LMFDB - Embedded newform 26.5.f.b.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [26,5,Mod(7,26)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(26, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([11]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("26.7");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	26.f (of order $12$, degree $4$, 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:	$2.68761904018$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 494x^{6} + 90747x^{4} - 7343258x^{2} + 221087161 $ x^8 - 494x^6 + 90747x^4 - 7343258*x^2 + 221087161
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.1
Root			$-12.0941 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	26.19
Dual form			26.5.f.b.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.732051 - 2.73205i) q^{2} +(-4.74800 + 8.22378i) q^{3} +(-6.92820 + 4.00000i) q^{4} +(-19.2341 + 19.2341i) q^{5} +(25.9436 + 6.95155i) q^{6} +(-5.11403 + 19.0858i) q^{7} +(16.0000 + 16.0000i) q^{8} +(-4.58700 - 7.94492i) q^{9} +O(q^{10})$	\(q+(-0.732051 - 2.73205i) q^{2} +(-4.74800 + 8.22378i) q^{3} +(-6.92820 + 4.00000i) q^{4} +(-19.2341 + 19.2341i) q^{5} +(25.9436 + 6.95155i) q^{6} +(-5.11403 + 19.0858i) q^{7} +(16.0000 + 16.0000i) q^{8} +(-4.58700 - 7.94492i) q^{9} +(66.6289 + 38.4682i) q^{10} +(-31.7929 + 8.51887i) q^{11} -75.9680i q^{12} +(-94.3282 - 140.225i) q^{13} +55.8871 q^{14} +(-66.8535 - 249.501i) q^{15} +(32.0000 - 55.4256i) q^{16} +(-186.163 + 107.481i) q^{17} +(-18.3480 + 18.3480i) q^{18} +(407.726 + 109.250i) q^{19} +(56.3214 - 210.194i) q^{20} +(-132.676 - 132.676i) q^{21} +(46.5480 + 80.6235i) q^{22} +(833.208 + 481.053i) q^{23} +(-207.548 + 55.6124i) q^{24} -114.902i q^{25} +(-314.050 + 360.362i) q^{26} -682.060 q^{27} +(-40.9122 - 152.686i) q^{28} +(-772.393 + 1337.82i) q^{29} +(-632.708 + 365.294i) q^{30} +(750.040 - 750.040i) q^{31} +(-174.851 - 46.8513i) q^{32} +(80.8952 - 301.905i) q^{33} +(429.924 + 429.924i) q^{34} +(-268.735 - 465.462i) q^{35} +(63.5593 + 36.6960i) q^{36} +(680.735 - 182.402i) q^{37} -1193.90i q^{38} +(1601.05 - 109.944i) q^{39} -615.491 q^{40} +(146.998 + 548.605i) q^{41} +(-265.352 + 459.603i) q^{42} +(-141.756 + 81.8426i) q^{43} +(186.192 - 186.192i) q^{44} +(241.040 + 64.5865i) q^{45} +(704.310 - 2628.52i) q^{46} +(-1733.01 - 1733.01i) q^{47} +(303.872 + 526.322i) q^{48} +(1741.21 + 1005.29i) q^{49} +(-313.917 + 84.1139i) q^{50} -2041.28i q^{51} +(1214.43 + 594.198i) q^{52} -4534.85 q^{53} +(499.302 + 1863.42i) q^{54} +(447.654 - 775.360i) q^{55} +(-387.197 + 223.548i) q^{56} +(-2834.33 + 2834.33i) q^{57} +(4220.44 + 1130.86i) q^{58} +(-201.708 + 752.785i) q^{59} +(1461.18 + 1461.18i) q^{60} +(-1974.23 - 3419.47i) q^{61} +(-2598.22 - 1500.08i) q^{62} +(175.093 - 46.9161i) q^{63} +512.000i q^{64} +(4511.43 + 882.793i) q^{65} -884.039 q^{66} +(1784.27 + 6658.99i) q^{67} +(859.849 - 1489.30i) q^{68} +(-7912.14 + 4568.08i) q^{69} +(-1074.94 + 1074.94i) q^{70} +(5330.87 + 1428.40i) q^{71} +(53.7267 - 200.511i) q^{72} +(-2496.58 - 2496.58i) q^{73} +(-996.665 - 1726.27i) q^{74} +(944.926 + 545.554i) q^{75} +(-3261.81 + 873.998i) q^{76} -650.358i q^{77} +(-1472.42 - 4293.67i) q^{78} +6710.05 q^{79} +(450.571 + 1681.55i) q^{80} +(3609.97 - 6252.64i) q^{81} +(1391.21 - 803.214i) q^{82} +(1361.30 - 1361.30i) q^{83} +(1449.91 + 388.502i) q^{84} +(1513.37 - 5647.98i) q^{85} +(327.370 + 327.370i) q^{86} +(-7334.65 - 12704.0i) q^{87} +(-644.988 - 372.384i) q^{88} +(6033.51 - 1616.67i) q^{89} -705.815i q^{90} +(3158.71 - 1083.21i) q^{91} -7696.84 q^{92} +(2606.97 + 9729.36i) q^{93} +(-3466.01 + 6003.31i) q^{94} +(-9943.56 + 5740.92i) q^{95} +(1215.49 - 1215.49i) q^{96} +(-4670.76 - 1251.53i) q^{97} +(1471.85 - 5493.00i) q^{98} +(213.516 + 213.516i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 18 q^{5} - 36 q^{6} + 4 q^{7} + 128 q^{8} - 198 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 - 18 * q^5 - 36 * q^6 + 4 * q^7 + 128 * q^8 - 198 * q^9	\( 8 q + 8 q^{2} - 18 q^{5} - 36 q^{6} + 4 q^{7} + 128 q^{8} - 198 q^{9} + 348 q^{10} + 144 q^{11} - 318 q^{13} - 40 q^{14} - 924 q^{15} + 256 q^{16} - 390 q^{17} - 792 q^{18} + 2278 q^{19} + 624 q^{20} - 678 q^{21} - 756 q^{22} + 744 q^{23} + 288 q^{24} + 424 q^{26} - 1404 q^{27} + 32 q^{28} - 732 q^{29} - 2496 q^{30} + 368 q^{31} - 512 q^{32} + 7746 q^{33} - 312 q^{34} - 342 q^{35} + 1248 q^{36} - 280 q^{37} + 2808 q^{39} - 576 q^{40} + 744 q^{41} - 1356 q^{42} - 13014 q^{43} - 3024 q^{44} + 5766 q^{45} + 1884 q^{46} - 10896 q^{47} - 1842 q^{49} + 1508 q^{50} + 2624 q^{52} - 4728 q^{53} + 6372 q^{54} + 6630 q^{55} + 288 q^{56} + 18990 q^{57} + 8064 q^{58} + 3576 q^{59} - 4800 q^{60} - 13170 q^{61} + 4704 q^{62} - 6396 q^{63} + 6792 q^{65} + 4824 q^{66} + 3490 q^{67} - 624 q^{68} - 45354 q^{69} - 1368 q^{70} + 22710 q^{71} - 672 q^{72} - 7586 q^{73} - 10592 q^{74} - 7128 q^{75} - 18224 q^{76} - 6396 q^{78} + 37824 q^{79} + 4992 q^{80} + 17088 q^{81} + 4368 q^{82} + 21864 q^{83} + 9456 q^{84} + 6198 q^{85} - 2592 q^{86} - 39708 q^{87} - 1440 q^{88} + 17238 q^{89} + 12160 q^{91} + 3168 q^{92} - 258 q^{93} - 21792 q^{94} - 8280 q^{95} - 19450 q^{97} - 20548 q^{98} - 55296 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - 18 * q^5 - 36 * q^6 + 4 * q^7 + 128 * q^8 - 198 * q^9 + 348 * q^10 + 144 * q^11 - 318 * q^13 - 40 * q^14 - 924 * q^15 + 256 * q^16 - 390 * q^17 - 792 * q^18 + 2278 * q^19 + 624 * q^20 - 678 * q^21 - 756 * q^22 + 744 * q^23 + 288 * q^24 + 424 * q^26 - 1404 * q^27 + 32 * q^28 - 732 * q^29 - 2496 * q^30 + 368 * q^31 - 512 * q^32 + 7746 * q^33 - 312 * q^34 - 342 * q^35 + 1248 * q^36 - 280 * q^37 + 2808 * q^39 - 576 * q^40 + 744 * q^41 - 1356 * q^42 - 13014 * q^43 - 3024 * q^44 + 5766 * q^45 + 1884 * q^46 - 10896 * q^47 - 1842 * q^49 + 1508 * q^50 + 2624 * q^52 - 4728 * q^53 + 6372 * q^54 + 6630 * q^55 + 288 * q^56 + 18990 * q^57 + 8064 * q^58 + 3576 * q^59 - 4800 * q^60 - 13170 * q^61 + 4704 * q^62 - 6396 * q^63 + 6792 * q^65 + 4824 * q^66 + 3490 * q^67 - 624 * q^68 - 45354 * q^69 - 1368 * q^70 + 22710 * q^71 - 672 * q^72 - 7586 * q^73 - 10592 * q^74 - 7128 * q^75 - 18224 * q^76 - 6396 * q^78 + 37824 * q^79 + 4992 * q^80 + 17088 * q^81 + 4368 * q^82 + 21864 * q^83 + 9456 * q^84 + 6198 * q^85 - 2592 * q^86 - 39708 * q^87 - 1440 * q^88 + 17238 * q^89 + 12160 * q^91 + 3168 * q^92 - 258 * q^93 - 21792 * q^94 - 8280 * q^95 - 19450 * q^97 - 20548 * q^98 - 55296 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$15$
$\chi(n)$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−0.732051	−	2.73205i	−0.183013	−	0.683013i
$2$	−0.732051	−	2.73205i	−0.183013	−	0.683013i
$3$	−4.74800	+	8.22378i	−0.527556	+	0.913753i	0.471929	+	0.881637i	$0.343558\pi$
$3$	−4.74800	+	8.22378i	−0.527556	+	0.913753i	−0.999484	+	0.0321162i	$0.989775\pi$
$4$	−6.92820	+	4.00000i	−0.433013	+	0.250000i
$5$	−19.2341	+	19.2341i	−0.769364	+	0.769364i	−0.977995	−	0.208630i	$-0.933099\pi$
$5$	−19.2341	+	19.2341i	−0.769364	+	0.769364i	0.208630	+	0.977995i	$0.433099\pi$
$6$	25.9436	+	6.95155i	0.720654	+	0.193099i
$7$	−5.11403	+	19.0858i	−0.104368	+	0.389506i	−0.998273	−	0.0587506i	$-0.981288\pi$
$7$	−5.11403	+	19.0858i	−0.104368	+	0.389506i	0.893905	+	0.448257i	$0.147955\pi$
$8$	16.0000	+	16.0000i	0.250000	+	0.250000i
$9$	−4.58700	−	7.94492i	−0.0566296	−	0.0980854i
$10$	66.6289	+	38.4682i	0.666289	+	0.384682i
$11$	−31.7929	+	8.51887i	−0.262751	+	0.0704039i	−0.387789	−	0.921748i	$-0.626761\pi$
$11$	−31.7929	+	8.51887i	−0.262751	+	0.0704039i	0.125038	+	0.992152i	$0.460095\pi$
$12$		−	75.9680i		−	0.527556i
$13$	−94.3282	−	140.225i	−0.558155	−	0.829737i
$13$	−94.3282	−	140.225i	−0.558155	−	0.829737i
$14$	55.8871			0.285138
$15$	−66.8535	−	249.501i	−0.297127	−	1.10889i
$16$	32.0000	−	55.4256i	0.125000	−	0.216506i
$17$	−186.163	+	107.481i	−0.644162	+	0.371907i	−0.786216	−	0.617952i	$-0.787963\pi$
$17$	−186.163	+	107.481i	−0.644162	+	0.371907i	0.142054	+	0.989859i	$0.454629\pi$
$18$	−18.3480	+	18.3480i	−0.0566296	+	0.0566296i
$19$	407.726	+	109.250i	1.12943	+	0.302631i	0.774695	−	0.632335i	$-0.217903\pi$
$19$	407.726	+	109.250i	1.12943	+	0.302631i	0.354739	+	0.934965i	$0.384570\pi$
$20$	56.3214	−	210.194i	0.140803	−	0.525486i
$21$	−132.676	−	132.676i	−0.300853	−	0.300853i
$22$	46.5480	+	80.6235i	0.0961735	+	0.166577i
$23$	833.208	+	481.053i	1.57506	+	0.909362i	0.995533	+	0.0944099i	$0.0300964\pi$
$23$	833.208	+	481.053i	1.57506	+	0.909362i	0.579528	+	0.814952i	$0.303237\pi$
$24$	−207.548	+	55.6124i	−0.360327	+	0.0965494i
$25$		−	114.902i		−	0.183843i
$26$	−314.050	+	360.362i	−0.464571	+	0.533079i
$27$	−682.060			−0.935610
$28$	−40.9122	−	152.686i	−0.0521839	−	0.194753i
$29$	−772.393	+	1337.82i	−0.918422	+	1.59075i	−0.116610	+	0.993178i	$0.537203\pi$
$29$	−772.393	+	1337.82i	−0.918422	+	1.59075i	−0.801812	+	0.597576i	$0.796130\pi$
$30$	−632.708	+	365.294i	−0.703009	+	0.405882i
$31$	750.040	−	750.040i	0.780479	−	0.780479i	−0.199432	−	0.979912i	$-0.563910\pi$
$31$	750.040	−	750.040i	0.780479	−	0.780479i	0.979912	+	0.199432i	$0.0639099\pi$
$32$	−174.851	−	46.8513i	−0.170753	−	0.0457532i
$33$	80.8952	−	301.905i	0.0742839	−	0.277231i
$34$	429.924	+	429.924i	0.371907	+	0.371907i
$35$	−268.735	−	465.462i	−0.219375	−	0.379969i
$36$	63.5593	+	36.6960i	0.0490427	+	0.0283148i
$37$	680.735	−	182.402i	0.497250	−	0.133238i	−0.00147363	−	0.999999i	$-0.500469\pi$
$37$	680.735	−	182.402i	0.497250	−	0.133238i	0.498723	+	0.866761i	$0.333802\pi$
$38$		−	1193.90i		−	0.826803i
$39$	1601.05	−	109.944i	1.05263	−	0.0722838i
$40$	−615.491			−0.384682
$41$	146.998	+	548.605i	0.0874470	+	0.326357i	0.995766	−	0.0919209i	$-0.0293007\pi$
$41$	146.998	+	548.605i	0.0874470	+	0.326357i	−0.908319	+	0.418277i	$0.862634\pi$
$42$	−265.352	+	459.603i	−0.150426	+	0.260546i
$43$	−141.756	+	81.8426i	−0.0766661	+	0.0442632i	−0.537843	−	0.843045i	$-0.680761\pi$
$43$	−141.756	+	81.8426i	−0.0766661	+	0.0442632i	0.461177	+	0.887308i	$0.347427\pi$
$44$	186.192	−	186.192i	0.0961735	−	0.0961735i
$45$	241.040	+	64.5865i	0.119032	+	0.0318946i
$46$	704.310	−	2628.52i	0.332850	−	1.24221i
$47$	−1733.01	−	1733.01i	−0.784521	−	0.784521i	0.196069	−	0.980590i	$-0.437182\pi$
$47$	−1733.01	−	1733.01i	−0.784521	−	0.784521i	−0.980590	+	0.196069i	$0.937182\pi$
$48$	303.872	+	526.322i	0.131889	+	0.228438i
$49$	1741.21	+	1005.29i	0.725203	+	0.418696i
$50$	−313.917	+	84.1139i	−0.125567	+	0.0336456i
$51$		−	2041.28i		−	0.784806i
$52$	1214.43	+	594.198i	0.449122	+	0.219748i
$53$	−4534.85			−1.61440			−0.807200	−	0.590278i	$-0.799018\pi$
$53$	−4534.85			−1.61440			−0.807200	+	0.590278i	$0.799018\pi$
$54$	499.302	+	1863.42i	0.171228	+	0.639033i
$55$	447.654	−	775.360i	0.147985	−	0.256317i
$56$	−387.197	+	223.548i	−0.123469	+	0.0712846i
$57$	−2834.33	+	2834.33i	−0.872369	+	0.872369i
$58$	4220.44	+	1130.86i	1.25459	+	0.336166i
$59$	−201.708	+	752.785i	−0.0579454	+	0.216255i	−0.988827	−	0.149065i	$-0.952374\pi$
$59$	−201.708	+	752.785i	−0.0579454	+	0.216255i	0.930882	+	0.365320i	$0.119040\pi$
$60$	1461.18	+	1461.18i	0.405882	+	0.405882i
$61$	−1974.23	−	3419.47i	−0.530564	−	0.918965i	−0.999364	−	0.0356600i	$-0.988647\pi$
$61$	−1974.23	−	3419.47i	−0.530564	−	0.918965i	0.468800	−	0.883305i	$-0.344687\pi$
$62$	−2598.22	−	1500.08i	−0.675915	−	0.390240i
$63$	175.093	−	46.9161i	0.0441152	−	0.0118206i
$64$			512.000i			0.125000i
$65$	4511.43	+	882.793i	1.06779	+	0.208945i
$66$	−884.039			−0.202947
$67$	1784.27	+	6658.99i	0.397476	+	1.48340i	0.817522	+	0.575898i	$0.195347\pi$
$67$	1784.27	+	6658.99i	0.397476	+	1.48340i	−0.420045	+	0.907503i	$0.637986\pi$
$68$	859.849	−	1489.30i	0.185953	−	0.322081i
$69$	−7912.14	+	4568.08i	−1.66186	+	0.959478i
$70$	−1074.94	+	1074.94i	−0.219375	+	0.219375i
$71$	5330.87	+	1428.40i	1.05750	+	0.283357i	0.745349	−	0.666675i	$-0.232283\pi$
$71$	5330.87	+	1428.40i	1.05750	+	0.283357i	0.312154	+	0.950032i	$0.398950\pi$
$72$	53.7267	−	200.511i	0.0103639	−	0.0386788i
$73$	−2496.58	−	2496.58i	−0.468489	−	0.468489i	0.432936	−	0.901425i	$-0.357478\pi$
$73$	−2496.58	−	2496.58i	−0.468489	−	0.468489i	−0.901425	+	0.432936i	$0.857478\pi$
$74$	−996.665	−	1726.27i	−0.182006	−	0.315244i
$75$	944.926	+	545.554i	0.167987	+	0.0969873i
$76$	−3261.81	+	873.998i	−0.564717	+	0.151315i
$77$		−	650.358i		−	0.109691i
$78$	−1472.42	−	4293.67i	−0.242016	−	0.705732i
$79$	6710.05			1.07516			0.537578	−	0.843214i	$-0.319339\pi$
$79$	6710.05			1.07516			0.537578	+	0.843214i	$0.319339\pi$
$80$	450.571	+	1681.55i	0.0704017	+	0.262743i
$81$	3609.97	−	6252.64i	0.550216	−	0.953002i
$82$	1391.21	−	803.214i	0.206902	−	0.119455i
$83$	1361.30	−	1361.30i	0.197605	−	0.197605i	−0.601368	−	0.798972i	$-0.705377\pi$
$83$	1361.30	−	1361.30i	0.197605	−	0.197605i	0.798972	+	0.601368i	$0.205377\pi$
$84$	1449.91	+	388.502i	0.205486	+	0.0550598i
$85$	1513.37	−	5647.98i	0.209463	−	0.781727i
$86$	327.370	+	327.370i	0.0442632	+	0.0442632i
$87$	−7334.65	−	12704.0i	−0.969038	−	1.67842i
$88$	−644.988	−	372.384i	−0.0832887	−	0.0480868i
$89$	6033.51	−	1616.67i	0.761711	−	0.204100i	0.143004	−	0.989722i	$-0.454324\pi$
$89$	6033.51	−	1616.67i	0.761711	−	0.204100i	0.618707	+	0.785622i	$0.287657\pi$
$90$		−	705.815i		−	0.0871376i
$91$	3158.71	−	1083.21i	0.381441	−	0.130807i
$92$	−7696.84			−0.909362
$93$	2606.97	+	9729.36i	0.301419	+	1.12491i
$94$	−3466.01	+	6003.31i	−0.392260	+	0.679415i
$95$	−9943.56	+	5740.92i	−1.10178	+	0.636113i
$96$	1215.49	−	1215.49i	0.131889	−	0.131889i
$97$	−4670.76	−	1251.53i	−0.496414	−	0.133014i	0.00192128	−	0.999998i	$-0.499388\pi$
$97$	−4670.76	−	1251.53i	−0.496414	−	0.133014i	−0.498335	+	0.866984i	$0.666055\pi$
$98$	1471.85	−	5493.00i	0.153253	−	0.571950i
$99$	213.516	+	213.516i	0.0217851	+	0.0217851i
$100$	459.607	+	796.063i	0.0459607	+	0.0796063i
$101$	7300.50	+	4214.95i	0.715665	+	0.413190i	0.813155	−	0.582047i	$-0.197748\pi$
$101$	7300.50	+	4214.95i	0.715665	+	0.413190i	−0.0974899	+	0.995237i	$0.531081\pi$
$102$	−5576.88	+	1494.32i	−0.536033	+	0.143629i
$103$			2398.45i			0.226076i	0.993591	+	0.113038i	$0.0360583\pi$
$103$			2398.45i			0.226076i	−0.993591	+	0.113038i	$0.963942\pi$
$104$	734.356	−	3752.86i	0.0678954	−	0.346973i
$105$	5103.81			0.462930
$106$	3319.74	+	12389.4i	0.295456	+	1.10266i
$107$	−4706.11	+	8151.21i	−0.411049	+	0.711959i	−0.995005	−	0.0998272i	$-0.968171\pi$
$107$	−4706.11	+	8151.21i	−0.411049	+	0.711959i	0.583955	+	0.811786i	$0.301504\pi$
$108$	4725.45	−	2728.24i	0.405131	−	0.233902i
$109$	14993.7	−	14993.7i	1.26199	−	1.26199i	0.311860	−	0.950128i	$-0.399048\pi$
$109$	14993.7	−	14993.7i	1.26199	−	1.26199i	0.950128	−	0.311860i	$-0.100952\pi$
$110$	−2446.03	−	655.412i	−0.202151	−	0.0541662i
$111$	−1732.09	+	6464.26i	−0.140580	+	0.524654i
$112$	894.194	+	894.194i	0.0712846	+	0.0712846i
$113$	8782.46	+	15211.7i	0.687795	+	1.19130i	0.972550	+	0.232696i	$0.0747547\pi$
$113$	8782.46	+	15211.7i	0.687795	+	1.19130i	−0.284754	+	0.958601i	$0.591912\pi$
$114$	9818.40	+	5668.65i	0.755494	+	0.436185i
$115$	−25278.6	+	6773.39i	−1.91143	+	0.512165i
$116$		−	12358.3i		−	0.918422i
$117$	−681.396	+	1392.64i	−0.0497769	+	0.101735i
$118$	2204.31			0.158310
$119$	−1099.32	−	4102.73i	−0.0776303	−	0.289720i
$120$	2922.35	−	5061.66i	0.202941	−	0.351504i
$121$	−11741.3	+	6778.82i	−0.801944	+	0.463003i
$122$	−7896.92	+	7896.92i	−0.530564	+	0.530564i
$123$	−5209.56	−	1395.90i	−0.344342	−	0.0922663i
$124$	−2196.27	+	8196.59i	−0.142838	+	0.533077i
$125$	−9811.28	−	9811.28i	−0.627922	−	0.627922i
$126$	−256.354	−	444.018i	−0.0161473	−	0.0279679i
$127$	−14061.3	−	8118.27i	−0.871800	−	0.503334i	−0.00385399	−	0.999993i	$-0.501227\pi$
$127$	−14061.3	−	8118.27i	−0.871800	−	0.503334i	−0.867946	+	0.496659i	$0.834560\pi$
$128$	1398.81	−	374.810i	0.0853766	−	0.0228766i
$129$		−	1554.35i		−	0.0934051i
$130$	−890.762	−	12971.7i	−0.0527078	−	0.767557i
$131$	9149.90			0.533180			0.266590	−	0.963810i	$-0.414103\pi$
$131$	9149.90			0.533180			0.266590	+	0.963810i	$0.414103\pi$
$132$	647.162	+	2415.24i	0.0371420	+	0.138616i
$133$	−4170.24	+	7223.07i	−0.235753	+	0.408337i
$134$	16886.5	−	9749.43i	0.940439	−	0.542962i
$135$	13118.8	−	13118.8i	0.719825	−	0.719825i
$136$	−4698.30	−	1258.91i	−0.254017	−	0.0680637i
$137$	3049.09	−	11379.4i	0.162454	−	0.606286i	−0.835898	−	0.548886i	$-0.815052\pi$
$137$	3049.09	−	11379.4i	0.162454	−	0.606286i	0.998351	−	0.0574001i	$-0.0182811\pi$
$138$	18272.3	+	18272.3i	0.959478	+	0.959478i
$139$	1013.40	+	1755.27i	0.0524509	+	0.0908476i	0.891059	−	0.453888i	$-0.149963\pi$
$139$	1013.40	+	1755.27i	0.0524509	+	0.0908476i	−0.838608	+	0.544736i	$0.816630\pi$
$140$	3723.70	+	2149.88i	0.189985	+	0.109688i
$141$	22480.2	−	6023.54i	1.13074	−	0.302980i
$142$		−	15609.9i		−	0.774145i
$143$	4193.53	+	3654.60i	0.205072	+	0.178718i
$144$	−587.136			−0.0283148
$145$	−10875.6	−	40588.1i	−0.517268	−	1.93047i
$146$	−4993.15	+	8648.39i	−0.234244	+	0.405723i
$147$	−16534.6	+	9546.23i	−0.765170	+	0.441771i
$148$	−3986.66	+	3986.66i	−0.182006	+	0.182006i
$149$	23213.0	+	6219.90i	1.04558	+	0.280163i	0.740425	−	0.672139i	$-0.234624\pi$
$149$	23213.0	+	6219.90i	1.04558	+	0.280163i	0.305157	+	0.952302i	$0.401291\pi$
$150$	798.746	−	2980.96i	0.0354998	−	0.132487i
$151$	−1109.89	−	1109.89i	−0.0486774	−	0.0486774i	0.682349	−	0.731026i	$-0.260958\pi$
$151$	−1109.89	−	1109.89i	−0.0486774	−	0.0486774i	−0.731026	+	0.682349i	$0.760958\pi$
$152$	4775.62	+	8271.61i	0.206701	+	0.358016i
$153$	1707.86	+	986.032i	0.0729573	+	0.0421219i
$154$	−1776.81	+	476.095i	−0.0749204	+	0.0200748i
$155$			28852.7i			1.20095i
$156$	−10652.6	+	7165.93i	−0.437732	+	0.294458i
$157$	−17982.1			−0.729525			−0.364762	−	0.931101i	$-0.618850\pi$
$157$	−17982.1			−0.729525			−0.364762	+	0.931101i	$0.618850\pi$
$158$	−4912.10	−	18332.2i	−0.196767	−	0.734345i
$159$	21531.5	−	37293.6i	0.851685	−	1.47516i
$160$	4264.25	−	2461.97i	0.166572	−	0.0961705i
$161$	−13442.3	+	13442.3i	−0.518588	+	0.518588i
$162$	−19725.2	−	5285.36i	−0.751609	−	0.201393i
$163$	−12052.9	+	44982.0i	−0.453645	+	1.69303i	0.238397	+	0.971168i	$0.423378\pi$
$163$	−12052.9	+	44982.0i	−0.453645	+	1.69303i	−0.692041	+	0.721858i	$0.743288\pi$
$164$	−3212.86	−	3212.86i	−0.119455	−	0.119455i
$165$	4250.93	+	7362.82i	0.156141	+	0.270443i
$166$	−4715.68	−	2722.60i	−0.171131	−	0.0988024i
$167$	16884.4	−	4524.16i	0.605415	−	0.162220i	0.0569261	−	0.998378i	$-0.481870\pi$
$167$	16884.4	−	4524.16i	0.605415	−	0.162220i	0.548489	+	0.836158i	$0.315203\pi$
$168$		−	4245.63i		−	0.150426i
$169$	−10765.4	+	26454.4i	−0.376926	+	0.926244i
$170$	−16538.4			−0.572264
$171$	−1002.26	−	3740.48i	−0.0342758	−	0.127919i
$172$	654.741	−	1134.04i	0.0221316	−	0.0383330i
$173$	27983.5	−	16156.3i	0.934995	−	0.539820i	0.0466071	−	0.998913i	$-0.485159\pi$
$173$	27983.5	−	16156.3i	0.934995	−	0.539820i	0.888388	+	0.459094i	$0.151826\pi$
$174$	−29338.6	+	29338.6i	−0.969038	+	0.969038i
$175$	2192.99	+	587.610i	0.0716079	+	0.0191873i
$176$	−545.208	+	2034.74i	−0.0176010	+	0.0656877i
$177$	−5233.02	−	5233.02i	−0.167034	−	0.167034i
$178$	−8833.68	−	15300.4i	−0.278806	−	0.482905i
$179$	−11550.5	−	6668.66i	−0.360490	−	0.208129i	0.308806	−	0.951125i	$-0.400071\pi$
$179$	−11550.5	−	6668.66i	−0.360490	−	0.208129i	−0.669296	+	0.742996i	$0.733404\pi$
$180$	−1928.32	+	516.692i	−0.0595161	+	0.0159473i
$181$			46226.0i			1.41101i	0.708706	+	0.705504i	$0.249279\pi$
$181$			46226.0i			1.41101i	−0.708706	+	0.705504i	$0.750721\pi$
$182$	−5271.73	−	7836.80i	−0.159151	−	0.236590i
$183$	37494.6			1.11961
$184$	5634.48	+	21028.2i	0.166425	+	0.621106i
$185$	−9584.98	+	16601.7i	−0.280058	+	0.485074i
$186$	24672.7	−	14244.8i	0.713165	−	0.411746i
$187$	5003.03	−	5003.03i	0.143070	−	0.143070i
$188$	18938.6	+	5074.60i	0.535838	+	0.143577i
$189$	3488.07	−	13017.7i	0.0976476	−	0.364426i
$190$	22963.7	+	22963.7i	0.636113	+	0.636113i
$191$	−5958.51	−	10320.4i	−0.163332	−	0.282899i	0.772730	−	0.634735i	$-0.218891\pi$
$191$	−5958.51	−	10320.4i	−0.163332	−	0.282899i	−0.936062	+	0.351836i	$0.885557\pi$
$192$	−4210.57	−	2430.98i	−0.114219	−	0.0659444i
$193$	40675.2	−	10898.9i	1.09198	−	0.292595i	0.332485	−	0.943108i	$-0.392113\pi$
$193$	40675.2	−	10898.9i	1.09198	−	0.292595i	0.759495	+	0.650513i	$0.225446\pi$
$194$			13676.9i			0.363400i
$195$	−28680.2	+	32909.5i	−0.754245	+	0.865470i
$196$	−16084.6			−0.418696
$197$	−14295.4	−	53351.2i	−0.368353	−	1.37471i	−0.862818	−	0.505515i	$-0.831303\pi$
$197$	−14295.4	−	53351.2i	−0.368353	−	1.37471i	0.494465	−	0.869198i	$-0.335364\pi$
$198$	427.031	−	739.640i	0.0108925	−	0.0188664i
$199$	58463.5	−	33753.9i	1.47631	−	0.852350i	0.476671	−	0.879082i	$-0.341843\pi$
$199$	58463.5	−	33753.9i	1.47631	−	0.852350i	0.999643	+	0.0267315i	$0.00850991\pi$
$200$	1838.43	−	1838.43i	0.0459607	−	0.0459607i
$201$	−63233.7	−	16943.4i	−1.56515	−	0.419381i
$202$	6171.11	−	23030.9i	0.151238	−	0.564427i
$203$	−21583.4	−	21583.4i	−0.523755	−	0.523755i
$204$	8165.12	+	14142.4i	0.196202	+	0.339831i
$205$	−13379.3	−	7724.55i	−0.318366	−	0.183808i
$206$	6552.67	−	1755.78i	0.154413	−	0.0413749i
$207$		−	8826.35i		−	0.205987i
$208$	−10790.6	+	740.985i	−0.249413	+	0.0171271i
$209$	−13893.5			−0.318066
$210$	−3736.25	−	13943.9i	−0.0847221	−	0.316187i
$211$	2183.67	−	3782.23i	0.0490481	−	0.0849538i	−0.840459	−	0.541875i	$-0.817715\pi$
$211$	2183.67	−	3782.23i	0.0490481	−	0.0849538i	0.889507	+	0.456921i	$0.151048\pi$
$212$	31418.3	−	18139.4i	0.699055	−	0.403600i
$213$	−37057.8	+	37057.8i	−0.816809	+	0.816809i
$214$	25714.6	+	6890.22i	0.561504	+	0.150455i
$215$	1152.37	−	4300.71i	0.0249296	−	0.0930386i
$216$	−10913.0	−	10913.0i	−0.233902	−	0.233902i
$217$	10479.4	+	18150.8i	0.222544	+	0.385458i
$218$	−51939.6	−	29987.4i	−1.09291	−	0.630994i
$219$	32385.0	−	8677.54i	0.675236	−	0.180929i
$220$			7162.47i			0.147985i
$221$	32632.0	+	15966.3i	0.668127	+	0.326903i
$222$	18928.7			0.384073
$223$	−5915.63	−	22077.4i	−0.118957	−	0.443955i	0.880595	−	0.473870i	$-0.157143\pi$
$223$	−5915.63	−	22077.4i	−0.118957	−	0.443955i	−0.999552	+	0.0299144i	$0.990477\pi$
$224$	1788.39	−	3097.58i	0.0356423	−	0.0617343i
$225$	−912.885	+	527.054i	−0.0180323	+	0.0104110i
$226$	35129.8	−	35129.8i	0.687795	−	0.687795i
$227$	−42663.3	−	11431.6i	−0.827946	−	0.221848i	−0.180129	−	0.983643i	$-0.557651\pi$
$227$	−42663.3	−	11431.6i	−0.827946	−	0.221848i	−0.647818	+	0.761795i	$0.724318\pi$
$228$	8299.49	−	30974.1i	0.159655	−	0.595839i
$229$	−10025.3	−	10025.3i	−0.191172	−	0.191172i	0.605030	−	0.796202i	$-0.293161\pi$
$229$	−10025.3	−	10025.3i	−0.191172	−	0.191172i	−0.796202	+	0.605030i	$0.793161\pi$
$230$	37010.5	+	64104.0i	0.699631	+	1.21180i
$231$	5348.40	+	3087.90i	0.100230	+	0.0578681i
$232$	−33763.5	+	9046.90i	−0.627294	+	0.168083i
$233$		−	3033.83i		−	0.0558829i	−0.999610	−	0.0279415i	$-0.991105\pi$
$233$		−	3033.83i		−	0.0558829i	0.999610	−	0.0279415i	$-0.00889520\pi$
$234$	4303.59	+	842.123i	0.0785958	+	0.0153796i
$235$	66665.7			1.20716
$236$	−1613.66	−	6022.28i	−0.0289727	−	0.108128i
$237$	−31859.3	+	55181.9i	−0.567204	+	0.982427i
$238$	−10404.1	+	6006.81i	−0.183675	+	0.106045i
$239$	−27446.8	+	27446.8i	−0.480503	+	0.480503i	−0.905292	−	0.424789i	$-0.860348\pi$
$239$	−27446.8	+	27446.8i	−0.480503	+	0.480503i	0.424789	+	0.905292i	$0.360348\pi$
$240$	−15968.0	−	4278.62i	−0.277223	−	0.0742816i
$241$	−15000.4	+	55982.4i	−0.258267	+	0.963867i	0.707976	+	0.706236i	$0.249608\pi$
$241$	−15000.4	+	55982.4i	−0.258267	+	0.963867i	−0.966243	+	0.257631i	$0.917058\pi$
$242$	27115.3	+	27115.3i	0.463003	+	0.463003i
$243$	6656.82	+	11529.9i	0.112734	+	0.195261i
$244$	27355.7	+	15793.8i	0.459482	+	0.265282i
$245$	−52826.5	+	14154.8i	−0.880075	+	0.235815i
$246$			15254.6i			0.252076i
$247$	−23140.4	−	67478.9i	−0.379296	−	1.10605i
$248$	24001.3			0.390240
$249$	4731.57	+	17658.5i	0.0763145	+	0.284810i
$250$	−19622.6	+	33987.3i	−0.313961	+	0.543797i
$251$	−48211.8	+	27835.1i	−0.765254	+	0.441820i	−0.831179	−	0.556005i	$-0.812334\pi$
$251$	−48211.8	+	27835.1i	−0.765254	+	0.441820i	0.0659249	+	0.997825i	$0.479000\pi$
$252$	−1025.42	+	1025.42i	−0.0161473	+	0.0161473i
$253$	−30588.1	−	8196.05i	−0.477872	−	0.128045i
$254$	−11886.0	+	44359.1i	−0.184233	+	0.687567i
$255$	39262.2	+	39262.2i	0.603802	+	0.603802i
$256$	−2048.00	−	3547.24i	−0.0312500	−	0.0541266i
$257$	17277.8	+	9975.36i	0.261591	+	0.151030i	0.625060	−	0.780577i	$-0.285074\pi$
$257$	17277.8	+	9975.36i	0.261591	+	0.151030i	−0.363469	+	0.931606i	$0.618408\pi$
$258$	−4246.58	+	1137.87i	−0.0637969	+	0.0170943i
$259$			13925.2i			0.207588i
$260$	−34787.3	+	11929.6i	−0.514605	+	0.176473i
$261$	14171.9			0.208040
$262$	−6698.19	−	24998.0i	−0.0975787	−	0.364169i
$263$	59229.8	−	102589.i	0.856305	−	1.48316i	−0.0191233	−	0.999817i	$-0.506087\pi$
$263$	59229.8	−	102589.i	0.856305	−	1.48316i	0.875429	−	0.483347i	$-0.160579\pi$
$264$	6124.80	−	3536.16i	0.0878788	−	0.0507369i
$265$	87223.8	−	87223.8i	1.24206	−	1.24206i
$266$	22786.6	+	6105.65i	0.322045	+	0.0862917i
$267$	−15351.9	+	57294.2i	−0.215348	+	0.803690i
$268$	−38997.7	−	38997.7i	−0.542962	−	0.542962i
$269$	6430.00	+	11137.1i	0.0888600	+	0.153910i	0.907030	−	0.421067i	$-0.138344\pi$
$269$	6430.00	+	11137.1i	0.0888600	+	0.153910i	−0.818170	+	0.574977i	$0.805011\pi$
$270$	−45444.9	−	26237.6i	−0.623387	−	0.359912i
$271$	−15408.0	+	4128.56i	−0.209801	+	0.0562161i	−0.362189	−	0.932105i	$-0.617970\pi$
$271$	−15408.0	+	4128.56i	−0.209801	+	0.0562161i	0.152388	+	0.988321i	$0.451304\pi$
$272$			13757.6i			0.185953i
$273$	−6089.46	+	31119.6i	−0.0817060	+	0.417551i
$274$	−33321.1			−0.443832
$275$	978.833	+	3653.06i	0.0129433	+	0.0483049i
$276$	36544.6	−	63297.1i	0.479739	−	0.830932i
$277$	52769.8	−	30466.6i	0.687742	−	0.397068i	−0.115024	−	0.993363i	$-0.536694\pi$
$277$	52769.8	−	30466.6i	0.687742	−	0.397068i	0.802766	+	0.596295i	$0.203361\pi$
$278$	4053.62	−	4053.62i	0.0524509	−	0.0524509i
$279$	−9399.45	−	2518.57i	−0.120752	−	0.0323554i
$280$	3147.64	−	11747.1i	0.0401485	−	0.149836i
$281$	−30774.2	−	30774.2i	−0.389739	−	0.389739i	0.484855	−	0.874594i	$-0.338872\pi$
$281$	−30774.2	−	30774.2i	−0.389739	−	0.389739i	−0.874594	+	0.484855i	$0.838872\pi$
$282$	−32913.3	−	57007.4i	−0.413878	−	0.716858i
$283$	95997.5	+	55424.2i	1.19864	+	0.692033i	0.960251	−	0.279138i	$-0.0900487\pi$
$283$	95997.5	+	55424.2i	1.19864	+	0.692033i	0.238385	+	0.971171i	$0.423382\pi$
$284$	−42647.0	+	11427.2i	−0.528751	+	0.141678i
$285$		−	109032.i		−	1.34234i
$286$	6914.68	−	14132.3i	0.0845356	−	0.172775i
$287$	−11222.3			−0.136245
$288$	429.813	+	1604.09i	0.00518197	+	0.0193394i
$289$	−18656.1	+	32313.4i	−0.223371	+	0.386889i
$290$	−102927.	+	59425.2i	−1.22387	+	0.706601i
$291$	32469.0	−	32469.0i	0.383428	−	0.383428i
$292$	27283.1	+	7310.48i	0.319984	+	0.0857394i
$293$	−8755.66	+	32676.6i	−0.101989	+	0.380628i	−0.997986	−	0.0634315i	$-0.979796\pi$
$293$	−8755.66	+	32676.6i	−0.101989	+	0.380628i	0.895997	+	0.444060i	$0.146462\pi$
$294$	38184.9	+	38184.9i	0.441771	+	0.441771i
$295$	−10599.5	−	18358.8i	−0.121798	−	0.210960i
$296$	13810.2	+	7973.32i	0.157622	+	0.0910030i
$297$	21684.6	−	5810.38i	0.245832	−	0.0658706i
$298$		−	67972.3i		−	0.765419i
$299$	−11139.2	−	162214.i	−0.124598	−	1.81445i
$300$	−8728.86			−0.0969873
$301$	−837.090	−	3124.06i	−0.00923931	−	0.0344816i
$302$	−2219.78	+	3844.78i	−0.0243387	+	0.0421558i
$303$	−69325.6	+	40025.1i	−0.755106	+	0.435961i
$304$	19102.5	−	19102.5i	0.206701	−	0.206701i
$305$	103743.	+	27797.8i	1.11522	+	0.298821i
$306$	1443.65	−	5387.78i	0.0154177	−	0.0575396i
$307$	98055.5	+	98055.5i	1.04039	+	1.04039i	0.999149	+	0.0412382i	$0.0131302\pi$
$307$	98055.5	+	98055.5i	1.04039	+	1.04039i	0.0412382	+	0.999149i	$0.486870\pi$
$308$	2601.43	+	4505.81i	0.0274228	+	0.0474976i
$309$	−19724.3	−	11387.8i	−0.206578	−	0.119268i
$310$	78827.1	−	21121.7i	0.820261	−	0.219788i
$311$			68074.1i			0.703819i	0.936034	+	0.351910i	$0.114468\pi$
$311$			68074.1i			0.703819i	−0.936034	+	0.351910i	$0.885532\pi$
$312$	27376.0	+	23857.8i	0.281229	+	0.245087i
$313$	−55684.0			−0.568383			−0.284192	−	0.958767i	$-0.591725\pi$
$313$	−55684.0			−0.568383			−0.284192	+	0.958767i	$0.591725\pi$
$314$	13163.8	+	49127.9i	0.133512	+	0.498275i
$315$	−2465.37	+	4270.15i	−0.0248463	+	0.0430350i
$316$	−46488.6	+	26840.2i	−0.465556	+	0.268789i
$317$	−23137.2	+	23137.2i	−0.230246	+	0.230246i	−0.812795	−	0.582549i	$-0.802055\pi$
$317$	−23137.2	+	23137.2i	−0.230246	+	0.230246i	0.582549	+	0.812795i	$0.302055\pi$
$318$	−117650.	−	31524.2i	−1.16342	−	0.311738i
$319$	13159.8	−	49113.2i	0.129321	−	0.482633i
$320$	−9847.86	−	9847.86i	−0.0961705	−	0.0961705i
$321$	−44689.2	−	77403.9i	−0.433703	−	0.751195i
$322$	46565.6	+	26884.6i	0.449110	+	0.259294i
$323$	−87645.6	+	23484.6i	−0.840089	+	0.225101i
$324$			57759.5i			0.550216i
$325$	−16112.2	+	10838.5i	−0.152541	+	0.102613i
$326$	131716.			1.23938
$327$	52114.7	+	194495.i	0.487377	+	1.81891i
$328$	−6425.71	+	11129.7i	−0.0597274	+	0.103451i
$329$	41938.5	−	24213.2i	0.387454	−	0.223697i
$330$	17003.7	−	17003.7i	0.156141	−	0.156141i
$331$	74041.0	+	19839.2i	0.675797	+	0.181079i	0.580365	−	0.814357i	$-0.302910\pi$
$331$	74041.0	+	19839.2i	0.675797	+	0.181079i	0.0954323	+	0.995436i	$0.469577\pi$
$332$	−3986.16	+	14876.6i	−0.0361642	+	0.134967i
$333$	−4571.70	−	4571.70i	−0.0412277	−	0.0412277i
$334$	−24720.5	−	42817.2i	−0.221597	−	0.383818i
$335$	−162399.	−	93760.8i	−1.44708	−	0.835472i
$336$	−11599.3	+	3108.02i	−0.102743	+	0.0275299i
$337$			15606.4i			0.137418i	0.997637	+	0.0687090i	$0.0218880\pi$
$337$			15606.4i			0.137418i	−0.997637	+	0.0687090i	$0.978112\pi$
$338$	80155.7	+	10045.6i	0.701618	+	0.0879307i
$339$	−166796.			−1.45140
$340$	12107.0	+	45183.8i	0.104732	+	0.390863i
$341$	−17456.4	+	30235.4i	−0.150123	+	0.260020i
$342$	−9485.47	+	5476.44i	−0.0810973	+	0.0468216i
$343$	−61637.6	+	61637.6i	−0.523911	+	0.523911i
$344$	−3577.57	−	958.607i	−0.0302323	−	0.00810072i
$345$	64320.1	−	240046.i	0.540391	−	2.01677i
$346$	−64625.0	−	64625.0i	−0.539820	−	0.539820i
$347$	−3570.79	−	6184.79i	−0.0296555	−	0.0513649i	0.850817	−	0.525463i	$-0.176108\pi$
$347$	−3570.79	−	6184.79i	−0.0296555	−	0.0513649i	−0.880472	+	0.474098i	$0.842774\pi$
$348$	101632.	+	58677.2i	0.839211	+	0.484519i
$349$	−173668.	+	46534.1i	−1.42583	+	0.382050i	−0.887548	−	0.460714i	$-0.847593\pi$
$349$	−173668.	+	46534.1i	−1.42583	+	0.382050i	−0.538282	+	0.842765i	$0.680927\pi$
$350$		−	6421.53i		−	0.0524206i
$351$	64337.5	+	95642.1i	0.522215	+	0.776310i
$352$	5958.14			0.0480868
$353$	54339.4	+	202797.i	0.436079	+	1.62747i	0.738470	+	0.674286i	$0.235549\pi$
$353$	54339.4	+	202797.i	0.436079	+	1.62747i	−0.302391	+	0.953184i	$0.597785\pi$
$354$	−10466.0	+	18127.7i	−0.0835172	+	0.144656i
$355$	−130009.	+	75060.5i	−1.03161	+	0.595600i
$356$	−35334.7	+	35334.7i	−0.278806	+	0.278806i
$357$	38959.5	+	10439.2i	0.305687	+	0.0819085i
$358$	−9763.59	+	36438.2i	−0.0761805	+	0.284309i
$359$	−111995.	−	111995.i	−0.868976	−	0.868976i	0.123383	−	0.992359i	$-0.460626\pi$
$359$	−111995.	−	111995.i	−0.868976	−	0.868976i	−0.992359	+	0.123383i	$0.960626\pi$
$360$	2823.26	+	4890.03i	0.0217844	+	0.0377317i
$361$	41443.5	+	23927.4i	0.318011	+	0.183603i
$362$	126292.	−	33839.8i	0.963737	−	0.258232i
$363$		−	128743.i		−	0.977038i
$364$	−17551.4	+	20139.6i	−0.132467	+	0.152001i
$365$	96038.8			0.720877
$366$	−27447.9	−	102437.i	−0.204903	−	0.764707i
$367$	−29488.8	+	51076.1i	−0.218940	+	0.379215i	−0.954484	−	0.298262i	$-0.903593\pi$
$367$	−29488.8	+	51076.1i	−0.218940	+	0.379215i	0.735544	+	0.677477i	$0.236927\pi$
$368$	53325.3	−	30787.4i	0.393765	−	0.227341i
$369$	3684.34	−	3684.34i	0.0270587	−	0.0270587i
$370$	52373.3	+	14033.4i	0.382566	+	0.102508i
$371$	23191.3	−	86551.2i	0.168491	−	0.628818i
$372$	−56979.1	−	56979.1i	−0.411746	−	0.411746i
$373$	27999.8	+	48497.1i	0.201251	+	0.348577i	0.948932	−	0.315482i	$-0.102166\pi$
$373$	27999.8	+	48497.1i	0.201251	+	0.348577i	−0.747681	+	0.664058i	$0.768833\pi$
$374$	−17331.0	−	10006.1i	−0.123903	−	0.0715352i
$375$	127270.	−	34101.8i	0.905030	−	0.242502i
$376$		−	55456.2i		−	0.392260i
$377$	260456.	−	17885.4i	1.83253	−	0.125839i
$378$	−38118.3			−0.266778
$379$	−27378.2	−	102177.i	−0.190601	−	0.711334i	−0.993362	−	0.115032i	$-0.963303\pi$
$379$	−27378.2	−	102177.i	−0.190601	−	0.711334i	0.802760	−	0.596302i	$-0.203364\pi$
$380$	45927.3	−	79548.5i	0.318056	−	0.550890i
$381$	133526.	−	77091.1i	0.919846	−	0.531073i
$382$	−23834.0	+	23834.0i	−0.163332	+	0.163332i
$383$	190137.	+	50947.1i	1.29619	+	0.347314i	0.840009	−	0.542572i	$-0.182550\pi$
$383$	190137.	+	50947.1i	1.29619	+	0.347314i	0.456183	+	0.889886i	$0.349216\pi$
$384$	−3559.20	+	13283.1i	−0.0241373	+	0.0900818i
$385$	12509.1	+	12509.1i	0.0843923	+	0.0843923i
$386$	−59552.6	−	103148.i	−0.399692	−	0.692288i
$387$	1300.47	+	750.824i	0.00868314	+	0.00501322i
$388$	37366.1	−	10012.2i	0.248207	−	0.0665069i
$389$		−	178816.i		−	1.18170i	−0.806780	−	0.590852i	$-0.798792\pi$
$389$		−	178816.i		−	1.18170i	0.806780	−	0.590852i	$-0.201208\pi$
$390$	110906.	+	54264.2i	0.729163	+	0.356767i
$391$	−206816.			−1.35279
$392$	11774.8	+	43944.0i	0.0766267	+	0.285975i
$393$	−43443.7	+	75246.8i	−0.281282	+	0.487195i
$394$	−135293.	+	78111.6i	−0.871533	+	0.503180i
$395$	−129062.	+	129062.i	−0.827186	+	0.827186i
$396$	−2333.34	−	625.217i	−0.0148795	−	0.00398695i
$397$	65796.0	−	245554.i	0.417463	−	1.55799i	−0.362386	−	0.932028i	$-0.618038\pi$
$397$	65796.0	−	245554.i	0.417463	−	1.55799i	0.779850	−	0.625967i	$-0.215295\pi$
$398$	−135016.	−	135016.i	−0.852350	−	0.852350i
$399$	−39600.6	−	68590.2i	−0.248746	−	0.430840i
$400$	−6368.50	−	3676.86i	−0.0398031	−	0.0229804i
$401$	−42604.7	+	11415.9i	−0.264953	+	0.0709939i	−0.388850	−	0.921301i	$-0.627127\pi$
$401$	−42604.7	+	11415.9i	−0.264953	+	0.0709939i	0.123897	+	0.992295i	$0.460461\pi$
$402$			185161.i			1.14577i
$403$	−175925.	−	34424.8i	−1.08322	−	0.211964i
$404$	−67439.1			−0.413190
$405$	50829.6	+	189699.i	0.309889	+	1.15652i
$406$	−43166.8	+	74767.1i	−0.261877	+	0.453585i
$407$	−20088.6	+	11598.2i	−0.121272	+	0.0700166i
$408$	32660.5	−	32660.5i	0.196202	−	0.196202i
$409$	−116159.	−	31124.6i	−0.694392	−	0.186062i	−0.105675	−	0.994401i	$-0.533700\pi$
$409$	−116159.	−	31124.6i	−0.694392	−	0.186062i	−0.588717	+	0.808339i	$0.700367\pi$
$410$	−11309.5	+	42207.7i	−0.0672786	+	0.251087i
$411$	79104.3	+	79104.3i	0.468292	+	0.468292i
$412$	−9593.78	−	16616.9i	−0.0565191	−	0.0978940i
$413$	−13336.0	−	7699.52i	−0.0781851	−	0.0451402i
$414$	−24114.0	+	6461.34i	−0.140692	+	0.0376983i
$415$			52366.8i			0.304060i
$416$	9923.67	+	28938.0i	0.0573437	+	0.167218i
$417$	−19246.6			−0.110683
$418$	10170.7	+	37957.6i	0.0582102	+	0.217243i
$419$	80827.3	−	139997.i	0.460394	−	0.797427i	−0.538586	−	0.842571i	$-0.681041\pi$
$419$	80827.3	−	139997.i	0.460394	−	0.797427i	0.998980	+	0.0451439i	$0.0143746\pi$
$420$	−35360.2	+	20415.2i	−0.200455	+	0.115733i
$421$	80144.5	−	80144.5i	0.452178	−	0.452178i	−0.443899	−	0.896077i	$-0.646405\pi$
$421$	80144.5	−	80144.5i	0.452178	−	0.452178i	0.896077	+	0.443899i	$0.146405\pi$
$422$	−11931.8	−	3197.11i	−0.0670009	−	0.0179528i
$423$	−5819.29	+	21717.9i	−0.0325229	+	0.121377i
$424$	−72557.6	−	72557.6i	−0.403600	−	0.403600i
$425$	12349.8	+	21390.4i	0.0683724	+	0.118424i
$426$	128372.	+	74115.6i	0.707378	+	0.408405i
$427$	75359.5	−	20192.5i	0.413316	−	0.110748i
$428$		−	75297.7i		−	0.411049i
$429$	−49965.5	+	17134.6i	−0.271491	+	0.0931020i
$430$	−12593.4			−0.0681090
$431$	−22499.7	−	83970.1i	−0.121122	−	0.452033i	0.878550	−	0.477650i	$-0.158511\pi$
$431$	−22499.7	−	83970.1i	−0.121122	−	0.452033i	−0.999672	+	0.0256176i	$0.991845\pi$
$432$	−21825.9	+	37803.6i	−0.116951	+	0.202565i
$433$	−186500.	+	107676.i	−0.994725	+	0.574305i	−0.906683	−	0.421812i	$-0.861394\pi$
$433$	−186500.	+	107676.i	−0.994725	+	0.574305i	−0.0880419	+	0.996117i	$0.528061\pi$
$434$	41917.6	−	41917.6i	0.222544	−	0.222544i
$435$	385425.	+	103274.i	2.03686	+	0.545775i
$436$	−43904.5	+	163854.i	−0.230960	+	0.861954i
$437$	287165.	+	287165.i	1.50373	+	1.50373i
$438$	−47415.0	−	82125.1i	−0.247154	−	0.428083i
$439$	254975.	+	147210.i	1.32303	+	0.763850i	0.984210	−	0.177003i	$-0.0566401\pi$
$439$	254975.	+	147210.i	1.32303	+	0.763850i	0.338816	+	0.940852i	$0.389973\pi$
$440$	19568.2	−	5243.29i	0.101076	−	0.0270831i
$441$		−	18445.1i		−	0.0948424i
$442$	19732.4	−	100840.i	0.101003	−	0.516167i
$443$	−75284.4			−0.383617			−0.191808	−	0.981432i	$-0.561435\pi$
$443$	−75284.4			−0.383617			−0.191808	+	0.981432i	$0.561435\pi$
$444$	−13856.7	−	51714.1i	−0.0702902	−	0.262327i
$445$	−84953.9	+	147145.i	−0.429006	+	0.743060i
$446$	−55986.2	+	32323.6i	−0.281456	+	0.162499i
$447$	−161366.	+	161366.i	−0.807602	+	0.807602i
$448$	−9771.93	−	2618.38i	−0.0486883	−	0.0130460i
$449$	−36394.3	+	135825.i	−0.180526	+	0.673733i	0.815018	+	0.579436i	$0.196727\pi$
$449$	−36394.3	+	135825.i	−0.180526	+	0.673733i	−0.995544	+	0.0942974i	$0.969940\pi$
$450$	2108.22	+	2108.22i	0.0104110	+	0.0104110i
$451$	−9347.00	−	16189.5i	−0.0459535	−	0.0795939i
$452$	−121693.	−	70259.7i	−0.595648	−	0.343898i
$453$	14397.3	−	3857.74i	0.0701591	−	0.0187991i
$454$			124927.i			0.606099i
$455$	−39920.4	+	81589.7i	−0.192829	+	0.394105i
$456$	−90698.5			−0.436185
$457$	−50410.3	−	188134.i	−0.241372	−	0.900813i	−0.975172	−	0.221447i	$-0.928922\pi$
$457$	−50410.3	−	188134.i	−0.241372	−	0.900813i	0.733800	−	0.679365i	$-0.237745\pi$
$458$	−20050.5	+	34728.5i	−0.0955861	+	0.165560i
$459$	126974.	−	73308.5i	0.602684	−	0.347960i
$460$	148042.	−	148042.i	0.699631	−	0.699631i
$461$	−316815.	−	84890.4i	−1.49075	−	0.399445i	−0.580758	−	0.814076i	$-0.697244\pi$
$461$	−316815.	−	84890.4i	−1.49075	−	0.399445i	−0.909989	+	0.414632i	$0.863910\pi$
$462$	4521.00	−	16872.6i	0.0211812	−	0.0790493i
$463$	195600.	+	195600.i	0.912447	+	0.912447i	0.996464	−	0.0840177i	$-0.0267752\pi$
$463$	195600.	+	195600.i	0.912447	+	0.912447i	−0.0840177	+	0.996464i	$0.526775\pi$
$464$	49433.2	+	85620.8i	0.229606	+	0.397689i
$465$	−237278.	−	136993.i	−1.09737	−	0.633565i
$466$	−8288.57	+	2220.92i	−0.0381687	+	0.0102273i
$467$		−	213346.i		−	0.978252i	−0.872213	−	0.489126i	$-0.837316\pi$
$467$		−	213346.i		−	0.978252i	0.872213	−	0.489126i	$-0.162684\pi$
$468$	−849.725	−	12374.1i	−0.00387960	−	0.0564966i
$469$	−136217.			−0.619278
$470$	−48802.7	−	182134.i	−0.220926	−	0.824509i
$471$	85378.8	−	147880.i	0.384865	−	0.666606i
$472$	−15271.9	+	8817.23i	−0.0685502	+	0.0395775i
$473$	3809.61	−	3809.61i	0.0170278	−	0.0170278i
$474$	174082.	+	46645.3i	0.774816	+	0.207611i
$475$	12553.0	−	46848.4i	0.0556365	−	0.207638i
$476$	24027.2	+	24027.2i	0.106045	+	0.106045i
$477$	20801.4	+	36029.0i	0.0914229	+	0.158349i
$478$	95078.6	+	54893.6i	0.416128	+	0.240252i
$479$	−139412.	+	37355.3i	−0.607615	+	0.162810i	−0.549491	−	0.835499i	$-0.685179\pi$
$479$	−139412.	+	37355.3i	−0.607615	+	0.162810i	−0.0581239	+	0.998309i	$0.518512\pi$
$480$			46757.6i			0.202941i
$481$	−89790.0	−	78250.7i	−0.388095	−	0.338219i
$482$	163928.			0.705600
$483$	−46722.5	−	174371.i	−0.200277	−	0.747445i
$484$	54230.6	−	93930.1i	0.231501	−	0.400972i
$485$	113910.	−	65765.9i	0.484259	−	0.279587i
$486$	26627.3	−	26627.3i	0.112734	−	0.112734i
$487$	−77919.1	−	20878.3i	−0.328538	−	0.0880315i	0.0907798	−	0.995871i	$-0.471064\pi$
$487$	−77919.1	−	20878.3i	−0.328538	−	0.0880315i	−0.419318	+	0.907839i	$0.637731\pi$
$488$	23123.8	−	86299.2i	0.0971000	−	0.362382i
$489$	−312695.	−	312695.i	−1.30768	−	1.30768i
$490$	77343.4	+	133963.i	0.322130	+	0.557945i
$491$	282641.	+	163183.i	1.17239	+	0.676880i	0.954242	−	0.299035i	$-0.0966648\pi$
$491$	282641.	+	163183.i	1.17239	+	0.676880i	0.218149	+	0.975915i	$0.429998\pi$
$492$	41676.4	−	11167.2i	0.172171	−	0.0461331i
$493$		−	332071.i		−	1.36627i
$494$	−167416.	+	112619.i	−0.686029	+	0.461484i
$495$	−8213.56			−0.0335213
$496$	−17570.2	−	65572.8i	−0.0714188	−	0.266539i
$497$	−54524.4	+	94439.0i	−0.220738	+	0.382330i
$498$	44780.1	−	25853.8i	0.180562	−	0.104248i
$499$	321163.	−	321163.i	1.28981	−	1.28981i	0.354902	−	0.934904i	$-0.384514\pi$
$499$	321163.	−	321163.i	1.28981	−	1.28981i	0.934904	−	0.354902i	$-0.115486\pi$
$500$	107220.	+	28729.4i	0.428879	+	0.114918i
$501$	−42961.5	+	160334.i	−0.171161	+	0.638780i
$502$	111340.	+	111340.i	0.441820	+	0.441820i
$503$	−38564.6	−	66795.9i	−0.152424	−	0.264006i	0.779694	−	0.626161i	$-0.215375\pi$
$503$	−38564.6	−	66795.9i	−0.152424	−	0.264006i	−0.932118	+	0.362155i	$0.882041\pi$
$504$	3552.15	+	2050.83i	0.0139840	+	0.00807364i
$505$	−221489.	+	59347.9i	−0.868501	+	0.232714i
$506$			89568.1i			0.349826i
$507$	−166441.	−	214138.i	−0.647509	−	0.833062i
$508$	129892.			0.503334
$509$	94717.1	+	353489.i	0.365589	+	1.36440i	0.866621	+	0.498967i	$0.166287\pi$
$509$	94717.1	+	353489.i	0.365589	+	1.36440i	−0.501032	+	0.865429i	$0.667046\pi$
$510$	78524.4	−	136008.i	0.301901	−	0.522908i
$511$	60416.7	−	34881.6i	0.231374	−	0.133584i
$512$	−8192.00	+	8192.00i	−0.0312500	+	0.0312500i
$513$	−278093.	−	74514.9i	−1.05671	−	0.283145i
$514$	14604.9	−	54506.4i	0.0552807	−	0.206310i
$515$	−46131.9	−	46131.9i	−0.173935	−	0.173935i
$516$	6217.42	+	10768.9i	0.0233513	+	0.0404456i
$517$	69860.5	+	40334.0i	0.261367	+	0.150900i
$518$	38044.3	−	10193.9i	0.141785	−	0.0379912i
$519$			306840.i			1.13914i
$520$	58058.2	+	86307.6i	0.214712	+	0.319185i
$521$	384986.			1.41830			0.709152	−	0.705055i	$-0.249078\pi$
$521$	384986.			1.41830			0.709152	+	0.705055i	$0.249078\pi$
$522$	−10374.5	−	38718.3i	−0.0380739	−	0.142094i
$523$	−50951.0	+	88249.7i	−0.186273	+	0.322634i	−0.944005	−	0.329932i	$-0.892974\pi$
$523$	−50951.0	+	88249.7i	−0.186273	+	0.322634i	0.757732	+	0.652566i	$0.226307\pi$
$524$	−63392.4	+	36599.6i	−0.230874	+	0.133295i
$525$	−15244.7	+	15244.7i	−0.0553096	+	0.0553096i
$526$	−323638.	−	86718.4i	−1.16973	−	0.313430i
$527$	−59014.4	+	220245.i	−0.212489	+	0.793020i
$528$	−14144.6	−	14144.6i	−0.0507369	−	0.0507369i
$529$	322903.	+	559284.i	1.15388	+	1.99858i
$530$	−302152.	−	174448.i	−1.07566	−	0.621031i
$531$	6906.05	−	1850.47i	0.0244929	−	0.00656286i
$532$		−	66723.8i		−	0.235753i
$533$	63062.3	−	72361.9i	0.221981	−	0.254716i
$534$	167769.			0.588342
$535$	−66263.6	−	247299.i	−0.231509	−	0.864002i
$536$	−77995.5	+	135092.i	−0.271481	+	0.470219i
$537$	109683.	−	63325.6i	0.380357	−	0.219599i
$538$	25720.0	−	25720.0i	0.0888600	−	0.0888600i
$539$	−63922.1	−	17127.9i	−0.220026	−	0.0589557i
$540$	−38414.5	+	143365.i	−0.131737	+	0.491650i
$541$	−52761.7	−	52761.7i	−0.180270	−	0.180270i	0.611203	−	0.791474i	$-0.290686\pi$
$541$	−52761.7	−	52761.7i	−0.180270	−	0.180270i	−0.791474	+	0.611203i	$0.790686\pi$
$542$	22558.9	+	39073.2i	0.0767926	+	0.133009i
$543$	−380153.	−	219481.i	−1.28931	−	0.744385i
$544$	37586.4	−	10071.2i	0.127009	−	0.0340318i
$545$			576780.i			1.94186i
$546$	89478.2	−	6144.43i	0.300146	−	0.0206109i
$547$	414681.			1.38592			0.692961	−	0.720975i	$-0.256306\pi$
$547$	414681.			1.38592			0.692961	+	0.720975i	$0.256306\pi$
$548$	24392.8	+	91035.0i	0.0812269	+	0.303143i
$549$	−18111.6	+	31370.2i	−0.0600913	+	0.104081i
$550$	9263.78	−	5348.45i	0.0306241	−	0.0176808i
$551$	−461082.	+	461082.i	−1.51871	+	1.51871i
$552$	−199683.	−	53505.0i	−0.655336	−	0.175597i
$553$	−34315.4	+	128067.i	−0.112212	+	0.418780i
$554$	−121867.	−	121867.i	−0.397068	−	0.397068i
$555$	−91019.0	−	157649.i	−0.295492	−	0.511807i
$556$	−14042.1	−	8107.23i	−0.0454238	−	0.0262255i
$557$	224316.	−	60105.3i	0.723019	−	0.193732i	0.121501	−	0.992591i	$-0.461229\pi$
$557$	224316.	−	60105.3i	0.723019	−	0.193732i	0.601518	+	0.798859i	$0.294563\pi$
$558$			27523.5i			0.0883965i
$559$	24848.0	+	12157.7i	0.0795183	+	0.0389069i
$560$	−34398.0			−0.109688
$561$	17389.4	+	64898.2i	0.0552534	+	0.206209i
$562$	−61548.4	+	106605.i	−0.194870	+	0.337524i
$563$	414896.	−	239540.i	1.30895	−	0.755721i	0.327027	−	0.945015i	$-0.393953\pi$
$563$	414896.	−	239540.i	1.30895	−	0.755721i	0.981921	+	0.189293i	$0.0606197\pi$
$564$	−131653.	+	131653.i	−0.413878	+	0.413878i
$565$	−461505.	−	123660.i	−1.44571	−	0.387376i
$566$	81146.7	−	302843.i	0.253302	−	0.945334i
$567$	100875.	+	100875.i	0.313775	+	0.313775i
$568$	62439.5	+	108148.i	0.193536	+	0.335215i
$569$	−113561.	−	65564.7i	−0.350757	−	0.202510i	0.314262	−	0.949336i	$-0.398243\pi$
$569$	−113561.	−	65564.7i	−0.350757	−	0.202510i	−0.665019	+	0.746827i	$0.731576\pi$
$570$	−297880.	+	79816.6i	−0.916835	+	0.245665i
$571$		−	131069.i		−	0.402003i	−0.979591	−	0.201002i	$-0.935580\pi$
$571$		−	131069.i		−	0.402003i	0.979591	−	0.201002i	$-0.0644196\pi$
$572$	−43672.0	−	8545.70i	−0.133478	−	0.0261189i
$573$	113164.			0.344667
$574$	8215.31	+	30660.0i	0.0249345	+	0.0930567i
$575$	55273.8	−	95737.0i	0.167180	−	0.289564i
$576$	4067.80	−	2348.54i	0.0122607	−	0.00707870i
$577$	265150.	−	265150.i	0.796416	−	0.796416i	−0.186112	−	0.982528i	$-0.559589\pi$
$577$	265150.	−	265150.i	0.796416	−	0.796416i	0.982528	+	0.186112i	$0.0595888\pi$
$578$	101939.	+	27314.5i	0.305130	+	0.0817593i
$579$	−103496.	+	386251.i	−0.308720	+	1.15216i
$580$	237701.	+	237701.i	0.706601	+	0.706601i
$581$	19019.8	+	32943.2i	0.0563447	+	0.0975919i
$582$	−112476.	−	64938.1i	−0.332058	−	0.191714i
$583$	144176.	−	38631.8i	0.424185	−	0.113660i
$584$		−	79890.4i		−	0.234244i
$585$	−13680.2	−	39892.3i	−0.0399743	−	0.116568i
$586$	95683.6			0.278639
$587$	−145082.	−	541455.i	−0.421055	−	1.57140i	−0.772390	−	0.635149i	$-0.780939\pi$
$587$	−145082.	−	541455.i	−0.421055	−	1.57140i	0.351335	−	0.936250i	$-0.385728\pi$
$588$	76369.8	−	132276.i	0.220885	−	0.382585i
$589$	387753.	−	223869.i	1.11770	−	0.645303i
$590$	−42397.9	+	42397.9i	−0.121798	+	0.121798i
$591$	506623.	+	135749.i	1.45047	+	0.388653i
$592$	11673.7	−	43567.0i	0.0333094	−	0.124312i
$593$	−284953.	−	284953.i	−0.810335	−	0.810335i	0.174349	−	0.984684i	$-0.444218\pi$
$593$	−284953.	−	284953.i	−0.810335	−	0.810335i	−0.984684	+	0.174349i	$0.944218\pi$
$594$	−31748.5	−	54990.0i	−0.0899809	−	0.155851i
$595$	100057.	+	57767.8i	0.282626	+	0.163174i
$596$	−185704.	+	49759.2i	−0.522791	+	0.140081i
$597$			641054.i			1.79865i
$598$	−435022.	+	149181.i	−1.21649	+	0.417169i
$599$	−311888.			−0.869251			−0.434625	−	0.900611i	$-0.643119\pi$
$599$	−311888.			−0.869251			−0.434625	+	0.900611i	$0.643119\pi$
$600$	6389.97	+	23847.7i	0.0177499	+	0.0662436i
$601$	174272.	−	301847.i	0.482478	−	0.835677i	−0.517319	−	0.855792i	$-0.673070\pi$
$601$	174272.	−	301847.i	0.482478	−	0.835677i	0.999798	+	0.0201155i	$0.00640338\pi$
$602$	−7922.31	+	4573.95i	−0.0218604	+	0.0126211i
$603$	44720.7	−	44720.7i	0.122991	−	0.122991i
$604$	12129.1	+	3249.99i	0.0332473	+	0.00890857i
$605$	95448.1	−	356217.i	0.260769	−	0.973205i
$606$	160101.	+	160101.i	0.435961	+	0.435961i
$607$	−187866.	−	325393.i	−0.509882	−	0.883142i	−0.999934	−	0.0114491i	$-0.996356\pi$
$607$	−187866.	−	325393.i	−0.509882	−	0.883142i	0.490052	−	0.871693i	$-0.336978\pi$
$608$	−66172.9	−	38204.9i	−0.179008	−	0.103350i
$609$	279975.	−	75019.1i	0.754892	−	0.202273i
$610$		−	303780.i		−	0.816395i
$611$	−79540.3	+	406483.i	−0.213061	+	1.08883i
$612$	−15776.5			−0.0421219
$613$	102859.	+	383876.i	0.273730	+	1.02158i	0.956688	+	0.291117i	$0.0940268\pi$
$613$	102859.	+	383876.i	0.273730	+	1.02158i	−0.682957	+	0.730458i	$0.739306\pi$
$614$	196111.	−	339674.i	0.520194	−	0.901002i
$615$	127050.	−	73352.3i	0.335911	−	0.193938i
$616$	10405.7	−	10405.7i	0.0274228	−	0.0274228i
$617$	−529221.	−	141804.i	−1.39017	−	0.372494i	−0.515363	−	0.856972i	$-0.672343\pi$
$617$	−529221.	−	141804.i	−1.39017	−	0.372494i	−0.874804	+	0.484478i	$0.839010\pi$
$618$	−16672.9	+	62224.2i	−0.0436551	+	0.162923i
$619$	104044.	+	104044.i	0.271540	+	0.271540i	0.829720	−	0.558180i	$-0.188500\pi$
$619$	104044.	+	104044.i	0.271540	+	0.271540i	−0.558180	+	0.829720i	$0.688500\pi$
$620$	−115411.	−	199897.i	−0.300236	−	0.520025i
$621$	−568297.	−	328107.i	−1.47364	−	0.850808i
$622$	185982.	−	49833.7i	0.480717	−	0.128808i
$623$			123422.i			0.317993i
$624$	45140.0	−	92257.6i	0.115929	−	0.236937i
$625$	449236.			1.15004
$626$	40763.5	+	152131.i	0.104021	+	0.388213i
$627$	65966.1	−	114257.i	0.167798	−	0.290634i
$628$	124583.	−	71928.2i	0.315894	−	0.182381i
$629$	−107123.	+	107123.i	−0.270757	+	0.270757i
$630$	13471.0	+	3609.55i	0.0339406	+	0.00909437i
$631$	−101850.	+	380110.i	−0.255802	+	0.954664i	0.711841	+	0.702340i	$0.247862\pi$
$631$	−101850.	+	380110.i	−0.255802	+	0.954664i	−0.967643	+	0.252324i	$0.918805\pi$
$632$	107361.	+	107361.i	0.268789	+	0.268789i
$633$	20736.1	+	35916.0i	0.0517512	+	0.0896356i
$634$	80149.6	+	46274.4i	0.199399	+	0.115123i
$635$	426604.	−	114308.i	1.05798	−	0.283485i
$636$			344503.i			0.851685i
$637$	−23278.3	−	338990.i	−0.0573683	−	0.835425i
$638$	−143813.			−0.353312
$639$	−13104.2	−	48905.4i	−0.0320928	−	0.119772i
$640$	−19695.7	+	34114.0i	−0.0480853	+	0.0832861i
$641$	84097.8	−	48553.9i	0.204677	−	0.118170i	−0.394158	−	0.919043i	$-0.628964\pi$
$641$	84097.8	−	48553.9i	0.204677	−	0.118170i	0.598835	+	0.800872i	$0.295630\pi$
$642$	−178757.	+	178757.i	−0.433703	+	0.433703i
$643$	238628.	+	63940.1i	0.577164	+	0.154651i	0.535580	−	0.844484i	$-0.320093\pi$
$643$	238628.	+	63940.1i	0.577164	+	0.154651i	0.0415838	+	0.999135i	$0.486760\pi$
$644$	39361.8	−	146900.i	0.0949082	−	0.354202i
$645$	29896.6	+	29896.6i	0.0718626	+	0.0718626i
$646$	128322.	+	222260.i	0.307494	+	0.532595i
$647$	−95982.0	−	55415.2i	−0.229288	−	0.132379i	0.380956	−	0.924593i	$-0.375595\pi$
$647$	−95982.0	−	55415.2i	−0.229288	−	0.132379i	−0.610243	+	0.792214i	$0.708928\pi$
$648$	157802.	−	42282.9i	0.375804	−	0.100696i
$649$		−	25651.5i		−	0.0609009i
$650$	41406.2	+	36084.9i	0.0980028	+	0.0854081i
$651$	−199025.			−0.469618
$652$	−96423.1	−	359856.i	−0.226822	−	0.846513i
$653$	86718.6	−	150201.i	0.203370	−	0.352246i	−0.746242	−	0.665674i	$-0.768144\pi$
$653$	86718.6	−	150201.i	0.203370	−	0.352246i	0.949612	+	0.313428i	$0.101477\pi$
$654$	493219.	−	284760.i	1.15315	−	0.665769i
$655$	−175990.	+	175990.i	−0.410210	+	0.410210i
$656$	35110.7	+	9407.89i	0.0815891	+	0.0218617i
$657$	−8383.29	+	31286.9i	−0.0194216	+	0.0724822i
$658$	−96852.7	−	96852.7i	−0.223697	−	0.223697i
$659$	−49301.9	−	85393.3i	−0.113525	−	0.196632i	0.803664	−	0.595083i	$-0.202881\pi$
$659$	−49301.9	−	85393.3i	−0.113525	−	0.196632i	−0.917189	+	0.398452i	$0.869548\pi$
$660$	−58902.6	−	34007.4i	−0.135222	−	0.0780703i
$661$	−760411.	+	203751.i	−1.74039	+	0.466335i	−0.982532	−	0.186091i	$-0.940418\pi$
$661$	−760411.	+	203751.i	−1.74039	+	0.466335i	−0.757853	+	0.652426i	$0.773751\pi$
$662$		−	216807.i		−	0.494718i
$663$	−286240.	+	192550.i	−0.651182	+	0.438044i
$664$	43561.6			0.0988024
$665$	−58718.4	−	219140.i	−0.132779	−	0.495540i
$666$	−9143.40	+	15836.8i	−0.0206139	+	0.0357043i
$667$	−1.28713e6	+	743124.i	−2.89314	+	1.67036i
$668$	−98882.0	+	98882.0i	−0.221597	+	0.221597i
$669$	209647.	+	56174.9i	0.468422	+	0.125513i
$670$	−137275.	+	512319.i	−0.305804	+	1.14128i
$671$	91896.4	+	91896.4i	0.204105	+	0.204105i
$672$	16982.5	+	29414.6i	0.0376066	+	0.0651365i
$673$	426080.	+	245997.i	0.940721	+	0.543125i	0.890186	−	0.455597i	$-0.150574\pi$
$673$	426080.	+	245997.i	0.940721	+	0.543125i	0.0505345	+	0.998722i	$0.483908\pi$
$674$	42637.6	−	11424.7i	0.0938583	−	0.0251492i
$675$			78369.9i			0.172005i
$676$	−31233.1	−	226343.i	−0.0683473	−	0.495307i
$677$	−556471.			−1.21413			−0.607065	−	0.794652i	$-0.707653\pi$
$677$	−556471.			−1.21413			−0.607065	+	0.794652i	$0.707653\pi$
$678$	122103.	+	455696.i	0.265625	+	0.991325i
$679$	47772.8	−	82744.8i	0.103619	−	0.179474i
$680$	114582.	−	66153.7i	0.247797	−	0.143066i
$681$	296576.	−	296576.i	0.639502	−	0.639502i
$682$	95383.7	+	25558.0i	0.205072	+	0.0549488i
$683$	−121235.	+	452456.i	−0.259889	+	0.969918i	0.705416	+	0.708793i	$0.250760\pi$
$683$	−121235.	+	452456.i	−0.259889	+	0.969918i	−0.965305	+	0.261125i	$0.915907\pi$
$684$	21905.7	+	21905.7i	0.0468216	+	0.0468216i
$685$	160226.	+	277519.i	0.341468	+	0.591441i
$686$	213519.	+	123275.i	0.453720	+	0.261955i
$687$	130045.	−	34845.6i	0.275538	−	0.0738302i
$688$			10475.9i			0.0221316i
$689$	427764.	+	635901.i	0.901085	+	1.33953i
$690$	−702903.			−1.47638
$691$	−158812.	−	592695.i	−0.332604	−	1.24129i	−0.906444	−	0.422327i	$-0.861213\pi$
$691$	−158812.	−	592695.i	−0.332604	−	1.24129i	0.573840	−	0.818968i	$-0.305453\pi$
$692$	−129250.	+	223868.i	−0.269910	+	0.467497i
$693$	−5167.04	+	2983.19i	−0.0107591	+	0.00621176i
$694$	−14283.2	+	14283.2i	−0.0296555	+	0.0296555i
$695$	−53252.9	−	14269.1i	−0.110249	−	0.0295411i
$696$	85909.3	−	320618.i	0.177346	−	0.661865i
$697$	−86330.3	−	86330.3i	−0.177704	−	0.177704i
$698$	254267.	+	440403.i	0.521890	+	0.903941i
$699$	24949.5	+	14404.6i	0.0510632	+	0.0294813i
$700$	−17543.9	+	4700.88i	−0.0358040	+	0.00959364i
$701$		−	445654.i		−	0.906905i	−0.891280	−	0.453453i	$-0.850192\pi$
$701$		−	445654.i		−	0.906905i	0.891280	−	0.453453i	$-0.149808\pi$
$702$	214201.	−	245788.i	0.434657	−	0.498754i
$703$	297480.			0.601933
$704$	−4361.66	−	16277.9i	−0.00880049	−	0.0328439i
$705$	−316529.	+	548244.i	−0.636846	+	1.10305i
$706$	514274.	−	296916.i	1.03177	−	0.595695i
$707$	−117781.	+	117781.i	−0.235632	+	0.235632i
$708$	57187.5	+	15323.4i	0.114087	+	0.0305694i
$709$	128823.	−	480775.i	0.256273	−	0.956422i	−0.711105	−	0.703085i	$-0.751805\pi$
$709$	128823.	−	480775.i	0.256273	−	0.956422i	0.967378	−	0.253337i	$-0.0815282\pi$
$710$	300242.	+	300242.i	0.595600	+	0.595600i
$711$	−30779.0	−	53310.8i	−0.0608857	−	0.105457i
$712$	122403.	+	70669.4i	0.241453	+	0.139403i
$713$	985748.	−	264130.i	1.93904	−	0.519564i
$714$		−	114081.i		−	0.223778i
$715$	−150952.	+	10365.8i	−0.295275	+	0.0202764i
$716$	106699.			0.208129
$717$	−95399.0	−	356034.i	−0.185569	−	0.692553i
$718$	−223989.	+	387960.i	−0.434488	+	0.752555i
$719$	−53204.8	+	30717.8i	−0.102918	+	0.0594200i	−0.550576	−	0.834785i	$-0.685592\pi$
$719$	−53204.8	+	30717.8i	−0.102918	+	0.0594200i	0.447657	+	0.894205i	$0.352258\pi$
$720$	11293.0	−	11293.0i	0.0217844	−	0.0217844i
$721$	−45776.2	−	12265.7i	−0.0880582	−	0.0235951i
$722$	35032.1	−	130742.i	0.0672035	−	0.250807i
$723$	−389164.	−	389164.i	−0.744486	−	0.744486i
$724$	−184904.	−	320263.i	−0.352752	−	0.610984i
$725$	153718.	+	88749.3i	0.292449	+	0.168845i
$726$	−351733.	+	94246.7i	−0.667330	+	0.178810i
$727$		−	121549.i		−	0.229975i	−0.993367	−	0.114988i	$-0.963317\pi$
$727$		−	121549.i		−	0.229975i	0.993367	−	0.114988i	$-0.0366828\pi$
$728$	67870.8	+	33208.0i	0.128062	+	0.0626585i
$729$	458388.			0.862538
$730$	−70305.3	−	262383.i	−0.131930	−	0.492368i
$731$	17593.1	−	30472.1i	0.0329236	−	0.0570253i
$732$	−259770.	+	149978.i	−0.484805	+	0.279902i
$733$	450529.	−	450529.i	0.838522	−	0.838522i	−0.150142	−	0.988664i	$-0.547973\pi$
$733$	450529.	−	450529.i	0.838522	−	0.838522i	0.988664	+	0.150142i	$0.0479732\pi$
$734$	161130.	+	43174.6i	0.299077	+	0.0801376i
$735$	134414.	−	501641.i	0.248811	−	0.928577i
$736$	−123149.	−	123149.i	−0.227341	−	0.227341i
$737$	−113454.	−	196508.i	−0.208874	−	0.361781i
$738$	−12762.9	−	7368.69i	−0.0234335	−	0.0135294i
$739$	−653211.	+	175027.i	−1.19609	+	0.320492i	−0.801291	−	0.598275i	$-0.795853\pi$
$739$	−653211.	+	175027.i	−1.19609	+	0.320492i	−0.394801	+	0.918767i	$0.629186\pi$
$740$		−	153360.i		−	0.280058i
$741$	664802.	+	130088.i	1.21075	+	0.236919i
$742$	−253440.			−0.460327
$743$	−17244.2	−	64356.2i	−0.0312367	−	0.116577i	0.948547	−	0.316636i	$-0.102553\pi$
$743$	−17244.2	−	64356.2i	−0.0312367	−	0.116577i	−0.979784	+	0.200059i	$0.935887\pi$
$744$	−113958.	+	197381.i	−0.205873	+	0.356583i
$745$	−566115.	+	326847.i	−1.01998	+	0.588886i
$746$	111999.	−	111999.i	0.201251	−	0.201251i
$747$	−17059.7	−	4571.13i	−0.0305724	−	0.00819186i
$748$	−14649.9	+	54674.1i	−0.0261837	+	0.0977189i
$749$	−131505.	−	131505.i	−0.234412	−	0.234412i
$750$	−186336.	−	322743.i	−0.331264	−	0.573766i
$751$	741981.	+	428383.i	1.31557	+	0.759543i	0.983012	−	0.183540i	$-0.0587558\pi$
$751$	741981.	+	428383.i	1.31557	+	0.759543i	0.332555	+	0.943084i	$0.392089\pi$
$752$	−151509.	+	40596.8i	−0.267919	+	0.0717886i
$753$		−	528644.i		−	0.932338i
$754$	−239530.	−	698485.i	−0.421326	−	1.22861i
$755$	42695.6			0.0749012
$756$	27904.6	+	104141.i	0.0488238	+	0.182213i
$757$	−485289.	+	840544.i	−0.846853	+	1.46679i	0.0371484	+	0.999310i	$0.488173\pi$
$757$	−485289.	+	840544.i	−0.846853	+	1.46679i	−0.884002	+	0.467483i	$0.845161\pi$
$758$	−259110.	+	149597.i	−0.450968	+	0.260366i
$759$	212635.	−	212635.i	0.369106	−	0.369106i
$760$	−250952.	−	67242.3i	−0.434473	−	0.116417i
$761$	106461.	−	397319.i	0.183833	−	0.686073i	−0.811045	−	0.584984i	$-0.801101\pi$
$761$	106461.	−	397319.i	0.183833	−	0.686073i	0.994877	−	0.101089i	$-0.0322327\pi$
$762$	−308364.	−	308364.i	−0.531073	−	0.531073i
$763$	209488.	+	362844.i	0.359841	+	0.623263i
$764$	82563.6	+	47668.1i	0.141450	+	0.0816660i
$765$	−51814.5	+	13883.7i	−0.0885378	+	0.0237236i
$766$		−	556760.i		−	0.948879i
$767$	124586.	−	42724.2i	0.211777	−	0.0726246i
$768$	38895.6			0.0659444
$769$	39128.5	+	146030.i	0.0661669	+	0.246938i	0.991086	−	0.133227i	$-0.0425339\pi$
$769$	39128.5	+	146030.i	0.0661669	+	0.246938i	−0.924919	+	0.380165i	$0.875867\pi$
$770$	25018.1	−	43332.6i	0.0421962	−	0.0730859i
$771$	−164070.	+	94726.0i	−0.276008	+	0.159353i
$772$	−238210.	+	238210.i	−0.399692	+	0.399692i
$773$	258234.	+	69193.5i	0.432169	+	0.115799i	0.468344	−	0.883546i	$-0.344851\pi$
$773$	258234.	+	69193.5i	0.432169	+	0.115799i	−0.0361751	+	0.999345i	$0.511517\pi$
$774$	1099.28	−	4102.58i	0.00183496	−	0.00684818i
$775$	−86181.0	−	86181.0i	−0.143485	−	0.143485i
$776$	−54707.7	−	94756.6i	−0.0908501	−	0.157357i
$777$	−114518.	−	66116.7i	−0.189684	−	0.109514i
$778$	−488536.	+	130903.i	−0.807118	+	0.216267i
$779$			239740.i			0.395062i
$780$	67064.0	−	342724.i	0.110230	−	0.563321i
$781$	−181652.			−0.297809
$782$	151400.	+	565032.i	0.247578	+	0.923974i
$783$	526818.	−	912476.i	0.859285	−	1.48833i
$784$	111438.	−	64338.5i	0.181301	−	0.104674i
$785$	345869.	−	345869.i	0.561270	−	0.561270i
$786$	237381.	+	63606.0i	0.384238	+	0.102956i
$787$	118929.	−	443851.i	0.192017	−	0.716617i	−0.801002	−	0.598662i	$-0.795699\pi$
$787$	118929.	−	443851.i	0.192017	−	0.716617i	0.993019	−	0.117955i	$-0.0376340\pi$
$788$	312446.	+	312446.i	0.503180	+	0.503180i
$789$	562446.	+	974185.i	0.903497	+	1.56490i
$790$	447083.	+	258124.i	0.716365	+	0.413593i
$791$	−335240.	+	89827.4i	−0.535801	+	0.143567i
$792$			6832.50i			0.0108925i
$793$	−293271.	+	599390.i	−0.466361	+	0.953154i
$794$	−719032.			−1.14053
$795$	303170.	+	1.13145e6i	0.479681	+	1.79019i
$796$	−270031.	+	467708.i	−0.426175	+	0.738157i
$797$	−220514.	+	127314.i	−0.347153	+	0.200429i	−0.663430	−	0.748238i	$-0.730900\pi$
$797$	−220514.	+	127314.i	−0.347153	+	0.200429i	0.316278	+	0.948667i	$0.397567\pi$
$798$	−158402.	+	158402.i	−0.248746	+	0.248746i
$799$	508887.	+	136356.i	0.797127	+	0.213590i
$800$	−5383.29	+	20090.7i	−0.00841139	+	0.0313917i
$801$	−40520.1	−	40520.1i	−0.0631546	−	0.0631546i
$802$	62377.6	+	108041.i	0.0969794	+	0.167973i
$803$	100641.	+	58105.3i	0.156079	+	0.0901124i
$804$	505870.	−	135547.i	0.782576	−	0.209691i
$805$		−	517102.i		−	0.797966i
$806$	34735.6	+	505836.i	0.0534693	+	0.778645i
$807$	−122119.			−0.187514
$808$	49368.9	+	184247.i	0.0756189	+	0.282214i
$809$	−74499.9	+	129038.i	−0.113830	+	0.197160i	−0.917312	−	0.398170i	$-0.869645\pi$
$809$	−74499.9	+	129038.i	−0.113830	+	0.197160i	0.803481	+	0.595330i	$0.202979\pi$
$810$	481056.	−	277738.i	0.733205	−	0.423316i
$811$	129192.	−	129192.i	0.196424	−	0.196424i	−0.602041	−	0.798465i	$-0.705646\pi$
$811$	129192.	−	129192.i	0.196424	−	0.196424i	0.798465	+	0.602041i	$0.205646\pi$
$812$	235868.	+	63200.6i	0.357731	+	0.0958538i
$813$	39204.8	−	146314.i	0.0593142	−	0.221364i
$814$	46392.7	+	46392.7i	0.0700166	+	0.0700166i
$815$	−633362.	−	1.09702e6i	−0.953535	−	1.65157i
$816$	−113139.	−	65321.0i	−0.169916	−	0.0981008i
$817$	−66738.7	+	17882.6i	−0.0999847	+	0.0267908i
$818$			340136.i			0.508330i
$819$	−23095.1	−	20127.0i	−0.0344311	−	0.0300062i
$820$	123593.			0.183808
$821$	123564.	+	461148.i	0.183319	+	0.684155i	0.994984	+	0.100032i	$0.0318946\pi$
$821$	123564.	+	461148.i	0.183319	+	0.684155i	−0.811666	+	0.584122i	$0.801439\pi$
$822$	158209.	−	274025.i	0.234146	−	0.405553i
$823$	−917060.	+	529465.i	−1.35394	+	0.781695i	−0.988798	−	0.149258i	$-0.952312\pi$
$823$	−917060.	+	529465.i	−1.35394	+	0.781695i	−0.365138	+	0.930953i	$0.618978\pi$
$824$	−38375.1	+	38375.1i	−0.0565191	+	0.0565191i
$825$	−34689.4	−	9295.00i	−0.0509670	−	0.0136566i
$826$	−11272.9	+	42071.0i	−0.0165225	+	0.0616627i
$827$	114562.	+	114562.i	0.167506	+	0.167506i	0.785882	−	0.618376i	$-0.212209\pi$
$827$	114562.	+	114562.i	0.167506	+	0.167506i	−0.618376	+	0.785882i	$0.712209\pi$
$828$	35305.4	+	61150.8i	0.0514969	+	0.0891952i
$829$	362084.	+	209050.i	0.526867	+	0.304187i	0.739740	−	0.672893i	$-0.234949\pi$
$829$	362084.	+	209050.i	0.526867	+	0.304187i	−0.212873	+	0.977080i	$0.568282\pi$
$830$	143069.	−	38335.1i	0.207677	−	0.0556469i
$831$			578622.i			0.837902i
$832$	71795.4	−	48296.0i	0.103717	−	0.0697694i
$833$	−432198.			−0.622864
$834$	14089.5	+	52582.6i	0.0202564	+	0.0755979i
$835$	−237738.	+	411775.i	−0.340978	+	0.590591i
$836$	96256.7	−	55573.8i	0.137727	−	0.0795166i
$837$	−511572.	+	511572.i	−0.730224	+	0.730224i
$838$	−441649.	−	118339.i	−0.628911	−	0.168516i
$839$	34000.3	−	126891.i	0.0483013	−	0.180263i	−0.937561	−	0.347821i	$-0.886922\pi$
$839$	34000.3	−	126891.i	0.0483013	−	0.180263i	0.985862	+	0.167558i	$0.0535882\pi$
$840$	81660.9	+	81660.9i	0.115733	+	0.115733i
$841$	−839542.	−	1.45413e6i	−1.18700	−	2.05594i
$842$	−277629.	−	160289.i	−0.391598	−	0.226089i
$843$	399196.	−	106964.i	0.561734	−	0.150516i
$844$			34938.7i			0.0490481i
$845$	−301765.	−	715890.i	−0.422626	−	1.00261i
$846$	63594.4			0.0888543
$847$	−69334.1	−	258758.i	−0.0966452	−	0.360685i
$848$	−145115.	+	251347.i	−0.201800	+	0.349528i
$849$	−911593.	+	526308.i	−1.26469	+	0.730171i
$850$	49399.1	−	49399.1i	0.0683724	−	0.0683724i
$851$	654938.	+	175490.i	0.904360	+	0.242323i
$852$	108513.	−	404975.i	0.149486	−	0.557891i
$853$	−73320.6	−	73320.6i	−0.100769	−	0.100769i	0.654925	−	0.755694i	$-0.272700\pi$
$853$	−73320.6	−	73320.6i	−0.100769	−	0.100769i	−0.755694	+	0.654925i	$0.772700\pi$
$854$	−110334.	−	191104.i	−0.151284	−	0.262032i
$855$	91222.3	+	52667.2i	0.124787	+	0.0720457i
$856$	−205717.	+	55121.7i	−0.280752	+	0.0752273i
$857$			973943.i			1.32609i	0.748581	+	0.663043i	$0.230735\pi$
$857$			973943.i			1.32609i	−0.748581	+	0.663043i	$0.769265\pi$
$858$	83389.8	+	123965.i	0.113276	+	0.168393i
$859$	−220355.			−0.298632			−0.149316	−	0.988790i	$-0.547707\pi$
$859$	−220355.			−0.298632			−0.149316	+	0.988790i	$0.547707\pi$
$860$	9218.98	+	34405.7i	0.0124648	+	0.0465193i
$861$	53283.6	−	92289.9i	0.0718765	−	0.124494i
$862$	−212940.	+	122941.i	−0.286577	+	0.165455i
$863$	224496.	−	224496.i	0.301430	−	0.301430i	−0.540143	−	0.841573i	$-0.681630\pi$
$863$	224496.	−	224496.i	0.301430	−	0.301430i	0.841573	+	0.540143i	$0.181630\pi$
$864$	119259.	+	31955.3i	0.159758	+	0.0428071i
$865$	−227486.	+	848988.i	−0.304034	+	1.13467i
$866$	430703.	+	430703.i	0.574305	+	0.574305i
$867$	−177159.	−	306848.i	−0.235681	−	0.408211i
$868$	−145207.	−	83835.2i	−0.192729	−	0.111272i
$869$	−213332.	+	57162.0i	−0.282498	+	0.0756952i
$870$		−	1.12860e6i		−	1.49109i
$871$	765453.	−	878331.i	1.00898	−	1.15777i
$872$	479798.			0.630994
$873$	11481.5	+	42849.5i	0.0150650	+	0.0562235i
$874$	574331.	−	994770.i	0.751864	−	1.30227i
$875$	237431.	−	137081.i	0.310114	−	0.179045i
$876$	−189660.	+	189660.i	−0.247154	+	0.247154i
$877$	389692.	+	104418.i	0.506667	+	0.135761i	0.503093	−	0.864233i	$-0.332195\pi$
$877$	389692.	+	104418.i	0.506667	+	0.135761i	0.00357470	+	0.999994i	$0.498862\pi$
$878$	215530.	−	804370.i	0.279588	−	1.04344i
$879$	−227153.	−	227153.i	−0.293995	−	0.293995i
$880$	−28649.9	−	49623.1i	−0.0369962	−	0.0640794i
$881$	−339319.	−	195906.i	−0.437176	−	0.252403i	0.265223	−	0.964187i	$-0.414554\pi$
$881$	−339319.	−	195906.i	−0.437176	−	0.252403i	−0.702399	+	0.711784i	$0.747888\pi$
$882$	−50392.8	+	13502.7i	−0.0647786	+	0.0173574i
$883$		−	579331.i		−	0.743029i	−0.928427	−	0.371514i	$-0.878839\pi$
$883$		−	579331.i		−	0.743029i	0.928427	−	0.371514i	$-0.121161\pi$
$884$	−289946.	+	19910.5i	−0.371033	+	0.0254787i
$885$	201305.			0.257021
$886$	55112.0	+	205681.i	0.0702067	+	0.262015i
$887$	646770.	−	1.12024e6i	0.822059	−	1.42385i	−0.0820875	−	0.996625i	$-0.526159\pi$
$887$	646770.	−	1.12024e6i	0.822059	−	1.42385i	0.904146	−	0.427223i	$-0.140508\pi$
$888$	−131142.	+	75714.6i	−0.166309	+	0.0960183i
$889$	226853.	−	226853.i	0.287040	−	0.287040i
$890$	464197.	+	124381.i	0.586033	+	0.157027i
$891$	−61505.7	+	229542.i	−0.0774747	+	0.289139i
$892$	129295.	+	129295.i	0.162499	+	0.162499i
$893$	−517261.	−	895922.i	−0.648644	−	1.12349i
$894$	558989.	+	322732.i	0.699404	+	0.403801i
$895$	350428.	−	93897.0i	0.437475	−	0.117221i
$896$			28614.2i			0.0356423i
$897$	1.38690e6	+	678585.i	1.72369	+	0.843372i
$898$	397724.			0.493207
$899$	424096.	+	1.58275e6i	0.524741	+	1.95836i
$900$	4216.44	−	7303.08i	0.00520548	−	0.00901615i
$901$	844220.	−	487410.i	1.03993	−	0.600406i
$902$	−37388.0	+	37388.0i	−0.0459535	+	0.0459535i
$903$	29666.1	+	7949.01i	0.0363819	+	0.00974849i
$904$	−102867.	+	383906.i	−0.125875	+	0.469773i
$905$	−889117.	−	889117.i	−1.08558	−	1.08558i
$906$	−21079.1	−	36510.0i	−0.0256800	−	0.0444791i
$907$	−1.15385e6	−	666178.i	−1.40261	−	0.809797i	−0.407949	−	0.913005i	$-0.633756\pi$
$907$	−1.15385e6	−	666178.i	−1.40261	−	0.809797i	−0.994660	+	0.103208i	$0.967089\pi$
$908$	341306.	−	91452.7i	0.413973	−	0.110924i
$909$		−	77335.9i		−	0.0935951i
$910$	252131.	+	49336.7i	0.304469	+	0.0595782i
$911$	224303.			0.270271			0.135135	−	0.990827i	$-0.456853\pi$
$911$	224303.			0.270271			0.135135	+	0.990827i	$0.456853\pi$
$912$	66395.9	+	247793.i	0.0798273	+	0.297920i
$913$	−31682.9	+	54876.4i	−0.0380087	+	0.0658330i
$914$	−477088.	+	275447.i	−0.571092	+	0.329720i
$915$	−721175.	+	721175.i	−0.861387	+	0.861387i
$916$	109558.	+	29356.0i	0.130573	+	0.0349869i
$917$	−46792.8	+	174633.i	−0.0556469	+	0.207677i
$918$	−293234.	−	293234.i	−0.347960	−	0.347960i
$919$	580970.	+	1.00627e6i	0.687896	+	1.19147i	0.972517	+	0.232831i	$0.0747990\pi$
$919$	580970.	+	1.00627e6i	0.687896	+	1.19147i	−0.284621	+	0.958640i	$0.591868\pi$
$920$	−512832.	−	296084.i	−0.605898	−	0.349815i
$921$	−1.27195e6	+	340819.i	−1.49952	+	0.401795i
$922$			927699.i			1.09130i
$923$	−302553.	−	882262.i	−0.355139	−	1.03561i
$924$	−49406.4			−0.0578681
$925$	−20958.3	−	78217.6i	−0.0244948	−	0.0914158i
$926$	391201.	−	677579.i	0.456223	−	0.790202i
$927$	19055.4	−	11001.7i	0.0221748	−	0.0128026i
$928$	197733.	−	197733.i	0.229606	−	0.229606i
$929$	−939320.	−	251690.i	−1.08838	−	0.291632i	−0.330358	−	0.943856i	$-0.607169\pi$
$929$	−939320.	−	251690.i	−1.08838	−	0.291632i	−0.758026	+	0.652224i	$0.773836\pi$
$930$	−200571.	+	748542.i	−0.231901	+	0.865466i
$931$	600109.	+	600109.i	0.692359	+	0.692359i
$932$	12135.3	+	21019.0i	0.0139707	+	0.0241980i
$933$	−559826.	−	323216.i	−0.643117	−	0.371304i
$934$	−582872.	+	156180.i	−0.668158	+	0.179033i
$935$			192458.i			0.220146i
$936$	−33184.7	+	11380.0i	−0.0378779	+	0.0129894i
$937$	−237066.			−0.270016			−0.135008	−	0.990845i	$-0.543106\pi$
$937$	−237066.			−0.270016			−0.135008	+	0.990845i	$0.543106\pi$
$938$	99717.7	+	372152.i	0.113336	+	0.422974i
$939$	264387.	−	457932.i	0.299854	−	0.519362i
$940$	−461873.	+	266663.i	−0.522718	+	0.301791i
$941$	−488611.	+	488611.i	−0.551803	+	0.551803i	−0.926961	−	0.375158i	$-0.877589\pi$
$941$	−488611.	+	488611.i	−0.551803	+	0.551803i	0.375158	+	0.926961i	$0.377589\pi$
$942$	−466519.	−	125003.i	−0.525735	−	0.140870i
$943$	−141428.	+	527816.i	−0.159042	+	0.593553i
$944$	35268.9	+	35268.9i	0.0395775	+	0.0395775i
$945$	183293.	+	317473.i	0.205250	+	0.355503i
$946$	−13196.9	−	7619.22i	−0.0147465	−	0.00851389i
$947$	1.53497e6	−	411293.i	1.71159	−	0.458618i	0.735773	−	0.677228i	$-0.236819\pi$
$947$	1.53497e6	−	411293.i	1.71159	−	0.458618i	0.975812	+	0.218610i	$0.0701523\pi$
$948$		−	509749.i		−	0.567204i
$949$	−114586.	+	585581.i	−0.127233	+	0.650211i
$950$	−137182.			−0.152002
$951$	−80419.7	−	300131.i	−0.0889204	−	0.331856i
$952$	48054.5	−	83232.8i	0.0530224	−	0.0918376i
$953$	469282.	−	270940.i	0.516711	−	0.298323i	−0.218877	−	0.975753i	$-0.570239\pi$
$953$	469282.	−	270940.i	0.516711	−	0.298323i	0.735588	+	0.677429i	$0.236906\pi$
$954$	83205.4	−	83205.4i	0.0914229	−	0.0914229i
$955$	313111.	+	83897.9i	0.343314	+	0.0919908i
$956$	80369.8	−	299944.i	0.0879382	−	0.328190i
$957$	341413.	+	341413.i	0.372783	+	0.372783i
$958$	204113.	+	353534.i	0.222403	+	0.385213i
$959$	201591.	+	116389.i	0.219197	+	0.126553i
$960$	127744.	−	34229.0i	0.138611	−	0.0371408i
$961$		−	201600.i		−	0.218295i
$962$	−148054.	+	302594.i	−0.159982	+	0.326972i
$963$	86347.6			0.0931103
$964$	−120003.	−	447859.i	−0.129134	−	0.481934i
$965$	−572720.	+	991981.i	−0.615018	+	1.06524i
$966$	−442186.	+	255296.i	−0.473861	+	0.273584i
$967$	906789.	−	906789.i	0.969735	−	0.969735i	−0.0298202	−	0.999555i	$-0.509493\pi$
$967$	906789.	−	906789.i	0.969735	−	0.969735i	0.999555	+	0.0298202i	$0.00949348\pi$
$968$	−296321.	−	79399.1i	−0.316237	−	0.0847354i
$969$	223009.	−	832283.i	0.237507	−	0.886387i
$970$	−263064.	−	263064.i	−0.279587	−	0.279587i
$971$	56975.0	+	98683.6i	0.0604291	+	0.104666i	0.894657	−	0.446753i	$-0.147420\pi$
$971$	56975.0	+	98683.6i	0.0604291	+	0.104666i	−0.834228	+	0.551419i	$0.814086\pi$
$972$	−92239.6	−	53254.5i	−0.0976303	−	0.0563669i
$973$	−38683.3	+	10365.1i	−0.0408599	+	0.0109484i
$974$			228163.i			0.240507i
$975$	−12632.7	−	183964.i	−0.0132889	−	0.193519i
$976$	−252701.			−0.265282
$977$	114361.	+	426801.i	0.119809	+	0.447133i	0.999602	−	0.0282246i	$-0.00898535\pi$
$977$	114361.	+	426801.i	0.119809	+	0.447133i	−0.879793	+	0.475358i	$0.842319\pi$
$978$	−625390.	+	1.08321e6i	−0.653842	+	1.13249i
$979$	−178050.	+	102797.i	−0.185771	+	0.107255i
$980$	309374.	−	309374.i	0.322130	−	0.322130i
$981$	−187900.	−	50347.5i	−0.195249	−	0.0523167i
$982$	238916.	−	891648.i	0.247755	−	0.924636i
$983$	810.786	+	810.786i	0.000839072	+	0.000839072i	0.707526	−	0.706687i	$-0.249811\pi$
$983$	810.786	+	810.786i	0.000839072	+	0.000839072i	−0.706687	+	0.707526i	$0.749811\pi$
$984$	−61018.5	−	105687.i	−0.0630190	−	0.109152i
$985$	1.30112e6	+	751203.i	1.34105	+	0.774257i
$986$	−907234.	+	243093.i	−0.933180	+	0.250045i
$987$			459857.i			0.472050i
$988$	430237.	+	374946.i	0.440752	+	0.384109i
$989$	−157482.			−0.161005
$990$	6012.75	+	22439.9i	0.00613483	+	0.0228955i
$991$	−137486.	+	238132.i	−0.139994	+	0.242477i	−0.927494	−	0.373838i	$-0.878042\pi$
$991$	−137486.	+	238132.i	−0.139994	+	0.242477i	0.787500	+	0.616315i	$0.211375\pi$
$992$	−166286.	+	96005.2i	−0.168979	+	0.0975599i
$993$	−514700.	+	514700.i	−0.521982	+	0.521982i
$994$	297927.	+	79829.3i	0.301534	+	0.0807959i
$995$	−475267.	+	1.77372e6i	−0.480055	+	1.79159i
$996$	−103415.	−	103415.i	−0.104248	−	0.104248i
$997$	769228.	+	1.33234e6i	0.773864	+	1.34037i	0.935431	+	0.353510i	$0.115012\pi$
$997$	769228.	+	1.33234e6i	0.773864	+	1.34037i	−0.161567	+	0.986862i	$0.551655\pi$
$998$	−1.11254e6	−	642326.i	−1.11700	−	0.644903i
$999$	−464302.	+	124409.i	−0.465232	+	0.124658i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.5.f.b.19.1	yes	8
3.2	odd	2		234.5.bb.a.19.2		8
13.4	even	6		338.5.d.g.239.3		8
13.6	odd	12		338.5.d.g.99.3		8
13.7	odd	12		338.5.d.f.99.3		8
13.9	even	3		338.5.d.f.239.3		8
13.11	odd	12	inner	26.5.f.b.11.1	✓	8
39.11	even	12		234.5.bb.a.37.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.5.f.b.11.1	✓	8	13.11	odd	12	inner
26.5.f.b.19.1	yes	8	1.1	even	1	trivial
234.5.bb.a.19.2		8	3.2	odd	2
234.5.bb.a.37.2		8	39.11	even	12
338.5.d.f.99.3		8	13.7	odd	12
338.5.d.f.239.3		8	13.9	even	3
338.5.d.g.99.3		8	13.6	odd	12
338.5.d.g.239.3		8	13.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	26.f (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.732051 - 2.73205i) q^{2} +(-4.74800 + 8.22378i) q^{3} +(-6.92820 + 4.00000i) q^{4} +(-19.2341 + 19.2341i) q^{5} +(25.9436 + 6.95155i) q^{6} +(-5.11403 + 19.0858i) q^{7} +(16.0000 + 16.0000i) q^{8} +(-4.58700 - 7.94492i) q^{9} +O(q^{10})\)	\(q+(-0.732051 - 2.73205i) q^{2} +(-4.74800 + 8.22378i) q^{3} +(-6.92820 + 4.00000i) q^{4} +(-19.2341 + 19.2341i) q^{5} +(25.9436 + 6.95155i) q^{6} +(-5.11403 + 19.0858i) q^{7} +(16.0000 + 16.0000i) q^{8} +(-4.58700 - 7.94492i) q^{9} +(66.6289 + 38.4682i) q^{10} +(-31.7929 + 8.51887i) q^{11} -75.9680i q^{12} +(-94.3282 - 140.225i) q^{13} +55.8871 q^{14} +(-66.8535 - 249.501i) q^{15} +(32.0000 - 55.4256i) q^{16} +(-186.163 + 107.481i) q^{17} +(-18.3480 + 18.3480i) q^{18} +(407.726 + 109.250i) q^{19} +(56.3214 - 210.194i) q^{20} +(-132.676 - 132.676i) q^{21} +(46.5480 + 80.6235i) q^{22} +(833.208 + 481.053i) q^{23} +(-207.548 + 55.6124i) q^{24} -114.902i q^{25} +(-314.050 + 360.362i) q^{26} -682.060 q^{27} +(-40.9122 - 152.686i) q^{28} +(-772.393 + 1337.82i) q^{29} +(-632.708 + 365.294i) q^{30} +(750.040 - 750.040i) q^{31} +(-174.851 - 46.8513i) q^{32} +(80.8952 - 301.905i) q^{33} +(429.924 + 429.924i) q^{34} +(-268.735 - 465.462i) q^{35} +(63.5593 + 36.6960i) q^{36} +(680.735 - 182.402i) q^{37} -1193.90i q^{38} +(1601.05 - 109.944i) q^{39} -615.491 q^{40} +(146.998 + 548.605i) q^{41} +(-265.352 + 459.603i) q^{42} +(-141.756 + 81.8426i) q^{43} +(186.192 - 186.192i) q^{44} +(241.040 + 64.5865i) q^{45} +(704.310 - 2628.52i) q^{46} +(-1733.01 - 1733.01i) q^{47} +(303.872 + 526.322i) q^{48} +(1741.21 + 1005.29i) q^{49} +(-313.917 + 84.1139i) q^{50} -2041.28i q^{51} +(1214.43 + 594.198i) q^{52} -4534.85 q^{53} +(499.302 + 1863.42i) q^{54} +(447.654 - 775.360i) q^{55} +(-387.197 + 223.548i) q^{56} +(-2834.33 + 2834.33i) q^{57} +(4220.44 + 1130.86i) q^{58} +(-201.708 + 752.785i) q^{59} +(1461.18 + 1461.18i) q^{60} +(-1974.23 - 3419.47i) q^{61} +(-2598.22 - 1500.08i) q^{62} +(175.093 - 46.9161i) q^{63} +512.000i q^{64} +(4511.43 + 882.793i) q^{65} -884.039 q^{66} +(1784.27 + 6658.99i) q^{67} +(859.849 - 1489.30i) q^{68} +(-7912.14 + 4568.08i) q^{69} +(-1074.94 + 1074.94i) q^{70} +(5330.87 + 1428.40i) q^{71} +(53.7267 - 200.511i) q^{72} +(-2496.58 - 2496.58i) q^{73} +(-996.665 - 1726.27i) q^{74} +(944.926 + 545.554i) q^{75} +(-3261.81 + 873.998i) q^{76} -650.358i q^{77} +(-1472.42 - 4293.67i) q^{78} +6710.05 q^{79} +(450.571 + 1681.55i) q^{80} +(3609.97 - 6252.64i) q^{81} +(1391.21 - 803.214i) q^{82} +(1361.30 - 1361.30i) q^{83} +(1449.91 + 388.502i) q^{84} +(1513.37 - 5647.98i) q^{85} +(327.370 + 327.370i) q^{86} +(-7334.65 - 12704.0i) q^{87} +(-644.988 - 372.384i) q^{88} +(6033.51 - 1616.67i) q^{89} -705.815i q^{90} +(3158.71 - 1083.21i) q^{91} -7696.84 q^{92} +(2606.97 + 9729.36i) q^{93} +(-3466.01 + 6003.31i) q^{94} +(-9943.56 + 5740.92i) q^{95} +(1215.49 - 1215.49i) q^{96} +(-4670.76 - 1251.53i) q^{97} +(1471.85 - 5493.00i) q^{98} +(213.516 + 213.516i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 18 q^{5} - 36 q^{6} + 4 q^{7} + 128 q^{8} - 198 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 - 18 * q^5 - 36 * q^6 + 4 * q^7 + 128 * q^8 - 198 * q^9	\( 8 q + 8 q^{2} - 18 q^{5} - 36 q^{6} + 4 q^{7} + 128 q^{8} - 198 q^{9} + 348 q^{10} + 144 q^{11} - 318 q^{13} - 40 q^{14} - 924 q^{15} + 256 q^{16} - 390 q^{17} - 792 q^{18} + 2278 q^{19} + 624 q^{20} - 678 q^{21} - 756 q^{22} + 744 q^{23} + 288 q^{24} + 424 q^{26} - 1404 q^{27} + 32 q^{28} - 732 q^{29} - 2496 q^{30} + 368 q^{31} - 512 q^{32} + 7746 q^{33} - 312 q^{34} - 342 q^{35} + 1248 q^{36} - 280 q^{37} + 2808 q^{39} - 576 q^{40} + 744 q^{41} - 1356 q^{42} - 13014 q^{43} - 3024 q^{44} + 5766 q^{45} + 1884 q^{46} - 10896 q^{47} - 1842 q^{49} + 1508 q^{50} + 2624 q^{52} - 4728 q^{53} + 6372 q^{54} + 6630 q^{55} + 288 q^{56} + 18990 q^{57} + 8064 q^{58} + 3576 q^{59} - 4800 q^{60} - 13170 q^{61} + 4704 q^{62} - 6396 q^{63} + 6792 q^{65} + 4824 q^{66} + 3490 q^{67} - 624 q^{68} - 45354 q^{69} - 1368 q^{70} + 22710 q^{71} - 672 q^{72} - 7586 q^{73} - 10592 q^{74} - 7128 q^{75} - 18224 q^{76} - 6396 q^{78} + 37824 q^{79} + 4992 q^{80} + 17088 q^{81} + 4368 q^{82} + 21864 q^{83} + 9456 q^{84} + 6198 q^{85} - 2592 q^{86} - 39708 q^{87} - 1440 q^{88} + 17238 q^{89} + 12160 q^{91} + 3168 q^{92} - 258 q^{93} - 21792 q^{94} - 8280 q^{95} - 19450 q^{97} - 20548 q^{98} - 55296 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - 18 * q^5 - 36 * q^6 + 4 * q^7 + 128 * q^8 - 198 * q^9 + 348 * q^10 + 144 * q^11 - 318 * q^13 - 40 * q^14 - 924 * q^15 + 256 * q^16 - 390 * q^17 - 792 * q^18 + 2278 * q^19 + 624 * q^20 - 678 * q^21 - 756 * q^22 + 744 * q^23 + 288 * q^24 + 424 * q^26 - 1404 * q^27 + 32 * q^28 - 732 * q^29 - 2496 * q^30 + 368 * q^31 - 512 * q^32 + 7746 * q^33 - 312 * q^34 - 342 * q^35 + 1248 * q^36 - 280 * q^37 + 2808 * q^39 - 576 * q^40 + 744 * q^41 - 1356 * q^42 - 13014 * q^43 - 3024 * q^44 + 5766 * q^45 + 1884 * q^46 - 10896 * q^47 - 1842 * q^49 + 1508 * q^50 + 2624 * q^52 - 4728 * q^53 + 6372 * q^54 + 6630 * q^55 + 288 * q^56 + 18990 * q^57 + 8064 * q^58 + 3576 * q^59 - 4800 * q^60 - 13170 * q^61 + 4704 * q^62 - 6396 * q^63 + 6792 * q^65 + 4824 * q^66 + 3490 * q^67 - 624 * q^68 - 45354 * q^69 - 1368 * q^70 + 22710 * q^71 - 672 * q^72 - 7586 * q^73 - 10592 * q^74 - 7128 * q^75 - 18224 * q^76 - 6396 * q^78 + 37824 * q^79 + 4992 * q^80 + 17088 * q^81 + 4368 * q^82 + 21864 * q^83 + 9456 * q^84 + 6198 * q^85 - 2592 * q^86 - 39708 * q^87 - 1440 * q^88 + 17238 * q^89 + 12160 * q^91 + 3168 * q^92 - 258 * q^93 - 21792 * q^94 - 8280 * q^95 - 19450 * q^97 - 20548 * q^98 - 55296 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more