LMFDB - Embedded newform 33.4.f.a.8.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,4,Mod(2,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 1]))

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

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

chi := DirichletCharacter("33.2");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	33.f (of order $10$, degree $4$, 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:	$1.94706303019$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			8.10
Character	$\chi$	$=$	33.8
Dual form			33.4.f.a.29.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.83133 - 2.78363i) q^{2} +(-4.74741 - 2.11237i) q^{3} +(4.45840 - 13.7215i) q^{4} +(-2.11757 + 2.91459i) q^{5} +(-24.0689 + 5.12183i) q^{6} +(28.5187 + 9.26628i) q^{7} +(-9.40652 - 28.9503i) q^{8} +(18.0758 + 20.0566i) q^{9} +17.0613i q^{10} +(-32.5614 + 16.4546i) q^{11} +(-50.1508 + 55.7240i) q^{12} +(-23.3577 - 32.1491i) q^{13} +(135.058 - 43.8831i) q^{14} +(16.2097 - 9.36366i) q^{15} +(-23.2483 - 16.8909i) q^{16} +(-18.3339 - 13.3204i) q^{17} +(125.084 + 26.5271i) q^{18} +(-74.0299 + 24.0538i) q^{19} +(30.5517 + 42.0508i) q^{20} +(-115.816 - 104.233i) q^{21} +(-78.9503 + 153.682i) q^{22} +39.4710i q^{23} +(-16.4971 + 157.309i) q^{24} +(34.6164 + 106.538i) q^{25} +(-178.982 - 58.1549i) q^{26} +(-43.4464 - 133.399i) q^{27} +(254.295 - 350.007i) q^{28} +(60.7406 - 186.940i) q^{29} +(36.0397 - 80.9969i) q^{30} +(-125.194 + 90.9588i) q^{31} +107.431 q^{32} +(189.341 - 9.33491i) q^{33} -107.322 q^{34} +(-87.3978 + 63.4982i) q^{35} +(355.796 - 158.608i) q^{36} +(103.703 - 319.166i) q^{37} +(-216.676 + 298.229i) q^{38} +(42.9778 + 201.965i) q^{39} +(104.297 + 33.8882i) q^{40} +(-67.1986 - 206.816i) q^{41} +(-733.875 - 76.9619i) q^{42} +193.093i q^{43} +(80.6104 + 520.154i) q^{44} +(-96.7335 + 10.2123i) q^{45} +(109.872 + 151.226i) q^{46} +(-188.238 + 61.1622i) q^{47} +(74.6896 + 129.297i) q^{48} +(449.958 + 326.914i) q^{49} +(429.190 + 311.825i) q^{50} +(58.9010 + 101.965i) q^{51} +(-545.274 + 177.170i) q^{52} +(28.7649 + 39.5915i) q^{53} +(-537.792 - 390.159i) q^{54} +(20.9929 - 129.747i) q^{55} -912.787i q^{56} +(402.260 + 42.1853i) q^{57} +(-287.654 - 885.309i) q^{58} +(105.494 + 34.2770i) q^{59} +(-56.2146 - 264.169i) q^{60} +(-187.195 + 257.652i) q^{61} +(-226.465 + 696.987i) q^{62} +(329.648 + 739.482i) q^{63} +(597.590 - 434.175i) q^{64} +143.163 q^{65} +(699.442 - 562.819i) q^{66} -329.164 q^{67} +(-264.516 + 192.182i) q^{68} +(83.3772 - 187.385i) q^{69} +(-158.095 + 486.565i) q^{70} +(348.236 - 479.306i) q^{71} +(410.613 - 711.962i) q^{72} +(286.826 + 93.1954i) q^{73} +(-491.116 - 1511.50i) q^{74} +(60.7100 - 578.904i) q^{75} +1123.04i q^{76} +(-1081.08 + 167.540i) q^{77} +(726.858 + 654.162i) q^{78} +(-324.935 - 447.235i) q^{79} +(98.4601 - 31.9916i) q^{80} +(-75.5309 + 725.077i) q^{81} +(-833.159 - 605.325i) q^{82} +(508.644 + 369.552i) q^{83} +(-1946.59 + 1124.46i) q^{84} +(77.6467 - 25.2289i) q^{85} +(537.499 + 739.804i) q^{86} +(-683.247 + 759.175i) q^{87} +(782.654 + 787.882i) q^{88} -1054.22i q^{89} +(-342.191 + 308.397i) q^{90} +(-368.228 - 1133.29i) q^{91} +(541.603 + 175.977i) q^{92} +(786.486 - 167.363i) q^{93} +(-550.949 + 758.317i) q^{94} +(86.6568 - 266.702i) q^{95} +(-510.019 - 226.934i) q^{96} +(402.482 - 292.420i) q^{97} +2633.94 q^{98} +(-918.596 - 355.640i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 3 q^{3} - 38 q^{4} + 45 q^{6} - 10 q^{7} - 65 q^{9} - 90 q^{12} - 10 q^{13} + 33 q^{15} + 310 q^{16} + 225 q^{18} - 460 q^{19} - 340 q^{22} - 565 q^{24} - 604 q^{25} - 435 q^{27} + 1190 q^{28} + 910 q^{30}+ \cdots + 955 q^{99}+O(q^{100}) $ 40 * q - 3 * q^3 - 38 * q^4 + 45 * q^6 - 10 * q^7 - 65 * q^9 - 90 * q^12 - 10 * q^13 + 33 * q^15 + 310 * q^16 + 225 * q^18 - 460 * q^19 - 340 * q^22 - 565 * q^24 - 604 * q^25 - 435 * q^27 + 1190 * q^28 + 910 * q^30 + 840 * q^31 + 1208 * q^33 - 188 * q^34 + 1991 * q^36 + 126 * q^37 - 1075 * q^39 - 90 * q^40 - 3340 * q^42 - 1662 * q^45 + 430 * q^46 - 346 * q^48 + 376 * q^49 - 210 * q^51 - 4270 * q^52 - 546 * q^55 + 1800 * q^57 - 4582 * q^58 + 674 * q^60 + 650 * q^61 + 3945 * q^63 + 7238 * q^64 + 3504 * q^66 + 4556 * q^67 + 3860 * q^69 + 2964 * q^70 - 1640 * q^72 + 3860 * q^73 - 6048 * q^75 - 7640 * q^78 - 3550 * q^79 - 2453 * q^81 - 5812 * q^82 - 7080 * q^84 - 8230 * q^85 - 9298 * q^88 + 9220 * q^90 - 6766 * q^91 + 5659 * q^93 + 3530 * q^94 + 14890 * q^96 + 8004 * q^97 + 955 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$

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 $

$2$	3.83133	−	2.78363i	1.35458	−	0.984160i	0.355812	−	0.934558i	$-0.384205\pi$
$2$	3.83133	−	2.78363i	1.35458	−	0.984160i	0.998769	−	0.0496026i	$-0.0157955\pi$
$3$	−4.74741	−	2.11237i	−0.913639	−	0.406525i
$3$	−4.74741	−	2.11237i	−0.913639	−	0.406525i
$4$	4.45840	−	13.7215i	0.557300	−	1.71519i
$5$	−2.11757	+	2.91459i	−0.189402	+	0.260689i	−0.893149	−	0.449762i	$-0.851509\pi$
$5$	−2.11757	+	2.91459i	−0.189402	+	0.260689i	0.703747	+	0.710451i	$0.251509\pi$
$6$	−24.0689	+	5.12183i	−1.63768	+	0.348496i
$7$	28.5187	+	9.26628i	1.53986	+	0.500332i	0.951339	−	0.308147i	$-0.0997089\pi$
$7$	28.5187	+	9.26628i	1.53986	+	0.500332i	0.588525	+	0.808479i	$0.299709\pi$
$8$	−9.40652	−	28.9503i	−0.415713	−	1.27943i
$9$	18.0758	+	20.0566i	0.669474	+	0.742835i
$10$			17.0613i			0.539525i
$11$	−32.5614	+	16.4546i	−0.892513	+	0.451022i
$11$	−32.5614	+	16.4546i	−0.892513	+	0.451022i
$12$	−50.1508	+	55.7240i	−1.20644	+	1.34051i
$13$	−23.3577	−	32.1491i	−0.498328	−	0.685890i	0.483569	−	0.875306i	$-0.339340\pi$
$13$	−23.3577	−	32.1491i	−0.498328	−	0.685890i	−0.981897	+	0.189417i	$0.939340\pi$
$14$	135.058	−	43.8831i	2.57828	−	0.837733i
$15$	16.2097	−	9.36366i	0.279021	−	0.161179i
$16$	−23.2483	−	16.8909i	−0.363255	−	0.263920i
$17$	−18.3339	−	13.3204i	−0.261566	−	0.190039i	0.449271	−	0.893395i	$-0.351684\pi$
$17$	−18.3339	−	13.3204i	−0.261566	−	0.190039i	−0.710837	+	0.703357i	$0.751684\pi$
$18$	125.084	+	26.5271i	1.63793	+	0.347361i
$19$	−74.0299	+	24.0538i	−0.893874	+	0.290437i	−0.719706	−	0.694279i	$-0.755724\pi$
$19$	−74.0299	+	24.0538i	−0.893874	+	0.290437i	−0.174168	+	0.984716i	$0.555724\pi$
$20$	30.5517	+	42.0508i	0.341578	+	0.470142i
$21$	−115.816	−	104.233i	−1.20348	−	1.08312i
$22$	−78.9503	+	153.682i	−0.765102	+	1.48932i
$23$			39.4710i			0.357838i	0.983864	+	0.178919i	$0.0572600\pi$
$23$			39.4710i			0.357838i	−0.983864	+	0.178919i	$0.942740\pi$
$24$	−16.4971	+	157.309i	−0.140310	+	1.33794i
$25$	34.6164	+	106.538i	0.276931	+	0.852307i
$26$	−178.982	−	58.1549i	−1.35005	−	0.438658i
$27$	−43.4464	−	133.399i	−0.309676	−	0.950842i
$28$	254.295	−	350.007i	1.71633	−	2.36233i
$29$	60.7406	−	186.940i	0.388939	−	1.19703i	−0.544643	−	0.838668i	$-0.683335\pi$
$29$	60.7406	−	186.940i	0.388939	−	1.19703i	0.933582	−	0.358364i	$-0.116665\pi$
$30$	36.0397	−	80.9969i	0.219331	−	0.492932i
$31$	−125.194	+	90.9588i	−0.725339	+	0.526990i	−0.888086	−	0.459678i	$-0.847965\pi$
$31$	−125.194	+	90.9588i	−0.725339	+	0.526990i	0.162746	+	0.986668i	$0.447965\pi$
$32$	107.431			0.593478
$33$	189.341	−	9.33491i	0.998787	−	0.0492424i
$34$	−107.322			−0.541341
$35$	−87.3978	+	63.4982i	−0.422083	+	0.306662i
$36$	355.796	−	158.608i	1.64720	−	0.734295i
$37$	103.703	−	319.166i	0.460776	−	1.41812i	−0.403442	−	0.915005i	$-0.632186\pi$
$37$	103.703	−	319.166i	0.460776	−	1.41812i	0.864218	−	0.503117i	$-0.167814\pi$
$38$	−216.676	+	298.229i	−0.924988	+	1.27314i
$39$	42.9778	+	201.965i	0.176461	+	0.829239i
$40$	104.297	+	33.8882i	0.412271	+	0.133955i
$41$	−67.1986	−	206.816i	−0.255967	−	0.787787i	−0.993638	−	0.112625i	$-0.964074\pi$
$41$	−67.1986	−	206.816i	−0.255967	−	0.787787i	0.737670	−	0.675161i	$-0.235926\pi$
$42$	−733.875	−	76.9619i	−2.69617	−	0.282749i
$43$			193.093i			0.684801i	0.939554	+	0.342400i	$0.111240\pi$
$43$			193.093i			0.684801i	−0.939554	+	0.342400i	$0.888760\pi$
$44$	80.6104	+	520.154i	0.276192	+	1.78219i
$45$	−96.7335	+	10.2123i	−0.320448	+	0.0338302i
$46$	109.872	+	151.226i	0.352170	+	0.484720i
$47$	−188.238	+	61.1622i	−0.584198	+	0.189818i	−0.586181	−	0.810180i	$-0.699369\pi$
$47$	−188.238	+	61.1622i	−0.584198	+	0.189818i	0.00198212	+	0.999998i	$0.499369\pi$
$48$	74.6896	+	129.297i	0.224594	+	0.388801i
$49$	449.958	+	326.914i	1.31183	+	0.953101i
$50$	429.190	+	311.825i	1.21393	+	0.881973i
$51$	58.9010	+	101.965i	0.161721	+	0.279960i
$52$	−545.274	+	177.170i	−1.45415	+	0.472482i
$53$	28.7649	+	39.5915i	0.0745502	+	0.102610i	0.844664	−	0.535297i	$-0.179800\pi$
$53$	28.7649	+	39.5915i	0.0745502	+	0.102610i	−0.770113	+	0.637907i	$0.779800\pi$
$54$	−537.792	−	390.159i	−1.35526	−	0.983221i
$55$	20.9929	−	129.747i	0.0514669	−	0.318092i
$56$		−	912.787i		−	2.17815i
$57$	402.260	+	42.1853i	0.934749	+	0.0980277i
$58$	−287.654	−	885.309i	−0.651222	−	2.00425i
$59$	105.494	+	34.2770i	0.232782	+	0.0756354i	0.423085	−	0.906090i	$-0.360947\pi$
$59$	105.494	+	34.2770i	0.232782	+	0.0756354i	−0.190303	+	0.981725i	$0.560947\pi$
$60$	−56.2146	−	264.169i	−0.120955	−	0.568400i
$61$	−187.195	+	257.652i	−0.392916	+	0.540803i	−0.958949	−	0.283580i	$-0.908478\pi$
$61$	−187.195	+	257.652i	−0.392916	+	0.540803i	0.566032	+	0.824383i	$0.308478\pi$
$62$	−226.465	+	696.987i	−0.463888	+	1.42770i
$63$	329.648	+	739.482i	0.659234	+	1.47882i
$64$	597.590	−	434.175i	1.16717	−	0.847998i
$65$	143.163			0.273188
$66$	699.442	−	562.819i	1.30447	−	1.04967i
$67$	−329.164			−0.600206			−0.300103	−	0.953907i	$-0.597021\pi$
$67$	−329.164			−0.600206			−0.300103	+	0.953907i	$0.597021\pi$
$68$	−264.516	+	192.182i	−0.471724	+	0.342727i
$69$	83.3772	−	187.385i	0.145470	−	0.326935i
$70$	−158.095	+	486.565i	−0.269942	+	0.830796i
$71$	348.236	−	479.306i	0.582085	−	0.801172i	−0.411837	−	0.911258i	$-0.635113\pi$
$71$	348.236	−	479.306i	0.582085	−	0.801172i	0.993922	+	0.110086i	$0.0351126\pi$
$72$	410.613	−	711.962i	0.672100	−	1.16535i
$73$	286.826	+	93.1954i	0.459869	+	0.149420i	0.529784	−	0.848132i	$-0.322273\pi$
$73$	286.826	+	93.1954i	0.459869	+	0.149420i	−0.0699154	+	0.997553i	$0.522273\pi$
$74$	−491.116	−	1511.50i	−0.771502	−	2.37444i
$75$	60.7100	−	578.904i	0.0934691	−	0.891281i
$76$			1123.04i			1.69503i
$77$	−1081.08	+	167.540i	−1.60001	+	0.247960i
$78$	726.858	+	654.162i	1.05513	+	0.949606i
$79$	−324.935	−	447.235i	−0.462760	−	0.636935i	0.512318	−	0.858796i	$-0.328787\pi$
$79$	−324.935	−	447.235i	−0.462760	−	0.636935i	−0.975078	+	0.221861i	$0.928787\pi$
$80$	98.4601	−	31.9916i	0.137602	−	0.0447097i
$81$	−75.5309	+	725.077i	−0.103609	+	0.994618i
$82$	−833.159	−	605.325i	−1.12204	−	0.815208i
$83$	508.644	+	369.552i	0.672662	+	0.488718i	0.870915	−	0.491433i	$-0.163527\pi$
$83$	508.644	+	369.552i	0.672662	+	0.488718i	−0.198253	+	0.980151i	$0.563527\pi$
$84$	−1946.59	+	1124.46i	−2.52845	+	1.46058i
$85$	77.6467	−	25.2289i	0.0990820	−	0.0321937i
$86$	537.499	+	739.804i	0.673954	+	0.927618i
$87$	−683.247	+	759.175i	−0.841974	+	0.935542i
$88$	782.654	+	787.882i	0.948082	+	0.954415i
$89$		−	1054.22i		−	1.25558i	−0.778381	−	0.627792i	$-0.783959\pi$
$89$		−	1054.22i		−	1.25558i	0.778381	−	0.627792i	$-0.216041\pi$
$90$	−342.191	+	308.397i	−0.400779	+	0.361198i
$91$	−368.228	−	1133.29i	−0.424185	−	1.30551i
$92$	541.603	+	175.977i	0.613761	+	0.199423i
$93$	786.486	−	167.363i	0.876933	−	0.186610i
$94$	−550.949	+	758.317i	−0.604533	+	0.832068i
$95$	86.6568	−	266.702i	0.0935874	−	0.288032i
$96$	−510.019	−	226.934i	−0.542225	−	0.241264i
$97$	402.482	−	292.420i	0.421298	−	0.306091i	−0.356862	−	0.934157i	$-0.616153\pi$
$97$	402.482	−	292.420i	0.421298	−	0.306091i	0.778160	+	0.628066i	$0.216153\pi$
$98$	2633.94			2.71499
$99$	−918.596	−	355.640i	−0.932549	−	0.361043i
$100$	1616.20			1.61620
$101$	562.026	−	408.336i	0.553699	−	0.402286i	−0.275448	−	0.961316i	$-0.588826\pi$
$101$	562.026	−	408.336i	0.553699	−	0.402286i	0.829148	+	0.559030i	$0.188826\pi$
$102$	509.502	+	226.704i	0.494590	+	0.220069i
$103$	−114.604	+	352.716i	−0.109634	+	0.337419i	−0.990790	−	0.135407i	$-0.956766\pi$
$103$	−114.604	+	352.716i	−0.109634	+	0.337419i	0.881156	+	0.472825i	$0.156766\pi$
$104$	−711.012	+	978.624i	−0.670389	+	0.922712i
$105$	549.045	−	116.836i	0.510298	−	0.108590i
$106$	220.416	+	71.6174i	0.201969	+	0.0656236i
$107$	383.755	+	1181.08i	0.346720	+	1.06709i	0.960657	+	0.277739i	$0.0895851\pi$
$107$	383.755	+	1181.08i	0.346720	+	1.06709i	−0.613937	+	0.789355i	$0.710415\pi$
$108$	−2024.15	+	1.40349i	−1.80346	+	0.00125047i
$109$		−	789.909i		−	0.694124i	−0.937842	−	0.347062i	$-0.887179\pi$
$109$		−	789.909i		−	0.694124i	0.937842	−	0.347062i	$-0.112821\pi$
$110$	−280.736	−	555.540i	−0.243338	−	0.481533i
$111$	−1166.52	+	1296.15i	−0.997486	+	1.10834i
$112$	−506.496	−	697.132i	−0.427316	−	0.588150i
$113$	−1764.55	+	573.337i	−1.46898	+	0.477301i	−0.930800	−	0.365529i	$-0.880888\pi$
$113$	−1764.55	+	573.337i	−1.46898	+	0.477301i	−0.538180	+	0.842830i	$0.680888\pi$
$114$	1658.62	−	958.117i	1.36267	−	0.787157i
$115$	−115.042	−	83.5827i	−0.0932843	−	0.0677750i
$116$	−2294.30	−	1666.91i	−1.83638	−	1.33421i
$117$	222.592	−	1049.60i	0.175886	−	0.829361i
$118$	499.597	−	162.329i	0.389759	−	0.126640i
$119$	−399.428	−	549.766i	−0.307693	−	0.423504i
$120$	−423.557	−	381.195i	−0.322211	−	0.289985i
$121$	789.493	−	1071.57i	0.593158	−	0.805086i
$122$			1508.23i			1.11925i
$123$	−117.852	+	1123.79i	−0.0863934	+	0.823810i
$124$	689.930	+	2123.39i	0.499657	+	1.53779i
$125$	−812.107	−	263.869i	−0.581096	−	0.188810i
$126$	3321.43	+	1915.58i	2.34839	+	1.35439i
$127$	−691.974	+	952.420i	−0.483486	+	0.665462i	−0.979170	−	0.203041i	$-0.934917\pi$
$127$	−691.974	+	952.420i	−0.483486	+	0.665462i	0.495684	+	0.868503i	$0.334917\pi$
$128$	815.403	−	2509.55i	0.563064	−	1.73293i
$129$	407.884	−	916.692i	0.278389	−	0.625661i
$130$	548.506	−	398.513i	0.370055	−	0.268861i
$131$	−297.471			−0.198398			−0.0991990	−	0.995068i	$-0.531628\pi$
$131$	−297.471			−0.198398			−0.0991990	+	0.995068i	$0.531628\pi$
$132$	716.067	−	2639.66i	0.472164	−	1.74055i
$133$	−2334.12			−1.52176
$134$	−1261.14	+	916.270i	−0.813028	+	0.590699i
$135$	480.806	+	155.855i	0.306527	+	0.0993617i
$136$	−213.170	+	656.070i	−0.134406	+	0.413658i
$137$	−730.280	+	1005.14i	−0.455416	+	0.626826i	−0.973550	−	0.228473i	$-0.926627\pi$
$137$	−730.280	+	1005.14i	−0.455416	+	0.626826i	0.518134	+	0.855299i	$0.326627\pi$
$138$	−202.164	−	950.025i	−0.124705	−	0.586025i
$139$	1544.43	+	501.815i	0.942422	+	0.306211i	0.739632	−	0.673011i	$-0.234999\pi$
$139$	1544.43	+	501.815i	0.942422	+	0.306211i	0.202789	+	0.979222i	$0.434999\pi$
$140$	481.639	+	1482.33i	0.290757	+	0.894857i
$141$	1022.84	+	107.266i	0.610912	+	0.0640667i
$142$		−	2805.74i		−	1.65812i
$143$	1289.56	+	662.481i	0.754116	+	0.387408i
$144$	−81.4589	−	771.598i	−0.0471406	−	0.446527i
$145$	416.231	+	572.893i	0.238387	+	0.328112i
$146$	1358.35	−	441.353i	0.769983	−	0.250183i
$147$	−1445.57	−	2502.47i	−0.811081	−	1.40408i
$148$	−3917.10	−	2845.94i	−2.17556	−	1.58064i
$149$	2846.16	+	2067.85i	1.56487	+	1.13695i	0.931867	+	0.362801i	$0.118180\pi$
$149$	2846.16	+	2067.85i	1.56487	+	1.13695i	0.633007	+	0.774146i	$0.281820\pi$
$150$	−1378.85	−	2386.97i	−0.750552	−	1.29930i
$151$	1035.49	−	336.450i	0.558058	−	0.181324i	−0.0163894	−	0.999866i	$-0.505217\pi$
$151$	1035.49	−	336.450i	0.558058	−	0.181324i	0.574447	+	0.818542i	$0.305217\pi$
$152$	1392.73	+	1916.92i	0.743191	+	1.02291i
$153$	−64.2394	−	608.491i	−0.0339441	−	0.321527i
$154$	−3675.62	+	3651.23i	−1.92331	+	1.91055i
$155$		−	557.501i		−	0.288900i
$156$	2962.89	+	310.720i	1.52065	+	0.159471i
$157$	642.100	+	1976.18i	0.326402	+	1.00456i	0.970804	+	0.239875i	$0.0771065\pi$
$157$	642.100	+	1976.18i	0.326402	+	1.00456i	−0.644402	+	0.764687i	$0.722893\pi$
$158$	−2489.87	−	809.007i	−1.25369	−	0.407349i
$159$	−52.9269	−	248.719i	−0.0263986	−	0.124055i
$160$	−227.493	+	313.117i	−0.112406	+	0.154713i
$161$	−365.749	+	1125.66i	−0.179038	+	0.551021i
$162$	1728.96	+	2988.26i	0.838517	+	1.44926i
$163$	−734.978	+	533.993i	−0.353177	+	0.256598i	−0.750201	−	0.661210i	$-0.770043\pi$
$163$	−734.978	+	533.993i	−0.353177	+	0.256598i	0.397023	+	0.917809i	$0.370043\pi$
$164$	−3137.43			−1.49386
$165$	−373.735	+	571.617i	−0.176335	+	0.269699i
$166$	2977.48			1.39215
$167$	2216.50	−	1610.38i	1.02705	−	0.746197i	0.0593351	−	0.998238i	$-0.481102\pi$
$167$	2216.50	−	1610.38i	1.02705	−	0.746197i	0.967716	+	0.252042i	$0.0811020\pi$
$168$	−1928.14	+	4333.37i	−0.885473	+	1.99004i
$169$	190.926	−	587.609i	0.0869030	−	0.267460i
$170$	227.262	−	312.800i	0.102531	−	0.141122i
$171$	−1820.58	−	1049.99i	−0.814173	−	0.469561i
$172$	2649.54	+	860.886i	1.17456	+	0.381639i
$173$	−272.961	−	840.087i	−0.119959	−	0.369194i	0.872990	−	0.487737i	$-0.162178\pi$
$173$	−272.961	−	840.087i	−0.119959	−	0.369194i	−0.992949	+	0.118543i	$0.962178\pi$
$174$	−504.486	+	4810.56i	−0.219799	+	2.09590i
$175$			3359.10i			1.45099i
$176$	1034.93	+	167.450i	0.443244	+	0.0717162i
$177$	−428.417	−	385.569i	−0.181931	−	0.163735i
$178$	−2934.55	−	4039.06i	−1.23570	−	1.70079i
$179$	−1371.30	+	445.562i	−0.572602	+	0.186050i	−0.580984	−	0.813915i	$-0.697332\pi$
$179$	−1371.30	+	445.562i	−0.572602	+	0.186050i	0.00838162	+	0.999965i	$0.497332\pi$
$180$	−291.148	+	1372.86i	−0.120560	+	0.568484i
$181$	−276.077	−	200.581i	−0.113374	−	0.0823707i	0.529654	−	0.848214i	$-0.322322\pi$
$181$	−276.077	−	200.581i	−0.113374	−	0.0823707i	−0.643027	+	0.765843i	$0.722322\pi$
$182$	−4565.46	−	3317.00i	−1.85942	−	1.35095i
$183$	1432.95	−	827.755i	0.578834	−	0.334368i
$184$	1142.70	−	371.284i	0.457830	−	0.148758i
$185$	710.638	+	978.109i	0.282417	+	0.388714i
$186$	2547.41	−	2830.50i	1.00422	−	1.11582i
$187$	816.159	+	132.053i	0.319163	+	0.0516400i
$188$			2855.60i			1.10780i
$189$	−2.91700	−	4206.96i	−0.00112265	−	1.61911i
$190$	−410.388	−	1263.05i	−0.156698	−	0.482268i
$191$	1550.59	+	503.817i	0.587418	+	0.190864i	0.587621	−	0.809136i	$-0.300065\pi$
$191$	1550.59	+	503.817i	0.587418	+	0.190864i	−0.000203108		1.00000i	$0.500065\pi$
$192$	−3754.14	+	798.875i	−1.41110	+	0.300280i
$193$	71.0415	−	97.7803i	0.0264958	−	0.0364683i	−0.795564	−	0.605870i	$-0.792825\pi$
$193$	71.0415	−	97.7803i	0.0264958	−	0.0364683i	0.822059	+	0.569402i	$0.192825\pi$
$194$	728.054	−	2240.72i	0.269439	−	0.829249i
$195$	−679.655	−	302.414i	−0.249595	−	0.111058i
$196$	6491.85	−	4716.61i	2.36584	−	1.71888i
$197$	−2346.99			−0.848812			−0.424406	−	0.905472i	$-0.639517\pi$
$197$	−2346.99			−0.848812			−0.424406	+	0.905472i	$0.639517\pi$
$198$	−4509.42	+	1194.45i	−1.61854	+	0.428717i
$199$	754.043			0.268606			0.134303	−	0.990940i	$-0.457120\pi$
$199$	754.043			0.268606			0.134303	+	0.990940i	$0.457120\pi$
$200$	2758.70	−	2004.31i	0.975346	−	0.708631i
$201$	1562.68	+	695.316i	0.548372	+	0.243999i
$202$	1016.65	−	3128.94i	0.354116	−	1.08986i
$203$	3464.48	−	4768.45i	1.19783	−	1.64867i
$204$	1661.72	−	353.611i	0.570313	−	0.121362i
$205$	745.082	+	242.092i	0.253848	+	0.0824801i
$206$	542.742	+	1670.39i	0.183566	+	0.564958i
$207$	−791.652	+	713.469i	−0.265815	+	0.239563i
$208$			1141.95i			0.380672i
$209$	2014.72	−	2001.36i	0.666801	−	0.662376i
$210$	1778.35	−	1975.97i	0.584369	−	0.649309i
$211$	−1329.30	−	1829.63i	−0.433711	−	0.596952i	0.535089	−	0.844796i	$-0.320278\pi$
$211$	−1329.30	−	1829.63i	−0.433711	−	0.596952i	−0.968800	+	0.247844i	$0.920278\pi$
$212$	671.501	−	218.184i	0.217542	−	0.0706837i
$213$	−2665.69	+	1539.86i	−0.857513	+	0.495349i
$214$	4757.97	+	3456.87i	1.51985	+	1.10424i
$215$	−562.787	−	408.889i	−0.178520	−	0.129702i
$216$	−3453.27	+	2512.61i	−1.08780	+	0.791488i
$217$	−4413.22	+	1433.94i	−1.38059	+	0.448582i
$218$	−2198.81	−	3026.40i	−0.683130	−	0.940247i
$219$	−1164.82	−	1048.32i	−0.359411	−	0.323465i
$220$	−1686.73	−	866.518i	−0.516907	−	0.265548i
$221$			900.552i			0.274107i
$222$	−861.316	+	8213.13i	−0.260395	+	2.48302i
$223$	−15.2917	−	47.0630i	−0.00459196	−	0.0141326i	0.948734	−	0.316075i	$-0.102365\pi$
$223$	−15.2917	−	47.0630i	−0.00459196	−	0.0141326i	−0.953326	+	0.301942i	$0.902365\pi$
$224$	3063.79	+	995.485i	0.913875	+	0.296936i
$225$	−1511.07	+	2620.05i	−0.447725	+	0.776312i
$226$	−5164.62	+	7108.49i	−1.52011	+	2.09225i
$227$	−1915.35	+	5894.83i	−0.560027	+	1.72358i	0.122258	+	0.992498i	$0.460986\pi$
$227$	−1915.35	+	5894.83i	−0.560027	+	1.72358i	−0.682285	+	0.731086i	$0.739014\pi$
$228$	2372.28	−	5331.55i	0.689072	−	1.54864i
$229$	791.662	−	575.176i	0.228448	−	0.165977i	−0.467673	−	0.883901i	$-0.654908\pi$
$229$	791.662	−	575.176i	0.228448	−	0.165977i	0.696121	+	0.717924i	$0.254908\pi$
$230$	−673.426			−0.193063
$231$	5486.24	+	1488.26i	1.56263	+	0.423899i
$232$	−5983.33			−1.69321
$233$	−1295.79	+	941.448i	−0.364335	+	0.264705i	−0.754858	−	0.655888i	$-0.772294\pi$
$233$	−1295.79	+	941.448i	−0.364335	+	0.264705i	0.390523	+	0.920593i	$0.372294\pi$
$234$	−2068.86	−	4640.97i	−0.577973	−	1.29654i
$235$	220.345	−	678.152i	0.0611647	−	0.188246i
$236$	940.668	−	1294.72i	0.259459	−	0.357114i
$237$	597.875	+	2809.59i	0.163866	+	0.770052i
$238$	−3060.68	−	994.477i	−0.833591	−	0.270850i
$239$	680.388	+	2094.02i	0.184145	+	0.566740i	0.999933	−	0.0116119i	$-0.00369626\pi$
$239$	680.388	+	2094.02i	0.184145	+	0.566740i	−0.815788	+	0.578351i	$0.803696\pi$
$240$	−535.009	−	56.1067i	−0.143894	−	0.0150903i
$241$			3376.06i			0.902371i	0.892430	+	0.451185i	$0.148999\pi$
$241$			3376.06i			0.902371i	−0.892430	+	0.451185i	$0.851001\pi$
$242$	41.9635	−	6303.19i	0.0111468	−	1.67432i
$243$	1890.21	−	3282.69i	0.498999	−	0.866603i
$244$	2700.79	+	3717.32i	0.708609	+	0.975317i
$245$	−1905.64	+	619.179i	−0.496926	+	0.161461i
$246$	2676.68	+	4633.67i	0.693735	+	1.20094i
$247$	2502.48	+	1818.16i	0.644651	+	0.468366i
$248$	3810.92	+	2768.80i	0.975782	+	0.708947i
$249$	−1634.11	−	2828.86i	−0.415895	−	0.719966i
$250$	−3845.96	+	1249.63i	−0.972960	+	0.316134i
$251$	−2875.33	−	3957.56i	−0.723066	−	0.995214i	−0.999416	−	0.0341575i	$-0.989125\pi$
$251$	−2875.33	−	3957.56i	−0.723066	−	0.995214i	0.276351	−	0.961057i	$-0.410875\pi$
$252$	11616.5	−	1226.38i	2.90386	−	0.306565i
$253$	−649.478	−	1285.23i	−0.161393	−	0.319375i
$254$			5575.24i			1.37725i
$255$	−421.914	−	44.2463i	−0.103613	−	0.0108659i
$256$	−2035.50	−	6264.63i	−0.496949	−	1.52945i
$257$	1460.91	+	474.680i	0.354589	+	0.115213i	0.480894	−	0.876778i	$-0.340312\pi$
$257$	1460.91	+	474.680i	0.354589	+	0.115213i	−0.126306	+	0.991991i	$0.540312\pi$
$258$	−988.990	−	4647.55i	−0.238650	−	1.12149i
$259$	5914.96	−	8141.24i	1.41906	−	1.95317i
$260$	638.279	−	1964.42i	0.152248	−	0.468570i
$261$	4847.31	−	2160.85i	1.14958	−	0.512464i
$262$	−1139.71	+	828.047i	−0.268746	+	0.195255i
$263$	6003.58			1.40759			0.703796	−	0.710402i	$-0.251487\pi$
$263$	6003.58			1.40759			0.703796	+	0.710402i	$0.251487\pi$
$264$	−2051.28	−	5393.65i	−0.478211	−	1.25741i
$265$	−176.305			−0.0408691
$266$	−8942.80	+	6497.32i	−2.06135	+	1.49766i
$267$	−2226.90	+	5004.81i	−0.510427	+	1.14715i
$268$	−1467.55	+	4516.64i	−0.334495	+	1.02947i
$269$	−4342.40	+	5976.80i	−0.984241	+	1.35469i	−0.0497278	+	0.998763i	$0.515835\pi$
$269$	−4342.40	+	5976.80i	−0.984241	+	1.35469i	−0.934513	+	0.355929i	$0.884165\pi$
$270$	2275.97	−	741.252i	0.513003	−	0.167078i
$271$	−6539.66	−	2124.87i	−1.46589	−	0.476297i	−0.536027	−	0.844201i	$-0.680075\pi$
$271$	−6539.66	−	2124.87i	−1.46589	−	0.476297i	−0.929864	+	0.367905i	$0.880075\pi$
$272$	201.240	+	619.352i	0.0448601	+	0.138065i
$273$	−645.796	+	6158.03i	−0.143170	+	1.36520i
$274$			5883.87i			1.29729i
$275$	−2880.20	−	2899.44i	−0.631574	−	0.635793i
$276$	−2199.48	−	1979.50i	−0.479685	−	0.431710i
$277$	−830.961	−	1143.72i	−0.180244	−	0.248085i	0.709329	−	0.704878i	$-0.248998\pi$
$277$	−830.961	−	1143.72i	−0.180244	−	0.248085i	−0.889573	+	0.456793i	$0.848998\pi$
$278$	7314.08	−	2376.49i	1.57795	−	0.512706i
$279$	−4087.30	−	866.808i	−0.877062	−	0.186002i
$280$	2660.40	+	1932.89i	0.567819	+	0.412545i
$281$	257.927	+	187.395i	0.0547566	+	0.0397830i	0.614827	−	0.788662i	$-0.289226\pi$
$281$	257.927	+	187.395i	0.0547566	+	0.0397830i	−0.560070	+	0.828445i	$0.689226\pi$
$282$	4217.43	−	2436.23i	0.890582	−	0.514452i
$283$	6900.66	−	2242.16i	1.44948	−	0.470964i	0.524639	−	0.851325i	$-0.324200\pi$
$283$	6900.66	−	2242.16i	1.44948	−	0.470964i	0.924838	+	0.380361i	$0.124200\pi$
$284$	−5024.24	−	6915.28i	−1.04977	−	1.44488i
$285$	−974.769	+	1083.09i	−0.202598	+	0.225112i
$286$	6784.84	−	1051.47i	1.40278	−	0.217395i
$287$		−	6520.80i		−	1.34115i
$288$	1941.90	+	2154.69i	0.397318	+	0.440856i
$289$	−1359.50	−	4184.11i	−0.276715	−	0.851641i
$290$	3189.44	+	1036.31i	0.645829	+	0.209843i
$291$	−2528.45	+	538.049i	−0.509348	+	0.108388i
$292$	2557.57	−	3520.19i	0.512570	−	0.705492i
$293$	−2649.09	+	8153.07i	−0.528197	+	1.62562i	0.229710	+	0.973259i	$0.426222\pi$
$293$	−2649.09	+	8153.07i	−0.528197	+	1.62562i	−0.757906	+	0.652363i	$0.773778\pi$
$294$	−12504.4	−	5563.86i	−2.48052	−	1.10371i
$295$	−323.295	+	234.887i	−0.0638066	+	0.0463582i
$296$	−10215.4			−2.00594
$297$	3609.71	+	3628.78i	0.705241	+	0.708968i
$298$	16660.7			3.23869
$299$	1268.96	−	921.952i	0.245437	−	0.178321i
$300$	−7672.78	−	3414.02i	−1.47663	−	0.657028i
$301$	−1789.25	+	5506.76i	−0.342628	+	1.05450i
$302$	3030.74	−	4171.46i	0.577482	−	0.794836i
$303$	−3530.72	+	751.331i	−0.669421	+	0.142452i
$304$	2127.36	+	691.222i	0.401357	+	0.130409i
$305$	−354.551	−	1091.19i	−0.0665623	−	0.204858i
$306$	−1939.93	−	2152.51i	−0.362414	−	0.402127i
$307$		−	5127.03i		−	0.953143i	−0.879136	−	0.476571i	$-0.841879\pi$
$307$		−	5127.03i		−	0.953143i	0.879136	−	0.476571i	$-0.158121\pi$
$308$	−2520.99	+	15581.1i	−0.466386	+	2.88251i
$309$	1289.14	−	1432.40i	0.237335	−	0.263710i
$310$	−1551.87	−	2135.97i	−0.284324	−	0.391339i
$311$	4460.43	−	1449.28i	0.813272	−	0.264248i	0.127289	−	0.991866i	$-0.459372\pi$
$311$	4460.43	−	1449.28i	0.813272	−	0.264248i	0.685983	+	0.727618i	$0.259372\pi$
$312$	5442.68	−	3144.01i	0.987600	−	0.570495i
$313$	−8309.42	−	6037.15i	−1.50056	−	1.09022i	−0.970157	−	0.242479i	$-0.922039\pi$
$313$	−8309.42	−	6037.15i	−1.50056	−	1.09022i	−0.530406	−	0.847743i	$-0.677961\pi$
$314$	7961.04	+	5784.04i	1.43079	+	1.03953i
$315$	−2853.34	−	605.118i	−0.510373	−	0.108237i
$316$	−7585.44	+	2464.66i	−1.35036	+	0.438759i
$317$	−3912.82	−	5385.53i	−0.693268	−	0.954201i	−0.999997	−	0.00240424i	$-0.999235\pi$
$317$	−3912.82	−	5385.53i	−0.693268	−	0.954201i	0.306730	−	0.951797i	$-0.400765\pi$
$318$	−895.121	−	805.596i	−0.157849	−	0.142062i
$319$	1098.22	+	7086.50i	0.192755	+	1.24379i
$320$			2661.13i			0.464880i
$321$	673.027	−	6417.69i	0.117024	−	1.11589i
$322$	1732.11	+	5330.89i	0.299772	+	0.922605i
$323$	1677.66	+	545.105i	0.289002	+	0.0939023i
$324$	9612.42	+	4269.08i	1.64822	+	0.732010i
$325$	2616.56	−	3601.38i	0.446586	−	0.614673i
$326$	−1329.51	+	4091.81i	−0.225873	+	0.695166i
$327$	−1668.58	+	3750.02i	−0.282179	+	0.634179i
$328$	−5355.28	+	3890.84i	−0.901512	+	0.654987i
$329$	−5935.04			−0.994558
$330$	159.266	+	3230.40i	0.0265675	+	0.538871i
$331$	−10658.5			−1.76993			−0.884963	−	0.465661i	$-0.845817\pi$
$331$	−10658.5			−1.76993			−0.884963	+	0.465661i	$0.845817\pi$
$332$	7338.56	−	5331.78i	1.21312	−	0.881383i
$333$	8275.89	−	3689.25i	1.36191	−	0.607115i
$334$	4009.44	−	12339.8i	0.656847	−	2.02157i
$335$	697.030	−	959.379i	0.113680	−	0.156467i
$336$	931.945	+	4379.48i	0.151315	+	0.711072i
$337$	7996.29	+	2598.15i	1.29254	+	0.419971i	0.872980	−	0.487756i	$-0.162185\pi$
$337$	7996.29	+	2598.15i	1.29254	+	0.419971i	0.419560	+	0.907728i	$0.362185\pi$
$338$	−904.184	−	2782.79i	−0.145506	−	0.447823i
$339$	9588.13	+	1005.51i	1.53615	+	0.161097i
$340$		−	1177.91i		−	0.187886i
$341$	2579.81	−	5021.76i	0.409690	−	0.797489i
$342$	−9898.05	+	1044.95i	−1.56499	+	0.165218i
$343$	3757.39	+	5171.60i	0.591486	+	0.814111i
$344$	5590.10	−	1816.33i	0.876157	−	0.284681i
$345$	369.593	+	639.812i	0.0576759	+	0.0998444i
$346$	−3384.29	−	2458.83i	−0.525840	−	0.382045i
$347$	−6028.90	−	4380.26i	−0.932705	−	0.677650i	0.0139489	−	0.999903i	$-0.495560\pi$
$347$	−6028.90	−	4380.26i	−0.932705	−	0.677650i	−0.946654	+	0.322253i	$0.895560\pi$
$348$	7370.87	+	12759.9i	1.13540	+	1.96553i
$349$	−1741.35	+	565.799i	−0.267084	+	0.0867809i	−0.439498	−	0.898244i	$-0.644843\pi$
$349$	−1741.35	+	565.799i	−0.267084	+	0.0867809i	0.172413	+	0.985025i	$0.444843\pi$
$350$	9350.47	+	12869.8i	1.42801	+	1.96549i
$351$	−3273.87	+	4512.67i	−0.497852	+	0.686235i
$352$	−3498.11	+	1767.73i	−0.529686	+	0.267672i
$353$		−	3878.68i		−	0.584819i	−0.956293	−	0.292410i	$-0.905543\pi$
$353$		−	3878.68i		−	0.584819i	0.956293	−	0.292410i	$-0.0944570\pi$
$354$	−2714.69	−	284.691i	−0.407582	−	0.0427434i
$355$	659.565	+	2029.93i	0.0986086	+	0.303486i
$356$	−14465.5	−	4700.13i	−2.15357	−	0.699737i
$357$	734.942	+	3453.70i	0.108956	+	0.512015i
$358$	−4013.63	+	5524.28i	−0.592533	+	0.815552i
$359$	1553.45	−	4781.02i	0.228378	−	0.702876i	−0.769553	−	0.638583i	$-0.779521\pi$
$359$	1553.45	−	4781.02i	0.228378	−	0.702876i	0.997931	−	0.0642928i	$-0.0204792\pi$
$360$	1205.57	+	2704.40i	0.176498	+	0.395929i
$361$	−647.211	+	470.226i	−0.0943593	+	0.0685561i
$362$	−1616.09			−0.234640
$363$	−6011.60	+	3419.48i	−0.869221	+	0.494424i
$364$	−17192.2			−2.47559
$365$	−879.001	+	638.632i	−0.126052	+	0.0915822i
$366$	3185.94	−	7160.20i	0.455005	−	1.02259i
$367$	−2489.43	+	7661.67i	−0.354079	+	1.08974i	0.602462	+	0.798147i	$0.294186\pi$
$367$	−2489.43	+	7661.67i	−0.354079	+	1.08974i	−0.956541	+	0.291596i	$0.905814\pi$
$368$	666.701	−	917.635i	0.0944407	−	0.129986i
$369$	2933.35	−	5086.14i	0.413832	−	0.717544i
$370$	5445.38	+	1769.31i	0.765113	+	0.248600i
$371$	453.471	+	1395.64i	0.0634583	+	0.195305i
$372$	1209.99	−	11538.0i	0.168643	−	1.60811i
$373$			1236.05i			0.171582i	0.996313	+	0.0857912i	$0.0273418\pi$
$373$			1236.05i			0.171582i	−0.996313	+	0.0857912i	$0.972658\pi$
$374$	3494.56	−	1765.94i	0.483154	−	0.244157i
$375$	3298.01	+	2968.16i	0.454156	+	0.408734i
$376$	3541.33	+	4874.22i	0.485718	+	0.668534i
$377$	−7428.73	+	2413.74i	−1.01485	+	0.329745i
$378$	−11721.8	−	16110.1i	−1.59498	−	2.19211i
$379$	−3110.63	−	2260.00i	−0.421589	−	0.306302i	0.356688	−	0.934224i	$-0.383906\pi$
$379$	−3110.63	−	2260.00i	−0.421589	−	0.306302i	−0.778277	+	0.627921i	$0.783906\pi$
$380$	−3273.21	−	2378.13i	−0.441875	−	0.321041i
$381$	5296.95	−	3059.83i	0.712259	−	0.411443i
$382$	7343.27	−	2385.97i	0.983545	−	0.319573i
$383$	7203.22	+	9914.38i	0.961011	+	1.32272i	0.946459	+	0.322824i	$0.104632\pi$
$383$	7203.22	+	9914.38i	0.961011	+	1.32272i	0.0145520	+	0.999894i	$0.495368\pi$
$384$	−9172.15	+	10191.4i	−1.21892	+	1.35437i
$385$	1800.96	−	3505.69i	0.238404	−	0.464068i
$386$		−	572.382i		−	0.0754753i
$387$	−3872.78	+	3490.31i	−0.508694	+	0.458456i
$388$	−2218.03	−	6826.40i	−0.290215	−	0.893191i
$389$	7905.29	+	2568.59i	1.03037	+	0.334788i	0.774937	−	0.632039i	$-0.217782\pi$
$389$	7905.29	+	2568.59i	1.03037	+	0.334788i	0.255434	+	0.966827i	$0.417782\pi$
$390$	−3445.79	+	733.257i	−0.447396	+	0.0952050i
$391$	525.767	−	723.657i	0.0680031	−	0.0935982i
$392$	5231.71	−	16101.5i	0.674084	−	2.07462i
$393$	1412.22	+	628.368i	0.181264	+	0.0806539i
$394$	−8992.09	+	6533.14i	−1.14978	+	0.835367i
$395$	1991.58			0.253689
$396$	−8975.40	+	11019.0i	−1.13897	+	1.39829i
$397$	15216.8			1.92370			0.961851	−	0.273572i	$-0.0882053\pi$
$397$	15216.8			1.92370			0.961851	+	0.273572i	$0.0882053\pi$
$398$	2888.99	−	2098.97i	0.363849	−	0.264352i
$399$	11081.0	+	4930.53i	1.39034	+	0.618634i
$400$	994.756	−	3061.54i	0.124344	−	0.382693i
$401$	2779.16	−	3825.19i	0.346097	−	0.476361i	−0.600113	−	0.799915i	$-0.704878\pi$
$401$	2779.16	−	3825.19i	0.346097	−	0.476361i	0.946210	+	0.323554i	$0.104878\pi$
$402$	7922.64	−	1685.92i	0.982949	−	0.209170i
$403$	5848.50	+	1900.29i	0.722914	+	0.234889i
$404$	−3097.26	−	9532.38i	−0.381422	−	1.17390i
$405$	−1953.36	−	1755.54i	−0.239662	−	0.215392i
$406$		−	27913.3i		−	3.41211i
$407$	1875.01	+	12098.9i	0.228356	+	1.47351i
$408$	2397.87	−	2664.34i	0.290961	−	0.323295i
$409$	2525.42	+	3475.94i	0.305315	+	0.420230i	0.933913	−	0.357500i	$-0.116371\pi$
$409$	2525.42	+	3475.94i	0.305315	+	0.420230i	−0.628598	+	0.777730i	$0.716371\pi$
$410$	3528.55	−	1146.50i	0.425031	−	0.138101i
$411$	5590.17	−	3229.21i	0.670907	−	0.387555i
$412$	4328.85	+	3145.09i	0.517639	+	0.376087i
$413$	2690.93	+	1955.07i	0.320610	+	0.232937i
$414$	−1047.05	+	4937.20i	−0.124299	+	0.586112i
$415$	−2154.18	+	699.937i	−0.254807	+	0.0827917i
$416$	−2509.34	−	3453.81i	−0.295747	−	0.407060i
$417$	−6272.01	−	5644.72i	−0.736551	−	0.662885i
$418$	2148.05	−	13276.1i	0.251351	−	1.55348i
$419$		−	14558.6i		−	1.69746i	−0.528826	−	0.848730i	$-0.677368\pi$
$419$		−	14558.6i		−	1.69746i	0.528826	−	0.848730i	$-0.322632\pi$
$420$	844.695	−	8054.64i	0.0981354	−	0.935777i
$421$	2275.11	+	7002.06i	0.263378	+	0.810593i	0.992063	+	0.125744i	$0.0401318\pi$
$421$	2275.11	+	7002.06i	0.263378	+	0.810593i	−0.728685	+	0.684849i	$0.759868\pi$
$422$	−10186.0	−	3309.63i	−1.17499	−	0.381778i
$423$	−4629.25	−	2669.85i	−0.532109	−	0.306885i
$424$	875.607	−	1205.17i	0.100291	−	0.138038i
$425$	784.475	−	2414.37i	0.0895356	−	0.275562i
$426$	−5926.76	+	13320.0i	−0.674067	+	1.51492i
$427$	−7726.04	+	5613.30i	−0.875619	+	0.636174i
$428$	17917.1			2.02350
$429$	−4722.67	−	5869.10i	−0.531499	−	0.660519i
$430$	−3294.42			−0.369467
$431$	−11648.5	+	8463.12i	−1.30183	+	0.945834i	−0.999972	−	0.00751966i	$-0.997606\pi$
$431$	−11648.5	+	8463.12i	−1.30183	+	0.945834i	−0.301857	+	0.953353i	$0.597606\pi$
$432$	−1243.18	+	3835.16i	−0.138455	+	0.427128i
$433$	518.298	−	1595.16i	0.0575238	−	0.177040i	−0.918166	−	0.396196i	$-0.870330\pi$
$433$	518.298	−	1595.16i	0.0575238	−	0.177040i	0.975690	+	0.219155i	$0.0703302\pi$
$434$	−12916.9	+	17778.7i	−1.42865	+	1.96637i
$435$	−765.859	−	3598.99i	−0.0844141	−	0.396686i
$436$	−10838.8	−	3521.73i	−1.19056	−	0.386835i
$437$	−949.425	−	2922.03i	−0.103929	−	0.319862i
$438$	−7380.93	−	774.042i	−0.805193	−	0.0844410i
$439$			3555.94i			0.386596i	0.981140	+	0.193298i	$0.0619184\pi$
$439$			3555.94i			0.386596i	−0.981140	+	0.193298i	$0.938082\pi$
$440$	−3953.68	+	612.718i	−0.428374	+	0.0663868i
$441$	1576.59	+	14933.8i	0.170240	+	1.61255i
$442$	2506.80	+	3450.31i	0.269765	+	0.371300i
$443$	−10807.1	+	3511.45i	−1.15906	+	0.376600i	−0.824548	−	0.565792i	$-0.808570\pi$
$443$	−10807.1	+	3511.45i	−1.15906	+	0.376600i	−0.334509	+	0.942393i	$0.608570\pi$
$444$	12584.4	+	21785.2i	1.34511	+	2.32856i
$445$	3072.62	+	2232.39i	0.327317	+	0.237810i
$446$	−189.593	−	137.748i	−0.0201289	−	0.0146245i
$447$	−9143.80	−	15829.1i	−0.967532	−	1.67492i
$448$	21065.7	−	6844.65i	2.22156	−	0.721829i
$449$	−4710.80	−	6483.87i	−0.495137	−	0.681498i	0.486188	−	0.873854i	$-0.338387\pi$
$449$	−4710.80	−	6483.87i	−0.495137	−	0.681498i	−0.981325	+	0.192356i	$0.938387\pi$
$450$	1503.82	+	14244.6i	0.157535	+	1.49221i
$451$	5591.16	+	5628.50i	0.583763	+	0.587663i
$452$			26768.5i			2.78558i
$453$	−5626.59	−	590.063i	−0.583576	−	0.0612000i
$454$	9070.68	+	27916.7i	0.937683	+	2.88589i
$455$	4082.83	+	1326.59i	0.420672	+	0.136685i
$456$	−2562.59	−	12042.4i	−0.263168	−	1.23670i
$457$	1365.24	−	1879.09i	0.139744	−	0.192341i	−0.733409	−	0.679788i	$-0.762072\pi$
$457$	1365.24	−	1879.09i	0.139744	−	0.192341i	0.873153	+	0.487447i	$0.162072\pi$
$458$	1432.05	−	4407.38i	0.146103	−	0.449658i
$459$	−980.386	+	3024.45i	−0.0996961	+	0.307558i
$460$	−1659.78	+	1205.90i	−0.168234	+	0.122230i
$461$	7704.57			0.778390			0.389195	−	0.921155i	$-0.372753\pi$
$461$	7704.57			0.778390			0.389195	+	0.921155i	$0.372753\pi$
$462$	25162.4	−	9569.61i	2.53390	−	0.963677i
$463$	−6615.47			−0.664032			−0.332016	−	0.943274i	$-0.607729\pi$
$463$	−6615.47			−0.664032			−0.332016	+	0.943274i	$0.607729\pi$
$464$	−4569.71	+	3320.09i	−0.457206	+	0.332179i
$465$	−1177.65	+	2646.69i	−0.117445	+	0.263951i
$466$	−2343.97	+	7214.00i	−0.233009	+	0.717129i
$467$	2820.00	−	3881.39i	0.279430	−	0.384603i	−0.646115	−	0.763240i	$-0.723607\pi$
$467$	2820.00	−	3881.39i	0.279430	−	0.384603i	0.925545	+	0.378637i	$0.123607\pi$
$468$	−13409.7	−	7733.82i	−1.32449	−	0.763881i
$469$	−9387.33	−	3050.13i	−0.924236	−	0.300302i
$470$	−1043.51	−	3211.58i	−0.102411	−	0.315190i
$471$	1126.11	−	10738.1i	0.110166	−	1.05050i
$472$		−	3376.51i		−	0.329272i
$473$	−3177.27	−	6287.39i	−0.308860	−	0.611193i
$474$	10111.5	+	9100.21i	0.979824	+	0.881828i
$475$	−5125.30	−	7054.36i	−0.495084	−	0.681424i
$476$	−9324.44	+	3029.70i	−0.897868	+	0.291735i
$477$	−274.120	+	1292.57i	−0.0263126	+	0.124073i
$478$	8435.75	+	6128.93i	0.807202	+	0.586466i
$479$	2237.37	+	1625.54i	0.213420	+	0.155058i	0.689360	−	0.724419i	$-0.257892\pi$
$479$	2237.37	+	1625.54i	0.213420	+	0.155058i	−0.475940	+	0.879478i	$0.657892\pi$
$480$	1741.42	−	1005.95i	0.165593	−	0.0956562i
$481$	−12683.2	+	4121.01i	−1.20229	+	0.390649i
$482$	9397.70	+	12934.8i	0.888078	+	1.22233i
$483$	4114.17	−	4571.37i	0.387580	−	0.430651i
$484$	−11183.7	−	15610.6i	−1.05031	−	1.46605i
$485$			1792.29i			0.167802i
$486$	−1895.77	−	17838.7i	−0.176942	−	1.66498i
$487$	−6266.13	−	19285.2i	−0.583051	−	1.79445i	−0.606962	−	0.794731i	$-0.707612\pi$
$487$	−6266.13	−	19285.2i	−0.583051	−	1.79445i	0.0239114	−	0.999714i	$-0.492388\pi$
$488$	9219.96	+	2995.75i	0.855262	+	0.277892i
$489$	4617.23	−	982.538i	0.426991	−	0.0908628i
$490$	−5577.57	+	7676.87i	−0.514222	+	0.707766i
$491$	−4140.97	+	12744.6i	−0.380610	+	1.17140i	0.559005	+	0.829164i	$0.311183\pi$
$491$	−4140.97	+	12744.6i	−0.380610	+	1.17140i	−0.939615	+	0.342233i	$0.888817\pi$
$492$	14894.7	+	6627.42i	1.36485	+	0.607291i
$493$	−3603.72	+	2618.26i	−0.329216	+	0.239189i
$494$	14648.9			1.33418
$495$	2981.74	−	1924.24i	0.270746	−	0.174723i
$496$	4446.93			0.402567
$497$	14372.6	−	10442.3i	1.29718	−	0.942459i
$498$	−14135.3	−	6289.53i	−1.27193	−	0.565945i
$499$	6230.41	−	19175.2i	0.558940	−	1.72024i	−0.126363	−	0.991984i	$-0.540330\pi$
$499$	6230.41	−	19175.2i	0.558940	−	1.72024i	0.685303	−	0.728258i	$-0.259670\pi$
$500$	−7241.39	+	9966.92i	−0.647690	+	0.891468i
$501$	−13924.3	+	2963.07i	−1.24170	+	0.264232i
$502$	−22032.7	−	7158.86i	−1.95890	−	0.636486i
$503$	2567.73	+	7902.65i	0.227613	+	0.700520i	0.998016	+	0.0629630i	$0.0200550\pi$
$503$	2567.73	+	7902.65i	0.227613	+	0.700520i	−0.770403	+	0.637557i	$0.779945\pi$
$504$	18307.4	−	16499.4i	1.61801	−	1.45821i
$505$			2502.75i			0.220537i
$506$	−6065.97	−	3116.24i	−0.532935	−	0.273782i
$507$	−2147.65	+	2386.32i	−0.188127	+	0.209034i
$508$	9983.58	+	13741.2i	0.871948	+	1.20013i
$509$	5285.57	−	1717.39i	0.460273	−	0.149552i	−0.0696971	−	0.997568i	$-0.522203\pi$
$509$	5285.57	−	1717.39i	0.460273	−	0.149552i	0.529970	+	0.848017i	$0.322203\pi$
$510$	−1739.66	+	1004.93i	−0.151046	+	0.0872528i
$511$	7316.32	+	5315.62i	0.633375	+	0.460174i
$512$	−8159.05	−	5927.90i	−0.704263	−	0.511677i
$513$	6425.09	+	8830.49i	0.552972	+	0.759992i
$514$	6918.58	−	2247.98i	0.593707	−	0.192907i
$515$	−785.339	−	1080.93i	−0.0671964	−	0.0924879i
$516$	−10759.9	−	9683.77i	−0.917983	−	0.826171i
$517$	5122.90	−	5088.91i	0.435793	−	0.432901i
$518$		−	47656.8i		−	4.04232i
$519$	−478.716	+	4564.83i	−0.0404881	+	0.386077i
$520$	−1346.67	−	4144.62i	−0.113568	−	0.349526i
$521$	−13655.4	−	4436.90i	−1.14828	−	0.373098i	−0.327783	−	0.944753i	$-0.606302\pi$
$521$	−13655.4	−	4436.90i	−1.14828	−	0.373098i	−0.820494	+	0.571655i	$0.806302\pi$
$522$	12556.7	−	21772.0i	1.05286	−	1.82555i
$523$	−10872.8	+	14965.1i	−0.909053	+	1.25120i	0.0584360	+	0.998291i	$0.481389\pi$
$523$	−10872.8	+	14965.1i	−0.909053	+	1.25120i	−0.967489	+	0.252913i	$0.918611\pi$
$524$	−1326.24	+	4081.76i	−0.110567	+	0.340291i
$525$	7095.65	−	15947.0i	0.589866	−	1.32569i
$526$	23001.7	−	16711.7i	1.90670	−	1.38530i
$527$	3506.90			0.289873
$528$	−4559.53	−	2981.11i	−0.375811	−	0.245713i
$529$	10609.0			0.871952
$530$	−675.482	+	490.766i	−0.0553605	+	0.0402217i
$531$	1219.41	+	2735.43i	0.0996568	+	0.223555i
$532$	−10406.4	+	32027.8i	−0.848077	+	2.61011i
$533$	−5079.36	+	6991.13i	−0.412779	+	0.568142i
$534$	5399.53	+	25373.9i	0.437566	+	2.05625i
$535$	−4254.99	−	1382.53i	−0.343849	−	0.111723i
$536$	3096.29	+	9529.40i	0.249514	+	0.767924i
$537$	7451.32	+	781.424i	0.598786	+	0.0627950i
$538$			34986.7i			2.80369i
$539$	−20030.5	−	3240.91i	−1.60070	−	0.258990i
$540$	4282.19	−	5902.53i	0.341252	−	0.470379i
$541$	587.839	+	809.091i	0.0467157	+	0.0642986i	0.831736	−	0.555172i	$-0.187347\pi$
$541$	587.839	+	809.091i	0.0467157	+	0.0642986i	−0.785020	+	0.619470i	$0.787347\pi$
$542$	−30970.5	+	10062.9i	−2.45442	+	0.797489i
$543$	886.947	+	1535.42i	0.0700968	+	0.121346i
$544$	−1969.63	−	1431.02i	−0.155234	−	0.112784i
$545$	2302.26	+	1672.69i	0.180950	+	0.131468i
$546$	14667.4	+	25391.1i	1.14964	+	1.99018i
$547$	−377.124	+	122.535i	−0.0294783	+	0.00957809i	−0.323719	−	0.946153i	$-0.604933\pi$
$547$	−377.124	+	122.535i	−0.0294783	+	0.00957809i	0.294241	+	0.955731i	$0.404933\pi$
$548$	10536.2	+	14501.9i	0.821325	+	1.13046i
$549$	−8551.32	+	902.777i	−0.664775	+	0.0701814i
$550$	−19106.0	−	3091.32i	−1.48124	−	0.239662i
$551$			15300.2i			1.18296i
$552$	−6209.14	−	651.156i	−0.478765	−	0.0502084i
$553$	−5122.52	−	15765.5i	−0.393909	−	1.21233i
$554$	−6367.37	−	2068.89i	−0.488310	−	0.158662i
$555$	−1307.56	−	6144.61i	−0.100005	−	0.469954i
$556$	13771.3	−	18954.6i	1.05042	−	1.44578i
$557$	−547.966	+	1686.46i	−0.0416841	+	0.128290i	−0.969733	−	0.244168i	$-0.921485\pi$
$557$	−547.966	+	1686.46i	−0.0416841	+	0.128290i	0.928049	+	0.372459i	$0.121485\pi$
$558$	−18072.7	+	8056.49i	−1.37111	+	0.611216i
$559$	6207.78	−	4510.22i	0.469698	−	0.341255i
$560$	3104.40			0.234258
$561$	−3595.69	−	2350.94i	−0.270607	−	0.176928i
$562$	1509.84			0.113325
$563$	−3873.68	+	2814.39i	−0.289975	+	0.210679i	−0.723257	−	0.690579i	$-0.757356\pi$
$563$	−3873.68	+	2814.39i	−0.289975	+	0.210679i	0.433281	+	0.901259i	$0.357356\pi$
$564$	6032.08	−	13556.7i	0.450348	−	1.01213i
$565$	2065.52	−	6357.02i	0.153800	−	0.473348i
$566$	20197.4	−	27799.3i	1.49993	−	2.06448i
$567$	−8872.80	+	19978.3i	−0.657183	+	1.47974i
$568$	−17151.7	−	5572.94i	−1.26703	−	0.411682i
$569$	−2817.82	−	8672.36i	−0.207608	−	0.638953i	−0.999596	−	0.0284161i	$-0.990954\pi$
$569$	−2817.82	−	8672.36i	−0.207608	−	0.638953i	0.791988	−	0.610537i	$-0.209046\pi$
$570$	−719.735	+	6863.08i	−0.0528884	+	0.504321i
$571$		−	2615.36i		−	0.191680i	−0.995397	−	0.0958401i	$-0.969446\pi$
$571$		−	2615.36i		−	0.191680i	0.995397	−	0.0958401i	$-0.0305537\pi$
$572$	14839.6	−	14741.2i	1.08475	−	1.07755i
$573$	−6297.04	−	5667.25i	−0.459097	−	0.413181i
$574$	−18151.5	−	24983.4i	−1.31991	−	1.81670i
$575$	−4205.17	+	1366.34i	−0.304988	+	0.0990965i
$576$	19510.0	+	4137.55i	1.41131	+	0.299302i
$577$	16380.0	+	11900.8i	1.18182	+	0.858639i	0.992375	−	0.123253i	$-0.0393326\pi$
$577$	16380.0	+	11900.8i	1.18182	+	0.858639i	0.189440	+	0.981892i	$0.439333\pi$
$578$	−16855.7	−	12246.4i	−1.21298	−	0.881285i
$579$	−543.811	+	314.137i	−0.0390329	+	0.0225477i
$580$	9716.71	−	3157.15i	0.695628	−	0.226023i
$581$	11081.5	+	15252.4i	0.791287	+	1.08911i
$582$	−8189.59	+	9099.70i	−0.583281	+	0.648101i
$583$	−1588.09	−	815.841i	−0.112816	−	0.0579566i
$584$		−	9180.33i		−	0.650488i
$585$	2587.79	+	2871.36i	0.182892	+	0.202934i
$586$	12545.5	+	38611.2i	0.884388	+	2.72187i
$587$	25073.9	+	8147.01i	1.76305	+	0.572850i	0.997509	−	0.0705343i	$-0.0224704\pi$
$587$	25073.9	+	8147.01i	1.76305	+	0.572850i	0.765543	+	0.643385i	$0.222470\pi$
$588$	−40782.7	+	8678.48i	−2.86029	+	0.608664i
$589$	7080.20	−	9745.05i	0.495305	−	0.681728i
$590$	−584.811	+	1799.86i	−0.0408072	+	0.125592i
$591$	11142.1	+	4957.70i	0.775508	+	0.345064i
$592$	−7801.93	+	5668.43i	−0.541651	+	0.393532i
$593$	25415.1			1.75999			0.879994	−	0.474984i	$-0.157546\pi$
$593$	25415.1			1.75999			0.879994	+	0.474984i	$0.157546\pi$
$594$	23931.2	+	3855.00i	1.65304	+	0.266284i
$595$	2448.16			0.168680
$596$	41063.4	−	29834.3i	2.82219	−	2.05044i
$597$	−3579.75	−	1592.82i	−0.245409	−	0.109195i
$598$	2295.43	−	7064.61i	0.156968	−	0.483099i
$599$	−389.495	+	536.094i	−0.0265682	+	0.0365679i	−0.822094	−	0.569351i	$-0.807194\pi$
$599$	−389.495	+	536.094i	−0.0265682	+	0.0365679i	0.795526	+	0.605919i	$0.207194\pi$
$600$	−17330.5	+	3687.90i	−1.17919	+	0.250930i
$601$	11979.2	+	3892.29i	0.813051	+	0.264176i	0.685889	−	0.727706i	$-0.259413\pi$
$601$	11979.2	+	3892.29i	0.813051	+	0.264176i	0.127161	+	0.991882i	$0.459413\pi$
$602$	8473.53	+	26078.8i	0.573680	+	1.76561i
$603$	−5949.91	−	6601.90i	−0.401823	−	0.445855i
$604$		−	15708.5i		−	1.05823i
$605$	1451.37	+	4570.18i	0.0975319	+	0.307114i
$606$	−11435.9	+	12706.8i	−0.766590	+	0.851780i
$607$	1265.09	+	1741.25i	0.0845937	+	0.116433i	0.849216	−	0.528045i	$-0.177075\pi$
$607$	1265.09	+	1741.25i	0.0845937	+	0.116433i	−0.764623	+	0.644478i	$0.777075\pi$
$608$	−7953.10	+	2584.12i	−0.530495	+	0.172368i
$609$	−26520.0	+	15319.5i	−1.76461	+	1.01934i
$610$	−4395.88	−	3193.79i	−0.291777	−	0.211988i
$611$	6363.12	+	4623.08i	0.421317	+	0.306104i
$612$	−8635.84	−	1831.43i	−0.570397	−	0.120966i
$613$	−22207.2	+	7215.55i	−1.46320	+	0.475422i	−0.929045	−	0.369966i	$-0.879369\pi$
$613$	−22207.2	+	7215.55i	−1.46320	+	0.475422i	−0.534152	+	0.845388i	$0.679369\pi$
$614$	−14271.7	−	19643.3i	−0.938045	−	1.29111i
$615$	−3025.82	−	2723.20i	−0.198395	−	0.178553i
$616$	15019.5	+	29721.7i	0.982393	+	1.94403i
$617$			18404.8i			1.20089i	0.799666	+	0.600444i	$0.205010\pi$
$617$			18404.8i			1.20089i	−0.799666	+	0.600444i	$0.794990\pi$
$618$	951.856	−	9076.48i	0.0619567	−	0.590792i
$619$	988.749	+	3043.06i	0.0642022	+	0.197594i	0.978012	−	0.208548i	$-0.0668738\pi$
$619$	988.749	+	3043.06i	0.0642022	+	0.197594i	−0.913810	+	0.406142i	$0.866874\pi$
$620$	−7649.77	−	2485.56i	−0.495520	−	0.161004i
$621$	5265.41	−	1714.87i	0.340247	−	0.110814i
$622$	13055.1	−	17968.8i	0.841580	−	1.15834i
$623$	9768.69	−	30064.9i	0.628209	−	1.93343i
$624$	2412.21	−	5421.29i	0.154753	−	0.347797i
$625$	−8839.60	+	6422.35i	−0.565734	+	0.411030i
$626$	−48641.3			−3.10559
$627$	−13792.3	+	5245.41i	−0.878488	+	0.334102i
$628$	29979.0			1.90492
$629$	−6152.68	+	4470.19i	−0.390022	+	0.283367i
$630$	−12616.5	+	5624.22i	−0.797864	+	0.355674i
$631$	1039.41	−	3198.96i	0.0655754	−	0.201820i	−0.912900	−	0.408183i	$-0.866163\pi$
$631$	1039.41	−	3198.96i	0.0655754	−	0.201820i	0.978476	+	0.206362i	$0.0661626\pi$
$632$	−9891.07	+	13613.9i	−0.622540	+	0.856853i
$633$	2445.90	+	11494.0i	0.153579	+	0.721713i
$634$	−29982.6	−	9741.94i	−1.87817	−	0.610256i
$635$	−1310.61	−	4033.64i	−0.0819054	−	0.252079i
$636$	−3648.78	−	382.649i	−0.227490	−	0.0238570i
$637$		−	22101.7i		−	1.37473i
$638$	23933.8	+	24093.7i	1.48519	+	1.49511i
$639$	15907.9	−	1679.42i	0.984830	−	0.103970i
$640$	5587.64	+	7690.73i	0.345111	+	0.475004i
$641$	12629.5	−	4103.58i	0.778215	−	0.252857i	0.107137	−	0.994244i	$-0.465832\pi$
$641$	12629.5	−	4103.58i	0.778215	−	0.252857i	0.671078	+	0.741387i	$0.265832\pi$
$642$	−15285.9	−	26461.8i	−0.939696	−	1.62673i
$643$	2328.32	+	1691.62i	0.142799	+	0.103750i	0.656891	−	0.753985i	$-0.271871\pi$
$643$	2328.32	+	1691.62i	0.142799	+	0.103750i	−0.514092	+	0.857735i	$0.671871\pi$
$644$	13815.1	+	10037.3i	0.845330	+	0.614168i
$645$	1808.06	+	3129.98i	0.110376	+	0.191074i
$646$	7945.04	−	2581.50i	0.483891	−	0.157226i
$647$	−12931.5	−	17798.7i	−0.785765	−	1.08151i	−0.994623	−	0.103566i	$-0.966975\pi$
$647$	−12931.5	−	17798.7i	−0.785765	−	1.08151i	0.208858	−	0.977946i	$-0.433025\pi$
$648$	21701.7	−	4633.80i	1.31562	−	0.280915i
$649$	−3999.05	+	619.748i	−0.241874	+	0.0374842i
$650$		−	21081.6i		−	1.27214i
$651$	23980.4	+	2514.83i	1.44372	+	0.151404i
$652$	4050.38	+	12465.8i	0.243290	+	0.748770i
$653$	−18419.3	−	5984.78i	−1.10383	−	0.358656i	−0.300255	−	0.953859i	$-0.597072\pi$
$653$	−18419.3	−	5984.78i	−1.10383	−	0.358656i	−0.803575	+	0.595203i	$0.797072\pi$
$654$	4045.78	+	19012.3i	0.241900	+	1.13676i
$655$	629.916	−	867.005i	0.0375769	−	0.0517201i
$656$	−1931.06	+	5943.18i	−0.114931	+	0.353723i
$657$	3315.43	+	7437.32i	0.196875	+	0.441640i
$658$	−22739.1	+	16520.9i	−1.34721	+	0.978804i
$659$	−18331.7			−1.08361			−0.541806	−	0.840504i	$-0.682259\pi$
$659$	−18331.7			−1.08361			−0.541806	+	0.840504i	$0.682259\pi$
$660$	6177.21	+	7676.72i	0.364315	+	0.452751i
$661$	−25570.9			−1.50468			−0.752338	−	0.658777i	$-0.771074\pi$
$661$	−25570.9			−1.50468			−0.752338	+	0.658777i	$0.771074\pi$
$662$	−40836.4	+	29669.3i	−2.39751	+	1.74189i
$663$	1902.30	−	4275.29i	0.111432	−	0.250435i
$664$	5914.06	−	18201.6i	0.345648	−	1.06379i
$665$	4942.68	−	6803.01i	0.288224	−	0.396706i
$666$	21438.2	−	37171.7i	1.24732	−	2.16272i
$667$	7378.71	+	2397.49i	0.428343	+	0.139177i
$668$	−12214.9	−	37593.4i	−0.707495	−	2.17745i
$669$	−26.8185	+	255.729i	−0.00154987	+	0.0147789i
$670$		−	5615.97i		−	0.323827i
$671$	1855.79	−	11469.7i	0.106769	−	0.659888i
$672$	−12442.2	−	11197.8i	−0.714240	−	0.642806i
$673$	14931.5	+	20551.4i	0.855226	+	1.17712i	0.982687	+	0.185274i	$0.0593172\pi$
$673$	14931.5	+	20551.4i	0.855226	+	1.17712i	−0.127461	+	0.991844i	$0.540683\pi$
$674$	37868.7	−	12304.3i	2.16417	−	0.703181i
$675$	12708.2	−	9246.52i	0.724650	−	0.527257i
$676$	−7211.68	−	5239.59i	−0.410314	−	0.298111i
$677$	2170.78	+	1577.16i	0.123235	+	0.0895351i	0.647695	−	0.761900i	$-0.275733\pi$
$677$	2170.78	+	1577.16i	0.123235	+	0.0895351i	−0.524461	+	0.851435i	$0.675733\pi$
$678$	39534.3	−	22837.3i	2.23939	−	1.29360i
$679$	14187.9	−	4609.93i	0.801888	−	0.260549i
$680$	−1460.77	−	2010.58i	−0.0823794	−	0.113386i
$681$	21545.0	−	23939.3i	1.21234	−	1.34707i
$682$	−4094.61	−	26421.3i	−0.229898	−	1.48346i
$683$			23150.1i			1.29694i	0.761239	+	0.648472i	$0.224592\pi$
$683$			23150.1i			1.29694i	−0.761239	+	0.648472i	$0.775408\pi$
$684$	−22524.4	+	20299.9i	−1.25913	+	1.13478i
$685$	−1383.16	−	4256.93i	−0.0771501	−	0.237444i
$686$	28791.6	+	9354.95i	1.60243	+	0.520661i
$687$	−4973.33	+	1058.32i	−0.276193	+	0.0587733i
$688$	3261.52	−	4489.10i	0.180733	−	0.248757i
$689$	600.950	−	1849.53i	0.0332284	−	0.102266i
$690$	3197.03	+	1422.52i	0.176390	+	0.0784848i
$691$	−9343.66	+	6788.57i	−0.514399	+	0.373733i	−0.814490	−	0.580178i	$-0.802983\pi$
$691$	−9343.66	+	6788.57i	−0.514399	+	0.373733i	0.300091	+	0.953911i	$0.402983\pi$
$692$	−12744.3			−0.700092
$693$	−22901.7	−	18654.4i	−1.25536	−	1.02254i
$694$	−35291.7			−1.93034
$695$	−4733.02	+	3438.74i	−0.258322	+	0.187682i
$696$	28405.3	+	12639.0i	1.54698	+	0.688333i
$697$	−1522.85	+	4686.85i	−0.0827577	+	0.254702i
$698$	−5096.72	+	7015.03i	−0.276381	+	0.380405i
$699$	8140.34	−	1732.25i	0.440481	−	0.0937335i
$700$	46092.0	+	14976.2i	2.48873	+	0.808639i
$701$	−3137.61	−	9656.57i	−0.169053	−	0.520291i	0.830259	−	0.557377i	$-0.188192\pi$
$701$	−3137.61	−	9656.57i	−0.169053	−	0.520291i	−0.999312	+	0.0370867i	$0.988192\pi$
$702$	18.3070	+	26402.8i	0.000984264	+	1.41953i
$703$			26122.2i			1.40145i
$704$	−12314.2	+	23970.5i	−0.659247	+	1.28327i
$705$	−2478.57	+	2754.01i	−0.132409	+	0.147124i
$706$	−10796.8	−	14860.5i	−0.575556	−	0.792185i
$707$	19812.0	−	6437.30i	1.05390	−	0.342432i
$708$	−7200.66	+	4159.52i	−0.382228	+	0.220797i
$709$	−8211.02	−	5965.65i	−0.434938	−	0.316001i	0.348682	−	0.937241i	$-0.386629\pi$
$709$	−8211.02	−	5965.65i	−0.434938	−	0.316001i	−0.783620	+	0.621240i	$0.786629\pi$
$710$	8177.58	+	5941.36i	0.432252	+	0.314050i
$711$	3096.53	−	14601.2i	0.163332	−	0.770166i
$712$	−30519.9	+	9916.53i	−1.60644	+	0.521963i
$713$	−3590.23	−	4941.53i	−0.188577	−	0.259554i
$714$	12429.6	+	11186.5i	0.651494	+	0.586336i
$715$	−4661.60	+	2355.69i	−0.243824	+	0.123214i
$716$			20802.8i			1.08581i
$717$	1193.26	−	11378.4i	0.0621521	−	0.592655i
$718$	−7356.79	−	22641.9i	−0.382386	−	1.17686i
$719$	−21065.9	−	6844.74i	−1.09267	−	0.355029i	−0.293390	−	0.955993i	$-0.594783\pi$
$719$	−21065.9	−	6844.74i	−1.09267	−	0.355029i	−0.799276	+	0.600964i	$0.794783\pi$
$720$	2421.39	+	1396.50i	0.125333	+	0.0722838i
$721$	−6536.73	+	8997.03i	−0.337643	+	0.464725i
$722$	−1170.75	+	3603.18i	−0.0603472	+	0.185729i
$723$	7131.49	−	16027.6i	0.366837	−	0.824442i
$724$	−3983.15	+	2893.92i	−0.204465	+	0.148552i
$725$	22018.9			1.12795
$726$	−13513.9	+	29835.2i	−0.690836	+	1.52519i
$727$	−9165.45			−0.467576			−0.233788	−	0.972288i	$-0.575112\pi$
$727$	−9165.45			−0.467576			−0.233788	+	0.972288i	$0.575112\pi$
$728$	−29345.3	+	21320.6i	−1.49397	+	1.08543i
$729$	−15907.8	+	11591.4i	−0.808201	+	0.588907i
$730$	−1590.03	+	4893.62i	−0.0806161	+	0.248111i
$731$	2572.07	−	3540.15i	0.130139	−	0.179121i
$732$	−4969.42	−	23352.7i	−0.250922	−	1.17916i
$733$	14562.5	+	4731.64i	0.733803	+	0.238427i	0.651997	−	0.758221i	$-0.273931\pi$
$733$	14562.5	+	4731.64i	0.733803	+	0.238427i	0.0818055	+	0.996648i	$0.473931\pi$
$734$	11789.4	+	36284.0i	0.592854	+	1.82462i
$735$	10354.8	+	1085.91i	0.519649	+	0.0544959i
$736$			4240.40i			0.212369i
$737$	10718.1	−	5416.26i	0.535692	−	0.270706i
$738$	−2919.27	−	27652.0i	−0.145610	−	1.37925i
$739$	20556.2	+	28293.2i	1.02324	+	1.40836i	0.909909	+	0.414807i	$0.136151\pi$
$739$	20556.2	+	28293.2i	1.02324	+	1.40836i	0.113328	+	0.993558i	$0.463849\pi$
$740$	16589.5	−	5390.25i	0.824110	−	0.267769i
$741$	−8039.67	−	13917.7i	−0.398576	−	0.689985i
$742$	5622.34	+	4084.87i	0.278170	+	0.202103i
$743$	−6106.25	−	4436.45i	−0.301503	−	0.219054i	0.426739	−	0.904375i	$-0.359662\pi$
$743$	−6106.25	−	4436.45i	−0.301503	−	0.219054i	−0.728242	+	0.685320i	$0.759662\pi$
$744$	−12243.3	−	21194.7i	−0.603308	−	1.04440i
$745$	−12053.9	+	3916.54i	−0.592779	+	0.192606i
$746$	3440.70	+	4735.72i	0.168865	+	0.232422i
$747$	1782.22	+	16881.6i	0.0872931	+	0.826861i
$748$	5450.73	−	10610.2i	0.266442	−	0.518647i
$749$			37238.8i			1.81666i
$750$	20898.0	+	2191.59i	1.01745	+	0.106701i
$751$	−4729.28	−	14555.2i	−0.229792	−	0.707227i	−0.997770	−	0.0667507i	$-0.978737\pi$
$751$	−4729.28	−	14555.2i	−0.229792	−	0.707227i	0.767978	−	0.640477i	$-0.221263\pi$
$752$	5409.31	+	1757.59i	0.262310	+	0.0852297i
$753$	5290.57	+	24861.9i	0.256041	+	1.20321i
$754$	−21743.0	+	29926.6i	−1.05018	+	1.44544i
$755$	−1212.11	+	3730.48i	−0.0584278	+	0.179822i
$756$	−57739.0	−	18716.3i	−2.77771	−	0.900403i
$757$	18433.0	−	13392.4i	0.885020	−	0.643005i	−0.0495547	−	0.998771i	$-0.515780\pi$
$757$	18433.0	−	13392.4i	0.885020	−	0.643005i	0.934575	+	0.355767i	$0.115780\pi$
$758$	−18208.9			−0.872527
$759$	368.458	+	7473.46i	0.0176208	+	0.357404i
$760$	−8536.24			−0.407424
$761$	−6732.74	+	4891.62i	−0.320712	+	0.233011i	−0.736479	−	0.676460i	$-0.763513\pi$
$761$	−6732.74	+	4891.62i	−0.320712	+	0.233011i	0.415767	+	0.909471i	$0.363513\pi$
$762$	11777.0	−	26467.9i	0.559887	−	1.25831i
$763$	7319.52	−	22527.2i	0.347293	−	1.06886i
$764$	13826.3	−	19030.3i	0.654736	−	0.901166i
$765$	1909.53	+	1101.29i	0.0902474	+	0.0520488i
$766$	55195.8	+	17934.2i	2.60353	+	0.845939i
$767$	−1362.12	−	4192.17i	−0.0641242	−	0.197354i
$768$	−3569.85	+	34040.5i	−0.167729	+	1.59939i
$769$		−	21833.4i		−	1.02384i	−0.859033	−	0.511920i	$-0.828934\pi$
$769$		−	21833.4i		−	1.02384i	0.859033	−	0.511920i	$-0.171066\pi$
$770$	−2858.44	−	18444.6i	−0.133781	−	0.863246i
$771$	−5932.86	−	5339.49i	−0.277129	−	0.249412i
$772$	−1024.96	−	1410.74i	−0.0477840	−	0.0657691i
$773$	2247.96	−	730.407i	0.104597	−	0.0339857i	−0.256251	−	0.966610i	$-0.582487\pi$
$773$	2247.96	−	730.407i	0.104597	−	0.0339857i	0.360848	+	0.932625i	$0.382487\pi$
$774$	−5122.20	+	24152.9i	−0.237873	+	1.12165i
$775$	−14024.4	−	10189.3i	−0.650026	−	0.472272i
$776$	−12251.6	−	8901.31i	−0.566762	−	0.411777i
$777$	−45278.0	+	26155.2i	−2.09053	+	1.20761i
$778$	37437.8	−	12164.3i	1.72521	−	0.560553i
$779$	9949.41	+	13694.2i	0.457605	+	0.629840i
$780$	−7179.75	+	7977.63i	−0.329585	+	0.366211i
$781$	−3452.29	+	21337.0i	−0.158172	+	0.977589i
$782$		−	4236.11i		−	0.193712i
$783$	−27576.7	+	19.1210i	−1.25863	+	0.000872705i
$784$	−4938.91	−	15200.4i	−0.224987	−	0.692438i
$785$	−7119.45	−	2313.25i	−0.323699	−	0.105176i
$786$	7159.81	−	1523.59i	0.324913	−	0.0691410i
$787$	−2059.32	+	2834.42i	−0.0932744	+	0.128381i	−0.853104	−	0.521742i	$-0.825283\pi$
$787$	−2059.32	+	2834.42i	−0.0932744	+	0.128381i	0.759829	+	0.650123i	$0.225283\pi$
$788$	−10463.8	+	32204.3i	−0.473043	+	1.45588i
$789$	−28501.5	−	12681.8i	−1.28603	−	0.572222i
$790$	7630.40	−	5543.81i	0.343642	−	0.249671i
$791$	−55635.3			−2.50084
$792$	−1655.10	+	29939.0i	−0.0742569	+	1.34323i
$793$	12655.8			0.566733
$794$	58300.7	−	42357.9i	2.60581	−	1.89323i
$795$	836.990	+	372.420i	0.0373396	+	0.0166143i
$796$	3361.82	−	10346.6i	0.149694	−	0.460712i
$797$	6218.98	−	8559.69i	0.276396	−	0.380426i	−0.648140	−	0.761521i	$-0.724453\pi$
$797$	6218.98	−	8559.69i	0.276396	−	0.380426i	0.924536	+	0.381095i	$0.124453\pi$
$798$	56179.9	−	11955.0i	2.49216	−	0.530328i
$799$	4265.84	+	1386.05i	0.188879	+	0.0613706i
$800$	3718.87	+	11445.5i	0.164353	+	0.505825i
$801$	21144.0	−	19055.9i	0.932692	−	0.840581i
$802$		−	22391.7i		−	0.985884i
$803$	−10873.0	+	1685.02i	−0.477831	+	0.0740513i
$804$	16507.9	−	18342.4i	0.724113	−	0.804583i
$805$	−2506.34	−	3449.68i	−0.109735	−	0.151037i
$806$	27697.2	−	8999.38i	1.21041	−	0.393287i
$807$	33240.4	−	19201.6i	1.44996	−	0.837581i
$808$	−17108.1	−	12429.8i	−0.744879	−	0.541186i
$809$	−10339.0	−	7511.72i	−0.449320	−	0.326450i	0.340007	−	0.940423i	$-0.389570\pi$
$809$	−10339.0	−	7511.72i	−0.449320	−	0.326450i	−0.789327	+	0.613973i	$0.789570\pi$
$810$	−12370.7	−	1288.66i	−0.536622	−	0.0558997i
$811$	2674.98	−	869.153i	0.115821	−	0.0376327i	−0.250533	−	0.968108i	$-0.580606\pi$
$811$	2674.98	−	869.153i	0.115821	−	0.0376327i	0.366354	+	0.930475i	$0.380606\pi$
$812$	−49984.4	−	68797.7i	−2.16023	−	2.97331i
$813$	26558.0	+	23901.8i	1.14567	+	1.03109i
$814$	40862.6	+	41135.5i	1.75950	+	1.77125i
$815$		−	3272.93i		−	0.140670i
$816$	352.933	−	3365.41i	0.0151411	−	0.144379i
$817$	−4644.62	−	14294.7i	−0.198892	−	0.612126i
$818$	19351.4	+	6287.66i	0.827147	+	0.268756i
$819$	16073.9	−	27870.5i	0.685796	−	1.18910i
$820$	6643.75	−	9144.33i	0.282939	−	0.389432i
$821$	−5396.04	+	16607.3i	−0.229383	+	0.705967i	0.768435	+	0.639928i	$0.221036\pi$
$821$	−5396.04	+	16607.3i	−0.229383	+	0.705967i	−0.997817	+	0.0660384i	$0.978964\pi$
$822$	12428.9	−	27933.1i	0.527381	−	1.18525i
$823$	7263.11	−	5276.96i	0.307626	−	0.223503i	−0.423251	−	0.906012i	$-0.639111\pi$
$823$	7263.11	−	5276.96i	0.307626	−	0.223503i	0.730877	+	0.682509i	$0.239111\pi$
$824$	11289.2			0.477281
$825$	7548.82	+	19848.9i	0.318565	+	0.837636i
$826$	15752.0			0.663539
$827$	12478.5	−	9066.20i	0.524694	−	0.381212i	−0.293675	−	0.955905i	$-0.594878\pi$
$827$	12478.5	−	9066.20i	0.524694	−	0.381212i	0.818369	+	0.574693i	$0.194878\pi$
$828$	6260.40	+	14043.6i	0.262758	+	0.589432i
$829$	−13225.8	+	40704.9i	−0.554103	+	1.70535i	0.144198	+	0.989549i	$0.453940\pi$
$829$	−13225.8	+	40704.9i	−0.554103	+	1.70535i	−0.698301	+	0.715805i	$0.746060\pi$
$830$	−6305.03	+	8678.13i	−0.263676	+	0.362919i
$831$	1528.95	+	7185.00i	0.0638253	+	0.299934i
$832$	−27916.7	−	9070.69i	−1.16327	−	0.377968i
$833$	−3894.88	−	11987.2i	−0.162004	−	0.498598i
$834$	−39743.0	−	4167.87i	−1.65010	−	0.173047i
$835$			9870.27i			0.409072i
$836$	−18479.2	−	36567.9i	−0.764495	−	1.51283i
$837$	17573.1	+	12749.0i	0.725704	+	0.526487i
$838$	−40525.8	−	55779.0i	−1.67057	−	2.29935i
$839$	−6014.79	+	1954.32i	−0.247501	+	0.0804180i	−0.430140	−	0.902762i	$-0.641536\pi$
$839$	−6014.79	+	1954.32i	−0.247501	+	0.0804180i	0.182639	+	0.983180i	$0.441536\pi$
$840$	−8547.02	−	14796.0i	−0.351072	−	0.607750i
$841$	−11526.1	−	8374.21i	−0.472595	−	0.343360i
$842$	28207.8	+	20494.2i	1.15452	+	0.838808i
$843$	−828.637	−	1434.48i	−0.0338550	−	0.0586073i
$844$	−31031.9	+	10082.9i	−1.26559	+	0.411216i
$845$	1308.34	+	1800.78i	0.0532643	+	0.0733120i
$846$	−25168.1	+	2657.03i	−1.02281	+	0.107980i
$847$	32444.8	−	23244.1i	1.31619	−	0.942947i
$848$		−	1406.30i		−	0.0569488i
$849$	−37496.6	−	3932.28i	−1.51576	−	0.158958i
$850$	−3715.11	−	11433.9i	−0.149914	−	0.461389i
$851$	12597.8	+	4093.27i	0.507458	+	0.164883i
$852$	9244.53	+	43442.7i	0.371728	+	1.74686i
$853$	2300.51	−	3166.38i	0.0923423	−	0.127098i	−0.760346	−	0.649518i	$-0.774971\pi$
$853$	2300.51	−	3166.38i	0.0923423	−	0.127098i	0.852688	+	0.522420i	$0.174971\pi$
$854$	−13975.7	+	43012.8i	−0.559999	+	1.72350i
$855$	6915.52	−	3082.82i	0.276615	−	0.123310i
$856$	30582.7	−	22219.7i	1.22114	−	0.887211i
$857$	8792.80			0.350474			0.175237	−	0.984526i	$-0.443931\pi$
$857$	8792.80			0.350474			0.175237	+	0.984526i	$0.443931\pi$
$858$	−34431.5	−	9340.30i	−1.37001	−	0.371646i
$859$	4177.56			0.165933			0.0829666	−	0.996552i	$-0.473561\pi$
$859$	4177.56			0.165933			0.0829666	+	0.996552i	$0.473561\pi$
$860$	−8119.71	+	5899.32i	−0.321953	+	0.233913i
$861$	−13774.3	+	30956.9i	−0.545213	+	1.22533i
$862$	−21071.1	+	64850.1i	−0.832579	+	2.56242i
$863$	−19276.4	+	26531.7i	−0.760344	+	1.04652i	0.236841	+	0.971548i	$0.423888\pi$
$863$	−19276.4	+	26531.7i	−0.760344	+	1.04652i	−0.997185	+	0.0749756i	$0.976112\pi$
$864$	−4667.49	−	14331.2i	−0.183786	−	0.564304i
$865$	3026.52	+	983.377i	0.118965	+	0.0386541i
$866$	−2454.55	−	7554.33i	−0.0963153	−	0.296428i
$867$	−2384.28	+	22735.5i	−0.0933961	+	0.890585i
$868$			66949.2i			2.61798i
$869$	17939.4	+	9215.93i	0.700291	+	0.359757i
$870$	−12952.5	−	11657.1i	−0.504749	−	0.454267i
$871$	7688.53	+	10582.4i	0.299100	+	0.411675i
$872$	−22868.1	+	7430.29i	−0.888086	+	0.288557i
$873$	13140.1	+	2786.67i	0.509423	+	0.108035i
$874$	−11771.4	−	8552.43i	−0.455576	−	0.330996i
$875$	−20715.1	−	15050.4i	−0.800341	−	0.581482i
$876$	−19577.8	+	11309.3i	−0.755104	+	0.436192i
$877$	−30301.8	+	9845.67i	−1.16673	+	0.379093i	−0.827421	−	0.561583i	$-0.810193\pi$
$877$	−30301.8	+	9845.67i	−1.16673	+	0.379093i	−0.339307	+	0.940676i	$0.610193\pi$
$878$	9898.39	+	13624.0i	0.380472	+	0.523675i
$879$	29798.6	−	33110.1i	1.14344	−	1.27051i
$880$	−2679.59	+	2661.81i	−0.102647	+	0.101966i
$881$		−	48533.5i		−	1.85600i	−0.372580	−	0.928000i	$-0.621527\pi$
$881$		−	48533.5i		−	1.85600i	0.372580	−	0.928000i	$-0.378473\pi$
$882$	47610.7	+	52827.9i	1.81761	+	2.01679i
$883$	−1711.94	−	5268.80i	−0.0652450	−	0.200803i	0.913120	−	0.407692i	$-0.133666\pi$
$883$	−1711.94	−	5268.80i	−0.0652450	−	0.200803i	−0.978365	+	0.206889i	$0.933666\pi$
$884$	12357.0	+	4015.02i	0.470147	+	0.152760i
$885$	2030.98	−	432.189i	0.0771420	−	0.0164157i
$886$	−31631.1	+	43536.5i	−1.19940	+	1.65083i
$887$	13039.9	−	40132.7i	0.493616	−	1.51919i	−0.325487	−	0.945547i	$-0.605528\pi$
$887$	13039.9	−	40132.7i	0.493616	−	1.51919i	0.819103	−	0.573647i	$-0.194472\pi$
$888$	48496.8	+	21578.7i	1.83271	+	0.815468i
$889$	−28559.6	+	20749.7i	−1.07745	+	0.782817i
$890$	17986.3			0.677420
$891$	−9471.44	−	24852.4i	−0.356122	−	0.934439i
$892$	−713.953			−0.0267992
$893$	12464.0	−	9055.66i	0.467070	−	0.339346i
$894$	−79095.2	−	35193.5i	−2.95899	−	1.31661i
$895$	1605.20	−	4940.29i	0.0599506	−	0.184509i
$896$	46508.4	−	64013.4i	1.73408	−	2.38676i
$897$	−7971.77	+	1696.38i	−0.296733	+	0.0631442i
$898$	−36097.3	−	11728.7i	−1.34141	−	0.435849i
$899$	9399.50	+	28928.7i	0.348711	+	1.07322i
$900$	29214.2	+	32415.5i	1.08201	+	1.20057i
$901$		−	1109.02i		−	0.0410066i
$902$	37089.2	+	6000.98i	1.36911	+	0.221520i
$903$	20126.6	−	22363.3i	0.741719	−	0.824146i
$904$	33196.5	+	45691.1i	1.22135	+	1.68104i
$905$	1169.23	−	379.904i	0.0429463	−	0.0139541i
$906$	−23199.8	+	13401.6i	−0.850732	+	0.491432i
$907$	1454.65	+	1056.87i	0.0532535	+	0.0386909i	0.614094	−	0.789233i	$-0.289522\pi$
$907$	1454.65	+	1056.87i	0.0532535	+	0.0386909i	−0.560840	+	0.827924i	$0.689522\pi$
$908$	72346.8	+	52563.0i	2.64418	+	1.92111i
$909$	18348.9	+	3891.31i	0.669520	+	0.141987i
$910$	19335.4	−	6282.45i	0.704354	−	0.228858i
$911$	−10729.9	−	14768.4i	−0.390228	−	0.537102i	0.568030	−	0.823008i	$-0.307706\pi$
$911$	−10729.9	−	14768.4i	−0.390228	−	0.537102i	−0.958258	+	0.285905i	$0.907706\pi$
$912$	−8639.34	−	7775.28i	−0.313681	−	0.282309i
$913$	−22643.0	−	3663.60i	−0.820782	−	0.132801i
$914$		−	10999.7i		−	0.398072i
$915$	−621.808	+	5929.29i	−0.0224659	+	0.214225i
$916$	−4362.76	−	13427.2i	−0.157369	−	0.484331i
$917$	−8483.47	−	2756.45i	−0.305506	−	0.0992649i
$918$	4662.76	+	14316.7i	0.167640	+	0.514730i
$919$	20840.0	−	28683.8i	0.748040	−	1.02959i	−0.250075	−	0.968226i	$-0.580455\pi$
$919$	20840.0	−	28683.8i	0.748040	−	1.02959i	0.998116	−	0.0613626i	$-0.0195446\pi$
$920$	−1337.60	+	4116.71i	−0.0479341	+	0.147526i
$921$	−10830.2	+	24340.1i	−0.387477	+	0.870829i
$922$	29518.8	−	21446.6i	1.05439	−	0.766060i
$923$	−23543.3			−0.839585
$924$	44881.1	−	68644.4i	1.59792	−	2.44398i
$925$	37593.2			1.33628
$926$	−25346.1	+	18415.0i	−0.899485	+	0.653514i
$927$	−9145.83	+	4077.05i	−0.324044	+	0.144453i
$928$	6525.42	−	20083.2i	0.230827	−	0.710412i
$929$	3174.30	−	4369.05i	0.112105	−	0.154299i	−0.749278	−	0.662256i	$-0.769599\pi$
$929$	3174.30	−	4369.05i	0.112105	−	0.154299i	0.861382	+	0.507957i	$0.169599\pi$
$930$	2855.42	+	13418.5i	0.100681	+	0.473128i
$931$	−41173.8	−	13378.2i	−1.44943	−	0.470948i
$932$	7140.96	+	21977.6i	0.250976	+	0.772426i
$933$	−24236.9	−	2541.74i	−0.850461	−	0.0891883i
$934$		−	22720.7i		−	0.795980i
$935$	−2113.16	+	2099.13i	−0.0739119	+	0.0734214i
$936$	−32479.9	+	3428.96i	−1.13423	+	0.119743i
$937$	−31021.4	−	42697.3i	−1.08156	−	1.48864i	−0.857789	−	0.514002i	$-0.828162\pi$
$937$	−31021.4	−	42697.3i	−1.08156	−	1.48864i	−0.223774	−	0.974641i	$-0.571838\pi$
$938$	−44456.4	+	14444.8i	−1.54750	+	0.502813i
$939$	26695.5	+	46213.4i	0.927770	+	1.60609i
$940$	−8322.90	−	6046.94i	−0.288791	−	0.209819i
$941$	20671.9	+	15019.0i	0.716137	+	0.520304i	0.885148	−	0.465310i	$-0.154057\pi$
$941$	20671.9	+	15019.0i	0.716137	+	0.520304i	−0.169011	+	0.985614i	$0.554057\pi$
$942$	−25576.3	−	44275.8i	−0.884630	−	1.53141i
$943$	8163.23	−	2652.40i	0.281900	−	0.0915948i
$944$	−1873.59	−	2578.77i	−0.0645975	−	0.0889109i
$945$	12267.7	+	8900.05i	0.422296	+	0.306369i
$946$	−29674.9	−	15244.8i	−1.01989	−	0.523943i
$947$		−	29385.9i		−	1.00836i	−0.863600	−	0.504178i	$-0.831796\pi$
$947$		−	29385.9i		−	1.00836i	0.863600	−	0.504178i	$-0.168204\pi$
$948$	41217.5	+	4322.50i	1.41211	+	0.148089i
$949$	−3703.45	−	11398.0i	−0.126680	−	0.389880i
$950$	−39273.4	−	12760.7i	−1.34126	−	0.435802i
$951$	7199.53	+	33832.7i	0.245490	+	1.15363i
$952$	−12158.6	+	16734.9i	−0.413933	+	0.569730i
$953$	2213.92	−	6813.74i	0.0752527	−	0.231604i	−0.906354	−	0.422520i	$-0.861146\pi$
$953$	2213.92	−	6813.74i	0.0752527	−	0.231604i	0.981606	+	0.190916i	$0.0611457\pi$
$954$	2547.79	+	5715.32i	0.0864652	+	0.193963i
$955$	−4751.91	+	3452.46i	−0.161014	+	0.116983i
$956$	31766.6			1.07469
$957$	9755.58	−	35962.4i	0.329523	−	1.21473i
$958$	13097.0			0.441696
$959$	−30140.6	+	21898.4i	−1.01490	+	0.737368i
$960$	5621.28	−	12633.5i	0.188986	−	0.424733i
$961$	−1805.88	+	5557.93i	−0.0606183	+	0.186564i
$962$	−37122.1	+	51094.2i	−1.24414	+	1.71241i
$963$	−16751.7	+	29045.7i	−0.560556	+	0.971948i
$964$	46324.8	+	15051.8i	1.54774	+	0.502891i
$965$	134.554	+	414.114i	0.00448854	+	0.0138143i
$966$	3037.76	−	28966.8i	0.101178	−	0.964793i
$967$			7152.16i			0.237847i	0.992903	+	0.118923i	$0.0379443\pi$
$967$			7152.16i			0.237847i	−0.992903	+	0.118923i	$0.962056\pi$
$968$	−38448.6	−	12776.3i	−1.27664	−	0.424222i
$969$	−6813.08	−	6131.67i	−0.225870	−	0.203279i
$970$	4989.07	+	6866.87i	0.165144	+	0.227301i
$971$	34305.3	−	11146.5i	1.13379	−	0.368391i	0.318775	−	0.947830i	$-0.396728\pi$
$971$	34305.3	−	11146.5i	1.13379	−	0.368391i	0.815015	+	0.579439i	$0.196728\pi$
$972$	−36616.2	−	40572.1i	−1.20830	−	1.33884i
$973$	39395.1	+	28622.2i	1.29799	+	0.943048i
$974$	−77690.4	−	56445.3i	−2.55581	−	1.85691i
$975$	−20029.3	+	11570.1i	−0.657899	+	0.380041i
$976$	8703.96	−	2828.09i	0.285458	−	0.0927509i
$977$	−17592.3	−	24213.8i	−0.576079	−	0.792904i	0.417180	−	0.908824i	$-0.363019\pi$
$977$	−17592.3	−	24213.8i	−0.576079	−	0.792904i	−0.993259	+	0.115920i	$0.963019\pi$
$978$	14955.1	−	16617.1i	0.488970	−	0.543308i
$979$	17346.7	+	34326.9i	0.566296	+	1.12062i
$980$			28908.8i			0.942305i
$981$	15842.9	−	14278.2i	0.515620	−	0.464698i
$982$	19610.8	+	60355.7i	0.637276	+	1.96133i
$983$	41628.8	+	13526.0i	1.35071	+	0.438874i	0.892932	−	0.450191i	$-0.148644\pi$
$983$	41628.8	+	13526.0i	1.35071	+	0.438874i	0.457782	+	0.889065i	$0.348644\pi$
$984$	33642.6	−	7159.08i	1.08993	−	0.231934i
$985$	4969.92	−	6840.51i	0.160766	−	0.221276i
$986$	−6518.81	+	20062.8i	−0.210549	+	0.648002i
$987$	28176.1	+	12537.0i	0.908667	+	0.404313i
$988$	36104.9	−	26231.8i	1.16260	−	0.844680i
$989$	−7621.57			−0.245047
$990$	6067.69	−	15672.4i	0.194792	−	0.503134i
$991$	−33372.4			−1.06974			−0.534868	−	0.844936i	$-0.679639\pi$
$991$	−33372.4			−1.06974			−0.534868	+	0.844936i	$0.679639\pi$
$992$	−13449.7	+	9771.79i	−0.430473	+	0.312757i
$993$	50600.4	+	22514.7i	1.61707	+	0.719520i
$994$	25998.8	−	80016.0i	0.829609	−	2.55327i
$995$	−1596.74	+	2197.73i	−0.0508745	+	0.0700227i
$996$	−46101.8	+	9810.38i	−1.46666	+	0.312102i
$997$	11261.5	+	3659.07i	0.357728	+	0.116233i	0.482367	−	0.875969i	$-0.339777\pi$
$997$	11261.5	+	3659.07i	0.357728	+	0.116233i	−0.124639	+	0.992202i	$0.539777\pi$
$998$	−29505.9	−	90809.8i	−0.935864	−	2.88029i
$999$	−47082.1	+	32.6455i	−1.49110	+	0.00103389i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.4.f.a.8.10	yes	40
3.2	odd	2	inner	33.4.f.a.8.1	✓	40
11.2	odd	10		363.4.d.d.362.37		40
11.7	odd	10	inner	33.4.f.a.29.1	yes	40
11.9	even	5		363.4.d.d.362.3		40
33.2	even	10		363.4.d.d.362.4		40
33.20	odd	10		363.4.d.d.362.38		40
33.29	even	10	inner	33.4.f.a.29.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.4.f.a.8.1	✓	40	3.2	odd	2	inner
33.4.f.a.8.10	yes	40	1.1	even	1	trivial
33.4.f.a.29.1	yes	40	11.7	odd	10	inner
33.4.f.a.29.10	yes	40	33.29	even	10	inner
363.4.d.d.362.3		40	11.9	even	5
363.4.d.d.362.4		40	33.2	even	10
363.4.d.d.362.37		40	11.2	odd	10
363.4.d.d.362.38		40	33.20	odd	10

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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	33.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.83133 - 2.78363i) q^{2} +(-4.74741 - 2.11237i) q^{3} +(4.45840 - 13.7215i) q^{4} +(-2.11757 + 2.91459i) q^{5} +(-24.0689 + 5.12183i) q^{6} +(28.5187 + 9.26628i) q^{7} +(-9.40652 - 28.9503i) q^{8} +(18.0758 + 20.0566i) q^{9} +17.0613i q^{10} +(-32.5614 + 16.4546i) q^{11} +(-50.1508 + 55.7240i) q^{12} +(-23.3577 - 32.1491i) q^{13} +(135.058 - 43.8831i) q^{14} +(16.2097 - 9.36366i) q^{15} +(-23.2483 - 16.8909i) q^{16} +(-18.3339 - 13.3204i) q^{17} +(125.084 + 26.5271i) q^{18} +(-74.0299 + 24.0538i) q^{19} +(30.5517 + 42.0508i) q^{20} +(-115.816 - 104.233i) q^{21} +(-78.9503 + 153.682i) q^{22} +39.4710i q^{23} +(-16.4971 + 157.309i) q^{24} +(34.6164 + 106.538i) q^{25} +(-178.982 - 58.1549i) q^{26} +(-43.4464 - 133.399i) q^{27} +(254.295 - 350.007i) q^{28} +(60.7406 - 186.940i) q^{29} +(36.0397 - 80.9969i) q^{30} +(-125.194 + 90.9588i) q^{31} +107.431 q^{32} +(189.341 - 9.33491i) q^{33} -107.322 q^{34} +(-87.3978 + 63.4982i) q^{35} +(355.796 - 158.608i) q^{36} +(103.703 - 319.166i) q^{37} +(-216.676 + 298.229i) q^{38} +(42.9778 + 201.965i) q^{39} +(104.297 + 33.8882i) q^{40} +(-67.1986 - 206.816i) q^{41} +(-733.875 - 76.9619i) q^{42} +193.093i q^{43} +(80.6104 + 520.154i) q^{44} +(-96.7335 + 10.2123i) q^{45} +(109.872 + 151.226i) q^{46} +(-188.238 + 61.1622i) q^{47} +(74.6896 + 129.297i) q^{48} +(449.958 + 326.914i) q^{49} +(429.190 + 311.825i) q^{50} +(58.9010 + 101.965i) q^{51} +(-545.274 + 177.170i) q^{52} +(28.7649 + 39.5915i) q^{53} +(-537.792 - 390.159i) q^{54} +(20.9929 - 129.747i) q^{55} -912.787i q^{56} +(402.260 + 42.1853i) q^{57} +(-287.654 - 885.309i) q^{58} +(105.494 + 34.2770i) q^{59} +(-56.2146 - 264.169i) q^{60} +(-187.195 + 257.652i) q^{61} +(-226.465 + 696.987i) q^{62} +(329.648 + 739.482i) q^{63} +(597.590 - 434.175i) q^{64} +143.163 q^{65} +(699.442 - 562.819i) q^{66} -329.164 q^{67} +(-264.516 + 192.182i) q^{68} +(83.3772 - 187.385i) q^{69} +(-158.095 + 486.565i) q^{70} +(348.236 - 479.306i) q^{71} +(410.613 - 711.962i) q^{72} +(286.826 + 93.1954i) q^{73} +(-491.116 - 1511.50i) q^{74} +(60.7100 - 578.904i) q^{75} +1123.04i q^{76} +(-1081.08 + 167.540i) q^{77} +(726.858 + 654.162i) q^{78} +(-324.935 - 447.235i) q^{79} +(98.4601 - 31.9916i) q^{80} +(-75.5309 + 725.077i) q^{81} +(-833.159 - 605.325i) q^{82} +(508.644 + 369.552i) q^{83} +(-1946.59 + 1124.46i) q^{84} +(77.6467 - 25.2289i) q^{85} +(537.499 + 739.804i) q^{86} +(-683.247 + 759.175i) q^{87} +(782.654 + 787.882i) q^{88} -1054.22i q^{89} +(-342.191 + 308.397i) q^{90} +(-368.228 - 1133.29i) q^{91} +(541.603 + 175.977i) q^{92} +(786.486 - 167.363i) q^{93} +(-550.949 + 758.317i) q^{94} +(86.6568 - 266.702i) q^{95} +(-510.019 - 226.934i) q^{96} +(402.482 - 292.420i) q^{97} +2633.94 q^{98} +(-918.596 - 355.640i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 3 q^{3} - 38 q^{4} + 45 q^{6} - 10 q^{7} - 65 q^{9} - 90 q^{12} - 10 q^{13} + 33 q^{15} + 310 q^{16} + 225 q^{18} - 460 q^{19} - 340 q^{22} - 565 q^{24} - 604 q^{25} - 435 q^{27} + 1190 q^{28} + 910 q^{30}+ \cdots + 955 q^{99}+O(q^{100}) \) 40 * q - 3 * q^3 - 38 * q^4 + 45 * q^6 - 10 * q^7 - 65 * q^9 - 90 * q^12 - 10 * q^13 + 33 * q^15 + 310 * q^16 + 225 * q^18 - 460 * q^19 - 340 * q^22 - 565 * q^24 - 604 * q^25 - 435 * q^27 + 1190 * q^28 + 910 * q^30 + 840 * q^31 + 1208 * q^33 - 188 * q^34 + 1991 * q^36 + 126 * q^37 - 1075 * q^39 - 90 * q^40 - 3340 * q^42 - 1662 * q^45 + 430 * q^46 - 346 * q^48 + 376 * q^49 - 210 * q^51 - 4270 * q^52 - 546 * q^55 + 1800 * q^57 - 4582 * q^58 + 674 * q^60 + 650 * q^61 + 3945 * q^63 + 7238 * q^64 + 3504 * q^66 + 4556 * q^67 + 3860 * q^69 + 2964 * q^70 - 1640 * q^72 + 3860 * q^73 - 6048 * q^75 - 7640 * q^78 - 3550 * q^79 - 2453 * q^81 - 5812 * q^82 - 7080 * q^84 - 8230 * q^85 - 9298 * q^88 + 9220 * q^90 - 6766 * q^91 + 5659 * q^93 + 3530 * q^94 + 14890 * q^96 + 8004 * q^97 + 955 * q^99

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