LMFDB - Embedded newform 65.5.g.a.34.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,5,Mod(34,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("65.34");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	65.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.71904760045$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			34.3
Character	$\chi$	$=$	65.34
Dual form			65.5.g.a.44.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.94726 + 4.94726i) q^{2} -3.40815i q^{3} -32.9507i q^{4} +(-22.9591 - 9.89351i) q^{5} +(16.8610 + 16.8610i) q^{6} +(9.32308 + 9.32308i) q^{7} +(83.8595 + 83.8595i) q^{8} +69.3845 q^{9} +O(q^{10})$	\(q+(-4.94726 + 4.94726i) q^{2} -3.40815i q^{3} -32.9507i q^{4} +(-22.9591 - 9.89351i) q^{5} +(16.8610 + 16.8610i) q^{6} +(9.32308 + 9.32308i) q^{7} +(83.8595 + 83.8595i) q^{8} +69.3845 q^{9} +(162.530 - 64.6387i) q^{10} +(-32.0590 + 32.0590i) q^{11} -112.301 q^{12} +(114.986 + 123.852i) q^{13} -92.2473 q^{14} +(-33.7186 + 78.2480i) q^{15} -302.538 q^{16} -430.937 q^{17} +(-343.263 + 343.263i) q^{18} +(315.570 + 315.570i) q^{19} +(-325.998 + 756.517i) q^{20} +(31.7745 - 31.7745i) q^{21} -317.209i q^{22} +360.475 q^{23} +(285.806 - 285.806i) q^{24} +(429.237 + 454.291i) q^{25} +(-1181.59 - 43.8629i) q^{26} -512.533i q^{27} +(307.202 - 307.202i) q^{28} +975.115 q^{29} +(-220.298 - 553.927i) q^{30} +(488.592 + 488.592i) q^{31} +(154.981 - 154.981i) q^{32} +(109.262 + 109.262i) q^{33} +(2131.96 - 2131.96i) q^{34} +(-121.811 - 306.287i) q^{35} -2286.27i q^{36} +(480.250 + 480.250i) q^{37} -3122.42 q^{38} +(422.106 - 391.889i) q^{39} +(-1095.67 - 2755.00i) q^{40} +(1241.43 + 1241.43i) q^{41} +314.393i q^{42} +391.593 q^{43} +(1056.37 + 1056.37i) q^{44} +(-1593.00 - 686.456i) q^{45} +(-1783.36 + 1783.36i) q^{46} +(1757.33 + 1757.33i) q^{47} +1031.10i q^{48} -2227.16i q^{49} +(-4371.04 - 123.950i) q^{50} +1468.70i q^{51} +(4081.01 - 3788.86i) q^{52} -1486.64i q^{53} +(2535.63 + 2535.63i) q^{54} +(1053.22 - 418.869i) q^{55} +1563.66i q^{56} +(1075.51 - 1075.51i) q^{57} +(-4824.15 + 4824.15i) q^{58} +(-4385.14 + 4385.14i) q^{59} +(2578.33 + 1111.05i) q^{60} -962.100 q^{61} -4834.38 q^{62} +(646.877 + 646.877i) q^{63} -3307.15i q^{64} +(-1414.64 - 3981.13i) q^{65} -1081.10 q^{66} +(1083.51 - 1083.51i) q^{67} +14199.7i q^{68} -1228.55i q^{69} +(2117.91 + 912.650i) q^{70} +(-3281.37 - 3281.37i) q^{71} +(5818.55 + 5818.55i) q^{72} +(496.118 + 496.118i) q^{73} -4751.85 q^{74} +(1548.29 - 1462.91i) q^{75} +(10398.3 - 10398.3i) q^{76} -597.778 q^{77} +(-149.492 + 4027.04i) q^{78} -293.532 q^{79} +(6945.99 + 2993.16i) q^{80} +3873.35 q^{81} -12283.3 q^{82} +(7793.88 - 7793.88i) q^{83} +(-1046.99 - 1046.99i) q^{84} +(9893.92 + 4263.48i) q^{85} +(-1937.31 + 1937.31i) q^{86} -3323.34i q^{87} -5376.91 q^{88} +(-1665.04 + 1665.04i) q^{89} +(11277.1 - 4484.92i) q^{90} +(-82.6594 + 2226.70i) q^{91} -11877.9i q^{92} +(1665.20 - 1665.20i) q^{93} -17388.0 q^{94} +(-4123.10 - 10367.3i) q^{95} +(-528.199 - 528.199i) q^{96} +(-3012.05 + 3012.05i) q^{97} +(11018.3 + 11018.3i) q^{98} +(-2224.40 + 2224.40i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 58 q^{5} + 60 q^{6} - 1196 q^{9}+O(q^{10}) $ 52 * q + 58 * q^5 + 60 * q^6 - 1196 * q^9	$ 52 q + 58 q^{5} + 60 q^{6} - 1196 q^{9} + 8 q^{11} + 424 q^{14} - 508 q^{15} - 3128 q^{16} + 268 q^{19} + 2116 q^{20} - 668 q^{21} + 2032 q^{24} + 1100 q^{26} - 3704 q^{29} - 1660 q^{31} + 1252 q^{34} + 6692 q^{35} + 7408 q^{39} + 3644 q^{40} + 5960 q^{41} + 1444 q^{44} - 8674 q^{45} + 17620 q^{46} - 3928 q^{50} - 30588 q^{54} + 14784 q^{55} - 5548 q^{59} - 13976 q^{60} - 20008 q^{61} - 15614 q^{65} + 24752 q^{66} + 26908 q^{70} - 16360 q^{71} - 7304 q^{74} - 5760 q^{76} - 9536 q^{79} - 62348 q^{80} - 36516 q^{81} + 66564 q^{84} - 11604 q^{85} - 5264 q^{86} - 940 q^{89} + 37644 q^{91} + 55448 q^{94} - 61644 q^{96} + 16140 q^{99}+O(q^{100}) $ 52 * q + 58 * q^5 + 60 * q^6 - 1196 * q^9 + 8 * q^11 + 424 * q^14 - 508 * q^15 - 3128 * q^16 + 268 * q^19 + 2116 * q^20 - 668 * q^21 + 2032 * q^24 + 1100 * q^26 - 3704 * q^29 - 1660 * q^31 + 1252 * q^34 + 6692 * q^35 + 7408 * q^39 + 3644 * q^40 + 5960 * q^41 + 1444 * q^44 - 8674 * q^45 + 17620 * q^46 - 3928 * q^50 - 30588 * q^54 + 14784 * q^55 - 5548 * q^59 - 13976 * q^60 - 20008 * q^61 - 15614 * q^65 + 24752 * q^66 + 26908 * q^70 - 16360 * q^71 - 7304 * q^74 - 5760 * q^76 - 9536 * q^79 - 62348 * q^80 - 36516 * q^81 + 66564 * q^84 - 11604 * q^85 - 5264 * q^86 - 940 * q^89 + 37644 * q^91 + 55448 * q^94 - 61644 * q^96 + 16140 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−4.94726	+	4.94726i	−1.23681	+	1.23681i	−0.275519	+	0.961296i	$0.588850\pi$
$2$	−4.94726	+	4.94726i	−1.23681	+	1.23681i	−0.961296	+	0.275519i	$0.911150\pi$
$3$		−	3.40815i		−	0.378684i	−0.981911	−	0.189342i	$-0.939365\pi$
$3$		−	3.40815i		−	0.378684i	0.981911	−	0.189342i	$-0.0606354\pi$
$4$		−	32.9507i		−	2.05942i
$5$	−22.9591	−	9.89351i	−0.918362	−	0.395740i
$5$	−22.9591	−	9.89351i	−0.918362	−	0.395740i
$6$	16.8610	+	16.8610i	0.468361	+	0.468361i
$7$	9.32308	+	9.32308i	0.190267	+	0.190267i	0.795811	−	0.605545i	$-0.207045\pi$
$7$	9.32308	+	9.32308i	0.190267	+	0.190267i	−0.605545	+	0.795811i	$0.707045\pi$
$8$	83.8595	+	83.8595i	1.31031	+	1.31031i
$9$	69.3845			0.856599
$10$	162.530	−	64.6387i	1.62530	−	0.646387i
$11$	−32.0590	+	32.0590i	−0.264951	+	0.264951i	−0.827062	−	0.562111i	$-0.809989\pi$
$11$	−32.0590	+	32.0590i	−0.264951	+	0.264951i	0.562111	+	0.827062i	$0.309989\pi$
$12$	−112.301			−0.779868
$13$	114.986	+	123.852i	0.680389	+	0.732851i
$13$	114.986	+	123.852i	0.680389	+	0.732851i
$14$	−92.2473			−0.470650
$15$	−33.7186	+	78.2480i	−0.149860	+	0.347769i
$16$	−302.538			−1.18179
$17$	−430.937			−1.49113			−0.745567	−	0.666431i	$-0.767821\pi$
$17$	−430.937			−1.49113			−0.745567	+	0.666431i	$0.767821\pi$
$18$	−343.263	+	343.263i	−1.05945	+	1.05945i
$19$	315.570	+	315.570i	0.874156	+	0.874156i	0.992922	−	0.118766i	$-0.0378938\pi$
$19$	315.570	+	315.570i	0.874156	+	0.874156i	−0.118766	+	0.992922i	$0.537894\pi$
$20$	−325.998	+	756.517i	−0.814995	+	1.89129i
$21$	31.7745	−	31.7745i	0.0720509	−	0.0720509i
$22$		−	317.209i		−	0.655390i
$23$	360.475			0.681428			0.340714	−	0.940167i	$-0.389331\pi$
$23$	360.475			0.681428			0.340714	+	0.940167i	$0.389331\pi$
$24$	285.806	−	285.806i	0.496191	−	0.496191i
$25$	429.237	+	454.291i	0.686779	+	0.726866i
$26$	−1181.59	−	43.8629i	−1.74792	−	0.0648860i
$27$		−	512.533i		−	0.703063i
$28$	307.202	−	307.202i	0.391839	−	0.391839i
$29$	975.115			1.15947			0.579736	−	0.814805i	$-0.303156\pi$
$29$	975.115			1.15947			0.579736	+	0.814805i	$0.303156\pi$
$30$	−220.298	−	553.927i	−0.244776	−	0.615475i
$31$	488.592	+	488.592i	0.508421	+	0.508421i	0.914041	−	0.405621i	$-0.132945\pi$
$31$	488.592	+	488.592i	0.508421	+	0.508421i	−0.405621	+	0.914041i	$0.632945\pi$
$32$	154.981	−	154.981i	0.151349	−	0.151349i
$33$	109.262	+	109.262i	0.100332	+	0.100332i
$34$	2131.96	−	2131.96i	1.84425	−	1.84425i
$35$	−121.811	−	306.287i	−0.0994377	−	0.250030i
$36$		−	2286.27i		−	1.76410i
$37$	480.250	+	480.250i	0.350804	+	0.350804i	0.860409	−	0.509605i	$-0.170208\pi$
$37$	480.250	+	480.250i	0.350804	+	0.350804i	−0.509605	+	0.860409i	$0.670208\pi$
$38$	−3122.42			−2.16234
$39$	422.106	−	391.889i	0.277519	−	0.257652i
$40$	−1095.67	−	2755.00i	−0.684795	−	1.72188i
$41$	1241.43	+	1241.43i	0.738505	+	0.738505i	0.972289	−	0.233783i	$-0.0751106\pi$
$41$	1241.43	+	1241.43i	0.738505	+	0.738505i	−0.233783	+	0.972289i	$0.575111\pi$
$42$			314.393i			0.178227i
$43$	391.593			0.211786			0.105893	−	0.994378i	$-0.466230\pi$
$43$	391.593			0.211786			0.105893	+	0.994378i	$0.466230\pi$
$44$	1056.37	+	1056.37i	0.545645	+	0.545645i
$45$	−1593.00	−	686.456i	−0.786668	−	0.338991i
$46$	−1783.36	+	1783.36i	−0.842800	+	0.842800i
$47$	1757.33	+	1757.33i	0.795534	+	0.795534i	0.982388	−	0.186854i	$-0.0598290\pi$
$47$	1757.33	+	1757.33i	0.795534	+	0.795534i	−0.186854	+	0.982388i	$0.559829\pi$
$48$			1031.10i			0.447524i
$49$		−	2227.16i		−	0.927597i
$50$	−4371.04	−	123.950i	−1.74842	−	0.0495801i
$51$			1468.70i			0.564668i
$52$	4081.01	−	3788.86i	1.50925	−	1.40121i
$53$		−	1486.64i		−	0.529241i	−0.964353	−	0.264621i	$-0.914753\pi$
$53$		−	1486.64i		−	0.529241i	0.964353	−	0.264621i	$-0.0852468\pi$
$54$	2535.63	+	2535.63i	0.869559	+	0.869559i
$55$	1053.22	−	418.869i	0.348172	−	0.138469i
$56$			1563.66i			0.498615i
$57$	1075.51	−	1075.51i	0.331029	−	0.331029i
$58$	−4824.15	+	4824.15i	−1.43405	+	1.43405i
$59$	−4385.14	+	4385.14i	−1.25974	+	1.25974i	−0.308516	+	0.951219i	$0.599832\pi$
$59$	−4385.14	+	4385.14i	−1.25974	+	1.25974i	−0.951219	+	0.308516i	$0.900168\pi$
$60$	2578.33	+	1111.05i	0.716202	+	0.308625i
$61$	−962.100			−0.258559			−0.129280	−	0.991608i	$-0.541267\pi$
$61$	−962.100			−0.258559			−0.129280	+	0.991608i	$0.541267\pi$
$62$	−4834.38			−1.25764
$63$	646.877	+	646.877i	0.162982	+	0.162982i
$64$		−	3307.15i		−	0.807409i
$65$	−1414.64	−	3981.13i	−0.334825	−	0.942280i
$66$	−1081.10			−0.248185
$67$	1083.51	−	1083.51i	0.241369	−	0.241369i	−0.576047	−	0.817416i	$-0.695406\pi$
$67$	1083.51	−	1083.51i	0.241369	−	0.241369i	0.817416	+	0.576047i	$0.195406\pi$
$68$			14199.7i			3.07087i
$69$		−	1228.55i		−	0.258045i
$70$	2117.91	+	912.650i	0.432227	+	0.186255i
$71$	−3281.37	−	3281.37i	−0.650937	−	0.650937i	0.302282	−	0.953219i	$-0.402252\pi$
$71$	−3281.37	−	3281.37i	−0.650937	−	0.650937i	−0.953219	+	0.302282i	$0.902252\pi$
$72$	5818.55	+	5818.55i	1.12241	+	1.12241i
$73$	496.118	+	496.118i	0.0930977	+	0.0930977i	0.752122	−	0.659024i	$-0.229030\pi$
$73$	496.118	+	496.118i	0.0930977	+	0.0930977i	−0.659024	+	0.752122i	$0.729030\pi$
$74$	−4751.85			−0.867758
$75$	1548.29	−	1462.91i	0.275252	−	0.260072i
$76$	10398.3	−	10398.3i	1.80025	−	1.80025i
$77$	−597.778			−0.100823
$78$	−149.492	+	4027.04i	−0.0245713	+	0.661907i
$79$	−293.532			−0.0470328			−0.0235164	−	0.999723i	$-0.507486\pi$
$79$	−293.532			−0.0470328			−0.0235164	+	0.999723i	$0.507486\pi$
$80$	6945.99	+	2993.16i	1.08531	+	0.467682i
$81$	3873.35			0.590360
$82$	−12283.3			−1.82679
$83$	7793.88	−	7793.88i	1.13135	−	1.13135i	0.141399	−	0.989953i	$-0.454840\pi$
$83$	7793.88	−	7793.88i	1.13135	−	1.13135i	0.989953	−	0.141399i	$-0.0451601\pi$
$84$	−1046.99	−	1046.99i	−0.148383	−	0.148383i
$85$	9893.92	+	4263.48i	1.36940	+	0.590102i
$86$	−1937.31	+	1937.31i	−0.261940	+	0.261940i
$87$		−	3323.34i		−	0.439073i
$88$	−5376.91			−0.694333
$89$	−1665.04	+	1665.04i	−0.210206	+	0.210206i	−0.804355	−	0.594149i	$-0.797489\pi$
$89$	−1665.04	+	1665.04i	−0.210206	+	0.210206i	0.594149	+	0.804355i	$0.297489\pi$
$90$	11277.1	−	4484.92i	1.39223	−	0.553694i
$91$	−82.6594	+	2226.70i	−0.00998182	+	0.268893i
$92$		−	11877.9i		−	1.40335i
$93$	1665.20	−	1665.20i	0.192531	−	0.192531i
$94$	−17388.0			−1.96786
$95$	−4123.10	−	10367.3i	−0.456853	−	1.14873i
$96$	−528.199	−	528.199i	−0.0573133	−	0.0573133i
$97$	−3012.05	+	3012.05i	−0.320124	+	0.320124i	−0.848815	−	0.528691i	$-0.822683\pi$
$97$	−3012.05	+	3012.05i	−0.320124	+	0.320124i	0.528691	+	0.848815i	$0.322683\pi$
$98$	11018.3	+	11018.3i	1.14727	+	1.14727i
$99$	−2224.40	+	2224.40i	−0.226956	+	0.226956i
$100$	14969.2	−	14143.7i	1.49692	−	1.41437i
$101$			19914.2i			1.95218i	0.217358	+	0.976092i	$0.430256\pi$
$101$			19914.2i			1.95218i	−0.217358	+	0.976092i	$0.569744\pi$
$102$	−7266.04	−	7266.04i	−0.698389	−	0.698389i
$103$	−19675.6			−1.85461			−0.927307	−	0.374301i	$-0.877883\pi$
$103$	−19675.6			−1.85461			−0.927307	+	0.374301i	$0.877883\pi$
$104$	−743.508	+	20028.8i	−0.0687415	+	1.85178i
$105$	−1043.87	+	415.151i	−0.0946823	+	0.0376554i
$106$	7354.79	+	7354.79i	0.654573	+	0.654573i
$107$		−	6292.51i		−	0.549612i	−0.961500	−	0.274806i	$-0.911386\pi$
$107$		−	6292.51i		−	0.549612i	0.961500	−	0.274806i	$-0.0886137\pi$
$108$	−16888.3			−1.44790
$109$	−9581.19	−	9581.19i	−0.806429	−	0.806429i	0.177662	−	0.984092i	$-0.443147\pi$
$109$	−9581.19	−	9581.19i	−0.806429	−	0.806429i	−0.984092	+	0.177662i	$0.943147\pi$
$110$	−3138.31	+	7282.81i	−0.259364	+	0.601885i
$111$	1636.77	−	1636.77i	0.132844	−	0.132844i
$112$	−2820.59	−	2820.59i	−0.224855	−	0.224855i
$113$			16440.2i			1.28751i	0.765233	+	0.643754i	$0.222624\pi$
$113$			16440.2i			1.28751i	−0.765233	+	0.643754i	$0.777376\pi$
$114$			10641.7i			0.818842i
$115$	−8276.17	−	3566.36i	−0.625798	−	0.269668i
$116$		−	32130.7i		−	2.38784i
$117$	7978.23	+	8593.40i	0.582820	+	0.627759i
$118$		−	43388.8i		−	3.11612i
$119$	−4017.66	−	4017.66i	−0.283713	−	0.283713i
$120$	−9389.46	+	3734.21i	−0.652046	+	0.259320i
$121$			12585.4i			0.859602i
$122$	4759.75	−	4759.75i	0.319790	−	0.319790i
$123$	4230.97	−	4230.97i	0.279660	−	0.279660i
$124$	16099.5	−	16099.5i	1.04705	−	1.04705i
$125$	−5360.34	−	14676.8i	−0.343062	−	0.939313i
$126$	−6400.53			−0.403158
$127$	6628.00			0.410937			0.205468	−	0.978664i	$-0.434128\pi$
$127$	6628.00			0.410937			0.205468	+	0.978664i	$0.434128\pi$
$128$	18841.0	+	18841.0i	1.14996	+	1.14996i
$129$		−	1334.61i		−	0.0802000i
$130$	26694.3	+	12697.1i	1.57954	+	0.751310i
$131$	23087.8			1.34536			0.672681	−	0.739932i	$-0.265143\pi$
$131$	23087.8			1.34536			0.672681	+	0.739932i	$0.265143\pi$
$132$	3600.26	−	3600.26i	0.206627	−	0.206627i
$133$			5884.17i			0.332646i
$134$			10720.8i			0.597058i
$135$	−5070.75	+	11767.3i	−0.278231	+	0.645667i
$136$	−36138.2	−	36138.2i	−1.95384	−	1.95384i
$137$	17371.1	+	17371.1i	0.925521	+	0.925521i	0.997412	−	0.0718917i	$-0.0229036\pi$
$137$	17371.1	+	17371.1i	0.925521	+	0.925521i	−0.0718917	+	0.997412i	$0.522904\pi$
$138$	6077.98	+	6077.98i	0.319154	+	0.319154i
$139$	36289.8			1.87825			0.939127	−	0.343569i	$-0.111636\pi$
$139$	36289.8			1.87825			0.939127	+	0.343569i	$0.111636\pi$
$140$	−10092.4	+	4013.76i	−0.514917	+	0.204784i
$141$	5989.26	−	5989.26i	0.301256	−	0.301256i
$142$	32467.6			1.61018
$143$	−7656.90	−	284.239i	−0.374439	−	0.0138999i
$144$	−20991.5			−1.01232
$145$	−22387.7	−	9647.31i	−1.06482	−	0.458850i
$146$	−4908.84			−0.230289
$147$	−7590.50			−0.351266
$148$	15824.6	−	15824.6i	0.722452	−	0.722452i
$149$	−6589.06	−	6589.06i	−0.296791	−	0.296791i	0.542964	−	0.839756i	$-0.317302\pi$
$149$	−6589.06	−	6589.06i	−0.296791	−	0.296791i	−0.839756	+	0.542964i	$0.817302\pi$
$150$	−422.441	+	14897.2i	−0.0187752	+	0.662097i
$151$	−9088.42	+	9088.42i	−0.398597	+	0.398597i	−0.877738	−	0.479141i	$-0.840948\pi$
$151$	−9088.42	+	9088.42i	−0.398597	+	0.398597i	0.479141	+	0.877738i	$0.340948\pi$
$152$			52927.2i			2.29082i
$153$	−29900.4			−1.27730
$154$	2957.36	−	2957.36i	0.124699	−	0.124699i
$155$	−6383.73	−	16051.5i	−0.265712	−	0.668117i
$156$	−12913.0	−	13908.7i	−0.530614	−	0.571527i
$157$			12710.4i			0.515657i	0.966191	+	0.257829i	$0.0830070\pi$
$157$			12710.4i			0.515657i	−0.966191	+	0.257829i	$0.916993\pi$
$158$	1452.18	−	1452.18i	0.0581708	−	0.0581708i
$159$	−5066.69			−0.200415
$160$	−5091.53	+	2024.91i	−0.198888	+	0.0790982i
$161$	3360.74	+	3360.74i	0.129653	+	0.129653i
$162$	−19162.5	+	19162.5i	−0.730166	+	0.730166i
$163$	−10279.8	−	10279.8i	−0.386908	−	0.386908i	0.486675	−	0.873583i	$-0.338210\pi$
$163$	−10279.8	−	10279.8i	−0.386908	−	0.386908i	−0.873583	+	0.486675i	$0.838210\pi$
$164$	40905.9	−	40905.9i	1.52089	−	1.52089i
$165$	−1427.57	−	3589.54i	−0.0524360	−	0.131847i
$166$			77116.7i			2.79854i
$167$	−27045.5	−	27045.5i	−0.969756	−	0.969756i	0.0298002	−	0.999556i	$-0.490513\pi$
$167$	−27045.5	−	27045.5i	−0.969756	−	0.969756i	−0.999556	+	0.0298002i	$0.990513\pi$
$168$	5329.18			0.188817
$169$	−2117.56	+	28482.4i	−0.0741417	+	0.997248i
$170$	−70040.3	+	27855.2i	−2.42354	+	0.963848i
$171$	21895.7	+	21895.7i	0.748801	+	0.748801i
$172$		−	12903.3i		−	0.436157i
$173$	38831.3			1.29745			0.648724	−	0.761024i	$-0.275303\pi$
$173$	38831.3			1.29745			0.648724	+	0.761024i	$0.275303\pi$
$174$	16441.4	+	16441.4i	0.543052	+	0.543052i
$175$	−233.583	+	8237.20i	−0.00762721	+	0.268970i
$176$	9699.08	−	9699.08i	0.313116	−	0.313116i
$177$	14945.2	+	14945.2i	0.477041	+	0.477041i
$178$		−	16474.8i		−	0.519972i
$179$		−	47004.4i		−	1.46701i	−0.679685	−	0.733504i	$-0.737884\pi$
$179$		−	47004.4i		−	1.46701i	0.679685	−	0.733504i	$-0.262116\pi$
$180$	−22619.2	+	52490.6i	−0.698124	+	1.62008i
$181$			32251.5i			0.984449i	0.870468	+	0.492224i	$0.163816\pi$
$181$			32251.5i			0.984449i	−0.870468	+	0.492224i	$0.836184\pi$
$182$	−10607.1	−	11425.0i	−0.320225	−	0.344916i
$183$			3278.98i			0.0979122i
$184$	30229.3	+	30229.3i	0.892878	+	0.892878i
$185$	−6274.74	−	15777.5i	−0.183338	−	0.460992i
$186$			16476.3i			0.476249i
$187$	13815.4	−	13815.4i	0.395077	−	0.395077i
$188$	57905.4	−	57905.4i	1.63834	−	1.63834i
$189$	4778.39	−	4778.39i	0.133770	−	0.133770i
$190$	71687.8	+	30891.7i	1.98581	+	0.855725i
$191$	−45257.7			−1.24058			−0.620292	−	0.784371i	$-0.712986\pi$
$191$	−45257.7			−1.24058			−0.620292	+	0.784371i	$0.712986\pi$
$192$	−11271.3			−0.305752
$193$	−11332.7	−	11332.7i	−0.304242	−	0.304242i	0.538429	−	0.842671i	$-0.319018\pi$
$193$	−11332.7	−	11332.7i	−0.304242	−	0.304242i	−0.842671	+	0.538429i	$0.819018\pi$
$194$		−	29802.7i		−	0.791868i
$195$	−13568.3	+	4821.29i	−0.356826	+	0.126793i
$196$	−73386.5			−1.91031
$197$	−37982.2	+	37982.2i	−0.978696	+	0.978696i	−0.999778	−	0.0210821i	$-0.993289\pi$
$197$	−37982.2	+	37982.2i	−0.978696	+	0.978696i	0.0210821	+	0.999778i	$0.493289\pi$
$198$		−	22009.4i		−	0.561406i
$199$		−	6460.09i		−	0.163130i	−0.996668	−	0.0815648i	$-0.974008\pi$
$199$		−	6460.09i		−	0.163130i	0.996668	−	0.0815648i	$-0.0259917\pi$
$200$	−2101.04	+	74092.3i	−0.0525261	+	1.85231i
$201$	−3692.75	−	3692.75i	−0.0914025	−	0.0914025i
$202$	−98520.8	−	98520.8i	−2.41449	−	2.41449i
$203$	9091.08	+	9091.08i	0.220609	+	0.220609i
$204$	48394.7			1.16289
$205$	−16219.9	−	40784.1i	−0.385959	−	0.970472i
$206$	97340.3	−	97340.3i	2.29381	−	2.29381i
$207$	25011.4			0.583710
$208$	−34787.6	−	37469.9i	−0.804076	−	0.866076i
$209$	−20233.8			−0.463217
$210$	3110.45	−	7218.17i	0.0705317	−	0.163677i
$211$	28703.0			0.644706			0.322353	−	0.946620i	$-0.395526\pi$
$211$	28703.0			0.644706			0.322353	+	0.946620i	$0.395526\pi$
$212$	−48985.8			−1.08993
$213$	−11183.4	+	11183.4i	−0.246499	+	0.246499i
$214$	31130.7	+	31130.7i	0.679769	+	0.679769i
$215$	−8990.60	−	3874.23i	−0.194496	−	0.0838123i
$216$	42980.8	−	42980.8i	0.921228	−	0.921228i
$217$			9110.36i			0.193471i
$218$	94801.2			1.99481
$219$	1690.84	−	1690.84i	0.0352546	−	0.0352546i
$220$	−13802.0	−	34704.4i	−0.285166	−	0.717033i
$221$	−49551.7	−	53372.4i	−1.01455	−	1.09278i
$222$			16195.0i			0.328606i
$223$	−14709.7	+	14709.7i	−0.295797	+	0.295797i	−0.839365	−	0.543568i	$-0.817073\pi$
$223$	−14709.7	+	14709.7i	−0.295797	+	0.295797i	0.543568	+	0.839365i	$0.317073\pi$
$224$	2889.80			0.0575933
$225$	29782.4	+	31520.8i	0.588294	+	0.622633i
$226$	−81333.8	−	81333.8i	−1.59241	−	1.59241i
$227$	58120.1	−	58120.1i	1.12791	−	1.12791i	0.137395	−	0.990516i	$-0.456127\pi$
$227$	58120.1	−	58120.1i	1.12791	−	1.12791i	0.990516	−	0.137395i	$-0.0438729\pi$
$228$	−35438.9	−	35438.9i	−0.681727	−	0.681727i
$229$	13653.9	−	13653.9i	0.260367	−	0.260367i	−0.564836	−	0.825203i	$-0.691061\pi$
$229$	13653.9	−	13653.9i	0.260367	−	0.260367i	0.825203	+	0.564836i	$0.191061\pi$
$230$	58588.1	−	23300.6i	1.10753	−	0.440466i
$231$			2037.32i			0.0381799i
$232$	81772.7	+	81772.7i	1.51926	+	1.51926i
$233$	−8914.23			−0.164200			−0.0820998	−	0.996624i	$-0.526163\pi$
$233$	−8914.23			−0.164200			−0.0820998	+	0.996624i	$0.526163\pi$
$234$	−81984.1	−	3043.41i	−1.49726	−	0.0555813i
$235$	−22960.6	−	57733.0i	−0.415764	−	1.04541i
$236$	144493.	+	144493.i	2.59432	+	2.59432i
$237$			1000.40i			0.0178105i
$238$	39752.8			0.701801
$239$	−5748.78	−	5748.78i	−0.100642	−	0.100642i	0.654993	−	0.755635i	$-0.272672\pi$
$239$	−5748.78	−	5748.78i	−0.100642	−	0.100642i	−0.755635	+	0.654993i	$0.772672\pi$
$240$	10201.2	−	23673.0i	0.177103	−	0.410989i
$241$	−4921.64	+	4921.64i	−0.0847375	+	0.0847375i	−0.748205	−	0.663468i	$-0.769084\pi$
$241$	−4921.64	+	4921.64i	−0.0847375	+	0.0847375i	0.663468	+	0.748205i	$0.269084\pi$
$242$	−62263.4	−	62263.4i	−1.06317	−	1.06317i
$243$		−	54716.2i		−	0.926623i
$244$			31701.9i			0.532482i
$245$	−22034.4	+	51133.5i	−0.367088	+	0.851870i
$246$			41863.4i			0.691775i
$247$	−2797.88	+	75370.1i	−0.0458602	+	1.23539i
$248$			81946.2i			1.33237i
$249$	−26562.7	−	26562.7i	−0.428424	−	0.428424i
$250$	99128.7	+	46090.7i	1.58606	+	0.737452i
$251$			83425.9i			1.32420i	0.749416	+	0.662100i	$0.230334\pi$
$251$			83425.9i			1.32420i	−0.749416	+	0.662100i	$0.769666\pi$
$252$	21315.1	−	21315.1i	0.335649	−	0.335649i
$253$	−11556.5	+	11556.5i	−0.180545	+	0.180545i
$254$	−32790.4	+	32790.4i	−0.508252	+	0.508252i
$255$	14530.6	−	33720.0i	0.223462	−	0.518570i
$256$	−133508.			−2.03717
$257$	91303.2			1.38236			0.691178	−	0.722684i	$-0.257092\pi$
$257$	91303.2			1.38236			0.691178	+	0.722684i	$0.257092\pi$
$258$	6602.65	+	6602.65i	0.0991925	+	0.0991925i
$259$			8954.82i			0.133493i
$260$	−131181.	+	46613.2i	−1.94055	+	0.689545i
$261$	67657.9			0.993202
$262$	−114221.	+	114221.i	−1.66396	+	1.66396i
$263$		−	113061.i		−	1.63456i	−0.576242	−	0.817279i	$-0.695481\pi$
$263$		−	113061.i		−	1.63456i	0.576242	−	0.817279i	$-0.304519\pi$
$264$			18325.3i			0.262932i
$265$	−14708.1	+	34131.8i	−0.209442	+	0.486035i
$266$	−29110.5	−	29110.5i	−0.411421	−	0.411421i
$267$	5674.72	+	5674.72i	0.0796016	+	0.0796016i
$268$	−35702.3	−	35702.3i	−0.497080	−	0.497080i
$269$	−111536.			−1.54138			−0.770688	−	0.637212i	$-0.780087\pi$
$269$	−111536.			−1.54138			−0.770688	+	0.637212i	$0.780087\pi$
$270$	−33129.5	−	83302.1i	−0.454451	−	1.14269i
$271$	26668.9	−	26668.9i	0.363134	−	0.363134i	−0.501831	−	0.864965i	$-0.667340\pi$
$271$	26668.9	−	26668.9i	0.363134	−	0.363134i	0.864965	+	0.501831i	$0.167340\pi$
$272$	130375.			1.76221
$273$	7588.94	+	281.716i	0.101825	+	0.00377995i
$274$	−171879.			−2.28939
$275$	−28325.1	−	803.218i	−0.374546	−	0.0106211i
$276$	−40481.7			−0.531424
$277$	64254.7			0.837424			0.418712	−	0.908119i	$-0.362482\pi$
$277$	64254.7			0.837424			0.418712	+	0.908119i	$0.362482\pi$
$278$	−179535.	+	179535.i	−2.32305	+	2.32305i
$279$	33900.7	+	33900.7i	0.435512	+	0.435512i
$280$	15470.1	−	35900.1i	0.197322	−	0.457910i
$281$	−3362.36	+	3362.36i	−0.0425825	+	0.0425825i	−0.728077	−	0.685495i	$-0.759586\pi$
$281$	−3362.36	+	3362.36i	−0.0425825	+	0.0425825i	0.685495	+	0.728077i	$0.259586\pi$
$282$			59260.9i			0.745195i
$283$	−26675.6			−0.333074			−0.166537	−	0.986035i	$-0.553259\pi$
$283$	−26675.6			−0.333074			−0.166537	+	0.986035i	$0.553259\pi$
$284$	−108124.	+	108124.i	−1.34055	+	1.34055i
$285$	−35333.3	+	14052.2i	−0.435006	+	0.173003i
$286$	39286.9	−	36474.5i	0.480303	−	0.445920i
$287$			23147.8i			0.281026i
$288$	10753.3	−	10753.3i	0.129645	−	0.129645i
$289$	102186.			1.22348
$290$	158486.	−	63030.2i	1.88449	−	0.749467i
$291$	10265.5	+	10265.5i	0.121226	+	0.121226i
$292$	16347.4	−	16347.4i	0.191727	−	0.191727i
$293$	69964.0	+	69964.0i	0.814965	+	0.814965i	0.985374	−	0.170408i	$-0.0545086\pi$
$293$	69964.0	+	69964.0i	0.814965	+	0.814965i	−0.170408	+	0.985374i	$0.554509\pi$
$294$	37552.2	−	37552.2i	0.434451	−	0.434451i
$295$	144063.	−	57294.3i	1.65542	−	0.658365i
$296$			80547.2i			0.919320i
$297$	16431.3	+	16431.3i	0.186277	+	0.186277i
$298$	65195.6			0.734151
$299$	41449.5	+	44645.5i	0.463636	+	0.499385i
$300$	−48203.8	−	51017.4i	−0.535597	−	0.566860i
$301$	3650.85	+	3650.85i	0.0402959	+	0.0402959i
$302$		−	89925.5i		−	0.985982i
$303$	67870.7			0.739260
$304$	−95472.1	−	95472.1i	−1.03307	−	1.03307i
$305$	22088.9	+	9518.54i	0.237451	+	0.102322i
$306$	147925.	−	147925.i	1.57979	−	1.57979i
$307$	25492.7	+	25492.7i	0.270482	+	0.270482i	0.829294	−	0.558812i	$-0.188743\pi$
$307$	25492.7	+	25492.7i	0.270482	+	0.270482i	−0.558812	+	0.829294i	$0.688743\pi$
$308$			19697.2i			0.207636i
$309$			67057.5i			0.702312i
$310$	110993.	+	47829.0i	1.15497	+	0.497700i
$311$		−	111844.i		−	1.15636i	−0.815911	−	0.578178i	$-0.803764\pi$
$311$		−	111844.i		−	1.15636i	0.815911	−	0.578178i	$-0.196236\pi$
$312$	68261.2	+	2533.99i	0.701237	+	0.0260313i
$313$			135446.i			1.38254i	0.722597	+	0.691270i	$0.242948\pi$
$313$			135446.i			1.38254i	−0.722597	+	0.691270i	$0.757052\pi$
$314$	−62881.8	−	62881.8i	−0.637772	−	0.637772i
$315$	−8451.80	−	21251.6i	−0.0851782	−	0.214176i
$316$			9672.08i			0.0968603i
$317$	111311.	−	111311.i	1.10769	−	1.10769i	0.114236	−	0.993454i	$-0.463558\pi$
$317$	111311.	−	111311.i	1.10769	−	1.10769i	0.993454	−	0.114236i	$-0.0364421\pi$
$318$	25066.2	−	25066.2i	0.247876	−	0.247876i
$319$	−31261.3	+	31261.3i	−0.307203	+	0.307203i
$320$	−32719.3	+	75929.0i	−0.319524	+	0.741494i
$321$	−21445.8			−0.208129
$322$	−33252.9			−0.320714
$323$	−135991.	−	135991.i	−1.30348	−	1.30348i
$324$		−	127630.i		−	1.21580i
$325$	−6908.69	+	105399.i	−0.0654077	+	0.997859i
$326$	101713.			0.957066
$327$	−32654.1	+	32654.1i	−0.305382	+	0.305382i
$328$			208211.i			1.93534i
$329$			32767.5i			0.302728i
$330$	24820.9	+	10695.8i	0.227924	+	0.0982169i
$331$	−102119.	−	102119.i	−0.932072	−	0.932072i	0.0657637	−	0.997835i	$-0.479052\pi$
$331$	−102119.	−	102119.i	−0.932072	−	0.932072i	−0.997835	+	0.0657637i	$0.979052\pi$
$332$	−256814.	−	256814.i	−2.32993	−	2.32993i
$333$	33321.9	+	33321.9i	0.300498	+	0.300498i
$334$	267602.			2.39882
$335$	−35596.0	+	14156.6i	−0.317184	+	0.126145i
$336$	−9612.99	+	9612.99i	−0.0851490	+	0.0851490i
$337$	−86813.4			−0.764411			−0.382206	−	0.924077i	$-0.624835\pi$
$337$	−86813.4			−0.764411			−0.382206	+	0.924077i	$0.624835\pi$
$338$	−130434.	−	151386.i	−1.14171	−	1.32511i
$339$	56030.6			0.487558
$340$	140485.	−	326012.i	1.21527	−	2.82017i
$341$	−31327.6			−0.269413
$342$	−216647.			−1.85226
$343$	43148.7	−	43148.7i	0.366758	−	0.366758i
$344$	32838.8	+	32838.8i	0.277505	+	0.277505i
$345$	−12154.7	+	28206.5i	−0.102119	+	0.236979i
$346$	−192108.	+	192108.i	−1.60470	+	1.60470i
$347$			132494.i			1.10037i	0.835043	+	0.550185i	$0.185443\pi$
$347$			132494.i			1.10037i	−0.835043	+	0.550185i	$0.814557\pi$
$348$	−109506.			−0.904235
$349$	58582.6	−	58582.6i	0.480970	−	0.480970i	−0.424472	−	0.905441i	$-0.639540\pi$
$349$	58582.6	−	58582.6i	0.480970	−	0.480970i	0.905441	+	0.424472i	$0.139540\pi$
$350$	−39596.0	−	41907.2i	−0.323232	−	0.342099i
$351$	63478.2	−	58934.0i	0.515241	−	0.478357i
$352$			9937.09i			0.0801999i
$353$	−67051.9	+	67051.9i	−0.538099	+	0.538099i	−0.922970	−	0.384872i	$-0.874246\pi$
$353$	−67051.9	+	67051.9i	−0.538099	+	0.538099i	0.384872	+	0.922970i	$0.374246\pi$
$354$	−147876.			−1.18002
$355$	42872.9	+	107802.i	0.340194	+	0.855398i
$356$	54864.3	+	54864.3i	0.432902	+	0.432902i
$357$	−13692.8	+	13692.8i	−0.107438	+	0.107438i
$358$	232543.	+	232543.i	1.81442	+	1.81442i
$359$	−53377.3	+	53377.3i	−0.414159	+	0.414159i	−0.883185	−	0.469025i	$-0.844605\pi$
$359$	−53377.3	+	53377.3i	−0.414159	+	0.414159i	0.469025	+	0.883185i	$0.344605\pi$
$360$	−76022.6	−	191154.i	−0.586594	−	1.47496i
$361$			68848.4i			0.528299i
$362$	−159557.	−	159557.i	−1.21758	−	1.21758i
$363$	42893.1			0.325517
$364$	73371.4	+	2723.69i	0.553763	+	0.0205568i
$365$	−6482.05	−	16298.7i	−0.0486549	−	0.122340i
$366$	−16222.0	−	16222.0i	−0.121099	−	0.121099i
$367$		−	162793.i		−	1.20866i	−0.796734	−	0.604330i	$-0.793441\pi$
$367$		−	162793.i		−	1.20866i	0.796734	−	0.604330i	$-0.206559\pi$
$368$	−109057.			−0.805304
$369$	86135.8	+	86135.8i	0.632603	+	0.632603i
$370$	109098.	+	47012.4i	0.796917	+	0.343407i
$371$	13860.1	−	13860.1i	0.100697	−	0.100697i
$372$	−54869.4	−	54869.4i	−0.396501	−	0.396501i
$373$		−	132620.i		−	0.953215i	−0.879116	−	0.476607i	$-0.841866\pi$
$373$		−	132620.i		−	0.953215i	0.879116	−	0.476607i	$-0.158134\pi$
$374$			136697.i			0.977273i
$375$	−50020.6	+	18268.9i	−0.355702	+	0.129912i
$376$			294739.i			2.08479i
$377$	112124.	+	120770.i	0.788892	+	0.849720i
$378$			47279.8i			0.330897i
$379$	−45353.7	−	45353.7i	−0.315743	−	0.315743i	0.531386	−	0.847130i	$-0.321671\pi$
$379$	−45353.7	−	45353.7i	−0.315743	−	0.315743i	−0.847130	+	0.531386i	$0.821671\pi$
$380$	−341610.	+	135859.i	−2.36572	+	0.940853i
$381$		−	22589.2i		−	0.155615i
$382$	223902.	−	223902.i	1.53437	−	1.53437i
$383$	−106919.	+	106919.i	−0.728880	+	0.728880i	−0.970397	−	0.241517i	$-0.922355\pi$
$383$	−106919.	+	106919.i	−0.728880	+	0.728880i	0.241517	+	0.970397i	$0.422355\pi$
$384$	64213.0	−	64213.0i	0.435472	−	0.435472i
$385$	13724.4	+	5914.12i	0.0925918	+	0.0398996i
$386$	112132.			0.752583
$387$	27170.5			0.181416
$388$	99249.1	+	99249.1i	0.659270	+	0.659270i
$389$		−	61087.9i		−	0.403697i	−0.979417	−	0.201849i	$-0.935305\pi$
$389$		−	61087.9i		−	0.403697i	0.979417	−	0.201849i	$-0.0646949\pi$
$390$	43273.8	−	90978.1i	0.284509	−	0.598147i
$391$	−155342.			−1.01610
$392$	186769.	−	186769.i	1.21544	−	1.21544i
$393$		−	78686.6i		−	0.509467i
$394$		−	375815.i		−	2.42093i
$395$	6739.21	+	2904.06i	0.0431931	+	0.0186128i
$396$	73295.6	+	73295.6i	0.467399	+	0.467399i
$397$	12554.9	+	12554.9i	0.0796586	+	0.0796586i	0.745813	−	0.666155i	$-0.232061\pi$
$397$	12554.9	+	12554.9i	0.0796586	+	0.0796586i	−0.666155	+	0.745813i	$0.732061\pi$
$398$	31959.7	+	31959.7i	0.201761	+	0.201761i
$399$	20054.2			0.125968
$400$	−129861.	−	137440.i	−0.811628	−	0.859003i
$401$	67377.3	−	67377.3i	0.419010	−	0.419010i	−0.465852	−	0.884863i	$-0.654252\pi$
$401$	67377.3	−	67377.3i	0.419010	−	0.419010i	0.884863	+	0.465852i	$0.154252\pi$
$402$	36538.0			0.226096
$403$	−4331.91	+	116694.i	−0.0266729	+	0.718520i
$404$	656188.			4.02037
$405$	−88928.5	−	38321.0i	−0.542165	−	0.233629i
$406$	−89951.8			−0.545705
$407$	−30792.7			−0.185891
$408$	−123165.	+	123165.i	−0.739887	+	0.739887i
$409$	−132917.	−	132917.i	−0.794575	−	0.794575i	0.187659	−	0.982234i	$-0.439910\pi$
$409$	−132917.	−	132917.i	−0.794575	−	0.794575i	−0.982234	+	0.187659i	$0.939910\pi$
$410$	282014.	+	121525.i	1.67765	+	0.722934i
$411$	59203.3	−	59203.3i	0.350479	−	0.350479i
$412$			648325.i			3.81943i
$413$	−81765.9			−0.479372
$414$	−123738.	+	123738.i	−0.721941	+	0.721941i
$415$	−256049.	+	101831.i	−1.48671	+	0.591270i
$416$	37015.3	+	1374.08i	0.213892	+	0.00794009i
$417$		−	123681.i		−	0.711264i
$418$	100102.	−	100102.i	0.572913	−	0.572913i
$419$	137730.			0.784516			0.392258	−	0.919855i	$-0.371694\pi$
$419$	137730.			0.784516			0.392258	+	0.919855i	$0.371694\pi$
$420$	13679.5	+	34396.4i	0.0775483	+	0.194991i
$421$	−73964.7	−	73964.7i	−0.417312	−	0.417312i	0.466964	−	0.884276i	$-0.345348\pi$
$421$	−73964.7	−	73964.7i	−0.417312	−	0.417312i	−0.884276	+	0.466964i	$0.845348\pi$
$422$	−142001.	+	142001.i	−0.797382	+	0.797382i
$423$	121932.	+	121932.i	0.681453	+	0.681453i
$424$	124669.	−	124669.i	0.693468	−	0.693468i
$425$	−184974.	−	195771.i	−1.02408	−	1.08385i
$426$		−	110654.i		−	0.609747i
$427$	−8969.73	−	8969.73i	−0.0491953	−	0.0491953i
$428$	−207343.			−1.13188
$429$	−968.730	+	26095.9i	−0.00526366	+	0.141794i
$430$	63645.6	−	25312.0i	0.344216	−	0.136896i
$431$	−192676.	−	192676.i	−1.03723	−	1.03723i	−0.999280	−	0.0379481i	$-0.987918\pi$
$431$	−192676.	−	192676.i	−1.03723	−	1.03723i	−0.0379481	−	0.999280i	$-0.512082\pi$
$432$			155061.i			0.830873i
$433$	−127612.			−0.680636			−0.340318	−	0.940310i	$-0.610535\pi$
$433$	−127612.			−0.680636			−0.340318	+	0.940310i	$0.610535\pi$
$434$	−45071.3	−	45071.3i	−0.239288	−	0.239288i
$435$	−32879.5	+	76300.8i	−0.173759	+	0.403228i
$436$	−315707.	+	315707.i	−1.66078	+	1.66078i
$437$	113755.	+	113755.i	0.595674	+	0.595674i
$438$			16730.1i			0.0872067i
$439$		−	128526.i		−	0.666903i	−0.942767	−	0.333452i	$-0.891787\pi$
$439$		−	128526.i		−	0.666903i	0.942767	−	0.333452i	$-0.108213\pi$
$440$	123449.	+	53196.5i	0.637649	+	0.274775i
$441$		−	154530.i		−	0.794578i
$442$	509192.	+	18902.2i	2.60638	+	0.0967537i
$443$		−	340629.i		−	1.73570i	−0.496827	−	0.867850i	$-0.665502\pi$
$443$		−	340629.i		−	1.73570i	0.496827	−	0.867850i	$-0.334498\pi$
$444$	−53932.6	−	53932.6i	−0.273581	−	0.273581i
$445$	54700.9	−	21754.7i	0.276232	−	0.109858i
$446$		−	145545.i		−	0.731692i
$447$	−22456.5	+	22456.5i	−0.112390	+	0.112390i
$448$	30832.8	−	30832.8i	0.153623	−	0.153623i
$449$	−36187.4	+	36187.4i	−0.179500	+	0.179500i	−0.791138	−	0.611638i	$-0.790511\pi$
$449$	−36187.4	+	36187.4i	−0.179500	+	0.179500i	0.611638	+	0.791138i	$0.290511\pi$
$450$	−303283.	−	8600.23i	−1.49769	−	0.0424702i
$451$	−79597.9			−0.391335
$452$	541716.			2.65152
$453$	30974.7	+	30974.7i	0.150942	+	0.150942i
$454$			575071.i			2.79003i
$455$	23927.7	−	50305.2i	0.115579	−	0.242991i
$456$	180384.			0.867497
$457$	−127105.	+	127105.i	−0.608598	+	0.608598i	−0.942580	−	0.333981i	$-0.891608\pi$
$457$	−127105.	+	127105.i	−0.608598	+	0.608598i	0.333981	+	0.942580i	$0.391608\pi$
$458$			135099.i			0.644052i
$459$			220870.i			1.04836i
$460$	−117514.	+	272706.i	−0.555360	+	1.28878i
$461$	−25843.5	−	25843.5i	−0.121604	−	0.121604i	0.643686	−	0.765290i	$-0.277404\pi$
$461$	−25843.5	−	25843.5i	−0.121604	−	0.121604i	−0.765290	+	0.643686i	$0.777404\pi$
$462$	−10079.1	−	10079.1i	−0.0472214	−	0.0472214i
$463$	−27483.8	−	27483.8i	−0.128208	−	0.128208i	0.640091	−	0.768299i	$-0.278897\pi$
$463$	−27483.8	−	27483.8i	−0.128208	−	0.128208i	−0.768299	+	0.640091i	$0.778897\pi$
$464$	−295010.			−1.37025
$465$	−54706.0	+	21756.7i	−0.253005	+	0.100621i
$466$	44101.0	−	44101.0i	0.203084	−	0.203084i
$467$	290604.			1.33250			0.666251	−	0.745727i	$-0.267898\pi$
$467$	290604.			1.33250			0.666251	+	0.745727i	$0.267898\pi$
$468$	283159.	−	262888.i	1.29282	−	1.20027i
$469$	20203.2			0.0918491
$470$	399212.	+	172028.i	1.80721	+	0.778760i
$471$	43319.1			0.195271
$472$	−735471.			−3.30128
$473$	−12554.1	+	12554.1i	−0.0561129	+	0.0561129i
$474$	−4949.24	−	4949.24i	−0.0220283	−	0.0220283i
$475$	−7906.41	+	278815.i	−0.0350423	+	1.23575i
$476$	−132385.	+	132385.i	−0.584285	+	0.584285i
$477$		−	103150.i		−	0.453348i
$478$	56881.4			0.248952
$479$	−152898.	+	152898.i	−0.666391	+	0.666391i	−0.956879	−	0.290487i	$-0.906183\pi$
$479$	−152898.	+	152898.i	−0.666391	+	0.666391i	0.290487	+	0.956879i	$0.406183\pi$
$480$	6901.22	+	17352.7i	0.0299532	+	0.0753156i
$481$	−4257.95	+	114702.i	−0.0184039	+	0.495770i
$482$		−	48697.2i		−	0.209609i
$483$	11453.9	−	11453.9i	0.0490975	−	0.0490975i
$484$	414699.			1.77028
$485$	98953.5	−	39354.1i	0.420676	−	0.167304i
$486$	270695.	+	270695.i	1.14606	+	1.14606i
$487$	−251528.	+	251528.i	−1.06054	+	1.06054i	−0.0624963	+	0.998045i	$0.519906\pi$
$487$	−251528.	+	251528.i	−1.06054	+	1.06054i	−0.998045	+	0.0624963i	$0.980094\pi$
$488$	−80681.2	−	80681.2i	−0.338792	−	0.338792i
$489$	−35035.0	+	35035.0i	−0.146516	+	0.146516i
$490$	−143961.	−	361981.i	−0.599586	−	1.50762i
$491$		−	302653.i		−	1.25540i	−0.778455	−	0.627701i	$-0.783996\pi$
$491$		−	302653.i		−	1.25540i	0.778455	−	0.627701i	$-0.216004\pi$
$492$	−139414.	−	139414.i	−0.575937	−	0.575937i
$493$	−420214.			−1.72893
$494$	−359033.	−	386717.i	−1.47123	−	1.58467i
$495$	73077.3	−	29063.0i	0.298244	−	0.118612i
$496$	−147818.	−	147818.i	−0.600846	−	0.600846i
$497$		−	61185.0i		−	0.247703i
$498$	262825.			1.05976
$499$	−201469.	−	201469.i	−0.809110	−	0.809110i	0.175389	−	0.984499i	$-0.443882\pi$
$499$	−201469.	−	201469.i	−0.809110	−	0.809110i	−0.984499	+	0.175389i	$0.943882\pi$
$500$	−483610.	+	176627.i	−1.93444	+	0.706509i
$501$	−92175.2	+	92175.2i	−0.367231	+	0.367231i
$502$	−412729.	−	412729.i	−1.63779	−	1.63779i
$503$		−	27845.1i		−	0.110056i	−0.998485	−	0.0550278i	$-0.982475\pi$
$503$		−	27845.1i		−	0.110056i	0.998485	−	0.0550278i	$-0.0175248\pi$
$504$			108494.i			0.427113i
$505$	197022.	−	457212.i	0.772558	−	1.79281i
$506$		−	114346.i		−	0.446601i
$507$	97072.3	+	7216.97i	0.377641	+	0.0280762i
$508$		−	218397.i		−	0.846291i
$509$	231881.	+	231881.i	0.895012	+	0.895012i	0.994990	−	0.0999780i	$-0.0318772\pi$
$509$	231881.	+	231881.i	0.895012	+	0.895012i	−0.0999780	+	0.994990i	$0.531877\pi$
$510$	94934.8	+	238708.i	0.364994	+	0.917755i
$511$			9250.69i			0.0354268i
$512$	359044.	−	359044.i	1.36964	−	1.36964i
$513$	161740.	−	161740.i	0.614587	−	0.614587i
$514$	−451701.	+	451701.i	−1.70972	+	1.70972i
$515$	451733.	+	194661.i	1.70321	+	0.733946i
$516$	−43976.3			−0.165165
$517$	−112677.			−0.421555
$518$	−44301.8	−	44301.8i	−0.165106	−	0.165106i
$519$		−	132343.i		−	0.491322i
$520$	215225.	−	452487.i	0.795952	−	1.67340i
$521$	375447.			1.38316			0.691581	−	0.722299i	$-0.256915\pi$
$521$	375447.			1.38316			0.691581	+	0.722299i	$0.256915\pi$
$522$	−334721.	+	334721.i	−1.22841	+	1.22841i
$523$			252258.i			0.922236i	0.887339	+	0.461118i	$0.152551\pi$
$523$			252258.i			0.922236i	−0.887339	+	0.461118i	$0.847449\pi$
$524$		−	760758.i		−	2.77067i
$525$	28073.6	+	796.088i	0.101854	+	0.00288830i
$526$	559341.	+	559341.i	2.02165	+	2.02165i
$527$	−210553.	−	210553.i	−0.758123	−	0.758123i
$528$	−33055.9	−	33055.9i	−0.118572	−	0.118572i
$529$	−149899.			−0.535656
$530$	−96094.4	−	241624.i	−0.342095	−	0.860177i
$531$	−304261.	+	304261.i	−1.07909	+	1.07909i
$532$	193888.			0.685058
$533$	−11006.6	+	296500.i	−0.0387436	+	1.04369i
$534$	−56148.6			−0.196905
$535$	−62255.0	+	144470.i	−0.217504	+	0.504743i
$536$	181725.			0.632535
$537$	−160198.			−0.555532
$538$	551795.	−	551795.i	1.90640	−	1.90640i
$539$	71400.6	+	71400.6i	0.245768	+	0.245768i
$540$	387740.	+	167085.i	1.32970	+	0.572993i
$541$	257129.	−	257129.i	0.878530	−	0.878530i	−0.114852	−	0.993383i	$-0.536639\pi$
$541$	257129.	−	257129.i	0.878530	−	0.878530i	0.993383	+	0.114852i	$0.0366394\pi$
$542$			263876.i			0.898259i
$543$	109918.			0.372795
$544$	−66787.2	+	66787.2i	−0.225681	+	0.225681i
$545$	125184.	+	314767.i	0.421458	+	1.05973i
$546$	−38938.1	+	36150.7i	−0.130614	+	0.121264i
$547$			85940.9i			0.287227i	0.989634	+	0.143614i	$0.0458722\pi$
$547$			85940.9i			0.287227i	−0.989634	+	0.143614i	$0.954128\pi$
$548$	572390.	−	572390.i	1.90604	−	1.90604i
$549$	−66754.8			−0.221482
$550$	144105.	−	136158.i	0.476381	−	0.450108i
$551$	307718.	+	307718.i	1.01356	+	1.01356i
$552$	103026.	−	103026.i	0.338118	−	0.338118i
$553$	−2736.62	−	2736.62i	−0.00894878	−	0.00894878i
$554$	−317884.	+	317884.i	−1.03574	+	1.03574i
$555$	−53772.0	+	21385.3i	−0.174570	+	0.0694270i
$556$		−	1.19577e6i		−	3.86812i
$557$	−347608.	−	347608.i	−1.12042	−	1.12042i	−0.991679	−	0.128736i	$-0.958908\pi$
$557$	−347608.	−	347608.i	−1.12042	−	1.12042i	−0.128736	−	0.991679i	$-0.541092\pi$
$558$	−335431.			−1.07730
$559$	45027.6	+	48499.5i	0.144097	+	0.155208i
$560$	36852.5	+	92663.5i	0.117514	+	0.295483i
$561$	−47085.1	−	47085.1i	−0.149609	−	0.149609i
$562$		−	33268.9i		−	0.105333i
$563$	346068.			1.09180			0.545902	−	0.837849i	$-0.316187\pi$
$563$	346068.			1.09180			0.545902	+	0.837849i	$0.316187\pi$
$564$	−197351.	−	197351.i	−0.620412	−	0.620412i
$565$	162651.	−	377451.i	0.509518	−	1.18240i
$566$	131971.	−	131971.i	0.411951	−	0.411951i
$567$	36111.6	+	36111.6i	0.112326	+	0.112326i
$568$		−	550349.i		−	1.70585i
$569$			34415.5i			0.106299i	0.998587	+	0.0531496i	$0.0169260\pi$
$569$			34415.5i			0.106299i	−0.998587	+	0.0531496i	$0.983074\pi$
$570$	105283.	−	244323.i	0.324049	−	0.751994i
$571$			104755.i			0.321295i	0.987012	+	0.160648i	$0.0513583\pi$
$571$			104755.i			0.321295i	−0.987012	+	0.160648i	$0.948642\pi$
$572$	−9365.88	+	252300.i	−0.0286257	+	0.771127i
$573$			154245.i			0.469789i
$574$	−114518.	−	114518.i	−0.347577	−	0.347577i
$575$	154729.	+	163761.i	0.467990	+	0.495307i
$576$		−	229465.i		−	0.691625i
$577$	222398.	−	222398.i	0.668005	−	0.668005i	−0.289249	−	0.957254i	$-0.593406\pi$
$577$	222398.	−	222398.i	0.668005	−	0.668005i	0.957254	+	0.289249i	$0.0934057\pi$
$578$	−505541.	+	505541.i	−1.51322	+	1.51322i
$579$	−38623.7	+	38623.7i	−0.115212	+	0.115212i
$580$	−317886.	+	737692.i	−0.944964	+	2.19290i
$581$	145326.			0.430518
$582$	−101572.			−0.299867
$583$	47660.2	+	47660.2i	0.140223	+	0.140223i
$584$			83208.4i			0.243973i
$585$	−98153.8	−	276229.i	−0.286811	−	0.807156i
$586$	−692259.			−2.01592
$587$	−173731.	+	173731.i	−0.504198	+	0.504198i	−0.912740	−	0.408541i	$-0.866038\pi$
$587$	−173731.	+	173731.i	−0.504198	+	0.504198i	0.408541	+	0.912740i	$0.366038\pi$
$588$			250112.i			0.723404i
$589$			308371.i			0.888878i
$590$	−429268.	+	996166.i	−1.23317	+	2.86172i
$591$	129449.	+	129449.i	0.370616	+	0.370616i
$592$	−145294.	−	145294.i	−0.414576	−	0.414576i
$593$	3471.77	+	3471.77i	0.00987282	+	0.00987282i	0.712026	−	0.702153i	$-0.247778\pi$
$593$	3471.77	+	3471.77i	0.00987282	+	0.00987282i	−0.702153	+	0.712026i	$0.747778\pi$
$594$	−162580.			−0.460781
$595$	52493.0	+	131991.i	0.148275	+	0.372828i
$596$	−217114.	+	217114.i	−0.611218	+	0.611218i
$597$	−22017.0			−0.0617745
$598$	−425934.	−	15811.5i	−1.19108	−	0.0442151i
$599$	258039.			0.719169			0.359585	−	0.933112i	$-0.382918\pi$
$599$	258039.			0.719169			0.359585	+	0.933112i	$0.382918\pi$
$600$	252518.	+	7160.68i	0.701438	+	0.0198908i
$601$	110797.			0.306747			0.153373	−	0.988168i	$-0.450986\pi$
$601$	110797.			0.306747			0.153373	+	0.988168i	$0.450986\pi$
$602$	−36123.4			−0.0996771
$603$	75178.5	−	75178.5i	0.206757	−	0.206757i
$604$	299470.	+	299470.i	0.820879	+	0.820879i
$605$	124514.	−	288950.i	0.340179	−	0.789426i
$606$	−335774.	+	335774.i	−0.914327	+	0.914327i
$607$			392316.i			1.06478i	0.846500	+	0.532388i	$0.178705\pi$
$607$			392316.i			1.06478i	−0.846500	+	0.532388i	$0.821295\pi$
$608$	97815.0			0.264605
$609$	30983.8	−	30983.8i	0.0835410	−	0.0835410i
$610$	−156370.	+	62188.8i	−0.420237	+	0.167129i
$611$	−15580.7	+	419718.i	−0.0417355	+	1.12428i
$612$			985239.i			2.63050i
$613$	161072.	−	161072.i	0.428645	−	0.428645i	−0.459521	−	0.888167i	$-0.651979\pi$
$613$	161072.	−	161072.i	0.428645	−	0.428645i	0.888167	+	0.459521i	$0.151979\pi$
$614$	−252238.			−0.669072
$615$	−138998.	+	55280.0i	−0.367502	+	0.146156i
$616$	−50129.4	−	50129.4i	−0.132108	−	0.132108i
$617$	49793.8	−	49793.8i	0.130799	−	0.130799i	−0.638676	−	0.769476i	$-0.720518\pi$
$617$	49793.8	−	49793.8i	0.130799	−	0.130799i	0.769476	+	0.638676i	$0.220518\pi$
$618$	−331751.	−	331751.i	−0.868630	−	0.868630i
$619$	218128.	−	218128.i	0.569284	−	0.569284i	−0.362644	−	0.931928i	$-0.618126\pi$
$619$	218128.	−	218128.i	0.569284	−	0.569284i	0.931928	+	0.362644i	$0.118126\pi$
$620$	−528909.	+	210348.i	−1.37593	+	0.547212i
$621$		−	184756.i		−	0.479087i
$622$	553321.	+	553321.i	1.43020	+	1.43020i
$623$	−31046.6			−0.0799905
$624$	−127703.	+	118561.i	−0.327969	+	0.304491i
$625$	−22136.2	+	389997.i	−0.0566687	+	0.998393i
$626$	−670086.	−	670086.i	−1.70994	−	1.70994i
$627$			68959.8i			0.175413i
$628$	418818.			1.06195
$629$	−206958.	−	206958.i	−0.523095	−	0.523095i
$630$	146950.	+	63323.7i	0.370245	+	0.159546i
$631$	55187.0	−	55187.0i	0.138605	−	0.138605i	−0.634400	−	0.773005i	$-0.718753\pi$
$631$	55187.0	−	55187.0i	0.138605	−	0.138605i	0.773005	+	0.634400i	$0.218753\pi$
$632$	−24615.4	−	24615.4i	−0.0616273	−	0.0616273i
$633$		−	97824.0i		−	0.244140i
$634$			1.10136e6i			2.74001i
$635$	−152173.	−	65574.1i	−0.377389	−	0.162624i
$636$			166951.i			0.412739i
$637$	275838.	−	256092.i	0.679791	−	0.631127i
$638$		−	309315.i		−	0.759906i
$639$	−227676.	−	227676.i	−0.557592	−	0.557592i
$640$	−246168.	−	618975.i	−0.600996	−	1.51117i
$641$			709653.i			1.72715i	0.504220	+	0.863575i	$0.331780\pi$
$641$			709653.i			1.72715i	−0.504220	+	0.863575i	$0.668220\pi$
$642$	106098.	−	106098.i	0.257417	−	0.257417i
$643$	414102.	−	414102.i	1.00158	−	1.00158i	0.00158102	−	0.999999i	$-0.499497\pi$
$643$	414102.	−	414102.i	1.00158	−	1.00158i	0.999999	−	0.00158102i	$-0.000503255\pi$
$644$	110739.	−	110739.i	0.267010	−	0.267010i
$645$	−13204.0	+	30641.3i	−0.0317384	+	0.0736526i
$646$	1.34557e6			3.22433
$647$	397484.			0.949535			0.474768	−	0.880111i	$-0.342532\pi$
$647$	397484.			0.949535			0.474768	+	0.880111i	$0.342532\pi$
$648$	324818.	+	324818.i	0.773552	+	0.773552i
$649$		−	281167.i		−	0.667535i
$650$	−487256.	−	555614.i	−1.15327	−	1.31506i
$651$	31049.5			0.0732644
$652$	−338725.	+	338725.i	−0.796805	+	0.796805i
$653$		−	192589.i		−	0.451653i	−0.974168	−	0.225826i	$-0.927492\pi$
$653$		−	192589.i		−	0.451653i	0.974168	−	0.225826i	$-0.0725082\pi$
$654$		−	323097.i		−	0.755401i
$655$	−530073.	−	228419.i	−1.23553	−	0.532414i
$656$	−375579.	−	375579.i	−0.872758	−	0.872758i
$657$	34422.9	+	34422.9i	0.0797474	+	0.0797474i
$658$	−162109.	−	162109.i	−0.374418	−	0.374418i
$659$	−90823.9			−0.209136			−0.104568	−	0.994518i	$-0.533346\pi$
$659$	−90823.9			−0.209136			−0.104568	+	0.994518i	$0.533346\pi$
$660$	−118278.	+	47039.4i	−0.271529	+	0.107988i
$661$	−536007.	+	536007.i	−1.22678	+	1.22678i	−0.261608	+	0.965174i	$0.584253\pi$
$661$	−536007.	+	536007.i	−1.22678	+	1.22678i	−0.965174	+	0.261608i	$0.915747\pi$
$662$	1.01041e6			2.30560
$663$	−181901.	+	168880.i	−0.413817	+	0.384194i
$664$	1.30718e6			2.96483
$665$	58215.1	−	135095.i	0.131641	−	0.305490i
$666$	−329704.			−0.743321
$667$	351505.			0.790096
$668$	−891169.	+	891169.i	−1.99713	+	1.99713i
$669$	50132.9	+	50132.9i	0.112013	+	0.112013i
$670$	106066.	−	246139.i	0.236280	−	0.548315i
$671$	30844.0	−	30844.0i	0.0685055	−	0.0685055i
$672$		−	9848.89i		−	0.0218096i
$673$	−39935.3			−0.0881712			−0.0440856	−	0.999028i	$-0.514037\pi$
$673$	−39935.3			−0.0881712			−0.0440856	+	0.999028i	$0.514037\pi$
$674$	429488.	−	429488.i	0.945435	−	0.945435i
$675$	232839.	−	219998.i	0.511033	−	0.482849i
$676$	938515.	+	69775.1i	2.05375	+	0.152689i
$677$		−	158413.i		−	0.345631i	−0.984954	−	0.172815i	$-0.944714\pi$
$677$		−	158413.i		−	0.345631i	0.984954	−	0.172815i	$-0.0552864\pi$
$678$	−277198.	+	277198.i	−0.603019	+	0.603019i
$679$	−56163.1			−0.121818
$680$	472166.	+	1.18723e6i	1.02112	+	2.56755i
$681$	−198082.	−	198082.i	−0.427121	−	0.427121i
$682$	154986.	−	154986.i	0.333214	−	0.333214i
$683$	165607.	+	165607.i	0.355007	+	0.355007i	0.861969	−	0.506961i	$-0.169231\pi$
$683$	165607.	+	165607.i	0.355007	+	0.355007i	−0.506961	+	0.861969i	$0.669231\pi$
$684$	721479.	−	721479.i	1.54210	−	1.54210i
$685$	−226963.	−	570685.i	−0.483698	−	1.21623i
$686$			426935.i			0.907223i
$687$	−46534.6	−	46534.6i	−0.0985968	−	0.0985968i
$688$	−118472.			−0.250287
$689$	184123.	−	170942.i	0.387855	−	0.360090i
$690$	−79412.1	−	199677.i	−0.166797	−	0.419402i
$691$	−91451.0	−	91451.0i	−0.191528	−	0.191528i	0.604828	−	0.796356i	$-0.293242\pi$
$691$	−91451.0	−	91451.0i	−0.191528	−	0.191528i	−0.796356	+	0.604828i	$0.793242\pi$
$692$		−	1.27952e6i		−	2.67199i
$693$	−41476.5			−0.0863646
$694$	−655484.	−	655484.i	−1.36095	−	1.36095i
$695$	−833179.	−	359033.i	−1.72492	−	0.743301i
$696$	278694.	−	278694.i	0.575319	−	0.575319i
$697$	−534978.	−	534978.i	−1.10121	−	1.10121i
$698$			579646.i			1.18974i
$699$			30381.1i			0.0621797i
$700$	271422.	+	7696.74i	0.553922	+	0.0157076i
$701$			207821.i			0.422916i	0.977387	+	0.211458i	$0.0678212\pi$
$701$			207821.i			0.422916i	−0.977387	+	0.211458i	$0.932179\pi$
$702$	−22481.2	+	605605.i	−0.0456190	+	1.22890i
$703$			303106.i			0.613315i
$704$	106024.	+	106024.i	0.213924	+	0.213924i
$705$	−196763.	+	78253.1i	−0.395881	+	0.157443i
$706$		−	663446.i		−	1.33106i
$707$	−185662.	+	185662.i	−0.371436	+	0.371436i
$708$	492456.	−	492456.i	0.982428	−	0.982428i
$709$	455659.	−	455659.i	0.906457	−	0.906457i	−0.0895274	−	0.995984i	$-0.528536\pi$
$709$	455659.	−	455659.i	0.906457	−	0.906457i	0.995984	+	0.0895274i	$0.0285357\pi$
$710$	−745425.	−	321218.i	−1.47872	−	0.637211i
$711$	−20366.5			−0.0402882
$712$	−279259.			−0.550868
$713$	176125.	+	176125.i	0.346452	+	0.346452i
$714$		−	135484.i		−	0.265761i
$715$	172983.	+	82279.5i	0.338370	+	0.160946i
$716$	−1.54883e6			−3.02118
$717$	−19592.7	+	19592.7i	−0.0381116	+	0.0381116i
$718$		−	528142.i		−	1.02448i
$719$		−	6972.79i		−	0.0134880i	−0.999977	−	0.00674402i	$-0.997853\pi$
$719$		−	6972.79i		−	0.0134880i	0.999977	−	0.00674402i	$-0.00214670\pi$
$720$	481944.	+	207679.i	0.929676	+	0.400616i
$721$	−183437.	−	183437.i	−0.352872	−	0.352872i
$722$	−340611.	−	340611.i	−0.653408	−	0.653408i
$723$	16773.7	+	16773.7i	0.0320887	+	0.0320887i
$724$	1.06271e6			2.02739
$725$	418556.	+	442986.i	0.796301	+	0.842780i
$726$	−212203.	+	212203.i	−0.402604	+	0.402604i
$727$	−331312.			−0.626858			−0.313429	−	0.949612i	$-0.601478\pi$
$727$	−331312.			−0.626858			−0.313429	+	0.949612i	$0.601478\pi$
$728$	−193662.	+	179798.i	−0.365411	+	0.339252i
$729$	127261.			0.239463
$730$	112702.	+	48565.7i	0.211489	+	0.0911347i
$731$	−168752.			−0.315801
$732$	108045.			0.201642
$733$	−345436.	+	345436.i	−0.642925	+	0.642925i	−0.951273	−	0.308349i	$-0.900224\pi$
$733$	−345436.	+	345436.i	−0.642925	+	0.642925i	0.308349	+	0.951273i	$0.400224\pi$
$734$	805380.	+	805380.i	1.49489	+	1.49489i
$735$	174271.	+	75096.7i	0.322589	+	0.139010i
$736$	55866.9	−	55866.9i	0.103133	−	0.103133i
$737$			69472.3i			0.127902i
$738$	−852272.			−1.56482
$739$	−128169.	+	128169.i	−0.234689	+	0.234689i	−0.814647	−	0.579958i	$-0.803069\pi$
$739$	−128169.	+	128169.i	−0.234689	+	0.234689i	0.579958	+	0.814647i	$0.303069\pi$
$740$	−519879.	+	206757.i	−0.949377	+	0.377570i
$741$	256873.	+	9535.61i	0.467823	+	0.0173665i
$742$			137138.i			0.249087i
$743$	293951.	−	293951.i	0.532473	−	0.532473i	−0.388835	−	0.921308i	$-0.627122\pi$
$743$	293951.	−	293951.i	0.532473	−	0.532473i	0.921308	+	0.388835i	$0.127122\pi$
$744$	279285.			0.504548
$745$	86089.8	+	216468.i	0.155110	+	0.390014i
$746$	656104.	+	656104.i	1.17895	+	1.17895i
$747$	540775.	−	540775.i	0.969115	−	0.969115i
$748$	−455229.	−	455229.i	−0.813629	−	0.813629i
$749$	58665.6	−	58665.6i	0.104573	−	0.104573i
$750$	157084.	−	337846.i	0.279261	−	0.600615i
$751$			331790.i			0.588280i	0.955762	+	0.294140i	$0.0950331\pi$
$751$			331790.i			0.588280i	−0.955762	+	0.294140i	$0.904967\pi$
$752$	−531661.	−	531661.i	−0.940154	−	0.940154i
$753$	284328.			0.501452
$754$	−1.15219e6	−	42771.4i	−2.02666	−	0.0752335i
$755$	298578.	−	118745.i	0.523798	−	0.208316i
$756$	−157451.	−	157451.i	−0.275488	−	0.275488i
$757$		−	67675.9i		−	0.118098i	−0.998255	−	0.0590490i	$-0.981193\pi$
$757$		−	67675.9i		−	0.118098i	0.998255	−	0.0590490i	$-0.0188068\pi$
$758$	448753.			0.781031
$759$	39386.3	+	39386.3i	0.0683693	+	0.0683693i
$760$	523636.	−	1.21516e6i	0.906571	−	2.10381i
$761$	15879.2	−	15879.2i	0.0274195	−	0.0274195i	−0.693264	−	0.720684i	$-0.743828\pi$
$761$	15879.2	−	15879.2i	0.0274195	−	0.0274195i	0.720684	+	0.693264i	$0.243828\pi$
$762$	111755.	+	111755.i	0.192467	+	0.192467i
$763$		−	178652.i		−	0.306874i
$764$			1.49127e6i			2.55488i
$765$	686485.	+	295820.i	1.17303	+	0.505480i
$766$		−	1.05791e6i		−	1.80298i
$767$	−1.04734e6	−	38879.1i	−1.78031	−	0.0660885i
$768$			455016.i			0.771444i
$769$	−368759.	−	368759.i	−0.623577	−	0.623577i	0.322867	−	0.946444i	$-0.395353\pi$
$769$	−368759.	−	368759.i	−0.623577	−	0.623577i	−0.946444	+	0.322867i	$0.895353\pi$
$770$	−97156.9	+	38639.5i	−0.163867	+	0.0651704i
$771$		−	311175.i		−	0.523476i
$772$	−373421.	+	373421.i	−0.626563	+	0.626563i
$773$	−142556.	+	142556.i	−0.238576	+	0.238576i	−0.816260	−	0.577684i	$-0.803956\pi$
$773$	−142556.	+	142556.i	−0.238576	+	0.238576i	0.577684	+	0.816260i	$0.303956\pi$
$774$	−134419.	+	134419.i	−0.224378	+	0.224378i
$775$	−12241.4	+	431685.i	−0.0203810	+	0.718726i
$776$	−505178.			−0.838920
$777$	30519.4			0.0505515
$778$	302218.	+	302218.i	0.499299	+	0.499299i
$779$			783516.i			1.29114i
$780$	158865.	+	447086.i	0.261119	+	0.734855i
$781$	210395.			0.344932
$782$	768518.	−	768518.i	1.25673	−	1.25673i
$783$		−	499779.i		−	0.815182i
$784$			673801.i			1.09622i
$785$	125751.	−	291820.i	0.204066	−	0.473560i
$786$	389283.	+	389283.i	0.630116	+	0.630116i
$787$	−700110.	−	700110.i	−1.13036	−	1.13036i	−0.990117	−	0.140243i	$-0.955212\pi$
$787$	−700110.	−	700110.i	−1.13036	−	1.13036i	−0.140243	−	0.990117i	$-0.544788\pi$
$788$	1.25154e6	+	1.25154e6i	2.01555	+	2.01555i
$789$	−385328.			−0.618981
$790$	−47707.7	+	18973.5i	−0.0764425	+	0.0304014i
$791$	−153273.	+	153273.i	−0.244970	+	0.244970i
$792$	−373074.			−0.594765
$793$	−110628.	−	119158.i	−0.175921	−	0.189486i
$794$	−124225.			−0.197046
$795$	116327.	+	50127.4i	0.184054	+	0.0793123i
$796$	−212865.			−0.335952
$797$	−671817.			−1.05763			−0.528816	−	0.848737i	$-0.677364\pi$
$797$	−671817.			−1.05763			−0.528816	+	0.848737i	$0.677364\pi$
$798$	−99213.1	+	99213.1i	−0.155799	+	0.155799i
$799$	−757301.	−	757301.i	−1.18625	−	1.18625i
$800$	136930.	+	3882.95i	0.213954	+	0.00606711i
$801$	−115528.	+	115528.i	−0.180062	+	0.180062i
$802$			666665.i			1.03648i
$803$	−31810.1			−0.0493326
$804$	−121679.	+	121679.i	−0.188236	+	0.188236i
$805$	−43909.9	−	110409.i	−0.0677596	−	0.170378i
$806$	−555885.	−	598747.i	−0.855687	−	0.921666i
$807$			380130.i			0.583694i
$808$	−1.67000e6	+	1.67000e6i	−2.55796	+	2.55796i
$809$	649071.			0.991733			0.495867	−	0.868399i	$-0.334850\pi$
$809$	649071.			0.991733			0.495867	+	0.868399i	$0.334850\pi$
$810$	629537.	−	250368.i	0.959513	−	0.381601i
$811$	714587.	+	714587.i	1.08646	+	1.08646i	0.995890	+	0.0905687i	$0.0288685\pi$
$811$	714587.	+	714587.i	1.08646	+	1.08646i	0.0905687	+	0.995890i	$0.471132\pi$
$812$	299557.	−	299557.i	0.454326	−	0.454326i
$813$	−90891.8	−	90891.8i	−0.137513	−	0.137513i
$814$	152340.	−	152340.i	0.229913	−	0.229913i
$815$	134311.	+	337716.i	0.202207	+	0.508437i
$816$		−	444338.i		−	0.667318i
$817$	123575.	+	123575.i	0.185134	+	0.185134i
$818$	1.31515e6			1.96548
$819$	−5735.28	+	154499.i	−0.00855041	+	0.230333i
$820$	−1.34386e6	+	534458.i	−1.99861	+	0.794852i
$821$	646116.	+	646116.i	0.958571	+	0.958571i	0.999175	−	0.0406046i	$-0.0129284\pi$
$821$	646116.	+	646116.i	0.958571	+	0.958571i	−0.0406046	+	0.999175i	$0.512928\pi$
$822$			585788.i			0.866956i
$823$	−1.18625e6			−1.75137			−0.875683	−	0.482887i	$-0.839588\pi$
$823$	−1.18625e6			−1.75137			−0.875683	+	0.482887i	$0.839588\pi$
$824$	−1.64999e6	−	1.64999e6i	−2.43011	−	2.43011i
$825$	−2737.49	+	96536.1i	−0.00402202	+	0.141835i
$826$	404517.	−	404517.i	0.592894	−	0.592894i
$827$	555171.	+	555171.i	0.811737	+	0.811737i	0.984894	−	0.173157i	$-0.0553968\pi$
$827$	555171.	+	555171.i	0.811737	+	0.811737i	−0.173157	+	0.984894i	$0.555397\pi$
$828$		−	824143.i		−	1.20210i
$829$		−	520297.i		−	0.757081i	−0.925585	−	0.378540i	$-0.876426\pi$
$829$		−	520297.i		−	0.757081i	0.925585	−	0.378540i	$-0.123574\pi$
$830$	762955.	−	1.77053e6i	1.10750	−	2.57008i
$831$		−	218990.i		−	0.317119i
$832$	409596.	−	380275.i	0.591710	−	0.549352i
$833$			959767.i			1.38317i
$834$	611882.	+	611882.i	0.879702	+	0.879702i
$835$	353365.	+	888515.i	0.506816	+	1.27436i
$836$			666717.i			0.953958i
$837$	250420.	−	250420.i	0.357452	−	0.357452i
$838$	−681388.	+	681388.i	−0.970301	+	0.970301i
$839$	91437.7	−	91437.7i	0.129898	−	0.129898i	−0.639169	−	0.769066i	$-0.720721\pi$
$839$	91437.7	−	91437.7i	0.129898	−	0.129898i	0.769066	+	0.639169i	$0.220721\pi$
$840$	−122353.	−	52724.3i	−0.173403	−	0.0747227i
$841$	243569.			0.344374
$842$	731845.			1.03227
$843$	11459.4	+	11459.4i	0.0161253	+	0.0161253i
$844$		−	945783.i		−	1.32772i
$845$	330408.	−	632979.i	0.462740	−	0.886494i
$846$	−1.20646e6			−1.68566
$847$	−117335.	+	117335.i	−0.163554	+	0.163554i
$848$			449765.i			0.625452i
$849$			90914.5i			0.126130i
$850$	1.88365e6	+	53414.8i	2.60712	+	0.0739305i
$851$	173118.	+	173118.i	0.239047	+	0.239047i
$852$	368502.	+	368502.i	0.507645	+	0.507645i
$853$	−215261.	−	215261.i	−0.295847	−	0.295847i	0.543538	−	0.839385i	$-0.317084\pi$
$853$	−215261.	−	215261.i	−0.295847	−	0.295847i	−0.839385	+	0.543538i	$0.817084\pi$
$854$	88751.1			0.121691
$855$	−286079.	−	719330.i	−0.391340	−	0.984002i
$856$	527687.	−	527687.i	0.720160	−	0.720160i
$857$	−645011.			−0.878224			−0.439112	−	0.898432i	$-0.644707\pi$
$857$	−645011.			−0.878224			−0.439112	+	0.898432i	$0.644707\pi$
$858$	−124311.	−	133896.i	−0.168863	−	0.181883i
$859$	−600338.			−0.813598			−0.406799	−	0.913518i	$-0.633355\pi$
$859$	−600338.			−0.813598			−0.406799	+	0.913518i	$0.633355\pi$
$860$	−127658.	+	296247.i	−0.172605	+	0.400550i
$861$	78891.4			0.106420
$862$	1.90644e6			2.56572
$863$	280491.	−	280491.i	0.376614	−	0.376614i	−0.493265	−	0.869879i	$-0.664197\pi$
$863$	280491.	−	280491.i	0.376614	−	0.376614i	0.869879	+	0.493265i	$0.164197\pi$
$864$	−79433.0	−	79433.0i	−0.106408	−	0.106408i
$865$	−891530.	−	384178.i	−1.19153	−	0.513452i
$866$	631329.	−	631329.i	0.841821	−	0.841821i
$867$		−	348266.i		−	0.463311i
$868$	300193.			0.398438
$869$	9410.34	−	9410.34i	0.0124614	−	0.0124614i
$870$	−214816.	−	540143.i	−0.283811	−	0.713626i
$871$	258782.	+	9606.49i	0.341113	+	0.0126628i
$872$		−	1.60695e6i		−	2.11334i
$873$	−208989.	+	208989.i	−0.274218	+	0.274218i
$874$	−1.12555e6			−1.47348
$875$	86857.7	−	186807.i	0.113447	−	0.243993i
$876$	−55714.5	−	55714.5i	−0.0726040	−	0.0726040i
$877$	−639864.	+	639864.i	−0.831934	+	0.831934i	−0.987781	−	0.155848i	$-0.950189\pi$
$877$	−639864.	+	639864.i	−0.831934	+	0.831934i	0.155848	+	0.987781i	$0.450189\pi$
$878$	635852.	+	635852.i	0.824835	+	0.824835i
$879$	238448.	−	238448.i	0.308614	−	0.308614i
$880$	−318640.	+	126724.i	−0.411467	+	0.163641i
$881$		−	818092.i		−	1.05402i	−0.849858	−	0.527012i	$-0.823312\pi$
$881$		−	818092.i		−	1.05402i	0.849858	−	0.527012i	$-0.176688\pi$
$882$	764502.	+	764502.i	0.982746	+	0.982746i
$883$	1.32115e6			1.69446			0.847230	−	0.531226i	$-0.178268\pi$
$883$	1.32115e6			1.69446			0.847230	+	0.531226i	$0.178268\pi$
$884$	−1.75866e6	+	1.63276e6i	−2.25049	+	2.08939i
$885$	−195268.	−	490989.i	−0.249312	−	0.626881i
$886$	1.68518e6	+	1.68518e6i	2.14674	+	2.14674i
$887$			788792.i			1.00257i	0.865282	+	0.501286i	$0.167139\pi$
$887$			788792.i			1.00257i	−0.865282	+	0.501286i	$0.832861\pi$
$888$	274517.			0.348132
$889$	61793.3	+	61793.3i	0.0781876	+	0.0781876i
$890$	−162993.	+	378246.i	−0.205774	+	0.477522i
$891$	−124176.	+	124176.i	−0.156416	+	0.156416i
$892$	484695.	+	484695.i	0.609170	+	0.609170i
$893$			1.10913e6i			1.39084i
$894$		−	222196.i		−	0.278011i
$895$	−465038.	+	1.07918e6i	−0.580554	+	1.34724i
$896$			351312.i			0.437600i
$897$	152159.	−	141266.i	0.189109	−	0.175571i
$898$		−	358057.i		−	0.444017i
$899$	476434.	+	476434.i	0.589499	+	0.589499i
$900$	1.03863e6	−	981351.i	1.28226	−	1.21154i
$901$			640649.i			0.789170i
$902$	393792.	−	393792.i	0.484009	−	0.484009i
$903$	12442.6	−	12442.6i	0.0152594	−	0.0152594i
$904$	−1.37867e6	+	1.37867e6i	−1.68703	+	1.68703i
$905$	319081.	−	740465.i	0.389586	−	0.904081i
$906$	−306480.			−0.373375
$907$	238436.			0.289840			0.144920	−	0.989443i	$-0.453708\pi$
$907$	238436.			0.289840			0.144920	+	0.989443i	$0.453708\pi$
$908$	−1.91510e6	−	1.91510e6i	−2.32284	−	2.32284i
$909$			1.38174e6i			1.67224i
$910$	130496.	+	367249.i	0.157585	+	0.443484i
$911$	62882.9			0.0757697			0.0378849	−	0.999282i	$-0.487938\pi$
$911$	62882.9			0.0757697			0.0378849	+	0.999282i	$0.487938\pi$
$912$	−325383.	+	325383.i	−0.391206	+	0.391206i
$913$			499729.i			0.599505i
$914$		−	1.25764e6i		−	1.50545i
$915$	32440.6	−	75282.3i	0.0387478	−	0.0899189i
$916$	−449906.	−	449906.i	−0.536205	−	0.536205i
$917$	215249.	+	215249.i	0.255978	+	0.255978i
$918$	−1.09270e6	−	1.09270e6i	−1.29663	−	1.29663i
$919$	−133666.			−0.158266			−0.0791332	−	0.996864i	$-0.525215\pi$
$919$	−133666.			−0.158266			−0.0791332	+	0.996864i	$0.525215\pi$
$920$	−394962.	−	993110.i	−0.466638	−	1.17333i
$921$	86882.9	−	86882.9i	0.102427	−	0.102427i
$922$	255709.			0.300804
$923$	29093.0	−	783715.i	0.0341496	−	0.919930i
$924$	67131.1			0.0786284
$925$	−12032.4	+	424315.i	−0.0140627	+	0.495912i
$926$	271939.			0.317139
$927$	−1.36518e6			−1.58866
$928$	151125.	−	151125.i	0.175485	−	0.175485i
$929$	−210287.	−	210287.i	−0.243658	−	0.243658i	0.574703	−	0.818362i	$-0.305117\pi$
$929$	−210287.	−	210287.i	−0.243658	−	0.243658i	−0.818362	+	0.574703i	$0.805117\pi$
$930$	163009.	−	378281.i	0.188471	−	0.437369i
$931$	702826.	−	702826.i	0.810865	−	0.810865i
$932$			293730.i			0.338156i
$933$	−381181.			−0.437893
$934$	−1.43769e6	+	1.43769e6i	−1.64806	+	1.64806i
$935$	−453873.	+	180506.i	−0.519172	+	0.206476i
$936$	−51587.9	+	1.38969e6i	−0.0588839	+	1.58623i
$937$		−	751353.i		−	0.855786i	−0.903829	−	0.427893i	$-0.859256\pi$
$937$		−	751353.i		−	0.855786i	0.903829	−	0.427893i	$-0.140744\pi$
$938$	−99950.5	+	99950.5i	−0.113600	+	0.113600i
$939$	461620.			0.523545
$940$	−1.90234e6	+	756567.i	−2.15295	+	0.856232i
$941$	−1.00149e6	−	1.00149e6i	−1.13101	−	1.13101i	−0.990009	−	0.141005i	$-0.954966\pi$
$941$	−1.00149e6	−	1.00149e6i	−1.13101	−	1.13101i	−0.141005	−	0.990009i	$-0.545034\pi$
$942$	−214311.	+	214311.i	−0.241514	+	0.241514i
$943$	447504.	+	447504.i	0.503238	+	0.503238i
$944$	1.32667e6	−	1.32667e6i	1.48874	−	1.48874i
$945$	−156982.	+	62432.3i	−0.175787	+	0.0699110i
$946$		−	124217.i		−	0.138802i
$947$	−329421.	−	329421.i	−0.367325	−	0.367325i	0.499176	−	0.866501i	$-0.333636\pi$
$947$	−329421.	−	329421.i	−0.367325	−	0.367325i	−0.866501	+	0.499176i	$0.833636\pi$
$948$	32963.9			0.0366794
$949$	−4398.64	+	118492.i	−0.00488411	+	0.131569i
$950$	−1.34026e6	−	1.41849e6i	−1.48505	−	1.57173i
$951$	−379364.	−	379364.i	−0.419464	−	0.419464i
$952$		−	673839.i		−	0.743502i
$953$	−531140.			−0.584821			−0.292410	−	0.956293i	$-0.594457\pi$
$953$	−531140.			−0.584821			−0.292410	+	0.956293i	$0.594457\pi$
$954$	510308.	+	510308.i	0.560707	+	0.560707i
$955$	1.03907e6	+	447758.i	1.13931	+	0.490949i
$956$	−189427.	+	189427.i	−0.207265	+	0.207265i
$957$	106543.	+	106543.i	0.116333	+	0.116333i
$958$		−	1.51285e6i		−	1.64841i
$959$			323904.i			0.352192i
$960$	258777.	+	111512.i	0.280792	+	0.120999i
$961$		−	446076.i		−	0.483017i
$962$	−546394.	−	588525.i	−0.590413	−	0.635938i
$963$		−	436603.i		−	0.470797i
$964$	162171.	+	162171.i	0.174510	+	0.174510i
$965$	148068.	+	372309.i	0.159004	+	0.399806i
$966$			113331.i			0.121449i
$967$	−1.03459e6	+	1.03459e6i	−1.10640	+	1.10640i	−0.112785	+	0.993619i	$0.535977\pi$
$967$	−1.03459e6	+	1.03459e6i	−1.10640	+	1.10640i	−0.993619	+	0.112785i	$0.964023\pi$
$968$	−1.05541e6	+	1.05541e6i	−1.12634	+	1.12634i
$969$	−463479.	+	463479.i	−0.493608	+	0.493608i
$970$	−294854.	+	684243.i	−0.313374	+	0.727222i
$971$	−1.54819e6			−1.64205			−0.821024	−	0.570894i	$-0.806597\pi$
$971$	−1.54819e6			−1.64205			−0.821024	+	0.570894i	$0.806597\pi$
$972$	−1.80294e6			−1.90831
$973$	338332.	+	338332.i	0.357370	+	0.357370i
$974$		−	2.48874e6i		−	2.62339i
$975$	359215.	+	23545.9i	0.377873	+	0.0247688i
$976$	291072.			0.305563
$977$	1.18194e6	−	1.18194e6i	1.23824	−	1.23824i	0.277525	−	0.960718i	$-0.410486\pi$
$977$	1.18194e6	−	1.18194e6i	1.23824	−	1.23824i	0.960718	−	0.277525i	$-0.0895141\pi$
$978$		−	346654.i		−	0.362425i
$979$		−	106759.i		−	0.111388i
$980$	1.68489e6	+	726050.i	1.75436	+	0.755987i
$981$	−664786.	−	664786.i	−0.690786	−	0.690786i
$982$	1.49730e6	+	1.49730e6i	1.55270	+	1.55270i
$983$	−494564.	−	494564.i	−0.511818	−	0.511818i	0.403265	−	0.915083i	$-0.367875\pi$
$983$	−494564.	−	494564.i	−0.511818	−	0.511818i	−0.915083	+	0.403265i	$0.867875\pi$
$984$	709615.			0.732880
$985$	1.24781e6	−	496258.i	1.28611	−	0.511488i
$986$	2.07891e6	−	2.07891e6i	2.13836	−	2.13836i
$987$	111677.			0.114638
$988$	2.48350e6	+	92192.3i	2.54419	+	0.0944453i
$989$	141159.			0.144317
$990$	−217750.	+	505314.i	−0.222171	+	0.515574i
$991$	11676.7			0.0118898			0.00594490	−	0.999982i	$-0.498108\pi$
$991$	11676.7			0.0118898			0.00594490	+	0.999982i	$0.498108\pi$
$992$	151445.			0.153898
$993$	−348036.	+	348036.i	−0.352960	+	0.352960i
$994$	302698.	+	302698.i	0.306363	+	0.306363i
$995$	−63913.0	+	148318.i	−0.0645569	+	0.149812i
$996$	−875261.	+	875261.i	−0.882306	+	0.882306i
$997$		−	892062.i		−	0.897439i	−0.893673	−	0.448720i	$-0.851880\pi$
$997$		−	892062.i		−	0.897439i	0.893673	−	0.448720i	$-0.148120\pi$
$998$	1.99344e6			2.00144
$999$	246144.	−	246144.i	0.246637	−	0.246637i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.5.g.a.34.3	✓	52
5.4	even	2	inner	65.5.g.a.34.24	yes	52
13.5	odd	4	inner	65.5.g.a.44.24	yes	52
65.44	odd	4	inner	65.5.g.a.44.3	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.5.g.a.34.3	✓	52	1.1	even	1	trivial
65.5.g.a.34.24	yes	52	5.4	even	2	inner
65.5.g.a.44.3	yes	52	65.44	odd	4	inner
65.5.g.a.44.24	yes	52	13.5	odd	4	inner

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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	65.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.94726 + 4.94726i) q^{2} -3.40815i q^{3} -32.9507i q^{4} +(-22.9591 - 9.89351i) q^{5} +(16.8610 + 16.8610i) q^{6} +(9.32308 + 9.32308i) q^{7} +(83.8595 + 83.8595i) q^{8} +69.3845 q^{9} +O(q^{10})\)	\(q+(-4.94726 + 4.94726i) q^{2} -3.40815i q^{3} -32.9507i q^{4} +(-22.9591 - 9.89351i) q^{5} +(16.8610 + 16.8610i) q^{6} +(9.32308 + 9.32308i) q^{7} +(83.8595 + 83.8595i) q^{8} +69.3845 q^{9} +(162.530 - 64.6387i) q^{10} +(-32.0590 + 32.0590i) q^{11} -112.301 q^{12} +(114.986 + 123.852i) q^{13} -92.2473 q^{14} +(-33.7186 + 78.2480i) q^{15} -302.538 q^{16} -430.937 q^{17} +(-343.263 + 343.263i) q^{18} +(315.570 + 315.570i) q^{19} +(-325.998 + 756.517i) q^{20} +(31.7745 - 31.7745i) q^{21} -317.209i q^{22} +360.475 q^{23} +(285.806 - 285.806i) q^{24} +(429.237 + 454.291i) q^{25} +(-1181.59 - 43.8629i) q^{26} -512.533i q^{27} +(307.202 - 307.202i) q^{28} +975.115 q^{29} +(-220.298 - 553.927i) q^{30} +(488.592 + 488.592i) q^{31} +(154.981 - 154.981i) q^{32} +(109.262 + 109.262i) q^{33} +(2131.96 - 2131.96i) q^{34} +(-121.811 - 306.287i) q^{35} -2286.27i q^{36} +(480.250 + 480.250i) q^{37} -3122.42 q^{38} +(422.106 - 391.889i) q^{39} +(-1095.67 - 2755.00i) q^{40} +(1241.43 + 1241.43i) q^{41} +314.393i q^{42} +391.593 q^{43} +(1056.37 + 1056.37i) q^{44} +(-1593.00 - 686.456i) q^{45} +(-1783.36 + 1783.36i) q^{46} +(1757.33 + 1757.33i) q^{47} +1031.10i q^{48} -2227.16i q^{49} +(-4371.04 - 123.950i) q^{50} +1468.70i q^{51} +(4081.01 - 3788.86i) q^{52} -1486.64i q^{53} +(2535.63 + 2535.63i) q^{54} +(1053.22 - 418.869i) q^{55} +1563.66i q^{56} +(1075.51 - 1075.51i) q^{57} +(-4824.15 + 4824.15i) q^{58} +(-4385.14 + 4385.14i) q^{59} +(2578.33 + 1111.05i) q^{60} -962.100 q^{61} -4834.38 q^{62} +(646.877 + 646.877i) q^{63} -3307.15i q^{64} +(-1414.64 - 3981.13i) q^{65} -1081.10 q^{66} +(1083.51 - 1083.51i) q^{67} +14199.7i q^{68} -1228.55i q^{69} +(2117.91 + 912.650i) q^{70} +(-3281.37 - 3281.37i) q^{71} +(5818.55 + 5818.55i) q^{72} +(496.118 + 496.118i) q^{73} -4751.85 q^{74} +(1548.29 - 1462.91i) q^{75} +(10398.3 - 10398.3i) q^{76} -597.778 q^{77} +(-149.492 + 4027.04i) q^{78} -293.532 q^{79} +(6945.99 + 2993.16i) q^{80} +3873.35 q^{81} -12283.3 q^{82} +(7793.88 - 7793.88i) q^{83} +(-1046.99 - 1046.99i) q^{84} +(9893.92 + 4263.48i) q^{85} +(-1937.31 + 1937.31i) q^{86} -3323.34i q^{87} -5376.91 q^{88} +(-1665.04 + 1665.04i) q^{89} +(11277.1 - 4484.92i) q^{90} +(-82.6594 + 2226.70i) q^{91} -11877.9i q^{92} +(1665.20 - 1665.20i) q^{93} -17388.0 q^{94} +(-4123.10 - 10367.3i) q^{95} +(-528.199 - 528.199i) q^{96} +(-3012.05 + 3012.05i) q^{97} +(11018.3 + 11018.3i) q^{98} +(-2224.40 + 2224.40i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 58 q^{5} + 60 q^{6} - 1196 q^{9}+O(q^{10}) \) 52 * q + 58 * q^5 + 60 * q^6 - 1196 * q^9	\( 52 q + 58 q^{5} + 60 q^{6} - 1196 q^{9} + 8 q^{11} + 424 q^{14} - 508 q^{15} - 3128 q^{16} + 268 q^{19} + 2116 q^{20} - 668 q^{21} + 2032 q^{24} + 1100 q^{26} - 3704 q^{29} - 1660 q^{31} + 1252 q^{34} + 6692 q^{35} + 7408 q^{39} + 3644 q^{40} + 5960 q^{41} + 1444 q^{44} - 8674 q^{45} + 17620 q^{46} - 3928 q^{50} - 30588 q^{54} + 14784 q^{55} - 5548 q^{59} - 13976 q^{60} - 20008 q^{61} - 15614 q^{65} + 24752 q^{66} + 26908 q^{70} - 16360 q^{71} - 7304 q^{74} - 5760 q^{76} - 9536 q^{79} - 62348 q^{80} - 36516 q^{81} + 66564 q^{84} - 11604 q^{85} - 5264 q^{86} - 940 q^{89} + 37644 q^{91} + 55448 q^{94} - 61644 q^{96} + 16140 q^{99}+O(q^{100}) \) 52 * q + 58 * q^5 + 60 * q^6 - 1196 * q^9 + 8 * q^11 + 424 * q^14 - 508 * q^15 - 3128 * q^16 + 268 * q^19 + 2116 * q^20 - 668 * q^21 + 2032 * q^24 + 1100 * q^26 - 3704 * q^29 - 1660 * q^31 + 1252 * q^34 + 6692 * q^35 + 7408 * q^39 + 3644 * q^40 + 5960 * q^41 + 1444 * q^44 - 8674 * q^45 + 17620 * q^46 - 3928 * q^50 - 30588 * q^54 + 14784 * q^55 - 5548 * q^59 - 13976 * q^60 - 20008 * q^61 - 15614 * q^65 + 24752 * q^66 + 26908 * q^70 - 16360 * q^71 - 7304 * q^74 - 5760 * q^76 - 9536 * q^79 - 62348 * q^80 - 36516 * q^81 + 66564 * q^84 - 11604 * q^85 - 5264 * q^86 - 940 * q^89 + 37644 * q^91 + 55448 * q^94 - 61644 * q^96 + 16140 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more