LMFDB - Embedded newform 80.7.p.d.17.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [80,7,Mod(17,80)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("80.17"); S:= CuspForms(chi, 7); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(80, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 7, names="a")

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	80.p (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,-32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$18.4043266896$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} - 450x^{3} + 23409x^{2} - 115668x + 285768 $ x^6 - 2x^5 + 2x^4 - 450x^3 + 23409x^2 - 115668*x + 285768
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{7}\cdot 5 $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.1
Root			$7.73238 + 7.73238i$ of defining polynomial
Character	$\chi$	$=$	80.17
Dual form			80.7.p.d.33.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-35.6344 + 35.6344i) q^{3} +(-115.493 - 47.8149i) q^{5} +(-53.9521 - 53.9521i) q^{7} -1810.62i q^{9} -1895.82 q^{11} +(-954.888 + 954.888i) q^{13} +(5819.40 - 2411.69i) q^{15} +(3807.14 + 3807.14i) q^{17} -2616.92i q^{19} +3845.11 q^{21} +(-1210.32 + 1210.32i) q^{23} +(11052.5 + 11044.6i) q^{25} +(38543.0 + 38543.0i) q^{27} +26815.4i q^{29} -4635.89 q^{31} +(67556.4 - 67556.4i) q^{33} +(3651.41 + 8810.83i) q^{35} +(-36098.6 - 36098.6i) q^{37} -68053.7i q^{39} +40561.4 q^{41} +(74613.4 - 74613.4i) q^{43} +(-86574.7 + 209115. i) q^{45} +(22549.0 + 22549.0i) q^{47} -111827. i q^{49} -271330. q^{51} +(67918.4 - 67918.4i) q^{53} +(218955. + 90648.3i) q^{55} +(93252.6 + 93252.6i) q^{57} +35389.7i q^{59} -261549. q^{61} +(-97687.0 + 97687.0i) q^{63} +(155941. - 64625.5i) q^{65} +(301383. + 301383. i) q^{67} -86258.3i q^{69} -274465. q^{71} +(-48363.4 + 48363.4i) q^{73} +(-787417. + 280.559i) q^{75} +(102283. + 102283. i) q^{77} -781918. i q^{79} -1.42697e6 q^{81} +(432869. - 432869. i) q^{83} +(-257662. - 621737. i) q^{85} +(-955551. - 955551. i) q^{87} +480927. i q^{89} +103036. q^{91} +(165197. - 165197. i) q^{93} +(-125128. + 302238. i) q^{95} +(165268. + 165268. i) q^{97} +3.43261e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 32 q^{3} - 156 q^{5} + 264 q^{7} - 2200 q^{11} + 858 q^{13} + 7768 q^{15} - 3278 q^{17} + 33176 q^{21} - 19984 q^{23} - 24174 q^{25} + 115528 q^{27} - 104976 q^{31} + 177320 q^{33} + 116072 q^{35}+ \cdots + 3338406 q^{97}+O(q^{100}) $ 6 * q - 32 * q^3 - 156 * q^5 + 264 * q^7 - 2200 * q^11 + 858 * q^13 + 7768 * q^15 - 3278 * q^17 + 33176 * q^21 - 19984 * q^23 - 24174 * q^25 + 115528 * q^27 - 104976 * q^31 + 177320 * q^33 + 116072 * q^35 - 241554 * q^37 + 351736 * q^41 - 60720 * q^43 - 287846 * q^45 + 355248 * q^47 - 641872 * q^51 + 346526 * q^53 + 310200 * q^55 - 112816 * q^57 - 492888 * q^61 - 2288 * q^63 - 5082 * q^65 + 230304 * q^67 - 174128 * q^71 - 332442 * q^73 - 1855048 * q^75 + 1618760 * q^77 - 3085166 * q^81 + 2190936 * q^83 - 164934 * q^85 - 2614304 * q^87 + 2186976 * q^91 + 242072 * q^93 - 3484184 * q^95 + 3338406 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−35.6344	+	35.6344i	−1.31979	+	1.31979i	−0.405856	+	0.913937i	$0.633027\pi$
$3$	−35.6344	+	35.6344i	−1.31979	+	1.31979i	−0.913937	+	0.405856i	$0.866973\pi$
$4$		0			0
$5$	−115.493	−	47.8149i	−0.923948	−	0.382519i
$5$	−115.493	−	47.8149i	−0.923948	−	0.382519i
$6$		0			0
$7$	−53.9521	−	53.9521i	−0.157295	−	0.157295i	0.624072	−	0.781367i	$-0.285477\pi$
$7$	−53.9521	−	53.9521i	−0.157295	−	0.157295i	−0.781367	+	0.624072i	$0.785477\pi$
$8$		0			0
$9$		−	1810.62i		−	2.48371i
$10$		0			0
$11$	−1895.82			−1.42436			−0.712178	−	0.701999i	$-0.752291\pi$
$11$	−1895.82			−1.42436			−0.712178	+	0.701999i	$0.752291\pi$
$12$		0			0
$13$	−954.888	+	954.888i	−0.434633	+	0.434633i	−0.890201	−	0.455568i	$-0.849436\pi$
$13$	−954.888	+	954.888i	−0.434633	+	0.434633i	0.455568	+	0.890201i	$0.349436\pi$
$14$		0			0
$15$	5819.40	−	2411.69i	1.72427	−	0.714574i
$16$		0			0
$17$	3807.14	+	3807.14i	0.774911	+	0.774911i	0.978960	−	0.204050i	$-0.0654105\pi$
$17$	3807.14	+	3807.14i	0.774911	+	0.774911i	−0.204050	+	0.978960i	$0.565410\pi$
$18$		0			0
$19$		−	2616.92i		−	0.381531i	−0.981636	−	0.190766i	$-0.938903\pi$
$19$		−	2616.92i		−	0.381531i	0.981636	−	0.190766i	$-0.0610971\pi$
$20$		0			0
$21$	3845.11			0.415193
$22$		0			0
$23$	−1210.32	+	1210.32i	−0.0994759	+	0.0994759i	−0.755093	−	0.655617i	$-0.772408\pi$
$23$	−1210.32	+	1210.32i	−0.0994759	+	0.0994759i	0.655617	+	0.755093i	$0.272408\pi$
$24$		0			0
$25$	11052.5	+	11044.6i	0.707359	+	0.706855i
$26$		0			0
$27$	38543.0	+	38543.0i	1.95819	+	1.95819i
$28$		0			0
$29$			26815.4i			1.09949i	0.835333	+	0.549744i	$0.185275\pi$
$29$			26815.4i			1.09949i	−0.835333	+	0.549744i	$0.814725\pi$
$30$		0			0
$31$	−4635.89			−0.155614			−0.0778069	−	0.996968i	$-0.524792\pi$
$31$	−4635.89			−0.155614			−0.0778069	+	0.996968i	$0.524792\pi$
$32$		0			0
$33$	67556.4	−	67556.4i	1.87986	−	1.87986i
$34$		0			0
$35$	3651.41	+	8810.83i	0.0851640	+	0.205500i
$36$		0			0
$37$	−36098.6	−	36098.6i	−0.712665	−	0.712665i	0.254427	−	0.967092i	$-0.418113\pi$
$37$	−36098.6	−	36098.6i	−0.712665	−	0.712665i	−0.967092	+	0.254427i	$0.918113\pi$
$38$		0			0
$39$		−	68053.7i		−	1.14725i
$40$		0			0
$41$	40561.4			0.588520			0.294260	−	0.955725i	$-0.404927\pi$
$41$	40561.4			0.588520			0.294260	+	0.955725i	$0.404927\pi$
$42$		0			0
$43$	74613.4	−	74613.4i	0.938451	−	0.938451i	−0.0597614	−	0.998213i	$-0.519034\pi$
$43$	74613.4	−	74613.4i	0.938451	−	0.938451i	0.998213	+	0.0597614i	$0.0190340\pi$
$44$		0			0
$45$	−86574.7	+	209115.i	−0.950065	+	2.29482i
$46$		0			0
$47$	22549.0	+	22549.0i	0.217187	+	0.217187i	0.807312	−	0.590125i	$-0.200922\pi$
$47$	22549.0	+	22549.0i	0.217187	+	0.217187i	−0.590125	+	0.807312i	$0.700922\pi$
$48$		0			0
$49$		−	111827.i		−	0.950517i
$50$		0			0
$51$	−271330.			−2.04544
$52$		0			0
$53$	67918.4	−	67918.4i	0.456205	−	0.456205i	−0.441203	−	0.897407i	$-0.645448\pi$
$53$	67918.4	−	67918.4i	0.456205	−	0.456205i	0.897407	+	0.441203i	$0.145448\pi$
$54$		0			0
$55$	218955.	+	90648.3i	1.31603	+	0.544843i
$56$		0			0
$57$	93252.6	+	93252.6i	0.503543	+	0.503543i
$58$		0			0
$59$			35389.7i			0.172314i	0.996282	+	0.0861570i	$0.0274587\pi$
$59$			35389.7i			0.172314i	−0.996282	+	0.0861570i	$0.972541\pi$
$60$		0			0
$61$	−261549.			−1.15230			−0.576148	−	0.817345i	$-0.695445\pi$
$61$	−261549.			−1.15230			−0.576148	+	0.817345i	$0.695445\pi$
$62$		0			0
$63$	−97687.0	+	97687.0i	−0.390674	+	0.390674i
$64$		0			0
$65$	155941.	−	64625.5i	0.567833	−	0.235323i
$66$		0			0
$67$	301383.	+	301383.i	1.00206	+	1.00206i	0.999998	+	0.00206356i	$0.000656853\pi$
$67$	301383.	+	301383.i	1.00206	+	1.00206i	0.00206356	+	0.999998i	$0.499343\pi$
$68$		0			0
$69$		−	86258.3i		−	0.262575i
$70$		0			0
$71$	−274465.			−0.766852			−0.383426	−	0.923572i	$-0.625256\pi$
$71$	−274465.			−0.766852			−0.383426	+	0.923572i	$0.625256\pi$
$72$		0			0
$73$	−48363.4	+	48363.4i	−0.124322	+	0.124322i	−0.766530	−	0.642208i	$-0.778018\pi$
$73$	−48363.4	+	48363.4i	−0.124322	+	0.124322i	0.642208	+	0.766530i	$0.278018\pi$
$74$		0			0
$75$	−787417.	+	280.559i	−1.86647	+	0.000665030i
$76$		0			0
$77$	102283.	+	102283.i	0.224044	+	0.224044i
$78$		0			0
$79$		−	781918.i		−	1.58592i	−0.609276	−	0.792958i	$-0.708540\pi$
$79$		−	781918.i		−	1.58592i	0.609276	−	0.792958i	$-0.291460\pi$
$80$		0			0
$81$	−1.42697e6			−2.68510
$82$		0			0
$83$	432869.	−	432869.i	0.757047	−	0.757047i	−0.218737	−	0.975784i	$-0.570194\pi$
$83$	432869.	−	432869.i	0.757047	−	0.757047i	0.975784	+	0.218737i	$0.0701937\pi$
$84$		0			0
$85$	−257662.	−	621737.i	−0.419559	−	1.01239i
$86$		0			0
$87$	−955551.	−	955551.i	−1.45110	−	1.45110i
$88$		0			0
$89$			480927.i			0.682196i	0.940028	+	0.341098i	$0.110799\pi$
$89$			480927.i			0.682196i	−0.940028	+	0.341098i	$0.889201\pi$
$90$		0			0
$91$	103036.			0.136731
$92$		0			0
$93$	165197.	−	165197.i	0.205378	−	0.205378i
$94$		0			0
$95$	−125128.	+	302238.i	−0.145943	+	0.352515i
$96$		0			0
$97$	165268.	+	165268.i	0.181082	+	0.181082i	0.791827	−	0.610745i	$-0.209130\pi$
$97$	165268.	+	165268.i	0.181082	+	0.181082i	−0.610745	+	0.791827i	$0.709130\pi$
$98$		0			0
$99$			3.43261e6i			3.53769i
$100$		0			0
$101$	1.97736e6			1.91920			0.959602	−	0.281361i	$-0.0907859\pi$
$101$	1.97736e6			1.91920			0.959602	+	0.281361i	$0.0907859\pi$
$102$		0			0
$103$	1.00960e6	−	1.00960e6i	0.923928	−	0.923928i	−0.0733759	−	0.997304i	$-0.523377\pi$
$103$	1.00960e6	−	1.00960e6i	0.923928	−	0.923928i	0.997304	+	0.0733759i	$0.0233773\pi$
$104$		0			0
$105$	−444085.	−	183853.i	−0.383617	−	0.158819i
$106$		0			0
$107$	−153055.	−	153055.i	−0.124938	−	0.124938i	0.641873	−	0.766811i	$-0.278158\pi$
$107$	−153055.	−	153055.i	−0.124938	−	0.124938i	−0.766811	+	0.641873i	$0.778158\pi$
$108$		0			0
$109$		−	732355.i		−	0.565512i	−0.959192	−	0.282756i	$-0.908751\pi$
$109$		−	732355.i		−	0.565512i	0.959192	−	0.282756i	$-0.0912487\pi$
$110$		0			0
$111$	2.57270e6			1.88114
$112$		0			0
$113$	−175540.	+	175540.i	−0.121658	+	0.121658i	−0.765314	−	0.643657i	$-0.777416\pi$
$113$	−175540.	+	175540.i	−0.121658	+	0.121658i	0.643657	+	0.765314i	$0.277416\pi$
$114$		0			0
$115$	197656.	−	81913.0i	0.129962	−	0.0538591i
$116$		0			0
$117$	1.72894e6	+	1.72894e6i	1.07950	+	1.07950i
$118$		0			0
$119$		−	410806.i		−	0.243779i
$120$		0			0
$121$	1.82257e6			1.02879
$122$		0			0
$123$	−1.44538e6	+	1.44538e6i	−0.776725	+	0.776725i
$124$		0			0
$125$	−748393.	−	1.80405e6i	−0.383177	−	0.923675i
$126$		0			0
$127$	1.57305e6	+	1.57305e6i	0.767947	+	0.767947i	0.977745	−	0.209798i	$-0.0672806\pi$
$127$	1.57305e6	+	1.57305e6i	0.767947	+	0.767947i	−0.209798	+	0.977745i	$0.567281\pi$
$128$		0			0
$129$			5.31761e6i			2.47712i
$130$		0			0
$131$	818974.			0.364298			0.182149	−	0.983271i	$-0.441695\pi$
$131$	818974.			0.364298			0.182149	+	0.983271i	$0.441695\pi$
$132$		0			0
$133$	−141189.	+	141189.i	−0.0600129	+	0.0600129i
$134$		0			0
$135$	−2.60854e6	−	6.29439e6i	−1.06022	−	2.55831i
$136$		0			0
$137$	−2.67122e6	−	2.67122e6i	−1.03884	−	1.03884i	−0.999215	−	0.0396222i	$-0.987385\pi$
$137$	−2.67122e6	−	2.67122e6i	−1.03884	−	1.03884i	−0.0396222	−	0.999215i	$-0.512615\pi$
$138$		0			0
$139$		−	1.75737e6i		−	0.654362i	−0.944962	−	0.327181i	$-0.893901\pi$
$139$		−	1.75737e6i		−	0.654362i	0.944962	−	0.327181i	$-0.106099\pi$
$140$		0			0
$141$	−1.60704e6			−0.573284
$142$		0			0
$143$	1.81029e6	−	1.81029e6i	0.619072	−	0.619072i
$144$		0			0
$145$	1.28218e6	−	3.09700e6i	0.420575	−	1.01587i
$146$		0			0
$147$	3.98490e6	+	3.98490e6i	1.25449	+	1.25449i
$148$		0			0
$149$		−	116045.i		−	0.0350808i	−0.999846	−	0.0175404i	$-0.994416\pi$
$149$		−	116045.i		−	0.0350808i	0.999846	−	0.0175404i	$-0.00558357\pi$
$150$		0			0
$151$	−4.90253e6			−1.42393			−0.711966	−	0.702214i	$-0.752195\pi$
$151$	−4.90253e6			−1.42393			−0.711966	+	0.702214i	$0.752195\pi$
$152$		0			0
$153$	6.89329e6	−	6.89329e6i	1.92465	−	1.92465i
$154$		0			0
$155$	535415.	+	221665.i	0.143779	+	0.0595252i
$156$		0			0
$157$	1.98980e6	+	1.98980e6i	0.514176	+	0.514176i	0.915803	−	0.401627i	$-0.131555\pi$
$157$	1.98980e6	+	1.98980e6i	0.514176	+	0.514176i	−0.401627	+	0.915803i	$0.631555\pi$
$158$		0			0
$159$			4.84046e6i			1.20419i
$160$		0			0
$161$	130599.			0.0312941
$162$		0			0
$163$	−2.38346e6	+	2.38346e6i	−0.550358	+	0.550358i	−0.926544	−	0.376186i	$-0.877235\pi$
$163$	−2.38346e6	+	2.38346e6i	−0.550358	+	0.550358i	0.376186	+	0.926544i	$0.377235\pi$
$164$		0			0
$165$	−1.10325e7	+	4.57212e6i	−2.45597	+	1.01781i
$166$		0			0
$167$	1.31144e6	+	1.31144e6i	0.281579	+	0.281579i	0.833739	−	0.552159i	$-0.186196\pi$
$167$	1.31144e6	+	1.31144e6i	0.281579	+	0.281579i	−0.552159	+	0.833739i	$0.686196\pi$
$168$		0			0
$169$			3.00319e6i			0.622189i
$170$		0			0
$171$	−4.73826e6			−0.947613
$172$		0			0
$173$	−3.84996e6	+	3.84996e6i	−0.743562	+	0.743562i	−0.973262	−	0.229699i	$-0.926226\pi$
$173$	−3.84996e6	+	3.84996e6i	−0.743562	+	0.743562i	0.229699	+	0.973262i	$0.426226\pi$
$174$		0			0
$175$	−424.780	−	1.19219e6i	−7.92592e−5	−	0.222449i
$176$		0			0
$177$	−1.26109e6	−	1.26109e6i	−0.227419	−	0.227419i
$178$		0			0
$179$			4.64255e6i			0.809464i	0.914435	+	0.404732i	$0.132635\pi$
$179$			4.64255e6i			0.809464i	−0.914435	+	0.404732i	$0.867365\pi$
$180$		0			0
$181$	2.75799e6			0.465112			0.232556	−	0.972583i	$-0.425291\pi$
$181$	2.75799e6			0.465112			0.232556	+	0.972583i	$0.425291\pi$
$182$		0			0
$183$	9.32016e6	−	9.32016e6i	1.52079	−	1.52079i
$184$		0			0
$185$	2.44310e6	+	5.89520e6i	0.385857	+	0.931072i
$186$		0			0
$187$	−7.21764e6	−	7.21764e6i	−1.10375	−	1.10375i
$188$		0			0
$189$		−	4.15895e6i		−	0.616026i
$190$		0			0
$191$	−6.44180e6			−0.924501			−0.462251	−	0.886749i	$-0.652958\pi$
$191$	−6.44180e6			−0.924501			−0.462251	+	0.886749i	$0.652958\pi$
$192$		0			0
$193$	4.82157e6	−	4.82157e6i	0.670682	−	0.670682i	−0.287191	−	0.957873i	$-0.592721\pi$
$193$	4.82157e6	−	4.82157e6i	0.670682	−	0.670682i	0.957873	+	0.287191i	$0.0927214\pi$
$194$		0			0
$195$	−3.25398e6	+	7.85976e6i	−0.438845	+	1.06000i
$196$		0			0
$197$	666959.	+	666959.i	0.0872369	+	0.0872369i	0.749379	−	0.662142i	$-0.230352\pi$
$197$	666959.	+	666959.i	0.0872369	+	0.0872369i	−0.662142	+	0.749379i	$0.730352\pi$
$198$		0			0
$199$		−	9.63418e6i		−	1.22252i	−0.791430	−	0.611259i	$-0.790663\pi$
$199$		−	9.63418e6i		−	1.22252i	0.791430	−	0.611259i	$-0.209337\pi$
$200$		0			0
$201$	−2.14792e7			−2.64503
$202$		0			0
$203$	1.44675e6	−	1.44675e6i	0.172944	−	0.172944i
$204$		0			0
$205$	−4.68458e6	−	1.93944e6i	−0.543762	−	0.225120i
$206$		0			0
$207$	2.19144e6	+	2.19144e6i	0.247069	+	0.247069i
$208$		0			0
$209$			4.96121e6i			0.543437i
$210$		0			0
$211$	2.80218e6			0.298296			0.149148	−	0.988815i	$-0.452347\pi$
$211$	2.80218e6			0.298296			0.149148	+	0.988815i	$0.452347\pi$
$212$		0			0
$213$	9.78039e6	−	9.78039e6i	1.01209	−	1.01209i
$214$		0			0
$215$	−1.21850e7	+	5.04973e6i	−1.22606	+	0.508105i
$216$		0			0
$217$	250116.	+	250116.i	0.0244773	+	0.0244773i
$218$		0			0
$219$		−	3.44680e6i		−	0.328159i
$220$		0			0
$221$	−7.27077e6			−0.673603
$222$		0			0
$223$	−619198.	+	619198.i	−0.0558361	+	0.0558361i	−0.734473	−	0.678637i	$-0.762571\pi$
$223$	−619198.	+	619198.i	−0.0558361	+	0.0558361i	0.678637	+	0.734473i	$0.262571\pi$
$224$		0			0
$225$	1.99976e7	−	2.00119e7i	1.75562	−	1.75687i
$226$		0			0
$227$	1.18276e7	+	1.18276e7i	1.01116	+	1.01116i	0.999937	+	0.0112211i	$0.00357185\pi$
$227$	1.18276e7	+	1.18276e7i	1.01116	+	1.01116i	0.0112211	+	0.999937i	$0.496428\pi$
$228$		0			0
$229$		−	1.98645e7i		−	1.65414i	−0.562100	−	0.827069i	$-0.690007\pi$
$229$		−	1.98645e7i		−	1.65414i	0.562100	−	0.827069i	$-0.309993\pi$
$230$		0			0
$231$	−7.28962e6			−0.591383
$232$		0			0
$233$	−8.61338e6	+	8.61338e6i	−0.680935	+	0.680935i	−0.960211	−	0.279276i	$-0.909906\pi$
$233$	−8.61338e6	+	8.61338e6i	−0.680935	+	0.680935i	0.279276	+	0.960211i	$0.409906\pi$
$234$		0			0
$235$	−1.52609e6	−	3.68244e6i	−0.117591	−	0.283748i
$236$		0			0
$237$	2.78632e7	+	2.78632e7i	2.09308	+	2.09308i
$238$		0			0
$239$			1.42020e7i			1.04029i	0.854077	+	0.520146i	$0.174122\pi$
$239$			1.42020e7i			1.04029i	−0.854077	+	0.520146i	$0.825878\pi$
$240$		0			0
$241$	−1.76895e7			−1.26376			−0.631881	−	0.775065i	$-0.717717\pi$
$241$	−1.76895e7			−1.26376			−0.631881	+	0.775065i	$0.717717\pi$
$242$		0			0
$243$	2.27514e7	−	2.27514e7i	1.58558	−	1.58558i
$244$		0			0
$245$	−5.34701e6	+	1.29153e7i	−0.363591	+	0.878228i
$246$		0			0
$247$	2.49887e6	+	2.49887e6i	0.165826	+	0.165826i
$248$		0			0
$249$			3.08501e7i			1.99829i
$250$		0			0
$251$	7.78236e6			0.492142			0.246071	−	0.969252i	$-0.420860\pi$
$251$	7.78236e6			0.492142			0.246071	+	0.969252i	$0.420860\pi$
$252$		0			0
$253$	2.29455e6	−	2.29455e6i	0.141689	−	0.141689i
$254$		0			0
$255$	3.13369e7	+	1.29736e7i	1.88988	+	0.782421i
$256$		0			0
$257$	1.39276e7	+	1.39276e7i	0.820499	+	0.820499i	0.986179	−	0.165681i	$-0.0529821\pi$
$257$	1.39276e7	+	1.39276e7i	0.820499	+	0.820499i	−0.165681	+	0.986179i	$0.552982\pi$
$258$		0			0
$259$			3.89519e6i			0.224197i
$260$		0			0
$261$	4.85526e7			2.73081
$262$		0			0
$263$	−1.52537e7	+	1.52537e7i	−0.838508	+	0.838508i	−0.988663	−	0.150154i	$-0.952023\pi$
$263$	−1.52537e7	+	1.52537e7i	−0.838508	+	0.838508i	0.150154	+	0.988663i	$0.452023\pi$
$264$		0			0
$265$	−1.10916e7	+	4.59662e6i	−0.596016	+	0.247002i
$266$		0			0
$267$	−1.71375e7	−	1.71375e7i	−0.900357	−	0.900357i
$268$		0			0
$269$		−	3.62826e7i		−	1.86398i	−0.362481	−	0.931991i	$-0.618070\pi$
$269$		−	3.62826e7i		−	1.86398i	0.362481	−	0.931991i	$-0.381930\pi$
$270$		0			0
$271$	3.51878e7			1.76801			0.884003	−	0.467480i	$-0.154838\pi$
$271$	3.51878e7			1.76801			0.884003	+	0.467480i	$0.154838\pi$
$272$		0			0
$273$	−3.67164e6	+	3.67164e6i	−0.180457	+	0.180457i
$274$		0			0
$275$	−2.09535e7	−	2.09386e7i	−1.00753	−	1.00681i
$276$		0			0
$277$	−2.06619e7	−	2.06619e7i	−0.972144	−	0.972144i	0.0274784	−	0.999622i	$-0.491252\pi$
$277$	−2.06619e7	−	2.06619e7i	−0.972144	−	0.972144i	−0.999622	+	0.0274784i	$0.991252\pi$
$278$		0			0
$279$			8.39385e6i			0.386499i
$280$		0			0
$281$	2.53204e7			1.14117			0.570587	−	0.821237i	$-0.306716\pi$
$281$	2.53204e7			1.14117			0.570587	+	0.821237i	$0.306716\pi$
$282$		0			0
$283$	9.14358e6	−	9.14358e6i	0.403420	−	0.403420i	−0.476017	−	0.879436i	$-0.657920\pi$
$283$	9.14358e6	−	9.14358e6i	0.403420	−	0.403420i	0.879436	+	0.476017i	$0.157920\pi$
$284$		0			0
$285$	−6.31120e6	−	1.52289e7i	−0.272632	−	0.657862i
$286$		0			0
$287$	−2.18837e6	−	2.18837e6i	−0.0925712	−	0.0925712i
$288$		0			0
$289$			4.85099e6i			0.200973i
$290$		0			0
$291$	−1.17785e7			−0.477981
$292$		0			0
$293$	−1.89469e7	+	1.89469e7i	−0.753244	+	0.753244i	−0.975083	−	0.221839i	$-0.928794\pi$
$293$	−1.89469e7	+	1.89469e7i	−0.753244	+	0.753244i	0.221839	+	0.975083i	$0.428794\pi$
$294$		0			0
$295$	1.69215e6	−	4.08727e6i	0.0659133	−	0.159209i
$296$		0			0
$297$	−7.30705e7	−	7.30705e7i	−2.78916	−	2.78916i
$298$		0			0
$299$		−	2.31145e6i		−	0.0864709i
$300$		0			0
$301$	−8.05111e6			−0.295227
$302$		0			0
$303$	−7.04620e7	+	7.04620e7i	−2.53295	+	2.53295i
$304$		0			0
$305$	3.02072e7	+	1.25059e7i	1.06466	+	0.440775i
$306$		0			0
$307$	−1.88276e7	−	1.88276e7i	−0.650699	−	0.650699i	0.302462	−	0.953161i	$-0.402191\pi$
$307$	−1.88276e7	−	1.88276e7i	−0.650699	−	0.650699i	−0.953161	+	0.302462i	$0.902191\pi$
$308$		0			0
$309$			7.19531e7i			2.43879i
$310$		0			0
$311$	−214842.			−0.00714231			−0.00357116	−	0.999994i	$-0.501137\pi$
$311$	−214842.			−0.00714231			−0.00357116	+	0.999994i	$0.501137\pi$
$312$		0			0
$313$	3.74790e7	−	3.74790e7i	1.22223	−	1.22223i	0.255399	−	0.966836i	$-0.417793\pi$
$313$	3.74790e7	−	3.74790e7i	1.22223	−	1.22223i	0.966836	−	0.255399i	$-0.0822067\pi$
$314$		0			0
$315$	1.59531e7	−	6.61132e6i	0.510403	−	0.211522i
$316$		0			0
$317$	−1.23169e7	−	1.23169e7i	−0.386656	−	0.386656i	0.486837	−	0.873493i	$-0.338151\pi$
$317$	−1.23169e7	−	1.23169e7i	−0.386656	−	0.386656i	−0.873493	+	0.486837i	$0.838151\pi$
$318$		0			0
$319$		−	5.08372e7i		−	1.56606i
$320$		0			0
$321$	1.09080e7			0.329785
$322$		0			0
$323$	9.96298e6	−	9.96298e6i	0.295653	−	0.295653i
$324$		0			0
$325$	−2.11002e7	+	7518.09i	−0.614663	+	0.000219007i
$326$		0			0
$327$	2.60970e7	+	2.60970e7i	0.746359	+	0.746359i
$328$		0			0
$329$		−	2.43313e6i		−	0.0683248i
$330$		0			0
$331$	3.46935e7			0.956675			0.478338	−	0.878176i	$-0.341240\pi$
$331$	3.46935e7			0.956675			0.478338	+	0.878176i	$0.341240\pi$
$332$		0			0
$333$	−6.53609e7	+	6.53609e7i	−1.77005	+	1.77005i
$334$		0			0
$335$	−2.03972e7	−	4.92184e7i	−0.542545	−	1.30916i
$336$		0			0
$337$	3.50117e7	+	3.50117e7i	0.914794	+	0.914794i	0.996645	−	0.0818508i	$-0.0260831\pi$
$337$	3.50117e7	+	3.50117e7i	0.914794	+	0.914794i	−0.0818508	+	0.996645i	$0.526083\pi$
$338$		0			0
$339$		−	1.25105e7i		−	0.321126i
$340$		0			0
$341$	8.78881e6			0.221650
$342$		0			0
$343$	−1.23807e7	+	1.23807e7i	−0.306806	+	0.306806i
$344$		0			0
$345$	−4.12443e6	+	9.96227e6i	−0.100440	+	0.242606i
$346$		0			0
$347$	2.37166e7	+	2.37166e7i	0.567627	+	0.567627i	0.931463	−	0.363836i	$-0.118533\pi$
$347$	2.37166e7	+	2.37166e7i	0.567627	+	0.567627i	−0.363836	+	0.931463i	$0.618533\pi$
$348$		0			0
$349$		−	5.40891e7i		−	1.27243i	−0.771513	−	0.636214i	$-0.780500\pi$
$349$		−	5.40891e7i		−	1.27243i	0.771513	−	0.636214i	$-0.219500\pi$
$350$		0			0
$351$	−7.36085e7			−1.70218
$352$		0			0
$353$	−3.36765e7	+	3.36765e7i	−0.765601	+	0.765601i	−0.977329	−	0.211728i	$-0.932091\pi$
$353$	−3.36765e7	+	3.36765e7i	−0.765601	+	0.765601i	0.211728	+	0.977329i	$0.432091\pi$
$354$		0			0
$355$	3.16989e7	+	1.31235e7i	0.708531	+	0.293335i
$356$		0			0
$357$	1.46388e7	+	1.46388e7i	0.321738	+	0.321738i
$358$		0			0
$359$			6.68407e7i			1.44463i	0.691562	+	0.722317i	$0.256923\pi$
$359$			6.68407e7i			1.44463i	−0.691562	+	0.722317i	$0.743077\pi$
$360$		0			0
$361$	4.01976e7			0.854434
$362$		0			0
$363$	−6.49461e7	+	6.49461e7i	−1.35779	+	1.35779i
$364$		0			0
$365$	7.89815e6	−	3.27317e6i	0.162423	−	0.0673116i
$366$		0			0
$367$	−1.83094e7	−	1.83094e7i	−0.370404	−	0.370404i	0.497220	−	0.867624i	$-0.334354\pi$
$367$	−1.83094e7	−	1.83094e7i	−0.370404	−	0.370404i	−0.867624	+	0.497220i	$0.834354\pi$
$368$		0			0
$369$		−	7.34414e7i		−	1.46171i
$370$		0			0
$371$	−7.32868e6			−0.143517
$372$		0			0
$373$	3.36562e7	−	3.36562e7i	0.648542	−	0.648542i	−0.304099	−	0.952641i	$-0.598355\pi$
$373$	3.36562e7	−	3.36562e7i	0.648542	−	0.648542i	0.952641	+	0.304099i	$0.0983552\pi$
$374$		0			0
$375$	9.09549e7	+	3.76178e7i	1.72477	+	0.713345i
$376$		0			0
$377$	−2.56057e7	−	2.56057e7i	−0.477873	−	0.477873i
$378$		0			0
$379$		−	6.14439e7i		−	1.12866i	−0.825551	−	0.564328i	$-0.809135\pi$
$379$		−	6.14439e7i		−	1.12866i	0.825551	−	0.564328i	$-0.190865\pi$
$380$		0			0
$381$	−1.12109e8			−2.02706
$382$		0			0
$383$	7.00364e7	−	7.00364e7i	1.24660	−	1.24660i	0.289390	−	0.957211i	$-0.406547\pi$
$383$	7.00364e7	−	7.00364e7i	1.24660	−	1.24660i	0.957211	−	0.289390i	$-0.0934525\pi$
$384$		0			0
$385$	−6.92240e6	−	1.67037e7i	−0.121304	−	0.292706i
$386$		0			0
$387$	−1.35097e8	−	1.35097e8i	−2.33084	−	2.33084i
$388$		0			0
$389$		−	5.13746e7i		−	0.872770i	−0.899760	−	0.436385i	$-0.856259\pi$
$389$		−	5.13746e7i		−	0.872770i	0.899760	−	0.436385i	$-0.143741\pi$
$390$		0			0
$391$	−9.21573e6			−0.154170
$392$		0			0
$393$	−2.91837e7	+	2.91837e7i	−0.480798	+	0.480798i
$394$		0			0
$395$	−3.73873e7	+	9.03065e7i	−0.606643	+	1.46530i
$396$		0			0
$397$	−1.95795e7	−	1.95795e7i	−0.312918	−	0.312918i	0.533121	−	0.846039i	$-0.321019\pi$
$397$	−1.95795e7	−	1.95795e7i	−0.312918	−	0.312918i	−0.846039	+	0.533121i	$0.821019\pi$
$398$		0			0
$399$		−	1.00624e7i		−	0.158409i
$400$		0			0
$401$	3.73749e7			0.579625			0.289813	−	0.957083i	$-0.406407\pi$
$401$	3.73749e7			0.579625			0.289813	+	0.957083i	$0.406407\pi$
$402$		0			0
$403$	4.42676e6	−	4.42676e6i	0.0676349	−	0.0676349i
$404$		0			0
$405$	1.64806e8	+	6.82304e7i	2.48089	+	1.02710i
$406$		0			0
$407$	6.84364e7	+	6.84364e7i	1.01509	+	1.01509i
$408$		0			0
$409$		−	1.69502e7i		−	0.247745i	−0.992298	−	0.123873i	$-0.960469\pi$
$409$		−	1.69502e7i		−	0.247745i	0.992298	−	0.123873i	$-0.0395314\pi$
$410$		0			0
$411$	1.90374e8			2.74210
$412$		0			0
$413$	1.90935e6	−	1.90935e6i	0.0271041	−	0.0271041i
$414$		0			0
$415$	−7.06912e7	+	2.92960e7i	−0.989056	+	0.409887i
$416$		0			0
$417$	6.26227e7	+	6.26227e7i	0.863622	+	0.863622i
$418$		0			0
$419$		−	8.39101e7i		−	1.14070i	−0.821401	−	0.570351i	$-0.806807\pi$
$419$		−	8.39101e7i		−	1.14070i	0.821401	−	0.570351i	$-0.193193\pi$
$420$		0			0
$421$	7.82429e7			1.04857			0.524286	−	0.851542i	$-0.324332\pi$
$421$	7.82429e7			1.04857			0.524286	+	0.851542i	$0.324332\pi$
$422$		0			0
$423$	4.08277e7	−	4.08277e7i	0.539429	−	0.539429i
$424$		0			0
$425$	29974.6	+	8.41266e7i	0.000390469	+	1.09589i
$426$		0			0
$427$	1.41112e7	+	1.41112e7i	0.181250	+	0.181250i
$428$		0			0
$429$			1.29018e8i			1.63409i
$430$		0			0
$431$	3.26426e7			0.407711			0.203856	−	0.979001i	$-0.434653\pi$
$431$	3.26426e7			0.407711			0.203856	+	0.979001i	$0.434653\pi$
$432$		0			0
$433$	−1.48344e7	+	1.48344e7i	−0.182728	+	0.182728i	−0.792544	−	0.609815i	$-0.791244\pi$
$433$	−1.48344e7	+	1.48344e7i	−0.182728	+	0.182728i	0.609815	+	0.792544i	$0.291244\pi$
$434$		0			0
$435$	6.46704e7	+	1.56050e8i	0.785666	+	1.89581i
$436$		0			0
$437$	3.16732e6	+	3.16732e6i	0.0379532	+	0.0379532i
$438$		0			0
$439$		−	1.17186e8i		−	1.38510i	−0.721371	−	0.692549i	$-0.756488\pi$
$439$		−	1.17186e8i		−	1.38510i	0.721371	−	0.692549i	$-0.243512\pi$
$440$		0			0
$441$	−2.02477e8			−2.36081
$442$		0			0
$443$	4.20807e7	−	4.20807e7i	0.484030	−	0.484030i	−0.422386	−	0.906416i	$-0.638807\pi$
$443$	4.20807e7	−	4.20807e7i	0.484030	−	0.484030i	0.906416	+	0.422386i	$0.138807\pi$
$444$		0			0
$445$	2.29954e7	−	5.55439e7i	0.260953	−	0.630313i
$446$		0			0
$447$	4.13521e6	+	4.13521e6i	0.0462994	+	0.0462994i
$448$		0			0
$449$		−	9.43574e7i		−	1.04241i	−0.853433	−	0.521203i	$-0.825483\pi$
$449$		−	9.43574e7i		−	1.04241i	0.853433	−	0.521203i	$-0.174517\pi$
$450$		0			0
$451$	−7.68970e7			−0.838262
$452$		0			0
$453$	1.74699e8	−	1.74699e8i	1.87930	−	1.87930i
$454$		0			0
$455$	−1.19000e7	−	4.92667e6i	−0.126332	−	0.0523022i
$456$		0			0
$457$	1.23071e8	+	1.23071e8i	1.28946	+	1.28946i	0.935114	+	0.354347i	$0.115297\pi$
$457$	1.23071e8	+	1.23071e8i	1.28946	+	1.28946i	0.354347	+	0.935114i	$0.384703\pi$
$458$		0			0
$459$			2.93477e8i			3.03484i
$460$		0			0
$461$	4.52473e7			0.461838			0.230919	−	0.972973i	$-0.425827\pi$
$461$	4.52473e7			0.461838			0.230919	+	0.972973i	$0.425827\pi$
$462$		0			0
$463$	−3.94536e7	+	3.94536e7i	−0.397506	+	0.397506i	−0.877353	−	0.479846i	$-0.840692\pi$
$463$	−3.94536e7	+	3.94536e7i	−0.397506	+	0.397506i	0.479846	+	0.877353i	$0.340692\pi$
$464$		0			0
$465$	−2.69781e7	+	1.11803e7i	−0.268320	+	0.111198i
$466$		0			0
$467$	3.51660e7	+	3.51660e7i	0.345281	+	0.345281i	0.858348	−	0.513067i	$-0.171491\pi$
$467$	3.51660e7	+	3.51660e7i	0.345281	+	0.345281i	−0.513067	+	0.858348i	$0.671491\pi$
$468$		0			0
$469$		−	3.25205e7i		−	0.315238i
$470$		0			0
$471$	−1.41811e8			−1.35721
$472$		0			0
$473$	−1.41454e8	+	1.41454e8i	−1.33669	+	1.33669i
$474$		0			0
$475$	2.89029e7	−	2.89235e7i	0.269687	−	0.269880i
$476$		0			0
$477$	−1.22975e8	−	1.22975e8i	−1.13308	−	1.13308i
$478$		0			0
$479$		−	4.02821e7i		−	0.366527i	−0.983064	−	0.183263i	$-0.941334\pi$
$479$		−	4.02821e7i		−	0.366527i	0.983064	−	0.183263i	$-0.0586661\pi$
$480$		0			0
$481$	6.89402e7			0.619494
$482$		0			0
$483$	−4.65382e6	+	4.65382e6i	−0.0413017	+	0.0413017i
$484$		0			0
$485$	−1.11851e7	−	2.69897e7i	−0.0980429	−	0.236577i
$486$		0			0
$487$	2.30857e7	+	2.30857e7i	0.199874	+	0.199874i	0.799946	−	0.600072i	$-0.204861\pi$
$487$	2.30857e7	+	2.30857e7i	0.199874	+	0.199874i	−0.600072	+	0.799946i	$0.704861\pi$
$488$		0			0
$489$		−	1.69867e8i		−	1.45272i
$490$		0			0
$491$	−1.30781e8			−1.10484			−0.552420	−	0.833566i	$-0.686296\pi$
$491$	−1.30781e8			−1.10484			−0.552420	+	0.833566i	$0.686296\pi$
$492$		0			0
$493$	−1.02090e8	+	1.02090e8i	−0.852005	+	0.852005i
$494$		0			0
$495$	1.64130e8	−	3.96444e8i	1.35323	−	3.26864i
$496$		0			0
$497$	1.48080e7	+	1.48080e7i	0.120622	+	0.120622i
$498$		0			0
$499$		−	5.56395e7i		−	0.447798i	−0.974612	−	0.223899i	$-0.928121\pi$
$499$		−	5.56395e7i		−	0.447798i	0.974612	−	0.223899i	$-0.0718785\pi$
$500$		0			0
$501$	−9.34651e7			−0.743252
$502$		0			0
$503$	−5.26610e7	+	5.26610e7i	−0.413795	+	0.413795i	−0.883058	−	0.469263i	$-0.844520\pi$
$503$	−5.26610e7	+	5.26610e7i	−0.413795	+	0.413795i	0.469263	+	0.883058i	$0.344520\pi$
$504$		0			0
$505$	−2.28372e8	−	9.45471e7i	−1.77324	−	0.734132i
$506$		0			0
$507$	−1.07017e8	−	1.07017e8i	−0.821161	−	0.821161i
$508$		0			0
$509$			1.12045e8i			0.849650i	0.905276	+	0.424825i	$0.139664\pi$
$509$			1.12045e8i			0.849650i	−0.905276	+	0.424825i	$0.860336\pi$
$510$		0			0
$511$	5.21862e6			0.0391105
$512$		0			0
$513$	1.00864e8	−	1.00864e8i	0.747110	−	0.747110i
$514$		0			0
$515$	−1.64876e8	+	6.83284e7i	−1.20708	+	0.500242i
$516$		0			0
$517$	−4.27488e7	−	4.27488e7i	−0.309352	−	0.309352i
$518$		0			0
$519$		−	2.74382e8i		−	1.96270i
$520$		0			0
$521$	2.03940e8			1.44208			0.721038	−	0.692895i	$-0.243665\pi$
$521$	2.03940e8			1.44208			0.721038	+	0.692895i	$0.243665\pi$
$522$		0			0
$523$	−9.98000e7	+	9.98000e7i	−0.697631	+	0.697631i	−0.963899	−	0.266268i	$-0.914209\pi$
$523$	−9.98000e7	+	9.98000e7i	−0.697631	+	0.697631i	0.266268	+	0.963899i	$0.414209\pi$
$524$		0			0
$525$	4.24980e7	+	4.24677e7i	0.293691	+	0.293481i
$526$		0			0
$527$	−1.76495e7	−	1.76495e7i	−0.120587	−	0.120587i
$528$		0			0
$529$			1.45106e8i			0.980209i
$530$		0			0
$531$	6.40773e7			0.427977
$532$		0			0
$533$	−3.87316e7	+	3.87316e7i	−0.255790	+	0.255790i
$534$		0			0
$535$	1.03585e7	+	2.49951e7i	0.0676452	+	0.163228i
$536$		0			0
$537$	−1.65435e8	−	1.65435e8i	−1.06832	−	1.06832i
$538$		0			0
$539$			2.12004e8i			1.35387i
$540$		0			0
$541$	−2.21560e8			−1.39927			−0.699633	−	0.714502i	$-0.746653\pi$
$541$	−2.21560e8			−1.39927			−0.699633	+	0.714502i	$0.746653\pi$
$542$		0			0
$543$	−9.82794e7	+	9.82794e7i	−0.613851	+	0.613851i
$544$		0			0
$545$	−3.50174e7	+	8.45822e7i	−0.216319	+	0.522504i
$546$		0			0
$547$	1.99416e8	+	1.99416e8i	1.21842	+	1.21842i	0.968184	+	0.250240i	$0.0805096\pi$
$547$	1.99416e8	+	1.99416e8i	1.21842	+	1.21842i	0.250240	+	0.968184i	$0.419490\pi$
$548$		0			0
$549$			4.73567e8i			2.86197i
$550$		0			0
$551$	7.01739e7			0.419489
$552$		0			0
$553$	−4.21862e7	+	4.21862e7i	−0.249456	+	0.249456i
$554$		0			0
$555$	−2.97131e8	−	1.23014e8i	−1.73807	−	0.719571i
$556$		0			0
$557$	−2.12978e8	−	2.12978e8i	−1.23245	−	1.23245i	−0.963019	−	0.269433i	$-0.913164\pi$
$557$	−2.12978e8	−	2.12978e8i	−1.23245	−	1.23245i	−0.269433	−	0.963019i	$-0.586836\pi$
$558$		0			0
$559$			1.42495e8i			0.815763i
$560$		0			0
$561$	5.14393e8			2.91344
$562$		0			0
$563$	8.58027e7	−	8.58027e7i	0.480812	−	0.480812i	−0.424579	−	0.905391i	$-0.639578\pi$
$563$	8.58027e7	−	8.58027e7i	0.480812	−	0.480812i	0.905391	+	0.424579i	$0.139578\pi$
$564$		0			0
$565$	2.86671e7	−	1.18803e7i	0.158942	−	0.0658690i
$566$		0			0
$567$	7.69881e7	+	7.69881e7i	0.422352	+	0.422352i
$568$		0			0
$569$		−	1.16983e8i		−	0.635019i	−0.948255	−	0.317510i	$-0.897153\pi$
$569$		−	1.16983e8i		−	0.635019i	0.948255	−	0.317510i	$-0.102847\pi$
$570$		0			0
$571$	2.93057e8			1.57414			0.787070	−	0.616864i	$-0.211597\pi$
$571$	2.93057e8			1.57414			0.787070	+	0.616864i	$0.211597\pi$
$572$		0			0
$573$	2.29550e8	−	2.29550e8i	1.22015	−	1.22015i
$574$		0			0
$575$	−2.67446e7	+	9529.21i	−0.140680	+	5.01249e-5i
$576$		0			0
$577$	4.74773e7	+	4.74773e7i	0.247149	+	0.247149i	0.819799	−	0.572651i	$-0.194085\pi$
$577$	4.74773e7	+	4.74773e7i	0.247149	+	0.247149i	−0.572651	+	0.819799i	$0.694085\pi$
$578$		0			0
$579$			3.43628e8i			1.77032i
$580$		0			0
$581$	−4.67085e7			−0.238159
$582$		0			0
$583$	−1.28761e8	+	1.28761e8i	−0.649798	+	0.649798i
$584$		0			0
$585$	−1.17012e8	−	2.82351e8i	−0.584473	−	1.41033i
$586$		0			0
$587$	−1.77321e8	−	1.77321e8i	−0.876690	−	0.876690i	0.116501	−	0.993191i	$-0.462832\pi$
$587$	−1.77321e8	−	1.77321e8i	−0.876690	−	0.876690i	−0.993191	+	0.116501i	$0.962832\pi$
$588$		0			0
$589$			1.21318e7i			0.0593716i
$590$		0			0
$591$	−4.75334e7			−0.230269
$592$		0			0
$593$	2.39503e8	−	2.39503e8i	1.14854	−	1.14854i	0.161705	−	0.986839i	$-0.448301\pi$
$593$	2.39503e8	−	2.39503e8i	1.14854	−	1.14854i	0.986839	−	0.161705i	$-0.0516992\pi$
$594$		0			0
$595$	−1.96426e7	+	4.74454e7i	−0.0932500	+	0.225239i
$596$		0			0
$597$	3.43308e8	+	3.43308e8i	1.61347	+	1.61347i
$598$		0			0
$599$		−	3.12890e8i		−	1.45583i	−0.685665	−	0.727917i	$-0.740489\pi$
$599$		−	3.12890e8i		−	1.45583i	0.685665	−	0.727917i	$-0.259511\pi$
$600$		0			0
$601$	−1.78301e8			−0.821354			−0.410677	−	0.911781i	$-0.634708\pi$
$601$	−1.78301e8			−0.821354			−0.410677	+	0.911781i	$0.634708\pi$
$602$		0			0
$603$	5.45691e8	−	5.45691e8i	2.48883	−	2.48883i
$604$		0			0
$605$	−2.10495e8	−	8.71458e7i	−0.950549	−	0.393532i
$606$		0			0
$607$	8.83561e7	+	8.83561e7i	0.395067	+	0.395067i	0.876489	−	0.481422i	$-0.159880\pi$
$607$	8.83561e7	+	8.83561e7i	0.395067	+	0.395067i	−0.481422	+	0.876489i	$0.659880\pi$
$608$		0			0
$609$			1.03108e8i			0.456500i
$610$		0			0
$611$	−4.30635e7			−0.188793
$612$		0			0
$613$	−2.76511e8	+	2.76511e8i	−1.20041	+	1.20041i	−0.226373	+	0.974041i	$0.572687\pi$
$613$	−2.76511e8	+	2.76511e8i	−1.20041	+	1.20041i	−0.974041	+	0.226373i	$0.927313\pi$
$614$		0			0
$615$	2.36043e8	−	9.78214e7i	1.01476	−	0.420541i
$616$		0			0
$617$	2.19011e8	+	2.19011e8i	0.932420	+	0.932420i	0.997857	−	0.0654371i	$-0.0208442\pi$
$617$	2.19011e8	+	2.19011e8i	0.932420	+	0.932420i	−0.0654371	+	0.997857i	$0.520844\pi$
$618$		0			0
$619$			2.33037e8i			0.982546i	0.871006	+	0.491273i	$0.163468\pi$
$619$			2.33037e8i			0.982546i	−0.871006	+	0.491273i	$0.836532\pi$
$620$		0			0
$621$	−9.32990e7			−0.389585
$622$		0			0
$623$	2.59470e7	−	2.59470e7i	0.107306	−	0.107306i
$624$		0			0
$625$	173976.	+	2.44141e8i	0.000712607	+	1.00000i
$626$		0			0
$627$	−1.76790e8	−	1.76790e8i	−0.717224	−	0.717224i
$628$		0			0
$629$		−	2.74864e8i		−	1.10450i
$630$		0			0
$631$	−3.76944e8			−1.50034			−0.750168	−	0.661247i	$-0.770028\pi$
$631$	−3.76944e8			−1.50034			−0.750168	+	0.661247i	$0.770028\pi$
$632$		0			0
$633$	−9.98539e7	+	9.98539e7i	−0.393690	+	0.393690i
$634$		0			0
$635$	−1.06462e8	−	2.56892e8i	−0.415789	−	1.00330i
$636$		0			0
$637$	1.06783e8	+	1.06783e8i	0.413126	+	0.413126i
$638$		0			0
$639$			4.96952e8i			1.90464i
$640$		0			0
$641$	−1.78061e8			−0.676076			−0.338038	−	0.941132i	$-0.609763\pi$
$641$	−1.78061e8			−0.676076			−0.338038	+	0.941132i	$0.609763\pi$
$642$		0			0
$643$	1.11035e8	−	1.11035e8i	0.417663	−	0.417663i	−0.466735	−	0.884397i	$-0.654570\pi$
$643$	1.11035e8	−	1.11035e8i	0.417663	−	0.417663i	0.884397	+	0.466735i	$0.154570\pi$
$644$		0			0
$645$	2.54261e8	−	6.14150e8i	0.947546	−	2.28873i
$646$		0			0
$647$	8.46874e7	+	8.46874e7i	0.312684	+	0.312684i	0.845949	−	0.533264i	$-0.179035\pi$
$647$	8.46874e7	+	8.46874e7i	0.312684	+	0.312684i	−0.533264	+	0.845949i	$0.679035\pi$
$648$		0			0
$649$		−	6.70924e7i		−	0.245436i
$650$		0			0
$651$	−1.78255e7			−0.0646098
$652$		0			0
$653$	1.46524e8	−	1.46524e8i	0.526224	−	0.526224i	−0.393220	−	0.919444i	$-0.628639\pi$
$653$	1.46524e8	−	1.46524e8i	0.526224	−	0.526224i	0.919444	+	0.393220i	$0.128639\pi$
$654$		0			0
$655$	−9.45862e7	−	3.91591e7i	−0.336592	−	0.139351i
$656$		0			0
$657$	8.75679e7	+	8.75679e7i	0.308780	+	0.308780i
$658$		0			0
$659$		−	3.05403e8i		−	1.06713i	−0.845759	−	0.533565i	$-0.820852\pi$
$659$		−	3.05403e8i		−	1.06713i	0.845759	−	0.533565i	$-0.179148\pi$
$660$		0			0
$661$	1.97303e8			0.683172			0.341586	−	0.939851i	$-0.389036\pi$
$661$	1.97303e8			0.683172			0.341586	+	0.939851i	$0.389036\pi$
$662$		0			0
$663$	2.59090e8	−	2.59090e8i	0.889016	−	0.889016i
$664$		0			0
$665$	2.30573e7	−	9.55545e6i	0.0784049	−	0.0324927i
$666$		0			0
$667$	−3.24553e7	−	3.24553e7i	−0.109373	−	0.109373i
$668$		0			0
$669$		−	4.41295e7i		−	0.147384i
$670$		0			0
$671$	4.95850e8			1.64128
$672$		0			0
$673$	1.38405e8	−	1.38405e8i	0.454055	−	0.454055i	−0.442643	−	0.896698i	$-0.645959\pi$
$673$	1.38405e8	−	1.38405e8i	0.454055	−	0.454055i	0.896698	+	0.442643i	$0.145959\pi$
$674$		0			0
$675$	303460.	+	8.51688e8i	0.000986710	+	2.76929i
$676$		0			0
$677$	3.58335e8	+	3.58335e8i	1.15484	+	1.15484i	0.985569	+	0.169274i	$0.0541424\pi$
$677$	3.58335e8	+	3.58335e8i	1.15484	+	1.15484i	0.169274	+	0.985569i	$0.445858\pi$
$678$		0			0
$679$		−	1.78332e7i		−	0.0569665i
$680$		0			0
$681$	−8.42939e8			−2.66904
$682$		0			0
$683$	−4.06177e8	+	4.06177e8i	−1.27483	+	1.27483i	−0.331311	+	0.943522i	$0.607491\pi$
$683$	−4.06177e8	+	4.06177e8i	−1.27483	+	1.27483i	−0.943522	+	0.331311i	$0.892509\pi$
$684$		0			0
$685$	1.80784e8	+	4.36232e8i	0.562456	+	1.35721i
$686$		0			0
$687$	7.07861e8	+	7.07861e8i	2.18312	+	2.18312i
$688$		0			0
$689$			1.29709e8i			0.396563i
$690$		0			0
$691$	3.30348e8			1.00124			0.500620	−	0.865667i	$-0.333106\pi$
$691$	3.30348e8			1.00124			0.500620	+	0.865667i	$0.333106\pi$
$692$		0			0
$693$	1.85197e8	−	1.85197e8i	0.556460	−	0.556460i
$694$		0			0
$695$	−8.40282e7	+	2.02964e8i	−0.250306	+	0.604596i
$696$		0			0
$697$	1.54423e8	+	1.54423e8i	0.456050	+	0.456050i
$698$		0			0
$699$		−	6.13865e8i		−	1.79739i
$700$		0			0
$701$	9.85520e7			0.286096			0.143048	−	0.989716i	$-0.454310\pi$
$701$	9.85520e7			0.286096			0.143048	+	0.989716i	$0.454310\pi$
$702$		0			0
$703$	−9.44673e7	+	9.44673e7i	−0.271904	+	0.271904i
$704$		0			0
$705$	1.85603e8	+	7.68404e7i	0.529684	+	0.219292i
$706$		0			0
$707$	−1.06683e8	−	1.06683e8i	−0.301881	−	0.301881i
$708$		0			0
$709$		−	2.86500e8i		−	0.803870i	−0.915668	−	0.401935i	$-0.868338\pi$
$709$		−	2.86500e8i		−	0.803870i	0.915668	−	0.401935i	$-0.131662\pi$
$710$		0			0
$711$	−1.41576e9			−3.93895
$712$		0			0
$713$	5.61093e6	−	5.61093e6i	0.0154798	−	0.0154798i
$714$		0			0
$715$	−2.95636e8	+	1.22518e8i	−0.808797	+	0.335183i
$716$		0			0
$717$	−5.06079e8	−	5.06079e8i	−1.37297	−	1.37297i
$718$		0			0
$719$			1.68198e8i			0.452517i	0.974067	+	0.226259i	$0.0726494\pi$
$719$			1.68198e8i			0.452517i	−0.974067	+	0.226259i	$0.927351\pi$
$720$		0			0
$721$	−1.08940e8			−0.290658
$722$		0			0
$723$	6.30356e8	−	6.30356e8i	1.66790	−	1.66790i
$724$		0			0
$725$	−2.96166e8	+	2.96377e8i	−0.777178	+	0.777732i
$726$		0			0
$727$	−1.47001e8	−	1.47001e8i	−0.382575	−	0.382575i	0.489454	−	0.872029i	$-0.337196\pi$
$727$	−1.47001e8	−	1.47001e8i	−0.382575	−	0.382575i	−0.872029	+	0.489454i	$0.837196\pi$
$728$		0			0
$729$			5.81204e8i			1.50019i
$730$		0			0
$731$	5.68127e8			1.45443
$732$		0			0
$733$	2.20507e8	−	2.20507e8i	0.559899	−	0.559899i	−0.369379	−	0.929279i	$-0.620430\pi$
$733$	2.20507e8	−	2.20507e8i	0.559899	−	0.559899i	0.929279	+	0.369379i	$0.120430\pi$
$734$		0			0
$735$	−2.69693e8	−	6.50768e8i	−0.679215	−	1.63894i
$736$		0			0
$737$	−5.71367e8	−	5.71367e8i	−1.42729	−	1.42729i
$738$		0			0
$739$		−	2.00165e7i		−	0.0495970i	−0.999692	−	0.0247985i	$-0.992106\pi$
$739$		−	2.00165e7i		−	0.0495970i	0.999692	−	0.0247985i	$-0.00789442\pi$
$740$		0			0
$741$	−1.78091e8			−0.437712
$742$		0			0
$743$	2.26439e8	−	2.26439e8i	0.552057	−	0.552057i	−0.374977	−	0.927034i	$-0.622349\pi$
$743$	2.26439e8	−	2.26439e8i	0.552057	−	0.552057i	0.927034	+	0.374977i	$0.122349\pi$
$744$		0			0
$745$	−5.54869e6	+	1.34025e7i	−0.0134191	+	0.0324128i
$746$		0			0
$747$	−7.83763e8	−	7.83763e8i	−1.88028	−	1.88028i
$748$		0			0
$749$			1.65153e7i			0.0393043i
$750$		0			0
$751$	−3.47339e8			−0.820037			−0.410019	−	0.912077i	$-0.634478\pi$
$751$	−3.47339e8			−0.820037			−0.410019	+	0.912077i	$0.634478\pi$
$752$		0			0
$753$	−2.77320e8	+	2.77320e8i	−0.649526	+	0.649526i
$754$		0			0
$755$	5.66210e8	+	2.34414e8i	1.31564	+	0.544681i
$756$		0			0
$757$	1.19148e8	+	1.19148e8i	0.274661	+	0.274661i	0.830973	−	0.556312i	$-0.187784\pi$
$757$	1.19148e8	+	1.19148e8i	0.274661	+	0.274661i	−0.556312	+	0.830973i	$0.687784\pi$
$758$		0			0
$759$			1.63530e8i			0.374001i
$760$		0			0
$761$	−2.72659e8			−0.618680			−0.309340	−	0.950952i	$-0.600108\pi$
$761$	−2.72659e8			−0.618680			−0.309340	+	0.950952i	$0.600108\pi$
$762$		0			0
$763$	−3.95121e7	+	3.95121e7i	−0.0889522	+	0.0889522i
$764$		0			0
$765$	−1.12573e9	+	4.66528e8i	−2.51449	+	1.04206i
$766$		0			0
$767$	−3.37932e7	−	3.37932e7i	−0.0748932	−	0.0748932i
$768$		0			0
$769$		−	4.45104e7i		−	0.0978774i	−0.998802	−	0.0489387i	$-0.984416\pi$
$769$		−	4.45104e7i		−	0.0978774i	0.998802	−	0.0489387i	$-0.0155839\pi$
$770$		0			0
$771$	−9.92606e8			−2.16578
$772$		0			0
$773$	3.76356e8	−	3.76356e8i	0.814818	−	0.814818i	−0.170534	−	0.985352i	$-0.554549\pi$
$773$	3.76356e8	−	3.76356e8i	0.814818	−	0.814818i	0.985352	+	0.170534i	$0.0545491\pi$
$774$		0			0
$775$	−5.12381e7	−	5.12016e7i	−0.110075	−	0.109996i
$776$		0			0
$777$	−1.38803e8	−	1.38803e8i	−0.295894	−	0.295894i
$778$		0			0
$779$		−	1.06146e8i		−	0.224539i
$780$		0			0
$781$	5.20336e8			1.09227
$782$		0			0
$783$	−1.03355e9	+	1.03355e9i	−2.15300	+	2.15300i
$784$		0			0
$785$	−1.34667e8	−	3.24952e8i	−0.278390	−	0.671753i
$786$		0			0
$787$	2.30940e8	+	2.30940e8i	0.473778	+	0.473778i	0.903135	−	0.429357i	$-0.141260\pi$
$787$	2.30940e8	+	2.30940e8i	0.473778	+	0.473778i	−0.429357	+	0.903135i	$0.641260\pi$
$788$		0			0
$789$		−	1.08711e9i		−	2.21332i
$790$		0			0
$791$	1.89415e7			0.0382723
$792$		0			0
$793$	2.49750e8	−	2.49750e8i	0.500826	−	0.500826i
$794$		0			0
$795$	2.31446e8	−	5.59042e8i	0.460626	−	1.11261i
$796$		0			0
$797$	2.32522e8	+	2.32522e8i	0.459293	+	0.459293i	0.898423	−	0.439131i	$-0.144713\pi$
$797$	2.32522e8	+	2.32522e8i	0.459293	+	0.459293i	−0.439131	+	0.898423i	$0.644713\pi$
$798$		0			0
$799$			1.71694e8i			0.336601i
$800$		0			0
$801$	8.70777e8			1.69437
$802$		0			0
$803$	9.16882e7	−	9.16882e7i	0.177079	−	0.177079i
$804$		0			0
$805$	−1.50833e7	−	6.24458e6i	−0.0289141	−	0.0119706i
$806$		0			0
$807$	1.29291e9	+	1.29291e9i	2.46007	+	2.46007i
$808$		0			0
$809$		−	9.11846e7i		−	0.172217i	−0.996286	−	0.0861085i	$-0.972557\pi$
$809$		−	9.11846e7i		−	0.172217i	0.996286	−	0.0861085i	$-0.0274432\pi$
$810$		0			0
$811$	3.05011e8			0.571812			0.285906	−	0.958258i	$-0.407706\pi$
$811$	3.05011e8			0.571812			0.285906	+	0.958258i	$0.407706\pi$
$812$		0			0
$813$	−1.25390e9	+	1.25390e9i	−2.33340	+	2.33340i
$814$		0			0
$815$	3.89239e8	−	1.61309e8i	0.719024	−	0.297980i
$816$		0			0
$817$	−1.95258e8	−	1.95258e8i	−0.358049	−	0.358049i
$818$		0			0
$819$		−	1.86560e8i		−	0.339600i
$820$		0			0
$821$	4.77855e8			0.863508			0.431754	−	0.901991i	$-0.357895\pi$
$821$	4.77855e8			0.863508			0.431754	+	0.901991i	$0.357895\pi$
$822$		0			0
$823$	2.56987e7	−	2.56987e7i	0.0461011	−	0.0461011i	−0.683680	−	0.729782i	$-0.739622\pi$
$823$	2.56987e7	−	2.56987e7i	0.0461011	−	0.0461011i	0.729782	+	0.683680i	$0.239622\pi$
$824$		0			0
$825$	1.49280e9	−	531890.i	2.65852	−	0.000947240i
$826$		0			0
$827$	−4.48704e8	−	4.48704e8i	−0.793310	−	0.793310i	0.188721	−	0.982031i	$-0.439566\pi$
$827$	−4.48704e8	−	4.48704e8i	−0.793310	−	0.793310i	−0.982031	+	0.188721i	$0.939566\pi$
$828$		0			0
$829$			6.67875e8i			1.17228i	0.810209	+	0.586141i	$0.199353\pi$
$829$			6.67875e8i			1.17228i	−0.810209	+	0.586141i	$0.800647\pi$
$830$		0			0
$831$	1.47255e9			2.56606
$832$		0			0
$833$	4.25742e8	−	4.25742e8i	0.736565	−	0.736565i
$834$		0			0
$835$	−8.87567e7	−	2.14170e8i	−0.152455	−	0.367874i
$836$		0			0
$837$	−1.78681e8	−	1.78681e8i	−0.304721	−	0.304721i
$838$		0			0
$839$		−	2.91494e8i		−	0.493564i	−0.969071	−	0.246782i	$-0.920627\pi$
$839$		−	2.91494e8i		−	0.493564i	0.969071	−	0.246782i	$-0.0793732\pi$
$840$		0			0
$841$	−1.24243e8			−0.208874
$842$		0			0
$843$	−9.02279e8	+	9.02279e8i	−1.50611	+	1.50611i
$844$		0			0
$845$	1.43597e8	−	3.46849e8i	0.237999	−	0.574870i
$846$		0			0
$847$	−9.83314e7	−	9.83314e7i	−0.161824	−	0.161824i
$848$		0			0
$849$			6.51652e8i			1.06486i
$850$		0			0
$851$	8.73820e7			0.141786
$852$		0			0
$853$	−8.06735e8	+	8.06735e8i	−1.29982	+	1.29982i	−0.371314	+	0.928507i	$0.621093\pi$
$853$	−8.06735e8	+	8.06735e8i	−1.29982	+	1.29982i	−0.928507	+	0.371314i	$0.878907\pi$
$854$		0			0
$855$	5.47238e8	+	2.26559e8i	0.875544	+	0.362480i
$856$		0			0
$857$	−4.48305e7	−	4.48305e7i	−0.0712248	−	0.0712248i	0.670597	−	0.741822i	$-0.266038\pi$
$857$	−4.48305e7	−	4.48305e7i	−0.0712248	−	0.0712248i	−0.741822	+	0.670597i	$0.766038\pi$
$858$		0			0
$859$			5.21914e8i			0.823417i	0.911316	+	0.411708i	$0.135068\pi$
$859$			5.21914e8i			0.823417i	−0.911316	+	0.411708i	$0.864932\pi$
$860$		0			0
$861$	1.55963e8			0.244350
$862$		0			0
$863$	−6.04145e8	+	6.04145e8i	−0.939959	+	0.939959i	−0.998297	−	0.0583383i	$-0.981420\pi$
$863$	−6.04145e8	+	6.04145e8i	−0.939959	+	0.939959i	0.0583383	+	0.998297i	$0.481420\pi$
$864$		0			0
$865$	6.28730e8	−	2.60560e8i	0.971439	−	0.402586i
$866$		0			0
$867$	−1.72862e8	−	1.72862e8i	−0.265242	−	0.265242i
$868$		0			0
$869$			1.48238e9i			2.25891i
$870$		0			0
$871$	−5.75574e8			−0.871057
$872$		0			0
$873$	2.99239e8	−	2.99239e8i	0.449754	−	0.449754i
$874$		0			0
$875$	−5.69551e7	+	1.37710e8i	−0.0850175	+	0.205561i
$876$		0			0
$877$	−4.32194e7	−	4.32194e7i	−0.0640737	−	0.0640737i	0.674344	−	0.738418i	$-0.264427\pi$
$877$	−4.32194e7	−	4.32194e7i	−0.0640737	−	0.0640737i	−0.738418	+	0.674344i	$0.764427\pi$
$878$		0			0
$879$		−	1.35032e9i		−	1.98825i
$880$		0			0
$881$	−4.38003e8			−0.640545			−0.320273	−	0.947325i	$-0.603775\pi$
$881$	−4.38003e8			−0.640545			−0.320273	+	0.947325i	$0.603775\pi$
$882$		0			0
$883$	6.70815e8	−	6.70815e8i	0.974363	−	0.974363i	−0.0253168	−	0.999679i	$-0.508059\pi$
$883$	6.70815e8	−	6.70815e8i	0.974363	−	0.974363i	0.999679	+	0.0253168i	$0.00805945\pi$
$884$		0			0
$885$	8.53488e7	+	2.05946e8i	0.123131	+	0.297115i
$886$		0			0
$887$	−6.04117e8	−	6.04117e8i	−0.865665	−	0.865665i	0.126324	−	0.991989i	$-0.459682\pi$
$887$	−6.04117e8	−	6.04117e8i	−0.865665	−	0.865665i	−0.991989	+	0.126324i	$0.959682\pi$
$888$		0			0
$889$		−	1.69739e8i		−	0.241588i
$890$		0			0
$891$	2.70528e9			3.82453
$892$		0			0
$893$	5.90090e7	−	5.90090e7i	0.0828637	−	0.0828637i
$894$		0			0
$895$	2.21983e8	−	5.36184e8i	0.309635	−	0.747902i
$896$		0			0
$897$	8.23670e7	+	8.23670e7i	0.114124	+	0.114124i
$898$		0			0
$899$		−	1.24313e8i		−	0.171096i
$900$		0			0
$901$	5.17149e8			0.707036
$902$		0			0
$903$	2.86897e8	−	2.86897e8i	0.389639	−	0.389639i
$904$		0			0
$905$	−3.18530e8	−	1.31873e8i	−0.429739	−	0.177914i
$906$		0			0
$907$	4.89905e8	+	4.89905e8i	0.656583	+	0.656583i	0.954570	−	0.297987i	$-0.0963152\pi$
$907$	4.89905e8	+	4.89905e8i	0.656583	+	0.656583i	−0.297987	+	0.954570i	$0.596315\pi$
$908$		0			0
$909$		−	3.58025e9i		−	4.76674i
$910$		0			0
$911$	−3.10050e8			−0.410087			−0.205044	−	0.978753i	$-0.565734\pi$
$911$	−3.10050e8			−0.410087			−0.205044	+	0.978753i	$0.565734\pi$
$912$		0			0
$913$	−8.20642e8	+	8.20642e8i	−1.07830	+	1.07830i
$914$		0			0
$915$	−1.52206e9	+	6.30775e8i	−1.98687	+	0.823401i
$916$		0			0
$917$	−4.41854e7	−	4.41854e7i	−0.0573022	−	0.0573022i
$918$		0			0
$919$			3.80950e8i			0.490818i	0.969420	+	0.245409i	$0.0789223\pi$
$919$			3.80950e8i			0.490818i	−0.969420	+	0.245409i	$0.921078\pi$
$920$		0			0
$921$	1.34182e9			1.71758
$922$		0			0
$923$	2.62083e8	−	2.62083e8i	0.333299	−	0.333299i
$924$		0			0
$925$	−284214.	−	7.97674e8i	−0.000359104	−	1.00786i
$926$		0			0
$927$	−1.82801e9	−	1.82801e9i	−2.29477	−	2.29477i
$928$		0			0
$929$			4.56924e8i			0.569897i	0.958543	+	0.284949i	$0.0919765\pi$
$929$			4.56924e8i			0.569897i	−0.958543	+	0.284949i	$0.908023\pi$
$930$		0			0
$931$	−2.92644e8			−0.362652
$932$		0			0
$933$	7.65578e6	−	7.65578e6i	0.00942637	−	0.00942637i
$934$		0			0
$935$	4.88480e8	+	1.17870e9i	0.597601	+	1.44201i
$936$		0			0
$937$	−8.80343e8	−	8.80343e8i	−1.07012	−	1.07012i	−0.997349	−	0.0727732i	$-0.976815\pi$
$937$	−8.80343e8	−	8.80343e8i	−1.07012	−	1.07012i	−0.0727732	−	0.997349i	$-0.523185\pi$
$938$		0			0
$939$			2.67108e9i			3.22619i
$940$		0			0
$941$	6.71533e8			0.805932			0.402966	−	0.915215i	$-0.367979\pi$
$941$	6.71533e8			0.805932			0.402966	+	0.915215i	$0.367979\pi$
$942$		0			0
$943$	−4.90924e7	+	4.90924e7i	−0.0585436	+	0.0585436i
$944$		0			0
$945$	−1.98860e8	+	4.80332e8i	−0.235641	+	0.569175i
$946$		0			0
$947$	−4.25809e8	−	4.25809e8i	−0.501377	−	0.501377i	0.410489	−	0.911866i	$-0.365358\pi$
$947$	−4.25809e8	−	4.25809e8i	−0.501377	−	0.501377i	−0.911866	+	0.410489i	$0.865358\pi$
$948$		0			0
$949$		−	9.23633e7i		−	0.108069i
$950$		0			0
$951$	8.77814e8			1.02061
$952$		0			0
$953$	1.76321e8	−	1.76321e8i	0.203716	−	0.203716i	−0.597874	−	0.801590i	$-0.703988\pi$
$953$	1.76321e8	−	1.76321e8i	0.203716	−	0.203716i	0.801590	+	0.597874i	$0.203988\pi$
$954$		0			0
$955$	7.43986e8	+	3.08014e8i	0.854191	+	0.353639i
$956$		0			0
$957$	1.81155e9	+	1.81155e9i	2.06688	+	2.06688i
$958$		0			0
$959$			2.88236e8i			0.326807i
$960$		0			0
$961$	−8.66012e8			−0.975784
$962$		0			0
$963$	−2.77124e8	+	2.77124e8i	−0.310310	+	0.310310i
$964$		0			0
$965$	−7.87403e8	+	3.26317e8i	−0.876224	+	0.363127i
$966$		0			0
$967$	1.87686e8	+	1.87686e8i	0.207564	+	0.207564i	0.803231	−	0.595667i	$-0.203112\pi$
$967$	1.87686e8	+	1.87686e8i	0.207564	+	0.207564i	−0.595667	+	0.803231i	$0.703112\pi$
$968$		0			0
$969$			7.10050e8i			0.780401i
$970$		0			0
$971$	−6.70884e8			−0.732807			−0.366404	−	0.930456i	$-0.619411\pi$
$971$	−6.70884e8			−0.732807			−0.366404	+	0.930456i	$0.619411\pi$
$972$		0			0
$973$	−9.48137e7	+	9.48137e7i	−0.102928	+	0.102928i
$974$		0			0
$975$	7.51627e8	−	7.52162e8i	0.810939	−	0.811517i
$976$		0			0
$977$	−4.17576e8	−	4.17576e8i	−0.447767	−	0.447767i	0.446845	−	0.894612i	$-0.352548\pi$
$977$	−4.17576e8	−	4.17576e8i	−0.447767	−	0.447767i	−0.894612	+	0.446845i	$0.852548\pi$
$978$		0			0
$979$		−	9.11750e8i		−	0.971690i
$980$		0			0
$981$	−1.32602e9			−1.40457
$982$		0			0
$983$	−7.39716e7	+	7.39716e7i	−0.0778761	+	0.0778761i	−0.744972	−	0.667096i	$-0.767537\pi$
$983$	−7.39716e7	+	7.39716e7i	−0.0778761	+	0.0778761i	0.667096	+	0.744972i	$0.267537\pi$
$984$		0			0
$985$	−4.51388e7	−	1.08920e8i	−0.0472326	−	0.113972i
$986$		0			0
$987$	8.67033e7	+	8.67033e7i	0.0901746	+	0.0901746i
$988$		0			0
$989$			1.80613e8i			0.186707i
$990$		0			0
$991$	3.99604e8			0.410591			0.205295	−	0.978700i	$-0.434185\pi$
$991$	3.99604e8			0.410591			0.205295	+	0.978700i	$0.434185\pi$
$992$		0			0
$993$	−1.23628e9	+	1.23628e9i	−1.26261	+	1.26261i
$994$		0			0
$995$	−4.60657e8	+	1.11268e9i	−0.467636	+	1.12954i
$996$		0			0
$997$	−2.12005e7	−	2.12005e7i	−0.0213924	−	0.0213924i	0.696330	−	0.717722i	$-0.254815\pi$
$997$	−2.12005e7	−	2.12005e7i	−0.0213924	−	0.0213924i	−0.717722	+	0.696330i	$0.754815\pi$
$998$		0			0
$999$		−	2.78270e9i		−	2.79106i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.7.p.d.17.1		6
4.3	odd	2		20.7.f.a.17.3	yes	6
5.3	odd	4	inner	80.7.p.d.33.1		6
12.11	even	2		180.7.l.a.37.3		6
20.3	even	4		20.7.f.a.13.3	✓	6
20.7	even	4		100.7.f.b.93.1		6
20.19	odd	2		100.7.f.b.57.1		6
60.23	odd	4		180.7.l.a.73.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.7.f.a.13.3	✓	6	20.3	even	4
20.7.f.a.17.3	yes	6	4.3	odd	2
80.7.p.d.17.1		6	1.1	even	1	trivial
80.7.p.d.33.1		6	5.3	odd	4	inner
100.7.f.b.57.1		6	20.19	odd	2
100.7.f.b.93.1		6	20.7	even	4
180.7.l.a.37.3		6	12.11	even	2
180.7.l.a.73.3		6	60.23	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	80.p (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-35.6344 + 35.6344i) q^{3} +(-115.493 - 47.8149i) q^{5} +(-53.9521 - 53.9521i) q^{7} -1810.62i q^{9} -1895.82 q^{11} +(-954.888 + 954.888i) q^{13} +(5819.40 - 2411.69i) q^{15} +(3807.14 + 3807.14i) q^{17} -2616.92i q^{19} +3845.11 q^{21} +(-1210.32 + 1210.32i) q^{23} +(11052.5 + 11044.6i) q^{25} +(38543.0 + 38543.0i) q^{27} +26815.4i q^{29} -4635.89 q^{31} +(67556.4 - 67556.4i) q^{33} +(3651.41 + 8810.83i) q^{35} +(-36098.6 - 36098.6i) q^{37} -68053.7i q^{39} +40561.4 q^{41} +(74613.4 - 74613.4i) q^{43} +(-86574.7 + 209115. i) q^{45} +(22549.0 + 22549.0i) q^{47} -111827. i q^{49} -271330. q^{51} +(67918.4 - 67918.4i) q^{53} +(218955. + 90648.3i) q^{55} +(93252.6 + 93252.6i) q^{57} +35389.7i q^{59} -261549. q^{61} +(-97687.0 + 97687.0i) q^{63} +(155941. - 64625.5i) q^{65} +(301383. + 301383. i) q^{67} -86258.3i q^{69} -274465. q^{71} +(-48363.4 + 48363.4i) q^{73} +(-787417. + 280.559i) q^{75} +(102283. + 102283. i) q^{77} -781918. i q^{79} -1.42697e6 q^{81} +(432869. - 432869. i) q^{83} +(-257662. - 621737. i) q^{85} +(-955551. - 955551. i) q^{87} +480927. i q^{89} +103036. q^{91} +(165197. - 165197. i) q^{93} +(-125128. + 302238. i) q^{95} +(165268. + 165268. i) q^{97} +3.43261e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 32 q^{3} - 156 q^{5} + 264 q^{7} - 2200 q^{11} + 858 q^{13} + 7768 q^{15} - 3278 q^{17} + 33176 q^{21} - 19984 q^{23} - 24174 q^{25} + 115528 q^{27} - 104976 q^{31} + 177320 q^{33} + 116072 q^{35}+ \cdots + 3338406 q^{97}+O(q^{100}) \) 6 * q - 32 * q^3 - 156 * q^5 + 264 * q^7 - 2200 * q^11 + 858 * q^13 + 7768 * q^15 - 3278 * q^17 + 33176 * q^21 - 19984 * q^23 - 24174 * q^25 + 115528 * q^27 - 104976 * q^31 + 177320 * q^33 + 116072 * q^35 - 241554 * q^37 + 351736 * q^41 - 60720 * q^43 - 287846 * q^45 + 355248 * q^47 - 641872 * q^51 + 346526 * q^53 + 310200 * q^55 - 112816 * q^57 - 492888 * q^61 - 2288 * q^63 - 5082 * q^65 + 230304 * q^67 - 174128 * q^71 - 332442 * q^73 - 1855048 * q^75 + 1618760 * q^77 - 3085166 * q^81 + 2190936 * q^83 - 164934 * q^85 - 2614304 * q^87 + 2186976 * q^91 + 242072 * q^93 - 3484184 * q^95 + 3338406 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more