LMFDB - Embedded newform 55.6.e.b.32.14

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			32.14
Character	$\chi$	$=$	55.32
Dual form			55.6.e.b.43.14

$q$-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} +(380.070 + 268.419i) 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} +(-1045.33 - 738.246i) 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} +(22382.8 - 1515.12i) 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} +(40830.2 + 28835.7i) 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} +(-16818.0 + 23813.6i) 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	−0.630919	−	0.775849i	$-0.717322\pi$
$2$	0.819850	−	0.819850i	0.144930	−	0.144930i	0.775849	+	0.630919i	$0.217322\pi$
$3$	−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	−0.280487	−	0.959858i	$-0.590496\pi$
$7$	88.0749	−	88.0749i	0.679371	−	0.679371i	0.959858	+	0.280487i	$0.0904958\pi$
$8$	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	$0.0799515\pi$
$13$	741.664	+	741.664i	1.21716	+	1.21716i	0.248542	+	0.968621i	$0.420049\pi$
$14$		−	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	−0.283005	−	0.959118i	$-0.591331\pi$
$17$	805.641	−	805.641i	0.676113	−	0.676113i	0.959118	+	0.283005i	$0.0913314\pi$
$18$	190.887	+	190.887i	0.138865	+	0.138865i
$19$	1851.56			1.17667			0.588334	−	0.808618i	$-0.299784\pi$
$19$	1851.56			1.17667			0.588334	+	0.808618i	$0.299784\pi$
$20$	1704.64	+	176.049i	0.952922	+	0.0984145i
$21$			397.196i			0.196542i
$22$	380.070	+	268.419i	0.167420	+	0.118238i
$23$	−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	$-0.644956\pi$
$29$	−3983.79			−0.879632			−0.439816	+	0.898088i	$0.644956\pi$
$30$	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
$33$	−1045.33	−	738.246i	−0.167096	−	0.118009i
$34$		−	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	$-0.770188\pi$
$41$		−	14226.7i		−	1.32174i	0.750502	−	0.660868i	$-0.229812\pi$
$42$	325.641	+	325.641i	0.0284849	+	0.0284849i
$43$	−3129.47	−	3129.47i	−0.258107	−	0.258107i	0.566177	−	0.824284i	$-0.308422\pi$
$43$	−3129.47	−	3129.47i	−0.258107	−	0.258107i	−0.824284	+	0.566177i	$0.808422\pi$
$44$	−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
$55$	22382.8	−	1515.12i	0.997717	−	0.0675368i
$56$	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	$-0.774106\pi$
$61$		−	37872.4i		−	1.30316i	0.758579	−	0.651581i	$-0.225894\pi$
$62$	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	0.931449	−	0.363873i	$-0.118546\pi$
$73$	25842.3	+	25842.3i	0.567575	+	0.567575i	−0.363873	+	0.931449i	$0.618546\pi$
$74$	9252.11			0.196409
$75$	8337.86	−	5457.64i	0.171160	−	0.112034i
$76$			56760.9i			1.12724i
$77$	40830.2	+	28835.7i	0.784793	+	0.554248i
$78$	−2742.16	+	2742.16i	−0.0510337	+	0.0510337i
$79$	−41319.9			−0.744889			−0.372445	−	0.928054i	$-0.621480\pi$
$79$	−41319.9			−0.744889			−0.372445	+	0.928054i	$0.621480\pi$
$80$	−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	$0.0271977\pi$
$83$	67888.9	+	67888.9i	1.08169	+	1.08169i	0.0853401	+	0.996352i	$0.472802\pi$
$84$	−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
$88$	−16818.0	+	23813.6i	−0.231508	+	0.327807i
$89$		−	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	$-0.833589\pi$
$101$		−	102376.i		−	0.998606i	0.866427	−	0.499303i	$-0.166411\pi$
$102$	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	−0.709170	−	0.705037i	$-0.750930\pi$
$107$	−489.464	+	489.464i	−0.00413296	+	0.00413296i	0.705037	+	0.709170i	$0.250930\pi$
$108$	32891.7	−	32891.7i	0.271348	−	0.271348i
$109$	−134140.			−1.08141			−0.540706	−	0.841212i	$-0.681843\pi$
$109$	−134140.			−1.08141			−0.540706	+	0.841212i	$0.681843\pi$
$110$	17108.3	−	19592.7i	0.134811	−	0.154388i
$111$	−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	−0.477290	−	0.878746i	$-0.658381\pi$
$127$	72970.4	−	72970.4i	0.401455	−	0.401455i	0.878746	+	0.477290i	$0.158381\pi$
$128$	−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	$-0.856794\pi$
$131$		−	170832.i		−	0.869741i	0.900493	−	0.434871i	$-0.143206\pi$
$132$	22631.4	−	32045.2i	0.113052	−	0.160077i
$133$	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	$-0.208696\pi$
$139$	361121.			1.58532			0.792659	+	0.609665i	$0.208696\pi$
$140$	165641.	−	134630.i	0.714248	−	0.580528i
$141$	83132.9			0.352148
$142$	−2681.85	+	2681.85i	−0.0111613	+	0.0111613i
$143$	−242821.	+	343824.i	−0.992992	+	1.40604i
$144$		−	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	$-0.593573\pi$
$149$	−157044.			−0.579505			−0.289752	+	0.957102i	$0.593573\pi$
$150$	2361.35	−	11310.2i	0.00856904	−	0.0410434i
$151$			406149.i			1.44958i	0.688968	+	0.724792i	$0.258064\pi$
$151$			406149.i			1.44958i	−0.688968	+	0.724792i	$0.741936\pi$
$152$	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
$165$	−47053.9	+	53886.7i	−0.134551	+	0.154089i
$166$	111317.			0.313540
$167$	285860.	−	285860.i	0.793164	−	0.793164i	−0.188843	−	0.982007i	$-0.560474\pi$
$167$	285860.	−	285860.i	0.793164	−	0.793164i	0.982007	+	0.188843i	$0.0604739\pi$
$168$	−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	$-0.971027\pi$
$173$	−427806.	−	427806.i	−1.08675	−	1.08675i	−0.0908942	−	0.995861i	$-0.528973\pi$
$174$		−	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
$187$	373483.	+	263767.i	0.781029	+	0.551590i
$188$	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	0.169080	−	0.985602i	$-0.445920\pi$
$193$	−422534.	−	422534.i	−0.816522	−	0.816522i	−0.985602	+	0.169080i	$0.945920\pi$
$194$	−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	−0.612608	−	0.790387i	$-0.709879\pi$
$197$	96838.2	−	96838.2i	0.177779	−	0.177779i	0.790387	+	0.612608i	$0.209879\pi$
$198$	−62496.3	+	88492.2i	−0.113290	+	0.160414i
$199$		−	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	$0.193110\pi$
$211$			737422.i			1.14028i	−0.821549	+	0.570138i	$0.806890\pi$
$212$	−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
$220$	46447.1	+	686160.i	0.0646996	+	0.955803i
$221$	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	−0.439704	−	0.898143i	$-0.644917\pi$
$227$	355915.	−	355915.i	0.458439	−	0.458439i	0.898143	+	0.439704i	$0.144917\pi$
$228$	−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	0.582094	−	0.813122i	$-0.302234\pi$
$233$	−191449.	−	191449.i	−0.231028	−	0.231028i	−0.813122	+	0.582094i	$0.802234\pi$
$234$			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	$-0.314390\pi$
$239$	972477.			1.10125			0.550624	+	0.834754i	$0.314390\pi$
$240$	−100827.	−	124051.i	−0.112992	−	0.139019i
$241$			169545.i			0.188037i	0.995570	+	0.0940186i	$0.0299713\pi$
$241$			169545.i			0.188037i	−0.995570	+	0.0940186i	$0.970029\pi$
$242$	−80277.7	+	168592.i	−0.0881164	+	0.185054i
$243$	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
$253$	−260158.	−	183733.i	−0.255527	−	0.180462i
$254$		−	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	0.882762	−	0.469820i	$-0.155681\pi$
$263$	463210.	+	463210.i	0.412942	+	0.412942i	−0.469820	+	0.882762i	$0.655681\pi$
$264$	−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	$0.0214442\pi$
$271$			162774.i			0.134636i	−0.997732	+	0.0673181i	$0.978556\pi$
$272$	−722461.	+	722461.i	−0.592096	+	0.592096i
$273$	−294586.	+	294586.i	−0.239224	+	0.239224i
$274$	238197.			0.191673
$275$	44289.9	−	1.25332e6i	0.0353161	−	0.999376i
$276$	77583.9			0.0613054
$277$	322956.	−	322956.i	0.252897	−	0.252897i	−0.569260	−	0.822157i	$-0.692770\pi$
$277$	322956.	−	322956.i	0.252897	−	0.252897i	0.822157	+	0.569260i	$0.192770\pi$
$278$	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	$0.0163361\pi$
$281$			135801.i			0.102598i	−0.998683	+	0.0512988i	$0.983664\pi$
$282$	68156.5	−	68156.5i	0.0510369	−	0.0510369i
$283$	1.20597e6	+	1.20597e6i	0.895099	+	0.895099i	0.994998	−	0.0998984i	$-0.0318518\pi$
$283$	1.20597e6	+	1.20597e6i	0.895099	+	0.895099i	−0.0998984	+	0.994998i	$0.531852\pi$
$284$		−	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	0.616315	−	0.787500i	$-0.288625\pi$
$293$	−251556.	−	251556.i	−0.171185	−	0.171185i	−0.787500	+	0.616315i	$0.788625\pi$
$294$	−4779.20			−0.00322468
$295$	1.26895e6	+	131053.i	0.848963	+	0.0876780i
$296$			579697.i			0.384567i
$297$	351280.	−	497398.i	0.231080	−	0.327200i
$298$	−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	$-0.484085\pi$
$307$	1.73184e6	−	1.73184e6i	1.04873	−	1.04873i	0.998750	−	0.0499766i	$-0.0159147\pi$
$308$	−883979.	+	1.25168e6i	−0.530964	+	0.751824i
$309$		−	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
$330$	5601.88	+	82756.2i	0.00283171	+	0.0418327i
$331$	−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	−0.677526	−	0.735499i	$-0.736948\pi$
$337$	120865.	−	120865.i	0.0579729	−	0.0579729i	0.735499	+	0.677526i	$0.236948\pi$
$338$	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	−0.946193	−	0.323602i	$-0.895106\pi$
$347$	−1.39645e6	+	1.39645e6i	−0.622591	+	0.622591i	0.323602	+	0.946193i	$0.395106\pi$
$348$	275378.	+	275378.i	0.121894	+	0.121894i
$349$	−3.13019e6			−1.37565			−0.687824	−	0.725878i	$-0.741434\pi$
$349$	−3.13019e6			−1.37565			−0.687824	+	0.725878i	$0.741434\pi$
$350$	−92233.9	+	441776.i	−0.0402458	+	0.192767i
$351$		−	1.59152e6i		−	0.689516i
$352$	−1.10286e6	−	778881.i	−0.474422	−	0.335054i
$353$	−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	$-0.545140\pi$
$359$	−690277.			−0.282675			−0.141338	+	0.989961i	$0.545140\pi$
$360$	596370.	+	733739.i	0.242527	+	0.298391i
$361$	952181.			0.384549
$362$	−518353.	+	518353.i	−0.207900	+	0.207900i
$363$	220792.	−	463688.i	0.0879460	−	0.184697i
$364$			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	0.931579	−	0.363538i	$-0.118431\pi$
$373$	1.52634e6	+	1.52634e6i	0.568042	+	0.568042i	−0.363538	+	0.931579i	$0.618431\pi$
$374$	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
$385$	1.83792e6	−	2.10481e6i	0.631938	−	0.723703i
$386$	−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
$407$	−1.84738e6	+	2.61581e6i	−0.552802	+	0.782745i
$408$	−186633.	+	186633.i	−0.0555058	+	0.0555058i
$409$	−2.72097e6			−0.804295			−0.402148	−	0.915575i	$-0.631736\pi$
$409$	−2.72097e6			−0.804295			−0.402148	+	0.915575i	$0.631736\pi$
$410$	−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
$418$	703723.	+	496994.i	0.196998	+	0.139127i
$419$			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	$0.171000\pi$
$431$			3.94706e6i			1.02348i	−0.859139	+	0.511742i	$0.829000\pi$
$432$	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	$-0.473217\pi$
$439$	678707.			0.168082			0.0840409	+	0.996462i	$0.473217\pi$
$440$	1.22759e6	+	1.07194e6i	0.302289	+	0.263959i
$441$	−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	−0.389235	−	0.921139i	$-0.627261\pi$
$457$	2.37478e6	−	2.37478e6i	0.531904	−	0.531904i	0.921139	+	0.389235i	$0.127261\pi$
$458$	−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	$-0.819903\pi$
$461$		−	4.89233e6i		−	1.07217i	0.844164	−	0.536084i	$-0.180097\pi$
$462$	−106615.	+	150962.i	−0.0232387	+	0.0329051i
$463$	−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
$473$	1.02459e6	−	1.45078e6i	0.210570	−	0.298159i
$474$		−	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	$-0.722256\pi$
$479$	−6.45641e6			−1.28574			−0.642869	+	0.765976i	$0.722256\pi$
$480$	−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	$0.0856507\pi$
$491$			2.84028e6i			0.531689i	−0.964016	+	0.265844i	$0.914349\pi$
$492$	−983417.	+	983417.i	−0.183158	+	0.183158i
$493$	−3.20950e6	+	3.20950e6i	−0.594730	+	0.594730i
$494$	2.25170e6			0.415138
$495$	352767.	+	5.21141e6i	0.0647106	+	0.955965i
$496$	−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	$-0.975081\pi$
$503$	−6.10079e6	−	6.10079e6i	−1.07514	−	1.07514i	−0.0782056	−	0.996937i	$-0.524919\pi$
$504$			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
$517$	6.03531e6	−	8.54575e6i	0.993054	−	1.40612i
$518$	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	0.866201	−	0.499695i	$-0.166555\pi$
$523$	2.29263e6	+	2.29263e6i	0.366506	+	0.366506i	−0.499695	+	0.866201i	$0.666555\pi$
$524$	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
$528$	937400.	+	662024.i	0.146332	+	0.103345i
$529$			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	$-0.949849\pi$
$541$		−	2.13626e6i		−	0.313805i	0.987614	−	0.156903i	$-0.0501509\pi$
$542$	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	−0.410106	−	0.912038i	$-0.634508\pi$
$547$	3.51247e6	−	3.51247e6i	0.501932	−	0.501932i	0.912038	+	0.410106i	$0.134508\pi$
$548$	−4.45332e6	+	4.45332e6i	−0.633479	+	0.633479i
$549$	8.81787e6			1.24863
$550$	−991220.	−	1.06384e6i	−0.139722	−	0.149958i
$551$	−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	−0.617852	−	0.786294i	$-0.711997\pi$
$557$	1.23335e6	−	1.23335e6i	0.168442	−	0.168442i	0.786294	+	0.617852i	$0.211997\pi$
$558$	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	0.332087	−	0.943249i	$-0.392247\pi$
$563$	−4.59650e6	−	4.59650e6i	−0.611161	−	0.611161i	−0.943249	+	0.332087i	$0.892247\pi$
$564$			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	$-0.167455\pi$
$569$	1.33573e7			1.72957			0.864785	+	0.502143i	$0.167455\pi$
$570$	380667.	+	39314.0i	0.0490748	+	0.00506828i
$571$			9.47840e6i			1.21659i	0.793711	+	0.608296i	$0.208146\pi$
$571$			9.47840e6i			1.21659i	−0.793711	+	0.608296i	$0.791854\pi$
$572$	−1.05402e7	−	7.44384e6i	−1.34697	−	0.951277i
$573$	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
$583$	−1.11446e6	−	787073.i	−0.135798	−	0.0959056i
$584$			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	0.199539	−	0.979890i	$-0.436055\pi$
$593$	−6.68231e6	−	6.68231e6i	−0.780351	−	0.780351i	−0.979890	+	0.199539i	$0.936055\pi$
$594$	−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	$0.0231164\pi$
$601$			1.28500e6i			0.145117i	−0.997364	+	0.0725584i	$0.976884\pi$
$602$	−451947.	+	451947.i	−0.0508272	+	0.0508272i
$603$	−1.32313e6	+	1.32313e6i	−0.148186	+	0.148186i
$604$	−1.24508e7			−1.38869
$605$	2.12332e6	+	8.74906e6i	0.235845	+	0.971791i
$606$	378516.			0.0418700
$607$	2.93816e6	−	2.93816e6i	0.323671	−	0.323671i	−0.526502	−	0.850174i	$-0.676497\pi$
$607$	2.93816e6	−	2.93816e6i	0.323671	−	0.323671i	0.850174	+	0.526502i	$0.176497\pi$
$608$	−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	0.815975	−	0.578087i	$-0.196200\pi$
$613$	2.21322e6	+	2.21322e6i	0.237889	+	0.237889i	−0.578087	+	0.815975i	$0.696200\pi$
$614$		−	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
$627$	−1.93548e6	−	1.36691e6i	−0.196617	−	0.138858i
$628$	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
$638$	−1.51412e6	−	1.06932e6i	−0.147268	−	0.104006i
$639$		−	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	$-0.765184\pi$
$659$	−1.65001e7			−1.48004			−0.740020	+	0.672585i	$0.765184\pi$
$660$	−1.65193e6	−	1.44247e6i	−0.147616	−	0.128898i
$661$	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	0.766690	−	0.642018i	$-0.221902\pi$
$673$	1.46489e6	+	1.46489e6i	0.124672	+	0.124672i	−0.642018	+	0.766690i	$0.721902\pi$
$674$		−	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	−0.748490	−	0.663146i	$-0.769221\pi$
$677$	−1.01776e6	+	1.01776e6i	−0.0853441	+	0.0853441i	0.663146	+	0.748490i	$0.269221\pi$
$678$	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
$682$	1.52463e6	+	1.07675e6i	0.125518	+	0.0886449i
$683$	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
$693$	−6.71386e6	+	9.50655e6i	−0.531054	+	0.751951i
$694$			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	$-0.807938\pi$
$701$		−	1.47651e7i		−	1.13486i	0.823422	−	0.567429i	$-0.192062\pi$
$702$	−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
$715$	1.77242e7	+	1.54768e7i	1.29659	+	1.13218i
$716$	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	0.992657	−	0.120966i	$-0.0385991\pi$
$733$	1.26801e7	+	1.26801e7i	0.871691	+	0.871691i	−0.120966	+	0.992657i	$0.538599\pi$
$734$	−138179.			−0.00946677
$735$	−178812.	+	145335.i	−0.0122089	+	0.00992321i
$736$		−	2.67012e6i		−	0.181692i
$737$	−1.86054e6	+	2.63445e6i	−0.126174	+	0.178657i
$738$	2.71569e6	−	2.71569e6i	0.183543	−	0.183543i
$739$	−8.77406e6			−0.591002			−0.295501	−	0.955342i	$-0.595487\pi$
$739$	−8.77406e6			−0.591002			−0.295501	+	0.955342i	$0.595487\pi$
$740$	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	0.954147	−	0.299340i	$-0.0967664\pi$
$743$	9.85338e6	+	9.85338e6i	0.654807	+	0.654807i	−0.299340	+	0.954147i	$0.596766\pi$
$744$	−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
$748$	−8.08596e6	+	1.14494e7i	−0.528418	+	0.748218i
$749$			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	$0.103497\pi$
$761$			1.02068e7i			0.638891i	−0.947605	+	0.319446i	$0.896503\pi$
$762$	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	$-0.126298\pi$
$769$	3.02499e7			1.84462			0.922312	+	0.386447i	$0.126298\pi$
$770$	−218808.	−	3.23244e6i	−0.0132995	−	0.196473i
$771$	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	−0.741776	−	0.670648i	$-0.766016\pi$
$787$	−1.23587e6	+	1.23587e6i	−0.0711273	+	0.0711273i	0.670648	+	0.741776i	$0.266016\pi$
$788$	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
$792$	−5.54454e6	−	3.91575e6i	−0.314089	−	0.221820i
$793$	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
$803$	−8.46076e6	+	1.19801e7i	−0.463042	+	0.655649i
$804$		−	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	$-0.529469\pi$
$809$	−3.44189e6			−0.184895			−0.0924477	+	0.995718i	$0.529469\pi$
$810$	2.11512e6	+	2.60232e6i	0.113272	+	0.139363i
$811$			1.27797e7i			0.682291i	0.940010	+	0.341146i	$0.110815\pi$
$811$			1.27797e7i			0.682291i	−0.940010	+	0.341146i	$0.889185\pi$
$812$	−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	$-0.757871\pi$
$821$		−	2.66295e7i		−	1.37881i	0.724374	−	0.689407i	$-0.242129\pi$
$822$	−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
$825$	2.72620e6	+	2.92594e6i	0.139451	+	0.149668i
$826$	3.29564e6			0.168070
$827$	−2.40113e7	+	2.40113e7i	−1.22082	+	1.22082i	−0.253478	+	0.967341i	$0.581574\pi$
$827$	−2.40113e7	+	2.40113e7i	−1.22082	+	1.22082i	−0.967341	+	0.253478i	$0.918426\pi$
$828$	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
$847$	−8.62409e6	+	1.81116e7i	−0.413052	+	0.867455i
$848$	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	$-0.938642\pi$
$853$	−2.49281e7	−	2.49281e7i	−1.17305	−	1.17305i	−0.191569	−	0.981479i	$-0.561358\pi$
$854$	−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	−0.986624	−	0.163015i	$-0.947878\pi$
$857$	−1.77081e7	+	1.77081e7i	−0.823609	+	0.823609i	0.163015	+	0.986624i	$0.447878\pi$
$858$	−1.27123e6	−	897785.i	−0.0589529	−	0.0416346i
$859$		−	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	$-0.315805\pi$
$877$	3.15258e7	−	3.15258e7i	1.38410	−	1.38410i	0.837193	−	0.546907i	$-0.184195\pi$
$878$	556438.	−	556438.i	0.0243602	−	0.0243602i
$879$	1.13445e6			0.0495239
$880$	−2.00718e7	+	1.35869e6i	−0.873737	+	0.0591444i
$881$	−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	−0.951916	−	0.306358i	$-0.900889\pi$
$887$	−1.51267e7	+	1.51267e7i	−0.645558	+	0.645558i	0.306358	+	0.951916i	$0.400889\pi$
$888$	−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
$902$	3.81872e6	−	5.40715e6i	0.156279	−	0.221285i
$903$	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
$913$	−2.22268e7	+	3.14723e7i	−0.882471	+	1.24954i
$914$		−	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	$-0.379246\pi$
$919$	1.89628e7			0.740650			0.370325	+	0.928902i	$0.379246\pi$
$920$	−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
$935$	1.68118e7	−	1.92531e7i	0.628907	−	0.720232i
$936$	−1.77408e7			−0.661886
$937$	1.04846e7	−	1.04846e7i	0.390123	−	0.390123i	−0.484608	−	0.874731i	$-0.661038\pi$
$937$	1.04846e7	−	1.04846e7i	0.390123	−	0.390123i	0.874731	+	0.484608i	$0.161038\pi$
$938$	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	$0.101028\pi$
$941$			1.69543e7i			0.624173i	−0.950054	+	0.312086i	$0.898972\pi$
$942$	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	0.921898	−	0.387434i	$-0.126638\pi$
$953$	1.49848e7	+	1.49848e7i	0.534464	+	0.534464i	−0.387434	+	0.921898i	$0.626638\pi$
$954$	−917787.			−0.0326491
$955$	−46557.6	+	450805.i	−0.00165189	+	0.0159949i
$956$			2.98120e7i			1.05498i
$957$	4.16435e6	+	2.94101e6i	0.146983	+	0.103805i
$958$	−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	$-0.468903\pi$
$967$	3.17757e7	−	3.17757e7i	1.09277	−	1.09277i	0.995232	−	0.0975384i	$-0.0310969\pi$
$968$	−1.05633e7	−	5.02986e6i	−0.362335	−	0.172531i
$969$			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
$990$	4.56179e6	+	3.98335e6i	0.147927	+	0.129170i
$991$	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	−0.357970	−	0.933733i	$-0.616531\pi$
$997$	1.80710e7	−	1.80710e7i	0.575764	−	0.575764i	0.933733	+	0.357970i	$0.116531\pi$
$998$	−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.32.14	yes	52
5.3	odd	4	inner	55.6.e.b.43.13	yes	52
11.10	odd	2	inner	55.6.e.b.32.13	✓	52
55.43	even	4	inner	55.6.e.b.43.14	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.6.e.b.32.13	✓	52	11.10	odd	2	inner
55.6.e.b.32.14	yes	52	1.1	even	1	trivial
55.6.e.b.43.13	yes	52	5.3	odd	4	inner
55.6.e.b.43.14	yes	52	55.43	even	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 $\F_{q}$
Belyi maps

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} +(380.070 + 268.419i) 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} +(-1045.33 - 738.246i) 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} +(22382.8 - 1515.12i) 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} +(40830.2 + 28835.7i) 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} +(-16818.0 + 23813.6i) 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

Related objects

Downloads

Learn more