LMFDB - Embedded newform 33.4.f.a.29.1

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			29.1
Character	$\chi$	$=$	33.29
Dual form			33.4.f.a.8.1

$q$-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} +(2.59912 + 4.49940i) q^{3} +(4.45840 + 13.7215i) q^{4} +(2.11757 + 2.91459i) q^{5} +(2.56657 - 24.4737i) q^{6} +(28.5187 - 9.26628i) q^{7} +(9.40652 - 28.9503i) q^{8} +(-13.4892 + 23.3889i) 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} +(-7.61008 + 17.1032i) q^{15} +(-23.2483 + 16.8909i) q^{16} +(18.3339 - 13.3204i) q^{17} +(116.788 - 52.0619i) 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} +(154.708 - 32.9215i) q^{24} +(34.6164 - 106.538i) q^{25} +(178.982 - 58.1549i) q^{26} +(-140.296 + 0.0972777i) q^{27} +(254.295 + 350.007i) q^{28} +(-60.7406 - 186.940i) q^{29} +(76.7656 - 44.3443i) q^{30} +(-125.194 - 90.9588i) q^{31} -107.431 q^{32} +(10.5952 + 189.274i) q^{33} -107.322 q^{34} +(87.3978 + 63.4982i) q^{35} +(-381.072 - 80.8153i) q^{36} +(103.703 + 319.166i) q^{37} +(216.676 + 298.229i) q^{38} +(-205.361 - 21.5364i) q^{39} +(104.297 - 33.8882i) q^{40} +(67.1986 - 206.816i) q^{41} +(-153.585 - 721.739i) 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} +(-136.424 - 60.7021i) q^{48} +(449.958 - 326.914i) q^{49} +(-429.190 + 311.825i) q^{50} +(107.586 + 47.8704i) 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} +(-84.1847 - 395.608i) q^{57} +(-287.654 + 885.309i) q^{58} +(-105.494 + 34.2770i) q^{59} +(-268.611 - 28.1693i) q^{60} +(-187.195 - 257.652i) q^{61} +(226.465 + 696.987i) q^{62} +(-167.966 + 792.016i) q^{63} +(597.590 + 434.175i) q^{64} -143.163 q^{65} +(486.275 - 754.666i) q^{66} -329.164 q^{67} +(264.516 + 192.182i) q^{68} +(-177.596 + 102.590i) q^{69} +(-158.095 - 486.565i) q^{70} +(-348.236 - 479.306i) q^{71} +(550.230 + 610.524i) q^{72} +(286.826 - 93.1954i) q^{73} +(491.116 - 1511.50i) q^{74} +(569.331 - 121.153i) 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} +(-365.084 - 630.995i) q^{81} +(-833.159 + 605.325i) q^{82} +(-508.644 + 369.552i) q^{83} +(-913.880 + 2053.89i) 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} +(399.045 + 230.143i) q^{90} +(-368.228 + 1133.29i) q^{91} +(-541.603 + 175.977i) q^{92} +(83.8661 - 799.710i) q^{93} +(-550.949 - 758.317i) q^{94} +(-86.6568 - 266.702i) q^{95} +(-279.225 - 483.375i) q^{96} +(402.482 + 292.420i) q^{97} -2633.94 q^{98} +(-824.082 + 539.618i) 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 $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$

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	−0.998769	−	0.0496026i	$-0.984205\pi$
$2$	−3.83133	−	2.78363i	−1.35458	−	0.984160i	−0.355812	−	0.934558i	$-0.615795\pi$
$3$	2.59912	+	4.49940i	0.500200	+	0.865910i
$3$	2.59912	+	4.49940i	0.500200	+	0.865910i
$4$	4.45840	+	13.7215i	0.557300	+	1.71519i
$5$	2.11757	+	2.91459i	0.189402	+	0.260689i	0.893149	−	0.449762i	$-0.148491\pi$
$5$	2.11757	+	2.91459i	0.189402	+	0.260689i	−0.703747	+	0.710451i	$0.748491\pi$
$6$	2.56657	−	24.4737i	0.174633	−	1.66522i
$7$	28.5187	−	9.26628i	1.53986	−	0.500332i	0.588525	−	0.808479i	$-0.299709\pi$
$7$	28.5187	−	9.26628i	1.53986	−	0.500332i	0.951339	+	0.308147i	$0.0997089\pi$
$8$	9.40652	−	28.9503i	0.415713	−	1.27943i
$9$	−13.4892	+	23.3889i	−0.499600	+	0.866256i
$10$		−	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	−0.981897	−	0.189417i	$-0.939340\pi$
$13$	−23.3577	+	32.1491i	−0.498328	+	0.685890i	0.483569	+	0.875306i	$0.339340\pi$
$14$	−135.058	−	43.8831i	−2.57828	−	0.837733i
$15$	−7.61008	+	17.1032i	−0.130994	+	0.294401i
$16$	−23.2483	+	16.8909i	−0.363255	+	0.263920i
$17$	18.3339	−	13.3204i	0.261566	−	0.190039i	−0.449271	−	0.893395i	$-0.648316\pi$
$17$	18.3339	−	13.3204i	0.261566	−	0.190039i	0.710837	+	0.703357i	$0.248316\pi$
$18$	116.788	−	52.0619i	1.52928	−	0.681728i
$19$	−74.0299	−	24.0538i	−0.893874	−	0.290437i	−0.174168	−	0.984716i	$-0.555724\pi$
$19$	−74.0299	−	24.0538i	−0.893874	−	0.290437i	−0.719706	+	0.694279i	$0.755724\pi$
$20$	−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	$0.942740\pi$
$24$	154.708	−	32.9215i	1.31581	−	0.280003i
$25$	34.6164	−	106.538i	0.276931	−	0.852307i
$26$	178.982	−	58.1549i	1.35005	−	0.438658i
$27$	−140.296	+	0.0972777i	−1.00000	+	0.000693374i
$28$	254.295	+	350.007i	1.71633	+	2.36233i
$29$	−60.7406	−	186.940i	−0.388939	−	1.19703i	−0.933582	−	0.358364i	$-0.883335\pi$
$29$	−60.7406	−	186.940i	−0.388939	−	1.19703i	0.544643	−	0.838668i	$-0.316665\pi$
$30$	76.7656	−	44.3443i	0.467180	−	0.269871i
$31$	−125.194	−	90.9588i	−0.725339	−	0.526990i	0.162746	−	0.986668i	$-0.447965\pi$
$31$	−125.194	−	90.9588i	−0.725339	−	0.526990i	−0.888086	+	0.459678i	$0.847965\pi$
$32$	−107.431			−0.593478
$33$	10.5952	+	189.274i	0.0558906	+	0.998437i
$34$	−107.322			−0.541341
$35$	87.3978	+	63.4982i	0.422083	+	0.306662i
$36$	−381.072	−	80.8153i	−1.76422	−	0.374145i
$37$	103.703	+	319.166i	0.460776	+	1.41812i	0.864218	+	0.503117i	$0.167814\pi$
$37$	103.703	+	319.166i	0.460776	+	1.41812i	−0.403442	+	0.915005i	$0.632186\pi$
$38$	216.676	+	298.229i	0.924988	+	1.27314i
$39$	−205.361	−	21.5364i	−0.843183	−	0.0884250i
$40$	104.297	−	33.8882i	0.412271	−	0.133955i
$41$	67.1986	−	206.816i	0.255967	−	0.787787i	−0.737670	−	0.675161i	$-0.764074\pi$
$41$	67.1986	−	206.816i	0.255967	−	0.787787i	0.993638	−	0.112625i	$-0.0359260\pi$
$42$	−153.585	−	721.739i	−0.564253	−	2.65159i
$43$		−	193.093i		−	0.684801i	−0.939554	−	0.342400i	$-0.888760\pi$
$43$		−	193.093i		−	0.684801i	0.939554	−	0.342400i	$-0.111240\pi$
$44$	−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	$-0.300631\pi$
$47$	188.238	+	61.1622i	0.584198	+	0.189818i	−0.00198212	+	0.999998i	$0.500631\pi$
$48$	−136.424	−	60.7021i	−0.410232	−	0.182533i
$49$	449.958	−	326.914i	1.31183	−	0.953101i
$50$	−429.190	+	311.825i	−1.21393	+	0.881973i
$51$	107.586	+	47.8704i	0.295392	+	0.131435i
$52$	−545.274	−	177.170i	−1.45415	−	0.472482i
$53$	−28.7649	+	39.5915i	−0.0745502	+	0.102610i	−0.844664	−	0.535297i	$-0.820200\pi$
$53$	−28.7649	+	39.5915i	−0.0745502	+	0.102610i	0.770113	+	0.637907i	$0.220200\pi$
$54$	537.792	+	390.159i	1.35526	+	0.983221i
$55$	20.9929	+	129.747i	0.0514669	+	0.318092i
$56$		−	912.787i		−	2.17815i
$57$	−84.1847	−	395.608i	−0.195624	−	0.919292i
$58$	−287.654	+	885.309i	−0.651222	+	2.00425i
$59$	−105.494	+	34.2770i	−0.232782	+	0.0756354i	−0.423085	−	0.906090i	$-0.639053\pi$
$59$	−105.494	+	34.2770i	−0.232782	+	0.0756354i	0.190303	+	0.981725i	$0.439053\pi$
$60$	−268.611	−	28.1693i	−0.577958	−	0.0606108i
$61$	−187.195	−	257.652i	−0.392916	−	0.540803i	0.566032	−	0.824383i	$-0.308478\pi$
$61$	−187.195	−	257.652i	−0.392916	−	0.540803i	−0.958949	+	0.283580i	$0.908478\pi$
$62$	226.465	+	696.987i	0.463888	+	1.42770i
$63$	−167.966	+	792.016i	−0.335899	+	1.58388i
$64$	597.590	+	434.175i	1.16717	+	0.847998i
$65$	−143.163			−0.273188
$66$	486.275	−	754.666i	0.906914	−	1.40747i
$67$	−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
$69$	−177.596	+	102.590i	−0.309855	+	0.178990i
$70$	−158.095	−	486.565i	−0.269942	−	0.830796i
$71$	−348.236	−	479.306i	−0.582085	−	0.801172i	0.411837	−	0.911258i	$-0.364887\pi$
$71$	−348.236	−	479.306i	−0.582085	−	0.801172i	−0.993922	+	0.110086i	$0.964887\pi$
$72$	550.230	+	610.524i	0.900628	+	0.999319i
$73$	286.826	−	93.1954i	0.459869	−	0.149420i	−0.0699154	−	0.997553i	$-0.522273\pi$
$73$	286.826	−	93.1954i	0.459869	−	0.149420i	0.529784	+	0.848132i	$0.322273\pi$
$74$	491.116	−	1511.50i	0.771502	−	2.37444i
$75$	569.331	−	121.153i	0.876542	−	0.186526i
$76$		−	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	−0.975078	−	0.221861i	$-0.928787\pi$
$79$	−324.935	+	447.235i	−0.462760	+	0.636935i	0.512318	+	0.858796i	$0.328787\pi$
$80$	−98.4601	−	31.9916i	−0.137602	−	0.0447097i
$81$	−365.084	−	630.995i	−0.500800	−	0.865563i
$82$	−833.159	+	605.325i	−1.12204	+	0.815208i
$83$	−508.644	+	369.552i	−0.672662	+	0.488718i	−0.870915	−	0.491433i	$-0.836473\pi$
$83$	−508.644	+	369.552i	−0.672662	+	0.488718i	0.198253	+	0.980151i	$0.436473\pi$
$84$	−913.880	+	2053.89i	−1.18705	+	2.66783i
$85$	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	$-0.216041\pi$
$90$	399.045	+	230.143i	0.467367	+	0.269547i
$91$	−368.228	+	1133.29i	−0.424185	+	1.30551i
$92$	−541.603	+	175.977i	−0.613761	+	0.199423i
$93$	83.8661	−	799.710i	0.0935108	−	0.891679i
$94$	−550.949	−	758.317i	−0.604533	−	0.832068i
$95$	−86.6568	−	266.702i	−0.0935874	−	0.288032i
$96$	−279.225	−	483.375i	−0.296858	−	0.513898i
$97$	402.482	+	292.420i	0.421298	+	0.306091i	0.778160	−	0.628066i	$-0.216153\pi$
$97$	402.482	+	292.420i	0.421298	+	0.306091i	−0.356862	+	0.934157i	$0.616153\pi$
$98$	−2633.94			−2.71499
$99$	−824.082	+	539.618i	−0.836600	+	0.547814i
$100$	1616.20			1.61620
$101$	−562.026	−	408.336i	−0.553699	−	0.402286i	0.275448	−	0.961316i	$-0.411174\pi$
$101$	−562.026	−	408.336i	−0.553699	−	0.402286i	−0.829148	+	0.559030i	$0.811174\pi$
$102$	−278.943	−	482.885i	−0.270779	−	0.468752i
$103$	−114.604	−	352.716i	−0.109634	−	0.337419i	0.881156	−	0.472825i	$-0.156766\pi$
$103$	−114.604	−	352.716i	−0.109634	−	0.337419i	−0.990790	+	0.135407i	$0.956766\pi$
$104$	711.012	+	978.624i	0.670389	+	0.922712i
$105$	−58.5468	+	558.277i	−0.0544151	+	0.518878i
$106$	220.416	−	71.6174i	0.201969	−	0.0656236i
$107$	−383.755	+	1181.08i	−0.346720	+	1.06709i	0.613937	+	0.789355i	$0.289585\pi$
$107$	−383.755	+	1181.08i	−0.346720	+	1.06709i	−0.960657	+	0.277739i	$0.910415\pi$
$108$	−626.831	−	1924.64i	−0.558489	−	1.71481i
$109$			789.909i			0.694124i	0.937842	+	0.347062i	$0.112821\pi$
$109$			789.909i			0.694124i	−0.937842	+	0.347062i	$0.887179\pi$
$110$	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	$-0.119112\pi$
$113$	1764.55	+	573.337i	1.46898	+	0.477301i	0.538180	+	0.842830i	$0.319112\pi$
$114$	−778.686	+	1750.05i	−0.639742	+	1.43778i
$115$	−115.042	+	83.5827i	−0.0932843	+	0.0677750i
$116$	2294.30	−	1666.91i	1.83638	−	1.33421i
$117$	−436.857	−	979.978i	−0.345192	−	0.774350i
$118$	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
$123$	1105.21	−	235.186i	0.810187	−	0.172406i
$124$	689.930	−	2123.39i	0.499657	−	1.53779i
$125$	812.107	−	263.869i	0.581096	−	0.188810i
$126$	2848.21	−	2566.92i	2.01380	−	1.81492i
$127$	−691.974	−	952.420i	−0.483486	−	0.665462i	0.495684	−	0.868503i	$-0.334917\pi$
$127$	−691.974	−	952.420i	−0.483486	−	0.665462i	−0.979170	+	0.203041i	$0.934917\pi$
$128$	−815.403	−	2509.55i	−0.563064	−	1.73293i
$129$	868.803	−	501.871i	0.592976	−	0.342537i
$130$	548.506	+	398.513i	0.370055	+	0.268861i
$131$	297.471			0.198398			0.0991990	−	0.995068i	$-0.468372\pi$
$131$	297.471			0.198398			0.0991990	+	0.995068i	$0.468372\pi$
$132$	−2549.90	+	989.243i	−1.68136	+	0.652292i
$133$	−2334.12			−1.52176
$134$	1261.14	+	916.270i	0.813028	+	0.590699i
$135$	−297.371	−	408.699i	−0.189582	−	0.260557i
$136$	−213.170	−	656.070i	−0.134406	−	0.413658i
$137$	730.280	+	1005.14i	0.455416	+	0.626826i	0.973550	−	0.228473i	$-0.0733732\pi$
$137$	730.280	+	1005.14i	0.455416	+	0.626826i	−0.518134	+	0.855299i	$0.673373\pi$
$138$	965.999	+	101.305i	0.595879	+	0.0624902i
$139$	1544.43	−	501.815i	0.942422	−	0.306211i	0.202789	−	0.979222i	$-0.434999\pi$
$139$	1544.43	−	501.815i	0.942422	−	0.306211i	0.739632	+	0.673011i	$0.234999\pi$
$140$	−481.639	+	1482.33i	−0.290757	+	0.894857i
$141$	214.059	+	1005.93i	0.127851	+	0.600810i
$142$			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
$147$	2640.41	+	1174.85i	1.48148	+	0.659186i
$148$	−3917.10	+	2845.94i	−2.17556	+	1.58064i
$149$	−2846.16	+	2067.85i	−1.56487	+	1.13695i	−0.633007	+	0.774146i	$0.718180\pi$
$149$	−2846.16	+	2067.85i	−1.56487	+	1.13695i	−0.931867	+	0.362801i	$0.881820\pi$
$150$	−2518.54	−	1120.63i	−1.37092	−	0.609993i
$151$	1035.49	+	336.450i	0.558058	+	0.181324i	0.574447	−	0.818542i	$-0.305217\pi$
$151$	1035.49	+	336.450i	0.558058	+	0.181324i	−0.0163894	+	0.999866i	$0.505217\pi$
$152$	−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
$156$	−620.071	−	2913.89i	−0.318240	−	1.49550i
$157$	642.100	−	1976.18i	0.326402	−	1.00456i	−0.644402	−	0.764687i	$-0.722893\pi$
$157$	642.100	−	1976.18i	0.326402	−	1.00456i	0.970804	−	0.239875i	$-0.0771065\pi$
$158$	2489.87	−	809.007i	1.25369	−	0.407349i
$159$	−252.901	−	26.5219i	−0.126141	−	0.0132284i
$160$	−227.493	−	313.117i	−0.112406	−	0.154713i
$161$	365.749	+	1125.66i	0.179038	+	0.551021i
$162$	−357.699	+	3433.81i	−0.173478	+	1.66534i
$163$	−734.978	−	533.993i	−0.353177	−	0.256598i	0.397023	−	0.917809i	$-0.370043\pi$
$163$	−734.978	−	533.993i	−0.353177	−	0.256598i	−0.750201	+	0.661210i	$0.770043\pi$
$164$	3137.43			1.49386
$165$	−529.221	+	431.683i	−0.249696	+	0.203675i
$166$	2977.48			1.39215
$167$	−2216.50	−	1610.38i	−1.02705	−	0.746197i	−0.0593351	−	0.998238i	$-0.518898\pi$
$167$	−2216.50	−	1610.38i	−1.02705	−	0.746197i	−0.967716	+	0.252042i	$0.918898\pi$
$168$	4106.99	−	2372.44i	1.88608	−	1.08951i
$169$	190.926	+	587.609i	0.0869030	+	0.267460i
$170$	−227.262	−	312.800i	−0.102531	−	0.141122i
$171$	1561.19	−	1407.01i	0.698173	−	0.629222i
$172$	2649.54	−	860.886i	1.17456	−	0.381639i
$173$	272.961	−	840.087i	0.119959	−	0.369194i	−0.872990	−	0.487737i	$-0.837822\pi$
$173$	272.961	−	840.087i	0.119959	−	0.369194i	0.992949	+	0.118543i	$0.0378223\pi$
$174$	−4731.01	+	1006.75i	−2.06125	+	0.438629i
$175$		−	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	$-0.302668\pi$
$179$	1371.30	+	445.562i	0.572602	+	0.186050i	−0.00838162	+	0.999965i	$0.502668\pi$
$180$	−571.405	−	1281.80i	−0.236611	−	0.530777i
$181$	−276.077	+	200.581i	−0.113374	+	0.0823707i	−0.643027	−	0.765843i	$-0.722322\pi$
$181$	−276.077	+	200.581i	−0.113374	+	0.0823707i	0.529654	+	0.848214i	$0.322322\pi$
$182$	4565.46	−	3317.00i	1.85942	−	1.35095i
$183$	672.738	−	1511.93i	0.271750	−	0.610740i
$184$	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
$189$	−4000.16	+	1302.80i	−1.53952	+	0.501400i
$190$	−410.388	+	1263.05i	−0.156698	+	0.482268i
$191$	−1550.59	+	503.817i	−0.587418	+	0.190864i	−0.587621	−	0.809136i	$-0.699935\pi$
$191$	−1550.59	+	503.817i	−0.587418	+	0.190864i	0.000203108		1.00000i	$0.499935\pi$
$192$	−400.319	+	3817.27i	−0.150472	+	1.43483i
$193$	71.0415	+	97.7803i	0.0264958	+	0.0364683i	0.822059	−	0.569402i	$-0.192825\pi$
$193$	71.0415	+	97.7803i	0.0264958	+	0.0364683i	−0.795564	+	0.605870i	$0.792825\pi$
$194$	−728.054	−	2240.72i	−0.269439	−	0.829249i
$195$	−372.098	−	644.149i	−0.136649	−	0.236556i
$196$	6491.85	+	4716.61i	2.36584	+	1.71888i
$197$	2346.99			0.848812			0.424406	−	0.905472i	$-0.360483\pi$
$197$	2346.99			0.848812			0.424406	+	0.905472i	$0.360483\pi$
$198$	4659.43	+	226.481i	1.67238	+	0.0812896i
$199$	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
$201$	−855.536	−	1481.04i	−0.300223	−	0.519725i
$202$	1016.65	+	3128.94i	0.354116	+	1.08986i
$203$	−3464.48	−	4768.45i	−1.19783	−	1.64867i
$204$	−177.196	+	1689.66i	−0.0608147	+	0.579903i
$205$	745.082	−	242.092i	0.253848	−	0.0824801i
$206$	−542.742	+	1670.39i	−0.183566	+	0.564958i
$207$	−923.184	−	532.431i	−0.309979	−	0.178776i
$208$		−	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	−0.968800	−	0.247844i	$-0.920278\pi$
$211$	−1329.30	+	1829.63i	−0.433711	+	0.596952i	0.535089	+	0.844796i	$0.320278\pi$
$212$	−671.501	−	218.184i	−0.217542	−	0.0706837i
$213$	1251.48	−	2812.63i	0.402583	−	0.904779i
$214$	4757.97	−	3456.87i	1.51985	−	1.10424i
$215$	562.787	−	408.889i	0.178520	−	0.129702i
$216$	−1316.88	+	4062.53i	−0.414826	+	1.27972i
$217$	−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
$222$	8077.32	−	1718.84i	2.44195	−	0.519643i
$223$	−15.2917	+	47.0630i	−0.00459196	+	0.0141326i	−0.953326	−	0.301942i	$-0.902365\pi$
$223$	−15.2917	+	47.0630i	−0.00459196	+	0.0141326i	0.948734	+	0.316075i	$0.102365\pi$
$224$	−3063.79	+	995.485i	−0.913875	+	0.296936i
$225$	2024.87	+	2246.76i	0.599962	+	0.665706i
$226$	−5164.62	−	7108.49i	−1.52011	−	2.09225i
$227$	1915.35	+	5894.83i	0.560027	+	1.72358i	0.682285	+	0.731086i	$0.260986\pi$
$227$	1915.35	+	5894.83i	0.560027	+	1.72358i	−0.122258	+	0.992498i	$0.539014\pi$
$228$	5053.03	−	2918.92i	1.46774	−	0.847853i
$229$	791.662	+	575.176i	0.228448	+	0.165977i	0.696121	−	0.717924i	$-0.254908\pi$
$229$	791.662	+	575.176i	0.228448	+	0.165977i	−0.467673	+	0.883901i	$0.654908\pi$
$230$	673.426			0.193063
$231$	2056.03	+	5299.67i	0.585614	+	1.50949i
$232$	−5983.33			−1.69321
$233$	1295.79	+	941.448i	0.364335	+	0.264705i	0.754858	−	0.655888i	$-0.227706\pi$
$233$	1295.79	+	941.448i	0.364335	+	0.264705i	−0.390523	+	0.920593i	$0.627706\pi$
$234$	−1054.15	+	4970.67i	−0.294495	+	1.38864i
$235$	220.345	+	678.152i	0.0611647	+	0.188246i
$236$	−940.668	−	1294.72i	−0.259459	−	0.357114i
$237$	−2856.83	−	299.598i	−0.783001	−	0.0821137i
$238$	−3060.68	+	994.477i	−0.833591	+	0.270850i
$239$	−680.388	+	2094.02i	−0.184145	+	0.566740i	−0.999933	−	0.0116119i	$-0.996304\pi$
$239$	−680.388	+	2094.02i	−0.184145	+	0.566740i	0.815788	+	0.578351i	$0.196304\pi$
$240$	−111.966	−	526.161i	−0.0301141	−	0.141515i
$241$		−	3376.06i		−	0.902371i	−0.892430	−	0.451185i	$-0.851001\pi$
$241$		−	3376.06i		−	0.902371i	0.892430	−	0.451185i	$-0.148999\pi$
$242$	−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
$246$	−4889.08	−	2175.40i	−1.26714	−	0.563816i
$247$	2502.48	−	1818.16i	0.644651	−	0.468366i
$248$	−3810.92	+	2768.80i	−0.975782	+	0.708947i
$249$	−2984.79	−	1328.09i	−0.759651	−	0.338008i
$250$	−3845.96	−	1249.63i	−0.972960	−	0.316134i
$251$	2875.33	−	3957.56i	0.723066	−	0.995214i	−0.276351	−	0.961057i	$-0.589125\pi$
$251$	2875.33	−	3957.56i	0.723066	−	0.995214i	0.999416	−	0.0341575i	$-0.0108748\pi$
$252$	−11616.5	+	1226.38i	−2.90386	+	0.306565i
$253$	−649.478	+	1285.23i	−0.161393	+	0.319375i
$254$			5575.24i			1.37725i
$255$	88.2977	+	414.937i	0.0216840	+	0.101899i
$256$	−2035.50	+	6264.63i	−0.496949	+	1.52945i
$257$	−1460.91	+	474.680i	−0.354589	+	0.115213i	−0.480894	−	0.876778i	$-0.659688\pi$
$257$	−1460.91	+	474.680i	−0.354589	+	0.115213i	0.126306	+	0.991991i	$0.459688\pi$
$258$	−4725.70	−	495.586i	−1.14034	−	0.119589i
$259$	5914.96	+	8141.24i	1.41906	+	1.95317i
$260$	−638.279	−	1964.42i	−0.152248	−	0.468570i
$261$	5191.67	+	1101.02i	1.23125	+	0.261116i
$262$	−1139.71	−	828.047i	−0.268746	−	0.195255i
$263$	−6003.58			−1.40759			−0.703796	−	0.710402i	$-0.748513\pi$
$263$	−6003.58			−1.40759			−0.703796	+	0.710402i	$0.748513\pi$
$264$	5579.21	+	1473.68i	1.30067	+	0.343555i
$265$	−176.305			−0.0408691
$266$	8942.80	+	6497.32i	2.06135	+	1.49766i
$267$	4743.35	−	2740.04i	1.08722	−	0.628043i
$268$	−1467.55	−	4516.64i	−0.334495	−	1.02947i
$269$	4342.40	+	5976.80i	0.984241	+	1.35469i	0.934513	+	0.355929i	$0.115835\pi$
$269$	4342.40	+	5976.80i	0.984241	+	1.35469i	0.0497278	+	0.998763i	$0.484165\pi$
$270$	1.65968	+	2393.63i	0.000374093	+	0.539525i
$271$	−6539.66	+	2124.87i	−1.46589	+	0.476297i	−0.929864	−	0.367905i	$-0.880075\pi$
$271$	−6539.66	+	2124.87i	−1.46589	+	0.476297i	−0.536027	+	0.844201i	$0.680075\pi$
$272$	−201.240	+	619.352i	−0.0448601	+	0.138065i
$273$	−6056.19	+	1288.75i	−1.34263	+	0.285709i
$274$		−	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	−0.889573	−	0.456793i	$-0.848998\pi$
$277$	−830.961	+	1143.72i	−0.180244	+	0.248085i	0.709329	+	0.704878i	$0.248998\pi$
$278$	−7314.08	−	2376.49i	−1.57795	−	0.512706i
$279$	3816.19	−	1701.19i	0.818887	−	0.365046i
$280$	2660.40	−	1932.89i	0.567819	−	0.412545i
$281$	−257.927	+	187.395i	−0.0547566	+	0.0397830i	−0.614827	−	0.788662i	$-0.710774\pi$
$281$	−257.927	+	187.395i	−0.0547566	+	0.0397830i	0.560070	+	0.828445i	$0.310774\pi$
$282$	1979.99	−	4449.89i	0.418109	−	0.939672i
$283$	6900.66	+	2242.16i	1.44948	+	0.470964i	0.924838	−	0.380361i	$-0.124200\pi$
$283$	6900.66	+	2242.16i	1.44948	+	0.470964i	0.524639	+	0.851325i	$0.324200\pi$
$284$	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
$288$	1449.16	−	2512.69i	0.296501	−	0.514104i
$289$	−1359.50	+	4184.11i	−0.276715	+	0.851641i
$290$	−3189.44	+	1036.31i	−0.645829	+	0.209843i
$291$	−269.618	+	2570.96i	−0.0543138	+	0.517912i
$292$	2557.57	+	3520.19i	0.512570	+	0.705492i
$293$	2649.09	+	8153.07i	0.528197	+	1.62562i	0.757906	+	0.652363i	$0.226222\pi$
$293$	2649.09	+	8153.07i	0.528197	+	1.62562i	−0.229710	+	0.973259i	$0.573778\pi$
$294$	−6845.93	−	11851.2i	−1.35804	−	2.35093i
$295$	−323.295	−	234.887i	−0.0638066	−	0.0463582i
$296$	10215.4			2.00594
$297$	−4569.84	−	2305.35i	−0.892825	−	0.450403i
$298$	16660.7			3.23869
$299$	−1268.96	−	921.952i	−0.245437	−	0.178321i
$300$	4200.70	+	7271.95i	0.808425	+	1.39949i
$301$	−1789.25	−	5506.76i	−0.342628	−	1.05450i
$302$	−3030.74	−	4171.46i	−0.577482	−	0.794836i
$303$	376.495	−	3590.09i	0.0713830	−	0.680677i
$304$	2127.36	−	691.222i	0.401357	−	0.130409i
$305$	354.551	−	1091.19i	0.0665623	−	0.204858i
$306$	1447.69	−	2510.15i	0.270454	−	0.468940i
$307$			5127.03i			0.953143i	0.879136	+	0.476571i	$0.158121\pi$
$307$			5127.03i			0.953143i	−0.879136	+	0.476571i	$0.841879\pi$
$308$	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	$-0.540628\pi$
$311$	−4460.43	−	1449.28i	−0.813272	−	0.264248i	−0.685983	+	0.727618i	$0.740628\pi$
$312$	−2555.22	+	5742.69i	−0.463656	+	1.04204i
$313$	−8309.42	+	6037.15i	−1.50056	+	1.09022i	−0.530406	+	0.847743i	$0.677961\pi$
$313$	−8309.42	+	6037.15i	−1.50056	+	1.09022i	−0.970157	+	0.242479i	$0.922039\pi$
$314$	−7961.04	+	5784.04i	−1.43079	+	1.03953i
$315$	−2664.08	+	1187.60i	−0.476520	+	0.212425i
$316$	−7585.44	−	2464.66i	−1.35036	−	0.438759i
$317$	3912.82	−	5385.53i	0.693268	−	0.954201i	−0.306730	−	0.951797i	$-0.599235\pi$
$317$	3912.82	−	5385.53i	0.693268	−	0.954201i	0.999997	−	0.00240424i	$-0.000765296\pi$
$318$	895.121	+	805.596i	0.157849	+	0.142062i
$319$	1098.22	−	7086.50i	0.192755	−	1.24379i
$320$			2661.13i			0.464880i
$321$	−6311.57	+	1343.09i	−1.09744	+	0.233533i
$322$	1732.11	−	5330.89i	0.299772	−	0.922605i
$323$	−1677.66	+	545.105i	−0.289002	+	0.0939023i
$324$	7030.54	−	7822.74i	1.20551	−	1.34135i
$325$	2616.56	+	3601.38i	0.446586	+	0.614673i
$326$	1329.51	+	4091.81i	0.225873	+	0.695166i
$327$	−3554.12	+	2053.07i	−0.601049	+	0.347201i
$328$	−5355.28	−	3890.84i	−0.901512	−	0.654987i
$329$	5935.04			0.994558
$330$	3229.26	−	180.768i	0.538682	−	0.0301544i
$331$	−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
$333$	−8863.82	−	1879.78i	−1.45866	−	0.309343i
$334$	4009.44	+	12339.8i	0.656847	+	2.02157i
$335$	−697.030	−	959.379i	−0.113680	−	0.156467i
$336$	−4453.12	−	467.001i	−0.723028	−	0.0758244i
$337$	7996.29	−	2598.15i	1.29254	−	0.419971i	0.419560	−	0.907728i	$-0.362185\pi$
$337$	7996.29	−	2598.15i	1.29254	−	0.419971i	0.872980	+	0.487756i	$0.162185\pi$
$338$	904.184	−	2782.79i	0.145506	−	0.447823i
$339$	2006.60	+	9429.58i	0.321485	+	1.51075i
$340$			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
$345$	−675.079	−	300.377i	−0.105348	−	0.0468747i
$346$	−3384.29	+	2458.83i	−0.525840	+	0.382045i
$347$	6028.90	−	4380.26i	0.932705	−	0.677650i	−0.0139489	−	0.999903i	$-0.504440\pi$
$347$	6028.90	−	4380.26i	0.932705	−	0.677650i	0.946654	+	0.322253i	$0.104440\pi$
$348$	13463.2	+	5990.49i	2.07387	+	0.922771i
$349$	−1741.35	−	565.799i	−0.267084	−	0.0867809i	0.172413	−	0.985025i	$-0.444843\pi$
$349$	−1741.35	−	565.799i	−0.267084	−	0.0867809i	−0.439498	+	0.898244i	$0.644843\pi$
$350$	−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	$-0.0944570\pi$
$354$	568.128	+	2669.80i	0.0852984	+	0.400842i
$355$	659.565	−	2029.93i	0.0986086	−	0.303486i
$356$	14465.5	−	4700.13i	2.15357	−	0.699737i
$357$	3511.78	+	368.282i	0.520624	+	0.0545982i
$358$	−4013.63	−	5524.28i	−0.592533	−	0.815552i
$359$	−1553.45	−	4781.02i	−0.228378	−	0.702876i	−0.997931	−	0.0642928i	$-0.979521\pi$
$359$	−1553.45	−	4781.02i	−0.228378	−	0.702876i	0.769553	−	0.638583i	$-0.220479\pi$
$360$	−614.276	+	2896.52i	−0.0899310	+	0.424056i
$361$	−647.211	−	470.226i	−0.0943593	−	0.0685561i
$362$	1616.09			0.234640
$363$	−2769.43	+	6337.38i	−0.400434	+	0.916326i
$364$	−17192.2			−2.47559
$365$	879.001	+	638.632i	0.126052	+	0.0915822i
$366$	−6786.14	+	3920.07i	−0.969173	+	0.559851i
$367$	−2489.43	−	7661.67i	−0.354079	−	1.08974i	−0.956541	−	0.291596i	$-0.905814\pi$
$367$	−2489.43	−	7661.67i	−0.354079	−	1.08974i	0.602462	−	0.798147i	$-0.294186\pi$
$368$	−666.701	−	917.635i	−0.0944407	−	0.129986i
$369$	3930.75	+	4361.49i	0.554544	+	0.615311i
$370$	5445.38	−	1769.31i	0.765113	−	0.248600i
$371$	−453.471	+	1395.64i	−0.0634583	+	0.195305i
$372$	11347.2	−	2414.66i	1.58151	−	0.336543i
$373$		−	1236.05i		−	0.171582i	−0.996313	−	0.0857912i	$-0.972658\pi$
$373$		−	1236.05i		−	0.171582i	0.996313	−	0.0857912i	$-0.0273418\pi$
$374$	−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
$378$	18952.4	+	6143.49i	2.57886	+	0.835945i
$379$	−3110.63	+	2260.00i	−0.421589	+	0.306302i	−0.778277	−	0.627921i	$-0.783906\pi$
$379$	−3110.63	+	2260.00i	−0.421589	+	0.306302i	0.356688	+	0.934224i	$0.383906\pi$
$380$	3273.21	−	2378.13i	0.441875	−	0.321041i
$381$	2486.80	−	5588.92i	0.334390	−	0.751520i
$382$	7343.27	+	2385.97i	0.983545	+	0.319573i
$383$	−7203.22	+	9914.38i	−0.961011	+	1.32272i	−0.0145520	+	0.999894i	$0.504632\pi$
$383$	−7203.22	+	9914.38i	−0.961011	+	1.32272i	−0.946459	+	0.322824i	$0.895368\pi$
$384$	9172.15	−	10191.4i	1.21892	−	1.35437i
$385$	1800.96	+	3505.69i	0.238404	+	0.464068i
$386$		−	572.382i		−	0.0754753i
$387$	4516.24	+	2604.67i	0.593213	+	0.342126i
$388$	−2218.03	+	6826.40i	−0.290215	+	0.893191i
$389$	−7905.29	+	2568.59i	−1.03037	+	0.334788i	−0.774937	−	0.632039i	$-0.782218\pi$
$389$	−7905.29	+	2568.59i	−1.03037	+	0.334788i	−0.255434	+	0.966827i	$0.582218\pi$
$390$	−367.438	+	3503.73i	−0.0477076	+	0.454918i
$391$	525.767	+	723.657i	0.0680031	+	0.0935982i
$392$	−5231.71	−	16101.5i	−0.674084	−	2.07462i
$393$	773.161	+	1338.44i	0.0992387	+	0.171795i
$394$	−8992.09	−	6533.14i	−1.14978	−	0.835367i
$395$	−1991.58			−0.253689
$396$	−11078.5	−	8901.85i	−1.40584	−	1.12963i
$397$	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
$399$	−6066.66	−	10502.1i	−0.761185	−	1.31771i
$400$	994.756	+	3061.54i	0.124344	+	0.382693i
$401$	−2779.16	−	3825.19i	−0.346097	−	0.476361i	0.600113	−	0.799915i	$-0.295122\pi$
$401$	−2779.16	−	3825.19i	−0.346097	−	0.476361i	−0.946210	+	0.323554i	$0.895122\pi$
$402$	−844.822	+	8055.86i	−0.104816	+	0.999477i
$403$	5848.50	−	1900.29i	0.722914	−	0.234889i
$404$	3097.26	−	9532.38i	0.381422	−	1.17390i
$405$	1066.00	−	2400.25i	0.130790	−	0.294492i
$406$			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	−0.628598	−	0.777730i	$-0.716371\pi$
$409$	2525.42	−	3475.94i	0.305315	−	0.420230i	0.933913	+	0.357500i	$0.116371\pi$
$410$	−3528.55	−	1146.50i	−0.425031	−	0.138101i
$411$	−2624.46	+	5898.31i	−0.314976	+	0.707888i
$412$	4328.85	−	3145.09i	0.517639	−	0.376087i
$413$	−2690.93	+	1955.07i	−0.320610	+	0.232937i
$414$	2054.93	+	4609.72i	0.243948	+	0.547235i
$415$	−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	$-0.322632\pi$
$420$	−7921.44	+	1685.67i	−0.920302	+	0.195839i
$421$	2275.11	−	7002.06i	0.263378	−	0.810593i	−0.728685	−	0.684849i	$-0.759868\pi$
$421$	2275.11	−	7002.06i	0.263378	−	0.810593i	0.992063	−	0.125744i	$-0.0401318\pi$
$422$	10186.0	−	3309.63i	1.17499	−	0.381778i
$423$	−3969.70	+	3577.65i	−0.456296	+	0.411233i
$424$	875.607	+	1205.17i	0.100291	+	0.138038i
$425$	−784.475	−	2414.37i	−0.0895356	−	0.275562i
$426$	−12624.1	+	7292.45i	−1.43578	+	0.829390i
$427$	−7726.04	−	5613.30i	−0.875619	−	0.636174i
$428$	−17917.1			−2.02350
$429$	−6332.49	−	4080.39i	−0.712670	−	0.459214i
$430$	−3294.42			−0.369467
$431$	11648.5	+	8463.12i	1.30183	+	0.945834i	0.999972	−	0.00751966i	$-0.00239360\pi$
$431$	11648.5	+	8463.12i	1.30183	+	0.945834i	0.301857	+	0.953353i	$0.402394\pi$
$432$	3260.01	−	2371.99i	0.363072	−	0.264172i
$433$	518.298	+	1595.16i	0.0575238	+	0.177040i	0.975690	−	0.219155i	$-0.0703302\pi$
$433$	518.298	+	1595.16i	0.0575238	+	0.177040i	−0.918166	+	0.396196i	$0.870330\pi$
$434$	12916.9	+	17778.7i	1.42865	+	1.96637i
$435$	3659.51	+	383.775i	0.403356	+	0.0423002i
$436$	−10838.8	+	3521.73i	−1.19056	+	0.386835i
$437$	949.425	−	2922.03i	0.103929	−	0.319862i
$438$	−1544.67	−	7258.87i	−0.168510	−	0.791877i
$439$		−	3555.94i		−	0.386596i	−0.981140	−	0.193298i	$-0.938082\pi$
$439$		−	3555.94i		−	0.386596i	0.981140	−	0.193298i	$-0.0619184\pi$
$440$	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	$-0.191430\pi$
$443$	10807.1	+	3511.45i	1.15906	+	0.376600i	0.334509	+	0.942393i	$0.391430\pi$
$444$	−22986.0	−	10227.7i	−2.45691	−	1.09321i
$445$	3072.62	−	2232.39i	0.327317	−	0.237810i
$446$	189.593	−	137.748i	0.0201289	−	0.0146245i
$447$	−16701.6	−	7431.40i	−1.76724	−	0.786338i
$448$	21065.7	+	6844.65i	2.22156	+	0.721829i
$449$	4710.80	−	6483.87i	0.495137	−	0.681498i	−0.486188	−	0.873854i	$-0.661613\pi$
$449$	4710.80	−	6483.87i	0.495137	−	0.681498i	0.981325	+	0.192356i	$0.0616129\pi$
$450$	−1503.82	−	14244.6i	−0.157535	−	1.49221i
$451$	5591.16	−	5628.50i	0.583763	−	0.587663i
$452$			26768.5i			2.78558i
$453$	1177.53	+	5533.54i	0.122130	+	0.573926i
$454$	9070.68	−	27916.7i	0.937683	−	2.88589i
$455$	−4082.83	+	1326.59i	−0.420672	+	0.136685i
$456$	−12244.9	−	1284.13i	−1.25750	−	0.131874i
$457$	1365.24	+	1879.09i	0.139744	+	0.192341i	0.873153	−	0.487447i	$-0.162072\pi$
$457$	1365.24	+	1879.09i	0.139744	+	0.192341i	−0.733409	+	0.679788i	$0.762072\pi$
$458$	−1432.05	−	4407.38i	−0.146103	−	0.449658i
$459$	−2570.88	+	1870.58i	−0.261434	+	0.190220i
$460$	−1659.78	−	1205.90i	−0.168234	−	0.122230i
$461$	−7704.57			−0.778390			−0.389195	−	0.921155i	$-0.627247\pi$
$461$	−7704.57			−0.778390			−0.389195	+	0.921155i	$0.627247\pi$
$462$	6874.97	−	26028.0i	0.692322	−	2.62107i
$463$	−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
$465$	2508.42	−	1449.01i	0.250162	−	0.144508i
$466$	−2343.97	−	7214.00i	−0.233009	−	0.717129i
$467$	−2820.00	−	3881.39i	−0.279430	−	0.384603i	0.646115	−	0.763240i	$-0.276393\pi$
$467$	−2820.00	−	3881.39i	−0.279430	−	0.384603i	−0.925545	+	0.378637i	$0.876393\pi$
$468$	11499.1	−	10363.5i	1.13578	−	1.02362i
$469$	−9387.33	+	3050.13i	−0.924236	+	0.300302i
$470$	1043.51	−	3211.58i	0.102411	−	0.315190i
$471$	10560.5	−	2247.26i	1.03313	−	0.219847i
$472$			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
$477$	−537.987	−	1206.84i	−0.0516409	−	0.115843i
$478$	8435.75	−	6128.93i	0.807202	−	0.586466i
$479$	−2237.37	+	1625.54i	−0.213420	+	0.155058i	−0.689360	−	0.724419i	$-0.742108\pi$
$479$	−2237.37	+	1625.54i	−0.213420	+	0.155058i	0.475940	+	0.879478i	$0.342108\pi$
$480$	817.558	−	1837.41i	0.0777422	−	0.174721i
$481$	−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
$486$	−16379.8	+	7315.44i	−1.52881	+	0.682788i
$487$	−6266.13	+	19285.2i	−0.583051	+	1.79445i	0.0239114	+	0.999714i	$0.492388\pi$
$487$	−6266.13	+	19285.2i	−0.583051	+	1.79445i	−0.606962	+	0.794731i	$0.707612\pi$
$488$	−9219.96	+	2995.75i	−0.855262	+	0.277892i
$489$	492.354	−	4694.87i	0.0455317	−	0.434170i
$490$	−5577.57	−	7676.87i	−0.514222	−	0.707766i
$491$	4140.97	+	12744.6i	0.380610	+	1.17140i	0.939615	+	0.342233i	$0.111183\pi$
$491$	4140.97	+	12744.6i	0.380610	+	1.17140i	−0.559005	+	0.829164i	$0.688817\pi$
$492$	8154.56	+	14116.6i	0.747227	+	1.29354i
$493$	−3603.72	−	2618.26i	−0.329216	−	0.239189i
$494$	−14648.9			−1.33418
$495$	−3317.82	−	1259.18i	−0.301262	−	0.114335i
$496$	4446.93			0.402567
$497$	−14372.6	−	10442.3i	−1.29718	−	0.942459i
$498$	7738.82	+	13396.9i	0.696355	+	1.20548i
$499$	6230.41	+	19175.2i	0.558940	+	1.72024i	0.685303	+	0.728258i	$0.259670\pi$
$499$	6230.41	+	19175.2i	0.558940	+	1.72024i	−0.126363	+	0.991984i	$0.540330\pi$
$500$	7241.39	+	9966.92i	0.647690	+	0.891468i
$501$	1484.81	−	14158.5i	0.132408	−	1.26258i
$502$	−22032.7	+	7158.86i	−1.95890	+	0.636486i
$503$	−2567.73	+	7902.65i	−0.227613	+	0.700520i	0.770403	+	0.637557i	$0.220055\pi$
$503$	−2567.73	+	7902.65i	−0.227613	+	0.700520i	−0.998016	+	0.0629630i	$0.979945\pi$
$504$	21349.1	+	12312.8i	1.88684	+	1.08820i
$505$		−	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	$-0.477797\pi$
$509$	−5285.57	−	1717.39i	−0.460273	−	0.149552i	−0.529970	+	0.848017i	$0.677797\pi$
$510$	816.730	−	1835.55i	0.0709126	−	0.159371i
$511$	7316.32	−	5315.62i	0.633375	−	0.460174i
$512$	8159.05	−	5927.90i	0.704263	−	0.511677i
$513$	10388.4	+	3367.45i	0.894076	+	0.289818i
$514$	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
$519$	4489.34	−	955.324i	0.379692	−	0.0807978i
$520$	−1346.67	+	4144.62i	−0.113568	+	0.349526i
$521$	13655.4	−	4436.90i	1.14828	−	0.373098i	0.327783	−	0.944753i	$-0.393698\pi$
$521$	13655.4	−	4436.90i	1.14828	−	0.373098i	0.820494	+	0.571655i	$0.193698\pi$
$522$	−16826.2	−	18670.0i	−1.41085	−	1.56545i
$523$	−10872.8	−	14965.1i	−0.909053	−	1.25120i	−0.967489	−	0.252913i	$-0.918611\pi$
$523$	−10872.8	−	14965.1i	−0.909053	−	1.25120i	0.0584360	−	0.998291i	$-0.481389\pi$
$524$	1326.24	+	4081.76i	0.110567	+	0.340291i
$525$	15113.9	−	8730.69i	1.25643	−	0.725787i
$526$	23001.7	+	16711.7i	1.90670	+	1.38530i
$527$	−3506.90			−0.289873
$528$	−3443.34	−	4221.35i	−0.283810	−	0.347937i
$529$	10609.0			0.871952
$530$	675.482	+	490.766i	0.0553605	+	0.0402217i
$531$	621.324	−	2929.76i	0.0507781	−	0.239436i
$532$	−10406.4	−	32027.8i	−0.848077	−	2.61011i
$533$	5079.36	+	6991.13i	0.412779	+	0.568142i
$534$	−25800.6	−	2705.72i	−2.09083	−	0.219266i
$535$	−4254.99	+	1382.53i	−0.343849	+	0.111723i
$536$	−3096.29	+	9529.40i	−0.249514	+	0.767924i
$537$	1559.41	+	7328.10i	0.125313	+	0.588884i
$538$		−	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	−0.785020	−	0.619470i	$-0.787347\pi$
$541$	587.839	−	809.091i	0.0467157	−	0.0642986i	0.831736	+	0.555172i	$0.187347\pi$
$542$	30970.5	+	10062.9i	2.45442	+	0.797489i
$543$	−1620.05	−	720.845i	−0.128035	−	0.0569694i
$544$	−1969.63	+	1431.02i	−0.155234	+	0.112784i
$545$	−2302.26	+	1672.69i	−0.180950	+	0.131468i
$546$	26790.7	+	11920.6i	2.09988	+	0.934346i
$547$	−377.124	−	122.535i	−0.0294783	−	0.00957809i	0.294241	−	0.955731i	$-0.404933\pi$
$547$	−377.124	−	122.535i	−0.0294783	−	0.00957809i	−0.323719	+	0.946153i	$0.604933\pi$
$548$	−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
$552$	1299.44	+	6106.46i	0.100196	+	0.470848i
$553$	−5122.52	+	15765.5i	−0.393909	+	1.21233i
$554$	6367.37	−	2068.89i	0.488310	−	0.158662i
$555$	−6247.93	−	655.224i	−0.477856	−	0.0501130i
$556$	13771.3	+	18954.6i	1.05042	+	1.44578i
$557$	547.966	+	1686.46i	0.0416841	+	0.128290i	0.969733	−	0.244168i	$-0.0785149\pi$
$557$	547.966	+	1686.46i	0.0416841	+	0.128290i	−0.928049	+	0.372459i	$0.878515\pi$
$558$	−19356.6	−	4105.02i	−1.46851	−	0.311433i
$559$	6207.78	+	4510.22i	0.469698	+	0.341255i
$560$	−3104.40			−0.234258
$561$	2715.45	+	3329.00i	0.204361	+	0.250536i
$562$	1509.84			0.113325
$563$	3873.68	+	2814.39i	0.289975	+	0.210679i	0.723257	−	0.690579i	$-0.242644\pi$
$563$	3873.68	+	2814.39i	0.289975	+	0.210679i	−0.433281	+	0.901259i	$0.642644\pi$
$564$	−12848.5	+	7422.04i	−0.959253	+	0.554121i
$565$	2065.52	+	6357.02i	0.153800	+	0.473348i
$566$	−20197.4	−	27799.3i	−1.49993	−	2.06448i
$567$	−16258.7	−	14612.2i	−1.20423	−	1.08228i
$568$	−17151.7	+	5572.94i	−1.26703	+	0.411682i
$569$	2817.82	−	8672.36i	0.207608	−	0.638953i	−0.791988	−	0.610537i	$-0.790954\pi$
$569$	2817.82	−	8672.36i	0.207608	−	0.638953i	0.999596	−	0.0284161i	$-0.00904634\pi$
$570$	−6749.59	+	1436.30i	−0.495981	+	0.105544i
$571$			2615.36i			0.191680i	0.995397	+	0.0958401i	$0.0305537\pi$
$571$			2615.36i			0.191680i	−0.995397	+	0.0958401i	$0.969446\pi$
$572$	−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
$576$	−18215.9	+	8120.33i	−1.31770	+	0.587408i
$577$	16380.0	−	11900.8i	1.18182	−	0.858639i	0.189440	−	0.981892i	$-0.439333\pi$
$577$	16380.0	−	11900.8i	1.18182	−	0.858639i	0.992375	+	0.123253i	$0.0393326\pi$
$578$	16855.7	−	12246.4i	1.21298	−	0.881285i
$579$	−255.307	+	573.786i	−0.0183251	+	0.0411844i
$580$	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
$585$	1931.16	−	3348.43i	0.136485	−	0.236651i
$586$	12545.5	−	38611.2i	0.884388	−	2.72187i
$587$	−25073.9	+	8147.01i	−1.76305	+	0.572850i	−0.997509	−	0.0705343i	$-0.977530\pi$
$587$	−25073.9	+	8147.01i	−1.76305	+	0.572850i	−0.765543	+	0.643385i	$0.777530\pi$
$588$	−4348.82	+	41468.4i	−0.305004	+	2.90838i
$589$	7080.20	+	9745.05i	0.495305	+	0.681728i
$590$	584.811	+	1799.86i	0.0408072	+	0.125592i
$591$	6100.09	+	10560.0i	0.424576	+	0.734995i
$592$	−7801.93	−	5668.43i	−0.541651	−	0.393532i
$593$	−25415.1			−1.75999			−0.879994	−	0.474984i	$-0.842454\pi$
$593$	−25415.1			−1.75999			−0.879994	+	0.474984i	$0.842454\pi$
$594$	11091.4	+	21553.3i	0.766135	+	1.48879i
$595$	2448.16			0.168680
$596$	−41063.4	−	29834.3i	−2.82219	−	2.05044i
$597$	1959.85	+	3392.74i	0.134357	+	0.232589i
$598$	2295.43	+	7064.61i	0.156968	+	0.483099i
$599$	389.495	+	536.094i	0.0265682	+	0.0365679i	0.822094	−	0.569351i	$-0.192806\pi$
$599$	389.495	+	536.094i	0.0265682	+	0.0365679i	−0.795526	+	0.605919i	$0.792806\pi$
$600$	1848.02	−	17621.9i	0.125742	−	1.19902i
$601$	11979.2	−	3892.29i	0.813051	−	0.264176i	0.127161	−	0.991882i	$-0.459413\pi$
$601$	11979.2	−	3892.29i	0.813051	−	0.264176i	0.685889	+	0.727706i	$0.259413\pi$
$602$	−8473.53	+	26078.8i	−0.573680	+	1.76561i
$603$	4440.16	−	7698.80i	0.299863	−	0.519933i
$604$			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	−0.764623	−	0.644478i	$-0.777075\pi$
$607$	1265.09	−	1741.25i	0.0845937	−	0.116433i	0.849216	+	0.528045i	$0.177075\pi$
$608$	7953.10	+	2584.12i	0.530495	+	0.172368i
$609$	12450.6	−	27981.8i	0.828444	−	1.86187i
$610$	−4395.88	+	3193.79i	−0.291777	+	0.211988i
$611$	−6363.12	+	4623.08i	−0.421317	+	0.306104i
$612$	−8063.03	+	3594.36i	−0.532563	+	0.237407i
$613$	−22207.2	−	7215.55i	−1.46320	−	0.475422i	−0.534152	−	0.845388i	$-0.679369\pi$
$613$	−22207.2	−	7215.55i	−1.46320	−	0.475422i	−0.929045	+	0.369966i	$0.879369\pi$
$614$	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	$0.794990\pi$
$618$	−8926.39	+	1899.52i	−0.581022	+	0.123641i
$619$	988.749	−	3043.06i	0.0642022	−	0.197594i	−0.913810	−	0.406142i	$-0.866874\pi$
$619$	988.749	−	3043.06i	0.0642022	−	0.197594i	0.978012	+	0.208548i	$0.0668738\pi$
$620$	7649.77	−	2485.56i	0.495520	−	0.161004i
$621$	−3.83965	−	5537.62i	−0.000248116	−	0.357838i
$622$	13055.1	+	17968.8i	0.841580	+	1.15834i
$623$	−9768.69	−	30064.9i	−0.628209	−	1.93343i
$624$	5138.08	−	2968.05i	0.329628	−	0.190412i
$625$	−8839.60	−	6422.35i	−0.565734	−	0.411030i
$626$	48641.3			3.10559
$627$	3768.40	−	14266.8i	0.240024	−	0.908710i
$628$	29979.0			1.90492
$629$	6152.68	+	4470.19i	0.390022	+	0.283367i
$630$	13512.8	+	2865.71i	0.854545	+	0.181226i
$631$	1039.41	+	3198.96i	0.0655754	+	0.201820i	0.978476	−	0.206362i	$-0.0661626\pi$
$631$	1039.41	+	3198.96i	0.0655754	+	0.201820i	−0.912900	+	0.408183i	$0.866163\pi$
$632$	9891.07	+	13613.9i	0.622540	+	0.856853i
$633$	−11687.2	−	1225.65i	−0.733848	−	0.0769591i
$634$	−29982.6	+	9741.94i	−1.87817	+	0.610256i
$635$	1310.61	−	4033.64i	0.0819054	−	0.252079i
$636$	−763.613	−	3588.44i	−0.0476088	−	0.223728i
$637$			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	$-0.534168\pi$
$641$	−12629.5	−	4103.58i	−0.778215	−	0.252857i	−0.671078	+	0.741387i	$0.734168\pi$
$642$	27920.4	+	12423.2i	1.71640	+	0.763715i
$643$	2328.32	−	1691.62i	0.142799	−	0.103750i	−0.514092	−	0.857735i	$-0.671871\pi$
$643$	2328.32	−	1691.62i	0.142799	−	0.103750i	0.656891	+	0.753985i	$0.271871\pi$
$644$	−13815.1	+	10037.3i	−0.845330	+	0.614168i
$645$	3302.50	+	1469.45i	0.201606	+	0.0897050i
$646$	7945.04	+	2581.50i	0.483891	+	0.157226i
$647$	12931.5	−	17798.7i	0.785765	−	1.08151i	−0.208858	−	0.977946i	$-0.566975\pi$
$647$	12931.5	−	17798.7i	0.785765	−	1.08151i	0.994623	−	0.103566i	$-0.0330254\pi$
$648$	−21701.7	+	4633.80i	−1.31562	+	0.280915i
$649$	−3999.05	−	619.748i	−0.241874	−	0.0374842i
$650$		−	21081.6i		−	1.27214i
$651$	−5018.59	−	23583.8i	−0.302141	−	1.41985i
$652$	4050.38	−	12465.8i	0.243290	−	0.748770i
$653$	18419.3	−	5984.78i	1.10383	−	0.358656i	0.300255	−	0.953859i	$-0.402928\pi$
$653$	18419.3	−	5984.78i	1.10383	−	0.358656i	0.803575	+	0.595203i	$0.202928\pi$
$654$	19332.0	+	2027.35i	1.15587	+	0.121217i
$655$	629.916	+	867.005i	0.0375769	+	0.0517201i
$656$	1931.06	+	5943.18i	0.114931	+	0.353723i
$657$	−1689.31	+	7965.68i	−0.100314	+	0.473015i
$658$	−22739.1	−	16520.9i	−1.34721	−	0.978804i
$659$	18331.7			1.08361			0.541806	−	0.840504i	$-0.317741\pi$
$659$	18331.7			1.08361			0.541806	+	0.840504i	$0.317741\pi$
$660$	−8282.83	−	5337.11i	−0.488498	−	0.314768i
$661$	−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
$663$	−4051.94	+	2340.64i	−0.237352	+	0.137108i
$664$	5914.06	+	18201.6i	0.345648	+	1.06379i
$665$	−4942.68	−	6803.01i	−0.288224	−	0.396706i
$666$	28727.6	+	31875.6i	1.67143	+	1.85459i
$667$	7378.71	−	2397.49i	0.428343	−	0.139177i
$668$	12214.9	−	37593.4i	0.707495	−	2.17745i
$669$	−251.500	+	53.5188i	−0.0145345	+	0.00309291i
$670$			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	−0.127461	−	0.991844i	$-0.540683\pi$
$673$	14931.5	−	20551.4i	0.855226	−	1.17712i	0.982687	−	0.185274i	$-0.0593172\pi$
$674$	−37868.7	−	12304.3i	−2.16417	−	0.703181i
$675$	−4846.18	+	14950.3i	−0.276340	+	0.852499i
$676$	−7211.68	+	5239.59i	−0.410314	+	0.298111i
$677$	−2170.78	+	1577.16i	−0.123235	+	0.0895351i	−0.647695	−	0.761900i	$-0.724267\pi$
$677$	−2170.78	+	1577.16i	−0.123235	+	0.0895351i	0.524461	+	0.851435i	$0.324267\pi$
$678$	18560.5	−	41713.5i	1.05134	−	2.36283i
$679$	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	$0.775408\pi$
$684$	26266.8	+	15149.0i	1.46833	+	0.846835i
$685$	−1383.16	+	4256.93i	−0.0771501	+	0.237444i
$686$	−28791.6	+	9354.95i	−1.60243	+	0.520661i
$687$	−530.326	+	5056.96i	−0.0294515	+	0.280837i
$688$	3261.52	+	4489.10i	0.180733	+	0.248757i
$689$	−600.950	−	1849.53i	−0.0332284	−	0.102266i
$690$	1750.31	+	3030.01i	0.0965699	+	0.167175i
$691$	−9343.66	−	6788.57i	−0.514399	−	0.373733i	0.300091	−	0.953911i	$-0.402983\pi$
$691$	−9343.66	−	6788.57i	−0.514399	−	0.373733i	−0.814490	+	0.580178i	$0.802983\pi$
$692$	12744.3			0.700092
$693$	−18501.5	+	23025.4i	−1.01416	+	1.26214i
$694$	−35291.7			−1.93034
$695$	4733.02	+	3438.74i	0.258322	+	0.187682i
$696$	−15551.4	−	26921.4i	−0.846944	−	1.46617i
$697$	−1522.85	−	4686.85i	−0.0827577	−	0.254702i
$698$	5096.72	+	7015.03i	0.276381	+	0.380405i
$699$	−868.037	+	8277.22i	−0.0469702	+	0.447887i
$700$	46092.0	−	14976.2i	2.48873	−	0.808639i
$701$	3137.61	−	9656.57i	0.169053	−	0.520291i	−0.830259	−	0.557377i	$-0.811808\pi$
$701$	3137.61	−	9656.57i	0.169053	−	0.520291i	0.999312	+	0.0370867i	$0.0118078\pi$
$702$	−25104.9	+	8176.32i	−1.34975	+	0.439594i
$703$		−	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
$708$	3380.55	−	7597.56i	0.179447	−	0.403296i
$709$	−8211.02	+	5965.65i	−0.434938	+	0.316001i	−0.783620	−	0.621240i	$-0.786629\pi$
$709$	−8211.02	+	5965.65i	−0.434938	+	0.316001i	0.348682	+	0.937241i	$0.386629\pi$
$710$	−8177.58	+	5941.36i	−0.432252	+	0.314050i
$711$	−6077.23	−	13632.7i	−0.320554	−	0.719081i
$712$	−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
$717$	−11190.2	+	2381.26i	−0.582855	+	0.124030i
$718$	−7356.79	+	22641.9i	−0.382386	+	1.17686i
$719$	21065.9	−	6844.74i	1.09267	−	0.355029i	0.293390	−	0.955993i	$-0.405217\pi$
$719$	21065.9	−	6844.74i	1.09267	−	0.355029i	0.799276	+	0.600964i	$0.205217\pi$
$720$	2076.40	−	1871.34i	0.107476	−	0.0968619i
$721$	−6536.73	−	8997.03i	−0.337643	−	0.464725i
$722$	1170.75	+	3603.18i	0.0603472	+	0.185729i
$723$	15190.3	−	8774.78i	0.781372	−	0.451366i
$724$	−3983.15	−	2893.92i	−0.204465	−	0.148552i
$725$	−22018.9			−1.12795
$726$	28251.5	−	16571.5i	1.44423	−	0.847145i
$727$	−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
$729$	19683.0	−	27.2954i	0.999999	−	0.00138675i
$730$	−1590.03	−	4893.62i	−0.0806161	−	0.248111i
$731$	−2572.07	−	3540.15i	−0.130139	−	0.179121i
$732$	23745.4	+	2490.19i	1.19898	+	0.125738i
$733$	14562.5	−	4731.64i	0.733803	−	0.238427i	0.0818055	−	0.996648i	$-0.473931\pi$
$733$	14562.5	−	4731.64i	0.733803	−	0.238427i	0.651997	+	0.758221i	$0.273931\pi$
$734$	−11789.4	+	36284.0i	−0.592854	+	1.82462i
$735$	2167.04	+	10183.5i	0.108752	+	0.511056i
$736$		−	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	0.113328	−	0.993558i	$-0.463849\pi$
$739$	20556.2	−	28293.2i	1.02324	−	1.40836i	0.909909	−	0.414807i	$-0.136151\pi$
$740$	−16589.5	−	5390.25i	−0.824110	−	0.267769i
$741$	14684.8	+	6534.04i	0.728017	+	0.323933i
$742$	5622.34	−	4084.87i	0.278170	−	0.202103i
$743$	6106.25	−	4436.45i	0.301503	−	0.219054i	−0.426739	−	0.904375i	$-0.640338\pi$
$743$	6106.25	−	4436.45i	0.301503	−	0.219054i	0.728242	+	0.685320i	$0.240338\pi$
$744$	−22363.0	−	9950.44i	−1.10197	−	0.490324i
$745$	−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
$750$	−4373.52	−	20552.5i	−0.212931	−	1.00063i
$751$	−4729.28	+	14555.2i	−0.229792	+	0.707227i	0.767978	+	0.640477i	$0.221263\pi$
$751$	−4729.28	+	14555.2i	−0.229792	+	0.707227i	−0.997770	+	0.0667507i	$0.978737\pi$
$752$	−5409.31	+	1757.59i	−0.262310	+	0.0852297i
$753$	25280.0	+	2651.12i	1.22344	+	0.128303i
$754$	−21743.0	−	29926.6i	−1.05018	−	1.44544i
$755$	1212.11	+	3730.48i	0.0584278	+	0.179822i
$756$	−35710.7	−	49079.9i	−1.71797	−	2.36114i
$757$	18433.0	+	13392.4i	0.885020	+	0.643005i	0.934575	−	0.355767i	$-0.115780\pi$
$757$	18433.0	+	13392.4i	0.885020	+	0.643005i	−0.0495547	+	0.998771i	$0.515780\pi$
$758$	18208.9			0.872527
$759$	−7470.84	+	418.203i	−0.357278	+	0.0199998i
$760$	−8536.24			−0.407424
$761$	6732.74	+	4891.62i	0.320712	+	0.233011i	0.736479	−	0.676460i	$-0.236487\pi$
$761$	6732.74	+	4891.62i	0.320712	+	0.233011i	−0.415767	+	0.909471i	$0.636487\pi$
$762$	−25085.2	+	14490.7i	−1.19257	+	0.688901i
$763$	7319.52	+	22527.2i	0.347293	+	1.06886i
$764$	−13826.3	−	19030.3i	−0.654736	−	0.901166i
$765$	−1637.47	+	1475.76i	−0.0773893	+	0.0697465i
$766$	55195.8	−	17934.2i	2.60353	−	0.845939i
$767$	1362.12	−	4192.17i	0.0641242	−	0.197354i
$768$	−33477.6	+	7123.97i	−1.57294	+	0.334719i
$769$			21833.4i			1.02384i	0.859033	+	0.511920i	$0.171066\pi$
$769$			21833.4i			1.02384i	−0.859033	+	0.511920i	$0.828934\pi$
$770$	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	$-0.417513\pi$
$773$	−2247.96	−	730.407i	−0.104597	−	0.0339857i	−0.360848	+	0.932625i	$0.617513\pi$
$774$	−10052.8	−	22550.9i	−0.466848	−	1.04725i
$775$	−14024.4	+	10189.3i	−0.650026	+	0.472272i
$776$	12251.6	−	8901.31i	0.566762	−	0.411777i
$777$	−21257.0	+	47773.8i	−0.981457	+	2.20576i
$778$	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
$783$	8539.85	+	26221.1i	0.389769	+	1.19676i
$784$	−4938.91	+	15200.4i	−0.224987	+	0.692438i
$785$	7119.45	−	2313.25i	0.323699	−	0.105176i
$786$	763.479	−	7280.20i	0.0346468	−	0.330377i
$787$	−2059.32	−	2834.42i	−0.0932744	−	0.128381i	0.759829	−	0.650123i	$-0.225283\pi$
$787$	−2059.32	−	2834.42i	−0.0932744	−	0.128381i	−0.853104	+	0.521742i	$0.825283\pi$
$788$	10463.8	+	32204.3i	0.473043	+	1.45588i
$789$	−15604.0	−	27012.5i	−0.704078	−	1.21885i
$790$	7630.40	+	5543.81i	0.343642	+	0.249671i
$791$	55635.3			2.50084
$792$	7870.35	+	28933.3i	0.353107	+	1.29811i
$793$	12655.8			0.566733
$794$	−58300.7	−	42357.9i	−2.60581	−	1.89323i
$795$	−458.236	−	793.265i	−0.0204427	−	0.0353889i
$796$	3361.82	+	10346.6i	0.149694	+	0.460712i
$797$	−6218.98	−	8559.69i	−0.276396	−	0.380426i	0.648140	−	0.761521i	$-0.275547\pi$
$797$	−6218.98	−	8559.69i	−0.276396	−	0.380426i	−0.924536	+	0.381095i	$0.875547\pi$
$798$	−5990.68	+	57124.5i	−0.265749	+	2.53407i
$799$	4265.84	−	1386.05i	0.188879	−	0.0613706i
$800$	−3718.87	+	11445.5i	−0.164353	+	0.505825i
$801$	24657.0	+	14220.6i	1.08766	+	0.627289i
$802$			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
$807$	−15605.6	+	35072.6i	−0.680723	+	1.52988i
$808$	−17108.1	+	12429.8i	−0.744879	+	0.541186i
$809$	10339.0	−	7511.72i	0.449320	−	0.326450i	−0.340007	−	0.940423i	$-0.610430\pi$
$809$	10339.0	−	7511.72i	0.449320	−	0.326450i	0.789327	+	0.613973i	$0.210430\pi$
$810$	−10765.6	+	6228.80i	−0.466993	+	0.270195i
$811$	2674.98	+	869.153i	0.115821	+	0.0376327i	0.366354	−	0.930475i	$-0.380606\pi$
$811$	2674.98	+	869.153i	0.115821	+	0.0376327i	−0.250533	+	0.968108i	$0.580606\pi$
$812$	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
$816$	−3309.76	+	704.310i	−0.141991	+	0.0302154i
$817$	−4644.62	+	14294.7i	−0.198892	+	0.612126i
$818$	−19351.4	+	6287.66i	−0.827147	+	0.268756i
$819$	−21539.3	−	23899.6i	−0.918981	−	1.01968i
$820$	6643.75	+	9144.33i	0.282939	+	0.389432i
$821$	5396.04	+	16607.3i	0.229383	+	0.705967i	0.997817	+	0.0660384i	$0.0210360\pi$
$821$	5396.04	+	16607.3i	0.229383	+	0.705967i	−0.768435	+	0.639928i	$0.778964\pi$
$822$	26473.9	−	15292.8i	1.12334	−	0.648904i
$823$	7263.11	+	5276.96i	0.307626	+	0.223503i	0.730877	−	0.682509i	$-0.239111\pi$
$823$	7263.11	+	5276.96i	0.307626	+	0.223503i	−0.423251	+	0.906012i	$0.639111\pi$
$824$	−11289.2			−0.477281
$825$	20531.7	+	5423.20i	0.866452	+	0.228862i
$826$	15752.0			0.663539
$827$	−12478.5	−	9066.20i	−0.524694	−	0.381212i	0.293675	−	0.955905i	$-0.405122\pi$
$827$	−12478.5	−	9066.20i	−0.524694	−	0.381212i	−0.818369	+	0.574693i	$0.805122\pi$
$828$	3189.86	−	15041.3i	0.133883	−	0.631306i
$829$	−13225.8	−	40704.9i	−0.554103	−	1.70535i	−0.698301	−	0.715805i	$-0.746060\pi$
$829$	−13225.8	−	40704.9i	−0.554103	−	1.70535i	0.144198	−	0.989549i	$-0.453940\pi$
$830$	6305.03	+	8678.13i	0.263676	+	0.362919i
$831$	−7305.81	−	766.165i	−0.304977	−	0.0319831i
$832$	−27916.7	+	9070.69i	−1.16327	+	0.377968i
$833$	3894.88	−	11987.2i	0.162004	−	0.498598i
$834$	−8317.37	−	39085.7i	−0.345332	−	1.62282i
$835$		−	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	$-0.358464\pi$
$839$	6014.79	+	1954.32i	0.247501	+	0.0804180i	−0.182639	+	0.983180i	$0.558464\pi$
$840$	15611.5	+	6946.39i	0.641250	+	0.285325i
$841$	−11526.1	+	8374.21i	−0.472595	+	0.343360i
$842$	−28207.8	+	20494.2i	−1.15452	+	0.838808i
$843$	−1513.54	−	673.454i	−0.0618378	−	0.0275148i
$844$	−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
$849$	7847.25	+	36876.5i	0.317217	+	1.49069i
$850$	−3715.11	+	11433.9i	−0.149914	+	0.461389i
$851$	−12597.8	+	4093.27i	−0.507458	+	0.164883i
$852$	44173.2	+	4632.47i	1.77623	+	0.186274i
$853$	2300.51	+	3166.38i	0.0923423	+	0.127098i	0.852688	−	0.522420i	$-0.174971\pi$
$853$	2300.51	+	3166.38i	0.0923423	+	0.127098i	−0.760346	+	0.649518i	$0.774971\pi$
$854$	13975.7	+	43012.8i	0.559999	+	1.72350i
$855$	7406.81	+	1570.79i	0.296266	+	0.0628302i
$856$	30582.7	+	22219.7i	1.22114	+	0.887211i
$857$	−8792.80			−0.350474			−0.175237	−	0.984526i	$-0.556069\pi$
$857$	−8792.80			−0.350474			−0.175237	+	0.984526i	$0.556069\pi$
$858$	12903.6	+	33260.6i	0.513428	+	1.32342i
$859$	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
$861$	29339.7	−	16948.3i	1.16132	−	0.670845i
$862$	−21071.1	−	64850.1i	−0.832579	−	2.56242i
$863$	19276.4	+	26531.7i	0.760344	+	1.04652i	0.997185	+	0.0749756i	$0.0238879\pi$
$863$	19276.4	+	26531.7i	0.760344	+	1.04652i	−0.236841	+	0.971548i	$0.576112\pi$
$864$	15072.1	−	10.4506i	0.593478	−	0.000411502i
$865$	3026.52	−	983.377i	0.118965	−	0.0386541i
$866$	2454.55	−	7554.33i	0.0963153	−	0.296428i
$867$	−22359.5	+	4758.06i	−0.875857	+	0.186381i
$868$		−	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
$873$	−12268.6	+	5469.11i	−0.475633	+	0.212029i
$874$	−11771.4	+	8552.43i	−0.455576	+	0.330996i
$875$	20715.1	−	15050.4i	0.800341	−	0.581482i
$876$	−9191.33	+	20656.9i	−0.354505	+	0.796726i
$877$	−30301.8	−	9845.67i	−1.16673	−	0.379093i	−0.339307	−	0.940676i	$-0.610193\pi$
$877$	−30301.8	−	9845.67i	−1.16673	−	0.379093i	−0.827421	+	0.561583i	$0.810193\pi$
$878$	−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	$-0.378473\pi$
$882$	35529.8	−	61605.1i	1.35641	−	2.35187i
$883$	−1711.94	+	5268.80i	−0.0652450	+	0.200803i	−0.978365	−	0.206889i	$-0.933666\pi$
$883$	−1711.94	+	5268.80i	−0.0652450	+	0.200803i	0.913120	+	0.407692i	$0.133666\pi$
$884$	−12357.0	+	4015.02i	−0.470147	+	0.152760i
$885$	216.571	−	2065.13i	0.00822595	−	0.0784391i
$886$	−31631.1	−	43536.5i	−1.19940	−	1.65083i
$887$	−13039.9	−	40132.7i	−0.493616	−	1.51919i	−0.819103	−	0.573647i	$-0.805528\pi$
$887$	−13039.9	−	40132.7i	−0.493616	−	1.51919i	0.325487	−	0.945547i	$-0.394472\pi$
$888$	26551.1	+	45963.3i	1.00337	+	1.73697i
$889$	−28559.6	−	20749.7i	−1.07745	−	0.782817i
$890$	−17986.3			−0.677420
$891$	−1504.88	−	26553.4i	−0.0565828	−	0.998398i
$892$	−713.953			−0.0267992
$893$	−12464.0	−	9055.66i	−0.467070	−	0.339346i
$894$	43303.1	+	74963.1i	1.61999	+	2.80441i
$895$	1605.20	+	4940.29i	0.0599506	+	0.184509i
$896$	−46508.4	−	64013.4i	−1.73408	−	2.38676i
$897$	850.061	−	8105.81i	0.0316418	−	0.301723i
$898$	−36097.3	+	11728.7i	−1.34141	+	0.435849i
$899$	−9399.50	+	28928.7i	−0.348711	+	1.07322i
$900$	−21801.3	+	37801.3i	−0.807455	+	1.40005i
$901$			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
$906$	10891.8	−	24478.6i	0.399400	−	0.897625i
$907$	1454.65	−	1056.87i	0.0532535	−	0.0386909i	−0.560840	−	0.827924i	$-0.689522\pi$
$907$	1454.65	−	1056.87i	0.0532535	−	0.0386909i	0.614094	+	0.789233i	$0.289522\pi$
$908$	−72346.8	+	52563.0i	−2.64418	+	1.92111i
$909$	17131.8	−	7637.06i	0.625111	−	0.278664i
$910$	19335.4	+	6282.45i	0.704354	+	0.228858i
$911$	10729.9	−	14768.4i	0.390228	−	0.537102i	−0.568030	−	0.823008i	$-0.692294\pi$
$911$	10729.9	−	14768.4i	0.390228	−	0.537102i	0.958258	+	0.285905i	$0.0922943\pi$
$912$	8639.34	+	7775.28i	0.313681	+	0.282309i
$913$	−22643.0	+	3663.60i	−0.820782	+	0.132801i
$914$		−	10999.7i		−	0.398072i
$915$	5831.24	−	1240.88i	0.210683	−	0.0448329i
$916$	−4362.76	+	13427.2i	−0.157369	+	0.484331i
$917$	8483.47	−	2756.45i	0.305506	−	0.0992649i
$918$	15056.9	−	10.4401i	0.541341	−	0.000375352i
$919$	20840.0	+	28683.8i	0.748040	+	1.02959i	0.998116	+	0.0613626i	$0.0195446\pi$
$919$	20840.0	+	28683.8i	0.748040	+	1.02959i	−0.250075	+	0.968226i	$0.580455\pi$
$920$	1337.60	+	4116.71i	0.0479341	+	0.147526i
$921$	−23068.5	+	13325.7i	−0.825336	+	0.476762i
$922$	29518.8	+	21446.6i	1.05439	+	0.766060i
$923$	23543.3			0.839585
$924$	−63553.1	+	51839.9i	−2.26271	+	1.84568i
$925$	37593.2			1.33628
$926$	25346.1	+	18415.0i	0.899485	+	0.653514i
$927$	9795.56	+	2077.38i	0.347064	+	0.0736031i
$928$	6525.42	+	20083.2i	0.230827	+	0.710412i
$929$	−3174.30	−	4369.05i	−0.112105	−	0.154299i	0.749278	−	0.662256i	$-0.230401\pi$
$929$	−3174.30	−	4369.05i	−0.112105	−	0.154299i	−0.861382	+	0.507957i	$0.830401\pi$
$930$	−13644.1	−	1430.86i	−0.481083	−	0.0504515i
$931$	−41173.8	+	13378.2i	−1.44943	+	0.470948i
$932$	−7140.96	+	21977.6i	−0.250976	+	0.772426i
$933$	−5072.27	−	23836.1i	−0.177984	−	0.836397i
$934$			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	−0.223774	+	0.974641i	$0.571838\pi$
$937$	−31021.4	+	42697.3i	−1.08156	+	1.48864i	−0.857789	+	0.514002i	$0.828162\pi$
$938$	44456.4	+	14444.8i	1.54750	+	0.502813i
$939$	−48760.7	−	21696.2i	−1.69462	−	0.754023i
$940$	−8322.90	+	6046.94i	−0.288791	+	0.209819i
$941$	−20671.9	+	15019.0i	−0.716137	+	0.520304i	−0.885148	−	0.465310i	$-0.845943\pi$
$941$	−20671.9	+	15019.0i	−0.716137	+	0.520304i	0.169011	+	0.985614i	$0.445943\pi$
$942$	−46716.4	−	20786.5i	−1.61582	−	0.718961i
$943$	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	$-0.168204\pi$
$948$	−8625.96	−	40535.9i	−0.295525	−	1.38876i
$949$	−3703.45	+	11398.0i	−0.126680	+	0.389880i
$950$	39273.4	−	12760.7i	1.34126	−	0.435802i
$951$	34401.5	+	3607.71i	1.17302	+	0.123016i
$952$	−12158.6	−	16734.9i	−0.413933	−	0.569730i
$953$	−2213.92	−	6813.74i	−0.0752527	−	0.231604i	0.906354	−	0.422520i	$-0.138854\pi$
$953$	−2213.92	−	6813.74i	−0.0752527	−	0.231604i	−0.981606	+	0.190916i	$0.938854\pi$
$954$	−1298.18	+	6121.35i	−0.0440566	+	0.207742i
$955$	−4751.91	−	3452.46i	−0.161014	−	0.116983i
$956$	−31766.6			−1.07469
$957$	34739.4	−	13477.3i	1.17342	−	0.455234i
$958$	13097.0			0.441696
$959$	30140.6	+	21898.4i	1.01490	+	0.737368i
$960$	−11973.5	+	6916.58i	−0.402544	+	0.232533i
$961$	−1805.88	−	5557.93i	−0.0606183	−	0.186564i
$962$	37122.1	+	51094.2i	1.24414	+	1.71241i
$963$	−22447.6	−	24907.4i	−0.751156	−	0.833468i
$964$	46324.8	−	15051.8i	1.54774	−	0.502891i
$965$	−134.554	+	414.114i	−0.00448854	+	0.0138143i
$966$	28487.7	−	6062.14i	0.948839	−	0.201911i
$967$		−	7152.16i		−	0.237847i	−0.992903	−	0.118923i	$-0.962056\pi$
$967$		−	7152.16i		−	0.237847i	0.992903	−	0.118923i	$-0.0379443\pi$
$968$	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	$-0.603272\pi$
$971$	−34305.3	−	11146.5i	−1.13379	−	0.368391i	−0.815015	+	0.579439i	$0.803272\pi$
$972$	53470.8	+	11301.0i	1.76448	+	0.372922i
$973$	39395.1	−	28622.2i	1.29799	−	0.943048i
$974$	77690.4	−	56445.3i	2.55581	−	1.85691i
$975$	−9403.32	+	21133.3i	−0.308869	+	0.694163i
$976$	8703.96	+	2828.09i	0.285458	+	0.0927509i
$977$	17592.3	−	24213.8i	0.576079	−	0.792904i	−0.417180	−	0.908824i	$-0.636981\pi$
$977$	17592.3	−	24213.8i	0.576079	−	0.792904i	0.993259	+	0.115920i	$0.0369815\pi$
$978$	−14955.1	+	16617.1i	−0.488970	+	0.543308i
$979$	17346.7	−	34326.9i	0.566296	−	1.12062i
$980$			28908.8i			0.942305i
$981$	−18475.1	−	10655.2i	−0.601290	−	0.346784i
$982$	19610.8	−	60355.7i	0.637276	−	1.96133i
$983$	−41628.8	+	13526.0i	−1.35071	+	0.438874i	−0.892932	−	0.450191i	$-0.851356\pi$
$983$	−41628.8	+	13526.0i	−1.35071	+	0.438874i	−0.457782	+	0.889065i	$0.651356\pi$
$984$	3587.44	−	34208.3i	0.116223	−	1.10825i
$985$	4969.92	+	6840.51i	0.160766	+	0.221276i
$986$	6518.81	+	20062.8i	0.210549	+	0.648002i
$987$	15425.9	+	26704.1i	0.497478	+	0.861197i
$988$	36104.9	+	26231.8i	1.16260	+	0.844680i
$989$	7621.57			0.245047
$990$	9206.58	+	14059.9i	0.295560	+	0.451367i
$991$	−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
$993$	−27702.7	−	47957.0i	−0.885317	−	1.53260i
$994$	25998.8	+	80016.0i	0.829609	+	2.55327i
$995$	1596.74	+	2197.73i	0.0508745	+	0.0700227i
$996$	4916.02	−	46877.0i	0.156396	−	1.49132i
$997$	11261.5	−	3659.07i	0.357728	−	0.116233i	−0.124639	−	0.992202i	$-0.539777\pi$
$997$	11261.5	−	3659.07i	0.357728	−	0.116233i	0.482367	+	0.875969i	$0.339777\pi$
$998$	29505.9	−	90809.8i	0.935864	−	2.88029i
$999$	−14580.2	−	44767.6i	−0.461759	−	1.41780i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.4.f.a.29.1	yes	40
3.2	odd	2	inner	33.4.f.a.29.10	yes	40
11.5	even	5		363.4.d.d.362.37		40
11.6	odd	10		363.4.d.d.362.3		40
11.8	odd	10	inner	33.4.f.a.8.10	yes	40
33.5	odd	10		363.4.d.d.362.4		40
33.8	even	10	inner	33.4.f.a.8.1	✓	40
33.17	even	10		363.4.d.d.362.38		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.4.f.a.8.1	✓	40	33.8	even	10	inner
33.4.f.a.8.10	yes	40	11.8	odd	10	inner
33.4.f.a.29.1	yes	40	1.1	even	1	trivial
33.4.f.a.29.10	yes	40	3.2	odd	2	inner
363.4.d.d.362.3		40	11.6	odd	10
363.4.d.d.362.4		40	33.5	odd	10
363.4.d.d.362.37		40	11.5	even	5
363.4.d.d.362.38		40	33.17	even	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} +(2.59912 + 4.49940i) q^{3} +(4.45840 + 13.7215i) q^{4} +(2.11757 + 2.91459i) q^{5} +(2.56657 - 24.4737i) q^{6} +(28.5187 - 9.26628i) q^{7} +(9.40652 - 28.9503i) q^{8} +(-13.4892 + 23.3889i) 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} +(-7.61008 + 17.1032i) q^{15} +(-23.2483 + 16.8909i) q^{16} +(18.3339 - 13.3204i) q^{17} +(116.788 - 52.0619i) 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} +(154.708 - 32.9215i) q^{24} +(34.6164 - 106.538i) q^{25} +(178.982 - 58.1549i) q^{26} +(-140.296 + 0.0972777i) q^{27} +(254.295 + 350.007i) q^{28} +(-60.7406 - 186.940i) q^{29} +(76.7656 - 44.3443i) q^{30} +(-125.194 - 90.9588i) q^{31} -107.431 q^{32} +(10.5952 + 189.274i) q^{33} -107.322 q^{34} +(87.3978 + 63.4982i) q^{35} +(-381.072 - 80.8153i) q^{36} +(103.703 + 319.166i) q^{37} +(216.676 + 298.229i) q^{38} +(-205.361 - 21.5364i) q^{39} +(104.297 - 33.8882i) q^{40} +(67.1986 - 206.816i) q^{41} +(-153.585 - 721.739i) 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} +(-136.424 - 60.7021i) q^{48} +(449.958 - 326.914i) q^{49} +(-429.190 + 311.825i) q^{50} +(107.586 + 47.8704i) 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} +(-84.1847 - 395.608i) q^{57} +(-287.654 + 885.309i) q^{58} +(-105.494 + 34.2770i) q^{59} +(-268.611 - 28.1693i) q^{60} +(-187.195 - 257.652i) q^{61} +(226.465 + 696.987i) q^{62} +(-167.966 + 792.016i) q^{63} +(597.590 + 434.175i) q^{64} -143.163 q^{65} +(486.275 - 754.666i) q^{66} -329.164 q^{67} +(264.516 + 192.182i) q^{68} +(-177.596 + 102.590i) q^{69} +(-158.095 - 486.565i) q^{70} +(-348.236 - 479.306i) q^{71} +(550.230 + 610.524i) q^{72} +(286.826 - 93.1954i) q^{73} +(491.116 - 1511.50i) q^{74} +(569.331 - 121.153i) 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} +(-365.084 - 630.995i) q^{81} +(-833.159 + 605.325i) q^{82} +(-508.644 + 369.552i) q^{83} +(-913.880 + 2053.89i) 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} +(399.045 + 230.143i) q^{90} +(-368.228 + 1133.29i) q^{91} +(-541.603 + 175.977i) q^{92} +(83.8661 - 799.710i) q^{93} +(-550.949 - 758.317i) q^{94} +(-86.6568 - 266.702i) q^{95} +(-279.225 - 483.375i) q^{96} +(402.482 + 292.420i) q^{97} -2633.94 q^{98} +(-824.082 + 539.618i) 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

Introduction

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