LMFDB - Embedded newform 182.4.g.a.113.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [182,4,Mod(29,182)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("182.29"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(182, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 182 = 2 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	182.g (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.7383476210$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 34x^{6} + 57x^{5} + 915x^{4} + 720x^{3} + 5490x^{2} - 1944x + 26244 $ x^8 - x^7 + 34x^6 + 57x^5 + 915x^4 + 720x^3 + 5490x^2 - 1944x + 26244
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			113.3
Root			$-1.60142 + 2.77373i$ of defining polynomial
Character	$\chi$	$=$	182.113
Dual form			182.4.g.a.29.3

$q$-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} +(2.60142 - 4.50578i) q^{3} +(-2.00000 - 3.46410i) q^{4} +17.5606 q^{5} +(5.20283 + 9.01157i) q^{6} +(3.50000 + 6.06218i) q^{7} +8.00000 q^{8} +(-0.0347256 - 0.0601466i) q^{9} +(-17.5606 + 30.4158i) q^{10} +(17.7770 - 30.7907i) q^{11} -20.8113 q^{12} +(-13.4505 + 44.9008i) q^{13} -14.0000 q^{14} +(45.6823 - 79.1241i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(9.71858 + 16.8331i) q^{17} +0.138903 q^{18} +(-36.3425 - 62.9471i) q^{19} +(-35.1211 - 60.8316i) q^{20} +36.4198 q^{21} +(35.5540 + 61.5814i) q^{22} +(27.6808 - 47.9445i) q^{23} +(20.8113 - 36.0463i) q^{24} +183.374 q^{25} +(-64.3200 - 68.1978i) q^{26} +140.115 q^{27} +(14.0000 - 24.2487i) q^{28} +(62.5178 - 108.284i) q^{29} +(91.3647 + 158.248i) q^{30} +71.0166 q^{31} +(-16.0000 - 27.7128i) q^{32} +(-92.4908 - 160.199i) q^{33} -38.8743 q^{34} +(61.4620 + 106.455i) q^{35} +(-0.138903 + 0.240586i) q^{36} +(-176.179 + 305.151i) q^{37} +145.370 q^{38} +(167.323 + 177.411i) q^{39} +140.485 q^{40} +(120.262 - 208.299i) q^{41} +(-36.4198 + 63.0810i) q^{42} +(122.466 + 212.117i) q^{43} -142.216 q^{44} +(-0.609802 - 1.05621i) q^{45} +(55.3616 + 95.8891i) q^{46} -237.059 q^{47} +(41.6226 + 72.0925i) q^{48} +(-24.5000 + 42.4352i) q^{49} +(-183.374 + 317.613i) q^{50} +101.128 q^{51} +(182.442 - 43.2078i) q^{52} -152.742 q^{53} +(-140.115 + 242.686i) q^{54} +(312.175 - 540.702i) q^{55} +(28.0000 + 48.4974i) q^{56} -378.168 q^{57} +(125.036 + 216.568i) q^{58} +(-12.2980 - 21.3008i) q^{59} -365.459 q^{60} +(-357.336 - 618.923i) q^{61} +(-71.0166 + 123.004i) q^{62} +(0.243080 - 0.421026i) q^{63} +64.0000 q^{64} +(-236.198 + 788.484i) q^{65} +369.963 q^{66} +(480.333 - 831.960i) q^{67} +(38.8743 - 67.3323i) q^{68} +(-144.018 - 249.447i) q^{69} -245.848 q^{70} +(229.188 + 396.965i) q^{71} +(-0.277805 - 0.481173i) q^{72} -100.872 q^{73} +(-352.358 - 610.302i) q^{74} +(477.031 - 826.242i) q^{75} +(-145.370 + 251.788i) q^{76} +248.878 q^{77} +(-474.607 + 112.401i) q^{78} -1145.74 q^{79} +(-140.485 + 243.326i) q^{80} +(365.435 - 632.952i) q^{81} +(240.523 + 416.599i) q^{82} -861.573 q^{83} +(-72.8396 - 126.162i) q^{84} +(170.664 + 295.598i) q^{85} -489.863 q^{86} +(-325.270 - 563.383i) q^{87} +(142.216 - 246.326i) q^{88} +(-528.592 + 915.549i) q^{89} +2.43921 q^{90} +(-319.274 + 75.6136i) q^{91} -221.446 q^{92} +(184.744 - 319.985i) q^{93} +(237.059 - 410.599i) q^{94} +(-638.196 - 1105.39i) q^{95} -166.491 q^{96} +(451.789 + 782.521i) q^{97} +(-49.0000 - 84.8705i) q^{98} -2.46927 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 7 q^{3} - 16 q^{4} - 2 q^{5} + 14 q^{6} + 28 q^{7} + 64 q^{8} + 29 q^{9} + 2 q^{10} + 15 q^{11} - 56 q^{12} + 64 q^{13} - 112 q^{14} - 67 q^{15} - 64 q^{16} + 24 q^{17} - 116 q^{18} - 21 q^{19}+ \cdots - 258 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 + 7 * q^3 - 16 * q^4 - 2 * q^5 + 14 * q^6 + 28 * q^7 + 64 * q^8 + 29 * q^9 + 2 * q^10 + 15 * q^11 - 56 * q^12 + 64 * q^13 - 112 * q^14 - 67 * q^15 - 64 * q^16 + 24 * q^17 - 116 * q^18 - 21 * q^19 + 4 * q^20 + 98 * q^21 + 30 * q^22 + 182 * q^23 + 56 * q^24 + 730 * q^25 - 136 * q^26 + 184 * q^27 + 112 * q^28 - 133 * q^29 - 134 * q^30 - 564 * q^31 - 128 * q^32 - 95 * q^33 - 96 * q^34 - 7 * q^35 + 116 * q^36 - 730 * q^37 + 84 * q^38 + 792 * q^39 - 16 * q^40 + 182 * q^41 - 98 * q^42 - 83 * q^43 - 120 * q^44 + 73 * q^45 + 364 * q^46 - 1120 * q^47 + 112 * q^48 - 196 * q^49 - 730 * q^50 + 418 * q^51 + 16 * q^52 - 212 * q^53 - 184 * q^54 + 997 * q^55 + 224 * q^56 - 682 * q^57 - 266 * q^58 + 782 * q^59 + 536 * q^60 + 708 * q^61 + 564 * q^62 - 203 * q^63 + 512 * q^64 - 801 * q^65 + 380 * q^66 + 528 * q^67 + 96 * q^68 - 1198 * q^69 + 28 * q^70 + 82 * q^71 + 232 * q^72 + 1120 * q^73 - 1460 * q^74 + 2873 * q^75 - 84 * q^76 + 210 * q^77 - 1566 * q^78 - 3996 * q^79 + 16 * q^80 + 1220 * q^81 + 364 * q^82 - 716 * q^83 - 196 * q^84 + 547 * q^85 + 332 * q^86 + 245 * q^87 + 120 * q^88 - 2385 * q^89 - 292 * q^90 - 28 * q^91 - 1456 * q^92 + 1963 * q^93 + 1120 * q^94 - 1117 * q^95 - 448 * q^96 + 1155 * q^97 - 392 * q^98 - 258 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/182\mathbb{Z}\right)^\times$.

$n$	$15$	$157$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$3$	2.60142	−	4.50578i	0.500643	−	0.867139i	−0.499357	−	0.866396i	$-0.666430\pi$
$3$	2.60142	−	4.50578i	0.500643	−	0.867139i	1.00000		0.000742233i	$-0.000236260\pi$
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	17.5606			1.57067			0.785333	−	0.619074i	$-0.212492\pi$
$5$	17.5606			1.57067			0.785333	+	0.619074i	$0.212492\pi$
$6$	5.20283	+	9.01157i	0.354008	+	0.613160i
$7$	3.50000	+	6.06218i	0.188982	+	0.327327i
$7$	3.50000	+	6.06218i	0.188982	+	0.327327i
$8$	8.00000			0.353553
$9$	−0.0347256	−	0.0601466i	−0.00128614	−	0.00222765i
$10$	−17.5606	+	30.4158i	−0.555314	+	0.961832i
$11$	17.7770	−	30.7907i	0.487270	−	0.843977i	−0.512623	−	0.858614i	$-0.671326\pi$
$11$	17.7770	−	30.7907i	0.487270	−	0.843977i	0.999893	+	0.0146372i	$0.00465934\pi$
$12$	−20.8113			−0.500643
$13$	−13.4505	+	44.9008i	−0.286961	+	0.957942i
$13$	−13.4505	+	44.9008i	−0.286961	+	0.957942i
$14$	−14.0000			−0.267261
$15$	45.6823	−	79.1241i	0.786342	−	1.36198i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	9.71858	+	16.8331i	0.138653	+	0.240154i	0.926987	−	0.375093i	$-0.122389\pi$
$17$	9.71858	+	16.8331i	0.138653	+	0.240154i	−0.788334	+	0.615248i	$0.789056\pi$
$18$	0.138903			0.00181887
$19$	−36.3425	−	62.9471i	−0.438818	−	0.760056i	0.558780	−	0.829316i	$-0.311270\pi$
$19$	−36.3425	−	62.9471i	−0.438818	−	0.760056i	−0.997599	+	0.0692600i	$0.977936\pi$
$20$	−35.1211	−	60.8316i	−0.392666	−	0.680118i
$21$	36.4198			0.378450
$22$	35.5540	+	61.5814i	0.344552	+	0.596782i
$23$	27.6808	−	47.9445i	0.250950	−	0.434658i	−0.712838	−	0.701329i	$-0.752590\pi$
$23$	27.6808	−	47.9445i	0.250950	−	0.434658i	0.963788	+	0.266671i	$0.0859238\pi$
$24$	20.8113	−	36.0463i	0.177004	−	0.306580i
$25$	183.374			1.46699
$26$	−64.3200	−	68.1978i	−0.485161	−	0.514411i
$27$	140.115			0.998710
$28$	14.0000	−	24.2487i	0.0944911	−	0.163663i
$29$	62.5178	−	108.284i	0.400319	−	0.693374i	−0.593445	−	0.804875i	$-0.702232\pi$
$29$	62.5178	−	108.284i	0.400319	−	0.693374i	0.993764	+	0.111501i	$0.0355658\pi$
$30$	91.3647	+	158.248i	0.556028	+	0.963068i
$31$	71.0166			0.411450			0.205725	−	0.978610i	$-0.434045\pi$
$31$	71.0166			0.411450			0.205725	+	0.978610i	$0.434045\pi$
$32$	−16.0000	−	27.7128i	−0.0883883	−	0.153093i
$33$	−92.4908	−	160.199i	−0.487897	−	0.845062i
$34$	−38.8743			−0.196085
$35$	61.4620	+	106.455i	0.296828	+	0.514121i
$36$	−0.138903	+	0.240586i	−0.000643068	+	0.00111383i
$37$	−176.179	+	305.151i	−0.782801	+	1.35585i	0.147503	+	0.989062i	$0.452876\pi$
$37$	−176.179	+	305.151i	−0.782801	+	1.35585i	−0.930304	+	0.366790i	$0.880457\pi$
$38$	145.370			0.620583
$39$	167.323	+	177.411i	0.687004	+	0.728422i
$40$	140.485			0.555314
$41$	120.262	−	208.299i	0.458091	−	0.793436i	−0.540769	−	0.841171i	$-0.681867\pi$
$41$	120.262	−	208.299i	0.458091	−	0.793436i	0.998860	+	0.0477347i	$0.0152002\pi$
$42$	−36.4198	+	63.0810i	−0.133802	+	0.231753i
$43$	122.466	+	212.117i	0.434322	+	0.752269i	0.997240	−	0.0742444i	$-0.0236545\pi$
$43$	122.466	+	212.117i	0.434322	+	0.752269i	−0.562918	+	0.826513i	$0.690321\pi$
$44$	−142.216			−0.487270
$45$	−0.609802	−	1.05621i	−0.00202009	−	0.00349889i
$46$	55.3616	+	95.8891i	0.177448	+	0.307349i
$47$	−237.059			−0.735716			−0.367858	−	0.929882i	$-0.619909\pi$
$47$	−237.059			−0.735716			−0.367858	+	0.929882i	$0.619909\pi$
$48$	41.6226	+	72.0925i	0.125161	+	0.216785i
$49$	−24.5000	+	42.4352i	−0.0714286	+	0.123718i
$50$	−183.374	+	317.613i	−0.518659	+	0.898344i
$51$	101.128			0.277662
$52$	182.442	−	43.2078i	0.486541	−	0.115228i
$53$	−152.742			−0.395863			−0.197932	−	0.980216i	$-0.563422\pi$
$53$	−152.742			−0.395863			−0.197932	+	0.980216i	$0.563422\pi$
$54$	−140.115	+	242.686i	−0.353097	+	0.611582i
$55$	312.175	−	540.702i	0.765338	−	1.32561i
$56$	28.0000	+	48.4974i	0.0668153	+	0.115728i
$57$	−378.168			−0.878765
$58$	125.036	+	216.568i	0.283069	+	0.490289i
$59$	−12.2980	−	21.3008i	−0.0271367	−	0.0470021i	0.852138	−	0.523317i	$-0.175306\pi$
$59$	−12.2980	−	21.3008i	−0.0271367	−	0.0470021i	−0.879275	+	0.476315i	$0.841972\pi$
$60$	−365.459			−0.786342
$61$	−357.336	−	618.923i	−0.750035	−	1.29910i	−0.947805	−	0.318850i	$-0.896703\pi$
$61$	−357.336	−	618.923i	−0.750035	−	1.29910i	0.197770	−	0.980248i	$-0.436630\pi$
$62$	−71.0166	+	123.004i	−0.145470	+	0.251961i
$63$	0.243080	−	0.421026i	0.000486113	−	0.000841973i
$64$	64.0000			0.125000
$65$	−236.198	+	788.484i	−0.450720	+	1.50461i
$66$	369.963			0.689990
$67$	480.333	−	831.960i	0.875850	−	1.51702i	0.0199959	−	0.999800i	$-0.493635\pi$
$67$	480.333	−	831.960i	0.875850	−	1.51702i	0.855854	−	0.517217i	$-0.173032\pi$
$68$	38.8743	−	67.3323i	0.0693265	−	0.120077i
$69$	−144.018	−	249.447i	−0.251272	−	0.435216i
$70$	−245.848			−0.419778
$71$	229.188	+	396.965i	0.383093	+	0.663536i	0.991503	−	0.130087i	$-0.0415256\pi$
$71$	229.188	+	396.965i	0.383093	+	0.663536i	−0.608410	+	0.793623i	$0.708192\pi$
$72$	−0.277805	−	0.481173i	−0.000454717	−	0.000787594i
$73$	−100.872			−0.161729			−0.0808645	−	0.996725i	$-0.525768\pi$
$73$	−100.872			−0.161729			−0.0808645	+	0.996725i	$0.525768\pi$
$74$	−352.358	−	610.302i	−0.553524	−	0.958732i
$75$	477.031	−	826.242i	0.734438	−	1.27208i
$76$	−145.370	+	251.788i	−0.219409	+	0.380028i
$77$	248.878			0.368342
$78$	−474.607	+	112.401i	−0.688958	+	0.163166i
$79$	−1145.74			−1.63172			−0.815862	−	0.578246i	$-0.803737\pi$
$79$	−1145.74			−1.63172			−0.815862	+	0.578246i	$0.803737\pi$
$80$	−140.485	+	243.326i	−0.196333	+	0.340059i
$81$	365.435	−	632.952i	0.501283	−	0.868247i
$82$	240.523	+	416.599i	0.323919	+	0.561044i
$83$	−861.573			−1.13940			−0.569698	−	0.821854i	$-0.692940\pi$
$83$	−861.573			−1.13940			−0.569698	+	0.821854i	$0.692940\pi$
$84$	−72.8396	−	126.162i	−0.0946126	−	0.163874i
$85$	170.664	+	295.598i	0.217778	+	0.377202i
$86$	−489.863			−0.614225
$87$	−325.270	−	563.383i	−0.400834	−	0.694265i
$88$	142.216	−	246.326i	0.172276	−	0.298391i
$89$	−528.592	+	915.549i	−0.629558	+	1.09043i	0.358082	+	0.933690i	$0.383431\pi$
$89$	−528.592	+	915.549i	−0.629558	+	1.09043i	−0.987640	+	0.156737i	$0.949903\pi$
$90$	2.43921			0.00285684
$91$	−319.274	+	75.6136i	−0.367791	+	0.0871040i
$92$	−221.446			−0.250950
$93$	184.744	−	319.985i	0.205989	−	0.356784i
$94$	237.059	−	410.599i	0.260115	−	0.450533i
$95$	−638.196	−	1105.39i	−0.689237	−	1.19379i
$96$	−166.491			−0.177004
$97$	451.789	+	782.521i	0.472909	+	0.819103i	0.999519	−	0.0310042i	$-0.00987052\pi$
$97$	451.789	+	782.521i	0.472909	+	0.819103i	−0.526610	+	0.850107i	$0.676537\pi$
$98$	−49.0000	−	84.8705i	−0.0505076	−	0.0874818i
$99$	−2.46927			−0.00250678
$100$	−366.747	−	635.225i	−0.366747	−	0.635225i
$101$	−464.420	+	804.398i	−0.457539	+	0.792481i	−0.998830	−	0.0483540i	$-0.984602\pi$
$101$	−464.420	+	804.398i	−0.457539	+	0.792481i	0.541291	+	0.840835i	$0.317936\pi$
$102$	−101.128	+	175.159i	−0.0981685	+	0.170033i
$103$	−386.662			−0.369893			−0.184946	−	0.982749i	$-0.559211\pi$
$103$	−386.662			−0.369893			−0.184946	+	0.982749i	$0.559211\pi$
$104$	−107.604	+	359.207i	−0.101456	+	0.338684i
$105$	639.553			0.594419
$106$	152.742	−	264.557i	0.139959	−	0.242416i
$107$	−508.543	+	880.823i	−0.459465	+	0.795816i	−0.998933	−	0.0461897i	$-0.985292\pi$
$107$	−508.543	+	880.823i	−0.459465	+	0.795816i	0.539468	+	0.842006i	$0.318625\pi$
$108$	−280.230	−	485.373i	−0.249677	−	0.432454i
$109$	−1889.22			−1.66013			−0.830066	−	0.557665i	$-0.811697\pi$
$109$	−1889.22			−1.66013			−0.830066	+	0.557665i	$0.811697\pi$
$110$	624.349	+	1081.40i	0.541176	+	0.937344i
$111$	916.629	+	1587.65i	0.783807	+	1.35759i
$112$	−112.000			−0.0944911
$113$	−28.8195	−	49.9168i	−0.0239921	−	0.0415556i	0.853780	−	0.520634i	$-0.174304\pi$
$113$	−28.8195	−	49.9168i	−0.0239921	−	0.0415556i	−0.877772	+	0.479078i	$0.840971\pi$
$114$	378.168	−	655.006i	0.310690	−	0.538131i
$115$	486.091	−	841.934i	0.394158	−	0.682702i
$116$	−500.142			−0.400319
$117$	3.16771	−	0.750209i	0.00250303	−	0.000592794i
$118$	49.1920			0.0383771
$119$	−68.0300	+	117.831i	−0.0524059	+	0.0907697i
$120$	365.459	−	632.993i	0.278014	−	0.481534i
$121$	33.4553	+	57.9462i	0.0251354	+	0.0435358i
$122$	1429.34			1.06071
$123$	−625.701	−	1083.75i	−0.458679	−	0.794456i
$124$	−142.033	−	246.009i	−0.102863	−	0.178163i
$125$	1025.08			0.733485
$126$	0.486159	+	0.842052i	0.000343734	+	0.000595365i
$127$	−478.285	+	828.414i	−0.334181	+	0.578818i	−0.983327	−	0.181846i	$-0.941793\pi$
$127$	−478.285	+	828.414i	−0.334181	+	0.578818i	0.649146	+	0.760663i	$0.275126\pi$
$128$	−64.0000	+	110.851i	−0.0441942	+	0.0765466i
$129$	1274.34			0.869761
$130$	−1129.50	−	1197.59i	−0.762026	−	0.807967i
$131$	2119.14			1.41336			0.706678	−	0.707535i	$-0.250193\pi$
$131$	2119.14			1.41336			0.706678	+	0.707535i	$0.250193\pi$
$132$	−369.963	+	640.795i	−0.243948	+	0.422531i
$133$	254.398	−	440.630i	0.165858	−	0.287274i
$134$	960.665	+	1663.92i	0.619320	+	1.07269i
$135$	2460.50			1.56864
$136$	77.7486	+	134.665i	0.0490212	+	0.0849073i
$137$	1228.87	+	2128.46i	0.766344	+	1.32735i	0.939533	+	0.342458i	$0.111259\pi$
$137$	1228.87	+	2128.46i	0.766344	+	1.32735i	−0.173189	+	0.984889i	$0.555407\pi$
$138$	576.074			0.355353
$139$	1104.87	+	1913.69i	0.674200	+	1.16775i	0.976702	+	0.214599i	$0.0688446\pi$
$139$	1104.87	+	1913.69i	0.674200	+	1.16775i	−0.302503	+	0.953149i	$0.597822\pi$
$140$	245.848	−	425.821i	0.148414	−	0.257060i
$141$	−616.690	+	1068.14i	−0.368331	+	0.637968i
$142$	−916.751			−0.541775
$143$	1143.42	+	1212.35i	0.668653	+	0.708965i
$144$	1.11122			0.000643068
$145$	1097.85	−	1901.53i	0.628768	−	1.08906i
$146$	100.872	−	174.716i	0.0571798	−	0.0990384i
$147$	127.469	+	220.783i	0.0715204	+	0.123877i
$148$	1409.43			0.782801
$149$	354.031	+	613.200i	0.194654	+	0.337150i	0.946787	−	0.321861i	$-0.104308\pi$
$149$	354.031	+	613.200i	0.194654	+	0.337150i	−0.752133	+	0.659011i	$0.770975\pi$
$150$	954.062	+	1652.48i	0.519326	+	0.899499i
$151$	−1080.25			−0.582181			−0.291091	−	0.956695i	$-0.594018\pi$
$151$	−1080.25			−0.582181			−0.291091	+	0.956695i	$0.594018\pi$
$152$	−290.740	−	503.577i	−0.155146	−	0.268720i
$153$	0.674968	−	1.16908i	0.000356653	−	0.000617741i
$154$	−248.878	+	431.070i	−0.130228	+	0.225562i
$155$	1247.09			0.646250
$156$	279.922	−	934.446i	0.143665	−	0.479587i
$157$	−1253.02			−0.636954			−0.318477	−	0.947931i	$-0.603171\pi$
$157$	−1253.02			−0.636954			−0.318477	+	0.947931i	$0.603171\pi$
$158$	1145.74	−	1984.49i	0.576902	−	0.999223i
$159$	−397.346	+	688.223i	−0.198186	+	0.343268i
$160$	−280.969	−	486.653i	−0.138829	−	0.240458i
$161$	387.531			0.189700
$162$	730.870	+	1265.90i	0.354460	+	0.613944i
$163$	−1720.89	−	2980.67i	−0.826936	−	1.43230i	−0.900431	−	0.434999i	$-0.856749\pi$
$163$	−1720.89	−	2980.67i	−0.826936	−	1.43230i	0.0734948	−	0.997296i	$-0.476585\pi$
$164$	−962.093			−0.458091
$165$	−1624.19	−	2813.18i	−0.766322	−	1.32731i
$166$	861.573	−	1492.29i	0.402838	−	0.697735i
$167$	−1174.38	+	2034.09i	−0.544171	+	0.942532i	0.454488	+	0.890753i	$0.349822\pi$
$167$	−1174.38	+	2034.09i	−0.544171	+	0.942532i	−0.998659	+	0.0517786i	$0.983511\pi$
$168$	291.359			0.133802
$169$	−1835.17	−	1207.88i	−0.835307	−	0.549784i
$170$	−682.655			−0.307984
$171$	−2.52404	+	4.37176i	−0.00112876	+	0.00195507i
$172$	489.863	−	848.468i	0.217161	−	0.376134i
$173$	−2174.81	−	3766.88i	−0.955768	−	1.65544i	−0.732601	−	0.680658i	$-0.761694\pi$
$173$	−2174.81	−	3766.88i	−0.955768	−	1.65544i	−0.223167	−	0.974780i	$-0.571639\pi$
$174$	1301.08			0.566865
$175$	641.808	+	1111.64i	0.277235	+	0.480185i
$176$	284.432	+	492.651i	0.121818	+	0.210994i
$177$	−127.969			−0.0543431
$178$	−1057.18	−	1831.10i	−0.445165	−	0.771048i
$179$	1743.41	−	3019.68i	0.727981	−	1.26090i	−0.229754	−	0.973249i	$-0.573792\pi$
$179$	1743.41	−	3019.68i	0.727981	−	1.26090i	0.957735	−	0.287652i	$-0.0928747\pi$
$180$	−2.43921	+	4.22483i	−0.00101004	+	0.00174945i
$181$	238.968			0.0981344			0.0490672	−	0.998795i	$-0.484375\pi$
$181$	238.968			0.0981344			0.0490672	+	0.998795i	$0.484375\pi$
$182$	188.307	−	628.612i	0.0766936	−	0.256021i
$183$	−3718.31			−1.50200
$184$	221.446	−	383.556i	0.0887241	−	0.153675i
$185$	−3093.80	+	5358.62i	−1.22952	+	2.12959i
$186$	369.487	+	639.971i	0.145657	+	0.252285i
$187$	691.069			0.270246
$188$	474.119	+	821.198i	0.183929	+	0.318575i
$189$	490.403	+	849.403i	0.188738	+	0.326904i
$190$	2552.78			0.974728
$191$	1477.63	+	2559.33i	0.559779	+	0.969565i	0.997514	+	0.0704616i	$0.0224472\pi$
$191$	1477.63	+	2559.33i	0.559779	+	0.969565i	−0.437736	+	0.899104i	$0.644219\pi$
$192$	166.491	−	288.370i	0.0625803	−	0.108392i
$193$	−1360.84	+	2357.05i	−0.507543	+	0.879090i	0.492419	+	0.870358i	$0.336113\pi$
$193$	−1360.84	+	2357.05i	−0.507543	+	0.879090i	−0.999962	+	0.00873172i	$0.997221\pi$
$194$	−1807.15			−0.668795
$195$	2938.29	+	3115.43i	1.07905	+	1.14411i
$196$	196.000			0.0714286
$197$	297.542	−	515.359i	0.107609	−	0.186385i	−0.807192	−	0.590289i	$-0.799014\pi$
$197$	297.542	−	515.359i	0.107609	−	0.186385i	0.914801	+	0.403904i	$0.132347\pi$
$198$	2.46927	−	4.27691i	0.000886281	−	0.00153508i
$199$	83.6477	+	144.882i	0.0297971	+	0.0516102i	0.880539	−	0.473973i	$-0.157181\pi$
$199$	83.6477	+	144.882i	0.0297971	+	0.0516102i	−0.850742	+	0.525583i	$0.823847\pi$
$200$	1466.99			0.518659
$201$	−2499.09	−	4328.55i	−0.876976	−	1.51897i
$202$	−928.839	−	1608.80i	−0.323529	−	0.560369i
$203$	875.249			0.302613
$204$	−202.256	−	350.319i	−0.0694156	−	0.120231i
$205$	2111.86	−	3657.85i	0.719507	−	1.24622i
$206$	386.662	−	669.718i	0.130777	−	0.226512i
$207$	−3.84493			−0.00129102
$208$	−514.560	−	545.582i	−0.171530	−	0.181872i
$209$	−2584.25			−0.855293
$210$	−639.553	+	1107.74i	−0.210159	+	0.364006i
$211$	1100.87	−	1906.76i	0.359181	−	0.622119i	−0.628644	−	0.777694i	$-0.716390\pi$
$211$	1100.87	−	1906.76i	0.359181	−	0.622119i	0.987824	+	0.155575i	$0.0497229\pi$
$212$	305.484	+	529.114i	0.0989658	+	0.171414i
$213$	2384.85			0.767170
$214$	−1017.09	−	1761.65i	−0.324891	−	0.562727i
$215$	2150.57	+	3724.90i	0.682175	+	1.18156i
$216$	1120.92			0.353097
$217$	248.558	+	430.515i	0.0777567	+	0.134679i
$218$	1889.22	−	3272.22i	0.586945	−	1.01662i
$219$	−262.411	+	454.509i	−0.0809684	+	0.140241i
$220$	−2497.40			−0.765338
$221$	−886.538	+	209.959i	−0.269842	+	0.0639067i
$222$	−3666.52			−1.10847
$223$	2957.46	−	5122.47i	0.888099	−	1.53823i	0.0459800	−	0.998942i	$-0.485359\pi$
$223$	2957.46	−	5122.47i	0.888099	−	1.53823i	0.842119	−	0.539291i	$-0.181308\pi$
$224$	112.000	−	193.990i	0.0334077	−	0.0578638i
$225$	−6.36777	−	11.0293i	−0.00188675	−	0.00326794i
$226$	115.278			0.0339300
$227$	2785.52	+	4824.66i	0.814456	+	1.41068i	0.909718	+	0.415227i	$0.136298\pi$
$227$	2785.52	+	4824.66i	0.814456	+	1.41068i	−0.0952617	+	0.995452i	$0.530369\pi$
$228$	756.336	+	1310.01i	0.219691	+	0.380516i
$229$	−3027.24			−0.873562			−0.436781	−	0.899568i	$-0.643882\pi$
$229$	−3027.24			−0.873562			−0.436781	+	0.899568i	$0.643882\pi$
$230$	972.181	+	1683.87i	0.278712	+	0.482743i
$231$	647.436	−	1121.39i	0.184408	−	0.319403i
$232$	500.142	−	866.272i	0.141534	−	0.245145i
$233$	−3763.80			−1.05826			−0.529131	−	0.848540i	$-0.677482\pi$
$233$	−3763.80			−1.05826			−0.529131	+	0.848540i	$0.677482\pi$
$234$	−1.86831	+	6.23684i	−0.000521945	+	0.00174237i
$235$	−4162.90			−1.15556
$236$	−49.1920	+	85.2031i	−0.0135683	+	0.0235010i
$237$	−2980.56	+	5162.47i	−0.816911	+	1.41493i
$238$	−136.060	−	235.663i	−0.0370566	−	0.0641839i
$239$	836.766			0.226468			0.113234	−	0.993568i	$-0.463879\pi$
$239$	836.766			0.226468			0.113234	+	0.993568i	$0.463879\pi$
$240$	730.918	+	1265.99i	0.196586	+	0.340496i
$241$	2487.17	+	4307.91i	0.664784	+	1.15144i	0.979344	+	0.202202i	$0.0648096\pi$
$241$	2487.17	+	4307.91i	0.664784	+	1.15144i	−0.314560	+	0.949237i	$0.601857\pi$
$242$	−133.821			−0.0355469
$243$	−9.74372	−	16.8766i	−0.00257226	−	0.00445529i
$244$	−1429.34	+	2475.69i	−0.375018	+	0.649549i
$245$	−430.234	+	745.187i	−0.112190	+	0.194319i
$246$	2502.80			0.648671
$247$	3315.20	−	785.141i	0.854013	−	0.202256i
$248$	568.133			0.145470
$249$	−2241.31	+	3882.06i	−0.570431	+	0.988015i
$250$	−1025.08	+	1775.48i	−0.259326	+	0.449166i
$251$	−1070.16	−	1853.58i	−0.269116	−	0.466123i	0.699518	−	0.714615i	$-0.253398\pi$
$251$	−1070.16	−	1853.58i	−0.269116	−	0.466123i	−0.968634	+	0.248493i	$0.920065\pi$
$252$	−1.94464			−0.000486113
$253$	−984.164	−	1704.62i	−0.244561	−	0.423592i
$254$	−956.570	−	1656.83i	−0.236301	−	0.409286i
$255$	1775.87			0.436115
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	2534.11	−	4389.20i	0.615071	−	1.06533i	−0.375301	−	0.926903i	$-0.622461\pi$
$257$	2534.11	−	4389.20i	0.615071	−	1.06533i	0.990372	−	0.138432i	$-0.0442062\pi$
$258$	−1274.34	+	2207.22i	−0.307507	+	0.532618i
$259$	−2466.51			−0.591742
$260$	3203.79	−	758.754i	0.764194	−	0.180984i
$261$	−8.68388			−0.00205946
$262$	−2119.14	+	3670.45i	−0.499697	+	0.865501i
$263$	−1649.55	+	2857.10i	−0.386751	+	0.669872i	−0.992010	−	0.126156i	$-0.959736\pi$
$263$	−1649.55	+	2857.10i	−0.386751	+	0.669872i	0.605260	+	0.796028i	$0.293069\pi$
$264$	−739.927	−	1281.59i	−0.172497	−	0.298774i
$265$	−2682.24			−0.621768
$266$	508.796	+	881.260i	0.117279	+	0.203133i
$267$	2750.18	+	4763.45i	0.630367	+	1.09183i
$268$	−3842.66			−0.875850
$269$	−2375.96	−	4115.28i	−0.538531	−	0.932762i	−0.998983	−	0.0450781i	$-0.985646\pi$
$269$	−2375.96	−	4115.28i	−0.538531	−	0.932762i	0.460453	−	0.887684i	$-0.347687\pi$
$270$	−2460.50	+	4261.71i	−0.554598	+	0.960591i
$271$	686.818	−	1189.60i	0.153953	−	0.266654i	−0.778724	−	0.627366i	$-0.784133\pi$
$271$	686.818	−	1189.60i	0.153953	−	0.266654i	0.932677	+	0.360712i	$0.117466\pi$
$272$	−310.994			−0.0693265
$273$	−489.864	+	1635.28i	−0.108601	+	0.362534i
$274$	−4915.46			−1.08377
$275$	3259.84	−	5646.20i	0.714820	−	1.23811i
$276$	−576.074	+	997.789i	−0.125636	+	0.217608i
$277$	−1789.80	−	3100.02i	−0.388226	−	0.672427i	0.603985	−	0.796996i	$-0.293579\pi$
$277$	−1789.80	−	3100.02i	−0.388226	−	0.672427i	−0.992211	+	0.124569i	$0.960245\pi$
$278$	−4419.47			−0.953462
$279$	−2.46610	−	4.27140i	−0.000529180	−	0.000916567i
$280$	491.696	+	851.643i	0.104944	+	0.181769i
$281$	−7576.39			−1.60843			−0.804216	−	0.594337i	$-0.797415\pi$
$281$	−7576.39			−1.60843			−0.804216	+	0.594337i	$0.797415\pi$
$282$	−1233.38	−	2136.28i	−0.260449	−	0.451112i
$283$	3129.30	−	5420.11i	0.657307	−	1.13849i	−0.324003	−	0.946056i	$-0.605029\pi$
$283$	3129.30	−	5420.11i	0.657307	−	1.13849i	0.981310	−	0.192433i	$-0.0616377\pi$
$284$	916.751	−	1587.86i	0.191546	−	0.331768i
$285$	−6640.85			−1.38025
$286$	−3243.27	+	768.106i	−0.670555	+	0.158808i
$287$	1683.66			0.346284
$288$	−1.11122	+	1.92469i	−0.000227359	+	0.000393797i
$289$	2267.60	−	3927.60i	0.461551	−	0.799429i
$290$	2195.70	+	3803.06i	0.444606	+	0.770080i
$291$	4701.16			0.947034
$292$	201.745	+	349.432i	0.0404322	+	0.0700307i
$293$	966.542	+	1674.10i	0.192717	+	0.333795i	0.946150	−	0.323730i	$-0.104937\pi$
$293$	966.542	+	1674.10i	0.192717	+	0.333795i	−0.753433	+	0.657525i	$0.771603\pi$
$294$	−509.877			−0.101145
$295$	−215.960	−	374.054i	−0.0426226	−	0.0738246i
$296$	−1409.43	+	2441.21i	−0.276762	+	0.479366i
$297$	2490.83	−	4314.24i	0.486642	−	0.842888i
$298$	−1416.13			−0.275282
$299$	1780.43	+	1887.77i	0.344364	+	0.365125i
$300$	−3816.25			−0.734438
$301$	−857.261	+	1484.82i	−0.164158	+	0.284331i
$302$	1080.25	−	1871.05i	0.205832	−	0.356512i
$303$	2416.30	+	4185.15i	0.458127	+	0.793500i
$304$	1162.96			0.219409
$305$	−6275.02	−	10868.6i	−1.17805	−	2.04045i
$306$	1.34994	+	2.33816i	0.000252192	+	0.000436809i
$307$	4886.39			0.908408			0.454204	−	0.890898i	$-0.349924\pi$
$307$	4886.39			0.908408			0.454204	+	0.890898i	$0.349924\pi$
$308$	−497.757	−	862.140i	−0.0920854	−	0.159497i
$309$	−1005.87	+	1742.22i	−0.185184	+	0.320748i
$310$	−1247.09	+	2160.03i	−0.228484	+	0.395746i
$311$	−8145.44			−1.48516			−0.742581	−	0.669756i	$-0.766399\pi$
$311$	−8145.44			−1.48516			−0.742581	+	0.669756i	$0.766399\pi$
$312$	1338.58	+	1419.29i	0.242892	+	0.257536i
$313$	10759.6			1.94304			0.971518	−	0.236966i	$-0.0761531\pi$
$313$	10759.6			1.94304			0.971518	+	0.236966i	$0.0761531\pi$
$314$	1253.02	−	2170.29i	0.225197	−	0.390053i
$315$	4.26862	−	7.39346i	0.000763521	−	0.00132246i
$316$	2291.49	+	3968.97i	0.407931	+	0.706557i
$317$	5799.15			1.02748			0.513742	−	0.857945i	$-0.328259\pi$
$317$	5799.15			1.02748			0.513742	+	0.857945i	$0.328259\pi$
$318$	−794.691	−	1376.45i	−0.140139	−	0.242727i
$319$	−2222.76	−	3849.93i	−0.390128	−	0.675721i
$320$	1123.88			0.196333
$321$	2645.87	+	4582.77i	0.460055	+	0.796839i
$322$	−387.531	+	671.224i	−0.0670691	+	0.116167i
$323$	706.396	−	1223.51i	0.121687	−	0.210768i
$324$	−2923.48			−0.501283
$325$	−2466.47	+	8233.63i	−0.420969	+	1.40529i
$326$	6883.56			1.16946
$327$	−4914.65	+	8512.42i	−0.831133	+	1.43956i
$328$	962.093	−	1666.39i	0.161959	−	0.280522i
$329$	−829.708	−	1437.10i	−0.139037	−	0.240820i
$330$	6496.77			1.08374
$331$	−3249.60	−	5628.47i	−0.539620	−	0.934649i	−0.998924	−	0.0463699i	$-0.985235\pi$
$331$	−3249.60	−	5628.47i	−0.539620	−	0.934649i	0.459305	−	0.888279i	$-0.348099\pi$
$332$	1723.15	+	2984.58i	0.284849	+	0.493373i
$333$	24.4717			0.00402715
$334$	−2348.77	−	4068.18i	−0.384787	−	0.666470i
$335$	8434.91	−	14609.7i	1.37567	−	2.38273i
$336$	−291.359	+	504.648i	−0.0473063	+	0.0819369i
$337$	−3846.02			−0.621680			−0.310840	−	0.950462i	$-0.600610\pi$
$337$	−3846.02			−0.621680			−0.310840	+	0.950462i	$0.600610\pi$
$338$	3927.27	−	1970.73i	0.631998	−	0.317141i
$339$	−299.886			−0.0480459
$340$	682.655	−	1182.39i	0.108889	−	0.188601i
$341$	1262.46	−	2186.65i	0.200487	−	0.347254i
$342$	−5.04807	−	8.74352i	−0.000798153	−	0.00138244i
$343$	−343.000			−0.0539949
$344$	979.727	+	1696.94i	0.153556	+	0.265967i
$345$	−2529.05	−	4380.44i	−0.394665	−	0.683579i
$346$	8699.25			1.35166
$347$	−3223.83	−	5583.83i	−0.498744	−	0.863849i	0.501255	−	0.865299i	$-0.332872\pi$
$347$	−3223.83	−	5583.83i	−0.498744	−	0.863849i	−0.999999	+	0.00145003i	$0.999538\pi$
$348$	−1301.08	+	2253.53i	−0.200417	+	0.347132i
$349$	1318.35	−	2283.45i	0.202205	−	0.350230i	−0.747033	−	0.664787i	$-0.768522\pi$
$349$	1318.35	−	2283.45i	0.202205	−	0.350230i	0.949239	+	0.314557i	$0.101856\pi$
$350$	−2567.23			−0.392069
$351$	−1884.62	+	6291.28i	−0.286591	+	0.956706i
$352$	−1137.73			−0.172276
$353$	−2048.05	+	3547.33i	−0.308801	+	0.534859i	−0.978100	−	0.208134i	$-0.933261\pi$
$353$	−2048.05	+	3547.33i	−0.308801	+	0.534859i	0.669299	+	0.742993i	$0.266594\pi$
$354$	127.969	−	221.649i	0.0192132	−	0.0332782i
$355$	4024.67	+	6970.93i	0.601710	+	1.04219i
$356$	4228.74			0.629558
$357$	353.949	+	613.057i	0.0524733	+	0.0908864i
$358$	3486.82	+	6039.35i	0.514761	+	0.891592i
$359$	−4036.48			−0.593418			−0.296709	−	0.954968i	$-0.595889\pi$
$359$	−4036.48			−0.593418			−0.296709	+	0.954968i	$0.595889\pi$
$360$	−4.87842	−	8.44967i	−0.000714209	−	0.00123705i
$361$	787.940	−	1364.75i	0.114877	−	0.198973i
$362$	−238.968	+	413.904i	−0.0346957	+	0.0600948i
$363$	348.124			0.0503355
$364$	900.480	+	954.769i	0.129665	+	0.137482i
$365$	−1771.38			−0.254022
$366$	3718.31	−	6440.31i	0.531037	−	0.919782i
$367$	6682.31	−	11574.1i	0.950446	−	1.64622i	0.205985	−	0.978555i	$-0.433960\pi$
$367$	6682.31	−	11574.1i	0.950446	−	1.64622i	0.744461	−	0.667666i	$-0.232707\pi$
$368$	442.893	+	767.113i	0.0627374	+	0.108664i
$369$	−16.7047			−0.00235667
$370$	−6187.61	−	10717.2i	−0.869401	−	1.50585i
$371$	−534.597	−	925.950i	−0.0748111	−	0.129577i
$372$	−1477.95			−0.205989
$373$	3436.92	+	5952.92i	0.477097	+	0.826356i	0.999655	−	0.0262476i	$-0.00835584\pi$
$373$	3436.92	+	5952.92i	0.477097	+	0.826356i	−0.522559	+	0.852603i	$0.675023\pi$
$374$	−691.069	+	1196.97i	−0.0955464	+	0.165491i
$375$	2666.65	−	4618.77i	0.367214	−	0.636033i
$376$	−1896.48			−0.260115
$377$	4021.15	+	4263.57i	0.549336	+	0.582454i
$378$	−1961.61			−0.266916
$379$	−4922.25	+	8525.59i	−0.667122	+	1.15549i	0.311584	+	0.950219i	$0.399141\pi$
$379$	−4922.25	+	8525.59i	−0.667122	+	1.15549i	−0.978705	+	0.205270i	$0.934193\pi$
$380$	−2552.78	+	4421.55i	−0.344618	+	0.596897i
$381$	2488.44	+	4310.10i	0.334610	+	0.579562i
$382$	−5910.53			−0.791647
$383$	4582.43	+	7937.01i	0.611361	+	1.05891i	0.991011	+	0.133779i	$0.0427111\pi$
$383$	4582.43	+	7937.01i	0.611361	+	1.05891i	−0.379650	+	0.925130i	$0.623956\pi$
$384$	332.981	+	576.740i	0.0442510	+	0.0766449i
$385$	4370.44			0.578542
$386$	−2721.69	−	4714.11i	−0.358887	−	0.621610i
$387$	8.50541	−	14.7318i	0.00111719	−	0.00193504i
$388$	1807.15	−	3130.08i	0.236455	−	0.409551i
$389$	5545.20			0.722758			0.361379	−	0.932419i	$-0.382306\pi$
$389$	5545.20			0.722758			0.361379	+	0.932419i	$0.382306\pi$
$390$	−8334.38	+	1973.83i	−1.08212	+	0.256279i
$391$	1076.07			0.139180
$392$	−196.000	+	339.482i	−0.0252538	+	0.0437409i
$393$	5512.75	−	9548.36i	0.707587	−	1.22558i
$394$	595.085	+	1030.72i	0.0760912	+	0.131794i
$395$	−20119.9			−2.56289
$396$	4.93855	+	8.55382i	0.000626695	+	0.00108547i
$397$	6091.52	+	10550.8i	0.770088	+	1.33383i	0.937514	+	0.347946i	$0.113121\pi$
$397$	6091.52	+	10550.8i	0.770088	+	1.33383i	−0.167427	+	0.985884i	$0.553546\pi$
$398$	−334.591			−0.0421395
$399$	−1323.59	−	2292.52i	−0.166071	−	0.287643i
$400$	−1466.99	+	2540.90i	−0.183374	+	0.317613i
$401$	−5621.15	+	9736.12i	−0.700018	+	1.21247i	0.268442	+	0.963296i	$0.413491\pi$
$401$	−5621.15	+	9736.12i	−0.700018	+	1.21247i	−0.968460	+	0.249170i	$0.919842\pi$
$402$	9996.36			1.24023
$403$	−955.207	+	3188.70i	−0.118070	+	0.394145i
$404$	3715.36			0.457539
$405$	6417.25	−	11115.0i	0.787348	−	1.36373i
$406$	−875.249	+	1515.98i	−0.106990	+	0.185312i
$407$	6263.87	+	10849.3i	0.762871	+	1.32133i
$408$	809.026			0.0981685
$409$	−6062.21	−	10500.1i	−0.732902	−	1.26942i	−0.955638	−	0.294545i	$-0.904832\pi$
$409$	−6062.21	−	10500.1i	−0.732902	−	1.26942i	0.222736	−	0.974879i	$-0.428501\pi$
$410$	4223.73	+	7315.71i	0.508768	+	0.881213i
$411$	12787.2			1.53466
$412$	773.324	+	1339.44i	0.0924732	+	0.160168i
$413$	86.0860	−	149.105i	0.0102567	−	0.0177651i
$414$	3.84493	−	6.65962i	0.000456445	−	0.000790586i
$415$	−15129.7			−1.78961
$416$	1459.54	−	345.662i	0.172018	−	0.0407392i
$417$	11496.9			1.35013
$418$	2584.25	−	4476.05i	0.302392	−	0.523758i
$419$	3666.43	−	6350.45i	0.427487	−	0.740429i	−0.569162	−	0.822225i	$-0.692732\pi$
$419$	3666.43	−	6350.45i	0.427487	−	0.740429i	0.996649	+	0.0817966i	$0.0260658\pi$
$420$	−1279.11	−	2215.48i	−0.148605	−	0.257391i
$421$	8750.98			1.01306			0.506528	−	0.862223i	$-0.330929\pi$
$421$	8750.98			1.01306			0.506528	+	0.862223i	$0.330929\pi$
$422$	2201.74	+	3813.53i	0.253979	+	0.439904i
$423$	8.23204	+	14.2583i	0.000946231	+	0.00163892i
$424$	−1221.94			−0.139959
$425$	1782.13	+	3086.74i	0.203403	+	0.352304i
$426$	−2384.85	+	4130.68i	−0.271236	+	0.469794i
$427$	2501.35	−	4332.46i	0.283487	−	0.491013i
$428$	4068.35			0.459465
$429$	8437.11	−	1998.16i	0.949528	−	0.224877i
$430$	−8602.28			−0.964742
$431$	1222.07	−	2116.70i	0.136578	−	0.236561i	−0.789621	−	0.613595i	$-0.789723\pi$
$431$	1222.07	−	2116.70i	0.136578	−	0.236561i	0.926199	+	0.377034i	$0.123056\pi$
$432$	−1120.92	+	1941.49i	−0.124839	+	0.216227i
$433$	5009.03	+	8675.89i	0.555932	+	0.962902i	0.997830	+	0.0658372i	$0.0209718\pi$
$433$	5009.03	+	8675.89i	0.555932	+	0.962902i	−0.441898	+	0.897065i	$0.645695\pi$
$434$	−994.232			−0.109965
$435$	−5711.92	−	9893.34i	−0.629576	−	1.09046i
$436$	3778.44	+	6544.45i	0.415033	+	0.718858i
$437$	−4023.96			−0.440485
$438$	−524.822	−	909.018i	−0.0572533	−	0.0991656i
$439$	821.158	−	1422.29i	0.0892750	−	0.154629i	−0.817930	−	0.575318i	$-0.804878\pi$
$439$	821.158	−	1422.29i	0.0892750	−	0.154629i	0.907205	+	0.420689i	$0.138212\pi$
$440$	2497.40	−	4325.62i	0.270588	−	0.468672i
$441$	3.40311			0.000367467
$442$	522.878	−	1745.49i	0.0562688	−	0.187838i
$443$	−2864.36			−0.307201			−0.153600	−	0.988133i	$-0.549087\pi$
$443$	−2864.36			−0.307201			−0.153600	+	0.988133i	$0.549087\pi$
$444$	3666.52	−	6350.59i	0.391904	−	0.678797i
$445$	−9282.38	+	16077.6i	−0.988825	+	1.71270i
$446$	5914.92	+	10244.9i	0.627981	+	1.08770i
$447$	3683.93			0.389807
$448$	224.000	+	387.979i	0.0236228	+	0.0409159i
$449$	−7115.34	−	12324.1i	−0.747870	−	1.29535i	−0.948842	−	0.315751i	$-0.897744\pi$
$449$	−7115.34	−	12324.1i	−0.747870	−	1.29535i	0.200973	−	0.979597i	$-0.435590\pi$
$450$	25.4711			0.00266826
$451$	−4275.79	−	7405.88i	−0.446428	−	0.773236i
$452$	−115.278	+	199.667i	−0.0119961	+	0.0207778i
$453$	−2810.18	+	4867.37i	−0.291465	+	0.504832i
$454$	−11142.1			−1.15181
$455$	−5606.63	+	1327.82i	−0.577676	+	0.136811i
$456$	−3025.35			−0.310690
$457$	8529.32	−	14773.2i	0.873052	−	1.51217i	0.0142290	−	0.999899i	$-0.495471\pi$
$457$	8529.32	−	14773.2i	0.873052	−	1.51217i	0.858823	−	0.512272i	$-0.171196\pi$
$458$	3027.24	−	5243.34i	0.308851	−	0.534945i
$459$	1361.72	+	2358.57i	0.138474	+	0.239844i
$460$	−3888.72			−0.394158
$461$	5562.03	+	9633.72i	0.561930	+	0.973291i	0.997328	+	0.0730527i	$0.0232741\pi$
$461$	5562.03	+	9633.72i	0.561930	+	0.973291i	−0.435399	+	0.900238i	$0.643393\pi$
$462$	1294.87	+	2242.78i	0.130396	+	0.225852i
$463$	−4793.11			−0.481112			−0.240556	−	0.970635i	$-0.577330\pi$
$463$	−4793.11			−0.481112			−0.240556	+	0.970635i	$0.577330\pi$
$464$	1000.28	+	1732.54i	0.100080	+	0.173343i
$465$	3244.20	−	5619.12i	0.323540	−	0.560389i
$466$	3763.80	−	6519.10i	0.374152	−	0.648050i
$467$	1176.28			0.116557			0.0582783	−	0.998300i	$-0.481439\pi$
$467$	1176.28			0.116557			0.0582783	+	0.998300i	$0.481439\pi$
$468$	−8.93422	−	9.47284i	−0.000882445	−	0.000935646i
$469$	6724.66			0.662081
$470$	4162.90	−	7210.35i	0.408554	−	0.707636i
$471$	−3259.62	+	5645.84i	−0.318887	+	0.552328i
$472$	−98.3840	−	170.406i	−0.00959426	−	0.0166178i
$473$	8708.31			0.846530
$474$	−5961.11	−	10324.9i	−0.577643	−	1.00051i
$475$	−6664.27	−	11542.8i	−0.643742	−	1.11499i
$476$	544.240			0.0524059
$477$	5.30407	+	9.18692i	0.000509133	+	0.000881845i
$478$	−836.766	+	1449.32i	−0.0800686	+	0.138683i
$479$	−3397.44	+	5884.53i	−0.324077	+	0.561318i	−0.981325	−	0.192356i	$-0.938387\pi$
$479$	−3397.44	+	5884.53i	−0.324077	+	0.561318i	0.657248	+	0.753674i	$0.271720\pi$
$480$	−2923.67			−0.278014
$481$	−11331.8	−	12015.0i	−1.07419	−	1.13895i
$482$	−9948.69			−0.940146
$483$	1008.13	−	1746.13i	0.0949720	−	0.164496i
$484$	133.821	−	231.785i	0.0125677	−	0.0217679i
$485$	7933.67	+	13741.5i	0.742782	+	1.28654i
$486$	38.9749			0.00363773
$487$	7537.49	+	13055.3i	0.701348	+	1.21477i	0.967994	+	0.250975i	$0.0807513\pi$
$487$	7537.49	+	13055.3i	0.701348	+	1.21477i	−0.266646	+	0.963795i	$0.585915\pi$
$488$	−2858.68	−	4951.39i	−0.265177	−	0.459301i
$489$	−17907.0			−1.65600
$490$	−860.468	−	1490.37i	−0.0793306	−	0.137405i
$491$	350.389	−	606.891i	0.0322053	−	0.0557813i	−0.849474	−	0.527631i	$-0.823080\pi$
$491$	350.389	−	606.891i	0.0322053	−	0.0557813i	0.881679	+	0.471850i	$0.156414\pi$
$492$	−2502.80	+	4334.98i	−0.229340	+	0.397228i
$493$	2430.34			0.222022
$494$	−1955.30	+	6527.24i	−0.178083	+	0.594483i
$495$	−43.3619			−0.00393731
$496$	−568.133	+	984.034i	−0.0514313	+	0.0890815i
$497$	−1604.31	+	2778.75i	−0.144795	+	0.250793i
$498$	−4482.62	−	7764.13i	−0.403355	−	0.698632i
$499$	−1528.64			−0.137137			−0.0685683	−	0.997646i	$-0.521843\pi$
$499$	−1528.64			−0.137137			−0.0685683	+	0.997646i	$0.521843\pi$
$500$	−2050.15	−	3550.97i	−0.183371	−	0.317608i
$501$	6110.12	+	10583.0i	0.544870	+	0.943743i
$502$	4280.66			0.380588
$503$	2006.91	+	3476.07i	0.177900	+	0.308132i	0.941161	−	0.337958i	$-0.109736\pi$
$503$	2006.91	+	3476.07i	0.177900	+	0.308132i	−0.763261	+	0.646090i	$0.776403\pi$
$504$	1.94464	−	3.36821i	0.000171867	−	0.000297682i
$505$	−8155.47	+	14125.7i	−0.718641	+	1.24472i
$506$	3936.66			0.345861
$507$	−10216.5	+	5126.69i	−0.894929	+	0.449081i
$508$	3826.28			0.334181
$509$	447.209	−	774.589i	0.0389434	−	0.0674520i	−0.845897	−	0.533347i	$-0.820934\pi$
$509$	447.209	−	774.589i	0.0389434	−	0.0674520i	0.884840	+	0.465895i	$0.154267\pi$
$510$	−1775.87	+	3075.90i	−0.154190	+	0.267065i
$511$	−353.053	−	611.506i	−0.0305639	−	0.0529382i
$512$	512.000			0.0441942
$513$	−5092.14	−	8819.84i	−0.438252	−	0.759075i
$514$	5068.22	+	8778.41i	0.434921	+	0.753306i
$515$	−6790.01			−0.580978
$516$	−2548.68	−	4414.44i	−0.217440	−	0.376618i
$517$	−4214.21	+	7299.23i	−0.358493	+	0.620928i
$518$	2466.51	−	4272.11i	0.209212	−	0.362366i
$519$	−22630.4			−1.91399
$520$	−1889.59	+	6307.87i	−0.159354	+	0.531959i
$521$	−586.692			−0.0493349			−0.0246674	−	0.999696i	$-0.507853\pi$
$521$	−586.692			−0.0493349			−0.0246674	+	0.999696i	$0.507853\pi$
$522$	8.68388	−	15.0409i	0.000728129	−	0.00126116i
$523$	6509.24	−	11274.3i	0.544224	−	0.942624i	−0.454431	−	0.890782i	$-0.650157\pi$
$523$	6509.24	−	11274.3i	0.544224	−	0.942624i	0.998655	−	0.0518421i	$-0.0165092\pi$
$524$	−4238.27	−	7340.90i	−0.353339	−	0.612001i
$525$	6678.44			0.555183
$526$	−3299.09	−	5714.20i	−0.273474	−	0.473671i
$527$	690.180	+	1195.43i	0.0570488	+	0.0988114i
$528$	2959.71			0.243948
$529$	4551.05	+	7882.65i	0.374048	+	0.647871i
$530$	2682.24	−	4645.77i	0.219828	−	0.380754i
$531$	−0.854112	+	1.47937i	−6.98029e−5	+	0.000120902i
$532$	−2035.18			−0.165858
$533$	7735.23	+	8201.57i	0.628612	+	0.666510i
$534$	−11000.7			−0.891474
$535$	−8930.31	+	15467.8i	−0.721666	+	1.24996i
$536$	3842.66	−	6655.68i	0.309660	−	0.536347i
$537$	−9070.67	−	15710.9i	−0.728917	−	1.26252i
$538$	9503.83			0.761597
$539$	871.074	+	1508.74i	0.0696100	+	0.120568i
$540$	−4921.00	−	8523.43i	−0.392160	−	0.679241i
$541$	−4069.61			−0.323413			−0.161706	−	0.986839i	$-0.551700\pi$
$541$	−4069.61			−0.323413			−0.161706	+	0.986839i	$0.551700\pi$
$542$	1373.64	+	2379.21i	0.108861	+	0.188553i
$543$	621.654	−	1076.74i	0.0491303	−	0.0850961i
$544$	310.994	−	538.658i	0.0245106	−	0.0424536i
$545$	−33175.8			−2.60751
$546$	−2342.52	−	2483.75i	−0.183609	−	0.194679i
$547$	−13272.7			−1.03748			−0.518740	−	0.854932i	$-0.673599\pi$
$547$	−13272.7			−1.03748			−0.518740	+	0.854932i	$0.673599\pi$
$548$	4915.46	−	8513.83i	0.383172	−	0.663673i
$549$	−24.8174	+	42.9850i	−0.00192929	+	0.00334163i
$550$	6519.68	+	11292.4i	0.505454	+	0.875473i
$551$	−9088.22			−0.702670
$552$	−1152.15	−	1995.58i	−0.0888382	−	0.153872i
$553$	−4010.10	−	6945.70i	−0.308367	−	0.534107i
$554$	7159.19			0.549034
$555$	16096.5	+	27880.0i	1.23110	+	2.13233i
$556$	4419.47	−	7654.75i	0.337100	−	0.583874i
$557$	−6119.66	+	10599.6i	−0.465527	+	0.806316i	−0.999225	−	0.0393589i	$-0.987468\pi$
$557$	−6119.66	+	10599.6i	−0.465527	+	0.806316i	0.533698	+	0.845675i	$0.320802\pi$
$558$	9.86438			0.000748374
$559$	−11171.5	+	2645.74i	−0.845264	+	0.200184i
$560$	−1966.78			−0.148414
$561$	1797.76	−	3113.81i	0.135297	−	0.234341i
$562$	7576.39	−	13122.7i	0.568667	−	0.984960i
$563$	−9813.48	−	16997.5i	−0.734616	−	1.27239i	−0.954891	−	0.296955i	$-0.904029\pi$
$563$	−9813.48	−	16997.5i	−0.734616	−	1.27239i	0.220275	−	0.975438i	$-0.429305\pi$
$564$	4933.52			0.368331
$565$	−506.087	−	876.568i	−0.0376836	−	0.0652699i
$566$	6258.61	+	10840.2i	0.464786	+	0.805033i
$567$	5116.09			0.378934
$568$	1833.50	+	3175.72i	0.135444	+	0.234595i
$569$	−8433.43	+	14607.1i	−0.621349	+	1.07621i	0.367885	+	0.929871i	$0.380082\pi$
$569$	−8433.43	+	14607.1i	−0.621349	+	1.07621i	−0.989235	+	0.146338i	$0.953251\pi$
$570$	6640.85	−	11502.3i	0.487990	−	0.845224i
$571$	3470.38			0.254345			0.127173	−	0.991881i	$-0.459410\pi$
$571$	3470.38			0.254345			0.127173	+	0.991881i	$0.459410\pi$
$572$	1912.88	−	6385.62i	0.139828	−	0.466777i
$573$	15375.7			1.12100
$574$	−1683.66	+	2916.19i	−0.122430	+	0.212055i
$575$	5075.93	−	8791.77i	0.368141	−	0.637638i
$576$	−2.22244	−	3.84938i	−0.000160767	−	0.000278456i
$577$	7642.02			0.551372			0.275686	−	0.961248i	$-0.411095\pi$
$577$	7642.02			0.551372			0.275686	+	0.961248i	$0.411095\pi$
$578$	4535.20	+	7855.19i	0.326366	+	0.565282i
$579$	7080.25	+	12263.3i	0.508195	+	0.880220i
$580$	−8782.79			−0.628768
$581$	−3015.51	−	5223.01i	−0.215326	−	0.372955i
$582$	−4701.16	+	8142.65i	−0.334827	+	0.579938i
$583$	−2715.30	+	4703.04i	−0.192892	+	0.334099i
$584$	−806.979			−0.0571798
$585$	55.6268	−	13.1741i	0.00393143	−	0.000931081i
$586$	−3866.17			−0.272543
$587$	2127.99	−	3685.79i	0.149628	−	0.259163i	−0.781462	−	0.623953i	$-0.785526\pi$
$587$	2127.99	−	3685.79i	0.149628	−	0.259163i	0.931090	+	0.364789i	$0.118859\pi$
$588$	509.877	−	883.134i	0.0357602	−	0.0619385i
$589$	−2580.92	−	4470.29i	−0.180552	−	0.312725i
$590$	863.840			0.0602775
$591$	−1548.06	−	2681.32i	−0.107748	−	0.186624i
$592$	−2818.86	−	4882.41i	−0.195700	−	0.338963i
$593$	25016.9			1.73242			0.866208	−	0.499684i	$-0.166551\pi$
$593$	25016.9			1.73242			0.866208	+	0.499684i	$0.166551\pi$
$594$	4981.66	+	8628.48i	0.344108	+	0.596012i
$595$	−1194.65	+	2069.19i	−0.0823122	+	0.142569i
$596$	1416.13	−	2452.80i	0.0973268	−	0.168575i
$597$	870.410			0.0596709
$598$	−5050.14	+	1196.03i	−0.345344	+	0.0817879i
$599$	7004.91			0.477818			0.238909	−	0.971042i	$-0.423210\pi$
$599$	7004.91			0.477818			0.238909	+	0.971042i	$0.423210\pi$
$600$	3816.25	−	6609.94i	0.259663	−	0.449749i
$601$	8949.64	−	15501.2i	0.607427	−	1.05209i	−0.384236	−	0.923235i	$-0.625535\pi$
$601$	8949.64	−	15501.2i	0.607427	−	1.05209i	0.991663	−	0.128859i	$-0.0411316\pi$
$602$	−1714.52	−	2969.64i	−0.116078	−	0.201052i
$603$	−66.7194			−0.00450585
$604$	2160.50	+	3742.09i	0.145545	+	0.252092i
$605$	587.493	+	1017.57i	0.0394793	+	0.0683802i
$606$	−9665.19			−0.647890
$607$	−157.690	−	273.127i	−0.0105444	−	0.0182634i	0.860705	−	0.509104i	$-0.170023\pi$
$607$	−157.690	−	273.127i	−0.0105444	−	0.0182634i	−0.871249	+	0.490841i	$0.836690\pi$
$608$	−1162.96	+	2014.31i	−0.0775729	+	0.134360i
$609$	2276.89	−	3943.68i	0.151501	−	0.262407i
$610$	25100.1			1.66602
$611$	3188.57	−	10644.2i	0.211122	−	0.704774i
$612$	−5.39974			−0.000356653
$613$	−14024.3	+	24290.8i	−0.924041	+	1.60049i	−0.130944	+	0.991390i	$0.541801\pi$
$613$	−14024.3	+	24290.8i	−0.924041	+	1.60049i	−0.793097	+	0.609096i	$0.791533\pi$
$614$	−4886.39	+	8463.48i	−0.321171	+	0.556284i
$615$	−10987.7	−	19031.2i	−0.720432	−	1.24782i
$616$	1991.03			0.130228
$617$	−13478.1	−	23344.8i	−0.879432	−	1.52322i	−0.851966	−	0.523598i	$-0.824590\pi$
$617$	−13478.1	−	23344.8i	−0.879432	−	1.52322i	−0.0274660	−	0.999623i	$-0.508744\pi$
$618$	−2011.74	−	3484.43i	−0.130945	−	0.226803i
$619$	9116.91			0.591986			0.295993	−	0.955190i	$-0.404349\pi$
$619$	9116.91			0.591986			0.295993	+	0.955190i	$0.404349\pi$
$620$	−2494.18	−	4320.05i	−0.161563	−	0.279835i
$621$	3878.50	−	6717.75i	0.250626	−	0.434097i
$622$	8145.44	−	14108.3i	0.525084	−	0.909472i
$623$	−7400.29			−0.475901
$624$	−3796.86	+	899.212i	−0.243583	+	0.0576879i
$625$	−4920.80			−0.314931
$626$	−10759.6	+	18636.2i	−0.686967	+	1.18986i
$627$	−6722.70	+	11644.1i	−0.428196	+	0.741657i
$628$	2506.04	+	4340.59i	0.159239	+	0.275809i
$629$	−6848.84			−0.434151
$630$	8.53723	+	14.7869i	0.000539891	+	0.000935119i
$631$	−9251.39	−	16023.9i	−0.583664	−	1.01094i	−0.995041	−	0.0994700i	$-0.968285\pi$
$631$	−9251.39	−	16023.9i	−0.583664	−	1.01094i	0.411377	−	0.911465i	$-0.365048\pi$
$632$	−9165.95			−0.576902
$633$	−5727.65	−	9920.57i	−0.359642	−	0.622919i
$634$	−5799.15	+	10044.4i	−0.363271	+	0.629203i
$635$	−8398.96	+	14547.4i	−0.524886	+	0.909129i
$636$	3178.77			0.198186
$637$	−1575.84	−	1670.85i	−0.0980174	−	0.103927i
$638$	8891.04			0.551724
$639$	15.9174	−	27.5697i	0.000985418	−	0.00170679i
$640$	−1123.88	+	1946.61i	−0.0694143	+	0.120229i
$641$	−6041.50	−	10464.2i	−0.372269	−	0.644790i	0.617645	−	0.786457i	$-0.288087\pi$
$641$	−6041.50	−	10464.2i	−0.372269	−	0.644790i	−0.989914	+	0.141668i	$0.954754\pi$
$642$	−10583.5			−0.650617
$643$	4782.65	+	8283.79i	0.293327	+	0.508057i	0.974594	−	0.223977i	$-0.0719042\pi$
$643$	4782.65	+	8283.79i	0.293327	+	0.508057i	−0.681267	+	0.732035i	$0.738571\pi$
$644$	−775.062	−	1342.45i	−0.0474250	−	0.0821426i
$645$	22378.1			1.36610
$646$	1412.79	+	2447.03i	0.0860457	+	0.149036i
$647$	16082.0	−	27854.8i	0.977199	−	1.69256i	0.304720	−	0.952442i	$-0.401437\pi$
$647$	16082.0	−	27854.8i	0.977199	−	1.69256i	0.672479	−	0.740116i	$-0.265230\pi$
$648$	2923.48	−	5063.62i	0.177230	−	0.306972i
$649$	−874.487			−0.0528916
$650$	−11794.6	−	12505.7i	−0.711727	−	0.754635i
$651$	2586.41			0.155713
$652$	−6883.56	+	11922.7i	−0.413468	+	0.716148i
$653$	−2251.94	+	3900.47i	−0.134954	+	0.233748i	−0.925580	−	0.378552i	$-0.876422\pi$
$653$	−2251.94	+	3900.47i	−0.134954	+	0.233748i	0.790626	+	0.612300i	$0.209755\pi$
$654$	−9829.29	−	17024.8i	−0.587700	−	1.01793i
$655$	37213.2			2.21991
$656$	1924.19	+	3332.79i	0.114523	+	0.198359i
$657$	3.50286	+	6.06713i	0.000208005	+	0.000360276i
$658$	3318.83			0.196629
$659$	−7798.15	−	13506.8i	−0.460960	−	0.798407i	0.538049	−	0.842914i	$-0.319162\pi$
$659$	−7798.15	−	13506.8i	−0.460960	−	0.798407i	−0.999009	+	0.0445071i	$0.985828\pi$
$660$	−6496.77	+	11252.7i	−0.383161	+	0.663654i
$661$	−6213.94	+	10762.9i	−0.365649	+	0.633323i	−0.988880	−	0.148715i	$-0.952486\pi$
$661$	−6213.94	+	10762.9i	−0.365649	+	0.633323i	0.623231	+	0.782038i	$0.285820\pi$
$662$	12998.4			0.763137
$663$	−1360.22	+	4540.74i	−0.0796783	+	0.265985i
$664$	−6892.59			−0.402838
$665$	4467.37	−	7737.71i	0.260507	−	0.451211i
$666$	−24.4717	+	42.3862i	−0.00142381	+	0.00246612i
$667$	−3461.08	−	5994.77i	−0.200920	−	0.348004i
$668$	9395.07			0.544171
$669$	−15387.2	−	26651.4i	−0.889241	−	1.54021i
$670$	16869.8	+	29219.4i	0.972744	+	1.68484i
$671$	−25409.4			−1.46188
$672$	−582.717	−	1009.30i	−0.0334506	−	0.0579381i
$673$	−6562.47	+	11366.5i	−0.375876	+	0.651036i	−0.990458	−	0.137817i	$-0.955991\pi$
$673$	−6562.47	+	11366.5i	−0.375876	+	0.651036i	0.614582	+	0.788853i	$0.289325\pi$
$674$	3846.02	−	6661.51i	0.219797	−	0.380700i
$675$	25693.4			1.46510
$676$	−513.868	+	8772.96i	−0.0292369	+	0.499144i
$677$	15546.9			0.882595			0.441297	−	0.897361i	$-0.354518\pi$
$677$	15546.9			0.882595			0.441297	+	0.897361i	$0.354518\pi$
$678$	299.886	−	519.418i	0.0169868	−	0.0294220i
$679$	−3162.52	+	5477.65i	−0.178743	+	0.309592i
$680$	1365.31	+	2364.79i	0.0769960	+	0.133361i
$681$	28985.2			1.63101
$682$	2524.93	+	4373.30i	0.141766	+	0.245546i
$683$	12275.0	+	21261.0i	0.687688	+	1.19111i	0.972584	+	0.232552i	$0.0747077\pi$
$683$	12275.0	+	21261.0i	0.687688	+	1.19111i	−0.284896	+	0.958558i	$0.591959\pi$
$684$	20.1923			0.00112876
$685$	21579.6	+	37377.0i	1.20367	+	2.08482i
$686$	343.000	−	594.093i	0.0190901	−	0.0330650i
$687$	−7875.11	+	13640.1i	−0.437343	+	0.757499i
$688$	−3918.91			−0.217161
$689$	2054.46	−	6858.25i	0.113597	−	0.379214i
$690$	10116.2			0.558140
$691$	5163.62	−	8943.65i	0.284274	−	0.492377i	−0.688159	−	0.725560i	$-0.741581\pi$
$691$	5163.62	−	8943.65i	0.284274	−	0.492377i	0.972433	+	0.233183i	$0.0749142\pi$
$692$	−8699.25	+	15067.5i	−0.477884	+	0.827719i
$693$	−8.64246	−	14.9692i	−0.000473737	−	0.000820537i
$694$	12895.3			0.705330
$695$	19402.1	+	33605.5i	1.05894	+	1.83414i
$696$	−2602.16	−	4507.07i	−0.141716	−	0.245460i
$697$	4675.09			0.254063
$698$	2636.70	+	4566.90i	0.142981	+	0.247650i
$699$	−9791.22	+	16958.9i	−0.529811	+	0.917659i
$700$	2567.23	−	4446.58i	0.138617	−	0.240093i
$701$	19970.4			1.07599			0.537996	−	0.842947i	$-0.319181\pi$
$701$	19970.4			1.07599			0.537996	+	0.842947i	$0.319181\pi$
$702$	−9012.21	−	9555.54i	−0.484535	−	0.513747i
$703$	25611.2			1.37403
$704$	1137.73	−	1970.60i	0.0609088	−	0.105497i
$705$	−10829.4	+	18757.1i	−0.578525	+	1.00203i
$706$	−4096.10	−	7094.65i	−0.218355	−	0.378202i
$707$	−6501.87			−0.345867
$708$	255.938	+	443.297i	0.0135858	+	0.0235313i
$709$	−7037.69	−	12189.6i	−0.372787	−	0.645686i	0.617206	−	0.786802i	$-0.288264\pi$
$709$	−7037.69	−	12189.6i	−0.372787	−	0.645686i	−0.989993	+	0.141115i	$0.954931\pi$
$710$	−16098.7			−0.850947
$711$	39.7867	+	68.9126i	0.00209862	+	0.00363491i
$712$	−4228.74	+	7324.39i	−0.222582	+	0.385524i
$713$	1965.79	−	3404.86i	0.103253	−	0.178840i
$714$	−1415.80			−0.0742084
$715$	20079.1	+	21289.6i	1.05023	+	1.11355i
$716$	−13947.3			−0.727981
$717$	2176.78	−	3770.29i	0.113380	−	0.196379i
$718$	4036.48	−	6991.38i	0.209805	−	0.363393i
$719$	−13300.2	−	23036.6i	−0.689867	−	1.19488i	−0.971881	−	0.235474i	$-0.924336\pi$
$719$	−13300.2	−	23036.6i	−0.689867	−	1.19488i	0.282014	−	0.959410i	$-0.408997\pi$
$720$	19.5137			0.00101004
$721$	−1353.32	−	2344.01i	−0.0699032	−	0.121076i
$722$	1575.88	+	2729.50i	0.0812302	+	0.140695i
$723$	25880.7			1.33128
$724$	−477.935	−	827.808i	−0.0245336	−	0.0424934i
$725$	11464.1	−	19856.4i	0.587265	−	1.01717i
$726$	−348.124	+	602.969i	−0.0177963	+	0.0308241i
$727$	25153.0			1.28318			0.641591	−	0.767047i	$-0.278275\pi$
$727$	25153.0			1.28318			0.641591	+	0.767047i	$0.278275\pi$
$728$	−2554.19	+	604.909i	−0.130034	+	0.0307959i
$729$	19632.1			0.997415
$730$	1771.38	−	3068.11i	0.0898104	−	0.155556i
$731$	−2380.39	+	4122.95i	−0.120440	+	0.208609i
$732$	7436.63	+	12880.6i	0.375500	+	0.650384i
$733$	18255.3			0.919886			0.459943	−	0.887948i	$-0.347870\pi$
$733$	18255.3			0.919886			0.459943	+	0.887948i	$0.347870\pi$
$734$	13364.6	+	23148.2i	0.672067	+	1.16405i
$735$	2238.43	+	3877.08i	0.112335	+	0.194569i
$736$	−1771.57			−0.0887241
$737$	−17077.8	−	29579.6i	−0.853551	−	1.47839i
$738$	16.7047	−	28.9333i	0.000833207	−	0.00144316i
$739$	−10927.5	+	18927.0i	−0.543943	+	0.942138i	0.454729	+	0.890630i	$0.349736\pi$
$739$	−10927.5	+	18927.0i	−0.543943	+	0.942138i	−0.998673	+	0.0515079i	$0.983597\pi$
$740$	24750.4			1.22952
$741$	5086.55	−	16980.1i	0.252171	−	0.841806i
$742$	2138.39			0.105799
$743$	−6108.29	+	10579.9i	−0.301604	+	0.522393i	−0.976499	−	0.215520i	$-0.930855\pi$
$743$	−6108.29	+	10579.9i	−0.301604	+	0.522393i	0.674896	+	0.737913i	$0.264189\pi$
$744$	1477.95	−	2559.88i	0.0728283	−	0.126142i
$745$	6216.99	+	10768.1i	0.305736	+	0.529550i
$746$	−13747.7			−0.674716
$747$	29.9187	+	51.8207i	0.00146542	+	0.00253818i
$748$	−1382.14	−	2393.93i	−0.0675615	−	0.117020i
$749$	−7119.61			−0.347323
$750$	5333.30	+	9237.54i	0.259659	+	0.449743i
$751$	8766.53	−	15184.1i	0.425959	−	0.737783i	−0.570550	−	0.821263i	$-0.693270\pi$
$751$	8766.53	−	15184.1i	0.425959	−	0.737783i	0.996509	+	0.0834798i	$0.0266034\pi$
$752$	1896.48	−	3284.79i	0.0919646	−	0.159287i
$753$	−11135.8			−0.538924
$754$	−11405.9	+	2701.26i	−0.550898	+	0.130469i
$755$	−18969.8			−0.914412
$756$	1961.61	−	3397.61i	0.0943692	−	0.163452i
$757$	16608.2	−	28766.2i	0.797403	−	1.38114i	−0.123899	−	0.992295i	$-0.539540\pi$
$757$	16608.2	−	28766.2i	0.797403	−	1.38114i	0.921302	−	0.388848i	$-0.127127\pi$
$758$	−9844.51	−	17051.2i	−0.471726	−	0.817054i
$759$	−10240.9			−0.489750
$760$	−5105.57	−	8843.10i	−0.243682	−	0.422070i
$761$	6299.21	+	10910.6i	0.300061	+	0.519720i	0.976149	−	0.217100i	$-0.0696597\pi$
$761$	6299.21	+	10910.6i	0.300061	+	0.519720i	−0.676089	+	0.736820i	$0.736326\pi$
$762$	−9953.75			−0.473210
$763$	−6612.27	−	11452.8i	−0.313736	−	0.543406i
$764$	5910.53	−	10237.3i	0.279889	−	0.484783i
$765$	11.8528	−	20.5297i	0.000560183	−	0.000970265i
$766$	−18329.7			−0.864596
$767$	1121.84	−	265.685i	0.0528125	−	0.0125076i
$768$	−1331.92			−0.0625803
$769$	−4325.52	+	7492.01i	−0.202838	+	0.351325i	−0.949442	−	0.313944i	$-0.898350\pi$
$769$	−4325.52	+	7492.01i	−0.202838	+	0.351325i	0.746604	+	0.665269i	$0.231683\pi$
$770$	−4370.44	+	7569.83i	−0.204545	+	0.354283i
$771$	−13184.5	−	22836.3i	−0.615862	−	1.06670i
$772$	10886.8			0.507543
$773$	8483.89	+	14694.5i	0.394753	+	0.683732i	0.993070	−	0.117527i	$-0.0374968\pi$
$773$	8483.89	+	14694.5i	0.394753	+	0.683732i	−0.598317	+	0.801260i	$0.704163\pi$
$774$	17.0108	+	29.4636i	0.000789976	+	0.00136828i
$775$	13022.6			0.603593
$776$	3614.31	+	6260.17i	0.167199	+	0.289597i
$777$	−6416.40	+	11113.5i	−0.296251	+	0.513122i
$778$	−5545.20	+	9604.57i	−0.255533	+	0.442597i
$779$	−17482.5			−0.804074
$780$	4915.60	−	16409.4i	0.225650	−	0.753270i
$781$	16297.1			0.746679
$782$	−1076.07	+	1863.81i	−0.0492075	+	0.0852299i
$783$	8759.69	−	15172.2i	0.399803	−	0.692479i
$784$	−392.000	−	678.964i	−0.0178571	−	0.0309295i
$785$	−22003.7			−1.00044
$786$	11025.5	+	19096.7i	0.500339	+	0.866613i
$787$	−14077.7	−	24383.4i	−0.637633	−	1.10441i	−0.985951	−	0.167036i	$-0.946580\pi$
$787$	−14077.7	−	24383.4i	−0.637633	−	1.10441i	0.348318	−	0.937377i	$-0.386753\pi$
$788$	−2380.34			−0.107609
$789$	8582.31	+	14865.0i	0.387248	+	0.670733i
$790$	20119.9	−	34848.7i	0.906119	−	1.56944i
$791$	201.736	−	349.418i	0.00906817	−	0.0157065i
$792$	−19.7542			−0.000886281
$793$	32596.5	−	7719.84i	1.45969	−	0.345699i
$794$	−24366.1			−1.08907
$795$	−6977.62	+	12085.6i	−0.311284	+	0.539159i
$796$	334.591	−	579.528i	0.0148986	−	0.0258051i
$797$	7813.98	+	13534.2i	0.347284	+	0.601514i	0.985766	−	0.168123i	$-0.0537707\pi$
$797$	7813.98	+	13534.2i	0.347284	+	0.601514i	−0.638482	+	0.769637i	$0.720437\pi$
$798$	5294.35			0.234860
$799$	−2303.88	−	3990.44i	−0.102009	−	0.176685i
$800$	−2933.98	−	5081.80i	−0.129665	−	0.224586i
$801$	73.4228			0.00323879
$802$	−11242.3	−	19472.2i	−0.494987	−	0.857343i
$803$	−1793.21	+	3105.93i	−0.0788057	+	0.136495i
$804$	−9996.36	+	17314.2i	−0.438488	+	0.759483i
$805$	6805.27			0.297956
$806$	−4567.79	−	4843.17i	−0.199620	−	0.211654i
$807$	−24723.4			−1.07845
$808$	−3715.36	+	6435.19i	−0.161765	+	0.280184i
$809$	−3114.28	+	5394.08i	−0.135343	+	0.234420i	−0.925728	−	0.378189i	$-0.876547\pi$
$809$	−3114.28	+	5394.08i	−0.135343	+	0.234420i	0.790386	+	0.612610i	$0.209880\pi$
$810$	12834.5	+	22230.0i	0.556739	+	0.964300i
$811$	−20273.2			−0.877790			−0.438895	−	0.898538i	$-0.644630\pi$
$811$	−20273.2			−0.877790			−0.438895	+	0.898538i	$0.644630\pi$
$812$	−1750.50	−	3031.95i	−0.0756533	−	0.131035i
$813$	−3573.40	−	6189.31i	−0.154151	−	0.266997i
$814$	−25055.5			−1.07886
$815$	−30219.8	−	52342.3i	−1.29884	−	2.24966i
$816$	−809.026	+	1401.27i	−0.0347078	+	0.0601157i
$817$	8901.44	−	15417.7i	0.381177	−	0.660219i
$818$	24248.8			1.03648
$819$	15.6349	+	16.5775i	0.000667066	+	0.000707282i
$820$	−16894.9			−0.719507
$821$	10770.2	−	18654.4i	0.457833	−	0.792990i	−0.541013	−	0.841014i	$-0.681959\pi$
$821$	10770.2	−	18654.4i	0.457833	−	0.792990i	0.998846	+	0.0480241i	$0.0152924\pi$
$822$	−12787.2	+	22148.0i	−0.542583	+	0.939782i
$823$	−2892.48	−	5009.92i	−0.122510	−	0.212193i	0.798247	−	0.602330i	$-0.205761\pi$
$823$	−2892.48	−	5009.92i	−0.122510	−	0.212193i	−0.920757	+	0.390137i	$0.872428\pi$
$824$	−3093.30			−0.130777
$825$	−16960.4	−	29376.2i	−0.715739	−	1.23970i
$826$	172.172	+	298.211i	0.00725258	+	0.0125618i
$827$	−5065.76			−0.213003			−0.106502	−	0.994313i	$-0.533965\pi$
$827$	−5065.76			−0.213003			−0.106502	+	0.994313i	$0.533965\pi$
$828$	7.68987	+	13.3192i	0.000322755	+	0.000559029i
$829$	−13055.6	+	22612.9i	−0.546971	+	0.947381i	0.451509	+	0.892266i	$0.350886\pi$
$829$	−13055.6	+	22612.9i	−0.546971	+	0.947381i	−0.998480	+	0.0551147i	$0.982448\pi$
$830$	15129.7	−	26205.4i	0.632723	−	1.09591i
$831$	−18624.0			−0.777450
$832$	−860.831	+	2873.65i	−0.0358701	+	0.119743i
$833$	−952.421			−0.0396151
$834$	−11496.9	+	19913.2i	−0.477344	+	0.826784i
$835$	−20622.8	+	35719.8i	−0.854710	+	1.48040i
$836$	5168.50	+	8952.10i	0.213823	+	0.370353i
$837$	9950.49			0.410919
$838$	7332.86	+	12700.9i	0.302279	+	0.523562i
$839$	−18418.1	−	31901.1i	−0.757882	−	1.31269i	−0.943929	−	0.330149i	$-0.892901\pi$
$839$	−18418.1	−	31901.1i	−0.757882	−	1.31269i	0.186047	−	0.982541i	$-0.440432\pi$
$840$	5116.42			0.210159
$841$	4377.55	+	7582.14i	0.179489	+	0.310883i
$842$	−8750.98	+	15157.1i	−0.358169	+	0.620368i
$843$	−19709.3	+	34137.6i	−0.805250	+	1.39473i
$844$	−8806.97			−0.359181
$845$	−32226.6	−	21211.0i	−1.31199	−	0.863527i
$846$	−32.9282			−0.00133817
$847$	−234.187	+	405.623i	−0.00950030	+	0.0164550i
$848$	1221.94	−	2116.46i	0.0494829	−	0.0857069i
$849$	−16281.2	−	28199.9i	−0.658152	−	1.13995i
$850$	−7128.53			−0.287655
$851$	9753.55	+	16893.6i	0.392887	+	0.680501i
$852$	−4769.70	−	8261.36i	−0.191793	−	0.332194i
$853$	37518.2			1.50598			0.752989	−	0.658033i	$-0.228611\pi$
$853$	37518.2			1.50598			0.752989	+	0.658033i	$0.228611\pi$
$854$	5002.70	+	8664.93i	0.200455	+	0.347199i
$855$	−44.3235	+	76.7706i	−0.00177290	+	0.00307076i
$856$	−4068.35	+	7046.58i	−0.162445	+	0.281364i
$857$	28899.8			1.15192			0.575962	−	0.817477i	$-0.304628\pi$
$857$	28899.8			1.15192			0.575962	+	0.817477i	$0.304628\pi$
$858$	−4976.19	+	16611.7i	−0.198000	+	0.660970i
$859$	−23027.2			−0.914643			−0.457322	−	0.889301i	$-0.651191\pi$
$859$	−23027.2			−0.914643			−0.457322	+	0.889301i	$0.651191\pi$
$860$	8602.28	−	14899.6i	0.341088	−	0.590781i
$861$	4379.91	−	7586.22i	0.173365	−	0.300276i
$862$	2444.15	+	4233.39i	0.0965755	+	0.167274i
$863$	−13042.4			−0.514450			−0.257225	−	0.966352i	$-0.582808\pi$
$863$	−13042.4			−0.514450			−0.257225	+	0.966352i	$0.582808\pi$
$864$	−2241.84	−	3882.98i	−0.0882743	−	0.152896i
$865$	−38190.9	−	66148.6i	−1.50119	−	2.60014i
$866$	−20036.1			−0.786206
$867$	−11797.9	−	20434.6i	−0.462144	−	0.800457i
$868$	994.232	−	1722.06i	0.0388784	−	0.0673393i
$869$	−20367.9	+	35278.2i	−0.795091	+	1.37714i
$870$	22847.7			0.890355
$871$	30895.0	+	32757.6i	1.20188	+	1.27434i
$872$	−15113.8			−0.586945
$873$	31.3773	−	54.3471i	0.00121645	−	0.00210695i
$874$	4023.96	−	6969.70i	0.155735	−	0.269741i
$875$	3587.77	+	6214.19i	0.138616	+	0.240089i
$876$	2099.29			0.0809684
$877$	3430.15	+	5941.20i	0.132073	+	0.228757i	0.924476	−	0.381241i	$-0.124503\pi$
$877$	3430.15	+	5941.20i	0.132073	+	0.228757i	−0.792403	+	0.609999i	$0.791170\pi$
$878$	1642.32	+	2844.57i	0.0631270	+	0.109339i
$879$	10057.5			0.385929
$880$	4994.79	+	8651.24i	0.191335	+	0.331401i
$881$	2893.62	−	5011.90i	0.110657	−	0.191663i	−0.805379	−	0.592761i	$-0.798038\pi$
$881$	2893.62	−	5011.90i	0.110657	−	0.191663i	0.916035	+	0.401098i	$0.131371\pi$
$882$	−3.40311	+	5.89437i	−0.000129919	+	0.000225027i
$883$	35206.6			1.34178			0.670892	−	0.741555i	$-0.265911\pi$
$883$	35206.6			1.34178			0.670892	+	0.741555i	$0.265911\pi$
$884$	2500.40	+	2651.14i	0.0951329	+	0.100868i
$885$	−2247.21			−0.0853548
$886$	2864.36	−	4961.22i	0.108612	−	0.188121i
$887$	−1626.01	+	2816.33i	−0.0615513	+	0.106610i	−0.895159	−	0.445747i	$-0.852938\pi$
$887$	−1626.01	+	2816.33i	−0.0615513	+	0.106610i	0.833608	+	0.552357i	$0.186271\pi$
$888$	7333.03	+	12701.2i	0.277118	+	0.479982i
$889$	−6695.99			−0.252617
$890$	−18564.8	−	32155.1i	−0.699205	−	1.21106i
$891$	−12992.7	−	22504.0i	−0.488520	−	0.846142i
$892$	−23659.7			−0.888099
$893$	8615.34	+	14922.2i	0.322846	+	0.559186i
$894$	−3683.93	+	6380.75i	−0.137818	+	0.238707i
$895$	30615.3	−	53027.3i	1.14342	−	1.98045i
$896$	−896.000			−0.0334077
$897$	13137.5	−	3111.36i	0.489018	−	0.115814i
$898$	28461.3			1.05765
$899$	4439.80	−	7689.96i	0.164711	−	0.285289i
$900$	−25.4711	+	44.1172i	−0.000943373	+	0.00163397i
$901$	−1484.44	−	2571.12i	−0.0548876	−	0.0950681i
$902$	17103.1			0.631344
$903$	4460.18	+	7725.27i	0.164369	+	0.284696i
$904$	−230.556	−	399.335i	−0.00848250	−	0.0146921i
$905$	4196.41			0.154136
$906$	−5620.35	−	9734.74i	−0.206097	−	0.356970i
$907$	−25691.5	+	44498.9i	−0.940541	+	1.62907i	−0.176100	+	0.984372i	$0.556348\pi$
$907$	−25691.5	+	44498.9i	−0.940541	+	1.62907i	−0.764441	+	0.644693i	$0.776985\pi$
$908$	11142.1	−	19298.7i	0.407228	−	0.705340i
$909$	64.5091			0.00235383
$910$	3306.78	−	11038.8i	0.120460	−	0.402123i
$911$	2406.21			0.0875096			0.0437548	−	0.999042i	$-0.486068\pi$
$911$	2406.21			0.0875096			0.0437548	+	0.999042i	$0.486068\pi$
$912$	3025.35	−	5240.05i	0.109846	−	0.190258i
$913$	−15316.2	+	26528.4i	−0.555194	+	0.961625i
$914$	17058.6	+	29546.4i	0.617341	+	1.06927i
$915$	−65295.7			−2.35914
$916$	6054.48	+	10486.7i	0.218391	+	0.378264i
$917$	7416.97	+	12846.6i	0.267099	+	0.462629i
$918$	−5446.88			−0.195832
$919$	1584.47	+	2744.38i	0.0568736	+	0.0985080i	0.893060	−	0.449937i	$-0.148553\pi$
$919$	1584.47	+	2744.38i	0.0568736	+	0.0985080i	−0.836187	+	0.548445i	$0.815220\pi$
$920$	3888.72	−	6735.47i	0.139356	−	0.241372i
$921$	12711.5	−	22017.0i	0.454788	−	0.787716i
$922$	−22248.1			−0.794688
$923$	−20906.7	+	4951.35i	−0.745562	+	0.176572i
$924$	−5179.49			−0.184408
$925$	−32306.6	+	55956.6i	−1.14836	+	1.98902i
$926$	4793.11	−	8301.92i	0.170099	−	0.294620i
$927$	13.4271	+	23.2564i	0.000475732	+	0.000823992i
$928$	−4001.14			−0.141534
$929$	13990.4	+	24232.1i	0.494090	+	0.855789i	0.999977	−	0.00681092i	$-0.00216800\pi$
$929$	13990.4	+	24232.1i	0.494090	+	0.855789i	−0.505887	+	0.862600i	$0.668835\pi$
$930$	6488.41	+	11238.2i	0.228778	+	0.396255i
$931$	3561.57			0.125377
$932$	7527.61	+	13038.2i	0.264565	+	0.458241i
$933$	−21189.7	+	36701.6i	−0.743536	+	1.28784i
$934$	−1176.28	+	2037.38i	−0.0412090	+	0.0713760i
$935$	12135.6			0.424466
$936$	25.3417	−	6.00168i	0.000884955	−	0.000209584i
$937$	39522.4			1.37795			0.688975	−	0.724785i	$-0.258061\pi$
$937$	39522.4			1.37795			0.688975	+	0.724785i	$0.258061\pi$
$938$	−6724.66	+	11647.4i	−0.234081	+	0.405440i
$939$	27990.3	−	48480.6i	0.972767	−	1.68488i
$940$	8325.80	+	14420.7i	0.288891	+	0.500374i
$941$	4246.22			0.147102			0.0735509	−	0.997291i	$-0.476567\pi$
$941$	4246.22			0.147102			0.0735509	+	0.997291i	$0.476567\pi$
$942$	−6519.25	−	11291.7i	−0.225487	−	0.390555i
$943$	−6657.88	−	11531.8i	−0.229915	−	0.398225i
$944$	393.536			0.0135683
$945$	8611.75	+	14916.0i	0.296445	+	0.513458i
$946$	−8708.31	+	15083.2i	−0.299293	+	0.518391i
$947$	12031.8	−	20839.6i	0.412861	−	0.715097i	−0.582340	−	0.812945i	$-0.697863\pi$
$947$	12031.8	−	20839.6i	0.412861	−	0.715097i	0.995201	+	0.0978487i	$0.0311961\pi$
$948$	23844.4			0.816911
$949$	1356.78	−	4529.25i	0.0464099	−	0.154927i
$950$	26657.1			0.910389
$951$	15086.0	−	26129.7i	0.514403	−	0.890972i
$952$	−544.240	+	942.652i	−0.0185283	+	0.0320919i
$953$	23910.9	+	41414.9i	0.812750	+	1.40772i	0.910932	+	0.412556i	$0.135364\pi$
$953$	23910.9	+	41414.9i	0.812750	+	1.40772i	−0.0981826	+	0.995168i	$0.531303\pi$
$954$	−21.2163			−0.000720023
$955$	25948.1	+	44943.4i	0.879225	+	1.52286i
$956$	−1673.53	−	2898.64i	−0.0566171	−	0.0980636i
$957$	−23129.3			−0.781258
$958$	−6794.88	−	11769.1i	−0.229157	−	0.396912i
$959$	−8602.06	+	14899.2i	−0.289651	+	0.501690i
$960$	2923.67	−	5063.95i	0.0982928	−	0.170248i
$961$	−24747.6			−0.830709
$962$	32142.4	−	7612.30i	1.07725	−	0.255125i
$963$	70.6380			0.00236374
$964$	9948.69	−	17231.6i	0.332392	−	0.575719i
$965$	−23897.2	+	41391.2i	−0.797180	+	1.38076i
$966$	2016.26	+	3492.26i	0.0671553	+	0.116316i
$967$	−45369.7			−1.50878			−0.754391	−	0.656425i	$-0.772068\pi$
$967$	−45369.7			−1.50878			−0.754391	+	0.656425i	$0.772068\pi$
$968$	267.642	+	463.570i	0.00888672	+	0.0153922i
$969$	−3675.26	−	6365.73i	−0.121843	−	0.211039i
$970$	−31734.7			−1.05045
$971$	6271.11	+	10861.9i	0.207260	+	0.358985i	0.950850	−	0.309650i	$-0.100212\pi$
$971$	6271.11	+	10861.9i	0.207260	+	0.358985i	−0.743590	+	0.668635i	$0.766879\pi$
$972$	−38.9749	+	67.5065i	−0.00128613	+	0.00222765i
$973$	−7734.08	+	13395.8i	−0.254823	+	0.441367i
$974$	−30150.0			−0.991855
$975$	30682.7	+	32532.5i	1.00783	+	1.06859i
$976$	11434.7			0.375018
$977$	−9256.37	+	16032.5i	−0.303109	+	0.525000i	−0.976839	−	0.213978i	$-0.931358\pi$
$977$	−9256.37	+	16032.5i	−0.303109	+	0.525000i	0.673729	+	0.738978i	$0.264691\pi$
$978$	17907.0	−	31015.8i	0.585484	−	1.01409i
$979$	18793.6	+	32551.5i	0.613530	+	1.06267i
$980$	3441.87			0.112190
$981$	65.6044	+	113.630i	0.00213515	+	0.00369820i
$982$	700.777	+	1213.78i	0.0227726	+	0.0394433i
$983$	−28145.6			−0.913231			−0.456615	−	0.889664i	$-0.650938\pi$
$983$	−28145.6			−0.913231			−0.456615	+	0.889664i	$0.650938\pi$
$984$	−5005.61	−	8669.97i	−0.162168	−	0.280883i
$985$	5225.02	−	9049.99i	0.169018	−	0.292748i
$986$	−2430.34	+	4209.47i	−0.0784966	+	0.135960i
$987$	−8633.66			−0.278432
$988$	−9350.21	−	9913.92i	−0.301083	−	0.319235i
$989$	13559.8			0.435972
$990$	43.3619	−	75.1049i	0.00139205	−	0.00241110i
$991$	12217.3	−	21161.1i	0.391621	−	0.678308i	−0.601042	−	0.799217i	$-0.705248\pi$
$991$	12217.3	−	21161.1i	0.391621	−	0.678308i	0.992664	+	0.120909i	$0.0385810\pi$
$992$	−1136.27	−	1968.07i	−0.0363674	−	0.0629902i
$993$	−33814.2			−1.08063
$994$	−3208.63	−	5557.51i	−0.102386	−	0.177337i
$995$	1468.90	+	2544.21i	0.0468013	+	0.0810623i
$996$	17930.5			0.570431
$997$	−3310.07	−	5733.21i	−0.105146	−	0.182119i	0.808652	−	0.588288i	$-0.200198\pi$
$997$	−3310.07	−	5733.21i	−0.105146	−	0.182119i	−0.913798	+	0.406169i	$0.866864\pi$
$998$	1528.64	−	2647.68i	0.0484851	−	0.0839787i
$999$	−24685.3	+	42756.2i	−0.781791	+	1.35410i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	182.4.g.a.113.3	yes	8
13.3	even	3	inner	182.4.g.a.29.3	✓	8
13.4	even	6		2366.4.a.q.1.2		4
13.9	even	3		2366.4.a.r.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.4.g.a.29.3	✓	8	13.3	even	3	inner
182.4.g.a.113.3	yes	8	1.1	even	1	trivial
2366.4.a.q.1.2		4	13.4	even	6
2366.4.a.r.1.2		4	13.9	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 182 = 2 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	182.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +(2.60142 - 4.50578i) q^{3} +(-2.00000 - 3.46410i) q^{4} +17.5606 q^{5} +(5.20283 + 9.01157i) q^{6} +(3.50000 + 6.06218i) q^{7} +8.00000 q^{8} +(-0.0347256 - 0.0601466i) q^{9} +(-17.5606 + 30.4158i) q^{10} +(17.7770 - 30.7907i) q^{11} -20.8113 q^{12} +(-13.4505 + 44.9008i) q^{13} -14.0000 q^{14} +(45.6823 - 79.1241i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(9.71858 + 16.8331i) q^{17} +0.138903 q^{18} +(-36.3425 - 62.9471i) q^{19} +(-35.1211 - 60.8316i) q^{20} +36.4198 q^{21} +(35.5540 + 61.5814i) q^{22} +(27.6808 - 47.9445i) q^{23} +(20.8113 - 36.0463i) q^{24} +183.374 q^{25} +(-64.3200 - 68.1978i) q^{26} +140.115 q^{27} +(14.0000 - 24.2487i) q^{28} +(62.5178 - 108.284i) q^{29} +(91.3647 + 158.248i) q^{30} +71.0166 q^{31} +(-16.0000 - 27.7128i) q^{32} +(-92.4908 - 160.199i) q^{33} -38.8743 q^{34} +(61.4620 + 106.455i) q^{35} +(-0.138903 + 0.240586i) q^{36} +(-176.179 + 305.151i) q^{37} +145.370 q^{38} +(167.323 + 177.411i) q^{39} +140.485 q^{40} +(120.262 - 208.299i) q^{41} +(-36.4198 + 63.0810i) q^{42} +(122.466 + 212.117i) q^{43} -142.216 q^{44} +(-0.609802 - 1.05621i) q^{45} +(55.3616 + 95.8891i) q^{46} -237.059 q^{47} +(41.6226 + 72.0925i) q^{48} +(-24.5000 + 42.4352i) q^{49} +(-183.374 + 317.613i) q^{50} +101.128 q^{51} +(182.442 - 43.2078i) q^{52} -152.742 q^{53} +(-140.115 + 242.686i) q^{54} +(312.175 - 540.702i) q^{55} +(28.0000 + 48.4974i) q^{56} -378.168 q^{57} +(125.036 + 216.568i) q^{58} +(-12.2980 - 21.3008i) q^{59} -365.459 q^{60} +(-357.336 - 618.923i) q^{61} +(-71.0166 + 123.004i) q^{62} +(0.243080 - 0.421026i) q^{63} +64.0000 q^{64} +(-236.198 + 788.484i) q^{65} +369.963 q^{66} +(480.333 - 831.960i) q^{67} +(38.8743 - 67.3323i) q^{68} +(-144.018 - 249.447i) q^{69} -245.848 q^{70} +(229.188 + 396.965i) q^{71} +(-0.277805 - 0.481173i) q^{72} -100.872 q^{73} +(-352.358 - 610.302i) q^{74} +(477.031 - 826.242i) q^{75} +(-145.370 + 251.788i) q^{76} +248.878 q^{77} +(-474.607 + 112.401i) q^{78} -1145.74 q^{79} +(-140.485 + 243.326i) q^{80} +(365.435 - 632.952i) q^{81} +(240.523 + 416.599i) q^{82} -861.573 q^{83} +(-72.8396 - 126.162i) q^{84} +(170.664 + 295.598i) q^{85} -489.863 q^{86} +(-325.270 - 563.383i) q^{87} +(142.216 - 246.326i) q^{88} +(-528.592 + 915.549i) q^{89} +2.43921 q^{90} +(-319.274 + 75.6136i) q^{91} -221.446 q^{92} +(184.744 - 319.985i) q^{93} +(237.059 - 410.599i) q^{94} +(-638.196 - 1105.39i) q^{95} -166.491 q^{96} +(451.789 + 782.521i) q^{97} +(-49.0000 - 84.8705i) q^{98} -2.46927 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 7 q^{3} - 16 q^{4} - 2 q^{5} + 14 q^{6} + 28 q^{7} + 64 q^{8} + 29 q^{9} + 2 q^{10} + 15 q^{11} - 56 q^{12} + 64 q^{13} - 112 q^{14} - 67 q^{15} - 64 q^{16} + 24 q^{17} - 116 q^{18} - 21 q^{19}+ \cdots - 258 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 7 * q^3 - 16 * q^4 - 2 * q^5 + 14 * q^6 + 28 * q^7 + 64 * q^8 + 29 * q^9 + 2 * q^10 + 15 * q^11 - 56 * q^12 + 64 * q^13 - 112 * q^14 - 67 * q^15 - 64 * q^16 + 24 * q^17 - 116 * q^18 - 21 * q^19 + 4 * q^20 + 98 * q^21 + 30 * q^22 + 182 * q^23 + 56 * q^24 + 730 * q^25 - 136 * q^26 + 184 * q^27 + 112 * q^28 - 133 * q^29 - 134 * q^30 - 564 * q^31 - 128 * q^32 - 95 * q^33 - 96 * q^34 - 7 * q^35 + 116 * q^36 - 730 * q^37 + 84 * q^38 + 792 * q^39 - 16 * q^40 + 182 * q^41 - 98 * q^42 - 83 * q^43 - 120 * q^44 + 73 * q^45 + 364 * q^46 - 1120 * q^47 + 112 * q^48 - 196 * q^49 - 730 * q^50 + 418 * q^51 + 16 * q^52 - 212 * q^53 - 184 * q^54 + 997 * q^55 + 224 * q^56 - 682 * q^57 - 266 * q^58 + 782 * q^59 + 536 * q^60 + 708 * q^61 + 564 * q^62 - 203 * q^63 + 512 * q^64 - 801 * q^65 + 380 * q^66 + 528 * q^67 + 96 * q^68 - 1198 * q^69 + 28 * q^70 + 82 * q^71 + 232 * q^72 + 1120 * q^73 - 1460 * q^74 + 2873 * q^75 - 84 * q^76 + 210 * q^77 - 1566 * q^78 - 3996 * q^79 + 16 * q^80 + 1220 * q^81 + 364 * q^82 - 716 * q^83 - 196 * q^84 + 547 * q^85 + 332 * q^86 + 245 * q^87 + 120 * q^88 - 2385 * q^89 - 292 * q^90 - 28 * q^91 - 1456 * q^92 + 1963 * q^93 + 1120 * q^94 - 1117 * q^95 - 448 * q^96 + 1155 * q^97 - 392 * q^98 - 258 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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