LMFDB - Embedded newform 105.4.i.b.46.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(16,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("105.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.i (of order $3$, degree $2$, 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:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	105.46
Dual form			105.4.i.b.16.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.70711 + 2.95680i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-1.82843 + 3.16693i) q^{4} +(2.50000 + 4.33013i) q^{5} +10.2426 q^{6} +(16.7426 - 7.91732i) q^{7} +14.8284 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(1.70711 + 2.95680i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-1.82843 + 3.16693i) q^{4} +(2.50000 + 4.33013i) q^{5} +10.2426 q^{6} +(16.7426 - 7.91732i) q^{7} +14.8284 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-8.53553 + 14.7840i) q^{10} +(-18.8701 + 32.6839i) q^{11} +(5.48528 + 9.50079i) q^{12} +43.7696 q^{13} +(51.9914 + 35.9889i) q^{14} +15.0000 q^{15} +(39.9411 + 69.1801i) q^{16} +(-19.0416 + 32.9811i) q^{17} +(15.3640 - 26.6112i) q^{18} +(-49.7548 - 86.1779i) q^{19} -18.2843 q^{20} +(4.54416 - 55.3746i) q^{21} -128.853 q^{22} +(-1.38478 - 2.39850i) q^{23} +(22.2426 - 38.5254i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(74.7193 + 129.418i) q^{26} -27.0000 q^{27} +(-5.53911 + 67.4990i) q^{28} -174.485 q^{29} +(25.6066 + 44.3519i) q^{30} +(8.95584 - 15.5120i) q^{31} +(-77.0538 + 133.461i) q^{32} +(56.6102 + 98.0517i) q^{33} -130.024 q^{34} +(76.1396 + 52.7045i) q^{35} +32.9117 q^{36} +(-161.478 - 279.688i) q^{37} +(169.874 - 294.230i) q^{38} +(65.6543 - 113.717i) q^{39} +(37.0711 + 64.2090i) q^{40} +248.534 q^{41} +(171.489 - 81.0943i) q^{42} -474.740 q^{43} +(-69.0051 - 119.520i) q^{44} +(22.5000 - 38.9711i) q^{45} +(4.72792 - 8.18900i) q^{46} +(-31.8528 - 55.1707i) q^{47} +239.647 q^{48} +(217.632 - 265.114i) q^{49} -85.3553 q^{50} +(57.1249 + 98.9432i) q^{51} +(-80.0294 + 138.615i) q^{52} +(131.598 - 227.934i) q^{53} +(-46.0919 - 79.8335i) q^{54} -188.701 q^{55} +(248.267 - 117.401i) q^{56} -298.529 q^{57} +(-297.865 - 515.917i) q^{58} +(166.522 - 288.424i) q^{59} +(-27.4264 + 47.5039i) q^{60} +(140.574 + 243.481i) q^{61} +61.1543 q^{62} +(-137.051 - 94.8680i) q^{63} +112.902 q^{64} +(109.424 + 189.528i) q^{65} +(-193.279 + 334.769i) q^{66} +(-443.277 + 767.778i) q^{67} +(-69.6325 - 120.607i) q^{68} -8.30866 q^{69} +(-25.8579 + 315.101i) q^{70} -951.897 q^{71} +(-66.7279 - 115.576i) q^{72} +(-406.429 + 703.956i) q^{73} +(551.319 - 954.913i) q^{74} +(37.5000 + 64.9519i) q^{75} +363.892 q^{76} +(-57.1657 + 696.615i) q^{77} +448.316 q^{78} +(-260.873 - 451.845i) q^{79} +(-199.706 + 345.900i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(424.274 + 734.864i) q^{82} +339.750 q^{83} +(167.059 + 115.640i) q^{84} -190.416 q^{85} +(-810.432 - 1403.71i) q^{86} +(-261.728 + 453.326i) q^{87} +(-279.813 + 484.651i) q^{88} +(688.634 + 1192.75i) q^{89} +153.640 q^{90} +(732.818 - 346.538i) q^{91} +10.1279 q^{92} +(-26.8675 - 46.5359i) q^{93} +(108.752 - 188.365i) q^{94} +(248.774 - 430.890i) q^{95} +(231.161 + 400.383i) q^{96} -194.861 q^{97} +(1155.41 + 190.916i) q^{98} +339.661 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 6 q^{3} + 4 q^{4} + 10 q^{5} + 24 q^{6} + 50 q^{7} + 48 q^{8} - 18 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 6 * q^3 + 4 * q^4 + 10 * q^5 + 24 * q^6 + 50 * q^7 + 48 * q^8 - 18 * q^9	\( 4 q + 4 q^{2} + 6 q^{3} + 4 q^{4} + 10 q^{5} + 24 q^{6} + 50 q^{7} + 48 q^{8} - 18 q^{9} - 20 q^{10} + 32 q^{11} - 12 q^{12} + 28 q^{13} + 92 q^{14} + 60 q^{15} + 24 q^{16} + 20 q^{17} + 36 q^{18} - 18 q^{19} + 40 q^{20} + 120 q^{21} - 176 q^{22} + 68 q^{23} + 72 q^{24} - 50 q^{25} + 132 q^{26} - 108 q^{27} + 272 q^{28} - 664 q^{29} + 60 q^{30} - 66 q^{31} - 48 q^{32} - 96 q^{33} - 192 q^{34} + 50 q^{35} - 72 q^{36} - 18 q^{37} + 292 q^{38} + 42 q^{39} + 120 q^{40} + 304 q^{41} + 372 q^{42} - 1684 q^{43} - 672 q^{44} + 90 q^{45} - 32 q^{46} + 212 q^{47} + 144 q^{48} + 22 q^{49} - 200 q^{50} - 60 q^{51} - 388 q^{52} + 368 q^{53} - 108 q^{54} + 320 q^{55} + 648 q^{56} - 108 q^{57} - 688 q^{58} + 140 q^{59} + 60 q^{60} + 732 q^{61} + 24 q^{62} - 90 q^{63} - 544 q^{64} + 70 q^{65} - 264 q^{66} - 1066 q^{67} - 584 q^{68} + 408 q^{69} - 160 q^{70} - 2416 q^{71} - 216 q^{72} - 1654 q^{73} + 924 q^{74} + 150 q^{75} + 1976 q^{76} + 2464 q^{77} + 792 q^{78} - 1134 q^{79} - 120 q^{80} - 162 q^{81} + 792 q^{82} + 1936 q^{83} + 804 q^{84} + 200 q^{85} - 1836 q^{86} - 996 q^{87} + 80 q^{88} - 204 q^{89} + 360 q^{90} + 974 q^{91} + 1104 q^{92} + 198 q^{93} + 56 q^{94} + 90 q^{95} + 144 q^{96} + 3384 q^{97} + 1912 q^{98} - 576 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 6 * q^3 + 4 * q^4 + 10 * q^5 + 24 * q^6 + 50 * q^7 + 48 * q^8 - 18 * q^9 - 20 * q^10 + 32 * q^11 - 12 * q^12 + 28 * q^13 + 92 * q^14 + 60 * q^15 + 24 * q^16 + 20 * q^17 + 36 * q^18 - 18 * q^19 + 40 * q^20 + 120 * q^21 - 176 * q^22 + 68 * q^23 + 72 * q^24 - 50 * q^25 + 132 * q^26 - 108 * q^27 + 272 * q^28 - 664 * q^29 + 60 * q^30 - 66 * q^31 - 48 * q^32 - 96 * q^33 - 192 * q^34 + 50 * q^35 - 72 * q^36 - 18 * q^37 + 292 * q^38 + 42 * q^39 + 120 * q^40 + 304 * q^41 + 372 * q^42 - 1684 * q^43 - 672 * q^44 + 90 * q^45 - 32 * q^46 + 212 * q^47 + 144 * q^48 + 22 * q^49 - 200 * q^50 - 60 * q^51 - 388 * q^52 + 368 * q^53 - 108 * q^54 + 320 * q^55 + 648 * q^56 - 108 * q^57 - 688 * q^58 + 140 * q^59 + 60 * q^60 + 732 * q^61 + 24 * q^62 - 90 * q^63 - 544 * q^64 + 70 * q^65 - 264 * q^66 - 1066 * q^67 - 584 * q^68 + 408 * q^69 - 160 * q^70 - 2416 * q^71 - 216 * q^72 - 1654 * q^73 + 924 * q^74 + 150 * q^75 + 1976 * q^76 + 2464 * q^77 + 792 * q^78 - 1134 * q^79 - 120 * q^80 - 162 * q^81 + 792 * q^82 + 1936 * q^83 + 804 * q^84 + 200 * q^85 - 1836 * q^86 - 996 * q^87 + 80 * q^88 - 204 * q^89 + 360 * q^90 + 974 * q^91 + 1104 * q^92 + 198 * q^93 + 56 * q^94 + 90 * q^95 + 144 * q^96 + 3384 * q^97 + 1912 * q^98 - 576 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.70711	+	2.95680i	0.603553	+	1.04539i	0.992278	+	0.124031i	$0.0395823\pi$
$2$	1.70711	+	2.95680i	0.603553	+	1.04539i	−0.388725	+	0.921354i	$0.627084\pi$
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$4$	−1.82843	+	3.16693i	−0.228553	+	0.395866i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$6$	10.2426			0.696923
$7$	16.7426	−	7.91732i	0.904018	−	0.427495i
$7$	16.7426	−	7.91732i	0.904018	−	0.427495i
$8$	14.8284			0.655330
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$	−8.53553	+	14.7840i	−0.269917	+	0.467510i
$11$	−18.8701	+	32.6839i	−0.517231	+	0.895870i	0.482569	+	0.875858i	$0.339704\pi$
$11$	−18.8701	+	32.6839i	−0.517231	+	0.895870i	−0.999800	+	0.0200118i	$0.993630\pi$
$12$	5.48528	+	9.50079i	0.131955	+	0.228553i
$13$	43.7696			0.933807			0.466903	−	0.884308i	$-0.345370\pi$
$13$	43.7696			0.933807			0.466903	+	0.884308i	$0.345370\pi$
$14$	51.9914	+	35.9889i	0.992520	+	0.687030i
$15$	15.0000			0.258199
$16$	39.9411	+	69.1801i	0.624080	+	1.08094i
$17$	−19.0416	+	32.9811i	−0.271663	+	0.470534i	−0.969288	−	0.245929i	$-0.920907\pi$
$17$	−19.0416	+	32.9811i	−0.271663	+	0.470534i	0.697625	+	0.716463i	$0.254240\pi$
$18$	15.3640	−	26.6112i	0.201184	−	0.348462i
$19$	−49.7548	−	86.1779i	−0.600765	−	1.04056i	−0.992705	−	0.120565i	$-0.961529\pi$
$19$	−49.7548	−	86.1779i	−0.600765	−	1.04056i	0.391940	−	0.919991i	$-0.371804\pi$
$20$	−18.2843			−0.204424
$21$	4.54416	−	55.3746i	0.0472198	−	0.575416i
$22$	−128.853			−1.24871
$23$	−1.38478	−	2.39850i	−0.0125542	−	0.0217445i	0.859680	−	0.510833i	$-0.170663\pi$
$23$	−1.38478	−	2.39850i	−0.0125542	−	0.0217445i	−0.872234	+	0.489088i	$0.837330\pi$
$24$	22.2426	−	38.5254i	0.189178	−	0.327665i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	74.7193	+	129.418i	0.563602	+	0.976188i
$27$	−27.0000			−0.192450
$28$	−5.53911	+	67.4990i	−0.0373854	+	0.455575i
$29$	−174.485			−1.11728			−0.558640	−	0.829410i	$-0.688677\pi$
$29$	−174.485			−1.11728			−0.558640	+	0.829410i	$0.688677\pi$
$30$	25.6066	+	44.3519i	0.155837	+	0.269917i
$31$	8.95584	−	15.5120i	0.0518876	−	0.0898720i	−0.838915	−	0.544262i	$-0.816810\pi$
$31$	8.95584	−	15.5120i	0.0518876	−	0.0898720i	0.890803	+	0.454390i	$0.150143\pi$
$32$	−77.0538	+	133.461i	−0.425666	+	0.737276i
$33$	56.6102	+	98.0517i	0.298623	+	0.517231i
$34$	−130.024			−0.655853
$35$	76.1396	+	52.7045i	0.367713	+	0.254534i
$36$	32.9117			0.152369
$37$	−161.478	−	279.688i	−0.717480	−	1.24271i	−0.961995	−	0.273067i	$-0.911962\pi$
$37$	−161.478	−	279.688i	−0.717480	−	1.24271i	0.244515	−	0.969646i	$-0.421371\pi$
$38$	169.874	−	294.230i	0.725188	−	1.25606i
$39$	65.6543	−	113.717i	0.269567	−	0.466903i
$40$	37.0711	+	64.2090i	0.146536	+	0.253808i
$41$	248.534			0.946695			0.473348	−	0.880876i	$-0.343045\pi$
$41$	248.534			0.946695			0.473348	+	0.880876i	$0.343045\pi$
$42$	171.489	−	81.0943i	0.630031	−	0.297931i
$43$	−474.740			−1.68366			−0.841828	−	0.539746i	$-0.818520\pi$
$43$	−474.740			−1.68366			−0.841828	+	0.539746i	$0.818520\pi$
$44$	−69.0051	−	119.520i	−0.236430	−	0.409508i
$45$	22.5000	−	38.9711i	0.0745356	−	0.129099i
$46$	4.72792	−	8.18900i	0.0151542	−	0.0262479i
$47$	−31.8528	−	55.1707i	−0.0988555	−	0.171223i	0.812356	−	0.583162i	$-0.198185\pi$
$47$	−31.8528	−	55.1707i	−0.0988555	−	0.171223i	−0.911211	+	0.411939i	$0.864852\pi$
$48$	239.647			0.720626
$49$	217.632	−	265.114i	0.634496	−	0.772926i
$50$	−85.3553			−0.241421
$51$	57.1249	+	98.9432i	0.156845	+	0.271663i
$52$	−80.0294	+	138.615i	−0.213425	+	0.369662i
$53$	131.598	−	227.934i	0.341064	−	0.590740i	−0.643567	−	0.765390i	$-0.722546\pi$
$53$	131.598	−	227.934i	0.341064	−	0.590740i	0.984631	+	0.174650i	$0.0558795\pi$
$54$	−46.0919	−	79.8335i	−0.116154	−	0.201184i
$55$	−188.701			−0.462625
$56$	248.267	−	117.401i	0.592430	−	0.280150i
$57$	−298.529			−0.693704
$58$	−297.865	−	515.917i	−0.674338	−	1.16799i
$59$	166.522	−	288.424i	0.367446	−	0.636435i	−0.621720	−	0.783240i	$-0.713566\pi$
$59$	166.522	−	288.424i	0.367446	−	0.636435i	0.989165	+	0.146805i	$0.0468990\pi$
$60$	−27.4264	+	47.5039i	−0.0590122	+	0.102212i
$61$	140.574	+	243.481i	0.295059	+	0.511057i	0.974999	−	0.222211i	$-0.0713273\pi$
$61$	140.574	+	243.481i	0.295059	+	0.511057i	−0.679940	+	0.733268i	$0.737994\pi$
$62$	61.1543			0.125268
$63$	−137.051	−	94.8680i	−0.274077	−	0.189718i
$64$	112.902			0.220511
$65$	109.424	+	189.528i	0.208806	+	0.361662i
$66$	−193.279	+	334.769i	−0.360470	+	0.624353i
$67$	−443.277	+	767.778i	−0.808282	+	1.39998i	0.105772	+	0.994390i	$0.466269\pi$
$67$	−443.277	+	767.778i	−0.808282	+	1.39998i	−0.914053	+	0.405594i	$0.867065\pi$
$68$	−69.6325	−	120.607i	−0.124179	−	0.215084i
$69$	−8.30866			−0.0144963
$70$	−25.8579	+	315.101i	−0.0441515	+	0.538026i
$71$	−951.897			−1.59112			−0.795559	−	0.605877i	$-0.792823\pi$
$71$	−951.897			−1.59112			−0.795559	+	0.605877i	$0.792823\pi$
$72$	−66.7279	−	115.576i	−0.109222	−	0.189178i
$73$	−406.429	+	703.956i	−0.651629	+	1.12865i	0.331099	+	0.943596i	$0.392581\pi$
$73$	−406.429	+	703.956i	−0.651629	+	1.12865i	−0.982728	+	0.185058i	$0.940753\pi$
$74$	551.319	−	954.913i	0.866075	−	1.50009i
$75$	37.5000	+	64.9519i	0.0577350	+	0.100000i
$76$	363.892			0.549228
$77$	−57.1657	+	696.615i	−0.0846056	+	1.03100i
$78$	448.316			0.650792
$79$	−260.873	−	451.845i	−0.371525	−	0.643500i	0.618276	−	0.785961i	$-0.287832\pi$
$79$	−260.873	−	451.845i	−0.371525	−	0.643500i	−0.989800	+	0.142462i	$0.954498\pi$
$80$	−199.706	+	345.900i	−0.279097	+	0.483410i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	424.274	+	734.864i	0.571381	+	0.989661i
$83$	339.750			0.449306			0.224653	−	0.974439i	$-0.427875\pi$
$83$	339.750			0.449306			0.224653	+	0.974439i	$0.427875\pi$
$84$	167.059	+	115.640i	0.216995	+	0.150206i
$85$	−190.416			−0.242983
$86$	−810.432	−	1403.71i	−1.01618	−	1.76007i
$87$	−261.728	+	453.326i	−0.322531	+	0.558640i
$88$	−279.813	+	484.651i	−0.338957	+	0.587090i
$89$	688.634	+	1192.75i	0.820169	+	1.42057i	0.905556	+	0.424226i	$0.139454\pi$
$89$	688.634	+	1192.75i	0.820169	+	1.42057i	−0.0853874	+	0.996348i	$0.527213\pi$
$90$	153.640			0.179945
$91$	732.818	−	346.538i	0.844178	−	0.399198i
$92$	10.1279			0.0114772
$93$	−26.8675	−	46.5359i	−0.0299573	−	0.0518876i
$94$	108.752	−	188.365i	0.119329	−	0.206684i
$95$	248.774	−	430.890i	0.268670	−	0.465351i
$96$	231.161	+	400.383i	0.245759	+	0.425666i
$97$	−194.861			−0.203971			−0.101985	−	0.994786i	$-0.532519\pi$
$97$	−194.861			−0.203971			−0.101985	+	0.994786i	$0.532519\pi$
$98$	1155.41	+	190.916i	1.19096	+	0.196790i
$99$	339.661			0.344820
$100$	−45.7107	−	79.1732i	−0.0457107	−	0.0791732i
$101$	−267.591	+	463.481i	−0.263627	+	0.456615i	−0.967203	−	0.254005i	$-0.918252\pi$
$101$	−267.591	+	463.481i	−0.263627	+	0.456615i	0.703576	+	0.710620i	$0.251585\pi$
$102$	−195.037	+	337.813i	−0.189328	+	0.327926i
$103$	−619.497	−	1073.00i	−0.592630	−	1.02646i	−0.993877	−	0.110495i	$-0.964756\pi$
$103$	−619.497	−	1073.00i	−0.592630	−	1.02646i	0.401247	−	0.915970i	$-0.368577\pi$
$104$	649.034			0.611952
$105$	251.140	−	118.760i	0.233416	−	0.110379i
$106$	898.607			0.823400
$107$	687.257	+	1190.36i	0.620931	+	1.07548i	0.989313	+	0.145810i	$0.0465787\pi$
$107$	687.257	+	1190.36i	0.620931	+	1.07548i	−0.368382	+	0.929675i	$0.620088\pi$
$108$	49.3675	−	85.5071i	0.0439851	−	0.0761845i
$109$	448.221	−	776.341i	0.393869	−	0.682202i	−0.599087	−	0.800684i	$-0.704470\pi$
$109$	448.221	−	776.341i	0.393869	−	0.682202i	0.992956	+	0.118482i	$0.0378029\pi$
$110$	−322.132	−	557.949i	−0.279219	−	0.483621i
$111$	−968.866			−0.828475
$112$	1216.44	+	842.030i	1.02628	+	0.710396i
$113$	−252.794			−0.210450			−0.105225	−	0.994448i	$-0.533556\pi$
$113$	−252.794			−0.210450			−0.105225	+	0.994448i	$0.533556\pi$
$114$	−509.621	−	882.689i	−0.418687	−	0.725188i
$115$	6.92388	−	11.9925i	0.00561439	−	0.00972442i
$116$	319.034	−	552.582i	0.255358	−	0.442293i
$117$	−196.963	−	341.150i	−0.155634	−	0.269567i
$118$	1137.08			0.887093
$119$	−57.6854	+	702.949i	−0.0444371	+	0.541506i
$120$	222.426			0.169206
$121$	−46.6582	−	80.8143i	−0.0350550	−	0.0607170i
$122$	−479.948	+	831.295i	−0.356168	+	0.616901i
$123$	372.801	−	645.710i	0.273287	−	0.473348i
$124$	32.7502	+	56.7250i	0.0237182	+	0.0410811i
$125$	−125.000			−0.0894427
$126$	46.5442	−	567.183i	0.0329086	−	0.401021i
$127$	2289.44			1.59965			0.799824	−	0.600235i	$-0.204926\pi$
$127$	2289.44			1.59965			0.799824	+	0.600235i	$0.204926\pi$
$128$	809.166	+	1401.52i	0.558756	+	0.967794i
$129$	−712.110	+	1233.41i	−0.486029	+	0.841828i
$130$	−373.597	+	647.088i	−0.252051	+	0.436564i
$131$	−1458.83	−	2526.77i	−0.972967	−	1.68523i	−0.686486	−	0.727143i	$-0.740848\pi$
$131$	−1458.83	−	2526.77i	−0.972967	−	1.68523i	−0.286481	−	0.958086i	$-0.592486\pi$
$132$	−414.030			−0.273005
$133$	−1515.33	−	1048.92i	−0.987935	−	0.683857i
$134$	−3026.88			−1.95136
$135$	−67.5000	−	116.913i	−0.0430331	−	0.0745356i
$136$	−282.357	+	489.057i	−0.178029	+	0.308355i
$137$	−1320.80	+	2287.70i	−0.823678	+	1.42665i	0.0792468	+	0.996855i	$0.474748\pi$
$137$	−1320.80	+	2287.70i	−0.823678	+	1.42665i	−0.902925	+	0.429798i	$0.858585\pi$
$138$	−14.1838	−	24.5670i	−0.00874929	−	0.0151542i
$139$	2946.18			1.79778			0.898892	−	0.438171i	$-0.144373\pi$
$139$	2946.18			1.79778			0.898892	+	0.438171i	$0.144373\pi$
$140$	−306.127	+	144.762i	−0.184803	+	0.0873904i
$141$	−191.117			−0.114149
$142$	−1624.99	−	2814.56i	−0.960324	−	1.66333i
$143$	−825.934	+	1430.56i	−0.482993	+	0.836569i
$144$	359.470	−	622.621i	0.208027	−	0.360313i
$145$	−436.213	−	755.543i	−0.249831	−	0.432720i
$146$	−2775.27			−1.57317
$147$	−362.338	−	963.095i	−0.203300	−	0.540372i
$148$	1181.00			0.655930
$149$	303.437	+	525.569i	0.166836	+	0.288968i	0.937306	−	0.348508i	$-0.113312\pi$
$149$	303.437	+	525.569i	0.166836	+	0.288968i	−0.770470	+	0.637477i	$0.779978\pi$
$150$	−128.033	+	221.760i	−0.0696923	+	0.120711i
$151$	797.034	−	1380.50i	0.429548	−	0.743998i	−0.567286	−	0.823521i	$-0.692006\pi$
$151$	797.034	−	1380.50i	0.429548	−	0.743998i	0.996833	+	0.0795231i	$0.0253397\pi$
$152$	−737.786	−	1277.88i	−0.393700	−	0.681908i
$153$	342.749			0.181109
$154$	−2157.34	+	1020.17i	−1.12885	+	0.533815i
$155$	89.5584			0.0464097
$156$	240.088	+	415.845i	0.123221	+	0.213425i
$157$	224.377	−	388.632i	0.114059	−	0.197555i	−0.803344	−	0.595515i	$-0.796948\pi$
$157$	224.377	−	388.632i	0.114059	−	0.197555i	0.917403	+	0.397959i	$0.130281\pi$
$158$	890.675	−	1542.69i	0.448470	−	0.776773i
$159$	−394.794	−	683.803i	−0.196913	−	0.341064i
$160$	−770.538			−0.380727
$161$	−42.1745	−	29.1936i	−0.0206448	−	0.0142905i
$162$	−276.551			−0.134123
$163$	−872.079	−	1510.49i	−0.419058	−	0.725830i	0.576787	−	0.816895i	$-0.304306\pi$
$163$	−872.079	−	1510.49i	−0.419058	−	0.725830i	−0.995845	+	0.0910645i	$0.970973\pi$
$164$	−454.426	+	787.090i	−0.216370	+	0.374764i
$165$	−283.051	+	490.258i	−0.133548	+	0.231313i
$166$	579.990	+	1004.57i	0.271180	+	0.469698i
$167$	2514.33			1.16506			0.582528	−	0.812811i	$-0.302064\pi$
$167$	2514.33			1.16506			0.582528	+	0.812811i	$0.302064\pi$
$168$	67.3827	−	821.119i	0.0309446	−	0.377087i
$169$	−281.226			−0.128005
$170$	−325.061	−	563.022i	−0.146653	−	0.254011i
$171$	−447.794	+	775.601i	−0.200255	+	0.346852i
$172$	868.028	−	1503.47i	0.384805	−	0.666502i
$173$	−933.622	−	1617.08i	−0.410301	−	0.710661i	0.584622	−	0.811306i	$-0.301243\pi$
$173$	−933.622	−	1617.08i	−0.410301	−	0.710661i	−0.994922	+	0.100644i	$0.967910\pi$
$174$	−1787.19			−0.778658
$175$	−37.8680	+	461.455i	−0.0163574	+	0.199330i
$176$	−3014.77			−1.29117
$177$	−499.566	−	865.273i	−0.212145	−	0.367446i
$178$	−2351.14	+	4072.30i	−0.990031	+	1.71478i
$179$	1202.87	−	2083.43i	0.502271	−	0.869960i	−0.497725	−	0.867335i	$-0.665831\pi$
$179$	1202.87	−	2083.43i	0.502271	−	0.869960i	0.999997	−	0.00262473i	$-0.000835477\pi$
$180$	82.2792	+	142.512i	0.0340707	+	0.0590122i
$181$	4565.55			1.87489			0.937443	−	0.348138i	$-0.113186\pi$
$181$	4565.55			1.87489			0.937443	+	0.348138i	$0.113186\pi$
$182$	2275.64	+	1575.22i	0.926822	+	0.641554i
$183$	843.442			0.340705
$184$	−20.5341	−	35.5660i	−0.00822712	−	0.0142498i
$185$	807.389	−	1398.44i	0.320867	−	0.555758i
$186$	91.7315	−	158.884i	0.0361617	−	0.0626339i
$187$	−718.633	−	1244.71i	−0.281025	−	0.486750i
$188$	232.962			0.0903751
$189$	−452.051	+	213.768i	−0.173978	+	0.0822715i
$190$	1698.74			0.648628
$191$	1970.27	+	3412.60i	0.746406	+	1.29281i	0.949535	+	0.313661i	$0.101556\pi$
$191$	1970.27	+	3412.60i	0.746406	+	1.29281i	−0.203129	+	0.979152i	$0.565111\pi$
$192$	169.352	−	293.327i	0.0636560	−	0.110255i
$193$	568.066	−	983.918i	0.211867	−	0.366964i	−0.740432	−	0.672131i	$-0.765379\pi$
$193$	568.066	−	983.918i	0.211867	−	0.366964i	0.952299	+	0.305167i	$0.0987124\pi$
$194$	−332.649	−	576.165i	−0.123107	−	0.213228i
$195$	656.543			0.241108
$196$	441.672	+	1173.97i	0.160959	+	0.427830i
$197$	1302.42			0.471032			0.235516	−	0.971870i	$-0.424322\pi$
$197$	1302.42			0.471032			0.235516	+	0.971870i	$0.424322\pi$
$198$	579.838	+	1004.31i	0.208118	+	0.360470i
$199$	521.025	−	902.442i	0.185601	−	0.321470i	−0.758178	−	0.652047i	$-0.773910\pi$
$199$	521.025	−	902.442i	0.185601	−	0.321470i	0.943779	+	0.330578i	$0.107244\pi$
$200$	−185.355	+	321.045i	−0.0655330	+	0.113507i
$201$	1329.83	+	2303.33i	0.466662	+	0.808282i
$202$	−1827.22			−0.636451
$203$	−2921.34	+	1381.46i	−1.01004	+	0.477632i
$204$	−417.795			−0.143390
$205$	621.335	+	1076.18i	0.211687	+	0.366653i
$206$	2115.10	−	3663.45i	0.715367	−	1.23905i
$207$	−12.4630	+	21.5865i	−0.00418472	+	0.00724815i
$208$	1748.21	+	3027.98i	0.582770	+	1.00939i
$209$	3755.51			1.24294
$210$	779.871	+	539.833i	0.256268	+	0.177390i
$211$	2098.50			0.684677			0.342338	−	0.939577i	$-0.388781\pi$
$211$	2098.50			0.684677			0.342338	+	0.939577i	$0.388781\pi$
$212$	481.235	+	833.523i	0.155903	+	0.270031i
$213$	−1427.84	+	2473.10i	−0.459316	+	0.795559i
$214$	−2346.44	+	4064.16i	−0.749530	+	1.29822i
$215$	−1186.85	−	2055.69i	−0.376477	−	0.652077i
$216$	−400.368			−0.126118
$217$	27.1312	−	330.618i	0.00848748	−	0.103428i
$218$	3060.64			0.950885
$219$	1219.29	+	2111.87i	0.376218	+	0.651629i
$220$	345.025	−	597.601i	0.105735	−	0.183138i
$221$	−833.444	+	1443.57i	−0.253681	+	0.439388i
$222$	−1653.96	−	2864.74i	−0.500029	−	0.866075i
$223$	−122.225			−0.0367032			−0.0183516	−	0.999832i	$-0.505842\pi$
$223$	−122.225			−0.0367032			−0.0183516	+	0.999832i	$0.505842\pi$
$224$	−233.430	+	2844.55i	−0.0696280	+	0.848480i
$225$	225.000			0.0666667
$226$	−431.546	−	747.460i	−0.127018	−	0.220001i
$227$	2539.21	−	4398.05i	0.742438	−	1.28594i	−0.208944	−	0.977928i	$-0.567003\pi$
$227$	2539.21	−	4398.05i	0.742438	−	1.28594i	0.951382	−	0.308013i	$-0.0996641\pi$
$228$	545.839	−	945.420i	0.158548	−	0.274614i
$229$	1245.22	+	2156.78i	0.359328	+	0.622375i	0.987849	−	0.155418i	$-0.0496725\pi$
$229$	1245.22	+	2156.78i	0.359328	+	0.622375i	−0.628521	+	0.777793i	$0.716339\pi$
$230$	47.2792			0.0135543
$231$	1724.11	+	1193.44i	0.491074	+	0.339926i
$232$	−2587.34			−0.732187
$233$	−825.610	−	1430.00i	−0.232135	−	0.402070i	0.726301	−	0.687377i	$-0.241238\pi$
$233$	−825.610	−	1430.00i	−0.232135	−	0.402070i	−0.958436	+	0.285307i	$0.907904\pi$
$234$	672.474	−	1164.76i	0.187867	−	0.325396i
$235$	159.264	−	275.853i	0.0442095	−	0.0765732i
$236$	608.946	+	1054.73i	0.167962	+	0.290919i
$237$	−1565.24			−0.429000
$238$	−2176.95	+	1029.44i	−0.592903	+	0.280374i
$239$	−2773.60			−0.750666			−0.375333	−	0.926890i	$-0.622472\pi$
$239$	−2773.60			−0.750666			−0.375333	+	0.926890i	$0.622472\pi$
$240$	599.117	+	1037.70i	0.161137	+	0.279097i
$241$	−2441.07	+	4228.05i	−0.652460	+	1.13009i	0.330064	+	0.943959i	$0.392930\pi$
$241$	−2441.07	+	4228.05i	−0.652460	+	1.13009i	−0.982524	+	0.186135i	$0.940404\pi$
$242$	159.301	−	275.917i	0.0423151	−	0.0732919i
$243$	121.500	+	210.444i	0.0320750	+	0.0555556i
$244$	−1028.11			−0.269747
$245$	1692.06	+	279.590i	0.441231	+	0.0729075i
$246$	2545.65			0.659774
$247$	−2177.75	−	3771.97i	−0.560999	−	0.971678i
$248$	132.801	−	230.018i	0.0340035	−	0.0588959i
$249$	509.625	−	882.697i	0.129704	−	0.224653i
$250$	−213.388	−	369.599i	−0.0539835	−	0.0935021i
$251$	24.7358			0.00622035			0.00311018	−	0.999995i	$-0.499010\pi$
$251$	24.7358			0.00622035			0.00311018	+	0.999995i	$0.499010\pi$
$252$	551.029	−	260.572i	0.137744	−	0.0651370i
$253$	104.523			0.0259736
$254$	3908.32	+	6769.42i	0.965473	+	1.67225i
$255$	−285.624	+	494.716i	−0.0701431	+	0.121491i
$256$	−2311.06	+	4002.87i	−0.564223	+	0.977263i
$257$	−2362.06	−	4091.20i	−0.573311	−	0.993004i	−0.996223	−	0.0868333i	$-0.972325\pi$
$257$	−2362.06	−	4091.20i	−0.573311	−	0.993004i	0.422912	−	0.906171i	$-0.361008\pi$
$258$	−4862.59			−1.17338
$259$	−4917.94	−	3404.24i	−1.17987	−	0.816714i
$260$	−800.294			−0.190893
$261$	785.184	+	1359.98i	0.186213	+	0.322531i
$262$	4980.76	−	8626.93i	1.17448	−	2.03425i
$263$	328.136	−	568.349i	0.0769344	−	0.133254i	−0.824991	−	0.565145i	$-0.808820\pi$
$263$	328.136	−	568.349i	0.0769344	−	0.133254i	0.901926	+	0.431891i	$0.142153\pi$
$264$	839.440	+	1453.95i	0.195697	+	0.338957i
$265$	1315.98			0.305057
$266$	514.621	−	6271.13i	0.118622	−	1.44552i
$267$	4131.80			0.947049
$268$	−1621.00	−	2807.65i	−0.369471	−	0.639943i
$269$	−1540.70	+	2668.57i	−0.349213	+	0.604854i	−0.986110	−	0.166094i	$-0.946884\pi$
$269$	−1540.70	+	2668.57i	−0.349213	+	0.604854i	0.636897	+	0.770949i	$0.280218\pi$
$270$	230.459	−	399.167i	0.0519456	−	0.0899724i
$271$	2031.57	+	3518.79i	0.455385	+	0.788749i	0.998710	−	0.0507729i	$-0.0161685\pi$
$271$	2031.57	+	3518.79i	0.455385	+	0.788749i	−0.543326	+	0.839522i	$0.682835\pi$
$272$	−3042.18			−0.678158
$273$	198.896	−	2423.72i	0.0440942	−	0.537327i
$274$	−9019.02			−1.98854
$275$	−471.751	−	817.097i	−0.103446	−	0.179174i
$276$	15.1918	−	26.3129i	0.00331318	−	0.00573859i
$277$	−4176.56	+	7234.02i	−0.905939	+	1.56913i	−0.0862883	+	0.996270i	$0.527501\pi$
$277$	−4176.56	+	7234.02i	−0.905939	+	1.56913i	−0.819651	+	0.572863i	$0.805833\pi$
$278$	5029.45	+	8711.26i	1.08506	+	1.87938i
$279$	−161.205			−0.0345918
$280$	1129.03	+	781.524i	0.240973	+	0.166804i
$281$	−3215.56			−0.682649			−0.341325	−	0.939946i	$-0.610876\pi$
$281$	−3215.56			−0.682649			−0.341325	+	0.939946i	$0.610876\pi$
$282$	−326.257	−	565.094i	−0.0688947	−	0.119329i
$283$	2227.93	−	3858.89i	0.467974	−	0.810555i	−0.531356	−	0.847148i	$-0.678317\pi$
$283$	2227.93	−	3858.89i	0.467974	−	0.810555i	0.999330	+	0.0365937i	$0.0116507\pi$
$284$	1740.47	−	3014.59i	0.363655	−	0.629869i
$285$	−746.323	−	1292.67i	−0.155117	−	0.268670i
$286$	−5639.83			−1.16605
$287$	4161.12	−	1967.72i	0.855829	−	0.404708i
$288$	1386.97			0.283778
$289$	1731.33	+	2998.76i	0.352398	+	0.610372i
$290$	1489.33	−	2579.59i	0.301573	−	0.522340i
$291$	−292.292	+	506.264i	−0.0588813	+	0.101985i
$292$	−1486.25	−	2574.26i	−0.297864	−	0.515916i
$293$	−8088.97			−1.61284			−0.806421	−	0.591342i	$-0.798598\pi$
$293$	−8088.97			−1.61284			−0.806421	+	0.591342i	$0.798598\pi$
$294$	2229.13	−	2715.46i	0.442195	−	0.538670i
$295$	1665.22			0.328653
$296$	−2394.46	−	4147.33i	−0.470186	−	0.814387i
$297$	509.492	−	882.465i	0.0995411	−	0.172410i
$298$	−1036.00	+	1794.40i	−0.201389	+	0.348816i
$299$	−60.6110	−	104.981i	−0.0117232	−	0.0203051i
$300$	−274.264			−0.0527821
$301$	−7948.40	+	3758.67i	−1.52205	+	0.719755i
$302$	5442.49			1.03702
$303$	802.773	+	1390.44i	0.152205	+	0.263627i
$304$	3974.53	−	6884.08i	0.749851	−	1.29878i
$305$	−702.868	+	1217.40i	−0.131954	+	0.228552i
$306$	585.110	+	1013.44i	0.109309	+	0.189328i
$307$	−2025.28			−0.376511			−0.188255	−	0.982120i	$-0.560283\pi$
$307$	−2025.28			−0.376511			−0.188255	+	0.982120i	$0.560283\pi$
$308$	−2101.61	−	1454.75i	−0.388799	−	0.269130i
$309$	−3716.98			−0.684310
$310$	152.886	+	264.806i	0.0280107	+	0.0485160i
$311$	828.235	−	1434.55i	0.151013	−	0.261561i	−0.780587	−	0.625047i	$-0.785080\pi$
$311$	828.235	−	1434.55i	0.151013	−	0.261561i	0.931600	+	0.363485i	$0.118413\pi$
$312$	973.550	−	1686.24i	0.176655	−	0.305976i
$313$	883.292	+	1529.91i	0.159510	+	0.276279i	0.934692	−	0.355459i	$-0.115675\pi$
$313$	883.292	+	1529.91i	0.159510	+	0.276279i	−0.775182	+	0.631738i	$0.782342\pi$
$314$	1532.14			0.275362
$315$	68.1623	−	830.620i	0.0121921	−	0.148572i
$316$	1907.95			0.339653
$317$	3060.95	+	5301.73i	0.542335	+	0.939352i	0.998769	+	0.0495948i	$0.0157930\pi$
$317$	3060.95	+	5301.73i	0.542335	+	0.939352i	−0.456434	+	0.889757i	$0.650874\pi$
$318$	1347.91	−	2334.65i	0.237695	−	0.411700i
$319$	3292.55	−	5702.86i	0.577891	−	1.00094i
$320$	282.254	+	488.878i	0.0493077	+	0.0854035i
$321$	4123.54			0.716990
$322$	14.3229	−	174.538i	0.00247884	−	0.0302069i
$323$	3789.65			0.652823
$324$	−148.103	−	256.521i	−0.0253948	−	0.0439851i
$325$	−547.119	+	947.639i	−0.0933807	+	0.161740i
$326$	2977.46	−	5157.12i	0.505848	−	0.876155i
$327$	−1344.66	−	2329.02i	−0.227401	−	0.393869i
$328$	3685.37			0.620398
$329$	−970.104	−	671.514i	−0.162564	−	0.112528i
$330$	−1932.79			−0.322414
$331$	−3430.41	−	5941.64i	−0.569644	−	0.986653i	−0.996601	−	0.0823805i	$-0.973748\pi$
$331$	−3430.41	−	5941.64i	−0.569644	−	0.986653i	0.426957	−	0.904272i	$-0.359586\pi$
$332$	−621.209	+	1075.96i	−0.102691	+	0.177865i
$333$	−1453.30	+	2517.19i	−0.239160	+	0.414237i
$334$	4292.22	+	7434.35i	0.703173	+	1.21793i
$335$	−4432.77			−0.722949
$336$	4012.32	−	1897.36i	0.651458	−	0.308064i
$337$	4191.48			0.677520			0.338760	−	0.940873i	$-0.389993\pi$
$337$	4191.48			0.677520			0.338760	+	0.940873i	$0.389993\pi$
$338$	−480.083	−	831.529i	−0.0772577	−	0.133814i
$339$	−379.191	+	656.778i	−0.0607517	+	0.105225i
$340$	348.162	−	603.035i	0.0555346	−	0.0961887i
$341$	337.995	+	585.424i	0.0536758	+	0.0929691i
$342$	−3057.73			−0.483459
$343$	1544.74	−	6161.77i	0.243173	−	0.969983i
$344$	−7039.65			−1.10335
$345$	−20.7716	−	35.9775i	−0.00324147	−	0.00561439i
$346$	3187.59	−	5521.06i	0.495277	−	0.857844i
$347$	−4369.87	+	7568.84i	−0.676044	+	1.17094i	0.300119	+	0.953902i	$0.402974\pi$
$347$	−4369.87	+	7568.84i	−0.676044	+	1.17094i	−0.976163	+	0.217040i	$0.930360\pi$
$348$	−957.101	−	1657.75i	−0.147431	−	0.255358i
$349$	237.613			0.0364445			0.0182223	−	0.999834i	$-0.494199\pi$
$349$	237.613			0.0364445			0.0182223	+	0.999834i	$0.494199\pi$
$350$	−1429.07	+	675.786i	−0.218249	+	0.103206i
$351$	−1181.78			−0.179711
$352$	−2908.02	−	5036.84i	−0.440335	−	0.762683i
$353$	−2561.68	+	4436.96i	−0.386245	+	0.668995i	−0.991941	−	0.126700i	$-0.959561\pi$
$353$	−2561.68	+	4436.96i	−0.386245	+	0.668995i	0.605696	+	0.795696i	$0.292895\pi$
$354$	1705.62	−	2954.23i	0.256082	−	0.443546i
$355$	−2379.74	−	4121.83i	−0.355785	−	0.616237i
$356$	−5036.47			−0.749809
$357$	1739.79	+	1204.29i	0.257925	+	0.178538i
$358$	8213.70			1.21259
$359$	4802.62	+	8318.39i	0.706052	+	1.22292i	0.966311	+	0.257379i	$0.0828589\pi$
$359$	4802.62	+	8318.39i	0.706052	+	1.22292i	−0.260258	+	0.965539i	$0.583808\pi$
$360$	333.640	−	577.881i	0.0488454	−	0.0846028i
$361$	−1521.59	+	2635.47i	−0.221838	+	0.384235i
$362$	7793.88	+	13499.4i	1.13159	+	1.95998i
$363$	−279.949			−0.0404780
$364$	−242.444	+	2954.40i	−0.0349108	+	0.425419i
$365$	−4064.29			−0.582835
$366$	1439.84	+	2493.88i	0.205634	+	0.356168i
$367$	−2635.34	+	4564.54i	−0.374833	+	0.649230i	−0.990302	−	0.138931i	$-0.955633\pi$
$367$	−2635.34	+	4564.54i	−0.374833	+	0.649230i	0.615469	+	0.788161i	$0.288967\pi$
$368$	110.619	−	191.598i	0.0156696	−	0.0271406i
$369$	−1118.40	−	1937.13i	−0.157783	−	0.273287i
$370$	5513.19			0.774641
$371$	398.668	−	4858.13i	0.0557892	−	0.679842i
$372$	196.501			0.0273874
$373$	123.193	+	213.377i	0.0171011	+	0.0296200i	0.874449	−	0.485117i	$-0.161223\pi$
$373$	123.193	+	213.377i	0.0171011	+	0.0296200i	−0.857348	+	0.514737i	$0.827890\pi$
$374$	2453.57	−	4249.70i	0.339227	−	0.587559i
$375$	−187.500	+	324.760i	−0.0258199	+	0.0447214i
$376$	−472.327	−	818.095i	−0.0647830	−	0.112207i
$377$	−7637.14			−1.04332
$378$	−1403.77	−	971.699i	−0.191011	−	0.132219i
$379$	−10120.5			−1.37165			−0.685826	−	0.727766i	$-0.740559\pi$
$379$	−10120.5			−1.37165			−0.685826	+	0.727766i	$0.740559\pi$
$380$	909.731	+	1575.70i	0.122811	+	0.212715i
$381$	3434.16	−	5948.15i	0.461778	−	0.799824i
$382$	−6726.91	+	11651.4i	−0.900992	+	1.56056i
$383$	−1706.78	−	2956.23i	−0.227709	−	0.394403i	0.729420	−	0.684066i	$-0.239790\pi$
$383$	−1706.78	−	2956.23i	−0.227709	−	0.394403i	−0.957129	+	0.289663i	$0.906457\pi$
$384$	4854.99			0.645196
$385$	−3159.35	+	1494.00i	−0.418221	+	0.197770i
$386$	3878.99			0.511491
$387$	2136.33	+	3700.23i	0.280609	+	0.486029i
$388$	356.289	−	617.111i	0.0466182	−	0.0807451i
$389$	−2450.91	+	4245.10i	−0.319450	+	0.553303i	−0.980373	−	0.197150i	$-0.936831\pi$
$389$	−2450.91	+	4245.10i	−0.319450	+	0.553303i	0.660924	+	0.750453i	$0.270165\pi$
$390$	1120.79	+	1941.26i	0.145521	+	0.252051i
$391$	105.474			0.0136420
$392$	3227.14	−	3931.22i	0.415804	−	0.506522i
$393$	−8752.99			−1.12349
$394$	2223.36	+	3850.98i	0.284293	+	0.492410i
$395$	1304.36	−	2259.22i	0.166151	−	0.287782i
$396$	−621.045	+	1075.68i	−0.0788099	+	0.136503i
$397$	2205.15	+	3819.43i	0.278774	+	0.482851i	0.971080	−	0.238753i	$-0.0767385\pi$
$397$	2205.15	+	3819.43i	0.278774	+	0.482851i	−0.692306	+	0.721604i	$0.743405\pi$
$398$	3557.78			0.448079
$399$	−4998.16	+	2363.55i	−0.627121	+	0.296555i
$400$	−1997.06			−0.249632
$401$	−3113.69	−	5393.08i	−0.387757	−	0.671614i	0.604391	−	0.796688i	$-0.293417\pi$
$401$	−3113.69	−	5393.08i	−0.387757	−	0.671614i	−0.992147	+	0.125074i	$0.960083\pi$
$402$	−4540.32	+	7864.07i	−0.563310	+	0.975682i
$403$	391.993	−	678.952i	0.0484530	−	0.0839231i
$404$	−978.541	−	1694.88i	−0.120505	−	0.208722i
$405$	−405.000			−0.0496904
$406$	−9071.73	−	6279.53i	−1.10892	−	0.767605i
$407$	12188.4			1.48441
$408$	847.072	+	1467.17i	0.102785	+	0.178029i
$409$	4360.55	−	7552.69i	0.527177	−	0.913097i	−0.472322	−	0.881426i	$-0.656584\pi$
$409$	4360.55	−	7552.69i	0.527177	−	0.913097i	0.999498	−	0.0316707i	$-0.0100828\pi$
$410$	−2121.37	+	3674.32i	−0.255529	+	0.442590i
$411$	3962.41	+	6863.10i	0.475551	+	0.823678i
$412$	4530.82			0.541790
$413$	504.468	−	6147.39i	0.0601047	−	0.732430i
$414$	−85.1026			−0.0101028
$415$	849.376	+	1471.16i	0.100468	+	0.174016i
$416$	−3372.61	+	5841.53i	−0.397490	+	0.688473i
$417$	4419.27	−	7654.41i	0.518975	−	0.898892i
$418$	6411.05	+	11104.3i	0.750179	+	1.29935i
$419$	−4007.88			−0.467298			−0.233649	−	0.972321i	$-0.575067\pi$
$419$	−4007.88			−0.467298			−0.233649	+	0.972321i	$0.575067\pi$
$420$	−83.0866	+	1012.48i	−0.00965288	+	0.117629i
$421$	13518.9			1.56501			0.782504	−	0.622645i	$-0.213942\pi$
$421$	13518.9			1.56501			0.782504	+	0.622645i	$0.213942\pi$
$422$	3582.37	+	6204.84i	0.413239	+	0.715751i
$423$	−286.675	+	496.536i	−0.0329518	+	0.0570743i
$424$	1951.39	−	3379.91i	0.223509	−	0.387129i
$425$	−476.041	−	824.527i	−0.0543326	−	0.0941069i
$426$	−9749.93			−1.10889
$427$	4281.29	+	2963.54i	0.485213	+	0.335868i
$428$	−5026.40			−0.567664
$429$	2477.80	+	4291.68i	0.278856	+	0.482993i
$430$	4052.16	−	7018.55i	0.454448	−	0.787127i
$431$	−1225.85	+	2123.24i	−0.137001	+	0.237292i	−0.926360	−	0.376639i	$-0.877080\pi$
$431$	−1225.85	+	2123.24i	−0.137001	+	0.237292i	0.789359	+	0.613932i	$0.210413\pi$
$432$	−1078.41	−	1867.86i	−0.120104	−	0.208027i
$433$	9390.37			1.04220			0.521100	−	0.853496i	$-0.325522\pi$
$433$	9390.37			1.04220			0.521100	+	0.853496i	$0.325522\pi$
$434$	1023.88	−	484.178i	0.113244	−	0.0535514i
$435$	−2617.28			−0.288480
$436$	1639.08	+	2838.97i	0.180040	+	0.311839i
$437$	−137.799	+	238.674i	−0.0150842	+	0.0261266i
$438$	−4162.91	+	7210.36i	−0.454135	+	0.786586i
$439$	−2954.86	−	5117.96i	−0.321247	−	0.556417i	0.659498	−	0.751706i	$-0.270769\pi$
$439$	−2954.86	−	5117.96i	−0.321247	−	0.556417i	−0.980746	+	0.195289i	$0.937435\pi$
$440$	−2798.13			−0.303172
$441$	−3045.70	−	503.262i	−0.328874	−	0.0543421i
$442$	−5691.11			−0.612440
$443$	−866.692	−	1501.15i	−0.0929521	−	0.160998i	0.815800	−	0.578334i	$-0.196297\pi$
$443$	−866.692	−	1501.15i	−0.0929521	−	0.160998i	−0.908752	+	0.417336i	$0.862964\pi$
$444$	1771.50	−	3068.33i	0.189351	−	0.327965i
$445$	−3443.17	+	5963.74i	−0.366791	+	0.635300i
$446$	−208.652	−	361.396i	−0.0221524	−	0.0383690i
$447$	1820.62			0.192646
$448$	1890.27	−	893.878i	0.199346	−	0.0942674i
$449$	15810.3			1.66177			0.830883	−	0.556447i	$-0.187836\pi$
$449$	15810.3			1.66177			0.830883	+	0.556447i	$0.187836\pi$
$450$	384.099	+	665.279i	0.0402369	+	0.0696923i
$451$	−4689.85	+	8123.06i	−0.489660	+	0.848115i
$452$	462.215	−	800.580i	0.0480991	−	0.0833100i
$453$	−2391.10	−	4141.51i	−0.247999	−	0.429548i
$454$	17338.8			1.79240
$455$	3332.60	+	2306.85i	0.343373	+	0.237685i
$456$	−4426.72			−0.454605
$457$	3537.54	+	6127.20i	0.362099	+	0.627174i	0.988306	−	0.152483i	$-0.0487269\pi$
$457$	3537.54	+	6127.20i	0.362099	+	0.627174i	−0.626207	+	0.779657i	$0.715394\pi$
$458$	−4251.43	+	7363.70i	−0.433748	+	0.751273i
$459$	514.124	−	890.489i	0.0522816	−	0.0905544i
$460$	25.3196	+	43.8549i	0.00256638	+	0.00444510i
$461$	7778.66			0.785875			0.392938	−	0.919565i	$-0.371459\pi$
$461$	7778.66			0.785875			0.392938	+	0.919565i	$0.371459\pi$
$462$	−585.527	+	7135.18i	−0.0589636	+	0.718525i
$463$	11287.4			1.13298			0.566489	−	0.824069i	$-0.308301\pi$
$463$	11287.4			1.13298			0.566489	+	0.824069i	$0.308301\pi$
$464$	−6969.14	−	12070.9i	−0.697272	−	1.20771i
$465$	134.338	−	232.680i	0.0133973	−	0.0232049i
$466$	2818.81	−	4882.32i	0.280212	−	0.485341i
$467$	−9332.61	−	16164.5i	−0.924757	−	1.60173i	−0.791951	−	0.610584i	$-0.790935\pi$
$467$	−9332.61	−	16164.5i	−0.924757	−	1.60173i	−0.132806	−	0.991142i	$-0.542399\pi$
$468$	1440.53			0.142283
$469$	−1342.88	+	16364.2i	−0.132214	+	1.61115i
$470$	1087.52			0.106731
$471$	−673.130	−	1165.90i	−0.0658518	−	0.114059i
$472$	2469.26	−	4276.88i	0.240798	−	0.417075i
$473$	8958.37	−	15516.4i	0.870838	−	1.50834i
$474$	−2672.02	−	4628.08i	−0.258924	−	0.448470i
$475$	2487.74			0.240306
$476$	−2120.72	−	1467.98i	−0.204208	−	0.141354i
$477$	−2368.76			−0.227376
$478$	−4734.83	−	8200.96i	−0.453067	−	0.784735i
$479$	3140.65	−	5439.77i	0.299583	−	0.518893i	−0.676458	−	0.736481i	$-0.736486\pi$
$479$	3140.65	−	5439.77i	0.299583	−	0.518893i	0.976041	+	0.217589i	$0.0698192\pi$
$480$	−1155.81	+	2001.92i	−0.109907	+	0.190364i
$481$	−7067.81	−	12241.8i	−0.669988	−	1.16045i
$482$	−16668.6			−1.57518
$483$	−139.109	+	65.7823i	−0.0131049	+	0.00619710i
$484$	341.244			0.0320477
$485$	−487.153	−	843.774i	−0.0456092	−	0.0789975i
$486$	−414.827	+	718.501i	−0.0387180	+	0.0670615i
$487$	−3382.23	+	5858.19i	−0.314709	+	0.545092i	−0.979376	−	0.202048i	$-0.935240\pi$
$487$	−3382.23	+	5858.19i	−0.314709	+	0.545092i	0.664666	+	0.747140i	$0.268574\pi$
$488$	2084.49	+	3610.43i	0.193361	+	0.334911i
$489$	−5232.47			−0.483887
$490$	2061.83	+	5480.35i	0.190090	+	0.505260i
$491$	13331.6			1.22535			0.612676	−	0.790334i	$-0.290093\pi$
$491$	13331.6			1.22535			0.612676	+	0.790334i	$0.290093\pi$
$492$	1363.28	+	2361.27i	0.124921	+	0.216370i
$493$	3322.48	−	5754.71i	0.303524	−	0.525718i
$494$	7435.29	−	12878.3i	0.677185	−	1.17292i
$495$	849.153	+	1470.78i	0.0771042	+	0.133548i
$496$	1430.83			0.129528
$497$	−15937.3	+	7536.47i	−1.43840	+	0.680195i
$498$	3479.94			0.313132
$499$	−5870.49	−	10168.0i	−0.526651	−	0.912187i	−0.999518	−	0.0310529i	$-0.990114\pi$
$499$	−5870.49	−	10168.0i	−0.526651	−	0.912187i	0.472866	−	0.881134i	$-0.343219\pi$
$500$	228.553	−	395.866i	0.0204424	−	0.0354073i
$501$	3771.49	−	6532.41i	0.336323	−	0.582528i
$502$	42.2266	+	73.1387i	0.00375432	+	0.00650267i
$503$	−20470.6			−1.81459			−0.907293	−	0.420498i	$-0.861855\pi$
$503$	−20470.6			−1.81459			−0.907293	+	0.420498i	$0.861855\pi$
$504$	−2032.26	−	1406.74i	−0.179611	−	0.124328i
$505$	−2675.91			−0.235795
$506$	178.432	+	309.054i	0.0156765	+	0.0271524i
$507$	−421.839	+	730.647i	−0.0369518	+	0.0640023i
$508$	−4186.08	+	7250.50i	−0.365605	+	0.633246i
$509$	−8428.34	−	14598.3i	−0.733948	−	1.27124i	−0.955183	−	0.296015i	$-0.904342\pi$
$509$	−8428.34	−	14598.3i	−0.733948	−	1.27124i	0.221235	−	0.975221i	$-0.428991\pi$
$510$	−1950.37			−0.169340
$511$	−1231.25	+	15003.9i	−0.106590	+	1.29889i
$512$	−2834.24			−0.244642
$513$	1343.38	+	2326.80i	0.115617	+	0.200255i
$514$	8064.56	−	13968.2i	0.692048	−	1.19866i
$515$	3097.49	−	5365.00i	0.265032	−	0.459049i
$516$	−2604.08	−	4510.40i	−0.222167	−	0.384805i
$517$	2404.26			0.204524
$518$	1670.19	−	20352.7i	0.141668	−	1.72635i
$519$	−5601.73			−0.473774
$520$	1622.58	+	2810.40i	0.136837	+	0.237008i
$521$	−7933.98	+	13742.1i	−0.667167	+	1.15557i	0.311526	+	0.950238i	$0.399160\pi$
$521$	−7933.98	+	13742.1i	−0.667167	+	1.15557i	−0.978693	+	0.205329i	$0.934174\pi$
$522$	−2680.79	+	4643.26i	−0.224779	+	0.389329i
$523$	−5326.58	−	9225.91i	−0.445344	−	0.771359i	0.552732	−	0.833359i	$-0.313585\pi$
$523$	−5326.58	−	9225.91i	−0.445344	−	0.771359i	−0.998076	+	0.0620000i	$0.980252\pi$
$524$	10669.5			0.889500
$525$	1142.09	+	790.567i	0.0949430	+	0.0657203i
$526$	2240.65			0.185736
$527$	341.068	+	590.747i	0.0281919	+	0.0488298i
$528$	−4522.15	+	7832.59i	−0.372730	+	0.645587i
$529$	6079.66	−	10530.3i	0.499685	−	0.865479i
$530$	2246.52	+	3891.08i	0.184118	+	0.318902i
$531$	−2997.39			−0.244964
$532$	6092.52	−	2881.05i	0.496512	−	0.234792i
$533$	10878.2			0.884030
$534$	7053.43	+	12216.9i	0.571595	+	0.990031i
$535$	−3436.28	+	5951.82i	−0.277689	+	0.480971i
$536$	−6573.10	+	11384.9i	−0.529691	+	0.917452i
$537$	−3608.60	−	6250.29i	−0.289987	−	0.502271i
$538$	−10520.6			−0.843075
$539$	4558.22	+	12115.8i	0.364261	+	0.968207i
$540$	493.675			0.0393415
$541$	1020.16	+	1766.96i	0.0810720	+	0.140421i	0.903711	−	0.428144i	$-0.140832\pi$
$541$	1020.16	+	1766.96i	0.0810720	+	0.140421i	−0.822639	+	0.568565i	$0.807499\pi$
$542$	−6936.22	+	12013.9i	−0.549698	+	0.952104i
$543$	6848.32	−	11861.6i	0.541233	−	0.937443i
$544$	−2934.46	−	5082.64i	−0.231276	−	0.400581i
$545$	4482.21			0.352287
$546$	7505.99	−	3549.46i	0.588327	−	0.278210i
$547$	−19582.0			−1.53065			−0.765325	−	0.643644i	$-0.777422\pi$
$547$	−19582.0			−1.53065			−0.765325	+	0.643644i	$0.777422\pi$
$548$	−4829.99	−	8365.79i	−0.376509	−	0.652133i
$549$	1265.16	−	2191.33i	0.0983530	−	0.170352i
$550$	1610.66	−	2789.75i	0.124871	−	0.216282i
$551$	8681.49	+	15036.8i	0.671223	+	1.16259i
$552$	−123.204			−0.00949986
$553$	−7945.09	−	5499.66i	−0.610958	−	0.422910i
$554$	−28519.3			−2.18713
$555$	−2422.17	−	4195.31i	−0.185253	−	0.320867i
$556$	−5386.88	+	9330.35i	−0.410890	+	0.711682i
$557$	1606.58	−	2782.67i	0.122213	−	0.211680i	−0.798427	−	0.602092i	$-0.794334\pi$
$557$	1606.58	−	2782.67i	0.122213	−	0.211680i	0.920640	+	0.390412i	$0.127667\pi$
$558$	−275.194	−	476.651i	−0.0208780	−	0.0361617i
$559$	−20779.2			−1.57221
$560$	−604.996	+	7372.42i	−0.0456531	+	0.556324i
$561$	−4311.80			−0.324500
$562$	−5489.31	−	9507.76i	−0.412015	−	0.713631i
$563$	−10134.5	+	17553.5i	−0.758650	+	1.31402i	0.184889	+	0.982759i	$0.440807\pi$
$563$	−10134.5	+	17553.5i	−0.758650	+	1.31402i	−0.943539	+	0.331261i	$0.892526\pi$
$564$	349.443	−	605.254i	0.0260890	−	0.0451875i
$565$	−631.985	−	1094.63i	−0.0470581	−	0.0815069i
$566$	15213.3			1.12979
$567$	−122.692	+	1495.12i	−0.00908746	+	0.110739i
$568$	−14115.1			−1.04271
$569$	−1078.55	−	1868.10i	−0.0794642	−	0.137636i	0.823555	−	0.567237i	$-0.191988\pi$
$569$	−1078.55	−	1868.10i	−0.0794642	−	0.137636i	−0.903019	+	0.429601i	$0.858654\pi$
$570$	2548.10	−	4413.45i	0.187243	−	0.324314i
$571$	6634.49	−	11491.3i	0.486243	−	0.842197i	−0.513632	−	0.858011i	$-0.671700\pi$
$571$	6634.49	−	11491.3i	0.486243	−	0.842197i	0.999875	+	0.0158132i	$0.00503372\pi$
$572$	−3020.32	−	5231.35i	−0.220780	−	0.382401i
$573$	11821.6			0.861875
$574$	12921.6	+	8944.46i	0.939614	+	0.650408i
$575$	69.2388			0.00502167
$576$	−508.057	−	879.981i	−0.0367518	−	0.0636560i
$577$	−6850.77	+	11865.9i	−0.494283	+	0.856123i	−0.999978	−	0.00658894i	$-0.997903\pi$
$577$	−6850.77	+	11865.9i	−0.494283	+	0.856123i	0.505695	+	0.862712i	$0.331236\pi$
$578$	−5911.14	+	10238.4i	−0.425382	+	0.736784i
$579$	−1704.20	−	2951.76i	−0.122321	−	0.211867i
$580$	3190.34			0.228399
$581$	5688.32	−	2689.91i	0.406181	−	0.192076i
$582$	−1995.89			−0.142152
$583$	4966.52	+	8602.27i	0.352817	+	0.611097i
$584$	−6026.70	+	10438.6i	−0.427032	+	0.739641i
$585$	984.815	−	1705.75i	0.0696019	−	0.120554i
$586$	−13808.7	−	23917.4i	−0.973436	−	1.68604i
$587$	18697.5			1.31470			0.657351	−	0.753585i	$-0.271677\pi$
$587$	18697.5			1.31470			0.657351	+	0.753585i	$0.271677\pi$
$588$	3712.56	+	613.452i	0.260380	+	0.0430244i
$589$	−1782.39			−0.124689
$590$	2842.71	+	4923.71i	0.198360	+	0.343569i
$591$	1953.62	−	3383.78i	0.135975	−	0.235516i
$592$	12899.2	−	22342.1i	0.895530	−	1.55110i
$593$	7143.52	+	12372.9i	0.494686	+	0.856822i	0.999981	−	0.00612480i	$-0.00194960\pi$
$593$	7143.52	+	12372.9i	0.494686	+	0.856822i	−0.505295	+	0.862947i	$0.668616\pi$
$594$	3479.03			0.240313
$595$	−3188.07	+	1507.59i	−0.219661	+	0.103874i
$596$	−2219.25			−0.152524
$597$	−1563.08	−	2707.33i	−0.107157	−	0.185601i
$598$	206.939	−	358.429i	0.0141511	−	0.0245104i
$599$	2210.28	−	3828.31i	0.150767	−	0.261136i	−0.780743	−	0.624853i	$-0.785159\pi$
$599$	2210.28	−	3828.31i	0.150767	−	0.261136i	0.931510	+	0.363717i	$0.118492\pi$
$600$	556.066	+	963.135i	0.0378355	+	0.0655330i
$601$	25208.4			1.71093			0.855467	−	0.517857i	$-0.173270\pi$
$601$	25208.4			1.71093			0.855467	+	0.517857i	$0.173270\pi$
$602$	−24682.4	−	17085.4i	−1.67106	−	1.15672i
$603$	7978.98			0.538854
$604$	2914.64	+	5048.30i	0.196349	+	0.340087i
$605$	233.291	−	404.071i	0.0156771	−	0.0271535i
$606$	−2740.84	+	4747.27i	−0.183728	+	0.318225i
$607$	11194.3	+	19389.0i	0.748536	+	1.29650i	0.948524	+	0.316704i	$0.102576\pi$
$607$	11194.3	+	19389.0i	0.748536	+	1.29650i	−0.199989	+	0.979798i	$0.564091\pi$
$608$	15335.2			1.02290
$609$	−792.888	+	9662.06i	−0.0527577	+	0.642901i
$610$	−4799.48			−0.318566
$611$	−1394.18	−	2414.80i	−0.0923120	−	0.159889i
$612$	−626.692	+	1085.46i	−0.0413930	+	0.0716948i
$613$	−2322.41	+	4022.53i	−0.153020	+	0.265038i	−0.932336	−	0.361592i	$-0.882233\pi$
$613$	−2322.41	+	4022.53i	−0.153020	+	0.265038i	0.779316	+	0.626631i	$0.215567\pi$
$614$	−3457.37	−	5988.34i	−0.227244	−	0.393599i
$615$	3728.01			0.244436
$616$	−847.677	+	10329.7i	−0.0554446	+	0.675642i
$617$	17799.0			1.16137			0.580683	−	0.814130i	$-0.302786\pi$
$617$	17799.0			1.16137			0.580683	+	0.814130i	$0.302786\pi$
$618$	−6345.29	−	10990.4i	−0.413018	−	0.715367i
$619$	91.0870	−	157.767i	0.00591453	−	0.0102443i	−0.863053	−	0.505113i	$-0.831451\pi$
$619$	91.0870	−	157.767i	0.00591453	−	0.0102443i	0.868968	+	0.494869i	$0.164784\pi$
$620$	−163.751	+	283.625i	−0.0106071	+	0.0183720i
$621$	37.3890	+	64.7596i	0.00241605	+	0.00418472i
$622$	5655.54			0.364577
$623$	20972.9	+	14517.6i	1.34874	+	0.933606i
$624$	10489.2			0.672925
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	−3015.75	+	5223.43i	−0.192546	+	0.333499i
$627$	5633.26	−	9757.09i	0.358805	−	0.621468i
$628$	820.513	+	1421.17i	0.0521370	+	0.0903039i
$629$	12299.2			0.779652
$630$	2572.33	−	1216.41i	0.162673	−	0.0769256i
$631$	24442.1			1.54203			0.771017	−	0.636814i	$-0.219748\pi$
$631$	24442.1			1.54203			0.771017	+	0.636814i	$0.219748\pi$
$632$	−3868.33	−	6700.14i	−0.243471	−	0.421705i
$633$	3147.75	−	5452.07i	0.197649	−	0.342338i
$634$	−10450.7	+	18101.2i	−0.654656	+	1.13390i
$635$	5723.61	+	9913.58i	0.357692	+	0.619541i
$636$	2887.41			0.180021
$637$	9525.66	−	11603.9i	0.592496	−	0.721764i
$638$	22482.9			1.39515
$639$	4283.53	+	7419.30i	0.265186	+	0.459316i
$640$	−4045.83	+	7007.58i	−0.249883	+	0.432811i
$641$	−8190.86	+	14187.0i	−0.504711	+	0.874184i	0.495275	+	0.868737i	$0.335067\pi$
$641$	−8190.86	+	14187.0i	−0.504711	+	0.874184i	−0.999985	+	0.00544791i	$0.998266\pi$
$642$	7039.33	+	12192.5i	0.432741	+	0.749530i
$643$	−22374.1			−1.37223			−0.686117	−	0.727491i	$-0.740686\pi$
$643$	−22374.1			−1.37223			−0.686117	+	0.727491i	$0.740686\pi$
$644$	169.567	−	80.1854i	0.0103756	−	0.00490644i
$645$	−7121.10			−0.434718
$646$	6469.34	+	11205.2i	0.394014	+	0.682452i
$647$	−543.166	+	940.791i	−0.0330047	+	0.0571659i	−0.882056	−	0.471145i	$-0.843841\pi$
$647$	−543.166	+	940.791i	−0.0330047	+	0.0571659i	0.849051	+	0.528311i	$0.177174\pi$
$648$	−600.551	+	1040.19i	−0.0364072	+	0.0630592i
$649$	6284.55	+	10885.2i	0.380108	+	0.658367i
$650$	−3735.97			−0.225441
$651$	−818.273	−	566.415i	−0.0492637	−	0.0341007i
$652$	6378.13			0.383109
$653$	−9381.49	−	16249.2i	−0.562215	−	0.973785i	−0.997303	−	0.0733966i	$-0.976616\pi$
$653$	−9381.49	−	16249.2i	−0.562215	−	0.973785i	0.435088	−	0.900388i	$-0.356717\pi$
$654$	4590.96	−	7951.78i	0.274497	−	0.475442i
$655$	7294.16	−	12633.9i	0.435124	−	0.753657i
$656$	9926.73	+	17193.6i	0.590814	+	1.02332i
$657$	7315.72			0.434419
$658$	329.458	−	4014.75i	0.0195192	−	0.237859i
$659$	−13722.2			−0.811138			−0.405569	−	0.914064i	$-0.632927\pi$
$659$	−13722.2			−0.811138			−0.405569	+	0.914064i	$0.632927\pi$
$660$	−1035.08	−	1792.80i	−0.0610459	−	0.105735i
$661$	−5289.08	+	9160.95i	−0.311227	+	0.539062i	−0.978628	−	0.205637i	$-0.934073\pi$
$661$	−5289.08	+	9160.95i	−0.311227	+	0.539062i	0.667401	+	0.744699i	$0.267407\pi$
$662$	11712.1	−	20286.0i	0.687621	−	1.19099i
$663$	2500.33	+	4330.70i	0.146463	+	0.253681i
$664$	5037.96			0.294444
$665$	753.646	−	9183.85i	0.0439476	−	0.535541i
$666$	−9923.75			−0.577384
$667$	241.623	+	418.503i	0.0140265	+	0.0242946i
$668$	−4597.26	+	7962.69i	−0.266277	+	0.461206i
$669$	−183.338	+	317.551i	−0.0105953	+	0.0183516i
$670$	−7567.21	−	13106.8i	−0.436338	−	0.755760i
$671$	−10610.5			−0.610454
$672$	7040.22	+	4873.30i	0.404140	+	0.279749i
$673$	10959.9			0.627748			0.313874	−	0.949465i	$-0.398373\pi$
$673$	10959.9			0.627748			0.313874	+	0.949465i	$0.398373\pi$
$674$	7155.30	+	12393.3i	0.408920	+	0.708270i
$675$	337.500	−	584.567i	0.0192450	−	0.0333333i
$676$	514.202	−	890.624i	0.0292559	−	0.0506727i
$677$	−11387.5	−	19723.7i	−0.646466	−	1.11971i	−0.983961	−	0.178384i	$-0.942913\pi$
$677$	−11387.5	−	19723.7i	−0.646466	−	1.11971i	0.337495	−	0.941327i	$-0.390420\pi$
$678$	−2589.28			−0.146668
$679$	−3262.49	+	1542.78i	−0.184393	+	0.0871965i
$680$	−2823.57			−0.159234
$681$	−7617.64	−	13194.1i	−0.428647	−	0.742438i
$682$	−1153.99	+	1998.76i	−0.0647924	+	0.112224i
$683$	−10081.1	+	17461.0i	−0.564776	+	0.978222i	0.432294	+	0.901733i	$0.357704\pi$
$683$	−10081.1	+	17461.0i	−0.564776	+	0.978222i	−0.997070	+	0.0764888i	$0.975629\pi$
$684$	−1637.52	−	2836.26i	−0.0915380	−	0.158548i
$685$	−13208.0			−0.736720
$686$	20856.1	−	5951.30i	1.16077	−	0.331227i
$687$	7471.29			0.414917
$688$	−18961.7	−	32842.5i	−1.05074	−	1.81993i
$689$	5759.98	−	9976.59i	0.318488	−	0.551637i
$690$	70.9188	−	122.835i	0.00391280	−	0.00677717i
$691$	−8150.10	−	14116.4i	−0.448689	−	0.777153i	0.549612	−	0.835420i	$-0.314776\pi$
$691$	−8150.10	−	14116.4i	−0.448689	−	0.777153i	−0.998301	+	0.0582676i	$0.981442\pi$
$692$	6828.24			0.375102
$693$	5686.82	−	2689.21i	0.311724	−	0.147409i
$694$	−29839.4			−1.63211
$695$	7365.46	+	12757.3i	0.401997	+	0.696279i
$696$	−3881.01	+	6722.11i	−0.211364	+	0.366093i
$697$	−4732.49	+	8196.92i	−0.257182	+	0.445453i
$698$	405.631	+	702.574i	0.0219962	+	0.0380986i
$699$	−4953.66			−0.268047
$700$	−1392.16	−	963.663i	−0.0751694	−	0.0520329i
$701$	−5644.95			−0.304147			−0.152073	−	0.988369i	$-0.548595\pi$
$701$	−5644.95			−0.304147			−0.152073	+	0.988369i	$0.548595\pi$
$702$	−2017.42	−	3494.28i	−0.108465	−	0.187867i
$703$	−16068.6	+	27831.6i	−0.862075	+	1.49316i
$704$	−2130.46	+	3690.06i	−0.114055	+	0.197549i
$705$	−477.792	−	827.560i	−0.0255244	−	0.0442095i
$706$	−17492.2			−0.932477
$707$	−810.650	+	9878.50i	−0.0431225	+	0.525487i
$708$	3653.68			0.193946
$709$	3373.06	+	5842.31i	0.178671	+	0.309468i	0.941426	−	0.337221i	$-0.109487\pi$
$709$	3373.06	+	5842.31i	0.178671	+	0.309468i	−0.762754	+	0.646688i	$0.776153\pi$
$710$	8124.95	−	14072.8i	0.429470	−	0.743864i
$711$	−2347.85	+	4066.60i	−0.123842	+	0.214500i
$712$	10211.4	+	17686.6i	0.537481	+	0.930945i
$713$	−49.6074			−0.00260562
$714$	−590.851	+	7200.05i	−0.0309693	+	0.377388i
$715$	−8259.34			−0.432003
$716$	4398.71	+	7618.79i	0.229592	+	0.397664i
$717$	−4160.40	+	7206.02i	−0.216699	+	0.375333i
$718$	−16397.2	+	28400.7i	−0.852280	+	1.47619i
$719$	4387.54	+	7599.45i	0.227577	+	0.394175i	0.957089	−	0.289793i	$-0.0935864\pi$
$719$	4387.54	+	7599.45i	0.227577	+	0.394175i	−0.729513	+	0.683967i	$0.760253\pi$
$720$	3594.70			0.186065
$721$	−18867.3	−	13060.1i	−0.974556	−	0.674596i
$722$	−10390.0			−0.535564
$723$	7323.20	+	12684.1i	0.376698	+	0.652460i
$724$	−8347.77	+	14458.8i	−0.428512	+	0.742204i
$725$	2181.07	−	3777.72i	0.111728	−	0.193518i
$726$	−477.903	−	827.752i	−0.0244306	−	0.0423151i
$727$	11113.0			0.566931			0.283466	−	0.958982i	$-0.408516\pi$
$727$	11113.0			0.566931			0.283466	+	0.958982i	$0.408516\pi$
$728$	10866.5	−	5138.61i	0.553215	−	0.261606i
$729$	729.000			0.0370370
$730$	−6938.18	−	12017.3i	−0.351772	−	0.609287i
$731$	9039.83	−	15657.4i	0.457387	−	0.792218i
$732$	−1542.17	+	2671.12i	−0.0778693	+	0.134874i
$733$	14359.9	+	24872.2i	0.723597	+	1.25331i	0.959549	+	0.281542i	$0.0908460\pi$
$733$	14359.9	+	24872.2i	0.723597	+	1.25331i	−0.235951	+	0.971765i	$0.575821\pi$
$734$	−17995.2			−0.904927
$735$	3264.48	−	3976.71i	0.163826	−	0.199569i
$736$	426.809			0.0213755
$737$	−16729.3	−	28976.0i	−0.836136	−	1.44823i
$738$	3818.47	−	6613.78i	0.190460	−	0.329887i
$739$	−10312.0	+	17860.9i	−0.513304	+	0.889069i	0.486577	+	0.873638i	$0.338245\pi$
$739$	−10312.0	+	17860.9i	−0.513304	+	0.889069i	−0.999881	+	0.0154313i	$0.995088\pi$
$740$	2952.50	+	5113.88i	0.146670	+	0.254041i
$741$	−13066.5			−0.647786
$742$	15045.1	−	7114.56i	0.744369	−	0.352000i
$743$	−1217.72			−0.0601265			−0.0300633	−	0.999548i	$-0.509571\pi$
$743$	−1217.72			−0.0601265			−0.0300633	+	0.999548i	$0.509571\pi$
$744$	−398.403	−	690.055i	−0.0196320	−	0.0340035i
$745$	−1517.19	+	2627.84i	−0.0746113	+	0.129231i
$746$	−420.608	+	728.515i	−0.0206428	+	0.0357545i
$747$	−1528.88	−	2648.09i	−0.0748844	−	0.129704i
$748$	5255.87			0.256917
$749$	20931.0	+	14488.6i	1.02110	+	0.706812i
$750$	−1280.33			−0.0623347
$751$	−12483.9	−	21622.7i	−0.606582	−	1.05063i	−0.991799	−	0.127805i	$-0.959207\pi$
$751$	−12483.9	−	21622.7i	−0.606582	−	1.05063i	0.385217	−	0.922826i	$-0.374127\pi$
$752$	2544.47	−	4407.16i	0.123388	−	0.213714i
$753$	37.1037	−	64.2654i	0.00179566	−	0.00311018i
$754$	−13037.4	−	22581.5i	−0.629701	−	1.09067i
$755$	7970.34			0.384199
$756$	149.556	−	1822.47i	0.00719483	−	0.0876755i
$757$	−32766.2			−1.57319			−0.786596	−	0.617468i	$-0.788158\pi$
$757$	−32766.2			−1.57319			−0.786596	+	0.617468i	$0.788158\pi$
$758$	−17276.8	−	29924.3i	−0.827865	−	1.43390i
$759$	156.785	−	271.559i	0.00749793	−	0.0129868i
$760$	3688.93	−	6389.41i	0.176068	−	0.304958i
$761$	−9123.13	−	15801.7i	−0.434577	−	0.752710i	0.562684	−	0.826672i	$-0.309769\pi$
$761$	−9123.13	−	15801.7i	−0.434577	−	0.752710i	−0.997261	+	0.0739624i	$0.976436\pi$
$762$	23449.9			1.11483
$763$	1357.86	−	16546.7i	0.0644269	−	0.785100i
$764$	−14410.0			−0.682374
$765$	856.873	+	1484.15i	0.0404972	+	0.0701431i
$766$	5827.32	−	10093.2i	0.274869	−	0.476087i
$767$	7288.59	−	12624.2i	0.343123	−	0.594307i
$768$	6933.17	+	12008.6i	0.325754	+	0.564223i
$769$	15150.4			0.710451			0.355225	−	0.934781i	$-0.384404\pi$
$769$	15150.4			0.710451			0.355225	+	0.934781i	$0.384404\pi$
$770$	−9810.80	−	6791.12i	−0.459165	−	0.317838i
$771$	−14172.3			−0.662003
$772$	2077.33	+	3598.05i	0.0968457	+	0.167742i
$773$	6365.80	−	11025.9i	0.296199	−	0.513032i	−0.679064	−	0.734079i	$-0.737614\pi$
$773$	6365.80	−	11025.9i	0.296199	−	0.513032i	0.975263	+	0.221047i	$0.0709475\pi$
$774$	−7293.89	+	12633.4i	−0.338725	+	0.586689i
$775$	223.896	+	387.799i	0.0103775	+	0.0179744i
$776$	−2889.48			−0.133668
$777$	−16221.4	+	7670.83i	−0.748956	+	0.354169i
$778$	−16735.8			−0.771220
$779$	−12365.8	−	21418.1i	−0.568742	−	0.985089i
$780$	−1200.44	+	2079.23i	−0.0551060	+	0.0954464i
$781$	17962.3	−	31111.7i	0.822975	−	1.42543i
$782$	180.055	+	311.864i	0.00823369	+	0.0142612i
$783$	4711.10			0.215021
$784$	27033.1	+	4466.86i	1.23146	+	0.203483i
$785$	2243.77			0.102017
$786$	−14942.3	−	25880.8i	−0.678084	−	1.17448i
$787$	16020.6	−	27748.4i	0.725631	−	1.25683i	−0.233083	−	0.972457i	$-0.574881\pi$
$787$	16020.6	−	27748.4i	0.725631	−	1.25683i	0.958714	−	0.284373i	$-0.0917853\pi$
$788$	−2381.37	+	4124.66i	−0.107656	+	0.186466i
$789$	−984.409	−	1705.05i	−0.0444181	−	0.0769344i
$790$	8906.75			0.401124
$791$	−4232.44	+	2001.45i	−0.190251	+	0.0899664i
$792$	5036.64			0.225971
$793$	6152.84	+	10657.0i	0.275528	+	0.477229i
$794$	−7528.86	+	13040.4i	−0.336510	+	0.582853i
$795$	1973.97	−	3419.02i	0.0880623	−	0.152528i
$796$	1905.31	+	3300.10i	0.0848393	+	0.146946i
$797$	1301.58			0.0578472			0.0289236	−	0.999582i	$-0.490792\pi$
$797$	1301.58			0.0578472			0.0289236	+	0.999582i	$0.490792\pi$
$798$	−15520.9	−	10743.7i	−0.688515	−	0.476596i
$799$	2426.12			0.107422
$800$	−1926.35	−	3336.53i	−0.0851333	−	0.147455i
$801$	6197.70	−	10734.7i	0.273390	−	0.473525i
$802$	10630.8	−	18413.1i	0.468064	−	0.810710i
$803$	−15338.7	−	26567.4i	−0.674085	−	1.16755i
$804$	−9725.99			−0.426628
$805$	20.9755	−	255.605i	0.000918370	−	0.0111912i
$806$	2676.70			0.116976
$807$	4622.11	+	8005.72i	0.201618	+	0.349213i
$808$	−3967.95	+	6872.69i	−0.172762	+	0.299233i
$809$	−7892.44	+	13670.1i	−0.342996	+	0.594086i	−0.984988	−	0.172626i	$-0.944775\pi$
$809$	−7892.44	+	13670.1i	−0.342996	+	0.594086i	0.641992	+	0.766711i	$0.278108\pi$
$810$	−691.378	−	1197.50i	−0.0299908	−	0.0519456i
$811$	−27422.7			−1.18735			−0.593676	−	0.804704i	$-0.702324\pi$
$811$	−27422.7			−1.18735			−0.593676	+	0.804704i	$0.702324\pi$
$812$	966.492	−	11777.6i	0.0417700	−	0.509005i
$813$	12189.4			0.525833
$814$	20806.9	+	36038.5i	0.895921	+	1.55178i
$815$	4360.40	−	7552.43i	0.187409	−	0.324601i
$816$	−4563.26	+	7903.81i	−0.195767	+	0.339079i
$817$	23620.6	+	40912.1i	1.01148	+	1.75194i
$818$	29775.7			1.27272
$819$	−5998.67	−	4152.33i	−0.255935	−	0.177160i
$820$	−4544.26			−0.193528
$821$	−2775.25	−	4806.87i	−0.117974	−	0.204337i	0.800991	−	0.598677i	$-0.204307\pi$
$821$	−2775.25	−	4806.87i	−0.117974	−	0.204337i	−0.918965	+	0.394340i	$0.870973\pi$
$822$	−13528.5	+	23432.1i	−0.574041	+	0.994268i
$823$	7413.14	−	12839.9i	0.313980	−	0.543830i	−0.665240	−	0.746630i	$-0.731671\pi$
$823$	7413.14	−	12839.9i	0.313980	−	0.543830i	0.979220	+	0.202800i	$0.0650041\pi$
$824$	−9186.17	−	15910.9i	−0.388368	−	0.672673i
$825$	−2830.51			−0.119449
$826$	19037.8	−	9002.65i	0.801947	−	0.379228i
$827$	−25067.8			−1.05404			−0.527021	−	0.849852i	$-0.676691\pi$
$827$	−25067.8			−1.05404			−0.527021	+	0.849852i	$0.676691\pi$
$828$	−45.5753	−	78.9388i	−0.00191286	−	0.00331318i
$829$	9308.74	−	16123.2i	0.389995	−	0.675491i	−0.602453	−	0.798154i	$-0.705810\pi$
$829$	9308.74	−	16123.2i	0.389995	−	0.675491i	0.992448	+	0.122663i	$0.0391434\pi$
$830$	−2899.95	+	5022.86i	−0.121276	+	0.210055i
$831$	12529.7	+	21702.0i	0.523044	+	0.905939i
$832$	4941.65			0.205915
$833$	4599.67	+	12225.9i	0.191319	+	0.508528i
$834$	30176.7			1.25292
$835$	6285.81	+	10887.3i	0.260514	+	0.451224i
$836$	−6866.67	+	11893.4i	−0.284077	+	0.492037i
$837$	−241.808	+	418.823i	−0.00998578	+	0.0172959i
$838$	−6841.88	−	11850.5i	−0.282039	−	0.488506i
$839$	9100.36			0.374469			0.187234	−	0.982315i	$-0.440048\pi$
$839$	9100.36			0.374469			0.187234	+	0.982315i	$0.440048\pi$
$840$	3724.01	−	1761.02i	0.152965	−	0.0723345i
$841$	6056.11			0.248313
$842$	23078.1	+	39972.5i	0.944566	+	1.63604i
$843$	−4823.34	+	8354.28i	−0.197064	+	0.341325i
$844$	−3836.96	+	6645.80i	−0.156485	+	0.271040i
$845$	−703.066	−	1217.75i	−0.0286227	−	0.0495760i
$846$	−1957.54			−0.0795528
$847$	−1421.01	−	983.637i	−0.0576465	−	0.0399034i
$848$	21024.7			0.851404
$849$	−6683.79	−	11576.7i	−0.270185	−	0.467974i
$850$	1625.30	−	2815.11i	0.0655853	−	0.113597i
$851$	−447.221	+	774.609i	−0.0180147	+	0.0312024i
$852$	−5221.42	−	9043.77i	−0.209956	−	0.363655i
$853$	−43589.1			−1.74966			−0.874831	−	0.484429i	$-0.839027\pi$
$853$	−43589.1			−1.74966			−0.874831	+	0.484429i	$0.839027\pi$
$854$	−1453.97	+	17718.0i	−0.0582599	+	0.709949i
$855$	−4477.94			−0.179114
$856$	10190.9	+	17651.2i	0.406915	+	0.704797i
$857$	17632.4	−	30540.1i	0.702812	−	1.21731i	−0.264664	−	0.964341i	$-0.585261\pi$
$857$	17632.4	−	30540.1i	0.702812	−	1.21731i	0.967475	−	0.252965i	$-0.0814057\pi$
$858$	−8459.75	+	14652.7i	−0.336609	+	0.583025i
$859$	7677.48	+	13297.8i	0.304950	+	0.528189i	0.977250	−	0.212090i	$-0.0680269\pi$
$859$	7677.48	+	13297.8i	0.304950	+	0.528189i	−0.672300	+	0.740279i	$0.734694\pi$
$860$	8680.28			0.344180
$861$	1129.38	−	13762.5i	0.0447028	−	0.544744i
$862$	−8370.65			−0.330749
$863$	4275.81	+	7405.93i	0.168656	+	0.292121i	0.937948	−	0.346777i	$-0.112724\pi$
$863$	4275.81	+	7405.93i	0.168656	+	0.292121i	−0.769291	+	0.638898i	$0.779391\pi$
$864$	2080.45	−	3603.45i	0.0819195	−	0.141889i
$865$	4668.11	−	8085.41i	0.183492	−	0.317817i
$866$	16030.4	+	27765.4i	0.629023	+	1.08950i
$867$	10388.0			0.406914
$868$	997.435	+	690.433i	0.0390036	+	0.0269986i
$869$	19690.7			0.768656
$870$	−4467.98	−	7738.76i	−0.174113	−	0.301573i
$871$	−19402.0	+	33605.3i	−0.754779	+	1.30732i
$872$	6646.41	−	11511.9i	0.258114	−	0.447067i
$873$	876.875	+	1518.79i	0.0339951	+	0.0588813i
$874$	−940.948			−0.0364165
$875$	−2092.83	+	989.665i	−0.0808578	+	0.0382363i
$876$	−8917.51			−0.343944
$877$	−24431.5	−	42316.5i	−0.940697	−	1.62934i	−0.764145	−	0.645044i	$-0.776839\pi$
$877$	−24431.5	−	42316.5i	−0.940697	−	1.62934i	−0.176552	−	0.984291i	$-0.556494\pi$
$878$	10088.5	−	17473.8i	0.387780	−	0.671654i
$879$	−12133.5	+	21015.8i	−0.465587	+	0.806421i
$880$	−7536.91	−	13054.3i	−0.288715	−	0.500069i
$881$	−23123.4			−0.884278			−0.442139	−	0.896947i	$-0.645780\pi$
$881$	−23123.4			−0.884278			−0.442139	+	0.896947i	$0.645780\pi$
$882$	−3711.29	−	9864.64i	−0.141685	−	0.376598i
$883$	16904.0			0.644243			0.322121	−	0.946698i	$-0.395604\pi$
$883$	16904.0			0.644243			0.322121	+	0.946698i	$0.395604\pi$
$884$	−3047.78	−	5278.91i	−0.115959	−	0.200847i
$885$	2497.83	−	4326.36i	0.0948741	−	0.164327i
$886$	2959.07	−	5125.26i	0.112203	−	0.194342i
$887$	21809.1	+	37774.5i	0.825567	+	1.42992i	0.901485	+	0.432811i	$0.142478\pi$
$887$	21809.1	+	37774.5i	0.825567	+	1.42992i	−0.0759175	+	0.997114i	$0.524189\pi$
$888$	−14366.8			−0.542925
$889$	38331.3	−	18126.3i	1.44611	−	0.683842i
$890$	−23511.4			−0.885511
$891$	−1528.47	−	2647.40i	−0.0574701	−	0.0995411i
$892$	223.480	−	387.079i	0.00838865	−	0.0145296i
$893$	−3169.66	+	5490.02i	−0.118778	+	0.205729i
$894$	3108.00	+	5383.21i	0.116272	+	0.201389i
$895$	12028.7			0.449245
$896$	24643.8	+	17058.7i	0.918853	+	0.636038i
$897$	−363.666			−0.0135367
$898$	26989.8	+	46747.8i	1.00296	+	1.73719i
$899$	−1562.66	+	2706.61i	−0.0579730	+	0.100412i
$900$	−411.396	+	712.559i	−0.0152369	+	0.0263911i
$901$	5011.68	+	8680.48i	0.185309	+	0.320964i
$902$	−32024.3			−1.18214
$903$	−2157.29	+	26288.6i	−0.0795019	+	0.968802i
$904$	−3748.54			−0.137914
$905$	11413.9	+	19769.4i	0.419237	+	0.726141i
$906$	8163.73	−	14140.0i	0.299362	−	0.518510i
$907$	19793.2	−	34282.8i	0.724612	−	1.25506i	−0.234522	−	0.972111i	$-0.575353\pi$
$907$	19793.2	−	34282.8i	0.724612	−	1.25506i	0.959134	−	0.282953i	$-0.0913141\pi$
$908$	9285.53	+	16083.0i	0.339374	+	0.587812i
$909$	4816.64			0.175751
$910$	−1131.79	+	13791.8i	−0.0412290	+	0.502412i
$911$	−36388.3			−1.32338			−0.661690	−	0.749778i	$-0.730160\pi$
$911$	−36388.3			−1.32338			−0.661690	+	0.749778i	$0.730160\pi$
$912$	−11923.6	−	20652.3i	−0.432927	−	0.749851i
$913$	−6411.11	+	11104.4i	−0.232395	+	0.402520i
$914$	−12077.9	+	20919.6i	−0.437092	+	0.757066i
$915$	2108.60	+	3652.21i	0.0761839	+	0.131954i
$916$	−9107.14			−0.328503
$917$	−44430.0	−	30754.8i	−1.60001	−	1.10754i
$918$	3510.66			0.126219
$919$	−2473.44	−	4284.12i	−0.0887826	−	0.153776i	0.818214	−	0.574914i	$-0.194964\pi$
$919$	−2473.44	−	4284.12i	−0.0887826	−	0.153776i	−0.906997	+	0.421138i	$0.861631\pi$
$920$	102.670	−	177.830i	0.00367928	−	0.00637270i
$921$	−3037.92	+	5261.83i	−0.108689	+	0.188255i
$922$	13279.0	+	22999.9i	0.474318	+	0.821542i
$923$	−41664.1			−1.48580
$924$	−6931.96	+	3278.01i	−0.246802	+	0.116708i
$925$	8073.89			0.286992
$926$	19268.8	+	33374.5i	0.683813	+	1.18440i
$927$	−5575.47	+	9657.00i	−0.197543	+	0.342155i
$928$	13444.8	−	23287.0i	0.475588	−	0.823743i
$929$	−26728.8	−	46295.7i	−0.943966	−	1.63500i	−0.757809	−	0.652477i	$-0.773730\pi$
$929$	−26728.8	−	46295.7i	−0.943966	−	1.63500i	−0.186157	−	0.982520i	$-0.559603\pi$
$930$	917.315			0.0323440
$931$	−33675.2	−	5564.38i	−1.18546	−	0.195881i
$932$	6038.27			0.212221
$933$	−2484.70	−	4303.64i	−0.0871871	−	0.151013i
$934$	31863.5	−	55189.2i	1.11628	−	1.93345i
$935$	3593.17	−	6223.55i	0.125678	−	0.217681i
$936$	−2920.65	−	5058.72i	−0.101992	−	0.176655i
$937$	1214.58			0.0423464			0.0211732	−	0.999776i	$-0.493260\pi$
$937$	1214.58			0.0423464			0.0211732	+	0.999776i	$0.493260\pi$
$938$	−50678.0	+	23964.8i	−1.76407	+	0.834199i
$939$	5299.75			0.184186
$940$	582.405	+	1008.76i	0.0202085	+	0.0350021i
$941$	6117.84	−	10596.4i	0.211940	−	0.367091i	−0.740381	−	0.672187i	$-0.765355\pi$
$941$	6117.84	−	10596.4i	0.211940	−	0.367091i	0.952322	+	0.305096i	$0.0986884\pi$
$942$	2298.21	−	3980.62i	0.0794902	−	0.137681i
$943$	−344.164	−	596.110i	−0.0118850	−	0.0205854i
$944$	26604.3			0.917262
$945$	−2055.77	−	1423.02i	−0.0707663	−	0.0489850i
$946$	61171.6			2.10239
$947$	15020.0	+	26015.4i	0.515400	+	0.892699i	0.999840	+	0.0178744i	$0.00568990\pi$
$947$	15020.0	+	26015.4i	0.515400	+	0.892699i	−0.484440	+	0.874824i	$0.660977\pi$
$948$	2861.92	−	4956.99i	0.0980494	−	0.169827i
$949$	−17789.2	+	30811.8i	−0.608496	+	1.05395i
$950$	4246.84	+	7355.74i	0.145038	+	0.251212i
$951$	18365.7			0.626235
$952$	−855.384	+	10423.6i	−0.0291210	+	0.354865i
$953$	−58329.9			−1.98268			−0.991339	−	0.131327i	$-0.958076\pi$
$953$	−58329.9			−1.98268			−0.991339	+	0.131327i	$0.958076\pi$
$954$	−4043.73	−	7003.95i	−0.137233	−	0.237695i
$955$	−9851.34	+	17063.0i	−0.333803	+	0.578164i
$956$	5071.32	−	8783.79i	0.171567	−	0.297163i
$957$	−9877.64	−	17108.6i	−0.333646	−	0.577891i
$958$	21445.7			0.723257
$959$	−4001.29	+	48759.4i	−0.134733	+	1.64184i
$960$	1693.52			0.0569357
$961$	14735.1	+	25521.9i	0.494615	+	0.856699i
$962$	24131.0	−	41796.1i	0.808747	−	1.40079i
$963$	6185.31	−	10713.3i	0.206977	−	0.358495i
$964$	−8926.62	−	15461.4i	−0.298244	−	0.516574i
$965$	5680.66			0.189499
$966$	−431.979	−	299.019i	−0.0143879	−	0.00995940i
$967$	33211.1			1.10444			0.552222	−	0.833697i	$-0.313780\pi$
$967$	33211.1			1.10444			0.552222	+	0.833697i	$0.313780\pi$
$968$	−691.867	−	1198.35i	−0.0229726	−	0.0397897i
$969$	5684.48	−	9845.81i	0.188454	−	0.326412i
$970$	1663.24	−	2880.82i	0.0550552	−	0.0953584i
$971$	16715.4	+	28951.9i	0.552443	+	0.956860i	0.998098	+	0.0616546i	$0.0196377\pi$
$971$	16715.4	+	28951.9i	0.552443	+	0.956860i	−0.445654	+	0.895205i	$0.647029\pi$
$972$	−888.616			−0.0293234
$973$	49326.9	−	23325.9i	1.62523	−	0.768544i
$974$	−23095.3			−0.759775
$975$	1641.36	+	2842.92i	0.0539134	+	0.0933807i
$976$	−11229.3	+	19449.8i	−0.368281	+	0.637881i
$977$	−24700.4	+	42782.3i	−0.808839	+	1.40095i	0.104830	+	0.994490i	$0.466570\pi$
$977$	−24700.4	+	42782.3i	−0.808839	+	1.40095i	−0.913669	+	0.406460i	$0.866763\pi$
$978$	−8932.39	−	15471.4i	−0.292052	−	0.505848i
$979$	−51978.2			−1.69687
$980$	−3979.24	+	4847.41i	−0.129706	+	0.158005i
$981$	−8067.97			−0.262580
$982$	22758.5	+	39418.9i	0.739565	+	1.28096i
$983$	−5762.56	+	9981.05i	−0.186976	+	0.323852i	−0.944241	−	0.329256i	$-0.893202\pi$
$983$	−5762.56	+	9981.05i	−0.186976	+	0.323852i	0.757265	+	0.653108i	$0.226535\pi$
$984$	5528.05	−	9574.87i	0.179093	−	0.310199i
$985$	3256.04	+	5639.63i	0.105326	+	0.182430i
$986$	22687.3			0.732771
$987$	−3199.80	+	1513.13i	−0.103192	+	0.0487980i
$988$	15927.4			0.512873
$989$	657.409	+	1138.67i	0.0211369	+	0.0366102i
$990$	−2899.19	+	5021.54i	−0.0930730	+	0.161207i
$991$	−426.143	+	738.101i	−0.0136598	+	0.0236595i	−0.872775	−	0.488124i	$-0.837682\pi$
$991$	−426.143	+	738.101i	−0.0136598	+	0.0236595i	0.859115	+	0.511783i	$0.171015\pi$
$992$	1380.16	+	2390.51i	0.0441736	+	0.0765110i
$993$	−20582.4			−0.657768
$994$	−49490.4	−	34257.7i	−1.57922	−	1.09315i
$995$	5210.25			0.166006
$996$	1863.63	+	3227.89i	0.0592884	+	0.102691i
$997$	−22412.8	+	38820.1i	−0.711957	+	1.23315i	0.252164	+	0.967684i	$0.418858\pi$
$997$	−22412.8	+	38820.1i	−0.711957	+	1.23315i	−0.964121	+	0.265461i	$0.914476\pi$
$998$	20043.1	−	34715.7i	0.635725	−	1.10111i
$999$	4359.90	+	7551.56i	0.138079	+	0.239160i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.i.b.46.2	yes	4
3.2	odd	2		315.4.j.d.46.1		4
7.2	even	3	inner	105.4.i.b.16.2	✓	4
7.3	odd	6		735.4.a.n.1.1		2
7.4	even	3		735.4.a.l.1.1		2
21.2	odd	6		315.4.j.d.226.1		4
21.11	odd	6		2205.4.a.bd.1.2		2
21.17	even	6		2205.4.a.bc.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.i.b.16.2	✓	4	7.2	even	3	inner
105.4.i.b.46.2	yes	4	1.1	even	1	trivial
315.4.j.d.46.1		4	3.2	odd	2
315.4.j.d.226.1		4	21.2	odd	6
735.4.a.l.1.1		2	7.4	even	3
735.4.a.n.1.1		2	7.3	odd	6
2205.4.a.bc.1.2		2	21.17	even	6
2205.4.a.bd.1.2		2	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.70711 + 2.95680i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-1.82843 + 3.16693i) q^{4} +(2.50000 + 4.33013i) q^{5} +10.2426 q^{6} +(16.7426 - 7.91732i) q^{7} +14.8284 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.70711 + 2.95680i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-1.82843 + 3.16693i) q^{4} +(2.50000 + 4.33013i) q^{5} +10.2426 q^{6} +(16.7426 - 7.91732i) q^{7} +14.8284 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-8.53553 + 14.7840i) q^{10} +(-18.8701 + 32.6839i) q^{11} +(5.48528 + 9.50079i) q^{12} +43.7696 q^{13} +(51.9914 + 35.9889i) q^{14} +15.0000 q^{15} +(39.9411 + 69.1801i) q^{16} +(-19.0416 + 32.9811i) q^{17} +(15.3640 - 26.6112i) q^{18} +(-49.7548 - 86.1779i) q^{19} -18.2843 q^{20} +(4.54416 - 55.3746i) q^{21} -128.853 q^{22} +(-1.38478 - 2.39850i) q^{23} +(22.2426 - 38.5254i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(74.7193 + 129.418i) q^{26} -27.0000 q^{27} +(-5.53911 + 67.4990i) q^{28} -174.485 q^{29} +(25.6066 + 44.3519i) q^{30} +(8.95584 - 15.5120i) q^{31} +(-77.0538 + 133.461i) q^{32} +(56.6102 + 98.0517i) q^{33} -130.024 q^{34} +(76.1396 + 52.7045i) q^{35} +32.9117 q^{36} +(-161.478 - 279.688i) q^{37} +(169.874 - 294.230i) q^{38} +(65.6543 - 113.717i) q^{39} +(37.0711 + 64.2090i) q^{40} +248.534 q^{41} +(171.489 - 81.0943i) q^{42} -474.740 q^{43} +(-69.0051 - 119.520i) q^{44} +(22.5000 - 38.9711i) q^{45} +(4.72792 - 8.18900i) q^{46} +(-31.8528 - 55.1707i) q^{47} +239.647 q^{48} +(217.632 - 265.114i) q^{49} -85.3553 q^{50} +(57.1249 + 98.9432i) q^{51} +(-80.0294 + 138.615i) q^{52} +(131.598 - 227.934i) q^{53} +(-46.0919 - 79.8335i) q^{54} -188.701 q^{55} +(248.267 - 117.401i) q^{56} -298.529 q^{57} +(-297.865 - 515.917i) q^{58} +(166.522 - 288.424i) q^{59} +(-27.4264 + 47.5039i) q^{60} +(140.574 + 243.481i) q^{61} +61.1543 q^{62} +(-137.051 - 94.8680i) q^{63} +112.902 q^{64} +(109.424 + 189.528i) q^{65} +(-193.279 + 334.769i) q^{66} +(-443.277 + 767.778i) q^{67} +(-69.6325 - 120.607i) q^{68} -8.30866 q^{69} +(-25.8579 + 315.101i) q^{70} -951.897 q^{71} +(-66.7279 - 115.576i) q^{72} +(-406.429 + 703.956i) q^{73} +(551.319 - 954.913i) q^{74} +(37.5000 + 64.9519i) q^{75} +363.892 q^{76} +(-57.1657 + 696.615i) q^{77} +448.316 q^{78} +(-260.873 - 451.845i) q^{79} +(-199.706 + 345.900i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(424.274 + 734.864i) q^{82} +339.750 q^{83} +(167.059 + 115.640i) q^{84} -190.416 q^{85} +(-810.432 - 1403.71i) q^{86} +(-261.728 + 453.326i) q^{87} +(-279.813 + 484.651i) q^{88} +(688.634 + 1192.75i) q^{89} +153.640 q^{90} +(732.818 - 346.538i) q^{91} +10.1279 q^{92} +(-26.8675 - 46.5359i) q^{93} +(108.752 - 188.365i) q^{94} +(248.774 - 430.890i) q^{95} +(231.161 + 400.383i) q^{96} -194.861 q^{97} +(1155.41 + 190.916i) q^{98} +339.661 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 6 q^{3} + 4 q^{4} + 10 q^{5} + 24 q^{6} + 50 q^{7} + 48 q^{8} - 18 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 6 * q^3 + 4 * q^4 + 10 * q^5 + 24 * q^6 + 50 * q^7 + 48 * q^8 - 18 * q^9	\( 4 q + 4 q^{2} + 6 q^{3} + 4 q^{4} + 10 q^{5} + 24 q^{6} + 50 q^{7} + 48 q^{8} - 18 q^{9} - 20 q^{10} + 32 q^{11} - 12 q^{12} + 28 q^{13} + 92 q^{14} + 60 q^{15} + 24 q^{16} + 20 q^{17} + 36 q^{18} - 18 q^{19} + 40 q^{20} + 120 q^{21} - 176 q^{22} + 68 q^{23} + 72 q^{24} - 50 q^{25} + 132 q^{26} - 108 q^{27} + 272 q^{28} - 664 q^{29} + 60 q^{30} - 66 q^{31} - 48 q^{32} - 96 q^{33} - 192 q^{34} + 50 q^{35} - 72 q^{36} - 18 q^{37} + 292 q^{38} + 42 q^{39} + 120 q^{40} + 304 q^{41} + 372 q^{42} - 1684 q^{43} - 672 q^{44} + 90 q^{45} - 32 q^{46} + 212 q^{47} + 144 q^{48} + 22 q^{49} - 200 q^{50} - 60 q^{51} - 388 q^{52} + 368 q^{53} - 108 q^{54} + 320 q^{55} + 648 q^{56} - 108 q^{57} - 688 q^{58} + 140 q^{59} + 60 q^{60} + 732 q^{61} + 24 q^{62} - 90 q^{63} - 544 q^{64} + 70 q^{65} - 264 q^{66} - 1066 q^{67} - 584 q^{68} + 408 q^{69} - 160 q^{70} - 2416 q^{71} - 216 q^{72} - 1654 q^{73} + 924 q^{74} + 150 q^{75} + 1976 q^{76} + 2464 q^{77} + 792 q^{78} - 1134 q^{79} - 120 q^{80} - 162 q^{81} + 792 q^{82} + 1936 q^{83} + 804 q^{84} + 200 q^{85} - 1836 q^{86} - 996 q^{87} + 80 q^{88} - 204 q^{89} + 360 q^{90} + 974 q^{91} + 1104 q^{92} + 198 q^{93} + 56 q^{94} + 90 q^{95} + 144 q^{96} + 3384 q^{97} + 1912 q^{98} - 576 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 6 * q^3 + 4 * q^4 + 10 * q^5 + 24 * q^6 + 50 * q^7 + 48 * q^8 - 18 * q^9 - 20 * q^10 + 32 * q^11 - 12 * q^12 + 28 * q^13 + 92 * q^14 + 60 * q^15 + 24 * q^16 + 20 * q^17 + 36 * q^18 - 18 * q^19 + 40 * q^20 + 120 * q^21 - 176 * q^22 + 68 * q^23 + 72 * q^24 - 50 * q^25 + 132 * q^26 - 108 * q^27 + 272 * q^28 - 664 * q^29 + 60 * q^30 - 66 * q^31 - 48 * q^32 - 96 * q^33 - 192 * q^34 + 50 * q^35 - 72 * q^36 - 18 * q^37 + 292 * q^38 + 42 * q^39 + 120 * q^40 + 304 * q^41 + 372 * q^42 - 1684 * q^43 - 672 * q^44 + 90 * q^45 - 32 * q^46 + 212 * q^47 + 144 * q^48 + 22 * q^49 - 200 * q^50 - 60 * q^51 - 388 * q^52 + 368 * q^53 - 108 * q^54 + 320 * q^55 + 648 * q^56 - 108 * q^57 - 688 * q^58 + 140 * q^59 + 60 * q^60 + 732 * q^61 + 24 * q^62 - 90 * q^63 - 544 * q^64 + 70 * q^65 - 264 * q^66 - 1066 * q^67 - 584 * q^68 + 408 * q^69 - 160 * q^70 - 2416 * q^71 - 216 * q^72 - 1654 * q^73 + 924 * q^74 + 150 * q^75 + 1976 * q^76 + 2464 * q^77 + 792 * q^78 - 1134 * q^79 - 120 * q^80 - 162 * q^81 + 792 * q^82 + 1936 * q^83 + 804 * q^84 + 200 * q^85 - 1836 * q^86 - 996 * q^87 + 80 * q^88 - 204 * q^89 + 360 * q^90 + 974 * q^91 + 1104 * q^92 + 198 * q^93 + 56 * q^94 + 90 * q^95 + 144 * q^96 + 3384 * q^97 + 1912 * q^98 - 576 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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