LMFDB - Embedded newform 55.6.e.b.32.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [55,6,Mod(32,55)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(55, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("55.32");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 55 = 5 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	55.e (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:	$8.82111008971$
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			32.2
Character	$\chi$	$=$	55.32
Dual form			55.6.e.b.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-7.05963 + 7.05963i) q^{2} +(1.68959 - 1.68959i) q^{3} -67.6769i q^{4} +(55.5275 - 6.45743i) q^{5} +23.8558i q^{6} +(-73.3168 + 73.3168i) q^{7} +(251.866 + 251.866i) q^{8} +237.291i q^{9} +(-346.417 + 437.591i) q^{10} +(-370.662 - 153.819i) q^{11} +(-114.346 - 114.346i) q^{12} +(432.912 + 432.912i) q^{13} -1035.18i q^{14} +(82.9084 - 104.729i) q^{15} -1390.50 q^{16} +(475.007 - 475.007i) q^{17} +(-1675.18 - 1675.18i) q^{18} -2637.86 q^{19} +(-437.019 - 3757.93i) q^{20} +247.751i q^{21} +(3702.65 - 1530.83i) q^{22} +(-3016.80 + 3016.80i) q^{23} +851.101 q^{24} +(3041.60 - 717.130i) q^{25} -6112.40 q^{26} +(811.495 + 811.495i) q^{27} +(4961.85 + 4961.85i) q^{28} -6444.84 q^{29} +(154.047 + 1324.65i) q^{30} -1472.27 q^{31} +(1756.72 - 1756.72i) q^{32} +(-886.161 + 366.376i) q^{33} +6706.75i q^{34} +(-3597.66 + 4544.54i) q^{35} +16059.1 q^{36} +(3361.98 + 3361.98i) q^{37} +(18622.3 - 18622.3i) q^{38} +1462.89 q^{39} +(15611.9 + 12359.1i) q^{40} +896.031i q^{41} +(-1749.03 - 1749.03i) q^{42} +(2457.51 + 2457.51i) q^{43} +(-10410.0 + 25085.3i) q^{44} +(1532.29 + 13176.1i) q^{45} -42595.0i q^{46} +(-11145.2 - 11145.2i) q^{47} +(-2349.38 + 2349.38i) q^{48} +6056.29i q^{49} +(-16409.9 + 26535.3i) q^{50} -1605.14i q^{51} +(29298.1 - 29298.1i) q^{52} +(-6204.06 + 6204.06i) q^{53} -11457.7 q^{54} +(-21575.2 - 6147.68i) q^{55} -36932.0 q^{56} +(-4456.91 + 4456.91i) q^{57} +(45498.2 - 45498.2i) q^{58} +25999.2i q^{59} +(-7087.75 - 5610.98i) q^{60} +5048.02i q^{61} +(10393.7 - 10393.7i) q^{62} +(-17397.4 - 17397.4i) q^{63} -19692.4i q^{64} +(26834.0 + 21243.0i) q^{65} +(3669.49 - 8842.45i) q^{66} +(-5544.59 - 5544.59i) q^{67} +(-32147.0 - 32147.0i) q^{68} +10194.3i q^{69} +(-6684.61 - 57480.9i) q^{70} +20276.1 q^{71} +(-59765.4 + 59765.4i) q^{72} +(17677.6 + 17677.6i) q^{73} -47468.7 q^{74} +(3927.41 - 6350.73i) q^{75} +178522. i q^{76} +(38453.3 - 15898.2i) q^{77} +(-10327.5 + 10327.5i) q^{78} +83992.0 q^{79} +(-77211.0 + 8979.06i) q^{80} -54919.4 q^{81} +(-6325.65 - 6325.65i) q^{82} +(78380.4 + 78380.4i) q^{83} +16767.0 q^{84} +(23308.6 - 29443.3i) q^{85} -34698.2 q^{86} +(-10889.1 + 10889.1i) q^{87} +(-54615.3 - 132099. i) q^{88} -48297.8i q^{89} +(-103836. - 82201.4i) q^{90} -63479.5 q^{91} +(204167. + 204167. i) q^{92} +(-2487.54 + 2487.54i) q^{93} +157362. q^{94} +(-146474. + 17033.8i) q^{95} -5936.27i q^{96} +(45539.3 + 45539.3i) q^{97} +(-42755.2 - 42755.2i) q^{98} +(36499.9 - 87954.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 56 q^{3} - 48 q^{5} - 364 q^{11} + 4792 q^{12} + 2564 q^{15} - 6416 q^{16} + 18272 q^{20} + 2680 q^{22} - 144 q^{23} - 12248 q^{25} + 2432 q^{26} + 3644 q^{27} + 9672 q^{31} + 30576 q^{33} - 148776 q^{36}+ \cdots - 633128 q^{97}+O(q^{100}) $ 52 * q + 56 * q^3 - 48 * q^5 - 364 * q^11 + 4792 * q^12 + 2564 * q^15 - 6416 * q^16 + 18272 * q^20 + 2680 * q^22 - 144 * q^23 - 12248 * q^25 + 2432 * q^26 + 3644 * q^27 + 9672 * q^31 + 30576 * q^33 - 148776 * q^36 + 24152 * q^37 + 4400 * q^38 - 43480 * q^42 - 4984 * q^45 - 44148 * q^47 + 26416 * q^48 + 75596 * q^53 + 59092 * q^55 + 304264 * q^56 - 220200 * q^58 - 240016 * q^60 + 207000 * q^66 - 17888 * q^67 - 216880 * q^70 + 285704 * q^71 + 278404 * q^75 - 341160 * q^77 + 15160 * q^78 + 616192 * q^80 - 397204 * q^81 + 349720 * q^82 - 94768 * q^86 + 539000 * q^88 - 864768 * q^91 + 242072 * q^92 + 15772 * q^93 - 633128 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$.

$n$	$12$	$46$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−7.05963	+	7.05963i	−1.24798	+	1.24798i	−0.291368	+	0.956611i	$0.594110\pi$
$2$	−7.05963	+	7.05963i	−1.24798	+	1.24798i	−0.956611	+	0.291368i	$0.905890\pi$
$3$	1.68959	−	1.68959i	0.108387	−	0.108387i	−0.650833	−	0.759221i	$-0.725580\pi$
$3$	1.68959	−	1.68959i	0.108387	−	0.108387i	0.759221	+	0.650833i	$0.225580\pi$
$4$		−	67.6769i		−	2.11490i
$5$	55.5275	−	6.45743i	0.993306	−	0.115514i
$5$	55.5275	−	6.45743i	0.993306	−	0.115514i
$6$			23.8558i			0.270530i
$7$	−73.3168	+	73.3168i	−0.565534	+	0.565534i	−0.930874	−	0.365340i	$-0.880953\pi$
$7$	−73.3168	+	73.3168i	−0.565534	+	0.565534i	0.365340	+	0.930874i	$0.380953\pi$
$8$	251.866	+	251.866i	1.39137	+	1.39137i
$9$			237.291i			0.976504i
$10$	−346.417	+	437.591i	−1.09547	+	1.38378i
$11$	−370.662	−	153.819i	−0.923627	−	0.383292i
$11$	−370.662	−	153.819i	−0.923627	−	0.383292i
$12$	−114.346	−	114.346i	−0.229229	−	0.229229i
$13$	432.912	+	432.912i	0.710463	+	0.710463i	0.966632	−	0.256169i	$-0.0824604\pi$
$13$	432.912	+	432.912i	0.710463	+	0.710463i	−0.256169	+	0.966632i	$0.582460\pi$
$14$		−	1035.18i		−	1.41155i
$15$	82.9084	−	104.729i	0.0951416	−	0.120182i
$16$	−1390.50			−1.35791
$17$	475.007	−	475.007i	0.398637	−	0.398637i	−0.479115	−	0.877752i	$-0.659042\pi$
$17$	475.007	−	475.007i	0.398637	−	0.398637i	0.877752	+	0.479115i	$0.159042\pi$
$18$	−1675.18	−	1675.18i	−1.21866	−	1.21866i
$19$	−2637.86			−1.67636			−0.838180	−	0.545394i	$-0.816380\pi$
$19$	−2637.86			−1.67636			−0.838180	+	0.545394i	$0.816380\pi$
$20$	−437.019	−	3757.93i	−0.244301	−	2.10074i
$21$			247.751i			0.122594i
$22$	3702.65	−	1530.83i	1.63101	−	0.674327i
$23$	−3016.80	+	3016.80i	−1.18912	+	1.18912i	−0.211812	+	0.977310i	$0.567936\pi$
$23$	−3016.80	+	3016.80i	−1.18912	+	1.18912i	−0.977310	+	0.211812i	$0.932064\pi$
$24$	851.101			0.301615
$25$	3041.60	−	717.130i	0.973313	−	0.229482i
$26$	−6112.40			−1.77329
$27$	811.495	+	811.495i	0.214228	+	0.214228i
$28$	4961.85	+	4961.85i	1.19605	+	1.19605i
$29$	−6444.84			−1.42304			−0.711520	−	0.702666i	$-0.751993\pi$
$29$	−6444.84			−1.42304			−0.711520	+	0.702666i	$0.751993\pi$
$30$	154.047	+	1324.65i	0.0312501	+	0.268719i
$31$	−1472.27			−0.275159			−0.137579	−	0.990491i	$-0.543932\pi$
$31$	−1472.27			−0.275159			−0.137579	+	0.990491i	$0.543932\pi$
$32$	1756.72	−	1756.72i	0.303268	−	0.303268i
$33$	−886.161	+	366.376i	−0.141654	+	0.0585656i
$34$			6706.75i			0.994982i
$35$	−3597.66	+	4544.54i	−0.496421	+	0.627075i
$36$	16059.1			2.06521
$37$	3361.98	+	3361.98i	0.403729	+	0.403729i	0.879545	−	0.475816i	$-0.157847\pi$
$37$	3361.98	+	3361.98i	0.403729	+	0.403729i	−0.475816	+	0.879545i	$0.657847\pi$
$38$	18622.3	−	18622.3i	2.09206	−	2.09206i
$39$	1462.89			0.154011
$40$	15611.9	+	12359.1i	1.54278	+	1.22134i
$41$			896.031i			0.0832460i	0.999133	+	0.0416230i	$0.0132528\pi$
$41$			896.031i			0.0832460i	−0.999133	+	0.0416230i	$0.986747\pi$
$42$	−1749.03	−	1749.03i	−0.152994	−	0.152994i
$43$	2457.51	+	2457.51i	0.202686	+	0.202686i	0.801150	−	0.598464i	$-0.204222\pi$
$43$	2457.51	+	2457.51i	0.202686	+	0.202686i	−0.598464	+	0.801150i	$0.704222\pi$
$44$	−10410.0	+	25085.3i	−0.810625	+	1.95338i
$45$	1532.29	+	13176.1i	0.112800	+	0.969967i
$46$		−	42595.0i		−	2.96800i
$47$	−11145.2	−	11145.2i	−0.735943	−	0.735943i	0.235847	−	0.971790i	$-0.424213\pi$
$47$	−11145.2	−	11145.2i	−0.735943	−	0.735943i	−0.971790	+	0.235847i	$0.924213\pi$
$48$	−2349.38	+	2349.38i	−0.147180	+	0.147180i
$49$			6056.29i			0.360343i
$50$	−16409.9	+	26535.3i	−0.928286	+	1.50106i
$51$		−	1605.14i		−	0.0864145i
$52$	29298.1	−	29298.1i	1.50256	−	1.50256i
$53$	−6204.06	+	6204.06i	−0.303380	+	0.303380i	−0.842335	−	0.538955i	$-0.818819\pi$
$53$	−6204.06	+	6204.06i	−0.303380	+	0.303380i	0.538955	+	0.842335i	$0.318819\pi$
$54$	−11457.7			−0.534705
$55$	−21575.2	−	6147.68i	−0.961720	−	0.274034i
$56$	−36932.0			−1.57374
$57$	−4456.91	+	4456.91i	−0.181696	+	0.181696i
$58$	45498.2	−	45498.2i	1.77592	−	1.77592i
$59$			25999.2i			0.972366i	0.873857	+	0.486183i	$0.161611\pi$
$59$			25999.2i			0.972366i	−0.873857	+	0.486183i	$0.838389\pi$
$60$	−7087.75	−	5610.98i	−0.254173	−	0.201215i
$61$			5048.02i			0.173699i	0.996221	+	0.0868493i	$0.0276799\pi$
$61$			5048.02i			0.173699i	−0.996221	+	0.0868493i	$0.972320\pi$
$62$	10393.7	−	10393.7i	0.343392	−	0.343392i
$63$	−17397.4	−	17397.4i	−0.552246	−	0.552246i
$64$		−	19692.4i		−	0.600965i
$65$	26834.0	+	21243.0i	0.787775	+	0.623639i
$66$	3669.49	−	8842.45i	0.103692	−	0.249869i
$67$	−5544.59	−	5544.59i	−0.150898	−	0.150898i	0.627621	−	0.778519i	$-0.284029\pi$
$67$	−5544.59	−	5544.59i	−0.150898	−	0.150898i	−0.778519	+	0.627621i	$0.784029\pi$
$68$	−32147.0	−	32147.0i	−0.843079	−	0.843079i
$69$			10194.3i			0.257772i
$70$	−6684.61	−	57480.9i	−0.163054	−	1.40210i
$71$	20276.1			0.477351			0.238675	−	0.971099i	$-0.423287\pi$
$71$	20276.1			0.477351			0.238675	+	0.971099i	$0.423287\pi$
$72$	−59765.4	+	59765.4i	−1.35868	+	1.35868i
$73$	17677.6	+	17677.6i	0.388254	+	0.388254i	0.874064	−	0.485811i	$-0.161476\pi$
$73$	17677.6	+	17677.6i	0.388254	+	0.388254i	−0.485811	+	0.874064i	$0.661476\pi$
$74$	−47468.7			−1.00769
$75$	3927.41	−	6350.73i	0.0806220	−	0.130368i
$76$			178522.i			3.54534i
$77$	38453.3	−	15898.2i	0.739107	−	0.305578i
$78$	−10327.5	+	10327.5i	−0.192202	+	0.192202i
$79$	83992.0			1.51416			0.757078	−	0.653325i	$-0.226626\pi$
$79$	83992.0			1.51416			0.757078	+	0.653325i	$0.226626\pi$
$80$	−77211.0	+	8979.06i	−1.34882	+	0.156858i
$81$	−54919.4			−0.930065
$82$	−6325.65	−	6325.65i	−0.103889	−	0.103889i
$83$	78380.4	+	78380.4i	1.24886	+	1.24886i	0.956226	+	0.292629i	$0.0945301\pi$
$83$	78380.4	+	78380.4i	1.24886	+	1.24886i	0.292629	+	0.956226i	$0.405470\pi$
$84$	16767.0			0.259273
$85$	23308.6	−	29443.3i	0.349920	−	0.442017i
$86$	−34698.2			−0.505895
$87$	−10889.1	+	10889.1i	−0.154240	+	0.154240i
$88$	−54615.3	−	132099.i	−0.751809	−	1.81841i
$89$		−	48297.8i		−	0.646327i	−0.946343	−	0.323163i	$-0.895254\pi$
$89$		−	48297.8i		−	0.646327i	0.946343	−	0.323163i	$-0.104746\pi$
$90$	−103836.	−	82201.4i	−1.35127	−	1.06973i
$91$	−63479.5			−0.803582
$92$	204167.	+	204167.i	2.51488	+	2.51488i
$93$	−2487.54	+	2487.54i	−0.0298237	+	0.0298237i
$94$	157362.			1.83688
$95$	−146474.	+	17033.8i	−1.66514	+	0.193643i
$96$		−	5936.27i		−	0.0657409i
$97$	45539.3	+	45539.3i	0.491425	+	0.491425i	0.908755	−	0.417330i	$-0.137034\pi$
$97$	45539.3	+	45539.3i	0.491425	+	0.491425i	−0.417330	+	0.908755i	$0.637034\pi$
$98$	−42755.2	−	42755.2i	−0.449700	−	0.449700i
$99$	36499.9	−	87954.7i	0.374286	−	0.901926i
$100$	−48533.1	−	205846.i	−0.485331	−	2.05846i
$101$		−	198542.i		−	1.93664i	−0.249715	−	0.968320i	$-0.580337\pi$
$101$		−	198542.i		−	1.93664i	0.249715	−	0.968320i	$-0.419663\pi$
$102$	11331.7	+	11331.7i	0.107844	+	0.107844i
$103$	61797.6	−	61797.6i	0.573956	−	0.573956i	−0.359276	−	0.933232i	$-0.616976\pi$
$103$	61797.6	−	61797.6i	0.573956	−	0.573956i	0.933232	+	0.359276i	$0.116976\pi$
$104$			218071.i			1.97704i
$105$	1599.84	+	13757.0i	0.0141613	+	0.121773i
$106$		−	87596.8i		−	0.757223i
$107$	2252.62	−	2252.62i	0.0190208	−	0.0190208i	−0.697532	−	0.716553i	$-0.745719\pi$
$107$	2252.62	−	2252.62i	0.0190208	−	0.0190208i	0.716553	+	0.697532i	$0.245719\pi$
$108$	54919.5	−	54919.5i	0.453072	−	0.453072i
$109$	70586.6			0.569057			0.284529	−	0.958668i	$-0.408163\pi$
$109$	70586.6			0.569057			0.284529	+	0.958668i	$0.408163\pi$
$110$	195714.	−	108913.i	1.54219	−	0.858217i
$111$	11360.7			0.0875184
$112$	101947.	−	101947.i	0.767944	−	0.767944i
$113$	−142467.	+	142467.i	−1.04959	+	1.04959i	−0.0508832	+	0.998705i	$0.516204\pi$
$113$	−142467.	+	142467.i	−1.04959	+	1.04959i	−0.998705	+	0.0508832i	$0.983796\pi$
$114$		−	62928.2i		−	0.453506i
$115$	−148034.	+	186996.i	−1.04380	+	1.31852i
$116$			436166.i			3.00959i
$117$	−102726.	+	102726.i	−0.693770	+	0.693770i
$118$	−183545.	−	183545.i	−1.21349	−	1.21349i
$119$			69652.0i			0.450886i
$120$	47259.5	−	5495.93i	0.299596	−	0.0348408i
$121$	113730.	+	114030.i	0.706175	+	0.708038i
$122$	−35637.2	−	35637.2i	−0.216772	−	0.216772i
$123$	1513.93	+	1513.93i	0.00902282	+	0.00902282i
$124$			99638.6i			0.581934i
$125$	164262.	−	59461.4i	0.940289	−	0.340377i
$126$	245638.			1.37838
$127$	−92818.2	+	92818.2i	−0.510650	+	0.510650i	−0.914726	−	0.404075i	$-0.867593\pi$
$127$	−92818.2	+	92818.2i	−0.510650	+	0.510650i	0.404075	+	0.914726i	$0.367593\pi$
$128$	195236.	+	195236.i	1.05326	+	1.05326i
$129$	8304.37			0.0439372
$130$	−339406.	+	39470.4i	−1.76141	+	0.204839i
$131$		−	34355.9i		−	0.174913i	−0.996168	−	0.0874566i	$-0.972126\pi$
$131$		−	34355.9i		−	0.174913i	0.996168	−	0.0874566i	$-0.0278739\pi$
$132$	24795.2	+	59972.6i	0.123860	+	0.299584i
$133$	193399.	−	193399.i	0.948038	−	0.948038i
$134$	78285.5			0.376634
$135$	50300.5	+	39820.1i	0.237541	+	0.188048i
$136$	239276.			1.10931
$137$	−212155.	−	212155.i	−0.965723	−	0.965723i	0.0337084	−	0.999432i	$-0.489268\pi$
$137$	−212155.	−	212155.i	−0.965723	−	0.965723i	−0.999432	+	0.0337084i	$0.989268\pi$
$138$	−71968.1	−	71968.1i	−0.321694	−	0.321694i
$139$	176187.			0.773458			0.386729	−	0.922193i	$-0.373605\pi$
$139$	176187.			0.773458			0.386729	+	0.922193i	$0.373605\pi$
$140$	307560.	+	243478.i	1.32620	+	1.04988i
$141$	−37661.8			−0.159534
$142$	−143142.	+	143142.i	−0.595724	+	0.595724i
$143$	−93873.9	−	227055.i	−0.383888	−	0.928518i
$144$		−	329952.i		−	1.32600i
$145$	−357866.	+	41617.1i	−1.41351	+	0.164381i
$146$	−249594.			−0.969064
$147$	10232.7	+	10232.7i	0.0390567	+	0.0390567i
$148$	227528.	−	227528.i	0.853848	−	0.853848i
$149$	−353969.			−1.30617			−0.653084	−	0.757285i	$-0.726525\pi$
$149$	−353969.			−1.30617			−0.653084	+	0.757285i	$0.726525\pi$
$150$	17107.7	+	72559.9i	0.0620818	+	0.263311i
$151$		−	125710.i		−	0.448672i	−0.974512	−	0.224336i	$-0.927979\pi$
$151$		−	125710.i		−	0.448672i	0.974512	−	0.224336i	$-0.0720213\pi$
$152$	−664386.	−	664386.i	−2.33245	−	2.33245i
$153$	112715.	+	112715.i	0.389271	+	0.389271i
$154$	−159231.	+	383702.i	−0.541035	+	1.30374i
$155$	−81751.5	+	9507.09i	−0.273317	+	0.0317847i
$156$		−	99003.9i		−	0.325717i
$157$	268661.	+	268661.i	0.869872	+	0.869872i	0.992458	−	0.122586i	$-0.0391187\pi$
$157$	268661.	+	268661.i	0.869872	+	0.869872i	−0.122586	+	0.992458i	$0.539119\pi$
$158$	−592953.	+	592953.i	−1.88963	+	1.88963i
$159$			20964.7i			0.0657651i
$160$	86202.2	−	108890.i	0.266206	−	0.336270i
$161$		−	442364.i		−	1.34498i
$162$	387711.	−	387711.i	1.16070	−	1.16070i
$163$	188897.	−	188897.i	0.556874	−	0.556874i	−0.371542	−	0.928416i	$-0.621171\pi$
$163$	188897.	−	188897.i	0.556874	−	0.556874i	0.928416	+	0.371542i	$0.121171\pi$
$164$	60640.6			0.176057
$165$	−46840.4	+	26066.3i	−0.133940	+	0.0745365i
$166$	−1.10667e6			−3.11709
$167$	−268846.	+	268846.i	−0.745955	+	0.745955i	−0.973717	−	0.227762i	$-0.926859\pi$
$167$	−268846.	+	268846.i	−0.745955	+	0.745955i	0.227762	+	0.973717i	$0.426859\pi$
$168$	−62400.0	+	62400.0i	−0.170574	+	0.170574i
$169$			3532.94i			0.00951523i
$170$	43308.4	+	372409.i	0.114934	+	0.988321i
$171$		−	625939.i		−	1.63697i
$172$	166316.	−	166316.i	0.428661	−	0.428661i
$173$	355552.	+	355552.i	0.903209	+	0.903209i	0.995712	−	0.0925033i	$-0.0294869\pi$
$173$	355552.	+	355552.i	0.903209	+	0.903209i	−0.0925033	+	0.995712i	$0.529487\pi$
$174$		−	153747.i		−	0.384975i
$175$	−170423.	+	275578.i	−0.420662	+	0.680221i
$176$	515406.	+	213886.i	1.25420	+	0.520476i
$177$	43928.1	+	43928.1i	0.105392	+	0.105392i
$178$	340965.	+	340965.i	0.806602	+	0.806602i
$179$		−	656048.i		−	1.53039i	−0.643797	−	0.765196i	$-0.722642\pi$
$179$		−	656048.i		−	1.53039i	0.643797	−	0.765196i	$-0.277358\pi$
$180$	891721.	−	103700.i	2.05139	−	0.238561i
$181$	387629.			0.879469			0.439734	−	0.898128i	$-0.355073\pi$
$181$	387629.			0.879469			0.439734	+	0.898128i	$0.355073\pi$
$182$	448142.	−	448142.i	1.00285	−	1.00285i
$183$	8529.09	+	8529.09i	0.0188267	+	0.0188267i
$184$	−1.51966e6			−3.30903
$185$	208392.	+	164972.i	0.447663	+	0.354390i
$186$		−	35122.2i		−	0.0744388i
$187$	−249133.	+	103002.i	−0.520987	+	0.215398i
$188$	−754274.	+	754274.i	−1.55645	+	1.55645i
$189$	−118993.			−0.242307
$190$	913798.	−	1.15430e6i	1.83639	−	2.31972i
$191$	−534904.			−1.06094			−0.530472	−	0.847702i	$-0.677985\pi$
$191$	−534904.			−1.06094			−0.530472	+	0.847702i	$0.677985\pi$
$192$	−33272.2	−	33272.2i	−0.0651371	−	0.0651371i
$193$	26979.2	+	26979.2i	0.0521358	+	0.0521358i	0.732694	−	0.680558i	$-0.238263\pi$
$193$	26979.2	+	26979.2i	0.0521358	+	0.0521358i	−0.680558	+	0.732694i	$0.738263\pi$
$194$	−642982.			−1.22658
$195$	81230.6	−	9446.52i	0.152980	−	0.0177904i
$196$	409870.			0.762090
$197$	543493.	−	543493.i	0.997766	−	0.997766i	−0.00223173	−	0.999998i	$-0.500710\pi$
$197$	543493.	−	543493.i	0.997766	−	0.997766i	0.999998	+	0.00223173i	$0.000710383\pi$
$198$	363252.	+	878604.i	0.658483	+	1.59269i
$199$			115409.i			0.206589i	0.994651	+	0.103295i	$0.0329384\pi$
$199$			115409.i			0.206589i	−0.994651	+	0.103295i	$0.967062\pi$
$200$	946696.	+	585455.i	1.67354	+	1.03495i
$201$	−18736.2			−0.0327108
$202$	1.40163e6	+	1.40163e6i	2.41688	+	2.41688i
$203$	472515.	−	472515.i	0.804777	−	0.804777i
$204$	−108631.			−0.182758
$205$	5786.06	+	49754.3i	0.00961608	+	0.0826887i
$206$			872537.i			1.43257i
$207$	−715857.	−	715857.i	−1.16118	−	1.16118i
$208$	−601964.	−	601964.i	−0.964745	−	0.964745i
$209$	977755.	+	405754.i	1.54833	+	0.642535i
$210$	−108414.	−	85825.1i	−0.169643	−	0.134297i
$211$			477898.i			0.738974i	0.929236	+	0.369487i	$0.120467\pi$
$211$			477898.i			0.738974i	−0.929236	+	0.369487i	$0.879533\pi$
$212$	419871.	+	419871.i	0.641618	+	0.641618i
$213$	34258.3	−	34258.3i	0.0517388	−	0.0517388i
$214$			31805.3i			0.0474750i
$215$	152328.	+	120590.i	0.224742	+	0.177916i
$216$			408776.i			0.596143i
$217$	107942.	−	107942.i	0.155612	−	0.155612i
$218$	−498315.	+	498315.i	−0.710171	+	0.710171i
$219$	59735.8			0.0841636
$220$	−416056.	+	1.46014e6i	−0.579555	+	2.03394i
$221$	411273.			0.566434
$222$	−80202.7	+	80202.7i	−0.109221	+	0.109221i
$223$	−319940.	+	319940.i	−0.430830	+	0.430830i	−0.888911	−	0.458080i	$-0.848537\pi$
$223$	−319940.	+	319940.i	−0.430830	+	0.430830i	0.458080	+	0.888911i	$0.348537\pi$
$224$			257594.i			0.343017i
$225$	170168.	+	721744.i	0.224090	+	0.950444i
$226$		−	2.01153e6i		−	2.61973i
$227$	−418191.	+	418191.i	−0.538655	+	0.538655i	−0.923134	−	0.384479i	$-0.874381\pi$
$227$	−418191.	+	418191.i	−0.538655	+	0.538655i	0.384479	+	0.923134i	$0.374381\pi$
$228$	301629.	+	301629.i	0.384270	+	0.384270i
$229$			511.775i			0.000644898i	1.00000		0.000322449i	$0.000102639\pi$
$229$			511.775i			0.000644898i	−1.00000		0.000322449i	$0.999897\pi$
$230$	−275054.	−	2.36519e6i	−0.342846	−	2.94813i
$231$	38109.0	−	91832.0i	0.0469891	−	0.113231i
$232$	−1.62323e6	−	1.62323e6i	−1.97998	−	1.97998i
$233$	−185639.	−	185639.i	−0.224016	−	0.224016i	0.586171	−	0.810187i	$-0.300635\pi$
$233$	−185639.	−	185639.i	−0.224016	−	0.224016i	−0.810187	+	0.586171i	$0.800635\pi$
$234$		−	1.45042e6i		−	1.73162i
$235$	−690836.	−	546896.i	−0.816028	−	0.646004i
$236$	1.75954e6			2.05646
$237$	141912.	−	141912.i	0.164115	−	0.164115i
$238$	−491718.	−	491718.i	−0.562696	−	0.562696i
$239$	1.02372e6			1.15928			0.579638	−	0.814874i	$-0.303194\pi$
$239$	1.02372e6			1.15928			0.579638	+	0.814874i	$0.303194\pi$
$240$	−115284.	+	145626.i	−0.129194	+	0.163197i
$241$		−	706594.i		−	0.783659i	−0.920038	−	0.391830i	$-0.871842\pi$
$241$		−	706594.i		−	0.783659i	0.920038	−	0.391830i	$-0.128158\pi$
$242$	−1.60790e6	−	2118.04i	−1.76491	−	0.00232486i
$243$	−289985.	+	289985.i	−0.315036	+	0.315036i
$244$	341634.			0.367356
$245$	39108.1	+	336290.i	0.0416247	+	0.357931i
$246$	−21375.5			−0.0225206
$247$	−1.14196e6	−	1.14196e6i	−1.19099	−	1.19099i
$248$	−370814.	−	370814.i	−0.382849	−	0.382849i
$249$	264862.			0.270720
$250$	−739852.	+	1.57940e6i	−0.748678	+	1.59824i
$251$	236229.			0.236673			0.118336	−	0.992974i	$-0.462244\pi$
$251$	236229.			0.236673			0.118336	+	0.992974i	$0.462244\pi$
$252$	−1.17740e6	+	1.17740e6i	−1.16795	+	1.16795i
$253$	1.58226e6	−	654171.i	1.55409	−	0.642525i
$254$		−	1.31052e6i		−	1.27456i
$255$	−10365.1	−	89129.2i	−0.00998209	−	0.0858361i
$256$	−2.12644e6			−2.02793
$257$	1.27361e6	+	1.27361e6i	1.20283	+	1.20283i	0.973303	+	0.229525i	$0.0737172\pi$
$257$	1.27361e6	+	1.27361e6i	1.20283	+	1.20283i	0.229525	+	0.973303i	$0.426283\pi$
$258$	−58625.8	+	58625.8i	−0.0548327	+	0.0548327i
$259$	−492979.			−0.456645
$260$	1.43766e6	−	1.81604e6i	1.31893	−	1.66607i
$261$		−	1.52930e6i		−	1.38960i
$262$	242540.	+	242540.i	0.218288	+	0.218288i
$263$	−415831.	−	415831.i	−0.370704	−	0.370704i	0.497029	−	0.867734i	$-0.334424\pi$
$263$	−415831.	−	415831.i	−0.370704	−	0.370704i	−0.867734	+	0.497029i	$0.834424\pi$
$264$	−315471.	−	130916.i	−0.278580	−	0.115607i
$265$	−304434.	+	384558.i	−0.266304	+	0.336393i
$266$			2.73066e6i			2.36626i
$267$	−81603.6	−	81603.6i	−0.0700537	−	0.0700537i
$268$	−375240.	+	375240.i	−0.319134	+	0.319134i
$269$			1.35554e6i			1.14218i	0.820889	+	0.571088i	$0.193478\pi$
$269$			1.35554e6i			1.14218i	−0.820889	+	0.571088i	$0.806522\pi$
$270$	−636219.	+	73987.5i	−0.531125	+	0.0617659i
$271$			1.71988e6i			1.42257i	0.702902	+	0.711287i	$0.251887\pi$
$271$			1.71988e6i			1.42257i	−0.702902	+	0.711287i	$0.748113\pi$
$272$	−660497.	+	660497.i	−0.541313	+	0.541313i
$273$	−107255.	+	107255.i	−0.0870981	+	0.0870981i
$274$	2.99548e6			2.41040
$275$	−1.23772e6	−	202045.i	−0.986937	−	0.161107i
$276$	689920.			0.545162
$277$	−1.09856e6	+	1.09856e6i	−0.860251	+	0.860251i	−0.991367	−	0.131116i	$-0.958144\pi$
$277$	−1.09856e6	+	1.09856e6i	−0.860251	+	0.860251i	0.131116	+	0.991367i	$0.458144\pi$
$278$	−1.24382e6	+	1.24382e6i	−0.965260	+	0.965260i
$279$		−	349356.i		−	0.268694i
$280$	−2.05074e6	+	238486.i	−1.56320	+	0.181789i
$281$			546569.i			0.412933i	0.978454	+	0.206466i	$0.0661964\pi$
$281$			546569.i			0.412933i	−0.978454	+	0.206466i	$0.933804\pi$
$282$	265878.	−	265878.i	0.199095	−	0.199095i
$283$	1.62747e6	+	1.62747e6i	1.20794	+	1.20794i	0.971693	+	0.236249i	$0.0759180\pi$
$283$	1.62747e6	+	1.62747e6i	1.20794	+	1.20794i	0.236249	+	0.971693i	$0.424082\pi$
$284$		−	1.37222e6i		−	1.00955i
$285$	−218701.	+	276261.i	−0.159492	+	0.201469i
$286$	2.26564e6	+	940207.i	1.63785	+	0.679686i
$287$	−65694.1	−	65694.1i	−0.0470784	−	0.0470784i
$288$	416852.	+	416852.i	0.296143	+	0.296143i
$289$			968593.i			0.682177i
$290$	2.23260e6	−	2.82020e6i	1.55889	−	1.96918i
$291$	153886.			0.106529
$292$	1.19636e6	−	1.19636e6i	0.821118	−	0.821118i
$293$	−1.63944e6	−	1.63944e6i	−1.11565	−	1.11565i	−0.992372	−	0.123277i	$-0.960660\pi$
$293$	−1.63944e6	−	1.63944e6i	−1.11565	−	1.11565i	−0.123277	−	0.992372i	$-0.539340\pi$
$294$	−144478.			−0.0974838
$295$	167888.	+	1.44367e6i	0.112322	+	0.965857i
$296$			1.69353e6i			1.12348i
$297$	−175967.	−	425615.i	−0.115755	−	0.279979i
$298$	2.49889e6	−	2.49889e6i	1.63007	−	1.63007i
$299$	−2.61202e6			−1.68965
$300$	−429797.	−	265795.i	−0.275715	−	0.170508i
$301$	−360353.			−0.229251
$302$	887470.	+	887470.i	0.559933	+	0.559933i
$303$	−335455.	−	335455.i	−0.209907	−	0.209907i
$304$	3.66794e6			2.27635
$305$	32597.2	+	280304.i	0.0200646	+	0.172536i
$306$	−1.59145e6			−0.971604
$307$	−721052.	+	721052.i	−0.436637	+	0.436637i	−0.890879	−	0.454241i	$-0.849910\pi$
$307$	−721052.	+	721052.i	−0.436637	+	0.436637i	0.454241	+	0.890879i	$0.349910\pi$
$308$	−1.07594e6	−	2.60240e6i	−0.646268	−	1.56314i
$309$		−	208826.i		−	0.124419i
$310$	510019.	−	644252.i	0.301427	−	0.380760i
$311$	76553.5			0.0448812			0.0224406	−	0.999748i	$-0.492856\pi$
$311$	76553.5			0.0448812			0.0224406	+	0.999748i	$0.492856\pi$
$312$	368452.	+	368452.i	0.214286	+	0.214286i
$313$	−141184.	+	141184.i	−0.0814565	+	0.0814565i	−0.746661	−	0.665205i	$-0.768344\pi$
$313$	−141184.	+	141184.i	−0.0814565	+	0.0814565i	0.665205	+	0.746661i	$0.268344\pi$
$314$	−3.79329e6			−2.17116
$315$	−1.07838e6	−	853691.i	−0.612342	−	0.484757i
$316$		−	5.68432e6i		−	3.20229i
$317$	−405222.	−	405222.i	−0.226488	−	0.226488i	0.584736	−	0.811224i	$-0.301198\pi$
$317$	−405222.	−	405222.i	−0.226488	−	0.226488i	−0.811224	+	0.584736i	$0.801198\pi$
$318$	−148003.	−	148003.i	−0.0820734	−	0.0820734i
$319$	2.38886e6	+	991341.i	1.31436	+	0.545439i
$320$	−127163.	−	1.09347e6i	−0.0694200	−	0.596942i
$321$		−	7612.01i		−	0.00412322i
$322$	3.12293e6	+	3.12293e6i	1.67850	+	1.67850i
$323$	−1.25300e6	+	1.25300e6i	−0.668260	+	0.668260i
$324$			3.71677e6i			1.96700i
$325$	1.62720e6	+	1.00629e6i	0.854541	+	0.528465i
$326$			2.66709e6i			1.38993i
$327$	119263.	−	119263.i	0.0616786	−	0.0616786i
$328$	−225679.	+	225679.i	−0.115826	+	0.115826i
$329$	1.63426e6			0.832401
$330$	146658.	−	514695.i	0.0741346	−	0.260175i
$331$	−1.21401e6			−0.609049			−0.304525	−	0.952504i	$-0.598498\pi$
$331$	−1.21401e6			−0.609049			−0.304525	+	0.952504i	$0.598498\pi$
$332$	5.30454e6	−	5.30454e6i	2.64121	−	2.64121i
$333$	−797765.	+	797765.i	−0.394244	+	0.394244i
$334$		−	3.79591e6i		−	1.86187i
$335$	−343681.	−	272073.i	−0.167318	−	0.132457i
$336$		−	344498.i		−	0.166471i
$337$	−892817.	+	892817.i	−0.428240	+	0.428240i	−0.888029	−	0.459788i	$-0.847925\pi$
$337$	−892817.	+	892817.i	−0.428240	+	0.428240i	0.459788	+	0.888029i	$0.347925\pi$
$338$	−24941.2	−	24941.2i	−0.0118748	−	0.0118748i
$339$			481423.i			0.227524i
$340$	−1.99263e6	−	1.57746e6i	−0.934823	−	0.740048i
$341$	545715.	+	226464.i	0.254144	+	0.105466i
$342$	4.41890e6	+	4.41890e6i	2.04291	+	2.04291i
$343$	−1.67626e6	−	1.67626e6i	−0.769320	−	0.769320i
$344$			1.23792e6i			0.564024i
$345$	65829.1	+	566065.i	0.0297763	+	0.256046i
$346$	−5.02014e6			−2.25437
$347$	1.51034e6	−	1.51034e6i	0.673364	−	0.673364i	−0.285126	−	0.958490i	$-0.592036\pi$
$347$	1.51034e6	−	1.51034e6i	0.673364	−	0.673364i	0.958490	+	0.285126i	$0.0920355\pi$
$348$	736944.	+	736944.i	0.326202	+	0.326202i
$349$	−212015.			−0.0931759			−0.0465879	−	0.998914i	$-0.514835\pi$
$349$	−212015.			−0.0931759			−0.0465879	+	0.998914i	$0.514835\pi$
$350$	−742359.	−	3.14861e6i	−0.323924	−	1.37388i
$351$			702613.i			0.304402i
$352$	−921366.	+	380931.i	−0.396347	+	0.163867i
$353$	297680.	−	297680.i	0.127149	−	0.127149i	−0.640669	−	0.767817i	$-0.721343\pi$
$353$	297680.	−	297680.i	0.127149	−	0.127149i	0.767817	+	0.640669i	$0.221343\pi$
$354$	−620232.			−0.263055
$355$	1.12588e6	−	130931.i	0.474155	−	0.0551407i
$356$	−3.26864e6			−1.36692
$357$	117684.	+	117684.i	0.0488703	+	0.0488703i
$358$	4.63146e6	+	4.63146e6i	1.90990	+	1.90990i
$359$	−3.57440e6			−1.46375			−0.731875	−	0.681439i	$-0.761354\pi$
$359$	−3.57440e6			−1.46375			−0.731875	+	0.681439i	$0.761354\pi$
$360$	−2.93269e6	+	3.70455e6i	−1.19264	+	1.50654i
$361$	4.48219e6			1.81018
$362$	−2.73652e6	+	2.73652e6i	−1.09756	+	1.09756i
$363$	384822.	+	506.914i	0.153283	+	0.000201915i
$364$			4.29609e6i			1.69950i
$365$	1.09574e6	+	867439.i	0.430503	+	0.340806i
$366$	−120425.			−0.0469907
$367$	−1.08140e6	−	1.08140e6i	−0.419102	−	0.419102i	0.465792	−	0.884894i	$-0.345770\pi$
$367$	−1.08140e6	−	1.08140e6i	−0.419102	−	0.419102i	−0.884894	+	0.465792i	$0.845770\pi$
$368$	4.19486e6	−	4.19486e6i	1.61472	−	1.61472i
$369$	−212620.			−0.0812901
$370$	−2.63582e6	+	306526.i	−1.00095	+	0.116403i
$371$		−	909724.i		−	0.343143i
$372$	168349.	+	168349.i	0.0630743	+	0.0630743i
$373$	458117.	+	458117.i	0.170492	+	0.170492i	0.787196	−	0.616703i	$-0.211532\pi$
$373$	458117.	+	458117.i	0.170492	+	0.170492i	−0.616703	+	0.787196i	$0.711532\pi$
$374$	1.03163e6	−	2.48594e6i	0.381368	−	0.918992i
$375$	177070.	−	378001.i	0.0650230	−	0.138808i
$376$		−	5.61420e6i		−	2.04794i
$377$	−2.79005e6	−	2.79005e6i	−1.01102	−	1.01102i
$378$	840044.	−	840044.i	0.302394	−	0.302394i
$379$		−	4.98915e6i		−	1.78414i	−0.451897	−	0.892070i	$-0.649253\pi$
$379$		−	4.98915e6i		−	1.78414i	0.451897	−	0.892070i	$-0.350747\pi$
$380$	1.15279e6	+	9.91288e6i	0.409536	+	3.52161i
$381$			313650.i			0.110696i
$382$	3.77623e6	−	3.77623e6i	1.32404	−	1.32404i
$383$	1.47061e6	−	1.47061e6i	0.512273	−	0.512273i	−0.402950	−	0.915222i	$-0.632015\pi$
$383$	1.47061e6	−	1.47061e6i	0.512273	−	0.512273i	0.915222	+	0.402950i	$0.132015\pi$
$384$	659740.			0.228320
$385$	2.03256e6	−	1.13110e6i	0.698861	−	0.388910i
$386$	−380927.			−0.130129
$387$	−583143.	+	583143.i	−0.197924	+	0.197924i
$388$	3.08196e6	−	3.08196e6i	1.03932	−	1.03932i
$389$			4.69895e6i			1.57444i	0.616672	+	0.787221i	$0.288481\pi$
$389$			4.69895e6i			1.57444i	−0.616672	+	0.787221i	$0.711519\pi$
$390$	−506770.	+	640148.i	−0.168713	+	0.213117i
$391$			2.86600e6i			0.948057i
$392$	−1.52537e6	+	1.52537e6i	−0.501372	+	0.501372i
$393$	−58047.4	−	58047.4i	−0.0189584	−	0.0189584i
$394$			7.67373e6i			2.49038i
$395$	4.66387e6	−	542373.i	1.50402	−	0.174906i
$396$	−5.95250e6	−	2.47020e6i	−1.90749	−	0.791579i
$397$	−1.88349e6	−	1.88349e6i	−0.599773	−	0.599773i	0.340479	−	0.940252i	$-0.389411\pi$
$397$	−1.88349e6	−	1.88349e6i	−0.599773	−	0.599773i	−0.940252	+	0.340479i	$0.889411\pi$
$398$	−814746.	−	814746.i	−0.257819	−	0.257819i
$399$		−	653532.i		−	0.205511i
$400$	−4.22935e6	+	997169.i	−1.32167	+	0.311615i
$401$	4.30526e6			1.33702			0.668511	−	0.743702i	$-0.266932\pi$
$401$	4.30526e6			1.33702			0.668511	+	0.743702i	$0.266932\pi$
$402$	132271.	−	132271.i	0.0408224	−	0.0408224i
$403$	−637364.	−	637364.i	−0.195490	−	0.195490i
$404$	−1.34367e7			−4.09580
$405$	−3.04954e6	+	354638.i	−0.923839	+	0.107436i
$406$			6.67157e6i			2.00869i
$407$	−729021.	−	1.76330e6i	−0.218149	−	0.527642i
$408$	404279.	−	404279.i	0.120235	−	0.120235i
$409$	−3.69322e6			−1.09169			−0.545843	−	0.837888i	$-0.683790\pi$
$409$	−3.69322e6			−1.09169			−0.545843	+	0.837888i	$0.683790\pi$
$410$	−392095.	−	310400.i	−0.115194	−	0.0911931i
$411$	−716913.			−0.209345
$412$	−4.18227e6	−	4.18227e6i	−1.21386	−	1.21386i
$413$	−1.90618e6	−	1.90618e6i	−0.549906	−	0.549906i
$414$	1.01074e7			2.89826
$415$	4.85840e6	+	3.84613e6i	1.38476	+	1.09623i
$416$	1.52101e6			0.430922
$417$	297684.	−	297684.i	0.0838331	−	0.0838331i
$418$	−9.76706e6	+	4.03812e6i	−2.73416	+	1.13042i
$419$			4.89485e6i			1.36209i	0.732243	+	0.681043i	$0.238473\pi$
$419$			4.89485e6i			1.36209i	−0.732243	+	0.681043i	$0.761527\pi$
$420$	931031.	−	108272.i	0.257538	−	0.0299497i
$421$	3.25503e6			0.895054			0.447527	−	0.894270i	$-0.352305\pi$
$421$	3.25503e6			0.895054			0.447527	+	0.894270i	$0.352305\pi$
$422$	−3.37379e6	−	3.37379e6i	−0.922224	−	0.922224i
$423$	2.64466e6	−	2.64466e6i	0.718651	−	0.718651i
$424$	−3.12518e6			−0.844229
$425$	1.10414e6	−	1.78543e6i	0.296519	−	0.479479i
$426$			483702.i			0.129138i
$427$	−370105.	−	370105.i	−0.0982324	−	0.0982324i
$428$	−152450.	−	152450.i	−0.0402270	−	0.0402270i
$429$	−542238.	−	225021.i	−0.142248	−	0.0590310i
$430$	−1.92670e6	+	224061.i	−0.502509	+	0.0584380i
$431$		−	5.40279e6i		−	1.40096i	−0.713674	−	0.700478i	$-0.752970\pi$
$431$		−	5.40279e6i		−	1.40096i	0.713674	−	0.700478i	$-0.247030\pi$
$432$	−1.12838e6	−	1.12838e6i	−0.290903	−	0.290903i
$433$	2.25397e6	−	2.25397e6i	0.577734	−	0.577734i	−0.356544	−	0.934278i	$-0.616045\pi$
$433$	2.25397e6	−	2.25397e6i	0.577734	−	0.577734i	0.934278	+	0.356544i	$0.116045\pi$
$434$			1.52406e6i			0.388400i
$435$	−534331.	+	674963.i	−0.135390	+	0.171024i
$436$		−	4.77708e6i		−	1.20350i
$437$	7.95788e6	−	7.95788e6i	1.99340	−	1.99340i
$438$	−421713.	+	421713.i	−0.105034	+	0.105034i
$439$	2.84191e6			0.703799			0.351900	−	0.936038i	$-0.385536\pi$
$439$	2.84191e6			0.703799			0.351900	+	0.936038i	$0.385536\pi$
$440$	−3.88567e6	−	6.98245e6i	−0.956829	−	1.71940i
$441$	−1.43710e6			−0.351877
$442$	−2.90344e6	+	2.90344e6i	−0.706898	+	0.706898i
$443$	2.80766e6	−	2.80766e6i	0.679728	−	0.679728i	−0.280211	−	0.959939i	$-0.590404\pi$
$443$	2.80766e6	−	2.80766e6i	0.679728	−	0.679728i	0.959939	+	0.280211i	$0.0904043\pi$
$444$		−	768860.i		−	0.185093i
$445$	−311880.	−	2.68185e6i	−0.0746598	−	0.642000i
$446$		−	4.51732e6i		−	1.07533i
$447$	−598063.	+	598063.i	−0.141572	+	0.141572i
$448$	1.44379e6	+	1.44379e6i	0.339866	+	0.339866i
$449$		−	5.75071e6i		−	1.34619i	−0.739557	−	0.673094i	$-0.764965\pi$
$449$		−	5.75071e6i		−	1.34619i	0.739557	−	0.673094i	$-0.235035\pi$
$450$	−6.29657e6	−	3.89392e6i	−1.46579	−	0.906475i
$451$	137827.	−	332125.i	0.0319075	−	0.0768883i
$452$	9.64173e6	+	9.64173e6i	2.21978	+	2.21978i
$453$	−212399.	−	212399.i	−0.0486304	−	0.0486304i
$454$		−	5.90456e6i		−	1.34446i
$455$	−3.52486e6	+	409915.i	−0.798202	+	0.0928250i
$456$	−2.24508e6			−0.505615
$457$	−4.14760e6	+	4.14760e6i	−0.928980	+	0.928980i	−0.997640	−	0.0686605i	$-0.978127\pi$
$457$	−4.14760e6	+	4.14760e6i	−0.928980	+	0.928980i	0.0686605	+	0.997640i	$0.478127\pi$
$458$	−3612.95	−	3612.95i	−0.000804819	−	0.000804819i
$459$	770932.			0.170799
$460$	1.26553e7	+	1.00185e7i	2.78855	+	2.20754i
$461$			6.64180e6i			1.45557i	0.685805	+	0.727786i	$0.259450\pi$
$461$			6.64180e6i			1.45557i	−0.685805	+	0.727786i	$0.740550\pi$
$462$	379265.	+	917336.i	0.0826681	+	0.199951i
$463$	−2.95352e6	+	2.95352e6i	−0.640306	+	0.640306i	−0.950631	−	0.310325i	$-0.899562\pi$
$463$	−2.95352e6	+	2.95352e6i	−0.640306	+	0.640306i	0.310325	+	0.950631i	$0.399562\pi$
$464$	8.96154e6			1.93236
$465$	−122064.	+	154190.i	−0.0261790	+	0.0330692i
$466$	2.62109e6			0.559135
$467$	3.82802e6	+	3.82802e6i	0.812236	+	0.812236i	0.984969	−	0.172733i	$-0.0552597\pi$
$467$	3.82802e6	+	3.82802e6i	0.812236	+	0.812236i	−0.172733	+	0.984969i	$0.555260\pi$
$468$	6.95217e6	+	6.95217e6i	1.46726	+	1.46726i
$469$	813023.			0.170675
$470$	8.73794e6	−	1.01616e6i	1.82459	−	0.212186i
$471$	907855.			0.188566
$472$	−6.54831e6	+	6.54831e6i	−1.35293	+	1.35293i
$473$	−532893.	−	1.28892e6i	−0.109518	−	0.264894i
$474$			2.00370e6i			0.409625i
$475$	−8.02332e6	+	1.89169e6i	−1.63162	+	0.384694i
$476$	4.71383e6			0.953579
$477$	−1.47216e6	−	1.47216e6i	−0.296251	−	0.296251i
$478$	−7.22710e6	+	7.22710e6i	−1.44675	+	1.44675i
$479$	−5.34164e6			−1.06374			−0.531871	−	0.846826i	$-0.678511\pi$
$479$	−5.34164e6			−1.06374			−0.531871	+	0.846826i	$0.678511\pi$
$480$	−38333.1	−	329626.i	−0.00759400	−	0.0653008i
$481$			2.91088e6i			0.573670i
$482$	4.98830e6	+	4.98830e6i	0.977990	+	0.977990i
$483$	−747415.	−	747415.i	−0.145779	−	0.145779i
$484$	7.71721e6	−	7.69690e6i	1.49743	−	1.49349i
$485$	2.82275e6	+	2.23462e6i	0.544902	+	0.431369i
$486$		−	4.09437e6i		−	0.786315i
$487$	272539.	+	272539.i	0.0520723	+	0.0520723i	0.732663	−	0.680591i	$-0.238277\pi$
$487$	272539.	+	272539.i	0.0520723	+	0.0520723i	−0.680591	+	0.732663i	$0.738277\pi$
$488$	−1.27142e6	+	1.27142e6i	−0.241680	+	0.241680i
$489$		−	638319.i		−	0.120716i
$490$	−2.65018e6	−	2.09800e6i	−0.498637	−	0.394743i
$491$			6.85187e6i			1.28264i	0.767273	+	0.641321i	$0.221613\pi$
$491$			6.85187e6i			1.28264i	−0.767273	+	0.641321i	$0.778387\pi$
$492$	102458.	−	102458.i	0.0190824	−	0.0190824i
$493$	−3.06134e6	+	3.06134e6i	−0.567276	+	0.567276i
$494$	1.61237e7			2.97267
$495$	1.45879e6	−	5.11960e6i	0.267595	−	0.939124i
$496$	2.04719e6			0.373641
$497$	−1.48658e6	+	1.48658e6i	−0.269958	+	0.269958i
$498$	−1.86983e6	+	1.86983e6i	−0.337853	+	0.337853i
$499$			5.35048e6i			0.961926i	0.876741	+	0.480963i	$0.159713\pi$
$499$			5.35048e6i			0.961926i	−0.876741	+	0.480963i	$0.840287\pi$
$500$	−4.02416e6	−	1.11167e7i	−0.719864	−	1.98862i
$501$			908481.i			0.161704i
$502$	−1.66769e6	+	1.66769e6i	−0.295363	+	0.295363i
$503$	−3.66869e6	−	3.66869e6i	−0.646533	−	0.646533i	0.305620	−	0.952153i	$-0.401136\pi$
$503$	−3.66869e6	−	3.66869e6i	−0.646533	−	0.646533i	−0.952153	+	0.305620i	$0.901136\pi$
$504$		−	8.76361e6i		−	1.53676i
$505$	−1.28207e6	−	1.10245e7i	−0.223709	−	1.92367i
$506$	−6.55193e6	+	1.57884e7i	−1.13761	+	2.74132i
$507$	5969.23	+	5969.23i	0.00103133	+	0.00103133i
$508$	6.28164e6	+	6.28164e6i	1.07998	+	1.07998i
$509$			6.92179e6i			1.18420i	0.805866	+	0.592098i	$0.201700\pi$
$509$			6.92179e6i			1.18420i	−0.805866	+	0.592098i	$0.798300\pi$
$510$	702393.	+	556046.i	0.119579	+	0.0946641i
$511$	−2.59213e6			−0.439141
$512$	8.76430e6	−	8.76430e6i	1.47755	−	1.47755i
$513$	−2.14061e6	−	2.14061e6i	−0.359124	−	0.359124i
$514$	−1.79824e7			−3.00221
$515$	3.03241e6	−	3.83052e6i	0.503814	−	0.636414i
$516$		−	562014.i		−	0.0929229i
$517$	2.41676e6	+	5.84546e6i	0.397656	+	0.961818i
$518$	3.48025e6	−	3.48025e6i	0.569884	−	0.569884i
$519$	1.20148e6			0.195793
$520$	1.40818e6	+	1.21090e7i	0.228376	+	1.96381i
$521$	3.32671e6			0.536934			0.268467	−	0.963289i	$-0.413483\pi$
$521$	3.32671e6			0.536934			0.268467	+	0.963289i	$0.413483\pi$
$522$	1.07963e7	+	1.07963e7i	1.73420	+	1.73420i
$523$	−2.95109e6	−	2.95109e6i	−0.471768	−	0.471768i	0.430718	−	0.902487i	$-0.358260\pi$
$523$	−2.95109e6	−	2.95109e6i	−0.471768	−	0.471768i	−0.902487	+	0.430718i	$0.858260\pi$
$524$	−2.32510e6			−0.369924
$525$	177670.	+	753561.i	0.0281330	+	0.119322i
$526$	5.87123e6			0.925262
$527$	−699339.	+	699339.i	−0.109688	+	0.109688i
$528$	1.23221e6	−	509446.i	0.192353	−	0.0795268i
$529$		−	1.17658e7i		−	1.82802i
$530$	−565650.	−	4.86403e6i	−0.0874699	−	0.752154i
$531$	−6.16936e6			−0.949520
$532$	−1.30887e7	−	1.30887e7i	−2.00501	−	2.00501i
$533$	−387903.	+	387903.i	−0.0591432	+	0.0591432i
$534$	1.15218e6			0.174851
$535$	110536.	−	139628.i	0.0166963	−	0.0210906i
$536$		−	2.79298e6i		−	0.419910i
$537$	−1.10845e6	−	1.10845e6i	−0.165875	−	0.165875i
$538$	−9.56964e6	−	9.56964e6i	−1.42541	−	1.42541i
$539$	931575.	−	2.24484e6i	0.138117	−	0.332823i
$540$	2.69490e6	−	3.40418e6i	0.397703	−	0.502375i
$541$		−	317033.i		−	0.0465706i	−0.999729	−	0.0232853i	$-0.992587\pi$
$541$		−	317033.i		−	0.0465706i	0.999729	−	0.0232853i	$-0.00741261\pi$
$542$	−1.21417e7	−	1.21417e7i	−1.77534	−	1.77534i
$543$	654936.	−	654936.i	0.0953233	−	0.0953233i
$544$		−	1.66891e6i		−	0.241788i
$545$	3.91950e6	−	455808.i	0.565248	−	0.0657341i
$546$		−	1.51436e6i		−	0.217393i
$547$	1.20290e6	−	1.20290e6i	0.171894	−	0.171894i	−0.615917	−	0.787811i	$-0.711214\pi$
$547$	1.20290e6	−	1.20290e6i	0.171894	−	0.171894i	0.787811	+	0.615917i	$0.211214\pi$
$548$	−1.43580e7	+	1.43580e7i	−2.04241	+	2.04241i
$549$	−1.19785e6			−0.169617
$550$	1.01642e7	−	7.31146e6i	1.43274	−	1.03062i
$551$	1.70006e7			2.38553
$552$	−2.56760e6	+	2.56760e6i	−0.358657	+	0.358657i
$553$	−6.15803e6	+	6.15803e6i	−0.856306	+	0.856306i
$554$		−	1.55109e7i		−	2.14715i
$555$	630834.	−	73361.3i	0.0869325	−	0.0101096i
$556$		−	1.19238e7i		−	1.63579i
$557$	−7.86659e6	+	7.86659e6i	−1.07436	+	1.07436i	−0.0773526	+	0.997004i	$0.524647\pi$
$557$	−7.86659e6	+	7.86659e6i	−1.07436	+	1.07436i	−0.997004	+	0.0773526i	$0.975353\pi$
$558$	2.46632e6	+	2.46632e6i	0.335324	+	0.335324i
$559$			2.12777e6i			0.288002i
$560$	5.00255e6	−	6.31918e6i	0.674095	−	0.851512i
$561$	−246901.	+	594964.i	−0.0331220	+	0.0798148i
$562$	−3.85858e6	−	3.85858e6i	−0.515332	−	0.515332i
$563$	5.42677e6	+	5.42677e6i	0.721557	+	0.721557i	0.968922	−	0.247365i	$-0.0795647\pi$
$563$	5.42677e6	+	5.42677e6i	0.721557	+	0.721557i	−0.247365	+	0.968922i	$0.579565\pi$
$564$			2.54883e6i			0.337399i
$565$	−6.99087e6	+	8.83082e6i	−0.921320	+	1.16380i
$566$	−2.29786e7			−3.01497
$567$	4.02652e6	−	4.02652e6i	0.525983	−	0.525983i
$568$	5.10684e6	+	5.10684e6i	0.664174	+	0.664174i
$569$	−2.03385e6			−0.263352			−0.131676	−	0.991293i	$-0.542036\pi$
$569$	−2.03385e6			−0.263352			−0.131676	+	0.991293i	$0.542036\pi$
$570$	−406355.	−	3.49425e6i	−0.0523864	−	0.450471i
$571$		−	3.09413e6i		−	0.397144i	−0.980086	−	0.198572i	$-0.936370\pi$
$571$		−	3.09413e6i		−	0.397144i	0.980086	−	0.198572i	$-0.0636304\pi$
$572$	−1.53663e7	+	6.35309e6i	−1.96372	+	0.811886i
$573$	−903771.	+	903771.i	−0.114993	+	0.114993i
$574$	927553.			0.117506
$575$	−7.01246e6	+	1.13393e7i	−0.884506	+	1.43027i
$576$	4.67283e6			0.586845
$577$	−2.29378e6	−	2.29378e6i	−0.286821	−	0.286821i	0.549001	−	0.835822i	$-0.315008\pi$
$577$	−2.29378e6	−	2.29378e6i	−0.286821	−	0.286821i	−0.835822	+	0.549001i	$0.815008\pi$
$578$	−6.83792e6	−	6.83792e6i	−0.851342	−	0.851342i
$579$	91167.8			0.0113017
$580$	2.81652e6	+	2.42192e7i	0.347650	+	2.98944i
$581$	−1.14932e7			−1.41254
$582$	−1.08638e6	+	1.08638e6i	−0.132945	+	0.132945i
$583$	3.25392e6	−	1.34531e6i	0.396493	−	0.163927i
$584$			8.90475e6i			1.08041i
$585$	−5.04077e6	+	6.36746e6i	−0.608986	+	0.769266i
$586$	2.31478e7			2.78461
$587$	−2.73651e6	−	2.73651e6i	−0.327795	−	0.327795i	0.523952	−	0.851748i	$-0.324457\pi$
$587$	−2.73651e6	−	2.73651e6i	−0.327795	−	0.327795i	−0.851748	+	0.523952i	$0.824457\pi$
$588$	692514.	−	692514.i	0.0826010	−	0.0826010i
$589$	3.88364e6			0.461265
$590$	−1.13770e7	−	9.00656e6i	−1.34554	−	1.06519i
$591$		−	1.83656e6i		−	0.216291i
$592$	−4.67483e6	−	4.67483e6i	−0.548228	−	0.548228i
$593$	3.54340e6	+	3.54340e6i	0.413793	+	0.413793i	0.883058	−	0.469265i	$-0.155481\pi$
$593$	3.54340e6	+	3.54340e6i	0.413793	+	0.413793i	−0.469265	+	0.883058i	$0.655481\pi$
$594$	4.24695e6	+	1.76242e6i	0.493868	+	0.204948i
$595$	449773.	+	3.86760e6i	0.0520836	+	0.447867i
$596$			2.39555e7i			2.76242i
$597$	194994.	+	194994.i	0.0223917	+	0.0223917i
$598$	1.84399e7	−	1.84399e7i	2.10865	−	2.10865i
$599$			6.01044e6i			0.684447i	0.939619	+	0.342223i	$0.111180\pi$
$599$			6.01044e6i			0.684447i	−0.939619	+	0.342223i	$0.888820\pi$
$600$	2.58871e6	−	610350.i	0.293566	−	0.0692151i
$601$		−	1.28995e7i		−	1.45675i	−0.685178	−	0.728375i	$-0.740276\pi$
$601$		−	1.28995e7i		−	1.45675i	0.685178	−	0.728375i	$-0.259724\pi$
$602$	2.54396e6	−	2.54396e6i	0.286101	−	0.286101i
$603$	1.31568e6	−	1.31568e6i	0.147352	−	0.147352i
$604$	−8.50769e6			−0.948897
$605$	7.05149e6	+	5.59740e6i	0.783236	+	0.621725i
$606$	4.73638e6			0.523920
$607$	−1.95058e6	+	1.95058e6i	−0.214878	+	0.214878i	−0.806336	−	0.591458i	$-0.798552\pi$
$607$	−1.95058e6	+	1.95058e6i	−0.214878	+	0.214878i	0.591458	+	0.806336i	$0.298552\pi$
$608$	−4.63397e6	+	4.63397e6i	−0.508387	+	0.508387i
$609$		−	1.59672e6i		−	0.174455i
$610$	−2.20897e6	−	1.74872e6i	−0.240361	−	0.190281i
$611$		−	9.64980e6i		−	1.04572i
$612$	7.62818e6	−	7.62818e6i	0.823270	−	0.823270i
$613$	1.05507e7	+	1.05507e7i	1.13404	+	1.13404i	0.989498	+	0.144546i	$0.0461722\pi$
$613$	1.05507e7	+	1.05507e7i	1.13404	+	1.13404i	0.144546	+	0.989498i	$0.453828\pi$
$614$		−	1.01807e7i		−	1.08983i
$615$	93840.6	+	74288.5i	0.0100047	+	0.00792015i
$616$	1.36893e7	+	5.68086e6i	1.45355	+	0.603201i
$617$	−7.29509e6	−	7.29509e6i	−0.771468	−	0.771468i	0.206895	−	0.978363i	$-0.433664\pi$
$617$	−7.29509e6	−	7.29509e6i	−0.771468	−	0.771468i	−0.978363	+	0.206895i	$0.933664\pi$
$618$	1.47423e6	+	1.47423e6i	0.155273	+	0.155273i
$619$			7.23061e6i			0.758487i	0.925297	+	0.379244i	$0.123816\pi$
$619$			7.23061e6i			0.758487i	−0.925297	+	0.379244i	$0.876184\pi$
$620$	643410.	+	5.53268e6i	0.0672215	+	0.578038i
$621$	−4.89623e6			−0.509487
$622$	−540440.	+	540440.i	−0.0560108	+	0.0560108i
$623$	3.54104e6	+	3.54104e6i	0.365520	+	0.365520i
$624$	−2.03415e6			−0.209132
$625$	8.73707e6	−	4.36245e6i	0.894676	−	0.446715i
$626$		−	1.99342e6i		−	0.203312i
$627$	2.33757e6	−	966448.i	0.237462	−	0.0981770i
$628$	1.81821e7	−	1.81821e7i	1.83969	−	1.83969i
$629$	3.19393e6			0.321883
$630$	1.36397e7	−	1.58619e6i	1.36916	−	0.159223i
$631$	−4.36014e6			−0.435940			−0.217970	−	0.975955i	$-0.569944\pi$
$631$	−4.36014e6			−0.435940			−0.217970	+	0.975955i	$0.569944\pi$
$632$	2.11547e7	+	2.11547e7i	2.10676	+	2.10676i
$633$	807453.	+	807453.i	0.0800955	+	0.0800955i
$634$	5.72144e6			0.565304
$635$	−4.55459e6	+	5.75333e6i	−0.448245	+	0.566219i
$636$	1.41882e6			0.139087
$637$	−2.62184e6	+	2.62184e6i	−0.256010	+	0.256010i
$638$	−2.38630e7	+	9.86596e6i	−2.32099	+	0.959594i
$639$			4.81132e6i			0.466135i
$640$	1.21017e7	+	9.58026e6i	1.16788	+	0.924543i
$641$	−980859.			−0.0942891			−0.0471446	−	0.998888i	$-0.515012\pi$
$641$	−980859.			−0.0942891			−0.0471446	+	0.998888i	$0.515012\pi$
$642$	53738.0	+	53738.0i	0.00514569	+	0.00514569i
$643$	6.67773e6	−	6.67773e6i	0.636945	−	0.636945i	−0.312856	−	0.949801i	$-0.601286\pi$
$643$	6.67773e6	−	6.67773e6i	0.636945	−	0.636945i	0.949801	+	0.312856i	$0.101286\pi$
$644$	−2.99378e7			−2.84450
$645$	461121.	−	53624.9i	0.0436431	−	0.00507537i
$646$		−	1.76915e7i		−	1.66795i
$647$	9.70368e6	+	9.70368e6i	0.911330	+	0.911330i	0.996377	−	0.0850468i	$-0.0271040\pi$
$647$	9.70368e6	+	9.70368e6i	0.911330	+	0.911330i	−0.0850468	+	0.996377i	$0.527104\pi$
$648$	−1.38323e7	−	1.38323e7i	−1.29407	−	1.29407i
$649$	3.99918e6	−	9.63692e6i	0.372700	−	0.898104i
$650$	−1.85915e7	+	4.38339e6i	−1.72596	+	0.406936i
$651$		−	364757.i		−	0.0337327i
$652$	−1.27840e7	−	1.27840e7i	−1.17773	−	1.17773i
$653$	−9.71690e6	+	9.71690e6i	−0.891753	+	0.891753i	−0.994688	−	0.102935i	$-0.967177\pi$
$653$	−9.71690e6	+	9.71690e6i	−0.891753	+	0.891753i	0.102935	+	0.994688i	$0.467177\pi$
$654$			1.68390e6i			0.153947i
$655$	−221851.	−	1.90769e6i	−0.0202049	−	0.173742i
$656$		−	1.24593e6i		−	0.113041i
$657$	−4.19472e6	+	4.19472e6i	−0.379131	+	0.379131i
$658$	−1.15373e7	+	1.15373e7i	−1.03882	+	1.03882i
$659$	1.58163e7			1.41870			0.709350	−	0.704856i	$-0.248988\pi$
$659$	1.58163e7			1.41870			0.709350	+	0.704856i	$0.248988\pi$
$660$	1.76408e6	+	3.17001e6i	0.157637	+	0.283270i
$661$	−1.90687e7			−1.69753			−0.848767	−	0.528767i	$-0.822654\pi$
$661$	−1.90687e7			−1.69753			−0.848767	+	0.528767i	$0.822654\pi$
$662$	8.57047e6	−	8.57047e6i	0.760080	−	0.760080i
$663$	694884.	−	694884.i	0.0613943	−	0.0613943i
$664$			3.94827e7i			3.47525i
$665$	9.49012e6	−	1.19878e7i	0.832180	−	1.05120i
$666$		−	1.12639e7i		−	0.984015i
$667$	1.94428e7	−	1.94428e7i	1.69217	−	1.69217i
$668$	1.81947e7	+	1.81947e7i	1.57762	+	1.57762i
$669$			1.08114e6i			0.0933932i
$670$	4.34700e6	−	505523.i	0.374113	−	0.0435065i
$671$	776483.	−	1.87111e6i	0.0665772	−	0.160433i
$672$	435229.	+	435229.i	0.0371787	+	0.0371787i
$673$	401618.	+	401618.i	0.0341803	+	0.0341803i	0.723990	−	0.689810i	$-0.242306\pi$
$673$	401618.	+	401618.i	0.0341803	+	0.0341803i	−0.689810	+	0.723990i	$0.742306\pi$
$674$		−	1.26059e7i		−	1.06887i
$675$	3.05019e6	+	1.88630e6i	0.257673	+	0.159350i
$676$	239098.			0.0201238
$677$	5.95662e6	−	5.95662e6i	0.499492	−	0.499492i	−0.411788	−	0.911280i	$-0.635096\pi$
$677$	5.95662e6	−	5.95662e6i	0.499492	−	0.499492i	0.911280	+	0.411788i	$0.135096\pi$
$678$	−3.39867e6	−	3.39867e6i	−0.283945	−	0.283945i
$679$	−6.67760e6			−0.555835
$680$	1.32864e7	−	1.54511e6i	1.10188	−	0.128141i
$681$			1.41315e6i			0.116767i
$682$	−5.45130e6	+	2.25380e6i	−0.448786	+	0.185547i
$683$	1.33363e6	−	1.33363e6i	0.109392	−	0.109392i	−0.650292	−	0.759684i	$-0.725354\pi$
$683$	1.33363e6	−	1.33363e6i	0.109392	−	0.109392i	0.759684	+	0.650292i	$0.225354\pi$
$684$	−4.23616e7			−3.46204
$685$	−1.31504e7	−	1.04105e7i	−1.07081	−	0.847704i
$686$	2.36676e7			1.92019
$687$	864.692	+	864.692i	6.98988e−5	+	6.98988e-5i
$688$	−3.41716e6	−	3.41716e6i	−0.275229	−	0.275229i
$689$	−5.37163e6			−0.431080
$690$	−4.46094e6	−	3.53148e6i	−0.356700	−	0.282380i
$691$	−1.07522e6			−0.0856646			−0.0428323	−	0.999082i	$-0.513638\pi$
$691$	−1.07522e6			−0.0856646			−0.0428323	+	0.999082i	$0.513638\pi$
$692$	2.40627e7	−	2.40627e7i	1.91020	−	1.91020i
$693$	3.77250e6	+	9.12461e6i	0.298398	+	0.721741i
$694$			2.13248e7i			1.68069i
$695$	9.78322e6	−	1.13772e6i	0.768281	−	0.0893453i
$696$	−5.48521e6			−0.429210
$697$	425621.	+	425621.i	0.0331849	+	0.0331849i
$698$	1.49675e6	−	1.49675e6i	0.116282	−	0.116282i
$699$	−627309.			−0.0485611
$700$	1.86503e7	+	1.15337e7i	1.43860	+	0.889659i
$701$		−	1.51552e7i		−	1.16484i	−0.812888	−	0.582419i	$-0.802106\pi$
$701$		−	1.51552e7i		−	1.16484i	0.812888	−	0.582419i	$-0.197894\pi$
$702$	−4.96019e6	−	4.96019e6i	−0.379888	−	0.379888i
$703$	−8.86842e6	−	8.86842e6i	−0.676796	−	0.676796i
$704$	−3.02908e6	+	7.29924e6i	−0.230345	+	0.555068i
$705$	−2.09126e6	+	243198.i	−0.158466	+	0.0184284i
$706$			4.20302e6i			0.317358i
$707$	1.45565e7	+	1.45565e7i	1.09523	+	1.09523i
$708$	2.97291e6	−	2.97291e6i	0.222894	−	0.222894i
$709$		−	1.15731e7i		−	0.864639i	−0.901721	−	0.432319i	$-0.857695\pi$
$709$		−	1.15731e7i		−	0.864639i	0.901721	−	0.432319i	$-0.142305\pi$
$710$	−7.02396e6	+	8.87262e6i	−0.522921	+	0.660550i
$711$			1.99305e7i			1.47858i
$712$	1.21646e7	−	1.21646e7i	0.899283	−	0.899283i
$713$	4.44154e6	−	4.44154e6i	0.327197	−	0.327197i
$714$	−1.66161e6			−0.121978
$715$	−6.67877e6	−	1.20016e7i	−0.488575	−	0.877957i
$716$	−4.43993e7			−3.23663
$717$	1.72967e6	−	1.72967e6i	0.125651	−	0.125651i
$718$	2.52339e7	−	2.52339e7i	1.82673	−	1.82673i
$719$			3.22580e6i			0.232710i	0.993208	+	0.116355i	$0.0371211\pi$
$719$			3.22580e6i			0.232710i	−0.993208	+	0.116355i	$0.962879\pi$
$720$	−2.13065e6	−	1.83214e7i	−0.153172	−	1.31713i
$721$			9.06161e6i			0.649183i
$722$	−3.16427e7	+	3.16427e7i	−2.25907	+	2.25907i
$723$	−1.19386e6	−	1.19386e6i	−0.0849388	−	0.0849388i
$724$		−	2.62336e7i		−	1.85999i
$725$	−1.96026e7	+	4.62179e6i	−1.38506	+	0.326561i
$726$	−2.72028e6	+	2.71313e6i	−0.191546	+	0.191042i
$727$	1.32304e7	+	1.32304e7i	0.928404	+	0.928404i	0.997603	−	0.0691987i	$-0.0220443\pi$
$727$	1.32304e7	+	1.32304e7i	0.928404	+	0.928404i	−0.0691987	+	0.997603i	$0.522044\pi$
$728$	−1.59883e7	−	1.59883e7i	−1.11808	−	1.11808i
$729$		−	1.23655e7i		−	0.861773i
$730$	−1.38593e7	+	1.61174e6i	−0.962577	+	0.111941i
$731$	2.33467e6			0.161596
$732$	577222.	−	577222.i	0.0398167	−	0.0398167i
$733$	−931738.	−	931738.i	−0.0640521	−	0.0640521i	0.674355	−	0.738407i	$-0.264422\pi$
$733$	−931738.	−	931738.i	−0.0640521	−	0.0640521i	−0.738407	+	0.674355i	$0.764422\pi$
$734$	1.52685e7			1.04606
$735$	634270.	+	502117.i	0.0433068	+	0.0342836i
$736$			1.05993e7i			0.721246i
$737$	1.20230e6	+	2.90803e6i	0.0815353	+	0.197211i
$738$	1.50102e6	−	1.50102e6i	0.101448	−	0.101448i
$739$	2.10979e7			1.42111			0.710554	−	0.703642i	$-0.248444\pi$
$739$	2.10979e7			1.42111			0.710554	+	0.703642i	$0.248444\pi$
$740$	1.11648e7	−	1.41033e7i	0.749501	−	0.946764i
$741$	−3.85890e6			−0.258177
$742$	6.42232e6	+	6.42232e6i	0.428235	+	0.428235i
$743$	1.25181e7	+	1.25181e7i	0.831892	+	0.831892i	0.987775	−	0.155883i	$-0.0498224\pi$
$743$	1.25181e7	+	1.25181e7i	0.831892	+	0.831892i	−0.155883	+	0.987775i	$0.549822\pi$
$744$	−1.25305e6			−0.0829920
$745$	−1.96550e7	+	2.28573e6i	−1.29743	+	0.150881i
$746$	−6.46828e6			−0.425541
$747$	−1.85989e7	+	1.85989e7i	−1.21951	+	1.21951i
$748$	6.97085e6	+	1.68605e7i	0.455545	+	1.10184i
$749$			330309.i			0.0215138i
$750$	1.41850e6	+	3.91860e6i	0.0920823	+	0.254377i
$751$	−1.05132e7			−0.680197			−0.340098	−	0.940390i	$-0.610460\pi$
$751$	−1.05132e7			−0.680197			−0.340098	+	0.940390i	$0.610460\pi$
$752$	1.54974e7	+	1.54974e7i	0.999344	+	0.999344i
$753$	399131.	−	399131.i	0.0256524	−	0.0256524i
$754$	3.93934e7			2.52345
$755$	−811767.	−	6.98038e6i	−0.0518279	−	0.445668i
$756$			8.05304e6i			0.512455i
$757$	−8.65481e6	−	8.65481e6i	−0.548931	−	0.548931i	0.377201	−	0.926132i	$-0.376887\pi$
$757$	−8.65481e6	−	8.65481e6i	−0.548931	−	0.548931i	−0.926132	+	0.377201i	$0.876887\pi$
$758$	3.52216e7	+	3.52216e7i	2.22657	+	2.22657i
$759$	1.56808e6	−	3.77865e6i	0.0988018	−	0.238085i
$760$	−4.11819e7	−	3.26015e7i	−2.58626	−	2.04740i
$761$		−	1.10844e7i		−	0.693828i	−0.937897	−	0.346914i	$-0.887230\pi$
$761$		−	1.10844e7i		−	0.693828i	0.937897	−	0.346914i	$-0.112770\pi$
$762$	−2.21425e6	−	2.21425e6i	−0.138146	−	0.138146i
$763$	−5.17518e6	+	5.17518e6i	−0.321821	+	0.321821i
$764$			3.62007e7i			2.24379i
$765$	6.98661e6	+	5.53092e6i	0.431631	+	0.341699i
$766$			2.07640e7i			1.27861i
$767$	−1.12554e7	+	1.12554e7i	−0.690830	+	0.690830i
$768$	−3.59281e6	+	3.59281e6i	−0.219802	+	0.219802i
$769$	−2.18944e6			−0.133511			−0.0667554	−	0.997769i	$-0.521265\pi$
$769$	−2.18944e6			−0.133511			−0.0667554	+	0.997769i	$0.521265\pi$
$770$	−6.36396e6	+	2.23342e7i	−0.386812	+	1.35751i
$771$	4.30376e6			0.260743
$772$	1.82587e6	−	1.82587e6i	0.110262	−	0.110262i
$773$	−1.42991e6	+	1.42991e6i	−0.0860718	+	0.0860718i	−0.748832	−	0.662760i	$-0.769385\pi$
$773$	−1.42991e6	+	1.42991e6i	−0.0860718	+	0.0860718i	0.662760	+	0.748832i	$0.269385\pi$
$774$		−	8.23355e6i		−	0.494009i
$775$	−4.47806e6	+	1.05581e6i	−0.267816	+	0.0631439i
$776$			2.29396e7i			1.36751i
$777$	−832934.	+	832934.i	−0.0494946	+	0.0494946i
$778$	−3.31728e7	−	3.31728e7i	−1.96487	−	1.96487i
$779$		−	2.36360e6i		−	0.139550i
$780$	−639311.	−	5.49744e6i	−0.0376249	−	0.323537i
$781$	−7.51557e6	−	3.11885e6i	−0.440894	−	0.182965i
$782$	−2.02329e7	−	2.02329e7i	−1.18315	−	1.18315i
$783$	−5.22996e6	−	5.22996e6i	−0.304855	−	0.304855i
$784$		−	8.42126e6i		−	0.489313i
$785$	1.66529e7	+	1.31832e7i	0.964531	+	0.763566i
$786$	819587.			0.0473193
$787$	−1.12675e6	+	1.12675e6i	−0.0648469	+	0.0648469i	−0.738786	−	0.673940i	$-0.764601\pi$
$787$	−1.12675e6	+	1.12675e6i	−0.0648469	+	0.0648469i	0.673940	+	0.738786i	$0.264601\pi$
$788$	−3.67819e7	−	3.67819e7i	−2.11018	−	2.11018i
$789$	−1.40517e6			−0.0803594
$790$	−2.90962e7	+	3.67542e7i	−1.65871	+	2.09526i
$791$		−	2.08905e7i		−	1.18715i
$792$	3.13458e7	−	1.29597e7i	1.77569	−	0.734145i
$793$	−2.18535e6	+	2.18535e6i	−0.123406	+	0.123406i
$794$	2.65935e7			1.49701
$795$	135378.	+	1.16412e6i	0.00759679	+	0.0653248i
$796$	7.81053e6			0.436916
$797$	1.10544e7	+	1.10544e7i	0.616440	+	0.616440i	0.944617	−	0.328176i	$-0.106434\pi$
$797$	1.10544e7	+	1.10544e7i	0.616440	+	0.616440i	−0.328176	+	0.944617i	$0.606434\pi$
$798$	4.61370e6	+	4.61370e6i	0.256473	+	0.256473i
$799$	−1.05881e7			−0.586748
$800$	4.08344e6	−	6.60303e6i	0.225580	−	0.364769i
$801$	1.14606e7			0.631141
$802$	−3.03936e7	+	3.03936e7i	−1.66858	+	1.66858i
$803$	−3.83326e6	−	9.27156e6i	−0.209787	−	0.507416i
$804$			1.26801e6i			0.0691801i
$805$	−2.85654e6	−	2.45634e7i	−0.155364	−	1.33597i
$806$	8.99911e6			0.487935
$807$	2.29032e6	+	2.29032e6i	0.123797	+	0.123797i
$808$	5.00059e7	−	5.00059e7i	2.69459	−	2.69459i
$809$	−1.98990e7			−1.06896			−0.534479	−	0.845182i	$-0.679492\pi$
$809$	−1.98990e7			−1.06896			−0.534479	+	0.845182i	$0.679492\pi$
$810$	1.90250e7	−	2.40322e7i	1.01885	−	1.28701i
$811$		−	1.61708e6i		−	0.0863336i	−0.999068	−	0.0431668i	$-0.986255\pi$
$811$		−	1.61708e6i		−	0.0863336i	0.999068	−	0.0431668i	$-0.0137447\pi$
$812$	−3.19783e7	−	3.19783e7i	−1.70202	−	1.70202i
$813$	2.90590e6	+	2.90590e6i	0.154189	+	0.154189i
$814$	1.75948e7	+	7.30160e6i	0.930732	+	0.386240i
$815$	9.26920e6	−	1.17088e7i	0.488819	−	0.617473i
$816$			2.23194e6i			0.117343i
$817$	−6.48255e6	−	6.48255e6i	−0.339775	−	0.339775i
$818$	2.60728e7	−	2.60728e7i	1.36240	−	1.36240i
$819$		−	1.50631e7i		−	0.784701i
$820$	3.36722e6	−	391582.i	0.174879	−	0.0203371i
$821$			9.79645e6i			0.507237i	0.967304	+	0.253618i	$0.0816207\pi$
$821$			9.79645e6i			0.507237i	−0.967304	+	0.253618i	$0.918379\pi$
$822$	5.06114e6	−	5.06114e6i	0.261258	−	0.261258i
$823$	8.91968e6	−	8.91968e6i	0.459039	−	0.459039i	−0.439301	−	0.898340i	$-0.644774\pi$
$823$	8.91968e6	−	8.91968e6i	0.459039	−	0.459039i	0.898340	+	0.439301i	$0.144774\pi$
$824$	3.11294e7			1.59718
$825$	−2.43261e6	+	1.74986e6i	−0.124434	+	0.0895095i
$826$	2.69139e7			1.37254
$827$	−1.91864e6	+	1.91864e6i	−0.0975506	+	0.0975506i	−0.754198	−	0.656647i	$-0.771974\pi$
$827$	−1.91864e6	+	1.91864e6i	−0.0975506	+	0.0975506i	0.656647	+	0.754198i	$0.271974\pi$
$828$	−4.84470e7	+	4.84470e7i	−2.45579	+	2.45579i
$829$			1.66748e7i			0.842703i	0.906897	+	0.421352i	$0.138444\pi$
$829$			1.66748e7i			0.842703i	−0.906897	+	0.421352i	$0.861556\pi$
$830$	−6.14508e7	+	7.14627e6i	−3.09622	+	0.360068i
$831$			3.71224e6i			0.186481i
$832$	8.52510e6	−	8.52510e6i	0.426964	−	0.426964i
$833$	2.87678e6	+	2.87678e6i	0.143646	+	0.143646i
$834$			4.20308e6i			0.209244i
$835$	−1.31923e7	+	1.66644e7i	−0.654793	+	0.827130i
$836$	2.74602e7	−	6.61714e7i	1.35890	−	3.27457i
$837$	−1.19474e6	−	1.19474e6i	−0.0589468	−	0.0589468i
$838$	−3.45559e7	−	3.45559e7i	−1.69986	−	1.69986i
$839$			5.52151e6i			0.270803i	0.990791	+	0.135401i	$0.0432324\pi$
$839$			5.52151e6i			0.270803i	−0.990791	+	0.135401i	$0.956768\pi$
$840$	−3.06197e6	+	3.86786e6i	−0.149728	+	0.189135i
$841$	2.10248e7			1.02504
$842$	−2.29793e7	+	2.29793e7i	−1.11701	+	1.11701i
$843$	923480.	+	923480.i	0.0447567	+	0.0447567i
$844$	3.23427e7			1.56286
$845$	22813.7	+	196175.i	0.00109914	+	0.00945153i
$846$			3.73406e7i			1.79372i
$847$	−1.66987e7	−	21996.6i	−0.799785	−	0.00105353i
$848$	8.62674e6	−	8.62674e6i	0.411962	−	0.411962i
$849$	5.49951e6			0.261851
$850$	4.80961e6	+	2.03993e7i	0.228330	+	0.968429i
$851$	−2.02848e7			−0.960167
$852$	−2.31849e6	−	2.31849e6i	−0.109423	−	0.109423i
$853$	−9.28882e6	−	9.28882e6i	−0.437107	−	0.437107i	0.453930	−	0.891037i	$-0.350022\pi$
$853$	−9.28882e6	−	9.28882e6i	−0.437107	−	0.437107i	−0.891037	+	0.453930i	$0.850022\pi$
$854$	5.22561e6			0.245184
$855$	−4.04196e6	−	3.47568e7i	−0.189093	−	1.62601i
$856$	1.13471e6			0.0529300
$857$	1.86631e7	−	1.86631e7i	0.868023	−	0.868023i	−0.124230	−	0.992253i	$-0.539646\pi$
$857$	1.86631e7	−	1.86631e7i	0.868023	−	0.868023i	0.992253	+	0.124230i	$0.0396461\pi$
$858$	5.41657e6	−	2.23944e6i	0.251192	−	0.103853i
$859$		−	8.39919e6i		−	0.388378i	−0.980964	−	0.194189i	$-0.937793\pi$
$859$		−	8.39919e6i		−	0.388378i	0.980964	−	0.194189i	$-0.0622075\pi$
$860$	8.16115e6	−	1.03091e7i	0.376275	−	0.475308i
$861$	−221993.			−0.0102054
$862$	3.81417e7	+	3.81417e7i	1.74836	+	1.74836i
$863$	1.46923e7	−	1.46923e7i	0.671527	−	0.671527i	−0.286541	−	0.958068i	$-0.592505\pi$
$863$	1.46923e7	−	1.46923e7i	0.671527	−	0.671527i	0.958068	+	0.286541i	$0.0925054\pi$
$864$	2.85114e6			0.129937
$865$	2.20389e7	+	1.74470e7i	1.00150	+	0.792830i
$866$			3.18244e7i			1.44200i
$867$	1.63653e6	+	1.63653e6i	0.0739394	+	0.0739394i
$868$	−7.30519e6	−	7.30519e6i	−0.329103	−	0.329103i
$869$	−3.11327e7	−	1.29196e7i	−1.39852	−	0.580363i
$870$	−992810.	−	8.53717e6i	−0.0444701	−	0.382398i
$871$		−	4.80064e6i		−	0.214414i
$872$	1.77783e7	+	1.77783e7i	0.791772	+	0.791772i
$873$	−1.08061e7	+	1.08061e7i	−0.479879	+	0.479879i
$874$			1.12359e8i			4.97544i
$875$	−7.68363e6	+	1.64027e7i	−0.339271	+	0.724260i
$876$		−	4.04273e6i		−	0.177998i
$877$	−1.36305e7	+	1.36305e7i	−0.598429	+	0.598429i	−0.939894	−	0.341466i	$-0.889077\pi$
$877$	−1.36305e7	+	1.36305e7i	−0.598429	+	0.598429i	0.341466	+	0.939894i	$0.389077\pi$
$878$	−2.00628e7	+	2.00628e7i	−0.878327	+	0.878327i
$879$	−5.53999e6			−0.241845
$880$	3.00003e7	+	8.54835e6i	1.30593	+	0.372114i
$881$	−1.21154e7			−0.525893			−0.262946	−	0.964810i	$-0.584694\pi$
$881$	−1.21154e7			−0.525893			−0.262946	+	0.964810i	$0.584694\pi$
$882$	1.01454e7	−	1.01454e7i	0.439134	−	0.439134i
$883$	−1.74392e7	+	1.74392e7i	−0.752706	+	0.752706i	−0.974984	−	0.222277i	$-0.928651\pi$
$883$	−1.74392e7	+	1.74392e7i	−0.752706	+	0.752706i	0.222277	+	0.974984i	$0.428651\pi$
$884$		−	2.78337e7i		−	1.19795i
$885$	2.72288e6	+	2.15555e6i	0.116861	+	0.0925125i
$886$			3.96421e7i			1.69657i
$887$	2.12954e7	−	2.12954e7i	0.908819	−	0.908819i	−0.0873579	−	0.996177i	$-0.527842\pi$
$887$	2.12954e7	−	2.12954e7i	0.908819	−	0.908819i	0.996177	+	0.0873579i	$0.0278424\pi$
$888$	2.86138e6	+	2.86138e6i	0.121771	+	0.121771i
$889$		−	1.36103e7i		−	0.577580i
$890$	2.11347e7	+	1.67312e7i	0.894376	+	0.708029i
$891$	2.03566e7	+	8.44767e6i	0.859033	+	0.356486i
$892$	2.16525e7	+	2.16525e7i	0.911164	+	0.911164i
$893$	2.93995e7	+	2.93995e7i	1.23371	+	1.23371i
$894$		−	8.44421e6i		−	0.353358i
$895$	−4.23638e6	−	3.64287e7i	−0.176782	−	1.52015i
$896$	−2.86282e7			−1.19131
$897$	−4.41324e6	+	4.41324e6i	−0.183137	+	0.183137i
$898$	4.05979e7	+	4.05979e7i	1.68001	+	1.68001i
$899$	9.48854e6			0.391562
$900$	4.88454e7	−	1.15165e7i	2.01010	−	0.473928i
$901$			5.89395e6i			0.241877i
$902$	1.37167e6	+	3.31769e6i	0.0561350	+	0.135775i
$903$	−608850.	+	608850.i	−0.0248480	+	0.0248480i
$904$	−7.17652e7			−2.92074
$905$	2.15241e7	−	2.50309e6i	0.873581	−	0.101591i
$906$	2.99892e6			0.121379
$907$	3.99980e6	+	3.99980e6i	0.161443	+	0.161443i	0.783206	−	0.621762i	$-0.213583\pi$
$907$	3.99980e6	+	3.99980e6i	0.161443	+	0.161443i	−0.621762	+	0.783206i	$0.713583\pi$
$908$	2.83019e7	+	2.83019e7i	1.13920	+	1.13920i
$909$	4.71121e7			1.89114
$910$	2.19904e7	−	2.77780e7i	0.880296	−	1.11198i
$911$	4.89525e6			0.195424			0.0977122	−	0.995215i	$-0.468848\pi$
$911$	4.89525e6			0.195424			0.0977122	+	0.995215i	$0.468848\pi$
$912$	6.19733e6	−	6.19733e6i	0.246727	−	0.246727i
$913$	−1.69962e7	−	4.11091e7i	−0.674801	−	1.63215i
$914$		−	5.85611e7i		−	2.31869i
$915$	528675.	+	418523.i	0.0208755	+	0.0165260i
$916$	34635.4			0.00136390
$917$	2.51886e6	+	2.51886e6i	0.0989193	+	0.0989193i
$918$	−5.44250e6	+	5.44250e6i	−0.213153	+	0.213153i
$919$	8.59032e6			0.335522			0.167761	−	0.985828i	$-0.446346\pi$
$919$	8.59032e6			0.335522			0.167761	+	0.985828i	$0.446346\pi$
$920$	−8.43826e7	+	9.81307e6i	−3.28688	+	0.382239i
$921$			2.43657e6i			0.0946520i
$922$	−4.68887e7	−	4.68887e7i	−1.81652	−	1.81652i
$923$	8.77775e6	+	8.77775e6i	0.339140	+	0.339140i
$924$	−6.21491e6	−	2.57909e6i	−0.239472	−	0.0993773i
$925$	1.26368e7	+	7.81483e6i	0.485604	+	0.300307i
$926$		−	4.17015e7i		−	1.59818i
$927$	1.46640e7	+	1.46640e7i	0.560470	+	0.560470i
$928$	−1.13218e7	+	1.13218e7i	−0.431562	+	0.431562i
$929$		−	2.90030e7i		−	1.10256i	−0.834320	−	0.551281i	$-0.814139\pi$
$929$		−	2.90030e7i		−	1.10256i	0.834320	−	0.551281i	$-0.185861\pi$
$930$	−226799.	−	1.95025e6i	−0.00859873	−	0.0739405i
$931$		−	1.59756e7i		−	0.604065i
$932$	−1.25635e7	+	1.25635e7i	−0.473773	+	0.473773i
$933$	129344.	−	129344.i	0.00486456	−	0.00486456i
$934$	−5.40489e7			−2.02731
$935$	−1.31686e7	+	7.32819e6i	−0.492618	+	0.274137i
$936$	−5.17463e7			−1.93059
$937$	1.64007e7	−	1.64007e7i	0.610256	−	0.610256i	−0.332757	−	0.943013i	$-0.607979\pi$
$937$	1.64007e7	−	1.64007e7i	0.610256	−	0.610256i	0.943013	+	0.332757i	$0.107979\pi$
$938$	−5.73964e6	+	5.73964e6i	−0.212999	+	0.212999i
$939$			477088.i			0.0176577i
$940$	−3.70122e7	+	4.67536e7i	−1.36624	+	1.72582i
$941$			2.32821e6i			0.0857133i	0.999081	+	0.0428567i	$0.0136459\pi$
$941$			2.32821e6i			0.0857133i	−0.999081	+	0.0428567i	$0.986354\pi$
$942$	−6.40912e6	+	6.40912e6i	−0.235327	+	0.235327i
$943$	−2.70314e6	−	2.70314e6i	−0.0989896	−	0.0989896i
$944$		−	3.61519e7i		−	1.32039i
$945$	−6.60736e6	+	768386.i	−0.240685	+	0.0279898i
$946$	1.28613e7	+	5.33726e6i	0.467259	+	0.193906i
$947$	1.09360e7	+	1.09360e7i	0.396264	+	0.396264i	0.876913	−	0.480649i	$-0.159599\pi$
$947$	1.09360e7	+	1.09360e7i	0.396264	+	0.396264i	−0.480649	+	0.876913i	$0.659599\pi$
$948$	−9.60419e6	−	9.60419e6i	−0.347088	−	0.347088i
$949$			1.53057e7i			0.551679i
$950$	4.32871e7	−	6.99963e7i	1.55614	−	2.51632i
$951$	−1.36932e6			−0.0490969
$952$	−1.75430e7	+	1.75430e7i	−0.627351	+	0.627351i
$953$	1.35026e7	+	1.35026e7i	0.481598	+	0.481598i	0.905642	−	0.424044i	$-0.139390\pi$
$953$	1.35026e7	+	1.35026e7i	0.481598	+	0.481598i	−0.424044	+	0.905642i	$0.639390\pi$
$954$	2.07859e7			0.739431
$955$	−2.97019e7	+	3.45411e6i	−1.05384	+	0.122554i
$956$		−	6.92822e7i		−	2.45176i
$957$	5.71116e6	−	2.36123e6i	0.201579	−	0.0833411i
$958$	3.77100e7	−	3.77100e7i	1.32753	−	1.32753i
$959$	3.11091e7			1.09230
$960$	−2.06237e6	−	1.63267e6i	−0.0722253	−	0.0571768i
$961$	−2.64616e7			−0.924288
$962$	−2.05498e7	−	2.05498e7i	−0.715928	−	0.715928i
$963$	534525.	+	534525.i	0.0185739	+	0.0185739i
$964$	−4.78201e7			−1.65736
$965$	1.67230e6	+	1.32387e6i	0.0578092	+	0.0457644i
$966$	1.05530e7			0.363857
$967$	1.38601e7	−	1.38601e7i	0.476650	−	0.476650i	−0.427408	−	0.904059i	$-0.640573\pi$
$967$	1.38601e7	−	1.38601e7i	0.476650	−	0.476650i	0.904059	+	0.427408i	$0.140573\pi$
$968$	−75565.1	+	5.73650e7i	−0.00259199	+	1.96770i
$969$			4.23412e6i			0.144862i
$970$	−3.57032e7	+	4.15201e6i	−1.21837	+	0.141687i
$971$	−5.06634e7			−1.72443			−0.862217	−	0.506539i	$-0.830925\pi$
$971$	−5.06634e7			−1.72443			−0.862217	+	0.506539i	$0.830925\pi$
$972$	1.96253e7	+	1.96253e7i	0.666270	+	0.666270i
$973$	−1.29175e7	+	1.29175e7i	−0.437417	+	0.437417i
$974$	−3.84805e6			−0.129970
$975$	4.44953e6	−	1.04908e6i	0.149900	−	0.0353426i
$976$		−	7.01927e6i		−	0.235867i
$977$	4.42563e6	+	4.42563e6i	0.148333	+	0.148333i	0.777373	−	0.629040i	$-0.216552\pi$
$977$	4.42563e6	+	4.42563e6i	0.148333	+	0.148333i	−0.629040	+	0.777373i	$0.716552\pi$
$978$	4.50630e6	+	4.50630e6i	0.150651	+	0.150651i
$979$	−7.42914e6	+	1.79022e7i	−0.247732	+	0.596965i
$980$	2.27591e7	−	2.64671e6i	0.756989	−	0.0880322i
$981$			1.67495e7i			0.555687i
$982$	−4.83717e7	−	4.83717e7i	−1.60071	−	1.60071i
$983$	−1.94690e7	+	1.94690e7i	−0.642628	+	0.642628i	−0.951201	−	0.308573i	$-0.900149\pi$
$983$	−1.94690e7	+	1.94690e7i	−0.642628	+	0.642628i	0.308573	+	0.951201i	$0.400149\pi$
$984$			762613.i			0.0251082i
$985$	2.66692e7	−	3.36884e7i	0.875831	−	1.10634i
$986$		−	4.32239e7i		−	1.41590i
$987$	2.76124e6	−	2.76124e6i	0.0902218	−	0.0902218i
$988$	−7.72843e7	+	7.72843e7i	−2.51883	+	2.51883i
$989$	−1.48276e7			−0.482037
$990$	2.58440e7	+	4.64410e7i	0.838053	+	1.50596i
$991$	−2.03618e7			−0.658617			−0.329309	−	0.944222i	$-0.606816\pi$
$991$	−2.03618e7			−0.658617			−0.329309	+	0.944222i	$0.606816\pi$
$992$	−2.58636e6	+	2.58636e6i	−0.0834469	+	0.0834469i
$993$	−2.05118e6	+	2.05118e6i	−0.0660133	+	0.0660133i
$994$		−	2.09894e7i		−	0.673804i
$995$	745247.	+	6.40838e6i	0.0238639	+	0.205206i
$996$		−	1.79250e7i		−	0.572547i
$997$	2.20214e6	−	2.20214e6i	0.0701628	−	0.0701628i	−0.671155	−	0.741317i	$-0.734201\pi$
$997$	2.20214e6	−	2.20214e6i	0.0701628	−	0.0701628i	0.741317	+	0.671155i	$0.234201\pi$
$998$	−3.77725e7	−	3.77725e7i	−1.20046	−	1.20046i
$999$			5.45646e6i			0.172980i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.6.e.b.32.2	✓	52
5.3	odd	4	inner	55.6.e.b.43.25	yes	52
11.10	odd	2	inner	55.6.e.b.32.25	yes	52
55.43	even	4	inner	55.6.e.b.43.2	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.6.e.b.32.2	✓	52	1.1	even	1	trivial
55.6.e.b.32.25	yes	52	11.10	odd	2	inner
55.6.e.b.43.2	yes	52	55.43	even	4	inner
55.6.e.b.43.25	yes	52	5.3	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:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	55.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.05963 + 7.05963i) q^{2} +(1.68959 - 1.68959i) q^{3} -67.6769i q^{4} +(55.5275 - 6.45743i) q^{5} +23.8558i q^{6} +(-73.3168 + 73.3168i) q^{7} +(251.866 + 251.866i) q^{8} +237.291i q^{9} +(-346.417 + 437.591i) q^{10} +(-370.662 - 153.819i) q^{11} +(-114.346 - 114.346i) q^{12} +(432.912 + 432.912i) q^{13} -1035.18i q^{14} +(82.9084 - 104.729i) q^{15} -1390.50 q^{16} +(475.007 - 475.007i) q^{17} +(-1675.18 - 1675.18i) q^{18} -2637.86 q^{19} +(-437.019 - 3757.93i) q^{20} +247.751i q^{21} +(3702.65 - 1530.83i) q^{22} +(-3016.80 + 3016.80i) q^{23} +851.101 q^{24} +(3041.60 - 717.130i) q^{25} -6112.40 q^{26} +(811.495 + 811.495i) q^{27} +(4961.85 + 4961.85i) q^{28} -6444.84 q^{29} +(154.047 + 1324.65i) q^{30} -1472.27 q^{31} +(1756.72 - 1756.72i) q^{32} +(-886.161 + 366.376i) q^{33} +6706.75i q^{34} +(-3597.66 + 4544.54i) q^{35} +16059.1 q^{36} +(3361.98 + 3361.98i) q^{37} +(18622.3 - 18622.3i) q^{38} +1462.89 q^{39} +(15611.9 + 12359.1i) q^{40} +896.031i q^{41} +(-1749.03 - 1749.03i) q^{42} +(2457.51 + 2457.51i) q^{43} +(-10410.0 + 25085.3i) q^{44} +(1532.29 + 13176.1i) q^{45} -42595.0i q^{46} +(-11145.2 - 11145.2i) q^{47} +(-2349.38 + 2349.38i) q^{48} +6056.29i q^{49} +(-16409.9 + 26535.3i) q^{50} -1605.14i q^{51} +(29298.1 - 29298.1i) q^{52} +(-6204.06 + 6204.06i) q^{53} -11457.7 q^{54} +(-21575.2 - 6147.68i) q^{55} -36932.0 q^{56} +(-4456.91 + 4456.91i) q^{57} +(45498.2 - 45498.2i) q^{58} +25999.2i q^{59} +(-7087.75 - 5610.98i) q^{60} +5048.02i q^{61} +(10393.7 - 10393.7i) q^{62} +(-17397.4 - 17397.4i) q^{63} -19692.4i q^{64} +(26834.0 + 21243.0i) q^{65} +(3669.49 - 8842.45i) q^{66} +(-5544.59 - 5544.59i) q^{67} +(-32147.0 - 32147.0i) q^{68} +10194.3i q^{69} +(-6684.61 - 57480.9i) q^{70} +20276.1 q^{71} +(-59765.4 + 59765.4i) q^{72} +(17677.6 + 17677.6i) q^{73} -47468.7 q^{74} +(3927.41 - 6350.73i) q^{75} +178522. i q^{76} +(38453.3 - 15898.2i) q^{77} +(-10327.5 + 10327.5i) q^{78} +83992.0 q^{79} +(-77211.0 + 8979.06i) q^{80} -54919.4 q^{81} +(-6325.65 - 6325.65i) q^{82} +(78380.4 + 78380.4i) q^{83} +16767.0 q^{84} +(23308.6 - 29443.3i) q^{85} -34698.2 q^{86} +(-10889.1 + 10889.1i) q^{87} +(-54615.3 - 132099. i) q^{88} -48297.8i q^{89} +(-103836. - 82201.4i) q^{90} -63479.5 q^{91} +(204167. + 204167. i) q^{92} +(-2487.54 + 2487.54i) q^{93} +157362. q^{94} +(-146474. + 17033.8i) q^{95} -5936.27i q^{96} +(45539.3 + 45539.3i) q^{97} +(-42755.2 - 42755.2i) q^{98} +(36499.9 - 87954.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 56 q^{3} - 48 q^{5} - 364 q^{11} + 4792 q^{12} + 2564 q^{15} - 6416 q^{16} + 18272 q^{20} + 2680 q^{22} - 144 q^{23} - 12248 q^{25} + 2432 q^{26} + 3644 q^{27} + 9672 q^{31} + 30576 q^{33} - 148776 q^{36}+ \cdots - 633128 q^{97}+O(q^{100}) \) 52 * q + 56 * q^3 - 48 * q^5 - 364 * q^11 + 4792 * q^12 + 2564 * q^15 - 6416 * q^16 + 18272 * q^20 + 2680 * q^22 - 144 * q^23 - 12248 * q^25 + 2432 * q^26 + 3644 * q^27 + 9672 * q^31 + 30576 * q^33 - 148776 * q^36 + 24152 * q^37 + 4400 * q^38 - 43480 * q^42 - 4984 * q^45 - 44148 * q^47 + 26416 * q^48 + 75596 * q^53 + 59092 * q^55 + 304264 * q^56 - 220200 * q^58 - 240016 * q^60 + 207000 * q^66 - 17888 * q^67 - 216880 * q^70 + 285704 * q^71 + 278404 * q^75 - 341160 * q^77 + 15160 * q^78 + 616192 * q^80 - 397204 * q^81 + 349720 * q^82 - 94768 * q^86 + 539000 * q^88 - 864768 * q^91 + 242072 * q^92 + 15772 * q^93 - 633128 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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