LMFDB - Embedded newform 200.6.d.c.101.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,6,Mod(101,200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(200, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("200.101");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	200.d (of order $2$, degree $1$, 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:	$32.0767639626$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} - 130 x^{17} + 144 x^{16} + 1560 x^{15} - 12320 x^{14} - 56128 x^{13} + \cdots + 11\!\cdots\!24 $ x^20 - x^19 - 130x^17 + 144x^16 + 1560x^15 - 12320x^14 - 56128x^13 + 672256x^12 - 4183040x^11 + 25763840x^10 - 133857280x^9 + 688390144x^8 - 1839202304x^7 - 12918456320x^6 + 52344913920x^5 + 154618822656x^4 - 4466765987840x^3 - 35184372088832x + 1125899906842624
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{49}\cdot 5^{4}\cdot 31 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.14
Root			$-2.73024 - 4.95437i$ of defining polynomial
Character	$\chi$	$=$	200.101
Dual form			200.6.d.c.101.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.73024 + 4.95437i) q^{2} -18.7068i q^{3} +(-17.0916 + 27.0532i) q^{4} +(92.6806 - 51.0741i) q^{6} +207.924 q^{7} +(-180.696 - 10.8164i) q^{8} -106.946 q^{9} +O(q^{10})$	\(q+(2.73024 + 4.95437i) q^{2} -18.7068i q^{3} +(-17.0916 + 27.0532i) q^{4} +(92.6806 - 51.0741i) q^{6} +207.924 q^{7} +(-180.696 - 10.8164i) q^{8} -106.946 q^{9} -248.376i q^{11} +(506.080 + 319.730i) q^{12} +532.796i q^{13} +(567.682 + 1030.13i) q^{14} +(-439.755 - 924.766i) q^{16} -710.880 q^{17} +(-291.987 - 529.849i) q^{18} -1347.48i q^{19} -3889.60i q^{21} +(1230.55 - 678.126i) q^{22} +2543.16 q^{23} +(-202.340 + 3380.25i) q^{24} +(-2639.67 + 1454.66i) q^{26} -2545.15i q^{27} +(-3553.75 + 5625.02i) q^{28} +4919.10i q^{29} +7820.61 q^{31} +(3381.00 - 4703.54i) q^{32} -4646.33 q^{33} +(-1940.87 - 3521.96i) q^{34} +(1827.87 - 2893.23i) q^{36} -556.924i q^{37} +(6675.91 - 3678.94i) q^{38} +9966.92 q^{39} +16600.7 q^{41} +(19270.5 - 10619.5i) q^{42} -20896.2i q^{43} +(6719.38 + 4245.14i) q^{44} +(6943.44 + 12599.8i) q^{46} +18789.0 q^{47} +(-17299.4 + 8226.42i) q^{48} +26425.4 q^{49} +13298.3i q^{51} +(-14413.8 - 9106.33i) q^{52} -16768.4i q^{53} +(12609.6 - 6948.85i) q^{54} +(-37571.0 - 2248.98i) q^{56} -25207.1 q^{57} +(-24371.0 + 13430.3i) q^{58} -30302.5i q^{59} -7339.65i q^{61} +(21352.1 + 38746.2i) q^{62} -22236.6 q^{63} +(32534.0 + 3908.94i) q^{64} +(-12685.6 - 23019.6i) q^{66} +34639.2i q^{67} +(12150.1 - 19231.6i) q^{68} -47574.5i q^{69} +50039.0 q^{71} +(19324.6 + 1156.76i) q^{72} -63284.7 q^{73} +(2759.21 - 1520.54i) q^{74} +(36453.7 + 23030.6i) q^{76} -51643.4i q^{77} +(27212.1 + 49379.8i) q^{78} -62964.6 q^{79} -73599.4 q^{81} +(45324.0 + 82246.2i) q^{82} +101298. i q^{83} +(105226. + 66479.5i) q^{84} +(103528. - 57051.6i) q^{86} +92020.7 q^{87} +(-2686.52 + 44880.5i) q^{88} +89208.0 q^{89} +110781. i q^{91} +(-43466.7 + 68800.7i) q^{92} -146299. i q^{93} +(51298.5 + 93087.7i) q^{94} +(-87988.3 - 63247.8i) q^{96} -72491.6 q^{97} +(72147.7 + 130921. i) q^{98} +26562.8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - q^{2} + q^{4} + 33 q^{6} - 196 q^{7} - 391 q^{8} - 1620 q^{9}+O(q^{10}) $ 20 * q - q^2 + q^4 + 33 * q^6 - 196 * q^7 - 391 * q^8 - 1620 * q^9	$ 20 q - q^{2} + q^{4} + 33 q^{6} - 196 q^{7} - 391 q^{8} - 1620 q^{9} - 241 q^{12} - 424 q^{14} - 55 q^{16} - 3368 q^{18} + 1197 q^{22} - 7184 q^{23} + 9459 q^{24} + 9172 q^{26} - 13492 q^{28} + 7160 q^{31} + 7869 q^{32} - 2836 q^{33} - 9591 q^{34} + 14828 q^{36} + 21505 q^{38} + 22452 q^{39} - 5804 q^{41} - 14272 q^{42} - 11593 q^{44} - 37612 q^{46} + 44180 q^{47} + 66571 q^{48} + 62652 q^{49} + 6136 q^{52} + 88947 q^{54} - 36908 q^{56} + 43696 q^{57} - 84012 q^{58} + 87460 q^{62} - 1240 q^{63} + 115177 q^{64} + 131439 q^{66} - 143341 q^{68} - 7724 q^{71} - 25772 q^{72} - 105136 q^{73} + 2112 q^{74} + 55951 q^{76} - 10948 q^{78} - 7780 q^{79} + 96984 q^{81} + 117501 q^{82} - 97556 q^{84} - 65986 q^{86} - 106188 q^{87} - 122597 q^{88} - 3160 q^{89} + 88908 q^{92} - 58540 q^{94} + 57791 q^{96} - 73688 q^{97} + 164655 q^{98}+O(q^{100}) $ 20 * q - q^2 + q^4 + 33 * q^6 - 196 * q^7 - 391 * q^8 - 1620 * q^9 - 241 * q^12 - 424 * q^14 - 55 * q^16 - 3368 * q^18 + 1197 * q^22 - 7184 * q^23 + 9459 * q^24 + 9172 * q^26 - 13492 * q^28 + 7160 * q^31 + 7869 * q^32 - 2836 * q^33 - 9591 * q^34 + 14828 * q^36 + 21505 * q^38 + 22452 * q^39 - 5804 * q^41 - 14272 * q^42 - 11593 * q^44 - 37612 * q^46 + 44180 * q^47 + 66571 * q^48 + 62652 * q^49 + 6136 * q^52 + 88947 * q^54 - 36908 * q^56 + 43696 * q^57 - 84012 * q^58 + 87460 * q^62 - 1240 * q^63 + 115177 * q^64 + 131439 * q^66 - 143341 * q^68 - 7724 * q^71 - 25772 * q^72 - 105136 * q^73 + 2112 * q^74 + 55951 * q^76 - 10948 * q^78 - 7780 * q^79 + 96984 * q^81 + 117501 * q^82 - 97556 * q^84 - 65986 * q^86 - 106188 * q^87 - 122597 * q^88 - 3160 * q^89 + 88908 * q^92 - 58540 * q^94 + 57791 * q^96 - 73688 * q^97 + 164655 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	2.73024	+	4.95437i	0.482643	+	0.875817i
$2$	2.73024	+	4.95437i	0.482643	+	0.875817i
$3$		−	18.7068i		−	1.20004i	−0.799983	−	0.600022i	$-0.795158\pi$
$3$		−	18.7068i		−	1.20004i	0.799983	−	0.600022i	$-0.204842\pi$
$4$	−17.0916	+	27.0532i	−0.534112	+	0.845413i
$5$		0			0
$5$		0			0
$6$	92.6806	−	51.0741i	1.05102	−	0.579192i
$7$	207.924			1.60384			0.801918	−	0.597435i	$-0.203813\pi$
$7$	207.924			1.60384			0.801918	+	0.597435i	$0.203813\pi$
$8$	−180.696	−	10.8164i	−0.998213	−	0.0597525i
$9$	−106.946			−0.440106
$10$		0			0
$11$		−	248.376i		−	0.618911i	−0.950914	−	0.309455i	$-0.899853\pi$
$11$		−	248.376i		−	0.618911i	0.950914	−	0.309455i	$-0.100147\pi$
$12$	506.080	+	319.730i	1.01453	+	0.640958i
$13$			532.796i			0.874384i	0.899368	+	0.437192i	$0.144027\pi$
$13$			532.796i			0.874384i	−0.899368	+	0.437192i	$0.855973\pi$
$14$	567.682	+	1030.13i	0.774079	+	1.40467i
$15$		0			0
$16$	−439.755	−	924.766i	−0.429448	−	0.903092i
$17$	−710.880			−0.596587			−0.298294	−	0.954474i	$-0.596417\pi$
$17$	−710.880			−0.596587			−0.298294	+	0.954474i	$0.596417\pi$
$18$	−291.987	−	529.849i	−0.212414	−	0.385452i
$19$		−	1347.48i		−	0.856324i	−0.903702	−	0.428162i	$-0.859161\pi$
$19$		−	1347.48i		−	0.856324i	0.903702	−	0.428162i	$-0.140839\pi$
$20$		0			0
$21$		−	3889.60i		−	1.92467i
$22$	1230.55	−	678.126i	0.542053	−	0.298713i
$23$	2543.16			1.00243			0.501215	−	0.865323i	$-0.332886\pi$
$23$	2543.16			1.00243			0.501215	+	0.865323i	$0.332886\pi$
$24$	−202.340	+	3380.25i	−0.0717056	+	1.19790i
$25$		0			0
$26$	−2639.67	+	1454.66i	−0.765801	+	0.422015i
$27$		−	2545.15i		−	0.671898i
$28$	−3553.75	+	5625.02i	−0.856628	+	1.35590i
$29$			4919.10i			1.08615i	0.839684	+	0.543076i	$0.182740\pi$
$29$			4919.10i			1.08615i	−0.839684	+	0.543076i	$0.817260\pi$
$30$		0			0
$31$	7820.61			1.46163			0.730814	−	0.682577i	$-0.239141\pi$
$31$	7820.61			1.46163			0.730814	+	0.682577i	$0.239141\pi$
$32$	3381.00	−	4703.54i	0.583674	−	0.811988i
$33$	−4646.33			−0.742720
$34$	−1940.87	−	3521.96i	−0.287938	−	0.522502i
$35$		0			0
$36$	1827.87	−	2893.23i	0.235066	−	0.372071i
$37$		−	556.924i		−	0.0668793i	−0.999441	−	0.0334397i	$-0.989354\pi$
$37$		−	556.924i		−	0.0668793i	0.999441	−	0.0334397i	$-0.0106462\pi$
$38$	6675.91	−	3678.94i	0.749984	−	0.413298i
$39$	9966.92			1.04930
$40$		0			0
$41$	16600.7			1.54230			0.771148	−	0.636656i	$-0.219683\pi$
$41$	16600.7			1.54230			0.771148	+	0.636656i	$0.219683\pi$
$42$	19270.5	−	10619.5i	1.68566	−	0.928929i
$43$		−	20896.2i		−	1.72344i	−0.507383	−	0.861720i	$-0.669387\pi$
$43$		−	20896.2i		−	1.72344i	0.507383	−	0.861720i	$-0.330613\pi$
$44$	6719.38	+	4245.14i	0.523236	+	0.330568i
$45$		0			0
$46$	6943.44	+	12599.8i	0.483816	+	0.877946i
$47$	18789.0			1.24068			0.620339	−	0.784334i	$-0.286995\pi$
$47$	18789.0			1.24068			0.620339	+	0.784334i	$0.286995\pi$
$48$	−17299.4	+	8226.42i	−1.08375	+	0.515356i
$49$	26425.4			1.57229
$50$		0			0
$51$			13298.3i			0.715931i
$52$	−14413.8	−	9106.33i	−0.739216	−	0.467019i
$53$		−	16768.4i		−	0.819979i	−0.912090	−	0.409989i	$-0.865532\pi$
$53$		−	16768.4i		−	0.819979i	0.912090	−	0.409989i	$-0.134468\pi$
$54$	12609.6	−	6948.85i	0.588460	−	0.324286i
$55$		0			0
$56$	−37571.0	−	2248.98i	−1.60097	−	0.0958331i
$57$	−25207.1			−1.02763
$58$	−24371.0	+	13430.3i	−0.951270	+	0.524223i
$59$		−	30302.5i		−	1.13331i	−0.823955	−	0.566656i	$-0.808237\pi$
$59$		−	30302.5i		−	1.13331i	0.823955	−	0.566656i	$-0.191763\pi$
$60$		0			0
$61$		−	7339.65i		−	0.252552i	−0.991995	−	0.126276i	$-0.959698\pi$
$61$		−	7339.65i		−	0.252552i	0.991995	−	0.126276i	$-0.0403025\pi$
$62$	21352.1	+	38746.2i	0.705443	+	1.28012i
$63$	−22236.6			−0.705857
$64$	32534.0	+	3908.94i	0.992859	+	0.119291i
$65$		0			0
$66$	−12685.6	−	23019.6i	−0.358468	−	0.650487i
$67$			34639.2i			0.942717i	0.881942	+	0.471358i	$0.156236\pi$
$67$			34639.2i			0.942717i	−0.881942	+	0.471358i	$0.843764\pi$
$68$	12150.1	−	19231.6i	0.318645	−	0.504363i
$69$		−	47574.5i		−	1.20296i
$70$		0			0
$71$	50039.0			1.17805			0.589023	−	0.808116i	$-0.299513\pi$
$71$	50039.0			1.17805			0.589023	+	0.808116i	$0.299513\pi$
$72$	19324.6	+	1156.76i	0.439319	+	0.0262974i
$73$	−63284.7			−1.38993			−0.694963	−	0.719045i	$-0.744579\pi$
$73$	−63284.7			−1.38993			−0.694963	+	0.719045i	$0.744579\pi$
$74$	2759.21	−	1520.54i	0.0585741	−	0.0322788i
$75$		0			0
$76$	36453.7	+	23030.6i	0.723948	+	0.457373i
$77$		−	51643.4i		−	0.992631i
$78$	27212.1	+	49379.8i	0.506437	+	0.918995i
$79$	−62964.6			−1.13509			−0.567543	−	0.823344i	$-0.692106\pi$
$79$	−62964.6			−1.13509			−0.567543	+	0.823344i	$0.692106\pi$
$80$		0			0
$81$	−73599.4			−1.24641
$82$	45324.0	+	82246.2i	0.744378	+	1.35077i
$83$			101298.i			1.61401i	0.590547	+	0.807004i	$0.298912\pi$
$83$			101298.i			1.61401i	−0.590547	+	0.807004i	$0.701088\pi$
$84$	105226.	+	66479.5i	1.62714	+	1.02799i
$85$		0			0
$86$	103528.	−	57051.6i	1.50942	−	0.831806i
$87$	92020.7			1.30343
$88$	−2686.52	+	44880.5i	−0.0369815	+	0.617805i
$89$	89208.0			1.19379			0.596896	−	0.802318i	$-0.296400\pi$
$89$	89208.0			1.19379			0.596896	+	0.802318i	$0.296400\pi$
$90$		0			0
$91$			110781.i			1.40237i
$92$	−43466.7	+	68800.7i	−0.535411	+	0.847468i
$93$		−	146299.i		−	1.75402i
$94$	51298.5	+	93087.7i	0.598804	+	1.08661i
$95$		0			0
$96$	−87988.3	−	63247.8i	−0.974422	−	0.700434i
$97$	−72491.6			−0.782274			−0.391137	−	0.920333i	$-0.627918\pi$
$97$	−72491.6			−0.782274			−0.391137	+	0.920333i	$0.627918\pi$
$98$	72147.7	+	130921.i	0.758853	+	1.37704i
$99$			26562.8i			0.272386i
$100$		0			0
$101$			93768.8i			0.914650i	0.889300	+	0.457325i	$0.151192\pi$
$101$			93768.8i			0.914650i	−0.889300	+	0.457325i	$0.848808\pi$
$102$	−65884.8	+	36307.6i	−0.627025	+	0.345539i
$103$	−144773.			−1.34461			−0.672304	−	0.740275i	$-0.734695\pi$
$103$	−144773.			−1.34461			−0.672304	+	0.740275i	$0.734695\pi$
$104$	5762.91	−	96274.0i	0.0522466	−	0.872822i
$105$		0			0
$106$	83077.0	−	45781.8i	0.718151	−	0.395756i
$107$		−	83252.5i		−	0.702972i	−0.936193	−	0.351486i	$-0.885676\pi$
$107$		−	83252.5i		−	0.702972i	0.936193	−	0.351486i	$-0.114324\pi$
$108$	68854.4	+	43500.6i	0.568031	+	0.358869i
$109$			8812.12i			0.0710418i	0.999369	+	0.0355209i	$0.0113090\pi$
$109$			8812.12i			0.0710418i	−0.999369	+	0.0355209i	$0.988691\pi$
$110$		0			0
$111$	−10418.3			−0.0802581
$112$	−91435.6	−	192281.i	−0.688764	−	1.44841i
$113$	−57082.3			−0.420538			−0.210269	−	0.977644i	$-0.567434\pi$
$113$	−57082.3			−0.420538			−0.210269	+	0.977644i	$0.567434\pi$
$114$	−68821.3	−	124885.i	−0.495976	−	0.900013i
$115$		0			0
$116$	−133077.	−	84075.2i	−0.918247	−	0.580127i
$117$		−	56980.2i		−	0.384821i
$118$	150130.	−	82733.2i	0.992574	−	0.546984i
$119$	−147809.			−0.956828
$120$		0			0
$121$	99360.3			0.616949
$122$	36363.4	−	20039.0i	0.221189	−	0.121892i
$123$		−	310547.i		−	1.85082i
$124$	−133667.	+	211573.i	−0.780673	+	1.23568i
$125$		0			0
$126$	−60711.2	−	110168.i	−0.340677	−	0.618202i
$127$	38513.8			0.211888			0.105944	−	0.994372i	$-0.466214\pi$
$127$	38513.8			0.211888			0.105944	+	0.994372i	$0.466214\pi$
$128$	69459.3	+	171858.i	0.374719	+	0.927139i
$129$	−390902.			−2.06820
$130$		0			0
$131$			330785.i			1.68410i	0.539402	+	0.842049i	$0.318650\pi$
$131$			330785.i			1.68410i	−0.539402	+	0.842049i	$0.681350\pi$
$132$	79413.2	−	125698.i	0.396696	−	0.627906i
$133$		−	280173.i		−	1.37340i
$134$	−171616.	+	94573.4i	−0.825648	+	0.454995i
$135$		0			0
$136$	128453.	+	7689.13i	0.595521	+	0.0356476i
$137$	−116224.			−0.529046			−0.264523	−	0.964379i	$-0.585214\pi$
$137$	−116224.			−0.529046			−0.264523	+	0.964379i	$0.585214\pi$
$138$	235702.	−	129890.i	1.05357	−	0.580600i
$139$		−	247733.i		−	1.08755i	−0.839233	−	0.543773i	$-0.816995\pi$
$139$		−	247733.i		−	1.08755i	0.839233	−	0.543773i	$-0.183005\pi$
$140$		0			0
$141$		−	351483.i		−	1.48887i
$142$	136618.	+	247912.i	0.568576	+	1.03175i
$143$	132334.			0.541166
$144$	47029.9	+	98899.7i	0.189002	+	0.397456i
$145$		0			0
$146$	−172782.	−	313536.i	−0.670838	−	1.21732i
$147$		−	494336.i		−	1.88681i
$148$	15066.6	+	9518.72i	0.0565407	+	0.0357211i
$149$		−	219932.i		−	0.811566i	−0.913970	−	0.405783i	$-0.866999\pi$
$149$		−	219932.i		−	0.811566i	0.913970	−	0.405783i	$-0.133001\pi$
$150$		0			0
$151$	−265570.			−0.947845			−0.473923	−	0.880566i	$-0.657162\pi$
$151$	−265570.			−0.947845			−0.473923	+	0.880566i	$0.657162\pi$
$152$	−14574.8	+	243484.i	−0.0511675	+	0.854794i
$153$	76025.6			0.262562
$154$	255860.	−	140999.i	0.869363	−	0.479086i
$155$		0			0
$156$	−170351.	+	269637.i	−0.560444	+	0.887092i
$157$			263705.i			0.853825i	0.904293	+	0.426913i	$0.140399\pi$
$157$			263705.i			0.853825i	−0.904293	+	0.426913i	$0.859601\pi$
$158$	−171908.	−	311950.i	−0.547841	−	0.994129i
$159$	−313684.			−0.984010
$160$		0			0
$161$	528785.			1.60773
$162$	−200944.	−	364639.i	−0.601572	−	1.09163i
$163$		−	165569.i		−	0.488102i	−0.969762	−	0.244051i	$-0.921524\pi$
$163$		−	165569.i		−	0.488102i	0.969762	−	0.244051i	$-0.0784764\pi$
$164$	−283733.	+	449104.i	−0.823759	+	1.30388i
$165$		0			0
$166$	−501868.	+	276568.i	−1.41358	+	0.778988i
$167$	−522240.			−1.44903			−0.724517	−	0.689257i	$-0.757937\pi$
$167$	−522240.			−1.44903			−0.724517	+	0.689257i	$0.757937\pi$
$168$	−42071.3	+	702835.i	−0.115004	+	1.92123i
$169$	87421.7			0.235452
$170$		0			0
$171$			144107.i			0.376873i
$172$	565310.	+	357150.i	1.45702	+	0.920511i
$173$			86351.3i			0.219358i	0.993967	+	0.109679i	$0.0349823\pi$
$173$			86351.3i			0.219358i	−0.993967	+	0.109679i	$0.965018\pi$
$174$	251238.	+	455905.i	0.629090	+	1.14157i
$175$		0			0
$176$	−229690.	+	109225.i	−0.558933	+	0.265790i
$177$	−566865.			−1.36002
$178$	243559.	+	441970.i	0.576175	+	1.04554i
$179$			259789.i			0.606021i	0.952987	+	0.303011i	$0.0979918\pi$
$179$			259789.i			0.606021i	−0.952987	+	0.303011i	$0.902008\pi$
$180$		0			0
$181$		−	252177.i		−	0.572149i	−0.958207	−	0.286075i	$-0.907649\pi$
$181$		−	252177.i		−	0.572149i	0.958207	−	0.286075i	$-0.0923506\pi$
$182$	−548851.	+	302459.i	−1.22822	+	0.676843i
$183$	−137302.			−0.303074
$184$	−459539.	−	27507.7i	−1.00064	−	0.0598977i
$185$		0			0
$186$	724819.	−	399431.i	1.53620	−	0.846563i
$187$			176566.i			0.369234i
$188$	−321134.	+	508303.i	−0.662661	+	1.04889i
$189$		−	529197.i		−	1.07761i
$190$		0			0
$191$	−83016.5			−0.164657			−0.0823286	−	0.996605i	$-0.526236\pi$
$191$	−83016.5			−0.164657			−0.0823286	+	0.996605i	$0.526236\pi$
$192$	73123.9	−	608608.i	0.143155	−	1.19147i
$193$	840228.			1.62369			0.811847	−	0.583871i	$-0.198462\pi$
$193$	840228.			1.62369			0.811847	+	0.583871i	$0.198462\pi$
$194$	−197919.	−	359151.i	−0.377558	−	0.685129i
$195$		0			0
$196$	−451653.	+	714893.i	−0.839778	+	1.32923i
$197$			837383.i			1.53730i	0.639670	+	0.768650i	$0.279071\pi$
$197$			837383.i			1.53730i	−0.639670	+	0.768650i	$0.720929\pi$
$198$	−131602.	+	72522.6i	−0.238561	+	0.131465i
$199$	617977.			1.10621			0.553107	−	0.833110i	$-0.313442\pi$
$199$	617977.			1.10621			0.553107	+	0.833110i	$0.313442\pi$
$200$		0			0
$201$	647990.			1.13130
$202$	−464565.	+	256011.i	−0.801066	+	0.441449i
$203$			1.02280e6i			1.74201i
$204$	−359762.	−	227289.i	−0.605258	−	0.382388i
$205$		0			0
$206$	−395266.	−	717261.i	−0.648965	−	1.17763i
$207$	−271980.			−0.441175
$208$	492711.	−	234299.i	0.789649	−	0.375502i
$209$	−334682.			−0.529988
$210$		0			0
$211$			790210.i			1.22190i	0.791668	+	0.610951i	$0.209213\pi$
$211$			790210.i			1.22190i	−0.791668	+	0.610951i	$0.790787\pi$
$212$	453640.	+	286599.i	0.693221	+	0.437961i
$213$		−	936071.i		−	1.41371i
$214$	412464.	−	227299.i	0.615675	−	0.339284i
$215$		0			0
$216$	−27529.2	+	459897.i	−0.0401476	+	0.670697i
$217$	1.62609e6			2.34421
$218$	−43658.5	+	24059.2i	−0.0622197	+	0.0342878i
$219$			1.18386e6i			1.66797i
$220$		0			0
$221$		−	378754.i		−	0.521647i
$222$	−28444.4	−	51616.1i	−0.0387360	−	0.0702915i
$223$	−1.18057e6			−1.58976			−0.794879	−	0.606769i	$-0.792465\pi$
$223$	−1.18057e6			−1.58976			−0.794879	+	0.606769i	$0.792465\pi$
$224$	702991.	−	977979.i	0.936116	−	1.30230i
$225$		0			0
$226$	−155848.	−	282807.i	−0.202970	−	0.368315i
$227$		−	787220.i		−	1.01398i	−0.861951	−	0.506992i	$-0.830757\pi$
$227$		−	787220.i		−	1.01398i	0.861951	−	0.506992i	$-0.169243\pi$
$228$	430829.	−	681933.i	0.548868	−	0.868769i
$229$		−	449368.i		−	0.566257i	−0.959082	−	0.283129i	$-0.908628\pi$
$229$		−	449368.i		−	0.566257i	0.959082	−	0.283129i	$-0.0913723\pi$
$230$		0			0
$231$	−966084.			−1.19120
$232$	53206.7	−	888860.i	0.0649002	−	1.08421i
$233$	−577938.			−0.697415			−0.348708	−	0.937232i	$-0.613379\pi$
$233$	−577938.			−0.697415			−0.348708	+	0.937232i	$0.613379\pi$
$234$	282301.	−	155570.i	0.337033	−	0.185731i
$235$		0			0
$236$	819782.	+	517919.i	0.958116	+	0.605315i
$237$			1.17787e6i			1.36215i
$238$	−403554.	−	732301.i	−0.461806	−	0.838006i
$239$	470229.			0.532494			0.266247	−	0.963905i	$-0.414216\pi$
$239$	470229.			0.532494			0.266247	+	0.963905i	$0.414216\pi$
$240$		0			0
$241$	−348925.			−0.386981			−0.193490	−	0.981102i	$-0.561981\pi$
$241$	−348925.			−0.386981			−0.193490	+	0.981102i	$0.561981\pi$
$242$	271277.	+	492268.i	0.297766	+	0.540335i
$243$			758342.i			0.823852i
$244$	198561.	+	125446.i	0.213511	+	0.134891i
$245$		0			0
$246$	1.53857e6	−	847868.i	1.62098	−	0.893286i
$247$	717931.			0.748756
$248$	−1.41315e6	−	84590.5i	−1.45902	−	0.0873358i
$249$	1.89496e6			1.93688
$250$		0			0
$251$		−	261709.i		−	0.262201i	−0.991369	−	0.131100i	$-0.958149\pi$
$251$		−	261709.i		−	0.262201i	0.991369	−	0.131100i	$-0.0418510\pi$
$252$	380059.	−	601571.i	0.377007	−	0.596741i
$253$		−	631661.i		−	0.620415i
$254$	105152.	+	190812.i	0.102266	+	0.185575i
$255$		0			0
$256$	−661808.	+	813340.i	−0.631149	+	0.775662i
$257$	−333856.			−0.315301			−0.157651	−	0.987495i	$-0.550392\pi$
$257$	−333856.			−0.315301			−0.157651	+	0.987495i	$0.550392\pi$
$258$	−1.06726e6	−	1.93667e6i	−0.998204	−	1.81137i
$259$		−	115798.i		−	0.107263i
$260$		0			0
$261$		−	526076.i		−	0.478021i
$262$	−1.63883e6	+	903121.i	−1.47496	+	0.812817i
$263$	−656633.			−0.585374			−0.292687	−	0.956208i	$-0.594549\pi$
$263$	−656633.			−0.585374			−0.292687	+	0.956208i	$0.594549\pi$
$264$	839573.	+	50256.3i	0.741393	+	0.0443794i
$265$		0			0
$266$	1.38808e6	−	764940.i	1.20285	−	0.662863i
$267$		−	1.66880e6i		−	1.43260i
$268$	−937103.	−	592040.i	−0.796986	−	0.503517i
$269$			55281.5i			0.0465799i	0.999729	+	0.0232900i	$0.00741410\pi$
$269$			55281.5i			0.0465799i	−0.999729	+	0.0232900i	$0.992586\pi$
$270$		0			0
$271$	−1.54431e6			−1.27735			−0.638676	−	0.769476i	$-0.720517\pi$
$271$	−1.54431e6			−1.27735			−0.638676	+	0.769476i	$0.720517\pi$
$272$	312613.	+	657398.i	0.256203	+	0.538773i
$273$	2.07236e6			1.68290
$274$	−317318.	−	575815.i	−0.255340	−	0.463348i
$275$		0			0
$276$	1.28704e6	+	813124.i	1.01700	+	0.642516i
$277$		−	2.13142e6i		−	1.66905i	−0.550968	−	0.834527i	$-0.685741\pi$
$277$		−	2.13142e6i		−	1.66905i	0.550968	−	0.834527i	$-0.314259\pi$
$278$	1.22736e6	−	676371.i	0.952491	−	0.524896i
$279$	−836381.			−0.643270
$280$		0			0
$281$	1.14339e6			0.863830			0.431915	−	0.901914i	$-0.357838\pi$
$281$	1.14339e6			0.863830			0.431915	+	0.901914i	$0.357838\pi$
$282$	1.74138e6	−	959632.i	1.30398	−	0.718591i
$283$			2.20775e6i			1.63864i	0.573334	+	0.819321i	$0.305650\pi$
$283$			2.20775e6i			1.63864i	−0.573334	+	0.819321i	$0.694350\pi$
$284$	−855246.	+	1.35372e6i	−0.629209	+	0.995937i
$285$		0			0
$286$	361303.	+	655630.i	0.261190	+	0.473962i
$287$	3.45169e6			2.47359
$288$	−361583.	+	503023.i	−0.256878	+	0.357361i
$289$	−914506.			−0.644083
$290$		0			0
$291$			1.35609e6i			0.938763i
$292$	1.08164e6	−	1.71206e6i	0.742377	−	1.17506i
$293$			2.76500e6i			1.88159i	0.338970	+	0.940797i	$0.389921\pi$
$293$			2.76500e6i			1.88159i	−0.338970	+	0.940797i	$0.610079\pi$
$294$	2.44913e6	−	1.34966e6i	1.65250	−	0.910657i
$295$		0			0
$296$	−6023.89	+	100634.i	−0.00399620	+	0.0667598i
$297$	−632153.			−0.415845
$298$	1.08963e6	−	600468.i	0.710783	−	0.391696i
$299$			1.35499e6i			0.876510i
$300$		0			0
$301$		−	4.34483e6i		−	2.76412i
$302$	−725071.	−	1.31573e6i	−0.457470	−	0.830139i
$303$	1.75412e6			1.09762
$304$	−1.24610e6	+	592560.i	−0.773339	+	0.367747i
$305$		0			0
$306$	207568.	+	376659.i	0.126723	+	0.229956i
$307$			1.14034e6i			0.690537i	0.938504	+	0.345268i	$0.112212\pi$
$307$			1.14034e6i			0.690537i	−0.938504	+	0.345268i	$0.887788\pi$
$308$	1.39712e6	+	882668.i	0.839184	+	0.530176i
$309$			2.70825e6i			1.61359i
$310$		0			0
$311$	396745.			0.232600			0.116300	−	0.993214i	$-0.462897\pi$
$311$	396745.			0.232600			0.116300	+	0.993214i	$0.462897\pi$
$312$	−1.80098e6	−	107806.i	−1.04742	−	0.0626982i
$313$	−2.25272e6			−1.29971			−0.649854	−	0.760059i	$-0.725170\pi$
$313$	−2.25272e6			−1.29971			−0.649854	+	0.760059i	$0.725170\pi$
$314$	−1.30649e6	+	719977.i	−0.747795	+	0.412092i
$315$		0			0
$316$	1.07617e6	−	1.70340e6i	0.606264	−	0.959617i
$317$			3.20646e6i			1.79216i	0.443890	+	0.896082i	$0.353598\pi$
$317$			3.20646e6i			1.79216i	−0.443890	+	0.896082i	$0.646402\pi$
$318$	−856432.	−	1.55411e6i	−0.474925	−	0.861813i
$319$	1.22179e6			0.672231
$320$		0			0
$321$	−1.55739e6			−0.843597
$322$	1.44371e6	+	2.61980e6i	0.775961	+	1.40808i
$323$			957896.i			0.510872i
$324$	1.25793e6	−	1.99110e6i	0.665724	−	1.05373i
$325$		0			0
$326$	820291.	−	452043.i	0.427488	−	0.235579i
$327$	164847.			0.0852533
$328$	−2.99969e6	−	179559.i	−1.53954	−	0.0921560i
$329$	3.90669e6			1.98984
$330$		0			0
$331$			3.04724e6i			1.52875i	0.644772	+	0.764375i	$0.276952\pi$
$331$			3.04724e6i			1.52875i	−0.644772	+	0.764375i	$0.723048\pi$
$332$	−2.74044e6	−	1.73134e6i	−1.36450	−	0.862061i
$333$			59560.6i			0.0294340i
$334$	−1.42584e6	−	2.58737e6i	−0.699366	−	1.26909i
$335$		0			0
$336$	−3.59697e6	+	1.71047e6i	−1.73816	+	0.826547i
$337$	−1.97900e6			−0.949230			−0.474615	−	0.880194i	$-0.657413\pi$
$337$	−1.97900e6			−0.949230			−0.474615	+	0.880194i	$0.657413\pi$
$338$	238682.	+	433120.i	0.113639	+	0.206213i
$339$			1.06783e6i			0.504664i
$340$		0			0
$341$		−	1.94245e6i		−	0.904617i
$342$	−713960.	+	393447.i	−0.330072	+	0.181895i
$343$	1.99990e6			0.917854
$344$	−226021.	+	3.77586e6i	−0.102980	+	1.72036i
$345$		0			0
$346$	−427817.	+	235760.i	−0.192118	+	0.105872i
$347$			1.24203e6i			0.553743i	0.960907	+	0.276871i	$0.0892976\pi$
$347$			1.24203e6i			0.553743i	−0.960907	+	0.276871i	$0.910702\pi$
$348$	−1.57278e6	+	2.48946e6i	−0.696178	+	1.10194i
$349$			82246.3i			0.0361454i	0.999837	+	0.0180727i	$0.00575303\pi$
$349$			82246.3i			0.0361454i	−0.999837	+	0.0180727i	$0.994247\pi$
$350$		0			0
$351$	1.35604e6			0.587497
$352$	−1.16825e6	−	839759.i	−0.502548	−	0.361242i
$353$	644542.			0.275305			0.137653	−	0.990481i	$-0.456044\pi$
$353$	644542.			0.275305			0.137653	+	0.990481i	$0.456044\pi$
$354$	−1.54768e6	−	2.80846e6i	−0.656405	−	1.19113i
$355$		0			0
$356$	−1.52471e6	+	2.41337e6i	−0.637620	+	1.00925i
$357$			2.76504e6i			1.14824i
$358$	−1.28709e6	+	709285.i	−0.530764	+	0.292492i
$359$	−868645.			−0.355718			−0.177859	−	0.984056i	$-0.556917\pi$
$359$	−868645.			−0.355718			−0.177859	+	0.984056i	$0.556917\pi$
$360$		0			0
$361$	660398.			0.266709
$362$	1.24938e6	−	688504.i	0.501098	−	0.276144i
$363$		−	1.85872e6i		−	0.740366i
$364$	−2.99699e6	−	1.89343e6i	−1.18558	−	0.749022i
$365$		0			0
$366$	−374866.	−	680243.i	−0.146276	−	0.265437i
$367$	−1.09793e6			−0.425510			−0.212755	−	0.977106i	$-0.568244\pi$
$367$	−1.09793e6			−0.425510			−0.212755	+	0.977106i	$0.568244\pi$
$368$	−1.11837e6	−	2.35183e6i	−0.430492	−	0.905287i
$369$	−1.77538e6			−0.678773
$370$		0			0
$371$		−	3.48656e6i		−	1.31511i
$372$	3.95786e6	+	2.50048e6i	1.48287	+	0.936842i
$373$		−	1.06332e6i		−	0.395724i	−0.980230	−	0.197862i	$-0.936600\pi$
$373$		−	1.06332e6i		−	0.395724i	0.980230	−	0.197862i	$-0.0633999\pi$
$374$	−874772.	+	482066.i	−0.323382	+	0.178208i
$375$		0			0
$376$	−3.39510e6	−	203228.i	−1.23846	−	0.0741336i
$377$	−2.62087e6			−0.949713
$378$	2.62184e6	−	1.44483e6i	0.943793	−	0.520102i
$379$		−	3.34165e6i		−	1.19499i	−0.801874	−	0.597493i	$-0.796163\pi$
$379$		−	3.34165e6i		−	1.19499i	0.801874	−	0.597493i	$-0.203837\pi$
$380$		0			0
$381$		−	720471.i		−	0.254275i
$382$	−226655.	−	411295.i	−0.0794706	−	0.144210i
$383$	1.62135e6			0.564780			0.282390	−	0.959300i	$-0.408873\pi$
$383$	1.62135e6			0.564780			0.282390	+	0.959300i	$0.408873\pi$
$384$	3.21492e6	−	1.29936e6i	1.11261	−	0.449679i
$385$		0			0
$386$	2.29402e6	+	4.16280e6i	0.783663	+	1.42206i
$387$			2.23476e6i			0.758496i
$388$	1.23900e6	−	1.96113e6i	0.417822	−	0.661345i
$389$		−	3.12030e6i		−	1.04550i	−0.852487	−	0.522749i	$-0.824907\pi$
$389$		−	3.12030e6i		−	1.04550i	0.852487	−	0.522749i	$-0.175093\pi$
$390$		0			0
$391$	−1.80788e6			−0.598038
$392$	−4.77497e6	−	285827.i	−1.56948	−	0.0939480i
$393$	6.18793e6			2.02099
$394$	−4.14871e6	+	2.28625e6i	−1.34639	+	0.741966i
$395$		0			0
$396$	−718608.	−	454000.i	−0.230279	−	0.145485i
$397$		−	4.39289e6i		−	1.39886i	−0.714701	−	0.699430i	$-0.753437\pi$
$397$		−	4.39289e6i		−	1.39886i	0.714701	−	0.699430i	$-0.246563\pi$
$398$	1.68722e6	+	3.06169e6i	0.533906	+	0.968842i
$399$	−5.24116e6			−1.64814
$400$		0			0
$401$	−504022.			−0.156527			−0.0782634	−	0.996933i	$-0.524938\pi$
$401$	−504022.			−0.156527			−0.0782634	+	0.996933i	$0.524938\pi$
$402$	1.76917e6	+	3.21039e6i	0.546014	+	0.990814i
$403$			4.16679e6i			1.27802i
$404$	−2.53675e6	−	1.60266e6i	−0.773257	−	0.488526i
$405$		0			0
$406$	−5.06732e6	+	2.79248e6i	−1.52568	+	0.840767i
$407$	−138327.			−0.0413923
$408$	143839.	−	2.40295e6i	0.0427787	−	0.714652i
$409$	−778374.			−0.230080			−0.115040	−	0.993361i	$-0.536700\pi$
$409$	−778374.			−0.230080			−0.115040	+	0.993361i	$0.536700\pi$
$410$		0			0
$411$			2.17418e6i			0.634878i
$412$	2.47441e6	−	3.91659e6i	0.718172	−	1.13675i
$413$		−	6.30063e6i		−	1.81764i
$414$	−742571.	−	1.34749e6i	−0.212930	−	0.386389i
$415$		0			0
$416$	2.50603e6	+	1.80138e6i	0.709990	+	0.510355i
$417$	−4.63431e6			−1.30510
$418$	−913761.	−	1.65814e6i	−0.255795	−	0.464173i
$419$			142016.i			0.0395186i	0.999805	+	0.0197593i	$0.00628999\pi$
$419$			142016.i			0.0395186i	−0.999805	+	0.0197593i	$0.993710\pi$
$420$		0			0
$421$			6.74295e6i			1.85415i	0.374878	+	0.927074i	$0.377685\pi$
$421$			6.74295e6i			1.85415i	−0.374878	+	0.927074i	$0.622315\pi$
$422$	−3.91499e6	+	2.15746e6i	−1.07016	+	0.589742i
$423$	−2.00940e6			−0.546029
$424$	−181373.	+	3.02998e6i	−0.0489957	+	0.818513i
$425$		0			0
$426$	4.63764e6	−	2.55570e6i	1.23815	−	0.682316i
$427$		−	1.52609e6i		−	0.405052i
$428$	2.25225e6	+	1.42292e6i	0.594302	+	0.375466i
$429$		−	2.47554e6i		−	0.649423i
$430$		0			0
$431$	2.72061e6			0.705462			0.352731	−	0.935725i	$-0.385253\pi$
$431$	2.72061e6			0.705462			0.352731	+	0.935725i	$0.385253\pi$
$432$	−2.35366e6	+	1.11924e6i	−0.606785	+	0.288545i
$433$	−2.02929e6			−0.520145			−0.260073	−	0.965589i	$-0.583747\pi$
$433$	−2.02929e6			−0.520145			−0.260073	+	0.965589i	$0.583747\pi$
$434$	4.43962e6	+	8.05627e6i	1.13141	+	2.05310i
$435$		0			0
$436$	−238396.	−	150613.i	−0.0600597	−	0.0379443i
$437$		−	3.42686e6i		−	0.858406i
$438$	−5.86527e6	+	3.23221e6i	−1.46084	+	0.805035i
$439$	−714833.			−0.177028			−0.0885142	−	0.996075i	$-0.528212\pi$
$439$	−714833.			−0.177028			−0.0885142	+	0.996075i	$0.528212\pi$
$440$		0			0
$441$	−2.82609e6			−0.691973
$442$	1.87649e6	−	1.03409e6i	0.456867	−	0.251769i
$443$			570008.i			0.137998i	0.997617	+	0.0689988i	$0.0219805\pi$
$443$			570008.i			0.137998i	−0.997617	+	0.0689988i	$0.978020\pi$
$444$	178065.	−	281848.i	0.0428669	−	0.0678513i
$445$		0			0
$446$	−3.22325e6	−	5.84900e6i	−0.767284	−	1.39234i
$447$	−4.11424e6			−0.973915
$448$	6.76461e6	+	812763.i	1.59238	+	0.191324i
$449$	−2.75906e6			−0.645871			−0.322935	−	0.946421i	$-0.604670\pi$
$449$	−2.75906e6			−0.645871			−0.322935	+	0.946421i	$0.604670\pi$
$450$		0			0
$451$		−	4.12323e6i		−	0.954544i
$452$	975628.	−	1.54426e6i	0.224615	−	0.355529i
$453$			4.96798e6i			1.13746i
$454$	3.90018e6	−	2.14930e6i	0.888065	−	0.489392i
$455$		0			0
$456$	4.55482e6	+	272649.i	1.02579	+	0.0614032i
$457$	6.21046e6			1.39102			0.695509	−	0.718517i	$-0.255179\pi$
$457$	6.21046e6			1.39102			0.695509	+	0.718517i	$0.255179\pi$
$458$	2.22634e6	−	1.22688e6i	0.495938	−	0.273300i
$459$			1.80929e6i			0.400846i
$460$		0			0
$461$		−	440438.i		−	0.0965233i	−0.998835	−	0.0482616i	$-0.984632\pi$
$461$		−	440438.i		−	0.0965233i	0.998835	−	0.0482616i	$-0.0153681\pi$
$462$	−2.63764e6	−	4.78634e6i	−0.574924	−	1.04327i
$463$	−2.73560e6			−0.593062			−0.296531	−	0.955023i	$-0.595830\pi$
$463$	−2.73560e6			−0.593062			−0.296531	+	0.955023i	$0.595830\pi$
$464$	4.54901e6	−	2.16319e6i	0.980894	−	0.466445i
$465$		0			0
$466$	−1.57791e6	−	2.86332e6i	−0.336602	−	0.610808i
$467$		−	1.58504e6i		−	0.336315i	−0.985760	−	0.168158i	$-0.946218\pi$
$467$		−	1.58504e6i		−	0.336315i	0.985760	−	0.168158i	$-0.0537818\pi$
$468$	1.54150e6	+	973883.i	0.325333	+	0.205538i
$469$			7.20233e6i			1.51196i
$470$		0			0
$471$	4.93308e6			1.02463
$472$	−327763.	+	5.47555e6i	−0.0677181	+	1.13129i
$473$	−5.19012e6			−1.06666
$474$	−5.83560e6	+	3.21586e6i	−1.19300	+	0.657433i
$475$		0			0
$476$	2.52629e6	−	3.99871e6i	0.511054	−	0.808915i
$477$			1.79331e6i			0.360877i
$478$	1.28384e6	+	2.32969e6i	0.257004	+	0.466368i
$479$	3.74059e6			0.744906			0.372453	−	0.928051i	$-0.378517\pi$
$479$	3.74059e6			0.744906			0.372453	+	0.928051i	$0.378517\pi$
$480$		0			0
$481$	296727.			0.0584782
$482$	−952648.	−	1.72870e6i	−0.186773	−	0.338925i
$483$		−	9.89189e6i		−	1.92935i
$484$	−1.69823e6	+	2.68802e6i	−0.329520	+	0.521577i
$485$		0			0
$486$	−3.75711e6	+	2.07045e6i	−0.721544	+	0.397626i
$487$	4.32680e6			0.826694			0.413347	−	0.910574i	$-0.364360\pi$
$487$	4.32680e6			0.826694			0.413347	+	0.910574i	$0.364360\pi$
$488$	−79388.2	+	1.32624e6i	−0.0150906	+	0.252101i
$489$	−3.09728e6			−0.585744
$490$		0			0
$491$		−	1.43888e6i		−	0.269352i	−0.990890	−	0.134676i	$-0.957001\pi$
$491$		−	1.43888e6i		−	0.269352i	0.990890	−	0.134676i	$-0.0429994\pi$
$492$	8.40131e6	+	5.30775e6i	1.56471	+	0.988548i
$493$		−	3.49689e6i		−	0.647984i
$494$	1.96012e6	+	3.55690e6i	0.361382	+	0.655774i
$495$		0			0
$496$	−3.43915e6	−	7.23224e6i	−0.627693	−	1.31998i
$497$	1.04043e7			1.88939
$498$	5.17370e6	+	9.38836e6i	0.934820	+	1.69635i
$499$			1.56596e6i			0.281532i	0.990043	+	0.140766i	$0.0449566\pi$
$499$			1.56596e6i			0.281532i	−0.990043	+	0.140766i	$0.955043\pi$
$500$		0			0
$501$			9.76945e6i			1.73891i
$502$	1.29660e6	−	714527.i	0.229640	−	0.126549i
$503$	−1.79997e6			−0.317209			−0.158604	−	0.987342i	$-0.550699\pi$
$503$	−1.79997e6			−0.317209			−0.158604	+	0.987342i	$0.550699\pi$
$504$	4.01806e6	+	240519.i	0.704596	+	0.0421767i
$505$		0			0
$506$	3.12948e6	−	1.72458e6i	0.543370	−	0.299439i
$507$		−	1.63538e6i		−	0.282553i
$508$	−658262.	+	1.04192e6i	−0.113172	+	0.179133i
$509$		−	3.91215e6i		−	0.669301i	−0.942342	−	0.334651i	$-0.891382\pi$
$509$		−	3.91215e6i		−	0.669301i	0.942342	−	0.334651i	$-0.108618\pi$
$510$		0			0
$511$	−1.31584e7			−2.22921
$512$	−5.83648e6	−	1.05823e6i	−0.983957	−	0.178404i
$513$	−3.42953e6			−0.575362
$514$	−911505.	−	1.65404e6i	−0.152178	−	0.276146i
$515$		0			0
$516$	6.68114e6	−	1.05752e7i	1.10465	−	1.74849i
$517$		−	4.66674e6i		−	0.767869i
$518$	573706.	−	316156.i	0.0939431	−	0.0517699i
$519$	1.61536e6			0.263239
$520$		0			0
$521$	4.76005e6			0.768276			0.384138	−	0.923276i	$-0.374499\pi$
$521$	4.76005e6			0.768276			0.384138	+	0.923276i	$0.374499\pi$
$522$	2.60638e6	−	1.43631e6i	0.418659	−	0.230713i
$523$		−	9.46692e6i		−	1.51340i	−0.653761	−	0.756701i	$-0.726810\pi$
$523$		−	9.46692e6i		−	1.51340i	0.653761	−	0.756701i	$-0.273190\pi$
$524$	−8.94879e6	−	5.65364e6i	−1.42376	−	0.899497i
$525$		0			0
$526$	−1.79276e6	−	3.25320e6i	−0.282526	−	0.512680i
$527$	−5.55952e6			−0.871988
$528$	2.04325e6	+	4.29677e6i	0.318960	+	0.670744i
$529$	31328.4			0.00486742
$530$		0			0
$531$			3.24073e6i			0.498777i
$532$	7.57960e6	+	4.78861e6i	1.16109	+	0.733551i
$533$			8.84480e6i			1.34856i
$534$	8.26786e6	−	4.55622e6i	1.25470	−	0.691436i
$535$		0			0
$536$	374670.	−	6.25917e6i	0.0563297	−	0.941032i
$537$	4.85983e6			0.727252
$538$	−273885.	+	150932.i	−0.0407955	+	0.0224815i
$539$		−	6.56345e6i		−	0.973106i
$540$		0			0
$541$		−	207950.i		−	0.0305468i	−0.999883	−	0.0152734i	$-0.995138\pi$
$541$		−	207950.i		−	0.0305468i	0.999883	−	0.0152734i	$-0.00486187\pi$
$542$	−4.21633e6	−	7.65107e6i	−0.616504	−	1.11873i
$543$	−4.71744e6			−0.686605
$544$	−2.40348e6	+	3.34365e6i	−0.348212	+	0.484422i
$545$		0			0
$546$	5.65805e6	+	1.02673e7i	0.812241	+	1.47392i
$547$		−	5.52015e6i		−	0.788829i	−0.918933	−	0.394414i	$-0.870947\pi$
$547$		−	5.52015e6i		−	0.788829i	0.918933	−	0.394414i	$-0.129053\pi$
$548$	1.98645e6	−	3.14423e6i	0.282570	−	0.447262i
$549$			784944.i			0.111150i
$550$		0			0
$551$	6.62838e6			0.930097
$552$	−514583.	+	8.59652e6i	−0.0718799	+	1.20081i
$553$	−1.30919e7			−1.82049
$554$	1.05599e7	−	5.81929e6i	1.46179	−	0.805556i
$555$		0			0
$556$	6.70199e6	+	4.23416e6i	0.919426	+	0.580871i
$557$			2.82029e6i			0.385174i	0.981280	+	0.192587i	$0.0616877\pi$
$557$			2.82029e6i			0.385174i	−0.981280	+	0.192587i	$0.938312\pi$
$558$	−2.28352e6	−	4.14374e6i	−0.310470	−	0.563387i
$559$	1.11334e7			1.50695
$560$		0			0
$561$	3.30298e6			0.443098
$562$	3.12172e6	+	5.66477e6i	0.416921	+	0.756557i
$563$		−	1.03425e7i		−	1.37516i	−0.726110	−	0.687579i	$-0.758674\pi$
$563$		−	1.03425e7i		−	1.37516i	0.726110	−	0.687579i	$-0.241326\pi$
$564$	9.50874e6	+	6.00740e6i	1.25871	+	0.795223i
$565$		0			0
$566$	−1.09380e7	+	6.02769e6i	−1.43515	+	0.790879i
$567$	−1.53031e7			−1.99904
$568$	−9.04184e6	−	541239.i	−1.17594	−	0.0703912i
$569$	−1.29533e7			−1.67726			−0.838629	−	0.544704i	$-0.816642\pi$
$569$	−1.29533e7			−1.67726			−0.838629	+	0.544704i	$0.816642\pi$
$570$		0			0
$571$		−	9.98316e6i		−	1.28138i	−0.767800	−	0.640690i	$-0.778648\pi$
$571$		−	9.98316e6i		−	1.28138i	0.767800	−	0.640690i	$-0.221352\pi$
$572$	−2.26179e6	+	3.58005e6i	−0.289043	+	0.457509i
$573$			1.55298e6i			0.197596i
$574$	9.42395e6	+	1.71010e7i	1.19386	+	2.16641i
$575$		0			0
$576$	−3.47937e6	−	418044.i	−0.436963	−	0.0525008i
$577$	4.57444e6			0.572004			0.286002	−	0.958229i	$-0.407674\pi$
$577$	4.57444e6			0.572004			0.286002	+	0.958229i	$0.407674\pi$
$578$	−2.49682e6	−	4.53080e6i	−0.310862	−	0.564100i
$579$		−	1.57180e7i		−	1.94850i
$580$		0			0
$581$			2.10623e7i			2.58860i
$582$	−6.71857e6	+	3.70245e6i	−0.822185	+	0.453087i
$583$	−4.16487e6			−0.507494
$584$	1.14353e7	+	684510.i	1.38744	+	0.0830515i
$585$		0			0
$586$	−1.36988e7	+	7.54911e6i	−1.64793	+	0.908137i
$587$			8.26669e6i			0.990230i	0.868827	+	0.495115i	$0.164874\pi$
$587$			8.26669e6i			0.990230i	−0.868827	+	0.495115i	$0.835126\pi$
$588$	1.33734e7	+	8.44900e6i	1.59514	+	1.00777i
$589$		−	1.05381e7i		−	1.25163i
$590$		0			0
$591$	1.56648e7			1.84483
$592$	−515024.	+	244910.i	−0.0603981	+	0.0287212i
$593$	348483.			0.0406953			0.0203477	−	0.999793i	$-0.493523\pi$
$593$	348483.			0.0406953			0.0203477	+	0.999793i	$0.493523\pi$
$594$	−1.72593e6	−	3.13192e6i	−0.200704	−	0.364204i
$595$		0			0
$596$	5.94988e6	+	3.75900e6i	0.686109	+	0.433467i
$597$		−	1.15604e7i		−	1.32751i
$598$	−6.71310e6	+	3.69943e6i	−0.767662	+	0.423041i
$599$	6.67173e6			0.759751			0.379875	−	0.925038i	$-0.375967\pi$
$599$	6.67173e6			0.759751			0.379875	+	0.925038i	$0.375967\pi$
$600$		0			0
$601$	−9.44178e6			−1.06627			−0.533136	−	0.846030i	$-0.678986\pi$
$601$	−9.44178e6			−1.06627			−0.533136	+	0.846030i	$0.678986\pi$
$602$	2.15259e7	−	1.18624e7i	2.42086	−	1.33408i
$603$		−	3.70452e6i		−	0.414895i
$604$	4.53902e6	−	7.18454e6i	0.506256	−	0.801321i
$605$		0			0
$606$	4.78916e6	+	8.69055e6i	0.529758	+	0.961315i
$607$	5.47399e6			0.603021			0.301510	−	0.953463i	$-0.402509\pi$
$607$	5.47399e6			0.603021			0.301510	+	0.953463i	$0.402509\pi$
$608$	−6.33792e6	−	4.55583e6i	−0.695325	−	0.499814i
$609$	1.91333e7			2.09049
$610$		0			0
$611$			1.00107e7i			1.08483i
$612$	−1.29940e6	+	2.05674e6i	−0.140237	+	0.221973i
$613$			2.24517e6i			0.241322i	0.992694	+	0.120661i	$0.0385014\pi$
$613$			2.24517e6i			0.241322i	−0.992694	+	0.120661i	$0.961499\pi$
$614$	−5.64965e6	+	3.11339e6i	−0.604784	+	0.333282i
$615$		0			0
$616$	−558593.	+	9.33175e6i	−0.0593122	+	0.990857i
$617$	−1.34351e7			−1.42078			−0.710391	−	0.703808i	$-0.751482\pi$
$617$	−1.34351e7			−1.42078			−0.710391	+	0.703808i	$0.751482\pi$
$618$	−1.34177e7	+	7.39418e6i	−1.41321	+	0.778787i
$619$			2.46771e6i			0.258862i	0.991588	+	0.129431i	$0.0413150\pi$
$619$			2.46771e6i			0.258862i	−0.991588	+	0.129431i	$0.958685\pi$
$620$		0			0
$621$		−	6.47272e6i		−	0.673531i
$622$	1.08321e6	+	1.96562e6i	0.112263	+	0.203715i
$623$	1.85485e7			1.91465
$624$	−4.38300e6	−	9.21707e6i	−0.450619	−	0.947614i
$625$		0			0
$626$	−6.15045e6	−	1.11608e7i	−0.627294	−	1.13831i
$627$			6.26084e6i			0.636009i
$628$	−7.13407e6	−	4.50714e6i	−0.721835	−	0.456039i
$629$			395906.i			0.0398993i
$630$		0			0
$631$	5.15502e6			0.515414			0.257707	−	0.966223i	$-0.417033\pi$
$631$	5.15502e6			0.515414			0.257707	+	0.966223i	$0.417033\pi$
$632$	1.13775e7	+	681048.i	1.13306	+	0.0678242i
$633$	1.47823e7			1.46634
$634$	−1.58860e7	+	8.75440e6i	−1.56961	+	0.864974i
$635$		0			0
$636$	5.36136e6	−	8.48617e6i	0.525572	−	0.831896i
$637$			1.40794e7i			1.37478i
$638$	3.33577e6	+	6.05318e6i	0.324447	+	0.588751i
$639$	−5.35145e6			−0.518465
$640$		0			0
$641$	1.37383e7			1.32065			0.660326	−	0.750979i	$-0.270418\pi$
$641$	1.37383e7			1.32065			0.660326	+	0.750979i	$0.270418\pi$
$642$	−4.25205e6	−	7.71590e6i	−0.407156	−	0.738837i
$643$			2.04942e6i			0.195480i	0.995212	+	0.0977401i	$0.0311614\pi$
$643$			2.04942e6i			0.195480i	−0.995212	+	0.0977401i	$0.968839\pi$
$644$	−9.03777e6	+	1.43053e7i	−0.858711	+	1.35920i
$645$		0			0
$646$	−4.74577e6	+	2.61529e6i	−0.447431	+	0.246569i
$647$	5.13222e6			0.481998			0.240999	−	0.970525i	$-0.422525\pi$
$647$	5.13222e6			0.481998			0.240999	+	0.970525i	$0.422525\pi$
$648$	1.32991e7	+	796077.i	1.24419	+	0.0744762i
$649$	−7.52643e6			−0.701418
$650$		0			0
$651$		−	3.04191e7i		−	2.81315i
$652$	4.47918e6	+	2.82984e6i	0.412648	+	0.260701i
$653$		−	8.58895e6i		−	0.788237i	−0.919060	−	0.394119i	$-0.871050\pi$
$653$		−	8.58895e6i		−	0.788237i	0.919060	−	0.394119i	$-0.128950\pi$
$654$	450071.	+	816712.i	0.0411469	+	0.0746663i
$655$		0			0
$656$	−7.30025e6	−	1.53518e7i	−0.662336	−	1.39283i
$657$	6.76803e6			0.611715
$658$	1.06662e7	+	1.93552e7i	0.960383	+	1.74274i
$659$		−	2.45187e6i		−	0.219930i	−0.993935	−	0.109965i	$-0.964926\pi$
$659$		−	2.45187e6i		−	0.219930i	0.993935	−	0.109965i	$-0.0350739\pi$
$660$		0			0
$661$			1.14993e7i			1.02369i	0.859078	+	0.511845i	$0.171038\pi$
$661$			1.14993e7i			1.02369i	−0.859078	+	0.511845i	$0.828962\pi$
$662$	−1.50972e7	+	8.31969e6i	−1.33891	+	0.737840i
$663$	−7.08529e6			−0.625999
$664$	1.09567e6	−	1.83041e7i	0.0964409	−	1.61112i
$665$		0			0
$666$	−295086.	+	162615.i	−0.0257788	+	0.0142061i
$667$			1.25101e7i			1.08879i
$668$	8.92591e6	−	1.41283e7i	0.773947	−	1.22503i
$669$			2.20848e7i			1.90778i
$670$		0			0
$671$	−1.82299e6			−0.156307
$672$	−1.82949e7	−	1.31507e7i	−1.56281	−	1.12338i
$673$	−1.49709e7			−1.27412			−0.637060	−	0.770814i	$-0.719850\pi$
$673$	−1.49709e7			−1.27412			−0.637060	+	0.770814i	$0.719850\pi$
$674$	−5.40315e6	−	9.80471e6i	−0.458139	−	0.831352i
$675$		0			0
$676$	−1.49418e6	+	2.36504e6i	−0.125758	+	0.199054i
$677$		−	1.98421e7i		−	1.66386i	−0.554882	−	0.831929i	$-0.687236\pi$
$677$		−	1.98421e7i		−	1.66386i	0.554882	−	0.831929i	$-0.312764\pi$
$678$	−5.29042e6	+	2.91543e6i	−0.441994	+	0.243572i
$679$	−1.50728e7			−1.25464
$680$		0			0
$681$	−1.47264e7			−1.21683
$682$	9.62364e6	−	5.30336e6i	0.792279	−	0.436607i
$683$			1.04995e7i			0.861226i	0.902537	+	0.430613i	$0.141703\pi$
$683$			1.04995e7i			0.861226i	−0.902537	+	0.430613i	$0.858297\pi$
$684$	−3.89856e6	−	2.46302e6i	−0.318614	−	0.201293i
$685$		0			0
$686$	5.46021e6	+	9.90827e6i	0.442996	+	0.803873i
$687$	−8.40626e6			−0.679534
$688$	−1.93241e7	+	9.18921e6i	−1.55643	+	0.740128i
$689$	8.93414e6			0.716976
$690$		0			0
$691$		−	2.20215e7i		−	1.75449i	−0.480041	−	0.877246i	$-0.659378\pi$
$691$		−	2.20215e7i		−	1.75449i	0.480041	−	0.877246i	$-0.340622\pi$
$692$	−2.33608e6	−	1.47588e6i	−0.185448	−	0.117162i
$693$			5.52304e6i			0.436863i
$694$	−6.15347e6	+	3.39103e6i	−0.484977	+	0.267260i
$695$		0			0
$696$	−1.66278e7	−	995328.i	−1.30110	−	0.0778831i
$697$	−1.18011e7			−0.920114
$698$	−407479.	+	224552.i	−0.0316567	+	0.0174453i
$699$			1.08114e7i			0.836929i
$700$		0			0
$701$		−	2.06117e6i		−	0.158424i	−0.996858	−	0.0792118i	$-0.974760\pi$
$701$		−	2.06117e6i		−	0.158424i	0.996858	−	0.0792118i	$-0.0252403\pi$
$702$	3.70232e6	+	6.71834e6i	0.283551	+	0.514540i
$703$	−750444.			−0.0572704
$704$	970887.	−	8.08067e6i	0.0738307	−	0.614491i
$705$		0			0
$706$	1.75975e6	+	3.19330e6i	0.132874	+	0.241117i
$707$			1.94968e7i			1.46695i
$708$	9.68862e6	−	1.53355e7i	0.726405	−	1.14978i
$709$			1.22382e7i			0.914330i	0.889382	+	0.457165i	$0.151135\pi$
$709$			1.22382e7i			0.914330i	−0.889382	+	0.457165i	$0.848865\pi$
$710$		0			0
$711$	6.73380e6			0.499558
$712$	−1.61195e7	−	964906.i	−1.19166	−	0.0713321i
$713$	1.98891e7			1.46518
$714$	−1.36990e7	+	7.54922e6i	−1.00564	+	0.554187i
$715$		0			0
$716$	−7.02813e6	−	4.44021e6i	−0.512339	−	0.323683i
$717$		−	8.79650e6i		−	0.639016i
$718$	−2.37161e6	−	4.30359e6i	−0.171685	−	0.311544i
$719$	5.55400e6			0.400667			0.200333	−	0.979728i	$-0.435797\pi$
$719$	5.55400e6			0.400667			0.200333	+	0.979728i	$0.435797\pi$
$720$		0			0
$721$	−3.01019e7			−2.15653
$722$	1.80304e6	+	3.27186e6i	0.128725	+	0.233588i
$723$			6.52728e6i			0.464394i
$724$	6.82221e6	+	4.31011e6i	0.483703	+	0.305592i
$725$		0			0
$726$	9.20878e6	−	5.07474e6i	0.648426	−	0.357332i
$727$	5.54744e6			0.389275			0.194638	−	0.980875i	$-0.437647\pi$
$727$	5.54744e6			0.389275			0.194638	+	0.980875i	$0.437647\pi$
$728$	1.19825e6	−	2.00177e7i	0.0837950	−	1.39986i
$729$	−3.69848e6			−0.257754
$730$		0			0
$731$			1.48547e7i			1.02818i
$732$	2.34670e6	−	3.71445e6i	0.161875	−	0.256222i
$733$			2.94032e6i			0.202132i	0.994880	+	0.101066i	$0.0322253\pi$
$733$			2.94032e6i			0.202132i	−0.994880	+	0.101066i	$0.967775\pi$
$734$	−2.99761e6	−	5.43956e6i	−0.205369	−	0.372669i
$735$		0			0
$736$	8.59843e6	−	1.19619e7i	0.585092	−	0.813962i
$737$	8.60356e6			0.583458
$738$	−4.84720e6	−	8.79588e6i	−0.327605	−	0.594482i
$739$			2.36648e7i			1.59401i	0.603971	+	0.797006i	$0.293584\pi$
$739$			2.36648e7i			1.59401i	−0.603971	+	0.797006i	$0.706416\pi$
$740$		0			0
$741$		−	1.34302e7i		−	0.898541i
$742$	1.72737e7	−	9.51914e6i	1.15180	−	0.634728i
$743$	2.82262e7			1.87577			0.937887	−	0.346940i	$-0.112779\pi$
$743$	2.82262e7			1.87577			0.937887	+	0.346940i	$0.112779\pi$
$744$	−1.58242e6	+	2.64356e7i	−0.104807	+	1.75088i
$745$		0			0
$746$	5.26809e6	−	2.90312e6i	0.346582	−	0.190993i
$747$		−	1.08334e7i		−	0.710334i
$748$	−4.77667e6	−	3.01779e6i	−0.312156	−	0.197213i
$749$		−	1.73102e7i		−	1.12745i
$750$		0			0
$751$	9.19289e6			0.594774			0.297387	−	0.954757i	$-0.403885\pi$
$751$	9.19289e6			0.594774			0.297387	+	0.954757i	$0.403885\pi$
$752$	−8.26255e6	−	1.73754e7i	−0.532807	−	1.12045i
$753$	−4.89574e6			−0.314652
$754$	−7.15561e6	−	1.29848e7i	−0.458372	−	0.831776i
$755$		0			0
$756$	1.43165e7	+	9.04482e6i	0.911029	+	0.575567i
$757$		−	4.78577e6i		−	0.303537i	−0.988416	−	0.151769i	$-0.951503\pi$
$757$		−	4.78577e6i		−	0.303537i	0.988416	−	0.151769i	$-0.0484969\pi$
$758$	1.65558e7	−	9.12350e6i	1.04659	−	0.576751i
$759$	−1.18164e7			−0.744526
$760$		0			0
$761$	−4.21229e6			−0.263668			−0.131834	−	0.991272i	$-0.542087\pi$
$761$	−4.21229e6			−0.263668			−0.131834	+	0.991272i	$0.542087\pi$
$762$	3.56948e6	−	1.96706e6i	0.222699	−	0.122724i
$763$			1.83225e6i			0.113939i
$764$	1.41888e6	−	2.24586e6i	0.0879455	−	0.139203i
$765$		0			0
$766$	4.42667e6	+	8.03276e6i	0.272587	+	0.494644i
$767$	1.61451e7			0.990949
$768$	1.52150e7	+	1.23803e7i	0.930828	+	0.757407i
$769$	−1.71941e7			−1.04849			−0.524246	−	0.851567i	$-0.675653\pi$
$769$	−1.71941e7			−1.04849			−0.524246	+	0.851567i	$0.675653\pi$
$770$		0			0
$771$			6.24538e6i			0.378375i
$772$	−1.43608e7	+	2.27309e7i	−0.867235	+	1.37269i
$773$			1.39162e7i			0.837667i	0.908063	+	0.418834i	$0.137561\pi$
$773$			1.39162e7i			0.837667i	−0.908063	+	0.418834i	$0.862439\pi$
$774$	−1.10718e7	+	6.10143e6i	−0.664304	+	0.366082i
$775$		0			0
$776$	1.30989e7	+	784095.i	0.780876	+	0.0467428i
$777$	−2.16621e6			−0.128721
$778$	1.54591e7	−	8.51917e6i	0.915665	−	0.504601i
$779$		−	2.23692e7i		−	1.32071i
$780$		0			0
$781$		−	1.24285e7i		−	0.729106i
$782$	−4.93595e6	−	8.95692e6i	−0.288638	−	0.523772i
$783$	1.25198e7			0.729783
$784$	−1.16207e7	−	2.44373e7i	−0.675215	−	1.41992i
$785$		0			0
$786$	1.68945e7	+	3.06573e7i	0.975416	+	1.77002i
$787$		−	2.67319e7i		−	1.53849i	−0.638957	−	0.769243i	$-0.720634\pi$
$787$		−	2.67319e7i		−	1.53849i	0.638957	−	0.769243i	$-0.279366\pi$
$788$	−2.26539e7	−	1.43122e7i	−1.29965	−	0.821091i
$789$			1.22835e7i			0.702474i
$790$		0			0
$791$	−1.18688e7			−0.674474
$792$	287312.	−	4.79978e6i	0.0162757	−	0.271899i
$793$	3.91053e6			0.220827
$794$	2.17640e7	−	1.19936e7i	1.22515	−	0.675149i
$795$		0			0
$796$	−1.05622e7	+	1.67183e7i	−0.590843	+	0.935209i
$797$			1.09380e7i			0.609947i	0.952361	+	0.304973i	$0.0986476\pi$
$797$			1.09380e7i			0.609947i	−0.952361	+	0.304973i	$0.901352\pi$
$798$	−1.43096e7	−	2.59666e7i	−0.795464	−	1.44347i
$799$	−1.33567e7			−0.740173
$800$		0			0
$801$	−9.54041e6			−0.525395
$802$	−1.37610e6	−	2.49711e6i	−0.0755465	−	0.137089i
$803$			1.57184e7i			0.860241i
$804$	−1.10752e7	+	1.75302e7i	−0.604242	+	0.956418i
$805$		0			0
$806$	−2.06438e7	+	1.13763e7i	−1.11932	+	0.616829i
$807$	1.03414e6			0.0558980
$808$	1.01424e6	−	1.69436e7i	0.0546526	−	0.913016i
$809$	−6.00240e6			−0.322444			−0.161222	−	0.986918i	$-0.551543\pi$
$809$	−6.00240e6			−0.322444			−0.161222	+	0.986918i	$0.551543\pi$
$810$		0			0
$811$			1.72122e7i			0.918936i	0.888194	+	0.459468i	$0.151960\pi$
$811$			1.72122e7i			0.918936i	−0.888194	+	0.459468i	$0.848040\pi$
$812$	−2.76700e7	−	1.74813e7i	−1.47272	−	0.930428i
$813$			2.88891e7i			1.53288i
$814$	−377665.	−	685322.i	−0.0199777	−	0.0362521i
$815$		0			0
$816$	1.22978e7	−	5.84800e6i	0.646551	−	0.307455i
$817$	−2.81572e7			−1.47582
$818$	−2.12515e6	−	3.85635e6i	−0.111047	−	0.201508i
$819$		−	1.18476e7i		−	0.617190i
$820$		0			0
$821$			3.42311e7i			1.77241i	0.463297	+	0.886203i	$0.346666\pi$
$821$			3.42311e7i			1.77241i	−0.463297	+	0.886203i	$0.653334\pi$
$822$	−1.07717e7	+	5.93602e6i	−0.556037	+	0.306419i
$823$	7.23069e6			0.372117			0.186059	−	0.982539i	$-0.440429\pi$
$823$	7.23069e6			0.372117			0.186059	+	0.982539i	$0.440429\pi$
$824$	2.61600e7	+	1.56592e6i	1.34221	+	0.0803437i
$825$		0			0
$826$	3.12157e7	−	1.72022e7i	1.59192	−	0.877272i
$827$			3.05073e7i			1.55110i	0.631285	+	0.775551i	$0.282528\pi$
$827$			3.05073e7i			1.55110i	−0.631285	+	0.775551i	$0.717472\pi$
$828$	4.64858e6	−	7.35794e6i	0.235637	−	0.372976i
$829$			1.67535e7i			0.846677i	0.905972	+	0.423339i	$0.139142\pi$
$829$			1.67535e7i			0.846677i	−0.905972	+	0.423339i	$0.860858\pi$
$830$		0			0
$831$	−3.98722e7			−2.00294
$832$	−2.08267e6	+	1.73340e7i	−0.104307	+	0.868141i
$833$	−1.87853e7			−0.938007
$834$	−1.26528e7	−	2.29601e7i	−0.629898	−	1.14303i
$835$		0			0
$836$	5.72024e6	−	9.05422e6i	0.283073	−	0.448059i
$837$		−	1.99046e7i		−	0.982064i
$838$	−703599.	+	387737.i	−0.0346111	+	0.0190733i
$839$	−1.49253e7			−0.732012			−0.366006	−	0.930612i	$-0.619275\pi$
$839$	−1.49253e7			−0.732012			−0.366006	+	0.930612i	$0.619275\pi$
$840$		0			0
$841$	−3.68635e6			−0.179724
$842$	−3.34071e7	+	1.84099e7i	−1.62390	+	0.894891i
$843$		−	2.13892e7i		−	1.03663i
$844$	−2.13777e7	−	1.35060e7i	−1.03301	−	0.652633i
$845$		0			0
$846$	−5.48615e6	−	9.95533e6i	−0.263537	−	0.478222i
$847$	2.06594e7			0.989485
$848$	−1.55069e7	+	7.37399e6i	−0.740516	+	0.352138i
$849$	4.13001e7			1.96644
$850$		0			0
$851$		−	1.41635e6i		−	0.0670419i
$852$	2.53237e7	+	1.59989e7i	1.19517	+	0.755079i
$853$			1.62162e7i			0.763089i	0.924350	+	0.381545i	$0.124608\pi$
$853$			1.62162e7i			0.763089i	−0.924350	+	0.381545i	$0.875392\pi$
$854$	7.56082e6	−	4.16659e6i	0.354751	−	0.195495i
$855$		0			0
$856$	−900489.	+	1.50434e7i	−0.0420043	+	0.701716i
$857$	2.31595e6			0.107715			0.0538577	−	0.998549i	$-0.482848\pi$
$857$	2.31595e6			0.107715			0.0538577	+	0.998549i	$0.482848\pi$
$858$	1.22648e7	−	6.75883e6i	0.568776	−	0.313439i
$859$		−	9.99784e6i		−	0.462299i	−0.972918	−	0.231150i	$-0.925751\pi$
$859$		−	9.99784e6i		−	0.462299i	0.972918	−	0.231150i	$-0.0742487\pi$
$860$		0			0
$861$		−	6.45703e7i		−	2.96842i
$862$	7.42792e6	+	1.34789e7i	0.340486	+	0.617856i
$863$	6.13760e6			0.280525			0.140263	−	0.990114i	$-0.455205\pi$
$863$	6.13760e6			0.280525			0.140263	+	0.990114i	$0.455205\pi$
$864$	−1.19712e7	−	8.60513e6i	−0.545573	−	0.392169i
$865$		0			0
$866$	−5.54045e6	−	1.00539e7i	−0.251044	−	0.455552i
$867$			1.71075e7i			0.772929i
$868$	−2.77925e7	+	4.39911e7i	−1.25207	+	1.98183i
$869$			1.56389e7i			0.702517i
$870$		0			0
$871$	−1.84556e7			−0.824297
$872$	95315.0	−	1.59231e6i	0.00424492	−	0.0709149i
$873$	7.75267e6			0.344283
$874$	1.69779e7	−	9.35614e6i	0.751807	−	0.414303i
$875$		0			0
$876$	−3.20272e7	−	2.02340e7i	−1.41013	−	0.890885i
$877$			4.19683e7i			1.84256i	0.388897	+	0.921281i	$0.372856\pi$
$877$			4.19683e7i			1.84256i	−0.388897	+	0.921281i	$0.627144\pi$
$878$	−1.95166e6	−	3.54155e6i	−0.0854415	−	0.155045i
$879$	5.17244e7			2.25800
$880$		0			0
$881$	2.66178e7			1.15540			0.577700	−	0.816249i	$-0.303950\pi$
$881$	2.66178e7			1.15540			0.577700	+	0.816249i	$0.303950\pi$
$882$	−7.71589e6	−	1.40015e7i	−0.333975	−	0.606042i
$883$			1.99925e7i			0.862908i	0.902135	+	0.431454i	$0.141999\pi$
$883$			1.99925e7i			0.862908i	−0.902135	+	0.431454i	$0.858001\pi$
$884$	1.02465e7	+	6.47351e6i	0.441007	+	0.278618i
$885$		0			0
$886$	−2.82403e6	+	1.55626e6i	−0.120861	+	0.0666035i
$887$	−8.27857e6			−0.353302			−0.176651	−	0.984274i	$-0.556526\pi$
$887$	−8.27857e6			−0.353302			−0.176651	+	0.984274i	$0.556526\pi$
$888$	1.88254e6	+	112688.i	0.0801147	+	0.00479562i
$889$	8.00795e6			0.339834
$890$		0			0
$891$			1.82803e7i			0.771418i
$892$	2.01779e7	−	3.19383e7i	0.849109	−	1.34400i
$893$		−	2.53178e7i		−	1.06242i
$894$	−1.12329e7	−	2.03835e7i	−0.470053	−	0.852971i
$895$		0			0
$896$	1.44423e7	+	3.57334e7i	0.600987	+	1.48698i
$897$	2.53475e7			1.05185
$898$	−7.53290e6	−	1.36694e7i	−0.311725	−	0.565665i
$899$			3.84703e7i			1.58755i
$900$		0			0
$901$			1.19203e7i			0.489189i
$902$	2.04280e7	−	1.12574e7i	0.836006	−	0.460703i
$903$	−8.12779e7			−3.31706
$904$	1.03145e7	+	617422.i	0.419787	+	0.0251282i
$905$		0			0
$906$	−2.46132e7	+	1.35638e7i	−0.996204	+	0.548985i
$907$		−	3.08214e7i		−	1.24404i	−0.783001	−	0.622020i	$-0.786312\pi$
$907$		−	3.08214e7i		−	1.24404i	0.783001	−	0.622020i	$-0.213688\pi$
$908$	2.12968e7	+	1.34548e7i	0.857236	+	0.541582i
$909$		−	1.00282e7i		−	0.402543i
$910$		0			0
$911$	2.02396e7			0.807991			0.403995	−	0.914761i	$-0.367621\pi$
$911$	2.02396e7			0.807991			0.403995	+	0.914761i	$0.367621\pi$
$912$	1.10849e7	+	2.33106e7i	0.441312	+	0.928041i
$913$	2.51600e7			0.998926
$914$	1.69560e7	+	3.07689e7i	0.671365	+	1.21828i
$915$		0			0
$916$	1.21569e7	+	7.68042e6i	0.478721	+	0.302445i
$917$			6.87781e7i			2.70101i
$918$	−8.96391e6	+	4.93980e6i	−0.351068	+	0.193465i
$919$	4.42883e7			1.72982			0.864909	−	0.501928i	$-0.167376\pi$
$919$	4.42883e7			1.72982			0.864909	+	0.501928i	$0.167376\pi$
$920$		0			0
$921$	2.13321e7			0.828675
$922$	2.18209e6	−	1.20250e6i	0.0845368	−	0.0465862i
$923$			2.66606e7i			1.03007i
$924$	1.65119e7	−	2.61357e7i	0.636235	−	1.00706i
$925$		0			0
$926$	−7.46884e6	−	1.35532e7i	−0.286237	−	0.519414i
$927$	1.54829e7			0.591770
$928$	2.31372e7	+	1.66315e7i	0.881942	+	0.633958i
$929$	−1.43005e7			−0.543641			−0.271820	−	0.962348i	$-0.587626\pi$
$929$	−1.43005e7			−0.543641			−0.271820	+	0.962348i	$0.587626\pi$
$930$		0			0
$931$		−	3.56077e7i		−	1.34639i
$932$	9.87788e6	−	1.56351e7i	0.372498	−	0.589604i
$933$		−	7.42184e6i		−	0.279130i
$934$	7.85285e6	−	4.32752e6i	0.294551	−	0.162320i
$935$		0			0
$936$	−616318.	+	1.02961e7i	−0.0229940	+	0.384134i
$937$	408897.			0.0152147			0.00760737	−	0.999971i	$-0.497578\pi$
$937$	408897.			0.0152147			0.00760737	+	0.999971i	$0.497578\pi$
$938$	−3.56830e7	+	1.96641e7i	−1.32420	+	0.729737i
$939$			4.21412e7i			1.55971i
$940$		0			0
$941$		−	2.02821e7i		−	0.746686i	−0.927693	−	0.373343i	$-0.878212\pi$
$941$		−	2.02821e7i		−	0.746686i	0.927693	−	0.373343i	$-0.121788\pi$
$942$	1.34685e7	+	2.44403e7i	0.494529	+	0.897387i
$943$	4.22184e7			1.54605
$944$	−2.80228e7	+	1.33257e7i	−1.02348	+	0.486698i
$945$		0			0
$946$	−1.41703e7	−	2.57138e7i	−0.514814	−	0.934196i
$947$			1.11440e7i			0.403801i	0.979406	+	0.201900i	$0.0647117\pi$
$947$			1.11440e7i			0.403801i	−0.979406	+	0.201900i	$0.935288\pi$
$948$	−3.18652e7	−	2.01317e7i	−1.15158	−	0.727543i
$949$		−	3.37178e7i		−	1.21533i
$950$		0			0
$951$	5.99827e7			2.15067
$952$	2.67085e7	+	1.59876e6i	0.955118	+	0.0571728i
$953$	−1.36818e7			−0.487990			−0.243995	−	0.969776i	$-0.578458\pi$
$953$	−1.36818e7			−0.487990			−0.243995	+	0.969776i	$0.578458\pi$
$954$	−8.88473e6	+	4.89616e6i	−0.316063	+	0.174175i
$955$		0			0
$956$	−8.03697e6	+	1.27212e7i	−0.284412	+	0.450178i
$957$		−	2.28557e7i		−	0.806706i
$958$	1.02127e7	+	1.85323e7i	0.359523	+	0.652402i
$959$	−2.41657e7			−0.848502
$960$		0			0
$961$	3.25328e7			1.13635
$962$	810135.	+	1.47009e6i	0.0282241	+	0.0512162i
$963$			8.90350e6i			0.309382i
$964$	5.96368e6	−	9.43955e6i	0.206691	−	0.327159i
$965$		0			0
$966$	4.90081e7	−	2.70072e7i	1.68976	−	0.931187i
$967$	−5.23654e7			−1.80085			−0.900427	−	0.435007i	$-0.856746\pi$
$967$	−5.23654e7			−1.80085			−0.900427	+	0.435007i	$0.856746\pi$
$968$	−1.79540e7	−	1.07472e6i	−0.615847	−	0.0368643i
$969$	1.79192e7			0.613069
$970$		0			0
$971$			7.06911e6i			0.240612i	0.992737	+	0.120306i	$0.0383875\pi$
$971$			7.06911e6i			0.240612i	−0.992737	+	0.120306i	$0.961612\pi$
$972$	−2.05156e7	−	1.29613e7i	−0.696496	−	0.440030i
$973$		−	5.15097e7i		−	1.74424i
$974$	1.18132e7	+	2.14366e7i	0.398998	+	0.724033i
$975$		0			0
$976$	−6.78746e6	+	3.22765e6i	−0.228078	+	0.108458i
$977$	3.98296e7			1.33496			0.667482	−	0.744626i	$-0.267372\pi$
$977$	3.98296e7			1.33496			0.667482	+	0.744626i	$0.267372\pi$
$978$	−8.45630e6	−	1.53451e7i	−0.282705	−	0.513005i
$979$		−	2.21571e7i		−	0.738851i
$980$		0			0
$981$		−	942418.i		−	0.0312659i
$982$	7.12874e6	−	3.92848e6i	0.235903	−	0.130001i
$983$	−1.64462e7			−0.542851			−0.271425	−	0.962459i	$-0.587495\pi$
$983$	−1.64462e7			−0.542851			−0.271425	+	0.962459i	$0.587495\pi$
$984$	−3.35899e6	+	5.61146e7i	−0.110591	+	1.84752i
$985$		0			0
$986$	1.73249e7	−	9.54734e6i	0.567516	−	0.312745i
$987$		−	7.30817e7i		−	2.38790i
$988$	−1.22706e7	+	1.94224e7i	−0.399920	+	0.633009i
$989$		−	5.31424e7i		−	1.72763i
$990$		0			0
$991$	−5.51196e7			−1.78288			−0.891440	−	0.453139i	$-0.850304\pi$
$991$	−5.51196e7			−1.78288			−0.891440	+	0.453139i	$0.850304\pi$
$992$	2.64415e7	−	3.67846e7i	0.853113	−	1.18682i
$993$	5.70042e7			1.83457
$994$	2.84062e7	+	5.15468e7i	0.911901	+	1.65476i
$995$		0			0
$996$	−3.23880e7	+	5.12649e7i	−1.03451	+	1.63746i
$997$		−	3.06324e7i		−	0.975986i	−0.872848	−	0.487993i	$-0.837729\pi$
$997$		−	3.06324e7i		−	0.975986i	0.872848	−	0.487993i	$-0.162271\pi$
$998$	−7.75833e6	+	4.27544e6i	−0.246571	+	0.135880i
$999$	−1.41745e6			−0.0449361

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.6.d.c.101.14	yes	20
4.3	odd	2		800.6.d.d.401.17		20
5.2	odd	4		200.6.f.d.149.6		40
5.3	odd	4		200.6.f.d.149.35		40
5.4	even	2		200.6.d.d.101.7	yes	20
8.3	odd	2		800.6.d.d.401.4		20
8.5	even	2	inner	200.6.d.c.101.13	✓	20
20.3	even	4		800.6.f.d.49.8		40
20.7	even	4		800.6.f.d.49.33		40
20.19	odd	2		800.6.d.b.401.4		20
40.3	even	4		800.6.f.d.49.34		40
40.13	odd	4		200.6.f.d.149.5		40
40.19	odd	2		800.6.d.b.401.17		20
40.27	even	4		800.6.f.d.49.7		40
40.29	even	2		200.6.d.d.101.8	yes	20
40.37	odd	4		200.6.f.d.149.36		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.6.d.c.101.13	✓	20	8.5	even	2	inner
200.6.d.c.101.14	yes	20	1.1	even	1	trivial
200.6.d.d.101.7	yes	20	5.4	even	2
200.6.d.d.101.8	yes	20	40.29	even	2
200.6.f.d.149.5		40	40.13	odd	4
200.6.f.d.149.6		40	5.2	odd	4
200.6.f.d.149.35		40	5.3	odd	4
200.6.f.d.149.36		40	40.37	odd	4
800.6.d.b.401.4		20	20.19	odd	2
800.6.d.b.401.17		20	40.19	odd	2
800.6.d.d.401.4		20	8.3	odd	2
800.6.d.d.401.17		20	4.3	odd	2
800.6.f.d.49.7		40	40.27	even	4
800.6.f.d.49.8		40	20.3	even	4
800.6.f.d.49.33		40	20.7	even	4
800.6.f.d.49.34		40	40.3	even	4

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:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	200.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(2.73024 + 4.95437i) q^{2} -18.7068i q^{3} +(-17.0916 + 27.0532i) q^{4} +(92.6806 - 51.0741i) q^{6} +207.924 q^{7} +(-180.696 - 10.8164i) q^{8} -106.946 q^{9} +O(q^{10})\)	\(q+(2.73024 + 4.95437i) q^{2} -18.7068i q^{3} +(-17.0916 + 27.0532i) q^{4} +(92.6806 - 51.0741i) q^{6} +207.924 q^{7} +(-180.696 - 10.8164i) q^{8} -106.946 q^{9} -248.376i q^{11} +(506.080 + 319.730i) q^{12} +532.796i q^{13} +(567.682 + 1030.13i) q^{14} +(-439.755 - 924.766i) q^{16} -710.880 q^{17} +(-291.987 - 529.849i) q^{18} -1347.48i q^{19} -3889.60i q^{21} +(1230.55 - 678.126i) q^{22} +2543.16 q^{23} +(-202.340 + 3380.25i) q^{24} +(-2639.67 + 1454.66i) q^{26} -2545.15i q^{27} +(-3553.75 + 5625.02i) q^{28} +4919.10i q^{29} +7820.61 q^{31} +(3381.00 - 4703.54i) q^{32} -4646.33 q^{33} +(-1940.87 - 3521.96i) q^{34} +(1827.87 - 2893.23i) q^{36} -556.924i q^{37} +(6675.91 - 3678.94i) q^{38} +9966.92 q^{39} +16600.7 q^{41} +(19270.5 - 10619.5i) q^{42} -20896.2i q^{43} +(6719.38 + 4245.14i) q^{44} +(6943.44 + 12599.8i) q^{46} +18789.0 q^{47} +(-17299.4 + 8226.42i) q^{48} +26425.4 q^{49} +13298.3i q^{51} +(-14413.8 - 9106.33i) q^{52} -16768.4i q^{53} +(12609.6 - 6948.85i) q^{54} +(-37571.0 - 2248.98i) q^{56} -25207.1 q^{57} +(-24371.0 + 13430.3i) q^{58} -30302.5i q^{59} -7339.65i q^{61} +(21352.1 + 38746.2i) q^{62} -22236.6 q^{63} +(32534.0 + 3908.94i) q^{64} +(-12685.6 - 23019.6i) q^{66} +34639.2i q^{67} +(12150.1 - 19231.6i) q^{68} -47574.5i q^{69} +50039.0 q^{71} +(19324.6 + 1156.76i) q^{72} -63284.7 q^{73} +(2759.21 - 1520.54i) q^{74} +(36453.7 + 23030.6i) q^{76} -51643.4i q^{77} +(27212.1 + 49379.8i) q^{78} -62964.6 q^{79} -73599.4 q^{81} +(45324.0 + 82246.2i) q^{82} +101298. i q^{83} +(105226. + 66479.5i) q^{84} +(103528. - 57051.6i) q^{86} +92020.7 q^{87} +(-2686.52 + 44880.5i) q^{88} +89208.0 q^{89} +110781. i q^{91} +(-43466.7 + 68800.7i) q^{92} -146299. i q^{93} +(51298.5 + 93087.7i) q^{94} +(-87988.3 - 63247.8i) q^{96} -72491.6 q^{97} +(72147.7 + 130921. i) q^{98} +26562.8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{2} + q^{4} + 33 q^{6} - 196 q^{7} - 391 q^{8} - 1620 q^{9}+O(q^{10}) \) 20 * q - q^2 + q^4 + 33 * q^6 - 196 * q^7 - 391 * q^8 - 1620 * q^9	\( 20 q - q^{2} + q^{4} + 33 q^{6} - 196 q^{7} - 391 q^{8} - 1620 q^{9} - 241 q^{12} - 424 q^{14} - 55 q^{16} - 3368 q^{18} + 1197 q^{22} - 7184 q^{23} + 9459 q^{24} + 9172 q^{26} - 13492 q^{28} + 7160 q^{31} + 7869 q^{32} - 2836 q^{33} - 9591 q^{34} + 14828 q^{36} + 21505 q^{38} + 22452 q^{39} - 5804 q^{41} - 14272 q^{42} - 11593 q^{44} - 37612 q^{46} + 44180 q^{47} + 66571 q^{48} + 62652 q^{49} + 6136 q^{52} + 88947 q^{54} - 36908 q^{56} + 43696 q^{57} - 84012 q^{58} + 87460 q^{62} - 1240 q^{63} + 115177 q^{64} + 131439 q^{66} - 143341 q^{68} - 7724 q^{71} - 25772 q^{72} - 105136 q^{73} + 2112 q^{74} + 55951 q^{76} - 10948 q^{78} - 7780 q^{79} + 96984 q^{81} + 117501 q^{82} - 97556 q^{84} - 65986 q^{86} - 106188 q^{87} - 122597 q^{88} - 3160 q^{89} + 88908 q^{92} - 58540 q^{94} + 57791 q^{96} - 73688 q^{97} + 164655 q^{98}+O(q^{100}) \) 20 * q - q^2 + q^4 + 33 * q^6 - 196 * q^7 - 391 * q^8 - 1620 * q^9 - 241 * q^12 - 424 * q^14 - 55 * q^16 - 3368 * q^18 + 1197 * q^22 - 7184 * q^23 + 9459 * q^24 + 9172 * q^26 - 13492 * q^28 + 7160 * q^31 + 7869 * q^32 - 2836 * q^33 - 9591 * q^34 + 14828 * q^36 + 21505 * q^38 + 22452 * q^39 - 5804 * q^41 - 14272 * q^42 - 11593 * q^44 - 37612 * q^46 + 44180 * q^47 + 66571 * q^48 + 62652 * q^49 + 6136 * q^52 + 88947 * q^54 - 36908 * q^56 + 43696 * q^57 - 84012 * q^58 + 87460 * q^62 - 1240 * q^63 + 115177 * q^64 + 131439 * q^66 - 143341 * q^68 - 7724 * q^71 - 25772 * q^72 - 105136 * q^73 + 2112 * q^74 + 55951 * q^76 - 10948 * q^78 - 7780 * q^79 + 96984 * q^81 + 117501 * q^82 - 97556 * q^84 - 65986 * q^86 - 106188 * q^87 - 122597 * q^88 - 3160 * q^89 + 88908 * q^92 - 58540 * q^94 + 57791 * q^96 - 73688 * q^97 + 164655 * q^98

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