LMFDB - Embedded newform 55.6.e.b.32.13

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			32.13
Character	$\chi$	$=$	55.32
Dual form			55.6.e.b.43.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.819850 + 0.819850i) q^{2} +(-2.25487 + 2.25487i) q^{3} +30.6557i q^{4} +(5.74279 - 55.6059i) q^{5} -3.69731i q^{6} +(-88.0749 + 88.0749i) q^{7} +(-51.3683 - 51.3683i) q^{8} +232.831i q^{9} +(40.8803 + 50.2967i) q^{10} +(68.0926 - 395.493i) q^{11} +(-69.1247 - 69.1247i) q^{12} +(-741.664 - 741.664i) q^{13} -144.416i q^{14} +(112.435 + 138.334i) q^{15} -896.754 q^{16} +(-805.641 + 805.641i) q^{17} +(-190.887 - 190.887i) q^{18} -1851.56 q^{19} +(1704.64 + 176.049i) q^{20} -397.196i q^{21} +(268.419 + 380.070i) q^{22} +(-561.188 + 561.188i) q^{23} +231.658 q^{24} +(-3059.04 - 638.666i) q^{25} +1216.11 q^{26} +(-1072.94 - 1072.94i) q^{27} +(-2700.00 - 2700.00i) q^{28} +3983.79 q^{29} +(-205.593 - 21.2329i) q^{30} +4011.45 q^{31} +(2378.99 - 2378.99i) q^{32} +(738.246 + 1045.33i) q^{33} -1321.01i q^{34} +(4391.69 + 5403.28i) q^{35} -7137.60 q^{36} +(5642.57 + 5642.57i) q^{37} +(1518.00 - 1518.00i) q^{38} +3344.72 q^{39} +(-3151.38 + 2561.38i) q^{40} +14226.7i q^{41} +(325.641 + 325.641i) q^{42} +(3129.47 + 3129.47i) q^{43} +(12124.1 + 2087.42i) q^{44} +(12946.8 + 1337.10i) q^{45} -920.180i q^{46} +(-18434.0 - 18434.0i) q^{47} +(2022.07 - 2022.07i) q^{48} +1292.61i q^{49} +(3031.56 - 1984.34i) q^{50} -3633.24i q^{51} +(22736.2 - 22736.2i) q^{52} +(-2404.01 + 2404.01i) q^{53} +1759.30 q^{54} +(-21600.7 - 6057.58i) q^{55} +9048.51 q^{56} +(4175.04 - 4175.04i) q^{57} +(-3266.11 + 3266.11i) q^{58} +22820.4i q^{59} +(-4240.71 + 3446.77i) q^{60} +37872.4i q^{61} +(-3288.79 + 3288.79i) q^{62} +(-20506.6 - 20506.6i) q^{63} -24795.3i q^{64} +(-45500.1 + 36981.7i) q^{65} +(-1462.26 - 251.760i) q^{66} +(5682.77 + 5682.77i) q^{67} +(-24697.5 - 24697.5i) q^{68} -2530.82i q^{69} +(-8030.41 - 829.353i) q^{70} -3271.14 q^{71} +(11960.1 - 11960.1i) q^{72} +(-25842.3 - 25842.3i) q^{73} -9252.11 q^{74} +(8337.86 - 5457.64i) q^{75} -56760.9i q^{76} +(28835.7 + 40830.2i) q^{77} +(-2742.16 + 2742.16i) q^{78} +41319.9 q^{79} +(-5149.87 + 49864.8i) q^{80} -51739.3 q^{81} +(-11663.8 - 11663.8i) q^{82} +(-67888.9 - 67888.9i) q^{83} +12176.3 q^{84} +(40171.8 + 49425.0i) q^{85} -5131.39 q^{86} +(-8982.93 + 8982.93i) q^{87} +(-23813.6 + 16818.0i) q^{88} -86508.1i q^{89} +(-11710.6 + 9518.20i) q^{90} +130644. q^{91} +(-17203.6 - 17203.6i) q^{92} +(-9045.31 + 9045.31i) q^{93} +30226.3 q^{94} +(-10633.1 + 102958. i) q^{95} +10728.6i q^{96} +(-24593.2 - 24593.2i) q^{97} +(-1059.75 - 1059.75i) q^{98} +(92083.0 + 15854.1i) 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 $

$2$	−0.819850	+	0.819850i	−0.144930	+	0.144930i	−0.775849	−	0.630919i	$-0.782678\pi$
$2$	−0.819850	+	0.819850i	−0.144930	+	0.144930i	0.630919	+	0.775849i	$0.282678\pi$
$3$	−2.25487	+	2.25487i	−0.144650	+	0.144650i	−0.775723	−	0.631073i	$-0.782615\pi$
$3$	−2.25487	+	2.25487i	−0.144650	+	0.144650i	0.631073	+	0.775723i	$0.282615\pi$
$4$			30.6557i			0.957990i
$5$	5.74279	−	55.6059i	0.102730	−	0.994709i
$5$	5.74279	−	55.6059i	0.102730	−	0.994709i
$6$		−	3.69731i		−	0.0419284i
$7$	−88.0749	+	88.0749i	−0.679371	+	0.679371i	−0.959858	−	0.280487i	$-0.909504\pi$
$7$	−88.0749	+	88.0749i	−0.679371	+	0.679371i	0.280487	+	0.959858i	$0.409504\pi$
$8$	−51.3683	−	51.3683i	−0.283772	−	0.283772i
$9$			232.831i			0.958153i
$10$	40.8803	+	50.2967i	0.129275	+	0.159052i
$11$	68.0926	−	395.493i	0.169675	−	0.985500i
$11$	68.0926	−	395.493i	0.169675	−	0.985500i
$12$	−69.1247	−	69.1247i	−0.138573	−	0.138573i
$13$	−741.664	−	741.664i	−1.21716	−	1.21716i	−0.968621	−	0.248542i	$-0.920049\pi$
$13$	−741.664	−	741.664i	−1.21716	−	1.21716i	−0.248542	−	0.968621i	$-0.579951\pi$
$14$		−	144.416i		−	0.196923i
$15$	112.435	+	138.334i	0.129025	+	0.158745i
$16$	−896.754			−0.875736
$17$	−805.641	+	805.641i	−0.676113	+	0.676113i	−0.959118	−	0.283005i	$-0.908669\pi$
$17$	−805.641	+	805.641i	−0.676113	+	0.676113i	0.283005	+	0.959118i	$0.408669\pi$
$18$	−190.887	−	190.887i	−0.138865	−	0.138865i
$19$	−1851.56			−1.17667			−0.588334	−	0.808618i	$-0.700216\pi$
$19$	−1851.56			−1.17667			−0.588334	+	0.808618i	$0.700216\pi$
$20$	1704.64	+	176.049i	0.952922	+	0.0984145i
$21$		−	397.196i		−	0.196542i
$22$	268.419	+	380.070i	0.118238	+	0.167420i
$23$	−561.188	+	561.188i	−0.221202	+	0.221202i	−0.809004	−	0.587803i	$-0.799993\pi$
$23$	−561.188	+	561.188i	−0.221202	+	0.221202i	0.587803	+	0.809004i	$0.299993\pi$
$24$	231.658			0.0820954
$25$	−3059.04	−	638.666i	−0.978893	−	0.204373i
$26$	1216.11			0.352808
$27$	−1072.94	−	1072.94i	−0.283247	−	0.283247i
$28$	−2700.00	−	2700.00i	−0.650831	−	0.650831i
$29$	3983.79			0.879632			0.439816	−	0.898088i	$-0.355044\pi$
$29$	3983.79			0.879632			0.439816	+	0.898088i	$0.355044\pi$
$30$	−205.593	−	21.2329i	−0.0417066	−	0.00430731i
$31$	4011.45			0.749717			0.374859	−	0.927082i	$-0.377691\pi$
$31$	4011.45			0.749717			0.374859	+	0.927082i	$0.377691\pi$
$32$	2378.99	−	2378.99i	0.410693	−	0.410693i
$33$	738.246	+	1045.33i	0.118009	+	0.167096i
$34$		−	1321.01i		−	0.195979i
$35$	4391.69	+	5403.28i	0.605985	+	0.745569i
$36$	−7137.60			−0.917901
$37$	5642.57	+	5642.57i	0.677598	+	0.677598i	0.959456	−	0.281858i	$-0.0909507\pi$
$37$	5642.57	+	5642.57i	0.677598	+	0.677598i	−0.281858	+	0.959456i	$0.590951\pi$
$38$	1518.00	−	1518.00i	0.170535	−	0.170535i
$39$	3344.72			0.352126
$40$	−3151.38	+	2561.38i	−0.311423	+	0.253119i
$41$			14226.7i			1.32174i	0.750502	+	0.660868i	$0.229812\pi$
$41$			14226.7i			1.32174i	−0.750502	+	0.660868i	$0.770188\pi$
$42$	325.641	+	325.641i	0.0284849	+	0.0284849i
$43$	3129.47	+	3129.47i	0.258107	+	0.258107i	0.824284	−	0.566177i	$-0.191578\pi$
$43$	3129.47	+	3129.47i	0.258107	+	0.258107i	−0.566177	+	0.824284i	$0.691578\pi$
$44$	12124.1	+	2087.42i	0.944100	+	0.162547i
$45$	12946.8	+	1337.10i	0.953083	+	0.0984311i
$46$		−	920.180i		−	0.0641177i
$47$	−18434.0	−	18434.0i	−1.21724	−	1.21724i	−0.968595	−	0.248645i	$-0.920015\pi$
$47$	−18434.0	−	18434.0i	−1.21724	−	1.21724i	−0.248645	−	0.968595i	$-0.579985\pi$
$48$	2022.07	−	2022.07i	0.126675	−	0.126675i
$49$			1292.61i			0.0769093i
$50$	3031.56	−	1984.34i	0.171491	−	0.112251i
$51$		−	3633.24i		−	0.195600i
$52$	22736.2	−	22736.2i	1.16603	−	1.16603i
$53$	−2404.01	+	2404.01i	−0.117557	+	0.117557i	−0.763438	−	0.645881i	$-0.776490\pi$
$53$	−2404.01	+	2404.01i	−0.117557	+	0.117557i	0.645881	+	0.763438i	$0.276490\pi$
$54$	1759.30			0.0821022
$55$	−21600.7	−	6057.58i	−0.962855	−	0.270018i
$56$	9048.51			0.385573
$57$	4175.04	−	4175.04i	0.170205	−	0.170205i
$58$	−3266.11	+	3266.11i	−0.127485	+	0.127485i
$59$			22820.4i			0.853479i	0.904375	+	0.426739i	$0.140338\pi$
$59$			22820.4i			0.853479i	−0.904375	+	0.426739i	$0.859662\pi$
$60$	−4240.71	+	3446.77i	−0.152076	+	0.123605i
$61$			37872.4i			1.30316i	0.758579	+	0.651581i	$0.225894\pi$
$61$			37872.4i			1.30316i	−0.758579	+	0.651581i	$0.774106\pi$
$62$	−3288.79	+	3288.79i	−0.108657	+	0.108657i
$63$	−20506.6	−	20506.6i	−0.650941	−	0.650941i
$64$		−	24795.3i		−	0.756692i
$65$	−45500.1	+	36981.7i	−1.33576	+	1.08568i
$66$	−1462.26	−	251.760i	−0.0413204	−	0.00711420i
$67$	5682.77	+	5682.77i	0.154658	+	0.154658i	0.780195	−	0.625537i	$-0.215120\pi$
$67$	5682.77	+	5682.77i	0.154658	+	0.154658i	−0.625537	+	0.780195i	$0.715120\pi$
$68$	−24697.5	−	24697.5i	−0.647710	−	0.647710i
$69$		−	2530.82i		−	0.0639938i
$70$	−8030.41	−	829.353i	−0.195881	−	0.0202299i
$71$	−3271.14			−0.0770111			−0.0385056	−	0.999258i	$-0.512260\pi$
$71$	−3271.14			−0.0770111			−0.0385056	+	0.999258i	$0.512260\pi$
$72$	11960.1	−	11960.1i	0.271897	−	0.271897i
$73$	−25842.3	−	25842.3i	−0.567575	−	0.567575i	0.363873	−	0.931449i	$-0.381454\pi$
$73$	−25842.3	−	25842.3i	−0.567575	−	0.567575i	−0.931449	+	0.363873i	$0.881454\pi$
$74$	−9252.11			−0.196409
$75$	8337.86	−	5457.64i	0.171160	−	0.112034i
$76$		−	56760.9i		−	1.12724i
$77$	28835.7	+	40830.2i	0.554248	+	0.784793i
$78$	−2742.16	+	2742.16i	−0.0510337	+	0.0510337i
$79$	41319.9			0.744889			0.372445	−	0.928054i	$-0.378520\pi$
$79$	41319.9			0.744889			0.372445	+	0.928054i	$0.378520\pi$
$80$	−5149.87	+	49864.8i	−0.0899645	+	0.871103i
$81$	−51739.3			−0.876209
$82$	−11663.8	−	11663.8i	−0.191560	−	0.191560i
$83$	−67888.9	−	67888.9i	−1.08169	−	1.08169i	−0.996352	−	0.0853401i	$-0.972802\pi$
$83$	−67888.9	−	67888.9i	−1.08169	−	1.08169i	−0.0853401	−	0.996352i	$-0.527198\pi$
$84$	12176.3			0.188286
$85$	40171.8	+	49425.0i	0.603079	+	0.741993i
$86$	−5131.39			−0.0748151
$87$	−8982.93	+	8982.93i	−0.127239	+	0.127239i
$88$	−23813.6	+	16818.0i	−0.327807	+	0.231508i
$89$		−	86508.1i		−	1.15766i	−0.815447	−	0.578831i	$-0.803509\pi$
$89$		−	86508.1i		−	1.15766i	0.815447	−	0.578831i	$-0.196491\pi$
$90$	−11710.6	+	9518.20i	−0.152396	+	0.123865i
$91$	130644.			1.65381
$92$	−17203.6	−	17203.6i	−0.211909	−	0.211909i
$93$	−9045.31	+	9045.31i	−0.108447	+	0.108447i
$94$	30226.3			0.352830
$95$	−10633.1	+	102958.i	−0.120879	+	1.17044i
$96$			10728.6i			0.118814i
$97$	−24593.2	−	24593.2i	−0.265390	−	0.265390i	0.561849	−	0.827240i	$-0.310090\pi$
$97$	−24593.2	−	24593.2i	−0.265390	−	0.265390i	−0.827240	+	0.561849i	$0.810090\pi$
$98$	−1059.75	−	1059.75i	−0.0111465	−	0.0111465i
$99$	92083.0	+	15854.1i	0.944260	+	0.162575i
$100$	19578.8	−	93777.0i	0.195788	−	0.937770i
$101$			102376.i			0.998606i	0.866427	+	0.499303i	$0.166411\pi$
$101$			102376.i			0.998606i	−0.866427	+	0.499303i	$0.833589\pi$
$102$	2978.71	+	2978.71i	0.0283483	+	0.0283483i
$103$	−99062.9	+	99062.9i	−0.920064	+	0.920064i	−0.997033	−	0.0769694i	$-0.975476\pi$
$103$	−99062.9	+	99062.9i	−0.920064	+	0.920064i	0.0769694	+	0.997033i	$0.475476\pi$
$104$			76196.0i			0.690794i
$105$	−22086.4	−	2281.01i	−0.195502	−	0.0201908i
$106$		−	3941.86i		−	0.0340750i
$107$	489.464	−	489.464i	0.00413296	−	0.00413296i	−0.705037	−	0.709170i	$-0.749070\pi$
$107$	489.464	−	489.464i	0.00413296	−	0.00413296i	0.709170	+	0.705037i	$0.249070\pi$
$108$	32891.7	−	32891.7i	0.271348	−	0.271348i
$109$	134140.			1.08141			0.540706	−	0.841212i	$-0.318157\pi$
$109$	134140.			1.08141			0.540706	+	0.841212i	$0.318157\pi$
$110$	22675.6	−	12743.0i	0.178681	−	0.100413i
$111$	−25446.5			−0.196029
$112$	78981.5	−	78981.5i	0.594950	−	0.594950i
$113$	113964.	−	113964.i	0.839601	−	0.839601i	−0.149205	−	0.988806i	$-0.547671\pi$
$113$	113964.	−	113964.i	0.839601	−	0.839601i	0.988806	+	0.149205i	$0.0476715\pi$
$114$			6845.80i			0.0493358i
$115$	27982.6	+	34428.2i	0.197307	+	0.242756i
$116$			122126.i			0.842679i
$117$	172682.	−	172682.i	1.16623	−	1.16623i
$118$	−18709.3	−	18709.3i	−0.123695	−	0.123695i
$119$		−	141914.i		−	0.918663i
$120$	1330.36	−	12881.5i	0.00843367	−	0.0816610i
$121$	−151778.	−	53860.2i	−0.942421	−	0.334430i
$122$	−31049.7	−	31049.7i	−0.188868	−	0.188868i
$123$	−32079.4	−	32079.4i	−0.191189	−	0.191189i
$124$			122974.i			0.718222i
$125$	−53081.1	+	166433.i	−0.303854	+	0.952719i
$126$	33624.6			0.188682
$127$	−72970.4	+	72970.4i	−0.401455	+	0.401455i	−0.878746	−	0.477290i	$-0.841619\pi$
$127$	−72970.4	+	72970.4i	−0.401455	+	0.401455i	0.477290	+	0.878746i	$0.341619\pi$
$128$	96456.0	+	96456.0i	0.520361	+	0.520361i
$129$	−14113.1			−0.0746704
$130$	6983.84	−	67622.7i	0.0362440	−	0.350941i
$131$			170832.i			0.869741i	0.900493	+	0.434871i	$0.143206\pi$
$131$			170832.i			0.869741i	−0.900493	+	0.434871i	$0.856794\pi$
$132$	−32045.2	+	22631.4i	−0.160077	+	0.113052i
$133$	163076.	−	163076.i	0.799395	−	0.799395i
$134$	−9318.04			−0.0448294
$135$	−65823.4	+	53500.1i	−0.310847	+	0.252651i
$136$	82768.7			0.383724
$137$	145269.	+	145269.i	0.661258	+	0.661258i	0.955677	−	0.294418i	$-0.0951259\pi$
$137$	145269.	+	145269.i	0.661258	+	0.661258i	−0.294418	+	0.955677i	$0.595126\pi$
$138$	2074.89	+	2074.89i	0.00927464	+	0.00927464i
$139$	−361121.			−1.58532			−0.792659	−	0.609665i	$-0.791304\pi$
$139$	−361121.			−1.58532			−0.792659	+	0.609665i	$0.791304\pi$
$140$	−165641.	+	134630.i	−0.714248	+	0.580528i
$141$	83132.9			0.352148
$142$	2681.85	−	2681.85i	0.0111613	−	0.0111613i
$143$	−343824.	+	242821.i	−1.40604	+	0.992992i
$144$		−	208792.i		−	0.839089i
$145$	22878.0	−	221522.i	0.0903647	−	0.874978i
$146$	42373.6			0.164518
$147$	−2914.68	−	2914.68i	−0.0111249	−	0.0111249i
$148$	−172977.	+	172977.i	−0.649133	+	0.649133i
$149$	157044.			0.579505			0.289752	−	0.957102i	$-0.406427\pi$
$149$	157044.			0.579505			0.289752	+	0.957102i	$0.406427\pi$
$150$	−2361.35	+	11310.2i	−0.00856904	+	0.0410434i
$151$		−	406149.i		−	1.44958i	−0.688968	−	0.724792i	$-0.741936\pi$
$151$		−	406149.i		−	1.44958i	0.688968	−	0.724792i	$-0.258064\pi$
$152$	95111.5	+	95111.5i	0.333906	+	0.333906i
$153$	−187578.	−	187578.i	−0.647819	−	0.647819i
$154$	−57115.6	−	9833.68i	−0.194068	−	0.0334129i
$155$	23036.9	−	223061.i	0.0770185	−	0.745750i
$156$			102535.i			0.337333i
$157$	−294046.	−	294046.i	−0.952063	−	0.952063i	0.0468397	−	0.998902i	$-0.485085\pi$
$157$	−294046.	−	294046.i	−0.952063	−	0.952063i	−0.998902	+	0.0468397i	$0.985085\pi$
$158$	−33876.1	+	33876.1i	−0.107957	+	0.107957i
$159$		−	10841.5i		−	0.0340091i
$160$	−118624.	−	145948.i	−0.366330	−	0.450711i
$161$		−	98853.2i		−	0.300556i
$162$	42418.4	−	42418.4i	0.126989	−	0.126989i
$163$	321782.	−	321782.i	0.948620	−	0.948620i	−0.0501226	−	0.998743i	$-0.515961\pi$
$163$	321782.	−	321782.i	0.948620	−	0.948620i	0.998743	+	0.0501226i	$0.0159612\pi$
$164$	−436130.			−1.26621
$165$	62365.9	−	35047.7i	0.178335	−	0.100219i
$166$	111317.			0.313540
$167$	−285860.	+	285860.i	−0.793164	+	0.793164i	−0.982007	−	0.188843i	$-0.939526\pi$
$167$	−285860.	+	285860.i	−0.793164	+	0.793164i	0.188843	+	0.982007i	$0.439526\pi$
$168$	−20403.2	+	20403.2i	−0.0557733	+	0.0557733i
$169$			728838.i			1.96297i
$170$	−73455.9	−	7586.28i	−0.194942	−	0.0201329i
$171$		−	431101.i		−	1.12743i
$172$	−95936.1	+	95936.1i	−0.247264	+	0.247264i
$173$	427806.	+	427806.i	1.08675	+	1.08675i	0.995861	+	0.0908942i	$0.0289725\pi$
$173$	427806.	+	427806.i	1.08675	+	1.08675i	0.0908942	+	0.995861i	$0.471027\pi$
$174$		−	14729.3i		−	0.0368815i
$175$	325675.	−	213174.i	0.803877	−	0.526187i
$176$	−61062.3	+	354659.i	−0.148591	+	0.863038i
$177$	−51457.0	−	51457.0i	−0.123456	−	0.123456i
$178$	70923.7	+	70923.7i	0.167780	+	0.167780i
$179$		−	241635.i		−	0.563672i	−0.959463	−	0.281836i	$-0.909057\pi$
$179$		−	241635.i		−	0.563672i	0.959463	−	0.281836i	$-0.0909434\pi$
$180$	−40989.7	+	396893.i	−0.0942961	+	0.913045i
$181$	−632254.			−1.43448			−0.717241	−	0.696825i	$-0.754595\pi$
$181$	−632254.			−1.43448			−0.717241	+	0.696825i	$0.754595\pi$
$182$	−107108.	+	107108.i	−0.239687	+	0.239687i
$183$	−85397.4	−	85397.4i	−0.188503	−	0.188503i
$184$	57654.5			0.125542
$185$	346164.	−	281356.i	0.743623	−	0.604404i
$186$		−	14831.6i		−	0.0314344i
$187$	263767.	+	373483.i	0.551590	+	0.781029i
$188$	565108.	−	565108.i	1.16610	−	1.16610i
$189$	188998.			0.384860
$190$	−75692.4	−	93127.5i	−0.152114	−	0.187152i
$191$	−8107.14			−0.0160799			−0.00803997	−	0.999968i	$-0.502559\pi$
$191$	−8107.14			−0.0160799			−0.00803997	+	0.999968i	$0.502559\pi$
$192$	55910.2	+	55910.2i	0.109456	+	0.109456i
$193$	422534.	+	422534.i	0.816522	+	0.816522i	0.985602	−	0.169080i	$-0.0540797\pi$
$193$	422534.	+	422534.i	0.816522	+	0.816522i	−0.169080	+	0.985602i	$0.554080\pi$
$194$	40325.4			0.0769263
$195$	19208.0	−	185986.i	0.0361739	−	0.350263i
$196$	−39626.0			−0.0736783
$197$	−96838.2	+	96838.2i	−0.177779	+	0.177779i	−0.790387	−	0.612608i	$-0.790121\pi$
$197$	−96838.2	+	96838.2i	−0.177779	+	0.177779i	0.612608	+	0.790387i	$0.290121\pi$
$198$	−88492.2	+	62496.3i	−0.160414	+	0.113290i
$199$		−	377063.i		−	0.674965i	−0.941332	−	0.337482i	$-0.890425\pi$
$199$		−	377063.i		−	0.674965i	0.941332	−	0.337482i	$-0.109575\pi$
$200$	124330.	+	189945.i	0.219787	+	0.335778i
$201$	−25627.9			−0.0447427
$202$	−83932.9	−	83932.9i	−0.144728	−	0.144728i
$203$	−350872.	+	350872.i	−0.597597	+	0.597597i
$204$	111379.			0.187383
$205$	791090.	+	81701.0i	1.31474	+	0.135782i
$206$		−	162433.i		−	0.266690i
$207$	−130662.	−	130662.i	−0.211945	−	0.211945i
$208$	665090.	+	665090.i	1.06591	+	1.06591i
$209$	−126078.	+	732279.i	−0.199651	+	1.15961i
$210$	19977.6	−	16237.5i	0.0312605	−	0.0254080i
$211$		−	737422.i		−	1.14028i	−0.821549	−	0.570138i	$-0.806890\pi$
$211$		−	737422.i		−	1.14028i	0.821549	−	0.570138i	$-0.193110\pi$
$212$	−73696.6	−	73696.6i	−0.112618	−	0.112618i
$213$	7376.01	−	7376.01i	0.0111397	−	0.0111397i
$214$			802.574i			0.00119798i
$215$	191989.	−	156045.i	0.283257	−	0.230226i
$216$			110230.i			0.160755i
$217$	−353308.	+	353308.i	−0.509336	+	0.509336i
$218$	−109974.	+	109974.i	−0.156729	+	0.156729i
$219$	116542.			0.164200
$220$	185699.	−	662184.i	0.258675	−	0.922406i
$221$	1.19503e6			1.64588
$222$	20862.3	−	20862.3i	0.0284106	−	0.0284106i
$223$	16331.6	−	16331.6i	0.0219921	−	0.0219921i	−0.696025	−	0.718017i	$-0.745050\pi$
$223$	16331.6	−	16331.6i	0.0219921	−	0.0219921i	0.718017	+	0.696025i	$0.245050\pi$
$224$			419058.i			0.558026i
$225$	148701.	−	712240.i	0.195821	−	0.937929i
$226$			186867.i			0.243367i
$227$	−355915.	+	355915.i	−0.458439	+	0.458439i	−0.898143	−	0.439704i	$-0.855083\pi$
$227$	−355915.	+	355915.i	−0.458439	+	0.458439i	0.439704	+	0.898143i	$0.355083\pi$
$228$	127989.	+	127989.i	0.163055	+	0.163055i
$229$		−	1.50015e6i		−	1.89036i	−0.326544	−	0.945182i	$-0.605884\pi$
$229$		−	1.50015e6i		−	1.89036i	0.326544	−	0.945182i	$-0.394116\pi$
$230$	−51167.5	−	5284.40i	−0.0637785	−	0.00658682i
$231$	−157088.	−	27046.1i	−0.193692	−	0.0333483i
$232$	−204640.	−	204640.i	−0.249615	−	0.249615i
$233$	191449.	+	191449.i	0.231028	+	0.231028i	0.813122	−	0.582094i	$-0.197766\pi$
$233$	191449.	+	191449.i	0.231028	+	0.231028i	−0.582094	+	0.813122i	$0.697766\pi$
$234$			283147.i			0.338044i
$235$	−1.13091e6	+	919180.i	−1.33585	+	1.08575i
$236$	−699574.			−0.817625
$237$	−93171.1	+	93171.1i	−0.107748	+	0.107748i
$238$	116348.	+	116348.i	0.133142	+	0.133142i
$239$	−972477.			−1.10125			−0.550624	−	0.834754i	$-0.685610\pi$
$239$	−972477.			−1.10125			−0.550624	+	0.834754i	$0.685610\pi$
$240$	−100827.	−	124051.i	−0.112992	−	0.139019i
$241$		−	169545.i		−	0.188037i	−0.995570	−	0.0940186i	$-0.970029\pi$
$241$		−	169545.i		−	0.188037i	0.995570	−	0.0940186i	$-0.0299713\pi$
$242$	168592.	−	80277.7i	0.185054	−	0.0881164i
$243$	377390.	−	377390.i	0.409991	−	0.409991i
$244$	−1.16100e6			−1.24842
$245$	71877.0	+	7423.21i	0.0765024	+	0.00790090i
$246$	52600.6			0.0554183
$247$	1.37324e6	+	1.37324e6i	1.43220	+	1.43220i
$248$	−206061.	−	206061.i	−0.212749	−	0.212749i
$249$	306162.			0.312934
$250$	−92931.6	−	179969.i	−0.0940402	−	0.182115i
$251$	−550651.			−0.551686			−0.275843	−	0.961203i	$-0.588957\pi$
$251$	−550651.			−0.551686			−0.275843	+	0.961203i	$0.588957\pi$
$252$	628643.	−	628643.i	0.623596	−	0.623596i
$253$	183733.	+	260158.i	0.180462	+	0.255527i
$254$		−	119649.i		−	0.116366i
$255$	−202029.	−	20864.9i	−0.194565	−	0.0200940i
$256$	635291.			0.605860
$257$	−708471.	−	708471.i	−0.669097	−	0.669097i	0.288410	−	0.957507i	$-0.406873\pi$
$257$	−708471.	−	708471.i	−0.669097	−	0.669097i	−0.957507	+	0.288410i	$0.906873\pi$
$258$	11570.6	−	11570.6i	0.0108220	−	0.0108220i
$259$	−993937.			−0.920682
$260$	−1.13370e6	−	1.39484e6i	−1.04008	−	1.27965i
$261$			927549.i			0.842822i
$262$	−140056.	−	140056.i	−0.126052	−	0.126052i
$263$	−463210.	−	463210.i	−0.412942	−	0.412942i	0.469820	−	0.882762i	$-0.344319\pi$
$263$	−463210.	−	463210.i	−0.412942	−	0.412942i	−0.882762	+	0.469820i	$0.844319\pi$
$264$	15774.2	−	91618.9i	0.0139295	−	0.0809050i
$265$	119872.	+	147483.i	0.104858	+	0.129011i
$266$			267396.i			0.231713i
$267$	195065.	+	195065.i	0.167456	+	0.167456i
$268$	−174209.	+	174209.i	−0.148161	+	0.148161i
$269$			657951.i			0.554387i	0.960814	+	0.277193i	$0.0894043\pi$
$269$			657951.i			0.554387i	−0.960814	+	0.277193i	$0.910596\pi$
$270$	10103.3	−	97827.4i	0.00843437	−	0.0816678i
$271$		−	162774.i		−	0.134636i	−0.997732	−	0.0673181i	$-0.978556\pi$
$271$		−	162774.i		−	0.134636i	0.997732	−	0.0673181i	$-0.0214442\pi$
$272$	722461.	−	722461.i	0.592096	−	0.592096i
$273$	−294586.	+	294586.i	−0.239224	+	0.239224i
$274$	−238197.			−0.191673
$275$	−460886.	+	1.16634e6i	−0.367504	+	0.930022i
$276$	77583.9			0.0613054
$277$	−322956.	+	322956.i	−0.252897	+	0.252897i	−0.822157	−	0.569260i	$-0.807230\pi$
$277$	−322956.	+	322956.i	−0.252897	+	0.252897i	0.569260	+	0.822157i	$0.307230\pi$
$278$	296065.	−	296065.i	0.229761	−	0.229761i
$279$			933991.i			0.718343i
$280$	51963.7	−	503151.i	0.0396100	−	0.383533i
$281$		−	135801.i		−	0.102598i	−0.998683	−	0.0512988i	$-0.983664\pi$
$281$		−	135801.i		−	0.102598i	0.998683	−	0.0512988i	$-0.0163361\pi$
$282$	−68156.5	+	68156.5i	−0.0510369	+	0.0510369i
$283$	−1.20597e6	−	1.20597e6i	−0.895099	−	0.895099i	0.0998984	−	0.994998i	$-0.468148\pi$
$283$	−1.20597e6	−	1.20597e6i	−0.895099	−	0.895099i	−0.994998	+	0.0998984i	$0.968148\pi$
$284$		−	100279.i		−	0.0737759i
$285$	−208180.	−	256133.i	−0.151820	−	0.186790i
$286$	82807.8	−	480961.i	0.0598627	−	0.347692i
$287$	−1.25302e6	−	1.25302e6i	−0.897950	−	0.897950i
$288$	553902.	+	553902.i	0.393506	+	0.393506i
$289$			121742.i			0.0857427i
$290$	162858.	+	200371.i	0.113714	+	0.139907i
$291$	110909.			0.0767776
$292$	792213.	−	792213.i	0.543732	−	0.543732i
$293$	251556.	+	251556.i	0.171185	+	0.171185i	0.787500	−	0.616315i	$-0.211375\pi$
$293$	251556.	+	251556.i	0.171185	+	0.171185i	−0.616315	+	0.787500i	$0.711375\pi$
$294$	4779.20			0.00322468
$295$	1.26895e6	+	131053.i	0.848963	+	0.0876780i
$296$		−	579697.i		−	0.384567i
$297$	−497398.	+	351280.i	−0.327200	+	0.231080i
$298$	−128753.	+	128753.i	−0.0839878	+	0.0839878i
$299$	832426.			0.538478
$300$	167308.	+	255603.i	0.107328	+	0.163969i
$301$	−551256.			−0.350701
$302$	332981.	+	332981.i	0.210089	+	0.210089i
$303$	−230845.	−	230845.i	−0.144449	−	0.144449i
$304$	1.66039e6			1.03045
$305$	2.10593e6	+	217493.i	1.29627	+	0.133874i
$306$	307572.			0.187777
$307$	−1.73184e6	+	1.73184e6i	−1.04873	+	1.04873i	−0.0499766	+	0.998750i	$0.515915\pi$
$307$	−1.73184e6	+	1.73184e6i	−1.04873	+	1.04873i	−0.998750	+	0.0499766i	$0.984085\pi$
$308$	−1.25168e6	+	883979.i	−0.751824	+	0.530964i
$309$		−	446749.i		−	0.266175i
$310$	163989.	+	201763.i	0.0969195	+	0.119244i
$311$	750807.			0.440177			0.220088	−	0.975480i	$-0.429365\pi$
$311$	750807.			0.440177			0.220088	+	0.975480i	$0.429365\pi$
$312$	−171812.	−	171812.i	−0.0999235	−	0.0999235i
$313$	−15556.4	+	15556.4i	−0.00897526	+	0.00897526i	−0.711580	−	0.702605i	$-0.752020\pi$
$313$	−15556.4	+	15556.4i	−0.00897526	+	0.00897526i	0.702605	+	0.711580i	$0.252020\pi$
$314$	482146.			0.275966
$315$	−1.25805e6	+	1.02252e6i	−0.714369	+	0.580626i
$316$			1.26669e6i			0.713597i
$317$	1.39427e6	+	1.39427e6i	0.779289	+	0.779289i	0.979710	−	0.200421i	$-0.0642308\pi$
$317$	1.39427e6	+	1.39427e6i	0.779289	+	0.779289i	−0.200421	+	0.979710i	$0.564231\pi$
$318$	8888.38	+	8888.38i	0.00492896	+	0.00492896i
$319$	271266.	−	1.57556e6i	0.149252	−	0.866877i
$320$	−1.37877e6	−	142394.i	−0.752689	−	0.0777351i
$321$			2207.36i			0.00119567i
$322$	81044.8	+	81044.8i	0.0435597	+	0.0435597i
$323$	1.49169e6	−	1.49169e6i	0.795561	−	0.795561i
$324$		−	1.58610e6i		−	0.839400i
$325$	1.79510e6	+	2.74246e6i	0.942717	+	1.44023i
$326$			527626.i			0.274968i
$327$	−302468.	+	302468.i	−0.156426	+	0.156426i
$328$	730801.	−	730801.i	0.375072	−	0.375072i
$329$	3.24715e6			1.65391
$330$	−22396.8	+	79864.6i	−0.0113214	+	0.0403710i
$331$	−1.98487e6			−0.995779			−0.497889	−	0.867241i	$-0.665891\pi$
$331$	−1.98487e6			−0.995779			−0.497889	+	0.867241i	$0.665891\pi$
$332$	2.08118e6	−	2.08118e6i	1.03625	−	1.03625i
$333$	−1.31376e6	+	1.31376e6i	−0.649243	+	0.649243i
$334$		−	468725.i		−	0.229907i
$335$	348631.	−	283361.i	0.169728	−	0.137952i
$336$			356187.i			0.172119i
$337$	−120865.	+	120865.i	−0.0579729	+	0.0579729i	−0.735499	−	0.677526i	$-0.763052\pi$
$337$	−120865.	+	120865.i	−0.0579729	+	0.0579729i	0.677526	+	0.735499i	$0.263052\pi$
$338$	−597538.	−	597538.i	−0.284494	−	0.284494i
$339$			513950.i			0.242897i
$340$	−1.51516e6	+	1.23149e6i	−0.710822	+	0.577744i
$341$	273150.	−	1.58650e6i	0.127208	−	0.738846i
$342$	353438.	+	353438.i	0.163399	+	0.163399i
$343$	−1.59412e6	−	1.59412e6i	−0.731621	−	0.731621i
$344$		−	321511.i		−	0.146487i
$345$	−140728.	−	14533.9i	−0.0636552	−	0.00657409i
$346$	−701473.			−0.315007
$347$	1.39645e6	−	1.39645e6i	0.622591	−	0.622591i	−0.323602	−	0.946193i	$-0.604894\pi$
$347$	1.39645e6	−	1.39645e6i	0.622591	−	0.622591i	0.946193	+	0.323602i	$0.104894\pi$
$348$	−275378.	−	275378.i	−0.121894	−	0.121894i
$349$	3.13019e6			1.37565			0.687824	−	0.725878i	$-0.258566\pi$
$349$	3.13019e6			1.37565			0.687824	+	0.725878i	$0.258566\pi$
$350$	−92233.9	+	441776.i	−0.0402458	+	0.192767i
$351$			1.59152e6i			0.689516i
$352$	−778881.	−	1.10286e6i	−0.335054	−	0.474422i
$353$	−23224.5	+	23224.5i	−0.00991995	+	0.00991995i	−0.712049	−	0.702129i	$-0.752233\pi$
$353$	−23224.5	+	23224.5i	−0.00991995	+	0.00991995i	0.702129	+	0.712049i	$0.252233\pi$
$354$	84374.1			0.0357850
$355$	−18785.5	+	181895.i	−0.00791136	+	0.0766037i
$356$	2.65197e6			1.10903
$357$	319997.	+	319997.i	0.132885	+	0.132885i
$358$	198104.	+	198104.i	0.0816932	+	0.0816932i
$359$	690277.			0.282675			0.141338	−	0.989961i	$-0.454860\pi$
$359$	690277.			0.282675			0.141338	+	0.989961i	$0.454860\pi$
$360$	−596370.	−	733739.i	−0.242527	−	0.298391i
$361$	952181.			0.384549
$362$	518353.	−	518353.i	0.207900	−	0.207900i
$363$	463688.	−	220792.i	0.184697	−	0.0879460i
$364$			4.00498e6i			1.58434i
$365$	−1.58539e6	+	1.28858e6i	−0.622880	+	0.506265i
$366$	140026.			0.0546395
$367$	−84271.0	−	84271.0i	−0.0326597	−	0.0326597i	0.690588	−	0.723248i	$-0.257352\pi$
$367$	−84271.0	−	84271.0i	−0.0326597	−	0.0326597i	−0.723248	+	0.690588i	$0.757352\pi$
$368$	503247.	−	503247.i	0.193714	−	0.193714i
$369$	−3.31242e6			−1.26643
$370$	−53132.9	+	514472.i	−0.0201771	+	0.195370i
$371$		−	423466.i		−	0.159729i
$372$	−277290.	−	277290.i	−0.103891	−	0.103891i
$373$	−1.52634e6	−	1.52634e6i	−0.568042	−	0.568042i	0.363538	−	0.931579i	$-0.381569\pi$
$373$	−1.52634e6	−	1.52634e6i	−0.568042	−	0.568042i	−0.931579	+	0.363538i	$0.881569\pi$
$374$	−522449.	−	89950.9i	−0.193137	−	0.0332527i
$375$	−255594.	−	494977.i	−0.0938584	−	0.181763i
$376$			1.89385e6i			0.690837i
$377$	−2.95463e6	−	2.95463e6i	−1.07066	−	1.07066i
$378$	−154950.	+	154950.i	−0.0557779	+	0.0557779i
$379$			2.00045e6i			0.715368i	0.933843	+	0.357684i	$0.116433\pi$
$379$			2.00045e6i			0.715368i	−0.933843	+	0.357684i	$0.883567\pi$
$380$	−3.15624e6	−	325966.i	−1.12127	−	0.115801i
$381$		−	329078.i		−	0.116141i
$382$	6646.64	−	6646.64i	0.00233047	−	0.00233047i
$383$	−3.76908e6	+	3.76908e6i	−1.31292	+	1.31292i	−0.393665	+	0.919254i	$0.628793\pi$
$383$	−3.76908e6	+	3.76908e6i	−1.31292	+	1.31292i	−0.919254	+	0.393665i	$0.871207\pi$
$384$	−434992.			−0.150540
$385$	2.43600e6	−	1.36896e6i	0.837579	−	0.470694i
$386$	−692828.			−0.236678
$387$	−728638.	+	728638.i	−0.247306	+	0.247306i
$388$	753921.	−	753921.i	0.254242	−	0.254242i
$389$		−	4.53726e6i		−	1.52026i	−0.649768	−	0.760132i	$-0.725134\pi$
$389$		−	4.53726e6i		−	1.52026i	0.649768	−	0.760132i	$-0.274866\pi$
$390$	136733.	+	168228.i	0.0455210	+	0.0560064i
$391$		−	904232.i		−	0.299115i
$392$	66399.3	−	66399.3i	0.0218247	−	0.0218247i
$393$	−385204.	−	385204.i	−0.125808	−	0.125808i
$394$		−	158786.i		−	0.0515312i
$395$	237291.	−	2.29763e6i	0.0765225	−	0.740948i
$396$	−486017.	+	2.82287e6i	−0.155745	+	0.904592i
$397$	3.97395e6	+	3.97395e6i	1.26545	+	1.26545i	0.948412	+	0.317041i	$0.102689\pi$
$397$	3.97395e6	+	3.97395e6i	1.26545	+	1.26545i	0.317041	+	0.948412i	$0.397311\pi$
$398$	309135.	+	309135.i	0.0978228	+	0.0978228i
$399$			735432.i			0.231265i
$400$	2.74321e6	+	572726.i	0.857252	+	0.178977i
$401$	185273.			0.0575374			0.0287687	−	0.999586i	$-0.490841\pi$
$401$	185273.			0.0575374			0.0287687	+	0.999586i	$0.490841\pi$
$402$	21011.0	−	21011.0i	0.00648457	−	0.00648457i
$403$	−2.97515e6	−	2.97515e6i	−0.912528	−	0.912528i
$404$	−3.13840e6			−0.956655
$405$	−297128.	+	2.87701e6i	−0.0900131	+	0.871573i
$406$		−	575324.i		−	0.173220i
$407$	2.61581e6	−	1.84738e6i	0.782745	−	0.552802i
$408$	−186633.	+	186633.i	−0.0555058	+	0.0555058i
$409$	2.72097e6			0.804295			0.402148	−	0.915575i	$-0.368264\pi$
$409$	2.72097e6			0.804295			0.402148	+	0.915575i	$0.368264\pi$
$410$	−715557.	+	581592.i	−0.210225	+	0.170867i
$411$	−655126.			−0.191302
$412$	−3.03684e6	−	3.03684e6i	−0.881413	−	0.881413i
$413$	−2.00990e6	−	2.00990e6i	−0.579829	−	0.579829i
$414$	214246.			0.0614346
$415$	−4.16490e6	+	3.38515e6i	−1.18709	+	0.964847i
$416$	−3.52882e6			−0.999761
$417$	814283.	−	814283.i	0.229316	−	0.229316i
$418$	−496994.	−	703723.i	−0.139127	−	0.196998i
$419$			3.36223e6i			0.935604i	0.883833	+	0.467802i	$0.154954\pi$
$419$			3.36223e6i			0.935604i	−0.883833	+	0.467802i	$0.845046\pi$
$420$	69925.9	−	677075.i	0.0193426	−	0.187290i
$421$	−798459.			−0.219557			−0.109778	−	0.993956i	$-0.535014\pi$
$421$	−798459.			−0.219557			−0.109778	+	0.993956i	$0.535014\pi$
$422$	604576.	+	604576.i	0.165261	+	0.165261i
$423$	4.29202e6	−	4.29202e6i	1.16630	−	1.16630i
$424$	246980.			0.0667186
$425$	2.97902e6	−	1.94995e6i	0.800022	−	0.523663i
$426$			12094.4i			0.00322895i
$427$	−3.33561e6	−	3.33561e6i	−0.885330	−	0.885330i
$428$	15004.9	+	15004.9i	0.00395934	+	0.00395934i
$429$	227750.	−	1.32281e6i	0.0597469	−	0.347020i
$430$	−29468.5	+	285336.i	−0.00768576	+	0.0744192i
$431$		−	3.94706e6i		−	1.02348i	−0.859139	−	0.511742i	$-0.829000\pi$
$431$		−	3.94706e6i		−	1.02348i	0.859139	−	0.511742i	$-0.171000\pi$
$432$	962162.	+	962162.i	0.248050	+	0.248050i
$433$	1.70841e6	−	1.70841e6i	0.437897	−	0.437897i	−0.453407	−	0.891304i	$-0.649792\pi$
$433$	1.70841e6	−	1.70841e6i	0.437897	−	0.437897i	0.891304	+	0.453407i	$0.149792\pi$
$434$		−	579320.i		−	0.147637i
$435$	447917.	+	551091.i	0.113494	+	0.139637i
$436$			4.11214e6i			1.03598i
$437$	1.03907e6	−	1.03907e6i	0.260281	−	0.260281i
$438$	−95547.0	+	95547.0i	−0.0237975	+	0.0237975i
$439$	−678707.			−0.168082			−0.0840409	−	0.996462i	$-0.526783\pi$
$439$	−678707.			−0.168082			−0.0840409	+	0.996462i	$0.526783\pi$
$440$	798423.	+	1.42076e6i	0.196608	+	0.349855i
$441$	−300961.			−0.0736908
$442$	−979745.	+	979745.i	−0.238538	+	0.238538i
$443$	−1.67407e6	+	1.67407e6i	−0.405289	+	0.405289i	−0.880092	−	0.474803i	$-0.842519\pi$
$443$	−1.67407e6	+	1.67407e6i	−0.405289	+	0.405289i	0.474803	+	0.880092i	$0.342519\pi$
$444$		−	780081.i		−	0.187794i
$445$	−4.81036e6	−	496798.i	−1.15154	−	0.118927i
$446$			26779.0i			0.00637466i
$447$	−354115.	+	354115.i	−0.0838255	+	0.0838255i
$448$	2.18384e6	+	2.18384e6i	0.514075	+	0.514075i
$449$			1.54007e6i			0.360515i	0.983619	+	0.180258i	$0.0576931\pi$
$449$			1.54007e6i			0.360515i	−0.983619	+	0.180258i	$0.942307\pi$
$450$	462017.	+	705842.i	0.107554	+	0.164315i
$451$	5.62656e6	+	968733.i	1.30257	+	0.224266i
$452$	3.49366e6	+	3.49366e6i	0.804330	+	0.804330i
$453$	915815.	+	915815.i	0.209683	+	0.209683i
$454$		−	583594.i		−	0.132884i
$455$	750261.	−	7.26458e6i	0.169896	−	1.64506i
$456$	−428929.			−0.0965991
$457$	−2.37478e6	+	2.37478e6i	−0.531904	+	0.531904i	−0.921139	−	0.389235i	$-0.872739\pi$
$457$	−2.37478e6	+	2.37478e6i	−0.531904	+	0.531904i	0.389235	+	0.921139i	$0.372739\pi$
$458$	1.22990e6	+	1.22990e6i	0.273971	+	0.273971i
$459$	1.72881e6			0.383014
$460$	−1.05542e6	+	857826.i	−0.232558	+	0.189019i
$461$			4.89233e6i			1.07217i	0.844164	+	0.536084i	$0.180097\pi$
$461$			4.89233e6i			1.07217i	−0.844164	+	0.536084i	$0.819903\pi$
$462$	150962.	−	106615.i	0.0329051	−	0.0232387i
$463$	−5.39140e6	+	5.39140e6i	−1.16882	+	1.16882i	−0.186338	+	0.982486i	$0.559662\pi$
$463$	−5.39140e6	+	5.39140e6i	−1.16882	+	1.16882i	−0.982486	+	0.186338i	$0.940338\pi$
$464$	−3.57247e6			−0.770325
$465$	451028.	+	554919.i	0.0967322	+	0.119014i
$466$	−313919.			−0.0669659
$467$	692307.	+	692307.i	0.146895	+	0.146895i	0.776729	−	0.629835i	$-0.216877\pi$
$467$	692307.	+	692307.i	0.146895	+	0.146895i	−0.629835	+	0.776729i	$0.716877\pi$
$468$	5.29370e6	+	5.29370e6i	1.11724	+	1.11724i
$469$	−1.00102e6			−0.210141
$470$	173583.	−	1.68076e6i	0.0362462	−	0.350963i
$471$	1.32607e6			0.275432
$472$	1.17224e6	−	1.17224e6i	0.242194	−	0.242194i
$473$	1.45078e6	−	1.02459e6i	0.298159	−	0.210570i
$474$		−	152773.i		−	0.0312320i
$475$	5.66400e6	+	1.18253e6i	1.15183	+	0.240480i
$476$	4.35046e6			0.880071
$477$	−559729.	−	559729.i	−0.112637	−	0.112637i
$478$	797285.	−	797285.i	0.159604	−	0.159604i
$479$	6.45641e6			1.28574			0.642869	−	0.765976i	$-0.277744\pi$
$479$	6.45641e6			1.28574			0.642869	+	0.765976i	$0.277744\pi$
$480$	596575.	+	61612.2i	0.118185	+	0.0122057i
$481$		−	8.36978e6i		−	1.64950i
$482$	139002.	+	139002.i	0.0272523	+	0.0272523i
$483$	222901.	+	222901.i	0.0434755	+	0.0434755i
$484$	1.65112e6	−	4.65285e6i	0.320380	−	0.902830i
$485$	−1.50876e6	+	1.22629e6i	−0.291250	+	0.236723i
$486$			618806.i			0.118840i
$487$	1.03959e6	+	1.03959e6i	0.198627	+	0.198627i	0.799411	−	0.600784i	$-0.205145\pi$
$487$	1.03959e6	+	1.03959e6i	0.198627	+	0.198627i	−0.600784	+	0.799411i	$0.705145\pi$
$488$	1.94544e6	−	1.94544e6i	0.369801	−	0.369801i
$489$			1.45115e6i			0.274436i
$490$	−65014.3	+	52842.4i	−0.0122326	+	0.00994243i
$491$		−	2.84028e6i		−	0.531689i	−0.964016	−	0.265844i	$-0.914349\pi$
$491$		−	2.84028e6i		−	0.531689i	0.964016	−	0.265844i	$-0.0856507\pi$
$492$	983417.	−	983417.i	0.183158	−	0.183158i
$493$	−3.20950e6	+	3.20950e6i	−0.594730	+	0.594730i
$494$	−2.25170e6			−0.415138
$495$	1.41039e6	−	5.02931e6i	0.258718	−	0.922562i
$496$	−3.59728e6			−0.656554
$497$	288106.	−	288106.i	0.0523192	−	0.0523192i
$498$	−251007.	+	251007.i	−0.0453536	+	0.0453536i
$499$		−	3.97737e6i		−	0.715064i	−0.933901	−	0.357532i	$-0.883618\pi$
$499$		−	3.97737e6i		−	0.715064i	0.933901	−	0.357532i	$-0.116382\pi$
$500$	−5.10212e6	−	1.62724e6i	−0.912695	−	0.291089i
$501$		−	1.28916e6i		−	0.229463i
$502$	451451.	−	451451.i	0.0799560	−	0.0799560i
$503$	6.10079e6	+	6.10079e6i	1.07514	+	1.07514i	0.996937	+	0.0782056i	$0.0249191\pi$
$503$	6.10079e6	+	6.10079e6i	1.07514	+	1.07514i	0.0782056	+	0.996937i	$0.475081\pi$
$504$			2.10677e6i			0.369438i
$505$	5.69271e6	+	587923.i	0.993323	+	0.102587i
$506$	−363924.	−	62657.4i	−0.0631880	−	0.0108792i
$507$	−1.64344e6	−	1.64344e6i	−0.283944	−	0.283944i
$508$	−2.23696e6	−	2.23696e6i	−0.384590	−	0.384590i
$509$		−	1.28443e6i		−	0.219743i	−0.993946	−	0.109871i	$-0.964956\pi$
$509$		−	1.28443e6i		−	0.219743i	0.993946	−	0.109871i	$-0.0350439\pi$
$510$	182740.	−	148528.i	0.0311106	−	0.0252861i
$511$	4.55211e6			0.771189
$512$	−3.60744e6	+	3.60744e6i	−0.608168	+	0.608168i
$513$	1.98661e6	+	1.98661e6i	0.333288	+	0.333288i
$514$	1.16168e6			0.193945
$515$	4.93959e6	+	6.07738e6i	0.820678	+	1.00971i
$516$		−	432647.i		−	0.0715336i
$517$	−8.54575e6	+	6.03531e6i	−1.40612	+	0.993054i
$518$	814879.	−	814879.i	0.133435	−	0.133435i
$519$	−1.92930e6			−0.314399
$520$	4.23695e6	+	437577.i	0.687139	+	0.0709654i
$521$	−6.78721e6			−1.09546			−0.547731	−	0.836655i	$-0.684508\pi$
$521$	−6.78721e6			−1.09546			−0.547731	+	0.836655i	$0.684508\pi$
$522$	−760451.	−	760451.i	−0.122150	−	0.122150i
$523$	−2.29263e6	−	2.29263e6i	−0.366506	−	0.366506i	0.499695	−	0.866201i	$-0.333445\pi$
$523$	−2.29263e6	−	2.29263e6i	−0.366506	−	0.366506i	−0.866201	+	0.499695i	$0.833445\pi$
$524$	−5.23696e6			−0.833204
$525$	−253675.	+	1.21504e6i	−0.0401680	+	0.192394i
$526$	759526.			0.119696
$527$	−3.23179e6	+	3.23179e6i	−0.506893	+	0.506893i
$528$	−662024.	−	937400.i	−0.103345	−	0.146332i
$529$			5.80648e6i			0.902139i
$530$	−219191.	−	22637.2i	−0.0338947	−	0.00350053i
$531$	−5.31329e6			−0.817763
$532$	4.99921e6	+	4.99921e6i	0.765813	+	0.765813i
$533$	1.05514e7	−	1.05514e7i	1.60877	−	1.60877i
$534$	−319848.			−0.0485389
$535$	−24406.2	−	30028.0i	−0.00368652	−	0.00453568i
$536$		−	583828.i		−	0.0877755i
$537$	544855.	+	544855.i	0.0815353	+	0.0815353i
$538$	−539421.	−	539421.i	−0.0803475	−	0.0803475i
$539$	511219.	+	88017.4i	0.0757941	+	0.0130496i
$540$	−1.64008e6	−	2.01786e6i	−0.242037	−	0.297788i
$541$			2.13626e6i			0.313805i	0.987614	+	0.156903i	$0.0501509\pi$
$541$			2.13626e6i			0.313805i	−0.987614	+	0.156903i	$0.949849\pi$
$542$	133450.	+	133450.i	0.0195129	+	0.0195129i
$543$	1.42565e6	−	1.42565e6i	0.207498	−	0.207498i
$544$			3.83322e6i			0.555350i
$545$	770336.	−	7.45896e6i	0.111094	−	1.07569i
$546$		−	483032.i		−	0.0693417i
$547$	−3.51247e6	+	3.51247e6i	−0.501932	+	0.501932i	−0.912038	−	0.410106i	$-0.865492\pi$
$547$	−3.51247e6	+	3.51247e6i	−0.501932	+	0.501932i	0.410106	+	0.912038i	$0.365492\pi$
$548$	−4.45332e6	+	4.45332e6i	−0.633479	+	0.633479i
$549$	−8.81787e6			−1.24863
$550$	−578366.	−	1.33408e6i	−0.0815260	−	0.188051i
$551$	−7.37622e6			−1.03504
$552$	−130004.	+	130004.i	−0.0181597	+	0.0181597i
$553$	−3.63925e6	+	3.63925e6i	−0.506056	+	0.506056i
$554$		−	529550.i		−	0.0733049i
$555$	−146134.	+	1.41498e6i	−0.0201381	+	0.194992i
$556$		−	1.10704e7i		−	1.51872i
$557$	−1.23335e6	+	1.23335e6i	−0.168442	+	0.168442i	−0.786294	−	0.617852i	$-0.788003\pi$
$557$	−1.23335e6	+	1.23335e6i	−0.168442	+	0.168442i	0.617852	+	0.786294i	$0.288003\pi$
$558$	−765732.	−	765732.i	−0.104110	−	0.104110i
$559$		−	4.64203e6i		−	0.628317i
$560$	−3.93827e6	−	4.84542e6i	−0.530683	−	0.652921i
$561$	−1.43692e6	−	247396.i	−0.192764	−	0.0331884i
$562$	111336.	+	111336.i	0.0148695	+	0.0148695i
$563$	4.59650e6	+	4.59650e6i	0.611161	+	0.611161i	0.943249	−	0.332087i	$-0.107753\pi$
$563$	4.59650e6	+	4.59650e6i	0.611161	+	0.611161i	−0.332087	+	0.943249i	$0.607753\pi$
$564$			2.54850e6i			0.337354i
$565$	−5.68262e6	−	6.99157e6i	−0.748907	−	0.921411i
$566$	1.97743e6			0.259454
$567$	4.55693e6	−	4.55693e6i	0.595271	−	0.595271i
$568$	168033.	+	168033.i	0.0218536	+	0.0218536i
$569$	−1.33573e7			−1.72957			−0.864785	−	0.502143i	$-0.832545\pi$
$569$	−1.33573e7			−1.72957			−0.864785	+	0.502143i	$0.832545\pi$
$570$	380667.	+	39314.0i	0.0490748	+	0.00506828i
$571$		−	9.47840e6i		−	1.21659i	−0.793711	−	0.608296i	$-0.791854\pi$
$571$		−	9.47840e6i		−	1.21659i	0.793711	−	0.608296i	$-0.208146\pi$
$572$	−7.44384e6	−	1.05402e7i	−0.951277	−	1.34697i
$573$	18280.6	−	18280.6i	0.00232597	−	0.00232597i
$574$	2.05457e6			0.260280
$575$	2.07511e6	−	1.35829e6i	0.261741	−	0.171325i
$576$	5.77312e6			0.725027
$577$	6.28321e6	+	6.28321e6i	0.785674	+	0.785674i	0.980782	−	0.195108i	$-0.0625057\pi$
$577$	6.28321e6	+	6.28321e6i	0.785674	+	0.785674i	−0.195108	+	0.980782i	$0.562506\pi$
$578$	−99810.5	−	99810.5i	−0.0124267	−	0.0124267i
$579$	−1.90552e6			−0.236220
$580$	6.79091e6	+	701342.i	0.838220	+	0.0865685i
$581$	1.19586e7			1.46974
$582$	−90928.7	+	90928.7i	−0.0111274	+	0.0111274i
$583$	787073.	+	1.11446e6i	0.0959056	+	0.135798i
$584$			2.65494e6i			0.322124i
$585$	−8.61049e6	−	1.05938e7i	−1.04025	−	1.27986i
$586$	−412476.			−0.0496198
$587$	4.86606e6	+	4.86606e6i	0.582884	+	0.582884i	0.935695	−	0.352811i	$-0.114774\pi$
$587$	4.86606e6	+	4.86606e6i	0.582884	+	0.582884i	−0.352811	+	0.935695i	$0.614774\pi$
$588$	89351.6	−	89351.6i	0.0106576	−	0.0106576i
$589$	−7.42745e6			−0.882168
$590$	−1.14779e6	+	932904.i	−0.135748	+	0.110333i
$591$		−	436716.i		−	0.0514316i
$592$	−5.05999e6	−	5.05999e6i	−0.593397	−	0.593397i
$593$	6.68231e6	+	6.68231e6i	0.780351	+	0.780351i	0.979890	−	0.199539i	$-0.0639445\pi$
$593$	6.68231e6	+	6.68231e6i	0.780351	+	0.780351i	−0.199539	+	0.979890i	$0.563945\pi$
$594$	119795.	−	695789.i	0.0139307	−	0.0809117i
$595$	−7.89124e6	−	814979.i	−0.913803	−	0.0943744i
$596$			4.81431e6i			0.555160i
$597$	850229.	+	850229.i	0.0976337	+	0.0976337i
$598$	−682464.	+	682464.i	−0.0780417	+	0.0780417i
$599$			9.73065e6i			1.10809i	0.832487	+	0.554045i	$0.186916\pi$
$599$			9.73065e6i			1.10809i	−0.832487	+	0.554045i	$0.813084\pi$
$600$	−708651.	−	147952.i	−0.0803626	−	0.0167781i
$601$		−	1.28500e6i		−	0.145117i	−0.997364	−	0.0725584i	$-0.976884\pi$
$601$		−	1.28500e6i		−	0.145117i	0.997364	−	0.0725584i	$-0.0231164\pi$
$602$	451947.	−	451947.i	0.0508272	−	0.0508272i
$603$	−1.32313e6	+	1.32313e6i	−0.148186	+	0.148186i
$604$	1.24508e7			1.38869
$605$	−3.86658e6	+	8.13044e6i	−0.429475	+	0.903079i
$606$	378516.			0.0418700
$607$	−2.93816e6	+	2.93816e6i	−0.323671	+	0.323671i	−0.850174	−	0.526502i	$-0.823503\pi$
$607$	−2.93816e6	+	2.93816e6i	−0.323671	+	0.323671i	0.526502	+	0.850174i	$0.323503\pi$
$608$	−4.40484e6	+	4.40484e6i	−0.483249	+	0.483249i
$609$		−	1.58234e6i		−	0.172885i
$610$	−1.90486e6	+	1.54823e6i	−0.207271	+	0.168466i
$611$			2.73437e7i			2.96316i
$612$	5.75034e6	−	5.75034e6i	0.620605	−	0.620605i
$613$	−2.21322e6	−	2.21322e6i	−0.237889	−	0.237889i	0.578087	−	0.815975i	$-0.303800\pi$
$613$	−2.21322e6	−	2.21322e6i	−0.237889	−	0.237889i	−0.815975	+	0.578087i	$0.803800\pi$
$614$		−	2.83970e6i		−	0.303985i
$615$	−1.96803e6	+	1.59958e6i	−0.209819	+	0.170537i
$616$	616136.	−	3.57862e6i	0.0654222	−	0.379983i
$617$	1.25927e6	+	1.25927e6i	0.133170	+	0.133170i	0.770550	−	0.637380i	$-0.219982\pi$
$617$	1.25927e6	+	1.25927e6i	0.133170	+	0.133170i	−0.637380	+	0.770550i	$0.719982\pi$
$618$	366267.	+	366267.i	0.0385768	+	0.0385768i
$619$		−	1.33220e7i		−	1.39747i	−0.715380	−	0.698735i	$-0.753746\pi$
$619$		−	1.33220e7i		−	1.39747i	0.715380	−	0.698735i	$-0.246254\pi$
$620$	6.83808e6	+	706213.i	0.714422	+	0.0737830i
$621$	1.20424e6			0.125310
$622$	−615549.	+	615549.i	−0.0637950	+	0.0637950i
$623$	7.61920e6	+	7.61920e6i	0.786482	+	0.786482i
$624$	−2.99939e6			−0.308369
$625$	8.94984e6	+	3.90741e6i	0.916463	+	0.400119i
$626$		−	25507.8i		−	0.00260158i
$627$	−1.36691e6	−	1.93548e6i	−0.138858	−	0.196617i
$628$	9.01417e6	−	9.01417e6i	0.912067	−	0.912067i
$629$	−9.09176e6			−0.916266
$630$	193099.	−	1.86973e6i	0.0193834	−	0.187684i
$631$	−9.67806e6			−0.967642			−0.483821	−	0.875167i	$-0.660751\pi$
$631$	−9.67806e6			−0.967642			−0.483821	+	0.875167i	$0.660751\pi$
$632$	−2.12253e6	−	2.12253e6i	−0.211379	−	0.211379i
$633$	1.66279e6	+	1.66279e6i	0.164941	+	0.164941i
$634$	−2.28618e6			−0.225885
$635$	3.63853e6	+	4.47664e6i	0.358090	+	0.440573i
$636$	332353.			0.0325804
$637$	958685.	−	958685.i	0.0936111	−	0.0936111i
$638$	1.06932e6	+	1.51412e6i	0.104006	+	0.147268i
$639$		−	761624.i		−	0.0737884i
$640$	5.91745e6	−	4.80960e6i	0.571064	−	0.464151i
$641$	−4.75399e6			−0.456997			−0.228498	−	0.973544i	$-0.573382\pi$
$641$	−4.75399e6			−0.456997			−0.228498	+	0.973544i	$0.573382\pi$
$642$	−1809.70	−	1809.70i	−0.000173288	−	0.000173288i
$643$	8.80966e6	−	8.80966e6i	0.840295	−	0.840295i	−0.148602	−	0.988897i	$-0.547477\pi$
$643$	8.80966e6	−	8.80966e6i	0.840295	−	0.840295i	0.988897	+	0.148602i	$0.0474774\pi$
$644$	3.03041e6			0.287930
$645$	−81048.7	+	784773.i	−0.00767090	+	0.0742754i
$646$			2.44593e6i			0.230602i
$647$	−4.90324e6	−	4.90324e6i	−0.460492	−	0.460492i	0.438325	−	0.898817i	$-0.355572\pi$
$647$	−4.90324e6	−	4.90324e6i	−0.460492	−	0.460492i	−0.898817	+	0.438325i	$0.855572\pi$
$648$	2.65776e6	+	2.65776e6i	0.248644	+	0.248644i
$649$	9.02529e6	+	1.55390e6i	0.841103	+	0.144814i
$650$	−3.72012e6	−	776686.i	−0.345361	−	0.0721045i
$651$		−	1.59333e6i		−	0.147351i
$652$	9.86444e6	+	9.86444e6i	0.908769	+	0.908769i
$653$	−9.36700e6	+	9.36700e6i	−0.859642	+	0.859642i	−0.991296	−	0.131653i	$-0.957971\pi$
$653$	−9.36700e6	+	9.36700e6i	−0.859642	+	0.859642i	0.131653	+	0.991296i	$0.457971\pi$
$654$		−	495957.i		−	0.0453419i
$655$	9.49925e6	+	981050.i	0.865140	+	0.0893486i
$656$		−	1.27579e7i		−	1.15749i
$657$	6.01688e6	−	6.01688e6i	0.543824	−	0.543824i
$658$	−2.66218e6	+	2.66218e6i	−0.239702	+	0.239702i
$659$	1.65001e7			1.48004			0.740020	−	0.672585i	$-0.234816\pi$
$659$	1.65001e7			1.48004			0.740020	+	0.672585i	$0.234816\pi$
$660$	1.07441e6	+	1.91187e6i	0.0960089	+	0.170844i
$661$	3.06152e6			0.272542			0.136271	−	0.990672i	$-0.456488\pi$
$661$	3.06152e6			0.272542			0.136271	+	0.990672i	$0.456488\pi$
$662$	1.62730e6	−	1.62730e6i	0.144319	−	0.144319i
$663$	−2.69464e6	+	2.69464e6i	−0.238077	+	0.238077i
$664$			6.97467e6i			0.613908i
$665$	−8.13149e6	−	1.00045e7i	−0.713044	−	0.877287i
$666$		−	2.15418e6i		−	0.188190i
$667$	−2.23565e6	+	2.23565e6i	−0.194576	+	0.194576i
$668$	−8.76325e6	−	8.76325e6i	−0.759843	−	0.759843i
$669$			73651.5i			0.00636233i
$670$	−53511.5	+	518138.i	−0.00460533	+	0.0445922i
$671$	1.49783e7	+	2.57883e6i	1.28427	+	0.221114i
$672$	−944923.	−	944923.i	−0.0807185	−	0.0807185i
$673$	−1.46489e6	−	1.46489e6i	−0.124672	−	0.124672i	0.642018	−	0.766690i	$-0.278098\pi$
$673$	−1.46489e6	−	1.46489e6i	−0.124672	−	0.124672i	−0.766690	+	0.642018i	$0.778098\pi$
$674$		−	198182.i		−	0.0168041i
$675$	2.59691e6	+	3.96741e6i	0.219381	+	0.335157i
$676$	−2.23430e7			−1.88051
$677$	1.01776e6	−	1.01776e6i	0.0853441	−	0.0853441i	−0.663146	−	0.748490i	$-0.730779\pi$
$677$	1.01776e6	−	1.01776e6i	0.0853441	−	0.0853441i	0.748490	+	0.663146i	$0.230779\pi$
$678$	−421362.	−	421362.i	−0.0352031	−	0.0352031i
$679$	4.33208e6			0.360597
$680$	475323.	−	4.60243e6i	0.0394200	−	0.381694i
$681$		−	1.60509e6i		−	0.132627i
$682$	1.07675e6	+	1.52463e6i	0.0886449	+	0.125518i
$683$	1.70844e7	−	1.70844e7i	1.40136	−	1.40136i	0.605548	−	0.795809i	$-0.292954\pi$
$683$	1.70844e7	−	1.70844e7i	1.40136	−	1.40136i	0.795809	−	0.605548i	$-0.207046\pi$
$684$	1.32157e7			1.08007
$685$	8.91206e6	−	7.24357e6i	0.725691	−	0.589829i
$686$	2.61388e6			0.212068
$687$	3.38264e6	+	3.38264e6i	0.273441	+	0.273441i
$688$	−2.80636e6	−	2.80636e6i	−0.226034	−	0.226034i
$689$	3.56594e6			0.286171
$690$	127292.	−	103460.i	0.0101784	−	0.00827279i
$691$	1.82141e6			0.145115			0.0725577	−	0.997364i	$-0.476884\pi$
$691$	1.82141e6			0.145115			0.0725577	+	0.997364i	$0.476884\pi$
$692$	−1.31147e7	+	1.31147e7i	−1.04110	+	1.04110i
$693$	−9.50655e6	+	6.71386e6i	−0.751951	+	0.531054i
$694$			2.28977e6i			0.180465i
$695$	−2.07384e6	+	2.00805e7i	−0.162860	+	1.57693i
$696$	922875.			0.0722137
$697$	−1.14616e7	−	1.14616e7i	−0.893643	−	0.893643i
$698$	−2.56629e6	+	2.56629e6i	−0.199373	+	0.199373i
$699$	−863388.			−0.0668364
$700$	6.53501e6	+	9.98380e6i	0.504082	+	0.770107i
$701$			1.47651e7i			1.13486i	0.823422	+	0.567429i	$0.192062\pi$
$701$			1.47651e7i			1.13486i	−0.823422	+	0.567429i	$0.807938\pi$
$702$	−1.30481e6	−	1.30481e6i	−0.0999318	−	0.0999318i
$703$	−1.04476e7	−	1.04476e7i	−0.797309	−	0.797309i
$704$	−9.80636e6	−	1.68838e6i	−0.745720	−	0.128392i
$705$	477414.	−	4.62268e6i	0.0361762	−	0.350285i
$706$		−	38081.2i		−	0.00287540i
$707$	−9.01675e6	−	9.01675e6i	−0.678425	−	0.678425i
$708$	1.57745e6	−	1.57745e6i	0.118270	−	0.118270i
$709$			1.67676e7i			1.25273i	0.779532	+	0.626363i	$0.215457\pi$
$709$			1.67676e7i			1.25273i	−0.779532	+	0.626363i	$0.784543\pi$
$710$	−133725.	−	164528.i	−0.00995560	−	0.0122488i
$711$			9.62056e6i			0.713717i
$712$	−4.44377e6	+	4.44377e6i	−0.328512	+	0.328512i
$713$	−2.25118e6	+	2.25118e6i	−0.165839	+	0.165839i
$714$	−524699.			−0.0385181
$715$	1.15278e7	+	2.05131e7i	0.843296	+	1.50061i
$716$	7.40748e6			0.539993
$717$	2.19281e6	−	2.19281e6i	0.159296	−	0.159296i
$718$	−565924.	+	565924.i	−0.0409682	+	0.0409682i
$719$			1.39297e7i			1.00489i	0.864609	+	0.502445i	$0.167566\pi$
$719$			1.39297e7i			1.00489i	−0.864609	+	0.502445i	$0.832434\pi$
$720$	−1.16101e7	−	1.19905e6i	−0.834649	−	0.0861997i
$721$		−	1.74499e7i		−	1.25013i
$722$	−780646.	+	780646.i	−0.0557328	+	0.0557328i
$723$	382304.	+	382304.i	0.0271996	+	0.0271996i
$724$		−	1.93822e7i		−	1.37422i
$725$	−1.21866e7	−	2.54431e6i	−0.861065	−	0.179773i
$726$	−199138.	+	561170.i	−0.0140221	+	0.0395142i
$727$	8.02094e6	+	8.02094e6i	0.562846	+	0.562846i	0.930115	−	0.367269i	$-0.119707\pi$
$727$	8.02094e6	+	8.02094e6i	0.562846	+	0.562846i	−0.367269	+	0.930115i	$0.619707\pi$
$728$	−6.71095e6	−	6.71095e6i	−0.469306	−	0.469306i
$729$		−	1.08707e7i		−	0.757599i
$730$	243342.	−	2.35622e6i	0.0169009	−	0.163647i
$731$	−5.04246e6			−0.349019
$732$	2.61792e6	−	2.61792e6i	0.180584	−	0.180584i
$733$	−1.26801e7	−	1.26801e7i	−0.871691	−	0.871691i	0.120966	−	0.992657i	$-0.461401\pi$
$733$	−1.26801e7	−	1.26801e7i	−0.871691	−	0.871691i	−0.992657	+	0.120966i	$0.961401\pi$
$734$	138179.			0.00946677
$735$	−178812.	+	145335.i	−0.0122089	+	0.00992321i
$736$			2.67012e6i			0.181692i
$737$	2.63445e6	−	1.86054e6i	0.178657	−	0.126174i
$738$	2.71569e6	−	2.71569e6i	0.183543	−	0.183543i
$739$	8.77406e6			0.591002			0.295501	−	0.955342i	$-0.404513\pi$
$739$	8.77406e6			0.591002			0.295501	+	0.955342i	$0.404513\pi$
$740$	8.62517e6	+	1.06119e7i	0.579013	+	0.712384i
$741$	−6.19295e6			−0.414335
$742$	347179.	+	347179.i	0.0231496	+	0.0231496i
$743$	−9.85338e6	−	9.85338e6i	−0.654807	−	0.654807i	0.299340	−	0.954147i	$-0.403234\pi$
$743$	−9.85338e6	−	9.85338e6i	−0.654807	−	0.654807i	−0.954147	+	0.299340i	$0.903234\pi$
$744$	929284.			0.0615483
$745$	901873.	−	8.73261e6i	0.0595326	−	0.576439i
$746$	2.50275e6			0.164653
$747$	1.58066e7	−	1.58066e7i	1.03643	−	1.03643i
$748$	−1.14494e7	+	8.08596e6i	−0.748218	+	0.528418i
$749$			86219.0i			0.00561563i
$750$	615355.	+	196257.i	0.0399460	+	0.0127401i
$751$	−3.38585e6			−0.219063			−0.109531	−	0.993983i	$-0.534935\pi$
$751$	−3.38585e6			−0.219063			−0.109531	+	0.993983i	$0.534935\pi$
$752$	1.65308e7	+	1.65308e7i	1.06598	+	1.06598i
$753$	1.24165e6	−	1.24165e6i	0.0798015	−	0.0798015i
$754$	4.84471e6			0.310341
$755$	−2.25843e7	−	2.33243e6i	−1.44191	−	0.148916i
$756$			5.79386e6i			0.368692i
$757$	−1.13440e7	−	1.13440e7i	−0.719494	−	0.719494i	0.249007	−	0.968502i	$-0.419896\pi$
$757$	−1.13440e7	−	1.13440e7i	−0.719494	−	0.719494i	−0.968502	+	0.249007i	$0.919896\pi$
$758$	−1.64007e6	−	1.64007e6i	−0.103678	−	0.103678i
$759$	−1.00092e6	−	172330.i	−0.0630659	−	0.0108581i
$760$	5.83497e6	−	4.74256e6i	0.366441	−	0.297837i
$761$		−	1.02068e7i		−	0.638891i	−0.947605	−	0.319446i	$-0.896503\pi$
$761$		−	1.02068e7i		−	0.638891i	0.947605	−	0.319446i	$-0.103497\pi$
$762$	269794.	+	269794.i	0.0168324	+	0.0168324i
$763$	−1.18143e7	+	1.18143e7i	−0.734680	+	0.734680i
$764$		−	248530.i		−	0.0154044i
$765$	−1.15077e7	+	9.35324e6i	−0.710942	+	0.577841i
$766$		−	6.18015e6i		−	0.380563i
$767$	1.69251e7	−	1.69251e7i	1.03882	−	1.03882i
$768$	−1.43250e6	+	1.43250e6i	−0.0876378	+	0.0876378i
$769$	−3.02499e7			−1.84462			−0.922312	−	0.386447i	$-0.873702\pi$
$769$	−3.02499e7			−1.84462			−0.922312	+	0.386447i	$0.873702\pi$
$770$	−874814.	+	3.11950e6i	−0.0531727	+	0.189608i
$771$	3.19502e6			0.193570
$772$	−1.29531e7	+	1.29531e7i	−0.782220	+	0.782220i
$773$	−6.66230e6	+	6.66230e6i	−0.401028	+	0.401028i	−0.878595	−	0.477567i	$-0.841519\pi$
$773$	−6.66230e6	+	6.66230e6i	−0.401028	+	0.401028i	0.477567	+	0.878595i	$0.341519\pi$
$774$		−	1.19475e6i		−	0.0716843i
$775$	−1.22712e7	−	2.56198e6i	−0.733893	−	0.153222i
$776$			2.52662e6i			0.150621i
$777$	2.24120e6	−	2.24120e6i	0.133177	−	0.133177i
$778$	3.71987e6	+	3.71987e6i	0.220333	+	0.220333i
$779$		−	2.63416e7i		−	1.55525i
$780$	5.70153e6	+	588834.i	0.335548	+	0.0346543i
$781$	−222740.	+	1.29371e6i	−0.0130669	+	0.0758945i
$782$	741335.	+	741335.i	0.0433508	+	0.0433508i
$783$	−4.27436e6	−	4.27436e6i	−0.249153	−	0.249153i
$784$		−	1.15916e6i		−	0.0673522i
$785$	−1.80393e7	+	1.46620e7i	−1.04483	+	0.849220i
$786$	631618.			0.0364669
$787$	1.23587e6	−	1.23587e6i	0.0711273	−	0.0711273i	−0.670648	−	0.741776i	$-0.733984\pi$
$787$	1.23587e6	−	1.23587e6i	0.0711273	−	0.0711273i	0.741776	+	0.670648i	$0.233984\pi$
$788$	−2.96864e6	−	2.96864e6i	−0.170311	−	0.170311i
$789$	2.08896e6			0.119464
$790$	1.68917e6	+	2.07826e6i	0.0962954	+	0.118476i
$791$			2.00748e7i			1.14080i
$792$	−3.91575e6	−	5.54454e6i	−0.221820	−	0.314089i
$793$	2.80886e7	−	2.80886e7i	1.58616	−	1.58616i
$794$	−6.51608e6			−0.366805
$795$	−602851.	−	62260.3i	−0.0338292	−	0.00349376i
$796$	1.15591e7			0.646610
$797$	1.75174e7	+	1.75174e7i	0.976840	+	0.976840i	0.999738	−	0.0228981i	$-0.00728933\pi$
$797$	1.75174e7	+	1.75174e7i	0.976840	+	0.976840i	−0.0228981	+	0.999738i	$0.507289\pi$
$798$	−602944.	−	602944.i	−0.0335173	−	0.0335173i
$799$	2.97024e7			1.64598
$800$	−8.79680e6	+	5.75804e6i	−0.485959	+	0.318090i
$801$	2.01418e7			1.10922
$802$	−151896.	+	151896.i	−0.00833891	+	0.00833891i
$803$	−1.19801e7	+	8.46076e6i	−0.655649	+	0.463042i
$804$		−	785640.i		−	0.0428631i
$805$	−5.49682e6	−	567693.i	−0.298966	−	0.0308762i
$806$	4.87835e6			0.264506
$807$	−1.48360e6	−	1.48360e6i	−0.0801922	−	0.0801922i
$808$	5.25887e6	−	5.25887e6i	0.283377	−	0.283377i
$809$	3.44189e6			0.184895			0.0924477	−	0.995718i	$-0.470531\pi$
$809$	3.44189e6			0.184895			0.0924477	+	0.995718i	$0.470531\pi$
$810$	−2.11512e6	−	2.60232e6i	−0.113272	−	0.139363i
$811$		−	1.27797e7i		−	0.682291i	−0.940010	−	0.341146i	$-0.889185\pi$
$811$		−	1.27797e7i		−	0.682291i	0.940010	−	0.341146i	$-0.110815\pi$
$812$	−1.07562e7	−	1.07562e7i	−0.572492	−	0.572492i
$813$	367035.	+	367035.i	0.0194752	+	0.0194752i
$814$	−630000.	+	3.65914e6i	−0.0333257	+	0.193561i
$815$	−1.60451e7	−	1.97409e7i	−0.846150	−	1.04105i
$816$			3.25812e6i			0.171294i
$817$	−5.79441e6	−	5.79441e6i	−0.303706	−	0.303706i
$818$	−2.23079e6	+	2.23079e6i	−0.116567	+	0.116567i
$819$			3.04180e7i			1.58460i
$820$	−2.50460e6	+	2.42514e7i	−0.130078	+	1.25951i
$821$			2.66295e7i			1.37881i	0.724374	+	0.689407i	$0.242129\pi$
$821$			2.66295e7i			1.37881i	−0.724374	+	0.689407i	$0.757871\pi$
$822$	537105.	−	537105.i	0.0277255	−	0.0277255i
$823$	−1.61359e7	+	1.61359e7i	−0.830410	+	0.830410i	−0.987573	−	0.157163i	$-0.949765\pi$
$823$	−1.61359e7	+	1.61359e7i	−0.830410	+	0.830410i	0.157163	+	0.987573i	$0.449765\pi$
$824$	1.01774e7			0.522177
$825$	−1.59071e6	−	3.66919e6i	−0.0813684	−	0.187687i
$826$	3.29564e6			0.168070
$827$	2.40113e7	−	2.40113e7i	1.22082	−	1.22082i	0.253478	−	0.967341i	$-0.418426\pi$
$827$	2.40113e7	−	2.40113e7i	1.22082	−	1.22082i	0.967341	−	0.253478i	$-0.0815745\pi$
$828$	4.00554e6	−	4.00554e6i	0.203041	−	0.203041i
$829$			7.97873e6i			0.403225i	0.979465	+	0.201612i	$0.0646181\pi$
$829$			7.97873e6i			0.403225i	−0.979465	+	0.201612i	$0.935382\pi$
$830$	639272.	−	6.18991e6i	0.0322100	−	0.311881i
$831$		−	1.45645e6i		−	0.0731631i
$832$	−1.83898e7	+	1.83898e7i	−0.921018	+	0.921018i
$833$	−1.04138e6	−	1.04138e6i	−0.0519994	−	0.0519994i
$834$			1.33518e6i			0.0664698i
$835$	1.42539e7	+	1.75372e7i	0.707485	+	0.870449i
$836$	−2.24485e7	−	3.86500e6i	−1.11089	−	0.191264i
$837$	−4.30404e6	−	4.30404e6i	−0.212355	−	0.212355i
$838$	−2.75652e6	−	2.75652e6i	−0.135597	−	0.135597i
$839$		−	1.69830e7i		−	0.832931i	−0.909152	−	0.416465i	$-0.863269\pi$
$839$		−	1.69830e7i		−	0.832931i	0.909152	−	0.416465i	$-0.136731\pi$
$840$	1.01737e6	+	1.25171e6i	0.0497486	+	0.0612078i
$841$	−4.64060e6			−0.226248
$842$	654616.	−	654616.i	0.0318205	−	0.0318205i
$843$	306214.	+	306214.i	0.0148408	+	0.0148408i
$844$	2.26062e7			1.09237
$845$	4.05277e7	+	4.18556e6i	1.95259	+	0.201656i
$846$			7.03762e6i			0.338065i
$847$	1.81116e7	−	8.62409e6i	0.867455	−	0.413052i
$848$	2.15581e6	−	2.15581e6i	0.102948	−	0.102948i
$849$	5.43863e6			0.258953
$850$	−843684.	+	4.04102e6i	−0.0400528	+	0.191842i
$851$	−6.33308e6			−0.299772
$852$	226117.	+	226117.i	0.0106717	+	0.0106717i
$853$	2.49281e7	+	2.49281e7i	1.17305	+	1.17305i	0.981479	+	0.191569i	$0.0613575\pi$
$853$	2.49281e7	+	2.49281e7i	1.17305	+	1.17305i	0.191569	+	0.981479i	$0.438642\pi$
$854$	5.46940e6			0.256622
$855$	−2.39718e7	−	2.47572e6i	−1.12146	−	0.115821i
$856$	−50285.8			−0.00234564
$857$	1.77081e7	−	1.77081e7i	0.823609	−	0.823609i	−0.163015	−	0.986624i	$-0.552122\pi$
$857$	1.77081e7	−	1.77081e7i	0.823609	−	0.823609i	0.986624	+	0.163015i	$0.0521218\pi$
$858$	897785.	+	1.27123e6i	0.0416346	+	0.0589529i
$859$		−	2.11987e7i		−	0.980225i	−0.871659	−	0.490113i	$-0.836956\pi$
$859$		−	2.11987e7i		−	0.980225i	0.871659	−	0.490113i	$-0.163044\pi$
$860$	4.78368e6	+	5.88556e6i	0.220554	+	0.271357i
$861$	5.65079e6			0.259777
$862$	3.23600e6	+	3.23600e6i	0.148334	+	0.148334i
$863$	1.53434e7	−	1.53434e7i	0.701286	−	0.701286i	−0.263400	−	0.964687i	$-0.584844\pi$
$863$	1.53434e7	−	1.53434e7i	0.701286	−	0.701286i	0.964687	+	0.263400i	$0.0848440\pi$
$864$	−5.10502e6			−0.232655
$865$	2.62454e7	−	2.13318e7i	1.19265	−	0.969363i
$866$			2.80127e6i			0.126929i
$867$	−274514.	−	274514.i	−0.0124027	−	0.0124027i
$868$	−1.08309e7	−	1.08309e7i	−0.487939	−	0.487939i
$869$	2.81358e6	−	1.63417e7i	0.126389	−	0.734088i
$870$	−819037.	−	84587.3i	−0.0366864	−	0.00378885i
$871$		−	8.42942e6i		−	0.376489i
$872$	−6.89052e6	−	6.89052e6i	−0.306875	−	0.306875i
$873$	5.72606e6	−	5.72606e6i	0.254285	−	0.254285i
$874$			1.70377e6i			0.0754453i
$875$	−9.98347e6	−	1.93337e7i	−0.440820	−	0.853679i
$876$			3.57268e6i			0.157302i
$877$	−3.15258e7	+	3.15258e7i	−1.38410	+	1.38410i	−0.546907	+	0.837193i	$0.684195\pi$
$877$	−3.15258e7	+	3.15258e7i	−1.38410	+	1.38410i	−0.837193	+	0.546907i	$0.815805\pi$
$878$	556438.	−	556438.i	0.0243602	−	0.0243602i
$879$	−1.13445e6			−0.0495239
$880$	1.93705e7	+	5.43216e6i	0.843207	+	0.236464i
$881$	−2.91839e7			−1.26679			−0.633394	−	0.773829i	$-0.718339\pi$
$881$	−2.91839e7			−1.26679			−0.633394	+	0.773829i	$0.718339\pi$
$882$	246743.	−	246743.i	0.0106800	−	0.0106800i
$883$	−757927.	+	757927.i	−0.0327134	+	0.0327134i	−0.723274	−	0.690561i	$-0.757364\pi$
$883$	−757927.	+	757927.i	−0.0327134	+	0.0327134i	0.690561	+	0.723274i	$0.257364\pi$
$884$			3.66345e7i			1.57674i
$885$	−3.15682e6	+	2.56581e6i	−0.135485	+	0.110120i
$886$		−	2.74498e6i		−	0.117477i
$887$	1.51267e7	−	1.51267e7i	0.645558	−	0.645558i	−0.306358	−	0.951916i	$-0.599111\pi$
$887$	1.51267e7	−	1.51267e7i	0.645558	−	0.645558i	0.951916	+	0.306358i	$0.0991106\pi$
$888$	1.30714e6	+	1.30714e6i	0.0556277	+	0.0556277i
$889$		−	1.28537e7i		−	0.545475i
$890$	4.35108e6	−	3.53648e6i	0.184129	−	0.149657i
$891$	−3.52306e6	+	2.04625e7i	−0.148671	+	0.863504i
$892$	500658.	+	500658.i	0.0210683	+	0.0210683i
$893$	3.41318e7	+	3.41318e7i	1.43229	+	1.43229i
$894$		−	580643.i		−	0.0242977i
$895$	−1.34363e7	−	1.38766e6i	−0.560690	−	0.0579061i
$896$	−1.69907e7			−0.707036
$897$	−1.87701e6	+	1.87701e6i	−0.0778909	+	0.0778909i
$898$	−1.26262e6	−	1.26262e6i	−0.0522496	−	0.0522496i
$899$	1.59808e7			0.659475
$900$	2.18342e7	+	4.55854e6i	0.898527	+	0.187594i
$901$		−	3.87354e6i		−	0.158963i
$902$	−5.40715e6	+	3.81872e6i	−0.221285	+	0.156279i
$903$	1.24301e6	−	1.24301e6i	0.0507290	−	0.0507290i
$904$	−1.17083e7			−0.476511
$905$	−3.63090e6	+	3.51571e7i	−0.147365	+	1.42689i
$906$	−1.50166e6			−0.0607787
$907$	2.81619e7	+	2.81619e7i	1.13670	+	1.13670i	0.989039	+	0.147657i	$0.0471731\pi$
$907$	2.81619e7	+	2.81619e7i	1.13670	+	1.13670i	0.147657	+	0.989039i	$0.452827\pi$
$908$	−1.09108e7	−	1.09108e7i	−0.439180	−	0.439180i
$909$	−2.38363e7			−0.956817
$910$	5.34077e6	+	6.57097e6i	0.213796	+	0.263042i
$911$	4.14771e7			1.65582			0.827908	−	0.560864i	$-0.189531\pi$
$911$	4.14771e7			1.65582			0.827908	+	0.560864i	$0.189531\pi$
$912$	−3.74398e6	+	3.74398e6i	−0.149055	+	0.149055i
$913$	−3.14723e7	+	2.22268e7i	−1.24954	+	0.882471i
$914$		−	3.89393e6i		−	0.154178i
$915$	−5.23902e6	+	4.25819e6i	−0.206870	+	0.168140i
$916$	4.59881e7			1.81095
$917$	−1.50460e7	−	1.50460e7i	−0.590877	−	0.590877i
$918$	−1.41736e6	+	1.41736e6i	−0.0555104	+	0.0555104i
$919$	−1.89628e7			−0.740650			−0.370325	−	0.928902i	$-0.620754\pi$
$919$	−1.89628e7			−0.740650			−0.370325	+	0.928902i	$0.620754\pi$
$920$	331098.	−	3.20593e6i	0.0128969	−	0.124878i
$921$		−	7.81017e6i		−	0.303397i
$922$	−4.01097e6	−	4.01097e6i	−0.155390	−	0.155390i
$923$	2.42609e6	+	2.42609e6i	0.0937351	+	0.0937351i
$924$	829116.	−	4.81564e6i	0.0319474	−	0.185556i
$925$	−1.36571e7	−	2.08646e7i	−0.524813	−	0.801779i
$926$		−	8.84028e6i		−	0.338796i
$927$	−2.30649e7	−	2.30649e7i	−0.881562	−	0.881562i
$928$	9.47737e6	−	9.47737e6i	0.361259	−	0.361259i
$929$			1.78035e7i			0.676810i	0.941001	+	0.338405i	$0.109887\pi$
$929$			1.78035e7i			0.676810i	−0.941001	+	0.338405i	$0.890113\pi$
$930$	−824725.	−	85174.7i	−0.0312681	−	0.00322926i
$931$		−	2.39335e6i		−	0.0904967i
$932$	−5.86901e6	+	5.86901e6i	−0.221322	+	0.221322i
$933$	−1.69297e6	+	1.69297e6i	−0.0636716	+	0.0636716i
$934$	−1.13518e6			−0.0425790
$935$	2.22826e7	−	1.25222e7i	0.833561	−	0.468436i
$936$	−1.77408e7			−0.661886
$937$	−1.04846e7	+	1.04846e7i	−0.390123	+	0.390123i	−0.874731	−	0.484608i	$-0.838962\pi$
$937$	−1.04846e7	+	1.04846e7i	−0.390123	+	0.390123i	0.484608	+	0.874731i	$0.338962\pi$
$938$	820686.	−	820686.i	0.0304558	−	0.0304558i
$939$		−	70155.2i		−	0.00259655i
$940$	−2.81781e7	−	3.46687e7i	−1.04014	−	1.27973i
$941$		−	1.69543e7i		−	0.624173i	−0.950054	−	0.312086i	$-0.898972\pi$
$941$		−	1.69543e7i		−	0.624173i	0.950054	−	0.312086i	$-0.101028\pi$
$942$	−1.08718e6	+	1.08718e6i	−0.0399185	+	0.0399185i
$943$	−7.98386e6	−	7.98386e6i	−0.292371	−	0.292371i
$944$		−	2.04643e7i		−	0.747422i
$945$	1.08538e6	−	1.05094e7i	0.0395367	−	0.382824i
$946$	−349410.	+	2.02943e6i	−0.0126942	+	0.0737303i
$947$	1.12252e7	+	1.12252e7i	0.406741	+	0.406741i	0.880600	−	0.473860i	$-0.157140\pi$
$947$	1.12252e7	+	1.12252e7i	0.406741	+	0.406741i	−0.473860	+	0.880600i	$0.657140\pi$
$948$	−2.85623e6	−	2.85623e6i	−0.103222	−	0.103222i
$949$			3.83326e7i			1.38166i
$950$	−5.61313e6	+	3.67413e6i	−0.201788	+	0.132083i
$951$	−6.28780e6			−0.225449
$952$	−7.28985e6	+	7.28985e6i	−0.260691	+	0.260691i
$953$	−1.49848e7	−	1.49848e7i	−0.534464	−	0.534464i	0.387434	−	0.921898i	$-0.373362\pi$
$953$	−1.49848e7	−	1.49848e7i	−0.534464	−	0.534464i	−0.921898	+	0.387434i	$0.873362\pi$
$954$	917787.			0.0326491
$955$	−46557.6	+	450805.i	−0.00165189	+	0.0159949i
$956$		−	2.98120e7i		−	1.05498i
$957$	2.94101e6	+	4.16435e6i	0.103805	+	0.146983i
$958$	−5.29329e6	+	5.29329e6i	−0.186342	+	0.186342i
$959$	−2.55891e7			−0.898480
$960$	3.43002e6	−	2.78786e6i	0.120121	−	0.0976322i
$961$	−1.25374e7			−0.437924
$962$	6.86196e6	+	6.86196e6i	0.239062	+	0.239062i
$963$	113962.	+	113962.i	0.00396001	+	0.00396001i
$964$	5.19753e6			0.180138
$965$	2.59219e7	−	2.10689e7i	0.896083	−	0.728321i
$966$	−365491.			−0.0126018
$967$	−3.17757e7	+	3.17757e7i	−1.09277	+	1.09277i	−0.0975384	+	0.995232i	$0.531097\pi$
$967$	−3.17757e7	+	3.17757e7i	−1.09277	+	1.09277i	−0.995232	+	0.0975384i	$0.968903\pi$
$968$	5.02986e6	+	1.05633e7i	0.172531	+	0.362335i
$969$			6.72716e6i			0.230156i
$970$	231580.	−	2.24233e6i	0.00790264	−	0.0765193i
$971$	−9.35785e6			−0.318514			−0.159257	−	0.987237i	$-0.550910\pi$
$971$	−9.35785e6			−0.318514			−0.159257	+	0.987237i	$0.550910\pi$
$972$	1.15691e7	+	1.15691e7i	0.392767	+	0.392767i
$973$	3.18057e7	−	3.18057e7i	1.07702	−	1.07702i
$974$	−1.70461e6			−0.0575742
$975$	−1.02316e7	−	2.13616e6i	−0.344693	−	0.0719651i
$976$		−	3.39622e7i		−	1.14123i
$977$	1.40931e6	+	1.40931e6i	0.0472355	+	0.0472355i	0.730330	−	0.683094i	$-0.239366\pi$
$977$	1.40931e6	+	1.40931e6i	0.0472355	+	0.0472355i	−0.683094	+	0.730330i	$0.739366\pi$
$978$	−1.18973e6	−	1.18973e6i	−0.0397741	−	0.0397741i
$979$	−3.42133e7	−	5.89056e6i	−1.14088	−	0.196426i
$980$	−227564.	+	2.20344e6i	−0.00756899	+	0.0732885i
$981$			3.12319e7i			1.03616i
$982$	2.32860e6	+	2.32860e6i	0.0770578	+	0.0770578i
$983$	2.12347e6	−	2.12347e6i	0.0700910	−	0.0700910i	−0.671192	−	0.741283i	$-0.734218\pi$
$983$	2.12347e6	−	2.12347e6i	0.0700910	−	0.0700910i	0.741283	+	0.671192i	$0.234218\pi$
$984$			3.29573e6i			0.108508i
$985$	4.82866e6	+	5.94090e6i	0.158575	+	0.195102i
$986$		−	5.26262e6i		−	0.172389i
$987$	−7.32192e6	+	7.32192e6i	−0.239239	+	0.239239i
$988$	−4.20975e7	+	4.20975e7i	−1.37203	+	1.37203i
$989$	−3.51244e6			−0.114188
$990$	2.96697e6	+	5.27959e6i	0.0962111	+	0.171203i
$991$	7.24962e6			0.234494			0.117247	−	0.993103i	$-0.462593\pi$
$991$	7.24962e6			0.234494			0.117247	+	0.993103i	$0.462593\pi$
$992$	9.54319e6	−	9.54319e6i	0.307903	−	0.307903i
$993$	4.47564e6	−	4.47564e6i	0.144040	−	0.144040i
$994$			472407.i			0.0151653i
$995$	−2.09669e7	−	2.16539e6i	−0.671394	−	0.0693392i
$996$			9.38560e6i			0.299788i
$997$	−1.80710e7	+	1.80710e7i	−0.575764	+	0.575764i	−0.933733	−	0.357970i	$-0.883469\pi$
$997$	−1.80710e7	+	1.80710e7i	−0.575764	+	0.575764i	0.357970	+	0.933733i	$0.383469\pi$
$998$	3.26085e6	+	3.26085e6i	0.103634	+	0.103634i
$999$		−	1.21083e7i		−	0.383856i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.6.e.b.32.13	✓	52
5.3	odd	4	inner	55.6.e.b.43.14	yes	52
11.10	odd	2	inner	55.6.e.b.32.14	yes	52
55.43	even	4	inner	55.6.e.b.43.13	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.6.e.b.32.13	✓	52	1.1	even	1	trivial
55.6.e.b.32.14	yes	52	11.10	odd	2	inner
55.6.e.b.43.13	yes	52	55.43	even	4	inner
55.6.e.b.43.14	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+(-0.819850 + 0.819850i) q^{2} +(-2.25487 + 2.25487i) q^{3} +30.6557i q^{4} +(5.74279 - 55.6059i) q^{5} -3.69731i q^{6} +(-88.0749 + 88.0749i) q^{7} +(-51.3683 - 51.3683i) q^{8} +232.831i q^{9} +(40.8803 + 50.2967i) q^{10} +(68.0926 - 395.493i) q^{11} +(-69.1247 - 69.1247i) q^{12} +(-741.664 - 741.664i) q^{13} -144.416i q^{14} +(112.435 + 138.334i) q^{15} -896.754 q^{16} +(-805.641 + 805.641i) q^{17} +(-190.887 - 190.887i) q^{18} -1851.56 q^{19} +(1704.64 + 176.049i) q^{20} -397.196i q^{21} +(268.419 + 380.070i) q^{22} +(-561.188 + 561.188i) q^{23} +231.658 q^{24} +(-3059.04 - 638.666i) q^{25} +1216.11 q^{26} +(-1072.94 - 1072.94i) q^{27} +(-2700.00 - 2700.00i) q^{28} +3983.79 q^{29} +(-205.593 - 21.2329i) q^{30} +4011.45 q^{31} +(2378.99 - 2378.99i) q^{32} +(738.246 + 1045.33i) q^{33} -1321.01i q^{34} +(4391.69 + 5403.28i) q^{35} -7137.60 q^{36} +(5642.57 + 5642.57i) q^{37} +(1518.00 - 1518.00i) q^{38} +3344.72 q^{39} +(-3151.38 + 2561.38i) q^{40} +14226.7i q^{41} +(325.641 + 325.641i) q^{42} +(3129.47 + 3129.47i) q^{43} +(12124.1 + 2087.42i) q^{44} +(12946.8 + 1337.10i) q^{45} -920.180i q^{46} +(-18434.0 - 18434.0i) q^{47} +(2022.07 - 2022.07i) q^{48} +1292.61i q^{49} +(3031.56 - 1984.34i) q^{50} -3633.24i q^{51} +(22736.2 - 22736.2i) q^{52} +(-2404.01 + 2404.01i) q^{53} +1759.30 q^{54} +(-21600.7 - 6057.58i) q^{55} +9048.51 q^{56} +(4175.04 - 4175.04i) q^{57} +(-3266.11 + 3266.11i) q^{58} +22820.4i q^{59} +(-4240.71 + 3446.77i) q^{60} +37872.4i q^{61} +(-3288.79 + 3288.79i) q^{62} +(-20506.6 - 20506.6i) q^{63} -24795.3i q^{64} +(-45500.1 + 36981.7i) q^{65} +(-1462.26 - 251.760i) q^{66} +(5682.77 + 5682.77i) q^{67} +(-24697.5 - 24697.5i) q^{68} -2530.82i q^{69} +(-8030.41 - 829.353i) q^{70} -3271.14 q^{71} +(11960.1 - 11960.1i) q^{72} +(-25842.3 - 25842.3i) q^{73} -9252.11 q^{74} +(8337.86 - 5457.64i) q^{75} -56760.9i q^{76} +(28835.7 + 40830.2i) q^{77} +(-2742.16 + 2742.16i) q^{78} +41319.9 q^{79} +(-5149.87 + 49864.8i) q^{80} -51739.3 q^{81} +(-11663.8 - 11663.8i) q^{82} +(-67888.9 - 67888.9i) q^{83} +12176.3 q^{84} +(40171.8 + 49425.0i) q^{85} -5131.39 q^{86} +(-8982.93 + 8982.93i) q^{87} +(-23813.6 + 16818.0i) q^{88} -86508.1i q^{89} +(-11710.6 + 9518.20i) q^{90} +130644. q^{91} +(-17203.6 - 17203.6i) q^{92} +(-9045.31 + 9045.31i) q^{93} +30226.3 q^{94} +(-10633.1 + 102958. i) q^{95} +10728.6i q^{96} +(-24593.2 - 24593.2i) q^{97} +(-1059.75 - 1059.75i) q^{98} +(92083.0 + 15854.1i) 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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