LMFDB - Embedded newform 65.5.g.a.34.16

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			34.16
Character	$\chi$	$=$	65.34
Dual form			65.5.g.a.44.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.479269 - 0.479269i) q^{2} -2.62394i q^{3} +15.5406i q^{4} +(-11.7601 - 22.0613i) q^{5} +(-1.25757 - 1.25757i) q^{6} +(51.9642 + 51.9642i) q^{7} +(15.1164 + 15.1164i) q^{8} +74.1150 q^{9} +O(q^{10})$	\(q+(0.479269 - 0.479269i) q^{2} -2.62394i q^{3} +15.5406i q^{4} +(-11.7601 - 22.0613i) q^{5} +(-1.25757 - 1.25757i) q^{6} +(51.9642 + 51.9642i) q^{7} +(15.1164 + 15.1164i) q^{8} +74.1150 q^{9} +(-16.2095 - 4.93705i) q^{10} +(35.9335 - 35.9335i) q^{11} +40.7776 q^{12} +(32.0577 + 165.932i) q^{13} +49.8096 q^{14} +(-57.8874 + 30.8577i) q^{15} -234.160 q^{16} +416.497 q^{17} +(35.5210 - 35.5210i) q^{18} +(-28.5561 - 28.5561i) q^{19} +(342.846 - 182.759i) q^{20} +(136.351 - 136.351i) q^{21} -34.4436i q^{22} +315.223 q^{23} +(39.6645 - 39.6645i) q^{24} +(-348.402 + 518.885i) q^{25} +(94.8901 + 64.1616i) q^{26} -407.012i q^{27} +(-807.555 + 807.555i) q^{28} -1074.35 q^{29} +(-12.9545 + 42.5327i) q^{30} +(119.050 + 119.050i) q^{31} +(-354.088 + 354.088i) q^{32} +(-94.2873 - 94.2873i) q^{33} +(199.614 - 199.614i) q^{34} +(535.295 - 1757.50i) q^{35} +1151.79i q^{36} +(-1144.48 - 1144.48i) q^{37} -27.3721 q^{38} +(435.394 - 84.1174i) q^{39} +(155.718 - 511.258i) q^{40} +(-1151.81 - 1151.81i) q^{41} -130.697i q^{42} +557.016 q^{43} +(558.429 + 558.429i) q^{44} +(-871.597 - 1635.07i) q^{45} +(151.077 - 151.077i) q^{46} +(-669.259 - 669.259i) q^{47} +614.421i q^{48} +2999.55i q^{49} +(81.7072 + 415.663i) q^{50} -1092.86i q^{51} +(-2578.68 + 498.196i) q^{52} +2664.52i q^{53} +(-195.068 - 195.068i) q^{54} +(-1215.32 - 370.160i) q^{55} +1571.02i q^{56} +(-74.9294 + 74.9294i) q^{57} +(-514.903 + 514.903i) q^{58} +(854.485 - 854.485i) q^{59} +(-479.547 - 899.606i) q^{60} +3845.74 q^{61} +114.113 q^{62} +(3851.32 + 3851.32i) q^{63} -3407.15i q^{64} +(3283.67 - 2658.60i) q^{65} -90.3779 q^{66} +(5223.52 - 5223.52i) q^{67} +6472.62i q^{68} -827.126i q^{69} +(-585.764 - 1098.86i) q^{70} +(-2891.45 - 2891.45i) q^{71} +(1120.35 + 1120.35i) q^{72} +(2861.02 + 2861.02i) q^{73} -1097.02 q^{74} +(1361.52 + 914.184i) q^{75} +(443.779 - 443.779i) q^{76} +3734.51 q^{77} +(168.356 - 248.986i) q^{78} -5467.48 q^{79} +(2753.74 + 5165.87i) q^{80} +4935.34 q^{81} -1104.06 q^{82} +(-4971.13 + 4971.13i) q^{83} +(2118.97 + 2118.97i) q^{84} +(-4898.04 - 9188.47i) q^{85} +(266.960 - 266.960i) q^{86} +2819.03i q^{87} +1086.37 q^{88} +(3375.91 - 3375.91i) q^{89} +(-1201.37 - 365.910i) q^{90} +(-6956.65 + 10288.4i) q^{91} +4898.76i q^{92} +(312.379 - 312.379i) q^{93} -641.509 q^{94} +(-294.163 + 965.807i) q^{95} +(929.105 + 929.105i) q^{96} +(3665.84 - 3665.84i) q^{97} +(1437.59 + 1437.59i) q^{98} +(2663.21 - 2663.21i) 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 $

$2$	0.479269	−	0.479269i	0.119817	−	0.119817i	−0.644656	−	0.764473i	$-0.722999\pi$
$2$	0.479269	−	0.479269i	0.119817	−	0.119817i	0.764473	+	0.644656i	$0.222999\pi$
$3$		−	2.62394i		−	0.291549i	−0.989318	−	0.145774i	$-0.953433\pi$
$3$		−	2.62394i		−	0.291549i	0.989318	−	0.145774i	$-0.0465673\pi$
$4$			15.5406i			0.971288i
$5$	−11.7601	−	22.0613i	−0.470403	−	0.882452i
$5$	−11.7601	−	22.0613i	−0.470403	−	0.882452i
$6$	−1.25757	−	1.25757i	−0.0349325	−	0.0349325i
$7$	51.9642	+	51.9642i	1.06049	+	1.06049i	0.998048	+	0.0624452i	$0.0198899\pi$
$7$	51.9642	+	51.9642i	1.06049	+	1.06049i	0.0624452	+	0.998048i	$0.480110\pi$
$8$	15.1164	+	15.1164i	0.236194	+	0.236194i
$9$	74.1150			0.914999
$10$	−16.2095	−	4.93705i	−0.162095	−	0.0493705i
$11$	35.9335	−	35.9335i	0.296971	−	0.296971i	−0.542855	−	0.839826i	$-0.682657\pi$
$11$	35.9335	−	35.9335i	0.296971	−	0.296971i	0.839826	+	0.542855i	$0.182657\pi$
$12$	40.7776			0.283177
$13$	32.0577	+	165.932i	0.189691	+	0.981844i
$13$	32.0577	+	165.932i	0.189691	+	0.981844i
$14$	49.8096			0.254131
$15$	−57.8874	+	30.8577i	−0.257278	+	0.137145i
$16$	−234.160			−0.914688
$17$	416.497			1.44117			0.720584	−	0.693368i	$-0.243874\pi$
$17$	416.497			1.44117			0.720584	+	0.693368i	$0.243874\pi$
$18$	35.5210	−	35.5210i	0.109633	−	0.109633i
$19$	−28.5561	−	28.5561i	−0.0791028	−	0.0791028i	0.666448	−	0.745551i	$-0.267814\pi$
$19$	−28.5561	−	28.5561i	−0.0791028	−	0.0791028i	−0.745551	+	0.666448i	$0.767814\pi$
$20$	342.846	−	182.759i	0.857115	−	0.456896i
$21$	136.351	−	136.351i	0.309185	−	0.309185i
$22$		−	34.4436i		−	0.0711645i
$23$	315.223			0.595885			0.297943	−	0.954584i	$-0.403700\pi$
$23$	315.223			0.595885			0.297943	+	0.954584i	$0.403700\pi$
$24$	39.6645	−	39.6645i	0.0688620	−	0.0688620i
$25$	−348.402	+	518.885i	−0.557443	+	0.830216i
$26$	94.8901	+	64.1616i	0.140370	+	0.0949135i
$27$		−	407.012i		−	0.558315i
$28$	−807.555	+	807.555i	−1.03004	+	1.03004i
$29$	−1074.35			−1.27747			−0.638734	−	0.769427i	$-0.720542\pi$
$29$	−1074.35			−1.27747			−0.638734	+	0.769427i	$0.720542\pi$
$30$	−12.9545	+	42.5327i	−0.0143939	+	0.0472586i
$31$	119.050	+	119.050i	0.123881	+	0.123881i	0.766329	−	0.642448i	$-0.222081\pi$
$31$	119.050	+	119.050i	0.123881	+	0.123881i	−0.642448	+	0.766329i	$0.722081\pi$
$32$	−354.088	+	354.088i	−0.345789	+	0.345789i
$33$	−94.2873	−	94.2873i	−0.0865816	−	0.0865816i
$34$	199.614	−	199.614i	0.172677	−	0.172677i
$35$	535.295	−	1757.50i	0.436975	−	1.43469i
$36$			1151.79i			0.888728i
$37$	−1144.48	−	1144.48i	−0.835994	−	0.835994i	0.152335	−	0.988329i	$-0.451321\pi$
$37$	−1144.48	−	1144.48i	−0.835994	−	0.835994i	−0.988329	+	0.152335i	$0.951321\pi$
$38$	−27.3721			−0.0189557
$39$	435.394	−	84.1174i	0.286255	−	0.0553040i
$40$	155.718	−	511.258i	0.0973236	−	0.319536i
$41$	−1151.81	−	1151.81i	−0.685196	−	0.685196i	0.275970	−	0.961166i	$-0.411001\pi$
$41$	−1151.81	−	1151.81i	−0.685196	−	0.685196i	−0.961166	+	0.275970i	$0.911001\pi$
$42$		−	130.697i		−	0.0740914i
$43$	557.016			0.301253			0.150626	−	0.988591i	$-0.451871\pi$
$43$	557.016			0.301253			0.150626	+	0.988591i	$0.451871\pi$
$44$	558.429	+	558.429i	0.288445	+	0.288445i
$45$	−871.597	−	1635.07i	−0.430418	−	0.807443i
$46$	151.077	−	151.077i	0.0713973	−	0.0713973i
$47$	−669.259	−	669.259i	−0.302969	−	0.302969i	0.539205	−	0.842174i	$-0.318725\pi$
$47$	−669.259	−	669.259i	−0.302969	−	0.302969i	−0.842174	+	0.539205i	$0.818725\pi$
$48$			614.421i			0.266676i
$49$			2999.55i			1.24929i
$50$	81.7072	+	415.663i	0.0326829	+	0.166265i
$51$		−	1092.86i		−	0.420170i
$52$	−2578.68	+	498.196i	−0.953653	+	0.184244i
$53$			2664.52i			0.948564i	0.880373	+	0.474282i	$0.157292\pi$
$53$			2664.52i			0.948564i	−0.880373	+	0.474282i	$0.842708\pi$
$54$	−195.068	−	195.068i	−0.0668957	−	0.0668957i
$55$	−1215.32	−	370.160i	−0.401759	−	0.122367i
$56$			1571.02i			0.500965i
$57$	−74.9294	+	74.9294i	−0.0230623	+	0.0230623i
$58$	−514.903	+	514.903i	−0.153063	+	0.153063i
$59$	854.485	−	854.485i	0.245471	−	0.245471i	−0.573638	−	0.819109i	$-0.694468\pi$
$59$	854.485	−	854.485i	0.245471	−	0.245471i	0.819109	+	0.573638i	$0.194468\pi$
$60$	−479.547	−	899.606i	−0.133207	−	0.249891i
$61$	3845.74			1.03352			0.516762	−	0.856129i	$-0.327137\pi$
$61$	3845.74			1.03352			0.516762	+	0.856129i	$0.327137\pi$
$62$	114.113			0.0296861
$63$	3851.32	+	3851.32i	0.970351	+	0.970351i
$64$		−	3407.15i		−	0.831825i
$65$	3283.67	−	2658.60i	0.777199	−	0.629255i
$66$	−90.3779			−0.0207479
$67$	5223.52	−	5223.52i	1.16363	−	1.16363i	0.179950	−	0.983676i	$-0.442406\pi$
$67$	5223.52	−	5223.52i	1.16363	−	1.16363i	0.983676	−	0.179950i	$-0.0575937\pi$
$68$			6472.62i			1.39979i
$69$		−	827.126i		−	0.173729i
$70$	−585.764	−	1098.86i	−0.119544	−	0.224258i
$71$	−2891.45	−	2891.45i	−0.573587	−	0.573587i	0.359542	−	0.933129i	$-0.382933\pi$
$71$	−2891.45	−	2891.45i	−0.573587	−	0.573587i	−0.933129	+	0.359542i	$0.882933\pi$
$72$	1120.35	+	1120.35i	0.216117	+	0.216117i
$73$	2861.02	+	2861.02i	0.536877	+	0.536877i	0.922610	−	0.385733i	$-0.126051\pi$
$73$	2861.02	+	2861.02i	0.536877	+	0.536877i	−0.385733	+	0.922610i	$0.626051\pi$
$74$	−1097.02			−0.200333
$75$	1361.52	+	914.184i	0.242048	+	0.162522i
$76$	443.779	−	443.779i	0.0768316	−	0.0768316i
$77$	3734.51			0.629873
$78$	168.356	−	248.986i	0.0276719	−	0.0409246i
$79$	−5467.48			−0.876059			−0.438029	−	0.898961i	$-0.644323\pi$
$79$	−5467.48			−0.876059			−0.438029	+	0.898961i	$0.644323\pi$
$80$	2753.74	+	5165.87i	0.430272	+	0.807168i
$81$	4935.34			0.752223
$82$	−1104.06			−0.164196
$83$	−4971.13	+	4971.13i	−0.721604	+	0.721604i	−0.968932	−	0.247328i	$-0.920448\pi$
$83$	−4971.13	+	4971.13i	−0.721604	+	0.721604i	0.247328	+	0.968932i	$0.420448\pi$
$84$	2118.97	+	2118.97i	0.300308	+	0.300308i
$85$	−4898.04	−	9188.47i	−0.677929	−	1.27176i
$86$	266.960	−	266.960i	0.0360952	−	0.0360952i
$87$			2819.03i			0.372444i
$88$	1086.37			0.140286
$89$	3375.91	−	3375.91i	0.426197	−	0.426197i	−0.461134	−	0.887331i	$-0.652557\pi$
$89$	3375.91	−	3375.91i	0.426197	−	0.426197i	0.887331	+	0.461134i	$0.152557\pi$
$90$	−1201.37	−	365.910i	−0.148317	−	0.0451740i
$91$	−6956.65	+	10288.4i	−0.840073	+	1.24240i
$92$			4898.76i			0.578776i
$93$	312.379	−	312.379i	0.0361173	−	0.0361173i
$94$	−641.509			−0.0726018
$95$	−294.163	+	965.807i	−0.0325942	+	0.107015i
$96$	929.105	+	929.105i	0.100814	+	0.100814i
$97$	3665.84	−	3665.84i	0.389610	−	0.389610i	−0.484938	−	0.874549i	$-0.661158\pi$
$97$	3665.84	−	3665.84i	0.389610	−	0.389610i	0.874549	+	0.484938i	$0.161158\pi$
$98$	1437.59	+	1437.59i	0.149687	+	0.149687i
$99$	2663.21	−	2663.21i	0.271729	−	0.271729i
$100$	−8063.78	−	5414.37i	−0.806378	−	0.541437i
$101$		−	6926.06i		−	0.678959i	−0.940614	−	0.339479i	$-0.889749\pi$
$101$		−	6926.06i		−	0.678959i	0.940614	−	0.339479i	$-0.110251\pi$
$102$	−523.775	−	523.775i	−0.0503436	−	0.0503436i
$103$	−12416.4			−1.17036			−0.585180	−	0.810903i	$-0.698976\pi$
$103$	−12416.4			−1.17036			−0.585180	+	0.810903i	$0.698976\pi$
$104$	−2023.69	+	2992.89i	−0.187102	+	0.276709i
$105$	−4611.57	−	1404.58i	−0.418283	−	0.127400i
$106$	1277.02	+	1277.02i	0.113654	+	0.113654i
$107$		−	19015.0i		−	1.66084i	−0.557137	−	0.830421i	$-0.688100\pi$
$107$		−	19015.0i		−	1.66084i	0.557137	−	0.830421i	$-0.311900\pi$
$108$	6325.21			0.542285
$109$	−4688.71	−	4688.71i	−0.394640	−	0.394640i	0.481698	−	0.876337i	$-0.340020\pi$
$109$	−4688.71	−	4688.71i	−0.394640	−	0.394640i	−0.876337	+	0.481698i	$0.840020\pi$
$110$	−759.871	+	405.060i	−0.0627993	+	0.0334760i
$111$	−3003.03	+	3003.03i	−0.243733	+	0.243733i
$112$	−12167.9	−	12167.9i	−0.970020	−	0.970020i
$113$			2134.17i			0.167137i	0.996502	+	0.0835684i	$0.0266317\pi$
$113$			2134.17i			0.167137i	−0.996502	+	0.0835684i	$0.973368\pi$
$114$			71.8226i			0.00552652i
$115$	−3707.05	−	6954.24i	−0.280306	−	0.525840i
$116$		−	16696.1i		−	1.24079i
$117$	2375.96	+	12298.0i	0.173567	+	0.898387i
$118$		−	819.056i		−	0.0588233i
$119$	21643.0	+	21643.0i	1.52835	+	1.52835i
$120$	−1341.51	−	408.593i	−0.0931603	−	0.0283745i
$121$			12058.6i			0.823616i
$122$	1843.14	−	1843.14i	0.123834	−	0.123834i
$123$	−3022.29	+	3022.29i	−0.199768	+	0.199768i
$124$	−1850.10	+	1850.10i	−0.120324	+	0.120324i
$125$	15544.5	+	1584.07i	0.994848	+	0.101381i
$126$	3691.64			0.232529
$127$	−31777.0			−1.97018			−0.985088	−	0.172053i	$-0.944960\pi$
$127$	−31777.0			−1.97018			−0.985088	+	0.172053i	$0.944960\pi$
$128$	−7298.35	−	7298.35i	−0.445456	−	0.445456i
$129$		−	1461.58i		−	0.0878298i
$130$	299.573	−	2847.94i	0.0177262	−	0.168517i
$131$	−30288.1			−1.76494			−0.882468	−	0.470373i	$-0.844119\pi$
$131$	−30288.1			−1.76494			−0.882468	+	0.470373i	$0.844119\pi$
$132$	1465.28	−	1465.28i	0.0840956	−	0.0840956i
$133$		−	2967.79i		−	0.167776i
$134$		−	5006.94i		−	0.278845i
$135$	−8979.21	+	4786.49i	−0.492686	+	0.262633i
$136$	6295.95	+	6295.95i	0.340395	+	0.340395i
$137$	18069.0	+	18069.0i	0.962704	+	0.962704i	0.999329	−	0.0366247i	$-0.0116606\pi$
$137$	18069.0	+	18069.0i	0.962704	+	0.962704i	−0.0366247	+	0.999329i	$0.511661\pi$
$138$	−396.416	−	396.416i	−0.0208158	−	0.0208158i
$139$	7012.09			0.362926			0.181463	−	0.983398i	$-0.441917\pi$
$139$	7012.09			0.362926			0.181463	+	0.983398i	$0.441917\pi$
$140$	27312.6	+	8318.81i	1.39350	+	0.424429i
$141$	−1756.09	+	1756.09i	−0.0883302	+	0.0883302i
$142$	−2771.56			−0.137451
$143$	7114.46	+	4810.56i	0.347912	+	0.235247i
$144$	−17354.8			−0.836939
$145$	12634.4	+	23701.6i	0.600925	+	1.12730i
$146$	2742.39			0.128654
$147$	7870.64			0.364230
$148$	17785.8	−	17785.8i	0.811990	−	0.811990i
$149$	−26975.3	−	26975.3i	−1.21505	−	1.21505i	−0.969345	−	0.245703i	$-0.920981\pi$
$149$	−26975.3	−	26975.3i	−1.21505	−	1.21505i	−0.245703	−	0.969345i	$-0.579019\pi$
$150$	1090.67	−	214.395i	0.0484744	−	0.00952865i
$151$	26348.8	−	26348.8i	1.15560	−	1.15560i	0.170186	−	0.985412i	$-0.445563\pi$
$151$	26348.8	−	26348.8i	1.15560	−	1.15560i	0.985412	−	0.170186i	$-0.0544369\pi$
$152$		−	863.332i		−	0.0373672i
$153$	30868.7			1.31867
$154$	1789.84	−	1789.84i	0.0754695	−	0.0754695i
$155$	1226.36	−	4026.42i	0.0510450	−	0.167593i
$156$	1307.24	+	6766.29i	0.0537161	+	0.278036i
$157$			35186.8i			1.42752i	0.700393	+	0.713758i	$0.253008\pi$
$157$			35186.8i			1.42752i	−0.700393	+	0.713758i	$0.746992\pi$
$158$	−2620.39	+	2620.39i	−0.104967	+	0.104967i
$159$	6991.52			0.276552
$160$	11975.7	+	3647.54i	0.467803	+	0.142482i
$161$	16380.3	+	16380.3i	0.631933	+	0.631933i
$162$	2365.35	−	2365.35i	0.0901293	−	0.0901293i
$163$	−25216.0	−	25216.0i	−0.949075	−	0.949075i	0.0496899	−	0.998765i	$-0.484177\pi$
$163$	−25216.0	−	25216.0i	−0.949075	−	0.949075i	−0.998765	+	0.0496899i	$0.984177\pi$
$164$	17899.9	−	17899.9i	0.665522	−	0.665522i
$165$	−971.275	+	3188.93i	−0.0356759	+	0.117132i
$166$			4765.01i			0.172921i
$167$	11599.8	+	11599.8i	0.415927	+	0.415927i	0.883797	−	0.467870i	$-0.154979\pi$
$167$	11599.8	+	11599.8i	0.415927	+	0.415927i	−0.467870	+	0.883797i	$0.654979\pi$
$168$	4122.27			0.146055
$169$	−26505.6	+	10638.8i	−0.928035	+	0.372493i
$170$	−6751.22	−	2056.27i	−0.233606	−	0.0711512i
$171$	−2116.44	−	2116.44i	−0.0723790	−	0.0723790i
$172$			8656.37i			0.292603i
$173$	−9980.66			−0.333478			−0.166739	−	0.986001i	$-0.553324\pi$
$173$	−9980.66			−0.333478			−0.166739	+	0.986001i	$0.553324\pi$
$174$	1351.07	+	1351.07i	0.0446252	+	0.0446252i
$175$	−45067.8	+	8859.02i	−1.47160	+	0.289274i
$176$	−8414.20	+	8414.20i	−0.271636	+	0.271636i
$177$	−2242.11	−	2242.11i	−0.0715668	−	0.0715668i
$178$		−	3235.93i		−	0.102131i
$179$			37894.8i			1.18270i	0.806416	+	0.591349i	$0.201404\pi$
$179$			37894.8i			1.18270i	−0.806416	+	0.591349i	$0.798596\pi$
$180$	25410.0	−	13545.1i	0.784259	−	0.418060i
$181$		−	31024.7i		−	0.947002i	−0.880793	−	0.473501i	$-0.842990\pi$
$181$		−	31024.7i		−	0.947002i	0.880793	−	0.473501i	$-0.157010\pi$
$182$	1596.78	+	8264.99i	0.0482062	+	0.249517i
$183$		−	10091.0i		−	0.301322i
$184$	4765.05	+	4765.05i	0.140745	+	0.140745i
$185$	−11789.5	+	38707.7i	−0.344470	+	1.13098i
$186$		−	299.426i		−	0.00865494i
$187$	14966.2	−	14966.2i	0.427986	−	0.427986i
$188$	10400.7	−	10400.7i	0.294270	−	0.294270i
$189$	21150.0	−	21150.0i	0.592090	−	0.592090i
$190$	321.898	+	603.864i	0.00891683	+	0.0167275i
$191$	58112.5			1.59295			0.796476	−	0.604670i	$-0.206695\pi$
$191$	58112.5			1.59295			0.796476	+	0.604670i	$0.206695\pi$
$192$	−8940.15			−0.242517
$193$	−12474.0	−	12474.0i	−0.334880	−	0.334880i	0.519556	−	0.854436i	$-0.326097\pi$
$193$	−12474.0	−	12474.0i	−0.334880	−	0.334880i	−0.854436	+	0.519556i	$0.826097\pi$
$194$		−	3513.85i		−	0.0933640i
$195$	−6976.00	−	8616.13i	−0.183458	−	0.226591i
$196$	−46614.9			−1.21342
$197$	32300.5	−	32300.5i	0.832295	−	0.832295i	−0.155535	−	0.987830i	$-0.549710\pi$
$197$	32300.5	−	32300.5i	0.832295	−	0.832295i	0.987830	+	0.155535i	$0.0497103\pi$
$198$		−	2552.79i		−	0.0651155i
$199$			54634.7i			1.37963i	0.723986	+	0.689815i	$0.242308\pi$
$199$			54634.7i			1.37963i	−0.723986	+	0.689815i	$0.757692\pi$
$200$	−13110.3	+	2577.09i	−0.327757	+	0.0644274i
$201$	−13706.2	−	13706.2i	−0.339253	−	0.339253i
$202$	−3319.44	−	3319.44i	−0.0813509	−	0.0813509i
$203$	−55827.8	−	55827.8i	−1.35475	−	1.35475i
$204$	16983.7			0.408106
$205$	−11865.1	+	38955.9i	−0.282334	+	0.926970i
$206$	−5950.77	+	5950.77i	−0.140229	+	0.140229i
$207$	23362.8			0.545235
$208$	−7506.64	−	38854.5i	−0.173508	−	0.898080i
$209$	−2052.24			−0.0469826
$210$	−2883.35	+	1537.01i	−0.0653821	+	0.0348528i
$211$	−51568.8			−1.15830			−0.579151	−	0.815220i	$-0.696616\pi$
$211$	−51568.8			−1.15830			−0.579151	+	0.815220i	$0.696616\pi$
$212$	−41408.2			−0.921328
$213$	−7586.98	+	7586.98i	−0.167228	+	0.167228i
$214$	−9113.28	−	9113.28i	−0.198997	−	0.198997i
$215$	−6550.55	−	12288.5i	−0.141710	−	0.265841i
$216$	6152.56	−	6152.56i	0.131871	−	0.131871i
$217$			12372.6i			0.262750i
$218$	−4494.31			−0.0945692
$219$	7507.13	−	7507.13i	0.156526	−	0.156526i
$220$	5752.50	−	18886.8i	0.118853	−	0.390224i
$221$	13352.0	+	69110.1i	0.273376	+	1.41500i
$222$			2878.52i			0.0584067i
$223$	21840.9	−	21840.9i	0.439199	−	0.439199i	−0.452543	−	0.891742i	$-0.649483\pi$
$223$	21840.9	−	21840.9i	0.439199	−	0.439199i	0.891742	+	0.452543i	$0.149483\pi$
$224$	−36799.8			−0.733415
$225$	−25821.8	+	38457.1i	−0.510060	+	0.759647i
$226$	1022.84	+	1022.84i	0.0200258	+	0.0200258i
$227$	−21796.2	+	21796.2i	−0.422989	+	0.422989i	−0.886232	−	0.463242i	$-0.846686\pi$
$227$	−21796.2	+	21796.2i	−0.422989	+	0.422989i	0.463242	+	0.886232i	$0.346686\pi$
$228$	−1164.45	−	1164.45i	−0.0224001	−	0.0224001i
$229$	23467.0	−	23467.0i	0.447493	−	0.447493i	−0.447027	−	0.894520i	$-0.647517\pi$
$229$	23467.0	−	23467.0i	0.447493	−	0.447493i	0.894520	+	0.447027i	$0.147517\pi$
$230$	−5109.62	−	1556.27i	−0.0965901	−	0.0294192i
$231$		−	9799.13i		−	0.183638i
$232$	−16240.3	−	16240.3i	−0.301730	−	0.301730i
$233$	−30076.3			−0.554003			−0.277001	−	0.960870i	$-0.589341\pi$
$233$	−30076.3			−0.554003			−0.277001	+	0.960870i	$0.589341\pi$
$234$	7032.77	+	4755.33i	0.128438	+	0.0868458i
$235$	−6894.19	+	22635.2i	−0.124838	+	0.409873i
$236$	13279.2	+	13279.2i	0.238423	+	0.238423i
$237$			14346.3i			0.255414i
$238$	20745.6			0.366245
$239$	−39023.2	−	39023.2i	−0.683168	−	0.683168i	0.277545	−	0.960713i	$-0.410479\pi$
$239$	−39023.2	−	39023.2i	−0.683168	−	0.683168i	−0.960713	+	0.277545i	$0.910479\pi$
$240$	13554.9	−	7225.63i	0.235329	−	0.125445i
$241$	56411.7	−	56411.7i	0.971259	−	0.971259i	−0.0283394	−	0.999598i	$-0.509022\pi$
$241$	56411.7	−	56411.7i	0.971259	−	0.971259i	0.999598	+	0.0283394i	$0.00902193\pi$
$242$	5779.29	+	5779.29i	0.0986833	+	0.0986833i
$243$		−	45918.0i		−	0.777625i
$244$			59765.1i			1.00385i
$245$	66174.0	−	35275.0i	1.10244	−	0.587671i
$246$			2896.97i			0.0478712i
$247$	3822.92	−	5653.81i	0.0626615	−	0.0926717i
$248$			3599.21i			0.0585199i
$249$	13043.9	+	13043.9i	0.210383	+	0.210383i
$250$	8209.18	−	6690.79i	0.131347	−	0.107053i
$251$		−	15686.3i		−	0.248984i	−0.992221	−	0.124492i	$-0.960270\pi$
$251$		−	15686.3i		−	0.248984i	0.992221	−	0.124492i	$-0.0397301\pi$
$252$	−59851.9	+	59851.9i	−0.942490	+	0.942490i
$253$	11327.1	−	11327.1i	0.176961	−	0.176961i
$254$	−15229.7	+	15229.7i	−0.236061	+	0.236061i
$255$	−24110.0	+	12852.1i	−0.370780	+	0.197649i
$256$	47518.7			0.725078
$257$	82709.5			1.25224			0.626122	−	0.779725i	$-0.284641\pi$
$257$	82709.5			1.25224			0.626122	+	0.779725i	$0.284641\pi$
$258$	−700.487	−	700.487i	−0.0105235	−	0.0105235i
$259$		−	118943.i		−	1.77313i
$260$	41316.3	+	51030.1i	0.611188	+	0.754884i
$261$	−79625.5			−1.16888
$262$	−14516.1	+	14516.1i	−0.211469	+	0.211469i
$263$			9882.57i			0.142876i	0.997445	+	0.0714379i	$0.0227588\pi$
$263$			9882.57i			0.142876i	−0.997445	+	0.0714379i	$0.977241\pi$
$264$		−	2850.57i		−	0.0409001i
$265$	58782.7	−	31334.9i	0.837062	−	0.446207i
$266$	−1422.37	−	1422.37i	−0.0201024	−	0.0201024i
$267$	−8858.16	−	8858.16i	−0.124257	−	0.124257i
$268$	81176.6	+	81176.6i	1.13022	+	1.13022i
$269$	−55591.2			−0.768247			−0.384124	−	0.923282i	$-0.625496\pi$
$269$	−55591.2			−0.768247			−0.384124	+	0.923282i	$0.625496\pi$
$270$	−2009.44	+	6597.46i	−0.0275643	+	0.0905002i
$271$	−82338.1	+	82338.1i	−1.12115	+	1.12115i	−0.129576	+	0.991569i	$0.541362\pi$
$271$	−82338.1	+	82338.1i	−1.12115	+	1.12115i	−0.991569	+	0.129576i	$0.958638\pi$
$272$	−97527.0			−1.31822
$273$	26996.0	+	18253.8i	0.362221	+	0.244922i
$274$	17319.8			0.230697
$275$	6126.06	+	31164.7i	0.0810058	+	0.412095i
$276$	12854.0			0.168741
$277$	109781.			1.43076			0.715378	−	0.698737i	$-0.246254\pi$
$277$	109781.			1.43076			0.715378	+	0.698737i	$0.246254\pi$
$278$	3360.67	−	3360.67i	0.0434847	−	0.0434847i
$279$	8823.35	+	8823.35i	0.113351	+	0.113351i
$280$	34658.8	−	18475.4i	0.442077	−	0.235655i
$281$	23819.8	−	23819.8i	0.301666	−	0.301666i	−0.540000	−	0.841665i	$-0.681576\pi$
$281$	23819.8	−	23819.8i	0.301666	−	0.301666i	0.841665	+	0.540000i	$0.181576\pi$
$282$			1683.28i			0.0211669i
$283$	−17223.0			−0.215049			−0.107524	−	0.994202i	$-0.534292\pi$
$283$	−17223.0			−0.215049			−0.107524	+	0.994202i	$0.534292\pi$
$284$	44934.9	−	44934.9i	0.557118	−	0.557118i
$285$	2534.22	+	771.865i	0.0311999	+	0.00950280i
$286$	5715.29	−	1104.18i	0.0698725	−	0.0134992i
$287$		−	119706.i		−	1.45329i
$288$	−26243.2	+	26243.2i	−0.316397	+	0.316397i
$289$	89949.1			1.07696
$290$	17414.7	+	5304.13i	0.207071	+	0.0630693i
$291$	−9618.94	−	9618.94i	−0.113590	−	0.113590i
$292$	−44462.0	+	44462.0i	−0.521462	+	0.521462i
$293$	109838.	+	109838.i	1.27944	+	1.27944i	0.940984	+	0.338452i	$0.109903\pi$
$293$	109838.	+	109838.i	1.27944	+	1.27944i	0.338452	+	0.940984i	$0.390097\pi$
$294$	3772.15	−	3772.15i	0.0436410	−	0.0436410i
$295$	−28899.9	−	8802.25i	−0.332087	−	0.101146i
$296$		−	34600.7i		−	0.394913i
$297$	−14625.4	−	14625.4i	−0.165804	−	0.165804i
$298$	−25856.8			−0.291167
$299$	10105.3	+	52305.5i	0.113034	+	0.585066i
$300$	−14207.0	+	21158.9i	−0.157855	+	0.235098i
$301$	28944.9	+	28944.9i	0.319477	+	0.319477i
$302$		−	25256.3i		−	0.276921i
$303$	−18173.5			−0.197949
$304$	6686.70	+	6686.70i	0.0723544	+	0.0723544i
$305$	−45226.2	−	84842.0i	−0.486172	−	0.912034i
$306$	14794.4	−	14794.4i	0.157999	−	0.157999i
$307$	60286.3	+	60286.3i	0.639649	+	0.639649i	0.950469	−	0.310820i	$-0.100604\pi$
$307$	60286.3	+	60286.3i	0.639649	+	0.639649i	−0.310820	+	0.950469i	$0.600604\pi$
$308$			58036.6i			0.611788i
$309$			32579.7i			0.341217i
$310$	−1341.98	−	2517.49i	−0.0139644	−	0.0261966i
$311$			5551.14i			0.0573933i	0.999588	+	0.0286967i	$0.00913569\pi$
$311$			5551.14i			0.0573933i	−0.999588	+	0.0286967i	$0.990864\pi$
$312$	7853.15	+	5310.05i	0.0806742	+	0.0545493i
$313$			113364.i			1.15714i	0.815633	+	0.578569i	$0.196389\pi$
$313$			113364.i			1.15714i	−0.815633	+	0.578569i	$0.803611\pi$
$314$	16863.9	+	16863.9i	0.171041	+	0.171041i
$315$	39673.4	−	130257.i	0.399832	−	1.31274i
$316$		−	84968.0i		−	0.850905i
$317$	14781.3	−	14781.3i	0.147094	−	0.147094i	−0.629725	−	0.776818i	$-0.716832\pi$
$317$	14781.3	−	14781.3i	0.147094	−	0.147094i	0.776818	+	0.629725i	$0.216832\pi$
$318$	3350.82	−	3350.82i	0.0331357	−	0.0331357i
$319$	−38605.2	+	38605.2i	−0.379372	+	0.379372i
$320$	−75166.2	+	40068.4i	−0.734045	+	0.391293i
$321$	−49894.1			−0.484216
$322$	15701.1			0.151433
$323$	−11893.5	−	11893.5i	−0.114000	−	0.114000i
$324$			76698.1i			0.730625i
$325$	−97268.3	−	41176.6i	−0.920884	−	0.389837i
$326$	−24170.4			−0.227431
$327$	−12302.9	+	12302.9i	−0.115057	+	0.115057i
$328$		−	34822.6i		−	0.323678i
$329$		−	69555.0i		−	0.642593i
$330$	1062.85	+	1993.85i	0.00975988	+	0.0183090i
$331$	55097.3	+	55097.3i	0.502892	+	0.502892i	0.912335	−	0.409444i	$-0.134277\pi$
$331$	55097.3	+	55097.3i	0.502892	+	0.502892i	−0.409444	+	0.912335i	$0.634277\pi$
$332$	−77254.4	−	77254.4i	−0.700885	−	0.700885i
$333$	−84822.7	−	84822.7i	−0.764934	−	0.764934i
$334$	11118.8			0.0996703
$335$	−176666.	−	53808.6i	−1.57422	−	0.479471i
$336$	−31927.9	+	31927.9i	−0.282808	+	0.282808i
$337$	41077.7			0.361698			0.180849	−	0.983511i	$-0.442115\pi$
$337$	41077.7			0.361698			0.180849	+	0.983511i	$0.442115\pi$
$338$	−7604.47	+	17802.1i	−0.0665634	+	0.155826i
$339$	5599.92			0.0487285
$340$	142794.	−	76118.5i	1.23525	−	0.658464i
$341$	8555.75			0.0735782
$342$	−2028.68			−0.0173445
$343$	−31103.3	+	31103.3i	−0.264374	+	0.264374i
$344$	8420.09	+	8420.09i	0.0711541	+	0.0711541i
$345$	−18247.5	+	9727.06i	−0.153308	+	0.0817228i
$346$	−4783.41	+	4783.41i	−0.0399563	+	0.0399563i
$347$		−	182137.i		−	1.51266i	−0.654193	−	0.756328i	$-0.726992\pi$
$347$		−	182137.i		−	1.51266i	0.654193	−	0.756328i	$-0.273008\pi$
$348$	−43809.4			−0.361750
$349$	−55489.2	+	55489.2i	−0.455572	+	0.455572i	−0.897199	−	0.441627i	$-0.854402\pi$
$349$	−55489.2	+	55489.2i	−0.455572	+	0.455572i	0.441627	+	0.897199i	$0.354402\pi$
$350$	−17353.7	+	25845.4i	−0.141663	+	0.210983i
$351$	67536.1	−	13047.9i	0.548178	−	0.105907i
$352$			25447.3i			0.205379i
$353$	−7288.04	+	7288.04i	−0.0584873	+	0.0584873i	−0.735745	−	0.677258i	$-0.763168\pi$
$353$	−7288.04	+	7288.04i	−0.0584873	+	0.0584873i	0.677258	+	0.735745i	$0.263168\pi$
$354$	−2149.15			−0.0171498
$355$	−29785.5	+	97792.8i	−0.236346	+	0.775979i
$356$	52463.6	+	52463.6i	0.413960	+	0.413960i
$357$	56789.7	−	56789.7i	0.445588	−	0.445588i
$358$	18161.8	+	18161.8i	0.141707	+	0.141707i
$359$	42309.8	−	42309.8i	0.328286	−	0.328286i	−0.523648	−	0.851934i	$-0.675429\pi$
$359$	42309.8	−	42309.8i	0.328286	−	0.328286i	0.851934	+	0.523648i	$0.175429\pi$
$360$	11541.0	−	37891.9i	0.0890510	−	0.292375i
$361$		−	128690.i		−	0.987485i
$362$	−14869.2	−	14869.2i	−0.113467	−	0.113467i
$363$	31640.9			0.240124
$364$	−159887.	−	108111.i	−1.20673	−	0.815953i
$365$	29472.0	−	96763.6i	0.221220	−	0.726317i
$366$	−4836.29	−	4836.29i	−0.0361036	−	0.0361036i
$367$			186972.i			1.38818i	0.719890	+	0.694088i	$0.244192\pi$
$367$			186972.i			1.38818i	−0.719890	+	0.694088i	$0.755808\pi$
$368$	−73812.7			−0.545049
$369$	−85366.7	−	85366.7i	−0.626954	−	0.626954i
$370$	12901.1	+	24201.7i	0.0942371	+	0.176784i
$371$	−138459.	+	138459.i	−1.00595	+	1.00595i
$372$	4854.55	+	4854.55i	0.0350803	+	0.0350803i
$373$			257810.i			1.85303i	0.376258	+	0.926515i	$0.377211\pi$
$373$			257810.i			1.85303i	−0.376258	+	0.926515i	$0.622789\pi$
$374$		−	14345.7i		−	0.102560i
$375$	4156.50	−	40787.8i	0.0295573	−	0.290046i
$376$		−	20233.6i		−	0.143119i
$377$	−34441.2	−	178269.i	−0.242324	−	1.25427i
$378$		−	20273.1i		−	0.141885i
$379$	−58076.7	−	58076.7i	−0.404319	−	0.404319i	0.475433	−	0.879752i	$-0.342291\pi$
$379$	−58076.7	−	58076.7i	−0.404319	−	0.404319i	−0.879752	+	0.475433i	$0.842291\pi$
$380$	−15009.2	−	4571.47i	−0.103942	−	0.0316584i
$381$			83380.7i			0.574402i
$382$	27851.5	−	27851.5i	0.190863	−	0.190863i
$383$	−51109.5	+	51109.5i	−0.348421	+	0.348421i	−0.859521	−	0.511100i	$-0.829238\pi$
$383$	−51109.5	+	51109.5i	−0.348421	+	0.348421i	0.511100	+	0.859521i	$0.329238\pi$
$384$	−19150.4	+	19150.4i	−0.129872	+	0.129872i
$385$	−43918.2	−	82388.2i	−0.296294	−	0.555832i
$386$	−11956.8			−0.0802488
$387$	41283.2			0.275646
$388$	56969.4	+	56969.4i	0.378424	+	0.378424i
$389$			162430.i			1.07342i	0.843768	+	0.536708i	$0.180332\pi$
$389$			162430.i			1.07342i	−0.843768	+	0.536708i	$0.819668\pi$
$390$	−7472.82	−	786.061i	−0.0491310	−	0.00516806i
$391$	131290.			0.858771
$392$	−45342.5	+	45342.5i	−0.295076	+	0.295076i
$393$			79473.9i			0.514564i
$394$		−	30961.3i		−	0.199446i
$395$	64298.0	+	120620.i	0.412100	+	0.773080i
$396$	41387.9	+	41387.9i	0.263927	+	0.263927i
$397$	−20845.7	−	20845.7i	−0.132262	−	0.132262i	0.637876	−	0.770139i	$-0.279813\pi$
$397$	−20845.7	−	20845.7i	−0.132262	−	0.132262i	−0.770139	+	0.637876i	$0.779813\pi$
$398$	26184.7	+	26184.7i	0.165303	+	0.165303i
$399$	−7787.29			−0.0489149
$400$	81581.7	−	121502.i	0.509886	−	0.759388i
$401$	121310.	−	121310.i	0.754412	−	0.754412i	−0.220887	−	0.975299i	$-0.570895\pi$
$401$	121310.	−	121310.i	0.754412	−	0.754412i	0.975299	+	0.220887i	$0.0708953\pi$
$402$	−13137.9			−0.0812968
$403$	−15937.6	+	23570.5i	−0.0981327	+	0.145131i
$404$	107635.			0.659464
$405$	−58039.9	−	108880.i	−0.353848	−	0.663801i
$406$	−53513.0			−0.324644
$407$	−82250.1			−0.496532
$408$	16520.2	−	16520.2i	0.0992417	−	0.0992417i
$409$	114075.	+	114075.i	0.681936	+	0.681936i	0.960436	−	0.278500i	$-0.0898372\pi$
$409$	114075.	+	114075.i	0.681936	+	0.681936i	−0.278500	+	0.960436i	$0.589837\pi$
$410$	12983.8	+	24356.9i	0.0772384	+	0.144895i
$411$	47411.9	−	47411.9i	0.280675	−	0.280675i
$412$		−	192958.i		−	1.13676i
$413$	88805.3			0.520641
$414$	11197.0	−	11197.0i	0.0653285	−	0.0653285i
$415$	168130.	+	51208.8i	0.976225	+	0.297336i
$416$	−70105.7	−	47403.2i	−0.405104	−	0.273918i
$417$		−	18399.3i		−	0.105810i
$418$	−983.576	+	983.576i	−0.00562932	+	0.00562932i
$419$	54894.4			0.312680			0.156340	−	0.987703i	$-0.450030\pi$
$419$	54894.4			0.312680			0.156340	+	0.987703i	$0.450030\pi$
$420$	21828.0	−	71666.5i	0.123742	−	0.406273i
$421$	66684.3	+	66684.3i	0.376235	+	0.376235i	0.869742	−	0.493507i	$-0.164285\pi$
$421$	66684.3	+	66684.3i	0.376235	+	0.376235i	−0.493507	+	0.869742i	$0.664285\pi$
$422$	−24715.3	+	24715.3i	−0.138784	+	0.138784i
$423$	−49602.1	−	49602.1i	−0.277216	−	0.277216i
$424$	−40277.9	+	40277.9i	−0.224045	+	0.224045i
$425$	−145108.	+	216114.i	−0.803368	+	1.19648i
$426$			7272.41i			0.0400737i
$427$	199841.	+	199841.i	1.09604	+	1.09604i
$428$	295504.			1.61315
$429$	12622.6	−	18667.9i	0.0685859	−	0.101433i
$430$	−9028.96	−	2750.02i	−0.0488316	−	0.0148730i
$431$	−208525.	−	208525.i	−1.12254	−	1.12254i	−0.991358	−	0.131187i	$-0.958121\pi$
$431$	−208525.	−	208525.i	−1.12254	−	1.12254i	−0.131187	−	0.991358i	$-0.541879\pi$
$432$			95305.9i			0.510684i
$433$	66262.9			0.353423			0.176712	−	0.984263i	$-0.443454\pi$
$433$	66262.9			0.353423			0.176712	+	0.984263i	$0.443454\pi$
$434$	5929.81	+	5929.81i	0.0314819	+	0.0314819i
$435$	62191.4	−	33152.0i	0.328664	−	0.175199i
$436$	72865.5	−	72865.5i	0.383309	−	0.383309i
$437$	−9001.55	−	9001.55i	−0.0471362	−	0.0471362i
$438$		−	7195.86i		−	0.0375089i
$439$		−	9461.70i		−	0.0490953i	−0.999699	−	0.0245477i	$-0.992185\pi$
$439$		−	9461.70i		−	0.0490953i	0.999699	−	0.0245477i	$-0.00781455\pi$
$440$	−12775.8	−	23966.8i	−0.0659908	−	0.123795i
$441$			222312.i			1.14310i
$442$	39521.5	+	26723.1i	0.202297	+	0.136786i
$443$			176515.i			0.899442i	0.893169	+	0.449721i	$0.148477\pi$
$443$			176515.i			0.899442i	−0.893169	+	0.449721i	$0.851523\pi$
$444$	−46668.9	−	46668.9i	−0.236735	−	0.236735i
$445$	−114178.	−	34776.0i	−0.576583	−	0.175614i
$446$		−	20935.3i		−	0.105247i
$447$	−70781.4	+	70781.4i	−0.354245	+	0.354245i
$448$	177050.	−	177050.i	0.882145	−	0.882145i
$449$	−72764.6	+	72764.6i	−0.360934	+	0.360934i	−0.864157	−	0.503223i	$-0.832147\pi$
$449$	−72764.6	+	72764.6i	−0.360934	+	0.360934i	0.503223	+	0.864157i	$0.332147\pi$
$450$	6055.73	+	30806.8i	0.0299048	+	0.152133i
$451$	−82777.5			−0.406967
$452$	−33166.3			−0.162338
$453$	−69137.6	−	69137.6i	−0.336913	−	0.336913i
$454$			20892.5i			0.101363i
$455$	308785.	+	32480.9i	1.49154	+	0.156894i
$456$	−2265.33			−0.0108944
$457$	−170622.	+	170622.i	−0.816962	+	0.816962i	−0.985667	−	0.168705i	$-0.946042\pi$
$457$	−170622.	+	170622.i	−0.816962	+	0.816962i	0.168705	+	0.985667i	$0.446042\pi$
$458$		−	22494.0i		−	0.107235i
$459$		−	169519.i		−	0.804626i
$460$	108073.	−	57609.8i	0.510742	−	0.272258i
$461$	−98289.4	−	98289.4i	−0.462493	−	0.462493i	0.436979	−	0.899472i	$-0.356048\pi$
$461$	−98289.4	−	98289.4i	−0.462493	−	0.462493i	−0.899472	+	0.436979i	$0.856048\pi$
$462$	−4696.42	−	4696.42i	−0.0220030	−	0.0220030i
$463$	−3551.65	−	3551.65i	−0.0165679	−	0.0165679i	0.698774	−	0.715342i	$-0.253729\pi$
$463$	−3551.65	−	3551.65i	−0.0165679	−	0.0165679i	−0.715342	+	0.698774i	$0.753729\pi$
$464$	251570.			1.16848
$465$	−10565.1	−	3217.88i	−0.0488615	−	0.0148821i
$466$	−14414.6	+	14414.6i	−0.0663790	+	0.0663790i
$467$	5559.97			0.0254940			0.0127470	−	0.999919i	$-0.495942\pi$
$467$	5559.97			0.0254940			0.0127470	+	0.999919i	$0.495942\pi$
$468$	−191119.	+	36923.8i	−0.872592	+	0.168583i
$469$	542872.			2.46804
$470$	7544.19	+	14152.5i	0.0341521	+	0.0640676i
$471$	92328.0			0.416190
$472$	25833.5			0.115958
$473$	20015.6	−	20015.6i	0.0894634	−	0.0894634i
$474$	6875.74	+	6875.74i	0.0306029	+	0.0306029i
$475$	24766.3	−	4868.34i	0.109768	−	0.0215771i
$476$	−336345.	+	336345.i	−1.48447	+	1.48447i
$477$			197480.i			0.867935i
$478$	−37405.2			−0.163711
$479$	−272904.	+	272904.i	−1.18943	+	1.18943i	−0.212203	+	0.977226i	$0.568064\pi$
$479$	−272904.	+	272904.i	−1.18943	+	1.18943i	−0.977226	+	0.212203i	$0.931936\pi$
$480$	9570.92	−	31423.6i	0.0415405	−	0.136387i
$481$	153215.	−	226594.i	0.662235	−	0.979395i
$482$		−	54072.7i		−	0.232747i
$483$	42980.9	−	42980.9i	0.184239	−	0.184239i
$484$	−187397.			−0.799968
$485$	−123984.	−	37762.7i	−0.527086	−	0.160539i
$486$	−22007.0	−	22007.0i	−0.0931728	−	0.0931728i
$487$	−973.959	+	973.959i	−0.00410660	+	0.00410660i	−0.709157	−	0.705050i	$-0.750924\pi$
$487$	−973.959	+	973.959i	−0.00410660	+	0.00410660i	0.705050	+	0.709157i	$0.250924\pi$
$488$	58133.8	+	58133.8i	0.244112	+	0.244112i
$489$	−66165.1	+	66165.1i	−0.276701	+	0.276701i
$490$	14809.0	−	48621.3i	0.0616783	−	0.202504i
$491$		−	93124.1i		−	0.386277i	−0.981171	−	0.193139i	$-0.938133\pi$
$491$		−	93124.1i		−	0.386277i	0.981171	−	0.193139i	$-0.0618667\pi$
$492$	−46968.2	−	46968.2i	−0.194032	−	0.194032i
$493$	−447464.			−1.84105
$494$	−877.487	−	4541.90i	−0.00359573	−	0.0186116i
$495$	−90073.5	−	27434.4i	−0.367609	−	0.111966i
$496$	−27876.6	−	27876.6i	−0.113312	−	0.113312i
$497$		−	300504.i		−	1.21657i
$498$	12503.1			0.0504149
$499$	−241247.	−	241247.i	−0.968859	−	0.968859i	0.0306701	−	0.999530i	$-0.490236\pi$
$499$	−241247.	−	241247.i	−0.968859	−	0.968859i	−0.999530	+	0.0306701i	$0.990236\pi$
$500$	−24617.4	+	241571.i	−0.0984697	+	0.966283i
$501$	30437.1	−	30437.1i	0.121263	−	0.121263i
$502$	−7517.93	−	7517.93i	−0.0298326	−	0.0298326i
$503$		−	266332.i		−	1.05266i	−0.850280	−	0.526330i	$-0.823568\pi$
$503$		−	266332.i		−	1.05266i	0.850280	−	0.526330i	$-0.176432\pi$
$504$			116436.i			0.458382i
$505$	−152798.	+	81450.9i	−0.599148	+	0.319384i
$506$		−	10857.4i		−	0.0424059i
$507$	27915.5	+	69549.0i	0.108600	+	0.270567i
$508$		−	493833.i		−	1.91361i
$509$	−161947.	−	161947.i	−0.625082	−	0.625082i	0.321745	−	0.946826i	$-0.395731\pi$
$509$	−161947.	−	161947.i	−0.625082	−	0.625082i	−0.946826	+	0.321745i	$0.895731\pi$
$510$	−5395.52	+	17714.8i	−0.0207440	+	0.0681076i
$511$			297341.i			1.13871i
$512$	139548.	−	139548.i	0.532333	−	0.532333i
$513$	−11622.7	+	11622.7i	−0.0441643	+	0.0441643i
$514$	39640.1	−	39640.1i	0.150040	−	0.150040i
$515$	146017.	+	273921.i	0.550541	+	1.03279i
$516$	22713.8			0.0853080
$517$	−48097.7			−0.179946
$518$	−57005.9	−	57005.9i	−0.212452	−	0.212452i
$519$			26188.6i			0.0972249i
$520$	89825.8	+	9448.72i	0.332196	+	0.0349435i
$521$	411981.			1.51775			0.758877	−	0.651234i	$-0.225748\pi$
$521$	411981.			1.51775			0.758877	+	0.651234i	$0.225748\pi$
$522$	−38162.0	+	38162.0i	−0.140052	+	0.140052i
$523$		−	332890.i		−	1.21702i	−0.793547	−	0.608509i	$-0.791768\pi$
$523$		−	332890.i		−	1.21702i	0.793547	−	0.608509i	$-0.208232\pi$
$524$		−	470695.i		−	1.71426i
$525$	23245.5	+	118255.i	0.0843374	+	0.429044i
$526$	4736.41	+	4736.41i	0.0171190	+	0.0171190i
$527$	49583.8	+	49583.8i	0.178533	+	0.178533i
$528$	22078.3	+	22078.3i	0.0791951	+	0.0791951i
$529$	−180475.			−0.644921
$530$	13154.9	−	43190.5i	0.0468311	−	0.153758i
$531$	63330.1	−	63330.1i	0.224606	−	0.224606i
$532$	46121.3			0.162959
$533$	154198.	−	228047.i	0.542780	−	0.802731i
$534$	−8490.88			−0.0297763
$535$	−419495.	+	223617.i	−1.46561	+	0.781264i
$536$	157922.			0.549683
$537$	99433.6			0.344814
$538$	−26643.1	+	26643.1i	−0.0920492	+	0.0920492i
$539$	107785.	+	107785.i	0.371004	+	0.371004i
$540$	−74384.9	−	139542.i	−0.255092	−	0.478540i
$541$	−343982.	+	343982.i	−1.17528	+	1.17528i	−0.194346	+	0.980933i	$0.562259\pi$
$541$	−343982.	+	343982.i	−1.17528	+	1.17528i	−0.980933	+	0.194346i	$0.937741\pi$
$542$			78924.1i			0.268665i
$543$	−81406.9			−0.276097
$544$	−147477.	+	147477.i	−0.498340	+	0.498340i
$545$	−48299.5	+	158579.i	−0.162611	+	0.533890i
$546$	21686.8	−	4189.86i	0.0727462	−	0.0140544i
$547$		−	121676.i		−	0.406659i	−0.979110	−	0.203329i	$-0.934824\pi$
$547$		−	121676.i		−	0.406659i	0.979110	−	0.203329i	$-0.0651762\pi$
$548$	−280803.	+	280803.i	−0.935063	+	0.935063i
$549$	285027.			0.945673
$550$	17872.3	+	12000.2i	0.0590819	+	0.0396701i
$551$	30679.3	+	30679.3i	0.101051	+	0.101051i
$552$	12503.2	−	12503.2i	0.0410339	−	0.0410339i
$553$	−284113.	−	284113.i	−0.929055	−	0.929055i
$554$	52614.4	−	52614.4i	0.171429	−	0.171429i
$555$	101567.	+	30934.9i	0.329735	+	0.100430i
$556$			108972.i			0.352505i
$557$	−158646.	−	158646.i	−0.511351	−	0.511351i	0.403590	−	0.914940i	$-0.367762\pi$
$557$	−158646.	−	158646.i	−0.511351	−	0.511351i	−0.914940	+	0.403590i	$0.867762\pi$
$558$	8457.51			0.0271628
$559$	17856.7	+	92426.6i	0.0571448	+	0.295783i
$560$	−125345.	+	411536.i	−0.399696	+	1.31230i
$561$	−39270.4	−	39270.4i	−0.124779	−	0.124779i
$562$		−	22832.2i		−	0.0722895i
$563$	114113.			0.360012			0.180006	−	0.983666i	$-0.442388\pi$
$563$	114113.			0.360012			0.180006	+	0.983666i	$0.442388\pi$
$564$	−27290.7	−	27290.7i	−0.0857940	−	0.0857940i
$565$	47082.5	−	25098.0i	0.147490	−	0.0786216i
$566$	−8254.46	+	8254.46i	−0.0257665	+	0.0257665i
$567$	256461.	+	256461.i	0.797728	+	0.797728i
$568$		−	87416.8i		−	0.270956i
$569$			227763.i			0.703492i	0.936095	+	0.351746i	$0.114412\pi$
$569$			227763.i			0.703492i	−0.936095	+	0.351746i	$0.885588\pi$
$570$	1584.50	−	844.639i	0.00487689	−	0.00259969i
$571$		−	78397.6i		−	0.240453i	−0.992746	−	0.120227i	$-0.961638\pi$
$571$		−	78397.6i		−	0.240453i	0.992746	−	0.120227i	$-0.0383621\pi$
$572$	−74759.1	+	110563.i	−0.228492	+	0.337923i
$573$		−	152484.i		−	0.464423i
$574$	−57371.4	−	57371.4i	−0.174129	−	0.174129i
$575$	−109824.	+	163565.i	−0.332172	+	0.494713i
$576$		−	252521.i		−	0.761119i
$577$	−366805.	+	366805.i	−1.10175	+	1.10175i	−0.107553	+	0.994199i	$0.534302\pi$
$577$	−366805.	+	366805.i	−1.10175	+	1.10175i	−0.994199	+	0.107553i	$0.965698\pi$
$578$	43109.8	−	43109.8i	0.129039	−	0.129039i
$579$	−32730.9	+	32730.9i	−0.0976339	+	0.0976339i
$580$	−368337.	+	196347.i	−1.09494	+	0.583671i
$581$	−516642.			−1.53051
$582$	−9220.12			−0.0272201
$583$	95745.5	+	95745.5i	0.281696	+	0.281696i
$584$			86496.7i			0.253614i
$585$	243369.	−	197042.i	0.711137	−	0.575768i
$586$	105284.			0.306597
$587$	382935.	−	382935.i	1.11135	−	1.11135i	0.118377	−	0.992969i	$-0.462231\pi$
$587$	382935.	−	382935.i	1.11135	−	1.11135i	0.992969	−	0.118377i	$-0.0377692\pi$
$588$			122314.i			0.353772i
$589$		−	6799.19i		−	0.0195987i
$590$	−18069.4	+	9632.15i	−0.0519087	+	0.0276706i
$591$	−84754.5	−	84754.5i	−0.242654	−	0.242654i
$592$	267990.	+	267990.i	0.764673	+	0.764673i
$593$	42846.4	+	42846.4i	0.121844	+	0.121844i	0.765400	−	0.643555i	$-0.222541\pi$
$593$	42846.4	+	42846.4i	0.121844	+	0.121844i	−0.643555	+	0.765400i	$0.722541\pi$
$594$	−14019.0			−0.0397322
$595$	222949.	−	731994.i	0.629755	−	2.06763i
$596$	419212.	−	419212.i	1.18016	−	1.18016i
$597$	143358.			0.402229
$598$	29911.6	+	20225.2i	0.0836444	+	0.0565576i
$599$	529127.			1.47471			0.737354	−	0.675506i	$-0.236075\pi$
$599$	529127.			1.47471			0.737354	+	0.675506i	$0.236075\pi$
$600$	6762.13	+	34400.5i	0.0187837	+	0.0955569i
$601$	−137757.			−0.381387			−0.190694	−	0.981650i	$-0.561074\pi$
$601$	−137757.			−0.381387			−0.190694	+	0.981650i	$0.561074\pi$
$602$	27744.8			0.0765575
$603$	387141.	−	387141.i	1.06472	−	1.06472i
$604$	409476.	+	409476.i	1.12242	+	1.12242i
$605$	266027.	−	141809.i	0.726801	−	0.387431i
$606$	−8710.00	+	8710.00i	−0.0237177	+	0.0237177i
$607$			384287.i			1.04299i	0.853256	+	0.521493i	$0.174625\pi$
$607$			384287.i			1.04299i	−0.853256	+	0.521493i	$0.825375\pi$
$608$	20222.8			0.0547058
$609$	−146489.	+	146489.i	−0.394975	+	0.394975i
$610$	−62337.6	−	18986.6i	−0.167529	−	0.0510256i
$611$	89596.3	−	132506.i	0.239998	−	0.354939i
$612$			479718.i			1.28081i
$613$	271532.	−	271532.i	0.722602	−	0.722602i	−0.246532	−	0.969135i	$-0.579291\pi$
$613$	271532.	−	271532.i	0.722602	−	0.722602i	0.969135	+	0.246532i	$0.0792911\pi$
$614$	57786.7			0.153282
$615$	102218.	+	31133.3i	0.270257	+	0.0823142i
$616$	56452.5	+	56452.5i	0.148772	+	0.148772i
$617$	165999.	−	165999.i	0.436049	−	0.436049i	−0.454631	−	0.890680i	$-0.650229\pi$
$617$	165999.	−	165999.i	0.436049	−	0.436049i	0.890680	+	0.454631i	$0.150229\pi$
$618$	15614.4	+	15614.4i	0.0408836	+	0.0408836i
$619$	354544.	−	354544.i	0.925312	−	0.925312i	−0.0720860	−	0.997398i	$-0.522966\pi$
$619$	354544.	−	354544.i	0.925312	−	0.925312i	0.997398	+	0.0720860i	$0.0229656\pi$
$620$	62573.0	+	19058.3i	0.162781	+	0.0495794i
$621$		−	128300.i		−	0.332692i
$622$	2660.49	+	2660.49i	0.00687671	+	0.00687671i
$623$	350852.			0.903958
$624$	−101952.	+	19696.9i	−0.261834	+	0.0505859i
$625$	−147858.	−	361561.i	−0.378516	−	0.925595i
$626$	54331.6	+	54331.6i	0.138645	+	0.138645i
$627$			5384.96i			0.0136977i
$628$	−546824.			−1.38653
$629$	−476671.	−	476671.i	−1.20481	−	1.20481i
$630$	−43413.9	−	81442.3i	−0.109382	−	0.205196i
$631$	−15264.1	+	15264.1i	−0.0383366	+	0.0383366i	−0.726015	−	0.687679i	$-0.758630\pi$
$631$	−15264.1	+	15264.1i	−0.0383366	+	0.0383366i	0.687679	+	0.726015i	$0.258630\pi$
$632$	−82648.7	−	82648.7i	−0.206920	−	0.206920i
$633$			135313.i			0.337701i
$634$		−	14168.4i		−	0.0352486i
$635$	373699.	+	701041.i	0.926776	+	1.73858i
$636$			108652.i			0.268612i
$637$	−497721.	+	96158.8i	−1.22661	+	0.236979i
$638$			37004.6i			0.0909105i
$639$	−214300.	−	214300.i	−0.524832	−	0.524832i
$640$	−75182.0	+	246840.i	−0.183550	+	0.602637i
$641$			403493.i			0.982019i	0.871154	+	0.491009i	$0.163372\pi$
$641$			403493.i			0.982019i	−0.871154	+	0.491009i	$0.836628\pi$
$642$	−23912.7	+	23912.7i	−0.0580174	+	0.0580174i
$643$	−65395.4	+	65395.4i	−0.158170	+	0.158170i	−0.781756	−	0.623585i	$-0.785676\pi$
$643$	−65395.4	+	65395.4i	−0.158170	+	0.158170i	0.623585	+	0.781756i	$0.285676\pi$
$644$	−254560.	+	254560.i	−0.613788	+	0.613788i
$645$	−32244.2	+	17188.2i	−0.0775055	+	0.0413154i
$646$	−11400.4			−0.0273184
$647$	−709187.			−1.69415			−0.847076	−	0.531472i	$-0.821639\pi$
$647$	−709187.			−1.69415			−0.847076	+	0.531472i	$0.821639\pi$
$648$	74604.6	+	74604.6i	0.177671	+	0.177671i
$649$		−	61409.4i		−	0.145796i
$650$	−66352.3	+	26883.0i	−0.157047	+	0.0636284i
$651$	32465.0			0.0766043
$652$	391871.	−	391871.i	0.921825	−	0.921825i
$653$			390503.i			0.915794i	0.889005	+	0.457897i	$0.151397\pi$
$653$			390503.i			0.915794i	−0.889005	+	0.457897i	$0.848603\pi$
$654$			11792.8i			0.0275715i
$655$	356190.	+	668194.i	0.830230	+	1.55747i
$656$	269709.	+	269709.i	0.626740	+	0.626740i
$657$	212044.	+	212044.i	0.491242	+	0.491242i
$658$	−33335.5	−	33335.5i	−0.0769937	−	0.0769937i
$659$	−2969.87			−0.00683859			−0.00341930	−	0.999994i	$-0.501088\pi$
$659$	−2969.87			−0.00683859			−0.00341930	+	0.999994i	$0.501088\pi$
$660$	−49557.8	−	15094.2i	−0.113769	−	0.0346515i
$661$	107353.	−	107353.i	0.245703	−	0.245703i	−0.573502	−	0.819204i	$-0.694415\pi$
$661$	107353.	−	107353.i	0.245703	−	0.245703i	0.819204	+	0.573502i	$0.194415\pi$
$662$	52812.8			0.120510
$663$	181341.	−	35034.7i	0.412542	−	0.0797024i
$664$	−150291.			−0.340877
$665$	−65473.3	+	34901.4i	−0.148054	+	0.0789223i
$666$	−81305.7			−0.183304
$667$	−338660.			−0.761225
$668$	−180268.	+	180268.i	−0.403984	+	0.403984i
$669$	−57309.2	−	57309.2i	−0.128048	−	0.128048i
$670$	−110459.	+	58881.9i	−0.246067	+	0.131169i
$671$	138191.	−	138191.i	0.306927	−	0.306927i
$672$			96560.4i			0.213826i
$673$	190638.			0.420901			0.210451	−	0.977604i	$-0.432507\pi$
$673$	190638.			0.420901			0.210451	+	0.977604i	$0.432507\pi$
$674$	19687.2	−	19687.2i	0.0433376	−	0.0433376i
$675$	211192.	+	141804.i	0.463522	+	0.311229i
$676$	−165333.	−	411913.i	−0.361798	−	0.901389i
$677$		−	283530.i		−	0.618617i	−0.950962	−	0.309308i	$-0.899903\pi$
$677$		−	283530.i		−	0.618617i	0.950962	−	0.309308i	$-0.100097\pi$
$678$	2683.87	−	2683.87i	0.00583851	−	0.00583851i
$679$	380985.			0.826359
$680$	64856.0	−	212938.i	0.140260	−	0.460505i
$681$	57191.9	+	57191.9i	0.123322	+	0.123322i
$682$	4100.50	−	4100.50i	0.00881593	−	0.00881593i
$683$	−137747.	−	137747.i	−0.295285	−	0.295285i	0.543879	−	0.839164i	$-0.316955\pi$
$683$	−137747.	−	137747.i	−0.295285	−	0.295285i	−0.839164	+	0.543879i	$0.816955\pi$
$684$	32890.7	−	32890.7i	0.0703009	−	0.0703009i
$685$	186133.	−	611118.i	0.396682	−	1.30240i
$686$			29813.7i			0.0633531i
$687$	−61575.9	−	61575.9i	−0.130466	−	0.130466i
$688$	−130431.			−0.275552
$689$	−442127.	+	85418.3i	−0.931342	+	0.179934i
$690$	−4083.57	+	13407.3i	−0.00857712	+	0.0281607i
$691$	344843.	+	344843.i	0.722212	+	0.722212i	0.969055	−	0.246843i	$-0.0793933\pi$
$691$	344843.	+	344843.i	0.722212	+	0.722212i	−0.246843	+	0.969055i	$0.579393\pi$
$692$		−	155105.i		−	0.323903i
$693$	276783.			0.576333
$694$	−87292.7	−	87292.7i	−0.181242	−	0.181242i
$695$	−82462.7	−	154696.i	−0.170721	−	0.320265i
$696$	−42613.6	+	42613.6i	−0.0879691	+	0.0879691i
$697$	−479728.	−	479728.i	−0.987482	−	0.987482i
$698$			53188.4i			0.109171i
$699$			78918.2i			0.161519i
$700$	−137674.	−	700381.i	−0.280968	−	1.42935i
$701$			487268.i			0.991589i	0.868440	+	0.495795i	$0.165123\pi$
$701$			487268.i			0.991589i	−0.868440	+	0.495795i	$0.834877\pi$
$702$	26114.5	−	38621.4i	0.0529917	−	0.0783707i
$703$			65363.5i			0.132259i
$704$	−122431.	−	122431.i	−0.247028	−	0.247028i
$705$	59393.4	+	18089.9i	0.119498	+	0.0363964i
$706$			6985.86i			0.0140156i
$707$	359907.	−	359907.i	0.720031	−	0.720031i
$708$	34843.8	−	34843.8i	0.0695119	−	0.0695119i
$709$	−577672.	+	577672.i	−1.14918	+	1.14918i	−0.162468	+	0.986714i	$0.551945\pi$
$709$	−577672.	+	577672.i	−1.14918	+	1.14918i	−0.986714	+	0.162468i	$0.948055\pi$
$710$	32593.8	+	61144.3i	0.0646573	+	0.121294i
$711$	−405222.			−0.801593
$712$	102063.			0.201330
$713$	37527.2	+	37527.2i	0.0738188	+	0.0738188i
$714$		−	54435.1i		−	0.106778i
$715$	22460.8	−	213527.i	0.0439352	−	0.417677i
$716$	−588908.			−1.14874
$717$	−102395.	+	102395.i	−0.199177	+	0.199177i
$718$		−	40555.5i		−	0.0786686i
$719$		−	96895.4i		−	0.187433i	−0.995599	−	0.0937163i	$-0.970125\pi$
$719$		−	96895.4i		−	0.187433i	0.995599	−	0.0937163i	$-0.0298747\pi$
$720$	204093.	+	382868.i	0.393698	+	0.738558i
$721$	−645206.	−	645206.i	−1.24116	−	1.24116i
$722$	−61677.1	−	61677.1i	−0.118318	−	0.118318i
$723$	−148021.	−	148021.i	−0.283169	−	0.283169i
$724$	482143.			0.919811
$725$	374306.	−	557464.i	0.712115	−	1.06057i
$726$	15164.5	−	15164.5i	0.0287710	−	0.0287710i
$727$	−95621.8			−0.180921			−0.0904603	−	0.995900i	$-0.528834\pi$
$727$	−95621.8			−0.180921			−0.0904603	+	0.995900i	$0.528834\pi$
$728$	−260683.	+	50363.5i	−0.491869	+	0.0950283i
$729$	279277.			0.525508
$730$	−32250.7	−	60500.7i	−0.0605193	−	0.113531i
$731$	231996.			0.434156
$732$	156820.			0.292670
$733$	−306759.	+	306759.i	−0.570939	+	0.570939i	−0.932391	−	0.361452i	$-0.882281\pi$
$733$	−306759.	+	306759.i	−0.570939	+	0.570939i	0.361452	+	0.932391i	$0.382281\pi$
$734$	89609.9	+	89609.9i	0.166327	+	0.166327i
$735$	−92559.2	−	173636.i	−0.171335	−	0.321415i
$736$	−111617.	+	111617.i	−0.206051	+	0.206051i
$737$		−	375399.i		−	0.691127i
$738$	−81827.1			−0.150240
$739$	−580950.	+	580950.i	−1.06377	+	1.06377i	−0.0659518	+	0.997823i	$0.521008\pi$
$739$	−580950.	+	580950.i	−1.06377	+	1.06377i	−0.997823	+	0.0659518i	$0.978992\pi$
$740$	−601541.	−	183216.i	−1.09850	−	0.334580i
$741$	−14835.2	−	10031.1i	−0.0270183	−	0.0182689i
$742$			132718.i			0.241059i
$743$	−371231.	+	371231.i	−0.672461	+	0.672461i	−0.958283	−	0.285822i	$-0.907733\pi$
$743$	−371231.	+	371231.i	−0.672461	+	0.672461i	0.285822	+	0.958283i	$0.407733\pi$
$744$	9444.09			0.0170614
$745$	−277879.	+	912341.i	−0.500660	+	1.64378i
$746$	123560.	+	123560.i	0.222025	+	0.222025i
$747$	−368435.	+	368435.i	−0.660267	+	0.660267i
$748$	232584.	+	232584.i	0.415697	+	0.415697i
$749$	988097.	−	988097.i	1.76131	−	1.76131i
$750$	−17556.2	−	21540.4i	−0.0312111	−	0.0382940i
$751$		−	66652.5i		−	0.118178i	−0.998253	−	0.0590890i	$-0.981180\pi$
$751$		−	66652.5i		−	0.118178i	0.998253	−	0.0590890i	$-0.0188196\pi$
$752$	156714.	+	156714.i	0.277122	+	0.277122i
$753$	−41159.7			−0.0725910
$754$	−101945.	−	68932.0i	−0.179318	−	0.121249i
$755$	−891152.	−	271425.i	−1.56336	−	0.476163i
$756$	328684.	+	328684.i	0.575090	+	0.575090i
$757$		−	405707.i		−	0.707980i	−0.935249	−	0.353990i	$-0.884825\pi$
$757$		−	405707.i		−	0.707980i	0.935249	−	0.353990i	$-0.115175\pi$
$758$	−55668.7			−0.0968886
$759$	−29721.6	−	29721.6i	−0.0515927	−	0.0515927i
$760$	−19046.2	+	10152.8i	−0.0329748	+	0.0175776i
$761$	496089.	−	496089.i	0.856624	−	0.856624i	−0.134315	−	0.990939i	$-0.542883\pi$
$761$	496089.	−	496089.i	0.856624	−	0.856624i	0.990939	+	0.134315i	$0.0428834\pi$
$762$	39961.8	+	39961.8i	0.0688232	+	0.0688232i
$763$		−	487290.i		−	0.837026i
$764$			903103.i			1.54722i
$765$	−363018.	−	681003.i	−0.620305	−	1.16366i
$766$			48990.4i			0.0834936i
$767$	169179.	+	114393.i	0.287578	+	0.194451i
$768$		−	124686.i		−	0.211395i
$769$	353439.	+	353439.i	0.597671	+	0.597671i	0.939692	−	0.342022i	$-0.111112\pi$
$769$	353439.	+	353439.i	0.597671	+	0.597671i	−0.342022	+	0.939692i	$0.611112\pi$
$770$	−60534.7	−	18437.5i	−0.102099	−	0.0310972i
$771$		−	217024.i		−	0.365090i
$772$	193853.	−	193853.i	0.325265	−	0.325265i
$773$	−714038.	+	714038.i	−1.19498	+	1.19498i	−0.219335	+	0.975650i	$0.570389\pi$
$773$	−714038.	+	714038.i	−1.19498	+	1.19498i	−0.975650	+	0.219335i	$0.929611\pi$
$774$	19785.8	−	19785.8i	0.0330271	−	0.0330271i
$775$	−103250.	+	20295.9i	−0.171904	+	0.0337914i
$776$	110829.			0.184047
$777$	−312100.			−0.516954
$778$	77847.8	+	77847.8i	0.128614	+	0.128614i
$779$			65782.7i			0.108402i
$780$	133900.	−	108411.i	0.220085	−	0.178191i
$781$	−207800.			−0.340678
$782$	62923.0	−	62923.0i	0.102895	−	0.102895i
$783$			437274.i			0.713230i
$784$		−	702375.i		−	1.14271i
$785$	776267.	−	413799.i	1.25971	−	0.671507i
$786$	38089.4	+	38089.4i	0.0616536	+	0.0616536i
$787$	546646.	+	546646.i	0.882585	+	0.882585i	0.993797	−	0.111212i	$-0.0354733\pi$
$787$	546646.	+	546646.i	0.882585	+	0.882585i	−0.111212	+	0.993797i	$0.535473\pi$
$788$	501970.	+	501970.i	0.808398	+	0.808398i
$789$	25931.2			0.0416552
$790$	88625.2	+	26993.3i	0.142005	+	0.0432515i
$791$	−110900.	+	110900.i	−0.177247	+	0.177247i
$792$	80516.5			0.128361
$793$	123286.	+	638130.i	0.196050	+	1.01476i
$794$	−19981.4			−0.0316946
$795$	−82220.8	−	154242.i	−0.130091	−	0.244044i
$796$	−849056.			−1.34002
$797$	439943.			0.692596			0.346298	−	0.938125i	$-0.387439\pi$
$797$	439943.			0.692596			0.346298	+	0.938125i	$0.387439\pi$
$798$	−3732.21	+	3732.21i	−0.00586084	+	0.00586084i
$799$	−278744.	−	278744.i	−0.436629	−	0.436629i
$800$	−60366.1	−	307096.i	−0.0943220	−	0.479837i
$801$	250205.	−	250205.i	0.389970	−	0.389970i
$802$		−	116280.i		−	0.180783i
$803$	205613.			0.318874
$804$	213002.	−	213002.i	0.329513	−	0.329513i
$805$	168737.	−	554005.i	0.260387	−	0.854913i
$806$	3658.22	+	18935.0i	0.00563118	+	0.0291471i
$807$			145868.i			0.223981i
$808$	104697.	−	104697.i	0.160366	−	0.160366i
$809$	161836.			0.247273			0.123637	−	0.992328i	$-0.460544\pi$
$809$	161836.			0.247273			0.123637	+	0.992328i	$0.460544\pi$
$810$	−79999.4	−	24366.0i	−0.121932	−	0.0371377i
$811$	−128433.	−	128433.i	−0.195270	−	0.195270i	0.602699	−	0.797969i	$-0.294092\pi$
$811$	−128433.	−	128433.i	−0.195270	−	0.195270i	−0.797969	+	0.602699i	$0.794092\pi$
$812$	867597.	−	867597.i	1.31585	−	1.31585i
$813$	216050.	+	216050.i	0.326868	+	0.326868i
$814$	−39419.9	+	39419.9i	−0.0594931	+	0.0594931i
$815$	−259755.	+	852838.i	−0.391065	+	1.28396i
$816$			255905.i			0.384325i
$817$	−15906.2	−	15906.2i	−0.0238299	−	0.0238299i
$818$	109345.			0.163415
$819$	−515592.	+	762521.i	−0.768667	+	1.13680i
$820$	−605399.	−	184391.i	−0.900355	−	0.274228i
$821$	528675.	+	528675.i	0.784337	+	0.784337i	0.980559	−	0.196222i	$-0.0628674\pi$
$821$	528675.	+	528675.i	0.784337	+	0.784337i	−0.196222	+	0.980559i	$0.562867\pi$
$822$		−	45446.1i		−	0.0672594i
$823$	966486.			1.42691			0.713454	−	0.700702i	$-0.247130\pi$
$823$	966486.			1.42691			0.713454	+	0.700702i	$0.247130\pi$
$824$	−187691.	−	187691.i	−0.276432	−	0.276432i
$825$	81774.1	−	16074.4i	0.120146	−	0.0236171i
$826$	42561.6	−	42561.6i	0.0623817	−	0.0623817i
$827$	−410946.	−	410946.i	−0.600861	−	0.600861i	0.339680	−	0.940541i	$-0.389681\pi$
$827$	−410946.	−	410946.i	−0.600861	−	0.600861i	−0.940541	+	0.339680i	$0.889681\pi$
$828$			363071.i			0.529580i
$829$			825127.i			1.20064i	0.799761	+	0.600319i	$0.204960\pi$
$829$			825127.i			1.20064i	−0.799761	+	0.600319i	$0.795040\pi$
$830$	105122.	−	56036.9i	0.152595	−	0.0813425i
$831$		−	288057.i		−	0.417135i
$832$	565354.	−	109226.i	0.816722	−	0.157789i
$833$			1.24931e6i			1.80044i
$834$	−8818.20	−	8818.20i	−0.0126779	−	0.0126779i
$835$	119492.	−	392320.i	0.171382	−	0.562688i
$836$		−	31893.1i		−	0.0456336i
$837$	48454.6	−	48454.6i	0.0691646	−	0.0691646i
$838$	26309.2	−	26309.2i	0.0374644	−	0.0374644i
$839$	455609.	−	455609.i	0.647245	−	0.647245i	−0.305082	−	0.952326i	$-0.598684\pi$
$839$	455609.	−	455609.i	0.647245	−	0.647245i	0.952326	+	0.305082i	$0.0986837\pi$
$840$	−48478.2	−	90942.6i	−0.0687049	−	0.128887i
$841$	446949.			0.631926
$842$	63919.4			0.0901589
$843$	−62501.7	−	62501.7i	−0.0879502	−	0.0879502i
$844$		−	801410.i		−	1.12504i
$845$	546413.	+	459635.i	0.765257	+	0.643724i
$846$	−47545.4			−0.0664306
$847$	−626613.	+	626613.i	−0.873439	+	0.873439i
$848$		−	623923.i		−	0.867640i
$849$			45192.1i			0.0626971i
$850$	34030.8	+	173123.i	0.0471015	+	0.239616i
$851$	−360765.	−	360765.i	−0.498156	−	0.498156i
$852$	−117906.	−	117906.i	−0.162427	−	0.162427i
$853$	381778.	+	381778.i	0.524702	+	0.524702i	0.918988	−	0.394286i	$-0.129008\pi$
$853$	381778.	+	381778.i	0.524702	+	0.524702i	−0.394286	+	0.918988i	$0.629008\pi$
$854$	191555.			0.262650
$855$	−21801.9	+	71580.7i	−0.0298237	+	0.0979183i
$856$	287438.	−	287438.i	0.392281	−	0.392281i
$857$	−605829.			−0.824876			−0.412438	−	0.910986i	$-0.635323\pi$
$857$	−605829.			−0.824876			−0.412438	+	0.910986i	$0.635323\pi$
$858$	−2897.31	−	14996.6i	−0.00393569	−	0.0203712i
$859$	468066.			0.634338			0.317169	−	0.948369i	$-0.397268\pi$
$859$	468066.			0.634338			0.317169	+	0.948369i	$0.397268\pi$
$860$	190971.	−	101799.i	0.258208	−	0.137641i
$861$	−314101.			−0.423705
$862$	−199879.			−0.269000
$863$	−465007.	+	465007.i	−0.624364	+	0.624364i	−0.946644	−	0.322280i	$-0.895551\pi$
$863$	−465007.	+	465007.i	−0.624364	+	0.624364i	0.322280	+	0.946644i	$0.395551\pi$
$864$	144118.	+	144118.i	0.193059	+	0.193059i
$865$	117373.	+	220186.i	0.156869	+	0.294278i
$866$	31757.7	−	31757.7i	0.0423461	−	0.0423461i
$867$		−	236021.i		−	0.313987i
$868$	−192278.			−0.255206
$869$	−196466.	+	196466.i	−0.260164	+	0.260164i
$870$	13917.7	−	45695.1i	0.0183878	−	0.0603714i
$871$	1.03420e6	+	699293.i	1.36323	+	0.921770i
$872$		−	141753.i		−	0.186423i
$873$	271694.	−	271694.i	0.356493	−	0.356493i
$874$	−8628.32			−0.0112954
$875$	725442.	+	890072.i	0.947516	+	1.16254i
$876$	116665.	+	116665.i	0.152032	+	0.152032i
$877$	−545086.	+	545086.i	−0.708706	+	0.708706i	−0.966263	−	0.257557i	$-0.917082\pi$
$877$	−545086.	+	545086.i	−0.708706	+	0.708706i	0.257557	+	0.966263i	$0.417082\pi$
$878$	−4534.69	−	4534.69i	−0.00588246	−	0.00588246i
$879$	288209.	−	288209.i	0.373018	−	0.373018i
$880$	284580.	+	86676.6i	0.367484	+	0.111927i
$881$		−	24667.2i		−	0.0317810i	−0.999874	−	0.0158905i	$-0.994942\pi$
$881$		−	24667.2i		−	0.0317810i	0.999874	−	0.0158905i	$-0.00505831\pi$
$882$	106547.	+	106547.i	0.136963	+	0.136963i
$883$	17866.0			0.0229143			0.0114571	−	0.999934i	$-0.496353\pi$
$883$	17866.0			0.0229143			0.0114571	+	0.999934i	$0.496353\pi$
$884$	−1.07401e6	+	207497.i	−1.37437	+	0.265527i
$885$	−23096.5	+	75831.4i	−0.0294890	+	0.0968194i
$886$	84597.9	+	84597.9i	0.107769	+	0.107769i
$887$			773614.i			0.983280i	0.870799	+	0.491640i	$0.163602\pi$
$887$			773614.i			0.983280i	−0.870799	+	0.491640i	$0.836398\pi$
$888$	−90790.1			−0.115136
$889$	−1.65126e6	−	1.65126e6i	−2.08936	−	2.08936i
$890$	−71388.8	+	38054.8i	−0.0901260	+	0.0480429i
$891$	177344.	−	177344.i	0.223389	−	0.223389i
$892$	339421.	+	339421.i	0.426589	+	0.426589i
$893$			38222.8i			0.0479314i
$894$			67846.6i			0.0848894i
$895$	836009.	−	445646.i	1.04367	−	0.556344i
$896$		−	758506.i		−	0.944807i
$897$	137246.	−	26515.8i	0.170575	−	0.0329549i
$898$			69747.6i			0.0864921i
$899$	−127901.	−	127901.i	−0.158254	−	0.158254i
$900$	−597647.	−	401286.i	−0.737836	−	0.495415i
$901$			1.10976e6i			1.36704i
$902$	−39672.7	+	39672.7i	−0.0487616	+	0.0487616i
$903$	75949.6	−	75949.6i	0.0931429	−	0.0931429i
$904$	−32261.0	+	32261.0i	−0.0394767	+	0.0394767i
$905$	−684446.	+	364853.i	−0.835683	+	0.445472i
$906$	−66270.9			−0.0807359
$907$	888296.			1.07980			0.539900	−	0.841729i	$-0.318462\pi$
$907$	888296.			1.07980			0.539900	+	0.841729i	$0.318462\pi$
$908$	−338726.	−	338726.i	−0.410844	−	0.410844i
$909$		−	513324.i		−	0.621247i
$910$	163558.	−	132424.i	0.197510	−	0.159913i
$911$	−1.43510e6			−1.72920			−0.864599	−	0.502463i	$-0.832427\pi$
$911$	−1.43510e6			−1.72920			−0.864599	+	0.502463i	$0.832427\pi$
$912$	17545.5	−	17545.5i	0.0210948	−	0.0210948i
$913$			357261.i			0.428592i
$914$			163547.i			0.195772i
$915$	−222620.	+	118671.i	−0.265902	+	0.141743i
$916$	364691.	+	364691.i	0.434645	+	0.434645i
$917$	−1.57389e6	−	1.57389e6i	−1.87170	−	1.87170i
$918$	−81245.3	−	81245.3i	−0.0964080	−	0.0964080i
$919$	1.42685e6			1.68946			0.844730	−	0.535192i	$-0.179761\pi$
$919$	1.42685e6			1.68946			0.844730	+	0.535192i	$0.179761\pi$
$920$	49085.8	−	161160.i	0.0579937	−	0.190407i
$921$	158187.	−	158187.i	0.186489	−	0.186489i
$922$	−94214.0			−0.110829
$923$	387090.	−	572476.i	0.454369	−	0.671977i
$924$	152284.			0.178366
$925$	992588.	−	195114.i	1.16007	−	0.228036i
$926$	−3404.39			−0.00397024
$927$	−920237.			−1.07088
$928$	380415.	−	380415.i	0.441735	−	0.441735i
$929$	−38299.7	−	38299.7i	−0.0443777	−	0.0443777i	0.684570	−	0.728947i	$-0.259990\pi$
$929$	−38299.7	−	38299.7i	−0.0443777	−	0.0443777i	−0.728947	+	0.684570i	$0.759990\pi$
$930$	−6605.74	+	3521.28i	−0.00763757	+	0.00407131i
$931$	85655.6	−	85655.6i	0.0988226	−	0.0988226i
$932$		−	467403.i		−	0.538096i
$933$	14565.8			0.0167329
$934$	2664.72	−	2664.72i	0.00305462	−	0.00305462i
$935$	−506178.	−	154171.i	−0.579002	−	0.176351i
$936$	−149986.	+	221818.i	−0.171198	+	0.253189i
$937$			263245.i			0.299834i	0.988699	+	0.149917i	$0.0479007\pi$
$937$			263245.i			0.299834i	−0.988699	+	0.149917i	$0.952099\pi$
$938$	260181.	−	260181.i	0.295713	−	0.295713i
$939$	297459.			0.337362
$940$	−351765.	−	107140.i	−0.398105	−	0.121254i
$941$	351385.	+	351385.i	0.396830	+	0.396830i	0.877113	−	0.480284i	$-0.159466\pi$
$941$	351385.	+	351385.i	0.396830	+	0.396830i	−0.480284	+	0.877113i	$0.659466\pi$
$942$	44249.9	−	44249.9i	0.0498667	−	0.0498667i
$943$	−363079.	−	363079.i	−0.408298	−	0.408298i
$944$	−200086.	+	200086.i	−0.224529	+	0.224529i
$945$	−715323.	−	217871.i	−0.801011	−	0.243970i
$946$		−	19185.7i		−	0.0214385i
$947$	−281368.	−	281368.i	−0.313744	−	0.313744i	0.532614	−	0.846358i	$-0.321210\pi$
$947$	−281368.	−	281368.i	−0.313744	−	0.313744i	−0.846358	+	0.532614i	$0.821210\pi$
$948$	−222951.			−0.248080
$949$	−383016.	+	566451.i	−0.425289	+	0.628970i
$950$	9536.48	−	14203.0i	0.0105667	−	0.0157374i
$951$	−38785.1	−	38785.1i	−0.0428849	−	0.0428849i
$952$			654328.i			0.721974i
$953$	−1.31753e6			−1.45069			−0.725344	−	0.688387i	$-0.758319\pi$
$953$	−1.31753e6			−1.45069			−0.725344	+	0.688387i	$0.758319\pi$
$954$	94646.2	+	94646.2i	0.103994	+	0.103994i
$955$	−683407.	−	1.28204e6i	−0.749329	−	1.40570i
$956$	606445.	−	606445.i	0.663553	−	0.663553i
$957$	101298.	+	101298.i	0.110605	+	0.110605i
$958$			261588.i			0.285028i
$959$			1.87788e6i			2.04188i
$960$	105137.	+	197231.i	0.114081	+	0.214010i
$961$		−	895175.i		−	0.969307i
$962$	−35168.0	−	182031.i	−0.0380012	−	0.196695i
$963$		−	1.40929e6i		−	1.51967i
$964$	876672.	+	876672.i	0.943372	+	0.943372i
$965$	−128497.	+	421886.i	−0.137987	+	0.453044i
$966$		−	41198.8i		−	0.0441500i
$967$	−471348.	+	471348.i	−0.504067	+	0.504067i	−0.912699	−	0.408632i	$-0.866006\pi$
$967$	−471348.	+	471348.i	−0.504067	+	0.504067i	0.408632	+	0.912699i	$0.366006\pi$
$968$	−182282.	+	182282.i	−0.194533	+	0.194533i
$969$	−31207.9	+	31207.9i	−0.0332367	+	0.0332367i
$970$	−77520.0	+	41323.1i	−0.0823893	+	0.0439187i
$971$	−764822.			−0.811189			−0.405594	−	0.914053i	$-0.632935\pi$
$971$	−764822.			−0.811189			−0.405594	+	0.914053i	$0.632935\pi$
$972$	713593.			0.755298
$973$	364378.	+	364378.i	0.384880	+	0.384880i
$974$			933.576i			0.000984083i
$975$	−108045.	+	255226.i	−0.113657	+	0.268482i
$976$	−900518.			−0.945351
$977$	54557.6	−	54557.6i	0.0571565	−	0.0571565i	−0.677951	−	0.735107i	$-0.737132\pi$
$977$	54557.6	−	54557.6i	0.0571565	−	0.0571565i	0.735107	+	0.677951i	$0.237132\pi$
$978$			63421.7i			0.0663071i
$979$		−	242617.i		−	0.253137i
$980$	548194.	+	1.02838e6i	0.570798	+	1.07079i
$981$	−347504.	−	347504.i	−0.361095	−	0.361095i
$982$	−44631.4	−	44631.4i	−0.0462826	−	0.0462826i
$983$	−1.14985e6	−	1.14985e6i	−1.18996	−	1.18996i	−0.977078	−	0.212883i	$-0.931715\pi$
$983$	−1.14985e6	−	1.14985e6i	−1.18996	−	1.18996i	−0.212883	−	0.977078i	$-0.568285\pi$
$984$	−91372.3			−0.0943679
$985$	−1.09245e6	−	332735.i	−1.12597	−	0.342946i
$986$	−214456.	+	214456.i	−0.220589	+	0.220589i
$987$	−182508.			−0.187347
$988$	87863.6	+	59410.5i	0.0900109	+	0.0608624i
$989$	175585.			0.179512
$990$	−56317.8	+	30021.0i	−0.0574613	+	0.0306305i
$991$	286562.			0.291791			0.145895	−	0.989300i	$-0.453394\pi$
$991$	286562.			0.291791			0.145895	+	0.989300i	$0.453394\pi$
$992$	−84308.1			−0.0856734
$993$	144572.	−	144572.i	0.146617	−	0.146617i
$994$	−144022.	−	144022.i	−0.145766	−	0.145766i
$995$	1.20531e6	−	642508.i	1.21746	−	0.648981i
$996$	−202711.	+	202711.i	−0.204342	+	0.204342i
$997$			746036.i			0.750532i	0.926917	+	0.375266i	$0.122449\pi$
$997$			746036.i			0.750532i	−0.926917	+	0.375266i	$0.877551\pi$
$998$	−231244.			−0.232172
$999$	−465815.	+	465815.i	−0.466748	+	0.466748i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.5.g.a.34.16	yes	52
5.4	even	2	inner	65.5.g.a.34.11	✓	52
13.5	odd	4	inner	65.5.g.a.44.11	yes	52
65.44	odd	4	inner	65.5.g.a.44.16	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.5.g.a.34.11	✓	52	5.4	even	2	inner
65.5.g.a.34.16	yes	52	1.1	even	1	trivial
65.5.g.a.44.11	yes	52	13.5	odd	4	inner
65.5.g.a.44.16	yes	52	65.44	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)

\(f(q)\)	\(=\)	\(q+(0.479269 - 0.479269i) q^{2} -2.62394i q^{3} +15.5406i q^{4} +(-11.7601 - 22.0613i) q^{5} +(-1.25757 - 1.25757i) q^{6} +(51.9642 + 51.9642i) q^{7} +(15.1164 + 15.1164i) q^{8} +74.1150 q^{9} +O(q^{10})\)	\(q+(0.479269 - 0.479269i) q^{2} -2.62394i q^{3} +15.5406i q^{4} +(-11.7601 - 22.0613i) q^{5} +(-1.25757 - 1.25757i) q^{6} +(51.9642 + 51.9642i) q^{7} +(15.1164 + 15.1164i) q^{8} +74.1150 q^{9} +(-16.2095 - 4.93705i) q^{10} +(35.9335 - 35.9335i) q^{11} +40.7776 q^{12} +(32.0577 + 165.932i) q^{13} +49.8096 q^{14} +(-57.8874 + 30.8577i) q^{15} -234.160 q^{16} +416.497 q^{17} +(35.5210 - 35.5210i) q^{18} +(-28.5561 - 28.5561i) q^{19} +(342.846 - 182.759i) q^{20} +(136.351 - 136.351i) q^{21} -34.4436i q^{22} +315.223 q^{23} +(39.6645 - 39.6645i) q^{24} +(-348.402 + 518.885i) q^{25} +(94.8901 + 64.1616i) q^{26} -407.012i q^{27} +(-807.555 + 807.555i) q^{28} -1074.35 q^{29} +(-12.9545 + 42.5327i) q^{30} +(119.050 + 119.050i) q^{31} +(-354.088 + 354.088i) q^{32} +(-94.2873 - 94.2873i) q^{33} +(199.614 - 199.614i) q^{34} +(535.295 - 1757.50i) q^{35} +1151.79i q^{36} +(-1144.48 - 1144.48i) q^{37} -27.3721 q^{38} +(435.394 - 84.1174i) q^{39} +(155.718 - 511.258i) q^{40} +(-1151.81 - 1151.81i) q^{41} -130.697i q^{42} +557.016 q^{43} +(558.429 + 558.429i) q^{44} +(-871.597 - 1635.07i) q^{45} +(151.077 - 151.077i) q^{46} +(-669.259 - 669.259i) q^{47} +614.421i q^{48} +2999.55i q^{49} +(81.7072 + 415.663i) q^{50} -1092.86i q^{51} +(-2578.68 + 498.196i) q^{52} +2664.52i q^{53} +(-195.068 - 195.068i) q^{54} +(-1215.32 - 370.160i) q^{55} +1571.02i q^{56} +(-74.9294 + 74.9294i) q^{57} +(-514.903 + 514.903i) q^{58} +(854.485 - 854.485i) q^{59} +(-479.547 - 899.606i) q^{60} +3845.74 q^{61} +114.113 q^{62} +(3851.32 + 3851.32i) q^{63} -3407.15i q^{64} +(3283.67 - 2658.60i) q^{65} -90.3779 q^{66} +(5223.52 - 5223.52i) q^{67} +6472.62i q^{68} -827.126i q^{69} +(-585.764 - 1098.86i) q^{70} +(-2891.45 - 2891.45i) q^{71} +(1120.35 + 1120.35i) q^{72} +(2861.02 + 2861.02i) q^{73} -1097.02 q^{74} +(1361.52 + 914.184i) q^{75} +(443.779 - 443.779i) q^{76} +3734.51 q^{77} +(168.356 - 248.986i) q^{78} -5467.48 q^{79} +(2753.74 + 5165.87i) q^{80} +4935.34 q^{81} -1104.06 q^{82} +(-4971.13 + 4971.13i) q^{83} +(2118.97 + 2118.97i) q^{84} +(-4898.04 - 9188.47i) q^{85} +(266.960 - 266.960i) q^{86} +2819.03i q^{87} +1086.37 q^{88} +(3375.91 - 3375.91i) q^{89} +(-1201.37 - 365.910i) q^{90} +(-6956.65 + 10288.4i) q^{91} +4898.76i q^{92} +(312.379 - 312.379i) q^{93} -641.509 q^{94} +(-294.163 + 965.807i) q^{95} +(929.105 + 929.105i) q^{96} +(3665.84 - 3665.84i) q^{97} +(1437.59 + 1437.59i) q^{98} +(2663.21 - 2663.21i) 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

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