LMFDB - Embedded newform 28.4.f.a.3.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [28,4,Mod(3,28)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(28, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("28.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 28 = 2^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	28.f (of order $6$, 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:	$1.65205348016$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{18} - 24 x^{17} + 28 x^{16} + 56 x^{15} - 192 x^{14} + 352 x^{13} - 448 x^{12} + \cdots + 1073741824 $ x^20 - 2x^18 - 24x^17 + 28x^16 + 56x^15 - 192x^14 + 352x^13 - 448x^12 + 5376x^11 - 41472x^10 + 43008x^9 - 28672x^8 + 180224x^7 - 786432x^6 + 1835008x^5 + 7340032x^4 - 50331648x^3 - 33554432*x^2 + 1073741824
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{24} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			3.3
Root			$-1.03939 + 2.63053i$ of defining polynomial
Character	$\chi$	$=$	28.3
Dual form			28.4.f.a.19.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.75840 - 2.21540i) q^{2} +(-3.44104 + 5.96006i) q^{3} +(-1.81602 + 7.79115i) q^{4} +(-4.17670 + 2.41142i) q^{5} +(19.2547 - 2.85690i) q^{6} +(-5.03893 + 17.8216i) q^{7} +(20.4539 - 9.67677i) q^{8} +(-10.1816 - 17.6350i) q^{9} +O(q^{10})$	\(q+(-1.75840 - 2.21540i) q^{2} +(-3.44104 + 5.96006i) q^{3} +(-1.81602 + 7.79115i) q^{4} +(-4.17670 + 2.41142i) q^{5} +(19.2547 - 2.85690i) q^{6} +(-5.03893 + 17.8216i) q^{7} +(20.4539 - 9.67677i) q^{8} +(-10.1816 - 17.6350i) q^{9} +(12.6866 + 5.01283i) q^{10} +(-36.6380 - 21.1529i) q^{11} +(-40.1867 - 37.6333i) q^{12} +3.39776i q^{13} +(48.3425 - 20.1743i) q^{14} -33.1912i q^{15} +(-57.4041 - 28.2978i) q^{16} +(101.660 + 58.6935i) q^{17} +(-21.1653 + 53.5656i) q^{18} +(45.5858 + 78.9570i) q^{19} +(-11.2028 - 36.9205i) q^{20} +(-88.8786 - 91.3572i) q^{21} +(17.5621 + 118.363i) q^{22} +(147.782 - 85.3222i) q^{23} +(-12.7084 + 155.204i) q^{24} +(-50.8701 + 88.1096i) q^{25} +(7.52740 - 5.97463i) q^{26} -45.6757 q^{27} +(-129.700 - 71.6235i) q^{28} -131.473 q^{29} +(-73.5319 + 58.3636i) q^{30} +(5.70011 - 9.87288i) q^{31} +(38.2485 + 176.932i) q^{32} +(252.146 - 145.576i) q^{33} +(-48.7299 - 328.425i) q^{34} +(-21.9293 - 86.5865i) q^{35} +(155.887 - 47.3005i) q^{36} +(59.2181 + 102.569i) q^{37} +(94.7632 - 239.829i) q^{38} +(-20.2508 - 11.6918i) q^{39} +(-62.0949 + 89.7399i) q^{40} +109.956i q^{41} +(-46.1084 + 357.545i) q^{42} +82.5542i q^{43} +(231.341 - 247.038i) q^{44} +(85.0507 + 49.1040i) q^{45} +(-448.885 - 177.367i) q^{46} +(-36.7384 - 63.6328i) q^{47} +(366.187 - 244.758i) q^{48} +(-292.218 - 179.603i) q^{49} +(284.648 - 42.2346i) q^{50} +(-699.634 + 403.934i) q^{51} +(-26.4724 - 6.17041i) q^{52} +(87.2160 - 151.062i) q^{53} +(80.3164 + 101.190i) q^{54} +204.035 q^{55} +(69.3900 + 413.281i) q^{56} -627.451 q^{57} +(231.182 + 291.265i) q^{58} +(-166.628 + 288.607i) q^{59} +(258.598 + 60.2761i) q^{60} +(472.266 - 272.663i) q^{61} +(-31.8955 + 4.73248i) q^{62} +(365.587 - 92.5901i) q^{63} +(324.720 - 395.855i) q^{64} +(-8.19342 - 14.1914i) q^{65} +(-765.885 - 302.622i) q^{66} +(516.318 + 298.096i) q^{67} +(-641.907 + 685.461i) q^{68} +1174.39i q^{69} +(-153.264 + 200.836i) q^{70} -384.641i q^{71} +(-378.901 - 262.178i) q^{72} +(187.557 + 108.286i) q^{73} +(123.102 - 311.550i) q^{74} +(-350.092 - 606.378i) q^{75} +(-697.951 + 211.778i) q^{76} +(561.595 - 546.359i) q^{77} +(9.70706 + 65.4227i) q^{78} +(868.356 - 501.346i) q^{79} +(307.998 - 20.2338i) q^{80} +(432.074 - 748.374i) q^{81} +(243.596 - 193.346i) q^{82} -459.471 q^{83} +(873.183 - 526.560i) q^{84} -566.139 q^{85} +(182.891 - 145.164i) q^{86} +(452.403 - 783.585i) q^{87} +(-954.080 - 78.1218i) q^{88} +(-771.258 + 445.286i) q^{89} +(-40.7683 - 274.766i) q^{90} +(-60.5534 - 17.1210i) q^{91} +(396.382 + 1306.34i) q^{92} +(39.2287 + 67.9460i) q^{93} +(-76.3713 + 193.283i) q^{94} +(-380.797 - 219.853i) q^{95} +(-1186.14 - 380.868i) q^{96} +282.888i q^{97} +(115.944 + 963.197i) q^{98} +861.479i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{4} - 6 q^{5} + 72 q^{8} - 56 q^{9}+O(q^{10}) $ 20 * q + 4 * q^4 - 6 * q^5 + 72 * q^8 - 56 * q^9	$ 20 q + 4 q^{4} - 6 q^{5} + 72 q^{8} - 56 q^{9} - 12 q^{10} - 168 q^{12} - 56 q^{14} - 104 q^{16} - 6 q^{17} + 68 q^{18} + 238 q^{21} - 184 q^{22} + 348 q^{24} - 36 q^{25} + 396 q^{26} + 448 q^{28} - 352 q^{29} + 644 q^{30} - 40 q^{32} + 30 q^{33} + 208 q^{36} + 258 q^{37} - 1620 q^{38} - 1548 q^{40} - 980 q^{42} - 1248 q^{44} - 504 q^{45} + 232 q^{46} - 644 q^{49} - 864 q^{50} + 2592 q^{52} + 570 q^{53} + 4572 q^{54} + 1904 q^{56} + 1452 q^{57} + 2244 q^{58} - 736 q^{60} + 294 q^{61} + 2560 q^{64} - 124 q^{65} - 4272 q^{66} - 6084 q^{68} - 4144 q^{70} - 4672 q^{72} + 966 q^{73} + 832 q^{74} - 378 q^{77} - 4056 q^{78} + 7032 q^{80} - 1262 q^{81} + 7692 q^{82} + 6188 q^{84} - 2980 q^{85} + 5696 q^{86} - 1396 q^{88} - 3186 q^{89} + 3312 q^{92} - 306 q^{93} - 6780 q^{94} - 11784 q^{96} - 4900 q^{98}+O(q^{100}) $ 20 * q + 4 * q^4 - 6 * q^5 + 72 * q^8 - 56 * q^9 - 12 * q^10 - 168 * q^12 - 56 * q^14 - 104 * q^16 - 6 * q^17 + 68 * q^18 + 238 * q^21 - 184 * q^22 + 348 * q^24 - 36 * q^25 + 396 * q^26 + 448 * q^28 - 352 * q^29 + 644 * q^30 - 40 * q^32 + 30 * q^33 + 208 * q^36 + 258 * q^37 - 1620 * q^38 - 1548 * q^40 - 980 * q^42 - 1248 * q^44 - 504 * q^45 + 232 * q^46 - 644 * q^49 - 864 * q^50 + 2592 * q^52 + 570 * q^53 + 4572 * q^54 + 1904 * q^56 + 1452 * q^57 + 2244 * q^58 - 736 * q^60 + 294 * q^61 + 2560 * q^64 - 124 * q^65 - 4272 * q^66 - 6084 * q^68 - 4144 * q^70 - 4672 * q^72 + 966 * q^73 + 832 * q^74 - 378 * q^77 - 4056 * q^78 + 7032 * q^80 - 1262 * q^81 + 7692 * q^82 + 6188 * q^84 - 2980 * q^85 + 5696 * q^86 - 1396 * q^88 - 3186 * q^89 + 3312 * q^92 - 306 * q^93 - 6780 * q^94 - 11784 * q^96 - 4900 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/28\mathbb{Z}\right)^\times$.

$n$	$15$	$17$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.75840	−	2.21540i	−0.621690	−	0.783263i
$2$	−1.75840	−	2.21540i	−0.621690	−	0.783263i
$3$	−3.44104	+	5.96006i	−0.662229	+	1.14701i	0.317800	+	0.948158i	$0.397056\pi$
$3$	−3.44104	+	5.96006i	−0.662229	+	1.14701i	−0.980029	+	0.198856i	$0.936277\pi$
$4$	−1.81602	+	7.79115i	−0.227003	+	0.973894i
$5$	−4.17670	+	2.41142i	−0.373576	+	0.215684i	−0.675020	−	0.737800i	$-0.735865\pi$
$5$	−4.17670	+	2.41142i	−0.373576	+	0.215684i	0.301444	+	0.953484i	$0.402531\pi$
$6$	19.2547	−	2.85690i	1.31012	−	0.194388i
$7$	−5.03893	+	17.8216i	−0.272077	+	0.962276i
$7$	−5.03893	+	17.8216i	−0.272077	+	0.962276i
$8$	20.4539	−	9.67677i	0.903941	−	0.427657i
$9$	−10.1816	−	17.6350i	−0.377094	−	0.653147i
$10$	12.6866	+	5.01283i	0.401186	+	0.158520i
$11$	−36.6380	−	21.1529i	−1.00425	−	0.579805i	−0.0947480	−	0.995501i	$-0.530205\pi$
$11$	−36.6380	−	21.1529i	−1.00425	−	0.579805i	−0.909503	+	0.415696i	$0.863538\pi$
$12$	−40.1867	−	37.6333i	−0.966742	−	0.905317i
$13$			3.39776i			0.0724898i	0.999343	+	0.0362449i	$0.0115396\pi$
$13$			3.39776i			0.0724898i	−0.999343	+	0.0362449i	$0.988460\pi$
$14$	48.3425	−	20.1743i	0.922863	−	0.385130i
$15$		−	33.1912i		−	0.571329i
$16$	−57.4041	−	28.2978i	−0.896939	−	0.442154i
$17$	101.660	+	58.6935i	1.45036	+	0.837369i	0.998502	−	0.0547188i	$-0.0174262\pi$
$17$	101.660	+	58.6935i	1.45036	+	0.837369i	0.451863	+	0.892087i	$0.350760\pi$
$18$	−21.1653	+	53.5656i	−0.277150	+	0.701419i
$19$	45.5858	+	78.9570i	0.550427	+	0.953367i	0.998244	+	0.0592419i	$0.0188683\pi$
$19$	45.5858	+	78.9570i	0.550427	+	0.953367i	−0.447817	+	0.894125i	$0.647798\pi$
$20$	−11.2028	−	36.9205i	−0.125251	−	0.412784i
$21$	−88.8786	−	91.3572i	−0.923567	−	0.949322i
$22$	17.5621	+	118.363i	0.170193	+	1.14705i
$23$	147.782	−	85.3222i	1.33977	−	0.773518i	0.352999	−	0.935624i	$-0.385162\pi$
$23$	147.782	−	85.3222i	1.33977	−	0.773518i	0.986773	+	0.162105i	$0.0518285\pi$
$24$	−12.7084	+	155.204i	−0.108087	+	1.32004i
$25$	−50.8701	+	88.1096i	−0.406961	+	0.704877i
$26$	7.52740	−	5.97463i	0.0567786	−	0.0450662i
$27$	−45.6757			−0.325566
$28$	−129.700	−	71.6235i	−0.875392	−	0.483413i
$29$	−131.473			−0.841857			−0.420928	−	0.907094i	$-0.638296\pi$
$29$	−131.473			−0.841857			−0.420928	+	0.907094i	$0.638296\pi$
$30$	−73.5319	+	58.3636i	−0.447501	+	0.355190i
$31$	5.70011	−	9.87288i	0.0330249	−	0.0572007i	−0.849041	−	0.528328i	$-0.822819\pi$
$31$	5.70011	−	9.87288i	0.0330249	−	0.0572007i	0.882065	+	0.471127i	$0.156153\pi$
$32$	38.2485	+	176.932i	0.211295	+	0.977422i
$33$	252.146	−	145.576i	1.33009	−	0.767927i
$34$	−48.7299	−	328.425i	−0.245797	−	1.65660i
$35$	−21.9293	−	86.5865i	−0.105906	−	0.418166i
$36$	155.887	−	47.3005i	0.721697	−	0.218984i
$37$	59.2181	+	102.569i	0.263119	+	0.455735i	0.967069	−	0.254514i	$-0.0819155\pi$
$37$	59.2181	+	102.569i	0.263119	+	0.455735i	−0.703950	+	0.710249i	$0.748582\pi$
$38$	94.7632	−	239.829i	0.404543	−	1.02383i
$39$	−20.2508	−	11.6918i	−0.0831469	−	0.0480049i
$40$	−62.0949	+	89.7399i	−0.245452	+	0.354728i
$41$			109.956i			0.418833i	0.977826	+	0.209417i	$0.0671565\pi$
$41$			109.956i			0.418833i	−0.977826	+	0.209417i	$0.932844\pi$
$42$	−46.1084	+	357.545i	−0.169397	+	1.31358i
$43$			82.5542i			0.292777i	0.989227	+	0.146388i	$0.0467649\pi$
$43$			82.5542i			0.292777i	−0.989227	+	0.146388i	$0.953235\pi$
$44$	231.341	−	247.038i	0.792637	−	0.846417i
$45$	85.0507	+	49.1040i	0.281747	+	0.162667i
$46$	−448.885	−	177.367i	−1.43879	−	0.568506i
$47$	−36.7384	−	63.6328i	−0.114018	−	0.197485i	0.803369	−	0.595482i	$-0.203039\pi$
$47$	−36.7384	−	63.6328i	−0.114018	−	0.197485i	−0.917387	+	0.397997i	$0.869706\pi$
$48$	366.187	−	244.758i	1.10114	−	0.735995i
$49$	−292.218	−	179.603i	−0.851949	−	0.523625i
$50$	284.648	−	42.2346i	0.805107	−	0.119457i
$51$	−699.634	+	403.934i	−1.92095	+	1.10906i
$52$	−26.4724	−	6.17041i	−0.0705974	−	0.0164554i
$53$	87.2160	−	151.062i	0.226038	−	0.391510i	−0.730592	−	0.682814i	$-0.760756\pi$
$53$	87.2160	−	151.062i	0.226038	−	0.391510i	0.956630	+	0.291304i	$0.0940892\pi$
$54$	80.3164	+	101.190i	0.202401	+	0.255004i
$55$	204.035			0.500219
$56$	69.3900	+	413.281i	0.165583	+	0.986196i
$57$	−627.451			−1.45803
$58$	231.182	+	291.265i	0.523374	+	0.659396i
$59$	−166.628	+	288.607i	−0.367679	+	0.636839i	−0.989202	−	0.146557i	$-0.953181\pi$
$59$	−166.628	+	288.607i	−0.367679	+	0.636839i	0.621523	+	0.783396i	$0.286514\pi$
$60$	258.598	+	60.2761i	0.556414	+	0.129693i
$61$	472.266	−	272.663i	0.991271	−	0.572310i	0.0856167	−	0.996328i	$-0.472714\pi$
$61$	472.266	−	272.663i	0.991271	−	0.572310i	0.905654	+	0.424018i	$0.139381\pi$
$62$	−31.8955	+	4.73248i	−0.0653345	+	0.00969396i
$63$	365.587	−	92.5901i	0.731106	−	0.185163i
$64$	324.720	−	395.855i	0.634219	−	0.773154i
$65$	−8.19342	−	14.1914i	−0.0156349	−	0.0270805i
$66$	−765.885	−	302.622i	−1.42839	−	0.564397i
$67$	516.318	+	298.096i	0.941466	+	0.543556i	0.890420	−	0.455141i	$-0.150411\pi$
$67$	516.318	+	298.096i	0.941466	+	0.543556i	0.0510465	+	0.998696i	$0.483744\pi$
$68$	−641.907	+	685.461i	−1.14475	+	1.22242i
$69$			1174.39i			2.04898i
$70$	−153.264	+	200.836i	−0.261693	+	0.342922i
$71$		−	384.641i		−	0.642937i	−0.946920	−	0.321468i	$-0.895824\pi$
$71$		−	384.641i		−	0.642937i	0.946920	−	0.321468i	$-0.104176\pi$
$72$	−378.901	−	262.178i	−0.620194	−	0.429139i
$73$	187.557	+	108.286i	0.300710	+	0.173615i	0.642762	−	0.766066i	$-0.277788\pi$
$73$	187.557	+	108.286i	0.300710	+	0.173615i	−0.342052	+	0.939681i	$0.611122\pi$
$74$	123.102	−	311.550i	0.193382	−	0.489418i
$75$	−350.092	−	606.378i	−0.539002	−	0.933580i
$76$	−697.951	+	211.778i	−1.05343	+	0.319640i
$77$	561.595	−	546.359i	0.831165	−	0.808615i
$78$	9.70706	+	65.4227i	0.0140911	+	0.0949701i
$79$	868.356	−	501.346i	1.23668	−	0.713997i	0.268266	−	0.963345i	$-0.413549\pi$
$79$	868.356	−	501.346i	1.23668	−	0.713997i	0.968414	+	0.249347i	$0.0802161\pi$
$80$	307.998	−	20.2338i	0.430440	−	0.0282776i
$81$	432.074	−	748.374i	0.592694	−	1.02658i
$82$	243.596	−	193.346i	0.328057	−	0.260384i
$83$	−459.471			−0.607632			−0.303816	−	0.952731i	$-0.598261\pi$
$83$	−459.471			−0.607632			−0.303816	+	0.952731i	$0.598261\pi$
$84$	873.183	−	526.560i	1.13419	−	0.683957i
$85$	−566.139			−0.722428
$86$	182.891	−	145.164i	0.229321	−	0.182016i
$87$	452.403	−	783.585i	0.557502	−	0.965622i
$88$	−954.080	−	78.1218i	−1.15574	−	0.0946342i
$89$	−771.258	+	445.286i	−0.918575	+	0.530340i	−0.883180	−	0.469034i	$-0.844602\pi$
$89$	−771.258	+	445.286i	−0.918575	+	0.530340i	−0.0353951	+	0.999373i	$0.511269\pi$
$90$	−40.7683	−	274.766i	−0.0477484	−	0.321810i
$91$	−60.5534	−	17.1210i	−0.0697552	−	0.0197228i
$92$	396.382	+	1306.34i	0.449192	+	1.48039i
$93$	39.2287	+	67.9460i	0.0437400	+	0.0757600i
$94$	−76.3713	+	193.283i	−0.0837989	+	0.212081i
$95$	−380.797	−	219.853i	−0.411252	−	0.237437i
$96$	−1186.14	−	380.868i	−1.26104	−	0.404919i
$97$			282.888i			0.296113i	0.988979	+	0.148056i	$0.0473017\pi$
$97$			282.888i			0.296113i	−0.988979	+	0.148056i	$0.952698\pi$
$98$	115.944	+	963.197i	0.119511	+	0.992833i
$99$			861.479i			0.874565i
$100$	−594.094	−	556.346i	−0.594094	−	0.556346i
$101$	−696.516	−	402.134i	−0.686197	−	0.396176i	0.115988	−	0.993251i	$-0.462996\pi$
$101$	−696.516	−	402.134i	−0.686197	−	0.396176i	−0.802186	+	0.597074i	$0.796330\pi$
$102$	2125.12	+	839.692i	2.06292	+	0.815116i
$103$	887.054	+	1536.42i	0.848583	+	1.46979i	0.882473	+	0.470363i	$0.155877\pi$
$103$	887.054	+	1536.42i	0.848583	+	1.46979i	−0.0338902	+	0.999426i	$0.510790\pi$
$104$	32.8793	+	69.4972i	0.0310008	+	0.0655265i
$105$	591.520	+	167.248i	0.549776	+	0.155445i
$106$	−488.025	+	72.4105i	−0.447181	+	0.0663502i
$107$	−64.5675	+	37.2781i	−0.0583362	+	0.0336804i	−0.528884	−	0.848694i	$-0.677390\pi$
$107$	−64.5675	+	37.2781i	−0.0583362	+	0.0336804i	0.470548	+	0.882374i	$0.344056\pi$
$108$	82.9482	−	355.866i	0.0739046	−	0.317067i
$109$	−38.8638	+	67.3141i	−0.0341512	+	0.0591516i	−0.882596	−	0.470133i	$-0.844206\pi$
$109$	−38.8638	+	67.3141i	−0.0341512	+	0.0591516i	0.848445	+	0.529284i	$0.177539\pi$
$110$	−358.776	−	452.019i	−0.310981	−	0.391803i
$111$	−815.089			−0.696980
$112$	793.568	−	880.442i	0.669510	−	0.742803i
$113$	1026.99			0.854969			0.427484	−	0.904023i	$-0.359400\pi$
$113$	1026.99			0.854969			0.427484	+	0.904023i	$0.359400\pi$
$114$	1103.31	+	1390.06i	0.906445	+	1.14202i
$115$	−411.496	+	712.732i	−0.333671	+	0.577935i
$116$	238.757	−	1024.32i	0.191104	−	0.819879i
$117$	59.9193	−	34.5944i	0.0473465	−	0.0273355i
$118$	932.380	−	138.341i	0.727395	−	0.107927i
$119$	−1558.27	+	1515.99i	−1.20039	+	1.16782i
$120$	−321.184	−	678.888i	−0.244333	−	0.516448i
$121$	229.394	+	397.322i	0.172347	+	0.298514i
$122$	−1434.49	−	566.808i	−1.06453	−	0.420626i
$123$	−655.342	−	378.362i	−0.480408	−	0.277364i
$124$	66.5696	+	62.3398i	0.0482107	+	0.0451474i
$125$		−	1093.53i		−	0.782468i
$126$	−847.975	−	647.112i	−0.599552	−	0.457534i
$127$		−	1645.64i		−	1.14982i	−0.818217	−	0.574909i	$-0.805037\pi$
$127$		−	1645.64i		−	1.14982i	0.818217	−	0.574909i	$-0.194963\pi$
$128$	−1447.97	−	23.3133i	−0.999870	−	0.0160986i
$129$	−492.028	−	284.072i	−0.335819	−	0.193885i
$130$	−17.0324	+	43.1060i	−0.0114911	+	0.0290819i
$131$	−381.520	−	660.812i	−0.254455	−	0.440729i	0.710293	−	0.703907i	$-0.248563\pi$
$131$	−381.520	−	660.812i	−0.254455	−	0.440729i	−0.964747	+	0.263178i	$0.915229\pi$
$132$	676.305	+	2228.88i	0.445945	+	1.46969i
$133$	−1636.84	+	414.554i	−1.06716	+	0.270273i
$134$	−247.492	−	1668.03i	−0.159553	−	1.07534i
$135$	190.774	−	110.143i	0.121624	−	0.0702195i
$136$	2647.30	+	216.766i	1.66915	+	0.136673i
$137$	−361.462	+	626.070i	−0.225414	+	0.390429i	−0.956444	−	0.291917i	$-0.905707\pi$
$137$	−361.462	+	626.070i	−0.225414	+	0.390429i	0.731029	+	0.682346i	$0.239040\pi$
$138$	2601.75	−	2065.05i	1.60489	−	1.27383i
$139$	1639.34			1.00034			0.500168	−	0.865928i	$-0.333271\pi$
$139$	1639.34			1.00034			0.500168	+	0.865928i	$0.333271\pi$
$140$	714.433	−	13.6110i	0.431290	−	0.00821670i
$141$	505.674			0.302024
$142$	−852.136	+	676.355i	−0.503589	+	0.399707i
$143$	71.8725	−	124.487i	0.0420300	−	0.0727980i
$144$	85.4314	+	1300.44i	0.0494395	+	0.752567i
$145$	549.122	−	317.036i	0.314497	−	0.181575i
$146$	−89.9037	−	605.924i	−0.0509622	−	0.343470i
$147$	2075.98	−	1123.62i	1.16479	−	0.630437i
$148$	−906.671	+	275.110i	−0.503567	+	0.152797i
$149$	−30.1479	−	52.2177i	−0.0165759	−	0.0287103i	0.857618	−	0.514286i	$-0.171943\pi$
$149$	−30.1479	−	52.2177i	−0.0165759	−	0.0287103i	−0.874194	+	0.485576i	$0.838610\pi$
$150$	−727.767	+	1841.85i	−0.396146	+	1.00258i
$151$	−816.384	−	471.339i	−0.439976	−	0.254020i	0.263611	−	0.964629i	$-0.415086\pi$
$151$	−816.384	−	471.339i	−0.439976	−	0.254020i	−0.703587	+	0.710609i	$0.748420\pi$
$152$	1696.46	+	1173.85i	0.905268	+	0.626394i
$153$		−	2390.36i		−	1.26307i
$154$	−2197.92	−	283.440i	−1.15009	−	0.148313i
$155$			54.9815i			0.0284917i
$156$	127.869	−	136.545i	0.0656263	−	0.0700790i
$157$	1152.45	+	665.369i	0.585833	+	0.338231i	0.763448	−	0.645869i	$-0.223505\pi$
$157$	1152.45	+	665.369i	0.585833	+	0.338231i	−0.177615	+	0.984100i	$0.556838\pi$
$158$	−2637.60	−	1042.19i	−1.32808	−	0.524761i
$159$	600.228	+	1039.62i	0.299378	+	0.518538i
$160$	−586.411	−	646.761i	−0.289749	−	0.319568i
$161$	775.913	+	3063.65i	0.379817	+	1.49969i
$162$	−2417.71	+	358.726i	−1.17255	+	0.173977i
$163$	−853.496	+	492.766i	−0.410129	+	0.236788i	−0.690845	−	0.723003i	$-0.742761\pi$
$163$	−853.496	+	492.766i	−0.410129	+	0.236788i	0.280716	+	0.959791i	$0.409428\pi$
$164$	−856.680	−	199.682i	−0.407899	−	0.0950764i
$165$	−702.092	+	1216.06i	−0.331259	+	0.573758i
$166$	807.936	+	1017.91i	0.377759	+	0.475936i
$167$	1020.34			0.472793			0.236396	−	0.971657i	$-0.424034\pi$
$167$	1020.34			0.472793			0.236396	+	0.971657i	$0.424034\pi$
$168$	−2701.95	−	1008.55i	−1.24083	−	0.463162i
$169$	2185.46			0.994745
$170$	995.502	+	1254.23i	0.449127	+	0.565852i
$171$	928.269	−	1607.81i	0.415126	−	0.719019i
$172$	−643.192	−	149.920i	−0.285133	−	0.0664612i
$173$	−1538.61	+	888.319i	−0.676177	+	0.390391i	−0.798413	−	0.602110i	$-0.794327\pi$
$173$	−1538.61	+	888.319i	−0.676177	+	0.390391i	0.122236	+	0.992501i	$0.460993\pi$
$174$	−2531.46	+	375.604i	−1.10293	+	0.163647i
$175$	−1313.92	−	1350.56i	−0.567561	−	0.583389i
$176$	1504.59	+	2251.04i	0.644390	+	0.964083i
$177$	−1146.74	−	1986.22i	−0.486975	−	0.843466i
$178$	2342.67	+	925.655i	0.986465	+	0.389780i
$179$	3863.93	+	2230.84i	1.61343	+	0.931513i	0.988568	+	0.150777i	$0.0481775\pi$
$179$	3863.93	+	2230.84i	1.61343	+	0.931513i	0.624860	+	0.780736i	$0.285156\pi$
$180$	−537.031	+	573.469i	−0.222377	+	0.237466i
$181$		−	2630.44i		−	1.08021i	−0.841596	−	0.540107i	$-0.818384\pi$
$181$		−	2630.44i		−	1.08021i	0.841596	−	0.540107i	$-0.181616\pi$
$182$	68.5474	+	164.256i	0.0279180	+	0.0668982i
$183$			3752.98i			1.51600i
$184$	2197.08	−	3175.23i	0.880275	−	1.27218i
$185$	−494.673	−	285.600i	−0.196590	−	0.113501i
$186$	81.5480	−	206.384i	0.0321473	−	0.0813592i
$187$	−2483.08	−	4300.82i	−0.971021	−	1.68186i
$188$	562.491	−	170.676i	0.218212	−	0.0662118i
$189$	230.157	−	814.014i	0.0885790	−	0.313285i
$190$	182.532	+	1230.21i	0.0696960	+	0.469731i
$191$	350.362	−	202.282i	0.132729	−	0.0766313i	−0.432165	−	0.901795i	$-0.642250\pi$
$191$	350.362	−	202.282i	0.132729	−	0.0766313i	0.564894	+	0.825163i	$0.308917\pi$
$192$	1241.94	+	3297.50i	0.466820	+	1.23946i
$193$	−1508.72	+	2613.17i	−0.562693	+	0.974613i	0.434567	+	0.900640i	$0.356901\pi$
$193$	−1508.72	+	2613.17i	−0.562693	+	0.974613i	−0.997260	+	0.0739738i	$0.976432\pi$
$194$	626.711	−	497.432i	0.231934	−	0.184090i
$195$	112.776			0.0414156
$196$	1929.99	−	1950.55i	0.703350	−	0.710843i
$197$	2643.88			0.956185			0.478093	−	0.878309i	$-0.341328\pi$
$197$	2643.88			0.956185			0.478093	+	0.878309i	$0.341328\pi$
$198$	1908.52	−	1514.83i	0.685015	−	0.543708i
$199$	−2077.01	+	3597.48i	−0.739875	+	1.28150i	0.212676	+	0.977123i	$0.431782\pi$
$199$	−2077.01	+	3597.48i	−0.739875	+	1.28150i	−0.952551	+	0.304378i	$0.901551\pi$
$200$	−187.873	+	2294.44i	−0.0664230	+	0.811207i
$201$	−3553.34	+	2051.52i	−1.24693	+	0.719917i
$202$	333.869	+	2250.18i	0.116292	+	0.783772i
$203$	662.481	−	2343.05i	0.229049	−	0.810098i
$204$	−1876.56	−	6184.51i	−0.644046	−	2.12256i
$205$	−265.149	−	459.252i	−0.0903357	−	0.156466i
$206$	1844.00	−	4666.84i	0.623676	−	1.57842i
$207$	−3009.31	−	1737.43i	−1.01044	−	0.583379i
$208$	96.1492	−	195.045i	0.0320517	−	0.0650190i
$209$		−	3857.10i		−	1.27656i
$210$	−669.610	−	1604.55i	−0.220036	−	0.527258i
$211$			592.260i			0.193236i	0.995322	+	0.0966182i	$0.0308026\pi$
$211$			592.260i			0.193236i	−0.995322	+	0.0966182i	$0.969197\pi$
$212$	1018.56	+	953.846i	0.329978	+	0.309011i
$213$	2292.49	+	1323.57i	0.737458	+	0.425771i
$214$	196.122	+	77.4931i	0.0626477	+	0.0247538i
$215$	−199.073	−	344.804i	−0.0631473	−	0.109374i
$216$	−934.244	+	441.994i	−0.294293	+	0.139231i
$217$	147.228	+	151.334i	0.0460576	+	0.0473420i
$218$	217.466	−	32.2664i	0.0675627	−	0.0100246i
$219$	−1290.78	+	745.233i	−0.398278	+	0.229946i
$220$	−370.532	+	1589.67i	−0.113551	+	0.487160i
$221$	−199.426	+	345.416i	−0.0607007	+	0.105137i
$222$	1433.26	+	1805.75i	0.433306	+	0.545919i
$223$	−3985.59			−1.19684			−0.598419	−	0.801183i	$-0.704204\pi$
$223$	−3985.59			−1.19684			−0.598419	+	0.801183i	$0.704204\pi$
$224$	−3345.95	−	209.900i	−0.998038	−	0.0626094i
$225$	2071.75			0.613851
$226$	−1805.87	−	2275.21i	−0.531525	−	0.669666i
$227$	−119.836	+	207.561i	−0.0350386	+	0.0606887i	−0.883013	−	0.469349i	$-0.844489\pi$
$227$	−119.836	+	207.561i	−0.0350386	+	0.0606887i	0.847974	+	0.530037i	$0.177822\pi$
$228$	1139.47	−	4888.57i	0.330978	−	1.41997i
$229$	3722.53	−	2149.20i	1.07420	−	0.620190i	0.144874	−	0.989450i	$-0.453722\pi$
$229$	3722.53	−	2149.20i	1.07420	−	0.620190i	0.929326	+	0.369261i	$0.120389\pi$
$230$	2302.56	−	341.642i	0.660116	−	0.0979443i
$231$	1323.86	+	5227.19i	0.377072	+	1.48885i
$232$	−2689.12	+	1272.23i	−0.760989	+	0.360026i
$233$	−617.944	−	1070.31i	−0.173746	−	0.300937i	0.765981	−	0.642864i	$-0.222254\pi$
$233$	−617.944	−	1070.31i	−0.173746	−	0.300937i	−0.939727	+	0.341927i	$0.888921\pi$
$234$	−182.003	−	71.9144i	−0.0508458	−	0.0200906i
$235$	306.891	+	177.184i	0.0851888	+	0.0491838i
$236$	−1945.98	−	1822.34i	−0.536749	−	0.502645i
$237$			6900.61i			1.89132i
$238$	6098.61	+	786.467i	1.66098	+	0.214198i
$239$		−	1777.38i		−	0.481042i	−0.970644	−	0.240521i	$-0.922682\pi$
$239$		−	1777.38i		−	0.481042i	0.970644	−	0.240521i	$-0.0773183\pi$
$240$	−939.240	+	1905.31i	−0.252615	+	0.512447i
$241$	−4291.94	−	2477.95i	−1.14717	−	0.662320i	−0.198975	−	0.980005i	$-0.563761\pi$
$241$	−4291.94	−	2477.95i	−1.14717	−	0.662320i	−0.948196	+	0.317685i	$0.897095\pi$
$242$	476.861	−	1206.85i	0.126669	−	0.320577i
$243$	2356.95	+	4082.35i	0.622215	+	1.07771i
$244$	1266.71	+	4174.66i	0.332348	+	1.09531i
$245$	1653.61	+	45.4889i	0.431205	+	0.0118620i
$246$	314.132	+	2117.16i	0.0814160	+	0.548720i
$247$	−268.277	+	154.890i	−0.0691094	+	0.0399003i
$248$	21.0516	−	257.097i	0.00539023	−	0.0658294i
$249$	1581.06	−	2738.47i	0.402392	−	0.696963i
$250$	−2422.62	+	1922.87i	−0.612879	+	0.486453i
$251$	5191.12			1.30542			0.652710	−	0.757608i	$-0.273632\pi$
$251$	5191.12			1.30542			0.652710	+	0.757608i	$0.273632\pi$
$252$	57.4686	+	3016.49i	0.0143658	+	0.754052i
$253$	−7219.27			−1.79396
$254$	−3645.75	+	2893.70i	−0.900610	+	0.714830i
$255$	1948.11	−	3374.22i	0.478413	−	0.828636i
$256$	2494.46	+	3248.83i	0.609000	+	0.793170i
$257$	−3574.00	+	2063.45i	−0.867471	+	0.500835i	−0.866507	−	0.499165i	$-0.833640\pi$
$257$	−3574.00	+	2063.45i	−0.867471	+	0.500835i	−0.000963893		1.00000i	$0.500307\pi$
$258$	235.849	+	1589.55i	0.0569121	+	0.383571i
$259$	−2126.34	+	538.525i	−0.510132	+	0.129198i
$260$	125.447	−	38.0642i	0.0299227	−	0.00907940i
$261$	1338.59	+	2318.51i	0.317459	+	0.549856i
$262$	−793.099	+	2007.20i	−0.187015	+	0.473302i
$263$	−543.813	−	313.970i	−0.127502	−	0.0736131i	0.434893	−	0.900482i	$-0.356786\pi$
$263$	−543.813	−	313.970i	−0.127502	−	0.0736131i	−0.562394	+	0.826869i	$0.690120\pi$
$264$	3748.64	−	5417.55i	0.873912	−	1.26298i
$265$			841.258i			0.195012i
$266$	3796.64	+	2897.31i	0.875138	+	0.667841i
$267$		−	6128.99i		−	1.40483i
$268$	−3260.16	+	3481.36i	−0.743081	+	0.793499i
$269$	−2662.88	−	1537.42i	−0.603565	−	0.348468i	0.166878	−	0.985978i	$-0.446631\pi$
$269$	−2662.88	−	1537.42i	−0.603565	−	0.348468i	−0.770443	+	0.637509i	$0.779965\pi$
$270$	−579.470	−	228.965i	−0.130613	−	0.0516087i
$271$	944.601	+	1636.10i	0.211736	+	0.366737i	0.952258	−	0.305295i	$-0.0987550\pi$
$271$	944.601	+	1636.10i	0.211736	+	0.366737i	−0.740522	+	0.672032i	$0.765422\pi$
$272$	−4174.81	−	6246.01i	−0.930643	−	1.39235i
$273$	310.409	−	301.988i	0.0688162	−	0.0669492i
$274$	2022.59	−	300.101i	0.445946	−	0.0661670i
$275$	3727.55	−	2152.10i	0.817382	−	0.471916i
$276$	−9149.85	−	2132.72i	−1.99549	−	0.465126i
$277$	4255.31	−	7370.41i	0.923020	−	1.59872i	0.128305	−	0.991735i	$-0.459046\pi$
$277$	4255.31	−	7370.41i	0.923020	−	1.59872i	0.794715	−	0.606983i	$-0.207620\pi$
$278$	−2882.62	−	3631.79i	−0.621899	−	0.783527i
$279$	−232.144			−0.0498140
$280$	−1286.42	−	1558.82i	−0.274565	−	0.332705i
$281$	6028.10			1.27974			0.639869	−	0.768484i	$-0.278989\pi$
$281$	6028.10			1.27974			0.639869	+	0.768484i	$0.278989\pi$
$282$	−889.179	−	1120.27i	−0.187765	−	0.236565i
$283$	2229.39	−	3861.42i	0.468281	−	0.811087i	−0.531062	−	0.847333i	$-0.678207\pi$
$283$	2229.39	−	3861.42i	0.468281	−	0.811087i	0.999343	+	0.0362463i	$0.0115401\pi$
$284$	2996.80	+	698.518i	0.626152	+	0.145949i
$285$	2620.68	−	1513.05i	0.544686	−	0.314475i
$286$	−402.170	+	59.6717i	−0.0831496	+	0.0123373i
$287$	−1959.58	−	554.058i	−0.403033	−	0.113955i
$288$	2730.77	−	2475.96i	0.558722	−	0.506587i
$289$	4433.35	+	7678.80i	0.902372	+	1.56295i
$290$	−1667.94	−	659.050i	−0.337741	−	0.133451i
$291$	−1686.03	−	973.430i	−0.339646	−	0.196094i
$292$	−1184.28	+	1264.63i	−0.237345	+	0.253449i
$293$			3220.71i			0.642171i	0.947050	+	0.321085i	$0.104048\pi$
$293$			3220.71i			0.642171i	−0.947050	+	0.321085i	$0.895952\pi$
$294$	−6139.68	−	2623.37i	−1.21794	−	0.520401i
$295$		−	1607.24i		−	0.317210i
$296$	2203.77	+	1524.89i	0.432743	+	0.299433i
$297$	1673.47	+	966.176i	0.326951	+	0.188765i
$298$	−62.6710	+	158.610i	−0.0121827	+	0.0308322i
$299$	289.904	+	502.129i	0.0560722	+	0.0971199i
$300$	5360.16	−	1626.43i	1.03156	−	0.313006i
$301$	−1471.25	−	415.985i	−0.281732	−	0.0796577i
$302$	391.326	+	2637.43i	0.0745639	+	0.502539i
$303$	4793.48	−	2767.52i	0.908840	−	0.524719i
$304$	−382.502	−	5822.44i	−0.0721645	−	1.09849i
$305$	−1315.01	+	2277.67i	−0.246876	+	0.427603i
$306$	−5295.62	+	4203.23i	−0.989315	+	0.785237i
$307$	−6242.78			−1.16057			−0.580284	−	0.814414i	$-0.697058\pi$
$307$	−6242.78			−1.16057			−0.580284	+	0.814414i	$0.697058\pi$
$308$	3236.89	+	5367.68i	0.598829	+	0.993025i
$309$	−12209.6			−2.24782
$310$	121.806	−	96.6797i	0.0223165	−	0.0177130i
$311$	−1146.70	+	1986.14i	−0.209078	+	0.362134i	−0.951424	−	0.307883i	$-0.900380\pi$
$311$	−1146.70	+	1986.14i	−0.209078	+	0.362134i	0.742346	+	0.670016i	$0.233713\pi$
$312$	−527.347	−	43.1801i	−0.0956895	−	0.00783523i
$313$	4989.49	−	2880.68i	0.901030	−	0.520210i	0.0234959	−	0.999724i	$-0.492520\pi$
$313$	4989.49	−	2880.68i	0.901030	−	0.520210i	0.877534	+	0.479514i	$0.159187\pi$
$314$	−552.418	−	3723.14i	−0.0992827	−	0.669136i
$315$	−1303.68	+	1268.31i	−0.233187	+	0.226860i
$316$	2329.10	+	7675.95i	0.414628	+	1.36647i
$317$	−2197.71	−	3806.54i	−0.389386	−	0.674437i	0.602981	−	0.797756i	$-0.293980\pi$
$317$	−2197.71	−	3806.54i	−0.389386	−	0.674437i	−0.992367	+	0.123319i	$0.960646\pi$
$318$	1247.75	−	3157.83i	0.220032	−	0.556862i
$319$	4816.89	+	2781.03i	0.845436	+	0.488113i
$320$	−401.688	+	2436.40i	−0.0701719	+	0.425622i
$321$		−	513.102i		−	0.0892166i
$322$	5422.85	−	7106.10i	0.938521	−	1.22984i
$323$			10702.4i			1.84364i
$324$	5046.04	+	4725.42i	0.865233	+	0.810257i
$325$	−299.375	−	172.844i	−0.0510964	−	0.0295005i
$326$	2592.47	+	1024.36i	0.440440	+	0.174030i
$327$	−267.464	−	463.262i	−0.0452318	−	0.0783438i
$328$	1064.01	+	2249.01i	0.179117	+	0.378601i
$329$	1319.16	−	334.096i	0.221057	−	0.0559857i
$330$	3928.62	−	582.907i	0.655344	−	0.0972363i
$331$	−5522.08	+	3188.18i	−0.916983	+	0.529420i	−0.882671	−	0.469991i	$-0.844257\pi$
$331$	−5522.08	+	3188.18i	−0.916983	+	0.529420i	−0.0343114	+	0.999411i	$0.510924\pi$
$332$	834.410	−	3579.81i	0.137934	−	0.591769i
$333$	1205.87	−	2088.62i	0.198441	−	0.343711i
$334$	−1794.17	−	2260.47i	−0.293930	−	0.370321i
$335$	−2875.34			−0.468945
$336$	2516.79	+	7759.35i	0.408637	+	1.25984i
$337$	−5111.05			−0.826163			−0.413081	−	0.910694i	$-0.635547\pi$
$337$	−5111.05			−0.826163			−0.413081	+	0.910694i	$0.635547\pi$
$338$	−3842.92	−	4841.66i	−0.618423	−	0.779148i
$339$	−3533.93	+	6120.95i	−0.566185	+	0.980661i
$340$	1028.12	−	4410.88i	0.163993	−	0.703569i
$341$	−417.681	+	241.148i	−0.0663305	+	0.0382959i
$342$	−5194.22	+	770.689i	−0.821261	+	0.121854i
$343$	4673.29	−	4302.79i	0.735667	−	0.677343i
$344$	798.858	+	1688.55i	0.125208	+	0.264653i
$345$	−2831.95	−	4905.08i	−0.441933	−	0.765451i
$346$	4673.49	+	1846.62i	0.726151	+	0.286922i
$347$	−4393.00	−	2536.30i	−0.679621	−	0.392379i	0.120091	−	0.992763i	$-0.461681\pi$
$347$	−4393.00	−	2536.30i	−0.679621	−	0.392379i	−0.799712	+	0.600384i	$0.795015\pi$
$348$	5283.45	+	4947.75i	0.813859	+	0.762147i
$349$			11661.1i			1.78856i	0.447512	+	0.894278i	$0.352310\pi$
$349$			11661.1i			1.78856i	−0.447512	+	0.894278i	$0.647690\pi$
$350$	−681.636	+	5285.71i	−0.104100	+	0.807237i
$351$		−	155.195i		−	0.0236003i
$352$	2341.29	−	7291.51i	0.354521	−	1.10409i
$353$	5552.29	+	3205.62i	0.837163	+	0.483337i	0.856299	−	0.516480i	$-0.172758\pi$
$353$	5552.29	+	3205.62i	0.837163	+	0.483337i	−0.0191356	+	0.999817i	$0.506091\pi$
$354$	−2383.84	+	6033.08i	−0.357908	+	0.905804i
$355$	927.532	+	1606.53i	0.138671	+	0.240186i
$356$	−2068.67	−	6817.64i	−0.307975	−	1.01498i
$357$	−3673.34	−	14504.0i	−0.544576	−	2.15023i
$358$	−1852.14	−	12482.9i	−0.273432	−	1.84285i
$359$	−8337.73	+	4813.79i	−1.22576	+	0.707694i	−0.966140	−	0.258017i	$-0.916931\pi$
$359$	−8337.73	+	4813.79i	−1.22576	+	0.707694i	−0.259621	+	0.965711i	$0.583598\pi$
$360$	2214.78	+	181.350i	0.324248	+	0.0265500i
$361$	−726.638	+	1258.57i	−0.105939	+	0.183492i
$362$	−5827.48	+	4625.37i	−0.846093	+	0.671559i
$363$	−3157.42			−0.456533
$364$	243.359	−	440.689i	0.0350425	−	0.0634570i
$365$	−1044.49			−0.149784
$366$	8314.37	−	6599.26i	1.18743	−	0.942483i
$367$	1753.92	−	3037.88i	0.249466	−	0.432087i	−0.713912	−	0.700235i	$-0.753078\pi$
$367$	1753.92	−	3037.88i	0.249466	−	0.432087i	0.963378	+	0.268148i	$0.0864117\pi$
$368$	−10897.8	+	715.923i	−1.54371	+	0.101413i
$369$	1939.06	−	1119.52i	0.273560	−	0.157940i
$370$	237.117	+	1598.10i	0.0333166	+	0.224544i
$371$	2252.70	+	2315.52i	0.315241	+	0.324032i
$372$	−600.618	+	182.245i	−0.0837113	+	0.0254004i
$373$	4053.65	+	7021.12i	0.562707	+	0.974638i	0.997259	+	0.0739909i	$0.0235736\pi$
$373$	4053.65	+	7021.12i	0.562707	+	0.974638i	−0.434551	+	0.900647i	$0.643093\pi$
$374$	−5161.79	+	13063.6i	−0.713663	+	1.80616i
$375$	6517.52	+	3762.89i	0.897502	+	0.518173i
$376$	−1367.20	−	946.027i	−0.187521	−	0.129754i
$377$		−	446.712i		−	0.0610261i
$378$	−2208.08	+	921.476i	−0.300453	+	0.125385i
$379$		−	6838.23i		−	0.926798i	−0.886150	−	0.463399i	$-0.846630\pi$
$379$		−	6838.23i		−	0.926798i	0.886150	−	0.463399i	$-0.153370\pi$
$380$	2404.45	−	2567.59i	0.324594	−	0.346617i
$381$	9808.11	+	5662.71i	1.31886	+	0.761443i
$382$	−1064.21	−	420.500i	−0.142539	−	0.0563211i
$383$	−6010.60	−	10410.7i	−0.801899	−	1.38893i	−0.918365	−	0.395735i	$-0.870490\pi$
$383$	−6010.60	−	10410.7i	−0.801899	−	1.38893i	0.116466	−	0.993195i	$-0.462843\pi$
$384$	5121.46	−	8549.75i	0.680608	−	1.13620i
$385$	−1028.12	+	3636.22i	−0.136098	+	0.481348i
$386$	8442.17	−	1252.60i	1.11320	−	0.165170i
$387$	1455.84	−	840.530i	0.191226	−	0.110404i
$388$	−2204.02	−	513.732i	−0.288382	−	0.0672185i
$389$	−1922.93	+	3330.62i	−0.250634	+	0.434111i	−0.963701	−	0.266986i	$-0.913972\pi$
$389$	−1922.93	+	3330.62i	−0.250634	+	0.434111i	0.713067	+	0.701096i	$0.247306\pi$
$390$	−198.305	−	249.844i	−0.0257476	−	0.0324393i
$391$	20031.4			2.59088
$392$	−7714.97	−	845.851i	−0.994043	−	0.108985i
$393$	5251.31			0.674029
$394$	−4649.01	−	5857.25i	−0.594451	−	0.748945i
$395$	−2417.91	+	4187.95i	−0.307996	+	0.533464i
$396$	−6711.91	−	1564.47i	−0.851733	−	0.198529i
$397$	10023.9	−	5787.30i	1.26722	−	0.731628i	0.292756	−	0.956187i	$-0.405428\pi$
$397$	10023.9	−	5787.30i	1.26722	−	0.731628i	0.974460	+	0.224560i	$0.0720943\pi$
$398$	11622.1	−	1724.42i	1.46373	−	0.217179i
$399$	3161.68	−	11182.2i	0.396697	−	1.40303i
$400$	5413.46	−	3618.34i	0.676683	−	0.452292i
$401$	−6583.03	−	11402.1i	−0.819803	−	1.41994i	−0.905827	−	0.423647i	$-0.860750\pi$
$401$	−6583.03	−	11402.1i	−0.819803	−	1.41994i	0.0860245	−	0.996293i	$-0.472584\pi$
$402$	10793.2	+	4264.68i	1.33909	+	0.529111i
$403$	33.5456	+	19.3676i	0.00414647	+	0.00239397i
$404$	4397.98	−	4696.38i	0.541603	−	0.578350i
$405$			4167.65i			0.511339i
$406$	−6355.71	+	2652.37i	−0.776918	+	0.324224i
$407$		−	5010.55i		−	0.610231i
$408$	−10401.4	+	15032.2i	−1.26213	+	1.82403i
$409$	−9916.78	−	5725.46i	−1.19891	−	0.692190i	−0.238596	−	0.971119i	$-0.576687\pi$
$409$	−9916.78	−	5725.46i	−1.19891	−	0.692190i	−0.960312	+	0.278929i	$0.910021\pi$
$410$	−551.188	+	1394.96i	−0.0663933	+	0.168030i
$411$	−2487.61	−	4308.67i	−0.298552	−	0.517107i
$412$	−13581.4	+	4120.99i	−1.62405	+	0.492783i
$413$	−4303.82	−	4423.84i	−0.512777	−	0.527077i
$414$	1442.49	+	9721.93i	0.171242	+	1.15412i
$415$	1919.07	−	1107.98i	0.226997	−	0.131057i
$416$	−601.173	+	129.959i	−0.0708532	+	0.0153168i
$417$	−5641.03	+	9770.55i	−0.662452	+	1.14740i
$418$	−8545.03	+	6782.34i	−0.999883	+	0.793625i
$419$	−4195.08			−0.489124			−0.244562	−	0.969634i	$-0.578644\pi$
$419$	−4195.08			−0.489124			−0.244562	+	0.969634i	$0.578644\pi$
$420$	−2377.27	+	4304.90i	−0.276188	+	0.500137i
$421$	−3710.27			−0.429520			−0.214760	−	0.976667i	$-0.568897\pi$
$421$	−3710.27			−0.429520			−0.214760	+	0.976667i	$0.568897\pi$
$422$	1312.10	−	1041.43i	0.151355	−	0.120133i
$423$	−748.108	+	1295.76i	−0.0859912	+	0.148941i
$424$	322.105	−	3933.78i	0.0368934	−	0.450569i
$425$	−10342.9	+	5971.49i	−1.18048	+	0.681552i
$426$	−1098.88	−	7406.15i	−0.124979	−	0.842322i
$427$	2479.57	+	9790.47i	0.281019	+	1.10959i
$428$	−173.183	−	570.753i	−0.0195587	−	0.0644589i
$429$	494.633	+	856.729i	0.0556669	+	0.0964179i
$430$	−413.830	+	1047.33i	−0.0464108	+	0.117458i
$431$	−2084.43	−	1203.45i	−0.232955	−	0.134497i	0.378979	−	0.925405i	$-0.376275\pi$
$431$	−2084.43	−	1203.45i	−0.232955	−	0.134497i	−0.611935	+	0.790908i	$0.709608\pi$
$432$	2621.97	+	1292.52i	0.292013	+	0.143950i
$433$		−	15138.8i		−	1.68019i	−0.542436	−	0.840097i	$-0.682498\pi$
$433$		−	15138.8i		−	1.68019i	0.542436	−	0.840097i	$-0.317502\pi$
$434$	76.3789	−	592.276i	0.00844771	−	0.0655072i
$435$			4363.74i			0.480977i
$436$	−453.877	−	425.038i	−0.0498550	−	0.0466872i
$437$	13473.6	+	7778.97i	1.47489	+	0.851530i
$438$	3920.71	+	1549.18i	0.427714	+	0.169002i
$439$	2889.10	+	5004.08i	0.314099	+	0.544035i	0.979246	−	0.202677i	$-0.0649643\pi$
$439$	2889.10	+	5004.08i	0.314099	+	0.544035i	−0.665147	+	0.746713i	$0.731631\pi$
$440$	4173.29	−	1974.40i	0.452168	−	0.213922i
$441$	−192.064	+	6981.90i	−0.0207390	+	0.753904i
$442$	1115.91	−	165.572i	0.120087	−	0.0178178i
$443$	7143.22	−	4124.14i	0.766106	−	0.442311i	−0.0653780	−	0.997861i	$-0.520825\pi$
$443$	7143.22	−	4124.14i	0.766106	−	0.442311i	0.831484	+	0.555549i	$0.187492\pi$
$444$	1480.22	−	6350.48i	0.158217	−	0.678785i
$445$	2147.55	−	3719.66i	0.228772	−	0.396244i
$446$	7008.28	+	8829.69i	0.744062	+	0.937440i
$447$	414.961			0.0439082
$448$	5418.52	+	7781.71i	0.571431	+	0.820650i
$449$	6493.19			0.682478			0.341239	−	0.939977i	$-0.389153\pi$
$449$	6493.19			0.682478			0.341239	+	0.939977i	$0.389153\pi$
$450$	−3642.97	−	4589.75i	−0.381625	−	0.480807i
$451$	2325.88	−	4028.55i	0.242842	−	0.420614i
$452$	−1865.05	+	8001.47i	−0.194080	+	0.832649i
$453$	5618.42	−	3243.80i	0.582730	−	0.336439i
$454$	670.551	−	99.4927i	0.0693184	−	0.0102851i
$455$	294.200	−	74.5103i	0.0303127	−	0.00767713i
$456$	−12833.8	+	6071.70i	−1.31798	+	0.623539i
$457$	5548.06	+	9609.52i	0.567893	+	0.983620i	0.996774	+	0.0802591i	$0.0255748\pi$
$457$	5548.06	+	9609.52i	0.567893	+	0.983620i	−0.428881	+	0.903361i	$0.641092\pi$
$458$	−11307.1	−	4467.74i	−1.15359	−	0.455816i
$459$	−4643.40	−	2680.87i	−0.472190	−	0.272619i
$460$	−4805.71	−	4500.36i	−0.487103	−	0.456153i
$461$		−	4976.01i		−	0.502724i	−0.967893	−	0.251362i	$-0.919122\pi$
$461$		−	4976.01i		−	0.502724i	0.967893	−	0.251362i	$-0.0808784\pi$
$462$	9252.45	−	12124.4i	0.931738	−	1.22095i
$463$			16003.8i			1.60639i	0.595716	+	0.803195i	$0.296868\pi$
$463$			16003.8i			1.60639i	−0.595716	+	0.803195i	$0.703132\pi$
$464$	7547.07	+	3720.39i	0.755094	+	0.372230i
$465$	−327.693	−	189.194i	−0.0326804	−	0.0188681i
$466$	−1284.57	+	3251.03i	−0.127697	+	0.323178i
$467$	8856.55	+	15340.0i	0.877585	+	1.52002i	0.853984	+	0.520300i	$0.174180\pi$
$467$	8856.55	+	15340.0i	0.877585	+	1.52002i	0.0236011	+	0.999721i	$0.492487\pi$
$468$	160.716	+	529.665i	0.0158741	+	0.0523157i
$469$	−7914.23	+	7699.52i	−0.779201	+	0.758061i
$470$	−147.106	−	991.448i	−0.0144372	−	0.0973023i
$471$	−7931.28	+	4579.13i	−0.775911	+	0.447972i
$472$	−615.387	+	7515.55i	−0.0600116	+	0.732905i
$473$	1746.26	−	3024.62i	0.169753	−	0.294021i
$474$	15287.6	−	12134.1i	1.48140	−	1.17581i
$475$	−9275.82			−0.896008
$476$	−8981.48	−	14893.8i	−0.864843	−	1.43415i
$477$	−3551.97			−0.340951
$478$	−3937.61	+	3125.35i	−0.376783	+	0.299059i
$479$	5044.30	−	8736.99i	0.481169	−	0.833410i	−0.518597	−	0.855019i	$-0.673546\pi$
$479$	5044.30	−	8736.99i	0.481169	−	0.833410i	0.999766	+	0.0216091i	$0.00687893\pi$
$480$	5872.60	−	1269.52i	0.558430	−	0.120719i
$481$	−348.504	+	201.209i	−0.0330362	+	0.0190735i
$482$	2057.30	+	13865.6i	0.194414	+	1.31029i
$483$	−20929.5	−	5917.67i	−1.97169	−	0.557481i
$484$	−3512.18	+	1065.70i	−0.329844	+	0.100084i
$485$	−682.162	−	1181.54i	−0.0638668	−	0.110621i
$486$	4899.59	−	12400.0i	0.457304	−	1.15736i
$487$	−2053.73	−	1185.72i	−0.191095	−	0.110329i	0.401400	−	0.915903i	$-0.368524\pi$
$487$	−2053.73	−	1185.72i	−0.191095	−	0.110329i	−0.592495	+	0.805574i	$0.701857\pi$
$488$	7021.17	−	10147.0i	0.651298	−	0.941259i
$489$		−	6782.52i		−	0.627231i
$490$	−2806.94	−	3743.40i	−0.258785	−	0.345122i
$491$		−	11069.3i		−	1.01741i	−0.860940	−	0.508706i	$-0.830124\pi$
$491$		−	11069.3i		−	1.01741i	0.860940	−	0.508706i	$-0.169876\pi$
$492$	4137.99	−	4418.75i	0.379177	−	0.404904i
$493$	−13365.5	−	7716.59i	−1.22100	−	0.704944i
$494$	814.882	+	321.982i	0.0742171	+	0.0293252i
$495$	−2077.39	−	3598.14i	−0.188630	−	0.326716i
$496$	−606.591	+	405.443i	−0.0549128	+	0.0367035i
$497$	6854.92	+	1938.18i	0.618682	+	0.174928i
$498$	−8846.97	+	1312.66i	−0.796068	+	0.118116i
$499$	9842.36	−	5682.49i	0.882975	−	0.509786i	0.0113371	−	0.999936i	$-0.496391\pi$
$499$	9842.36	−	5682.49i	0.882975	−	0.509786i	0.871638	+	0.490150i	$0.163058\pi$
$500$	8519.88	+	1985.88i	0.762041	+	0.177623i
$501$	−3511.04	+	6081.30i	−0.313097	+	0.542300i
$502$	−9128.08	−	11500.4i	−0.811566	−	1.02249i
$503$	−11337.8			−1.00503			−0.502513	−	0.864570i	$-0.667591\pi$
$503$	−11337.8			−1.00503			−0.502513	+	0.864570i	$0.667591\pi$
$504$	6581.69	−	5431.53i	0.581690	−	0.480039i
$505$	3878.86			0.341796
$506$	12694.4	+	15993.6i	1.11529	+	1.40514i
$507$	−7520.24	+	13025.4i	−0.658749	+	1.14099i
$508$	12821.4	+	2988.52i	1.11980	+	0.261012i
$509$	2352.86	−	1358.43i	0.204890	−	0.118293i	−0.394045	−	0.919091i	$-0.628924\pi$
$509$	2352.86	−	1358.43i	0.204890	−	0.118293i	0.598934	+	0.800798i	$0.295591\pi$
$510$	−10900.8	+	1617.40i	−0.946465	+	0.140431i
$511$	−2874.91	+	2796.92i	−0.248882	+	0.242130i
$512$	2811.18	−	11239.0i	0.242652	−	0.970113i
$513$	−2082.17	−	3606.42i	−0.179200	−	0.310384i
$514$	10855.9	+	4289.47i	0.931583	+	0.368094i
$515$	−7409.93	−	4278.12i	−0.634020	−	0.366052i
$516$	3106.79	−	3317.58i	0.265056	−	0.283040i
$517$			3108.50i			0.264433i
$518$	4932.01	+	3763.75i	0.418340	+	0.319246i
$519$		−	12227.0i		−	1.03411i
$520$	−304.914	−	210.983i	−0.0257142	−	0.0177928i
$521$	−6728.44	−	3884.67i	−0.565793	−	0.326661i	0.189674	−	0.981847i	$-0.439257\pi$
$521$	−6728.44	−	3884.67i	−0.565793	−	0.326661i	−0.755467	+	0.655186i	$0.772590\pi$
$522$	2782.65	−	7042.41i	0.233321	−	0.590494i
$523$	8189.91	+	14185.3i	0.684742	+	1.18601i	0.973518	+	0.228611i	$0.0734182\pi$
$523$	8189.91	+	14185.3i	0.684742	+	1.18601i	−0.288776	+	0.957397i	$0.593248\pi$
$524$	5841.34	−	1772.43i	0.486985	−	0.147765i
$525$	12570.7	−	3183.71i	1.04501	−	0.264664i
$526$	260.672	+	1756.85i	0.0216080	+	0.145632i
$527$	1158.95	−	669.119i	0.0957962	−	0.0553079i
$528$	−18593.7	+	1221.50i	−1.53255	+	0.100680i
$529$	8476.27	−	14681.3i	0.696661	−	1.20665i
$530$	1863.73	−	1479.27i	0.152745	−	0.121237i
$531$	6786.11			0.554599
$532$	−257.304	−	13505.7i	−0.0209691	−	1.10065i
$533$	−373.602			−0.0303612
$534$	−13578.2	+	10777.3i	−1.10035	+	0.873366i
$535$	179.786	−	311.399i	0.0145287	−	0.0251644i
$536$	13445.3	+	1100.92i	1.08349	+	0.0887177i
$537$	−26591.9	+	15352.8i	−2.13692	+	1.23375i
$538$	1276.43	+	8602.76i	0.102288	+	0.689389i
$539$	6907.15	+	12761.6i	0.551970	+	1.01982i
$540$	511.694	+	1686.37i	0.0407774	+	0.134389i
$541$	3348.80	+	5800.29i	0.266129	+	0.460950i	0.967859	−	0.251494i	$-0.0809218\pi$
$541$	3348.80	+	5800.29i	0.266129	+	0.460950i	−0.701729	+	0.712444i	$0.747588\pi$
$542$	1963.62	−	4969.59i	0.155618	−	0.393842i
$543$	15677.6	+	9051.45i	1.23902	+	0.715350i
$544$	−6496.43	+	20231.9i	−0.512007	+	1.59455i
$545$		−	374.868i		−	0.0294635i
$546$	−1214.85	−	156.665i	−0.0952212	−	0.0122796i
$547$			2582.34i			0.201851i	0.994894	+	0.100926i	$0.0321804\pi$
$547$			2582.34i			0.201851i	−0.994894	+	0.100926i	$0.967820\pi$
$548$	−4221.38	−	3953.16i	−0.329067	−	0.308158i
$549$	−9616.81	−	5552.27i	−0.747605	−	0.431630i
$550$	−11322.3	−	4473.77i	−0.877792	−	0.346840i
$551$	−5993.29	−	10380.7i	−0.463380	−	0.802599i
$552$	11364.3	+	24020.8i	0.876263	+	1.85216i
$553$	4559.19	+	18001.7i	0.350591	+	1.38429i
$554$	−23811.0	+	3532.94i	−1.82605	+	0.270939i
$555$	3404.38	−	1965.52i	0.260375	−	0.150328i
$556$	−2977.08	+	12772.3i	−0.227080	+	0.974222i
$557$	−224.120	+	388.188i	−0.0170490	+	0.0295297i	−0.874424	−	0.485162i	$-0.838760\pi$
$557$	−224.120	+	388.188i	−0.0170490	+	0.0295297i	0.857375	+	0.514692i	$0.172094\pi$
$558$	408.203	+	514.292i	0.0309688	+	0.0390174i
$559$	−280.499			−0.0212233
$560$	−1191.38	+	5590.97i	−0.0899019	+	0.421896i
$561$	34177.5			2.57215
$562$	−10599.8	−	13354.7i	−0.795600	−	1.00237i
$563$	12501.7	−	21653.5i	0.935849	−	1.62094i	0.162736	−	0.986670i	$-0.447968\pi$
$563$	12501.7	−	21653.5i	0.935849	−	1.62094i	0.773113	−	0.634268i	$-0.218698\pi$
$564$	−918.316	+	3939.78i	−0.0685604	+	0.294140i
$565$	−4289.45	+	2476.52i	−0.319396	+	0.184403i
$566$	−12474.8	+	1850.94i	−0.926420	+	0.137457i
$567$	11160.0	+	11471.2i	0.826591	+	0.849642i
$568$	−3722.09	−	7867.40i	−0.274956	−	0.581177i
$569$	3287.22	+	5693.64i	0.242193	+	0.419490i	0.961339	−	0.275369i	$-0.0888001\pi$
$569$	3287.22	+	5693.64i	0.242193	+	0.419490i	−0.719146	+	0.694859i	$0.755467\pi$
$570$	−7960.23	−	3145.31i	−0.584943	−	0.231127i
$571$	−9610.58	−	5548.67i	−0.704361	−	0.406663i	0.104608	−	0.994513i	$-0.466641\pi$
$571$	−9610.58	−	5548.67i	−0.704361	−	0.406663i	−0.808970	+	0.587850i	$0.799974\pi$
$572$	839.374	+	786.041i	0.0613566	+	0.0574581i
$573$			2784.24i			0.202990i
$574$	2218.28	+	5315.52i	0.161305	+	0.386526i
$575$			17361.4i			1.25917i
$576$	−10287.0	−	1696.01i	−0.744143	−	0.122686i
$577$	−1236.76	−	714.046i	−0.0892325	−	0.0515184i	0.454720	−	0.890635i	$-0.349739\pi$
$577$	−1236.76	−	714.046i	−0.0892325	−	0.0515184i	−0.543952	+	0.839116i	$0.683073\pi$
$578$	9216.00	−	23324.1i	0.663209	−	1.67847i
$579$	−10383.1	−	17984.1i	−0.745264	−	1.29083i
$580$	1472.86	+	4854.04i	0.105443	+	0.347505i
$581$	2315.24	−	8188.50i	0.165322	−	0.584710i
$582$	808.184	+	5446.92i	0.0575606	+	0.387942i
$583$	−6390.83	+	3689.75i	−0.453999	+	0.262116i
$584$	4884.12	+	399.920i	0.346072	+	0.0283370i
$585$	−166.843	+	288.981i	−0.0117917	+	0.0204238i
$586$	7135.18	−	5663.32i	0.502989	−	0.399231i
$587$	27212.3			1.91341			0.956704	−	0.291063i	$-0.0940089\pi$
$587$	27212.3			1.91341			0.956704	+	0.291063i	$0.0940089\pi$
$588$	4984.23	+	18214.8i	0.349568	+	1.27749i
$589$	1039.38			0.0727111
$590$	−3560.68	+	2826.17i	−0.248459	+	0.197206i
$591$	−9097.69	+	15757.7i	−0.633213	+	1.09676i
$592$	−496.888	−	7563.62i	−0.0344966	−	0.525106i
$593$	−7855.97	+	4535.65i	−0.544024	+	0.314092i	−0.746708	−	0.665152i	$-0.768367\pi$
$593$	−7855.97	+	4535.65i	−0.544024	+	0.314092i	0.202684	+	0.979244i	$0.435033\pi$
$594$	−802.161	−	5406.33i	−0.0554092	−	0.373442i
$595$	2852.73	−	10089.5i	0.196556	−	0.695175i
$596$	461.585	−	140.058i	0.0317236	−	0.00962585i
$597$	−14294.1	−	24758.2i	−0.979933	−	1.69729i
$598$	602.649	−	1525.20i	0.0412109	−	0.104298i
$599$	−6261.35	−	3614.99i	−0.427098	−	0.246585i	0.271011	−	0.962576i	$-0.412642\pi$
$599$	−6261.35	−	3614.99i	−0.427098	−	0.246585i	−0.698110	+	0.715991i	$0.745975\pi$
$600$	−13028.5	−	9014.99i	−0.886478	−	0.613393i
$601$		−	18772.6i		−	1.27413i	−0.770810	−	0.637065i	$-0.780148\pi$
$601$		−	18772.6i		−	1.27413i	0.770810	−	0.637065i	$-0.219852\pi$
$602$	1665.47	+	3990.88i	0.112757	+	0.270193i
$603$		−	12140.3i		−	0.819887i
$604$	5154.85	−	5504.61i	0.347265	−	0.370827i
$605$	−1916.22	−	1106.33i	−0.128770	−	0.0743451i
$606$	−14560.1	−	5753.08i	−0.976010	−	0.385648i
$607$	−6114.97	−	10591.4i	−0.408895	−	0.708226i	0.585871	−	0.810404i	$-0.300752\pi$
$607$	−6114.97	−	10591.4i	−0.408895	−	0.708226i	−0.994766	+	0.102178i	$0.967419\pi$
$608$	−12226.5	+	11085.6i	−0.815540	+	0.739441i
$609$	11685.1	+	12011.0i	0.777511	+	0.799193i
$610$	7358.27	−	1091.78i	0.488406	−	0.0724670i
$611$	216.209	−	124.828i	0.0143157	−	0.00826515i
$612$	18623.7	+	4340.96i	1.23009	+	0.286720i
$613$	−5994.59	+	10382.9i	−0.394974	+	0.684116i	−0.993098	−	0.117288i	$-0.962580\pi$
$613$	−5994.59	+	10382.9i	−0.394974	+	0.684116i	0.598124	+	0.801404i	$0.295913\pi$
$614$	10977.3	+	13830.3i	0.721513	+	0.909030i
$615$	3649.56			0.239292
$616$	6199.80	−	16609.6i	0.405514	−	1.08639i
$617$	−1209.26			−0.0789030			−0.0394515	−	0.999221i	$-0.512561\pi$
$617$	−1209.26			−0.0789030			−0.0394515	+	0.999221i	$0.512561\pi$
$618$	21469.4	+	27049.1i	1.39745	+	1.76064i
$619$	9171.91	−	15886.2i	0.595558	−	1.03154i	−0.397910	−	0.917424i	$-0.630264\pi$
$619$	9171.91	−	15886.2i	0.595558	−	1.03154i	0.993468	−	0.114112i	$-0.0364022\pi$
$620$	−428.369	−	99.8477i	−0.0277479	−	0.00646771i
$621$	−6750.07	+	3897.15i	−0.436185	+	0.251832i
$622$	6416.46	−	952.038i	0.413628	−	0.0613718i
$623$	−4049.39	−	15988.8i	−0.260410	−	1.02822i
$624$	831.628	+	1244.21i	0.0533522	+	0.0798212i
$625$	−3721.79	−	6446.34i	−0.238195	−	0.412565i
$626$	−15155.4	−	5988.32i	−0.967623	−	0.382335i
$627$	22988.5	+	13272.4i	1.46423	+	0.845375i
$628$	−7276.87	+	7770.61i	−0.462387	+	0.493760i
$629$			13902.9i			0.881310i
$630$	5102.20	+	657.972i	0.322661	+	0.0416099i
$631$		−	7055.98i		−	0.445157i	−0.974915	−	0.222579i	$-0.928553\pi$
$631$		−	7055.98i		−	0.445157i	0.974915	−	0.222579i	$-0.0714474\pi$
$632$	12909.8	−	18657.3i	0.812540	−	1.17429i
$633$	−3529.91	−	2037.99i	−0.221645	−	0.127967i
$634$	−4568.56	+	11562.2i	−0.286184	+	0.724283i
$635$	3968.33	+	6873.35i	0.247997	+	0.429544i
$636$	−9189.90	+	2788.48i	−0.572961	+	0.173853i
$637$	610.249	−	992.887i	0.0379575	−	0.0617576i
$638$	−2308.93	−	15561.5i	−0.143278	−	0.965654i
$639$	−6783.13	+	3916.24i	−0.419932	+	0.242448i
$640$	6103.95	−	3394.29i	0.377000	−	0.209642i
$641$	−5116.60	+	8862.20i	−0.315278	+	0.546078i	−0.979497	−	0.201461i	$-0.935431\pi$
$641$	−5116.60	+	8862.20i	−0.315278	+	0.546078i	0.664218	+	0.747539i	$0.268765\pi$
$642$	−1136.73	+	902.241i	−0.0698801	+	0.0554651i
$643$	−20543.5			−1.25996			−0.629982	−	0.776610i	$-0.716938\pi$
$643$	−20543.5			−1.25996			−0.629982	+	0.776610i	$0.716938\pi$
$644$	−25278.5	+	481.591i	−1.54676	+	0.0294679i
$645$	2740.07			0.167272
$646$	23710.1	−	18819.1i	1.44406	−	1.14617i
$647$	−12712.8	+	22019.1i	−0.772473	+	1.33796i	0.163731	+	0.986505i	$0.447647\pi$
$647$	−12712.8	+	22019.1i	−0.772473	+	1.33796i	−0.936204	+	0.351457i	$0.885686\pi$
$648$	1595.73	−	19488.2i	0.0967379	−	1.18143i
$649$	12209.8	−	7049.33i	0.738484	−	0.426364i
$650$	143.503	+	967.166i	0.00865944	+	0.0583621i
$651$	−1408.58	+	356.742i	−0.0848026	+	0.0214775i
$652$	−2289.25	−	7544.59i	−0.137506	−	0.453174i
$653$	9127.03	+	15808.5i	0.546965	+	0.947371i	0.998480	+	0.0551081i	$0.0175503\pi$
$653$	9127.03	+	15808.5i	0.546965	+	0.947371i	−0.451515	+	0.892263i	$0.649116\pi$
$654$	−556.001	+	1407.14i	−0.0332437	+	0.0841340i
$655$	3186.99	+	1840.01i	0.190116	+	0.109764i
$656$	3111.50	−	6311.90i	0.185189	−	0.375668i
$657$		−	4410.08i		−	0.261877i
$658$	−3059.78	−	2335.00i	−0.181280	−	0.138340i
$659$			16252.1i			0.960683i	0.877081	+	0.480342i	$0.159487\pi$
$659$			16252.1i			0.960683i	−0.877081	+	0.480342i	$0.840513\pi$
$660$	−8199.49	−	7678.50i	−0.483583	−	0.452856i
$661$	6622.84	+	3823.70i	0.389711	+	0.224999i	0.682035	−	0.731320i	$-0.261095\pi$
$661$	6622.84	+	3823.70i	0.389711	+	0.224999i	−0.292324	+	0.956319i	$0.594429\pi$
$662$	16773.2	+	6627.54i	0.984754	+	0.389104i
$663$	−1372.47	−	2377.18i	−0.0803955	−	0.139249i
$664$	−9397.95	+	4446.20i	−0.549264	+	0.259858i
$665$	5836.95	−	5678.59i	0.340372	−	0.331137i
$666$	−6747.53	+	1001.16i	−0.392585	+	0.0582496i
$667$	−19429.3	+	11217.5i	−1.12790	+	0.651191i
$668$	−1852.96	+	7949.63i	−0.107325	+	0.460450i
$669$	13714.6	−	23754.4i	0.792581	−	1.37279i
$670$	5056.01	+	6370.04i	0.291539	+	0.367308i
$671$	−23070.5			−1.32731
$672$	12764.6	−	19219.8i	0.732744	−	1.10330i
$673$	−4057.51			−0.232400			−0.116200	−	0.993226i	$-0.537071\pi$
$673$	−4057.51			−0.232400			−0.116200	+	0.993226i	$0.537071\pi$
$674$	8987.30	+	11323.0i	0.513617	+	0.647103i
$675$	2323.53	−	4024.47i	0.132493	−	0.229484i
$676$	−3968.84	+	17027.2i	−0.225810	+	0.968776i
$677$	3916.39	−	2261.13i	0.222333	−	0.128364i	−0.384697	−	0.923043i	$-0.625694\pi$
$677$	3916.39	−	2261.13i	0.222333	−	0.128364i	0.607030	+	0.794679i	$0.292361\pi$
$678$	19774.4	−	2934.02i	1.12011	−	0.166195i
$679$	−5041.52	−	1425.45i	−0.284942	−	0.0805653i
$680$	−11579.7	+	5478.40i	−0.653033	+	0.308952i
$681$	−824.719	−	1428.45i	−0.0464072	−	0.0803796i
$682$	1268.69	+	501.296i	0.0712328	+	0.0281461i
$683$	12667.7	+	7313.73i	0.709690	+	0.409739i	0.810946	−	0.585121i	$-0.198953\pi$
$683$	12667.7	+	7313.73i	0.709690	+	0.409739i	−0.101257	+	0.994860i	$0.532286\pi$
$684$	10840.9	+	10152.1i	0.606013	+	0.567508i
$685$		−	3486.55i		−	0.194473i
$686$	−17749.9	−	2787.17i	−0.987895	−	0.155124i
$687$			29582.0i			1.64283i
$688$	2336.11	−	4738.95i	0.129452	−	0.262603i
$689$	513.273	+	296.339i	0.0283805	+	0.0163855i
$690$	−5887.02	+	14899.0i	−0.324804	+	0.822024i
$691$	−6100.92	−	10567.1i	−0.335875	−	0.581753i	0.647777	−	0.761830i	$-0.275699\pi$
$691$	−6100.92	−	10567.1i	−0.335875	−	0.581753i	−0.983653	+	0.180077i	$0.942365\pi$
$692$	−4126.87	−	13600.8i	−0.226705	−	0.747145i
$693$	−15352.9	−	4340.93i	−0.841572	−	0.237949i
$694$	2105.74	+	14192.1i	0.115177	+	0.776260i
$695$	−6847.03	+	3953.13i	−0.373702	+	0.215757i
$696$	1670.81	−	20405.1i	0.0909940	−	1.11128i
$697$	−6453.67	+	11178.1i	−0.350718	+	0.607461i
$698$	25834.1	−	20505.0i	1.40091	−	1.11193i
$699$	8505.48			0.460239
$700$	12908.6	−	7784.31i	0.696997	−	0.420313i
$701$	−31433.5			−1.69362			−0.846808	−	0.531898i	$-0.821479\pi$
$701$	−31433.5			−1.69362			−0.846808	+	0.531898i	$0.821479\pi$
$702$	−343.819	+	272.895i	−0.0184852	+	0.0146720i
$703$	−5399.02	+	9351.37i	−0.289655	+	0.501698i
$704$	−20270.6	+	7634.53i	−1.08519	+	0.408717i
$705$	−2112.05	+	1219.39i	−0.112829	+	0.0651418i
$706$	−2661.44	−	17937.3i	−0.141876	−	0.956205i
$707$	10676.4	−	10386.7i	0.567929	−	0.552521i
$708$	17557.5	−	5327.44i	0.931991	−	0.282793i
$709$	12216.8	+	21160.2i	0.647126	+	1.12086i	0.983806	+	0.179237i	$0.0573628\pi$
$709$	12216.8	+	21160.2i	0.647126	+	1.12086i	−0.336680	+	0.941619i	$0.609304\pi$
$710$	1928.14	−	4879.79i	0.101918	−	0.257937i
$711$	−17682.4	−	10209.0i	−0.932690	−	0.538489i
$712$	−11466.3	+	16571.1i	−0.603534	+	0.872231i
$713$		−	1945.39i		−	0.102181i
$714$	−25673.0	+	33641.8i	−1.34564	+	1.76332i
$715$			693.260i			0.0362608i
$716$	−24397.8	+	26053.2i	−1.27345	+	1.35985i
$717$	10593.3	+	6116.04i	0.551762	+	0.318560i
$718$	25325.6	+	10006.8i	1.31635	+	0.520128i
$719$	14584.0	+	25260.1i	0.756453	+	1.31021i	0.944649	+	0.328083i	$0.106403\pi$
$719$	14584.0	+	25260.1i	0.756453	+	1.31021i	−0.188196	+	0.982132i	$0.560264\pi$
$720$	−3492.72	−	5225.52i	−0.180786	−	0.270477i
$721$	−31851.3	+	8066.79i	−1.64522	+	0.416676i
$722$	4065.97	−	603.286i	0.209584	−	0.0310969i
$723$	29537.5	−	17053.5i	1.51938	−	0.877215i
$724$	20494.1	+	4776.94i	1.05201	+	0.245212i
$725$	6688.02	−	11584.0i	0.342603	−	0.593405i
$726$	5552.02	+	6994.96i	0.283822	+	0.357586i
$727$	14802.2			0.755135			0.377567	−	0.925982i	$-0.376761\pi$
$727$	14802.2			0.755135			0.377567	+	0.925982i	$0.376761\pi$
$728$	−1404.23	+	235.770i	−0.0714892	+	0.0120031i
$729$	−9109.44			−0.462807
$730$	1836.64	+	2313.97i	0.0931193	+	0.117320i
$731$	−4845.39	+	8392.47i	−0.245162	+	0.424633i
$732$	−29240.0	−	6815.51i	−1.47643	−	0.344137i
$733$	24302.0	−	14030.8i	1.22458	−	0.707010i	0.258687	−	0.965961i	$-0.416710\pi$
$733$	24302.0	−	14030.8i	1.22458	−	0.707010i	0.965890	+	0.258951i	$0.0833769\pi$
$734$	−9814.23	+	1456.18i	−0.493529	+	0.0732270i
$735$	−5961.26	+	9699.09i	−0.299162	+	0.486743i
$736$	20748.7	+	22884.0i	1.03914	+	1.14608i
$737$	−12611.2	−	21843.3i	−0.630312	−	1.09173i
$738$	−5889.84	−	2327.24i	−0.293778	−	0.116080i
$739$	−19623.3	−	11329.5i	−0.976798	−	0.563955i	−0.0754963	−	0.997146i	$-0.524054\pi$
$739$	−19623.3	−	11329.5i	−0.976798	−	0.563955i	−0.901302	+	0.433191i	$0.857387\pi$
$740$	3123.49	−	3335.42i	0.155165	−	0.165693i
$741$		−	2131.93i		−	0.105693i
$742$	1168.65	−	9062.26i	0.0578203	−	0.448364i
$743$		−	36038.3i		−	1.77943i	−0.456514	−	0.889716i	$-0.650902\pi$
$743$		−	36038.3i		−	1.77943i	0.456514	−	0.889716i	$-0.349098\pi$
$744$	1459.88	+	1010.15i	0.0719377	+	0.0497768i
$745$	251.838	+	145.398i	0.0123847	+	0.00715032i
$746$	8426.67	−	21326.4i	0.413569	−	1.04667i
$747$	4678.13	+	8102.75i	0.229135	+	0.396873i
$748$	38017.7	−	11535.7i	1.85838	−	0.563885i
$749$	−339.004	−	1338.54i	−0.0165379	−	0.0652992i
$750$	−3124.12	−	21055.6i	−0.152102	−	1.02512i
$751$	10031.0	−	5791.41i	0.487399	−	0.281400i	−0.236096	−	0.971730i	$-0.575868\pi$
$751$	10031.0	−	5791.41i	0.487399	−	0.281400i	0.723495	+	0.690330i	$0.242535\pi$
$752$	308.265	+	4692.40i	0.0149485	+	0.227546i
$753$	−17862.9	+	30939.4i	−0.864487	+	1.49733i
$754$	−989.647	+	785.500i	−0.0477995	+	0.0379393i
$755$	4546.39			0.219153
$756$	5924.14	+	3271.45i	0.284998	+	0.157383i
$757$	24698.1			1.18582			0.592910	−	0.805268i	$-0.297979\pi$
$757$	24698.1			1.18582			0.592910	+	0.805268i	$0.297979\pi$
$758$	−15149.4	+	12024.4i	−0.725927	+	0.576181i
$759$	24841.8	−	43027.3i	1.18801	−	2.05770i
$760$	−9916.24	−	811.960i	−0.473289	−	0.0387538i
$761$	21831.6	−	12604.5i	1.03994	−	0.600410i	0.120124	−	0.992759i	$-0.461671\pi$
$761$	21831.6	−	12604.5i	1.03994	−	0.600410i	0.919816	+	0.392349i	$0.128338\pi$
$762$	−4701.43	−	31686.3i	−0.223510	−	1.50639i
$763$	−1003.81	−	1031.81i	−0.0476284	−	0.0489566i
$764$	939.741	+	3097.07i	0.0445008	+	0.146660i
$765$	5764.17	+	9983.84i	0.272424	+	0.471852i
$766$	−12494.7	+	31622.1i	−0.589365	+	1.49158i
$767$	−980.617	−	566.160i	−0.0461643	−	0.0266530i
$768$	−27946.8	+	3687.81i	−1.31307	+	0.173271i
$769$		−	16983.7i		−	0.796423i	−0.917294	−	0.398212i	$-0.869631\pi$
$769$		−	16983.7i		−	0.796423i	0.917294	−	0.398212i	$-0.130369\pi$
$770$	9863.55	−	4116.26i	0.461633	−	0.192649i
$771$		−	28401.7i		−	1.32667i
$772$	−17619.8	−	16500.2i	−0.821437	−	0.769244i
$773$	26702.2	+	15416.5i	1.24245	+	0.717326i	0.969591	−	0.244730i	$-0.0786992\pi$
$773$	26702.2	+	15416.5i	1.24245	+	0.717326i	0.272854	+	0.962056i	$0.412033\pi$
$774$	−4422.07	−	1747.28i	−0.205359	−	0.0811431i
$775$	579.930	+	1004.47i	0.0268796	+	0.0465569i
$776$	2737.44	+	5786.15i	0.126635	+	0.267668i
$777$	4107.17	−	14526.2i	0.189632	−	0.670687i
$778$	10760.0	−	1596.50i	0.495840	−	0.0735699i
$779$	−8681.76	+	5012.41i	−0.399302	+	0.230537i
$780$	−204.803	+	878.652i	−0.00940146	+	0.0403344i
$781$	−8136.30	+	14092.5i	−0.372778	+	0.645670i
$782$	−35223.4	−	44377.7i	−1.61072	−	2.02934i
$783$	6005.10			0.274080
$784$	11692.1	+	18579.1i	0.532623	+	0.846352i
$785$	−6417.94			−0.291804
$786$	−9233.93	−	11633.8i	−0.419037	−	0.527942i
$787$	−7483.59	+	12962.0i	−0.338960	+	0.587095i	−0.984237	−	0.176853i	$-0.943408\pi$
$787$	−7483.59	+	12962.0i	−0.338960	+	0.587095i	0.645278	+	0.763948i	$0.276742\pi$
$788$	−4801.35	+	20598.8i	−0.217057	+	0.931223i
$789$	3742.56	−	2160.77i	0.168871	−	0.0974974i
$790$	13529.7	−	2007.45i	0.609321	−	0.0904077i
$791$	−5174.95	+	18302.7i	−0.232617	+	0.822715i
$792$	8336.34	+	17620.6i	0.374014	+	0.790555i
$793$	926.443	+	1604.65i	0.0414867	+	0.0718570i
$794$	−30447.3	−	12030.6i	−1.36087	−	0.537719i
$795$	−5013.95	−	2894.80i	−0.223681	−	0.129142i
$796$	−24256.6	−	22715.4i	−1.08009	−	1.01146i
$797$			39166.5i			1.74071i	0.492421	+	0.870357i	$0.336112\pi$
$797$			39166.5i			1.74071i	−0.492421	+	0.870357i	$0.663888\pi$
$798$	−30332.6	+	12658.4i	−1.34557	+	0.561532i
$799$		−	8625.23i		−	0.381901i
$800$	−17535.1	−	5630.50i	−0.774951	−	0.248835i
$801$	15705.2	+	9067.41i	0.692779	+	0.399976i
$802$	−13684.7	+	34633.7i	−0.602524	+	1.52488i
$803$	−4581.13	−	7934.76i	−0.201326	−	0.348707i
$804$	−9530.77	−	31410.2i	−0.418065	−	1.37780i
$805$	−10628.5	−	10924.9i	−0.465349	−	0.478326i
$806$	−16.0798	−	108.373i	−0.000702714	−	0.00473608i
$807$	18326.2	−	10580.6i	0.799396	−	0.461532i
$808$	−18137.8	−	1485.16i	−0.789710	−	0.0646628i
$809$	13908.0	−	24089.3i	0.604422	−	1.04689i	−0.387720	−	0.921777i	$-0.626737\pi$
$809$	13908.0	−	24089.3i	0.604422	−	1.04689i	0.992143	−	0.125113i	$-0.0399293\pi$
$810$	9233.03	−	7328.42i	0.400513	−	0.317894i
$811$	20600.5			0.891962			0.445981	−	0.895042i	$-0.352855\pi$
$811$	20600.5			0.891962			0.445981	+	0.895042i	$0.352855\pi$
$812$	17052.0	+	9416.53i	0.736955	+	0.406965i
$813$	−13001.7			−0.560871
$814$	−11100.4	+	8810.58i	−0.477971	+	0.379374i
$815$	2376.53	−	4116.28i	0.102143	−	0.176916i
$816$	51592.3	−	3389.33i	2.21335	−	0.145405i
$817$	−6518.23	+	3763.30i	−0.279124	+	0.161152i
$818$	4753.52	+	32037.3i	0.203182	+	1.36939i
$819$	314.599	+	1242.18i	0.0134224	+	0.0529977i
$820$	4059.62	−	1231.80i	0.172888	−	0.0524591i
$821$	−8179.13	−	14166.7i	−0.347690	−	0.602217i	0.638149	−	0.769913i	$-0.279701\pi$
$821$	−8179.13	−	14166.7i	−0.347690	−	0.602217i	−0.985839	+	0.167696i	$0.946367\pi$
$822$	−5171.21	+	13087.4i	−0.219424	+	0.555325i
$823$	−8972.43	−	5180.24i	−0.380024	−	0.219407i	0.297805	−	0.954627i	$-0.403745\pi$
$823$	−8972.43	−	5180.24i	−0.380024	−	0.219407i	−0.677828	+	0.735220i	$0.737079\pi$
$824$	33011.3	+	22841.9i	1.39563	+	0.965700i
$825$			29621.9i			1.25006i
$826$	−2232.73	+	17313.6i	−0.0940518	+	0.729318i
$827$			9204.30i			0.387019i	0.981098	+	0.193510i	$0.0619871\pi$
$827$			9204.30i			0.387019i	−0.981098	+	0.193510i	$0.938013\pi$
$828$	19001.5	−	20290.8i	0.797523	−	0.851634i
$829$	−26296.5	−	15182.3i	−1.10171	−	0.636071i	−0.165039	−	0.986287i	$-0.552775\pi$
$829$	−26296.5	−	15182.3i	−1.10171	−	0.636071i	−0.936669	+	0.350216i	$0.886108\pi$
$830$	−5829.13	−	2303.25i	−0.243773	−	0.0963216i
$831$	29285.4	+	50723.8i	1.22250	+	2.11743i
$832$	1345.02	+	1103.32i	0.0560458	+	0.0459744i
$833$	−19165.4	−	35409.8i	−0.797169	−	1.47284i
$834$	31564.9	−	4683.43i	1.31056	−	0.194453i
$835$	−4261.66	+	2460.47i	−0.176624	+	0.101974i
$836$	30051.2	+	7004.59i	1.24323	+	0.289783i
$837$	−260.357	+	450.951i	−0.0107518	+	0.0186226i
$838$	7376.65	+	9293.79i	0.304084	+	0.383113i
$839$	−7688.40			−0.316369			−0.158184	−	0.987410i	$-0.550564\pi$
$839$	−7688.40			−0.316369			−0.158184	+	0.987410i	$0.550564\pi$
$840$	13717.3	−	2303.14i	0.563442	−	0.0946022i
$841$	−7103.96			−0.291277
$842$	6524.17	+	8219.76i	0.267028	+	0.336427i
$843$	−20742.9	+	35927.8i	−0.847479	+	1.46788i
$844$	−4614.39	−	1075.56i	−0.188192	−	0.0438652i
$845$	−9128.00	+	5270.05i	−0.371613	+	0.214551i
$846$	4186.11	−	621.112i	0.170120	−	0.0252414i
$847$	−8236.82	+	2086.09i	−0.334145	+	0.0846268i
$848$	−9281.30	+	6203.58i	−0.375850	+	0.251217i
$849$	15342.9	+	26574.6i	0.620219	+	1.07425i
$850$	31416.3	+	12413.4i	1.26773	+	0.500915i
$851$	17502.8	+	10105.2i	0.705039	+	0.407055i
$852$	−14475.3	+	15457.5i	−0.582061	+	0.621554i
$853$		−	16264.6i		−	0.652860i	−0.945221	−	0.326430i	$-0.894154\pi$
$853$		−	16264.6i		−	0.652860i	0.945221	−	0.326430i	$-0.105846\pi$
$854$	17329.7	−	22708.9i	0.694393	−	0.909931i
$855$			8953.79i			0.358144i
$856$	−959.923	+	1387.29i	−0.0383288	+	0.0553930i
$857$	9676.46	+	5586.71i	0.385696	+	0.222682i	0.680294	−	0.732940i	$-0.261852\pi$
$857$	9676.46	+	5586.71i	0.385696	+	0.222682i	−0.294598	+	0.955621i	$0.595186\pi$
$858$	1028.24	−	2602.29i	0.0409131	−	0.103544i
$859$	−10035.8	−	17382.6i	−0.398624	−	0.690437i	0.594932	−	0.803776i	$-0.297179\pi$
$859$	−10035.8	−	17382.6i	−0.398624	−	0.690437i	−0.993556	+	0.113339i	$0.963845\pi$
$860$	3047.95	−	924.834i	0.120854	−	0.0366705i
$861$	10045.2	−	9772.69i	0.397608	−	0.386821i
$862$	999.155	+	6734.01i	0.0394795	+	0.266080i
$863$	16644.7	−	9609.81i	0.656537	−	0.379052i	−0.134419	−	0.990925i	$-0.542917\pi$
$863$	16644.7	−	9609.81i	0.656537	−	0.379052i	0.790956	+	0.611873i	$0.209584\pi$
$864$	−1747.03	−	8081.51i	−0.0687907	−	0.318216i
$865$	4284.22	−	7420.49i	0.168402	−	0.291681i
$866$	−33538.5	+	26620.1i	−1.31603	+	1.04456i
$867$	−61021.5			−2.39031
$868$	−1446.43	+	872.250i	−0.0565613	+	0.0341084i
$869$	−42419.8			−1.65592
$870$	9667.43	−	7673.21i	0.376732	−	0.299019i
$871$	−1012.86	+	1754.32i	−0.0394023	+	0.0682467i
$872$	−143.531	+	1752.91i	−0.00557407	+	0.0680745i
$873$	4988.72	−	2880.24i	0.193405	−	0.111662i
$874$	−6458.44	−	43528.0i	−0.249954	−	1.68462i
$875$	19488.5	+	5510.23i	0.752950	+	0.212891i
$876$	−3462.13	−	11410.0i	−0.133533	−	0.440079i
$877$	−15336.1	−	26563.0i	−0.590496	−	1.02277i	−0.994166	−	0.107864i	$-0.965599\pi$
$877$	−15336.1	−	26563.0i	−0.590496	−	1.02277i	0.403670	−	0.914905i	$-0.367734\pi$
$878$	6005.83	−	15199.7i	0.230851	−	0.584244i
$879$	−19195.6	−	11082.6i	−0.736579	−	0.425264i
$880$	−11712.4	−	5773.74i	−0.448666	−	0.221174i
$881$			37453.2i			1.43227i	0.697962	+	0.716135i	$0.254091\pi$
$881$			37453.2i			1.43227i	−0.697962	+	0.716135i	$0.745909\pi$
$882$	15805.5	−	11851.5i	0.603398	−	0.452450i
$883$			28915.6i			1.10202i	0.834497	+	0.551012i	$0.185758\pi$
$883$			28915.6i			1.10202i	−0.834497	+	0.551012i	$0.814242\pi$
$884$	−2329.03	−	2181.04i	−0.0886128	−	0.0829824i
$885$	9579.23	+	5530.57i	0.363844	+	0.210066i
$886$	−21697.3	−	8573.21i	−0.822726	−	0.325082i
$887$	−18831.9	−	32617.7i	−0.712866	−	1.23472i	−0.963777	−	0.266710i	$-0.914064\pi$
$887$	−18831.9	−	32617.7i	−0.712866	−	1.23472i	0.250911	−	0.968010i	$-0.419270\pi$
$888$	−16671.7	+	7887.43i	−0.630029	+	0.298068i
$889$	29327.9	+	8292.26i	1.10644	+	0.312838i
$890$	−12016.8	+	1782.98i	−0.452589	+	0.0671526i
$891$	−31660.6	+	18279.3i	−1.19043	+	0.687294i
$892$	7237.93	−	31052.3i	0.271686	−	1.16559i
$893$	3349.50	−	5801.51i	0.125517	−	0.217402i
$894$	−729.669	−	919.305i	−0.0272973	−	0.0343917i
$895$	−21518.0			−0.803650
$896$	7711.68	−	25687.6i	0.287533	−	0.957771i
$897$	−3990.29			−0.148531
$898$	−11417.7	−	14385.0i	−0.424290	−	0.534560i
$899$	−749.408	+	1298.01i	−0.0278022	+	0.0481548i
$900$	−3762.34	+	16141.3i	−0.139346	+	0.597825i
$901$	17732.8	−	10238.0i	0.655676	−	0.378555i
$902$	−13014.7	+	1931.05i	−0.480424	+	0.0712826i
$903$	7541.92	−	7337.30i	0.277939	−	0.270399i
$904$	21006.0	−	9937.99i	0.772841	−	0.365633i
$905$	6343.09	+	10986.6i	0.232985	+	0.403542i
$906$	−17065.8	−	6743.16i	−0.625798	−	0.247270i
$907$	18222.8	+	10520.9i	0.667119	+	0.385161i	0.794984	−	0.606630i	$-0.207479\pi$
$907$	18222.8	+	10520.9i	0.667119	+	0.385161i	−0.127865	+	0.991792i	$0.540813\pi$
$908$	−1399.52	−	1310.59i	−0.0511505	−	0.0479004i
$909$			16377.4i			0.597584i
$910$	−682.393	−	520.752i	−0.0248584	−	0.0189701i
$911$		−	9510.87i		−	0.345894i	−0.984931	−	0.172947i	$-0.944671\pi$
$911$		−	9510.87i		−	0.345894i	0.984931	−	0.172947i	$-0.0553289\pi$
$912$	36018.3	+	17755.5i	1.30777	+	0.644675i
$913$	16834.1	+	9719.16i	0.610215	+	0.352308i
$914$	11533.2	−	29188.6i	0.417380	−	1.05632i
$915$	−9050.02	−	15675.1i	−0.326978	−	0.566342i
$916$	9984.57	+	32905.8i	0.360152	+	1.18694i
$917$	13699.2	−	3469.51i	0.493333	−	0.124944i
$918$	2225.77	+	15001.1i	0.0800233	+	0.539334i
$919$	6898.95	−	3983.11i	0.247634	−	0.142971i	−0.371047	−	0.928614i	$-0.621001\pi$
$919$	6898.95	−	3983.11i	0.247634	−	0.142971i	0.618680	+	0.785643i	$0.287668\pi$
$920$	−1519.73	+	18560.1i	−0.0544609	+	0.665116i
$921$	21481.7	−	37207.4i	0.768562	−	1.33119i
$922$	−11023.9	+	8749.83i	−0.393765	+	0.312538i
$923$	1306.92			0.0466064
$924$	−43130.0	+	821.689i	−1.53558	+	0.0292549i
$925$	−12049.7			−0.428316
$926$	35454.8	−	28141.1i	1.25823	−	0.998676i
$927$	18063.2	−	31286.3i	0.639992	−	1.10850i
$928$	−5028.63	−	23261.7i	−0.177880	−	0.822849i
$929$	1439.51	−	831.103i	0.0508384	−	0.0293516i	−0.474365	−	0.880328i	$-0.657322\pi$
$929$	1439.51	−	831.103i	0.0508384	−	0.0293516i	0.525204	+	0.850976i	$0.323989\pi$
$930$	157.077	+	1058.65i	0.00553844	+	0.0373275i
$931$	859.929	−	31260.1i	0.0302718	−	1.10044i
$932$	9461.15	−	2870.78i	0.332522	−	0.100897i
$933$	−7891.67	−	13668.8i	−0.276915	−	0.479631i
$934$	18410.9	−	46594.7i	0.644991	−	1.63236i
$935$	20742.2	+	11975.5i	0.725500	+	0.418867i
$936$	890.818	−	1287.41i	0.0311082	−	0.0449578i
$937$			11523.9i			0.401783i	0.979614	+	0.200891i	$0.0643838\pi$
$937$			11523.9i			0.401783i	−0.979614	+	0.200891i	$0.935616\pi$
$938$	30974.0	+	3994.35i	1.07818	+	0.139041i
$939$			39650.2i			1.37799i
$940$	−1937.79	+	2069.27i	−0.0672379	+	0.0718000i
$941$	−13692.6	−	7905.45i	−0.474354	−	0.273868i	0.243707	−	0.969849i	$-0.421637\pi$
$941$	−13692.6	−	7905.45i	−0.474354	−	0.273868i	−0.718061	+	0.695981i	$0.754970\pi$
$942$	24091.0	+	9519.02i	0.833256	+	0.329243i
$943$	9381.65	+	16249.5i	0.323975	+	0.561141i
$944$	17732.1	−	11852.0i	0.611366	−	0.408635i
$945$	1001.63	+	3954.90i	0.0344795	+	0.136141i
$946$	−9771.39	+	1449.82i	−0.335830	+	0.0498286i
$947$	−20479.9	+	11824.1i	−0.702752	+	0.405734i	−0.808372	−	0.588672i	$-0.799651\pi$
$947$	−20479.9	+	11824.1i	−0.702752	+	0.405734i	0.105619	+	0.994407i	$0.466317\pi$
$948$	−53763.7	−	12531.7i	−1.84194	−	0.429335i
$949$	−367.929	+	637.272i	−0.0125853	+	0.0217984i
$950$	16310.7	+	20549.7i	0.557039	+	0.701811i
$951$	30249.6			1.03145
$952$	−17202.7	+	46086.9i	−0.585654	+	1.56900i
$953$	23736.6			0.806825			0.403413	−	0.915018i	$-0.367824\pi$
$953$	23736.6			0.806825			0.403413	+	0.915018i	$0.367824\pi$
$954$	6245.81	+	7869.06i	0.211966	+	0.267055i
$955$	−975.572	+	1689.74i	−0.0330563	+	0.0572552i
$956$	13847.8	+	3227.76i	0.468484	+	0.109198i
$957$	−33150.2	+	19139.3i	−1.11974	+	0.646485i
$958$	−28225.9	+	4188.00i	−0.951917	+	0.141240i
$959$	−9336.18	−	9596.54i	−0.314370	−	0.323137i
$960$	−13138.9	−	10777.9i	−0.441725	−	0.362348i
$961$	14830.5	+	25687.2i	0.497819	+	0.862247i
$962$	1058.57	+	418.270i	0.0354778	+	0.0140183i
$963$	1314.79	+	759.097i	0.0439965	+	0.0254014i
$964$	27100.4	−	28939.2i	0.905441	−	0.966875i
$965$		−	14552.6i		−	0.485456i
$966$	23692.5	+	56772.9i	0.789124	+	1.89093i
$967$		−	37667.0i		−	1.25263i	−0.779571	−	0.626314i	$-0.784563\pi$
$967$		−	37667.0i		−	1.25263i	0.779571	−	0.626314i	$-0.215437\pi$
$968$	8536.79	+	5906.98i	0.283453	+	0.196134i
$969$	−63786.8	−	36827.3i	−2.11468	−	1.22091i
$970$	−1418.07	+	3588.89i	−0.0469397	+	0.118796i
$971$	−14502.0	−	25118.3i	−0.479292	−	0.830159i	0.520426	−	0.853907i	$-0.325773\pi$
$971$	−14502.0	−	25118.3i	−0.479292	−	0.830159i	−0.999718	+	0.0237484i	$0.992440\pi$
$972$	−36086.5	+	10949.7i	−1.19082	+	0.361329i
$973$	−8260.51	+	29215.6i	−0.272168	+	0.962600i
$974$	984.436	+	6634.81i	0.0323854	+	0.218268i
$975$	2060.32	−	1189.53i	0.0676750	−	0.0390722i
$976$	−34825.8	+	2287.86i	−1.14216	+	0.0750335i
$977$	−11699.4	+	20263.9i	−0.383108	+	0.663563i	−0.991505	−	0.130070i	$-0.958480\pi$
$977$	−11699.4	+	20263.9i	−0.383108	+	0.663563i	0.608397	+	0.793633i	$0.291813\pi$
$978$	−15026.0	+	11926.4i	−0.491287	+	0.389943i
$979$	37676.5			1.22997
$980$	−3357.41	+	12800.9i	−0.109437	+	0.417255i
$981$	1582.78			0.0515129
$982$	−24522.9	+	19464.3i	−0.796901	+	0.632515i
$983$	−5578.49	+	9662.22i	−0.181003	+	0.313507i	−0.942222	−	0.334988i	$-0.891268\pi$
$983$	−5578.49	+	9662.22i	−0.181003	+	0.313507i	0.761219	+	0.648495i	$0.224601\pi$
$984$	−17065.6	−	1397.36i	−0.552877	−	0.0452705i
$985$	−11042.7	+	6375.50i	−0.357208	+	0.206234i
$986$	6406.64	+	43178.9i	0.206926	+	1.39462i
$987$	−2548.05	+	9011.91i	−0.0821737	+	0.290631i
$988$	−719.571	−	2371.47i	−0.0231707	−	0.0763628i
$989$	7043.71	+	12200.1i	0.226468	+	0.392254i
$990$	−4318.45	+	10929.2i	−0.138636	+	0.350863i
$991$	49165.5	+	28385.7i	1.57598	+	0.909892i	0.995412	+	0.0956788i	$0.0305022\pi$
$991$	49165.5	+	28385.7i	1.57598	+	0.909892i	0.580566	+	0.814213i	$0.302831\pi$
$992$	1964.85	+	630.911i	0.0628873	+	0.0201930i
$993$		−	43882.6i		−	1.40239i
$994$	−7759.88	−	18594.5i	−0.247614	−	0.593342i
$995$		−	20034.2i		−	0.638317i
$996$	18464.6	+	17291.4i	0.587424	+	0.550100i
$997$	8650.18	+	4994.18i	0.274778	+	0.158643i	0.631057	−	0.775736i	$-0.282621\pi$
$997$	8650.18	+	4994.18i	0.274778	+	0.158643i	−0.356279	+	0.934380i	$0.615955\pi$
$998$	−29895.9	−	11812.7i	−0.948234	−	0.374673i
$999$	−2704.83	−	4684.90i	−0.0856627	−	0.148372i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	28.4.f.a.3.3	✓	20
4.3	odd	2	inner	28.4.f.a.3.5	yes	20
7.2	even	3		196.4.f.d.19.5		20
7.3	odd	6		196.4.d.b.195.17		20
7.4	even	3		196.4.d.b.195.18		20
7.5	odd	6	inner	28.4.f.a.19.5	yes	20
7.6	odd	2		196.4.f.d.31.3		20
8.3	odd	2		448.4.p.h.255.2		20
8.5	even	2		448.4.p.h.255.9		20
28.3	even	6		196.4.d.b.195.20		20
28.11	odd	6		196.4.d.b.195.19		20
28.19	even	6	inner	28.4.f.a.19.3	yes	20
28.23	odd	6		196.4.f.d.19.3		20
28.27	even	2		196.4.f.d.31.5		20
56.5	odd	6		448.4.p.h.383.2		20
56.19	even	6		448.4.p.h.383.9		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.4.f.a.3.3	✓	20	1.1	even	1	trivial
28.4.f.a.3.5	yes	20	4.3	odd	2	inner
28.4.f.a.19.3	yes	20	28.19	even	6	inner
28.4.f.a.19.5	yes	20	7.5	odd	6	inner
196.4.d.b.195.17		20	7.3	odd	6
196.4.d.b.195.18		20	7.4	even	3
196.4.d.b.195.19		20	28.11	odd	6
196.4.d.b.195.20		20	28.3	even	6
196.4.f.d.19.3		20	28.23	odd	6
196.4.f.d.19.5		20	7.2	even	3
196.4.f.d.31.3		20	7.6	odd	2
196.4.f.d.31.5		20	28.27	even	2
448.4.p.h.255.2		20	8.3	odd	2
448.4.p.h.255.9		20	8.5	even	2
448.4.p.h.383.2		20	56.5	odd	6
448.4.p.h.383.9		20	56.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	28.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.75840 - 2.21540i) q^{2} +(-3.44104 + 5.96006i) q^{3} +(-1.81602 + 7.79115i) q^{4} +(-4.17670 + 2.41142i) q^{5} +(19.2547 - 2.85690i) q^{6} +(-5.03893 + 17.8216i) q^{7} +(20.4539 - 9.67677i) q^{8} +(-10.1816 - 17.6350i) q^{9} +O(q^{10})\)	\(q+(-1.75840 - 2.21540i) q^{2} +(-3.44104 + 5.96006i) q^{3} +(-1.81602 + 7.79115i) q^{4} +(-4.17670 + 2.41142i) q^{5} +(19.2547 - 2.85690i) q^{6} +(-5.03893 + 17.8216i) q^{7} +(20.4539 - 9.67677i) q^{8} +(-10.1816 - 17.6350i) q^{9} +(12.6866 + 5.01283i) q^{10} +(-36.6380 - 21.1529i) q^{11} +(-40.1867 - 37.6333i) q^{12} +3.39776i q^{13} +(48.3425 - 20.1743i) q^{14} -33.1912i q^{15} +(-57.4041 - 28.2978i) q^{16} +(101.660 + 58.6935i) q^{17} +(-21.1653 + 53.5656i) q^{18} +(45.5858 + 78.9570i) q^{19} +(-11.2028 - 36.9205i) q^{20} +(-88.8786 - 91.3572i) q^{21} +(17.5621 + 118.363i) q^{22} +(147.782 - 85.3222i) q^{23} +(-12.7084 + 155.204i) q^{24} +(-50.8701 + 88.1096i) q^{25} +(7.52740 - 5.97463i) q^{26} -45.6757 q^{27} +(-129.700 - 71.6235i) q^{28} -131.473 q^{29} +(-73.5319 + 58.3636i) q^{30} +(5.70011 - 9.87288i) q^{31} +(38.2485 + 176.932i) q^{32} +(252.146 - 145.576i) q^{33} +(-48.7299 - 328.425i) q^{34} +(-21.9293 - 86.5865i) q^{35} +(155.887 - 47.3005i) q^{36} +(59.2181 + 102.569i) q^{37} +(94.7632 - 239.829i) q^{38} +(-20.2508 - 11.6918i) q^{39} +(-62.0949 + 89.7399i) q^{40} +109.956i q^{41} +(-46.1084 + 357.545i) q^{42} +82.5542i q^{43} +(231.341 - 247.038i) q^{44} +(85.0507 + 49.1040i) q^{45} +(-448.885 - 177.367i) q^{46} +(-36.7384 - 63.6328i) q^{47} +(366.187 - 244.758i) q^{48} +(-292.218 - 179.603i) q^{49} +(284.648 - 42.2346i) q^{50} +(-699.634 + 403.934i) q^{51} +(-26.4724 - 6.17041i) q^{52} +(87.2160 - 151.062i) q^{53} +(80.3164 + 101.190i) q^{54} +204.035 q^{55} +(69.3900 + 413.281i) q^{56} -627.451 q^{57} +(231.182 + 291.265i) q^{58} +(-166.628 + 288.607i) q^{59} +(258.598 + 60.2761i) q^{60} +(472.266 - 272.663i) q^{61} +(-31.8955 + 4.73248i) q^{62} +(365.587 - 92.5901i) q^{63} +(324.720 - 395.855i) q^{64} +(-8.19342 - 14.1914i) q^{65} +(-765.885 - 302.622i) q^{66} +(516.318 + 298.096i) q^{67} +(-641.907 + 685.461i) q^{68} +1174.39i q^{69} +(-153.264 + 200.836i) q^{70} -384.641i q^{71} +(-378.901 - 262.178i) q^{72} +(187.557 + 108.286i) q^{73} +(123.102 - 311.550i) q^{74} +(-350.092 - 606.378i) q^{75} +(-697.951 + 211.778i) q^{76} +(561.595 - 546.359i) q^{77} +(9.70706 + 65.4227i) q^{78} +(868.356 - 501.346i) q^{79} +(307.998 - 20.2338i) q^{80} +(432.074 - 748.374i) q^{81} +(243.596 - 193.346i) q^{82} -459.471 q^{83} +(873.183 - 526.560i) q^{84} -566.139 q^{85} +(182.891 - 145.164i) q^{86} +(452.403 - 783.585i) q^{87} +(-954.080 - 78.1218i) q^{88} +(-771.258 + 445.286i) q^{89} +(-40.7683 - 274.766i) q^{90} +(-60.5534 - 17.1210i) q^{91} +(396.382 + 1306.34i) q^{92} +(39.2287 + 67.9460i) q^{93} +(-76.3713 + 193.283i) q^{94} +(-380.797 - 219.853i) q^{95} +(-1186.14 - 380.868i) q^{96} +282.888i q^{97} +(115.944 + 963.197i) q^{98} +861.479i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{4} - 6 q^{5} + 72 q^{8} - 56 q^{9}+O(q^{10}) \) 20 * q + 4 * q^4 - 6 * q^5 + 72 * q^8 - 56 * q^9	\( 20 q + 4 q^{4} - 6 q^{5} + 72 q^{8} - 56 q^{9} - 12 q^{10} - 168 q^{12} - 56 q^{14} - 104 q^{16} - 6 q^{17} + 68 q^{18} + 238 q^{21} - 184 q^{22} + 348 q^{24} - 36 q^{25} + 396 q^{26} + 448 q^{28} - 352 q^{29} + 644 q^{30} - 40 q^{32} + 30 q^{33} + 208 q^{36} + 258 q^{37} - 1620 q^{38} - 1548 q^{40} - 980 q^{42} - 1248 q^{44} - 504 q^{45} + 232 q^{46} - 644 q^{49} - 864 q^{50} + 2592 q^{52} + 570 q^{53} + 4572 q^{54} + 1904 q^{56} + 1452 q^{57} + 2244 q^{58} - 736 q^{60} + 294 q^{61} + 2560 q^{64} - 124 q^{65} - 4272 q^{66} - 6084 q^{68} - 4144 q^{70} - 4672 q^{72} + 966 q^{73} + 832 q^{74} - 378 q^{77} - 4056 q^{78} + 7032 q^{80} - 1262 q^{81} + 7692 q^{82} + 6188 q^{84} - 2980 q^{85} + 5696 q^{86} - 1396 q^{88} - 3186 q^{89} + 3312 q^{92} - 306 q^{93} - 6780 q^{94} - 11784 q^{96} - 4900 q^{98}+O(q^{100}) \) 20 * q + 4 * q^4 - 6 * q^5 + 72 * q^8 - 56 * q^9 - 12 * q^10 - 168 * q^12 - 56 * q^14 - 104 * q^16 - 6 * q^17 + 68 * q^18 + 238 * q^21 - 184 * q^22 + 348 * q^24 - 36 * q^25 + 396 * q^26 + 448 * q^28 - 352 * q^29 + 644 * q^30 - 40 * q^32 + 30 * q^33 + 208 * q^36 + 258 * q^37 - 1620 * q^38 - 1548 * q^40 - 980 * q^42 - 1248 * q^44 - 504 * q^45 + 232 * q^46 - 644 * q^49 - 864 * q^50 + 2592 * q^52 + 570 * q^53 + 4572 * q^54 + 1904 * q^56 + 1452 * q^57 + 2244 * q^58 - 736 * q^60 + 294 * q^61 + 2560 * q^64 - 124 * q^65 - 4272 * q^66 - 6084 * q^68 - 4144 * q^70 - 4672 * q^72 + 966 * q^73 + 832 * q^74 - 378 * q^77 - 4056 * q^78 + 7032 * q^80 - 1262 * q^81 + 7692 * q^82 + 6188 * q^84 - 2980 * q^85 + 5696 * q^86 - 1396 * q^88 - 3186 * q^89 + 3312 * q^92 - 306 * q^93 - 6780 * q^94 - 11784 * q^96 - 4900 * q^98

Introduction

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