	14426.7i	−0.841476	−	0.996525i
$595$	−5494.70			−0.378590
$596$	773.658	+	650.298i	0.0531716	+	0.0446933i
$597$	6130.58	+	16782.1i	0.420281	+	1.15050i
$598$	−7328.28	+	20107.7i	−0.501130	+	1.37502i
$599$	−12370.2			−0.843794			−0.421897	−	0.906644i	$-0.638636\pi$
$599$	−12370.2			−0.843794			−0.421897	+	0.906644i	$0.638636\pi$
$600$	2251.52	+	1889.62i	0.153196	+	0.128572i
$601$	20999.7			1.42528			0.712642	−	0.701528i	$-0.247499\pi$
$601$	20999.7			1.42528			0.712642	+	0.701528i	$0.247499\pi$
$602$	−3948.39	+	10833.8i	−0.267316	+	0.733475i
$603$	9497.05	−	8007.17i	0.641376	−	0.540758i
$604$	2361.71	−	2809.72i	0.159100	−	0.189281i
$605$	−4666.12			−0.313561
$606$	−3277.74	+	2.46668i	−0.219718	+	0.000165350i
$607$		−	11458.0i		−	0.766168i	−0.923713	−	0.383084i	$-0.874862\pi$
$607$		−	11458.0i		−	0.766168i	0.923713	−	0.383084i	$-0.125138\pi$
$608$	−3925.39	+	21988.6i	−0.261835	+	1.46670i
$609$	2672.13	+	7314.81i	0.177800	+	0.486718i
$610$	1533.30	−	4207.14i	0.101773	−	0.279250i
$611$		−	3089.52i		−	0.204564i
$612$	29.3153	+	19477.1i	0.00193628	+	1.28647i
$613$			12071.4i			0.795365i	0.917523	+	0.397683i	$0.130186\pi$
$613$			12071.4i			0.795365i	−0.917523	+	0.397683i	$0.869814\pi$
$614$	2499.45	+	910.928i	0.164283	+	0.0598731i
$615$	−1411.63	−	3864.26i	−0.0925570	−	0.253369i
$616$	−6546.45	−	11372.3i	−0.428188	−	0.743833i
$617$		−	3983.60i		−	0.259925i	−0.991519	−	0.129962i	$-0.958514\pi$
$617$		−	3983.60i		−	0.259925i	0.991519	−	0.129962i	$-0.0414857\pi$
$618$	8.86663	+	11782.0i	0.000577133	+	0.766897i
$619$	−16728.2			−1.08621			−0.543103	−	0.839666i	$-0.682751\pi$
$619$	−16728.2			−1.08621			−0.543103	+	0.839666i	$0.682751\pi$
$620$	−5594.84	+	6656.16i	−0.362410	+	0.431158i
$621$	9537.87	−	16655.7i	0.616331	−	1.07628i
$622$	−5005.91	−	1824.41i	−0.322699	−	0.117608i
$623$	−41.3534			−0.00265937
$624$	15933.7	−	9188.25i	1.02221	−	0.589462i
$625$	625.000			0.0400000
$626$	−2491.74	−	908.120i	−0.159090	−	0.0579805i
$627$	−10468.4	−	28656.7i	−0.666775	−	1.82526i
$628$	10782.2	−	12827.6i	0.685124	−	0.815090i
$629$	32394.6			2.05351
$630$	−1600.03	−	4369.79i	−0.101185	−	0.276344i
$631$		−	24619.9i		−	1.55325i	−0.629961	−	0.776627i	$-0.716929\pi$
$631$		−	24619.9i		−	1.55325i	0.629961	−	0.776627i	$-0.283071\pi$
$632$	7350.03	−	4231.05i	0.462608	−	0.266301i
$633$	−14248.1	+	5204.89i	−0.894646	+	0.326818i
$634$	−28531.5	−	10398.3i	−1.78727	−	0.651373i
$635$		−	9100.61i		−	0.568735i
$636$	19302.1	+	7018.24i	1.20343	+	0.437565i
$637$			10756.1i			0.669029i
$638$	5667.39	−	15550.5i	0.351684	−	0.964966i
$639$	1142.07	−	962.905i	0.0707037	−	0.0596118i
$640$	5560.58	−	4637.75i	0.343439	−	0.286443i
$641$			6804.36i			0.419276i	0.977779	+	0.209638i	$0.0672286\pi$
$641$			6804.36i			0.419276i	−0.977779	+	0.209638i	$0.932771\pi$
$642$	−4.92714	−	6547.21i	−0.000302895	−	0.402489i
$643$	6258.56			0.383847			0.191924	−	0.981410i	$-0.438527\pi$
$643$	6258.56			0.383847			0.191924	+	0.981410i	$0.438527\pi$
$644$	8582.30	−	10210.3i	0.525140	−	0.624758i
$645$	8163.29	−	2982.09i	0.498340	−	0.182046i
$646$	−10776.1	+	29567.9i	−0.656314	+	1.80083i
$647$	8923.55			0.542227			0.271114	−	0.962547i	$-0.412608\pi$
$647$	8923.55			0.542227			0.271114	+	0.962547i	$0.412608\pi$
$648$	−15481.1	+	5694.97i	−0.938512	+	0.345246i
$649$	7207.97			0.435959
$650$	1339.18	−	3674.50i	0.0808105	−	0.221732i
$651$	12930.2	−	4723.44i	0.778452	−	0.284372i
$652$	16907.6	+	14211.7i	1.01557	+	0.853638i
$653$	−23271.1			−1.39459			−0.697295	−	0.716784i	$-0.745613\pi$
$653$	−23271.1			−1.39459			−0.697295	+	0.716784i	$0.745613\pi$
$654$	11.8503	+	15746.8i	0.000708540	+	0.941511i
$655$		−	10282.7i		−	0.613403i
$656$	−9983.36	+	1742.84i	−0.594184	+	0.103729i
$657$	−5873.45	+	4952.03i	−0.348775	+	0.294059i
$658$	−659.330	+	1809.10i	−0.0390629	+	0.107183i
$659$			23993.2i			1.41827i	0.705072	+	0.709136i	$0.250915\pi$
$659$			23993.2i			1.41827i	−0.705072	+	0.709136i	$0.749085\pi$
$660$	−3379.58	+	9294.78i	−0.199318	+	0.548180i
$661$			10707.4i			0.630058i	0.949082	+	0.315029i	$0.102014\pi$
$661$			10707.4i			0.630058i	−0.949082	+	0.315029i	$0.897986\pi$
$662$	−310.328	−	113.099i	−0.0182194	−	0.00664008i
$663$	24341.5	−	8892.06i	1.42586	−	0.520873i
$664$	11003.2	−	6334.02i	0.643084	−	0.370192i
$665$		−	7518.95i		−	0.438455i
$666$	9433.17	+	25762.6i	0.548840	+	1.49892i
$667$	16823.8			0.976642
$668$	−20186.0	−	16967.4i	−1.16919	−	0.982765i
$669$	−194.107	−	531.356i	−0.0112176	−	0.0307076i
$670$	−6113.15	−	2227.95i	−0.352495	−	0.128467i
$671$	15066.5			0.866821
$672$	−11291.0	+	1979.88i	−0.648155	+	0.113654i
$673$	−3532.35			−0.202321			−0.101161	−	0.994870i	$-0.532256\pi$
$673$	−3532.35			−0.202321			−0.101161	+	0.994870i	$0.532256\pi$
$674$	−22183.2	−	8084.71i	−1.26775	−	0.462035i
$675$	−1742.96	+	3043.68i	−0.0993874	+	0.173557i
$676$	−5279.26	−	4437.48i	−0.300367	−	0.252474i
$677$	8946.41			0.507885			0.253943	−	0.967219i	$-0.418273\pi$
$677$	8946.41			0.507885			0.253943	+	0.967219i	$0.418273\pi$
$678$	8.60541	+	11434.9i	0.000487447	+	0.647722i
$679$			12755.3i			0.720917i
$680$	8841.52	−	5089.63i	0.498613	−	0.287027i
$681$	−10139.0	−	27755.0i	−0.570527	−	1.56178i
$682$	−27488.0	−	10018.1i	−1.54336	−	0.562480i
$683$		−	9783.65i		−	0.548113i	−0.961714	−	0.274056i	$-0.911634\pi$
$683$		−	9783.65i		−	0.548113i	0.961714	−	0.274056i	$-0.0883655\pi$
$684$	−26652.5	+	40.1150i	−1.48989	+	0.00224245i
$685$			2447.05i			0.136492i
$686$	6343.99	−	17407.0i	0.353083	−	0.968805i
$687$	5294.70	+	14493.9i	0.294040	+	0.804918i
$688$	−3681.76	−	21089.9i	−0.204020	−	1.16867i
$689$		−	27326.9i		−	1.51099i
$690$	−10053.1	+	7.56554i	−0.554661	+	0.000417413i
$691$	2000.60			0.110139			0.0550697	−	0.998483i	$-0.482462\pi$
$691$	2000.60			0.110139			0.0550697	+	0.998483i	$0.482462\pi$
$692$	−13886.5	−	11672.3i	−0.762838	−	0.641203i
$693$	11970.7	−	10092.7i	0.656174	−	0.553235i
$694$	3240.04	−	8890.16i	0.177219	−	0.486262i
$695$	9455.24			0.516054
$696$	−11075.3	−	9295.12i	−0.603172	−	0.506222i
$697$	−14278.7			−0.775959
$698$	−6158.64	+	16898.4i	−0.333965	+	0.916350i
$699$	8738.54	+	23921.2i	0.472849	+	1.29440i
$700$	−1568.34	+	1865.85i	−0.0846822	+	0.100746i
$701$	−13253.5			−0.714089			−0.357045	−	0.934087i	$-0.616216\pi$
$701$	−13253.5			−0.714089			−0.357045	+	0.934087i	$0.616216\pi$
$702$	14159.8	+	16768.8i	0.761290	+	0.901565i
$703$			44328.8i			2.37822i
$704$	21067.8	+	12235.2i	1.12787	+	0.655019i
$705$	1363.17	−	497.970i	0.0728224	−	0.0266023i
$706$	−5165.37	+	14173.0i	−0.275356	+	0.755534i
$707$		−	2718.01i		−	0.144584i
$708$	2151.72	−	5917.84i	0.114218	−	0.314133i
$709$			34854.0i			1.84622i	0.384540	+	0.923108i	$0.374360\pi$
$709$			34854.0i			1.84622i	−0.384540	+	0.923108i	$0.625640\pi$
$710$	−735.139	−	267.923i	−0.0388581	−	0.0141619i
$711$	6523.06	+	7736.80i	0.344070	+	0.408091i
$712$	66.5416	−	38.3048i	0.00350246	−	0.00201620i
$713$		−	29738.9i		−	1.56203i
$714$	−16151.1	+	12.1546i	−0.846552	+	0.000637078i
$715$	13159.0			0.688279
$716$	−17400.9	+	20701.8i	−0.908241	+	1.08053i
$717$	−18914.7	+	6909.62i	−0.985191	+	0.359895i
$718$	−32628.8	−	11891.6i	−1.69595	−	0.618093i
$719$	5597.88			0.290356			0.145178	−	0.989406i	$-0.453625\pi$
$719$	5597.88			0.290356			0.145178	+	0.989406i	$0.453625\pi$
$720$	6622.26	+	5549.35i	0.342774	+	0.287239i
$721$	−9770.01			−0.504652
$722$	−22233.3	−	8102.97i	−1.14604	−	0.417675i
$723$	31086.4	−	11356.0i	1.59905	−	0.584141i
$724$	−12485.5	+	14853.9i	−0.640910	+	0.762489i
$725$	−3074.40			−0.157490
$726$	−13715.5	+	10.3217i	−0.701144	+	0.000527650i
$727$			5447.92i			0.277926i	0.990298	+	0.138963i	$0.0443769\pi$
$727$			5447.92i			0.277926i	−0.990298	+	0.138963i	$0.955623\pi$
$728$	7609.23	+	13218.5i	0.387386	+	0.672952i
$729$	−9961.70	−	16976.0i	−0.506107	−	0.862471i
$730$	3780.68	+	1377.87i	0.191684	+	0.0698594i
$731$		−	30163.8i		−	1.52620i
$732$	4497.66	−	12369.8i	0.227101	−	0.624592i
$733$			6940.15i			0.349714i	0.984594	+	0.174857i	$0.0559463\pi$
$733$			6940.15i			0.349714i	−0.984594	+	0.174857i	$0.944054\pi$
$734$	−773.835	+	2123.29i	−0.0389139	+	0.106774i
$735$	−4745.82	+	1733.67i	−0.238166	+	0.0870032i
$736$	−4352.14	+	24379.1i	−0.217964	+	1.22096i
$737$		−	21892.3i		−	1.09418i
$738$	−4157.88	−	11355.4i	−0.207390	−	0.566395i
$739$	−1766.63			−0.0879387			−0.0439693	−	0.999033i	$-0.514000\pi$
$739$	−1766.63			−0.0879387			−0.0439693	+	0.999033i	$0.514000\pi$
$740$	9246.30	−	11000.3i	0.459325	−	0.546458i
$741$	12167.9	+	33308.9i	0.603237	+	1.65133i
$742$	−5831.79	+	16001.5i	−0.288533	+	0.791691i
$743$	−8562.00			−0.422758			−0.211379	−	0.977404i	$-0.567795\pi$
$743$	−8562.00			−0.422758			−0.211379	+	0.977404i	$0.567795\pi$
$744$	−16430.7	+	19577.4i	−0.809647	+	0.964708i
$745$	631.663			0.0310635
$746$	3362.41	−	9225.95i	0.165022	−	0.452796i
$747$	9765.23	+	11582.2i	0.478301	+	0.567298i
$748$	26276.4	+	22086.6i	1.28444	+	1.07963i
$749$	5429.15			0.264855
$750$	1837.12	−	1.38253i	0.0894427	−	6.73106e-5i
$751$			14814.4i			0.719820i	0.932987	+	0.359910i	$0.117193\pi$
$751$			14814.4i			0.719820i	−0.932987	+	0.359910i	$0.882807\pi$
$752$	−614.806	−	3521.75i	−0.0298134	−	0.170778i
$753$	−1655.20	−	4531.01i	−0.0801047	−	0.219282i
$754$	−6587.46	+	18075.0i	−0.318171	+	0.873013i
$755$		−	2294.03i		−	0.110581i
$756$	−4712.78	−	12841.0i	−0.226723	−	0.617753i
$757$		−	33629.1i		−	1.61462i	−0.590126	−	0.807311i	$-0.700922\pi$
$757$		−	33629.1i		−	1.61462i	0.590126	−	0.807311i	$-0.299078\pi$
$758$	17909.9	+	6527.29i	0.858202	+	0.312773i
$759$	−11606.5	−	31772.0i	−0.555057	−	1.51944i
$760$	6964.65	+	12098.7i	0.332414	+	0.577457i
$761$			40718.2i			1.93960i	0.243906	+	0.969799i	$0.421571\pi$
$761$			40718.2i			1.93960i	−0.243906	+	0.969799i	$0.578429\pi$
$762$	−20.1310	−	26750.2i	−0.000957048	−	1.27173i
$763$	−13057.7			−0.619556
$764$	3333.13	+	2801.66i	0.157838	+	0.132671i
$765$	7846.74	+	9306.78i	0.370849	+	0.439853i
$766$	−2601.89	−	948.262i	−0.122728	−	0.0447286i
$767$	−8378.14			−0.394416
$768$	16334.4	−	13644.5i	0.767472	−	0.641083i
$769$	−23764.9			−1.11441			−0.557206	−	0.830374i	$-0.688127\pi$
$769$	−23764.9			−1.11441			−0.557206	+	0.830374i	$0.688127\pi$
$770$	−7705.40	−	2808.25i	−0.360628	−	0.131431i
$771$	7043.83	+	19282.1i	0.329024	+	0.900684i
$772$	−24278.1	−	20406.9i	−1.13185	−	0.951375i
$773$	20722.3			0.964204			0.482102	−	0.876115i	$-0.339873\pi$
$773$	20722.3			0.964204			0.482102	+	0.876115i	$0.339873\pi$
$774$	23988.5	−	8783.57i	1.11402	−	0.407905i
$775$			5434.51i			0.251888i
$776$	−11815.0	−	20524.5i	−0.546562	−	0.949467i
$777$	−21369.0	+	7806.19i	−0.986626	+	0.360419i
$778$	23945.2	+	8726.86i	1.10344	+	0.402151i
$779$		−	19538.9i		−	0.898658i
$780$	3928.23	−	10803.7i	0.180325	−	0.495943i
$781$		−	2632.66i		−	0.120620i
$782$	−11947.6	+	32782.3i	−0.546349	+	1.49910i
$783$	8573.68	−	14972.0i	0.391313	−	0.683338i
$784$	2140.43	+	12260.9i	0.0975050	+	0.558531i
$785$		−	10473.2i		−	0.476186i
$786$	−22.7459	−	30224.9i	−0.00103221	−	1.37161i
$787$	4696.17			0.212707			0.106354	−	0.994328i	$-0.466082\pi$
$787$	4696.17			0.212707			0.106354	+	0.994328i	$0.466082\pi$
$788$	19492.5	+	16384.4i	0.881209	+	0.740700i
$789$	−9596.04	+	3505.48i	−0.432989	+	0.158173i
$790$	1815.01	−	4980.10i	0.0817405	−	0.224283i
$791$	−9482.19			−0.426230
$792$	−9913.32	+	27328.4i	−0.444766	+	1.22610i
$793$	−17512.5			−0.784220
$794$	−676.176	+	1855.33i	−0.0302224	+	0.0829257i
$795$	12057.2	−	4404.55i	0.537894	−	0.196495i
$796$	17699.6	−	21057.1i	0.788121	−	0.937626i
$797$	−12468.5			−0.554151			−0.277075	−	0.960848i	$-0.589365\pi$
$797$	−12468.5			−0.554151			−0.277075	+	0.960848i	$0.589365\pi$
$798$	−16.6323	−	22101.1i	−0.000737816	−	0.980414i
$799$		−	5036.97i		−	0.223023i
$800$	795.313	−	4455.05i	0.0351482	−	0.196887i
$801$	59.0549	+	70.0432i	0.00260500	+	0.00308971i
$802$	−4355.81	+	11951.7i	−0.191782	+	0.526219i
$803$			13539.3i			0.595007i
$804$	−17973.8	−	6535.28i	−0.788419	−	0.286669i
$805$		−	8336.36i		−	0.364991i
$806$	31950.5	+	11644.4i	1.39629	+	0.508880i
$807$	39801.2	−	14539.6i	1.73615	−	0.634222i
$808$	2517.63	+	4373.54i	0.109616	+	0.190421i
$809$			8761.63i			0.380770i	0.981710	+	0.190385i	$0.0609736\pi$
$809$			8761.63i			0.380770i	−0.981710	+	0.190385i	$0.939026\pi$
$810$	−5116.50	+	8950.40i	−0.221945	+	0.388253i
$811$	1598.54			0.0692136			0.0346068	−	0.999401i	$-0.488982\pi$
$811$	1598.54			0.0692136			0.0346068	+	0.999401i	$0.488982\pi$
$812$	7714.70	−	9178.17i	0.333415	−	0.396663i
$813$	−7753.81	−	21225.6i	−0.334487	−	0.915639i
$814$	45428.0	+	16556.3i	1.95608	+	0.712898i
$815$	13804.4			0.593310
$816$	25977.4	−	14980.0i	1.11445	−	0.642651i
$817$	41276.1			1.76753
$818$	−1920.21	−	699.823i	−0.0820764	−	0.0299129i
$819$	−13914.1	+	11731.2i	−0.593646	+	0.500516i
$820$	−4075.52	+	4848.64i	−0.173565	+	0.206490i
$821$	−13201.8			−0.561201			−0.280601	−	0.959825i	$-0.590534\pi$
$821$	−13201.8			−0.561201			−0.280601	+	0.959825i	$0.590534\pi$
$822$	5.41300	+	7192.82i	0.000229684	+	0.305205i
$823$		−	30716.2i		−	1.30097i	−0.759518	−	0.650486i	$-0.774565\pi$
$823$		−	30716.2i		−	1.30097i	0.759518	−	0.650486i	$-0.225435\pi$
$824$	15720.9	−	9049.76i	0.664641	−	0.382601i
$825$	2120.98	+	5806.05i	0.0895066	+	0.245019i
$826$	4905.91	+	1787.97i	0.206657	+	0.0753163i
$827$			45110.8i			1.89680i	0.317070	+	0.948402i	$0.397301\pi$
$827$			45110.8i			1.89680i	−0.317070	+	0.948402i	$0.602699\pi$
$828$	−29550.0	+	44.4761i	−1.24026	+	0.00186673i
$829$			37703.0i			1.57959i	0.613373	+	0.789794i	$0.289812\pi$
$829$			37703.0i			1.57959i	−0.613373	+	0.789794i	$0.710188\pi$
$830$	2717.12	−	7455.36i	0.113630	−	0.311782i
$831$	−14408.4	−	39442.1i	−0.601469	−	1.64649i
$832$	−24488.0	−	14221.6i	−1.02040	−	0.592601i
$833$			17536.1i			0.729398i
$834$	27792.6	−	20.9155i	1.15393	−	0.000868399i
$835$	−16481.1			−0.683058
$836$	−30223.3	+	35956.6i	−1.25035	+	1.48754i
$837$	−26465.4	−	15155.4i	−1.09293	−	0.625863i
$838$	5190.22	−	14241.2i	0.213954	−	0.587056i
$839$	−41663.4			−1.71440			−0.857200	−	0.514983i	$-0.827798\pi$
$839$	−41663.4			−1.71440			−0.857200	+	0.514983i	$0.827798\pi$
$840$	−4605.82	+	5487.92i	−0.189186	+	0.225418i
$841$	−9265.93			−0.379923
$842$	−8219.84	+	22554.0i	−0.336430	+	0.923114i
$843$	−7239.03	−	19816.4i	−0.295760	−	0.809626i
$844$	17877.6	+	15027.0i	0.729115	+	0.612857i
$845$	−4310.31			−0.175478
$846$	4005.77	−	1466.74i	0.162791	−	0.0596072i
$847$		−	11373.3i		−	0.461384i
$848$	−5437.97	−	31149.9i	−0.220213	−	1.26143i
$849$	3704.94	−	1353.43i	0.149768	−	0.0547111i
$850$	2183.31	−	5990.67i	0.0881023	−	0.241739i
$851$			49147.9i			1.97975i
$852$	−2161.45	−	785.902i	−0.0869132	−	0.0316016i
$853$		−	4555.33i		−	0.182850i	−0.995812	−	0.0914252i	$-0.970858\pi$
$853$		−	4555.33i		−	0.182850i	0.995812	−	0.0914252i	$-0.0291423\pi$
$854$	10254.6	+	3737.31i	0.410897	+	0.149752i
$855$	−12735.4	+	10737.5i	−0.509405	+	0.429490i
$856$	−8736.03	+	5028.91i	−0.348822	+	0.200800i
$857$			35895.8i			1.43078i	0.698727	+	0.715388i	$0.253750\pi$
$857$			35895.8i			1.43078i	−0.698727	+	0.715388i	$0.746250\pi$
$858$	38679.5	−	29.1085i	1.53904	−	0.00115821i
$859$	−11545.7			−0.458597			−0.229298	−	0.973356i	$-0.573643\pi$
$859$	−11545.7			−0.458597			−0.229298	+	0.973356i	$0.573643\pi$
$860$	−10242.8	−	8609.57i	−0.406135	−	0.341377i
$861$	9418.88	−	3440.76i	0.372816	−	0.136191i
$862$	−21388.9	−	7795.22i	−0.845137	−	0.308012i
$863$	15731.1			0.620502			0.310251	−	0.950655i	$-0.399587\pi$
$863$	15731.1			0.620502			0.310251	+	0.950655i	$0.399587\pi$
$864$	19477.7	+	16297.0i	0.766948	+	0.641709i
$865$	−11337.8			−0.445660
$866$	17409.2	+	6344.82i	0.683128	+	0.248967i
$867$	15706.1	−	5737.50i	0.615233	−	0.224747i
$868$	−16223.9	−	13637.0i	−0.634420	−	0.533261i
$869$	17834.6			0.696200
$870$	−9036.84	+	6.80073i	−0.352158	+	0.000265019i
$871$			25446.4i			0.989916i
$872$	21011.2	−	12095.1i	0.815973	−	0.469715i
$873$	21604.5	−	18215.2i	0.837575	−	0.706177i
$874$	−44859.3	−	16349.1i	−1.73614	−	0.632740i
$875$			1523.39i			0.0588573i
$876$	11115.9	+	4041.74i	0.428735	+	0.155888i
$877$		−	14736.3i		−	0.567401i	−0.958913	−	0.283701i	$-0.908438\pi$
$877$		−	14736.3i		−	0.567401i	0.958913	−	0.283701i	$-0.0915622\pi$
$878$	11398.8	−	31276.6i	0.438145	−	1.20220i
$879$	−37111.7	+	13557.1i	−1.42406	+	0.520214i
$880$	15000.0	−	2618.61i	0.574601	−	0.100311i
$881$		−	19926.0i		−	0.762002i	−0.924575	−	0.381001i	$-0.875579\pi$
$881$		−	19926.0i		−	0.762002i	0.924575	−	0.381001i	$-0.124421\pi$
$882$	−13946.0	+	5106.42i	−0.532409	+	0.194946i
$883$	−695.922			−0.0265228			−0.0132614	−	0.999912i	$-0.504221\pi$
$883$	−695.922			−0.0265228			−0.0132614	+	0.999912i	$0.504221\pi$
$884$	−30542.2	−	25672.2i	−1.16204	−	0.976754i
$885$	−1350.39	−	3696.62i	−0.0512914	−	0.140407i
$886$	7003.15	−	19215.6i	0.265548	−	0.728623i
$887$	−10875.3			−0.411678			−0.205839	−	0.978586i	$-0.565992\pi$
$887$	−10875.3			−0.411678			−0.205839	+	0.978586i	$0.565992\pi$
$888$	27154.1	−	32354.6i	1.02616	−	1.22269i
$889$	22182.1			0.836855
$890$	16.4317	−	45.0860i	0.000618867	−	0.00169808i
$891$	−34189.6	−	5862.63i	−1.28552	−	0.220433i
$892$	−560.404	+	666.711i	−0.0210356	+	0.0250260i
$893$	6892.59			0.258288
$894$	1856.70	−	1.39727i	0.0694601	−	5.22726e-5i
$895$			16902.2i			0.631261i
$896$	11304.2	+	13553.5i	0.421481	+	0.505348i
$897$	13490.7	+	36930.0i	0.502165	+	1.37465i
$898$	4910.52	−	13473.7i	0.182479	−	0.500694i
$899$		−	26732.5i		−	0.991746i
$900$	5399.99	−	8.12760i	0.200000	−	0.000301022i
$901$		−	44552.1i		−	1.64733i
$902$	−20023.4	−	7297.58i	−0.739144	−	0.269382i
$903$	7268.63	+	19897.5i	0.267868	+	0.733274i
$904$	15257.8	−	8783.15i	0.561356	−	0.323145i
$905$			12127.7i			0.445456i
$906$	−5.07452	−	6743.05i	−0.000186081	−	0.247266i
$907$	6504.96			0.238141			0.119070	−	0.992886i	$-0.462009\pi$
$907$	6504.96			0.238141			0.119070	+	0.992886i	$0.462009\pi$
$908$	−29272.4	+	34825.3i	−1.06987	+	1.27282i
$909$	−4603.68	+	3881.46i	−0.167981	+	0.141628i
$910$	8956.33	+	3264.15i	0.326263	+	0.118907i
$911$	8613.24			0.313248			0.156624	−	0.987658i	$-0.449939\pi$
$911$	8613.24			0.313248			0.156624	+	0.987658i	$0.449939\pi$
$912$	20498.6	+	35547.4i	0.744271	+	1.29067i
$913$	26699.0			0.967806
$914$	3479.39	+	1268.07i	0.125917	+	0.0458906i
$915$	−2822.67	−	7726.89i	−0.101983	−	0.279173i
$916$	15286.3	−	18186.1i	0.551390	−	0.655988i
$917$	25063.4			0.902581
$918$	23085.2	+	27338.9i	0.829984	+	0.982916i
$919$		−	13181.9i		−	0.473156i	−0.971613	−	0.236578i	$-0.923974\pi$
$919$		−	13181.9i		−	0.473156i	0.971613	−	0.236578i	$-0.0760258\pi$
$920$	7721.80	+	13414.0i	0.276718	+	0.480704i
$921$	4590.52	−	1676.94i	0.164237	−	0.0599967i
$922$	46821.1	+	17064.0i	1.67242	+	0.609516i
$923$			3060.06i			0.109126i
$924$	−22655.4	−	8237.48i	−0.806609	−	0.293283i
$925$		−	8981.33i		−	0.319248i
$926$	−12674.3	+	34776.4i	−0.449788	+	1.23415i
$927$	13952.1	+	16548.2i	0.494334	+	0.586315i
$928$	−3912.17	+	21914.6i	−0.138387	+	0.775194i
$929$		−	10313.6i		−	0.364241i	−0.983276	−	0.182120i	$-0.941704\pi$
$929$		−	10313.6i		−	0.364241i	0.983276	−	0.182120i	$-0.0582960\pi$
$930$	12.0214	+	15974.1i	0.000423869	+	0.563239i
$931$	−23996.3			−0.844735
$932$	25229.0	−	30014.9i	0.886698	−	1.05490i
$933$	−9193.91	+	3358.58i	−0.322610	+	0.117851i
$934$	−14024.0	+	38479.8i	−0.491306	+	1.34807i
$935$	21453.7			0.750385
$936$	11522.7	−	31765.0i	0.402383	−	1.10927i
$937$	7841.52			0.273395			0.136698	−	0.990613i	$-0.456351\pi$
$937$	7841.52			0.273395			0.136698	+	0.990613i	$0.456351\pi$
$938$	5430.47	−	14900.4i	0.189031	−	0.518672i
$939$	−4576.37	+	1671.77i	−0.159046	+	0.0581002i
$940$	−1710.41	−	1437.69i	−0.0593485	−	0.0498853i
$941$	−36976.7			−1.28099			−0.640493	−	0.767964i	$-0.721270\pi$
$941$	−36976.7			−1.28099			−0.640493	+	0.767964i	$0.721270\pi$
$942$	−23.1674	−	30784.9i	−0.000801310	−	1.06478i
$943$		−	21663.1i		−	0.748088i
$944$	−9550.25	+	1667.23i	−0.329273	+	0.0574826i
$945$	−7418.75	−	4248.34i	−0.255378	−	0.146242i
$946$	15416.2	−	42299.7i	0.529835	−	1.45379i
$947$		−	38104.4i		−	1.30753i	−0.756699	−	0.653763i	$-0.773189\pi$
$947$		−	38104.4i		−	1.30753i	0.756699	−	0.653763i	$-0.226811\pi$
$948$	5323.99	−	14642.4i	0.182400	−	0.501650i
$949$		−	15737.3i		−	0.538308i
$950$	8197.63	+	2987.64i	0.279965	+	0.102034i
$951$	−52401.2	+	19142.4i	−1.78678	+	0.652718i
$952$	12405.6	+	21550.6i	0.422341	+	0.733675i
$953$		−	39022.1i		−	1.32639i	−0.748447	−	0.663195i	$-0.769200\pi$
$953$		−	39022.1i		−	1.32639i	0.748447	−	0.663195i	$-0.230800\pi$
$954$	35431.1	−	12973.4i	1.20244	−	0.440281i
$955$	2721.37			0.0922111
$956$	23733.0	+	19948.7i	0.802906	+	0.674883i
$957$	−10433.2	−	28560.2i	−0.352410	−	0.964701i
$958$	10630.7	+	3874.37i	0.358519	+	0.130663i
$959$	−5964.51			−0.200838
$960$	2327.88	−	13096.9i	0.0782624	−	0.440312i
$961$	−17463.2			−0.586190
$962$	−52803.0	−	19244.1i	−1.76968	−	0.644965i
$963$	−7753.12	−	9195.74i	−0.259440	−	0.307714i
$964$	−39005.2	−	32785.8i	−1.30319	−	1.09539i
$965$	−19822.1			−0.661241
$966$	−18.4405	−	24503.8i	−0.000614195	−	0.816145i
$967$		−	17707.6i		−	0.588870i	−0.955671	−	0.294435i	$-0.904868\pi$
$967$		−	17707.6i		−	0.588870i	0.955671	−	0.294435i	$-0.0951315\pi$
$968$	10534.9	+	18300.8i	0.349798	+	0.607655i
$969$	19837.8	+	54304.8i	0.657669	+	1.80033i
$970$	−13906.6	−	5068.29i	−0.460324	−	0.167766i
$971$		−	20263.5i		−	0.669708i	−0.942270	−	0.334854i	$-0.891313\pi$
$971$		−	20263.5i		−	0.669708i	0.942270	−	0.334854i	$-0.108687\pi$
$972$	−15019.6	+	26320.0i	−0.495631	+	0.868533i
$973$			23046.5i			0.759339i
$974$	16491.6	−	45250.4i	0.542531	−	1.48862i
$975$	−2465.30	−	6748.63i	−0.0809773	−	0.221671i
$976$	−19962.5	+	3484.94i	−0.654696	+	0.114293i
$977$			22715.7i			0.743847i	0.928263	+	0.371924i	$0.121302\pi$
$977$			22715.7i			0.743847i	−0.928263	+	0.371924i	$0.878698\pi$
$978$	40576.5	−	30.5361i	1.32668	−	0.000998402i
$979$	161.461			0.00527101
$980$	5954.76	+	5005.27i	0.194100	+	0.163150i
$981$	18647.2	+	22116.8i	0.606889	+	0.719812i
$982$	9666.01	−	26522.1i	0.314109	−	0.861866i
$983$	−42669.4			−1.38448			−0.692239	−	0.721669i	$-0.743375\pi$
$983$	−42669.4			−1.38448			−0.692239	+	0.721669i	$0.743375\pi$
$984$	−11968.8	+	14261.0i	−0.387755	+	0.462017i
$985$	15914.9			0.514814
$986$	−10739.8	+	29468.3i	−0.346881	+	0.951788i
$987$	1213.77	+	3322.62i	0.0391435	+	0.107153i
$988$	35129.8	−	41793.9i	1.13120	−	1.34579i
$989$	45763.4			1.47138
$990$	6247.21	+	17061.5i	0.200555	+	0.547729i
$991$			10989.6i			0.352267i	0.984366	+	0.176133i	$0.0563590\pi$
$991$			10989.6i			0.352267i	−0.984366	+	0.176133i	$0.943641\pi$
$992$	38737.6	+	6915.42i	1.23984	+	0.221335i
$993$	−569.952	+	208.206i	−0.0182144	+	0.00665379i
$994$	653.043	−	1791.85i	0.0208383	−	0.0571771i
$995$		−	17192.4i		−	0.547773i
$996$	7970.17	−	21920.2i	0.253559	−	0.697357i
$997$		−	20204.6i		−	0.641813i	−0.947111	−	0.320906i	$-0.896013\pi$
$997$		−	20204.6i		−	0.641813i	0.947111	−	0.320906i	$-0.103987\pi$
$998$	−24224.0	−	8828.49i	−0.768335	−	0.280021i
$999$	43738.0	+	25046.6i	1.38520	+	0.793231i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.4.b.a.11.3	✓	24
3.2	odd	2		120.4.b.b.11.22	yes	24
4.3	odd	2		480.4.b.b.431.21		24
8.3	odd	2		120.4.b.b.11.21	yes	24
8.5	even	2		480.4.b.a.431.21		24
12.11	even	2		480.4.b.a.431.22		24
24.5	odd	2		480.4.b.b.431.22		24
24.11	even	2	inner	120.4.b.a.11.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.4.b.a.11.3	✓	24	1.1	even	1	trivial
120.4.b.a.11.4	yes	24	24.11	even	2	inner
120.4.b.b.11.21	yes	24	8.3	odd	2
120.4.b.b.11.22	yes	24	3.2	odd	2
480.4.b.a.431.21		24	8.5	even	2
480.4.b.a.431.22		24	12.11	even	2
480.4.b.b.431.21		24	4.3	odd	2
480.4.b.b.431.22		24	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	120.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.65744 - 0.968509i) q^{2} +(-4.88069 + 1.78294i) q^{3} +(6.12398 + 5.14751i) q^{4} +5.00000 q^{5} +(14.6969 - 0.0110603i) q^{6} +12.1872i q^{7} +(-11.2887 - 19.6103i) q^{8} +(20.6423 - 17.4039i) q^{9} +O(q^{10})\)	\(q+(-2.65744 - 0.968509i) q^{2} +(-4.88069 + 1.78294i) q^{3} +(6.12398 + 5.14751i) q^{4} +5.00000 q^{5} +(14.6969 - 0.0110603i) q^{6} +12.1872i q^{7} +(-11.2887 - 19.6103i) q^{8} +(20.6423 - 17.4039i) q^{9} +(-13.2872 - 4.84254i) q^{10} -47.5839i q^{11} +(-39.0669 - 14.2047i) q^{12} +55.3088i q^{13} +(11.8034 - 32.3866i) q^{14} +(-24.4034 + 8.91469i) q^{15} +(11.0063 + 63.0465i) q^{16} +90.1721i q^{17} +(-71.7115 + 26.2577i) q^{18} -123.391 q^{19} +(30.6199 + 25.7375i) q^{20} +(-21.7289 - 59.4817i) q^{21} +(-46.0854 + 126.451i) q^{22} -136.806 q^{23} +(90.0607 + 75.5849i) q^{24} +25.0000 q^{25} +(53.5671 - 146.980i) q^{26} +(-69.7184 + 121.747i) q^{27} +(-62.7335 + 74.6339i) q^{28} -122.976 q^{29} +(73.4847 - 0.0553013i) q^{30} +217.380i q^{31} +(31.8125 - 178.202i) q^{32} +(84.8391 + 232.242i) q^{33} +(87.3325 - 239.627i) q^{34} +60.9358i q^{35} +(216.000 - 0.325104i) q^{36} -359.253i q^{37} +(327.905 + 119.506i) q^{38} +(-98.6121 - 269.945i) q^{39} +(-56.4435 - 98.0517i) q^{40} +158.349i q^{41} +(0.134793 + 179.114i) q^{42} -334.514 q^{43} +(244.938 - 291.403i) q^{44} +(103.211 - 87.0197i) q^{45} +(363.553 + 132.498i) q^{46} -55.8595 q^{47} +(-166.126 - 288.087i) q^{48} +194.473 q^{49} +(-66.4360 - 24.2127i) q^{50} +(-160.771 - 440.102i) q^{51} +(-284.703 + 338.710i) q^{52} -494.078 q^{53} +(303.186 - 256.013i) q^{54} -237.919i q^{55} +(238.994 - 137.577i) q^{56} +(602.235 - 219.999i) q^{57} +(326.801 + 119.103i) q^{58} +151.479i q^{59} +(-195.335 - 71.0236i) q^{60} +316.631i q^{61} +(210.535 - 577.675i) q^{62} +(212.104 + 251.570i) q^{63} +(-257.130 + 442.751i) q^{64} +276.544i q^{65} +(-0.526290 - 699.337i) q^{66} +460.078 q^{67} +(-464.162 + 552.212i) q^{68} +(667.706 - 243.916i) q^{69} +(59.0168 - 161.933i) q^{70} +55.3268 q^{71} +(-574.321 - 208.334i) q^{72} -284.535 q^{73} +(-347.940 + 954.694i) q^{74} +(-122.017 + 44.5734i) q^{75} +(-755.647 - 635.158i) q^{76} +579.912 q^{77} +(0.611730 + 812.870i) q^{78} +374.804i q^{79} +(55.0315 + 315.233i) q^{80} +(123.206 - 718.513i) q^{81} +(153.363 - 420.803i) q^{82} +561.093i q^{83} +(173.115 - 476.115i) q^{84} +450.860i q^{85} +(888.951 + 323.980i) q^{86} +(600.207 - 219.258i) q^{87} +(-933.135 + 537.160i) q^{88} +3.39319i q^{89} +(-358.557 + 131.289i) q^{90} -674.057 q^{91} +(-837.796 - 704.209i) q^{92} +(-387.576 - 1060.97i) q^{93} +(148.443 + 54.1005i) q^{94} -616.957 q^{95} +(162.456 + 926.469i) q^{96} +1046.62 q^{97} +(-516.801 - 188.349i) q^{98} +(-828.146 - 982.239i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} - 3 q^{4} + 120 q^{5} + 19 q^{6} + 21 q^{8}+O(q^{10}) \) 24 * q - 3 * q^2 - 3 * q^4 + 120 * q^5 + 19 * q^6 + 21 * q^8	\( 24 q - 3 q^{2} - 3 q^{4} + 120 q^{5} + 19 q^{6} + 21 q^{8} - 15 q^{10} + 65 q^{12} - 54 q^{14} + 153 q^{16} - 175 q^{18} + 12 q^{19} - 15 q^{20} - 4 q^{21} - 102 q^{22} + 228 q^{23} - 407 q^{24} + 600 q^{25} + 336 q^{26} + 132 q^{27} - 186 q^{28} + 95 q^{30} + 177 q^{32} + 116 q^{33} + 408 q^{34} + 673 q^{36} + 312 q^{38} - 656 q^{39} + 105 q^{40} - 990 q^{42} - 450 q^{44} - 1104 q^{46} - 924 q^{47} - 535 q^{48} - 816 q^{49} - 75 q^{50} - 700 q^{51} - 1548 q^{52} + 528 q^{53} + 1331 q^{54} - 390 q^{56} - 172 q^{57} + 1410 q^{58} + 325 q^{60} - 978 q^{62} + 476 q^{63} + 1137 q^{64} - 2794 q^{66} + 1632 q^{67} - 1608 q^{68} + 980 q^{69} - 270 q^{70} + 216 q^{71} - 3699 q^{72} - 216 q^{73} + 768 q^{74} - 1812 q^{76} + 4140 q^{78} + 765 q^{80} + 152 q^{81} + 2244 q^{82} + 5086 q^{84} - 2808 q^{86} + 252 q^{87} + 2622 q^{88} - 875 q^{90} - 1800 q^{91} - 1836 q^{92} - 1968 q^{94} + 60 q^{95} - 5455 q^{96} + 792 q^{97} + 4851 q^{98} - 1328 q^{99}+O(q^{100}) \) 24 * q - 3 * q^2 - 3 * q^4 + 120 * q^5 + 19 * q^6 + 21 * q^8 - 15 * q^10 + 65 * q^12 - 54 * q^14 + 153 * q^16 - 175 * q^18 + 12 * q^19 - 15 * q^20 - 4 * q^21 - 102 * q^22 + 228 * q^23 - 407 * q^24 + 600 * q^25 + 336 * q^26 + 132 * q^27 - 186 * q^28 + 95 * q^30 + 177 * q^32 + 116 * q^33 + 408 * q^34 + 673 * q^36 + 312 * q^38 - 656 * q^39 + 105 * q^40 - 990 * q^42 - 450 * q^44 - 1104 * q^46 - 924 * q^47 - 535 * q^48 - 816 * q^49 - 75 * q^50 - 700 * q^51 - 1548 * q^52 + 528 * q^53 + 1331 * q^54 - 390 * q^56 - 172 * q^57 + 1410 * q^58 + 325 * q^60 - 978 * q^62 + 476 * q^63 + 1137 * q^64 - 2794 * q^66 + 1632 * q^67 - 1608 * q^68 + 980 * q^69 - 270 * q^70 + 216 * q^71 - 3699 * q^72 - 216 * q^73 + 768 * q^74 - 1812 * q^76 + 4140 * q^78 + 765 * q^80 + 152 * q^81 + 2244 * q^82 + 5086 * q^84 - 2808 * q^86 + 252 * q^87 + 2622 * q^88 - 875 * q^90 - 1800 * q^91 - 1836 * q^92 - 1968 * q^94 + 60 * q^95 - 5455 * q^96 + 792 * q^97 + 4851 * q^98 - 1328 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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