LMFDB - Embedded newform 33.4.e.a.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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([0, 2]))

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

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

chi := DirichletCharacter("33.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	33.e (of order $5$, 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:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			25.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	33.25
Dual form			33.4.e.a.4.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.61803 - 2.62866i) q^{2} +(0.927051 + 2.85317i) q^{3} +(3.70820 - 11.4127i) q^{4} +(-4.69098 - 3.40820i) q^{5} +(10.8541 + 7.88597i) q^{6} +(-4.72542 + 14.5434i) q^{7} +(-5.52786 - 17.0130i) q^{8} +(-7.28115 + 5.29007i) q^{9} +O(q^{10})$	\(q+(3.61803 - 2.62866i) q^{2} +(0.927051 + 2.85317i) q^{3} +(3.70820 - 11.4127i) q^{4} +(-4.69098 - 3.40820i) q^{5} +(10.8541 + 7.88597i) q^{6} +(-4.72542 + 14.5434i) q^{7} +(-5.52786 - 17.0130i) q^{8} +(-7.28115 + 5.29007i) q^{9} -25.9311 q^{10} +(-7.07953 - 35.7894i) q^{11} +36.0000 q^{12} +(-37.6976 + 27.3889i) q^{13} +(21.1327 + 65.0399i) q^{14} +(5.37539 - 16.5437i) q^{15} +(12.9443 + 9.40456i) q^{16} +(91.6033 + 66.5537i) q^{17} +(-12.4377 + 38.2793i) q^{18} +(-34.2426 - 105.388i) q^{19} +(-56.2918 + 40.8984i) q^{20} -45.8754 q^{21} +(-119.692 - 110.878i) q^{22} +12.1935 q^{23} +(43.4164 - 31.5439i) q^{24} +(-28.2376 - 86.9065i) q^{25} +(-64.3951 + 198.188i) q^{26} +(-21.8435 - 15.8702i) q^{27} +(148.456 + 107.860i) q^{28} +(86.7295 - 266.926i) q^{29} +(-24.0395 - 73.9859i) q^{30} +(-74.0967 + 53.8344i) q^{31} +214.663 q^{32} +(95.5501 - 53.3777i) q^{33} +506.371 q^{34} +(71.7336 - 52.1175i) q^{35} +(33.3738 + 102.714i) q^{36} +(-86.7092 + 266.863i) q^{37} +(-400.920 - 291.285i) q^{38} +(-113.093 - 82.1666i) q^{39} +(-32.0526 + 98.6478i) q^{40} +(1.85004 + 5.69383i) q^{41} +(-165.979 + 120.591i) q^{42} -126.915 q^{43} +(-434.705 - 51.9180i) q^{44} +52.1854 q^{45} +(44.1165 - 32.0525i) q^{46} +(72.3075 + 222.539i) q^{47} +(-14.8328 + 45.6507i) q^{48} +(88.3131 + 64.1632i) q^{49} +(-330.612 - 240.204i) q^{50} +(-104.968 + 323.059i) q^{51} +(172.790 + 531.794i) q^{52} +(-7.78367 + 5.65516i) q^{53} -120.748 q^{54} +(-88.7674 + 192.016i) q^{55} +273.548 q^{56} +(268.945 - 195.400i) q^{57} +(-387.866 - 1193.73i) q^{58} +(-96.3309 + 296.476i) q^{59} +(-168.875 - 122.695i) q^{60} +(719.565 + 522.795i) q^{61} +(-126.572 + 389.550i) q^{62} +(-42.5288 - 130.890i) q^{63} +(673.102 - 489.037i) q^{64} +270.185 q^{65} +(205.392 - 444.291i) q^{66} -589.717 q^{67} +(1099.24 - 798.645i) q^{68} +(11.3040 + 34.7901i) q^{69} +(122.536 - 377.126i) q^{70} +(-212.804 - 154.611i) q^{71} +(130.249 + 94.6316i) q^{72} +(-52.0801 + 160.286i) q^{73} +(387.775 + 1193.45i) q^{74} +(221.781 - 161.133i) q^{75} -1329.74 q^{76} +(553.952 + 66.1599i) q^{77} -625.161 q^{78} +(-403.586 + 293.222i) q^{79} +(-28.6687 - 88.2333i) q^{80} +(25.0304 - 77.0356i) q^{81} +(21.6606 + 15.7374i) q^{82} +(-261.316 - 189.857i) q^{83} +(-170.115 + 523.561i) q^{84} +(-202.881 - 624.405i) q^{85} +(-459.182 + 333.615i) q^{86} +841.988 q^{87} +(-569.751 + 318.283i) q^{88} -1183.82 q^{89} +(188.808 - 137.177i) q^{90} +(-220.189 - 677.673i) q^{91} +(45.2160 - 139.160i) q^{92} +(-222.290 - 161.503i) q^{93} +(846.591 + 615.084i) q^{94} +(-198.552 + 611.079i) q^{95} +(199.003 + 612.469i) q^{96} +(938.191 - 681.636i) q^{97} +488.183 q^{98} +(240.875 + 223.137i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 10 q^{2} - 3 q^{3} - 12 q^{4} - 21 q^{5} + 30 q^{6} + 37 q^{7} - 40 q^{8} - 9 q^{9}+O(q^{10}) $ 4 * q + 10 * q^2 - 3 * q^3 - 12 * q^4 - 21 * q^5 + 30 * q^6 + 37 * q^7 - 40 * q^8 - 9 * q^9	\( 4 q + 10 q^{2} - 3 q^{3} - 12 q^{4} - 21 q^{5} + 30 q^{6} + 37 q^{7} - 40 q^{8} - 9 q^{9} - 220 q^{10} + 41 q^{11} + 144 q^{12} - 77 q^{13} + 250 q^{14} + 102 q^{15} + 16 q^{16} + 192 q^{17} - 90 q^{18} - 52 q^{19} - 252 q^{20} - 264 q^{21} + 40 q^{22} - 148 q^{23} + 120 q^{24} - 426 q^{25} - 110 q^{26} - 27 q^{27} + 84 q^{28} + 414 q^{29} + 360 q^{30} - 198 q^{31} - 27 q^{33} + 1140 q^{34} + 477 q^{35} - 108 q^{36} + 201 q^{37} - 830 q^{38} - 231 q^{39} + 480 q^{40} - 129 q^{41} - 570 q^{42} - 132 q^{43} - 1068 q^{44} - 234 q^{45} - 150 q^{46} - 35 q^{47} + 48 q^{48} + 474 q^{49} - 30 q^{50} - 279 q^{51} + 396 q^{52} + 188 q^{53} + 356 q^{55} - 480 q^{56} + 519 q^{57} + 300 q^{58} - 1320 q^{59} - 756 q^{60} + 1275 q^{61} + 330 q^{62} + 333 q^{63} + 832 q^{64} + 638 q^{65} + 30 q^{66} + 150 q^{67} + 2304 q^{68} + 441 q^{69} - 3660 q^{70} + 117 q^{71} + 360 q^{72} - 982 q^{73} + 2450 q^{74} + 867 q^{75} - 2904 q^{76} + 1583 q^{77} - 1320 q^{78} - 1469 q^{79} - 544 q^{80} - 81 q^{81} + 270 q^{82} - 967 q^{83} + 1332 q^{84} + 27 q^{85} - 750 q^{86} + 792 q^{87} - 2440 q^{88} - 5424 q^{89} - 90 q^{90} - 561 q^{91} + 1764 q^{92} - 594 q^{93} + 2000 q^{94} - 707 q^{95} + 1440 q^{96} + 2391 q^{97} + 5280 q^{98} + 1044 q^{99}+O(q^{100}) \) 4 * q + 10 * q^2 - 3 * q^3 - 12 * q^4 - 21 * q^5 + 30 * q^6 + 37 * q^7 - 40 * q^8 - 9 * q^9 - 220 * q^10 + 41 * q^11 + 144 * q^12 - 77 * q^13 + 250 * q^14 + 102 * q^15 + 16 * q^16 + 192 * q^17 - 90 * q^18 - 52 * q^19 - 252 * q^20 - 264 * q^21 + 40 * q^22 - 148 * q^23 + 120 * q^24 - 426 * q^25 - 110 * q^26 - 27 * q^27 + 84 * q^28 + 414 * q^29 + 360 * q^30 - 198 * q^31 - 27 * q^33 + 1140 * q^34 + 477 * q^35 - 108 * q^36 + 201 * q^37 - 830 * q^38 - 231 * q^39 + 480 * q^40 - 129 * q^41 - 570 * q^42 - 132 * q^43 - 1068 * q^44 - 234 * q^45 - 150 * q^46 - 35 * q^47 + 48 * q^48 + 474 * q^49 - 30 * q^50 - 279 * q^51 + 396 * q^52 + 188 * q^53 + 356 * q^55 - 480 * q^56 + 519 * q^57 + 300 * q^58 - 1320 * q^59 - 756 * q^60 + 1275 * q^61 + 330 * q^62 + 333 * q^63 + 832 * q^64 + 638 * q^65 + 30 * q^66 + 150 * q^67 + 2304 * q^68 + 441 * q^69 - 3660 * q^70 + 117 * q^71 + 360 * q^72 - 982 * q^73 + 2450 * q^74 + 867 * q^75 - 2904 * q^76 + 1583 * q^77 - 1320 * q^78 - 1469 * q^79 - 544 * q^80 - 81 * q^81 + 270 * q^82 - 967 * q^83 + 1332 * q^84 + 27 * q^85 - 750 * q^86 + 792 * q^87 - 2440 * q^88 - 5424 * q^89 - 90 * q^90 - 561 * q^91 + 1764 * q^92 - 594 * q^93 + 2000 * q^94 - 707 * q^95 + 1440 * q^96 + 2391 * q^97 + 5280 * q^98 + 1044 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	3.61803	−	2.62866i	1.27917	−	0.929370i	0.279641	−	0.960105i	$-0.409785\pi$
$2$	3.61803	−	2.62866i	1.27917	−	0.929370i	0.999528	+	0.0307347i	$0.00978469\pi$
$3$	0.927051	+	2.85317i	0.178411	+	0.549093i
$3$	0.927051	+	2.85317i	0.178411	+	0.549093i
$4$	3.70820	−	11.4127i	0.463525	−	1.42658i
$5$	−4.69098	−	3.40820i	−0.419574	−	0.304839i	0.357892	−	0.933763i	$-0.383496\pi$
$5$	−4.69098	−	3.40820i	−0.419574	−	0.304839i	−0.777467	+	0.628924i	$0.783496\pi$
$6$	10.8541	+	7.88597i	0.738528	+	0.536572i
$7$	−4.72542	+	14.5434i	−0.255149	+	0.785268i	0.738651	+	0.674088i	$0.235463\pi$
$7$	−4.72542	+	14.5434i	−0.255149	+	0.785268i	−0.993800	+	0.111180i	$0.964537\pi$
$8$	−5.52786	−	17.0130i	−0.244299	−	0.751876i
$9$	−7.28115	+	5.29007i	−0.269672	+	0.195928i
$10$	−25.9311			−0.820014
$11$	−7.07953	−	35.7894i	−0.194051	−	0.980992i
$11$	−7.07953	−	35.7894i	−0.194051	−	0.980992i
$12$	36.0000			0.866025
$13$	−37.6976	+	27.3889i	−0.804263	+	0.584331i	−0.912162	−	0.409830i	$-0.865588\pi$
$13$	−37.6976	+	27.3889i	−0.804263	+	0.584331i	0.107898	+	0.994162i	$0.465588\pi$
$14$	21.1327	+	65.0399i	0.403426	+	1.24162i
$15$	5.37539	−	16.5437i	0.0925280	−	0.284772i
$16$	12.9443	+	9.40456i	0.202254	+	0.146946i
$17$	91.6033	+	66.5537i	1.30689	+	0.949509i	0.999997	−	0.00223673i	$-0.000711975\pi$
$17$	91.6033	+	66.5537i	1.30689	+	0.949509i	0.306889	+	0.951745i	$0.400712\pi$
$18$	−12.4377	+	38.2793i	−0.162866	+	0.501251i
$19$	−34.2426	−	105.388i	−0.413463	−	1.27251i	−0.913618	−	0.406573i	$-0.866724\pi$
$19$	−34.2426	−	105.388i	−0.413463	−	1.27251i	0.500155	−	0.865936i	$-0.333276\pi$
$20$	−56.2918	+	40.8984i	−0.629361	+	0.457258i
$21$	−45.8754			−0.476706
$22$	−119.692	−	110.878i	−1.15993	−	1.07451i
$23$	12.1935			0.110544			0.0552722	−	0.998471i	$-0.482397\pi$
$23$	12.1935			0.110544			0.0552722	+	0.998471i	$0.482397\pi$
$24$	43.4164	−	31.5439i	0.369264	−	0.268286i
$25$	−28.2376	−	86.9065i	−0.225901	−	0.695252i
$26$	−64.3951	+	198.188i	−0.485728	+	1.49492i
$27$	−21.8435	−	15.8702i	−0.155695	−	0.113119i
$28$	148.456	+	107.860i	1.00198	+	0.727983i
$29$	86.7295	−	266.926i	0.555354	−	1.70920i	−0.139653	−	0.990200i	$-0.544599\pi$
$29$	86.7295	−	266.926i	0.555354	−	1.70920i	0.695007	−	0.719003i	$-0.255401\pi$
$30$	−24.0395	−	73.9859i	−0.146300	−	0.450264i
$31$	−74.0967	+	53.8344i	−0.429296	+	0.311902i	−0.781367	−	0.624071i	$-0.785477\pi$
$31$	−74.0967	+	53.8344i	−0.429296	+	0.311902i	0.352071	+	0.935973i	$0.385477\pi$
$32$	214.663			1.18585
$33$	95.5501	−	53.3777i	0.504035	−	0.281572i
$34$	506.371			2.55417
$35$	71.7336	−	52.1175i	0.346434	−	0.251699i
$36$	33.3738	+	102.714i	0.154508	+	0.475528i
$37$	−86.7092	+	266.863i	−0.385268	+	1.18573i	0.551018	+	0.834493i	$0.314239\pi$
$37$	−86.7092	+	266.863i	−0.385268	+	1.18573i	−0.936286	+	0.351239i	$0.885761\pi$
$38$	−400.920	−	291.285i	−1.71152	−	1.24349i
$39$	−113.093	−	82.1666i	−0.464342	−	0.337364i
$40$	−32.0526	+	98.6478i	−0.126699	+	0.389940i
$41$	1.85004	+	5.69383i	0.00704700	+	0.0216884i	0.954518	−	0.298153i	$-0.0963705\pi$
$41$	1.85004	+	5.69383i	0.00704700	+	0.0216884i	−0.947471	+	0.319841i	$0.896370\pi$
$42$	−165.979	+	120.591i	−0.609787	+	0.443036i
$43$	−126.915			−0.450101			−0.225050	−	0.974347i	$-0.572255\pi$
$43$	−126.915			−0.450101			−0.225050	+	0.974347i	$0.572255\pi$
$44$	−434.705	−	51.9180i	−1.48941	−	0.177885i
$45$	52.1854			0.172874
$46$	44.1165	−	32.0525i	0.141405	−	0.102737i
$47$	72.3075	+	222.539i	0.224407	+	0.690654i	0.998351	+	0.0574000i	$0.0182810\pi$
$47$	72.3075	+	222.539i	0.224407	+	0.690654i	−0.773944	+	0.633254i	$0.781719\pi$
$48$	−14.8328	+	45.6507i	−0.0446028	+	0.137273i
$49$	88.3131	+	64.1632i	0.257473	+	0.187065i
$50$	−330.612	−	240.204i	−0.935111	−	0.679398i
$51$	−104.968	+	323.059i	−0.288205	+	0.887005i
$52$	172.790	+	531.794i	0.460802	+	1.41820i
$53$	−7.78367	+	5.65516i	−0.0201730	+	0.0146565i	−0.597826	−	0.801626i	$-0.703969\pi$
$53$	−7.78367	+	5.65516i	−0.0201730	+	0.0146565i	0.577653	+	0.816282i	$0.303969\pi$
$54$	−120.748			−0.304290
$55$	−88.7674	+	192.016i	−0.217625	+	0.470753i
$56$	273.548			0.652757
$57$	268.945	−	195.400i	0.624959	−	0.454059i
$58$	−387.866	−	1193.73i	−0.878092	−	2.70249i
$59$	−96.3309	+	296.476i	−0.212563	+	0.654202i	0.786755	+	0.617266i	$0.211760\pi$
$59$	−96.3309	+	296.476i	−0.212563	+	0.654202i	−0.999318	+	0.0369357i	$0.988240\pi$
$60$	−168.875	−	122.695i	−0.363362	−	0.263998i
$61$	719.565	+	522.795i	1.51034	+	1.09733i	0.966025	+	0.258448i	$0.0832112\pi$
$61$	719.565	+	522.795i	1.51034	+	1.09733i	0.544317	+	0.838879i	$0.316789\pi$
$62$	−126.572	+	389.550i	−0.259269	+	0.797949i
$63$	−42.5288	−	130.890i	−0.0850497	−	0.261756i
$64$	673.102	−	489.037i	1.31465	−	0.955151i
$65$	270.185			0.515575
$66$	205.392	−	444.291i	0.383061	−	0.828612i
$67$	−589.717			−1.07530			−0.537652	−	0.843167i	$-0.680689\pi$
$67$	−589.717			−1.07530			−0.537652	+	0.843167i	$0.680689\pi$
$68$	1099.24	−	798.645i	1.96033	−	1.42426i
$69$	11.3040	+	34.7901i	0.0197223	+	0.0606991i
$70$	122.536	−	377.126i	0.209226	−	0.643930i
$71$	−212.804	−	154.611i	−0.355707	−	0.258437i	0.395552	−	0.918444i	$-0.370553\pi$
$71$	−212.804	−	154.611i	−0.355707	−	0.258437i	−0.751259	+	0.660007i	$0.770553\pi$
$72$	130.249	+	94.6316i	0.213195	+	0.154895i
$73$	−52.0801	+	160.286i	−0.0835002	+	0.256987i	−0.984087	−	0.177690i	$-0.943138\pi$
$73$	−52.0801	+	160.286i	−0.0835002	+	0.256987i	0.900586	+	0.434677i	$0.143138\pi$
$74$	387.775	+	1193.45i	0.609161	+	1.87481i
$75$	221.781	−	161.133i	0.341454	−	0.248081i
$76$	−1329.74			−2.00699
$77$	553.952	+	66.1599i	0.819853	+	0.0979172i
$78$	−625.161			−0.907507
$79$	−403.586	+	293.222i	−0.574772	+	0.417596i	−0.836836	−	0.547454i	$-0.815597\pi$
$79$	−403.586	+	293.222i	−0.574772	+	0.417596i	0.262064	+	0.965051i	$0.415597\pi$
$80$	−28.6687	−	88.2333i	−0.0400658	−	0.123310i
$81$	25.0304	−	77.0356i	0.0343352	−	0.105673i
$82$	21.6606	+	15.7374i	0.0291709	+	0.0211939i
$83$	−261.316	−	189.857i	−0.345580	−	0.251078i	0.401433	−	0.915889i	$-0.368512\pi$
$83$	−261.316	−	189.857i	−0.345580	−	0.251078i	−0.747012	+	0.664810i	$0.768512\pi$
$84$	−170.115	+	523.561i	−0.220965	+	0.680062i
$85$	−202.881	−	624.405i	−0.258889	−	0.796779i
$86$	−459.182	+	333.615i	−0.575755	+	0.418310i
$87$	841.988			1.03759
$88$	−569.751	+	318.283i	−0.690178	+	0.385558i
$89$	−1183.82			−1.40994			−0.704972	−	0.709235i	$-0.749040\pi$
$89$	−1183.82			−1.40994			−0.704972	+	0.709235i	$0.749040\pi$
$90$	188.808	−	137.177i	0.221135	−	0.160664i
$91$	−220.189	−	677.673i	−0.253650	−	0.780654i
$92$	45.2160	−	139.160i	0.0512401	−	0.157701i
$93$	−222.290	−	161.503i	−0.247854	−	0.180076i
$94$	846.591	+	615.084i	0.928927	+	0.674905i
$95$	−198.552	+	611.079i	−0.214431	+	0.659952i
$96$	199.003	+	612.469i	0.211569	+	0.651144i
$97$	938.191	−	681.636i	0.982051	−	0.713501i	0.0238846	−	0.999715i	$-0.492397\pi$
$97$	938.191	−	681.636i	0.982051	−	0.713501i	0.958166	+	0.286213i	$0.0923966\pi$
$98$	488.183			0.503203
$99$	240.875	+	223.137i	0.244534	+	0.226526i
$100$	−1096.55			−1.09655
$101$	778.869	−	565.881i	0.767330	−	0.557498i	−0.133820	−	0.991006i	$-0.542724\pi$
$101$	778.869	−	565.881i	0.767330	−	0.557498i	0.901150	+	0.433508i	$0.142724\pi$
$102$	469.431	+	1444.76i	0.455693	+	1.40248i
$103$	−168.973	+	520.044i	−0.161644	+	0.497490i	−0.998773	−	0.0495155i	$-0.984232\pi$
$103$	−168.973	+	520.044i	−0.161644	+	0.497490i	0.837129	+	0.547005i	$0.184232\pi$
$104$	674.354	+	489.947i	0.635826	+	0.461955i
$105$	215.201	+	156.352i	0.200014	+	0.145318i
$106$	−13.2961	+	40.9212i	−0.0121833	+	0.0374964i
$107$	−481.994	−	1483.42i	−0.435477	−	1.34026i	−0.892597	−	0.450856i	$-0.851119\pi$
$107$	−481.994	−	1483.42i	−0.435477	−	1.34026i	0.457119	−	0.889405i	$-0.348881\pi$
$108$	−262.122	+	190.442i	−0.233543	+	0.169679i
$109$	784.644			0.689498			0.344749	−	0.938695i	$-0.387964\pi$
$109$	784.644			0.689498			0.344749	+	0.938695i	$0.387964\pi$
$110$	183.580	+	928.059i	0.159124	+	0.804427i
$111$	−841.790			−0.719813
$112$	−197.941	+	143.813i	−0.166997	+	0.121331i
$113$	−477.022	−	1468.12i	−0.397119	−	1.22221i	−0.927299	−	0.374322i	$-0.877875\pi$
$113$	−477.022	−	1468.12i	−0.397119	−	1.22221i	0.530179	−	0.847885i	$-0.322125\pi$
$114$	459.413	−	1413.93i	0.377439	−	1.16164i
$115$	−57.1995	−	41.5579i	−0.0463816	−	0.0336982i
$116$	−2724.73	−	1979.63i	−2.18090	−	1.58452i
$117$	129.593	−	398.845i	0.102400	−	0.315156i
$118$	430.805	+	1325.88i	0.336092	+	1.03438i
$119$	−1400.78	+	1017.73i	−1.07907	+	0.783990i
$120$	−311.173			−0.236718
$121$	−1230.76	+	506.744i	−0.924689	+	0.380724i
$122$	3977.66			2.95181
$123$	−14.5304	+	10.5569i	−0.0106517	+	0.00773892i
$124$	339.629	+	1045.27i	0.245965	+	0.757001i
$125$	−387.707	+	1193.24i	−0.277420	+	0.853812i
$126$	−497.936	−	361.772i	−0.352061	−	0.255787i
$127$	259.068	+	188.224i	0.181012	+	0.131513i	0.674602	−	0.738182i	$-0.264315\pi$
$127$	259.068	+	188.224i	0.181012	+	0.131513i	−0.493589	+	0.869695i	$0.664315\pi$
$128$	619.121	−	1905.46i	0.427524	−	1.31578i
$129$	−117.657	−	362.110i	−0.0803030	−	0.247147i
$130$	977.540	−	710.224i	0.659507	−	0.479160i
$131$	551.281			0.367676			0.183838	−	0.982957i	$-0.441148\pi$
$131$	551.281			0.367676			0.183838	+	0.982957i	$0.441148\pi$
$132$	−254.863	−	1288.42i	−0.168053	−	0.849564i
$133$	1694.51			1.10476
$134$	−2133.62	+	1550.16i	−1.37550	+	0.999356i
$135$	48.3785	+	148.894i	0.0308427	+	0.0949239i
$136$	625.909	−	1926.35i	0.394641	−	1.21458i
$137$	1378.00	+	1001.18i	0.859349	+	0.624353i	0.927708	−	0.373307i	$-0.121776\pi$
$137$	1378.00	+	1001.18i	0.859349	+	0.624353i	−0.0683591	+	0.997661i	$0.521776\pi$
$138$	132.349	+	96.1575i	0.0816401	+	0.0593150i
$139$	772.257	−	2376.76i	0.471237	−	1.45032i	−0.379729	−	0.925098i	$-0.623983\pi$
$139$	772.257	−	2376.76i	0.471237	−	1.45032i	0.850966	−	0.525221i	$-0.176017\pi$
$140$	−328.797	−	1011.93i	−0.198489	−	0.610886i
$141$	−567.910	+	412.611i	−0.339196	+	0.246440i
$142$	−1176.35			−0.695193
$143$	1247.11	+	1155.27i	0.729292	+	0.675585i
$144$	−144.000			−0.0833333
$145$	−1316.58	+	956.554i	−0.754043	+	0.547845i
$146$	232.909	+	716.821i	0.132025	+	0.406333i
$147$	−101.198	+	311.455i	−0.0567800	+	0.174751i
$148$	2724.09	+	1979.17i	1.51297	+	1.09923i
$149$	−60.2223	−	43.7541i	−0.0331114	−	0.0240569i	0.571106	−	0.820876i	$-0.306514\pi$
$149$	−60.2223	−	43.7541i	−0.0331114	−	0.0240569i	−0.604218	+	0.796819i	$0.706514\pi$
$150$	378.847	−	1165.97i	0.206218	−	0.634675i
$151$	−693.835	−	2135.41i	−0.373931	−	1.15084i	−0.944197	−	0.329381i	$-0.893160\pi$
$151$	−693.835	−	2135.41i	−0.373931	−	1.15084i	0.570267	−	0.821460i	$-0.306840\pi$
$152$	−1603.68	+	1165.14i	−0.855760	+	0.621746i
$153$	−1019.05			−0.538467
$154$	2178.13	−	1216.78i	1.13973	−	0.636694i
$155$	531.065			0.275201
$156$	−1357.11	+	986.000i	−0.696512	+	0.506046i
$157$	802.781	+	2470.71i	0.408082	+	1.25595i	0.918294	+	0.395899i	$0.129567\pi$
$157$	802.781	+	2470.71i	0.408082	+	1.25595i	−0.510212	+	0.860049i	$0.670433\pi$
$158$	−689.407	+	2121.78i	−0.347129	+	1.06835i
$159$	−23.3510	−	16.9655i	−0.0116469	−	0.00846196i
$160$	−1006.98	−	731.613i	−0.497554	−	0.361494i
$161$	−57.6194	+	177.334i	−0.0282053	+	0.0868069i
$162$	−111.939	−	344.514i	−0.0542888	−	0.167084i
$163$	−2230.33	+	1620.43i	−1.07174	+	0.778663i	−0.976224	−	0.216765i	$-0.930449\pi$
$163$	−2230.33	+	1620.43i	−1.07174	+	0.778663i	−0.0955137	+	0.995428i	$0.530449\pi$
$164$	71.8421			0.0342069
$165$	−630.146	−	75.2600i	−0.297314	−	0.0355090i
$166$	−1444.52			−0.675399
$167$	−668.854	+	485.951i	−0.309925	+	0.225174i	−0.731864	−	0.681450i	$-0.761350\pi$
$167$	−668.854	+	485.951i	−0.309925	+	0.225174i	0.421939	+	0.906624i	$0.361350\pi$
$168$	253.593	+	780.479i	0.116459	+	0.358424i
$169$	−7.95506	+	24.4831i	−0.00362087	+	0.0111439i
$170$	−2375.38	−	1725.81i	−1.07167	−	0.778610i
$171$	806.836	+	586.200i	0.360820	+	0.262151i
$172$	−470.626	+	1448.44i	−0.208633	+	0.642107i
$173$	−542.583	−	1669.90i	−0.238450	−	0.733873i	−0.996645	−	0.0818457i	$-0.973919\pi$
$173$	−542.583	−	1669.90i	−0.238450	−	0.733873i	0.758195	−	0.652028i	$-0.226081\pi$
$174$	3046.34	−	2213.30i	1.32726	−	0.964307i
$175$	1397.35			0.603597
$176$	244.944	−	529.847i	0.104906	−	0.226925i
$177$	−935.200			−0.397141
$178$	−4283.11	+	3111.86i	−1.80355	+	1.31036i
$179$	212.369	+	653.605i	0.0886771	+	0.272920i	0.985554	−	0.169359i	$-0.0541699\pi$
$179$	212.369	+	653.605i	0.0886771	+	0.272920i	−0.896877	+	0.442280i	$0.854170\pi$
$180$	193.514	−	595.575i	0.0801316	−	0.246620i
$181$	−1282.03	−	931.448i	−0.526478	−	0.382508i	0.292561	−	0.956247i	$-0.405493\pi$
$181$	−1282.03	−	931.448i	−0.526478	−	0.382508i	−0.819039	+	0.573738i	$0.805493\pi$
$182$	−2578.02	−	1873.04i	−1.04998	−	0.762853i
$183$	−824.548	+	2537.70i	−0.333073	+	1.02509i
$184$	−67.4040	−	207.448i	−0.0270059	−	0.0831156i
$185$	1316.27	−	956.329i	0.523105	−	0.380058i
$186$	−1228.79			−0.484405
$187$	1733.41	−	3749.60i	0.677858	−	1.46630i
$188$	2807.90			1.08929
$189$	334.026	−	242.684i	0.128554	−	0.0934003i
$190$	887.950	+	2732.83i	0.339046	+	1.04348i
$191$	936.850	−	2883.33i	0.354911	−	1.09230i	−0.601150	−	0.799137i	$-0.705290\pi$
$191$	936.850	−	2883.33i	0.354911	−	1.09230i	0.956061	−	0.293168i	$-0.0947096\pi$
$192$	2019.31	+	1467.11i	0.759015	+	0.551457i
$193$	3176.76	+	2308.05i	1.18481	+	0.860815i	0.992706	−	0.120560i	$-0.0384690\pi$
$193$	3176.76	+	2308.05i	1.18481	+	0.860815i	0.192104	+	0.981375i	$0.438469\pi$
$194$	1602.62	−	4932.36i	0.593101	−	1.82538i
$195$	250.476	+	770.885i	0.0919843	+	0.283098i
$196$	1059.76	−	769.959i	0.386209	−	0.280597i
$197$	1769.43			0.639933			0.319967	−	0.947429i	$-0.396328\pi$
$197$	1769.43			0.639933			0.319967	+	0.947429i	$0.396328\pi$
$198$	1458.05	+	174.138i	0.523327	+	0.0625023i
$199$	−786.483			−0.280162			−0.140081	−	0.990140i	$-0.544736\pi$
$199$	−786.483			−0.280162			−0.140081	+	0.990140i	$0.544736\pi$
$200$	−1322.45	+	960.814i	−0.467556	+	0.339699i
$201$	−546.698	−	1682.56i	−0.191846	−	0.590442i
$202$	1330.47	−	4094.75i	0.463422	−	1.42627i
$203$	3472.17	+	2522.68i	1.20048	+	0.872203i
$204$	3297.72	+	2395.93i	1.13180	+	0.822299i
$205$	10.7272	−	33.0149i	0.00365473	−	0.0112481i
$206$	755.668	+	2325.71i	0.255582	+	0.786600i
$207$	−88.7827	+	64.5044i	−0.0298107	+	0.0216588i
$208$	−745.548			−0.248531
$209$	−3529.35	+	1971.62i	−1.16809	+	0.652535i
$210$	1189.60			0.390906
$211$	2931.88	−	2130.13i	0.956581	−	0.694997i	0.00422692	−	0.999991i	$-0.498655\pi$
$211$	2931.88	−	2130.13i	0.956581	−	0.694997i	0.952354	+	0.304994i	$0.0986545\pi$
$212$	35.6771	+	109.803i	0.0115581	+	0.0355722i
$213$	243.852	−	750.500i	0.0784435	−	0.241424i
$214$	−5643.28	−	4100.08i	−1.80265	−	1.30970i
$215$	595.355	+	432.551i	0.188851	+	0.137208i
$216$	−149.252	+	459.351i	−0.0470154	+	0.144699i
$217$	−432.795	−	1332.01i	−0.135392	−	0.416693i
$218$	2838.87	−	2062.56i	0.881984	−	0.640799i
$219$	−505.604			−0.156007
$220$	1862.25	+	1725.11i	0.570694	+	0.528667i
$221$	−5276.05			−1.60591
$222$	−3045.63	+	2212.78i	−0.920761	+	0.668972i
$223$	−151.169	−	465.249i	−0.0453946	−	0.139710i	0.925790	−	0.378037i	$-0.123401\pi$
$223$	−151.169	−	465.249i	−0.0453946	−	0.139710i	−0.971185	+	0.238327i	$0.923401\pi$
$224$	−1014.37	+	3121.91i	−0.302569	+	0.931213i
$225$	665.343	+	483.400i	0.197139	+	0.143230i
$226$	−5585.07	−	4057.79i	−1.64387	−	1.19434i
$227$	574.931	−	1769.46i	0.168104	−	0.517370i	−0.831148	−	0.556051i	$-0.812316\pi$
$227$	574.931	−	1769.46i	0.168104	−	0.517370i	0.999252	+	0.0386815i	$0.0123158\pi$
$228$	−1232.74	−	3793.97i	−0.358070	−	1.10203i
$229$	−5265.21	+	3825.40i	−1.51937	+	1.10388i	−0.557566	+	0.830132i	$0.688265\pi$
$229$	−5265.21	+	3825.40i	−1.51937	+	1.10388i	−0.961800	+	0.273752i	$0.911735\pi$
$230$	−316.191			−0.0906479
$231$	324.776	+	1641.85i	0.0925052	+	0.467645i
$232$	−5020.64			−1.42078
$233$	188.501	−	136.954i	0.0530006	−	0.0385072i	−0.560970	−	0.827836i	$-0.689572\pi$
$233$	188.501	−	136.954i	0.0530006	−	0.0385072i	0.613970	+	0.789329i	$0.289572\pi$
$234$	−579.556	−	1783.69i	−0.161909	−	0.498305i
$235$	419.266	−	1290.37i	0.116382	−	0.358188i
$236$	3026.37	+	2198.79i	0.834746	+	0.606478i
$237$	−1210.76	−	879.667i	−0.331845	−	0.241099i
$238$	−2392.82	+	7364.33i	−0.651694	+	2.00571i
$239$	1964.36	+	6045.67i	0.531647	+	1.63624i	0.750784	+	0.660548i	$0.229676\pi$
$239$	1964.36	+	6045.67i	0.531647	+	1.63624i	−0.219137	+	0.975694i	$0.570324\pi$
$240$	225.167	−	163.594i	0.0605603	−	0.0439997i
$241$	−128.649			−0.0343860			−0.0171930	−	0.999852i	$-0.505473\pi$
$241$	−128.649			−0.0343860			−0.0171930	+	0.999852i	$0.505473\pi$
$242$	−3120.88	+	5068.66i	−0.828999	+	1.34639i
$243$	243.000			0.0641500
$244$	8634.78	−	6273.54i	2.26551	−	1.64599i
$245$	−195.594	−	601.977i	−0.0510043	−	0.156975i
$246$	−24.8208	+	76.3907i	−0.00643301	+	0.0197988i
$247$	4177.32	+	3035.00i	1.07610	+	0.781833i
$248$	1325.48	+	963.020i	0.339388	+	0.246580i
$249$	299.441	−	921.585i	0.0762101	−	0.234550i
$250$	1733.88	+	5336.33i	0.438640	+	1.35000i
$251$	85.3177	−	61.9870i	0.0214550	−	0.0155880i	−0.577006	−	0.816740i	$-0.695779\pi$
$251$	85.3177	−	61.9870i	0.0214550	−	0.0155880i	0.598461	+	0.801152i	$0.295779\pi$
$252$	−1651.51			−0.412840
$253$	−86.3242	−	436.398i	−0.0214512	−	0.108443i
$254$	1432.09			0.353769
$255$	1593.45	−	1157.71i	0.391317	−	0.284308i
$256$	−711.975	−	2191.23i	−0.173822	−	0.534969i
$257$	−80.4268	+	247.528i	−0.0195210	+	0.0600793i	−0.960342	−	0.278823i	$-0.910056\pi$
$257$	−80.4268	+	247.528i	−0.0195210	+	0.0600793i	0.940822	+	0.338902i	$0.110056\pi$
$258$	−1377.55	−	1000.85i	−0.332412	−	0.241512i
$259$	−3471.35	−	2522.09i	−0.832816	−	0.605076i
$260$	1001.90	−	3083.54i	0.238982	−	0.735511i
$261$	780.565	+	2402.33i	0.185118	+	0.569734i
$262$	1994.55	−	1449.13i	0.470320	−	0.341707i
$263$	−606.064			−0.142097			−0.0710485	−	0.997473i	$-0.522635\pi$
$263$	−606.064			−0.142097			−0.0710485	+	0.997473i	$0.522635\pi$
$264$	−1436.30	−	1330.53i	−0.334842	−	0.310184i
$265$	55.7870			0.0129319
$266$	6130.79	−	4454.28i	1.41317	−	1.02673i
$267$	−1097.46	−	3377.65i	−0.251549	−	0.774190i
$268$	−2186.79	+	6730.25i	−0.498431	+	1.53401i
$269$	−3591.18	−	2609.14i	−0.813970	−	0.591384i	0.101009	−	0.994885i	$-0.467793\pi$
$269$	−3591.18	−	2609.14i	−0.813970	−	0.591384i	−0.914979	+	0.403502i	$0.867793\pi$
$270$	566.425	+	411.532i	0.127672	+	0.0927594i
$271$	−1494.68	+	4600.15i	−0.335038	+	1.03114i	0.631666	+	0.775241i	$0.282372\pi$
$271$	−1494.68	+	4600.15i	−0.335038	+	1.03114i	−0.966703	+	0.255900i	$0.917628\pi$
$272$	559.830	+	1722.98i	0.124797	+	0.384084i
$273$	1729.39	−	1256.48i	0.383397	−	0.278554i
$274$	7617.41			1.67951
$275$	−2910.42	+	1625.86i	−0.638200	+	0.356521i
$276$	438.966			0.0957342
$277$	3717.23	−	2700.72i	0.806305	−	0.585815i	−0.106452	−	0.994318i	$-0.533949\pi$
$277$	3717.23	−	2700.72i	0.806305	−	0.585815i	0.912757	+	0.408503i	$0.133949\pi$
$278$	−3453.64	−	10629.2i	−0.745091	−	2.29316i
$279$	254.722	−	783.954i	0.0546588	−	0.168222i
$280$	−1283.21	−	932.306i	−0.273880	−	0.198985i
$281$	−3698.30	−	2686.97i	−0.785132	−	0.570431i	0.121383	−	0.992606i	$-0.461267\pi$
$281$	−3698.30	−	2686.97i	−0.785132	−	0.570431i	−0.906515	+	0.422174i	$0.861267\pi$
$282$	−970.106	+	2985.68i	−0.204855	+	0.630478i
$283$	−2494.55	−	7677.43i	−0.523977	−	1.61263i	−0.766331	−	0.642447i	$-0.777919\pi$
$283$	−2494.55	−	7677.43i	−0.523977	−	1.61263i	0.242354	−	0.970188i	$-0.422081\pi$
$284$	−2553.65	+	1855.34i	−0.533561	+	0.387655i
$285$	−1927.58			−0.400632
$286$	7548.91	+	901.586i	1.56076	+	0.186405i
$287$	−91.5496			−0.0188293
$288$	−1562.99	+	1135.58i	−0.319792	+	0.232343i
$289$	2443.57	+	7520.54i	0.497369	+	1.53074i
$290$	−2248.99	+	6921.69i	−0.455398	+	1.40157i
$291$	2814.57	+	2044.91i	0.566987	+	0.411940i
$292$	1636.17	+	1188.75i	0.327910	+	0.238240i
$293$	44.4461	−	136.791i	0.00886200	−	0.0272744i	−0.946528	−	0.322622i	$-0.895436\pi$
$293$	44.4461	−	136.791i	0.00886200	−	0.0272744i	0.955390	+	0.295348i	$0.0954356\pi$
$294$	452.570	+	1392.87i	0.0897770	+	0.276305i
$295$	1462.34	−	1062.45i	0.288612	−	0.209689i
$296$	5019.47			0.985644
$297$	−413.343	+	894.118i	−0.0807563	+	0.174687i
$298$	−332.901			−0.0647128
$299$	−459.665	+	333.966i	−0.0889067	+	0.0645945i
$300$	−1016.55	−	3128.63i	−0.195636	−	0.602106i
$301$	599.727	−	1845.77i	0.114843	−	0.353450i
$302$	−8123.57	−	5902.12i	−1.54788	−	1.12460i
$303$	2336.61	+	1697.64i	0.443018	+	0.321872i
$304$	547.882	−	1686.21i	0.103366	−	0.318127i
$305$	−1593.68	−	4904.84i	−0.299193	−	0.920821i
$306$	−3686.96	+	2678.74i	−0.688790	+	0.500435i
$307$	−954.997			−0.177539			−0.0887697	−	0.996052i	$-0.528294\pi$
$307$	−954.997			−0.177539			−0.0887697	+	0.996052i	$0.528294\pi$
$308$	2809.23	−	6076.74i	0.519710	−	1.12420i
$309$	−1640.42			−0.302007
$310$	1921.41	−	1395.99i	0.352028	−	0.255764i
$311$	−575.737	−	1771.94i	−0.104974	−	0.323078i	0.884750	−	0.466066i	$-0.154329\pi$
$311$	−575.737	−	1771.94i	−0.104974	−	0.323078i	−0.989724	+	0.142988i	$0.954329\pi$
$312$	−772.741	+	2378.25i	−0.140218	+	0.431545i
$313$	−1247.35	−	906.249i	−0.225253	−	0.163656i	0.469435	−	0.882967i	$-0.344458\pi$
$313$	−1247.35	−	906.249i	−0.225253	−	0.163656i	−0.694688	+	0.719311i	$0.744458\pi$
$314$	9399.12	+	6828.86i	1.68925	+	1.22731i
$315$	−246.598	+	758.951i	−0.0441086	+	0.135752i
$316$	1849.87	+	5693.33i	0.329315	+	1.01353i
$317$	1451.60	−	1054.65i	0.257192	−	0.186861i	−0.451716	−	0.892162i	$-0.649188\pi$
$317$	1451.60	−	1054.65i	0.257192	−	0.186861i	0.708908	+	0.705301i	$0.249188\pi$
$318$	−129.081			−0.0227626
$319$	−10167.1	−	1214.29i	−1.78448	−	0.213125i
$320$	−4824.25			−0.842761
$321$	3785.63	−	2750.42i	0.658234	−	0.478235i
$322$	257.682	+	793.064i	0.0445964	+	0.137254i
$323$	3877.22	−	11932.9i	0.667909	−	2.05561i
$324$	−786.365	−	571.327i	−0.134836	−	0.0979642i
$325$	3444.76	+	2502.76i	0.587941	+	0.427164i
$326$	−3809.86	+	11725.6i	−0.647267	+	1.99208i
$327$	727.405	+	2238.72i	0.123014	+	0.378598i
$328$	86.6424	−	62.9494i	0.0145855	−	0.0105969i
$329$	−3578.16			−0.599605
$330$	−2477.72	+	1384.14i	−0.413315	+	0.230893i
$331$	11429.1			1.89788			0.948939	−	0.315458i	$-0.102158\pi$
$331$	11429.1			1.89788			0.948939	+	0.315458i	$0.102158\pi$
$332$	−3135.79	+	2278.28i	−0.518370	+	0.376617i
$333$	−780.382	−	2401.77i	−0.128423	−	0.395244i
$334$	−1142.54	+	3516.37i	−0.187176	+	0.576070i
$335$	2766.35	+	2009.87i	0.451170	+	0.327794i
$336$	−593.823	−	431.438i	−0.0964159	−	0.0700502i
$337$	494.332	−	1521.40i	0.0799050	−	0.245922i	−0.903122	−	0.429385i	$-0.858731\pi$
$337$	494.332	−	1521.40i	0.0799050	−	0.245922i	0.983027	+	0.183462i	$0.0587305\pi$
$338$	35.5761	+	109.492i	0.00572510	+	0.0176200i
$339$	3746.58	−	2722.05i	0.600255	−	0.436111i
$340$	−7878.45			−1.25667
$341$	2451.27	+	2270.75i	0.389278	+	0.360611i
$342$	4460.08			0.705185
$343$	−5593.83	+	4064.15i	−0.880578	+	0.639778i
$344$	701.568	+	2159.20i	0.109959	+	0.338420i
$345$	65.5448	−	201.726i	0.0102284	−	0.0314799i
$346$	−6352.68	−	4615.49i	−0.987058	−	0.717139i
$347$	1806.74	+	1312.67i	0.279512	+	0.203077i	0.718705	−	0.695316i	$-0.244735\pi$
$347$	1806.74	+	1312.67i	0.279512	+	0.203077i	−0.439192	+	0.898393i	$0.644735\pi$
$348$	3122.26	−	9609.33i	0.480951	−	1.48021i
$349$	2204.01	+	6783.25i	0.338046	+	1.04040i	0.965202	+	0.261504i	$0.0842186\pi$
$349$	2204.01	+	6783.25i	0.338046	+	1.04040i	−0.627157	+	0.778893i	$0.715781\pi$
$350$	5055.65	−	3673.14i	0.772102	−	0.560965i
$351$	1258.11			0.191319
$352$	−1519.71	−	7682.64i	−0.230116	−	1.16331i
$353$	5585.03			0.842100			0.421050	−	0.907037i	$-0.361662\pi$
$353$	5585.03			0.842100			0.421050	+	0.907037i	$0.361662\pi$
$354$	−3383.59	+	2458.32i	−0.508010	+	0.369091i
$355$	471.315	+	1450.56i	0.0704643	+	0.216867i
$356$	−4389.86	+	13510.6i	−0.653545	+	2.01140i
$357$	−4202.34	−	3053.18i	−0.623001	−	0.452637i
$358$	2486.46	+	1806.52i	0.367077	+	0.266697i
$359$	−2659.42	+	8184.87i	−0.390972	+	1.20329i	0.541082	+	0.840970i	$0.318015\pi$
$359$	−2659.42	+	8184.87i	−0.390972	+	1.20329i	−0.932054	+	0.362319i	$0.881985\pi$
$360$	−288.474	−	887.830i	−0.0422330	−	0.129980i
$361$	−4385.03	+	3185.91i	−0.639310	+	0.464486i
$362$	−7086.88			−1.02895
$363$	−2586.80	−	3041.79i	−0.374028	−	0.439814i
$364$	−8550.58			−1.23124
$365$	790.594	−	574.400i	0.113374	−	0.0823712i
$366$	3687.49	+	11348.9i	0.526635	+	1.62082i
$367$	−635.906	+	1957.12i	−0.0904469	+	0.278367i	−0.986040	−	0.166506i	$-0.946751\pi$
$367$	−635.906	+	1957.12i	−0.0904469	+	0.278367i	0.895593	+	0.444873i	$0.146751\pi$
$368$	157.836	+	114.675i	0.0223581	+	0.0162441i
$369$	−43.5911	−	31.6708i	−0.00614977	−	0.00446807i
$370$	2248.47	−	6920.06i	0.315925	−	0.972316i
$371$	−45.4640	−	139.924i	−0.00636219	−	0.0195808i
$372$	−2667.48	+	1938.04i	−0.371781	+	0.270115i
$373$	−10090.3			−1.40069			−0.700344	−	0.713805i	$-0.746970\pi$
$373$	−10090.3			−1.40069			−0.700344	+	0.713805i	$0.746970\pi$
$374$	−3584.87	−	18122.7i	−0.495639	−	2.50562i
$375$	−3763.94			−0.518317
$376$	3386.36	−	2460.34i	0.464464	−	0.337453i
$377$	4041.31	+	12437.9i	0.552091	+	1.69916i
$378$	570.584	−	1756.08i	0.0776394	−	0.238949i
$379$	−5770.80	−	4192.73i	−0.782127	−	0.568249i	0.123489	−	0.992346i	$-0.460591\pi$
$379$	−5770.80	−	4192.73i	−0.782127	−	0.568249i	−0.905617	+	0.424097i	$0.860591\pi$
$380$	6237.78	+	4532.01i	0.842083	+	0.611809i
$381$	−296.865	+	913.657i	−0.0399183	+	0.122856i
$382$	−4189.72	−	12894.6i	−0.561164	−	1.72709i
$383$	−5396.98	+	3921.13i	−0.720033	+	0.523135i	−0.886395	−	0.462930i	$-0.846798\pi$
$383$	−5396.98	+	3921.13i	−0.720033	+	0.523135i	0.166362	+	0.986065i	$0.446798\pi$
$384$	6010.55			0.798762
$385$	−2373.09	−	2198.33i	−0.314140	−	0.291006i
$386$	17560.7			2.31559
$387$	924.086	−	671.388i	0.121380	−	0.0881875i
$388$	−4300.29	−	13234.9i	−0.562665	−	1.73170i
$389$	1034.07	−	3182.55i	0.134780	−	0.414811i	−0.860775	−	0.508985i	$-0.830021\pi$
$389$	1034.07	−	3182.55i	0.134780	−	0.414811i	0.995556	+	0.0941736i	$0.0300209\pi$
$390$	2932.62	+	2130.67i	0.380767	+	0.276643i
$391$	1116.96	+	811.522i	0.144469	+	0.104963i
$392$	603.427	−	1857.16i	0.0777492	−	0.239287i
$393$	511.065	+	1572.90i	0.0655975	+	0.201888i
$394$	6401.87	−	4651.23i	0.818582	−	0.594735i
$395$	2892.58			0.368459
$396$	3439.80	−	1921.60i	0.436507	−	0.243848i
$397$	8174.27			1.03339			0.516694	−	0.856170i	$-0.327163\pi$
$397$	8174.27			1.03339			0.516694	+	0.856170i	$0.327163\pi$
$398$	−2845.52	+	2067.39i	−0.358375	+	0.260374i
$399$	1570.89	+	4834.72i	0.197100	+	0.606613i
$400$	451.802	−	1390.50i	0.0564752	−	0.173813i
$401$	9953.83	+	7231.88i	1.23958	+	0.900605i	0.997570	−	0.0696693i	$-0.0221944\pi$
$401$	9953.83	+	7231.88i	1.23958	+	0.900605i	0.242007	+	0.970275i	$0.422194\pi$
$402$	−6400.85	−	4650.49i	−0.794143	−	0.576978i
$403$	1318.80	−	4058.85i	0.163013	−	0.501702i
$404$	−3570.02	−	10987.4i	−0.439641	−	1.35308i
$405$	−379.970	+	276.064i	−0.0466194	+	0.0338710i
$406$	19193.7			2.34622
$407$	10164.7	+	1214.00i	1.23795	+	0.147852i
$408$	6076.45			0.737326
$409$	−510.899	+	371.190i	−0.0617661	+	0.0448757i	−0.618240	−	0.785989i	$-0.712154\pi$
$409$	−510.899	+	371.190i	−0.0617661	+	0.0448757i	0.556474	+	0.830865i	$0.312154\pi$
$410$	−47.9735	−	147.647i	−0.00577864	−	0.0177848i
$411$	−1579.05	+	4859.82i	−0.189511	+	0.583254i
$412$	5308.51	+	3856.86i	0.634785	+	0.461198i
$413$	−3856.55	−	2801.95i	−0.459488	−	0.333838i
$414$	−151.659	+	466.758i	−0.0180039	+	0.0554104i
$415$	578.757	+	1781.23i	0.0684580	+	0.210692i
$416$	−8092.25	+	5879.37i	−0.953739	+	0.692932i
$417$	7497.23			0.880433
$418$	−7586.60	+	16410.8i	−0.887734	+	1.92029i
$419$	−3416.77			−0.398378			−0.199189	−	0.979961i	$-0.563831\pi$
$419$	−3416.77			−0.398378			−0.199189	+	0.979961i	$0.563831\pi$
$420$	2582.41	−	1876.23i	0.300020	−	0.217978i
$421$	1166.73	+	3590.82i	0.135066	+	0.415690i	0.995600	−	0.0937022i	$-0.0298702\pi$
$421$	1166.73	+	3590.82i	0.135066	+	0.415690i	−0.860534	+	0.509392i	$0.829870\pi$
$422$	5008.24	−	15413.8i	0.577719	−	1.77804i
$423$	−1703.73	−	1237.83i	−0.195835	−	0.142282i
$424$	139.238	+	101.163i	0.0159482	+	0.0115870i
$425$	3197.29	−	9840.24i	0.364921	−	1.12311i
$426$	−1090.54	−	3356.34i	−0.124030	−	0.381725i
$427$	−11003.4	+	7994.47i	−1.24706	+	0.906041i
$428$	−18717.2			−2.11385
$429$	−2140.05	+	4629.22i	−0.240845	+	0.520981i
$430$	3291.04			0.369089
$431$	366.901	−	266.569i	0.0410046	−	0.0297916i	−0.567094	−	0.823653i	$-0.691932\pi$
$431$	366.901	−	266.569i	0.0410046	−	0.0297916i	0.608099	+	0.793861i	$0.291932\pi$
$432$	−133.495	−	410.856i	−0.0148676	−	0.0457577i
$433$	−3032.72	+	9333.75i	−0.336589	+	1.03592i	0.629345	+	0.777126i	$0.283323\pi$
$433$	−3032.72	+	9333.75i	−0.336589	+	1.03592i	−0.965934	+	0.258789i	$0.916677\pi$
$434$	−5067.25	−	3681.58i	−0.560452	−	0.407192i
$435$	−3949.75	−	2869.66i	−0.435347	−	0.316298i
$436$	2909.62	−	8954.89i	0.319600	−	0.983627i
$437$	−417.538	−	1285.05i	−0.0457060	−	0.140669i
$438$	−1829.29	+	1329.06i	−0.199559	+	0.144988i
$439$	−614.875			−0.0668483			−0.0334241	−	0.999441i	$-0.510641\pi$
$439$	−614.875			−0.0668483			−0.0334241	+	0.999441i	$0.510641\pi$
$440$	3757.46	+	448.764i	0.407114	+	0.0486227i
$441$	−982.449			−0.106085
$442$	−19088.9	+	13868.9i	−2.05423	+	1.49248i
$443$	−3859.24	−	11877.5i	−0.413901	−	1.27386i	−0.913230	−	0.407444i	$-0.866420\pi$
$443$	−3859.24	−	11877.5i	−0.413901	−	1.27386i	0.499329	−	0.866413i	$-0.333580\pi$
$444$	−3121.53	+	9607.08i	−0.333651	+	1.02687i
$445$	5553.29	+	4034.70i	0.591576	+	0.429805i
$446$	−1769.91	−	1285.92i	−0.187910	−	0.136525i
$447$	69.0086	−	212.387i	0.00730201	−	0.0224733i
$448$	3931.55	+	12100.1i	0.414617	+	1.27606i
$449$	7373.12	−	5356.88i	0.774964	−	0.563044i	−0.128499	−	0.991710i	$-0.541016\pi$
$449$	7373.12	−	5356.88i	0.774964	−	0.563044i	0.903463	+	0.428665i	$0.141016\pi$
$450$	3677.93			0.385287
$451$	190.681	−	106.521i	0.0199087	−	0.0111217i
$452$	−18524.1			−1.92766
$453$	5449.45	−	3959.26i	0.565205	−	0.410645i
$454$	−2571.17	−	7913.25i	−0.265795	−	0.818034i
$455$	−1276.74	+	3929.40i	−0.131548	+	0.404864i
$456$	−4811.04	−	3495.42i	−0.494074	−	0.358965i
$457$	−1415.77	−	1028.62i	−0.144917	−	0.105288i	0.512964	−	0.858410i	$-0.328547\pi$
$457$	−1415.77	−	1028.62i	−0.144917	−	0.105288i	−0.657882	+	0.753121i	$0.728547\pi$
$458$	−8994.05	+	27680.9i	−0.917608	+	2.82411i
$459$	−944.713	−	2907.53i	−0.0960684	−	0.295668i
$460$	−686.394	+	498.694i	−0.0695723	+	0.0505473i
$461$	−1394.82			−0.140918			−0.0704589	−	0.997515i	$-0.522446\pi$
$461$	−1394.82			−0.140918			−0.0704589	+	0.997515i	$0.522446\pi$
$462$	5490.91	+	5086.55i	0.552945	+	0.512225i
$463$	9007.16			0.904099			0.452050	−	0.891993i	$-0.350693\pi$
$463$	9007.16			0.904099			0.452050	+	0.891993i	$0.350693\pi$
$464$	3632.97	−	2639.51i	0.363484	−	0.264086i
$465$	492.324	+	1515.22i	0.0490989	+	0.151111i
$466$	321.999	−	991.010i	0.0320092	−	0.0985143i
$467$	−7754.99	−	5634.33i	−0.768432	−	0.558299i	0.133053	−	0.991109i	$-0.457522\pi$
$467$	−7754.99	−	5634.33i	−0.768432	−	0.558299i	−0.901485	+	0.432810i	$0.857522\pi$
$468$	−4071.34	−	2958.00i	−0.402132	−	0.292166i
$469$	2786.66	−	8576.47i	0.274363	−	0.844402i
$470$	−1875.01	−	5770.70i	−0.184017	−	0.566346i
$471$	−6305.12	+	4580.94i	−0.616825	+	0.448150i
$472$	5576.46			0.543808
$473$	898.497	+	4542.21i	0.0873424	+	0.441545i
$474$	−6692.91			−0.648556
$475$	−8191.97	+	5951.81i	−0.791312	+	0.574922i
$476$	6420.60	+	19760.6i	0.618252	+	1.90278i
$477$	26.7579	−	82.3522i	0.00256847	−	0.00790493i
$478$	22999.1	+	16709.8i	2.20074	+	1.59893i
$479$	−4562.49	−	3314.84i	−0.435210	−	0.316199i	0.348519	−	0.937302i	$-0.386685\pi$
$479$	−4562.49	−	3314.84i	−0.435210	−	0.316199i	−0.783729	+	0.621103i	$0.786685\pi$
$480$	1153.89	−	3551.32i	0.109725	−	0.337698i
$481$	−4040.37	−	12435.0i	−0.383004	−	1.17876i
$482$	−465.457	+	338.174i	−0.0439855	+	0.0319573i
$483$	−559.381			−0.0526972
$484$	1219.39	+	15925.4i	0.114519	+	1.49562i
$485$	−6724.19			−0.629546
$486$	879.182	−	638.763i	0.0820587	−	0.0596191i
$487$	−5230.42	−	16097.6i	−0.486680	−	1.49785i	−0.829533	−	0.558457i	$-0.811394\pi$
$487$	−5230.42	−	16097.6i	−0.486680	−	1.49785i	0.342854	−	0.939389i	$-0.388606\pi$
$488$	4916.66	−	15131.9i	0.456079	−	1.40367i
$489$	−6691.00	−	4861.30i	−0.618768	−	0.449561i
$490$	−2290.06	−	1663.82i	−0.211131	−	0.153396i
$491$	1608.35	−	4950.01i	0.147829	−	0.454971i	−0.849535	−	0.527532i	$-0.823117\pi$
$491$	1608.35	−	4950.01i	0.147829	−	0.454971i	0.997364	+	0.0725615i	$0.0231174\pi$
$492$	66.6013	+	204.978i	0.00610288	+	0.0187827i
$493$	25709.6	−	18679.1i	2.34869	−	1.70642i
$494$	23091.7			2.10313
$495$	−369.448	−	1867.68i	−0.0335463	−	0.169588i
$496$	−1465.42			−0.132660
$497$	3254.16	−	2364.29i	0.293700	−	0.213386i
$498$	−1339.14	−	4121.45i	−0.120499	−	0.370857i
$499$	512.588	−	1577.58i	0.0459852	−	0.141528i	−0.925428	−	0.378924i	$-0.876294\pi$
$499$	512.588	−	1577.58i	0.0459852	−	0.141528i	0.971413	+	0.237396i	$0.0762941\pi$
$500$	12180.4	+	8849.55i	1.08944	+	0.791527i
$501$	−2006.56	−	1457.85i	−0.178935	−	0.130004i
$502$	145.740	−	448.542i	0.0129576	−	0.0398793i
$503$	4733.44	+	14568.0i	0.419590	+	1.29136i	0.908080	+	0.418796i	$0.137548\pi$
$503$	4733.44	+	14568.0i	0.419590	+	1.29136i	−0.488491	+	0.872569i	$0.662452\pi$
$504$	−1991.74	+	1447.09i	−0.176030	+	0.127894i
$505$	−5582.29			−0.491899
$506$	−1459.46	−	1351.99i	−0.128223	−	0.118781i
$507$	−77.2293			−0.00676504
$508$	3108.81	−	2258.68i	0.271518	−	0.197270i
$509$	4088.97	+	12584.5i	0.356071	+	1.09587i	0.955386	+	0.295361i	$0.0954399\pi$
$509$	4088.97	+	12584.5i	0.356071	+	1.09587i	−0.599314	+	0.800514i	$0.704560\pi$
$510$	2721.94	−	8377.27i	0.236332	−	0.727356i
$511$	−2085.00	−	1514.84i	−0.180499	−	0.131140i
$512$	4631.08	+	3364.68i	0.399740	+	0.290428i
$513$	−924.551	+	2845.48i	−0.0795710	+	0.244894i
$514$	359.680	+	1106.98i	0.0308654	+	0.0949938i
$515$	2565.06	−	1863.63i	0.219476	−	0.159459i
$516$	−4568.93			−0.389799
$517$	7452.65	−	4163.31i	0.633979	−	0.354163i
$518$	−19189.2			−1.62765
$519$	4261.50	−	3096.16i	0.360422	−	0.261862i
$520$	−1493.55	−	4596.67i	−0.125955	−	0.387649i
$521$	4129.84	−	12710.3i	0.347277	−	1.06881i	−0.613076	−	0.790024i	$-0.710068\pi$
$521$	4129.84	−	12710.3i	0.347277	−	1.06881i	0.960353	−	0.278786i	$-0.0899320\pi$
$522$	9139.02	+	6639.89i	0.766291	+	0.556743i
$523$	6790.77	+	4933.78i	0.567762	+	0.412503i	0.834292	−	0.551323i	$-0.185877\pi$
$523$	6790.77	+	4933.78i	0.567762	+	0.412503i	−0.266529	+	0.963827i	$0.585877\pi$
$524$	2044.26	−	6291.59i	0.170427	−	0.524522i
$525$	1295.41	+	3986.87i	0.107688	+	0.331431i
$526$	−2192.76	+	1593.13i	−0.181766	+	0.132061i
$527$	−10370.4			−0.857194
$528$	1738.82	+	207.672i	0.143319	+	0.0171170i
$529$	−12018.3			−0.987780
$530$	201.839	−	146.645i	0.0165421	−	0.0120186i
$531$	−866.978	−	2668.28i	−0.0708543	−	0.218067i
$532$	6283.58	−	19338.9i	0.512082	−	1.57603i
$533$	−225.689	−	163.973i	−0.0183409	−	0.0133254i
$534$	−12849.3	−	9335.59i	−1.04128	−	0.756536i
$535$	−2794.78	+	8601.44i	−0.225848	+	0.695090i
$536$	3259.88	+	10032.9i	0.262696	+	0.808496i
$537$	−1667.97	+	1211.85i	−0.134037	+	0.0973839i
$538$	−19851.5			−1.59082
$539$	1671.15	−	3614.92i	0.133546	−	0.288878i
$540$	1878.67			0.149713
$541$	1474.19	−	1071.06i	0.117154	−	0.0851174i	−0.527665	−	0.849452i	$-0.676933\pi$
$541$	1474.19	−	1071.06i	0.117154	−	0.0851174i	0.644820	+	0.764335i	$0.276933\pi$
$542$	6684.41	+	20572.5i	0.529741	+	1.63038i
$543$	1469.07	−	4521.35i	0.116103	−	0.357329i
$544$	19663.8	+	14286.6i	1.54978	+	1.12598i
$545$	−3680.75	−	2674.22i	−0.289296	−	0.210185i
$546$	2954.15	−	9091.94i	0.231549	−	0.712636i
$547$	3461.10	+	10652.2i	0.270541	+	0.832639i	0.990365	+	0.138482i	$0.0442224\pi$
$547$	3461.10	+	10652.2i	0.270541	+	0.832639i	−0.719824	+	0.694156i	$0.755778\pi$
$548$	16536.0	−	12014.1i	1.28902	−	0.936530i
$549$	−8004.88			−0.622295
$550$	−6256.16	+	13532.9i	−0.485025	+	1.04917i
$551$	−31100.6			−2.40460
$552$	529.398	−	384.630i	0.0408200	−	0.0296575i
$553$	−2357.32	−	7255.10i	−0.181272	−	0.557899i
$554$	6349.78	−	19542.6i	0.486961	−	1.49871i
$555$	3948.82	+	2868.99i	0.302015	+	0.219427i
$556$	−24261.5	−	17627.0i	−1.85057	−	1.34452i
$557$	−2084.88	+	6416.60i	−0.158598	+	0.488115i	−0.998508	−	0.0546116i	$-0.982608\pi$
$557$	−2084.88	+	6416.60i	−0.158598	+	0.488115i	0.839910	+	0.542726i	$0.182608\pi$
$558$	−1139.15	−	3505.95i	−0.0864231	−	0.265983i
$559$	4784.38	−	3476.06i	0.362000	−	0.263008i
$560$	1418.68			0.107054
$561$	12305.2	+	1469.64i	0.926070	+	0.110603i
$562$	−20443.7			−1.53446
$563$	−17495.7	+	12711.3i	−1.30969	+	0.951544i	−0.309688	+	0.950838i	$0.600225\pi$
$563$	−17495.7	+	12711.3i	−1.30969	+	0.951544i	−1.00000		0.000705699i	$0.999775\pi$
$564$	2603.07	+	8011.42i	0.194342	+	0.598124i
$565$	−2765.95	+	8512.73i	−0.205955	+	0.633864i
$566$	−29206.7	−	21219.9i	−2.16899	−	1.57586i
$567$	1002.08	+	728.052i	0.0742210	+	0.0539247i
$568$	−1454.05	+	4475.11i	−0.107413	+	0.330584i
$569$	336.611	+	1035.98i	0.0248005	+	0.0763280i	0.962691	−	0.270604i	$-0.0872234\pi$
$569$	336.611	+	1035.98i	0.0248005	+	0.0763280i	−0.937890	+	0.346932i	$0.887223\pi$
$570$	−6974.05	+	5066.94i	−0.512475	+	0.372335i
$571$	19919.7			1.45992			0.729960	−	0.683490i	$-0.239539\pi$
$571$	19919.7			1.45992			0.729960	+	0.683490i	$0.239539\pi$
$572$	17809.3	−	9948.90i	1.30183	−	0.727246i
$573$	9095.13			0.663097
$574$	−331.230	+	240.652i	−0.0240858	+	0.0174994i
$575$	−344.315	−	1059.69i	−0.0249721	−	0.0768561i
$576$	−2313.92	+	7121.51i	−0.167384	+	0.515156i
$577$	−9332.54	−	6780.48i	−0.673342	−	0.489212i	0.197800	−	0.980242i	$-0.436620\pi$
$577$	−9332.54	−	6780.48i	−0.673342	−	0.489212i	−0.871142	+	0.491031i	$0.836620\pi$
$578$	28609.8	+	20786.3i	2.05885	+	1.49584i
$579$	−3640.24	+	11203.5i	−0.261284	+	0.804149i
$580$	6034.68	+	18572.8i	0.432028	+	1.32965i
$581$	3995.98	−	2903.25i	0.285338	−	0.207310i
$582$	15558.6			1.10812
$583$	257.500	+	238.537i	0.0182925	+	0.0169454i
$584$	3014.84			0.213622
$585$	−1967.26	+	1429.30i	−0.139036	+	0.101016i
$586$	−198.769	−	611.747i	−0.0140121	−	0.0431247i
$587$	−3881.56	+	11946.2i	−0.272929	+	0.839989i	0.716831	+	0.697247i	$0.245592\pi$
$587$	−3881.56	+	11946.2i	−0.272929	+	0.839989i	−0.989760	+	0.142742i	$0.954408\pi$
$588$	3179.27	+	2309.88i	0.222978	+	0.162003i
$589$	8210.77	+	5965.48i	0.574396	+	0.417323i
$590$	2497.97	−	7687.95i	0.174305	−	0.536454i
$591$	1640.35	+	5048.49i	0.114171	+	0.351383i
$592$	−3632.12	+	2638.89i	−0.252161	+	0.183206i
$593$	7070.92			0.489659			0.244830	−	0.969566i	$-0.421268\pi$
$593$	7070.92			0.489659			0.244830	+	0.969566i	$0.421268\pi$
$594$	854.836	+	4321.49i	0.0590477	+	0.298506i
$595$	10039.6			0.691740
$596$	−722.668	+	525.049i	−0.0496672	+	0.0360853i
$597$	−729.110	−	2243.97i	−0.0499840	−	0.153835i
$598$	−785.202	+	2416.60i	−0.0536945	+	0.165255i
$599$	15260.5	+	11087.4i	1.04095	+	0.756293i	0.970470	−	0.241221i	$-0.0775478\pi$
$599$	15260.5	+	11087.4i	1.04095	+	0.756293i	0.0704773	+	0.997513i	$0.477548\pi$
$600$	−3967.34	−	2882.44i	−0.269943	−	0.196125i
$601$	−1029.55	+	3168.64i	−0.0698775	+	0.215061i	−0.979897	−	0.199505i	$-0.936067\pi$
$601$	−1029.55	+	3168.64i	−0.0698775	+	0.215061i	0.910019	+	0.414566i	$0.136067\pi$
$602$	−2682.06	−	8254.53i	−0.181582	−	0.558853i
$603$	4293.82	−	3119.64i	0.289980	−	0.210683i
$604$	−26943.6			−1.81510
$605$	7500.56	+	1817.55i	0.504035	+	0.122139i
$606$	12916.4			0.865832
$607$	4736.96	−	3441.60i	0.316750	−	0.230132i	−0.418038	−	0.908430i	$-0.637282\pi$
$607$	4736.96	−	3441.60i	0.316750	−	0.230132i	0.734787	+	0.678298i	$0.237282\pi$
$608$	−7350.61	−	22622.9i	−0.490307	−	1.50901i
$609$	−3978.75	+	12245.3i	−0.264741	+	0.814788i
$610$	−18659.1	−	13556.7i	−1.23850	−	0.899824i
$611$	−8820.92	−	6408.78i	−0.584053	−	0.424339i
$612$	−3778.85	+	11630.1i	−0.249593	+	0.768169i
$613$	−3678.51	−	11321.3i	−0.242371	−	0.745943i	−0.996058	−	0.0887082i	$-0.971726\pi$
$613$	−3678.51	−	11321.3i	−0.242371	−	0.745943i	0.753686	−	0.657234i	$-0.228274\pi$
$614$	−3455.21	+	2510.36i	−0.227103	+	0.165000i
$615$	104.142			0.00682830
$616$	−1936.59	−	9790.11i	−0.126668	−	0.640349i
$617$	−7655.61			−0.499519			−0.249759	−	0.968308i	$-0.580352\pi$
$617$	−7655.61			−0.499519			−0.249759	+	0.968308i	$0.580352\pi$
$618$	−5935.09	+	4312.10i	−0.386318	+	0.280676i
$619$	−1925.29	−	5925.44i	−0.125015	−	0.384755i	0.868889	−	0.495007i	$-0.164834\pi$
$619$	−1925.29	−	5925.44i	−0.125015	−	0.384755i	−0.993904	+	0.110251i	$0.964834\pi$
$620$	1969.30	−	6060.87i	0.127563	−	0.392598i
$621$	−266.348	−	193.513i	−0.0172112	−	0.0125047i
$622$	−6740.84	−	4897.51i	−0.434539	−	0.315711i
$623$	5594.07	−	17216.8i	0.359746	−	1.10718i
$624$	−691.161	−	2127.17i	−0.0443407	−	0.136467i
$625$	−3355.36	+	2437.81i	−0.214743	+	0.156020i
$626$	−6895.15			−0.440233
$627$	−8897.26	−	8242.04i	−0.566702	−	0.524969i
$628$	31174.2			1.98087
$629$	−25703.6	+	18674.8i	−1.62936	+	1.18380i
$630$	1102.82	+	3394.13i	0.0697419	+	0.214643i
$631$	−2545.93	+	7835.56i	−0.160621	+	0.494340i	−0.998687	−	0.0512284i	$-0.983686\pi$
$631$	−2545.93	+	7835.56i	−0.160621	+	0.494340i	0.838066	+	0.545569i	$0.183686\pi$
$632$	7219.57	+	5245.32i	0.454397	+	0.330139i
$633$	8795.63	+	6390.40i	0.552282	+	0.401257i
$634$	2479.62	−	7631.49i	0.155329	−	0.478053i
$635$	−573.778	−	1765.91i	−0.0358578	−	0.110359i
$636$	−280.212	+	203.586i	−0.0174703	+	0.0126929i
$637$	−5086.55			−0.316384
$638$	−39976.9	+	22332.5i	−2.48072	+	1.38582i
$639$	2367.37			0.146560
$640$	−9398.46	+	6828.38i	−0.580480	+	0.421743i
$641$	2196.12	+	6758.97i	0.135322	+	0.416479i	0.995640	−	0.0932791i	$-0.0297349\pi$
$641$	2196.12	+	6758.97i	0.135322	+	0.416479i	−0.860318	+	0.509758i	$0.829735\pi$
$642$	6466.62	−	19902.2i	0.397535	−	1.22349i
$643$	787.679	+	572.282i	0.0483095	+	0.0350989i	0.611678	−	0.791107i	$-0.290495\pi$
$643$	787.679	+	572.282i	0.0483095	+	0.0350989i	−0.563368	+	0.826206i	$0.690495\pi$
$644$	1810.20	+	1315.18i	0.110764	+	0.0804744i
$645$	−682.217	+	2099.65i	−0.0416469	+	0.128176i
$646$	−17339.5	−	53365.4i	−1.05606	−	3.25021i
$647$	6220.87	−	4519.73i	0.378003	−	0.274635i	−0.382519	−	0.923948i	$-0.624943\pi$
$647$	6220.87	−	4519.73i	0.378003	−	0.274635i	0.760522	+	0.649313i	$0.224943\pi$
$648$	−1448.97			−0.0878410
$649$	11292.7	+	1348.71i	0.683014	+	0.0815742i
$650$	19042.2			1.14907
$651$	3399.22	−	2469.68i	0.204648	−	0.148685i
$652$	10222.9	+	31463.0i	0.614051	+	1.88985i
$653$	−9224.44	+	28389.9i	−0.552803	+	1.70135i	0.148875	+	0.988856i	$0.452435\pi$
$653$	−9224.44	+	28389.9i	−0.552803	+	1.70135i	−0.701677	+	0.712495i	$0.747565\pi$
$654$	8516.60	+	6187.68i	0.509213	+	0.369965i
$655$	−2586.05	−	1878.87i	−0.154268	−	0.112082i
$656$	−29.6006	+	91.1012i	−0.00176175	+	0.00542211i
$657$	−468.721	−	1442.58i	−0.0278334	−	0.0856624i
$658$	−12945.9	+	9405.74i	−0.766996	+	0.557255i
$659$	30312.9			1.79184			0.895921	−	0.444213i	$-0.146517\pi$
$659$	30312.9			1.79184			0.895921	+	0.444213i	$0.146517\pi$
$660$	−3195.63	+	6912.57i	−0.188469	+	0.407684i
$661$	16789.0			0.987922			0.493961	−	0.869484i	$-0.335549\pi$
$661$	16789.0			0.987922			0.493961	+	0.869484i	$0.335549\pi$
$662$	41350.7	−	30043.1i	2.42771	−	1.76383i
$663$	−4891.17	−	15053.5i	−0.286512	−	0.881793i
$664$	−1785.52	+	5495.27i	−0.104355	+	0.321171i
$665$	−7948.90	−	5775.22i	−0.463527	−	0.336772i
$666$	−9136.88	−	6638.33i	−0.531602	−	0.386231i
$667$	1057.54	−	3254.76i	0.0613912	−	0.188943i
$668$	3065.75	+	9435.42i	0.177571	+	0.546508i
$669$	1187.29	−	862.619i	0.0686150	−	0.0498517i
$670$	15292.0			0.881765
$671$	13616.3	−	29453.9i	0.783386	−	1.69457i
$672$	−9847.73			−0.565304
$673$	−2339.32	+	1699.61i	−0.133988	+	0.0973481i	−0.652761	−	0.757564i	$-0.726389\pi$
$673$	−2339.32	+	1699.61i	−0.133988	+	0.0973481i	0.518772	+	0.854912i	$0.326389\pi$
$674$	−2210.72	−	6803.90i	−0.126341	−	0.388837i
$675$	−762.416	+	2346.47i	−0.0434747	+	0.133801i
$676$	249.919	+	181.577i	0.0142193	+	0.0103310i
$677$	1441.42	+	1047.26i	0.0818293	+	0.0594525i	0.627948	−	0.778255i	$-0.283895\pi$
$677$	1441.42	+	1047.26i	0.0818293	+	0.0594525i	−0.546118	+	0.837708i	$0.683895\pi$
$678$	6399.93	−	19696.9i	0.362519	−	1.11572i
$679$	5479.93	+	16865.5i	0.309721	+	0.953222i
$680$	−9501.51	+	6903.25i	−0.535833	+	0.389305i
$681$	5581.55			0.314076
$682$	14837.8	+	1772.12i	0.833093	+	0.0994985i
$683$	30297.1			1.69734			0.848672	−	0.528920i	$-0.177403\pi$
$683$	30297.1			1.69734			0.848672	+	0.528920i	$0.177403\pi$
$684$	9682.03	−	7034.41i	0.541230	−	0.393227i
$685$	−3051.98	−	9393.02i	−0.170234	−	0.523925i
$686$	−9555.40	+	29408.5i	−0.531818	+	1.63677i
$687$	−15795.6	−	11476.2i	−0.877207	−	0.637328i
$688$	−1642.82	−	1193.58i	−0.0910348	−	0.0661407i
$689$	138.537	−	426.372i	0.00766012	−	0.0235754i
$690$	−293.125	−	902.146i	−0.0161726	−	0.0497741i
$691$	−22181.6	+	16115.9i	−1.22117	+	0.887232i	−0.996197	−	0.0871327i	$-0.972230\pi$
$691$	−22181.6	+	16115.9i	−1.22117	+	0.887232i	−0.224974	+	0.974365i	$0.572230\pi$
$692$	−21070.0			−1.15746
$693$	−4383.40	+	2448.72i	−0.240276	+	0.134227i
$694$	9987.39			0.546277
$695$	−11723.1	+	8517.35i	−0.639832	+	0.464865i
$696$	−4654.39	−	14324.7i	−0.253483	−	0.780141i
$697$	−209.476	+	644.700i	−0.0113837	+	0.0350355i
$698$	25805.0	+	18748.4i	1.39933	+	1.01667i
$699$	565.504	+	410.863i	0.0305999	+	0.0222321i
$700$	5181.65	−	15947.5i	0.279783	−	0.861082i
$701$	−6690.31	−	20590.7i	−0.360470	−	1.10941i	−0.952769	−	0.303695i	$-0.901780\pi$
$701$	−6690.31	−	20590.7i	−0.360470	−	1.10941i	0.592299	−	0.805718i	$-0.298220\pi$
$702$	4551.89	−	3307.14i	0.244730	−	0.177806i
$703$	31093.4			1.66815
$704$	−22267.6	−	20627.8i	−1.19210	−	1.10432i
$705$	4070.32			0.217443
$706$	20206.8	−	14681.1i	1.07719	−	0.782623i
$707$	4549.33	+	14001.4i	0.242002	+	0.744804i
$708$	−3467.91	+	10673.1i	−0.184085	+	0.566555i
$709$	−22584.3	−	16408.5i	−1.19629	−	0.869158i	−0.202379	−	0.979307i	$-0.564867\pi$
$709$	−22584.3	−	16408.5i	−1.19629	−	0.869158i	−0.993915	+	0.110149i	$0.964867\pi$
$710$	5518.25	+	4009.25i	0.291685	+	0.211922i
$711$	1387.41	−	4270.00i	0.0731811	−	0.225228i
$712$	6544.01	+	20140.4i	0.344448	+	1.06010i
$713$	−903.498	+	656.430i	−0.0474562	+	0.0344790i
$714$	−23230.0			−1.21759
$715$	−1912.78	−	9669.77i	−0.100048	−	0.505775i
$716$	8246.89			0.430448
$717$	−15428.3	+	11209.3i	−0.803597	+	0.583847i
$718$	11893.3	+	36603.8i	0.618181	+	1.90257i
$719$	7451.10	−	22932.1i	0.386480	−	1.18946i	−0.548921	−	0.835874i	$-0.684961\pi$
$719$	7451.10	−	22932.1i	0.386480	−	1.18946i	0.935401	−	0.353589i	$-0.115039\pi$
$720$	675.502	+	490.781i	0.0349645	+	0.0254032i
$721$	−6764.72	−	4914.86i	−0.349419	−	0.253868i
$722$	−7490.53	+	23053.5i	−0.386106	+	1.18831i
$723$	−119.264	−	367.058i	−0.00613484	−	0.0188811i
$724$	−15384.3	+	11177.4i	−0.789716	+	0.573763i
$725$	−25646.6			−1.31378
$726$	−17355.0	−	4205.49i	−0.887195	−	0.214987i
$727$	−27063.6			−1.38065			−0.690327	−	0.723498i	$-0.742533\pi$
$727$	−27063.6			−1.38065			−0.690327	+	0.723498i	$0.742533\pi$
$728$	−10312.1	+	7492.17i	−0.524988	+	0.381426i
$729$	225.273	+	693.320i	0.0114451	+	0.0352243i
$730$	1350.50	−	4156.40i	0.0684714	−	0.210733i
$731$	−11625.8	−	8446.65i	−0.588231	−	0.427375i
$732$	25904.3	+	18820.6i	1.30799	+	0.950314i
$733$	632.598	−	1946.94i	0.0318766	−	0.0981060i	−0.933852	−	0.357659i	$-0.883575\pi$
$733$	632.598	−	1946.94i	0.0318766	−	0.0981060i	0.965729	+	0.259553i	$0.0835751\pi$
$734$	2843.86	+	8752.49i	0.143009	+	0.440137i
$735$	1536.22	−	1116.13i	0.0770942	−	0.0560122i
$736$	2617.49			0.131089
$737$	4174.92	+	21105.6i	0.208664	+	1.05486i
$738$	−240.966			−0.0120191
$739$	14282.1	−	10376.5i	0.710926	−	0.516518i	−0.172546	−	0.985001i	$-0.555199\pi$
$739$	14282.1	−	10376.5i	0.710926	−	0.516518i	0.883472	+	0.468484i	$0.155199\pi$
$740$	−6033.27	−	18568.5i	−0.299713	−	0.922420i
$741$	−4786.79	+	14732.2i	−0.237310	+	0.730366i
$742$	−532.301	−	386.740i	−0.0263361	−	0.0191343i
$743$	5142.74	+	3736.42i	0.253929	+	0.184490i	0.707466	−	0.706747i	$-0.249838\pi$
$743$	5142.74	+	3736.42i	0.253929	+	0.184490i	−0.453537	+	0.891237i	$0.649838\pi$
$744$	−1518.87	+	4674.60i	−0.0748446	+	0.230348i
$745$	133.379	+	410.499i	0.00655925	+	0.0201873i
$746$	−36507.1	+	26524.0i	−1.79172	+	1.30176i
$747$	2907.03			0.142387
$748$	−36365.1	−	33687.1i	−1.77759	−	1.64669i
$749$	23851.6			1.16358
$750$	−13618.1	+	9894.09i	−0.663015	+	0.481708i
$751$	8394.53	+	25835.7i	0.407884	+	1.25534i	0.918463	+	0.395506i	$0.129431\pi$
$751$	8394.53	+	25835.7i	0.407884	+	1.25534i	−0.510580	+	0.859830i	$0.670569\pi$
$752$	−1156.92	+	3560.63i	−0.0561017	+	0.172663i
$753$	255.953	+	185.961i	0.0123871	+	0.00899972i
$754$	47316.5	+	34377.5i	2.28537	+	1.66042i
$755$	−4023.12	+	12381.9i	−0.193929	+	0.596851i
$756$	−1531.04	−	4712.05i	−0.0736552	−	0.226687i
$757$	10245.1	−	7443.49i	0.491894	−	0.357382i	−0.314018	−	0.949417i	$-0.601675\pi$
$757$	10245.1	−	7443.49i	0.491894	−	0.357382i	0.805912	+	0.592035i	$0.201675\pi$
$758$	−31900.2			−1.52859
$759$	1165.09	−	650.860i	0.0557182	−	0.0311261i
$760$	11493.9			0.548587
$761$	10660.1	−	7745.04i	0.507792	−	0.368932i	−0.304194	−	0.952610i	$-0.598387\pi$
$761$	10660.1	−	7745.04i	0.507792	−	0.368932i	0.811985	+	0.583678i	$0.198387\pi$
$762$	1327.62	+	4086.00i	0.0631163	+	0.194252i
$763$	−3707.78	+	11411.4i	−0.175925	+	0.541440i
$764$	−29432.4	−	21383.9i	−1.39375	−	1.01262i
$765$	4780.35	+	3473.13i	0.225927	+	0.164145i
$766$	−9219.14	+	28373.6i	−0.434858	+	1.33835i
$767$	−4488.71	−	13814.8i	−0.211314	−	0.650357i
$768$	5591.93	−	4062.77i	0.262736	−	0.190889i
$769$	−28039.9			−1.31488			−0.657442	−	0.753505i	$-0.728361\pi$
$769$	−28039.9			−1.31488			−0.657442	+	0.753505i	$0.728361\pi$
$770$	−14364.6	−	1715.60i	−0.672291	−	0.0802935i
$771$	−780.800			−0.0364719
$772$	38121.1	−	27696.6i	1.77721	−	1.29122i
$773$	−9037.91	−	27815.8i	−0.420532	−	1.29426i	−0.907208	−	0.420682i	$-0.861791\pi$
$773$	−9037.91	−	27815.8i	−0.420532	−	1.29426i	0.486677	−	0.873582i	$-0.338209\pi$
$774$	1578.53	−	4858.21i	0.0733062	−	0.225613i
$775$	6770.88	+	4919.33i	0.313828	+	0.228010i
$776$	−16782.9	−	12193.5i	−0.776379	−	0.564072i
$777$	3977.82	−	12242.5i	0.183659	−	0.565246i
$778$	−4624.51	−	14232.8i	−0.213107	−	0.655874i
$779$	536.711	−	389.943i	0.0246851	−	0.0179348i
$780$	9726.67			0.446501
$781$	−4026.89	+	8710.71i	−0.184499	+	0.399096i
$782$	6174.43			0.282349
$783$	−6130.64	+	4454.17i	−0.279810	+	0.203294i
$784$	539.722	+	1661.09i	0.0245864	+	0.0756693i
$785$	4654.82	−	14326.1i	0.211640	−	0.651362i
$786$	5983.66	+	4347.38i	0.271539	+	0.197285i
$787$	−8346.87	−	6064.36i	−0.378061	−	0.274677i	0.382485	−	0.923962i	$-0.375068\pi$
$787$	−8346.87	−	6064.36i	−0.378061	−	0.274677i	−0.760546	+	0.649284i	$0.775068\pi$
$788$	6561.42	−	20194.0i	0.296625	−	0.912919i
$789$	−561.852	−	1729.20i	−0.0253517	−	0.0780244i
$790$	10465.4	−	7603.59i	0.471321	−	0.342435i
$791$	23605.6			1.06108
$792$	2464.70	−	5331.49i	0.110580	−	0.239200i
$793$	−41444.6			−1.85592
$794$	29574.8	−	21487.3i	1.32188	−	0.960399i
$795$	51.7174	+	159.170i	0.00230720	+	0.00710084i
$796$	−2916.44	+	8975.88i	−0.129862	+	0.399675i
$797$	19617.0	+	14252.6i	0.871858	+	0.633442i	0.931085	−	0.364803i	$-0.118864\pi$
$797$	19617.0	+	14252.6i	0.871858	+	0.633442i	−0.0592269	+	0.998245i	$0.518864\pi$
$798$	18392.4	+	13362.8i	0.815893	+	0.592781i
$799$	−8187.23	+	25197.7i	−0.362507	+	1.11568i
$800$	−6061.56	−	18655.6i	−0.267886	−	0.824467i
$801$	8619.59	−	6262.50i	0.380223	−	0.276248i
$802$	55023.4			2.42262
$803$	6105.25	+	729.166i	0.268306	+	0.0320445i
$804$	−21229.8			−0.931241
$805$	874.683	−	635.494i	0.0382963	−	0.0278239i
$806$	−5897.86	−	18151.7i	−0.257746	−	0.793261i
$807$	4115.12	−	12665.0i	0.179503	−	0.552454i
$808$	−13932.8	−	10122.8i	−0.606628	−	0.440741i
$809$	11721.2	+	8515.97i	0.509390	+	0.370094i	0.812592	−	0.582833i	$-0.198056\pi$
$809$	11721.2	+	8515.97i	0.509390	+	0.370094i	−0.303202	+	0.952926i	$0.598056\pi$
$810$	−649.066	+	1997.62i	−0.0281554	+	0.0866533i
$811$	13272.0	+	40847.0i	0.574651	+	1.76859i	0.637364	+	0.770563i	$0.280025\pi$
$811$	13272.0	+	40847.0i	0.574651	+	1.76859i	−0.0627122	+	0.998032i	$0.519975\pi$
$812$	41666.0	−	30272.1i	1.80073	−	1.30830i
$813$	−14510.6			−0.625966
$814$	39967.6	−	22327.3i	1.72096	−	0.961390i
$815$	15985.2			0.687040
$816$	−4396.96	+	3194.58i	−0.188633	+	0.137050i
$817$	4345.90	+	13375.3i	0.186100	+	0.572757i
$818$	−872.720	+	2685.96i	−0.0373031	+	0.114807i
$819$	5188.17	+	3769.43i	0.221355	+	0.160823i
$820$	−337.010	−	244.852i	−0.0143523	−	0.0104276i
$821$	1805.41	−	5556.47i	0.0767468	−	0.236202i	−0.905322	−	0.424726i	$-0.860370\pi$
$821$	1805.41	−	5556.47i	0.0767468	−	0.236202i	0.982069	+	0.188524i	$0.0603703\pi$
$822$	7061.73	+	21733.8i	0.299643	+	0.922205i
$823$	23800.1	−	17291.8i	1.00804	−	0.732386i	0.0442452	−	0.999021i	$-0.485912\pi$
$823$	23800.1	−	17291.8i	1.00804	−	0.732386i	0.963798	+	0.266635i	$0.0859117\pi$
$824$	9781.57			0.413540
$825$	−7336.97	−	6796.66i	−0.309625	−	0.286824i
$826$	−21318.5			−0.898021
$827$	−30948.0	+	22485.0i	−1.30129	+	0.945442i	−0.999967	−	0.00807991i	$-0.997428\pi$
$827$	−30948.0	+	22485.0i	−1.30129	+	0.945442i	−0.301322	+	0.953522i	$0.597428\pi$
$828$	406.944	+	1252.44i	0.0170800	+	0.0525670i
$829$	3890.89	−	11974.9i	0.163011	−	0.501696i	−0.835873	−	0.548923i	$-0.815038\pi$
$829$	3890.89	−	11974.9i	0.163011	−	0.501696i	0.998884	+	0.0472263i	$0.0150382\pi$
$830$	6776.21	+	4923.20i	0.283380	+	0.205888i
$831$	11151.7	+	8102.17i	0.465520	+	0.338220i
$832$	−11980.1	+	36871.0i	−0.499202	+	1.53639i
$833$	3819.47	+	11755.1i	0.158868	+	0.488945i
$834$	27125.2	−	19707.6i	1.12622	−	0.818248i
$835$	4793.80			0.198678
$836$	9413.92	+	47590.5i	0.389458	+	1.96884i
$837$	2472.89			0.102121
$838$	−12362.0	+	8981.52i	−0.509592	+	0.370240i
$839$	−9726.63	−	29935.5i	−0.400239	−	1.23181i	−0.924806	−	0.380439i	$-0.875773\pi$
$839$	−9726.63	−	29935.5i	−0.400239	−	1.23181i	0.524567	−	0.851369i	$-0.324227\pi$
$840$	1470.43	−	4525.51i	0.0603983	−	0.185887i
$841$	−43996.3	−	31965.2i	−1.80394	−	1.31064i
$842$	13660.3	+	9924.77i	0.559102	+	0.406212i
$843$	4237.87	−	13042.8i	0.173144	−	0.532881i
$844$	−13438.5	−	41359.5i	−0.548072	−	1.68679i
$845$	120.760	−	87.7376i	0.00491631	−	0.00357191i
$846$	−9417.99			−0.382739
$847$	−1553.89	−	20294.0i	−0.0630371	−	0.823270i
$848$	−153.938			−0.00623380
$849$	19592.4	−	14234.7i	0.792003	−	0.575424i
$850$	−14298.7	−	44006.9i	−0.576990	−	1.77579i
$851$	−1057.29	+	3254.00i	−0.0425891	+	0.131076i
$852$	−7660.96	−	5566.01i	−0.308052	−	0.223813i
$853$	−13596.5	−	9878.47i	−0.545764	−	0.396521i	0.280457	−	0.959867i	$-0.409514\pi$
$853$	−13596.5	−	9878.47i	−0.545764	−	0.396521i	−0.826221	+	0.563346i	$0.809514\pi$
$854$	−18796.1	+	57848.5i	−0.753150	+	2.31796i
$855$	−1786.96	−	5499.71i	−0.0714771	−	0.219984i
$856$	−22573.1	+	16400.3i	−0.901324	+	0.654850i
$857$	−42475.1			−1.69302			−0.846512	−	0.532369i	$-0.821302\pi$
$857$	−42475.1			−1.69302			−0.846512	+	0.532369i	$0.821302\pi$
$858$	4425.84	+	22374.1i	0.176102	+	0.890257i
$859$	−25306.4			−1.00517			−0.502586	−	0.864527i	$-0.667618\pi$
$859$	−25306.4			−1.00517			−0.502586	+	0.864527i	$0.667618\pi$
$860$	7144.27	−	5190.61i	0.283276	−	0.205812i
$861$	−84.8711	−	261.207i	−0.00335935	−	0.0103390i
$862$	626.742	−	1928.91i	0.0247644	−	0.0762170i
$863$	−10675.6	−	7756.28i	−0.421091	−	0.305941i	0.356986	−	0.934110i	$-0.383805\pi$
$863$	−10675.6	−	7756.28i	−0.421091	−	0.305941i	−0.778077	+	0.628169i	$0.783805\pi$
$864$	−4688.97	−	3406.74i	−0.184632	−	0.134143i
$865$	−3146.10	+	9682.70i	−0.123665	+	0.380603i
$866$	13562.7	+	41741.8i	0.532194	+	1.63793i
$867$	−19192.1	+	13943.9i	−0.751784	+	0.546203i
$868$	−16806.7			−0.657206
$869$	13351.5	+	12368.2i	0.521193	+	0.482812i
$870$	−21833.7			−0.850840
$871$	22230.9	−	16151.7i	0.864828	−	0.628334i
$872$	−4337.40	−	13349.2i	−0.168444	−	0.518417i
$873$	−3225.21	+	9926.19i	−0.125037	+	0.384823i
$874$	−4888.61	−	3551.79i	−0.189199	−	0.137461i
$875$	−15521.6	−	11277.1i	−0.599688	−	0.435699i
$876$	−1874.88	+	5770.30i	−0.0723133	+	0.222558i
$877$	8959.63	+	27574.9i	0.344977	+	1.06173i	0.961596	+	0.274469i	$0.0885022\pi$
$877$	8959.63	+	27574.9i	0.344977	+	1.06173i	−0.616618	+	0.787262i	$0.711498\pi$
$878$	−2224.64	+	1616.29i	−0.0855102	+	0.0621268i
$879$	431.491			0.0165573
$880$	−2954.85	+	1650.69i	−0.113191	+	0.0632325i
$881$	9676.79			0.370056			0.185028	−	0.982733i	$-0.440762\pi$
$881$	9676.79			0.370056			0.185028	+	0.982733i	$0.440762\pi$
$882$	−3554.53	+	2582.52i	−0.135700	+	0.0985918i
$883$	−6694.81	−	20604.5i	−0.255151	−	0.785274i	−0.993800	−	0.111184i	$-0.964536\pi$
$883$	−6694.81	−	20604.5i	−0.255151	−	0.785274i	0.738649	−	0.674091i	$-0.235464\pi$
$884$	−19564.7	+	60213.9i	−0.744380	+	2.29096i
$885$	4387.01	+	3187.35i	0.166630	+	0.121064i
$886$	−45184.8	−	32828.7i	−1.71333	−	1.24481i
$887$	8370.05	−	25760.4i	0.316842	−	0.975139i	−0.658148	−	0.752889i	$-0.728660\pi$
$887$	8370.05	−	25760.4i	0.316842	−	0.975139i	0.974990	−	0.222250i	$-0.0713402\pi$
$888$	4653.30	+	14321.4i	0.175850	+	0.541210i
$889$	−3961.61	+	2878.28i	−0.149458	+	0.108588i
$890$	30697.8			1.15617
$891$	−2934.26	−	350.446i	−0.110327	−	0.0131767i
$892$	−5870.30			−0.220350
$893$	20977.0	−	15240.7i	0.786079	−	0.571120i
$894$	−308.616	−	949.822i	−0.0115455	−	0.0355333i
$895$	1231.40	−	3789.84i	0.0459899	−	0.141542i
$896$	24786.2	+	18008.2i	0.924160	+	0.671441i
$897$	−1379.00	−	1001.90i	−0.0513303	−	0.0372937i
$898$	12594.8	−	38762.8i	0.468033	−	1.44046i
$899$	7943.43	+	24447.4i	0.294692	+	0.906970i
$900$	7984.12	−	5800.80i	0.295708	−	0.214845i
$901$	−1089.38			−0.0402803
$902$	409.883	−	886.633i	0.0151304	−	0.0327291i
$903$	5822.27			0.214566
$904$	−22340.3	+	16231.2i	−0.821933	+	0.597169i
$905$	2839.41	+	8738.82i	0.104293	+	0.320981i
$906$	9308.78	−	28649.5i	0.341350	−	1.05057i
$907$	30624.4	+	22250.0i	1.12113	+	0.814551i	0.984380	−	0.176054i	$-0.0563335\pi$
$907$	30624.4	+	22250.0i	1.12113	+	0.814551i	0.136753	+	0.990605i	$0.456333\pi$
$908$	−18062.3	−	13123.0i	−0.660152	−	0.479628i
$909$	−2677.51	+	8240.53i	−0.0976980	+	0.300683i
$910$	5709.76	+	17572.8i	0.207996	+	0.640147i
$911$	−16018.5	+	11638.1i	−0.582566	+	0.423259i	−0.839648	−	0.543131i	$-0.817239\pi$
$911$	−16018.5	+	11638.1i	−0.582566	+	0.423259i	0.257082	+	0.966389i	$0.417239\pi$
$912$	5318.95			0.193123
$913$	−4944.87	+	10696.4i	−0.179246	+	0.387733i
$914$	−7826.21			−0.283225
$915$	12516.9	−	9094.08i	0.452237	−	0.328569i
$916$	24133.6	+	74275.5i	0.870520	+	2.67918i
$917$	−2605.03	+	8017.47i	−0.0938122	+	0.288724i
$918$	−11060.9	−	8036.21i	−0.397673	−	0.288926i
$919$	−4256.70	−	3092.68i	−0.152792	−	0.111010i	0.508763	−	0.860907i	$-0.330103\pi$
$919$	−4256.70	−	3092.68i	−0.152792	−	0.111010i	−0.661555	+	0.749897i	$0.730103\pi$
$920$	−390.834	+	1202.86i	−0.0140059	+	0.0431056i
$921$	−885.331	−	2724.77i	−0.0316750	−	0.0974856i
$922$	−5046.50	+	3666.50i	−0.180258	+	0.130965i
$923$	12256.8			0.437095
$924$	19942.3	+	2381.76i	0.710013	+	0.0847988i
$925$	25640.6			0.911414
$926$	32588.2	−	23676.7i	1.15650	−	0.840243i
$927$	−1520.75	−	4680.40i	−0.0538814	−	0.165830i
$928$	18617.6	−	57299.0i	0.658569	−	2.02687i
$929$	35922.3	+	26099.1i	1.26865	+	0.921725i	0.999148	−	0.0412761i	$-0.0131423\pi$
$929$	35922.3	+	26099.1i	1.26865	+	0.921725i	0.269498	+	0.963001i	$0.413142\pi$
$930$	5764.23	+	4187.96i	0.203244	+	0.147665i
$931$	3737.96	−	11504.3i	0.131586	−	0.404981i
$932$	−864.013	−	2659.16i	−0.0303666	−	0.0934589i
$933$	4521.90	−	3285.35i	0.158671	−	0.115281i
$934$	−42868.5			−1.50182
$935$	−20910.8	+	11681.5i	−0.731396	+	0.408583i
$936$	−7501.93			−0.261975
$937$	24473.0	−	17780.7i	0.853253	−	0.619924i	−0.0727882	−	0.997347i	$-0.523190\pi$
$937$	24473.0	−	17780.7i	0.853253	−	0.619924i	0.926041	+	0.377423i	$0.123190\pi$
$938$	−12462.3	−	38355.1i	−0.433806	−	1.33512i
$939$	1429.33	−	4399.03i	0.0496746	−	0.152883i
$940$	−13171.8	−	9569.89i	−0.457040	−	0.332059i
$941$	−41839.6	−	30398.2i	−1.44945	−	1.05309i	−0.985960	−	0.166984i	$-0.946597\pi$
$941$	−41839.6	−	30398.2i	−1.44945	−	1.05309i	−0.463490	−	0.886102i	$-0.653403\pi$
$942$	−10770.4	+	33148.0i	−0.372526	+	1.14652i
$943$	22.5584	+	69.4277i	0.000779006	+	0.00239754i
$944$	−4035.16	+	2931.72i	−0.139124	+	0.101080i
$945$	−2394.02			−0.0824102
$946$	15190.7	+	14072.0i	0.522084	+	0.483637i
$947$	−8455.69			−0.290151			−0.145075	−	0.989421i	$-0.546342\pi$
$947$	−8455.69			−0.290151			−0.145075	+	0.989421i	$0.546342\pi$
$948$	−14529.1	+	10556.0i	−0.497767	+	0.361649i
$949$	−2426.76	−	7468.81i	−0.0830096	−	0.255477i
$950$	−13993.6	+	43067.7i	−0.477906	+	1.47084i
$951$	4354.79	+	3163.94i	0.148490	+	0.107884i
$952$	25057.9	+	18205.6i	0.853079	+	0.619798i
$953$	7375.49	−	22699.4i	0.250699	−	0.771571i	−0.743948	−	0.668237i	$-0.767049\pi$
$953$	7375.49	−	22699.4i	0.250699	−	0.771571i	0.994647	−	0.103334i	$-0.0329509\pi$
$954$	−119.665	−	368.290i	−0.00406110	−	0.0124988i
$955$	−14221.7	+	10332.7i	−0.481888	+	0.350112i
$956$	76281.5			2.58067
$957$	−5960.87	−	30134.2i	−0.201346	−	1.01787i
$958$	−25220.8			−0.850572
$959$	−21072.1	+	15309.8i	−0.709546	+	0.515516i
$960$	−4472.32	−	13764.4i	−0.150358	−	0.462754i
$961$	−6613.74	+	20355.0i	−0.222005	+	0.683260i
$962$	−47305.4	−	34369.4i	−1.58543	−	1.15189i
$963$	11356.9	+	8251.26i	0.380032	+	0.276109i
$964$	−477.057	+	1468.23i	−0.0159388	+	0.0490545i
$965$	−7035.83	−	21654.1i	−0.234706	−	0.722351i
$966$	−2023.86	+	1470.42i	−0.0674085	+	0.0489752i
$967$	9812.37			0.326313			0.163156	−	0.986600i	$-0.447832\pi$
$967$	9812.37			0.326313			0.163156	+	0.986600i	$0.447832\pi$
$968$	15424.7	+	18137.7i	0.512158	+	0.602241i
$969$	37640.9			1.24788
$970$	−24328.3	+	17675.6i	−0.805295	+	0.585081i
$971$	7331.56	+	22564.2i	0.242308	+	0.745747i	0.996068	+	0.0885966i	$0.0282382\pi$
$971$	7331.56	+	22564.2i	0.242308	+	0.745747i	−0.753760	+	0.657150i	$0.771762\pi$
$972$	901.094	−	2773.28i	0.0297352	−	0.0915155i
$973$	30916.9	+	22462.4i	1.01865	+	0.740095i
$974$	−61238.8	−	44492.6i	−2.01460	−	1.46369i
$975$	−3947.34	+	12148.7i	−0.129658	+	0.399045i
$976$	4397.59	+	13534.4i	0.144225	+	0.443878i
$977$	11792.9	−	8568.03i	0.386170	−	0.280569i	−0.377714	−	0.925922i	$-0.623290\pi$
$977$	11792.9	−	8568.03i	0.386170	−	0.280569i	0.763884	+	0.645353i	$0.223290\pi$
$978$	−36986.9			−1.20932
$979$	8380.91	+	42368.3i	0.273600	+	1.38314i
$980$	−7595.47			−0.247580
$981$	−5713.11	+	4150.82i	−0.185938	+	0.135092i
$982$	−7192.78	−	22137.1i	−0.233738	−	0.719372i
$983$	14679.6	−	45179.3i	0.476305	−	1.46592i	−0.367884	−	0.929872i	$-0.619918\pi$
$983$	14679.6	−	45179.3i	0.476305	−	1.46592i	0.844189	−	0.536045i	$-0.180082\pi$
$984$	259.927	+	188.848i	0.00842091	+	0.00611815i
$985$	−8300.38	−	6030.58i	−0.268499	−	0.195076i
$986$	43917.3	−	135163.i	1.41847	−	4.36560i
$987$	−3317.13	−	10209.1i	−0.106976	−	0.329239i
$988$	50127.9	−	36420.0i	1.61415	−	1.17275i
$989$	−1547.54			−0.0497561
$990$	−6246.17	−	5786.19i	−0.200521	−	0.185755i
$991$	−3389.37			−0.108645			−0.0543224	−	0.998523i	$-0.517300\pi$
$991$	−3389.37			−0.108645			−0.0543224	+	0.998523i	$0.517300\pi$
$992$	−15905.8	+	11556.2i	−0.509082	+	0.369870i
$993$	10595.3	+	32609.0i	0.338603	+	1.04211i
$994$	5558.77	−	17108.1i	0.177378	−	0.545913i
$995$	3689.38	+	2680.49i	0.117549	+	0.0854043i
$996$	−9407.36	−	6834.85i	−0.299281	−	0.217440i
$997$	−10326.2	+	31780.6i	−0.328017	+	1.00953i	0.642044	+	0.766668i	$0.278087\pi$
$997$	−10326.2	+	31780.6i	−0.328017	+	1.00953i	−0.970060	+	0.242863i	$0.921913\pi$
$998$	−2292.36	−	7055.17i	−0.0727090	−	0.223775i
$999$	6129.20	−	4453.13i	0.194114	−	0.141032i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.4.e.a.25.1	yes	4
3.2	odd	2		99.4.f.a.91.1		4
11.2	odd	10		363.4.a.o.1.2		2
11.4	even	5	inner	33.4.e.a.4.1	✓	4
11.9	even	5		363.4.a.n.1.1		2
33.2	even	10		1089.4.a.q.1.1		2
33.20	odd	10		1089.4.a.p.1.2		2
33.26	odd	10		99.4.f.a.37.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.4.e.a.4.1	✓	4	11.4	even	5	inner
33.4.e.a.25.1	yes	4	1.1	even	1	trivial
99.4.f.a.37.1		4	33.26	odd	10
99.4.f.a.91.1		4	3.2	odd	2
363.4.a.n.1.1		2	11.9	even	5
363.4.a.o.1.2		2	11.2	odd	10
1089.4.a.p.1.2		2	33.20	odd	10
1089.4.a.q.1.1		2	33.2	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.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.61803 - 2.62866i) q^{2} +(0.927051 + 2.85317i) q^{3} +(3.70820 - 11.4127i) q^{4} +(-4.69098 - 3.40820i) q^{5} +(10.8541 + 7.88597i) q^{6} +(-4.72542 + 14.5434i) q^{7} +(-5.52786 - 17.0130i) q^{8} +(-7.28115 + 5.29007i) q^{9} +O(q^{10})\)	\(q+(3.61803 - 2.62866i) q^{2} +(0.927051 + 2.85317i) q^{3} +(3.70820 - 11.4127i) q^{4} +(-4.69098 - 3.40820i) q^{5} +(10.8541 + 7.88597i) q^{6} +(-4.72542 + 14.5434i) q^{7} +(-5.52786 - 17.0130i) q^{8} +(-7.28115 + 5.29007i) q^{9} -25.9311 q^{10} +(-7.07953 - 35.7894i) q^{11} +36.0000 q^{12} +(-37.6976 + 27.3889i) q^{13} +(21.1327 + 65.0399i) q^{14} +(5.37539 - 16.5437i) q^{15} +(12.9443 + 9.40456i) q^{16} +(91.6033 + 66.5537i) q^{17} +(-12.4377 + 38.2793i) q^{18} +(-34.2426 - 105.388i) q^{19} +(-56.2918 + 40.8984i) q^{20} -45.8754 q^{21} +(-119.692 - 110.878i) q^{22} +12.1935 q^{23} +(43.4164 - 31.5439i) q^{24} +(-28.2376 - 86.9065i) q^{25} +(-64.3951 + 198.188i) q^{26} +(-21.8435 - 15.8702i) q^{27} +(148.456 + 107.860i) q^{28} +(86.7295 - 266.926i) q^{29} +(-24.0395 - 73.9859i) q^{30} +(-74.0967 + 53.8344i) q^{31} +214.663 q^{32} +(95.5501 - 53.3777i) q^{33} +506.371 q^{34} +(71.7336 - 52.1175i) q^{35} +(33.3738 + 102.714i) q^{36} +(-86.7092 + 266.863i) q^{37} +(-400.920 - 291.285i) q^{38} +(-113.093 - 82.1666i) q^{39} +(-32.0526 + 98.6478i) q^{40} +(1.85004 + 5.69383i) q^{41} +(-165.979 + 120.591i) q^{42} -126.915 q^{43} +(-434.705 - 51.9180i) q^{44} +52.1854 q^{45} +(44.1165 - 32.0525i) q^{46} +(72.3075 + 222.539i) q^{47} +(-14.8328 + 45.6507i) q^{48} +(88.3131 + 64.1632i) q^{49} +(-330.612 - 240.204i) q^{50} +(-104.968 + 323.059i) q^{51} +(172.790 + 531.794i) q^{52} +(-7.78367 + 5.65516i) q^{53} -120.748 q^{54} +(-88.7674 + 192.016i) q^{55} +273.548 q^{56} +(268.945 - 195.400i) q^{57} +(-387.866 - 1193.73i) q^{58} +(-96.3309 + 296.476i) q^{59} +(-168.875 - 122.695i) q^{60} +(719.565 + 522.795i) q^{61} +(-126.572 + 389.550i) q^{62} +(-42.5288 - 130.890i) q^{63} +(673.102 - 489.037i) q^{64} +270.185 q^{65} +(205.392 - 444.291i) q^{66} -589.717 q^{67} +(1099.24 - 798.645i) q^{68} +(11.3040 + 34.7901i) q^{69} +(122.536 - 377.126i) q^{70} +(-212.804 - 154.611i) q^{71} +(130.249 + 94.6316i) q^{72} +(-52.0801 + 160.286i) q^{73} +(387.775 + 1193.45i) q^{74} +(221.781 - 161.133i) q^{75} -1329.74 q^{76} +(553.952 + 66.1599i) q^{77} -625.161 q^{78} +(-403.586 + 293.222i) q^{79} +(-28.6687 - 88.2333i) q^{80} +(25.0304 - 77.0356i) q^{81} +(21.6606 + 15.7374i) q^{82} +(-261.316 - 189.857i) q^{83} +(-170.115 + 523.561i) q^{84} +(-202.881 - 624.405i) q^{85} +(-459.182 + 333.615i) q^{86} +841.988 q^{87} +(-569.751 + 318.283i) q^{88} -1183.82 q^{89} +(188.808 - 137.177i) q^{90} +(-220.189 - 677.673i) q^{91} +(45.2160 - 139.160i) q^{92} +(-222.290 - 161.503i) q^{93} +(846.591 + 615.084i) q^{94} +(-198.552 + 611.079i) q^{95} +(199.003 + 612.469i) q^{96} +(938.191 - 681.636i) q^{97} +488.183 q^{98} +(240.875 + 223.137i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 10 q^{2} - 3 q^{3} - 12 q^{4} - 21 q^{5} + 30 q^{6} + 37 q^{7} - 40 q^{8} - 9 q^{9}+O(q^{10}) \) 4 * q + 10 * q^2 - 3 * q^3 - 12 * q^4 - 21 * q^5 + 30 * q^6 + 37 * q^7 - 40 * q^8 - 9 * q^9	\( 4 q + 10 q^{2} - 3 q^{3} - 12 q^{4} - 21 q^{5} + 30 q^{6} + 37 q^{7} - 40 q^{8} - 9 q^{9} - 220 q^{10} + 41 q^{11} + 144 q^{12} - 77 q^{13} + 250 q^{14} + 102 q^{15} + 16 q^{16} + 192 q^{17} - 90 q^{18} - 52 q^{19} - 252 q^{20} - 264 q^{21} + 40 q^{22} - 148 q^{23} + 120 q^{24} - 426 q^{25} - 110 q^{26} - 27 q^{27} + 84 q^{28} + 414 q^{29} + 360 q^{30} - 198 q^{31} - 27 q^{33} + 1140 q^{34} + 477 q^{35} - 108 q^{36} + 201 q^{37} - 830 q^{38} - 231 q^{39} + 480 q^{40} - 129 q^{41} - 570 q^{42} - 132 q^{43} - 1068 q^{44} - 234 q^{45} - 150 q^{46} - 35 q^{47} + 48 q^{48} + 474 q^{49} - 30 q^{50} - 279 q^{51} + 396 q^{52} + 188 q^{53} + 356 q^{55} - 480 q^{56} + 519 q^{57} + 300 q^{58} - 1320 q^{59} - 756 q^{60} + 1275 q^{61} + 330 q^{62} + 333 q^{63} + 832 q^{64} + 638 q^{65} + 30 q^{66} + 150 q^{67} + 2304 q^{68} + 441 q^{69} - 3660 q^{70} + 117 q^{71} + 360 q^{72} - 982 q^{73} + 2450 q^{74} + 867 q^{75} - 2904 q^{76} + 1583 q^{77} - 1320 q^{78} - 1469 q^{79} - 544 q^{80} - 81 q^{81} + 270 q^{82} - 967 q^{83} + 1332 q^{84} + 27 q^{85} - 750 q^{86} + 792 q^{87} - 2440 q^{88} - 5424 q^{89} - 90 q^{90} - 561 q^{91} + 1764 q^{92} - 594 q^{93} + 2000 q^{94} - 707 q^{95} + 1440 q^{96} + 2391 q^{97} + 5280 q^{98} + 1044 q^{99}+O(q^{100}) \) 4 * q + 10 * q^2 - 3 * q^3 - 12 * q^4 - 21 * q^5 + 30 * q^6 + 37 * q^7 - 40 * q^8 - 9 * q^9 - 220 * q^10 + 41 * q^11 + 144 * q^12 - 77 * q^13 + 250 * q^14 + 102 * q^15 + 16 * q^16 + 192 * q^17 - 90 * q^18 - 52 * q^19 - 252 * q^20 - 264 * q^21 + 40 * q^22 - 148 * q^23 + 120 * q^24 - 426 * q^25 - 110 * q^26 - 27 * q^27 + 84 * q^28 + 414 * q^29 + 360 * q^30 - 198 * q^31 - 27 * q^33 + 1140 * q^34 + 477 * q^35 - 108 * q^36 + 201 * q^37 - 830 * q^38 - 231 * q^39 + 480 * q^40 - 129 * q^41 - 570 * q^42 - 132 * q^43 - 1068 * q^44 - 234 * q^45 - 150 * q^46 - 35 * q^47 + 48 * q^48 + 474 * q^49 - 30 * q^50 - 279 * q^51 + 396 * q^52 + 188 * q^53 + 356 * q^55 - 480 * q^56 + 519 * q^57 + 300 * q^58 - 1320 * q^59 - 756 * q^60 + 1275 * q^61 + 330 * q^62 + 333 * q^63 + 832 * q^64 + 638 * q^65 + 30 * q^66 + 150 * q^67 + 2304 * q^68 + 441 * q^69 - 3660 * q^70 + 117 * q^71 + 360 * q^72 - 982 * q^73 + 2450 * q^74 + 867 * q^75 - 2904 * q^76 + 1583 * q^77 - 1320 * q^78 - 1469 * q^79 - 544 * q^80 - 81 * q^81 + 270 * q^82 - 967 * q^83 + 1332 * q^84 + 27 * q^85 - 750 * q^86 + 792 * q^87 - 2440 * q^88 - 5424 * q^89 - 90 * q^90 - 561 * q^91 + 1764 * q^92 - 594 * q^93 + 2000 * q^94 - 707 * q^95 + 1440 * q^96 + 2391 * q^97 + 5280 * q^98 + 1044 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more