LMFDB - Embedded newform 55.6.e.b.32.9

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			32.9
Character	$\chi$	$=$	55.32
Dual form			55.6.e.b.43.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.04500 + 4.04500i) q^{2} +(-4.18256 + 4.18256i) q^{3} -0.723976i q^{4} +(-55.4681 - 6.94934i) q^{5} -33.8369i q^{6} +(23.8782 - 23.8782i) q^{7} +(-126.511 - 126.511i) q^{8} +208.012i q^{9} +(252.478 - 196.258i) q^{10} +(-162.470 - 366.953i) q^{11} +(3.02807 + 3.02807i) q^{12} +(251.625 + 251.625i) q^{13} +193.175i q^{14} +(261.065 - 202.933i) q^{15} +1046.64 q^{16} +(1136.35 - 1136.35i) q^{17} +(-841.409 - 841.409i) q^{18} +362.422 q^{19} +(-5.03115 + 40.1576i) q^{20} +199.744i q^{21} +(2141.51 + 827.134i) q^{22} +(2137.53 - 2137.53i) q^{23} +1058.28 q^{24} +(3028.41 + 770.933i) q^{25} -2035.65 q^{26} +(-1886.39 - 1886.39i) q^{27} +(-17.2873 - 17.2873i) q^{28} -4083.07 q^{29} +(-235.144 + 1876.87i) q^{30} -7668.76 q^{31} +(-185.303 + 185.303i) q^{32} +(2214.34 + 855.263i) q^{33} +9193.05i q^{34} +(-1490.42 + 1158.54i) q^{35} +150.596 q^{36} +(-6841.32 - 6841.32i) q^{37} +(-1466.00 + 1466.00i) q^{38} -2104.88 q^{39} +(6138.17 + 7896.51i) q^{40} +810.545i q^{41} +(-807.965 - 807.965i) q^{42} +(-11090.7 - 11090.7i) q^{43} +(-265.665 + 117.624i) q^{44} +(1445.55 - 11538.0i) q^{45} +17292.6i q^{46} +(-1807.14 - 1807.14i) q^{47} +(-4377.65 + 4377.65i) q^{48} +15666.7i q^{49} +(-15368.3 + 9131.50i) q^{50} +9505.70i q^{51} +(182.171 - 182.171i) q^{52} +(15473.0 - 15473.0i) q^{53} +15260.9 q^{54} +(6461.81 + 21483.2i) q^{55} -6041.74 q^{56} +(-1515.85 + 1515.85i) q^{57} +(16516.0 - 16516.0i) q^{58} -17175.6i q^{59} +(-146.918 - 189.005i) q^{60} -44695.7i q^{61} +(31020.1 - 31020.1i) q^{62} +(4966.97 + 4966.97i) q^{63} +31993.5i q^{64} +(-12208.5 - 15705.8i) q^{65} +(-12416.5 + 5497.47i) q^{66} +(34101.9 + 34101.9i) q^{67} +(-822.690 - 822.690i) q^{68} +17880.7i q^{69} +(1342.44 - 10715.0i) q^{70} -3689.67 q^{71} +(26315.9 - 26315.9i) q^{72} +(-40158.6 - 40158.6i) q^{73} +55346.2 q^{74} +(-15891.0 + 9442.05i) q^{75} -262.385i q^{76} +(-12641.7 - 4882.70i) q^{77} +(8514.21 - 8514.21i) q^{78} +44415.1 q^{79} +(-58055.3 - 7273.48i) q^{80} -34767.2 q^{81} +(-3278.65 - 3278.65i) q^{82} +(-77966.2 - 77966.2i) q^{83} +144.610 q^{84} +(-70928.0 + 55134.2i) q^{85} +89723.8 q^{86} +(17077.7 - 17077.7i) q^{87} +(-25869.5 + 66978.0i) q^{88} -29435.8i q^{89} +(40824.1 + 52518.6i) q^{90} +12016.7 q^{91} +(-1547.52 - 1547.52i) q^{92} +(32075.0 - 32075.0i) q^{93} +14619.8 q^{94} +(-20102.9 - 2518.59i) q^{95} -1550.08i q^{96} +(84004.1 + 84004.1i) q^{97} +(-63371.6 - 63371.6i) q^{98} +(76330.8 - 33795.7i) 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 $

$2$	−4.04500	+	4.04500i	−0.715061	+	0.715061i	−0.967589	−	0.252529i	$-0.918738\pi$
$2$	−4.04500	+	4.04500i	−0.715061	+	0.715061i	0.252529	+	0.967589i	$0.418738\pi$
$3$	−4.18256	+	4.18256i	−0.268311	+	0.268311i	−0.828420	−	0.560108i	$-0.810760\pi$
$3$	−4.18256	+	4.18256i	−0.268311	+	0.268311i	0.560108	+	0.828420i	$0.310760\pi$
$4$		−	0.723976i		−	0.0226243i
$5$	−55.4681	−	6.94934i	−0.992243	−	0.124314i
$5$	−55.4681	−	6.94934i	−0.992243	−	0.124314i
$6$		−	33.8369i		−	0.383718i
$7$	23.8782	−	23.8782i	0.184186	−	0.184186i	−0.608991	−	0.793177i	$-0.708425\pi$
$7$	23.8782	−	23.8782i	0.184186	−	0.184186i	0.793177	+	0.608991i	$0.208425\pi$
$8$	−126.511	−	126.511i	−0.698883	−	0.698883i
$9$			208.012i			0.856018i
$10$	252.478	−	196.258i	0.798406	−	0.620622i
$11$	−162.470	−	366.953i	−0.404847	−	0.914384i
$11$	−162.470	−	366.953i	−0.404847	−	0.914384i
$12$	3.02807	+	3.02807i	0.00607035	+	0.00607035i
$13$	251.625	+	251.625i	0.412949	+	0.412949i	0.882764	−	0.469816i	$-0.155680\pi$
$13$	251.625	+	251.625i	0.412949	+	0.412949i	−0.469816	+	0.882764i	$0.655680\pi$
$14$			193.175i			0.263409i
$15$	261.065	−	202.933i	0.299585	−	0.232875i
$16$	1046.64			1.02211
$17$	1136.35	−	1136.35i	0.953651	−	0.953651i	−0.0453215	−	0.998972i	$-0.514431\pi$
$17$	1136.35	−	1136.35i	0.953651	−	0.953651i	0.998972	+	0.0453215i	$0.0144312\pi$
$18$	−841.409	−	841.409i	−0.612105	−	0.612105i
$19$	362.422			0.230320			0.115160	−	0.993347i	$-0.463262\pi$
$19$	362.422			0.230320			0.115160	+	0.993347i	$0.463262\pi$
$20$	−5.03115	+	40.1576i	−0.00281250	+	0.0224488i
$21$			199.744i			0.0988385i
$22$	2141.51	+	827.134i	0.943331	+	0.364350i
$23$	2137.53	−	2137.53i	0.842543	−	0.842543i	−0.146646	−	0.989189i	$-0.546848\pi$
$23$	2137.53	−	2137.53i	0.842543	−	0.842543i	0.989189	+	0.146646i	$0.0468479\pi$
$24$	1058.28			0.375037
$25$	3028.41	+	770.933i	0.969092	+	0.246698i
$26$	−2035.65			−0.590567
$27$	−1886.39	−	1886.39i	−0.497991	−	0.497991i
$28$	−17.2873	−	17.2873i	−0.00416707	−	0.00416707i
$29$	−4083.07			−0.901553			−0.450777	−	0.892637i	$-0.648853\pi$
$29$	−4083.07			−0.901553			−0.450777	+	0.892637i	$0.648853\pi$
$30$	−235.144	+	1876.87i	−0.0477013	+	0.380741i
$31$	−7668.76			−1.43325			−0.716623	−	0.697461i	$-0.754313\pi$
$31$	−7668.76			−1.43325			−0.716623	+	0.697461i	$0.754313\pi$
$32$	−185.303	+	185.303i	−0.0319894	+	0.0319894i
$33$	2214.34	+	855.263i	0.353965	+	0.136715i
$34$			9193.05i			1.36384i
$35$	−1490.42	+	1158.54i	−0.205654	+	0.159861i
$36$	150.596			0.0193668
$37$	−6841.32	−	6841.32i	−0.821553	−	0.821553i	0.164777	−	0.986331i	$-0.447309\pi$
$37$	−6841.32	−	6841.32i	−0.821553	−	0.821553i	−0.986331	+	0.164777i	$0.947309\pi$
$38$	−1466.00	+	1466.00i	−0.164692	+	0.164692i
$39$	−2104.88			−0.221598
$40$	6138.17	+	7896.51i	0.606581	+	0.780343i
$41$			810.545i			0.0753039i	0.999291	+	0.0376520i	$0.0119878\pi$
$41$			810.545i			0.0753039i	−0.999291	+	0.0376520i	$0.988012\pi$
$42$	−807.965	−	807.965i	−0.0706756	−	0.0706756i
$43$	−11090.7	−	11090.7i	−0.914721	−	0.914721i	0.0819181	−	0.996639i	$-0.473895\pi$
$43$	−11090.7	−	11090.7i	−0.914721	−	0.914721i	−0.996639	+	0.0819181i	$0.973895\pi$
$44$	−265.665	+	117.624i	−0.0206873	+	0.00915936i
$45$	1445.55	−	11538.0i	0.106415	−	0.849378i
$46$			17292.6i			1.20494i
$47$	−1807.14	−	1807.14i	−0.119330	−	0.119330i	0.644920	−	0.764250i	$-0.276891\pi$
$47$	−1807.14	−	1807.14i	−0.119330	−	0.119330i	−0.764250	+	0.644920i	$0.776891\pi$
$48$	−4377.65	+	4377.65i	−0.274244	+	0.274244i
$49$			15666.7i			0.932151i
$50$	−15368.3	+	9131.50i	−0.869364	+	0.516556i
$51$			9505.70i			0.511751i
$52$	182.171	−	182.171i	0.00934265	−	0.00934265i
$53$	15473.0	−	15473.0i	0.756633	−	0.756633i	−0.219075	−	0.975708i	$-0.570304\pi$
$53$	15473.0	−	15473.0i	0.756633	−	0.756633i	0.975708	+	0.219075i	$0.0703039\pi$
$54$	15260.9			0.712188
$55$	6461.81	+	21483.2i	0.288036	+	0.957619i
$56$	−6041.74			−0.257449
$57$	−1515.85	+	1515.85i	−0.0617974	+	0.0617974i
$58$	16516.0	−	16516.0i	0.644665	−	0.644665i
$59$		−	17175.6i		−	0.642366i	−0.947017	−	0.321183i	$-0.895920\pi$
$59$		−	17175.6i		−	0.642366i	0.947017	−	0.321183i	$-0.104080\pi$
$60$	−146.918	−	189.005i	−0.00526863	−	0.00677788i
$61$		−	44695.7i		−	1.53795i	−0.639282	−	0.768973i	$-0.720768\pi$
$61$		−	44695.7i		−	1.53795i	0.639282	−	0.768973i	$-0.279232\pi$
$62$	31020.1	−	31020.1i	1.02486	−	1.02486i
$63$	4966.97	+	4966.97i	0.157667	+	0.157667i
$64$			31993.5i			0.976364i
$65$	−12208.5	−	15705.8i	−0.358410	−	0.461080i
$66$	−12416.5	+	5497.47i	−0.350866	+	0.155347i
$67$	34101.9	+	34101.9i	0.928094	+	0.928094i	0.997583	−	0.0694889i	$-0.0221368\pi$
$67$	34101.9	+	34101.9i	0.928094	+	0.928094i	−0.0694889	+	0.997583i	$0.522137\pi$
$68$	−822.690	−	822.690i	−0.0215756	−	0.0215756i
$69$			17880.7i			0.452128i
$70$	1342.44	−	10715.0i	0.0327453	−	0.261365i
$71$	−3689.67			−0.0868643			−0.0434322	−	0.999056i	$-0.513829\pi$
$71$	−3689.67			−0.0868643			−0.0434322	+	0.999056i	$0.513829\pi$
$72$	26315.9	−	26315.9i	0.598257	−	0.598257i
$73$	−40158.6	−	40158.6i	−0.882006	−	0.882006i	0.111732	−	0.993738i	$-0.464360\pi$
$73$	−40158.6	−	40158.6i	−0.882006	−	0.882006i	−0.993738	+	0.111732i	$0.964360\pi$
$74$	55346.2			1.17492
$75$	−15891.0	+	9442.05i	−0.326211	+	0.193827i
$76$		−	262.385i		−	0.00521081i
$77$	−12641.7	−	4882.70i	−0.242984	−	0.0938497i
$78$	8514.21	−	8514.21i	0.158456	−	0.158456i
$79$	44415.1			0.800687			0.400344	−	0.916365i	$-0.368891\pi$
$79$	44415.1			0.800687			0.400344	+	0.916365i	$0.368891\pi$
$80$	−58055.3	−	7273.48i	−1.01418	−	0.127062i
$81$	−34767.2			−0.588785
$82$	−3278.65	−	3278.65i	−0.0538469	−	0.0538469i
$83$	−77966.2	−	77966.2i	−1.24226	−	1.24226i	−0.959063	−	0.283194i	$-0.908606\pi$
$83$	−77966.2	−	77966.2i	−1.24226	−	1.24226i	−0.283194	−	0.959063i	$-0.591394\pi$
$84$	144.610			0.00223615
$85$	−70928.0	+	55134.2i	−1.06481	+	0.827702i
$86$	89723.8			1.30816
$87$	17077.7	−	17077.7i	0.241897	−	0.241897i
$88$	−25869.5	+	66978.0i	−0.356107	+	0.921989i
$89$		−	29435.8i		−	0.393913i	−0.980412	−	0.196957i	$-0.936894\pi$
$89$		−	29435.8i		−	0.393913i	0.980412	−	0.196957i	$-0.0631058\pi$
$90$	40824.1	+	52518.6i	0.531264	+	0.683450i
$91$	12016.7			0.152119
$92$	−1547.52	−	1547.52i	−0.0190619	−	0.0190619i
$93$	32075.0	−	32075.0i	0.384556	−	0.384556i
$94$	14619.8			0.170656
$95$	−20102.9	−	2518.59i	−0.228533	−	0.0286318i
$96$		−	1550.08i		−	0.0171663i
$97$	84004.1	+	84004.1i	0.906507	+	0.906507i	0.995988	−	0.0894817i	$-0.0285211\pi$
$97$	84004.1	+	84004.1i	0.906507	+	0.906507i	−0.0894817	+	0.995988i	$0.528521\pi$
$98$	−63371.6	−	63371.6i	−0.666545	−	0.666545i
$99$	76330.8	−	33795.7i	0.782729	−	0.346556i
$100$	558.137	−	2192.50i	0.00558137	−	0.0219250i
$101$			170716.i			1.66521i	0.553864	+	0.832607i	$0.313153\pi$
$101$			170716.i			1.66521i	−0.553864	+	0.832607i	$0.686847\pi$
$102$	−38450.5	−	38450.5i	−0.365933	−	0.365933i
$103$	19007.6	−	19007.6i	0.176536	−	0.176536i	−0.613308	−	0.789844i	$-0.710161\pi$
$103$	19007.6	−	19007.6i	0.176536	−	0.176536i	0.789844	+	0.613308i	$0.210161\pi$
$104$		−	63666.9i		−	0.577206i
$105$	1388.09	−	11079.4i	0.0122870	−	0.0980718i
$106$			125177.i			1.08208i
$107$	−50406.0	+	50406.0i	−0.425621	+	0.425621i	−0.887134	−	0.461513i	$-0.847307\pi$
$107$	−50406.0	+	50406.0i	−0.425621	+	0.425621i	0.461513	+	0.887134i	$0.347307\pi$
$108$	−1365.70	+	1365.70i	−0.0112667	+	0.0112667i
$109$	−28125.2			−0.226741			−0.113370	−	0.993553i	$-0.536165\pi$
$109$	−28125.2			−0.226741			−0.113370	+	0.993553i	$0.536165\pi$
$110$	−113038.	−	60761.6i	−0.890720	−	0.478793i
$111$	57228.5			0.440864
$112$	24992.0	−	24992.0i	0.188259	−	0.188259i
$113$	−7537.31	+	7537.31i	−0.0555290	+	0.0555290i	−0.734326	−	0.678797i	$-0.762502\pi$
$113$	−7537.31	+	7537.31i	−0.0555290	+	0.0555290i	0.678797	+	0.734326i	$0.262502\pi$
$114$		−	12263.2i		−	0.0883777i
$115$	−133419.	+	103710.i	−0.940747	+	0.731268i
$116$			2956.04i			0.0203970i
$117$	−52341.2	+	52341.2i	−0.353491	+	0.353491i
$118$	69475.4	+	69475.4i	0.459331	+	0.459331i
$119$		−	54268.0i		−	0.351299i
$120$	−58700.9	−	7354.37i	−0.372128	−	0.0466221i
$121$	−108258.	+	119238.i	−0.672198	+	0.740372i
$122$	180794.	+	180794.i	1.09972	+	1.09972i
$123$	−3390.15	−	3390.15i	−0.0202049	−	0.0202049i
$124$			5552.00i			0.0324261i
$125$	−162623.	−	63807.6i	−0.930907	−	0.365256i
$126$	−40182.7			−0.225483
$127$	83816.2	−	83816.2i	0.461125	−	0.461125i	−0.437899	−	0.899024i	$-0.644277\pi$
$127$	83816.2	−	83816.2i	0.461125	−	0.461125i	0.899024	+	0.437899i	$0.144277\pi$
$128$	−135343.	−	135343.i	−0.730149	−	0.730149i
$129$	92775.2			0.490860
$130$	112913.	+	14146.4i	0.585986	+	0.0734154i
$131$		−	258051.i		−	1.31379i	−0.753980	−	0.656897i	$-0.771868\pi$
$131$		−	258051.i		−	1.31379i	0.753980	−	0.656897i	$-0.228132\pi$
$132$	619.190	−	1603.13i	0.00309307	−	0.00800819i
$133$	8654.00	−	8654.00i	0.0424217	−	0.0424217i
$134$	−275884.			−1.32729
$135$	91525.1	+	117743.i	0.432221	+	0.556035i
$136$	−287522.			−1.33298
$137$	−149076.	−	149076.i	−0.678589	−	0.678589i	0.281092	−	0.959681i	$-0.409303\pi$
$137$	−149076.	−	149076.i	−0.678589	−	0.678589i	−0.959681	+	0.281092i	$0.909303\pi$
$138$	−72327.2	−	72327.2i	−0.323299	−	0.323299i
$139$	344167.			1.51089			0.755443	−	0.655214i	$-0.227422\pi$
$139$	344167.			1.51089			0.755443	+	0.655214i	$0.227422\pi$
$140$	838.756	+	1079.03i	0.00361673	+	0.00465277i
$141$	15117.0			0.0640350
$142$	14924.7	−	14924.7i	0.0621133	−	0.0621133i
$143$	51453.1	−	133216.i	0.210413	−	0.544775i
$144$			217715.i			0.874947i
$145$	226480.	+	28374.6i	0.894560	+	0.112075i
$146$	324883.			1.26138
$147$	−65526.8	−	65526.8i	−0.250107	−	0.250107i
$148$	−4952.95	+	4952.95i	−0.0185870	+	0.0185870i
$149$	−222770.			−0.822037			−0.411019	−	0.911627i	$-0.634827\pi$
$149$	−222770.			−0.822037			−0.411019	+	0.911627i	$0.634827\pi$
$150$	26086.0	−	102472.i	0.0946626	−	0.371858i
$151$		−	234294.i		−	0.836215i	−0.908398	−	0.418107i	$-0.862694\pi$
$151$		−	234294.i		−	0.836215i	0.908398	−	0.418107i	$-0.137306\pi$
$152$	−45850.5	−	45850.5i	−0.160966	−	0.160966i
$153$	236375.	+	236375.i	0.816342	+	0.816342i
$154$	70886.0	−	31385.1i	0.240857	−	0.106640i
$155$	425371.	+	53292.8i	1.42213	+	0.178172i
$156$			1523.88i			0.00501348i
$157$	55271.7	+	55271.7i	0.178959	+	0.178959i	0.790902	−	0.611943i	$-0.209612\pi$
$157$	55271.7	+	55271.7i	0.178959	+	0.178959i	−0.611943	+	0.790902i	$0.709612\pi$
$158$	−179659.	+	179659.i	−0.572540	+	0.572540i
$159$			129434.i			0.406027i
$160$	11566.1	−	8990.65i	0.0357180	−	0.0277646i
$161$		−	102081.i		−	0.310369i
$162$	140633.	−	140633.i	0.421017	−	0.421017i
$163$	89316.4	−	89316.4i	0.263307	−	0.263307i	−0.563089	−	0.826396i	$-0.690387\pi$
$163$	89316.4	−	89316.4i	0.263307	−	0.263307i	0.826396	+	0.563089i	$0.190387\pi$
$164$	586.815			0.00170369
$165$	−116882.	−	62828.0i	−0.334224	−	0.179657i
$166$	630746.			1.77658
$167$	61089.6	−	61089.6i	0.169502	−	0.169502i	−0.617258	−	0.786761i	$-0.711757\pi$
$167$	61089.6	−	61089.6i	0.169502	−	0.169502i	0.786761	+	0.617258i	$0.211757\pi$
$168$	25269.9	−	25269.9i	0.0690766	−	0.0690766i
$169$		−	244662.i		−	0.658947i
$170$	63885.6	−	509921.i	0.169543	−	1.35326i
$171$			75388.3i			0.197158i
$172$	−8029.42	+	8029.42i	−0.0206949	+	0.0206949i
$173$	63235.1	+	63235.1i	0.160636	+	0.160636i	0.782848	−	0.622212i	$-0.213766\pi$
$173$	63235.1	+	63235.1i	0.160636	+	0.160636i	−0.622212	+	0.782848i	$0.713766\pi$
$174$			138158.i			0.345942i
$175$	90721.7	−	53904.6i	0.223932	−	0.133055i
$176$	−170048.	−	384069.i	−0.413799	−	0.934604i
$177$	71838.1	+	71838.1i	0.172354	+	0.172354i
$178$	119068.	+	119068.i	0.281672	+	0.281672i
$179$			310676.i			0.724729i	0.932036	+	0.362365i	$0.118030\pi$
$179$			310676.i			0.724729i	−0.932036	+	0.362365i	$0.881970\pi$
$180$	−8353.27	−	1046.54i	−0.0192165	−	0.00240755i
$181$	−392715.			−0.891007			−0.445503	−	0.895280i	$-0.646975\pi$
$181$	−392715.			−0.891007			−0.445503	+	0.895280i	$0.646975\pi$
$182$	−48607.6	+	48607.6i	−0.108774	+	0.108774i
$183$	186942.	+	186942.i	0.412648	+	0.412648i
$184$	−540843.			−1.17768
$185$	331932.	+	427018.i	0.713050	+	0.917311i
$186$			259487.i			0.549962i
$187$	−601609.	−	232364.i	−1.25809	−	0.485921i
$188$	−1308.33	+	1308.33i	−0.00269974	+	0.00269974i
$189$	−90087.2			−0.183446
$190$	91503.7	−	71128.3i	0.183888	−	0.142941i
$191$	−574417.			−1.13932			−0.569658	−	0.821882i	$-0.692924\pi$
$191$	−574417.			−1.13932			−0.569658	+	0.821882i	$0.692924\pi$
$192$	−133815.	−	133815.i	−0.261969	−	0.261969i
$193$	445869.	+	445869.i	0.861617	+	0.861617i	0.991526	−	0.129909i	$-0.0414684\pi$
$193$	445869.	+	445869.i	0.861617	+	0.861617i	−0.129909	+	0.991526i	$0.541468\pi$
$194$	−679592.			−1.29642
$195$	116753.	+	14627.5i	0.219879	+	0.0275476i
$196$	11342.3			0.0210892
$197$	−634401.	+	634401.i	−1.16466	+	1.16466i	−0.181215	+	0.983444i	$0.558003\pi$
$197$	−634401.	+	634401.i	−1.16466	+	1.16466i	−0.983444	+	0.181215i	$0.941997\pi$
$198$	−172054.	+	445461.i	−0.311890	+	0.807508i
$199$			188538.i			0.337494i	0.985659	+	0.168747i	$0.0539721\pi$
$199$			188538.i			0.337494i	−0.985659	+	0.168747i	$0.946028\pi$
$200$	−285597.	−	480660.i	−0.504869	−	0.849696i
$201$	−285267.			−0.498036
$202$	−690545.	−	690545.i	−1.19073	−	1.19073i
$203$	−97496.4	+	97496.4i	−0.166054	+	0.166054i
$204$	6881.90			0.0115780
$205$	5632.75	−	44959.4i	0.00936129	−	0.0747198i
$206$			153771.i			0.252468i
$207$	444632.	+	444632.i	0.721232	+	0.721232i
$208$	263362.	+	263362.i	0.422080	+	0.422080i
$209$	−58882.7	−	132992.i	−0.0932442	−	0.210601i
$210$	39201.4	+	50431.1i	0.0613414	+	0.0789132i
$211$		−	1.11562e6i		−	1.72509i	−0.505982	−	0.862544i	$-0.668870\pi$
$211$		−	1.11562e6i		−	1.72509i	0.505982	−	0.862544i	$-0.331130\pi$
$212$	−11202.1	−	11202.1i	−0.0171183	−	0.0171183i
$213$	15432.3	−	15432.3i	0.0233067	−	0.0233067i
$214$		−	407784.i		−	0.608690i
$215$	538108.	+	692254.i	0.793913	+	1.02134i
$216$			477299.i			0.696075i
$217$	−183116.	+	183116.i	−0.263984	+	0.263984i
$218$	113766.	−	113766.i	0.162133	−	0.162133i
$219$	335932.			0.473305
$220$	15553.3	−	4678.19i	0.0216654	−	0.00651661i
$221$	571868.			0.787617
$222$	−231489.	+	231489.i	−0.315245	+	0.315245i
$223$	−175677.	+	175677.i	−0.236566	+	0.236566i	−0.815427	−	0.578861i	$-0.803498\pi$
$223$	−175677.	+	175677.i	−0.236566	+	0.236566i	0.578861	+	0.815427i	$0.303498\pi$
$224$			8849.40i			0.0117840i
$225$	−160364.	+	629947.i	−0.211178	+	0.829560i
$226$		−	60976.8i		−	0.0794133i
$227$	−32427.0	+	32427.0i	−0.0417678	+	0.0417678i	−0.727682	−	0.685914i	$-0.759402\pi$
$227$	−32427.0	+	32427.0i	−0.0417678	+	0.0417678i	0.685914	+	0.727682i	$0.259402\pi$
$228$	1097.44	+	1097.44i	0.00139812	+	0.00139812i
$229$		−	237994.i		−	0.299900i	−0.988694	−	0.149950i	$-0.952089\pi$
$229$		−	237994.i		−	0.299900i	0.988694	−	0.149950i	$-0.0479113\pi$
$230$	120172.	−	959185.i	0.149790	−	1.19559i
$231$	73296.8	−	32452.4i	0.0903764	−	0.0400145i
$232$	516554.	+	516554.i	0.630080	+	0.630080i
$233$	−153761.	−	153761.i	−0.185549	−	0.185549i	0.608220	−	0.793769i	$-0.291884\pi$
$233$	−153761.	−	153761.i	−0.185549	−	0.185549i	−0.793769	+	0.608220i	$0.791884\pi$
$234$		−	423440.i		−	0.505536i
$235$	87680.3	+	112797.i	0.103570	+	0.133238i
$236$	−12434.7			−0.0145331
$237$	−185769.	+	185769.i	−0.214834	+	0.214834i
$238$	219514.	+	219514.i	0.251200	+	0.251200i
$239$	−1.09332e6			−1.23809			−0.619047	−	0.785354i	$-0.712481\pi$
$239$	−1.09332e6			−1.23809			−0.619047	+	0.785354i	$0.712481\pi$
$240$	273241.	−	212398.i	0.306209	−	0.238025i
$241$			871234.i			0.966256i	0.875550	+	0.483128i	$0.160500\pi$
$241$			871234.i			0.966256i	−0.875550	+	0.483128i	$0.839500\pi$
$242$	−44412.1	−	920219.i	−0.0487487	−	1.01007i
$243$	603808.	−	603808.i	0.655968	−	0.655968i
$244$	−32358.6			−0.0347949
$245$	108873.	−	868999.i	0.115879	−	0.924920i
$246$	27426.3			0.0288955
$247$	91194.6	+	91194.6i	0.0951101	+	0.0951101i
$248$	970185.	+	970185.i	1.00167	+	1.00167i
$249$	652197.			0.666623
$250$	915910.	−	399707.i	0.926836	−	0.404475i
$251$	1.53392e6			1.53680			0.768401	−	0.639969i	$-0.221053\pi$
$251$	1.53392e6			1.53680			0.768401	+	0.639969i	$0.221053\pi$
$252$	3595.97	−	3595.97i	0.00356709	−	0.00356709i
$253$	−1.13166e6	−	437088.i	−1.11151	−	0.429307i
$254$			678072.i			0.659465i
$255$	66058.3	−	527263.i	0.0636176	−	0.507781i
$256$	71133.6			0.0678383
$257$	−102083.	−	102083.i	−0.0964099	−	0.0964099i	0.657257	−	0.753667i	$-0.271717\pi$
$257$	−102083.	−	102083.i	−0.0964099	−	0.0964099i	−0.753667	+	0.657257i	$0.771717\pi$
$258$	−375275.	+	375275.i	−0.350995	+	0.350995i
$259$	−326717.			−0.302638
$260$	−11370.6	+	8838.69i	−0.0104316	+	0.00810876i
$261$		−	849328.i		−	0.771746i
$262$	1.04382e6	+	1.04382e6i	0.939443	+	0.939443i
$263$	−457272.	−	457272.i	−0.407648	−	0.407648i	0.473270	−	0.880917i	$-0.343074\pi$
$263$	−457272.	−	457272.i	−0.407648	−	0.407648i	−0.880917	+	0.473270i	$0.843074\pi$
$264$	−171939.	−	388340.i	−0.151833	−	0.342928i
$265$	−965786.	+	750731.i	−0.844824	+	0.656704i
$266$			70010.8i			0.0606682i
$267$	123117.	+	123117.i	0.105691	+	0.105691i
$268$	24689.0	−	24689.0i	0.0209974	−	0.0209974i
$269$		−	158324.i		−	0.133403i	−0.997773	−	0.0667014i	$-0.978753\pi$
$269$		−	158324.i		−	0.133403i	0.997773	−	0.0667014i	$-0.0212475\pi$
$270$	−846490.	−	106053.i	−0.706663	−	0.0885345i
$271$		−	1.15776e6i		−	0.957625i	−0.877917	−	0.478812i	$-0.841067\pi$
$271$		−	1.15776e6i		−	0.957625i	0.877917	−	0.478812i	$-0.158933\pi$
$272$	1.18935e6	−	1.18935e6i	0.974738	−	0.974738i
$273$	−50260.7	+	50260.7i	−0.0408152	+	0.0408152i
$274$	1.20602e6			0.970465
$275$	−209130.	−	1.23654e6i	−0.166757	−	0.985998i
$276$	12945.2			0.0102291
$277$	−10185.1	+	10185.1i	−0.00797561	+	0.00797561i	−0.711083	−	0.703108i	$-0.751795\pi$
$277$	−10185.1	+	10185.1i	−0.00797561	+	0.00797561i	0.703108	+	0.711083i	$0.251795\pi$
$278$	−1.39215e6	+	1.39215e6i	−1.08038	+	1.08038i
$279$		−	1.59520e6i		−	1.22688i
$280$	335123.	+	41986.1i	0.255452	+	0.0320044i
$281$		−	116911.i		−	0.0883261i	−0.999024	−	0.0441631i	$-0.985938\pi$
$281$		−	116911.i		−	0.0883261i	0.999024	−	0.0441631i	$-0.0140621\pi$
$282$	−61148.1	+	61148.1i	−0.0457889	+	0.0457889i
$283$	−406779.	−	406779.i	−0.301920	−	0.301920i	0.539845	−	0.841765i	$-0.318483\pi$
$283$	−406779.	−	406779.i	−0.301920	−	0.301920i	−0.841765	+	0.539845i	$0.818483\pi$
$284$			2671.23i			0.00196524i
$285$	94615.6	−	73547.3i	0.0690002	−	0.0536357i
$286$	330731.	+	746987.i	0.239089	+	0.540005i
$287$	19354.4	+	19354.4i	0.0138699	+	0.0138699i
$288$	−38545.2	−	38545.2i	−0.0273835	−	0.0273835i
$289$		−	1.16272e6i		−	0.818900i
$290$	−1.03088e6	+	801334.i	−0.719805	+	0.559524i
$291$	−702704.			−0.486452
$292$	−29073.9	+	29073.9i	−0.0199547	+	0.0199547i
$293$	−160045.	−	160045.i	−0.108912	−	0.108912i	0.650551	−	0.759463i	$-0.274538\pi$
$293$	−160045.	−	160045.i	−0.108912	−	0.108912i	−0.759463	+	0.650551i	$0.774538\pi$
$294$	530111.			0.357683
$295$	−119359.	+	952699.i	−0.0798548	+	0.637383i
$296$			1.73101e6i			1.14834i
$297$	−385734.	+	998696.i	−0.253745	+	0.656965i
$298$	901105.	−	901105.i	0.587807	−	0.587807i
$299$	1.07571e6			0.695854
$300$	6835.82	+	11504.7i	0.00438518	+	0.00738027i
$301$	−529654.			−0.336958
$302$	947716.	+	947716.i	0.597945	+	0.597945i
$303$	−714029.	−	714029.i	−0.446796	−	0.446796i
$304$	379327.			0.235412
$305$	−310605.	+	2.47918e6i	−0.191187	+	1.52602i
$306$	−1.91227e6			−1.16747
$307$	−431604.	+	431604.i	−0.261360	+	0.261360i	−0.825607	−	0.564246i	$-0.809167\pi$
$307$	−431604.	+	431604.i	−0.261360	+	0.261360i	0.564246	+	0.825607i	$0.309167\pi$
$308$	−3534.96	+	9152.28i	−0.00212328	+	0.00549734i
$309$			159001.i			0.0947334i
$310$	−1.93619e6	+	1.50506e6i	−1.14431	+	0.889505i
$311$	1.54156e6			0.903771			0.451886	−	0.892076i	$-0.350752\pi$
$311$	1.54156e6			0.903771			0.451886	+	0.892076i	$0.350752\pi$
$312$	266291.	+	266291.i	0.154871	+	0.154871i
$313$	735171.	−	735171.i	0.424158	−	0.424158i	−0.462475	−	0.886633i	$-0.653038\pi$
$313$	735171.	−	735171.i	0.424158	−	0.424158i	0.886633	+	0.462475i	$0.153038\pi$
$314$	−447148.			−0.255933
$315$	−240991.	−	310025.i	−0.136844	−	0.176044i
$316$		−	32155.5i		−	0.0181150i
$317$	−2.15280e6	−	2.15280e6i	−1.20325	−	1.20325i	−0.973173	−	0.230073i	$-0.926103\pi$
$317$	−2.15280e6	−	2.15280e6i	−1.20325	−	1.20325i	−0.230073	−	0.973173i	$-0.573897\pi$
$318$	−523559.	−	523559.i	−0.290334	−	0.290334i
$319$	663375.	+	1.49829e6i	0.364991	+	0.824366i
$320$	222334.	−	1.77462e6i	0.121375	−	0.968790i
$321$		−	421652.i		−	0.228398i
$322$	412916.	+	412916.i	0.221933	+	0.221933i
$323$	411838.	−	411838.i	0.219644	−	0.219644i
$324$			25170.6i			0.0133208i
$325$	568039.	+	956012.i	0.298311	+	0.502059i
$326$			722569.i			0.376561i
$327$	117635.	−	117635.i	0.0608371	−	0.0608371i
$328$	102543.	−	102543.i	0.0526286	−	0.0526286i
$329$	−86302.8			−0.0439577
$330$	726926.	−	218647.i	0.367456	−	0.110525i
$331$	655579.			0.328893			0.164447	−	0.986386i	$-0.447416\pi$
$331$	655579.			0.328893			0.164447	+	0.986386i	$0.447416\pi$
$332$	−56445.7	+	56445.7i	−0.0281051	+	0.0281051i
$333$	1.42308e6	−	1.42308e6i	0.703264	−	0.703264i
$334$			494214.i			0.242409i
$335$	−1.65458e6	−	2.12855e6i	−0.805520	−	1.03627i
$336$			209061.i			0.101024i
$337$	−1.94942e6	+	1.94942e6i	−0.935043	+	0.935043i	−0.998015	−	0.0629724i	$-0.979942\pi$
$337$	−1.94942e6	+	1.94942e6i	−0.935043	+	0.935043i	0.0629724	+	0.998015i	$0.479942\pi$
$338$	989658.	+	989658.i	0.471187	+	0.471187i
$339$		−	63050.5i		−	0.0297982i
$340$	39915.9	+	51350.1i	0.0187261	+	0.0240904i
$341$	1.24594e6	+	2.81407e6i	0.580246	+	1.31054i
$342$	−304945.	−	304945.i	−0.140980	−	0.140980i
$343$	775414.	+	775414.i	0.355875	+	0.355875i
$344$			2.80620e6i			1.27857i
$345$	124259.	−	991806.i	0.0562056	−	0.448620i
$346$	−511572.			−0.229729
$347$	1.93078e6	−	1.93078e6i	0.860814	−	0.860814i	−0.130619	−	0.991433i	$-0.541696\pi$
$347$	1.93078e6	−	1.93078e6i	0.860814	−	0.860814i	0.991433	+	0.130619i	$0.0416963\pi$
$348$	−12363.8	−	12363.8i	−0.00547274	−	0.00547274i
$349$	−3.56184e6			−1.56535			−0.782673	−	0.622433i	$-0.786144\pi$
$349$	−3.56184e6			−1.56535			−0.782673	+	0.622433i	$0.786144\pi$
$350$	−148925.	+	585013.i	−0.0649825	+	0.255267i
$351$		−	949325.i		−	0.411289i
$352$	98103.4	+	37891.3i	0.0422015	+	0.0162998i
$353$	−2.51808e6	+	2.51808e6i	−1.07556	+	1.07556i	−0.0786537	+	0.996902i	$0.525062\pi$
$353$	−2.51808e6	+	2.51808e6i	−1.07556	+	1.07556i	−0.996902	+	0.0786537i	$0.974938\pi$
$354$	−581170.			−0.246487
$355$	204659.	+	25640.7i	0.0861905	+	0.0107984i
$356$	−21310.8			−0.00891200
$357$	226979.	+	226979.i	0.0942574	+	0.0942574i
$358$	−1.25669e6	−	1.25669e6i	−0.518226	−	0.518226i
$359$	3.65670e6			1.49745			0.748726	−	0.662880i	$-0.230666\pi$
$359$	3.65670e6			1.49745			0.748726	+	0.662880i	$0.230666\pi$
$360$	−1.64257e6	+	1.27682e6i	−0.667987	+	0.519245i
$361$	−2.34475e6			−0.946953
$362$	1.58853e6	−	1.58853e6i	0.637124	−	0.637124i
$363$	−45922.5	−	951515.i	−0.0182919	−	0.379008i
$364$		−	8699.83i		−	0.00344157i
$365$	1.94844e6	+	2.50660e6i	0.765519	+	0.984810i
$366$	−1.51236e6			−0.590137
$367$	755105.	+	755105.i	0.292646	+	0.292646i	0.838125	−	0.545479i	$-0.183652\pi$
$367$	755105.	+	755105.i	0.292646	+	0.292646i	−0.545479	+	0.838125i	$0.683652\pi$
$368$	2.23723e6	−	2.23723e6i	0.861173	−	0.861173i
$369$	−168603.			−0.0644615
$370$	−3.06995e6	−	384620.i	−1.16581	−	0.146059i
$371$		−	738937.i		−	0.278723i
$372$	−23221.6	−	23221.6i	−0.00870030	−	0.00870030i
$373$	−3.54521e6	−	3.54521e6i	−1.31938	−	1.31938i	−0.914265	−	0.405116i	$-0.867231\pi$
$373$	−3.54521e6	−	3.54521e6i	−1.31938	−	1.31938i	−0.405116	−	0.914265i	$-0.632769\pi$
$374$	3.37342e6	−	1.49359e6i	1.24707	−	0.552146i
$375$	947059.	−	413300.i	0.347775	−	0.151771i
$376$			457248.i			0.166795i
$377$	−1.02740e6	−	1.02740e6i	−0.372295	−	0.372295i
$378$	364402.	−	364402.i	0.131175	−	0.131175i
$379$			5.18541e6i			1.85432i	0.374662	+	0.927162i	$0.377759\pi$
$379$			5.18541e6i			1.85432i	−0.374662	+	0.927162i	$0.622241\pi$
$380$	−1823.40	+	14554.0i	−0.000647774	+	0.00517039i
$381$			701133.i			0.247450i
$382$	2.32352e6	−	2.32352e6i	0.814680	−	0.814680i
$383$	−573566.	+	573566.i	−0.199796	+	0.199796i	−0.799912	−	0.600117i	$-0.795121\pi$
$383$	−573566.	+	573566.i	−0.199796	+	0.199796i	0.600117	+	0.799912i	$0.295121\pi$
$384$	1.13216e6			0.391815
$385$	667278.	+	358685.i	0.229433	+	0.123328i
$386$	−3.60708e6			−1.23222
$387$	2.30701e6	−	2.30701e6i	0.783018	−	0.783018i
$388$	60816.9	−	60816.9i	0.0205090	−	0.0205090i
$389$			5.37420e6i			1.80069i	0.435172	+	0.900347i	$0.356688\pi$
$389$			5.37420e6i			1.80069i	−0.435172	+	0.900347i	$0.643312\pi$
$390$	−531435.	+	413099.i	−0.176925	+	0.137528i
$391$		−	4.85795e6i		−	1.60698i
$392$	1.98201e6	−	1.98201e6i	0.651465	−	0.651465i
$393$	1.07931e6	+	1.07931e6i	0.352506	+	0.352506i
$394$		−	5.13230e6i		−	1.66560i
$395$	−2.46362e6	−	308656.i	−0.794476	−	0.0995363i
$396$	−24467.3	−	55261.7i	−0.00784058	−	0.0177087i
$397$	−2.28040e6	−	2.28040e6i	−0.726163	−	0.726163i	0.243690	−	0.969853i	$-0.421642\pi$
$397$	−2.28040e6	−	2.28040e6i	−0.726163	−	0.726163i	−0.969853	+	0.243690i	$0.921642\pi$
$398$	−762635.	−	762635.i	−0.241329	−	0.241329i
$399$			72391.8i			0.0227644i
$400$	3.16967e6	+	806891.i	0.990521	+	0.252154i
$401$	2.04742e6			0.635837			0.317919	−	0.948118i	$-0.397016\pi$
$401$	2.04742e6			0.635837			0.317919	+	0.948118i	$0.397016\pi$
$402$	1.15390e6	−	1.15390e6i	0.356126	−	0.356126i
$403$	−1.92965e6	−	1.92965e6i	−0.591857	−	0.591857i
$404$	123594.			0.0376742
$405$	1.92847e6	+	241609.i	0.584218	+	0.0731939i
$406$		−	788745.i		−	0.237477i
$407$	−1.39894e6	+	3.62195e6i	−0.418612	+	1.08382i
$408$	1.20258e6	−	1.20258e6i	0.357654	−	0.357654i
$409$	2.17148e6			0.641872			0.320936	−	0.947101i	$-0.396003\pi$
$409$	2.17148e6			0.641872			0.320936	+	0.947101i	$0.396003\pi$
$410$	159076.	+	204645.i	0.0467353	+	0.0601231i
$411$	1.24704e6			0.364146
$412$	−13761.0	−	13761.0i	−0.00399400	−	0.00399400i
$413$	−410124.	−	410124.i	−0.118315	−	0.118315i
$414$	−3.59707e6			−1.03145
$415$	3.78282e6	+	4.86645e6i	1.07819	+	1.38705i
$416$	−93253.6			−0.0264200
$417$	−1.43950e6	+	1.43950e6i	−0.405388	+	0.405388i
$418$	776132.	+	299772.i	0.217268	+	0.0839170i
$419$		−	382192.i		−	0.106352i	−0.998585	−	0.0531762i	$-0.983066\pi$
$419$		−	382192.i		−	0.106352i	0.998585	−	0.0531762i	$-0.0169345\pi$
$420$	−8021.24	−	1004.94i	−0.00221880	−	0.000277983i
$421$	2.41346e6			0.663643			0.331822	−	0.943342i	$-0.392337\pi$
$421$	2.41346e6			0.663643			0.331822	+	0.943342i	$0.392337\pi$
$422$	4.51269e6	+	4.51269e6i	1.23354	+	1.23354i
$423$	375908.	−	375908.i	0.102148	−	0.102148i
$424$	−3.91503e6			−1.05760
$425$	4.31738e6	−	2.56529e6i	1.15944	−	0.688912i
$426$			124847.i			0.0333314i
$427$	−1.06725e6	−	1.06725e6i	−0.283268	−	0.283268i
$428$	36492.8	+	36492.8i	0.00962935	+	0.00962935i
$429$	341979.	+	772391.i	0.0897132	+	0.202625i
$430$	−4.97681e6	−	623521.i	−1.29802	−	0.162622i
$431$			4.74684e6i			1.23087i	0.788188	+	0.615434i	$0.211019\pi$
$431$			4.74684e6i			1.23087i	−0.788188	+	0.615434i	$0.788981\pi$
$432$	−1.97437e6	−	1.97437e6i	−0.509003	−	0.509003i
$433$	4.94661e6	−	4.94661e6i	1.26791	−	1.26791i	0.320744	−	0.947166i	$-0.396067\pi$
$433$	4.94661e6	−	4.94661e6i	1.26791	−	1.26791i	0.947166	−	0.320744i	$-0.103933\pi$
$434$		−	1.48141e6i		−	0.377529i
$435$	−1.06594e6	+	828587.i	−0.270092	+	0.209950i
$436$			20362.0i			0.00512984i
$437$	774687.	−	774687.i	0.194054	−	0.194054i
$438$	−1.35884e6	+	1.35884e6i	−0.338442	+	0.338442i
$439$	7.74504e6			1.91806			0.959031	−	0.283302i	$-0.0914298\pi$
$439$	7.74504e6			1.91806			0.959031	+	0.283302i	$0.0914298\pi$
$440$	1.90038e6	−	3.53537e6i	0.467960	−	0.870568i
$441$	−3.25886e6			−0.797938
$442$	−2.31320e6	+	2.31320e6i	−0.563194	+	0.563194i
$443$	−1.91880e6	+	1.91880e6i	−0.464536	+	0.464536i	−0.900139	−	0.435603i	$-0.856535\pi$
$443$	−1.91880e6	+	1.91880e6i	−0.464536	+	0.464536i	0.435603	+	0.900139i	$0.356535\pi$
$444$		−	41432.1i		−	0.00997422i
$445$	−204559.	+	1.63275e6i	−0.0489688	+	0.390858i
$446$		−	1.42122e6i		−	0.338318i
$447$	931750.	−	931750.i	0.220562	−	0.220562i
$448$	763948.	+	763948.i	0.179833	+	0.179833i
$449$			513053.i			0.120101i	0.998195	+	0.0600504i	$0.0191262\pi$
$449$			513053.i			0.120101i	−0.998195	+	0.0600504i	$0.980874\pi$
$450$	−1.89946e6	−	3.19680e6i	−0.442181	−	0.744192i
$451$	297432.	−	131689.i	0.0688567	−	0.0304866i
$452$	5456.83	+	5456.83i	0.00125630	+	0.00125630i
$453$	979947.	+	979947.i	0.224366	+	0.224366i
$454$		−	262334.i		−	0.0597331i
$455$	−666545.	−	83508.3i	−0.150939	−	0.0189104i
$456$	383545.			0.0863783
$457$	−583728.	+	583728.i	−0.130744	+	0.130744i	−0.769450	−	0.638707i	$-0.779470\pi$
$457$	−583728.	+	583728.i	−0.130744	+	0.130744i	0.638707	+	0.769450i	$0.279470\pi$
$458$	962684.	+	962684.i	0.214447	+	0.214447i
$459$	−4.28719e6			−0.949819
$460$	75083.6	+	96592.1i	0.0165444	+	0.0212837i
$461$			3.50076e6i			0.767202i	0.923499	+	0.383601i	$0.125316\pi$
$461$			3.50076e6i			0.767202i	−0.923499	+	0.383601i	$0.874684\pi$
$462$	−165215.	+	427755.i	−0.0360118	+	0.0932374i
$463$	−51801.0	+	51801.0i	−0.0112302	+	0.0112302i	−0.712700	−	0.701469i	$-0.752528\pi$
$463$	−51801.0	+	51801.0i	−0.0112302	+	0.0112302i	0.701469	+	0.712700i	$0.252528\pi$
$464$	−4.27351e6			−0.921489
$465$	−2.00204e6	+	1.55624e6i	−0.429379	+	0.333768i
$466$	1.24393e6			0.265357
$467$	1.40004e6	+	1.40004e6i	0.297064	+	0.297064i	0.839863	−	0.542799i	$-0.182635\pi$
$467$	1.40004e6	+	1.40004e6i	0.297064	+	0.297064i	−0.542799	+	0.839863i	$0.682635\pi$
$468$	37893.8	+	37893.8i	0.00799748	+	0.00799748i
$469$	1.62859e6			0.341884
$470$	−810931.	−	101598.i	−0.169332	−	0.0212148i
$471$	−462355.			−0.0960336
$472$	−2.17291e6	+	2.17291e6i	−0.448939	+	0.448939i
$473$	−2.26787e6	+	5.87168e6i	−0.466084	+	1.20673i
$474$		−	1.50287e6i		−	0.307238i
$475$	1.09756e6	+	279403.i	0.223201	+	0.0568195i
$476$	−39288.7			−0.00794787
$477$	3.21858e6	+	3.21858e6i	0.647692	+	0.647692i
$478$	4.42248e6	−	4.42248e6i	0.885312	−	0.885312i
$479$	−5.27611e6			−1.05069			−0.525346	−	0.850889i	$-0.676064\pi$
$479$	−5.27611e6			−1.05069			−0.525346	+	0.850889i	$0.676064\pi$
$480$	−10772.0	+	85979.9i	−0.00213400	+	0.0170331i
$481$		−	3.44290e6i		−	0.678518i
$482$	−3.52414e6	−	3.52414e6i	−0.690932	−	0.690932i
$483$	426959.	+	426959.i	0.0832757	+	0.0832757i
$484$	86325.2	+	78376.3i	0.0167504	+	0.0152080i
$485$	−4.07577e6	−	5.24332e6i	−0.786784	−	1.01217i
$486$			4.88480e6i			0.938115i
$487$	−4.74171e6	−	4.74171e6i	−0.905967	−	0.905967i	0.0899768	−	0.995944i	$-0.471321\pi$
$487$	−4.74171e6	−	4.74171e6i	−0.905967	−	0.905967i	−0.995944	+	0.0899768i	$0.971321\pi$
$488$	−5.65451e6	+	5.65451e6i	−1.07484	+	1.07484i
$489$			747143.i			0.141297i
$490$	3.07471e6	+	3.95549e6i	0.578514	+	0.744235i
$491$			4.98492e6i			0.933157i	0.884480	+	0.466579i	$0.154514\pi$
$491$			4.98492e6i			0.933157i	−0.884480	+	0.466579i	$0.845486\pi$
$492$	−2454.39	+	2454.39i	−0.000457121	+	0.000457121i
$493$	−4.63979e6	+	4.63979e6i	−0.859767	+	0.859767i
$494$	−737763.			−0.136019
$495$	−4.46878e6	+	1.34414e6i	−0.819739	+	0.246564i
$496$	−8.02645e6			−1.46494
$497$	−88102.7	+	88102.7i	−0.0159992	+	0.0159992i
$498$	−2.63813e6	+	2.63813e6i	−0.476676	+	0.476676i
$499$		−	5.44333e6i		−	0.978618i	−0.872111	−	0.489309i	$-0.837249\pi$
$499$		−	5.44333e6i		−	0.978618i	0.872111	−	0.489309i	$-0.162751\pi$
$500$	−46195.2	+	117735.i	−0.00826365	+	0.0210611i
$501$			511022.i			0.0909589i
$502$	−6.20469e6	+	6.20469e6i	−1.09891	+	1.09891i
$503$	−12630.0	−	12630.0i	−0.00222578	−	0.00222578i	0.705993	−	0.708219i	$-0.250501\pi$
$503$	−12630.0	−	12630.0i	−0.00222578	−	0.00222578i	−0.708219	+	0.705993i	$0.750501\pi$
$504$		−	1.25676e6i		−	0.220381i
$505$	1.18636e6	−	9.46927e6i	0.207009	−	1.65230i
$506$	6.34556e6	−	2.80952e6i	1.10178	−	0.487816i
$507$	1.02332e6	+	1.02332e6i	0.176803	+	0.176803i
$508$	−60680.9	−	60680.9i	−0.0104326	−	0.0104326i
$509$		−	6.23451e6i		−	1.06662i	−0.845921	−	0.533308i	$-0.820949\pi$
$509$		−	6.23451e6i		−	1.06662i	0.845921	−	0.533308i	$-0.179051\pi$
$510$	1.86557e6	+	2.39998e6i	0.317604	+	0.408585i
$511$	−1.91783e6			−0.324907
$512$	4.04325e6	−	4.04325e6i	0.681640	−	0.681640i
$513$	−683668.	−	683668.i	−0.114697	−	0.114697i
$514$	825853.			0.137878
$515$	−1.18640e6	+	922224.i	−0.197113	+	0.153221i
$516$		−	67167.1i		−	0.0111053i
$517$	−369531.	+	956743.i	−0.0608029	+	0.157423i
$518$	1.32157e6	−	1.32157e6i	0.216404	−	0.216404i
$519$	−528969.			−0.0862010
$520$	−442443.	+	3.53148e6i	−0.0717545	+	0.572728i
$521$	1.07105e7			1.72869			0.864343	−	0.502904i	$-0.167735\pi$
$521$	1.07105e7			1.72869			0.864343	+	0.502904i	$0.167735\pi$
$522$	3.43553e6	+	3.43553e6i	0.551845	+	0.551845i
$523$	6.06097e6	+	6.06097e6i	0.968920	+	0.968920i	0.999531	−	0.0306109i	$-0.00974527\pi$
$523$	6.06097e6	+	6.06097e6i	0.968920	+	0.968920i	−0.0306109	+	0.999531i	$0.509745\pi$
$524$	−186823.			−0.0297236
$525$	−153989.	+	604908.i	−0.0243833	+	0.0957836i
$526$	3.69932e6			0.582986
$527$	−8.71438e6	+	8.71438e6i	−1.36682	+	1.36682i
$528$	2.31763e6	+	895156.i	0.361792	+	0.139738i
$529$		−	2.70170e6i		−	0.419756i
$530$	869894.	−	6.94330e6i	0.134517	−	1.07368i
$531$	3.57274e6			0.549877
$532$	−6265.29	−	6265.29i	−0.000959759	−	0.000959759i
$533$	−203954.	+	203954.i	−0.0310966	+	0.0310966i
$534$	−996015.			−0.151152
$535$	3.14621e6	−	2.44564e6i	0.475230	−	0.369409i
$536$		−	8.62856e6i		−	1.29726i
$537$	−1.29942e6	−	1.29942e6i	−0.194453	−	0.194453i
$538$	640418.	+	640418.i	0.0953911	+	0.0953911i
$539$	5.74893e6	−	2.54536e6i	0.852344	−	0.377379i
$540$	85243.4	−	66262.0i	0.0125799	−	0.00977867i
$541$		−	1.30520e7i		−	1.91727i	−0.284637	−	0.958635i	$-0.591873\pi$
$541$		−	1.30520e7i		−	1.91727i	0.284637	−	0.958635i	$-0.408127\pi$
$542$	4.68313e6	+	4.68313e6i	0.684760	+	0.684760i
$543$	1.64255e6	−	1.64255e6i	0.239067	−	0.239067i
$544$			421137.i			0.0610135i
$545$	1.56005e6	+	195452.i	0.224982	+	0.0281869i
$546$		−	406609.i		−	0.0583707i
$547$	−668156.	+	668156.i	−0.0954794	+	0.0954794i	−0.753233	−	0.657754i	$-0.771507\pi$
$547$	−668156.	+	668156.i	−0.0954794	+	0.0954794i	0.657754	+	0.753233i	$0.271507\pi$
$548$	−107928.	+	107928.i	−0.0153526	+	0.0153526i
$549$	9.29725e6			1.31651
$550$	5.84772e6	+	4.15587e6i	0.824290	+	0.585807i
$551$	−1.47979e6			−0.207645
$552$	2.26211e6	−	2.26211e6i	0.315984	−	0.315984i
$553$	1.06055e6	−	1.06055e6i	0.147476	−	0.147476i
$554$		−	82397.0i		−	0.0114061i
$555$	−3.17435e6	−	397700.i	−0.437444	−	0.0548054i
$556$		−	249168.i		−	0.0341827i
$557$	2.21811e6	−	2.21811e6i	0.302931	−	0.302931i	−0.539228	−	0.842160i	$-0.681284\pi$
$557$	2.21811e6	−	2.21811e6i	0.302931	−	0.302931i	0.842160	+	0.539228i	$0.181284\pi$
$558$	6.45256e6	+	6.45256e6i	0.877297	+	0.877297i
$559$		−	5.58141e6i		−	0.755465i
$560$	−1.55993e6	+	1.21258e6i	−0.210202	+	0.163396i
$561$	3.48814e6	−	1.54439e6i	0.467937	−	0.207181i
$562$	472904.	+	472904.i	0.0631586	+	0.0631586i
$563$	−3.44662e6	−	3.44662e6i	−0.458271	−	0.458271i	0.439817	−	0.898087i	$-0.355043\pi$
$563$	−3.44662e6	−	3.44662e6i	−0.458271	−	0.458271i	−0.898087	+	0.439817i	$0.855043\pi$
$564$		−	10944.3i		−	0.00144874i
$565$	470459.	−	365701.i	0.0620013	−	0.0481953i
$566$	3.29084e6			0.431783
$567$	−830178.	+	830178.i	−0.108446	+	0.108446i
$568$	466785.	+	466785.i	0.0607080	+	0.0607080i
$569$	−1.16987e7			−1.51480			−0.757402	−	0.652949i	$-0.773531\pi$
$569$	−1.16987e7			−1.51480			−0.757402	+	0.652949i	$0.773531\pi$
$570$	−85221.4	+	680218.i	−0.0109865	+	0.0876922i
$571$			4.00112e6i			0.513560i	0.966470	+	0.256780i	$0.0826615\pi$
$571$			4.00112e6i			0.513560i	−0.966470	+	0.256780i	$0.917338\pi$
$572$	−96445.3	−	37250.8i	−0.0123251	−	0.00476043i
$573$	2.40254e6	−	2.40254e6i	0.305691	−	0.305691i
$574$	−156577.			−0.0198357
$575$	8.12120e6	−	4.82542e6i	1.02436	−	0.608648i
$576$	−6.65504e6			−0.835785
$577$	8.17756e6	+	8.17756e6i	1.02255	+	1.02255i	0.999740	+	0.0228095i	$0.00726112\pi$
$577$	8.17756e6	+	8.17756e6i	1.02255	+	1.02255i	0.0228095	+	0.999740i	$0.492739\pi$
$578$	4.70320e6	+	4.70320e6i	0.585563	+	0.585563i
$579$	−3.72975e6			−0.462364
$580$	20542.5	−	163966.i	0.00253562	−	0.0202387i
$581$	−3.72339e6			−0.457613
$582$	2.84244e6	−	2.84244e6i	0.347843	−	0.347843i
$583$	−8.19177e6	−	3.16397e6i	−0.998174	−	0.385533i
$584$			1.01610e7i			1.23284i
$585$	3.26700e6	−	2.53953e6i	0.394693	−	0.306806i
$586$	1.29477e6			0.155757
$587$	−9.94234e6	−	9.94234e6i	−1.19095	−	1.19095i	−0.976801	−	0.214148i	$-0.931303\pi$
$587$	−9.94234e6	−	9.94234e6i	−1.19095	−	1.19095i	−0.214148	−	0.976801i	$-0.568697\pi$
$588$	−47439.8	+	47439.8i	−0.00565848	+	0.00565848i
$589$	−2.77933e6			−0.330105
$590$	−3.37086e6	−	4.33647e6i	−0.398667	−	0.512869i
$591$		−	5.30684e6i		−	0.624982i
$592$	−7.16042e6	−	7.16042e6i	−0.839720	−	0.839720i
$593$	4.17369e6	+	4.17369e6i	0.487398	+	0.487398i	0.907484	−	0.420086i	$-0.138000\pi$
$593$	4.17369e6	+	4.17369e6i	0.487398	+	0.487398i	−0.420086	+	0.907484i	$0.638000\pi$
$594$	−2.47943e6	−	5.60002e6i	−0.288327	−	0.651213i
$595$	−377127.	+	3.01014e6i	−0.0436712	+	0.348574i
$596$			161280.i			0.0185980i
$597$	−788572.	−	788572.i	−0.0905535	−	0.0905535i
$598$	−4.35125e6	+	4.35125e6i	−0.497578	+	0.497578i
$599$			1.39134e7i			1.58441i	0.610257	+	0.792204i	$0.291066\pi$
$599$			1.39134e7i			1.58441i	−0.610257	+	0.792204i	$0.708934\pi$
$600$	3.20492e6	+	815865.i	0.363445	+	0.0925210i
$601$		−	338828.i		−	0.0382643i	−0.999817	−	0.0191321i	$-0.993910\pi$
$601$		−	338828.i		−	0.0382643i	0.999817	−	0.0191321i	$-0.00609032\pi$
$602$	2.14245e6	−	2.14245e6i	0.240945	−	0.240945i
$603$	−7.09362e6	+	7.09362e6i	−0.794465	+	0.794465i
$604$	−169623.			−0.0189187
$605$	6.83349e6	−	5.86156e6i	0.759022	−	0.651065i
$606$	5.77649e6			0.638973
$607$	1.93606e6	−	1.93606e6i	0.213279	−	0.213279i	−0.592380	−	0.805659i	$-0.701812\pi$
$607$	1.93606e6	−	1.93606e6i	0.213279	−	0.213279i	0.805659	+	0.592380i	$0.201812\pi$
$608$	−67157.8	+	67157.8i	−0.00736779	+	0.00736779i
$609$		−	815569.i		−	0.0891082i
$610$	−8.77189e6	−	1.12847e7i	−0.954483	−	1.22790i
$611$		−	909446.i		−	0.0985539i
$612$	171130.	−	171130.i	0.0184691	−	0.0184691i
$613$	504356.	+	504356.i	0.0542108	+	0.0542108i	0.733692	−	0.679482i	$-0.237795\pi$
$613$	504356.	+	504356.i	0.0542108	+	0.0542108i	−0.679482	+	0.733692i	$0.737795\pi$
$614$		−	3.49167e6i		−	0.373777i
$615$	164486.	+	211605.i	0.0175364	+	0.0225599i
$616$	981600.	+	2.21703e6i	0.104228	+	0.235408i
$617$	−1.52938e6	−	1.52938e6i	−0.161735	−	0.161735i	0.621600	−	0.783335i	$-0.286483\pi$
$617$	−1.52938e6	−	1.52938e6i	−0.161735	−	0.161735i	−0.783335	+	0.621600i	$0.786483\pi$
$618$	−643158.	−	643158.i	−0.0677402	−	0.0677402i
$619$			2.63399e6i			0.276304i	0.990411	+	0.138152i	$0.0441162\pi$
$619$			2.63399e6i			0.276304i	−0.990411	+	0.138152i	$0.955884\pi$
$620$	38582.7	−	307959.i	0.00403101	−	0.0321746i
$621$	−8.06440e6			−0.839157
$622$	−6.23559e6	+	6.23559e6i	−0.646251	+	0.646251i
$623$	−702875.	−	702875.i	−0.0725534	−	0.0725534i
$624$	−2.20305e6			−0.226498
$625$	8.57695e6	+	4.66941e6i	0.878280	+	0.478147i
$626$			5.94753e6i			0.606598i
$627$	802527.	+	309966.i	0.0815250	+	0.0314881i
$628$	40015.4	−	40015.4i	0.00404882	−	0.00404882i
$629$	−1.55483e7			−1.56695
$630$	2.22886e6	+	279243.i	0.223733	+	0.0280305i
$631$	−1.69570e6			−0.169542			−0.0847709	−	0.996400i	$-0.527016\pi$
$631$	−1.69570e6			−0.169542			−0.0847709	+	0.996400i	$0.527016\pi$
$632$	−5.61902e6	−	5.61902e6i	−0.559587	−	0.559587i
$633$	4.66616e6	+	4.66616e6i	0.462861	+	0.462861i
$634$	1.74161e7			1.72079
$635$	−5.23159e6	+	4.06666e6i	−0.514872	+	0.400224i
$636$	93706.9			0.00918605
$637$	−3.94213e6	+	3.94213e6i	−0.384930	+	0.384930i
$638$	−8.74394e6	−	3.37724e6i	−0.850463	−	0.328481i
$639$		−	767496.i		−	0.0743574i
$640$	6.56668e6	+	8.44777e6i	0.633718	+	0.815253i
$641$	−1.25948e7			−1.21073			−0.605365	−	0.795948i	$-0.706973\pi$
$641$	−1.25948e7			−1.21073			−0.605365	+	0.795948i	$0.706973\pi$
$642$	1.70558e6	+	1.70558e6i	0.163318	+	0.163318i
$643$	6.06150e6	−	6.06150e6i	0.578166	−	0.578166i	−0.356232	−	0.934398i	$-0.615939\pi$
$643$	6.06150e6	−	6.06150e6i	0.578166	−	0.578166i	0.934398	+	0.356232i	$0.115939\pi$
$644$	−73904.0			−0.00702188
$645$	−5.14606e6	−	644726.i	−0.487053	−	0.0610206i
$646$			3.33177e6i			0.314118i
$647$	2.17837e6	+	2.17837e6i	0.204584	+	0.204584i	0.801961	−	0.597377i	$-0.203790\pi$
$647$	2.17837e6	+	2.17837e6i	0.204584	+	0.204584i	−0.597377	+	0.801961i	$0.703790\pi$
$648$	4.39844e6	+	4.39844e6i	0.411492	+	0.411492i
$649$	−6.30265e6	+	2.79052e6i	−0.587370	+	0.260060i
$650$	−6.16478e6	−	1.56935e6i	−0.572314	−	0.145692i
$651$		−	1.53179e6i		−	0.141660i
$652$	−64663.0	−	64663.0i	−0.00595712	−	0.00595712i
$653$	1.09329e7	−	1.09329e7i	1.00335	−	1.00335i	0.00335867	−	0.999994i	$-0.498931\pi$
$653$	1.09329e7	−	1.09329e7i	1.00335	−	1.00335i	0.999994	−	0.00335867i	$-0.00106910\pi$
$654$			951669.i			0.0870045i
$655$	−1.79328e6	+	1.43136e7i	−0.163322	+	1.30360i
$656$			848351.i			0.0769691i
$657$	8.35349e6	−	8.35349e6i	0.755013	−	0.755013i
$658$	349094.	−	349094.i	0.0314324	−	0.0314324i
$659$	−1.26138e7			−1.13145			−0.565723	−	0.824595i	$-0.691403\pi$
$659$	−1.26138e7			−1.13145			−0.565723	+	0.824595i	$0.691403\pi$
$660$	−45486.0	+	84619.7i	−0.00406460	+	0.00756156i
$661$	4.63511e6			0.412626			0.206313	−	0.978486i	$-0.433854\pi$
$661$	4.63511e6			0.412626			0.206313	+	0.978486i	$0.433854\pi$
$662$	−2.65181e6	+	2.65181e6i	−0.235179	+	0.235179i
$663$	−2.39187e6	+	2.39187e6i	−0.211327	+	0.211327i
$664$			1.97272e7i			1.73638i
$665$	−540160.	+	419881.i	−0.0473662	+	0.0368190i
$666$			1.15127e7i			1.00575i
$667$	−8.72766e6	+	8.72766e6i	−0.759597	+	0.759597i
$668$	−44227.4	−	44227.4i	−0.00383487	−	0.00383487i
$669$		−	1.46956e6i		−	0.126947i
$670$	1.53028e7	+	1.91721e6i	1.31699	+	0.165000i
$671$	−1.64012e7	+	7.26170e6i	−1.40627	+	0.622633i
$672$	−37013.1	−	37013.1i	−0.00316179	−	0.00316179i
$673$	5.17190e6	+	5.17190e6i	0.440162	+	0.440162i	0.892066	−	0.451905i	$-0.149255\pi$
$673$	5.17190e6	+	5.17190e6i	0.440162	+	0.440162i	−0.451905	+	0.892066i	$0.649255\pi$
$674$		−	1.57708e7i		−	1.33723i
$675$	−4.25848e6	−	7.16704e6i	−0.359745	−	0.605453i
$676$	−177130.			−0.0149082
$677$	6.79262e6	−	6.79262e6i	0.569594	−	0.569594i	−0.362421	−	0.932015i	$-0.618050\pi$
$677$	6.79262e6	−	6.79262e6i	0.569594	−	0.569594i	0.932015	+	0.362421i	$0.118050\pi$
$678$	255039.	+	255039.i	0.0213075	+	0.0213075i
$679$	4.01174e6			0.333932
$680$	1.59483e7	+	1.99809e6i	1.32264	+	0.165708i
$681$		−	271256.i		−	0.0224136i
$682$	−1.64227e7	−	6.34309e6i	−1.35203	−	0.522203i
$683$	1.70346e7	−	1.70346e7i	1.39727	−	1.39727i	0.589494	−	0.807773i	$-0.299327\pi$
$683$	1.70346e7	−	1.70346e7i	1.39727	−	1.39727i	0.807773	−	0.589494i	$-0.200673\pi$
$684$	54579.3			0.00446054
$685$	7.23299e6	+	9.30495e6i	0.588967	+	0.757683i
$686$	−6.27309e6			−0.508945
$687$	995424.	+	995424.i	0.0804667	+	0.0804667i
$688$	−1.16080e7	−	1.16080e7i	−0.934948	−	0.934948i
$689$	7.78681e6			0.624901
$690$	3.50923e6	+	4.51448e6i	0.280601	+	0.360981i
$691$	1.74062e7			1.38678			0.693391	−	0.720562i	$-0.256116\pi$
$691$	1.74062e7			1.38678			0.693391	+	0.720562i	$0.256116\pi$
$692$	45780.7	−	45780.7i	0.00363427	−	0.00363427i
$693$	1.01566e6	−	2.62963e6i	0.0803370	−	0.207999i
$694$			1.56200e7i			1.23107i
$695$	−1.90903e7	−	2.39173e6i	−1.49917	−	0.187824i
$696$	−4.32104e6			−0.338115
$697$	921062.	+	921062.i	0.0718136	+	0.0718136i
$698$	1.44076e7	−	1.44076e7i	1.11932	−	1.11932i
$699$	1.28623e6			0.0995696
$700$	−39025.7	−	65680.3i	−0.00301027	−	0.00506629i
$701$		−	3.44331e6i		−	0.264656i	−0.991206	−	0.132328i	$-0.957755\pi$
$701$		−	3.44331e6i		−	0.264656i	0.991206	−	0.132328i	$-0.0422452\pi$
$702$	3.84002e6	+	3.84002e6i	0.294097	+	0.294097i
$703$	−2.47945e6	−	2.47945e6i	−0.189220	−	0.189220i
$704$	1.17401e7	−	5.19798e6i	0.892772	−	0.395278i
$705$	−838509.	−	105053.i	−0.0635382	−	0.00796041i
$706$		−	2.03713e7i		−	1.53818i
$707$	4.07639e6	+	4.07639e6i	0.306710	+	0.306710i
$708$	52009.1	−	52009.1i	0.00389938	−	0.00389938i
$709$			5.79095e6i			0.432647i	0.976322	+	0.216324i	$0.0694066\pi$
$709$			5.79095e6i			0.432647i	−0.976322	+	0.216324i	$0.930593\pi$
$710$	−931560.	+	724127.i	−0.0693530	+	0.0539099i
$711$			9.23889e6i			0.685403i
$712$	−3.72396e6	+	3.72396e6i	−0.275299	+	0.275299i
$713$	−1.63922e7	+	1.63922e7i	−1.20757	+	1.20757i
$714$	−1.83626e6			−0.134800
$715$	−3.77977e6	+	7.03168e6i	−0.276503	+	0.514392i
$716$	224922.			0.0163965
$717$	4.57289e6	−	4.57289e6i	0.332195	−	0.332195i
$718$	−1.47913e7	+	1.47913e7i	−1.07077	+	1.07077i
$719$		−	1.15861e7i		−	0.835821i	−0.908488	−	0.417910i	$-0.862763\pi$
$719$		−	1.15861e7i		−	0.835821i	0.908488	−	0.417910i	$-0.137237\pi$
$720$	1.51297e6	−	1.20762e7i	0.108768	−	0.868160i
$721$		−	907736.i		−	0.0650311i
$722$	9.48450e6	−	9.48450e6i	0.677129	−	0.677129i
$723$	−3.64399e6	−	3.64399e6i	−0.259258	−	0.259258i
$724$			284316.i			0.0201584i
$725$	−1.23652e7	−	3.14777e6i	−0.873688	−	0.222412i
$726$	4.03463e6	+	3.66312e6i	0.284094	+	0.257934i
$727$	1.34606e7	+	1.34606e7i	0.944560	+	0.944560i	0.998542	−	0.0539815i	$-0.0171912\pi$
$727$	1.34606e7	+	1.34606e7i	0.944560	+	0.944560i	−0.0539815	+	0.998542i	$0.517191\pi$
$728$	−1.52025e6	−	1.52025e6i	−0.106313	−	0.106313i
$729$		−	3.39749e6i		−	0.236777i
$730$	−1.80206e7	−	2.25772e6i	−1.25159	−	0.156806i
$731$	−2.52059e7			−1.74465
$732$	135342.	−	135342.i	0.00933586	−	0.00933586i
$733$	−7.34614e6	−	7.34614e6i	−0.505009	−	0.505009i	0.407981	−	0.912990i	$-0.366233\pi$
$733$	−7.34614e6	−	7.34614e6i	−0.505009	−	0.505009i	−0.912990	+	0.407981i	$0.866233\pi$
$734$	−6.10879e6			−0.418519
$735$	3.17928e6	+	4.09001e6i	0.217075	+	0.279258i
$736$			792178.i			0.0539049i
$737$	6.97327e6	−	1.80543e7i	0.472898	−	1.22437i
$738$	682000.	−	682000.i	0.0460939	−	0.0460939i
$739$	1.81881e7			1.22512			0.612558	−	0.790426i	$-0.290141\pi$
$739$	1.81881e7			1.22512			0.612558	+	0.790426i	$0.290141\pi$
$740$	309151.	−	240311.i	0.0207535	−	0.0161322i
$741$	−762854.			−0.0510382
$742$	2.98900e6	+	2.98900e6i	0.199304	+	0.199304i
$743$	866311.	+	866311.i	0.0575708	+	0.0575708i	0.735306	−	0.677735i	$-0.237038\pi$
$743$	866311.	+	866311.i	0.0575708	+	0.0575708i	−0.677735	+	0.735306i	$0.737038\pi$
$744$	−8.11572e6			−0.537520
$745$	1.23566e7	+	1.54811e6i	0.815661	+	0.102190i
$746$	2.86807e7			1.88688
$747$	1.62179e7	−	1.62179e7i	1.06339	−	1.06339i
$748$	−168226.	+	435551.i	−0.0109936	+	0.0284633i
$749$			2.40721e6i			0.156787i
$750$	−2.15905e6	+	5.50265e6i	−0.140155	+	0.357206i
$751$	7.59592e6			0.491451			0.245726	−	0.969339i	$-0.420974\pi$
$751$	7.59592e6			0.491451			0.245726	+	0.969339i	$0.420974\pi$
$752$	−1.89143e6	−	1.89143e6i	−0.121968	−	0.121968i
$753$	−6.41570e6	+	6.41570e6i	−0.412341	+	0.412341i
$754$	8.31168e6			0.532427
$755$	−1.62818e6	+	1.29958e7i	−0.103953	+	0.829728i
$756$			65220.9i			0.00415033i
$757$	−6.58446e6	−	6.58446e6i	−0.417619	−	0.417619i	0.466763	−	0.884382i	$-0.345420\pi$
$757$	−6.58446e6	−	6.58446e6i	−0.417619	−	0.417619i	−0.884382	+	0.466763i	$0.845420\pi$
$758$	−2.09750e7	−	2.09750e7i	−1.32595	−	1.32595i
$759$	6.56137e6	−	2.90507e6i	0.413418	−	0.183043i
$760$	2.22461e6	+	2.86187e6i	0.139708	+	0.179728i
$761$			1.70427e7i			1.06678i	0.845868	+	0.533392i	$0.179083\pi$
$761$			1.70427e7i			1.06678i	−0.845868	+	0.533392i	$0.820917\pi$
$762$	−2.83608e6	−	2.83608e6i	−0.176942	−	0.176942i
$763$	−671580.	+	671580.i	−0.0417625	+	0.0417625i
$764$			415865.i			0.0257762i
$765$	−1.14686e7	−	1.47539e7i	−0.708528	−	0.911492i
$766$		−	4.64014e6i		−	0.285732i
$767$	4.32182e6	−	4.32182e6i	0.265264	−	0.265264i
$768$	−297521.	+	297521.i	−0.0182018	+	0.0182018i
$769$	1.89828e7			1.15756			0.578781	−	0.815483i	$-0.303529\pi$
$769$	1.89828e7			1.15756			0.578781	+	0.815483i	$0.303529\pi$
$770$	−4.15002e6	+	1.24826e6i	−0.252245	+	0.0758713i
$771$	853939.			0.0517358
$772$	322799.	−	322799.i	0.0194935	−	0.0194935i
$773$	9.29605e6	−	9.29605e6i	0.559564	−	0.559564i	−0.369619	−	0.929183i	$-0.620512\pi$
$773$	9.29605e6	−	9.29605e6i	0.559564	−	0.559564i	0.929183	+	0.369619i	$0.120512\pi$
$774$			1.86637e7i			1.11981i
$775$	−2.32242e7	−	5.91210e6i	−1.38895	−	0.353580i
$776$		−	2.12549e7i		−	1.26708i
$777$	1.36652e6	−	1.36652e6i	0.0812011	−	0.0812011i
$778$	−2.17386e7	−	2.17386e7i	−1.28761	−	1.28761i
$779$			293759.i			0.0173440i
$780$	10590.0	−	84526.7i	0.000623243	−	0.00497459i
$781$	599460.	+	1.35393e6i	0.0351668	+	0.0794274i
$782$	1.96504e7	+	1.96504e7i	1.14909	+	1.14909i
$783$	7.70224e6	+	7.70224e6i	0.448965	+	0.448965i
$784$			1.63974e7i			0.952763i
$785$	−2.68171e6	−	3.44992e6i	−0.155324	−	0.199818i
$786$	−8.73164e6			−0.504127
$787$	1.18976e7	−	1.18976e7i	0.684737	−	0.684737i	−0.276327	−	0.961064i	$-0.589117\pi$
$787$	1.18976e7	−	1.18976e7i	0.684737	−	0.684737i	0.961064	+	0.276327i	$0.0891172\pi$
$788$	459291.	+	459291.i	0.0263495	+	0.0263495i
$789$	3.82513e6			0.218753
$790$	1.12138e7	−	8.71682e6i	0.639273	−	0.496924i
$791$			359955.i			0.0204554i
$792$	−1.39323e7	−	5.38117e6i	−0.789239	−	0.304834i
$793$	1.12466e7	−	1.12466e7i	0.635092	−	0.635092i
$794$	1.84484e7			1.03850
$795$	899478.	−	7.17944e6i	0.0504746	−	0.402877i
$796$	136497.			0.00763555
$797$	2.11535e7	+	2.11535e7i	1.17961	+	1.17961i	0.979845	+	0.199761i	$0.0640166\pi$
$797$	2.11535e7	+	2.11535e7i	1.17961	+	1.17961i	0.199761	+	0.979845i	$0.435983\pi$
$798$	−292824.	−	292824.i	−0.0162780	−	0.0162780i
$799$	−4.10709e6			−0.227597
$800$	−704029.	+	418317.i	−0.0388925	+	0.0231090i
$801$	6.12301e6			0.337197
$802$	−8.28180e6	+	8.28180e6i	−0.454662	+	0.454662i
$803$	−8.21176e6	+	2.12609e7i	−0.449415	+	1.16357i
$804$			206526.i			0.0112677i
$805$	−709393.	+	5.66222e6i	−0.0385831	+	0.307962i
$806$	1.56109e7			0.846427
$807$	662198.	+	662198.i	0.0357935	+	0.0357935i
$808$	2.15975e7	−	2.15975e7i	1.16379	−	1.16379i
$809$	6.25369e6			0.335943			0.167971	−	0.985792i	$-0.446278\pi$
$809$	6.25369e6			0.335943			0.167971	+	0.985792i	$0.446278\pi$
$810$	−8.77795e6	+	6.82333e6i	−0.470089	+	0.365413i
$811$			2.35193e7i			1.25566i	0.778350	+	0.627831i	$0.216057\pi$
$811$			2.35193e7i			1.25566i	−0.778350	+	0.627831i	$0.783943\pi$
$812$	70585.0	+	70585.0i	0.00375684	+	0.00375684i
$813$	4.84240e6	+	4.84240e6i	0.256942	+	0.256942i
$814$	−8.99209e6	−	2.03095e7i	−0.475664	−	1.07433i
$815$	−5.57490e6	+	4.33352e6i	−0.293997	+	0.228532i
$816$			9.94907e6i			0.523067i
$817$	−4.01952e6	−	4.01952e6i	−0.210678	−	0.210678i
$818$	−8.78365e6	+	8.78365e6i	−0.458978	+	0.458978i
$819$			2.49963e6i			0.130216i
$820$	−32549.5	−	4077.98i	−0.00169048	−	0.000211792i
$821$		−	1.86375e7i		−	0.965007i	−0.875894	−	0.482504i	$-0.839728\pi$
$821$		−	1.86375e7i		−	0.965007i	0.875894	−	0.482504i	$-0.160272\pi$
$822$	−5.04427e6	+	5.04427e6i	−0.260387	+	0.260387i
$823$	4.58805e6	−	4.58805e6i	0.236118	−	0.236118i	−0.579123	−	0.815240i	$-0.696605\pi$
$823$	4.58805e6	−	4.58805e6i	0.236118	−	0.236118i	0.815240	+	0.579123i	$0.196605\pi$
$824$	−4.80935e6			−0.246757
$825$	6.04660e6	+	4.29720e6i	0.309297	+	0.219812i
$826$	3.31790e6			0.169205
$827$	−2.31865e7	+	2.31865e7i	−1.17888	+	1.17888i	−0.198854	+	0.980029i	$0.563722\pi$
$827$	−2.31865e7	+	2.31865e7i	−1.17888	+	1.17888i	−0.980029	+	0.198854i	$0.936278\pi$
$828$	321903.	−	321903.i	0.0163173	−	0.0163173i
$829$		−	3.64658e7i		−	1.84289i	−0.388506	−	0.921446i	$-0.627009\pi$
$829$		−	3.64658e7i		−	1.84289i	0.388506	−	0.921446i	$-0.372991\pi$
$830$	−3.49863e7	−	4.38327e6i	−1.76280	−	0.220853i
$831$		−	85199.2i		−	0.00427989i
$832$	−8.05037e6	+	8.05037e6i	−0.403188	+	0.403188i
$833$	1.78028e7	+	1.78028e7i	0.888947	+	0.888947i
$834$		−	1.16455e7i		−	0.579754i
$835$	−3.81305e6	+	2.96399e6i	−0.189259	+	0.147116i
$836$	−96283.0	+	42629.7i	−0.00476468	+	0.00210958i
$837$	1.44662e7	+	1.44662e7i	0.713743	+	0.713743i
$838$	1.54597e6	+	1.54597e6i	0.0760484	+	0.0760484i
$839$		−	2.13160e7i		−	1.04544i	−0.852504	−	0.522721i	$-0.824917\pi$
$839$		−	2.13160e7i		−	1.04544i	0.852504	−	0.522721i	$-0.175083\pi$
$840$	−1.57728e6	+	1.22606e6i	−0.0771279	+	0.0599536i
$841$	−3.83973e6			−0.187202
$842$	−9.76243e6	+	9.76243e6i	−0.474546	+	0.474546i
$843$	488987.	+	488987.i	0.0236989	+	0.0236989i
$844$	−807684.			−0.0390288
$845$	−1.70024e6	+	1.35710e7i	−0.0819160	+	0.653836i
$846$			3.04109e6i			0.146084i
$847$	262172.	+	5.43220e6i	0.0125567	+	0.260176i
$848$	1.61947e7	−	1.61947e7i	0.773364	−	0.773364i
$849$	3.40275e6			0.162017
$850$	−7.08722e6	+	2.78404e7i	−0.336456	+	1.32168i
$851$	−2.92470e7			−1.38439
$852$	−11172.6	−	11172.6i	−0.000527296	−	0.000527296i
$853$	−2.06563e7	−	2.06563e7i	−0.972031	−	0.972031i	0.0275888	−	0.999619i	$-0.491217\pi$
$853$	−2.06563e7	−	2.06563e7i	−0.972031	−	0.972031i	−0.999619	+	0.0275888i	$0.991217\pi$
$854$	8.63407e6			0.405108
$855$	523899.	−	4.18164e6i	0.0245094	−	0.195628i
$856$	1.27539e7			0.594919
$857$	−4.82211e6	+	4.82211e6i	−0.224277	+	0.224277i	−0.810297	−	0.586020i	$-0.800694\pi$
$857$	−4.82211e6	+	4.82211e6i	−0.224277	+	0.224277i	0.586020	+	0.810297i	$0.300694\pi$
$858$	−4.50762e6	−	1.74101e6i	−0.209040	−	0.0807391i
$859$			3.35791e7i			1.55269i	0.630306	+	0.776347i	$0.282930\pi$
$859$			3.35791e7i			1.55269i	−0.630306	+	0.776347i	$0.717070\pi$
$860$	501175.	−	389577.i	0.0231070	−	0.0179617i
$861$	−161902.			−0.00744293
$862$	−1.92010e7	−	1.92010e7i	−0.880146	−	0.880146i
$863$	5.78092e6	−	5.78092e6i	0.264223	−	0.264223i	−0.562544	−	0.826767i	$-0.690177\pi$
$863$	5.78092e6	−	5.78092e6i	0.264223	−	0.264223i	0.826767	+	0.562544i	$0.190177\pi$
$864$	699105.			0.0318609
$865$	−3.06809e6	−	3.94697e6i	−0.139421	−	0.179359i
$866$			4.00181e7i			1.81327i
$867$	4.86315e6	+	4.86315e6i	0.219720	+	0.219720i
$868$	132572.	+	132572.i	0.00597244	+	0.00597244i
$869$	−7.21611e6	−	1.62983e7i	−0.324156	−	0.732136i
$870$	960108.	−	7.66337e6i	0.0430053	−	0.343259i
$871$			1.71618e7i			0.766510i
$872$	3.55816e6	+	3.55816e6i	0.158465	+	0.158465i
$873$	−1.74739e7	+	1.74739e7i	−0.775986	+	0.775986i
$874$			6.26721e6i			0.277521i
$875$	−5.40676e6	+	2.35953e6i	−0.238735	+	0.104185i
$876$		−	243207.i		−	0.0107082i
$877$	−2.13675e6	+	2.13675e6i	−0.0938113	+	0.0938113i	−0.752455	−	0.658644i	$-0.771130\pi$
$877$	−2.13675e6	+	2.13675e6i	−0.0938113	+	0.0938113i	0.658644	+	0.752455i	$0.271130\pi$
$878$	−3.13287e7	+	3.13287e7i	−1.37153	+	1.37153i
$879$	1.33880e6			0.0584444
$880$	6.76321e6	+	2.24853e7i	0.294406	+	0.978795i
$881$	2.45552e6			0.106587			0.0532935	−	0.998579i	$-0.483028\pi$
$881$	2.45552e6			0.106587			0.0532935	+	0.998579i	$0.483028\pi$
$882$	1.31821e7	−	1.31821e7i	0.570574	−	0.570574i
$883$	3.84035e6	−	3.84035e6i	0.165756	−	0.165756i	−0.619355	−	0.785111i	$-0.712606\pi$
$883$	3.84035e6	−	3.84035e6i	0.165756	−	0.165756i	0.785111	+	0.619355i	$0.212606\pi$
$884$		−	414019.i		−	0.0178193i
$885$	−3.48549e6	−	4.48395e6i	−0.149591	−	0.192443i
$886$		−	1.55230e7i		−	0.664343i
$887$	2.85124e7	−	2.85124e7i	1.21681	−	1.21681i	0.248074	−	0.968741i	$-0.420203\pi$
$887$	2.85124e7	−	2.85124e7i	1.21681	−	1.21681i	0.968741	−	0.248074i	$-0.0797975\pi$
$888$	−7.24006e6	−	7.24006e6i	−0.308113	−	0.308113i
$889$		−	4.00276e6i		−	0.169866i
$890$	−5.77701e6	−	7.43189e6i	−0.244471	−	0.314503i
$891$	5.64861e6	+	1.27579e7i	0.238368	+	0.538376i
$892$	127186.	+	127186.i	0.00535213	+	0.00535213i
$893$	−654949.	−	654949.i	−0.0274839	−	0.0274839i
$894$			7.53785e6i			0.315430i
$895$	2.15900e6	−	1.72326e7i	0.0900937	−	0.719108i
$896$	−6.46351e6			−0.268967
$897$	−4.49923e6	+	4.49923e6i	−0.186705	+	0.186705i
$898$	−2.07530e6	−	2.07530e6i	−0.0858794	−	0.0858794i
$899$	3.13120e7			1.29215
$900$	456067.	+	116099.i	0.0187682	+	0.00477775i
$901$		−	3.51655e7i		−	1.44313i
$902$	−670429.	+	1.73579e6i	−0.0274370	+	0.0710365i
$903$	2.21531e6	−	2.21531e6i	0.0904097	−	0.0904097i
$904$	1.90711e6			0.0776166
$905$	2.17831e7	+	2.72911e6i	0.884095	+	0.110764i
$906$	−7.92776e6			−0.320871
$907$	−2.42882e7	−	2.42882e7i	−0.980341	−	0.980341i	0.0194695	−	0.999810i	$-0.493802\pi$
$907$	−2.42882e7	−	2.42882e7i	−0.980341	−	0.980341i	−0.999810	+	0.0194695i	$0.993802\pi$
$908$	23476.4	+	23476.4i	0.000944966	+	0.000944966i
$909$	−3.55110e7			−1.42545
$910$	3.03396e6	−	2.35838e6i	0.121453	−	0.0944084i
$911$	−1.18804e7			−0.474281			−0.237141	−	0.971475i	$-0.576210\pi$
$911$	−1.18804e7			−0.474281			−0.237141	+	0.971475i	$0.576210\pi$
$912$	−1.58656e6	+	1.58656e6i	−0.0631638	+	0.0631638i
$913$	−1.59428e7	+	4.12771e7i	−0.632976	+	1.63882i
$914$		−	4.72236e6i		−	0.186979i
$915$	−9.07021e6	−	1.16685e7i	−0.358150	−	0.460745i
$916$	−172302.			−0.00678502
$917$	−6.16180e6	−	6.16180e6i	−0.241983	−	0.241983i
$918$	1.73417e7	−	1.73417e7i	0.679178	−	0.679178i
$919$	−3.05751e7			−1.19421			−0.597103	−	0.802165i	$-0.703681\pi$
$919$	−3.05751e7			−1.19421			−0.597103	+	0.802165i	$0.703681\pi$
$920$	2.99995e7	+	3.75850e6i	1.16854	+	0.146401i
$921$		−	3.61042e6i		−	0.140252i
$922$	−1.41605e7	−	1.41605e7i	−0.548596	−	0.548596i
$923$	−928414.	−	928414.i	−0.0358705	−	0.0358705i
$924$	−23494.8	−	53065.1i	−0.000905298	−	0.00204470i
$925$	−1.54442e7	−	2.59926e7i	−0.593485	−	0.998837i
$926$		−	419070.i		−	0.0160605i
$927$	3.95382e6	+	3.95382e6i	0.151118	+	0.151118i
$928$	756602.	−	756602.i	0.0288402	−	0.0288402i
$929$			4.75462e7i			1.80749i	0.428067	+	0.903747i	$0.359195\pi$
$929$			4.75462e7i			1.80749i	−0.428067	+	0.903747i	$0.640805\pi$
$930$	1.80326e6	−	1.43932e7i	0.0683678	−	0.545696i
$931$			5.67794e6i			0.214693i
$932$	−111320.	+	111320.i	−0.00419790	+	0.00419790i
$933$	−6.44765e6	+	6.44765e6i	−0.242492	+	0.242492i
$934$	−1.13263e7			−0.424837
$935$	3.17553e7	+	1.70696e7i	1.18792	+	0.638549i
$936$	1.32435e7			0.494098
$937$	−6.43779e6	+	6.43779e6i	−0.239545	+	0.239545i	−0.816662	−	0.577117i	$-0.804178\pi$
$937$	−6.43779e6	+	6.43779e6i	−0.239545	+	0.239545i	0.577117	+	0.816662i	$0.304178\pi$
$938$	−6.58763e6	+	6.58763e6i	−0.244468	+	0.244468i
$939$			6.14980e6i			0.227613i
$940$	81662.5	−	63478.5i	0.00301441	−	0.00234319i
$941$			3.67572e7i			1.35322i	0.736342	+	0.676609i	$0.236551\pi$
$941$			3.67572e7i			1.35322i	−0.736342	+	0.676609i	$0.763449\pi$
$942$	1.87022e6	−	1.87022e6i	0.0686699	−	0.0686699i
$943$	1.73256e6	+	1.73256e6i	0.0634468	+	0.0634468i
$944$		−	1.79768e7i		−	0.656570i
$945$	4.99696e6	+	626046.i	0.182023	+	0.0228048i
$946$	−1.45774e7	−	3.29244e7i	−0.529606	−	1.19616i
$947$	2.68412e7	+	2.68412e7i	0.972585	+	0.972585i	0.999634	−	0.0270491i	$-0.00861106\pi$
$947$	2.68412e7	+	2.68412e7i	0.972585	+	0.972585i	−0.0270491	+	0.999634i	$0.508611\pi$
$948$	134492.	+	134492.i	0.00486045	+	0.00486045i
$949$		−	2.02098e7i		−	0.728446i
$950$	−5.56983e6	+	3.30946e6i	−0.200232	+	0.118973i
$951$	1.80084e7			0.645689
$952$	−6.86552e6	+	6.86552e6i	−0.245517	+	0.245517i
$953$	3.56521e7	+	3.56521e7i	1.27161	+	1.27161i	0.945244	+	0.326365i	$0.105824\pi$
$953$	3.56521e7	+	3.56521e7i	1.27161	+	1.27161i	0.326365	+	0.945244i	$0.394176\pi$
$954$	−2.60383e7			−0.926278
$955$	3.18618e7	+	3.99182e6i	1.13048	+	0.141632i
$956$			791539.i			0.0280109i
$957$	−9.04131e6	−	3.49210e6i	−0.319118	−	0.123256i
$958$	2.13419e7	−	2.13419e7i	0.751309	−	0.751309i
$959$	−7.11935e6			−0.249973
$960$	6.49252e6	+	8.35237e6i	0.227371	+	0.292504i
$961$	3.01807e7			1.05419
$962$	1.39265e7	+	1.39265e7i	0.485182	+	0.485182i
$963$	−1.04851e7	−	1.04851e7i	−0.364339	−	0.364339i
$964$	630753.			0.0218608
$965$	−2.16330e7	−	2.78300e7i	−0.747823	−	0.962045i
$966$	−3.45409e6			−0.119094
$967$	3.23095e7	−	3.23095e7i	1.11113	−	1.11113i	0.118131	−	0.992998i	$-0.462310\pi$
$967$	3.23095e7	−	3.23095e7i	1.11113	−	1.11113i	0.992998	−	0.118131i	$-0.0376902\pi$
$968$	2.87808e7	−	1.38903e6i	0.987221	−	0.0476458i
$969$			3.44508e6i			0.117866i
$970$	3.76957e7	+	4.72272e6i	1.28636	+	0.161162i
$971$	7.40830e6			0.252157			0.126078	−	0.992020i	$-0.459761\pi$
$971$	7.40830e6			0.252157			0.126078	+	0.992020i	$0.459761\pi$
$972$	−437142.	−	437142.i	−0.0148408	−	0.0148408i
$973$	8.21809e6	−	8.21809e6i	0.278284	−	0.278284i
$974$	3.83604e7			1.29564
$975$	−6.37444e6	−	1.62272e6i	−0.214749	−	0.0546678i
$976$		−	4.67804e7i		−	1.57195i
$977$	−2.06272e6	−	2.06272e6i	−0.0691360	−	0.0691360i	0.671693	−	0.740829i	$-0.265567\pi$
$977$	−2.06272e6	−	2.06272e6i	−0.0691360	−	0.0691360i	−0.740829	+	0.671693i	$0.765567\pi$
$978$	−3.02219e6	−	3.02219e6i	−0.101036	−	0.101036i
$979$	−1.08016e7	+	4.78243e6i	−0.360188	+	0.159475i
$980$	−629135.	−	78821.4i	−0.0209256	−	0.00262168i
$981$		−	5.85039e6i		−	0.194094i
$982$	−2.01640e7	−	2.01640e7i	−0.667264	−	0.667264i
$983$	2.40841e7	−	2.40841e7i	0.794964	−	0.794964i	−0.187333	−	0.982297i	$-0.559984\pi$
$983$	2.40841e7	−	2.40841e7i	0.794964	−	0.794964i	0.982297	+	0.187333i	$0.0599843\pi$
$984$			857786.i			0.0282417i
$985$	3.95977e7	−	3.07803e7i	1.30041	−	1.01084i
$986$		−	3.75358e7i		−	1.22957i
$987$	360967.	−	360967.i	0.0117944	−	0.0117944i
$988$	66022.7	−	66022.7i	0.00215180	−	0.00215180i
$989$	−4.74134e7			−1.54138
$990$	1.26392e7	−	2.35132e7i	0.409855	−	0.762472i
$991$	−3.82954e7			−1.23869			−0.619345	−	0.785119i	$-0.712602\pi$
$991$	−3.82954e7			−1.23869			−0.619345	+	0.785119i	$0.712602\pi$
$992$	1.42104e6	−	1.42104e6i	0.0458487	−	0.0458487i
$993$	−2.74200e6	+	2.74200e6i	−0.0882458	+	0.0882458i
$994$		−	712750.i		−	0.0228808i
$995$	1.31021e6	−	1.04578e7i	0.0419551	−	0.334876i
$996$		−	472175.i		−	0.0150819i
$997$	−3.55877e7	+	3.55877e7i	−1.13387	+	1.13387i	−0.144339	+	0.989528i	$0.546106\pi$
$997$	−3.55877e7	+	3.55877e7i	−1.13387	+	1.13387i	−0.989528	+	0.144339i	$0.953894\pi$
$998$	2.20182e7	+	2.20182e7i	0.699771	+	0.699771i
$999$			2.58108e7i			0.818252i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.6.e.b.32.9	✓	52
5.3	odd	4	inner	55.6.e.b.43.18	yes	52
11.10	odd	2	inner	55.6.e.b.32.18	yes	52
55.43	even	4	inner	55.6.e.b.43.9	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.6.e.b.32.9	✓	52	1.1	even	1	trivial
55.6.e.b.32.18	yes	52	11.10	odd	2	inner
55.6.e.b.43.9	yes	52	55.43	even	4	inner
55.6.e.b.43.18	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+(-4.04500 + 4.04500i) q^{2} +(-4.18256 + 4.18256i) q^{3} -0.723976i q^{4} +(-55.4681 - 6.94934i) q^{5} -33.8369i q^{6} +(23.8782 - 23.8782i) q^{7} +(-126.511 - 126.511i) q^{8} +208.012i q^{9} +(252.478 - 196.258i) q^{10} +(-162.470 - 366.953i) q^{11} +(3.02807 + 3.02807i) q^{12} +(251.625 + 251.625i) q^{13} +193.175i q^{14} +(261.065 - 202.933i) q^{15} +1046.64 q^{16} +(1136.35 - 1136.35i) q^{17} +(-841.409 - 841.409i) q^{18} +362.422 q^{19} +(-5.03115 + 40.1576i) q^{20} +199.744i q^{21} +(2141.51 + 827.134i) q^{22} +(2137.53 - 2137.53i) q^{23} +1058.28 q^{24} +(3028.41 + 770.933i) q^{25} -2035.65 q^{26} +(-1886.39 - 1886.39i) q^{27} +(-17.2873 - 17.2873i) q^{28} -4083.07 q^{29} +(-235.144 + 1876.87i) q^{30} -7668.76 q^{31} +(-185.303 + 185.303i) q^{32} +(2214.34 + 855.263i) q^{33} +9193.05i q^{34} +(-1490.42 + 1158.54i) q^{35} +150.596 q^{36} +(-6841.32 - 6841.32i) q^{37} +(-1466.00 + 1466.00i) q^{38} -2104.88 q^{39} +(6138.17 + 7896.51i) q^{40} +810.545i q^{41} +(-807.965 - 807.965i) q^{42} +(-11090.7 - 11090.7i) q^{43} +(-265.665 + 117.624i) q^{44} +(1445.55 - 11538.0i) q^{45} +17292.6i q^{46} +(-1807.14 - 1807.14i) q^{47} +(-4377.65 + 4377.65i) q^{48} +15666.7i q^{49} +(-15368.3 + 9131.50i) q^{50} +9505.70i q^{51} +(182.171 - 182.171i) q^{52} +(15473.0 - 15473.0i) q^{53} +15260.9 q^{54} +(6461.81 + 21483.2i) q^{55} -6041.74 q^{56} +(-1515.85 + 1515.85i) q^{57} +(16516.0 - 16516.0i) q^{58} -17175.6i q^{59} +(-146.918 - 189.005i) q^{60} -44695.7i q^{61} +(31020.1 - 31020.1i) q^{62} +(4966.97 + 4966.97i) q^{63} +31993.5i q^{64} +(-12208.5 - 15705.8i) q^{65} +(-12416.5 + 5497.47i) q^{66} +(34101.9 + 34101.9i) q^{67} +(-822.690 - 822.690i) q^{68} +17880.7i q^{69} +(1342.44 - 10715.0i) q^{70} -3689.67 q^{71} +(26315.9 - 26315.9i) q^{72} +(-40158.6 - 40158.6i) q^{73} +55346.2 q^{74} +(-15891.0 + 9442.05i) q^{75} -262.385i q^{76} +(-12641.7 - 4882.70i) q^{77} +(8514.21 - 8514.21i) q^{78} +44415.1 q^{79} +(-58055.3 - 7273.48i) q^{80} -34767.2 q^{81} +(-3278.65 - 3278.65i) q^{82} +(-77966.2 - 77966.2i) q^{83} +144.610 q^{84} +(-70928.0 + 55134.2i) q^{85} +89723.8 q^{86} +(17077.7 - 17077.7i) q^{87} +(-25869.5 + 66978.0i) q^{88} -29435.8i q^{89} +(40824.1 + 52518.6i) q^{90} +12016.7 q^{91} +(-1547.52 - 1547.52i) q^{92} +(32075.0 - 32075.0i) q^{93} +14619.8 q^{94} +(-20102.9 - 2518.59i) q^{95} -1550.08i q^{96} +(84004.1 + 84004.1i) q^{97} +(-63371.6 - 63371.6i) q^{98} +(76330.8 - 33795.7i) 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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