LMFDB - Embedded newform 28.4.f.a.19.5

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			19.5
Root			$-1.75840 - 2.21540i$ of defining polynomial
Character	$\chi$	$=$	28.19
Dual form			28.4.f.a.3.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.03939 + 2.63053i) q^{2} +(3.44104 + 5.96006i) q^{3} +(-5.83932 - 5.46830i) q^{4} +(-4.17670 - 2.41142i) q^{5} +(-19.2547 + 2.85690i) q^{6} +(5.03893 + 17.8216i) q^{7} +(20.4539 - 9.67677i) q^{8} +(-10.1816 + 17.6350i) q^{9} +O(q^{10})$	\(q+(-1.03939 + 2.63053i) q^{2} +(3.44104 + 5.96006i) q^{3} +(-5.83932 - 5.46830i) 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} +(10.6845 - 8.48051i) q^{10} +(36.6380 - 21.1529i) q^{11} +(12.4980 - 53.6194i) q^{12} -3.39776i q^{13} +(-52.1176 - 5.26861i) q^{14} -33.1912i q^{15} +(4.19540 + 63.8623i) q^{16} +(101.660 - 58.6935i) q^{17} +(-35.8066 - 45.1125i) 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} +(128.057 + 88.6080i) q^{24} +(-50.8701 - 88.1096i) q^{25} +(8.93788 + 3.53160i) q^{26} +45.6757 q^{27} +(68.0299 - 131.620i) q^{28} -131.473 q^{29} +(87.3103 + 34.4987i) q^{30} +(-5.70011 - 9.87288i) q^{31} +(-172.352 - 55.3420i) 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} +(-160.317 - 201.982i) q^{38} +(20.2508 - 11.6918i) q^{39} +(-108.764 - 8.90583i) q^{40} -109.956i q^{41} +(-147.938 - 328.753i) q^{42} +82.5542i q^{43} +(-329.612 - 76.8285i) q^{44} +(85.0507 - 49.1040i) q^{45} +(378.046 - 300.062i) 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} +(-18.5799 + 19.8406i) q^{52} +(87.2160 + 151.062i) q^{53} +(-47.4750 + 120.151i) q^{54} -204.035 q^{55} +(275.521 + 315.760i) q^{56} -627.451 q^{57} +(136.652 - 345.842i) q^{58} +(166.628 + 288.607i) q^{59} +(-181.500 + 193.814i) 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} +(-645.021 + 511.964i) q^{66} +(-516.318 + 298.096i) q^{67} +(-914.580 - 213.178i) q^{68} -1174.39i q^{69} +(204.975 + 147.683i) q^{70} -384.641i q^{71} +(-37.6024 + 459.227i) q^{72} +(187.557 - 108.286i) q^{73} +(208.259 + 262.384i) 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} +(136.476 - 276.851i) q^{80} +(432.074 + 748.374i) q^{81} +(289.241 + 114.287i) q^{82} +459.471 q^{83} +(1018.56 - 47.4493i) q^{84} -566.139 q^{85} +(-217.161 - 85.8063i) q^{86} +(-452.403 - 783.585i) q^{87} +(544.695 - 787.197i) 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} +(129.202 + 162.781i) q^{94} +(380.797 - 219.853i) q^{95} +(-263.230 - 1217.66i) q^{96} -282.888i q^{97} +(-168.722 - 955.366i) 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 $\left(\mathbb{Z}/28\mathbb{Z}\right)^\times$.

$n$	$15$	$17$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.03939	+	2.63053i	−0.367481	+	0.930031i
$2$	−1.03939	+	2.63053i	−0.367481	+	0.930031i
$3$	3.44104	+	5.96006i	0.662229	+	1.14701i	0.980029	+	0.198856i	$0.0637227\pi$
$3$	3.44104	+	5.96006i	0.662229	+	1.14701i	−0.317800	+	0.948158i	$0.602944\pi$
$4$	−5.83932	−	5.46830i	−0.729915	−	0.683537i
$5$	−4.17670	−	2.41142i	−0.373576	−	0.215684i	0.301444	−	0.953484i	$-0.402531\pi$
$5$	−4.17670	−	2.41142i	−0.373576	−	0.215684i	−0.675020	+	0.737800i	$0.735865\pi$
$6$	−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
$10$	10.6845	−	8.48051i	0.337875	−	0.268177i
$11$	36.6380	−	21.1529i	1.00425	−	0.579805i	0.0947480	−	0.995501i	$-0.469795\pi$
$11$	36.6380	−	21.1529i	1.00425	−	0.579805i	0.909503	+	0.415696i	$0.136462\pi$
$12$	12.4980	−	53.6194i	0.300656	−	1.28988i
$13$		−	3.39776i		−	0.0724898i	−0.999343	−	0.0362449i	$-0.988460\pi$
$13$		−	3.39776i		−	0.0724898i	0.999343	−	0.0362449i	$-0.0115396\pi$
$14$	−52.1176	−	5.26861i	−0.994929	−	0.100578i
$15$		−	33.1912i		−	0.571329i
$16$	4.19540	+	63.8623i	0.0655532	+	0.997849i
$17$	101.660	−	58.6935i	1.45036	−	0.837369i	0.451863	−	0.892087i	$-0.350760\pi$
$17$	101.660	−	58.6935i	1.45036	−	0.837369i	0.998502	+	0.0547188i	$0.0174262\pi$
$18$	−35.8066	−	45.1125i	−0.468872	−	0.590729i
$19$	−45.5858	+	78.9570i	−0.550427	+	0.953367i	0.447817	+	0.894125i	$0.352202\pi$
$19$	−45.5858	+	78.9570i	−0.550427	+	0.953367i	−0.998244	+	0.0592419i	$0.981132\pi$
$20$	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	$-0.614838\pi$
$23$	−147.782	−	85.3222i	−1.33977	−	0.773518i	−0.986773	+	0.162105i	$0.948172\pi$
$24$	128.057	+	88.6080i	1.08914	+	0.753626i
$25$	−50.8701	−	88.1096i	−0.406961	−	0.704877i
$26$	8.93788	+	3.53160i	0.0674178	+	0.0266386i
$27$	45.6757			0.325566
$28$	68.0299	−	131.620i	0.459158	−	0.888354i
$29$	−131.473			−0.841857			−0.420928	−	0.907094i	$-0.638296\pi$
$29$	−131.473			−0.841857			−0.420928	+	0.907094i	$0.638296\pi$
$30$	87.3103	+	34.4987i	0.531354	+	0.209953i
$31$	−5.70011	−	9.87288i	−0.0330249	−	0.0572007i	0.849041	−	0.528328i	$-0.177181\pi$
$31$	−5.70011	−	9.87288i	−0.0330249	−	0.0572007i	−0.882065	+	0.471127i	$0.843847\pi$
$32$	−172.352	−	55.3420i	−0.952120	−	0.305724i
$33$	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	−0.703950	−	0.710249i	$-0.748582\pi$
$37$	59.2181	−	102.569i	0.263119	−	0.455735i	0.967069	+	0.254514i	$0.0819155\pi$
$38$	−160.317	−	201.982i	−0.684390	−	0.862258i
$39$	20.2508	−	11.6918i	0.0831469	−	0.0480049i
$40$	−108.764	−	8.90583i	−0.429929	−	0.0352034i
$41$		−	109.956i		−	0.418833i	−0.977826	−	0.209417i	$-0.932844\pi$
$41$		−	109.956i		−	0.418833i	0.977826	−	0.209417i	$-0.0671565\pi$
$42$	−147.938	−	328.753i	−0.543506	−	1.20780i
$43$			82.5542i			0.292777i	0.989227	+	0.146388i	$0.0467649\pi$
$43$			82.5542i			0.292777i	−0.989227	+	0.146388i	$0.953235\pi$
$44$	−329.612	−	76.8285i	−1.12934	−	0.263235i
$45$	85.0507	−	49.1040i	0.281747	−	0.162667i
$46$	378.046	−	300.062i	1.21174	−	0.961777i
$47$	36.7384	−	63.6328i	0.114018	−	0.197485i	−0.803369	−	0.595482i	$-0.796961\pi$
$47$	36.7384	−	63.6328i	0.114018	−	0.197485i	0.917387	+	0.397997i	$0.130294\pi$
$48$	−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
$52$	−18.5799	+	19.8406i	−0.0495495	+	0.0529115i
$53$	87.2160	+	151.062i	0.226038	+	0.391510i	0.956630	−	0.291304i	$-0.0940892\pi$
$53$	87.2160	+	151.062i	0.226038	+	0.391510i	−0.730592	+	0.682814i	$0.760756\pi$
$54$	−47.4750	+	120.151i	−0.119639	+	0.302787i
$55$	−204.035			−0.500219
$56$	275.521	+	315.760i	0.657465	+	0.753485i
$57$	−627.451			−1.45803
$58$	136.652	−	345.842i	0.309366	−	0.782953i
$59$	166.628	+	288.607i	0.367679	+	0.636839i	0.989202	−	0.146557i	$-0.0468192\pi$
$59$	166.628	+	288.607i	0.367679	+	0.636839i	−0.621523	+	0.783396i	$0.713486\pi$
$60$	−181.500	+	193.814i	−0.390525	+	0.417022i
$61$	472.266	+	272.663i	0.991271	+	0.572310i	0.905654	−	0.424018i	$-0.139381\pi$
$61$	472.266	+	272.663i	0.991271	+	0.572310i	0.0856167	+	0.996328i	$0.472714\pi$
$62$	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
$66$	−645.021	+	511.964i	−1.20298	+	0.954825i
$67$	−516.318	+	298.096i	−0.941466	+	0.543556i	−0.890420	−	0.455141i	$-0.849589\pi$
$67$	−516.318	+	298.096i	−0.941466	+	0.543556i	−0.0510465	+	0.998696i	$0.516256\pi$
$68$	−914.580	−	213.178i	−1.63102	−	0.380170i
$69$		−	1174.39i		−	2.04898i
$70$	204.975	+	147.683i	0.349988	+	0.252164i
$71$		−	384.641i		−	0.642937i	−0.946920	−	0.321468i	$-0.895824\pi$
$71$		−	384.641i		−	0.642937i	0.946920	−	0.321468i	$-0.104176\pi$
$72$	−37.6024	+	459.227i	−0.0615484	+	0.751673i
$73$	187.557	−	108.286i	0.300710	−	0.173615i	−0.342052	−	0.939681i	$-0.611122\pi$
$73$	187.557	−	108.286i	0.300710	−	0.173615i	0.642762	+	0.766066i	$0.277788\pi$
$74$	208.259	+	262.384i	0.327157	+	0.412183i
$75$	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	$-0.586451\pi$
$79$	−868.356	−	501.346i	−1.23668	−	0.713997i	−0.968414	+	0.249347i	$0.919784\pi$
$80$	136.476	−	276.851i	0.190731	−	0.386911i
$81$	432.074	+	748.374i	0.592694	+	1.02658i
$82$	289.241	+	114.287i	0.389528	+	0.153913i
$83$	459.471			0.607632			0.303816	−	0.952731i	$-0.401739\pi$
$83$	459.471			0.607632			0.303816	+	0.952731i	$0.401739\pi$
$84$	1018.56	−	47.4493i	1.32302	−	0.0616327i
$85$	−566.139			−0.722428
$86$	−217.161	−	85.8063i	−0.272291	−	0.107590i
$87$	−452.403	−	783.585i	−0.557502	−	0.965622i
$88$	544.695	−	787.197i	0.659826	−	0.953585i
$89$	−771.258	−	445.286i	−0.918575	−	0.530340i	−0.0353951	−	0.999373i	$-0.511269\pi$
$89$	−771.258	−	445.286i	−0.918575	−	0.530340i	−0.883180	+	0.469034i	$0.844602\pi$
$90$	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
$94$	129.202	+	162.781i	0.141768	+	0.178612i
$95$	380.797	−	219.853i	0.411252	−	0.237437i
$96$	−263.230	−	1217.66i	−0.279852	−	1.29455i
$97$		−	282.888i		−	0.296113i	−0.988979	−	0.148056i	$-0.952698\pi$
$97$		−	282.888i		−	0.296113i	0.988979	−	0.148056i	$-0.0473017\pi$
$98$	−168.722	−	955.366i	−0.173913	−	0.984761i
$99$			861.479i			0.874565i
$100$	−184.763	+	792.673i	−0.184763	+	0.792673i
$101$	−696.516	+	402.134i	−0.686197	+	0.396176i	−0.802186	−	0.597074i	$-0.796330\pi$
$101$	−696.516	+	402.134i	−0.686197	+	0.396176i	0.115988	+	0.993251i	$0.462996\pi$
$102$	−1789.75	+	1420.56i	−1.73737	+	1.37898i
$103$	−887.054	+	1536.42i	−0.848583	+	1.46979i	0.0338902	+	0.999426i	$0.489210\pi$
$103$	−887.054	+	1536.42i	−0.848583	+	1.46979i	−0.882473	+	0.470363i	$0.844123\pi$
$104$	−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	$-0.322610\pi$
$107$	64.5675	+	37.2781i	0.0583362	+	0.0336804i	−0.470548	+	0.882374i	$0.655944\pi$
$108$	−266.715	−	249.768i	−0.237636	−	0.222537i
$109$	−38.8638	−	67.3141i	−0.0341512	−	0.0591516i	0.848445	−	0.529284i	$-0.177539\pi$
$109$	−38.8638	−	67.3141i	−0.0341512	−	0.0591516i	−0.882596	+	0.470133i	$0.844206\pi$
$110$	212.072	−	536.718i	0.183821	−	0.465219i
$111$	815.089			0.696980
$112$	−1116.99	+	396.567i	−0.942370	+	0.334572i
$113$	1026.99			0.854969			0.427484	−	0.904023i	$-0.359400\pi$
$113$	1026.99			0.854969			0.427484	+	0.904023i	$0.359400\pi$
$114$	652.169	−	1650.53i	0.535800	−	1.35602i
$115$	411.496	+	712.732i	0.333671	+	0.577935i
$116$	767.711	+	718.931i	0.614484	+	0.575441i
$117$	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
$122$	−1208.12	+	958.904i	−0.896539	+	0.711599i
$123$	655.342	−	378.362i	0.480408	−	0.277364i
$124$	−20.7031	+	88.8209i	−0.0149935	+	0.0643254i
$125$			1093.53i			0.782468i
$126$	623.550	−	865.449i	0.440875	−	0.611907i
$127$		−	1645.64i		−	1.14982i	−0.818217	−	0.574909i	$-0.805037\pi$
$127$		−	1645.64i		−	1.14982i	0.818217	−	0.574909i	$-0.194963\pi$
$128$	703.794	+	1265.63i	0.485993	+	0.873962i
$129$	−492.028	+	284.072i	−0.335819	+	0.193885i
$130$	−28.8147	−	36.3035i	−0.0194401	−	0.0244925i
$131$	381.520	−	660.812i	0.254455	−	0.440729i	−0.710293	−	0.703907i	$-0.751437\pi$
$131$	381.520	−	660.812i	0.254455	−	0.440729i	0.964747	+	0.263178i	$0.0847707\pi$
$132$	−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
$136$	1511.38	−	2184.25i	0.952938	−	1.37719i
$137$	−361.462	−	626.070i	−0.225414	−	0.390429i	0.731029	−	0.682346i	$-0.239040\pi$
$137$	−361.462	−	626.070i	−0.225414	−	0.390429i	−0.956444	+	0.291917i	$0.905707\pi$
$138$	3089.26	+	1220.65i	1.90562	+	0.752963i
$139$	−1639.34			−1.00034			−0.500168	−	0.865928i	$-0.666729\pi$
$139$	−1639.34			−1.00034			−0.500168	+	0.865928i	$0.666729\pi$
$140$	−601.533	+	385.691i	−0.363134	+	0.232835i
$141$	505.674			0.302024
$142$	1011.81	+	399.793i	0.597951	+	0.236267i
$143$	−71.8725	−	124.487i	−0.0420300	−	0.0727980i
$144$	−1168.93	−	576.232i	−0.676462	−	0.333468i
$145$	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	−0.874194	−	0.485576i	$-0.838610\pi$
$149$	−30.1479	+	52.2177i	−0.0165759	+	0.0287103i	0.857618	+	0.514286i	$0.171943\pi$
$150$	1231.21	+	1551.19i	0.670185	+	0.844362i
$151$	816.384	−	471.339i	0.439976	−	0.254020i	−0.263611	−	0.964629i	$-0.584914\pi$
$151$	816.384	−	471.339i	0.439976	−	0.254020i	0.703587	+	0.710609i	$0.251580\pi$
$152$	−168.357	+	2056.10i	−0.0898392	+	1.09718i
$153$			2390.36i			1.26307i
$154$	−2020.93	+	909.409i	−1.05747	+	0.475859i
$155$			54.9815i			0.0284917i
$156$	−182.186	−	42.4653i	−0.0935033	−	0.0217945i
$157$	1152.45	−	665.369i	0.585833	−	0.338231i	−0.177615	−	0.984100i	$-0.556838\pi$
$157$	1152.45	−	665.369i	0.585833	−	0.338231i	0.763448	+	0.645869i	$0.223505\pi$
$158$	2221.37	−	1763.14i	1.11850	−	0.887770i
$159$	−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	$-0.257239\pi$
$163$	853.496	+	492.766i	0.410129	+	0.236788i	−0.280716	+	0.959791i	$0.590572\pi$
$164$	−601.270	+	642.066i	−0.286288	+	0.305713i
$165$	−702.092	−	1216.06i	−0.331259	−	0.573758i
$166$	−477.571	+	1208.65i	−0.223293	+	0.565117i
$167$	−1020.34			−0.472793			−0.236396	−	0.971657i	$-0.575966\pi$
$167$	−1020.34			−0.472793			−0.236396	+	0.971657i	$0.575966\pi$
$168$	−933.867	+	2728.66i	−0.428866	+	1.25310i
$169$	2185.46			0.994745
$170$	588.441	−	1489.24i	0.265479	−	0.671881i
$171$	−928.269	−	1607.81i	−0.415126	−	0.719019i
$172$	451.431	−	482.061i	0.200124	−	0.213702i
$173$	−1538.61	−	888.319i	−0.676177	−	0.390391i	0.122236	−	0.992501i	$-0.460993\pi$
$173$	−1538.61	−	888.319i	−0.676177	−	0.390391i	−0.798413	+	0.602110i	$0.794327\pi$
$174$	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
$178$	1972.98	−	1565.99i	0.830791	−	0.659414i
$179$	−3863.93	+	2230.84i	−1.61343	+	0.931513i	−0.624860	+	0.780736i	$0.714844\pi$
$179$	−3863.93	+	2230.84i	−1.61343	+	0.931513i	−0.988568	+	0.150777i	$0.951823\pi$
$180$	−765.154	−	178.348i	−0.316840	−	0.0738516i
$181$			2630.44i			1.08021i	0.841596	+	0.540107i	$0.181616\pi$
$181$			2630.44i			1.08021i	−0.841596	+	0.540107i	$0.818384\pi$
$182$	−17.9015	+	177.083i	−0.00729091	+	0.0721223i
$183$			3752.98i			1.51600i
$184$	−3848.36	−	315.111i	−1.54188	−	0.126252i
$185$	−494.673	+	285.600i	−0.196590	+	0.113501i
$186$	137.960	+	173.815i	0.0543855	+	0.0685199i
$187$	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	$-0.357750\pi$
$191$	−350.362	−	202.282i	−0.132729	−	0.0766313i	−0.564894	+	0.825163i	$0.691083\pi$
$192$	3476.69	+	573.199i	1.30682	+	0.215453i
$193$	−1508.72	−	2613.17i	−0.562693	−	0.974613i	−0.997260	−	0.0739738i	$-0.976432\pi$
$193$	−1508.72	−	2613.17i	−0.562693	−	0.974613i	0.434567	−	0.900640i	$-0.356901\pi$
$194$	744.144	+	294.032i	0.275394	+	0.108816i
$195$	−112.776			−0.0414156
$196$	2688.48	+	549.175i	0.979768	+	0.200137i
$197$	2643.88			0.956185			0.478093	−	0.878309i	$-0.341328\pi$
$197$	2643.88			0.956185			0.478093	+	0.878309i	$0.341328\pi$
$198$	−2266.14	−	895.415i	−0.813372	−	0.321386i
$199$	2077.01	+	3597.48i	0.739875	+	1.28150i	0.952551	+	0.304378i	$0.0984487\pi$
$199$	2077.01	+	3597.48i	0.739875	+	1.28150i	−0.212676	+	0.977123i	$0.568218\pi$
$200$	−1893.11	−	1309.92i	−0.669314	−	0.463127i
$201$	−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
$206$	−3119.60	−	3930.37i	−1.05511	−	1.32933i
$207$	3009.31	−	1737.43i	1.01044	−	0.583379i
$208$	216.989	−	14.2550i	0.0723339	−	0.00475194i
$209$			3857.10i			1.27656i
$210$	−174.872	+	1729.85i	−0.0574633	+	0.568432i
$211$			592.260i			0.193236i	0.995322	+	0.0966182i	$0.0308026\pi$
$211$			592.260i			0.193236i	−0.995322	+	0.0966182i	$0.969197\pi$
$212$	316.773	−	1359.03i	0.102623	−	0.440275i
$213$	2292.49	−	1323.57i	0.737458	−	0.425771i
$214$	−165.172	+	131.100i	−0.0527613	+	0.0418776i
$215$	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
$220$	1191.42	+	1115.72i	0.365117	+	0.341918i
$221$	−199.426	−	345.416i	−0.0607007	−	0.105137i
$222$	−847.198	+	2144.11i	−0.256127	+	0.648213i
$223$	3985.59			1.19684			0.598419	−	0.801183i	$-0.295796\pi$
$223$	3985.59			1.19684			0.598419	+	0.801183i	$0.295796\pi$
$224$	117.812	−	3350.45i	0.0351412	−	0.999382i
$225$	2071.75			0.613851
$226$	−1067.45	+	2701.53i	−0.314185	+	0.795147i
$227$	119.836	+	207.561i	0.0350386	+	0.0606887i	0.883013	−	0.469349i	$-0.155511\pi$
$227$	119.836	+	207.561i	0.0350386	+	0.0606887i	−0.847974	+	0.530037i	$0.822178\pi$
$228$	3663.89	+	3431.09i	1.06424	+	0.996621i
$229$	3722.53	+	2149.20i	1.07420	+	0.620190i	0.929326	−	0.369261i	$-0.120389\pi$
$229$	3722.53	+	2149.20i	1.07420	+	0.620190i	0.144874	+	0.989450i	$0.453722\pi$
$230$	−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	−0.939727	−	0.341927i	$-0.888921\pi$
$233$	−617.944	+	1070.31i	−0.173746	+	0.300937i	0.765981	+	0.642864i	$0.222254\pi$
$234$	−153.281	+	121.662i	−0.0428218	+	0.0339884i
$235$	−306.891	+	177.184i	−0.0851888	+	0.0491838i
$236$	605.199	−	2596.44i	0.166928	−	0.716161i
$237$		−	6900.61i		−	1.89132i
$238$	−5607.51	+	2523.36i	−1.52723	+	0.687247i
$239$		−	1777.38i		−	0.481042i	−0.970644	−	0.240521i	$-0.922682\pi$
$239$		−	1777.38i		−	0.481042i	0.970644	−	0.240521i	$-0.0773183\pi$
$240$	2119.67	−	139.251i	0.570100	−	0.0374524i
$241$	−4291.94	+	2477.95i	−1.14717	+	0.662320i	−0.948196	−	0.317685i	$-0.897095\pi$
$241$	−4291.94	+	2477.95i	−1.14717	+	0.662320i	−0.198975	+	0.980005i	$0.563761\pi$
$242$	806.736	+	1016.40i	0.214293	+	0.269987i
$243$	−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
$248$	−212.127	−	146.780i	−0.0543148	−	0.0375828i
$249$	1581.06	+	2738.47i	0.402392	+	0.696963i
$250$	−2876.56	−	1136.61i	−0.727720	−	0.287542i
$251$	−5191.12			−1.30542			−0.652710	−	0.757608i	$-0.726368\pi$
$251$	−5191.12			−1.30542			−0.652710	+	0.757608i	$0.726368\pi$
$252$	1628.47	+	2539.80i	0.407080	+	0.634891i
$253$	−7219.27			−1.79396
$254$	4328.89	+	1710.47i	1.06937	+	0.422536i
$255$	−1948.11	−	3374.22i	−0.478413	−	0.828636i
$256$	−4060.80	+	535.857i	−0.991406	+	0.130824i
$257$	−3574.00	−	2063.45i	−0.867471	−	0.500835i	−0.000963893	−	1.00000i	$-0.500307\pi$
$257$	−3574.00	−	2063.45i	−0.867471	−	0.500835i	−0.866507	+	0.499165i	$0.833640\pi$
$258$	−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
$262$	1341.73	+	1690.44i	0.316384	+	0.398610i
$263$	543.813	−	313.970i	0.127502	−	0.0736131i	−0.434893	−	0.900482i	$-0.643214\pi$
$263$	543.813	−	313.970i	0.127502	−	0.0736131i	0.562394	+	0.826869i	$0.309880\pi$
$264$	6566.06	+	537.641i	1.53073	+	0.125339i
$265$		−	841.258i		−	0.195012i
$266$	2791.82	−	3874.87i	0.643524	−	0.893172i
$267$		−	6128.99i		−	1.40483i
$268$	4645.02	+	1082.70i	1.05873	+	0.246778i
$269$	−2662.88	+	1537.42i	−0.603565	+	0.348468i	−0.770443	−	0.637509i	$-0.779965\pi$
$269$	−2662.88	+	1537.42i	−0.603565	+	0.348468i	0.166878	+	0.985978i	$0.446631\pi$
$270$	488.024	−	387.353i	0.110001	−	0.0873095i
$271$	−944.601	+	1636.10i	−0.211736	+	0.366737i	−0.952258	−	0.305295i	$-0.901245\pi$
$271$	−944.601	+	1636.10i	−0.211736	+	0.366737i	0.740522	+	0.672032i	$0.234578\pi$
$272$	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
$276$	−6421.92	+	6857.64i	−1.40056	+	1.49559i
$277$	4255.31	+	7370.41i	0.923020	+	1.59872i	0.794715	+	0.606983i	$0.207620\pi$
$277$	4255.31	+	7370.41i	0.923020	+	1.59872i	0.128305	+	0.991735i	$0.459046\pi$
$278$	1703.92	−	4312.32i	0.367605	−	0.930344i
$279$	232.144			0.0498140
$280$	−389.340	−	1983.23i	−0.0830983	−	0.423289i
$281$	6028.10			1.27974			0.639869	−	0.768484i	$-0.278989\pi$
$281$	6028.10			1.27974			0.639869	+	0.768484i	$0.278989\pi$
$282$	−525.594	+	1330.19i	−0.110988	+	0.280892i
$283$	−2229.39	−	3861.42i	−0.468281	−	0.811087i	0.531062	−	0.847333i	$-0.321793\pi$
$283$	−2229.39	−	3861.42i	−0.468281	−	0.811087i	−0.999343	+	0.0362463i	$0.988460\pi$
$284$	−2103.33	+	2246.04i	−0.439471	+	0.469290i
$285$	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
$290$	−1404.72	+	1114.95i	−0.284442	+	0.225767i
$291$	1686.03	−	973.430i	0.339646	−	0.196094i
$292$	−1687.34	−	393.300i	−0.338166	−	0.0788224i
$293$		−	3220.71i		−	0.642171i	−0.947050	−	0.321085i	$-0.895952\pi$
$293$		−	3220.71i		−	0.642171i	0.947050	−	0.321085i	$-0.104048\pi$
$294$	5113.46	−	4293.05i	1.01436	−	0.851618i
$295$		−	1607.24i		−	0.317210i
$296$	218.704	−	2670.97i	0.0429456	−	0.524483i
$297$	1673.47	−	966.176i	0.326951	−	0.188765i
$298$	−106.024	−	133.579i	−0.0206102	−	0.0259666i
$299$	−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
$304$	−5233.63	−	2579.96i	−0.987399	−	0.486747i
$305$	−1315.01	−	2277.67i	−0.246876	−	0.427603i
$306$	−6287.91	−	2484.53i	−1.17469	−	0.464154i
$307$	6242.78			1.16057			0.580284	−	0.814414i	$-0.302942\pi$
$307$	6242.78			1.16057			0.580284	+	0.814414i	$0.302942\pi$
$308$	−291.683	−	6261.34i	−0.0539616	−	1.15835i
$309$	−12209.6			−2.24782
$310$	−144.630	−	57.1474i	−0.0264982	−	0.0104702i
$311$	1146.70	+	1986.14i	0.209078	+	0.362134i	0.951424	−	0.307883i	$-0.0996204\pi$
$311$	1146.70	+	1986.14i	0.209078	+	0.362134i	−0.742346	+	0.670016i	$0.766287\pi$
$312$	301.068	−	435.106i	0.0546303	−	0.0789519i
$313$	4989.49	+	2880.68i	0.901030	+	0.520210i	0.877534	−	0.479514i	$-0.159187\pi$
$313$	4989.49	+	2880.68i	0.901030	+	0.520210i	0.0234959	+	0.999724i	$0.492520\pi$
$314$	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	−0.992367	−	0.123319i	$-0.960646\pi$
$317$	−2197.71	+	3806.54i	−0.389386	+	0.674437i	0.602981	+	0.797756i	$0.293980\pi$
$318$	−2110.89	−	2659.49i	−0.372241	−	0.468984i
$319$	−4816.89	+	2781.03i	−0.845436	+	0.488113i
$320$	−2310.83	+	870.331i	−0.403686	+	0.152041i
$321$			513.102i			0.0892166i
$322$	7252.53	+	5225.40i	1.25518	+	0.904348i
$323$			10702.4i			1.84364i
$324$	1569.31	−	6732.71i	0.269087	−	1.15444i
$325$	−299.375	+	172.844i	−0.0510964	+	0.0295005i
$326$	−2183.35	+	1732.97i	−0.370935	+	0.294417i
$327$	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	$-0.155743\pi$
$331$	5522.08	+	3188.18i	0.916983	+	0.529420i	0.0343114	+	0.999411i	$0.489076\pi$
$332$	−2683.00	−	2512.52i	−0.443520	−	0.415339i
$333$	1205.87	+	2088.62i	0.198441	+	0.343711i
$334$	1060.54	−	2684.03i	0.173742	−	0.439712i
$335$	2875.34			0.468945
$336$	−6207.17	−	5292.72i	−1.00782	−	0.859349i
$337$	−5111.05			−0.826163			−0.413081	−	0.910694i	$-0.635547\pi$
$337$	−5111.05			−0.826163			−0.413081	+	0.910694i	$0.635547\pi$
$338$	−2271.55	+	5748.89i	−0.365550	+	0.925144i
$339$	3533.93	+	6120.95i	0.566185	+	0.980661i
$340$	3305.87	+	3095.82i	0.527312	+	0.493807i
$341$	−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
$346$	3935.97	−	3124.05i	0.611558	−	0.485404i
$347$	4393.00	−	2536.30i	0.679621	−	0.392379i	−0.120091	−	0.992763i	$-0.538319\pi$
$347$	4393.00	−	2536.30i	0.679621	−	0.392379i	0.799712	+	0.600384i	$0.204985\pi$
$348$	−1643.15	+	7049.48i	−0.253109	+	1.08590i
$349$		−	11661.1i		−	1.78856i	−0.447512	−	0.894278i	$-0.647690\pi$
$349$		−	11661.1i		−	1.78856i	0.447512	−	0.894278i	$-0.352310\pi$
$350$	2187.01	+	4860.07i	0.334002	+	0.742234i
$351$		−	155.195i		−	0.0236003i
$352$	−7485.28	+	1618.14i	−1.13343	+	0.245020i
$353$	5552.29	−	3205.62i	0.837163	−	0.483337i	−0.0191356	−	0.999817i	$-0.506091\pi$
$353$	5552.29	−	3205.62i	0.837163	−	0.483337i	0.856299	+	0.516480i	$0.172758\pi$
$354$	−4032.88	−	5081.00i	−0.605495	−	0.762860i
$355$	−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	$-0.0830690\pi$
$359$	8337.73	+	4813.79i	1.22576	+	0.707694i	0.259621	+	0.965711i	$0.416402\pi$
$360$	1264.45	−	1827.38i	0.185117	−	0.267532i
$361$	−726.638	−	1258.57i	−0.105939	−	0.183492i
$362$	−6919.43	−	2734.06i	−1.00463	−	0.396958i
$363$	3157.42			0.456533
$364$	−447.214	−	231.149i	−0.0643967	−	0.0332843i
$365$	−1044.49			−0.149784
$366$	−9872.31	−	3900.82i	−1.40993	−	0.557102i
$367$	−1753.92	−	3037.88i	−0.249466	−	0.432087i	0.713912	−	0.700235i	$-0.246922\pi$
$367$	−1753.92	−	3037.88i	−0.249466	−	0.432087i	−0.963378	+	0.268148i	$0.913588\pi$
$368$	4828.87	−	9795.69i	0.684028	−	1.38760i
$369$	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	−0.434551	−	0.900647i	$-0.643093\pi$
$373$	4053.65	−	7021.12i	0.562707	−	0.974638i	0.997259	−	0.0739909i	$-0.0235736\pi$
$374$	8732.52	+	11002.1i	1.20735	+	1.52113i
$375$	−6517.52	+	3762.89i	−0.897502	+	0.518173i
$376$	135.682	−	1657.05i	0.0186097	−	0.227275i
$377$			446.712i			0.0610261i
$378$	−2380.51	−	240.648i	−0.323916	−	0.0327449i
$379$		−	6838.23i		−	0.926798i	−0.886150	−	0.463399i	$-0.846630\pi$
$379$		−	6838.23i		−	0.926798i	0.886150	−	0.463399i	$-0.153370\pi$
$380$	−3425.82	−	798.518i	−0.462476	−	0.107798i
$381$	9808.11	−	5662.71i	1.31886	−	0.761443i
$382$	896.270	−	711.386i	0.120045	−	0.0952818i
$383$	6010.60	−	10410.7i	0.801899	−	1.38893i	−0.116466	−	0.993195i	$-0.537157\pi$
$383$	6010.60	−	10410.7i	0.801899	−	1.38893i	0.918365	−	0.395735i	$-0.129510\pi$
$384$	−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
$388$	−1546.92	+	1651.88i	−0.202404	+	0.216137i
$389$	−1922.93	−	3330.62i	−0.250634	−	0.434111i	0.713067	−	0.701096i	$-0.247306\pi$
$389$	−1922.93	−	3330.62i	−0.250634	−	0.434111i	−0.963701	+	0.266986i	$0.913972\pi$
$390$	117.218	−	296.659i	0.0152194	−	0.0385177i
$391$	−20031.4			−2.59088
$392$	−4239.01	+	6501.31i	−0.546179	+	0.837668i
$393$	5251.31			0.674029
$394$	−2748.03	+	6954.79i	−0.351380	+	0.889282i
$395$	2417.91	+	4187.95i	0.307996	+	0.533464i
$396$	4710.83	−	5030.46i	0.597798	−	0.638358i
$397$	10023.9	+	5787.30i	1.26722	+	0.731628i	0.974460	−	0.224560i	$-0.0720943\pi$
$397$	10023.9	+	5787.30i	1.26722	+	0.731628i	0.292756	+	0.956187i	$0.405428\pi$
$398$	−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	0.0860245	+	0.996293i	$0.472584\pi$
$401$	−6583.03	+	11402.1i	−0.819803	+	1.41994i	−0.905827	+	0.423647i	$0.860750\pi$
$402$	9089.90	−	7214.81i	1.12777	−	0.895130i
$403$	−33.5456	+	19.3676i	−0.00414647	+	0.00239397i
$404$	6266.17	+	1460.57i	0.771667	+	0.179866i
$405$		−	4167.65i		−	0.511339i
$406$	6852.03	+	692.678i	0.837588	+	0.0846725i
$407$		−	5010.55i		−	0.610231i
$408$	18219.0	+	1491.80i	2.21072	+	0.181018i
$409$	−9916.78	+	5725.46i	−1.19891	+	0.692190i	−0.960312	−	0.278929i	$-0.910021\pi$
$409$	−9916.78	+	5725.46i	−1.19891	+	0.692190i	−0.238596	+	0.971119i	$0.576687\pi$
$410$	−932.479	−	1174.82i	−0.112322	−	0.141513i
$411$	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
$416$	−188.038	+	585.611i	−0.0221619	+	0.0690190i
$417$	−5641.03	−	9770.55i	−0.662452	−	1.14740i
$418$	−10146.2	−	4009.04i	−1.18724	−	0.469112i
$419$	4195.08			0.489124			0.244562	−	0.969634i	$-0.421356\pi$
$419$	4195.08			0.489124			0.244562	+	0.969634i	$0.421356\pi$
$420$	−4368.64	−	2257.99i	−0.507543	−	0.262331i
$421$	−3710.27			−0.429520			−0.214760	−	0.976667i	$-0.568897\pi$
$421$	−3710.27			−0.429520			−0.214760	+	0.976667i	$0.568897\pi$
$422$	−1557.96	−	615.591i	−0.179716	−	0.0710107i
$423$	748.108	+	1295.76i	0.0859912	+	0.148941i
$424$	3245.70	+	2245.84i	0.371757	+	0.257235i
$425$	−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
$430$	700.102	+	882.054i	0.0785161	+	0.0989219i
$431$	2084.43	−	1203.45i	0.232955	−	0.134497i	−0.378979	−	0.925405i	$-0.623725\pi$
$431$	2084.43	−	1203.45i	0.232955	−	0.134497i	0.611935	+	0.790908i	$0.290392\pi$
$432$	191.628	+	2916.96i	0.0213419	+	0.324866i
$433$			15138.8i			1.68019i	0.542436	+	0.840097i	$0.317502\pi$
$433$			15138.8i			1.68019i	−0.542436	+	0.840097i	$0.682498\pi$
$434$	245.060	+	544.582i	0.0271042	+	0.0602322i
$435$			4363.74i			0.480977i
$436$	−141.155	+	605.588i	−0.0155048	+	0.0665193i
$437$	13473.6	−	7778.97i	1.47489	−	0.851530i
$438$	−3301.98	+	2620.84i	−0.360217	+	0.285910i
$439$	−2889.10	+	5004.08i	−0.314099	+	0.544035i	−0.979246	−	0.202677i	$-0.935036\pi$
$439$	−2889.10	+	5004.08i	−0.314099	+	0.544035i	0.665147	+	0.746713i	$0.268369\pi$
$440$	−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	$-0.479175\pi$
$443$	−7143.22	−	4124.14i	−0.766106	−	0.442311i	−0.831484	+	0.555549i	$0.812508\pi$
$444$	−4759.57	−	4457.15i	−0.508737	−	0.476412i
$445$	2147.55	+	3719.66i	0.228772	+	0.396244i
$446$	−4142.60	+	10484.2i	−0.439815	+	1.11310i
$447$	−414.961			−0.0439082
$448$	8691.00	+	3792.35i	0.916543	+	0.399936i
$449$	6493.19			0.682478			0.341239	−	0.939977i	$-0.389153\pi$
$449$	6493.19			0.682478			0.341239	+	0.939977i	$0.389153\pi$
$450$	−2153.36	+	5449.78i	−0.225578	+	0.570900i
$451$	−2325.88	−	4028.55i	−0.242842	−	0.420614i
$452$	−5996.95	−	5615.91i	−0.624055	−	0.584403i
$453$	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	−0.428881	−	0.903361i	$-0.641092\pi$
$457$	5548.06	−	9609.52i	0.567893	−	0.983620i	0.996774	−	0.0802591i	$-0.0255748\pi$
$458$	−9522.71	+	7558.34i	−0.971544	+	0.771131i
$459$	4643.40	−	2680.87i	0.472190	−	0.272619i
$460$	1494.57	−	6412.05i	0.151489	−	0.649921i
$461$			4976.01i			0.502724i	0.967893	+	0.251362i	$0.0808784\pi$
$461$			4976.01i			0.502724i	−0.967893	+	0.251362i	$0.919122\pi$
$462$	−12374.2	−	8915.55i	−1.24611	−	0.897811i
$463$			16003.8i			1.60639i	0.595716	+	0.803195i	$0.296868\pi$
$463$			16003.8i			1.60639i	−0.595716	+	0.803195i	$0.703132\pi$
$464$	−551.581	−	8396.15i	−0.0551864	−	0.840046i
$465$	−327.693	+	189.194i	−0.0326804	+	0.0188681i
$466$	−2173.19	−	2737.99i	−0.216032	−	0.272178i
$467$	−8856.55	+	15340.0i	−0.877585	+	1.52002i	−0.0236011	+	0.999721i	$0.507513\pi$
$467$	−8856.55	+	15340.0i	−0.877585	+	1.52002i	−0.853984	+	0.520300i	$0.825820\pi$
$468$	−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
$472$	6200.96	+	4290.71i	0.604709	+	0.418424i
$473$	1746.26	+	3024.62i	0.169753	+	0.294021i
$474$	18152.2	+	7172.44i	1.75899	+	0.695024i
$475$	9275.82			0.896008
$476$	−809.338	−	17373.5i	−0.0779327	−	1.67292i
$477$	−3551.97			−0.340951
$478$	4675.44	+	1847.40i	0.447384	+	0.176774i
$479$	−5044.30	−	8736.99i	−0.481169	−	0.833410i	0.518597	−	0.855019i	$-0.326454\pi$
$479$	−5044.30	−	8736.99i	−0.481169	−	0.833410i	−0.999766	+	0.0216091i	$0.993121\pi$
$480$	−1836.87	+	5720.58i	−0.174669	+	0.543974i
$481$	−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
$486$	−8288.94	−	10443.2i	−0.773650	−	0.974717i
$487$	2053.73	−	1185.72i	0.191095	−	0.110329i	−0.401400	−	0.915903i	$-0.631476\pi$
$487$	2053.73	−	1185.72i	0.191095	−	0.110329i	0.592495	+	0.805574i	$0.298143\pi$
$488$	12298.2	+	1007.00i	1.14080	+	0.0934110i
$489$			6782.52i			0.627231i
$490$	−1599.09	+	4397.14i	−0.147428	+	0.405393i
$491$		−	11069.3i		−	1.01741i	−0.860940	−	0.508706i	$-0.830124\pi$
$491$		−	11069.3i		−	1.01741i	0.860940	−	0.508706i	$-0.169876\pi$
$492$	−5895.75	−	1374.23i	−0.540245	−	0.125925i
$493$	−13365.5	+	7716.59i	−1.22100	+	0.704944i
$494$	−686.286	+	544.717i	−0.0625050	+	0.0496113i
$495$	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	$-0.503609\pi$
$499$	−9842.36	−	5682.49i	−0.882975	−	0.509786i	−0.871638	+	0.490150i	$0.836942\pi$
$500$	5979.76	−	6385.49i	0.534846	−	0.571136i
$501$	−3511.04	−	6081.30i	−0.313097	−	0.542300i
$502$	5395.61	−	13655.4i	0.479717	−	1.21408i
$503$	11337.8			1.00503			0.502513	−	0.864570i	$-0.332409\pi$
$503$	11337.8			1.00503			0.502513	+	0.864570i	$0.332409\pi$
$504$	−8373.64	+	1643.88i	−0.740063	+	0.145286i
$505$	3878.86			0.341796
$506$	7503.66	−	18990.5i	0.659245	−	1.66844i
$507$	7520.24	+	13025.4i	0.658749	+	1.14099i
$508$	−8998.85	+	9609.42i	−0.785943	+	0.839270i
$509$	2352.86	+	1358.43i	0.204890	+	0.118293i	0.598934	−	0.800798i	$-0.295591\pi$
$509$	2352.86	+	1358.43i	0.204890	+	0.118293i	−0.394045	+	0.919091i	$0.628924\pi$
$510$	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
$514$	9142.75	−	7256.76i	0.784571	−	0.622728i
$515$	7409.93	−	4278.12i	0.634020	−	0.366052i
$516$	4426.50	+	1031.77i	0.377647	+	0.0880250i
$517$		−	3108.50i		−	0.264433i
$518$	−3626.70	+	5033.64i	−0.307622	+	0.426960i
$519$		−	12227.0i		−	1.03411i
$520$	−30.2598	+	369.555i	−0.00255189	+	0.0311655i
$521$	−6728.44	+	3884.67i	−0.565793	+	0.326661i	−0.755467	−	0.655186i	$-0.772590\pi$
$521$	−6728.44	+	3884.67i	−0.565793	+	0.326661i	0.189674	+	0.981847i	$0.439257\pi$
$522$	4707.58	+	5931.05i	0.394723	+	0.497309i
$523$	−8189.91	+	14185.3i	−0.684742	+	1.18601i	0.288776	+	0.957397i	$0.406752\pi$
$523$	−8189.91	+	14185.3i	−0.684742	+	1.18601i	−0.973518	+	0.228611i	$0.926582\pi$
$524$	−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
$528$	−8239.00	+	16713.4i	−0.679084	+	1.37757i
$529$	8476.27	+	14681.3i	0.696661	+	1.20665i
$530$	2212.95	+	874.398i	0.181367	+	0.0716630i
$531$	−6786.11			−0.554599
$532$	7291.15	+	11371.5i	0.594195	+	0.926721i
$533$	−373.602			−0.0303612
$534$	16122.5	+	6370.43i	1.30653	+	0.516247i
$535$	−179.786	−	311.399i	−0.0145287	−	0.0251644i
$536$	−7676.07	+	11093.5i	−0.618574	+	0.893967i
$537$	−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	−0.701729	−	0.712444i	$-0.747588\pi$
$541$	3348.80	−	5800.29i	0.266129	−	0.460950i	0.967859	+	0.251494i	$0.0809218\pi$
$542$	−3321.98	−	4185.35i	−0.263268	−	0.331690i
$543$	−15677.6	+	9051.45i	−1.23902	+	0.715350i
$544$	−20769.6	+	4489.88i	−1.63693	+	0.353864i
$545$			374.868i			0.0294635i
$546$	−1117.02	+	502.656i	−0.0875535	+	0.0393987i
$547$			2582.34i			0.201851i	0.994894	+	0.100926i	$0.0321804\pi$
$547$			2582.34i			0.201851i	−0.994894	+	0.100926i	$0.967820\pi$
$548$	−1312.85	+	5632.41i	−0.102339	+	0.439059i
$549$	−9616.81	+	5552.27i	−0.747605	+	0.431630i
$550$	9535.56	−	7568.54i	0.739268	−	0.586770i
$551$	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
$556$	9572.62	+	8964.39i	0.730161	+	0.683768i
$557$	−224.120	−	388.188i	−0.0170490	−	0.0295297i	0.857375	−	0.514692i	$-0.172094\pi$
$557$	−224.120	−	388.188i	−0.0170490	−	0.0295297i	−0.874424	+	0.485162i	$0.838760\pi$
$558$	−241.289	+	610.660i	−0.0183057	+	0.0463285i
$559$	280.499			0.0212233
$560$	5621.62	+	1037.19i	0.424209	+	0.0782664i
$561$	34177.5			2.57215
$562$	−6265.56	+	15857.1i	−0.470279	+	1.19020i
$563$	−12501.7	−	21653.5i	−0.935849	−	1.62094i	−0.773113	−	0.634268i	$-0.781302\pi$
$563$	−12501.7	−	21653.5i	−0.935849	−	1.62094i	−0.162736	−	0.986670i	$-0.552032\pi$
$564$	−2952.79	−	2765.18i	−0.220452	−	0.206445i
$565$	−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	−0.719146	−	0.694859i	$-0.755467\pi$
$569$	3287.22	−	5693.64i	0.242193	−	0.419490i	0.961339	+	0.275369i	$0.0888001\pi$
$570$	−6704.03	+	5321.11i	−0.492633	+	0.391012i
$571$	9610.58	−	5548.67i	0.704361	−	0.406663i	−0.104608	−	0.994513i	$-0.533359\pi$
$571$	9610.58	−	5548.67i	0.704361	−	0.406663i	0.808970	+	0.587850i	$0.200026\pi$
$572$	−261.045	+	1119.94i	−0.0190819	+	0.0818654i
$573$		−	2784.24i		−	0.202990i
$574$	−579.313	+	5730.61i	−0.0421256	+	0.416709i
$575$			17361.4i			1.25917i
$576$	3674.73	+	9756.84i	0.265822	+	0.705790i
$577$	−1236.76	+	714.046i	−0.0892325	+	0.0515184i	−0.543952	−	0.839116i	$-0.683073\pi$
$577$	−1236.76	+	714.046i	−0.0892325	+	0.0515184i	0.454720	+	0.890635i	$0.349739\pi$
$578$	15591.3	+	19643.3i	1.12199	+	1.41359i
$579$	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
$584$	2788.40	−	4029.81i	0.197577	−	0.285539i
$585$	−166.843	−	288.981i	−0.0117917	−	0.0204238i
$586$	8472.17	+	3347.59i	0.597239	+	0.235986i
$587$	−27212.3			−1.91341			−0.956704	−	0.291063i	$-0.905991\pi$
$587$	−27212.3			−1.91341			−0.956704	+	0.291063i	$0.905991\pi$
$588$	5978.07	+	17913.3i	0.419271	+	1.25634i
$589$	1039.38			0.0727111
$590$	4227.88	+	1670.55i	0.295015	+	0.116569i
$591$	9097.69	+	15757.7i	0.633213	+	1.09676i
$592$	6798.73	+	3351.49i	0.472003	+	0.232678i
$593$	−7855.97	−	4535.65i	−0.544024	−	0.314092i	0.202684	−	0.979244i	$-0.435033\pi$
$593$	−7855.97	−	4535.65i	−0.544024	−	0.314092i	−0.746708	+	0.665152i	$0.768367\pi$
$594$	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
$598$	−1019.54	−	1284.51i	−0.0697191	−	0.0878386i
$599$	6261.35	−	3614.99i	0.427098	−	0.246585i	−0.271011	−	0.962576i	$-0.587358\pi$
$599$	6261.35	−	3614.99i	0.427098	−	0.246585i	0.698110	+	0.715991i	$0.254025\pi$
$600$	1292.96	−	15790.5i	0.0879745	−	1.07441i
$601$			18772.6i			1.27413i	0.770810	+	0.637065i	$0.219852\pi$
$601$			18772.6i			1.27413i	−0.770810	+	0.637065i	$0.780148\pi$
$602$	434.946	−	4302.52i	0.0294470	−	0.291292i
$603$		−	12140.3i		−	0.819887i
$604$	−7344.55	−	1711.93i	−0.494778	−	0.115327i
$605$	−1916.22	+	1106.33i	−0.128770	+	0.0743451i
$606$	12262.3	−	9732.84i	0.821986	−	0.652425i
$607$	6114.97	−	10591.4i	0.408895	−	0.708226i	−0.585871	−	0.810404i	$-0.699248\pi$
$607$	6114.97	−	10591.4i	0.408895	−	0.708226i	0.994766	+	0.102178i	$0.0325810\pi$
$608$	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
$612$	13071.2	−	13958.1i	0.863354	−	0.921933i
$613$	−5994.59	−	10382.9i	−0.394974	−	0.684116i	0.598124	−	0.801404i	$-0.295913\pi$
$613$	−5994.59	−	10382.9i	−0.394974	−	0.684116i	−0.993098	+	0.117288i	$0.962580\pi$
$614$	−6488.70	+	16421.8i	−0.426487	+	1.07936i
$615$	−3649.56			−0.239292
$616$	16773.8	+	5740.71i	1.09713	+	0.375487i
$617$	−1209.26			−0.0789030			−0.0394515	−	0.999221i	$-0.512561\pi$
$617$	−1209.26			−0.0789030			−0.0394515	+	0.999221i	$0.512561\pi$
$618$	12690.5	−	32117.6i	0.826033	−	2.09055i
$619$	−9171.91	−	15886.2i	−0.595558	−	1.03154i	−0.993468	−	0.114112i	$-0.963598\pi$
$619$	−9171.91	−	15886.2i	−0.595558	−	1.03154i	0.397910	−	0.917424i	$-0.369736\pi$
$620$	300.655	−	321.055i	0.0194752	−	0.0207966i
$621$	−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
$626$	−12763.7	+	10130.8i	−0.814923	+	0.646819i
$627$	−22988.5	+	13272.4i	−1.46423	+	0.845375i
$628$	−10368.0	−	2416.65i	−0.658802	−	0.153559i
$629$		−	13902.9i		−	0.881310i
$630$	−4691.34	+	2111.08i	−0.296679	+	0.133504i
$631$		−	7055.98i		−	0.445157i	−0.974915	−	0.222579i	$-0.928553\pi$
$631$		−	7055.98i		−	0.445157i	0.974915	−	0.222579i	$-0.0714474\pi$
$632$	−22612.6	−	1851.56i	−1.42323	−	0.116537i
$633$	−3529.91	+	2037.99i	−0.221645	+	0.127967i
$634$	−7728.91	−	9737.61i	−0.484155	−	0.609984i
$635$	−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
$640$	112.436	−	6983.32i	0.00694443	−	0.431312i
$641$	−5116.60	−	8862.20i	−0.315278	−	0.546078i	0.664218	−	0.747539i	$-0.268765\pi$
$641$	−5116.60	−	8862.20i	−0.315278	−	0.546078i	−0.979497	+	0.201461i	$0.935431\pi$
$642$	−1349.73	−	533.314i	−0.0829743	−	0.0327854i
$643$	20543.5			1.25996			0.629982	−	0.776610i	$-0.283062\pi$
$643$	20543.5			1.25996			0.629982	+	0.776610i	$0.283062\pi$
$644$	−21283.8	+	13646.7i	−1.30233	+	0.835026i
$645$	2740.07			0.167272
$646$	−28152.9	−	11124.0i	−1.71464	−	0.677503i
$647$	12712.8	+	22019.1i	0.772473	+	1.33796i	0.936204	+	0.351457i	$0.114314\pi$
$647$	12712.8	+	22019.1i	0.772473	+	1.33796i	−0.163731	+	0.986505i	$0.552353\pi$
$648$	16079.4	+	11126.0i	0.974783	+	0.674495i
$649$	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	−0.451515	−	0.892263i	$-0.649116\pi$
$653$	9127.03	−	15808.5i	0.546965	−	0.947371i	0.998480	−	0.0551081i	$-0.0175503\pi$
$654$	940.621	+	1185.08i	0.0562403	+	0.0708568i
$655$	−3186.99	+	1840.01i	−0.190116	+	0.109764i
$656$	7022.02	−	461.308i	0.417932	−	0.0274559i
$657$			4410.08i			0.261877i
$658$	−2249.97	+	3122.83i	−0.133303	+	0.185016i
$659$			16252.1i			0.960683i	0.877081	+	0.480342i	$0.159487\pi$
$659$			16252.1i			0.960683i	−0.877081	+	0.480342i	$0.840513\pi$
$660$	−2550.03	+	10940.2i	−0.150394	+	0.645223i
$661$	6622.84	−	3823.70i	0.389711	−	0.224999i	−0.292324	−	0.956319i	$-0.594429\pi$
$661$	6622.84	−	3823.70i	0.389711	−	0.224999i	0.682035	+	0.731320i	$0.261095\pi$
$662$	−14126.2	+	11212.2i	−0.829351	+	0.658270i
$663$	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
$668$	5958.10	+	5579.53i	0.345099	+	0.323171i
$669$	13714.6	+	23754.4i	0.792581	+	1.37279i
$670$	−2988.61	+	7563.66i	−0.172328	+	0.436134i
$671$	23070.5			1.32731
$672$	20374.3	−	10826.9i	1.16958	−	0.621512i
$673$	−4057.51			−0.232400			−0.116200	−	0.993226i	$-0.537071\pi$
$673$	−4057.51			−0.232400			−0.116200	+	0.993226i	$0.537071\pi$
$674$	5312.39	−	13444.8i	0.303599	−	0.768357i
$675$	−2323.53	−	4024.47i	−0.132493	−	0.229484i
$676$	−12761.6	−	11950.7i	−0.726080	−	0.679946i
$677$	3916.39	+	2261.13i	0.222333	+	0.128364i	0.607030	−	0.794679i	$-0.292361\pi$
$677$	3916.39	+	2261.13i	0.222333	+	0.128364i	−0.384697	+	0.923043i	$0.625694\pi$
$678$	−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
$682$	1068.48	−	848.073i	0.0599916	−	0.0476164i
$683$	−12667.7	+	7313.73i	−0.709690	+	0.409739i	−0.810946	−	0.585121i	$-0.801047\pi$
$683$	−12667.7	+	7313.73i	−0.709690	+	0.409739i	0.101257	+	0.994860i	$0.467714\pi$
$684$	−3371.52	+	14464.6i	−0.188470	+	0.808577i
$685$			3486.55i			0.194473i
$686$	16176.0	−	7820.91i	0.900294	−	0.435282i
$687$			29582.0i			1.64283i
$688$	−5272.10	+	346.348i	−0.292147	+	0.0191924i
$689$	513.273	−	296.339i	0.0283805	−	0.0163855i
$690$	−9959.43	−	12547.8i	−0.549491	−	0.692301i
$691$	6100.92	−	10567.1i	0.335875	−	0.581753i	−0.647777	−	0.761830i	$-0.724301\pi$
$691$	6100.92	−	10567.1i	0.335875	−	0.581753i	0.983653	+	0.180077i	$0.0576346\pi$
$692$	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
$696$	−16835.9	−	11649.5i	−0.916904	−	0.634445i
$697$	−6453.67	−	11178.1i	−0.350718	−	0.607461i
$698$	30674.9	+	12120.5i	1.66341	+	0.657260i
$699$	−8505.48			−0.460239
$700$	−15057.7	+	701.459i	−0.813040	+	0.0378752i
$701$	−31433.5			−1.69362			−0.846808	−	0.531898i	$-0.821479\pi$
$701$	−31433.5			−1.69362			−0.846808	+	0.531898i	$0.821479\pi$
$702$	408.244	+	161.309i	0.0219490	+	0.00867265i
$703$	5399.02	+	9351.37i	0.289655	+	0.501698i
$704$	3523.60	−	21372.1i	0.188637	−	1.14416i
$705$	−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	−0.336680	−	0.941619i	$-0.609304\pi$
$709$	12216.8	−	21160.2i	0.647126	−	1.12086i	0.983806	−	0.179237i	$-0.0573628\pi$
$710$	−3261.95	−	4109.72i	−0.172421	−	0.217232i
$711$	17682.4	−	10209.0i	0.932690	−	0.538489i
$712$	−20084.1	−	1644.52i	−1.05714	−	0.0865606i
$713$			1945.39i			0.102181i
$714$	−34335.0	−	24738.1i	−1.79966	−	1.29664i
$715$			693.260i			0.0362608i
$716$	34761.6	+	8102.52i	1.81439	+	0.422913i
$717$	10593.3	−	6116.04i	0.551762	−	0.318560i
$718$	−21329.0	+	16929.2i	−1.10862	+	0.879932i
$719$	−14584.0	+	25260.1i	−0.756453	+	1.31021i	0.188196	+	0.982132i	$0.439736\pi$
$719$	−14584.0	+	25260.1i	−0.756453	+	1.31021i	−0.944649	+	0.328083i	$0.893597\pi$
$720$	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
$724$	14384.0	−	15360.0i	0.738367	−	0.788466i
$725$	6688.02	+	11584.0i	0.342603	+	0.593405i
$726$	−3281.80	+	8305.67i	−0.167767	+	0.424590i
$727$	−14802.2			−0.755135			−0.377567	−	0.925982i	$-0.623239\pi$
$727$	−14802.2			−0.755135			−0.377567	+	0.925982i	$0.623239\pi$
$728$	1072.87	−	936.153i	0.0546200	−	0.0476595i
$729$	−9109.44			−0.462807
$730$	1085.64	−	2747.56i	0.0550428	−	0.139304i
$731$	4845.39	+	8392.47i	0.245162	+	0.424633i
$732$	20522.4	−	21914.9i	1.03624	−	1.10655i
$733$	24302.0	+	14030.8i	1.22458	+	0.707010i	0.965890	−	0.258951i	$-0.0833769\pi$
$733$	24302.0	+	14030.8i	1.22458	+	0.707010i	0.258687	+	0.965961i	$0.416710\pi$
$734$	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
$738$	−4960.37	+	3937.13i	−0.247417	+	0.196379i
$739$	19623.3	−	11329.5i	0.976798	−	0.563955i	0.0754963	−	0.997146i	$-0.475946\pi$
$739$	19623.3	−	11329.5i	0.976798	−	0.563955i	0.901302	+	0.433191i	$0.142613\pi$
$740$	4450.30	+	1037.31i	0.221076	+	0.0515302i
$741$			2131.93i			0.105693i
$742$	−3749.59	−	8332.52i	−0.185515	−	0.412259i
$743$		−	36038.3i		−	1.77943i	−0.456514	−	0.889716i	$-0.650902\pi$
$743$		−	36038.3i		−	1.77943i	0.456514	−	0.889716i	$-0.349098\pi$
$744$	144.879	−	1769.36i	0.00713913	−	0.0871883i
$745$	251.838	−	145.398i	0.0123847	−	0.00715032i
$746$	14255.9	+	17960.9i	0.699659	+	0.881496i
$747$	−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	$-0.424132\pi$
$751$	−10031.0	−	5791.41i	−0.487399	−	0.281400i	−0.723495	+	0.690330i	$0.757465\pi$
$752$	4217.87	+	2079.24i	0.204535	+	0.100827i
$753$	−17862.9	−	30939.4i	−0.864487	−	1.49733i
$754$	−1175.09	−	464.309i	−0.0567561	−	0.0224259i
$755$	−4546.39			−0.219153
$756$	3107.31	−	6011.86i	0.149487	−	0.289218i
$757$	24698.1			1.18582			0.592910	−	0.805268i	$-0.297979\pi$
$757$	24698.1			1.18582			0.592910	+	0.805268i	$0.297979\pi$
$758$	17988.1	+	7107.61i	0.861951	+	0.340581i
$759$	−24841.8	−	43027.3i	−1.18801	−	2.05770i
$760$	5661.30	−	8181.74i	0.270206	−	0.390504i
$761$	21831.6	+	12604.5i	1.03994	+	0.600410i	0.919816	−	0.392349i	$-0.128338\pi$
$761$	21831.6	+	12604.5i	1.03994	+	0.600410i	0.120124	+	0.992759i	$0.461671\pi$
$762$	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
$766$	21138.1	+	26631.8i	0.997065	+	1.25620i
$767$	980.617	−	566.160i	0.0461643	−	0.0266530i
$768$	−17167.1	−	22358.7i	−0.806595	−	1.05052i
$769$			16983.7i			0.796423i	0.917294	+	0.398212i	$0.130369\pi$
$769$			16983.7i			0.796423i	−0.917294	+	0.398212i	$0.869631\pi$
$770$	10633.8	+	1074.98i	0.497682	+	0.0503112i
$771$		−	28401.7i		−	1.32667i
$772$	−5479.73	+	23509.3i	−0.255466	+	1.09601i
$773$	26702.2	−	15416.5i	1.24245	−	0.717326i	0.272854	−	0.962056i	$-0.412033\pi$
$773$	26702.2	−	15416.5i	1.24245	−	0.717326i	0.969591	+	0.244730i	$0.0786992\pi$
$774$	3724.22	−	2955.98i	0.172952	−	0.137275i
$775$	−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
$780$	658.534	+	616.691i	0.0302299	+	0.0283091i
$781$	−8136.30	−	14092.5i	−0.372778	−	0.645670i
$782$	20820.5	−	52693.2i	0.952099	−	2.40960i
$783$	−6005.10			−0.274080
$784$	−12695.9	−	17908.2i	−0.578347	−	0.815791i
$785$	−6417.94			−0.291804
$786$	−5458.17	+	13813.7i	−0.247693	+	0.626868i
$787$	7483.59	+	12962.0i	0.338960	+	0.587095i	0.984237	−	0.176853i	$-0.0565917\pi$
$787$	7483.59	+	12962.0i	0.338960	+	0.587095i	−0.645278	+	0.763948i	$0.723258\pi$
$788$	−15438.5	−	14457.5i	−0.697934	−	0.653588i
$789$	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
$794$	−25642.4	+	20352.8i	−1.14611	+	0.909691i
$795$	5013.95	−	2894.80i	0.223681	−	0.129142i
$796$	7543.79	−	32364.6i	0.335908	−	1.44112i
$797$		−	39166.5i		−	1.74071i	−0.492421	−	0.870357i	$-0.663888\pi$
$797$		−	39166.5i		−	1.74071i	0.492421	−	0.870357i	$-0.336112\pi$
$798$	32701.2	+	3305.80i	1.45064	+	0.146647i
$799$		−	8625.23i		−	0.381901i
$800$	3891.41	+	18001.1i	0.171978	+	0.795545i
$801$	15705.2	−	9067.41i	0.692779	−	0.399976i
$802$	−23151.3	−	29168.1i	−1.01933	−	1.28424i
$803$	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
$808$	−10355.1	+	14965.2i	−0.450854	+	0.651577i
$809$	13908.0	+	24089.3i	0.604422	+	1.04689i	0.992143	+	0.125113i	$0.0399293\pi$
$809$	13908.0	+	24089.3i	0.604422	+	1.04689i	−0.387720	+	0.921777i	$0.626737\pi$
$810$	10963.1	+	4331.83i	0.475561	+	0.187907i
$811$	−20600.5			−0.891962			−0.445981	−	0.895042i	$-0.647145\pi$
$811$	−20600.5			−0.891962			−0.445981	+	0.895042i	$0.647145\pi$
$812$	−8944.06	+	17304.5i	−0.386546	+	0.747867i
$813$	−13001.7			−0.560871
$814$	13180.4	+	5207.93i	0.567533	+	0.224248i
$815$	−2376.53	−	4116.28i	−0.102143	−	0.176916i
$816$	−22860.9	+	46374.9i	−0.980750	+	1.98952i
$817$	−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	−0.985839	−	0.167696i	$-0.946367\pi$
$821$	−8179.13	+	14166.7i	−0.347690	+	0.602217i	0.638149	+	0.769913i	$0.279701\pi$
$822$	8748.45	+	11022.1i	0.371213	+	0.467689i
$823$	8972.43	−	5180.24i	0.380024	−	0.219407i	−0.297805	−	0.954627i	$-0.596255\pi$
$823$	8972.43	−	5180.24i	0.380024	−	0.219407i	0.677828	+	0.735220i	$0.262921\pi$
$824$	−3276.06	+	40009.6i	−0.138503	+	1.69150i
$825$		−	29621.9i		−	1.25006i
$826$	−7163.66	−	15919.4i	−0.301762	−	0.670590i
$827$			9204.30i			0.387019i	0.981098	+	0.193510i	$0.0619871\pi$
$827$			9204.30i			0.387019i	−0.981098	+	0.193510i	$0.938013\pi$
$828$	−27073.1	−	6310.41i	−1.13630	−	0.264858i
$829$	−26296.5	+	15182.3i	−1.10171	+	0.636071i	−0.936669	−	0.350216i	$-0.886108\pi$
$829$	−26296.5	+	15182.3i	−1.10171	+	0.636071i	−0.165039	+	0.986287i	$0.552775\pi$
$830$	4909.24	−	3896.55i	0.205304	−	0.162953i
$831$	−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
$836$	21091.8	−	22522.9i	0.872577	−	0.931781i
$837$	−260.357	−	450.951i	−0.0107518	−	0.0186226i
$838$	−4360.34	+	11035.3i	−0.179744	+	0.454901i
$839$	7688.40			0.316369			0.158184	−	0.987410i	$-0.449436\pi$
$839$	7688.40			0.316369			0.158184	+	0.987410i	$0.449436\pi$
$840$	10480.4	−	9144.88i	0.430488	−	0.375629i
$841$	−7103.96			−0.291277
$842$	3856.43	−	9759.97i	0.157840	−	0.399466i
$843$	20742.9	+	35927.8i	0.847479	+	1.46788i
$844$	3238.66	−	3458.40i	0.132084	−	0.141046i
$845$	−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
$850$	26458.5	−	21000.6i	1.06767	−	0.847428i
$851$	−17502.8	+	10105.2i	−0.705039	+	0.407055i
$852$	−20624.2	−	4807.26i	−0.829313	−	0.193303i
$853$			16264.6i			0.652860i	0.945221	+	0.326430i	$0.105846\pi$
$853$			16264.6i			0.652860i	−0.945221	+	0.326430i	$0.894154\pi$
$854$	−23176.8	−	16698.7i	−0.928682	−	0.669109i
$855$			8953.79i			0.358144i
$856$	1681.39	+	137.675i	0.0671362	+	0.00549723i
$857$	9676.46	−	5586.71i	0.385696	−	0.222682i	−0.294598	−	0.955621i	$-0.595186\pi$
$857$	9676.46	−	5586.71i	0.385696	−	0.222682i	0.680294	+	0.732940i	$0.261852\pi$
$858$	1739.53	+	2191.62i	0.0692151	+	0.0872037i
$859$	10035.8	−	17382.6i	0.398624	−	0.690437i	−0.594932	−	0.803776i	$-0.702821\pi$
$859$	10035.8	−	17382.6i	0.398624	−	0.690437i	0.993556	+	0.113339i	$0.0361545\pi$
$860$	−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	$-0.457083\pi$
$863$	−16644.7	−	9609.81i	−0.656537	−	0.379052i	−0.790956	+	0.611873i	$0.790416\pi$
$864$	−7872.31	−	2527.78i	−0.309978	−	0.0995335i
$865$	4284.22	+	7420.49i	0.168402	+	0.291681i
$866$	−39823.0	−	15735.2i	−1.56263	−	0.617439i
$867$	61021.5			2.39031
$868$	−1687.25	+	78.6001i	−0.0659782	+	0.00307357i
$869$	−42419.8			−1.65592
$870$	−11478.9	−	4535.64i	−0.447324	−	0.176750i
$871$	1012.86	+	1754.32i	0.0394023	+	0.0682467i
$872$	−1446.30	−	1000.76i	−0.0561673	−	0.0388646i
$873$	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	0.403670	+	0.914905i	$0.367734\pi$
$877$	−15336.1	+	26563.0i	−0.590496	+	1.02277i	−0.994166	+	0.107864i	$0.965599\pi$
$878$	−10160.4	−	12801.1i	−0.390544	−	0.492044i
$879$	19195.6	−	11082.6i	0.736579	−	0.425264i
$880$	−856.008	−	13030.1i	−0.0327909	−	0.499143i
$881$		−	37453.2i		−	1.43227i	−0.697962	−	0.716135i	$-0.745909\pi$
$881$		−	37453.2i		−	1.43227i	0.697962	−	0.716135i	$-0.254091\pi$
$882$	18565.7	+	6751.71i	0.708775	+	0.257757i
$883$			28915.6i			1.10202i	0.834497	+	0.551012i	$0.185758\pi$
$883$			28915.6i			1.10202i	−0.834497	+	0.551012i	$0.814242\pi$
$884$	−724.326	+	3107.52i	−0.0275585	+	0.118232i
$885$	9579.23	−	5530.57i	0.363844	−	0.210066i
$886$	18273.3	−	14503.8i	0.692892	−	0.549961i
$887$	18831.9	−	32617.7i	0.712866	−	1.23472i	−0.250911	−	0.968010i	$-0.580730\pi$
$887$	18831.9	−	32617.7i	0.712866	−	1.23472i	0.963777	−	0.266710i	$-0.0859365\pi$
$888$	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
$892$	−23273.2	−	21794.4i	−0.873591	−	0.818084i
$893$	3349.50	+	5801.51i	0.125517	+	0.217402i
$894$	431.307	−	1091.56i	0.0161354	−	0.0408360i
$895$	21518.0			0.803650
$896$	−19009.2	+	18920.2i	−0.708765	+	0.705444i
$897$	−3990.29			−0.148531
$898$	−6748.98	+	17080.5i	−0.250798	+	0.634726i
$899$	749.408	+	1298.01i	0.0278022	+	0.0481548i
$900$	−12097.6	−	11328.9i	−0.448059	−	0.419590i
$901$	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
$906$	−14372.6	+	11407.8i	−0.527041	+	0.418322i
$907$	−18222.8	+	10520.9i	−0.667119	+	0.385161i	−0.794984	−	0.606630i	$-0.792521\pi$
$907$	−18222.8	+	10520.9i	−0.667119	+	0.385161i	0.127865	+	0.991792i	$0.459187\pi$
$908$	435.249	−	1867.31i	0.0159077	−	0.0682478i
$909$		−	16377.4i		−	0.597584i
$910$	501.790	−	696.455i	0.0182793	−	0.0253706i
$911$		−	9510.87i		−	0.345894i	−0.984931	−	0.172947i	$-0.944671\pi$
$911$		−	9510.87i		−	0.345894i	0.984931	−	0.172947i	$-0.0553289\pi$
$912$	−2632.41	−	40070.5i	−0.0955788	−	1.45490i
$913$	16834.1	−	9719.16i	0.610215	−	0.352308i
$914$	19511.5	+	24582.4i	0.706107	+	0.889620i
$915$	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	$-0.378999\pi$
$919$	−6898.95	−	3983.11i	−0.247634	−	0.142971i	−0.618680	+	0.785643i	$0.712332\pi$
$920$	15313.6	+	10596.2i	0.548777	+	0.379723i
$921$	21481.7	+	37207.4i	0.768562	+	1.33119i
$922$	−13089.5	−	5172.03i	−0.467549	−	0.184741i
$923$	−1306.92			−0.0466064
$924$	36314.3	−	23284.0i	1.29291	−	0.828990i
$925$	−12049.7			−0.428316
$926$	−42098.3	−	16634.2i	−1.49399	−	0.590318i
$927$	−18063.2	−	31286.3i	−0.639992	−	1.10850i
$928$	22659.6	+	7275.95i	0.801549	+	0.257376i
$929$	1439.51	+	831.103i	0.0508384	+	0.0293516i	0.525204	−	0.850976i	$-0.323989\pi$
$929$	1439.51	+	831.103i	0.0508384	+	0.0293516i	−0.474365	+	0.880328i	$0.657322\pi$
$930$	−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
$934$	−31146.8	−	39241.6i	−1.09117	−	1.37476i
$935$	−20742.2	+	11975.5i	−0.725500	+	0.418867i
$936$	1560.34	+	127.764i	0.0544887	+	0.00446163i
$937$		−	11523.9i		−	0.401783i	−0.979614	−	0.200891i	$-0.935616\pi$
$937$		−	11523.9i		−	0.401783i	0.979614	−	0.200891i	$-0.0643838\pi$
$938$	28479.8	−	12815.8i	0.991362	−	0.446108i
$939$			39650.2i			1.37799i
$940$	2760.93	+	643.540i	0.0957996	+	0.0223297i
$941$	−13692.6	+	7905.45i	−0.474354	+	0.273868i	−0.718061	−	0.695981i	$-0.754970\pi$
$941$	−13692.6	+	7905.45i	−0.474354	+	0.273868i	0.243707	+	0.969849i	$0.421637\pi$
$942$	−20289.2	+	16103.9i	−0.701761	+	0.557000i
$943$	−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	$-0.200349\pi$
$947$	20479.9	+	11824.1i	0.702752	+	0.405734i	−0.105619	+	0.994407i	$0.533683\pi$
$948$	−37734.6	+	40294.9i	−1.29279	+	1.38050i
$949$	−367.929	−	637.272i	−0.0125853	−	0.0217984i
$950$	−9641.23	+	24400.3i	−0.329266	+	0.833316i
$951$	−30249.6			−1.03145
$952$	46542.5	+	15928.9i	1.58451	+	0.542288i
$953$	23736.6			0.806825			0.403413	−	0.915018i	$-0.367824\pi$
$953$	23736.6			0.806825			0.403413	+	0.915018i	$0.367824\pi$
$954$	3691.90	−	9343.56i	0.125293	−	0.317095i
$955$	975.572	+	1689.74i	0.0330563	+	0.0572552i
$956$	−9719.24	+	10378.7i	−0.328810	+	0.351120i
$957$	−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
$962$	891.517	−	707.613i	0.0298791	−	0.0237156i
$963$	−1314.79	+	759.097i	−0.0439965	+	0.0254014i
$964$	38612.2	+	9000.05i	1.29006	+	0.300697i
$965$			14552.6i			0.485456i
$966$	−6187.41	+	61206.4i	−0.206083	+	2.03859i
$967$		−	37667.0i		−	1.25263i	−0.779571	−	0.626314i	$-0.784563\pi$
$967$		−	37667.0i		−	1.25263i	0.779571	−	0.626314i	$-0.215437\pi$
$968$	847.195	−	10346.6i	0.0281301	−	0.343545i
$969$	−63786.8	+	36827.3i	−2.11468	+	1.22091i
$970$	−2399.04	−	3022.53i	−0.0794107	−	0.100049i
$971$	14502.0	−	25118.3i	0.479292	−	0.830159i	−0.520426	−	0.853907i	$-0.674227\pi$
$971$	14502.0	−	25118.3i	0.479292	−	0.830159i	0.999718	+	0.0237484i	$0.00756006\pi$
$972$	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
$976$	−15431.6	+	31304.0i	−0.506098	+	1.02666i
$977$	−11699.4	−	20263.9i	−0.383108	−	0.663563i	0.608397	−	0.793633i	$-0.291813\pi$
$977$	−11699.4	−	20263.9i	−0.383108	−	0.663563i	−0.991505	+	0.130070i	$0.958480\pi$
$978$	−17841.6	−	7049.70i	−0.583345	−	0.230496i
$979$	−37676.5			−1.22997
$980$	−9904.71	−	8776.81i	−0.322851	−	0.286087i
$981$	1582.78			0.0515129
$982$	29118.0	+	11505.3i	0.946224	+	0.373879i
$983$	5578.49	+	9662.22i	0.181003	+	0.313507i	0.942222	−	0.334988i	$-0.108732\pi$
$983$	5578.49	+	9662.22i	0.181003	+	0.313507i	−0.761219	+	0.648495i	$0.775399\pi$
$984$	9742.94	−	14080.5i	0.315644	−	0.456170i
$985$	−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
$990$	7305.78	+	9204.51i	0.234538	+	0.295493i
$991$	−49165.5	+	28385.7i	−1.57598	+	0.909892i	−0.580566	+	0.814213i	$0.697169\pi$
$991$	−49165.5	+	28385.7i	−1.57598	+	0.909892i	−0.995412	+	0.0956788i	$0.969498\pi$
$992$	436.042	+	2017.07i	0.0139560	+	0.0645585i
$993$			43882.6i			1.40239i
$994$	−2026.53	+	20046.6i	−0.0646655	+	0.639677i
$995$		−	20034.2i		−	0.638317i
$996$	5742.48	−	24636.5i	0.182688	−	0.783774i
$997$	8650.18	−	4994.18i	0.274778	−	0.158643i	−0.356279	−	0.934380i	$-0.615955\pi$
$997$	8650.18	−	4994.18i	0.274778	−	0.158643i	0.631057	+	0.775736i	$0.282621\pi$
$998$	25178.0	−	19984.2i	0.798594	−	0.633858i
$999$	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.19.5	yes	20
4.3	odd	2	inner	28.4.f.a.19.3	yes	20
7.2	even	3		196.4.d.b.195.17		20
7.3	odd	6	inner	28.4.f.a.3.3	✓	20
7.4	even	3		196.4.f.d.31.3		20
7.5	odd	6		196.4.d.b.195.18		20
7.6	odd	2		196.4.f.d.19.5		20
8.3	odd	2		448.4.p.h.383.9		20
8.5	even	2		448.4.p.h.383.2		20
28.3	even	6	inner	28.4.f.a.3.5	yes	20
28.11	odd	6		196.4.f.d.31.5		20
28.19	even	6		196.4.d.b.195.19		20
28.23	odd	6		196.4.d.b.195.20		20
28.27	even	2		196.4.f.d.19.3		20
56.3	even	6		448.4.p.h.255.2		20
56.45	odd	6		448.4.p.h.255.9		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.4.f.a.3.3	✓	20	7.3	odd	6	inner
28.4.f.a.3.5	yes	20	28.3	even	6	inner
28.4.f.a.19.3	yes	20	4.3	odd	2	inner
28.4.f.a.19.5	yes	20	1.1	even	1	trivial
196.4.d.b.195.17		20	7.2	even	3
196.4.d.b.195.18		20	7.5	odd	6
196.4.d.b.195.19		20	28.19	even	6
196.4.d.b.195.20		20	28.23	odd	6
196.4.f.d.19.3		20	28.27	even	2
196.4.f.d.19.5		20	7.6	odd	2
196.4.f.d.31.3		20	7.4	even	3
196.4.f.d.31.5		20	28.11	odd	6
448.4.p.h.255.2		20	56.3	even	6
448.4.p.h.255.9		20	56.45	odd	6
448.4.p.h.383.2		20	8.5	even	2
448.4.p.h.383.9		20	8.3	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-1.03939 + 2.63053i) q^{2} +(3.44104 + 5.96006i) q^{3} +(-5.83932 - 5.46830i) q^{4} +(-4.17670 - 2.41142i) q^{5} +(-19.2547 + 2.85690i) q^{6} +(5.03893 + 17.8216i) q^{7} +(20.4539 - 9.67677i) q^{8} +(-10.1816 + 17.6350i) q^{9} +O(q^{10})\)	\(q+(-1.03939 + 2.63053i) q^{2} +(3.44104 + 5.96006i) q^{3} +(-5.83932 - 5.46830i) 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} +(10.6845 - 8.48051i) q^{10} +(36.6380 - 21.1529i) q^{11} +(12.4980 - 53.6194i) q^{12} -3.39776i q^{13} +(-52.1176 - 5.26861i) q^{14} -33.1912i q^{15} +(4.19540 + 63.8623i) q^{16} +(101.660 - 58.6935i) q^{17} +(-35.8066 - 45.1125i) 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} +(128.057 + 88.6080i) q^{24} +(-50.8701 - 88.1096i) q^{25} +(8.93788 + 3.53160i) q^{26} +45.6757 q^{27} +(68.0299 - 131.620i) q^{28} -131.473 q^{29} +(87.3103 + 34.4987i) q^{30} +(-5.70011 - 9.87288i) q^{31} +(-172.352 - 55.3420i) 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} +(-160.317 - 201.982i) q^{38} +(20.2508 - 11.6918i) q^{39} +(-108.764 - 8.90583i) q^{40} -109.956i q^{41} +(-147.938 - 328.753i) q^{42} +82.5542i q^{43} +(-329.612 - 76.8285i) q^{44} +(85.0507 - 49.1040i) q^{45} +(378.046 - 300.062i) 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} +(-18.5799 + 19.8406i) q^{52} +(87.2160 + 151.062i) q^{53} +(-47.4750 + 120.151i) q^{54} -204.035 q^{55} +(275.521 + 315.760i) q^{56} -627.451 q^{57} +(136.652 - 345.842i) q^{58} +(166.628 + 288.607i) q^{59} +(-181.500 + 193.814i) 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} +(-645.021 + 511.964i) q^{66} +(-516.318 + 298.096i) q^{67} +(-914.580 - 213.178i) q^{68} -1174.39i q^{69} +(204.975 + 147.683i) q^{70} -384.641i q^{71} +(-37.6024 + 459.227i) q^{72} +(187.557 - 108.286i) q^{73} +(208.259 + 262.384i) 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} +(136.476 - 276.851i) q^{80} +(432.074 + 748.374i) q^{81} +(289.241 + 114.287i) q^{82} +459.471 q^{83} +(1018.56 - 47.4493i) q^{84} -566.139 q^{85} +(-217.161 - 85.8063i) q^{86} +(-452.403 - 783.585i) q^{87} +(544.695 - 787.197i) 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} +(129.202 + 162.781i) q^{94} +(380.797 - 219.853i) q^{95} +(-263.230 - 1217.66i) q^{96} -282.888i q^{97} +(-168.722 - 955.366i) 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

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