LMFDB - Embedded newform 570.4.i.h.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,4,Mod(121,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, 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("570.121");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	570.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:	$33.6310887033$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{385})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 97x^{2} + 96x + 9216 $ x^4 - x^3 + 97x^2 + 96x + 9216
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.2
Root			$-4.65535 + 8.06331i$ of defining polynomial
Character	$\chi$	$=$	570.121
Dual form			570.4.i.h.391.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} +(3.00000 - 5.19615i) q^{6} +28.6214 q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} +(3.00000 - 5.19615i) q^{6} +28.6214 q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(5.00000 - 8.66025i) q^{10} +4.31071 q^{11} -12.0000 q^{12} +(23.0000 - 39.8372i) q^{13} +(-28.6214 - 49.5737i) q^{14} +(-7.50000 + 12.9904i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-40.9661 - 70.9553i) q^{17} +18.0000 q^{18} +(63.4321 - 53.2482i) q^{19} -20.0000 q^{20} +(42.9321 + 74.3606i) q^{21} +(-4.31071 - 7.46637i) q^{22} +(64.4857 - 111.692i) q^{23} +(12.0000 + 20.7846i) q^{24} +(-12.5000 + 21.6506i) q^{25} -92.0000 q^{26} -27.0000 q^{27} +(-57.2428 + 99.1475i) q^{28} +(-35.3303 + 61.1939i) q^{29} +30.0000 q^{30} +189.486 q^{31} +(-16.0000 + 27.7128i) q^{32} +(6.46606 + 11.1995i) q^{33} +(-81.9321 + 141.911i) q^{34} +(71.5535 + 123.934i) q^{35} +(-18.0000 - 31.1769i) q^{36} -271.379 q^{37} +(-155.661 - 56.6195i) q^{38} +138.000 q^{39} +(20.0000 + 34.6410i) q^{40} +(60.7285 + 105.185i) q^{41} +(85.8643 - 148.721i) q^{42} +(-13.7572 - 23.8281i) q^{43} +(-8.62142 + 14.9327i) q^{44} -45.0000 q^{45} -257.943 q^{46} +(-24.1018 + 41.7456i) q^{47} +(24.0000 - 41.5692i) q^{48} +476.186 q^{49} +50.0000 q^{50} +(122.898 - 212.866i) q^{51} +(92.0000 + 159.349i) q^{52} +(-77.3160 + 133.915i) q^{53} +(27.0000 + 46.7654i) q^{54} +(10.7768 + 18.6659i) q^{55} +228.971 q^{56} +(233.491 + 84.9293i) q^{57} +141.321 q^{58} +(39.6697 + 68.7099i) q^{59} +(-30.0000 - 51.9615i) q^{60} +(256.505 - 444.280i) q^{61} +(-189.486 - 328.199i) q^{62} +(-128.796 + 223.082i) q^{63} +64.0000 q^{64} +230.000 q^{65} +(12.9321 - 22.3991i) q^{66} +(451.243 - 781.576i) q^{67} +327.729 q^{68} +386.914 q^{69} +(143.107 - 247.869i) q^{70} +(-89.0091 - 154.168i) q^{71} +(-36.0000 + 62.3538i) q^{72} +(280.186 + 485.296i) q^{73} +(271.379 + 470.041i) q^{74} -75.0000 q^{75} +(57.5928 + 326.232i) q^{76} +123.379 q^{77} +(-138.000 - 239.023i) q^{78} +(472.069 + 817.648i) q^{79} +(40.0000 - 69.2820i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(121.457 - 210.370i) q^{82} +107.446 q^{83} -343.457 q^{84} +(204.830 - 354.777i) q^{85} +(-27.5143 + 47.6562i) q^{86} -211.982 q^{87} +34.4857 q^{88} +(-297.612 + 515.480i) q^{89} +(45.0000 + 77.9423i) q^{90} +(658.293 - 1140.20i) q^{91} +(257.943 + 446.770i) q^{92} +(284.229 + 492.298i) q^{93} +96.4072 q^{94} +(389.152 + 141.549i) q^{95} -96.0000 q^{96} +(-331.175 - 573.612i) q^{97} +(-476.186 - 824.777i) q^{98} +(-19.3982 + 33.5986i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} + 10 q^{5} + 12 q^{6} + 36 q^{7} + 32 q^{8} - 18 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 6 * q^3 - 8 * q^4 + 10 * q^5 + 12 * q^6 + 36 * q^7 + 32 * q^8 - 18 * q^9	\( 4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} + 10 q^{5} + 12 q^{6} + 36 q^{7} + 32 q^{8} - 18 q^{9} + 20 q^{10} - 22 q^{11} - 48 q^{12} + 92 q^{13} - 36 q^{14} - 30 q^{15} - 32 q^{16} - 105 q^{17} + 72 q^{18} + 136 q^{19} - 80 q^{20} + 54 q^{21} + 22 q^{22} - 56 q^{23} + 48 q^{24} - 50 q^{25} - 368 q^{26} - 108 q^{27} - 72 q^{28} + 153 q^{29} + 120 q^{30} + 444 q^{31} - 64 q^{32} - 33 q^{33} - 210 q^{34} + 90 q^{35} - 72 q^{36} - 1164 q^{37} - 34 q^{38} + 552 q^{39} + 80 q^{40} - 228 q^{41} + 108 q^{42} - 212 q^{43} + 44 q^{44} - 180 q^{45} + 224 q^{46} - 273 q^{47} + 96 q^{48} + 492 q^{49} + 200 q^{50} + 315 q^{51} + 368 q^{52} + 299 q^{53} + 108 q^{54} - 55 q^{55} + 288 q^{56} + 51 q^{57} - 612 q^{58} + 453 q^{59} - 120 q^{60} + 457 q^{61} - 444 q^{62} - 162 q^{63} + 256 q^{64} + 920 q^{65} - 66 q^{66} + 1648 q^{67} + 840 q^{68} - 336 q^{69} + 180 q^{70} - 1239 q^{71} - 144 q^{72} - 292 q^{73} + 1164 q^{74} - 300 q^{75} - 476 q^{76} + 572 q^{77} - 552 q^{78} - 15 q^{79} + 160 q^{80} - 162 q^{81} - 456 q^{82} + 626 q^{83} - 432 q^{84} + 525 q^{85} - 424 q^{86} + 918 q^{87} - 176 q^{88} - 229 q^{89} + 180 q^{90} + 828 q^{91} - 224 q^{92} + 666 q^{93} + 1092 q^{94} + 85 q^{95} - 384 q^{96} - 1050 q^{97} - 492 q^{98} + 99 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 6 * q^3 - 8 * q^4 + 10 * q^5 + 12 * q^6 + 36 * q^7 + 32 * q^8 - 18 * q^9 + 20 * q^10 - 22 * q^11 - 48 * q^12 + 92 * q^13 - 36 * q^14 - 30 * q^15 - 32 * q^16 - 105 * q^17 + 72 * q^18 + 136 * q^19 - 80 * q^20 + 54 * q^21 + 22 * q^22 - 56 * q^23 + 48 * q^24 - 50 * q^25 - 368 * q^26 - 108 * q^27 - 72 * q^28 + 153 * q^29 + 120 * q^30 + 444 * q^31 - 64 * q^32 - 33 * q^33 - 210 * q^34 + 90 * q^35 - 72 * q^36 - 1164 * q^37 - 34 * q^38 + 552 * q^39 + 80 * q^40 - 228 * q^41 + 108 * q^42 - 212 * q^43 + 44 * q^44 - 180 * q^45 + 224 * q^46 - 273 * q^47 + 96 * q^48 + 492 * q^49 + 200 * q^50 + 315 * q^51 + 368 * q^52 + 299 * q^53 + 108 * q^54 - 55 * q^55 + 288 * q^56 + 51 * q^57 - 612 * q^58 + 453 * q^59 - 120 * q^60 + 457 * q^61 - 444 * q^62 - 162 * q^63 + 256 * q^64 + 920 * q^65 - 66 * q^66 + 1648 * q^67 + 840 * q^68 - 336 * q^69 + 180 * q^70 - 1239 * q^71 - 144 * q^72 - 292 * q^73 + 1164 * q^74 - 300 * q^75 - 476 * q^76 + 572 * q^77 - 552 * q^78 - 15 * q^79 + 160 * q^80 - 162 * q^81 - 456 * q^82 + 626 * q^83 - 432 * q^84 + 525 * q^85 - 424 * q^86 + 918 * q^87 - 176 * q^88 - 229 * q^89 + 180 * q^90 + 828 * q^91 - 224 * q^92 + 666 * q^93 + 1092 * q^94 + 85 * q^95 - 384 * q^96 - 1050 * q^97 - 492 * q^98 + 99 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$6$	3.00000	−	5.19615i	0.204124	−	0.353553i
$7$	28.6214			1.54541			0.772706	−	0.634765i	$-0.218903\pi$
$7$	28.6214			1.54541			0.772706	+	0.634765i	$0.218903\pi$
$8$	8.00000			0.353553
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	5.00000	−	8.66025i	0.158114	−	0.273861i
$11$	4.31071			0.118157			0.0590785	−	0.998253i	$-0.481184\pi$
$11$	4.31071			0.118157			0.0590785	+	0.998253i	$0.481184\pi$
$12$	−12.0000			−0.288675
$13$	23.0000	−	39.8372i	0.490696	−	0.849911i	−0.509246	−	0.860621i	$-0.670076\pi$
$13$	23.0000	−	39.8372i	0.490696	−	0.849911i	0.999943	+	0.0107098i	$0.00340911\pi$
$14$	−28.6214	−	49.5737i	−0.546385	−	0.946367i
$15$	−7.50000	+	12.9904i	−0.129099	+	0.223607i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−40.9661	−	70.9553i	−0.584455	−	1.01231i	−0.994943	−	0.100439i	$-0.967975\pi$
$17$	−40.9661	−	70.9553i	−0.584455	−	1.01231i	0.410488	−	0.911866i	$-0.365358\pi$
$18$	18.0000			0.235702
$19$	63.4321	−	53.2482i	0.765912	−	0.642945i
$19$	63.4321	−	53.2482i	0.765912	−	0.642945i
$20$	−20.0000			−0.223607
$21$	42.9321	+	74.3606i	0.446122	+	0.772706i
$22$	−4.31071	−	7.46637i	−0.0417748	−	0.0723561i
$23$	64.4857	−	111.692i	0.584617	−	1.01259i	−0.410306	−	0.911948i	$-0.634578\pi$
$23$	64.4857	−	111.692i	0.584617	−	1.01259i	0.994923	−	0.100638i	$-0.0320885\pi$
$24$	12.0000	+	20.7846i	0.102062	+	0.176777i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	−92.0000			−0.693949
$27$	−27.0000			−0.192450
$28$	−57.2428	+	99.1475i	−0.386353	+	0.669183i
$29$	−35.3303	+	61.1939i	−0.226230	+	0.391842i	−0.956688	−	0.291116i	$-0.905973\pi$
$29$	−35.3303	+	61.1939i	−0.226230	+	0.391842i	0.730458	+	0.682958i	$0.239307\pi$
$30$	30.0000			0.182574
$31$	189.486			1.09783			0.548913	−	0.835879i	$-0.315042\pi$
$31$	189.486			1.09783			0.548913	+	0.835879i	$0.315042\pi$
$32$	−16.0000	+	27.7128i	−0.0883883	+	0.153093i
$33$	6.46606	+	11.1995i	0.0341090	+	0.0590785i
$34$	−81.9321	+	141.911i	−0.413272	+	0.715808i
$35$	71.5535	+	123.934i	0.345564	+	0.598535i
$36$	−18.0000	−	31.1769i	−0.0833333	−	0.144338i
$37$	−271.379			−1.20579			−0.602897	−	0.797819i	$-0.705987\pi$
$37$	−271.379			−1.20579			−0.602897	+	0.797819i	$0.705987\pi$
$38$	−155.661	−	56.6195i	−0.664513	−	0.241708i
$39$	138.000			0.566607
$40$	20.0000	+	34.6410i	0.0790569	+	0.136931i
$41$	60.7285	+	105.185i	0.231322	+	0.400661i	0.958197	−	0.286108i	$-0.0923616\pi$
$41$	60.7285	+	105.185i	0.231322	+	0.400661i	−0.726875	+	0.686769i	$0.759028\pi$
$42$	85.8643	−	148.721i	0.315456	−	0.546385i
$43$	−13.7572	−	23.8281i	−0.0487895	−	0.0845059i	0.840599	−	0.541657i	$-0.182203\pi$
$43$	−13.7572	−	23.8281i	−0.0487895	−	0.0845059i	−0.889389	+	0.457152i	$0.848870\pi$
$44$	−8.62142	+	14.9327i	−0.0295393	+	0.0511635i
$45$	−45.0000			−0.149071
$46$	−257.943			−0.826773
$47$	−24.1018	+	41.7456i	−0.0748002	+	0.129558i	−0.900999	−	0.433820i	$-0.857165\pi$
$47$	−24.1018	+	41.7456i	−0.0748002	+	0.129558i	0.826199	+	0.563378i	$0.190499\pi$
$48$	24.0000	−	41.5692i	0.0721688	−	0.125000i
$49$	476.186			1.38830
$50$	50.0000			0.141421
$51$	122.898	−	212.866i	0.337435	−	0.584455i
$52$	92.0000	+	159.349i	0.245348	+	0.424955i
$53$	−77.3160	+	133.915i	−0.200381	+	0.347069i	−0.948651	−	0.316324i	$-0.897551\pi$
$53$	−77.3160	+	133.915i	−0.200381	+	0.347069i	0.748271	+	0.663394i	$0.230885\pi$
$54$	27.0000	+	46.7654i	0.0680414	+	0.117851i
$55$	10.7768	+	18.6659i	0.0264207	+	0.0457620i
$56$	228.971			0.546385
$57$	233.491	+	84.9293i	0.542572	+	0.197354i
$58$	141.321			0.319938
$59$	39.6697	+	68.7099i	0.0875348	+	0.151615i	0.906469	−	0.422273i	$-0.138768\pi$
$59$	39.6697	+	68.7099i	0.0875348	+	0.151615i	−0.818934	+	0.573888i	$0.805434\pi$
$60$	−30.0000	−	51.9615i	−0.0645497	−	0.111803i
$61$	256.505	−	444.280i	0.538396	−	0.932529i	−0.460595	−	0.887610i	$-0.652364\pi$
$61$	256.505	−	444.280i	0.538396	−	0.932529i	0.998991	−	0.0449182i	$-0.0143027\pi$
$62$	−189.486	−	328.199i	−0.388140	−	0.672279i
$63$	−128.796	+	223.082i	−0.257569	+	0.446122i
$64$	64.0000			0.125000
$65$	230.000			0.438892
$66$	12.9321	−	22.3991i	0.0241187	−	0.0417748i
$67$	451.243	−	781.576i	0.822807	−	1.42514i	−0.0807764	−	0.996732i	$-0.525740\pi$
$67$	451.243	−	781.576i	0.822807	−	1.42514i	0.903584	−	0.428412i	$-0.140927\pi$
$68$	327.729			0.584455
$69$	386.914			0.675058
$70$	143.107	−	247.869i	0.244351	−	0.423228i
$71$	−89.0091	−	154.168i	−0.148781	−	0.257696i	0.781996	−	0.623283i	$-0.214202\pi$
$71$	−89.0091	−	154.168i	−0.148781	−	0.257696i	−0.930777	+	0.365587i	$0.880868\pi$
$72$	−36.0000	+	62.3538i	−0.0589256	+	0.102062i
$73$	280.186	+	485.296i	0.449222	+	0.778076i	0.998336	−	0.0576720i	$-0.0183678\pi$
$73$	280.186	+	485.296i	0.449222	+	0.778076i	−0.549113	+	0.835748i	$0.685034\pi$
$74$	271.379	+	470.041i	0.426312	+	0.738395i
$75$	−75.0000			−0.115470
$76$	57.5928	+	326.232i	0.0869255	+	0.492386i
$77$	123.379			0.182601
$78$	−138.000	−	239.023i	−0.200326	−	0.346975i
$79$	472.069	+	817.648i	0.672303	+	1.16446i	0.977249	+	0.212094i	$0.0680282\pi$
$79$	472.069	+	817.648i	0.672303	+	1.16446i	−0.304946	+	0.952370i	$0.598638\pi$
$80$	40.0000	−	69.2820i	0.0559017	−	0.0968246i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	121.457	−	210.370i	0.163569	−	0.283310i
$83$	107.446			0.142094			0.0710469	−	0.997473i	$-0.477366\pi$
$83$	107.446			0.142094			0.0710469	+	0.997473i	$0.477366\pi$
$84$	−343.457			−0.446122
$85$	204.830	−	354.777i	0.261376	−	0.452717i
$86$	−27.5143	+	47.6562i	−0.0344994	+	0.0597547i
$87$	−211.982			−0.261228
$88$	34.4857			0.0417748
$89$	−297.612	+	515.480i	−0.354459	+	0.613941i	−0.987025	−	0.160565i	$-0.948668\pi$
$89$	−297.612	+	515.480i	−0.354459	+	0.613941i	0.632566	+	0.774506i	$0.282002\pi$
$90$	45.0000	+	77.9423i	0.0527046	+	0.0912871i
$91$	658.293	−	1140.20i	0.758328	−	1.31346i
$92$	257.943	+	446.770i	0.292309	+	0.506293i
$93$	284.229	+	492.298i	0.316915	+	0.548913i
$94$	96.4072			0.105783
$95$	389.152	+	141.549i	0.420275	+	0.152869i
$96$	−96.0000			−0.102062
$97$	−331.175	−	573.612i	−0.346657	−	0.600427i	0.638996	−	0.769210i	$-0.279350\pi$
$97$	−331.175	−	573.612i	−0.346657	−	0.600427i	−0.985653	+	0.168782i	$0.946017\pi$
$98$	−476.186	−	824.777i	−0.490837	−	0.850154i
$99$	−19.3982	+	33.5986i	−0.0196928	+	0.0341090i
$100$	−50.0000	−	86.6025i	−0.0500000	−	0.0866025i
$101$	390.730	−	676.764i	0.384941	−	0.666738i	−0.606820	−	0.794840i	$-0.707555\pi$
$101$	390.730	−	676.764i	0.384941	−	0.666738i	0.991761	+	0.128101i	$0.0408883\pi$
$102$	−491.593			−0.477205
$103$	852.314			0.815349			0.407675	−	0.913127i	$-0.366340\pi$
$103$	852.314			0.815349			0.407675	+	0.913127i	$0.366340\pi$
$104$	184.000	−	318.697i	0.173487	−	0.300489i
$105$	−214.661	+	371.803i	−0.199512	+	0.345564i
$106$	309.264			0.283381
$107$	792.903			0.716382			0.358191	−	0.933648i	$-0.383394\pi$
$107$	792.903			0.716382			0.358191	+	0.933648i	$0.383394\pi$
$108$	54.0000	−	93.5307i	0.0481125	−	0.0833333i
$109$	290.918	+	503.884i	0.255641	+	0.442783i	0.965069	−	0.261994i	$-0.0843802\pi$
$109$	290.918	+	503.884i	0.255641	+	0.442783i	−0.709428	+	0.704778i	$0.751047\pi$
$110$	21.5535	−	37.3318i	0.0186823	−	0.0323586i
$111$	−407.068	−	705.062i	−0.348083	−	0.602897i
$112$	−228.971	−	396.590i	−0.193176	−	0.334591i
$113$	−682.747			−0.568384			−0.284192	−	0.958767i	$-0.591725\pi$
$113$	−682.747			−0.568384			−0.284192	+	0.958767i	$0.591725\pi$
$114$	−86.3891	−	489.347i	−0.0709744	−	0.402031i
$115$	644.857			0.522897
$116$	−141.321	−	244.776i	−0.113115	−	0.195921i
$117$	207.000	+	358.535i	0.163565	+	0.283304i
$118$	79.3394	−	137.420i	0.0618965	−	0.107208i
$119$	−1172.51	−	2030.84i	−0.903223	−	1.56443i
$120$	−60.0000	+	103.923i	−0.0456435	+	0.0790569i
$121$	−1312.42			−0.986039
$122$	−1026.02			−0.761406
$123$	−182.186	+	315.555i	−0.133554	+	0.231322i
$124$	−378.971	+	656.398i	−0.274457	+	0.475373i
$125$	−125.000			−0.0894427
$126$	515.186			0.364257
$127$	866.293	−	1500.46i	0.605284	−	1.04838i	−0.386723	−	0.922196i	$-0.626393\pi$
$127$	866.293	−	1500.46i	0.605284	−	1.04838i	0.992007	−	0.126186i	$-0.0402737\pi$
$128$	−64.0000	−	110.851i	−0.0441942	−	0.0765466i
$129$	41.2715	−	71.4843i	0.0281686	−	0.0487895i
$130$	−230.000	−	398.372i	−0.155172	−	0.268765i
$131$	906.350	+	1569.84i	0.604490	+	1.04701i	0.992132	+	0.125197i	$0.0399563\pi$
$131$	906.350	+	1569.84i	0.604490	+	1.04701i	−0.387642	+	0.921810i	$0.626710\pi$
$132$	−51.7285			−0.0341090
$133$	1815.52	−	1524.04i	1.18365	−	0.993615i
$134$	−1804.97			−1.16363
$135$	−67.5000	−	116.913i	−0.0430331	−	0.0745356i
$136$	−327.729	−	567.642i	−0.206636	−	0.357904i
$137$	−971.577	+	1682.82i	−0.605894	+	1.04944i	0.386016	+	0.922492i	$0.373851\pi$
$137$	−971.577	+	1682.82i	−0.605894	+	1.04944i	−0.991910	+	0.126946i	$0.959482\pi$
$138$	−386.914	−	670.155i	−0.238669	−	0.413387i
$139$	−1003.92	+	1738.84i	−0.612599	+	1.06105i	0.378201	+	0.925723i	$0.376543\pi$
$139$	−1003.92	+	1738.84i	−0.612599	+	1.06105i	−0.990801	+	0.135330i	$0.956791\pi$
$140$	−572.428			−0.345564
$141$	−144.611			−0.0863719
$142$	−178.018	+	308.336i	−0.105204	+	0.182218i
$143$	99.1463	−	171.726i	0.0579792	−	0.100423i
$144$	144.000			0.0833333
$145$	−353.303			−0.202346
$146$	560.371	−	970.591i	0.317648	−	0.550183i
$147$	714.278	+	1237.17i	0.400767	+	0.694148i
$148$	542.757	−	940.083i	0.301448	−	0.522124i
$149$	−1150.17	−	1992.15i	−0.632386	−	1.09532i	−0.987063	−	0.160336i	$-0.948742\pi$
$149$	−1150.17	−	1992.15i	−0.632386	−	1.09532i	0.354677	−	0.934989i	$-0.384591\pi$
$150$	75.0000	+	129.904i	0.0408248	+	0.0707107i
$151$	637.507			0.343573			0.171787	−	0.985134i	$-0.445046\pi$
$151$	637.507			0.343573			0.171787	+	0.985134i	$0.445046\pi$
$152$	507.457	−	425.985i	0.270791	−	0.227316i
$153$	737.389			0.389636
$154$	−123.379	−	213.698i	−0.0645593	−	0.111820i
$155$	473.714	+	820.497i	0.245482	+	0.425186i
$156$	−276.000	+	478.046i	−0.141652	+	0.245348i
$157$	−527.979	−	914.486i	−0.268390	−	0.464866i	0.700056	−	0.714088i	$-0.253158\pi$
$157$	−527.979	−	914.486i	−0.268390	−	0.464866i	−0.968446	+	0.249222i	$0.919825\pi$
$158$	944.139	−	1635.30i	0.475390	−	0.823400i
$159$	−463.896			−0.231379
$160$	−160.000			−0.0790569
$161$	1845.67	−	3196.80i	0.903474	−	1.56486i
$162$	−81.0000	+	140.296i	−0.0392837	+	0.0680414i
$163$	3251.73			1.56255			0.781275	−	0.624188i	$-0.214570\pi$
$163$	3251.73			1.56255			0.781275	+	0.624188i	$0.214570\pi$
$164$	−485.828			−0.231322
$165$	−32.3303	+	55.9977i	−0.0152540	+	0.0264207i
$166$	−107.446	−	186.103i	−0.0502377	−	0.0870143i
$167$	820.501	−	1421.15i	0.380193	−	0.658514i	−0.610896	−	0.791711i	$-0.709191\pi$
$167$	820.501	−	1421.15i	0.380193	−	0.658514i	0.991090	+	0.133196i	$0.0425241\pi$
$168$	343.457	+	594.885i	0.157728	+	0.273193i
$169$	40.5000	+	70.1481i	0.0184342	+	0.0319290i
$170$	−819.321			−0.369642
$171$	129.584	+	734.021i	0.0579504	+	0.328257i
$172$	110.057			0.0487895
$173$	1897.55	+	3286.65i	0.833919	+	1.44439i	0.894908	+	0.446251i	$0.147241\pi$
$173$	1897.55	+	3286.65i	0.833919	+	1.44439i	−0.0609887	+	0.998138i	$0.519425\pi$
$174$	211.982	+	367.163i	0.0923581	+	0.159969i
$175$	−357.768	+	619.672i	−0.154541	+	0.267673i
$176$	−34.4857	−	59.7309i	−0.0147696	−	0.0255818i
$177$	−119.009	+	206.130i	−0.0505382	+	0.0875348i
$178$	1190.45			0.501281
$179$	−1668.07			−0.696520			−0.348260	−	0.937398i	$-0.613227\pi$
$179$	−1668.07			−0.696520			−0.348260	+	0.937398i	$0.613227\pi$
$180$	90.0000	−	155.885i	0.0372678	−	0.0645497i
$181$	576.966	−	999.335i	0.236937	−	0.410386i	−0.722897	−	0.690956i	$-0.757190\pi$
$181$	576.966	−	999.335i	0.236937	−	0.410386i	0.959834	+	0.280569i	$0.0905233\pi$
$182$	−2633.17			−1.07244
$183$	1539.03			0.621686
$184$	515.885	−	893.540i	0.206693	−	0.358003i
$185$	−678.446	−	1175.10i	−0.269624	−	0.467002i
$186$	568.457	−	984.596i	0.224093	−	0.388140i
$187$	−176.593	−	305.868i	−0.0690574	−	0.119611i
$188$	−96.4072	−	166.982i	−0.0374001	−	0.0647789i
$189$	−772.778			−0.297415
$190$	−143.982	−	815.579i	−0.0549765	−	0.311412i
$191$	−2740.14			−1.03806			−0.519031	−	0.854755i	$-0.673707\pi$
$191$	−2740.14			−1.03806			−0.519031	+	0.854755i	$0.673707\pi$
$192$	96.0000	+	166.277i	0.0360844	+	0.0625000i
$193$	2578.97	+	4466.91i	0.961858	+	1.66599i	0.717829	+	0.696219i	$0.245136\pi$
$193$	2578.97	+	4466.91i	0.961858	+	1.66599i	0.244029	+	0.969768i	$0.421531\pi$
$194$	−662.350	+	1147.22i	−0.245123	+	0.424566i
$195$	345.000	+	597.558i	0.126697	+	0.219446i
$196$	−952.371	+	1649.55i	−0.347074	+	0.601150i
$197$	−3205.90			−1.15945			−0.579723	−	0.814813i	$-0.696839\pi$
$197$	−3205.90			−1.15945			−0.579723	+	0.814813i	$0.696839\pi$
$198$	77.5928			0.0278499
$199$	−409.988	+	710.120i	−0.146047	+	0.252960i	−0.929763	−	0.368159i	$-0.879988\pi$
$199$	−409.988	+	710.120i	−0.146047	+	0.252960i	0.783716	+	0.621119i	$0.213322\pi$
$200$	−100.000	+	173.205i	−0.0353553	+	0.0612372i
$201$	2707.46			0.950096
$202$	−1562.92			−0.544389
$203$	−1011.20	+	1751.46i	−0.349619	+	0.605557i
$204$	491.593	+	851.464i	0.168718	+	0.292227i
$205$	−303.643	+	525.924i	−0.103450	+	0.179181i
$206$	−852.314	−	1476.25i	−0.288269	−	0.499297i
$207$	580.371	+	1005.23i	0.194872	+	0.337529i
$208$	−736.000			−0.245348
$209$	273.437	−	229.537i	0.0904979	−	0.0759685i
$210$	858.643			0.282152
$211$	1263.76	+	2188.90i	0.412327	+	0.714172i	0.995144	−	0.0984318i	$-0.0313826\pi$
$211$	1263.76	+	2188.90i	0.412327	+	0.714172i	−0.582816	+	0.812604i	$0.698049\pi$
$212$	−309.264	−	535.661i	−0.100190	−	0.173535i
$213$	267.027	−	462.505i	0.0858986	−	0.148781i
$214$	−792.903	−	1373.35i	−0.253279	−	0.438693i
$215$	68.7858	−	119.141i	0.0218193	−	0.0377922i
$216$	−216.000			−0.0680414
$217$	5423.35			1.69659
$218$	581.836	−	1007.77i	0.180765	−	0.313095i
$219$	−840.557	+	1455.89i	−0.259359	+	0.449222i
$220$	−86.2142			−0.0264207
$221$	−3768.88			−1.14716
$222$	−814.136	+	1410.12i	−0.246132	+	0.426312i
$223$	975.431	+	1689.50i	0.292914	+	0.507341i	0.974497	−	0.224399i	$-0.0720419\pi$
$223$	975.431	+	1689.50i	0.292914	+	0.507341i	−0.681584	+	0.731740i	$0.738709\pi$
$224$	−457.943	+	793.180i	−0.136596	+	0.236592i
$225$	−112.500	−	194.856i	−0.0333333	−	0.0577350i
$226$	682.747	+	1182.55i	0.200954	+	0.348063i
$227$	−3629.36			−1.06119			−0.530593	−	0.847627i	$-0.678031\pi$
$227$	−3629.36			−1.06119			−0.530593	+	0.847627i	$0.678031\pi$
$228$	−761.186	+	638.978i	−0.221100	+	0.185602i
$229$	−145.350			−0.0419432			−0.0209716	−	0.999780i	$-0.506676\pi$
$229$	−145.350			−0.0419432			−0.0209716	+	0.999780i	$0.506676\pi$
$230$	−644.857	−	1116.92i	−0.184872	−	0.320208i
$231$	185.068	+	320.547i	0.0527124	+	0.0913006i
$232$	−282.643	+	489.551i	−0.0799844	+	0.138537i
$233$	−2093.44	−	3625.94i	−0.588609	−	1.01950i	−0.994415	−	0.105541i	$-0.966343\pi$
$233$	−2093.44	−	3625.94i	−0.588609	−	1.01950i	0.405806	−	0.913959i	$-0.366991\pi$
$234$	414.000	−	717.069i	0.115658	−	0.200326i
$235$	−241.018			−0.0669034
$236$	−317.357			−0.0875348
$237$	−1416.21	+	2452.94i	−0.388154	+	0.672303i
$238$	−2345.01	+	4061.68i	−0.638675	+	1.10622i
$239$	−5470.20			−1.48049			−0.740247	−	0.672335i	$-0.765291\pi$
$239$	−5470.20			−1.48049			−0.740247	+	0.672335i	$0.765291\pi$
$240$	240.000			0.0645497
$241$	−2905.25	+	5032.05i	−0.776530	+	1.34499i	0.157400	+	0.987535i	$0.449689\pi$
$241$	−2905.25	+	5032.05i	−0.776530	+	1.34499i	−0.933930	+	0.357455i	$0.883645\pi$
$242$	1312.42	+	2273.17i	0.348617	+	0.603823i
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$	1026.02	+	1777.12i	0.269198	+	0.466264i
$245$	1190.46	+	2061.94i	0.310432	+	0.537685i
$246$	728.742			0.188874
$247$	−662.317	−	3751.66i	−0.170616	−	0.966448i
$248$	1515.89			0.388140
$249$	161.170	+	279.154i	0.0410189	+	0.0710469i
$250$	125.000	+	216.506i	0.0316228	+	0.0547723i
$251$	−1298.77	+	2249.53i	−0.326604	+	0.565695i	−0.981836	−	0.189733i	$-0.939238\pi$
$251$	−1298.77	+	2249.53i	−0.326604	+	0.565695i	0.655232	+	0.755428i	$0.272571\pi$
$252$	−515.186	−	892.327i	−0.128784	−	0.223061i
$253$	277.979	−	481.474i	0.0690766	−	0.119644i
$254$	−3465.17			−0.856000
$255$	1228.98			0.301811
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−2230.58	+	3863.47i	−0.541399	+	0.937731i	0.457425	+	0.889248i	$0.348772\pi$
$257$	−2230.58	+	3863.47i	−0.541399	+	0.937731i	−0.998824	+	0.0484827i	$0.984561\pi$
$258$	−165.086			−0.0398365
$259$	−7767.24			−1.86345
$260$	−460.000	+	796.743i	−0.109723	+	0.190046i
$261$	−317.973	−	550.745i	−0.0754101	−	0.130614i
$262$	1812.70	−	3139.69i	0.427439	−	0.740346i
$263$	−2707.67	−	4689.83i	−0.634838	−	1.09957i	−0.986550	−	0.163463i	$-0.947734\pi$
$263$	−2707.67	−	4689.83i	−0.634838	−	1.09957i	0.351712	−	0.936108i	$-0.385600\pi$
$264$	51.7285	+	89.5964i	0.0120594	+	0.0208874i
$265$	−773.160			−0.179226
$266$	−4455.23	−	1620.53i	−1.02695	−	0.373538i
$267$	−1785.67			−0.409294
$268$	1804.97	+	3126.30i	0.411404	+	0.712572i
$269$	3613.08	+	6258.04i	0.818934	+	1.41844i	0.906468	+	0.422275i	$0.138768\pi$
$269$	3613.08	+	6258.04i	0.818934	+	1.41844i	−0.0875335	+	0.996162i	$0.527898\pi$
$270$	−135.000	+	233.827i	−0.0304290	+	0.0527046i
$271$	417.557	+	723.231i	0.0935971	+	0.162115i	0.909022	−	0.416748i	$-0.136830\pi$
$271$	417.557	+	723.231i	0.0935971	+	0.162115i	−0.815425	+	0.578863i	$0.803497\pi$
$272$	−655.457	+	1135.28i	−0.146114	+	0.253076i
$273$	3949.76			0.875641
$274$	3886.31			0.856863
$275$	−53.8839	+	93.3296i	−0.0118157	+	0.0204654i
$276$	−773.828	+	1340.31i	−0.168764	+	0.292309i
$277$	−209.858			−0.0455204			−0.0227602	−	0.999741i	$-0.507245\pi$
$277$	−209.858			−0.0455204			−0.0227602	+	0.999741i	$0.507245\pi$
$278$	4015.68			0.866346
$279$	−852.686	+	1476.89i	−0.182971	+	0.316915i
$280$	572.428	+	991.475i	0.122175	+	0.211614i
$281$	859.842	−	1489.29i	0.182540	−	0.316169i	−0.760205	−	0.649684i	$-0.774901\pi$
$281$	859.842	−	1489.29i	0.182540	−	0.316169i	0.942745	+	0.333515i	$0.108235\pi$
$282$	144.611	+	250.473i	0.0305371	+	0.0528917i
$283$	−147.157	−	254.883i	−0.0309101	−	0.0535379i	0.850157	−	0.526530i	$-0.176507\pi$
$283$	−147.157	−	254.883i	−0.0309101	−	0.0535379i	−0.881067	+	0.472992i	$0.843174\pi$
$284$	712.072			0.148781
$285$	215.973	+	1223.37i	0.0448882	+	0.254267i
$286$	−396.585			−0.0819950
$287$	1738.14	+	3010.54i	0.357487	+	0.619186i
$288$	−144.000	−	249.415i	−0.0294628	−	0.0510310i
$289$	−899.937	+	1558.74i	−0.183175	+	0.317268i
$290$	353.303	+	611.939i	0.0715403	+	0.123911i
$291$	993.525	−	1720.84i	0.200142	−	0.346657i
$292$	−2241.48			−0.449222
$293$	6457.02			1.28745			0.643725	−	0.765257i	$-0.277388\pi$
$293$	6457.02			1.28745			0.643725	+	0.765257i	$0.277388\pi$
$294$	1428.56	−	2474.33i	0.283385	−	0.490837i
$295$	−198.348	+	343.550i	−0.0391468	+	0.0678042i
$296$	−2171.03			−0.426312
$297$	−116.389			−0.0227393
$298$	−2300.34	+	3984.30i	−0.447164	+	0.774511i
$299$	−2966.34	−	5137.85i	−0.573739	−	0.993745i
$300$	150.000	−	259.808i	0.0288675	−	0.0500000i
$301$	−393.750	−	681.994i	−0.0753998	−	0.130596i
$302$	−637.507	−	1104.19i	−0.121471	−	0.210395i
$303$	2344.38			0.444492
$304$	−1245.29	−	452.956i	−0.234941	−	0.0854566i
$305$	2565.05			0.481556
$306$	−737.389	−	1277.20i	−0.137757	−	0.238603i
$307$	1926.96	+	3337.59i	0.358232	+	0.620476i	0.987666	−	0.156578i	$-0.0500464\pi$
$307$	1926.96	+	3337.59i	0.358232	+	0.620476i	−0.629434	+	0.777054i	$0.716713\pi$
$308$	−246.757	+	427.396i	−0.0456503	+	0.0790687i
$309$	1278.47	+	2214.38i	0.235371	+	0.407675i
$310$	947.428	−	1640.99i	0.173582	−	0.300652i
$311$	−8358.72			−1.52405			−0.762025	−	0.647548i	$-0.775795\pi$
$311$	−8358.72			−1.52405			−0.762025	+	0.647548i	$0.775795\pi$
$312$	1104.00			0.200326
$313$	−1925.35	+	3334.80i	−0.347690	+	0.602218i	−0.985839	−	0.167696i	$-0.946367\pi$
$313$	−1925.35	+	3334.80i	−0.347690	+	0.602218i	0.638148	+	0.769913i	$0.279701\pi$
$314$	−1055.96	+	1828.97i	−0.189781	+	0.328710i
$315$	−1287.96			−0.230376
$316$	−3776.55			−0.672303
$317$	3892.71	−	6742.37i	0.689704	−	1.19460i	−0.282229	−	0.959347i	$-0.591074\pi$
$317$	3892.71	−	6742.37i	0.689704	−	1.19460i	0.971933	−	0.235256i	$-0.0755928\pi$
$318$	463.896	+	803.491i	0.0818050	+	0.141690i
$319$	−152.299	+	263.789i	−0.0267307	+	0.0462989i
$320$	160.000	+	277.128i	0.0279508	+	0.0484123i
$321$	1189.36	+	2060.02i	0.206802	+	0.358191i
$322$	−7382.68			−1.27770
$323$	−6376.80	−	2319.48i	−1.09850	−	0.399564i
$324$	324.000			0.0555556
$325$	575.000	+	995.929i	0.0981393	+	0.169982i
$326$	−3251.73	−	5632.17i	−0.552445	−	0.956862i
$327$	−872.753	+	1511.65i	−0.147594	+	0.255641i
$328$	485.828	+	841.479i	0.0817846	+	0.141655i
$329$	−689.828	+	1194.82i	−0.115597	+	0.200220i
$330$	129.321			0.0215724
$331$	−3570.70			−0.592940			−0.296470	−	0.955042i	$-0.595810\pi$
$331$	−3570.70			−0.592940			−0.296470	+	0.955042i	$0.595810\pi$
$332$	−214.893	+	372.205i	−0.0355234	+	0.0615284i
$333$	1221.20	−	2115.19i	0.200966	−	0.348083i
$334$	−3282.01			−0.537675
$335$	4512.43			0.735941
$336$	686.914	−	1189.77i	0.111530	−	0.193176i
$337$	−1633.33	−	2829.01i	−0.264015	−	0.457287i	0.703290	−	0.710903i	$-0.251713\pi$
$337$	−1633.33	−	2829.01i	−0.264015	−	0.457287i	−0.967305	+	0.253616i	$0.918380\pi$
$338$	81.0000	−	140.296i	0.0130350	−	0.0225772i
$339$	−1024.12	−	1773.83i	−0.164078	−	0.284192i
$340$	819.321	+	1419.11i	0.130688	+	0.226358i
$341$	816.817			0.129716
$342$	1141.78	−	958.467i	0.180527	−	0.151544i
$343$	3811.96			0.600077
$344$	−110.057	−	190.625i	−0.0172497	−	0.0298773i
$345$	967.285	+	1675.39i	0.150947	+	0.261449i
$346$	3795.10	−	6573.30i	0.589670	−	1.02134i
$347$	2745.92	+	4756.07i	0.424808	+	0.735790i	0.996403	−	0.0847468i	$-0.0270081\pi$
$347$	2745.92	+	4756.07i	0.424808	+	0.735790i	−0.571594	+	0.820537i	$0.693675\pi$
$348$	423.964	−	734.327i	0.0653070	−	0.113115i
$349$	4375.75			0.671142			0.335571	−	0.942015i	$-0.391071\pi$
$349$	4375.75			0.671142			0.335571	+	0.942015i	$0.391071\pi$
$350$	1431.07			0.218554
$351$	−621.000	+	1075.60i	−0.0944346	+	0.163565i
$352$	−68.9713	+	119.462i	−0.0104437	+	0.0180890i
$353$	9525.41			1.43622			0.718111	−	0.695929i	$-0.245007\pi$
$353$	9525.41			1.43622			0.718111	+	0.695929i	$0.245007\pi$
$354$	476.036			0.0714719
$355$	445.045	−	770.841i	0.0665368	−	0.115245i
$356$	−1190.45	−	2061.92i	−0.177229	−	0.306970i
$357$	3517.52	−	6092.52i	0.521476	−	0.903223i
$358$	1668.07	+	2889.18i	0.246257	+	0.426530i
$359$	627.576	+	1086.99i	0.0922624	+	0.159803i	0.908463	−	0.417966i	$-0.137257\pi$
$359$	627.576	+	1086.99i	0.0922624	+	0.159803i	−0.816200	+	0.577769i	$0.803923\pi$
$360$	−360.000			−0.0527046
$361$	1188.27	−	6755.29i	0.173242	−	0.984879i
$362$	−2307.86			−0.335079
$363$	−1968.63	−	3409.76i	−0.284645	−	0.493019i
$364$	2633.17	+	4560.78i	0.379164	+	0.656731i
$365$	−1400.93	+	2426.48i	−0.200898	+	0.347966i
$366$	−1539.03	−	2665.68i	−0.219799	−	0.380703i
$367$	−5243.43	+	9081.88i	−0.745789	+	1.29174i	0.204036	+	0.978963i	$0.434594\pi$
$367$	−5243.43	+	9081.88i	−0.745789	+	1.29174i	−0.949825	+	0.312781i	$0.898739\pi$
$368$	−2063.54			−0.292309
$369$	−1093.11			−0.154215
$370$	−1356.89	+	2350.21i	−0.190653	+	0.330220i
$371$	−2212.89	+	3832.84i	−0.309670	+	0.536365i
$372$	−2273.83			−0.316915
$373$	−7848.84			−1.08954			−0.544769	−	0.838586i	$-0.683383\pi$
$373$	−7848.84			−1.08954			−0.544769	+	0.838586i	$0.683383\pi$
$374$	−353.186	+	611.735i	−0.0488310	+	0.0845777i
$375$	−187.500	−	324.760i	−0.0258199	−	0.0447214i
$376$	−192.814	+	333.965i	−0.0264459	+	0.0458056i
$377$	1625.19	+	2814.92i	0.222021	+	0.384551i
$378$	772.778	+	1338.49i	0.105152	+	0.182128i
$379$	4137.48			0.560760			0.280380	−	0.959889i	$-0.409540\pi$
$379$	4137.48			0.560760			0.280380	+	0.959889i	$0.409540\pi$
$380$	−1268.64	+	1064.96i	−0.171263	+	0.143767i
$381$	5197.76			0.698921
$382$	2740.14	+	4746.07i	0.367010	+	0.635681i
$383$	−39.5605	−	68.5207i	−0.00527792	−	0.00914163i	0.863374	−	0.504564i	$-0.168347\pi$
$383$	−39.5605	−	68.5207i	−0.00527792	−	0.00914163i	−0.868652	+	0.495422i	$0.835013\pi$
$384$	192.000	−	332.554i	0.0255155	−	0.0441942i
$385$	308.446	+	534.245i	0.0408309	+	0.0707212i
$386$	5157.95	−	8933.83i	0.680136	−	1.17803i
$387$	247.629			0.0325263
$388$	2649.40			0.346657
$389$	3676.32	−	6367.58i	0.479170	−	0.829946i	−0.520545	−	0.853834i	$-0.674271\pi$
$389$	3676.32	−	6367.58i	0.479170	−	0.829946i	0.999715	+	0.0238880i	$0.00760450\pi$
$390$	690.000	−	1195.12i	0.0895885	−	0.155172i
$391$	−10566.9			−1.36673
$392$	3809.48			0.490837
$393$	−2719.05	+	4709.53i	−0.349002	+	0.604490i
$394$	3205.90	+	5552.78i	0.409926	+	0.710013i
$395$	−2360.35	+	4088.24i	−0.300663	+	0.520764i
$396$	−77.5928	−	134.395i	−0.00984642	−	0.0170545i
$397$	−5491.24	−	9511.11i	−0.694201	−	1.20239i	−0.970449	−	0.241305i	$-0.922425\pi$
$397$	−5491.24	−	9511.11i	−0.694201	−	1.20239i	0.276249	−	0.961086i	$-0.410909\pi$
$398$	1639.95			0.206541
$399$	6682.84	+	2430.80i	0.838498	+	0.304993i
$400$	400.000			0.0500000
$401$	−1035.41	−	1793.39i	−0.128943	−	0.223335i	0.794325	−	0.607494i	$-0.207825\pi$
$401$	−1035.41	−	1793.39i	−0.128943	−	0.223335i	−0.923267	+	0.384158i	$0.874492\pi$
$402$	−2707.46	−	4689.45i	−0.335910	−	0.581813i
$403$	4358.17	−	7548.57i	0.538700	−	0.933055i
$404$	1562.92	+	2707.06i	0.192471	+	0.333369i
$405$	202.500	−	350.740i	0.0248452	−	0.0430331i
$406$	4044.81			0.494435
$407$	−1169.83			−0.142473
$408$	983.186	−	1702.93i	0.119301	−	0.206636i
$409$	4531.55	−	7848.87i	0.547850	−	0.948904i	−0.450572	−	0.892740i	$-0.648780\pi$
$409$	4531.55	−	7848.87i	0.547850	−	0.948904i	0.998422	−	0.0561638i	$-0.0178869\pi$
$410$	1214.57			0.146301
$411$	−5829.46			−0.699626
$412$	−1704.63	+	2952.50i	−0.203837	+	0.353057i
$413$	1135.40	+	1966.58i	0.135277	+	0.234307i
$414$	1160.74	−	2010.46i	0.137796	−	0.238669i
$415$	268.616	+	465.257i	0.0317731	+	0.0550327i
$416$	736.000	+	1274.79i	0.0867437	+	0.150244i
$417$	−6023.52			−0.707369
$418$	−671.008	−	244.070i	−0.0785169	−	0.0285595i
$419$	−1690.59			−0.197113			−0.0985567	−	0.995131i	$-0.531423\pi$
$419$	−1690.59			−0.197113			−0.0985567	+	0.995131i	$0.531423\pi$
$420$	−858.643	−	1487.21i	−0.0997559	−	0.172782i
$421$	−7501.22	−	12992.5i	−0.868378	−	1.50407i	−0.863654	−	0.504086i	$-0.831830\pi$
$421$	−7501.22	−	12992.5i	−0.868378	−	1.50407i	−0.00472430	−	0.999989i	$-0.501504\pi$
$422$	2527.53	−	4377.81i	0.291560	−	0.504996i
$423$	−216.916	−	375.710i	−0.0249334	−	0.0431859i
$424$	−618.528	+	1071.32i	−0.0708452	+	0.122707i
$425$	2048.30			0.233782
$426$	−1068.11			−0.121479
$427$	7341.54	−	12715.9i	0.832043	−	1.44114i
$428$	−1585.81	+	2746.70i	−0.179095	+	0.310202i
$429$	594.878			0.0669486
$430$	−275.143			−0.0308572
$431$	−6820.70	+	11813.8i	−0.762277	+	1.32030i	0.179397	+	0.983777i	$0.442585\pi$
$431$	−6820.70	+	11813.8i	−0.762277	+	1.32030i	−0.941674	+	0.336526i	$0.890748\pi$
$432$	216.000	+	374.123i	0.0240563	+	0.0416667i
$433$	5415.71	−	9380.29i	0.601068	−	1.04108i	−0.391591	−	0.920139i	$-0.628075\pi$
$433$	5415.71	−	9380.29i	0.601068	−	1.04108i	0.992660	−	0.120942i	$-0.0385914\pi$
$434$	−5423.35	−	9393.51i	−0.599837	−	1.03895i
$435$	−529.955	−	917.908i	−0.0584124	−	0.101173i
$436$	−2327.34			−0.255641
$437$	−1856.95	−	10518.6i	−0.203273	−	1.15143i
$438$	3362.23			0.366789
$439$	−6346.96	−	10993.3i	−0.690032	−	1.19517i	−0.971827	−	0.235695i	$-0.924263\pi$
$439$	−6346.96	−	10993.3i	−0.690032	−	1.19517i	0.281795	−	0.959475i	$-0.409070\pi$
$440$	86.2142	+	149.327i	0.00934113	+	0.0161793i
$441$	−2142.83	+	3711.50i	−0.231383	+	0.400767i
$442$	3768.88	+	6527.89i	0.405582	+	0.702489i
$443$	−1450.82	+	2512.89i	−0.155599	+	0.269505i	−0.933277	−	0.359157i	$-0.883064\pi$
$443$	−1450.82	+	2512.89i	−0.155599	+	0.269505i	0.777678	+	0.628663i	$0.216397\pi$
$444$	3256.54			0.348083
$445$	−2976.12			−0.317038
$446$	1950.86	−	3378.99i	0.207121	−	0.358744i
$447$	3450.51	−	5976.45i	0.365108	−	0.632386i
$448$	1831.77			0.193176
$449$	−50.5038			−0.00530829			−0.00265414	−	0.999996i	$-0.500845\pi$
$449$	−50.5038			−0.00530829			−0.00265414	+	0.999996i	$0.500845\pi$
$450$	−225.000	+	389.711i	−0.0235702	+	0.0408248i
$451$	261.783	+	453.421i	0.0273323	+	0.0473410i
$452$	1365.49	−	2365.10i	0.142096	−	0.246118i
$453$	956.260	+	1656.29i	0.0991811	+	0.171787i
$454$	3629.36	+	6286.24i	0.375186	+	0.649841i
$455$	6582.93			0.678269
$456$	1867.93	+	679.434i	0.191828	+	0.0697750i
$457$	−10840.4			−1.10961			−0.554804	−	0.831981i	$-0.687207\pi$
$457$	−10840.4			−1.10961			−0.554804	+	0.831981i	$0.687207\pi$
$458$	145.350	+	251.753i	0.0148292	+	0.0256849i
$459$	1106.08	+	1915.79i	0.112478	+	0.194818i
$460$	−1289.71	+	2233.85i	−0.130724	+	0.226421i
$461$	−1804.67	−	3125.77i	−0.182325	−	0.315795i	0.760347	−	0.649517i	$-0.225029\pi$
$461$	−1804.67	−	3125.77i	−0.182325	−	0.315795i	−0.942672	+	0.333721i	$0.891695\pi$
$462$	370.136	−	641.094i	0.0372733	−	0.0645593i
$463$	9096.20			0.913038			0.456519	−	0.889714i	$-0.349096\pi$
$463$	9096.20			0.913038			0.456519	+	0.889714i	$0.349096\pi$
$464$	1130.57			0.113115
$465$	−1421.14	+	2461.49i	−0.141729	+	0.245482i
$466$	−4186.88	+	7251.89i	−0.416209	+	0.720895i
$467$	1927.45			0.190989			0.0954943	−	0.995430i	$-0.469557\pi$
$467$	1927.45			0.190989			0.0954943	+	0.995430i	$0.469557\pi$
$468$	−1656.00			−0.163565
$469$	12915.2	−	22369.8i	1.27158	−	2.20243i
$470$	241.018	+	417.456i	0.0236539	+	0.0409698i
$471$	1583.94	−	2743.46i	0.154955	−	0.268390i
$472$	317.357	+	549.679i	0.0309482	+	0.0536039i
$473$	−59.3031	−	102.716i	−0.00576482	−	0.00998497i
$474$	5664.83			0.548933
$475$	359.955	+	2038.95i	0.0347702	+	0.196954i
$476$	9380.05			0.903223
$477$	−695.844	−	1205.24i	−0.0667935	−	0.115690i
$478$	5470.20	+	9474.67i	0.523434	+	0.906613i
$479$	9349.27	−	16193.4i	0.891814	−	1.54467i	0.0541151	−	0.998535i	$-0.482766\pi$
$479$	9349.27	−	16193.4i	0.891814	−	1.54467i	0.837699	−	0.546132i	$-0.183900\pi$
$480$	−240.000	−	415.692i	−0.0228218	−	0.0395285i
$481$	−6241.71	+	10811.0i	−0.591679	+	1.02482i
$482$	11621.0			1.09818
$483$	11074.0			1.04324
$484$	2624.84	−	4546.35i	0.246510	−	0.426967i
$485$	1655.87	−	2868.06i	0.155030	−	0.268519i
$486$	−486.000			−0.0453609
$487$	9370.36			0.871892			0.435946	−	0.899973i	$-0.356414\pi$
$487$	9370.36			0.871892			0.435946	+	0.899973i	$0.356414\pi$
$488$	2052.04	−	3554.24i	0.190352	−	0.329699i
$489$	4877.60	+	8448.25i	0.451069	+	0.781275i
$490$	2380.93	−	4123.89i	0.219509	−	0.380200i
$491$	−8801.87	−	15245.3i	−0.809008	−	1.40124i	−0.913552	−	0.406723i	$-0.866671\pi$
$491$	−8801.87	−	15245.3i	−0.809008	−	1.40124i	0.104544	−	0.994520i	$-0.466662\pi$
$492$	−728.742	−	1262.22i	−0.0667769	−	0.115661i
$493$	5789.38			0.528885
$494$	−5835.76	+	4898.83i	−0.531504	+	0.446172i
$495$	−193.982			−0.0176138
$496$	−1515.89	−	2625.59i	−0.137228	−	0.237686i
$497$	−2547.57	−	4412.51i	−0.229927	−	0.398246i
$498$	322.339	−	558.308i	0.0290048	−	0.0502377i
$499$	−9161.02	−	15867.3i	−0.821851	−	1.42349i	−0.904303	−	0.426892i	$-0.859608\pi$
$499$	−9161.02	−	15867.3i	−0.821851	−	1.42349i	0.0824520	−	0.996595i	$-0.473725\pi$
$500$	250.000	−	433.013i	0.0223607	−	0.0387298i
$501$	4923.01			0.439010
$502$	5195.08			0.461888
$503$	−5635.20	+	9760.45i	−0.499525	+	0.865203i	−1.00000		0.000548122i	$-0.999826\pi$
$503$	−5635.20	+	9760.45i	−0.499525	+	0.865203i	0.500475	+	0.865751i	$0.333159\pi$
$504$	−1030.37	+	1784.65i	−0.0910642	+	0.157728i
$505$	3907.30			0.344302
$506$	−1111.92			−0.0976891
$507$	−121.500	+	210.444i	−0.0106430	+	0.0184342i
$508$	3465.17	+	6001.85i	0.302642	+	0.524191i
$509$	−2067.88	+	3581.68i	−0.180073	+	0.311896i	−0.941905	−	0.335878i	$-0.890967\pi$
$509$	−2067.88	+	3581.68i	−0.180073	+	0.311896i	0.761832	+	0.647775i	$0.224300\pi$
$510$	−1228.98	−	2128.66i	−0.106706	−	0.184821i
$511$	8019.31	+	13889.8i	0.694233	+	1.20245i
$512$	512.000			0.0441942
$513$	−1712.67	+	1437.70i	−0.147400	+	0.123735i
$514$	8922.31			0.765654
$515$	2130.78	+	3690.63i	0.182318	+	0.315783i
$516$	165.086	+	285.937i	0.0140843	+	0.0243947i
$517$	−103.896	+	179.953i	−0.00883817	+	0.0153082i
$518$	7767.24	+	13453.3i	0.658828	+	1.14112i
$519$	−5692.65	+	9859.95i	−0.481463	+	0.833919i
$520$	1840.00			0.155172
$521$	−5893.76			−0.495606			−0.247803	−	0.968810i	$-0.579709\pi$
$521$	−5893.76			−0.495606			−0.247803	+	0.968810i	$0.579709\pi$
$522$	−635.946	+	1101.49i	−0.0533230	+	0.0923581i
$523$	−2513.85	+	4354.11i	−0.210178	+	0.364038i	−0.951770	−	0.306812i	$-0.900738\pi$
$523$	−2513.85	+	4354.11i	−0.210178	+	0.364038i	0.741592	+	0.670851i	$0.234071\pi$
$524$	−7250.80			−0.604490
$525$	−2146.61			−0.178449
$526$	−5415.35	+	9379.66i	−0.448898	+	0.777514i
$527$	−7762.48	−	13445.0i	−0.641630	−	1.11134i
$528$	103.457	−	179.193i	0.00852725	−	0.0147696i
$529$	−2233.30	−	3868.19i	−0.183554	−	0.317925i
$530$	773.160	+	1339.15i	0.0633659	+	0.109753i
$531$	−714.054			−0.0583565
$532$	1648.39	+	9337.21i	0.134336	+	0.760939i
$533$	5587.02			0.454035
$534$	1785.67	+	3092.88i	0.144707	+	0.250640i
$535$	1982.26	+	3433.37i	0.160188	+	0.277454i
$536$	3609.94	−	6252.60i	0.290906	−	0.503864i
$537$	−2502.10	−	4333.76i	−0.201068	−	0.348260i
$538$	7226.16	−	12516.1i	0.579074	−	1.00299i
$539$	2052.70			0.164037
$540$	540.000			0.0430331
$541$	−7786.73	+	13487.0i	−0.618813	+	1.07181i	0.370890	+	0.928677i	$0.379053\pi$
$541$	−7786.73	+	13487.0i	−0.618813	+	1.07181i	−0.989703	+	0.143138i	$0.954281\pi$
$542$	835.115	−	1446.46i	0.0661831	−	0.114633i
$543$	3461.80			0.273591
$544$	2621.83			0.206636
$545$	−1454.59	+	2519.42i	−0.114326	+	0.198019i
$546$	−3949.76	−	6841.18i	−0.309586	−	0.536219i
$547$	−3746.10	+	6488.44i	−0.292819	+	0.507177i	−0.974475	−	0.224496i	$-0.927927\pi$
$547$	−3746.10	+	6488.44i	−0.292819	+	0.507177i	0.681656	+	0.731672i	$0.261260\pi$
$548$	−3886.31	−	6731.28i	−0.302947	−	0.524719i
$549$	2308.55	+	3998.52i	0.179465	+	0.310843i
$550$	215.535			0.0167099
$551$	1017.38	+	5762.93i	0.0786607	+	0.445570i
$552$	3095.31			0.238669
$553$	13511.3	+	23402.2i	1.03898	+	1.79957i
$554$	209.858	+	363.485i	0.0160939	+	0.0278755i
$555$	2035.34	−	3525.31i	0.155667	−	0.269624i
$556$	−4015.68	−	6955.36i	−0.306300	−	0.530527i
$557$	2062.15	−	3571.75i	0.156869	−	0.271705i	−0.776869	−	0.629662i	$-0.783193\pi$
$557$	2062.15	−	3571.75i	0.156869	−	0.271705i	0.933738	+	0.357957i	$0.116527\pi$
$558$	3410.74			0.258760
$559$	−1265.66			−0.0957633
$560$	1144.86	−	1982.95i	0.0863911	−	0.149634i
$561$	529.778	−	917.603i	0.0398703	−	0.0690574i
$562$	−3439.37			−0.258151
$563$	7596.95			0.568691			0.284346	−	0.958722i	$-0.408224\pi$
$563$	7596.95			0.568691			0.284346	+	0.958722i	$0.408224\pi$
$564$	289.222	−	500.947i	0.0215930	−	0.0374001i
$565$	−1706.87	−	2956.38i	−0.127095	−	0.220134i
$566$	−294.314	+	509.766i	−0.0218568	+	0.0378570i
$567$	−1159.17	−	2007.74i	−0.0858562	−	0.148707i
$568$	−712.072	−	1233.35i	−0.0526019	−	0.0911092i
$569$	−25780.6			−1.89943			−0.949717	−	0.313108i	$-0.898630\pi$
$569$	−25780.6			−1.89943			−0.949717	+	0.313108i	$0.898630\pi$
$570$	1902.96	−	1597.44i	0.139836	−	0.117385i
$571$	−16636.4			−1.21928			−0.609642	−	0.792677i	$-0.708687\pi$
$571$	−16636.4			−1.21928			−0.609642	+	0.792677i	$0.708687\pi$
$572$	396.585	+	686.906i	0.0289896	+	0.0502115i
$573$	−4110.22	−	7119.10i	−0.299663	−	0.519031i
$574$	3476.27	−	6021.08i	0.252782	−	0.437831i
$575$	1612.14	+	2792.31i	0.116923	+	0.202517i
$576$	−288.000	+	498.831i	−0.0208333	+	0.0360844i
$577$	1857.95			0.134051			0.0670254	−	0.997751i	$-0.478649\pi$
$577$	1857.95			0.134051			0.0670254	+	0.997751i	$0.478649\pi$
$578$	3599.75			0.259048
$579$	−7736.92	+	13400.7i	−0.555329	+	0.961858i
$580$	706.606	−	1223.88i	0.0505866	−	0.0876186i
$581$	3075.27			0.219593
$582$	−3974.10			−0.283044
$583$	−333.287	+	577.269i	−0.0236764	+	0.0410087i
$584$	2241.48	+	3882.36i	0.158824	+	0.275091i
$585$	−1035.00	+	1792.67i	−0.0731487	+	0.126697i
$586$	−6457.02	−	11183.9i	−0.455183	−	0.788399i
$587$	12908.6	+	22358.4i	0.907658	+	1.57211i	0.817309	+	0.576199i	$0.195465\pi$
$587$	12908.6	+	22358.4i	0.907658	+	1.57211i	0.0903484	+	0.995910i	$0.471202\pi$
$588$	−5714.23			−0.400767
$589$	12019.5	−	10089.8i	0.840839	−	0.705843i
$590$	793.394			0.0553619
$591$	−4808.85	−	8329.18i	−0.334704	−	0.579723i
$592$	2171.03	+	3760.33i	0.150724	+	0.261062i
$593$	−241.613	+	418.486i	−0.0167316	+	0.0289801i	−0.874270	−	0.485440i	$-0.838659\pi$
$593$	−241.613	+	418.486i	−0.0167316	+	0.0289801i	0.857538	+	0.514420i	$0.171993\pi$
$594$	116.389	+	201.592i	0.00803957	+	0.0139249i
$595$	5862.53	−	10154.2i	0.403934	−	0.699633i
$596$	9201.35			0.632386
$597$	−2459.93			−0.168640
$598$	−5932.68	+	10275.7i	−0.405695	+	0.702684i
$599$	−3337.55	+	5780.80i	−0.227660	+	0.394319i	−0.957114	−	0.289711i	$-0.906441\pi$
$599$	−3337.55	+	5780.80i	−0.227660	+	0.394319i	0.729454	+	0.684030i	$0.239774\pi$
$600$	−600.000			−0.0408248
$601$	−1767.06			−0.119933			−0.0599665	−	0.998200i	$-0.519099\pi$
$601$	−1767.06			−0.119933			−0.0599665	+	0.998200i	$0.519099\pi$
$602$	−787.499	+	1363.99i	−0.0533157	+	0.0923456i
$603$	4061.19	+	7034.18i	0.274269	+	0.475048i
$604$	−1275.01	+	2208.39i	−0.0858933	+	0.148772i
$605$	−3281.04	−	5682.94i	−0.220485	−	0.381891i
$606$	−2344.38	−	4060.59i	−0.157152	−	0.272195i
$607$	−25376.2			−1.69685			−0.848426	−	0.529314i	$-0.822449\pi$
$607$	−25376.2			−1.69685			−0.848426	+	0.529314i	$0.822449\pi$
$608$	460.742	+	2609.85i	0.0307328	+	0.174085i
$609$	−6067.22			−0.403705
$610$	−2565.05	−	4442.80i	−0.170256	−	0.294891i
$611$	1108.68	+	1920.30i	0.0734084	+	0.127147i
$612$	−1474.78	+	2554.39i	−0.0974091	+	0.168718i
$613$	10802.8	+	18711.0i	0.711780	+	1.23284i	0.964189	+	0.265218i	$0.0854438\pi$
$613$	10802.8	+	18711.0i	0.711780	+	1.23284i	−0.252409	+	0.967621i	$0.581223\pi$
$614$	3853.91	−	6675.17i	0.253308	−	0.438743i
$615$	−1821.86			−0.119454
$616$	987.029			0.0645593
$617$	6471.86	−	11209.6i	0.422281	−	0.731412i	−0.573881	−	0.818938i	$-0.694563\pi$
$617$	6471.86	−	11209.6i	0.422281	−	0.731412i	0.996162	+	0.0875266i	$0.0278963\pi$
$618$	2556.94	−	4428.75i	0.166432	−	0.288269i
$619$	−10134.0			−0.658030			−0.329015	−	0.944325i	$-0.606717\pi$
$619$	−10134.0			−0.658030			−0.329015	+	0.944325i	$0.606717\pi$
$620$	−3789.71			−0.245482
$621$	−1741.11	+	3015.70i	−0.112510	+	0.194872i
$622$	8358.72	+	14477.7i	0.538833	+	0.933286i
$623$	−8518.09	+	14753.8i	−0.547785	+	0.948791i
$624$	−1104.00	−	1912.18i	−0.0708259	−	0.122674i
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	7701.39			0.491709
$627$	1006.51	+	366.105i	0.0641088	+	0.0233187i
$628$	4223.83			0.268390
$629$	11117.3	+	19255.7i	0.704732	+	1.22063i
$630$	1287.96	+	2230.82i	0.0814503	+	0.141076i
$631$	3914.47	−	6780.07i	0.246962	−	0.427750i	−0.715720	−	0.698388i	$-0.753901\pi$
$631$	3914.47	−	6780.07i	0.246962	−	0.427750i	0.962681	+	0.270638i	$0.0872345\pi$
$632$	3776.55	+	6541.18i	0.237695	+	0.411700i
$633$	−3791.29	+	6566.71i	−0.238057	+	0.412327i
$634$	−15570.8			−0.975389
$635$	8662.93			0.541382
$636$	927.792	−	1606.98i	0.0578449	−	0.100190i
$637$	10952.3	−	18969.9i	0.681232	−	1.17993i
$638$	609.195			0.0378029
$639$	1602.16			0.0991872
$640$	320.000	−	554.256i	0.0197642	−	0.0342327i
$641$	−2251.98	−	3900.55i	−0.138764	−	0.240347i	0.788265	−	0.615336i	$-0.210980\pi$
$641$	−2251.98	−	3900.55i	−0.138764	−	0.240347i	−0.927029	+	0.374989i	$0.877646\pi$
$642$	2378.71	−	4120.05i	0.146231	−	0.253279i
$643$	−8593.07	−	14883.6i	−0.527026	−	0.912836i	−0.999504	−	0.0314933i	$-0.989974\pi$
$643$	−8593.07	−	14883.6i	−0.527026	−	0.912836i	0.472478	−	0.881342i	$-0.343360\pi$
$644$	7382.68	+	12787.2i	0.451737	+	0.782431i
$645$	412.715			0.0251948
$646$	2359.35	+	13364.4i	0.143696	+	0.813957i
$647$	−8654.23			−0.525862			−0.262931	−	0.964815i	$-0.584689\pi$
$647$	−8654.23			−0.525862			−0.262931	+	0.964815i	$0.584689\pi$
$648$	−324.000	−	561.184i	−0.0196419	−	0.0340207i
$649$	171.004	+	296.188i	0.0103429	+	0.0179143i
$650$	1150.00	−	1991.86i	0.0693949	−	0.120196i
$651$	8135.02	+	14090.3i	0.489764	+	0.848297i
$652$	−6503.47	+	11264.3i	−0.390637	+	0.676604i
$653$	−3442.22			−0.206286			−0.103143	−	0.994667i	$-0.532890\pi$
$653$	−3442.22			−0.206286			−0.103143	+	0.994667i	$0.532890\pi$
$654$	3491.01			0.208730
$655$	−4531.75	+	7849.22i	−0.270336	+	0.468236i
$656$	971.656	−	1682.96i	0.0578305	−	0.100165i
$657$	−5043.34			−0.299482
$658$	2759.31			0.163479
$659$	607.674	−	1052.52i	0.0359205	−	0.0622162i	−0.847506	−	0.530785i	$-0.821897\pi$
$659$	607.674	−	1052.52i	0.0359205	−	0.0622162i	0.883427	+	0.468569i	$0.155230\pi$
$660$	−129.321	−	223.991i	−0.00762700	−	0.0132104i
$661$	9794.68	−	16964.9i	0.576352	−	0.998271i	−0.419541	−	0.907736i	$-0.637809\pi$
$661$	9794.68	−	16964.9i	0.576352	−	0.998271i	0.995893	−	0.0905351i	$-0.0288577\pi$
$662$	3570.70	+	6184.63i	0.209636	+	0.363100i
$663$	−5653.32	−	9791.83i	−0.331156	−	0.573580i
$664$	859.572			0.0502377
$665$	11138.1	+	4051.33i	0.649497	+	0.236246i
$666$	−4884.81			−0.284208
$667$	4556.60	+	7892.26i	0.264516	+	0.458155i
$668$	3282.01	+	5684.60i	0.190097	+	0.329257i
$669$	−2926.29	+	5068.49i	−0.169114	+	0.292914i
$670$	−4512.43	−	7815.76i	−0.260195	−	0.450670i
$671$	1105.72	−	1915.16i	0.0636152	−	0.110185i
$672$	−2747.66			−0.157728
$673$	17853.2			1.02257			0.511284	−	0.859412i	$-0.329170\pi$
$673$	17853.2			1.02257			0.511284	+	0.859412i	$0.329170\pi$
$674$	−3266.65	+	5658.01i	−0.186687	+	0.323351i
$675$	337.500	−	584.567i	0.0192450	−	0.0333333i
$676$	−324.000			−0.0184342
$677$	20443.0			1.16054			0.580271	−	0.814423i	$-0.302947\pi$
$677$	20443.0			1.16054			0.580271	+	0.814423i	$0.302947\pi$
$678$	−2048.24	+	3547.66i	−0.116021	+	0.200954i
$679$	−9478.70	−	16417.6i	−0.535728	−	0.927907i
$680$	1638.64	−	2838.21i	0.0924104	−	0.160060i
$681$	−5444.05	−	9429.36i	−0.306338	−	0.530593i
$682$	−816.817	−	1414.77i	−0.0458615	−	0.0794345i
$683$	−3882.95			−0.217536			−0.108768	−	0.994067i	$-0.534691\pi$
$683$	−3882.95			−0.217536			−0.108768	+	0.994067i	$0.534691\pi$
$684$	−2801.89	−	1019.15i	−0.156627	−	0.0569711i
$685$	−9715.77			−0.541928
$686$	−3811.96	−	6602.50i	−0.212159	−	0.367471i
$687$	−218.025	−	377.630i	−0.0121080	−	0.0209716i
$688$	−220.115	+	381.250i	−0.0121974	+	0.0211265i
$689$	3556.54	+	6160.10i	0.196652	+	0.340611i
$690$	1934.57	−	3350.77i	0.106736	−	0.184872i
$691$	12415.2			0.683496			0.341748	−	0.939792i	$-0.388981\pi$
$691$	12415.2			0.683496			0.341748	+	0.939792i	$0.388981\pi$
$692$	−15180.4			−0.833919
$693$	−555.204	+	961.641i	−0.0304335	+	0.0527124i
$694$	5491.83	−	9512.13i	0.300385	−	0.520282i
$695$	−10039.2			−0.547926
$696$	−1695.86			−0.0923581
$697$	4975.62	−	8618.02i	0.270394	−	0.468337i
$698$	−4375.75	−	7579.02i	−0.237285	−	0.410989i
$699$	6280.32	−	10877.8i	0.339833	−	0.588609i
$700$	−1431.07	−	2478.69i	−0.0772706	−	0.133837i
$701$	18484.8	+	32016.6i	0.995950	+	1.72504i	0.575839	+	0.817563i	$0.304676\pi$
$701$	18484.8	+	32016.6i	0.995950	+	1.72504i	0.420111	+	0.907473i	$0.361991\pi$
$702$	2484.00			0.133551
$703$	−17214.1	+	14450.4i	−0.923532	+	0.775260i
$704$	275.885			0.0147696
$705$	−361.527	−	626.183i	−0.0193133	−	0.0334517i
$706$	−9525.41	−	16498.5i	−0.507781	−	0.879503i
$707$	11183.2	−	19369.9i	0.594893	−	1.03038i
$708$	−476.036	−	824.519i	−0.0252691	−	0.0437674i
$709$	−1299.50	+	2250.80i	−0.0688346	+	0.119225i	−0.898389	−	0.439201i	$-0.855261\pi$
$709$	−1299.50	+	2250.80i	−0.0688346	+	0.119225i	0.829554	+	0.558427i	$0.188595\pi$
$710$	−1780.18			−0.0940972
$711$	−8497.25			−0.448202
$712$	−2380.90	+	4123.84i	−0.125320	+	0.217061i
$713$	12219.1	−	21164.1i	0.641808	−	1.11164i
$714$	−14070.1			−0.737478
$715$	991.463			0.0518582
$716$	3336.13	−	5778.35i	0.174130	−	0.301602i
$717$	−8205.30	−	14212.0i	−0.427382	−	0.740247i
$718$	1255.15	−	2173.99i	0.0652394	−	0.112998i
$719$	1928.66	+	3340.54i	0.100037	+	0.173270i	0.911700	−	0.410857i	$-0.134770\pi$
$719$	1928.66	+	3340.54i	0.100037	+	0.173270i	−0.811662	+	0.584127i	$0.801437\pi$
$720$	360.000	+	623.538i	0.0186339	+	0.0322749i
$721$	24394.4			1.26005
$722$	−12888.8	+	4697.14i	−0.664363	+	0.242119i
$723$	−17431.5			−0.896660
$724$	2307.86	+	3997.34i	0.118468	+	0.205193i
$725$	−883.258	−	1529.85i	−0.0452460	−	0.0783684i
$726$	−3937.25	+	6819.52i	−0.201274	+	0.348617i
$727$	−6751.68	−	11694.2i	−0.344437	−	0.596583i	0.640814	−	0.767696i	$-0.278597\pi$
$727$	−6751.68	−	11694.2i	−0.344437	−	0.596583i	−0.985251	+	0.171113i	$0.945264\pi$
$728$	5266.34	−	9121.57i	0.268109	−	0.464379i
$729$	729.000			0.0370370
$730$	5603.71			0.284113
$731$	−1127.15	+	1952.29i	−0.0570305	+	0.0987797i
$732$	−3078.06	+	5331.36i	−0.155421	+	0.269198i
$733$	−39035.0			−1.96697			−0.983485	−	0.180987i	$-0.942071\pi$
$733$	−39035.0			−1.96697			−0.983485	+	0.180987i	$0.942071\pi$
$734$	20973.7			1.05470
$735$	−3571.39	+	6185.83i	−0.179228	+	0.310432i
$736$	2063.54	+	3574.16i	0.103347	+	0.179002i
$737$	1945.18	−	3369.14i	0.0972205	−	0.168391i
$738$	1093.11	+	1893.33i	0.0545231	+	0.0944368i
$739$	−4629.94	−	8019.30i	−0.230467	−	0.399181i	0.727479	−	0.686130i	$-0.240692\pi$
$739$	−4629.94	−	8019.30i	−0.230467	−	0.399181i	−0.957946	+	0.286950i	$0.907359\pi$
$740$	5427.57			0.269624
$741$	8753.63	−	7348.24i	0.433971	−	0.364298i
$742$	8851.57			0.437940
$743$	14970.9	+	25930.4i	0.739205	+	1.28034i	0.952854	+	0.303430i	$0.0981320\pi$
$743$	14970.9	+	25930.4i	0.739205	+	1.28034i	−0.213648	+	0.976911i	$0.568535\pi$
$744$	2273.83	+	3938.39i	0.112046	+	0.194070i
$745$	5750.84	−	9960.75i	0.282812	−	0.489844i
$746$	7848.84	+	13594.6i	0.385210	+	0.667203i
$747$	−483.509	+	837.462i	−0.0236823	+	0.0410189i
$748$	1412.74			0.0690574
$749$	22694.0			1.10710
$750$	−375.000	+	649.519i	−0.0182574	+	0.0316228i
$751$	−14364.7	+	24880.5i	−0.697972	+	1.20892i	0.271196	+	0.962524i	$0.412581\pi$
$751$	−14364.7	+	24880.5i	−0.697972	+	1.20892i	−0.969168	+	0.246399i	$0.920753\pi$
$752$	771.258			0.0374001
$753$	−7792.62			−0.377130
$754$	3250.39	−	5629.84i	0.156992	−	0.271919i
$755$	1593.77	+	2760.49i	0.0768253	+	0.133065i
$756$	1545.56	−	2676.98i	0.0743536	−	0.128784i
$757$	−16105.9	−	27896.2i	−0.773286	−	1.33937i	−0.935753	−	0.352656i	$-0.885279\pi$
$757$	−16105.9	−	27896.2i	−0.773286	−	1.33937i	0.162468	−	0.986714i	$-0.448055\pi$
$758$	−4137.48	−	7166.32i	−0.198259	−	0.343394i
$759$	1667.87			0.0797628
$760$	3113.21	+	1132.39i	0.148590	+	0.0540475i
$761$	−26848.7			−1.27893			−0.639465	−	0.768820i	$-0.720844\pi$
$761$	−26848.7			−1.27893			−0.639465	+	0.768820i	$0.720844\pi$
$762$	−5197.76	−	9002.78i	−0.247106	−	0.428000i
$763$	8326.48	+	14421.9i	0.395071	+	0.684282i
$764$	5480.29	−	9492.14i	0.259516	−	0.449494i
$765$	1843.47	+	3192.99i	0.0871254	+	0.150906i
$766$	−79.1209	+	137.041i	−0.00373206	+	0.00646411i
$767$	3649.61			0.171812
$768$	−768.000			−0.0360844
$769$	−752.838	+	1303.95i	−0.0353030	+	0.0611467i	−0.883137	−	0.469115i	$-0.844573\pi$
$769$	−752.838	+	1303.95i	−0.0353030	+	0.0611467i	0.847834	+	0.530262i	$0.177906\pi$
$770$	616.893	−	1068.49i	0.0288718	−	0.0500074i
$771$	−13383.5			−0.625154
$772$	−20631.8			−0.961858
$773$	−2065.25	+	3577.12i	−0.0960957	+	0.166443i	−0.910065	−	0.414465i	$-0.863969\pi$
$773$	−2065.25	+	3577.12i	−0.0960957	+	0.166443i	0.813970	+	0.580907i	$0.197302\pi$
$774$	−247.629	−	428.906i	−0.0114998	−	0.0199182i
$775$	−2368.57	+	4102.49i	−0.109783	+	0.190149i
$776$	−2649.40	−	4588.89i	−0.122562	−	0.212283i
$777$	−11650.9	−	20179.9i	−0.537931	−	0.931724i
$778$	−14705.3			−0.677648
$779$	9453.04	+	3438.42i	0.434776	+	0.158144i
$780$	−2760.00			−0.126697
$781$	−383.692	−	664.574i	−0.0175795	−	0.0304486i
$782$	10566.9	+	18302.4i	0.483212	+	0.836947i
$783$	953.918	−	1652.24i	0.0435380	−	0.0754101i
$784$	−3809.48	−	6598.22i	−0.173537	−	0.300575i
$785$	2639.89	−	4572.43i	0.120028	−	0.207894i
$786$	10876.2			0.493564
$787$	−40000.2			−1.81176			−0.905878	−	0.423540i	$-0.860787\pi$
$787$	−40000.2			−1.81176			−0.905878	+	0.423540i	$0.860787\pi$
$788$	6411.80	−	11105.6i	0.289862	−	0.502055i
$789$	8123.02	−	14069.5i	0.366524	−	0.634838i
$790$	9441.39			0.425202
$791$	−19541.2			−0.878387
$792$	−155.186	+	268.789i	−0.00696247	+	0.0120594i
$793$	−11799.2	−	20436.9i	−0.528378	−	0.915177i
$794$	−10982.5	+	19022.2i	−0.490874	+	0.850219i
$795$	−1159.74	−	2008.73i	−0.0517380	−	0.0896129i
$796$	−1639.95	−	2840.48i	−0.0730233	−	0.126480i
$797$	−37984.2			−1.68817			−0.844085	−	0.536210i	$-0.819856\pi$
$797$	−37984.2			−1.68817			−0.844085	+	0.536210i	$0.819856\pi$
$798$	−2472.58	−	14005.8i	−0.109685	−	0.621304i
$799$	3949.43			0.174869
$800$	−400.000	−	692.820i	−0.0176777	−	0.0306186i
$801$	−2678.51	−	4639.32i	−0.118153	−	0.204647i
$802$	−2070.82	+	3586.77i	−0.0911762	+	0.157922i
$803$	1207.80	+	2091.97i	0.0530788	+	0.0919352i
$804$	−5414.91	+	9378.91i	−0.237524	+	0.411404i
$805$	18456.7			0.808091
$806$	−17432.7			−0.761836
$807$	−10839.2	+	18774.1i	−0.472812	+	0.818934i
$808$	3125.84	−	5414.11i	0.136097	−	0.235728i
$809$	−2726.35			−0.118484			−0.0592418	−	0.998244i	$-0.518868\pi$
$809$	−2726.35			−0.118484			−0.0592418	+	0.998244i	$0.518868\pi$
$810$	−810.000			−0.0351364
$811$	−8725.27	+	15112.6i	−0.377787	+	0.654347i	−0.990740	−	0.135773i	$-0.956648\pi$
$811$	−8725.27	+	15112.6i	−0.377787	+	0.654347i	0.612953	+	0.790120i	$0.289982\pi$
$812$	−4044.81	−	7005.82i	−0.174809	−	0.302779i
$813$	−1252.67	+	2169.69i	−0.0540383	+	0.0935971i
$814$	1169.83	+	2026.21i	0.0503718	+	0.0872465i
$815$	8129.34	+	14080.4i	0.349397	+	0.605173i
$816$	−3932.74			−0.168718
$817$	−2141.45	−	778.924i	−0.0917011	−	0.0333551i
$818$	−18126.2			−0.774777
$819$	5924.63	+	10261.8i	0.252776	+	0.437821i
$820$	−1214.57	−	2103.70i	−0.0517252	−	0.0895906i
$821$	7041.11	−	12195.6i	0.299313	−	0.518426i	−0.676666	−	0.736290i	$-0.736576\pi$
$821$	7041.11	−	12195.6i	0.299313	−	0.518426i	0.975979	+	0.217864i	$0.0699090\pi$
$822$	5829.46	+	10096.9i	0.247355	+	0.428431i
$823$	−18673.4	+	32343.3i	−0.790905	+	1.36989i	0.134503	+	0.990913i	$0.457056\pi$
$823$	−18673.4	+	32343.3i	−0.790905	+	1.36989i	−0.925407	+	0.378974i	$0.876277\pi$
$824$	6818.51			0.288269
$825$	−323.303			−0.0136436
$826$	2270.81	−	3933.15i	0.0956555	−	0.165680i
$827$	−2252.06	+	3900.68i	−0.0946939	+	0.164015i	−0.909481	−	0.415746i	$-0.863521\pi$
$827$	−2252.06	+	3900.68i	−0.0946939	+	0.164015i	0.814787	+	0.579761i	$0.196854\pi$
$828$	−4642.97			−0.194872
$829$	34842.9			1.45976			0.729881	−	0.683574i	$-0.239575\pi$
$829$	34842.9			1.45976			0.729881	+	0.683574i	$0.239575\pi$
$830$	537.232	−	930.514i	0.0224670	−	0.0389140i
$831$	−314.787	−	545.228i	−0.0131406	−	0.0227602i
$832$	1472.00	−	2549.58i	0.0613370	−	0.106239i
$833$	−19507.4	−	33787.9i	−0.811396	−	1.40538i
$834$	6023.52	+	10433.0i	0.250093	+	0.433173i
$835$	8205.01			0.340055
$836$	248.266	+	1406.29i	0.0102709	+	0.0581789i
$837$	−5116.11			−0.211277
$838$	1690.59	+	2928.18i	0.0696901	+	0.120707i
$839$	−180.915	−	313.355i	−0.00744445	−	0.0128942i	0.862279	−	0.506433i	$-0.169036\pi$
$839$	−180.915	−	313.355i	−0.00744445	−	0.0128942i	−0.869724	+	0.493539i	$0.835703\pi$
$840$	−1717.29	+	2974.42i	−0.0705381	+	0.122175i
$841$	9698.04	+	16797.5i	0.397640	+	0.688732i
$842$	−15002.4	+	25985.0i	−0.614036	+	1.06354i
$843$	5159.05			0.210779
$844$	−10110.1			−0.412327
$845$	−202.500	+	350.740i	−0.00824404	+	0.0142791i
$846$	−433.833	+	751.420i	−0.0176306	+	0.0305371i
$847$	−37563.3			−1.52384
$848$	2474.11			0.100190
$849$	441.471	−	764.649i	0.0178460	−	0.0309101i
$850$	−2048.30	−	3547.77i	−0.0826544	−	0.143162i
$851$	−17500.0	+	30310.9i	−0.704927	+	1.22097i
$852$	1068.11	+	1850.02i	0.0429493	+	0.0743904i
$853$	−7499.86	−	12990.1i	−0.301044	−	0.521423i	0.675329	−	0.737517i	$-0.264002\pi$
$853$	−7499.86	−	12990.1i	−0.301044	−	0.521423i	−0.976373	+	0.216094i	$0.930668\pi$
$854$	−29366.2			−1.17669
$855$	−2854.45	+	2396.17i	−0.114175	+	0.0958446i
$856$	6343.23			0.253279
$857$	18382.3	+	31839.1i	0.732705	+	1.26908i	0.955723	+	0.294268i	$0.0950758\pi$
$857$	18382.3	+	31839.1i	0.732705	+	1.26908i	−0.223018	+	0.974814i	$0.571591\pi$
$858$	−594.878	−	1030.36i	−0.0236699	−	0.0409975i
$859$	12909.2	−	22359.4i	0.512754	−	0.888116i	−0.487137	−	0.873326i	$-0.661959\pi$
$859$	12909.2	−	22359.4i	0.512754	−	0.888116i	0.999891	−	0.0147901i	$-0.00470802\pi$
$860$	275.143	+	476.562i	0.0109097	+	0.0188961i
$861$	−5214.41	+	9031.62i	−0.206395	+	0.357487i
$862$	27282.8			1.07802
$863$	24106.5			0.950863			0.475431	−	0.879753i	$-0.342292\pi$
$863$	24106.5			0.950863			0.475431	+	0.879753i	$0.342292\pi$
$864$	432.000	−	748.246i	0.0170103	−	0.0294628i
$865$	−9487.74	+	16433.3i	−0.372940	+	0.645951i
$866$	−21662.9			−0.850039
$867$	−5399.62			−0.211512
$868$	−10846.7	+	18787.0i	−0.424148	+	0.734647i
$869$	2034.95	+	3524.64i	0.0794374	+	0.137590i
$870$	−1059.91	+	1835.82i	−0.0413038	+	0.0715403i
$871$	−20757.2	−	35952.5i	−0.807497	−	1.39863i
$872$	2327.34	+	4031.08i	0.0903827	+	0.156548i
$873$	5961.15			0.231105
$874$	−16361.9	+	13735.0i	−0.633236	+	0.531570i
$875$	−3577.68			−0.138226
$876$	−3362.23	−	5823.55i	−0.129679	−	0.224611i
$877$	21466.0	+	37180.2i	0.826517	+	1.43157i	0.900754	+	0.434329i	$0.143014\pi$
$877$	21466.0	+	37180.2i	0.826517	+	1.43157i	−0.0742374	+	0.997241i	$0.523652\pi$
$878$	−12693.9	+	21986.5i	−0.487926	+	0.845113i
$879$	9685.53	+	16775.8i	0.371655	+	0.643725i
$880$	172.428	−	298.655i	0.00660518	−	0.0114405i
$881$	24231.9			0.926667			0.463334	−	0.886184i	$-0.346653\pi$
$881$	24231.9			0.926667			0.463334	+	0.886184i	$0.346653\pi$
$882$	8571.34			0.327224
$883$	2388.34	−	4136.72i	0.0910237	−	0.157658i	−0.816918	−	0.576753i	$-0.804319\pi$
$883$	2388.34	−	4136.72i	0.0910237	−	0.157658i	0.907942	+	0.419095i	$0.137653\pi$
$884$	7537.76	−	13055.8i	0.286790	−	0.496734i
$885$	−1190.09			−0.0452028
$886$	5803.27			0.220050
$887$	12767.7	−	22114.3i	0.483311	−	0.837120i	−0.516505	−	0.856284i	$-0.672767\pi$
$887$	12767.7	−	22114.3i	0.483311	−	0.837120i	0.999816	+	0.0191644i	$0.00610058\pi$
$888$	−3256.54	−	5640.50i	−0.123066	−	0.213156i
$889$	24794.5	−	42945.4i	0.935412	−	1.62018i
$890$	2976.12	+	5154.80i	0.112090	+	0.194145i
$891$	−174.584	−	302.388i	−0.00656428	−	0.0113697i
$892$	−7803.45			−0.292914
$893$	694.045	+	3931.39i	0.0260082	+	0.147322i
$894$	−13802.0			−0.516341
$895$	−4170.17	−	7222.94i	−0.155747	−	0.269761i
$896$	−1831.77	−	3172.72i	−0.0682982	−	0.118296i
$897$	8899.02	−	15413.6i	0.331248	−	0.573739i
$898$	50.5038	+	87.4751i	0.00187676	+	0.00325065i
$899$	−6694.59	+	11595.4i	−0.248362	+	0.430175i
$900$	900.000			0.0333333
$901$	12669.3			0.468453
$902$	523.566	−	906.842i	0.0193269	−	0.0334751i
$903$	1181.25	−	2045.98i	0.0435321	−	0.0753998i
$904$	−5461.97			−0.200954
$905$	5769.66			0.211923
$906$	1912.52	−	3312.58i	0.0701316	−	0.121471i
$907$	8162.61	+	14138.1i	0.298826	+	0.517582i	0.975868	−	0.218363i	$-0.0700717\pi$
$907$	8162.61	+	14138.1i	0.298826	+	0.517582i	−0.677042	+	0.735945i	$0.736738\pi$
$908$	7258.73	−	12572.5i	0.265297	−	0.459507i
$909$	3516.57	+	6090.88i	0.128314	+	0.222246i
$910$	−6582.93	−	11402.0i	−0.239804	−	0.415353i
$911$	8345.82			0.303523			0.151761	−	0.988417i	$-0.451505\pi$
$911$	8345.82			0.303523			0.151761	+	0.988417i	$0.451505\pi$
$912$	−691.113	−	3914.78i	−0.0250932	−	0.142140i
$913$	463.170			0.0167894
$914$	10840.4	+	18776.0i	0.392305	+	0.679493i
$915$	3847.58	+	6664.20i	0.139013	+	0.240778i
$916$	290.700	−	503.507i	0.0104858	−	0.0181619i
$917$	25941.0	+	44931.2i	0.934185	+	1.61806i
$918$	2212.17	−	3831.59i	0.0795342	−	0.137757i
$919$	−43563.2			−1.56367			−0.781837	−	0.623483i	$-0.785717\pi$
$919$	−43563.2			−1.56367			−0.781837	+	0.623483i	$0.785717\pi$
$920$	5158.85			0.184872
$921$	−5780.87	+	10012.8i	−0.206825	+	0.358232i
$922$	−3609.33	+	6251.54i	−0.128923	+	0.223301i
$923$	−8188.83			−0.292025
$924$	−1480.54			−0.0527124
$925$	3392.23	−	5875.52i	0.120579	−	0.208850i
$926$	−9096.20	−	15755.1i	−0.322808	−	0.559119i
$927$	−3835.41	+	6643.13i	−0.135892	+	0.235371i
$928$	−1130.57	−	1958.20i	−0.0399922	−	0.0692686i
$929$	−13485.0	−	23356.7i	−0.476241	−	0.824874i	0.523388	−	0.852094i	$-0.324668\pi$
$929$	−13485.0	−	23356.7i	−0.476241	−	0.824874i	−0.999629	+	0.0272201i	$0.991335\pi$
$930$	5684.57			0.200435
$931$	30205.5	−	25356.0i	1.06331	−	0.892599i
$932$	16747.5			0.588609
$933$	−12538.1	−	21716.6i	−0.439955	−	0.762025i
$934$	−1927.45	−	3338.44i	−0.0675247	−	0.116956i
$935$	882.964	−	1529.34i	0.0308834	−	0.0534917i
$936$	1656.00	+	2868.28i	0.0578291	+	0.100163i
$937$	1035.57	−	1793.67i	0.0361054	−	0.0625364i	−0.847408	−	0.530942i	$-0.821838\pi$
$937$	1035.57	−	1793.67i	0.0361054	−	0.0625364i	0.883513	+	0.468406i	$0.155171\pi$
$938$	−51660.8			−1.79828
$939$	−11552.1			−0.401478
$940$	482.036	−	834.911i	0.0167258	−	0.0289700i
$941$	11248.2	−	19482.4i	0.389670	−	0.674928i	−0.602735	−	0.797941i	$-0.705922\pi$
$941$	11248.2	−	19482.4i	0.389670	−	0.674928i	0.992405	+	0.123013i	$0.0392558\pi$
$942$	−6335.75			−0.219140
$943$	15664.5			0.540939
$944$	634.715	−	1099.36i	0.0218837	−	0.0379037i
$945$	−1931.95	−	3346.23i	−0.0665039	−	0.115188i
$946$	−118.606	+	205.432i	−0.00407634	+	0.00706044i
$947$	13834.8	+	23962.6i	0.474732	+	0.822261i	0.999581	−	0.0289347i	$-0.00921150\pi$
$947$	13834.8	+	23962.6i	0.474732	+	0.822261i	−0.524849	+	0.851195i	$0.675878\pi$
$948$	−5664.83	−	9811.78i	−0.194077	−	0.336152i
$949$	25777.1			0.881727
$950$	3171.61	−	2662.41i	0.108316	−	0.0909262i
$951$	23356.2			0.796402
$952$	−9380.05	−	16246.7i	−0.319337	−	0.553109i
$953$	−12059.6	−	20887.8i	−0.409914	−	0.709991i	0.584966	−	0.811058i	$-0.301108\pi$
$953$	−12059.6	−	20887.8i	−0.409914	−	0.709991i	−0.994880	+	0.101067i	$0.967775\pi$
$954$	−1391.69	+	2410.47i	−0.0472301	+	0.0818050i
$955$	−6850.36	−	11865.2i	−0.232118	−	0.402040i
$956$	10940.4	−	18949.3i	0.370123	−	0.641073i
$957$	−913.792			−0.0308659
$958$	−37397.1			−1.26122
$959$	−27807.9	+	48164.7i	−0.936355	+	1.62181i
$960$	−480.000	+	831.384i	−0.0161374	+	0.0279508i
$961$	6113.82			0.205224
$962$	24966.8			0.836760
$963$	−3568.07	+	6180.07i	−0.119397	+	0.206802i
$964$	−11621.0	−	20128.2i	−0.388265	−	0.672495i
$965$	−12894.9	+	22334.6i	−0.430156	+	0.745052i
$966$	−11074.0	−	19180.8i	−0.368842	−	0.638852i
$967$	−24174.6	−	41871.6i	−0.803931	−	1.39245i	−0.917010	−	0.398864i	$-0.869405\pi$
$967$	−24174.6	−	41871.6i	−0.803931	−	1.39245i	0.113079	−	0.993586i	$-0.463929\pi$
$968$	−10499.3			−0.348617
$969$	−3539.02	−	20046.6i	−0.117327	−	0.664593i
$970$	−6623.50			−0.219245
$971$	18108.4	+	31364.7i	0.598484	+	1.03660i	0.993045	+	0.117735i	$0.0375632\pi$
$971$	18108.4	+	31364.7i	0.598484	+	1.03660i	−0.394561	+	0.918870i	$0.629103\pi$
$972$	486.000	+	841.777i	0.0160375	+	0.0277778i
$973$	−28733.6	+	49768.0i	−0.946718	+	1.63976i
$974$	−9370.36	−	16229.9i	−0.308260	−	0.533923i
$975$	−1725.00	+	2987.79i	−0.0566607	+	0.0981393i
$976$	−8208.17			−0.269198
$977$	6145.65			0.201245			0.100623	−	0.994925i	$-0.467917\pi$
$977$	6145.65			0.201245			0.100623	+	0.994925i	$0.467917\pi$
$978$	9755.20	−	16896.5i	0.318954	−	0.552445i
$979$	−1282.92	+	2222.08i	−0.0418818	+	0.0725414i
$980$	−9523.71			−0.310432
$981$	−5236.52			−0.170427
$982$	−17603.7	+	30490.6i	−0.572055	+	0.990828i
$983$	13123.1	+	22729.9i	0.425801	+	0.737510i	0.996495	−	0.0836535i	$-0.0266589\pi$
$983$	13123.1	+	22729.9i	0.425801	+	0.737510i	−0.570693	+	0.821163i	$0.693326\pi$
$984$	−1457.48	+	2524.44i	−0.0472184	+	0.0817846i
$985$	−8014.75	−	13882.0i	−0.259260	−	0.449052i
$986$	−5789.38	−	10027.5i	−0.186989	−	0.323875i
$987$	−4138.97			−0.133480
$988$	14320.8	+	5209.00i	0.461138	+	0.167733i
$989$	−3548.56			−0.114093
$990$	193.982	+	335.986i	0.00622742	+	0.0107862i
$991$	16444.3	+	28482.4i	0.527116	+	0.912991i	0.999501	+	0.0315988i	$0.0100599\pi$
$991$	16444.3	+	28482.4i	0.527116	+	0.912991i	−0.472385	+	0.881392i	$0.656607\pi$
$992$	−3031.77	+	5251.18i	−0.0970351	+	0.168070i
$993$	−5356.04	−	9276.94i	−0.171167	−	0.296470i
$994$	−5095.13	+	8825.03i	−0.162583	+	0.281602i
$995$	−4099.88			−0.130628
$996$	−1289.36			−0.0410189
$997$	7911.13	−	13702.5i	0.251302	−	0.435268i	−0.712583	−	0.701588i	$-0.752475\pi$
$997$	7911.13	−	13702.5i	0.251302	−	0.435268i	0.963885	+	0.266320i	$0.0858079\pi$
$998$	−18322.0	+	31734.7i	−0.581136	+	1.00656i
$999$	7327.22			0.232055

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.4.i.h.121.2	✓	4
19.11	even	3	inner	570.4.i.h.391.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.4.i.h.121.2	✓	4	1.1	even	1	trivial
570.4.i.h.391.2	yes	4	19.11	even	3	inner

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	570.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} +(3.00000 - 5.19615i) q^{6} +28.6214 q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} +(3.00000 - 5.19615i) q^{6} +28.6214 q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(5.00000 - 8.66025i) q^{10} +4.31071 q^{11} -12.0000 q^{12} +(23.0000 - 39.8372i) q^{13} +(-28.6214 - 49.5737i) q^{14} +(-7.50000 + 12.9904i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-40.9661 - 70.9553i) q^{17} +18.0000 q^{18} +(63.4321 - 53.2482i) q^{19} -20.0000 q^{20} +(42.9321 + 74.3606i) q^{21} +(-4.31071 - 7.46637i) q^{22} +(64.4857 - 111.692i) q^{23} +(12.0000 + 20.7846i) q^{24} +(-12.5000 + 21.6506i) q^{25} -92.0000 q^{26} -27.0000 q^{27} +(-57.2428 + 99.1475i) q^{28} +(-35.3303 + 61.1939i) q^{29} +30.0000 q^{30} +189.486 q^{31} +(-16.0000 + 27.7128i) q^{32} +(6.46606 + 11.1995i) q^{33} +(-81.9321 + 141.911i) q^{34} +(71.5535 + 123.934i) q^{35} +(-18.0000 - 31.1769i) q^{36} -271.379 q^{37} +(-155.661 - 56.6195i) q^{38} +138.000 q^{39} +(20.0000 + 34.6410i) q^{40} +(60.7285 + 105.185i) q^{41} +(85.8643 - 148.721i) q^{42} +(-13.7572 - 23.8281i) q^{43} +(-8.62142 + 14.9327i) q^{44} -45.0000 q^{45} -257.943 q^{46} +(-24.1018 + 41.7456i) q^{47} +(24.0000 - 41.5692i) q^{48} +476.186 q^{49} +50.0000 q^{50} +(122.898 - 212.866i) q^{51} +(92.0000 + 159.349i) q^{52} +(-77.3160 + 133.915i) q^{53} +(27.0000 + 46.7654i) q^{54} +(10.7768 + 18.6659i) q^{55} +228.971 q^{56} +(233.491 + 84.9293i) q^{57} +141.321 q^{58} +(39.6697 + 68.7099i) q^{59} +(-30.0000 - 51.9615i) q^{60} +(256.505 - 444.280i) q^{61} +(-189.486 - 328.199i) q^{62} +(-128.796 + 223.082i) q^{63} +64.0000 q^{64} +230.000 q^{65} +(12.9321 - 22.3991i) q^{66} +(451.243 - 781.576i) q^{67} +327.729 q^{68} +386.914 q^{69} +(143.107 - 247.869i) q^{70} +(-89.0091 - 154.168i) q^{71} +(-36.0000 + 62.3538i) q^{72} +(280.186 + 485.296i) q^{73} +(271.379 + 470.041i) q^{74} -75.0000 q^{75} +(57.5928 + 326.232i) q^{76} +123.379 q^{77} +(-138.000 - 239.023i) q^{78} +(472.069 + 817.648i) q^{79} +(40.0000 - 69.2820i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(121.457 - 210.370i) q^{82} +107.446 q^{83} -343.457 q^{84} +(204.830 - 354.777i) q^{85} +(-27.5143 + 47.6562i) q^{86} -211.982 q^{87} +34.4857 q^{88} +(-297.612 + 515.480i) q^{89} +(45.0000 + 77.9423i) q^{90} +(658.293 - 1140.20i) q^{91} +(257.943 + 446.770i) q^{92} +(284.229 + 492.298i) q^{93} +96.4072 q^{94} +(389.152 + 141.549i) q^{95} -96.0000 q^{96} +(-331.175 - 573.612i) q^{97} +(-476.186 - 824.777i) q^{98} +(-19.3982 + 33.5986i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} + 10 q^{5} + 12 q^{6} + 36 q^{7} + 32 q^{8} - 18 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 6 * q^3 - 8 * q^4 + 10 * q^5 + 12 * q^6 + 36 * q^7 + 32 * q^8 - 18 * q^9	\( 4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} + 10 q^{5} + 12 q^{6} + 36 q^{7} + 32 q^{8} - 18 q^{9} + 20 q^{10} - 22 q^{11} - 48 q^{12} + 92 q^{13} - 36 q^{14} - 30 q^{15} - 32 q^{16} - 105 q^{17} + 72 q^{18} + 136 q^{19} - 80 q^{20} + 54 q^{21} + 22 q^{22} - 56 q^{23} + 48 q^{24} - 50 q^{25} - 368 q^{26} - 108 q^{27} - 72 q^{28} + 153 q^{29} + 120 q^{30} + 444 q^{31} - 64 q^{32} - 33 q^{33} - 210 q^{34} + 90 q^{35} - 72 q^{36} - 1164 q^{37} - 34 q^{38} + 552 q^{39} + 80 q^{40} - 228 q^{41} + 108 q^{42} - 212 q^{43} + 44 q^{44} - 180 q^{45} + 224 q^{46} - 273 q^{47} + 96 q^{48} + 492 q^{49} + 200 q^{50} + 315 q^{51} + 368 q^{52} + 299 q^{53} + 108 q^{54} - 55 q^{55} + 288 q^{56} + 51 q^{57} - 612 q^{58} + 453 q^{59} - 120 q^{60} + 457 q^{61} - 444 q^{62} - 162 q^{63} + 256 q^{64} + 920 q^{65} - 66 q^{66} + 1648 q^{67} + 840 q^{68} - 336 q^{69} + 180 q^{70} - 1239 q^{71} - 144 q^{72} - 292 q^{73} + 1164 q^{74} - 300 q^{75} - 476 q^{76} + 572 q^{77} - 552 q^{78} - 15 q^{79} + 160 q^{80} - 162 q^{81} - 456 q^{82} + 626 q^{83} - 432 q^{84} + 525 q^{85} - 424 q^{86} + 918 q^{87} - 176 q^{88} - 229 q^{89} + 180 q^{90} + 828 q^{91} - 224 q^{92} + 666 q^{93} + 1092 q^{94} + 85 q^{95} - 384 q^{96} - 1050 q^{97} - 492 q^{98} + 99 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 6 * q^3 - 8 * q^4 + 10 * q^5 + 12 * q^6 + 36 * q^7 + 32 * q^8 - 18 * q^9 + 20 * q^10 - 22 * q^11 - 48 * q^12 + 92 * q^13 - 36 * q^14 - 30 * q^15 - 32 * q^16 - 105 * q^17 + 72 * q^18 + 136 * q^19 - 80 * q^20 + 54 * q^21 + 22 * q^22 - 56 * q^23 + 48 * q^24 - 50 * q^25 - 368 * q^26 - 108 * q^27 - 72 * q^28 + 153 * q^29 + 120 * q^30 + 444 * q^31 - 64 * q^32 - 33 * q^33 - 210 * q^34 + 90 * q^35 - 72 * q^36 - 1164 * q^37 - 34 * q^38 + 552 * q^39 + 80 * q^40 - 228 * q^41 + 108 * q^42 - 212 * q^43 + 44 * q^44 - 180 * q^45 + 224 * q^46 - 273 * q^47 + 96 * q^48 + 492 * q^49 + 200 * q^50 + 315 * q^51 + 368 * q^52 + 299 * q^53 + 108 * q^54 - 55 * q^55 + 288 * q^56 + 51 * q^57 - 612 * q^58 + 453 * q^59 - 120 * q^60 + 457 * q^61 - 444 * q^62 - 162 * q^63 + 256 * q^64 + 920 * q^65 - 66 * q^66 + 1648 * q^67 + 840 * q^68 - 336 * q^69 + 180 * q^70 - 1239 * q^71 - 144 * q^72 - 292 * q^73 + 1164 * q^74 - 300 * q^75 - 476 * q^76 + 572 * q^77 - 552 * q^78 - 15 * q^79 + 160 * q^80 - 162 * q^81 - 456 * q^82 + 626 * q^83 - 432 * q^84 + 525 * q^85 - 424 * q^86 + 918 * q^87 - 176 * q^88 - 229 * q^89 + 180 * q^90 + 828 * q^91 - 224 * q^92 + 666 * q^93 + 1092 * q^94 + 85 * q^95 - 384 * q^96 - 1050 * q^97 - 492 * q^98 + 99 * q^99

Introduction

L-functions

Modular forms

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