LMFDB - Embedded newform 52.4.f.b.47.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [52,4,Mod(31,52)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(52, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("52.31");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 52 = 2^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	52.f (of order $4$, 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:	$3.06809932030$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.18
Character	$\chi$	$=$	52.47
Dual form			52.4.f.b.31.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.81360 + 0.289217i) q^{2} +7.82965i q^{3} +(7.83271 + 1.62748i) q^{4} +(-8.33093 - 8.33093i) q^{5} +(-2.26447 + 22.0295i) q^{6} +(11.3199 + 11.3199i) q^{7} +(21.5674 + 6.84443i) q^{8} -34.3035 q^{9} +(-21.0305 - 25.8494i) q^{10} +(-25.6362 - 25.6362i) q^{11} +(-12.7426 + 61.3274i) q^{12} +(46.5752 - 5.26830i) q^{13} +(28.5758 + 35.1236i) q^{14} +(65.2283 - 65.2283i) q^{15} +(58.7026 + 25.4952i) q^{16} -78.9448i q^{17} +(-96.5163 - 9.92113i) q^{18} +(40.6150 - 40.6150i) q^{19} +(-51.6953 - 78.8122i) q^{20} +(-88.6309 + 88.6309i) q^{21} +(-64.7157 - 79.5445i) q^{22} -16.5644 q^{23} +(-53.5895 + 168.865i) q^{24} +13.8089i q^{25} +(132.568 - 1.35260i) q^{26} -57.1838i q^{27} +(70.2426 + 107.088i) q^{28} -273.273 q^{29} +(202.392 - 164.661i) q^{30} +(-166.461 + 166.461i) q^{31} +(157.792 + 88.7110i) q^{32} +(200.723 - 200.723i) q^{33} +(22.8321 - 222.119i) q^{34} -188.611i q^{35} +(-268.689 - 55.8282i) q^{36} +(88.3479 - 88.3479i) q^{37} +(126.021 - 102.528i) q^{38} +(41.2490 + 364.667i) q^{39} +(-122.656 - 236.697i) q^{40} +(341.169 + 341.169i) q^{41} +(-275.006 + 223.739i) q^{42} -381.339 q^{43} +(-159.079 - 242.523i) q^{44} +(285.780 + 285.780i) q^{45} +(-46.6056 - 4.79069i) q^{46} +(251.611 + 251.611i) q^{47} +(-199.618 + 459.621i) q^{48} -86.7195i q^{49} +(-3.99375 + 38.8527i) q^{50} +618.110 q^{51} +(373.384 + 34.5351i) q^{52} -400.479 q^{53} +(16.5385 - 160.892i) q^{54} +427.147i q^{55} +(166.663 + 321.619i) q^{56} +(318.001 + 318.001i) q^{57} +(-768.881 - 79.0350i) q^{58} +(-449.591 - 449.591i) q^{59} +(617.072 - 404.757i) q^{60} +157.121 q^{61} +(-516.499 + 420.212i) q^{62} +(-388.312 - 388.312i) q^{63} +(418.308 + 295.233i) q^{64} +(-431.904 - 344.125i) q^{65} +(622.806 - 506.701i) q^{66} +(-138.141 + 138.141i) q^{67} +(128.481 - 618.351i) q^{68} -129.693i q^{69} +(54.5493 - 530.675i) q^{70} +(236.698 - 236.698i) q^{71} +(-739.838 - 234.788i) q^{72} +(59.1869 - 59.1869i) q^{73} +(274.128 - 223.024i) q^{74} -108.119 q^{75} +(384.225 - 252.025i) q^{76} -580.399i q^{77} +(10.5904 + 1037.96i) q^{78} +559.485i q^{79} +(-276.649 - 701.446i) q^{80} -478.465 q^{81} +(861.243 + 1058.59i) q^{82} +(140.344 - 140.344i) q^{83} +(-838.465 + 549.975i) q^{84} +(-657.684 + 657.684i) q^{85} +(-1072.94 - 110.290i) q^{86} -2139.63i q^{87} +(-377.442 - 728.372i) q^{88} +(137.575 - 137.575i) q^{89} +(721.419 + 886.723i) q^{90} +(586.863 + 467.590i) q^{91} +(-129.744 - 26.9582i) q^{92} +(-1303.33 - 1303.33i) q^{93} +(635.163 + 780.703i) q^{94} -676.722 q^{95} +(-694.576 + 1235.46i) q^{96} +(598.653 + 598.653i) q^{97} +(25.0807 - 243.994i) q^{98} +(879.412 + 879.412i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 2 q^{2} - 20 q^{5} - 16 q^{6} - 40 q^{8} - 332 q^{9} - 96 q^{13} + 204 q^{14} + 52 q^{16} + 330 q^{18} + 500 q^{20} + 224 q^{21} - 48 q^{22} - 496 q^{24} + 570 q^{26} - 356 q^{28} + 560 q^{29} + 292 q^{32}+ \cdots + 3226 q^{98}+O(q^{100}) $ 36 * q + 2 * q^2 - 20 * q^5 - 16 * q^6 - 40 * q^8 - 332 * q^9 - 96 * q^13 + 204 * q^14 + 52 * q^16 + 330 * q^18 + 500 * q^20 + 224 * q^21 - 48 * q^22 - 496 * q^24 + 570 * q^26 - 356 * q^28 + 560 * q^29 + 292 * q^32 + 104 * q^33 - 416 * q^34 - 788 * q^37 - 2788 * q^40 + 1124 * q^41 - 1172 * q^42 - 156 * q^44 - 972 * q^45 - 668 * q^46 + 1332 * q^48 + 1354 * q^50 - 164 * q^52 + 1208 * q^53 + 2272 * q^54 - 1248 * q^57 - 2972 * q^58 + 692 * q^60 + 2632 * q^61 + 596 * q^65 + 3312 * q^66 + 2948 * q^68 - 1008 * q^70 - 908 * q^72 - 196 * q^73 - 1504 * q^74 - 3472 * q^76 - 2688 * q^78 - 1096 * q^80 - 764 * q^81 + 3744 * q^84 + 600 * q^85 - 3952 * q^86 - 2748 * q^89 - 1224 * q^92 - 6128 * q^93 + 2884 * q^94 + 4792 * q^96 - 1820 * q^97 + 3226 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/52\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	2.81360	+	0.289217i	0.994758	+	0.102253i
$2$	2.81360	+	0.289217i	0.994758	+	0.102253i
$3$			7.82965i			1.50682i	0.657552	+	0.753409i	$0.271592\pi$
$3$			7.82965i			1.50682i	−0.657552	+	0.753409i	$0.728408\pi$
$4$	7.83271	+	1.62748i	0.979088	+	0.203435i
$5$	−8.33093	−	8.33093i	−0.745141	−	0.745141i	0.228421	−	0.973562i	$-0.426644\pi$
$5$	−8.33093	−	8.33093i	−0.745141	−	0.745141i	−0.973562	+	0.228421i	$0.926644\pi$
$6$	−2.26447	+	22.0295i	−0.154077	+	1.49892i
$7$	11.3199	+	11.3199i	0.611217	+	0.611217i	0.943263	−	0.332046i	$-0.107739\pi$
$7$	11.3199	+	11.3199i	0.611217	+	0.611217i	−0.332046	+	0.943263i	$0.607739\pi$
$8$	21.5674	+	6.84443i	0.953155	+	0.302484i
$9$	−34.3035			−1.27050
$10$	−21.0305	−	25.8494i	−0.665042	−	0.817429i
$11$	−25.6362	−	25.6362i	−0.702692	−	0.702692i	0.262296	−	0.964988i	$-0.415520\pi$
$11$	−25.6362	−	25.6362i	−0.702692	−	0.702692i	−0.964988	+	0.262296i	$0.915520\pi$
$12$	−12.7426	+	61.3274i	−0.306539	+	1.47531i
$13$	46.5752	−	5.26830i	0.993663	−	0.112397i
$13$	46.5752	−	5.26830i	0.993663	−	0.112397i
$14$	28.5758	+	35.1236i	0.545515	+	0.670513i
$15$	65.2283	−	65.2283i	1.12279	−	1.12279i
$16$	58.7026	+	25.4952i	0.917228	+	0.398362i
$17$		−	78.9448i		−	1.12629i	−0.826358	−	0.563145i	$-0.809591\pi$
$17$		−	78.9448i		−	1.12629i	0.826358	−	0.563145i	$-0.190409\pi$
$18$	−96.5163	−	9.92113i	−1.26384	−	0.129913i
$19$	40.6150	−	40.6150i	0.490406	−	0.490406i	−0.418028	−	0.908434i	$-0.637279\pi$
$19$	40.6150	−	40.6150i	0.490406	−	0.490406i	0.908434	+	0.418028i	$0.137279\pi$
$20$	−51.6953	−	78.8122i	−0.577971	−	0.881147i
$21$	−88.6309	+	88.6309i	−0.920993	+	0.920993i
$22$	−64.7157	−	79.5445i	−0.627156	−	0.770861i
$23$	−16.5644			−0.150170			−0.0750851	−	0.997177i	$-0.523923\pi$
$23$	−16.5644			−0.150170			−0.0750851	+	0.997177i	$0.523923\pi$
$24$	−53.5895	+	168.865i	−0.455788	+	1.43623i
$25$			13.8089i			0.110471i
$26$	132.568	−	1.35260i	0.999948	−	0.0102026i
$27$		−	57.1838i		−	0.407594i
$28$	70.2426	+	107.088i	0.474093	+	0.722779i
$29$	−273.273			−1.74984			−0.874922	−	0.484263i	$-0.839088\pi$
$29$	−273.273			−1.74984			−0.874922	+	0.484263i	$0.839088\pi$
$30$	202.392	−	164.661i	1.23172	−	1.00210i
$31$	−166.461	+	166.461i	−0.964429	+	0.964429i	−0.999389	−	0.0349596i	$-0.988870\pi$
$31$	−166.461	+	166.461i	−0.964429	+	0.964429i	0.0349596	+	0.999389i	$0.488870\pi$
$32$	157.792	+	88.7110i	0.871687	+	0.490063i
$33$	200.723	−	200.723i	1.05883	−	1.05883i
$34$	22.8321	−	222.119i	0.115167	−	1.12039i
$35$		−	188.611i		−	0.910887i
$36$	−268.689	−	55.8282i	−1.24393	−	0.258464i
$37$	88.3479	−	88.3479i	0.392549	−	0.392549i	−0.483046	−	0.875595i	$-0.660470\pi$
$37$	88.3479	−	88.3479i	0.392549	−	0.392549i	0.875595	+	0.483046i	$0.160470\pi$
$38$	126.021	−	102.528i	0.537981	−	0.437690i
$39$	41.2490	+	364.667i	0.169362	+	1.49727i
$40$	−122.656	−	236.697i	−0.484842	−	0.935628i
$41$	341.169	+	341.169i	1.29955	+	1.29955i	0.928685	+	0.370869i	$0.120940\pi$
$41$	341.169	+	341.169i	1.29955	+	1.29955i	0.370869	+	0.928685i	$0.379060\pi$
$42$	−275.006	+	223.739i	−1.01034	+	0.821991i
$43$	−381.339			−1.35241			−0.676206	−	0.736713i	$-0.736377\pi$
$43$	−381.339			−1.35241			−0.676206	+	0.736713i	$0.736377\pi$
$44$	−159.079	−	242.523i	−0.545045	−	0.830949i
$45$	285.780	+	285.780i	0.946702	+	0.946702i
$46$	−46.6056	−	4.79069i	−0.149383	−	0.0153554i
$47$	251.611	+	251.611i	0.780877	+	0.780877i	0.979979	−	0.199102i	$-0.0638025\pi$
$47$	251.611	+	251.611i	0.780877	+	0.780877i	−0.199102	+	0.979979i	$0.563802\pi$
$48$	−199.618	+	459.621i	−0.600258	+	1.38210i
$49$		−	86.7195i		−	0.252826i
$50$	−3.99375	+	38.8527i	−0.0112960	+	0.109892i
$51$	618.110			1.69711
$52$	373.384	+	34.5351i	0.995750	+	0.0920991i
$53$	−400.479			−1.03792			−0.518962	−	0.854797i	$-0.673681\pi$
$53$	−400.479			−1.03792			−0.518962	+	0.854797i	$0.673681\pi$
$54$	16.5385	−	160.892i	0.0416779	−	0.405457i
$55$			427.147i			1.04721i
$56$	166.663	+	321.619i	0.397701	+	0.767468i
$57$	318.001	+	318.001i	0.738953	+	0.738953i
$58$	−768.881	−	79.0350i	−1.74067	−	0.178928i
$59$	−449.591	−	449.591i	−0.992064	−	0.992064i	0.00790438	−	0.999969i	$-0.497484\pi$
$59$	−449.591	−	449.591i	−0.992064	−	0.992064i	−0.999969	+	0.00790438i	$0.997484\pi$
$60$	617.072	−	404.757i	1.32773	−	0.870898i
$61$	157.121			0.329791			0.164896	−	0.986311i	$-0.447271\pi$
$61$	157.121			0.329791			0.164896	+	0.986311i	$0.447271\pi$
$62$	−516.499	+	420.212i	−1.05799	+	0.860758i
$63$	−388.312	−	388.312i	−0.776551	−	0.776551i
$64$	418.308	+	295.233i	0.817007	+	0.576628i
$65$	−431.904	−	344.125i	−0.824171	−	0.656668i
$66$	622.806	−	506.701i	1.16155	−	0.945010i
$67$	−138.141	+	138.141i	−0.251890	+	0.251890i	−0.821745	−	0.569855i	$-0.806999\pi$
$67$	−138.141	+	138.141i	−0.251890	+	0.251890i	0.569855	+	0.821745i	$0.306999\pi$
$68$	128.481	−	618.351i	0.229127	−	1.10274i
$69$		−	129.693i		−	0.226279i
$70$	54.5493	−	530.675i	0.0931413	−	0.906112i
$71$	236.698	−	236.698i	0.395646	−	0.395646i	−0.481048	−	0.876694i	$-0.659744\pi$
$71$	236.698	−	236.698i	0.395646	−	0.395646i	0.876694	+	0.481048i	$0.159744\pi$
$72$	−739.838	−	234.788i	−1.21098	−	0.384306i
$73$	59.1869	−	59.1869i	0.0948946	−	0.0948946i	−0.658066	−	0.752960i	$-0.728625\pi$
$73$	59.1869	−	59.1869i	0.0948946	−	0.0948946i	0.752960	+	0.658066i	$0.228625\pi$
$74$	274.128	−	223.024i	0.430631	−	0.350352i
$75$	−108.119			−0.166460
$76$	384.225	−	252.025i	0.579917	−	0.380385i
$77$		−	580.399i		−	0.858995i
$78$	10.5904	+	1037.96i	0.0153734	+	1.50674i
$79$			559.485i			0.796797i	0.917212	+	0.398399i	$0.130434\pi$
$79$			559.485i			0.796797i	−0.917212	+	0.398399i	$0.869566\pi$
$80$	−276.649	−	701.446i	−0.386629	−	0.980300i
$81$	−478.465			−0.656330
$82$	861.243	+	1058.59i	1.15986	+	1.42563i
$83$	140.344	−	140.344i	0.185599	−	0.185599i	−0.608191	−	0.793791i	$-0.708105\pi$
$83$	140.344	−	140.344i	0.185599	−	0.185599i	0.793791	+	0.608191i	$0.208105\pi$
$84$	−838.465	+	549.975i	−1.08910	+	0.714372i
$85$	−657.684	+	657.684i	−0.839245	+	0.839245i
$86$	−1072.94	−	110.290i	−1.34532	−	0.138289i
$87$		−	2139.63i		−	2.63670i
$88$	−377.442	−	728.372i	−0.457221	−	0.882327i
$89$	137.575	−	137.575i	0.163853	−	0.163853i	−0.620418	−	0.784271i	$-0.713037\pi$
$89$	137.575	−	137.575i	0.163853	−	0.163853i	0.784271	+	0.620418i	$0.213037\pi$
$90$	721.419	+	886.723i	0.844936	+	1.03854i
$91$	586.863	+	467.590i	0.676044	+	0.538645i
$92$	−129.744	−	26.9582i	−0.147030	−	0.0305499i
$93$	−1303.33	−	1303.33i	−1.45322	−	1.45322i
$94$	635.163	+	780.703i	0.696936	+	0.856631i
$95$	−676.722			−0.730844
$96$	−694.576	+	1235.46i	−0.738436	+	1.31347i
$97$	598.653	+	598.653i	0.626639	+	0.626639i	0.947221	−	0.320582i	$-0.103878\pi$
$97$	598.653	+	598.653i	0.626639	+	0.626639i	−0.320582	+	0.947221i	$0.603878\pi$
$98$	25.0807	−	243.994i	0.0258524	−	0.251501i
$99$	879.412	+	879.412i	0.892770	+	0.892770i
$100$	−22.4737	+	108.161i	−0.0224737	+	0.108161i
$101$			115.142i			0.113436i	0.998390	+	0.0567181i	$0.0180636\pi$
$101$			115.142i			0.113436i	−0.998390	+	0.0567181i	$0.981936\pi$
$102$	1739.12	+	178.768i	1.68822	+	0.173536i
$103$	961.255			0.919566			0.459783	−	0.888031i	$-0.347927\pi$
$103$	961.255			0.919566			0.459783	+	0.888031i	$0.347927\pi$
$104$	1040.56	+	205.157i	0.981113	+	0.193435i
$105$	1476.76			1.37254
$106$	−1126.79	−	115.825i	−1.03248	−	0.106131i
$107$		−	1104.88i		−	0.998253i	−0.866529	−	0.499126i	$-0.833654\pi$
$107$		−	1104.88i		−	0.998253i	0.866529	−	0.499126i	$-0.166346\pi$
$108$	93.0655	−	447.904i	0.0829188	−	0.399070i
$109$	624.968	+	624.968i	0.549184	+	0.549184i	0.926205	−	0.377020i	$-0.123051\pi$
$109$	624.968	+	624.968i	0.549184	+	0.549184i	−0.377020	+	0.926205i	$0.623051\pi$
$110$	−123.538	+	1201.82i	−0.107081	+	1.04172i
$111$	691.734	+	691.734i	0.591500	+	0.591500i
$112$	375.905	+	953.111i	0.317140	+	0.804112i
$113$	305.701			0.254495			0.127248	−	0.991871i	$-0.459386\pi$
$113$	305.701			0.254495			0.127248	+	0.991871i	$0.459386\pi$
$114$	802.758	+	986.700i	0.659519	+	0.810640i
$115$	137.997	+	137.997i	0.111898	+	0.111898i
$116$	−2140.47	−	444.746i	−1.71325	−	0.355980i
$117$	−1597.69	+	180.721i	−1.26245	+	0.142801i
$118$	−1134.94	−	1395.00i	−0.885422	−	1.08831i
$119$	893.648	−	893.648i	0.688408	−	0.688408i
$120$	1853.26	−	960.356i	1.40982	−	0.730568i
$121$		−	16.5690i		−	0.0124486i
$122$	442.075	+	45.4419i	0.328062	+	0.0337223i
$123$	−2671.24	+	2671.24i	−1.95819	+	1.95819i
$124$	−1574.75	+	1032.93i	−1.14046	+	0.748063i
$125$	−926.326	+	926.326i	−0.662825	+	0.662825i
$126$	−980.250	−	1204.86i	−0.693076	−	0.851886i
$127$	−1806.31			−1.26208			−0.631040	−	0.775750i	$-0.717372\pi$
$127$	−1806.31			−1.26208			−0.631040	+	0.775750i	$0.717372\pi$
$128$	1091.56	+	951.651i	0.753762	+	0.657147i
$129$		−	2985.76i		−	2.03784i
$130$	−1115.68	−	1093.14i	−0.752705	−	0.737500i
$131$			684.759i			0.456700i	0.973579	+	0.228350i	$0.0733330\pi$
$131$			684.759i			0.456700i	−0.973579	+	0.228350i	$0.926667\pi$
$132$	1898.87	−	1245.53i	1.25209	−	0.821284i
$133$	919.516			0.599490
$134$	−428.627	+	348.721i	−0.276326	+	0.224813i
$135$	−476.394	+	476.394i	−0.303715	+	0.303715i
$136$	540.332	−	1702.64i	0.340684	−	1.07353i
$137$	1583.71	−	1583.71i	0.987634	−	0.987634i	−0.0122902	−	0.999924i	$-0.503912\pi$
$137$	1583.71	−	1583.71i	0.987634	−	0.987634i	0.999924	+	0.0122902i	$0.00391218\pi$
$138$	37.5095	−	364.906i	0.0231378	−	0.225093i
$139$			79.6284i			0.0485899i	0.999705	+	0.0242949i	$0.00773408\pi$
$139$			79.6284i			0.0485899i	−0.999705	+	0.0242949i	$0.992266\pi$
$140$	306.960	−	1477.33i	0.185306	−	0.891839i
$141$	−1970.03	+	1970.03i	−1.17664	+	1.17664i
$142$	734.430	−	597.516i	0.434028	−	0.353116i
$143$	−1329.07	−	1058.95i	−0.777220	−	0.619258i
$144$	−2013.70	−	874.573i	−1.16534	−	0.506118i
$145$	2276.62	+	2276.62i	1.30388	+	1.30388i
$146$	183.646	−	149.411i	0.104100	−	0.0846939i
$147$	678.984			0.380963
$148$	835.788	−	548.219i	0.464198	−	0.304482i
$149$	−560.398	−	560.398i	−0.308118	−	0.308118i	0.536061	−	0.844179i	$-0.319912\pi$
$149$	−560.398	−	560.398i	−0.308118	−	0.308118i	−0.844179	+	0.536061i	$0.819912\pi$
$150$	−304.203	−	31.2697i	−0.165587	−	0.0170211i
$151$	540.614	+	540.614i	0.291355	+	0.291355i	0.837615	−	0.546261i	$-0.183949\pi$
$151$	540.614	+	540.614i	0.291355	+	0.291355i	−0.546261	+	0.837615i	$0.683949\pi$
$152$	1153.95	−	597.974i	0.615773	−	0.319093i
$153$			2708.08i			1.43095i
$154$	167.861	−	1633.01i	0.0878352	−	0.854492i
$155$	2773.55			1.43727
$156$	−270.398	+	2923.46i	−0.138777	+	1.50041i
$157$	2172.91			1.10457			0.552283	−	0.833657i	$-0.313757\pi$
$157$	2172.91			1.10457			0.552283	+	0.833657i	$0.313757\pi$
$158$	−161.812	+	1574.17i	−0.0814753	+	0.792621i
$159$		−	3135.61i		−	1.56396i
$160$	−575.511	−	2053.60i	−0.284363	−	1.01470i
$161$	−187.507	−	187.507i	−0.0917866	−	0.0917866i
$162$	−1346.21	−	138.380i	−0.652890	−	0.0671121i
$163$	−1000.42	−	1000.42i	−0.480730	−	0.480730i	0.424635	−	0.905365i	$-0.360402\pi$
$163$	−1000.42	−	1000.42i	−0.480730	−	0.480730i	−0.905365	+	0.424635i	$0.860402\pi$
$164$	2117.03	+	3227.53i	1.00800	+	1.53675i
$165$	−3344.41			−1.57795
$166$	435.462	−	354.282i	0.203605	−	0.165648i
$167$	−334.621	−	334.621i	−0.155053	−	0.155053i	0.625318	−	0.780370i	$-0.284969\pi$
$167$	−334.621	−	334.621i	−0.155053	−	0.155053i	−0.780370	+	0.625318i	$0.784969\pi$
$168$	−2518.17	+	1304.91i	−1.15643	+	0.599263i
$169$	2141.49	−	490.744i	0.974734	−	0.223370i
$170$	−2040.67	+	1660.25i	−0.920662	+	0.749030i
$171$	−1393.24	+	1393.24i	−0.623061	+	0.623061i
$172$	−2986.92	−	620.622i	−1.32413	−	0.275128i
$173$			2881.58i			1.26637i	0.773999	+	0.633187i	$0.218253\pi$
$173$			2881.58i			1.26637i	−0.773999	+	0.633187i	$0.781747\pi$
$174$	618.817	−	6020.07i	0.269611	−	2.62288i
$175$	−156.315	+	156.315i	−0.0675218	+	0.0675218i
$176$	−851.314	−	2158.51i	−0.364603	−	0.924454i
$177$	3520.14	−	3520.14i	1.49486	−	1.49486i
$178$	426.869	−	347.291i	0.179748	−	0.146239i
$179$	2412.92			1.00754			0.503772	−	0.863837i	$-0.331945\pi$
$179$	2412.92			1.00754			0.503772	+	0.863837i	$0.331945\pi$
$180$	1773.33	+	2703.53i	0.734312	+	1.11950i
$181$		−	1049.11i		−	0.430829i	−0.976523	−	0.215414i	$-0.930890\pi$
$181$		−	1049.11i		−	0.430829i	0.976523	−	0.215414i	$-0.0691102\pi$
$182$	1515.96	+	1485.34i	0.617422	+	0.604950i
$183$			1230.20i			0.496935i
$184$	−357.251	−	113.374i	−0.143135	−	0.0454241i
$185$	−1472.04			−0.585009
$186$	−3290.11	−	4044.01i	−1.29701	−	1.59420i
$187$	−2023.85	+	2023.85i	−0.791434	+	0.791434i
$188$	1561.30	+	2380.29i	0.605690	+	0.923405i
$189$	647.315	−	647.315i	0.249128	−	0.249128i
$190$	−1904.02	−	195.719i	−0.727013	−	0.0747313i
$191$			4047.74i			1.53343i	0.641990	+	0.766713i	$0.278109\pi$
$191$			4047.74i			1.53343i	−0.641990	+	0.766713i	$0.721891\pi$
$192$	−2311.58	+	3275.20i	−0.868873	+	1.23108i
$193$	−2852.15	+	2852.15i	−1.06374	+	1.06374i	−0.0659166	+	0.997825i	$0.520997\pi$
$193$	−2852.15	+	2852.15i	−1.06374	+	1.06374i	−0.997825	+	0.0659166i	$0.979003\pi$
$194$	1511.23	+	1857.51i	0.559278	+	0.687430i
$195$	2694.38	−	3381.66i	0.989479	−	1.24188i
$196$	141.134	−	679.248i	0.0514338	−	0.247539i
$197$	414.273	+	414.273i	0.149826	+	0.149826i	0.778040	−	0.628214i	$-0.216214\pi$
$197$	414.273	+	414.273i	0.149826	+	0.149826i	−0.628214	+	0.778040i	$0.716214\pi$
$198$	2219.97	+	2728.65i	0.796801	+	0.979379i
$199$	−159.956			−0.0569797			−0.0284898	−	0.999594i	$-0.509070\pi$
$199$	−159.956			−0.0569797			−0.0284898	+	0.999594i	$0.509070\pi$
$200$	−94.5139	+	297.822i	−0.0334157	+	0.105296i
$201$	−1081.60	−	1081.60i	−0.379552	−	0.379552i
$202$	−33.3010	+	323.964i	−0.0115993	+	0.112842i
$203$	−3093.42	−	3093.42i	−1.06954	−	1.06954i
$204$	4841.48	+	1005.96i	1.66162	+	0.345252i
$205$		−	5684.52i		−	1.93670i
$206$	2704.59	+	278.011i	0.914746	+	0.0940288i
$207$	568.216			0.190791
$208$	2868.40	+	878.177i	0.956191	+	0.292744i
$209$	−2082.43			−0.689209
$210$	4155.01	+	427.102i	1.36535	+	0.140347i
$211$		−	1482.87i		−	0.483816i	−0.970299	−	0.241908i	$-0.922227\pi$
$211$		−	1482.87i		−	0.483816i	0.970299	−	0.241908i	$-0.0777732\pi$
$212$	−3136.83	−	651.771i	−1.01622	−	0.211150i
$213$	1853.26	+	1853.26i	0.596166	+	0.596166i
$214$	319.550	−	3108.70i	0.102075	−	0.993020i
$215$	3176.91	+	3176.91i	1.00774	+	1.00774i
$216$	391.390	−	1233.31i	0.123290	−	0.388500i
$217$	−3768.65			−1.17895
$218$	1577.66	+	1939.16i	0.490150	+	0.602462i
$219$	463.413	+	463.413i	0.142989	+	0.142989i
$220$	−695.173	+	3345.72i	−0.213039	+	1.02531i
$221$	−415.905	−	3676.87i	−0.126592	−	1.11915i
$222$	1746.20	+	2146.32i	0.527916	+	0.648882i
$223$	−1531.16	+	1531.16i	−0.459795	+	0.459795i	−0.898588	−	0.438793i	$-0.855406\pi$
$223$	−1531.16	+	1531.16i	−0.459795	+	0.459795i	0.438793	+	0.898588i	$0.355406\pi$
$224$	781.993	+	2790.39i	0.233255	+	0.832325i
$225$		−	473.693i		−	0.140353i
$226$	860.121	+	88.4138i	0.253161	+	0.0260230i
$227$	−1709.23	+	1709.23i	−0.499760	+	0.499760i	−0.911363	−	0.411603i	$-0.864969\pi$
$227$	−1709.23	+	1709.23i	−0.499760	+	0.499760i	0.411603	+	0.911363i	$0.364969\pi$
$228$	1973.27	+	3008.35i	0.573171	+	0.873829i
$229$	−1492.21	+	1492.21i	−0.430604	+	0.430604i	−0.888834	−	0.458230i	$-0.848484\pi$
$229$	−1492.21	+	1492.21i	−0.430604	+	0.430604i	0.458230	+	0.888834i	$0.348484\pi$
$230$	348.357	+	428.179i	0.0998695	+	0.122753i
$231$	4544.32			1.29435
$232$	−5893.79	−	1870.40i	−1.66787	−	0.529300i
$233$			2553.26i			0.717894i	0.933358	+	0.358947i	$0.116864\pi$
$233$			2553.26i			0.717894i	−0.933358	+	0.358947i	$0.883136\pi$
$234$	−4547.53	+	46.3989i	−1.27043	+	0.0129623i
$235$		−	4192.31i		−	1.16373i
$236$	−2789.82	−	4253.22i	−0.769498	−	1.17314i
$237$	−4380.57			−1.20063
$238$	2772.83	−	2255.91i	0.755192	−	0.614407i
$239$	−923.193	+	923.193i	−0.249859	+	0.249859i	−0.820913	−	0.571053i	$-0.806535\pi$
$239$	−923.193	+	923.193i	−0.249859	+	0.249859i	0.571053	+	0.820913i	$0.306535\pi$
$240$	5492.08	−	2166.07i	1.47713	−	0.582579i
$241$	966.059	−	966.059i	0.258213	−	0.258213i	−0.566114	−	0.824327i	$-0.691554\pi$
$241$	966.059	−	966.059i	0.258213	−	0.258213i	0.824327	+	0.566114i	$0.191554\pi$
$242$	4.79204	−	46.6187i	0.00127291	−	0.0123833i
$243$		−	5290.18i		−	1.39656i
$244$	1230.68	+	255.711i	0.322895	+	0.0670911i
$245$	−722.454	+	722.454i	−0.188391	+	0.188391i
$246$	−8288.37	+	6743.24i	−2.14816	+	1.74770i
$247$	1677.68	−	2105.62i	0.432178	−	0.542419i
$248$	−4729.47	+	2450.81i	−1.21097	+	0.627526i
$249$	1098.84	+	1098.84i	0.279664	+	0.279664i
$250$	−2874.22	+	2338.40i	−0.727127	+	0.591574i
$251$	2634.63			0.662535			0.331268	−	0.943537i	$-0.392524\pi$
$251$	2634.63			0.662535			0.331268	+	0.943537i	$0.392524\pi$
$252$	−2409.57	−	3673.51i	−0.602335	−	0.918290i
$253$	424.648	+	424.648i	0.105523	+	0.105523i
$254$	−5082.24	−	522.415i	−1.25546	−	0.129052i
$255$	−5149.44	−	5149.44i	−1.26459	−	1.26459i
$256$	2795.99	+	2993.26i	0.682616	+	0.730777i
$257$		−	4970.67i		−	1.20647i	−0.797565	−	0.603233i	$-0.793879\pi$
$257$		−	4970.67i		−	1.20647i	0.797565	−	0.603233i	$-0.206121\pi$
$258$	863.530	−	8400.73i	0.208376	−	2.02716i
$259$	2000.18			0.479865
$260$	−2822.92	−	3398.34i	−0.673347	−	0.810601i
$261$	9374.21			2.22318
$262$	−198.044	+	1926.64i	−0.0466991	+	0.454306i
$263$			2705.57i			0.634345i	0.948368	+	0.317173i	$0.102734\pi$
$263$			2705.57i			0.634345i	−0.948368	+	0.317173i	$0.897266\pi$
$264$	5702.90	−	2955.24i	1.32951	−	0.688949i
$265$	3336.36	+	3336.36i	0.773400	+	0.773400i
$266$	2587.15	+	265.939i	0.596347	+	0.0612999i
$267$	1077.16	+	1077.16i	0.246896	+	0.246896i
$268$	−1306.84	+	857.197i	−0.297866	+	0.195379i
$269$	1593.16			0.361103			0.180551	−	0.983566i	$-0.442212\pi$
$269$	1593.16			0.361103			0.180551	+	0.983566i	$0.442212\pi$
$270$	−1478.16	+	1202.60i	−0.333179	+	0.271067i
$271$	−3493.98	−	3493.98i	−0.783189	−	0.783189i	0.197179	−	0.980368i	$-0.436822\pi$
$271$	−3493.98	−	3493.98i	−0.783189	−	0.783189i	−0.980368	+	0.197179i	$0.936822\pi$
$272$	2012.71	−	4634.27i	0.448671	−	1.03306i
$273$	−3661.07	+	4594.93i	−0.811640	+	1.01867i
$274$	4913.98	−	3997.91i	1.08345	−	0.881468i
$275$	354.007	−	354.007i	0.0776271	−	0.0776271i
$276$	211.073	−	1015.85i	0.0460331	−	0.221547i
$277$			4783.66i			1.03763i	0.854888	+	0.518813i	$0.173626\pi$
$277$			4783.66i			1.03763i	−0.854888	+	0.518813i	$0.826374\pi$
$278$	−23.0299	+	224.043i	−0.00496848	+	0.0483352i
$279$	5710.20	−	5710.20i	1.22531	−	1.22531i
$280$	1290.93	−	4067.85i	0.275529	−	0.868216i
$281$	745.228	−	745.228i	0.158208	−	0.158208i	−0.623564	−	0.781772i	$-0.714316\pi$
$281$	745.228	−	745.228i	0.158208	−	0.158208i	0.781772	+	0.623564i	$0.214316\pi$
$282$	−6112.63	+	4973.10i	−1.29079	+	1.05016i
$283$	−8851.69			−1.85929			−0.929644	−	0.368459i	$-0.879886\pi$
$283$	−8851.69			−1.85929			−0.929644	+	0.368459i	$0.879886\pi$
$284$	2239.20	−	1468.76i	0.467860	−	0.306884i
$285$		−	5298.50i		−	1.10125i
$286$	−3433.21	−	3363.86i	−0.709824	−	0.695486i
$287$			7724.01i			1.58862i
$288$	−5412.82	−	3043.10i	−1.10748	−	0.622625i
$289$	−1319.28			−0.268528
$290$	5747.06	+	7063.93i	1.16372	+	1.43037i
$291$	−4687.24	+	4687.24i	−0.944230	+	0.944230i
$292$	559.919	−	367.268i	0.112215	−	0.0736053i
$293$	2823.92	−	2823.92i	0.563055	−	0.563055i	−0.367119	−	0.930174i	$-0.619656\pi$
$293$	2823.92	−	2823.92i	0.563055	−	0.563055i	0.930174	+	0.367119i	$0.119656\pi$
$294$	1910.39	+	196.373i	0.378967	+	0.0389548i
$295$			7491.03i			1.47846i
$296$	2510.13	−	1300.75i	0.492899	−	0.255420i
$297$	−1465.98	+	1465.98i	−0.286413	+	0.286413i
$298$	−1414.66	−	1738.81i	−0.274997	−	0.338009i
$299$	−771.489	+	87.2662i	−0.149219	+	0.0168787i
$300$	−846.862	−	175.961i	−0.162979	−	0.0338637i
$301$	−4316.73	−	4316.73i	−0.826618	−	0.826618i
$302$	1364.72	+	1677.43i	0.260036	+	0.319620i
$303$	−901.523			−0.170928
$304$	3419.69	−	1348.72i	0.645174	−	0.254455i
$305$	−1308.96	−	1308.96i	−0.245741	−	0.245741i
$306$	−783.222	+	7619.46i	−0.146320	+	1.42345i
$307$	6618.79	+	6618.79i	1.23047	+	1.23047i	0.963783	+	0.266686i	$0.0859286\pi$
$307$	6618.79	+	6618.79i	1.23047	+	1.23047i	0.266686	+	0.963783i	$0.414071\pi$
$308$	944.588	−	4546.10i	0.174750	−	0.841032i
$309$			7526.30i			1.38562i
$310$	7803.67	+	802.157i	1.42974	+	0.146966i
$311$	−6512.49			−1.18743			−0.593713	−	0.804677i	$-0.702339\pi$
$311$	−6512.49			−1.18743			−0.593713	+	0.804677i	$0.702339\pi$
$312$	−1606.31	+	8147.26i	−0.291472	+	1.47836i
$313$	−4369.28			−0.789030			−0.394515	−	0.918889i	$-0.629087\pi$
$313$	−4369.28			−0.789030			−0.394515	+	0.918889i	$0.629087\pi$
$314$	6113.69	+	628.440i	1.09878	+	0.112946i
$315$			6470.01i			1.15728i
$316$	−910.551	+	4382.28i	−0.162096	+	0.780135i
$317$	3150.54	+	3150.54i	0.558208	+	0.558208i	0.928797	−	0.370589i	$-0.120844\pi$
$317$	3150.54	+	3150.54i	0.558208	+	0.558208i	−0.370589	+	0.928797i	$0.620844\pi$
$318$	906.870	−	8822.35i	0.159921	−	1.55576i
$319$	7005.68	+	7005.68i	1.22960	+	1.22960i
$320$	−1025.32	−	5944.46i	−0.179117	−	1.03845i
$321$	8650.85			1.50419
$322$	−473.341	−	581.801i	−0.0819200	−	0.100691i
$323$	−3206.34	−	3206.34i	−0.552339	−	0.552339i
$324$	−3747.68	−	778.692i	−0.642606	−	0.133521i
$325$	72.7493	+	643.150i	0.0124166	+	0.109771i
$326$	−2525.45	−	3104.12i	−0.429054	−	0.527366i
$327$	−4893.29	+	4893.29i	−0.827521	+	0.827521i
$328$	5023.04	+	9693.26i	0.845582	+	1.63177i
$329$			5696.42i			0.954571i
$330$	−9409.85	−	967.260i	−1.56968	−	0.161351i
$331$	6836.90	−	6836.90i	1.13532	−	1.13532i	0.146039	−	0.989279i	$-0.453347\pi$
$331$	6836.90	−	6836.90i	1.13532	−	1.13532i	0.989279	−	0.146039i	$-0.0466526\pi$
$332$	1327.68	−	870.866i	0.219476	−	0.143961i
$333$	−3030.64	+	3030.64i	−0.498733	+	0.498733i
$334$	−844.713	−	1038.27i	−0.138385	−	0.170094i
$335$	2301.69			0.375387
$336$	−7462.53	+	2943.21i	−1.21165	+	0.477873i
$337$		−	9303.15i		−	1.50378i	−0.659287	−	0.751892i	$-0.729142\pi$
$337$		−	9303.15i		−	1.50378i	0.659287	−	0.751892i	$-0.270858\pi$
$338$	6167.23	−	761.404i	0.992465	−	0.122529i
$339$			2393.53i			0.383478i
$340$	−6221.81	+	4081.08i	−0.992427	+	0.650963i
$341$	8534.87			1.35539
$342$	−4322.96	+	3517.06i	−0.683505	+	0.556085i
$343$	4864.38	−	4864.38i	0.765749	−	0.765749i
$344$	−8224.51	−	2610.05i	−1.28906	−	0.409083i
$345$	−1080.47	+	1080.47i	−0.168610	+	0.168610i
$346$	−833.401	+	8107.62i	−0.129491	+	1.25974i
$347$		−	2807.63i		−	0.434356i	−0.976132	−	0.217178i	$-0.930315\pi$
$347$		−	2807.63i		−	0.434356i	0.976132	−	0.217178i	$-0.0696853\pi$
$348$	3482.21	−	16759.1i	0.536396	−	2.58156i
$349$	7057.12	−	7057.12i	1.08240	−	1.08240i	0.0861192	−	0.996285i	$-0.472553\pi$
$349$	7057.12	−	7057.12i	1.08240	−	1.08240i	0.996285	−	0.0861192i	$-0.0274466\pi$
$350$	−485.018	+	394.600i	−0.0740722	+	0.0602635i
$351$	−301.261	−	2663.34i	−0.0458124	−	0.405011i
$352$	−1770.98	−	6319.41i	−0.268164	−	0.956891i
$353$	603.023	+	603.023i	0.0909226	+	0.0909226i	0.751105	−	0.660183i	$-0.229521\pi$
$353$	603.023	+	603.023i	0.0909226	+	0.0909226i	−0.660183	+	0.751105i	$0.729521\pi$
$354$	10922.4	−	8886.20i	1.63988	−	1.33417i
$355$	−3943.82			−0.589624
$356$	1301.48	−	853.682i	0.193759	−	0.127093i
$357$	6996.95	+	6996.95i	1.03731	+	1.03731i
$358$	6789.01	+	697.858i	1.00226	+	0.103025i
$359$	−5777.00	−	5777.00i	−0.849299	−	0.849299i	0.140747	−	0.990046i	$-0.455050\pi$
$359$	−5777.00	−	5777.00i	−0.849299	−	0.849299i	−0.990046	+	0.140747i	$0.955050\pi$
$360$	4207.54	+	8119.54i	0.615991	+	1.18871i
$361$			3559.84i			0.519003i
$362$	303.421	−	2951.79i	0.0440538	−	0.428571i
$363$	129.730			0.0187577
$364$	3835.73	+	4617.60i	0.552327	+	0.664912i
$365$	−986.165			−0.141420
$366$	−355.795	+	3461.30i	−0.0508133	+	0.494330i
$367$		−	7484.67i		−	1.06457i	−0.846566	−	0.532284i	$-0.821334\pi$
$367$		−	7484.67i		−	1.06457i	0.846566	−	0.532284i	$-0.178666\pi$
$368$	−972.373	−	422.312i	−0.137740	−	0.0598220i
$369$	−11703.3	−	11703.3i	−1.65108	−	1.65108i
$370$	−4141.74	−	425.739i	−0.581942	−	0.0598192i
$371$	−4533.38	−	4533.38i	−0.634397	−	0.634397i
$372$	−8087.48	−	12329.8i	−1.12719	−	1.71847i
$373$	−5362.28			−0.744365			−0.372183	−	0.928160i	$-0.621390\pi$
$373$	−5362.28			−0.744365			−0.372183	+	0.928160i	$0.621390\pi$
$374$	−6279.62	+	5108.97i	−0.868213	+	0.706359i
$375$	−7252.81	−	7252.81i	−0.998756	−	0.998756i
$376$	3704.47	+	7148.73i	0.508094	+	0.980499i
$377$	−12727.7	+	1439.68i	−1.73876	+	0.196678i
$378$	2008.50	−	1634.07i	0.273297	−	0.222348i
$379$	3373.09	−	3373.09i	0.457160	−	0.457160i	−0.440562	−	0.897722i	$-0.645221\pi$
$379$	3373.09	−	3373.09i	0.457160	−	0.457160i	0.897722	+	0.440562i	$0.145221\pi$
$380$	−5300.56	−	1101.35i	−0.715561	−	0.148679i
$381$		−	14142.8i		−	1.90172i
$382$	−1170.67	+	11388.7i	−0.156798	+	1.52539i
$383$	8389.54	−	8389.54i	1.11928	−	1.11928i	0.127437	−	0.991847i	$-0.459325\pi$
$383$	8389.54	−	8389.54i	1.11928	−	1.11928i	0.991847	−	0.127437i	$-0.0406750\pi$
$384$	−7451.10	+	8546.57i	−0.990201	+	1.13578i
$385$	−4835.27	+	4835.27i	−0.640073	+	0.640073i
$386$	−8849.70	+	7199.92i	−1.16694	+	0.949395i
$387$	13081.3			1.71824
$388$	3714.78	+	5663.36i	0.486054	+	0.741015i
$389$			10641.1i			1.38695i	0.720478	+	0.693477i	$0.243922\pi$
$389$			10641.1i			1.38695i	−0.720478	+	0.693477i	$0.756078\pi$
$390$	8558.93	−	8735.39i	1.11128	−	1.13419i
$391$			1307.67i			0.169135i
$392$	593.545	−	1870.32i	0.0764759	−	0.240983i
$393$	−5361.43			−0.688163
$394$	1045.79	+	1285.41i	0.133721	+	0.164361i
$395$	4661.03	−	4661.03i	0.593726	−	0.593726i
$396$	5456.95	+	8319.40i	0.692480	+	1.05572i
$397$	−2077.52	+	2077.52i	−0.262640	+	0.262640i	−0.826126	−	0.563486i	$-0.809460\pi$
$397$	−2077.52	+	2077.52i	−0.262640	+	0.262640i	0.563486	+	0.826126i	$0.309460\pi$
$398$	−450.051	−	46.2618i	−0.0566810	−	0.00582637i
$399$			7199.49i			0.903322i
$400$	−352.059	+	810.617i	−0.0440074	+	0.101327i
$401$	180.680	−	180.680i	0.0225006	−	0.0225006i	−0.695767	−	0.718268i	$-0.744935\pi$
$401$	180.680	−	180.680i	0.0225006	−	0.0225006i	0.718268	+	0.695767i	$0.244935\pi$
$402$	−2730.37	−	3356.00i	−0.338752	−	0.416373i
$403$	−6875.99	+	8629.92i	−0.849919	+	1.06672i
$404$	−187.391	+	901.874i	−0.0230769	+	0.111064i
$405$	3986.06	+	3986.06i	0.489059	+	0.489059i
$406$	−7808.99	−	9598.33i	−0.954566	−	1.17329i
$407$	−4529.81			−0.551682
$408$	13331.0	+	4230.61i	1.61761	+	0.513349i
$409$	192.163	+	192.163i	0.0232319	+	0.0232319i	0.718627	−	0.695395i	$-0.244771\pi$
$409$	192.163	+	192.163i	0.0232319	+	0.0232319i	−0.695395	+	0.718627i	$0.744771\pi$
$410$	1644.06	−	15994.0i	0.198035	−	1.92655i
$411$	12399.9	+	12399.9i	1.48818	+	1.48818i
$412$	7529.23	+	1564.42i	0.900336	+	0.187072i
$413$		−	10178.7i		−	1.21273i
$414$	1598.73	+	164.338i	0.189791	+	0.0195091i
$415$	−2338.39			−0.276596
$416$	7816.55	+	3300.43i	0.921245	+	0.388983i
$417$	−623.463			−0.0732161
$418$	−5859.13	−	602.273i	−0.685596	−	0.0704740i
$419$			3850.84i			0.448988i	0.974475	+	0.224494i	$0.0720730\pi$
$419$			3850.84i			0.448988i	−0.974475	+	0.224494i	$0.927927\pi$
$420$	11567.0	+	2403.39i	1.34384	+	0.279223i
$421$	−950.379	−	950.379i	−0.110020	−	0.110020i	0.649954	−	0.759974i	$-0.274788\pi$
$421$	−950.379	−	950.379i	−0.110020	−	0.110020i	−0.759974	+	0.649954i	$0.774788\pi$
$422$	428.871	−	4172.21i	0.0494718	−	0.481280i
$423$	−8631.13	−	8631.13i	−0.992104	−	0.992104i
$424$	−8637.29	−	2741.05i	−0.989302	−	0.313955i
$425$	1090.14			0.124422
$426$	4678.34	+	5750.33i	0.532081	+	0.654001i
$427$	1778.59	+	1778.59i	0.201574	+	0.201574i
$428$	1798.17	−	8654.22i	0.203080	−	0.977378i
$429$	8291.22	−	10406.2i	0.933110	−	1.17113i
$430$	8019.75	+	9857.38i	0.899411	+	1.10550i
$431$	6807.46	−	6807.46i	0.760798	−	0.760798i	−0.215669	−	0.976467i	$-0.569193\pi$
$431$	6807.46	−	6807.46i	0.760798	−	0.760798i	0.976467	+	0.215669i	$0.0691931\pi$
$432$	1457.91	−	3356.84i	0.162370	−	0.373856i
$433$		−	13910.7i		−	1.54389i	−0.635686	−	0.771947i	$-0.719283\pi$
$433$		−	13910.7i		−	1.54389i	0.635686	−	0.771947i	$-0.280717\pi$
$434$	−10603.5	−	1089.96i	−1.17277	−	0.120552i
$435$	−17825.1	+	17825.1i	−1.96471	+	1.96471i
$436$	3878.07	+	5912.32i	0.425977	+	0.649424i
$437$	−672.763	+	672.763i	−0.0736444	+	0.0736444i
$438$	1169.83	+	1437.89i	0.127618	+	0.156860i
$439$	3859.01			0.419545			0.209773	−	0.977750i	$-0.432728\pi$
$439$	3859.01			0.419545			0.209773	+	0.977750i	$0.432728\pi$
$440$	−2923.58	+	9212.46i	−0.316764	+	0.998152i
$441$			2974.78i			0.321216i
$442$	−106.781	−	10465.5i	−0.0114910	−	1.12623i
$443$			6880.31i			0.737908i	0.929448	+	0.368954i	$0.120284\pi$
$443$			6880.31i			0.737908i	−0.929448	+	0.368954i	$0.879716\pi$
$444$	4292.36	+	6543.93i	0.458799	+	0.699462i
$445$	−2292.25			−0.244187
$446$	−4750.92	+	3865.24i	−0.504400	+	0.410369i
$447$	4387.73	−	4387.73i	0.464278	−	0.464278i
$448$	1393.19	+	8077.22i	0.146924	+	0.851814i
$449$	−4272.88	+	4272.88i	−0.449109	+	0.449109i	−0.895058	−	0.445949i	$-0.852866\pi$
$449$	−4272.88	+	4272.88i	−0.449109	+	0.449109i	0.445949	+	0.895058i	$0.352866\pi$
$450$	137.000	−	1332.78i	0.0143516	−	0.139618i
$451$		−	17492.6i		−	1.82637i
$452$	2394.47	+	497.523i	0.249173	+	0.0517732i
$453$	−4232.82	+	4232.82i	−0.439019	+	0.439019i
$454$	−5303.43	+	4314.75i	−0.548243	+	0.446038i
$455$	−993.658	−	8784.57i	−0.102381	−	0.905115i
$456$	4681.93	+	9035.01i	0.480815	+	0.927857i
$457$	1999.48	+	1999.48i	0.204665	+	0.204665i	0.801995	−	0.597330i	$-0.203772\pi$
$457$	1999.48	+	1999.48i	0.204665	+	0.204665i	−0.597330	+	0.801995i	$0.703772\pi$
$458$	−4630.07	+	3766.92i	−0.472378	+	0.384316i
$459$	−4514.36			−0.459068
$460$	856.302	+	1305.48i	0.0867941	+	0.132322i
$461$	−3543.23	−	3543.23i	−0.357971	−	0.357971i	0.505094	−	0.863065i	$-0.331458\pi$
$461$	−3543.23	−	3543.23i	−0.357971	−	0.357971i	−0.863065	+	0.505094i	$0.831458\pi$
$462$	12785.9	+	1314.29i	1.28756	+	0.132352i
$463$	4677.60	+	4677.60i	0.469517	+	0.469517i	0.901758	−	0.432241i	$-0.142277\pi$
$463$	4677.60	+	4677.60i	0.469517	+	0.469517i	−0.432241	+	0.901758i	$0.642277\pi$
$464$	−16041.8	−	6967.13i	−1.60501	−	0.697071i
$465$			21716.0i			2.16571i
$466$	−738.444	+	7183.84i	−0.0734072	+	0.714131i
$467$	1260.64			0.124915			0.0624577	−	0.998048i	$-0.480106\pi$
$467$	1260.64			0.124915			0.0624577	+	0.998048i	$0.480106\pi$
$468$	−12808.4	−	1184.67i	−1.26510	−	0.117012i
$469$	−3127.49			−0.307919
$470$	1212.48	−	11795.5i	0.118995	−	1.15763i
$471$			17013.1i			1.66438i
$472$	−6619.33	−	12773.7i	−0.645507	−	1.24567i
$473$	9776.10	+	9776.10i	0.950329	+	0.950329i
$474$	−12325.2	−	1266.93i	−1.19433	−	0.122768i
$475$	560.847	+	560.847i	0.0541757	+	0.0541757i
$476$	8454.07	−	5545.29i	0.814058	−	0.533966i
$477$	13737.8			1.31868
$478$	−2864.50	+	2330.50i	−0.274099	+	0.223001i
$479$	9685.16	+	9685.16i	0.923854	+	0.923854i	0.997299	−	0.0734449i	$-0.0233993\pi$
$479$	9685.16	+	9685.16i	0.923854	+	0.923854i	−0.0734449	+	0.997299i	$0.523399\pi$
$480$	16079.0	−	4506.05i	1.52896	−	0.428484i
$481$	3649.37	−	4580.26i	0.345940	−	0.434183i
$482$	2997.51	−	2438.71i	0.283263	−	0.230456i
$483$	1468.12	−	1468.12i	0.138306	−	0.138306i
$484$	26.9658	−	129.780i	0.00253247	−	0.0121882i
$485$		−	9974.67i		−	0.933869i
$486$	1530.01	−	14884.5i	0.142804	−	1.38924i
$487$	1674.95	−	1674.95i	0.155850	−	0.155850i	−0.624875	−	0.780725i	$-0.714850\pi$
$487$	1674.95	−	1674.95i	0.155850	−	0.155850i	0.780725	+	0.624875i	$0.214850\pi$
$488$	3388.69	+	1075.40i	0.314342	+	0.0997565i
$489$	7832.95	−	7832.95i	0.724372	−	0.724372i
$490$	−2241.64	+	1823.75i	−0.206668	+	0.168140i
$491$	−17057.1			−1.56777			−0.783884	−	0.620907i	$-0.786765\pi$
$491$	−17057.1			−1.56777			−0.783884	+	0.620907i	$0.786765\pi$
$492$	−25270.4	+	16575.6i	−2.31561	+	1.51888i
$493$			21573.5i			1.97083i
$494$	5329.30	−	5439.17i	0.485377	−	0.495384i
$495$		−	14652.6i		−	1.33048i
$496$	−14015.7	+	5527.75i	−1.26879	+	0.500410i
$497$	5358.79			0.483651
$498$	2773.91	+	3409.52i	0.249602	+	0.306795i
$499$	4398.18	−	4398.18i	0.394568	−	0.394568i	−0.481744	−	0.876312i	$-0.659996\pi$
$499$	4398.18	−	4398.18i	0.394568	−	0.394568i	0.876312	+	0.481744i	$0.159996\pi$
$500$	−8763.22	+	5748.06i	−0.783806	+	0.514122i
$501$	2619.97	−	2619.97i	0.233636	−	0.233636i
$502$	7412.80	+	761.979i	0.659063	+	0.0677466i
$503$			5852.18i			0.518759i	0.965775	+	0.259380i	$0.0835180\pi$
$503$			5852.18i			0.518759i	−0.965775	+	0.259380i	$0.916482\pi$
$504$	−5717.12	−	11032.7i	−0.505279	−	0.975068i
$505$	959.241	−	959.241i	0.0845261	−	0.0845261i
$506$	1071.98	+	1317.61i	0.0941801	+	0.115760i
$507$	3842.36	+	16767.1i	0.336578	+	1.46875i
$508$	−14148.3	−	2939.73i	−1.23569	−	0.256751i
$509$	7272.18	+	7272.18i	0.633268	+	0.633268i	0.948886	−	0.315618i	$-0.102212\pi$
$509$	7272.18	+	7272.18i	0.633268	+	0.633268i	−0.315618	+	0.948886i	$0.602212\pi$
$510$	−12999.2	−	15977.8i	−1.12865	−	1.38727i
$511$	1339.98			0.116002
$512$	7001.11	+	9230.50i	0.604313	+	0.796747i
$513$	−2322.52	−	2322.52i	−0.199886	−	0.199886i
$514$	1437.60	−	13985.5i	0.123365	−	1.20014i
$515$	−8008.15	−	8008.15i	−0.685206	−	0.685206i
$516$	4859.26	−	23386.5i	0.414568	−	1.99522i
$517$		−	12900.7i		−	1.09743i
$518$	5627.71	+	578.485i	0.477350	+	0.0490679i
$519$	−22561.8			−1.90819
$520$	−6959.73	−	10378.0i	−0.586931	−	0.875204i
$521$	−8450.83			−0.710629			−0.355314	−	0.934747i	$-0.615626\pi$
$521$	−8450.83			−0.710629			−0.355314	+	0.934747i	$0.615626\pi$
$522$	26375.3	+	2711.18i	2.21152	+	0.227328i
$523$		−	20588.0i		−	1.72132i	−0.509183	−	0.860658i	$-0.670052\pi$
$523$		−	20588.0i		−	1.72132i	0.509183	−	0.860658i	$-0.329948\pi$
$524$	−1114.43	+	5363.52i	−0.0929087	+	0.447149i
$525$	−1223.89	−	1223.89i	−0.101743	−	0.101743i
$526$	−782.497	+	7612.41i	−0.0648640	+	0.631020i
$527$	13141.2	+	13141.2i	1.08623	+	1.08623i
$528$	16900.4	−	6665.49i	1.39298	−	0.549391i
$529$	−11892.6			−0.977449
$530$	8422.26	+	10352.1i	0.690263	+	0.848429i
$531$	15422.5	+	15422.5i	1.26042	+	1.26042i
$532$	7202.30	+	1496.49i	0.586953	+	0.121957i
$533$	17687.4	+	14092.6i	1.43739	+	1.14525i
$534$	2719.17	+	3342.24i	0.220356	+	0.270848i
$535$	−9204.71	+	9204.71i	−0.743839	+	0.743839i
$536$	−3924.85	+	2033.85i	−0.316283	+	0.163897i
$537$			18892.4i			1.51819i
$538$	4482.51	+	460.768i	0.359210	+	0.0369240i
$539$	−2223.16	+	2223.16i	−0.177659	+	0.177659i
$540$	−4506.78	+	2956.13i	−0.359150	+	0.235577i
$541$	7981.77	−	7981.77i	0.634313	−	0.634313i	−0.314834	−	0.949147i	$-0.601949\pi$
$541$	7981.77	−	7981.77i	0.634313	−	0.634313i	0.949147	+	0.314834i	$0.101949\pi$
$542$	−8820.15	−	10841.2i	−0.699000	−	0.859167i
$543$	8214.20			0.649181
$544$	7003.27	−	12456.9i	0.551953	−	0.981772i
$545$		−	10413.1i		−	0.818440i
$546$	−11629.7	+	11869.5i	−0.911549	+	0.930342i
$547$		−	12318.8i		−	0.962912i	−0.876470	−	0.481456i	$-0.840108\pi$
$547$		−	12318.8i		−	0.962912i	0.876470	−	0.481456i	$-0.159892\pi$
$548$	14982.2	−	9827.31i	1.16790	−	0.766062i
$549$	−5389.79			−0.418999
$550$	1098.42	−	893.651i	0.0851578	−	0.0692825i
$551$	−11099.0	+	11099.0i	−0.858135	+	0.858135i
$552$	887.678	−	2797.15i	0.0684458	−	0.215679i
$553$	−6333.32	+	6333.32i	−0.487016	+	0.487016i
$554$	−1383.51	+	13459.3i	−0.106101	+	1.03219i
$555$		−	11525.6i		−	0.881501i
$556$	−129.594	+	623.706i	−0.00988488	+	0.0475738i
$557$	5792.59	−	5792.59i	0.440646	−	0.440646i	−0.451583	−	0.892229i	$-0.649140\pi$
$557$	5792.59	−	5792.59i	0.440646	−	0.440646i	0.892229	+	0.451583i	$0.149140\pi$
$558$	17717.7	−	14414.7i	1.34418	−	1.09359i
$559$	−17760.9	+	2009.01i	−1.34384	+	0.152007i
$560$	4808.66	−	11071.9i	0.362862	−	0.835491i
$561$	−15846.0	−	15846.0i	−1.19255	−	1.19255i
$562$	2312.31	−	1881.24i	0.173557	−	0.141202i
$563$	−7611.40			−0.569773			−0.284887	−	0.958561i	$-0.591956\pi$
$563$	−7611.40			−0.569773			−0.284887	+	0.958561i	$0.591956\pi$
$564$	−18636.8	+	12224.5i	−1.39140	+	0.912664i
$565$	−2546.78	−	2546.78i	−0.189635	−	0.189635i
$566$	−24905.1	−	2560.06i	−1.84954	−	0.190119i
$567$	−5416.18	−	5416.18i	−0.401161	−	0.401161i
$568$	6725.02	−	3484.90i	0.496788	−	0.257435i
$569$			4350.28i			0.320515i	0.987075	+	0.160258i	$0.0512325\pi$
$569$			4350.28i			0.320515i	−0.987075	+	0.160258i	$0.948768\pi$
$570$	1532.41	−	14907.9i	0.112606	−	1.09548i
$571$	23139.5			1.69590			0.847949	−	0.530077i	$-0.177837\pi$
$571$	23139.5			1.69590			0.847949	+	0.530077i	$0.177837\pi$
$572$	−8686.79	−	10457.5i	−0.634988	−	0.764422i
$573$	−31692.4			−2.31059
$574$	−2233.91	+	21732.3i	−0.162442	+	1.58029i
$575$		−	228.736i		−	0.0165894i
$576$	−14349.4	−	10127.5i	−1.03801	−	0.732605i
$577$	−11827.6	−	11827.6i	−0.853361	−	0.853361i	0.137184	−	0.990546i	$-0.456195\pi$
$577$	−11827.6	−	11827.6i	−0.853361	−	0.853361i	−0.990546	+	0.137184i	$0.956195\pi$
$578$	−3711.93	−	381.557i	−0.267121	−	0.0274580i
$579$	−22331.3	−	22331.3i	−1.60286	−	1.60286i
$580$	14126.9	+	21537.2i	1.01136	+	1.54187i
$581$	3177.36			0.226883
$582$	−14543.7	+	11832.4i	−1.03583	+	0.842730i
$583$	10266.8	+	10266.8i	0.729340	+	0.729340i
$584$	1681.61	−	871.409i	0.119153	−	0.0617451i
$585$	14815.8	+	11804.7i	1.04711	+	0.834296i
$586$	8762.11	−	7128.66i	0.617678	−	0.502529i
$587$	16220.6	−	16220.6i	1.14054	−	1.14054i	0.152187	−	0.988352i	$-0.451368\pi$
$587$	16220.6	−	16220.6i	1.14054	−	1.14054i	0.988352	−	0.152187i	$-0.0486316\pi$
$588$	5318.28	+	1105.03i	0.372997	+	0.0775013i
$589$			13521.6i			0.945924i
$590$	−2166.53	+	21076.8i	−0.151177	+	1.47071i
$591$	−3243.62	+	3243.62i	−0.225761	+	0.225761i
$592$	7438.70	−	2933.81i	0.516433	−	0.203681i
$593$	−5684.80	+	5684.80i	−0.393671	+	0.393671i	−0.875994	−	0.482323i	$-0.839793\pi$
$593$	−5684.80	+	5684.80i	−0.393671	+	0.393671i	0.482323	+	0.875994i	$0.339793\pi$
$594$	−4548.66	+	3700.69i	−0.314198	+	0.255625i
$595$	−14889.8			−1.02592
$596$	−3477.40	−	5301.47i	−0.238993	−	0.364357i
$597$		−	1252.40i		−	0.0858580i
$598$	−2195.90	+	22.4050i	−0.150162	+	0.00153212i
$599$		−	580.437i		−	0.0395927i	−0.999804	−	0.0197963i	$-0.993698\pi$
$599$		−	580.437i		−	0.0395927i	0.999804	−	0.0197963i	$-0.00630178\pi$
$600$	−2331.84	−	740.011i	−0.158662	−	0.0503514i
$601$	24529.0			1.66483			0.832413	−	0.554156i	$-0.186959\pi$
$601$	24529.0			1.66483			0.832413	+	0.554156i	$0.186959\pi$
$602$	−10897.1	−	13394.0i	−0.737760	−	0.906809i
$603$	4738.72	−	4738.72i	0.320026	−	0.320026i
$604$	3354.64	+	5114.31i	0.225990	+	0.344534i
$605$	−138.036	+	138.036i	−0.00927594	+	0.00927594i
$606$	−2536.53	−	260.735i	−0.170032	−	0.0174780i
$607$			7465.91i			0.499229i	0.968345	+	0.249614i	$0.0803038\pi$
$607$			7465.91i			0.499229i	−0.968345	+	0.249614i	$0.919696\pi$
$608$	10011.7	−	2805.73i	0.667811	−	0.187150i
$609$	24220.4	−	24220.4i	1.61160	−	1.61160i
$610$	−3304.33	−	4061.47i	−0.219325	−	0.269581i
$611$	13044.4	+	10393.3i	0.863697	+	0.688160i
$612$	−4407.35	+	21211.6i	−0.291105	+	1.40103i
$613$	−11158.0	−	11158.0i	−0.735186	−	0.735186i	0.236456	−	0.971642i	$-0.424014\pi$
$613$	−11158.0	−	11158.0i	−0.735186	−	0.735186i	−0.971642	+	0.236456i	$0.924014\pi$
$614$	16708.4	+	20536.9i	1.09820	+	1.34984i
$615$	44507.8			2.91826
$616$	3972.50	−	12517.7i	0.259832	−	0.818755i
$617$	−3043.59	−	3043.59i	−0.198591	−	0.198591i	0.600805	−	0.799396i	$-0.294847\pi$
$617$	−3043.59	−	3043.59i	−0.198591	−	0.198591i	−0.799396	+	0.600805i	$0.794847\pi$
$618$	−2176.73	+	21176.0i	−0.141684	+	1.37836i
$619$	−756.784	−	756.784i	−0.0491401	−	0.0491401i	0.682110	−	0.731250i	$-0.261063\pi$
$619$	−756.784	−	756.784i	−0.0491401	−	0.0491401i	−0.731250	+	0.682110i	$0.761063\pi$
$620$	21724.4	+	4513.90i	1.40722	+	0.292391i
$621$			947.215i			0.0612084i
$622$	−18323.6	−	1883.52i	−1.18120	−	0.121418i
$623$	3114.66			0.200299
$624$	−6875.83	+	22458.6i	−0.441111	+	1.44081i
$625$	17160.4			1.09827
$626$	−12293.4	−	1263.67i	−0.784894	−	0.0806811i
$627$		−	16304.7i		−	1.03851i
$628$	17019.7	+	3536.36i	1.08147	+	0.224707i
$629$	−6974.61	−	6974.61i	−0.442124	−	0.442124i
$630$	−1871.23	+	18204.0i	−0.118336	+	1.15122i
$631$	−3051.61	−	3051.61i	−0.192524	−	0.192524i	0.604262	−	0.796786i	$-0.293468\pi$
$631$	−3051.61	−	3051.61i	−0.192524	−	0.192524i	−0.796786	+	0.604262i	$0.793468\pi$
$632$	−3829.35	+	12066.6i	−0.241018	+	0.759471i
$633$	11610.4			0.729022
$634$	7953.17	+	9775.54i	0.498203	+	0.612360i
$635$	15048.2	+	15048.2i	0.940428	+	0.940428i
$636$	5103.14	−	24560.3i	0.318165	−	1.53126i
$637$	−456.864	−	4038.97i	−0.0284170	−	0.251224i
$638$	17685.0	+	21737.4i	1.09743	+	1.34889i
$639$	−8119.55	+	8119.55i	−0.502668	+	0.502668i
$640$	−1165.61	−	17021.9i	−0.0719921	−	1.05133i
$641$		−	6342.25i		−	0.390801i	−0.980723	−	0.195401i	$-0.937399\pi$
$641$		−	6342.25i		−	0.390801i	0.980723	−	0.195401i	$-0.0626007\pi$
$642$	24340.0	+	2501.97i	1.49630	+	0.153808i
$643$	−16479.3	+	16479.3i	−1.01070	+	1.01070i	−0.0107603	+	0.999942i	$0.503425\pi$
$643$	−16479.3	+	16479.3i	−1.01070	+	1.01070i	−0.999942	+	0.0107603i	$0.996575\pi$
$644$	−1163.53	−	1773.85i	−0.0711946	−	0.108540i
$645$	−24874.1	+	24874.1i	−1.51848	+	1.51848i
$646$	−8094.04	−	9948.70i	−0.492966	−	0.605923i
$647$	−13626.7			−0.828010			−0.414005	−	0.910275i	$-0.635870\pi$
$647$	−13626.7			−0.828010			−0.414005	+	0.910275i	$0.635870\pi$
$648$	−10319.3	−	3274.82i	−0.625584	−	0.198529i
$649$			23051.6i			1.39423i
$650$	18.6779	+	1830.61i	0.00112709	+	0.110465i
$651$		−	29507.2i		−	1.77647i
$652$	−6207.84	−	9464.16i	−0.372880	−	0.568474i
$653$	−3063.46			−0.183587			−0.0917935	−	0.995778i	$-0.529260\pi$
$653$	−3063.46			−0.183587			−0.0917935	+	0.995778i	$0.529260\pi$
$654$	−15183.0	+	12352.5i	−0.907800	+	0.738566i
$655$	5704.68	−	5704.68i	0.340306	−	0.340306i
$656$	11329.4	+	28725.7i	0.674295	+	1.70968i
$657$	−2030.32	+	2030.32i	−0.120564	+	0.120564i
$658$	−1647.50	+	16027.5i	−0.0976082	+	0.949568i
$659$			28687.3i			1.69575i	0.530197	+	0.847875i	$0.322118\pi$
$659$			28687.3i			1.69575i	−0.530197	+	0.847875i	$0.677882\pi$
$660$	−26195.8	−	5442.97i	−1.54496	−	0.321011i
$661$	−14074.8	+	14074.8i	−0.828208	+	0.828208i	−0.987269	−	0.159061i	$-0.949153\pi$
$661$	−14074.8	+	14074.8i	−0.828208	+	0.828208i	0.159061	+	0.987269i	$0.449153\pi$
$662$	21213.7	−	17259.0i	1.24546	−	1.01328i
$663$	28788.6	−	3256.39i	1.68636	−	0.190751i
$664$	3987.43	−	2066.28i	0.233046	−	0.120764i
$665$	−7660.42	−	7660.42i	−0.446705	−	0.446705i
$666$	−9403.53	+	7650.51i	−0.547116	+	0.445122i
$667$	4526.60			0.262774
$668$	−2076.40	−	3165.58i	−0.120267	−	0.183353i
$669$	−11988.5	−	11988.5i	−0.692827	−	0.692827i
$670$	6476.04	+	665.687i	0.373420	+	0.0383846i
$671$	−4027.98	−	4027.98i	−0.231742	−	0.231742i
$672$	−21847.8	+	6122.73i	−1.25416	+	0.351472i
$673$		−	23395.6i		−	1.34002i	−0.742352	−	0.670010i	$-0.766290\pi$
$673$		−	23395.6i		−	1.34002i	0.742352	−	0.670010i	$-0.233710\pi$
$674$	2690.62	−	26175.4i	0.153767	−	1.49590i
$675$	789.644			0.0450273
$676$	17572.3	−	358.622i	0.999792	−	0.0204041i
$677$	2942.64			0.167053			0.0835264	−	0.996506i	$-0.473382\pi$
$677$	2942.64			0.167053			0.0835264	+	0.996506i	$0.473382\pi$
$678$	−692.250	+	6734.45i	−0.0392119	+	0.381468i
$679$			13553.4i			0.766025i
$680$	−18686.0	+	9683.07i	−1.05379	+	0.546072i
$681$	−13382.7	−	13382.7i	−0.753048	−	0.753048i
$682$	24013.7	+	2468.42i	1.34829	+	0.138594i
$683$	−21017.1	−	21017.1i	−1.17745	−	1.17745i	−0.980392	−	0.197056i	$-0.936862\pi$
$683$	−21017.1	−	21017.1i	−1.17745	−	1.17745i	−0.197056	−	0.980392i	$-0.563138\pi$
$684$	−13180.3	+	8645.35i	−0.736784	+	0.483279i
$685$	−26387.6			−1.47185
$686$	15093.3	−	12279.6i	0.840036	−	0.683435i
$687$	−11683.5	−	11683.5i	−0.648841	−	0.648841i
$688$	−22385.6	−	9722.30i	−1.24047	−	0.538749i
$689$	−18652.4	+	2109.84i	−1.03135	+	0.116660i
$690$	−3352.49	+	2727.52i	−0.184967	+	0.150485i
$691$	1650.19	−	1650.19i	0.0908483	−	0.0908483i	−0.660222	−	0.751070i	$-0.729538\pi$
$691$	1650.19	−	1650.19i	0.0908483	−	0.0908483i	0.751070	+	0.660222i	$0.229538\pi$
$692$	−4689.72	+	22570.6i	−0.257625	+	1.23989i
$693$			19909.7i			1.09135i
$694$	812.014	−	7899.56i	0.0444144	−	0.432080i
$695$	663.379	−	663.379i	0.0362063	−	0.0362063i
$696$	14644.6	−	46146.4i	0.797558	−	2.51318i
$697$	26933.5	−	26933.5i	1.46367	−	1.46367i
$698$	21897.0	−	17814.9i	1.18741	−	0.966051i
$699$	−19991.1			−1.08174
$700$	−1478.77	+	969.971i	−0.0798461	+	0.0523735i
$701$		−	9962.53i		−	0.536775i	−0.963311	−	0.268388i	$-0.913509\pi$
$701$		−	9962.53i		−	0.536775i	0.963311	−	0.268388i	$-0.0864908\pi$
$702$	−77.3467	−	7580.72i	−0.00415850	−	0.407572i
$703$		−	7176.50i		−	0.385017i
$704$	−3155.16	−	18292.5i	−0.168913	−	0.979296i
$705$	32824.3			1.75352
$706$	1522.26	+	1871.07i	0.0811489	+	0.0997432i
$707$	−1303.40	+	1303.40i	−0.0693342	+	0.0693342i
$708$	33301.2	−	21843.3i	1.76771	−	1.15949i
$709$	−14478.0	+	14478.0i	−0.766903	+	0.766903i	−0.977560	−	0.210657i	$-0.932440\pi$
$709$	−14478.0	+	14478.0i	−0.766903	+	0.766903i	0.210657	+	0.977560i	$0.432440\pi$
$710$	−11096.3	−	1140.62i	−0.586533	−	0.0602911i
$711$		−	19192.3i		−	1.01233i
$712$	3908.75	−	2025.51i	0.205740	−	0.106614i
$713$	2757.33	−	2757.33i	0.144828	−	0.144828i
$714$	17663.0	+	21710.3i	0.925800	+	1.13794i
$715$	2250.34	+	19894.4i	0.117703	+	1.04057i
$716$	18899.7	+	3926.99i	0.986475	+	0.204970i
$717$	−7228.29	−	7228.29i	−0.376493	−	0.376493i
$718$	−14583.4	−	17925.0i	−0.758003	−	0.931691i
$719$	−6501.99			−0.337251			−0.168625	−	0.985680i	$-0.553933\pi$
$719$	−6501.99			−0.337251			−0.168625	+	0.985680i	$0.553933\pi$
$720$	9490.03	+	24062.0i	0.491212	+	1.24547i
$721$	10881.3	+	10881.3i	0.562055	+	0.562055i
$722$	−1029.57	+	10016.0i	−0.0530699	+	0.516283i
$723$	7563.91	+	7563.91i	0.389080	+	0.389080i
$724$	1707.41	−	8217.40i	0.0876457	−	0.421820i
$725$		−	3773.59i		−	0.193307i
$726$	365.008	+	37.5200i	0.0186594	+	0.00191804i
$727$	−27724.7			−1.41437			−0.707187	−	0.707026i	$-0.750036\pi$
$727$	−27724.7			−1.41437			−0.707187	+	0.707026i	$0.750036\pi$
$728$	9456.74	+	14101.4i	0.481442	+	0.717904i
$729$	28501.7			1.44804
$730$	−2774.67	−	285.215i	−0.140678	−	0.0144607i
$731$			30104.8i			1.52321i
$732$	−2002.13	+	9635.81i	−0.101094	+	0.486543i
$733$	10665.7	+	10665.7i	0.537443	+	0.537443i	0.922777	−	0.385334i	$-0.125914\pi$
$733$	10665.7	+	10665.7i	0.537443	+	0.537443i	−0.385334	+	0.922777i	$0.625914\pi$
$734$	2164.69	−	21058.9i	0.108856	−	1.05899i
$735$	−5656.57	−	5656.57i	−0.283872	−	0.283872i
$736$	−2613.73	−	1469.44i	−0.130901	−	0.0735929i
$737$	7082.83			0.354002
$738$	−29543.6	−	36313.2i	−1.47360	−	1.81126i
$739$	−14431.1	−	14431.1i	−0.718343	−	0.718343i	0.249922	−	0.968266i	$-0.419595\pi$
$739$	−14431.1	−	14431.1i	−0.718343	−	0.718343i	−0.968266	+	0.249922i	$0.919595\pi$
$740$	−11530.1	−	2395.72i	−0.572775	−	0.119011i
$741$	16486.3	+	13135.6i	0.817327	+	0.651214i
$742$	−11444.0	−	14066.3i	−0.566203	−	0.695941i
$743$	15096.1	−	15096.1i	0.745388	−	0.745388i	−0.228221	−	0.973609i	$-0.573291\pi$
$743$	15096.1	−	15096.1i	0.745388	−	0.745388i	0.973609	+	0.228221i	$0.0732910\pi$
$744$	−19189.0	−	37030.1i	−0.945567	−	1.82472i
$745$			9337.28i			0.459183i
$746$	−15087.3	−	1550.86i	−0.740464	−	0.0761139i
$747$	−4814.29	+	4814.29i	−0.235804	+	0.235804i
$748$	−19146.0	+	12558.4i	−0.935890	+	0.613879i
$749$	12507.2	−	12507.2i	0.610150	−	0.610150i
$750$	−18308.9	−	22504.2i	−0.891395	−	1.09565i
$751$	19669.8			0.955741			0.477871	−	0.878430i	$-0.341409\pi$
$751$	19669.8			0.955741			0.477871	+	0.878430i	$0.341409\pi$
$752$	8355.36	+	21185.1i	0.405171	+	1.02731i
$753$			20628.2i			0.998320i
$754$	−36227.1	+	369.629i	−1.74975	+	0.0178529i
$755$		−	9007.64i		−	0.434201i
$756$	6123.72	−	4016.74i	0.294600	−	0.193237i
$757$	1667.11			0.0800426			0.0400213	−	0.999199i	$-0.487257\pi$
$757$	1667.11			0.0800426			0.0400213	+	0.999199i	$0.487257\pi$
$758$	10466.1	−	8514.97i	0.501510	−	0.408018i
$759$	−3324.85	+	3324.85i	−0.159004	+	0.159004i
$760$	−14595.1	−	4631.77i	−0.696607	−	0.221068i
$761$	−26197.2	+	26197.2i	−1.24790	+	1.24790i	−0.291249	+	0.956647i	$0.594071\pi$
$761$	−26197.2	+	26197.2i	−1.24790	+	1.24790i	−0.956647	+	0.291249i	$0.905929\pi$
$762$	4090.33	−	39792.2i	0.194458	−	1.89176i
$763$			14149.2i			0.671342i
$764$	−6587.62	+	31704.8i	−0.311953	+	1.50136i
$765$	22560.8	−	22560.8i	1.06626	−	1.06626i
$766$	26031.2	−	21178.4i	1.22787	−	0.998966i
$767$	−23308.4	−	18571.2i	−1.09728	−	0.874273i
$768$	−23436.2	+	21891.7i	−1.10115	+	1.02858i
$769$	22929.7	+	22929.7i	1.07525	+	1.07525i	0.996928	+	0.0783191i	$0.0249553\pi$
$769$	22929.7	+	22929.7i	1.07525	+	1.07525i	0.0783191	+	0.996928i	$0.475045\pi$
$770$	−15002.9	+	12206.1i	−0.702167	+	0.571268i
$771$	38918.6			1.81793
$772$	−26981.9	+	17698.2i	−1.25790	+	0.825095i
$773$	3716.38	+	3716.38i	0.172922	+	0.172922i	0.788262	−	0.615340i	$-0.210981\pi$
$773$	3716.38	+	3716.38i	0.172922	+	0.172922i	−0.615340	+	0.788262i	$0.710981\pi$
$774$	36805.5	+	3783.32i	1.70923	+	0.175696i
$775$	−2298.64	−	2298.64i	−0.106541	−	0.106541i
$776$	8813.96	+	17008.8i	0.407735	+	0.786832i
$777$			15660.7i			0.723070i
$778$	−3077.58	+	29939.8i	−0.141821	+	1.37968i
$779$	27713.2			1.27462
$780$	26607.9	−	22102.5i	1.22143	−	1.01461i
$781$	−12136.1			−0.556034
$782$	−378.200	+	3679.27i	−0.0172947	+	0.168249i
$783$			15626.8i			0.713225i
$784$	2210.93	−	5090.66i	0.100716	−	0.231900i
$785$	−18102.3	−	18102.3i	−0.823057	−	0.823057i
$786$	−15084.9	−	1550.61i	−0.684556	−	0.0703671i
$787$	26575.1	+	26575.1i	1.20369	+	1.20369i	0.973037	+	0.230650i	$0.0740853\pi$
$787$	26575.1	+	26575.1i	1.20369	+	1.20369i	0.230650	+	0.973037i	$0.425915\pi$
$788$	2570.66	+	3919.10i	0.116213	+	0.177173i
$789$	−21183.7			−0.955843
$790$	14462.3	−	11766.2i	0.651325	−	0.529904i
$791$	3460.51	+	3460.51i	0.155552	+	0.155552i
$792$	12947.6	+	24985.7i	0.580899	+	1.12100i
$793$	7317.93	−	827.760i	0.327701	−	0.0370676i
$794$	−6446.18	+	5244.47i	−0.288119	+	0.234407i
$795$	−26122.5	+	26122.5i	−1.16537	+	1.16537i
$796$	−1252.89	−	260.325i	−0.0557881	−	0.0115917i
$797$		−	17195.0i		−	0.764215i	−0.924118	−	0.382108i	$-0.875198\pi$
$797$		−	17195.0i		−	0.764215i	0.924118	−	0.382108i	$-0.124802\pi$
$798$	−2082.21	+	20256.5i	−0.0923678	+	0.898587i
$799$	19863.4	−	19863.4i	0.879494	−	0.879494i
$800$	−1225.00	+	2178.93i	−0.0541378	+	0.0962961i
$801$	−4719.29	+	4719.29i	−0.208175	+	0.208175i
$802$	560.617	−	456.106i	0.0246834	−	0.0200819i
$803$	−3034.66			−0.133363
$804$	−6711.56	−	10232.1i	−0.294401	−	0.448829i
$805$			3124.22i			0.136788i
$806$	−21842.2	+	22292.5i	−0.954539	+	0.974219i
$807$			12473.9i			0.544116i
$808$	−788.082	+	2483.32i	−0.0343127	+	0.108122i
$809$	−19454.5			−0.845467			−0.422733	−	0.906254i	$-0.638929\pi$
$809$	−19454.5			−0.845467			−0.422733	+	0.906254i	$0.638929\pi$
$810$	10062.3	+	12368.0i	0.436487	+	0.536503i
$811$	−2380.03	+	2380.03i	−0.103051	+	0.103051i	−0.756752	−	0.653702i	$-0.773215\pi$
$811$	−2380.03	+	2380.03i	−0.103051	+	0.103051i	0.653702	+	0.756752i	$0.273215\pi$
$812$	−19195.4	−	29264.4i	−0.829589	−	1.26475i
$813$	27356.7	−	27356.7i	1.18012	−	1.18012i
$814$	−12745.1	−	1310.10i	−0.548790	−	0.0564114i
$815$			16668.9i			0.716423i
$816$	36284.7	+	15758.8i	1.55664	+	0.676065i
$817$	−15488.1	+	15488.1i	−0.663231	+	0.663231i
$818$	485.093	+	596.246i	0.0207346	+	0.0254856i
$819$	−20131.4	−	16040.0i	−0.858913	−	0.684349i
$820$	9251.44	−	44525.2i	0.393993	−	1.89620i
$821$	22630.8	+	22630.8i	0.962024	+	0.962024i	0.999305	−	0.0372811i	$-0.0118697\pi$
$821$	22630.8	+	22630.8i	0.962024	+	0.962024i	−0.0372811	+	0.999305i	$0.511870\pi$
$822$	31302.2	+	38474.8i	1.32821	+	1.63256i
$823$	−28020.6			−1.18680			−0.593400	−	0.804907i	$-0.702215\pi$
$823$	−28020.6			−1.18680			−0.593400	+	0.804907i	$0.702215\pi$
$824$	20731.8	+	6579.24i	0.876488	+	0.278154i
$825$	2771.75	+	2771.75i	0.116970	+	0.116970i
$826$	2943.84	−	28638.7i	0.124006	−	1.20638i
$827$	−6750.61	−	6750.61i	−0.283847	−	0.283847i	0.550794	−	0.834641i	$-0.314325\pi$
$827$	−6750.61	−	6750.61i	−0.283847	−	0.283847i	−0.834641	+	0.550794i	$0.814325\pi$
$828$	4450.67	+	924.761i	0.186801	+	0.0388136i
$829$			34588.0i			1.44908i	0.689232	+	0.724541i	$0.257948\pi$
$829$			34588.0i			1.44908i	−0.689232	+	0.724541i	$0.742052\pi$
$830$	−6579.30	−	676.302i	−0.275146	−	0.0282829i
$831$	−37454.4			−1.56351
$832$	21038.1	+	11546.8i	0.876641	+	0.481145i
$833$	−6846.05			−0.284756
$834$	−1754.18	−	180.316i	−0.0728323	−	0.00748660i
$835$			5575.42i			0.231072i
$836$	−16311.1	−	3389.11i	−0.674796	−	0.140209i
$837$	9518.88	+	9518.88i	0.393095	+	0.393095i
$838$	−1113.73	+	10834.7i	−0.0459106	+	0.446635i
$839$	1054.50	+	1054.50i	0.0433915	+	0.0433915i	0.728470	−	0.685078i	$-0.240232\pi$
$839$	1054.50	+	1054.50i	0.0433915	+	0.0433915i	−0.685078	+	0.728470i	$0.740232\pi$
$840$	31849.8	+	10107.6i	1.30824	+	0.415171i
$841$	50289.1			2.06196
$842$	−2399.12	−	2948.85i	−0.0981938	−	0.120694i
$843$	5834.88	+	5834.88i	0.238391	+	0.238391i
$844$	2413.34	−	11614.9i	0.0984250	−	0.473698i
$845$	−21929.0	−	13752.3i	−0.892757	−	0.559872i
$846$	−21788.3	−	26780.8i	−0.885457	−	1.08835i
$847$	187.560	−	187.560i	0.00760878	−	0.00760878i
$848$	−23509.1	−	10210.3i	−0.952013	−	0.413469i
$849$		−	69305.7i		−	2.80161i
$850$	3067.22	+	315.286i	0.123770	+	0.0127226i
$851$	−1463.43	+	1463.43i	−0.0589491	+	0.0589491i
$852$	11499.9	+	17532.2i	0.462418	+	0.704980i
$853$	19643.1	−	19643.1i	0.788474	−	0.788474i	−0.192770	−	0.981244i	$-0.561747\pi$
$853$	19643.1	−	19643.1i	0.788474	−	0.788474i	0.981244	+	0.192770i	$0.0617471\pi$
$854$	4489.85	+	5518.65i	0.179906	+	0.221129i
$855$	23213.9			0.928537
$856$	7562.29	−	23829.5i	0.301955	−	0.951489i
$857$			20116.1i			0.801812i	0.916119	+	0.400906i	$0.131305\pi$
$857$			20116.1i			0.801812i	−0.916119	+	0.400906i	$0.868695\pi$
$858$	26337.8	−	26880.8i	1.04797	−	1.06958i
$859$			32320.3i			1.28377i	0.766803	+	0.641883i	$0.221847\pi$
$859$			32320.3i			1.28377i	−0.766803	+	0.641883i	$0.778153\pi$
$860$	19713.5	+	30054.2i	0.781655	+	1.19167i
$861$	−60476.3			−2.39376
$862$	21122.3	−	17184.7i	0.834605	−	0.679016i
$863$	13386.6	−	13386.6i	0.528025	−	0.528025i	−0.391958	−	0.919983i	$-0.628202\pi$
$863$	13386.6	−	13386.6i	0.528025	−	0.528025i	0.919983	+	0.391958i	$0.128202\pi$
$864$	5072.83	−	9023.15i	0.199747	−	0.355294i
$865$	24006.3	−	24006.3i	0.943627	−	0.943627i
$866$	4023.21	−	39139.2i	0.157869	−	1.53580i
$867$		−	10329.5i		−	0.404623i
$868$	−29518.7	−	6133.40i	−1.15430	−	0.239840i
$869$	14343.1	−	14343.1i	0.559903	−	0.559903i
$870$	−55308.1	+	44997.5i	−2.15531	+	1.75351i
$871$	−5706.18	+	7161.72i	−0.221982	+	0.278606i
$872$	9201.41	+	17756.5i	0.357338	+	0.689577i
$873$	−20535.9	−	20535.9i	−0.796144	−	0.796144i
$874$	−2087.46	+	1698.31i	−0.0807888	+	0.0657280i
$875$	−20971.8			−0.810260
$876$	2875.58	+	4383.98i	0.110910	+	0.169088i
$877$	−12721.1	−	12721.1i	−0.489807	−	0.489807i	0.418438	−	0.908245i	$-0.362578\pi$
$877$	−12721.1	−	12721.1i	−0.489807	−	0.489807i	−0.908245	+	0.418438i	$0.862578\pi$
$878$	10857.7	+	1116.09i	0.417346	+	0.0429000i
$879$	22110.3	+	22110.3i	0.848421	+	0.848421i
$880$	−10890.2	+	25074.7i	−0.417168	+	0.960530i
$881$			24612.2i			0.941208i	0.882344	+	0.470604i	$0.155964\pi$
$881$			24612.2i			0.941208i	−0.882344	+	0.470604i	$0.844036\pi$
$882$	−860.356	+	8369.85i	−0.0328454	+	0.319532i
$883$	−6348.96			−0.241970			−0.120985	−	0.992654i	$-0.538605\pi$
$883$	−6348.96			−0.241970			−0.120985	+	0.992654i	$0.538605\pi$
$884$	2726.36	−	29476.7i	0.103730	−	1.12150i
$885$	−58652.2			−2.22776
$886$	−1989.90	+	19358.5i	−0.0754537	+	0.734041i
$887$		−	13629.4i		−	0.515932i	−0.966154	−	0.257966i	$-0.916948\pi$
$887$		−	13629.4i		−	0.515932i	0.966154	−	0.257966i	$-0.0830523\pi$
$888$	10184.4	+	19653.4i	0.384871	+	0.742710i
$889$	−20447.3	−	20447.3i	−0.771405	−	0.771405i
$890$	−6449.48	−	662.956i	−0.242907	−	0.0249689i
$891$	12266.0	+	12266.0i	0.461198	+	0.461198i
$892$	−14485.1	+	9501.21i	−0.543718	+	0.356641i
$893$	20438.3			0.765894
$894$	13614.3	−	11076.3i	0.509319	−	0.414371i
$895$	−20101.9	−	20101.9i	−0.750763	−	0.750763i
$896$	1583.81	+	23129.0i	0.0590530	+	0.862372i
$897$	−683.264	−	6040.49i	−0.0254331	−	0.224845i
$898$	−13258.0	+	10786.4i	−0.492678	+	0.400832i
$899$	45489.3	−	45489.3i	1.68760	−	1.68760i
$900$	770.925	−	3710.30i	0.0285528	−	0.137418i
$901$			31615.7i			1.16900i
$902$	5059.14	−	49217.2i	0.186753	−	1.81680i
$903$	33798.5	−	33798.5i	1.24556	−	1.24556i
$904$	6593.19	+	2092.35i	0.242573	+	0.0769807i
$905$	−8740.10	+	8740.10i	−0.321028	+	0.321028i
$906$	−13133.7	+	10685.3i	−0.481609	+	0.391826i
$907$	−33608.2			−1.23037			−0.615183	−	0.788384i	$-0.710918\pi$
$907$	−33608.2			−1.23037			−0.615183	+	0.788384i	$0.710918\pi$
$908$	−16169.6	+	10606.2i	−0.590978	+	0.387641i
$909$		−	3949.78i		−	0.144121i
$910$	−255.115	−	25003.7i	−0.00929337	−	0.910839i
$911$			7660.22i			0.278589i	0.990251	+	0.139294i	$0.0444834\pi$
$911$			7660.22i			0.278589i	−0.990251	+	0.139294i	$0.955517\pi$
$912$	10560.0	+	26775.0i	0.383418	+	0.972159i
$913$	−7195.78			−0.260838
$914$	5047.46	+	6204.03i	0.182664	+	0.224520i
$915$	10248.7	−	10248.7i	0.370287	−	0.370287i
$916$	−14116.6	+	9259.53i	−0.509199	+	0.333999i
$917$	−7751.41	+	7751.41i	−0.279143	+	0.279143i
$918$	−12701.6	−	1305.63i	−0.456662	−	0.0469413i
$919$		−	24824.8i		−	0.891073i	−0.895264	−	0.445537i	$-0.853013\pi$
$919$		−	24824.8i		−	0.891073i	0.895264	−	0.445537i	$-0.146987\pi$
$920$	2031.73	+	3920.75i	0.0728087	+	0.140503i
$921$	−51822.8	+	51822.8i	−1.85409	+	1.85409i
$922$	−8944.47	−	10994.0i	−0.319491	−	0.392698i
$923$	9777.23	−	12271.2i	0.348669	−	0.437608i
$924$	35594.4	+	7395.80i	1.26728	+	0.263316i
$925$	1219.99	+	1219.99i	0.0433653	+	0.0433653i
$926$	11808.1	+	14513.7i	0.419046	+	0.515066i
$927$	−32974.4			−1.16831
$928$	−43120.3	−	24242.3i	−1.52532	−	0.857535i
$929$	27381.9	+	27381.9i	0.967030	+	0.967030i	0.999474	−	0.0324437i	$-0.0103290\pi$
$929$	27381.9	+	27381.9i	0.967030	+	0.967030i	−0.0324437	+	0.999474i	$0.510329\pi$
$930$	−6280.61	+	61100.1i	−0.221451	+	2.15435i
$931$	−3522.11	−	3522.11i	−0.123988	−	0.123988i
$932$	−4155.37	+	19998.9i	−0.146045	+	0.702882i
$933$		−	50990.6i		−	1.78924i
$934$	3546.94	+	364.598i	0.124261	+	0.0127730i
$935$	33721.0			1.17946
$936$	−35695.0	−	7037.59i	−1.24650	−	0.245759i
$937$	35295.2			1.23057			0.615284	−	0.788305i	$-0.289041\pi$
$937$	35295.2			1.23057			0.615284	+	0.788305i	$0.289041\pi$
$938$	−8799.51	−	904.522i	−0.306305	−	0.0314858i
$939$		−	34210.0i		−	1.18892i
$940$	6822.89	−	32837.1i	0.236743	−	1.13939i
$941$	14419.7	+	14419.7i	0.499541	+	0.499541i	0.911295	−	0.411754i	$-0.135084\pi$
$941$	14419.7	+	14419.7i	0.499541	+	0.499541i	−0.411754	+	0.911295i	$0.635084\pi$
$942$	−4920.47	+	47868.1i	−0.170188	+	1.65565i
$943$	−5651.26	−	5651.26i	−0.195154	−	0.195154i
$944$	−14929.8	−	37854.6i	−0.514749	−	1.30515i
$945$	−10785.5			−0.371272
$946$	24678.6	+	30333.5i	0.848173	+	1.04252i
$947$	4592.42	+	4592.42i	0.157586	+	0.157586i	0.781496	−	0.623910i	$-0.214457\pi$
$947$	4592.42	+	4592.42i	0.157586	+	0.157586i	−0.623910	+	0.781496i	$0.714457\pi$
$948$	−34311.8	−	7129.30i	−1.17552	−	0.244250i
$949$	2444.83	−	3068.45i	0.0836274	−	0.104959i
$950$	1415.79	+	1740.21i	0.0483520	+	0.0594313i
$951$	−24667.6	+	24667.6i	−0.841117	+	0.841117i
$952$	25390.2	−	13157.2i	0.864391	−	0.447927i
$953$		−	45329.1i		−	1.54077i	−0.637579	−	0.770385i	$-0.720064\pi$
$953$		−	45329.1i		−	1.54077i	0.637579	−	0.770385i	$-0.279936\pi$
$954$	38652.7	+	3973.20i	1.31177	+	0.134840i
$955$	33721.5	−	33721.5i	1.14262	−	1.14262i
$956$	−8733.58	+	5728.62i	−0.295465	+	0.193804i
$957$	−54852.1	+	54852.1i	−1.85279	+	1.85279i
$958$	24449.1	+	30051.3i	0.824545	+	1.01348i
$959$	35855.0			1.20732
$960$	46543.1	−	8027.92i	1.56476	−	0.269896i
$961$		−	25627.6i		−	0.860247i
$962$	11592.6	−	11831.6i	0.388523	−	0.396533i
$963$			37901.3i			1.26828i
$964$	9139.10	−	5994.62i	0.305343	−	0.200284i
$965$	47522.1			1.58528
$966$	4555.30	−	3706.09i	0.151723	−	0.123439i
$967$	26619.2	−	26619.2i	0.885228	−	0.885228i	−0.108832	−	0.994060i	$-0.534711\pi$
$967$	26619.2	−	26619.2i	0.885228	−	0.885228i	0.994060	+	0.108832i	$0.0347112\pi$
$968$	113.406	−	357.352i	0.00376549	−	0.0118654i
$969$	25104.6	−	25104.6i	0.832275	−	0.832275i
$970$	2884.84	−	28064.7i	0.0954913	−	0.928974i
$971$		−	37752.3i		−	1.24771i	−0.781539	−	0.623857i	$-0.785565\pi$
$971$		−	37752.3i		−	1.24771i	0.781539	−	0.623857i	$-0.214435\pi$
$972$	8609.66	−	41436.4i	0.284110	−	1.36736i
$973$	−901.386	+	901.386i	−0.0296990	+	0.0296990i
$974$	5197.06	−	4228.21i	0.170970	−	0.139097i
$975$	−5035.65	+	569.602i	−0.165405	+	0.0187096i
$976$	9223.40	+	4005.82i	0.302494	+	0.131376i
$977$	−10803.3	−	10803.3i	−0.353766	−	0.353766i	0.507743	−	0.861509i	$-0.330480\pi$
$977$	−10803.3	−	10803.3i	−0.353766	−	0.353766i	−0.861509	+	0.507743i	$0.830480\pi$
$978$	24304.2	−	19773.4i	0.794645	−	0.646506i
$979$	−7053.78			−0.230276
$980$	−6834.55	+	4482.99i	−0.222777	+	0.146126i
$981$	−21438.6	−	21438.6i	−0.697739	−	0.697739i
$982$	−47991.8	−	4933.18i	−1.55955	−	0.160310i
$983$	−19472.5	−	19472.5i	−0.631816	−	0.631816i	0.316707	−	0.948523i	$-0.397423\pi$
$983$	−19472.5	−	19472.5i	−0.631816	−	0.631816i	−0.948523	+	0.316707i	$0.897423\pi$
$984$	−75894.8	+	39328.6i	−2.45878	+	1.27414i
$985$		−	6902.57i		−	0.223283i
$986$	−6239.40	+	60699.1i	−0.201524	+	1.96050i
$987$	−44601.0			−1.43836
$988$	16567.6	−	13762.3i	0.533488	−	0.443156i
$989$	6316.65			0.203092
$990$	4237.78	−	41226.7i	0.136046	−	1.32351i
$991$			4706.86i			0.150876i	0.997150	+	0.0754381i	$0.0240355\pi$
$991$			4706.86i			0.150876i	−0.997150	+	0.0754381i	$0.975964\pi$
$992$	−41033.2	+	11499.3i	−1.31331	+	0.368049i
$993$	53530.6	+	53530.6i	1.71072	+	1.71072i
$994$	15077.5	+	1549.85i	0.481116	+	0.0494550i
$995$	1332.58	+	1332.58i	0.0424579	+	0.0424579i
$996$	6818.58	+	10395.3i	0.216923	+	0.330710i
$997$	6926.54			0.220026			0.110013	−	0.993930i	$-0.464911\pi$
$997$	6926.54			0.220026			0.110013	+	0.993930i	$0.464911\pi$
$998$	13646.7	−	11102.7i	0.432846	−	0.352154i
$999$	−5052.07	−	5052.07i	−0.160000	−	0.160000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	52.4.f.b.47.18	yes	36
4.3	odd	2	inner	52.4.f.b.47.10	yes	36
13.5	odd	4	inner	52.4.f.b.31.10	✓	36
52.31	even	4	inner	52.4.f.b.31.18	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.4.f.b.31.10	✓	36	13.5	odd	4	inner
52.4.f.b.31.18	yes	36	52.31	even	4	inner
52.4.f.b.47.10	yes	36	4.3	odd	2	inner
52.4.f.b.47.18	yes	36	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 52 = 2^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	52.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.81360 + 0.289217i) q^{2} +7.82965i q^{3} +(7.83271 + 1.62748i) q^{4} +(-8.33093 - 8.33093i) q^{5} +(-2.26447 + 22.0295i) q^{6} +(11.3199 + 11.3199i) q^{7} +(21.5674 + 6.84443i) q^{8} -34.3035 q^{9} +(-21.0305 - 25.8494i) q^{10} +(-25.6362 - 25.6362i) q^{11} +(-12.7426 + 61.3274i) q^{12} +(46.5752 - 5.26830i) q^{13} +(28.5758 + 35.1236i) q^{14} +(65.2283 - 65.2283i) q^{15} +(58.7026 + 25.4952i) q^{16} -78.9448i q^{17} +(-96.5163 - 9.92113i) q^{18} +(40.6150 - 40.6150i) q^{19} +(-51.6953 - 78.8122i) q^{20} +(-88.6309 + 88.6309i) q^{21} +(-64.7157 - 79.5445i) q^{22} -16.5644 q^{23} +(-53.5895 + 168.865i) q^{24} +13.8089i q^{25} +(132.568 - 1.35260i) q^{26} -57.1838i q^{27} +(70.2426 + 107.088i) q^{28} -273.273 q^{29} +(202.392 - 164.661i) q^{30} +(-166.461 + 166.461i) q^{31} +(157.792 + 88.7110i) q^{32} +(200.723 - 200.723i) q^{33} +(22.8321 - 222.119i) q^{34} -188.611i q^{35} +(-268.689 - 55.8282i) q^{36} +(88.3479 - 88.3479i) q^{37} +(126.021 - 102.528i) q^{38} +(41.2490 + 364.667i) q^{39} +(-122.656 - 236.697i) q^{40} +(341.169 + 341.169i) q^{41} +(-275.006 + 223.739i) q^{42} -381.339 q^{43} +(-159.079 - 242.523i) q^{44} +(285.780 + 285.780i) q^{45} +(-46.6056 - 4.79069i) q^{46} +(251.611 + 251.611i) q^{47} +(-199.618 + 459.621i) q^{48} -86.7195i q^{49} +(-3.99375 + 38.8527i) q^{50} +618.110 q^{51} +(373.384 + 34.5351i) q^{52} -400.479 q^{53} +(16.5385 - 160.892i) q^{54} +427.147i q^{55} +(166.663 + 321.619i) q^{56} +(318.001 + 318.001i) q^{57} +(-768.881 - 79.0350i) q^{58} +(-449.591 - 449.591i) q^{59} +(617.072 - 404.757i) q^{60} +157.121 q^{61} +(-516.499 + 420.212i) q^{62} +(-388.312 - 388.312i) q^{63} +(418.308 + 295.233i) q^{64} +(-431.904 - 344.125i) q^{65} +(622.806 - 506.701i) q^{66} +(-138.141 + 138.141i) q^{67} +(128.481 - 618.351i) q^{68} -129.693i q^{69} +(54.5493 - 530.675i) q^{70} +(236.698 - 236.698i) q^{71} +(-739.838 - 234.788i) q^{72} +(59.1869 - 59.1869i) q^{73} +(274.128 - 223.024i) q^{74} -108.119 q^{75} +(384.225 - 252.025i) q^{76} -580.399i q^{77} +(10.5904 + 1037.96i) q^{78} +559.485i q^{79} +(-276.649 - 701.446i) q^{80} -478.465 q^{81} +(861.243 + 1058.59i) q^{82} +(140.344 - 140.344i) q^{83} +(-838.465 + 549.975i) q^{84} +(-657.684 + 657.684i) q^{85} +(-1072.94 - 110.290i) q^{86} -2139.63i q^{87} +(-377.442 - 728.372i) q^{88} +(137.575 - 137.575i) q^{89} +(721.419 + 886.723i) q^{90} +(586.863 + 467.590i) q^{91} +(-129.744 - 26.9582i) q^{92} +(-1303.33 - 1303.33i) q^{93} +(635.163 + 780.703i) q^{94} -676.722 q^{95} +(-694.576 + 1235.46i) q^{96} +(598.653 + 598.653i) q^{97} +(25.0807 - 243.994i) q^{98} +(879.412 + 879.412i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 2 q^{2} - 20 q^{5} - 16 q^{6} - 40 q^{8} - 332 q^{9} - 96 q^{13} + 204 q^{14} + 52 q^{16} + 330 q^{18} + 500 q^{20} + 224 q^{21} - 48 q^{22} - 496 q^{24} + 570 q^{26} - 356 q^{28} + 560 q^{29} + 292 q^{32}+ \cdots + 3226 q^{98}+O(q^{100}) \) 36 * q + 2 * q^2 - 20 * q^5 - 16 * q^6 - 40 * q^8 - 332 * q^9 - 96 * q^13 + 204 * q^14 + 52 * q^16 + 330 * q^18 + 500 * q^20 + 224 * q^21 - 48 * q^22 - 496 * q^24 + 570 * q^26 - 356 * q^28 + 560 * q^29 + 292 * q^32 + 104 * q^33 - 416 * q^34 - 788 * q^37 - 2788 * q^40 + 1124 * q^41 - 1172 * q^42 - 156 * q^44 - 972 * q^45 - 668 * q^46 + 1332 * q^48 + 1354 * q^50 - 164 * q^52 + 1208 * q^53 + 2272 * q^54 - 1248 * q^57 - 2972 * q^58 + 692 * q^60 + 2632 * q^61 + 596 * q^65 + 3312 * q^66 + 2948 * q^68 - 1008 * q^70 - 908 * q^72 - 196 * q^73 - 1504 * q^74 - 3472 * q^76 - 2688 * q^78 - 1096 * q^80 - 764 * q^81 + 3744 * q^84 + 600 * q^85 - 3952 * q^86 - 2748 * q^89 - 1224 * q^92 - 6128 * q^93 + 2884 * q^94 + 4792 * q^96 - 1820 * q^97 + 3226 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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