LMFDB - Embedded newform 65.5.g.a.34.1

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			34.1
Character	$\chi$	$=$	65.34
Dual form			65.5.g.a.44.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.15266 + 5.15266i) q^{2} -15.6320i q^{3} -37.0999i q^{4} +(22.4978 + 10.9017i) q^{5} +(80.5463 + 80.5463i) q^{6} +(-43.9050 - 43.9050i) q^{7} +(108.720 + 108.720i) q^{8} -163.359 q^{9} +O(q^{10})$	\(q+(-5.15266 + 5.15266i) q^{2} -15.6320i q^{3} -37.0999i q^{4} +(22.4978 + 10.9017i) q^{5} +(80.5463 + 80.5463i) q^{6} +(-43.9050 - 43.9050i) q^{7} +(108.720 + 108.720i) q^{8} -163.359 q^{9} +(-172.097 + 59.7510i) q^{10} +(38.6628 - 38.6628i) q^{11} -579.944 q^{12} +(-29.6319 + 166.382i) q^{13} +452.455 q^{14} +(170.415 - 351.686i) q^{15} -526.801 q^{16} -82.2374 q^{17} +(841.731 - 841.731i) q^{18} +(-336.190 - 336.190i) q^{19} +(404.451 - 834.667i) q^{20} +(-686.322 + 686.322i) q^{21} +398.433i q^{22} -489.563 q^{23} +(1699.51 - 1699.51i) q^{24} +(387.306 + 490.529i) q^{25} +(-704.626 - 1009.99i) q^{26} +1287.43i q^{27} +(-1628.87 + 1628.87i) q^{28} -973.662 q^{29} +(934.027 + 2690.21i) q^{30} +(-236.013 - 236.013i) q^{31} +(974.903 - 974.903i) q^{32} +(-604.376 - 604.376i) q^{33} +(423.741 - 423.741i) q^{34} +(-509.129 - 1466.41i) q^{35} +6060.58i q^{36} +(178.519 + 178.519i) q^{37} +3464.54 q^{38} +(2600.88 + 463.206i) q^{39} +(1260.74 + 3631.21i) q^{40} +(302.631 + 302.631i) q^{41} -7072.77i q^{42} -1446.29 q^{43} +(-1434.38 - 1434.38i) q^{44} +(-3675.22 - 1780.89i) q^{45} +(2522.55 - 2522.55i) q^{46} +(1597.00 + 1597.00i) q^{47} +8234.94i q^{48} +1454.30i q^{49} +(-4523.19 - 531.875i) q^{50} +1285.53i q^{51} +(6172.75 + 1099.34i) q^{52} -1950.93i q^{53} +(-6633.67 - 6633.67i) q^{54} +(1291.32 - 448.339i) q^{55} -9546.74i q^{56} +(-5255.30 + 5255.30i) q^{57} +(5016.95 - 5016.95i) q^{58} +(3071.64 - 3071.64i) q^{59} +(-13047.5 - 6322.37i) q^{60} +2210.65 q^{61} +2432.19 q^{62} +(7172.26 + 7172.26i) q^{63} +1617.87i q^{64} +(-2480.50 + 3420.20i) q^{65} +6228.29 q^{66} +(964.245 - 964.245i) q^{67} +3050.99i q^{68} +7652.83i q^{69} +(10179.3 + 4932.53i) q^{70} +(-1933.53 - 1933.53i) q^{71} +(-17760.4 - 17760.4i) q^{72} +(-1810.35 - 1810.35i) q^{73} -1839.70 q^{74} +(7667.94 - 6054.36i) q^{75} +(-12472.6 + 12472.6i) q^{76} -3394.98 q^{77} +(-15788.2 + 11014.7i) q^{78} -8326.35 q^{79} +(-11851.9 - 5743.03i) q^{80} +6892.97 q^{81} -3118.71 q^{82} +(5573.75 - 5573.75i) q^{83} +(25462.4 + 25462.4i) q^{84} +(-1850.16 - 896.527i) q^{85} +(7452.22 - 7452.22i) q^{86} +15220.3i q^{87} +8406.87 q^{88} +(3792.03 - 3792.03i) q^{89} +(28113.4 - 9760.84i) q^{90} +(8605.99 - 6004.01i) q^{91} +18162.7i q^{92} +(-3689.35 + 3689.35i) q^{93} -16457.6 q^{94} +(-3898.50 - 11228.6i) q^{95} +(-15239.7 - 15239.7i) q^{96} +(7917.02 - 7917.02i) q^{97} +(-7493.52 - 7493.52i) q^{98} +(-6315.90 + 6315.90i) 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 $

$2$	−5.15266	+	5.15266i	−1.28817	+	1.28817i	−0.352265	+	0.935900i	$0.614589\pi$
$2$	−5.15266	+	5.15266i	−1.28817	+	1.28817i	−0.935900	+	0.352265i	$0.885411\pi$
$3$		−	15.6320i		−	1.73689i	−0.495789	−	0.868443i	$-0.665121\pi$
$3$		−	15.6320i		−	1.73689i	0.495789	−	0.868443i	$-0.334879\pi$
$4$		−	37.0999i		−	2.31874i
$5$	22.4978	+	10.9017i	0.899914	+	0.436068i
$5$	22.4978	+	10.9017i	0.899914	+	0.436068i
$6$	80.5463	+	80.5463i	2.23740	+	2.23740i
$7$	−43.9050	−	43.9050i	−0.896021	−	0.896021i	0.0990607	−	0.995081i	$-0.468416\pi$
$7$	−43.9050	−	43.9050i	−0.896021	−	0.896021i	−0.995081	+	0.0990607i	$0.968416\pi$
$8$	108.720	+	108.720i	1.69876	+	1.69876i
$9$	−163.359			−2.01677
$10$	−172.097	+	59.7510i	−1.72097	+	0.597510i
$11$	38.6628	−	38.6628i	0.319527	−	0.319527i	−0.529058	−	0.848585i	$-0.677455\pi$
$11$	38.6628	−	38.6628i	0.319527	−	0.319527i	0.848585	+	0.529058i	$0.177455\pi$
$12$	−579.944			−4.02739
$13$	−29.6319	+	166.382i	−0.175337	+	0.984508i
$13$	−29.6319	+	166.382i	−0.175337	+	0.984508i
$14$	452.455			2.30845
$15$	170.415	−	351.686i	0.757400	−	1.56305i
$16$	−526.801			−2.05782
$17$	−82.2374			−0.284558			−0.142279	−	0.989827i	$-0.545443\pi$
$17$	−82.2374			−0.284558			−0.142279	+	0.989827i	$0.545443\pi$
$18$	841.731	−	841.731i	2.59794	−	2.59794i
$19$	−336.190	−	336.190i	−0.931273	−	0.931273i	0.0665127	−	0.997786i	$-0.478813\pi$
$19$	−336.190	−	336.190i	−0.931273	−	0.931273i	−0.997786	+	0.0665127i	$0.978813\pi$
$20$	404.451	−	834.667i	1.01113	−	2.08667i
$21$	−686.322	+	686.322i	−1.55629	+	1.55629i
$22$			398.433i			0.823208i
$23$	−489.563			−0.925449			−0.462724	−	0.886502i	$-0.653128\pi$
$23$	−489.563			−0.925449			−0.462724	+	0.886502i	$0.653128\pi$
$24$	1699.51	−	1699.51i	2.95055	−	2.95055i
$25$	387.306	+	490.529i	0.619690	+	0.784847i
$26$	−704.626	−	1009.99i	−1.04235	−	1.49407i
$27$			1287.43i			1.76602i
$28$	−1628.87	+	1628.87i	−2.07764	+	2.07764i
$29$	−973.662			−1.15774			−0.578872	−	0.815419i	$-0.696507\pi$
$29$	−973.662			−1.15774			−0.578872	+	0.815419i	$0.696507\pi$
$30$	934.027	+	2690.21i	1.03781	+	2.98912i
$31$	−236.013	−	236.013i	−0.245591	−	0.245591i	0.573567	−	0.819158i	$-0.305559\pi$
$31$	−236.013	−	236.013i	−0.245591	−	0.245591i	−0.819158	+	0.573567i	$0.805559\pi$
$32$	974.903	−	974.903i	0.952054	−	0.952054i
$33$	−604.376	−	604.376i	−0.554982	−	0.554982i
$34$	423.741	−	423.741i	0.366558	−	0.366558i
$35$	−509.129	−	1466.41i	−0.415616	−	1.19707i
$36$			6060.58i			4.67637i
$37$	178.519	+	178.519i	0.130401	+	0.130401i	0.769295	−	0.638894i	$-0.220608\pi$
$37$	178.519	+	178.519i	0.130401	+	0.130401i	−0.638894	+	0.769295i	$0.720608\pi$
$38$	3464.54			2.39927
$39$	2600.88	+	463.206i	1.70998	+	0.304540i
$40$	1260.74	+	3631.21i	0.787961	+	2.26951i
$41$	302.631	+	302.631i	0.180031	+	0.180031i	0.791369	−	0.611339i	$-0.209369\pi$
$41$	302.631	+	302.631i	0.180031	+	0.180031i	−0.611339	+	0.791369i	$0.709369\pi$
$42$		−	7072.77i		−	4.00951i
$43$	−1446.29			−0.782199			−0.391099	−	0.920348i	$-0.627905\pi$
$43$	−1446.29			−0.782199			−0.391099	+	0.920348i	$0.627905\pi$
$44$	−1434.38	−	1434.38i	−0.740901	−	0.740901i
$45$	−3675.22	−	1780.89i	−1.81492	−	0.879449i
$46$	2522.55	−	2522.55i	1.19213	−	1.19213i
$47$	1597.00	+	1597.00i	0.722954	+	0.722954i	0.969206	−	0.246252i	$-0.0791991\pi$
$47$	1597.00	+	1597.00i	0.722954	+	0.722954i	−0.246252	+	0.969206i	$0.579199\pi$
$48$			8234.94i			3.57419i
$49$			1454.30i			0.605706i
$50$	−4523.19	−	531.875i	−1.80928	−	0.212750i
$51$			1285.53i			0.494245i
$52$	6172.75	+	1099.34i	2.28282	+	0.406561i
$53$		−	1950.93i		−	0.694529i	−0.937767	−	0.347265i	$-0.887111\pi$
$53$		−	1950.93i		−	0.694529i	0.937767	−	0.347265i	$-0.112889\pi$
$54$	−6633.67	−	6633.67i	−2.27492	−	2.27492i
$55$	1291.32	−	448.339i	0.426882	−	0.148211i
$56$		−	9546.74i		−	3.04424i
$57$	−5255.30	+	5255.30i	−1.61751	+	1.61751i
$58$	5016.95	−	5016.95i	1.49137	−	1.49137i
$59$	3071.64	−	3071.64i	0.882403	−	0.882403i	−0.111376	−	0.993778i	$-0.535526\pi$
$59$	3071.64	−	3071.64i	0.882403	−	0.882403i	0.993778	+	0.111376i	$0.0355257\pi$
$60$	−13047.5	−	6322.37i	−3.62430	−	1.75621i
$61$	2210.65			0.594100			0.297050	−	0.954862i	$-0.403997\pi$
$61$	2210.65			0.594100			0.297050	+	0.954862i	$0.403997\pi$
$62$	2432.19			0.632724
$63$	7172.26	+	7172.26i	1.80707	+	1.80707i
$64$			1617.87i			0.394988i
$65$	−2480.50	+	3420.20i	−0.587101	+	0.809514i
$66$	6228.29			1.42982
$67$	964.245	−	964.245i	0.214802	−	0.214802i	−0.591502	−	0.806304i	$-0.701465\pi$
$67$	964.245	−	964.245i	0.214802	−	0.214802i	0.806304	+	0.591502i	$0.201465\pi$
$68$			3050.99i			0.659817i
$69$			7652.83i			1.60740i
$70$	10179.3	+	4932.53i	2.07740	+	1.00664i
$71$	−1933.53	−	1933.53i	−0.383562	−	0.383562i	0.488822	−	0.872384i	$-0.337427\pi$
$71$	−1933.53	−	1933.53i	−0.383562	−	0.383562i	−0.872384	+	0.488822i	$0.837427\pi$
$72$	−17760.4	−	17760.4i	−3.42600	−	3.42600i
$73$	−1810.35	−	1810.35i	−0.339718	−	0.339718i	0.516543	−	0.856261i	$-0.327218\pi$
$73$	−1810.35	−	1810.35i	−0.339718	−	0.339718i	−0.856261	+	0.516543i	$0.827218\pi$
$74$	−1839.70			−0.335957
$75$	7667.94	−	6054.36i	1.36319	−	1.07633i
$76$	−12472.6	+	12472.6i	−2.15938	+	2.15938i
$77$	−3394.98			−0.572606
$78$	−15788.2	+	11014.7i	−2.59503	+	1.81044i
$79$	−8326.35			−1.33414			−0.667068	−	0.744997i	$-0.732451\pi$
$79$	−8326.35			−1.33414			−0.667068	+	0.744997i	$0.732451\pi$
$80$	−11851.9	−	5743.03i	−1.85186	−	0.897348i
$81$	6892.97			1.05060
$82$	−3118.71			−0.463818
$83$	5573.75	−	5573.75i	0.809080	−	0.809080i	−0.175415	−	0.984495i	$-0.556127\pi$
$83$	5573.75	−	5573.75i	0.809080	−	0.809080i	0.984495	+	0.175415i	$0.0561266\pi$
$84$	25462.4	+	25462.4i	3.60862	+	3.60862i
$85$	−1850.16	−	896.527i	−0.256078	−	0.124087i
$86$	7452.22	−	7452.22i	1.00760	−	1.00760i
$87$			15220.3i			2.01087i
$88$	8406.87			1.08560
$89$	3792.03	−	3792.03i	0.478731	−	0.478731i	−0.425994	−	0.904726i	$-0.640076\pi$
$89$	3792.03	−	3792.03i	0.478731	−	0.478731i	0.904726	+	0.425994i	$0.140076\pi$
$90$	28113.4	−	9760.84i	3.47080	−	1.20504i
$91$	8605.99	−	6004.01i	1.03925	−	0.725034i
$92$			18162.7i			2.14588i
$93$	−3689.35	+	3689.35i	−0.426563	+	0.426563i
$94$	−16457.6			−1.86257
$95$	−3898.50	−	11228.6i	−0.431967	−	1.24416i
$96$	−15239.7	−	15239.7i	−1.65361	−	1.65361i
$97$	7917.02	−	7917.02i	0.841430	−	0.841430i	−0.147615	−	0.989045i	$-0.547160\pi$
$97$	7917.02	−	7917.02i	0.841430	−	0.841430i	0.989045	+	0.147615i	$0.0471596\pi$
$98$	−7493.52	−	7493.52i	−0.780250	−	0.780250i
$99$	−6315.90	+	6315.90i	−0.644414	+	0.644414i
$100$	18198.6	−	14369.0i	1.81986	−	1.43690i
$101$		−	6101.67i		−	0.598144i	−0.954231	−	0.299072i	$-0.903323\pi$
$101$		−	6101.67i		−	0.598144i	0.954231	−	0.299072i	$-0.0966771\pi$
$102$	−6623.91	−	6623.91i	−0.636670	−	0.636670i
$103$	−17499.6			−1.64950			−0.824751	−	0.565495i	$-0.808685\pi$
$103$	−17499.6			−1.64950			−0.824751	+	0.565495i	$0.808685\pi$
$104$	−21310.7	+	14867.5i	−1.97029	+	1.37459i
$105$	−22922.8	+	7958.69i	−2.07917	+	0.721877i
$106$	10052.5	+	10052.5i	0.894669	+	0.894669i
$107$		−	17295.4i		−	1.51064i	−0.655354	−	0.755322i	$-0.727481\pi$
$107$		−	17295.4i		−	1.51064i	0.655354	−	0.755322i	$-0.272519\pi$
$108$	47763.3			4.09494
$109$	5415.44	+	5415.44i	0.455807	+	0.455807i	0.897276	−	0.441469i	$-0.145543\pi$
$109$	5415.44	+	5415.44i	0.455807	+	0.455807i	−0.441469	+	0.897276i	$0.645543\pi$
$110$	−4343.59	+	8963.87i	−0.358974	+	0.740816i
$111$	2790.61	−	2790.61i	0.226492	−	0.226492i
$112$	23129.2	+	23129.2i	1.84385	+	1.84385i
$113$		−	8994.00i		−	0.704362i	−0.935932	−	0.352181i	$-0.885440\pi$
$113$		−	8994.00i		−	0.704362i	0.935932	−	0.352181i	$-0.114560\pi$
$114$		−	54157.6i		−	4.16725i
$115$	−11014.1	−	5337.06i	−0.832824	−	0.403559i
$116$			36122.7i			2.68451i
$117$	4840.63	−	27179.9i	0.353615	−	1.98553i
$118$			31654.3i			2.27336i
$119$	3610.63	+	3610.63i	0.254970	+	0.254970i
$120$	56763.0	−	19707.8i	3.94187	−	1.36860i
$121$			11651.4i			0.795805i
$122$	−11390.7	+	11390.7i	−0.765299	+	0.765299i
$123$	4730.72	−	4730.72i	0.312692	−	0.312692i
$124$	−8756.04	+	8756.04i	−0.569462	+	0.569462i
$125$	3365.95	+	15258.1i	0.215421	+	0.976521i
$126$	−73912.5			−4.65561
$127$	22334.0			1.38471			0.692356	−	0.721556i	$-0.256573\pi$
$127$	22334.0			1.38471			0.692356	+	0.721556i	$0.256573\pi$
$128$	7262.11	+	7262.11i	0.443244	+	0.443244i
$129$			22608.3i			1.35859i
$130$	−4841.94	−	30404.3i	−0.286505	−	1.79907i
$131$	4171.01			0.243051			0.121526	−	0.992588i	$-0.461221\pi$
$131$	4171.01			0.243051			0.121526	+	0.992588i	$0.461221\pi$
$132$	−22422.2	+	22422.2i	−1.28686	+	1.28686i
$133$			29520.8i			1.66888i
$134$			9936.86i			0.553400i
$135$	−14035.1	+	28964.3i	−0.770103	+	1.58926i
$136$	−8940.88	−	8940.88i	−0.483395	−	0.483395i
$137$	−9253.83	−	9253.83i	−0.493038	−	0.493038i	0.416224	−	0.909262i	$-0.363353\pi$
$137$	−9253.83	−	9253.83i	−0.493038	−	0.493038i	−0.909262	+	0.416224i	$0.863353\pi$
$138$	−39432.4	−	39432.4i	−2.07060	−	2.07060i
$139$	636.320			0.0329341			0.0164670	−	0.999864i	$-0.494758\pi$
$139$	636.320			0.0329341			0.0164670	+	0.999864i	$0.494758\pi$
$140$	−54403.5	+	18888.6i	−2.77569	+	0.963705i
$141$	24964.3	−	24964.3i	1.25569	−	1.25569i
$142$	19925.7			0.988182
$143$	5287.14	+	7578.44i	0.258552	+	0.370602i
$144$	86057.5			4.15015
$145$	−21905.3	−	10614.6i	−1.04187	−	0.504855i
$146$	18656.3			0.875225
$147$	22733.6			1.05204
$148$	6623.05	−	6623.05i	0.302367	−	0.302367i
$149$	6698.16	+	6698.16i	0.301705	+	0.301705i	0.841681	−	0.539975i	$-0.181567\pi$
$149$	6698.16	+	6698.16i	0.301705	+	0.301705i	−0.539975	+	0.841681i	$0.681567\pi$
$150$	−8314.25	+	70706.4i	−0.369522	+	3.14251i
$151$	−29076.2	+	29076.2i	−1.27522	+	1.27522i	−0.331903	+	0.943313i	$0.607691\pi$
$151$	−29076.2	+	29076.2i	−1.27522	+	1.27522i	−0.943313	+	0.331903i	$0.892309\pi$
$152$		−	73101.3i		−	3.16401i
$153$	13434.2			0.573889
$154$	17493.2	−	17493.2i	0.737611	−	0.737611i
$155$	−2736.84	−	7882.72i	−0.113916	−	0.328105i
$156$	17184.9	−	96492.2i	0.706150	−	3.96500i
$157$		−	33308.6i		−	1.35132i	−0.737215	−	0.675658i	$-0.763859\pi$
$157$		−	33308.6i		−	1.35132i	0.737215	−	0.675658i	$-0.236141\pi$
$158$	42902.9	−	42902.9i	1.71859	−	1.71859i
$159$	−30496.9			−1.20632
$160$	32561.3	−	11305.1i	1.27193	−	0.441606i
$161$	21494.2	+	21494.2i	0.829221	+	0.829221i
$162$	−35517.2	+	35517.2i	−1.35334	+	1.35334i
$163$	−14902.2	−	14902.2i	−0.560888	−	0.560888i	0.368672	−	0.929560i	$-0.379813\pi$
$163$	−14902.2	−	14902.2i	−0.560888	−	0.560888i	−0.929560	+	0.368672i	$0.879813\pi$
$164$	11227.6	−	11227.6i	0.417444	−	0.417444i
$165$	−7008.43	−	20185.9i	−0.257426	−	0.741446i
$166$			57439.3i			2.08446i
$167$	31497.1	+	31497.1i	1.12938	+	1.12938i	0.990279	+	0.139096i	$0.0444197\pi$
$167$	31497.1	+	31497.1i	1.12938	+	1.12938i	0.139096	+	0.990279i	$0.455580\pi$
$168$	−149234.			−5.28750
$169$	−26804.9	−	9860.44i	−0.938514	−	0.345241i
$170$	14152.8	−	4913.77i	0.489715	−	0.170027i
$171$	54919.4	+	54919.4i	1.87817	+	1.87817i
$172$			53657.0i			1.81372i
$173$	−33223.7			−1.11008			−0.555041	−	0.831823i	$-0.687298\pi$
$173$	−33223.7			−1.11008			−0.555041	+	0.831823i	$0.687298\pi$
$174$	−78424.9	−	78424.9i	−2.59033	−	2.59033i
$175$	4532.02	−	38541.4i	0.147984	−	1.25849i
$176$	−20367.6	+	20367.6i	−0.657529	+	0.657529i
$177$	−48015.8	−	48015.8i	−1.53263	−	1.53263i
$178$			39078.1i			1.23337i
$179$		−	51139.2i		−	1.59606i	−0.602621	−	0.798028i	$-0.705877\pi$
$179$		−	51139.2i		−	1.59606i	0.602621	−	0.798028i	$-0.294123\pi$
$180$	−66070.6	+	136350.i	−2.03922	+	4.20833i
$181$		−	29871.7i		−	0.911808i	−0.890029	−	0.455904i	$-0.849316\pi$
$181$		−	29871.7i		−	0.911808i	0.890029	−	0.455904i	$-0.150684\pi$
$182$	−13407.1	+	75280.4i	−0.404756	+	2.27268i
$183$		−	34556.7i		−	1.03188i
$184$	−53225.4	−	53225.4i	−1.57211	−	1.57211i
$185$	2070.14	+	5962.47i	0.0604861	+	0.174214i
$186$		−	38019.9i		−	1.09897i
$187$	−3179.53	+	3179.53i	−0.0909241	+	0.0909241i
$188$	59248.6	−	59248.6i	1.67634	−	1.67634i
$189$	56524.5	−	56524.5i	1.58239	−	1.58239i
$190$	77944.7	+	37769.4i	2.15913	+	1.04624i
$191$	36116.1			0.989997			0.494998	−	0.868894i	$-0.335169\pi$
$191$	36116.1			0.989997			0.494998	+	0.868894i	$0.335169\pi$
$192$	25290.5			0.686049
$193$	−19502.2	−	19502.2i	−0.523562	−	0.523562i	0.395083	−	0.918645i	$-0.370716\pi$
$193$	−19502.2	−	19502.2i	−0.523562	−	0.523562i	−0.918645	+	0.395083i	$0.870716\pi$
$194$			81587.4i			2.16780i
$195$	53464.4	+	38775.1i	1.40603	+	1.01973i
$196$	53954.3			1.40448
$197$	−3484.13	+	3484.13i	−0.0897763	+	0.0897763i	−0.750569	−	0.660792i	$-0.770220\pi$
$197$	−3484.13	+	3484.13i	−0.0897763	+	0.0897763i	0.660792	+	0.750569i	$0.270220\pi$
$198$		−	65087.4i		−	1.66022i
$199$			31507.9i			0.795633i	0.917465	+	0.397816i	$0.130232\pi$
$199$			31507.9i			0.795633i	−0.917465	+	0.397816i	$0.869768\pi$
$200$	−11222.5	+	95438.6i	−0.280562	+	2.38597i
$201$	−15073.1	−	15073.1i	−0.373086	−	0.373086i
$202$	31439.8	+	31439.8i	0.770509	+	0.770509i
$203$	42748.7	+	42748.7i	1.03736	+	1.03736i
$204$	47693.1			1.14603
$205$	3509.36	+	10107.7i	0.0835064	+	0.240517i
$206$	90169.4	−	90169.4i	2.12483	−	2.12483i
$207$	79974.2			1.86642
$208$	15610.2	−	87650.2i	0.360812	−	2.02594i
$209$	−25996.0			−0.595134
$210$	77105.2	−	159122.i	1.74842	−	3.60821i
$211$	−77877.8			−1.74924			−0.874619	−	0.484811i	$-0.838888\pi$
$211$	−77877.8			−1.74924			−0.874619	+	0.484811i	$0.838888\pi$
$212$	−72379.3			−1.61043
$213$	−30224.9	+	30224.9i	−0.666203	+	0.666203i
$214$	89117.2	+	89117.2i	1.94596	+	1.94596i
$215$	−32538.3	−	15767.0i	−0.703912	−	0.341092i
$216$	−139970.	+	139970.i	−3.00003	+	3.00003i
$217$			20724.3i			0.440109i
$218$	−55807.9			−1.17431
$219$	−28299.4	+	28299.4i	−0.590051	+	0.590051i
$220$	−16633.3	−	47907.8i	−0.343664	−	0.989830i
$221$	2436.85	−	13682.8i	0.0498936	−	0.280150i
$222$			28758.2i			0.583519i
$223$	27970.3	−	27970.3i	0.562455	−	0.562455i	−0.367549	−	0.930004i	$-0.619803\pi$
$223$	27970.3	−	27970.3i	0.562455	−	0.562455i	0.930004	+	0.367549i	$0.119803\pi$
$224$	−85606.3			−1.70612
$225$	−63269.8	−	80132.2i	−1.24977	−	1.58286i
$226$	46343.0	+	46343.0i	0.907335	+	0.907335i
$227$	−70475.8	+	70475.8i	−1.36769	+	1.36769i	−0.503971	+	0.863721i	$0.668128\pi$
$227$	−70475.8	+	70475.8i	−1.36769	+	1.36769i	−0.863721	+	0.503971i	$0.831872\pi$
$228$	194971.	+	194971.i	3.75060	+	3.75060i
$229$	46752.0	−	46752.0i	0.891517	−	0.891517i	−0.103149	−	0.994666i	$-0.532892\pi$
$229$	46752.0	−	46752.0i	0.891517	−	0.891517i	0.994666	+	0.103149i	$0.0328918\pi$
$230$	84252.0	−	29251.9i	1.59267	−	0.552965i
$231$			53070.2i			0.994551i
$232$	−105857.	−	105857.i	−1.96672	−	1.96672i
$233$	64884.3			1.19516			0.597582	−	0.801808i	$-0.296128\pi$
$233$	64884.3			1.19516			0.597582	+	0.801808i	$0.296128\pi$
$234$	115107.	+	164991.i	2.10218	+	3.01320i
$235$	18519.1	+	53339.2i	0.335339	+	0.965853i
$236$	−113958.	−	113958.i	−2.04606	−	2.04606i
$237$			130157.i			2.31724i
$238$	−37208.7			−0.656888
$239$	1940.70	+	1940.70i	0.0339753	+	0.0339753i	0.723890	−	0.689915i	$-0.242352\pi$
$239$	1940.70	+	1940.70i	0.0339753	+	0.0339753i	−0.689915	+	0.723890i	$0.742352\pi$
$240$	−89774.9	+	185269.i	−1.55859	+	3.21647i
$241$	40098.2	−	40098.2i	0.690384	−	0.690384i	−0.271932	−	0.962316i	$-0.587663\pi$
$241$	40098.2	−	40098.2i	0.690384	−	0.690384i	0.962316	+	0.271932i	$0.0876626\pi$
$242$	−60035.6	−	60035.6i	−1.02513	−	1.02513i
$243$		−	3469.19i		−	0.0587511i
$244$		−	82014.6i		−	1.37756i
$245$	−15854.3	+	32718.6i	−0.264129	+	0.545083i
$246$			48751.6i			0.805599i
$247$	65897.8	−	45973.9i	1.08013	−	0.753559i
$248$		−	51318.8i		−	0.834398i
$249$	−87128.7	−	87128.7i	−1.40528	−	1.40528i
$250$	−95963.7	−	61276.5i	−1.53542	−	0.980423i
$251$			42177.8i			0.669478i	0.942311	+	0.334739i	$0.108648\pi$
$251$			42177.8i			0.669478i	−0.942311	+	0.334739i	$0.891352\pi$
$252$	266090.	−	266090.i	4.19013	−	4.19013i
$253$	−18927.9	+	18927.9i	−0.295706	+	0.295706i
$254$	−115080.	+	115080.i	−1.78374	+	1.78374i
$255$	−14014.5	+	28921.7i	−0.215524	+	0.444778i
$256$	−100724.			−1.53693
$257$	40573.9			0.614300			0.307150	−	0.951661i	$-0.400625\pi$
$257$	40573.9			0.614300			0.307150	+	0.951661i	$0.400625\pi$
$258$	−116493.	−	116493.i	−1.75009	−	1.75009i
$259$		−	15675.8i		−	0.233685i
$260$	126889.	+	92026.2i	1.87705	+	1.36133i
$261$	159056.			2.33491
$262$	−21491.8	+	21491.8i	−0.313091	+	0.313091i
$263$			99954.1i			1.44507i	0.691334	+	0.722536i	$0.257023\pi$
$263$			99954.1i			1.44507i	−0.691334	+	0.722536i	$0.742977\pi$
$264$		−	131416.i		−	1.88556i
$265$	21268.5	−	43891.8i	0.302862	−	0.625017i
$266$	−152111.	−	152111.i	−2.14979	−	2.14979i
$267$	−59276.9	−	59276.9i	−0.831502	−	0.831502i
$268$	−35773.4	−	35773.4i	−0.498070	−	0.498070i
$269$	25990.6			0.359179			0.179590	−	0.983742i	$-0.442523\pi$
$269$	25990.6			0.359179			0.179590	+	0.983742i	$0.442523\pi$
$270$	−76925.1	−	221562.i	−1.05521	−	3.03925i
$271$	−69665.1	+	69665.1i	−0.948586	+	0.948586i	−0.998741	−	0.0501552i	$-0.984028\pi$
$271$	−69665.1	+	69665.1i	−0.948586	+	0.948586i	0.0501552	+	0.998741i	$0.484028\pi$
$272$	43322.8			0.585569
$273$	−93854.5	−	134529.i	−1.25930	−	1.80505i
$274$	95363.8			1.27023
$275$	33939.6	+	3990.90i	0.448788	+	0.0527722i
$276$	283919.			3.72714
$277$	15301.0			0.199416			0.0997078	−	0.995017i	$-0.468209\pi$
$277$	15301.0			0.199416			0.0997078	+	0.995017i	$0.468209\pi$
$278$	−3278.74	+	3278.74i	−0.0424246	+	0.0424246i
$279$	38554.7	+	38554.7i	0.495301	+	0.495301i
$280$	104076.	−	214781.i	1.32750	−	2.73956i
$281$	39407.5	−	39407.5i	0.499075	−	0.499075i	−0.412075	−	0.911150i	$-0.635196\pi$
$281$	39407.5	−	39407.5i	0.499075	−	0.499075i	0.911150	+	0.412075i	$0.135196\pi$
$282$			257266.i			3.23507i
$283$	28989.8			0.361969			0.180985	−	0.983486i	$-0.442072\pi$
$283$	28989.8			0.361969			0.180985	+	0.983486i	$0.442072\pi$
$284$	−71733.8	+	71733.8i	−0.889380	+	0.889380i
$285$	−175525.	+	60941.3i	−2.16097	+	0.750278i
$286$	−66292.0	−	11806.3i	−0.810455	−	0.144339i
$287$		−	26574.1i		−	0.322622i
$288$	−159259.	+	159259.i	−1.92008	+	1.92008i
$289$	−76758.0			−0.919027
$290$	167564.	−	58177.3i	1.99244	−	0.691764i
$291$	−123759.	−	123759.i	−1.46147	−	1.46147i
$292$	−67163.9	+	67163.9i	−0.787717	+	0.787717i
$293$	9105.83	+	9105.83i	0.106068	+	0.106068i	0.758149	−	0.652081i	$-0.226104\pi$
$293$	9105.83	+	9105.83i	0.106068	+	0.106068i	−0.652081	+	0.758149i	$0.726104\pi$
$294$	−117138.	+	117138.i	−1.35520	+	1.35520i
$295$	102591.	−	35619.2i	1.17887	−	0.409299i
$296$			38817.4i			0.443040i
$297$	49775.5	+	49775.5i	0.564290	+	0.564290i
$298$	−69026.7			−0.777293
$299$	14506.7	−	81454.4i	0.162265	−	0.911112i
$300$	−224616.	−	284479.i	−2.49573	−	3.16088i
$301$	63499.2	+	63499.2i	0.700866	+	0.700866i
$302$		−	299640.i		−	3.28538i
$303$	−95381.1			−1.03891
$304$	177105.	+	177105.i	1.91639	+	1.91639i
$305$	49734.8	+	24099.8i	0.534639	+	0.259068i
$306$	−69221.8	+	69221.8i	−0.739264	+	0.739264i
$307$	−11380.3	−	11380.3i	−0.120748	−	0.120748i	0.644151	−	0.764898i	$-0.277211\pi$
$307$	−11380.3	−	11380.3i	−0.120748	−	0.120748i	−0.764898	+	0.644151i	$0.777211\pi$
$308$			125953.i			1.32772i
$309$			273553.i			2.86500i
$310$	54719.0	+	26515.0i	0.569397	+	0.275910i
$311$		−	91213.2i		−	0.943055i	−0.881851	−	0.471527i	$-0.843703\pi$
$311$		−	91213.2i		−	0.943055i	0.881851	−	0.471527i	$-0.156297\pi$
$312$	232409.	+	333128.i	2.38750	+	3.42218i
$313$			73740.9i			0.752696i	0.926478	+	0.376348i	$0.122820\pi$
$313$			73740.9i			0.752696i	−0.926478	+	0.376348i	$0.877180\pi$
$314$	171628.	+	171628.i	1.74072	+	1.74072i
$315$	83170.6	+	239550.i	0.838202	+	2.41421i
$316$			308906.i			3.09352i
$317$	31671.7	−	31671.7i	0.315175	−	0.315175i	−0.531735	−	0.846911i	$-0.678460\pi$
$317$	31671.7	−	31671.7i	0.315175	−	0.315175i	0.846911	+	0.531735i	$0.178460\pi$
$318$	157140.	−	157140.i	1.55394	−	1.55394i
$319$	−37644.5	+	37644.5i	−0.369931	+	0.369931i
$320$	−17637.5	+	36398.6i	−0.172241	+	0.355455i
$321$	−270361.			−2.62382
$322$	−221505.			−2.13635
$323$	27647.3	+	27647.3i	0.265001	+	0.265001i
$324$		−	255728.i		−	2.43606i
$325$	−93091.8	+	49905.4i	−0.881343	+	0.472477i
$326$	153572.			1.44503
$327$	84654.1	−	84654.1i	0.791685	−	0.791685i
$328$			65804.4i			0.611656i
$329$		−	140233.i		−	1.29556i
$330$	140123.	+	67898.9i	1.28671	+	0.623498i
$331$	29812.9	+	29812.9i	0.272113	+	0.272113i	0.829950	−	0.557838i	$-0.188369\pi$
$331$	29812.9	+	29812.9i	0.272113	+	0.272113i	−0.557838	+	0.829950i	$0.688369\pi$
$332$	−206785.	−	206785.i	−1.87605	−	1.87605i
$333$	−29162.7	−	29162.7i	−0.262990	−	0.262990i
$334$	−324588.			−2.90964
$335$	32205.3	−	11181.5i	0.286971	−	0.0996349i
$336$	361555.	−	361555.i	3.20255	−	3.20255i
$337$	18539.8			0.163247			0.0816234	−	0.996663i	$-0.473990\pi$
$337$	18539.8			0.163247			0.0816234	+	0.996663i	$0.473990\pi$
$338$	188924.	−	87309.0i	1.65369	−	0.764233i
$339$	−140594.			−1.22340
$340$	−33261.0	+	68640.8i	−0.287725	+	0.593778i
$341$	−18249.8			−0.156946
$342$	−565962.			−4.83878
$343$	−41564.8	+	41564.8i	−0.353295	+	0.353295i
$344$	−157241.	−	157241.i	−1.32877	−	1.32877i
$345$	−83428.8	+	172172.i	−0.700935	+	1.44652i
$346$	171190.	−	171190.i	1.42997	−	1.42997i
$347$			53245.0i			0.442202i	0.975251	+	0.221101i	$0.0709650\pi$
$347$			53245.0i			0.442202i	−0.975251	+	0.221101i	$0.929035\pi$
$348$	564670.			4.66268
$349$	−28521.1	+	28521.1i	−0.234161	+	0.234161i	−0.814427	−	0.580266i	$-0.802949\pi$
$349$	−28521.1	+	28521.1i	−0.234161	+	0.234161i	0.580266	+	0.814427i	$0.302949\pi$
$350$	175239.	+	221943.i	1.43052	+	1.81178i
$351$	−214204.	−	38148.9i	−1.73866	−	0.309648i
$352$		−	75384.9i		−	0.608414i
$353$	−118709.	+	118709.i	−0.952651	+	0.952651i	−0.998929	−	0.0462775i	$-0.985264\pi$
$353$	−118709.	+	118709.i	−0.952651	+	0.952651i	0.0462775	+	0.998929i	$0.485264\pi$
$354$	494819.			3.94857
$355$	−22421.5	−	64579.1i	−0.177913	−	0.512431i
$356$	−140684.	−	140684.i	−1.11005	−	1.11005i
$357$	56441.3	−	56441.3i	0.442854	−	0.442854i
$358$	263503.	+	263503.i	2.05598	+	2.05598i
$359$	145412.	−	145412.i	1.12826	−	1.12826i	0.137803	−	0.990460i	$-0.455996\pi$
$359$	145412.	−	145412.i	1.12826	−	1.12826i	0.990460	−	0.137803i	$-0.0440042\pi$
$360$	−205952.	−	593189.i	−1.58914	−	4.57708i
$361$			95725.8i			0.734538i
$362$	153919.	+	153919.i	1.17456	+	1.17456i
$363$	182134.			1.38222
$364$	−222748.	−	319281.i	−1.68117	−	2.40974i
$365$	−20993.1	−	60465.0i	−0.157577	−	0.453856i
$366$	178059.	+	178059.i	1.32924	+	1.32924i
$367$		−	139128.i		−	1.03296i	−0.856301	−	0.516478i	$-0.827243\pi$
$367$		−	139128.i		−	1.03296i	0.856301	−	0.516478i	$-0.172757\pi$
$368$	257902.			1.90441
$369$	−49437.4	−	49437.4i	−0.363081	−	0.363081i
$370$	−41389.3	−	20055.9i	−0.302332	−	0.146500i
$371$	−85655.8	+	85655.8i	−0.622313	+	0.622313i
$372$	136874.	+	136874.i	0.989090	+	0.989090i
$373$		−	45806.2i		−	0.329236i	−0.986357	−	0.164618i	$-0.947361\pi$
$373$		−	45806.2i		−	0.329236i	0.986357	−	0.164618i	$-0.0526391\pi$
$374$		−	32766.0i		−	0.234251i
$375$	238515.	−	52616.4i	1.69611	−	0.374161i
$376$			347254.i			2.45624i
$377$	28851.5	−	162000.i	0.202995	−	1.13981i
$378$			582503.i			4.07675i
$379$	34.2978	+	34.2978i	0.000238774	+	0.000238774i	0.707226	−	0.706987i	$-0.249946\pi$
$379$	34.2978	+	34.2978i	0.000238774	+	0.000238774i	−0.706987	+	0.707226i	$0.749946\pi$
$380$	−416578.	+	144634.i	−2.88489	+	1.00162i
$381$		−	349125.i		−	2.40509i
$382$	−186094.	+	186094.i	−1.27528	+	1.27528i
$383$	−61341.4	+	61341.4i	−0.418173	+	0.418173i	−0.884574	−	0.466401i	$-0.845550\pi$
$383$	−61341.4	+	61341.4i	−0.418173	+	0.418173i	0.466401	+	0.884574i	$0.345550\pi$
$384$	113521.	−	113521.i	0.769865	−	0.769865i
$385$	−76379.8	−	37011.0i	−0.515296	−	0.249695i
$386$	200976.			1.34887
$387$	236263.			1.57752
$388$	−293720.	−	293720.i	−1.95106	−	1.95106i
$389$			265582.i			1.75509i	0.479496	+	0.877544i	$0.340820\pi$
$389$			265582.i			1.75509i	−0.479496	+	0.877544i	$0.659180\pi$
$390$	−475279.	+	75689.0i	−3.12478	+	0.497627i
$391$	40260.3			0.263344
$392$	−158112.	+	158112.i	−1.02895	+	1.02895i
$393$		−	65201.1i		−	0.422153i
$394$		−	35905.1i		−	0.231293i
$395$	−187325.	−	90771.3i	−1.20061	−	0.581774i
$396$	234319.	+	234319.i	1.49423	+	1.49423i
$397$	−178801.	−	178801.i	−1.13446	−	1.13446i	−0.989427	−	0.145035i	$-0.953671\pi$
$397$	−178801.	−	178801.i	−1.13446	−	1.13446i	−0.145035	−	0.989427i	$-0.546329\pi$
$398$	−162349.	−	162349.i	−1.02491	−	1.02491i
$399$	461468.			2.89865
$400$	−204033.	−	258412.i	−1.27521	−	1.61507i
$401$	48328.4	−	48328.4i	0.300548	−	0.300548i	−0.540680	−	0.841228i	$-0.681833\pi$
$401$	48328.4	−	48328.4i	0.300548	−	0.300548i	0.841228	+	0.540680i	$0.181833\pi$
$402$	155333.			0.961193
$403$	46261.8	−	32274.8i	0.284848	−	0.198725i
$404$	−226371.			−1.38694
$405$	155077.	+	75145.1i	0.945447	+	0.458132i
$406$	−440539.			−2.67259
$407$	13804.1			0.0833336
$408$	−139764.	+	139764.i	−0.839602	+	0.839602i
$409$	−28247.1	−	28247.1i	−0.168860	−	0.168860i	0.617618	−	0.786478i	$-0.288098\pi$
$409$	−28247.1	−	28247.1i	−0.168860	−	0.168860i	−0.786478	+	0.617618i	$0.788098\pi$
$410$	−70164.3	−	33999.3i	−0.417396	−	0.202256i
$411$	−144656.	+	144656.i	−0.856351	+	0.856351i
$412$			649232.i			3.82477i
$413$	−269721.			−1.58130
$414$	−412080.	+	412080.i	−2.40426	+	2.40426i
$415$	186161.	−	64634.1i	1.08092	−	0.375289i
$416$	133318.	+	191095.i	0.770375	+	1.10424i
$417$		−	9946.93i		−	0.0572027i
$418$	133949.	−	133949.i	0.766631	−	0.766631i
$419$	268334.			1.52844			0.764220	−	0.644956i	$-0.223124\pi$
$419$	268334.			1.52844			0.764220	+	0.644956i	$0.223124\pi$
$420$	295266.	+	850434.i	1.67385	+	4.82105i
$421$	197933.	+	197933.i	1.11675	+	1.11675i	0.992216	+	0.124529i	$0.0397420\pi$
$421$	197933.	+	197933.i	1.11675	+	1.11675i	0.124529	+	0.992216i	$0.460258\pi$
$422$	401278.	−	401278.i	2.25331	−	2.25331i
$423$	−260884.	−	260884.i	−1.45803	−	1.45803i
$424$	212106.	−	212106.i	1.17984	−	1.17984i
$425$	−31851.0	−	40339.8i	−0.176338	−	0.223335i
$426$		−	311478.i		−	1.71636i
$427$	−97058.4	−	97058.4i	−0.532326	−	0.532326i
$428$	−641655.			−3.50279
$429$	118466.	−	82648.4i	0.643694	−	0.449076i
$430$	248901.	−	86417.1i	1.34614	−	0.467372i
$431$	−97251.1	−	97251.1i	−0.523528	−	0.523528i	0.395107	−	0.918635i	$-0.370708\pi$
$431$	−97251.1	−	97251.1i	−0.523528	−	0.523528i	−0.918635	+	0.395107i	$0.870708\pi$
$432$		−	678218.i		−	3.63414i
$433$	55736.0			0.297276			0.148638	−	0.988892i	$-0.452511\pi$
$433$	55736.0			0.297276			0.148638	+	0.988892i	$0.452511\pi$
$434$	−106785.	−	106785.i	−0.566933	−	0.566933i
$435$	−165927.	+	342423.i	−0.876875	+	1.80961i
$436$	200912.	−	200912.i	1.05690	−	1.05690i
$437$	164586.	+	164586.i	0.861846	+	0.861846i
$438$		−	291635.i		−	1.52017i
$439$			18640.8i			0.0967243i	0.998830	+	0.0483622i	$0.0154002\pi$
$439$			18640.8i			0.0967243i	−0.998830	+	0.0483622i	$0.984600\pi$
$440$	189136.	+	91649.1i	0.976944	+	0.473394i
$441$		−	237572.i		−	1.22157i
$442$	57946.6	+	83059.2i	0.296609	+	0.425151i
$443$			29547.9i			0.150563i	0.997162	+	0.0752817i	$0.0239856\pi$
$443$			29547.9i			0.150563i	−0.997162	+	0.0752817i	$0.976014\pi$
$444$	−103531.	−	103531.i	−0.525177	−	0.525177i
$445$	126652.	−	43973.0i	0.639576	−	0.222058i
$446$			288243.i			1.44907i
$447$	104705.	−	104705.i	0.524028	−	0.524028i
$448$	71032.6	−	71032.6i	0.353917	−	0.353917i
$449$	−90656.6	+	90656.6i	−0.449684	+	0.449684i	−0.895249	−	0.445566i	$-0.853003\pi$
$449$	−90656.6	+	90656.6i	−0.449684	+	0.449684i	0.445566	+	0.895249i	$0.353003\pi$
$450$	738902.	+	86886.3i	3.64890	+	0.429068i
$451$	23401.1			0.115049
$452$	−333676.			−1.63323
$453$	454519.	+	454519.i	2.21491	+	2.21491i
$454$		−	726276.i		−	3.52363i
$455$	259070.	−	41257.4i	1.25140	−	0.199287i
$456$	−1.14272e6			−5.49553
$457$	189607.	−	189607.i	0.907864	−	0.907864i	−0.0882353	−	0.996100i	$-0.528123\pi$
$457$	189607.	−	189607.i	0.907864	−	0.907864i	0.996100	+	0.0882353i	$0.0281227\pi$
$458$			481795.i			2.29684i
$459$		−	105875.i		−	0.502535i
$460$	−198004.	+	408622.i	−0.935748	+	1.93110i
$461$	261344.	+	261344.i	1.22973	+	1.22973i	0.964065	+	0.265668i	$0.0855924\pi$
$461$	261344.	+	261344.i	1.22973	+	1.22973i	0.265668	+	0.964065i	$0.414408\pi$
$462$	−273453.	−	273453.i	−1.28115	−	1.28115i
$463$	−32654.1	−	32654.1i	−0.152327	−	0.152327i	0.626830	−	0.779156i	$-0.284352\pi$
$463$	−32654.1	−	32654.1i	−0.152327	−	0.152327i	−0.779156	+	0.626830i	$0.784352\pi$
$464$	512927.			2.38243
$465$	−123222.	+	42782.2i	−0.569881	+	0.197860i
$466$	−334327.	+	334327.i	−1.53957	+	1.53957i
$467$	−42372.2			−0.194289			−0.0971443	−	0.995270i	$-0.530971\pi$
$467$	−42372.2			−0.194289			−0.0971443	+	0.995270i	$0.530971\pi$
$468$	−1.00837e6	−	179587.i	−4.60393	−	0.819941i
$469$	−84670.4			−0.384934
$470$	−370262.	−	179416.i	−1.67615	−	0.812206i
$471$	−520679.			−2.34708
$472$	667901.			2.99797
$473$	−55917.4	+	55917.4i	−0.249934	+	0.249934i
$474$	−670656.	−	670656.i	−2.98499	−	2.98499i
$475$	34702.6	−	295119.i	0.153806	−	1.30801i
$476$	133954.	−	133954.i	0.591210	−	0.591210i
$477$			318702.i			1.40071i
$478$	−19999.6			−0.0875317
$479$	98169.3	−	98169.3i	0.427863	−	0.427863i	−0.460037	−	0.887900i	$-0.652164\pi$
$479$	98169.3	−	98169.3i	0.427863	−	0.427863i	0.887900	+	0.460037i	$0.152164\pi$
$480$	−176721.	−	508998.i	−0.767020	−	2.20919i
$481$	−34992.3	+	24412.5i	−0.151245	+	0.105517i
$482$			413225.i			1.77866i
$483$	335997.	−	335997.i	1.44026	−	1.44026i
$484$	432264.			1.84526
$485$	264425.	−	91806.9i	1.12414	−	0.390294i
$486$	17875.6	+	17875.6i	0.0756811	+	0.0756811i
$487$	−80584.9	+	80584.9i	−0.339778	+	0.339778i	−0.856284	−	0.516506i	$-0.827233\pi$
$487$	−80584.9	+	80584.9i	−0.339778	+	0.339778i	0.516506	+	0.856284i	$0.327233\pi$
$488$	240342.	+	240342.i	1.00923	+	1.00923i
$489$	−232951.	+	232951.i	−0.974198	+	0.974198i
$490$	−86896.0	−	250280.i	−0.361916	−	1.04240i
$491$		−	239274.i		−	0.992506i	−0.868178	−	0.496253i	$-0.834709\pi$
$491$		−	239274.i		−	0.992506i	0.868178	−	0.496253i	$-0.165291\pi$
$492$	−175509.	−	175509.i	−0.725053	−	0.725053i
$493$	80071.4			0.329446
$494$	−102661.	+	576437.i	−0.420680	+	2.36210i
$495$	−210948.	+	73240.1i	−0.860925	+	0.298909i
$496$	124332.	+	124332.i	0.505381	+	0.505381i
$497$			169784.i			0.687358i
$498$	897890.			3.62047
$499$	171858.	+	171858.i	0.690191	+	0.690191i	0.962274	−	0.272083i	$-0.0877124\pi$
$499$	171858.	+	171858.i	0.690191	+	0.690191i	−0.272083	+	0.962274i	$0.587712\pi$
$500$	566075.	−	124876.i	2.26430	−	0.499505i
$501$	492362.	−	492362.i	1.96160	−	1.96160i
$502$	−217328.	−	217328.i	−0.862398	−	0.862398i
$503$		−	13319.1i		−	0.0526429i	−0.999654	−	0.0263214i	$-0.991621\pi$
$503$		−	13319.1i		−	0.0526429i	0.999654	−	0.0263214i	$-0.00837934\pi$
$504$			1.55954e6i			6.13954i
$505$	66518.5	−	137274.i	0.260831	−	0.538278i
$506$		−	195058.i		−	0.761837i
$507$	−154138.	+	419013.i	−0.599645	+	1.63009i
$508$		−	828589.i		−	3.21079i
$509$	63649.4	+	63649.4i	0.245674	+	0.245674i	0.819192	−	0.573519i	$-0.194422\pi$
$509$	63649.4	+	63649.4i	0.245674	+	0.245674i	−0.573519	+	0.819192i	$0.694422\pi$
$510$	−76811.9	−	221236.i	−0.295317	−	0.850579i
$511$			158967.i			0.608788i
$512$	402805.	−	402805.i	1.53658	−	1.53658i
$513$	432819.	−	432819.i	1.64464	−	1.64464i
$514$	−209064.	+	209064.i	−0.791320	+	0.791320i
$515$	−393703.	−	190775.i	−1.48441	−	0.719295i
$516$	838765.			3.15022
$517$	123489.			0.462007
$518$	80772.1	+	80772.1i	0.301025	+	0.301025i
$519$			519351.i			1.92809i
$520$	−641526.	+	102164.i	−2.37251	+	0.377826i
$521$	−94374.7			−0.347680			−0.173840	−	0.984774i	$-0.555618\pi$
$521$	−94374.7			−0.347680			−0.173840	+	0.984774i	$0.555618\pi$
$522$	−819562.	+	819562.i	−3.00774	+	3.00774i
$523$		−	188571.i		−	0.689400i	−0.938713	−	0.344700i	$-0.887981\pi$
$523$		−	188571.i		−	0.689400i	0.938713	−	0.344700i	$-0.112019\pi$
$524$		−	154744.i		−	0.563573i
$525$	−602478.	−	70844.4i	−2.18586	−	0.257032i
$526$	−515030.	−	515030.i	−1.86149	−	1.86149i
$527$	19409.1	+	19409.1i	0.0698850	+	0.0698850i
$528$	318386.	+	318386.i	1.14205	+	1.14205i
$529$	−40169.6			−0.143544
$530$	116570.	+	335749.i	0.414989	+	1.19526i
$531$	−501779.	+	501779.i	−1.77960	+	1.77960i
$532$	1.09522e6			3.86970
$533$	−59319.9	+	41384.8i	−0.208808	+	0.145676i
$534$	610868.			2.14222
$535$	188549.	−	389108.i	0.658743	−	1.35945i
$536$	209666.			0.729792
$537$	−799407.			−2.77217
$538$	−133921.	+	133921.i	−0.462682	+	0.462682i
$539$	56227.3	+	56227.3i	0.193540	+	0.193540i
$540$	1.07457e6	+	520701.i	3.68509	+	1.78567i
$541$	−10397.4	+	10397.4i	−0.0355248	+	0.0355248i	−0.724646	−	0.689121i	$-0.757997\pi$
$541$	−10397.4	+	10397.4i	−0.0355248	+	0.0355248i	0.689121	+	0.724646i	$0.257997\pi$
$542$		−	717922.i		−	2.44387i
$543$	−466954.			−1.58371
$544$	−80173.5	+	80173.5i	−0.270915	+	0.270915i
$545$	62798.3	+	180873.i	0.211424	+	0.608950i
$546$	1.17678e6	+	209580.i	3.94739	+	0.703015i
$547$			410344.i			1.37143i	0.727870	+	0.685715i	$0.240510\pi$
$547$			410344.i			1.37143i	−0.727870	+	0.685715i	$0.759490\pi$
$548$	−343316.	+	343316.i	−1.14323	+	1.14323i
$549$	−361128.			−1.19816
$550$	−195443.	+	154315.i	−0.646092	+	0.510133i
$551$	327335.	+	327335.i	1.07818	+	1.07818i
$552$	−832019.	+	832019.i	−2.73058	+	2.73058i
$553$	365568.	+	365568.i	1.19541	+	1.19541i
$554$	−78840.6	+	78840.6i	−0.256880	+	0.256880i
$555$	93205.1	−	32360.3i	0.302590	−	0.105058i
$556$		−	23607.4i		−	0.0763656i
$557$	−152228.	−	152228.i	−0.490663	−	0.490663i	0.417852	−	0.908515i	$-0.362783\pi$
$557$	−152228.	−	152228.i	−0.490663	−	0.490663i	−0.908515	+	0.417852i	$0.862783\pi$
$558$	−397319.			−1.27606
$559$	42856.3	−	240636.i	0.137148	−	0.770081i
$560$	268210.	+	772505.i	0.855261	+	2.46335i
$561$	49702.3	+	49702.3i	0.157925	+	0.157925i
$562$			406107.i			1.28578i
$563$	−320222.			−1.01026			−0.505132	−	0.863042i	$-0.668556\pi$
$563$	−320222.			−1.01026			−0.505132	+	0.863042i	$0.668556\pi$
$564$	−926173.	−	926173.i	−2.91161	−	2.91161i
$565$	98049.8	−	202346.i	0.307150	−	0.633865i
$566$	−149374.	+	149374.i	−0.466276	+	0.466276i
$567$	−302636.	−	302636.i	−0.941357	−	0.941357i
$568$		−	420429.i		−	1.30316i
$569$			13756.2i			0.0424887i	0.999774	+	0.0212443i	$0.00676279\pi$
$569$			13756.2i			0.0424887i	−0.999774	+	0.0212443i	$0.993237\pi$
$570$	590410.	−	1.21843e6i	1.81720	−	3.75017i
$571$		−	644788.i		−	1.97763i	−0.149152	−	0.988814i	$-0.547654\pi$
$571$		−	644788.i		−	1.97763i	0.149152	−	0.988814i	$-0.452346\pi$
$572$	281159.	−	196152.i	0.859330	−	0.599516i
$573$		−	564565.i		−	1.71951i
$574$	136927.	+	136927.i	0.415591	+	0.415591i
$575$	−189611.	−	240145.i	−0.573491	−	0.726336i
$576$		−	264293.i		−	0.796600i
$577$	−150478.	+	150478.i	−0.451983	+	0.451983i	−0.896012	−	0.444029i	$-0.853549\pi$
$577$	−150478.	+	150478.i	−0.451983	+	0.451983i	0.444029	+	0.896012i	$0.353549\pi$
$578$	395508.	−	395508.i	1.18386	−	1.18386i
$579$	−304857.	+	304857.i	−0.909367	+	0.909367i
$580$	−393799.	+	812684.i	−1.17063	+	2.41583i
$581$	−489431.			−1.44991
$582$	1.27537e6			3.76523
$583$	−75428.5	−	75428.5i	−0.221921	−	0.221921i
$584$		−	393645.i		−	1.15419i
$585$	405211.	−	558718.i	1.18405	−	1.63261i
$586$	−93838.5			−0.273266
$587$	−58926.8	+	58926.8i	−0.171016	+	0.171016i	−0.787426	−	0.616410i	$-0.788587\pi$
$587$	−58926.8	+	58926.8i	−0.171016	+	0.171016i	0.616410	+	0.787426i	$0.288587\pi$
$588$		−	843413.i		−	2.43941i
$589$			158690.i			0.457424i
$590$	−345085.	+	712153.i	−0.991340	+	2.04583i
$591$	54463.8	+	54463.8i	0.155931	+	0.155931i
$592$	−94044.3	−	94044.3i	−0.268342	−	0.268342i
$593$	28704.1	+	28704.1i	0.0816273	+	0.0816273i	0.746742	−	0.665114i	$-0.231617\pi$
$593$	28704.1	+	28704.1i	0.0816273	+	0.0816273i	−0.665114	+	0.746742i	$0.731617\pi$
$594$	−512953.			−1.45380
$595$	41869.4	+	120593.i	0.118267	+	0.340635i
$596$	248501.	−	248501.i	0.699576	−	0.699576i
$597$	492530.			1.38192
$598$	344959.	+	494455.i	0.964639	+	1.38269i
$599$	−458810.			−1.27873			−0.639366	−	0.768903i	$-0.720803\pi$
$599$	−458810.			−1.27873			−0.639366	+	0.768903i	$0.720803\pi$
$600$	1.49189e6	+	175429.i	4.14415	+	0.487304i
$601$	88231.5			0.244273			0.122136	−	0.992513i	$-0.461025\pi$
$601$	88231.5			0.244273			0.122136	+	0.992513i	$0.461025\pi$
$602$	−654380.			−1.80566
$603$	−157518.	+	157518.i	−0.433206	+	0.433206i
$604$	1.07872e6	+	1.07872e6i	2.95690	+	2.95690i
$605$	−127020.	+	262131.i	−0.347025	+	0.716156i
$606$	491467.	−	491467.i	1.33829	−	1.33829i
$607$			45108.0i			0.122427i	0.998125	+	0.0612134i	$0.0194970\pi$
$607$			45108.0i			0.122427i	−0.998125	+	0.0612134i	$0.980503\pi$
$608$	−655504.			−1.77324
$609$	668246.	−	668246.i	1.80178	−	1.80178i
$610$	−380444.	+	132088.i	−1.02243	+	0.354981i
$611$	−313035.	+	218390.i	−0.838514	+	0.584993i
$612$		−	498406.i		−	1.33070i
$613$	−106294.	+	106294.i	−0.282870	+	0.282870i	−0.834253	−	0.551382i	$-0.814101\pi$
$613$	−106294.	+	106294.i	−0.282870	+	0.282870i	0.551382	+	0.834253i	$0.314101\pi$
$614$	117278.			0.311086
$615$	158004.	−	54858.2i	0.417751	−	0.145041i
$616$	−369104.	−	369104.i	−0.972718	−	0.972718i
$617$	454876.	−	454876.i	1.19488	−	1.19488i	0.219194	−	0.975681i	$-0.429657\pi$
$617$	454876.	−	454876.i	1.19488	−	1.19488i	0.975681	−	0.219194i	$-0.0703428\pi$
$618$	−1.40953e6	−	1.40953e6i	−3.69059	−	3.69059i
$619$	89601.7	−	89601.7i	0.233849	−	0.233849i	−0.580448	−	0.814297i	$-0.697123\pi$
$619$	89601.7	−	89601.7i	0.233849	−	0.233849i	0.814297	+	0.580448i	$0.197123\pi$
$620$	−292448.	+	101536.i	−0.760790	+	0.264143i
$621$		−	630276.i		−	1.63436i
$622$	469991.	+	469991.i	1.21481	+	1.21481i
$623$	−332978.			−0.857906
$624$	−1.37015e6	−	244017.i	−3.51883	−	0.626688i
$625$	−90613.0	+	379970.i	−0.231969	+	0.972723i
$626$	−379962.	−	379962.i	−0.969597	−	0.969597i
$627$			406369.i			1.03368i
$628$	−1.23574e6			−3.13335
$629$	−14681.0	−	14681.0i	−0.0371068	−	0.0371068i
$630$	−1.66287e6	−	805771.i	−4.18965	−	2.03016i
$631$	443560.	−	443560.i	1.11402	−	1.11402i	0.121420	−	0.992601i	$-0.461255\pi$
$631$	443560.	−	443560.i	1.11402	−	1.11402i	0.992601	−	0.121420i	$-0.0387447\pi$
$632$	−905244.	−	905244.i	−2.26637	−	2.26637i
$633$			1.21738e6i			3.03823i
$634$			326387.i			0.811996i
$635$	502467.	+	243479.i	1.24612	+	0.603828i
$636$			1.13143e6i			2.79714i
$637$	−241969.	−	43093.8i	−0.596323	−	0.106203i
$638$		−	387939.i		−	0.953064i
$639$	315859.	+	315859.i	0.773556	+	0.773556i
$640$	84212.6	+	242551.i	0.205597	+	0.592166i
$641$			261622.i			0.636734i	0.947967	+	0.318367i	$0.103134\pi$
$641$			261622.i			0.636734i	−0.947967	+	0.318367i	$0.896866\pi$
$642$	1.39308e6	−	1.39308e6i	3.37991	−	3.37991i
$643$	−197717.	+	197717.i	−0.478213	+	0.478213i	−0.904560	−	0.426347i	$-0.859800\pi$
$643$	−197717.	+	197717.i	−0.478213	+	0.478213i	0.426347	+	0.904560i	$0.359800\pi$
$644$	797433.	−	797433.i	1.92275	−	1.92275i
$645$	−246469.	+	508638.i	−0.592437	+	1.22261i
$646$	−284915.			−0.682732
$647$	60908.9			0.145503			0.0727515	−	0.997350i	$-0.476822\pi$
$647$	60908.9			0.145503			0.0727515	+	0.997350i	$0.476822\pi$
$648$	749407.	+	749407.i	1.78471	+	1.78471i
$649$		−	237517.i		−	0.563903i
$650$	222525.	−	736816.i	0.526687	−	1.74394i
$651$	323962.			0.764419
$652$	−552871.	+	552871.i	−1.30055	+	1.30055i
$653$			244735.i			0.573944i	0.957939	+	0.286972i	$0.0926487\pi$
$653$			244735.i			0.573944i	−0.957939	+	0.286972i	$0.907351\pi$
$654$			872388.i			2.03964i
$655$	93838.7	+	45471.0i	0.218725	+	0.105987i
$656$	−159427.	−	159427.i	−0.370470	−	0.370470i
$657$	295737.	+	295737.i	0.685133	+	0.685133i
$658$	722573.	+	722573.i	1.66890	+	1.66890i
$659$	−732439.			−1.68656			−0.843278	−	0.537478i	$-0.819377\pi$
$659$	−732439.			−1.68656			−0.843278	+	0.537478i	$0.819377\pi$
$660$	−748893.	+	260012.i	−1.71922	+	0.596905i
$661$	−234413.	+	234413.i	−0.536512	+	0.536512i	−0.922503	−	0.385991i	$-0.873860\pi$
$661$	−234413.	+	234413.i	−0.536512	+	0.536512i	0.385991	+	0.922503i	$0.373860\pi$
$662$	−307232.			−0.701052
$663$	−213889.	−	38092.8i	−0.486589	−	0.0866595i
$664$	1.21196e6			2.74886
$665$	−321827.	+	664155.i	−0.727745	+	1.50185i
$666$	300531.			0.677549
$667$	476669.			1.07143
$668$	1.16854e6	−	1.16854e6i	2.61873	−	2.61873i
$669$	−437231.	−	437231.i	−0.976920	−	0.976920i
$670$	−108329.	+	223558.i	−0.241320	+	0.498013i
$671$	85469.7	−	85469.7i	0.189831	−	0.189831i
$672$			1.33819e6i			2.96334i
$673$	−201880.			−0.445722			−0.222861	−	0.974850i	$-0.571540\pi$
$673$	−201880.			−0.445722			−0.222861	+	0.974850i	$0.571540\pi$
$674$	−95529.2	+	95529.2i	−0.210289	+	0.210289i
$675$	−631520.	+	498628.i	−1.38605	+	1.09438i
$676$	−365821.	+	994458.i	−0.800525	+	2.17617i
$677$		−	105415.i		−	0.229998i	−0.993366	−	0.114999i	$-0.963313\pi$
$677$		−	105415.i		−	0.229998i	0.993366	−	0.114999i	$-0.0366865\pi$
$678$	724433.	−	724433.i	1.57594	−	1.57594i
$679$	−695194.			−1.50788
$680$	−103680.	−	298621.i	−0.224221	−	0.645807i
$681$	1.10168e6	+	1.10168e6i	2.37552	+	2.37552i
$682$	94035.2	−	94035.2i	0.202172	−	0.202172i
$683$	505930.	+	505930.i	1.08455	+	1.08455i	0.996079	+	0.0884688i	$0.0281974\pi$
$683$	505930.	+	505930.i	1.08455	+	1.08455i	0.0884688	+	0.996079i	$0.471803\pi$
$684$	2.03750e6	−	2.03750e6i	4.35498	−	4.35498i
$685$	−107309.	−	309074.i	−0.228694	−	0.658690i
$686$		−	428339.i		−	0.910206i
$687$	−730827.	−	730827.i	−1.54846	−	1.54846i
$688$	761905.			1.60962
$689$	324600.	+	57810.0i	0.683770	+	0.121777i
$690$	−457264.	−	1.31703e6i	−0.960438	−	2.76628i
$691$	627031.	+	627031.i	1.31321	+	1.31321i	0.919038	+	0.394169i	$0.128968\pi$
$691$	627031.	+	627031.i	1.31321	+	1.31321i	0.394169	+	0.919038i	$0.371032\pi$
$692$			1.23259e6i			2.57399i
$693$	554599.			1.15482
$694$	−274354.	−	274354.i	−0.569629	−	0.569629i
$695$	14315.8	+	6936.96i	0.0296378	+	0.0143615i
$696$	−1.65475e6	+	1.65475e6i	−3.41598	+	3.41598i
$697$	−24887.6	−	24887.6i	−0.0512292	−	0.0512292i
$698$		−	293919.i		−	0.603277i
$699$		−	1.01427e6i		−	2.07586i
$700$	−1.42988e6	−	168137.i	−2.91812	−	0.343137i
$701$		−	490442.i		−	0.998049i	−0.866588	−	0.499025i	$-0.833692\pi$
$701$		−	490442.i		−	0.998049i	0.866588	−	0.499025i	$-0.166308\pi$
$702$	1.30029e6	−	907155.i	2.63856	−	1.84080i
$703$		−	120033.i		−	0.242879i
$704$	62551.4	+	62551.4i	0.126209	+	0.126209i
$705$	833797.	−	289490.i	1.67758	−	0.582446i
$706$		−	1.22333e6i		−	2.45434i
$707$	−267894.	+	267894.i	−0.535949	+	0.535949i
$708$	−1.78138e6	+	1.78138e6i	−3.55378	+	3.55378i
$709$	−137372.	+	137372.i	−0.273278	+	0.273278i	−0.830419	−	0.557140i	$-0.811899\pi$
$709$	−137372.	+	137372.i	−0.273278	+	0.273278i	0.557140	+	0.830419i	$0.311899\pi$
$710$	448285.	+	217224.i	0.889278	+	0.430914i
$711$	1.36018e6			2.69065
$712$	824542.			1.62650
$713$	115543.	+	115543.i	0.227282	+	0.227282i
$714$			581646.i			1.14094i
$715$	36331.3	+	228137.i	0.0710671	+	0.446256i
$716$	−1.89726e6			−3.70084
$717$	30337.0	−	30337.0i	0.0590113	−	0.0590113i
$718$			1.49851e6i			2.90678i
$719$		−	890512.i		−	1.72259i	−0.508105	−	0.861295i	$-0.669654\pi$
$719$		−	890512.i		−	1.72259i	0.508105	−	0.861295i	$-0.330346\pi$
$720$	1.93611e6	+	938173.i	3.73478	+	1.80975i
$721$	768319.	+	768319.i	1.47799	+	1.47799i
$722$	−493242.	−	493242.i	−0.946207	−	0.946207i
$723$	−626814.	−	626814.i	−1.19912	−	1.19912i
$724$	−1.10824e6			−2.11425
$725$	−377105.	−	477610.i	−0.717442	−	0.908652i
$726$	−938475.	+	938475.i	−1.78053	+	1.78053i
$727$	−99031.5			−0.187372			−0.0936860	−	0.995602i	$-0.529865\pi$
$727$	−99031.5			−0.187372			−0.0936860	+	0.995602i	$0.529865\pi$
$728$	1.58841e6	+	282889.i	2.99708	+	0.533768i
$729$	504100.			0.948554
$730$	419726.	+	203385.i	0.787627	+	0.381657i
$731$	118939.			0.222581
$732$	−1.28205e6			−2.39267
$733$	483767.	−	483767.i	0.900385	−	0.900385i	−0.0950840	−	0.995469i	$-0.530312\pi$
$733$	483767.	−	483767.i	0.900385	−	0.900385i	0.995469	+	0.0950840i	$0.0303120\pi$
$734$	716878.	+	716878.i	1.33062	+	1.33062i
$735$	511457.	+	247835.i	0.946748	+	0.458762i
$736$	−477276.	+	477276.i	−0.881077	+	0.881077i
$737$		−	74560.8i		−	0.137270i
$738$	509469.			0.935416
$739$	643742.	−	643742.i	1.17875	−	1.17875i	0.198690	−	0.980062i	$-0.436331\pi$
$739$	643742.	−	643742.i	1.17875	−	1.17875i	0.980062	−	0.198690i	$-0.0636688\pi$
$740$	221207.	−	76801.8i	0.403957	−	0.140252i
$741$	−718663.	−	1.03011e6i	−1.30885	−	1.87607i
$742$		−	882710.i		−	1.60328i
$743$	471401.	−	471401.i	0.853911	−	0.853911i	−0.136701	−	0.990612i	$-0.543650\pi$
$743$	471401.	−	471401.i	0.853911	−	0.853911i	0.990612	+	0.136701i	$0.0436499\pi$
$744$	−802215.			−1.44925
$745$	77672.8	+	223715.i	0.139945	+	0.403073i
$746$	236024.	+	236024.i	0.424110	+	0.424110i
$747$	−910520.	+	910520.i	−1.63173	+	1.63173i
$748$	117960.	+	117960.i	0.210829	+	0.210829i
$749$	−759353.	+	759353.i	−1.35357	+	1.35357i
$750$	−957872.	+	1.50010e6i	−1.70288	+	2.66685i
$751$			55715.2i			0.0987856i	0.998779	+	0.0493928i	$0.0157286\pi$
$751$			55715.2i			0.0987856i	−0.998779	+	0.0493928i	$0.984271\pi$
$752$	−841304.	−	841304.i	−1.48771	−	1.48771i
$753$	659321.			1.16281
$754$	686068.	+	983393.i	1.20677	+	1.72975i
$755$	−971132.	+	337172.i	−1.70367	+	0.591504i
$756$	−2.09705e6	−	2.09705e6i	−3.66915	−	3.66915i
$757$		−	1.06857e6i		−	1.86471i	−0.361544	−	0.932355i	$-0.617750\pi$
$757$		−	1.06857e6i		−	1.86471i	0.361544	−	0.932355i	$-0.382250\pi$
$758$	−353.450			−0.000615161
$759$	295880.	+	295880.i	0.513608	+	0.513608i
$760$	796928.	−	1.64462e6i	1.37972	−	2.84734i
$761$	−631595.	+	631595.i	−1.09061	+	1.09061i	−0.0951458	+	0.995463i	$0.530332\pi$
$761$	−631595.	+	631595.i	−1.09061	+	1.09061i	−0.995463	+	0.0951458i	$0.969668\pi$
$762$	1.79892e6	+	1.79892e6i	3.09815	+	3.09815i
$763$		−	475530.i		−	0.816825i
$764$		−	1.33990e6i		−	2.29555i
$765$	302240.	+	146455.i	0.516451	+	0.250255i
$766$		−	632143.i		−	1.07735i
$767$	420047.	+	602085.i	0.714015	+	1.02345i
$768$			1.57452e6i			2.66947i
$769$	−515335.	−	515335.i	−0.871439	−	0.871439i	0.121191	−	0.992629i	$-0.461329\pi$
$769$	−515335.	−	515335.i	−0.871439	−	0.871439i	−0.992629	+	0.121191i	$0.961329\pi$
$770$	584264.	−	202854.i	0.985435	−	0.342138i
$771$		−	634250.i		−	1.06697i
$772$	−723527.	+	723527.i	−1.21400	+	1.21400i
$773$	−272846.	+	272846.i	−0.456624	+	0.456624i	−0.897546	−	0.440922i	$-0.854652\pi$
$773$	−272846.	+	272846.i	−0.456624	+	0.456624i	0.440922	+	0.897546i	$0.354652\pi$
$774$	−1.21738e6	+	1.21738e6i	−2.03210	+	2.03210i
$775$	24362.0	−	207180.i	0.0405611	−	0.344941i
$776$	1.72148e6			2.85877
$777$	−245044.			−0.405884
$778$	−1.36845e6	−	1.36845e6i	−2.26084	−	2.26084i
$779$		−	203483.i		−	0.335315i
$780$	1.43855e6	−	1.98352e6i	2.36448	−	3.26023i
$781$	−149512.			−0.245117
$782$	−207448.	+	207448.i	−0.339231	+	0.339231i
$783$		−	1.25352e6i		−	2.04460i
$784$		−	766128.i		−	1.24643i
$785$	363120.	−	749372.i	0.589266	−	1.21607i
$786$	335959.	+	335959.i	0.543802	+	0.543802i
$787$	−487093.	−	487093.i	−0.786435	−	0.786435i	0.194473	−	0.980908i	$-0.437700\pi$
$787$	−487093.	−	487093.i	−0.786435	−	0.786435i	−0.980908	+	0.194473i	$0.937700\pi$
$788$	129261.	+	129261.i	0.208168	+	0.208168i
$789$	1.56248e6			2.50992
$790$	1.43294e6	−	497508.i	2.29600	−	0.797161i
$791$	−394882.	+	394882.i	−0.631123	+	0.631123i
$792$	−1.37333e6			−2.18940
$793$	−65505.7	+	367811.i	−0.104168	+	0.584896i
$794$	1.84261e6			2.92275
$795$	−686115.	−	332468.i	−1.08558	−	0.526037i
$796$	1.16894e6			1.84487
$797$	−696225.			−1.09606			−0.548029	−	0.836460i	$-0.684622\pi$
$797$	−696225.			−1.09606			−0.548029	+	0.836460i	$0.684622\pi$
$798$	−2.37779e6	+	2.37779e6i	−3.73394	+	3.73394i
$799$	−131333.	−	131333.i	−0.205722	−	0.205722i
$800$	855804.	+	100633.i	1.33719	+	0.157239i
$801$	−619461.	+	619461.i	−0.965492	+	0.965492i
$802$			498040.i			0.774310i
$803$	−139987.			−0.217098
$804$	−559208.	+	559208.i	−0.865090	+	0.865090i
$805$	249251.	+	717898.i	0.384631	+	1.10782i
$806$	−72070.5	+	404672.i	−0.110940	+	0.622922i
$807$		−	406284.i		−	0.623853i
$808$	663376.	−	663376.i	1.01610	−	1.01610i
$809$	−78183.5			−0.119459			−0.0597294	−	0.998215i	$-0.519024\pi$
$809$	−78183.5			−0.119459			−0.0597294	+	0.998215i	$0.519024\pi$
$810$	−1.18626e6	+	411862.i	−1.80804	+	0.627743i
$811$	−162602.	−	162602.i	−0.247220	−	0.247220i	0.572609	−	0.819829i	$-0.305931\pi$
$811$	−162602.	−	162602.i	−0.247220	−	0.247220i	−0.819829	+	0.572609i	$0.805931\pi$
$812$	1.58597e6	−	1.58597e6i	2.40537	−	2.40537i
$813$	1.08900e6	+	1.08900e6i	1.64759	+	1.64759i
$814$	−71128.0	+	71128.0i	−0.107347	+	0.107347i
$815$	−172808.	−	497728.i	−0.260166	−	0.749336i
$816$		−	677220.i		−	1.01707i
$817$	486226.	+	486226.i	0.728441	+	0.728441i
$818$	291095.			0.435039
$819$	−1.40586e6	+	980806.i	−2.09592	+	1.46223i
$820$	374996.	−	130197.i	0.557698	−	0.193630i
$821$	129092.	+	129092.i	0.191520	+	0.191520i	0.796352	−	0.604833i	$-0.206760\pi$
$821$	129092.	+	129092.i	0.191520	+	0.191520i	−0.604833	+	0.796352i	$0.706760\pi$
$822$		−	1.49072e6i		−	2.20624i
$823$	200717.			0.296335			0.148168	−	0.988962i	$-0.452662\pi$
$823$	200717.			0.296335			0.148168	+	0.988962i	$0.452662\pi$
$824$	−1.90256e6	−	1.90256e6i	−2.80210	−	2.80210i
$825$	62385.6	−	530542.i	0.0916593	−	0.779493i
$826$	1.38978e6	−	1.38978e6i	2.03698	−	2.03698i
$827$	267148.	+	267148.i	0.390607	+	0.390607i	0.874904	−	0.484297i	$-0.160924\pi$
$827$	267148.	+	267148.i	0.390607	+	0.390607i	−0.484297	+	0.874904i	$0.660924\pi$
$828$		−	2.96703e6i		−	4.32774i
$829$			890085.i			1.29516i	0.761999	+	0.647579i	$0.224218\pi$
$829$			890085.i			1.29516i	−0.761999	+	0.647579i	$0.775782\pi$
$830$	−626186.	+	1.29226e6i	−0.908965	+	1.87583i
$831$		−	239184.i		−	0.346362i
$832$	−269184.	−	47940.6i	−0.388869	−	0.0692559i
$833$		−	119598.i		−	0.172359i
$834$	51253.2	+	51253.2i	0.0736866	+	0.0736866i
$835$	365246.	+	1.05199e6i	0.523856	+	1.50882i
$836$			964450.i			1.37996i
$837$	303849.	−	303849.i	0.433718	−	0.433718i
$838$	−1.38264e6	+	1.38264e6i	−1.96888	+	1.96888i
$839$	259979.	−	259979.i	0.369330	−	0.369330i	−0.497903	−	0.867233i	$-0.665896\pi$
$839$	259979.	−	259979.i	0.369330	−	0.369330i	0.867233	+	0.497903i	$0.165896\pi$
$840$	−3.35745e6	−	1.62691e6i	−4.75829	−	2.30571i
$841$	240738.			0.340371
$842$	−2.03976e6			−2.87710
$843$	−616017.	−	616017.i	−0.866837	−	0.866837i
$844$			2.88926e6i			4.05603i
$845$	−495557.	−	514057.i	−0.694033	−	0.719943i
$846$	2.68850e6			3.75637
$847$	511554.	−	511554.i	0.713058	−	0.713058i
$848$			1.02775e6i			1.42922i
$849$		−	453167.i		−	0.628699i
$850$	371975.	+	43740.0i	0.514844	+	0.0605397i
$851$	−87396.4	−	87396.4i	−0.120680	−	0.120680i
$852$	1.12134e6	+	1.12134e6i	1.54475	+	1.54475i
$853$	124.423	+	124.423i	0.000171003	+	0.000171003i	0.707192	−	0.707021i	$-0.249962\pi$
$853$	124.423	+	124.423i	0.000171003	+	0.000171003i	−0.707021	+	0.707192i	$0.749962\pi$
$854$	1.00022e6			1.37145
$855$	636854.	+	1.83428e6i	0.871179	+	2.50919i
$856$	1.88036e6	−	1.88036e6i	2.56622	−	2.56622i
$857$	−465991.			−0.634477			−0.317239	−	0.948346i	$-0.602756\pi$
$857$	−465991.			−0.634477			−0.317239	+	0.948346i	$0.602756\pi$
$858$	−184556.	+	1.03627e6i	−0.250700	+	1.40767i
$859$	−706293.			−0.957191			−0.478595	−	0.878036i	$-0.658854\pi$
$859$	−706293.			−0.957191			−0.478595	+	0.878036i	$0.658854\pi$
$860$	−584952.	+	1.20717e6i	−0.790903	+	1.63219i
$861$	−415405.			−0.560358
$862$	1.00220e6			1.34878
$863$	584073.	−	584073.i	0.784234	−	0.784234i	−0.196308	−	0.980542i	$-0.562895\pi$
$863$	584073.	−	584073.i	0.784234	−	0.784234i	0.980542	+	0.196308i	$0.0628953\pi$
$864$	1.25512e6	+	1.25512e6i	1.68134	+	1.68134i
$865$	−747461.	−	362194.i	−0.998978	−	0.484071i
$866$	−287189.	+	287189.i	−0.382941	+	0.382941i
$867$			1.19988e6i			1.59624i
$868$	768868.			1.02050
$869$	−321920.	+	321920.i	−0.426293	+	0.426293i
$870$	−909427.	−	2.61935e6i	−1.20151	−	3.46064i
$871$	131861.	+	189005.i	0.173811	+	0.249137i
$872$			1.17754e6i			1.54861i
$873$	−1.29331e6	+	1.29331e6i	−1.69697	+	1.69697i
$874$	−1.69611e6			−2.22040
$875$	522127.	−	817691.i	0.681962	−	1.06800i
$876$	1.04990e6	+	1.04990e6i	1.36817	+	1.36817i
$877$	−903081.	+	903081.i	−1.17416	+	1.17416i	−0.192952	+	0.981208i	$0.561806\pi$
$877$	−903081.	+	903081.i	−1.17416	+	1.17416i	−0.981208	+	0.192952i	$0.938194\pi$
$878$	−96049.8	−	96049.8i	−0.124597	−	0.124597i
$879$	142342.	−	142342.i	0.184228	−	0.184228i
$880$	−680269.	+	236186.i	−0.878446	+	0.304992i
$881$			1.43322e6i			1.84655i	0.384144	+	0.923273i	$0.374497\pi$
$881$			1.43322e6i			1.84655i	−0.384144	+	0.923273i	$0.625503\pi$
$882$	1.22413e6	+	1.22413e6i	1.57359	+	1.57359i
$883$	−226067.			−0.289945			−0.144972	−	0.989436i	$-0.546309\pi$
$883$	−226067.			−0.289945			−0.144972	+	0.989436i	$0.546309\pi$
$884$	−507630.	−	90406.9i	−0.649595	−	0.115690i
$885$	−556799.	−	1.60371e6i	−0.710905	−	2.04757i
$886$	−152251.	−	152251.i	−0.193951	−	0.193951i
$887$		−	564525.i		−	0.717523i	−0.933429	−	0.358761i	$-0.883199\pi$
$887$		−	564525.i		−	0.717523i	0.933429	−	0.358761i	$-0.116801\pi$
$888$	606793.			0.769510
$889$	−980575.	−	980575.i	−1.24073	−	1.24073i
$890$	−426018.	+	879173.i	−0.537833	+	1.10993i
$891$	266501.	−	266501.i	0.335695	−	0.335695i
$892$	−1.03769e6	−	1.03769e6i	−1.30419	−	1.30419i
$893$		−	1.07379e6i		−	1.34653i
$894$			1.07902e6i			1.35007i
$895$	557504.	−	1.15052e6i	0.695988	−	1.43631i
$896$		−	637686.i		−	0.794312i
$897$	−1.27329e6	−	226768.i	−1.58250	−	0.281836i
$898$		−	934246.i		−	1.15853i
$899$	229797.	+	229797.i	0.284331	+	0.284331i
$900$	−2.97289e6	+	2.34730e6i	−3.67024	+	2.89790i
$901$			160440.i			0.197634i
$902$	−120578.	+	120578.i	−0.148203	+	0.148203i
$903$	992618.	−	992618.i	1.21732	−	1.21732i
$904$	977831.	−	977831.i	1.19654	−	1.19654i
$905$	325653.	−	672050.i	0.397610	−	0.820548i
$906$	−4.68396e6			−5.70633
$907$	525617.			0.638933			0.319466	−	0.947598i	$-0.396496\pi$
$907$	525617.			0.638933			0.319466	+	0.947598i	$0.396496\pi$
$908$	2.61464e6	+	2.61464e6i	3.17132	+	3.17132i
$909$			996760.i			1.20632i
$910$	−1.12232e6	+	1.54749e6i	−1.35529	+	1.86872i
$911$	1.01637e6			1.22466			0.612332	−	0.790600i	$-0.290231\pi$
$911$	1.01637e6			1.22466			0.612332	+	0.790600i	$0.290231\pi$
$912$	2.76850e6	−	2.76850e6i	3.32855	−	3.32855i
$913$		−	430994.i		−	0.517046i
$914$			1.95396e6i			2.33896i
$915$	376727.	−	777452.i	0.449971	−	0.928606i
$916$	−1.73449e6	−	1.73449e6i	−2.06720	−	2.06720i
$917$	−183128.	−	183128.i	−0.217779	−	0.217779i
$918$	545536.	+	545536.i	0.647348	+	0.647348i
$919$	−984928.			−1.16620			−0.583101	−	0.812400i	$-0.698161\pi$
$919$	−984928.			−1.16620			−0.583101	+	0.812400i	$0.698161\pi$
$920$	−617210.	−	1.77771e6i	−0.729218	−	2.10031i
$921$	−177897.	+	177897.i	−0.209725	+	0.209725i
$922$	−2.69323e6			−3.16820
$923$	378999.	−	264411.i	0.444872	−	0.310367i
$924$	1.96890e6			2.30611
$925$	−18427.4	+	156711.i	−0.0215367	+	0.183153i
$926$	336511.			0.392444
$927$	2.85871e6			3.32667
$928$	−949227.	+	949227.i	−1.10223	+	1.10223i
$929$	718926.	+	718926.i	0.833015	+	0.833015i	0.987928	−	0.154913i	$-0.0495099\pi$
$929$	718926.	+	718926.i	0.833015	+	0.833015i	−0.154913	+	0.987928i	$0.549510\pi$
$930$	414482.	−	855366.i	0.479225	−	0.988977i
$931$	488921.	−	488921.i	0.564078	−	0.564078i
$932$		−	2.40720e6i		−	2.77128i
$933$	−1.42584e6			−1.63798
$934$	218330.	−	218330.i	0.250276	−	0.250276i
$935$	−106195.	+	36870.3i	−0.121473	+	0.0421748i
$936$	3.48129e6	−	2.42874e6i	3.97364	−	2.77223i
$937$		−	1.12059e6i		−	1.27634i	−0.769895	−	0.638170i	$-0.779692\pi$
$937$		−	1.12059e6i		−	1.27634i	0.769895	−	0.638170i	$-0.220308\pi$
$938$	436278.	−	436278.i	0.495858	−	0.495858i
$939$	1.15272e6			1.30735
$940$	1.97888e6	−	687056.i	2.23956	−	0.777564i
$941$	−911478.	−	911478.i	−1.02936	−	1.02936i	−0.999556	−	0.0298031i	$-0.990512\pi$
$941$	−911478.	−	911478.i	−1.02936	−	1.02936i	−0.0298031	−	0.999556i	$-0.509488\pi$
$942$	2.68288e6	−	2.68288e6i	3.02343	−	3.02343i
$943$	−148157.	−	148157.i	−0.166609	−	0.166609i
$944$	−1.61815e6	+	1.61815e6i	−1.81582	+	1.81582i
$945$	1.88789e6	−	655466.i	2.11404	−	0.733984i
$946$		−	576247.i		−	0.643912i
$947$	−76180.1	−	76180.1i	−0.0849457	−	0.0849457i	0.663357	−	0.748303i	$-0.269131\pi$
$947$	−76180.1	−	76180.1i	−0.0849457	−	0.0849457i	−0.748303	+	0.663357i	$0.769131\pi$
$948$	4.82881e6			5.37309
$949$	354855.	−	247566.i	0.394020	−	0.274890i
$950$	1.34184e6	+	1.69946e6i	1.48680	+	1.88306i
$951$	−495090.	−	495090.i	−0.547424	−	0.547424i
$952$			785099.i			0.866264i
$953$	−953191.			−1.04953			−0.524764	−	0.851248i	$-0.675846\pi$
$953$	−953191.			−1.04953			−0.524764	+	0.851248i	$0.675846\pi$
$954$	−1.64216e6	−	1.64216e6i	−1.80434	−	1.80434i
$955$	812534.	+	393726.i	0.890912	+	0.431706i
$956$	71999.9	−	71999.9i	0.0787800	−	0.0787800i
$957$	588458.	+	588458.i	0.642527	+	0.642527i
$958$			1.01167e6i			1.10232i
$959$			812579.i			0.883545i
$960$	568982.	+	275709.i	0.617385	+	0.299164i
$961$		−	812117.i		−	0.879370i
$962$	54513.9	−	306093.i	0.0589057	−	0.330753i
$963$			2.82535e6i			3.04662i
$964$	−1.48764e6	−	1.48764e6i	−1.60082	−	1.60082i
$965$	−226150.	−	651363.i	−0.242852	−	0.699469i
$966$			3.46256e6i			3.71059i
$967$	−1.02453e6	+	1.02453e6i	−1.09565	+	1.09565i	−0.100732	+	0.994914i	$0.532118\pi$
$967$	−1.02453e6	+	1.02453e6i	−1.09565	+	1.09565i	−0.994914	+	0.100732i	$0.967882\pi$
$968$	−1.26674e6	+	1.26674e6i	−1.35188	+	1.35188i
$969$	432182.	−	432182.i	0.460277	−	0.460277i
$970$	−889441.	+	1.83554e6i	−0.945309	+	1.95084i
$971$	294898.			0.312775			0.156388	−	0.987696i	$-0.450015\pi$
$971$	294898.			0.312775			0.156388	+	0.987696i	$0.450015\pi$
$972$	−128706.			−0.136228
$973$	−27937.6	−	27937.6i	−0.0295096	−	0.0295096i
$974$		−	830453.i		−	0.875381i
$975$	780120.	+	1.45521e6i	0.820639	+	1.53079i
$976$	−1.16457e6			−1.22255
$977$	−725729.	+	725729.i	−0.760301	+	0.760301i	−0.976377	−	0.216076i	$-0.930674\pi$
$977$	−725729.	+	725729.i	−0.760301	+	0.760301i	0.216076	+	0.976377i	$0.430674\pi$
$978$		−	2.40064e6i		−	2.50986i
$979$		−	293221.i		−	0.305935i
$980$	1.21386e6	+	588194.i	1.26391	+	0.612447i
$981$	−884659.	−	884659.i	−0.919259	−	0.919259i
$982$	1.23290e6	+	1.23290e6i	1.27851	+	1.27851i
$983$	−457102.	−	457102.i	−0.473049	−	0.473049i	0.429851	−	0.902900i	$-0.358566\pi$
$983$	−457102.	−	457102.i	−0.473049	−	0.473049i	−0.902900	+	0.429851i	$0.858566\pi$
$984$	1.02865e6			1.06238
$985$	−116368.	+	40402.5i	−0.119939	+	0.0416424i
$986$	−412581.	+	412581.i	−0.424381	+	0.424381i
$987$	−2.19212e6			−2.25024
$988$	−1.70563e6	−	2.44480e6i	−1.74731	−	2.50455i
$989$	708047.			0.723885
$990$	709563.	−	1.46433e6i	0.723970	−	1.49406i
$991$	121266.			0.123478			0.0617391	−	0.998092i	$-0.480335\pi$
$991$	121266.			0.123478			0.0617391	+	0.998092i	$0.480335\pi$
$992$	−460179.			−0.467632
$993$	466035.	−	466035.i	0.472629	−	0.472629i
$994$	−874838.	−	874838.i	−0.885431	−	0.885431i
$995$	−343489.	+	708859.i	−0.346950	+	0.716001i
$996$	−3.23246e6	+	3.23246e6i	−3.25848	+	3.25848i
$997$			1.97377e6i			1.98566i	0.119522	+	0.992832i	$0.461864\pi$
$997$			1.97377e6i			1.98566i	−0.119522	+	0.992832i	$0.538136\pi$
$998$	−1.77106e6			−1.77816
$999$	−229831.	+	229831.i	−0.230291	+	0.230291i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.5.g.a.34.1	✓	52
5.4	even	2	inner	65.5.g.a.34.26	yes	52
13.5	odd	4	inner	65.5.g.a.44.26	yes	52
65.44	odd	4	inner	65.5.g.a.44.1	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.5.g.a.34.1	✓	52	1.1	even	1	trivial
65.5.g.a.34.26	yes	52	5.4	even	2	inner
65.5.g.a.44.1	yes	52	65.44	odd	4	inner
65.5.g.a.44.26	yes	52	13.5	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-5.15266 + 5.15266i) q^{2} -15.6320i q^{3} -37.0999i q^{4} +(22.4978 + 10.9017i) q^{5} +(80.5463 + 80.5463i) q^{6} +(-43.9050 - 43.9050i) q^{7} +(108.720 + 108.720i) q^{8} -163.359 q^{9} +O(q^{10})\)	\(q+(-5.15266 + 5.15266i) q^{2} -15.6320i q^{3} -37.0999i q^{4} +(22.4978 + 10.9017i) q^{5} +(80.5463 + 80.5463i) q^{6} +(-43.9050 - 43.9050i) q^{7} +(108.720 + 108.720i) q^{8} -163.359 q^{9} +(-172.097 + 59.7510i) q^{10} +(38.6628 - 38.6628i) q^{11} -579.944 q^{12} +(-29.6319 + 166.382i) q^{13} +452.455 q^{14} +(170.415 - 351.686i) q^{15} -526.801 q^{16} -82.2374 q^{17} +(841.731 - 841.731i) q^{18} +(-336.190 - 336.190i) q^{19} +(404.451 - 834.667i) q^{20} +(-686.322 + 686.322i) q^{21} +398.433i q^{22} -489.563 q^{23} +(1699.51 - 1699.51i) q^{24} +(387.306 + 490.529i) q^{25} +(-704.626 - 1009.99i) q^{26} +1287.43i q^{27} +(-1628.87 + 1628.87i) q^{28} -973.662 q^{29} +(934.027 + 2690.21i) q^{30} +(-236.013 - 236.013i) q^{31} +(974.903 - 974.903i) q^{32} +(-604.376 - 604.376i) q^{33} +(423.741 - 423.741i) q^{34} +(-509.129 - 1466.41i) q^{35} +6060.58i q^{36} +(178.519 + 178.519i) q^{37} +3464.54 q^{38} +(2600.88 + 463.206i) q^{39} +(1260.74 + 3631.21i) q^{40} +(302.631 + 302.631i) q^{41} -7072.77i q^{42} -1446.29 q^{43} +(-1434.38 - 1434.38i) q^{44} +(-3675.22 - 1780.89i) q^{45} +(2522.55 - 2522.55i) q^{46} +(1597.00 + 1597.00i) q^{47} +8234.94i q^{48} +1454.30i q^{49} +(-4523.19 - 531.875i) q^{50} +1285.53i q^{51} +(6172.75 + 1099.34i) q^{52} -1950.93i q^{53} +(-6633.67 - 6633.67i) q^{54} +(1291.32 - 448.339i) q^{55} -9546.74i q^{56} +(-5255.30 + 5255.30i) q^{57} +(5016.95 - 5016.95i) q^{58} +(3071.64 - 3071.64i) q^{59} +(-13047.5 - 6322.37i) q^{60} +2210.65 q^{61} +2432.19 q^{62} +(7172.26 + 7172.26i) q^{63} +1617.87i q^{64} +(-2480.50 + 3420.20i) q^{65} +6228.29 q^{66} +(964.245 - 964.245i) q^{67} +3050.99i q^{68} +7652.83i q^{69} +(10179.3 + 4932.53i) q^{70} +(-1933.53 - 1933.53i) q^{71} +(-17760.4 - 17760.4i) q^{72} +(-1810.35 - 1810.35i) q^{73} -1839.70 q^{74} +(7667.94 - 6054.36i) q^{75} +(-12472.6 + 12472.6i) q^{76} -3394.98 q^{77} +(-15788.2 + 11014.7i) q^{78} -8326.35 q^{79} +(-11851.9 - 5743.03i) q^{80} +6892.97 q^{81} -3118.71 q^{82} +(5573.75 - 5573.75i) q^{83} +(25462.4 + 25462.4i) q^{84} +(-1850.16 - 896.527i) q^{85} +(7452.22 - 7452.22i) q^{86} +15220.3i q^{87} +8406.87 q^{88} +(3792.03 - 3792.03i) q^{89} +(28113.4 - 9760.84i) q^{90} +(8605.99 - 6004.01i) q^{91} +18162.7i q^{92} +(-3689.35 + 3689.35i) q^{93} -16457.6 q^{94} +(-3898.50 - 11228.6i) q^{95} +(-15239.7 - 15239.7i) q^{96} +(7917.02 - 7917.02i) q^{97} +(-7493.52 - 7493.52i) q^{98} +(-6315.90 + 6315.90i) 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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