LMFDB - Embedded newform 65.5.g.a.44.3

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			44.3
Character	$\chi$	$=$	65.44
Dual form			65.5.g.a.34.3

$q$-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 $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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	−0.961296	−	0.275519i	$-0.911150\pi$
$2$	−4.94726	−	4.94726i	−1.23681	−	1.23681i	−0.275519	−	0.961296i	$-0.588850\pi$
$3$			3.40815i			0.378684i	0.981911	+	0.189342i	$0.0606354\pi$
$3$			3.40815i			0.378684i	−0.981911	+	0.189342i	$0.939365\pi$
$4$			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	−0.605545	−	0.795811i	$-0.707045\pi$
$7$	9.32308	−	9.32308i	0.190267	−	0.190267i	0.795811	+	0.605545i	$0.207045\pi$
$8$	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	0.562111	−	0.827062i	$-0.309989\pi$
$11$	−32.0590	−	32.0590i	−0.264951	−	0.264951i	−0.827062	+	0.562111i	$0.809989\pi$
$12$	−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	−0.118766	−	0.992922i	$-0.537894\pi$
$19$	315.570	−	315.570i	0.874156	−	0.874156i	0.992922	+	0.118766i	$0.0378938\pi$
$20$	−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	−0.405621	−	0.914041i	$-0.632945\pi$
$31$	488.592	−	488.592i	0.508421	−	0.508421i	0.914041	+	0.405621i	$0.132945\pi$
$32$	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	−0.509605	−	0.860409i	$-0.670208\pi$
$37$	480.250	−	480.250i	0.350804	−	0.350804i	0.860409	+	0.509605i	$0.170208\pi$
$38$	−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	−0.233783	−	0.972289i	$-0.575111\pi$
$41$	1241.43	−	1241.43i	0.738505	−	0.738505i	0.972289	+	0.233783i	$0.0751106\pi$
$42$		−	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	−0.186854	−	0.982388i	$-0.559829\pi$
$47$	1757.33	−	1757.33i	0.795534	−	0.795534i	0.982388	+	0.186854i	$0.0598290\pi$
$48$		−	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	$0.0852468\pi$
$53$			1486.64i			0.529241i	−0.964353	+	0.264621i	$0.914753\pi$
$54$	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	−0.951219	−	0.308516i	$-0.900168\pi$
$59$	−4385.14	−	4385.14i	−1.25974	−	1.25974i	−0.308516	−	0.951219i	$-0.599832\pi$
$60$	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	0.817416	−	0.576047i	$-0.195406\pi$
$67$	1083.51	+	1083.51i	0.241369	+	0.241369i	−0.576047	+	0.817416i	$0.695406\pi$
$68$		−	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	−0.953219	−	0.302282i	$-0.902252\pi$
$71$	−3281.37	+	3281.37i	−0.650937	+	0.650937i	0.302282	+	0.953219i	$0.402252\pi$
$72$	5818.55	−	5818.55i	1.12241	−	1.12241i
$73$	496.118	−	496.118i	0.0930977	−	0.0930977i	−0.659024	−	0.752122i	$-0.729030\pi$
$73$	496.118	−	496.118i	0.0930977	−	0.0930977i	0.752122	+	0.659024i	$0.229030\pi$
$74$	−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	0.989953	+	0.141399i	$0.0451601\pi$
$83$	7793.88	+	7793.88i	1.13135	+	1.13135i	0.141399	+	0.989953i	$0.454840\pi$
$84$	−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	0.594149	−	0.804355i	$-0.297489\pi$
$89$	−1665.04	−	1665.04i	−0.210206	−	0.210206i	−0.804355	+	0.594149i	$0.797489\pi$
$90$	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	0.528691	−	0.848815i	$-0.322683\pi$
$97$	−3012.05	−	3012.05i	−0.320124	−	0.320124i	−0.848815	+	0.528691i	$0.822683\pi$
$98$	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	$-0.569744\pi$
$101$		−	19914.2i		−	1.95218i	0.217358	−	0.976092i	$-0.430256\pi$
$102$	−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	$0.0886137\pi$
$107$			6292.51i			0.549612i	−0.961500	+	0.274806i	$0.911386\pi$
$108$	−16888.3			−1.44790
$109$	−9581.19	+	9581.19i	−0.806429	+	0.806429i	−0.984092	−	0.177662i	$-0.943147\pi$
$109$	−9581.19	+	9581.19i	−0.806429	+	0.806429i	0.177662	+	0.984092i	$0.443147\pi$
$110$	−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	$-0.777376\pi$
$113$		−	16440.2i		−	1.28751i	0.765233	−	0.643754i	$-0.222624\pi$
$114$		−	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	−0.0718917	−	0.997412i	$-0.522904\pi$
$137$	17371.1	−	17371.1i	0.925521	−	0.925521i	0.997412	+	0.0718917i	$0.0229036\pi$
$138$	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	−0.839756	−	0.542964i	$-0.817302\pi$
$149$	−6589.06	+	6589.06i	−0.296791	+	0.296791i	0.542964	+	0.839756i	$0.317302\pi$
$150$	−422.441	−	14897.2i	−0.0187752	−	0.662097i
$151$	−9088.42	−	9088.42i	−0.398597	−	0.398597i	0.479141	−	0.877738i	$-0.340948\pi$
$151$	−9088.42	−	9088.42i	−0.398597	−	0.398597i	−0.877738	+	0.479141i	$0.840948\pi$
$152$		−	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	$-0.916993\pi$
$157$		−	12710.4i		−	0.515657i	0.966191	−	0.257829i	$-0.0830070\pi$
$158$	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	−0.873583	−	0.486675i	$-0.838210\pi$
$163$	−10279.8	+	10279.8i	−0.386908	+	0.386908i	0.486675	+	0.873583i	$0.338210\pi$
$164$	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	−0.999556	−	0.0298002i	$-0.990513\pi$
$167$	−27045.5	+	27045.5i	−0.969756	+	0.969756i	0.0298002	+	0.999556i	$0.490513\pi$
$168$	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	$0.262116\pi$
$179$			47004.4i			1.46701i	−0.679685	+	0.733504i	$0.737884\pi$
$180$	−22619.2	−	52490.6i	−0.698124	−	1.62008i
$181$		−	32251.5i		−	0.984449i	−0.870468	−	0.492224i	$-0.836184\pi$
$181$		−	32251.5i		−	0.984449i	0.870468	−	0.492224i	$-0.163816\pi$
$182$	−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	−0.842671	−	0.538429i	$-0.819018\pi$
$193$	−11332.7	+	11332.7i	−0.304242	+	0.304242i	0.538429	+	0.842671i	$0.319018\pi$
$194$			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	0.0210821	−	0.999778i	$-0.493289\pi$
$197$	−37982.2	−	37982.2i	−0.978696	−	0.978696i	−0.999778	+	0.0210821i	$0.993289\pi$
$198$			22009.4i			0.561406i
$199$			6460.09i			0.163130i	0.996668	+	0.0815648i	$0.0259917\pi$
$199$			6460.09i			0.163130i	−0.996668	+	0.0815648i	$0.974008\pi$
$200$	−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	0.543568	−	0.839365i	$-0.317073\pi$
$223$	−14709.7	−	14709.7i	−0.295797	−	0.295797i	−0.839365	+	0.543568i	$0.817073\pi$
$224$	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	0.990516	+	0.137395i	$0.0438729\pi$
$227$	58120.1	+	58120.1i	1.12791	+	1.12791i	0.137395	+	0.990516i	$0.456127\pi$
$228$	−35438.9	+	35438.9i	−0.681727	+	0.681727i
$229$	13653.9	+	13653.9i	0.260367	+	0.260367i	0.825203	−	0.564836i	$-0.191061\pi$
$229$	13653.9	+	13653.9i	0.260367	+	0.260367i	−0.564836	+	0.825203i	$0.691061\pi$
$230$	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	−0.755635	−	0.654993i	$-0.772672\pi$
$239$	−5748.78	+	5748.78i	−0.100642	+	0.100642i	0.654993	+	0.755635i	$0.272672\pi$
$240$	10201.2	+	23673.0i	0.177103	+	0.410989i
$241$	−4921.64	−	4921.64i	−0.0847375	−	0.0847375i	0.663468	−	0.748205i	$-0.269084\pi$
$241$	−4921.64	−	4921.64i	−0.0847375	−	0.0847375i	−0.748205	+	0.663468i	$0.769084\pi$
$242$	−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	$-0.769666\pi$
$251$		−	83425.9i		−	1.32420i	0.749416	−	0.662100i	$-0.230334\pi$
$252$	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	$0.304519\pi$
$263$			113061.i			1.63456i	−0.576242	+	0.817279i	$0.695481\pi$
$264$		−	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	0.864965	−	0.501831i	$-0.167340\pi$
$271$	26668.9	+	26668.9i	0.363134	+	0.363134i	−0.501831	+	0.864965i	$0.667340\pi$
$272$	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	0.685495	−	0.728077i	$-0.259586\pi$
$281$	−3362.36	−	3362.36i	−0.0425825	−	0.0425825i	−0.728077	+	0.685495i	$0.759586\pi$
$282$		−	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	−0.170408	−	0.985374i	$-0.554509\pi$
$293$	69964.0	−	69964.0i	0.814965	−	0.814965i	0.985374	+	0.170408i	$0.0545086\pi$
$294$	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	−0.558812	−	0.829294i	$-0.688743\pi$
$307$	25492.7	−	25492.7i	0.270482	−	0.270482i	0.829294	+	0.558812i	$0.188743\pi$
$308$		−	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	$0.196236\pi$
$311$			111844.i			1.15636i	−0.815911	+	0.578178i	$0.803764\pi$
$312$	68261.2	−	2533.99i	0.701237	−	0.0260313i
$313$		−	135446.i		−	1.38254i	−0.722597	−	0.691270i	$-0.757052\pi$
$313$		−	135446.i		−	1.38254i	0.722597	−	0.691270i	$-0.242948\pi$
$314$	−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	0.993454	+	0.114236i	$0.0364421\pi$
$317$	111311.	+	111311.i	1.10769	+	1.10769i	0.114236	+	0.993454i	$0.463558\pi$
$318$	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	−0.997835	−	0.0657637i	$-0.979052\pi$
$331$	−102119.	+	102119.i	−0.932072	+	0.932072i	0.0657637	+	0.997835i	$0.479052\pi$
$332$	−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	$-0.814557\pi$
$347$		−	132494.i		−	1.10037i	0.835043	−	0.550185i	$-0.185443\pi$
$348$	−109506.			−0.904235
$349$	58582.6	+	58582.6i	0.480970	+	0.480970i	0.905441	−	0.424472i	$-0.139540\pi$
$349$	58582.6	+	58582.6i	0.480970	+	0.480970i	−0.424472	+	0.905441i	$0.639540\pi$
$350$	−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	0.384872	−	0.922970i	$-0.374246\pi$
$353$	−67051.9	−	67051.9i	−0.538099	−	0.538099i	−0.922970	+	0.384872i	$0.874246\pi$
$354$	−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	0.469025	−	0.883185i	$-0.344605\pi$
$359$	−53377.3	−	53377.3i	−0.414159	−	0.414159i	−0.883185	+	0.469025i	$0.844605\pi$
$360$	−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	$0.206559\pi$
$367$			162793.i			1.20866i	−0.796734	+	0.604330i	$0.793441\pi$
$368$	−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	$0.158134\pi$
$373$			132620.i			0.953215i	−0.879116	+	0.476607i	$0.841866\pi$
$374$		−	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	−0.847130	−	0.531386i	$-0.821671\pi$
$379$	−45353.7	+	45353.7i	−0.315743	+	0.315743i	0.531386	+	0.847130i	$0.321671\pi$
$380$	−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	0.241517	−	0.970397i	$-0.422355\pi$
$383$	−106919.	−	106919.i	−0.728880	−	0.728880i	−0.970397	+	0.241517i	$0.922355\pi$
$384$	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	$0.0646949\pi$
$389$			61087.9i			0.403697i	−0.979417	+	0.201849i	$0.935305\pi$
$390$	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	−0.666155	−	0.745813i	$-0.732061\pi$
$397$	12554.9	−	12554.9i	0.0796586	−	0.0796586i	0.745813	+	0.666155i	$0.232061\pi$
$398$	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	0.884863	−	0.465852i	$-0.154252\pi$
$401$	67377.3	+	67377.3i	0.419010	+	0.419010i	−0.465852	+	0.884863i	$0.654252\pi$
$402$	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	−0.982234	−	0.187659i	$-0.939910\pi$
$409$	−132917.	+	132917.i	−0.794575	+	0.794575i	0.187659	+	0.982234i	$0.439910\pi$
$410$	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	−0.884276	−	0.466964i	$-0.845348\pi$
$421$	−73964.7	+	73964.7i	−0.417312	+	0.417312i	0.466964	+	0.884276i	$0.345348\pi$
$422$	−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	−0.0379481	+	0.999280i	$0.512082\pi$
$431$	−192676.	+	192676.i	−1.03723	+	1.03723i	−0.999280	+	0.0379481i	$0.987918\pi$
$432$		−	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	$0.108213\pi$
$439$			128526.i			0.666903i	−0.942767	+	0.333452i	$0.891787\pi$
$440$	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	$0.334498\pi$
$443$			340629.i			1.73570i	−0.496827	+	0.867850i	$0.665502\pi$
$444$	−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	0.611638	−	0.791138i	$-0.290511\pi$
$449$	−36187.4	−	36187.4i	−0.179500	−	0.179500i	−0.791138	+	0.611638i	$0.790511\pi$
$450$	−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	0.333981	−	0.942580i	$-0.391608\pi$
$457$	−127105.	−	127105.i	−0.608598	−	0.608598i	−0.942580	+	0.333981i	$0.891608\pi$
$458$		−	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	−0.765290	−	0.643686i	$-0.777404\pi$
$461$	−25843.5	+	25843.5i	−0.121604	+	0.121604i	0.643686	+	0.765290i	$0.277404\pi$
$462$	−10079.1	+	10079.1i	−0.0472214	+	0.0472214i
$463$	−27483.8	+	27483.8i	−0.128208	+	0.128208i	−0.768299	−	0.640091i	$-0.778897\pi$
$463$	−27483.8	+	27483.8i	−0.128208	+	0.128208i	0.640091	+	0.768299i	$0.278897\pi$
$464$	−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	0.290487	−	0.956879i	$-0.406183\pi$
$479$	−152898.	−	152898.i	−0.666391	−	0.666391i	−0.956879	+	0.290487i	$0.906183\pi$
$480$	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	−0.998045	−	0.0624963i	$-0.980094\pi$
$487$	−251528.	−	251528.i	−1.06054	−	1.06054i	−0.0624963	−	0.998045i	$-0.519906\pi$
$488$	−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	$0.216004\pi$
$491$			302653.i			1.25540i	−0.778455	+	0.627701i	$0.783996\pi$
$492$	−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	−0.984499	−	0.175389i	$-0.943882\pi$
$499$	−201469.	+	201469.i	−0.809110	+	0.809110i	0.175389	+	0.984499i	$0.443882\pi$
$500$	−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	$0.0175248\pi$
$503$			27845.1i			0.110056i	−0.998485	+	0.0550278i	$0.982475\pi$
$504$		−	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	−0.0999780	−	0.994990i	$-0.531877\pi$
$509$	231881.	−	231881.i	0.895012	−	0.895012i	0.994990	+	0.0999780i	$0.0318772\pi$
$510$	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	$-0.847449\pi$
$523$		−	252258.i		−	0.922236i	0.887339	−	0.461118i	$-0.152551\pi$
$524$			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	0.993383	−	0.114852i	$-0.0366394\pi$
$541$	257129.	+	257129.i	0.878530	+	0.878530i	−0.114852	+	0.993383i	$0.536639\pi$
$542$		−	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	$-0.954128\pi$
$547$		−	85940.9i		−	0.287227i	0.989634	−	0.143614i	$-0.0458722\pi$
$548$	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	−0.128736	+	0.991679i	$0.541092\pi$
$557$	−347608.	+	347608.i	−1.12042	+	1.12042i	−0.991679	+	0.128736i	$0.958908\pi$
$558$	−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	$-0.983074\pi$
$569$		−	34415.5i		−	0.106299i	0.998587	−	0.0531496i	$-0.0169260\pi$
$570$	105283.	+	244323.i	0.324049	+	0.751994i
$571$		−	104755.i		−	0.321295i	−0.987012	−	0.160648i	$-0.948642\pi$
$571$		−	104755.i		−	0.321295i	0.987012	−	0.160648i	$-0.0513583\pi$
$572$	−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	0.957254	−	0.289249i	$-0.0934057\pi$
$577$	222398.	+	222398.i	0.668005	+	0.668005i	−0.289249	+	0.957254i	$0.593406\pi$
$578$	−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	0.408541	−	0.912740i	$-0.366038\pi$
$587$	−173731.	−	173731.i	−0.504198	−	0.504198i	−0.912740	+	0.408541i	$0.866038\pi$
$588$		−	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	−0.702153	−	0.712026i	$-0.747778\pi$
$593$	3471.77	−	3471.77i	0.00987282	−	0.00987282i	0.712026	+	0.702153i	$0.247778\pi$
$594$	−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	$-0.821295\pi$
$607$		−	392316.i		−	1.06478i	0.846500	−	0.532388i	$-0.178705\pi$
$608$	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	0.888167	−	0.459521i	$-0.151979\pi$
$613$	161072.	+	161072.i	0.428645	+	0.428645i	−0.459521	+	0.888167i	$0.651979\pi$
$614$	−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	0.769476	−	0.638676i	$-0.220518\pi$
$617$	49793.8	+	49793.8i	0.130799	+	0.130799i	−0.638676	+	0.769476i	$0.720518\pi$
$618$	−331751.	+	331751.i	−0.868630	+	0.868630i
$619$	218128.	+	218128.i	0.569284	+	0.569284i	0.931928	−	0.362644i	$-0.118126\pi$
$619$	218128.	+	218128.i	0.569284	+	0.569284i	−0.362644	+	0.931928i	$0.618126\pi$
$620$	−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	0.773005	−	0.634400i	$-0.218753\pi$
$631$	55187.0	+	55187.0i	0.138605	+	0.138605i	−0.634400	+	0.773005i	$0.718753\pi$
$632$	−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	$-0.668220\pi$
$641$		−	709653.i		−	1.72715i	0.504220	−	0.863575i	$-0.331780\pi$
$642$	106098.	+	106098.i	0.257417	+	0.257417i
$643$	414102.	+	414102.i	1.00158	+	1.00158i	0.999999	+	0.00158102i	$0.000503255\pi$
$643$	414102.	+	414102.i	1.00158	+	1.00158i	0.00158102	+	0.999999i	$0.499497\pi$
$644$	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	$0.0725082\pi$
$653$			192589.i			0.451653i	−0.974168	+	0.225826i	$0.927492\pi$
$654$			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	−0.965174	−	0.261608i	$-0.915747\pi$
$661$	−536007.	−	536007.i	−1.22678	−	1.22678i	−0.261608	−	0.965174i	$-0.584253\pi$
$662$	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	$0.0552864\pi$
$677$			158413.i			0.345631i	−0.984954	+	0.172815i	$0.944714\pi$
$678$	−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	−0.506961	−	0.861969i	$-0.669231\pi$
$683$	165607.	−	165607.i	0.355007	−	0.355007i	0.861969	+	0.506961i	$0.169231\pi$
$684$	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	−0.796356	−	0.604828i	$-0.793242\pi$
$691$	−91451.0	+	91451.0i	−0.191528	+	0.191528i	0.604828	+	0.796356i	$0.293242\pi$
$692$			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	$-0.932179\pi$
$701$		−	207821.i		−	0.422916i	0.977387	−	0.211458i	$-0.0678212\pi$
$702$	−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	0.995984	−	0.0895274i	$-0.0285357\pi$
$709$	455659.	+	455659.i	0.906457	+	0.906457i	−0.0895274	+	0.995984i	$0.528536\pi$
$710$	−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	$0.00214670\pi$
$719$			6972.79i			0.0134880i	−0.999977	+	0.00674402i	$0.997853\pi$
$720$	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	0.308349	−	0.951273i	$-0.400224\pi$
$733$	−345436.	−	345436.i	−0.642925	−	0.642925i	−0.951273	+	0.308349i	$0.900224\pi$
$734$	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	0.579958	−	0.814647i	$-0.303069\pi$
$739$	−128169.	−	128169.i	−0.234689	−	0.234689i	−0.814647	+	0.579958i	$0.803069\pi$
$740$	−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	0.921308	−	0.388835i	$-0.127122\pi$
$743$	293951.	+	293951.i	0.532473	+	0.532473i	−0.388835	+	0.921308i	$0.627122\pi$
$744$	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	$-0.904967\pi$
$751$		−	331790.i		−	0.588280i	0.955762	−	0.294140i	$-0.0950331\pi$
$752$	−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	$0.0188068\pi$
$757$			67675.9i			0.118098i	−0.998255	+	0.0590490i	$0.981193\pi$
$758$	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	0.720684	−	0.693264i	$-0.243828\pi$
$761$	15879.2	+	15879.2i	0.0274195	+	0.0274195i	−0.693264	+	0.720684i	$0.743828\pi$
$762$	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	−0.946444	−	0.322867i	$-0.895353\pi$
$769$	−368759.	+	368759.i	−0.623577	+	0.623577i	0.322867	+	0.946444i	$0.395353\pi$
$770$	−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	0.577684	−	0.816260i	$-0.303956\pi$
$773$	−142556.	−	142556.i	−0.238576	−	0.238576i	−0.816260	+	0.577684i	$0.803956\pi$
$774$	−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	−0.140243	+	0.990117i	$0.544788\pi$
$787$	−700110.	+	700110.i	−1.13036	+	1.13036i	−0.990117	+	0.140243i	$0.955212\pi$
$788$	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	0.0905687	−	0.995890i	$-0.471132\pi$
$811$	714587.	−	714587.i	1.08646	−	1.08646i	0.995890	−	0.0905687i	$-0.0288685\pi$
$812$	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	−0.0406046	−	0.999175i	$-0.512928\pi$
$821$	646116.	−	646116.i	0.958571	−	0.958571i	0.999175	+	0.0406046i	$0.0129284\pi$
$822$		−	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	−0.173157	−	0.984894i	$-0.555397\pi$
$827$	555171.	−	555171.i	0.811737	−	0.811737i	0.984894	+	0.173157i	$0.0553968\pi$
$828$			824143.i			1.20210i
$829$			520297.i			0.757081i	0.925585	+	0.378540i	$0.123574\pi$
$829$			520297.i			0.757081i	−0.925585	+	0.378540i	$0.876426\pi$
$830$	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	0.769066	−	0.639169i	$-0.220721\pi$
$839$	91437.7	+	91437.7i	0.129898	+	0.129898i	−0.639169	+	0.769066i	$0.720721\pi$
$840$	−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	−0.839385	−	0.543538i	$-0.817084\pi$
$853$	−215261.	+	215261.i	−0.295847	+	0.295847i	0.543538	+	0.839385i	$0.317084\pi$
$854$	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	0.869879	−	0.493265i	$-0.164197\pi$
$863$	280491.	+	280491.i	0.376614	+	0.376614i	−0.493265	+	0.869879i	$0.664197\pi$
$864$	−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	0.155848	−	0.987781i	$-0.450189\pi$
$877$	−639864.	−	639864.i	−0.831934	−	0.831934i	−0.987781	+	0.155848i	$0.950189\pi$
$878$	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	$0.176688\pi$
$881$			818092.i			1.05402i	−0.849858	+	0.527012i	$0.823312\pi$
$882$	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	$-0.832861\pi$
$887$		−	788792.i		−	1.00257i	0.865282	−	0.501286i	$-0.167139\pi$
$888$	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	−0.818362	−	0.574703i	$-0.805117\pi$
$929$	−210287.	+	210287.i	−0.243658	+	0.243658i	0.574703	+	0.818362i	$0.305117\pi$
$930$	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	$0.140744\pi$
$937$			751353.i			0.855786i	−0.903829	+	0.427893i	$0.859256\pi$
$938$	−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	−0.141005	+	0.990009i	$0.545034\pi$
$941$	−1.00149e6	+	1.00149e6i	−1.13101	+	1.13101i	−0.990009	+	0.141005i	$0.954966\pi$
$942$	−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	−0.866501	−	0.499176i	$-0.833636\pi$
$947$	−329421.	+	329421.i	−0.367325	+	0.367325i	0.499176	+	0.866501i	$0.333636\pi$
$948$	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	−0.993619	−	0.112785i	$-0.964023\pi$
$967$	−1.03459e6	−	1.03459e6i	−1.10640	−	1.10640i	−0.112785	−	0.993619i	$-0.535977\pi$
$968$	−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	0.960718	+	0.277525i	$0.0895141\pi$
$977$	1.18194e6	+	1.18194e6i	1.23824	+	1.23824i	0.277525	+	0.960718i	$0.410486\pi$
$978$			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	−0.915083	−	0.403265i	$-0.867875\pi$
$983$	−494564.	+	494564.i	−0.511818	+	0.511818i	0.403265	+	0.915083i	$0.367875\pi$
$984$	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	$0.148120\pi$
$997$			892062.i			0.897439i	−0.893673	+	0.448720i	$0.851880\pi$
$998$	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.44.3	yes	52
5.4	even	2	inner	65.5.g.a.44.24	yes	52
13.8	odd	4	inner	65.5.g.a.34.24	yes	52
65.34	odd	4	inner	65.5.g.a.34.3	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.5.g.a.34.3	✓	52	65.34	odd	4	inner
65.5.g.a.34.24	yes	52	13.8	odd	4	inner
65.5.g.a.44.3	yes	52	1.1	even	1	trivial
65.5.g.a.44.24	yes	52	5.4	even	2	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

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Database

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