LMFDB - Embedded newform 26.4.c.b.3.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [26,4,Mod(3,26)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(26, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("26.3"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	26.c (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.53404966015$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{217})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 55x^{2} + 54x + 2916 $ x^4 - x^3 + 55x^2 + 54x + 2916
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			3.2
Root			$3.93273 + 6.81169i$ of defining polynomial
Character	$\chi$	$=$	26.3
Dual form			26.4.c.b.9.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.73205i) q^{2} +(4.43273 + 7.67771i) q^{3} +(-2.00000 + 3.46410i) q^{4} +3.86546 q^{5} +(8.86546 - 15.3554i) q^{6} +(7.56727 - 13.1069i) q^{7} +8.00000 q^{8} +(-25.7982 + 44.6838i) q^{9} +(-3.86546 - 6.69517i) q^{10} +(-27.0291 - 46.8158i) q^{11} -35.4618 q^{12} +(-19.7982 + 42.4857i) q^{13} -30.2691 q^{14} +(17.1345 + 29.6779i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(61.9618 - 107.321i) q^{17} +103.193 q^{18} +(-4.43273 + 7.67771i) q^{19} +(-7.73092 + 13.3903i) q^{20} +134.175 q^{21} +(-54.0582 + 93.6316i) q^{22} +(-19.2982 - 33.4254i) q^{23} +(35.4618 + 61.4217i) q^{24} -110.058 q^{25} +(93.3855 - 8.19419i) q^{26} -218.058 q^{27} +(30.2691 + 52.4276i) q^{28} +(93.6928 + 162.281i) q^{29} +(34.2691 - 59.3558i) q^{30} -36.7710 q^{31} +(-16.0000 + 27.7128i) q^{32} +(239.625 - 415.044i) q^{33} -247.847 q^{34} +(29.2510 - 50.6642i) q^{35} +(-103.193 - 178.735i) q^{36} +(160.769 + 278.460i) q^{37} +17.7309 q^{38} +(-413.953 + 36.3226i) q^{39} +30.9237 q^{40} +(13.1546 + 22.7844i) q^{41} +(-134.175 - 232.397i) q^{42} +(-68.8182 + 119.197i) q^{43} +216.233 q^{44} +(-99.7219 + 172.723i) q^{45} +(-38.5964 + 66.8509i) q^{46} -300.466 q^{47} +(70.9237 - 122.843i) q^{48} +(56.9728 + 98.6799i) q^{49} +(110.058 + 190.626i) q^{50} +1098.64 q^{51} +(-107.578 - 153.554i) q^{52} -260.135 q^{53} +(218.058 + 377.688i) q^{54} +(-104.480 - 180.965i) q^{55} +(60.5382 - 104.855i) q^{56} -78.5964 q^{57} +(187.386 - 324.561i) q^{58} +(123.029 - 213.093i) q^{59} -137.076 q^{60} +(-45.6526 + 79.0727i) q^{61} +(36.7710 + 63.6893i) q^{62} +(390.444 + 676.268i) q^{63} +64.0000 q^{64} +(-76.5291 + 164.227i) q^{65} -958.502 q^{66} +(-205.262 - 355.524i) q^{67} +(247.847 + 429.284i) q^{68} +(171.087 - 296.332i) q^{69} -117.004 q^{70} +(212.222 - 367.579i) q^{71} +(-206.386 + 357.470i) q^{72} -421.982 q^{73} +(321.538 - 556.920i) q^{74} +(-487.858 - 844.995i) q^{75} +(-17.7309 - 30.7109i) q^{76} -818.146 q^{77} +(476.865 + 680.665i) q^{78} +733.542 q^{79} +(-30.9237 - 53.5614i) q^{80} +(-270.042 - 467.727i) q^{81} +(26.3092 - 45.5689i) q^{82} -616.843 q^{83} +(-268.349 + 464.795i) q^{84} +(239.511 - 414.845i) q^{85} +275.273 q^{86} +(-830.629 + 1438.69i) q^{87} +(-216.233 - 374.526i) q^{88} +(103.585 + 179.415i) q^{89} +398.887 q^{90} +(407.037 + 580.993i) q^{91} +154.386 q^{92} +(-162.996 - 282.317i) q^{93} +(300.466 + 520.422i) q^{94} +(-17.1345 + 29.6779i) q^{95} -283.695 q^{96} +(370.742 - 642.144i) q^{97} +(113.946 - 197.360i) q^{98} +2789.21 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 3 q^{3} - 8 q^{4} - 14 q^{5} + 6 q^{6} + 45 q^{7} + 32 q^{8} - 59 q^{9} + 14 q^{10} - 5 q^{11} - 24 q^{12} - 35 q^{13} - 180 q^{14} + 98 q^{15} - 32 q^{16} + 130 q^{17} + 236 q^{18} - 3 q^{19}+ \cdots + 4852 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + 3 * q^3 - 8 * q^4 - 14 * q^5 + 6 * q^6 + 45 * q^7 + 32 * q^8 - 59 * q^9 + 14 * q^10 - 5 * q^11 - 24 * q^12 - 35 * q^13 - 180 * q^14 + 98 * q^15 - 32 * q^16 + 130 * q^17 + 236 * q^18 - 3 * q^19 + 28 * q^20 - 82 * q^21 - 10 * q^22 - 33 * q^23 + 24 * q^24 - 234 * q^25 + 20 * q^26 - 666 * q^27 + 180 * q^28 + 198 * q^29 + 196 * q^30 + 560 * q^31 - 64 * q^32 + 767 * q^33 - 520 * q^34 - 266 * q^35 - 236 * q^36 + 702 * q^37 + 12 * q^38 - 1317 * q^39 - 112 * q^40 - 242 * q^41 + 82 * q^42 + 93 * q^43 + 40 * q^44 - 119 * q^45 - 66 * q^46 + 448 * q^47 + 48 * q^48 - 435 * q^49 + 234 * q^50 + 2126 * q^51 + 100 * q^52 - 1070 * q^53 + 666 * q^54 - 742 * q^55 + 360 * q^56 - 226 * q^57 + 396 * q^58 + 389 * q^59 - 784 * q^60 - 654 * q^61 - 560 * q^62 + 1002 * q^63 + 256 * q^64 - 203 * q^65 - 3068 * q^66 + 107 * q^67 + 520 * q^68 + 375 * q^69 + 1064 * q^70 + 569 * q^71 - 472 * q^72 - 1246 * q^73 + 1404 * q^74 - 935 * q^75 - 12 * q^76 + 1294 * q^77 + 1878 * q^78 + 1520 * q^79 + 112 * q^80 + 334 * q^81 - 484 * q^82 - 3528 * q^83 + 164 * q^84 + 413 * q^85 - 372 * q^86 - 1599 * q^87 - 40 * q^88 + 871 * q^89 + 476 * q^90 - 1539 * q^91 + 264 * q^92 - 2184 * q^93 - 448 * q^94 - 98 * q^95 - 192 * q^96 + 879 * q^97 - 870 * q^98 + 4852 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$3$	4.43273	+	7.67771i	0.853079	+	1.47758i	0.878416	+	0.477898i	$0.158601\pi$
$3$	4.43273	+	7.67771i	0.853079	+	1.47758i	−0.0253362	+	0.999679i	$0.508066\pi$
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	3.86546			0.345737			0.172869	−	0.984945i	$-0.444696\pi$
$5$	3.86546			0.345737			0.172869	+	0.984945i	$0.444696\pi$
$6$	8.86546	−	15.3554i	0.603218	−	1.04480i
$7$	7.56727	−	13.1069i	0.408594	−	0.707706i	−0.586138	−	0.810211i	$-0.699352\pi$
$7$	7.56727	−	13.1069i	0.408594	−	0.707706i	0.994732	+	0.102505i	$0.0326858\pi$
$8$	8.00000			0.353553
$9$	−25.7982	+	44.6838i	−0.955489	+	1.65495i
$10$	−3.86546	−	6.69517i	−0.122237	−	0.211720i
$11$	−27.0291	−	46.8158i	−0.740871	−	1.28323i	−0.952099	−	0.305790i	$-0.901080\pi$
$11$	−27.0291	−	46.8158i	−0.740871	−	1.28323i	0.211228	−	0.977437i	$-0.432254\pi$
$12$	−35.4618			−0.853079
$13$	−19.7982	+	42.4857i	−0.422387	+	0.906416i
$13$	−19.7982	+	42.4857i	−0.422387	+	0.906416i
$14$	−30.2691			−0.577839
$15$	17.1345	+	29.6779i	0.294941	+	0.510853i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	61.9618	−	107.321i	0.883997	−	1.53113i	0.0371386	−	0.999310i	$-0.488176\pi$
$17$	61.9618	−	107.321i	0.883997	−	1.53113i	0.846859	−	0.531818i	$-0.178491\pi$
$18$	103.193			1.35126
$19$	−4.43273	+	7.67771i	−0.0535231	+	0.0927046i	−0.891546	−	0.452931i	$-0.850378\pi$
$19$	−4.43273	+	7.67771i	−0.0535231	+	0.0927046i	0.838023	+	0.545636i	$0.183712\pi$
$20$	−7.73092	+	13.3903i	−0.0864343	+	0.149709i
$21$	134.175			1.39425
$22$	−54.0582	+	93.6316i	−0.523875	+	0.907378i
$23$	−19.2982	−	33.4254i	−0.174954	−	0.303030i	0.765191	−	0.643803i	$-0.222644\pi$
$23$	−19.2982	−	33.4254i	−0.174954	−	0.303030i	−0.940145	+	0.340773i	$0.889311\pi$
$24$	35.4618	+	61.4217i	0.301609	+	0.522402i
$25$	−110.058			−0.880466
$26$	93.3855	−	8.19419i	0.704400	−	0.0618082i
$27$	−218.058			−1.55427
$28$	30.2691	+	52.4276i	0.204297	+	0.353853i
$29$	93.6928	+	162.281i	0.599942	+	1.03913i	0.992829	+	0.119543i	$0.0381429\pi$
$29$	93.6928	+	162.281i	0.599942	+	1.03913i	−0.392887	+	0.919587i	$0.628524\pi$
$30$	34.2691	−	59.3558i	0.208555	−	0.361228i
$31$	−36.7710			−0.213041			−0.106521	−	0.994311i	$-0.533971\pi$
$31$	−36.7710			−0.213041			−0.106521	+	0.994311i	$0.533971\pi$
$32$	−16.0000	+	27.7128i	−0.0883883	+	0.153093i
$33$	239.625	−	415.044i	1.26404	−	2.18939i
$34$	−247.847			−1.25016
$35$	29.2510	−	50.6642i	0.141266	−	0.244680i
$36$	−103.193	−	178.735i	−0.477744	−	0.827477i
$37$	160.769	+	278.460i	0.714332	+	1.23726i	0.963217	+	0.268726i	$0.0866025\pi$
$37$	160.769	+	278.460i	0.714332	+	1.23726i	−0.248885	+	0.968533i	$0.580064\pi$
$38$	17.7309			0.0756930
$39$	−413.953	+	36.3226i	−1.69963	+	0.149135i
$40$	30.9237			0.122237
$41$	13.1546	+	22.7844i	0.0501074	+	0.0867886i	0.889991	−	0.455978i	$-0.150710\pi$
$41$	13.1546	+	22.7844i	0.0501074	+	0.0867886i	−0.839884	+	0.542766i	$0.817377\pi$
$42$	−134.175	−	232.397i	−0.492943	−	0.853802i
$43$	−68.8182	+	119.197i	−0.244062	+	0.422729i	−0.961868	−	0.273515i	$-0.911814\pi$
$43$	−68.8182	+	119.197i	−0.244062	+	0.422729i	0.717805	+	0.696244i	$0.245147\pi$
$44$	216.233			0.740871
$45$	−99.7219	+	172.723i	−0.330348	+	0.572179i
$46$	−38.5964	+	66.8509i	−0.123711	+	0.214274i
$47$	−300.466			−0.932499			−0.466249	−	0.884653i	$-0.654395\pi$
$47$	−300.466			−0.932499			−0.466249	+	0.884653i	$0.654395\pi$
$48$	70.9237	−	122.843i	0.213270	−	0.369394i
$49$	56.9728	+	98.6799i	0.166102	+	0.287696i
$50$	110.058	+	190.626i	0.311292	+	0.539173i
$51$	1098.64			3.01648
$52$	−107.578	−	153.554i	−0.286893	−	0.409503i
$53$	−260.135			−0.674193			−0.337096	−	0.941470i	$-0.609445\pi$
$53$	−260.135			−0.674193			−0.337096	+	0.941470i	$0.609445\pi$
$54$	218.058	+	377.688i	0.549518	+	0.951793i
$55$	−104.480	−	180.965i	−0.256147	−	0.443659i
$56$	60.5382	−	104.855i	0.144460	−	0.250212i
$57$	−78.5964			−0.182638
$58$	187.386	−	324.561i	0.424223	−	0.734775i
$59$	123.029	−	213.093i	0.271475	−	0.470209i	−0.697765	−	0.716327i	$-0.745822\pi$
$59$	123.029	−	213.093i	0.271475	−	0.470209i	0.969240	+	0.246118i	$0.0791552\pi$
$60$	−137.076			−0.294941
$61$	−45.6526	+	79.0727i	−0.0958233	+	0.165971i	−0.909952	−	0.414714i	$-0.863882\pi$
$61$	−45.6526	+	79.0727i	−0.0958233	+	0.165971i	0.814129	+	0.580685i	$0.197215\pi$
$62$	36.7710	+	63.6893i	0.0753214	+	0.130460i
$63$	390.444	+	676.268i	0.780814	+	1.35241i
$64$	64.0000			0.125000
$65$	−76.5291	+	164.227i	−0.146035	+	0.313382i
$66$	−958.502			−1.78763
$67$	−205.262	−	355.524i	−0.374280	−	0.648272i	0.615939	−	0.787794i	$-0.288777\pi$
$67$	−205.262	−	355.524i	−0.374280	−	0.648272i	−0.990219	+	0.139522i	$0.955443\pi$
$68$	247.847	+	429.284i	0.441999	+	0.765564i
$69$	171.087	−	296.332i	0.298500	−	0.517017i
$70$	−117.004			−0.199781
$71$	212.222	−	367.579i	0.354734	−	0.614417i	−0.632339	−	0.774692i	$-0.717905\pi$
$71$	212.222	−	367.579i	0.354734	−	0.614417i	0.987072	+	0.160275i	$0.0512382\pi$
$72$	−206.386	+	357.470i	−0.337816	+	0.585115i
$73$	−421.982			−0.676565			−0.338283	−	0.941045i	$-0.609846\pi$
$73$	−421.982			−0.676565			−0.338283	+	0.941045i	$0.609846\pi$
$74$	321.538	−	556.920i	0.505109	−	0.874874i
$75$	−487.858	−	844.995i	−0.751107	−	1.30096i
$76$	−17.7309	−	30.7109i	−0.0267615	−	0.0463523i
$77$	−818.146			−1.21086
$78$	476.865	+	680.665i	0.692236	+	0.988078i
$79$	733.542			1.04468			0.522341	−	0.852736i	$-0.325059\pi$
$79$	733.542			1.04468			0.522341	+	0.852736i	$0.325059\pi$
$80$	−30.9237	−	53.5614i	−0.0432172	−	0.0748543i
$81$	−270.042	−	467.727i	−0.370428	−	0.641600i
$82$	26.3092	−	45.5689i	0.0354313	−	0.0613688i
$83$	−616.843			−0.815751			−0.407876	−	0.913037i	$-0.633730\pi$
$83$	−616.843			−0.815751			−0.407876	+	0.913037i	$0.633730\pi$
$84$	−268.349	+	464.795i	−0.348563	+	0.603729i
$85$	239.511	−	414.845i	0.305631	−	0.529368i
$86$	275.273			0.345156
$87$	−830.629	+	1438.69i	−1.02360	+	1.77292i
$88$	−216.233	−	374.526i	−0.261938	−	0.453689i
$89$	103.585	+	179.415i	0.123371	+	0.213685i	0.921095	−	0.389338i	$-0.127296\pi$
$89$	103.585	+	179.415i	0.123371	+	0.213685i	−0.797724	+	0.603023i	$0.793963\pi$
$90$	398.887			0.467183
$91$	407.037	+	580.993i	0.468891	+	0.669282i
$92$	154.386			0.174954
$93$	−162.996	−	282.317i	−0.181741	−	0.314785i
$94$	300.466	+	520.422i	0.329688	+	0.571036i
$95$	−17.1345	+	29.6779i	−0.0185049	+	0.0320514i
$96$	−283.695			−0.301609
$97$	370.742	−	642.144i	0.388074	−	0.672163i	−0.604117	−	0.796896i	$-0.706474\pi$
$97$	370.742	−	642.144i	0.388074	−	0.672163i	0.992190	+	0.124733i	$0.0398073\pi$
$98$	113.946	−	197.360i	0.117452	−	0.203432i
$99$	2789.21			2.83158
$100$	220.116	−	381.253i	0.220116	−	0.381253i
$101$	206.653	+	357.933i	0.203591	+	0.352630i	0.949683	−	0.313213i	$-0.101405\pi$
$101$	206.653	+	357.933i	0.203591	+	0.352630i	−0.746092	+	0.665843i	$0.768072\pi$
$102$	−1098.64	−	1902.90i	−1.06649	−	1.84721i
$103$	−3.76712			−0.00360374			−0.00180187	−	0.999998i	$-0.500574\pi$
$103$	−3.76712			−0.00360374			−0.00180187	+	0.999998i	$0.500574\pi$
$104$	−158.386	+	339.885i	−0.149336	+	0.320466i
$105$	518.647			0.482045
$106$	260.135	+	450.566i	0.238363	+	0.412857i
$107$	−56.9127	−	98.5756i	−0.0514201	−	0.0890623i	0.839170	−	0.543870i	$-0.183041\pi$
$107$	−56.9127	−	98.5756i	−0.0514201	−	0.0890623i	−0.890590	+	0.454807i	$0.849708\pi$
$108$	436.116	−	755.376i	0.388568	−	0.673019i
$109$	1935.63			1.70092			0.850458	−	0.526044i	$-0.176325\pi$
$109$	1935.63			1.70092			0.850458	+	0.526044i	$0.176325\pi$
$110$	−208.960	+	361.929i	−0.181123	+	0.313714i
$111$	−1425.29	+	2468.68i	−1.21876	+	2.11096i
$112$	−242.153			−0.204297
$113$	−949.391	+	1644.39i	−0.790365	+	1.36895i	0.135376	+	0.990794i	$0.456776\pi$
$113$	−949.391	+	1644.39i	−0.790365	+	1.36895i	−0.925741	+	0.378158i	$0.876558\pi$
$114$	78.5964	+	136.133i	0.0645722	+	0.111842i
$115$	−74.5964	−	129.205i	−0.0604882	−	0.104769i
$116$	−749.542			−0.599942
$117$	−1387.66	−	1980.71i	−1.09649	−	1.56510i
$118$	−492.116			−0.383924
$119$	−937.764	−	1624.25i	−0.722392	−	1.25122i
$120$	137.076	+	237.423i	0.104277	+	0.180614i
$121$	−795.646	+	1378.10i	−0.597780	+	1.03539i
$122$	182.611			0.135515
$123$	−116.622	+	201.994i	−0.0854912	+	0.148075i
$124$	73.5421	−	127.379i	0.0532603	−	0.0922495i
$125$	−908.608			−0.650147
$126$	780.887	−	1352.54i	0.552119	−	0.956298i
$127$	−122.302	−	211.833i	−0.0854532	−	0.148009i	0.820131	−	0.572176i	$-0.193900\pi$
$127$	−122.302	−	211.833i	−0.0854532	−	0.148009i	−0.905584	+	0.424166i	$0.860567\pi$
$128$	−64.0000	−	110.851i	−0.0441942	−	0.0765466i
$129$	−1220.21			−0.832818
$130$	360.978	−	31.6743i	0.243537	−	0.0213694i
$131$	1615.62			1.07754			0.538769	−	0.842453i	$-0.318889\pi$
$131$	1615.62			1.07754			0.538769	+	0.842453i	$0.318889\pi$
$132$	958.502	+	1660.17i	0.632022	+	1.09469i
$133$	67.0873	+	116.199i	0.0437384	+	0.0757572i
$134$	−410.524	+	711.048i	−0.264656	+	0.458397i
$135$	−842.895			−0.537369
$136$	495.695	−	858.568i	0.312540	−	0.541336i
$137$	1150.97	−	1993.54i	0.717769	−	1.24321i	−0.244113	−	0.969747i	$-0.578497\pi$
$137$	1150.97	−	1993.54i	0.717769	−	1.24321i	0.961882	−	0.273465i	$-0.0881698\pi$
$138$	−684.349			−0.422143
$139$	1404.53	−	2432.73i	0.857058	−	1.48447i	−0.0176640	−	0.999844i	$-0.505623\pi$
$139$	1404.53	−	2432.73i	0.857058	−	1.48447i	0.874722	−	0.484625i	$-0.161044\pi$
$140$	117.004	+	202.657i	0.0706331	+	0.122340i
$141$	−1331.88	−	2306.89i	−0.795495	−	1.37784i
$142$	−848.887			−0.501669
$143$	2524.13	−	221.482i	1.47607	−	0.129519i
$144$	825.542			0.477744
$145$	362.166	+	627.289i	0.207422	+	0.359266i
$146$	421.982	+	730.894i	0.239202	+	0.414310i
$147$	−505.091	+	874.842i	−0.283396	+	0.490856i
$148$	−1286.15			−0.714332
$149$	−1266.58	+	2193.79i	−0.696393	+	1.20619i	0.273315	+	0.961925i	$0.411880\pi$
$149$	−1266.58	+	2193.79i	−0.696393	+	1.20619i	−0.969709	+	0.244264i	$0.921454\pi$
$150$	−975.717	+	1689.99i	−0.531113	+	0.919915i
$151$	−2391.10			−1.28864			−0.644321	−	0.764755i	$-0.722860\pi$
$151$	−2391.10			−1.28864			−0.644321	+	0.764755i	$0.722860\pi$
$152$	−35.4618	+	61.4217i	−0.0189233	+	0.0327760i
$153$	3197.01	+	5537.38i	1.68930	+	2.92595i
$154$	818.146	+	1417.07i	0.428105	+	0.741499i
$155$	−142.137			−0.0736562
$156$	702.080	−	1506.62i	0.360330	−	0.773244i
$157$	1927.49			0.979811			0.489905	−	0.871776i	$-0.337031\pi$
$157$	1927.49			0.979811			0.489905	+	0.871776i	$0.337031\pi$
$158$	−733.542	−	1270.53i	−0.369351	−	0.639735i
$159$	−1153.11	−	1997.24i	−0.575140	−	0.996172i
$160$	−61.8474	+	107.123i	−0.0305591	+	0.0529300i
$161$	−584.138			−0.285941
$162$	−540.084	+	935.453i	−0.261932	+	0.453680i
$163$	1109.26	−	1921.30i	0.533031	−	0.923237i	−0.466225	−	0.884666i	$-0.654386\pi$
$163$	1109.26	−	1921.30i	0.533031	−	0.923237i	0.999256	−	0.0385709i	$-0.0122805\pi$
$164$	−105.237			−0.0501074
$165$	926.263	−	1604.33i	0.437027	−	0.756953i
$166$	616.843	+	1068.40i	0.288412	+	0.499544i
$167$	754.135	+	1306.20i	0.349442	+	0.605251i	0.986150	−	0.165854i	$-0.0530380\pi$
$167$	754.135	+	1306.20i	0.349442	+	0.605251i	−0.636709	+	0.771104i	$0.719705\pi$
$168$	1073.40			0.492943
$169$	−1413.06	−	1682.28i	−0.643179	−	0.765716i
$170$	−958.044			−0.432227
$171$	−228.713	−	396.142i	−0.102281	−	0.177156i
$172$	−275.273	−	476.787i	−0.122031	−	0.211364i
$173$	853.236	−	1477.85i	0.374973	−	0.649472i	−0.615350	−	0.788254i	$-0.710985\pi$
$173$	853.236	−	1477.85i	0.374973	−	0.649472i	0.990323	+	0.138782i	$0.0443186\pi$
$174$	3322.52			1.44758
$175$	−832.840	+	1442.52i	−0.359753	+	0.623111i
$176$	−432.466	+	749.053i	−0.185218	+	0.320807i
$177$	2181.42			0.926359
$178$	207.171	−	358.830i	0.0872365	−	0.151098i
$179$	−297.611	−	515.478i	−0.124271	−	0.215244i	0.797177	−	0.603746i	$-0.206326\pi$
$179$	−297.611	−	515.478i	−0.124271	−	0.215244i	−0.921448	+	0.388502i	$0.872993\pi$
$180$	−398.887	−	690.893i	−0.165174	−	0.286090i
$181$	403.006			0.165498			0.0827492	−	0.996570i	$-0.473630\pi$
$181$	403.006			0.165498			0.0827492	+	0.996570i	$0.473630\pi$
$182$	599.273	−	1286.00i	0.244072	−	0.523763i
$183$	−809.463			−0.326980
$184$	−154.386	−	267.404i	−0.0618557	−	0.107137i
$185$	621.446	+	1076.38i	0.246971	+	0.427766i
$186$	−325.992	+	564.635i	−0.128510	+	0.222586i
$187$	−6699.09			−2.61971
$188$	600.932	−	1040.84i	0.233125	−	0.403784i
$189$	−1650.11	+	2858.07i	−0.635066	+	1.09997i
$190$	68.5382			0.0261699
$191$	306.848	−	531.476i	0.116245	−	0.201342i	−0.802032	−	0.597281i	$-0.796248\pi$
$191$	306.848	−	531.476i	0.116245	−	0.201342i	0.918277	+	0.395939i	$0.129581\pi$
$192$	283.695	+	491.374i	0.106635	+	0.184697i
$193$	−1002.66	−	1736.67i	−0.373955	−	0.647709i	0.616215	−	0.787578i	$-0.288665\pi$
$193$	−1002.66	−	1736.67i	−0.373955	−	0.647709i	−0.990170	+	0.139869i	$0.955332\pi$
$194$	−1482.97			−0.548819
$195$	−1600.12	+	140.404i	−0.587625	+	0.0515616i
$196$	−455.783			−0.166102
$197$	278.750	+	482.809i	0.100813	+	0.174613i	0.912020	−	0.410146i	$-0.134522\pi$
$197$	278.750	+	482.809i	0.100813	+	0.174613i	−0.811207	+	0.584759i	$0.801189\pi$
$198$	−2789.21	−	4831.05i	−1.00111	−	1.73398i
$199$	−2766.99	+	4792.56i	−0.985661	+	1.70721i	−0.346698	+	0.937977i	$0.612697\pi$
$199$	−2766.99	+	4792.56i	−0.985661	+	1.70721i	−0.638963	+	0.769237i	$0.720636\pi$
$200$	−880.466			−0.311292
$201$	1819.74	−	3151.89i	0.638581	−	1.10605i
$202$	413.305	−	715.866i	0.143961	−	0.249347i
$203$	2835.99			0.980531
$204$	−2197.28	+	3805.80i	−0.754120	+	1.30617i
$205$	50.8486	+	88.0723i	0.0173240	+	0.0300060i
$206$	3.76712	+	6.52485i	0.00127412	+	0.00220683i
$207$	1991.43			0.668668
$208$	747.084	−	65.5535i	0.249043	−	0.0218525i
$209$	479.251			0.158615
$210$	−518.647	−	898.323i	−0.170429	−	0.295191i
$211$	2341.87	+	4056.23i	0.764079	+	1.32342i	0.940732	+	0.339151i	$0.110140\pi$
$211$	2341.87	+	4056.23i	0.764079	+	1.32342i	−0.176653	+	0.984273i	$0.556527\pi$
$212$	520.269	−	901.132i	0.168548	−	0.291934i
$213$	3762.89			1.21046
$214$	−113.825	+	197.151i	−0.0363595	+	0.0629766i
$215$	−266.014	+	460.750i	−0.0843815	+	0.146153i
$216$	−1744.47			−0.549518
$217$	−278.256	+	481.954i	−0.0870473	+	0.150770i
$218$	−1935.63	−	3352.61i	−0.601364	−	1.04159i
$219$	−1870.53	−	3239.86i	−0.577164	−	0.999677i
$220$	835.840			0.256147
$221$	3332.87	+	4757.25i	1.01445	+	1.44800i
$222$	5701.17			1.72359
$223$	1191.93	+	2064.48i	0.357926	+	0.619947i	0.987614	−	0.156902i	$-0.0501505\pi$
$223$	1191.93	+	2064.48i	0.357926	+	0.619947i	−0.629688	+	0.776848i	$0.716817\pi$
$224$	242.153	+	419.421i	0.0722299	+	0.125106i
$225$	2839.30	−	4917.82i	0.841275	−	1.45713i
$226$	3797.57			1.11774
$227$	777.037	−	1345.87i	0.227197	−	0.393517i	−0.729779	−	0.683683i	$-0.760377\pi$
$227$	777.037	−	1345.87i	0.227197	−	0.393517i	0.956976	+	0.290166i	$0.0937105\pi$
$228$	157.193	−	272.266i	0.0456594	−	0.0790844i
$229$	−2915.60			−0.841346			−0.420673	−	0.907212i	$-0.638206\pi$
$229$	−2915.60			−0.841346			−0.420673	+	0.907212i	$0.638206\pi$
$230$	−149.193	+	258.409i	−0.0427716	+	0.0740827i
$231$	−3626.62	−	6281.49i	−1.03296	−	1.78914i
$232$	749.542	+	1298.24i	0.212111	+	0.367388i
$233$	−4233.93			−1.19045			−0.595223	−	0.803561i	$-0.702936\pi$
$233$	−4233.93			−1.19045			−0.595223	+	0.803561i	$0.702936\pi$
$234$	−2043.03	+	4384.21i	−0.570757	+	1.22481i
$235$	−1161.44			−0.322400
$236$	492.116	+	852.371i	0.135738	+	0.235104i
$237$	3251.59	+	5631.93i	0.891197	+	1.54360i
$238$	−1875.53	+	3248.51i	−0.510808	+	0.884746i
$239$	2372.55			0.642124			0.321062	−	0.947058i	$-0.395960\pi$
$239$	2372.55			0.642124			0.321062	+	0.947058i	$0.395960\pi$
$240$	274.153	−	474.846i	0.0737353	−	0.127713i
$241$	−162.882	+	282.119i	−0.0435358	+	0.0754062i	−0.886972	−	0.461823i	$-0.847196\pi$
$241$	−162.882	+	282.119i	−0.0435358	+	0.0754062i	0.843436	+	0.537229i	$0.180529\pi$
$242$	3182.58			0.845389
$243$	−549.739	+	952.175i	−0.145127	+	0.251367i
$244$	−182.611	−	316.291i	−0.0479117	−	0.0829854i
$245$	220.226	+	381.443i	0.0574275	+	0.0994674i
$246$	466.486			0.120903
$247$	−238.433	−	340.332i	−0.0614215	−	0.0876714i
$248$	−294.168			−0.0753214
$249$	−2734.30	−	4735.95i	−0.695901	−	1.20534i
$250$	908.608	+	1573.76i	0.229862	+	0.398132i
$251$	1300.88	−	2253.20i	0.327136	−	0.566616i	−0.654806	−	0.755797i	$-0.727250\pi$
$251$	1300.88	−	2253.20i	0.327136	−	0.566616i	0.981942	+	0.189181i	$0.0605832\pi$
$252$	−3123.55			−0.780814
$253$	−1043.23	+	1806.92i	−0.259237	+	0.449012i
$254$	−244.604	+	423.667i	−0.0604245	+	0.104658i
$255$	4246.75			1.04291
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−2108.55	−	3652.11i	−0.511781	−	0.886430i	−0.999907	−	0.0136569i	$-0.995653\pi$
$257$	−2108.55	−	3652.11i	−0.511781	−	0.886430i	0.488126	−	0.872773i	$-0.337681\pi$
$258$	1220.21	+	2113.47i	0.294446	+	0.509995i
$259$	4866.33			1.16749
$260$	−415.840	−	593.558i	−0.0991895	−	0.141580i
$261$	−9668.41			−2.29295
$262$	−1615.62	−	2798.34i	−0.380967	−	0.659855i
$263$	−3237.16	−	5606.93i	−0.758981	−	1.31459i	−0.943371	−	0.331740i	$-0.892364\pi$
$263$	−3237.16	−	5606.93i	−0.758981	−	1.31459i	0.184390	−	0.982853i	$-0.440969\pi$
$264$	1917.00	−	3320.35i	0.446907	−	0.774066i
$265$	−1005.54			−0.233094
$266$	134.175	−	232.397i	0.0309277	−	0.0535684i
$267$	−918.332	+	1590.60i	−0.210491	+	0.364580i
$268$	1642.10			0.374280
$269$	650.517	−	1126.73i	0.147445	−	0.255382i	−0.782837	−	0.622226i	$-0.786228\pi$
$269$	650.517	−	1126.73i	0.147445	−	0.255382i	0.930282	+	0.366844i	$0.119562\pi$
$270$	842.895	+	1459.94i	0.189989	+	0.329070i
$271$	1539.82	+	2667.05i	0.345157	+	0.597829i	0.985382	−	0.170358i	$-0.0544923\pi$
$271$	1539.82	+	2667.05i	0.345157	+	0.597829i	−0.640225	+	0.768187i	$0.721159\pi$
$272$	−1982.78			−0.441999
$273$	−2656.42	+	5700.50i	−0.588914	+	1.26377i
$274$	−4603.89			−1.01508
$275$	2974.78	+	5152.46i	0.652312	+	1.12984i
$276$	684.349	+	1185.33i	0.149250	+	0.258509i
$277$	3143.95	−	5445.48i	0.681955	−	1.18118i	−0.292428	−	0.956288i	$-0.594463\pi$
$277$	3143.95	−	5445.48i	0.681955	−	1.18118i	0.974383	−	0.224894i	$-0.0722034\pi$
$278$	−5618.14			−1.21206
$279$	948.626	−	1643.07i	0.203558	−	0.352573i
$280$	234.008	−	405.313i	0.0499452	−	0.0865075i
$281$	−3226.00			−0.684864			−0.342432	−	0.939543i	$-0.611251\pi$
$281$	−3226.00			−0.684864			−0.342432	+	0.939543i	$0.611251\pi$
$282$	−2663.77	+	4613.78i	−0.562500	+	0.974279i
$283$	193.292	+	334.791i	0.0406007	+	0.0703225i	0.885612	−	0.464426i	$-0.153739\pi$
$283$	193.292	+	334.791i	0.0406007	+	0.0703225i	−0.845011	+	0.534749i	$0.820406\pi$
$284$	848.887	+	1470.32i	0.177367	+	0.307209i
$285$	−303.811			−0.0631446
$286$	−2907.75	−	4150.44i	−0.601184	−	0.858113i
$287$	398.178			0.0818944
$288$	−825.542	−	1429.88i	−0.168908	−	0.292557i
$289$	−5222.04	−	9044.84i	−1.06290	−	1.84100i
$290$	724.331	−	1254.58i	0.146670	−	0.254039i
$291$	6573.60			1.32423
$292$	843.964	−	1461.79i	0.169141	−	0.292961i
$293$	−1096.41	+	1899.04i	−0.218611	+	0.378645i	−0.954384	−	0.298583i	$-0.903486\pi$
$293$	−1096.41	+	1899.04i	−0.218611	+	0.378645i	0.735773	+	0.677229i	$0.236819\pi$
$294$	2020.36			0.400782
$295$	475.564	−	823.701i	0.0938590	−	0.162569i
$296$	1286.15	+	2227.68i	0.252554	+	0.437437i
$297$	5893.92	+	10208.6i	1.15151	+	1.99448i
$298$	5066.34			0.984849
$299$	1802.17	−	158.133i	0.348569	−	0.0305855i
$300$	3902.87			0.751107
$301$	1041.53	+	1803.99i	0.199445	+	0.345449i
$302$	2391.10	+	4141.51i	0.455604	+	0.789129i
$303$	−1832.07	+	3173.24i	−0.347359	+	0.601643i
$304$	141.847			0.0267615
$305$	−176.468	+	305.652i	−0.0331297	+	0.0573823i
$306$	6394.01	−	11074.8i	1.19451	−	2.06896i
$307$	−8083.96			−1.50285			−0.751427	−	0.659817i	$-0.770634\pi$
$307$	−8083.96			−1.50285			−0.751427	+	0.659817i	$0.770634\pi$
$308$	1636.29	−	2834.14i	0.302716	−	0.524319i
$309$	−16.6986	−	28.9229i	−0.00307428	−	0.00532481i
$310$	142.137	+	246.188i	0.0260414	+	0.0451050i
$311$	244.409			0.0445632			0.0222816	−	0.999752i	$-0.492907\pi$
$311$	244.409			0.0445632			0.0222816	+	0.999752i	$0.492907\pi$
$312$	−3311.62	+	290.581i	−0.600909	+	0.0527273i
$313$	4444.13			0.802546			0.401273	−	0.915958i	$-0.368568\pi$
$313$	4444.13			0.802546			0.401273	+	0.915958i	$0.368568\pi$
$314$	−1927.49	−	3338.51i	−0.346415	−	0.600009i
$315$	1509.24	+	2614.09i	0.269957	+	0.467578i
$316$	−1467.08	+	2541.06i	−0.261171	+	0.452361i
$317$	930.597			0.164882			0.0824409	−	0.996596i	$-0.473728\pi$
$317$	930.597			0.164882			0.0824409	+	0.996596i	$0.473728\pi$
$318$	−2306.21	+	3994.48i	−0.406685	+	0.704400i
$319$	5064.86	−	8772.60i	0.888959	−	1.53972i
$320$	247.389			0.0432172
$321$	504.557	−	873.918i	0.0877309	−	0.151954i
$322$	584.138	+	1011.76i	0.101096	+	0.175103i
$323$	549.320	+	951.451i	0.0946285	+	0.163901i
$324$	2160.34			0.370428
$325$	2178.95	−	4675.90i	0.371897	−	0.798068i
$326$	−4437.05			−0.753820
$327$	8580.13	+	14861.2i	1.45102	+	2.51323i
$328$	105.237	+	182.275i	0.0177156	+	0.0306844i
$329$	−2273.71	+	3938.17i	−0.381014	+	0.659935i
$330$	−3705.05			−0.618050
$331$	−2413.68	+	4180.61i	−0.400809	+	0.694221i	−0.993824	−	0.110970i	$-0.964604\pi$
$331$	−2413.68	+	4180.61i	−0.400809	+	0.694221i	0.593015	+	0.805191i	$0.297937\pi$
$332$	1233.69	−	2136.81i	0.203938	−	0.353231i
$333$	−16590.2			−2.73014
$334$	1508.27	−	2612.40i	0.247092	−	0.427977i
$335$	−793.432	−	1374.26i	−0.129402	−	0.224132i
$336$	−1073.40	−	1859.18i	−0.174282	−	0.301865i
$337$	10709.7			1.73115			0.865573	−	0.500782i	$-0.166954\pi$
$337$	10709.7			1.73115			0.865573	+	0.500782i	$0.166954\pi$
$338$	−1500.73	+	4129.78i	−0.241506	+	0.664586i
$339$	−16833.6			−2.69698
$340$	958.044	+	1659.38i	0.152815	+	0.264684i
$341$	993.888	+	1721.47i	0.157836	+	0.273380i
$342$	−457.426	+	792.284i	−0.0723238	+	0.125269i
$343$	6915.66			1.08866
$344$	−550.546	+	953.574i	−0.0862891	+	0.149457i
$345$	661.331	−	1145.46i	0.103203	−	0.178752i
$346$	−3412.94			−0.530292
$347$	−3200.54	+	5543.51i	−0.495142	+	0.857611i	−0.999984	−	0.00560066i	$-0.998217\pi$
$347$	−3200.54	+	5543.51i	−0.495142	+	0.857611i	0.504842	+	0.863211i	$0.331551\pi$
$348$	−3322.52	−	5754.77i	−0.511798	−	0.886460i
$349$	1215.01	+	2104.46i	0.186355	+	0.322777i	0.944032	−	0.329853i	$-0.106999\pi$
$349$	1215.01	+	2104.46i	0.186355	+	0.322777i	−0.757677	+	0.652630i	$0.773666\pi$
$350$	3331.36			0.508768
$351$	4317.16	−	9264.35i	0.656504	−	1.40882i
$352$	1729.86			0.261938
$353$	−4040.01	−	6997.51i	−0.609145	−	1.05507i	−0.991382	−	0.131006i	$-0.958179\pi$
$353$	−4040.01	−	6997.51i	−0.609145	−	1.05507i	0.382237	−	0.924064i	$-0.375154\pi$
$354$	−2181.42	−	3778.33i	−0.327517	−	0.567277i
$355$	820.335	−	1420.86i	0.122645	−	0.212427i
$356$	−828.683			−0.123371
$357$	8313.71	−	14399.8i	1.23252	−	2.13478i
$358$	−595.223	+	1030.96i	−0.0878729	+	0.152200i
$359$	8715.23			1.28126			0.640630	−	0.767850i	$-0.278673\pi$
$359$	8715.23			1.28126			0.640630	+	0.767850i	$0.278673\pi$
$360$	−797.775	+	1381.79i	−0.116796	+	0.202296i
$361$	3390.20	+	5872.00i	0.494271	+	0.856102i
$362$	−403.006	−	698.027i	−0.0585126	−	0.101347i
$363$	−14107.5			−2.03982
$364$	−2826.69	+	248.031i	−0.407030	+	0.0357152i
$365$	−1631.15			−0.233914
$366$	809.463	+	1402.03i	0.115605	+	0.200233i
$367$	−1410.44	−	2442.95i	−0.200611	−	0.347469i	0.748114	−	0.663570i	$-0.230959\pi$
$367$	−1410.44	−	2442.95i	−0.200611	−	0.347469i	−0.948726	+	0.316101i	$0.897626\pi$
$368$	−308.771	+	534.807i	−0.0437386	+	0.0757575i
$369$	−1357.46			−0.191508
$370$	1242.89	−	2152.75i	0.174635	−	0.302477i
$371$	−1968.51	+	3409.56i	−0.275471	+	0.477130i
$372$	1303.97			0.181741
$373$	6464.84	−	11197.4i	0.897418	−	1.55437i	0.0666351	−	0.997777i	$-0.478774\pi$
$373$	6464.84	−	11197.4i	0.897418	−	1.55437i	0.830783	−	0.556596i	$-0.187893\pi$
$374$	6699.09	+	11603.2i	0.926208	+	1.60424i
$375$	−4027.61	−	6976.03i	−0.554627	−	0.960642i
$376$	−2403.73			−0.329688
$377$	−8749.55	+	767.737i	−1.19529	+	0.104882i
$378$	6600.42			0.898119
$379$	1144.02	+	1981.51i	0.155052	+	0.268557i	0.933078	−	0.359675i	$-0.117112\pi$
$379$	1144.02	+	1981.51i	0.155052	+	0.268557i	−0.778026	+	0.628232i	$0.783779\pi$
$380$	−68.5382	−	118.712i	−0.00925246	−	0.0160257i
$381$	1084.26	−	1878.00i	0.145797	−	0.252527i
$382$	−1227.39			−0.164395
$383$	−6078.10	+	10527.6i	−0.810904	+	1.40453i	0.101328	+	0.994853i	$0.467691\pi$
$383$	−6078.10	+	10527.6i	−0.810904	+	1.40453i	−0.912232	+	0.409674i	$0.865642\pi$
$384$	567.389	−	982.747i	0.0754023	−	0.130601i
$385$	−3162.51			−0.418640
$386$	−2005.33	+	3473.33i	−0.264426	+	0.458000i
$387$	−3550.77	−	6150.12i	−0.466398	−	0.807825i
$388$	1482.97	+	2568.58i	0.194037	+	0.336082i
$389$	−1479.71			−0.192864			−0.0964322	−	0.995340i	$-0.530743\pi$
$389$	−1479.71			−0.192864			−0.0964322	+	0.995340i	$0.530743\pi$
$390$	1843.30	+	2631.08i	0.239332	+	0.341615i
$391$	−4783.01			−0.618637
$392$	455.783	+	789.439i	0.0587258	+	0.101716i
$393$	7161.62	+	12404.3i	0.919226	+	1.59215i
$394$	557.500	−	965.617i	0.0712853	−	0.123470i
$395$	2835.48			0.361186
$396$	−5578.42	+	9662.10i	−0.707894	+	1.22611i
$397$	−7635.63	+	13225.3i	−0.965292	+	1.67194i	−0.256465	+	0.966554i	$0.582558\pi$
$397$	−7635.63	+	13225.3i	−0.965292	+	1.67194i	−0.708827	+	0.705382i	$0.750775\pi$
$398$	11067.9			1.39393
$399$	−594.760	+	1030.15i	−0.0746247	+	0.129254i
$400$	880.466	+	1525.01i	0.110058	+	0.190626i
$401$	−1282.27	−	2220.96i	−0.159685	−	0.276582i	0.775070	−	0.631875i	$-0.217714\pi$
$401$	−1282.27	−	2220.96i	−0.159685	−	0.276582i	−0.934755	+	0.355293i	$0.884381\pi$
$402$	−7278.97			−0.903089
$403$	728.000	−	1562.24i	0.0899858	−	0.193104i
$404$	−1653.22			−0.203591
$405$	−1043.84	−	1807.98i	−0.128071	−	0.221825i
$406$	−2835.99	−	4912.09i	−0.346670	−	0.600450i
$407$	8690.89	−	15053.1i	1.05846	−	1.83330i
$408$	8789.12			1.06649
$409$	−526.235	+	911.465i	−0.0636201	+	0.110193i	−0.896081	−	0.443890i	$-0.853598\pi$
$409$	−526.235	+	911.465i	−0.0636201	+	0.110193i	0.832461	+	0.554084i	$0.186931\pi$
$410$	101.697	−	176.145i	0.0122499	−	0.0212175i
$411$	20407.8			2.44925
$412$	7.53424	−	13.0497i	0.000900936	−	0.00156047i
$413$	−1861.99	−	3225.06i	−0.221846	−	0.384249i
$414$	−1991.43	−	3449.26i	−0.236410	−	0.409474i
$415$	−2384.38			−0.282036
$416$	−860.626	−	1228.43i	−0.101432	−	0.144781i
$417$	24903.7			2.92455
$418$	−479.251	−	830.087i	−0.0560788	−	0.0971313i
$419$	−4355.81	−	7544.48i	−0.507864	−	0.879647i	−0.999959	−	0.00910485i	$-0.997102\pi$
$419$	−4355.81	−	7544.48i	−0.507864	−	0.879647i	0.492094	−	0.870542i	$-0.336232\pi$
$420$	−1037.29	+	1796.65i	−0.120511	+	0.208732i
$421$	213.335			0.0246967			0.0123484	−	0.999924i	$-0.496069\pi$
$421$	213.335			0.0246967			0.0123484	+	0.999924i	$0.496069\pi$
$422$	4683.73	−	8112.46i	0.540286	−	0.935802i
$423$	7751.47	−	13425.9i	0.890992	−	1.54324i
$424$	−2081.08			−0.238363
$425$	−6819.41	+	11811.6i	−0.778329	+	1.34811i
$426$	−3762.89	−	6517.51i	−0.427964	−	0.741255i
$427$	690.932	+	1196.73i	0.0783057	+	0.135629i
$428$	455.301			0.0514201
$429$	12889.2	+	18397.8i	1.45058	+	2.07052i
$430$	1064.06			0.119333
$431$	−4476.72	−	7753.91i	−0.500316	−	0.866573i	−1.00000		0.000364932i	$-0.999884\pi$
$431$	−4476.72	−	7753.91i	−0.500316	−	0.866573i	0.499684	−	0.866208i	$-0.333449\pi$
$432$	1744.47	+	3021.50i	0.194284	+	0.336510i
$433$	−2930.72	+	5076.16i	−0.325269	+	0.563382i	−0.981567	−	0.191120i	$-0.938788\pi$
$433$	−2930.72	+	5076.16i	−0.325269	+	0.563382i	0.656298	+	0.754502i	$0.272122\pi$
$434$	1113.03			0.123104
$435$	−3210.76	+	5561.21i	−0.353895	+	0.612964i
$436$	−3871.26	+	6705.22i	−0.425229	+	0.736518i
$437$	342.175			0.0374564
$438$	−3741.06	+	6479.71i	−0.408116	+	0.706878i
$439$	5221.77	+	9044.36i	0.567702	+	0.983289i	0.996793	+	0.0800275i	$0.0255008\pi$
$439$	5221.77	+	9044.36i	0.567702	+	0.983289i	−0.429090	+	0.903262i	$0.641166\pi$
$440$	−835.840	−	1447.72i	−0.0905616	−	0.156857i
$441$	−5879.19			−0.634833
$442$	4906.93	−	10530.0i	0.528052	−	1.13317i
$443$	8789.73			0.942692			0.471346	−	0.881948i	$-0.343768\pi$
$443$	8789.73			0.942692			0.471346	+	0.881948i	$0.343768\pi$
$444$	−5701.17	−	9874.71i	−0.609382	−	1.05548i
$445$	400.405	+	693.522i	0.0426540	+	0.0738789i
$446$	2383.86	−	4128.97i	0.253092	−	0.438369i
$447$	−22457.7			−2.37632
$448$	484.305	−	838.841i	0.0510743	−	0.0884632i
$449$	−4318.06	+	7479.09i	−0.453857	+	0.786103i	−0.998622	−	0.0524857i	$-0.983286\pi$
$449$	−4318.06	+	7479.09i	−0.453857	+	0.786103i	0.544765	+	0.838589i	$0.316619\pi$
$450$	−11357.2			−1.18974
$451$	711.114	−	1231.69i	0.0742463	−	0.128598i
$452$	−3797.57	−	6577.58i	−0.395182	−	0.684476i
$453$	−10599.1	−	18358.2i	−1.09931	−	1.90407i
$454$	−3108.15			−0.321305
$455$	1573.38	+	2245.81i	0.162113	+	0.231396i
$456$	−628.771			−0.0645722
$457$	−2438.48	−	4223.57i	−0.249600	−	0.432320i	0.713815	−	0.700335i	$-0.246966\pi$
$457$	−2438.48	−	4223.57i	−0.249600	−	0.432320i	−0.963415	+	0.268014i	$0.913633\pi$
$458$	2915.60	+	5049.97i	0.297461	+	0.515217i
$459$	−13511.3	+	23402.2i	−1.37397	+	2.37979i
$460$	596.771			0.0604882
$461$	5901.96	−	10222.5i	0.596272	−	1.03277i	−0.397094	−	0.917778i	$-0.629981\pi$
$461$	5901.96	−	10222.5i	0.596272	−	1.03277i	0.993366	−	0.114996i	$-0.0366855\pi$
$462$	−7253.24	+	12563.0i	−0.730414	+	1.26511i
$463$	−4797.53			−0.481555			−0.240777	−	0.970580i	$-0.577402\pi$
$463$	−4797.53			−0.481555			−0.240777	+	0.970580i	$0.577402\pi$
$464$	1499.08	−	2596.49i	0.149985	−	0.259782i
$465$	−630.055	−	1091.29i	−0.0628346	−	0.108833i
$466$	4233.93	+	7333.38i	0.420886	+	0.728996i
$467$	−13188.7			−1.30686			−0.653428	−	0.756989i	$-0.726670\pi$
$467$	−13188.7			−1.30686			−0.653428	+	0.756989i	$0.726670\pi$
$468$	9636.71	−	845.581i	0.951831	−	0.0835193i
$469$	−6213.09			−0.611714
$470$	1161.44	+	2011.67i	0.113985	+	0.197429i
$471$	8544.03	+	14798.7i	0.835856	+	1.44775i
$472$	984.233	−	1704.74i	0.0959809	−	0.166244i
$473$	7440.38			0.723275
$474$	6503.19	−	11263.9i	0.630172	−	1.09149i
$475$	487.858	−	844.995i	0.0471252	−	0.0816233i
$476$	7502.11			0.722392
$477$	6711.00	−	11623.8i	0.644184	−	1.11576i
$478$	−2372.55	−	4109.38i	−0.227025	−	0.393219i
$479$	−9024.41	−	15630.7i	−0.860827	−	1.49100i	−0.871132	−	0.491049i	$-0.836614\pi$
$479$	−9024.41	−	15630.7i	−0.860827	−	1.49100i	0.0103054	−	0.999947i	$-0.496720\pi$
$480$	−1096.61			−0.104277
$481$	−15013.5	+	1317.37i	−1.42320	+	0.124879i
$482$	651.526			0.0615689
$483$	−2589.33	−	4484.85i	−0.243931	−	0.422500i
$484$	−3182.58	−	5512.39i	−0.298890	−	0.517693i
$485$	1433.09	−	2482.18i	0.134171	−	0.232392i
$486$	2198.96			0.205240
$487$	−5750.62	+	9960.37i	−0.535084	+	0.926792i	0.464076	+	0.885796i	$0.346387\pi$
$487$	−5750.62	+	9960.37i	−0.535084	+	0.926792i	−0.999159	+	0.0409963i	$0.986947\pi$
$488$	−365.221	+	632.582i	−0.0338787	+	0.0586796i
$489$	19668.2			1.81887
$490$	440.453	−	762.886i	0.0406074	−	0.0703340i
$491$	2000.33	+	3464.67i	0.183856	+	0.318449i	0.943191	−	0.332252i	$-0.107809\pi$
$491$	2000.33	+	3464.67i	0.183856	+	0.318449i	−0.759334	+	0.650701i	$0.774475\pi$
$492$	−466.486	−	807.978i	−0.0427456	−	0.0740375i
$493$	23221.5			2.12139
$494$	−351.040	+	753.310i	−0.0319717	+	0.0686093i
$495$	10781.6			0.978981
$496$	294.168	+	509.514i	0.0266301	+	0.0461247i
$497$	−3211.88	−	5563.14i	−0.289884	−	0.502094i
$498$	−5468.60	+	9471.89i	−0.492076	+	0.852301i
$499$	−8322.72			−0.746645			−0.373323	−	0.927702i	$-0.621782\pi$
$499$	−8322.72			−0.746645			−0.373323	+	0.927702i	$0.621782\pi$
$500$	1817.22	−	3147.51i	0.162537	−	0.281522i
$501$	−6685.76	+	11580.1i	−0.596203	+	1.03265i
$502$	−5203.54			−0.462640
$503$	3563.74	−	6172.58i	0.315903	−	0.547160i	−0.663726	−	0.747976i	$-0.731026\pi$
$503$	3563.74	−	6172.58i	0.315903	−	0.547160i	0.979629	+	0.200816i	$0.0643592\pi$
$504$	3123.55	+	5410.15i	0.276059	+	0.478149i
$505$	798.808	+	1383.58i	0.0703890	+	0.121917i
$506$	4172.90			0.366617
$507$	6652.32	−	18306.2i	0.582722	−	1.60356i
$508$	978.417			0.0854532
$509$	7174.46	+	12426.5i	0.624759	+	1.08211i	0.988587	+	0.150649i	$0.0481362\pi$
$509$	7174.46	+	12426.5i	0.624759	+	1.08211i	−0.363828	+	0.931466i	$0.618530\pi$
$510$	−4246.75	−	7355.59i	−0.368724	−	0.638649i
$511$	−3193.25	+	5530.87i	−0.276441	+	0.478809i
$512$	512.000			0.0441942
$513$	966.593	−	1674.19i	0.0831893	−	0.144088i
$514$	−4217.10	+	7304.22i	−0.361884	+	0.626801i
$515$	−14.5617			−0.00124595
$516$	2440.42	−	4226.93i	0.208205	−	0.360621i
$517$	8121.32	+	14066.5i	0.690861	+	1.19661i
$518$	−4866.33	−	8428.73i	−0.412769	−	0.714937i
$519$	15128.7			1.27953
$520$	−612.233	+	1313.81i	−0.0516311	+	0.110797i
$521$	3535.86			0.297329			0.148665	−	0.988888i	$-0.452502\pi$
$521$	3535.86			0.297329			0.148665	+	0.988888i	$0.452502\pi$
$522$	9668.41	+	16746.2i	0.810680	+	1.40414i
$523$	−6982.44	−	12093.9i	−0.583787	−	1.01115i	−0.995025	−	0.0996211i	$-0.968237\pi$
$523$	−6982.44	−	12093.9i	−0.583787	−	1.01115i	0.411238	−	0.911528i	$-0.365096\pi$
$524$	−3231.24	+	5596.68i	−0.269385	+	0.466588i
$525$	−14767.0			−1.22759
$526$	−6474.32	+	11213.9i	−0.536680	+	0.929558i
$527$	−2278.40	+	3946.31i	−0.188328	+	0.326193i
$528$	−7668.02			−0.632022
$529$	5338.66	−	9246.83i	0.438782	−	0.759993i
$530$	1005.54	+	1741.65i	0.0824110	+	0.142740i
$531$	6347.86	+	10994.8i	0.518783	+	0.898558i
$532$	−536.699			−0.0437384
$533$	−1228.45	+	107.791i	−0.0998312	+	0.00875978i
$534$	3673.33			0.297679
$535$	−219.994	−	381.040i	−0.0177779	−	0.0307922i
$536$	−1642.10	−	2844.19i	−0.132328	−	0.229199i
$537$	2638.46	−	4569.95i	0.212026	−	0.367240i
$538$	−2602.07			−0.208519
$539$	3079.85	−	5334.46i	0.246120	−	0.426292i
$540$	1685.79	−	2919.88i	0.134342	−	0.232688i
$541$	−10661.6			−0.847277			−0.423638	−	0.905831i	$-0.639247\pi$
$541$	−10661.6			−0.847277			−0.423638	+	0.905831i	$0.639247\pi$
$542$	3079.64	−	5334.10i	0.244063	−	0.422729i
$543$	1786.42	+	3094.17i	0.141183	+	0.244537i
$544$	1982.78	+	3434.27i	0.156270	+	0.270668i
$545$	7482.10			0.588070
$546$	12530.0	−	1099.45i	0.982112	−	0.0861763i
$547$	−3393.59			−0.265264			−0.132632	−	0.991165i	$-0.542343\pi$
$547$	−3393.59			−0.265264			−0.132632	+	0.991165i	$0.542343\pi$
$548$	4603.89	+	7974.18i	0.358884	+	0.621606i
$549$	−2355.51	−	4079.86i	−0.183116	−	0.317166i
$550$	5949.55	−	10304.9i	0.461254	−	0.798915i
$551$	−1661.26			−0.128443
$552$	1368.70	−	2370.66i	0.105536	−	0.182793i
$553$	5550.91	−	9614.46i	0.426851	−	0.739328i
$554$	−12575.8			−0.964430
$555$	−5509.41	+	9542.58i	−0.421372	+	0.729837i
$556$	5618.14	+	9730.90i	0.428529	+	0.742234i
$557$	4124.51	+	7143.87i	0.313754	+	0.543439i	0.979172	−	0.203033i	$-0.0650798\pi$
$557$	4124.51	+	7143.87i	0.313754	+	0.543439i	−0.665418	+	0.746471i	$0.731746\pi$
$558$	−3794.50			−0.287875
$559$	−3701.67	−	5283.67i	−0.280079	−	0.399777i
$560$	−936.031			−0.0706331
$561$	−29695.3	−	51433.7i	−2.23482	−	3.87083i
$562$	3226.00	+	5587.59i	0.242136	+	0.419392i
$563$	−4434.39	+	7680.59i	−0.331949	+	0.574953i	−0.982894	−	0.184172i	$-0.941040\pi$
$563$	−4434.39	+	7680.59i	−0.331949	+	0.574953i	0.650945	+	0.759125i	$0.274373\pi$
$564$	10655.1			0.795495
$565$	−3669.83	+	6356.34i	−0.273259	+	0.473298i
$566$	386.584	−	669.583i	0.0287091	−	0.0497255i
$567$	−8173.93			−0.605419
$568$	1697.77	−	2940.63i	0.125417	−	0.217229i
$569$	3204.24	+	5549.91i	0.236079	+	0.408901i	0.959586	−	0.281417i	$-0.0908043\pi$
$569$	3204.24	+	5549.91i	0.236079	+	0.408901i	−0.723507	+	0.690317i	$0.757471\pi$
$570$	303.811	+	526.216i	0.0223250	+	0.0386680i
$571$	10045.2			0.736212			0.368106	−	0.929784i	$-0.380006\pi$
$571$	10045.2			0.736212			0.368106	+	0.929784i	$0.380006\pi$
$572$	−4281.02	+	9186.80i	−0.312934	+	0.671537i
$573$	5440.70			0.396664
$574$	−398.178	−	689.664i	−0.0289540	−	0.0501498i
$575$	2123.92	+	3678.75i	0.154041	+	0.266807i
$576$	−1651.08	+	2859.76i	−0.119436	+	0.206869i
$577$	−24528.9			−1.76976			−0.884880	−	0.465818i	$-0.845760\pi$
$577$	−24528.9			−1.76976			−0.884880	+	0.465818i	$0.845760\pi$
$578$	−10444.1	+	18089.7i	−0.751585	+	1.30178i
$579$	8889.08	−	15396.3i	0.638027	−	1.10510i
$580$	−2897.32			−0.207422
$581$	−4667.82	+	8084.90i	−0.333311	+	0.577312i
$582$	−6573.60	−	11385.8i	−0.468186	−	0.810922i
$583$	7031.21	+	12178.4i	0.499490	+	0.865142i
$584$	−3375.86			−0.239202
$585$	−5363.95	−	7656.36i	−0.379098	−	0.541114i
$586$	4385.64			0.309163
$587$	7951.88	+	13773.1i	0.559130	+	0.968441i	0.997569	+	0.0696803i	$0.0221979\pi$
$587$	7951.88	+	13773.1i	0.559130	+	0.968441i	−0.438440	+	0.898761i	$0.644469\pi$
$588$	−2020.36	−	3499.37i	−0.141698	−	0.245428i
$589$	162.996	−	282.317i	0.0114026	−	0.0197499i
$590$	−1902.26			−0.132737
$591$	−2471.24	+	4280.32i	−0.172002	+	0.297917i
$592$	2572.31	−	4455.36i	0.178583	−	0.309315i
$593$	−5436.51			−0.376477			−0.188238	−	0.982123i	$-0.560278\pi$
$593$	−5436.51			−0.376477			−0.188238	+	0.982123i	$0.560278\pi$
$594$	11787.8	−	20417.1i	0.814244	−	1.41031i
$595$	−3624.89	−	6278.49i	−0.249758	−	0.432593i
$596$	−5066.34	−	8775.15i	−0.348197	−	0.603094i
$597$	−49061.2			−3.36339
$598$	−2076.07	−	2963.32i	−0.141968	−	0.202641i
$599$	6872.46			0.468783			0.234392	−	0.972142i	$-0.424690\pi$
$599$	6872.46			0.468783			0.234392	+	0.972142i	$0.424690\pi$
$600$	−3902.87	−	6759.96i	−0.265556	−	0.459957i
$601$	708.911	+	1227.87i	0.0481149	+	0.0833375i	0.889080	−	0.457752i	$-0.151345\pi$
$601$	708.911	+	1227.87i	0.0481149	+	0.0833375i	−0.840965	+	0.541090i	$0.818012\pi$
$602$	2083.07	−	3607.97i	0.141029	−	0.244269i
$603$	21181.6			1.43048
$604$	4782.20	−	8283.01i	0.322161	−	0.557998i
$605$	−3075.54	+	5326.98i	−0.206675	+	0.357971i
$606$	7328.28			0.491240
$607$	6796.67	−	11772.2i	0.454478	−	0.787180i	−0.544180	−	0.838969i	$-0.683159\pi$
$607$	6796.67	−	11772.2i	0.454478	−	0.787180i	0.998658	+	0.0517890i	$0.0164923\pi$
$608$	−141.847	−	245.687i	−0.00946163	−	0.0163880i
$609$	12571.2	+	21773.9i	0.836470	+	1.44881i
$610$	705.874			0.0468525
$611$	5948.68	−	12765.5i	0.393875	−	0.845231i
$612$	−25576.1			−1.68930
$613$	8639.71	+	14964.4i	0.569257	+	0.985982i	0.996640	+	0.0819112i	$0.0261024\pi$
$613$	8639.71	+	14964.4i	0.569257	+	0.985982i	−0.427383	+	0.904071i	$0.640564\pi$
$614$	8083.96	+	14001.8i	0.531339	+	0.920306i
$615$	−450.796	+	780.802i	−0.0295575	+	0.0511951i
$616$	−6545.17			−0.428105
$617$	1088.54	−	1885.40i	0.0710256	−	0.123020i	−0.828325	−	0.560247i	$-0.810706\pi$
$617$	1088.54	−	1885.40i	0.0710256	−	0.123020i	0.899351	+	0.437227i	$0.144039\pi$
$618$	−33.3973	+	57.8458i	−0.00217384	+	0.00376521i
$619$	17067.5			1.10824			0.554121	−	0.832436i	$-0.313055\pi$
$619$	17067.5			1.10824			0.554121	+	0.832436i	$0.313055\pi$
$620$	284.274	−	492.377i	0.0184141	−	0.0318941i
$621$	4208.13	+	7288.69i	0.271927	+	0.470991i
$622$	−244.409	−	423.329i	−0.0157555	−	0.0272893i
$623$	3135.43			0.201635
$624$	3814.92	+	5445.32i	0.244742	+	0.349338i
$625$	10245.1			0.655686
$626$	−4444.13	−	7697.45i	−0.283743	−	0.491457i
$627$	2124.39	+	3679.55i	0.135311	+	0.234365i
$628$	−3854.98	+	6677.01i	−0.244953	+	0.424270i
$629$	39846.2			2.52587
$630$	3018.49	−	5228.18i	0.190888	−	0.330628i
$631$	3964.98	−	6867.55i	0.250148	−	0.433269i	−0.713418	−	0.700738i	$-0.752854\pi$
$631$	3964.98	−	6867.55i	0.250148	−	0.433269i	0.963566	+	0.267469i	$0.0861874\pi$
$632$	5868.34			0.369351
$633$	−20761.7	+	35960.4i	−1.30364	+	2.25797i
$634$	−930.597	−	1611.84i	−0.0582945	−	0.100969i
$635$	−472.754	−	818.834i	−0.0295444	−	0.0511723i
$636$	9224.85			0.575140
$637$	−5320.44	+	466.847i	−0.330932	+	0.0290379i
$638$	−20259.5			−1.25718
$639$	10949.9	+	18965.7i	0.677888	+	1.17414i
$640$	−247.389	−	428.491i	−0.0152796	−	0.0264650i
$641$	2919.53	−	5056.77i	0.179898	−	0.311592i	−0.761948	−	0.647639i	$-0.775757\pi$
$641$	2919.53	−	5056.77i	0.179898	−	0.311592i	0.941845	+	0.336047i	$0.109090\pi$
$642$	−2018.23			−0.124070
$643$	8511.42	−	14742.2i	0.522018	−	0.904161i	−0.477654	−	0.878548i	$-0.658513\pi$
$643$	8511.42	−	14742.2i	0.522018	−	0.904161i	0.999672	−	0.0256134i	$-0.00815390\pi$
$644$	1168.28	−	2023.51i	0.0714853	−	0.123816i
$645$	−4716.68			−0.287936
$646$	1098.64	−	1902.90i	0.0669124	−	0.115896i
$647$	−10889.6	−	18861.4i	−0.661694	−	1.14609i	−0.980170	−	0.198157i	$-0.936504\pi$
$647$	−10889.6	−	18861.4i	−0.661694	−	1.14609i	0.318476	−	0.947931i	$-0.396829\pi$
$648$	−2160.34	−	3741.81i	−0.130966	−	0.226840i
$649$	−13301.5			−0.804512
$650$	−10277.8	+	901.838i	−0.620200	+	0.0544200i
$651$	−4933.74			−0.297033
$652$	4437.05	+	7685.19i	0.266516	+	0.461619i
$653$	−8520.81	−	14758.5i	−0.510636	−	0.884447i	−0.999924	−	0.0123250i	$-0.996077\pi$
$653$	−8520.81	−	14758.5i	−0.510636	−	0.884447i	0.489288	−	0.872122i	$-0.337257\pi$
$654$	17160.3	−	29722.4i	1.02602	−	1.77712i
$655$	6245.12			0.372545
$656$	210.474	−	364.551i	0.0125268	−	0.0216971i
$657$	10886.4	−	18855.7i	0.646450	−	1.11968i
$658$	9094.82			0.538834
$659$	−15382.9	+	26644.0i	−0.909306	+	1.57496i	−0.0942763	+	0.995546i	$0.530054\pi$
$659$	−15382.9	+	26644.0i	−0.909306	+	1.57496i	−0.815030	+	0.579419i	$0.803280\pi$
$660$	3705.05	+	6417.34i	0.218514	+	0.378476i
$661$	−3872.35	−	6707.11i	−0.227862	−	0.394669i	0.729312	−	0.684181i	$-0.239840\pi$
$661$	−3872.35	−	6707.11i	−0.227862	−	0.394669i	−0.957174	+	0.289512i	$0.906507\pi$
$662$	9654.71			0.566829
$663$	−21751.1	+	46676.5i	−1.27412	+	2.73418i
$664$	−4934.75			−0.288412
$665$	259.323	+	449.161i	0.0151220	+	0.0261921i
$666$	16590.2	+	28735.1i	0.965251	+	1.67186i
$667$	3616.20	−	6263.44i	0.209925	−	0.363601i
$668$	−6033.08			−0.349442
$669$	−10567.0	+	18302.6i	−0.610679	+	1.05773i
$670$	−1586.86	+	2748.53i	−0.0915013	+	0.158485i
$671$	4935.80			0.283971
$672$	−2146.79	+	3718.36i	−0.123236	+	0.213451i
$673$	1151.23	+	1993.98i	0.0659384	+	0.114209i	0.897110	−	0.441808i	$-0.145663\pi$
$673$	1151.23	+	1993.98i	0.0659384	+	0.114209i	−0.831171	+	0.556016i	$0.812329\pi$
$674$	−10709.7	−	18549.8i	−0.612053	−	1.06011i
$675$	23999.1			1.36848
$676$	8653.71	−	1530.44i	0.492359	−	0.0870754i
$677$	−15932.6			−0.904488			−0.452244	−	0.891894i	$-0.649376\pi$
$677$	−15932.6			−0.904488			−0.452244	+	0.891894i	$0.649376\pi$
$678$	16833.6	+	29156.6i	0.953525	+	1.65155i
$679$	−5611.01	−	9718.55i	−0.317129	−	0.549284i
$680$	1916.09	−	3318.76i	0.108057	−	0.187160i
$681$	13777.6			0.775269
$682$	1987.78	−	3442.93i	0.111607	−	0.193309i
$683$	−9229.29	+	15985.6i	−0.517055	+	0.895566i	0.482748	+	0.875759i	$0.339639\pi$
$683$	−9229.29	+	15985.6i	−0.517055	+	0.895566i	−0.999804	+	0.0198072i	$0.993695\pi$
$684$	1829.70			0.102281
$685$	4449.04	−	7705.97i	0.248159	−	0.429825i
$686$	−6915.66	−	11978.3i	−0.384900	−	0.666666i
$687$	−12924.1	−	22385.1i	−0.717735	−	1.24315i
$688$	2202.18			0.122031
$689$	5150.19	−	11052.0i	0.284770	−	0.611099i
$690$	−2645.32			−0.145950
$691$	−11489.7	−	19900.7i	−0.632544	−	1.09560i	−0.987030	−	0.160537i	$-0.948677\pi$
$691$	−11489.7	−	19900.7i	−0.632544	−	1.09560i	0.354486	−	0.935061i	$-0.384656\pi$
$692$	3412.94	+	5911.39i	0.187487	+	0.324736i
$693$	21106.7	−	36557.9i	1.15697	−	2.00392i
$694$	12802.2			0.700236
$695$	5429.17	−	9403.60i	0.296317	−	0.513236i
$696$	−6645.04	+	11509.5i	−0.361896	+	0.626822i
$697$	3260.33			0.177179
$698$	2430.02	−	4208.92i	0.131773	−	0.228238i
$699$	−18767.9	−	32506.9i	−1.01554	−	1.75897i
$700$	−3331.36	−	5770.09i	−0.179877	−	0.311555i
$701$	8633.81			0.465185			0.232592	−	0.972574i	$-0.425279\pi$
$701$	8633.81			0.465185			0.232592	+	0.972574i	$0.425279\pi$
$702$	−20363.5	+	1786.81i	−1.09483	+	0.0960667i
$703$	−2850.58			−0.152933
$704$	−1729.86	−	2996.21i	−0.0926089	−	0.160403i
$705$	−5148.34	−	8917.19i	−0.275032	−	0.476370i
$706$	−8080.03	+	13995.0i	−0.430731	+	0.746047i
$707$	6255.19			0.332745
$708$	−4362.84	+	7556.66i	−0.231590	+	0.401125i
$709$	12811.2	−	22189.7i	0.678612	−	1.17539i	−0.296787	−	0.954944i	$-0.595915\pi$
$709$	12811.2	−	22189.7i	0.678612	−	1.17539i	0.975399	−	0.220447i	$-0.0707515\pi$
$710$	−3281.34			−0.173446
$711$	−18924.1	+	32777.4i	−0.998182	+	1.72890i
$712$	828.683	+	1435.32i	0.0436183	+	0.0755491i
$713$	709.614	+	1229.09i	0.0372725	+	0.0645578i
$714$	−33254.8			−1.74304
$715$	9756.91	−	856.129i	0.510333	−	0.0447796i
$716$	2380.89			0.124271
$717$	10516.9	+	18215.8i	0.547783	+	0.948788i
$718$	−8715.23	−	15095.2i	−0.452994	−	0.784608i
$719$	−17477.4	+	30271.7i	−0.906532	+	1.57016i	−0.0876845	+	0.996148i	$0.527947\pi$
$719$	−17477.4	+	30271.7i	−0.906532	+	1.57016i	−0.818847	+	0.574011i	$0.805387\pi$
$720$	3191.10			0.165174
$721$	−28.5068	+	49.3753i	−0.00147247	+	0.00255039i
$722$	6780.40	−	11744.0i	0.349502	−	0.605355i
$723$	−2888.04			−0.148558
$724$	−806.013	+	1396.05i	−0.0413746	+	0.0716629i
$725$	−10311.7	−	17860.3i	−0.528228	−	0.914918i
$726$	14107.5	+	24435.0i	0.721184	+	1.24913i
$727$	−23397.0			−1.19360			−0.596800	−	0.802390i	$-0.703562\pi$
$727$	−23397.0			−1.19360			−0.596800	+	0.802390i	$0.703562\pi$
$728$	3256.30	+	4647.95i	0.165778	+	0.236627i
$729$	−24329.6			−1.23607
$730$	1631.15	+	2825.24i	0.0827010	+	0.143242i
$731$	8528.21	+	14771.3i	0.431501	+	0.747382i
$732$	1618.93	−	2804.06i	0.0817449	−	0.141586i
$733$	−3541.17			−0.178440			−0.0892198	−	0.996012i	$-0.528437\pi$
$733$	−3541.17			−0.178440			−0.0892198	+	0.996012i	$0.528437\pi$
$734$	−2820.88	+	4885.90i	−0.141854	+	0.245698i
$735$	−1952.41	+	3381.67i	−0.0979804	+	0.169707i
$736$	1235.08			0.0618557
$737$	−11096.1	+	19219.0i	−0.554586	+	0.960571i
$738$	1357.46	+	2351.19i	0.0677084	+	0.117274i
$739$	19616.5	+	33976.8i	0.976460	+	1.69128i	0.675029	+	0.737791i	$0.264131\pi$
$739$	19616.5	+	33976.8i	0.976460	+	1.69128i	0.301431	+	0.953488i	$0.402536\pi$
$740$	−4971.57			−0.246971
$741$	1556.07	−	3339.22i	0.0771437	−	0.165546i
$742$	7874.03			0.389575
$743$	−19099.4	−	33081.1i	−0.943052	−	1.63341i	−0.759606	−	0.650383i	$-0.774608\pi$
$743$	−19099.4	−	33081.1i	−0.943052	−	1.63341i	−0.183446	−	0.983030i	$-0.558725\pi$
$744$	−1303.97	−	2258.54i	−0.0642551	−	0.111293i
$745$	−4895.93	+	8480.00i	−0.240769	+	0.417024i
$746$	−25859.4			−1.26914
$747$	15913.4	−	27562.9i	0.779441	−	1.35003i
$748$	13398.2	−	23206.3i	0.654928	−	1.13437i
$749$	−1722.69			−0.0840399
$750$	−8055.23	+	13952.1i	−0.392180	+	0.679277i
$751$	835.377	+	1446.92i	0.0405903	+	0.0703045i	0.885607	−	0.464436i	$-0.153743\pi$
$751$	835.377	+	1446.92i	0.0405903	+	0.0703045i	−0.845017	+	0.534740i	$0.820409\pi$
$752$	2403.73	+	4163.38i	0.116562	+	0.201892i
$753$	23065.9			1.11629
$754$	10079.3	+	14386.9i	0.486826	+	0.694882i
$755$	−9242.70			−0.445532
$756$	−6600.42	−	11432.3i	−0.317533	−	0.549983i
$757$	18974.3	+	32864.4i	0.911007	+	1.57791i	0.812645	+	0.582759i	$0.198027\pi$
$757$	18974.3	+	32864.4i	0.911007	+	1.57791i	0.0983617	+	0.995151i	$0.468640\pi$
$758$	2288.05	−	3963.01i	0.109638	−	0.189899i
$759$	−18497.4			−0.884600
$760$	−137.076	+	237.423i	−0.00654247	+	0.0113319i
$761$	18886.4	−	32712.1i	0.899645	−	1.55823i	0.0716969	−	0.997426i	$-0.477159\pi$
$761$	18886.4	−	32712.1i	0.899645	−	1.55823i	0.827948	−	0.560805i	$-0.189508\pi$
$762$	−4337.06			−0.206188
$763$	14647.4	−	25370.1i	0.694984	−	1.20375i
$764$	1227.39	+	2125.91i	0.0581224	+	0.100671i
$765$	12357.9	+	21404.5i	0.584053	+	1.01161i
$766$	24312.4			1.14679
$767$	6617.63	+	9445.82i	0.311537	+	0.444679i
$768$	−2269.56			−0.106635
$769$	6536.64	+	11321.8i	0.306524	+	0.530916i	0.977600	−	0.210474i	$-0.0675006\pi$
$769$	6536.64	+	11321.8i	0.306524	+	0.530916i	−0.671075	+	0.741389i	$0.734167\pi$
$770$	3162.51	+	5477.63i	0.148012	+	0.256364i
$771$	18693.2	−	32377.7i	0.873179	−	1.51239i
$772$	8021.32			0.373955
$773$	12571.5	−	21774.6i	0.584951	−	1.01316i	−0.409931	−	0.912117i	$-0.634447\pi$
$773$	12571.5	−	21774.6i	0.584951	−	1.01316i	0.994882	−	0.101048i	$-0.0322196\pi$
$774$	−7101.55	+	12300.2i	−0.329793	+	0.571218i
$775$	4046.96			0.187575
$776$	2965.94	−	5137.15i	0.137205	−	0.237646i
$777$	21571.1	+	37362.3i	0.995959	+	1.72505i
$778$	1479.71	+	2562.93i	0.0681879	+	0.118105i
$779$	−233.243			−0.0107276
$780$	2713.86	−	5823.78i	0.124579	−	0.267339i
$781$	−22944.7			−1.05125
$782$	4783.01	+	8284.41i	0.218721	+	0.378836i
$783$	−20430.5	−	35386.6i	−0.932472	−	1.61509i
$784$	911.566	−	1578.88i	0.0415254	−	0.0719241i
$785$	7450.63			0.338757
$786$	14323.2	−	24808.6i	0.649991	−	1.12582i
$787$	−9582.29	+	16597.0i	−0.434017	+	0.751740i	−0.997215	−	0.0745822i	$-0.976238\pi$
$787$	−9582.29	+	16597.0i	−0.434017	+	0.751740i	0.563197	+	0.826322i	$0.309571\pi$
$788$	−2230.00			−0.100813
$789$	28698.9	−	49708.0i	1.29494	−	2.24290i
$790$	−2835.48	−	4911.19i	−0.127698	−	0.221180i
$791$	14368.6	+	24887.1i	0.645877	+	1.11869i
$792$	22313.7			1.00111
$793$	−2455.62	−	3505.08i	−0.109964	−	0.156960i
$794$	30542.5			1.36513
$795$	−4457.29	−	7720.25i	−0.198847	−	0.344414i
$796$	−11067.9	−	19170.2i	−0.492830	−	0.853607i
$797$	−14495.7	+	25107.3i	−0.644246	+	1.11587i	0.340229	+	0.940343i	$0.389496\pi$
$797$	−14495.7	+	25107.3i	−0.644246	+	1.11587i	−0.984475	+	0.175525i	$0.943838\pi$
$798$	2379.04			0.105535
$799$	−18617.4	+	32246.3i	−0.824326	+	1.42777i
$800$	1760.93	−	3050.02i	0.0778229	−	0.134793i
$801$	−10689.3			−0.471519
$802$	−2564.54	+	4441.92i	−0.112914	+	0.195573i
$803$	11405.8	+	19755.4i	0.501248	+	0.868186i
$804$	7278.97	+	12607.5i	0.319290	+	0.553027i
$805$	−2257.96			−0.0988606
$806$	−3433.88	+	301.309i	−0.150066	+	0.0131677i
$807$	11534.3			0.503129
$808$	1653.22	+	2863.46i	0.0719803	+	0.124674i
$809$	8446.41	+	14629.6i	0.367070	+	0.635784i	0.989106	−	0.147204i	$-0.0470275\pi$
$809$	8446.41	+	14629.6i	0.367070	+	0.635784i	−0.622036	+	0.782989i	$0.713694\pi$
$810$	−2087.67	+	3615.96i	−0.0905597	+	0.156854i
$811$	−42182.9			−1.82644			−0.913220	−	0.407466i	$-0.866413\pi$
$811$	−42182.9			−1.82644			−0.913220	+	0.407466i	$0.866413\pi$
$812$	−5671.99	+	9824.17i	−0.245133	+	0.424582i
$813$	−13651.2	+	23644.6i	−0.588892	+	1.01999i
$814$	−34763.6			−1.49688
$815$	4287.81	−	7426.70i	0.184289	−	0.319198i
$816$	−8789.12	−	15223.2i	−0.377060	−	0.653087i
$817$	−610.105	−	1056.73i	−0.0261259	−	0.0452514i
$818$	2104.94			0.0899725
$819$	−36461.8	+	3199.37i	−1.55565	+	0.136502i
$820$	−406.789			−0.0173240
$821$	9250.39	+	16022.1i	0.393229	+	0.681092i	0.992873	−	0.119174i	$-0.0380247\pi$
$821$	9250.39	+	16022.1i	0.393229	+	0.681092i	−0.599645	+	0.800266i	$0.704691\pi$
$822$	−20407.8	−	35347.4i	−0.865942	−	1.49986i
$823$	13934.4	−	24135.0i	0.590184	−	1.02223i	−0.404024	−	0.914749i	$-0.632389\pi$
$823$	13934.4	−	24135.0i	0.590184	−	1.02223i	0.994207	−	0.107480i	$-0.0342780\pi$
$824$	−30.1370			−0.00127412
$825$	−26372.8	+	45679.0i	−1.11295	+	1.92768i
$826$	−3723.98	+	6450.12i	−0.156869	+	0.271705i
$827$	2541.96			0.106884			0.0534418	−	0.998571i	$-0.482981\pi$
$827$	2541.96			0.106884			0.0534418	+	0.998571i	$0.482981\pi$
$828$	−3982.87	+	6898.53i	−0.167167	+	0.289542i
$829$	−14785.0	−	25608.4i	−0.619427	−	1.07288i	−0.989590	−	0.143912i	$-0.954032\pi$
$829$	−14785.0	−	25608.4i	−0.619427	−	1.07288i	0.370164	−	0.928967i	$-0.379302\pi$
$830$	2384.38	+	4129.87i	0.0997147	+	0.172711i
$831$	55745.1			2.32705
$832$	−1267.08	+	2719.08i	−0.0527984	+	0.113302i
$833$	14120.6			0.587333
$834$	−24903.7	−	43134.5i	−1.03399	−	1.79092i
$835$	2915.08	+	5049.07i	0.120815	+	0.209258i
$836$	−958.502	+	1660.17i	−0.0396537	+	0.0686822i
$837$	8018.23			0.331124
$838$	−8711.62	+	15089.0i	−0.359114	+	0.622004i
$839$	−10803.7	+	18712.6i	−0.444561	+	0.770002i	−0.998022	−	0.0628731i	$-0.979974\pi$
$839$	−10803.7	+	18712.6i	−0.444561	+	0.770002i	0.553460	+	0.832875i	$0.313307\pi$
$840$	4149.17			0.170429
$841$	−5362.17	+	9287.54i	−0.219860	+	0.380809i
$842$	−213.335	−	369.507i	−0.00873161	−	0.0151236i
$843$	−14300.0	−	24768.3i	−0.584244	−	1.01194i
$844$	−18734.9			−0.764079
$845$	−5462.14	−	6502.78i	−0.222371	−	0.264737i
$846$	−31005.9			−1.26005
$847$	12041.7	+	20856.9i	0.488499	+	0.846105i
$848$	2081.08	+	3604.53i	0.0842741	+	0.145967i
$849$	−1713.62	+	2968.08i	−0.0692713	+	0.119981i
$850$	27277.6			1.10072
$851$	6205.10	−	10747.6i	0.249951	−	0.432928i
$852$	−7525.78	+	13035.0i	−0.302616	+	0.524146i
$853$	−28695.1			−1.15182			−0.575910	−	0.817513i	$-0.695352\pi$
$853$	−28695.1			−1.15182			−0.575910	+	0.817513i	$0.695352\pi$
$854$	1381.86	−	2393.46i	0.0553705	−	0.0959045i
$855$	−884.080	−	1531.27i	−0.0353625	−	0.0612496i
$856$	−455.301	−	788.605i	−0.0181798	−	0.0314883i
$857$	8720.01			0.347573			0.173786	−	0.984783i	$-0.444400\pi$
$857$	8720.01			0.347573			0.173786	+	0.984783i	$0.444400\pi$
$858$	18976.6	−	40722.6i	0.755071	−	1.62033i
$859$	−1750.23			−0.0695191			−0.0347596	−	0.999396i	$-0.511067\pi$
$859$	−1750.23			−0.0695191			−0.0347596	+	0.999396i	$0.511067\pi$
$860$	−1064.06	−	1843.00i	−0.0421907	−	0.0730765i
$861$	1765.01	+	3057.09i	0.0698624	+	0.121005i
$862$	−8953.45	+	15507.8i	−0.353777	+	0.612759i
$863$	−35493.3			−1.40001			−0.700004	−	0.714139i	$-0.746819\pi$
$863$	−35493.3			−1.40001			−0.700004	+	0.714139i	$0.746819\pi$
$864$	3488.93	−	6043.01i	0.137379	−	0.237948i
$865$	3298.15	−	5712.56i	0.129642	−	0.224547i
$866$	11722.9			0.460000
$867$	46295.8	−	80186.6i	1.81348	−	3.14104i
$868$	−1113.03	−	1927.82i	−0.0435237	−	0.0753852i
$869$	−19827.0	−	34341.4i	−0.773975	−	1.34056i
$870$	12843.1			0.500483
$871$	19168.5	−	1681.96i	0.745694	−	0.0654316i
$872$	15485.0			0.601364
$873$	19128.9	+	33132.3i	0.741600	+	1.28449i
$874$	−342.175	−	592.664i	−0.0132428	−	0.0229372i
$875$	−6875.68	+	11909.0i	−0.265646	+	0.460113i
$876$	14964.3			0.577164
$877$	13213.9	−	22887.2i	0.508782	−	0.881237i	−0.491166	−	0.871066i	$-0.663429\pi$
$877$	13213.9	−	22887.2i	0.508782	−	0.881237i	0.999948	−	0.0101709i	$-0.00323754\pi$
$878$	10443.5	−	18088.7i	0.401426	−	0.695290i
$879$	−19440.4			−0.745970
$880$	−1671.68	+	2895.43i	−0.0640367	+	0.110915i
$881$	−383.063	−	663.484i	−0.0146489	−	0.0253727i	0.858608	−	0.512633i	$-0.171330\pi$
$881$	−383.063	−	663.484i	−0.0146489	−	0.0253727i	−0.873257	+	0.487260i	$0.837996\pi$
$882$	5879.19	+	10183.0i	0.224447	+	0.388754i
$883$	6521.89			0.248561			0.124280	−	0.992247i	$-0.460338\pi$
$883$	6521.89			0.248561			0.124280	+	0.992247i	$0.460338\pi$
$884$	−23145.4	+	2030.91i	−0.880614	+	0.0772702i
$885$	8432.19			0.320277
$886$	−8789.73	−	15224.3i	−0.333292	−	0.577279i
$887$	−12675.8	−	21955.2i	−0.479834	−	0.831097i	0.519899	−	0.854228i	$-0.325970\pi$
$887$	−12675.8	−	21955.2i	−0.479834	−	0.831097i	−0.999732	+	0.0231313i	$0.992636\pi$
$888$	−11402.3	+	19749.4i	−0.430898	+	0.746337i
$889$	−3701.97			−0.139663
$890$	800.810	−	1387.04i	0.0301609	−	0.0522402i
$891$	−14598.0	+	25284.5i	−0.548879	+	0.950686i
$892$	−9535.45			−0.357926
$893$	1331.88	−	2306.89i	0.0499102	−	0.0864470i
$894$	22457.7	+	38897.9i	0.840154	+	1.45519i
$895$	−1150.40	−	1992.56i	−0.0429651	−	0.0744178i
$896$	−1937.22			−0.0722299
$897$	9202.64	+	13135.6i	0.342550	+	0.488946i
$898$	17272.2			0.641851
$899$	−3445.18	−	5967.23i	−0.127812	−	0.221377i
$900$	11357.2	+	19671.3i	0.420637	+	0.728565i
$901$	−16118.4	+	27917.9i	−0.595985	+	1.03228i
$902$	−2844.46			−0.105000
$903$	−9233.67	+	15993.2i	−0.340285	+	0.589390i
$904$	−7595.13	+	13155.2i	−0.279436	+	0.483998i
$905$	1557.80			0.0572190
$906$	−21198.2	+	36716.4i	−0.777332	+	1.34638i
$907$	4752.28	+	8231.20i	0.173977	+	0.301337i	0.939807	−	0.341707i	$-0.111005\pi$
$907$	4752.28	+	8231.20i	0.173977	+	0.301337i	−0.765830	+	0.643043i	$0.777672\pi$
$908$	3108.15	+	5383.47i	0.113599	+	0.196759i
$909$	−21325.1			−0.778116
$910$	2316.47	−	4970.99i	0.0843847	−	0.181084i
$911$	6435.82			0.234059			0.117030	−	0.993128i	$-0.462663\pi$
$911$	6435.82			0.234059			0.117030	+	0.993128i	$0.462663\pi$
$912$	628.771	+	1089.06i	0.0228297	+	0.0395422i
$913$	16672.7	+	28878.0i	0.604367	+	1.04679i
$914$	−4876.96	+	8447.14i	−0.176494	+	0.305697i
$915$	−3128.95			−0.113049
$916$	5831.20	−	10099.9i	0.210336	−	0.364313i
$917$	12225.9	−	21175.8i	0.440276	−	0.762581i
$918$	54045.2			1.94309
$919$	−7476.96	+	12950.5i	−0.268381	+	0.464849i	−0.968444	−	0.249232i	$-0.919822\pi$
$919$	−7476.96	+	12950.5i	−0.268381	+	0.464849i	0.700063	+	0.714081i	$0.253155\pi$
$920$	−596.771	−	1033.64i	−0.0213858	−	0.0370413i
$921$	−35834.0	−	62066.3i	−1.28205	−	2.22058i
$922$	−23607.8			−0.843256
$923$	11415.2	+	16293.8i	0.407082	+	0.581058i
$924$	29013.0			1.03296
$925$	−17694.0	−	30646.8i	−0.628945	−	1.08936i
$926$	4797.53	+	8309.56i	0.170255	+	0.294891i
$927$	97.1849	−	168.329i	0.00344334	−	0.00596403i
$928$	−5996.34			−0.212111
$929$	19030.9	−	32962.5i	0.672103	−	1.16412i	−0.305204	−	0.952287i	$-0.598725\pi$
$929$	19030.9	−	32962.5i	0.672103	−	1.16412i	0.977307	−	0.211829i	$-0.0679419\pi$
$930$	−1260.11	+	2182.57i	−0.0444308	+	0.0769564i
$931$	−1010.18			−0.0355611
$932$	8467.86	−	14666.8i	0.297611	−	0.515478i
$933$	1083.40	+	1876.50i	0.0380160	+	0.0658456i
$934$	13188.7	+	22843.6i	0.462043	+	0.800282i
$935$	−25895.1			−0.905732
$936$	−11101.3	−	15845.7i	−0.387668	−	0.553347i
$937$	14572.5			0.508072			0.254036	−	0.967195i	$-0.418242\pi$
$937$	14572.5			0.508072			0.254036	+	0.967195i	$0.418242\pi$
$938$	6213.09	+	10761.4i	0.216274	+	0.374597i
$939$	19699.6	+	34120.7i	0.684635	+	1.18582i
$940$	2322.88	−	4023.34i	0.0805999	−	0.139603i
$941$	32190.2			1.11516			0.557582	−	0.830122i	$-0.311729\pi$
$941$	32190.2			1.11516			0.557582	+	0.830122i	$0.311729\pi$
$942$	17088.1	−	29597.4i	0.591040	−	1.02371i
$943$	507.720	−	879.397i	0.0175330	−	0.0303681i
$944$	−3936.93			−0.135738
$945$	−6378.42	+	11047.7i	−0.219566	+	0.380300i
$946$	−7440.38	−	12887.1i	−0.255716	−	0.442914i
$947$	21115.5	+	36573.1i	0.724563	+	1.25498i	0.959154	+	0.282886i	$0.0912919\pi$
$947$	21115.5	+	36573.1i	0.724563	+	1.25498i	−0.234590	+	0.972094i	$0.575375\pi$
$948$	−26012.8			−0.891197
$949$	8354.48	−	17928.2i	0.285772	−	0.613249i
$950$	−1951.43			−0.0666451
$951$	4125.09	+	7144.86i	0.140657	+	0.243626i
$952$	−7502.11	−	12994.0i	−0.255404	−	0.442373i
$953$	4084.22	−	7074.07i	0.138826	−	0.240453i	−0.788227	−	0.615385i	$-0.789001\pi$
$953$	4084.22	−	7074.07i	0.138826	−	0.240453i	0.927052	+	0.374932i	$0.122334\pi$
$954$	−26844.0			−0.911013
$955$	1186.11	−	2054.40i	0.0401901	−	0.0696114i
$956$	−4745.11	+	8218.77i	−0.160531	+	0.278048i
$957$	89804.7			3.03341
$958$	−18048.8	+	31261.5i	−0.608696	+	1.05429i
$959$	−17419.5	−	30171.4i	−0.586552	−	1.01594i
$960$	1096.61	+	1899.39i	0.0368677	+	0.0638567i
$961$	−28438.9			−0.954613
$962$	17295.3	+	24686.8i	0.579648	+	0.827374i
$963$	5872.98			0.196525
$964$	−651.526	−	1128.48i	−0.0217679	−	0.0377031i
$965$	−3875.76	−	6713.01i	−0.129290	−	0.223937i
$966$	−5178.66	+	8969.70i	−0.172485	+	0.298753i
$967$	52022.1			1.73001			0.865003	−	0.501766i	$-0.167316\pi$
$967$	52022.1			1.73001			0.865003	+	0.501766i	$0.167316\pi$
$968$	−6365.16	+	11024.8i	−0.211347	+	0.366064i
$969$	−4869.98	+	8435.05i	−0.161451	+	0.279642i
$970$	−5732.35			−0.189747
$971$	5972.47	−	10344.6i	0.197390	−	0.341890i	−0.750291	−	0.661107i	$-0.770087\pi$
$971$	5972.47	−	10344.6i	0.197390	−	0.341890i	0.947681	+	0.319218i	$0.103420\pi$
$972$	−2198.96	−	3808.70i	−0.0725633	−	0.125683i
$973$	−21257.0	−	36818.2i	−0.700378	−	1.21309i
$974$	23002.5			0.756722
$975$	45558.9	−	3997.61i	1.49646	−	0.131309i
$976$	1460.88			0.0479117
$977$	−9494.95	−	16445.7i	−0.310922	−	0.538532i	0.667640	−	0.744484i	$-0.267304\pi$
$977$	−9494.95	−	16445.7i	−0.310922	−	0.538532i	−0.978562	+	0.205952i	$0.933971\pi$
$978$	−19668.2	−	34066.4i	−0.643068	−	1.11383i
$979$	5599.64	−	9698.86i	0.182804	−	0.316626i
$980$	−1761.81			−0.0574275
$981$	−49935.8	+	86491.3i	−1.62520	+	2.81494i
$982$	4000.65	−	6929.34i	0.130006	−	0.225177i
$983$	−47187.4			−1.53107			−0.765537	−	0.643392i	$-0.777526\pi$
$983$	−47187.4			−1.53107			−0.765537	+	0.643392i	$0.777526\pi$
$984$	−932.973	+	1615.96i	−0.0302257	+	0.0523524i
$985$	1077.50	+	1866.28i	0.0348547	+	0.0603701i
$986$	−23221.5	−	40220.8i	−0.750024	−	1.29908i
$987$	−40314.9			−1.30014
$988$	1655.81	−	145.291i	0.0533182	−	0.00467845i
$989$	5312.27			0.170799
$990$	−10781.6	−	18674.2i	−0.346122	−	0.599501i
$991$	15379.7	+	26638.5i	0.492991	+	0.853885i	0.999967	−	0.00807499i	$-0.00257038\pi$
$991$	15379.7	+	26638.5i	0.492991	+	0.853885i	−0.506977	+	0.861960i	$0.669237\pi$
$992$	588.337	−	1019.03i	0.0188303	−	0.0326151i
$993$	−42796.7			−1.36769
$994$	−6423.76	+	11126.3i	−0.204979	+	0.355034i
$995$	−10695.7	+	18525.5i	−0.340780	+	0.590248i
$996$	21874.4			0.695901
$997$	−24666.1	+	42722.9i	−0.783533	+	1.35712i	0.146338	+	0.989235i	$0.453251\pi$
$997$	−24666.1	+	42722.9i	−0.783533	+	1.35712i	−0.929871	+	0.367885i	$0.880082\pi$
$998$	8322.72	+	14415.4i	0.263979	+	0.457225i
$999$	−35057.0	−	60720.5i	−1.11027	−	1.92304i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.4.c.b.3.2	✓	4
3.2	odd	2		234.4.h.h.55.1		4
4.3	odd	2		208.4.i.d.81.1		4
13.2	odd	12		338.4.b.e.337.1		4
13.3	even	3		338.4.a.h.1.1		2
13.4	even	6		338.4.c.j.191.2		4
13.5	odd	4		338.4.e.f.23.2		8
13.6	odd	12		338.4.e.f.147.4		8
13.7	odd	12		338.4.e.f.147.2		8
13.8	odd	4		338.4.e.f.23.4		8
13.9	even	3	inner	26.4.c.b.9.2	yes	4
13.10	even	6		338.4.a.g.1.1		2
13.11	odd	12		338.4.b.e.337.3		4
13.12	even	2		338.4.c.j.315.2		4
39.35	odd	6		234.4.h.h.217.1		4
52.35	odd	6		208.4.i.d.113.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.4.c.b.3.2	✓	4	1.1	even	1	trivial
26.4.c.b.9.2	yes	4	13.9	even	3	inner
208.4.i.d.81.1		4	4.3	odd	2
208.4.i.d.113.1		4	52.35	odd	6
234.4.h.h.55.1		4	3.2	odd	2
234.4.h.h.217.1		4	39.35	odd	6
338.4.a.g.1.1		2	13.10	even	6
338.4.a.h.1.1		2	13.3	even	3
338.4.b.e.337.1		4	13.2	odd	12
338.4.b.e.337.3		4	13.11	odd	12
338.4.c.j.191.2		4	13.4	even	6
338.4.c.j.315.2		4	13.12	even	2
338.4.e.f.23.2		8	13.5	odd	4
338.4.e.f.23.4		8	13.8	odd	4
338.4.e.f.147.2		8	13.7	odd	12
338.4.e.f.147.4		8	13.6	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	26.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(4.43273 + 7.67771i) q^{3} +(-2.00000 + 3.46410i) q^{4} +3.86546 q^{5} +(8.86546 - 15.3554i) q^{6} +(7.56727 - 13.1069i) q^{7} +8.00000 q^{8} +(-25.7982 + 44.6838i) q^{9} +(-3.86546 - 6.69517i) q^{10} +(-27.0291 - 46.8158i) q^{11} -35.4618 q^{12} +(-19.7982 + 42.4857i) q^{13} -30.2691 q^{14} +(17.1345 + 29.6779i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(61.9618 - 107.321i) q^{17} +103.193 q^{18} +(-4.43273 + 7.67771i) q^{19} +(-7.73092 + 13.3903i) q^{20} +134.175 q^{21} +(-54.0582 + 93.6316i) q^{22} +(-19.2982 - 33.4254i) q^{23} +(35.4618 + 61.4217i) q^{24} -110.058 q^{25} +(93.3855 - 8.19419i) q^{26} -218.058 q^{27} +(30.2691 + 52.4276i) q^{28} +(93.6928 + 162.281i) q^{29} +(34.2691 - 59.3558i) q^{30} -36.7710 q^{31} +(-16.0000 + 27.7128i) q^{32} +(239.625 - 415.044i) q^{33} -247.847 q^{34} +(29.2510 - 50.6642i) q^{35} +(-103.193 - 178.735i) q^{36} +(160.769 + 278.460i) q^{37} +17.7309 q^{38} +(-413.953 + 36.3226i) q^{39} +30.9237 q^{40} +(13.1546 + 22.7844i) q^{41} +(-134.175 - 232.397i) q^{42} +(-68.8182 + 119.197i) q^{43} +216.233 q^{44} +(-99.7219 + 172.723i) q^{45} +(-38.5964 + 66.8509i) q^{46} -300.466 q^{47} +(70.9237 - 122.843i) q^{48} +(56.9728 + 98.6799i) q^{49} +(110.058 + 190.626i) q^{50} +1098.64 q^{51} +(-107.578 - 153.554i) q^{52} -260.135 q^{53} +(218.058 + 377.688i) q^{54} +(-104.480 - 180.965i) q^{55} +(60.5382 - 104.855i) q^{56} -78.5964 q^{57} +(187.386 - 324.561i) q^{58} +(123.029 - 213.093i) q^{59} -137.076 q^{60} +(-45.6526 + 79.0727i) q^{61} +(36.7710 + 63.6893i) q^{62} +(390.444 + 676.268i) q^{63} +64.0000 q^{64} +(-76.5291 + 164.227i) q^{65} -958.502 q^{66} +(-205.262 - 355.524i) q^{67} +(247.847 + 429.284i) q^{68} +(171.087 - 296.332i) q^{69} -117.004 q^{70} +(212.222 - 367.579i) q^{71} +(-206.386 + 357.470i) q^{72} -421.982 q^{73} +(321.538 - 556.920i) q^{74} +(-487.858 - 844.995i) q^{75} +(-17.7309 - 30.7109i) q^{76} -818.146 q^{77} +(476.865 + 680.665i) q^{78} +733.542 q^{79} +(-30.9237 - 53.5614i) q^{80} +(-270.042 - 467.727i) q^{81} +(26.3092 - 45.5689i) q^{82} -616.843 q^{83} +(-268.349 + 464.795i) q^{84} +(239.511 - 414.845i) q^{85} +275.273 q^{86} +(-830.629 + 1438.69i) q^{87} +(-216.233 - 374.526i) q^{88} +(103.585 + 179.415i) q^{89} +398.887 q^{90} +(407.037 + 580.993i) q^{91} +154.386 q^{92} +(-162.996 - 282.317i) q^{93} +(300.466 + 520.422i) q^{94} +(-17.1345 + 29.6779i) q^{95} -283.695 q^{96} +(370.742 - 642.144i) q^{97} +(113.946 - 197.360i) q^{98} +2789.21 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 3 q^{3} - 8 q^{4} - 14 q^{5} + 6 q^{6} + 45 q^{7} + 32 q^{8} - 59 q^{9} + 14 q^{10} - 5 q^{11} - 24 q^{12} - 35 q^{13} - 180 q^{14} + 98 q^{15} - 32 q^{16} + 130 q^{17} + 236 q^{18} - 3 q^{19}+ \cdots + 4852 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 3 * q^3 - 8 * q^4 - 14 * q^5 + 6 * q^6 + 45 * q^7 + 32 * q^8 - 59 * q^9 + 14 * q^10 - 5 * q^11 - 24 * q^12 - 35 * q^13 - 180 * q^14 + 98 * q^15 - 32 * q^16 + 130 * q^17 + 236 * q^18 - 3 * q^19 + 28 * q^20 - 82 * q^21 - 10 * q^22 - 33 * q^23 + 24 * q^24 - 234 * q^25 + 20 * q^26 - 666 * q^27 + 180 * q^28 + 198 * q^29 + 196 * q^30 + 560 * q^31 - 64 * q^32 + 767 * q^33 - 520 * q^34 - 266 * q^35 - 236 * q^36 + 702 * q^37 + 12 * q^38 - 1317 * q^39 - 112 * q^40 - 242 * q^41 + 82 * q^42 + 93 * q^43 + 40 * q^44 - 119 * q^45 - 66 * q^46 + 448 * q^47 + 48 * q^48 - 435 * q^49 + 234 * q^50 + 2126 * q^51 + 100 * q^52 - 1070 * q^53 + 666 * q^54 - 742 * q^55 + 360 * q^56 - 226 * q^57 + 396 * q^58 + 389 * q^59 - 784 * q^60 - 654 * q^61 - 560 * q^62 + 1002 * q^63 + 256 * q^64 - 203 * q^65 - 3068 * q^66 + 107 * q^67 + 520 * q^68 + 375 * q^69 + 1064 * q^70 + 569 * q^71 - 472 * q^72 - 1246 * q^73 + 1404 * q^74 - 935 * q^75 - 12 * q^76 + 1294 * q^77 + 1878 * q^78 + 1520 * q^79 + 112 * q^80 + 334 * q^81 - 484 * q^82 - 3528 * q^83 + 164 * q^84 + 413 * q^85 - 372 * q^86 - 1599 * q^87 - 40 * q^88 + 871 * q^89 + 476 * q^90 - 1539 * q^91 + 264 * q^92 - 2184 * q^93 - 448 * q^94 - 98 * q^95 - 192 * q^96 + 879 * q^97 - 870 * q^98 + 4852 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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